LMFDB - Embedded newform 74.5.g.a.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(23,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("74.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.g (of order $12$, 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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	74.29
Dual form			74.5.g.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.732051 - 2.73205i) q^{2} +(13.7481 + 7.93744i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(5.58720 + 20.8517i) q^{5} +(31.7498 - 31.7498i) q^{6} +(10.7825 - 18.6759i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(85.5060 + 148.101i) q^{9} +O(q^{10})$	\(q+(0.732051 - 2.73205i) q^{2} +(13.7481 + 7.93744i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(5.58720 + 20.8517i) q^{5} +(31.7498 - 31.7498i) q^{6} +(10.7825 - 18.6759i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(85.5060 + 148.101i) q^{9} +61.0580 q^{10} -84.9630i q^{11} +(-63.4995 - 109.984i) q^{12} +(66.1127 + 246.736i) q^{13} +(-43.1300 - 43.1300i) q^{14} +(-88.6961 + 331.019i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-68.7695 - 18.4267i) q^{17} +(467.213 - 125.189i) q^{18} +(-122.946 - 458.841i) q^{19} +(44.6976 - 166.814i) q^{20} +(296.477 - 171.171i) q^{21} +(-232.123 - 62.1972i) q^{22} +(340.952 - 340.952i) q^{23} +(-346.968 + 92.9698i) q^{24} +(137.689 - 79.4947i) q^{25} +722.494 q^{26} +1428.93i q^{27} +(-149.407 + 86.2601i) q^{28} +(302.089 + 302.089i) q^{29} +(839.429 + 484.645i) q^{30} +(-941.814 - 941.814i) q^{31} +(174.851 - 46.8513i) q^{32} +(674.389 - 1168.08i) q^{33} +(-100.686 + 174.392i) q^{34} +(449.668 + 120.488i) q^{35} -1368.10i q^{36} +(-615.430 - 1222.87i) q^{37} -1343.58 q^{38} +(-1049.53 + 3916.91i) q^{39} +(-423.023 - 244.232i) q^{40} +(-2613.28 - 1508.78i) q^{41} +(-250.612 - 935.296i) q^{42} +(-1783.94 + 1783.94i) q^{43} +(-339.852 + 588.641i) q^{44} +(-2610.41 + 2610.41i) q^{45} +(-681.903 - 1181.09i) q^{46} -42.3456 q^{47} +1015.99i q^{48} +(967.975 + 1676.58i) q^{49} +(-116.388 - 434.367i) q^{50} +(-799.186 - 799.186i) q^{51} +(528.902 - 1973.89i) q^{52} +(457.121 + 791.757i) q^{53} +(3903.91 + 1046.05i) q^{54} +(1771.62 - 474.705i) q^{55} +(126.294 + 471.334i) q^{56} +(1951.75 - 7284.04i) q^{57} +(1046.47 - 604.179i) q^{58} +(-3272.46 - 876.854i) q^{59} +(1938.58 - 1938.58i) q^{60} +(2614.07 - 700.438i) q^{61} +(-3262.54 + 1883.63i) q^{62} +3687.88 q^{63} -512.000i q^{64} +(-4775.49 + 2757.13i) q^{65} +(-2697.56 - 2697.56i) q^{66} +(4396.29 + 2538.20i) q^{67} +(402.742 + 402.742i) q^{68} +(7393.71 - 1981.14i) q^{69} +(658.359 - 1140.31i) q^{70} +(3192.16 - 5528.98i) q^{71} +(-3737.71 - 1001.52i) q^{72} +6020.79i q^{73} +(-3791.46 + 786.185i) q^{74} +2523.94 q^{75} +(-983.568 + 3670.73i) q^{76} +(-1586.76 - 916.114i) q^{77} +(9932.88 + 5734.75i) q^{78} +(-1307.86 - 4880.99i) q^{79} +(-976.929 + 976.929i) q^{80} +(-4416.06 + 7648.85i) q^{81} +(-6035.12 + 6035.12i) q^{82} +(-3998.24 - 6925.16i) q^{83} -2738.74 q^{84} -1536.92i q^{85} +(3567.87 + 6179.74i) q^{86} +(1755.32 + 6550.96i) q^{87} +(1359.41 + 1359.41i) q^{88} +(-1321.79 + 4932.98i) q^{89} +(5220.83 + 9042.74i) q^{90} +(5320.87 + 1425.72i) q^{91} +(-3725.99 + 998.376i) q^{92} +(-5472.52 - 20423.7i) q^{93} +(-30.9991 + 115.690i) q^{94} +(8880.69 - 5127.27i) q^{95} +(2775.74 + 743.758i) q^{96} +(-6689.12 + 6689.12i) q^{97} +(5289.11 - 1417.21i) q^{98} +(12583.1 - 7264.85i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9 - 72 * q^10 + 80 * q^12 + 248 * q^13 - 192 * q^14 - 852 * q^15 + 896 * q^16 + 1092 * q^17 + 1112 * q^18 - 320 * q^19 + 336 * q^20 - 858 * q^21 - 112 * q^22 + 2348 * q^23 + 160 * q^24 - 162 * q^25 - 184 * q^26 + 1584 * q^28 - 1308 * q^29 + 2652 * q^30 - 3444 * q^31 + 1792 * q^32 + 1052 * q^33 + 1428 * q^34 - 580 * q^35 - 5694 * q^37 - 824 * q^38 - 6514 * q^39 - 1056 * q^40 - 12186 * q^41 - 1276 * q^42 - 6220 * q^43 + 1280 * q^44 + 12804 * q^45 - 4696 * q^46 + 15928 * q^47 - 4892 * q^49 - 10792 * q^50 - 6218 * q^51 + 1984 * q^52 - 9662 * q^53 - 9836 * q^54 + 1744 * q^55 - 3936 * q^56 + 16046 * q^57 + 13800 * q^58 - 9356 * q^59 - 3024 * q^60 - 6682 * q^61 + 16128 * q^62 + 60268 * q^63 - 28086 * q^65 - 4208 * q^66 + 28086 * q^67 - 5712 * q^68 + 19878 * q^69 - 6028 * q^70 + 680 * q^71 - 8896 * q^72 - 2420 * q^74 + 11076 * q^75 - 2560 * q^76 - 32208 * q^77 + 23436 * q^78 - 15136 * q^79 + 1152 * q^80 - 21274 * q^81 - 2608 * q^82 - 19732 * q^83 + 23936 * q^84 + 12440 * q^86 - 31624 * q^87 - 5120 * q^88 + 45940 * q^89 - 25608 * q^90 - 13106 * q^91 - 6944 * q^92 - 37734 * q^93 - 16960 * q^94 - 37458 * q^95 - 1280 * q^96 + 31792 * q^97 + 5216 * q^98 + 141456 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$3$	13.7481	+	7.93744i	1.52756	+	0.881938i	0.999463	+	0.0327547i	$0.0104280\pi$
$3$	13.7481	+	7.93744i	1.52756	+	0.881938i	0.528098	+	0.849183i	$0.322905\pi$
$4$	−6.92820	−	4.00000i	−0.433013	−	0.250000i
$5$	5.58720	+	20.8517i	0.223488	+	0.834068i	0.983005	+	0.183581i	$0.0587688\pi$
$5$	5.58720	+	20.8517i	0.223488	+	0.834068i	−0.759517	+	0.650488i	$0.774564\pi$
$6$	31.7498	−	31.7498i	0.881938	−	0.881938i
$7$	10.7825	−	18.6759i	0.220051	−	0.381140i	−0.734772	−	0.678314i	$-0.762711\pi$
$7$	10.7825	−	18.6759i	0.220051	−	0.381140i	0.954823	+	0.297174i	$0.0960442\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	85.5060	+	148.101i	1.05563	+	1.82840i
$10$	61.0580			0.610580
$11$		−	84.9630i		−	0.702174i	−0.936343	−	0.351087i	$-0.885812\pi$
$11$		−	84.9630i		−	0.702174i	0.936343	−	0.351087i	$-0.114188\pi$
$12$	−63.4995	−	109.984i	−0.440969	−	0.763781i
$13$	66.1127	+	246.736i	0.391200	+	1.45998i	0.828158	+	0.560495i	$0.189389\pi$
$13$	66.1127	+	246.736i	0.391200	+	1.45998i	−0.436958	+	0.899482i	$0.643944\pi$
$14$	−43.1300	−	43.1300i	−0.220051	−	0.220051i
$15$	−88.6961	+	331.019i	−0.394205	+	1.47119i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	−68.7695	−	18.4267i	−0.237957	−	0.0637603i	0.137870	−	0.990450i	$-0.455974\pi$
$17$	−68.7695	−	18.4267i	−0.237957	−	0.0637603i	−0.375826	+	0.926690i	$0.622641\pi$
$18$	467.213	−	125.189i	1.44202	−	0.386387i
$19$	−122.946	−	458.841i	−0.340571	−	1.27103i	−0.897702	−	0.440603i	$-0.854765\pi$
$19$	−122.946	−	458.841i	−0.340571	−	1.27103i	0.557132	−	0.830424i	$-0.311902\pi$
$20$	44.6976	−	166.814i	0.111744	−	0.417034i
$21$	296.477	−	171.171i	0.672283	−	0.388143i
$22$	−232.123	−	62.1972i	−0.479594	−	0.128507i
$23$	340.952	−	340.952i	0.644521	−	0.644521i	−0.307143	−	0.951664i	$-0.599373\pi$
$23$	340.952	−	340.952i	0.644521	−	0.644521i	0.951664	+	0.307143i	$0.0993728\pi$
$24$	−346.968	+	92.9698i	−0.602375	+	0.161406i
$25$	137.689	−	79.4947i	0.220302	−	0.127191i
$26$	722.494			1.06878
$27$			1428.93i			1.96012i
$28$	−149.407	+	86.2601i	−0.190570	+	0.110026i
$29$	302.089	+	302.089i	0.359203	+	0.359203i	0.863519	−	0.504316i	$-0.168255\pi$
$29$	302.089	+	302.089i	0.359203	+	0.359203i	−0.504316	+	0.863519i	$0.668255\pi$
$30$	839.429	+	484.645i	0.932699	+	0.538494i
$31$	−941.814	−	941.814i	−0.980036	−	0.980036i	0.0197687	−	0.999805i	$-0.493707\pi$
$31$	−941.814	−	941.814i	−0.980036	−	0.980036i	−0.999805	+	0.0197687i	$0.993707\pi$
$32$	174.851	−	46.8513i	0.170753	−	0.0457532i
$33$	674.389	−	1168.08i	0.619274	−	1.07261i
$34$	−100.686	+	174.392i	−0.0870982	+	0.150859i
$35$	449.668	+	120.488i	0.367076	+	0.0983576i
$36$		−	1368.10i		−	1.05563i
$37$	−615.430	−	1222.87i	−0.449547	−	0.893257i
$37$	−615.430	−	1222.87i	−0.449547	−	0.893257i
$38$	−1343.58			−0.930456
$39$	−1049.53	+	3916.91i	−0.690028	+	2.57522i
$40$	−423.023	−	244.232i	−0.264389	−	0.152645i
$41$	−2613.28	−	1508.78i	−1.55460	−	0.897549i	−0.997758	−	0.0669312i	$-0.978679\pi$
$41$	−2613.28	−	1508.78i	−1.55460	−	0.897549i	−0.556843	−	0.830618i	$-0.687987\pi$
$42$	−250.612	−	935.296i	−0.142070	−	0.530213i
$43$	−1783.94	+	1783.94i	−0.964812	+	0.964812i	−0.999402	−	0.0345899i	$-0.988987\pi$
$43$	−1783.94	+	1783.94i	−0.964812	+	0.964812i	0.0345899	+	0.999402i	$0.488987\pi$
$44$	−339.852	+	588.641i	−0.175543	+	0.304050i
$45$	−2610.41	+	2610.41i	−1.28909	+	1.28909i
$46$	−681.903	−	1181.09i	−0.322260	−	0.558172i
$47$	−42.3456			−0.0191696			−0.00958479	−	0.999954i	$-0.503051\pi$
$47$	−42.3456			−0.0191696			−0.00958479	+	0.999954i	$0.503051\pi$
$48$			1015.99i			0.440969i
$49$	967.975	+	1676.58i	0.403155	+	0.698285i
$50$	−116.388	−	434.367i	−0.0465553	−	0.173747i
$51$	−799.186	−	799.186i	−0.307261	−	0.307261i
$52$	528.902	−	1973.89i	0.195600	−	0.729989i
$53$	457.121	+	791.757i	0.162734	+	0.281864i	0.935848	−	0.352403i	$-0.114635\pi$
$53$	457.121	+	791.757i	0.162734	+	0.281864i	−0.773114	+	0.634267i	$0.781302\pi$
$54$	3903.91	+	1046.05i	1.33879	+	0.358728i
$55$	1771.62	−	474.705i	0.585661	−	0.156927i
$56$	126.294	+	471.334i	0.0402722	+	0.150298i
$57$	1951.75	−	7284.04i	0.600724	−	2.24193i
$58$	1046.47	−	604.179i	0.311079	−	0.179601i
$59$	−3272.46	−	876.854i	−0.940093	−	0.251897i	−0.243940	−	0.969790i	$-0.578440\pi$
$59$	−3272.46	−	876.854i	−0.940093	−	0.251897i	−0.696153	+	0.717893i	$0.745107\pi$
$60$	1938.58	−	1938.58i	0.538494	−	0.538494i
$61$	2614.07	−	700.438i	0.702518	−	0.188239i	0.110160	−	0.993914i	$-0.464864\pi$
$61$	2614.07	−	700.438i	0.702518	−	0.188239i	0.592358	+	0.805675i	$0.298197\pi$
$62$	−3262.54	+	1883.63i	−0.848736	+	0.490018i
$63$	3687.88			0.929170
$64$		−	512.000i		−	0.125000i
$65$	−4775.49	+	2757.13i	−1.13029	+	0.652575i
$66$	−2697.56	−	2697.56i	−0.619274	−	0.619274i
$67$	4396.29	+	2538.20i	0.979348	+	0.565427i	0.902073	−	0.431583i	$-0.142045\pi$
$67$	4396.29	+	2538.20i	0.979348	+	0.565427i	0.0772749	+	0.997010i	$0.475378\pi$
$68$	402.742	+	402.742i	0.0870982	+	0.0870982i
$69$	7393.71	−	1981.14i	1.55297	−	0.416118i
$70$	658.359	−	1140.31i	0.134359	−	0.232717i
$71$	3192.16	−	5528.98i	0.633239	−	1.09680i	−0.353647	−	0.935379i	$-0.615058\pi$
$71$	3192.16	−	5528.98i	0.633239	−	1.09680i	0.986885	−	0.161423i	$-0.0516082\pi$
$72$	−3737.71	−	1001.52i	−0.721008	−	0.193194i
$73$			6020.79i			1.12982i	0.825154	+	0.564908i	$0.191088\pi$
$73$			6020.79i			1.12982i	−0.825154	+	0.564908i	$0.808912\pi$
$74$	−3791.46	+	786.185i	−0.692378	+	0.143569i
$75$	2523.94			0.448700
$76$	−983.568	+	3670.73i	−0.170285	+	0.635513i
$77$	−1586.76	−	916.114i	−0.267626	−	0.154514i
$78$	9932.88	+	5734.75i	1.63262	+	0.942595i
$79$	−1307.86	−	4880.99i	−0.209559	−	0.782084i	−0.988011	−	0.154381i	$-0.950662\pi$
$79$	−1307.86	−	4880.99i	−0.209559	−	0.782084i	0.778453	−	0.627703i	$-0.216005\pi$
$80$	−976.929	+	976.929i	−0.152645	+	0.152645i
$81$	−4416.06	+	7648.85i	−0.673078	+	1.16581i
$82$	−6035.12	+	6035.12i	−0.897549	+	0.897549i
$83$	−3998.24	−	6925.16i	−0.580381	−	1.00525i	−0.995434	−	0.0954516i	$-0.969570\pi$
$83$	−3998.24	−	6925.16i	−0.580381	−	1.00525i	0.415053	−	0.909797i	$-0.363763\pi$
$84$	−2738.74			−0.388143
$85$		−	1536.92i		−	0.212722i
$86$	3567.87	+	6179.74i	0.482406	+	0.835551i
$87$	1755.32	+	6550.96i	0.231910	+	0.865498i
$88$	1359.41	+	1359.41i	0.175543	+	0.175543i
$89$	−1321.79	+	4932.98i	−0.166871	+	0.622772i	0.830923	+	0.556388i	$0.187813\pi$
$89$	−1321.79	+	4932.98i	−0.166871	+	0.622772i	−0.997794	+	0.0663846i	$0.978854\pi$
$90$	5220.83	+	9042.74i	0.644547	+	1.11639i
$91$	5320.87	+	1425.72i	0.642539	+	0.172168i
$92$	−3725.99	+	998.376i	−0.440216	+	0.117956i
$93$	−5472.52	−	20423.7i	−0.632734	−	2.36140i
$94$	−30.9991	+	115.690i	−0.00350828	+	0.0130931i
$95$	8880.69	−	5127.27i	0.984010	−	0.568118i
$96$	2775.74	+	743.758i	0.301187	+	0.0807029i
$97$	−6689.12	+	6689.12i	−0.710928	+	0.710928i	−0.966729	−	0.255801i	$-0.917661\pi$
$97$	−6689.12	+	6689.12i	−0.710928	+	0.710928i	0.255801	+	0.966729i	$0.417661\pi$
$98$	5289.11	−	1417.21i	0.550720	−	0.147565i
$99$	12583.1	−	7264.85i	1.28386	−	0.741235i
$100$	−1271.91			−0.127191
$101$		−	17485.0i		−	1.71405i	−0.515273	−	0.857026i	$-0.672310\pi$
$101$		−	17485.0i		−	1.71405i	0.515273	−	0.857026i	$-0.327690\pi$
$102$	−2768.46	+	1598.37i	−0.266096	+	0.153630i
$103$	7350.34	+	7350.34i	0.692840	+	0.692840i	0.962856	−	0.270016i	$-0.0870289\pi$
$103$	7350.34	+	7350.34i	0.692840	+	0.692840i	−0.270016	+	0.962856i	$0.587029\pi$
$104$	−5005.58	−	2889.97i	−0.462794	−	0.267194i
$105$	5225.69	+	5225.69i	0.473985	+	0.473985i
$106$	2497.76	−	669.271i	0.222299	−	0.0595649i
$107$	−4548.65	+	7878.50i	−0.397297	+	0.688138i	−0.993391	−	0.114776i	$-0.963385\pi$
$107$	−4548.65	+	7878.50i	−0.397297	+	0.688138i	0.596095	+	0.802914i	$0.296718\pi$
$108$	5715.72	−	9899.92i	0.490031	−	0.848758i
$109$	12377.3	+	3316.48i	1.04177	+	0.279142i	0.738847	−	0.673873i	$-0.235371\pi$
$109$	12377.3	+	3316.48i	1.04177	+	0.279142i	0.302924	+	0.953015i	$0.402037\pi$
$110$		−	5187.68i		−	0.428734i
$111$	1245.48	−	21697.0i	0.101086	−	1.76098i
$112$	1380.16			0.110026
$113$	−4789.48	+	17874.6i	−0.375086	+	1.39984i	0.478132	+	0.878288i	$0.341314\pi$
$113$	−4789.48	+	17874.6i	−0.375086	+	1.39984i	−0.853218	+	0.521554i	$0.825353\pi$
$114$	−18471.6	−	10664.6i	−1.42133	−	0.820605i
$115$	9014.39	+	5204.46i	0.681617	+	0.393532i
$116$	−884.579	−	3301.29i	−0.0657386	−	0.245340i
$117$	−30888.8	+	30888.8i	−2.25647	+	2.25647i
$118$	−4791.22	+	8298.64i	−0.344098	+	0.595995i
$119$	−1085.64	+	1085.64i	−0.0766643	+	0.0766643i
$120$	−3877.16	−	6715.44i	−0.269247	−	0.466350i
$121$	7422.29			0.506952
$122$		−	7654.53i		−	0.514279i
$123$	−23951.7	−	41485.6i	−1.58317	−	2.74212i
$124$	2757.82	+	10292.3i	0.179359	+	0.669377i
$125$	11967.2	+	11967.2i	0.765902	+	0.765902i
$126$	2699.71	−	10075.5i	0.170050	−	0.634635i
$127$	−1514.51	−	2623.21i	−0.0939000	−	0.162640i	0.815249	−	0.579111i	$-0.196600\pi$
$127$	−1514.51	−	2623.21i	−0.0939000	−	0.162640i	−0.909149	+	0.416471i	$0.863267\pi$
$128$	−1398.81	−	374.810i	−0.0853766	−	0.0228766i
$129$	−38685.6	+	10365.8i	−2.32471	+	0.622905i
$130$	4036.72	+	15065.2i	0.238859	+	0.891434i
$131$	1069.14	−	3990.08i	0.0623004	−	0.232508i	−0.927754	−	0.373192i	$-0.878263\pi$
$131$	1069.14	−	3990.08i	0.0623004	−	0.232508i	0.990055	+	0.140683i	$0.0449300\pi$
$132$	−9344.61	+	5395.11i	−0.536307	+	0.309637i
$133$	−9894.91	−	2651.33i	−0.559382	−	0.149886i
$134$	10152.8	−	10152.8i	0.565427	−	0.565427i
$135$	−29795.6	+	7983.72i	−1.63488	+	0.438064i
$136$	1395.14	−	805.484i	0.0754293	−	0.0435491i
$137$	−20039.9			−1.06771			−0.533856	−	0.845576i	$-0.679257\pi$
$137$	−20039.9			−1.06771			−0.533856	+	0.845576i	$0.679257\pi$
$138$		−	21650.3i		−	1.13686i
$139$	32083.3	−	18523.3i	1.66054	−	0.958713i	0.688082	−	0.725633i	$-0.258453\pi$
$139$	32083.3	−	18523.3i	1.66054	−	0.958713i	0.972458	−	0.233080i	$-0.0748803\pi$
$140$	−2633.44	−	2633.44i	−0.134359	−	0.134359i
$141$	−582.170	−	336.116i	−0.0292827	−	0.0169064i
$142$	−12768.6	−	12768.6i	−0.633239	−	0.633239i
$143$	20963.4	−	5617.14i	1.02516	−	0.274690i
$144$	−5472.38	+	9478.45i	−0.263907	+	0.457101i
$145$	−4611.25	+	7986.91i	−0.219322	+	0.379877i
$146$	16449.1	+	4407.52i	0.771679	+	0.206771i
$147$			30733.0i			1.42223i
$148$	−627.647	+	10934.0i	−0.0286545	+	0.499178i
$149$	2615.82			0.117825			0.0589123	−	0.998263i	$-0.481237\pi$
$149$	2615.82			0.117825			0.0589123	+	0.998263i	$0.481237\pi$
$150$	1847.65	−	6895.52i	0.0821178	−	0.306468i
$151$	−1581.52	−	913.093i	−0.0693620	−	0.0400462i	0.464918	−	0.885354i	$-0.346084\pi$
$151$	−1581.52	−	913.093i	−0.0693620	−	0.0400462i	−0.534280	+	0.845308i	$0.679417\pi$
$152$	9308.59	+	5374.32i	0.402899	+	0.232614i
$153$	−3151.19	−	11760.4i	−0.134615	−	0.502388i
$154$	−3664.46	+	3664.46i	−0.154514	+	0.154514i
$155$	14376.3	−	24900.5i	0.598391	−	1.03644i
$156$	22939.0	−	22939.0i	0.942595	−	0.942595i
$157$	20857.0	+	36125.3i	0.846158	+	1.46559i	0.884611	+	0.466329i	$0.154424\pi$
$157$	20857.0	+	36125.3i	0.846158	+	1.46559i	−0.0384530	+	0.999260i	$0.512243\pi$
$158$	−14292.5			−0.572525
$159$			14513.5i			0.574087i
$160$	1953.86	+	3384.18i	0.0763226	+	0.132195i
$161$	−2691.25	−	10043.9i	−0.103825	−	0.387480i
$162$	17664.3	+	17664.3i	0.673078	+	0.673078i
$163$	−7201.89	+	26877.8i	−0.271064	+	1.01162i	0.687370	+	0.726308i	$0.258765\pi$
$163$	−7201.89	+	26877.8i	−0.271064	+	1.01162i	−0.958433	+	0.285316i	$0.907901\pi$
$164$	12070.2	+	20906.3i	0.448775	+	0.777300i
$165$	28124.3	+	7535.89i	1.03303	+	0.276800i
$166$	−21846.8	+	5853.83i	−0.792815	+	0.212434i
$167$	7812.95	+	29158.3i	0.280144	+	1.04551i	0.952315	+	0.305117i	$0.0986956\pi$
$167$	7812.95	+	29158.3i	0.280144	+	1.04551i	−0.672170	+	0.740396i	$0.734638\pi$
$168$	−2004.89	+	7482.37i	−0.0710351	+	0.265107i
$169$	−31773.3	+	18344.3i	−1.11247	+	0.642285i
$170$	−4198.93	−	1125.10i	−0.145292	−	0.0389308i
$171$	57442.0	−	57442.0i	1.96443	−	1.96443i
$172$	19495.2	−	5223.73i	0.658979	−	0.176573i
$173$	19521.5	−	11270.7i	0.652259	−	0.376582i	−0.137062	−	0.990562i	$-0.543766\pi$
$173$	19521.5	−	11270.7i	0.652259	−	0.376582i	0.789321	+	0.613980i	$0.210433\pi$
$174$	19182.5			0.633589
$175$		−	3428.61i		−	0.111955i
$176$	4709.13	−	2718.82i	0.152025	−	0.0877717i
$177$	−38030.0	−	38030.0i	−1.21389	−	1.21389i
$178$	12509.5	+	7222.38i	0.394822	+	0.227951i
$179$	−21254.5	−	21254.5i	−0.663352	−	0.663352i	0.292816	−	0.956169i	$-0.405408\pi$
$179$	−21254.5	−	21254.5i	−0.663352	−	0.663352i	−0.956169	+	0.292816i	$0.905408\pi$
$180$	28527.1	−	7643.82i	0.880467	−	0.235921i
$181$	−1788.15	+	3097.17i	−0.0545817	+	0.0945383i	−0.892025	−	0.451985i	$-0.850716\pi$
$181$	−1788.15	+	3097.17i	−0.0545817	+	0.0945383i	0.837444	+	0.546524i	$0.184049\pi$
$182$	7790.29	−	13493.2i	0.235186	−	0.407354i
$183$	41498.1	+	11119.4i	1.23916	+	0.332031i
$184$			10910.5i			0.322260i
$185$	22060.4	−	19665.2i	0.644569	−	0.574585i
$186$	−59804.8			−1.72866
$187$	−1565.59	+	5842.86i	−0.0447708	+	0.167087i
$188$	293.379	+	169.382i	0.00830067	+	0.00479239i
$189$	26686.5	+	15407.5i	0.747081	+	0.431328i
$190$	−7506.84	−	28015.9i	−0.207946	−	0.776064i
$191$	−45087.3	+	45087.3i	−1.23591	+	1.23591i	−0.274256	+	0.961657i	$0.588432\pi$
$191$	−45087.3	+	45087.3i	−1.23591	+	1.23591i	−0.961657	+	0.274256i	$0.911568\pi$
$192$	4063.97	−	7039.00i	0.110242	−	0.190945i
$193$	−30365.9	+	30365.9i	−0.815213	+	0.815213i	−0.985410	−	0.170197i	$-0.945560\pi$
$193$	−30365.9	+	30365.9i	−0.815213	+	0.815213i	0.170197	+	0.985410i	$0.445560\pi$
$194$	13378.2	+	23171.8i	0.355464	+	0.615682i
$195$	−87538.2			−2.30212
$196$		−	15487.6i		−	0.403155i
$197$	−27055.7	−	46861.9i	−0.697151	−	1.20750i	−0.969450	−	0.245288i	$-0.921118\pi$
$197$	−27055.7	−	46861.9i	−0.697151	−	1.20750i	0.272300	−	0.962212i	$-0.412216\pi$
$198$	−10636.5	−	39695.9i	−0.271311	−	1.01255i
$199$	43561.1	+	43561.1i	1.10000	+	1.10000i	0.994410	+	0.105591i	$0.0336733\pi$
$199$	43561.1	+	43561.1i	1.10000	+	1.10000i	0.105591	+	0.994410i	$0.466327\pi$
$200$	−931.106	+	3474.94i	−0.0232777	+	0.0868734i
$201$	40293.7	+	69790.7i	0.997343	+	1.72745i
$202$	−47770.0	−	12799.9i	−1.17072	−	0.313693i
$203$	8899.06	−	2384.50i	0.215949	−	0.0578635i
$204$	2340.18	+	8733.66i	0.0562327	+	0.209863i
$205$	16859.7	−	62921.3i	0.401183	−	1.49723i
$206$	25462.3	−	14700.7i	0.600017	−	0.346420i
$207$	79648.6	+	21341.8i	1.85882	+	0.498069i
$208$	−11559.9	+	11559.9i	−0.267194	+	0.267194i
$209$	−38984.5	+	10445.9i	−0.892482	+	0.239140i
$210$	18102.3	−	10451.4i	0.410483	−	0.236993i
$211$	22233.1			0.499384			0.249692	−	0.968325i	$-0.419671\pi$
$211$	22233.1			0.499384			0.249692	+	0.968325i	$0.419671\pi$
$212$		−	7313.93i		−	0.162734i
$213$	87771.9	−	50675.1i	1.93462	−	1.11695i
$214$	18194.6	+	18194.6i	0.397297	+	0.397297i
$215$	−47165.3	−	27230.9i	−1.02034	−	0.589095i
$216$	−22862.9	−	22862.9i	−0.490031	−	0.490031i
$217$	−27744.3	+	7434.07i	−0.589189	+	0.157873i
$218$	18121.6	−	31387.5i	0.381315	−	0.660456i
$219$	−47789.7	+	82774.1i	−0.996428	+	1.72586i
$220$	−14173.0	−	3797.64i	−0.292830	−	0.0784637i
$221$		−	18186.2i		−	0.372354i
$222$	−58365.6	−	19286.0i	−1.18427	−	0.391324i
$223$	−71074.0			−1.42923			−0.714614	−	0.699519i	$-0.753397\pi$
$223$	−71074.0			−1.42923			−0.714614	+	0.699519i	$0.753397\pi$
$224$	1010.35	−	3770.67i	0.0201361	−	0.0751489i
$225$	23546.4	+	13594.5i	0.465115	+	0.268534i
$226$	45328.1	+	26170.2i	0.887464	+	0.512378i
$227$	11464.9	+	42787.5i	0.222494	+	0.830358i	0.983393	+	0.181488i	$0.0580914\pi$
$227$	11464.9	+	42787.5i	0.222494	+	0.830358i	−0.760899	+	0.648870i	$0.775242\pi$
$228$	−42658.3	+	42658.3i	−0.820605	+	0.820605i
$229$	1278.25	−	2213.99i	0.0243750	−	0.0422187i	−0.853581	−	0.520961i	$-0.825574\pi$
$229$	1278.25	−	2213.99i	0.0243750	−	0.0422187i	0.877956	+	0.478742i	$0.158907\pi$
$230$	20817.8	−	20817.8i	0.393532	−	0.393532i
$231$	−14543.2	−	25189.6i	−0.272544	−	0.472060i
$232$	−9666.86			−0.179601
$233$		−	61126.3i		−	1.12594i	−0.826476	−	0.562972i	$-0.809658\pi$
$233$		−	61126.3i		−	1.12594i	0.826476	−	0.562972i	$-0.190342\pi$
$234$	61777.5	+	107002.i	1.12823	+	1.95416i
$235$	−236.593	−	882.978i	−0.00428417	−	0.0159887i
$236$	19164.9	+	19164.9i	0.344098	+	0.344098i
$237$	20762.1	−	77485.1i	0.369636	−	1.37950i
$238$	2171.29	+	3760.78i	0.0383321	+	0.0663932i
$239$	−46714.3	−	12517.1i	−0.817813	−	0.219132i	−0.174423	−	0.984671i	$-0.555806\pi$
$239$	−46714.3	−	12517.1i	−0.817813	−	0.219132i	−0.643390	+	0.765538i	$0.722473\pi$
$240$	−21185.2	+	5676.55i	−0.367798	+	0.0985513i
$241$	2438.25	+	9099.69i	0.0419802	+	0.156672i	0.983734	−	0.179630i	$-0.0574901\pi$
$241$	2438.25	+	9099.69i	0.0419802	+	0.156672i	−0.941754	+	0.336303i	$0.890823\pi$
$242$	5433.49	−	20278.1i	0.0927787	−	0.346255i
$243$	−21187.9	+	12232.9i	−0.358819	+	0.207165i
$244$	−20912.6	−	5603.51i	−0.351259	−	0.0941196i
$245$	−29551.3	+	29551.3i	−0.492317	+	0.492317i
$246$	−130875.	+	35067.7i	−2.16264	+	0.579479i
$247$	105084.	−	60670.4i	1.72244	−	0.994451i
$248$	30138.1			0.490018
$249$		−	126943.i		−	2.04744i
$250$	41455.6	−	23934.4i	0.663290	−	0.382951i
$251$	−6373.78	−	6373.78i	−0.101169	−	0.101169i	0.654710	−	0.755880i	$-0.272791\pi$
$251$	−6373.78	−	6373.78i	−0.101169	−	0.101169i	−0.755880	+	0.654710i	$0.772791\pi$
$252$	−25550.4	−	14751.5i	−0.402342	−	0.232293i
$253$	−28968.3	−	28968.3i	−0.452566	−	0.452566i
$254$	−8275.45	+	2217.40i	−0.128270	+	0.0343698i
$255$	12199.2	−	21129.6i	0.187608	−	0.324946i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	32125.3	+	8607.94i	0.486386	+	0.130327i	0.493674	−	0.869647i	$-0.335653\pi$
$257$	32125.3	+	8607.94i	0.486386	+	0.130327i	−0.00728881	+	0.999973i	$0.502320\pi$
$258$			113279.i			1.70181i
$259$	−29474.0	−	1691.90i	−0.439379	−	0.0252218i
$260$	44114.0			0.652575
$261$	−18909.2	+	70570.1i	−0.277583	+	1.03595i
$262$	−10118.4	−	5841.88i	−0.147404	−	0.0851040i
$263$	2089.26	+	1206.24i	0.0302052	+	0.0174390i	0.515027	−	0.857174i	$-0.327782\pi$
$263$	2089.26	+	1206.24i	0.0302052	+	0.0174390i	−0.484821	+	0.874613i	$0.661115\pi$
$264$	7898.99	+	29479.4i	0.113335	+	0.422972i
$265$	−13955.5	+	13955.5i	−0.198725	+	0.198725i
$266$	−14487.2	+	25092.5i	−0.204748	+	0.354634i
$267$	−57327.3	+	57327.3i	−0.804153	+	0.804153i
$268$	−20305.6	−	35170.4i	−0.282713	−	0.489674i
$269$	−58633.5			−0.810291			−0.405145	−	0.914252i	$-0.632779\pi$
$269$	−58633.5			−0.810291			−0.405145	+	0.914252i	$0.632779\pi$
$270$			87247.7i			1.19681i
$271$	41087.1	+	71164.9i	0.559457	+	0.969008i	0.997542	+	0.0700744i	$0.0223237\pi$
$271$	41087.1	+	71164.9i	0.559457	+	0.969008i	−0.438085	+	0.898934i	$0.644343\pi$
$272$	−1179.31	−	4401.25i	−0.0159401	−	0.0594892i
$273$	61835.0	+	61835.0i	0.829677	+	0.829677i
$274$	−14670.2	+	54750.0i	−0.195405	+	0.729260i
$275$	−6754.11	−	11698.5i	−0.0893105	−	0.154690i
$276$	−59149.6	−	15849.1i	−0.776487	−	0.208059i
$277$	−41044.1	+	10997.7i	−0.534923	+	0.143332i	−0.516160	−	0.856492i	$-0.672639\pi$
$277$	−41044.1	+	10997.7i	−0.534923	+	0.143332i	−0.0187621	+	0.999824i	$0.505973\pi$
$278$	−27120.0	−	101213.i	−0.350913	−	1.30963i
$279$	58952.6	−	220014.i	0.757347	−	2.82646i
$280$	−9122.49	+	5266.87i	−0.116358	+	0.0671795i
$281$	−125058.	−	33509.2i	−1.58379	−	0.424376i	−0.643696	−	0.765282i	$-0.722600\pi$
$281$	−125058.	−	33509.2i	−1.58379	−	0.424376i	−0.940098	+	0.340905i	$0.889266\pi$
$282$	−1344.46	+	1344.46i	−0.0169064	+	0.0169064i
$283$	−35615.7	+	9543.21i	−0.444702	+	0.119158i	−0.474219	−	0.880407i	$-0.657270\pi$
$283$	−35615.7	+	9543.21i	−0.444702	+	0.119158i	0.0295174	+	0.999564i	$0.490603\pi$
$284$	−44231.8	+	25537.3i	−0.548401	+	0.316619i
$285$	162790.			2.00418
$286$		−	61385.2i		−	0.750467i
$287$	−56355.5	+	32536.9i	−0.684183	+	0.395013i
$288$	21889.5	+	21889.5i	0.263907	+	0.263907i
$289$	−67941.6	−	39226.1i	−0.813467	−	0.469656i
$290$	18445.0	+	18445.0i	0.219322	+	0.219322i
$291$	−145057.	+	38867.9i	−1.71298	+	0.458992i
$292$	24083.2	−	41713.2i	0.282454	−	0.489225i
$293$	−5063.08	+	8769.50i	−0.0589765	+	0.102150i	−0.894006	−	0.448055i	$-0.852117\pi$
$293$	−5063.08	+	8769.50i	−0.0589765	+	0.102150i	0.835030	+	0.550205i	$0.185450\pi$
$294$	83964.1	+	22498.1i	0.971402	+	0.260286i
$295$		−	73135.6i		−	0.840398i
$296$	29412.8	+	9719.01i	0.335701	+	0.110927i
$297$	121406.			1.37635
$298$	1914.91	−	7146.56i	0.0215634	−	0.0804757i
$299$	106666.	+	61583.8i	1.19312	+	0.688849i
$300$	−17486.4	−	10095.7i	−0.194293	−	0.112175i
$301$	14081.2	+	52551.9i	0.155420	+	0.580036i
$302$	−3652.37	+	3652.37i	−0.0400462	+	0.0400462i
$303$	138787.	−	240385.i	1.51169	−	2.61832i
$304$	21497.3	−	21497.3i	0.232614	−	0.232614i
$305$	29210.7	+	50594.4i	0.314009	+	0.543879i
$306$	−34436.9			−0.367774
$307$		−	53438.5i		−	0.566993i	−0.958973	−	0.283497i	$-0.908506\pi$
$307$		−	53438.5i		−	0.566993i	0.958973	−	0.283497i	$-0.0914944\pi$
$308$	7328.92	+	12694.1i	0.0772571	+	0.133813i
$309$	42710.0	+	159396.i	0.447314	+	1.66940i
$310$	−57505.4	−	57505.4i	−0.598391	−	0.598391i
$311$	30150.9	−	112525.i	0.311730	−	1.16339i	−0.615265	−	0.788320i	$-0.710951\pi$
$311$	30150.9	−	112525.i	0.311730	−	1.16339i	0.926995	−	0.375073i	$-0.122382\pi$
$312$	−45878.0	−	79463.0i	−0.471298	−	0.816312i
$313$	185526.	+	49711.5i	1.89372	+	0.507421i	0.998030	+	0.0627444i	$0.0199853\pi$
$313$	185526.	+	49711.5i	1.89372	+	0.507421i	0.895691	+	0.444677i	$0.146681\pi$
$314$	113965.	−	30536.7i	1.15587	−	0.309715i
$315$	20604.9	+	76898.5i	0.207658	+	0.774992i
$316$	−10462.9	+	39047.9i	−0.104779	+	0.391042i
$317$	14447.4	−	8341.22i	0.143771	−	0.0830063i	−0.426389	−	0.904540i	$-0.640215\pi$
$317$	14447.4	−	8341.22i	0.143771	−	0.0830063i	0.570160	+	0.821534i	$0.306881\pi$
$318$	39651.6	+	10624.6i	0.392108	+	0.105065i
$319$	25666.4	−	25666.4i	0.252223	−	0.252223i
$320$	10676.1	−	2860.65i	0.104259	−	0.0279360i
$321$	−125070.	+	72209.3i	−1.21379	+	0.700782i
$322$	−29410.5			−0.283655
$323$			33819.7i			0.324164i
$324$	61190.8	−	35328.5i	0.582903	−	0.336539i
$325$	28717.2	+	28717.2i	0.271879	+	0.271879i
$326$	68159.5	+	39351.9i	0.641344	+	0.370280i
$327$	143839.	+	143839.i	1.34518	+	1.34518i
$328$	65953.0	−	17672.1i	0.613037	−	0.164263i
$329$	−456.592	+	790.840i	−0.00421829	+	0.00730629i
$330$	41176.9	−	71320.5i	0.378116	−	0.654917i
$331$	−187861.	−	50337.3i	−1.71467	−	0.459445i	−0.738111	−	0.674679i	$-0.764282\pi$
$331$	−187861.	−	50337.3i	−1.71467	−	0.459445i	−0.976563	+	0.215233i	$0.930949\pi$
$332$			63971.9i			0.580381i
$333$	128485.	−	195708.i	1.15868	−	1.76490i
$334$	85381.5			0.765369
$335$	−28362.9	+	105852.i	−0.252732	+	0.943210i
$336$	18974.5	+	10954.9i	0.168071	+	0.0970358i
$337$	67112.4	+	38747.4i	0.590939	+	0.341179i	0.765469	−	0.643473i	$-0.222507\pi$
$337$	67112.4	+	38747.4i	0.590939	+	0.341179i	−0.174529	+	0.984652i	$0.555840\pi$
$338$	26857.9	+	100235.i	0.235093	+	0.877378i
$339$	−207724.	+	207724.i	−1.80754	+	1.80754i
$340$	−6147.66	+	10648.1i	−0.0531805	+	0.0921113i
$341$	−80019.4	+	80019.4i	−0.688155	+	0.688155i
$342$	−114884.	−	198985.i	−0.982217	−	1.70125i
$343$	93526.4			0.794961
$344$		−	57086.0i		−	0.482406i
$345$	82620.2	+	143102.i	0.694142	+	1.20229i
$346$	−16501.5	−	61584.4i	−0.137839	−	0.514421i
$347$	−37720.2	−	37720.2i	−0.313267	−	0.313267i	0.532907	−	0.846174i	$-0.321100\pi$
$347$	−37720.2	−	37720.2i	−0.313267	−	0.313267i	−0.846174	+	0.532907i	$0.821100\pi$
$348$	14042.6	−	52407.7i	0.115955	−	0.432749i
$349$	−33282.1	−	57646.4i	−0.273250	−	0.473283i	0.696442	−	0.717613i	$-0.254765\pi$
$349$	−33282.1	−	57646.4i	−0.273250	−	0.473283i	−0.969692	+	0.244330i	$0.921432\pi$
$350$	−9367.13	−	2509.91i	−0.0764664	−	0.0204891i
$351$	−352569.	+	94470.5i	−2.86174	+	0.766800i
$352$	−3980.62	−	14855.9i	−0.0321267	−	0.119898i
$353$	−19606.3	+	73171.7i	−0.157343	+	0.587210i	0.841551	+	0.540178i	$0.181643\pi$
$353$	−19606.3	+	73171.7i	−0.157343	+	0.587210i	−0.998893	+	0.0470324i	$0.985024\pi$
$354$	−131740.	+	76060.1i	−1.05126	+	0.606946i
$355$	133124.	+	35670.4i	1.05633	+	0.283043i
$356$	28889.5	−	28889.5i	0.227951	−	0.227951i
$357$	−23542.7	+	6308.25i	−0.184723	+	0.0494963i
$358$	−73627.7	+	42509.0i	−0.574480	+	0.331676i
$359$	121559.			0.943190			0.471595	−	0.881815i	$-0.343678\pi$
$359$	121559.			0.943190			0.471595	+	0.881815i	$0.343678\pi$
$360$		−	83533.3i		−	0.644547i
$361$	−82557.8	+	47664.8i	−0.633496	+	0.365749i
$362$	7152.61	+	7152.61i	0.0545817	+	0.0545817i
$363$	102042.	+	58914.0i	0.774401	+	0.447100i
$364$	−31161.2	−	31161.2i	−0.235186	−	0.235186i
$365$	−125544.	+	33639.3i	−0.942344	+	0.252500i
$366$	60757.4	−	105235.i	0.453562	−	0.785593i
$367$	14675.0	−	25417.8i	0.108955	−	0.188715i	−0.806392	−	0.591381i	$-0.798583\pi$
$367$	14675.0	−	25417.8i	0.108955	−	0.188715i	0.915347	+	0.402666i	$0.131916\pi$
$368$	29807.9	+	7987.00i	0.220108	+	0.0589778i
$369$		−	516039.i		−	3.78992i
$370$	−37577.0	−	74665.9i	−0.274485	−	0.545405i
$371$	19715.6			0.143240
$372$	−43780.1	+	163390.i	−0.316367	+	1.18070i
$373$	−221805.	−	128059.i	−1.59424	−	0.920436i	−0.992568	−	0.121695i	$-0.961167\pi$
$373$	−221805.	−	128059.i	−1.59424	−	0.920436i	−0.601675	−	0.798741i	$-0.705500\pi$
$374$	14816.9	+	8554.55i	0.105929	+	0.0611581i
$375$	69536.8	+	259515.i	0.494484	+	1.84544i
$376$	677.530	−	677.530i	0.00479239	−	0.00479239i
$377$	−54564.4	+	94508.3i	−0.383908	+	0.664947i
$378$	61629.8	−	61629.8i	0.431328	−	0.431328i
$379$	29127.1	+	50449.7i	0.202777	+	0.351220i	0.949422	−	0.314002i	$-0.101670\pi$
$379$	29127.1	+	50449.7i	0.202777	+	0.351220i	−0.746645	+	0.665223i	$0.768337\pi$
$380$	−82036.3			−0.568118
$381$		−	48085.4i		−	0.331256i
$382$	90174.7	+	156187.i	0.617957	+	1.07033i
$383$	39260.9	+	146524.i	0.267647	+	0.998873i	0.960610	+	0.277900i	$0.0896382\pi$
$383$	39260.9	+	146524.i	0.267647	+	0.998873i	−0.692963	+	0.720973i	$0.743695\pi$
$384$	−16255.9	−	16255.9i	−0.110242	−	0.110242i
$385$	10237.0	−	38205.1i	0.0690641	−	0.257751i
$386$	60731.8	+	105190.i	0.407607	+	0.705995i
$387$	−416740.	−	111665.i	−2.78255	−	0.745582i
$388$	73100.1	−	19587.1i	0.485573	−	0.130109i
$389$	30291.7	+	113050.i	0.200181	+	0.747087i	0.990864	+	0.134861i	$0.0430589\pi$
$389$	30291.7	+	113050.i	0.200181	+	0.747087i	−0.790683	+	0.612226i	$0.790274\pi$
$390$	−64082.4	+	239159.i	−0.421318	+	1.57238i
$391$	−29729.7	+	17164.4i	−0.194463	+	0.112273i
$392$	−42312.9	−	11337.7i	−0.275360	−	0.0737825i
$393$	46369.6	−	46369.6i	0.300226	−	0.300226i
$394$	−147835.	+	39612.3i	−0.952325	+	0.255175i
$395$	94469.7	−	54542.1i	0.605478	−	0.349573i
$396$	−116238.			−0.741235
$397$		−	43050.6i		−	0.273148i	−0.990630	−	0.136574i	$-0.956391\pi$
$397$		−	43050.6i		−	0.273148i	0.990630	−	0.136574i	$-0.0436092\pi$
$398$	150900.	−	87122.2i	0.952628	−	0.550000i
$399$	−114991.	−	114991.i	−0.722300	−	0.722300i
$400$	8812.08	+	5087.66i	0.0550755	+	0.0317979i
$401$	21173.2	+	21173.2i	0.131674	+	0.131674i	0.769872	−	0.638198i	$-0.220320\pi$
$401$	21173.2	+	21173.2i	0.131674	+	0.131674i	−0.638198	+	0.769872i	$0.720320\pi$
$402$	220169.	−	58994.0i	1.36240	−	0.365053i
$403$	170114.	−	294646.i	1.04744	−	1.81422i
$404$	−69940.2	+	121140.i	−0.428513	+	0.742206i
$405$	−184165.	−	49346.9i	−1.12279	−	0.300850i
$406$		−	26058.2i		−	0.158086i
$407$	−103899.	+	52288.8i	−0.627221	+	0.315660i
$408$	25573.9			0.153630
$409$	45786.1	−	170876.i	0.273708	−	1.02149i	−0.682995	−	0.730423i	$-0.739323\pi$
$409$	45786.1	−	170876.i	0.273708	−	1.02149i	0.956702	−	0.291068i	$-0.0940105\pi$
$410$	−159562.	−	92123.2i	−0.949209	−	0.548026i
$411$	−275509.	−	159065.i	−1.63100	−	0.941655i
$412$	−21523.3	−	80326.0i	−0.126799	−	0.473219i
$413$	−51661.4	+	51661.4i	−0.302877	+	0.302877i
$414$	116614.	−	201981.i	0.680375	−	1.17844i
$415$	122062.	−	122062.i	0.708738	−	0.708738i
$416$	23119.8	+	40044.7i	0.133597	+	0.231397i
$417$	588110.			3.38210
$418$			114155.i			0.653342i
$419$	−66013.7	−	114339.i	−0.376015	−	0.651278i	0.614463	−	0.788946i	$-0.289373\pi$
$419$	−66013.7	−	114339.i	−0.376015	−	0.651278i	−0.990478	+	0.137668i	$0.956039\pi$
$420$	−15301.9	−	57107.4i	−0.0867453	−	0.323738i
$421$	186639.	+	186639.i	1.05302	+	1.05302i	0.998513	+	0.0545078i	$0.0173590\pi$
$421$	186639.	+	186639.i	1.05302	+	1.05302i	0.0545078	+	0.998513i	$0.482641\pi$
$422$	16275.7	−	60741.8i	0.0913936	−	0.341085i
$423$	−3620.80	−	6271.41i	−0.0202360	−	0.0350497i
$424$	−19982.0	−	5354.17i	−0.111150	−	0.0297825i
$425$	−10933.6	+	2929.65i	−0.0605321	+	0.0162195i
$426$	−74193.5	−	276894.i	−0.408834	−	1.52579i
$427$	15105.0	−	56372.5i	0.0828445	−	0.309180i
$428$	63028.0	−	36389.2i	0.344069	−	0.198648i
$429$	332792.	+	89171.4i	1.80825	+	0.484519i
$430$	−108924.	+	108924.i	−0.589095	+	0.589095i
$431$	111290.	−	29820.1i	0.599103	−	0.160529i	0.0534927	−	0.998568i	$-0.482965\pi$
$431$	111290.	−	29820.1i	0.599103	−	0.160529i	0.545610	+	0.838039i	$0.316298\pi$
$432$	−79199.3	+	45725.8i	−0.424379	+	0.245015i
$433$	−179261.			−0.956114			−0.478057	−	0.878329i	$-0.658659\pi$
$433$	−179261.			−0.956114			−0.478057	+	0.878329i	$0.658659\pi$
$434$			81241.0i			0.431316i
$435$	−126791.	+	73203.0i	−0.670056	+	0.386857i
$436$	−72486.4	−	72486.4i	−0.381315	−	0.381315i
$437$	−198361.	−	114524.i	−1.03871	−	0.599699i
$438$	191159.	+	191159.i	0.996428	+	0.996428i
$439$	−125960.	+	33750.9i	−0.653589	+	0.175129i	−0.570351	−	0.821401i	$-0.693193\pi$
$439$	−125960.	+	33750.9i	−0.653589	+	0.175129i	−0.0832378	+	0.996530i	$0.526526\pi$
$440$	−20750.7	+	35941.3i	−0.107183	+	0.185647i
$441$	−165535.	+	286716.i	−0.851165	+	1.47426i
$442$	−49685.5	−	13313.2i	−0.254323	−	0.0681456i
$443$			181957.i			0.927174i	0.886052	+	0.463587i	$0.153438\pi$
$443$			181957.i			0.927174i	−0.886052	+	0.463587i	$0.846562\pi$
$444$	−95416.9	+	145339.i	−0.484016	+	0.737254i
$445$	−110246.			−0.556729
$446$	−52029.8	+	194178.i	−0.261567	+	0.976180i
$447$	35962.5	+	20762.9i	0.179984	+	0.103914i
$448$	−9562.04	−	5520.64i	−0.0476425	−	0.0275064i
$449$	−24501.6	−	91441.2i	−0.121535	−	0.453575i	0.878157	−	0.478372i	$-0.158773\pi$
$449$	−24501.6	−	91441.2i	−0.121535	−	0.453575i	−0.999693	+	0.0247967i	$0.992106\pi$
$450$	54378.2	−	54378.2i	0.268534	−	0.268534i
$451$	−128190.	+	222032.i	−0.630235	+	1.09160i
$452$	104681.	−	104681.i	0.512378	−	0.512378i
$453$	−14495.2	−	25106.5i	−0.0706365	−	0.122346i
$454$	125291.			0.607864
$455$			118915.i			0.574399i
$456$	85316.6	+	147773.i	0.410302	+	0.710665i
$457$	−79075.8	−	295115.i	−0.378627	−	1.41305i	−0.847973	−	0.530040i	$-0.822177\pi$
$457$	−79075.8	−	295115.i	−0.378627	−	1.41305i	0.469346	−	0.883015i	$-0.344490\pi$
$458$	−5113.00	−	5113.00i	−0.0243750	−	0.0243750i
$459$	26330.5	−	98266.8i	0.124978	−	0.466425i
$460$	−41635.7	−	72115.1i	−0.196766	−	0.340809i
$461$	−99739.3	−	26725.1i	−0.469315	−	0.125753i	0.0164081	−	0.999865i	$-0.494777\pi$
$461$	−99739.3	−	26725.1i	−0.469315	−	0.125753i	−0.485723	+	0.874113i	$0.661444\pi$
$462$	−79465.6	+	21292.7i	−0.372302	+	0.0997580i
$463$	38820.7	+	144881.i	0.181093	+	0.675848i	0.995433	+	0.0954604i	$0.0304323\pi$
$463$	38820.7	+	144881.i	0.181093	+	0.675848i	−0.814340	+	0.580388i	$0.802901\pi$
$464$	−7076.63	+	26410.3i	−0.0328693	+	0.122670i
$465$	395293.	−	228223.i	1.82816	−	1.05549i
$466$	−167000.	−	44747.6i	−0.769034	−	0.206062i
$467$	117038.	−	117038.i	0.536651	−	0.536651i	−0.385892	−	0.922544i	$-0.626106\pi$
$467$	117038.	−	117038.i	0.536651	−	0.536651i	0.922544	+	0.385892i	$0.126106\pi$
$468$	337559.	−	90448.6i	1.54119	−	0.412962i
$469$	94806.2	−	54736.4i	0.431013	−	0.248846i
$470$	−2585.54			−0.0117046
$471$			662204.i			2.98504i
$472$	66389.1	−	38329.8i	0.297998	−	0.172049i
$473$	151569.	+	151569.i	0.677465	+	0.677465i
$474$	−196494.	−	113446.i	−0.874568	−	0.504932i
$475$	−53403.7	−	53403.7i	−0.236692	−	0.236692i
$476$	11864.1	−	3178.98i	0.0523627	−	0.0140305i
$477$	−78173.2	+	135400.i	−0.343574	+	0.595088i
$478$	−68394.5	+	118463.i	−0.299340	+	0.518473i
$479$	−185004.	−	49571.8i	−0.806327	−	0.216055i	−0.167967	−	0.985793i	$-0.553720\pi$
$479$	−185004.	−	49571.8i	−0.806327	−	0.216055i	−0.638360	+	0.769738i	$0.720387\pi$
$480$			62034.5i			0.269247i
$481$	261038.	−	232696.i	1.12827	−	1.00577i
$482$	26645.7			0.114692
$483$	42723.3	−	159445.i	0.183134	−	0.683467i
$484$	−51423.1	−	29689.1i	−0.219517	−	0.126738i
$485$	−176853.	−	102106.i	−0.751847	−	0.434079i
$486$	17910.1	+	66841.6i	0.0758275	+	0.282992i
$487$	172222.	−	172222.i	0.726159	−	0.726159i	−0.243694	−	0.969852i	$-0.578359\pi$
$487$	172222.	−	172222.i	0.726159	−	0.726159i	0.969852	+	0.243694i	$0.0783592\pi$
$488$	−30618.1	+	53032.2i	−0.128570	+	0.222689i
$489$	−312353.	+	312353.i	−1.30626	+	1.30626i
$490$	59102.7	+	102369.i	0.246159	+	0.426359i
$491$	396124.			1.64312			0.821559	−	0.570124i	$-0.193105\pi$
$491$	396124.			1.64312			0.821559	+	0.570124i	$0.193105\pi$
$492$			383227.i			1.58317i
$493$	−15208.0	−	26341.1i	−0.0625718	−	0.108378i
$494$	−88827.7	−	331509.i	−0.363994	−	1.35844i
$495$	221789.	+	221789.i	0.905168	+	0.905168i
$496$	22062.6	−	82338.7i	0.0896795	−	0.334688i
$497$	−68838.9	−	119232.i	−0.278690	−	0.482705i
$498$	−346815.	−	92928.9i	−1.39843	−	0.374707i
$499$	169361.	−	45380.1i	0.680161	−	0.182249i	0.0978333	−	0.995203i	$-0.468809\pi$
$499$	169361.	−	45380.1i	0.680161	−	0.182249i	0.582327	+	0.812954i	$0.302142\pi$
$500$	−35042.4	−	130780.i	−0.140170	−	0.523121i
$501$	−124030.	+	462885.i	−0.494140	+	1.84416i
$502$	−22079.4	+	12747.6i	−0.0876153	+	0.0505847i
$503$	241274.	+	64649.2i	0.953618	+	0.255521i	0.701897	−	0.712279i	$-0.252337\pi$
$503$	241274.	+	64649.2i	0.953618	+	0.255521i	0.251721	+	0.967800i	$0.419003\pi$
$504$	−59006.0	+	59006.0i	−0.232293	+	0.232293i
$505$	364593.	−	97692.4i	1.42964	−	0.383070i
$506$	−100349.	+	57936.6i	−0.391933	+	0.226283i
$507$	−582427.			−2.26582
$508$			24232.2i			0.0939000i
$509$	152742.	−	88185.6i	0.589553	−	0.340379i	−0.175368	−	0.984503i	$-0.556111\pi$
$509$	152742.	−	88185.6i	0.589553	−	0.340379i	0.764921	+	0.644124i	$0.222778\pi$
$510$	−48796.7	−	48796.7i	−0.187608	−	0.187608i
$511$	112443.	+	64919.2i	0.430618	+	0.248617i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	655651.	−	175681.i	2.49137	−	0.667561i
$514$	47034.7	−	81466.5i	0.178029	−	0.308356i
$515$	−112199.	+	194335.i	−0.423035	+	0.732718i
$516$	309484.	+	82926.1i	1.16236	+	0.311453i
$517$			3597.81i			0.0134604i
$518$	−26198.8	+	79285.9i	−0.0976388	+	0.295486i
$519$	357843.			1.32849
$520$	32293.7	−	120522.i	0.119429	−	0.445717i
$521$	−78718.8	−	45448.3i	−0.290003	−	0.167434i	0.347940	−	0.937517i	$-0.386881\pi$
$521$	−78718.8	−	45448.3i	−0.290003	−	0.167434i	−0.637943	+	0.770083i	$0.720215\pi$
$522$	178959.	+	103322.i	0.656767	+	0.379185i
$523$	−21173.3	−	79020.0i	−0.0774080	−	0.288891i	0.916361	−	0.400354i	$-0.131113\pi$
$523$	−21173.3	−	79020.0i	−0.0774080	−	0.288891i	−0.993769	+	0.111463i	$0.964446\pi$
$524$	−23367.5	+	23367.5i	−0.0851040	+	0.0851040i
$525$	27214.4	−	47136.7i	0.0987370	−	0.171017i
$526$	4824.95	−	4824.95i	0.0174390	−	0.0174390i
$527$	47413.5	+	82122.7i	0.170719	+	0.295694i
$528$	86321.8			0.309637
$529$			47345.0i			0.169185i
$530$	27910.9	+	48343.1i	0.0993624	+	0.172101i
$531$	−149953.	−	559631.i	−0.531820	−	1.98478i
$532$	57948.6	+	57948.6i	0.204748	+	0.204748i
$533$	199499.	−	744541.i	0.702242	−	2.62080i
$534$	114655.	+	198587.i	0.402076	+	0.696417i
$535$	−189694.	−	50828.4i	−0.662746	−	0.177582i
$536$	−110952.	+	29729.5i	−0.386194	+	0.103480i
$537$	−123501.	−	460914.i	−0.428276	−	1.59835i
$538$	−42922.7	+	160190.i	−0.148294	+	0.553439i
$539$	142447.	−	82242.1i	0.490317	−	0.283085i
$540$	238365.	+	63869.7i	0.817439	+	0.219032i
$541$	−133198.	+	133198.i	−0.455098	+	0.455098i	−0.897042	−	0.441945i	$-0.854289\pi$
$541$	−133198.	+	133198.i	−0.455098	+	0.455098i	0.441945	+	0.897042i	$0.354289\pi$
$542$	224504.	−	60155.7i	0.764233	−	0.204776i
$543$	−49167.2	+	28386.7i	−0.166754	+	0.0962754i
$544$	−12887.7			−0.0435491
$545$			276617.i			0.931293i
$546$	214203.	−	123670.i	0.718521	−	0.414839i
$547$	−109219.	−	109219.i	−0.365025	−	0.365025i	0.500634	−	0.865659i	$-0.333100\pi$
$547$	−109219.	−	109219.i	−0.365025	−	0.365025i	−0.865659	+	0.500634i	$0.833100\pi$
$548$	138840.	+	80159.5i	0.462333	+	0.266928i
$549$	327254.	+	327254.i	1.08578	+	1.08578i
$550$	−36905.1	+	9888.70i	−0.122000	+	0.0326899i
$551$	101470.	−	175752.i	0.334222	−	0.578890i
$552$	−86601.1	+	149997.i	−0.284214	+	0.492273i
$553$	−105259.	−	28203.9i	−0.344197	−	0.0922273i
$554$			120185.i			0.391590i
$555$	459378.	−	95255.1i	1.49137	−	0.309245i
$556$	−296373.			−0.958713
$557$	100899.	−	376560.i	0.325219	−	1.21373i	−0.588872	−	0.808226i	$-0.700428\pi$
$557$	100899.	−	376560.i	0.325219	−	1.21373i	0.914091	−	0.405508i	$-0.132905\pi$
$558$	−557934.	−	322123.i	−1.79190	−	1.03455i
$559$	−558103.	−	322221.i	−1.78604	−	1.03117i
$560$	7711.24	+	28778.7i	0.0245894	+	0.0917689i
$561$	−67901.2	+	67901.2i	−0.215751	+	0.215751i
$562$	−183097.	+	317134.i	−0.579709	+	1.00408i
$563$	−342627.	+	342627.i	−1.08095	+	1.08095i	−0.0845268	+	0.996421i	$0.526938\pi$
$563$	−342627.	+	342627.i	−1.08095	+	1.08095i	−0.996421	+	0.0845268i	$0.973062\pi$
$564$	2688.93	+	4657.36i	0.00845319	+	0.0146414i
$565$	−399475.			−1.25139
$566$			104290.i			0.325544i
$567$	95232.5	+	164948.i	0.296223	+	0.513074i
$568$	37389.1	+	139538.i	0.115891	+	0.432510i
$569$	−135904.	−	135904.i	−0.419767	−	0.419767i	0.465356	−	0.885123i	$-0.345926\pi$
$569$	−135904.	−	135904.i	−0.419767	−	0.419767i	−0.885123	+	0.465356i	$0.845926\pi$
$570$	119170.	−	444750.i	0.366791	−	1.36888i
$571$	−4479.51	−	7758.74i	−0.0137391	−	0.0237968i	0.859074	−	0.511851i	$-0.171040\pi$
$571$	−4479.51	−	7758.74i	−0.0137391	−	0.0237968i	−0.872813	+	0.488054i	$0.837707\pi$
$572$	−167708.	−	44937.1i	−0.512579	−	0.137345i
$573$	−977741.	+	261985.i	−2.97793	+	0.797934i
$574$	47637.3	+	177785.i	0.144585	+	0.539598i
$575$	19841.4	−	74049.0i	0.0600117	−	0.223967i
$576$	75827.6	−	43779.1i	0.228551	−	0.131954i
$577$	−143413.	−	38427.3i	−0.430760	−	0.115422i	0.0369227	−	0.999318i	$-0.488244\pi$
$577$	−143413.	−	38427.3i	−0.430760	−	0.115422i	−0.467683	+	0.883896i	$0.654911\pi$
$578$	−156904.	+	156904.i	−0.469656	+	0.469656i
$579$	−658499.	+	176444.i	−1.96426	+	0.526321i
$580$	63895.3	−	36890.0i	0.189938	−	0.109661i
$581$	−172444.			−0.510854
$582$			424756.i			1.25399i
$583$	67270.0	−	38838.4i	0.197918	−	0.114268i
$584$	−96332.6	−	96332.6i	−0.282454	−	0.282454i
$585$	−816665.	−	471502.i	−2.38634	−	1.37775i
$586$	20252.3	+	20252.3i	0.0589765	+	0.0589765i
$587$	305670.	−	81904.1i	0.887109	−	0.237700i	0.213637	−	0.976913i	$-0.431469\pi$
$587$	305670.	−	81904.1i	0.887109	−	0.237700i	0.673472	+	0.739213i	$0.264802\pi$
$588$	122932.	−	212924.i	0.355558	−	0.615844i
$589$	−316350.	+	547935.i	−0.911880	+	1.57942i
$590$	−199810.	−	53539.0i	−0.574003	−	0.153804i
$591$		−	859013.i		−	2.45937i
$592$	48084.5	−	73242.4i	0.137202	−	0.208987i
$593$	174574.			0.496444			0.248222	−	0.968703i	$-0.420154\pi$
$593$	174574.			0.496444			0.248222	+	0.968703i	$0.420154\pi$
$594$	88875.5	−	331688.i	0.251889	−	0.940063i
$595$	−28703.2	−	16571.8i	−0.0810768	−	0.0468097i
$596$	−18122.9	−	10463.3i	−0.0510195	−	0.0294561i
$597$	253117.	+	944644.i	0.710186	+	2.65045i
$598$	246335.	−	246335.i	0.688849	−	0.688849i
$599$	192009.	−	332569.i	0.535141	−	0.926891i	−0.464016	−	0.885827i	$-0.653592\pi$
$599$	192009.	−	332569.i	0.535141	−	0.926891i	0.999157	−	0.0410642i	$-0.0130748\pi$
$600$	−40383.0	+	40383.0i	−0.112175	+	0.112175i
$601$	307764.	+	533062.i	0.852056	+	1.47580i	0.879349	+	0.476177i	$0.157978\pi$
$601$	307764.	+	533062.i	0.852056	+	1.47580i	−0.0272929	+	0.999627i	$0.508689\pi$
$602$	153883.			0.424616
$603$			868126.i			2.38753i
$604$	7304.74	+	12652.2i	0.0200231	+	0.0346810i
$605$	41469.8	+	154767.i	0.113298	+	0.422833i
$606$	−555146.	−	555146.i	−1.51169	−	1.51169i
$607$	−90260.7	+	336857.i	−0.244975	+	0.914258i	0.728422	+	0.685129i	$0.240254\pi$
$607$	−90260.7	+	336857.i	−0.244975	+	0.914258i	−0.973396	+	0.229129i	$0.926412\pi$
$608$	−42994.5	−	74468.7i	−0.116307	−	0.201450i
$609$	141272.	+	37853.6i	0.380908	+	0.102064i
$610$	159610.	−	42767.4i	0.428944	−	0.114935i
$611$	−2799.58	−	10448.2i	−0.00749913	−	0.0279871i
$612$	−25209.5	+	94083.3i	−0.0673073	+	0.251194i
$613$	79666.5	−	45995.5i	0.212009	−	0.122404i	−0.390236	−	0.920715i	$-0.627606\pi$
$613$	79666.5	−	45995.5i	0.212009	−	0.122404i	0.602245	+	0.798311i	$0.294273\pi$
$614$	−145997.	−	39119.7i	−0.387263	−	0.103767i
$615$	731222.	−	731222.i	1.93330	−	1.93330i
$616$	40045.9	−	10730.3i	0.105535	−	0.0282781i
$617$	−526542.	+	303999.i	−1.38313	+	0.798550i	−0.992529	−	0.122010i	$-0.961066\pi$
$617$	−526542.	+	303999.i	−1.38313	+	0.798550i	−0.390601	+	0.920560i	$0.627733\pi$
$618$	466743.			1.22208
$619$			268422.i			0.700546i	0.936648	+	0.350273i	$0.113911\pi$
$619$			268422.i			0.700546i	−0.936648	+	0.350273i	$0.886089\pi$
$620$	−199204.	+	115011.i	−0.518222	+	0.299195i
$621$	487196.	+	487196.i	1.26334	+	1.26334i
$622$	−285351.	−	164747.i	−0.737562	−	0.425832i
$623$	77875.4	+	77875.4i	0.200643	+	0.200643i
$624$	−250682.	+	67170.1i	−0.643805	+	0.172507i
$625$	−132990.	+	230345.i	−0.340453	+	0.589682i
$626$	271629.	−	470475.i	0.693150	−	1.20057i
$627$	−618874.	−	165827.i	−1.57423	−	0.421813i
$628$		−	333711.i		−	0.846158i
$629$	19789.4	+	95436.4i	0.0500185	+	0.241220i
$630$	225175.			0.567333
$631$	3298.13	−	12308.8i	0.00828340	−	0.0309141i	−0.961660	−	0.274243i	$-0.911573\pi$
$631$	3298.13	−	12308.8i	0.00828340	−	0.0309141i	0.969944	+	0.243329i	$0.0782394\pi$
$632$	99021.5	+	57170.1i	0.247911	+	0.143131i
$633$	305661.	+	176474.i	0.762839	+	0.440425i
$634$	−12212.4	−	45577.3i	−0.0303824	−	0.113389i
$635$	46236.6	−	46236.6i	0.114667	−	0.114667i
$636$	58053.9	−	100552.i	0.143522	−	0.248587i
$637$	−349678.	+	349678.i	−0.861766	+	0.861766i
$638$	−51332.8	−	88911.1i	−0.126111	−	0.218431i
$639$	1.09179e6			2.67386
$640$		−	31261.7i		−	0.0763226i
$641$	37672.0	+	65249.8i	0.0916860	+	0.158805i	0.908221	−	0.418492i	$-0.137441\pi$
$641$	37672.0	+	65249.8i	0.0916860	+	0.158805i	−0.816535	+	0.577296i	$0.804108\pi$
$642$	105722.	+	394559.i	0.256504	+	0.957287i
$643$	397860.	+	397860.i	0.962295	+	0.962295i	0.999315	−	0.0370200i	$-0.0117865\pi$
$643$	397860.	+	397860.i	0.962295	+	0.962295i	−0.0370200	+	0.999315i	$0.511787\pi$
$644$	−21530.0	+	80351.0i	−0.0519125	+	0.193740i
$645$	−432288.	−	748744.i	−1.03909	−	1.79976i
$646$	92397.2	+	24757.8i	0.221408	+	0.0593262i
$647$	693730.	−	185884.i	1.65723	−	0.444052i	0.695603	−	0.718426i	$-0.255137\pi$
$647$	693730.	−	185884.i	1.65723	−	0.444052i	0.961623	+	0.274374i	$0.0884707\pi$
$648$	−51724.5	−	193039.i	−0.123182	−	0.459721i
$649$	−74500.2	+	278038.i	−0.176876	+	0.660109i
$650$	99479.3	−	57434.4i	0.235454	−	0.135939i
$651$	−440438.	−	118015.i	−1.03926	−	0.278468i
$652$	157408.	−	157408.i	0.370280	−	0.370280i
$653$	327415.	−	87730.6i	0.767843	−	0.205743i	0.146425	−	0.989222i	$-0.453223\pi$
$653$	327415.	−	87730.6i	0.767843	−	0.205743i	0.621418	+	0.783479i	$0.286557\pi$
$654$	498273.	−	287678.i	1.16496	−	0.672592i
$655$	89173.4			0.207851
$656$		−	193124.i		−	0.448775i
$657$	−891683.	+	514814.i	−2.06576	+	1.19267i
$658$	1826.37	+	1826.37i	0.00421829	+	0.00421829i
$659$	−494696.	−	285613.i	−1.13912	−	0.657669i	−0.192904	−	0.981218i	$-0.561791\pi$
$659$	−494696.	−	285613.i	−1.13912	−	0.657669i	−0.946212	+	0.323549i	$0.895124\pi$
$660$	−164708.	−	164708.i	−0.378116	−	0.378116i
$661$	689050.	−	184630.i	1.57706	−	0.422572i	0.639045	−	0.769169i	$-0.279330\pi$
$661$	689050.	−	184630.i	1.57706	−	0.422572i	0.938014	+	0.346597i	$0.112663\pi$
$662$	−275048.	+	476397.i	−0.627614	+	1.08706i
$663$	144352.	−	250024.i	0.328394	−	0.568794i
$664$	174774.	+	46830.7i	0.396407	+	0.106217i
$665$		−	221139.i		−	0.500061i
$666$	−440627.	−	494295.i	−0.993398	−	1.11439i
$667$	205996.			0.463027
$668$	62503.6	−	233267.i	0.140072	−	0.522757i
$669$	−977130.	−	564146.i	−2.18323	−	1.26049i
$670$	268429.	+	154978.i	0.597971	+	0.345239i
$671$	−59511.4	−	222099.i	−0.132177	−	0.493290i
$672$	43819.8	−	43819.8i	0.0970358	−	0.0970358i
$673$	325418.	−	563640.i	0.718474	−	1.24443i	−0.243130	−	0.969994i	$-0.578174\pi$
$673$	325418.	−	563640.i	0.718474	−	1.24443i	0.961604	−	0.274440i	$-0.0884926\pi$
$674$	154989.	−	154989.i	0.341179	−	0.341179i
$675$	113592.	+	196748.i	0.249311	+	0.431819i
$676$	293509.			0.642285
$677$			580336.i			1.26620i	0.774070	+	0.633100i	$0.218218\pi$
$677$			580336.i			1.26620i	−0.774070	+	0.633100i	$0.781782\pi$
$678$	415449.	+	719579.i	0.903771	+	1.56538i
$679$	52799.6	+	197051.i	0.114522	+	0.427404i
$680$	24590.7	+	24590.7i	0.0531805	+	0.0531805i
$681$	−182004.	+	679247.i	−0.392451	+	1.46465i
$682$	160039.	+	277195.i	0.344078	+	0.595960i
$683$	93149.4	+	24959.3i	0.199682	+	0.0535046i	0.357274	−	0.934000i	$-0.383706\pi$
$683$	93149.4	+	24959.3i	0.199682	+	0.0535046i	−0.157592	+	0.987504i	$0.550373\pi$
$684$	−627738.	+	168202.i	−1.34173	+	0.359516i
$685$	−111967.	−	417866.i	−0.238621	−	0.890544i
$686$	68466.1	−	255519.i	0.145488	−	0.542969i
$687$	35146.9	−	20292.1i	0.0744686	−	0.0429945i
$688$	−155962.	−	41789.8i	−0.329489	−	0.0882864i
$689$	−165133.	+	165133.i	−0.347854	+	0.347854i
$690$	451445.	−	120964.i	0.948215	−	0.254073i
$691$	−375694.	+	216907.i	−0.786826	+	0.454274i	−0.838844	−	0.544372i	$-0.816768\pi$
$691$	−375694.	+	216907.i	−0.786826	+	0.454274i	0.0520182	+	0.998646i	$0.483435\pi$
$692$	−180332.			−0.376582
$693$		−	313333.i		−	0.652439i
$694$	−130667.	+	75440.3i	−0.271297	+	0.156634i
$695$	565498.	+	565498.i	1.17074	+	1.17074i
$696$	−132901.	−	76730.1i	−0.274352	−	0.158397i
$697$	151912.	+	151912.i	0.312700	+	0.312700i
$698$	−181857.	+	48728.4i	−0.373267	+	0.100017i
$699$	485187.	−	840368.i	0.993012	−	1.71995i
$700$	−13714.4	+	23754.1i	−0.0279886	+	0.0484777i
$701$	−63539.8	−	17025.4i	−0.129303	−	0.0346467i	0.193587	−	0.981083i	$-0.437988\pi$
$701$	−63539.8	−	17025.4i	−0.129303	−	0.0346467i	−0.322890	+	0.946436i	$0.604654\pi$
$702$			1.03239e6i			2.09494i
$703$	−485437.	+	432731.i	−0.982250	+	0.875604i
$704$	−43501.1			−0.0877717
$705$	3755.89	−	14017.2i	0.00755675	−	0.0282022i
$706$	185556.	+	107131.i	0.372276	+	0.214934i
$707$	−326548.	−	188533.i	−0.653294	−	0.377179i
$708$	111360.	+	415600.i	0.222158	+	0.829104i
$709$	−323873.	+	323873.i	−0.644292	+	0.644292i	−0.951608	−	0.307316i	$-0.900569\pi$
$709$	−323873.	+	323873.i	−0.644292	+	0.644292i	0.307316	+	0.951608i	$0.400569\pi$
$710$	194907.	−	337589.i	0.386643	−	0.669686i
$711$	611048.	−	611048.i	1.20875	−	1.20875i
$712$	−57779.1	−	100076.i	−0.113975	−	0.197411i
$713$	−642226.			−1.26331
$714$			68937.8i			0.135226i
$715$	234254.	+	405740.i	0.458221	+	0.793662i
$716$	62237.4	+	232273.i	0.121402	+	0.453078i
$717$	−542877.	−	542877.i	−1.05600	−	1.05600i
$718$	88987.5	−	332106.i	0.172616	−	0.644211i
$719$	58296.8	+	100973.i	0.112768	+	0.195320i	0.916885	−	0.399150i	$-0.130695\pi$
$719$	58296.8	+	100973.i	0.112768	+	0.195320i	−0.804117	+	0.594471i	$0.797362\pi$
$720$	−228217.	−	61150.6i	−0.440234	−	0.117960i
$721$	216529.	−	58018.8i	0.416529	−	0.111609i
$722$	69786.0	+	260445.i	0.133873	+	0.499622i
$723$	−38707.0	+	144457.i	−0.0740479	+	0.276351i
$724$	24777.4	−	14305.2i	0.0472692	−	0.0272909i
$725$	65608.8	+	17579.8i	0.124821	+	0.0334456i
$726$	235656.	−	235656.i	0.447100	−	0.447100i
$727$	−268499.	+	71944.2i	−0.508012	+	0.136121i	−0.503716	−	0.863869i	$-0.668034\pi$
$727$	−268499.	+	71944.2i	−0.508012	+	0.136121i	−0.00429628	+	0.999991i	$0.501368\pi$
$728$	−107945.	+	62322.3i	−0.203677	+	0.117593i
$729$	327012.			0.615331
$730$			367618.i			0.689844i
$731$	155553.	−	89808.3i	0.291100	−	0.168067i
$732$	−243030.	−	243030.i	−0.453562	−	0.453562i
$733$	745442.	+	430381.i	1.38741	+	0.801023i	0.993023	−	0.117920i	$-0.0376225\pi$
$733$	745442.	+	430381.i	1.38741	+	0.801023i	0.394390	+	0.918943i	$0.370956\pi$
$734$	−58699.9	−	58699.9i	−0.108955	−	0.108955i
$735$	−640835.	+	171711.i	−1.18624	+	0.317851i
$736$	43641.8	−	75589.8i	0.0805651	−	0.139543i
$737$	215653.	−	373522.i	0.397028	−	0.687673i
$738$	−1.40984e6	−	377767.i	−2.58856	−	0.693603i
$739$		−	249552.i		−	0.456953i	−0.973549	−	0.228477i	$-0.926626\pi$
$739$		−	249552.i		−	0.456953i	0.973549	−	0.228477i	$-0.0733744\pi$
$740$	−231499.	+	48002.9i	−0.422753	+	0.0876606i
$741$	1.92627e6			3.50818
$742$	14432.9	−	53864.1i	0.0262147	−	0.0978345i
$743$	436633.	+	252090.i	0.790931	+	0.456644i	0.840290	−	0.542137i	$-0.182385\pi$
$743$	436633.	+	252090.i	0.790931	+	0.456644i	−0.0493593	+	0.998781i	$0.515718\pi$
$744$	414340.	+	239219.i	0.748533	+	0.432165i
$745$	14615.1	+	54544.4i	0.0263324	+	0.0982737i
$746$	−512237.	+	512237.i	−0.920436	+	0.920436i
$747$	683747.	−	1.18429e6i	1.22533	−	2.12234i
$748$	34218.2	−	34218.2i	0.0611581	−	0.0611581i
$749$	98091.7	+	169900.i	0.174851	+	0.302851i
$750$	759913.			1.35096
$751$		−	125536.i		−	0.222581i	−0.993788	−	0.111291i	$-0.964502\pi$
$751$		−	125536.i		−	0.222581i	0.993788	−	0.111291i	$-0.0354984\pi$
$752$	−1355.06	−	2347.03i	−0.00239620	−	0.00415034i
$753$	−37035.5	−	138219.i	−0.0653174	−	0.243768i
$754$	218258.	+	218258.i	0.383908	+	0.383908i
$755$	10203.3	−	38079.1i	0.0178997	−	0.0668025i
$756$	−123260.	−	213492.i	−0.215664	−	0.373541i
$757$	−192951.	−	51701.2i	−0.336710	−	0.0902212i	0.0865024	−	0.996252i	$-0.472431\pi$
$757$	−192951.	−	51701.2i	−0.336710	−	0.0902212i	−0.423213	+	0.906030i	$0.639098\pi$
$758$	159154.	−	42645.1i	0.276999	−	0.0742216i
$759$	−168323.	−	628191.i	−0.292187	−	1.09046i
$760$	−60054.7	+	224127.i	−0.103973	+	0.388032i
$761$	−119653.	+	69081.7i	−0.206612	+	0.119287i	−0.599736	−	0.800198i	$-0.704728\pi$
$761$	−119653.	+	69081.7i	−0.206612	+	0.119287i	0.393124	+	0.919485i	$0.371394\pi$
$762$	−131372.	−	35201.0i	−0.226252	−	0.0606240i
$763$	195396.	−	195396.i	0.335635	−	0.335635i
$764$	492724.	−	132025.i	0.844144	−	0.226188i
$765$	227618.	−	131416.i	0.388942	−	0.224556i
$766$	429051.			0.731226
$767$		−	865406.i		−	1.47106i
$768$	−56312.0	+	32511.8i	−0.0954726	+	0.0551211i
$769$	−334643.	−	334643.i	−0.565886	−	0.565886i	0.365087	−	0.930973i	$-0.381039\pi$
$769$	−334643.	−	334643.i	−0.565886	−	0.565886i	−0.930973	+	0.365087i	$0.881039\pi$
$770$	−96884.3	−	55936.2i	−0.163407	−	0.0943433i
$771$	373335.	+	373335.i	0.628044	+	0.628044i
$772$	331844.	−	88917.5i	0.556801	−	0.149194i
$773$	340586.	−	589912.i	0.569990	−	0.987252i	−0.426576	−	0.904452i	$-0.640280\pi$
$773$	340586.	−	589912.i	0.569990	−	0.987252i	0.996566	−	0.0828003i	$-0.0263863\pi$
$774$	−610149.	+	1.05681e6i	−1.01848	+	1.76407i
$775$	−204547.	−	54808.1i	−0.340556	−	0.0912517i
$776$		−	214052.i		−	0.355464i
$777$	−391781.	−	257208.i	−0.648935	−	0.426033i
$778$	331033.			0.546906
$779$	−370997.	+	1.38458e6i	−0.611358	+	2.28162i
$780$	606482.	+	350153.i	0.996848	+	0.575530i
$781$	−469759.	−	271215.i	−0.770145	−	0.444644i
$782$	25130.5	+	93788.3i	0.0410949	+	0.153368i
$783$	−431665.	+	431665.i	−0.704081	+	0.704081i
$784$	−61950.4	+	107301.i	−0.100789	+	0.174571i
$785$	−636743.	+	636743.i	−1.03330	+	1.03330i
$786$	−92739.1	−	160629.i	−0.150113	−	0.260003i
$787$	−401631.			−0.648452			−0.324226	−	0.945980i	$-0.605104\pi$
$787$	−401631.			−0.648452			−0.324226	+	0.945980i	$0.605104\pi$
$788$			432891.i			0.697151i
$789$	19148.9	+	33166.8i	0.0307602	+	0.0532782i
$790$	−79855.2	−	298024.i	−0.127953	−	0.477525i
$791$	282180.	+	282180.i	0.450997	+	0.450997i
$792$	−85091.8	+	317567.i	−0.135655	+	0.506273i
$793$	345647.	+	598678.i	0.549650	+	0.952022i
$794$	−117616.	−	31515.2i	−0.186564	−	0.0499896i
$795$	−302631.	+	81089.7i	−0.478828	+	0.128301i
$796$	−127556.	−	476045.i	−0.201314	−	0.751314i
$797$	230523.	−	860324.i	0.362909	−	1.35440i	−0.507324	−	0.861756i	$-0.669365\pi$
$797$	230523.	−	860324.i	0.362909	−	1.35440i	0.870233	−	0.492640i	$-0.163968\pi$
$798$	−398340.	+	229982.i	−0.625530	+	0.361150i
$799$	2912.09	+	780.291i	0.00456153	+	0.00122226i
$800$	20350.6	−	20350.6i	0.0317979	−	0.0317979i
$801$	−843599.	+	226042.i	−1.31483	+	0.352309i
$802$	73346.3	−	42346.5i	0.114033	−	0.0658368i
$803$	511544.			0.793327
$804$		−	644699.i		−	0.997343i
$805$	194395.	−	112234.i	0.299981	−	0.173194i
$806$	−680455.	−	680455.i	−1.04744	−	1.04744i
$807$	−806096.	−	465400.i	−1.23777	−	0.714626i
$808$	279761.	+	279761.i	0.428513	+	0.428513i
$809$	161720.	−	43332.6i	0.247096	−	0.0662092i	−0.133145	−	0.991097i	$-0.542508\pi$
$809$	161720.	−	43332.6i	0.247096	−	0.0662092i	0.380241	+	0.924887i	$0.375841\pi$
$810$	−269636.	+	467024.i	−0.410968	+	0.711818i
$811$	−5559.95	+	9630.12i	−0.00845336	+	0.0146416i	−0.870221	−	0.492661i	$-0.836024\pi$
$811$	−5559.95	+	9630.12i	−0.00845336	+	0.0146416i	0.861768	+	0.507303i	$0.169357\pi$
$812$	−71192.5	−	19076.0i	−0.107975	−	0.0289317i
$813$			1.30451e6i			1.97363i
$814$	66796.6	+	322134.i	0.100811	+	0.486170i
$815$	−600687.			−0.904343
$816$	18721.4	−	69869.3i	0.0281163	−	0.104932i
$817$	1.03787e6	+	599215.i	1.55489	+	0.897715i
$818$	−433324.	−	250180.i	−0.647599	−	0.373892i
$819$	243816.	+	909932.i	0.363491	+	1.35657i
$820$	−368493.	+	368493.i	−0.548026	+	0.548026i
$821$	−492837.	+	853618.i	−0.731167	+	1.26642i	0.225218	+	0.974308i	$0.427691\pi$
$821$	−492837.	+	853618.i	−0.731167	+	1.26642i	−0.956385	+	0.292110i	$0.905643\pi$
$822$	−636261.	+	636261.i	−0.941655	+	0.941655i
$823$	265830.	+	460431.i	0.392468	+	0.679775i	0.992774	−	0.119995i	$-0.0382879\pi$
$823$	265830.	+	460431.i	0.392468	+	0.679775i	−0.600306	+	0.799770i	$0.704955\pi$
$824$	−235211.			−0.346420
$825$		−	214441.i		−	0.315065i
$826$	103323.	+	178960.i	0.151438	+	0.262299i
$827$	−68128.9	−	254261.i	−0.0996140	−	0.371765i	0.898065	−	0.439864i	$-0.144973\pi$
$827$	−68128.9	−	254261.i	−0.0996140	−	0.371765i	−0.997679	+	0.0680991i	$0.978307\pi$
$828$	−466455.	−	466455.i	−0.680375	−	0.680375i
$829$	1081.36	−	4035.70i	0.00157348	−	0.00587232i	−0.965135	−	0.261754i	$-0.915699\pi$
$829$	1081.36	−	4035.70i	0.00157348	−	0.00587232i	0.966708	+	0.255882i	$0.0823658\pi$
$830$	−244125.	−	422837.i	−0.354369	−	0.613785i
$831$	−651570.	−	174588.i	−0.943537	−	0.252820i
$832$	126329.	−	33849.7i	0.182497	−	0.0489000i
$833$	−35673.2	−	133134.i	−0.0514106	−	0.191867i
$834$	430527.	−	1.60675e6i	0.618968	−	2.31002i
$835$	−564348.	+	325827.i	−0.809421	+	0.467319i
$836$	311876.	+	83566.9i	0.446241	+	0.119570i
$837$	1.34579e6	−	1.34579e6i	1.92099	−	1.92099i
$838$	−360705.	+	96650.7i	−0.513647	+	0.137631i
$839$	−56804.5	+	32796.1i	−0.0806973	+	0.0465906i	−0.539806	−	0.841790i	$-0.681502\pi$
$839$	−56804.5	+	32796.1i	−0.0806973	+	0.0465906i	0.459108	+	0.888380i	$0.348169\pi$
$840$	−167222.			−0.236993
$841$		−	524765.i		−	0.741947i
$842$	646535.	−	373277.i	0.911943	−	0.526511i
$843$	−1.45333e6	−	1.45333e6i	−2.04507	−	2.04507i
$844$	−154035.	−	88932.2i	−0.216239	−	0.124846i
$845$	−560034.	−	560034.i	−0.784333	−	0.784333i
$846$	−19784.4	+	5301.22i	−0.0276429	+	0.00740688i
$847$	80030.9	−	138618.i	0.111555	−	0.193220i
$848$	−29255.7	+	50672.4i	−0.0406836	+	0.0704661i
$849$	−565396.	−	151497.i	−0.784399	−	0.210179i
$850$			32015.9i			0.0443126i
$851$	−626771.	−	207107.i	−0.865465	−	0.285980i
$852$	−810802.			−1.11695
$853$	186231.	−	695023.i	0.255949	−	0.955215i	−0.711611	−	0.702574i	$-0.752034\pi$
$853$	186231.	−	695023.i	0.255949	−	0.955215i	0.967560	−	0.252641i	$-0.0812992\pi$
$854$	−142955.	−	82535.1i	−0.196012	−	0.113168i
$855$	1.51870e6	+	876824.i	2.07750	+	1.19945i
$856$	−53277.5	−	198834.i	−0.0727104	−	0.271359i
$857$	695178.	−	695178.i	0.946529	−	0.946529i	−0.0521119	−	0.998641i	$-0.516595\pi$
$857$	695178.	−	695178.i	0.946529	−	0.946529i	0.998641	+	0.0521119i	$0.0165952\pi$
$858$	487242.	−	843927.i	0.661866	−	1.14639i
$859$	−57024.4	+	57024.4i	−0.0772813	+	0.0772813i	−0.744691	−	0.667410i	$-0.767403\pi$
$859$	−57024.4	+	57024.4i	−0.0772813	+	0.0772813i	0.667410	+	0.744691i	$0.267403\pi$
$860$	217847.	+	377323.i	0.294548	+	0.510171i
$861$	−1.03304e6			−1.39351
$862$		−	325880.i		−	0.438574i
$863$	334819.	+	579923.i	0.449561	+	0.778662i	0.998357	−	0.0572941i	$-0.0182473\pi$
$863$	334819.	+	579923.i	0.449561	+	0.778662i	−0.548797	+	0.835956i	$0.684914\pi$
$864$	66947.2	+	249850.i	0.0896819	+	0.334697i
$865$	344084.	+	344084.i	0.459867	+	0.459867i
$866$	−131228.	+	489750.i	−0.174981	+	0.653038i
$867$	−622710.	−	1.07857e6i	−0.828414	−	1.43486i
$868$	221954.	+	59472.5i	0.294594	+	0.0789363i
$869$	−414703.	+	111119.i	−0.549159	+	0.147147i
$870$	107177.	+	399989.i	0.141599	+	0.528456i
$871$	−335615.	+	1.25253e6i	−0.442390	+	1.65102i
$872$	−251100.	+	144973.i	−0.330228	+	0.190657i
$873$	−1.56262e6	−	418704.i	−2.05034	−	0.549387i
$874$	−458095.	+	458095.i	−0.599699	+	0.599699i
$875$	352535.	−	94461.3i	0.460453	−	0.123378i
$876$	662193.	−	382317.i	0.862932	−	0.498214i
$877$	339432.			0.441320			0.220660	−	0.975351i	$-0.429179\pi$
$877$	339432.			0.441320			0.220660	+	0.975351i	$0.429179\pi$
$878$			368837.i			0.478460i
$879$	−139215.	+	80375.8i	−0.180181	+	0.104027i
$880$	83002.8	+	83002.8i	0.107183	+	0.107183i
$881$	−385361.	−	222488.i	−0.496496	−	0.286652i	0.230770	−	0.973008i	$-0.425876\pi$
$881$	−385361.	−	222488.i	−0.496496	−	0.286652i	−0.727265	+	0.686357i	$0.759209\pi$
$882$	662141.	+	662141.i	0.851165	+	0.851165i
$883$	−414151.	+	110971.i	−0.531174	+	0.142328i	−0.514430	−	0.857532i	$-0.671997\pi$
$883$	−414151.	+	110971.i	−0.531174	+	0.142328i	−0.0167437	+	0.999860i	$0.505330\pi$
$884$	−72744.6	+	125997.i	−0.0930886	+	0.161234i
$885$	580510.	−	1.00547e6i	0.741179	−	1.28376i
$886$	497115.	+	133202.i	0.633271	+	0.169685i
$887$		−	329892.i		−	0.419300i	−0.977776	−	0.209650i	$-0.932768\pi$
$887$		−	329892.i		−	0.419300i	0.977776	−	0.209650i	$-0.0672325\pi$
$888$	327224.	+	367080.i	0.414973	+	0.465516i
$889$	−65321.0			−0.0826512
$890$	−80705.8	+	301198.i	−0.101888	+	0.380253i
$891$	649869.	+	375202.i	0.818598	+	0.472618i
$892$	492415.	+	284296.i	0.618873	+	0.357307i
$893$	5206.22	+	19429.9i	0.00652859	+	0.0243650i
$894$	83051.8	−	83051.8i	0.103914	−	0.103914i
$895$	324439.	−	561945.i	0.405030	−	0.701533i
$896$	−22082.6	+	22082.6i	−0.0275064	+	0.0275064i
$897$	977636.	+	1.69332e6i	1.21505	+	2.10452i
$898$	−267758.			−0.332040
$899$		−	569024.i		−	0.704063i
$900$	−108756.	−	188371.i	−0.134267	−	0.232557i
$901$	−16846.5	−	62872.0i	−0.0207520	−	0.0774475i
$902$	512762.	+	512762.i	0.630235	+	0.630235i
$903$	−223538.	+	834255.i	−0.274142	+	1.02311i
$904$	−209362.	−	362625.i	−0.256189	−	0.443732i
$905$	−74572.1	−	19981.5i	−0.0910498	−	0.0243967i
$906$	−79203.5	+	21222.5i	−0.0964912	+	0.0258548i
$907$	−88886.5	−	331729.i	−0.108049	−	0.403245i	0.890624	−	0.454740i	$-0.150268\pi$
$907$	−88886.5	−	331729.i	−0.108049	−	0.403245i	−0.998673	+	0.0514954i	$0.983601\pi$
$908$	91719.0	−	342300.i	0.111247	−	0.415179i
$909$	2.58955e6	−	1.49508e6i	3.13398	−	1.80940i
$910$	324882.	+	87051.8i	0.392322	+	0.105122i
$911$	350788.	−	350788.i	0.422676	−	0.422676i	−0.463448	−	0.886124i	$-0.653388\pi$
$911$	350788.	−	350788.i	0.422676	−	0.422676i	0.886124	+	0.463448i	$0.153388\pi$
$912$	466179.	−	124912.i	0.560484	−	0.150181i
$913$	−588382.	+	339703.i	−0.705859	+	0.407528i
$914$	−864157.			−1.03443
$915$			927432.i			1.10775i
$916$	−17711.9	+	10226.0i	−0.0211094	+	0.0121875i
$917$	−62990.1	−	62990.1i	−0.0749089	−	0.0749089i
$918$	−249195.	−	143873.i	−0.295701	−	0.170723i
$919$	−486669.	−	486669.i	−0.576239	−	0.576239i	0.357626	−	0.933865i	$-0.383586\pi$
$919$	−486669.	−	486669.i	−0.576239	−	0.576239i	−0.933865	+	0.357626i	$0.883586\pi$
$920$	−227502.	+	60958.9i	−0.268787	+	0.0720213i
$921$	424165.	−	734676.i	0.500053	−	0.866117i
$922$	−146028.	+	252929.i	−0.171781	+	0.297534i
$923$	1.57524e6	+	422084.i	1.84903	+	0.495446i
$924$			232691.i			0.272544i
$925$	−181949.	−	119452.i	−0.212651	−	0.139608i
$926$	424241.			0.494755
$927$	−460093.	+	1.71709e6i	−0.535409	+	1.99817i
$928$	66974.0	+	38667.4i	0.0777696	+	0.0449003i
$929$	1.46827e6	+	847708.i	1.70128	+	0.982234i	0.944470	+	0.328597i	$0.106576\pi$
$929$	1.46827e6	+	847708.i	1.70128	+	0.982234i	0.756808	+	0.653637i	$0.226758\pi$
$930$	−334141.	−	1.24703e6i	−0.386335	−	1.44182i
$931$	650275.	−	650275.i	0.750236	−	0.750236i
$932$	−244505.	+	423496.i	−0.281486	+	0.487548i
$933$	1.30767e6	−	1.30767e6i	1.50223	−	1.50223i
$934$	−234076.	−	405431.i	−0.268326	−	0.464754i
$935$	−130581.			−0.149368
$936$		−	988440.i		−	1.12823i
$937$	−53304.5	−	92326.2i	−0.0607135	−	0.105159i	0.834071	−	0.551657i	$-0.186004\pi$
$937$	−53304.5	−	92326.2i	−0.0607135	−	0.105159i	−0.894785	+	0.446498i	$0.852671\pi$
$938$	−80139.6	−	299085.i	−0.0910839	−	0.339930i
$939$	2.15604e6	+	2.15604e6i	2.44526	+	2.44526i
$940$	−1892.75	+	7063.83i	−0.00214208	+	0.00799437i
$941$	429045.	+	743127.i	0.484533	+	0.839235i	0.999842	−	0.0177689i	$-0.00565633\pi$
$941$	429045.	+	743127.i	0.484533	+	0.839235i	−0.515309	+	0.857004i	$0.672323\pi$
$942$	1.80917e6	+	484767.i	2.03882	+	0.546300i
$943$	−1.40542e6	+	376582.i	−1.58046	+	0.423483i
$944$	−56118.7	−	209438.i	−0.0629743	−	0.235023i
$945$	−172169.	+	642543.i	−0.192793	+	0.719513i
$946$	525049.	−	303137.i	0.586702	−	0.338733i
$947$	−1.37739e6	−	369072.i	−1.53588	−	0.411539i	−0.610950	−	0.791669i	$-0.709212\pi$
$947$	−1.37739e6	−	369072.i	−1.53588	−	0.411539i	−0.924933	+	0.380130i	$0.875879\pi$
$948$	−453784.	+	453784.i	−0.504932	+	0.504932i
$949$	−1.48555e6	+	398051.i	−1.64951	+	0.441984i
$950$	−184996.	+	106807.i	−0.204981	+	0.118346i
$951$	264832.			0.292826
$952$		−	34740.6i		−	0.0383321i
$953$	699088.	−	403619.i	0.769744	−	0.444412i	−0.0630396	−	0.998011i	$-0.520079\pi$
$953$	699088.	−	403619.i	0.769744	−	0.444412i	0.832783	+	0.553599i	$0.186746\pi$
$954$	312693.	+	312693.i	0.343574	+	0.343574i
$955$	−1.19206e6	−	688236.i	−1.30705	−	0.754624i
$956$	273578.	+	273578.i	0.299340	+	0.299340i
$957$	556589.	−	149138.i	0.607730	−	0.162841i
$958$	−270865.	+	469153.i	−0.295136	+	0.511191i
$959$	−216080.	+	374262.i	−0.234951	+	0.406947i
$960$	169481.	+	45412.4i	0.183899	+	0.0492756i
$961$			850508.i			0.920941i
$962$	−444644.	−	883514.i	−0.480466	−	0.954692i
$963$	−1.55575e6			−1.67759
$964$	19506.0	−	72797.5i	0.0209901	−	0.0783362i
$965$	−802841.	−	463520.i	−0.862134	−	0.497753i
$966$	−404337.	−	233444.i	−0.433301	−	0.250166i
$967$	−332629.	−	1.24139e6i	−0.355719	−	1.32756i	−0.879577	−	0.475756i	$-0.842174\pi$
$967$	−332629.	−	1.24139e6i	−0.355719	−	1.32756i	0.523858	−	0.851806i	$-0.324492\pi$
$968$	−118757.	+	118757.i	−0.126738	+	0.126738i
$969$	−268442.	+	464956.i	−0.285893	+	0.495181i
$970$	−408425.	+	408425.i	−0.434079	+	0.434079i
$971$	450019.	+	779456.i	0.477301	+	0.826710i	0.999662	−	0.0260152i	$-0.00828181\pi$
$971$	450019.	+	779456.i	0.477301	+	0.826710i	−0.522361	+	0.852725i	$0.674948\pi$
$972$	195726.			0.207165
$973$		−	798910.i		−	0.843864i
$974$	−344445.	−	596596.i	−0.363079	−	0.628872i
$975$	166864.	+	622746.i	0.175531	+	0.655092i
$976$	122473.	+	122473.i	0.128570	+	0.128570i
$977$	240414.	−	897238.i	0.251867	−	0.939980i	−0.717940	−	0.696105i	$-0.754915\pi$
$977$	240414.	−	897238.i	0.251867	−	0.939980i	0.969807	−	0.243875i	$-0.0784186\pi$
$978$	624707.	+	1.08202e6i	0.653128	+	1.13125i
$979$	419121.	+	112303.i	0.437294	+	0.117173i
$980$	322943.	−	86532.3i	0.336259	−	0.0901003i
$981$	567158.	+	2.11666e6i	0.589340	+	2.19945i
$982$	289983.	−	1.08223e6i	0.300711	−	1.12227i
$983$	−564812.	+	326094.i	−0.584517	+	0.337471i	−0.762926	−	0.646485i	$-0.776238\pi$
$983$	−564812.	+	326094.i	−0.584517	+	0.337471i	0.178410	+	0.983956i	$0.442905\pi$
$984$	1.04700e6	+	280542.i	1.08132	+	0.289739i
$985$	825985.	−	825985.i	0.851333	−	0.851333i
$986$	−83098.1	+	22266.1i	−0.0854747	+	0.0229029i
$987$	−12554.5	+	7248.34i	−0.0128874	+	0.00744054i
$988$	−970727.			−0.994451
$989$			1.21647e6i			1.24368i
$990$	768299.	−	443577.i	0.783898	−	0.452584i
$991$	−93432.8	−	93432.8i	−0.0951376	−	0.0951376i	0.657936	−	0.753074i	$-0.271430\pi$
$991$	−93432.8	−	93432.8i	−0.0951376	−	0.0951376i	−0.753074	+	0.657936i	$0.771430\pi$
$992$	−208803.	−	120552.i	−0.212184	−	0.122504i
$993$	−2.18318e6	−	2.18318e6i	−2.21407	−	2.21407i
$994$	−376143.	+	100787.i	−0.380697	+	0.102008i
$995$	−664939.	+	1.15171e6i	−0.671639	+	1.16331i
$996$	−507773.	+	879489.i	−0.511860	+	0.886567i
$997$	1.42946e6	+	383023.i	1.43808	+	0.385331i	0.891860	−	0.452312i	$-0.149401\pi$
$997$	1.42946e6	+	383023.i	1.43808	+	0.385331i	0.546217	+	0.837644i	$0.316067\pi$
$998$		−	495923.i		−	0.497912i
$999$	1.74739e6	−	879407.i	1.75089	−	0.881168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.g.a.29.7	yes	28
37.23	odd	12	inner	74.5.g.a.23.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.g.a.23.7	✓	28	37.23	odd	12	inner
74.5.g.a.29.7	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.732051 - 2.73205i) q^{2} +(13.7481 + 7.93744i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(5.58720 + 20.8517i) q^{5} +(31.7498 - 31.7498i) q^{6} +(10.7825 - 18.6759i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(85.5060 + 148.101i) q^{9} +O(q^{10})\)	\(q+(0.732051 - 2.73205i) q^{2} +(13.7481 + 7.93744i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(5.58720 + 20.8517i) q^{5} +(31.7498 - 31.7498i) q^{6} +(10.7825 - 18.6759i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(85.5060 + 148.101i) q^{9} +61.0580 q^{10} -84.9630i q^{11} +(-63.4995 - 109.984i) q^{12} +(66.1127 + 246.736i) q^{13} +(-43.1300 - 43.1300i) q^{14} +(-88.6961 + 331.019i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-68.7695 - 18.4267i) q^{17} +(467.213 - 125.189i) q^{18} +(-122.946 - 458.841i) q^{19} +(44.6976 - 166.814i) q^{20} +(296.477 - 171.171i) q^{21} +(-232.123 - 62.1972i) q^{22} +(340.952 - 340.952i) q^{23} +(-346.968 + 92.9698i) q^{24} +(137.689 - 79.4947i) q^{25} +722.494 q^{26} +1428.93i q^{27} +(-149.407 + 86.2601i) q^{28} +(302.089 + 302.089i) q^{29} +(839.429 + 484.645i) q^{30} +(-941.814 - 941.814i) q^{31} +(174.851 - 46.8513i) q^{32} +(674.389 - 1168.08i) q^{33} +(-100.686 + 174.392i) q^{34} +(449.668 + 120.488i) q^{35} -1368.10i q^{36} +(-615.430 - 1222.87i) q^{37} -1343.58 q^{38} +(-1049.53 + 3916.91i) q^{39} +(-423.023 - 244.232i) q^{40} +(-2613.28 - 1508.78i) q^{41} +(-250.612 - 935.296i) q^{42} +(-1783.94 + 1783.94i) q^{43} +(-339.852 + 588.641i) q^{44} +(-2610.41 + 2610.41i) q^{45} +(-681.903 - 1181.09i) q^{46} -42.3456 q^{47} +1015.99i q^{48} +(967.975 + 1676.58i) q^{49} +(-116.388 - 434.367i) q^{50} +(-799.186 - 799.186i) q^{51} +(528.902 - 1973.89i) q^{52} +(457.121 + 791.757i) q^{53} +(3903.91 + 1046.05i) q^{54} +(1771.62 - 474.705i) q^{55} +(126.294 + 471.334i) q^{56} +(1951.75 - 7284.04i) q^{57} +(1046.47 - 604.179i) q^{58} +(-3272.46 - 876.854i) q^{59} +(1938.58 - 1938.58i) q^{60} +(2614.07 - 700.438i) q^{61} +(-3262.54 + 1883.63i) q^{62} +3687.88 q^{63} -512.000i q^{64} +(-4775.49 + 2757.13i) q^{65} +(-2697.56 - 2697.56i) q^{66} +(4396.29 + 2538.20i) q^{67} +(402.742 + 402.742i) q^{68} +(7393.71 - 1981.14i) q^{69} +(658.359 - 1140.31i) q^{70} +(3192.16 - 5528.98i) q^{71} +(-3737.71 - 1001.52i) q^{72} +6020.79i q^{73} +(-3791.46 + 786.185i) q^{74} +2523.94 q^{75} +(-983.568 + 3670.73i) q^{76} +(-1586.76 - 916.114i) q^{77} +(9932.88 + 5734.75i) q^{78} +(-1307.86 - 4880.99i) q^{79} +(-976.929 + 976.929i) q^{80} +(-4416.06 + 7648.85i) q^{81} +(-6035.12 + 6035.12i) q^{82} +(-3998.24 - 6925.16i) q^{83} -2738.74 q^{84} -1536.92i q^{85} +(3567.87 + 6179.74i) q^{86} +(1755.32 + 6550.96i) q^{87} +(1359.41 + 1359.41i) q^{88} +(-1321.79 + 4932.98i) q^{89} +(5220.83 + 9042.74i) q^{90} +(5320.87 + 1425.72i) q^{91} +(-3725.99 + 998.376i) q^{92} +(-5472.52 - 20423.7i) q^{93} +(-30.9991 + 115.690i) q^{94} +(8880.69 - 5127.27i) q^{95} +(2775.74 + 743.758i) q^{96} +(-6689.12 + 6689.12i) q^{97} +(5289.11 - 1417.21i) q^{98} +(12583.1 - 7264.85i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9 - 72 * q^10 + 80 * q^12 + 248 * q^13 - 192 * q^14 - 852 * q^15 + 896 * q^16 + 1092 * q^17 + 1112 * q^18 - 320 * q^19 + 336 * q^20 - 858 * q^21 - 112 * q^22 + 2348 * q^23 + 160 * q^24 - 162 * q^25 - 184 * q^26 + 1584 * q^28 - 1308 * q^29 + 2652 * q^30 - 3444 * q^31 + 1792 * q^32 + 1052 * q^33 + 1428 * q^34 - 580 * q^35 - 5694 * q^37 - 824 * q^38 - 6514 * q^39 - 1056 * q^40 - 12186 * q^41 - 1276 * q^42 - 6220 * q^43 + 1280 * q^44 + 12804 * q^45 - 4696 * q^46 + 15928 * q^47 - 4892 * q^49 - 10792 * q^50 - 6218 * q^51 + 1984 * q^52 - 9662 * q^53 - 9836 * q^54 + 1744 * q^55 - 3936 * q^56 + 16046 * q^57 + 13800 * q^58 - 9356 * q^59 - 3024 * q^60 - 6682 * q^61 + 16128 * q^62 + 60268 * q^63 - 28086 * q^65 - 4208 * q^66 + 28086 * q^67 - 5712 * q^68 + 19878 * q^69 - 6028 * q^70 + 680 * q^71 - 8896 * q^72 - 2420 * q^74 + 11076 * q^75 - 2560 * q^76 - 32208 * q^77 + 23436 * q^78 - 15136 * q^79 + 1152 * q^80 - 21274 * q^81 - 2608 * q^82 - 19732 * q^83 + 23936 * q^84 + 12440 * q^86 - 31624 * q^87 - 5120 * q^88 + 45940 * q^89 - 25608 * q^90 - 13106 * q^91 - 6944 * q^92 - 37734 * q^93 - 16960 * q^94 - 37458 * q^95 - 1280 * q^96 + 31792 * q^97 + 5216 * q^98 + 141456 * q^99

Introduction

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