LMFDB - Embedded newform 74.6.f.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(7,74)]

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([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, 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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	74.7
Dual form			74.6.f.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75877 + 1.36808i) q^{2} +(-13.8557 - 5.04306i) q^{3} +(12.2567 - 10.2846i) q^{4} +(11.2687 + 63.9081i) q^{5} +58.9797 q^{6} +(-40.1269 - 227.571i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-19.6009 - 16.4471i) q^{9} +O(q^{10})$	\(q+(-3.75877 + 1.36808i) q^{2} +(-13.8557 - 5.04306i) q^{3} +(12.2567 - 10.2846i) q^{4} +(11.2687 + 63.9081i) q^{5} +58.9797 q^{6} +(-40.1269 - 227.571i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-19.6009 - 16.4471i) q^{9} +(-129.788 - 224.799i) q^{10} +(69.4520 - 120.294i) q^{11} +(-221.691 + 80.6890i) q^{12} +(-515.565 + 432.610i) q^{13} +(462.163 + 800.490i) q^{14} +(166.157 - 942.321i) q^{15} +(44.4539 - 252.111i) q^{16} +(1502.60 + 1260.83i) q^{17} +(96.1761 + 35.0052i) q^{18} +(1228.43 + 447.113i) q^{19} +(795.387 + 667.409i) q^{20} +(-591.668 + 3355.52i) q^{21} +(-96.4817 + 547.175i) q^{22} +(761.300 + 1318.61i) q^{23} +(722.897 - 606.583i) q^{24} +(-1020.73 + 371.514i) q^{25} +(1346.04 - 2331.42i) q^{26} +(1980.15 + 3429.72i) q^{27} +(-2832.30 - 2376.58i) q^{28} +(-2977.19 + 5156.65i) q^{29} +(664.626 + 3769.28i) q^{30} -7894.34 q^{31} +(177.816 + 1008.44i) q^{32} +(-1568.96 + 1316.51i) q^{33} +(-7372.85 - 2683.50i) q^{34} +(14091.4 - 5128.87i) q^{35} -409.394 q^{36} +(3246.21 + 7668.51i) q^{37} -5229.09 q^{38} +(9325.19 - 3394.09i) q^{39} +(-3902.75 - 1420.48i) q^{40} +(10632.9 - 8922.08i) q^{41} +(-2366.67 - 13422.1i) q^{42} +17121.6 q^{43} +(-385.927 - 2188.70i) q^{44} +(830.225 - 1437.99i) q^{45} +(-4665.52 - 3914.84i) q^{46} +(-528.669 - 915.682i) q^{47} +(-1887.35 + 3268.99i) q^{48} +(-34384.9 + 12515.1i) q^{49} +(3328.41 - 2792.87i) q^{50} +(-14461.1 - 25047.4i) q^{51} +(-1869.90 + 10604.8i) q^{52} +(-2378.72 + 13490.4i) q^{53} +(-12135.1 - 10182.5i) q^{54} +(8470.43 + 3082.98i) q^{55} +(13897.3 + 5058.21i) q^{56} +(-14766.0 - 12390.1i) q^{57} +(4135.87 - 23455.7i) q^{58} +(-3126.40 + 17730.7i) q^{59} +(-7654.86 - 13258.6i) q^{60} +(26748.4 - 22444.6i) q^{61} +(29673.0 - 10800.1i) q^{62} +(-2956.35 + 5120.56i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-33457.1 - 28073.8i) q^{65} +(4096.26 - 7094.93i) q^{66} +(5262.80 + 29846.8i) q^{67} +31384.1 q^{68} +(-3898.51 - 22109.6i) q^{69} +(-45949.8 + 38556.5i) q^{70} +(-32833.4 - 11950.4i) q^{71} +(1538.82 - 560.084i) q^{72} +61059.2 q^{73} +(-22692.9 - 24383.1i) q^{74} +16016.4 q^{75} +(19654.9 - 7153.81i) q^{76} +(-30162.4 - 10978.2i) q^{77} +(-30407.8 + 25515.2i) q^{78} +(6854.09 + 38871.5i) q^{79} +16612.9 q^{80} +(-9060.38 - 51384.0i) q^{81} +(-27760.6 + 48082.7i) q^{82} +(5100.55 + 4279.87i) q^{83} +(27258.2 + 47212.7i) q^{84} +(-63645.0 + 110236. i) q^{85} +(-64356.0 + 23423.7i) q^{86} +(67256.4 - 56434.8i) q^{87} +(4444.93 + 7698.84i) q^{88} +(-4232.82 + 24005.5i) q^{89} +(-1153.34 + 6540.90i) q^{90} +(119137. + 99968.2i) q^{91} +(22892.4 + 8332.16i) q^{92} +(109382. + 39811.7i) q^{93} +(3239.87 + 2718.58i) q^{94} +(-14731.3 + 83545.3i) q^{95} +(2621.88 - 14869.4i) q^{96} +(-40137.4 - 69520.1i) q^{97} +(112123. - 94082.7i) q^{98} +(-3339.81 + 1215.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) $ 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−3.75877	+	1.36808i	−0.664463	+	0.241845i
$2$	−3.75877	+	1.36808i	−0.664463	+	0.241845i
$3$	−13.8557	−	5.04306i	−0.888844	−	0.323513i	−0.143070	−	0.989713i	$-0.545698\pi$
$3$	−13.8557	−	5.04306i	−0.888844	−	0.323513i	−0.745773	+	0.666200i	$0.767920\pi$
$4$	12.2567	−	10.2846i	0.383022	−	0.321394i
$5$	11.2687	+	63.9081i	0.201581	+	1.14322i	0.902730	+	0.430208i	$0.141560\pi$
$5$	11.2687	+	63.9081i	0.201581	+	1.14322i	−0.701149	+	0.713015i	$0.747329\pi$
$6$	58.9797			0.668844
$7$	−40.1269	−	227.571i	−0.309521	−	1.75538i	−0.601420	−	0.798933i	$-0.705398\pi$
$7$	−40.1269	−	227.571i	−0.309521	−	1.75538i	0.291899	−	0.956449i	$-0.405713\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	−19.6009	−	16.4471i	−0.0806620	−	0.0676834i
$10$	−129.788	−	224.799i	−0.410426	−	0.710878i
$11$	69.4520	−	120.294i	0.173063	−	0.299753i	−0.766427	−	0.642332i	$-0.777967\pi$
$11$	69.4520	−	120.294i	0.173063	−	0.299753i	0.939489	+	0.342579i	$0.111300\pi$
$12$	−221.691	+	80.6890i	−0.444422	+	0.161756i
$13$	−515.565	+	432.610i	−0.846106	+	0.709967i	−0.958928	−	0.283648i	$-0.908455\pi$
$13$	−515.565	+	432.610i	−0.846106	+	0.709967i	0.112823	+	0.993615i	$0.464011\pi$
$14$	462.163	+	800.490i	0.630195	+	1.09153i
$15$	166.157	−	942.321i	0.190673	−	1.08136i
$16$	44.4539	−	252.111i	0.0434120	−	0.246202i
$17$	1502.60	+	1260.83i	1.26102	+	1.05812i	0.995573	+	0.0939930i	$0.0299631\pi$
$17$	1502.60	+	1260.83i	1.26102	+	1.05812i	0.265444	+	0.964126i	$0.414481\pi$
$18$	96.1761	+	35.0052i	0.0699658	+	0.0254655i
$19$	1228.43	+	447.113i	0.780671	+	0.284141i	0.701452	−	0.712716i	$-0.252535\pi$
$19$	1228.43	+	447.113i	0.780671	+	0.284141i	0.0792183	+	0.996857i	$0.474758\pi$
$20$	795.387	+	667.409i	0.444635	+	0.373093i
$21$	−591.668	+	3355.52i	−0.292772	+	1.66039i
$22$	−96.4817	+	547.175i	−0.0424999	+	0.241029i
$23$	761.300	+	1318.61i	0.300080	+	0.519753i	0.976154	−	0.217080i	$-0.0696534\pi$
$23$	761.300	+	1318.61i	0.300080	+	0.519753i	−0.676074	+	0.736834i	$0.736320\pi$
$24$	722.897	−	606.583i	0.256182	−	0.214962i
$25$	−1020.73	+	371.514i	−0.326632	+	0.118884i
$26$	1346.04	−	2331.42i	0.390504	−	0.676373i
$27$	1980.15	+	3429.72i	0.522743	+	0.905418i
$28$	−2832.30	−	2376.58i	−0.682722	−	0.572872i
$29$	−2977.19	+	5156.65i	−0.657373	+	1.13860i	0.323920	+	0.946084i	$0.394999\pi$
$29$	−2977.19	+	5156.65i	−0.657373	+	1.13860i	−0.981293	+	0.192519i	$0.938334\pi$
$30$	664.626	+	3769.28i	0.134826	+	0.764638i
$31$	−7894.34			−1.47541			−0.737703	−	0.675125i	$-0.764090\pi$
$31$	−7894.34			−1.47541			−0.737703	+	0.675125i	$0.764090\pi$
$32$	177.816	+	1008.44i	0.0306970	+	0.174091i
$33$	−1568.96	+	1316.51i	−0.250799	+	0.210446i
$34$	−7372.85	−	2683.50i	−1.09380	−	0.398111i
$35$	14091.4	−	5128.87i	1.94440	−	0.707704i
$36$	−409.394			−0.0526484
$37$	3246.21	+	7668.51i	0.389828	+	0.920888i
$37$	3246.21	+	7668.51i	0.389828	+	0.920888i
$38$	−5229.09			−0.587445
$39$	9325.19	−	3394.09i	0.981739	−	0.357324i
$40$	−3902.75	−	1420.48i	−0.385674	−	0.140374i
$41$	10632.9	−	8922.08i	0.987854	−	0.828908i	0.00259828	−	0.999997i	$-0.499173\pi$
$41$	10632.9	−	8922.08i	0.987854	−	0.828908i	0.985256	+	0.171089i	$0.0547285\pi$
$42$	−2366.67	−	13422.1i	−0.207021	−	1.17408i
$43$	17121.6			1.41212			0.706061	−	0.708151i	$-0.250471\pi$
$43$	17121.6			1.41212			0.706061	+	0.708151i	$0.250471\pi$
$44$	−385.927	−	2188.70i	−0.0300520	−	0.170433i
$45$	830.225	−	1437.99i	0.0611174	−	0.105858i
$46$	−4665.52	−	3914.84i	−0.325091	−	0.272784i
$47$	−528.669	−	915.682i	−0.0349092	−	0.0604645i	0.848043	−	0.529927i	$-0.177781\pi$
$47$	−528.669	−	915.682i	−0.0349092	−	0.0604645i	−0.882952	+	0.469463i	$0.844448\pi$
$48$	−1887.35	+	3268.99i	−0.118236	+	0.204791i
$49$	−34384.9	+	12515.1i	−2.04587	+	0.744635i
$50$	3328.41	−	2792.87i	0.188283	−	0.157989i
$51$	−14461.1	−	25047.4i	−0.778532	−	1.34846i
$52$	−1869.90	+	10604.8i	−0.0958983	+	0.543866i
$53$	−2378.72	+	13490.4i	−0.116320	+	0.659683i	0.869768	+	0.493460i	$0.164268\pi$
$53$	−2378.72	+	13490.4i	−0.116320	+	0.659683i	−0.986088	+	0.166223i	$0.946843\pi$
$54$	−12135.1	−	10182.5i	−0.566314	−	0.475194i
$55$	8470.43	+	3082.98i	0.377571	+	0.137425i
$56$	13897.3	+	5058.21i	0.592190	+	0.215539i
$57$	−14766.0	−	12390.1i	−0.601971	−	0.505114i
$58$	4135.87	−	23455.7i	0.161435	−	0.915542i
$59$	−3126.40	+	17730.7i	−0.116927	+	0.663125i	0.868851	+	0.495073i	$0.164859\pi$
$59$	−3126.40	+	17730.7i	−0.116927	+	0.663125i	−0.985778	+	0.168052i	$0.946252\pi$
$60$	−7654.86	−	13258.6i	−0.274511	−	0.475466i
$61$	26748.4	−	22444.6i	0.920392	−	0.772301i	−0.0536752	−	0.998558i	$-0.517094\pi$
$61$	26748.4	−	22444.6i	0.920392	−	0.772301i	0.974067	+	0.226258i	$0.0726491\pi$
$62$	29673.0	−	10800.1i	0.980353	−	0.356819i
$63$	−2956.35	+	5120.56i	−0.0938437	+	0.162542i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−33457.1	−	28073.8i	−0.982210	−	0.824172i
$66$	4096.26	−	7094.93i	0.115752	−	0.200488i
$67$	5262.80	+	29846.8i	0.143229	+	0.812290i	0.968772	+	0.247952i	$0.0797575\pi$
$67$	5262.80	+	29846.8i	0.143229	+	0.812290i	−0.825544	+	0.564338i	$0.809131\pi$
$68$	31384.1			0.823071
$69$	−3898.51	−	22109.6i	−0.0985772	−	0.559059i
$70$	−45949.8	+	38556.5i	−1.12083	+	0.940486i
$71$	−32833.4	−	11950.4i	−0.772982	−	0.281343i	−0.0747391	−	0.997203i	$-0.523812\pi$
$71$	−32833.4	−	11950.4i	−0.772982	−	0.281343i	−0.698243	+	0.715861i	$0.746035\pi$
$72$	1538.82	−	560.084i	0.0349829	−	0.0127327i
$73$	61059.2			1.34105			0.670524	−	0.741888i	$-0.266070\pi$
$73$	61059.2			1.34105			0.670524	+	0.741888i	$0.266070\pi$
$74$	−22692.9	−	24383.1i	−0.481738	−	0.517618i
$75$	16016.4			0.328785
$76$	19654.9	−	7153.81i	0.390335	−	0.142070i
$77$	−30162.4	−	10978.2i	−0.579748	−	0.211011i
$78$	−30407.8	+	25515.2i	−0.565912	+	0.474857i
$79$	6854.09	+	38871.5i	0.123561	+	0.700751i	0.982152	+	0.188089i	$0.0602294\pi$
$79$	6854.09	+	38871.5i	0.123561	+	0.700751i	−0.858591	+	0.512662i	$0.828660\pi$
$80$	16612.9			0.290215
$81$	−9060.38	−	51384.0i	−0.153438	−	0.870192i
$82$	−27760.6	+	48082.7i	−0.455925	+	0.789686i
$83$	5100.55	+	4279.87i	0.0812684	+	0.0681923i	0.682517	−	0.730870i	$-0.260885\pi$
$83$	5100.55	+	4279.87i	0.0812684	+	0.0681923i	−0.601248	+	0.799062i	$0.705330\pi$
$84$	27258.2	+	47212.7i	0.421502	+	0.730063i
$85$	−63645.0	+	110236.i	−0.955469	+	1.65492i
$86$	−64356.0	+	23423.7i	−0.938303	+	0.341514i
$87$	67256.4	−	56434.8i	0.952654	−	0.799372i
$88$	4444.93	+	7698.84i	0.0611868	+	0.105979i
$89$	−4232.82	+	24005.5i	−0.0566441	+	0.321244i	−0.999943	−	0.0107007i	$-0.996594\pi$
$89$	−4232.82	+	24005.5i	−0.0566441	+	0.321244i	0.943299	+	0.331945i	$0.107705\pi$
$90$	−1153.34	+	6540.90i	−0.0150089	+	0.0851199i
$91$	119137.	+	99968.2i	1.50815	+	1.26549i
$92$	22892.4	+	8332.16i	0.281983	+	0.102633i
$93$	109382.	+	39811.7i	1.31141	+	0.477313i
$94$	3239.87	+	2718.58i	0.0378189	+	0.0317338i
$95$	−14731.3	+	83545.3i	−0.167468	+	0.949758i
$96$	2621.88	−	14869.4i	0.0290359	−	0.164671i
$97$	−40137.4	−	69520.1i	−0.433132	−	0.750206i	0.564009	−	0.825768i	$-0.309258\pi$
$97$	−40137.4	−	69520.1i	−0.433132	−	0.750206i	−0.997141	+	0.0755621i	$0.975925\pi$
$98$	112123.	−	94082.7i	1.17932	−	0.989565i
$99$	−3339.81	+	1215.59i	−0.0342479	+	0.0124652i
$100$	−8689.87	+	15051.3i	−0.0868987	+	0.150513i
$101$	−30857.5	−	53446.8i	−0.300994	−	0.521336i	0.675368	−	0.737481i	$-0.263985\pi$
$101$	−30857.5	−	53446.8i	−0.300994	−	0.521336i	−0.976361	+	0.216145i	$0.930652\pi$
$102$	88622.9	+	74363.4i	0.843423	+	0.707716i
$103$	254.994	−	441.663i	0.00236830	−	0.00410202i	−0.864839	−	0.502050i	$-0.832579\pi$
$103$	254.994	−	441.663i	0.00236830	−	0.00410202i	0.867207	+	0.497948i	$0.165913\pi$
$104$	−7479.62	−	42419.0i	−0.0678103	−	0.384572i
$105$	−221112.			−1.95722
$106$	−9514.89	−	53961.6i	−0.0822506	−	0.466467i
$107$	−4661.66	+	3911.59i	−0.0393623	+	0.0330289i	−0.662257	−	0.749277i	$-0.730401\pi$
$107$	−4661.66	+	3911.59i	−0.0393623	+	0.0330289i	0.622894	+	0.782306i	$0.285957\pi$
$108$	59543.4	+	21672.0i	0.491218	+	0.178789i
$109$	−144639.	+	52644.4i	−1.16606	+	0.424411i	−0.851258	−	0.524747i	$-0.824160\pi$
$109$	−144639.	+	52644.4i	−1.16606	+	0.424411i	−0.314801	+	0.949158i	$0.601938\pi$
$110$	−36056.2			−0.284117
$111$	−6305.78	−	122623.i	−0.0485771	−	0.944639i
$112$	−59156.9			−0.445615
$113$	184749.	−	67243.1i	1.36109	−	0.495395i	0.444696	−	0.895681i	$-0.353312\pi$
$113$	184749.	−	67243.1i	1.36109	−	0.495395i	0.916390	+	0.400286i	$0.131089\pi$
$114$	72452.7	+	26370.6i	0.522146	+	0.190046i
$115$	−75691.1	+	63512.4i	−0.533704	+	0.447830i
$116$	16543.5	+	93822.8i	0.114152	+	0.647386i
$117$	17220.7			0.116302
$118$	−12505.6	−	70922.7i	−0.0826797	−	0.468900i
$119$	226634.	−	392541.i	1.46709	−	2.54108i
$120$	46911.7	+	39363.6i	0.297391	+	0.249541i
$121$	70878.3	+	122765.i	0.440099	+	0.762273i
$122$	−69835.1	+	120958.i	−0.424790	+	0.735757i
$123$	−192321.	+	69999.1i	−1.14621	+	0.417186i
$124$	−96758.7	+	81190.2i	−0.565113	+	0.474186i
$125$	66151.9	+	114578.i	0.378675	+	0.655885i
$126$	4106.92	−	23291.5i	0.0230457	−	0.130699i
$127$	16003.7	−	90761.3i	0.0880461	−	0.499334i	−0.908612	−	0.417642i	$-0.862857\pi$
$127$	16003.7	−	90761.3i	0.0880461	−	0.499334i	0.996658	−	0.0816919i	$-0.0260324\pi$
$128$	12550.9	+	10531.4i	0.0677094	+	0.0568149i
$129$	−237231.	−	86345.1i	−1.25516	−	0.456839i
$130$	164165.	+	59751.0i	0.851964	+	0.310089i
$131$	−152982.	−	128368.i	−0.778867	−	0.653547i	0.164096	−	0.986444i	$-0.447529\pi$
$131$	−152982.	−	128368.i	−0.778867	−	0.653547i	−0.942963	+	0.332897i	$0.891974\pi$
$132$	−5690.46	+	32272.2i	−0.0284258	+	0.161211i
$133$	52456.8	−	297497.i	0.257142	−	1.45832i
$134$	−60614.5	−	104987.i	−0.291618	−	0.505098i
$135$	−196873.	+	165196.i	−0.929720	+	0.780127i
$136$	−117966.	+	42935.9i	−0.546900	+	0.199055i
$137$	−128329.	+	222273.i	−0.584150	+	1.01178i	0.410831	+	0.911712i	$0.365239\pi$
$137$	−128329.	+	222273.i	−0.584150	+	1.01178i	−0.994981	+	0.100066i	$0.968095\pi$
$138$	44901.3	+	77771.3i	0.200706	+	0.347634i
$139$	236486.	+	198436.i	1.03817	+	0.871130i	0.991801	−	0.127794i	$-0.0407898\pi$
$139$	236486.	+	198436.i	1.03817	+	0.871130i	0.0463714	+	0.998924i	$0.485234\pi$
$140$	119966.	−	207788.i	0.517297	−	0.895984i
$141$	2707.24	+	15353.5i	0.0114678	+	0.0650370i
$142$	139762.			0.581659
$143$	16233.6	+	92065.1i	0.0663856	+	0.376491i
$144$	−5017.82	+	4210.45i	−0.0201655	+	0.0169209i
$145$	−363101.	−	132158.i	−1.43419	−	0.522003i
$146$	−229508.	+	83533.9i	−0.891076	+	0.324325i
$147$	539542.			2.05936
$148$	118655.	+	60604.7i	0.445280	+	0.227432i
$149$	313783.			1.15788			0.578939	−	0.815371i	$-0.303467\pi$
$149$	313783.			1.15788			0.578939	+	0.815371i	$0.303467\pi$
$150$	−60202.1	+	21911.8i	−0.218466	+	0.0795150i
$151$	−429172.	−	156206.i	−1.53175	−	0.557513i	−0.567704	−	0.823233i	$-0.692168\pi$
$151$	−429172.	−	156206.i	−1.53175	−	0.557513i	−0.964050	+	0.265720i	$0.914390\pi$
$152$	−64091.4	+	53779.1i	−0.225004	+	0.188801i
$153$	−8715.27	−	49426.7i	−0.0300990	−	0.170700i
$154$	128393.			0.436253
$155$	−88959.2	−	504513.i	−0.297414	−	1.68672i
$156$	79389.2	−	137506.i	0.261186	−	0.452388i
$157$	−134158.	−	112572.i	−0.434376	−	0.364485i	0.399224	−	0.916854i	$-0.369280\pi$
$157$	−134158.	−	112572.i	−0.434376	−	0.364485i	−0.833600	+	0.552368i	$0.813724\pi$
$158$	−78942.3	−	136732.i	−0.251575	−	0.435740i
$159$	100992.	−	174923.i	0.316806	−	0.548724i
$160$	−62444.0	+	22727.7i	−0.192837	+	0.0701869i
$161$	269529.	−	226162.i	0.819484	−	0.687629i
$162$	104353.	+	180745.i	0.312405	+	0.541102i
$163$	−109559.	+	621340.i	−0.322982	+	1.83172i	0.200507	+	0.979692i	$0.435741\pi$
$163$	−109559.	+	621340.i	−0.322982	+	1.83172i	−0.523490	+	0.852032i	$0.675370\pi$
$164$	38564.6	−	218711.i	0.111964	−	0.634980i
$165$	−101816.	−	85433.8i	−0.291143	−	0.244298i
$166$	−25027.0	−	9109.09i	−0.0704918	−	0.0256569i
$167$	501778.	+	182632.i	1.39226	+	0.506741i	0.925872	−	0.377838i	$-0.123332\pi$
$167$	501778.	+	182632.i	1.39226	+	0.506741i	0.466389	+	0.884580i	$0.345555\pi$
$168$	−167048.	−	140170.i	−0.456634	−	0.383162i
$169$	14181.0	−	80424.5i	0.0381936	−	0.216607i
$170$	88414.7	−	501424.i	0.234640	−	1.33071i
$171$	−16724.7	−	28968.0i	−0.0437388	−	0.0757578i
$172$	209854.	−	176088.i	0.540874	−	0.453847i
$173$	−479245.	+	174431.i	−1.21743	+	0.443107i	−0.869274	−	0.494331i	$-0.835413\pi$
$173$	−479245.	+	174431.i	−1.21743	+	0.443107i	−0.348152	+	0.937438i	$0.613191\pi$
$174$	−175594.	+	304138.i	−0.439680	+	0.761547i
$175$	125504.	+	217380.i	0.309787	+	0.536567i
$176$	−27240.1	−	22857.2i	−0.0662868	−	0.0556212i
$177$	132735.	−	229904.i	0.318459	−	0.551587i
$178$	−16931.3	−	96022.0i	−0.0400534	−	0.227154i
$179$	−29880.8			−0.0697044			−0.0348522	−	0.999392i	$-0.511096\pi$
$179$	−29880.8			−0.0697044			−0.0348522	+	0.999392i	$0.511096\pi$
$180$	−4613.35	−	26163.6i	−0.0106129	−	0.0601888i
$181$	−105642.	+	88643.8i	−0.239684	+	0.201118i	−0.754715	−	0.656053i	$-0.772225\pi$
$181$	−105642.	+	88643.8i	−0.239684	+	0.201118i	0.515031	+	0.857171i	$0.327780\pi$
$182$	−584575.	−	212768.i	−1.30816	−	0.476132i
$183$	−483807.	+	176091.i	−1.06793	+	0.388696i
$184$	−97446.5			−0.212188
$185$	−453499.	+	293874.i	−0.974199	+	0.631294i
$186$	−465606.			−0.986816
$187$	256029.	−	93187.1i	0.535409	−	0.194873i
$188$	−15897.2	−	5786.10i	−0.0328039	−	0.0119396i
$189$	701047.	−	588248.i	1.42755	−	1.19786i
$190$	−58925.2	−	334181.i	−0.118418	−	0.671581i
$191$	576177.			1.14281			0.571403	−	0.820669i	$-0.306399\pi$
$191$	576177.			1.14281			0.571403	+	0.820669i	$0.306399\pi$
$192$	10487.5	+	59477.7i	0.0205315	+	0.116440i
$193$	−475615.	+	823788.i	−0.919098	+	1.59192i	−0.118310	+	0.992977i	$0.537748\pi$
$193$	−475615.	+	823788.i	−0.919098	+	1.59192i	−0.800788	+	0.598948i	$0.795586\pi$
$194$	245976.	+	206399.i	0.469234	+	0.393734i
$195$	321993.	+	557708.i	0.606401	+	1.05032i
$196$	−292733.	+	507029.i	−0.544292	+	0.942742i
$197$	−139209.	+	50667.9i	−0.255565	+	0.0930181i	−0.466626	−	0.884455i	$-0.654530\pi$
$197$	−139209.	+	50667.9i	−0.255565	+	0.0930181i	0.211061	+	0.977473i	$0.432308\pi$
$198$	10890.6	−	9138.26i	0.0197418	−	0.0165653i
$199$	−111298.	−	192773.i	−0.199229	−	0.345075i	0.749049	−	0.662514i	$-0.230511\pi$
$199$	−111298.	−	192773.i	−0.199229	−	0.345075i	−0.948279	+	0.317439i	$0.897177\pi$
$200$	12071.8	−	68462.8i	0.0213402	−	0.121026i
$201$	77599.6	−	440089.i	0.135478	−	0.768335i
$202$	189106.	+	158679.i	0.326082	+	0.273615i
$203$	1.29297e6	+	470602.i	2.20215	+	0.801518i
$204$	−434848.	−	158272.i	−0.731581	−	0.266274i
$205$	690013.	+	578989.i	1.14676	+	0.962245i
$206$	−354.234	+	2008.96i	−0.000581597	+	0.00329840i
$207$	6765.15	−	38367.1i	0.0109737	−	0.0622347i
$208$	86146.8	+	149211.i	0.138064	+	0.239134i
$209$	139102.	−	116721.i	0.220277	−	0.184834i
$210$	831110.	−	302499.i	1.30050	−	0.473343i
$211$	265869.	−	460498.i	0.411113	−	0.712068i	−0.583899	−	0.811826i	$-0.698474\pi$
$211$	265869.	−	460498.i	0.411113	−	0.712068i	0.995012	+	0.0997580i	$0.0318069\pi$
$212$	109588.	+	189812.i	0.167465	+	0.290058i
$213$	394663.	+	331161.i	0.596043	+	0.500139i
$214$	12170.7	−	21080.3i	0.0181669	−	0.0314661i
$215$	192938.	+	1.09421e6i	0.284657	+	1.61437i
$216$	−253459.			−0.369635
$217$	316775.	+	1.79652e6i	0.456670	+	2.58990i
$218$	471645.	−	395757.i	0.672161	−	0.564010i
$219$	−846018.	−	307925.i	−1.19198	−	0.433846i
$220$	135527.	−	49327.7i	0.188785	−	0.0687123i
$221$	−1.32014e6			−1.81818
$222$	191461.	+	452287.i	0.260734	+	0.615930i
$223$	−364043.			−0.490219			−0.245109	−	0.969495i	$-0.578824\pi$
$223$	−364043.			−0.490219			−0.245109	+	0.969495i	$0.578824\pi$
$224$	222357.	−	80931.4i	0.296095	−	0.107770i
$225$	26117.4	+	9505.96i	0.0343933	+	0.0125181i
$226$	−602435.	+	505503.i	−0.784583	+	0.658343i
$227$	45108.2	+	255821.i	0.0581019	+	0.329512i	0.999979	−	0.00644462i	$-0.00205140\pi$
$227$	45108.2	+	255821.i	0.0581019	+	0.329512i	−0.941877	+	0.335957i	$0.890940\pi$
$228$	−308410.			−0.392909
$229$	−91652.1	−	519785.i	−0.115492	−	0.654990i	−0.986505	−	0.163730i	$-0.947647\pi$
$229$	−91652.1	−	519785.i	−0.115492	−	0.654990i	0.871013	−	0.491260i	$-0.163464\pi$
$230$	197615.	−	342280.i	0.246321	−	0.426640i
$231$	362557.	+	304222.i	0.447040	+	0.375111i
$232$	−190540.	−	330025.i	−0.232416	−	0.402557i
$233$	−119280.	+	206598.i	−0.143938	+	0.249309i	−0.928976	−	0.370139i	$-0.879310\pi$
$233$	−119280.	+	206598.i	−0.143938	+	0.249309i	0.785038	+	0.619448i	$0.212643\pi$
$234$	−64728.6	+	23559.3i	−0.0772781	+	0.0281269i
$235$	52562.1	−	44104.9i	0.0620874	−	0.0520975i
$236$	144034.	+	249474.i	0.168339	+	0.291571i
$237$	101063.	−	573157.i	0.116875	−	0.662831i
$238$	−314836.	+	1.78553e6i	−0.360282	+	2.04326i
$239$	−7023.40	−	5893.33i	−0.00795340	−	0.00667369i	0.638802	−	0.769371i	$-0.279430\pi$
$239$	−7023.40	−	5893.33i	−0.00795340	−	0.00667369i	−0.646756	+	0.762697i	$0.723875\pi$
$240$	−230183.	−	83779.7i	−0.257956	−	0.0938882i
$241$	−654116.	−	238079.i	−0.725457	−	0.264045i	−0.0472166	−	0.998885i	$-0.515035\pi$
$241$	−654116.	−	238079.i	−0.725457	−	0.264045i	−0.678241	+	0.734840i	$0.737257\pi$
$242$	−434368.	−	364478.i	−0.476781	−	0.400067i
$243$	33516.1	−	190079.i	0.0364115	−	0.206500i
$244$	97013.9	−	550193.i	0.104318	−	0.591617i
$245$	−1.18729e6	−	2.05645e6i	−1.26369	−	2.18878i
$246$	627126.	−	526221.i	0.660720	−	0.554410i
$247$	−826763.	+	300917.i	−0.862260	+	0.313837i
$248$	252619.	−	437549.i	0.260817	−	0.451749i
$249$	−49088.1	−	85023.0i	−0.0501739	−	0.0869037i
$250$	−405402.	−	340173.i	−0.410238	−	0.344231i
$251$	−1462.00	+	2532.25i	−0.00146474	+	0.00253701i	−0.866757	−	0.498731i	$-0.833800\pi$
$251$	−1462.00	+	2532.25i	−0.00146474	+	0.00253701i	0.865292	+	0.501268i	$0.167133\pi$
$252$	16427.7	+	93166.1i	0.0162958	+	0.0924180i
$253$	211495.			0.207730
$254$	64014.7	+	363045.i	0.0622580	+	0.353083i
$255$	1.43777e6	−	1.20644e6i	1.38465	−	1.16186i
$256$	−61583.7	−	22414.6i	−0.0587308	−	0.0213763i
$257$	−1.49285e6	+	543353.i	−1.40989	+	0.513156i	−0.931096	−	0.364774i	$-0.881146\pi$
$257$	−1.49285e6	+	543353.i	−1.40989	+	0.513156i	−0.478789	+	0.877930i	$0.658924\pi$
$258$	1.00982e6			0.944488
$259$	1.61487e6	−	1.04646e6i	1.49585	−	0.969331i
$260$	−698801.			−0.641092
$261$	143167.	−	52108.6i	0.130090	−	0.0473487i
$262$	750643.	+	273212.i	0.675585	+	0.245893i
$263$	1.02822e6	−	862783.i	0.916639	−	0.769152i	−0.0567311	−	0.998389i	$-0.518068\pi$
$263$	1.02822e6	−	862783.i	0.916639	−	0.769152i	0.973370	+	0.229238i	$0.0736233\pi$
$264$	−22761.9	−	129089.i	−0.0201001	−	0.113993i
$265$	−888952.			−0.777613
$266$	209827.	+	1.18999e6i	0.181827	+	1.03119i
$267$	179710.	−	311267.i	0.154274	−	0.267211i
$268$	371467.	+	311698.i	0.315925	+	0.265092i
$269$	62366.8	+	108022.i	0.0525500	+	0.0910193i	0.891104	−	0.453800i	$-0.149932\pi$
$269$	62366.8	+	108022.i	0.0525500	+	0.0910193i	−0.838554	+	0.544819i	$0.816598\pi$
$270$	513999.	−	890273.i	0.429095	−	0.743214i
$271$	−183771.	+	66887.1i	−0.152003	+	0.0553247i	−0.416901	−	0.908952i	$-0.636884\pi$
$271$	−183771.	+	66887.1i	−0.152003	+	0.0553247i	0.264898	+	0.964276i	$0.414662\pi$
$272$	384666.	−	322773.i	0.315254	−	0.264530i
$273$	−1.14659e6	−	1.98595e6i	−0.931109	−	1.61273i
$274$	178273.	−	1.01104e6i	0.143453	−	0.813562i
$275$	−26200.4	+	148590.i	−0.0208918	+	0.118483i
$276$	−275171.	−	230896.i	−0.217435	−	0.182450i
$277$	−746198.	−	271594.i	−0.584325	−	0.212677i	0.0329063	−	0.999458i	$-0.489524\pi$
$277$	−746198.	−	271594.i	−0.584325	−	0.212677i	−0.617232	+	0.786781i	$0.711746\pi$
$278$	−1.16037e6	−	422342.i	−0.900505	−	0.327757i
$279$	154736.	+	129839.i	0.119009	+	0.0998606i
$280$	−166656.	+	945151.i	−0.127035	+	0.720454i
$281$	−191289.	+	1.08485e6i	−0.144518	+	0.819604i	0.823234	+	0.567702i	$0.192167\pi$
$281$	−191289.	+	1.08485e6i	−0.144518	+	0.819604i	−0.967753	+	0.251903i	$0.918944\pi$
$282$	−31180.8	−	54006.7i	−0.0233488	−	0.0404413i
$283$	−329958.	+	276868.i	−0.244902	+	0.205497i	−0.756974	−	0.653446i	$-0.773323\pi$
$283$	−329958.	+	276868.i	−0.244902	+	0.205497i	0.512071	+	0.858943i	$0.328878\pi$
$284$	−525334.	+	191206.i	−0.386491	+	0.140671i
$285$	625437.	−	1.08329e6i	0.456112	−	0.790008i
$286$	−186971.	−	323843.i	−0.135163	−	0.234110i
$287$	−2.45707e6	−	2.06173e6i	−1.76081	−	1.47750i
$288$	13100.6	−	22690.9i	0.00930700	−	0.0161202i
$289$	421556.	+	2.39076e6i	0.296900	+	1.68381i
$290$	1.54562e6			1.07921
$291$	205538.	+	1.16566e6i	0.142285	+	0.806940i
$292$	748385.	−	627970.i	0.513651	−	0.431004i
$293$	799123.	+	290857.i	0.543806	+	0.197929i	0.599293	−	0.800530i	$-0.295449\pi$
$293$	799123.	+	290857.i	0.543806	+	0.197929i	−0.0554861	+	0.998459i	$0.517671\pi$
$294$	−2.02801e6	+	738136.i	−1.36837	+	0.498045i
$295$	−1.16836e6			−0.781670
$296$	−528911.	−	65468.9i	−0.350876	−	0.0434316i
$297$	550101.			0.361869
$298$	−1.17944e6	+	429280.i	−0.769368	+	0.280027i
$299$	−962944.	−	350483.i	−0.622907	−	0.226719i
$300$	196309.	−	164723.i	0.125932	−	0.105670i
$301$	−687035.	−	3.89637e6i	−0.437081	−	2.47881i
$302$	1.82686e6			1.15263
$303$	158017.	+	896159.i	0.0988774	+	0.560762i
$304$	167331.	−	289825.i	0.103847	−	0.179867i
$305$	1.73581e6	+	1.45652e6i	1.06845	+	0.896533i
$306$	100378.	+	173861.i	0.0612826	+	0.106145i
$307$	1.11788e6	−	1.93622e6i	0.676938	−	1.17249i	−0.298961	−	0.954265i	$-0.596640\pi$
$307$	1.11788e6	−	1.93622e6i	0.676938	−	1.17249i	0.975898	−	0.218225i	$-0.0700267\pi$
$308$	−482598.	+	175651.i	−0.289874	+	0.105505i
$309$	−5760.46	+	4833.60i	−0.00343211	+	0.00287988i
$310$	1.02459e6	+	1.77464e6i	0.605545	+	1.04883i
$311$	−132214.	+	749822.i	−0.0775133	+	0.439600i	0.921209	+	0.389068i	$0.127203\pi$
$311$	−132214.	+	749822.i	−0.0775133	+	0.439600i	−0.998722	+	0.0505320i	$0.983908\pi$
$312$	−110286.	+	625465.i	−0.0641410	+	0.363761i
$313$	918165.	+	770432.i	0.529736	+	0.444502i	0.868010	−	0.496546i	$-0.165399\pi$
$313$	918165.	+	770432.i	0.529736	+	0.444502i	−0.338274	+	0.941048i	$0.609843\pi$
$314$	658275.	+	239592.i	0.376776	+	0.137135i
$315$	−360559.	−	131233.i	−0.204739	−	0.0745189i
$316$	483787.	+	405945.i	0.272544	+	0.228691i
$317$	95693.9	−	542707.i	0.0534855	−	0.303331i	−0.946316	−	0.323242i	$-0.895227\pi$
$317$	95693.9	−	542707.i	0.0534855	−	0.303331i	0.999802	+	0.0199109i	$0.00633824\pi$
$318$	−140296.	+	795661.i	−0.0777999	+	0.441225i
$319$	413544.	+	716279.i	0.227533	+	0.394099i
$320$	203619.	−	170857.i	0.111159	−	0.0932733i
$321$	84316.9	−	30688.8i	0.0456722	−	0.0166233i
$322$	−703690.	+	1.21883e6i	−0.378218	+	0.655092i
$323$	1.28211e6	+	2.22068e6i	0.683784	+	1.18435i
$324$	−639514.	−	536616.i	−0.338445	−	0.283989i
$325$	365529.	−	633115.i	0.191961	−	0.332487i
$326$	−438236.	−	2.48536e6i	−0.228383	−	1.29522i
$327$	2.26957e6			1.17375
$328$	154258.	+	874842.i	0.0791706	+	0.448999i
$329$	−187169.	+	157053.i	−0.0953331	+	0.0799940i
$330$	499583.	+	181833.i	0.252536	+	0.0919155i
$331$	−1.36389e6	+	496415.i	−0.684241	+	0.249043i	−0.660667	−	0.750679i	$-0.729727\pi$
$331$	−1.36389e6	+	496415.i	−0.684241	+	0.249043i	−0.0235736	+	0.999722i	$0.507504\pi$
$332$	106533.			0.0530442
$333$	62496.0	−	203700.i	0.0308846	−	0.100666i
$334$	−2.13592e6			−1.04766
$335$	−1.84815e6	+	672671.i	−0.899757	+	0.327485i
$336$	819660.	+	298332.i	0.396082	+	0.144162i
$337$	−437098.	+	366769.i	−0.209655	+	0.175921i	−0.741568	−	0.670878i	$-0.765918\pi$
$337$	−437098.	+	366769.i	−0.209655	+	0.175921i	0.531913	+	0.846799i	$0.321473\pi$
$338$	56724.0	+	321698.i	0.0270069	+	0.153164i
$339$	−2.89894e6			−1.37006
$340$	353659.	+	2.00570e6i	0.165916	+	0.940954i
$341$	−548278.	+	949645.i	−0.255338	+	0.442258i
$342$	102495.	+	86003.2i	0.0473845	+	0.0397603i
$343$	2.28594e6	+	3.95936e6i	1.04913	+	1.81714i
$344$	−547890.	+	948973.i	−0.249630	+	0.432372i
$345$	1.36905e6	−	498293.i	0.619258	−	0.225391i
$346$	1.56274e6	−	1.31129e6i	0.701772	−	0.588856i
$347$	−1.05827e6	−	1.83297e6i	−0.471815	−	0.817208i	0.527665	−	0.849453i	$-0.323068\pi$
$347$	−1.05827e6	−	1.83297e6i	−0.471815	−	0.817208i	−0.999480	+	0.0322447i	$0.989734\pi$
$348$	243932.	−	1.38341e6i	0.107975	−	0.612354i
$349$	391978.	−	2.22302e6i	0.172266	−	0.976966i	−0.768987	−	0.639264i	$-0.779239\pi$
$349$	391978.	−	2.22302e6i	0.172266	−	0.976966i	0.941253	−	0.337702i	$-0.109650\pi$
$350$	−769134.	−	645380.i	−0.335608	−	0.281608i
$351$	−2.50462e6	−	911609.i	−1.08511	−	0.394949i
$352$	133660.	+	48648.2i	0.0574968	+	0.0209271i
$353$	1.72223e6	+	1.44512e6i	0.735622	+	0.617260i	0.931658	−	0.363337i	$-0.118363\pi$
$353$	1.72223e6	+	1.44512e6i	0.735622	+	0.617260i	−0.196036	+	0.980597i	$0.562807\pi$
$354$	−184394.	+	1.04575e6i	−0.0782057	+	0.443527i
$355$	393735.	−	2.23298e6i	0.165819	−	0.940405i
$356$	195007.	+	337761.i	0.0815500	+	0.141249i
$357$	−5.11978e6	+	4.29600e6i	−2.12609	+	1.78400i
$358$	112315.	−	40879.4i	0.0463160	−	0.0168576i
$359$	−277900.	+	481337.i	−0.113803	+	0.197112i	−0.917301	−	0.398196i	$-0.869637\pi$
$359$	−277900.	+	481337.i	−0.113803	+	0.197112i	0.803498	+	0.595308i	$0.202970\pi$
$360$	53134.4	+	92031.5i	0.0216082	+	0.0374266i
$361$	−587662.	−	493107.i	−0.237334	−	0.199147i
$362$	275810.	−	477718.i	0.110621	−	0.191602i
$363$	−362958.	−	2.05844e6i	−0.144574	−	0.819919i
$364$	2.48837e6			0.984375
$365$	688060.	+	3.90218e6i	0.270330	+	1.53312i
$366$	1.57761e6	−	1.32377e6i	0.615598	−	0.516548i
$367$	762377.	+	277482.i	0.295464	+	0.107540i	0.485499	−	0.874237i	$-0.338638\pi$
$367$	762377.	+	277482.i	0.295464	+	0.107540i	−0.190035	+	0.981777i	$0.560860\pi$
$368$	366279.	−	133315.i	0.140991	−	0.0513166i
$369$	−355156.			−0.135786
$370$	1.30256e6	−	1.72503e6i	0.494644	−	0.655076i
$371$	3.16548e6			1.19400
$372$	1.75011e6	−	636986.i	0.655703	−	0.238656i
$373$	4.74552e6	+	1.72723e6i	1.76608	+	0.642802i	1.00000		6.22696e-5i	$1.98210e-5\pi$
$373$	4.74552e6	+	1.72723e6i	1.76608	+	0.642802i	0.766084	+	0.642740i	$0.222202\pi$
$374$	−834869.	+	700538.i	−0.308631	+	0.258972i
$375$	−338754.	−	1.92117e6i	−0.124396	−	0.705486i
$376$	67669.7			0.0246845
$377$	−695883.	−	3.94655e6i	−0.252164	−	1.43009i
$378$	−1.83030e6	+	3.17018e6i	−0.658861	+	1.14118i
$379$	−2.25272e6	−	1.89026e6i	−0.805580	−	0.675962i	0.143968	−	0.989582i	$-0.454014\pi$
$379$	−2.25272e6	−	1.89026e6i	−0.805580	−	0.675962i	−0.949549	+	0.313620i	$0.898458\pi$
$380$	678673.	+	1.17550e6i	0.241102	+	0.417602i
$381$	−679457.	+	1.17685e6i	−0.239800	+	0.415346i
$382$	−2.16572e6	+	788257.i	−0.759353	+	0.276382i
$383$	−1.42067e6	+	1.19208e6i	−0.494874	+	0.415249i	−0.855769	−	0.517358i	$-0.826916\pi$
$383$	−1.42067e6	+	1.19208e6i	−0.494874	+	0.415249i	0.360895	+	0.932606i	$0.382471\pi$
$384$	−120790.	−	209215.i	−0.0418027	−	0.0724044i
$385$	361705.	−	2.05133e6i	0.124366	−	0.705317i
$386$	660717.	−	3.74711e6i	0.225708	−	1.28005i
$387$	−335597.	−	281600.i	−0.113905	−	0.0955772i
$388$	−1.20694e6	−	439290.i	−0.407011	−	0.148140i
$389$	2.96793e6	+	1.08024e6i	0.994441	+	0.361947i	0.787438	−	0.616394i	$-0.211407\pi$
$389$	2.96793e6	+	1.08024e6i	0.994441	+	0.361947i	0.207003	+	0.978340i	$0.433629\pi$
$390$	−1.97329e6	−	1.65578e6i	−0.656945	−	0.551242i
$391$	−518616.	+	2.94122e6i	−0.171555	+	0.972938i
$392$	406661.	−	2.30629e6i	0.133665	−	0.758051i
$393$	1.47231e6	+	2.55012e6i	0.480860	+	0.832874i
$394$	453937.	−	380898.i	0.147318	−	0.123614i
$395$	−2.40697e6	+	876065.i	−0.776207	+	0.282516i
$396$	−28433.2	+	49247.8i	−0.00911146	+	0.0157815i
$397$	1.67130e6	+	2.89479e6i	0.532206	+	0.921807i	0.999293	+	0.0375960i	$0.0119700\pi$
$397$	1.67130e6	+	2.89479e6i	0.532206	+	0.921807i	−0.467087	+	0.884211i	$0.654697\pi$
$398$	682071.	+	572326.i	0.215835	+	0.181107i
$399$	−2.22712e6	+	3.85749e6i	−0.700344	+	1.21303i
$400$	48287.3	+	273851.i	0.0150898	+	0.0855785i
$401$	6.22315e6			1.93263			0.966317	−	0.257356i	$-0.0828513\pi$
$401$	6.22315e6			1.93263			0.966317	+	0.257356i	$0.0828513\pi$
$402$	310398.	+	1.76036e6i	0.0957976	+	0.543295i
$403$	4.07004e6	−	3.41517e6i	1.24835	−	1.04749i
$404$	−927890.	−	337724.i	−0.282842	−	0.102946i
$405$	3.18175e6	−	1.15806e6i	0.963893	−	0.350828i
$406$	−5.50379e6			−1.65709
$407$	1.14793e6	+	142092.i	0.343504	+	0.0425191i
$408$	1.85102e6			0.550505
$409$	−4.07345e6	+	1.48262e6i	−1.20408	+	0.438248i	−0.864645	−	0.502382i	$-0.832457\pi$
$409$	−4.07345e6	+	1.48262e6i	−1.20408	+	0.438248i	−0.339432	+	0.940631i	$0.610235\pi$
$410$	−3.38570e6	−	1.23230e6i	−0.994693	−	0.362039i
$411$	2.89903e6	−	2.43257e6i	0.846540	−	0.710332i
$412$	−1416.94	−	8035.85i	−0.000411251	−	0.00233232i
$413$	4.16044e6			1.20023
$414$	27060.6	+	153468.i	0.00775955	+	0.0440066i
$415$	−216042.	+	374195.i	−0.0615769	+	0.106654i
$416$	−527938.	−	442993.i	−0.149572	−	0.125506i
$417$	−2.27596e6	−	3.94208e6i	−0.640951	−	1.11016i
$418$	−363171.	+	629030.i	−0.101665	+	0.176088i
$419$	−2.54433e6	+	926062.i	−0.708010	+	0.257694i	−0.670827	−	0.741614i	$-0.734061\pi$
$419$	−2.54433e6	+	926062.i	−0.708010	+	0.257694i	−0.0371829	+	0.999308i	$0.511838\pi$
$420$	−2.71011e6	+	2.27405e6i	−0.749658	+	0.629038i
$421$	39711.4	+	68782.1i	0.0109197	+	0.0189134i	0.871434	−	0.490513i	$-0.163191\pi$
$421$	39711.4	+	68782.1i	0.0109197	+	0.0189134i	−0.860514	+	0.509427i	$0.829857\pi$
$422$	−369341.	+	2.09464e6i	−0.100959	+	0.572569i
$423$	−4697.92	+	26643.2i	−0.00127660	+	0.00723996i
$424$	−671595.	−	563535.i	−0.181423	−	0.152232i
$425$	−2.00216e6	−	728726.i	−0.537683	−	0.195700i
$426$	−1.93650e6	−	704829.i	−0.517004	−	0.188174i
$427$	−6.18106e6	−	5.18652e6i	−1.64056	−	1.37660i
$428$	−16907.4	+	95886.5i	−0.00446136	+	0.0253016i
$429$	239363.	−	1.35749e6i	0.0627933	−	0.356119i
$430$	−2.22217e6	−	3.84892e6i	−0.579571	−	1.00385i
$431$	−2.83197e6	+	2.37631e6i	−0.734338	+	0.616183i	−0.931311	−	0.364226i	$-0.881334\pi$
$431$	−2.83197e6	+	2.37631e6i	−0.734338	+	0.616183i	0.196972	+	0.980409i	$0.436889\pi$
$432$	952694.	−	346752.i	0.245609	−	0.0893944i
$433$	1.67046e6	−	2.89333e6i	0.428171	−	0.741614i	−0.568540	−	0.822656i	$-0.692491\pi$
$433$	1.67046e6	−	2.89333e6i	0.428171	−	0.741614i	0.996711	+	0.0810421i	$0.0258248\pi$
$434$	−3.64847e6	−	6.31934e6i	−0.929794	−	1.61045i
$435$	4.36454e6	+	3.66228e6i	1.10590	+	0.927958i
$436$	−1.23138e6	+	2.13281e6i	−0.310223	+	0.537323i
$437$	345639.	+	1.96021e6i	0.0865802	+	0.491021i
$438$	3.60125e6			0.896951
$439$	−675432.	−	3.83057e6i	−0.167271	−	0.948641i	−0.946692	−	0.322140i	$-0.895598\pi$
$439$	−675432.	−	3.83057e6i	−0.167271	−	0.948641i	0.779421	−	0.626501i	$-0.215513\pi$
$440$	−441930.	+	370823.i	−0.108823	+	0.0913135i
$441$	879811.	+	320225.i	0.215423	+	0.0784077i
$442$	4.96209e6	−	1.80605e6i	1.20812	−	0.439718i
$443$	4.44824e6			1.07691			0.538454	−	0.842655i	$-0.319008\pi$
$443$	4.44824e6			1.07691			0.538454	+	0.842655i	$0.319008\pi$
$444$	−1.33842e6	−	1.43811e6i	−0.322207	−	0.346206i
$445$	−1.58184e6			−0.378673
$446$	1.36835e6	−	498040.i	0.325732	−	0.118557i
$447$	−4.34768e6	−	1.58243e6i	−1.02917	−	0.374588i
$448$	−725069.	+	608405.i	−0.170681	+	0.143218i
$449$	−1.41742e6	−	8.03857e6i	−0.331804	−	1.88175i	−0.456758	−	0.889591i	$-0.650990\pi$
$449$	−1.41742e6	−	8.03857e6i	−0.331804	−	1.88175i	0.124955	−	0.992162i	$-0.460122\pi$
$450$	−111174.			−0.0258805
$451$	−334798.	−	1.89874e6i	−0.0775072	−	0.439565i
$452$	1.57285e6	−	2.72425e6i	0.362110	−	0.627192i
$453$	5.15872e6	+	4.32868e6i	1.18113	+	0.991084i
$454$	−519535.	−	899861.i	−0.118297	−	0.204897i
$455$	−5.04625e6	+	8.74036e6i	−1.14272	+	1.97925i
$456$	1.15924e6	−	421930.i	0.261073	−	0.0950229i
$457$	712871.	−	598169.i	0.159669	−	0.133978i	−0.559453	−	0.828862i	$-0.688989\pi$
$457$	712871.	−	598169.i	0.159669	−	0.133978i	0.719122	+	0.694884i	$0.244544\pi$
$458$	1.05561e6	+	1.82836e6i	0.235146	+	0.407286i
$459$	−1.34892e6	+	7.65013e6i	−0.298852	+	1.69487i
$460$	−274524.	+	1.55691e6i	−0.0604904	+	0.343058i
$461$	1.39910e6	+	1.17398e6i	0.306616	+	0.257282i	0.783092	−	0.621906i	$-0.213641\pi$
$461$	1.39910e6	+	1.17398e6i	0.306616	+	0.257282i	−0.476476	+	0.879188i	$0.658086\pi$
$462$	−1.77897e6	−	647492.i	−0.387760	−	0.141133i
$463$	−7.82053e6	−	2.84644e6i	−1.69545	−	0.617092i	−0.700152	−	0.713994i	$-0.746884\pi$
$463$	−7.82053e6	−	2.84644e6i	−1.69545	−	0.617092i	−0.995294	+	0.0969025i	$0.969106\pi$
$464$	1.16770e6	+	979815.i	0.251788	+	0.211276i
$465$	−1.31170e6	+	7.43900e6i	−0.281320	+	1.59545i
$466$	165702.	−	939740.i	0.0353478	−	0.200467i
$467$	−4.50612e6	−	7.80484e6i	−0.956117	−	1.65604i	−0.731792	−	0.681528i	$-0.761316\pi$
$467$	−4.50612e6	−	7.80484e6i	−0.956117	−	1.65604i	−0.224325	−	0.974514i	$-0.572018\pi$
$468$	211069.	−	177108.i	0.0445461	−	0.0373786i
$469$	6.58109e6	−	2.39532e6i	1.38155	−	0.502842i
$470$	−137230.	+	237689.i	−0.0286553	+	0.0496324i
$471$	1.29114e6	+	2.23632e6i	0.268177	+	0.464496i
$472$	−882689.	−	740664.i	−0.182370	−	0.153026i
$473$	1.18913e6	−	2.05963e6i	0.244385	−	0.423288i
$474$	404253.	+	2.29263e6i	0.0826432	+	0.468693i
$475$	−1.42000e6			−0.288772
$476$	−1.25935e6	−	7.14210e6i	−0.254758	−	1.44480i
$477$	268503.	−	225301.i	0.0540322	−	0.0453384i
$478$	34461.9	+	12543.1i	0.00689874	+	0.00251093i
$479$	3.56369e6	−	1.29708e6i	0.709677	−	0.258301i	0.0381401	−	0.999272i	$-0.487857\pi$
$479$	3.56369e6	−	1.29708e6i	0.709677	−	0.258301i	0.671537	+	0.740971i	$0.265634\pi$
$480$	979822.			0.194108
$481$	−4.99111e6	−	2.54927e6i	−0.983635	−	0.502404i
$482$	2.78438e6			0.545897
$483$	−4.87506e6	+	1.77438e6i	−0.950850	+	0.346081i
$484$	2.13132e6	+	775738.i	0.413558	+	0.150523i
$485$	3.99060e6	−	3.34851e6i	0.770342	−	0.646394i
$486$	134064.	+	760317.i	0.0257468	+	0.146017i
$487$	6.54180e6			1.24990			0.624949	−	0.780666i	$-0.285120\pi$
$487$	6.54180e6			1.24990			0.624949	+	0.780666i	$0.285120\pi$
$488$	388055.	+	2.20077e6i	0.0737640	+	0.418336i
$489$	4.65147e6	−	8.05658e6i	0.879667	−	1.52363i
$490$	7.27614e6	+	6.10540e6i	1.36902	+	1.14875i
$491$	2.06309e6	+	3.57338e6i	0.386202	+	0.668921i	0.991935	−	0.126747i	$-0.0404535\pi$
$491$	2.06309e6	+	3.57338e6i	0.386202	+	0.668921i	−0.605733	+	0.795668i	$0.707120\pi$
$492$	−1.63731e6	+	2.83590e6i	−0.304943	+	0.528176i
$493$	−1.09752e7	+	3.99464e6i	−2.03374	+	0.740219i
$494$	2.69593e6	−	2.26216e6i	0.497040	−	0.417066i
$495$	−115322.	−	199743.i	−0.0211542	−	0.0366402i
$496$	−350935.	+	1.99025e6i	−0.0640504	+	0.363248i
$497$	−1.40206e6	+	7.95145e6i	−0.254609	+	1.44396i
$498$	300829.	+	252426.i	0.0543559	+	0.0456100i
$499$	9.28844e6	+	3.38072e6i	1.66990	+	0.607795i	0.991872	−	0.127238i	$-0.0406112\pi$
$499$	9.28844e6	+	3.38072e6i	1.66990	+	0.607795i	0.678031	+	0.735033i	$0.262833\pi$
$500$	1.98920e6	+	724009.i	0.355839	+	0.129515i
$501$	−6.03146e6	−	5.06100e6i	−1.07356	−	0.900828i
$502$	2030.98	−	11518.3i	0.000359706	−	0.00203999i
$503$	−1.05553e6	+	5.98623e6i	−0.186017	+	1.05495i	0.738625	+	0.674116i	$0.235475\pi$
$503$	−1.05553e6	+	5.98623e6i	−0.186017	+	1.05495i	−0.924642	+	0.380838i	$0.875636\pi$
$504$	−189207.	−	327716.i	−0.0331788	−	0.0574673i
$505$	3.06796e6	−	2.57432e6i	0.535329	−	0.449195i
$506$	−794963.	+	289343.i	−0.138029	+	0.0502385i
$507$	−602073.	+	1.04282e6i	−0.104023	+	0.180173i
$508$	−737291.	−	1.27703e6i	−0.126759	−	0.219554i
$509$	−661845.	−	555354.i	−0.113230	−	0.0950113i	0.584415	−	0.811455i	$-0.301324\pi$
$509$	−661845.	−	555354.i	−0.113230	−	0.0950113i	−0.697645	+	0.716444i	$0.745769\pi$
$510$	−3.75376e6	+	6.50171e6i	−0.639059	+	1.10688i
$511$	−2.45012e6	−	1.38953e7i	−0.415082	−	2.35405i
$512$	262144.			0.0441942
$513$	899009.	+	5.09853e6i	0.150824	+	0.855366i
$514$	4.86793e6	−	4.08468e6i	0.812712	−	0.681947i
$515$	31099.3	+	11319.2i	0.00516693	+	0.00188061i
$516$	−3.79570e6	+	1.38152e6i	−0.627578	+	0.228420i
$517$	−146869.			−0.0241659
$518$	−4.63829e6	+	6.14266e6i	−0.759509	+	1.00585i
$519$	7.51995e6			1.22545
$520$	2.62663e6	−	956016.i	0.425982	−	0.155045i
$521$	6.15628e6	+	2.24070e6i	0.993628	+	0.361651i	0.787124	−	0.616795i	$-0.211569\pi$
$521$	6.15628e6	+	2.24070e6i	0.993628	+	0.361651i	0.206504	+	0.978446i	$0.433791\pi$
$522$	−466844.	+	391729.i	−0.0749887	+	0.0629230i
$523$	97659.5	+	553854.i	0.0156121	+	0.0885404i	0.991618	−	0.129202i	$-0.0412417\pi$
$523$	97659.5	+	553854.i	0.0156121	+	0.0885404i	−0.976006	+	0.217743i	$0.930131\pi$
$524$	−3.19527e6			−0.508369
$525$	−642689.	−	3.64487e6i	−0.101766	−	0.577144i
$526$	−2.68450e6	+	4.64970e6i	−0.423058	+	0.732757i
$527$	−1.18620e7	−	9.95343e6i	−1.86051	−	1.56116i
$528$	262161.	+	454075.i	0.0409244	+	0.0708832i
$529$	2.05901e6	−	3.56632e6i	0.319904	−	0.554091i
$530$	3.34137e6	−	1.21616e6i	0.516695	−	0.188062i
$531$	352898.	−	296116.i	0.0543141	−	0.0455750i
$532$	−2.41669e6	−	4.18583e6i	−0.370205	−	0.641214i
$533$	−1.62217e6	+	9.19981e6i	−0.247332	+	1.40269i
$534$	−249650.	+	1.41584e6i	−0.0378860	+	0.214862i
$535$	−302514.	−	253839.i	−0.0456941	−	0.0383419i
$536$	−1.82269e6	−	663404.i	−0.274032	−	0.0997393i
$537$	414020.	+	150691.i	0.0619563	+	0.0225502i
$538$	−382206.	−	320709.i	−0.0569301	−	0.0477700i
$539$	−882607.	+	5.00551e6i	−0.130856	+	0.742124i
$540$	−714040.	+	4.04952e6i	−0.105375	+	0.597612i
$541$	946288.	+	1.63902e6i	0.139005	+	0.240764i	0.927120	−	0.374764i	$-0.122276\pi$
$541$	946288.	+	1.63902e6i	0.139005	+	0.240764i	−0.788115	+	0.615528i	$0.788943\pi$
$542$	599246.	−	502827.i	0.0876207	−	0.0735225i
$543$	1.91077e6	−	695465.i	0.278106	−	0.101222i
$544$	−1.00429e6	+	1.73948e6i	−0.145500	+	0.252013i
$545$	−4.99431e6	−	8.65040e6i	−0.720252	−	1.24751i
$546$	7.02669e6	+	5.89609e6i	1.00872	+	0.846414i
$547$	2.77368e6	−	4.80416e6i	0.396359	−	0.686514i	−0.596915	−	0.802305i	$-0.703607\pi$
$547$	2.77368e6	−	4.80416e6i	0.396359	−	0.686514i	0.993274	+	0.115791i	$0.0369402\pi$
$548$	713093.	+	4.04415e6i	0.101437	+	0.575275i
$549$	−893439.			−0.126513
$550$	−104802.	−	594360.i	−0.0147727	−	0.0837804i
$551$	−5.96289e6	+	5.00346e6i	−0.836715	+	0.702087i
$552$	1.35019e6	+	491429.i	0.188602	+	0.0686456i
$553$	8.57099e6	−	3.11958e6i	1.19184	−	0.433794i
$554$	3.17635e6			0.439697
$555$	7.76558e6	−	1.78480e6i	1.07014	−	0.245956i
$556$	4.93938e6			0.677619
$557$	−9.47270e6	+	3.44778e6i	−1.29371	+	0.470871i	−0.894942	−	0.446183i	$-0.852783\pi$
$557$	−9.47270e6	+	3.44778e6i	−1.29371	+	0.470871i	−0.398764	+	0.917053i	$0.630561\pi$
$558$	−759247.	−	276343.i	−0.103228	−	0.0375719i
$559$	−8.82727e6	+	7.40696e6i	−1.19480	+	1.00256i
$560$	−666623.	−	3.78060e6i	−0.0898276	−	0.509438i
$561$	−4.01742e6			−0.538939
$562$	−765154.	−	4.33940e6i	−0.102190	−	0.579548i
$563$	387959.	−	671964.i	0.0515839	−	0.0893460i	−0.839080	−	0.544007i	$-0.816906\pi$
$563$	387959.	−	671964.i	0.0515839	−	0.0893460i	0.890664	+	0.454661i	$0.150240\pi$
$564$	191087.	+	160341.i	0.0252949	+	0.0212249i
$565$	6.37927e6	+	1.10492e7i	0.840717	+	1.45616i
$566$	861460.	−	1.49209e6i	0.113030	−	0.195774i
$567$	−1.13299e7	+	4.12376e6i	−1.48003	+	0.538686i
$568$	1.71302e6	−	1.43740e6i	0.222789	−	0.186942i
$569$	4.33248e6	+	7.50408e6i	0.560991	+	0.971666i	0.997410	+	0.0719220i	$0.0229133\pi$
$569$	4.33248e6	+	7.50408e6i	0.560991	+	0.971666i	−0.436419	+	0.899744i	$0.643753\pi$
$570$	−868847.	+	4.92748e6i	−0.112010	+	0.635240i
$571$	436660.	−	2.47642e6i	0.0560471	−	0.317859i	−0.943875	−	0.330301i	$-0.892850\pi$
$571$	436660.	−	2.47642e6i	0.0560471	−	0.317859i	0.999923	+	0.0124426i	$0.00396069\pi$
$572$	1.14582e6	+	961460.i	0.146429	+	0.122869i
$573$	−7.98334e6	−	2.90570e6i	−1.01578	−	0.369712i
$574$	1.20562e7	+	4.38809e6i	1.52732	+	0.555899i
$575$	−1.26696e6	−	1.06311e6i	−0.159806	−	0.134093i
$576$	−18199.2	+	103213.i	−0.00228557	+	0.0129621i
$577$	−987882.	+	5.60256e6i	−0.123528	+	0.700562i	0.858643	+	0.512574i	$0.171308\pi$
$577$	−987882.	+	5.60256e6i	−0.123528	+	0.700562i	−0.982171	+	0.187989i	$0.939803\pi$
$578$	−4.85529e6	−	8.40961e6i	−0.604499	−	1.04702i
$579$	1.07444e7	−	9.01561e6i	1.33194	−	1.11763i
$580$	−5.80961e6	+	2.11453e6i	−0.717096	+	0.261002i
$581$	769305.	−	1.33247e6i	0.0945492	−	0.163764i
$582$	−2.36729e6	−	4.10027e6i	−0.289697	−	0.501771i
$583$	1.45761e6	+	1.22308e6i	0.177611	+	0.149034i
$584$	−1.95389e6	+	3.38424e6i	−0.237066	+	0.410610i
$585$	194055.	+	1.10054e6i	0.0234442	+	0.132959i
$586$	−3.40163e6			−0.409207
$587$	1.04581e6	+	5.93110e6i	0.125273	+	0.710461i	0.981145	+	0.193273i	$0.0619102\pi$
$587$	1.04581e6	+	5.93110e6i	0.125273	+	0.710461i	−0.855872	+	0.517188i	$0.826979\pi$
$588$	6.61300e6	−	5.54897e6i	0.788779	−	0.661864i
$589$	−9.69768e6	−	3.52967e6i	−1.15181	−	0.419223i
$590$	4.39162e6	−	1.59842e6i	0.519391	−	0.189043i
$591$	2.18436e6			0.257250
$592$	2.07762e6	−	477510.i	0.243648	−	0.0559987i
$593$	7.56130e6			0.882998			0.441499	−	0.897262i	$-0.354447\pi$
$593$	7.56130e6			0.882998			0.441499	+	0.897262i	$0.354447\pi$
$594$	−2.06770e6	+	752583.i	−0.240449	+	0.0875161i
$595$	2.76404e7	+	1.00603e7i	3.20076	+	1.16498i
$596$	3.84594e6	−	3.22713e6i	0.443493	−	0.372135i
$597$	569939.	+	3.23229e6i	0.0654475	+	0.371171i
$598$	4.09897e6			0.468729
$599$	−2.33091e6	−	1.32193e7i	−0.265435	−	1.50536i	−0.767792	−	0.640699i	$-0.778645\pi$
$599$	−2.33091e6	−	1.32193e7i	−0.265435	−	1.50536i	0.502357	−	0.864660i	$-0.332466\pi$
$600$	−512526.	+	887721.i	−0.0581216	+	0.100670i
$601$	8.75638e6	+	7.34747e6i	0.988868	+	0.829759i	0.985403	−	0.170235i	$-0.0544528\pi$
$601$	8.75638e6	+	7.34747e6i	0.988868	+	0.829759i	0.00346455	+	0.999994i	$0.498897\pi$
$602$	7.91295e6	+	1.37056e7i	0.889912	+	1.54137i
$603$	387738.	−	671581.i	0.0434255	−	0.0752151i
$604$	−6.86675e6	+	2.49929e6i	−0.765877	+	0.278757i
$605$	−7.04697e6	+	5.91311e6i	−0.782733	+	0.656791i
$606$	−1.81997e6	−	3.15227e6i	−0.201318	−	0.348692i
$607$	588347.	−	3.33668e6i	0.0648129	−	0.367572i	−0.935100	−	0.354384i	$-0.884691\pi$
$607$	588347.	−	3.33668e6i	0.0648129	−	0.367572i	0.999913	−	0.0131887i	$-0.00419822\pi$
$608$	−232454.	+	1.31831e6i	−0.0255022	+	0.144630i
$609$	−1.55417e7	−	1.30410e7i	−1.69807	−	1.42485i
$610$	−8.51715e6	−	3.09999e6i	−0.926765	−	0.337315i
$611$	668697.	+	243386.i	0.0724646	+	0.0263750i
$612$	−615155.	−	516176.i	−0.0663905	−	0.0557082i
$613$	507050.	−	2.87563e6i	0.0545004	−	0.309087i	−0.945356	−	0.326040i	$-0.894285\pi$
$613$	507050.	−	2.87563e6i	0.0545004	−	0.309087i	0.999856	+	0.0169531i	$0.00539658\pi$
$614$	−1.55294e6	+	8.80716e6i	−0.166239	+	0.942790i
$615$	−6.64073e6	−	1.15021e7i	−0.707991	−	1.22628i
$616$	1.57367e6	−	1.32047e6i	0.167094	−	0.140209i
$617$	−5.05608e6	+	1.84026e6i	−0.534689	+	0.194611i	−0.595231	−	0.803555i	$-0.702939\pi$
$617$	−5.05608e6	+	1.84026e6i	−0.534689	+	0.194611i	0.0605418	+	0.998166i	$0.480717\pi$
$618$	15039.5	−	26049.1i	0.00158402	−	0.00274361i
$619$	−4.05541e6	−	7.02418e6i	−0.425411	−	0.736833i	0.571048	−	0.820917i	$-0.306537\pi$
$619$	−4.05541e6	−	7.02418e6i	−0.425411	−	0.736833i	−0.996459	+	0.0840836i	$0.973204\pi$
$620$	−6.27906e6	−	5.26876e6i	−0.656017	−	0.550464i
$621$	−3.01498e6	+	5.22209e6i	−0.313729	+	0.543395i
$622$	−528856.	−	2.99929e6i	−0.0548102	−	0.310844i
$623$	5.63280e6			0.581439
$624$	−441146.	−	2.50186e6i	−0.0453545	−	0.257218i
$625$	−9.17737e6	+	7.70072e6i	−0.939762	+	0.788554i
$626$	−4.50518e6	−	1.63975e6i	−0.459491	−	0.167241i
$627$	−2.51599e6	+	915746.i	−0.255588	+	0.0930264i
$628$	−2.80209e6			−0.283519
$629$	−4.79094e6	+	1.56156e7i	−0.482830	+	1.57374i
$630$	1.53480e6			0.154063
$631$	−1.39222e7	+	5.06727e6i	−1.39198	+	0.506641i	−0.925789	−	0.378041i	$-0.876598\pi$
$631$	−1.39222e7	+	5.06727e6i	−1.39198	+	0.506641i	−0.466195	+	0.884682i	$0.654376\pi$
$632$	−2.37381e6	−	863996.i	−0.236403	−	0.0860437i
$633$	−6.00612e6	+	5.03973e6i	−0.595778	+	0.499917i
$634$	382776.	+	2.17083e6i	0.0378200	+	0.214488i
$635$	5.98072e6			0.588599
$636$	−561186.	−	3.18264e6i	−0.0550128	−	0.311993i
$637$	1.23135e7	−	2.13276e7i	1.20235	−	2.08254i
$638$	−2.53434e6	−	2.12657e6i	−0.246498	−	0.206837i
$639$	447014.	+	774251.i	0.0433081	+	0.0750118i
$640$	−531612.	+	920779.i	−0.0513032	+	0.0888598i
$641$	3.99293e6	−	1.45331e6i	0.383837	−	0.139705i	−0.142893	−	0.989738i	$-0.545640\pi$
$641$	3.99293e6	−	1.45331e6i	0.383837	−	0.139705i	0.526729	+	0.850033i	$0.323418\pi$
$642$	−274943.	+	230705.i	−0.0263272	+	0.0220912i
$643$	−9.60020e6	−	1.66280e7i	−0.915699	−	1.58604i	−0.805874	−	0.592087i	$-0.798304\pi$
$643$	−9.60020e6	−	1.66280e7i	−0.915699	−	1.58604i	−0.109825	−	0.993951i	$-0.535029\pi$
$644$	977556.	−	5.54399e6i	0.0928810	−	0.526754i
$645$	2.84486e6	−	1.61340e7i	0.269254	−	1.52701i
$646$	−7.85723e6	−	6.59300e6i	−0.740778	−	0.621586i
$647$	1.22246e7	+	4.44939e6i	1.14808	+	0.417869i	0.844827	−	0.535040i	$-0.179703\pi$
$647$	1.22246e7	+	4.44939e6i	1.14808	+	0.417869i	0.303258	+	0.952908i	$0.401926\pi$
$648$	3.13792e6	+	1.14211e6i	0.293565	+	0.106849i
$649$	1.91577e6	+	1.60752e6i	0.178538	+	0.149811i
$650$	−507788.	+	2.87981e6i	−0.0471410	+	0.267350i
$651$	4.67083e6	−	2.64896e7i	0.431958	−	2.44976i
$652$	5.04740e6	+	8.74235e6i	0.464995	+	0.805396i
$653$	−541191.	+	454113.i	−0.0496670	+	0.0416755i	−0.667283	−	0.744804i	$-0.732543\pi$
$653$	−541191.	+	454113.i	−0.0496670	+	0.0416755i	0.617616	+	0.786480i	$0.288098\pi$
$654$	−8.53079e6	+	3.10495e6i	−0.779911	+	0.283864i
$655$	6.47981e6	−	1.12234e7i	0.590145	−	1.02216i
$656$	−1.77668e6	−	3.07729e6i	−0.161194	−	0.279196i
$657$	−1.19681e6	−	1.00425e6i	−0.108172	−	0.0907667i
$658$	488663.	−	846389.i	0.0439992	−	0.0762088i
$659$	3.13949e6	+	1.78049e7i	0.281608	+	1.59708i	0.717154	+	0.696914i	$0.245444\pi$
$659$	3.13949e6	+	1.78049e7i	0.281608	+	1.59708i	−0.435546	+	0.900166i	$0.643445\pi$
$660$	−2.12658e6			−0.190030
$661$	−3.30018e6	−	1.87163e7i	−0.293788	−	1.66616i	−0.672087	−	0.740472i	$-0.734602\pi$
$661$	−3.30018e6	−	1.87163e7i	−0.293788	−	1.66616i	0.378299	−	0.925683i	$-0.376509\pi$
$662$	4.44741e6	−	3.73182e6i	0.394423	−	0.330960i
$663$	1.82914e7	+	6.65752e6i	1.61608	+	0.588205i
$664$	−400432.	+	145745.i	−0.0352459	+	0.0128285i
$665$	1.96036e7			1.71902
$666$	43770.1	+	851162.i	0.00382377	+	0.0743578i
$667$	−9.06615e6			−0.789057
$668$	8.02845e6	−	2.92212e6i	0.696130	−	0.253371i
$669$	5.04407e6	+	1.83589e6i	0.435728	+	0.158592i
$670$	6.02650e6	−	5.05684e6i	0.518655	−	0.435203i
$671$	−842226.	−	4.77650e6i	−0.0722141	−	0.409547i
$672$	−3.48906e6			−0.298047
$673$	−502991.	−	2.85260e6i	−0.0428077	−	0.242775i	0.955894	−	0.293711i	$-0.0948905\pi$
$673$	−502991.	−	2.85260e6i	−0.0428077	−	0.242775i	−0.998702	+	0.0509366i	$0.983779\pi$
$674$	1.14118e6	−	1.97659e6i	0.0967621	−	0.167597i
$675$	−3.29538e6	−	2.76515e6i	−0.278385	−	0.233593i
$676$	−653321.	−	1.13159e6i	−0.0549870	−	0.0952403i
$677$	1.96324e6	−	3.40042e6i	0.164627	−	0.285142i	−0.771896	−	0.635749i	$-0.780691\pi$
$677$	1.96324e6	−	3.40042e6i	0.164627	−	0.285142i	0.936523	+	0.350607i	$0.114025\pi$
$678$	1.08964e7	−	3.96598e6i	0.910354	−	0.331342i
$679$	−1.42101e7	+	1.19237e7i	−1.18284	+	0.992517i
$680$	−4.07328e6	−	7.05512e6i	−0.337809	−	0.585103i
$681$	665117.	−	3.77206e6i	0.0549579	−	0.311682i
$682$	761660.	−	4.31959e6i	0.0627047	−	0.355616i
$683$	−1.10276e6	−	925329.i	−0.0904547	−	0.0759005i	0.596439	−	0.802658i	$-0.296582\pi$
$683$	−1.10276e6	−	925329.i	−0.0904547	−	0.0759005i	−0.686894	+	0.726758i	$0.741026\pi$
$684$	−502913.	−	183045.i	−0.0411010	−	0.0149596i
$685$	−1.56511e7	−	5.69655e6i	−1.27444	−	0.463859i
$686$	−1.40090e7	−	1.17550e7i	−1.13657	−	0.953699i
$687$	−1.35140e6	+	7.66419e6i	−0.109243	+	0.619547i
$688$	761120.	−	4.31653e6i	0.0613031	−	0.347667i
$689$	−4.60970e6	−	7.98424e6i	−0.369934	−	0.640745i
$690$	−4.46424e6	+	3.74594e6i	−0.356964	+	0.299529i
$691$	−1.48604e7	+	5.40873e6i	−1.18395	+	0.430923i	−0.857596	−	0.514324i	$-0.828043\pi$
$691$	−1.48604e7	+	5.40873e6i	−1.18395	+	0.430923i	−0.326356	+	0.945247i	$0.605821\pi$
$692$	−4.08002e6	+	7.06680e6i	−0.323889	+	0.560993i
$693$	410649.	+	711266.i	0.0324816	+	0.0562599i
$694$	6.48544e6	+	5.44193e6i	0.511141	+	0.428899i
$695$	−1.00168e7	+	1.73495e7i	−0.786620	+	1.36247i
$696$	975730.	+	5.53364e6i	0.0763495	+	0.433000i
$697$	2.72262e7			2.12278
$698$	1.56791e6	+	8.89208e6i	0.121810	+	0.690820i
$699$	2.69459e6	−	2.26103e6i	0.208593	−	0.175030i
$700$	3.77393e6	+	1.37360e6i	0.291105	+	0.105953i
$701$	−1.58334e7	+	5.76288e6i	−1.21697	+	0.442939i	−0.869115	−	0.494610i	$-0.835311\pi$
$701$	−1.58334e7	+	5.76288e6i	−1.21697	+	0.442939i	−0.347851	+	0.937550i	$0.613089\pi$
$702$	1.06615e7			0.816534
$703$	559065.	+	1.08717e7i	0.0426652	+	0.829676i
$704$	−568951.			−0.0432656
$705$	−950708.	+	346030.i	−0.0720401	+	0.0262205i
$706$	−8.45051e6	−	3.07574e6i	−0.638074	−	0.232240i
$707$	−1.09247e7	+	9.16692e6i	−0.821980	+	0.689723i
$708$	−737576.	−	4.18300e6i	−0.0552998	−	0.313621i
$709$	55978.6			0.00418222			0.00209111	−	0.999998i	$-0.499334\pi$
$709$	55978.6			0.00418222			0.00209111	+	0.999998i	$0.499334\pi$
$710$	1.57494e6	+	8.93194e6i	0.117252	+	0.664967i
$711$	504976.	−	874645.i	0.0374625	−	0.0648870i
$712$	−1.19507e6	−	1.00278e6i	−0.0883473	−	0.0741322i
$713$	−6.00997e6	−	1.04096e7i	−0.442739	−	0.766847i
$714$	1.33668e7	−	2.31520e7i	0.981255	−	1.69958i
$715$	−5.70078e6	+	2.07491e6i	−0.417032	+	0.151787i
$716$	−366241.	+	307312.i	−0.0266983	+	0.0224026i
$717$	67593.7	+	117076.i	0.00491030	+	0.00850489i
$718$	386055.	−	2.18943e6i	0.0279472	−	0.158496i
$719$	−3.79778e6	+	2.15383e7i	−0.273973	+	1.55378i	0.468232	+	0.883605i	$0.344891\pi$
$719$	−3.79778e6	+	2.15383e7i	−0.273973	+	1.55378i	−0.742205	+	0.670173i	$0.766220\pi$
$720$	−325627.	−	273233.i	−0.0234093	−	0.0196427i
$721$	−110742.	−	40306.7i	−0.00793365	−	0.00288761i
$722$	2.88350e6	+	1.04951e6i	0.205862	+	0.0749277i
$723$	7.86258e6	+	6.59749e6i	0.559396	+	0.469389i
$724$	−383152.	+	2.17296e6i	−0.0271659	+	0.154066i
$725$	1.12313e6	−	6.36959e6i	0.0793570	−	0.450056i
$726$	4.18038e6	+	7.24064e6i	0.294357	+	0.509842i
$727$	286580.	−	240469.i	0.0201099	−	0.0168742i	−0.632677	−	0.774416i	$-0.718044\pi$
$727$	286580.	−	240469.i	0.0201099	−	0.0168742i	0.652787	+	0.757541i	$0.273600\pi$
$728$	−9.35320e6	+	3.40429e6i	−0.654081	+	0.238066i
$729$	−7.76243e6	+	1.34449e7i	−0.540977	+	0.937000i
$730$	−7.92475e6	−	1.37261e7i	−0.550400	−	0.953321i
$731$	2.57268e7	+	2.15874e7i	1.78071	+	1.49419i
$732$	−4.11885e6	+	7.13406e6i	−0.284118	+	0.492107i
$733$	3.51426e6	+	1.99304e7i	0.241587	+	1.37011i	0.828286	+	0.560305i	$0.189316\pi$
$733$	3.51426e6	+	1.99304e7i	0.241587	+	1.37011i	−0.586699	+	0.809805i	$0.699573\pi$
$734$	−3.24522e6			−0.222333
$735$	6.07995e6	+	3.44811e7i	0.415127	+	2.35430i
$736$	−1.19437e6	+	1.00220e6i	−0.0812729	+	0.0681960i
$737$	3.95592e6	+	1.43984e6i	0.268274	+	0.0976437i
$738$	1.33495e6	−	485883.i	0.0902245	−	0.0328390i
$739$	9.61862e6			0.647891			0.323945	−	0.946076i	$-0.394991\pi$
$739$	9.61862e6			0.647891			0.323945	+	0.946076i	$0.394991\pi$
$740$	−2.53604e6	+	8.26599e6i	−0.170246	+	0.554901i
$741$	1.29729e7			0.867945
$742$	−1.18983e7	+	4.33063e6i	−0.793369	+	0.288763i
$743$	1.51099e7	+	5.49954e6i	1.00413	+	0.365472i	0.791174	−	0.611591i	$-0.209470\pi$
$743$	1.51099e7	+	5.49954e6i	1.00413	+	0.365472i	0.212952	+	0.977063i	$0.431692\pi$
$744$	−5.70680e6	+	4.78857e6i	−0.377972	+	0.317157i
$745$	3.53593e6	+	2.00533e7i	0.233407	+	1.32371i
$746$	−2.02003e7			−1.32896
$747$	−29583.8	−	167778.i	−0.00193978	−	0.0110011i
$748$	2.17969e6	−	3.77533e6i	0.142443	−	0.246718i
$749$	1.07722e6	+	903897.i	0.0701618	+	0.0588728i
$750$	3.90162e6	+	6.75780e6i	0.253275	+	0.438685i
$751$	2.17230e6	−	3.76253e6i	0.140546	−	0.243433i	−0.787156	−	0.616754i	$-0.788447\pi$
$751$	2.17230e6	−	3.76253e6i	0.140546	−	0.243433i	0.927702	+	0.373320i	$0.121781\pi$
$752$	−254355.	+	92577.6i	−0.0164019	+	0.00596982i
$753$	33027.3	−	27713.2i	0.00212268	−	0.00178114i
$754$	8.01486e6	+	1.38821e7i	0.513414	+	0.889259i
$755$	5.14660e6	−	2.91878e7i	0.328589	−	1.86352i
$756$	2.54263e6	−	1.44200e7i	0.161800	−	0.917614i
$757$	5.86587e6	+	4.92205e6i	0.372043	+	0.312181i	0.809569	−	0.587025i	$-0.199701\pi$
$757$	5.86587e6	+	4.92205e6i	0.372043	+	0.312181i	−0.437526	+	0.899206i	$0.644145\pi$
$758$	1.10535e7	+	4.02313e6i	0.698756	+	0.254326i
$759$	−2.93042e6	−	1.06658e6i	−0.184640	−	0.0672033i
$760$	−4.15915e6	−	3.48994e6i	−0.261198	−	0.219172i
$761$	5.07777e6	−	2.87974e7i	0.317842	−	1.80257i	−0.237981	−	0.971270i	$-0.576486\pi$
$761$	5.07777e6	−	2.87974e7i	0.317842	−	1.80257i	0.555823	−	0.831301i	$-0.312403\pi$
$762$	943891.	−	5.35307e6i	0.0588891	−	0.333976i
$763$	1.77843e7	+	3.08033e7i	1.10592	+	1.91551i
$764$	7.06204e6	−	5.92575e6i	0.437720	−	0.367291i
$765$	3.06056e6	−	1.11395e6i	0.189081	−	0.0688198i
$766$	3.70910e6	−	6.42434e6i	0.228400	−	0.395600i
$767$	−6.05861e6	−	1.04938e7i	−0.371864	−	0.644088i
$768$	740247.	+	621141.i	0.0452870	+	0.0380003i
$769$	−2.76202e6	+	4.78396e6i	−0.168427	+	0.291724i	−0.937867	−	0.346995i	$-0.887202\pi$
$769$	−2.76202e6	+	4.78396e6i	−0.168427	+	0.291724i	0.769440	+	0.638719i	$0.220535\pi$
$770$	1.44682e6	+	8.20533e6i	0.0879403	+	0.498734i
$771$	2.34247e7			1.41918
$772$	2.64287e6	+	1.49884e7i	0.159600	+	0.905135i
$773$	1.26848e7	−	1.06438e7i	0.763547	−	0.640692i	−0.175501	−	0.984479i	$-0.556154\pi$
$773$	1.26848e7	−	1.06438e7i	0.763547	−	0.640692i	0.939048	+	0.343787i	$0.111710\pi$
$774$	1.64668e6	+	599344.i	0.0988002	+	0.0359603i
$775$	8.05795e6	−	2.93286e6i	0.481915	−	0.175403i
$776$	5.13759e6			0.306270
$777$	−2.76525e7	+	6.35551e6i	−1.64317	+	0.377657i
$778$	−1.26336e7			−0.748304
$779$	1.70510e7	−	6.20606e6i	1.00672	−	0.366414i
$780$	9.68238e6	+	3.52410e6i	0.569830	+	0.207401i
$781$	−3.71791e6	+	3.11969e6i	−0.218108	+	0.183014i
$782$	−2.07446e6	−	1.17649e7i	−0.121308	−	0.687971i
$783$	−2.35811e7			−1.37455
$784$	1.62664e6	+	9.22515e6i	0.0945153	+	0.536023i
$785$	5.68246e6	−	9.84230e6i	0.329126	−	0.570063i
$786$	−9.02286e6	−	7.57108e6i	−0.520940	−	0.437121i
$787$	−6.48658e6	−	1.12351e7i	−0.373318	−	0.646606i	0.616756	−	0.787155i	$-0.288447\pi$
$787$	−6.48658e6	−	1.12351e7i	−0.373318	−	0.646606i	−0.990074	+	0.140549i	$0.955113\pi$
$788$	−1.18514e6	+	2.05273e6i	−0.0679917	+	0.117765i
$789$	−1.85978e7	+	6.76906e6i	−1.06358	+	0.387111i
$790$	7.84871e6	−	6.58585e6i	0.447436	−	0.375443i
$791$	−2.27160e7	−	3.93452e7i	−1.29089	−	2.23589i
$792$	39499.0	−	224010.i	0.00223755	−	0.0126898i
$793$	−4.08078e6	+	2.31432e7i	−0.230441	+	1.30690i
$794$	−1.02424e7	−	8.59435e6i	−0.576565	−	0.483796i
$795$	1.23171e7	+	4.48304e6i	0.691177	+	0.251568i
$796$	−3.34674e6	−	1.21811e6i	−0.187214	−	0.0681404i
$797$	−1.03095e7	−	8.65069e6i	−0.574899	−	0.482397i	0.308369	−	0.951267i	$-0.400217\pi$
$797$	−1.03095e7	−	8.65069e6i	−0.574899	−	0.482397i	−0.883267	+	0.468870i	$0.844661\pi$
$798$	3.09388e6	−	1.75463e7i	0.171987	−	0.975389i
$799$	360142.	−	2.04247e6i	0.0199575	−	0.113185i
$800$	−556151.	−	963283.i	−0.0307233	−	0.0532143i
$801$	477787.	−	400911.i	0.0263119	−	0.0220783i
$802$	−2.33914e7	+	8.51377e6i	−1.28416	+	0.467397i
$803$	4.24068e6	−	7.34508e6i	0.232085	−	0.401983i
$804$	−3.57503e6	−	6.19213e6i	−0.195047	−	0.337831i
$805$	1.74908e7	+	1.46765e7i	0.951306	+	0.798241i
$806$	−1.06261e7	+	1.84050e7i	−0.576152	+	0.997925i
$807$	−319372.	−	1.81125e6i	−0.0172628	−	0.0979025i
$808$	3.94976e6			0.212835
$809$	3.94502e6	+	2.23733e7i	0.211923	+	1.20187i	0.886167	+	0.463366i	$0.153358\pi$
$809$	3.94502e6	+	2.23733e7i	0.211923	+	1.20187i	−0.674244	+	0.738509i	$0.735530\pi$
$810$	−1.03752e7	+	8.70579e6i	−0.555625	+	0.466225i
$811$	−2.14636e6	−	781213.i	−0.114591	−	0.0417078i	0.284088	−	0.958798i	$-0.408309\pi$
$811$	−2.14636e6	−	781213.i	−0.114591	−	0.0417078i	−0.398679	+	0.917090i	$0.630531\pi$
$812$	2.06875e7	−	7.52963e6i	1.10108	−	0.400759i
$813$	2.88359e6			0.153006
$814$	−4.50922e6	+	1.03638e6i	−0.238528	+	0.0548222i
$815$	−4.09432e7			−2.15918
$816$	−6.95757e6	+	2.53235e6i	−0.365791	+	0.133137i
$817$	2.10327e7	+	7.65528e6i	1.10240	+	0.401241i
$818$	1.32828e7	−	1.11456e7i	0.694077	−	0.582399i
$819$	−691012.	−	3.91892e6i	−0.0359978	−	0.204154i
$820$	1.44120e7			0.748494
$821$	−2.84087e6	−	1.61114e7i	−0.147093	−	0.834208i	−0.965662	−	0.259800i	$-0.916343\pi$
$821$	−2.84087e6	−	1.61114e7i	−0.147093	−	0.834208i	0.818569	−	0.574408i	$-0.194768\pi$
$822$	−7.56882e6	+	1.31096e7i	−0.390705	+	0.676721i
$823$	906201.	+	760393.i	0.0466364	+	0.0391326i	0.665808	−	0.746123i	$-0.268087\pi$
$823$	906201.	+	760393.i	0.0466364	+	0.0391326i	−0.619172	+	0.785256i	$0.712531\pi$
$824$	16319.6	+	28266.4i	0.000837321	+	0.00145028i
$825$	1.11237e6	−	1.92669e6i	0.0569004	−	0.0985545i
$826$	−1.56381e7	+	5.69181e6i	−0.797507	+	0.290269i
$827$	6.25687e6	−	5.25014e6i	0.318122	−	0.266936i	−0.469717	−	0.882817i	$-0.655644\pi$
$827$	6.25687e6	−	5.25014e6i	0.318122	−	0.266936i	0.787839	+	0.615881i	$0.211200\pi$
$828$	−311672.	−	539831.i	−0.0157987	−	0.0273642i
$829$	2.68049e6	−	1.52018e7i	0.135465	−	0.768262i	−0.839069	−	0.544025i	$-0.816900\pi$
$829$	2.68049e6	−	1.52018e7i	0.135465	−	0.768262i	0.974535	−	0.224237i	$-0.0719891\pi$
$830$	300122.	−	1.70208e6i	0.0151218	−	0.0857599i
$831$	8.96943e6	+	7.52625e6i	0.450570	+	0.378073i
$832$	2.59045e6	+	942846.i	0.129738	+	0.0472207i
$833$	−6.74462e7	−	2.45484e7i	−3.36779	−	1.22578i
$834$	1.39479e7	+	1.17037e7i	0.694375	+	0.582650i
$835$	−6.01729e6	+	3.41257e7i	−0.298665	+	1.69381i
$836$	504511.	−	2.86123e6i	0.0249664	−	0.141591i
$837$	−1.56320e7	−	2.70754e7i	−0.771259	−	1.33586i
$838$	8.29664e6	−	6.96171e6i	0.408124	−	0.342457i
$839$	−4.60596e6	+	1.67643e6i	−0.225899	+	0.0822207i	−0.452490	−	0.891769i	$-0.649464\pi$
$839$	−4.60596e6	+	1.67643e6i	−0.225899	+	0.0822207i	0.226591	+	0.973990i	$0.427242\pi$
$840$	7.07559e6	−	1.22553e7i	0.345991	−	0.599273i
$841$	−7.47176e6	−	1.29415e7i	−0.364278	−	0.630948i
$842$	−243365.	−	204208.i	−0.0118298	−	0.00992641i
$843$	8.12141e6	−	1.40667e7i	0.393607	−	0.681747i
$844$	−1.47736e6	−	8.37855e6i	−0.0713890	−	0.404867i
$845$	5.29958e6			0.255329
$846$	−18791.7	−	106573.i	−0.000902692	−	0.00511942i
$847$	2.50936e7	−	2.10560e7i	1.20186	−	1.00848i
$848$	3.29533e6	+	1.19940e6i	0.157366	+	0.0572764i
$849$	5.96806e6	−	2.17220e6i	0.284161	−	0.103426i
$850$	8.52261e6			0.404599
$851$	−7.64044e6	+	1.01185e7i	−0.361655	+	0.478954i
$852$	8.24313e6			0.389039
$853$	−3.53086e7	+	1.28513e7i	−1.66153	+	0.604746i	−0.990602	−	0.136778i	$-0.956325\pi$
$853$	−3.53086e7	+	1.28513e7i	−1.66153	+	0.604746i	−0.670925	+	0.741525i	$0.734103\pi$
$854$	3.03288e7	+	1.10388e7i	1.42302	+	0.517936i
$855$	1.66282e6	−	1.39527e6i	0.0777912	−	0.0652746i
$856$	−67629.5	−	383546.i	−0.00315466	−	0.0178909i
$857$	−7.65517e6			−0.356043			−0.178022	−	0.984027i	$-0.556970\pi$
$857$	−7.65517e6			−0.356043			−0.178022	+	0.984027i	$0.556970\pi$
$858$	957451.	+	5.42998e6i	0.0444016	+	0.251814i
$859$	−7.03079e6	+	1.21777e7i	−0.325103	+	0.563095i	−0.981533	−	0.191292i	$-0.938732\pi$
$859$	−7.03079e6	+	1.21777e7i	−0.325103	+	0.563095i	0.656430	+	0.754387i	$0.272066\pi$
$860$	1.36183e7	+	1.14271e7i	0.627879	+	0.526853i
$861$	2.36470e7	+	4.09578e7i	1.08710	+	1.88291i
$862$	7.39376e6	−	1.28064e7i	0.338920	−	0.587027i
$863$	3.54922e7	−	1.29181e7i	1.62221	−	0.590435i	0.638406	−	0.769700i	$-0.279594\pi$
$863$	3.54922e7	−	1.29181e7i	1.62221	−	0.590435i	0.983801	+	0.179265i	$0.0573720\pi$
$864$	−3.10657e6	+	2.60673e6i	−0.141579	+	0.118798i
$865$	−1.65480e7	−	2.86621e7i	−0.751980	−	1.30247i
$866$	−2.32058e6	+	1.31607e7i	−0.105148	+	0.596326i
$867$	6.21581e6	−	3.52516e7i	0.280834	−	1.59269i
$868$	2.23591e7	+	1.87615e7i	1.00729	+	0.845219i
$869$	5.15205e6	+	1.87519e6i	0.231436	+	0.0842358i
$870$	−2.14156e7	−	7.79463e6i	−0.959250	−	0.349138i
$871$	−1.56253e7	−	1.31112e7i	−0.697886	−	0.585596i
$872$	1.71061e6	−	9.70135e6i	0.0761833	−	0.432057i
$873$	−356674.	+	2.02280e6i	−0.0158393	+	0.0898290i
$874$	−3.98091e6	−	6.89513e6i	−0.176280	−	0.305326i
$875$	2.34202e7	−	1.96519e7i	1.03412	−	0.867730i
$876$	−1.35363e7	+	4.92681e6i	−0.595991	+	0.216923i
$877$	630354.	−	1.09180e6i	0.0276748	−	0.0479342i	−0.851856	−	0.523776i	$-0.824523\pi$
$877$	630354.	−	1.09180e6i	0.0276748	−	0.0479342i	0.879531	+	0.475841i	$0.157856\pi$
$878$	7.77932e6	+	1.34742e7i	0.340569	+	0.589883i
$879$	−9.60559e6	−	8.06005e6i	−0.419326	−	0.351856i
$880$	1.15380e6	−	1.99843e6i	0.0502253	−	0.0869928i
$881$	−3.16391e6	−	1.79434e7i	−0.137336	−	0.778871i	−0.973205	−	0.229941i	$-0.926147\pi$
$881$	−3.16391e6	−	1.79434e7i	−0.137336	−	0.778871i	0.835869	−	0.548930i	$-0.184964\pi$
$882$	−3.74510e6			−0.162103
$883$	−4.60401e6	−	2.61106e7i	−0.198717	−	1.12698i	−0.907026	−	0.421075i	$-0.861653\pi$
$883$	−4.60401e6	−	2.61106e7i	−0.198717	−	1.12698i	0.708309	−	0.705902i	$-0.249458\pi$
$884$	−1.61805e7	+	1.35771e7i	−0.696405	+	0.584353i
$885$	1.61885e7	+	5.89214e6i	0.694782	+	0.252880i
$886$	−1.67199e7	+	6.08555e6i	−0.715566	+	0.260445i
$887$	−6.84301e6			−0.292037			−0.146019	−	0.989282i	$-0.546646\pi$
$887$	−6.84301e6			−0.292037			−0.146019	+	0.989282i	$0.546646\pi$
$888$	6.99827e6	+	3.57445e6i	0.297823	+	0.152117i
$889$	−2.12968e7			−0.903774
$890$	5.94579e6	−	2.16409e6i	0.251614	−	0.0915800i
$891$	−6.81046e6	−	2.47881e6i	−0.287397	−	0.104604i
$892$	−4.46197e6	+	3.74403e6i	−0.187765	+	0.157553i
$893$	−240022.	−	1.36123e6i	−0.0100721	−	0.0571220i
$894$	1.85068e7			0.774440
$895$	−336719.	−	1.90963e6i	−0.0140511	−	0.0796877i
$896$	1.89302e6	−	3.27881e6i	0.0787744	−	0.136441i
$897$	1.15748e7	+	9.71237e6i	0.480320	+	0.403036i
$898$	1.63251e7	+	2.82760e7i	0.675564	+	1.17011i
$899$	2.35030e7	−	4.07083e7i	0.969892	−	1.67990i
$900$	417879.	−	152095.i	0.0171966	−	0.00625907i
$901$	−2.05834e7	+	1.72715e7i	−0.844705	+	0.708792i
$902$	3.85605e6	+	6.67888e6i	0.157807	+	0.273330i
$903$	−1.01303e7	+	5.74517e7i	−0.413430	+	2.34468i
$904$	−2.18497e6	+	1.23916e7i	−0.0889253	+	0.504320i
$905$	−6.85550e6	−	5.75245e6i	−0.278239	−	0.233470i
$906$	−2.53125e7	−	9.21298e6i	−1.02450	−	0.372889i
$907$	3.49634e7	+	1.27256e7i	1.41122	+	0.513642i	0.931488	−	0.363772i	$-0.118511\pi$
$907$	3.49634e7	+	1.27256e7i	1.41122	+	0.513642i	0.479733	+	0.877415i	$0.340734\pi$
$908$	3.18390e6	+	2.67161e6i	0.128158	+	0.107537i
$909$	−274209.	+	1.55512e6i	−0.0110071	+	0.0624243i
$910$	7.01018e6	−	3.97567e7i	0.280625	−	1.59150i
$911$	−9.39672e6	−	1.62756e7i	−0.375129	−	0.649742i	0.615218	−	0.788357i	$-0.289068\pi$
$911$	−9.39672e6	−	1.62756e7i	−0.375129	−	0.649742i	−0.990346	+	0.138615i	$0.955735\pi$
$912$	−3.78009e6	+	3.17188e6i	−0.150493	+	0.126278i
$913$	869088.	−	316322.i	0.0345054	−	0.0125589i
$914$	−1.86117e6	+	3.22365e6i	−0.0736921	+	0.127639i
$915$	−1.67056e7	−	2.89349e7i	−0.659642	−	1.14253i
$916$	−6.46913e6	−	5.42825e6i	−0.254746	−	0.213757i
$917$	−2.30740e7	+	3.99653e7i	−0.906149	+	1.56950i
$918$	−5.39570e6	−	3.06005e7i	−0.211320	−	1.19846i
$919$	−2.20807e7			−0.862431			−0.431215	−	0.902249i	$-0.641915\pi$
$919$	−2.20807e7			−0.862431			−0.431215	+	0.902249i	$0.641915\pi$
$920$	−1.09810e6	−	6.22762e6i	−0.0427732	−	0.242579i
$921$	−2.52535e7	+	2.11902e7i	−0.981007	+	0.823163i
$922$	−6.86498e6	−	2.49865e6i	−0.265957	−	0.0968006i
$923$	2.20976e7	−	8.04286e6i	0.853769	−	0.310746i
$924$	7.57256e6			0.291785
$925$	−6.16245e6	−	6.62143e6i	−0.236809	−	0.254447i
$926$	3.32897e7			1.27580
$927$	−12262.2	+	4463.06i	−0.000468671	+	0.000170582i
$928$	−5.72958e6	−	2.08540e6i	−0.218400	−	0.0794911i
$929$	2.32930e7	−	1.95452e7i	0.885496	−	0.743020i	−0.0818052	−	0.996648i	$-0.526069\pi$
$929$	2.32930e7	−	1.95452e7i	0.885496	−	0.743020i	0.967302	+	0.253629i	$0.0816241\pi$
$930$	−5.24679e6	−	2.97560e7i	−0.198923	−	1.12815i
$931$	−4.78353e7			−1.80873
$932$	662806.	+	3.75896e6i	0.0249946	+	0.141752i
$933$	5.61332e6	−	9.72255e6i	0.211113	−	0.365659i
$934$	2.76151e7	+	2.31718e7i	1.03581	+	0.869147i
$935$	8.84054e6	+	1.53123e7i	0.330712	+	0.572810i
$936$	−551062.	+	954467.i	−0.0205594	+	0.0356099i
$937$	−3.87746e7	+	1.41128e7i	−1.44277	+	0.525127i	−0.940563	−	0.339618i	$-0.889702\pi$
$937$	−3.87746e7	+	1.41128e7i	−1.44277	+	0.525127i	−0.502211	+	0.864745i	$0.667480\pi$
$938$	−2.14598e7	+	1.80069e7i	−0.796377	+	0.668240i
$939$	−8.83648e6	−	1.53052e7i	−0.327051	−	0.566469i
$940$	190638.	−	1.08116e6i	0.00703703	−	0.0399090i
$941$	11217.0	−	63614.6i	0.000412954	−	0.00234198i	−0.984601	−	0.174819i	$-0.944066\pi$
$941$	11217.0	−	63614.6i	0.000412954	−	0.00234198i	0.985014	+	0.172477i	$0.0551771\pi$
$942$	−7.91258e6	−	6.63944e6i	−0.290530	−	0.243784i
$943$	1.98596e7	+	7.22830e6i	0.727262	+	0.264702i
$944$	4.33111e6	+	1.57640e6i	0.158187	+	0.0575752i
$945$	4.54937e7	+	3.81738e7i	1.65719	+	1.39055i
$946$	−1.65192e6	+	9.36849e6i	−0.0600151	+	0.340362i
$947$	6.43756e6	−	3.65092e7i	0.233263	−	1.32290i	−0.612978	−	0.790100i	$-0.710028\pi$
$947$	6.43756e6	−	3.65092e7i	0.233263	−	1.32290i	0.846241	−	0.532801i	$-0.178860\pi$
$948$	−4.65599e6	−	8.06442e6i	−0.168264	−	0.291442i
$949$	−3.14800e7	+	2.64148e7i	−1.13467	+	0.952099i
$950$	5.33746e6	−	1.94268e6i	0.191878	−	0.0698380i
$951$	−4.06281e6	+	7.03700e6i	−0.145672	+	0.252311i
$952$	1.45046e7	+	2.51226e7i	0.518695	+	0.898406i
$953$	−2.66773e7	−	2.23849e7i	−0.951501	−	0.798404i	0.0280486	−	0.999607i	$-0.491071\pi$
$953$	−2.66773e7	−	2.23849e7i	−0.951501	−	0.798404i	−0.979550	+	0.201202i	$0.935515\pi$
$954$	−701011.	+	1.21419e6i	−0.0249376	+	0.0431931i
$955$	6.49278e6	+	3.68224e7i	0.230368	+	1.30648i
$956$	−146694.			−0.00519121
$957$	−2.11770e6	−	1.20101e7i	−0.0747454	−	0.423902i
$958$	−1.16206e7	+	9.75082e6i	−0.409085	+	0.343263i
$959$	5.57323e7	+	2.02849e7i	1.95686	+	0.712240i
$960$	−3.68293e6	+	1.34048e6i	−0.128978	+	0.0469441i
$961$	3.36915e7			1.17682
$962$	2.22480e7	+	2.75388e6i	0.775093	+	0.0959415i
$963$	155707.			0.00541055
$964$	−1.04658e7	+	3.80926e6i	−0.362729	+	0.132022i
$965$	−5.80064e7	−	2.11126e7i	−2.00520	−	0.729832i
$966$	1.58967e7	−	1.33389e7i	0.548107	−	0.459916i
$967$	−1.35582e6	−	7.68924e6i	−0.0466269	−	0.264434i	0.952578	−	0.304293i	$-0.0984202\pi$
$967$	−1.35582e6	−	7.68924e6i	−0.0466269	−	0.264434i	−0.999205	+	0.0398591i	$0.987309\pi$
$968$	−9.07243e6			−0.311197
$969$	−6.56551e6	−	3.72348e7i	−0.224625	−	1.27391i
$970$	−1.04187e7	+	1.80457e7i	−0.355537	+	0.615808i
$971$	3.68240e7	+	3.08990e7i	1.25338	+	1.05171i	0.996355	+	0.0853061i	$0.0271868\pi$
$971$	3.68240e7	+	3.08990e7i	1.25338	+	1.05171i	0.257025	+	0.966405i	$0.417258\pi$
$972$	−1.54409e6	−	2.67445e6i	−0.0524213	−	0.0907963i
$973$	3.56687e7	−	6.17800e7i	1.20783	−	2.09202i
$974$	−2.45891e7	+	8.94970e6i	−0.830511	+	0.302281i
$975$	−8.25750e6	+	6.92887e6i	−0.278187	+	0.233427i
$976$	−4.46944e6	−	7.74131e6i	−0.150186	−	0.260130i
$977$	3.97128e6	−	2.25223e7i	0.133105	−	0.754876i	−0.843056	−	0.537826i	$-0.819246\pi$
$977$	3.97128e6	−	2.25223e7i	0.133105	−	0.754876i	0.976161	−	0.217050i	$-0.0696433\pi$
$978$	−6.46176e6	+	3.66464e7i	−0.216025	+	1.22514i
$979$	2.59375e6	+	2.17641e6i	0.0864910	+	0.0725746i
$980$	−3.57020e7	−	1.29945e7i	−1.18748	−	0.432209i
$981$	3.70090e6	+	1.34702e6i	0.122782	+	0.0446891i
$982$	−1.26433e7	−	1.06090e7i	−0.418392	−	0.351072i
$983$	−7.92305e6	+	4.49339e7i	−0.261522	+	1.48317i	0.517236	+	0.855843i	$0.326961\pi$
$983$	−7.92305e6	+	4.49339e7i	−0.261522	+	1.48317i	−0.778758	+	0.627324i	$0.784150\pi$
$984$	2.27453e6	−	1.28995e7i	0.0748865	−	0.424702i
$985$	−4.80680e6	−	8.32562e6i	−0.157858	−	0.273417i
$986$	3.57882e7	−	3.00299e7i	1.17232	−	0.983697i
$987$	3.38538e6	−	1.23218e6i	0.110615	−	0.0402607i
$988$	−7.03858e6	+	1.21912e7i	−0.229400	+	0.397332i
$989$	1.30346e7	+	2.25767e7i	0.423749	+	0.733955i
$990$	706732.	+	593018.i	0.0229175	+	0.0192300i
$991$	1.68786e6	−	2.92346e6i	0.0545950	−	0.0945614i	−0.837436	−	0.546535i	$-0.815947\pi$
$991$	1.68786e6	−	2.92346e6i	0.0545950	−	0.0945614i	0.892031	+	0.451974i	$0.149280\pi$
$992$	−1.40374e6	−	7.96099e6i	−0.0452905	−	0.256855i
$993$	2.14011e7			0.688752
$994$	−5.60822e6	−	3.18058e7i	−0.180036	−	1.02103i
$995$	1.10656e7	−	9.28513e6i	0.354337	−	0.297324i
$996$	−1.47609e6	−	537251.i	−0.0471480	−	0.0171605i
$997$	3.69007e7	−	1.34307e7i	1.17570	−	0.427920i	0.321019	−	0.947073i	$-0.395975\pi$
$997$	3.69007e7	−	1.34307e7i	1.17570	−	0.427920i	0.854681	+	0.519153i	$0.173753\pi$
$998$	−3.95382e7			−1.25658
$999$	−1.98728e7	+	2.63184e7i	−0.630008	+	0.834345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.f.a.7.3	✓	48
37.16	even	9	inner	74.6.f.a.53.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.f.a.7.3	✓	48	1.1	even	1	trivial
74.6.f.a.53.3	yes	48	37.16	even	9	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.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.75877 + 1.36808i) q^{2} +(-13.8557 - 5.04306i) q^{3} +(12.2567 - 10.2846i) q^{4} +(11.2687 + 63.9081i) q^{5} +58.9797 q^{6} +(-40.1269 - 227.571i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-19.6009 - 16.4471i) q^{9} +O(q^{10})\)	\(q+(-3.75877 + 1.36808i) q^{2} +(-13.8557 - 5.04306i) q^{3} +(12.2567 - 10.2846i) q^{4} +(11.2687 + 63.9081i) q^{5} +58.9797 q^{6} +(-40.1269 - 227.571i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-19.6009 - 16.4471i) q^{9} +(-129.788 - 224.799i) q^{10} +(69.4520 - 120.294i) q^{11} +(-221.691 + 80.6890i) q^{12} +(-515.565 + 432.610i) q^{13} +(462.163 + 800.490i) q^{14} +(166.157 - 942.321i) q^{15} +(44.4539 - 252.111i) q^{16} +(1502.60 + 1260.83i) q^{17} +(96.1761 + 35.0052i) q^{18} +(1228.43 + 447.113i) q^{19} +(795.387 + 667.409i) q^{20} +(-591.668 + 3355.52i) q^{21} +(-96.4817 + 547.175i) q^{22} +(761.300 + 1318.61i) q^{23} +(722.897 - 606.583i) q^{24} +(-1020.73 + 371.514i) q^{25} +(1346.04 - 2331.42i) q^{26} +(1980.15 + 3429.72i) q^{27} +(-2832.30 - 2376.58i) q^{28} +(-2977.19 + 5156.65i) q^{29} +(664.626 + 3769.28i) q^{30} -7894.34 q^{31} +(177.816 + 1008.44i) q^{32} +(-1568.96 + 1316.51i) q^{33} +(-7372.85 - 2683.50i) q^{34} +(14091.4 - 5128.87i) q^{35} -409.394 q^{36} +(3246.21 + 7668.51i) q^{37} -5229.09 q^{38} +(9325.19 - 3394.09i) q^{39} +(-3902.75 - 1420.48i) q^{40} +(10632.9 - 8922.08i) q^{41} +(-2366.67 - 13422.1i) q^{42} +17121.6 q^{43} +(-385.927 - 2188.70i) q^{44} +(830.225 - 1437.99i) q^{45} +(-4665.52 - 3914.84i) q^{46} +(-528.669 - 915.682i) q^{47} +(-1887.35 + 3268.99i) q^{48} +(-34384.9 + 12515.1i) q^{49} +(3328.41 - 2792.87i) q^{50} +(-14461.1 - 25047.4i) q^{51} +(-1869.90 + 10604.8i) q^{52} +(-2378.72 + 13490.4i) q^{53} +(-12135.1 - 10182.5i) q^{54} +(8470.43 + 3082.98i) q^{55} +(13897.3 + 5058.21i) q^{56} +(-14766.0 - 12390.1i) q^{57} +(4135.87 - 23455.7i) q^{58} +(-3126.40 + 17730.7i) q^{59} +(-7654.86 - 13258.6i) q^{60} +(26748.4 - 22444.6i) q^{61} +(29673.0 - 10800.1i) q^{62} +(-2956.35 + 5120.56i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-33457.1 - 28073.8i) q^{65} +(4096.26 - 7094.93i) q^{66} +(5262.80 + 29846.8i) q^{67} +31384.1 q^{68} +(-3898.51 - 22109.6i) q^{69} +(-45949.8 + 38556.5i) q^{70} +(-32833.4 - 11950.4i) q^{71} +(1538.82 - 560.084i) q^{72} +61059.2 q^{73} +(-22692.9 - 24383.1i) q^{74} +16016.4 q^{75} +(19654.9 - 7153.81i) q^{76} +(-30162.4 - 10978.2i) q^{77} +(-30407.8 + 25515.2i) q^{78} +(6854.09 + 38871.5i) q^{79} +16612.9 q^{80} +(-9060.38 - 51384.0i) q^{81} +(-27760.6 + 48082.7i) q^{82} +(5100.55 + 4279.87i) q^{83} +(27258.2 + 47212.7i) q^{84} +(-63645.0 + 110236. i) q^{85} +(-64356.0 + 23423.7i) q^{86} +(67256.4 - 56434.8i) q^{87} +(4444.93 + 7698.84i) q^{88} +(-4232.82 + 24005.5i) q^{89} +(-1153.34 + 6540.90i) q^{90} +(119137. + 99968.2i) q^{91} +(22892.4 + 8332.16i) q^{92} +(109382. + 39811.7i) q^{93} +(3239.87 + 2718.58i) q^{94} +(-14731.3 + 83545.3i) q^{95} +(2621.88 - 14869.4i) q^{96} +(-40137.4 - 69520.1i) q^{97} +(112123. - 94082.7i) q^{98} +(-3339.81 + 1215.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Introduction

L-functions

Modular forms

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