LMFDB - Embedded newform 74.6.f.a.7.2

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			7.2
Character	$\chi$	$=$	74.7
Dual form			74.6.f.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75877 + 1.36808i) q^{2} +(-20.0307 - 7.29057i) q^{3} +(12.2567 - 10.2846i) q^{4} +(-15.8864 - 90.0960i) q^{5} +85.2648 q^{6} +(-21.3019 - 120.809i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(161.927 + 135.873i) q^{9} +O(q^{10})$	\(q+(-3.75877 + 1.36808i) q^{2} +(-20.0307 - 7.29057i) q^{3} +(12.2567 - 10.2846i) q^{4} +(-15.8864 - 90.0960i) q^{5} +85.2648 q^{6} +(-21.3019 - 120.809i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(161.927 + 135.873i) q^{9} +(182.972 + 316.916i) q^{10} +(305.921 - 529.870i) q^{11} +(-320.491 + 116.649i) q^{12} +(156.904 - 131.658i) q^{13} +(245.345 + 424.950i) q^{14} +(-338.637 + 1920.50i) q^{15} +(44.4539 - 252.111i) q^{16} +(-1287.11 - 1080.01i) q^{17} +(-794.531 - 289.186i) q^{18} +(-2053.85 - 747.540i) q^{19} +(-1121.32 - 940.896i) q^{20} +(-454.075 + 2575.19i) q^{21} +(-424.981 + 2410.19i) q^{22} +(1757.58 + 3044.22i) q^{23} +(1045.07 - 876.915i) q^{24} +(-4928.37 + 1793.78i) q^{25} +(-409.646 + 709.528i) q^{26} +(337.003 + 583.707i) q^{27} +(-1503.56 - 1261.64i) q^{28} +(2768.44 - 4795.07i) q^{29} +(-1354.55 - 7682.02i) q^{30} +1022.87 q^{31} +(177.816 + 1008.44i) q^{32} +(-9990.86 + 8383.33i) q^{33} +(6315.49 + 2298.65i) q^{34} +(-10546.0 + 3838.43i) q^{35} +3382.09 q^{36} +(8224.20 - 1306.30i) q^{37} +8742.64 q^{38} +(-4102.74 + 1493.28i) q^{39} +(5501.99 + 2002.56i) q^{40} +(5171.27 - 4339.21i) q^{41} +(-1816.30 - 10300.8i) q^{42} -9135.81 q^{43} +(-1699.92 - 9640.74i) q^{44} +(9669.16 - 16747.5i) q^{45} +(-10771.1 - 9038.02i) q^{46} +(12589.5 + 21805.6i) q^{47} +(-2728.47 + 4725.86i) q^{48} +(1652.39 - 601.420i) q^{49} +(16070.6 - 13484.8i) q^{50} +(17907.8 + 31017.2i) q^{51} +(569.074 - 3227.38i) q^{52} +(134.868 - 764.877i) q^{53} +(-2065.28 - 1732.97i) q^{54} +(-52599.2 - 19144.5i) q^{55} +(7377.57 + 2685.22i) q^{56} +(35690.0 + 29947.5i) q^{57} +(-3845.87 + 21811.0i) q^{58} +(3696.32 - 20962.9i) q^{59} +(15601.0 + 27021.8i) q^{60} +(26240.3 - 22018.2i) q^{61} +(-3844.72 + 1399.36i) q^{62} +(12965.3 - 22456.6i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-14354.5 - 12044.8i) q^{65} +(26084.3 - 45179.3i) q^{66} +(4284.66 + 24299.5i) q^{67} -26883.2 q^{68} +(-13011.4 - 73791.6i) q^{69} +(34388.7 - 28855.5i) q^{70} +(45328.8 + 16498.3i) q^{71} +(-12712.5 + 4626.97i) q^{72} -75997.3 q^{73} +(-29125.8 + 16161.5i) q^{74} +111796. q^{75} +(-32861.6 + 11960.6i) q^{76} +(-70529.8 - 25670.7i) q^{77} +(13378.3 - 11225.8i) q^{78} +(2150.22 + 12194.5i) q^{79} -23420.4 q^{80} +(-11414.4 - 64734.1i) q^{81} +(-13501.2 + 23384.8i) q^{82} +(20256.2 + 16997.0i) q^{83} +(20919.3 + 36233.3i) q^{84} +(-76857.3 + 133121. i) q^{85} +(34339.4 - 12498.5i) q^{86} +(-90412.4 + 75865.0i) q^{87} +(19578.9 + 33911.7i) q^{88} +(-7760.25 + 44010.5i) q^{89} +(-13432.3 + 76178.1i) q^{90} +(-19247.8 - 16150.8i) q^{91} +(52850.8 + 19236.1i) q^{92} +(-20488.7 - 7457.28i) q^{93} +(-77152.7 - 64738.8i) q^{94} +(-34722.2 + 196919. i) q^{95} +(3790.36 - 21496.2i) q^{96} +(-78042.3 - 135173. i) q^{97} +(-5388.15 + 4521.20i) q^{98} +(121532. - 44233.9i) 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
$3$	−20.0307	−	7.29057i	−1.28497	−	0.467690i	−0.392896	−	0.919583i	$-0.628527\pi$
$3$	−20.0307	−	7.29057i	−1.28497	−	0.467690i	−0.892072	+	0.451892i	$0.850749\pi$
$4$	12.2567	−	10.2846i	0.383022	−	0.321394i
$5$	−15.8864	−	90.0960i	−0.284184	−	1.61169i	−0.708187	−	0.706025i	$-0.750487\pi$
$5$	−15.8864	−	90.0960i	−0.284184	−	1.61169i	0.424003	−	0.905661i	$-0.360625\pi$
$6$	85.2648			0.966923
$7$	−21.3019	−	120.809i	−0.164313	−	0.931867i	−0.949770	−	0.312950i	$-0.898683\pi$
$7$	−21.3019	−	120.809i	−0.164313	−	0.931867i	0.785456	−	0.618917i	$-0.212428\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	161.927	+	135.873i	0.666366	+	0.559147i
$10$	182.972	+	316.916i	0.578607	+	1.00218i
$11$	305.921	−	529.870i	0.762302	−	1.32035i	−0.179359	−	0.983784i	$-0.557402\pi$
$11$	305.921	−	529.870i	0.762302	−	1.32035i	0.941661	−	0.336563i	$-0.109264\pi$
$12$	−320.491	+	116.649i	−0.642484	+	0.233845i
$13$	156.904	−	131.658i	0.257498	−	0.216067i	−0.504895	−	0.863181i	$-0.668469\pi$
$13$	156.904	−	131.658i	0.257498	−	0.216067i	0.762393	+	0.647114i	$0.224024\pi$
$14$	245.345	+	424.950i	0.334547	+	0.579453i
$15$	−338.637	+	1920.50i	−0.388603	+	2.20388i
$16$	44.4539	−	252.111i	0.0434120	−	0.246202i
$17$	−1287.11	−	1080.01i	−1.08017	−	0.906372i	−0.0842373	−	0.996446i	$-0.526845\pi$
$17$	−1287.11	−	1080.01i	−1.08017	−	0.906372i	−0.995935	+	0.0900734i	$0.971290\pi$
$18$	−794.531	−	289.186i	−0.578002	−	0.210376i
$19$	−2053.85	−	747.540i	−1.30522	−	0.475062i	−0.406528	−	0.913638i	$-0.633261\pi$
$19$	−2053.85	−	747.540i	−1.30522	−	0.475062i	−0.898694	+	0.438576i	$0.855483\pi$
$20$	−1121.32	−	940.896i	−0.626834	−	0.525977i
$21$	−454.075	+	2575.19i	−0.224688	+	1.27427i
$22$	−424.981	+	2410.19i	−0.187203	+	1.06168i
$23$	1757.58	+	3044.22i	0.692781	+	1.19993i	0.970923	+	0.239392i	$0.0769481\pi$
$23$	1757.58	+	3044.22i	0.692781	+	1.19993i	−0.278142	+	0.960540i	$0.589719\pi$
$24$	1045.07	−	876.915i	0.370353	−	0.310763i
$25$	−4928.37	+	1793.78i	−1.57708	+	0.574009i
$26$	−409.646	+	709.528i	−0.118843	+	0.205843i
$27$	337.003	+	583.707i	0.0889662	+	0.154094i
$28$	−1503.56	−	1261.64i	−0.362432	−	0.304116i
$29$	2768.44	−	4795.07i	0.611279	−	1.05877i	−0.379746	−	0.925091i	$-0.623989\pi$
$29$	2768.44	−	4795.07i	0.611279	−	1.05877i	0.991025	−	0.133675i	$-0.0426779\pi$
$30$	−1354.55	−	7682.02i	−0.274784	−	1.55838i
$31$	1022.87			0.191168			0.0955839	−	0.995421i	$-0.469528\pi$
$31$	1022.87			0.191168			0.0955839	+	0.995421i	$0.469528\pi$
$32$	177.816	+	1008.44i	0.0306970	+	0.174091i
$33$	−9990.86	+	8383.33i	−1.59705	+	1.34008i
$34$	6315.49	+	2298.65i	0.936936	+	0.341017i
$35$	−10546.0	+	3838.43i	−1.45518	+	0.529643i
$36$	3382.09			0.434939
$37$	8224.20	−	1306.30i	0.987619	−	0.156870i
$37$	8224.20	−	1306.30i	0.987619	−	0.156870i
$38$	8742.64			0.982163
$39$	−4102.74	+	1493.28i	−0.431930	+	0.157209i
$40$	5501.99	+	2002.56i	0.543713	+	0.197895i
$41$	5171.27	−	4339.21i	0.480438	−	0.403136i	−0.370147	−	0.928973i	$-0.620693\pi$
$41$	5171.27	−	4339.21i	0.480438	−	0.403136i	0.850585	+	0.525838i	$0.176248\pi$
$42$	−1816.30	−	10300.8i	−0.158878	−	0.901043i
$43$	−9135.81			−0.753487			−0.376744	−	0.926318i	$-0.622956\pi$
$43$	−9135.81			−0.753487			−0.376744	+	0.926318i	$0.622956\pi$
$44$	−1699.92	−	9640.74i	−0.132372	−	0.750721i
$45$	9669.16	−	16747.5i	0.711799	−	1.23287i
$46$	−10771.1	−	9038.02i	−0.750525	−	0.629765i
$47$	12589.5	+	21805.6i	0.831309	+	1.43987i	0.897001	+	0.442029i	$0.145741\pi$
$47$	12589.5	+	21805.6i	0.831309	+	1.43987i	−0.0656917	+	0.997840i	$0.520925\pi$
$48$	−2728.47	+	4725.86i	−0.170929	+	0.296058i
$49$	1652.39	−	601.420i	0.0983154	−	0.0357839i
$50$	16070.6	−	13484.8i	0.909089	−	0.762816i
$51$	17907.8	+	31017.2i	0.964086	+	1.66985i
$52$	569.074	−	3227.38i	0.0291851	−	0.165517i
$53$	134.868	−	764.877i	0.00659509	−	0.0374026i	−0.981333	−	0.192318i	$-0.938399\pi$
$53$	134.868	−	764.877i	0.00659509	−	0.0374026i	0.987928	+	0.154916i	$0.0495106\pi$
$54$	−2065.28	−	1732.97i	−0.0963815	−	0.0808737i
$55$	−52599.2	−	19144.5i	−2.34462	−	0.853371i
$56$	7377.57	+	2685.22i	0.314372	+	0.114422i
$57$	35690.0	+	29947.5i	1.45499	+	1.22088i
$58$	−3845.87	+	21811.0i	−0.150115	+	0.851345i
$59$	3696.32	−	20962.9i	0.138242	−	0.784009i	−0.834305	−	0.551303i	$-0.814131\pi$
$59$	3696.32	−	20962.9i	0.138242	−	0.784009i	0.972547	−	0.232706i	$-0.0747581\pi$
$60$	15601.0	+	27021.8i	0.559469	+	0.969028i
$61$	26240.3	−	22018.2i	0.902910	−	0.757631i	−0.0678470	−	0.997696i	$-0.521613\pi$
$61$	26240.3	−	22018.2i	0.902910	−	0.757631i	0.970757	+	0.240064i	$0.0771685\pi$
$62$	−3844.72	+	1399.36i	−0.127024	+	0.0462329i
$63$	12965.3	−	22456.6i	0.411558	−	0.712840i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−14354.5	−	12044.8i	−0.421408	−	0.353604i
$66$	26084.3	−	45179.3i	0.737088	−	1.27667i
$67$	4284.66	+	24299.5i	0.116608	+	0.661319i	0.985941	+	0.167092i	$0.0534376\pi$
$67$	4284.66	+	24299.5i	0.116608	+	0.661319i	−0.869333	+	0.494227i	$0.835451\pi$
$68$	−26883.2			−0.705032
$69$	−13011.4	−	73791.6i	−0.329005	−	1.86588i
$70$	34388.7	−	28855.5i	0.838823	−	0.703856i
$71$	45328.8	+	16498.3i	1.06716	+	0.388413i	0.815113	−	0.579302i	$-0.196675\pi$
$71$	45328.8	+	16498.3i	1.06716	+	0.388413i	0.252044	+	0.967716i	$0.418897\pi$
$72$	−12712.5	+	4626.97i	−0.289001	+	0.105188i
$73$	−75997.3			−1.66913			−0.834566	−	0.550908i	$-0.814282\pi$
$73$	−75997.3			−1.66913			−0.834566	+	0.550908i	$0.814282\pi$
$74$	−29125.8	+	16161.5i	−0.618298	+	0.343085i
$75$	111796.			2.29495
$76$	−32861.6	+	11960.6i	−0.652611	+	0.237531i
$77$	−70529.8	−	25670.7i	−1.35564	−	0.493414i
$78$	13378.3	−	11225.8i	0.248981	−	0.208920i
$79$	2150.22	+	12194.5i	0.0387628	+	0.219835i	0.998036	−	0.0626458i	$-0.0199538\pi$
$79$	2150.22	+	12194.5i	0.0387628	+	0.219835i	−0.959273	+	0.282481i	$0.908843\pi$
$80$	−23420.4			−0.409137
$81$	−11414.4	−	64734.1i	−0.193303	−	1.09628i
$82$	−13501.2	+	23384.8i	−0.221737	+	0.384060i
$83$	20256.2	+	16997.0i	0.322748	+	0.270818i	0.789737	−	0.613445i	$-0.210217\pi$
$83$	20256.2	+	16997.0i	0.322748	+	0.270818i	−0.466989	+	0.884263i	$0.654661\pi$
$84$	20919.3	+	36233.3i	0.323481	+	0.560286i
$85$	−76857.3	+	133121.i	−1.15382	+	1.99847i
$86$	34339.4	−	12498.5i	0.500664	−	0.182227i
$87$	−90412.4	+	75865.0i	−1.28065	+	1.07459i
$88$	19578.9	+	33911.7i	0.269515	+	0.466813i
$89$	−7760.25	+	44010.5i	−0.103849	+	0.588954i	0.887825	+	0.460180i	$0.152215\pi$
$89$	−7760.25	+	44010.5i	−0.103849	+	0.588954i	−0.991674	+	0.128774i	$0.958896\pi$
$90$	−13432.3	+	76178.1i	−0.174801	+	0.991343i
$91$	−19247.8	−	16150.8i	−0.243656	−	0.204451i
$92$	52850.8	+	19236.1i	0.651001	+	0.236945i
$93$	−20488.7	−	7457.28i	−0.245645	−	0.0894073i
$94$	−77152.7	−	64738.8i	−0.900599	−	0.755692i
$95$	−34722.2	+	196919.i	−0.394728	+	2.23861i
$96$	3790.36	−	21496.2i	0.0419761	−	0.238058i
$97$	−78042.3	−	135173.i	−0.842172	−	1.45868i	−0.888055	−	0.459737i	$-0.847944\pi$
$97$	−78042.3	−	135173.i	−0.842172	−	1.45868i	0.0458832	−	0.998947i	$-0.485390\pi$
$98$	−5388.15	+	4521.20i	−0.0566728	+	0.0475541i
$99$	121532.	−	44233.9i	1.24624	−	0.453594i
$100$	−41957.3	+	72672.1i	−0.419573	+	0.726721i
$101$	−31810.5	−	55097.3i	−0.310289	−	0.537437i	0.668136	−	0.744039i	$-0.267093\pi$
$101$	−31810.5	−	55097.3i	−0.310289	−	0.537437i	−0.978425	+	0.206603i	$0.933759\pi$
$102$	−109745.	−	92087.1i	−1.04444	−	0.876392i
$103$	−9643.78	+	16703.5i	−0.0895683	+	0.155137i	−0.907329	−	0.420422i	$-0.861882\pi$
$103$	−9643.78	+	16703.5i	−0.0895683	+	0.155137i	0.817760	+	0.575559i	$0.195215\pi$
$104$	2276.30	+	12909.5i	0.0206370	+	0.117038i
$105$	239228.			2.11757
$106$	539.474	+	3059.51i	0.00466343	+	0.0264476i
$107$	−2749.42	+	2307.04i	−0.0232157	+	0.0194803i	−0.654322	−	0.756216i	$-0.727046\pi$
$107$	−2749.42	+	2307.04i	−0.0232157	+	0.0194803i	0.631106	+	0.775697i	$0.282601\pi$
$108$	10133.7	+	3688.38i	0.0836009	+	0.0304282i
$109$	−2084.66	+	758.752i	−0.0168061	+	0.00611693i	−0.350410	−	0.936597i	$-0.613958\pi$
$109$	−2084.66	+	758.752i	−0.0168061	+	0.00611693i	0.333603	+	0.942714i	$0.391735\pi$
$110$	223899.			1.76430
$111$	−174260.	−	33793.0i	−1.34243	−	0.260327i
$112$	−31404.2			−0.236561
$113$	127773.	−	46505.5i	0.941332	−	0.342617i	0.174640	−	0.984632i	$-0.444124\pi$
$113$	127773.	−	46505.5i	0.941332	−	0.342617i	0.766692	+	0.642016i	$0.221902\pi$
$114$	−175121.	−	63738.8i	−1.26205	−	0.459348i
$115$	246351.	−	206713.i	1.73704	−	1.45755i
$116$	−15383.5	−	87244.0i	−0.106147	−	0.601992i
$117$	43295.6			0.292401
$118$	14785.3	+	83851.6i	0.0977518	+	0.554378i
$119$	−103057.	+	178501.i	−0.667132	+	1.15551i
$120$	−95608.8	−	80225.3i	−0.606100	−	0.508579i
$121$	−106650.	−	184723.i	−0.662210	−	1.14698i
$122$	−68508.6	+	118660.i	−0.416721	+	0.721782i
$123$	−135219.	+	49215.8i	−0.805891	+	0.293320i
$124$	12537.0	−	10519.8i	0.0732215	−	0.0614401i
$125$	96959.5	+	167939.i	0.555028	+	0.961337i
$126$	−18011.2	+	102147.i	−0.101069	+	0.573189i
$127$	54374.8	−	308375.i	0.299150	−	1.69656i	−0.350691	−	0.936491i	$-0.614053\pi$
$127$	54374.8	−	308375.i	0.299150	−	1.69656i	0.649841	−	0.760070i	$-0.274836\pi$
$128$	12550.9	+	10531.4i	0.0677094	+	0.0568149i
$129$	182996.	+	66605.3i	0.968208	+	0.352399i
$130$	70433.4	+	25635.6i	0.365528	+	0.133041i
$131$	206310.	+	173115.i	1.05037	+	0.881365i	0.993132	−	0.116996i	$-0.0373264\pi$
$131$	206310.	+	173115.i	1.05037	+	0.881365i	0.0572373	+	0.998361i	$0.481771\pi$
$132$	−36235.9	+	205504.i	−0.181011	+	1.02656i
$133$	−46558.6	+	264047.i	−0.228229	+	1.29435i
$134$	−49348.8	−	85474.6i	−0.237418	−	0.411221i
$135$	47235.9	−	39635.6i	0.223068	−	0.187177i
$136$	101048.	−	36778.4i	0.468468	−	0.170508i
$137$	42103.7	−	72925.7i	0.191654	−	0.331955i	−0.754144	−	0.656709i	$-0.771948\pi$
$137$	42103.7	−	72925.7i	0.191654	−	0.331955i	0.945799	+	0.324754i	$0.105281\pi$
$138$	149860.	+	259565.i	0.669866	+	1.16024i
$139$	−122705.	−	102962.i	−0.538673	−	0.452001i	0.332411	−	0.943135i	$-0.392138\pi$
$139$	−122705.	−	102962.i	−0.538673	−	0.452001i	−0.871084	+	0.491134i	$0.836583\pi$
$140$	−89782.5	+	155508.i	−0.387143	+	0.670551i
$141$	−93200.3	−	528565.i	−0.394793	−	2.23898i
$142$	−192952.			−0.803022
$143$	−21761.5	−	123415.i	−0.0889914	−	0.504695i
$144$	41453.3	−	34783.4i	0.166591	−	0.139787i
$145$	−475997.	−	173249.i	−1.88011	−	0.684305i
$146$	285656.	−	103970.i	1.10908	−	0.403671i
$147$	−37483.1			−0.143068
$148$	87366.9	−	100594.i	0.327863	−	0.377499i
$149$	1971.72			0.00727577			0.00363788	−	0.999993i	$-0.498842\pi$
$149$	1971.72			0.00727577			0.00363788	+	0.999993i	$0.498842\pi$
$150$	−420216.	+	152946.i	−1.52491	+	0.555023i
$151$	−73208.1	−	26645.6i	−0.261286	−	0.0951005i	0.208055	−	0.978117i	$-0.433287\pi$
$151$	−73208.1	−	26645.6i	−0.261286	−	0.0951005i	−0.469342	+	0.883017i	$0.655509\pi$
$152$	107156.	−	89914.6i	0.376190	−	0.315661i
$153$	−61673.2	−	349766.i	−0.212994	−	1.20795i
$154$	300225.			1.02010
$155$	−16249.6	−	92156.1i	−0.0543267	−	0.308102i
$156$	−34928.4	+	60497.7i	−0.114912	+	0.199034i
$157$	362457.	+	304137.i	1.17356	+	0.984737i	1.00000		8.53347e-5i	$-2.71629e-5\pi$
$157$	362457.	+	304137.i	1.17356	+	0.984737i	0.173564	+	0.984823i	$0.444472\pi$
$158$	−24765.2	−	42894.7i	−0.0789223	−	0.136697i
$159$	−8277.89	+	14337.7i	−0.0259673	+	0.0449767i
$160$	88031.8	−	32041.0i	0.271857	−	0.0989477i
$161$	330329.	−	277179.i	1.00434	−	0.842745i
$162$	131465.	+	227705.i	0.393572	+	0.681687i
$163$	−65739.6	+	372828.i	−0.193802	+	1.09910i	0.720313	+	0.693649i	$0.243998\pi$
$163$	−65739.6	+	372828.i	−0.193802	+	1.09910i	−0.914115	+	0.405455i	$0.867113\pi$
$164$	18755.7	−	106369.i	0.0544532	−	0.308820i
$165$	914022.	+	766956.i	2.61365	+	2.19311i
$166$	−99391.8	−	36175.6i	−0.279950	−	0.101893i
$167$	−185288.	−	67439.3i	−0.514110	−	0.187121i	0.0719193	−	0.997410i	$-0.477088\pi$
$167$	−185288.	−	67439.3i	−0.514110	−	0.187121i	−0.586030	+	0.810290i	$0.699310\pi$
$168$	−128201.	−	107573.i	−0.350444	−	0.294057i
$169$	−57189.4	+	324337.i	−0.154028	+	0.873534i
$170$	106769.	−	605518.i	0.283350	−	1.60696i
$171$	−231003.	−	400109.i	−0.604126	−	1.04638i
$172$	−111975.	+	93958.2i	−0.288602	+	0.242166i
$173$	286182.	−	104162.i	0.726986	−	0.264601i	0.0480978	−	0.998843i	$-0.484684\pi$
$173$	286182.	−	104162.i	0.726986	−	0.264601i	0.678889	+	0.734241i	$0.262462\pi$
$174$	236050.	−	408851.i	0.591059	−	1.02374i
$175$	321688.	+	557180.i	0.794035	+	1.37531i
$176$	−119987.	−	100681.i	−0.291979	−	0.244999i
$177$	−226871.	+	392953.i	−0.544310	+	0.942773i
$178$	−31041.0	−	176042.i	−0.0734320	−	0.416454i
$179$	647240.			1.50985			0.754924	−	0.655813i	$-0.227674\pi$
$179$	647240.			1.50985			0.754924	+	0.655813i	$0.227674\pi$
$180$	−53729.0	−	304713.i	−0.123603	−	0.700986i
$181$	−86740.4	+	72783.9i	−0.196800	+	0.165135i	−0.735863	−	0.677131i	$-0.763223\pi$
$181$	−86740.4	+	72783.9i	−0.196800	+	0.165135i	0.539063	+	0.842266i	$0.318779\pi$
$182$	94443.5	+	34374.6i	0.211346	+	0.0769236i
$183$	−686137.	+	249733.i	−1.51455	+	0.551250i
$184$	−224970.			−0.489870
$185$	−248345.	−	720215.i	−0.533491	−	1.54715i
$186$	87214.5			0.184844
$187$	−966020.	+	351603.i	−2.02014	+	0.735272i
$188$	378567.	+	137787.i	0.781175	+	0.284324i
$189$	63338.2	−	53147.1i	0.128977	−	0.108224i
$190$	−138889.	−	787676.i	−0.279115	−	1.58294i
$191$	146377.			0.290328			0.145164	−	0.989408i	$-0.453629\pi$
$191$	146377.			0.290328			0.145164	+	0.989408i	$0.453629\pi$
$192$	15161.4	+	85984.7i	0.0296816	+	0.168333i
$193$	−7997.65	+	13852.3i	−0.0154550	+	0.0267688i	−0.873649	−	0.486556i	$-0.838253\pi$
$193$	−7997.65	+	13852.3i	−0.0154550	+	0.0267688i	0.858194	+	0.513325i	$0.171586\pi$
$194$	478271.	+	401317.i	0.912367	+	0.765567i
$195$	199716.	+	345918.i	0.376120	+	0.651458i
$196$	14067.5	−	24365.6i	0.0261563	−	0.0453040i
$197$	183050.	−	66624.6i	0.336049	−	0.122312i	−0.168483	−	0.985704i	$-0.553887\pi$
$197$	183050.	−	66624.6i	0.336049	−	0.122312i	0.504533	+	0.863393i	$0.331665\pi$
$198$	−396294.	+	332531.i	−0.718381	+	0.602793i
$199$	5762.80	+	9981.46i	0.0103158	+	0.0178674i	0.871137	−	0.491040i	$-0.163383\pi$
$199$	5762.80	+	9981.46i	0.0103158	+	0.0178674i	−0.860821	+	0.508907i	$0.830050\pi$
$200$	58286.4	−	330559.i	0.103037	−	0.584351i
$201$	91332.7	−	517974.i	0.159454	−	0.904310i
$202$	194946.	+	163579.i	0.336152	+	0.282065i
$203$	−638260.	−	232308.i	−1.08707	−	0.395661i
$204$	538489.	+	195994.i	0.905945	+	0.329737i
$205$	−473098.	−	396976.i	−0.786260	−	0.659751i
$206$	13397.0	−	75978.2i	0.0219958	−	0.124744i
$207$	−129027.	+	731749.i	−0.209293	+	1.18696i
$208$	−26217.3	−	45409.8i	−0.0420175	−	0.0727765i
$209$	−1.02441e6	+	859585.i	−1.62222	+	1.36120i
$210$	−899202.	+	327283.i	−1.40705	+	0.512124i
$211$	−569880.	+	987062.i	−0.881206	+	1.52629i	−0.0312055	+	0.999513i	$0.509935\pi$
$211$	−569880.	+	987062.i	−0.881206	+	1.52629i	−0.850001	+	0.526781i	$0.823399\pi$
$212$	−6213.41	−	10761.9i	−0.00949490	−	0.0164456i
$213$	−787684.	−	660945.i	−1.18961	−	0.998198i
$214$	7178.24	−	12433.1i	0.0107148	−	0.0185586i
$215$	145135.	+	823100.i	0.214129	+	1.21438i
$216$	−43136.4			−0.0629086
$217$	−21789.0	−	123571.i	−0.0314114	−	0.178143i
$218$	6797.71	−	5703.95i	0.00968771	−	0.00812895i
$219$	1.52228e6	+	554063.i	2.14478	+	0.780637i
$220$	−841586.	+	306312.i	−1.17231	+	0.426686i
$221$	−344144.			−0.473979
$222$	701235.	−	111382.i	0.954951	−	0.151681i
$223$	−1.23839e6			−1.66762			−0.833808	−	0.552054i	$-0.813844\pi$
$223$	−1.23839e6			−1.66762			−0.833808	+	0.552054i	$0.813844\pi$
$224$	118041.	−	42963.5i	0.157186	−	0.0572110i
$225$	−1.04176e6	−	379170.i	−1.37187	−	0.499319i
$226$	−416646.	+	349607.i	−0.542620	+	0.455312i
$227$	−36226.8	−	205452.i	−0.0466622	−	0.264634i	0.952547	−	0.304391i	$-0.0984529\pi$
$227$	−36226.8	−	205452.i	−0.0466622	−	0.264634i	−0.999209	+	0.0397565i	$0.987342\pi$
$228$	745439.			0.949675
$229$	−130336.	−	739174.i	−0.164239	−	0.931447i	−0.949845	−	0.312720i	$-0.898760\pi$
$229$	−130336.	−	739174.i	−0.164239	−	0.931447i	0.785606	−	0.618727i	$-0.212351\pi$
$230$	−643176.	+	1.11401e6i	−0.801696	+	1.38858i
$231$	1.22560e6	+	1.02840e6i	1.51119	+	1.26804i
$232$	177180.	+	306884.i	0.216120	+	0.374330i
$233$	−206704.	+	358022.i	−0.249436	+	0.432036i	−0.963369	−	0.268178i	$-0.913579\pi$
$233$	−206704.	+	358022.i	−0.249436	+	0.432036i	0.713933	+	0.700214i	$0.246912\pi$
$234$	−162738.	+	59231.9i	−0.194290	+	0.0707157i
$235$	1.76459e6	−	1.48067e6i	2.08437	−	1.74900i
$236$	−170290.	−	294951.i	−0.199026	−	0.344723i
$237$	45834.5	−	259940.i	0.0530056	−	0.300610i
$238$	143166.	−	811933.i	0.163831	−	0.929133i
$239$	157999.	+	132577.i	0.178920	+	0.150132i	0.727849	−	0.685737i	$-0.240520\pi$
$239$	157999.	+	132577.i	0.178920	+	0.150132i	−0.548929	+	0.835869i	$0.684964\pi$
$240$	469126.	+	170748.i	0.525728	+	0.191349i
$241$	−778335.	−	283291.i	−0.863224	−	0.314188i	−0.127804	−	0.991799i	$-0.540793\pi$
$241$	−778335.	−	283291.i	−0.863224	−	0.314188i	−0.735420	+	0.677611i	$0.763015\pi$
$242$	653587.	+	548424.i	0.717406	+	0.601975i
$243$	−214870.	+	1.21859e6i	−0.233432	+	1.32386i
$244$	95171.2	−	539742.i	0.102337	−	0.580379i
$245$	−80435.9	−	139319.i	−0.0856120	−	0.148284i
$246$	440927.	−	369982.i	0.464547	−	0.389801i
$247$	−420675.	+	153113.i	−0.438737	+	0.159687i
$248$	−32731.7	+	56693.0i	−0.0337940	+	0.0585329i
$249$	−281828.	−	488141.i	−0.288062	−	0.498938i
$250$	−594202.	−	498595.i	−0.601290	−	0.504542i
$251$	913173.	−	1.58166e6i	0.914890	−	1.58464i	0.107827	−	0.994170i	$-0.465611\pi$
$251$	913173.	−	1.58166e6i	0.914890	−	1.58464i	0.807063	−	0.590466i	$-0.201056\pi$
$252$	−72044.8	−	408586.i	−0.0714663	−	0.405306i
$253$	2.15072e6			2.11243
$254$	217499.	+	1.23350e6i	0.211531	+	1.19965i
$255$	2.51003e6	−	2.10617e6i	2.41729	−	2.02835i
$256$	−61583.7	−	22414.6i	−0.0587308	−	0.0213763i
$257$	−1.03396e6	+	376329.i	−0.976493	+	0.355414i	−0.780476	−	0.625186i	$-0.785023\pi$
$257$	−1.03396e6	+	376329.i	−0.976493	+	0.355414i	−0.196017	+	0.980600i	$0.562801\pi$
$258$	−778963.			−0.728564
$259$	−333004.	−	965730.i	−0.308461	−	0.894554i
$260$	−299814.			−0.275055
$261$	1.09980e6	−	400296.i	0.999341	−	0.363731i
$262$	−1.01231e6	−	368450.i	−0.911085	−	0.331608i
$263$	−355406.	+	298221.i	−0.316837	+	0.265858i	−0.787311	−	0.616556i	$-0.788527\pi$
$263$	−355406.	+	298221.i	−0.316837	+	0.265858i	0.470474	+	0.882414i	$0.344083\pi$
$264$	−144944.	−	822016.i	−0.127994	−	0.725890i
$265$	−71054.9			−0.0621555
$266$	−186235.	−	1.05619e6i	−0.161382	−	0.915245i
$267$	476305.	−	824984.i	0.408890	−	0.708219i
$268$	302427.	+	253766.i	0.257207	+	0.215823i
$269$	295859.	+	512443.i	0.249290	+	0.431782i	0.963329	−	0.268323i	$-0.0864695\pi$
$269$	295859.	+	512443.i	0.249290	+	0.431782i	−0.714039	+	0.700106i	$0.753136\pi$
$270$	−123324.	+	213604.i	−0.102953	+	0.178320i
$271$	506005.	−	184171.i	0.418535	−	0.152334i	−0.124164	−	0.992262i	$-0.539625\pi$
$271$	506005.	−	184171.i	0.418535	−	0.152334i	0.542699	+	0.839927i	$0.317403\pi$
$272$	−329500.	+	276483.i	−0.270043	+	0.226593i
$273$	267797.	+	463838.i	0.217470	+	0.376669i
$274$	−58489.8	+	331712.i	−0.0470656	+	0.266922i
$275$	−557220.	+	3.16015e6i	−0.444319	+	2.51986i
$276$	−918395.	−	770625.i	−0.725699	−	0.608934i
$277$	1.06631e6	+	388106.i	0.834998	+	0.303914i	0.723908	−	0.689896i	$-0.242344\pi$
$277$	1.06631e6	+	388106.i	0.834998	+	0.303914i	0.111089	+	0.993810i	$0.464566\pi$
$278$	602080.	+	219139.i	0.467243	+	0.170062i
$279$	165630.	+	138980.i	0.127388	+	0.106891i
$280$	124724.	−	707348.i	0.0950729	−	0.539185i
$281$	398489.	−	2.25994e6i	0.301058	−	1.70739i	−0.340445	−	0.940265i	$-0.610578\pi$
$281$	398489.	−	2.25994e6i	0.301058	−	1.70739i	0.641503	−	0.767121i	$-0.278311\pi$
$282$	1.07344e6	+	1.85925e6i	0.803811	+	1.39224i
$283$	−807359.	+	677455.i	−0.599240	+	0.502822i	−0.891201	−	0.453608i	$-0.850137\pi$
$283$	−807359.	+	677455.i	−0.599240	+	0.502822i	0.291961	+	0.956430i	$0.405692\pi$
$284$	725261.	−	263973.i	0.533578	−	0.194207i
$285$	2.13116e6	−	3.69128e6i	1.55419	−	2.69194i
$286$	250638.	+	434119.i	0.181189	+	0.313829i
$287$	−634373.	−	532302.i	−0.454611	−	0.381464i
$288$	−108227.	+	187454.i	−0.0768871	+	0.133172i
$289$	243667.	+	1.38190e6i	0.171614	+	0.973269i
$290$	2.02618e6			1.41476
$291$	577750.	+	3.27658e6i	0.399952	+	2.26824i
$292$	−931477.	+	781602.i	−0.639315	+	0.536449i
$293$	−2.40078e6	−	873812.i	−1.63374	−	0.594633i	−0.647813	−	0.761800i	$-0.724316\pi$
$293$	−2.40078e6	−	873812.i	−1.63374	−	0.594633i	−0.985929	+	0.167166i	$0.946538\pi$
$294$	140890.	−	51279.9i	0.0950634	−	0.0346002i
$295$	−1.94739e6			−1.30286
$296$	−190772.	+	497633.i	−0.126557	+	0.330126i
$297$	412385.			0.271277
$298$	−7411.23	+	2697.47i	−0.00483448	+	0.00175961i
$299$	676566.	+	246250.i	0.437655	+	0.159293i
$300$	1.37025e6	−	1.14978e6i	0.879019	−	0.737584i
$301$	194610.	+	1.10369e6i	0.123808	+	0.702150i
$302$	311626.			0.196615
$303$	235494.	+	1.33555e6i	0.147358	+	0.835708i
$304$	−279764.	+	484566.i	−0.173624	+	0.300725i
$305$	−2.40062e6	−	2.01436e6i	−1.47766	−	1.23990i
$306$	710324.	+	1.23032e6i	0.433663	+	0.751127i
$307$	708194.	−	1.22663e6i	0.428851	−	0.742791i	−0.567921	−	0.823083i	$-0.692252\pi$
$307$	708194.	−	1.22663e6i	0.428851	−	0.742791i	0.996771	+	0.0802921i	$0.0255853\pi$
$308$	−1.12848e6	+	410732.i	−0.677822	+	0.246707i
$309$	314950.	−	264274.i	0.187648	−	0.157456i
$310$	187156.	+	324163.i	0.110611	+	0.191584i
$311$	390659.	−	2.21554e6i	0.229032	−	1.29891i	−0.625792	−	0.779990i	$-0.715224\pi$
$311$	390659.	−	2.21554e6i	0.229032	−	1.29891i	0.854824	−	0.518917i	$-0.173665\pi$
$312$	48522.0	−	275182.i	0.0282197	−	0.160042i
$313$	1.21777e6	+	1.02183e6i	0.702597	+	0.589549i	0.922511	−	0.385970i	$-0.126133\pi$
$313$	1.21777e6	+	1.02183e6i	0.702597	+	0.589549i	−0.219914	+	0.975519i	$0.570578\pi$
$314$	−1.77848e6	−	647312.i	−1.01794	−	0.370501i
$315$	−2.22922e6	−	811369.i	−1.26583	−	0.460725i
$316$	151770.	+	127350.i	0.0855005	+	0.0717435i
$317$	−501827.	+	2.84600e6i	−0.280483	+	1.59070i	0.440506	+	0.897750i	$0.354799\pi$
$317$	−501827.	+	2.84600e6i	−0.280483	+	1.59070i	−0.720989	+	0.692947i	$0.756312\pi$
$318$	11499.5	−	65217.1i	0.00637694	−	0.0361654i
$319$	−1.69384e6	−	2.93382e6i	−0.931959	−	1.61420i
$320$	−287057.	+	240869.i	−0.156709	+	0.131494i
$321$	71892.5	−	26166.7i	0.0389422	−	0.0141738i
$322$	−862429.	+	1.49377e6i	−0.463536	+	0.802868i
$323$	1.83617e6	+	3.18035e6i	0.979282	+	1.69617i
$324$	−805667.	−	676035.i	−0.426376	−	0.357772i
$325$	−537114.	+	930308.i	−0.282071	+	0.488560i
$326$	−262958.	−	1.49131e6i	−0.137039	−	0.777184i
$327$	47288.8			0.0244562
$328$	75022.8	+	425476.i	0.0385043	+	0.218369i
$329$	2.36613e6	−	1.98542e6i	1.20517	−	1.01126i
$330$	−4.48486e6	−	1.63235e6i	−2.26706	−	0.825144i
$331$	−2.32031e6	+	844525.i	−1.16406	+	0.423684i	−0.850547	−	0.525898i	$-0.823729\pi$
$331$	−2.32031e6	+	844525.i	−1.16406	+	0.423684i	−0.313516	+	0.949583i	$0.601507\pi$
$332$	423082.			0.210659
$333$	1.50921e6	+	905920.i	0.745829	+	0.447692i
$334$	788718.			0.386861
$335$	2.12122e6	−	772062.i	1.03270	−	0.375872i
$336$	629047.	+	228954.i	0.303973	+	0.110637i
$337$	2.45685e6	−	2.06154e6i	1.17843	−	0.988821i	0.178442	−	0.983950i	$-0.442894\pi$
$337$	2.45685e6	−	2.06154e6i	1.17843	−	0.988821i	0.999988	−	0.00487033i	$-0.00155028\pi$
$338$	−228758.	−	1.29735e6i	−0.108914	−	0.617682i
$339$	−2.89843e6			−1.36982
$340$	427076.	+	2.42207e6i	0.200359	+	1.13629i
$341$	312916.	−	541986.i	0.145728	−	0.252408i
$342$	1.41567e6	+	1.18789e6i	0.654480	+	0.549174i
$343$	−1.13873e6	−	1.97235e6i	−0.522622	−	0.905207i
$344$	292346.	−	506358.i	0.133199	−	0.230707i
$345$	−6.44162e6	+	2.34456e6i	−2.91372	+	1.06051i
$346$	−933189.	+	783039.i	−0.419063	+	0.351636i
$347$	−1.88873e6	−	3.27138e6i	−0.842067	−	1.45850i	−0.888144	−	0.459565i	$-0.848005\pi$
$347$	−1.88873e6	−	3.27138e6i	−0.842067	−	1.45850i	0.0460767	−	0.998938i	$-0.485328\pi$
$348$	−327917.	+	1.85971e6i	−0.145150	+	0.823185i
$349$	−215064.	+	1.21969e6i	−0.0945156	+	0.536024i	0.900379	+	0.435106i	$0.143289\pi$
$349$	−215064.	+	1.21969e6i	−0.0945156	+	0.536024i	−0.994895	+	0.100918i	$0.967822\pi$
$350$	−1.97142e6	−	1.65422e6i	−0.860219	−	0.721809i
$351$	129727.	+	47216.6i	0.0562032	+	0.0204563i
$352$	588742.	+	214284.i	0.253261	+	0.0921794i
$353$	411215.	+	345050.i	0.175644	+	0.147382i	0.726371	−	0.687302i	$-0.241205\pi$
$353$	411215.	+	345050.i	0.175644	+	0.147382i	−0.550728	+	0.834685i	$0.685650\pi$
$354$	315166.	−	1.78740e6i	0.133669	−	0.758076i
$355$	766324.	−	4.34604e6i	0.322732	−	1.83030i
$356$	357516.	+	619236.i	0.149510	+	0.258959i
$357$	3.36568e6	−	2.82414e6i	1.39766	−	1.17278i
$358$	−2.43283e6	+	885477.i	−1.00324	+	0.365149i
$359$	−1.58721e6	+	2.74913e6i	−0.649977	+	1.12579i	0.333151	+	0.942874i	$0.391888\pi$
$359$	−1.58721e6	+	2.74913e6i	−0.649977	+	1.12579i	−0.983128	+	0.182920i	$0.941445\pi$
$360$	618826.	+	1.07184e6i	0.251659	+	0.435886i
$361$	1.76267e6	+	1.47906e6i	0.711876	+	0.597335i
$362$	226463.	−	392246.i	0.0908294	−	0.157321i
$363$	789531.	+	4.47765e6i	0.314487	+	1.78354i
$364$	−402019.			−0.159035
$365$	1.20732e6	+	6.84705e6i	0.474340	+	2.69012i
$366$	2.23738e6	−	1.87738e6i	0.873044	−	0.732571i
$367$	1.15477e6	+	420302.i	0.447538	+	0.162891i	0.555951	−	0.831215i	$-0.312354\pi$
$367$	1.15477e6	+	420302.i	0.447538	+	0.162891i	−0.108412	+	0.994106i	$0.534577\pi$
$368$	845612.	−	307778.i	0.325501	−	0.118473i
$369$	1.42695e6			0.545560
$370$	1.91879e6	+	2.36737e6i	0.728655	+	0.899003i
$371$	−95276.9			−0.0359379
$372$	−327819.	+	119316.i	−0.122822	+	0.0447036i
$373$	2.94204e6	+	1.07082e6i	1.09491	+	0.398513i	0.825436	−	0.564496i	$-0.190929\pi$
$373$	2.94204e6	+	1.07082e6i	1.09491	+	0.398513i	0.269469	+	0.963009i	$0.413152\pi$
$374$	3.15003e6	−	2.64319e6i	1.16449	−	0.977122i
$375$	−717795.	−	4.07082e6i	−0.263586	−	1.49487i
$376$	−1.61145e6			−0.587824
$377$	−196931.	−	1.11685e6i	−0.0713608	−	0.404707i
$378$	−165364.	+	286419.i	−0.0595268	+	0.103103i
$379$	1.52377e6	+	1.27860e6i	0.544907	+	0.457231i	0.873212	−	0.487340i	$-0.162033\pi$
$379$	1.52377e6	+	1.27860e6i	0.544907	+	0.457231i	−0.328305	+	0.944572i	$0.606477\pi$
$380$	1.59966e6	+	2.77068e6i	0.568287	+	0.984301i
$381$	−3.33739e6	+	5.78053e6i	−1.17786	+	2.04012i
$382$	−550197.	+	200255.i	−0.192912	+	0.0702143i
$383$	−4.00293e6	+	3.35885e6i	−1.39438	+	1.17002i	−0.430848	+	0.902425i	$0.641785\pi$
$383$	−4.00293e6	+	3.35885e6i	−1.39438	+	1.17002i	−0.963531	+	0.267598i	$0.913770\pi$
$384$	−174622.	−	302455.i	−0.0604327	−	0.104672i
$385$	−1.19237e6	+	6.76226e6i	−0.409976	+	2.32509i
$386$	11110.2	−	63009.1i	0.00379537	−	0.0215246i
$387$	−1.47933e6	−	1.24131e6i	−0.502098	−	0.421310i
$388$	−2.34674e6	−	854145.i	−0.791383	−	0.288040i
$389$	−1.46172e6	−	532021.i	−0.489766	−	0.178260i	0.0853192	−	0.996354i	$-0.472809\pi$
$389$	−1.46172e6	−	532021.i	−0.489766	−	0.178260i	−0.575085	+	0.818093i	$0.695031\pi$
$390$	−1.22393e6	−	1.02700e6i	−0.407469	−	0.341907i
$391$	1.02560e6	−	5.81646e6i	0.339262	−	1.92405i
$392$	−19542.3	+	110830.i	−0.00642334	+	0.0364286i
$393$	−2.87043e6	−	4.97172e6i	−0.937486	−	1.62377i
$394$	−596894.	+	500853.i	−0.193712	+	0.162544i
$395$	1.06452e6	−	387452.i	0.343289	−	0.124947i
$396$	1.03465e6	−	1.79207e6i	0.331555	−	0.574271i
$397$	−932269.	−	1.61474e6i	−0.296869	−	0.514192i	0.678549	−	0.734555i	$-0.262609\pi$
$397$	−932269.	−	1.61474e6i	−0.296869	−	0.514192i	−0.975418	+	0.220363i	$0.929276\pi$
$398$	−35316.5	−	29634.1i	−0.0111756	−	0.00937742i
$399$	2.85766e6	−	4.94961e6i	0.898623	−	1.55646i
$400$	233146.	+	1.32224e6i	0.0728581	+	0.413199i
$401$	−2.25091e6			−0.699032			−0.349516	−	0.936930i	$-0.613654\pi$
$401$	−2.25091e6			−0.699032			−0.349516	+	0.936930i	$0.613654\pi$
$402$	365331.	+	2.07189e6i	0.112751	+	0.639444i
$403$	160491.	−	134668.i	0.0492254	−	0.0413050i
$404$	−956546.	−	348154.i	−0.291576	−	0.106125i
$405$	−5.65095e6	+	2.05678e6i	−1.71192	+	0.623089i
$406$	2.71689e6			0.818007
$407$	1.82378e6	−	4.75739e6i	0.545742	−	1.42358i
$408$	−2.29219e6			−0.681712
$409$	−197323.	+	71819.7i	−0.0583270	+	0.0212293i	−0.371019	−	0.928625i	$-0.620991\pi$
$409$	−197323.	+	71819.7i	−0.0583270	+	0.0212293i	0.312692	+	0.949855i	$0.398769\pi$
$410$	2.32136e6	+	844907.i	0.681998	+	0.248227i
$411$	−1.37503e6	+	1.15379e6i	−0.401522	+	0.336917i
$412$	53588.0	+	303913.i	0.0155534	+	0.0882075i
$413$	−2.61124e6			−0.753307
$414$	−516108.	−	2.92700e6i	−0.147993	−	0.839308i
$415$	1.20956e6	−	2.09502e6i	0.344753	−	0.597130i
$416$	160669.	+	134817.i	0.0455197	+	0.0381956i
$417$	1.70722e6	+	2.95698e6i	0.480782	+	0.832739i
$418$	2.67456e6	−	4.63247e6i	0.748705	−	1.29680i
$419$	3.08093e6	−	1.12137e6i	0.857327	−	0.312042i	0.124303	−	0.992244i	$-0.460330\pi$
$419$	3.08093e6	−	1.12137e6i	0.857327	−	0.312042i	0.733024	+	0.680203i	$0.238108\pi$
$420$	2.93214e6	−	2.46036e6i	0.811077	−	0.680574i
$421$	147099.	+	254782.i	0.0404486	+	0.0700590i	0.885541	−	0.464561i	$-0.153788\pi$
$421$	147099.	+	254782.i	0.0404486	+	0.0700590i	−0.845092	+	0.534620i	$0.820455\pi$
$422$	791670.	−	4.48978e6i	0.216403	−	1.22728i
$423$	−924214.	+	5.24148e6i	−0.251143	+	1.42430i
$424$	38078.0	+	31951.2i	0.0102863	+	0.00863123i
$425$	8.28065e6	+	3.01391e6i	2.22378	+	0.809391i
$426$	3.86495e6	+	1.40673e6i	1.03186	+	0.375566i
$427$	−3.21897e6	−	2.70103e6i	−0.854372	−	0.716903i
$428$	−9971.90	+	56553.5i	−0.00263129	+	0.0149228i
$429$	−463872.	+	2.63075e6i	−0.121690	+	0.690138i
$430$	−1.67159e6	−	2.89529e6i	−0.435973	−	0.755128i
$431$	−587382.	+	492872.i	−0.152310	+	0.127803i	−0.715758	−	0.698348i	$-0.753919\pi$
$431$	−587382.	+	492872.i	−0.152310	+	0.127803i	0.563449	+	0.826151i	$0.309474\pi$
$432$	162140.	−	59014.1i	0.0418004	−	0.0152141i
$433$	−1.81006e6	+	3.13511e6i	−0.463951	+	0.803587i	−0.999154	−	0.0411371i	$-0.986902\pi$
$433$	−1.81006e6	+	3.13511e6i	−0.463951	+	0.803587i	0.535203	+	0.844724i	$0.320235\pi$
$434$	250955.	+	434667.i	0.0639546	+	0.110773i
$435$	8.27146e6	+	6.94058e6i	2.09584	+	1.75862i
$436$	−17747.5	+	30739.7i	−0.00447118	+	0.00774431i
$437$	−1.33413e6	−	7.56623e6i	−0.334191	−	1.89529i
$438$	−6.47989e6			−1.61392
$439$	526642.	+	2.98673e6i	0.130423	+	0.739665i	0.977938	+	0.208894i	$0.0669865\pi$
$439$	526642.	+	2.98673e6i	0.130423	+	0.739665i	−0.847515	+	0.530771i	$0.821902\pi$
$440$	2.74427e6	−	2.30272e6i	0.675764	−	0.567034i
$441$	349282.	+	127128.i	0.0855225	+	0.0311276i
$442$	1.29356e6	−	470817.i	0.314942	−	0.114629i
$443$	−4.20793e6			−1.01873			−0.509365	−	0.860551i	$-0.670120\pi$
$443$	−4.20793e6			−1.01873			−0.509365	+	0.860551i	$0.670120\pi$
$444$	−2.48340e6	+	1.37800e6i	−0.597847	+	0.331737i
$445$	4.08845e6			0.978722
$446$	4.65483e6	−	1.69422e6i	1.10807	−	0.403304i
$447$	−39494.8	−	14374.9i	−0.00934913	−	0.00340281i
$448$	−384912.	+	322980.i	−0.0906080	+	0.0760291i
$449$	567198.	+	3.21674e6i	0.132776	+	0.753009i	0.976383	+	0.216048i	$0.0693168\pi$
$449$	567198.	+	3.21674e6i	0.132776	+	0.753009i	−0.843607	+	0.536961i	$0.819572\pi$
$450$	4.43448e6			1.03231
$451$	−717220.	−	4.06756e6i	−0.166039	−	0.941656i
$452$	1.08778e6	−	1.88410e6i	0.250436	−	0.433768i
$453$	1.27215e6	+	1.06746e6i	0.291267	+	0.244402i
$454$	417243.	+	722687.i	0.0950057	+	0.164555i
$455$	−1.14934e6	+	1.99072e6i	−0.260269	+	0.450798i
$456$	−2.80194e6	+	1.01982e6i	−0.631024	+	0.229674i
$457$	5.54938e6	−	4.65648e6i	1.24295	−	1.04296i	0.245664	−	0.969355i	$-0.420994\pi$
$457$	5.54938e6	−	4.65648e6i	1.24295	−	1.04296i	0.997287	−	0.0736047i	$-0.0234503\pi$
$458$	1.50115e6	+	2.60008e6i	0.334397	+	0.579192i
$459$	196651.	−	1.11526e6i	0.0435677	−	0.247085i
$460$	893490.	−	5.06723e6i	0.196877	−	1.11655i
$461$	−4.68676e6	−	3.93266e6i	−1.02712	−	0.861855i	−0.0366134	−	0.999330i	$-0.511657\pi$
$461$	−4.68676e6	−	3.93266e6i	−1.02712	−	0.861855i	−0.990505	+	0.137475i	$0.956101\pi$
$462$	−6.01371e6	−	2.18881e6i	−1.31080	−	0.477093i
$463$	4.42733e6	+	1.61142e6i	0.959819	+	0.349345i	0.773962	−	0.633232i	$-0.218272\pi$
$463$	4.42733e6	+	1.61142e6i	0.959819	+	0.349345i	0.185856	+	0.982577i	$0.440494\pi$
$464$	−1.08582e6	−	911112.i	−0.234133	−	0.196461i
$465$	−346380.	+	1.96442e6i	−0.0742883	+	0.421310i
$466$	287150.	−	1.62851e6i	0.0612554	−	0.347397i
$467$	−2.10808e6	−	3.65130e6i	−0.447296	−	0.774739i	0.550913	−	0.834563i	$-0.314280\pi$
$467$	−2.10808e6	−	3.65130e6i	−0.447296	−	0.774739i	−0.998209	+	0.0598233i	$0.980946\pi$
$468$	530662.	−	445278.i	0.111996	−	0.0939759i
$469$	2.84433e6	−	1.03525e6i	0.597101	−	0.217327i
$470$	−4.60703e6	+	7.97961e6i	−0.962003	+	1.66624i
$471$	−5.04292e6	−	8.73459e6i	−1.04744	−	1.81422i
$472$	1.04360e6	+	875684.i	0.215615	+	0.180922i
$473$	−2.79483e6	+	4.84080e6i	−0.574385	+	0.994864i
$474$	183338.	+	1.03976e6i	0.0374806	+	0.212563i
$475$	1.14630e7			2.33113
$476$	572663.	+	3.24773e6i	0.115846	+	0.656996i
$477$	125765.	−	105529.i	0.0253083	−	0.0212362i
$478$	−775257.	−	282170.i	−0.155194	−	0.0564861i
$479$	230858.	−	84025.3i	0.0459733	−	0.0167329i	−0.318931	−	0.947778i	$-0.603324\pi$
$479$	230858.	−	84025.3i	0.0459733	−	0.0167329i	0.364904	+	0.931045i	$0.381102\pi$
$480$	−1.99693e6			−0.395604
$481$	1.11842e6	−	1.28774e6i	0.220416	−	0.253785i
$482$	3.31315e6			0.649565
$483$	−8.63752e6	+	3.14380e6i	−1.68469	+	0.613178i
$484$	−3.20697e6	−	1.16724e6i	−0.622274	−	0.226489i
$485$	−1.09388e7	+	9.17870e6i	−2.11161	+	1.77185i
$486$	−859481.	−	4.87436e6i	−0.165061	−	0.936110i
$487$	5.74247e6			1.09718			0.548588	−	0.836093i	$-0.315166\pi$
$487$	5.74247e6			1.09718			0.548588	+	0.836093i	$0.315166\pi$
$488$	380685.	+	2.15897e6i	0.0723629	+	0.410390i
$489$	4.03493e6	−	6.98871e6i	0.763070	−	1.32168i
$490$	492940.	+	413626.i	0.0927478	+	0.0778247i
$491$	5.10216e6	+	8.83721e6i	0.955104	+	1.65429i	0.734130	+	0.679009i	$0.237590\pi$
$491$	5.10216e6	+	8.83721e6i	0.955104	+	1.65429i	0.220974	+	0.975280i	$0.429076\pi$
$492$	−1.15118e6	+	1.99390e6i	−0.214403	+	0.371356i
$493$	−8.74202e6	+	3.18183e6i	−1.61992	+	0.589604i
$494$	1.37175e6	−	1.15104e6i	0.252905	−	0.212213i
$495$	−5.91600e6	−	1.02468e7i	−1.08521	−	1.87964i
$496$	45470.4	−	257876.i	0.00829898	−	0.0470659i
$497$	1.02756e6	−	5.82757e6i	0.186601	−	1.05827i
$498$	1.72714e6	+	1.44925e6i	0.312072	+	0.261860i
$499$	−6.05022e6	−	2.20210e6i	−1.08773	−	0.395900i	−0.264948	−	0.964263i	$-0.585355\pi$
$499$	−6.05022e6	−	2.20210e6i	−1.08773	−	0.395900i	−0.822778	+	0.568363i	$0.807577\pi$
$500$	2.91559e6	+	1.06119e6i	0.521556	+	0.189831i
$501$	3.21977e6	+	2.70171e6i	0.573101	+	0.480889i
$502$	−1.26857e6	+	7.19440e6i	−0.224675	+	1.27419i
$503$	611474.	−	3.46784e6i	0.107760	−	0.611138i	−0.882322	−	0.470646i	$-0.844021\pi$
$503$	611474.	−	3.46784e6i	0.107760	−	0.611138i	0.990082	−	0.140491i	$-0.0448682\pi$
$504$	829779.	+	1.43722e6i	0.145508	+	0.252027i
$505$	−4.45870e6	+	3.74129e6i	−0.778000	+	0.652819i
$506$	−8.08408e6	+	2.94236e6i	−1.40363	+	0.510881i
$507$	3.51015e6	−	6.07975e6i	0.606464	−	1.05043i
$508$	−2.50506e6	−	4.33888e6i	−0.430683	−	0.745966i
$509$	3.63901e6	+	3.05349e6i	0.622571	+	0.522399i	0.898611	−	0.438747i	$-0.144578\pi$
$509$	3.63901e6	+	3.05349e6i	0.622571	+	0.522399i	−0.276039	+	0.961146i	$0.589022\pi$
$510$	−6.55323e6	+	1.13505e7i	−1.11565	+	1.93237i
$511$	1.61888e6	+	9.18115e6i	0.274261	+	1.55541i
$512$	262144.			0.0441942
$513$	−255810.	−	1.45077e6i	−0.0429164	−	0.243391i
$514$	3.37155e6	−	2.82907e6i	0.562888	−	0.472319i
$515$	1.65812e6	+	603508.i	0.275486	+	0.100269i
$516$	2.92794e6	−	1.06568e6i	0.484104	−	0.176199i
$517$	1.54055e7			2.53484
$518$	2.57288e6	+	3.17438e6i	0.421304	+	0.519798i
$519$	−6.49181e6			−1.05791
$520$	1.12693e6	−	410170.i	0.182764	−	0.0665206i
$521$	5.78180e6	+	2.10440e6i	0.933187	+	0.339652i	0.763472	−	0.645841i	$-0.223493\pi$
$521$	5.78180e6	+	2.10440e6i	0.933187	+	0.339652i	0.169715	+	0.985493i	$0.445715\pi$
$522$	−3.58627e6	+	3.00924e6i	−0.576059	+	0.483371i
$523$	−25185.3	−	142833.i	−0.00402618	−	0.0228336i	0.982728	−	0.185053i	$-0.0592458\pi$
$523$	−25185.3	−	142833.i	−0.00402618	−	0.0228336i	−0.986755	+	0.162220i	$0.948135\pi$
$524$	4.30910e6			0.685580
$525$	−2.38147e6	−	1.35060e7i	−0.377092	−	2.13859i
$526$	927899.	−	1.60717e6i	0.146230	−	0.253278i
$527$	−1.31654e6	−	1.10471e6i	−0.206494	−	0.173269i
$528$	1.66939e6	+	2.89148e6i	0.260600	+	0.451372i
$529$	−2.96002e6	+	5.12690e6i	−0.459891	+	0.796555i
$530$	267079.	−	97208.8i	0.0413000	−	0.0150320i
$531$	3.44682e6	−	2.89223e6i	0.530496	−	0.445139i
$532$	2.14496e6	+	3.71519e6i	0.328580	+	0.569117i
$533$	240100.	−	1.36167e6i	0.0366078	−	0.207613i
$534$	−661676.	+	3.75255e6i	−0.100414	+	0.569473i
$535$	251533.	+	211062.i	0.0379937	+	0.0318805i
$536$	−1.48393e6	−	540105.i	−0.223100	−	0.0812019i
$537$	−1.29647e7	−	4.71875e6i	−1.94011	−	0.706141i
$538$	−1.81313e6	−	1.52140e6i	−0.270068	−	0.226614i
$539$	186825.	−	1.05954e6i	0.0276990	−	0.157089i
$540$	171320.	−	971605.i	0.0252827	−	0.143386i
$541$	−1.92954e6	−	3.34206e6i	−0.283439	−	0.490931i	0.688790	−	0.724961i	$-0.258142\pi$
$541$	−1.92954e6	−	3.34206e6i	−0.283439	−	0.490931i	−0.972230	+	0.234029i	$0.924809\pi$
$542$	−1.65000e6	+	1.38451e6i	−0.241260	+	0.202441i
$543$	2.26811e6	−	825523.i	0.330114	−	0.120152i
$544$	860263.	−	1.49002e6i	0.124633	−	0.215871i
$545$	101478.	+	175765.i	0.0146346	+	0.0253479i
$546$	−1.64116e6	−	1.37709e6i	−0.235596	−	0.197689i
$547$	−131059.	+	227000.i	−0.0187283	+	0.0324383i	−0.875238	−	0.483693i	$-0.839295\pi$
$547$	−131059.	+	227000.i	−0.0187283	+	0.0324383i	0.856509	+	0.516131i	$0.172628\pi$
$548$	−233959.	−	1.32685e6i	−0.0332804	−	0.188743i
$549$	7.24069e6			1.02530
$550$	−2.22888e6	−	1.26406e7i	−0.314181	−	1.78181i
$551$	−9.27045e6	+	7.77883e6i	−1.30083	+	1.09153i
$552$	4.50631e6	+	1.64016e6i	0.629468	+	0.229108i
$553$	1.42740e6	−	519531.i	0.198488	−	0.0722435i
$554$	−4.53899e6			−0.628325
$555$	−276254.	+	1.62370e7i	−0.0380693	+	2.23755i
$556$	−2.56288e6			−0.351594
$557$	−7.32128e6	+	2.66473e6i	−0.999883	+	0.363928i	−0.789539	−	0.613700i	$-0.789680\pi$
$557$	−7.32128e6	+	2.66473e6i	−0.999883	+	0.363928i	−0.210344	+	0.977628i	$0.567458\pi$
$558$	−812699.	−	295798.i	−0.110495	−	0.0402170i
$559$	−1.43344e6	+	1.20280e6i	−0.194022	+	0.162804i
$560$	498898.	+	2.82939e6i	0.0672267	+	0.381261i
$561$	2.19134e7			2.93970
$562$	1.59396e6	+	9.03977e6i	0.212880	+	1.20730i
$563$	4.89401e6	−	8.47668e6i	0.650720	−	1.12708i	−0.332229	−	0.943199i	$-0.607801\pi$
$563$	4.89401e6	−	8.47668e6i	0.650720	−	1.12708i	0.982948	−	0.183881i	$-0.0588661\pi$
$564$	−6.57841e6	−	5.51994e6i	−0.870809	−	0.730696i
$565$	−6.21981e6	−	1.07730e7i	−0.819702	−	1.41976i
$566$	2.10786e6	−	3.65093e6i	0.276568	−	0.479030i
$567$	−7.57731e6	+	2.75792e6i	−0.989823	+	0.360266i
$568$	−2.36495e6	+	1.98443e6i	−0.307575	+	0.258086i
$569$	957242.	+	1.65799e6i	0.123948	+	0.214685i	0.921321	−	0.388802i	$-0.127111\pi$
$569$	957242.	+	1.65799e6i	0.123948	+	0.214685i	−0.797373	+	0.603487i	$0.793778\pi$
$570$	−2.96058e6	+	1.67903e7i	−0.381671	+	2.16456i
$571$	−170005.	+	964144.i	−0.0218208	+	0.123752i	−0.993772	−	0.111429i	$-0.964457\pi$
$571$	−170005.	+	964144.i	−0.0218208	+	0.123752i	0.971952	+	0.235181i	$0.0755683\pi$
$572$	−1.53600e6	−	1.28886e6i	−0.196292	−	0.164708i
$573$	−2.93203e6	−	1.06717e6i	−0.373062	−	0.135784i
$574$	3.11270e6	+	1.13293e6i	0.394327	+	0.143523i
$575$	−1.41227e7	−	1.18503e7i	−1.78134	−	1.49472i
$576$	150347.	−	852661.i	0.0188816	−	0.107083i
$577$	−1.85200e6	+	1.05032e7i	−0.231580	+	1.31335i	0.618119	+	0.786085i	$0.287895\pi$
$577$	−1.85200e6	+	1.05032e7i	−0.231580	+	1.31335i	−0.849698	+	0.527269i	$0.823216\pi$
$578$	−2.80644e6	−	4.86090e6i	−0.349411	−	0.605197i
$579$	261190.	−	219164.i	0.0323787	−	0.0271690i
$580$	−7.61595e6	+	2.77198e6i	−0.940057	+	0.342153i
$581$	1.62189e6	−	2.80920e6i	0.199334	−	0.345257i
$582$	−6.65426e6	−	1.15255e7i	−0.814315	−	1.41043i
$583$	−364027.	−	305455.i	−0.0443569	−	0.0372199i
$584$	2.43191e6	−	4.21220e6i	0.295064	−	0.511065i
$585$	−687809.	−	3.90076e6i	−0.0830956	−	0.471259i
$586$	1.02194e7			1.22937
$587$	238031.	+	1.34994e6i	0.0285127	+	0.161703i	0.995740	−	0.0922102i	$-0.0293932\pi$
$587$	238031.	+	1.34994e6i	0.0285127	+	0.161703i	−0.967227	+	0.253914i	$0.918282\pi$
$588$	−459420.	+	385499.i	−0.0547982	+	0.0459812i
$589$	−2.10081e6	−	764633.i	−0.249516	−	0.0908165i
$590$	7.31980e6	−	2.66419e6i	0.865704	−	0.315091i
$591$	−4.15234e6			−0.489017
$592$	36264.7	−	2.13148e6i	0.00425285	−	0.249964i
$593$	6.39782e6			0.747129			0.373564	−	0.927604i	$-0.378135\pi$
$593$	6.39782e6			0.747129			0.373564	+	0.927604i	$0.378135\pi$
$594$	−1.55006e6	+	564177.i	−0.180253	+	0.0656068i
$595$	1.77194e7	+	6.44933e6i	2.05190	+	0.746831i
$596$	24166.8	−	20278.3i	0.00278678	−	0.00233839i
$597$	−42662.2	−	241950.i	−0.00489901	−	0.0277836i
$598$	−2.87995e6			−0.329330
$599$	−2.79828e6	−	1.58699e7i	−0.318658	−	1.80720i	−0.550934	−	0.834549i	$-0.685728\pi$
$599$	−2.79828e6	−	1.58699e7i	−0.318658	−	1.80720i	0.232276	−	0.972650i	$-0.425383\pi$
$600$	−3.57748e6	+	6.19638e6i	−0.405694	+	0.702683i
$601$	937286.	+	786476.i	0.105849	+	0.0888177i	0.694176	−	0.719805i	$-0.255769\pi$
$601$	937286.	+	786476.i	0.105849	+	0.0888177i	−0.588327	+	0.808623i	$0.700213\pi$
$602$	−2.24143e6	−	3.88227e6i	−0.252077	−	0.436610i
$603$	−2.60784e6	+	4.51692e6i	−0.292071	+	0.505881i
$604$	−1.17133e6	+	426329.i	−0.130643	+	0.0475502i
$605$	−1.49485e7	+	1.25433e7i	−1.66038	+	1.39323i
$606$	−2.71231e6	−	4.69786e6i	−0.300026	−	0.519660i
$607$	204198.	−	1.15807e6i	0.0224947	−	0.127574i	−0.971492	−	0.237070i	$-0.923813\pi$
$607$	204198.	−	1.15807e6i	0.0224947	−	0.127574i	0.993987	+	0.109497i	$0.0349239\pi$
$608$	388645.	−	2.20411e6i	0.0426377	−	0.241810i
$609$	1.10911e7	+	9.30656e6i	1.21180	+	1.01682i
$610$	1.17792e7	+	4.28727e6i	1.28171	+	0.466505i
$611$	4.84620e6	+	1.76387e6i	0.525168	+	0.191146i
$612$	−4.35312e6	−	3.65270e6i	−0.469810	−	0.394217i
$613$	−1.72592e6	+	9.78816e6i	−0.185511	+	1.05208i	0.739787	+	0.672841i	$0.234926\pi$
$613$	−1.72592e6	+	9.78816e6i	−0.185511	+	1.05208i	−0.925298	+	0.379242i	$0.876185\pi$
$614$	−983812.	+	5.57948e6i	−0.105315	+	0.597273i
$615$	6.58229e6	+	1.14009e7i	0.701761	+	1.21549i
$616$	3.67977e6	−	3.08769e6i	0.390723	−	0.327855i
$617$	−1.25458e7	+	4.56629e6i	−1.32674	+	0.482893i	−0.905611	−	0.424109i	$-0.860587\pi$
$617$	−1.25458e7	+	4.56629e6i	−1.32674	+	0.482893i	−0.421127	+	0.907002i	$0.638365\pi$
$618$	−822275.	+	1.42422e6i	−0.0866056	+	0.150005i
$619$	6.38019e6	+	1.10508e7i	0.669279	+	1.15923i	0.978106	+	0.208107i	$0.0667302\pi$
$619$	6.38019e6	+	1.10508e7i	0.669279	+	1.15923i	−0.308827	+	0.951118i	$0.599936\pi$
$620$	−1.14696e6	−	962410.i	−0.119831	−	0.100550i
$621$	−1.18462e6	+	2.05183e6i	−0.123268	+	0.213507i
$622$	1.56264e6	+	8.86215e6i	0.161950	+	0.918466i
$623$	5.48217e6			0.565891
$624$	194088.	+	1.10073e6i	0.0199543	+	0.113167i
$625$	1.03514e6	−	868582.i	0.105998	−	0.0889428i
$626$	−5.97529e6	−	2.17483e6i	−0.609429	−	0.221814i
$627$	2.67866e7	−	9.74952e6i	2.72112	−	0.990408i
$628$	7.57045e6			0.765990
$629$	−1.19963e7	−	7.20089e6i	−1.20898	−	0.725704i
$630$	9.48913e6			0.952522
$631$	−9.44796e6	+	3.43877e6i	−0.944636	+	0.343819i	−0.767995	−	0.640456i	$-0.778745\pi$
$631$	−9.44796e6	+	3.43877e6i	−0.944636	+	0.343819i	−0.176641	+	0.984275i	$0.556523\pi$
$632$	−744695.	−	271047.i	−0.0741627	−	0.0269930i
$633$	1.86113e7	−	1.56168e7i	1.84616	−	1.54911i
$634$	−2.00731e6	−	1.13840e7i	−0.198331	−	1.12479i
$635$	−2.86471e7			−2.81934
$636$	45998.1	+	260868.i	0.00450918	+	0.0255728i
$637$	180084.	−	311914.i	0.0175843	−	0.0304570i
$638$	1.03805e7	+	8.71025e6i	1.00964	+	0.847187i
$639$	5.09827e6	+	8.83047e6i	0.493936	+	0.855523i
$640$	749452.	−	1.29809e6i	0.0723259	−	0.125272i
$641$	729992.	−	265695.i	0.0701734	−	0.0255410i	−0.306695	−	0.951808i	$-0.599223\pi$
$641$	729992.	−	265695.i	0.0701734	−	0.0255410i	0.376868	+	0.926267i	$0.377001\pi$
$642$	−234429.	+	196709.i	−0.0224478	+	0.0188360i
$643$	−147733.	−	255880.i	−0.0140912	−	0.0244067i	0.858894	−	0.512154i	$-0.171152\pi$
$643$	−147733.	−	255880.i	−0.0140912	−	0.0244067i	−0.872985	+	0.487747i	$0.837819\pi$
$644$	1.19807e6	−	6.79461e6i	0.113833	−	0.645580i
$645$	3.09372e6	−	1.75454e7i	0.292807	−	1.66059i
$646$	−1.12527e7	−	9.44216e6i	−1.06091	−	0.890205i
$647$	5.19578e6	+	1.89111e6i	0.487967	+	0.177605i	0.574274	−	0.818663i	$-0.305284\pi$
$647$	5.19578e6	+	1.89111e6i	0.487967	+	0.177605i	−0.0863072	+	0.996269i	$0.527507\pi$
$648$	3.95319e6	+	1.43884e6i	0.369837	+	0.134610i
$649$	−9.97683e6	−	8.37156e6i	−0.929782	−	0.780180i
$650$	746150.	−	4.23163e6i	0.0692696	−	0.392848i
$651$	−464458.	+	2.63407e6i	−0.0429530	+	0.243599i
$652$	3.02863e6	+	5.24575e6i	0.279015	+	0.483268i
$653$	4.20957e6	−	3.53225e6i	0.386327	−	0.324167i	−0.428853	−	0.903374i	$-0.641082\pi$
$653$	4.20957e6	−	3.53225e6i	0.386327	−	0.324167i	0.815180	+	0.579207i	$0.196638\pi$
$654$	−177748.	+	64694.9i	−0.0162502	+	0.00591460i
$655$	1.23194e7	−	2.13379e7i	1.12199	−	1.94334i
$656$	−864078.	−	1.49663e6i	−0.0783959	−	0.135786i
$657$	−1.23060e7	−	1.03260e7i	−1.11225	−	0.933291i
$658$	−6.17753e6	+	1.06998e7i	−0.556224	+	0.963409i
$659$	−430316.	−	2.44045e6i	−0.0385989	−	0.218905i	0.959407	−	0.282025i	$-0.0910061\pi$
$659$	−430316.	−	2.44045e6i	−0.0385989	−	0.218905i	−0.998006	+	0.0631199i	$0.979895\pi$
$660$	1.90907e7			1.70594
$661$	−2.73800e6	−	1.55279e7i	−0.243741	−	1.38233i	−0.823398	−	0.567465i	$-0.807924\pi$
$661$	−2.73800e6	−	1.55279e7i	−0.243741	−	1.38233i	0.579657	−	0.814861i	$-0.303187\pi$
$662$	7.56615e6	−	6.34875e6i	0.671011	−	0.563045i
$663$	6.89344e6	+	2.50901e6i	0.609049	+	0.221676i
$664$	−1.59027e6	+	578810.i	−0.139975	+	0.0509467i
$665$	2.45292e7			2.15095
$666$	−6.91215e6	−	1.34042e6i	−0.603848	−	0.117100i
$667$	1.94630e7			1.69393
$668$	−2.96461e6	+	1.07903e6i	−0.257055	+	0.0935604i
$669$	2.48059e7	+	9.02859e6i	2.14284	+	0.779928i
$670$	−6.91694e6	+	5.80400e6i	−0.595288	+	0.499506i
$671$	−3.63935e6	−	2.06398e7i	−0.312046	−	1.76970i
$672$	−2.67767e6			−0.228736
$673$	2.21318e6	+	1.25516e7i	0.188356	+	1.06822i	0.921568	+	0.388218i	$0.126909\pi$
$673$	2.21318e6	+	1.25516e7i	0.188356	+	1.06822i	−0.733212	+	0.680000i	$0.761980\pi$
$674$	−6.41438e6	+	1.11100e7i	−0.543882	+	0.942032i
$675$	−2.70792e6	−	2.27221e6i	−0.228758	−	0.191951i
$676$	2.63472e6	+	4.56348e6i	0.221752	+	0.384087i
$677$	7.92178e6	−	1.37209e7i	0.664280	−	1.15057i	−0.315200	−	0.949025i	$-0.602072\pi$
$677$	7.92178e6	−	1.37209e7i	0.664280	−	1.15057i	0.979480	−	0.201541i	$-0.0645951\pi$
$678$	1.08945e7	−	3.96529e6i	0.910195	−	0.331284i
$679$	−1.46677e7	+	1.23076e7i	−1.22092	+	1.02447i
$680$	−4.91887e6	−	8.51973e6i	−0.407937	−	0.706568i
$681$	−772217.	+	4.37946e6i	−0.0638075	+	0.361870i
$682$	−434698.	+	2.46530e6i	−0.0357871	+	0.202959i
$683$	−7.78979e6	−	6.53641e6i	−0.638960	−	0.536151i	0.264738	−	0.964320i	$-0.414714\pi$
$683$	−7.78979e6	−	6.53641e6i	−0.638960	−	0.536151i	−0.903699	+	0.428169i	$0.859159\pi$
$684$	−6.94630e6	−	2.52825e6i	−0.567692	−	0.206623i
$685$	−7.23918e6	−	2.63485e6i	−0.589472	−	0.214550i
$686$	6.97857e6	+	5.85572e6i	0.566182	+	0.475083i
$687$	−2.77828e6	+	1.57564e7i	−0.224587	+	1.27369i
$688$	−406123.	+	2.30324e6i	−0.0327104	+	0.185510i
$689$	−79540.6	−	137768.i	−0.00638323	−	0.0110561i
$690$	2.10050e7	−	1.76253e7i	1.67958	−	1.40933i
$691$	1.54992e7	−	5.64125e6i	1.23485	−	0.449449i	0.359594	−	0.933109i	$-0.382915\pi$
$691$	1.54992e7	−	5.64125e6i	1.23485	−	0.449449i	0.875256	+	0.483660i	$0.160693\pi$
$692$	2.43638e6	−	4.21994e6i	0.193411	−	0.334997i
$693$	−7.93271e6	−	1.37399e7i	−0.627464	−	1.08680i
$694$	1.15748e7	+	9.71243e6i	0.912254	+	0.765472i
$695$	−7.32711e6	+	1.26909e7i	−0.575401	+	0.996624i
$696$	−1.31167e6	−	7.43885e6i	−0.102636	−	0.582080i
$697$	−1.13424e7			−0.884347
$698$	−860254.	−	4.87875e6i	−0.0668326	−	0.379027i
$699$	6.75061e6	−	5.66443e6i	0.522577	−	0.438494i
$700$	9.67321e6	+	3.52076e6i	0.746149	+	0.271576i
$701$	1.25272e7	−	4.55954e6i	0.962853	−	0.350450i	0.187702	−	0.982226i	$-0.439896\pi$
$701$	1.25272e7	−	4.55954e6i	0.962853	−	0.350450i	0.775151	+	0.631776i	$0.217674\pi$
$702$	−552208.			−0.0422922
$703$	−1.78678e7	−	3.46497e6i	−1.36359	−	0.264430i
$704$	−2.50610e6			−0.190576
$705$	−4.61410e7	+	1.67939e7i	−3.49634	+	1.27256i
$706$	−2.01772e6	−	734390.i	−0.152352	−	0.0554517i
$707$	−5.97863e6	+	5.01666e6i	−0.449835	+	0.377456i
$708$	1.26067e6	+	7.14959e6i	0.0945185	+	0.536041i
$709$	−1.22311e7			−0.913799			−0.456900	−	0.889518i	$-0.651040\pi$
$709$	−1.22311e7			−0.913799			−0.456900	+	0.889518i	$0.651040\pi$
$710$	3.06530e6	+	1.73842e7i	0.228206	+	1.29422i
$711$	−1.30872e6	+	2.26677e6i	−0.0970898	+	0.168164i
$712$	−2.19098e6	−	1.83845e6i	−0.161972	−	0.135910i
$713$	1.79777e6	+	3.11383e6i	0.132437	+	0.229388i
$714$	−8.78717e6	+	1.52198e7i	−0.645065	+	1.11728i
$715$	−1.07735e7	+	3.92124e6i	−0.788120	+	0.286852i
$716$	7.93304e6	−	6.65661e6i	0.578305	−	0.485256i
$717$	−2.19826e6	−	3.80750e6i	−0.159692	−	0.276594i
$718$	2.20493e6	−	1.25048e7i	0.159619	−	0.905242i
$719$	−3.54267e6	+	2.00915e7i	−0.255569	+	1.44940i	0.539038	+	0.842281i	$0.318788\pi$
$719$	−3.54267e6	+	2.00915e7i	−0.255569	+	1.44940i	−0.794607	+	0.607124i	$0.792323\pi$
$720$	−3.79239e6	−	3.18219e6i	−0.272635	−	0.228768i
$721$	2.22336e6	+	809238.i	0.159284	+	0.0579747i
$722$	−8.64896e6	−	3.14797e6i	−0.617477	−	0.224743i
$723$	1.35252e7	+	1.13490e7i	0.962274	+	0.807443i
$724$	−314599.	+	1.78418e6i	−0.0223055	+	0.126501i
$725$	−5.04257e6	+	2.85978e7i	−0.356293	+	2.02064i
$726$	−9.09346e6	−	1.57503e7i	−0.640306	−	1.10904i
$727$	−1.31834e7	+	1.10622e7i	−0.925103	+	0.776254i	−0.974932	−	0.222504i	$-0.928577\pi$
$727$	−1.31834e7	+	1.10622e7i	−0.925103	+	0.776254i	0.0498288	+	0.998758i	$0.484132\pi$
$728$	1.51110e6	−	549994.i	0.105673	−	0.0384618i
$729$	5.20169e6	−	9.00959e6i	0.362515	−	0.627894i
$730$	−1.39053e7	−	2.40848e7i	−0.965772	−	1.67277i
$731$	1.17588e7	+	9.86679e6i	0.813896	+	0.682940i
$732$	−5.84137e6	+	1.01176e7i	−0.402937	+	0.697908i
$733$	3.78664e6	+	2.14751e7i	0.260312	+	1.47630i	0.782060	+	0.623203i	$0.214169\pi$
$733$	3.78664e6	+	2.14751e7i	0.260312	+	1.47630i	−0.521749	+	0.853099i	$0.674720\pi$
$734$	−4.91552e6			−0.336767
$735$	595470.	+	3.37708e6i	0.0406576	+	0.230581i
$736$	−2.75740e6	+	2.31373e6i	−0.187631	+	0.157441i
$737$	1.41864e7	+	5.16341e6i	0.962061	+	0.350161i
$738$	−5.36357e6	+	1.95218e6i	−0.362504	+	0.131941i
$739$	−1.45413e6			−0.0979471			−0.0489735	−	0.998800i	$-0.515595\pi$
$739$	−1.45413e6			−0.0979471			−0.0489735	+	0.998800i	$0.515595\pi$
$740$	−1.04510e7	−	6.27334e6i	−0.701584	−	0.421133i
$741$	9.54270e6			0.638448
$742$	358124.	−	130346.i	0.0238794	−	0.00869140i
$743$	−206160.	−	75036.2i	−0.0137004	−	0.00498653i	0.335161	−	0.942161i	$-0.391209\pi$
$743$	−206160.	−	75036.2i	−0.0137004	−	0.00498653i	−0.348861	+	0.937174i	$0.613432\pi$
$744$	1.06896e6	−	896966.i	0.0707995	−	0.0594078i
$745$	−31323.4	−	177644.i	−0.00206765	−	0.0117263i
$746$	−1.25234e7			−0.823902
$747$	970599.	+	5.50454e6i	0.0636412	+	0.360927i
$748$	−8.22414e6	+	1.42446e7i	−0.537448	+	0.930887i
$749$	337279.	+	283011.i	0.0219677	+	0.0184331i
$750$	8.26723e6	+	1.43193e7i	0.536670	+	0.929539i
$751$	1.15405e7	−	1.99887e7i	0.746662	−	1.29326i	−0.202752	−	0.979230i	$-0.564989\pi$
$751$	1.15405e7	−	1.99887e7i	0.746662	−	1.29326i	0.949414	−	0.314026i	$-0.101678\pi$
$752$	6.05707e6	−	2.20459e6i	0.390587	−	0.142162i
$753$	−2.98227e7	+	2.50242e7i	−1.91672	+	1.60832i
$754$	2.26816e6	+	3.92856e6i	0.145293	+	0.251655i
$755$	−1.23765e6	+	7.01906e6i	−0.0790188	+	0.448138i
$756$	229722.	−	1.30282e6i	0.0146183	−	0.0829046i
$757$	−4.70516e6	−	3.94810e6i	−0.298425	−	0.250408i	0.481263	−	0.876576i	$-0.340178\pi$
$757$	−4.70516e6	−	3.94810e6i	−0.298425	−	0.250408i	−0.779688	+	0.626168i	$0.784622\pi$
$758$	−7.47674e6	−	2.72131e6i	−0.472650	−	0.172030i
$759$	−4.30805e7	−	1.56800e7i	−2.71441	−	0.987965i
$760$	−9.80326e6	−	8.22591e6i	−0.615654	−	0.516595i
$761$	−4.19701e6	+	2.38024e7i	−0.262711	+	1.48991i	0.512763	+	0.858530i	$0.328622\pi$
$761$	−4.19701e6	+	2.38024e7i	−0.262711	+	1.48991i	−0.775474	+	0.631379i	$0.782489\pi$
$762$	4.63626e6	−	2.62935e7i	0.289255	−	1.64044i
$763$	136071.	+	235682.i	0.00846164	+	0.0146560i
$764$	1.79410e6	−	1.50543e6i	0.111202	−	0.0933096i
$765$	−3.05328e7	+	1.11130e7i	−1.88631	+	0.686560i
$766$	1.04509e7	−	1.81015e7i	0.643549	−	1.11466i
$767$	−2.17996e6	−	3.77580e6i	−0.133801	−	0.231751i
$768$	1.07015e6	+	897961.i	0.0654698	+	0.0549356i
$769$	1.14969e6	−	1.99133e6i	0.0701078	−	0.121430i	−0.828841	−	0.559485i	$-0.810999\pi$
$769$	1.14969e6	−	1.99133e6i	0.0701078	−	0.121430i	0.898948	+	0.438055i	$0.144332\pi$
$770$	−4.76948e6	−	2.70490e7i	−0.289897	−	1.64409i
$771$	2.34545e7			1.42099
$772$	44440.8	+	252037.i	0.00268373	+	0.0152202i
$773$	−69568.1	+	58374.6i	−0.00418757	+	0.00351379i	−0.644879	−	0.764285i	$-0.723092\pi$
$773$	−69568.1	+	58374.6i	−0.00418757	+	0.00351379i	0.640691	+	0.767798i	$0.278648\pi$
$774$	7.25868e6	+	2.64194e6i	0.435517	+	0.158515i
$775$	−5.04106e6	+	1.83480e6i	−0.301486	+	0.109732i
$776$	9.98941e6			0.595505
$777$	−370426.	+	2.17720e7i	−0.0220115	+	1.29374i
$778$	6.22210e6			0.368543
$779$	−1.38647e7	+	5.04635e6i	−0.818593	+	0.297943i
$780$	6.00549e6	+	2.18582e6i	0.353437	+	0.128640i
$781$	2.26090e7	−	1.89712e7i	1.32634	−	1.11293i
$782$	4.10239e6	+	2.32658e7i	0.239895	+	1.36051i
$783$	3.73189e6			0.217533
$784$	−78169.3	−	443320.i	−0.00454199	−	0.0257589i
$785$	2.16434e7	−	3.74875e7i	1.25358	−	2.17126i
$786$	1.75910e7	+	1.47606e7i	1.01563	+	0.852212i
$787$	1.06292e6	+	1.84103e6i	0.0611734	+	0.105956i	0.894990	−	0.446086i	$-0.147182\pi$
$787$	1.06292e6	+	1.84103e6i	0.0611734	+	0.105956i	−0.833817	+	0.552041i	$0.813849\pi$
$788$	1.55838e6	−	2.69919e6i	0.0894041	−	0.154852i
$789$	9.29323e6	−	3.38246e6i	0.531464	−	0.193437i
$790$	−3.47121e6	+	2.91269e6i	−0.197885	+	0.166045i
$791$	−8.34009e6	−	1.44455e7i	−0.473946	−	0.820899i
$792$	−1.43732e6	+	8.15146e6i	−0.0814219	+	0.461767i
$793$	1.21833e6	−	6.90948e6i	0.0687988	−	0.390178i
$794$	5.71327e6	+	4.79401e6i	0.321613	+	0.269865i
$795$	1.42328e6	+	518031.i	0.0798678	+	0.0290695i
$796$	173288.	+	63071.8i	0.00969364	+	0.00352820i
$797$	7.18556e6	+	6.02940e6i	0.400696	+	0.336224i	0.820762	−	0.571270i	$-0.193549\pi$
$797$	7.18556e6	+	6.02940e6i	0.400696	+	0.336224i	−0.420067	+	0.907493i	$0.637993\pi$
$798$	−3.96981e6	+	2.25139e7i	−0.220680	+	1.25154i
$799$	7.34630e6	−	4.16629e7i	0.407101	−	2.30878i
$800$	−2.68527e6	−	4.65102e6i	−0.148341	−	0.256935i
$801$	−7.23643e6	+	6.07208e6i	−0.398513	+	0.334392i
$802$	8.46066e6	−	3.07943e6i	0.464481	−	0.169057i
$803$	−2.32491e7	+	4.02687e7i	−1.27238	+	2.20383i
$804$	−4.20771e6	−	7.28797e6i	−0.229565	−	0.397619i
$805$	−3.02205e7	−	2.53580e7i	−1.64366	−	1.37919i
$806$	−419013.	+	725752.i	−0.0227190	+	0.0393505i
$807$	−2.19026e6	−	1.24216e7i	−0.118389	−	0.671417i
$808$	4.07174e6			0.219408
$809$	359183.	+	2.03703e6i	0.0192950	+	0.109427i	0.992934	−	0.118666i	$-0.0378619\pi$
$809$	359183.	+	2.03703e6i	0.0192950	+	0.109427i	−0.973639	+	0.228094i	$0.926751\pi$
$810$	1.84268e7	−	1.54619e7i	0.986818	−	0.828039i
$811$	1.65398e7	+	6.02001e6i	0.883037	+	0.321399i	0.743435	−	0.668808i	$-0.233195\pi$
$811$	1.65398e7	+	6.02001e6i	0.883037	+	0.321399i	0.139602	+	0.990208i	$0.455418\pi$
$812$	−1.02122e7	+	3.71692e6i	−0.543535	+	0.197831i
$813$	−1.14783e7			−0.609050
$814$	−346691.	+	2.03770e7i	−0.0183393	+	1.07790i
$815$	3.46346e7			1.82649
$816$	8.61583e6	−	3.13591e6i	0.452972	−	0.164868i
$817$	1.87636e7	+	6.82938e6i	0.983468	+	0.357953i
$818$	643437.	−	539908.i	0.0336219	−	0.0282122i
$819$	−922277.	−	5.23049e6i	−0.0480454	−	0.272479i
$820$	−9.88137e6			−0.513195
$821$	−1.23740e6	−	7.01766e6i	−0.0640698	−	0.363358i	−0.999939	−	0.0110112i	$-0.996495\pi$
$821$	−1.23740e6	−	7.01766e6i	−0.0640698	−	0.363358i	0.935870	−	0.352347i	$-0.114616\pi$
$822$	3.58996e6	−	6.21799e6i	0.185315	−	0.320975i
$823$	−2.16937e6	−	1.82031e6i	−0.111643	−	0.0936800i	0.585257	−	0.810848i	$-0.300994\pi$
$823$	−2.16937e6	−	1.82031e6i	−0.111643	−	0.0936800i	−0.696900	+	0.717168i	$0.745438\pi$
$824$	−617202.	−	1.06903e6i	−0.0316672	−	0.0548491i
$825$	3.42008e7	−	5.92375e7i	1.74945	−	3.03014i
$826$	9.81506e6	−	3.57239e6i	0.500545	−	0.182183i
$827$	2.11264e7	−	1.77272e7i	1.07414	−	0.901312i	0.0787207	−	0.996897i	$-0.474916\pi$
$827$	2.11264e7	−	1.77272e7i	1.07414	−	0.901312i	0.995421	+	0.0955845i	$0.0304720\pi$
$828$	5.94430e6	+	1.02958e7i	0.301318	+	0.521898i
$829$	−1.39899e6	+	7.93406e6i	−0.0707014	+	0.400967i	0.928834	+	0.370496i	$0.120812\pi$
$829$	−1.39899e6	+	7.93406e6i	−0.0707014	+	0.400967i	−0.999536	+	0.0304719i	$0.990299\pi$
$830$	−1.68031e6	+	9.52950e6i	−0.0846630	+	0.480148i
$831$	−1.85295e7	−	1.55481e7i	−0.930808	−	0.781041i
$832$	−788360.	−	286940.i	−0.0394835	−	0.0143708i
$833$	−2.77634e6	−	1.01051e6i	−0.138631	−	0.0504576i
$834$	−1.04624e7	−	8.77902e6i	−0.520856	−	0.437050i
$835$	−3.13246e6	+	1.77651e7i	−0.155478	+	0.881761i
$836$	−3.71545e6	+	2.10714e7i	−0.183864	+	1.04274i
$837$	344709.	+	597054.i	0.0170075	+	0.0294578i
$838$	−1.00464e7	+	8.42992e6i	−0.494197	+	0.414680i
$839$	−1.25518e6	+	456850.i	−0.0615606	+	0.0224062i	−0.372617	−	0.927985i	$-0.621539\pi$
$839$	−1.25518e6	+	456850.i	−0.0615606	+	0.0224062i	0.311056	+	0.950391i	$0.399317\pi$
$840$	−7.65528e6	+	1.32593e7i	−0.374337	+	0.648371i
$841$	−5.07289e6	−	8.78650e6i	−0.247324	−	0.428377i
$842$	−901473.	−	756426.i	−0.0438200	−	0.0367694i
$843$	−2.44583e7	+	4.23630e7i	−1.18538	+	2.05313i
$844$	3.16668e6	+	1.79591e7i	0.153020	+	0.867819i
$845$	3.01300e7			1.45163
$846$	−3.69685e6	−	2.09659e7i	−0.177585	−	1.00713i
$847$	−2.00443e7	+	1.68192e7i	−0.960024	+	0.805556i
$848$	−186838.	−	68003.6i	−0.00892229	−	0.00324745i
$849$	2.11110e7	−	7.68377e6i	1.00517	−	0.365852i
$850$	−3.52484e7			−1.67337
$851$	1.84314e7	+	2.27404e7i	0.872437	+	1.07640i
$852$	−1.64520e7			−0.776460
$853$	2.27726e7	−	8.28855e6i	1.07162	−	0.390037i	0.254836	−	0.966984i	$-0.417978\pi$
$853$	2.27726e7	−	8.28855e6i	1.07162	−	0.390037i	0.816781	+	0.576947i	$0.195756\pi$
$854$	1.57946e7	+	5.74876e6i	0.741078	+	0.269730i
$855$	−3.23784e7	+	2.71687e7i	−1.51475	+	1.27102i
$856$	−39887.6	−	226214.i	−0.00186060	−	0.0105520i
$857$	1.95744e7			0.910409			0.455205	−	0.890387i	$-0.349566\pi$
$857$	1.95744e7			0.910409			0.455205	+	0.890387i	$0.349566\pi$
$858$	−1.85549e6	−	1.05230e7i	−0.0860478	−	0.488001i
$859$	−9.54941e6	+	1.65401e7i	−0.441564	+	0.764811i	−0.997806	−	0.0662095i	$-0.978909\pi$
$859$	−9.54941e6	+	1.65401e7i	−0.441564	+	0.764811i	0.556242	+	0.831020i	$0.312243\pi$
$860$	1.02441e7	+	8.59584e6i	0.472312	+	0.396317i
$861$	8.82614e6	+	1.52873e7i	0.405754	+	0.702786i
$862$	1.53355e6	−	2.65618e6i	0.0702957	−	0.121756i
$863$	1.86388e7	−	6.78397e6i	0.851905	−	0.310068i	0.121088	−	0.992642i	$-0.461362\pi$
$863$	1.86388e7	−	6.78397e6i	0.851905	−	0.310068i	0.730817	+	0.682574i	$0.239139\pi$
$864$	−528711.	+	443641.i	−0.0240954	+	0.0202184i
$865$	−1.39309e7	−	2.41291e7i	−0.633052	−	1.09648i
$866$	2.51450e6	−	1.42605e7i	0.113935	−	0.646158i
$867$	5.19405e6	−	2.94569e7i	0.234670	−	1.33088i
$868$	−1.53794e6	−	1.29049e6i	−0.0692853	−	0.0581372i
$869$	7.11930e6	+	2.59121e6i	0.319807	+	0.116400i
$870$	−4.05858e7	−	1.47720e7i	−1.81792	−	0.661670i
$871$	3.87150e6	+	3.24857e6i	0.172915	+	0.145093i
$872$	24654.6	−	139823.i	0.00109801	−	0.00622714i
$873$	5.72922e6	−	3.24920e7i	0.254425	−	1.44292i
$874$	1.53659e7	+	2.66145e7i	0.680424	+	1.17853i
$875$	1.82231e7	−	1.52910e7i	0.804640	−	0.675173i
$876$	2.43564e7	−	8.86502e6i	1.07239	−	0.390319i
$877$	−9.91944e6	+	1.71810e7i	−0.435500	+	0.754308i	−0.997336	−	0.0729404i	$-0.976762\pi$
$877$	−9.91944e6	+	1.71810e7i	−0.435500	+	0.754308i	0.561836	+	0.827248i	$0.310095\pi$
$878$	−6.06562e6	−	1.05060e7i	−0.265545	−	0.459938i
$879$	4.17187e7	+	3.50061e7i	1.82120	+	1.52817i
$880$	−7.16478e6	+	1.24098e7i	−0.311886	+	0.540203i
$881$	−5.05632e6	−	2.86758e7i	−0.219480	−	1.24473i	−0.872961	−	0.487790i	$-0.837803\pi$
$881$	−5.05632e6	−	2.86758e7i	−0.219480	−	1.24473i	0.653481	−	0.756943i	$-0.273308\pi$
$882$	−1.48679e6			−0.0643546
$883$	900583.	+	5.10746e6i	0.0388707	+	0.220447i	0.998055	−	0.0623338i	$-0.0198543\pi$
$883$	900583.	+	5.10746e6i	0.0388707	+	0.220447i	−0.959185	+	0.282780i	$0.908743\pi$
$884$	−4.21807e6	+	3.53938e6i	−0.181545	+	0.152334i
$885$	3.90076e7	+	1.41976e7i	1.67414	+	0.609336i
$886$	1.58166e7	−	5.75678e6i	0.676908	−	0.246374i
$887$	2.14430e7			0.915117			0.457558	−	0.889180i	$-0.348724\pi$
$887$	2.14430e7			0.915117			0.457558	+	0.889180i	$0.348724\pi$
$888$	7.44932e6	−	8.57710e6i	0.317018	−	0.365013i
$889$	−3.84127e7			−1.63012
$890$	−1.53676e7	+	5.59334e6i	−0.650324	+	0.236699i
$891$	−3.77926e7	−	1.37554e7i	−1.59482	−	0.580468i
$892$	−1.51786e7	+	1.27364e7i	−0.638734	+	0.535962i
$893$	−9.55630e6	−	5.41965e7i	−0.401016	−	2.27427i
$894$	168118.			0.00703510
$895$	−1.02823e7	−	5.83138e7i	−0.429074	−	2.43340i
$896$	1.00493e6	−	1.74060e6i	0.0418184	−	0.0724316i
$897$	−1.17568e7	−	9.86510e6i	−0.487873	−	0.409374i
$898$	−6.53273e6	−	1.13150e7i	−0.270336	−	0.468236i
$899$	2.83174e6	−	4.90471e6i	0.116857	−	0.202402i
$900$	−1.66682e7	+	6.06672e6i	−0.685933	+	0.249659i
$901$	−999667.	+	838820.i	−0.0410245	+	0.0344237i
$902$	8.26061e6	+	1.43078e7i	0.338062	+	0.585540i
$903$	4.14834e6	−	2.35264e7i	0.169299	−	0.960144i
$904$	−1.51113e6	+	8.57007e6i	−0.0615010	+	0.348789i
$905$	7.93552e6	+	6.65869e6i	0.322073	+	0.270251i
$906$	−6.24208e6	−	2.27193e6i	−0.252644	−	0.0919548i
$907$	1.17315e7	+	4.26993e6i	0.473519	+	0.172347i	0.567746	−	0.823204i	$-0.307816\pi$
$907$	1.17315e7	+	4.26993e6i	0.473519	+	0.172347i	−0.0942269	+	0.995551i	$0.530038\pi$
$908$	−2.55702e6	−	2.14559e6i	−0.102924	−	0.0863639i
$909$	2.33526e6	−	1.32439e7i	0.0937401	−	0.531627i
$910$	1.59665e6	−	9.05507e6i	0.0639156	−	0.362483i
$911$	−6.98693e6	−	1.21017e7i	−0.278927	−	0.483115i	0.692191	−	0.721714i	$-0.256645\pi$
$911$	−6.98693e6	−	1.21017e7i	−0.278927	−	0.483115i	−0.971118	+	0.238598i	$0.923312\pi$
$912$	9.13664e6	−	7.66655e6i	0.363747	−	0.305220i
$913$	1.52030e7	−	5.53344e6i	0.603605	−	0.219694i
$914$	−1.44884e7	+	2.50947e7i	−0.573661	+	0.993609i
$915$	3.34002e7	+	5.78508e7i	1.31885	+	2.28432i
$916$	−9.19961e6	−	7.71939e6i	−0.362269	−	0.303979i
$917$	1.65190e7	−	2.86118e7i	0.648725	−	1.12362i
$918$	786604.	+	4.46105e6i	0.0308070	+	0.174715i
$919$	−2.32772e7			−0.909163			−0.454582	−	0.890705i	$-0.650211\pi$
$919$	−2.32772e7			−0.909163			−0.454582	+	0.890705i	$0.650211\pi$
$920$	3.57396e6	+	2.02689e7i	0.139213	+	0.789517i
$921$	−2.31284e7	+	1.94070e7i	−0.898456	+	0.753894i
$922$	2.29967e7	+	8.37010e6i	0.890918	+	0.324267i
$923$	9.28438e6	−	3.37924e6i	0.358714	−	0.130561i
$924$	2.55986e7			0.986362
$925$	−3.81887e7	+	2.11904e7i	−1.46751	+	0.814299i
$926$	−1.88459e7			−0.722251
$927$	−3.83114e6	+	1.39442e6i	−0.146430	+	0.0532960i
$928$	5.32783e6	+	1.93917e6i	0.203086	+	0.0739173i
$929$	1.51277e7	−	1.26936e7i	0.575087	−	0.482555i	−0.308243	−	0.951308i	$-0.599741\pi$
$929$	1.51277e7	−	1.26936e7i	0.575087	−	0.482555i	0.883330	+	0.468752i	$0.155296\pi$
$930$	−1.38552e6	−	7.85767e6i	−0.0525298	−	0.297911i
$931$	−3.84334e6			−0.145323
$932$	1.14860e6	+	6.51404e6i	0.0433141	+	0.245647i
$933$	−2.39777e7	+	4.15306e7i	−0.901786	+	1.56194i
$934$	1.29191e7	+	1.08404e7i	0.484578	+	0.406610i
$935$	4.70245e7	+	8.14489e7i	1.75912	+	3.04688i
$936$	−1.38546e6	+	2.39969e6i	−0.0516897	+	0.0895292i
$937$	−2.69279e7	+	9.80094e6i	−1.00197	+	0.364686i	−0.790342	−	0.612666i	$-0.790097\pi$
$937$	−2.69279e7	+	9.80094e6i	−1.00197	+	0.364686i	−0.211623	+	0.977351i	$0.567875\pi$
$938$	−9.27487e6	+	7.78254e6i	−0.344192	+	0.288811i
$939$	−1.69431e7	−	2.93463e7i	−0.627089	−	1.08615i
$940$	6.40002e6	−	3.62963e7i	0.236244	−	1.33981i
$941$	−1.09332e6	+	6.20050e6i	−0.0402505	+	0.228272i	−0.998297	−	0.0583420i	$-0.981419\pi$
$941$	−1.09332e6	+	6.20050e6i	−0.0402505	+	0.228272i	0.958046	+	0.286614i	$0.0925297\pi$
$942$	3.09048e7	+	2.59322e7i	1.13475	+	0.952165i
$943$	2.22984e7	+	8.11597e6i	0.816574	+	0.297209i
$944$	−5.12066e6	−	1.86377e6i	−0.187023	−	0.0680709i
$945$	−5.79455e6	−	4.86221e6i	−0.211077	−	0.177114i
$946$	3.88254e6	−	2.20190e7i	0.141055	−	0.799963i
$947$	4.35995e6	−	2.47265e7i	0.157982	−	0.895958i	−0.798028	−	0.602621i	$-0.794123\pi$
$947$	4.35995e6	−	2.47265e7i	0.157982	−	0.895958i	0.956009	−	0.293337i	$-0.0947658\pi$
$948$	−2.11160e6	−	3.65741e6i	−0.0763118	−	0.132176i
$949$	−1.19242e7	+	1.00056e7i	−0.429799	+	0.360644i
$950$	−4.30869e7	+	1.56824e7i	−1.54895	+	0.563771i
$951$	3.08009e7	−	5.33488e7i	1.10436	−	1.91282i
$952$	−6.59567e6	−	1.14240e7i	−0.235867	−	0.408533i
$953$	1.32840e7	+	1.11466e7i	0.473801	+	0.397567i	0.848179	−	0.529710i	$-0.177699\pi$
$953$	1.32840e7	+	1.11466e7i	0.473801	+	0.397567i	−0.374378	+	0.927276i	$0.622144\pi$
$954$	−328348.	+	568716.i	−0.0116806	+	0.0202313i
$955$	−2.32539e6	−	1.31880e7i	−0.0825065	−	0.467917i
$956$	3.30005e6			0.116782
$957$	1.25396e7	+	7.11156e7i	0.442592	+	2.51006i
$958$	−752787.	+	631663.i	−0.0265008	+	0.0222368i
$959$	−9.70696e6	−	3.53304e6i	−0.340829	−	0.124052i
$960$	7.50602e6	−	2.73197e6i	0.262864	−	0.0956747i
$961$	−2.75829e7			−0.963455
$962$	−2.44215e6	+	6.37042e6i	−0.0850815	+	0.221937i
$963$	−758670.			−0.0263625
$964$	−1.24534e7	+	4.53265e6i	−0.431612	+	0.157094i
$965$	1.37509e6	+	500493.i	0.0475350	+	0.0173013i
$966$	2.81655e7	−	2.36336e7i	0.971123	−	0.814869i
$967$	114280.	+	648113.i	0.00393010	+	0.0222887i	0.986710	−	0.162493i	$-0.0519534\pi$
$967$	114280.	+	648113.i	0.00393010	+	0.0222887i	−0.982780	+	0.184781i	$0.940842\pi$
$968$	1.36511e7			0.468253
$969$	−1.35933e7	−	7.70913e7i	−0.465066	−	2.63752i
$970$	2.85591e7	−	4.94657e7i	0.974573	−	1.68801i
$971$	−1.23380e7	−	1.03528e7i	−0.419950	−	0.352380i	0.408194	−	0.912895i	$-0.366159\pi$
$971$	−1.23380e7	−	1.03528e7i	−0.419950	−	0.352380i	−0.828144	+	0.560515i	$0.810603\pi$
$972$	9.89911e6	+	1.71458e7i	0.336071	+	0.582091i
$973$	−9.82486e6	+	1.70171e7i	−0.332693	+	0.576242i
$974$	−2.15846e7	+	7.85616e6i	−0.729033	+	0.265346i
$975$	1.75412e7	−	1.47188e7i	0.590947	−	0.495863i
$976$	−4.38455e6	−	7.59426e6i	−0.147333	−	0.255189i
$977$	−1.54284e6	+	8.74988e6i	−0.0517112	+	0.293269i	−0.999685	−	0.0250782i	$-0.992017\pi$
$977$	−1.54284e6	+	8.74988e6i	−0.0517112	+	0.293269i	0.947974	+	0.318347i	$0.103128\pi$
$978$	−5.60527e6	+	3.17891e7i	−0.187391	+	1.06275i
$979$	2.09459e7	+	1.75757e7i	0.698460	+	0.586078i
$980$	−2.41872e6	−	880342.i	−0.0804490	−	0.0292810i
$981$	−440656.	−	160385.i	−0.0146193	−	0.00532099i
$982$	−3.12679e7	−	2.62369e7i	−1.03471	−	0.868227i
$983$	5.95261e6	−	3.37589e7i	0.196482	−	1.11431i	−0.713809	−	0.700340i	$-0.753032\pi$
$983$	5.95261e6	−	3.37589e7i	0.196482	−	1.11431i	0.910292	−	0.413967i	$-0.135857\pi$
$984$	1.59920e6	−	9.06952e6i	0.0526521	−	0.298605i
$985$	−8.91060e6	−	1.54336e7i	−0.292628	−	0.506847i
$986$	2.85062e7	−	2.39196e7i	0.933786	−	0.783540i
$987$	−6.18700e7	+	2.25188e7i	−2.02156	+	0.735789i
$988$	−3.58139e6	+	6.20314e6i	−0.116724	+	0.202171i
$989$	−1.60569e7	−	2.78114e7i	−0.522002	−	0.904134i
$990$	3.62553e7	+	3.04218e7i	1.17567	+	0.986501i
$991$	−2.16912e7	+	3.75702e7i	−0.701615	+	1.21523i	0.266284	+	0.963895i	$0.414204\pi$
$991$	−2.16912e7	+	3.75702e7i	−0.701615	+	1.21523i	−0.967899	+	0.251339i	$0.919129\pi$
$992$	181882.	+	1.03150e6i	0.00586827	+	0.0332806i
$993$	5.26345e7			1.69394
$994$	4.11023e6	+	2.33103e7i	0.131947	+	0.748310i
$995$	807740.	−	677774.i	0.0258651	−	0.0217034i
$996$	−8.47462e6	−	3.08451e6i	−0.270690	−	0.0985230i
$997$	4.11120e7	−	1.49636e7i	1.30988	−	0.476757i	0.409677	−	0.912231i	$-0.365641\pi$
$997$	4.11120e7	−	1.49636e7i	1.30988	−	0.476757i	0.900201	+	0.435474i	$0.143419\pi$
$998$	2.57540e7			0.818500
$999$	3.53408e6	+	4.36030e6i	0.112037	+	0.138230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.f.a.7.2	✓	48
37.16	even	9	inner	74.6.f.a.53.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.f.a.7.2	✓	48	1.1	even	1	trivial
74.6.f.a.53.2	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)

\(f(q)\)	\(=\)	\(q+(-3.75877 + 1.36808i) q^{2} +(-20.0307 - 7.29057i) q^{3} +(12.2567 - 10.2846i) q^{4} +(-15.8864 - 90.0960i) q^{5} +85.2648 q^{6} +(-21.3019 - 120.809i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(161.927 + 135.873i) q^{9} +O(q^{10})\)	\(q+(-3.75877 + 1.36808i) q^{2} +(-20.0307 - 7.29057i) q^{3} +(12.2567 - 10.2846i) q^{4} +(-15.8864 - 90.0960i) q^{5} +85.2648 q^{6} +(-21.3019 - 120.809i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(161.927 + 135.873i) q^{9} +(182.972 + 316.916i) q^{10} +(305.921 - 529.870i) q^{11} +(-320.491 + 116.649i) q^{12} +(156.904 - 131.658i) q^{13} +(245.345 + 424.950i) q^{14} +(-338.637 + 1920.50i) q^{15} +(44.4539 - 252.111i) q^{16} +(-1287.11 - 1080.01i) q^{17} +(-794.531 - 289.186i) q^{18} +(-2053.85 - 747.540i) q^{19} +(-1121.32 - 940.896i) q^{20} +(-454.075 + 2575.19i) q^{21} +(-424.981 + 2410.19i) q^{22} +(1757.58 + 3044.22i) q^{23} +(1045.07 - 876.915i) q^{24} +(-4928.37 + 1793.78i) q^{25} +(-409.646 + 709.528i) q^{26} +(337.003 + 583.707i) q^{27} +(-1503.56 - 1261.64i) q^{28} +(2768.44 - 4795.07i) q^{29} +(-1354.55 - 7682.02i) q^{30} +1022.87 q^{31} +(177.816 + 1008.44i) q^{32} +(-9990.86 + 8383.33i) q^{33} +(6315.49 + 2298.65i) q^{34} +(-10546.0 + 3838.43i) q^{35} +3382.09 q^{36} +(8224.20 - 1306.30i) q^{37} +8742.64 q^{38} +(-4102.74 + 1493.28i) q^{39} +(5501.99 + 2002.56i) q^{40} +(5171.27 - 4339.21i) q^{41} +(-1816.30 - 10300.8i) q^{42} -9135.81 q^{43} +(-1699.92 - 9640.74i) q^{44} +(9669.16 - 16747.5i) q^{45} +(-10771.1 - 9038.02i) q^{46} +(12589.5 + 21805.6i) q^{47} +(-2728.47 + 4725.86i) q^{48} +(1652.39 - 601.420i) q^{49} +(16070.6 - 13484.8i) q^{50} +(17907.8 + 31017.2i) q^{51} +(569.074 - 3227.38i) q^{52} +(134.868 - 764.877i) q^{53} +(-2065.28 - 1732.97i) q^{54} +(-52599.2 - 19144.5i) q^{55} +(7377.57 + 2685.22i) q^{56} +(35690.0 + 29947.5i) q^{57} +(-3845.87 + 21811.0i) q^{58} +(3696.32 - 20962.9i) q^{59} +(15601.0 + 27021.8i) q^{60} +(26240.3 - 22018.2i) q^{61} +(-3844.72 + 1399.36i) q^{62} +(12965.3 - 22456.6i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-14354.5 - 12044.8i) q^{65} +(26084.3 - 45179.3i) q^{66} +(4284.66 + 24299.5i) q^{67} -26883.2 q^{68} +(-13011.4 - 73791.6i) q^{69} +(34388.7 - 28855.5i) q^{70} +(45328.8 + 16498.3i) q^{71} +(-12712.5 + 4626.97i) q^{72} -75997.3 q^{73} +(-29125.8 + 16161.5i) q^{74} +111796. q^{75} +(-32861.6 + 11960.6i) q^{76} +(-70529.8 - 25670.7i) q^{77} +(13378.3 - 11225.8i) q^{78} +(2150.22 + 12194.5i) q^{79} -23420.4 q^{80} +(-11414.4 - 64734.1i) q^{81} +(-13501.2 + 23384.8i) q^{82} +(20256.2 + 16997.0i) q^{83} +(20919.3 + 36233.3i) q^{84} +(-76857.3 + 133121. i) q^{85} +(34339.4 - 12498.5i) q^{86} +(-90412.4 + 75865.0i) q^{87} +(19578.9 + 33911.7i) q^{88} +(-7760.25 + 44010.5i) q^{89} +(-13432.3 + 76178.1i) q^{90} +(-19247.8 - 16150.8i) q^{91} +(52850.8 + 19236.1i) q^{92} +(-20488.7 - 7457.28i) q^{93} +(-77152.7 - 64738.8i) q^{94} +(-34722.2 + 196919. i) q^{95} +(3790.36 - 21496.2i) q^{96} +(-78042.3 - 135173. i) q^{97} +(-5388.15 + 4521.20i) q^{98} +(121532. - 44233.9i) 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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