LMFDB - Embedded newform 33.6.e.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} + \cdots + 25599187870096 $ x^20 - x^19 + 78x^18 + 79x^17 + 10573x^16 - 33409x^15 + 1262953x^14 - 1581925x^13 + 89291182x^12 - 100741271x^11 + 2277268901x^10 - 1144062486x^9 + 70677624924x^8 + 93641098134x^7 + 1732079176577x^6 + 1113900934906x^5 + 27749747552381x^4 + 4154923377746x^3 + 57625758470132x^2 + 60036938210920x + 25599187870096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.2
Root			$-1.64776 - 5.07128i$ of defining polynomial
Character	$\chi$	$=$	33.31
Dual form			33.6.e.b.16.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95678 + 6.02234i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-6.55106 - 4.75963i) q^{4} +(8.65323 + 26.6319i) q^{5} +(17.6110 + 54.2011i) q^{6} +(121.539 + 88.3034i) q^{7} +(-122.450 + 88.9651i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.95678 + 6.02234i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-6.55106 - 4.75963i) q^{4} +(8.65323 + 26.6319i) q^{5} +(17.6110 + 54.2011i) q^{6} +(121.539 + 88.3034i) q^{7} +(-122.450 + 88.9651i) q^{8} +(25.0304 - 77.0356i) q^{9} -177.319 q^{10} +(-364.758 + 167.341i) q^{11} -72.8780 q^{12} +(-95.6452 + 294.366i) q^{13} +(-769.618 + 559.160i) q^{14} +(203.890 + 148.135i) q^{15} +(-376.244 - 1157.96i) q^{16} +(279.891 + 861.416i) q^{17} +(414.956 + 301.483i) q^{18} +(1375.30 - 999.212i) q^{19} +(70.0700 - 215.653i) q^{20} +1352.08 q^{21} +(-294.034 - 2524.14i) q^{22} +2873.63 q^{23} +(-420.946 + 1295.54i) q^{24} +(1893.80 - 1375.93i) q^{25} +(-1585.61 - 1152.02i) q^{26} +(-225.273 - 693.320i) q^{27} +(-375.920 - 1156.96i) q^{28} +(-2018.20 - 1466.31i) q^{29} +(-1291.08 + 938.028i) q^{30} +(372.821 - 1147.42i) q^{31} +2866.45 q^{32} +(-1770.61 + 3148.03i) q^{33} -5735.43 q^{34} +(-1299.98 + 4000.93i) q^{35} +(-530.636 + 385.530i) q^{36} +(-9827.30 - 7139.95i) q^{37} +(3326.45 + 10237.7i) q^{38} +(860.806 + 2649.29i) q^{39} +(-3428.90 - 2491.24i) q^{40} +(13374.1 - 9716.82i) q^{41} +(-2645.71 + 8142.66i) q^{42} +13910.0 q^{43} +(3186.03 + 639.850i) q^{44} +2268.20 q^{45} +(-5623.05 + 17306.0i) q^{46} +(-12079.5 + 8776.30i) q^{47} +(-8865.18 - 6440.93i) q^{48} +(1780.63 + 5480.22i) q^{49} +(4580.55 + 14097.5i) q^{50} +(6594.88 + 4791.46i) q^{51} +(2027.65 - 1473.17i) q^{52} +(5156.42 - 15869.8i) q^{53} +4616.22 q^{54} +(-7612.93 - 8266.14i) q^{55} -22738.4 q^{56} +(4727.85 - 14550.8i) q^{57} +(12779.8 - 9285.05i) q^{58} +(-30229.6 - 21963.1i) q^{59} +(-630.630 - 1940.88i) q^{60} +(6319.71 + 19450.1i) q^{61} +(6180.65 + 4490.50i) q^{62} +(9844.67 - 7152.57i) q^{63} +(6430.81 - 19792.0i) q^{64} -8667.15 q^{65} +(-15493.8 - 16823.2i) q^{66} +10129.9 q^{67} +(2266.44 - 6975.37i) q^{68} +(20923.3 - 15201.7i) q^{69} +(-21551.2 - 15657.8i) q^{70} +(5254.17 + 16170.7i) q^{71} +(3788.51 + 11659.8i) q^{72} +(56559.7 + 41093.0i) q^{73} +(62229.1 - 45212.1i) q^{74} +(6510.30 - 20036.6i) q^{75} -13765.5 q^{76} +(-59109.1 - 11870.9i) q^{77} -17639.3 q^{78} +(-14674.8 + 45164.4i) q^{79} +(27582.9 - 20040.2i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(32348.0 + 99556.8i) q^{82} +(-6981.10 - 21485.6i) q^{83} +(-8857.53 - 6435.38i) q^{84} +(-20519.2 + 14908.1i) q^{85} +(-27218.7 + 83770.6i) q^{86} -22451.7 q^{87} +(29777.1 - 52941.6i) q^{88} +25397.8 q^{89} +(-4438.35 + 13659.9i) q^{90} +(-37618.1 + 27331.1i) q^{91} +(-18825.3 - 13677.4i) q^{92} +(-3355.39 - 10326.8i) q^{93} +(-29216.9 - 89920.4i) q^{94} +(38511.7 + 27980.4i) q^{95} +(20871.0 - 15163.7i) q^{96} +(-52256.2 + 160828. i) q^{97} -36488.1 q^{98} +(3761.18 + 32287.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−1.95678	+	6.02234i	−0.345913	+	1.06461i	0.615181	+	0.788386i	$0.289083\pi$
$2$	−1.95678	+	6.02234i	−0.345913	+	1.06461i	−0.961093	+	0.276223i	$0.910917\pi$
$3$	7.28115	−	5.29007i	0.467086	−	0.339358i
$3$	7.28115	−	5.29007i	0.467086	−	0.339358i
$4$	−6.55106	−	4.75963i	−0.204721	−	0.148738i
$5$	8.65323	+	26.6319i	0.154794	+	0.476406i	0.998140	−	0.0609647i	$-0.0194177\pi$
$5$	8.65323	+	26.6319i	0.154794	+	0.476406i	−0.843346	+	0.537370i	$0.819418\pi$
$6$	17.6110	+	54.2011i	0.199713	+	0.614653i
$7$	121.539	+	88.3034i	0.937500	+	0.681133i	0.947817	−	0.318813i	$-0.103284\pi$
$7$	121.539	+	88.3034i	0.937500	+	0.681133i	−0.0103179	+	0.999947i	$0.503284\pi$
$8$	−122.450	+	88.9651i	−0.676447	+	0.491468i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	−177.319			−0.560731
$11$	−364.758	+	167.341i	−0.908914	+	0.416985i
$11$	−364.758	+	167.341i	−0.908914	+	0.416985i
$12$	−72.8780			−0.146098
$13$	−95.6452	+	294.366i	−0.156966	+	0.483091i	−0.998355	−	0.0573392i	$-0.981738\pi$
$13$	−95.6452	+	294.366i	−0.156966	+	0.483091i	0.841389	+	0.540430i	$0.181738\pi$
$14$	−769.618	+	559.160i	−1.04943	+	0.762458i
$15$	203.890	+	148.135i	0.233974	+	0.169992i
$16$	−376.244	−	1157.96i	−0.367426	−	1.13082i
$17$	279.891	+	861.416i	0.234891	+	0.722921i	0.997136	+	0.0756318i	$0.0240974\pi$
$17$	279.891	+	861.416i	0.234891	+	0.722921i	−0.762245	+	0.647289i	$0.775903\pi$
$18$	414.956	+	301.483i	0.301870	+	0.219322i
$19$	1375.30	−	999.212i	0.874003	−	0.635000i	−0.0576553	−	0.998337i	$-0.518362\pi$
$19$	1375.30	−	999.212i	0.874003	−	0.635000i	0.931658	+	0.363336i	$0.118362\pi$
$20$	70.0700	−	215.653i	0.0391703	−	0.120554i
$21$	1352.08			0.669041
$22$	−294.034	−	2524.14i	−0.129521	−	1.11188i
$23$	2873.63			1.13269			0.566344	−	0.824169i	$-0.308357\pi$
$23$	2873.63			1.13269			0.566344	+	0.824169i	$0.308357\pi$
$24$	−420.946	+	1295.54i	−0.149176	+	0.459115i
$25$	1893.80	−	1375.93i	0.606016	−	0.440296i
$26$	−1585.61	−	1152.02i	−0.460006	−	0.334214i
$27$	−225.273	−	693.320i	−0.0594703	−	0.183031i
$28$	−375.920	−	1156.96i	−0.0906150	−	0.278884i
$29$	−2018.20	−	1466.31i	−0.445625	−	0.323765i	0.342241	−	0.939612i	$-0.388814\pi$
$29$	−2018.20	−	1466.31i	−0.445625	−	0.323765i	−0.787866	+	0.615847i	$0.788814\pi$
$30$	−1291.08	+	938.028i	−0.261910	+	0.190289i
$31$	372.821	−	1147.42i	0.0696780	−	0.214447i	−0.910154	−	0.414270i	$-0.864037\pi$
$31$	372.821	−	1147.42i	0.0696780	−	0.214447i	0.979832	+	0.199823i	$0.0640368\pi$
$32$	2866.45			0.494845
$33$	−1770.61	+	3148.03i	−0.283034	+	0.503215i
$34$	−5735.43			−0.850880
$35$	−1299.98	+	4000.93i	−0.179377	+	0.552065i
$36$	−530.636	+	385.530i	−0.0682403	+	0.0495794i
$37$	−9827.30	−	7139.95i	−1.18013	−	0.857415i	−0.187944	−	0.982180i	$-0.560182\pi$
$37$	−9827.30	−	7139.95i	−1.18013	−	0.857415i	−0.992186	+	0.124765i	$0.960182\pi$
$38$	3326.45	+	10237.7i	0.373699	+	1.15013i
$39$	860.806	+	2649.29i	0.0906242	+	0.278912i
$40$	−3428.90	−	2491.24i	−0.338848	−	0.246187i
$41$	13374.1	−	9716.82i	1.24252	−	0.902744i	0.244757	−	0.969584i	$-0.421292\pi$
$41$	13374.1	−	9716.82i	1.24252	−	0.902744i	0.997764	+	0.0668402i	$0.0212918\pi$
$42$	−2645.71	+	8142.66i	−0.231430	+	0.712267i
$43$	13910.0			1.14724			0.573621	−	0.819121i	$-0.305538\pi$
$43$	13910.0			1.14724			0.573621	+	0.819121i	$0.305538\pi$
$44$	3186.03	+	639.850i	0.248095	+	0.0498249i
$45$	2268.20			0.166974
$46$	−5623.05	+	17306.0i	−0.391811	+	1.20587i
$47$	−12079.5	+	8776.30i	−0.797638	+	0.579518i	−0.910220	−	0.414124i	$-0.864088\pi$
$47$	−12079.5	+	8776.30i	−0.797638	+	0.579518i	0.112582	+	0.993642i	$0.464088\pi$
$48$	−8865.18	−	6440.93i	−0.555373	−	0.403502i
$49$	1780.63	+	5480.22i	0.105946	+	0.326068i
$50$	4580.55	+	14097.5i	0.259115	+	0.797474i
$51$	6594.88	+	4791.46i	0.355043	+	0.257954i
$52$	2027.65	−	1473.17i	0.103988	−	0.0755519i
$53$	5156.42	−	15869.8i	0.252150	−	0.776038i	−0.742228	−	0.670148i	$-0.766231\pi$
$53$	5156.42	−	15869.8i	0.252150	−	0.776038i	0.994378	−	0.105890i	$-0.0337692\pi$
$54$	4616.22			0.215428
$55$	−7612.93	−	8266.14i	−0.339348	−	0.368465i
$56$	−22738.4			−0.968924
$57$	4727.85	−	14550.8i	0.192742	−	0.593200i
$58$	12779.8	−	9285.05i	0.498831	−	0.362422i
$59$	−30229.6	−	21963.1i	−1.13058	−	0.821418i	−0.144805	−	0.989460i	$-0.546255\pi$
$59$	−30229.6	−	21963.1i	−1.13058	−	0.821418i	−0.985780	+	0.168043i	$0.946255\pi$
$60$	−630.630	−	1940.88i	−0.0226150	−	0.0696018i
$61$	6319.71	+	19450.1i	0.217456	+	0.669262i	0.998970	+	0.0453740i	$0.0144480\pi$
$61$	6319.71	+	19450.1i	0.217456	+	0.669262i	−0.781514	+	0.623888i	$0.785552\pi$
$62$	6180.65	+	4490.50i	0.204200	+	0.148360i
$63$	9844.67	−	7152.57i	0.312500	−	0.227044i
$64$	6430.81	−	19792.0i	0.196253	−	0.604004i
$65$	−8667.15			−0.254444
$66$	−15493.8	−	16823.2i	−0.437822	−	0.475389i
$67$	10129.9			0.275689			0.137845	−	0.990454i	$-0.455983\pi$
$67$	10129.9			0.275689			0.137845	+	0.990454i	$0.455983\pi$
$68$	2266.44	−	6975.37i	0.0594389	−	0.182934i
$69$	20923.3	−	15201.7i	0.529063	−	0.384387i
$70$	−21551.2	−	15657.8i	−0.525685	−	0.381933i
$71$	5254.17	+	16170.7i	0.123697	+	0.380699i	0.993661	−	0.112415i	$-0.0358585\pi$
$71$	5254.17	+	16170.7i	0.123697	+	0.380699i	−0.869965	+	0.493114i	$0.835859\pi$
$72$	3788.51	+	11659.8i	0.0861266	+	0.265070i
$73$	56559.7	+	41093.0i	1.24222	+	0.902529i	0.997745	−	0.0671255i	$-0.0213828\pi$
$73$	56559.7	+	41093.0i	1.24222	+	0.902529i	0.244480	+	0.969654i	$0.421383\pi$
$74$	62229.1	−	45212.1i	1.32103	−	0.959788i
$75$	6510.30	−	20036.6i	0.133644	−	0.411312i
$76$	−13765.5			−0.273375
$77$	−59109.1	−	11870.9i	−1.13613	−	0.228168i
$78$	−17639.3			−0.328281
$79$	−14674.8	+	45164.4i	−0.264548	+	0.814195i	0.727249	+	0.686373i	$0.240798\pi$
$79$	−14674.8	+	45164.4i	−0.264548	+	0.814195i	−0.991797	+	0.127821i	$0.959202\pi$
$80$	27582.9	−	20040.2i	0.481854	−	0.350088i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	32348.0	+	99556.8i	0.531266	+	1.63507i
$83$	−6981.10	−	21485.6i	−0.111232	−	0.342336i	0.879911	−	0.475139i	$-0.157602\pi$
$83$	−6981.10	−	21485.6i	−0.111232	−	0.342336i	−0.991142	+	0.132803i	$0.957602\pi$
$84$	−8857.53	−	6435.38i	−0.136967	−	0.0995121i
$85$	−20519.2	+	14908.1i	−0.308044	+	0.223807i
$86$	−27218.7	+	83770.6i	−0.396846	+	1.22137i
$87$	−22451.7			−0.318017
$88$	29777.1	−	52941.6i	0.409898	−	0.728770i
$89$	25397.8			0.339876			0.169938	−	0.985455i	$-0.445643\pi$
$89$	25397.8			0.339876			0.169938	+	0.985455i	$0.445643\pi$
$90$	−4438.35	+	13659.9i	−0.0577585	+	0.177762i
$91$	−37618.1	+	27331.1i	−0.476204	+	0.345983i
$92$	−18825.3	−	13677.4i	−0.231885	−	0.168474i
$93$	−3355.39	−	10326.8i	−0.0402286	−	0.123811i
$94$	−29216.9	−	89920.4i	−0.341047	−	1.04964i
$95$	38511.7	+	27980.4i	0.437808	+	0.318086i
$96$	20871.0	−	15163.7i	0.231135	−	0.167930i
$97$	−52256.2	+	160828.i	−0.563908	+	1.73553i	0.107266	+	0.994230i	$0.465790\pi$
$97$	−52256.2	+	160828.i	−0.563908	+	1.73553i	−0.671174	+	0.741300i	$0.734210\pi$
$98$	−36488.1			−0.383783
$99$	3761.18	+	32287.9i	0.0385688	+	0.331094i
$100$	−18955.3			−0.189553
$101$	−8647.42	+	26614.0i	−0.0843496	+	0.259601i	−0.984332	−	0.176325i	$-0.943579\pi$
$101$	−8647.42	+	26614.0i	−0.0843496	+	0.259601i	0.899982	+	0.435926i	$0.143579\pi$
$102$	−41760.5	+	30340.8i	−0.397434	+	0.288753i
$103$	−124418.	−	90395.1i	−1.15556	−	0.839560i	−0.166346	−	0.986067i	$-0.553197\pi$
$103$	−124418.	−	90395.1i	−1.15556	−	0.839560i	−0.989210	+	0.146507i	$0.953197\pi$
$104$	−14476.5	−	44554.2i	−0.131244	−	0.403929i
$105$	11699.8	+	36008.3i	0.103563	+	0.318735i
$106$	85483.6	+	62107.5i	0.738955	+	0.536882i
$107$	68635.0	−	49866.2i	0.579544	−	0.421063i	−0.259016	−	0.965873i	$-0.583398\pi$
$107$	68635.0	−	49866.2i	0.579544	−	0.421063i	0.838559	+	0.544810i	$0.183398\pi$
$108$	−1824.16	+	5614.20i	−0.0150489	+	0.0463157i
$109$	−119569.			−0.963945			−0.481973	−	0.876186i	$-0.660080\pi$
$109$	−119569.			−0.963945			−0.481973	+	0.876186i	$0.660080\pi$
$110$	64678.3	−	29672.7i	0.509656	−	0.233816i
$111$	−109325.			−0.842193
$112$	56523.4	−	173961.i	0.425778	−	1.31041i
$113$	128780.	−	93564.1i	0.948750	−	0.689307i	−0.00176076	−	0.999998i	$-0.500560\pi$
$113$	128780.	−	93564.1i	0.948750	−	0.689307i	0.950511	+	0.310691i	$0.100560\pi$
$114$	78378.7	+	56945.5i	0.564854	+	0.410390i
$115$	24866.1	+	76530.1i	0.175333	+	0.539619i
$116$	6242.28	+	19211.8i	0.0430723	+	0.132563i
$117$	20282.6	+	14736.2i	0.136980	+	0.0995221i
$118$	191422.	−	139076.i	1.26557	−	0.919492i
$119$	−42048.2	+	129411.i	−0.272195	+	0.837730i
$120$	−38145.2			−0.241817
$121$	105045.	−	122078.i	0.652248	−	0.758006i
$122$	−129501.			−0.787724
$123$	45975.9	−	141499.i	0.274011	−	0.843319i
$124$	−7903.68	+	5742.36i	−0.0461610	+	0.0335379i
$125$	123826.	+	89964.9i	0.708822	+	0.514989i
$126$	23811.4	+	73283.9i	0.133616	+	0.411228i
$127$	−46475.2	−	143036.i	−0.255689	−	0.786929i	−0.993693	−	0.112133i	$-0.964232\pi$
$127$	−46475.2	−	143036.i	−0.255689	−	0.786929i	0.738004	−	0.674796i	$-0.235768\pi$
$128$	180819.	+	131372.i	0.975480	+	0.708728i
$129$	101281.	−	73584.7i	0.535861	−	0.389326i
$130$	16959.7	−	52196.5i	0.0880155	−	0.270884i
$131$	−336852.			−1.71499			−0.857494	−	0.514494i	$-0.827980\pi$
$131$	−336852.			−1.71499			−0.857494	+	0.514494i	$0.827980\pi$
$132$	26582.8	−	12195.5i	0.132790	−	0.0609205i
$133$	255386.			1.25190
$134$	−19822.0	+	61005.9i	−0.0953644	+	0.293501i
$135$	16515.1	−	11998.9i	0.0779913	−	0.0566640i
$136$	−110909.	−	80579.9i	−0.514184	−	0.373576i
$137$	−96654.5	−	297472.i	−0.439968	−	1.35408i	−0.887909	−	0.460019i	$-0.847843\pi$
$137$	−96654.5	−	297472.i	−0.439968	−	1.35408i	0.447941	−	0.894063i	$-0.352157\pi$
$138$	50607.4	+	155754.i	0.226212	+	0.696210i
$139$	−224652.	−	163219.i	−0.986219	−	0.716530i	−0.0271291	−	0.999632i	$-0.508637\pi$
$139$	−224652.	−	163219.i	−0.986219	−	0.716530i	−0.959090	+	0.283102i	$0.908637\pi$
$140$	27559.2	−	20022.9i	0.118835	−	0.0863390i
$141$	−41525.8	+	127803.i	−0.175902	+	0.541370i
$142$	−107666.			−0.448084
$143$	−14372.1	−	123377.i	−0.0587732	−	0.504540i
$144$	−98621.7			−0.396338
$145$	21586.6	−	66436.8i	0.0852638	−	0.262415i
$146$	−358151.	+	260212.i	−1.39054	+	1.01029i
$147$	41955.8	+	30482.7i	0.160140	+	0.116348i
$148$	30395.8	+	93548.6i	0.114067	+	0.351061i
$149$	125849.	+	387323.i	0.464391	+	1.42925i	0.859747	+	0.510720i	$0.170621\pi$
$149$	125849.	+	387323.i	0.464391	+	1.42925i	−0.395356	+	0.918528i	$0.629379\pi$
$150$	107928.	+	78414.5i	0.391658	+	0.284556i
$151$	−446201.	+	324184.i	−1.59253	+	1.15704i	−0.692320	+	0.721591i	$0.743411\pi$
$151$	−446201.	+	324184.i	−1.59253	+	1.15704i	−0.900212	+	0.435451i	$0.856589\pi$
$152$	−79510.2	+	244707.i	−0.279135	+	0.859088i
$153$	73365.5			0.253375
$154$	187154.	−	332746.i	0.635911	−	1.13061i
$155$	33784.2			0.112949
$156$	6970.43	−	21452.8i	0.0229323	−	0.0705785i
$157$	183038.	−	132985.i	0.592642	−	0.430580i	−0.250618	−	0.968086i	$-0.580634\pi$
$157$	183038.	−	132985.i	0.592642	−	0.430580i	0.843260	+	0.537507i	$0.180634\pi$
$158$	−243280.	−	176753.i	−0.775289	−	0.563280i
$159$	−46407.8	−	142829.i	−0.145579	−	0.448046i
$160$	24804.0	+	76338.9i	0.0765988	+	0.235747i
$161$	349258.	+	253751.i	1.06190	+	0.771512i
$162$	33611.4	−	24420.1i	0.100623	−	0.0731072i
$163$	−183643.	+	565194.i	−0.541383	+	1.66621i	0.188054	+	0.982159i	$0.439782\pi$
$163$	−183643.	+	565194.i	−0.541383	+	1.66621i	−0.729437	+	0.684048i	$0.760218\pi$
$164$	−133863.			−0.388642
$165$	−99159.4	−	19914.2i	−0.283546	−	0.0569445i
$166$	143054.			0.402930
$167$	80477.4	−	247684.i	0.223297	−	0.687237i	−0.775163	−	0.631761i	$-0.782332\pi$
$167$	80477.4	−	247684.i	0.223297	−	0.687237i	0.998460	−	0.0554760i	$-0.0176676\pi$
$168$	−165562.	+	120288.i	−0.452571	+	0.328812i
$169$	222879.	+	161931.i	0.600279	+	0.436128i
$170$	−49629.9	−	152745.i	−0.131711	−	0.405364i
$171$	−42550.7	−	130958.i	−0.111280	−	0.342484i
$172$	−91125.1	−	66206.3i	−0.234864	−	0.170639i
$173$	363003.	−	263737.i	0.922136	−	0.669971i	−0.0219186	−	0.999760i	$-0.506977\pi$
$173$	363003.	−	263737.i	0.922136	−	0.669971i	0.944055	+	0.329789i	$0.106977\pi$
$174$	43932.9	−	135212.i	0.110006	−	0.338564i
$175$	351670.			0.868040
$176$	331012.	+	359414.i	0.805493	+	0.874607i
$177$	−336293.			−0.806835
$178$	−49697.8	+	152954.i	−0.117568	+	0.361836i
$179$	398534.	−	289552.i	0.929679	−	0.675452i	−0.0162348	−	0.999868i	$-0.505168\pi$
$179$	398534.	−	289552.i	0.929679	−	0.675452i	0.945914	+	0.324417i	$0.105168\pi$
$180$	−14859.1	−	10795.8i	−0.0341831	−	0.0248355i
$181$	171460.	+	527701.i	0.389016	+	1.19727i	0.933525	+	0.358513i	$0.116716\pi$
$181$	171460.	+	527701.i	0.389016	+	1.19727i	−0.544509	+	0.838755i	$0.683284\pi$
$182$	−90987.2	−	280030.i	−0.203611	−	0.626651i
$183$	148907.	+	108187.i	0.328690	+	0.238808i
$184$	−351876.	+	255653.i	−0.766204	+	0.556680i
$185$	105113.	−	323503.i	0.225801	−	0.694943i
$186$	68757.3			0.145726
$187$	−246242.	−	267371.i	−0.514943	−	0.559127i
$188$	120906.			0.249490
$189$	33843.0	−	104158.i	0.0689150	−	0.212099i
$190$	−243866.	+	177179.i	−0.490080	+	0.356064i
$191$	−59841.4	−	43477.3i	−0.118691	−	0.0862342i	0.526856	−	0.849954i	$-0.323371\pi$
$191$	−59841.4	−	43477.3i	−0.118691	−	0.0862342i	−0.645547	+	0.763720i	$0.723371\pi$
$192$	−57877.3	−	178128.i	−0.113307	−	0.348722i
$193$	−241010.	−	741753.i	−0.465738	−	1.43340i	−0.858051	−	0.513564i	$-0.828325\pi$
$193$	−241010.	−	741753.i	−0.465738	−	1.43340i	0.392313	−	0.919832i	$-0.371675\pi$
$194$	−866307.	−	629409.i	−1.65260	−	1.20068i
$195$	−63106.8	+	45849.8i	−0.118847	+	0.0863477i
$196$	14418.8	−	44376.4i	0.0268095	−	0.0825110i
$197$	197885.			0.363285			0.181643	−	0.983365i	$-0.441859\pi$
$197$	197885.			0.363285			0.181643	+	0.983365i	$0.441859\pi$
$198$	−201809.	−	40529.2i	−0.365828	−	0.0734691i
$199$	75090.8			0.134417			0.0672084	−	0.997739i	$-0.478591\pi$
$199$	75090.8			0.134417			0.0672084	+	0.997739i	$0.478591\pi$
$200$	−109486.	+	336964.i	−0.193546	+	0.595674i
$201$	73757.6	−	53588.1i	0.128771	−	0.0935574i
$202$	−143358.	−	104155.i	−0.247196	−	0.179599i
$203$	−115810.	−	356428.i	−0.197246	−	0.607059i
$204$	−20397.9	−	62778.3i	−0.0343171	−	0.105617i
$205$	374506.	+	272095.i	0.622407	+	0.452205i
$206$	787849.	−	572406.i	1.29352	−	0.939801i
$207$	71927.9	−	221371.i	0.116673	−	0.359084i
$208$	376850.			0.603962
$209$	−334441.	+	594614.i	−0.529608	+	0.941606i
$210$	−239748.			−0.375152
$211$	−196695.	+	605364.i	−0.304149	+	0.936075i	0.675844	+	0.737045i	$0.263779\pi$
$211$	−196695.	+	605364.i	−0.304149	+	0.936075i	−0.979993	+	0.199030i	$0.936221\pi$
$212$	−109315.	+	79421.7i	−0.167047	+	0.121367i
$213$	123800.	+	89946.2i	0.186970	+	0.135842i
$214$	166008.	+	510920.i	0.247796	+	0.762638i
$215$	120366.	+	370449.i	0.177586	+	0.546553i
$216$	89266.1	+	64855.6i	0.130182	+	0.0945830i
$217$	146634.	−	106536.i	0.211390	−	0.153584i
$218$	233970.	−	720085.i	0.333441	−	1.02623i
$219$	629205.			0.886506
$220$	10529.0	+	90386.8i	0.0146667	+	0.125906i
$221$	−280342.			−0.386106
$222$	213925.	−	658392.i	0.291325	−	0.896607i
$223$	377838.	−	274515.i	0.508795	−	0.369661i	−0.303571	−	0.952809i	$-0.598179\pi$
$223$	377838.	−	274515.i	0.508795	−	0.369661i	0.812366	+	0.583147i	$0.198179\pi$
$224$	348386.	+	253117.i	0.463917	+	0.337055i
$225$	−58592.7	−	180330.i	−0.0771591	−	0.237471i
$226$	311481.	+	958640.i	0.405658	+	1.24849i
$227$	−352187.	−	255879.i	−0.453637	−	0.329586i	0.337393	−	0.941364i	$-0.390455\pi$
$227$	−352187.	−	255879.i	−0.453637	−	0.329586i	−0.791030	+	0.611777i	$0.790455\pi$
$228$	−100229.	+	72820.6i	−0.127690	+	0.0927721i
$229$	196019.	−	603285.i	0.247007	−	0.760210i	−0.748293	−	0.663369i	$-0.769126\pi$
$229$	196019.	−	603285.i	0.247007	−	0.760210i	0.995300	−	0.0968412i	$-0.0308739\pi$
$230$	−509548.			−0.635134
$231$	−493180.	+	226257.i	−0.608100	+	0.278980i
$232$	377579.			0.460562
$233$	−330548.	+	1.01732e6i	−0.398883	+	1.22763i	0.527014	+	0.849857i	$0.323312\pi$
$233$	−330548.	+	1.01732e6i	−0.398883	+	1.22763i	−0.925896	+	0.377778i	$0.876688\pi$
$234$	−128435.	+	93313.3i	−0.153335	+	0.111405i
$235$	−338257.	−	245758.i	−0.399555	−	0.290294i
$236$	93500.1	+	287764.i	0.109278	+	0.336323i
$237$	132073.	+	406479.i	0.152737	+	0.470075i
$238$	−697079.	−	506457.i	−0.797700	−	0.579563i
$239$	−1.22620e6	+	890886.i	−1.38857	+	1.00885i	−0.392544	+	0.919733i	$0.628405\pi$
$239$	−1.22620e6	+	890886.i	−1.38857	+	1.00885i	−0.996021	+	0.0891186i	$0.971595\pi$
$240$	94821.7	−	291831.i	0.106262	−	0.327042i
$241$	245818.			0.272628			0.136314	−	0.990666i	$-0.456474\pi$
$241$	245818.			0.272628			0.136314	+	0.990666i	$0.456474\pi$
$242$	529643.	+	871496.i	0.581360	+	0.956593i
$243$	−59049.0			−0.0641500
$244$	51174.2	−	157498.i	0.0550271	−	0.169356i
$245$	−130540.	+	94843.2i	−0.138941	+	0.100946i
$246$	762193.	+	553765.i	0.803021	+	0.583429i
$247$	162593.	+	500410.i	0.169574	+	0.521896i
$248$	56428.8	+	173670.i	0.0582602	+	0.179306i
$249$	−164491.	−	119509.i	−0.168129	−	0.122153i
$250$	−784099.	+	569682.i	−0.793453	+	0.576477i
$251$	213164.	−	656050.i	0.213564	−	0.657283i	−0.785688	−	0.618623i	$-0.787691\pi$
$251$	213164.	−	656050.i	0.213564	−	0.657283i	0.999252	−	0.0386605i	$-0.0123091\pi$
$252$	−98536.6			−0.0977454
$253$	−1.04818e6	+	480875.i	−1.02952	+	0.472314i
$254$	952352.			0.926218
$255$	−70538.7	+	217096.i	−0.0679324	+	0.209074i
$256$	−606237.	+	440457.i	−0.578152	+	0.420052i
$257$	−991734.	−	720537.i	−0.936618	−	0.680493i	0.0109863	−	0.999940i	$-0.496503\pi$
$257$	−991734.	−	720537.i	−0.936618	−	0.680493i	−0.947604	+	0.319447i	$0.896503\pi$
$258$	244968.	+	753935.i	0.229119	+	0.705155i
$259$	−563920.	−	1.73557e6i	−0.522358	−	1.60765i
$260$	56779.1	+	41252.4i	0.0520900	+	0.0378456i
$261$	−163474.	+	118771.i	−0.148542	+	0.107922i
$262$	659145.	−	2.02864e6i	0.593236	−	1.82579i
$263$	−941210.			−0.839068			−0.419534	−	0.907740i	$-0.637807\pi$
$263$	−941210.			−0.839068			−0.419534	+	0.907740i	$0.637807\pi$
$264$	−63253.2	−	542999.i	−0.0558563	−	0.479500i
$265$	467263.			0.408740
$266$	−499734.	+	1.53802e6i	−0.433047	+	1.33278i
$267$	184925.	−	134356.i	0.158752	−	0.115340i
$268$	−66361.9	−	48214.7i	−0.0564393	−	0.0410056i
$269$	−331386.	−	1.01990e6i	−0.279225	−	0.859365i	−0.988071	−	0.154002i	$-0.950784\pi$
$269$	−331386.	−	1.01990e6i	−0.279225	−	0.859365i	0.708846	−	0.705363i	$-0.249216\pi$
$270$	39945.2	+	122939.i	0.0333469	+	0.102631i
$271$	275315.	+	200028.i	0.227723	+	0.165451i	0.695796	−	0.718239i	$-0.255052\pi$
$271$	275315.	+	200028.i	0.227723	+	0.165451i	−0.468073	+	0.883690i	$0.655052\pi$
$272$	892179.	−	648206.i	0.731189	−	0.531240i
$273$	−129320.	+	398005.i	−0.105016	+	0.323207i
$274$	1.98061e6			1.59376
$275$	−460529.	+	818789.i	−0.367219	+	0.652890i
$276$	−209424.			−0.165483
$277$	521981.	−	1.60649e6i	0.408748	−	1.25800i	−0.508977	−	0.860780i	$-0.669976\pi$
$277$	521981.	−	1.60649e6i	0.408748	−	1.25800i	0.917725	−	0.397216i	$-0.130024\pi$
$278$	1.42256e6	−	1.03355e6i	1.10397	−	0.802081i
$279$	−79060.6	−	57440.9i	−0.0608064	−	0.0441785i
$280$	−196760.	−	605566.i	−0.149983	−	0.461601i
$281$	−54846.3	−	168799.i	−0.0414363	−	0.127528i	0.928198	−	0.372086i	$-0.121357\pi$
$281$	−54846.3	−	168799.i	−0.0414363	−	0.127528i	−0.969635	+	0.244558i	$0.921357\pi$
$282$	−688418.	−	500165.i	−0.515501	−	0.374533i
$283$	−1.64475e6	+	1.19498e6i	−1.22077	+	0.886944i	−0.996164	−	0.0875050i	$-0.972111\pi$
$283$	−1.64475e6	+	1.19498e6i	−1.22077	+	0.886944i	−0.224609	+	0.974449i	$0.572111\pi$
$284$	42545.9	−	130943.i	0.0313013	−	0.0963355i
$285$	428427.			0.312439
$286$	771144.	+	154869.i	0.557468	+	0.111956i
$287$	2.48350e6			1.77975
$288$	71748.3	−	220818.i	0.0509718	−	0.156875i
$289$	484989.	−	352365.i	0.341576	−	0.248170i
$290$	357865.	+	260004.i	0.249876	+	0.181545i
$291$	470306.	+	1.44745e6i	0.325572	+	1.00201i
$292$	−174939.	−	538406.i	−0.120068	−	0.369533i
$293$	595077.	+	432349.i	0.404953	+	0.294215i	0.771555	−	0.636162i	$-0.219479\pi$
$293$	595077.	+	432349.i	0.404953	+	0.294215i	−0.366603	+	0.930378i	$0.619479\pi$
$294$	−265675.	+	193024.i	−0.179260	+	0.130240i
$295$	323336.	−	995124.i	0.216321	−	0.665767i
$296$	1.83856e6			1.21969
$297$	198191.	+	215196.i	0.130374	+	0.141561i
$298$	−2.57885e6			−1.68223
$299$	−274848.	+	845896.i	−0.177793	+	0.547191i
$300$	−138016.	+	100275.i	−0.0885375	+	0.0643263i
$301$	1.69061e6	+	1.22830e6i	1.07554	+	0.781425i
$302$	−1.07923e6	−	3.32153e6i	−0.680921	−	2.09566i
$303$	77826.7	+	239526.i	0.0486992	+	0.149881i
$304$	−1.67450e6	−	1.21659e6i	−1.03920	−	0.755025i
$305$	−463306.	+	336611.i	−0.285179	+	0.207195i
$306$	−143560.	+	441832.i	−0.0876455	+	0.269745i
$307$	272950.			0.165286			0.0826431	−	0.996579i	$-0.473664\pi$
$307$	272950.			0.165286			0.0826431	+	0.996579i	$0.473664\pi$
$308$	330726.	+	359104.i	0.198652	+	0.215697i
$309$	−1.38410e6			−0.824655
$310$	−66108.1	+	203460.i	−0.0390706	+	0.120247i
$311$	772254.	−	561075.i	0.452751	−	0.328943i	−0.337930	−	0.941171i	$-0.609727\pi$
$311$	772254.	−	561075.i	0.452751	−	0.328943i	0.790681	+	0.612228i	$0.209727\pi$
$312$	−341100.	−	247824.i	−0.198379	−	0.144131i
$313$	−584705.	−	1.79954e6i	−0.337346	−	1.03825i	−0.965555	−	0.260200i	$-0.916211\pi$
$313$	−584705.	−	1.79954e6i	−0.337346	−	1.03825i	0.628208	−	0.778045i	$-0.283789\pi$
$314$	442716.	+	1.36254e6i	0.253397	+	0.779875i
$315$	275675.	+	200289.i	0.156538	+	0.113732i
$316$	311101.	−	226028.i	0.175260	−	0.127334i
$317$	−390811.	+	1.20279e6i	−0.218433	+	0.672267i	0.780459	+	0.625207i	$0.214985\pi$
$317$	−390811.	+	1.20279e6i	−0.218433	+	0.672267i	−0.998892	+	0.0470606i	$0.985015\pi$
$318$	950972.			0.527351
$319$	981527.	+	197120.i	0.540039	+	0.108456i
$320$	582746.			0.318130
$321$	235946.	−	726167.i	0.127806	−	0.393345i
$322$	−2.21159e6	+	1.60682e6i	−1.18868	+	0.863628i
$323$	1.24567e6	+	905033.i	0.664350	+	0.482679i
$324$	16417.5	+	50527.8i	0.00868849	+	0.0267404i
$325$	223892.	+	689070.i	0.117579	+	0.361872i
$326$	−3.04444e6	−	2.21192e6i	−1.58659	−	1.15272i
$327$	−870600.	+	632528.i	−0.450246	+	0.327123i
$328$	−773195.	+	2.37965e6i	−0.396830	+	1.22132i
$329$	−2.24311e6			−1.14251
$330$	313963.	−	558204.i	0.158706	−	0.282168i
$331$	−1.29373e6			−0.649042			−0.324521	−	0.945878i	$-0.605203\pi$
$331$	−1.29373e6			−0.649042			−0.324521	+	0.945878i	$0.605203\pi$
$332$	−56529.8	+	173981.i	−0.0281470	+	0.0866277i
$333$	−796012.	+	578336.i	−0.393377	+	0.285805i
$334$	1.33416e6	+	969324.i	0.654398	+	0.475448i
$335$	87656.7	+	269779.i	0.0426749	+	0.131340i
$336$	−508711.	−	1.56565e6i	−0.245823	−	0.756565i
$337$	1.15898e6	+	842046.i	0.555904	+	0.403888i	0.829958	−	0.557826i	$-0.188365\pi$
$337$	1.15898e6	+	842046.i	0.555904	+	0.403888i	−0.274053	+	0.961714i	$0.588365\pi$
$338$	−1.41133e6	+	1.02539e6i	−0.671950	+	0.488200i
$339$	442706.	−	1.36251e6i	0.209226	−	0.643932i
$340$	205379.			0.0963517
$341$	56021.7	+	480920.i	0.0260898	+	0.223968i
$342$	871933.			0.403105
$343$	512740.	−	1.57805e6i	0.235322	−	0.724245i
$344$	−1.70328e6	+	1.23750e6i	−0.776049	+	0.563832i
$345$	585903.	+	425684.i	0.265020	+	0.192548i
$346$	877999.	+	2.70220e6i	0.394279	+	1.21347i
$347$	−787144.	−	2.42258e6i	−0.350938	−	1.08008i	−0.958327	−	0.285672i	$-0.907783\pi$
$347$	−787144.	−	2.42258e6i	−0.350938	−	1.08008i	0.607389	−	0.794404i	$-0.292217\pi$
$348$	147082.	+	106862.i	0.0651048	+	0.0473014i
$349$	1.21385e6	−	881910.i	0.533458	−	0.387580i	−0.288192	−	0.957573i	$-0.593054\pi$
$349$	1.21385e6	−	881910.i	0.533458	−	0.387580i	0.821650	+	0.569993i	$0.193054\pi$
$350$	−688139.	+	2.11787e6i	−0.300266	+	0.924123i
$351$	225636.			0.0977553
$352$	−1.04556e6	+	479674.i	−0.449771	+	0.206343i
$353$	1.30139e6			0.555868			0.277934	−	0.960600i	$-0.410350\pi$
$353$	1.30139e6			0.555868			0.277934	+	0.960600i	$0.410350\pi$
$354$	658051.	−	2.02527e6i	0.279094	−	0.858964i
$355$	−385190.	+	279857.i	−0.162220	+	0.117860i
$356$	−166383.	−	120884.i	−0.0695798	−	0.0505527i
$357$	378434.	+	1.16470e6i	0.157152	+	0.483664i
$358$	963939.	+	2.96670e6i	0.397504	+	1.22339i
$359$	1.16326e6	+	845155.i	0.476364	+	0.346099i	0.799916	−	0.600111i	$-0.204877\pi$
$359$	1.16326e6	+	845155.i	0.476364	+	0.346099i	−0.323552	+	0.946210i	$0.604877\pi$
$360$	−277741.	+	201790.i	−0.112949	+	0.0820624i
$361$	127862.	−	393519.i	0.0516386	−	0.158927i
$362$	−3.51350e6			−1.40919
$363$	119051.	−	1.44456e6i	0.0474205	−	0.575400i
$364$	376525.			0.148950
$365$	−604961.	+	1.86188e6i	−0.237682	+	0.731508i
$366$	−942918.	+	685070.i	−0.367935	+	0.267320i
$367$	3.13489e6	+	2.27763e6i	1.21495	+	0.882711i	0.995671	−	0.0929523i	$-0.0296304\pi$
$367$	3.13489e6	+	2.27763e6i	1.21495	+	0.882711i	0.219276	+	0.975663i	$0.429630\pi$
$368$	−1.08118e6	−	3.32754e6i	−0.416179	−	1.28087i
$369$	−413783.	−	1.27349e6i	−0.158200	−	0.486890i
$370$	1.74257e6	+	1.26605e6i	0.661736	+	0.480779i
$371$	2.02807e6	−	1.47348e6i	0.764976	−	0.555787i
$372$	−27170.4	+	83622.0i	−0.0101798	+	0.0313302i
$373$	−2.44643e6			−0.910459			−0.455229	−	0.890374i	$-0.650443\pi$
$373$	−2.44643e6			−0.910459			−0.455229	+	0.890374i	$0.650443\pi$
$374$	2.09204e6	−	959771.i	0.773377	−	0.354804i
$375$	1.37752e6			0.505847
$376$	698355.	−	2.14932e6i	0.254746	−	0.784027i
$377$	624662.	−	453843.i	0.226356	−	0.164457i
$378$	561051.	+	407628.i	0.201964	+	0.146735i
$379$	−831534.	−	2.55920e6i	−0.297360	−	0.915179i	−0.982419	−	0.186691i	$-0.940224\pi$
$379$	−831534.	−	2.55920e6i	−0.297360	−	0.915179i	0.685059	−	0.728488i	$-0.259776\pi$
$380$	−119116.	−	366602.i	−0.0423168	−	0.130238i
$381$	−1.09506e6	−	795609.i	−0.386479	−	0.280794i
$382$	378932.	−	275310.i	0.132862	−	0.0965303i
$383$	548276.	−	1.68742e6i	0.190986	−	0.587795i	−0.809014	−	0.587790i	$-0.799998\pi$
$383$	548276.	−	1.68742e6i	0.190986	−	0.587795i	1.00000		5.63705e-6i	$-1.79433e-6\pi$
$384$	2.01154e6			0.696146
$385$	−195341.	−	1.67691e6i	−0.0671647	−	0.576577i
$386$	4.93869e6			1.68711
$387$	348172.	−	1.07156e6i	0.118172	−	0.363697i
$388$	1.10781e6	−	804874.i	0.373584	−	0.271424i
$389$	−2.09377e6	−	1.52122e6i	−0.701545	−	0.509703i	0.178890	−	0.983869i	$-0.442749\pi$
$389$	−2.09377e6	−	1.52122e6i	−0.701545	−	0.509703i	−0.880435	+	0.474167i	$0.842749\pi$
$390$	−152637.	−	469769.i	−0.0508158	−	0.156395i
$391$	804302.	+	2.47539e6i	0.266059	+	0.818845i
$392$	−705587.	−	512639.i	−0.231919	−	0.168499i
$393$	−2.45267e6	+	1.78197e6i	−0.801047	+	0.581995i
$394$	−387217.	+	1.19173e6i	−0.125665	+	0.386757i
$395$	−1.32980e6			−0.428837
$396$	129039.	−	229422.i	0.0413506	−	0.0735186i
$397$	−4.92643e6			−1.56876			−0.784378	−	0.620283i	$-0.787018\pi$
$397$	−4.92643e6			−1.56876			−0.784378	+	0.620283i	$0.787018\pi$
$398$	−146936.	+	452222.i	−0.0464965	+	0.143101i
$399$	1.85951e6	−	1.35101e6i	0.584744	−	0.424841i
$400$	−2.30580e6	−	1.67526e6i	−0.720562	−	0.523519i
$401$	516517.	+	1.58968e6i	0.160407	+	0.493683i	0.998669	−	0.0515859i	$-0.0164276\pi$
$401$	516517.	+	1.58968e6i	0.160407	+	0.493683i	−0.838261	+	0.545269i	$0.816428\pi$
$402$	178398.	+	549054.i	0.0550587	+	0.169453i
$403$	302104.	+	219491.i	0.0926602	+	0.0673216i
$404$	183323.	−	133192.i	0.0558808	−	0.0405998i
$405$	56773.8	−	174732.i	0.0171993	−	0.0529340i
$406$	2.37314e6			0.714511
$407$	4.77939e6	+	959843.i	1.43017	+	0.287220i
$408$	−1.23382e6			−0.366944
$409$	383159.	−	1.17924e6i	0.113258	−	0.348574i	−0.878321	−	0.478071i	$-0.841336\pi$
$409$	383159.	−	1.17924e6i	0.113258	−	0.348574i	0.991580	+	0.129497i	$0.0413363\pi$
$410$	−2.37147e6	+	1.72297e6i	−0.696720	+	0.506197i
$411$	−2.27740e6	−	1.65463e6i	−0.665021	−	0.483166i
$412$	384825.	+	1.18437e6i	0.111691	+	0.343751i
$413$	−1.73467e6	−	5.33876e6i	−0.500428	−	1.54016i
$414$	1.19243e6	+	866349.i	0.341925	+	0.248423i
$415$	511793.	−	371840.i	0.145873	−	0.105983i
$416$	−274162.	+	843783.i	−0.0776736	+	0.239055i
$417$	−2.49917e6			−0.703809
$418$	−2.92654e6	−	3.17765e6i	−0.819245	−	0.889539i
$419$	191033.			0.0531586			0.0265793	−	0.999647i	$-0.491539\pi$
$419$	191033.			0.0531586			0.0265793	+	0.999647i	$0.491539\pi$
$420$	94740.0	−	291580.i	0.0262066	−	0.0806555i
$421$	1.78615e6	−	1.29772e6i	0.491149	−	0.356841i	−0.314477	−	0.949265i	$-0.601829\pi$
$421$	1.78615e6	−	1.29772e6i	0.491149	−	0.356841i	0.805626	+	0.592424i	$0.201829\pi$
$422$	−3.26082e6	−	2.36913e6i	−0.891345	−	0.647600i
$423$	373732.	+	1.15023e6i	0.101557	+	0.312560i
$424$	780458.	+	2.40200e6i	0.210831	+	0.648872i
$425$	1.71530e6	+	1.24624e6i	0.460647	+	0.334680i
$426$	−783936.	+	569563.i	−0.209294	+	0.152061i
$427$	−949414.	+	2.92199e6i	−0.251991	+	0.775550i
$428$	−686977.			−0.181273
$429$	−757320.	−	822300.i	−0.198672	−	0.215718i
$430$	−2.46650e6			−0.643294
$431$	−915536.	+	2.81773e6i	−0.237401	+	0.730645i	0.759393	+	0.650632i	$0.225496\pi$
$431$	−915536.	+	2.81773e6i	−0.237401	+	0.730645i	−0.996794	+	0.0800127i	$0.974504\pi$
$432$	−718079.	+	521715.i	−0.185124	+	0.134501i
$433$	4.22810e6	+	3.07190e6i	1.08374	+	0.787384i	0.978332	−	0.207045i	$-0.0663845\pi$
$433$	4.22810e6	+	3.07190e6i	1.08374	+	0.787384i	0.105410	+	0.994429i	$0.466385\pi$
$434$	354664.	+	1.09154e6i	0.0903843	+	0.278174i
$435$	−194280.	−	597931.i	−0.0492271	−	0.151505i
$436$	783304.	+	569104.i	0.197340	+	0.143376i
$437$	3.95209e6	−	2.87136e6i	0.989973	−	0.719258i
$438$	−1.23121e6	+	3.78929e6i	−0.306654	+	0.943783i
$439$	−5.62144e6			−1.39215			−0.696075	−	0.717969i	$-0.745072\pi$
$439$	−5.62144e6			−1.39215			−0.696075	+	0.717969i	$0.745072\pi$
$440$	1.66760e6	+	334904.i	0.410640	+	0.0824686i
$441$	466742.			0.114283
$442$	548566.	−	1.68831e6i	0.133559	−	0.411052i
$443$	5.18608e6	−	3.76791e6i	1.25554	−	0.912202i	0.257008	−	0.966409i	$-0.417263\pi$
$443$	5.18608e6	−	3.76791e6i	1.25554	−	0.912202i	0.998530	+	0.0542077i	$0.0172633\pi$
$444$	716195.	+	520346.i	0.172414	+	0.125266i
$445$	219773.	+	676391.i	0.0526107	+	0.161919i
$446$	913879.	+	2.81263e6i	0.217546	+	0.669539i
$447$	2.96529e6	+	2.15441e6i	0.701937	+	0.509987i
$448$	2.52930e6	−	1.83764e6i	0.595394	−	0.432579i
$449$	−884100.	+	2.72098e6i	−0.206960	+	0.636956i	0.792668	+	0.609654i	$0.208692\pi$
$449$	−884100.	+	2.72098e6i	−0.206960	+	0.636956i	−0.999627	+	0.0273020i	$0.991308\pi$
$450$	1.20066e6			0.279505
$451$	−3.25227e6	+	5.78231e6i	−0.752913	+	1.33863i
$452$	−1.28898e6			−0.296755
$453$	−1.53390e6	+	4.72087e6i	−0.351198	+	1.08088i
$454$	2.23014e6	−	1.62029e6i	0.507800	−	0.368938i
$455$	−1.05340e6	−	765338.i	−0.238542	−	0.173311i
$456$	715592.	+	2.20236e6i	0.161158	+	0.495995i
$457$	−978169.	−	3.01049e6i	−0.219090	−	0.674291i	−0.998838	−	0.0481967i	$-0.984653\pi$
$457$	−978169.	−	3.01049e6i	−0.219090	−	0.674291i	0.779748	−	0.626094i	$-0.215347\pi$
$458$	3.24962e6	+	2.36099e6i	0.723884	+	0.525932i
$459$	534185.	−	388108.i	0.118348	−	0.0859847i
$460$	201355.	−	619707.i	0.0443678	−	0.136550i
$461$	−3.58110e6			−0.784810			−0.392405	−	0.919792i	$-0.628357\pi$
$461$	−3.58110e6			−0.784810			−0.392405	+	0.919792i	$0.628357\pi$
$462$	−397556.	−	3.41283e6i	−0.0866550	−	0.743892i
$463$	−1.60994e6			−0.349025			−0.174513	−	0.984655i	$-0.555835\pi$
$463$	−1.60994e6			−0.349025			−0.174513	+	0.984655i	$0.555835\pi$
$464$	−938591.	+	2.88868e6i	−0.202386	+	0.622881i
$465$	245988.	−	178720.i	0.0527571	−	0.0383303i
$466$	−5.47986e6	−	3.98135e6i	−1.16897	−	0.849308i
$467$	2.18073e6	+	6.71161e6i	0.462712	+	1.42408i	0.861838	+	0.507184i	$0.169314\pi$
$467$	2.18073e6	+	6.71161e6i	0.462712	+	1.42408i	−0.399126	+	0.916896i	$0.630686\pi$
$468$	−62733.9	−	193075.i	−0.0132400	−	0.0407485i
$469$	1.23118e6	+	894508.i	0.258459	+	0.187781i
$470$	2.14193e6	−	1.55620e6i	0.447261	−	0.324954i
$471$	629229.	−	1.93657e6i	0.130694	−	0.402236i
$472$	5.65557e6			1.16848
$473$	−5.07377e6	+	2.32771e6i	−1.04274	+	0.478382i
$474$	−2.70639e6			−0.553280
$475$	1.22970e6	−	3.78461e6i	0.250071	−	0.769640i
$476$	891409.	−	647647.i	0.180327	−	0.131015i
$477$	−1.09347e6	−	794456.i	−0.220046	−	0.159873i
$478$	−2.96582e6	−	9.12785e6i	−0.593711	−	1.82725i
$479$	1.85220e6	+	5.70050e6i	0.368850	+	1.13520i	0.947535	+	0.319653i	$0.103566\pi$
$479$	1.85220e6	+	5.70050e6i	0.368850	+	1.13520i	−0.578685	+	0.815551i	$0.696434\pi$
$480$	584440.	+	424620.i	0.115781	+	0.0841197i
$481$	3.04169e6	−	2.20992e6i	0.599449	−	0.435525i
$482$	−481011.	+	1.48040e6i	−0.0943055	+	0.290242i
$483$	3.88536e6			0.757815
$484$	−1.26920e6	+	299763.i	−0.246273	+	0.0581653i
$485$	−4.73534e6			−0.914106
$486$	115546.	−	355613.i	0.0221903	−	0.0682947i
$487$	−3.69276e6	+	2.68295e6i	−0.705552	+	0.512614i	−0.881736	−	0.471744i	$-0.843625\pi$
$487$	−3.69276e6	+	2.68295e6i	−0.705552	+	0.512614i	0.176184	+	0.984357i	$0.443625\pi$
$488$	−2.50423e6	−	1.81943e6i	−0.476019	−	0.345848i
$489$	1.65279e6	+	5.08675e6i	0.312568	+	0.961985i
$490$	−315739.	−	971746.i	−0.0594071	−	0.182836i
$491$	−4.34031e6	−	3.15342e6i	−0.812487	−	0.590307i	0.102063	−	0.994778i	$-0.467456\pi$
$491$	−4.34031e6	−	3.15342e6i	−0.812487	−	0.590307i	−0.914551	+	0.404471i	$0.867456\pi$
$492$	−974675.	+	708143.i	−0.181530	+	0.131889i
$493$	698225.	−	2.14892e6i	0.129383	−	0.398201i
$494$	−3.33180e6			−0.614273
$495$	−827342.	+	379562.i	−0.151765	+	0.0696257i
$496$	−1.46894e6			−0.268102
$497$	−789337.	+	2.42933e6i	−0.143341	+	0.441159i
$498$	1.04160e6	−	756766.i	0.188203	−	0.136738i
$499$	−5.82416e6	−	4.23150e6i	−1.04709	−	0.760752i	−0.0754296	−	0.997151i	$-0.524033\pi$
$499$	−5.82416e6	−	4.23150e6i	−1.04709	−	0.760752i	−0.971656	+	0.236399i	$0.924033\pi$
$500$	−382993.	−	1.17873e6i	−0.0685119	−	0.210858i
$501$	−724296.	−	2.22915e6i	−0.128920	−	0.396776i
$502$	3.53384e6	+	2.56749e6i	0.625876	+	0.454725i
$503$	3.88163e6	−	2.82017e6i	0.684060	−	0.496999i	−0.190642	−	0.981660i	$-0.561057\pi$
$503$	3.88163e6	−	2.82017e6i	0.684060	−	0.496999i	0.874702	+	0.484661i	$0.161057\pi$
$504$	−569150.	+	1.75167e6i	−0.0998046	+	0.307167i
$505$	−783609.			−0.136732
$506$	−844944.	−	7.25344e6i	−0.146707	−	1.25941i
$507$	2.47945e6			0.428385
$508$	−376336.	+	1.15824e6i	−0.0647017	+	0.199132i
$509$	−1.99220e6	+	1.44742e6i	−0.340831	+	0.247628i	−0.745012	−	0.667051i	$-0.767557\pi$
$509$	−1.99220e6	+	1.44742e6i	−0.340831	+	0.247628i	0.404181	+	0.914679i	$0.367557\pi$
$510$	−1.16940e6	−	849616.i	−0.199084	−	0.144643i
$511$	3.24557e6	+	9.98882e6i	0.549842	+	1.69224i
$512$	743820.	+	2.28924e6i	0.125399	+	0.385938i
$513$	−1.00259e6	−	728426.i	−0.168202	−	0.122206i
$514$	6.27992e6	−	4.56263e6i	1.04845	−	0.761741i
$515$	1.33077e6	−	4.09570e6i	0.221099	−	0.680472i
$516$	−1.01373e6			−0.167610
$517$	2.93747e6	−	5.22262e6i	0.483334	−	0.859335i
$518$	1.15556e7			1.89221
$519$	1.24789e6	−	3.84062e6i	0.203357	−	0.625869i
$520$	1.06129e6	−	771074.i	0.172118	−	0.125051i
$521$	−8.21678e6	−	5.96984e6i	−1.32619	−	0.963537i	−0.999833	−	0.0182917i	$-0.994177\pi$
$521$	−8.21678e6	−	5.96984e6i	−1.32619	−	0.963537i	−0.326362	−	0.945245i	$-0.605823\pi$
$522$	−395397.	−	1.21691e6i	−0.0635121	−	0.195470i
$523$	691516.	+	2.12827e6i	0.110547	+	0.340229i	0.990992	−	0.133919i	$-0.0427561\pi$
$523$	691516.	+	2.12827e6i	0.110547	+	0.340229i	−0.880445	+	0.474148i	$0.842756\pi$
$524$	2.20674e6	+	1.60329e6i	0.351094	+	0.255084i
$525$	2.56056e6	−	1.86036e6i	0.405449	−	0.294576i
$526$	1.84174e6	−	5.66829e6i	0.290244	−	0.893280i
$527$	1.09276e6			0.171395
$528$	4.31147e6	+	865872.i	0.673040	+	0.135166i
$529$	1.82138e6			0.282984
$530$	−914330.	+	2.81402e6i	−0.141388	+	0.435148i
$531$	−2.44860e6	+	1.77901e6i	−0.376862	+	0.273806i
$532$	−1.67305e6	−	1.21554e6i	−0.256289	−	0.186205i
$533$	1.58113e6	+	4.86623e6i	0.241074	+	0.741950i
$534$	447280.	+	1.37659e6i	0.0678776	+	0.208906i
$535$	1.92195e6	+	1.39638e6i	0.290306	+	0.210920i
$536$	−1.24041e6	+	901212.i	−0.186489	+	0.135492i
$537$	1.37004e6	−	4.21655e6i	0.205021	−	0.630988i
$538$	6.79065e6			1.01148
$539$	−1.56656e6	−	1.70098e6i	−0.232261	−	0.252190i
$540$	−165302.			−0.0243946
$541$	448295.	−	1.37971e6i	0.0658523	−	0.202673i	−0.912716	−	0.408594i	$-0.866019\pi$
$541$	448295.	−	1.37971e6i	0.0658523	−	0.202673i	0.978569	+	0.205922i	$0.0660192\pi$
$542$	−1.74337e6	+	1.26663e6i	−0.254912	+	0.185205i
$543$	4.04000e6	+	2.93523e6i	0.588007	+	0.427212i
$544$	802293.	+	2.46920e6i	0.116235	+	0.357734i
$545$	−1.03466e6	−	3.18435e6i	−0.149213	−	0.459229i
$546$	−2.14387e6	−	1.55761e6i	−0.307763	−	0.223603i
$547$	−866951.	+	629877.i	−0.123887	+	0.0900093i	−0.648003	−	0.761637i	$-0.724396\pi$
$547$	−866951.	+	629877.i	−0.123887	+	0.0900093i	0.524116	+	0.851647i	$0.324396\pi$
$548$	−782666.	+	2.40880e6i	−0.111333	+	0.342649i
$549$	1.65653e6			0.234568
$550$	−4.02987e6	−	4.37565e6i	−0.568048	−	0.616788i
$551$	−4.24078e6			−0.595068
$552$	−1.20964e6	+	3.72289e6i	−0.168970	+	0.520035i
$553$	−5.77173e6	+	4.19340e6i	−0.802588	+	0.583115i
$554$	8.65345e6	+	6.28710e6i	1.19788	+	0.870313i
$555$	−946013.	−	2.91153e6i	−0.130366	−	0.401226i
$556$	694847.	+	2.13852e6i	0.0953240	+	0.293377i
$557$	768386.	+	558265.i	0.104940	+	0.0762434i	0.639018	−	0.769192i	$-0.279341\pi$
$557$	768386.	+	558265.i	0.104940	+	0.0762434i	−0.534078	+	0.845435i	$0.679341\pi$
$558$	500633.	−	363731.i	0.0680665	−	0.0494532i
$559$	−1.33042e6	+	4.09462e6i	−0.180078	+	0.554222i
$560$	5.12202e6			0.690194
$561$	−3.20734e6	−	644129.i	−0.430267	−	0.0864104i
$562$	1.12389e6			0.150101
$563$	1.06534e6	−	3.27877e6i	0.141650	−	0.435953i	−0.854915	−	0.518768i	$-0.826391\pi$
$563$	1.06534e6	−	3.27877e6i	0.141650	−	0.435953i	0.996565	+	0.0828145i	$0.0263909\pi$
$564$	880334.	−	639600.i	0.116533	−	0.0846663i
$565$	3.60615e6	+	2.62002e6i	0.475250	+	0.345290i
$566$	−3.97818e6	−	1.22436e7i	−0.521968	−	1.60645i
$567$	−304587.	−	937421.i	−0.0397881	−	0.122455i
$568$	−2.08200e6	−	1.51266e6i	−0.270776	−	0.196730i
$569$	−2.06773e6	+	1.50229e6i	−0.267740	+	0.194524i	−0.713552	−	0.700602i	$-0.752915\pi$
$569$	−2.06773e6	+	1.50229e6i	−0.267740	+	0.194524i	0.445812	+	0.895126i	$0.352915\pi$
$570$	−838337.	+	2.58014e6i	−0.108077	+	0.332625i
$571$	−9.29638e6			−1.19323			−0.596614	−	0.802528i	$-0.703488\pi$
$571$	−9.29638e6			−1.19323			−0.596614	+	0.802528i	$0.703488\pi$
$572$	−493078.	+	876659.i	−0.0630123	+	0.112032i
$573$	−665712.			−0.0847033
$574$	−4.85966e6	+	1.49565e7i	−0.615639	+	1.89474i
$575$	5.44207e6	−	3.95390e6i	0.686427	−	0.498719i
$576$	−1.36372e6	−	990803.i	−0.171266	−	0.124432i
$577$	3.47832e6	+	1.07052e7i	0.434941	+	1.33861i	0.893147	+	0.449765i	$0.148492\pi$
$577$	3.47832e6	+	1.07052e7i	0.434941	+	1.33861i	−0.458206	+	0.888846i	$0.651508\pi$
$578$	1.17305e6	+	3.61027e6i	0.146048	+	0.449490i
$579$	−5.67876e6	−	4.12586e6i	−0.703974	−	0.511467i
$580$	−457629.	+	332487.i	−0.0564864	+	0.0410398i
$581$	1.04877e6	−	3.22780e6i	0.128897	−	0.396703i
$582$	−9.63733e6			−1.17937
$583$	774827.	+	6.65152e6i	0.0944133	+	0.810494i
$584$	−1.05816e7			−1.28386
$585$	−216942.	+	667679.i	−0.0262092	+	0.0806637i
$586$	−3.76819e6	+	2.73775e6i	−0.453303	+	0.329344i
$587$	−5.08801e6	−	3.69666e6i	−0.609470	−	0.442806i	0.239757	−	0.970833i	$-0.422932\pi$
$587$	−5.08801e6	−	3.69666e6i	−0.609470	−	0.442806i	−0.849228	+	0.528027i	$0.822932\pi$
$588$	−129769.	−	399388.i	−0.0154785	−	0.0476378i
$589$	−633781.	−	1.95058e6i	−0.0752750	−	0.231673i
$590$	5.36028e6	+	3.89447e6i	0.633954	+	0.460594i
$591$	1.44083e6	−	1.04683e6i	0.169685	−	0.123284i
$592$	−4.57032e6	+	1.40660e7i	−0.535972	+	1.64955i
$593$	4.49257e6			0.524636			0.262318	−	0.964982i	$-0.415513\pi$
$593$	4.49257e6			0.524636			0.262318	+	0.964982i	$0.415513\pi$
$594$	−1.68380e6	+	772482.i	−0.195805	+	0.0898302i
$595$	−3.81032e6			−0.441234
$596$	1.01907e6	−	3.13637e6i	0.117514	−	0.361670i
$597$	546747.	−	397235.i	0.0627843	−	0.0456154i
$598$	−4.55646e6	−	3.31046e6i	−0.521044	−	0.378561i
$599$	−973092.	−	2.99487e6i	−0.110812	−	0.341044i	0.880239	−	0.474532i	$-0.157383\pi$
$599$	−973092.	−	2.99487e6i	−0.110812	−	0.341044i	−0.991051	+	0.133487i	$0.957383\pi$
$600$	985377.	+	3.03268e6i	0.111744	+	0.343913i
$601$	829502.	+	602669.i	0.0936766	+	0.0680601i	0.633638	−	0.773630i	$-0.281561\pi$
$601$	829502.	+	602669.i	0.0936766	+	0.0680601i	−0.539961	+	0.841690i	$0.681561\pi$
$602$	−1.07054e7	+	7.77790e6i	−1.20395	+	0.874724i
$603$	253556.	−	780366.i	0.0283976	−	0.0873987i
$604$	4.46609e6			0.498121
$605$	4.16014e6	+	1.74118e6i	0.462082	+	0.193400i
$606$	−1.59480e6			−0.176410
$607$	1.29514e6	−	3.98603e6i	0.142674	−	0.439106i	−0.854031	−	0.520223i	$-0.825849\pi$
$607$	1.29514e6	−	3.98603e6i	0.142674	−	0.439106i	0.996705	+	0.0811174i	$0.0258489\pi$
$608$	3.94222e6	−	2.86419e6i	0.432496	−	0.314227i
$609$	−2.72876e6	−	1.98256e6i	−0.298141	−	0.216612i
$610$	−1.12060e6	−	3.44886e6i	−0.121935	−	0.375276i
$611$	−1.42809e6	−	4.39521e6i	−0.154758	−	0.476296i
$612$	−480622.	−	349192.i	−0.0518711	−	0.0376865i
$613$	−2.81915e6	+	2.04823e6i	−0.303017	+	0.220155i	−0.728894	−	0.684626i	$-0.759965\pi$
$613$	−2.81915e6	+	2.04823e6i	−0.303017	+	0.220155i	0.425877	+	0.904781i	$0.359965\pi$
$614$	−534102.	+	1.64380e6i	−0.0571746	+	0.175965i
$615$	4.16624e6			0.444177
$616$	8.29400e6	−	3.80506e6i	0.880668	−	0.404026i
$617$	9.64129e6			1.01958			0.509791	−	0.860298i	$-0.329723\pi$
$617$	9.64129e6			1.01958			0.509791	+	0.860298i	$0.329723\pi$
$618$	2.70838e6	−	8.33555e6i	0.285259	−	0.877936i
$619$	6.46901e6	−	4.70001e6i	0.678596	−	0.493029i	−0.194296	−	0.980943i	$-0.562242\pi$
$619$	6.46901e6	−	4.70001e6i	0.678596	−	0.493029i	0.872891	+	0.487914i	$0.162242\pi$
$620$	−221322.	−	160800.i	−0.0231231	−	0.0167999i
$621$	−647351.	−	1.99234e6i	−0.0673614	−	0.207317i
$622$	1.86786e6	+	5.74868e6i	0.193583	+	0.595788i
$623$	3.08683e6	+	2.24271e6i	0.318634	+	0.231501i
$624$	2.74390e6	−	1.99356e6i	0.282102	−	0.204959i
$625$	936081.	−	2.88096e6i	0.0958547	−	0.295010i
$626$	1.19816e7			1.22202
$627$	710428.	+	6.09869e6i	0.0721691	+	0.619538i
$628$	−1.83205e6			−0.185370
$629$	3.39990e6	−	1.04638e7i	0.342641	−	1.05454i
$630$	−1.74564e6	+	1.26828e6i	−0.175228	+	0.127311i
$631$	9.40979e6	+	6.83661e6i	0.940820	+	0.683545i	0.948618	−	0.316424i	$-0.102482\pi$
$631$	9.40979e6	+	6.83661e6i	0.940820	+	0.683545i	−0.00779821	+	0.999970i	$0.502482\pi$
$632$	−2.22113e6	−	6.83592e6i	−0.221198	−	0.680776i
$633$	1.77025e6	+	5.44828e6i	0.175601	+	0.540443i
$634$	−6.47889e6	−	4.70719e6i	−0.640144	−	0.465091i
$635$	3.40716e6	−	2.47544e6i	0.335319	−	0.243623i
$636$	−375790.	+	1.15656e6i	−0.0368385	+	0.113377i
$637$	−1.78350e6			−0.174150
$638$	−3.10775e6	+	5.52537e6i	−0.302270	+	0.537415i
$639$	1.37723e6			0.133430
$640$	−1.93403e6	+	5.95234e6i	−0.186644	+	0.574431i
$641$	−4.58812e6	+	3.33346e6i	−0.441052	+	0.320443i	−0.786053	−	0.618159i	$-0.787879\pi$
$641$	−4.58812e6	+	3.33346e6i	−0.441052	+	0.320443i	0.345001	+	0.938602i	$0.387879\pi$
$642$	3.91153e6	+	2.84189e6i	0.374550	+	0.272126i
$643$	−5.26772e6	−	1.62124e7i	−0.502453	−	1.54639i	−0.805010	−	0.593261i	$-0.797840\pi$
$643$	−5.26772e6	−	1.62124e7i	−0.502453	−	1.54639i	0.302557	−	0.953131i	$-0.402160\pi$
$644$	−1.08025e6	−	3.32468e6i	−0.102639	−	0.315889i
$645$	2.83610e6	+	2.06055e6i	0.268425	+	0.195022i
$646$	−7.88792e6	+	5.73091e6i	−0.743672	+	0.540309i
$647$	−3.30066e6	+	1.01584e7i	−0.309985	+	0.954035i	0.667785	+	0.744354i	$0.267243\pi$
$647$	−3.30066e6	+	1.01584e7i	−0.309985	+	0.954035i	−0.977770	+	0.209681i	$0.932757\pi$
$648$	993050.			0.0929039
$649$	1.47018e7	+	2.95256e6i	1.37012	+	0.275161i
$650$	−4.58792e6			−0.425924
$651$	504082.	−	1.55140e6i	0.0466174	−	0.143474i
$652$	3.89317e6	−	2.82855e6i	0.358661	−	0.260583i
$653$	1.34623e7	+	9.78096e6i	1.23549	+	0.897633i	0.997289	−	0.0735842i	$-0.0234438\pi$
$653$	1.34623e7	+	9.78096e6i	1.23549	+	0.897633i	0.238197	+	0.971217i	$0.423444\pi$
$654$	−2.10573e6	−	6.48077e6i	−0.192512	−	0.592491i
$655$	−2.91486e6	−	8.97101e6i	−0.265469	−	0.817030i
$656$	−1.62836e7	−	1.18307e7i	−1.47738	−	1.07338i
$657$	4.58134e6	−	3.32854e6i	0.414075	−	0.300843i
$658$	4.38928e6	−	1.35088e7i	0.395210	−	1.21633i
$659$	−8.20448e6			−0.735932			−0.367966	−	0.929839i	$-0.619946\pi$
$659$	−8.20448e6			−0.735932			−0.367966	+	0.929839i	$0.619946\pi$
$660$	554815.	+	602420.i	0.0495780	+	0.0538319i
$661$	2.23539e7			1.98998			0.994991	−	0.0999688i	$-0.0318743\pi$
$661$	2.23539e7			1.98998			0.994991	+	0.0999688i	$0.0318743\pi$
$662$	2.53154e6	−	7.79127e6i	0.224512	−	0.690977i
$663$	−2.04121e6	+	1.48303e6i	−0.180345	+	0.131028i
$664$	2.76631e6	+	2.00984e6i	0.243489	+	0.176905i
$665$	2.20992e6	+	6.80142e6i	0.193786	+	0.596411i
$666$	−1.92532e6	−	5.92553e6i	−0.168197	−	0.517656i
$667$	−5.79955e6	−	4.21362e6i	−0.504754	−	0.366725i
$668$	−1.70610e6	+	1.23955e6i	−0.147932	+	0.107479i
$669$	1.29889e6	−	3.99757e6i	0.112204	−	0.345327i
$670$	−1.79623e6			−0.154588
$671$	−5.55995e6	−	6.03701e6i	−0.476721	−	0.517625i
$672$	3.87565e6			0.331071
$673$	1.25557e6	−	3.86426e6i	0.106857	−	0.328873i	−0.883304	−	0.468800i	$-0.844687\pi$
$673$	1.25557e6	−	3.86426e6i	0.106857	−	0.328873i	0.990162	+	0.139926i	$0.0446866\pi$
$674$	−7.33895e6	+	5.33206e6i	−0.622277	+	0.452111i
$675$	−1.38058e6	−	1.00305e6i	−0.116628	−	0.0847350i
$676$	−689364.	−	2.12164e6i	−0.0580206	−	0.178569i
$677$	951919.	+	2.92971e6i	0.0798231	+	0.245670i	0.983002	−	0.183594i	$-0.0587731\pi$
$677$	951919.	+	2.92971e6i	0.0798231	+	0.245670i	−0.903179	+	0.429264i	$0.858773\pi$
$678$	7.33921e6	+	5.33225e6i	0.613162	+	0.445488i
$679$	−2.05528e7	+	1.49325e7i	−1.71079	+	1.24296i
$680$	1.18628e6	−	3.65098e6i	0.0983816	−	0.302787i
$681$	−3.91794e6			−0.323735
$682$	−3.00588e6	−	603671.i	−0.247463	−	0.0496980i
$683$	−1.98040e7			−1.62443			−0.812215	−	0.583358i	$-0.801738\pi$
$683$	−1.98040e7			−1.62443			−0.812215	+	0.583358i	$0.801738\pi$
$684$	−344557.	+	1.06044e6i	−0.0281592	+	0.0866651i
$685$	7.08587e6	−	5.14819e6i	0.576988	−	0.419206i
$686$	8.50024e6	+	6.17579e6i	0.689638	+	0.501051i
$687$	−1.76417e6	−	5.42956e6i	−0.142610	−	0.438907i
$688$	−5.23355e6	−	1.61072e7i	−0.421527	−	1.29733i
$689$	4.17835e6	+	3.03575e6i	0.335318	+	0.243623i
$690$	−3.71009e6	+	2.69554e6i	−0.296662	+	0.215538i
$691$	2.14688e6	−	6.60742e6i	0.171046	−	0.526425i	−0.828385	−	0.560159i	$-0.810740\pi$
$691$	2.14688e6	−	6.60742e6i	0.171046	−	0.526425i	0.999431	+	0.0337340i	$0.0107399\pi$
$692$	−3.63335e6			−0.288431
$693$	−2.39400e6	+	4.25637e6i	−0.189361	+	0.336671i
$694$	1.61299e7			1.27125
$695$	2.40287e6	−	7.39528e6i	0.188699	−	0.580755i
$696$	2.74921e6	−	1.99742e6i	0.215122	−	0.156295i
$697$	1.21135e7	+	8.80098e6i	0.944470	+	0.686198i
$698$	2.93594e6	+	9.03589e6i	0.228091	+	0.701993i
$699$	2.97493e6	+	9.15591e6i	0.230295	+	0.708775i
$700$	−2.30381e6	−	1.67382e6i	−0.177706	−	0.129111i
$701$	129661.	−	94204.5i	0.00996587	−	0.00724063i	−0.582791	−	0.812622i	$-0.698039\pi$
$701$	129661.	−	94204.5i	0.00996587	−	0.00724063i	0.592757	+	0.805381i	$0.298039\pi$
$702$	−441519.	+	1.35886e6i	−0.0338148	+	0.104071i
$703$	−2.06498e7			−1.57590
$704$	966322.	+	8.29542e6i	0.0734836	+	0.630822i
$705$	−3.76297e6			−0.285140
$706$	−2.54654e6	+	7.83744e6i	−0.192282	+	0.591783i
$707$	−3.40111e6	+	2.47105e6i	−0.255901	+	0.185923i
$708$	2.20308e6	+	1.60063e6i	0.165176	+	0.120007i
$709$	−993823.	−	3.05867e6i	−0.0742495	−	0.228516i	0.907043	−	0.421037i	$-0.138334\pi$
$709$	−993823.	−	3.05867e6i	−0.0742495	−	0.228516i	−0.981293	+	0.192521i	$0.938334\pi$
$710$	−931662.	−	2.86736e6i	−0.0693606	−	0.213470i
$711$	3.11195e6	+	2.26096e6i	0.230865	+	0.167733i
$712$	−3.10996e6	+	2.25952e6i	−0.229908	+	0.167038i
$713$	1.07135e6	−	3.29727e6i	0.0789235	−	0.242902i
$714$	−7.75473e6			−0.569274
$715$	3.16141e6	−	1.45037e6i	0.231268	−	0.106099i
$716$	−3.98898e6			−0.290790
$717$	−4.21530e6	+	1.29734e7i	−0.306218	+	0.942441i
$718$	−7.36604e6	+	5.35174e6i	−0.533241	+	0.387422i
$719$	1.60053e7	+	1.16285e7i	1.15463	+	0.838886i	0.989089	−	0.147318i	$-0.0470640\pi$
$719$	1.60053e7	+	1.16285e7i	1.15463	+	0.838886i	0.165538	+	0.986203i	$0.447064\pi$
$720$	−853396.	−	2.62648e6i	−0.0613506	−	0.188818i
$721$	−7.13949e6	−	2.19731e7i	−0.511480	−	1.57417i
$722$	2.11971e6	+	1.54006e6i	0.151333	+	0.109950i
$723$	1.78984e6	−	1.30039e6i	0.127341	−	0.0925185i
$724$	1.38841e6	−	4.27309e6i	0.0984400	−	0.302967i
$725$	−5.83959e6			−0.412608
$726$	8.46669e6	+	3.54365e6i	0.596172	+	0.249522i
$727$	1.50612e7			1.05687			0.528437	−	0.848973i	$-0.322778\pi$
$727$	1.50612e7			1.05687			0.528437	+	0.848973i	$0.322778\pi$
$728$	2.17482e6	−	6.69340e6i	0.152088	−	0.468078i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	−1.00291e7	−	7.28657e6i	−0.696554	−	0.506076i
$731$	3.89328e6	+	1.19823e7i	0.269477	+	0.829366i
$732$	−460568.	−	1.41748e6i	−0.0317699	−	0.0977777i
$733$	−1.57604e7	−	1.14506e7i	−1.08345	−	0.787172i	−0.105168	−	0.994454i	$-0.533538\pi$
$733$	−1.57604e7	−	1.14506e7i	−1.08345	−	0.787172i	−0.978281	+	0.207283i	$0.933538\pi$
$734$	−1.98510e7	+	1.44226e7i	−1.36001	+	0.988103i
$735$	−448758.	+	1.38114e6i	−0.0306404	+	0.0943013i
$736$	8.23710e6			0.560505
$737$	−3.69497e6	+	1.69515e6i	−0.250578	+	0.114958i
$738$	8.47910e6			0.573071
$739$	774808.	−	2.38461e6i	0.0521895	−	0.160623i	−0.921565	−	0.388225i	$-0.873088\pi$
$739$	774808.	−	2.38461e6i	0.0521895	−	0.160623i	0.973754	+	0.227602i	$0.0730885\pi$
$740$	−2.22835e6	+	1.61899e6i	−0.149591	+	0.108684i
$741$	3.83107e6	+	2.78343e6i	0.256315	+	0.186224i
$742$	4.90531e6	+	1.50970e7i	0.327082	+	1.00665i
$743$	8.22437e6	+	2.53120e7i	0.546551	+	1.68211i	0.717273	+	0.696792i	$0.245390\pi$
$743$	8.22437e6	+	2.53120e7i	0.546551	+	1.68211i	−0.170722	+	0.985319i	$0.554610\pi$
$744$	1.32959e6	+	966006.i	0.0880616	+	0.0639805i
$745$	−9.22615e6	+	6.70319e6i	−0.609017	+	0.442477i
$746$	4.78711e6	−	1.47332e7i	0.314939	−	0.969283i
$747$	−1.82990e6			−0.119984
$748$	340565.	+	2.92359e6i	0.0222559	+	0.191057i
$749$	1.27452e7			0.830122
$750$	−2.69549e6	+	8.29588e6i	−0.174979	+	0.538529i
$751$	28986.6	−	21060.0i	0.00187542	−	0.00136257i	−0.586847	−	0.809698i	$-0.699631\pi$
$751$	28986.6	−	21060.0i	0.00187542	−	0.00136257i	0.588723	+	0.808335i	$0.299631\pi$
$752$	1.47075e7	+	1.06856e7i	0.948404	+	0.689056i
$753$	−1.91847e6	−	5.90445e6i	−0.123301	−	0.379483i
$754$	1.51087e6	+	4.64999e6i	0.0967832	+	0.297868i
$755$	−1.24947e7	−	9.07794e6i	−0.797735	−	0.579589i
$756$	−717460.	+	521265.i	−0.0456555	+	0.0331707i
$757$	−3.77488e6	+	1.16179e7i	−0.239422	+	0.736864i	0.757082	+	0.653320i	$0.226624\pi$
$757$	−3.77488e6	+	1.16179e7i	−0.239422	+	0.736864i	−0.996504	+	0.0835449i	$0.973376\pi$
$758$	1.70395e7			1.07717
$759$	−5.08808e6	+	9.04625e6i	−0.320589	+	0.569986i
$760$	−7.20503e6			−0.452483
$761$	27516.8	−	84687.9i	0.00172241	−	0.00530102i	−0.950192	−	0.311666i	$-0.899113\pi$
$761$	27516.8	−	84687.9i	0.00172241	−	0.00530102i	0.951914	+	0.306365i	$0.0991129\pi$
$762$	6.93422e6	−	5.03801e6i	0.432624	−	0.314320i
$763$	−1.45323e7	−	1.05583e7i	−0.903698	−	0.656575i
$764$	185089.	+	569646.i	0.0114722	+	0.0353079i
$765$	634848.	+	1.95386e6i	0.0392208	+	0.120709i
$766$	9.08936e6	+	6.60381e6i	0.559708	+	0.406652i
$767$	9.35651e6	−	6.79790e6i	0.574282	−	0.417240i
$768$	−2.08406e6	+	6.41407e6i	−0.127499	+	0.392401i
$769$	2.03342e7			1.23997			0.619985	−	0.784613i	$-0.287139\pi$
$769$	2.03342e7			1.23997			0.619985	+	0.784613i	$0.287139\pi$
$770$	1.04811e7	+	2.10493e6i	0.637062	+	0.127941i
$771$	−1.10327e7			−0.668412
$772$	−1.95159e6	+	6.00639e6i	−0.117855	+	0.362719i
$773$	−1.86967e7	+	1.35839e7i	−1.12542	+	0.817668i	−0.985022	−	0.172427i	$-0.944839\pi$
$773$	−1.86967e7	+	1.35839e7i	−1.12542	+	0.817668i	−0.140401	+	0.990095i	$0.544839\pi$
$774$	5.77202e6	+	4.19362e6i	0.346318	+	0.251615i
$775$	−872722.	−	2.68596e6i	−0.0521941	−	0.160637i
$776$	−7.90931e6	−	2.43424e7i	−0.471503	−	1.45114i
$777$	−1.32873e7	−	9.65376e6i	−0.789556	−	0.573646i
$778$	1.32583e7	−	9.63274e6i	0.785308	−	0.570559i
$779$	8.68415e6	−	2.67271e7i	0.512724	−	1.57800i
$780$	631645.			0.0371738
$781$	−4.62251e6	−	5.01914e6i	−0.271175	−	0.294443i
$782$	−1.64815e7			−0.963783
$783$	−561974.	+	1.72958e6i	−0.0327576	+	0.100818i
$784$	5.67593e6	−	4.12380e6i	0.329797	−	0.239611i
$785$	5.12551e6	+	3.72390e6i	0.296868	+	0.215687i
$786$	−5.93230e6	−	1.82577e7i	−0.342505	−	1.05412i
$787$	3.05947e6	+	9.41609e6i	0.176080	+	0.541918i	0.999681	−	0.0252511i	$-0.00803854\pi$
$787$	3.05947e6	+	9.41609e6i	0.176080	+	0.541918i	−0.823601	+	0.567169i	$0.808039\pi$
$788$	−1.29636e6	−	941859.i	−0.0743720	−	0.0540344i
$789$	−6.85310e6	+	4.97907e6i	−0.391917	+	0.284744i
$790$	2.60212e6	−	8.00849e6i	0.148340	−	0.456544i
$791$	2.39138e7			1.35896
$792$	−3.33305e6	−	3.61904e6i	−0.188812	−	0.205013i
$793$	−6.32988e6			−0.357447
$794$	9.63992e6	−	2.96686e7i	0.542653	−	1.67011i
$795$	3.40222e6	−	2.47186e6i	0.190917	−	0.138709i
$796$	−491924.	−	357404.i	−0.0275179	−	0.0199929i
$797$	−3.11868e6	−	9.59830e6i	−0.173910	−	0.535240i	0.825672	−	0.564150i	$-0.190796\pi$
$797$	−3.11868e6	−	9.59830e6i	−0.173910	−	0.535240i	−0.999582	+	0.0289106i	$0.990796\pi$
$798$	4.49761e6	+	1.38422e7i	0.250020	+	0.769482i
$799$	−1.09410e7	−	7.94911e6i	−0.606304	−	0.440506i
$800$	5.42847e6	−	3.94402e6i	0.299884	−	0.217878i
$801$	635716.	−	1.95653e6i	0.0350092	−	0.107747i
$802$	−1.05843e7			−0.581066
$803$	−2.75071e7	−	5.52425e6i	−1.50542	−	0.302332i
$804$	−738250.			−0.0402776
$805$	−3.73566e6	+	1.14972e7i	−0.203178	+	0.625318i
$806$	−1.91300e6	+	1.38988e6i	−0.103723	+	0.0753595i
$807$	−7.80822e6	−	5.67301e6i	−0.422054	−	0.306640i
$808$	−1.30884e6	−	4.02820e6i	−0.0705276	−	0.217062i
$809$	−6.45089e6	−	1.98538e7i	−0.346536	−	1.06653i	−0.960756	−	0.277394i	$-0.910529\pi$
$809$	−6.45089e6	−	1.98538e7i	−0.346536	−	1.06653i	0.614220	−	0.789135i	$-0.289471\pi$
$810$	941201.	+	683822.i	0.0504046	+	0.0366211i
$811$	−5.54886e6	+	4.03148e6i	−0.296245	+	0.215235i	−0.725972	−	0.687724i	$-0.758610\pi$
$811$	−5.54886e6	+	4.03148e6i	−0.296245	+	0.215235i	0.429727	+	0.902959i	$0.358610\pi$
$812$	−937781.	+	2.88619e6i	−0.0499128	+	0.153616i
$813$	3.06278e6			0.162513
$814$	−1.51327e7	+	2.69049e7i	−0.800489	+	1.42321i
$815$	−1.66413e7			−0.877593
$816$	3.06704e6	−	9.43937e6i	0.161248	−	0.496269i
$817$	1.91304e7	−	1.38990e7i	1.00269	−	0.728499i
$818$	6.35204e6	+	4.61502e6i	0.331917	+	0.241152i
$819$	1.16388e6	+	3.58204e6i	0.0606313	+	0.186604i
$820$	−1.15834e6	−	3.56502e6i	−0.0601594	−	0.185151i
$821$	2.22188e7	+	1.61429e7i	1.15044	+	0.835842i	0.988539	−	0.150966i	$-0.0482384\pi$
$821$	2.22188e7	+	1.61429e7i	1.15044	+	0.835842i	0.161898	+	0.986807i	$0.448238\pi$
$822$	1.44211e7	−	1.04776e7i	0.744423	−	0.540855i
$823$	−6.86523e6	+	2.11290e7i	−0.353310	+	1.08737i	0.603674	+	0.797232i	$0.293703\pi$
$823$	−6.86523e6	+	2.11290e7i	−0.353310	+	1.08737i	−0.956983	+	0.290143i	$0.906297\pi$
$824$	2.32770e7			1.19429
$825$	978267.	+	8.39796e6i	0.0500406	+	0.429575i
$826$	3.55462e7			1.81277
$827$	−4.78793e6	+	1.47357e7i	−0.243435	+	0.749217i	0.752454	+	0.658644i	$0.228870\pi$
$827$	−4.78793e6	+	1.47357e7i	−0.243435	+	0.749217i	−0.995890	+	0.0905729i	$0.971130\pi$
$828$	−1.52485e6	+	1.10787e6i	−0.0772950	+	0.0561581i
$829$	−1.35112e7	−	9.81643e6i	−0.682820	−	0.496098i	0.191472	−	0.981498i	$-0.438674\pi$
$829$	−1.35112e7	−	9.81643e6i	−0.682820	−	0.496098i	−0.874292	+	0.485400i	$0.838674\pi$
$830$	1.23788e6	+	3.80980e6i	0.0623710	+	0.191958i
$831$	−4.69783e6	−	1.44584e7i	−0.235991	−	0.726305i
$832$	5.21101e6	+	3.78602e6i	0.260984	+	0.189616i
$833$	−4.22237e6	+	3.06773e6i	−0.210835	+	0.153181i
$834$	4.89031e6	−	1.50508e7i	0.243457	−	0.749282i
$835$	7.29268e6			0.361969
$836$	5.02109e6	−	2.30354e6i	0.248475	−	0.113993i
$837$	−879519.			−0.0433942
$838$	−373809.	+	1.15047e6i	−0.0183882	+	0.0565931i
$839$	1.11806e7	−	8.12317e6i	0.548352	−	0.398401i	−0.278825	−	0.960342i	$-0.589945\pi$
$839$	1.11806e7	−	8.12317e6i	0.548352	−	0.398401i	0.827178	+	0.561940i	$0.189945\pi$
$840$	−4.63613e6	−	3.36834e6i	−0.226703	−	0.164709i
$841$	−4.41522e6	−	1.35887e7i	−0.215260	−	0.662501i
$842$	4.32018e6	+	1.32962e7i	0.210001	+	0.646317i
$843$	−1.29230e6	−	938914.i	−0.0626319	−	0.0455048i
$844$	4.16987e6	−	3.02959e6i	0.201496	−	0.146395i
$845$	−2.38391e6	+	7.33692e6i	−0.114855	+	0.353486i
$846$	−7.65838e6			−0.367884
$847$	2.35470e7	−	5.56137e6i	1.12778	−	0.266363i
$848$	−2.03167e7			−0.970206
$849$	−5.65416e6	+	1.74017e7i	−0.269215	+	0.828558i
$850$	−1.08617e7	+	7.89152e6i	−0.515647	+	0.374639i
$851$	−2.82400e7	−	2.05176e7i	−1.33672	−	0.971185i
$852$	−382913.	−	1.17849e6i	−0.0180718	−	0.0556193i
$853$	2.02747e6	+	6.23991e6i	0.0954073	+	0.293634i	0.987360	−	0.158496i	$-0.0506645\pi$
$853$	2.02747e6	+	6.23991e6i	0.0954073	+	0.293634i	−0.891952	+	0.452129i	$0.850664\pi$
$854$	−1.57395e7	−	1.14354e7i	−0.738491	−	0.536545i
$855$	3.11945e6	−	2.26641e6i	0.145936	−	0.106029i
$856$	−3.96800e6	+	1.22122e7i	−0.185092	+	0.569654i
$857$	1.36240e7			0.633655			0.316827	−	0.948483i	$-0.397382\pi$
$857$	1.36240e7			0.633655			0.316827	+	0.948483i	$0.397382\pi$
$858$	6.43408e6	−	2.95178e6i	0.298379	−	0.136888i
$859$	1.77958e7			0.822875			0.411437	−	0.911438i	$-0.365027\pi$
$859$	1.77958e7			0.822875			0.411437	+	0.911438i	$0.365027\pi$
$860$	974672.	−	2.99973e6i	0.0449379	−	0.138305i
$861$	1.80827e7	−	1.31379e7i	0.831297	−	0.603973i
$862$	−1.51778e7	−	1.10273e7i	−0.695732	−	0.505479i
$863$	6.33321e6	+	1.94916e7i	0.289466	+	0.890884i	0.985024	+	0.172415i	$0.0551569\pi$
$863$	6.33321e6	+	1.94916e7i	0.289466	+	0.890884i	−0.695559	+	0.718469i	$0.744843\pi$
$864$	−645734.	−	1.98737e6i	−0.0294286	−	0.0905719i
$865$	1.01650e7	+	7.38528e6i	0.461919	+	0.335604i
$866$	−2.67735e7	+	1.94521e7i	−1.21314	+	0.881395i
$867$	1.66725e6	−	5.13125e6i	0.0753272	−	0.231833i
$868$	−1.46768e6			−0.0661197
$869$	−2.20510e6	−	1.89297e7i	−0.0990555	−	0.850345i
$870$	3.98110e6			0.178322
$871$	−968880.	+	2.98191e6i	−0.0432737	+	0.133183i
$872$	1.46412e7	−	1.06375e7i	0.652058	−	0.473748i
$873$	1.10815e7	+	8.05117e6i	0.492110	+	0.357539i
$874$	9.55896e6	+	2.94195e7i	0.423284	+	1.30274i
$875$	7.10551e6	+	2.18685e7i	0.313744	+	0.965604i
$876$	−4.12196e6	−	2.99478e6i	−0.181486	−	0.131857i
$877$	−499927.	+	363218.i	−0.0219486	+	0.0159466i	−0.598705	−	0.800969i	$-0.704318\pi$
$877$	−499927.	+	363218.i	−0.0219486	+	0.0159466i	0.576757	+	0.816916i	$0.304318\pi$
$878$	1.09999e7	−	3.38542e7i	0.481563	−	1.48210i
$879$	6.62000e6			0.288992
$880$	−6.70755e6	+	1.19256e7i	−0.291983	+	0.519125i
$881$	−2.54436e7			−1.10443			−0.552215	−	0.833702i	$-0.686217\pi$
$881$	−2.54436e7			−1.10443			−0.552215	+	0.833702i	$0.686217\pi$
$882$	−913310.	+	2.81088e6i	−0.0395318	+	0.121666i
$883$	−1.41673e7	+	1.02931e7i	−0.611483	+	0.444269i	−0.849936	−	0.526885i	$-0.823360\pi$
$883$	−1.41673e7	+	1.02931e7i	−0.611483	+	0.444269i	0.238453	+	0.971154i	$0.423360\pi$
$884$	1.83654e6	+	1.33432e6i	0.0790439	+	0.0574288i
$885$	−2.91002e6	−	8.95612e6i	−0.124893	−	0.384381i
$886$	1.25436e7	+	3.86053e7i	0.536832	+	1.65220i
$887$	9.27426e6	+	6.73814e6i	0.395795	+	0.287562i	0.767826	−	0.640658i	$-0.221339\pi$
$887$	9.27426e6	+	6.73814e6i	0.395795	+	0.287562i	−0.372031	+	0.928220i	$0.621339\pi$
$888$	1.33868e7	−	9.72611e6i	0.569699	−	0.413911i
$889$	6.98200e6	−	2.14884e7i	0.296296	−	0.911904i
$890$	−4.50351e6			−0.190579
$891$	2.58146e6	+	518434.i	0.108936	+	0.0218776i
$892$	−3.78183e6			−0.159144
$893$	−7.84358e6	+	2.41401e7i	−0.329144	+	1.01300i
$894$	−1.87770e7	+	1.36423e7i	−0.785746	+	0.570878i
$895$	1.11599e7	+	8.10816e6i	0.465697	+	0.338349i
$896$	1.03759e7	+	3.19338e7i	0.431774	+	1.32886i
$897$	2.47364e6	+	7.61307e6i	0.102649	+	0.315921i
$898$	−1.46567e7	−	1.06487e7i	−0.606519	−	0.440662i
$899$	−2.43490e6	+	1.76906e6i	−0.100481	+	0.0730035i
$900$	−474458.	+	1.46023e6i	−0.0195250	+	0.0600918i
$901$	1.51138e7			0.620242
$902$	−2.84591e7	−	3.09010e7i	−1.16467	−	1.26461i
$903$	1.88073e7			0.767552
$904$	−7.44516e6	+	2.29138e7i	−0.303007	+	0.932560i
$905$	−1.25700e7	+	9.13263e6i	−0.510168	+	0.370659i
$906$	−2.54292e7	−	1.84754e7i	−1.02923	−	0.747778i
$907$	−2.10432e6	−	6.47643e6i	−0.0849363	−	0.261407i	0.899564	−	0.436788i	$-0.143884\pi$
$907$	−2.10432e6	−	6.47643e6i	−0.0849363	−	0.261407i	−0.984501	+	0.175381i	$0.943884\pi$
$908$	1.08931e6	+	3.35255e6i	0.0438467	+	0.134946i
$909$	1.83378e6	+	1.33232e6i	0.0736100	+	0.0534808i
$910$	6.67039e6	−	4.84632e6i	0.267023	−	0.194003i
$911$	−1.20648e7	+	3.71315e7i	−0.481640	+	1.48234i	0.355149	+	0.934810i	$0.384430\pi$
$911$	−1.20648e7	+	3.71315e7i	−0.481640	+	1.48234i	−0.836789	+	0.547526i	$0.815570\pi$
$912$	−1.86281e7			−0.741621
$913$	6.14182e6	+	6.66881e6i	0.243849	+	0.264772i
$914$	2.00443e7			0.793642
$915$	−1.59270e6	+	4.90184e6i	−0.0628901	+	0.193556i
$916$	−4.15554e6	+	3.01918e6i	−0.163640	+	0.118891i
$917$	−4.09407e7	−	2.97452e7i	−1.60780	−	1.16814i
$918$	1.29204e6	+	3.97649e6i	0.0506021	+	0.155737i
$919$	1.42616e6	+	4.38926e6i	0.0557030	+	0.171436i	0.975037	−	0.222041i	$-0.0712720\pi$
$919$	1.42616e6	+	4.38926e6i	0.0557030	+	0.171436i	−0.919334	+	0.393477i	$0.871272\pi$
$920$	−9.85337e6	−	7.15889e6i	−0.383809	−	0.278854i
$921$	1.98739e6	−	1.44392e6i	0.0772029	−	0.0560912i
$922$	7.00742e6	−	2.15666e7i	0.271476	−	0.835516i
$923$	−5.26262e6			−0.203328
$924$	4.30775e6	+	865125.i	0.165986	+	0.0333349i
$925$	−2.84350e7			−1.09269
$926$	3.15029e6	−	9.69560e6i	0.120732	−	0.371576i
$927$	−1.00779e7	+	7.32200e6i	−0.385185	+	0.279853i
$928$	−5.78506e6	−	4.20309e6i	−0.220515	−	0.160214i
$929$	−9.56499e6	−	2.94380e7i	−0.363618	−	1.11910i	−0.950842	−	0.309677i	$-0.899779\pi$
$929$	−9.56499e6	−	2.94380e7i	−0.363618	−	1.11910i	0.587224	−	0.809425i	$-0.300221\pi$
$930$	594973.	+	1.83114e6i	0.0225574	+	0.0694246i
$931$	7.92480e6	+	5.75771e6i	0.299650	+	0.217708i
$932$	7.00752e6	−	5.09126e6i	0.264256	−	0.191993i
$933$	2.65477e6	−	8.17055e6i	0.0998443	−	0.307289i
$934$	−4.46868e7			−1.67615
$935$	4.98980e6	−	8.87152e6i	0.186661	−	0.331871i
$936$	−3.79461e6			−0.141572
$937$	−8.67714e6	+	2.67055e7i	−0.322870	+	0.993692i	0.649523	+	0.760342i	$0.274969\pi$
$937$	−8.67714e6	+	2.67055e7i	−0.322870	+	0.993692i	−0.972393	+	0.233350i	$0.925031\pi$
$938$	−7.79618e6	+	5.66426e6i	−0.289318	+	0.210202i
$939$	−1.37770e7	−	1.00096e7i	−0.509907	−	0.370469i
$940$	1.04623e6	+	3.21995e6i	0.0386194	+	0.118858i
$941$	2.33704e6	+	7.19266e6i	0.0860382	+	0.264798i	0.984815	−	0.173609i	$-0.0555428\pi$
$941$	2.33704e6	+	7.19266e6i	0.0860382	+	0.264798i	−0.898776	+	0.438407i	$0.855543\pi$
$942$	1.04314e7	+	7.57886e6i	0.383015	+	0.278277i
$943$	3.84320e7	−	2.79225e7i	1.40739	−	1.02253i
$944$	−1.40587e7	+	4.32682e7i	−0.513470	+	1.58030i
$945$	3.06677e6			0.111713
$946$	−4.09000e6	−	3.51108e7i	−0.148592	−	1.27559i
$947$	2.89705e7			1.04974			0.524870	−	0.851183i	$-0.324114\pi$
$947$	2.89705e7			1.04974			0.524870	+	0.851183i	$0.324114\pi$
$948$	1.06947e6	−	3.29149e6i	0.0386499	−	0.118952i
$949$	−1.75060e7	+	1.27189e7i	−0.630990	+	0.458441i
$950$	2.03860e7	+	1.48113e7i	0.732863	+	0.532456i
$951$	3.51729e6	+	1.08251e7i	0.126112	+	0.388134i
$952$	−6.36427e6	−	1.95872e7i	−0.227592	−	0.700455i
$953$	2.77765e7	+	2.01808e7i	0.990708	+	0.719791i	0.960076	−	0.279739i	$-0.0902480\pi$
$953$	2.77765e7	+	2.01808e7i	0.990708	+	0.719791i	0.0306319	+	0.999531i	$0.490248\pi$
$954$	6.92417e6	−	5.03070e6i	0.246318	−	0.178961i
$955$	640062.	−	1.96991e6i	0.0227098	−	0.0698937i
$956$	1.22732e7			0.434323
$957$	8.18942e6	−	3.75708e6i	0.289050	−	0.132608i
$958$	−3.79547e7			−1.33614
$959$	1.45205e7	−	4.46894e7i	0.509840	−	1.56913i
$960$	4.24306e6	−	3.08276e6i	0.148594	−	0.107960i
$961$	2.19839e7	+	1.59722e7i	0.767885	+	0.557901i
$962$	7.35697e6	+	2.26424e7i	0.256307	+	0.788833i
$963$	−2.12351e6	−	6.53551e6i	−0.0737886	−	0.227098i
$964$	−1.61037e6	−	1.17000e6i	−0.0558126	−	0.0405503i
$965$	1.76688e7	−	1.28371e7i	0.610785	−	0.443761i
$966$	−7.60278e6	+	2.33990e7i	−0.262138	+	0.806777i
$967$	1.24449e7			0.427980			0.213990	−	0.976836i	$-0.431354\pi$
$967$	1.24449e7			0.427980			0.213990	+	0.976836i	$0.431354\pi$
$968$	−2.00212e6	+	2.42938e7i	−0.0686756	+	0.833310i
$969$	1.38576e7			0.474110
$970$	9.26600e6	−	2.85178e7i	0.316201	−	0.973166i
$971$	3.16202e7	−	2.29734e7i	1.07626	−	0.781947i	0.0992317	−	0.995064i	$-0.468362\pi$
$971$	3.16202e7	−	2.29734e7i	1.07626	−	0.781947i	0.977027	+	0.213117i	$0.0683615\pi$
$972$	386834.	+	281051.i	0.0131328	+	0.00954157i
$973$	−1.28912e7	−	3.96751e7i	−0.436527	−	1.34349i
$974$	−8.93172e6	−	2.74890e7i	−0.301674	−	0.928457i
$975$	5.27542e6	+	3.83282e6i	0.177724	+	0.129124i
$976$	2.01446e7	−	1.46359e7i	0.676916	−	0.491809i
$977$	3.40982e6	−	1.04944e7i	0.114287	−	0.351738i	−0.877511	−	0.479557i	$-0.840798\pi$
$977$	3.40982e6	−	1.04944e7i	0.114287	−	0.351738i	0.991798	+	0.127819i	$0.0407975\pi$
$978$	−3.38683e7			−1.13226
$979$	−9.26404e6	+	4.25009e6i	−0.308918	+	0.141723i
$980$	1.30660e6			0.0434587
$981$	−2.99286e6	+	9.21107e6i	−0.0992918	+	0.305589i
$982$	2.74840e7	−	1.99683e7i	0.909496	−	0.660787i
$983$	−1.53291e6	−	1.11372e6i	−0.0505980	−	0.0367616i	0.562199	−	0.827002i	$-0.309956\pi$
$983$	−1.53291e6	−	1.11372e6i	−0.0505980	−	0.0367616i	−0.612797	+	0.790241i	$0.709956\pi$
$984$	6.95876e6	+	2.14169e7i	0.229110	+	0.705128i
$985$	1.71234e6	+	5.27005e6i	0.0562342	+	0.173071i
$986$	1.15752e7	+	8.40990e6i	0.379173	+	0.275485i
$987$	−1.63325e7	+	1.18662e7i	−0.533653	+	0.387721i
$988$	1.31661e6	−	4.05210e6i	0.0429105	−	0.132065i
$989$	3.99721e7			1.29947
$990$	−666927.	−	5.72525e6i	−0.0216267	−	0.185655i
$991$	3.70987e7			1.19998			0.599990	−	0.800007i	$-0.295171\pi$
$991$	3.70987e7			1.19998			0.599990	+	0.800007i	$0.295171\pi$
$992$	1.06867e6	−	3.28903e6i	0.0344798	−	0.106118i
$993$	−9.41983e6	+	6.84391e6i	−0.303159	+	0.220258i
$994$	−1.30857e7	−	9.50731e6i	−0.420079	−	0.305205i
$995$	649777.	+	1.99981e6i	0.0208069	+	0.0640370i
$996$	508769.	+	1.56583e6i	0.0162507	+	0.0500145i
$997$	4.77180e6	+	3.46692e6i	0.152035	+	0.110460i	0.661202	−	0.750208i	$-0.270046\pi$
$997$	4.77180e6	+	3.46692e6i	0.152035	+	0.110460i	−0.509167	+	0.860668i	$0.670046\pi$
$998$	3.68801e7	−	2.67950e7i	1.17210	−	0.851584i
$999$	−2.73644e6	+	8.42191e6i	−0.0867507	+	0.266991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.e.b.31.2	yes	20
3.2	odd	2		99.6.f.b.64.4		20
11.4	even	5		363.6.a.r.1.4		10
11.5	even	5	inner	33.6.e.b.16.2	✓	20
11.7	odd	10		363.6.a.t.1.7		10
33.5	odd	10		99.6.f.b.82.4		20
33.26	odd	10		1089.6.a.bk.1.7		10
33.29	even	10		1089.6.a.bi.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.b.16.2	✓	20	11.5	even	5	inner
33.6.e.b.31.2	yes	20	1.1	even	1	trivial
99.6.f.b.64.4		20	3.2	odd	2
99.6.f.b.82.4		20	33.5	odd	10
363.6.a.r.1.4		10	11.4	even	5
363.6.a.t.1.7		10	11.7	odd	10
1089.6.a.bi.1.4		10	33.29	even	10
1089.6.a.bk.1.7		10	33.26	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95678 + 6.02234i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-6.55106 - 4.75963i) q^{4} +(8.65323 + 26.6319i) q^{5} +(17.6110 + 54.2011i) q^{6} +(121.539 + 88.3034i) q^{7} +(-122.450 + 88.9651i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.95678 + 6.02234i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-6.55106 - 4.75963i) q^{4} +(8.65323 + 26.6319i) q^{5} +(17.6110 + 54.2011i) q^{6} +(121.539 + 88.3034i) q^{7} +(-122.450 + 88.9651i) q^{8} +(25.0304 - 77.0356i) q^{9} -177.319 q^{10} +(-364.758 + 167.341i) q^{11} -72.8780 q^{12} +(-95.6452 + 294.366i) q^{13} +(-769.618 + 559.160i) q^{14} +(203.890 + 148.135i) q^{15} +(-376.244 - 1157.96i) q^{16} +(279.891 + 861.416i) q^{17} +(414.956 + 301.483i) q^{18} +(1375.30 - 999.212i) q^{19} +(70.0700 - 215.653i) q^{20} +1352.08 q^{21} +(-294.034 - 2524.14i) q^{22} +2873.63 q^{23} +(-420.946 + 1295.54i) q^{24} +(1893.80 - 1375.93i) q^{25} +(-1585.61 - 1152.02i) q^{26} +(-225.273 - 693.320i) q^{27} +(-375.920 - 1156.96i) q^{28} +(-2018.20 - 1466.31i) q^{29} +(-1291.08 + 938.028i) q^{30} +(372.821 - 1147.42i) q^{31} +2866.45 q^{32} +(-1770.61 + 3148.03i) q^{33} -5735.43 q^{34} +(-1299.98 + 4000.93i) q^{35} +(-530.636 + 385.530i) q^{36} +(-9827.30 - 7139.95i) q^{37} +(3326.45 + 10237.7i) q^{38} +(860.806 + 2649.29i) q^{39} +(-3428.90 - 2491.24i) q^{40} +(13374.1 - 9716.82i) q^{41} +(-2645.71 + 8142.66i) q^{42} +13910.0 q^{43} +(3186.03 + 639.850i) q^{44} +2268.20 q^{45} +(-5623.05 + 17306.0i) q^{46} +(-12079.5 + 8776.30i) q^{47} +(-8865.18 - 6440.93i) q^{48} +(1780.63 + 5480.22i) q^{49} +(4580.55 + 14097.5i) q^{50} +(6594.88 + 4791.46i) q^{51} +(2027.65 - 1473.17i) q^{52} +(5156.42 - 15869.8i) q^{53} +4616.22 q^{54} +(-7612.93 - 8266.14i) q^{55} -22738.4 q^{56} +(4727.85 - 14550.8i) q^{57} +(12779.8 - 9285.05i) q^{58} +(-30229.6 - 21963.1i) q^{59} +(-630.630 - 1940.88i) q^{60} +(6319.71 + 19450.1i) q^{61} +(6180.65 + 4490.50i) q^{62} +(9844.67 - 7152.57i) q^{63} +(6430.81 - 19792.0i) q^{64} -8667.15 q^{65} +(-15493.8 - 16823.2i) q^{66} +10129.9 q^{67} +(2266.44 - 6975.37i) q^{68} +(20923.3 - 15201.7i) q^{69} +(-21551.2 - 15657.8i) q^{70} +(5254.17 + 16170.7i) q^{71} +(3788.51 + 11659.8i) q^{72} +(56559.7 + 41093.0i) q^{73} +(62229.1 - 45212.1i) q^{74} +(6510.30 - 20036.6i) q^{75} -13765.5 q^{76} +(-59109.1 - 11870.9i) q^{77} -17639.3 q^{78} +(-14674.8 + 45164.4i) q^{79} +(27582.9 - 20040.2i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(32348.0 + 99556.8i) q^{82} +(-6981.10 - 21485.6i) q^{83} +(-8857.53 - 6435.38i) q^{84} +(-20519.2 + 14908.1i) q^{85} +(-27218.7 + 83770.6i) q^{86} -22451.7 q^{87} +(29777.1 - 52941.6i) q^{88} +25397.8 q^{89} +(-4438.35 + 13659.9i) q^{90} +(-37618.1 + 27331.1i) q^{91} +(-18825.3 - 13677.4i) q^{92} +(-3355.39 - 10326.8i) q^{93} +(-29216.9 - 89920.4i) q^{94} +(38511.7 + 27980.4i) q^{95} +(20871.0 - 15163.7i) q^{96} +(-52256.2 + 160828. i) q^{97} -36488.1 q^{98} +(3761.18 + 32287.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Introduction

L-functions

Modular forms

Varieties

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