LMFDB - Embedded newform 50.6.e.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.e (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	50.19
Dual form			50.6.e.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.80423 + 1.23607i) q^{2} +(10.0418 + 13.8214i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-52.7366 + 18.5432i) q^{5} +(-55.2856 - 40.1674i) q^{6} +107.711i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-15.1017 + 46.4781i) q^{9} +O(q^{10})$	\(q+(-3.80423 + 1.23607i) q^{2} +(10.0418 + 13.8214i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-52.7366 + 18.5432i) q^{5} +(-55.2856 - 40.1674i) q^{6} +107.711i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-15.1017 + 46.4781i) q^{9} +(177.701 - 135.729i) q^{10} +(-33.7553 - 103.888i) q^{11} +(259.969 + 84.4689i) q^{12} +(-458.396 - 148.942i) q^{13} +(-133.139 - 409.759i) q^{14} +(-785.866 - 542.686i) q^{15} +(79.1084 - 243.470i) q^{16} +(-1085.98 + 1494.72i) q^{17} -195.480i q^{18} +(-2180.01 - 1583.87i) q^{19} +(-508.246 + 735.993i) q^{20} +(-1488.72 + 1081.62i) q^{21} +(256.826 + 353.490i) q^{22} +(-840.169 + 272.987i) q^{23} -1093.39 q^{24} +(2437.30 - 1955.81i) q^{25} +1927.94 q^{26} +(3154.23 - 1024.87i) q^{27} +(1012.98 + 1394.25i) q^{28} +(-3024.53 + 2197.45i) q^{29} +(3660.41 + 1093.12i) q^{30} +(5009.43 + 3639.56i) q^{31} +1024.00i q^{32} +(1096.92 - 1509.77i) q^{33} +(2283.73 - 7028.61i) q^{34} +(-1997.32 - 5680.34i) q^{35} +(241.627 + 743.650i) q^{36} +(5791.81 + 1881.87i) q^{37} +(10251.0 + 3330.76i) q^{38} +(-2544.55 - 7831.33i) q^{39} +(1023.74 - 3428.11i) q^{40} +(-5683.73 + 17492.7i) q^{41} +(4326.49 - 5954.90i) q^{42} +9071.17i q^{43} +(-1413.96 - 1027.30i) q^{44} +(-65.4446 - 2731.13i) q^{45} +(2858.76 - 2077.01i) q^{46} +(2985.41 + 4109.07i) q^{47} +(4159.50 - 1351.50i) q^{48} +5205.24 q^{49} +(-6854.51 + 10453.0i) q^{50} -31564.4 q^{51} +(-7334.34 + 2383.07i) q^{52} +(4692.58 + 6458.79i) q^{53} +(-10732.6 + 7797.69i) q^{54} +(3706.56 + 4852.77i) q^{55} +(-5576.99 - 4051.92i) q^{56} -46035.8i q^{57} +(8789.80 - 12098.1i) q^{58} +(3421.68 - 10530.8i) q^{59} +(-15276.2 + 366.055i) q^{60} +(1078.57 + 3319.49i) q^{61} +(-23555.8 - 7653.73i) q^{62} +(-5006.23 - 1626.62i) q^{63} +(-1265.73 - 3895.53i) q^{64} +(26936.1 - 645.455i) q^{65} +(-2306.73 + 7099.38i) q^{66} +(16665.4 - 22937.9i) q^{67} +29561.3i q^{68} +(-12209.9 - 8871.02i) q^{69} +(14619.5 + 19140.5i) q^{70} +(-51625.4 + 37508.0i) q^{71} +(-1838.40 - 2530.35i) q^{72} +(18186.0 - 5908.98i) q^{73} -24359.5 q^{74} +(51507.1 + 14046.9i) q^{75} -43114.3 q^{76} +(11189.9 - 3635.83i) q^{77} +(19360.1 + 26646.9i) q^{78} +(-73638.5 + 53501.5i) q^{79} +(342.824 + 14306.7i) q^{80} +(55446.9 + 40284.5i) q^{81} -73571.7i q^{82} +(732.917 - 1008.77i) q^{83} +(-9098.27 + 28001.6i) q^{84} +(29553.9 - 98964.2i) q^{85} +(-11212.6 - 34508.8i) q^{86} +(-60743.7 - 19736.8i) q^{87} +(6648.84 + 2160.34i) q^{88} +(-14733.3 - 45344.3i) q^{89} +(3624.83 + 10308.9i) q^{90} +(16042.7 - 49374.5i) q^{91} +(-8308.05 + 11435.0i) q^{92} +105785. i q^{93} +(-16436.3 - 11941.7i) q^{94} +(144337. + 43103.5i) q^{95} +(-14153.1 + 10282.8i) q^{96} +(-31859.5 - 43850.9i) q^{97} +(-19801.9 + 6434.03i) q^{98} +5338.29 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
$3$	10.0418	+	13.8214i	0.644184	+	0.886644i	0.998830	−	0.0483569i	$-0.0153985\pi$
$3$	10.0418	+	13.8214i	0.644184	+	0.886644i	−0.354646	+	0.935001i	$0.615398\pi$
$4$	12.9443	−	9.40456i	0.404508	−	0.293893i
$5$	−52.7366	+	18.5432i	−0.943381	+	0.331711i
$5$	−52.7366	+	18.5432i	−0.943381	+	0.331711i
$6$	−55.2856	−	40.1674i	−0.626952	−	0.455507i
$7$			107.711i			0.830839i	0.909630	+	0.415419i	$0.136365\pi$
$7$			107.711i			0.830839i	−0.909630	+	0.415419i	$0.863635\pi$
$8$	−37.6183	+	51.7771i	−0.207813	+	0.286031i
$9$	−15.1017	+	46.4781i	−0.0621467	+	0.191268i
$10$	177.701	−	135.729i	0.561941	−	0.429212i
$11$	−33.7553	−	103.888i	−0.0841125	−	0.258872i	0.900151	−	0.435578i	$-0.143456\pi$
$11$	−33.7553	−	103.888i	−0.0841125	−	0.258872i	−0.984264	+	0.176706i	$0.943456\pi$
$12$	259.969	+	84.4689i	0.521156	+	0.169334i
$13$	−458.396	−	148.942i	−0.752285	−	0.244432i	−0.0923209	−	0.995729i	$-0.529429\pi$
$13$	−458.396	−	148.942i	−0.752285	−	0.244432i	−0.659964	+	0.751297i	$0.729429\pi$
$14$	−133.139	−	409.759i	−0.181545	−	0.558738i
$15$	−785.866	−	542.686i	−0.901821	−	0.622760i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−1085.98	+	1494.72i	−0.911380	+	1.25441i	0.0553133	+	0.998469i	$0.482384\pi$
$17$	−1085.98	+	1494.72i	−0.911380	+	1.25441i	−0.966693	+	0.255938i	$0.917616\pi$
$18$		−	195.480i		−	0.142207i
$19$	−2180.01	−	1583.87i	−1.38540	−	1.00655i	−0.996352	−	0.0853333i	$-0.972805\pi$
$19$	−2180.01	−	1583.87i	−1.38540	−	1.00655i	−0.389047	−	0.921218i	$-0.627195\pi$
$20$	−508.246	+	735.993i	−0.284118	+	0.411433i
$21$	−1488.72	+	1081.62i	−0.736658	+	0.535214i
$22$	256.826	+	353.490i	0.113131	+	0.155711i
$23$	−840.169	+	272.987i	−0.331167	+	0.107603i	−0.469881	−	0.882730i	$-0.655703\pi$
$23$	−840.169	+	272.987i	−0.331167	+	0.107603i	0.138714	+	0.990332i	$0.455703\pi$
$24$	−1093.39			−0.387478
$25$	2437.30	−	1955.81i	0.779935	−	0.625860i
$26$	1927.94			0.559321
$27$	3154.23	−	1024.87i	0.832692	−	0.270558i
$28$	1012.98	+	1394.25i	0.244177	+	0.336081i
$29$	−3024.53	+	2197.45i	−0.667825	+	0.485204i	−0.869297	−	0.494291i	$-0.835428\pi$
$29$	−3024.53	+	2197.45i	−0.667825	+	0.485204i	0.201471	+	0.979494i	$0.435428\pi$
$30$	3660.41	+	1093.12i	0.742551	+	0.221750i
$31$	5009.43	+	3639.56i	0.936233	+	0.680213i	0.947511	−	0.319723i	$-0.103590\pi$
$31$	5009.43	+	3639.56i	0.936233	+	0.680213i	−0.0112778	+	0.999936i	$0.503590\pi$
$32$			1024.00i			0.176777i
$33$	1096.92	−	1509.77i	0.175343	−	0.241339i
$34$	2283.73	−	7028.61i	0.338804	−	1.04273i
$35$	−1997.32	−	5680.34i	−0.275599	−	0.783798i
$36$	241.627	+	743.650i	0.0310734	+	0.0956340i
$37$	5791.81	+	1881.87i	0.695521	+	0.225988i	0.635378	−	0.772201i	$-0.280844\pi$
$37$	5791.81	+	1881.87i	0.695521	+	0.225988i	0.0601430	+	0.998190i	$0.480844\pi$
$38$	10251.0	+	3330.76i	1.15162	+	0.374183i
$39$	−2544.55	−	7831.33i	−0.267886	−	0.824468i
$40$	1023.74	−	3428.11i	0.101168	−	0.338770i
$41$	−5683.73	+	17492.7i	−0.528048	+	1.62517i	0.230160	+	0.973153i	$0.426075\pi$
$41$	−5683.73	+	17492.7i	−0.528048	+	1.62517i	−0.758208	+	0.652013i	$0.773925\pi$
$42$	4326.49	−	5954.90i	0.378453	−	0.520896i
$43$			9071.17i			0.748156i	0.927397	+	0.374078i	$0.122041\pi$
$43$			9071.17i			0.748156i	−0.927397	+	0.374078i	$0.877959\pi$
$44$	−1413.96	−	1027.30i	−0.110105	−	0.0799957i
$45$	−65.4446	−	2731.13i	−0.00481773	−	0.201053i
$46$	2858.76	−	2077.01i	0.199197	−	0.144725i
$47$	2985.41	+	4109.07i	0.197133	+	0.271331i	0.896128	−	0.443797i	$-0.146369\pi$
$47$	2985.41	+	4109.07i	0.197133	+	0.271331i	−0.698994	+	0.715127i	$0.746369\pi$
$48$	4159.50	−	1351.50i	0.260578	−	0.0846670i
$49$	5205.24			0.309707
$50$	−6854.51	+	10453.0i	−0.387750	+	0.591312i
$51$	−31564.4			−1.69931
$52$	−7334.34	+	2383.07i	−0.376143	+	0.122216i
$53$	4692.58	+	6458.79i	0.229468	+	0.315836i	0.908189	−	0.418561i	$-0.137465\pi$
$53$	4692.58	+	6458.79i	0.229468	+	0.315836i	−0.678721	+	0.734396i	$0.737465\pi$
$54$	−10732.6	+	7797.69i	−0.500865	+	0.363900i
$55$	3706.56	+	4852.77i	0.165221	+	0.216313i
$56$	−5576.99	−	4051.92i	−0.237645	−	0.172660i
$57$		−	46035.8i		−	1.87676i
$58$	8789.80	−	12098.1i	0.343091	−	0.472224i
$59$	3421.68	−	10530.8i	0.127970	−	0.393852i	−0.866460	−	0.499246i	$-0.833610\pi$
$59$	3421.68	−	10530.8i	0.127970	−	0.393852i	0.994431	+	0.105394i	$0.0336104\pi$
$60$	−15276.2	+	366.055i	−0.547819	+	0.0131271i
$61$	1078.57	+	3319.49i	0.0371127	+	0.114221i	0.967897	−	0.251349i	$-0.0808741\pi$
$61$	1078.57	+	3319.49i	0.0371127	+	0.114221i	−0.930784	+	0.365570i	$0.880874\pi$
$62$	−23555.8	−	7653.73i	−0.778248	−	0.252868i
$63$	−5006.23	−	1626.62i	−0.158913	−	0.0516339i
$64$	−1265.73	−	3895.53i	−0.0386271	−	0.118882i
$65$	26936.1	−	645.455i	0.790772	−	0.0189488i
$66$	−2306.73	+	7099.38i	−0.0651834	+	0.200614i
$67$	16665.4	−	22937.9i	0.453553	−	0.624262i	−0.519603	−	0.854408i	$-0.673920\pi$
$67$	16665.4	−	22937.9i	0.453553	−	0.624262i	0.973156	+	0.230146i	$0.0739203\pi$
$68$			29561.3i			0.775266i
$69$	−12209.9	−	8871.02i	−0.308738	−	0.224311i
$70$	14619.5	+	19140.5i	0.356606	+	0.466882i
$71$	−51625.4	+	37508.0i	−1.21540	+	0.883036i	−0.995709	−	0.0925344i	$-0.970503\pi$
$71$	−51625.4	+	37508.0i	−1.21540	+	0.883036i	−0.219686	+	0.975571i	$0.570503\pi$
$72$	−1838.40	−	2530.35i	−0.0417936	−	0.0575239i
$73$	18186.0	−	5908.98i	0.399419	−	0.129779i	−0.102417	−	0.994742i	$-0.532658\pi$
$73$	18186.0	−	5908.98i	0.399419	−	0.129779i	0.501837	+	0.864962i	$0.332658\pi$
$74$	−24359.5			−0.517117
$75$	51507.1	+	14046.9i	1.05734	+	0.288355i
$76$	−43114.3			−0.856224
$77$	11189.9	−	3635.83i	0.215081	−	0.0698839i
$78$	19360.1	+	26646.9i	0.360306	+	0.495919i
$79$	−73638.5	+	53501.5i	−1.32751	+	0.964491i	−0.327703	+	0.944781i	$0.606274\pi$
$79$	−73638.5	+	53501.5i	−1.32751	+	0.964491i	−0.999806	+	0.0197104i	$0.993726\pi$
$80$	342.824	+	14306.7i	0.00598889	+	0.249928i
$81$	55446.9	+	40284.5i	0.938998	+	0.682222i
$82$		−	73571.7i		−	1.20830i
$83$	732.917	−	1008.77i	0.0116778	−	0.0160731i	−0.803138	−	0.595793i	$-0.796838\pi$
$83$	732.917	−	1008.77i	0.0116778	−	0.0160731i	0.814816	+	0.579720i	$0.196838\pi$
$84$	−9098.27	+	28001.6i	−0.140689	+	0.432997i
$85$	29553.9	−	98964.2i	0.443677	−	1.48570i
$86$	−11212.6	−	34508.8i	−0.163478	−	0.503134i
$87$	−60743.7	−	19736.8i	−0.860406	−	0.279563i
$88$	6648.84	+	2160.34i	0.0915249	+	0.0297382i
$89$	−14733.3	−	45344.3i	−0.197162	−	0.606803i	−0.999945	−	0.0105308i	$-0.996648\pi$
$89$	−14733.3	−	45344.3i	−0.197162	−	0.606803i	0.802782	−	0.596272i	$-0.203352\pi$
$90$	3624.83	+	10308.9i	0.0471717	+	0.134155i
$91$	16042.7	−	49374.5i	0.203084	−	0.625028i
$92$	−8308.05	+	11435.0i	−0.102336	+	0.140854i
$93$			105785.i			1.26829i
$94$	−16436.3	−	11941.7i	−0.191860	−	0.139394i
$95$	144337.	+	43103.5i	1.64084	+	0.490009i
$96$	−14153.1	+	10282.8i	−0.156738	+	0.113877i
$97$	−31859.5	−	43850.9i	−0.343803	−	0.473205i	0.601744	−	0.798689i	$-0.294473\pi$
$97$	−31859.5	−	43850.9i	−0.343803	−	0.473205i	−0.945547	+	0.325484i	$0.894473\pi$
$98$	−19801.9	+	6434.03i	−0.208277	+	0.0676734i
$99$	5338.29			0.0547412
$100$	13155.5	−	48238.3i	0.131555	−	0.482383i
$101$	48853.2			0.476529			0.238264	−	0.971200i	$-0.423421\pi$
$101$	48853.2			0.476529			0.238264	+	0.971200i	$0.423421\pi$
$102$	120078.	−	39015.8i	1.14278	−	0.371313i
$103$	87211.0	+	120036.i	0.809988	+	1.11485i	0.991325	+	0.131431i	$0.0419573\pi$
$103$	87211.0	+	120036.i	0.809988	+	1.11485i	−0.181338	+	0.983421i	$0.558043\pi$
$104$	24955.8	−	18131.5i	0.226250	−	0.164380i
$105$	58453.5	−	84646.8i	0.517413	−	0.749268i
$106$	−25835.1	−	18770.3i	−0.223330	−	0.162258i
$107$			178864.i			1.51030i	0.655551	+	0.755151i	$0.272436\pi$
$107$			178864.i			1.51030i	−0.655551	+	0.755151i	$0.727564\pi$
$108$	31190.8	−	42930.4i	0.257316	−	0.354165i
$109$	48908.1	−	150524.i	0.394289	−	1.21350i	−0.535225	−	0.844709i	$-0.679773\pi$
$109$	48908.1	−	150524.i	0.394289	−	1.21350i	0.929514	−	0.368787i	$-0.120227\pi$
$110$	−20099.0	−	13879.5i	−0.158377	−	0.109368i
$111$	32150.3	+	98948.5i	0.247673	+	0.762258i
$112$	26224.6	+	8520.88i	0.197544	+	0.0641858i
$113$	−177729.	−	57747.7i	−1.30937	−	0.425440i	−0.430539	−	0.902572i	$-0.641676\pi$
$113$	−177729.	−	57747.7i	−1.30937	−	0.425440i	−0.878832	+	0.477132i	$0.841676\pi$
$114$	56903.4	+	175131.i	0.410087	+	1.26212i
$115$	39245.6	−	29975.9i	0.276723	−	0.211362i
$116$	−18484.3	+	56888.8i	−0.127543	+	0.392538i
$117$	13845.1	−	19056.1i	0.0935041	−	0.128697i
$118$			44291.1i			0.292828i
$119$	−160999.	−	116972.i	−1.04221	−	0.757210i
$120$	57661.6	−	20275.0i	0.365539	−	0.128531i
$121$	120640.	−	87649.9i	0.749077	−	0.544237i
$122$	−8206.22	−	11294.9i	−0.0499165	−	0.0687041i
$123$	−298849.	+	97102.0i	−1.78110	+	0.578716i
$124$	99071.9			0.578624
$125$	−92267.6	+	148338.i	−0.528171	+	0.849138i
$126$	21055.4			0.118151
$127$	−41870.4	+	13604.5i	−0.230355	+	0.0748468i	−0.421920	−	0.906633i	$-0.638644\pi$
$127$	−41870.4	+	13604.5i	−0.230355	+	0.0748468i	0.191565	+	0.981480i	$0.438644\pi$
$128$	9630.27	+	13254.9i	0.0519534	+	0.0715077i
$129$	−125376.	+	91091.3i	−0.663348	+	0.481951i
$130$	−101673.	+	35750.3i	−0.527653	+	0.185533i
$131$	80461.6	+	58458.8i	0.409648	+	0.297627i	0.773459	−	0.633846i	$-0.218525\pi$
$131$	80461.6	+	58458.8i	0.409648	+	0.297627i	−0.363811	+	0.931473i	$0.618525\pi$
$132$		−	29858.9i		−	0.149156i
$133$	170601.	−	234812.i	0.836282	−	1.15104i
$134$	−35046.0	+	107860.i	−0.168607	+	0.518920i
$135$	−147339.	+	112538.i	−0.695798	+	0.531453i
$136$	−36539.7	−	112458.i	−0.169402	−	0.521365i
$137$	−247522.	−	80424.7i	−1.12671	−	0.366090i	−0.314384	−	0.949296i	$-0.601798\pi$
$137$	−247522.	−	80424.7i	−1.12671	−	0.366090i	−0.812324	+	0.583206i	$0.801798\pi$
$138$	57414.5	+	18655.1i	0.256639	+	0.0833872i
$139$	−77921.1	−	239816.i	−0.342072	−	1.05279i	−0.963133	−	0.269027i	$-0.913298\pi$
$139$	−77921.1	−	239816.i	−0.342072	−	1.05279i	0.621060	−	0.783763i	$-0.286702\pi$
$140$	−79274.9	−	54743.9i	−0.341834	−	0.236056i
$141$	−26814.1	+	82525.2i	−0.113583	+	0.349574i
$142$	150032.	−	206502.i	0.624401	−	0.859414i
$143$			52649.5i			0.215305i
$144$	10121.4	+	7353.62i	0.0406756	+	0.0295525i
$145$	118756.	−	171971.i	0.469066	−	0.679257i
$146$	−61879.6	+	44958.2i	−0.240251	+	0.174553i
$147$	52270.2	+	71943.8i	0.199508	+	0.274600i
$148$	92669.0	−	30110.0i	0.347760	−	0.112994i
$149$	311211.			1.14839			0.574195	−	0.818719i	$-0.305315\pi$
$149$	311211.			1.14839			0.574195	+	0.818719i	$0.305315\pi$
$150$	−213307.	+	10228.6i	−0.774066	+	0.0371183i
$151$	−326556.			−1.16551			−0.582755	−	0.812648i	$-0.698025\pi$
$151$	−326556.			−1.16551			−0.582755	+	0.812648i	$0.698025\pi$
$152$	164017.	−	53292.2i	0.575809	−	0.187092i
$153$	−53071.8	−	73047.1i	−0.183289	−	0.252275i
$154$	−38074.9	+	27663.1i	−0.129371	+	0.0939936i
$155$	−331670.	−	99047.2i	−1.10886	−	0.331141i
$156$	−106588.	−	77440.5i	−0.350667	−	0.254775i
$157$			563726.i			1.82524i	0.408813	+	0.912618i	$0.365943\pi$
$157$			563726.i			1.82524i	−0.408813	+	0.912618i	$0.634057\pi$
$158$	214006.	−	294554.i	0.681998	−	0.938690i
$159$	−42147.4	+	129716.i	−0.132214	+	0.406913i
$160$	−18988.3	−	54002.3i	−0.0586388	−	0.166768i
$161$	−29403.9	−	90495.8i	−0.0894005	−	0.275146i
$162$	−260727.	−	84715.3i	−0.780546	−	0.253615i
$163$	−306182.	−	99484.6i	−0.902632	−	0.293283i	−0.179309	−	0.983793i	$-0.557386\pi$
$163$	−306182.	−	99484.6i	−0.902632	−	0.293283i	−0.723323	+	0.690510i	$0.757386\pi$
$164$	90939.7	+	279884.i	0.264024	+	0.812583i
$165$	−29851.5	+	99960.7i	−0.0853603	+	0.285838i
$166$	−1541.27	+	4743.54i	−0.00434119	+	0.0133608i
$167$	−124417.	+	171245.i	−0.345213	+	0.475145i	−0.945955	−	0.324298i	$-0.894872\pi$
$167$	−124417.	+	171245.i	−0.345213	+	0.475145i	0.600742	+	0.799443i	$0.294872\pi$
$168$		−	117771.i		−	0.321931i
$169$	−112439.	−	81691.8i	−0.302831	−	0.220020i
$170$	9896.80	+	413013.i	0.0262647	+	1.09608i
$171$	106537.	−	77403.8i	0.278619	−	0.202429i
$172$	85310.4	+	117420.i	0.219878	+	0.302636i
$173$	670557.	−	217877.i	1.70341	−	0.553473i	0.714199	−	0.699942i	$-0.246791\pi$
$173$	670557.	−	217877.i	1.70341	−	0.553473i	0.989215	+	0.146469i	$0.0467910\pi$
$174$	255479.			0.639708
$175$	210664.	+	262525.i	0.519989	+	0.648000i
$176$	−27964.0			−0.0680484
$177$	179911.	−	58456.7i	0.431643	−	0.140249i
$178$	112097.	+	154289.i	0.265183	+	0.364993i
$179$	584285.	−	424508.i	1.36299	−	0.990268i	0.364739	−	0.931110i	$-0.381158\pi$
$179$	584285.	−	424508.i	1.36299	−	0.990268i	0.998249	−	0.0591585i	$-0.0188417\pi$
$180$	−26532.2	−	34737.0i	−0.0610369	−	0.0799119i
$181$	547065.	+	397466.i	1.24120	+	0.901786i	0.997678	−	0.0681085i	$-0.0216964\pi$
$181$	547065.	+	397466.i	1.24120	+	0.901786i	0.243524	+	0.969895i	$0.421696\pi$
$182$			207662.i			0.464706i
$183$	−35049.2	+	48241.1i	−0.0773660	+	0.106485i
$184$	17471.2	−	53770.8i	0.0380433	−	0.117085i
$185$	−340337.	+	8155.30i	−0.731104	+	0.0175191i
$186$	−130758.	−	402431.i	−0.277131	−	0.852922i
$187$	191942.	+	62365.6i	0.401389	+	0.130419i
$188$	77288.0	+	25112.4i	0.159484	+	0.0518195i
$189$	110390.	+	339747.i	0.224790	+	0.691833i
$190$	−602368.	+	14434.2i	−1.21054	+	0.0290074i
$191$	128201.	−	394563.i	0.254278	−	0.782587i	−0.739693	−	0.672944i	$-0.765029\pi$
$191$	128201.	−	394563.i	0.254278	−	0.782587i	0.993971	−	0.109643i	$-0.0349706\pi$
$192$	41131.4	−	56612.5i	0.0805231	−	0.110830i
$193$		−	790524.i		−	1.52764i	−0.645428	−	0.763821i	$-0.723321\pi$
$193$		−	790524.i		−	1.52764i	0.645428	−	0.763821i	$-0.276679\pi$
$194$	175403.	+	127438.i	0.334606	+	0.243106i
$195$	279409.	+	365813.i	0.526204	+	0.688927i
$196$	67378.0	−	48953.0i	0.125279	−	0.0910205i
$197$	427775.	+	588782.i	0.785326	+	1.08091i	0.994674	+	0.103067i	$0.0328656\pi$
$197$	427775.	+	588782.i	0.785326	+	1.08091i	−0.209349	+	0.977841i	$0.567134\pi$
$198$	−20308.1	+	6598.49i	−0.0368133	+	0.0119614i
$199$	811932.			1.45341			0.726703	−	0.686952i	$-0.241052\pi$
$199$	811932.			1.45341			0.726703	+	0.686952i	$0.241052\pi$
$200$	9579.48	+	199770.i	0.0169343	+	0.353148i
$201$	484385.			0.845669
$202$	−185848.	+	60385.8i	−0.320465	+	0.104125i
$203$	−236691.	−	325777.i	−0.403126	−	0.554855i
$204$	−408578.	+	296850.i	−0.687385	+	0.499414i
$205$	−24631.0	−	1.02790e6i	−0.0409353	−	1.70831i
$206$	−480143.	−	348844.i	−0.788320	−	0.572748i
$207$		−	43172.0i		−	0.0700288i
$208$	−72525.9	+	99823.3i	−0.116234	+	0.159983i
$209$	−90958.5	+	279941.i	−0.144038	+	0.443304i
$210$	−117741.	+	394268.i	−0.184238	+	0.616941i
$211$	17239.3	+	53057.2i	0.0266572	+	0.0820423i	0.963500	−	0.267708i	$-0.0862663\pi$
$211$	17239.3	+	53057.2i	0.0266572	+	0.0820423i	−0.936843	+	0.349751i	$0.886266\pi$
$212$	121484.	+	39472.6i	0.185644	+	0.0603193i
$213$	−1.03683e6	−	336886.i	−1.56588	−	0.508784i
$214$	−221088.	−	680439.i	−0.330013	−	1.01568i
$215$	−168209.	−	478383.i	−0.248172	−	0.705796i
$216$	−65591.8	+	201871.i	−0.0956567	+	0.294401i
$217$	−392023.	+	539573.i	−0.565148	+	0.777859i
$218$			633080.i			0.902230i
$219$	264291.	+	192019.i	0.372368	+	0.270541i
$220$	93617.0	+	27957.0i	0.130406	+	0.0389435i
$221$	720436.	−	523427.i	0.992235	−	0.720901i
$222$	−244614.	−	336683.i	−0.333119	−	0.458499i
$223$	−895179.	+	290861.i	−1.20545	+	0.391673i	−0.841762	−	0.539849i	$-0.818481\pi$
$223$	−895179.	+	290861.i	−1.20545	+	0.391673i	−0.363684	+	0.931522i	$0.618481\pi$
$224$	−110297.			−0.146873
$225$	54095.3	+	142817.i	0.0712367	+	0.188072i
$226$	747502.			0.973512
$227$	342232.	−	111198.i	0.440814	−	0.143229i	−0.0801971	−	0.996779i	$-0.525555\pi$
$227$	342232.	−	111198.i	0.440814	−	0.143229i	0.521011	+	0.853550i	$0.325555\pi$
$228$	−432947.	−	595900.i	−0.551566	−	0.759166i
$229$	−834893.	+	606586.i	−1.05206	+	0.764370i	−0.972604	−	0.232468i	$-0.925320\pi$
$229$	−834893.	+	606586.i	−1.05206	+	0.764370i	−0.0794606	+	0.996838i	$0.525320\pi$
$230$	−112247.	+	162545.i	−0.139912	+	0.202607i
$231$	162620.	+	118150.i	0.200514	+	0.145682i
$232$		−	239266.i		−	0.291850i
$233$	−678784.	+	934265.i	−0.819109	+	1.12741i	0.170745	+	0.985315i	$0.445383\pi$
$233$	−678784.	+	934265.i	−0.819109	+	1.12741i	−0.989854	+	0.142091i	$0.954617\pi$
$234$	−29115.2	+	89607.2i	−0.0347600	+	0.106980i
$235$	−233636.	−	161339.i	−0.275975	−	0.190577i
$236$	−54746.9	−	168494.i	−0.0639852	−	0.196926i
$237$	−1.47893e6	−	480534.i	−1.71032	−	0.555717i
$238$	757062.	+	245984.i	0.866341	+	0.281491i
$239$	−345718.	−	1.06401e6i	−0.391496	−	1.20490i	−0.931657	−	0.363338i	$-0.881637\pi$
$239$	−345718.	−	1.06401e6i	−0.391496	−	1.20490i	0.540162	−	0.841561i	$-0.318363\pi$
$240$	−194297.	+	148404.i	−0.217739	+	0.166310i
$241$	−222027.	+	683329.i	−0.246243	+	0.757857i	0.749187	+	0.662359i	$0.230445\pi$
$241$	−222027.	+	683329.i	−0.246243	+	0.757857i	−0.995430	+	0.0954986i	$0.969555\pi$
$242$	−350599.	+	482559.i	−0.384833	+	0.529678i
$243$			364962.i			0.396490i
$244$	45179.6	+	32824.9i	0.0485811	+	0.0352963i
$245$	−274507.	+	96522.0i	−0.292171	+	0.102733i
$246$	1.01687e6	−	738796.i	1.07134	−	0.778371i
$247$	763404.	+	1.05074e6i	0.796181	+	1.09585i
$248$	−376892.	+	122460.i	−0.389124	+	0.126434i
$249$	21302.5			0.0217737
$250$	167651.	−	678362.i	0.169651	−	0.686454i
$251$	−1.40462e6			−1.40726			−0.703631	−	0.710566i	$-0.748439\pi$
$251$	−1.40462e6			−1.40726			−0.703631	+	0.710566i	$0.748439\pi$
$252$	−80099.6	+	26025.9i	−0.0794564	+	0.0258170i
$253$	56720.3	+	78068.8i	0.0557105	+	0.0766790i
$254$	142468.	−	103509.i	0.138559	−	0.100669i
$255$	1.66460e6	−	585306.i	1.60310	−	0.563680i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$		−	878072.i		−	0.829272i	−0.909987	−	0.414636i	$-0.863909\pi$
$257$		−	878072.i		−	0.829272i	0.909987	−	0.414636i	$-0.136091\pi$
$258$	364365.	−	501506.i	0.340791	−	0.469058i
$259$	−202699.	+	623845.i	−0.187760	+	0.577866i
$260$	342598.	−	261677.i	0.314305	−	0.240067i
$261$	−56457.9	−	173760.i	−0.0513007	−	0.157887i
$262$	−378353.	−	122934.i	−0.340521	−	0.110642i
$263$	753192.	+	244727.i	0.671454	+	0.218169i	0.624850	−	0.780745i	$-0.285160\pi$
$263$	753192.	+	244727.i	0.671454	+	0.218169i	0.0466041	+	0.998913i	$0.485160\pi$
$264$	36907.7	+	113590.i	0.0325917	+	0.100307i
$265$	−367238.	−	253599.i	−0.321242	−	0.221836i
$266$	−358761.	+	1.10415e6i	−0.310886	+	0.956809i
$267$	478773.	−	658975.i	0.411009	−	0.565706i
$268$		−	453645.i		−	0.385815i
$269$	423627.	+	307783.i	0.356947	+	0.259337i	0.751777	−	0.659417i	$-0.229197\pi$
$269$	423627.	+	307783.i	0.356947	+	0.259337i	−0.394831	+	0.918754i	$0.629197\pi$
$270$	421406.	−	610241.i	0.351797	−	0.509439i
$271$	19235.2	−	13975.2i	0.0159102	−	0.0115594i	−0.579802	−	0.814758i	$-0.696870\pi$
$271$	19235.2	−	13975.2i	0.0159102	−	0.0115594i	0.595712	+	0.803198i	$0.296870\pi$
$272$	278011.	+	382649.i	0.227845	+	0.313602i
$273$	843524.	−	274078.i	0.685000	−	0.222570i
$274$	1.04104e6			0.837704
$275$	−285458.	−	187187.i	−0.227620	−	0.149260i
$276$	−241477.			−0.190810
$277$	696482.	−	226301.i	0.545395	−	0.177209i	−0.0233445	−	0.999727i	$-0.507431\pi$
$277$	696482.	−	226301.i	0.545395	−	0.177209i	0.568739	+	0.822518i	$0.307431\pi$
$278$	592859.	+	816000.i	0.460086	+	0.633254i
$279$	−244811.	+	177865.i	−0.188287	+	0.136798i
$280$	369247.	+	110269.i	0.281463	+	0.0840540i
$281$	62075.5	+	45100.5i	0.0468980	+	0.0340734i	0.610987	−	0.791640i	$-0.290773\pi$
$281$	62075.5	+	45100.5i	0.0468980	+	0.0340734i	−0.564089	+	0.825714i	$0.690773\pi$
$282$		−	347089.i		−	0.259907i
$283$	−979196.	+	1.34775e6i	−0.726781	+	1.00033i	0.272490	+	0.962159i	$0.412153\pi$
$283$	−979196.	+	1.34775e6i	−0.726781	+	1.00033i	−0.999271	+	0.0381697i	$0.987847\pi$
$284$	−315506.	+	971029.i	−0.232120	+	0.714391i
$285$	853653.	+	2.42777e6i	0.622543	+	1.77050i
$286$	−65078.4	−	200291.i	−0.0470459	−	0.144792i
$287$	−1.88417e6	−	612203.i	−1.35025	−	0.438723i
$288$	−47593.6	−	15464.1i	−0.0338117	−	0.0109861i
$289$	−616085.	−	1.89611e6i	−0.433906	−	1.33543i
$290$	−239206.	+	801005.i	−0.167023	+	0.559294i
$291$	286153.	−	880687.i	0.198091	−	0.609662i
$292$	179833.	−	247518.i	0.123427	−	0.169883i
$293$		−	1.52743e6i		−	1.03942i	−0.854342	−	0.519710i	$-0.826040\pi$
$293$		−	1.52743e6i		−	1.03942i	0.854342	−	0.519710i	$-0.173960\pi$
$294$	−287775.	−	209081.i	−0.194171	−	0.141074i
$295$	14828.2	+	618810.i	0.00992050	+	0.414002i
$296$	−315316.	+	229090.i	−0.209178	+	0.151977i
$297$	−212944.	−	293093.i	−0.140080	−	0.192803i
$298$	−1.18392e6	+	384678.i	−0.772290	+	0.250932i
$299$	425789.			0.275433
$300$	798826.	−	302574.i	0.512447	−	0.194102i
$301$	−977069.			−0.621597
$302$	1.24229e6	−	403646.i	0.783804	−	0.254673i
$303$	490576.	+	675220.i	0.306973	+	0.422511i
$304$	−558083.	+	405471.i	−0.346350	+	0.251638i
$305$	−118434.	−	155058.i	−0.0728999	−	0.0954433i
$306$	292188.	+	212287.i	0.178385	+	0.129605i
$307$		−	1.32034e6i		−	0.799537i	−0.916616	−	0.399768i	$-0.869091\pi$
$307$		−	1.32034e6i		−	0.799537i	0.916616	−	0.399768i	$-0.130909\pi$
$308$	110652.	−	152300.i	0.0664635	−	0.0914792i
$309$	−783303.	+	2.41076e6i	−0.466696	+	1.43634i
$310$	1.38418e6	−	33168.2i	0.818063	−	0.0196028i
$311$	−165664.	−	509860.i	−0.0971239	−	0.298917i	0.890677	−	0.454636i	$-0.150231\pi$
$311$	−165664.	−	509860.i	−0.0971239	−	0.298917i	−0.987801	+	0.155719i	$0.950231\pi$
$312$	501205.	+	162851.i	0.291494	+	0.0947120i
$313$	2.14955e6	+	698430.i	1.24018	+	0.402960i	0.854394	−	0.519626i	$-0.173929\pi$
$313$	2.14955e6	+	698430.i	1.24018	+	0.402960i	0.385790	+	0.922586i	$0.373929\pi$
$314$	−696804.	−	2.14454e6i	−0.398829	−	1.22747i
$315$	294174.	−	7049.14i	0.167043	−	0.00400276i
$316$	−450039.	+	1.38508e6i	−0.253532	+	0.780290i
$317$	−104124.	+	143314.i	−0.0581973	+	0.0801016i	−0.837124	−	0.547014i	$-0.815765\pi$
$317$	−104124.	+	143314.i	−0.0581973	+	0.0801016i	0.778926	+	0.627115i	$0.215765\pi$
$318$		−	545567.i		−	0.302538i
$319$	330383.	+	240037.i	0.181778	+	0.132069i
$320$	138986.	+	181966.i	0.0758746	+	0.0993380i
$321$	−2.47215e6	+	1.79613e6i	−1.33910	+	0.972913i
$322$	223718.	+	307921.i	0.120243	+	0.165501i
$323$	4.73490e6	−	1.53846e6i	2.52525	−	0.820503i
$324$	1.09658e6			0.580333
$325$	−1.40855e6	+	533522.i	−0.739714	+	0.280184i
$326$	1.28776e6			0.671104
$327$	2.57158e6	−	835556.i	1.32993	−	0.432122i
$328$	−691910.	−	952333.i	−0.355112	−	0.488769i
$329$	−442594.	+	321563.i	−0.225432	+	0.163786i
$330$	−9996.46	−	417172.i	−0.00505314	−	0.210877i
$331$	−355002.	−	257924.i	−0.178099	−	0.129396i	0.495164	−	0.868799i	$-0.335108\pi$
$331$	−355002.	−	257924.i	−0.178099	−	0.129396i	−0.673263	+	0.739403i	$0.735108\pi$
$332$		−	19950.6i		−	0.00993370i
$333$	−174932.	+	240773.i	−0.0864487	+	0.118986i
$334$	261639.	−	805242.i	0.128332	−	0.394966i
$335$	−453532.	+	1.51870e6i	−0.220798	+	0.739365i
$336$	145572.	+	448026.i	0.0703446	+	0.216498i
$337$	932905.	+	303119.i	0.447469	+	0.145391i	0.524079	−	0.851670i	$-0.324410\pi$
$337$	932905.	+	303119.i	0.447469	+	0.145391i	−0.0766101	+	0.997061i	$0.524410\pi$
$338$	528721.	+	171792.i	0.251730	+	0.0817919i
$339$	−986574.	−	3.03636e6i	−0.466262	−	1.43501i
$340$	−548161.	−	1.55896e6i	−0.257165	−	0.731371i
$341$	209013.	−	643275.i	0.0973390	−	0.299579i
$342$	−309615.	+	426149.i	−0.143139	+	0.197013i
$343$			2.37097e6i			1.08816i
$344$	−469679.	−	341242.i	−0.213996	−	0.155477i
$345$	808407.	+	241416.i	0.365664	+	0.109199i
$346$	−2.28164e6	+	1.65771e6i	−1.02461	+	0.744419i
$347$	−1.87327e6	−	2.57833e6i	−0.835173	−	1.14952i	−0.986938	−	0.161101i	$-0.948496\pi$
$347$	−1.87327e6	−	2.57833e6i	−0.835173	−	1.14952i	0.151765	−	0.988417i	$-0.451504\pi$
$348$	−971900.	+	315789.i	−0.430203	+	0.139781i
$349$	−1.64595e6			−0.723356			−0.361678	−	0.932303i	$-0.617796\pi$
$349$	−1.64595e6			−0.723356			−0.361678	+	0.932303i	$0.617796\pi$
$350$	−1.12591e6	−	738309.i	−0.491285	−	0.322157i
$351$	−1.59853e6			−0.692555
$352$	106381.	−	34565.4i	0.0457625	−	0.0148691i
$353$	336078.	+	462572.i	0.143550	+	0.197580i	0.874738	−	0.484597i	$-0.161034\pi$
$353$	336078.	+	462572.i	0.143550	+	0.197580i	−0.731188	+	0.682176i	$0.761034\pi$
$354$	−612166.	+	444765.i	−0.259634	+	0.188635i
$355$	2.02703e6	−	2.93535e6i	0.853667	−	1.23620i
$356$	−617155.	−	448389.i	−0.258089	−	0.187512i
$357$		−	3.39985e6i		−	1.41185i
$358$	−1.69803e6	+	2.33714e6i	−0.700225	+	0.963778i
$359$	−600738.	+	1.84888e6i	−0.246008	+	0.757135i	0.749461	+	0.662048i	$0.230313\pi$
$359$	−600738.	+	1.84888e6i	−0.246008	+	0.757135i	−0.995469	+	0.0950863i	$0.969687\pi$
$360$	143872.	+	99351.9i	0.0585086	+	0.0404036i
$361$	1.47865e6	+	4.55081e6i	0.597168	+	1.83789i
$362$	−2.57245e6	−	835841.i	−1.03175	−	0.335237i
$363$	2.42289e6	+	787244.i	0.965088	+	0.313576i
$364$	−256684.	−	789992.i	−0.101542	−	0.312514i
$365$	−849494.	+	648846.i	−0.333755	+	0.254923i
$366$	73705.8	−	226843.i	0.0287607	−	0.0885162i
$367$	−2.21477e6	+	3.04837e6i	−0.858349	+	1.18142i	0.123612	+	0.992331i	$0.460552\pi$
$367$	−2.21477e6	+	3.04837e6i	−0.858349	+	1.18142i	−0.981961	+	0.189085i	$0.939448\pi$
$368$			226152.i			0.0870524i
$369$	−727195.	−	528338.i	−0.278026	−	0.201998i
$370$	1.28464e6	−	451704.i	0.487838	−	0.171534i
$371$	−695685.	+	505445.i	−0.262409	+	0.190651i
$372$	994865.	+	1.36931e6i	0.372741	+	0.513033i
$373$	−1.31810e6	+	428277.i	−0.490543	+	0.159387i	−0.543835	−	0.839192i	$-0.683028\pi$
$373$	−1.31810e6	+	428277.i	−0.490543	+	0.159387i	0.0532926	+	0.998579i	$0.483028\pi$
$374$	−807277.			−0.298431
$375$	−2.97678e6	+	214321.i	−1.09312	+	0.0787022i
$376$	−325062.			−0.118576
$377$	1.71373e6	−	556823.i	0.620995	−	0.201773i
$378$	−839901.	−	1.15602e6i	−0.302342	−	0.416138i
$379$	790766.	−	574525.i	0.282781	−	0.205452i	−0.437349	−	0.899292i	$-0.644082\pi$
$379$	790766.	−	574525.i	0.282781	−	0.205452i	0.720129	+	0.693840i	$0.244082\pi$
$380$	2.27370e6	−	799478.i	0.807745	−	0.284019i
$381$	−608489.	−	442093.i	−0.214753	−	0.156028i
$382$			1.65947e6i			0.581850i
$383$	414237.	−	570149.i	0.144295	−	0.198606i	−0.730752	−	0.682643i	$-0.760830\pi$
$383$	414237.	−	570149.i	0.144295	−	0.198606i	0.875047	+	0.484038i	$0.160830\pi$
$384$	−86496.2	+	266208.i	−0.0299343	+	0.0921283i
$385$	−522699.	+	399239.i	−0.179722	+	0.137272i
$386$	977141.	+	3.00733e6i	0.333802	+	1.02734i
$387$	−421611.	−	136990.i	−0.143098	−	0.0464955i
$388$	−824797.	−	267993.i	−0.278143	−	0.0903740i
$389$	−1.55316e6	−	4.78013e6i	−0.520405	−	1.60164i	−0.773228	−	0.634129i	$-0.781359\pi$
$389$	−1.55316e6	−	4.78013e6i	−0.520405	−	1.60164i	0.252823	−	0.967513i	$-0.418641\pi$
$390$	−1.51511e6	−	1.04627e6i	−0.504408	−	0.348322i
$391$	504366.	−	1.55228e6i	0.166841	−	0.513485i
$392$	−195812.	+	269512.i	−0.0643612	+	0.0885856i
$393$			1.69913e6i			0.554938i
$394$	−2.35513e6	−	1.71110e6i	−0.764317	−	0.555309i
$395$	2.89135e6	−	4.18698e6i	0.932413	−	1.35023i
$396$	69100.2	−	50204.3i	0.0221433	−	0.0160880i
$397$	2.48450e6	+	3.41961e6i	0.791156	+	1.08893i	0.993963	+	0.109714i	$0.0349934\pi$
$397$	2.48450e6	+	3.41961e6i	0.791156	+	1.08893i	−0.202808	+	0.979219i	$0.565007\pi$
$398$	−3.08877e6	+	1.00360e6i	−0.977413	+	0.317581i
$399$	4.95859e6			1.55929
$400$	−283372.	−	748131.i	−0.0885539	−	0.233791i
$401$	1.77272e6			0.550528			0.275264	−	0.961369i	$-0.411235\pi$
$401$	1.77272e6			0.550528			0.275264	+	0.961369i	$0.411235\pi$
$402$	−1.84271e6	+	598733.i	−0.568711	+	0.184786i
$403$	−1.75422e6	−	2.41448e6i	−0.538048	−	0.740560i
$404$	632369.	−	459443.i	0.192760	−	0.140048i
$405$	−3.67109e6	−	1.09630e6i	−1.11213	−	0.332119i
$406$	1.30311e6	+	946762.i	0.392342	+	0.285053i
$407$		−	665224.i		−	0.199059i
$408$	1.18740e6	−	1.63431e6i	0.353139	−	0.486055i
$409$	−1.45094e6	+	4.46552e6i	−0.428884	+	1.31997i	0.470342	+	0.882484i	$0.344131\pi$
$409$	−1.45094e6	+	4.46552e6i	−0.428884	+	1.31997i	−0.899226	+	0.437485i	$0.855869\pi$
$410$	1.36426e6	+	3.87992e6i	0.400808	+	1.13989i
$411$	−1.37399e6	−	4.22871e6i	−0.401217	−	1.23482i
$412$	2.25777e6	+	733593.i	0.655294	+	0.212918i
$413$	1.13429e6	+	368554.i	0.327228	+	0.106323i
$414$	53363.6	+	164236.i	0.0153018	+	0.0470942i
$415$	−19945.6	+	66790.0i	−0.00568496	+	0.0190367i
$416$	152516.	−	469398.i	0.0432099	−	0.132986i
$417$	2.53213e6	−	3.48518e6i	0.713092	−	0.981488i
$418$		−	1.17739e6i		−	0.329595i
$419$	−1.04633e6	−	760201.i	−0.291161	−	0.211541i	0.432610	−	0.901581i	$-0.357593\pi$
$419$	−1.04633e6	−	760201.i	−0.291161	−	0.211541i	−0.723771	+	0.690041i	$0.757593\pi$
$420$	−39428.3	−	1.64542e6i	−0.0109065	−	0.455149i
$421$	3.68476e6	−	2.67714e6i	1.01322	−	0.736148i	0.0483385	−	0.998831i	$-0.484607\pi$
$421$	3.68476e6	−	2.67714e6i	1.01322	−	0.736148i	0.964882	+	0.262683i	$0.0846074\pi$
$422$	−131165.	−	180532.i	−0.0358538	−	0.0493485i
$423$	−236066.	+	76702.6i	−0.0641480	+	0.0208430i
$424$	−510944.			−0.138025
$425$	276545.	+	5.76706e6i	0.0742665	+	1.54875i
$426$	4.36074e6			1.16422
$427$	−357547.	+	116174.i	−0.0948993	+	0.0308347i
$428$	1.68214e6	+	2.31527e6i	0.443867	+	0.610930i
$429$	−727690.	+	528698.i	−0.190899	+	0.138696i
$430$	1.23122e6	+	1.61196e6i	0.321117	+	0.420419i
$431$	−526838.	−	382770.i	−0.136611	−	0.0992534i	0.517381	−	0.855755i	$-0.326907\pi$
$431$	−526838.	−	382770.i	−0.136611	−	0.0992534i	−0.653992	+	0.756502i	$0.726907\pi$
$432$		−	849038.i		−	0.218886i
$433$	−1.08911e6	+	1.49904e6i	−0.279160	+	0.384231i	−0.925456	−	0.378856i	$-0.876317\pi$
$433$	−1.08911e6	+	1.49904e6i	−0.279160	+	0.384231i	0.646295	+	0.763087i	$0.276317\pi$
$434$	824394.	−	2.53722e6i	0.210093	−	0.646598i
$435$	3.56940e6	−	85531.6i	0.904424	−	0.0216722i
$436$	−782529.	−	2.40838e6i	−0.197144	−	0.606748i
$437$	2.26395e6	+	735604.i	0.567106	+	0.184264i
$438$	−1.24277e6	−	403801.i	−0.309532	−	0.100573i
$439$	2.03408e6	+	6.26026e6i	0.503741	+	1.55035i	0.802877	+	0.596144i	$0.203301\pi$
$439$	2.03408e6	+	6.26026e6i	0.503741	+	1.55035i	−0.299137	+	0.954210i	$0.596699\pi$
$440$	−390697.	+	9362.06i	−0.0962074	+	0.00230536i
$441$	−78607.8	+	241930.i	−0.0192473	+	0.0592370i
$442$	−2.09371e6	+	2.88174e6i	−0.509754	+	0.701616i
$443$			770495.i			0.186535i	0.995641	+	0.0932675i	$0.0297312\pi$
$443$			770495.i			0.186535i	−0.995641	+	0.0932675i	$0.970269\pi$
$444$	1.34673e6	+	978457.i	0.324208	+	0.235551i
$445$	1.61781e6	+	2.11810e6i	0.387283	+	0.507045i
$446$	3.04594e6	−	2.21301e6i	0.725077	−	0.526799i
$447$	3.12513e6	+	4.30137e6i	0.739775	+	1.01821i
$448$	419593.	−	136334.i	0.0987718	−	0.0320929i
$449$	7.69472e6			1.80126			0.900632	−	0.434584i	$-0.143104\pi$
$449$	7.69472e6			1.80126			0.900632	+	0.434584i	$0.143104\pi$
$450$	−382322.	−	476443.i	−0.0890017	−	0.110912i
$451$	2.00914e6			0.465125
$452$	−2.84367e6	+	923963.i	−0.654685	+	0.212720i
$453$	−3.27923e6	−	4.51347e6i	−0.750803	−	1.03339i
$454$	−1.16448e6	+	846043.i	−0.265150	+	0.192643i
$455$	69522.9	+	2.90133e6i	0.0157434	+	0.657004i
$456$	2.38360e6	+	1.73179e6i	0.536811	+	0.390016i
$457$		−	5.14870e6i		−	1.15321i	−0.817024	−	0.576604i	$-0.804378\pi$
$457$		−	5.14870e6i		−	1.15321i	0.817024	−	0.576604i	$-0.195622\pi$
$458$	2.42634e6	−	3.33957e6i	0.540491	−	0.743922i
$459$	−1.89353e6	+	5.82769e6i	−0.419509	+	1.29112i
$460$	226095.	−	757103.i	0.0498192	−	0.166825i
$461$	−791451.	−	2.43584e6i	−0.173449	−	0.533821i	0.826110	−	0.563509i	$-0.190549\pi$
$461$	−791451.	−	2.43584e6i	−0.173449	−	0.533821i	−0.999559	+	0.0296873i	$0.990549\pi$
$462$	−764685.	−	248461.i	−0.166678	−	0.0541569i
$463$	−4.10527e6	−	1.33388e6i	−0.889998	−	0.289178i	−0.171895	−	0.985115i	$-0.554989\pi$
$463$	−4.10527e6	−	1.33388e6i	−0.889998	−	0.289178i	−0.718102	+	0.695937i	$0.754989\pi$
$464$	295749.	+	910221.i	0.0637717	+	0.196269i
$465$	−1.96160e6	−	5.57876e6i	−0.420706	−	1.19648i
$466$	1.42743e6	−	4.39318e6i	0.304502	−	0.937161i
$467$	−5.41527e6	+	7.45348e6i	−1.14902	+	1.58149i	−0.403546	+	0.914959i	$0.632222\pi$
$467$	−5.41527e6	+	7.45348e6i	−1.14902	+	1.58149i	−0.745475	+	0.666533i	$0.767778\pi$
$468$		−	376874.i		−	0.0795394i
$469$	2.47068e6	+	1.79505e6i	0.518661	+	0.376829i
$470$	1.08823e6	+	324980.i	0.227235	+	0.0678598i
$471$	−7.79149e6	+	5.66085e6i	−1.61833	+	1.17579i
$472$	416539.	+	573317.i	0.0860598	+	0.118451i
$473$	942387.	−	306200.i	0.193676	−	0.0629293i
$474$	6.22017e6			1.27162
$475$	−8.41109e6	+	403333.i	−1.71048	+	0.0820218i
$476$	−3.18409e6			−0.644121
$477$	−371058.	+	120564.i	−0.0746700	+	0.0242617i
$478$	2.63038e6	+	3.62040e6i	0.526560	+	0.724748i
$479$	−3.84118e6	+	2.79078e6i	−0.764937	+	0.555759i	−0.900421	−	0.435020i	$-0.856741\pi$
$479$	−3.84118e6	+	2.79078e6i	−0.764937	+	0.555759i	0.135483	+	0.990780i	$0.456741\pi$
$480$	555710.	−	804727.i	0.110089	−	0.159421i
$481$	−2.37465e6	−	1.72529e6i	−0.467991	−	0.340015i
$482$		−	2.87398e6i		−	0.563464i
$483$	955511.	−	1.31515e6i	0.186366	−	0.256511i
$484$	737284.	−	2.26913e6i	0.143061	−	0.440297i
$485$	2.49330e6	+	1.72177e6i	0.481305	+	0.332369i
$486$	−451118.	−	1.38840e6i	−0.0866362	−	0.266639i
$487$	−4.32601e6	−	1.40561e6i	−0.826542	−	0.268560i	−0.134954	−	0.990852i	$-0.543089\pi$
$487$	−4.32601e6	−	1.40561e6i	−0.826542	−	0.268560i	−0.691588	+	0.722292i	$0.743089\pi$
$488$	−212447.	−	69028.3i	−0.0403833	−	0.0131213i
$489$	−1.69962e6	−	5.23088e6i	−0.321424	−	0.989242i
$490$	924978.	−	706500.i	0.174037	−	0.132930i
$491$	2.13538e6	−	6.57201e6i	0.399734	−	1.23025i	−0.525480	−	0.850806i	$-0.676114\pi$
$491$	2.13538e6	−	6.57201e6i	0.399734	−	1.23025i	0.925213	−	0.379447i	$-0.123886\pi$
$492$	−2.95518e6	+	4.06746e6i	−0.550391	+	0.757549i
$493$		−	6.90722e6i		−	1.27993i
$494$	−4.20294e6	−	3.05362e6i	−0.774883	−	0.562985i
$495$	−281523.	+	98989.1i	−0.0516418	+	0.0181583i
$496$	1.28241e6	−	931728.i	0.234058	−	0.170053i
$497$	−4.04005e6	−	5.56065e6i	−0.733661	−	1.00980i
$498$	−81039.6	+	26331.4i	−0.0146428	+	0.00475773i
$499$	6.09448e6			1.09568			0.547842	−	0.836582i	$-0.315450\pi$
$499$	6.09448e6			1.09568			0.547842	+	0.836582i	$0.315450\pi$
$500$	200720.	+	2.78787e6i	0.0359059	+	0.498709i
$501$	−3.61622e6			−0.643666
$502$	5.34349e6	−	1.73621e6i	0.946381	−	0.307498i
$503$	2.83749e6	+	3.90547e6i	0.500051	+	0.688261i	0.982202	−	0.187827i	$-0.0601444\pi$
$503$	2.83749e6	+	3.90547e6i	0.500051	+	0.688261i	−0.482151	+	0.876088i	$0.660144\pi$
$504$	272547.	−	198017.i	0.0477931	−	0.0347237i
$505$	−2.57635e6	+	905896.i	−0.449548	+	0.158070i
$506$	−312275.	−	226881.i	−0.0542202	−	0.0393933i
$507$		−	2.37440e6i		−	0.410237i
$508$	−414037.	+	569873.i	−0.0711836	+	0.0979758i
$509$	125439.	−	386060.i	0.0214603	−	0.0660481i	−0.939753	−	0.341855i	$-0.888945\pi$
$509$	125439.	−	386060.i	0.0214603	−	0.0660481i	0.961213	+	0.275807i	$0.0889449\pi$
$510$	−5.60904e6	+	4.28420e6i	−0.954911	+	0.729363i
$511$	636465.	+	1.95884e6i	0.107826	+	0.331853i
$512$	249314.	+	81007.0i	0.0420312	+	0.0136568i
$513$	−8.49953e6	−	2.76167e6i	−1.42594	−	0.463316i
$514$	1.08536e6	+	3.34038e6i	0.181203	+	0.557684i
$515$	−6.82506e6	−	4.71310e6i	−1.13394	−	0.783048i
$516$	−766232.	+	2.35822e6i	−0.126688	+	0.389906i
$517$	326110.	−	448852.i	0.0536584	−	0.0738544i
$518$		−	2.62380e6i		−	0.429641i
$519$	9.74500e6	+	7.08015e6i	1.58805	+	1.15378i
$520$	−979870.	+	1.41895e6i	−0.158913	+	0.230123i
$521$	5.84092e6	−	4.24368e6i	0.942729	−	0.684933i	−0.00634674	−	0.999980i	$-0.502020\pi$
$521$	5.84092e6	−	4.24368e6i	0.942729	−	0.684933i	0.949076	+	0.315047i	$0.102020\pi$
$522$	429557.	+	591235.i	0.0689993	+	0.0949695i
$523$	−1.10967e6	+	360554.i	−0.177395	+	0.0576390i	−0.396368	−	0.918092i	$-0.629729\pi$
$523$	−1.10967e6	+	360554.i	−0.177395	+	0.0576390i	0.218973	+	0.975731i	$0.429729\pi$
$524$	1.59130e6			0.253176
$525$	−1.51301e6	+	5.54790e6i	−0.239577	+	0.878477i
$526$	−3.16781e6			−0.499223
$527$	−1.08803e7	+	3.53522e6i	−1.70653	+	0.554485i
$528$	−280810.	−	386502.i	−0.0438357	−	0.0603347i
$529$	−4.57575e6	+	3.32448e6i	−0.710924	+	0.516516i
$530$	1.71052e6	+	510816.i	0.264508	+	0.0789905i
$531$	437781.	+	318066.i	0.0673784	+	0.0489533i
$532$		−	4.64390e6i		−	0.711384i
$533$	5.21080e6	−	7.17205e6i	0.794486	−	1.09352i
$534$	−1.00682e6	+	3.09869e6i	−0.152792	+	0.470245i
$535$	−3.31672e6	−	9.43268e6i	−0.500984	−	1.42479i
$536$	560736.	+	1.72577e6i	0.0843037	+	0.259460i
$537$	1.17346e7	+	3.81280e6i	1.75603	+	0.570569i
$538$	−1.99201e6	−	647245.i	−0.296713	−	0.0964080i
$539$	−175704.	−	540763.i	−0.0260502	−	0.0801743i
$540$	−848826.	+	2.84238e6i	−0.125266	+	0.419467i
$541$	−554029.	+	1.70512e6i	−0.0813840	+	0.250474i	−0.983467	−	0.181089i	$-0.942038\pi$
$541$	−554029.	+	1.70512e6i	−0.0813840	+	0.250474i	0.902083	+	0.431563i	$0.142038\pi$
$542$	−55900.9	+	76941.0i	−0.00817374	+	0.0112502i
$543$			1.15525e7i			1.68142i
$544$	−1.53060e6	−	1.11204e6i	−0.221750	−	0.161111i
$545$	211948.	+	8.84502e6i	0.0305660	+	1.27558i
$546$	−2.87018e6	+	2.08531e6i	−0.412028	+	0.299356i
$547$	2.72391e6	+	3.74914e6i	0.389246	+	0.535751i	0.958004	−	0.286754i	$-0.0925761\pi$
$547$	2.72391e6	+	3.74914e6i	0.389246	+	0.535751i	−0.568759	+	0.822505i	$0.692576\pi$
$548$	−3.96035e6	+	1.28679e6i	−0.563354	+	0.183045i
$549$	−170572.			−0.0241533
$550$	1.31732e6	+	359257.i	0.185688	+	0.0506406i
$551$	1.00740e7			1.41359
$552$	918631.	−	298481.i	0.128320	−	0.0416936i
$553$	−5.76273e6	−	7.93171e6i	−0.801337	−	1.10295i
$554$	−2.36985e6	+	1.72180e6i	−0.328055	+	0.238346i
$555$	−3.53032e6	−	4.62204e6i	−0.486499	−	0.636944i
$556$	−3.26400e6	−	2.37144e6i	−0.447778	−	0.325330i
$557$			5.66290e6i			0.773394i	0.922207	+	0.386697i	$0.126384\pi$
$557$			5.66290e6i			0.773394i	−0.922207	+	0.386697i	$0.873616\pi$
$558$	711462.	−	979243.i	0.0967311	−	0.133139i
$559$	1.35108e6	−	4.15819e6i	0.182874	−	0.562827i
$560$	−1.54100e6	+	36926.1i	−0.207650	+	0.00497581i
$561$	1.06547e6	+	3.27917e6i	0.142933	+	0.439903i
$562$	−291897.	−	94843.0i	−0.0389842	−	0.0126667i
$563$	−2.36874e6	−	769650.i	−0.314954	−	0.102335i	0.147275	−	0.989096i	$-0.452950\pi$
$563$	−2.36874e6	−	769650.i	−0.314954	−	0.102335i	−0.462228	+	0.886761i	$0.652950\pi$
$564$	429025.	+	1.32040e6i	0.0567917	+	0.174787i
$565$	1.04437e7	−	250256.i	1.37636	−	0.0329809i
$566$	2.05918e6	−	6.33749e6i	0.270179	−	0.831527i
$567$	−4.33911e6	+	5.97227e6i	−0.566817	+	0.780156i
$568$		−	4.08400e6i		−	0.531147i
$569$	−5.91270e6	−	4.29583e6i	−0.765606	−	0.556245i	0.135019	−	0.990843i	$-0.456891\pi$
$569$	−5.91270e6	−	4.29583e6i	−0.765606	−	0.556245i	−0.900625	+	0.434598i	$0.856891\pi$
$570$	−6.24838e6	−	8.18062e6i	−0.805528	−	1.05463i
$571$	4.87660e6	−	3.54306e6i	0.625932	−	0.454766i	−0.229057	−	0.973413i	$-0.573564\pi$
$571$	4.87660e6	−	3.54306e6i	0.625932	−	0.454766i	0.854989	+	0.518647i	$0.173564\pi$
$572$	495146.	+	681509.i	0.0632765	+	0.0870927i
$573$	6.74079e6	−	2.19022e6i	0.857678	−	0.278676i
$574$	7.92452e6			1.00391
$575$	−1.51383e6	+	2.30856e6i	−0.190944	+	0.291187i
$576$	200171.			0.0251389
$577$	1.43993e7	−	4.67861e6i	1.80053	−	0.585029i	0.800632	−	0.599156i	$-0.204497\pi$
$577$	1.43993e7	−	4.67861e6i	1.80053	−	0.585029i	0.999900	+	0.0141272i	$0.00449699\pi$
$578$	4.68745e6	+	6.45172e6i	0.583602	+	0.803260i
$579$	1.09262e7	−	7.93831e6i	1.35447	−	0.984083i
$580$	−80103.6	−	3.34288e6i	−0.00988740	−	0.412620i
$581$	108657.	+	78943.6i	0.0133541	+	0.00970234i
$582$			3.70404e6i			0.453281i
$583$	512592.	−	705522.i	0.0624598	−	0.0859685i
$584$	−378175.	+	1.16390e6i	−0.0458839	+	0.141216i
$585$	−376780.	+	1.26169e6i	−0.0455196	+	0.152427i
$586$	1.88800e6	+	5.81068e6i	0.227122	+	0.699009i
$587$	−5.25384e6	−	1.70708e6i	−0.629334	−	0.204483i	−0.0230541	−	0.999734i	$-0.507339\pi$
$587$	−5.25384e6	−	1.70708e6i	−0.629334	−	0.204483i	−0.606280	+	0.795251i	$0.707339\pi$
$588$	1.35320e6	+	439681.i	0.161406	+	0.0524438i
$589$	−5.15602e6	−	1.58686e7i	−0.612387	−	1.88473i
$590$	−821301.	−	2.33576e6i	−0.0971342	−	0.276248i
$591$	−3.84215e6	+	1.18249e7i	−0.452486	+	1.39261i
$592$	916362.	−	1.26126e6i	0.107464	−	0.147911i
$593$			1.14179e7i			1.33336i	0.745344	+	0.666681i	$0.232285\pi$
$593$			1.14179e7i			1.33336i	−0.745344	+	0.666681i	$0.767715\pi$
$594$	1.17237e6	+	851777.i	0.136332	+	0.0990512i
$595$	1.06596e7	+	3.18329e6i	1.23438	+	0.368624i
$596$	4.02840e6	−	2.92680e6i	0.464533	−	0.337503i
$597$	8.15329e6	+	1.12220e7i	0.936262	+	1.28865i
$598$	−1.61980e6	+	526304.i	−0.185229	+	0.0601844i
$599$	−7.23732e6			−0.824158			−0.412079	−	0.911148i	$-0.635197\pi$
$599$	−7.23732e6			−0.824158			−0.412079	+	0.911148i	$0.635197\pi$
$600$	−2.66491e6	+	2.13847e6i	−0.302207	+	0.242507i
$601$	1.53017e7			1.72804			0.864018	−	0.503461i	$-0.167940\pi$
$601$	1.53017e7			1.72804			0.864018	+	0.503461i	$0.167940\pi$
$602$	3.71699e6	−	1.20772e6i	0.418023	−	0.135824i
$603$	814436.	+	1.12098e6i	0.0912145	+	0.125546i
$604$	−4.22704e6	+	3.07112e6i	−0.471459	+	0.342535i
$605$	−4.73681e6	+	6.85940e6i	−0.526136	+	0.761900i
$606$	−2.70088e6	−	1.96230e6i	−0.298761	−	0.217062i
$607$		−	2.95038e6i		−	0.325017i	−0.986707	−	0.162508i	$-0.948042\pi$
$607$		−	2.95038e6i		−	0.325017i	0.986707	−	0.162508i	$-0.0519584\pi$
$608$	1.62188e6	−	2.23233e6i	0.177935	−	0.244906i
$609$	2.12588e6	−	6.54279e6i	0.232272	−	0.714858i
$610$	642212.	+	443485.i	0.0698802	+	0.0482563i
$611$	−756489.	−	2.32823e6i	−0.0819784	−	0.252304i
$612$	−1.37395e6	−	446424.i	−0.148284	−	0.0481803i
$613$	−5.34483e6	−	1.73664e6i	−0.574491	−	0.186663i	0.00734027	−	0.999973i	$-0.497663\pi$
$613$	−5.34483e6	−	1.73664e6i	−0.574491	−	0.186663i	−0.581831	+	0.813310i	$0.697663\pi$
$614$	1.63202e6	+	5.02286e6i	0.174705	+	0.537687i
$615$	1.39597e7	−	1.06625e7i	1.48829	−	1.13676i
$616$	−232693.	+	716156.i	−0.0247077	+	0.0760425i
$617$	−3.49687e6	+	4.81302e6i	−0.369799	+	0.508985i	−0.952846	−	0.303453i	$-0.901860\pi$
$617$	−3.49687e6	+	4.81302e6i	−0.369799	+	0.508985i	0.583047	+	0.812438i	$0.301860\pi$
$618$		−	1.01393e7i		−	1.06791i
$619$	−3.18112e6	−	2.31122e6i	−0.333698	−	0.242446i	0.408300	−	0.912848i	$-0.366122\pi$
$619$	−3.18112e6	−	2.31122e6i	−0.333698	−	0.242446i	−0.741998	+	0.670402i	$0.766122\pi$
$620$	−5.22472e6	+	1.83711e6i	−0.545863	+	0.191936i
$621$	−2.37031e6	+	1.72213e6i	−0.246647	+	0.179200i
$622$	1.26044e6	+	1.73485e6i	0.130631	+	0.179799i
$623$	4.88410e6	−	1.58694e6i	0.504156	−	0.163810i
$624$	−2.10799e6			−0.216724
$625$	2.11521e6	−	9.53380e6i	0.216597	−	0.976261i
$626$	−9.04067e6			−0.922072
$627$	−4.78258e6	+	1.55395e6i	−0.485840	+	0.157859i
$628$	5.30160e6	+	7.29703e6i	0.536423	+	0.738324i
$629$	−9.10267e6	+	6.61348e6i	−0.917365	+	0.666505i
$630$	−1.11039e6	+	390436.i	−0.111461	+	0.0391921i
$631$	−3.74335e6	−	2.71970e6i	−0.374271	−	0.271924i	0.384708	−	0.923038i	$-0.374302\pi$
$631$	−3.74335e6	−	2.71970e6i	−0.374271	−	0.271924i	−0.758980	+	0.651114i	$0.774302\pi$
$632$		−	5.82542e6i		−	0.580142i
$633$	−560210.	+	771063.i	−0.0555702	+	0.0764858i
$634$	218965.	−	673904.i	0.0216347	−	0.0665848i
$635$	1.95583e6	−	1.49387e6i	0.192485	−	0.147020i
$636$	674358.	+	2.07546e6i	0.0661070	+	0.203456i
$637$	−2.38606e6	−	775278.i	−0.232988	−	0.0757023i
$638$	−1.55355e6	−	504780.i	−0.151104	−	0.0490965i
$639$	−963674.	−	2.96589e6i	−0.0933637	−	0.287344i
$640$	−753657.	−	520444.i	−0.0727317	−	0.0502255i
$641$	−2.57610e6	+	7.92842e6i	−0.247638	+	0.762152i	0.747553	+	0.664202i	$0.231229\pi$
$641$	−2.57610e6	+	7.92842e6i	−0.247638	+	0.762152i	−0.995191	+	0.0979501i	$0.968771\pi$
$642$	7.18450e6	−	9.88862e6i	0.687953	−	0.946887i
$643$			881269.i			0.0840584i	0.999116	+	0.0420292i	$0.0133823\pi$
$643$			881269.i			0.0840584i	−0.999116	+	0.0420292i	$0.986618\pi$
$644$	−1.23169e6	−	894872.i	−0.117027	−	0.0850249i
$645$	4.92280e6	−	7.12873e6i	0.465921	−	0.674703i
$646$	−1.61110e7	+	1.17053e7i	−1.51894	+	1.10357i
$647$	1.56722e6	+	2.15709e6i	0.147187	+	0.202585i	0.876244	−	0.481868i	$-0.160041\pi$
$647$	1.56722e6	+	2.15709e6i	0.147187	+	0.202585i	−0.729058	+	0.684452i	$0.760041\pi$
$648$	−4.17163e6	+	1.35545e6i	−0.390273	+	0.126807i
$649$	−1.20953e6			−0.112721
$650$	4.69897e6	−	3.77070e6i	0.436234	−	0.350057i
$651$	−1.13943e7			−1.05374
$652$	−4.89892e6	+	1.59175e6i	−0.451316	+	0.146642i
$653$	4.32721e6	+	5.95589e6i	0.397123	+	0.546593i	0.960019	−	0.279935i	$-0.0903129\pi$
$653$	4.32721e6	+	5.95589e6i	0.397123	+	0.546593i	−0.562896	+	0.826528i	$0.690313\pi$
$654$	−8.75005e6	+	6.35728e6i	−0.799956	+	0.581202i
$655$	−5.32729e6	−	1.59090e6i	−0.485180	−	0.144890i
$656$	3.80933e6	+	2.76764e6i	0.345612	+	0.251102i
$657$			934485.i			0.0844615i
$658$	1.28625e6	−	1.77037e6i	0.115814	−	0.159404i
$659$	1.51184e6	−	4.65298e6i	0.135611	−	0.417366i	−0.860074	−	0.510169i	$-0.829583\pi$
$659$	1.51184e6	−	4.65298e6i	0.135611	−	0.417366i	0.995684	+	0.0928030i	$0.0295827\pi$
$660$	553681.	+	1.57466e6i	0.0494766	+	0.140711i
$661$	553337.	+	1.70300e6i	0.0492590	+	0.151604i	0.972660	−	0.232232i	$-0.0746029\pi$
$661$	553337.	+	1.70300e6i	0.0492590	+	0.151604i	−0.923401	+	0.383836i	$0.874603\pi$
$662$	1.66932e6	+	542394.i	0.148045	+	0.0481028i
$663$	1.44690e7	+	4.70126e6i	1.27836	+	0.415366i
$664$	24660.3	+	75896.6i	0.00217059	+	0.00668040i
$665$	−4.64274e6	+	1.55467e7i	−0.407118	+	1.36328i
$666$	367869.	−	1.13218e6i	0.0321371	−	0.0989080i
$667$	1.94124e6	−	2.67189e6i	0.168952	−	0.232543i
$668$			3.38672e6i			0.293656i
$669$	−1.30094e7	−	9.45186e6i	−1.12380	−	0.816492i
$670$	−151876.	−	6.33806e6i	−0.0130708	−	0.545468i
$671$	308448.	−	224101.i	0.0264470	−	0.0192148i
$672$	−1.10758e6	−	1.52445e6i	−0.0946133	−	0.130224i
$673$	74061.9	−	24064.2i	0.00630314	−	0.00204802i	−0.305864	−	0.952075i	$-0.598945\pi$
$673$	74061.9	−	24064.2i	0.00630314	−	0.00204802i	0.312167	+	0.950027i	$0.398945\pi$
$674$	−3.92366e6			−0.332691
$675$	5.68334e6	−	8.66701e6i	0.480114	−	0.732167i
$676$	−2.22372e6			−0.187160
$677$	−4.32597e6	+	1.40559e6i	−0.362754	+	0.117866i	−0.484722	−	0.874668i	$-0.661079\pi$
$677$	−4.32597e6	+	1.40559e6i	−0.362754	+	0.117866i	0.121969	+	0.992534i	$0.461079\pi$
$678$	7.50630e6	+	1.03315e7i	0.627121	+	0.863158i
$679$	4.72324e6	−	3.43164e6i	0.393157	−	0.285645i
$680$	4.01231e6	+	5.25307e6i	0.332753	+	0.435654i
$681$	4.97355e6	+	3.61349e6i	0.410959	+	0.298579i
$682$			2.70552e6i			0.222735i
$683$	−7.99358e6	+	1.10022e7i	−0.655677	+	0.902461i	−0.999329	−	0.0366357i	$-0.988336\pi$
$683$	−7.99358e6	+	1.10022e7i	−0.655677	+	0.902461i	0.343652	+	0.939097i	$0.388336\pi$
$684$	651097.	−	2.00387e6i	0.0532115	−	0.163768i
$685$	1.45448e7	−	348529.i	1.18435	−	0.0283800i
$686$	−2.93068e6	−	9.01971e6i	−0.237771	−	0.731783i
$687$	−1.67677e7	−	5.44817e6i	−1.35545	−	0.440412i
$688$	2.20856e6	+	717606.i	0.177885	+	0.0577983i
$689$	−1.18908e6	−	3.65960e6i	−0.0954250	−	0.293688i
$690$	−3.37377e6	+	80843.8i	−0.269769	+	0.00646433i
$691$	−1.11934e6	+	3.44498e6i	−0.0891801	+	0.274468i	−0.985693	−	0.168549i	$-0.946092\pi$
$691$	−1.11934e6	+	3.44498e6i	−0.0891801	+	0.274468i	0.896513	+	0.443017i	$0.146092\pi$
$692$	6.63083e6	−	9.12656e6i	0.526384	−	0.724505i
$693$			574995.i			0.0454811i
$694$	1.03133e7	+	7.49308e6i	0.812832	+	0.590557i
$695$	8.55626e6	+	1.12022e7i	0.671927	+	0.879713i
$696$	3.30699e6	−	2.40267e6i	0.258767	−	0.188006i
$697$	−1.99744e7	−	2.74923e7i	−1.55737	−	2.14353i
$698$	6.26155e6	−	2.03450e6i	0.486456	−	0.158059i
$699$	−1.97291e7			−1.52726
$700$	5.19582e6	+	1.41699e6i	0.400783	+	0.109301i
$701$	1.32326e7			1.01707			0.508534	−	0.861042i	$-0.330188\pi$
$701$	1.32326e7			1.01707			0.508534	+	0.861042i	$0.330188\pi$
$702$	6.08118e6	−	1.97590e6i	0.465742	−	0.151329i
$703$	−9.64558e6	−	1.32760e7i	−0.736105	−	1.01316i
$704$	−361974.	+	262989.i	−0.0275262	+	0.0199989i
$705$	−116202.	−	4.84932e6i	−0.00880520	−	0.367458i
$706$	−1.85029e6	−	1.34431e6i	−0.139710	−	0.101505i
$707$			5.26205e6i			0.395919i
$708$	1.77906e6	−	2.44866e6i	0.133385	−	0.183589i
$709$	−5.47052e6	+	1.68365e7i	−0.408708	+	1.25787i	0.509051	+	0.860736i	$0.329996\pi$
$709$	−5.47052e6	+	1.68365e7i	−0.408708	+	1.25787i	−0.917759	+	0.397138i	$0.870004\pi$
$710$	−4.08298e6	+	1.36723e7i	−0.303970	+	1.01788i
$711$	−1.37459e6	−	4.23054e6i	−0.101976	−	0.313850i
$712$	2.90204e6	+	942929.i	0.214537	+	0.0697074i
$713$	−5.20232e6	−	1.69034e6i	−0.383242	−	0.124523i
$714$	4.20245e6	+	1.29338e7i	0.308501	+	0.949468i
$715$	−976292.	−	2.77655e6i	−0.0714191	−	0.203115i
$716$	3.57083e6	−	1.09899e7i	0.260307	−	0.801144i
$717$	1.12345e7	−	1.54629e7i	0.816121	−	1.12329i
$718$		−	7.77612e6i		−	0.562927i
$719$	965051.	+	701151.i	0.0696191	+	0.0505812i	0.622050	−	0.782977i	$-0.286300\pi$
$719$	965051.	+	701151.i	0.0696191	+	0.0505812i	−0.552431	+	0.833558i	$0.686300\pi$
$720$	−670127.	−	200121.i	−0.0481755	−	0.0143867i
$721$	−1.29292e7	+	9.39363e6i	−0.926263	+	0.672969i
$722$	−1.12502e7	−	1.54846e7i	−0.803189	−	1.10550i
$723$	−1.16741e7	+	3.79316e6i	−0.830575	+	0.269870i
$724$	1.08194e7			0.767105
$725$	−3.07388e6	+	1.12713e7i	−0.217191	+	0.796393i
$726$	−1.01903e7			−0.717539
$727$	1.74123e7	−	5.65761e6i	1.22186	−	0.397006i	0.374101	−	0.927388i	$-0.377951\pi$
$727$	1.74123e7	−	5.65761e6i	1.22186	−	0.397006i	0.847759	+	0.530382i	$0.177951\pi$
$728$	1.95297e6	+	2.68803e6i	0.136574	+	0.187977i
$729$	8.42931e6	−	6.12425e6i	0.587453	−	0.426809i
$730$	2.42965e6	−	3.51839e6i	0.168747	−	0.244364i
$731$	−1.35589e7	−	9.85111e6i	−0.938492	−	0.681855i
$732$			954068.i			0.0658115i
$733$	−6.09151e6	+	8.38424e6i	−0.418760	+	0.576373i	−0.965328	−	0.261042i	$-0.915934\pi$
$733$	−6.09151e6	+	8.38424e6i	−0.418760	+	0.576373i	0.546568	+	0.837415i	$0.315934\pi$
$734$	4.65750e6	−	1.43343e7i	0.319089	−	0.982056i
$735$	−4.09062e6	−	2.82481e6i	−0.279300	−	0.192873i
$736$	−279539.	−	860333.i	−0.0190216	−	0.0585426i
$737$	−2.94552e6	−	957058.i	−0.199753	−	0.0649037i
$738$	3.41948e6	+	1.11106e6i	0.231110	+	0.0750922i
$739$	7.21288e6	+	2.21990e7i	0.485845	+	1.49528i	0.830754	+	0.556640i	$0.187910\pi$
$739$	7.21288e6	+	2.21990e7i	0.485845	+	1.49528i	−0.344909	+	0.938636i	$0.612090\pi$
$740$	−4.32871e6	+	3.30628e6i	−0.290589	+	0.221953i
$741$	−6.85666e6	+	2.11026e7i	−0.458741	+	1.41186i
$742$	2.02178e6	−	2.78274e6i	0.134811	−	0.185551i
$743$			1.82321e7i			1.21162i	0.795611	+	0.605808i	$0.207150\pi$
$743$			1.82321e7i			1.21162i	−0.795611	+	0.605808i	$0.792850\pi$
$744$	−5.47726e6	−	3.97946e6i	−0.362769	−	0.263567i
$745$	−1.64122e7	+	5.77086e6i	−1.08337	+	0.380934i
$746$	4.48498e6	−	3.25853e6i	0.295062	−	0.214375i
$747$	35817.7	+	49298.8i	0.00234853	+	0.00323247i
$748$	3.07107e6	−	997850.i	0.200694	−	0.0652095i
$749$	−1.92657e7			−1.25482
$750$	1.10594e7	−	4.49483e6i	0.717926	−	0.291783i
$751$	−1.97574e7			−1.27829			−0.639147	−	0.769085i	$-0.720713\pi$
$751$	−1.97574e7			−1.27829			−0.639147	+	0.769085i	$0.720713\pi$
$752$	1.23661e6	−	401798.i	0.0797420	−	0.0259098i
$753$	−1.41050e7	−	1.94138e7i	−0.906536	−	1.24774i
$754$	−5.83113e6	+	4.23656e6i	−0.373529	+	0.271385i
$755$	1.72215e7	−	6.05541e6i	1.09952	−	0.386613i
$756$	4.62410e6	+	3.35960e6i	0.294254	+	0.213788i
$757$			4.01927e6i			0.254922i	0.991844	+	0.127461i	$0.0406828\pi$
$757$			4.01927e6i			0.254922i	−0.991844	+	0.127461i	$0.959317\pi$
$758$	−2.29810e6	+	3.16306e6i	−0.145277	+	0.199956i
$759$	−509445.	+	1.56791e6i	−0.0320991	+	0.0987908i
$760$	−7.66146e6	+	5.85184e6i	−0.481147	+	0.367501i
$761$	4.30625e6	+	1.32533e7i	0.269549	+	0.829587i	0.990610	+	0.136716i	$0.0436546\pi$
$761$	4.30625e6	+	1.32533e7i	0.269549	+	0.829587i	−0.721061	+	0.692871i	$0.756345\pi$
$762$	2.86129e6	+	929688.i	0.178515	+	0.0580029i
$763$	1.62131e7	+	5.26796e6i	1.00822	+	0.327590i
$764$	−2.05122e6	−	6.31300e6i	−0.127139	−	0.391293i
$765$	4.15336e6	+	2.86813e6i	0.256593	+	0.177193i
$766$	−871110.	+	2.68100e6i	−0.0536415	+	0.165092i
$767$	−3.13697e6	+	4.31767e6i	−0.192540	+	0.265009i
$768$		−	1.11963e6i		−	0.0684970i
$769$	1.79052e7	+	1.30089e7i	1.09185	+	0.793276i	0.979711	−	0.200417i	$-0.0642296\pi$
$769$	1.79052e7	+	1.30089e7i	1.09185	+	0.793276i	0.112140	+	0.993692i	$0.464230\pi$
$770$	1.49498e6	−	2.16489e6i	0.0908675	−	0.131586i
$771$	1.21362e7	−	8.81746e6i	0.735269	−	0.534204i
$772$	−7.43453e6	−	1.02328e7i	−0.448963	−	0.617944i
$773$	2.05191e7	−	6.66706e6i	1.23512	−	0.401315i	0.382554	−	0.923933i	$-0.375044\pi$
$773$	2.05191e7	−	6.66706e6i	1.23512	−	0.401315i	0.852567	+	0.522618i	$0.175044\pi$
$774$	1.77323e6			0.106393
$775$	1.93278e7	−	926814.i	1.15592	−	0.0554292i
$776$	3.46897e6			0.206798
$777$	−1.06579e7	+	3.46296e6i	−0.633313	+	0.205776i
$778$	1.18171e7	+	1.62649e7i	0.699943	+	0.963389i
$779$	4.00968e7	−	2.91320e7i	2.36737	−	1.72000i
$780$	7.05707e6	+	2.10747e6i	0.415325	+	0.124029i
$781$	5.63927e6	+	4.09717e6i	0.330823	+	0.240357i
$782$			6.52865e6i			0.381774i
$783$	−7.28797e6	+	1.00310e7i	−0.424817	+	0.584711i
$784$	411778.	−	1.26732e6i	0.0239262	−	0.0736371i
$785$	−1.04533e7	−	2.97290e7i	−0.605452	−	1.72189i
$786$	−2.10024e6	−	6.46386e6i	−0.121258	−	0.373195i
$787$	6.64439e6	+	2.15889e6i	0.382400	+	0.124249i	0.493908	−	0.869514i	$-0.335568\pi$
$787$	6.64439e6	+	2.15889e6i	0.382400	+	0.124249i	−0.111508	+	0.993764i	$0.535568\pi$
$788$	1.10745e7	+	3.59831e6i	0.635342	+	0.206435i
$789$	4.18096e6	+	1.28677e7i	0.239102	+	0.735882i
$790$	−5.82397e6	+	1.95021e7i	−0.332010	+	1.11177i
$791$	6.22009e6	−	1.91435e7i	0.353472	−	1.08788i
$792$	−200817.	+	276401.i	−0.0113759	+	0.0156577i
$793$		−	1.68228e6i		−	0.0949984i
$794$	−1.36785e7	−	9.93798e6i	−0.769991	−	0.559431i
$795$	−182650.	−	7.62234e6i	−0.0102495	−	0.427731i
$796$	1.05099e7	−	7.63587e6i	0.587915	−	0.427145i
$797$	−215742.	−	296944.i	−0.0120307	−	0.0165588i	0.802959	−	0.596034i	$-0.203258\pi$
$797$	−215742.	−	296944.i	−0.0120307	−	0.0165588i	−0.814990	+	0.579475i	$0.803258\pi$
$798$	−1.88636e7	+	6.12915e6i	−1.04862	+	0.340716i
$799$	−9.38402e6			−0.520022
$800$	2.00275e6	+	2.49579e6i	0.110638	+	0.137874i
$801$	2.33002e6			0.128315
$802$	−6.74383e6	+	2.19120e6i	−0.370229	+	0.120295i
$803$	−1.22775e6	−	1.68985e6i	−0.0671923	−	0.0924823i
$804$	6.27001e6	−	4.55543e6i	0.342080	−	0.248536i
$805$	3.22874e6	+	4.22720e6i	0.175608	+	0.229913i
$806$	9.65790e6	+	7.01688e6i	0.523655	+	0.380458i
$807$			8.94584e6i			0.483545i
$808$	−1.83777e6	+	2.52947e6i	−0.0990291	+	0.136302i
$809$	−108196.	+	332994.i	−0.00581221	+	0.0178881i	−0.953921	−	0.300059i	$-0.902994\pi$
$809$	−108196.	+	332994.i	−0.00581221	+	0.0178881i	0.948108	+	0.317947i	$0.102994\pi$
$810$	1.53207e7	−	367123.i	0.820479	−	0.0196607i
$811$	1.83396e6	+	5.64434e6i	0.0979123	+	0.301343i	0.988002	−	0.154443i	$-0.0493583\pi$
$811$	1.83396e6	+	5.64434e6i	0.0979123	+	0.301343i	−0.890089	+	0.455786i	$0.849358\pi$
$812$	−6.12757e6	−	1.99097e6i	−0.326136	−	0.105968i
$813$	386315.	+	125521.i	0.0204982	+	0.00666026i
$814$	822262.	+	2.53066e6i	0.0434960	+	0.133867i
$815$	1.79918e7	−	431127.i	0.948812	−	0.0227359i
$816$	−2.49701e6	+	7.68500e6i	−0.131279	+	0.404035i
$817$	1.43676e7	−	1.97753e7i	0.753058	−	1.03650i
$818$		−	1.87813e7i		−	0.981392i
$819$	2.05256e6	+	1.49127e6i	0.106927	+	0.0776869i
$820$	−9.98579e6	−	1.30738e7i	−0.518618	−	0.678995i
$821$	1.04357e7	−	7.58200e6i	0.540337	−	0.392578i	−0.283873	−	0.958862i	$-0.591619\pi$
$821$	1.04357e7	−	7.58200e6i	0.540337	−	0.392578i	0.824210	+	0.566284i	$0.191619\pi$
$822$	1.04539e7	+	1.43886e7i	0.539636	+	0.742745i
$823$	5.00270e6	−	1.62548e6i	0.257457	−	0.0836529i	−0.177445	−	0.984131i	$-0.556783\pi$
$823$	5.00270e6	−	1.62548e6i	0.257457	−	0.0836529i	0.434902	+	0.900478i	$0.356783\pi$
$824$	−9.49583e6			−0.487208
$825$	−279329.	−	5.82513e6i	−0.0142883	−	0.297969i
$826$	−4.77066e6			−0.243292
$827$	−8.54962e6	+	2.77794e6i	−0.434693	+	0.141240i	−0.518186	−	0.855268i	$-0.673392\pi$
$827$	−8.54962e6	+	2.77794e6i	−0.434693	+	0.141240i	0.0834927	+	0.996508i	$0.473392\pi$
$828$	−406014.	−	558830.i	−0.0205809	−	0.0283272i
$829$	−1.64068e7	+	1.19202e7i	−0.829159	+	0.602419i	−0.919321	−	0.393508i	$-0.871261\pi$
$829$	−1.64068e7	+	1.19202e7i	−0.829159	+	0.602419i	0.0901626	+	0.995927i	$0.471261\pi$
$830$	−6679.25	−	278738.i	−0.000336537	−	0.0140443i
$831$	1.01218e7	+	7.35389e6i	0.508456	+	0.369415i
$832$			1.97421e6i			0.0988749i
$833$	−5.65279e6	+	7.78039e6i	−0.282260	+	0.388498i
$834$	−5.32488e6	+	1.63883e7i	−0.265091	+	0.815865i
$835$	3.38588e6	−	1.13380e7i	0.168056	−	0.562754i
$836$	1.45534e6	+	4.47906e6i	0.0720191	+	0.221652i
$837$	1.95310e7	+	6.34601e6i	0.963631	+	0.313103i
$838$	4.92013e6	+	1.59865e6i	0.242028	+	0.0786398i
$839$	−5.70160e6	−	1.75477e7i	−0.279635	−	0.860629i	−0.987956	−	0.154738i	$-0.950547\pi$
$839$	−5.70160e6	−	1.75477e7i	−0.279635	−	0.860629i	0.708320	−	0.705891i	$-0.249453\pi$
$840$	2.18385e6	+	6.21082e6i	0.106788	+	0.303704i
$841$	−2.01930e6	+	6.21475e6i	−0.0984487	+	0.302994i
$842$	−1.07085e7	+	1.47390e7i	−0.520535	+	0.716455i
$843$			1.31086e6i			0.0635314i
$844$	722130.	+	524658.i	0.0348947	+	0.0253525i
$845$	7.44449e6	+	2.22316e6i	0.358668	+	0.107110i
$846$	803240.	−	583588.i	0.0385851	−	0.0280337i
$847$	9.44089e6	+	1.29943e7i	0.452173	+	0.622363i
$848$	1.94375e6	−	631561.i	0.0928218	−	0.0301596i
$849$	−2.84607e7			−1.35512
$850$	−8.18051e6	−	2.15974e7i	−0.388359	−	1.02531i
$851$	−5.37983e6			−0.254650
$852$	−1.65893e7	+	5.39017e6i	−0.782939	+	0.254392i
$853$	−2.02866e7	−	2.79221e7i	−0.954634	−	1.31394i	−0.949438	−	0.313955i	$-0.898346\pi$
$853$	−2.02866e7	−	2.79221e7i	−0.954634	−	1.31394i	−0.00519603	−	0.999987i	$-0.501654\pi$
$854$	1.21659e6	−	883904.i	0.0570820	−	0.0414725i
$855$	−4.18309e6	+	6.05756e6i	−0.195696	+	0.283388i
$856$	−9.26106e6	−	6.72856e6i	−0.431993	−	0.313861i
$857$			3.32093e7i			1.54457i	0.635277	+	0.772285i	$0.280886\pi$
$857$			3.32093e7i			1.54457i	−0.635277	+	0.772285i	$0.719114\pi$
$858$	2.11479e6	−	2.91076e6i	0.0980730	−	0.134986i
$859$	1.29479e6	−	3.98497e6i	0.0598712	−	0.184265i	−0.916648	−	0.399696i	$-0.869116\pi$
$859$	1.29479e6	−	3.98497e6i	0.0598712	−	0.184265i	0.976519	+	0.215431i	$0.0691157\pi$
$860$	−6.67632e6	−	4.61039e6i	−0.307816	−	0.212565i
$861$	−1.04590e7	−	3.21895e7i	−0.480820	−	1.47981i
$862$	2.47734e6	+	804937.i	0.113558	+	0.0368972i
$863$	1.20929e6	+	392923.i	0.0552720	+	0.0179589i	0.336522	−	0.941675i	$-0.390749\pi$
$863$	1.20929e6	+	392923.i	0.0552720	+	0.0179589i	−0.281251	+	0.959634i	$0.590749\pi$
$864$	1.04947e6	+	3.22993e6i	0.0478283	+	0.147201i
$865$	−3.13227e7	+	2.39244e7i	−1.42338	+	1.08718i
$866$	2.29032e6	−	7.04889e6i	0.103777	−	0.319394i
$867$	2.00203e7	−	2.75556e7i	0.904532	−	1.24498i
$868$			1.06712e7i			0.480743i
$869$	8.04386e6	+	5.84421e6i	0.361339	+	0.262528i
$870$	−1.34731e7	+	4.73740e6i	−0.603489	+	0.212199i
$871$	−1.10558e7	+	8.03247e6i	−0.493791	+	0.358760i
$872$	5.95384e6	+	8.19475e6i	0.265159	+	0.364960i
$873$	2.51924e6	−	818550.i	0.111875	−	0.0363504i
$874$	−9.52185e6			−0.421641
$875$	−1.59777e7	−	9.93828e6i	−0.705497	−	0.438825i
$876$	5.22691e6			0.230136
$877$	−1.73547e7	+	5.63887e6i	−0.761934	+	0.247567i	−0.664108	−	0.747636i	$-0.731189\pi$
$877$	−1.73547e7	+	5.63887e6i	−0.761934	+	0.247567i	−0.0978254	+	0.995204i	$0.531189\pi$
$878$	−1.54762e7	−	2.13012e7i	−0.677530	−	0.932540i
$879$	2.11112e7	−	1.53382e7i	0.921596	−	0.669579i
$880$	1.47473e6	−	518543.i	0.0641956	−	0.0225724i
$881$	3.40314e7	+	2.47253e7i	1.47720	+	1.07325i	0.978444	+	0.206511i	$0.0662109\pi$
$881$	3.40314e7	+	2.47253e7i	1.47720	+	1.07325i	0.498760	+	0.866740i	$0.333789\pi$
$882$		−	1.01752e6i		−	0.0440425i
$883$	−6.54409e6	+	9.00716e6i	−0.282454	+	0.388764i	−0.926545	−	0.376185i	$-0.877236\pi$
$883$	−6.54409e6	+	9.00716e6i	−0.282454	+	0.388764i	0.644091	+	0.764949i	$0.277236\pi$
$884$	4.40291e6	−	1.35508e7i	0.189500	−	0.583221i
$885$	−8.40392e6	+	6.41894e6i	−0.360682	+	0.275489i
$886$	−952384.	−	2.93114e6i	−0.0407594	−	0.125445i
$887$	3.39663e6	+	1.10363e6i	0.144957	+	0.0470993i	0.380597	−	0.924741i	$-0.375719\pi$
$887$	3.39663e6	+	1.10363e6i	0.144957	+	0.0470993i	−0.235640	+	0.971840i	$0.575719\pi$
$888$	−6.33270e6	−	2.05762e6i	−0.269499	−	0.0875655i
$889$	−1.46536e6	−	4.50992e6i	−0.0621856	−	0.191388i
$890$	−8.77264e6	−	6.05801e6i	−0.371241	−	0.256363i
$891$	2.31346e6	−	7.12009e6i	0.0976264	−	0.300463i
$892$	−8.85202e6	+	1.21838e7i	−0.372503	+	0.512707i
$893$		−	1.36863e7i		−	0.574326i
$894$	−1.72055e7	−	1.25005e7i	−0.719985	−	0.523100i
$895$	−2.29414e7	+	3.32216e7i	−0.957333	+	1.38632i
$896$	−1.42771e6	+	1.03729e6i	−0.0594114	+	0.0431649i
$897$	4.27571e6	+	5.88501e6i	0.177430	+	0.244211i
$898$	−2.92725e7	+	9.51120e6i	−1.21135	+	0.393590i
$899$	−2.31489e7			−0.955282
$900$	2.04336e6	+	1.33992e6i	0.0840887	+	0.0551407i
$901$	−1.47501e7			−0.605319
$902$	−7.64323e6	+	2.48344e6i	−0.312796	+	0.101633i
$903$	−9.81158e6	−	1.35045e7i	−0.400423	−	0.551135i
$904$	9.67587e6	−	7.02993e6i	0.393794	−	0.286108i
$905$	−3.62207e7	−	1.08167e7i	−1.47006	−	0.439007i
$906$	1.80539e7	+	1.31169e7i	0.730719	+	0.530898i
$907$			2.14771e7i			0.866878i	0.901183	+	0.433439i	$0.142700\pi$
$907$			2.14771e7i			0.866878i	−0.901183	+	0.433439i	$0.857300\pi$
$908$	3.38417e6	−	4.65791e6i	0.136219	−	0.187489i
$909$	−737764.	+	2.27060e6i	−0.0296147	+	0.0911447i
$910$	−3.85072e6	−	1.09514e7i	−0.154148	−	0.438394i
$911$	−1.07180e7	−	3.29867e7i	−0.427877	−	1.31687i	−0.900212	−	0.435451i	$-0.856589\pi$
$911$	−1.07180e7	−	3.29867e7i	−0.427877	−	1.31687i	0.472336	−	0.881419i	$-0.343411\pi$
$912$	−1.12084e7	−	3.64182e6i	−0.446226	−	0.144988i
$913$	−129540.	−	42089.9i	−0.00514310	−	0.00167110i
$914$	6.36415e6	+	1.95868e7i	0.251985	+	0.775530i
$915$	953830.	−	3.19400e6i	0.0376633	−	0.126119i
$916$	−5.10242e6	+	1.57036e7i	−0.200926	+	0.618388i
$917$	−6.29668e6	+	8.66664e6i	−0.247280	+	0.340351i
$918$		−	2.45104e7i		−	0.959939i
$919$	3.25650e7	+	2.36599e7i	1.27193	+	0.924109i	0.999278	−	0.0380041i	$-0.0121000\pi$
$919$	3.25650e7	+	2.36599e7i	1.27193	+	0.924109i	0.272650	+	0.962113i	$0.412100\pi$
$920$	75713.2	+	3.15966e6i	0.00294919	+	0.123075i
$921$	1.82489e7	−	1.32586e7i	0.708904	−	0.515049i
$922$	6.02172e6	+	8.28819e6i	0.233288	+	0.321094i
$923$	2.92514e7	−	9.50435e6i	1.13017	−	0.367213i
$924$	3.21615e6			0.123924
$925$	1.77970e7	−	6.74102e6i	0.683898	−	0.259043i
$926$	1.72661e7			0.661710
$927$	−6.89607e6	+	2.24067e6i	−0.263574	+	0.0856403i
$928$	−2.25019e6	−	3.09712e6i	−0.0857727	−	0.118056i
$929$	2.17987e7	−	1.58377e7i	0.828689	−	0.602078i	−0.0904993	−	0.995897i	$-0.528846\pi$
$929$	2.17987e7	−	1.58377e7i	0.828689	−	0.602078i	0.919188	+	0.393819i	$0.128846\pi$
$930$	1.43581e7	+	1.87982e7i	0.544364	+	0.712703i
$931$	−1.13475e7	−	8.24443e6i	−0.429067	−	0.311736i
$932$			1.84770e7i			0.696775i
$933$	5.38342e6	−	7.40964e6i	0.202467	−	0.278672i
$934$	1.13879e7	−	3.50484e7i	0.427146	−	1.31462i
$935$	−1.12788e7	+	270268.i	−0.421924	+	0.0101103i
$936$	465842.	+	1.43372e6i	0.0173800	+	0.0534901i
$937$	2.21215e7	+	7.18771e6i	0.823124	+	0.267449i	0.690146	−	0.723670i	$-0.257546\pi$
$937$	2.21215e7	+	7.18771e6i	0.823124	+	0.267449i	0.132978	+	0.991119i	$0.457546\pi$
$938$	−1.16178e7	−	3.77486e6i	−0.431139	−	0.140086i
$939$	1.19321e7	+	3.67233e7i	0.441625	+	1.35918i
$940$	−4.54157e6	+	108827.i	−0.167643	+	0.00401715i
$941$	7.60208e6	−	2.33968e7i	0.279871	−	0.861355i	−0.708018	−	0.706194i	$-0.750410\pi$
$941$	7.60208e6	−	2.33968e7i	0.279871	−	0.861355i	0.987889	−	0.155161i	$-0.0495896\pi$
$942$	2.26434e7	−	3.11660e7i	0.831408	−	1.14434i
$943$		−	1.62484e7i		−	0.595021i
$944$	−2.29327e6	−	1.66616e6i	−0.0837577	−	0.0608535i
$945$	−1.21216e7	−	1.58701e7i	−0.441552	−	0.578096i
$946$	−3.20657e6	+	2.32971e6i	−0.116497	+	0.0846397i
$947$	−1.04391e7	−	1.43681e7i	−0.378256	−	0.520625i	0.576865	−	0.816839i	$-0.304276\pi$
$947$	−1.04391e7	−	1.43681e7i	−0.378256	−	0.520625i	−0.955122	+	0.296214i	$0.904276\pi$
$948$	−2.36629e7	+	7.68855e6i	−0.855160	+	0.277858i
$949$	−9.21647e6			−0.332200
$950$	3.14992e7	−	1.19311e7i	1.13237	−	0.428914i
$951$	−3.02640e6			−0.108511
$952$	1.21130e7	−	3.93575e6i	0.433171	−	0.140746i
$953$	1.41734e7	+	1.95079e7i	0.505522	+	0.695792i	0.983156	−	0.182767i	$-0.0585054\pi$
$953$	1.41734e7	+	1.95079e7i	0.505522	+	0.695792i	−0.477634	+	0.878559i	$0.658505\pi$
$954$	1.26256e6	−	917306.i	0.0449141	−	0.0326320i
$955$	555573.	+	2.31852e7i	0.0197121	+	0.822624i
$956$	−1.44816e7	−	1.05215e7i	−0.512474	−	0.372334i
$957$			6.97678e6i			0.246249i
$958$	1.11631e7	−	1.53647e7i	0.392981	−	0.540892i
$959$	8.66266e6	−	2.66609e7i	0.304162	−	0.936114i
$960$	−1.11935e6	+	3.74826e6i	−0.0392002	+	0.131266i
$961$	3.00107e6	+	9.23634e6i	0.104826	+	0.322620i
$962$	1.11663e7	+	3.62815e6i	0.389019	+	0.126400i
$963$	−8.31327e6	−	2.70114e6i	−0.288872	−	0.0938603i
$964$	3.55243e6	+	1.09333e7i	0.123121	+	0.378929i
$965$	1.46589e7	+	4.16895e7i	0.506736	+	1.44115i
$966$	−2.00937e6	+	6.18419e6i	−0.0692814	+	0.213226i
$967$	−8.98267e6	+	1.23636e7i	−0.308915	+	0.425185i	−0.935043	−	0.354536i	$-0.884639\pi$
$967$	−8.98267e6	+	1.23636e7i	−0.308915	+	0.425185i	0.626127	+	0.779721i	$0.284639\pi$
$968$			9.54361e6i			0.327359i
$969$	6.88108e7	+	4.99940e7i	2.35422	+	1.71044i
$970$	−1.16133e7	−	3.46810e6i	−0.396302	−	0.118348i
$971$	−4.17001e6	+	3.02969e6i	−0.141935	+	0.103122i	−0.656487	−	0.754338i	$-0.727958\pi$
$971$	−4.17001e6	+	3.02969e6i	−0.141935	+	0.103122i	0.514552	+	0.857459i	$0.327958\pi$
$972$	3.43231e6	+	4.72417e6i	0.116525	+	0.160383i
$973$	2.58310e7	−	8.39299e6i	0.874699	−	0.284207i
$974$	1.81945e7			0.614531
$975$	−2.15185e7	−	1.41106e7i	−0.724936	−	0.475373i
$976$	893521.			0.0300248
$977$	−1.33434e7	+	4.33555e6i	−0.447231	+	0.145314i	−0.523969	−	0.851737i	$-0.675549\pi$
$977$	−1.33434e7	+	4.33555e6i	−0.447231	+	0.145314i	0.0767386	+	0.997051i	$0.475549\pi$
$978$	1.29314e7	+	1.77986e7i	0.432315	+	0.595030i
$979$	−4.21341e6	+	3.06122e6i	−0.140500	+	0.102079i
$980$	−2.64554e6	+	3.83102e6i	−0.0879933	+	0.127423i
$981$	6.25746e6	+	4.54631e6i	0.207599	+	0.150830i
$982$			2.76409e7i			0.914689i
$983$	1.41624e7	−	1.94929e7i	0.467470	−	0.643417i	−0.508567	−	0.861023i	$-0.669825\pi$
$983$	1.41624e7	−	1.94929e7i	0.467470	−	0.643417i	0.976037	+	0.217605i	$0.0698245\pi$
$984$	6.21453e6	−	1.91263e7i	0.204607	−	0.629715i
$985$	−3.34773e7	−	2.31180e7i	−1.09941	−	0.759207i
$986$	8.53780e6	+	2.62766e7i	0.279675	+	0.860751i
$987$	−8.88891e6	−	2.88818e6i	−0.290440	−	0.0943695i
$988$	1.97634e7	+	6.42152e6i	0.644124	+	0.209289i
$989$	−2.47632e6	−	7.62132e6i	−0.0805036	−	0.247765i
$990$	948620.	−	724559.i	0.0307613	−	0.0234955i
$991$	969103.	−	2.98259e6i	0.0313463	−	0.0964739i	−0.934159	−	0.356856i	$-0.883849\pi$
$991$	969103.	−	2.98259e6i	0.0313463	−	0.0964739i	0.965506	+	0.260382i	$0.0838486\pi$
$992$	−3.72691e6	+	5.12966e6i	−0.120246	+	0.165504i
$993$		−	7.49666e6i		−	0.241265i
$994$	2.22426e7	+	1.61602e7i	0.714035	+	0.518777i
$995$	−4.28185e7	+	1.50558e7i	−1.37112	+	0.482111i
$996$	275746.	−	200341.i	0.00880765	−	0.00639914i
$997$	−2.16652e7	−	2.98196e7i	−0.690279	−	0.950087i	0.309721	−	0.950827i	$-0.399764\pi$
$997$	−2.16652e7	−	2.98196e7i	−0.690279	−	0.950087i	−1.00000		0.000740281i	$0.999764\pi$
$998$	−2.31848e7	+	7.53319e6i	−0.736846	+	0.239416i
$999$	2.01974e7			0.640298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.e.a.19.6	✓	48
25.4	even	10	inner	50.6.e.a.29.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.e.a.19.6	✓	48	1.1	even	1	trivial
50.6.e.a.29.6	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)

\(f(q)\)	\(=\)	\(q+(-3.80423 + 1.23607i) q^{2} +(10.0418 + 13.8214i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-52.7366 + 18.5432i) q^{5} +(-55.2856 - 40.1674i) q^{6} +107.711i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-15.1017 + 46.4781i) q^{9} +O(q^{10})\)	\(q+(-3.80423 + 1.23607i) q^{2} +(10.0418 + 13.8214i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-52.7366 + 18.5432i) q^{5} +(-55.2856 - 40.1674i) q^{6} +107.711i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-15.1017 + 46.4781i) q^{9} +(177.701 - 135.729i) q^{10} +(-33.7553 - 103.888i) q^{11} +(259.969 + 84.4689i) q^{12} +(-458.396 - 148.942i) q^{13} +(-133.139 - 409.759i) q^{14} +(-785.866 - 542.686i) q^{15} +(79.1084 - 243.470i) q^{16} +(-1085.98 + 1494.72i) q^{17} -195.480i q^{18} +(-2180.01 - 1583.87i) q^{19} +(-508.246 + 735.993i) q^{20} +(-1488.72 + 1081.62i) q^{21} +(256.826 + 353.490i) q^{22} +(-840.169 + 272.987i) q^{23} -1093.39 q^{24} +(2437.30 - 1955.81i) q^{25} +1927.94 q^{26} +(3154.23 - 1024.87i) q^{27} +(1012.98 + 1394.25i) q^{28} +(-3024.53 + 2197.45i) q^{29} +(3660.41 + 1093.12i) q^{30} +(5009.43 + 3639.56i) q^{31} +1024.00i q^{32} +(1096.92 - 1509.77i) q^{33} +(2283.73 - 7028.61i) q^{34} +(-1997.32 - 5680.34i) q^{35} +(241.627 + 743.650i) q^{36} +(5791.81 + 1881.87i) q^{37} +(10251.0 + 3330.76i) q^{38} +(-2544.55 - 7831.33i) q^{39} +(1023.74 - 3428.11i) q^{40} +(-5683.73 + 17492.7i) q^{41} +(4326.49 - 5954.90i) q^{42} +9071.17i q^{43} +(-1413.96 - 1027.30i) q^{44} +(-65.4446 - 2731.13i) q^{45} +(2858.76 - 2077.01i) q^{46} +(2985.41 + 4109.07i) q^{47} +(4159.50 - 1351.50i) q^{48} +5205.24 q^{49} +(-6854.51 + 10453.0i) q^{50} -31564.4 q^{51} +(-7334.34 + 2383.07i) q^{52} +(4692.58 + 6458.79i) q^{53} +(-10732.6 + 7797.69i) q^{54} +(3706.56 + 4852.77i) q^{55} +(-5576.99 - 4051.92i) q^{56} -46035.8i q^{57} +(8789.80 - 12098.1i) q^{58} +(3421.68 - 10530.8i) q^{59} +(-15276.2 + 366.055i) q^{60} +(1078.57 + 3319.49i) q^{61} +(-23555.8 - 7653.73i) q^{62} +(-5006.23 - 1626.62i) q^{63} +(-1265.73 - 3895.53i) q^{64} +(26936.1 - 645.455i) q^{65} +(-2306.73 + 7099.38i) q^{66} +(16665.4 - 22937.9i) q^{67} +29561.3i q^{68} +(-12209.9 - 8871.02i) q^{69} +(14619.5 + 19140.5i) q^{70} +(-51625.4 + 37508.0i) q^{71} +(-1838.40 - 2530.35i) q^{72} +(18186.0 - 5908.98i) q^{73} -24359.5 q^{74} +(51507.1 + 14046.9i) q^{75} -43114.3 q^{76} +(11189.9 - 3635.83i) q^{77} +(19360.1 + 26646.9i) q^{78} +(-73638.5 + 53501.5i) q^{79} +(342.824 + 14306.7i) q^{80} +(55446.9 + 40284.5i) q^{81} -73571.7i q^{82} +(732.917 - 1008.77i) q^{83} +(-9098.27 + 28001.6i) q^{84} +(29553.9 - 98964.2i) q^{85} +(-11212.6 - 34508.8i) q^{86} +(-60743.7 - 19736.8i) q^{87} +(6648.84 + 2160.34i) q^{88} +(-14733.3 - 45344.3i) q^{89} +(3624.83 + 10308.9i) q^{90} +(16042.7 - 49374.5i) q^{91} +(-8308.05 + 11435.0i) q^{92} +105785. i q^{93} +(-16436.3 - 11941.7i) q^{94} +(144337. + 43103.5i) q^{95} +(-14153.1 + 10282.8i) q^{96} +(-31859.5 - 43850.9i) q^{97} +(-19801.9 + 6434.03i) q^{98} +5338.29 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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