LMFDB - Embedded newform 74.6.f.a.9.3

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			9.3
Character	$\chi$	$=$	74.9
Dual form			74.6.f.a.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694593 + 3.93923i) q^{2} +(-2.84323 + 16.1248i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(-37.4537 - 31.4274i) q^{5} -65.4941 q^{6} +(-21.7905 - 18.2844i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-23.5794 - 8.58219i) q^{9} +O(q^{10})$	\(q+(0.694593 + 3.93923i) q^{2} +(-2.84323 + 16.1248i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(-37.4537 - 31.4274i) q^{5} -65.4941 q^{6} +(-21.7905 - 18.2844i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-23.5794 - 8.58219i) q^{9} +(97.7847 - 169.368i) q^{10} +(-281.728 - 487.967i) q^{11} +(-45.4918 - 257.997i) q^{12} +(-128.358 + 46.7185i) q^{13} +(56.8909 - 98.5379i) q^{14} +(613.250 - 514.578i) q^{15} +(196.107 - 164.554i) q^{16} +(673.897 + 245.278i) q^{17} +(17.4292 - 98.8457i) q^{18} +(-166.435 + 943.901i) q^{19} +(735.100 + 267.555i) q^{20} +(356.787 - 299.380i) q^{21} +(1726.53 - 1448.73i) q^{22} +(1453.21 - 2517.03i) q^{23} +(984.710 - 358.405i) q^{24} +(-127.551 - 723.379i) q^{25} +(-273.191 - 473.181i) q^{26} +(-1783.96 + 3089.90i) q^{27} +(427.680 + 155.663i) q^{28} +(-4248.51 - 7358.64i) q^{29} +(2453.00 + 2058.31i) q^{30} -2026.24 q^{31} +(784.430 + 658.215i) q^{32} +(8669.38 - 3155.40i) q^{33} +(-498.124 + 2825.00i) q^{34} +(241.504 + 1369.64i) q^{35} +401.482 q^{36} +(-6747.08 - 4880.66i) q^{37} -3833.85 q^{38} +(-388.374 - 2202.58i) q^{39} +(-543.364 + 3081.57i) q^{40} +(-3268.60 + 1189.67i) q^{41} +(1427.15 + 1197.52i) q^{42} -3863.03 q^{43} +(6906.12 + 5794.92i) q^{44} +(613.419 + 1062.47i) q^{45} +(10924.6 + 3976.21i) q^{46} +(-6989.85 + 12106.8i) q^{47} +(2095.81 + 3630.05i) q^{48} +(-2778.00 - 15754.8i) q^{49} +(2760.96 - 1004.91i) q^{50} +(-5871.11 + 10169.1i) q^{51} +(1674.21 - 1404.83i) q^{52} +(-6094.48 + 5113.88i) q^{53} +(-13411.0 - 4881.19i) q^{54} +(-4783.78 + 27130.2i) q^{55} +(-316.128 + 1792.85i) q^{56} +(-14747.0 - 5367.46i) q^{57} +(26036.4 - 21847.1i) q^{58} +(-5751.29 + 4825.91i) q^{59} +(-6404.32 + 11092.6i) q^{60} +(-41099.4 + 14959.0i) q^{61} +(-1407.41 - 7981.84i) q^{62} +(356.886 + 618.144i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(6275.72 + 2284.18i) q^{65} +(18451.5 + 31959.0i) q^{66} +(-984.387 - 825.999i) q^{67} -11474.3 q^{68} +(36454.8 + 30589.2i) q^{69} +(-5227.57 + 1902.68i) q^{70} +(2172.00 - 12318.0i) q^{71} +(278.867 + 1581.53i) q^{72} -7404.31 q^{73} +(14539.6 - 29968.4i) q^{74} +12027.0 q^{75} +(-2662.96 - 15102.4i) q^{76} +(-2783.19 + 15784.3i) q^{77} +(8406.69 - 3059.79i) q^{78} +(8188.83 + 6871.24i) q^{79} -12516.4 q^{80} +(-49422.8 - 41470.6i) q^{81} +(-6956.74 - 12049.4i) q^{82} +(60562.2 + 22042.9i) q^{83} +(-3726.02 + 6453.66i) q^{84} +(-17531.5 - 30365.4i) q^{85} +(-2683.24 - 15217.4i) q^{86} +(130736. - 47584.0i) q^{87} +(-18030.6 + 31229.9i) q^{88} +(-14024.5 + 11767.9i) q^{89} +(-3759.25 + 3154.38i) q^{90} +(3651.20 + 1328.93i) q^{91} +(-8075.11 + 45796.2i) q^{92} +(5761.08 - 32672.7i) q^{93} +(-52546.5 - 19125.4i) q^{94} +(35898.0 - 30122.0i) q^{95} +(-12843.9 + 10777.3i) q^{96} +(47635.3 - 82506.8i) q^{97} +(60132.3 - 21886.4i) q^{98} +(2455.14 + 13923.8i) 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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.694593	+	3.93923i	0.122788	+	0.696364i
$2$	0.694593	+	3.93923i	0.122788	+	0.696364i
$3$	−2.84323	+	16.1248i	−0.182394	+	1.03441i	0.746865	+	0.664976i	$0.231558\pi$
$3$	−2.84323	+	16.1248i	−0.182394	+	1.03441i	−0.929259	+	0.369430i	$0.879553\pi$
$4$	−15.0351	+	5.47232i	−0.469846	+	0.171010i
$5$	−37.4537	−	31.4274i	−0.669992	−	0.562190i	0.243071	−	0.970009i	$-0.421845\pi$
$5$	−37.4537	−	31.4274i	−0.669992	−	0.562190i	−0.913063	+	0.407818i	$0.866290\pi$
$6$	−65.4941			−0.742719
$7$	−21.7905	−	18.2844i	−0.168082	−	0.141038i	0.554867	−	0.831939i	$-0.312769\pi$
$7$	−21.7905	−	18.2844i	−0.168082	−	0.141038i	−0.722949	+	0.690902i	$0.757214\pi$
$8$	−32.0000	−	55.4256i	−0.176777	−	0.306186i
$9$	−23.5794	−	8.58219i	−0.0970344	−	0.0353176i
$10$	97.7847	−	169.368i	0.309222	−	0.535589i
$11$	−281.728	−	487.967i	−0.702018	−	1.21593i	−0.967757	−	0.251886i	$-0.918949\pi$
$11$	−281.728	−	487.967i	−0.702018	−	1.21593i	0.265739	−	0.964045i	$-0.414384\pi$
$12$	−45.4918	−	257.997i	−0.0911968	−	0.517203i
$13$	−128.358	+	46.7185i	−0.210651	+	0.0766708i	−0.445191	−	0.895436i	$-0.646864\pi$
$13$	−128.358	+	46.7185i	−0.210651	+	0.0766708i	0.234539	+	0.972107i	$0.424642\pi$
$14$	56.8909	−	98.5379i	0.0775752	−	0.134364i
$15$	613.250	−	514.578i	0.703735	−	0.590504i
$16$	196.107	−	164.554i	0.191511	−	0.160697i
$17$	673.897	+	245.278i	0.565550	+	0.205843i	0.608942	−	0.793215i	$-0.291594\pi$
$17$	673.897	+	245.278i	0.565550	+	0.205843i	−0.0433920	+	0.999058i	$0.513816\pi$
$18$	17.4292	−	98.8457i	0.0126793	−	0.0719079i
$19$	−166.435	+	943.901i	−0.105770	+	0.599850i	0.885140	+	0.465324i	$0.154062\pi$
$19$	−166.435	+	943.901i	−0.105770	+	0.599850i	−0.990910	+	0.134526i	$0.957049\pi$
$20$	735.100	+	267.555i	0.410934	+	0.149568i
$21$	356.787	−	299.380i	0.176547	−	0.148141i
$22$	1726.53	−	1448.73i	0.760531	−	0.638162i
$23$	1453.21	−	2517.03i	0.572807	−	0.992131i	−0.423469	−	0.905911i	$-0.639188\pi$
$23$	1453.21	−	2517.03i	0.572807	−	0.992131i	0.996276	−	0.0862206i	$-0.0274790\pi$
$24$	984.710	−	358.405i	0.348964	−	0.127012i
$25$	−127.551	−	723.379i	−0.0408164	−	0.231481i
$26$	−273.191	−	473.181i	−0.0792563	−	0.137276i
$27$	−1783.96	+	3089.90i	−0.470950	+	0.815710i
$28$	427.680	+	155.663i	0.103092	+	0.0375223i
$29$	−4248.51	−	7358.64i	−0.938084	−	1.62481i	−0.769039	−	0.639202i	$-0.779265\pi$
$29$	−4248.51	−	7358.64i	−0.938084	−	1.62481i	−0.169045	−	0.985608i	$-0.554068\pi$
$30$	2453.00	+	2058.31i	0.497616	+	0.417549i
$31$	−2026.24			−0.378693			−0.189346	−	0.981910i	$-0.560637\pi$
$31$	−2026.24			−0.378693			−0.189346	+	0.981910i	$0.560637\pi$
$32$	784.430	+	658.215i	0.135419	+	0.113630i
$33$	8669.38	−	3155.40i	1.38581	−	0.504393i
$34$	−498.124	+	2825.00i	−0.0738993	+	0.419104i
$35$	241.504	+	1369.64i	0.0333237	+	0.188988i
$36$	401.482			0.0516309
$37$	−6747.08	−	4880.66i	−0.810236	−	0.586104i
$37$	−6747.08	−	4880.66i	−0.810236	−	0.586104i
$38$	−3833.85			−0.430701
$39$	−388.374	−	2202.58i	−0.0408873	−	0.231883i
$40$	−543.364	+	3081.57i	−0.0536959	+	0.304525i
$41$	−3268.60	+	1189.67i	−0.303670	+	0.110527i	−0.489361	−	0.872081i	$-0.662770\pi$
$41$	−3268.60	+	1189.67i	−0.303670	+	0.110527i	0.185691	+	0.982608i	$0.440548\pi$
$42$	1427.15	+	1197.52i	0.124838	+	0.104751i
$43$	−3863.03			−0.318609			−0.159304	−	0.987230i	$-0.550925\pi$
$43$	−3863.03			−0.318609			−0.159304	+	0.987230i	$0.550925\pi$
$44$	6906.12	+	5794.92i	0.537777	+	0.451248i
$45$	613.419	+	1062.47i	0.0451571	+	0.0782144i
$46$	10924.6	+	3976.21i	0.761218	+	0.277061i
$47$	−6989.85	+	12106.8i	−0.461555	+	0.799437i	−0.999039	−	0.0438375i	$-0.986042\pi$
$47$	−6989.85	+	12106.8i	−0.461555	+	0.799437i	0.537484	+	0.843274i	$0.319375\pi$
$48$	2095.81	+	3630.05i	0.131295	+	0.227410i
$49$	−2778.00	−	15754.8i	−0.165288	−	0.937396i
$50$	2760.96	−	1004.91i	0.156184	−	0.0568462i
$51$	−5871.11	+	10169.1i	−0.316078	+	0.547463i
$52$	1674.21	−	1404.83i	0.0858623	−	0.0720470i
$53$	−6094.48	+	5113.88i	−0.298021	+	0.250070i	−0.779520	−	0.626377i	$-0.784537\pi$
$53$	−6094.48	+	5113.88i	−0.298021	+	0.250070i	0.481499	+	0.876447i	$0.340093\pi$
$54$	−13411.0	−	4881.19i	−0.625858	−	0.227794i
$55$	−4783.78	+	27130.2i	−0.213238	+	1.20933i
$56$	−316.128	+	1792.85i	−0.0134708	+	0.0763966i
$57$	−14747.0	−	5367.46i	−0.601196	−	0.218817i
$58$	26036.4	−	21847.1i	1.01627	−	0.852755i
$59$	−5751.29	+	4825.91i	−0.215097	+	0.180488i	−0.743970	−	0.668213i	$-0.767059\pi$
$59$	−5751.29	+	4825.91i	−0.215097	+	0.180488i	0.528872	+	0.848701i	$0.322615\pi$
$60$	−6404.32	+	11092.6i	−0.229665	+	0.397792i
$61$	−41099.4	+	14959.0i	−1.41420	+	0.514727i	−0.932360	−	0.361532i	$-0.882254\pi$
$61$	−41099.4	+	14959.0i	−1.41420	+	0.514727i	−0.481840	+	0.876259i	$0.660032\pi$
$62$	−1407.41	−	7981.84i	−0.0464989	−	0.263708i
$63$	356.886	+	618.144i	0.0113286	+	0.0196218i
$64$	−2048.00	+	3547.24i	−0.0625000	+	0.108253i
$65$	6275.72	+	2284.18i	0.184238	+	0.0670573i
$66$	18451.5	+	31959.0i	0.521402	+	0.903094i
$67$	−984.387	−	825.999i	−0.0267904	−	0.0224798i	0.629294	−	0.777167i	$-0.283344\pi$
$67$	−984.387	−	825.999i	−0.0267904	−	0.0224798i	−0.656085	+	0.754687i	$0.727789\pi$
$68$	−11474.3			−0.300923
$69$	36454.8	+	30589.2i	0.921790	+	0.773473i
$70$	−5227.57	+	1902.68i	−0.127513	+	0.0464109i
$71$	2172.00	−	12318.0i	0.0511344	−	0.289997i	−0.948508	−	0.316754i	$-0.897407\pi$
$71$	2172.00	−	12318.0i	0.0511344	−	0.289997i	0.999642	+	0.0267569i	$0.00851801\pi$
$72$	278.867	+	1581.53i	0.00633965	+	0.0359539i
$73$	−7404.31			−0.162621			−0.0813107	−	0.996689i	$-0.525911\pi$
$73$	−7404.31			−0.162621			−0.0813107	+	0.996689i	$0.525911\pi$
$74$	14539.6	−	29968.4i	0.308655	−	0.636186i
$75$	12027.0			0.246890
$76$	−2662.96	−	15102.4i	−0.0528849	−	0.299925i
$77$	−2783.19	+	15784.3i	−0.0534954	+	0.303387i
$78$	8406.69	−	3059.79i	0.156455	−	0.0569449i
$79$	8188.83	+	6871.24i	0.147623	+	0.123870i	0.713608	−	0.700545i	$-0.247060\pi$
$79$	8188.83	+	6871.24i	0.147623	+	0.123870i	−0.565985	+	0.824415i	$0.691504\pi$
$80$	−12516.4			−0.218653
$81$	−49422.8	−	41470.6i	−0.836979	−	0.702309i
$82$	−6956.74	−	12049.4i	−0.114254	−	0.197894i
$83$	60562.2	+	22042.9i	0.964954	+	0.351215i	0.775973	−	0.630766i	$-0.217259\pi$
$83$	60562.2	+	22042.9i	0.964954	+	0.351215i	0.188981	+	0.981981i	$0.439481\pi$
$84$	−3726.02	+	6453.66i	−0.0576165	+	0.0997947i
$85$	−17531.5	−	30365.4i	−0.263191	−	0.455860i
$86$	−2683.24	−	15217.4i	−0.0391212	−	0.221868i
$87$	130736.	−	47584.0i	1.85181	−	0.674005i
$88$	−18030.6	+	31229.9i	−0.248201	+	0.429896i
$89$	−14024.5	+	11767.9i	−0.187677	+	0.157480i	−0.731785	−	0.681535i	$-0.761313\pi$
$89$	−14024.5	+	11767.9i	−0.187677	+	0.157480i	0.544108	+	0.839015i	$0.316868\pi$
$90$	−3759.25	+	3154.38i	−0.0489209	+	0.0410495i
$91$	3651.20	+	1328.93i	0.0462202	+	0.0168228i
$92$	−8075.11	+	45796.2i	−0.0994669	+	0.564105i
$93$	5761.08	−	32672.7i	0.0690712	−	0.391722i
$94$	−52546.5	−	19125.4i	−0.613372	−	0.223249i
$95$	35898.0	−	30122.0i	0.408095	−	0.342432i
$96$	−12843.9	+	10777.3i	−0.142239	+	0.119353i
$97$	47635.3	−	82506.8i	0.514043	−	0.890349i	−0.485824	−	0.874057i	$-0.661480\pi$
$97$	47635.3	−	82506.8i	0.514043	−	0.890349i	0.999867	−	0.0162923i	$-0.00518624\pi$
$98$	60132.3	−	21886.4i	0.632474	−	0.230202i
$99$	2455.14	+	13923.8i	0.0251761	+	0.142781i
$100$	5876.31	+	10178.1i	0.0587631	+	0.101781i
$101$	28822.8	−	49922.5i	0.281146	−	0.486959i	−0.690521	−	0.723312i	$-0.742619\pi$
$101$	28822.8	−	49922.5i	0.281146	−	0.486959i	0.971667	+	0.236353i	$0.0759521\pi$
$102$	−44136.3	−	16064.3i	−0.420045	−	0.152884i
$103$	−35782.9	−	61977.7i	−0.332339	−	0.575629i	0.650631	−	0.759394i	$-0.274505\pi$
$103$	−35782.9	−	61977.7i	−0.332339	−	0.575629i	−0.982970	+	0.183765i	$0.941171\pi$
$104$	6696.85	+	5619.33i	0.0607138	+	0.0509449i
$105$	−22771.7			−0.201569
$106$	−24377.9	−	20455.5i	−0.210733	−	0.176826i
$107$	51451.7	−	18726.9i	0.434451	−	0.158127i	−0.115531	−	0.993304i	$-0.536857\pi$
$107$	51451.7	−	18726.9i	0.434451	−	0.158127i	0.549982	+	0.835177i	$0.314635\pi$
$108$	9912.99	−	56219.3i	0.0817796	−	0.463795i
$109$	−6810.96	−	38626.9i	−0.0549088	−	0.311403i	0.944967	−	0.327166i	$-0.106094\pi$
$109$	−6810.96	−	38626.9i	−0.0549088	−	0.311403i	−0.999876	+	0.0157624i	$0.994982\pi$
$110$	−110195.			−0.868319
$111$	97883.2	−	94918.3i	0.754051	−	0.731211i
$112$	−7282.03			−0.0548539
$113$	18470.2	+	104750.i	0.136074	+	0.771714i	0.974106	+	0.226093i	$0.0725952\pi$
$113$	18470.2	+	104750.i	0.136074	+	0.771714i	−0.838032	+	0.545621i	$0.816294\pi$
$114$	10900.5	−	61820.0i	0.0785571	−	0.445520i
$115$	−133532.	+	48601.6i	−0.941543	+	0.342694i
$116$	104146.	+	87388.5i	0.718614	+	0.602989i
$117$	3427.54			0.0231483
$118$	−23005.2	−	19303.6i	−0.152097	−	0.127624i
$119$	−10199.8	−	17666.5i	−0.0660272	−	0.114362i
$120$	−48144.8	−	17523.3i	−0.305208	−	0.111087i
$121$	−78215.8	+	135474.i	−0.485658	+	0.841185i
$122$	−87474.1	−	151510.i	−0.532084	−	0.921596i
$123$	−9889.83	−	56088.0i	−0.0589421	−	0.334277i
$124$	30464.7	−	11088.3i	0.177928	−	0.0647603i
$125$	−94350.9	+	163421.i	−0.540096	+	0.935474i
$126$	−2187.12	+	1835.21i	−0.0122729	+	0.0102982i
$127$	−85552.2	+	71786.8i	−0.470676	+	0.394944i	−0.847041	−	0.531528i	$-0.821618\pi$
$127$	−85552.2	+	71786.8i	−0.470676	+	0.394944i	0.376365	+	0.926471i	$0.377174\pi$
$128$	−15395.9	−	5603.66i	−0.0830579	−	0.0302306i
$129$	10983.5	−	62290.6i	0.0581121	−	0.329570i
$130$	−4638.83	+	26308.1i	−0.0240741	+	0.136531i
$131$	285943.	+	104075.i	1.45580	+	0.529867i	0.944204	−	0.329361i	$-0.106833\pi$
$131$	285943.	+	104075.i	1.45580	+	0.529867i	0.511593	+	0.859228i	$0.329056\pi$
$132$	−113078.	+	94883.3i	−0.564861	+	0.473975i
$133$	20885.4	−	17524.9i	0.102379	−	0.0859065i
$134$	2570.05	−	4451.46i	0.0123646	−	0.0214161i
$135$	163923.	−	59663.3i	0.774117	−	0.281756i
$136$	−7969.99	−	45200.1i	−0.0369497	−	0.209552i
$137$	156934.	+	271818.i	0.714357	+	1.23730i	0.963207	+	0.268761i	$0.0866142\pi$
$137$	156934.	+	271818.i	0.714357	+	1.23730i	−0.248849	+	0.968542i	$0.580052\pi$
$138$	−95176.7	+	164851.i	−0.425435	+	0.736874i
$139$	−64451.0	−	23458.2i	−0.282939	−	0.102981i	0.196653	−	0.980473i	$-0.436993\pi$
$139$	−64451.0	−	23458.2i	−0.282939	−	0.102981i	−0.479591	+	0.877492i	$0.659215\pi$
$140$	−11126.1	−	19271.0i	−0.0479760	−	0.0830968i
$141$	−175345.	−	147132.i	−0.742757	−	0.623247i
$142$	50032.1			0.208223
$143$	58959.1	+	49472.6i	0.241107	+	0.202313i
$144$	−6036.32	+	2197.04i	−0.0242586	+	0.00882941i
$145$	−72140.3	+	409128.i	−0.284943	+	1.61599i
$146$	−5142.98	−	29167.3i	−0.0199679	−	0.113244i
$147$	261941.			0.999795
$148$	128151.	+	36459.0i	0.480916	+	0.136820i
$149$	22866.9			0.0843804			0.0421902	−	0.999110i	$-0.486566\pi$
$149$	22866.9			0.0843804			0.0421902	+	0.999110i	$0.486566\pi$
$150$	8353.86	+	47377.1i	0.0303151	+	0.171925i
$151$	−77475.7	+	439387.i	−0.276518	+	1.56821i	0.457581	+	0.889168i	$0.348716\pi$
$151$	−77475.7	+	439387.i	−0.276518	+	1.56821i	−0.734099	+	0.679043i	$0.762395\pi$
$152$	57642.2	−	20980.1i	0.202363	−	0.0736542i
$153$	−13785.0	−	11567.0i	−0.0476079	−	0.0399478i
$154$	−64111.0			−0.217837
$155$	75890.3	+	63679.5i	0.253721	+	0.212898i
$156$	17892.4	+	30990.6i	0.0588651	+	0.101957i
$157$	99800.5	+	36324.4i	0.323135	+	0.117611i	0.498494	−	0.866893i	$-0.333887\pi$
$157$	99800.5	+	36324.4i	0.323135	+	0.117611i	−0.175359	+	0.984504i	$0.556109\pi$
$158$	−21379.5	+	37030.4i	−0.0681326	+	0.118009i
$159$	−65132.2	−	112812.i	−0.204316	−	0.353886i
$160$	−8693.83	−	49305.2i	−0.0268480	−	0.152262i
$161$	−77688.5	+	28276.3i	−0.236207	+	0.0859722i
$162$	129034.	−	223493.i	0.386292	−	0.669077i
$163$	−153561.	+	128853.i	−0.452701	+	0.379861i	−0.840437	−	0.541909i	$-0.817702\pi$
$163$	−153561.	+	128853.i	−0.452701	+	0.379861i	0.387736	+	0.921770i	$0.373257\pi$
$164$	42633.4	−	35773.7i	0.123777	−	0.103861i
$165$	−423866.	−	154275.i	−1.21205	−	0.441149i
$166$	−44765.8	+	253879.i	−0.126089	+	0.715084i
$167$	99376.8	−	563594.i	0.275736	−	1.56378i	−0.460878	−	0.887464i	$-0.652465\pi$
$167$	99376.8	−	563594.i	0.275736	−	1.56378i	0.736614	−	0.676314i	$-0.236424\pi$
$168$	−28010.5	−	10195.0i	−0.0765681	−	0.0278685i
$169$	−270134.	+	226669.i	−0.727549	+	0.610486i
$170$	107439.	−	90152.1i	0.285128	−	0.239251i
$171$	12025.2	−	20828.2i	0.0314486	−	0.0544705i
$172$	58081.0	−	21139.8i	0.149697	−	0.0544853i
$173$	−94623.8	−	536639.i	−0.240373	−	1.36322i	−0.830998	−	0.556276i	$-0.812230\pi$
$173$	−94623.8	−	536639.i	−0.240373	−	1.36322i	0.590625	−	0.806946i	$-0.298881\pi$
$174$	278253.	+	481948.i	0.696733	+	1.20678i
$175$	−10447.1	+	18095.0i	−0.0257871	+	0.0446645i
$176$	−135546.	−	49334.6i	−0.329841	−	0.120052i
$177$	−61464.4	−	106459.i	−0.147466	−	0.255418i
$178$	−56097.8	−	47071.7i	−0.132708	−	0.111355i
$179$	−693481.			−1.61771			−0.808857	−	0.588005i	$-0.799914\pi$
$179$	−693481.			−1.61771			−0.808857	+	0.588005i	$0.799914\pi$
$180$	−15037.0	−	12617.5i	−0.0345923	−	0.0290264i
$181$	−548218.	+	199535.i	−1.24382	+	0.452713i	−0.878308	−	0.478095i	$-0.841328\pi$
$181$	−548218.	+	199535.i	−1.24382	+	0.452713i	−0.365510	+	0.930807i	$0.619105\pi$
$182$	−2698.86	+	15306.0i	−0.00603951	+	0.0342517i
$183$	−124355.	−	705251.i	−0.274495	−	1.55674i
$184$	−186011.			−0.405036
$185$	99316.7	+	394842.i	0.213350	+	0.848192i
$186$	132707.			0.281262
$187$	−70167.8	−	397941.i	−0.146735	−	0.832175i
$188$	38840.8	−	220277.i	0.0801482	−	0.454543i
$189$	95370.3	−	34711.9i	0.194204	−	0.0706845i
$190$	143592.	+	120488.i	0.288566	+	0.242136i
$191$	898668.			1.78244			0.891222	−	0.453567i	$-0.149849\pi$
$191$	898668.			1.78244			0.891222	+	0.453567i	$0.149849\pi$
$192$	−51375.5	−	43109.2i	−0.100578	−	0.0843950i
$193$	−133931.	−	231975.i	−0.258814	−	0.448279i	0.707110	−	0.707103i	$-0.249998\pi$
$193$	−133931.	−	231975.i	−0.258814	−	0.448279i	−0.965925	+	0.258824i	$0.916665\pi$
$194$	358100.	+	130338.i	0.683125	+	0.248637i
$195$	−54675.2	+	94700.2i	−0.102968	+	0.178346i
$196$	127983.	+	221673.i	0.237964	+	0.412166i
$197$	−137138.	−	777749.i	−0.251763	−	1.42782i	−0.804246	−	0.594297i	$-0.797431\pi$
$197$	−137138.	−	777749.i	−0.251763	−	1.42782i	0.552483	−	0.833524i	$-0.313681\pi$
$198$	−53143.7	+	19342.7i	−0.0963361	+	0.0350635i
$199$	93981.7	−	162781.i	0.168233	−	0.291388i	−0.769566	−	0.638568i	$-0.779527\pi$
$199$	93981.7	−	162781.i	0.168233	−	0.291388i	0.937799	+	0.347180i	$0.112861\pi$
$200$	−36012.1	+	30217.7i	−0.0636610	+	0.0534179i
$201$	16117.9	−	13524.5i	0.0281396	−	0.0236119i
$202$	216676.	+	78863.7i	0.373622	+	0.135987i
$203$	−41971.1	+	238030.i	−0.0714842	+	0.405407i
$204$	32624.2	−	185021.i	0.0548864	−	0.311276i
$205$	159810.	+	58165.9i	0.265594	+	0.0966683i
$206$	219290.	−	184006.i	0.360040	−	0.302110i
$207$	−55867.4	+	46878.3i	−0.0906217	+	0.0760407i
$208$	−17484.2	+	30283.6i	−0.0280213	+	0.0485343i
$209$	507482.	−	184708.i	0.803628	−	0.292497i
$210$	−15817.1	−	89703.1i	−0.0247502	−	0.140365i
$211$	360573.	+	624531.i	0.557554	+	0.965713i	0.997700	+	0.0677861i	$0.0215935\pi$
$211$	360573.	+	624531.i	0.557554	+	0.965713i	−0.440145	+	0.897926i	$0.645073\pi$
$212$	63646.3	−	110239.i	0.0972598	−	0.168459i
$213$	192450.	+	70045.9i	0.290648	+	0.105787i
$214$	109508.	+	189673.i	0.163459	+	0.283120i
$215$	144685.	+	121405.i	0.213465	+	0.179119i
$216$	228346.			0.333012
$217$	44152.8	+	37048.6i	0.0636515	+	0.0534100i
$218$	147429.	−	53659.9i	0.210108	−	0.0764731i
$219$	21052.2	−	119393.i	0.0296611	−	0.168216i
$220$	−76540.5	−	434082.i	−0.106619	−	0.604666i
$221$	−97959.0			−0.134916
$222$	441894.	+	319655.i	0.601777	+	0.435310i
$223$	1.00256e6			1.35004			0.675022	−	0.737798i	$-0.264134\pi$
$223$	1.00256e6			1.35004			0.675022	+	0.737798i	$0.264134\pi$
$224$	−5058.05	−	28685.6i	−0.00673539	−	0.0381983i
$225$	−3200.60	+	18151.5i	−0.00421478	+	0.0239032i
$226$	−399804.	+	145517.i	−0.520686	+	0.189514i
$227$	367289.	+	308192.i	0.473089	+	0.396969i	0.847920	−	0.530124i	$-0.177855\pi$
$227$	367289.	+	308192.i	0.473089	+	0.396969i	−0.374831	+	0.927093i	$0.622299\pi$
$228$	251095.			0.319890
$229$	−869419.	−	729529.i	−1.09557	−	0.919293i	−0.0984517	−	0.995142i	$-0.531389\pi$
$229$	−869419.	−	729529.i	−1.09557	−	0.919293i	−0.997119	+	0.0758486i	$0.975833\pi$
$230$	−284203.	−	492254.i	−0.354250	−	0.613578i
$231$	−246604.	−	89756.7i	−0.304068	−	0.110672i
$232$	−271905.	+	470953.i	−0.331663	+	0.574457i
$233$	−771965.	−	1.33708e6i	−0.931553	−	1.61350i	−0.780668	−	0.624946i	$-0.785121\pi$
$233$	−771965.	−	1.33708e6i	−0.931553	−	1.61350i	−0.150885	−	0.988551i	$-0.548212\pi$
$234$	2380.75	+	13501.9i	0.00284232	+	0.0161196i
$235$	642281.	−	233771.i	0.758674	−	0.276135i
$236$	60062.2	−	104031.i	0.0701974	−	0.121586i
$237$	−134080.	+	112507.i	−0.155058	+	0.130109i
$238$	62507.8	−	52450.3i	0.0715306	−	0.0600213i
$239$	704547.	+	256434.i	0.797839	+	0.290390i	0.708591	−	0.705620i	$-0.249331\pi$
$239$	704547.	+	256434.i	0.797839	+	0.290390i	0.0892485	+	0.996009i	$0.471553\pi$
$240$	35587.2	−	201825.i	0.0398809	−	0.226176i
$241$	−243008.	+	1.37817e6i	−0.269512	+	1.52848i	0.486359	+	0.873759i	$0.338325\pi$
$241$	−243008.	+	1.37817e6i	−0.269512	+	1.52848i	−0.755871	+	0.654720i	$0.772786\pi$
$242$	−587990.	−	214011.i	−0.645404	−	0.234908i
$243$	145063.	−	121722.i	0.157594	−	0.132237i
$244$	536073.	−	449818.i	0.576433	−	0.483685i
$245$	−391086.	+	677381.i	−0.416253	+	0.720972i
$246$	214074.	−	77916.6i	0.225542	−	0.0820904i
$247$	−22734.3	−	128933.i	−0.0237105	−	0.134469i
$248$	64839.8	+	112306.i	0.0669441	+	0.115951i
$249$	−527629.	+	913880.i	−0.539300	+	0.934094i
$250$	−709287.	−	258159.i	−0.717748	−	0.261239i
$251$	−194757.	−	337328.i	−0.195123	−	0.337963i	0.751818	−	0.659371i	$-0.229177\pi$
$251$	−194757.	−	337328.i	−0.195123	−	0.337963i	−0.946941	+	0.321408i	$0.895844\pi$
$252$	−8748.49	−	7340.85i	−0.00867824	−	0.00728191i
$253$	−1.63764e6			−1.60848
$254$	−342209.	−	287147.i	−0.332818	−	0.279267i
$255$	539482.	−	196355.i	0.519549	−	0.189100i
$256$	11380.2	−	64540.4i	0.0108530	−	0.0615505i
$257$	73381.6	+	416168.i	0.0693034	+	0.393039i	0.999652	+	0.0263639i	$0.00839285\pi$
$257$	73381.6	+	416168.i	0.0693034	+	0.393039i	−0.930349	+	0.366675i	$0.880496\pi$
$258$	253006.			0.236636
$259$	57782.2	+	229718.i	0.0535235	+	0.212787i
$260$	−106856.			−0.0980312
$261$	37024.0	+	209974.i	0.0336420	+	0.190793i
$262$	−211360.	+	1.19868e6i	−0.190226	+	1.07883i
$263$	−1.77759e6	+	646989.i	−1.58468	+	0.576777i	−0.976215	−	0.216804i	$-0.930437\pi$
$263$	−1.77759e6	+	646989.i	−1.58468	+	0.576777i	−0.608465	+	0.793580i	$0.708215\pi$
$264$	−452310.	−	379533.i	−0.399417	−	0.335151i
$265$	388977.			0.340259
$266$	83541.4	+	70099.6i	0.0723932	+	0.0607451i
$267$	−149880.	−	259600.i	−0.128667	−	0.222857i
$268$	19320.5	+	7032.08i	0.0164316	+	0.00598063i
$269$	−657710.	+	1.13919e6i	−0.554183	+	0.959874i	0.443783	+	0.896134i	$0.353636\pi$
$269$	−657710.	+	1.13919e6i	−0.554183	+	0.959874i	−0.997967	+	0.0637396i	$0.979697\pi$
$270$	348887.	+	604291.i	0.291257	+	0.504471i
$271$	148908.	+	844498.i	0.123167	+	0.698514i	0.982380	+	0.186896i	$0.0598427\pi$
$271$	148908.	+	844498.i	0.123167	+	0.698514i	−0.859213	+	0.511618i	$0.829046\pi$
$272$	172518.	−	62791.3i	0.141388	−	0.0514608i
$273$	−31809.9	+	55096.3i	−0.0258319	+	0.0447421i
$274$	−961747.	+	807002.i	−0.773899	+	0.649379i
$275$	−317050.	+	266037.i	−0.252811	+	0.212134i
$276$	−715495.	−	260419.i	−0.565371	−	0.205778i
$277$	102777.	−	582880.i	0.0804819	−	0.456435i	−0.917759	−	0.397139i	$-0.870003\pi$
$277$	102777.	−	582880.i	0.0804819	−	0.456435i	0.998240	−	0.0592966i	$-0.0188858\pi$
$278$	47640.2	−	270181.i	0.0369711	−	0.209673i
$279$	47777.5	+	17389.6i	0.0367463	+	0.0133745i
$280$	68184.8	−	57213.8i	0.0519748	−	0.0436120i
$281$	1.62245e6	−	1.36140e6i	1.22576	−	1.02853i	0.227257	−	0.973835i	$-0.427024\pi$
$281$	1.62245e6	−	1.36140e6i	1.22576	−	1.02853i	0.998503	−	0.0546997i	$-0.0174201\pi$
$282$	457794.	−	792923.i	0.342805	−	0.593756i
$283$	265494.	−	96631.8i	0.197055	−	0.0717223i	−0.241607	−	0.970374i	$-0.577675\pi$
$283$	265494.	−	96631.8i	0.197055	−	0.0717223i	0.438663	+	0.898652i	$0.355452\pi$
$284$	34751.9	+	197088.i	0.0255672	+	0.144999i
$285$	383644.	+	664491.i	0.279780	+	0.484593i
$286$	−153931.	+	266617.i	−0.111279	+	0.192740i
$287$	92976.8	+	33840.8i	0.0666300	+	0.0242513i
$288$	−12847.4	−	22252.4i	−0.00912715	−	0.0158087i
$289$	−693698.	−	582082.i	−0.488569	−	0.409958i
$290$	−1.66176e6			−1.16031
$291$	1.19497e6	+	1.00270e6i	0.827224	+	0.694123i
$292$	111324.	−	40518.8i	0.0764070	−	0.0278099i
$293$	325016.	−	1.84326e6i	0.221175	−	1.25434i	−0.648690	−	0.761053i	$-0.724683\pi$
$293$	325016.	−	1.84326e6i	0.221175	−	1.25434i	0.869864	−	0.493291i	$-0.164206\pi$
$294$	181943.	+	1.03185e6i	0.122763	+	0.696221i
$295$	367073.			0.245582
$296$	−54607.2	+	530142.i	−0.0362260	+	0.351693i
$297$	2.01036e6			1.32246
$298$	15883.2	+	90077.9i	0.0103609	+	0.0587595i
$299$	−68939.0	+	390973.i	−0.0445951	+	0.252911i
$300$	−180827.	+	65815.5i	−0.116000	+	0.0422207i
$301$	84177.4	+	70633.2i	0.0535524	+	0.0449358i
$302$	−1.78466e6			−1.12600
$303$	723039.	+	606702.i	0.452434	+	0.379637i
$304$	122683.	+	212494.i	0.0761379	+	0.131875i
$305$	2.00945e6	+	731378.i	1.23688	+	0.450187i
$306$	35990.2	−	62336.8i	0.0219725	−	0.0380575i
$307$	−164974.	−	285744.i	−0.0999010	−	0.173034i	0.811743	−	0.584016i	$-0.198519\pi$
$307$	−164974.	−	285744.i	−0.0999010	−	0.173034i	−0.911644	+	0.410982i	$0.865186\pi$
$308$	−44531.0	−	252548.i	−0.0267477	−	0.151694i
$309$	1.10112e6	−	400774.i	0.656050	−	0.238783i
$310$	−198136.	+	343181.i	−0.117100	+	0.202824i
$311$	1.67484e6	−	1.40536e6i	0.981912	−	0.823922i	−0.00246464	−	0.999997i	$-0.500785\pi$
$311$	1.67484e6	−	1.40536e6i	0.981912	−	0.823922i	0.984377	+	0.176075i	$0.0563401\pi$
$312$	−109651.	+	92008.3i	−0.0637715	+	0.0535107i
$313$	−2.66611e6	−	970384.i	−1.53821	−	0.559864i	−0.572598	−	0.819836i	$-0.694064\pi$
$313$	−2.66611e6	−	970384.i	−1.53821	−	0.559864i	−0.965616	+	0.259972i	$0.916287\pi$
$314$	−73769.6	+	418368.i	−0.0422234	+	0.239461i
$315$	6059.97	−	34367.8i	0.00344107	−	0.0195153i
$316$	−160721.	−	58497.8i	−0.0905432	−	0.0329550i
$317$	1.16016e6	−	973489.i	0.648439	−	0.544105i	−0.258158	−	0.966103i	$-0.583115\pi$
$317$	1.16016e6	−	973489.i	0.648439	−	0.544105i	0.906597	+	0.421998i	$0.138671\pi$
$318$	399153.	−	334929.i	0.221346	−	0.185731i
$319$	−2.39385e6	+	4.14627e6i	−1.31710	+	2.28129i
$320$	188186.	−	68494.0i	0.102733	−	0.0373919i
$321$	155678.	+	882893.i	0.0843265	+	0.478240i
$322$	−165349.	−	286392.i	−0.0888712	−	0.153929i
$323$	−343679.	+	595269.i	−0.183293	+	0.317473i
$324$	970016.	+	353057.i	0.513354	+	0.186845i
$325$	50167.4	+	86892.4i	0.0263459	+	0.0456324i
$326$	−614243.	−	515411.i	−0.320108	−	0.268602i
$327$	642215.			0.332132
$328$	170534.	+	143095.i	0.0875236	+	0.0734410i
$329$	373677.	−	136007.i	0.190330	−	0.0692744i
$330$	313309.	−	1.77687e6i	0.158376	−	0.898193i
$331$	−509293.	−	2.88834e6i	−0.255504	−	1.44904i	−0.794776	−	0.606903i	$-0.792412\pi$
$331$	−509293.	−	2.88834e6i	−0.255504	−	1.44904i	0.539272	−	0.842132i	$-0.318700\pi$
$332$	−1.03118e6			−0.513441
$333$	117205.	+	172988.i	0.0579210	+	0.0854878i
$334$	2.28915e6			1.12282
$335$	10910.0	+	61873.5i	0.00531143	+	0.0301226i
$336$	20704.5	−	117421.i	0.0100050	−	0.0567412i
$337$	−1.38652e6	+	504653.i	−0.665047	+	0.242057i	−0.652414	−	0.757863i	$-0.726244\pi$
$337$	−1.38652e6	+	504653.i	−0.665047	+	0.242057i	−0.0126333	+	0.999920i	$0.504021\pi$
$338$	−1.08054e6	−	906677.i	−0.514455	−	0.431679i
$339$	−1.74158e6			−0.823084
$340$	429756.	+	360608.i	0.201616	+	0.169176i
$341$	570849.	+	988740.i	0.265849	+	0.460464i
$342$	90399.7	+	32902.8i	0.0417928	+	0.0152113i
$343$	−466574.	+	808131.i	−0.214134	+	0.370891i
$344$	123617.	+	214111.i	0.0563226	+	0.0975535i
$345$	−404028.	−	2.29136e6i	−0.182753	−	1.03644i
$346$	2.04822e6	−	745490.i	0.919784	−	0.334774i
$347$	−295597.	+	511989.i	−0.131788	+	0.228264i	−0.924366	−	0.381507i	$-0.875405\pi$
$347$	−295597.	+	511989.i	−0.131788	+	0.228264i	0.792578	+	0.609771i	$0.208739\pi$
$348$	−1.70523e6	+	1.43086e6i	−0.754806	+	0.633357i
$349$	683239.	−	573306.i	0.300268	−	0.251955i	−0.480188	−	0.877166i	$-0.659431\pi$
$349$	683239.	−	573306.i	0.300268	−	0.251955i	0.780456	+	0.625211i	$0.214987\pi$
$350$	−78536.8	−	28585.0i	−0.0342691	−	0.0124729i
$351$	84629.4	−	479957.i	0.0366652	−	0.207939i
$352$	100191.	−	568213.i	0.0430996	−	0.244430i
$353$	2.30406e6	+	838609.i	0.984140	+	0.358198i	0.783449	−	0.621457i	$-0.213459\pi$
$353$	2.30406e6	+	838609.i	0.984140	+	0.358198i	0.200692	+	0.979654i	$0.435681\pi$
$354$	376676.	−	316069.i	0.159757	−	0.134052i
$355$	−468472.	+	393095.i	−0.197293	+	0.165549i
$356$	146461.	−	253678.i	0.0612487	−	0.106086i
$357$	313869.	−	114239.i	0.130340	−	0.0474399i
$358$	−481687.	−	2.73178e6i	−0.198636	−	1.12652i
$359$	−420679.	−	728637.i	−0.172272	−	0.298384i	0.766942	−	0.641717i	$-0.221777\pi$
$359$	−420679.	−	728637.i	−0.172272	−	0.298384i	−0.939214	+	0.343333i	$0.888444\pi$
$360$	39258.8	−	67998.2i	0.0159654	−	0.0276530i
$361$	1.46352e6	+	532679.i	0.591060	+	0.215128i
$362$	−1.16680e6	−	2.02096e6i	−0.467979	−	0.810563i
$363$	−1.96210e6	−	1.64640e6i	−0.781545	−	0.655794i
$364$	−62168.4			−0.0245933
$365$	277319.	+	232698.i	0.108955	+	0.0914241i
$366$	2.69177e6	−	979724.i	1.05035	−	0.382297i
$367$	854653.	−	4.84698e6i	0.331226	−	1.87848i	−0.130492	−	0.991449i	$-0.541656\pi$
$367$	854653.	−	4.84698e6i	0.331226	−	1.87848i	0.461718	−	0.887027i	$-0.347233\pi$
$368$	−129202.	−	732739.i	−0.0497335	−	0.282053i
$369$	87281.5			0.0333700
$370$	−1.48639e6	+	665486.i	−0.564454	+	0.252717i
$371$	226306.			0.0853613
$372$	92177.3	+	522764.i	0.0345356	+	0.195861i
$373$	277648.	−	1.57462e6i	0.103329	−	0.586009i	−0.888545	−	0.458789i	$-0.848283\pi$
$373$	277648.	−	1.57462e6i	0.103329	−	0.586009i	0.991875	−	0.127220i	$-0.0406054\pi$
$374$	1.51884e6	−	552814.i	0.561480	−	0.204362i
$375$	−2.36686e6	−	1.98603e6i	−0.869150	−	0.729303i
$376$	894701.			0.326369
$377$	889115.	+	746056.i	0.322184	+	0.270345i
$378$	202982.	+	351575.i	0.0730681	+	0.126558i
$379$	46241.2	+	16830.4i	0.0165360	+	0.00601862i	0.350275	−	0.936647i	$-0.386088\pi$
$379$	46241.2	+	16830.4i	0.0165360	+	0.00601862i	−0.333739	+	0.942666i	$0.608310\pi$
$380$	−374892.	+	649332.i	−0.133182	+	0.230679i
$381$	−914302.	−	1.58362e6i	−0.322684	−	0.558905i
$382$	624208.	+	3.54006e6i	0.218862	+	1.24123i
$383$	958132.	−	348732.i	0.333756	−	0.121477i	−0.169706	−	0.985495i	$-0.554282\pi$
$383$	958132.	−	348732.i	0.333756	−	0.121477i	0.503462	+	0.864018i	$0.332060\pi$
$384$	134132.	−	232323.i	0.0464199	−	0.0804016i
$385$	600299.	−	503711.i	0.206403	−	0.173193i
$386$	820777.	−	688714.i	0.280386	−	0.235272i
$387$	91087.9	+	33153.3i	0.0309160	+	0.0112525i
$388$	−264697.	+	1.50117e6i	−0.0892627	+	0.506234i
$389$	66875.6	−	379271.i	0.0224075	−	0.127079i	−0.971552	−	0.236826i	$-0.923893\pi$
$389$	66875.6	−	379271.i	0.0224075	−	0.127079i	0.993960	+	0.109747i	$0.0350040\pi$
$390$	−411023.	−	149600.i	−0.136837	−	0.0498047i
$391$	1.59669e6	−	1.33978e6i	0.528175	−	0.443191i
$392$	−784324.	+	658126.i	−0.257799	+	0.216319i
$393$	−2.49118e6	+	4.31486e6i	−0.813625	+	1.40924i
$394$	2.96848e6	−	1.08044e6i	0.963370	−	0.350638i
$395$	−90756.7	−	514707.i	−0.0292675	−	0.165984i
$396$	−113109.	−	195910.i	−0.0362458	−	0.0627796i
$397$	−1.29738e6	+	2.24713e6i	−0.413135	+	0.715570i	−0.995231	−	0.0975498i	$-0.968899\pi$
$397$	−1.29738e6	+	2.24713e6i	−0.413135	+	0.715570i	0.582096	+	0.813120i	$0.302233\pi$
$398$	706512.	+	257149.i	0.223569	+	0.0813725i
$399$	223203.	+	386599.i	0.0701888	+	0.121571i
$400$	−144048.	−	120871.i	−0.0450151	−	0.0377722i
$401$	−2.25512e6			−0.700340			−0.350170	−	0.936686i	$-0.613876\pi$
$401$	−2.25512e6			−0.700340			−0.350170	+	0.936686i	$0.613876\pi$
$402$	64471.6	+	54098.1i	0.0198977	+	0.0166962i
$403$	260084.	−	94663.0i	0.0797722	−	0.0290347i
$404$	−160161.	+	908316.i	−0.0488205	+	0.276875i
$405$	547753.	+	3.10646e6i	0.165938	+	0.941083i
$406$	−966807.			−0.291088
$407$	−480762.	+	4.66737e6i	−0.143861	+	1.39665i
$408$	751502.			0.223501
$409$	870366.	+	4.93609e6i	0.257273	+	1.45907i	0.790171	+	0.612886i	$0.209992\pi$
$409$	870366.	+	4.93609e6i	0.257273	+	1.45907i	−0.532899	+	0.846179i	$0.678897\pi$
$410$	−118126.	+	669928.i	−0.0347046	+	0.196820i
$411$	−4.82920e6	+	1.75769e6i	−1.41017	+	0.513259i
$412$	877160.	+	736025.i	0.254587	+	0.213624i
$413$	213562.			0.0616097
$414$	−223470.	−	187513.i	−0.0640792	−	0.0537689i
$415$	−1.57553e6	−	2.72890e6i	−0.449062	−	0.777799i
$416$	−131439.	−	47839.7i	−0.0372383	−	0.0135536i
$417$	561508.	−	972561.i	0.158131	−	0.273890i
$418$	1.08010e6	+	1.87079e6i	0.302360	+	0.523703i
$419$	−425386.	−	2.41248e6i	−0.118372	−	0.671319i	−0.985025	−	0.172409i	$-0.944845\pi$
$419$	−425386.	−	2.41248e6i	−0.118372	−	0.671319i	0.866654	−	0.498910i	$-0.166266\pi$
$420$	342375.	−	124614.i	0.0947063	−	0.0344703i
$421$	2.19057e6	−	3.79419e6i	0.602355	−	1.04331i	−0.390108	−	0.920769i	$-0.627562\pi$
$421$	2.19057e6	−	3.79419e6i	0.602355	−	1.04331i	0.992463	−	0.122541i	$-0.0391043\pi$
$422$	−2.20972e6	+	1.85418e6i	−0.604027	+	0.506839i
$423$	268719.	−	225482.i	0.0730209	−	0.0612718i
$424$	478463.	+	174146.i	0.129251	+	0.0470435i
$425$	91472.8	−	518768.i	0.0245652	−	0.139316i
$426$	−142253.	+	806757.i	−0.0379785	+	0.215387i
$427$	1.16909e6	+	425514.i	0.310298	+	0.112939i
$428$	−671101.	+	563121.i	−0.177084	+	0.148591i
$429$	−965369.	+	810041.i	−0.253250	+	0.212502i
$430$	−377746.	+	654275.i	−0.0985209	+	0.170643i
$431$	−1.11206e6	+	404757.i	−0.288360	+	0.104954i	−0.482150	−	0.876089i	$-0.660144\pi$
$431$	−1.11206e6	+	404757.i	−0.288360	+	0.104954i	0.193790	+	0.981043i	$0.437922\pi$
$432$	158608.	+	899510.i	0.0408898	+	0.231898i
$433$	−1.45581e6	−	2.52154e6i	−0.373152	−	0.646318i	0.616897	−	0.787044i	$-0.288390\pi$
$433$	−1.45581e6	−	2.52154e6i	−0.373152	−	0.646318i	−0.990049	+	0.140726i	$0.955056\pi$
$434$	−115275.	+	199662.i	−0.0293772	+	0.0508828i
$435$	−6.39199e6	−	2.32649e6i	−1.61962	−	0.589493i
$436$	313782.	+	543487.i	0.0790518	+	0.136922i
$437$	2.13396e6	+	1.79061e6i	0.534544	+	0.448536i
$438$	484939.			0.120782
$439$	−4.04830e6	−	3.39692e6i	−1.00256	−	0.841249i	−0.0152241	−	0.999884i	$-0.504846\pi$
$439$	−4.04830e6	−	3.39692e6i	−1.00256	−	0.841249i	−0.987337	+	0.158635i	$0.949291\pi$
$440$	1.65679e6	−	603021.i	0.407976	−	0.148491i
$441$	−69707.3	+	395330.i	−0.0170680	+	0.0967972i
$442$	−68041.6	−	385883.i	−0.0165661	−	0.0939507i
$443$	1.06693e6			0.258302			0.129151	−	0.991625i	$-0.458775\pi$
$443$	1.06693e6			0.258302			0.129151	+	0.991625i	$0.458775\pi$
$444$	−952258.	+	1.96275e6i	−0.229243	+	0.472507i
$445$	895103.			0.214276
$446$	696370.	+	3.94931e6i	0.165769	+	0.940122i
$447$	−65015.9	+	368724.i	−0.0153904	+	0.0872835i
$448$	109486.	−	39849.6i	0.0257729	−	0.00938057i
$449$	4.48217e6	+	3.76099e6i	1.04923	+	0.880412i	0.993013	−	0.118007i	$-0.0376504\pi$
$449$	4.48217e6	+	3.76099e6i	1.04923	+	0.880412i	0.0562209	+	0.998418i	$0.482095\pi$
$450$	−73726.0			−0.0171628
$451$	1.50138e6	+	1.25981e6i	0.347575	+	0.291650i
$452$	−850924.	−	1.47384e6i	−0.195905	−	0.339317i
$453$	−6.86473e6	−	2.49856e6i	−1.57173	−	0.572063i
$454$	−958923.	+	1.66090e6i	−0.218345	+	0.378185i
$455$	−94986.2	−	164521.i	−0.0215096	−	0.0372557i
$456$	174409.	+	989120.i	0.0392786	+	0.222760i
$457$	4.53958e6	−	1.65227e6i	1.01677	−	0.370076i	0.220744	−	0.975332i	$-0.429152\pi$
$457$	4.53958e6	−	1.65227e6i	1.01677	−	0.370076i	0.796031	+	0.605256i	$0.206929\pi$
$458$	2.26989e6	−	3.93157e6i	0.505640	−	0.875794i
$459$	−1.96009e6	+	1.64471e6i	−0.434254	+	0.364383i
$460$	1.74170e6	−	1.46146e6i	0.383776	−	0.322027i
$461$	2.39893e6	+	873139.i	0.525733	+	0.191351i	0.591232	−	0.806501i	$-0.298642\pi$
$461$	2.39893e6	+	873139.i	0.525733	+	0.191351i	−0.0654990	+	0.997853i	$0.520864\pi$
$462$	182283.	−	1.03378e6i	0.0397320	−	0.225331i
$463$	−296033.	+	1.67889e6i	−0.0641782	+	0.363973i	0.935758	+	0.352644i	$0.114717\pi$
$463$	−296033.	+	1.67889e6i	−0.0641782	+	0.363973i	−0.999936	+	0.0113289i	$0.996394\pi$
$464$	−2.04406e6	−	743975.i	−0.440755	−	0.160422i
$465$	−1.24259e6	+	1.04266e6i	−0.266500	+	0.223620i
$466$	4.73087e6	−	3.96968e6i	1.00920	−	0.846818i
$467$	−3.92232e6	+	6.79365e6i	−0.832243	+	1.44149i	0.0640117	+	0.997949i	$0.479610\pi$
$467$	−3.92232e6	+	6.79365e6i	−0.832243	+	1.44149i	−0.896255	+	0.443539i	$0.853723\pi$
$468$	−51533.4	+	18756.6i	−0.0108761	+	0.00395859i
$469$	6347.39	+	35997.8i	0.00133249	+	0.00755691i
$470$	1.36700e6	+	2.36772e6i	0.285446	+	0.494407i
$471$	−869480.	+	1.50598e6i	−0.180596	+	0.312801i
$472$	451520.	+	164340.i	0.0932872	+	0.0339538i
$473$	1.08832e6	+	1.88503e6i	0.223669	+	0.387406i
$474$	−536320.	−	450026.i	−0.109642	−	0.0920008i
$475$	704027.			0.143171
$476$	250031.	+	209801.i	0.0505798	+	0.0424415i
$477$	187592.	−	68278.0i	0.0377502	−	0.0137399i
$478$	−520780.	+	2.95349e6i	−0.104252	+	0.591243i
$479$	1.00339e6	+	5.69052e6i	0.199817	+	1.13322i	0.905390	+	0.424581i	$0.139578\pi$
$479$	1.00339e6	+	5.69052e6i	0.199817	+	1.13322i	−0.705573	+	0.708637i	$0.749310\pi$
$480$	819754.			0.162398
$481$	1.09406e6	+	311259.i	0.215614	+	0.0613421i
$482$	−5.59771e6			−1.09747
$483$	−235063.	−	1.33311e6i	−0.0458475	−	0.260014i
$484$	434625.	−	2.46488e6i	0.0843337	−	0.478280i
$485$	−4.37709e6	+	1.59313e6i	−0.844951	+	0.307537i
$486$	580251.	+	486889.i	0.111436	+	0.0935059i
$487$	9.20757e6			1.75923			0.879615	−	0.475686i	$-0.157800\pi$
$487$	9.20757e6			1.75923			0.879615	+	0.475686i	$0.157800\pi$
$488$	2.14429e6	+	1.79927e6i	0.407600	+	0.342017i
$489$	−1.64111e6	−	2.84249e6i	−0.310361	−	0.537561i
$490$	−2.94001e6	−	1.07008e6i	−0.553170	−	0.201337i
$491$	−2.90772e6	+	5.03632e6i	−0.544314	+	0.942779i	0.454336	+	0.890830i	$0.349877\pi$
$491$	−2.90772e6	+	5.03632e6i	−0.544314	+	0.942779i	−0.998650	+	0.0519487i	$0.983457\pi$
$492$	455626.	+	789167.i	0.0848586	+	0.146979i
$493$	−1.05814e6	−	6.00103e6i	−0.196077	−	1.11201i
$494$	492105.	−	179112.i	0.0907278	−	0.0330222i
$495$	345634.	−	598656.i	0.0634022	−	0.109816i
$496$	−397361.	+	333426.i	−0.0725239	+	0.0608548i
$497$	−272556.	+	228701.i	−0.0494954	+	0.0415315i
$498$	−3.96647e6	−	1.44368e6i	−0.716689	−	0.260854i
$499$	1.22400e6	−	6.94165e6i	0.220055	−	1.24799i	−0.651862	−	0.758337i	$-0.726012\pi$
$499$	1.22400e6	−	6.94165e6i	0.220055	−	1.24799i	0.871917	−	0.489654i	$-0.162877\pi$
$500$	524284.	−	2.97336e6i	0.0937867	−	0.531891i
$501$	8.80528e6	+	3.20486e6i	1.56729	+	0.570446i
$502$	1.19354e6	−	1.00150e6i	0.211386	−	0.177374i
$503$	−177735.	+	149137.i	−0.0313223	+	0.0262825i	−0.658314	−	0.752743i	$-0.728730\pi$
$503$	−177735.	+	149137.i	−0.0313223	+	0.0262825i	0.626992	+	0.779026i	$0.284286\pi$
$504$	22840.7	−	39561.2i	0.00400528	−	0.00693734i
$505$	−2.64845e6	+	963958.i	−0.462130	+	0.168201i
$506$	−1.13749e6	−	6.45104e6i	−0.197502	−	1.12009i
$507$	−2.88694e6	−	5.00032e6i	−0.498790	−	0.863929i
$508$	893444.	−	1.54749e6i	0.153606	−	0.266053i
$509$	4.31823e6	+	1.57171e6i	0.738773	+	0.268891i	0.683874	−	0.729600i	$-0.260294\pi$
$509$	4.31823e6	+	1.57171e6i	0.738773	+	0.268891i	0.0548995	+	0.998492i	$0.482516\pi$
$510$	1.14821e6	+	1.98876e6i	0.195477	+	0.338576i
$511$	161343.	+	135383.i	0.0273337	+	0.0229357i
$512$	262144.			0.0441942
$513$	−2.61965e6	−	2.19815e6i	−0.439491	−	0.368777i
$514$	−1.58841e6	+	578134.i	−0.265189	+	0.0965208i
$515$	−607598.	+	3.44586e6i	−0.100948	+	0.572505i
$516$	175736.	+	996649.i	0.0290561	+	0.164785i
$517$	7.87695e6			1.29608
$518$	−864778.	+	387178.i	−0.141606	+	0.0633996i
$519$	8.92222e6			1.45397
$520$	−74221.2	−	420929.i	−0.0120370	−	0.0682654i
$521$	1.32398e6	−	7.50868e6i	0.213692	−	1.21191i	−0.669470	−	0.742839i	$-0.733479\pi$
$521$	1.32398e6	−	7.50868e6i	0.213692	−	1.21191i	0.883162	−	0.469068i	$-0.155410\pi$
$522$	−801418.	+	291692.i	−0.128731	+	0.0468542i
$523$	−5.93585e6	−	4.98077e6i	−0.948918	−	0.796236i	0.0301973	−	0.999544i	$-0.490386\pi$
$523$	−5.93585e6	−	4.98077e6i	−0.948918	−	0.796236i	−0.979115	+	0.203308i	$0.934831\pi$
$524$	−4.86870e6			−0.774613
$525$	−262074.	−	219906.i	−0.0414978	−	0.0348208i
$526$	−3.78334e6	−	6.55294e6i	−0.596226	−	1.03269i
$527$	−1.36548e6	−	496993.i	−0.214170	−	0.0779514i
$528$	1.18090e6	−	2.04538e6i	0.184343	−	0.319292i
$529$	−1.00546e6	−	1.74151e6i	−0.156216	−	0.270575i
$530$	270181.	+	1.53227e6i	0.0417796	+	0.236944i
$531$	177029.	−	64433.1i	0.0272463	−	0.00991683i
$532$	−218111.	+	377780.i	−0.0334117	+	0.0578708i
$533$	363971.	−	305408.i	0.0554944	−	0.0465653i
$534$	918520.	−	770730.i	0.139391	−	0.116963i
$535$	−2.51560e6	−	915602.i	−0.379976	−	0.138300i
$536$	−14281.1	+	80992.2i	−0.00214709	+	0.0121768i
$537$	1.97173e6	−	1.11822e7i	0.295061	−	1.67337i
$538$	−4.94436e6	−	1.79960e6i	−0.736469	−	0.268053i
$539$	−6.90519e6	+	5.79414e6i	−1.02377	+	0.859048i
$540$	−2.13811e6	+	1.79408e6i	−0.315533	+	0.264764i
$541$	3.60086e6	−	6.23688e6i	0.528949	−	0.916166i	−0.470481	−	0.882410i	$-0.655920\pi$
$541$	3.60086e6	−	6.23688e6i	0.528949	−	0.916166i	0.999430	−	0.0337560i	$-0.0107469\pi$
$542$	−3.22324e6	+	1.17316e6i	−0.471297	+	0.171538i
$543$	−1.65875e6	−	9.40722e6i	−0.241424	−	1.36918i
$544$	367179.	+	635972.i	0.0531962	+	0.0921384i
$545$	−958847.	+	1.66077e6i	−0.138280	+	0.239507i
$546$	−239132.	−	87037.0i	−0.0343286	−	0.0124946i
$547$	6.11384e6	+	1.05895e7i	0.873667	+	1.51323i	0.858176	+	0.513355i	$0.171598\pi$
$547$	6.11384e6	+	1.05895e7i	0.873667	+	1.51323i	0.0154901	+	0.999880i	$0.495069\pi$
$548$	−3.84699e6	−	3.22801e6i	−0.547230	−	0.459180i
$549$	1.09748e6			0.155405
$550$	−1.26820e6	−	1.06415e6i	−0.178765	−	0.150001i
$551$	7.65293e6	−	2.78544e6i	1.07386	−	0.390854i
$552$	528872.	−	2.99938e6i	0.0738759	−	0.418971i
$553$	−52802.0	−	299455.i	−0.00734240	−	0.0416408i
$554$	2.36749e6			0.327728
$555$	−6.64912e6	+	478831.i	−0.916288	+	0.0659858i
$556$	1.09740e6			0.150549
$557$	1.95578e6	+	1.10918e7i	0.267104	+	1.51482i	0.762975	+	0.646428i	$0.223738\pi$
$557$	1.95578e6	+	1.10918e7i	0.267104	+	1.51482i	−0.495870	+	0.868397i	$0.665151\pi$
$558$	−35315.7	+	200285.i	−0.00480156	+	0.0272310i
$559$	495851.	−	180475.i	0.0671153	−	0.0244280i
$560$	272739.	+	228855.i	0.0367517	+	0.0308383i
$561$	6.61622e6			0.887570
$562$	6.48980e6	+	5.44559e6i	0.866743	+	0.727284i
$563$	1.82466e6	+	3.16040e6i	0.242611	+	0.420214i	0.961457	−	0.274955i	$-0.0886629\pi$
$563$	1.82466e6	+	3.16040e6i	0.242611	+	0.420214i	−0.718846	+	0.695169i	$0.755330\pi$
$564$	3.44149e6	+	1.25260e6i	0.455563	+	0.165811i
$565$	2.60023e6	−	4.50373e6i	0.342682	−	0.593542i
$566$	565065.	+	978721.i	0.0741408	+	0.128416i
$567$	318681.	+	1.80733e6i	0.0416293	+	0.236091i
$568$	−752237.	+	273792.i	−0.0978326	+	0.0356082i
$569$	6.47106e6	−	1.12082e7i	0.837905	−	1.45129i	−0.0537383	−	0.998555i	$-0.517114\pi$
$569$	6.47106e6	−	1.12082e7i	0.837905	−	1.45129i	0.891643	−	0.452739i	$-0.149553\pi$
$570$	−2.35111e6	+	1.97281e6i	−0.303099	+	0.254331i
$571$	−3.48043e6	+	2.92043e6i	−0.446728	+	0.374849i	−0.838220	−	0.545332i	$-0.816403\pi$
$571$	−3.48043e6	+	2.92043e6i	−0.446728	+	0.374849i	0.391492	+	0.920181i	$0.371959\pi$
$572$	−1.15718e6	−	421181.i	−0.147881	−	0.0538243i
$573$	−2.55512e6	+	1.44908e7i	−0.325106	+	1.84377i
$574$	−68725.7	+	389763.i	−0.00870641	+	0.0493765i
$575$	−2.00613e6	−	730170.i	−0.253040	−	0.0920989i
$576$	78733.6	−	66065.3i	0.00988790	−	0.00829693i
$577$	−2.65033e6	+	2.22389e6i	−0.331406	+	0.278083i	−0.793273	−	0.608867i	$-0.791624\pi$
$577$	−2.65033e6	+	2.22389e6i	−0.331406	+	0.278083i	0.461866	+	0.886950i	$0.347180\pi$
$578$	1.81112e6	−	3.13695e6i	0.225490	−	0.390560i
$579$	4.12135e6	−	1.50005e6i	0.510909	−	0.185956i
$580$	−1.15425e6	−	6.54605e6i	−0.142472	−	0.807996i
$581$	−916640.	−	1.58767e6i	−0.112657	−	0.195128i
$582$	−3.11983e6	+	5.40371e6i	−0.381789	+	0.661279i
$583$	4.21239e6	+	1.53319e6i	0.513284	+	0.186820i
$584$	236938.	+	410389.i	0.0287477	+	0.0497924i
$585$	−128374.	−	107719.i	−0.0155092	−	0.0130137i
$586$	7.48677e6			0.900638
$587$	4.93127e6	+	4.13783e6i	0.590696	+	0.495652i	0.888440	−	0.458993i	$-0.151790\pi$
$587$	4.93127e6	+	4.13783e6i	0.590696	+	0.495652i	−0.297744	+	0.954646i	$0.596234\pi$
$588$	−3.93831e6	+	1.43343e6i	−0.469750	+	0.170975i
$589$	337238.	−	1.91257e6i	0.0400542	−	0.227159i
$590$	254966.	+	1.44598e6i	0.0301545	+	0.171015i
$591$	1.29309e7			1.52287
$592$	−2.12628e6	+	153123.i	−0.249354	+	0.0179571i
$593$	−1.26035e7			−1.47181			−0.735907	−	0.677082i	$-0.763244\pi$
$593$	−1.26035e7			−1.47181			−0.735907	+	0.677082i	$0.763244\pi$
$594$	1.39638e6	+	7.91928e6i	0.162382	+	0.920915i
$595$	−173193.	+	982229.i	−0.0200558	+	0.113742i
$596$	−343806.	+	125135.i	−0.0396458	+	0.0144299i
$597$	2.35760e6	+	1.97826e6i	0.270729	+	0.227168i
$598$	−1.58802e6			−0.181594
$599$	−1.07029e7	−	8.98076e6i	−1.21880	−	1.02270i	−0.998887	−	0.0471758i	$-0.984978\pi$
$599$	−1.07029e7	−	8.98076e6i	−1.21880	−	1.02270i	−0.219914	−	0.975519i	$-0.570578\pi$
$600$	−384864.	−	666603.i	−0.0436444	−	0.0755943i
$601$	−1.99049e6	−	724478.i	−0.224788	−	0.0818161i	0.227171	−	0.973855i	$-0.427052\pi$
$601$	−1.99049e6	−	724478.i	−0.224788	−	0.0818161i	−0.451959	+	0.892039i	$0.649275\pi$
$602$	−219771.	+	380655.i	−0.0247161	+	0.0428096i
$603$	16122.3	+	27924.7i	0.00180566	+	0.00312749i
$604$	−1.23961e6	−	7.03018e6i	−0.138259	−	0.784105i
$605$	7.18706e6	−	2.61587e6i	0.798294	−	0.290555i
$606$	−1.88772e6	+	3.26963e6i	−0.208812	+	0.361674i
$607$	8.78898e6	−	7.37483e6i	0.968204	−	0.812419i	−0.0140643	−	0.999901i	$-0.504477\pi$
$607$	8.78898e6	−	7.37483e6i	0.968204	−	0.812419i	0.982268	+	0.187482i	$0.0600325\pi$
$608$	−751846.	+	630874.i	−0.0824841	+	0.0692123i
$609$	−3.71884e6	−	1.35355e6i	−0.406317	−	0.147887i
$610$	−1.48532e6	+	8.42368e6i	−0.161620	+	0.916595i
$611$	331593.	−	1.88056e6i	0.0359337	−	0.203790i
$612$	270557.	+	98474.9i	0.0291999	+	0.0106279i
$613$	−4.95310e6	+	4.15615e6i	−0.532386	+	0.446724i	−0.868924	−	0.494945i	$-0.835188\pi$
$613$	−4.95310e6	+	4.15615e6i	−0.532386	+	0.446724i	0.336539	+	0.941670i	$0.390744\pi$
$614$	1.01102e6	−	848347.i	0.108228	−	0.0908139i
$615$	−1.39229e6	+	2.41152e6i	−0.148437	+	0.257100i
$616$	963914.	−	350836.i	0.102350	−	0.0372523i
$617$	−2.16586e6	−	1.22832e7i	−0.229044	−	1.29897i	−0.854802	−	0.518954i	$-0.826322\pi$
$617$	−2.16586e6	−	1.22832e7i	−0.229044	−	1.29897i	0.625758	−	0.780017i	$-0.284790\pi$
$618$	2.34357e6	+	4.05918e6i	0.246835	+	0.427530i
$619$	−6.82938e6	+	1.18288e7i	−0.716399	+	1.24084i	0.246019	+	0.969265i	$0.420877\pi$
$619$	−6.82938e6	+	1.18288e7i	−0.716399	+	1.24084i	−0.962418	+	0.271574i	$0.912456\pi$
$620$	−1.48949e6	−	542131.i	−0.155618	−	0.0566402i
$621$	5.18492e6	+	8.98055e6i	0.539527	+	0.934489i
$622$	6.69936e6	+	5.62143e6i	0.694317	+	0.582601i
$623$	520769.			0.0537557
$624$	−438605.	−	368033.i	−0.0450933	−	0.0378378i
$625$	6.51268e6	−	2.37042e6i	0.666898	−	0.242731i
$626$	1.97071e6	−	1.11764e7i	0.200995	−	1.13990i
$627$	1.53549e6	+	8.70821e6i	0.155984	+	0.884627i
$628$	−1.69929e6			−0.171936
$629$	−3.34971e6	−	4.94398e6i	−0.337583	−	0.498253i
$630$	139592.			0.0140123
$631$	2.87067e6	+	1.62804e7i	0.287018	+	1.62776i	0.697985	+	0.716112i	$0.254080\pi$
$631$	2.87067e6	+	1.62804e7i	0.287018	+	1.62776i	−0.410967	+	0.911650i	$0.634809\pi$
$632$	118800.	−	673751.i	0.0118311	−	0.0670975i
$633$	−1.10956e7	+	4.03848e6i	−1.10063	+	0.400597i
$634$	4.64063e6	+	3.89395e6i	0.458516	+	0.384740i
$635$	5.46032e6			0.537383
$636$	1.59661e6	+	1.33972e6i	0.156515	+	0.131332i
$637$	1.09262e6	+	1.89247e6i	0.106689	+	0.184791i
$638$	−1.79959e7	−	6.54996e6i	−1.75033	−	0.637069i
$639$	−156930.	+	271810.i	−0.0152038	+	0.0263338i
$640$	400526.	+	693732.i	0.0386528	+	0.0669486i
$641$	697517.	+	3.95581e6i	0.0670517	+	0.380269i	0.999805	+	0.0197534i	$0.00628812\pi$
$641$	697517.	+	3.95581e6i	0.0670517	+	0.380269i	−0.932753	+	0.360516i	$0.882601\pi$
$642$	−3.36979e6	+	1.22650e6i	−0.322675	+	0.117444i
$643$	−8.85991e6	+	1.53458e7i	−0.845088	+	1.46373i	0.0404572	+	0.999181i	$0.487119\pi$
$643$	−8.85991e6	+	1.53458e7i	−0.845088	+	1.46373i	−0.885545	+	0.464554i	$0.846215\pi$
$644$	1.01332e6	−	850273.i	0.0962787	−	0.0807874i
$645$	−2.36900e6	+	1.98783e6i	−0.224216	+	0.188140i
$646$	−2.58362e6	−	940360.i	−0.243583	−	0.0886570i
$647$	2.46570e6	−	1.39837e7i	0.231569	−	1.31329i	−0.618152	−	0.786059i	$-0.712118\pi$
$647$	2.46570e6	−	1.39837e7i	0.231569	−	1.31329i	0.849721	−	0.527233i	$-0.176771\pi$
$648$	−717007.	+	4.06635e6i	−0.0670789	+	0.380423i
$649$	3.97518e6	+	1.44685e6i	0.370463	+	0.134838i
$650$	−307443.	+	257976.i	−0.0285418	+	0.0239494i
$651$	−722937.	+	606617.i	−0.0668572	+	0.0560999i
$652$	1.60368e6	−	2.77765e6i	0.147740	−	0.255893i
$653$	−1.56127e7	+	5.68255e6i	−1.43283	+	0.521507i	−0.937741	−	0.347335i	$-0.887087\pi$
$653$	−1.56127e7	+	5.68255e6i	−1.43283	+	0.521507i	−0.495089	+	0.868843i	$0.664864\pi$
$654$	446078.	+	2.52983e6i	0.0407818	+	0.231285i
$655$	−7.43882e6	−	1.28844e7i	−0.677487	−	1.17344i
$656$	−445232.	+	771164.i	−0.0403949	+	0.0699660i
$657$	174589.	+	63545.2i	0.0157799	+	0.00574340i
$658$	795318.	+	1.37753e6i	0.0716104	+	0.124033i
$659$	−1.30255e7	−	1.09297e7i	−1.16837	−	0.980378i	−0.168383	−	0.985722i	$-0.553854\pi$
$659$	−1.30255e7	−	1.09297e7i	−1.16837	−	0.980378i	−0.999986	+	0.00534405i	$0.998299\pi$
$660$	7.21711e6			0.644916
$661$	−3.40994e6	−	2.86128e6i	−0.303559	−	0.254716i	0.478265	−	0.878216i	$-0.341266\pi$
$661$	−3.40994e6	−	2.86128e6i	−0.303559	−	0.254716i	−0.781824	+	0.623499i	$0.785710\pi$
$662$	1.10241e7	−	4.01245e6i	0.977683	−	0.355848i
$663$	278520.	−	1.57957e6i	0.0246078	−	0.139558i
$664$	−716253.	−	4.06207e6i	−0.0630443	−	0.357542i
$665$	−1.33300e6			−0.116889
$666$	−600028.	+	581854.i	−0.0524187	+	0.0508310i
$667$	−2.46959e7			−2.14937
$668$	1.59003e6	+	9.01750e6i	0.137868	+	0.781889i
$669$	−2.85051e6	+	1.61660e7i	−0.246239	+	1.39649i
$670$	−236156.	+	85953.7i	−0.0203241	+	0.00739737i
$671$	1.88783e7	+	1.58408e7i	1.61867	+	1.35822i
$672$	476931.			0.0407410
$673$	−8.44962e6	−	7.09007e6i	−0.719117	−	0.603410i	0.208024	−	0.978124i	$-0.433297\pi$
$673$	−8.44962e6	−	7.09007e6i	−0.719117	−	0.603410i	−0.927141	+	0.374713i	$0.877741\pi$
$674$	−2.95102e6	−	5.11131e6i	−0.250220	−	0.433393i
$675$	2.46272e6	+	896356.i	0.208044	+	0.0757218i
$676$	2.82108e6	−	4.88625e6i	0.237437	−	0.411253i
$677$	−2.09990e6	−	3.63714e6i	−0.176087	−	0.304992i	0.764450	−	0.644683i	$-0.223011\pi$
$677$	−2.09990e6	−	3.63714e6i	−0.176087	−	0.304992i	−0.940537	+	0.339691i	$0.889677\pi$
$678$	−1.20969e6	−	6.86049e6i	−0.101065	−	0.573166i
$679$	−2.54658e6	+	926880.i	−0.211974	+	0.0771523i
$680$	−1.12201e6	+	1.94339e6i	−0.0930521	+	0.161171i
$681$	−6.01382e6	+	5.04619e6i	−0.496915	+	0.416961i
$682$	−3.49837e6	+	2.93548e6i	−0.288008	+	0.241667i
$683$	−1.41547e7	−	5.15187e6i	−1.16104	−	0.422584i	−0.311572	−	0.950223i	$-0.600855\pi$
$683$	−1.41547e7	−	5.15187e6i	−1.16104	−	0.422584i	−0.849469	+	0.527638i	$0.823078\pi$
$684$	−66820.8	+	378959.i	−0.00546099	+	0.0309708i
$685$	2.66476e6	−	1.51126e7i	0.216986	−	1.23059i
$686$	−3.50749e6	−	1.27662e6i	−0.284568	−	0.103574i
$687$	1.42355e7	−	1.19450e7i	1.15075	−	0.965591i
$688$	−757569.	+	635676.i	−0.0610171	+	0.0511994i
$689$	543363.	−	941132.i	0.0436056	−	0.0755270i
$690$	8.74555e6	−	3.18312e6i	0.699302	−	0.254525i
$691$	513719.	+	2.91345e6i	0.0409289	+	0.232120i	0.998409	−	0.0563783i	$-0.0179553\pi$
$691$	513719.	+	2.91345e6i	0.0409289	+	0.232120i	−0.957481	+	0.288498i	$0.906844\pi$
$692$	4.35934e6	+	7.55059e6i	0.346063	+	0.599399i
$693$	201089.	−	348297.i	0.0159058	−	0.0275497i
$694$	−2.22216e6	−	808802.i	−0.175137	−	0.0637446i
$695$	1.67670e6	+	2.90413e6i	0.131672	+	0.228062i
$696$	−6.82093e6	−	5.72344e6i	−0.533728	−	0.447851i
$697$	−2.49450e6			−0.194492
$698$	2.73296e6	+	2.29322e6i	0.212322	+	0.178159i
$699$	2.37550e7	−	8.64613e6i	1.83892	−	0.669312i
$700$	58052.0	−	329229.i	0.00447788	−	0.0253953i
$701$	3.77306e6	+	2.13981e7i	0.290000	+	1.64467i	0.686857	+	0.726793i	$0.258990\pi$
$701$	3.77306e6	+	2.13981e7i	0.290000	+	1.64467i	−0.396857	+	0.917881i	$0.629899\pi$
$702$	1.94945e6			0.149303
$703$	5.72981e6	−	5.55626e6i	0.437273	−	0.424028i
$704$	2.30792e6			0.175504
$705$	1.94335e6	+	1.10213e7i	0.147258	+	0.835142i
$706$	−1.70309e6	+	9.65872e6i	−0.128596	+	0.729302i
$707$	−1.54086e6	+	560828.i	−0.115935	+	0.0421970i
$708$	1.50670e6	+	1.26427e6i	0.112965	+	0.0947890i
$709$	1.38097e6			0.103174			0.0515868	−	0.998669i	$-0.483572\pi$
$709$	1.38097e6			0.103174			0.0515868	+	0.998669i	$0.483572\pi$
$710$	−1.87389e6	−	1.57238e6i	−0.139508	−	0.117061i
$711$	−134117.	−	232298.i	−0.00994970	−	0.0172334i
$712$	1.10103e6	+	400741.i	0.0813951	+	0.0296254i
$713$	−2.94455e6	+	5.10012e6i	−0.216918	+	0.375713i
$714$	668025.	+	1.15705e6i	0.0490396	+	0.0849391i
$715$	−653443.	−	3.70586e6i	−0.0478016	−	0.271097i
$716$	1.04265e7	−	3.79495e6i	0.760077	−	0.276646i
$717$	−6.13814e6	+	1.06316e7i	−0.445901	+	0.772324i
$718$	2.57807e6	−	2.16326e6i	0.186631	−	0.156602i
$719$	1.05620e7	−	8.86259e6i	0.761947	−	0.639349i	−0.176686	−	0.984267i	$-0.556538\pi$
$719$	1.05620e7	−	8.86259e6i	0.761947	−	0.639349i	0.938633	+	0.344918i	$0.112093\pi$
$720$	295130.	+	107418.i	0.0212169	+	0.00772232i
$721$	−353499.	+	2.00479e6i	−0.0253250	+	0.143625i
$722$	−1.08179e6	+	6.13515e6i	−0.0772327	+	0.438008i
$723$	−2.15317e7	−	7.83691e6i	−1.53191	−	0.557570i
$724$	7.15058e6	−	6.00005e6i	0.506985	−	0.425411i
$725$	−4.78118e6	+	4.01189e6i	−0.337824	+	0.283468i
$726$	5.12267e6	−	8.87273e6i	0.360708	−	0.624764i
$727$	6.98361e6	−	2.54182e6i	0.490054	−	0.178365i	−0.0851613	−	0.996367i	$-0.527141\pi$
$727$	6.98361e6	−	2.54182e6i	0.490054	−	0.178365i	0.575215	+	0.818002i	$0.304918\pi$
$728$	−43181.7	−	244896.i	−0.00301975	−	0.0171259i
$729$	−6.28850e6	−	1.08920e7i	−0.438257	−	0.759083i
$730$	−724028.	+	1.25405e6i	−0.0502861	+	0.0870982i
$731$	−2.60329e6	−	947519.i	−0.180189	−	0.0655835i
$732$	5.72904e6	+	9.92299e6i	0.395189	+	0.684487i
$733$	−8.78649e6	−	7.37274e6i	−0.604026	−	0.506838i	0.288711	−	0.957416i	$-0.406773\pi$
$733$	−8.78649e6	−	7.37274e6i	−0.604026	−	0.506838i	−0.892737	+	0.450579i	$0.851218\pi$
$734$	1.96870e7			1.34877
$735$	−9.81068e6	−	8.23214e6i	−0.669855	−	0.562075i
$736$	2.79669e6	−	1.01791e6i	0.190305	−	0.0692652i
$737$	−125731.	+	713056.i	−0.00852655	+	0.0483565i
$738$	60625.1	+	343822.i	0.00409743	+	0.0232377i
$739$	2.33343e7			1.57175			0.785874	−	0.618386i	$-0.212213\pi$
$739$	2.33343e7			1.57175			0.785874	+	0.618386i	$0.212213\pi$
$740$	−3.65394e6	−	5.39299e6i	−0.245291	−	0.362035i
$741$	2.14365e6			0.143420
$742$	157190.	+	891471.i	0.0104813	+	0.0594426i
$743$	1.73193e6	−	9.82226e6i	0.115096	−	0.652739i	−0.871607	−	0.490205i	$-0.836922\pi$
$743$	1.73193e6	−	9.82226e6i	0.115096	−	0.652739i	0.986703	−	0.162534i	$-0.0519669\pi$
$744$	−1.99526e6	+	726216.i	−0.132150	+	0.0480987i
$745$	−856450.	−	718647.i	−0.0565342	−	0.0474378i
$746$	6.39565e6			0.420763
$747$	−1.23884e6	−	1.03951e6i	−0.0812297	−	0.0681598i
$748$	3.23264e6	+	5.59910e6i	0.211253	+	0.365901i
$749$	−1.46357e6	−	532695.i	−0.0953253	−	0.0346956i
$750$	6.17943e6	−	1.07031e7i	0.401140	−	0.694794i
$751$	1.21321e7	+	2.10134e7i	0.784940	+	1.35956i	0.929035	+	0.369993i	$0.120640\pi$
$751$	1.21321e7	+	2.10134e7i	0.784940	+	1.35956i	−0.144094	+	0.989564i	$0.546027\pi$
$752$	621453.	+	3.52443e6i	0.0400741	+	0.227271i
$753$	5.99309e6	−	2.18130e6i	0.385179	−	0.140194i
$754$	−2.32131e6	+	4.02063e6i	−0.148698	+	0.257553i
$755$	1.67105e7	−	1.40218e7i	1.06690	−	0.895233i
$756$	−1.24394e6	+	1.04379e6i	−0.0791583	+	0.0664217i
$757$	−7.48813e6	−	2.72546e6i	−0.474935	−	0.172862i	0.0934518	−	0.995624i	$-0.470210\pi$
$757$	−7.48813e6	−	2.72546e6i	−0.474935	−	0.172862i	−0.568386	+	0.822762i	$0.692432\pi$
$758$	−34180.1	+	193845.i	−0.00216073	+	0.0122541i
$759$	4.65619e6	−	2.64066e7i	0.293377	−	1.66382i
$760$	−2.81826e6	−	1.02576e6i	−0.176990	−	0.0644189i
$761$	−8.28898e6	+	6.95528e6i	−0.518847	+	0.435365i	−0.864230	−	0.503097i	$-0.832194\pi$
$761$	−8.28898e6	+	6.95528e6i	−0.518847	+	0.435365i	0.345382	+	0.938462i	$0.387749\pi$
$762$	5.60317e6	−	4.70162e6i	0.349580	−	0.293332i
$763$	−557855.	+	966233.i	−0.0346904	+	0.0600856i
$764$	−1.35116e7	+	4.91780e6i	−0.837475	+	0.304816i
$765$	152779.	+	866455.i	0.00943868	+	0.0535294i
$766$	2.03925e6	+	3.53208e6i	0.125573	+	0.217500i
$767$	512765.	−	888135.i	0.0314724	−	0.0545118i
$768$	1.00834e6	+	367007.i	0.0616886	+	0.0224528i
$769$	8.68903e6	+	1.50498e7i	0.529853	+	0.917732i	0.999394	+	0.0348213i	$0.0110862\pi$
$769$	8.68903e6	+	1.50498e7i	0.529853	+	0.917732i	−0.469541	+	0.882911i	$0.655580\pi$
$770$	2.40120e6	+	2.01484e6i	0.145949	+	0.122466i
$771$	−6.91926e6			−0.419202
$772$	3.28311e6	+	2.75486e6i	0.198263	+	0.166363i
$773$	2.04772e7	−	7.45308e6i	1.23260	−	0.448629i	0.358111	−	0.933679i	$-0.383421\pi$
$773$	2.04772e7	−	7.45308e6i	1.23260	−	0.448629i	0.874486	+	0.485051i	$0.161199\pi$
$774$	−67329.4	+	381844.i	−0.00403973	+	0.0229105i
$775$	258450.	+	1.46574e6i	0.0154569	+	0.0876603i
$776$	−6.09732e6			−0.363483
$777$	−3.86844e6	+	278583.i	−0.229871	+	0.0165540i
$778$	1.54049e6			0.0912449
$779$	−578924.	−	3.28324e6i	−0.0341804	−	0.193847i
$780$	303816.	−	1.72303e6i	0.0178803	−	0.101404i
$781$	−6.62269e6	+	2.41046e6i	−0.388514	+	0.141408i
$782$	6.38674e6	+	5.35912e6i	0.373476	+	0.313384i
$783$	3.03167e7			1.76716
$784$	−3.13730e6	−	2.63251e6i	−0.182291	−	0.152960i
$785$	−2.59632e6	−	4.49696e6i	−0.150378	−	0.260462i
$786$	−1.87276e7	−	6.81628e6i	−1.08125	−	0.393542i
$787$	3.23255e6	−	5.59895e6i	0.186041	−	0.322233i	−0.757886	−	0.652387i	$-0.773768\pi$
$787$	3.23255e6	−	5.59895e6i	0.186041	−	0.322233i	0.943927	+	0.330155i	$0.107101\pi$
$788$	6.31797e6	+	1.09431e7i	0.362462	+	0.627802i
$789$	−5.37846e6	−	3.05028e7i	−0.307585	−	1.74440i
$790$	1.96451e6	−	715023.i	0.111992	−	0.0407617i
$791$	1.51281e6	−	2.62026e6i	0.0859691	−	0.148903i
$792$	693171.	−	581639.i	0.0392669	−	0.0329489i
$793$	4.57657e6	−	3.84020e6i	0.258439	−	0.216856i
$794$	−9.75312e6	−	3.54985e6i	−0.549026	−	0.199829i
$795$	−1.10595e6	+	6.27217e6i	−0.0620610	+	0.351965i
$796$	−522232.	+	2.96173e6i	−0.0292133	+	0.165677i
$797$	−1.68914e7	−	6.14795e6i	−0.941930	−	0.342835i	−0.175003	−	0.984568i	$-0.555993\pi$
$797$	−1.68914e7	−	6.14795e6i	−0.941930	−	0.342835i	−0.766928	+	0.641733i	$0.778216\pi$
$798$	−1.36787e6	+	1.14778e6i	−0.0760391	+	0.0638044i
$799$	−7.67997e6	+	6.44426e6i	−0.425591	+	0.357113i
$800$	376084.	−	651396.i	0.0207759	−	0.0359849i
$801$	431682.	−	157120.i	0.0237729	−	0.00865264i
$802$	−1.56639e6	−	8.88345e6i	−0.0859932	−	0.487692i
$803$	2.08600e6	+	3.61306e6i	0.114163	+	0.197736i
$804$	−168323.	+	291545.i	−0.00918342	+	0.0159061i
$805$	3.79837e6	+	1.38249e6i	0.206589	+	0.0751924i
$806$	553552.	+	958780.i	0.0300138	+	0.0519854i
$807$	−1.64991e7	−	1.38444e7i	−0.891819	−	0.748325i
$808$	−3.68931e6			−0.198800
$809$	−7.74344e6	−	6.49751e6i	−0.415970	−	0.349041i	0.410657	−	0.911790i	$-0.365299\pi$
$809$	−7.74344e6	−	6.49751e6i	−0.415970	−	0.349041i	−0.826628	+	0.562749i	$0.809744\pi$
$810$	−1.18566e7	+	4.31545e6i	−0.634962	+	0.231107i
$811$	1.48704e6	−	8.43344e6i	0.0793911	−	0.450249i	−0.919036	−	0.394175i	$-0.871030\pi$
$811$	1.48704e6	−	8.43344e6i	0.0793911	−	0.450249i	0.998427	−	0.0560744i	$-0.0178584\pi$
$812$	−671537.	−	3.80848e6i	−0.0357421	−	0.202703i
$813$	−1.40407e7			−0.745012
$814$	−1.87198e7	+	1.34809e6i	−0.990239	+	0.0713113i
$815$	9.80093e6			0.516860
$816$	521988.	+	2.96034e6i	0.0274432	+	0.155638i
$817$	642945.	−	3.64632e6i	0.0336991	−	0.191117i
$818$	−1.88398e7	+	6.85714e6i	−0.984451	+	0.358311i
$819$	−74687.8	−	62670.5i	−0.00389081	−	0.00326478i
$820$	−2.72105e6			−0.141320
$821$	−5.62802e6	−	4.72247e6i	−0.291406	−	0.244518i	0.485351	−	0.874320i	$-0.338692\pi$
$821$	−5.62802e6	−	4.72247e6i	−0.291406	−	0.244518i	−0.776756	+	0.629801i	$0.783136\pi$
$822$	−1.02783e7	−	1.78025e7i	−0.530567	−	0.918968i
$823$	−9.10350e6	−	3.31340e6i	−0.468499	−	0.170520i	0.0969733	−	0.995287i	$-0.469084\pi$
$823$	−9.10350e6	−	3.31340e6i	−0.468499	−	0.170520i	−0.565472	+	0.824767i	$0.691306\pi$
$824$	−2.29010e6	+	3.96657e6i	−0.117500	+	0.203516i
$825$	−3.38834e6	−	5.86877e6i	−0.173321	−	0.300201i
$826$	148339.	+	841270.i	0.00756492	+	0.0429028i
$827$	−1.48937e7	+	5.42085e6i	−0.757248	+	0.275616i	−0.691652	−	0.722231i	$-0.743117\pi$
$827$	−1.48937e7	+	5.42085e6i	−0.757248	+	0.275616i	−0.0655955	+	0.997846i	$0.520895\pi$
$828$	583437.	−	1.01054e6i	0.0295746	−	0.0512247i
$829$	8.33922e6	−	6.99744e6i	0.421443	−	0.353633i	−0.407269	−	0.913308i	$-0.633519\pi$
$829$	8.33922e6	−	6.99744e6i	0.421443	−	0.353633i	0.828712	+	0.559676i	$0.189074\pi$
$830$	9.65542e6	−	8.10186e6i	0.486492	−	0.408215i
$831$	9.10659e6	+	3.31453e6i	0.457460	+	0.166502i
$832$	97155.4	−	550996.i	0.00486585	−	0.0275956i
$833$	1.99223e6	−	1.12985e7i	0.0994780	−	0.564168i
$834$	4.22116e6	+	1.53638e6i	0.210144	+	0.0764861i
$835$	−2.14343e7	+	1.79855e7i	−1.06388	+	0.892703i
$836$	−6.61925e6	+	5.55421e6i	−0.327562	+	0.274857i
$837$	3.61473e6	−	6.26090e6i	0.178346	−	0.308904i
$838$	9.20785e6	−	3.35138e6i	0.452948	−	0.164860i
$839$	2.58723e6	+	1.46729e7i	0.126891	+	0.719632i	0.980167	+	0.198173i	$0.0635009\pi$
$839$	2.58723e6	+	1.46729e7i	0.126891	+	0.719632i	−0.853276	+	0.521459i	$0.825388\pi$
$840$	728696.	+	1.26214e6i	0.0356326	+	0.0617175i
$841$	−2.58441e7	+	4.47634e7i	−1.26000	+	2.18239i
$842$	1.64677e7	+	5.99376e6i	0.800486	+	0.291353i
$843$	1.73392e7	+	3.00324e7i	0.840351	+	1.45553i
$844$	−8.83888e6	−	7.41670e6i	−0.427111	−	0.358389i
$845$	1.72411e7			0.830661
$846$	1.07488e6	+	901928.i	0.0516336	+	0.0433257i
$847$	4.18141e6	−	1.52191e6i	0.200269	−	0.0728921i
$848$	−353666.	+	2.00574e6i	−0.0168890	+	0.0957822i
$849$	803306.	+	4.55577e6i	0.0382483	+	0.216917i
$850$	2.10708e6			0.100031
$851$	−2.20897e7	+	9.88999e6i	−1.04560	+	0.468136i
$852$	−3.27681e6			−0.154651
$853$	2.20041e6	+	1.24792e7i	0.103546	+	0.587237i	0.991791	+	0.127868i	$0.0408133\pi$
$853$	2.20041e6	+	1.24792e7i	0.103546	+	0.587237i	−0.888246	+	0.459369i	$0.848076\pi$
$854$	−864157.	+	4.90088e6i	−0.0405460	+	0.229948i
$855$	−1.10496e6	+	402174.i	−0.0516931	+	0.0188148i
$856$	−2.68441e6	−	2.25248e6i	−0.125217	−	0.105070i
$857$	3.95035e7			1.83731			0.918657	−	0.395056i	$-0.129275\pi$
$857$	3.95035e7			1.83731			0.918657	+	0.395056i	$0.129275\pi$
$858$	−3.86148e6	−	3.24016e6i	−0.179075	−	0.150262i
$859$	3.97471e6	+	6.88440e6i	0.183790	+	0.318334i	0.943168	−	0.332316i	$-0.107830\pi$
$859$	3.97471e6	+	6.88440e6i	0.183790	+	0.318334i	−0.759378	+	0.650650i	$0.774497\pi$
$860$	−2.83972e6	−	1.03357e6i	−0.130927	−	0.0476535i
$861$	−810030.	+	1.40301e6i	−0.0372386	+	0.0644992i
$862$	−2.36686e6	−	4.09952e6i	−0.108494	−	0.187916i
$863$	1.64554e6	+	9.33233e6i	0.0752111	+	0.426543i	0.999043	+	0.0437443i	$0.0139287\pi$
$863$	1.64554e6	+	9.33233e6i	0.0752111	+	0.426543i	−0.923832	+	0.382799i	$0.874960\pi$
$864$	−3.43321e6	+	1.24959e6i	−0.156464	+	0.0569484i
$865$	−1.33211e7	+	2.30729e7i	−0.605342	+	1.04848i
$866$	8.92173e6	−	7.48622e6i	0.404254	−	0.339210i
$867$	1.13583e7	−	9.53074e6i	0.513175	−	0.430605i
$868$	−866583.	−	315410.i	−0.0390401	−	0.0142094i
$869$	1.04592e6	−	5.93170e6i	0.0469838	−	0.266459i
$870$	4.72477e6	−	2.67955e7i	0.211632	−	1.20023i
$871$	164943.	+	60034.5i	0.00736698	+	0.00268136i
$872$	−1.92297e6	+	1.61356e6i	−0.0856409	+	0.0718612i
$873$	−1.83130e6	+	1.53664e6i	−0.0813249	+	0.0682397i
$874$	−5.57138e6	+	9.64992e6i	−0.246709	+	0.427312i
$875$	5.04400e6	−	1.83586e6i	0.222718	−	0.0810626i
$876$	336835.	+	1.91029e6i	0.0148305	+	0.0841082i
$877$	208073.	+	360393.i	0.00913516	+	0.0158226i	0.870557	−	0.492068i	$-0.163759\pi$
$877$	208073.	+	360393.i	0.00913516	+	0.0158226i	−0.861422	+	0.507890i	$0.830425\pi$
$878$	1.05694e7	−	1.83067e7i	0.462713	−	0.801443i
$879$	2.87980e7	+	1.04816e7i	1.25716	+	0.457569i
$880$	3.52623e6	+	6.10761e6i	0.153498	+	0.265867i
$881$	1.56404e7	+	1.31239e7i	0.678904	+	0.569668i	0.915686	−	0.401895i	$-0.131648\pi$
$881$	1.56404e7	+	1.31239e7i	0.678904	+	0.569668i	−0.236782	+	0.971563i	$0.576093\pi$
$882$	−1.60571e6			−0.0695019
$883$	−2.40448e6	−	2.01760e6i	−0.103781	−	0.0870829i	0.589421	−	0.807826i	$-0.299356\pi$
$883$	−2.40448e6	−	2.01760e6i	−0.103781	−	0.0870829i	−0.693202	+	0.720743i	$0.743801\pi$
$884$	1.47282e6	−	536063.i	0.0633898	−	0.0230720i
$885$	−1.04367e6	+	5.91897e6i	−0.0447926	+	0.254032i
$886$	741084.	+	4.20290e6i	0.0317164	+	0.179872i
$887$	−1.47340e7			−0.628800			−0.314400	−	0.949291i	$-0.601803\pi$
$887$	−1.47340e7			−0.628800			−0.314400	+	0.949291i	$0.601803\pi$
$888$	−8.39317e6	−	2.38785e6i	−0.357185	−	0.101619i
$889$	3.17680e6			0.134814
$890$	621732.	+	3.52602e6i	0.0263105	+	0.149214i
$891$	−6.31253e6	+	3.58001e7i	−0.266385	+	1.51074i
$892$	−1.50736e7	+	5.48632e6i	−0.634313	+	0.230871i
$893$	−1.02642e7	−	8.61273e6i	−0.430723	−	0.361420i
$894$	−1.49765e6			−0.0626709
$895$	2.59734e7	+	2.17943e7i	1.08386	+	0.909464i
$896$	233025.	+	403611.i	0.00969690	+	0.0167955i
$897$	−6.10834e6	−	2.22325e6i	−0.253479	−	0.0922588i
$898$	−1.17021e7	+	2.02686e7i	−0.484254	+	0.838753i
$899$	8.60852e6	+	1.49104e7i	0.355246	+	0.615304i
$900$	−51209.5	−	290424.i	−0.00210739	−	0.0119516i
$901$	−5.36138e6	+	1.95138e6i	−0.220021	+	0.0800811i
$902$	−3.91982e6	+	6.78932e6i	−0.160417	+	0.277850i
$903$	−1.37828e6	+	1.15651e6i	−0.0562495	+	0.0471989i
$904$	5.21477e6	−	4.37571e6i	0.212233	−	0.178085i
$905$	2.68037e7	+	9.75574e6i	1.08786	+	0.395948i
$906$	5.07420e6	−	2.87772e7i	0.205375	−	1.16474i
$907$	4.47500e6	−	2.53790e7i	0.180624	−	1.02437i	−0.750827	−	0.660499i	$-0.770345\pi$
$907$	4.47500e6	−	2.53790e7i	0.180624	−	1.02437i	0.931450	−	0.363868i	$-0.118544\pi$
$908$	−7.20874e6	−	2.62377e6i	−0.290165	−	0.105611i
$909$	−1.10807e6	+	929778.i	−0.0444791	+	0.0373224i
$910$	582109.	−	488448.i	0.0233024	−	0.0195531i
$911$	2.71686e6	−	4.70574e6i	0.108460	−	0.187859i	−0.806686	−	0.590980i	$-0.798741\pi$
$911$	2.71686e6	−	4.70574e6i	0.108460	−	0.187859i	0.915147	+	0.403121i	$0.132075\pi$
$912$	−3.77523e6	+	1.37407e6i	−0.150299	+	0.0547044i
$913$	−6.30589e6	−	3.57625e7i	−0.250363	−	1.41988i
$914$	9.66183e6	+	1.67348e7i	0.382555	+	0.662605i
$915$	−1.75066e7	+	3.03224e7i	−0.691274	+	1.19732i
$916$	1.70640e7	+	6.21079e6i	0.671958	+	0.244573i
$917$	−4.32789e6	−	7.49612e6i	−0.169962	−	0.294383i
$918$	−7.84036e6	−	6.57884e6i	−0.307064	−	0.257657i
$919$	115957.			0.00452908			0.00226454	−	0.999997i	$-0.499279\pi$
$919$	115957.			0.00452908			0.00226454	+	0.999997i	$0.499279\pi$
$920$	6.96679e6	+	5.84583e6i	0.271371	+	0.227707i
$921$	5.07661e6	−	1.84774e6i	0.197208	−	0.0717779i
$922$	−1.77322e6	+	1.00564e7i	−0.0686965	+	0.389597i
$923$	296685.	+	1.68258e6i	0.0114628	+	0.0650089i
$924$	4.19890e6			0.161791
$925$	−2.66997e6	+	5.50323e6i	−0.102601	+	0.211477i
$926$	−6.81915e6			−0.261338
$927$	311833.	+	1.76849e6i	0.0119185	+	0.0675933i
$928$	1.51090e6	−	8.56877e6i	0.0575927	−	0.326624i
$929$	−3.12866e7	+	1.13874e7i	−1.18938	+	0.432897i	−0.859504	−	0.511129i	$-0.829228\pi$
$929$	−3.12866e7	+	1.13874e7i	−1.18938	+	0.432897i	−0.329871	+	0.944026i	$0.607005\pi$
$930$	−4.97037e6	−	4.17064e6i	−0.188444	−	0.158123i
$931$	1.53333e7			0.579779
$932$	1.89235e7	+	1.58787e7i	0.713611	+	0.598791i
$933$	1.78991e7	+	3.10022e7i	0.673175	+	1.16597i
$934$	−2.94862e7	−	1.07321e7i	−1.10599	−	0.402547i
$935$	−9.87821e6	+	1.71096e7i	−0.369530	+	0.640044i
$936$	−109681.	−	189974.i	−0.00409207	−	0.00708768i
$937$	268072.	+	1.52031e6i	0.00997475	+	0.0565696i	0.989389	−	0.145292i	$-0.0464121\pi$
$937$	268072.	+	1.52031e6i	0.00997475	+	0.0565696i	−0.979414	+	0.201861i	$0.935301\pi$
$938$	−137395.	+	50007.7i	−0.00509875	+	0.00185579i
$939$	2.32276e7	−	4.02314e7i	0.859687	−	1.48902i
$940$	−8.37747e6	+	7.02953e6i	−0.309238	+	0.259482i
$941$	3.51429e7	−	2.94884e7i	1.29379	−	1.08562i	0.302606	−	0.953116i	$-0.402144\pi$
$941$	3.51429e7	−	2.94884e7i	1.29379	−	1.08562i	0.991183	−	0.132501i	$-0.0423009\pi$
$942$	−6.53635e6	−	2.37904e6i	−0.239998	−	0.0873522i
$943$	−1.75551e6	+	9.95602e6i	−0.0642873	+	0.364591i
$944$	−333750.	+	1.89279e6i	−0.0121897	+	0.0691310i
$945$	−4.66288e6	−	1.69715e6i	−0.169853	−	0.0618216i
$946$	−6.66964e6	+	5.59649e6i	−0.242312	+	0.203324i
$947$	2.22876e7	−	1.87015e7i	0.807585	−	0.677644i	−0.142445	−	0.989803i	$-0.545496\pi$
$947$	2.22876e7	−	1.87015e7i	0.807585	−	0.677644i	0.950030	+	0.312158i	$0.101052\pi$
$948$	1.40023e6	−	2.42527e6i	0.0506034	−	0.0876476i
$949$	950402.	−	345918.i	0.0342564	−	0.0124683i
$950$	489012.	+	2.77333e6i	0.0175797	+	0.0996993i
$951$	1.23987e7	+	2.14752e7i	0.444554	+	0.769990i
$952$	−652785.	+	1.13066e6i	−0.0233441	+	0.0404332i
$953$	−2.09495e7	−	7.62498e6i	−0.747206	−	0.271961i	−0.0597766	−	0.998212i	$-0.519039\pi$
$953$	−2.09495e7	−	7.62498e6i	−0.747206	−	0.271961i	−0.687430	+	0.726251i	$0.741261\pi$
$954$	399263.	+	691544.i	0.0142033	+	0.0246008i
$955$	−3.36585e7	−	2.82428e7i	−1.19422	−	1.00207i
$956$	−1.19962e7			−0.424521
$957$	−6.00514e7	−	5.03891e7i	−2.11955	−	1.77851i
$958$	−2.17193e7	+	7.90519e6i	−0.764597	+	0.278291i
$959$	1.55035e6	−	8.79248e6i	0.0544357	−	0.308720i
$960$	569395.	+	3.22920e6i	0.0199405	+	0.113088i
$961$	−2.45235e7			−0.856592
$962$	−466194.	+	4.52595e6i	−0.0162416	+	0.157678i
$963$	−1.37392e6			−0.0477413
$964$	−3.88813e6	−	2.20507e7i	−0.134756	−	0.764240i
$965$	−2.27417e6	+	1.28974e7i	−0.0786148	+	0.445847i
$966$	5.08814e6	−	1.85193e6i	0.175435	−	0.0638531i
$967$	7.32952e6	+	6.15020e6i	0.252063	+	0.211506i	0.760060	−	0.649853i	$-0.225169\pi$
$967$	7.32952e6	+	6.15020e6i	0.252063	+	0.211506i	−0.507997	+	0.861359i	$0.669614\pi$
$968$	1.00116e7			0.343412
$969$	−8.62142e6	−	7.23423e6i	−0.294964	−	0.247504i
$970$	−9.31601e6	−	1.61358e7i	−0.317907	−	0.550632i
$971$	−4.52804e7	−	1.64807e7i	−1.54121	−	0.560955i	−0.574876	−	0.818240i	$-0.694950\pi$
$971$	−4.52804e7	−	1.64807e7i	−1.54121	−	0.560955i	−0.966336	+	0.257285i	$0.917172\pi$
$972$	−1.51493e6	+	2.62393e6i	−0.0514312	+	0.0890814i
$973$	975498.	+	1.68961e6i	0.0330327	+	0.0572144i
$974$	6.39551e6	+	3.62707e7i	0.216012	+	1.22506i
$975$	−1.54376e6	+	561882.i	−0.0520077	+	0.0189293i
$976$	−5.59834e6	+	9.69662e6i	−0.188120	+	0.325833i
$977$	3.30428e7	−	2.77262e7i	1.10749	−	0.929296i	0.109586	−	0.993977i	$-0.465047\pi$
$977$	3.30428e7	−	2.77262e7i	1.10749	−	0.929296i	0.997906	+	0.0646809i	$0.0206030\pi$
$978$	1.00573e7	−	8.43910e6i	0.336229	−	0.282130i
$979$	9.69344e6	+	3.52812e6i	0.323237	+	0.117649i
$980$	2.17317e6	−	1.23246e7i	0.0722816	−	0.409929i
$981$	−170905.	+	969250.i	−0.00566999	+	0.0321561i
$982$	−2.18589e7	−	7.95600e6i	−0.723353	−	0.263279i
$983$	4.14664e7	−	3.47945e7i	1.36872	−	1.14849i	0.395533	−	0.918452i	$-0.370560\pi$
$983$	4.14664e7	−	3.47945e7i	1.36872	−	1.14849i	0.973182	−	0.230037i	$-0.0738846\pi$
$984$	−2.79224e6	+	2.34297e6i	−0.0919316	+	0.0771397i
$985$	−1.93063e7	+	3.34395e7i	−0.634028	+	1.09817i
$986$	2.29045e7	−	8.33655e6i	0.750288	−	0.273082i
$987$	1.13064e6	+	6.41217e6i	0.0369429	+	0.209513i
$988$	1.04737e6	+	1.81411e6i	0.0341358	+	0.0591249i
$989$	−5.61380e6	+	9.72338e6i	−0.182501	+	0.316101i
$990$	2.59832e6	+	945712.i	0.0842568	+	0.0306670i
$991$	−5.35488e6	−	9.27493e6i	−0.173207	−	0.300004i	0.766332	−	0.642445i	$-0.222080\pi$
$991$	−5.35488e6	−	9.27493e6i	−0.173207	−	0.300004i	−0.939539	+	0.342441i	$0.888746\pi$
$992$	−1.58944e6	−	1.33370e6i	−0.0512822	−	0.0430308i
$993$	4.80220e7			1.54549
$994$	−1.09022e6	−	914806.i	−0.0349985	−	0.0293672i
$995$	−8.63575e6	+	3.14316e6i	−0.276530	+	0.100649i
$996$	2.93190e6	−	1.66276e7i	0.0936484	−	0.531107i
$997$	3.71047e6	+	2.10431e7i	0.118220	+	0.670460i	0.985105	+	0.171952i	$0.0550074\pi$
$997$	3.71047e6	+	2.10431e7i	0.118220	+	0.670460i	−0.866885	+	0.498508i	$0.833881\pi$
$998$	2.81950e7			0.896077
$999$	2.71173e7	−	1.21409e7i	0.859671	−	0.384892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.f.a.9.3	✓	48
37.33	even	9	inner	74.6.f.a.33.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.f.a.9.3	✓	48	1.1	even	1	trivial
74.6.f.a.33.3	yes	48	37.33	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)

\(f(q)\)	\(=\)	\(q+(0.694593 + 3.93923i) q^{2} +(-2.84323 + 16.1248i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(-37.4537 - 31.4274i) q^{5} -65.4941 q^{6} +(-21.7905 - 18.2844i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-23.5794 - 8.58219i) q^{9} +O(q^{10})\)	\(q+(0.694593 + 3.93923i) q^{2} +(-2.84323 + 16.1248i) q^{3} +(-15.0351 + 5.47232i) q^{4} +(-37.4537 - 31.4274i) q^{5} -65.4941 q^{6} +(-21.7905 - 18.2844i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-23.5794 - 8.58219i) q^{9} +(97.7847 - 169.368i) q^{10} +(-281.728 - 487.967i) q^{11} +(-45.4918 - 257.997i) q^{12} +(-128.358 + 46.7185i) q^{13} +(56.8909 - 98.5379i) q^{14} +(613.250 - 514.578i) q^{15} +(196.107 - 164.554i) q^{16} +(673.897 + 245.278i) q^{17} +(17.4292 - 98.8457i) q^{18} +(-166.435 + 943.901i) q^{19} +(735.100 + 267.555i) q^{20} +(356.787 - 299.380i) q^{21} +(1726.53 - 1448.73i) q^{22} +(1453.21 - 2517.03i) q^{23} +(984.710 - 358.405i) q^{24} +(-127.551 - 723.379i) q^{25} +(-273.191 - 473.181i) q^{26} +(-1783.96 + 3089.90i) q^{27} +(427.680 + 155.663i) q^{28} +(-4248.51 - 7358.64i) q^{29} +(2453.00 + 2058.31i) q^{30} -2026.24 q^{31} +(784.430 + 658.215i) q^{32} +(8669.38 - 3155.40i) q^{33} +(-498.124 + 2825.00i) q^{34} +(241.504 + 1369.64i) q^{35} +401.482 q^{36} +(-6747.08 - 4880.66i) q^{37} -3833.85 q^{38} +(-388.374 - 2202.58i) q^{39} +(-543.364 + 3081.57i) q^{40} +(-3268.60 + 1189.67i) q^{41} +(1427.15 + 1197.52i) q^{42} -3863.03 q^{43} +(6906.12 + 5794.92i) q^{44} +(613.419 + 1062.47i) q^{45} +(10924.6 + 3976.21i) q^{46} +(-6989.85 + 12106.8i) q^{47} +(2095.81 + 3630.05i) q^{48} +(-2778.00 - 15754.8i) q^{49} +(2760.96 - 1004.91i) q^{50} +(-5871.11 + 10169.1i) q^{51} +(1674.21 - 1404.83i) q^{52} +(-6094.48 + 5113.88i) q^{53} +(-13411.0 - 4881.19i) q^{54} +(-4783.78 + 27130.2i) q^{55} +(-316.128 + 1792.85i) q^{56} +(-14747.0 - 5367.46i) q^{57} +(26036.4 - 21847.1i) q^{58} +(-5751.29 + 4825.91i) q^{59} +(-6404.32 + 11092.6i) q^{60} +(-41099.4 + 14959.0i) q^{61} +(-1407.41 - 7981.84i) q^{62} +(356.886 + 618.144i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(6275.72 + 2284.18i) q^{65} +(18451.5 + 31959.0i) q^{66} +(-984.387 - 825.999i) q^{67} -11474.3 q^{68} +(36454.8 + 30589.2i) q^{69} +(-5227.57 + 1902.68i) q^{70} +(2172.00 - 12318.0i) q^{71} +(278.867 + 1581.53i) q^{72} -7404.31 q^{73} +(14539.6 - 29968.4i) q^{74} +12027.0 q^{75} +(-2662.96 - 15102.4i) q^{76} +(-2783.19 + 15784.3i) q^{77} +(8406.69 - 3059.79i) q^{78} +(8188.83 + 6871.24i) q^{79} -12516.4 q^{80} +(-49422.8 - 41470.6i) q^{81} +(-6956.74 - 12049.4i) q^{82} +(60562.2 + 22042.9i) q^{83} +(-3726.02 + 6453.66i) q^{84} +(-17531.5 - 30365.4i) q^{85} +(-2683.24 - 15217.4i) q^{86} +(130736. - 47584.0i) q^{87} +(-18030.6 + 31229.9i) q^{88} +(-14024.5 + 11767.9i) q^{89} +(-3759.25 + 3154.38i) q^{90} +(3651.20 + 1328.93i) q^{91} +(-8075.11 + 45796.2i) q^{92} +(5761.08 - 32672.7i) q^{93} +(-52546.5 - 19125.4i) q^{94} +(35898.0 - 30122.0i) q^{95} +(-12843.9 + 10777.3i) q^{96} +(47635.3 - 82506.8i) q^{97} +(60132.3 - 21886.4i) q^{98} +(2455.14 + 13923.8i) 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

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