LMFDB - Embedded newform 50.6.e.a.19.11

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			19.11
Character	$\chi$	$=$	50.19
Dual form			50.6.e.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.80423 - 1.23607i) q^{2} +(12.0218 + 16.5465i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-33.0957 + 45.0519i) q^{5} +(66.1861 + 48.0870i) q^{6} +103.889i q^{7} +(37.6183 - 51.7771i) q^{8} +(-54.1737 + 166.730i) q^{9} +O(q^{10})$	\(q+(3.80423 - 1.23607i) q^{2} +(12.0218 + 16.5465i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-33.0957 + 45.0519i) q^{5} +(66.1861 + 48.0870i) q^{6} +103.889i q^{7} +(37.6183 - 51.7771i) q^{8} +(-54.1737 + 166.730i) q^{9} +(-70.2163 + 212.296i) q^{10} +(-4.59941 - 14.1555i) q^{11} +(311.226 + 101.123i) q^{12} +(-100.594 - 32.6850i) q^{13} +(128.414 + 395.217i) q^{14} +(-1143.32 - 6.01571i) q^{15} +(79.1084 - 243.470i) q^{16} +(343.421 - 472.678i) q^{17} +701.239i q^{18} +(1978.33 + 1437.34i) q^{19} +(-4.70606 + 894.415i) q^{20} +(-1719.00 + 1248.93i) q^{21} +(-34.9944 - 48.1656i) q^{22} +(4005.42 - 1301.44i) q^{23} +1308.97 q^{24} +(-934.350 - 2982.05i) q^{25} -423.083 q^{26} +(1316.68 - 427.816i) q^{27} +(977.029 + 1344.77i) q^{28} +(-1837.18 + 1334.79i) q^{29} +(-4356.89 + 1390.34i) q^{30} +(-6282.20 - 4564.28i) q^{31} -1024.00i q^{32} +(178.932 - 246.278i) q^{33} +(722.187 - 2222.66i) q^{34} +(-4680.39 - 3438.27i) q^{35} +(866.780 + 2667.67i) q^{36} +(-5284.96 - 1717.19i) q^{37} +(9302.68 + 3022.62i) q^{38} +(-668.493 - 2057.41i) q^{39} +(1087.65 + 3408.37i) q^{40} +(328.604 - 1011.34i) q^{41} +(-4995.70 + 6876.00i) q^{42} -19531.3i q^{43} +(-192.663 - 139.978i) q^{44} +(-5718.57 - 7958.66i) q^{45} +(13628.8 - 9901.93i) q^{46} +(8308.17 + 11435.2i) q^{47} +(4979.61 - 1617.97i) q^{48} +6014.11 q^{49} +(-7240.49 - 10189.5i) q^{50} +11949.7 q^{51} +(-1609.50 + 522.959i) q^{52} +(-15539.1 - 21387.8i) q^{53} +(4480.15 - 3255.02i) q^{54} +(789.954 + 261.275i) q^{55} +(5379.06 + 3908.12i) q^{56} +50013.9i q^{57} +(-5339.15 + 7348.71i) q^{58} +(-1213.21 + 3733.88i) q^{59} +(-14856.0 + 10674.6i) q^{60} +(11968.9 + 36836.4i) q^{61} +(-29540.7 - 9598.34i) q^{62} +(-17321.3 - 5628.05i) q^{63} +(-1265.73 - 3895.53i) q^{64} +(4801.75 - 3450.22i) q^{65} +(376.280 - 1158.07i) q^{66} +(-33136.2 + 45608.1i) q^{67} -9348.19i q^{68} +(69686.4 + 50630.1i) q^{69} +(-22055.2 - 7294.69i) q^{70} +(28132.6 - 20439.6i) q^{71} +(6594.85 + 9077.03i) q^{72} +(13129.6 - 4266.07i) q^{73} -22227.8 q^{74} +(38110.0 - 51309.7i) q^{75} +39125.7 q^{76} +(1470.60 - 477.827i) q^{77} +(-5086.20 - 7000.55i) q^{78} +(-23831.1 + 17314.3i) q^{79} +(8350.66 + 11621.8i) q^{80} +(57372.0 + 41683.2i) q^{81} -4253.53i q^{82} +(-33926.9 + 46696.4i) q^{83} +(-10505.6 + 32332.9i) q^{84} +(9929.30 + 31115.4i) q^{85} +(-24142.0 - 74301.5i) q^{86} +(-44172.2 - 14352.4i) q^{87} +(-905.954 - 294.362i) q^{88} +(-2404.58 - 7400.53i) q^{89} +(-31592.2 - 23208.0i) q^{90} +(3395.60 - 10450.6i) q^{91} +(39607.7 - 54515.4i) q^{92} -158819. i q^{93} +(45740.8 + 33232.7i) q^{94} +(-130229. + 41557.8i) q^{95} +(16943.6 - 12310.3i) q^{96} +(-71770.8 - 98784.0i) q^{97} +(22879.0 - 7433.84i) q^{98} +2609.31 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 $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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
$3$	12.0218	+	16.5465i	0.771196	+	1.06146i	0.996199	+	0.0871019i	$0.0277606\pi$
$3$	12.0218	+	16.5465i	0.771196	+	1.06146i	−0.225004	+	0.974358i	$0.572239\pi$
$4$	12.9443	−	9.40456i	0.404508	−	0.293893i
$5$	−33.0957	+	45.0519i	−0.592034	+	0.805913i
$5$	−33.0957	+	45.0519i	−0.592034	+	0.805913i
$6$	66.1861	+	48.0870i	0.750565	+	0.545318i
$7$			103.889i			0.801353i	0.916220	+	0.400676i	$0.131225\pi$
$7$			103.889i			0.801353i	−0.916220	+	0.400676i	$0.868775\pi$
$8$	37.6183	−	51.7771i	0.207813	−	0.286031i
$9$	−54.1737	+	166.730i	−0.222937	+	0.686130i
$10$	−70.2163	+	212.296i	−0.222043	+	0.671340i
$11$	−4.59941	−	14.1555i	−0.0114609	−	0.0352731i	0.945163	−	0.326600i	$-0.105903\pi$
$11$	−4.59941	−	14.1555i	−0.0114609	−	0.0352731i	−0.956623	+	0.291327i	$0.905903\pi$
$12$	311.226	+	101.123i	0.623910	+	0.202721i
$13$	−100.594	−	32.6850i	−0.165087	−	0.0536401i	0.225307	−	0.974288i	$-0.427661\pi$
$13$	−100.594	−	32.6850i	−0.165087	−	0.0536401i	−0.390395	+	0.920648i	$0.627661\pi$
$14$	128.414	+	395.217i	0.175102	+	0.538909i
$15$	−1143.32	−	6.01571i	−1.31202	−	0.00690333i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	343.421	−	472.678i	0.288207	−	0.396682i	−0.640224	−	0.768188i	$-0.721158\pi$
$17$	343.421	−	472.678i	0.288207	−	0.396682i	0.928431	+	0.371506i	$0.121158\pi$
$18$			701.239i			0.510135i
$19$	1978.33	+	1437.34i	1.25723	+	0.913432i	0.998618	−	0.0525486i	$-0.0167345\pi$
$19$	1978.33	+	1437.34i	1.25723	+	0.913432i	0.258613	+	0.965981i	$0.416734\pi$
$20$	−4.70606	+	894.415i	−0.00263077	+	0.499993i
$21$	−1719.00	+	1248.93i	−0.850604	+	0.618000i
$22$	−34.9944	−	48.1656i	−0.0154149	−	0.0212168i
$23$	4005.42	−	1301.44i	1.57880	−	0.512984i	0.617055	−	0.786920i	$-0.288326\pi$
$23$	4005.42	−	1301.44i	1.57880	−	0.512984i	0.961748	+	0.273936i	$0.0883256\pi$
$24$	1308.97			0.463875
$25$	−934.350	−	2982.05i	−0.298992	−	0.954256i
$26$	−423.083			−0.122742
$27$	1316.68	−	427.816i	0.347593	−	0.112940i
$28$	977.029	+	1344.77i	0.235512	+	0.324154i
$29$	−1837.18	+	1334.79i	−0.405655	+	0.294725i	−0.771840	−	0.635817i	$-0.780663\pi$
$29$	−1837.18	+	1334.79i	−0.405655	+	0.294725i	0.366186	+	0.930542i	$0.380663\pi$
$30$	−4356.89	+	1390.34i	−0.883839	+	0.282044i
$31$	−6282.20	−	4564.28i	−1.17411	−	0.853038i	−0.182612	−	0.983185i	$-0.558455\pi$
$31$	−6282.20	−	4564.28i	−1.17411	−	0.853038i	−0.991495	+	0.130147i	$0.958455\pi$
$32$		−	1024.00i		−	0.176777i
$33$	178.932	−	246.278i	0.0286024	−	0.0393678i
$34$	722.187	−	2222.66i	0.107140	−	0.329744i
$35$	−4680.39	−	3438.27i	−0.645821	−	0.474428i
$36$	866.780	+	2667.67i	0.111469	+	0.343065i
$37$	−5284.96	−	1717.19i	−0.634655	−	0.206212i	−0.0260189	−	0.999661i	$-0.508283\pi$
$37$	−5284.96	−	1717.19i	−0.634655	−	0.206212i	−0.608636	+	0.793450i	$0.708283\pi$
$38$	9302.68	+	3022.62i	1.04508	+	0.339567i
$39$	−668.493	−	2057.41i	−0.0703778	−	0.216601i
$40$	1087.65	+	3408.37i	0.107483	+	0.336819i
$41$	328.604	−	1011.34i	0.0305290	−	0.0939586i	−0.934631	−	0.355619i	$-0.884270\pi$
$41$	328.604	−	1011.34i	0.0305290	−	0.0939586i	0.965160	+	0.261660i	$0.0842701\pi$
$42$	−4995.70	+	6876.00i	−0.436992	+	0.601468i
$43$		−	19531.3i		−	1.61087i	−0.592685	−	0.805434i	$-0.701932\pi$
$43$		−	19531.3i		−	1.61087i	0.592685	−	0.805434i	$-0.298068\pi$
$44$	−192.663	−	139.978i	−0.0150026	−	0.0109000i
$45$	−5718.57	−	7958.66i	−0.420975	−	0.585880i
$46$	13628.8	−	9901.93i	0.949652	−	0.689962i
$47$	8308.17	+	11435.2i	0.548606	+	0.755091i	0.989822	−	0.142309i	$-0.0454528\pi$
$47$	8308.17	+	11435.2i	0.548606	+	0.755091i	−0.441216	+	0.897401i	$0.645453\pi$
$48$	4979.61	−	1617.97i	0.311955	−	0.101360i
$49$	6014.11			0.357833
$50$	−7240.49	−	10189.5i	−0.409584	−	0.576403i
$51$	11949.7			0.643326
$52$	−1609.50	+	522.959i	−0.0825436	+	0.0268201i
$53$	−15539.1	−	21387.8i	−0.759866	−	1.04587i	−0.997225	−	0.0744439i	$-0.976282\pi$
$53$	−15539.1	−	21387.8i	−0.759866	−	1.04587i	0.237359	−	0.971422i	$-0.423718\pi$
$54$	4480.15	−	3255.02i	0.209078	−	0.151904i
$55$	789.954	+	261.275i	0.0352124	+	0.0116464i
$56$	5379.06	+	3908.12i	0.229212	+	0.166532i
$57$			50013.9i			2.03894i
$58$	−5339.15	+	7348.71i	−0.208402	+	0.286841i
$59$	−1213.21	+	3733.88i	−0.0453739	+	0.139646i	−0.971177	−	0.238360i	$-0.923390\pi$
$59$	−1213.21	+	3733.88i	−0.0453739	+	0.139646i	0.925803	+	0.378006i	$0.123390\pi$
$60$	−14856.0	+	10674.6i	−0.532751	+	0.382800i
$61$	11968.9	+	36836.4i	0.411840	+	1.26751i	0.915047	+	0.403347i	$0.132153\pi$
$61$	11968.9	+	36836.4i	0.411840	+	1.26751i	−0.503207	+	0.864166i	$0.667847\pi$
$62$	−29540.7	−	9598.34i	−0.975980	−	0.317115i
$63$	−17321.3	−	5628.05i	−0.549832	−	0.178651i
$64$	−1265.73	−	3895.53i	−0.0386271	−	0.118882i
$65$	4801.75	−	3450.22i	0.140967	−	0.101289i
$66$	376.280	−	1158.07i	0.0106329	−	0.0327247i
$67$	−33136.2	+	45608.1i	−0.901811	+	1.24124i	0.0680752	+	0.997680i	$0.478314\pi$
$67$	−33136.2	+	45608.1i	−0.901811	+	1.24124i	−0.969887	+	0.243557i	$0.921686\pi$
$68$		−	9348.19i		−	0.245163i
$69$	69686.4	+	50630.1i	1.76208	+	1.28022i
$70$	−22055.2	−	7294.69i	−0.537980	−	0.177935i
$71$	28132.6	−	20439.6i	0.662315	−	0.481200i	−0.205129	−	0.978735i	$-0.565761\pi$
$71$	28132.6	−	20439.6i	0.662315	−	0.481200i	0.867444	+	0.497535i	$0.165761\pi$
$72$	6594.85	+	9077.03i	0.149925	+	0.206354i
$73$	13129.6	−	4266.07i	0.288367	−	0.0936960i	−0.161262	−	0.986912i	$-0.551556\pi$
$73$	13129.6	−	4266.07i	0.288367	−	0.0936960i	0.449629	+	0.893216i	$0.351556\pi$
$74$	−22227.8			−0.471863
$75$	38110.0	−	51309.7i	0.782323	−	1.05329i
$76$	39125.7			0.777012
$77$	1470.60	−	477.827i	0.0282662	−	0.00918426i
$78$	−5086.20	−	7000.55i	−0.0946579	−	0.130285i
$79$	−23831.1	+	17314.3i	−0.429612	+	0.312131i	−0.781494	−	0.623913i	$-0.785542\pi$
$79$	−23831.1	+	17314.3i	−0.429612	+	0.312131i	0.351882	+	0.936044i	$0.385542\pi$
$80$	8350.66	+	11621.8i	0.145880	+	0.203025i
$81$	57372.0	+	41683.2i	0.971601	+	0.705909i
$82$		−	4253.53i		−	0.0698579i
$83$	−33926.9	+	46696.4i	−0.540566	+	0.744026i	−0.988695	−	0.149944i	$-0.952091\pi$
$83$	−33926.9	+	46696.4i	−0.540566	+	0.744026i	0.448128	+	0.893969i	$0.352091\pi$
$84$	−10505.6	+	32332.9i	−0.162451	+	0.499972i
$85$	9929.30	+	31115.4i	0.149063	+	0.467119i
$86$	−24142.0	−	74301.5i	−0.351988	−	1.08331i
$87$	−44172.2	−	14352.4i	−0.625678	−	0.203295i
$88$	−905.954	−	294.362i	−0.0124709	−	0.00405205i
$89$	−2404.58	−	7400.53i	−0.0321784	−	0.0990348i	0.933677	−	0.358115i	$-0.116581\pi$
$89$	−2404.58	−	7400.53i	−0.0321784	−	0.0990348i	−0.965856	+	0.259080i	$0.916581\pi$
$90$	−31592.2	−	23208.0i	−0.411124	−	0.302017i
$91$	3395.60	−	10450.6i	0.0429847	−	0.132293i
$92$	39607.7	−	54515.4i	0.487877	−	0.671505i
$93$		−	158819.i		−	1.90413i
$94$	45740.8	+	33232.7i	0.533930	+	0.387923i
$95$	−130229.	+	41557.8i	−1.48047	+	0.472437i
$96$	16943.6	−	12310.3i	0.187641	−	0.136329i
$97$	−71770.8	−	98784.0i	−0.774494	−	1.06600i	−0.995868	−	0.0908110i	$-0.971054\pi$
$97$	−71770.8	−	98784.0i	−0.774494	−	1.06600i	0.221374	−	0.975189i	$-0.428946\pi$
$98$	22879.0	−	7433.84i	0.240642	−	0.0781895i
$99$	2609.31			0.0267570
$100$	−40139.3	−	29813.3i	−0.401393	−	0.298133i
$101$	82637.6			0.806073			0.403036	−	0.915184i	$-0.367955\pi$
$101$	82637.6			0.806073			0.403036	+	0.915184i	$0.367955\pi$
$102$	45459.3	−	14770.6i	0.432636	−	0.140572i
$103$	−95292.3	−	131159.i	−0.885044	−	1.21816i	−0.974998	−	0.222212i	$-0.928672\pi$
$103$	−95292.3	−	131159.i	−0.885044	−	1.21816i	0.0899545	−	0.995946i	$-0.471328\pi$
$104$	−5476.50	+	3978.91i	−0.0496501	+	0.0360729i
$105$	624.965	−	118778.i	0.00553200	−	1.05139i
$106$	−85551.1	−	62156.5i	−0.739539	−	0.537306i
$107$			9449.42i			0.0797895i	0.999204	+	0.0398948i	$0.0127023\pi$
$107$			9449.42i			0.0797895i	−0.999204	+	0.0398948i	$0.987298\pi$
$108$	13020.1	−	17920.6i	0.107412	−	0.147840i
$109$	−39705.1	+	122200.i	−0.320096	+	0.985153i	0.653510	+	0.756918i	$0.273296\pi$
$109$	−39705.1	+	122200.i	−0.320096	+	0.985153i	−0.973606	+	0.228235i	$0.926704\pi$
$110$	3328.12	+	17.5113i	0.0262251	+	0.000137986i
$111$	−35121.0	−	108091.i	−0.270558	−	0.832690i
$112$	25293.9	+	8218.48i	0.190533	+	0.0619079i
$113$	181777.	+	59063.0i	1.33919	+	0.435131i	0.889044	−	0.457822i	$-0.151370\pi$
$113$	181777.	+	59063.0i	1.33919	+	0.435131i	0.450150	+	0.892953i	$0.351370\pi$
$114$	61820.6	+	190264.i	0.445524	+	1.37118i
$115$	−73929.7	+	223524.i	−0.521284	+	1.57608i
$116$	−11227.8	+	34555.7i	−0.0774731	+	0.238438i
$117$	10899.1	−	15001.3i	0.0736082	−	0.101313i
$118$			15704.1i			0.103827i
$119$	49106.0	+	35677.6i	0.317883	+	0.230955i
$120$	−43321.2	+	58971.5i	−0.274630	+	0.373843i
$121$	130114.	−	94533.2i	0.807904	−	0.586977i
$122$	91064.5	+	125340.i	0.553923	+	0.762410i
$123$	20684.5	−	6720.81i	0.123277	−	0.0400552i
$124$	−124244.			−0.725638
$125$	165270.	+	56598.7i	0.946061	+	0.323990i
$126$	−72851.0			−0.408798
$127$	−262120.	+	85168.0i	−1.44209	+	0.468562i	−0.922547	−	0.385885i	$-0.873896\pi$
$127$	−262120.	+	85168.0i	−1.44209	+	0.468562i	−0.519539	+	0.854447i	$0.673896\pi$
$128$	−9630.27	−	13254.9i	−0.0519534	−	0.0715077i
$129$	323175.	−	234800.i	1.70987	−	1.24229i
$130$	14002.2	−	19060.7i	0.0726673	−	0.0989192i
$131$	42969.6	+	31219.2i	0.218767	+	0.158944i	0.691772	−	0.722116i	$-0.256830\pi$
$131$	42969.6	+	31219.2i	0.218767	+	0.158944i	−0.473004	+	0.881060i	$0.656830\pi$
$132$		−	4870.67i		−	0.0243307i
$133$	−149324.	+	205527.i	−0.731982	+	1.00749i
$134$	−69682.9	+	214462.i	−0.335247	+	1.03178i
$135$	−24302.6	+	73477.9i	−0.114767	+	0.346994i
$136$	−11555.0	−	35562.6i	−0.0535701	−	0.164872i
$137$	−76999.2	−	25018.6i	−0.350498	−	0.113884i	0.128477	−	0.991713i	$-0.458991\pi$
$137$	−76999.2	−	25018.6i	−0.350498	−	0.113884i	−0.478974	+	0.877829i	$0.658991\pi$
$138$	327685.	+	106471.i	1.46473	+	0.475921i
$139$	−120666.	−	371372.i	−0.529723	−	1.63032i	−0.754783	−	0.655974i	$-0.772258\pi$
$139$	−120666.	−	371372.i	−0.529723	−	1.63032i	0.225060	−	0.974345i	$-0.427742\pi$
$140$	−92919.7	−	488.907i	−0.400671	−	0.00210817i
$141$	−89334.2	+	274943.i	−0.378417	+	1.16465i
$142$	81758.2	−	112531.i	0.340260	−	0.468327i
$143$			1574.29i			0.00643791i
$144$	36308.1	+	26379.4i	0.145914	+	0.106013i
$145$	667.931	−	126944.i	0.00263822	−	0.501410i
$146$	44674.9	−	32458.2i	0.173453	−	0.126021i
$147$	72300.1	+	99512.5i	0.275960	+	0.379826i
$148$	−84559.4	+	27475.0i	−0.317327	+	0.103106i
$149$	−401488.			−1.48152			−0.740758	−	0.671772i	$-0.765534\pi$
$149$	−401488.			−1.48152			−0.740758	+	0.671772i	$0.765534\pi$
$150$	81556.8	−	242300.i	0.295959	−	0.879277i
$151$	−361831.			−1.29141			−0.645704	−	0.763588i	$-0.723436\pi$
$151$	−361831.			−1.29141			−0.645704	+	0.763588i	$0.723436\pi$
$152$	148843.	−	48362.0i	0.522539	−	0.169783i
$153$	60205.0	+	82865.1i	0.207924	+	0.286182i
$154$	5003.87	−	3635.53i	0.0170022	−	0.0123528i
$155$	413543.	−	131967.i	1.38259	−	0.441200i
$156$	−28002.2	−	20344.8i	−0.0921257	−	0.0669332i
$157$			448290.i			1.45148i	0.687970	+	0.725739i	$0.258502\pi$
$157$			448290.i			1.45148i	−0.687970	+	0.725739i	$0.741498\pi$
$158$	−69257.2	+	95324.3i	−0.220710	+	0.303781i
$159$	167086.	−	514237.i	0.524139	−	1.61313i
$160$	46133.2	+	33890.0i	0.142467	+	0.104658i
$161$	135205.	+	416118.i	0.411081	+	1.26518i
$162$	269780.	+	87656.7i	0.807647	+	0.262420i
$163$	−385547.	−	125272.i	−1.13660	−	0.369304i	−0.320520	−	0.947242i	$-0.603858\pi$
$163$	−385547.	−	125272.i	−1.13660	−	0.369304i	−0.816081	+	0.577937i	$0.803858\pi$
$164$	−5257.66	−	16181.4i	−0.0152645	−	0.0469793i
$165$	5173.44	+	16212.0i	0.0147935	+	0.0463581i
$166$	−71345.7	+	219579.i	−0.200954	+	0.618474i
$167$	310609.	−	427516.i	0.861832	−	1.18621i	−0.119297	−	0.992859i	$-0.538064\pi$
$167$	310609.	−	427516.i	0.861832	−	1.18621i	0.981130	−	0.193352i	$-0.0619358\pi$
$168$			135987.i			0.371728i
$169$	−291332.	−	211665.i	−0.784640	−	0.570075i
$170$	76234.0	+	106097.i	0.202314	+	0.281565i
$171$	−346821.	+	251980.i	−0.907017	+	0.658986i
$172$	−183683.	−	252818.i	−0.473422	−	0.651610i
$173$	178817.	−	58101.3i	0.454249	−	0.147595i	−0.0729512	−	0.997336i	$-0.523242\pi$
$173$	178817.	−	58101.3i	0.454249	−	0.147595i	0.527200	+	0.849741i	$0.323242\pi$
$174$	−185782.			−0.465189
$175$	309802.	−	97068.5i	0.764696	−	0.239598i
$176$	−3810.30			−0.00927210
$177$	−76367.5	+	24813.3i	−0.183221	+	0.0595322i
$178$	−18295.1	−	25181.1i	−0.0432798	−	0.0595695i
$179$	475197.	−	345251.i	1.10851	−	0.805383i	0.126085	−	0.992019i	$-0.459759\pi$
$179$	475197.	−	345251.i	1.10851	−	0.805383i	0.982429	+	0.186637i	$0.0597587\pi$
$180$	−148870.	−	49238.4i	−0.342474	−	0.113272i
$181$	508588.	+	369511.i	1.15390	+	0.838360i	0.988995	−	0.147949i	$-0.0472670\pi$
$181$	508588.	+	369511.i	1.15390	+	0.838360i	0.164909	+	0.986309i	$0.447267\pi$
$182$		−	43953.6i		−	0.0983595i
$183$	−465627.	+	640881.i	−1.02780	+	1.41465i
$184$	83292.0	−	256347.i	0.181367	−	0.558191i
$185$	252272.	−	181266.i	0.541926	−	0.389392i
$186$	−196311.	−	604184.i	−0.416067	−	1.28052i
$187$	−8270.53	−	2687.26i	−0.0172954	−	0.00561960i
$188$	215086.	+	69885.8i	0.443832	+	0.144210i
$189$	44445.3	+	136789.i	0.0905047	+	0.278545i
$190$	−444054.	+	319068.i	−0.892383	+	0.641208i
$191$	65473.7	−	201507.i	0.129862	−	0.399675i	−0.864893	−	0.501956i	$-0.832614\pi$
$191$	65473.7	−	201507.i	0.129862	−	0.399675i	0.994756	+	0.102281i	$0.0326139\pi$
$192$	49241.1	−	67774.6i	0.0963995	−	0.132682i
$193$		−	406833.i		−	0.786182i	−0.919500	−	0.393091i	$-0.871406\pi$
$193$		−	406833.i		−	0.786182i	0.919500	−	0.393091i	$-0.128594\pi$
$194$	−395136.	−	287083.i	−0.753776	−	0.547650i
$195$	114815.	+	37974.5i	0.216227	+	0.0715165i
$196$	77848.2	−	56560.0i	0.144747	−	0.105165i
$197$	−180726.	−	248748.i	−0.331783	−	0.456660i	0.610236	−	0.792220i	$-0.291075\pi$
$197$	−180726.	−	248748.i	−0.331783	−	0.456660i	−0.942019	+	0.335559i	$0.891075\pi$
$198$	9926.41	−	3225.29i	0.0179941	−	0.00584663i
$199$	−267695.			−0.479190			−0.239595	−	0.970873i	$-0.577015\pi$
$199$	−267695.			−0.479190			−0.239595	+	0.970873i	$0.577015\pi$
$200$	−189550.	−	63801.6i	−0.335081	−	0.112786i
$201$	−1.15301e6			−2.01300
$202$	314372.	−	102146.i	0.542083	−	0.176133i
$203$	−138670.	−	190862.i	−0.236179	−	0.325072i
$204$	154680.	−	112382.i	0.260231	−	0.189069i
$205$	34687.3	+	48275.1i	0.0576483	+	0.0802304i
$206$	−524634.	−	381169.i	−0.861368	−	0.625820i
$207$			738325.i			1.19763i
$208$	−15915.6	+	21906.0i	−0.0255074	+	0.0351079i
$209$	11247.2	−	34615.3i	0.0178106	−	0.0548153i
$210$	−144441.	−	452632.i	−0.226017	−	0.708267i
$211$	−18360.9	−	56509.1i	−0.0283915	−	0.0873801i	0.935857	−	0.352381i	$-0.114628\pi$
$211$	−18360.9	−	56509.1i	−0.0283915	−	0.0873801i	−0.964248	+	0.265001i	$0.914628\pi$
$212$	−402285.	−	130710.i	−0.614745	−	0.199743i
$213$	676407.	+	219778.i	1.02155	+	0.331921i
$214$	11680.1	+	35947.7i	0.0174346	+	0.0536583i
$215$	879922.	+	646402.i	1.29822	+	0.953688i
$216$	27380.2	−	84267.6i	0.0399303	−	0.122893i
$217$	474178.	−	652650.i	0.683585	−	0.940874i
$218$			513953.i			0.732457i
$219$	228430.	+	165964.i	0.321842	+	0.233832i
$220$	12682.6	−	4047.16i	0.0176665	−	0.00563760i
$221$	−49995.5	+	36323.9i	−0.0688573	+	0.0500278i
$222$	−267217.	−	367792.i	−0.363899	−	0.500864i
$223$	−221957.	+	72118.1i	−0.298886	+	0.0971140i	−0.454621	−	0.890685i	$-0.650225\pi$
$223$	−221957.	+	72118.1i	−0.298886	+	0.0971140i	0.155735	+	0.987799i	$0.450225\pi$
$224$	106382.			0.141661
$225$	547813.	+	5764.92i	0.721400	+	0.00759166i
$226$	764528.			0.995685
$227$	1.16802e6	−	379513.i	1.50448	−	0.488835i	0.563159	−	0.826349i	$-0.309586\pi$
$227$	1.16802e6	−	379513.i	1.50448	−	0.488835i	0.941321	+	0.337513i	$0.109586\pi$
$228$	470359.	+	647394.i	0.599228	+	0.824767i
$229$	−693319.	+	503726.i	−0.873664	+	0.634754i	−0.931568	−	0.363568i	$-0.881558\pi$
$229$	−693319.	+	503726.i	−0.873664	+	0.634754i	0.0579033	+	0.998322i	$0.481558\pi$
$230$	−4954.95	+	941717.i	−0.00617617	+	1.17382i
$231$	25585.6	+	18589.0i	0.0315475	+	0.0229206i
$232$			145336.i			0.177278i
$233$	303356.	−	417533.i	0.366068	−	0.503850i	−0.585759	−	0.810486i	$-0.699203\pi$
$233$	303356.	−	417533.i	0.366068	−	0.503850i	0.951827	+	0.306636i	$0.0992033\pi$
$234$	22920.0	−	70540.5i	0.0273637	−	0.0842168i
$235$	−790143.	−	4157.42i	−0.933331	−	0.00491083i
$236$	19411.4	+	59742.0i	0.0226869	+	0.0698232i
$237$	−572983.	−	186173.i	−0.662629	−	0.215301i
$238$	230910.	+	75027.2i	0.264241	+	0.0858572i
$239$	463482.	+	1.42645e6i	0.524853	+	1.61533i	0.764605	+	0.644499i	$0.222934\pi$
$239$	463482.	+	1.42645e6i	0.524853	+	1.61533i	−0.239752	+	0.970834i	$0.577066\pi$
$240$	−91910.9	+	277889.i	−0.103000	+	0.311418i
$241$	24392.4	−	75072.0i	0.0270527	−	0.0832598i	−0.936619	−	0.350351i	$-0.886062\pi$
$241$	24392.4	−	75072.0i	0.0270527	−	0.0832598i	0.963671	+	0.267091i	$0.0860624\pi$
$242$	378133.	−	520455.i	0.415055	−	0.571275i
$243$			1.11399e6i			1.21023i
$244$	501358.	+	364258.i	0.539105	+	0.391683i
$245$	−199041.	+	270947.i	−0.211849	+	0.288383i
$246$	70381.2	−	51134.9i	0.0741513	−	0.0538741i
$247$	−152029.	−	209250.i	−0.158556	−	0.218234i
$248$	−472651.	+	153574.i	−0.487990	+	0.158558i
$249$	−1.18052e6			−1.20664
$250$	698684.	+	11029.4i	0.707019	+	0.0111610i
$251$	−877883.			−0.879533			−0.439767	−	0.898112i	$-0.644939\pi$
$251$	−877883.			−0.879533			−0.439767	+	0.898112i	$0.644939\pi$
$252$	−277142.	+	90048.7i	−0.274916	+	0.0893257i
$253$	−36845.1	−	50712.9i	−0.0361891	−	0.0498101i
$254$	−891891.	+	647997.i	−0.867416	+	0.630215i
$255$	−395483.	+	538356.i	−0.380871	+	0.518465i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$		−	327744.i		−	0.309530i	−0.987951	−	0.154765i	$-0.950538\pi$
$257$		−	327744.i		−	0.309530i	0.987951	−	0.154765i	$-0.0494620\pi$
$258$	939202.	−	1.29270e6i	0.878435	−	1.20906i
$259$	178397.	−	549049.i	0.165249	−	0.508583i
$260$	29707.3	−	89818.9i	0.0272540	−	0.0824014i
$261$	−123022.	−	378622.i	−0.111784	−	0.344037i
$262$	202055.	+	65651.6i	0.181851	+	0.0590871i
$263$	−1.74240e6	−	566140.i	−1.55331	−	0.504701i	−0.598300	−	0.801272i	$-0.704157\pi$
$263$	−1.74240e6	−	566140.i	−1.55331	−	0.504701i	−0.955011	+	0.296571i	$0.904157\pi$
$264$	−6020.48	−	18529.1i	−0.00531644	−	0.0163623i
$265$	1.47784e6	+	7775.81i	1.29274	+	0.00680191i
$266$	−314017.	+	966445.i	−0.272113	+	0.837477i
$267$	93545.8	−	128755.i	0.0803056	−	0.110531i
$268$			901995.i			0.767127i
$269$	262982.	+	191067.i	0.221587	+	0.160993i	0.693041	−	0.720898i	$-0.256271\pi$
$269$	262982.	+	191067.i	0.221587	+	0.160993i	−0.471454	+	0.881891i	$0.656271\pi$
$270$	−1628.82	+	309566.i	−0.00135976	+	0.258431i
$271$	371947.	−	270236.i	0.307651	−	0.223521i	−0.423237	−	0.906019i	$-0.639106\pi$
$271$	371947.	−	270236.i	0.307651	−	0.223521i	0.730888	+	0.682498i	$0.239106\pi$
$272$	−87915.7	−	121006.i	−0.0720517	−	0.0991706i
$273$	213742.	−	69449.0i	0.173573	−	0.0563974i
$274$	−323847.			−0.260594
$275$	−37915.0	+	26941.9i	−0.0302329	+	0.0214831i
$276$	1.37819e6			1.08902
$277$	−1.21701e6	+	395431.i	−0.953006	+	0.309650i	−0.743936	−	0.668251i	$-0.767043\pi$
$277$	−1.21701e6	+	395431.i	−0.953006	+	0.309650i	−0.209069	+	0.977901i	$0.567043\pi$
$278$	−918083.	−	1.26363e6i	−0.712476	−	0.980639i
$279$	1.10133e6	−	800164.i	0.847047	−	0.615416i
$280$	−354092.	+	112995.i	−0.269911	+	0.0861321i
$281$	1.16899e6	+	849324.i	0.883175	+	0.641664i	0.934090	−	0.357039i	$-0.116214\pi$
$281$	1.16899e6	+	849324.i	0.883175	+	0.641664i	−0.0509146	+	0.998703i	$0.516214\pi$
$282$			1.15637e6i			0.865910i
$283$	722022.	−	993778.i	0.535900	−	0.737604i	−0.452115	−	0.891960i	$-0.649330\pi$
$283$	722022.	−	993778.i	0.535900	−	0.737604i	0.988015	+	0.154356i	$0.0493303\pi$
$284$	171931.	−	529150.i	0.126491	−	0.389299i
$285$	−2.25322e6	−	1.65524e6i	−1.64321	−	1.20712i
$286$	1945.93	+	5988.96i	0.00140674	+	0.00432949i
$287$	105067.	+	34138.2i	0.0752940	+	0.0244645i
$288$	170731.	+	55473.9i	0.121292	+	0.0394101i
$289$	333273.	+	1.02571e6i	0.234723	+	0.722404i
$290$	−154371.	−	483750.i	−0.107788	−	0.337774i
$291$	771721.	−	2.37511e6i	0.534229	−	1.64419i
$292$	129833.	−	178700.i	0.0891102	−	0.122650i
$293$		−	1.58060e6i		−	1.07560i	−0.843072	−	0.537801i	$-0.819255\pi$
$293$		−	1.58060e6i		−	1.07560i	0.843072	−	0.537801i	$-0.180745\pi$
$294$	398050.	+	289200.i	0.268577	+	0.195133i
$295$	−128066.	−	178233.i	−0.0856800	−	0.119243i
$296$	−287722.	+	209042.i	−0.190873	+	0.138677i
$297$	−12111.9	−	16670.6i	−0.00796749	−	0.0109663i
$298$	−1.52735e6	+	496266.i	−0.996318	+	0.323723i
$299$	−445458.			−0.288157
$300$	10761.1	−	1.02257e6i	0.00690323	−	0.655982i
$301$	2.02908e6			1.29087
$302$	−1.37649e6	+	447248.i	−0.868470	+	0.282183i
$303$	993449.	+	1.36736e6i	0.621640	+	0.855614i
$304$	506453.	−	367960.i	0.314308	−	0.228358i
$305$	−2.05567e6	−	679905.i	−1.26533	−	0.418503i
$306$	331460.	+	240820.i	0.202362	+	0.147024i
$307$			1.31146e6i			0.794164i	0.917783	+	0.397082i	$0.129977\pi$
$307$			1.31146e6i			0.794164i	−0.917783	+	0.397082i	$0.870023\pi$
$308$	14542.1	−	20015.5i	0.00873475	−	0.0120224i
$309$	1.02464e6	−	3.15351e6i	0.610484	−	1.87888i
$310$	1.41009e6	−	1.01320e6i	0.833381	−	0.598812i
$311$	−276210.	−	850086.i	−0.161934	−	0.498382i	0.836863	−	0.547412i	$-0.184387\pi$
$311$	−276210.	−	850086.i	−0.161934	−	0.498382i	−0.998797	+	0.0490304i	$0.984387\pi$
$312$	−131674.	−	42783.6i	−0.0765798	−	0.0248823i
$313$	−2.98990e6	−	971478.i	−1.72503	−	0.560496i	−0.732311	−	0.680970i	$-0.761558\pi$
$313$	−2.98990e6	−	971478.i	−1.72503	−	0.560496i	−0.992716	+	0.120474i	$0.961558\pi$
$314$	554117.	+	1.70540e6i	0.317159	+	0.976116i
$315$	826816.	−	594096.i	0.469497	−	0.337349i
$316$	−145643.	+	448242.i	−0.0820485	+	0.252519i
$317$	−594874.	+	818774.i	−0.332489	+	0.457632i	−0.942229	−	0.334970i	$-0.891274\pi$
$317$	−594874.	+	818774.i	−0.332489	+	0.457632i	0.609740	+	0.792602i	$0.291274\pi$
$318$		−	2.16280e6i		−	1.19936i
$319$	27344.6	+	19867.0i	0.0150451	+	0.0109309i
$320$	217391.	+	71901.5i	0.118677	+	0.0392521i
$321$	−156355.	+	113599.i	−0.0846934	+	0.0615333i
$322$	1.02870e6	+	1.41588e6i	0.552903	+	0.761006i
$323$	1.35880e6	−	441501.i	0.724685	−	0.235464i
$324$	1.13465e6			0.600482
$325$	−3478.18	+	330515.i	−0.00182660	+	0.173573i
$326$	−1.62155e6			−0.845059
$327$	−2.49930e6	+	812073.i	−1.29256	+	0.419977i
$328$	−40002.6	−	55058.9i	−0.0205307	−	0.0282581i
$329$	−1.18799e6	+	863126.i	−0.605095	+	0.439627i
$330$	39720.0	+	55279.3i	0.0200782	+	0.0279433i
$331$	1.86515e6	+	1.35511e6i	0.935716	+	0.679837i	0.947386	−	0.320095i	$-0.103715\pi$
$331$	1.86515e6	+	1.35511e6i	0.935716	+	0.679837i	−0.0116698	+	0.999932i	$0.503715\pi$
$332$			923518.i			0.459833i
$333$	572612.	−	788133.i	0.282976	−	0.389483i
$334$	653187.	−	2.01030e6i	0.320384	−	0.986042i
$335$	−958065.	−	3.00228e6i	−0.466426	−	1.46164i
$336$	168089.	+	517326.i	0.0812255	+	0.249986i
$337$	1.65231e6	+	536868.i	0.792532	+	0.257509i	0.677182	−	0.735816i	$-0.263201\pi$
$337$	1.65231e6	+	536868.i	0.792532	+	0.257509i	0.115350	+	0.993325i	$0.463201\pi$
$338$	−1.36992e6	−	445115.i	−0.652235	−	0.211924i
$339$	1.20799e6	+	3.71782e6i	0.570907	+	1.75707i
$340$	421154.	+	309385.i	0.197580	+	0.145145i
$341$	−35715.4	+	109921.i	−0.0166330	+	0.0511910i
$342$	−1.00792e6	+	1.38728e6i	−0.465974	+	0.641358i
$343$			2.37086e6i			1.08810i
$344$	−1.01127e6	−	734733.i	−0.460758	−	0.334760i
$345$	−4.58730e6	+	1.46387e6i	−2.07496	+	0.662146i
$346$	608444.	−	442061.i	0.273231	−	0.198514i
$347$	−590506.	−	812762.i	−0.263270	−	0.362360i	0.656834	−	0.754036i	$-0.271895\pi$
$347$	−590506.	−	812762.i	−0.263270	−	0.362360i	−0.920103	+	0.391676i	$0.871895\pi$
$348$	−706755.	+	229639.i	−0.312839	+	0.101648i
$349$	−1.29519e6			−0.569208			−0.284604	−	0.958645i	$-0.591862\pi$
$349$	−1.29519e6			−0.569208			−0.284604	+	0.958645i	$0.591862\pi$
$350$	1.05857e6	−	752207.i	0.461903	−	0.328221i
$351$	−146433.			−0.0634413
$352$	−14495.3	+	4709.79i	−0.00623547	+	0.00202603i
$353$	1.27131e6	+	1.74980e6i	0.543017	+	0.747398i	0.989044	−	0.147621i	$-0.0471616\pi$
$353$	1.27131e6	+	1.74980e6i	0.543017	+	0.747398i	−0.446027	+	0.895019i	$0.647162\pi$
$354$	−259848.	+	188791.i	−0.110208	+	0.0800706i
$355$	−10228.0	+	1.94389e6i	−0.00430744	+	0.818655i
$356$	−100724.	−	73180.5i	−0.0421220	−	0.0306034i
$357$			1.24144e6i			0.515531i
$358$	1.38100e6	−	1.90079e6i	0.569492	−	0.783838i
$359$	−694291.	+	2.13681e6i	−0.284319	+	0.875043i	0.702283	+	0.711898i	$0.252164\pi$
$359$	−694291.	+	2.13681e6i	−0.284319	+	0.875043i	−0.986602	+	0.163146i	$0.947836\pi$
$360$	−627199.	−	3300.08i	−0.255064	−	0.00134205i
$361$	1.08269e6	+	3.33217e6i	0.437256	+	1.34574i
$362$	2.39152e6	+	777053.i	0.959187	+	0.311659i
$363$	3.12839e6	+	1.01648e6i	1.24610	+	0.404884i
$364$	−54329.7	−	167209.i	−0.0214923	−	0.0661466i
$365$	−242339.	+	732703.i	−0.0952120	+	0.287870i
$366$	−979179.	+	3.01360e6i	−0.382084	+	1.17593i
$367$	−14933.4	+	20554.1i	−0.00578755	+	0.00796588i	−0.811901	−	0.583795i	$-0.801567\pi$
$367$	−14933.4	+	20554.1i	−0.00578755	+	0.00796588i	0.806113	+	0.591761i	$0.201567\pi$
$368$		−	1.07815e6i		−	0.415013i
$369$	150818.	+	109576.i	0.0576618	+	0.0418937i
$370$	735643.	−	1.00140e6i	0.279359	−	0.380281i
$371$	2.22195e6	−	1.61434e6i	0.838108	−	0.608921i
$372$	−1.49363e6	−	2.05580e6i	−0.559609	−	0.770235i
$373$	5.01359e6	−	1.62901e6i	1.86585	−	0.606251i	0.872873	−	0.487948i	$-0.162254\pi$
$373$	5.01359e6	−	1.62901e6i	1.86585	−	0.606251i	0.992977	−	0.118304i	$-0.0377456\pi$
$374$	−34784.6			−0.0128590
$375$	1.05032e6	+	3.41506e6i	0.385695	+	1.25406i
$376$	904621.			0.329987
$377$	228437.	−	74223.5i	0.0827775	−	0.0268960i
$378$	338160.	+	465437.i	0.121729	+	0.167545i
$379$	3.59784e6	−	2.61399e6i	1.28660	−	0.934771i	0.286871	−	0.957969i	$-0.407385\pi$
$379$	3.59784e6	−	2.61399e6i	1.28660	−	0.934771i	0.999731	+	0.0231977i	$0.00738472\pi$
$380$	−1.29489e6	+	1.76269e6i	−0.460017	+	0.626204i
$381$	−4.56038e6	−	3.31331e6i	−1.60949	−	1.16936i
$382$		−	847510.i		−	0.297157i
$383$	1.07947e6	−	1.48576e6i	0.376022	−	0.517549i	−0.578503	−	0.815680i	$-0.696363\pi$
$383$	1.07947e6	−	1.48576e6i	0.376022	−	0.517549i	0.954525	+	0.298130i	$0.0963631\pi$
$384$	103550.	−	318695.i	0.0358363	−	0.110293i
$385$	−27143.5	+	82067.4i	−0.00933286	+	0.0282175i
$386$	−502873.	−	1.54769e6i	−0.171787	−	0.528706i
$387$	3.25645e6	+	1.05808e6i	1.10526	+	0.359122i
$388$	−1.85804e6	−	603714.i	−0.626579	−	0.203588i
$389$	1.23051e6	+	3.78712e6i	0.412298	+	1.26892i	0.914645	+	0.404257i	$0.132470\pi$
$389$	1.23051e6	+	3.78712e6i	0.412298	+	1.26892i	−0.502347	+	0.864666i	$0.667530\pi$
$390$	483720.	+	2545.14i	0.161039	+	0.000847327i
$391$	760381.	−	2.34021e6i	0.251530	−	0.774129i
$392$	226240.	−	311393.i	0.0743626	−	0.102351i
$393$			1.08631e6i			0.354790i
$394$	−994990.	−	722903.i	−0.322908	−	0.234606i
$395$	8664.11	−	1.64666e6i	0.00279403	−	0.531022i
$396$	33775.6	−	24539.4i	0.0108234	−	0.00786370i
$397$	−1.03804e6	−	1.42874e6i	−0.330552	−	0.454965i	0.611101	−	0.791553i	$-0.290727\pi$
$397$	−1.03804e6	−	1.42874e6i	−0.330552	−	0.454965i	−0.941652	+	0.336588i	$0.890727\pi$
$398$	−1.01837e6	+	330890.i	−0.322255	+	0.104707i
$399$	−5.19589e6			−1.63391
$400$	−799956.	−	8418.34i	−0.249986	−	0.00263073i
$401$	−2.70823e6			−0.841055			−0.420527	−	0.907280i	$-0.638155\pi$
$401$	−2.70823e6			−0.841055			−0.420527	+	0.907280i	$0.638155\pi$
$402$	−4.38631e6	+	1.42520e6i	−1.35374	+	0.439856i
$403$	482768.	+	664473.i	0.148073	+	0.203805i
$404$	1.06968e6	−	777171.i	0.326063	−	0.236899i
$405$	−3.77668e6	+	1.20518e6i	−1.14412	+	0.365104i
$406$	−763449.	−	554678.i	−0.229861	−	0.167004i
$407$			82709.5i			0.0247497i
$408$	449526.	−	618720.i	0.133692	−	0.184011i
$409$	268287.	−	825702.i	0.0793032	−	0.244070i	−0.903543	−	0.428498i	$-0.859043\pi$
$409$	268287.	−	825702.i	0.0793032	−	0.244070i	0.982846	+	0.184427i	$0.0590430\pi$
$410$	191630.	+	140774.i	0.0562994	+	0.0413582i
$411$	−511695.	−	1.57484e6i	−0.149419	−	0.459866i
$412$	−2.46698e6	−	801570.i	−0.716015	−	0.232648i
$413$	−387908.	−	126039.i	−0.111906	−	0.0363605i
$414$	912620.	+	2.80876e6i	0.261691	+	0.805403i
$415$	−980926.	−	3.07392e6i	−0.279587	−	0.876138i
$416$	−33469.4	+	103008.i	−0.00948232	+	0.0291836i
$417$	4.69430e6	−	6.46115e6i	1.32200	−	1.81957i
$418$		−	145587.i		−	0.0407550i
$419$	3.38115e6	+	2.45655e6i	0.940868	+	0.683581i	0.948629	−	0.316389i	$-0.102471\pi$
$419$	3.38115e6	+	2.45655e6i	0.940868	+	0.683581i	−0.00776131	+	0.999970i	$0.502471\pi$
$420$	−1.10897e6	−	1.54338e6i	−0.306758	−	0.426922i
$421$	1.37337e6	−	997812.i	0.377644	−	0.274374i	−0.382730	−	0.923860i	$-0.625016\pi$
$421$	1.37337e6	−	997812.i	0.377644	−	0.274374i	0.760374	+	0.649486i	$0.225016\pi$
$422$	−139698.	−	192278.i	−0.0381865	−	0.0525592i
$423$	−2.35667e6	+	765729.i	−0.640396	+	0.208077i
$424$	−1.69195e6			−0.457060
$425$	−1.73042e6	−	582450.i	−0.464708	−	0.156418i
$426$	2.84487e6			0.759518
$427$	−3.82689e6	+	1.24343e6i	−1.01573	+	0.330029i
$428$	88867.7	+	122316.i	0.0234495	+	0.0322755i
$429$	−26049.1	+	18925.7i	−0.00683359	+	0.00496489i
$430$	4.14642e6	+	1.37142e6i	1.08144	+	0.357683i
$431$	−3.42428e6	−	2.48788e6i	−0.887924	−	0.645115i	0.0474118	−	0.998875i	$-0.484903\pi$
$431$	−3.42428e6	−	2.48788e6i	−0.887924	−	0.645115i	−0.935336	+	0.353761i	$0.884903\pi$
$432$		−	354417.i		−	0.0913703i
$433$	−3.38446e6	+	4.65831e6i	−0.867501	+	1.19401i	0.112227	+	0.993683i	$0.464201\pi$
$433$	−3.38446e6	+	4.65831e6i	−0.867501	+	1.19401i	−0.979728	+	0.200330i	$0.935799\pi$
$434$	997161.	−	3.06895e6i	0.254121	−	0.782105i
$435$	2.10851e6	−	1.51504e6i	0.534261	−	0.383885i
$436$	635281.	+	1.95519e6i	0.160048	+	0.492576i
$437$	9.79466e6	+	3.18248e6i	2.45350	+	0.797190i
$438$	1.07414e6	+	349010.i	0.267532	+	0.0869265i
$439$	1.04834e6	+	3.22645e6i	0.259621	+	0.799030i	0.992884	+	0.119085i	$0.0379962\pi$
$439$	1.04834e6	+	3.22645e6i	0.259621	+	0.799030i	−0.733264	+	0.679945i	$0.762004\pi$
$440$	43244.7	−	31072.8i	0.0106488	−	0.00765154i
$441$	−325807.	+	1.00273e6i	−0.0797744	+	0.245520i
$442$	−145295.	+	199982.i	−0.0353750	+	0.0486895i
$443$		−	1.63066e6i		−	0.394780i	−0.980325	−	0.197390i	$-0.936753\pi$
$443$		−	1.63066e6i		−	0.394780i	0.980325	−	0.197390i	$-0.0632465\pi$
$444$	−1.47117e6	−	1.06887e6i	−0.354164	−	0.257315i
$445$	412989.	+	136595.i	0.0988641	+	0.0326990i
$446$	−755230.	+	548707.i	−0.179780	+	0.130618i
$447$	−4.82658e6	−	6.64322e6i	−1.14254	−	1.57257i
$448$	404702.	−	131496.i	0.0952665	−	0.0309540i
$449$	−1.84737e6			−0.432453			−0.216227	−	0.976343i	$-0.569375\pi$
$449$	−1.84737e6			−0.432453			−0.216227	+	0.976343i	$0.569375\pi$
$450$	2.09113e6	−	655203.i	0.486799	−	0.152526i
$451$	−15827.4			−0.00366411
$452$	2.90844e6	−	945008.i	0.669597	−	0.217565i
$453$	−4.34984e6	−	5.98705e6i	−0.995929	−	1.37078i
$454$	3.97432e6	−	2.88751e6i	0.904946	−	0.657482i
$455$	358439.	+	498848.i	0.0811684	+	0.112964i
$456$	2.58957e6	+	1.88144e6i	0.583198	+	0.423718i
$457$		−	194715.i		−	0.0436123i	−0.999762	−	0.0218061i	$-0.993058\pi$
$457$		−	194715.i		−	0.0436123i	0.999762	−	0.0218061i	$-0.00694166\pi$
$458$	−2.01490e6	+	2.77328e6i	−0.448839	+	0.617774i
$459$	249956.	−	769287.i	0.0553774	−	0.170434i
$460$	1.14518e6	+	3.58863e6i	0.252335	+	0.790740i
$461$	−534507.	−	1.64504e6i	−0.117139	−	0.360516i	0.875248	−	0.483674i	$-0.160698\pi$
$461$	−534507.	−	1.64504e6i	−0.117139	−	0.360516i	−0.992387	+	0.123158i	$0.960698\pi$
$462$	120311.	+	39091.3i	0.0262240	+	0.00852070i
$463$	−411989.	−	133863.i	−0.0893168	−	0.0290208i	0.264018	−	0.964518i	$-0.414952\pi$
$463$	−411989.	−	133863.i	−0.0893168	−	0.0290208i	−0.353335	+	0.935497i	$0.614952\pi$
$464$	179645.	+	552892.i	0.0387366	+	0.119219i
$465$	7.15511e6	+	5.25623e6i	1.53456	+	1.12731i
$466$	637934.	−	1.96336e6i	0.136085	−	0.418827i
$467$	235525.	−	324173.i	0.0499741	−	0.0687835i	−0.783299	−	0.621646i	$-0.786464\pi$
$467$	235525.	−	324173.i	0.0499741	−	0.0687835i	0.833273	+	0.552862i	$0.186464\pi$
$468$		−	296683.i		−	0.0626148i
$469$	−4.73817e6	−	3.44248e6i	−0.994669	−	0.722669i
$470$	−3.01102e6	+	960854.i	−0.628737	+	0.200638i
$471$	−7.41765e6	+	5.38924e6i	−1.54069	+	1.11937i
$472$	147690.	+	203278.i	0.0305139	+	0.0419987i
$473$	−276476.	+	89832.4i	−0.0568204	+	0.0184621i
$474$	−2.40988e6			−0.492662
$475$	2.43777e6	−	7.24247e6i	0.495746	−	1.47283i
$476$	971173.			0.196462
$477$	4.40779e6	−	1.43218e6i	0.887002	−	0.288205i
$478$	3.52638e6	+	4.85365e6i	0.705926	+	0.971624i
$479$	−1.99741e6	+	1.45121e6i	−0.397767	+	0.288995i	−0.768631	−	0.639692i	$-0.779062\pi$
$479$	−1.99741e6	+	1.45121e6i	−0.397767	+	0.288995i	0.370864	+	0.928687i	$0.379062\pi$
$480$	−6160.09	+	1.17076e6i	−0.00122035	+	0.231934i
$481$	475509.	+	345478.i	0.0937122	+	0.0680859i
$482$		−	315741.i		−	0.0619033i
$483$	−5.25991e6	+	7.23964e6i	−1.02591	+	1.41205i
$484$	795185.	−	2.44733e6i	0.154296	−	0.474874i
$485$	6.82571e6	+	35914.2i	1.31763	+	0.00693286i
$486$	1.37697e6	+	4.23789e6i	0.264445	+	0.813877i
$487$	−4.43821e6	−	1.44206e6i	−0.847979	−	0.275525i	−0.147380	−	0.989080i	$-0.547084\pi$
$487$	−4.43821e6	−	1.44206e6i	−0.847979	−	0.275525i	−0.700599	+	0.713555i	$0.747084\pi$
$488$	2.35753e6	+	766007.i	0.448133	+	0.145607i
$489$	−2.56214e6	−	7.88545e6i	−0.484541	−	1.49126i
$490$	−422288.	+	1.27677e6i	−0.0794545	+	0.240228i
$491$	−620119.	+	1.90853e6i	−0.116084	+	0.357269i	−0.992172	−	0.124883i	$-0.960145\pi$
$491$	−620119.	+	1.90853e6i	−0.116084	+	0.357269i	0.876088	+	0.482151i	$0.160145\pi$
$492$	204540.	−	281525.i	0.0380947	−	0.0524329i
$493$			1.32679e6i			0.245858i
$494$	−836999.	−	608115.i	−0.154315	−	0.112116i
$495$	−86357.0	+	117554.i	−0.0158411	+	0.0215638i
$496$	−1.60824e6	+	1.16846e6i	−0.293527	+	0.213260i
$497$	2.12344e6	+	2.92267e6i	0.385611	+	0.530748i
$498$	−4.49098e6	+	1.45921e6i	−0.811461	+	0.263660i
$499$	−1.07827e7			−1.93854			−0.969271	−	0.245994i	$-0.920886\pi$
$499$	−1.07827e7			−1.93854			−0.969271	+	0.245994i	$0.920886\pi$
$500$	2.67159e6	−	821663.i	0.477908	−	0.146983i
$501$	1.08080e7			1.92376
$502$	−3.33966e6	+	1.08512e6i	−0.591485	+	0.192185i
$503$	−2.38177e6	−	3.27822e6i	−0.419739	−	0.577721i	0.545821	−	0.837902i	$-0.316218\pi$
$503$	−2.38177e6	−	3.27822e6i	−0.419739	−	0.577721i	−0.965560	+	0.260181i	$0.916218\pi$
$504$	−943003.	+	685132.i	−0.165362	+	0.120143i
$505$	−2.73495e6	+	3.72298e6i	−0.477222	+	0.649625i
$506$	−202852.	−	147380.i	−0.0352210	−	0.0255896i
$507$		−	7.36510e6i		−	1.27250i
$508$	−2.59199e6	+	3.56756e6i	−0.445629	+	0.613356i
$509$	11795.0	−	36301.3i	0.00201792	−	0.00621052i	−0.950042	−	0.312121i	$-0.898961\pi$
$509$	11795.0	−	36301.3i	0.00201792	−	0.00621052i	0.952060	+	0.305910i	$0.0989607\pi$
$510$	−839063.	+	2.53687e6i	−0.142846	+	0.431890i
$511$	443197.	+	1.36402e6i	0.0750836	+	0.231083i
$512$	−249314.	−	81007.0i	−0.0420312	−	0.0136568i
$513$	3.21975e6	+	1.04616e6i	0.540168	+	0.175511i
$514$	−405114.	−	1.24681e6i	−0.0676347	−	0.208158i
$515$	9.06271e6	+	47684.5i	1.50571	+	0.00792244i
$516$	1.97507e6	−	6.07864e6i	0.326556	−	1.00504i
$517$	123659.	−	170202.i	0.0203469	−	0.0280051i
$518$		−	2.30922e6i		−	0.378129i
$519$	3.11107e6	+	2.26032e6i	0.506981	+	0.368343i
$520$	1991.06	−	378412.i	0.000322905	−	0.0613700i
$521$	−5.20034e6	+	3.77827e6i	−0.839340	+	0.609816i	−0.922186	−	0.386746i	$-0.873599\pi$
$521$	−5.20034e6	+	3.77827e6i	−0.839340	+	0.609816i	0.0828464	+	0.996562i	$0.473599\pi$
$522$	−936006.	−	1.28830e6i	−0.150350	−	0.206939i
$523$	1.84711e6	−	600161.i	0.295283	−	0.0959431i	−0.157629	−	0.987498i	$-0.550385\pi$
$523$	1.84711e6	−	600161.i	0.295283	−	0.0959431i	0.452912	+	0.891555i	$0.350385\pi$
$524$	849813.			0.135206
$525$	5.33050e6	+	3.95921e6i	0.844054	+	0.626917i
$526$	−7.32827e6			−1.15488
$527$	−4.31487e6	+	1.40199e6i	−0.676770	+	0.219896i
$528$	−45806.5	−	63047.3i	−0.00715060	−	0.00984196i
$529$	9.14250e6	−	6.64241e6i	1.42045	−	1.03202i
$530$	5.63164e6	−	1.79713e6i	0.870854	−	0.277901i
$531$	−556823.	−	404556.i	−0.0857001	−	0.0622647i
$532$			4.06472e6i			0.622661i
$533$	−66111.1	+	90994.1i	−0.0100799	+	0.0138738i
$534$	196720.	−	605441.i	0.0298535	−	0.0918795i
$535$	−425715.	−	312735.i	−0.0643034	−	0.0472381i
$536$	1.11493e6	+	3.43139e6i	0.167623	+	0.515892i
$537$	1.14254e7	+	3.71234e6i	1.70976	+	0.555536i
$538$	1.23661e6	+	401800.i	0.184195	+	0.0598487i
$539$	−27661.3	−	85132.8i	−0.00410111	−	0.0126219i
$540$	376448.	+	1.17967e6i	0.0555547	+	0.174091i
$541$	−1.74340e6	+	5.36563e6i	−0.256096	+	0.788184i	0.737515	+	0.675330i	$0.235999\pi$
$541$	−1.74340e6	+	5.36563e6i	−0.256096	+	0.788184i	−0.993612	+	0.112853i	$0.964001\pi$
$542$	1.08094e6	−	1.48779e6i	0.158054	−	0.217542i
$543$			1.28575e7i			1.87136i
$544$	−484022.	−	351663.i	−0.0701242	−	0.0509482i
$545$	−4.19126e6	−	5.83307e6i	−0.604440	−	0.841213i
$546$	727279.	−	528399.i	0.104405	−	0.0758544i
$547$	171422.	+	235942.i	0.0244962	+	0.0337161i	0.821089	−	0.570800i	$-0.193367\pi$
$547$	171422.	+	235942.i	0.0244962	+	0.0337161i	−0.796593	+	0.604516i	$0.793367\pi$
$548$	−1.23199e6	+	400297.i	−0.175249	+	0.0569418i
$549$	−6.79011e6			−0.961493
$550$	−110935.	+	149359.i	−0.0156373	+	0.0210534i
$551$	−5.55310e6			−0.779213
$552$	5.24296e6	−	1.70354e6i	0.732367	−	0.237961i
$553$	−1.79876e6	−	2.47578e6i	−0.250127	−	0.344271i
$554$	−4.14101e6	+	3.00862e6i	−0.573234	+	0.416479i
$555$	6.03208e6	+	1.99509e6i	0.831255	+	0.274935i
$556$	−5.05453e6	−	3.67233e6i	−0.693416	−	0.503796i
$557$			9.28543e6i			1.26813i	0.773279	+	0.634066i	$0.218615\pi$
$557$			9.28543e6i			1.26813i	−0.773279	+	0.634066i	$0.781385\pi$
$558$	3.20066e6	−	4.40533e6i	0.435165	−	0.598953i
$559$	−638380.	+	1.96473e6i	−0.0864071	+	0.265934i
$560$	−1.20738e6	+	867541.i	−0.162694	+	0.116901i
$561$	−54961.5	−	169154.i	−0.00737312	−	0.0226921i
$562$	5.49694e6	+	1.78607e6i	0.734143	+	0.238537i
$563$	6.82892e6	+	2.21885e6i	0.907989	+	0.295024i	0.725531	−	0.688190i	$-0.241594\pi$
$563$	6.82892e6	+	2.21885e6i	0.907989	+	0.295024i	0.182459	+	0.983214i	$0.441594\pi$
$564$	1.42935e6	+	4.39908e6i	0.189208	+	0.582323i
$565$	−8.67695e6	+	6.23468e6i	−1.14353	+	0.821662i
$566$	1.51836e6	−	4.67302e6i	0.199220	−	0.613136i
$567$	−4.33042e6	+	5.96032e6i	−0.565682	+	0.778595i
$568$		−	2.22553e6i		−	0.289442i
$569$	9.60706e6	+	6.97994e6i	1.24397	+	0.903797i	0.997856	−	0.0654443i	$-0.0208465\pi$
$569$	9.60706e6	+	6.97994e6i	1.24397	+	0.903797i	0.246113	+	0.969241i	$0.420846\pi$
$570$	−1.06178e7	−	3.51179e6i	−1.36882	−	0.452732i
$571$	3.14145e6	−	2.28240e6i	0.403218	−	0.292955i	−0.367632	−	0.929971i	$-0.619832\pi$
$571$	3.14145e6	−	2.28240e6i	0.403218	−	0.292955i	0.770851	+	0.637016i	$0.219832\pi$
$572$	14805.5	+	20378.1i	0.00189206	+	0.00260419i
$573$	4.12135e6	−	1.33911e6i	0.524389	−	0.170384i
$574$	441895.			0.0559808
$575$	−7.62341e6	−	1.07283e7i	−0.961567	−	1.35320i
$576$	718069.			0.0901800
$577$	−3.53943e6	+	1.15003e6i	−0.442582	+	0.143804i	−0.521827	−	0.853052i	$-0.674749\pi$
$577$	−3.53943e6	+	1.15003e6i	−0.442582	+	0.143804i	0.0792445	+	0.996855i	$0.474749\pi$
$578$	2.53569e6	+	3.49008e6i	0.315702	+	0.434526i
$579$	6.73167e6	−	4.89085e6i	0.834500	−	0.606300i
$580$	−1.18521e6	−	1.64948e6i	−0.146293	−	0.203600i
$581$	−4.85123e6	−	3.52463e6i	−0.596227	−	0.433184i
$582$		−	9.98937e6i		−	1.22245i
$583$	−231284.	+	318336.i	−0.0281822	+	0.0387895i
$584$	273029.	−	840296.i	0.0331265	−	0.101953i
$585$	315125.	+	987505.i	0.0380709	+	0.119302i
$586$	−1.95372e6	−	6.01295e6i	−0.235028	−	0.723341i
$587$	−1.25052e7	−	4.06318e6i	−1.49794	−	0.486710i	−0.558524	−	0.829489i	$-0.688632\pi$
$587$	−1.25052e7	−	4.06318e6i	−1.49794	−	0.486710i	−0.939416	+	0.342778i	$0.888632\pi$
$588$	1.87174e6	+	608166.i	0.223256	+	0.0725403i
$589$	−5.86784e6	−	1.80593e7i	−0.696931	−	2.14493i
$590$	−707500.	−	519739.i	−0.0836752	−	0.0614688i
$591$	1.94327e6	−	5.98076e6i	0.228857	−	0.704349i
$592$	−836169.	+	1.15089e6i	−0.0980596	+	0.134967i
$593$		−	9.03065e6i		−	1.05459i	−0.849683	−	0.527294i	$-0.823207\pi$
$593$		−	9.03065e6i		−	1.05459i	0.849683	−	0.527294i	$-0.176793\pi$
$594$	−66682.5	−	48447.7i	−0.00775435	−	0.00563387i
$595$	−3.23254e6	+	1.03154e6i	−0.374327	+	0.119452i
$596$	−5.19697e6	+	3.77582e6i	−0.599286	+	0.435407i
$597$	−3.21817e6	−	4.42943e6i	−0.369550	−	0.508641i
$598$	−1.69462e6	+	550616.i	−0.193785	+	0.0629646i
$599$	1.83618e6			0.209097			0.104548	−	0.994520i	$-0.466660\pi$
$599$	1.83618e6			0.209097			0.104548	+	0.994520i	$0.466660\pi$
$600$	−1.22303e6	−	3.90341e6i	−0.138695	−	0.442655i
$601$	−3.14765e6			−0.355468			−0.177734	−	0.984079i	$-0.556877\pi$
$601$	−3.14765e6			−0.355468			−0.177734	+	0.984079i	$0.556877\pi$
$602$	7.71910e6	−	2.50809e6i	0.868111	−	0.282066i
$603$	−5.80910e6	−	7.99554e6i	−0.650603	−	0.895478i
$604$	−4.68364e6	+	3.40286e6i	−0.522386	+	0.379535i
$605$	−47304.6	+	8.99052e6i	−0.00525430	+	0.998611i
$606$	5.46946e6	+	3.97379e6i	0.605010	+	0.439566i
$607$		−	5.72657e6i		−	0.630845i	−0.948951	−	0.315423i	$-0.897854\pi$
$607$		−	5.72657e6i		−	0.630845i	0.948951	−	0.315423i	$-0.102146\pi$
$608$	1.47184e6	−	2.02581e6i	0.161474	−	0.222249i
$609$	1.49106e6	−	4.58900e6i	0.162911	−	0.501389i
$610$	−8.66063e6	−	45568.9i	−0.942378	−	0.00495843i
$611$	−461992.	−	1.42187e6i	−0.0500647	−	0.154083i
$612$	1.55862e6	+	506426.i	0.168214	+	0.0546560i
$613$	1.30565e7	+	4.24231e6i	1.40338	+	0.455985i	0.910282	−	0.413989i	$-0.135865\pi$
$613$	1.30565e7	+	4.24231e6i	1.40338	+	0.455985i	0.493097	+	0.869974i	$0.335865\pi$
$614$	1.62106e6	+	4.98910e6i	0.173531	+	0.534074i
$615$	−381783.	+	1.15431e6i	−0.0407032	+	0.123065i
$616$	30580.9	−	94118.5i	0.00324713	−	0.00999363i
$617$	5.29923e6	−	7.29376e6i	0.560402	−	0.771327i	−0.430976	−	0.902364i	$-0.641830\pi$
$617$	5.29923e6	−	7.29376e6i	0.560402	−	0.771327i	0.991378	+	0.131036i	$0.0418305\pi$
$618$		−	1.32632e7i		−	1.39694i
$619$	8.61474e6	+	6.25898e6i	0.903682	+	0.656563i	0.939409	−	0.342798i	$-0.111375\pi$
$619$	8.61474e6	+	6.25898e6i	0.903682	+	0.656563i	−0.0357271	+	0.999362i	$0.511375\pi$
$620$	4.11193e6	−	5.59741e6i	0.429602	−	0.584801i
$621$	4.71708e6	−	3.42716e6i	0.490845	−	0.356620i
$622$	−2.10153e6	−	2.89251e6i	−0.217801	−	0.299777i
$623$	768833.	−	249809.i	0.0793618	−	0.0257862i
$624$	−553802.			−0.0569368
$625$	−8.01961e6	+	5.57255e6i	−0.821208	+	0.570630i
$626$	−1.25751e7			−1.28255
$627$	707973.	−	230034.i	0.0719197	−	0.0233681i
$628$	4.21598e6	+	5.80279e6i	0.426579	+	0.587135i
$629$	−2.62664e6	+	1.90837e6i	−0.264712	+	0.192325i
$630$	2.41105e6	−	3.28208e6i	0.242022	−	0.329456i
$631$	3.53147e6	+	2.56576e6i	0.353087	+	0.256533i	0.750163	−	0.661253i	$-0.229975\pi$
$631$	3.53147e6	+	2.56576e6i	0.353087	+	0.256533i	−0.397076	+	0.917786i	$0.629975\pi$
$632$			1.88524e6i			0.187747i
$633$	714299.	−	983148.i	0.0708550	−	0.0975236i
$634$	−1.25098e6	+	3.85011e6i	−0.123602	+	0.380408i
$635$	4.83807e6	−	1.46277e7i	0.476143	−	1.43960i
$636$	−2.67337e6	−	8.22779e6i	−0.262070	−	0.806567i
$637$	−604983.	−	196571.i	−0.0590737	−	0.0191942i
$638$	128582.	+	41778.8i	0.0125063	+	0.00406353i
$639$	1.88383e6	+	5.79783e6i	0.182511	+	0.561712i
$640$	915881.	+	4819.01i	0.0883871	+	0.000465059i
$641$	−6.06647e6	+	1.86707e7i	−0.583164	+	1.79480i	0.0233558	+	0.999727i	$0.492565\pi$
$641$	−6.06647e6	+	1.86707e7i	−0.583164	+	1.79480i	−0.606520	+	0.795068i	$0.707435\pi$
$642$	−454394.	+	625420.i	−0.0435106	+	0.0598872i
$643$			8.01144e6i			0.764158i	0.924130	+	0.382079i	$0.124792\pi$
$643$			8.01144e6i			0.764158i	−0.924130	+	0.382079i	$0.875208\pi$
$644$	5.66354e6	+	4.11480e6i	0.538113	+	0.390962i
$645$	−117495.	+	2.23305e7i	−0.0111204	+	2.11349i
$646$	4.62346e6	−	3.35914e6i	0.435899	−	0.316699i
$647$	1.02901e7	+	1.41631e7i	0.966405	+	1.33014i	0.943842	+	0.330396i	$0.107182\pi$
$647$	1.02901e7	+	1.41631e7i	0.966405	+	1.33014i	0.0225623	+	0.999745i	$0.492818\pi$
$648$	4.31647e6	−	1.40251e6i	0.403823	−	0.131210i
$649$	58435.0			0.00544580
$650$	395308.	+	1.26165e6i	0.0366988	+	0.117127i
$651$	1.64995e7			1.52588
$652$	−6.16875e6	+	2.00435e6i	−0.568301	+	0.184652i
$653$	−7.85170e6	−	1.08069e7i	−0.720577	−	0.991790i	−0.999504	−	0.0314774i	$-0.989979\pi$
$653$	−7.85170e6	−	1.08069e7i	−0.720577	−	0.991790i	0.278927	−	0.960312i	$-0.410021\pi$
$654$	−8.50414e6	+	6.17862e6i	−0.777474	+	0.564868i
$655$	−2.82859e6	+	902639.i	−0.257613	+	0.0822074i
$656$	−220236.	−	160011.i	−0.0199815	−	0.0145174i
$657$			2.42021e6i			0.218745i
$658$	−3.45250e6	+	4.75196e6i	−0.310863	+	0.427867i
$659$	−809672.	+	2.49191e6i	−0.0726265	+	0.223522i	−0.980780	−	0.195115i	$-0.937492\pi$
$659$	−809672.	+	2.49191e6i	−0.0726265	+	0.223522i	0.908154	+	0.418637i	$0.137492\pi$
$660$	219433.	+	161198.i	0.0196084	+	0.0144046i
$661$	1.87443e6	+	5.76889e6i	0.166865	+	0.513557i	0.999169	−	0.0407622i	$-0.0129786\pi$
$661$	1.87443e6	+	5.76889e6i	0.166865	+	0.513557i	−0.832304	+	0.554319i	$0.812979\pi$
$662$	8.77046e6	+	2.84970e6i	0.777817	+	0.252728i
$663$	−1.20207e6	−	390575.i	−0.106205	−	0.0345081i
$664$	1.14153e6	+	3.51327e6i	0.100477	+	0.309237i
$665$	−4.31739e6	−	1.35294e7i	−0.378589	−	1.18638i
$666$	1.20416e6	−	3.70602e6i	0.105196	−	0.323760i
$667$	−5.62152e6	+	7.73735e6i	−0.489259	+	0.673407i
$668$		−	8.45503e6i		−	0.733118i
$669$	−3.86161e6	−	2.80562e6i	−0.333582	−	0.242362i
$670$	−7.35572e6	−	1.02371e7i	−0.633050	−	0.881030i
$671$	466389.	−	338851.i	0.0399891	−	0.0290538i
$672$	1.27890e6	+	1.76026e6i	0.109248	+	0.150367i
$673$	1.74915e6	−	568333.i	0.148864	−	0.0483688i	−0.233637	−	0.972324i	$-0.575063\pi$
$673$	1.74915e6	−	568333.i	0.148864	−	0.0483688i	0.382501	+	0.923955i	$0.375063\pi$
$674$	6.94936e6			0.589244
$675$	−2.50601e6	−	3.52668e6i	−0.211701	−	0.297925i
$676$	−5.76169e6			−0.484934
$677$	−8.67695e6	+	2.81931e6i	−0.727604	+	0.236413i	−0.649317	−	0.760518i	$-0.724945\pi$
$677$	−8.67695e6	+	2.81931e6i	−0.727604	+	0.236413i	−0.0782872	+	0.996931i	$0.524945\pi$
$678$	9.19096e6	+	1.26503e7i	0.767868	+	1.05688i
$679$	1.02626e7	−	7.45618e6i	0.854242	−	0.620643i
$680$	1.98459e6	+	656395.i	0.164588	+	0.0544369i
$681$	2.03213e7	+	1.47643e7i	1.67913	+	1.21996i
$682$			462310.i			0.0380603i
$683$	−2.83455e6	+	3.90143e6i	−0.232505	+	0.320016i	−0.909289	−	0.416166i	$-0.863373\pi$
$683$	−2.83455e6	+	3.90143e6i	−0.232505	+	0.320016i	0.676783	+	0.736182i	$0.263373\pi$
$684$	−2.11958e6	+	6.52340e6i	−0.173225	+	0.533131i
$685$	3.67548e6	−	2.64096e6i	0.299287	−	0.215048i
$686$	2.93054e6	+	9.01928e6i	0.237759	+	0.731748i
$687$	−1.66698e7	−	5.41635e6i	−1.34753	−	0.437840i
$688$	−4.75529e6	−	1.54509e6i	−0.383007	−	0.124446i
$689$	864084.	+	2.65938e6i	0.0693438	+	0.213418i
$690$	−1.56417e7	+	1.12391e7i	−1.25072	+	0.898687i
$691$	2.26866e6	−	6.98223e6i	0.180749	−	0.556287i	−0.819101	−	0.573650i	$-0.805527\pi$
$691$	2.26866e6	−	6.98223e6i	0.180749	−	0.556287i	0.999849	+	0.0173627i	$0.00552699\pi$
$692$	1.76824e6	−	2.43378e6i	0.140371	−	0.193204i
$693$			271078.i			0.0214418i
$694$	−3.25105e6	−	2.36202e6i	−0.256227	−	0.186160i
$695$	2.07246e7	+	6.85458e6i	1.62751	+	0.538294i
$696$	−2.40481e6	+	1.74719e6i	−0.188173	+	0.136716i
$697$	−365188.	−	502638.i	−0.0284731	−	0.0391898i
$698$	−4.92721e6	+	1.60095e6i	−0.382792	+	0.124377i
$699$	1.05556e7			0.817127
$700$	3.09727e6	−	4.17003e6i	0.238910	−	0.321658i
$701$	529304.			0.0406827			0.0203414	−	0.999793i	$-0.493525\pi$
$701$	529304.			0.0406827			0.0203414	+	0.999793i	$0.493525\pi$
$702$	−557066.	+	181002.i	−0.0426642	+	0.0138624i
$703$	−7.98723e6	−	1.09935e7i	−0.609548	−	0.838970i
$704$	−49321.6	+	35834.2i	−0.00375064	+	0.00272500i
$705$	−9.43011e6	−	1.31241e7i	−0.714569	−	0.994481i
$706$	6.99921e6	+	5.08522e6i	0.528490	+	0.383971i
$707$			8.58513e6i			0.645949i
$708$	−755164.	+	1.03939e6i	−0.0566185	+	0.0779286i
$709$	−3.45109e6	+	1.06213e7i	−0.257834	+	0.793531i	0.735424	+	0.677607i	$0.236983\pi$
$709$	−3.45109e6	+	1.06213e7i	−0.257834	+	0.793531i	−0.993258	+	0.115924i	$0.963017\pi$
$710$	2.36387e6	+	7.40764e6i	0.175986	+	0.551486i
$711$	−1.59579e6	−	4.91133e6i	−0.118386	−	0.364355i
$712$	−473634.	−	153893.i	−0.0350141	−	0.0113768i
$713$	−3.11029e7	−	1.01060e7i	−2.29128	−	0.744481i
$714$	1.53450e6	+	4.72272e6i	0.112648	+	0.346694i
$715$	−70924.9	−	52102.3i	−0.00518840	−	0.00381146i
$716$	2.90415e6	−	8.93805e6i	0.211707	−	0.651568i
$717$	−1.80309e7	+	2.48174e7i	−1.30985	+	1.80285i
$718$			8.98710e6i			0.650591i
$719$	−9.91388e6	−	7.20285e6i	−0.715190	−	0.519616i	0.169654	−	0.985504i	$-0.445735\pi$
$719$	−9.91388e6	−	7.20285e6i	−0.715190	−	0.519616i	−0.884844	+	0.465888i	$0.845735\pi$
$720$	−2.39009e6	+	762706.i	−0.171823	+	0.0548310i
$721$	1.36259e7	−	9.89981e6i	0.976175	−	0.709232i
$722$	8.23759e6	+	1.13381e7i	0.588108	+	0.809461i
$723$	1.53542e6	−	498888.i	0.109240	−	0.0354942i
$724$	1.00584e7			0.713152
$725$	5.69697e6	+	4.23140e6i	0.402531	+	0.298978i
$726$	1.31575e7			0.926474
$727$	−1.05247e7	+	3.41968e6i	−0.738540	+	0.239966i	−0.654043	−	0.756458i	$-0.726928\pi$
$727$	−1.05247e7	+	3.41968e6i	−0.738540	+	0.239966i	−0.0844971	+	0.996424i	$0.526928\pi$
$728$	−413365.	−	568948.i	−0.0289071	−	0.0397872i
$729$	−4.49132e6	+	3.26313e6i	−0.313008	+	0.227413i
$730$	−16242.2	+	3.08692e6i	−0.00112807	+	0.214397i
$731$	−9.23201e6	−	6.70745e6i	−0.639003	−	0.464263i
$732$			1.26748e7i			0.874303i
$733$	1.42093e7	−	1.95574e7i	0.976815	−	1.34447i	0.0382867	−	0.999267i	$-0.487810\pi$
$733$	1.42093e7	−	1.95574e7i	0.976815	−	1.34447i	0.938528	−	0.345203i	$-0.112190\pi$
$734$	−31403.9	+	96651.2i	−0.00215151	+	0.00662167i
$735$	−6.87605e6	−	36179.1i	−0.469484	−	0.00247024i
$736$	−1.33267e6	−	4.10155e6i	−0.0906837	−	0.279096i
$737$	798013.	+	259290.i	0.0541179	+	0.0175840i
$738$	709190.	+	230430.i	0.0479316	+	0.0155739i
$739$	4.82884e6	+	1.48617e7i	0.325261	+	1.00105i	0.971323	+	0.237765i	$0.0764150\pi$
$739$	4.82884e6	+	1.48617e7i	0.325261	+	1.00105i	−0.646061	+	0.763285i	$0.723585\pi$
$740$	1.56075e6	−	4.71887e6i	0.104774	−	0.316781i
$741$	1.63470e6	−	5.03110e6i	0.109369	−	0.336602i
$742$	6.45737e6	−	8.88781e6i	0.430572	−	0.592632i
$743$			501158.i			0.0333045i	0.999861	+	0.0166522i	$0.00530082\pi$
$743$			501158.i			0.0333045i	−0.999861	+	0.0166522i	$0.994699\pi$
$744$	−8.22320e6	−	5.97450e6i	−0.544638	−	0.395703i
$745$	1.32875e7	−	1.80878e7i	0.877108	−	1.19397i
$746$	1.70593e7	−	1.23943e7i	1.12231	−	0.815406i
$747$	−5.94772e6	−	8.18633e6i	−0.389986	−	0.536770i
$748$	−132329.	+	42996.1i	−0.00864768	+	0.00280980i
$749$	−981690.			−0.0639396
$750$	8.21691e6	+	1.16934e7i	0.533403	+	0.759079i
$751$	1.08254e7			0.700396			0.350198	−	0.936676i	$-0.386114\pi$
$751$	1.08254e7			0.700396			0.350198	+	0.936676i	$0.386114\pi$
$752$	3.44138e6	−	1.11817e6i	0.221916	−	0.0721048i
$753$	−1.05537e7	−	1.45259e7i	−0.678292	−	0.933589i
$754$	777279.	−	564726.i	0.0497907	−	0.0361751i
$755$	1.19751e7	−	1.63012e7i	0.764557	−	1.04076i
$756$	1.86175e6	+	1.35264e6i	0.118472	+	0.0860751i
$757$		−	434282.i		−	0.0275443i	−0.999905	−	0.0137722i	$-0.995616\pi$
$757$		−	434282.i		−	0.0275443i	0.999905	−	0.0137722i	$-0.00438395\pi$
$758$	1.04559e7	−	1.43914e7i	0.660983	−	0.909765i
$759$	396180.	−	1.21932e6i	0.0249625	−	0.0768266i
$760$	−2.74726e6	+	8.30623e6i	−0.172530	+	0.521639i
$761$	1.78926e6	+	5.50677e6i	0.111998	+	0.344695i	0.991309	−	0.131553i	$-0.0419963\pi$
$761$	1.78926e6	+	5.50677e6i	0.111998	+	0.344695i	−0.879311	+	0.476248i	$0.841996\pi$
$762$	−2.14442e7	−	6.96764e6i	−1.33789	−	0.434708i
$763$	−1.26952e7	−	4.12491e6i	−0.789455	−	0.256510i
$764$	−1.04758e6	−	3.22412e6i	−0.0649312	−	0.199838i
$765$	−5.72576e6	−	30126.7i	−0.353736	−	0.00186122i
$766$	2.27004e6	−	6.98646e6i	0.139785	−	0.430215i
$767$	244083.	−	335952.i	0.0149813	−	0.0206200i
$768$		−	1.34038e6i		−	0.0820023i
$769$	749710.	+	544696.i	0.0457170	+	0.0332153i	0.610409	−	0.792086i	$-0.291005\pi$
$769$	749710.	+	544696.i	0.0457170	+	0.0332153i	−0.564692	+	0.825302i	$0.691005\pi$
$770$	−1819.22	+	345754.i	−0.000110576	+	0.0210155i
$771$	5.42303e6	−	3.94006e6i	0.328553	−	0.238708i
$772$	−3.82609e6	−	5.26616e6i	−0.231053	−	0.318017i
$773$	3.71576e6	−	1.20732e6i	0.223665	−	0.0726733i	−0.195040	−	0.980795i	$-0.562484\pi$
$773$	3.71576e6	−	1.20732e6i	0.223665	−	0.0726733i	0.418706	+	0.908122i	$0.362484\pi$
$774$	1.36961e7			0.821760
$775$	−7.74115e6	+	2.29985e7i	−0.462968	+	1.37545i
$776$	−7.81464e6			−0.465859
$777$	1.12295e7	−	3.64868e6i	0.667279	−	0.216812i
$778$	9.36228e6	+	1.28861e7i	0.554540	+	0.763258i
$779$	2.10373e6	−	1.52845e6i	0.124207	−	0.0902416i
$780$	1.84332e6	−	588228.i	0.108484	−	0.0346186i
$781$	−418726.	−	304222.i	−0.0245642	−	0.0178469i
$782$		−	9.84258e6i		−	0.575562i
$783$	−1.84794e6	+	2.54346e6i	−0.107717	+	0.148259i
$784$	475766.	−	1.46426e6i	0.0276441	−	0.0850799i
$785$	−2.01963e7	−	1.48365e7i	−1.16976	−	0.859324i
$786$	1.34275e6	+	4.13256e6i	0.0775244	+	0.238596i
$787$	−1.76412e6	−	573197.i	−0.101529	−	0.0329888i	0.257812	−	0.966195i	$-0.416999\pi$
$787$	−1.76412e6	−	573197.i	−0.101529	−	0.0329888i	−0.359341	+	0.933206i	$0.616999\pi$
$788$	−4.67872e6	−	1.52021e6i	−0.268418	−	0.0872144i
$789$	−1.15790e7	−	3.56366e7i	−0.662187	−	2.03800i
$790$	−2.00243e6	−	6.27499e6i	−0.114154	−	0.357722i
$791$	−6.13599e6	+	1.88846e7i	−0.348693	+	1.07317i
$792$	98157.8	−	135103.i	0.00556047	−	0.00765333i
$793$		−	4.09672e6i		−	0.231341i
$794$	−5.71498e6	−	4.15217e6i	−0.321709	−	0.233735i
$795$	1.76375e7	+	2.45466e7i	0.989738	+	1.37744i
$796$	−3.46512e6	+	2.51756e6i	−0.193837	+	0.140831i
$797$	1.07781e6	+	1.48348e6i	0.0601031	+	0.0827248i	0.838010	−	0.545654i	$-0.183719\pi$
$797$	1.07781e6	+	1.48348e6i	0.0601031	+	0.0827248i	−0.777907	+	0.628379i	$0.783719\pi$
$798$	−1.97663e7	+	6.42247e6i	−1.09880	+	0.357022i
$799$	8.25837e6			0.457643
$800$	−3.05362e6	+	956774.i	−0.168690	+	0.0528548i
$801$	1.36415e6			0.0751245
$802$	−1.03027e7	+	3.34755e6i	−0.565608	+	0.183777i
$803$	−120777.	−	166235.i	−0.00660991	−	0.00909776i
$804$	−1.49249e7	+	1.08436e7i	−0.814274	+	0.591605i
$805$	−2.32216e7	−	7.68047e6i	−1.26300	−	0.417733i
$806$	2.65789e6	+	1.93107e6i	0.144112	+	0.104703i
$807$			6.64840e6i			0.359363i
$808$	3.10868e6	−	4.27873e6i	0.167513	−	0.230562i
$809$	−8.18234e6	+	2.51827e7i	−0.439548	+	1.35279i	0.448805	+	0.893629i	$0.351850\pi$
$809$	−8.18234e6	+	2.51827e7i	−0.439548	+	1.35279i	−0.888353	+	0.459160i	$0.848150\pi$
$810$	−1.28776e7	+	9.25303e6i	−0.689642	+	0.495531i
$811$	−6.72651e6	−	2.07021e7i	−0.359118	−	1.10525i	−0.953583	−	0.301131i	$-0.902636\pi$
$811$	−6.72651e6	−	2.07021e7i	−0.359118	−	1.10525i	0.594464	−	0.804122i	$-0.297364\pi$
$812$	−3.58995e6	−	1.16645e6i	−0.191073	−	0.0620833i
$813$	8.94292e6	+	2.90573e6i	0.474518	+	0.154180i
$814$	102235.	+	314646.i	0.00540800	+	0.0166441i
$815$	1.84037e7	−	1.32237e7i	0.970534	−	0.697362i
$816$	945320.	−	2.90940e6i	0.0496997	−	0.152960i
$817$	2.80732e7	−	3.86394e7i	1.47142	−	2.02523i
$818$		−	3.47278e6i		−	0.181465i
$819$	1.55847e6	+	1.13230e6i	0.0811874	+	0.0589861i
$820$	903009.	+	298667.i	0.0468983	+	0.0155115i
$821$	−2.13874e7	+	1.55388e7i	−1.10739	+	0.804564i	−0.982250	−	0.187575i	$-0.939937\pi$
$821$	−2.13874e7	+	1.55388e7i	−1.10739	+	0.804564i	−0.125138	+	0.992139i	$0.539937\pi$
$822$	−3.89321e6	−	5.35854e6i	−0.200969	−	0.276610i
$823$	9.42142e6	−	3.06121e6i	0.484861	−	0.157541i	−0.0563785	−	0.998409i	$-0.517955\pi$
$823$	9.42142e6	−	3.06121e6i	0.484861	−	0.157541i	0.541239	+	0.840869i	$0.317955\pi$
$824$	−1.03757e7			−0.532355
$825$	−901599.	−	303473.i	−0.0461189	−	0.0155233i
$826$	−1.63148e6			−0.0832017
$827$	3.64445e7	−	1.18415e7i	1.85297	−	0.602067i	0.856696	−	0.515821i	$-0.172513\pi$
$827$	3.64445e7	−	1.18415e7i	1.85297	−	0.602067i	0.996274	−	0.0862456i	$-0.0274870\pi$
$828$	6.94362e6	+	9.55708e6i	0.351974	+	0.484450i
$829$	−2.44907e7	+	1.77935e7i	−1.23770	+	0.899240i	−0.997443	−	0.0714694i	$-0.977231\pi$
$829$	−2.44907e7	+	1.77935e7i	−1.23770	+	0.899240i	−0.240255	+	0.970710i	$0.577231\pi$
$830$	−7.53124e6	−	1.04814e7i	−0.379465	−	0.528109i
$831$	−2.11736e7	−	1.53835e7i	−1.06364	−	0.772776i
$832$			433237.i			0.0216979i
$833$	2.06537e6	−	2.84273e6i	0.103130	−	0.141946i
$834$	9.87176e6	−	3.03822e7i	0.491450	−	1.51253i
$835$	8.98062e6	+	2.81425e7i	0.445749	+	1.39684i
$836$	−179955.	−	553844.i	−0.00890529	−	0.0274077i
$837$	−1.02243e7	−	3.32209e6i	−0.504453	−	0.163907i
$838$	1.58991e7	+	5.16593e6i	0.782100	+	0.254120i
$839$	1.05250e7	+	3.23926e7i	0.516199	+	1.58870i	0.781089	+	0.624419i	$0.214664\pi$
$839$	1.05250e7	+	3.23926e7i	0.516199	+	1.58870i	−0.264890	+	0.964279i	$0.585336\pi$
$840$	−6.12648e6	−	4.50059e6i	−0.299580	−	0.220075i
$841$	−4.74473e6	+	1.46028e7i	−0.231324	+	0.711943i
$842$	3.99125e6	−	5.49348e6i	0.194012	−	0.267035i
$843$			2.95532e7i			1.43230i
$844$	−769112.	−	558793.i	−0.0371650	−	0.0270019i
$845$	1.91777e7	−	6.11985e6i	0.923964	−	0.294849i
$846$	−8.01882e6	+	5.82601e6i	−0.385199	+	0.279863i
$847$	9.82094e6	+	1.35174e7i	0.470376	+	0.647416i
$848$	−6.43657e6	+	2.09137e6i	−0.307372	+	0.0998713i
$849$	2.51235e7			1.19622
$850$	−7.30287e6	−	76851.8i	−0.346694	−	0.00364844i
$851$	−2.34033e7			−1.10778
$852$	1.08225e7	−	3.51645e6i	0.510774	−	0.165961i
$853$	1.80090e7	+	2.47872e7i	0.847454	+	1.16642i	0.984418	+	0.175844i	$0.0562655\pi$
$853$	1.80090e7	+	2.47872e7i	0.847454	+	1.16642i	−0.136964	+	0.990576i	$0.543734\pi$
$854$	−1.30214e7	+	9.46059e6i	−0.610960	+	0.443888i
$855$	126091.	−	2.39644e7i	0.00589889	−	1.12112i
$856$	489264.	+	355471.i	0.0228222	+	0.0165813i
$857$		−	2.65878e6i		−	0.123660i	−0.998087	−	0.0618301i	$-0.980306\pi$
$857$		−	2.65878e6i		−	0.123660i	0.998087	−	0.0618301i	$-0.0196937\pi$
$858$	−75703.0	+	104196.i	−0.00351071	+	0.00483208i
$859$	−2.67376e6	+	8.22899e6i	−0.123635	+	0.380508i	−0.993650	−	0.112517i	$-0.964109\pi$
$859$	−2.67376e6	+	8.22899e6i	−0.123635	+	0.380508i	0.870015	+	0.493025i	$0.164109\pi$
$860$	1.74691e7	+	91915.5i	0.805423	+	0.00423782i
$861$	698217.	+	2.14889e6i	0.0320983	+	0.0987885i
$862$	−1.61019e7	−	5.23183e6i	−0.738090	−	0.239820i
$863$	−1.03480e7	−	3.36226e6i	−0.472965	−	0.153675i	0.0628294	−	0.998024i	$-0.479988\pi$
$863$	−1.03480e7	−	3.36226e6i	−0.472965	−	0.153675i	−0.535794	+	0.844349i	$0.679988\pi$
$864$	−438083.	−	1.34828e6i	−0.0199651	−	0.0614464i
$865$	−3.30051e6	+	9.97896e6i	−0.149983	+	0.453466i
$866$	−7.11727e6	+	2.19047e7i	−0.322492	+	0.992528i
$867$	−1.29654e7	+	1.78453e7i	−0.585785	+	0.806264i
$868$		−	1.29075e7i		−	0.581492i
$869$	354702.	+	257706.i	0.0159336	+	0.0115764i
$870$	6.14857e6	−	8.36982e6i	0.275408	−	0.374902i
$871$	4.82400e6	−	3.50484e6i	0.215458	−	0.156539i
$872$	4.83351e6	+	6.65275e6i	0.215264	+	0.296285i
$873$	2.03583e7	−	6.61481e6i	0.904078	−	0.293753i
$874$	4.11948e7			1.82417
$875$	−5.87998e6	+	1.71697e7i	−0.259630	+	0.758128i
$876$	4.51767e6			0.198909
$877$	3.27287e7	−	1.06342e7i	1.43691	−	0.466881i	0.515979	−	0.856602i	$-0.327428\pi$
$877$	3.27287e7	−	1.06342e7i	1.43691	−	0.466881i	0.920933	+	0.389721i	$0.127428\pi$
$878$	7.97621e6	+	1.09783e7i	0.349189	+	0.480617i
$879$	2.61534e7	−	1.90015e7i	1.14171	−	0.829500i
$880$	126105.	−	171661.i	0.00548939	−	0.00747250i
$881$	7.96745e6	+	5.78869e6i	0.345844	+	0.251270i	0.747123	−	0.664685i	$-0.231434\pi$
$881$	7.96745e6	+	5.78869e6i	0.345844	+	0.251270i	−0.401280	+	0.915956i	$0.631434\pi$
$882$			4.21733e6i			0.182543i
$883$	−8.09284e6	+	1.11388e7i	−0.349300	+	0.480771i	−0.947129	−	0.320853i	$-0.896030\pi$
$883$	−8.09284e6	+	1.11388e7i	−0.349300	+	0.480771i	0.597829	+	0.801624i	$0.296030\pi$
$884$	−305545.	+	940372.i	−0.0131506	+	0.0404733i
$885$	1.40955e6	−	4.26172e6i	0.0604954	−	0.182905i
$886$	−2.01561e6	−	6.20341e6i	−0.0862626	−	0.265489i
$887$	−5.11201e6	−	1.66099e6i	−0.218164	−	0.0708857i	0.197896	−	0.980223i	$-0.436589\pi$
$887$	−5.11201e6	−	1.66099e6i	−0.218164	−	0.0708857i	−0.416060	+	0.909337i	$0.636589\pi$
$888$	−6.91785e6	−	2.24774e6i	−0.294401	−	0.0956565i
$889$	−8.84801e6	−	2.72314e7i	−0.375484	−	1.15562i
$890$	1.73994e6	+	9154.91i	0.0736310	+	0.000387417i
$891$	326170.	−	1.00385e6i	0.0137642	−	0.0423618i
$892$	−2.19483e6	+	3.02092e6i	−0.0923609	+	0.127124i
$893$			3.45643e7i			1.45044i
$894$	−2.65729e7	−	1.93063e7i	−1.11198	−	0.807897i
$895$	−172764.	+	3.28349e7i	−0.00720935	+	1.37018i
$896$	1.37704e6	−	1.00048e6i	0.0573029	−	0.0416330i
$897$	−5.35519e6	−	7.37078e6i	−0.222225	−	0.305867i
$898$	−7.02783e6	+	2.28348e6i	−0.290824	+	0.0944945i
$899$	1.76339e7			0.727693
$900$	7.14526e6	−	5.07732e6i	0.294043	−	0.208943i
$901$	−1.54460e7			−0.633875
$902$	−60211.0	+	19563.7i	−0.00246411	+	0.000800637i
$903$	2.43931e7	+	3.35743e7i	0.995517	+	1.37021i
$904$	9.89626e6	−	7.19005e6i	0.402763	−	0.292625i
$905$	−3.34792e7	+	1.06836e7i	−1.35880	+	0.433609i
$906$	−2.39482e7	−	1.73994e7i	−0.969286	−	0.704228i
$907$		−	4.54428e6i		−	0.183420i	−0.995786	−	0.0917101i	$-0.970767\pi$
$907$		−	4.54428e6i		−	0.183420i	0.995786	−	0.0917101i	$-0.0292333\pi$
$908$	1.15500e7	−	1.58973e7i	0.464910	−	0.639893i
$909$	−4.47679e6	+	1.37781e7i	−0.179704	+	0.553071i
$910$	1.98019e6	+	1.45468e6i	0.0792692	+	0.0582321i
$911$	−7.77372e6	−	2.39251e7i	−0.310337	−	0.955118i	−0.977632	−	0.210325i	$-0.932548\pi$
$911$	−7.77372e6	−	2.39251e7i	−0.310337	−	0.955118i	0.667295	−	0.744794i	$-0.267452\pi$
$912$	1.21769e7	+	3.95652e6i	0.484786	+	0.157516i
$913$	817055.	+	265477.i	0.0324395	+	0.0105402i
$914$	−240681.	−	740740.i	−0.00952963	−	0.0293292i
$915$	−1.34627e7	−	4.21878e7i	−0.531591	−	1.66584i
$916$	−4.23719e6	+	1.30407e7i	−0.166855	+	0.513527i
$917$	−3.24333e6	+	4.46406e6i	−0.127370	+	0.175310i
$918$		−	3.23550e6i		−	0.126717i
$919$	−2.21692e7	−	1.61068e7i	−0.865886	−	0.629103i	0.0635938	−	0.997976i	$-0.479744\pi$
$919$	−2.21692e7	−	1.61068e7i	−0.865886	−	0.629103i	−0.929480	+	0.368873i	$0.879744\pi$
$920$	8.79230e6	+	1.22364e7i	0.342478	+	0.476634i
$921$	−2.17001e7	+	1.57661e7i	−0.842973	+	0.612456i
$922$	−4.06677e6	−	5.59743e6i	−0.157551	−	0.216851i
$923$	−3.49804e6	+	1.13658e6i	−0.135151	+	0.0439133i
$924$	506008.			0.0194974
$925$	−182735.	+	1.73645e7i	−0.00702212	+	0.667279i
$926$	−1.73276e6			−0.0664067
$927$	2.70304e7	−	8.78270e6i	1.03312	−	0.335682i
$928$	1.36682e6	+	1.88127e6i	0.0521006	+	0.0717103i
$929$	−3.89418e7	+	2.82929e7i	−1.48039	+	1.07557i	−0.502962	+	0.864308i	$0.667756\pi$
$929$	−3.89418e7	+	2.82929e7i	−1.48039	+	1.07557i	−0.977430	+	0.211259i	$0.932244\pi$
$930$	3.37167e7	+	1.11517e7i	1.27831	+	0.422799i
$931$	1.18979e7	+	8.64433e6i	0.449879	+	0.326857i
$932$		−	8.25759e6i		−	0.311396i
$933$	1.07454e7	−	1.47898e7i	0.404129	−	0.556236i
$934$	495292.	−	1.52435e6i	0.0185778	−	0.0571765i
$935$	394785.	−	283667.i	0.0147683	−	0.0106116i
$936$	−366720.	−	1.12865e6i	−0.0136818	−	0.0421084i
$937$	−2.73105e7	−	8.87371e6i	−1.01620	−	0.330184i	−0.246881	−	0.969046i	$-0.579406\pi$
$937$	−2.73105e7	−	8.87371e6i	−1.01620	−	0.330184i	−0.769322	+	0.638861i	$0.779406\pi$
$938$	−2.22802e7	−	7.23928e6i	−0.826822	−	0.268651i
$939$	−1.98693e7	−	6.11513e7i	−0.735391	−	2.26330i
$940$	−1.02669e7	+	7.37713e6i	−0.378984	+	0.272313i
$941$	4.36110e6	−	1.34221e7i	0.160554	−	0.494135i	−0.838127	−	0.545475i	$-0.816349\pi$
$941$	4.36110e6	−	1.34221e7i	0.160554	−	0.494135i	0.998681	+	0.0513398i	$0.0163492\pi$
$942$	−2.15569e7	+	2.96706e7i	−0.791516	+	1.08943i
$943$		−	4.47848e6i		−	0.164003i
$944$	813113.	+	590761.i	0.0296976	+	0.0215766i
$945$	−7.63353e6	−	2.52477e6i	−0.278065	−	0.0919690i
$946$	−940737.	+	683486.i	−0.0341775	+	0.0248314i
$947$	2.89097e7	+	3.97908e7i	1.04754	+	1.44181i	0.890927	+	0.454147i	$0.150056\pi$
$947$	2.89097e7	+	3.97908e7i	1.04754	+	1.44181i	0.156608	+	0.987661i	$0.449944\pi$
$948$	−9.16772e6	+	2.97877e6i	−0.331315	+	0.107651i
$949$	−1.46020e6			−0.0526315
$950$	321654.	−	3.05652e7i	0.0115632	−	1.09880i
$951$	−2.06993e7			−0.742172
$952$	3.69456e6	−	1.20044e6i	0.132121	−	0.0429286i
$953$	−7.92350e6	−	1.09058e7i	−0.282608	−	0.388977i	0.643987	−	0.765036i	$-0.277279\pi$
$953$	−7.92350e6	−	1.09058e7i	−0.282608	−	0.388977i	−0.926596	+	0.376059i	$0.877279\pi$
$954$	1.49980e7	−	1.08967e7i	0.533533	−	0.387634i
$955$	6.91139e6	+	9.61874e6i	0.245221	+	0.341279i
$956$	1.94146e7	+	1.41055e7i	0.687042	+	0.499165i
$957$			691293.i			0.0243996i
$958$	−5.80482e6	+	7.98966e6i	−0.204350	+	0.281264i
$959$	2.59915e6	−	7.99936e6i	0.0912609	−	0.280872i
$960$	1.42371e6	+	4.46145e6i	0.0498588	+	0.156242i
$961$	9.78643e6	+	3.01195e7i	0.341834	+	1.05206i
$962$	2.23598e6	+	726513.i	0.0778986	+	0.0253108i
$963$	−1.57550e6	−	511910.i	−0.0547460	−	0.0177880i
$964$	−390278.	−	1.20115e6i	−0.0135264	−	0.0416299i
$965$	1.83286e7	+	1.34644e7i	0.633594	+	0.465446i
$966$	−1.10612e7	+	3.40428e7i	−0.381381	+	1.17377i
$967$	2.17566e7	−	2.99453e7i	0.748211	−	1.02982i	−0.249893	−	0.968273i	$-0.580395\pi$
$967$	2.17566e7	−	2.99453e7i	0.748211	−	1.02982i	0.998104	−	0.0615507i	$-0.0196046\pi$
$968$		−	1.02931e7i		−	0.353067i
$969$	2.36405e7	+	1.71758e7i	0.808810	+	0.587635i
$970$	2.60109e7	−	8.30042e6i	0.887619	−	0.283250i
$971$	1.93330e7	−	1.40462e7i	0.658038	−	0.478092i	−0.207962	−	0.978137i	$-0.566683\pi$
$971$	1.93330e7	−	1.40462e7i	0.658038	−	0.478092i	0.866000	+	0.500045i	$0.166683\pi$
$972$	1.04766e7	+	1.44198e7i	0.355677	+	0.489547i
$973$	3.85815e7	−	1.25359e7i	1.30646	−	0.424495i
$974$	−1.86664e7			−0.630469
$975$	−5.51069e6	+	3.91582e6i	−0.185650	+	0.131920i
$976$	9.91541e6			0.333185
$977$	−1.53189e7	+	4.97742e6i	−0.513442	+	0.166828i	−0.554267	−	0.832339i	$-0.687001\pi$
$977$	−1.53189e7	+	4.97742e6i	−0.513442	+	0.166828i	0.0408248	+	0.999166i	$0.487001\pi$
$978$	−1.94939e7	−	2.68310e7i	−0.651706	−	0.896996i
$979$	−93698.7	+	68076.1i	−0.00312447	+	0.00227006i
$980$	−28302.8	+	5.37911e6i	−0.000941377	+	0.178914i
$981$	−1.82233e7	−	1.32400e7i	−0.604582	−	0.439254i
$982$			8.02698e6i			0.265628i
$983$	−1.41369e7	+	1.94578e7i	−0.466629	+	0.642260i	−0.975867	−	0.218366i	$-0.929927\pi$
$983$	−1.41369e7	+	1.94578e7i	−0.466629	+	0.642260i	0.509238	+	0.860626i	$0.329927\pi$
$984$	430132.	−	1.32381e6i	0.0141616	−	0.0435850i
$985$	1.71878e7	+	90435.5i	0.564455	+	0.00296994i
$986$	1.64000e6	+	5.04740e6i	0.0537219	+	0.165339i
$987$	−2.85635e7	−	9.28083e6i	−0.933293	−	0.303245i
$988$	−3.93581e6	−	1.27882e6i	−0.128275	−	0.0416790i
$989$	−2.54188e7	−	7.82310e7i	−0.826350	−	2.54324i
$990$	−183216.	+	553947.i	−0.00594122	+	0.0179631i
$991$	7.56547e6	−	2.32841e7i	0.244710	−	0.753140i	−0.750974	−	0.660332i	$-0.770416\pi$
$991$	7.56547e6	−	2.32841e7i	0.244710	−	0.753140i	0.995684	−	0.0928080i	$-0.0295843\pi$
$992$	−4.67383e6	+	6.43297e6i	−0.150797	+	0.207555i
$993$			4.71526e7i			1.51751i
$994$	1.16907e7	+	8.49377e6i	0.375296	+	0.272668i
$995$	8.85956e6	−	1.20602e7i	0.283697	−	0.386186i
$996$	−1.52810e7	+	1.11023e7i	−0.488094	+	0.354621i
$997$	1.43497e6	+	1.97507e6i	0.0457199	+	0.0629281i	0.831265	−	0.555877i	$-0.187617\pi$
$997$	1.43497e6	+	1.97507e6i	0.0457199	+	0.0629281i	−0.785545	+	0.618805i	$0.787617\pi$
$998$	−4.10198e7	+	1.33281e7i	−1.30367	+	0.423587i
$999$	−7.69325e6			−0.243891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.e.a.19.11	✓	48
25.4	even	10	inner	50.6.e.a.29.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.e.a.19.11	✓	48	1.1	even	1	trivial
50.6.e.a.29.11	yes	48	25.4	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)

\(f(q)\)	\(=\)	\(q+(3.80423 - 1.23607i) q^{2} +(12.0218 + 16.5465i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-33.0957 + 45.0519i) q^{5} +(66.1861 + 48.0870i) q^{6} +103.889i q^{7} +(37.6183 - 51.7771i) q^{8} +(-54.1737 + 166.730i) q^{9} +O(q^{10})\)	\(q+(3.80423 - 1.23607i) q^{2} +(12.0218 + 16.5465i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-33.0957 + 45.0519i) q^{5} +(66.1861 + 48.0870i) q^{6} +103.889i q^{7} +(37.6183 - 51.7771i) q^{8} +(-54.1737 + 166.730i) q^{9} +(-70.2163 + 212.296i) q^{10} +(-4.59941 - 14.1555i) q^{11} +(311.226 + 101.123i) q^{12} +(-100.594 - 32.6850i) q^{13} +(128.414 + 395.217i) q^{14} +(-1143.32 - 6.01571i) q^{15} +(79.1084 - 243.470i) q^{16} +(343.421 - 472.678i) q^{17} +701.239i q^{18} +(1978.33 + 1437.34i) q^{19} +(-4.70606 + 894.415i) q^{20} +(-1719.00 + 1248.93i) q^{21} +(-34.9944 - 48.1656i) q^{22} +(4005.42 - 1301.44i) q^{23} +1308.97 q^{24} +(-934.350 - 2982.05i) q^{25} -423.083 q^{26} +(1316.68 - 427.816i) q^{27} +(977.029 + 1344.77i) q^{28} +(-1837.18 + 1334.79i) q^{29} +(-4356.89 + 1390.34i) q^{30} +(-6282.20 - 4564.28i) q^{31} -1024.00i q^{32} +(178.932 - 246.278i) q^{33} +(722.187 - 2222.66i) q^{34} +(-4680.39 - 3438.27i) q^{35} +(866.780 + 2667.67i) q^{36} +(-5284.96 - 1717.19i) q^{37} +(9302.68 + 3022.62i) q^{38} +(-668.493 - 2057.41i) q^{39} +(1087.65 + 3408.37i) q^{40} +(328.604 - 1011.34i) q^{41} +(-4995.70 + 6876.00i) q^{42} -19531.3i q^{43} +(-192.663 - 139.978i) q^{44} +(-5718.57 - 7958.66i) q^{45} +(13628.8 - 9901.93i) q^{46} +(8308.17 + 11435.2i) q^{47} +(4979.61 - 1617.97i) q^{48} +6014.11 q^{49} +(-7240.49 - 10189.5i) q^{50} +11949.7 q^{51} +(-1609.50 + 522.959i) q^{52} +(-15539.1 - 21387.8i) q^{53} +(4480.15 - 3255.02i) q^{54} +(789.954 + 261.275i) q^{55} +(5379.06 + 3908.12i) q^{56} +50013.9i q^{57} +(-5339.15 + 7348.71i) q^{58} +(-1213.21 + 3733.88i) q^{59} +(-14856.0 + 10674.6i) q^{60} +(11968.9 + 36836.4i) q^{61} +(-29540.7 - 9598.34i) q^{62} +(-17321.3 - 5628.05i) q^{63} +(-1265.73 - 3895.53i) q^{64} +(4801.75 - 3450.22i) q^{65} +(376.280 - 1158.07i) q^{66} +(-33136.2 + 45608.1i) q^{67} -9348.19i q^{68} +(69686.4 + 50630.1i) q^{69} +(-22055.2 - 7294.69i) q^{70} +(28132.6 - 20439.6i) q^{71} +(6594.85 + 9077.03i) q^{72} +(13129.6 - 4266.07i) q^{73} -22227.8 q^{74} +(38110.0 - 51309.7i) q^{75} +39125.7 q^{76} +(1470.60 - 477.827i) q^{77} +(-5086.20 - 7000.55i) q^{78} +(-23831.1 + 17314.3i) q^{79} +(8350.66 + 11621.8i) q^{80} +(57372.0 + 41683.2i) q^{81} -4253.53i q^{82} +(-33926.9 + 46696.4i) q^{83} +(-10505.6 + 32332.9i) q^{84} +(9929.30 + 31115.4i) q^{85} +(-24142.0 - 74301.5i) q^{86} +(-44172.2 - 14352.4i) q^{87} +(-905.954 - 294.362i) q^{88} +(-2404.58 - 7400.53i) q^{89} +(-31592.2 - 23208.0i) q^{90} +(3395.60 - 10450.6i) q^{91} +(39607.7 - 54515.4i) q^{92} -158819. i q^{93} +(45740.8 + 33232.7i) q^{94} +(-130229. + 41557.8i) q^{95} +(16943.6 - 12310.3i) q^{96} +(-71770.8 - 98784.0i) q^{97} +(22879.0 - 7433.84i) q^{98} +2609.31 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

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Representations

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Database

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