LMFDB - Embedded newform 74.6.h.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(3,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("74.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.h (of order $18$, degree $6$, 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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	74.3
Dual form			74.6.h.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57115 + 3.06418i) q^{2} +(-5.46669 + 4.58709i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-35.9379 + 98.7386i) q^{5} -28.5450i q^{6} +(74.9073 + 27.2640i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-33.3533 + 189.156i) q^{9} +O(q^{10})$	\(q+(-2.57115 + 3.06418i) q^{2} +(-5.46669 + 4.58709i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-35.9379 + 98.7386i) q^{5} -28.5450i q^{6} +(74.9073 + 27.2640i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-33.3533 + 189.156i) q^{9} +(-210.151 - 363.992i) q^{10} +(38.7806 - 67.1699i) q^{11} +(87.4670 + 73.3935i) q^{12} +(-115.954 + 20.4459i) q^{13} +(-276.140 + 159.429i) q^{14} +(-256.462 - 704.624i) q^{15} +(-240.561 + 87.5572i) q^{16} +(-1211.04 - 213.539i) q^{17} +(-493.851 - 588.549i) q^{18} +(-121.992 - 145.385i) q^{19} +(1655.67 + 291.939i) q^{20} +(-534.557 + 194.563i) q^{21} +(106.110 + 291.535i) q^{22} +(1806.23 - 1042.83i) q^{23} +(-449.782 + 79.3086i) q^{24} +(-6063.89 - 5088.21i) q^{25} +(235.486 - 407.874i) q^{26} +(-1552.40 - 2688.83i) q^{27} +(221.477 - 1256.06i) q^{28} +(2029.26 + 1171.59i) q^{29} +(2818.49 + 1025.85i) q^{30} -9722.36i q^{31} +(350.229 - 962.245i) q^{32} +(96.1136 + 545.087i) q^{33} +(3768.08 - 3161.80i) q^{34} +(-5384.02 + 6416.43i) q^{35} +3073.18 q^{36} +(-4911.56 + 6724.62i) q^{37} +759.146 q^{38} +(540.098 - 643.664i) q^{39} +(-5151.52 + 4322.64i) q^{40} +(2695.09 + 15284.6i) q^{41} +(778.252 - 2138.23i) q^{42} +11261.2i q^{43} +(-1166.14 - 424.440i) q^{44} +(-17478.3 - 10091.1i) q^{45} +(-1448.68 + 8215.88i) q^{46} +(6084.42 + 10538.5i) q^{47} +(913.440 - 1582.13i) q^{48} +(-8007.14 - 6718.79i) q^{49} +(31182.3 - 5498.29i) q^{50} +(7599.89 - 4387.80i) q^{51} +(644.328 + 1770.28i) q^{52} +(20199.4 - 7351.99i) q^{53} +(12230.5 + 2156.57i) q^{54} +(5238.57 + 6243.09i) q^{55} +(3279.33 + 3908.16i) q^{56} +(1333.79 + 235.183i) q^{57} +(-8807.50 + 3205.67i) q^{58} +(1923.54 + 5284.89i) q^{59} +(-10390.2 + 5998.76i) q^{60} +(-6322.90 + 1114.90i) q^{61} +(29791.0 + 24997.7i) q^{62} +(-7655.55 + 13259.8i) q^{63} +(2048.00 + 3547.24i) q^{64} +(2148.36 - 12183.9i) q^{65} +(-1917.37 - 1106.99i) q^{66} +(-23795.7 - 8660.91i) q^{67} +19675.5i q^{68} +(-5090.54 + 13986.2i) q^{69} +(-5817.94 - 32995.2i) q^{70} +(-51631.5 + 43324.0i) q^{71} +(-7901.61 + 9416.78i) q^{72} +42735.7 q^{73} +(-7977.07 - 32339.9i) q^{74} +56489.5 q^{75} +(-1951.88 + 2326.16i) q^{76} +(4736.27 - 3974.20i) q^{77} +(583.627 + 3309.91i) q^{78} +(-8732.70 + 23992.9i) q^{79} -26899.3i q^{80} +(-23038.8 - 8385.42i) q^{81} +(-53764.3 - 31040.8i) q^{82} +(627.896 - 3560.98i) q^{83} +(4550.91 + 7882.41i) q^{84} +(64606.7 - 111902. i) q^{85} +(-34506.3 - 28954.2i) q^{86} +(-16467.5 + 2903.67i) q^{87} +(4298.88 - 2481.96i) q^{88} +(-31545.4 - 86670.4i) q^{89} +(75860.4 - 27610.9i) q^{90} +(-9243.25 - 1629.83i) q^{91} +(-21450.1 - 25563.3i) q^{92} +(44597.4 + 53149.1i) q^{93} +(-47935.9 - 8452.39i) q^{94} +(18739.3 - 6820.53i) q^{95} +(2499.32 + 6866.82i) q^{96} +(7615.85 - 4397.02i) q^{97} +(41175.1 - 7260.28i) q^{98} +(11412.1 + 9575.91i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9} + 600 q^{10} - 726 q^{11} - 96 q^{12} - 246 q^{13} + 3960 q^{14} - 3960 q^{15} - 1530 q^{17} + 3222 q^{19} + 1440 q^{20} - 16110 q^{21} + 8232 q^{25} + 13632 q^{26} + 2154 q^{27} - 10464 q^{28} - 18378 q^{29} - 25056 q^{30} + 78198 q^{33} + 37296 q^{34} + 82170 q^{35} - 124416 q^{36} - 5586 q^{37} - 39936 q^{38} + 58686 q^{39} - 16128 q^{40} - 59598 q^{41} - 26304 q^{42} + 480 q^{44} - 74646 q^{45} - 22536 q^{46} - 1266 q^{47} + 193320 q^{49} + 18864 q^{50} + 68352 q^{52} - 57432 q^{53} + 101520 q^{54} + 133830 q^{55} - 228936 q^{57} - 79224 q^{58} - 52800 q^{59} + 68664 q^{61} - 72720 q^{62} - 166254 q^{63} + 196608 q^{64} - 122058 q^{65} + 254946 q^{67} - 218094 q^{69} - 25872 q^{70} + 200052 q^{71} - 32244 q^{73} + 124368 q^{74} - 234036 q^{75} + 51552 q^{76} + 397188 q^{77} - 16584 q^{78} + 267462 q^{79} - 371496 q^{81} + 121440 q^{83} + 84672 q^{84} - 337260 q^{85} + 43920 q^{86} - 667500 q^{87} - 135936 q^{88} + 377850 q^{89} - 576408 q^{90} + 875826 q^{91} + 233376 q^{92} + 365868 q^{93} - 80256 q^{94} + 764592 q^{95} - 823212 q^{97} - 342192 q^{98} - 928650 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9 + 600 * q^10 - 726 * q^11 - 96 * q^12 - 246 * q^13 + 3960 * q^14 - 3960 * q^15 - 1530 * q^17 + 3222 * q^19 + 1440 * q^20 - 16110 * q^21 + 8232 * q^25 + 13632 * q^26 + 2154 * q^27 - 10464 * q^28 - 18378 * q^29 - 25056 * q^30 + 78198 * q^33 + 37296 * q^34 + 82170 * q^35 - 124416 * q^36 - 5586 * q^37 - 39936 * q^38 + 58686 * q^39 - 16128 * q^40 - 59598 * q^41 - 26304 * q^42 + 480 * q^44 - 74646 * q^45 - 22536 * q^46 - 1266 * q^47 + 193320 * q^49 + 18864 * q^50 + 68352 * q^52 - 57432 * q^53 + 101520 * q^54 + 133830 * q^55 - 228936 * q^57 - 79224 * q^58 - 52800 * q^59 + 68664 * q^61 - 72720 * q^62 - 166254 * q^63 + 196608 * q^64 - 122058 * q^65 + 254946 * q^67 - 218094 * q^69 - 25872 * q^70 + 200052 * q^71 - 32244 * q^73 + 124368 * q^74 - 234036 * q^75 + 51552 * q^76 + 397188 * q^77 - 16584 * q^78 + 267462 * q^79 - 371496 * q^81 + 121440 * q^83 + 84672 * q^84 - 337260 * q^85 + 43920 * q^86 - 667500 * q^87 - 135936 * q^88 + 377850 * q^89 - 576408 * q^90 + 875826 * q^91 + 233376 * q^92 + 365868 * q^93 - 80256 * q^94 + 764592 * q^95 - 823212 * q^97 - 342192 * q^98 - 928650 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−2.57115	+	3.06418i	−0.454519	+	0.541675i
$2$	−2.57115	+	3.06418i	−0.454519	+	0.541675i
$3$	−5.46669	+	4.58709i	−0.350688	+	0.294262i	−0.801066	−	0.598576i	$-0.795734\pi$
$3$	−5.46669	+	4.58709i	−0.350688	+	0.294262i	0.450378	+	0.892838i	$0.351289\pi$
$4$	−2.77837	−	15.7569i	−0.0868241	−	0.492404i
$5$	−35.9379	+	98.7386i	−0.642877	+	1.76629i	−0.000382109		1.00000i	$0.500122\pi$
$5$	−35.9379	+	98.7386i	−0.642877	+	1.76629i	−0.642495	+	0.766290i	$0.722101\pi$
$6$		−	28.5450i		−	0.323707i
$7$	74.9073	+	27.2640i	0.577802	+	0.210303i	0.614356	−	0.789029i	$-0.289416\pi$
$7$	74.9073	+	27.2640i	0.577802	+	0.210303i	−0.0365542	+	0.999332i	$0.511638\pi$
$8$	55.4256	+	32.0000i	0.306186	+	0.176777i
$9$	−33.3533	+	189.156i	−0.137256	+	0.778419i
$10$	−210.151	−	363.992i	−0.664555	−	1.15104i
$11$	38.7806	−	67.1699i	0.0966346	−	0.167376i	−0.813655	−	0.581348i	$-0.802526\pi$
$11$	38.7806	−	67.1699i	0.0966346	−	0.167376i	0.910290	+	0.413972i	$0.135859\pi$
$12$	87.4670	+	73.3935i	0.175344	+	0.147131i
$13$	−115.954	+	20.4459i	−0.190295	+	0.0335542i	−0.267983	−	0.963424i	$-0.586357\pi$
$13$	−115.954	+	20.4459i	−0.190295	+	0.0335542i	0.0776881	+	0.996978i	$0.475246\pi$
$14$	−276.140	+	159.429i	−0.376538	+	0.217394i
$15$	−256.462	−	704.624i	−0.294303	−	0.808591i
$16$	−240.561	+	87.5572i	−0.234923	+	0.0855050i
$17$	−1211.04	−	213.539i	−1.01633	−	0.179207i	−0.359421	−	0.933175i	$-0.617026\pi$
$17$	−1211.04	−	213.539i	−1.01633	−	0.179207i	−0.656910	+	0.753969i	$0.728137\pi$
$18$	−493.851	−	588.549i	−0.359265	−	0.428155i
$19$	−121.992	−	145.385i	−0.0775263	−	0.0923922i	0.725887	−	0.687814i	$-0.241429\pi$
$19$	−121.992	−	145.385i	−0.0775263	−	0.0923922i	−0.803413	+	0.595422i	$0.796985\pi$
$20$	1655.67	+	291.939i	0.925545	+	0.163199i
$21$	−534.557	+	194.563i	−0.264512	+	0.0962746i
$22$	106.110	+	291.535i	0.0467411	+	0.128420i
$23$	1806.23	−	1042.83i	0.711956	−	0.411048i	−0.0998286	−	0.995005i	$-0.531829\pi$
$23$	1806.23	−	1042.83i	0.711956	−	0.411048i	0.811785	+	0.583956i	$0.198496\pi$
$24$	−449.782	+	79.3086i	−0.159395	+	0.0281056i
$25$	−6063.89	−	5088.21i	−1.94044	−	1.62823i
$26$	235.486	−	407.874i	0.0683175	−	0.118329i
$27$	−1552.40	−	2688.83i	−0.409821	−	0.709830i
$28$	221.477	−	1256.06i	0.0533867	−	0.302771i
$29$	2029.26	+	1171.59i	0.448067	+	0.258691i	0.707013	−	0.707200i	$-0.250042\pi$
$29$	2029.26	+	1171.59i	0.448067	+	0.258691i	−0.258947	+	0.965892i	$0.583375\pi$
$30$	2818.49	+	1025.85i	0.571760	+	0.208104i
$31$		−	9722.36i		−	1.81705i	−0.417827	−	0.908526i	$-0.637208\pi$
$31$		−	9722.36i		−	1.81705i	0.417827	−	0.908526i	$-0.362792\pi$
$32$	350.229	−	962.245i	0.0604612	−	0.166116i
$33$	96.1136	+	545.087i	0.0153638	+	0.0871327i
$34$	3768.08	−	3161.80i	0.559014	−	0.469069i
$35$	−5384.02	+	6416.43i	−0.742911	+	0.885367i
$36$	3073.18			0.395214
$37$	−4911.56	+	6724.62i	−0.589814	+	0.807539i
$37$	−4911.56	+	6724.62i	−0.589814	+	0.807539i
$38$	759.146			0.0852838
$39$	540.098	−	643.664i	0.0568606	−	0.0677638i
$40$	−5151.52	+	4322.64i	−0.509079	+	0.427168i
$41$	2695.09	+	15284.6i	0.250388	+	1.42002i	0.807639	+	0.589677i	$0.200745\pi$
$41$	2695.09	+	15284.6i	0.250388	+	1.42002i	−0.557251	+	0.830344i	$0.688144\pi$
$42$	778.252	−	2138.23i	0.0680764	−	0.187038i
$43$			11261.2i			0.928781i	0.885631	+	0.464390i	$0.153727\pi$
$43$			11261.2i			0.928781i	−0.885631	+	0.464390i	$0.846273\pi$
$44$	−1166.14	−	424.440i	−0.0908068	−	0.0330510i
$45$	−17478.3	−	10091.1i	−1.28668	−	0.742862i
$46$	−1448.68	+	8215.88i	−0.100943	+	0.572479i
$47$	6084.42	+	10538.5i	0.401767	+	0.695882i	0.993939	−	0.109930i	$-0.0350627\pi$
$47$	6084.42	+	10538.5i	0.401767	+	0.695882i	−0.592172	+	0.805812i	$0.701729\pi$
$48$	913.440	−	1582.13i	0.0572239	−	0.0991146i
$49$	−8007.14	−	6718.79i	−0.476417	−	0.399761i
$50$	31182.3	−	5498.29i	1.76394	−	0.311030i
$51$	7599.89	−	4387.80i	0.409149	−	0.236222i
$52$	644.328	+	1770.28i	0.0330444	+	0.0907889i
$53$	20199.4	−	7351.99i	0.987755	−	0.359513i	0.202904	−	0.979199i	$-0.434962\pi$
$53$	20199.4	−	7351.99i	0.987755	−	0.359513i	0.784850	+	0.619685i	$0.212740\pi$
$54$	12230.5	+	2156.57i	0.570769	+	0.100642i
$55$	5238.57	+	6243.09i	0.233510	+	0.278287i
$56$	3279.33	+	3908.16i	0.139738	+	0.166534i
$57$	1333.79	+	235.183i	0.0543751	+	0.00958779i
$58$	−8807.50	+	3205.67i	−0.343782	+	0.125126i
$59$	1923.54	+	5284.89i	0.0719402	+	0.197654i	0.970451	−	0.241296i	$-0.0775726\pi$
$59$	1923.54	+	5284.89i	0.0719402	+	0.197654i	−0.898511	+	0.438950i	$0.855350\pi$
$60$	−10390.2	+	5998.76i	−0.372601	+	0.215121i
$61$	−6322.90	+	1114.90i	−0.217566	+	0.0383628i	−0.281369	−	0.959600i	$-0.590788\pi$
$61$	−6322.90	+	1114.90i	−0.217566	+	0.0383628i	0.0638024	+	0.997963i	$0.479677\pi$
$62$	29791.0	+	24997.7i	0.984253	+	0.825886i
$63$	−7655.55	+	13259.8i	−0.243011	+	0.420907i
$64$	2048.00	+	3547.24i	0.0625000	+	0.108253i
$65$	2148.36	−	12183.9i	0.0630700	−	0.357688i
$66$	−1917.37	−	1106.99i	−0.0541808	−	0.0312813i
$67$	−23795.7	−	8660.91i	−0.647606	−	0.235709i	−0.00272948	−	0.999996i	$-0.500869\pi$
$67$	−23795.7	−	8660.91i	−0.647606	−	0.235709i	−0.644876	+	0.764287i	$0.723091\pi$
$68$			19675.5i			0.516005i
$69$	−5090.54	+	13986.2i	−0.128719	+	0.353652i
$70$	−5817.94	−	32995.2i	−0.141914	−	0.804833i
$71$	−51631.5	+	43324.0i	−1.21554	+	1.01996i	−0.216494	+	0.976284i	$0.569462\pi$
$71$	−51631.5	+	43324.0i	−1.21554	+	1.01996i	−0.999046	+	0.0436750i	$0.986093\pi$
$72$	−7901.61	+	9416.78i	−0.179632	+	0.214078i
$73$	42735.7			0.938606			0.469303	−	0.883037i	$-0.344505\pi$
$73$	42735.7			0.938606			0.469303	+	0.883037i	$0.344505\pi$
$74$	−7977.07	−	32339.9i	−0.169342	−	0.686530i
$75$	56489.5			1.15962
$76$	−1951.88	+	2326.16i	−0.0387631	+	0.0461961i
$77$	4736.27	−	3974.20i	0.0910352	−	0.0763876i
$78$	583.627	+	3309.91i	0.0108617	+	0.0615999i
$79$	−8732.70	+	23992.9i	−0.157428	+	0.432529i	−0.993182	−	0.116575i	$-0.962808\pi$
$79$	−8732.70	+	23992.9i	−0.157428	+	0.432529i	0.835754	+	0.549103i	$0.185031\pi$
$80$		−	26899.3i		−	0.469912i
$81$	−23038.8	−	8385.42i	−0.390164	−	0.142008i
$82$	−53764.3	−	31040.8i	−0.882997	−	0.509798i
$83$	627.896	−	3560.98i	0.0100044	−	0.0567380i	−0.979397	−	0.201945i	$-0.935274\pi$
$83$	627.896	−	3560.98i	0.0100044	−	0.0567380i	0.989401	+	0.145207i	$0.0463849\pi$
$84$	4550.91	+	7882.41i	0.0703720	+	0.121888i
$85$	64606.7	−	111902.i	0.969907	−	1.67993i
$86$	−34506.3	−	28954.2i	−0.503098	−	0.422149i
$87$	−16467.5	+	2903.67i	−0.233255	+	0.0411291i
$88$	4298.88	−	2481.96i	0.0591763	−	0.0341655i
$89$	−31545.4	−	86670.4i	−0.422145	−	1.15983i	−0.950477	−	0.310795i	$-0.899405\pi$
$89$	−31545.4	−	86670.4i	−0.422145	−	1.15983i	0.528332	−	0.849038i	$-0.322818\pi$
$90$	75860.4	−	27610.9i	0.987209	−	0.359315i
$91$	−9243.25	−	1629.83i	−0.117010	−	0.0206319i
$92$	−21450.1	−	25563.3i	−0.264217	−	0.314881i
$93$	44597.4	+	53149.1i	0.534690	+	0.637219i
$94$	−47935.9	−	8452.39i	−0.559553	−	0.0986643i
$95$	18739.3	−	6820.53i	0.213031	−	0.0775371i
$96$	2499.32	+	6866.82i	0.0276786	+	0.0760463i
$97$	7615.85	−	4397.02i	0.0821844	−	0.0474492i	−0.458345	−	0.888775i	$-0.651557\pi$
$97$	7615.85	−	4397.02i	0.0821844	−	0.0474492i	0.540529	+	0.841325i	$0.318224\pi$
$98$	41175.1	−	7260.28i	0.433081	−	0.0763639i
$99$	11412.1	+	9575.91i	0.117025	+	0.0981956i
$100$	−63326.8	+	109685.i	−0.633268	+	1.09685i
$101$	−41454.6	−	71801.5i	−0.404361	−	0.700374i	0.589886	−	0.807487i	$-0.299173\pi$
$101$	−41454.6	−	71801.5i	−0.404361	−	0.700374i	−0.994247	+	0.107113i	$0.965839\pi$
$102$	−6095.46	+	34569.1i	−0.0580105	+	0.328994i
$103$	−164061.	−	94720.5i	−1.52374	−	0.879733i	−0.999605	−	0.0280991i	$-0.991055\pi$
$103$	−164061.	−	94720.5i	−1.52374	−	0.879733i	−0.524137	−	0.851634i	$-0.675612\pi$
$104$	−7081.10	−	2577.31i	−0.0641974	−	0.0233659i
$105$		−	59773.6i		−	0.529098i
$106$	−29407.9	+	80797.7i	−0.254214	+	0.698448i
$107$	23320.6	+	132258.i	0.196916	+	1.11677i	0.909664	+	0.415345i	$0.136339\pi$
$107$	23320.6	+	132258.i	0.196916	+	1.11677i	−0.712748	+	0.701420i	$0.752550\pi$
$108$	−38054.6	+	31931.6i	−0.313941	+	0.263428i
$109$	−47479.5	+	56583.9i	−0.382772	+	0.456170i	−0.922687	−	0.385550i	$-0.874012\pi$
$109$	−47479.5	+	56583.9i	−0.382772	+	0.456170i	0.539915	+	0.841719i	$0.318456\pi$
$110$	−32599.1			−0.256876
$111$	−3996.50	−	59291.2i	−0.0307874	−	0.456754i
$112$	−20406.9			−0.153721
$113$	−50554.8	+	60248.9i	−0.372449	+	0.443867i	−0.919416	−	0.393287i	$-0.871338\pi$
$113$	−50554.8	+	60248.9i	−0.372449	+	0.443867i	0.546967	+	0.837154i	$0.315782\pi$
$114$	−4150.01	+	3482.28i	−0.0299080	+	0.0250958i
$115$	38055.2	+	215822.i	0.268330	+	1.52177i
$116$	12822.7	−	35230.0i	0.0884777	−	0.243090i
$117$		−	22615.4i		−	0.152735i
$118$	−21139.6	−	7694.17i	−0.139763	−	0.0508694i
$119$	−84893.6	−	49013.4i	−0.549551	−	0.317283i
$120$	8333.39	−	47261.0i	0.0528285	−	0.299605i
$121$	77517.6	+	134264.i	0.481324	+	0.833677i
$122$	12840.9	−	22241.1i	0.0781079	−	0.135287i
$123$	−84845.2	−	71193.6i	−0.505667	−	0.424305i
$124$	−153195.	+	27012.3i	−0.894724	+	0.157764i
$125$	435957.	−	251700.i	2.49557	−	1.44082i
$126$	−20946.8	−	57550.9i	−0.117542	−	0.322943i
$127$	284839.	−	103673.i	1.56708	−	0.570369i	0.594733	−	0.803923i	$-0.297258\pi$
$127$	284839.	−	103673.i	1.56708	−	0.570369i	0.972344	+	0.233554i	$0.0750355\pi$
$128$	−16135.1	−	2845.05i	−0.0870455	−	0.0153485i
$129$	−51656.2	−	61561.4i	−0.273305	−	0.325712i
$130$	31810.0	+	37909.7i	0.165084	+	0.196740i
$131$	159305.	+	28089.7i	0.811055	+	0.143011i	0.563770	−	0.825932i	$-0.309351\pi$
$131$	159305.	+	28089.7i	0.811055	+	0.143011i	0.247285	+	0.968943i	$0.420462\pi$
$132$	8321.86	−	3028.91i	0.0415705	−	0.0151304i
$133$	−5174.34	−	14216.4i	−0.0253645	−	0.0696884i
$134$	87720.8	−	50645.6i	0.422027	−	0.243658i
$135$	321282.	−	56650.6i	1.51723	−	0.267529i
$136$	−60289.3	−	50588.7i	−0.279507	−	0.234534i
$137$	−56823.3	+	98420.8i	−0.258657	+	0.448008i	−0.965882	−	0.258981i	$-0.916613\pi$
$137$	−56823.3	+	98420.8i	−0.258657	+	0.448008i	0.707225	+	0.706988i	$0.249947\pi$
$138$	−29767.5	−	51558.8i	−0.133059	−	0.230465i
$139$	−55289.7	+	313564.i	−0.242721	+	1.37654i	0.583005	+	0.812468i	$0.301877\pi$
$139$	−55289.7	+	313564.i	−0.242721	+	1.37654i	−0.825726	+	0.564071i	$0.809234\pi$
$140$	116062.	+	67008.4i	0.500461	+	0.288941i
$141$	−81602.9	−	29701.0i	−0.345667	−	0.125812i
$142$		−	269601.i		−	1.12202i
$143$	−3123.42	+	8581.54i	−0.0127729	+	0.0350934i
$144$	−8538.44	−	48423.9i	−0.0343141	−	0.194605i
$145$	−188609.	+	158262.i	−0.744976	+	0.625109i
$146$	−109880.	+	130950.i	−0.426615	+	0.508420i
$147$	74592.2			0.284708
$148$	119605.	+	58707.6i	0.448845	+	0.220313i
$149$	−389443.			−1.43707			−0.718536	−	0.695490i	$-0.755188\pi$
$149$	−389443.			−1.43707			−0.718536	+	0.695490i	$0.755188\pi$
$150$	−145243.	+	173094.i	−0.527068	+	0.628136i
$151$	−408790.	+	343016.i	−1.45901	+	1.22425i	−0.533350	+	0.845895i	$0.679067\pi$
$151$	−408790.	+	343016.i	−1.45901	+	1.22425i	−0.925659	+	0.378359i	$0.876489\pi$
$152$	−2109.19	−	11961.8i	−0.00740469	−	0.0419941i
$153$	80784.2	−	221953.i	0.278996	−	0.766535i
$154$			24731.0i			0.0840312i
$155$	959973.	+	349401.i	3.20944	+	1.16814i
$156$	−11642.8	−	6721.95i	−0.0383040	−	0.0221148i
$157$	−30404.5	+	172432.i	−0.0984438	+	0.558303i	0.895194	+	0.445677i	$0.147037\pi$
$157$	−30404.5	+	172432.i	−0.0984438	+	0.558303i	−0.993638	+	0.112625i	$0.964074\pi$
$158$	−51065.4	−	88447.9i	−0.162736	−	0.281867i
$159$	−76699.6	+	132848.i	−0.240603	+	0.416736i
$160$	82424.3	+	69162.2i	0.254539	+	0.213584i
$161$	163731.	−	28870.3i	0.497814	−	0.0877781i
$162$	84930.6	−	49034.7i	0.254259	−	0.146797i
$163$	−92031.8	−	252855.i	−0.271312	−	0.745424i	−0.998273	−	0.0587449i	$-0.981290\pi$
$163$	−92031.8	−	252855.i	−0.271312	−	0.745424i	0.726961	−	0.686679i	$-0.240932\pi$
$164$	233351.	−	84932.7i	0.677484	−	0.246584i
$165$	−57275.3	−	10099.2i	−0.163779	−	0.0288786i
$166$	9297.05	+	11079.8i	0.0261863	+	0.0312077i
$167$	−197883.	−	235827.i	−0.549056	−	0.654340i	0.418136	−	0.908384i	$-0.362683\pi$
$167$	−197883.	−	235827.i	−0.549056	−	0.654340i	−0.967192	+	0.254045i	$0.918239\pi$
$168$	−35854.2	−	6322.06i	−0.0980091	−	0.0172817i
$169$	−335874.	+	122248.i	−0.904606	+	0.329250i
$170$	176774.	+	485683.i	0.469134	+	1.28893i
$171$	31569.3	−	18226.5i	0.0825608	−	0.0476665i
$172$	177442.	−	31287.8i	0.457335	−	0.0806405i
$173$	240605.	+	201892.i	0.611210	+	0.512866i	0.895027	−	0.446013i	$-0.147156\pi$
$173$	240605.	+	201892.i	0.611210	+	0.512866i	−0.283817	+	0.958878i	$0.591601\pi$
$174$	33443.2	−	57925.2i	0.0837402	−	0.145042i
$175$	−315504.	−	546470.i	−0.778772	−	1.34887i
$176$	−3447.90	+	19554.0i	−0.00839021	+	0.0475832i
$177$	−34757.7	−	20067.4i	−0.0833907	−	0.0481457i
$178$	346681.	+	126182.i	0.820126	+	0.298501i
$179$			409616.i			0.955531i	0.878488	+	0.477765i	$0.158553\pi$
$179$			409616.i			0.955531i	−0.878488	+	0.477765i	$0.841447\pi$
$180$	−110444.	+	303442.i	−0.254074	+	0.698062i
$181$	−30427.0	−	172560.i	−0.0690340	−	0.391511i	−0.999673	−	0.0255727i	$-0.991859\pi$
$181$	−30427.0	−	172560.i	−0.0690340	−	0.391511i	0.930639	−	0.365939i	$-0.119252\pi$
$182$	28759.9	−	24132.4i	0.0643589	−	0.0540035i
$183$	29451.2	−	35098.5i	0.0650092	−	0.0774749i
$184$	133482.			0.290655
$185$	−487468.	−	726630.i	−1.04717	−	1.56093i
$186$	−277525.			−0.588193
$187$	−61308.1	+	73064.2i	−0.128208	+	0.152792i
$188$	149150.	−	125152.i	0.307772	−	0.258251i
$189$	−42977.5	−	243738.i	−0.0875159	−	0.496327i
$190$	−27282.1	+	74957.0i	−0.0548270	+	0.150636i
$191$			413216.i			0.819584i	0.912179	+	0.409792i	$0.134399\pi$
$191$			413216.i			0.819584i	−0.912179	+	0.409792i	$0.865601\pi$
$192$	−27467.3	−	9997.28i	−0.0537728	−	0.0195717i
$193$	−792809.	−	457729.i	−1.53206	−	0.884535i	−0.999267	−	0.0382888i	$-0.987809\pi$
$193$	−792809.	−	457729.i	−1.53206	−	0.884535i	−0.532792	−	0.846246i	$-0.678857\pi$
$194$	−6108.27	+	34641.7i	−0.0116524	+	0.0660838i
$195$	44144.5	+	76460.5i	0.0831362	+	0.143996i
$196$	−83620.6	+	144835.i	−0.155480	+	0.269298i
$197$	459570.	+	385625.i	0.843697	+	0.707946i	0.958392	−	0.285455i	$-0.0921447\pi$
$197$	459570.	+	385625.i	0.843697	+	0.707946i	−0.114695	+	0.993401i	$0.536589\pi$
$198$	−58684.6	+	10347.7i	−0.106380	+	0.0187577i
$199$	338247.	−	195287.i	0.605483	−	0.349576i	−0.165713	−	0.986174i	$-0.552992\pi$
$199$	338247.	−	195287.i	0.605483	−	0.349576i	0.771195	+	0.636599i	$0.219659\pi$
$200$	−173272.	−	476062.i	−0.306305	−	0.841566i
$201$	169812.	−	61806.4i	0.296468	−	0.107905i
$202$	326598.	+	57588.1i	0.563165	+	0.0993012i
$203$	120064.	+	143087.i	0.204490	+	0.243702i
$204$	−90253.5	−	107560.i	−0.151841	−	0.180957i
$205$	−1.60604e6	−	283188.i	−2.66914	−	0.470641i
$206$	712065.	−	259171.i	1.16910	−	0.425518i
$207$	137013.	+	376441.i	0.222247	+	0.610620i
$208$	26103.9	−	15071.1i	0.0418357	−	0.0241539i
$209$	−14496.4	+	2556.11i	−0.0229560	+	0.00404775i
$210$	183157.	+	153687.i	0.286599	+	0.240485i
$211$	−318455.	+	551580.i	−0.492427	+	0.852908i	−0.999962	−	0.00872281i	$-0.997223\pi$
$211$	−318455.	+	551580.i	−0.492427	+	0.852908i	0.507535	+	0.861631i	$0.330557\pi$
$212$	−171966.	−	297854.i	−0.262787	−	0.455160i
$213$	83522.1	−	473677.i	0.126140	−	0.715375i
$214$	−465222.	−	268596.i	−0.694426	−	0.400927i
$215$	−1.11191e6	−	404704.i	−1.64050	−	0.597092i
$216$		−	198707.i		−	0.289787i
$217$	265071.	−	728276.i	0.382131	−	1.04990i
$218$	−51306.1	−	290971.i	−0.0731186	−	0.414676i
$219$	−233622.	+	196033.i	−0.329158	+	0.276196i
$220$	83817.1	−	99889.4i	0.116755	−	0.139143i
$221$	144791.			0.199416
$222$	191954.	+	140201.i	0.261406	+	0.190927i
$223$	−147158.			−0.198163			−0.0990814	−	0.995079i	$-0.531590\pi$
$223$	−147158.			−0.198163			−0.0990814	+	0.995079i	$0.531590\pi$
$224$	52469.3	−	62530.5i	0.0698692	−	0.0832668i
$225$	1.16472e6	−	977312.i	1.53378	−	1.28700i
$226$	−54629.2	−	309818.i	−0.0711466	−	0.403492i
$227$	−38903.5	+	106887.i	−0.0501100	+	0.137676i	−0.962223	−	0.272263i	$-0.912228\pi$
$227$	−38903.5	+	106887.i	−0.0501100	+	0.137676i	0.912113	+	0.409939i	$0.134450\pi$
$228$		−	21669.8i		−	0.0276070i
$229$	1.25693e6	+	457484.i	1.58388	+	0.576484i	0.976042	−	0.217580i	$-0.0698164\pi$
$229$	1.25693e6	+	457484.i	1.58388	+	0.576484i	0.607834	+	0.794064i	$0.292039\pi$
$230$	−759162.	−	438302.i	−0.946269	−	0.546329i
$231$	−7661.66	+	43451.4i	−0.00944698	+	0.0535765i
$232$	74982.0	+	129873.i	0.0914612	+	0.158415i
$233$	117883.	−	204179.i	0.142253	−	0.246389i	−0.786092	−	0.618110i	$-0.787899\pi$
$233$	117883.	−	204179.i	0.142253	−	0.246389i	0.928345	+	0.371721i	$0.121232\pi$
$234$	69297.5	+	58147.5i	0.0827328	+	0.0694211i
$235$	−1.25922e6	+	222035.i	−1.48742	+	0.262272i
$236$	77929.3	−	44992.5i	0.0910795	−	0.0525848i
$237$	−62318.7	−	171219.i	−0.0720689	−	0.198008i
$238$	368460.	−	134108.i	0.421646	−	0.153467i
$239$	−1.12625e6	−	198588.i	−1.27538	−	0.224884i	−0.505364	−	0.862906i	$-0.668642\pi$
$239$	−1.12625e6	−	198588.i	−1.27538	−	0.224884i	−0.770018	+	0.638022i	$0.779753\pi$
$240$	123390.	+	147050.i	0.138277	+	0.164792i
$241$	489804.	+	583726.i	0.543225	+	0.647391i	0.965908	−	0.258887i	$-0.0833559\pi$
$241$	489804.	+	583726.i	0.543225	+	0.647391i	−0.422682	+	0.906278i	$0.638911\pi$
$242$	−610720.	−	107686.i	−0.670353	−	0.118201i
$243$	873376.	−	317883.i	0.948824	−	0.345344i
$244$	35134.7	+	96531.8i	0.0377800	+	0.103800i
$245$	951163.	−	549154.i	1.01237	−	0.584493i
$246$	436299.	−	76931.4i	0.459671	−	0.0810524i
$247$	17118.1	+	14363.8i	0.0178530	+	0.0149805i
$248$	311116.	−	538868.i	0.321213	−	0.556357i
$249$	12902.0	+	22347.0i	0.0131874	+	0.0228413i
$250$	−349658.	+	1.98301e6i	−0.353829	+	2.00667i
$251$	416038.	+	240199.i	0.416820	+	0.240651i	0.693716	−	0.720249i	$-0.255972\pi$
$251$	416038.	+	240199.i	0.416820	+	0.240651i	−0.276896	+	0.960900i	$0.589306\pi$
$252$	230204.	+	83787.3i	0.228355	+	0.0831145i
$253$		−	161766.i		−	0.158886i
$254$	−414692.	+	1.13936e6i	−0.403312	+	1.10809i
$255$	160121.	+	908091.i	0.154205	+	0.874538i
$256$	50203.5	−	42125.7i	0.0478778	−	0.0401742i
$257$	89422.9	−	106570.i	0.0844532	−	0.100647i	−0.722163	−	0.691723i	$-0.756852\pi$
$257$	89422.9	−	106570.i	0.0844532	−	0.100647i	0.806616	+	0.591075i	$0.201296\pi$
$258$	321451.			0.300653
$259$	−551252.	+	369814.i	−0.510623	+	0.342558i
$260$	−197950.			−0.181603
$261$	−289296.	+	344770.i	−0.262870	+	0.313277i
$262$	−495668.	+	415915.i	−0.446106	+	0.374327i
$263$	101135.	+	573567.i	0.0901599	+	0.511322i	0.996123	+	0.0879665i	$0.0280368\pi$
$263$	101135.	+	573567.i	0.0901599	+	0.511322i	−0.905964	+	0.423356i	$0.860852\pi$
$264$	−12115.6	+	33287.4i	−0.0106988	+	0.0293948i
$265$			2.25868e6i			1.97578i
$266$	56865.6	+	20697.4i	0.0492771	+	0.0179354i
$267$	570014.	+	329098.i	0.489336	+	0.282518i
$268$	−70356.1	+	399009.i	−0.0598363	+	0.339349i
$269$	−208224.	−	360654.i	−0.175448	−	0.303886i	0.764868	−	0.644187i	$-0.222804\pi$
$269$	−208224.	−	360654.i	−0.175448	−	0.303886i	−0.940316	+	0.340301i	$0.889471\pi$
$270$	−652476.	+	1.13012e6i	−0.544697	+	0.943443i
$271$	217584.	+	182575.i	0.179971	+	0.151014i	0.728323	−	0.685234i	$-0.240300\pi$
$271$	217584.	+	182575.i	0.179971	+	0.151014i	−0.548352	+	0.836248i	$0.684744\pi$
$272$	310026.	−	54665.9i	0.254083	−	0.0448017i
$273$	58006.2	−	33489.9i	0.0471050	−	0.0271961i
$274$	−155478.	−	427171.i	−0.125110	−	0.343736i
$275$	−576936.	+	209987.i	−0.460040	+	0.167441i
$276$	234522.	+	41352.6i	0.185315	+	0.0326761i
$277$	271831.	+	323955.i	0.212863	+	0.253680i	0.861902	−	0.507075i	$-0.169273\pi$
$277$	271831.	+	323955.i	0.212863	+	0.253680i	−0.649039	+	0.760755i	$0.724829\pi$
$278$	−818656.	−	975637.i	−0.635316	−	0.757140i
$279$	1.83904e6	+	324273.i	1.41443	+	0.249402i
$280$	−503738.	+	183346.i	−0.383981	+	0.139758i
$281$	−598879.	−	1.64541e6i	−0.452453	−	1.24310i	−0.930992	−	0.365038i	$-0.881056\pi$
$281$	−598879.	−	1.64541e6i	−0.452453	−	1.24310i	0.478540	−	0.878066i	$-0.341166\pi$
$282$	300822.	−	173680.i	0.225262	−	0.130055i
$283$	2.18887e6	−	385958.i	1.62463	−	0.286466i	0.714143	−	0.700000i	$-0.246817\pi$
$283$	2.18887e6	−	385958.i	1.62463	−	0.286466i	0.910489	+	0.413534i	$0.135706\pi$
$284$	826105.	+	693184.i	0.607770	+	0.509979i
$285$	−71155.2	+	123244.i	−0.0518913	+	0.0898784i
$286$	−18264.6	−	31635.2i	−0.0132037	−	0.0228694i
$287$	−214838.	+	1.21841e6i	−0.153960	+	0.873148i
$288$	170333.	+	98341.8i	0.121009	+	0.0698646i
$289$	86785.1	+	31587.2i	0.0611224	+	0.0222467i
$290$		−	984846.i		−	0.687659i
$291$	−21464.0	+	58971.8i	−0.0148586	+	0.0408236i
$292$	−118736.	−	673383.i	−0.0814936	−	0.462173i
$293$	1.02327e6	−	858624.i	0.696338	−	0.584297i	−0.224391	−	0.974499i	$-0.572039\pi$
$293$	1.02327e6	−	858624.i	0.696338	−	0.584297i	0.920729	+	0.390202i	$0.127595\pi$
$294$	−191788.	+	228564.i	−0.129405	+	0.154219i
$295$	−590951.			−0.395363
$296$	−487414.	+	215546.i	−0.323347	+	0.142992i
$297$	−240812.			−0.158411
$298$	1.00132e6	−	1.19332e6i	0.653177	−	0.778427i
$299$	−188118.	+	157850.i	−0.121690	+	0.102110i
$300$	−156949.	−	890100.i	−0.100683	−	0.571000i
$301$	−307025.	+	843545.i	−0.195325	+	0.536651i
$302$		−	2.13455e6i		−	1.34676i
$303$	555979.	+	202360.i	0.347898	+	0.126625i
$304$	42076.2	+	24292.7i	0.0261127	+	0.0150762i
$305$	117148.	−	664381.i	0.0721085	−	0.408948i
$306$	472394.	+	818211.i	0.288404	+	0.499530i
$307$	1.08464e6	−	1.87865e6i	0.656809	−	1.13763i	−0.324628	−	0.945842i	$-0.605239\pi$
$307$	1.08464e6	−	1.87865e6i	0.656809	−	1.13763i	0.981437	−	0.191784i	$-0.0614274\pi$
$308$	−75780.3	−	63587.2i	−0.0455176	−	0.0381938i
$309$	1.33136e6	−	234755.i	0.793231	−	0.139868i
$310$	−3.53886e6	+	2.04316e6i	−2.09151	+	1.20753i
$311$	983591.	+	2.70240e6i	0.576652	+	1.58434i	0.793786	+	0.608197i	$0.208107\pi$
$311$	983591.	+	2.70240e6i	0.576652	+	1.58434i	−0.217135	+	0.976142i	$0.569671\pi$
$312$	50532.5	−	18392.3i	0.0293890	−	0.0106967i
$313$	−539858.	−	95191.6i	−0.311472	−	0.0549209i	0.0157271	−	0.999876i	$-0.494994\pi$
$313$	−539858.	−	95191.6i	−0.311472	−	0.0549209i	−0.327199	+	0.944955i	$0.606105\pi$
$314$	−450189.	−	536514.i	−0.257674	−	0.307084i
$315$	−1.03413e6	−	1.23243e6i	−0.587217	−	0.699818i
$316$	402317.	+	70939.3i	0.226647	+	0.0399640i
$317$	−2.25875e6	+	822118.i	−1.26247	+	0.459501i	−0.884596	−	0.466357i	$-0.845566\pi$
$317$	−2.25875e6	+	822118.i	−1.26247	+	0.459501i	−0.377872	+	0.925858i	$0.623344\pi$
$318$	−209862.	−	576592.i	−0.116377	−	0.319743i
$319$	157392.	−	90870.1i	0.0865975	−	0.0499971i
$320$	−423850.	+	74736.3i	−0.231386	+	0.0407996i
$321$	−734166.	−	616038.i	−0.397678	−	0.333691i
$322$	−332514.	+	575932.i	−0.178719	+	0.309550i
$323$	116692.	+	202117.i	0.0622351	+	0.107794i
$324$	−68118.3	+	386318.i	−0.0360497	+	0.204448i
$325$	807166.	+	466018.i	0.423892	+	0.244734i
$326$	1.01142e6	+	368127.i	0.527094	+	0.191847i
$327$		−	527119.i		−	0.272609i
$328$	−339731.	+	933402.i	−0.174361	+	0.479054i
$329$	168445.	+	955298.i	0.0857962	+	0.486574i
$330$	178209.	−	149535.i	0.0900834	−	0.0755889i
$331$	2.20543e6	−	2.62833e6i	1.10643	−	1.31859i	0.163144	−	0.986602i	$-0.447837\pi$
$331$	2.20543e6	−	2.62833e6i	1.10643	−	1.31859i	0.943284	−	0.331987i	$-0.107719\pi$
$332$	−57854.6			−0.0288066
$333$	−1.10818e6	−	1.15334e6i	−0.547648	−	0.569963i
$334$	1.23140e6			0.603996
$335$	1.71033e6	−	2.03829e6i	0.832661	−	0.992327i
$336$	111558.	−	93608.6i	0.0539081	−	0.0452343i
$337$	699604.	+	3.96765e6i	0.335566	+	1.90309i	0.421574	+	0.906794i	$0.361478\pi$
$337$	699604.	+	3.96765e6i	0.335566	+	1.90309i	−0.0860077	+	0.996294i	$0.527411\pi$
$338$	488992.	−	1.34350e6i	0.232815	−	0.639653i
$339$		−	561261.i		−	0.265256i
$340$	−1.94273e6	−	707097.i	−0.911415	−	0.331728i
$341$	−653050.	−	377039.i	−0.304131	−	0.175590i
$342$	−25320.0	+	143597.i	−0.0117057	+	0.0663865i
$343$	−1.08649e6	−	1.88186e6i	−0.498645	−	0.863679i
$344$	−360358.	+	624159.i	−0.164187	+	0.284380i
$345$	−1.19803e6	−	1.00527e6i	−0.541901	−	0.454709i
$346$	−1.23727e6	+	218163.i	−0.555613	+	0.0979696i
$347$	−801198.	+	462572.i	−0.357204	+	0.206232i	−0.667854	−	0.744293i	$-0.732787\pi$
$347$	−801198.	+	462572.i	−0.357204	+	0.206232i	0.310650	+	0.950524i	$0.399453\pi$
$348$	91505.8	+	251410.i	0.0405043	+	0.111285i
$349$	−1.16297e6	+	423288.i	−0.511100	+	0.186025i	−0.584680	−	0.811264i	$-0.698780\pi$
$349$	−1.16297e6	+	423288.i	−0.511100	+	0.186025i	0.0735797	+	0.997289i	$0.476558\pi$
$350$	2.48569e6	+	438294.i	1.08462	+	0.191247i
$351$	234983.	+	280041.i	0.101805	+	0.121326i
$352$	−51051.9	−	60841.3i	−0.0219611	−	0.0261723i
$353$	−186430.	−	32872.6i	−0.0796304	−	0.0140410i	0.133691	−	0.991023i	$-0.457317\pi$
$353$	−186430.	−	32872.6i	−0.0796304	−	0.0140410i	−0.213321	+	0.976982i	$0.568428\pi$
$354$	150857.	−	54907.5i	0.0639820	−	0.0232876i
$355$	−2.42222e6	−	6.65500e6i	−1.02010	−	2.80270i
$356$	−1.27801e6	+	737861.i	−0.534454	+	0.308567i
$357$	688916.	−	121474.i	0.286085	−	0.0504446i
$358$	−1.25514e6	−	1.05319e6i	−0.517587	−	0.434307i
$359$	−980406.	+	1.69811e6i	−0.401486	+	0.695393i	−0.993905	−	0.110236i	$-0.964839\pi$
$359$	−980406.	+	1.69811e6i	−0.401486	+	0.695393i	0.592420	+	0.805629i	$0.298173\pi$
$360$	−645832.	−	1.11861e6i	−0.262641	−	0.454908i
$361$	423715.	−	2.40301e6i	0.171122	−	0.970482i
$362$	606988.	+	350445.i	0.243449	+	0.140556i
$363$	−1.03965e6	−	378401.i	−0.414114	−	0.150725i
$364$			150173.i			0.0594073i
$365$	−1.53583e6	+	4.21966e6i	−0.603408	+	1.65785i
$366$	31824.8	+	180487.i	0.0124183	+	0.0704277i
$367$	−891623.	+	748160.i	−0.345554	+	0.289954i	−0.799002	−	0.601329i	$-0.794638\pi$
$367$	−891623.	+	748160.i	−0.345554	+	0.289954i	0.453448	+	0.891283i	$0.350194\pi$
$368$	−343202.	+	409012.i	−0.132108	+	0.157441i
$369$	−2.98106e6			−1.13974
$370$	3.47988e6	+	374584.i	1.32148	+	0.142248i
$371$	1.71353e6			0.646333
$372$	713558.	−	850386.i	0.267345	−	0.318609i
$373$	3.54470e6	−	2.97436e6i	1.31919	−	1.10693i	0.332714	−	0.943028i	$-0.392036\pi$
$373$	3.54470e6	−	2.97436e6i	1.31919	−	1.10693i	0.986476	−	0.163904i	$-0.0524088\pi$
$374$	−66249.2	−	375718.i	−0.0244907	−	0.138894i
$375$	−1.22867e6	+	3.37574e6i	−0.451188	+	1.23963i
$376$			778806.i			0.284092i
$377$	−259255.	−	94361.3i	−0.0939452	−	0.0341933i
$378$	857358.	+	494996.i	0.308626	+	0.178185i
$379$	150397.	−	852946.i	0.0537827	−	0.305017i	−0.946036	−	0.324062i	$-0.894951\pi$
$379$	150397.	−	852946.i	0.0537827	−	0.305017i	0.999819	+	0.0190450i	$0.00606259\pi$
$380$	−159535.	−	276323.i	−0.0566758	−	0.0981654i
$381$	−1.08157e6	+	1.87333e6i	−0.381717	+	0.661153i
$382$	−1.26617e6	−	1.06244e6i	−0.443948	−	0.372517i
$383$	4.32808e6	−	763157.i	1.50764	−	0.265838i	0.642079	−	0.766639i	$-0.278072\pi$
$383$	4.32808e6	−	763157.i	1.50764	−	0.265838i	0.865563	+	0.500801i	$0.166961\pi$
$384$	101256.	−	58460.2i	0.0350423	−	0.0202317i
$385$	222195.	+	610477.i	0.0763982	+	0.209902i
$386$	3.44099e6	−	1.25242e6i	1.17548	−	0.427840i
$387$	−2.13012e6	−	375598.i	−0.722981	−	0.127481i
$388$	−90443.1	−	107786.i	−0.0304997	−	0.0363482i
$389$	−1.90918e6	−	2.27527e6i	−0.639695	−	0.762358i	0.344627	−	0.938740i	$-0.388005\pi$
$389$	−1.90918e6	−	2.27527e6i	−0.639695	−	0.762358i	−0.984322	+	0.176381i	$0.943561\pi$
$390$	−347791.	−	61324.9i	−0.115786	−	0.0204162i
$391$	−2.41010e6	+	877204.i	−0.797246	+	0.290174i
$392$	−228799.	−	628621.i	−0.0752038	−	0.206621i
$393$	−999719.	+	577188.i	−0.326510	+	0.188511i
$394$	−2.36325e6	+	416705.i	−0.766953	+	0.135235i
$395$	−2.05519e6	−	1.72451e6i	−0.662764	−	0.556125i
$396$	119180.	−	206425.i	0.0381913	−	0.0661493i
$397$	2.99565e6	+	5.18861e6i	0.953925	+	1.65225i	0.736808	+	0.676102i	$0.236332\pi$
$397$	2.99565e6	+	5.18861e6i	0.953925	+	1.65225i	0.217117	+	0.976146i	$0.430335\pi$
$398$	−271290.	+	1.53856e6i	−0.0858472	+	0.486864i
$399$	93498.4	+	53981.3i	0.0294017	+	0.0169751i
$400$	1.90425e6	+	693089.i	0.595077	+	0.216590i
$401$			5.00402e6i			1.55403i	0.629484	+	0.777013i	$0.283266\pi$
$401$			5.00402e6i			1.55403i	−0.629484	+	0.777013i	$0.716734\pi$
$402$	−247226.	+	679247.i	−0.0763007	+	0.209634i
$403$	198782.	+	1.12735e6i	0.0609698	+	0.345777i
$404$	−1.01619e6	+	852688.i	−0.309758	+	0.259918i
$405$	1.65593e6	−	1.97346e6i	0.501654	−	0.597848i
$406$	−747145.			−0.224952
$407$	261219.	+	590694.i	0.0781662	+	0.176757i
$408$	561638.			0.167034
$409$	1.64226e6	−	1.95717e6i	0.485438	−	0.578522i	−0.466613	−	0.884461i	$-0.654526\pi$
$409$	1.64226e6	−	1.95717e6i	0.485438	−	0.578522i	0.952051	+	0.305939i	$0.0989705\pi$
$410$	4.99710e6	−	4.19307e6i	1.46811	−	1.23189i
$411$	−140830.	−	798689.i	−0.0411237	−	0.233224i
$412$	−1.03668e6	+	2.84826e6i	−0.300886	+	0.826679i
$413$			448320.i			0.129334i
$414$	−1.50576e6	−	548053.i	−0.431773	−	0.157153i
$415$	329041.	+	189972.i	0.0937841	+	0.0541463i
$416$	−20936.6	+	118737.i	−0.00593160	+	0.0336398i
$417$	−1.13609e6	−	1.96777e6i	−0.319944	−	0.554160i
$418$	29440.1	−	50991.8i	0.00824136	−	0.0142745i
$419$	−2.28965e6	−	1.92124e6i	−0.637139	−	0.534623i	0.265999	−	0.963973i	$-0.414298\pi$
$419$	−2.28965e6	−	1.92124e6i	−0.637139	−	0.534623i	−0.903138	+	0.429350i	$0.858743\pi$
$420$	−941848.	+	166073.i	−0.260530	+	0.0459385i
$421$	−5.62080e6	+	3.24517e6i	−1.54558	+	0.892343i	−0.547113	+	0.837059i	$0.684273\pi$
$421$	−5.62080e6	+	3.24517e6i	−1.54558	+	0.892343i	−0.998471	+	0.0552848i	$0.982393\pi$
$422$	−871344.	−	2.39400e6i	−0.238182	−	0.654399i
$423$	−2.19636e6	+	799410.i	−0.596833	+	0.217229i
$424$	1.35483e6	+	238893.i	0.365990	+	0.0645340i
$425$	6.25707e6	+	7.45689e6i	1.68035	+	2.00256i
$426$	1.23668e6	+	1.47382e6i	0.330168	+	0.393479i
$427$	−504028.	−	88873.7i	−0.133778	−	0.0235887i
$428$	2.01918e6	−	734923.i	0.532803	−	0.193924i
$429$	−22289.5	−	61240.0i	−0.00584734	−	0.0160654i
$430$	4.09898e6	−	2.36655e6i	1.06907	−	0.617226i
$431$	−2.11819e6	+	373495.i	−0.549253	+	0.0968482i	−0.441386	−	0.897317i	$-0.645513\pi$
$431$	−2.11819e6	+	373495.i	−0.549253	+	0.0968482i	−0.107867	+	0.994165i	$0.534402\pi$
$432$	608874.	+	510906.i	0.156970	+	0.131714i
$433$	1.68478e6	−	2.91812e6i	0.431840	−	0.747968i	−0.565192	−	0.824959i	$-0.691198\pi$
$433$	1.68478e6	−	2.91812e6i	0.431840	−	0.747968i	0.997032	+	0.0769910i	$0.0245313\pi$
$434$	1.55003e6	+	2.68473e6i	0.395017	+	0.684189i
$435$	305104.	−	1.73033e6i	0.0773082	−	0.438436i
$436$	1.02350e6	+	590920.i	0.257853	+	0.148872i
$437$	−371958.	−	135382.i	−0.0931730	−	0.0339122i
$438$		−	1.21989e6i		−	0.303833i
$439$	558683.	−	1.53497e6i	0.138358	−	0.380136i	−0.851091	−	0.525019i	$-0.824058\pi$
$439$	558683.	−	1.53497e6i	0.138358	−	0.380136i	0.989449	+	0.144883i	$0.0462806\pi$
$440$	90572.3	+	513661.i	0.0223030	+	0.126487i
$441$	1.53796e6	−	1.29050e6i	0.376573	−	0.315982i
$442$	−372279.	+	443665.i	−0.0906386	+	0.108019i
$443$	723445.			0.175144			0.0875721	−	0.996158i	$-0.472089\pi$
$443$	723445.			0.175144			0.0875721	+	0.996158i	$0.472089\pi$
$444$	−923143.	+	227706.i	−0.222235	+	0.0548171i
$445$	9.69139e6			2.31999
$446$	378366.	−	450919.i	0.0900688	−	0.107340i
$447$	2.12896e6	−	1.78641e6i	0.503964	−	0.422876i
$448$	56698.1	+	321551.i	0.0133467	+	0.0756928i
$449$	−694348.	+	1.90771e6i	−0.162540	+	0.446576i	−0.994049	−	0.108936i	$-0.965256\pi$
$449$	−694348.	+	1.90771e6i	−0.162540	+	0.446576i	0.831508	+	0.555512i	$0.187478\pi$
$450$			6.08171e6i			1.41578i
$451$	1.13118e6	+	411717.i	0.261874	+	0.0953142i
$452$	1.08980e6	+	629194.i	0.250899	+	0.144857i
$453$	661282.	−	3.75032e6i	0.151405	−	0.858662i
$454$	−227493.	−	394029.i	−0.0517997	−	0.0897198i
$455$	493111.	−	854093.i	0.111665	−	0.193409i
$456$	66400.2	+	55716.4i	0.0149540	+	0.0125479i
$457$	−938622.	+	165504.i	−0.210233	+	0.0370697i	−0.277773	−	0.960647i	$-0.589596\pi$
$457$	−938622.	+	165504.i	−0.210233	+	0.0370697i	0.0675398	+	0.997717i	$0.478485\pi$
$458$	−4.63356e6	+	2.67519e6i	−1.03217	+	0.595923i
$459$	1.30584e6	+	3.58778e6i	0.289307	+	0.794865i
$460$	3.29495e6	−	1.19927e6i	0.726030	−	0.264253i
$461$	−1.07499e6	−	189550.i	−0.235588	−	0.0415406i	0.0546074	−	0.998508i	$-0.482609\pi$
$461$	−1.07499e6	−	189550.i	−0.235588	−	0.0415406i	−0.290196	+	0.956967i	$0.593720\pi$
$462$	−113444.	−	135197.i	−0.0247272	−	0.0294687i
$463$	−5.09970e6	−	6.07758e6i	−1.10558	−	1.31758i	−0.943710	−	0.330773i	$-0.892690\pi$
$463$	−5.09970e6	−	6.07758e6i	−1.10558	−	1.31758i	−0.161874	−	0.986811i	$-0.551754\pi$
$464$	−590743.	−	104164.i	−0.127381	−	0.0224606i
$465$	−6.85061e6	+	2.49342e6i	−1.46925	+	0.534764i
$466$	322547.	+	886190.i	0.0688062	+	0.189044i
$467$	−1.40935e6	+	813691.i	−0.299039	+	0.172650i	−0.642011	−	0.766695i	$-0.721900\pi$
$467$	−1.40935e6	+	813691.i	−0.299039	+	0.172650i	0.342972	+	0.939346i	$0.388566\pi$
$468$	−356348.	+	62833.9i	−0.0752074	+	0.0132611i
$469$	−1.54634e6	−	1.29753e6i	−0.324617	−	0.272386i
$470$	2.55729e6	−	4.42936e6i	0.533993	−	0.924904i
$471$	−624752.	−	1.08210e6i	−0.129764	−	0.224758i
$472$	−62502.9	+	354472.i	−0.0129135	+	0.0732363i
$473$	756413.	+	436715.i	0.155456	+	0.0897523i
$474$	684877.	+	249275.i	0.140013	+	0.0509604i
$475$			1.50232e6i			0.305512i
$476$	−536434.	+	1.47384e6i	−0.108517	+	0.298149i
$477$	716954.	+	4.06605e6i	0.144276	+	0.818233i
$478$	3.50427e6	−	2.94043e6i	0.701500	−	0.588629i
$479$	−4.27906e6	+	5.09958e6i	−0.852137	+	1.01554i	0.147512	+	0.989060i	$0.452873\pi$
$479$	−4.27906e6	+	5.09958e6i	−0.852137	+	1.01554i	−0.999649	+	0.0264773i	$0.991571\pi$
$480$	−767841.			−0.152114
$481$	432026.	−	880169.i	0.0851426	−	0.173462i
$482$	−3.04800e6			−0.597582
$483$	−762638.	+	908876.i	−0.148748	+	0.177271i
$484$	1.90022e6	−	1.59448e6i	0.368715	−	0.309389i
$485$	160457.	+	909998.i	0.0309746	+	0.175665i
$486$	−1.27153e6	+	3.49351e6i	−0.244195	+	0.670920i
$487$		−	5.55086e6i		−	1.06057i	−0.847820	−	0.530283i	$-0.822085\pi$
$487$		−	5.55086e6i		−	1.06057i	0.847820	−	0.530283i	$-0.177915\pi$
$488$	−386127.	−	140539.i	−0.0733975	−	0.0267145i
$489$	1.66298e6	+	960122.i	0.314496	+	0.181574i
$490$	−762877.	+	4.32649e6i	−0.143537	+	0.814040i
$491$	2.25368e6	+	3.90349e6i	0.421880	+	0.730717i	0.996123	−	0.0879672i	$-0.0280371\pi$
$491$	2.25368e6	+	3.90349e6i	0.421880	+	0.730717i	−0.574243	+	0.818685i	$0.694704\pi$
$492$	−886060.	+	1.53470e6i	−0.165025	+	0.285832i
$493$	−2.20733e6	−	1.85217e6i	−0.409025	−	0.343213i
$494$	−88026.2	+	15521.4i	−0.0162291	+	0.00286163i
$495$	−1.35564e6	+	782679.i	−0.248675	+	0.143572i
$496$	851262.	+	2.33882e6i	0.155367	+	0.426868i
$497$	−5.04876e6	+	1.83760e6i	−0.916841	+	0.333703i
$498$	−101648.	−	17923.3i	−0.0183665	−	0.00323851i
$499$	4.40767e6	+	5.25286e6i	0.792425	+	0.944375i	0.999423	−	0.0339664i	$-0.0108139\pi$
$499$	4.40767e6	+	5.25286e6i	0.792425	+	0.944375i	−0.206998	+	0.978341i	$0.566369\pi$
$500$	−5.17727e6	−	6.17003e6i	−0.926138	−	1.10373i
$501$	2.16353e6	+	381488.i	0.385095	+	0.0679026i
$502$	−1.80571e6	+	657224.i	−0.319807	+	0.116400i
$503$	−2.56640e6	−	7.05111e6i	−0.452276	−	1.24262i	−0.931118	−	0.364717i	$-0.881166\pi$
$503$	−2.56640e6	−	7.05111e6i	−0.452276	−	1.24262i	0.478842	−	0.877901i	$-0.341057\pi$
$504$	−848627.	+	489955.i	−0.148813	+	0.0859172i
$505$	8.57937e6	−	1.51277e6i	1.49702	−	0.263965i
$506$	495679.	+	415924.i	0.0860645	+	0.0722167i
$507$	1.27535e6	−	2.20898e6i	0.220349	−	0.381655i
$508$	−2.42496e6	−	4.20015e6i	−0.416912	−	0.722113i
$509$	−655618.	+	3.71820e6i	−0.112165	+	0.636118i	0.875950	+	0.482402i	$0.160235\pi$
$509$	−655618.	+	3.71820e6i	−0.112165	+	0.636118i	−0.988115	+	0.153717i	$0.950876\pi$
$510$	−3.19425e6	−	1.84420e6i	−0.543805	−	0.313966i
$511$	3.20121e6	+	1.16515e6i	0.542328	+	0.197391i
$512$			262144.i			0.0441942i
$513$	−201535.	+	553713.i	−0.0338109	+	0.0928947i
$514$	96629.9	+	548015.i	0.0161326	+	0.0914924i
$515$	1.52486e7	−	1.27951e7i	2.53344	−	2.12581i
$516$	−826498.	+	984983.i	−0.136653	+	0.162856i
$517$	943830.			0.155298
$518$	284175.	−	2.63998e6i	0.0465331	−	0.432291i
$519$	−2.24141e6			−0.365261
$520$	508960.	−	606555.i	0.0825421	−	0.0983698i
$521$	−1.23143e6	+	1.03329e6i	−0.198753	+	0.166774i	−0.736732	−	0.676184i	$-0.763632\pi$
$521$	−1.23143e6	+	1.03329e6i	−0.198753	+	0.166774i	0.537979	+	0.842958i	$0.319188\pi$
$522$	−312612.	−	1.77291e6i	−0.0502145	−	0.284781i
$523$	2.28943e6	−	6.29016e6i	0.365994	−	1.00556i	−0.610877	−	0.791726i	$-0.709183\pi$
$523$	2.28943e6	−	6.29016e6i	0.365994	−	1.00556i	0.976870	−	0.213833i	$-0.0685949\pi$
$524$		−	2.58819e6i		−	0.411783i
$525$	4.23147e6	+	1.54013e6i	0.670028	+	0.243870i
$526$	−2.01754e6	−	1.16483e6i	−0.317950	−	0.183569i
$527$	−2.07610e6	+	1.17742e7i	−0.325628	+	1.84673i
$528$	−70847.5	−	122711.i	−0.0110596	−	0.0191558i
$529$	−1.04319e6	+	1.80686e6i	−0.162079	+	0.280728i
$530$	−6.92099e6	−	5.80740e6i	−1.07023	−	0.898032i
$531$	−1.06382e6	+	187581.i	−0.163732	+	0.0288704i
$532$	−209630.	+	121030.i	−0.0321126	+	0.0185402i
$533$	−625014.	−	1.71721e6i	−0.0952954	−	0.261822i
$534$	−2.47401e6	+	900465.i	−0.375446	+	0.136651i
$535$	−1.38970e7	−	2.45042e6i	−2.09912	−	0.370132i
$536$	−1.04174e6	−	1.24150e6i	−0.156620	−	0.186652i
$537$	−1.87895e6	−	2.23924e6i	−0.281177	−	0.335093i
$538$	1.64048e6	+	289261.i	0.244352	+	0.0430859i
$539$	−761822.	+	277280.i	−0.112949	+	0.0411100i
$540$	−1.78528e6	−	4.90501e6i	−0.263464	−	0.723862i
$541$	−5.33632e6	+	3.08093e6i	−0.783879	+	0.452573i	−0.837803	−	0.545972i	$-0.816160\pi$
$541$	−5.33632e6	+	3.08093e6i	−0.783879	+	0.452573i	0.0539242	+	0.998545i	$0.482827\pi$
$542$	−1.11888e6	+	197289.i	−0.163601	+	0.0288473i
$543$	957885.	+	803761.i	0.139416	+	0.116984i
$544$	−629617.	+	1.09053e6i	−0.0912177	+	0.157994i
$545$	−3.88070e6	−	6.72157e6i	−0.559653	−	0.969347i
$546$	−46523.6	+	263849.i	−0.00667870	+	0.0378768i
$547$	9.18093e6	+	5.30061e6i	1.31195	+	0.757457i	0.982419	−	0.186687i	$-0.0597750\pi$
$547$	9.18093e6	+	5.30061e6i	1.31195	+	0.757457i	0.329534	+	0.944144i	$0.393108\pi$
$548$	1.70868e6	+	621910.i	0.243058	+	0.0884660i
$549$		−	1.23320e6i		−	0.174623i
$550$	839950.	−	2.30774e6i	0.118399	−	0.325297i
$551$	−77222.3	−	437949.i	−0.0108359	−	0.0614533i
$552$	−729704.	+	612294.i	−0.101929	+	0.0855288i
$553$	−1.30828e6	+	1.55915e6i	−0.181924	+	0.216808i
$554$	−1.69158e6			−0.234162
$555$	5.99796e6	+	1.73619e6i	0.826553	+	0.239257i
$556$	5.09441e6			0.698887
$557$	−1.68666e6	+	2.01008e6i	−0.230351	+	0.274521i	−0.868822	−	0.495124i	$-0.835123\pi$
$557$	−1.68666e6	+	2.01008e6i	−0.230351	+	0.274521i	0.638471	+	0.769645i	$0.279567\pi$
$558$	−5.72208e6	+	4.80140e6i	−0.777980	+	0.652803i
$559$	−230245.	−	1.30578e6i	−0.0311645	−	0.176743i
$560$	733383.	−	2.01495e6i	0.0988236	−	0.271516i
$561$		−	680645.i		−	0.0913090i
$562$	6.58163e6	+	2.39552e6i	0.879008	+	0.319933i
$563$	−3.50429e6	−	2.02320e6i	−0.465938	−	0.269010i	0.248600	−	0.968606i	$-0.420030\pi$
$563$	−3.50429e6	−	2.02320e6i	−0.465938	−	0.269010i	−0.714538	+	0.699597i	$0.753363\pi$
$564$	−241274.	+	1.36833e6i	−0.0319383	+	0.181131i
$565$	−4.13205e6	−	7.15693e6i	−0.544559	−	0.943204i
$566$	−4.44528e6	+	7.69946e6i	−0.583255	+	1.01023i
$567$	−1.49715e6	−	1.25626e6i	−0.195573	−	0.164105i
$568$	−4.24808e6	+	749051.i	−0.552486	+	0.0974183i
$569$	5.82280e6	−	3.36179e6i	0.753964	−	0.435302i	−0.0731601	−	0.997320i	$-0.523308\pi$
$569$	5.82280e6	−	3.36179e6i	0.753964	−	0.435302i	0.827125	+	0.562019i	$0.189975\pi$
$570$	−194692.	−	534912.i	−0.0250993	−	0.0689597i
$571$	9.78009e6	−	3.55966e6i	1.25531	−	0.456897i	0.373120	−	0.927783i	$-0.378288\pi$
$571$	9.78009e6	−	3.55966e6i	1.25531	−	0.456897i	0.882194	+	0.470886i	$0.156066\pi$
$572$	143897.	+	25372.9i	0.0183891	+	0.00324250i
$573$	−1.89546e6	−	2.25892e6i	−0.241173	−	0.287418i
$574$	−3.18104e6	−	3.79101e6i	−0.402985	−	0.480259i
$575$	−1.62589e7	−	2.86688e6i	−2.05079	−	0.361610i
$576$	−739289.	+	269079.i	−0.0928449	+	0.0337928i
$577$	1.59186e6	+	4.37359e6i	0.199051	+	0.546889i	0.998553	−	0.0537750i	$-0.0171254\pi$
$577$	1.59186e6	+	4.37359e6i	0.199051	+	0.546889i	−0.799502	+	0.600664i	$0.794903\pi$
$578$	−319926.	+	184710.i	−0.0398318	+	0.0229969i
$579$	6.43369e6	−	1.13443e6i	0.797560	−	0.140631i
$580$	3.01774e6	+	2.53219e6i	0.372488	+	0.312554i
$581$	144120.	−	249624.i	0.0177127	−	0.0306793i
$582$	−125513.	−	217395.i	−0.0153596	−	0.0266037i
$583$	289513.	−	1.64191e6i	0.0352774	−	0.200068i
$584$	2.36865e6	+	1.36754e6i	0.287388	+	0.165924i
$585$	2.23301e6	+	812749.i	0.269774	+	0.0981899i
$586$			5.34313e6i			0.642764i
$587$	−2.01582e6	+	5.53842e6i	−0.241466	+	0.663423i	0.758465	+	0.651713i	$0.225949\pi$
$587$	−2.01582e6	+	5.53842e6i	−0.241466	+	0.663423i	−0.999931	+	0.0117093i	$0.996273\pi$
$588$	−207245.	−	1.17534e6i	−0.0247195	−	0.140191i
$589$	−1.41349e6	+	1.18605e6i	−0.167882	+	0.140869i
$590$	1.51942e6	−	1.81078e6i	0.179700	−	0.214158i
$591$	−4.28123e6			−0.504196
$592$	592743.	−	2.04773e6i	0.0695124	−	0.240142i
$593$	18706.5			0.00218452			0.00109226	−	0.999999i	$-0.499652\pi$
$593$	18706.5			0.00218452			0.00109226	+	0.999999i	$0.499652\pi$
$594$	619163.	−	737890.i	0.0720010	−	0.0858075i
$595$	7.89041e6	−	6.62084e6i	0.913707	−	0.766692i
$596$	1.08202e6	+	6.13643e6i	0.124773	+	0.707620i
$597$	−953291.	+	2.61915e6i	−0.109469	+	0.300763i
$598$		−	982285.i		−	0.112327i
$599$	1.08527e7	+	3.95007e6i	1.23587	+	0.449819i	0.875603	−	0.483031i	$-0.160464\pi$
$599$	1.08527e7	+	3.95007e6i	1.23587	+	0.449819i	0.360264	+	0.932850i	$0.382686\pi$
$600$	3.13096e6	+	1.80766e6i	0.355059	+	0.204993i
$601$	2.31972e6	−	1.31558e7i	0.261969	−	1.48570i	−0.515559	−	0.856854i	$-0.672416\pi$
$601$	2.31972e6	−	1.31558e7i	0.261969	−	1.48570i	0.777529	−	0.628847i	$-0.216473\pi$
$602$	−1.79536e6	−	3.10966e6i	−0.201912	−	0.349721i
$603$	2.43192e6	−	4.21222e6i	0.272368	−	0.471756i
$604$	6.54064e6	+	5.48825e6i	0.729504	+	0.612127i
$605$	−1.60429e7	+	2.82880e6i	−1.78195	+	0.314205i
$606$	−2.04957e6	+	1.18332e6i	−0.226716	+	0.130894i
$607$	−3.59041e6	−	9.86457e6i	−0.395523	−	1.08669i	−0.964441	−	0.264297i	$-0.914860\pi$
$607$	−3.59041e6	−	9.86457e6i	−0.395523	−	1.08669i	0.568918	−	0.822394i	$-0.307362\pi$
$608$	−182621.	+	66468.7i	−0.0200351	+	0.00729219i
$609$	−1.31270e6	−	231465.i	−0.143425	−	0.0252896i
$610$	1.73458e6	+	2.06719e6i	0.188742	+	0.224934i
$611$	−920984.	−	1.09759e6i	−0.0998042	−	0.118942i
$612$	−3.72174e6	−	656243.i	−0.401668	−	0.0708250i
$613$	1.32698e7	−	4.82983e6i	1.42631	−	0.519135i	0.490440	−	0.871475i	$-0.336836\pi$
$613$	1.32698e7	−	4.82983e6i	1.42631	−	0.519135i	0.935872	+	0.352340i	$0.114614\pi$
$614$	2.96774e6	+	8.15381e6i	0.317691	+	0.872850i
$615$	1.00787e7	−	5.81895e6i	1.07453	−	0.620378i
$616$	389685.	−	68712.0i	0.0413773	−	0.00729593i
$617$	1.35556e7	+	1.13745e7i	1.43353	+	1.20287i	0.943589	+	0.331120i	$0.107426\pi$
$617$	1.35556e7	+	1.13745e7i	1.43353	+	1.20287i	0.489942	+	0.871755i	$0.337018\pi$
$618$	−2.70380e6	+	4.68311e6i	−0.284776	+	0.493246i
$619$	−2.88870e6	−	5.00337e6i	−0.303023	−	0.524851i	0.673796	−	0.738917i	$-0.264663\pi$
$619$	−2.88870e6	−	5.00337e6i	−0.303023	−	0.524851i	−0.976819	+	0.214066i	$0.931329\pi$
$620$	2.83833e6	−	1.60970e7i	0.296540	−	1.68176i
$621$	−5.60798e6	−	3.23777e6i	−0.583549	−	0.336912i
$622$	−1.08096e7	−	3.93437e6i	−1.12030	−	0.407754i
$623$		−	7.35229e6i		−	0.758932i
$624$	−73569.4	+	202130.i	−0.00756372	+	0.0207812i
$625$	4.88958e6	+	2.77302e7i	0.500693	+	2.83957i
$626$	1.67974e6	−	1.40947e6i	0.171319	−	0.143754i
$627$	67522.3	−	80470.0i	0.00685928	−	0.00817457i
$628$	2.80148e6			0.283458
$629$	7.38405e6	−	7.09496e6i	0.744163	−	0.715029i
$630$	6.43528e6			0.645976
$631$	−8.10889e6	+	9.66380e6i	−0.810752	+	0.966216i	−0.999876	−	0.0157368i	$-0.994991\pi$
$631$	−8.10889e6	+	9.66380e6i	−0.810752	+	0.966216i	0.189124	+	0.981953i	$0.439435\pi$
$632$	−1.25179e6	+	1.05037e6i	−0.124663	+	0.104605i
$633$	−789257.	−	4.47610e6i	−0.0782905	−	0.444007i
$634$	3.28847e6	−	9.03501e6i	0.324916	−	0.892700i
$635$			3.18504e7i			3.13459i
$636$	2.30637e6	+	839450.i	0.226093	+	0.0822909i
$637$	1.06583e6	+	615359.i	0.104074	+	0.0600869i
$638$	−126235.	+	715917.i	−0.0122781	+	0.0696323i
$639$	−6.47291e6	−	1.12114e7i	−0.627115	−	1.08620i
$640$	860778.	−	1.49091e6i	0.0830694	−	0.143880i
$641$	2.19543e6	+	1.84219e6i	0.211045	+	0.177088i	0.742182	−	0.670198i	$-0.233791\pi$
$641$	2.19543e6	+	1.84219e6i	0.211045	+	0.177088i	−0.531137	+	0.847286i	$0.678235\pi$
$642$	3.77530e6	−	665687.i	0.361505	−	0.0637430i
$643$	−7.05991e6	+	4.07604e6i	−0.673398	+	0.388787i	−0.797363	−	0.603500i	$-0.793772\pi$
$643$	−7.05991e6	+	4.07604e6i	−0.673398	+	0.388787i	0.123965	+	0.992287i	$0.460439\pi$
$644$	−909813.	−	2.49969e6i	−0.0864445	−	0.237504i
$645$	7.93490e6	−	2.88807e6i	0.751004	−	0.273343i
$646$	−919355.	−	162107.i	−0.0866766	−	0.0152834i
$647$	8.20897e6	+	9.78306e6i	0.770953	+	0.918786i	0.998487	−	0.0549844i	$-0.0175109\pi$
$647$	8.20897e6	+	9.78306e6i	0.770953	+	0.918786i	−0.227535	+	0.973770i	$0.573066\pi$
$648$	−1.00860e6	−	1.20201e6i	−0.0943590	−	0.112453i
$649$	429582.	+	75746.9i	0.0400345	+	0.00705916i
$650$	−3.50331e6	+	1.27510e6i	−0.325233	+	0.118375i
$651$	1.89161e6	+	5.19716e6i	0.174936	+	0.480633i
$652$	−3.72852e6	+	2.15266e6i	−0.343493	+	0.198316i
$653$	−6.34990e6	+	1.11966e6i	−0.582753	+	0.102755i	−0.457250	−	0.889338i	$-0.651165\pi$
$653$	−6.34990e6	+	1.11966e6i	−0.582753	+	0.102755i	−0.125503	+	0.992093i	$0.540054\pi$
$654$	1.61519e6	+	1.35530e6i	0.147665	+	0.123906i
$655$	−8.49861e6	+	1.47200e7i	−0.774007	+	1.34062i
$656$	−1.98661e6	−	3.44091e6i	−0.180241	−	0.312186i
$657$	−1.42537e6	+	8.08370e6i	−0.128830	+	0.730629i
$658$	−3.36030e6	−	1.94007e6i	−0.302561	−	0.174684i
$659$	−1.48871e6	−	541846.i	−0.133535	−	0.0486029i	0.274388	−	0.961619i	$-0.411525\pi$
$659$	−1.48871e6	−	541846.i	−0.133535	−	0.0486029i	−0.407923	+	0.913016i	$0.633747\pi$
$660$			930541.i			0.0831526i
$661$	−6.88862e6	+	1.89263e7i	−0.613237	+	1.68486i	0.109720	+	0.993963i	$0.465004\pi$
$661$	−6.88862e6	+	1.89263e7i	−0.613237	+	1.68486i	−0.722957	+	0.690893i	$0.757218\pi$
$662$	2.38317e6	+	1.35156e7i	0.211354	+	1.19865i
$663$	−791527.	+	664170.i	−0.0699329	+	0.0586807i
$664$	148753.	−	177277.i	0.0130932	−	0.0156038i
$665$	1.58966e6			0.139396
$666$	6.38334e6	−	430267.i	0.557651	−	0.0375883i
$667$	4.88708e6			0.425339
$668$	−3.16612e6	+	3.77324e6i	−0.274528	+	0.327170i
$669$	804467.	−	675028.i	0.0694933	−	0.0583118i
$670$	1.84818e6	+	1.04815e7i	0.159058	+	0.902064i
$671$	−170318.	+	467945.i	−0.0146034	+	0.0401225i
$672$			582517.i			0.0497605i
$673$	−1.87115e6	−	681044.i	−0.159247	−	0.0579612i	0.261167	−	0.965294i	$-0.415893\pi$
$673$	−1.87115e6	−	681044.i	−0.159247	−	0.0579612i	−0.420414	+	0.907333i	$0.638115\pi$
$674$	−1.39564e7	−	8.05772e6i	−1.18338	−	0.683223i
$675$	−4.26777e6	+	2.42037e7i	−0.360530	+	2.04467i
$676$	2.85944e6	+	4.95269e6i	0.240665	+	0.416845i
$677$	5.89957e6	−	1.02184e7i	0.494708	−	0.856859i	−0.505273	−	0.862959i	$-0.668608\pi$
$677$	5.89957e6	−	1.02184e7i	0.494708	−	0.856859i	0.999981	+	0.00610001i	$0.00194171\pi$
$678$	1.71980e6	+	1.44309e6i	0.143683	+	0.120564i
$679$	690363.	−	121730.i	0.0574650	−	0.0101326i
$680$	7.16173e6	−	4.13483e6i	0.593944	−	0.342914i
$681$	−277625.	−	762769.i	−0.0229399	−	0.0630268i
$682$	2.83440e6	−	1.03164e6i	0.233346	−	0.0849311i
$683$	1.37298e7	+	2.42093e6i	1.12619	+	0.198578i	0.705557	−	0.708654i	$-0.250697\pi$
$683$	1.37298e7	+	2.42093e6i	1.12619	+	0.198578i	0.420633	+	0.907231i	$0.361808\pi$
$684$	−374905.	−	446794.i	−0.0306395	−	0.0365147i
$685$	−7.67582e6	−	9.14769e6i	−0.625027	−	0.744878i
$686$	8.55990e6	+	1.50934e6i	0.694478	+	0.122455i
$687$	−8.96975e6	+	3.26472e6i	−0.725084	+	0.263909i
$688$	−985998.	−	2.70901e6i	−0.0794154	−	0.218192i
$689$	−2.19189e6	+	1.26549e6i	−0.175902	+	0.101557i
$690$	6.16063e6	−	1.08629e6i	0.492609	−	0.0868603i
$691$	1.30882e7	+	1.09823e7i	1.04276	+	0.874983i	0.992314	−	0.123744i	$-0.0394900\pi$
$691$	1.30882e7	+	1.09823e7i	1.04276	+	0.874983i	0.0504500	+	0.998727i	$0.483934\pi$
$692$	2.51270e6	−	4.35213e6i	0.199469	−	0.345491i
$693$	593773.	+	1.02845e6i	0.0469664	+	0.0813483i
$694$	642598.	−	3.64436e6i	0.0506455	−	0.287225i
$695$	−2.89738e7	−	1.67281e7i	−2.27533	−	1.31366i
$696$	−1.00564e6	−	366023.i	−0.0786901	−	0.0286408i
$697$		−	1.90858e7i		−	1.48808i
$698$	1.69315e6	−	4.65189e6i	0.131540	−	0.361402i
$699$	292160.	+	1.65692e6i	0.0226167	+	0.128265i
$700$	−7.73409e6	+	6.48967e6i	−0.596574	+	0.500585i
$701$	−1.09623e7	+	1.30644e7i	−0.842572	+	1.00414i	0.157291	+	0.987552i	$0.449724\pi$
$701$	−1.09623e7	+	1.30644e7i	−0.842572	+	1.00414i	−0.999862	+	0.0165853i	$0.994720\pi$
$702$	−1.46227e6			−0.111992
$703$	1.57683e6	−	106286.i	0.120336	−	0.00811124i
$704$	317690.			0.0241586
$705$	5.86527e6	−	6.98996e6i	0.444442	−	0.529666i
$706$	580067.	−	486734.i	0.0437992	−	0.0367519i
$707$	−1.14765e6	−	6.50867e6i	−0.0863500	−	0.489715i
$708$	−219630.	+	603429.i	−0.0164668	+	0.0452421i
$709$		−	1.48896e7i		−	1.11242i	−0.831043	−	0.556208i	$-0.812256\pi$
$709$		−	1.48896e7i		−	1.11242i	0.831043	−	0.556208i	$-0.187744\pi$
$710$	2.66200e7	+	9.68889e6i	1.98181	+	0.721320i
$711$	−4.24713e6	−	2.45208e6i	−0.315081	−	0.181912i
$712$	1.02503e6	−	5.81321e6i	0.0757766	−	0.429750i
$713$	−1.01387e7	−	1.75608e7i	−0.746896	−	1.29366i
$714$	−1.39909e6	+	2.42329e6i	−0.102707	+	0.177893i
$715$	−735080.	−	616805.i	−0.0537736	−	0.0451214i
$716$	6.45429e6	−	1.13807e6i	0.470507	−	0.0829631i
$717$	7.06781e6	−	4.08060e6i	0.513436	−	0.296433i
$718$	−2.68255e6	−	7.37024e6i	−0.194194	−	0.533545i
$719$	1.20102e7	−	4.37137e6i	0.866421	−	0.315352i	0.129704	−	0.991553i	$-0.458597\pi$
$719$	1.20102e7	−	4.37137e6i	0.866421	−	0.315352i	0.736717	+	0.676201i	$0.236375\pi$
$720$	5.08816e6	+	897180.i	0.365788	+	0.0644983i
$721$	−9.70688e6	−	1.15682e7i	−0.695411	−	0.828758i
$722$	6.27381e6	+	7.47684e6i	0.447908	+	0.533796i
$723$	−5.35521e6	−	944268.i	−0.381005	−	0.0671815i
$724$	−2.63448e6	+	958873.i	−0.186788	+	0.0679852i
$725$	−6.34390e6	−	1.74297e7i	−0.448240	−	1.23153i
$726$	3.83258e6	−	2.21274e6i	0.269867	−	0.155808i
$727$	1.40815e7	−	2.48295e6i	0.988128	−	0.174234i	0.343849	−	0.939025i	$-0.388269\pi$
$727$	1.40815e7	−	2.48295e6i	0.988128	−	0.174234i	0.644278	+	0.764791i	$0.277158\pi$
$728$	−460158.	−	386119.i	−0.0321795	−	0.0270018i
$729$	−337458.	+	584495.i	−0.0235180	+	0.0407344i
$730$	−8.98094e6	−	1.55554e7i	−0.623756	−	1.08038i
$731$	2.40470e6	−	1.36377e7i	0.166444	−	0.943949i
$732$	−634871.	−	366543.i	−0.0437933	−	0.0252841i
$733$	−1.18150e7	−	4.30030e6i	−0.812218	−	0.295623i	−0.0976782	−	0.995218i	$-0.531142\pi$
$733$	−1.18150e7	−	4.30030e6i	−0.812218	−	0.295623i	−0.714540	+	0.699595i	$0.753364\pi$
$734$		−	4.65572e6i		−	0.318968i
$735$	−2.68069e6	+	7.36513e6i	−0.183032	+	0.502877i
$736$	−370862.	−	2.10326e6i	−0.0252359	−	0.143120i
$737$	−1.50456e6	+	1.26248e6i	−0.102033	+	0.0856160i
$738$	7.66477e6	−	9.13451e6i	0.518034	−	0.617368i
$739$	1.07715e7			0.725543			0.362772	−	0.931878i	$-0.381831\pi$
$739$	1.07715e7			0.725543			0.362772	+	0.931878i	$0.381831\pi$
$740$	−1.00951e7	+	9.69985e6i	−0.677689	+	0.651157i
$741$	−159467.			−0.0106690
$742$	−4.40574e6	+	5.25055e6i	−0.293771	+	0.350103i
$743$	−7.91001e6	+	6.63729e6i	−0.525660	+	0.441081i	−0.866600	−	0.499004i	$-0.833699\pi$
$743$	−7.91001e6	+	6.63729e6i	−0.525660	+	0.441081i	0.340940	+	0.940085i	$0.389255\pi$
$744$	771067.	+	4.37294e6i	0.0510693	+	0.289628i
$745$	1.39958e7	−	3.84531e7i	0.923861	−	2.53829i
$746$			1.85091e7i			1.21769i
$747$	652637.	+	237541.i	0.0427928	+	0.0155753i
$748$	1.32160e6	+	763028.i	0.0863669	+	0.0498639i
$749$	−1.85900e6	+	1.05429e7i	−0.121080	+	0.686681i
$750$	−7.18478e6	−	1.24444e7i	−0.466402	−	0.807832i
$751$	−7.85340e6	+	1.36025e7i	−0.508110	+	0.880073i	0.491846	+	0.870682i	$0.336322\pi$
$751$	−7.85340e6	+	1.36025e7i	−0.508110	+	0.880073i	−0.999956	+	0.00939026i	$0.997011\pi$
$752$	−2.38640e6	−	2.00243e6i	−0.153886	−	0.129126i
$753$	−3.37617e6	+	595309.i	−0.216988	+	0.0382609i
$754$	955725.	−	551788.i	0.0612216	−	0.0353463i
$755$	−1.91778e7	−	5.26906e7i	−1.22442	−	3.36408i
$756$	−3.72115e6	+	1.35439e6i	−0.236795	+	0.0861864i
$757$	7.10629e6	+	1.25303e6i	0.450716	+	0.0794734i	0.394399	−	0.918939i	$-0.370953\pi$
$757$	7.10629e6	+	1.25303e6i	0.450716	+	0.0794734i	0.0563177	+	0.998413i	$0.482064\pi$
$758$	2.22688e6	+	2.65390e6i	0.140775	+	0.167769i
$759$	742035.	+	884323.i	0.0467541	+	0.0557194i
$760$	1.25689e6	+	221624.i	0.0789340	+	0.0139182i
$761$	−1.76257e7	+	6.41521e6i	−1.10327	+	0.401559i	−0.828522	−	0.559956i	$-0.810818\pi$
$761$	−1.76257e7	+	6.41521e6i	−1.10327	+	0.401559i	−0.274752	+	0.961515i	$0.588596\pi$
$762$	−2.95935e6	−	8.13074e6i	−0.184633	−	0.507274i
$763$	−5.09926e6	+	2.94406e6i	−0.317100	+	0.183078i
$764$	6.51101e6	−	1.14807e6i	0.403566	−	0.0711596i
$765$	1.90121e7	+	1.59530e7i	1.17456	+	0.985575i
$766$	−8.78969e6	+	1.52242e7i	−0.541255	+	0.937480i
$767$	−331097.	−	573477.i	−0.0203220	−	0.0351988i
$768$	−81212.0	+	460576.i	−0.00496841	+	0.0281772i
$769$	9.08110e6	+	5.24298e6i	0.553762	+	0.319714i	0.750638	−	0.660714i	$-0.229746\pi$
$769$	9.08110e6	+	5.24298e6i	0.553762	+	0.319714i	−0.196876	+	0.980428i	$0.563080\pi$
$770$	−2.44191e6	−	888782.i	−0.148423	−	0.0540217i
$771$			992776.i			0.0601472i
$772$	−5.00968e6	+	1.37640e7i	−0.302529	+	0.831191i
$773$	178892.	+	1.01454e6i	0.0107682	+	0.0610692i	0.989718	−	0.143030i	$-0.0456846\pi$
$773$	178892.	+	1.01454e6i	0.0107682	+	0.0610692i	−0.978950	+	0.204099i	$0.934573\pi$
$774$	6.62776e6	−	5.56135e6i	0.397662	−	0.333678i
$775$	−4.94694e7	+	5.89553e7i	−2.95857	+	3.52589i
$776$	562818.			0.0335516
$777$	1.31715e6	−	4.55030e6i	0.0782676	−	0.270388i
$778$	1.18806e7			0.703704
$779$	1.89337e6	−	2.25643e6i	0.111787	−	0.133223i
$780$	1.08213e6	−	908017.i	0.0636860	−	0.0534389i
$781$	907769.	+	5.14822e6i	0.0532535	+	0.302015i
$782$	3.50881e6	−	9.64039e6i	0.205184	−	0.563738i
$783$		−	7.27512e6i		−	0.424068i
$784$	2.51449e6	+	915198.i	0.146103	+	0.0531771i
$785$	−1.59331e7	−	9.19896e6i	−0.922837	−	0.532800i
$786$	801821.	−	4.54735e6i	0.0462936	−	0.262544i
$787$	1.28654e7	+	2.22835e7i	0.740432	+	1.28247i	0.952299	+	0.305167i	$0.0987124\pi$
$787$	1.28654e7	+	2.22835e7i	0.740432	+	1.28247i	−0.211867	+	0.977299i	$0.567954\pi$
$788$	4.79941e6	−	8.31282e6i	0.275342	−	0.476906i
$789$	−3.18388e6	−	2.67159e6i	−0.182081	−	0.152784i
$790$	1.05684e7	−	1.86349e6i	0.602479	−	0.106233i
$791$	−5.42955e6	+	3.13475e6i	−0.308548	+	0.178140i
$792$	326095.	+	895939.i	0.0184727	+	0.0507534i
$793$	710372.	−	258554.i	0.0401146	−	0.0146005i
$794$	−2.36011e7	−	4.16151e6i	−1.32856	−	0.234261i
$795$	−1.03608e7	−	1.23475e7i	−0.581399	−	0.692884i
$796$	−4.01690e6	−	4.78716e6i	−0.224703	−	0.267790i
$797$	−6.32979e6	−	1.11611e6i	−0.352974	−	0.0622389i	−0.00565026	−	0.999984i	$-0.501799\pi$
$797$	−6.32979e6	−	1.11611e6i	−0.352974	−	0.0622389i	−0.347324	+	0.937745i	$0.612910\pi$
$798$	−405807.	+	147702.i	−0.0225586	+	0.00821066i
$799$	−5.11808e6	−	1.40618e7i	−0.283622	−	0.779246i
$800$	−7.01985e6	+	4.05291e6i	−0.387796	+	0.223894i
$801$	1.74464e7	−	3.07626e6i	0.960779	−	0.169411i
$802$	−1.53332e7	−	1.28661e7i	−0.841778	−	0.706335i
$803$	1.65731e6	−	2.87055e6i	0.0907018	−	0.157100i
$804$	−1.44568e6	−	2.50399e6i	−0.0788736	−	0.136613i
$805$	−3.03356e6	+	1.72041e7i	−0.164992	+	0.935715i
$806$	−3.96550e6	−	2.28948e6i	−0.215011	−	0.124136i
$807$	2.79265e6	+	1.01644e6i	0.150950	+	0.0549412i
$808$		−	5.30619e6i		−	0.285926i
$809$	−3.52772e6	+	9.69233e6i	−0.189506	+	0.520663i	−0.997665	−	0.0683014i	$-0.978242\pi$
$809$	−3.52772e6	+	9.69233e6i	−0.189506	+	0.520663i	0.808159	+	0.588965i	$0.200464\pi$
$810$	1.78939e6	+	1.01481e7i	0.0958280	+	0.543467i
$811$	642986.	−	539530.i	0.0343281	−	0.0288047i	−0.625462	−	0.780254i	$-0.715090\pi$
$811$	642986.	−	539530.i	0.0343281	−	0.0288047i	0.659790	+	0.751450i	$0.270645\pi$
$812$	1.92102e6	−	2.28939e6i	0.102245	−	0.121851i
$813$	−2.02695e6			−0.107552
$814$	−2.48162e6	−	718341.i	−0.131273	−	0.0379988i
$815$	2.82740e7			1.49105
$816$	−1.44406e6	+	1.72096e6i	−0.0759204	+	0.0904784i
$817$	1.63721e6	−	1.37378e6i	0.0858121	−	0.0720049i
$818$	1.77462e6	+	1.00643e7i	0.0927302	+	0.525899i
$819$	616585.	−	1.69405e6i	0.0321206	−	0.0882506i
$820$			2.60930e7i			1.35516i
$821$	2.49188e7	+	9.06970e6i	1.29024	+	0.469608i	0.893805	−	0.448457i	$-0.148026\pi$
$821$	2.49188e7	+	9.06970e6i	1.29024	+	0.469608i	0.396432	+	0.918064i	$0.370248\pi$
$822$	2.80942e6	+	1.62202e6i	0.145023	+	0.0837292i
$823$	−694452.	+	3.93843e6i	−0.0357390	+	0.202686i	−0.997449	−	0.0713833i	$-0.977259\pi$
$823$	−694452.	+	3.93843e6i	−0.0357390	+	0.202686i	0.961710	+	0.274069i	$0.0883698\pi$
$824$	−6.06211e6	−	1.04999e7i	−0.311033	−	0.538724i
$825$	2.19069e6	−	3.79439e6i	0.112059	−	0.194092i
$826$	−1.37373e6	−	1.15270e6i	−0.0700571	−	0.0587849i
$827$	3.03542e7	−	5.35227e6i	1.54332	−	0.272128i	0.663769	−	0.747938i	$-0.268956\pi$
$827$	3.03542e7	−	5.35227e6i	1.54332	−	0.272128i	0.879548	+	0.475809i	$0.157845\pi$
$828$	5.55087e6	−	3.20480e6i	0.281375	−	0.162452i
$829$	−5.86726e6	−	1.61202e7i	−0.296517	−	0.814672i	−0.995075	−	0.0991199i	$-0.968397\pi$
$829$	−5.86726e6	−	1.61202e7i	−0.296517	−	0.814672i	0.698559	−	0.715552i	$-0.253825\pi$
$830$	−1.42812e6	+	519793.i	−0.0719564	+	0.0261900i
$831$	−2.97203e6	−	524049.i	−0.149297	−	0.0263250i
$832$	−310001.	−	369444.i	−0.0155258	−	0.0185029i
$833$	8.26223e6	+	9.84654e6i	0.412558	+	0.491667i
$834$	8.95068e6	+	1.57825e6i	0.445595	+	0.0785705i
$835$	3.03968e7	−	1.10635e7i	1.50873	−	0.549132i
$836$	80552.9	+	221317.i	0.00398626	+	0.0109522i
$837$	−2.61418e7	+	1.50930e7i	−1.28980	+	0.744666i
$838$	1.17741e7	−	2.07609e6i	0.579184	−	0.102126i
$839$	2.39326e7	+	2.00819e7i	1.17378	+	0.984916i	1.00000		0.000130692i	$4.16005e-5\pi$
$839$	2.39326e7	+	2.00819e7i	1.17378	+	0.984916i	0.173777	+	0.984785i	$0.444403\pi$
$840$	1.91276e6	−	3.31299e6i	0.0935322	−	0.162003i
$841$	−7.51031e6	−	1.30082e7i	−0.366158	−	0.634203i
$842$	4.50814e6	−	2.55669e7i	0.219138	−	1.24279i
$843$	1.08215e7	+	6.24781e6i	0.524469	+	0.302802i
$844$	9.57599e6	+	3.48537e6i	0.462730	+	0.168420i
$845$		−	3.75571e7i		−	1.80946i
$846$	3.19764e6	−	8.78544e6i	0.153604	−	0.422024i
$847$	2.14605e6	+	1.21708e7i	0.102785	+	0.582923i
$848$	−4.21548e6	+	3.53721e6i	−0.201306	+	0.168916i
$849$	−1.01955e7	+	1.21505e7i	−0.485443	+	0.578528i
$850$	−3.89371e7			−1.84849
$851$	−1.85879e6	+	1.72681e7i	−0.0879846	+	0.817375i
$852$	−7.69576e6			−0.363205
$853$	6.67484e6	−	7.95476e6i	0.314100	−	0.374330i	−0.585778	−	0.810472i	$-0.699211\pi$
$853$	6.67484e6	−	7.95476e6i	0.314100	−	0.374330i	0.899878	+	0.436142i	$0.143655\pi$
$854$	1.56826e6	−	1.31592e6i	0.0735821	−	0.0617427i
$855$	665128.	+	3.77213e6i	0.0311164	+	0.176470i
$856$	−2.93969e6	+	8.07673e6i	−0.137125	+	0.376748i
$857$			2.00260e7i			0.931414i	0.884939	+	0.465707i	$0.154200\pi$
$857$			2.00260e7i			0.931414i	−0.884939	+	0.465707i	$0.845800\pi$
$858$	244960.	+	89158.2i	0.0113600	+	0.00413469i
$859$	1.50433e7	+	8.68528e6i	0.695603	+	0.401607i	0.805708	−	0.592313i	$-0.201785\pi$
$859$	1.50433e7	+	8.68528e6i	0.695603	+	0.401607i	−0.110105	+	0.993920i	$0.535119\pi$
$860$	−3.28758e6	+	1.86448e7i	−0.151576	+	0.859629i
$861$	−4.41450e6	−	7.64614e6i	−0.202943	−	0.351507i
$862$	4.30174e6	−	7.45084e6i	0.197186	−	0.341536i
$863$	1.97051e7	+	1.65346e7i	0.900643	+	0.755729i	0.970316	−	0.241841i	$-0.0777511\pi$
$863$	1.97051e7	+	1.65346e7i	0.900643	+	0.755729i	−0.0696729	+	0.997570i	$0.522196\pi$
$864$	−3.13101e6	+	552082.i	−0.142692	+	0.0251605i
$865$	−2.85814e7	+	1.65015e7i	−1.29880	+	0.749864i
$866$	4.60982e6	+	1.26654e7i	0.208876	+	0.573883i
$867$	−619320.	+	225414.i	−0.0279813	+	0.0101844i
$868$	−1.22118e7	−	2.15328e6i	−0.550151	−	0.0970065i
$869$	1.27294e6	+	1.51703e6i	0.0571819	+	0.0681468i
$870$	4.51758e6	+	5.38384e6i	0.202352	+	0.241154i
$871$	2.93629e6	+	517746.i	0.131145	+	0.0231245i
$872$	−4.44226e6	+	1.61685e6i	−0.197840	+	0.0720077i
$873$	577708.	+	1.58724e6i	0.0256550	+	0.0704866i
$874$	1.37119e6	−	791658.i	0.0607183	−	0.0350557i
$875$	3.95187e7	−	6.96822e6i	1.74495	−	0.307682i
$876$	3.73796e6	+	3.13652e6i	0.164579	+	0.138098i
$877$	−1.18898e6	+	2.05938e6i	−0.0522007	+	0.0904143i	−0.890945	−	0.454111i	$-0.849957\pi$
$877$	−1.18898e6	+	2.05938e6i	−0.0522007	+	0.0904143i	0.838744	+	0.544525i	$0.183290\pi$
$878$	3.26696e6	+	5.65854e6i	0.143024	+	0.247724i
$879$	−1.65530e6	+	9.38766e6i	−0.0722610	+	0.409812i
$880$	−1.80682e6	−	1.04317e6i	−0.0786519	−	0.0454097i
$881$	695623.	+	253186.i	0.0301949	+	0.0109901i	0.357073	−	0.934076i	$-0.383775\pi$
$881$	695623.	+	253186.i	0.0301949	+	0.0109901i	−0.326879	+	0.945066i	$0.605997\pi$
$882$			8.03067e6i			0.347600i
$883$	1.35676e6	−	3.72766e6i	0.0585599	−	0.160892i	−0.906963	−	0.421211i	$-0.861605\pi$
$883$	1.35676e6	−	3.72766e6i	0.0585599	−	0.160892i	0.965523	+	0.260318i	$0.0838276\pi$
$884$	−402283.	−	2.28146e6i	−0.0173141	−	0.0981934i
$885$	3.23054e6	−	2.71075e6i	0.138649	−	0.116340i
$886$	−1.86008e6	+	2.21676e6i	−0.0796065	+	0.0948713i
$887$	−2.52256e7			−1.07654			−0.538272	−	0.842771i	$-0.680923\pi$
$887$	−2.52256e7			−1.07654			−0.538272	+	0.842771i	$0.680923\pi$
$888$	1.67581e6	−	3.41414e6i	0.0713169	−	0.145294i
$889$	2.41631e7			1.02541
$890$	−2.49180e7	+	2.96961e7i	−1.05448	+	1.25668i
$891$	−1.45670e6	+	1.22232e6i	−0.0614720	+	0.0515811i
$892$	408860.	+	2.31876e6i	0.0172053	+	0.0975761i
$893$	789890.	−	2.17020e6i	0.0331465	−	0.0910693i
$894$			1.11167e7i			0.465190i
$895$	−4.04449e7	−	1.47208e7i	−1.68774	−	0.614289i
$896$	−1.13107e6	−	653022.i	−0.0470672	−	0.0271743i
$897$	304311.	−	1.72583e6i	0.0126281	−	0.0716173i
$898$	−4.06028e6	−	7.03261e6i	−0.168022	−	0.291022i
$899$	1.13907e7	−	1.97292e7i	0.470056	−	0.814161i
$900$	−1.86354e7	−	1.56370e7i	−0.766891	−	0.643498i
$901$	−2.60322e7	+	4.59018e6i	−1.06831	+	0.188372i
$902$	−4.17002e6	+	2.40756e6i	−0.170656	+	0.0985283i
$903$	−2.19101e6	−	6.01975e6i	−0.0894180	−	0.245674i
$904$	−4.73000e6	+	1.72158e6i	−0.192504	+	0.0700657i
$905$	1.81318e7	+	3.19713e6i	0.735903	+	0.129760i
$906$	9.79138e6	+	1.16689e7i	0.396299	+	0.472291i
$907$	−2.05588e7	−	2.45010e7i	−0.829812	−	0.988931i	−0.999994	−	0.00351835i	$-0.998880\pi$
$907$	−2.05588e7	−	2.45010e7i	−0.829812	−	0.988931i	0.170182	−	0.985413i	$-0.445564\pi$
$908$	1.79229e6	+	316029.i	0.0721430	+	0.0127207i
$909$	1.49643e7	−	5.44657e6i	0.600685	−	0.218632i
$910$	1.34923e6	+	3.70698e6i	0.0540110	+	0.148394i
$911$	1.63006e7	−	9.41117e6i	0.650741	−	0.375705i	−0.137999	−	0.990432i	$-0.544067\pi$
$911$	1.63006e7	−	9.41117e6i	0.650741	−	0.375705i	0.788740	+	0.614727i	$0.210734\pi$
$912$	−341450.	+	60206.8i	−0.0135938	+	0.00239695i
$913$	−214840.	−	180272.i	−0.00852980	−	0.00715735i
$914$	1.90620e6	−	3.30164e6i	0.0754751	−	0.130727i
$915$	2.40717e6	+	4.16933e6i	0.0950503	+	0.164632i
$916$	3.71633e6	−	2.10764e7i	0.146344	−	0.829959i
$917$	1.11672e7	+	6.44741e6i	0.438553	+	0.253199i
$918$	−1.43511e7	−	5.22338e6i	−0.562055	−	0.204571i
$919$			4.13215e7i			1.61394i	0.590591	+	0.806971i	$0.298895\pi$
$919$			4.13215e7i			1.61394i	−0.590591	+	0.806971i	$0.701105\pi$
$920$	−4.79706e6	+	1.31798e7i	−0.186855	+	0.513381i
$921$	2.68816e6	+	1.52453e7i	0.104425	+	0.592226i
$922$	3.34479e6	−	2.80661e6i	0.129581	−	0.108731i
$923$	5.10110e6	−	6.07925e6i	0.197088	−	0.234880i
$924$	705948.			0.0272015
$925$	6.39994e7	−	1.57863e7i	2.45936	−	0.606633i
$926$	3.17349e7			1.21621
$927$	2.33889e7	−	2.78738e7i	0.893944	−	1.06536i
$928$	1.83807e6	−	1.54232e6i	0.0700634	−	0.0587901i
$929$	−1.23691e6	−	7.01487e6i	−0.0470218	−	0.266674i	0.952229	−	0.305386i	$-0.0987855\pi$
$929$	−1.23691e6	−	7.01487e6i	−0.0470218	−	0.266674i	−0.999250	+	0.0387124i	$0.987674\pi$
$930$	9.97367e6	−	2.74024e7i	0.378136	−	1.03892i
$931$			1.98376e6i			0.0750092i
$932$	−3.54476e6	−	1.29019e6i	−0.133674	−	0.0486534i
$933$	−1.77731e7	−	1.02613e7i	−0.668436	−	0.385922i
$934$	1.13037e6	−	6.41063e6i	0.0423987	−	0.240455i
$935$	−5.01097e6	−	8.67925e6i	−0.187453	−	0.324678i
$936$	723691.	−	1.25347e6i	0.0270000	−	0.0467654i
$937$	5.76231e6	+	4.83515e6i	0.214411	+	0.179913i	0.743668	−	0.668550i	$-0.233085\pi$
$937$	5.76231e6	+	4.83515e6i	0.214411	+	0.179913i	−0.529256	+	0.848462i	$0.677529\pi$
$938$	7.95172e6	−	1.40210e6i	0.295090	−	0.0520323i
$939$	3.38789e6	−	1.95600e6i	0.125391	−	0.0723943i
$940$	6.99717e6	+	1.92246e7i	0.258287	+	0.709638i
$941$	−1.15983e7	+	4.22145e6i	−0.426994	+	0.155413i	−0.546573	−	0.837412i	$-0.684068\pi$
$941$	−1.15983e7	+	4.22145e6i	−0.426994	+	0.155413i	0.119579	+	0.992825i	$0.461846\pi$
$942$	4.92209e6	+	867896.i	0.180727	+	0.0318670i
$943$	2.08072e7	+	2.47970e7i	0.761963	+	0.908072i
$944$	−925460.	−	1.10292e6i	−0.0338008	−	0.0402823i
$945$	2.56108e7	+	4.51588e6i	0.932920	+	0.164499i
$946$	−3.28303e6	+	1.19492e6i	−0.119274	+	0.0434123i
$947$	6.45724e6	+	1.77411e7i	0.233976	+	0.642845i	1.00000		3.24476e-5i	$1.03284e-5\pi$
$947$	6.45724e6	+	1.77411e7i	0.233976	+	0.642845i	−0.766024	+	0.642812i	$0.777767\pi$
$948$	−2.52474e6	+	1.45766e6i	−0.0912424	+	0.0526788i
$949$	−4.95538e6	+	873767.i	−0.178612	+	0.0314942i
$950$	−4.60338e6	−	3.86269e6i	−0.165488	−	0.138861i
$951$	8.57675e6	−	1.48554e7i	0.307519	−	0.532638i
$952$	−3.13685e6	−	5.43319e6i	−0.112177	−	0.194295i
$953$	−830417.	+	4.70953e6i	−0.0296186	+	0.167975i	−0.996029	−	0.0890279i	$-0.971624\pi$
$953$	−830417.	+	4.70953e6i	−0.0296186	+	0.167975i	0.966411	+	0.257003i	$0.0827351\pi$
$954$	−1.43025e7	−	8.25755e6i	−0.508793	−	0.293752i
$955$	−4.08004e7	−	1.48501e7i	−1.44762	−	0.526892i
$956$			1.82980e7i			0.647529i
$957$	−443581.	+	1.21873e6i	−0.0156564	+	0.0430157i
$958$	−4.62393e6	−	2.62236e7i	−0.162779	−	0.923163i
$959$	−6.93982e6	+	5.82320e6i	−0.243670	+	0.204463i
$960$	1.97423e6	−	2.35280e6i	0.0691386	−	0.0823962i
$961$	−6.58952e7			−2.30168
$962$	1.58619e6	+	3.58685e6i	0.0552609	+	0.124961i
$963$	−2.57952e7			−0.896340
$964$	7.83687e6	−	9.33961e6i	0.271613	−	0.323695i
$965$	7.36874e7	−	6.18311e7i	2.54727	−	2.13741i
$966$	−824102.	−	4.67371e6i	−0.0284144	−	0.161146i
$967$	−9.66870e6	+	2.65645e7i	−0.332508	+	0.913558i	0.654950	+	0.755673i	$0.272690\pi$
$967$	−9.66870e6	+	2.65645e7i	−0.332508	+	0.913558i	−0.987457	+	0.157885i	$0.949532\pi$
$968$			9.92226e6i			0.340347i
$969$	−1.56505e6	−	569631.i	−0.0535449	−	0.0194888i
$970$	−3.20096e6	−	1.84807e6i	−0.109232	−	0.0630652i
$971$	−3.95571e6	+	2.24340e7i	−0.134641	+	0.763586i	0.840468	+	0.541860i	$0.182280\pi$
$971$	−3.95571e6	+	2.24340e7i	−0.134641	+	0.763586i	−0.975109	+	0.221725i	$0.928831\pi$
$972$	−7.43542e6	−	1.28785e7i	−0.252429	−	0.437221i
$973$	−1.26906e7	+	2.19808e7i	−0.429734	+	0.744322i
$974$	1.70088e7	+	1.42721e7i	0.574483	+	0.482048i
$975$	−6.55019e6	+	1.15498e6i	−0.220670	+	0.0389100i
$976$	1.42343e6	−	821816.i	0.0478311	−	0.0276153i
$977$	−4.55812e6	−	1.25233e7i	−0.152774	−	0.419743i	0.839570	−	0.543252i	$-0.182807\pi$
$977$	−4.55812e6	−	1.25233e7i	−0.152774	−	0.419743i	−0.992343	+	0.123510i	$0.960585\pi$
$978$	−7.21776e6	+	2.62705e6i	−0.241299	+	0.0878256i
$979$	−7.04499e6	−	1.24222e6i	−0.234922	−	0.0414231i
$980$	−1.12957e7	−	1.34617e7i	−0.375705	−	0.447748i
$981$	−9.11957e6	−	1.08683e7i	−0.302553	−	0.360569i
$982$	−1.77555e7	−	3.13078e6i	−0.587564	−	0.103603i
$983$	1.91054e7	−	6.95379e6i	0.630626	−	0.229529i	−0.00687793	−	0.999976i	$-0.502189\pi$
$983$	1.91054e7	−	6.95379e6i	0.630626	−	0.229529i	0.637504	+	0.770447i	$0.279967\pi$
$984$	−2.42440e6	−	6.66099e6i	−0.0798210	−	0.219306i
$985$	−5.45921e7	+	3.15188e7i	−1.79283	+	1.03509i
$986$	1.13508e7	−	2.00144e6i	0.371820	−	0.0655619i
$987$	−5.30288e6	−	4.44964e6i	−0.173268	−	0.145389i
$988$	178768.	−	309636.i	0.00582637	−	0.0100916i
$989$	1.17435e7	+	2.03403e7i	0.381774	+	0.661252i
$990$	1.08729e6	−	6.16631e6i	0.0352579	−	0.199957i
$991$	−2.07661e7	−	1.19893e7i	−0.671693	−	0.387802i	0.125025	−	0.992154i	$-0.460099\pi$
$991$	−2.07661e7	−	1.19893e7i	−0.671693	−	0.387802i	−0.796718	+	0.604351i	$0.793432\pi$
$992$	−9.35530e6	−	3.40505e6i	−0.301841	−	0.109861i
$993$			2.44848e7i			0.787993i
$994$	7.35040e6	−	2.01951e7i	0.235964	−	0.648304i
$995$	7.12648e6	+	4.04163e7i	0.228201	+	1.29419i
$996$	316273.	−	265384.i	0.0101021	−	0.00847670i
$997$	−2.00074e7	+	2.38439e7i	−0.637459	+	0.759694i	−0.983967	−	0.178353i	$-0.942923\pi$
$997$	−2.00074e7	+	2.38439e7i	−0.637459	+	0.759694i	0.346508	+	0.938047i	$0.387368\pi$
$998$	−2.74285e7			−0.871717
$999$	2.57061e7	+	2.76708e6i	0.814934	+	0.0877219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.h.a.3.3	✓	96
37.25	even	18	inner	74.6.h.a.25.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.h.a.3.3	✓	96	1.1	even	1	trivial
74.6.h.a.25.3	yes	96	37.25	even	18	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57115 + 3.06418i) q^{2} +(-5.46669 + 4.58709i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-35.9379 + 98.7386i) q^{5} -28.5450i q^{6} +(74.9073 + 27.2640i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-33.3533 + 189.156i) q^{9} +O(q^{10})\)	\(q+(-2.57115 + 3.06418i) q^{2} +(-5.46669 + 4.58709i) q^{3} +(-2.77837 - 15.7569i) q^{4} +(-35.9379 + 98.7386i) q^{5} -28.5450i q^{6} +(74.9073 + 27.2640i) q^{7} +(55.4256 + 32.0000i) q^{8} +(-33.3533 + 189.156i) q^{9} +(-210.151 - 363.992i) q^{10} +(38.7806 - 67.1699i) q^{11} +(87.4670 + 73.3935i) q^{12} +(-115.954 + 20.4459i) q^{13} +(-276.140 + 159.429i) q^{14} +(-256.462 - 704.624i) q^{15} +(-240.561 + 87.5572i) q^{16} +(-1211.04 - 213.539i) q^{17} +(-493.851 - 588.549i) q^{18} +(-121.992 - 145.385i) q^{19} +(1655.67 + 291.939i) q^{20} +(-534.557 + 194.563i) q^{21} +(106.110 + 291.535i) q^{22} +(1806.23 - 1042.83i) q^{23} +(-449.782 + 79.3086i) q^{24} +(-6063.89 - 5088.21i) q^{25} +(235.486 - 407.874i) q^{26} +(-1552.40 - 2688.83i) q^{27} +(221.477 - 1256.06i) q^{28} +(2029.26 + 1171.59i) q^{29} +(2818.49 + 1025.85i) q^{30} -9722.36i q^{31} +(350.229 - 962.245i) q^{32} +(96.1136 + 545.087i) q^{33} +(3768.08 - 3161.80i) q^{34} +(-5384.02 + 6416.43i) q^{35} +3073.18 q^{36} +(-4911.56 + 6724.62i) q^{37} +759.146 q^{38} +(540.098 - 643.664i) q^{39} +(-5151.52 + 4322.64i) q^{40} +(2695.09 + 15284.6i) q^{41} +(778.252 - 2138.23i) q^{42} +11261.2i q^{43} +(-1166.14 - 424.440i) q^{44} +(-17478.3 - 10091.1i) q^{45} +(-1448.68 + 8215.88i) q^{46} +(6084.42 + 10538.5i) q^{47} +(913.440 - 1582.13i) q^{48} +(-8007.14 - 6718.79i) q^{49} +(31182.3 - 5498.29i) q^{50} +(7599.89 - 4387.80i) q^{51} +(644.328 + 1770.28i) q^{52} +(20199.4 - 7351.99i) q^{53} +(12230.5 + 2156.57i) q^{54} +(5238.57 + 6243.09i) q^{55} +(3279.33 + 3908.16i) q^{56} +(1333.79 + 235.183i) q^{57} +(-8807.50 + 3205.67i) q^{58} +(1923.54 + 5284.89i) q^{59} +(-10390.2 + 5998.76i) q^{60} +(-6322.90 + 1114.90i) q^{61} +(29791.0 + 24997.7i) q^{62} +(-7655.55 + 13259.8i) q^{63} +(2048.00 + 3547.24i) q^{64} +(2148.36 - 12183.9i) q^{65} +(-1917.37 - 1106.99i) q^{66} +(-23795.7 - 8660.91i) q^{67} +19675.5i q^{68} +(-5090.54 + 13986.2i) q^{69} +(-5817.94 - 32995.2i) q^{70} +(-51631.5 + 43324.0i) q^{71} +(-7901.61 + 9416.78i) q^{72} +42735.7 q^{73} +(-7977.07 - 32339.9i) q^{74} +56489.5 q^{75} +(-1951.88 + 2326.16i) q^{76} +(4736.27 - 3974.20i) q^{77} +(583.627 + 3309.91i) q^{78} +(-8732.70 + 23992.9i) q^{79} -26899.3i q^{80} +(-23038.8 - 8385.42i) q^{81} +(-53764.3 - 31040.8i) q^{82} +(627.896 - 3560.98i) q^{83} +(4550.91 + 7882.41i) q^{84} +(64606.7 - 111902. i) q^{85} +(-34506.3 - 28954.2i) q^{86} +(-16467.5 + 2903.67i) q^{87} +(4298.88 - 2481.96i) q^{88} +(-31545.4 - 86670.4i) q^{89} +(75860.4 - 27610.9i) q^{90} +(-9243.25 - 1629.83i) q^{91} +(-21450.1 - 25563.3i) q^{92} +(44597.4 + 53149.1i) q^{93} +(-47935.9 - 8452.39i) q^{94} +(18739.3 - 6820.53i) q^{95} +(2499.32 + 6866.82i) q^{96} +(7615.85 - 4397.02i) q^{97} +(41175.1 - 7260.28i) q^{98} +(11412.1 + 9575.91i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9	\( 96 q + 6 q^{3} + 90 q^{5} - 228 q^{7} - 186 q^{9} + 600 q^{10} - 726 q^{11} - 96 q^{12} - 246 q^{13} + 3960 q^{14} - 3960 q^{15} - 1530 q^{17} + 3222 q^{19} + 1440 q^{20} - 16110 q^{21} + 8232 q^{25} + 13632 q^{26} + 2154 q^{27} - 10464 q^{28} - 18378 q^{29} - 25056 q^{30} + 78198 q^{33} + 37296 q^{34} + 82170 q^{35} - 124416 q^{36} - 5586 q^{37} - 39936 q^{38} + 58686 q^{39} - 16128 q^{40} - 59598 q^{41} - 26304 q^{42} + 480 q^{44} - 74646 q^{45} - 22536 q^{46} - 1266 q^{47} + 193320 q^{49} + 18864 q^{50} + 68352 q^{52} - 57432 q^{53} + 101520 q^{54} + 133830 q^{55} - 228936 q^{57} - 79224 q^{58} - 52800 q^{59} + 68664 q^{61} - 72720 q^{62} - 166254 q^{63} + 196608 q^{64} - 122058 q^{65} + 254946 q^{67} - 218094 q^{69} - 25872 q^{70} + 200052 q^{71} - 32244 q^{73} + 124368 q^{74} - 234036 q^{75} + 51552 q^{76} + 397188 q^{77} - 16584 q^{78} + 267462 q^{79} - 371496 q^{81} + 121440 q^{83} + 84672 q^{84} - 337260 q^{85} + 43920 q^{86} - 667500 q^{87} - 135936 q^{88} + 377850 q^{89} - 576408 q^{90} + 875826 q^{91} + 233376 q^{92} + 365868 q^{93} - 80256 q^{94} + 764592 q^{95} - 823212 q^{97} - 342192 q^{98} - 928650 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 + 90 * q^5 - 228 * q^7 - 186 * q^9 + 600 * q^10 - 726 * q^11 - 96 * q^12 - 246 * q^13 + 3960 * q^14 - 3960 * q^15 - 1530 * q^17 + 3222 * q^19 + 1440 * q^20 - 16110 * q^21 + 8232 * q^25 + 13632 * q^26 + 2154 * q^27 - 10464 * q^28 - 18378 * q^29 - 25056 * q^30 + 78198 * q^33 + 37296 * q^34 + 82170 * q^35 - 124416 * q^36 - 5586 * q^37 - 39936 * q^38 + 58686 * q^39 - 16128 * q^40 - 59598 * q^41 - 26304 * q^42 + 480 * q^44 - 74646 * q^45 - 22536 * q^46 - 1266 * q^47 + 193320 * q^49 + 18864 * q^50 + 68352 * q^52 - 57432 * q^53 + 101520 * q^54 + 133830 * q^55 - 228936 * q^57 - 79224 * q^58 - 52800 * q^59 + 68664 * q^61 - 72720 * q^62 - 166254 * q^63 + 196608 * q^64 - 122058 * q^65 + 254946 * q^67 - 218094 * q^69 - 25872 * q^70 + 200052 * q^71 - 32244 * q^73 + 124368 * q^74 - 234036 * q^75 + 51552 * q^76 + 397188 * q^77 - 16584 * q^78 + 267462 * q^79 - 371496 * q^81 + 121440 * q^83 + 84672 * q^84 - 337260 * q^85 + 43920 * q^86 - 667500 * q^87 - 135936 * q^88 + 377850 * q^89 - 576408 * q^90 + 875826 * q^91 + 233376 * q^92 + 365868 * q^93 - 80256 * q^94 + 764592 * q^95 - 823212 * q^97 - 342192 * q^98 - 928650 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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