LMFDB - Embedded newform 50.6.d.b.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.d (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:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	50.41
Dual form			50.6.d.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(-9.01407 - 27.7425i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-53.0123 + 17.7397i) q^{5} +(36.0563 - 110.970i) q^{6} +66.5258 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-491.799 + 357.313i) q^{9} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(-9.01407 - 27.7425i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-53.0123 + 17.7397i) q^{5} +(36.0563 - 110.970i) q^{6} +66.5258 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-491.799 + 357.313i) q^{9} +(-213.260 - 67.2326i) q^{10} +(-317.317 - 230.544i) q^{11} +(377.586 - 274.333i) q^{12} +(-716.419 + 520.509i) q^{13} +(215.282 + 156.412i) q^{14} +(969.999 + 1310.78i) q^{15} +(-207.108 + 150.473i) q^{16} +(-253.165 + 779.161i) q^{17} -2431.59 q^{18} +(910.313 - 2801.66i) q^{19} +(-532.050 - 718.973i) q^{20} +(-599.669 - 1845.59i) q^{21} +(-484.817 - 1492.11i) q^{22} +(-1796.02 - 1304.88i) q^{23} +1866.89 q^{24} +(2495.61 - 1880.84i) q^{25} -3542.17 q^{26} +(8611.27 + 6256.46i) q^{27} +(328.922 + 1012.32i) q^{28} +(-817.136 - 2514.89i) q^{29} +(57.1429 + 6522.39i) q^{30} +(399.902 - 1230.77i) q^{31} -1024.00 q^{32} +(-3535.54 + 10881.3i) q^{33} +(-2651.18 + 1926.19i) q^{34} +(-3526.69 + 1180.15i) q^{35} +(-7868.79 - 5717.01i) q^{36} +(4682.98 - 3402.39i) q^{37} +(9532.93 - 6926.08i) q^{38} +(20898.1 + 15183.3i) q^{39} +(-31.3432 - 3577.57i) q^{40} +(-3082.51 + 2239.58i) q^{41} +(2398.68 - 7382.36i) q^{42} -12449.3 q^{43} +(1939.27 - 5968.45i) q^{44} +(19732.8 - 27666.4i) q^{45} +(-2744.07 - 8445.38i) q^{46} +(1545.48 + 4756.50i) q^{47} +(6041.38 + 4389.32i) q^{48} -12381.3 q^{49} +(12498.1 - 219.009i) q^{50} +23897.9 q^{51} +(-11462.7 - 8328.14i) q^{52} +(-7993.88 - 24602.6i) q^{53} +(13156.9 + 40492.6i) q^{54} +(20911.5 + 6592.58i) q^{55} +(-1315.69 + 4049.27i) q^{56} -85930.5 q^{57} +(3268.54 - 10059.5i) q^{58} +(-13860.5 + 10070.2i) q^{59} +(-15150.1 + 21241.3i) q^{60} +(13003.6 + 9447.68i) q^{61} +(4187.83 - 3042.64i) q^{62} +(-32717.4 + 23770.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(28745.4 - 40302.4i) q^{65} +(-37024.7 + 26900.0i) q^{66} +(-3829.22 + 11785.1i) q^{67} -13108.1 q^{68} +(-20011.2 + 61588.3i) q^{69} +(-14187.3 - 4472.70i) q^{70} +(-8071.85 - 24842.6i) q^{71} +(-12022.4 - 37001.3i) q^{72} +(64338.8 + 46744.9i) q^{73} +23153.9 q^{74} +(-74674.8 - 52280.2i) q^{75} +47133.4 q^{76} +(-21109.8 - 15337.1i) q^{77} +(31929.4 + 98268.5i) q^{78} +(-14506.6 - 44646.6i) q^{79} +(8309.95 - 11651.0i) q^{80} +(50299.1 - 154805. i) q^{81} -15240.8 q^{82} +(-8792.25 + 27059.8i) q^{83} +(25119.3 - 18250.2i) q^{84} +(-401.222 - 45796.2i) q^{85} +(-40286.6 - 29269.9i) q^{86} +(-62403.4 + 45338.7i) q^{87} +(20308.3 - 14754.8i) q^{88} +(18770.0 + 13637.2i) q^{89} +(128904. - 43135.6i) q^{90} +(-47660.4 + 34627.3i) q^{91} +(10976.3 - 33781.5i) q^{92} -37749.4 q^{93} +(-6181.92 + 19026.0i) q^{94} +(1442.69 + 164671. i) q^{95} +(9230.41 + 28408.3i) q^{96} +(34977.3 + 107649. i) q^{97} +(-40066.8 - 29110.2i) q^{98} +238433. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9 - 220 * q^10 - 389 * q^11 + 192 * q^12 + 1047 * q^13 + 164 * q^14 - 640 * q^15 - 1792 * q^16 + 909 * q^17 - 11576 * q^18 + 260 * q^19 - 1040 * q^20 - 1849 * q^21 + 556 * q^22 + 817 * q^23 + 2432 * q^24 + 16055 * q^25 - 4528 * q^26 + 1675 * q^27 + 2544 * q^28 - 2445 * q^29 - 5440 * q^30 + 16731 * q^31 - 28672 * q^32 + 29629 * q^33 - 7576 * q^34 - 825 * q^35 - 7136 * q^36 + 39819 * q^37 + 3100 * q^38 + 26008 * q^39 + 10231 * q^41 + 7396 * q^42 - 86148 * q^43 - 2224 * q^44 - 7870 * q^45 - 11708 * q^46 + 10019 * q^47 + 3072 * q^48 + 147076 * q^49 + 16520 * q^50 - 108074 * q^51 + 16752 * q^52 + 74512 * q^53 + 4260 * q^54 + 2735 * q^55 - 10176 * q^56 - 176840 * q^57 + 9780 * q^58 - 13430 * q^59 + 5760 * q^60 - 29774 * q^61 + 63956 * q^62 - 206818 * q^63 - 28672 * q^64 + 51235 * q^65 + 23264 * q^66 - 85061 * q^67 - 89696 * q^68 - 185227 * q^69 - 25260 * q^70 + 148501 * q^71 + 64064 * q^72 + 189082 * q^73 + 305304 * q^74 + 93630 * q^75 + 16480 * q^76 + 127243 * q^77 + 32028 * q^78 + 46930 * q^79 + 39680 * q^80 - 179812 * q^81 - 338864 * q^82 + 66807 * q^83 - 34464 * q^84 - 877380 * q^85 + 121332 * q^86 - 226000 * q^87 + 24896 * q^88 - 347190 * q^89 + 628660 * q^90 + 197001 * q^91 + 46832 * q^92 - 64906 * q^93 - 40076 * q^94 + 85970 * q^95 - 7168 * q^96 + 502364 * q^97 + 185056 * q^98 + 1151018 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$	−9.01407	−	27.7425i	−0.578253	−	1.77968i	−0.624825	−	0.780765i	$-0.714830\pi$
$3$	−9.01407	−	27.7425i	−0.578253	−	1.77968i	0.0465721	−	0.998915i	$-0.485170\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−53.0123	+	17.7397i	−0.948313	+	0.317337i
$5$	−53.0123	+	17.7397i	−0.948313	+	0.317337i
$6$	36.0563	−	110.970i	0.408887	−	1.25842i
$7$	66.5258			0.513151			0.256576	−	0.966524i	$-0.417406\pi$
$7$	66.5258			0.513151			0.256576	+	0.966524i	$0.417406\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−491.799	+	357.313i	−2.02387	+	1.47042i
$10$	−213.260	−	67.2326i	−0.674387	−	0.212608i
$11$	−317.317	−	230.544i	−0.790699	−	0.574477i	0.117472	−	0.993076i	$-0.462521\pi$
$11$	−317.317	−	230.544i	−0.790699	−	0.574477i	−0.908171	+	0.418600i	$0.862521\pi$
$12$	377.586	−	274.333i	0.756943	−	0.549951i
$13$	−716.419	+	520.509i	−1.17573	+	0.854220i	−0.991684	−	0.128697i	$-0.958921\pi$
$13$	−716.419	+	520.509i	−1.17573	+	0.854220i	−0.184049	+	0.982917i	$0.558921\pi$
$14$	215.282	+	156.412i	0.293554	+	0.213279i
$15$	969.999	+	1310.78i	1.11312	+	1.50419i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−253.165	+	779.161i	−0.212462	+	0.653890i	0.786862	+	0.617129i	$0.211704\pi$
$17$	−253.165	+	779.161i	−0.212462	+	0.653890i	−0.999324	+	0.0367617i	$0.988296\pi$
$18$	−2431.59			−1.76892
$19$	910.313	−	2801.66i	0.578505	−	1.78045i	−0.0454173	−	0.998968i	$-0.514462\pi$
$19$	910.313	−	2801.66i	0.578505	−	1.78045i	0.623922	−	0.781487i	$-0.285538\pi$
$20$	−532.050	−	718.973i	−0.297425	−	0.401918i
$21$	−599.669	−	1845.59i	−0.296731	−	0.913245i
$22$	−484.817	−	1492.11i	−0.213561	−	0.657272i
$23$	−1796.02	−	1304.88i	−0.707931	−	0.514342i	0.174574	−	0.984644i	$-0.444145\pi$
$23$	−1796.02	−	1304.88i	−0.707931	−	0.514342i	−0.882506	+	0.470302i	$0.844145\pi$
$24$	1866.89			0.661592
$25$	2495.61	−	1880.84i	0.798594	−	0.601870i
$26$	−3542.17			−1.02763
$27$	8611.27	+	6256.46i	2.27331	+	1.65165i
$28$	328.922	+	1012.32i	0.0792862	+	0.244018i
$29$	−817.136	−	2514.89i	−0.180426	−	0.555294i	0.819414	−	0.573203i	$-0.194299\pi$
$29$	−817.136	−	2514.89i	−0.180426	−	0.555294i	−0.999840	+	0.0179084i	$0.994299\pi$
$30$	57.1429	+	6522.39i	0.0115920	+	1.32313i
$31$	399.902	−	1230.77i	0.0747394	−	0.230024i	−0.906707	−	0.421761i	$-0.861412\pi$
$31$	399.902	−	1230.77i	0.0747394	−	0.230024i	0.981446	+	0.191737i	$0.0614121\pi$
$32$	−1024.00			−0.176777
$33$	−3535.54	+	10881.3i	−0.565160	+	1.73938i
$34$	−2651.18	+	1926.19i	−0.393316	+	0.285761i
$35$	−3526.69	+	1180.15i	−0.486628	+	0.162842i
$36$	−7868.79	−	5717.01i	−1.01193	−	0.735212i
$37$	4682.98	−	3402.39i	0.562365	−	0.408582i	−0.269959	−	0.962872i	$-0.587010\pi$
$37$	4682.98	−	3402.39i	0.562365	−	0.408582i	0.832324	+	0.554290i	$0.187010\pi$
$38$	9532.93	−	6926.08i	1.07095	−	0.778087i
$39$	20898.1	+	15183.3i	2.20011	+	1.59847i
$40$	−31.3432	−	3577.57i	−0.00309737	−	0.353540i
$41$	−3082.51	+	2239.58i	−0.286382	+	0.208069i	−0.721696	−	0.692210i	$-0.756637\pi$
$41$	−3082.51	+	2239.58i	−0.286382	+	0.208069i	0.435314	+	0.900279i	$0.356637\pi$
$42$	2398.68	−	7382.36i	0.209821	−	0.645762i
$43$	−12449.3			−1.02677			−0.513384	−	0.858159i	$-0.671608\pi$
$43$	−12449.3			−1.02677			−0.513384	+	0.858159i	$0.671608\pi$
$44$	1939.27	−	5968.45i	0.151010	−	0.464761i
$45$	19732.8	−	27666.4i	1.45264	−	2.03667i
$46$	−2744.07	−	8445.38i	−0.191206	−	0.588471i
$47$	1545.48	+	4756.50i	0.102051	+	0.314082i	0.989027	−	0.147734i	$-0.0471981\pi$
$47$	1545.48	+	4756.50i	0.102051	+	0.314082i	−0.886976	+	0.461816i	$0.847198\pi$
$48$	6041.38	+	4389.32i	0.378471	+	0.274976i
$49$	−12381.3			−0.736676
$50$	12498.1	−	219.009i	0.706998	−	0.0123890i
$51$	23897.9			1.28657
$52$	−11462.7	−	8328.14i	−0.587867	−	0.427110i
$53$	−7993.88	−	24602.6i	−0.390902	−	1.20307i	−0.932107	−	0.362182i	$-0.882032\pi$
$53$	−7993.88	−	24602.6i	−0.390902	−	1.20307i	0.541206	−	0.840890i	$-0.317968\pi$
$54$	13156.9	+	40492.6i	0.613999	+	1.88969i
$55$	20911.5	+	6592.58i	0.932133	+	0.293865i
$56$	−1315.69	+	4049.27i	−0.0560638	+	0.172547i
$57$	−85930.5			−3.50316
$58$	3268.54	−	10059.5i	0.127580	−	0.392652i
$59$	−13860.5	+	10070.2i	−0.518381	+	0.376626i	−0.815994	−	0.578061i	$-0.803810\pi$
$59$	−13860.5	+	10070.2i	−0.518381	+	0.376626i	0.297613	+	0.954687i	$0.403810\pi$
$60$	−15150.1	+	21241.3i	−0.543299	+	0.761732i
$61$	13003.6	+	9447.68i	0.447445	+	0.325088i	0.788586	−	0.614924i	$-0.210813\pi$
$61$	13003.6	+	9447.68i	0.447445	+	0.325088i	−0.341141	+	0.940012i	$0.610813\pi$
$62$	4187.83	−	3042.64i	0.138360	−	0.100524i
$63$	−32717.4	+	23770.6i	−1.03855	+	0.754550i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	28745.4	−	40302.4i	0.843887	−	1.18317i
$66$	−37024.7	+	26900.0i	−1.04624	+	0.760139i
$67$	−3829.22	+	11785.1i	−0.104213	+	0.320736i	−0.989545	−	0.144224i	$-0.953931\pi$
$67$	−3829.22	+	11785.1i	−0.104213	+	0.320736i	0.885332	+	0.464960i	$0.153931\pi$
$68$	−13108.1			−0.343771
$69$	−20011.2	+	61588.3i	−0.506001	+	1.55731i
$70$	−14187.3	−	4472.70i	−0.346062	−	0.109100i
$71$	−8071.85	−	24842.6i	−0.190032	−	0.584859i	0.809967	−	0.586476i	$-0.199485\pi$
$71$	−8071.85	−	24842.6i	−0.190032	−	0.584859i	−0.999999	+	0.00161723i	$0.999485\pi$
$72$	−12022.4	−	37001.3i	−0.273314	−	0.841173i
$73$	64338.8	+	46744.9i	1.41308	+	1.02666i	0.992866	+	0.119234i	$0.0380437\pi$
$73$	64338.8	+	46744.9i	1.41308	+	1.02666i	0.420210	+	0.907427i	$0.361956\pi$
$74$	23153.9			0.491525
$75$	−74674.8	−	52280.2i	−1.53292	−	1.07321i
$76$	47133.4			0.936040
$77$	−21109.8	−	15337.1i	−0.405748	−	0.294793i
$78$	31929.4	+	98268.5i	0.594229	+	1.82885i
$79$	−14506.6	−	44646.6i	−0.261515	−	0.804861i	−0.992476	−	0.122441i	$-0.960928\pi$
$79$	−14506.6	−	44646.6i	−0.261515	−	0.804861i	0.730960	−	0.682420i	$-0.239072\pi$
$80$	8309.95	−	11651.0i	0.145169	−	0.203534i
$81$	50299.1	−	154805.i	0.851820	−	2.62163i
$82$	−15240.8			−0.250307
$83$	−8792.25	+	27059.8i	−0.140089	+	0.431150i	−0.996347	−	0.0853987i	$-0.972784\pi$
$83$	−8792.25	+	27059.8i	−0.140089	+	0.431150i	0.856258	+	0.516549i	$0.172784\pi$
$84$	25119.3	−	18250.2i	0.388426	−	0.282208i
$85$	−401.222	−	45796.2i	−0.00602333	−	0.687515i
$86$	−40286.6	−	29269.9i	−0.587374	−	0.426752i
$87$	−62403.4	+	45338.7i	−0.883914	+	0.642201i
$88$	20308.3	−	14754.8i	0.279554	−	0.203108i
$89$	18770.0	+	13637.2i	0.251183	+	0.182495i	0.706251	−	0.707962i	$-0.250385\pi$
$89$	18770.0	+	13637.2i	0.251183	+	0.182495i	−0.455068	+	0.890457i	$0.650385\pi$
$90$	128904.	−	43135.6i	1.67749	−	0.561345i
$91$	−47660.4	+	34627.3i	−0.603329	+	0.438344i
$92$	10976.3	−	33781.5i	0.135203	−	0.416111i
$93$	−37749.4			−0.452588
$94$	−6181.92	+	19026.0i	−0.0721612	+	0.222089i
$95$	1442.69	+	164671.i	0.0164007	+	1.87201i
$96$	9230.41	+	28408.3i	0.102222	+	0.314606i
$97$	34977.3	+	107649.i	0.377448	+	1.16167i	0.941812	+	0.336140i	$0.109121\pi$
$97$	34977.3	+	107649.i	0.377448	+	1.16167i	−0.564364	+	0.825526i	$0.690879\pi$
$98$	−40066.8	−	29110.2i	−0.421424	−	0.306182i
$99$	238433.			2.44499
$100$	40959.6	+	28676.0i	0.409596	+	0.286760i
$101$	90212.0			0.879956			0.439978	−	0.898008i	$-0.354986\pi$
$101$	90212.0			0.879956			0.439978	+	0.898008i	$0.354986\pi$
$102$	77335.2	+	56187.3i	0.735998	+	0.534734i
$103$	−32012.1	−	98523.0i	−0.297318	−	0.915050i	−0.982433	−	0.186615i	$-0.940248\pi$
$103$	−32012.1	−	98523.0i	−0.297318	−	0.915050i	0.685116	−	0.728434i	$-0.259752\pi$
$104$	−17513.5	−	53900.9i	−0.158777	−	0.488666i
$105$	64530.0	+	87201.1i	0.571200	+	0.771878i
$106$	31975.5	−	98410.5i	0.276409	−	0.850701i
$107$	−127652.			−1.07788			−0.538939	−	0.842345i	$-0.681175\pi$
$107$	−127652.			−1.07788			−0.538939	+	0.842345i	$0.681175\pi$
$108$	−52627.4	+	161971.i	−0.434163	+	1.33622i
$109$	116971.	−	84984.6i	0.943003	−	0.685132i	−0.00613888	−	0.999981i	$-0.501954\pi$
$109$	116971.	−	84984.6i	0.943003	−	0.685132i	0.949142	+	0.314850i	$0.101954\pi$
$110$	52170.9	+	70499.8i	0.411099	+	0.555529i
$111$	−136603.	−	99248.1i	−1.05233	−	0.764566i
$112$	−13778.1	+	10010.3i	−0.103787	+	0.0754057i
$113$	−144407.	+	104918.i	−1.06388	+	0.772956i	−0.974803	−	0.223069i	$-0.928393\pi$
$113$	−144407.	+	104918.i	−1.06388	+	0.772956i	−0.0890795	+	0.996025i	$0.528393\pi$
$114$	−278077.	−	202035.i	−2.00402	−	1.45601i
$115$	118359.	+	37314.1i	0.834560	+	0.263104i
$116$	34228.6	−	24868.6i	0.236181	−	0.171595i
$117$	166350.	−	511972.i	1.12346	−	3.45765i
$118$	−68530.1			−0.453081
$119$	−16842.0	+	51834.4i	−0.109025	+	0.335545i
$120$	−98968.1	+	33118.0i	−0.627397	+	0.209948i
$121$	−2228.17	−	6857.60i	−0.0138352	−	0.0425803i
$122$	19867.8	+	61146.7i	0.120851	+	0.371940i
$123$	89917.4	+	65328.8i	0.535897	+	0.389352i
$124$	20705.8			0.120931
$125$	−98932.3	+	143979.i	−0.566322	+	0.824184i
$126$	−161764.			−0.907725
$127$	160590.	+	116675.i	0.883503	+	0.641903i	0.934176	−	0.356812i	$-0.116136\pi$
$127$	160590.	+	116675.i	0.883503	+	0.641903i	−0.0506726	+	0.998715i	$0.516136\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	112218.	+	345373.i	0.593731	+	1.82732i
$130$	187779.	−	62837.0i	0.974513	−	0.326105i
$131$	2772.87	−	8534.02i	0.0141173	−	0.0434486i	−0.943750	−	0.330661i	$-0.892728\pi$
$131$	2772.87	−	8534.02i	0.0141173	−	0.0434486i	0.957867	+	0.287212i	$0.0927284\pi$
$132$	−183060.			−0.914448
$133$	60559.4	−	186383.i	0.296860	−	0.913642i
$134$	−40100.1	+	29134.4i	−0.192923	+	0.140167i
$135$	−567491.	−	178908.i	−2.67994	−	0.844880i
$136$	−42418.8	−	30819.1i	−0.196658	−	0.142880i
$137$	−218890.	+	159033.i	−0.996377	+	0.723910i	−0.961308	−	0.275475i	$-0.911165\pi$
$137$	−218890.	+	159033.i	−0.996377	+	0.723910i	−0.0350688	+	0.999385i	$0.511165\pi$
$138$	−209560.	+	152255.i	−0.936724	+	0.680570i
$139$	49234.2	+	35770.7i	0.216137	+	0.157033i	0.690586	−	0.723250i	$-0.257353\pi$
$139$	49234.2	+	35770.7i	0.216137	+	0.157033i	−0.474449	+	0.880283i	$0.657353\pi$
$140$	−35395.1	−	47830.3i	−0.152624	−	0.206245i
$141$	118026.	−	85750.8i	0.499953	−	0.363237i
$142$	32287.4	−	99370.4i	0.134373	−	0.413558i
$143$	347332.			1.42038
$144$	48089.8	−	148005.i	0.193262	−	0.594799i
$145$	87931.5	+	118824.i	0.347316	+	0.469337i
$146$	98300.9	+	302539.i	0.381659	+	1.17463i
$147$	111606.	+	343488.i	0.425985	+	1.31105i
$148$	74927.7	+	54438.2i	0.281182	+	0.204291i
$149$	−60333.2			−0.222634			−0.111317	−	0.993785i	$-0.535507\pi$
$149$	−60333.2			−0.222634			−0.111317	+	0.993785i	$0.535507\pi$
$150$	−118734.	−	344753.i	−0.430872	−	1.25107i
$151$	−145629.			−0.519764			−0.259882	−	0.965640i	$-0.583684\pi$
$151$	−145629.			−0.519764			−0.259882	+	0.965640i	$0.583684\pi$
$152$	152527.	+	110817.i	0.535473	+	0.389044i
$153$	−153898.	−	473650.i	−0.531502	−	1.63580i
$154$	−32252.8	−	99264.1i	−0.109589	−	0.337280i
$155$	633.775	+	72340.2i	0.00211888	+	0.241853i
$156$	−127718.	+	393074.i	−0.420184	+	1.29319i
$157$	−412406.			−1.33529			−0.667646	−	0.744479i	$-0.732698\pi$
$157$	−412406.			−1.33529			−0.667646	+	0.744479i	$0.732698\pi$
$158$	58026.3	−	178587.i	0.184919	−	0.569123i
$159$	−610480.	+	443540.i	−1.91504	+	1.39136i
$160$	54284.6	−	18165.4i	0.167640	−	0.0560978i
$161$	−119482.	−	86808.5i	−0.363276	−	0.263935i
$162$	526739.	−	382698.i	1.57691	−	1.14570i
$163$	520481.	−	378152.i	1.53439	−	1.11480i	0.580657	−	0.814149i	$-0.302796\pi$
$163$	520481.	−	378152.i	1.53439	−	1.11480i	0.953734	−	0.300651i	$-0.0972041\pi$
$164$	−49320.2	−	35833.2i	−0.143191	−	0.104034i
$165$	−5603.21	−	639562.i	−0.0160224	−	1.82883i
$166$	−92073.6	+	66895.4i	−0.259337	+	0.188420i
$167$	−74567.1	+	229494.i	−0.206898	+	0.636766i	0.792732	+	0.609570i	$0.208658\pi$
$167$	−74567.1	+	229494.i	−0.206898	+	0.636766i	−0.999630	+	0.0271963i	$0.991342\pi$
$168$	124196.			0.339497
$169$	127591.	−	392685.i	0.343640	−	1.05761i
$170$	106375.	−	149143.i	0.282304	−	0.395804i
$171$	553377.	+	1.70312e6i	1.44721	+	4.45405i
$172$	−61552.5	−	189439.i	−0.158644	−	0.488257i
$173$	−189939.	−	137999.i	−0.482502	−	0.350559i	0.319791	−	0.947488i	$-0.396387\pi$
$173$	−189939.	−	137999.i	−0.482502	−	0.350559i	−0.802294	+	0.596929i	$0.796387\pi$
$174$	−308539.			−0.772569
$175$	166022.	−	125125.i	0.409800	−	0.308850i
$176$	100410.			0.244339
$177$	404313.	+	293750.i	0.970028	+	0.704767i
$178$	28678.0	+	88261.9i	0.0678421	+	0.208797i
$179$	−80116.6	−	246573.i	−0.186892	−	0.575193i	0.813084	−	0.582146i	$-0.197787\pi$
$179$	−80116.6	−	246573.i	−0.186892	−	0.575193i	−0.999976	+	0.00695283i	$0.997787\pi$
$180$	518561.	+	163482.i	1.19294	+	0.376088i
$181$	262179.	−	806904.i	0.594842	−	1.83074i	0.0393305	−	0.999226i	$-0.487477\pi$
$181$	262179.	−	806904.i	0.594842	−	1.83074i	0.555511	−	0.831509i	$-0.312523\pi$
$182$	−235646.			−0.527329
$183$	144886.	−	445914.i	0.319816	−	0.984291i
$184$	114945.	−	83512.5i	0.250291	−	0.181847i
$185$	−187898.	+	263443.i	−0.403640	+	0.565923i
$186$	−122160.	−	88754.2i	−0.258908	−	0.188108i
$187$	259964.	−	188875.i	0.543638	−	0.394976i
$188$	−64737.9	+	47034.8i	−0.133587	+	0.0970565i
$189$	572872.	+	416216.i	1.16655	+	0.847548i
$190$	−382496.	+	536278.i	−0.768675	+	1.07772i
$191$	10063.7	−	7311.71i	0.0199606	−	0.0145023i	−0.577760	−	0.816207i	$-0.696073\pi$
$191$	10063.7	−	7311.71i	0.0199606	−	0.0145023i	0.597721	+	0.801704i	$0.296073\pi$
$192$	−36921.6	+	113633.i	−0.0722816	+	0.222460i
$193$	−519156.			−1.00324			−0.501619	−	0.865088i	$-0.667262\pi$
$193$	−519156.			−1.00324			−0.501619	+	0.865088i	$0.667262\pi$
$194$	−139909.	+	430596.i	−0.266896	+	0.821421i
$195$	−1.37720e6	−	434178.i	−2.59365	−	0.817676i
$196$	−61216.6	−	188405.i	−0.113823	−	0.350310i
$197$	−12832.5	−	39494.5i	−0.0235585	−	0.0725056i	0.938586	−	0.345045i	$-0.112136\pi$
$197$	−12832.5	−	39494.5i	−0.0235585	−	0.0725056i	−0.962145	+	0.272540i	$0.912136\pi$
$198$	771584.	+	560589.i	1.39869	+	1.01621i
$199$	−282921.			−0.506446			−0.253223	−	0.967408i	$-0.581491\pi$
$199$	−282921.			−0.506446			−0.253223	+	0.967408i	$0.581491\pi$
$200$	65126.5	+	189099.i	0.115129	+	0.334283i
$201$	361465.			0.631069
$202$	291932.	+	212101.i	0.503389	+	0.365734i
$203$	−54360.7	−	167305.i	−0.0925858	−	0.284950i
$204$	118158.	+	363652.i	0.198786	+	0.611801i
$205$	123682.	−	173408.i	0.205552	−	0.288194i
$206$	128048.	−	394092.i	0.210235	−	0.647038i
$207$	1.34953e6			2.18906
$208$	70053.8	−	215604.i	0.112273	−	0.345539i
$209$	−934763.	+	679145.i	−1.48025	+	1.07547i
$210$	3801.48	+	433908.i	0.00594845	+	0.678968i
$211$	367574.	+	267058.i	0.568380	+	0.412952i	0.834516	−	0.550983i	$-0.185747\pi$
$211$	367574.	+	267058.i	0.568380	+	0.412952i	−0.266136	+	0.963935i	$0.585747\pi$
$212$	334852.	−	243284.i	0.511697	−	0.371770i
$213$	−616435.	+	447866.i	−0.930975	+	0.676393i
$214$	−413092.	−	300129.i	−0.616613	−	0.447995i
$215$	659963.	−	220846.i	0.973697	−	0.325831i
$216$	−551121.	+	400413.i	−0.803735	+	0.583948i
$217$	26603.8	−	81878.2i	0.0383526	−	0.118037i
$218$	578338.			0.824215
$219$	716863.	−	2.20628e6i	1.01001	−	3.10849i
$220$	3073.40	+	350803.i	0.00428116	+	0.488660i
$221$	−224188.	−	689981.i	−0.308768	−	0.950290i
$222$	−208711.	−	642347.i	−0.284226	−	0.874757i
$223$	387785.	+	281742.i	0.522190	+	0.379393i	0.817428	−	0.576030i	$-0.195399\pi$
$223$	387785.	+	281742.i	0.522190	+	0.379393i	−0.295238	+	0.955424i	$0.595399\pi$
$224$	−68122.5			−0.0907132
$225$	−555289.	+	1.81671e6i	−0.731244	+	2.39238i
$226$	−713990.			−0.929867
$227$	−662314.	−	481199.i	−0.853099	−	0.619813i	0.0728998	−	0.997339i	$-0.476775\pi$
$227$	−662314.	−	481199.i	−0.853099	−	0.619813i	−0.925999	+	0.377527i	$0.876775\pi$
$228$	−424864.	−	1.30760e6i	−0.541268	−	1.66585i
$229$	−313261.	−	964118.i	−0.394746	−	1.21490i	−0.929159	−	0.369679i	$-0.879468\pi$
$229$	−313261.	−	964118.i	−0.394746	−	1.21490i	0.534414	−	0.845223i	$-0.320532\pi$
$230$	295288.	+	399030.i	0.368066	+	0.497377i
$231$	−235205.	+	723887.i	−0.290013	+	0.892567i
$232$	169236.			0.206430
$233$	52349.6	−	161116.i	0.0631719	−	0.194423i	−0.914489	−	0.404610i	$-0.867407\pi$
$233$	52349.6	−	161116.i	0.0631719	−	0.194423i	0.977661	+	0.210187i	$0.0674073\pi$
$234$	1.74204e6	−	1.26566e6i	2.07978	−	1.51105i
$235$	−166308.	−	224736.i	−0.196446	−	0.265463i
$236$	−221768.	−	161124.i	−0.259190	−	0.188313i
$237$	−1.10784e6	+	804896.i	−1.28117	+	0.930827i
$238$	−176372.	+	128142.i	−0.201830	+	0.146638i
$239$	−741806.	−	538954.i	−0.840032	−	0.610319i	0.0823476	−	0.996604i	$-0.473758\pi$
$239$	−741806.	−	538954.i	−0.840032	−	0.610319i	−0.922380	+	0.386285i	$0.873758\pi$
$240$	−398133.	−	125516.i	−0.446169	−	0.140660i
$241$	354334.	−	257439.i	0.392980	−	0.285517i	−0.373695	−	0.927551i	$-0.621909\pi$
$241$	354334.	−	257439.i	0.392980	−	0.285517i	0.766676	+	0.642035i	$0.221909\pi$
$242$	8912.68	−	27430.4i	0.00978295	−	0.0301088i
$243$	−2.16155e6			−2.34827
$244$	−79471.0	+	244587.i	−0.0854543	+	0.263001i
$245$	656362.	−	219641.i	0.698599	−	0.233775i
$246$	137382.	+	422817.i	0.144741	+	0.445466i
$247$	806121.	+	2.48099e6i	0.840733	+	2.58751i
$248$	67005.3	+	48682.2i	0.0691799	+	0.0502621i
$249$	829958.			0.848316
$250$	−658667.	+	233322.i	−0.666524	+	0.236105i
$251$	−1.69808e6			−1.70128			−0.850638	−	0.525751i	$-0.823784\pi$
$251$	−1.69808e6			−1.70128			−0.850638	+	0.525751i	$0.823784\pi$
$252$	−523478.	−	380329.i	−0.519275	−	0.377275i
$253$	269073.	+	828123.i	0.264283	+	0.813380i
$254$	245359.	+	755138.i	0.238626	+	0.734416i
$255$	−1.26688e6	+	423941.i	−1.22007	+	0.408277i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−91177.0			−0.0861098			−0.0430549	−	0.999073i	$-0.513709\pi$
$257$	−91177.0			−0.0861098			−0.0430549	+	0.999073i	$0.513709\pi$
$258$	−448874.	+	1.38149e6i	−0.419832	+	1.29211i
$259$	311539.	−	226347.i	0.288578	−	0.209664i
$260$	755403.	+	238149.i	0.693019	+	0.218482i
$261$	1.30047e6	+	944846.i	1.18168	+	0.858538i
$262$	29037.9	−	21097.3i	0.0261344	−	0.0189877i
$263$	1.34488e6	−	977115.i	1.19893	−	0.871077i	0.204755	−	0.978813i	$-0.434360\pi$
$263$	1.34488e6	−	977115.i	1.19893	−	0.871077i	0.994180	+	0.107736i	$0.0343602\pi$
$264$	−592395.	−	430400.i	−0.523121	−	0.380069i
$265$	860216.	+	1.16243e6i	0.752477	+	1.01684i
$266$	634186.	−	460763.i	0.549557	−	0.399276i
$267$	209136.	−	643653.i	0.179535	−	0.552553i
$268$	−198266.			−0.168621
$269$	−512217.	+	1.57644e6i	−0.431592	+	1.32830i	0.464947	+	0.885339i	$0.346074\pi$
$269$	−512217.	+	1.57644e6i	−0.431592	+	1.32830i	−0.896539	+	0.442965i	$0.853926\pi$
$270$	−1.41580e6	−	1.91321e6i	−1.18193	−	1.59718i
$271$	−735228.	−	2.26280e6i	−0.608133	−	1.87164i	−0.473618	−	0.880730i	$-0.657052\pi$
$271$	−735228.	−	2.26280e6i	−0.608133	−	1.87164i	−0.134515	−	0.990911i	$-0.542948\pi$
$272$	−64810.2	−	199465.i	−0.0531155	−	0.163473i
$273$	1.39026e6	+	1.01008e6i	1.12899	+	0.820258i
$274$	−1.08225e6			−0.870866
$275$	−1.22552e6	+	21475.2i	−0.977208	+	0.0171240i
$276$	−1.03612e6			−0.818727
$277$	−976291.	−	709317.i	−0.764504	−	0.555445i	0.135785	−	0.990738i	$-0.456645\pi$
$277$	−976291.	−	709317.i	−0.764504	−	0.555445i	−0.900288	+	0.435294i	$0.856645\pi$
$278$	75223.1	+	231513.i	0.0583767	+	0.179665i
$279$	243100.	+	748184.i	0.186971	+	0.575437i
$280$	−2085.13	−	238001.i	−0.00158942	−	0.181419i
$281$	117185.	−	360657.i	0.0885328	−	0.272476i	−0.896982	−	0.442068i	$-0.854245\pi$
$281$	117185.	−	360657.i	0.0885328	−	0.272476i	0.985514	+	0.169592i	$0.0542450\pi$
$282$	583552.			0.436975
$283$	−519460.	+	1.59873e6i	−0.385554	+	1.18661i	0.550523	+	0.834820i	$0.314428\pi$
$283$	−519460.	+	1.59873e6i	−0.385554	+	1.18661i	−0.936077	+	0.351795i	$0.885572\pi$
$284$	338118.	−	245657.i	0.248755	−	0.180731i
$285$	4.55537e6	−	1.52438e6i	3.32209	−	1.11168i
$286$	1.12399e6	+	816627.i	0.812545	+	0.590349i
$287$	−205067.	+	148990.i	−0.146957	+	0.106771i
$288$	503603.	−	365889.i	0.357772	−	0.259937i
$289$	605689.	+	440059.i	0.426584	+	0.309932i
$290$	5180.06	+	591262.i	0.00361693	+	0.412843i
$291$	2.67116e6	−	1.94071e6i	1.84913	−	1.34347i
$292$	−393204.	+	1.21016e6i	−0.269874	+	0.830586i
$293$	2.08541e6			1.41913			0.709566	−	0.704639i	$-0.248891\pi$
$293$	2.08541e6			1.41913			0.709566	+	0.704639i	$0.248891\pi$
$294$	−446424.	+	1.37395e6i	−0.301217	+	0.927050i
$295$	556134.	−	779728.i	0.372070	−	0.521660i
$296$	114479.	+	352331.i	0.0759448	+	0.233734i
$297$	−1.29011e6	−	3.97056e6i	−0.848665	−	2.61192i
$298$	−195242.	−	141852.i	−0.127360	−	0.0925325i
$299$	1.96590e6			1.27170
$300$	426331.	−	1.39481e6i	0.273491	−	0.894769i
$301$	−828197.			−0.526887
$302$	−471266.	−	342395.i	−0.297337	−	0.216028i
$303$	−813178.	−	2.50270e6i	−0.508837	−	1.56604i
$304$	233040.	+	717224.i	0.144626	+	0.445114i
$305$	−856950.	−	270163.i	−0.527480	−	0.166294i
$306$	615593.	−	1.89460e6i	0.375829	−	1.15668i
$307$	2.48465e6			1.50460			0.752298	−	0.658823i	$-0.228946\pi$
$307$	2.48465e6			1.50460			0.752298	+	0.658823i	$0.228946\pi$
$308$	129011.	−	397056.i	0.0774910	−	0.238493i
$309$	−2.44471e6	+	1.77619e6i	−1.45657	+	1.05826i
$310$	−168031.	+	235588.i	−0.0993083	+	0.139235i
$311$	582208.	+	422999.i	0.341332	+	0.247992i	0.745224	−	0.666815i	$-0.232343\pi$
$311$	582208.	+	422999.i	0.341332	+	0.247992i	−0.403891	+	0.914807i	$0.632343\pi$
$312$	−1.33748e6	+	971733.i	−0.777856	+	0.565146i
$313$	−463507.	+	336758.i	−0.267421	+	0.194293i	−0.713412	−	0.700745i	$-0.752851\pi$
$313$	−463507.	+	336758.i	−0.267421	+	0.194293i	0.445991	+	0.895037i	$0.352851\pi$
$314$	−1.33457e6	−	969625.i	−0.763869	−	0.554983i
$315$	1.31274e6	−	1.84053e6i	0.745423	−	1.04512i
$316$	607659.	−	441490.i	0.342328	−	0.248716i
$317$	−190881.	+	587472.i	−0.106688	+	0.328352i	−0.990123	−	0.140202i	$-0.955225\pi$
$317$	−190881.	+	587472.i	−0.106688	+	0.328352i	0.883435	+	0.468554i	$0.155225\pi$
$318$	−3.01838e6			−1.67381
$319$	−320501.	+	986401.i	−0.176341	+	0.542721i
$320$	218378.	+	68846.2i	0.119216	+	0.0375842i
$321$	1.15067e6	+	3.54139e6i	0.623286	+	1.91828i
$322$	−182552.	−	561836.i	−0.0981174	−	0.301974i
$323$	1.95248e6	+	1.41856e6i	1.04131	+	0.756557i
$324$	2.60434e6			1.37827
$325$	−808906.	+	2.64646e6i	−0.424805	+	1.38981i
$326$	2.57340e6			1.34111
$327$	−3.41207e6	−	2.47901e6i	−1.76461	−	1.28206i
$328$	−75354.6	−	231918.i	−0.0386745	−	0.119028i
$329$	102814.	+	316430.i	0.0523677	+	0.161171i
$330$	1.48557e6	−	2.08284e6i	0.750944	−	1.05286i
$331$	−752230.	+	2.31513e6i	−0.377382	+	1.16146i	0.564476	+	0.825449i	$0.309078\pi$
$331$	−752230.	+	2.31513e6i	−0.377382	+	1.16146i	−0.941858	+	0.336012i	$0.890922\pi$
$332$	−455237.			−0.226669
$333$	−1.08737e6	+	3.34658e6i	−0.537362	+	1.65383i
$334$	−780877.	+	567340.i	−0.383016	+	0.278277i
$335$	−6068.64	−	692686.i	−0.00295447	−	0.337229i
$336$	401908.	+	292003.i	0.194213	+	0.141104i
$337$	−2.03698e6	+	1.47995e6i	−0.977041	+	0.709862i	−0.957045	−	0.289939i	$-0.906365\pi$
$337$	−2.03698e6	+	1.47995e6i	−0.977041	+	0.709862i	−0.0199954	+	0.999800i	$0.506365\pi$
$338$	1.33615e6	−	970770.i	0.636156	−	0.462194i
$339$	4.21239e6	+	3.06048e6i	1.99081	+	1.44641i
$340$	694892.	−	232534.i	0.326002	−	0.109091i
$341$	−410643.	+	298350.i	−0.191240	+	0.138944i
$342$	−2.21351e6	+	6.81248e6i	−1.02333	+	3.14949i
$343$	−1.94178e6			−0.891177
$344$	246210.	−	757756.i	0.112178	−	0.345250i
$345$	−31714.3	−	3.61993e6i	−0.0143452	−	1.63739i
$346$	−290201.	−	893148.i	−0.130319	−	0.401082i
$347$	−761724.	−	2.34435e6i	−0.339605	−	1.04520i	−0.964409	−	0.264415i	$-0.914821\pi$
$347$	−761724.	−	2.34435e6i	−0.339605	−	1.04520i	0.624804	−	0.780782i	$-0.285179\pi$
$348$	−998454.	−	725419.i	−0.441957	−	0.321101i
$349$	−2.61891e6			−1.15095			−0.575476	−	0.817818i	$-0.695183\pi$
$349$	−2.61891e6			−1.15095			−0.575476	+	0.817818i	$0.695183\pi$
$350$	831445.	−	14569.7i	0.362797	−	0.00635743i
$351$	−9.42582e6			−4.08368
$352$	324932.	+	236077.i	0.139777	+	0.101554i
$353$	−641977.	−	1.97580e6i	−0.274210	−	0.843931i	−0.989427	−	0.145029i	$-0.953672\pi$
$353$	−641977.	−	1.97580e6i	−0.274210	−	0.843931i	0.715218	−	0.698902i	$-0.246328\pi$
$354$	617735.	+	1.90119e6i	0.261996	+	0.806340i
$355$	868607.	+	1.17377e6i	0.365807	+	0.494325i
$356$	−114712.	+	353048.i	−0.0479716	+	0.147641i
$357$	1.58983e6			0.660206
$358$	320466.	−	986294.i	0.132152	−	0.406723i
$359$	1.32787e6	−	964751.i	0.543774	−	0.395075i	−0.281711	−	0.959499i	$-0.590902\pi$
$359$	1.32787e6	−	964751.i	0.543774	−	0.395075i	0.825485	+	0.564425i	$0.190902\pi$
$360$	1.29373e6	+	1.74825e6i	0.526122	+	0.710963i
$361$	−5.01740e6	−	3.64536e6i	−2.02633	−	1.47222i
$362$	2.74557e6	−	1.99478e6i	1.10119	−	0.800061i
$363$	−170162.	+	123630.i	−0.0677791	+	0.0492444i
$364$	−762566.	−	554037.i	−0.301664	−	0.219172i
$365$	−4.23999e6	−	1.33670e6i	−1.66584	−	0.525174i
$366$	1.51727e6	−	1.10236e6i	0.592052	−	0.430151i
$367$	−361210.	+	1.11169e6i	−0.139989	+	0.430842i	−0.996333	−	0.0855643i	$-0.972731\pi$
$367$	−361210.	+	1.11169e6i	−0.139989	+	0.430842i	0.856343	+	0.516407i	$0.172731\pi$
$368$	568320.			0.218763
$369$	715748.	−	2.20285e6i	0.273649	−	0.842206i
$370$	−1.22744e6	+	410743.i	−0.466119	+	0.155979i
$371$	−531799.	−	1.63671e6i	−0.200592	−	0.617358i
$372$	−186643.	−	574429.i	−0.0699287	−	0.215218i
$373$	46413.2	+	33721.2i	0.0172731	+	0.0125496i	0.596388	−	0.802696i	$-0.296602\pi$
$373$	46413.2	+	33721.2i	0.0172731	+	0.0125496i	−0.579115	+	0.815246i	$0.696602\pi$
$374$	1.28533e6			0.475157
$375$	4.88612e6	+	1.44679e6i	1.79426	+	0.531284i
$376$	−320082.			−0.116759
$377$	1.89443e6	+	1.37639e6i	0.686477	+	0.498754i
$378$	875271.	+	2.69381e6i	0.315074	+	0.969699i
$379$	−393812.	−	1.21203e6i	−0.140829	−	0.433426i	0.855622	−	0.517601i	$-0.173175\pi$
$379$	−393812.	−	1.21203e6i	−0.140829	−	0.433426i	−0.996451	+	0.0841744i	$0.973175\pi$
$380$	−2.49865e6	+	836131.i	−0.887659	+	0.297040i
$381$	1.78929e6	−	5.50687e6i	0.631493	−	1.94354i
$382$	49757.7			0.0174462
$383$	−689077.	+	2.12076e6i	−0.240033	+	0.738745i	0.756381	+	0.654131i	$0.226966\pi$
$383$	−689077.	+	2.12076e6i	−0.240033	+	0.738745i	−0.996414	+	0.0846137i	$0.973034\pi$
$384$	−386648.	+	280917.i	−0.133810	+	0.0972186i
$385$	1.39115e6	+	438577.i	0.478325	+	0.150797i
$386$	−1.68002e6	−	1.22061e6i	−0.573914	−	0.416973i
$387$	6.12254e6	−	4.44828e6i	2.07804	−	1.50978i
$388$	−1.46515e6	+	1.06449e6i	−0.494086	+	0.358974i
$389$	306137.	+	222422.i	0.102575	+	0.0745252i	0.637890	−	0.770127i	$-0.279807\pi$
$389$	306137.	+	222422.i	0.102575	+	0.0745252i	−0.535315	+	0.844652i	$0.679807\pi$
$390$	−3.43590e6	−	4.64302e6i	−1.14388	−	1.54575i
$391$	1.47140e6	−	1.06904e6i	0.486732	−	0.353631i
$392$	244866.	−	753621.i	0.0804848	−	0.247707i
$393$	−261750.			−0.0854879
$394$	51330.2	−	157978.i	0.0166584	−	0.0512692i
$395$	1.56104e6	+	2.10948e6i	0.503411	+	0.680272i
$396$	1.17888e6	+	3.62821e6i	0.377772	+	1.16266i
$397$	575541.	+	1.77133e6i	0.183274	+	0.564059i	0.999914	−	0.0130879i	$-0.00416613\pi$
$397$	575541.	+	1.77133e6i	0.183274	+	0.564059i	−0.816641	+	0.577147i	$0.804166\pi$
$398$	−915553.	−	665188.i	−0.289718	−	0.210493i
$399$	−5.71660e6			−1.79765
$400$	−233845.	+	765060.i	−0.0730766	+	0.239081i
$401$	−4.75109e6			−1.47548			−0.737738	−	0.675087i	$-0.764106\pi$
$401$	−4.75109e6			−1.47548			−0.737738	+	0.675087i	$0.764106\pi$
$402$	1.16973e6	+	849856.i	0.361010	+	0.262289i
$403$	354131.	+	1.08990e6i	0.108618	+	0.334291i
$404$	446033.	+	1.37275e6i	0.135961	+	0.418444i
$405$	79715.2	+	9.09885e6i	0.0241493	+	2.75644i
$406$	217443.	−	669220.i	0.0654681	−	0.201490i
$407$	−2.27039e6			−0.679382
$408$	−472631.	+	1.45461e6i	−0.140563	+	0.432609i
$409$	4.60257e6	−	3.34396e6i	1.36048	−	0.988446i	0.362065	−	0.932153i	$-0.382072\pi$
$409$	4.60257e6	−	3.34396e6i	1.36048	−	0.988446i	0.998414	−	0.0562935i	$-0.0179282\pi$
$410$	807949.	−	270367.i	0.237369	−	0.0794317i
$411$	6.38504e6	+	4.63901e6i	1.86449	+	1.35463i
$412$	1.34094e6	−	974249.i	0.389194	−	0.282766i
$413$	−922081.	+	669931.i	−0.266008	+	0.193266i
$414$	4.36718e6	+	3.17294e6i	1.25228	+	0.909832i
$415$	−13934.2	−	1.59047e6i	−0.00397156	−	0.453321i
$416$	733613.	−	533001.i	0.207842	−	0.151006i
$417$	548567.	−	1.68832e6i	0.154486	−	0.475460i
$418$	−4.62172e6			−1.29379
$419$	−265427.	+	816900.i	−0.0738601	+	0.227318i	−0.981171	−	0.193143i	$-0.938132\pi$
$419$	−265427.	+	816900.i	−0.0738601	+	0.227318i	0.907310	+	0.420461i	$0.138132\pi$
$420$	−1.00788e6	+	1.41309e6i	−0.278794	+	0.390884i
$421$	1.15057e6	+	3.54109e6i	0.316379	+	0.973715i	0.975183	+	0.221400i	$0.0710628\pi$
$421$	1.15057e6	+	3.54109e6i	0.316379	+	0.973715i	−0.658804	+	0.752315i	$0.728937\pi$
$422$	561603.	+	1.72844e6i	0.153514	+	0.472468i
$423$	−2.45962e6	−	1.78702e6i	−0.668372	−	0.485600i
$424$	1.65560e6			0.447240
$425$	833679.	+	2.42064e6i	0.223886	+	0.650068i
$426$	−3.04782e6			−0.813702
$427$	865076.	+	628515.i	0.229607	+	0.166819i
$428$	−631149.	−	1.94248e6i	−0.166541	−	0.512562i
$429$	−3.13088e6	−	9.63585e6i	−0.821339	−	2.52782i
$430$	2.65493e6	+	836995.i	0.692439	+	0.218299i
$431$	344537.	−	1.06038e6i	0.0893394	−	0.274958i	−0.896398	−	0.443251i	$-0.853825\pi$
$431$	344537.	−	1.06038e6i	0.0893394	−	0.274958i	0.985737	+	0.168292i	$0.0538252\pi$
$432$	−2.72489e6			−0.702490
$433$	357956.	−	1.10168e6i	0.0917509	−	0.282380i	−0.894642	−	0.446783i	$-0.852570\pi$
$433$	357956.	−	1.10168e6i	0.0917509	−	0.282380i	0.986393	+	0.164403i	$0.0525696\pi$
$434$	278599.	−	202414.i	0.0709995	−	0.0515841i
$435$	2.50385e6	−	3.51053e6i	0.634433	−	0.889506i
$436$	1.87154e6	+	1.35975e6i	0.471501	+	0.342566i
$437$	−5.29077e6	+	3.84397e6i	−1.32530	+	0.962890i
$438$	7.50709e6	−	5.45422e6i	1.86976	−	1.35846i
$439$	−891543.	−	647744.i	−0.220791	−	0.160414i	0.471892	−	0.881656i	$-0.343571\pi$
$439$	−891543.	−	647744.i	−0.220791	−	0.160414i	−0.692683	+	0.721243i	$0.743571\pi$
$440$	−814842.	+	1.14245e6i	−0.200651	+	0.281323i
$441$	6.08912e6	−	4.42401e6i	1.49093	−	1.08323i
$442$	896753.	−	2.75992e6i	0.218332	−	0.671956i
$443$	536178.			0.129807			0.0649037	−	0.997892i	$-0.479326\pi$
$443$	536178.			0.129807			0.0649037	+	0.997892i	$0.479326\pi$
$444$	834845.	−	2.56939e6i	0.200978	−	0.618547i
$445$	−1.23696e6	−	389966.i	−0.296112	−	0.0933527i
$446$	592483.	+	1.82347e6i	0.141039	+	0.434073i
$447$	543848.	+	1.67379e6i	0.128739	+	0.396216i
$448$	−220449.	−	160166.i	−0.0518935	−	0.0377028i
$449$	3.31855e6			0.776842			0.388421	−	0.921482i	$-0.373021\pi$
$449$	3.31855e6			0.776842			0.388421	+	0.921482i	$0.373021\pi$
$450$	−6.06830e6	+	4.57344e6i	−1.41265	+	1.06466i
$451$	1.49445e6			0.345972
$452$	−2.31052e6	−	1.67869e6i	−0.531941	−	0.386478i
$453$	1.31271e6	+	4.04011e6i	0.300555	+	0.925013i
$454$	−1.01193e6	−	3.11439e6i	−0.230414	−	0.709142i
$455$	1.91231e6	−	2.68115e6i	0.433042	−	0.607146i
$456$	1.69945e6	−	5.23038e6i	0.382734	−	1.17794i
$457$	356547.			0.0798595			0.0399297	−	0.999202i	$-0.487287\pi$
$457$	356547.			0.0798595			0.0399297	+	0.999202i	$0.487287\pi$
$458$	1.25304e6	−	3.85647e6i	0.279127	−	0.859066i
$459$	−7.05486e6	+	5.12565e6i	−1.56299	+	1.13558i
$460$	17395.5	+	1.98555e6i	0.00383302	+	0.437509i
$461$	−87505.5	−	63576.5i	−0.0191771	−	0.0139330i	0.578155	−	0.815927i	$-0.303773\pi$
$461$	−87505.5	−	63576.5i	−0.0191771	−	0.0139330i	−0.597333	+	0.801994i	$0.703773\pi$
$462$	−2.46310e6	+	1.78955e6i	−0.536880	+	0.390066i
$463$	−1.86264e6	+	1.35329e6i	−0.403810	+	0.293385i	−0.771091	−	0.636725i	$-0.780289\pi$
$463$	−1.86264e6	+	1.35329e6i	−0.403810	+	0.293385i	0.367281	+	0.930110i	$0.380289\pi$
$464$	547658.	+	397897.i	0.118090	+	0.0857977i
$465$	2.00118e6	−	669662.i	0.429195	−	0.143623i
$466$	548212.	−	398300.i	0.116946	−	0.0849660i
$467$	2.00543e6	−	6.17207e6i	0.425515	−	1.30960i	−0.476985	−	0.878911i	$-0.658270\pi$
$467$	2.00543e6	−	6.17207e6i	0.425515	−	1.30960i	0.902500	−	0.430689i	$-0.141730\pi$
$468$	8.61311e6			1.81780
$469$	−254742.	+	784016.i	−0.0534772	+	0.164586i
$470$	−9797.25	−	1.11828e6i	−0.00204578	−	0.233509i
$471$	3.71746e6	+	1.14412e7i	0.772137	+	2.37639i
$472$	−338831.	−	1.04282e6i	−0.0700049	−	0.215453i
$473$	3.95036e6	+	2.87010e6i	0.811864	+	0.589854i
$474$	−5.47748e6			−1.11979
$475$	−2.99769e6	−	8.70399e6i	−0.609611	−	1.77005i
$476$	−872030.			−0.176406
$477$	1.27222e7	+	9.24324e6i	2.56016	+	1.86007i
$478$	−1.13338e6	−	3.48818e6i	−0.226885	−	0.698280i
$479$	1.31035e6	+	4.03283e6i	0.260944	+	0.803103i	0.992600	+	0.121429i	$0.0387477\pi$
$479$	1.31035e6	+	4.03283e6i	0.260944	+	0.803103i	−0.731656	+	0.681674i	$0.761252\pi$
$480$	−993279.	−	1.34224e6i	−0.196774	−	0.265906i
$481$	−1.58401e6	+	4.87507e6i	−0.312172	+	0.960767i
$482$	1.75193e6			0.343477
$483$	−1.33126e6	+	4.09721e6i	−0.259655	+	0.799136i
$484$	93334.8	−	67811.7i	0.0181105	−	0.0131580i
$485$	−3.76389e6	−	5.08624e6i	−0.726578	−	0.981844i
$486$	−6.99491e6	−	5.08210e6i	−1.34336	−	0.976006i
$487$	1.71797e6	−	1.24818e6i	0.328242	−	0.238482i	−0.411442	−	0.911436i	$-0.634975\pi$
$487$	1.71797e6	−	1.24818e6i	0.328242	−	0.238482i	0.739684	+	0.672954i	$0.234975\pi$
$488$	−832231.	+	604651.i	−0.158196	+	0.114936i
$489$	−1.51825e7	−	1.10307e7i	−2.87125	−	2.08609i
$490$	2.64044e6	+	832427.i	0.496805	+	0.156623i
$491$	−6.36298e6	+	4.62298e6i	−1.19112	+	0.865402i	−0.993383	−	0.114852i	$-0.963361\pi$
$491$	−6.36298e6	+	4.62298e6i	−1.19112	+	0.865402i	−0.197741	+	0.980254i	$0.563361\pi$
$492$	−549526.	+	1.69127e6i	−0.102347	+	0.314992i
$493$	2.16637e6			0.401435
$494$	−3.22449e6	+	9.92395e6i	−0.594488	+	1.82965i
$495$	−1.26399e7	+	4.22972e6i	−2.31862	+	0.775887i
$496$	102375.	+	315078.i	0.0186849	+	0.0575061i
$497$	−536987.	−	1.65267e6i	−0.0975152	−	0.300121i
$498$	2.68580e6	+	1.95135e6i	0.485289	+	0.352583i
$499$	3.33102e6			0.598860			0.299430	−	0.954118i	$-0.403203\pi$
$499$	3.33102e6			0.598860			0.299430	+	0.954118i	$0.403203\pi$
$500$	−2.68006e6	−	793572.i	−0.479424	−	0.141959i
$501$	7.03888e6			1.25288
$502$	−5.49512e6	−	3.99244e6i	−0.973235	−	0.707096i
$503$	−117278.	−	360945.i	−0.0206680	−	0.0636094i	0.940191	−	0.340649i	$-0.110647\pi$
$503$	−117278.	−	360945.i	−0.0206680	−	0.0636094i	−0.960859	+	0.277039i	$0.910647\pi$
$504$	−799803.	−	2.46154e6i	−0.140251	−	0.431649i
$505$	−4.78235e6	+	1.60033e6i	−0.834474	+	0.279243i
$506$	−1.07629e6	+	3.31249e6i	−0.186876	+	0.575146i
$507$	−1.20442e7			−2.08092
$508$	−981437.	+	3.02055e6i	−0.168734	+	0.519310i
$509$	6.61037e6	−	4.80271e6i	1.13092	−	0.821660i	0.145090	−	0.989418i	$-0.453653\pi$
$509$	6.61037e6	−	4.80271e6i	1.13092	−	0.821660i	0.985828	+	0.167758i	$0.0536529\pi$
$510$	−5.09646e6	−	1.60672e6i	−0.867648	−	0.273536i
$511$	4.28019e6	+	3.10974e6i	0.725122	+	0.526832i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	2.53674e7	−	1.84305e7i	4.25581	−	3.09203i
$514$	−295055.	−	214370.i	−0.0492601	−	0.0357896i
$515$	3.44480e6	+	4.65505e6i	0.572329	+	0.773403i
$516$	−4.70067e6	+	3.41524e6i	−0.777205	+	0.564672i
$517$	606176.	−	1.86562e6i	0.0997406	−	0.306970i
$518$	1.54034e6			0.252227
$519$	−2.11630e6	+	6.51332e6i	−0.344873	+	1.06141i
$520$	1.88461e6	+	2.54673e6i	0.305643	+	0.413023i
$521$	2.81520e6	+	8.66428e6i	0.454375	+	1.39842i	0.871867	+	0.489742i	$0.162909\pi$
$521$	2.81520e6	+	8.66428e6i	0.454375	+	1.39842i	−0.417492	+	0.908680i	$0.637091\pi$
$522$	1.98694e6	+	6.11517e6i	0.319160	+	0.982273i
$523$	−4.55289e6	−	3.30787e6i	−0.727835	−	0.528803i	0.161043	−	0.986947i	$-0.448514\pi$
$523$	−4.55289e6	−	3.30787e6i	−0.727835	−	0.528803i	−0.888878	+	0.458145i	$0.848514\pi$
$524$	143571.			0.0228423
$525$	−4.96780e6	−	3.47799e6i	−0.786622	−	0.550719i
$526$	6.64947e6			1.04791
$527$	857729.	+	623177.i	0.134531	+	0.0977428i
$528$	−905099.	−	2.78561e6i	−0.141290	−	0.434846i
$529$	−465980.	−	1.43414e6i	−0.0723983	−	0.222819i
$530$	50675.5	+	5.78420e6i	0.00783626	+	0.894445i
$531$	3.21836e6	−	9.90508e6i	0.495334	−	1.52448i
$532$	3.13559e6			0.480330
$533$	1.04265e6	−	3.20895e6i	0.158972	−	0.489266i
$534$	2.19010e6	−	1.59120e6i	0.332361	−	0.241474i
$535$	6.76715e6	−	2.26451e6i	1.02217	−	0.342051i
$536$	−641602.	−	466151.i	−0.0964614	−	0.0700833i
$537$	−6.11838e6	+	4.44526e6i	−0.915589	+	0.665214i
$538$	−5.36401e6	+	3.89718e6i	−0.798976	+	0.580490i
$539$	3.92880e6	+	2.85444e6i	0.582489	+	0.423203i
$540$	−83405.2	−	9.52002e6i	−0.0123086	−	1.40493i
$541$	−376173.	+	273306.i	−0.0552579	+	0.0401472i	−0.615071	−	0.788471i	$-0.710873\pi$
$541$	−376173.	+	273306.i	−0.0552579	+	0.0401472i	0.559813	+	0.828619i	$0.310873\pi$
$542$	2.94091e6	−	9.05120e6i	0.430015	−	1.32345i
$543$	−2.47488e7			−3.60209
$544$	259241.	−	797861.i	0.0375583	−	0.115593i
$545$	−4.69332e6	+	6.58026e6i	−0.676844	+	0.948969i
$546$	2.12413e6	+	6.53740e6i	0.304929	+	0.938476i
$547$	2.44717e6	+	7.53163e6i	0.349701	+	1.07627i	0.959019	+	0.283342i	$0.0914433\pi$
$547$	2.44717e6	+	7.53163e6i	0.349701	+	1.07627i	−0.609318	+	0.792926i	$0.708557\pi$
$548$	−3.50223e6	−	2.54452e6i	−0.498189	−	0.361955i
$549$	−9.77095e6			−1.38359
$550$	−4.01634e6	−	2.81186e6i	−0.566140	−	0.396358i
$551$	−7.78970e6			−1.09305
$552$	−3.35297e6	−	2.43607e6i	−0.468362	−	0.340285i
$553$	−965062.	−	2.97016e6i	−0.134197	−	0.413015i
$554$	−1.49164e6	−	4.59079e6i	−0.206485	−	0.635497i
$555$	9.00228e6	+	2.83807e6i	1.24057	+	0.391103i
$556$	−300892.	+	926052.i	−0.0412785	+	0.127042i
$557$	−3.10398e6			−0.423917			−0.211958	−	0.977279i	$-0.567984\pi$
$557$	−3.10398e6			−0.423917			−0.211958	+	0.977279i	$0.567984\pi$
$558$	−972399.	+	2.99273e6i	−0.132208	+	0.406895i
$559$	8.91888e6	−	6.47995e6i	1.20720	−	0.877086i
$560$	552826.	−	775090.i	0.0744935	−	0.104444i
$561$	−7.58320e6	−	5.50952e6i	−1.01729	−	0.739106i
$562$	1.22717e6	−	891593.i	0.163895	−	0.119076i
$563$	7.24800e6	−	5.26598e6i	0.963712	−	0.700178i	0.00970232	−	0.999953i	$-0.496912\pi$
$563$	7.24800e6	−	5.26598e6i	0.963712	−	0.700178i	0.954010	+	0.299775i	$0.0969116\pi$
$564$	1.88841e6	+	1.37201e6i	0.249977	+	0.181619i
$565$	5.79416e6	−	8.12370e6i	0.763606	−	1.07061i
$566$	−5.43985e6	+	3.95228e6i	−0.713750	+	0.518570i
$567$	3.34619e6	−	1.02985e7i	0.437112	−	1.34529i
$568$	1.67175e6			0.217420
$569$	416378.	−	1.28148e6i	0.0539147	−	0.165932i	−0.920473	−	0.390805i	$-0.872197\pi$
$569$	416378.	−	1.28148e6i	0.0539147	−	0.165932i	0.974388	+	0.224873i	$0.0721966\pi$
$570$	1.83255e7	+	5.77733e6i	2.36249	+	0.744800i
$571$	−1.58143e6	−	4.86715e6i	−0.202983	−	0.624719i	−0.999790	−	0.0204845i	$-0.993479\pi$
$571$	−1.58143e6	−	4.86715e6i	−0.202983	−	0.624719i	0.796807	−	0.604234i	$-0.206521\pi$
$572$	1.71730e6	+	5.28532e6i	0.219461	+	0.675431i
$573$	−293560.	−	213284.i	−0.0373517	−	0.0271376i
$574$	−1.01391e6			−0.128445
$575$	−6.93643e6	+	121550.i	−0.874917	+	0.0153315i
$576$	2.48995e6			0.312705
$577$	882029.	+	640832.i	0.110292	+	0.0801317i	0.641564	−	0.767069i	$-0.278286\pi$
$577$	882029.	+	640832.i	0.110292	+	0.0801317i	−0.531272	+	0.847201i	$0.678286\pi$
$578$	925410.	+	2.84812e6i	0.115216	+	0.354600i
$579$	4.67971e6	+	1.44027e7i	0.580126	+	1.78544i
$580$	−1.37338e6	+	1.92554e6i	−0.169520	+	0.237675i
$581$	−584912.	+	1.80017e6i	−0.0718870	+	0.221245i
$582$	1.32070e7			1.61620
$583$	−3.13540e6	+	9.64976e6i	−0.382051	+	1.17583i
$584$	−4.11768e6	+	2.99167e6i	−0.499598	+	0.362979i
$585$	263635.	+	3.00918e7i	0.0318503	+	3.63545i
$586$	6.74853e6	+	4.90310e6i	0.811831	+	0.589829i
$587$	4.34727e6	−	3.15848e6i	0.520741	−	0.378341i	−0.296142	−	0.955144i	$-0.595700\pi$
$587$	4.34727e6	−	3.15848e6i	0.520741	−	0.378341i	0.816883	+	0.576803i	$0.195700\pi$
$588$	−4.67501e6	+	3.39660e6i	−0.557622	+	0.405136i
$589$	−3.08417e6	−	2.24078e6i	−0.366311	−	0.266140i
$590$	3.63294e6	−	1.21570e6i	0.429663	−	0.143780i
$591$	−980002.	+	712013.i	−0.115414	+	0.0838531i
$592$	−457917.	+	1.40933e6i	−0.0537011	+	0.165275i
$593$	4.93112e6			0.575849			0.287924	−	0.957653i	$-0.407035\pi$
$593$	4.93112e6			0.575849			0.287924	+	0.957653i	$0.407035\pi$
$594$	5.16045e6	−	1.58822e7i	0.600097	−	1.84691i
$595$	−26691.6	−	3.04663e6i	−0.00309088	−	0.352799i
$596$	−298304.	−	918084.i	−0.0343988	−	0.105869i
$597$	2.55027e6	+	7.84894e6i	0.292854	+	0.901312i
$598$	6.36180e6	+	4.62212e6i	0.727490	+	0.528553i
$599$	8.84620e6			1.00737			0.503686	−	0.863887i	$-0.331977\pi$
$599$	8.84620e6			1.00737			0.503686	+	0.863887i	$0.331977\pi$
$600$	4.65902e6	−	3.51133e6i	0.528344	−	0.398192i
$601$	−608229.			−0.0686881			−0.0343440	−	0.999410i	$-0.510934\pi$
$601$	−608229.			−0.0686881			−0.0343440	+	0.999410i	$0.510934\pi$
$602$	−2.68010e6	−	1.94721e6i	−0.301412	−	0.218988i
$603$	−2.32777e6	−	7.16415e6i	−0.260704	−	0.802364i
$604$	−720030.	−	2.21603e6i	−0.0803079	−	0.247162i
$605$	239772.	+	324010.i	0.0266324	+	0.0359890i
$606$	3.25271e6	−	1.00108e7i	0.359802	−	1.10736i
$607$	3.20411e6			0.352968			0.176484	−	0.984303i	$-0.443528\pi$
$607$	3.20411e6			0.352968			0.176484	+	0.984303i	$0.443528\pi$
$608$	−932161.	+	2.86890e6i	−0.102266	+	0.314743i
$609$	−4.15144e6	+	3.01620e6i	−0.453582	+	0.329546i
$610$	−2.13796e6	−	2.88908e6i	−0.232635	−	0.314365i
$611$	−3.58301e6	−	2.60321e6i	−0.388280	−	0.282102i
$612$	6.44657e6	−	4.68371e6i	0.695746	−	0.505489i
$613$	−1.26571e7	+	9.19594e6i	−1.36045	+	0.988428i	−0.362038	+	0.932163i	$0.617919\pi$
$613$	−1.26571e7	+	9.19594e6i	−1.36045	+	0.988428i	−0.998416	+	0.0562643i	$0.982081\pi$
$614$	8.04050e6	+	5.84177e6i	0.860721	+	0.625350i
$615$	−5.92564e6	−	1.86812e6i	−0.631753	−	0.199167i
$616$	1.35102e6	−	981577.i	0.143454	−	0.104225i
$617$	3.84089e6	−	1.18210e7i	0.406180	−	1.25009i	−0.513726	−	0.857955i	$-0.671735\pi$
$617$	3.84089e6	−	1.18210e7i	0.406180	−	1.25009i	0.919906	−	0.392140i	$-0.128265\pi$
$618$	−1.20873e7			−1.27309
$619$	−1.43022e6	+	4.40176e6i	−0.150029	+	0.461743i	−0.997623	−	0.0689024i	$-0.978050\pi$
$619$	−1.43022e6	+	4.40176e6i	−0.150029	+	0.461743i	0.847594	+	0.530645i	$0.178050\pi$
$620$	−1.09766e6	+	367314.i	−0.114680	+	0.0383759i
$621$	−7.30205e6	−	2.24734e7i	−0.759829	−	2.33851i
$622$	889535.	+	2.73771e6i	0.0921907	+	0.283734i
$623$	1.24869e6	+	907227.i	0.128895	+	0.0936474i
$624$	−6.61284e6			−0.679871
$625$	2.69049e6	−	9.38769e6i	0.275506	−	0.961299i
$626$	−2.29171e6			−0.233735
$627$	2.72672e7	+	1.98108e7i	2.76995	+	2.01248i
$628$	−2.03905e6	−	6.27555e6i	−0.206314	−	0.634969i
$629$	1.46544e6	+	4.51016e6i	0.147687	+	0.454533i
$630$	8.57546e6	−	2.86963e6i	0.860808	−	0.288055i
$631$	2.97606e6	−	9.15937e6i	0.297556	−	0.915783i	−0.684795	−	0.728736i	$-0.740108\pi$
$631$	2.97606e6	−	9.15937e6i	0.297556	−	0.915783i	0.982351	−	0.187047i	$-0.0598917\pi$
$632$	3.00443e6			0.299206
$633$	4.09551e6	−	1.26047e7i	0.406255	−	1.25032i
$634$	−1.99893e6	+	1.45231e6i	−0.197504	+	0.143495i
$635$	−1.05830e7	−	3.33641e6i	−1.04154	−	0.328356i
$636$	−9.76768e6	−	7.09663e6i	−0.957522	−	0.695680i
$637$	8.87021e6	−	6.44458e6i	0.866134	−	0.629283i
$638$	−3.35633e6	+	2.43852e6i	−0.326447	+	0.237178i
$639$	1.28463e7	+	9.33340e6i	1.24459	+	0.904248i
$640$	544819.	+	736229.i	0.0525778	+	0.0710498i
$641$	1.75392e6	−	1.27430e6i	0.168603	−	0.122497i	−0.500284	−	0.865861i	$-0.666771\pi$
$641$	1.75392e6	−	1.27430e6i	0.168603	−	0.122497i	0.668887	+	0.743364i	$0.266771\pi$
$642$	−4.60267e6	+	1.41656e7i	−0.440730	+	1.35643i
$643$	9.32371e6			0.889327			0.444663	−	0.895698i	$-0.353323\pi$
$643$	9.32371e6			0.889327			0.444663	+	0.895698i	$0.353323\pi$
$644$	730207.	−	2.24734e6i	0.0693795	−	0.213528i
$645$	−1.20758e7	−	1.63183e7i	−1.14292	−	1.54446i
$646$	2.98313e6	+	9.18112e6i	0.281249	+	0.865595i
$647$	−6.06148e6	−	1.86553e7i	−0.569269	−	1.75203i	−0.654912	−	0.755705i	$-0.727294\pi$
$647$	−6.06148e6	−	1.86553e7i	−0.569269	−	1.75203i	0.0856430	−	0.996326i	$-0.472706\pi$
$648$	8.42783e6	+	6.12318e6i	0.788457	+	0.572848i
$649$	6.71980e6			0.626246
$650$	−8.83987e6	+	6.66227e6i	−0.820658	+	0.618498i
$651$	−2.51131e6			−0.232246
$652$	8.32770e6	+	6.05043e6i	0.767195	+	0.557400i
$653$	1.19021e6	+	3.66308e6i	0.109230	+	0.336174i	0.990700	−	0.136066i	$-0.0434458\pi$
$653$	1.19021e6	+	3.66308e6i	0.109230	+	0.336174i	−0.881470	+	0.472239i	$0.843446\pi$
$654$	−5.21318e6	−	1.60445e7i	−0.476605	−	1.46684i
$655$	4394.51	+	501598.i	0.000400228	+	0.0456828i
$656$	301418.	−	927671.i	0.0273470	−	0.0841655i
$657$	−4.83443e7			−4.36950
$658$	−411257.	+	1.26572e6i	−0.0370296	+	0.113965i
$659$	4.55202e6	−	3.30723e6i	0.408310	−	0.296655i	−0.364607	−	0.931161i	$-0.618797\pi$
$659$	4.55202e6	−	3.30723e6i	0.408310	−	0.296655i	0.772917	+	0.634507i	$0.218797\pi$
$660$	9.70444e6	−	3.24743e6i	0.867183	−	0.290188i
$661$	4.36608e6	+	3.17214e6i	0.388676	+	0.282390i	0.764913	−	0.644134i	$-0.222782\pi$
$661$	4.36608e6	+	3.17214e6i	0.388676	+	0.282390i	−0.376237	+	0.926524i	$0.622782\pi$
$662$	−7.87746e6	+	5.72331e6i	−0.698620	+	0.507577i
$663$	−1.71209e7	+	1.24391e7i	−1.51267	+	1.09902i
$664$	−1.47318e6	−	1.07033e6i	−0.129669	−	0.0942098i
$665$	95975.9	+	1.09549e7i	0.00841605	+	0.960624i
$666$	−1.13871e7	+	8.27321e6i	−0.994781	+	0.722751i
$667$	−1.81404e6	+	5.58305e6i	−0.157882	+	0.485911i
$668$	−3.86087e6			−0.334768
$669$	4.32070e6	−	1.32978e7i	0.373241	−	1.14872i
$670$	1.60896e6	−	2.25585e6i	0.138471	−	0.194143i
$671$	−1.94816e6	−	5.99581e6i	−0.167039	−	0.514093i
$672$	614061.	+	1.88988e6i	0.0524552	+	0.161440i
$673$	−3.05186e6	−	2.21731e6i	−0.259733	−	0.188707i	0.450296	−	0.892879i	$-0.351318\pi$
$673$	−3.05186e6	−	2.21731e6i	−0.259733	−	0.188707i	−0.710029	+	0.704172i	$0.751318\pi$
$674$	−1.00714e7			−0.853965
$675$	3.32578e7	−	582789.i	2.80953	−	0.0492325i
$676$	6.60629e6			0.556020
$677$	−1.07590e7	−	7.81690e6i	−0.902198	−	0.655485i	0.0368319	−	0.999321i	$-0.488273\pi$
$677$	−1.07590e7	−	7.81690e6i	−0.902198	−	0.655485i	−0.939030	+	0.343837i	$0.888273\pi$
$678$	6.43596e6	+	1.98078e7i	0.537698	+	1.65487i
$679$	2.32690e6	+	7.16145e6i	0.193688	+	0.596110i
$680$	2.79544e6	+	881294.i	0.231834	+	0.0730884i
$681$	−7.37951e6	+	2.27118e7i	−0.609761	+	1.87665i
$682$	−2.03033e6			−0.167150
$683$	−1.53792e6	+	4.73323e6i	−0.126149	+	0.388245i	−0.994109	−	0.108389i	$-0.965431\pi$
$683$	−1.53792e6	+	4.73323e6i	−0.126149	+	0.388245i	0.867960	+	0.496634i	$0.165431\pi$
$684$	−2.31802e7	+	1.68414e7i	−1.89442	+	1.37638i
$685$	8.78265e6	−	1.23137e7i	0.715154	−	1.00268i
$686$	−6.28372e6	−	4.56539e6i	−0.509808	−	0.370397i
$687$	−2.39232e7	+	1.73813e7i	−1.93387	+	1.40504i
$688$	2.57834e6	−	1.87328e6i	0.207668	−	0.150880i
$689$	1.85329e7	+	1.34649e7i	1.48728	+	1.08058i
$690$	8.40833e6	−	1.17889e7i	0.672337	−	0.942650i
$691$	−1.10675e7	+	8.04103e6i	−0.881770	+	0.640644i	−0.933719	−	0.358006i	$-0.883457\pi$
$691$	−1.10675e7	+	8.04103e6i	−0.881770	+	0.640644i	0.0519489	+	0.998650i	$0.483457\pi$
$692$	1.16081e6	−	3.57259e6i	0.0921498	−	0.283608i
$693$	1.58619e7			1.25465
$694$	3.04690e6	−	9.37739e6i	0.240137	−	0.739066i
$695$	−3.24458e6	−	1.02289e6i	−0.254798	−	0.0803279i
$696$	−1.52550e6	−	4.69501e6i	−0.119369	−	0.367379i
$697$	−964608.	−	2.96876e6i	−0.0752088	−	0.231469i
$698$	−8.47498e6	−	6.15743e6i	−0.658416	−	0.478367i
$699$	−4.94163e6			−0.382540
$700$	2.72487e6	+	1.90770e6i	0.210184	+	0.147151i
$701$	1.40227e7			1.07780			0.538898	−	0.842371i	$-0.318841\pi$
$701$	1.40227e7			1.07780			0.538898	+	0.842371i	$0.318841\pi$
$702$	−3.05026e7	−	2.21614e7i	−2.33611	−	1.69729i
$703$	−5.26934e6	−	1.62173e7i	−0.402131	−	1.23763i
$704$	496452.	+	1.52792e6i	0.0377525	+	0.116190i
$705$	−4.73563e6	+	6.63959e6i	−0.358843	+	0.503116i
$706$	2.56791e6	−	7.90321e6i	0.193896	−	0.596749i
$707$	6.00143e6			0.451551
$708$	−2.47094e6	+	7.60477e6i	−0.185259	+	0.570168i
$709$	−8.82382e6	+	6.41088e6i	−0.659236	+	0.478963i	−0.866405	−	0.499342i	$-0.833575\pi$
$709$	−8.82382e6	+	6.41088e6i	−0.659236	+	0.478963i	0.207169	+	0.978305i	$0.433575\pi$
$710$	51169.8	+	5.84062e6i	0.00380950	+	0.434824i
$711$	2.30872e7	+	1.67738e7i	1.71276	+	1.24439i
$712$	−1.20128e6	+	872782.i	−0.0888065	+	0.0645217i
$713$	−2.32425e6	+	1.68866e6i	−0.171221	+	0.124400i
$714$	5.14479e6	+	3.73791e6i	0.377678	+	0.274399i
$715$	−1.84129e7	+	6.16156e6i	−1.34697	+	0.450739i
$716$	3.35597e6	−	2.43825e6i	0.244644	−	0.177744i
$717$	−8.26521e6	+	2.54377e7i	−0.600421	+	1.84791i
$718$	6.56533e6			0.475276
$719$	−4.25095e6	+	1.30831e7i	−0.306665	+	0.943817i	0.672386	+	0.740201i	$0.265270\pi$
$719$	−4.25095e6	+	1.30831e7i	−0.306665	+	0.943817i	−0.979051	+	0.203617i	$0.934730\pi$
$720$	76213.8	+	8.69919e6i	0.00547901	+	0.625385i
$721$	−2.12963e6	−	6.55433e6i	−0.152569	−	0.469559i
$722$	−7.66591e6	−	2.35932e7i	−0.547294	−	1.68440i
$723$	−1.03360e7	−	7.50954e6i	−0.735371	−	0.534278i
$724$	1.35749e7			0.962474
$725$	−6.76935e6	−	4.73926e6i	−0.478302	−	0.334862i
$726$	−841327.			−0.0592411
$727$	−6.38538e6	−	4.63925e6i	−0.448075	−	0.325546i	0.340760	−	0.940150i	$-0.389316\pi$
$727$	−6.38538e6	−	4.63925e6i	−0.448075	−	0.325546i	−0.788835	+	0.614605i	$0.789316\pi$
$728$	−1.16510e6	−	3.58580e6i	−0.0814768	−	0.250760i
$729$	7.26163e6	+	2.23490e7i	0.506076	+	1.55754i
$730$	−1.05781e7	−	1.42945e7i	−0.734684	−	0.992798i
$731$	3.15171e6	−	9.69997e6i	0.218149	−	0.671393i
$732$	7.50179e6			0.517473
$733$	596010.	−	1.83433e6i	0.0409726	−	0.126101i	−0.928478	−	0.371388i	$-0.878882\pi$
$733$	596010.	−	1.83433e6i	0.0409726	−	0.126101i	0.969451	+	0.245287i	$0.0788821\pi$
$734$	−3.78264e6	+	2.74825e6i	−0.259152	+	0.188285i
$735$	−1.20099e7	−	1.62292e7i	−0.820011	−	1.10810i
$736$	1.83912e6	+	1.33620e6i	0.125146	+	0.0909237i
$737$	3.93207e6	−	2.85682e6i	0.266657	−	0.193737i
$738$	7.49541e6	−	5.44574e6i	0.506588	−	0.368058i
$739$	−1.63722e7	−	1.18951e7i	−1.10280	−	0.801228i	−0.121281	−	0.992618i	$-0.538700\pi$
$739$	−1.63722e7	−	1.18951e7i	−1.10280	−	0.801228i	−0.981514	+	0.191391i	$0.938700\pi$
$740$	−4.93781e6	−	1.55670e6i	−0.331478	−	0.104502i
$741$	6.15622e7	−	4.47276e7i	4.11878	−	2.99247i
$742$	2.12720e6	−	6.54684e6i	0.141840	−	0.436538i
$743$	1.52200e7			1.01144			0.505722	−	0.862696i	$-0.331226\pi$
$743$	1.52200e7			1.01144			0.505722	+	0.862696i	$0.331226\pi$
$744$	746573.	−	2.29772e6i	0.0494470	−	0.152182i
$745$	3.19840e6	−	1.07029e6i	0.211126	−	0.0706499i
$746$	70913.1	+	218248.i	0.00466530	+	0.0143583i
$747$	−5.34479e6	−	1.64496e7i	−0.350452	−	1.07858i
$748$	4.15943e6	+	3.02200e6i	0.271819	+	0.197488i
$749$	−8.49219e6			−0.553115
$750$	1.24102e7	+	1.61699e7i	0.805611	+	1.04967i
$751$	1.68477e6			0.109004			0.0545019	−	0.998514i	$-0.482643\pi$
$751$	1.68477e6			0.109004			0.0545019	+	0.998514i	$0.482643\pi$
$752$	−1.03581e6	−	752557.i	−0.0667934	−	0.0485283i
$753$	1.53067e7	+	4.71090e7i	0.983768	+	3.02773i
$754$	2.89443e6	+	8.90815e6i	0.185411	+	0.570636i
$755$	7.72014e6	−	2.58342e6i	0.492899	−	0.164940i
$756$	−3.50108e6	+	1.07752e7i	−0.222791	+	0.685681i
$757$	−298516.			−0.0189334			−0.00946668	−	0.999955i	$-0.503013\pi$
$757$	−298516.			−0.0189334			−0.00946668	+	0.999955i	$0.503013\pi$
$758$	1.57525e6	−	4.84812e6i	0.0995810	−	0.306479i
$759$	2.05487e7	−	1.49295e7i	1.29473	−	0.940678i
$760$	−1.00517e7	−	3.16890e6i	−0.631253	−	0.199010i
$761$	−1.70795e7	−	1.24090e7i	−1.06909	−	0.776739i	−0.0933414	−	0.995634i	$-0.529755\pi$
$761$	−1.70795e7	−	1.24090e7i	−1.06909	−	0.776739i	−0.975748	+	0.218895i	$0.929755\pi$
$762$	1.87377e7	−	1.36137e7i	1.16904	−	0.849356i
$763$	7.78161e6	−	5.65367e6i	0.483903	−	0.351576i
$764$	161019.	+	116987.i	0.00998032	+	0.00725113i
$765$	1.65609e7	+	2.23792e7i	1.02313	+	1.38258i
$766$	−7.21610e6	+	5.24281e6i	−0.444356	+	0.322843i
$767$	4.68828e6	−	1.44290e7i	0.287756	−	0.885623i
$768$	−1.91169e6			−0.116954
$769$	−7.31576e6	+	2.25156e7i	−0.446112	+	1.37299i	0.435148	+	0.900359i	$0.356696\pi$
$769$	−7.31576e6	+	2.25156e7i	−0.446112	+	1.37299i	−0.881260	+	0.472632i	$0.843304\pi$
$770$	3.47071e6	+	4.69006e6i	0.210956	+	0.285070i
$771$	821876.	+	2.52948e6i	0.0497933	+	0.153248i
$772$	−2.56685e6	−	7.89994e6i	−0.155009	−	0.477068i
$773$	1.83058e7	+	1.32999e7i	1.10189	+	0.800571i	0.981368	−	0.192139i	$-0.0615424\pi$
$773$	1.83058e7	+	1.32999e7i	1.10189	+	0.800571i	0.120524	+	0.992710i	$0.461542\pi$
$774$	3.02715e7			1.81627
$775$	−1.31689e6	−	3.82368e6i	−0.0787581	−	0.228679i
$776$	−7.24409e6			−0.431847
$777$	−9.08765e6	−	6.60256e6i	−0.540007	−	0.392338i
$778$	467736.	+	1.43954e6i	0.0277046	+	0.0852660i
$779$	3.46847e6	+	1.06749e7i	0.204783	+	0.630259i
$780$	−202410.	−	2.31034e7i	−0.0119123	−	1.35969i
$781$	−3.16598e6	+	9.74389e6i	−0.185729	+	0.571616i
$782$	7.27502e6			0.425419
$783$	8.69769e6	−	2.67687e7i	0.506990	−	1.56036i
$784$	2.56427e6	−	1.86305e6i	0.148996	−	0.108252i
$785$	2.18626e7	−	7.31596e6i	1.26627	−	0.423738i
$786$	−847040.	−	615410.i	−0.0489043	−	0.0355311i
$787$	−2.35121e7	+	1.70825e7i	−1.35318	+	0.983139i	−0.354329	+	0.935121i	$0.615291\pi$
$787$	−2.35121e7	+	1.70825e7i	−1.35318	+	0.983139i	−0.998846	+	0.0480183i	$0.984709\pi$
$788$	537537.	−	390543.i	0.0308385	−	0.0224055i
$789$	−3.92305e7	−	2.85026e7i	−2.24353	−	1.63002i
$790$	91961.4	+	1.04967e7i	0.00524249	+	0.598388i
$791$	−9.60683e6	+	6.97977e6i	−0.545932	+	0.396643i
$792$	−4.71550e6	+	1.45128e7i	−0.267125	+	0.822127i
$793$	−1.42336e7			−0.803772
$794$	−2.30217e6	+	7.08534e6i	−0.129594	+	0.398850i
$795$	2.44947e7	−	3.43428e7i	1.37453	−	1.92716i
$796$	−1.39884e6	−	4.30519e6i	−0.0782502	−	0.240829i
$797$	9.53472e6	+	2.93449e7i	0.531694	+	1.63639i	0.750685	+	0.660660i	$0.229724\pi$
$797$	9.53472e6	+	2.93449e7i	0.531694	+	1.63639i	−0.218990	+	0.975727i	$0.570276\pi$
$798$	−1.84993e7	−	1.34405e7i	−1.02837	−	0.747152i
$799$	−4.09734e6			−0.227057
$800$	−2.55550e6	+	1.92598e6i	−0.141173	+	0.106397i
$801$	−1.41038e7			−0.776705
$802$	−1.53748e7	−	1.11705e7i	−0.844063	−	0.613248i
$803$	−9.63902e6	−	2.96659e7i	−0.527526	−	1.62356i
$804$	1.78718e6	+	5.50039e6i	0.0975055	+	0.300091i
$805$	7.87395e6	+	2.48235e6i	0.428255	+	0.135012i
$806$	−1.41652e6	+	4.35961e6i	−0.0768043	+	0.236379i
$807$	4.83516e7			2.61353
$808$	−1.78413e6	+	5.49099e6i	−0.0961387	+	0.295885i
$809$	2.00002e7	−	1.45310e7i	1.07439	−	0.780591i	0.0976944	−	0.995216i	$-0.468853\pi$
$809$	2.00002e7	−	1.45310e7i	1.07439	−	0.780591i	0.976696	+	0.214626i	$0.0688532\pi$
$810$	−2.11347e7	+	2.96319e7i	−1.13184	+	1.58689i
$811$	1.41547e7	+	1.02840e7i	0.755699	+	0.549048i	0.897588	−	0.440835i	$-0.145318\pi$
$811$	1.41547e7	+	1.02840e7i	0.755699	+	0.549048i	−0.141889	+	0.989883i	$0.545318\pi$
$812$	2.27709e6	−	1.65440e6i	0.121196	−	0.0880544i
$813$	−5.61482e7	+	4.07941e7i	−2.97927	+	2.16457i
$814$	−7.34713e6	−	5.33800e6i	−0.388648	−	0.282370i
$815$	−2.08836e7	+	2.92799e7i	−1.10131	+	1.54410i
$816$	−4.94945e6	+	3.59599e6i	−0.260215	+	0.189057i
$817$	−1.13327e7	+	3.48785e7i	−0.593990	+	1.82811i
$818$	2.27564e7			1.18910
$819$	1.10666e7	−	3.40594e7i	0.576505	−	1.77430i
$820$	3.25025e6	+	1.02468e6i	0.168804	+	0.0532173i
$821$	−5.16704e6	−	1.59025e7i	−0.267537	−	0.823395i	−0.991098	−	0.133134i	$-0.957496\pi$
$821$	−5.16704e6	−	1.59025e7i	−0.267537	−	0.823395i	0.723561	−	0.690261i	$-0.242504\pi$
$822$	9.75548e6	+	3.00243e7i	0.503581	+	1.54986i
$823$	2.60159e7	+	1.89017e7i	1.33887	+	0.972748i	0.999485	+	0.0321017i	$0.0102200\pi$
$823$	2.60159e7	+	1.89017e7i	1.33887	+	0.972748i	0.339388	+	0.940646i	$0.389780\pi$
$824$	6.62997e6			0.340168
$825$	1.16427e7	+	3.38052e7i	0.595549	+	1.72921i
$826$	−4.55902e6			−0.232499
$827$	2.30817e6	+	1.67698e6i	0.117356	+	0.0852638i	0.644915	−	0.764254i	$-0.276893\pi$
$827$	2.30817e6	+	1.67698e6i	0.117356	+	0.0852638i	−0.527559	+	0.849518i	$0.676893\pi$
$828$	6.67246e6	+	2.05357e7i	0.338228	+	1.04096i
$829$	−8.27178e6	−	2.54579e7i	−0.418035	−	1.28658i	−0.909508	−	0.415687i	$-0.863541\pi$
$829$	−8.27178e6	−	2.54579e7i	−0.418035	−	1.28658i	0.491473	−	0.870893i	$-0.336459\pi$
$830$	3.69433e6	−	5.17964e6i	0.186140	−	0.260978i
$831$	−1.08778e7	+	3.34785e7i	−0.546437	+	1.68176i
$832$	3.62718e6			0.181661
$833$	3.13451e6	−	9.64704e6i	0.156516	−	0.481705i
$834$	5.74467e6	−	4.17375e6i	0.285989	−	0.207784i
$835$	−118176.	−	1.34888e7i	−0.00586559	−	0.669510i
$836$	−1.49562e7	−	1.08663e7i	−0.740126	−	0.537733i
$837$	1.11439e7	−	8.09655e6i	0.549826	−	0.399472i
$838$	−2.77959e6	+	2.01949e6i	−0.136732	+	0.0993416i
$839$	−8.94241e6	−	6.49704e6i	−0.438581	−	0.318648i	0.346490	−	0.938054i	$-0.387373\pi$
$839$	−8.94241e6	−	6.49704e6i	−0.438581	−	0.318648i	−0.785071	+	0.619406i	$0.787373\pi$
$840$	−6.58394e6	+	2.20320e6i	−0.321949	+	0.107735i
$841$	1.09369e7	−	7.94614e6i	0.533219	−	0.387406i
$842$	−4.60228e6	+	1.41644e7i	−0.223714	+	0.688521i
$843$	−1.10618e7			−0.536115
$844$	−2.24641e6	+	6.91375e6i	−0.108551	+	0.334085i
$845$	202209.	+	2.30805e7i	0.00974224	+	1.11200i
$846$	−3.75797e6	−	1.15658e7i	−0.180521	−	0.555586i
$847$	−148231.	−	456208.i	−0.00709954	−	0.0218501i
$848$	5.35763e6	+	3.89255e6i	0.255849	+	0.185885i
$849$	4.90352e7			2.33474
$850$	−2.99343e6	+	9.79346e6i	−0.142109	+	0.464932i
$851$	−1.28504e7			−0.608267
$852$	−9.86295e6	−	7.16585e6i	−0.465487	−	0.338196i
$853$	−8.74789e6	−	2.69232e7i	−0.411652	−	1.26694i	−0.915211	−	0.402975i	$-0.867976\pi$
$853$	−8.74789e6	−	2.69232e7i	−0.411652	−	1.26694i	0.503559	−	0.863961i	$-0.332024\pi$
$854$	1.32172e6	+	4.06783e6i	0.0620147	+	0.190862i
$855$	−5.95486e7	−	8.04696e7i	−2.78584	−	3.76458i
$856$	2.52459e6	−	7.76990e6i	0.117763	−	0.362436i
$857$	2.20251e7			1.02439			0.512195	−	0.858869i	$-0.328832\pi$
$857$	2.20251e7			1.02439			0.512195	+	0.858869i	$0.328832\pi$
$858$	1.25235e7	−	3.85434e7i	0.580775	−	1.78744i
$859$	−9.01320e6	+	6.54847e6i	−0.416769	+	0.302801i	−0.776337	−	0.630318i	$-0.782924\pi$
$859$	−9.01320e6	+	6.54847e6i	−0.416769	+	0.302801i	0.359567	+	0.933119i	$0.382924\pi$
$860$	6.62363e6	+	8.95068e6i	0.305386	+	0.412677i
$861$	5.98183e6	+	4.34606e6i	0.274996	+	0.199796i
$862$	3.60804e6	−	2.62139e6i	0.165388	−	0.120161i
$863$	−2.13071e7	+	1.54805e7i	−0.973861	+	0.707551i	−0.956328	−	0.292295i	$-0.905581\pi$
$863$	−2.13071e7	+	1.54805e7i	−0.973861	+	0.707551i	−0.0175324	+	0.999846i	$0.505581\pi$
$864$	−8.81794e6	−	6.40661e6i	−0.401868	−	0.291974i
$865$	1.25172e7	+	3.94618e6i	0.568809	+	0.179323i
$866$	3.74857e6	−	2.72349e6i	0.169852	−	0.123405i
$867$	6.74859e6	−	2.07700e7i	0.304905	−	0.938402i
$868$	1.37747e6			0.0620558
$869$	−5.68984e6	+	1.75115e7i	−0.255594	+	0.786637i
$870$	1.63564e7	−	5.47339e6i	0.732637	−	0.245165i
$871$	−3.39094e6	−	1.04362e7i	−0.151452	−	0.466121i
$872$	2.85946e6	+	8.80051e6i	0.127348	+	0.391937i
$873$	−5.56663e7	−	4.04439e7i	−2.47205	−	1.79605i
$874$	−2.61590e7			−1.15836
$875$	−6.58156e6	+	9.57833e6i	−0.290609	+	0.422931i
$876$	3.71171e7			1.63423
$877$	8.84345e6	+	6.42514e6i	0.388260	+	0.282087i	0.764742	−	0.644337i	$-0.222866\pi$
$877$	8.84345e6	+	6.42514e6i	0.388260	+	0.282087i	−0.376482	+	0.926424i	$0.622866\pi$
$878$	−1.36216e6	−	4.19228e6i	−0.0596335	−	0.183533i
$879$	−1.87980e7	−	5.78544e7i	−0.820617	−	2.52560i
$880$	−5.32294e6	+	1.78123e6i	−0.231710	+	0.0775380i
$881$	−6.45955e6	+	1.98805e7i	−0.280390	+	0.862952i	0.707353	+	0.706861i	$0.249889\pi$
$881$	−6.45955e6	+	1.98805e7i	−0.280390	+	0.862952i	−0.987743	+	0.156091i	$0.950111\pi$
$882$	3.01063e7			1.30312
$883$	−6.41076e6	+	1.97303e7i	−0.276699	+	0.851592i	0.712066	+	0.702113i	$0.247760\pi$
$883$	−6.41076e6	+	1.97303e7i	−0.276699	+	0.851592i	−0.988765	+	0.149480i	$0.952240\pi$
$884$	9.39092e6	−	6.82290e6i	0.404182	−	0.293656i
$885$	−2.66446e7	−	8.40001e6i	−1.14354	−	0.360513i
$886$	1.73511e6	+	1.26063e6i	0.0742578	+	0.0539515i
$887$	2.54997e7	−	1.85267e7i	1.08825	−	0.790657i	0.109143	−	0.994026i	$-0.465189\pi$
$887$	2.54997e7	−	1.85267e7i	1.08825	−	0.790657i	0.979102	+	0.203369i	$0.0651893\pi$
$888$	8.74261e6	−	6.35188e6i	0.372056	−	0.270315i
$889$	1.06834e7	+	7.76192e6i	0.453371	+	0.329393i
$890$	−3.08603e6	−	4.17023e6i	−0.130594	−	0.176476i
$891$	−5.16501e7	+	3.75260e7i	−2.17960	+	1.58357i
$892$	−2.36993e6	+	7.29390e6i	−0.0997295	+	0.306936i
$893$	1.47329e7			0.618245
$894$	−2.17539e6	+	6.69516e6i	−0.0910319	+	0.280167i
$895$	8.62130e6	+	1.16502e7i	0.359762	+	0.486155i
$896$	−336816.	−	1.03661e6i	−0.0140160	−	0.0431367i
$897$	−1.77208e7	−	5.45390e7i	−0.735364	−	2.26322i
$898$	1.07391e7	+	7.80238e6i	0.444401	+	0.322876i
$899$	−3.42203e6			−0.141216
$900$	−3.03902e7	+	532540.i	−1.25063	+	0.0219152i
$901$	2.11932e7			0.869729
$902$	4.83616e6	+	3.51367e6i	0.197917	+	0.143795i
$903$	7.46543e6	+	2.29762e7i	0.304674	+	0.937690i
$904$	−3.53016e6	−	1.08647e7i	−0.143672	−	0.442178i
$905$	415508.	+	4.74268e7i	0.0168639	+	1.92487i
$906$	−5.25085e6	+	1.61604e7i	−0.212524	+	0.654083i
$907$	9.17543e6			0.370346			0.185173	−	0.982706i	$-0.440715\pi$
$907$	9.17543e6			0.370346			0.185173	+	0.982706i	$0.440715\pi$
$908$	4.04770e6	−	1.24576e7i	0.162927	−	0.501439i
$909$	−4.43662e7	+	3.22340e7i	−1.78091	+	1.29391i
$910$	1.24921e7	−	4.18028e6i	0.500073	−	0.167341i
$911$	−1.30043e7	−	9.44818e6i	−0.519148	−	0.377183i	0.297135	−	0.954836i	$-0.403969\pi$
$911$	−1.30043e7	−	9.44818e6i	−0.519148	−	0.377183i	−0.816283	+	0.577652i	$0.803969\pi$
$912$	1.77969e7	−	1.29302e7i	0.708529	−	0.514777i
$913$	9.02840e6	−	6.55951e6i	0.358454	−	0.260432i
$914$	1.15381e6	+	838293.i	0.0456845	+	0.0331918i
$915$	229619.	+	2.62092e7i	0.00906683	+	1.03491i
$916$	1.31220e7	−	9.53372e6i	0.516729	−	0.375425i
$917$	184468.	−	567733.i	0.00724431	−	0.0222957i
$918$	−3.48811e7			−1.36610
$919$	−1.42292e7	+	4.37929e7i	−0.555764	+	1.71047i	0.138152	+	0.990411i	$0.455884\pi$
$919$	−1.42292e7	+	4.37929e7i	−0.555764	+	1.71047i	−0.693916	+	0.720056i	$0.744116\pi$
$920$	−4.61202e6	+	6.46628e6i	−0.179648	+	0.251875i
$921$	−2.23968e7	−	6.89304e7i	−0.870037	−	2.67770i
$922$	−133697.	−	411476.i	−0.00517956	−	0.0159411i
$923$	1.87136e7	+	1.35962e7i	0.723025	+	0.525309i
$924$	−1.21782e7			−0.469250
$925$	5.28753e6	−	1.72990e7i	0.203188	−	0.664762i
$926$	−9.20941e6			−0.352943
$927$	5.09471e7	+	3.70152e7i	1.94724	+	1.41475i
$928$	836747.	+	2.57524e6i	0.0318951	+	0.0981631i
$929$	489749.	+	1.50729e6i	0.0186180	+	0.0573004i	0.959934	−	0.280227i	$-0.0904096\pi$
$929$	489749.	+	1.50729e6i	0.0186180	+	0.0573004i	−0.941316	+	0.337527i	$0.890410\pi$
$930$	8.05043e6	+	2.53799e6i	0.305219	+	0.0962238i
$931$	−1.12709e7	+	3.46882e7i	−0.426171	+	1.31162i
$932$	2.71051e6			0.102214
$933$	6.48697e6	−	1.99648e7i	0.243971	−	0.750864i
$934$	2.10011e7	−	1.52582e7i	0.787726	−	0.572316i
$935$	−1.04307e7	+	1.46244e7i	−0.390198	+	0.547078i
$936$	2.78726e7	+	2.02506e7i	1.03989	+	0.755525i
$937$	−1.90718e7	+	1.38565e7i	−0.709649	+	0.515590i	−0.883060	−	0.469259i	$-0.844521\pi$
$937$	−1.90718e7	+	1.38565e7i	−0.709649	+	0.515590i	0.173412	+	0.984849i	$0.444521\pi$
$938$	−2.66770e6	+	1.93819e6i	−0.0989986	+	0.0719267i
$939$	1.35206e7	+	9.82327e6i	0.500416	+	0.363573i
$940$	2.59752e6	−	3.64185e6i	0.0958825	−	0.134432i
$941$	1.03272e6	−	750317.i	0.0380198	−	0.0276230i	−0.568613	−	0.822605i	$-0.692520\pi$
$941$	1.03272e6	−	750317.i	0.0380198	−	0.0276230i	0.606633	+	0.794982i	$0.292520\pi$
$942$	−1.48698e7	+	4.57647e7i	−0.545983	+	1.68036i
$943$	8.45864e6			0.309757
$944$	1.35533e6	−	4.17126e6i	0.0495010	−	0.152348i
$945$	−3.77528e7	−	1.19020e7i	−1.37521	−	0.433551i
$946$	6.03561e6	+	1.85757e7i	0.219277	+	0.674865i
$947$	−5.25101e6	−	1.61609e7i	−0.190269	−	0.585587i	0.809730	−	0.586802i	$-0.199613\pi$
$947$	−5.25101e6	−	1.61609e7i	−0.190269	−	0.585587i	−0.999999	+	0.00121470i	$0.999613\pi$
$948$	−1.77255e7	−	1.28783e7i	−0.640587	−	0.465413i
$949$	−7.04247e7			−2.53840
$950$	1.07636e7	−	3.52147e7i	0.386944	−	1.26595i
$951$	1.80185e7			0.646053
$952$	−2.82195e6	−	2.05027e6i	−0.100915	−	0.0733192i
$953$	3.65468e6	+	1.12479e7i	0.130352	+	0.401182i	0.994838	−	0.101475i	$-0.0323561\pi$
$953$	3.65468e6	+	1.12479e7i	0.130352	+	0.401182i	−0.864486	+	0.502656i	$0.832356\pi$
$954$	1.94378e7	+	5.98235e7i	0.691476	+	2.12814i
$955$	−403793.	+	566137.i	−0.0143268	+	0.0200869i
$956$	4.53352e6	−	1.39527e7i	0.160432	−	0.493758i
$957$	3.02542e7			1.06784
$958$	−5.24139e6	+	1.61313e7i	−0.184515	+	0.567880i
$959$	−1.45618e7	+	1.05798e7i	−0.511292	+	0.371475i
$960$	−58514.3	−	6.67893e6i	−0.00204920	−	0.233899i
$961$	2.18066e7	+	1.58434e7i	0.761692	+	0.553402i
$962$	−1.65879e7	+	1.20518e7i	−0.577902	+	0.419871i
$963$	6.27794e7	−	4.56119e7i	2.18148	−	1.58494i
$964$	5.66935e6	+	4.11902e6i	0.196490	+	0.142758i
$965$	2.75216e7	−	9.20965e6i	0.951384	−	0.318365i
$966$	−1.39412e7	+	1.01289e7i	−0.480681	+	0.349235i
$967$	−5.09539e6	+	1.56820e7i	−0.175231	+	0.539306i	−0.999644	−	0.0266831i	$-0.991506\pi$
$967$	−5.09539e6	+	1.56820e7i	−0.175231	+	0.539306i	0.824413	+	0.565989i	$0.191506\pi$
$968$	461473.			0.0158292
$969$	2.17546e7	−	6.69537e7i	0.744288	−	2.29068i
$970$	−221731.	−	2.53088e7i	−0.00756655	−	0.863661i
$971$	2.32112e6	+	7.14369e6i	0.0790042	+	0.243150i	0.982756	−	0.184907i	$-0.0591983\pi$
$971$	2.32112e6	+	7.14369e6i	0.0790042	+	0.243150i	−0.903752	+	0.428057i	$0.859198\pi$
$972$	−1.06873e7	−	3.28920e7i	−0.362828	−	1.11667i
$973$	3.27534e6	+	2.37968e6i	0.110911	+	0.0805816i
$974$	8.49413e6			0.286894
$975$	8.07108e7	−	1.41433e6i	2.71907	−	0.0476473i
$976$	−4.11478e6			−0.138268
$977$	−3.85430e7	−	2.80031e7i	−1.29184	−	0.938578i	−0.292001	−	0.956418i	$-0.594321\pi$
$977$	−3.85430e7	−	2.80031e7i	−1.29184	−	0.938578i	−0.999841	+	0.0178404i	$0.994321\pi$
$978$	−2.31968e7	−	7.13924e7i	−0.775499	−	2.38674i
$979$	−2.81206e6	−	8.65463e6i	−0.0937709	−	0.288597i
$980$	6.58748e6	+	8.90183e6i	0.219106	+	0.296083i
$981$	−2.71603e7	+	8.35908e7i	−0.901077	+	2.77323i
$982$	−3.14603e7			−1.04108
$983$	1.82893e7	−	5.62887e7i	0.603689	−	1.85796i	0.0981269	−	0.995174i	$-0.468715\pi$
$983$	1.82893e7	−	5.62887e7i	0.603689	−	1.85796i	0.505562	−	0.862790i	$-0.331285\pi$
$984$	−5.75471e6	+	4.18104e6i	−0.189468	+	0.137657i
$985$	1.38090e6	+	1.86605e6i	0.0453495	+	0.0612820i
$986$	7.01052e6	+	5.09344e6i	0.229646	+	0.166847i
$987$	7.85177e6	−	5.70464e6i	0.256552	−	0.186396i
$988$	−3.37673e7	+	2.45333e7i	−1.10053	+	0.799585i
$989$	2.23591e7	+	1.62448e7i	0.726881	+	0.528110i
$990$	−5.08481e7	−	1.60304e7i	−1.64887	−	0.519825i
$991$	−3.22200e7	+	2.34092e7i	−1.04218	+	0.757185i	−0.970709	−	0.240258i	$-0.922768\pi$
$991$	−3.22200e7	+	2.34092e7i	−1.04218	+	0.757185i	−0.0714664	+	0.997443i	$0.522768\pi$
$992$	−409500.	+	1.26031e6i	−0.0132122	+	0.0406629i
$993$	7.10080e7			2.28525
$994$	2.14795e6	−	6.61070e6i	0.0689537	−	0.212218i
$995$	1.49983e7	−	5.01894e6i	0.480269	−	0.160714i
$996$	4.10354e6	+	1.26294e7i	0.131072	+	0.403398i
$997$	456220.	+	1.40410e6i	0.0145357	+	0.0447363i	0.958061	−	0.286563i	$-0.0925129\pi$
$997$	456220.	+	1.40410e6i	0.0145357	+	0.0447363i	−0.943526	+	0.331300i	$0.892513\pi$
$998$	1.07794e7	+	7.83169e6i	0.342585	+	0.248903i
$999$	6.16133e7			1.95326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.b.41.1	yes	28
25.11	even	5	inner	50.6.d.b.11.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.b.11.1	✓	28	25.11	even	5	inner
50.6.d.b.41.1	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(-9.01407 - 27.7425i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-53.0123 + 17.7397i) q^{5} +(36.0563 - 110.970i) q^{6} +66.5258 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-491.799 + 357.313i) q^{9} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(-9.01407 - 27.7425i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-53.0123 + 17.7397i) q^{5} +(36.0563 - 110.970i) q^{6} +66.5258 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-491.799 + 357.313i) q^{9} +(-213.260 - 67.2326i) q^{10} +(-317.317 - 230.544i) q^{11} +(377.586 - 274.333i) q^{12} +(-716.419 + 520.509i) q^{13} +(215.282 + 156.412i) q^{14} +(969.999 + 1310.78i) q^{15} +(-207.108 + 150.473i) q^{16} +(-253.165 + 779.161i) q^{17} -2431.59 q^{18} +(910.313 - 2801.66i) q^{19} +(-532.050 - 718.973i) q^{20} +(-599.669 - 1845.59i) q^{21} +(-484.817 - 1492.11i) q^{22} +(-1796.02 - 1304.88i) q^{23} +1866.89 q^{24} +(2495.61 - 1880.84i) q^{25} -3542.17 q^{26} +(8611.27 + 6256.46i) q^{27} +(328.922 + 1012.32i) q^{28} +(-817.136 - 2514.89i) q^{29} +(57.1429 + 6522.39i) q^{30} +(399.902 - 1230.77i) q^{31} -1024.00 q^{32} +(-3535.54 + 10881.3i) q^{33} +(-2651.18 + 1926.19i) q^{34} +(-3526.69 + 1180.15i) q^{35} +(-7868.79 - 5717.01i) q^{36} +(4682.98 - 3402.39i) q^{37} +(9532.93 - 6926.08i) q^{38} +(20898.1 + 15183.3i) q^{39} +(-31.3432 - 3577.57i) q^{40} +(-3082.51 + 2239.58i) q^{41} +(2398.68 - 7382.36i) q^{42} -12449.3 q^{43} +(1939.27 - 5968.45i) q^{44} +(19732.8 - 27666.4i) q^{45} +(-2744.07 - 8445.38i) q^{46} +(1545.48 + 4756.50i) q^{47} +(6041.38 + 4389.32i) q^{48} -12381.3 q^{49} +(12498.1 - 219.009i) q^{50} +23897.9 q^{51} +(-11462.7 - 8328.14i) q^{52} +(-7993.88 - 24602.6i) q^{53} +(13156.9 + 40492.6i) q^{54} +(20911.5 + 6592.58i) q^{55} +(-1315.69 + 4049.27i) q^{56} -85930.5 q^{57} +(3268.54 - 10059.5i) q^{58} +(-13860.5 + 10070.2i) q^{59} +(-15150.1 + 21241.3i) q^{60} +(13003.6 + 9447.68i) q^{61} +(4187.83 - 3042.64i) q^{62} +(-32717.4 + 23770.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(28745.4 - 40302.4i) q^{65} +(-37024.7 + 26900.0i) q^{66} +(-3829.22 + 11785.1i) q^{67} -13108.1 q^{68} +(-20011.2 + 61588.3i) q^{69} +(-14187.3 - 4472.70i) q^{70} +(-8071.85 - 24842.6i) q^{71} +(-12022.4 - 37001.3i) q^{72} +(64338.8 + 46744.9i) q^{73} +23153.9 q^{74} +(-74674.8 - 52280.2i) q^{75} +47133.4 q^{76} +(-21109.8 - 15337.1i) q^{77} +(31929.4 + 98268.5i) q^{78} +(-14506.6 - 44646.6i) q^{79} +(8309.95 - 11651.0i) q^{80} +(50299.1 - 154805. i) q^{81} -15240.8 q^{82} +(-8792.25 + 27059.8i) q^{83} +(25119.3 - 18250.2i) q^{84} +(-401.222 - 45796.2i) q^{85} +(-40286.6 - 29269.9i) q^{86} +(-62403.4 + 45338.7i) q^{87} +(20308.3 - 14754.8i) q^{88} +(18770.0 + 13637.2i) q^{89} +(128904. - 43135.6i) q^{90} +(-47660.4 + 34627.3i) q^{91} +(10976.3 - 33781.5i) q^{92} -37749.4 q^{93} +(-6181.92 + 19026.0i) q^{94} +(1442.69 + 164671. i) q^{95} +(9230.41 + 28408.3i) q^{96} +(34977.3 + 107649. i) q^{97} +(-40066.8 - 29110.2i) q^{98} +238433. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9 - 220 * q^10 - 389 * q^11 + 192 * q^12 + 1047 * q^13 + 164 * q^14 - 640 * q^15 - 1792 * q^16 + 909 * q^17 - 11576 * q^18 + 260 * q^19 - 1040 * q^20 - 1849 * q^21 + 556 * q^22 + 817 * q^23 + 2432 * q^24 + 16055 * q^25 - 4528 * q^26 + 1675 * q^27 + 2544 * q^28 - 2445 * q^29 - 5440 * q^30 + 16731 * q^31 - 28672 * q^32 + 29629 * q^33 - 7576 * q^34 - 825 * q^35 - 7136 * q^36 + 39819 * q^37 + 3100 * q^38 + 26008 * q^39 + 10231 * q^41 + 7396 * q^42 - 86148 * q^43 - 2224 * q^44 - 7870 * q^45 - 11708 * q^46 + 10019 * q^47 + 3072 * q^48 + 147076 * q^49 + 16520 * q^50 - 108074 * q^51 + 16752 * q^52 + 74512 * q^53 + 4260 * q^54 + 2735 * q^55 - 10176 * q^56 - 176840 * q^57 + 9780 * q^58 - 13430 * q^59 + 5760 * q^60 - 29774 * q^61 + 63956 * q^62 - 206818 * q^63 - 28672 * q^64 + 51235 * q^65 + 23264 * q^66 - 85061 * q^67 - 89696 * q^68 - 185227 * q^69 - 25260 * q^70 + 148501 * q^71 + 64064 * q^72 + 189082 * q^73 + 305304 * q^74 + 93630 * q^75 + 16480 * q^76 + 127243 * q^77 + 32028 * q^78 + 46930 * q^79 + 39680 * q^80 - 179812 * q^81 - 338864 * q^82 + 66807 * q^83 - 34464 * q^84 - 877380 * q^85 + 121332 * q^86 - 226000 * q^87 + 24896 * q^88 - 347190 * q^89 + 628660 * q^90 + 197001 * q^91 + 46832 * q^92 - 64906 * q^93 - 40076 * q^94 + 85970 * q^95 - 7168 * q^96 + 502364 * q^97 + 185056 * q^98 + 1151018 * q^99

Introduction

L-functions

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