LMFDB - Embedded newform 16.6.e.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, 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:	$2.56614111701$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.4
Root			$-3.62794 - 1.68466i$ of defining polynomial
Character	$\chi$	$=$	16.5
Dual form			16.6.e.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94328 - 5.31260i) q^{2} +(13.2148 - 13.2148i) q^{3} +(-24.4473 + 20.6477i) q^{4} +(-26.0955 - 26.0955i) q^{5} +(-95.8850 - 44.5248i) q^{6} -106.802i q^{7} +(157.201 + 89.7545i) q^{8} -106.262i q^{9} +O(q^{10})$	\(q+(-1.94328 - 5.31260i) q^{2} +(13.2148 - 13.2148i) q^{3} +(-24.4473 + 20.6477i) q^{4} +(-26.0955 - 26.0955i) q^{5} +(-95.8850 - 44.5248i) q^{6} -106.802i q^{7} +(157.201 + 89.7545i) q^{8} -106.262i q^{9} +(-87.9240 + 189.346i) q^{10} +(407.630 + 407.630i) q^{11} +(-50.2112 + 595.922i) q^{12} +(684.623 - 684.623i) q^{13} +(-567.395 + 207.546i) q^{14} -689.694 q^{15} +(171.344 - 1009.56i) q^{16} +566.949 q^{17} +(-564.527 + 206.497i) q^{18} +(-1700.29 + 1700.29i) q^{19} +(1176.78 + 99.1530i) q^{20} +(-1411.37 - 1411.37i) q^{21} +(1373.43 - 2957.71i) q^{22} +838.931i q^{23} +(3263.47 - 891.291i) q^{24} -1763.05i q^{25} +(-4967.54 - 2306.71i) q^{26} +(1806.97 + 1806.97i) q^{27} +(2205.21 + 2611.02i) q^{28} +(-5523.73 + 5523.73i) q^{29} +(1340.27 + 3664.07i) q^{30} +2169.95 q^{31} +(-5696.37 + 1051.58i) q^{32} +10773.5 q^{33} +(-1101.74 - 3011.97i) q^{34} +(-2787.05 + 2787.05i) q^{35} +(2194.07 + 2597.82i) q^{36} +(-2842.06 - 2842.06i) q^{37} +(12337.1 + 5728.80i) q^{38} -18094.3i q^{39} +(-1760.05 - 6444.43i) q^{40} -1926.27i q^{41} +(-4755.34 + 10240.7i) q^{42} +(800.365 + 800.365i) q^{43} +(-18382.1 - 1548.84i) q^{44} +(-2772.96 + 2772.96i) q^{45} +(4456.90 - 1630.28i) q^{46} +441.674 q^{47} +(-11076.9 - 15605.5i) q^{48} +5400.36 q^{49} +(-9366.36 + 3426.10i) q^{50} +(7492.12 - 7492.12i) q^{51} +(-2601.31 + 30873.1i) q^{52} +(-4098.70 - 4098.70i) q^{53} +(6088.24 - 13111.1i) q^{54} -21274.6i q^{55} +(9585.95 - 16789.4i) q^{56} +44937.9i q^{57} +(40079.5 + 18611.2i) q^{58} +(18994.6 + 18994.6i) q^{59} +(16861.2 - 14240.6i) q^{60} +(-13660.7 + 13660.7i) q^{61} +(-4216.82 - 11528.1i) q^{62} -11349.0 q^{63} +(16656.3 + 28219.0i) q^{64} -35731.2 q^{65} +(-20935.9 - 57235.2i) q^{66} +(-22510.3 + 22510.3i) q^{67} +(-13860.4 + 11706.2i) q^{68} +(11086.3 + 11086.3i) q^{69} +(20222.5 + 9390.45i) q^{70} +34159.3i q^{71} +(9537.50 - 16704.5i) q^{72} -77379.2i q^{73} +(-9575.81 + 20621.7i) q^{74} +(-23298.3 - 23298.3i) q^{75} +(6460.44 - 76674.5i) q^{76} +(43535.7 - 43535.7i) q^{77} +(-96127.8 + 35162.3i) q^{78} -5843.36 q^{79} +(-30816.4 + 21873.7i) q^{80} +73579.1 q^{81} +(-10233.5 + 3743.28i) q^{82} +(22248.9 - 22248.9i) q^{83} +(63645.6 + 5362.65i) q^{84} +(-14794.8 - 14794.8i) q^{85} +(2696.68 - 5807.35i) q^{86} +145990. i q^{87} +(27493.2 + 100666. i) q^{88} -41863.5i q^{89} +(20120.3 + 9342.99i) q^{90} +(-73119.0 - 73119.0i) q^{91} +(-17322.0 - 20509.6i) q^{92} +(28675.5 - 28675.5i) q^{93} +(-858.297 - 2346.44i) q^{94} +88739.6 q^{95} +(-61379.9 + 89172.8i) q^{96} -156099. q^{97} +(-10494.4 - 28689.9i) q^{98} +(43315.6 - 43315.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.94328	−	5.31260i	−0.343526	−	0.939143i
$2$	−1.94328	−	5.31260i	−0.343526	−	0.939143i
$3$	13.2148	−	13.2148i	0.847730	−	0.847730i	−0.142119	−	0.989850i	$-0.545392\pi$
$3$	13.2148	−	13.2148i	0.847730	−	0.847730i	0.989850	+	0.142119i	$0.0453917\pi$
$4$	−24.4473	+	20.6477i	−0.763979	+	0.645241i
$5$	−26.0955	−	26.0955i	−0.466811	−	0.466811i	0.434069	−	0.900880i	$-0.357077\pi$
$5$	−26.0955	−	26.0955i	−0.466811	−	0.466811i	−0.900880	+	0.434069i	$0.857077\pi$
$6$	−95.8850	−	44.5248i	−1.08736	−	0.504922i
$7$		−	106.802i		−	0.823823i	−0.911224	−	0.411911i	$-0.864861\pi$
$7$		−	106.802i		−	0.823823i	0.911224	−	0.411911i	$-0.135139\pi$
$8$	157.201	+	89.7545i	0.868421	+	0.495828i
$9$		−	106.262i		−	0.437292i
$10$	−87.9240	+	189.346i	−0.278040	+	0.598764i
$11$	407.630	+	407.630i	1.01574	+	1.01574i	0.999874	+	0.0158703i	$0.00505187\pi$
$11$	407.630	+	407.630i	1.01574	+	1.01574i	0.0158703	+	0.999874i	$0.494948\pi$
$12$	−50.2112	+	595.922i	−0.100658	+	1.19464i
$13$	684.623	−	684.623i	1.12355	−	1.12355i	0.132349	−	0.991203i	$-0.457748\pi$
$13$	684.623	−	684.623i	1.12355	−	1.12355i	0.991203	−	0.132349i	$-0.0422519\pi$
$14$	−567.395	+	207.546i	−0.773687	+	0.283005i
$15$	−689.694			−0.791459
$16$	171.344	−	1009.56i	0.167328	−	0.985901i
$17$	566.949			0.475797			0.237899	−	0.971290i	$-0.423541\pi$
$17$	566.949			0.475797			0.237899	+	0.971290i	$0.423541\pi$
$18$	−564.527	+	206.497i	−0.410680	+	0.150222i
$19$	−1700.29	+	1700.29i	−1.08053	+	1.08053i	−0.0840731	+	0.996460i	$0.526793\pi$
$19$	−1700.29	+	1700.29i	−1.08053	+	1.08053i	−0.996460	+	0.0840731i	$0.973207\pi$
$20$	1176.78	+	99.1530i	0.657839	+	0.0554282i
$21$	−1411.37	−	1411.37i	−0.698379	−	0.698379i
$22$	1373.43	−	2957.71i	0.604994	−	1.30286i
$23$			838.931i			0.330679i	0.986237	+	0.165339i	$0.0528720\pi$
$23$			838.931i			0.330679i	−0.986237	+	0.165339i	$0.947128\pi$
$24$	3263.47	−	891.291i	1.15651	−	0.315858i
$25$		−	1763.05i		−	0.564176i
$26$	−4967.54	−	2306.71i	−1.44115	−	0.669206i
$27$	1806.97	+	1806.97i	0.477024	+	0.477024i
$28$	2205.21	+	2611.02i	0.531564	+	0.629383i
$29$	−5523.73	+	5523.73i	−1.21966	+	1.21966i	−0.251905	+	0.967752i	$0.581057\pi$
$29$	−5523.73	+	5523.73i	−1.21966	+	1.21966i	−0.967752	+	0.251905i	$0.918943\pi$
$30$	1340.27	+	3664.07i	0.271887	+	0.743293i
$31$	2169.95			0.405551			0.202776	−	0.979225i	$-0.435004\pi$
$31$	2169.95			0.405551			0.202776	+	0.979225i	$0.435004\pi$
$32$	−5696.37	+	1051.58i	−0.983384	+	0.181538i
$33$	10773.5			1.72215
$34$	−1101.74	−	3011.97i	−0.163449	−	0.446842i
$35$	−2787.05	+	2787.05i	−0.384569	+	0.384569i
$36$	2194.07	+	2597.82i	0.282159	+	0.334082i
$37$	−2842.06	−	2842.06i	−0.341295	−	0.341295i	0.515559	−	0.856854i	$-0.327584\pi$
$37$	−2842.06	−	2842.06i	−0.341295	−	0.341295i	−0.856854	+	0.515559i	$0.827584\pi$
$38$	12337.1	+	5728.80i	1.38597	+	0.643583i
$39$		−	18094.3i		−	1.90494i
$40$	−1760.05	−	6444.43i	−0.173930	−	0.636846i
$41$		−	1926.27i		−	0.178960i	−0.995989	−	0.0894802i	$-0.971479\pi$
$41$		−	1926.27i		−	0.178960i	0.995989	−	0.0894802i	$-0.0285206\pi$
$42$	−4755.34	+	10240.7i	−0.415966	+	0.895790i
$43$	800.365	+	800.365i	0.0660111	+	0.0660111i	0.739342	−	0.673330i	$-0.235137\pi$
$43$	800.365	+	800.365i	0.0660111	+	0.0660111i	−0.673330	+	0.739342i	$0.735137\pi$
$44$	−18382.1	−	1548.84i	−1.43141	−	0.120608i
$45$	−2772.96	+	2772.96i	−0.204133	+	0.204133i
$46$	4456.90	−	1630.28i	0.310555	−	0.113597i
$47$	441.674			0.0291647			0.0145824	−	0.999894i	$-0.495358\pi$
$47$	441.674			0.0291647			0.0145824	+	0.999894i	$0.495358\pi$
$48$	−11076.9	−	15605.5i	−0.693929	−	0.977627i
$49$	5400.36			0.321316
$50$	−9366.36	+	3426.10i	−0.529842	+	0.193809i
$51$	7492.12	−	7492.12i	0.403347	−	0.403347i
$52$	−2601.31	+	30873.1i	−0.133408	+	1.58333i
$53$	−4098.70	−	4098.70i	−0.200427	−	0.200427i	0.599756	−	0.800183i	$-0.295264\pi$
$53$	−4098.70	−	4098.70i	−0.200427	−	0.200427i	−0.800183	+	0.599756i	$0.795264\pi$
$54$	6088.24	−	13111.1i	0.284123	−	0.611864i
$55$		−	21274.6i		−	0.948321i
$56$	9585.95	−	16789.4i	0.408475	−	0.715425i
$57$			44937.9i			1.83200i
$58$	40079.5	+	18611.2i	1.56442	+	0.726448i
$59$	18994.6	+	18994.6i	0.710395	+	0.710395i	0.966618	−	0.256223i	$-0.0824781\pi$
$59$	18994.6	+	18994.6i	0.710395	+	0.710395i	−0.256223	+	0.966618i	$0.582478\pi$
$60$	16861.2	−	14240.6i	0.604658	−	0.510682i
$61$	−13660.7	+	13660.7i	−0.470056	+	0.470056i	−0.901933	−	0.431877i	$-0.857851\pi$
$61$	−13660.7	+	13660.7i	−0.470056	+	0.470056i	0.431877	+	0.901933i	$0.357851\pi$
$62$	−4216.82	−	11528.1i	−0.139318	−	0.380871i
$63$	−11349.0			−0.360251
$64$	16656.3	+	28219.0i	0.508309	+	0.861175i
$65$	−35731.2			−1.04897
$66$	−20935.9	−	57235.2i	−0.591605	−	1.61735i
$67$	−22510.3	+	22510.3i	−0.612624	+	0.612624i	−0.943629	−	0.331005i	$-0.892612\pi$
$67$	−22510.3	+	22510.3i	−0.612624	+	0.612624i	0.331005	+	0.943629i	$0.392612\pi$
$68$	−13860.4	+	11706.2i	−0.363499	+	0.307004i
$69$	11086.3	+	11086.3i	0.280326	+	0.280326i
$70$	20222.5	+	9390.45i	0.493275	+	0.229056i
$71$			34159.3i			0.804199i	0.915596	+	0.402099i	$0.131719\pi$
$71$			34159.3i			0.804199i	−0.915596	+	0.402099i	$0.868281\pi$
$72$	9537.50	−	16704.5i	0.216822	−	0.379754i
$73$		−	77379.2i		−	1.69948i	−0.527200	−	0.849741i	$-0.676758\pi$
$73$		−	77379.2i		−	1.69948i	0.527200	−	0.849741i	$-0.323242\pi$
$74$	−9575.81	+	20621.7i	−0.203281	+	0.437768i
$75$	−23298.3	−	23298.3i	−0.478269	−	0.478269i
$76$	6460.44	−	76674.5i	0.128300	−	1.52271i
$77$	43535.7	−	43535.7i	0.836793	−	0.836793i
$78$	−96127.8	+	35162.3i	−1.78901	+	0.654396i
$79$	−5843.36			−0.105340			−0.0526702	−	0.998612i	$-0.516773\pi$
$79$	−5843.36			−0.105340			−0.0526702	+	0.998612i	$0.516773\pi$
$80$	−30816.4	+	21873.7i	−0.538340	+	0.382119i
$81$	73579.1			1.24607
$82$	−10233.5	+	3743.28i	−0.168069	+	0.0614776i
$83$	22248.9	−	22248.9i	0.354498	−	0.354498i	−0.507282	−	0.861780i	$-0.669350\pi$
$83$	22248.9	−	22248.9i	0.354498	−	0.354498i	0.861780	+	0.507282i	$0.169350\pi$
$84$	63645.6	+	5362.65i	0.984170	+	0.0829243i
$85$	−14794.8	−	14794.8i	−0.222107	−	0.222107i
$86$	2696.68	−	5807.35i	0.0393173	−	0.0846705i
$87$			145990.i			2.06788i
$88$	27493.2	+	100666.i	0.378459	+	1.38573i
$89$		−	41863.5i		−	0.560222i	−0.959968	−	0.280111i	$-0.909629\pi$
$89$		−	41863.5i		−	0.560222i	0.959968	−	0.280111i	$-0.0903713\pi$
$90$	20120.3	+	9342.99i	0.261835	+	0.121585i
$91$	−73119.0	−	73119.0i	−0.925608	−	0.925608i
$92$	−17322.0	−	20509.6i	−0.213368	−	0.252632i
$93$	28675.5	−	28675.5i	0.343798	−	0.343798i
$94$	−858.297	−	2346.44i	−0.0100188	−	0.0273898i
$95$	88739.6			1.00881
$96$	−61379.9	+	89172.8i	−0.679749	+	0.987539i
$97$	−156099.			−1.68450			−0.842248	−	0.539090i	$-0.818768\pi$
$97$	−156099.			−1.68450			−0.842248	+	0.539090i	$0.818768\pi$
$98$	−10494.4	−	28689.9i	−0.110381	−	0.301762i
$99$	43315.6	−	43315.6i	0.444177	−	0.444177i
$100$	36402.9	+	43101.8i	0.364029	+	0.431018i
$101$	94579.5	+	94579.5i	0.922557	+	0.922557i	0.997210	−	0.0746522i	$-0.0237847\pi$
$101$	94579.5	+	94579.5i	0.922557	+	0.922557i	−0.0746522	+	0.997210i	$0.523785\pi$
$102$	−54361.9	−	25243.3i	−0.517362	−	0.240240i
$103$		−	22786.6i		−	0.211634i	−0.994386	−	0.105817i	$-0.966254\pi$
$103$		−	22786.6i		−	0.211634i	0.994386	−	0.105817i	$-0.0337458\pi$
$104$	169071.	−	46175.4i	1.53280	−	0.418627i
$105$			73660.6i			0.652022i
$106$	−13809.8	+	29739.6i	−0.119378	+	0.257082i
$107$	51699.8	+	51699.8i	0.436545	+	0.436545i	0.890848	−	0.454302i	$-0.150111\pi$
$107$	51699.8	+	51699.8i	0.436545	+	0.436545i	−0.454302	+	0.890848i	$0.650111\pi$
$108$	−81485.2	−	6865.78i	−0.672232	−	0.0566409i
$109$	61340.0	−	61340.0i	0.494513	−	0.494513i	−0.415212	−	0.909725i	$-0.636293\pi$
$109$	61340.0	−	61340.0i	0.494513	−	0.494513i	0.909725	+	0.415212i	$0.136293\pi$
$110$	−113023.	+	41342.5i	−0.890609	+	0.325773i
$111$	−75114.6			−0.578651
$112$	−107823.	−	18299.9i	−0.812208	−	0.137849i
$113$	−107766.			−0.793938			−0.396969	−	0.917832i	$-0.629938\pi$
$113$	−107766.			−0.793938			−0.396969	+	0.917832i	$0.629938\pi$
$114$	238737.	−	87326.9i	1.72051	−	0.629341i
$115$	21892.3	−	21892.3i	0.154364	−	0.154364i
$116$	20988.1	−	249093.i	0.144820	−	1.71877i
$117$	−72749.5	−	72749.5i	−0.491321	−	0.491321i
$118$	63998.8	−	137822.i	0.423123	−	0.911202i
$119$		−	60551.2i		−	0.391973i
$120$	−108421.	−	61903.1i	−0.687319	−	0.392428i
$121$			171273.i			1.06347i
$122$	99120.5	+	46027.3i	0.602926	+	0.279973i
$123$	−25455.2	−	25455.2i	−0.151710	−	0.151710i
$124$	−53049.5	+	44804.5i	−0.309833	+	0.261678i
$125$	−127556.	+	127556.i	−0.730174	+	0.730174i
$126$	22054.3	+	60292.6i	0.123756	+	0.338328i
$127$	−267429.			−1.47129			−0.735647	−	0.677365i	$-0.763122\pi$
$127$	−267429.			−1.47129			−0.735647	+	0.677365i	$0.763122\pi$
$128$	117548.	−	143325.i	0.634149	−	0.773211i
$129$	21153.3			0.111919
$130$	69435.7	+	189825.i	0.360350	+	0.985135i
$131$	−9397.10	+	9397.10i	−0.0478427	+	0.0478427i	−0.730623	−	0.682781i	$-0.760770\pi$
$131$	−9397.10	+	9397.10i	−0.0478427	+	0.0478427i	0.682781	+	0.730623i	$0.260770\pi$
$132$	−263383.	+	222448.i	−1.31569	+	1.11120i
$133$	181594.	+	181594.i	0.890168	+	0.890168i
$134$	163332.	+	75844.3i	0.785794	+	0.364889i
$135$		−	94307.3i		−	0.445360i
$136$	89124.9	+	50886.2i	0.413192	+	0.235914i
$137$		−	29494.1i		−	0.134256i	−0.997744	−	0.0671281i	$-0.978616\pi$
$137$		−	29494.1i		−	0.134256i	0.997744	−	0.0671281i	$-0.0213836\pi$
$138$	37353.3	−	80440.8i	0.166967	−	0.359566i
$139$	36678.6	+	36678.6i	0.161019	+	0.161019i	0.783018	−	0.621999i	$-0.213679\pi$
$139$	36678.6	+	36678.6i	0.161019	+	0.161019i	−0.621999	+	0.783018i	$0.713679\pi$
$140$	10589.7	−	125682.i	0.0456630	−	0.541943i
$141$	5836.64	−	5836.64i	0.0247238	−	0.0247238i
$142$	181475.	−	66381.1i	0.755258	−	0.276264i
$143$	558146.			2.28248
$144$	−107278.	−	18207.4i	−0.431127	−	0.0731713i
$145$	288289.			1.13870
$146$	−411084.	+	150369.i	−1.59606	+	0.583817i
$147$	71364.6	−	71364.6i	0.272389	−	0.272389i
$148$	128163.	+	10798.8i	0.480959	+	0.0405247i
$149$	−244564.	−	244564.i	−0.902457	−	0.902457i	0.0931915	−	0.995648i	$-0.470293\pi$
$149$	−244564.	−	244564.i	−0.902457	−	0.902457i	−0.995648	+	0.0931915i	$0.970293\pi$
$150$	−78499.5	+	169050.i	−0.284865	+	0.613461i
$151$		−	178219.i		−	0.636079i	−0.948077	−	0.318040i	$-0.896975\pi$
$151$		−	178219.i		−	0.636079i	0.948077	−	0.318040i	$-0.103025\pi$
$152$	−419895.	+	114678.i	−1.47412	+	0.402598i
$153$		−	60245.2i		−	0.208062i
$154$	−315889.	−	146685.i	−1.07333	−	0.498408i
$155$	−56626.0	−	56626.0i	−0.189316	−	0.189316i
$156$	373606.	+	442358.i	1.22914	+	1.45533i
$157$	−148493.	+	148493.i	−0.480791	+	0.480791i	−0.905384	−	0.424593i	$-0.860417\pi$
$157$	−148493.	+	148493.i	−0.480791	+	0.480791i	0.424593	+	0.905384i	$0.360417\pi$
$158$	11355.3	+	31043.4i	0.0361872	+	0.0989297i
$159$	−108327.			−0.339816
$160$	176091.	+	121208.i	0.543798	+	0.374310i
$161$	89599.4			0.272421
$162$	−142985.	−	390896.i	−0.428057	−	1.17024i
$163$	−190853.	+	190853.i	−0.562640	+	0.562640i	−0.930056	−	0.367417i	$-0.880242\pi$
$163$	−190853.	+	190853.i	−0.562640	+	0.562640i	0.367417	+	0.930056i	$0.380242\pi$
$164$	39773.0	+	47092.1i	0.115473	+	0.136722i
$165$	−281140.	−	281140.i	−0.803920	−	0.803920i
$166$	−161435.	−	74963.6i	−0.454703	−	0.211145i
$167$		−	105468.i		−	0.292636i	−0.989238	−	0.146318i	$-0.953258\pi$
$167$		−	105468.i		−	0.292636i	0.989238	−	0.146318i	$-0.0467423\pi$
$168$	−95191.6	−	348544.i	−0.260211	−	0.952763i
$169$		−	566125.i		−	1.52474i
$170$	−49848.4	+	107349.i	−0.132291	+	0.284890i
$171$	180676.	+	180676.i	0.472509	+	0.472509i
$172$	−36092.5	−	3041.08i	−0.0930242	−	0.00783804i
$173$	−109671.	+	109671.i	−0.278597	+	0.278597i	−0.832549	−	0.553952i	$-0.813119\pi$
$173$	−109671.	+	109671.i	−0.278597	+	0.278597i	0.553952	+	0.832549i	$0.313119\pi$
$174$	775586.	−	283700.i	1.94204	−	0.710372i
$175$	−188297.			−0.464781
$176$	481373.	−	341683.i	1.17139	−	0.831461i
$177$	502019.			1.20445
$178$	−222404.	+	81352.4i	−0.526129	+	0.192451i
$179$	−355752.	+	355752.i	−0.829880	+	0.829880i	−0.987500	−	0.157620i	$-0.949618\pi$
$179$	−355752.	+	355752.i	−0.829880	+	0.829880i	0.157620	+	0.987500i	$0.449618\pi$
$180$	10536.2	−	125047.i	0.0242383	−	0.287668i
$181$	352209.	+	352209.i	0.799105	+	0.799105i	0.982954	−	0.183849i	$-0.0588559\pi$
$181$	352209.	+	352209.i	0.799105	+	0.799105i	−0.183849	+	0.982954i	$0.558856\pi$
$182$	−246361.	+	530543.i	−0.551307	+	1.18725i
$183$			361048.i			0.796961i
$184$	−75297.8	+	131881.i	−0.163960	+	0.287168i
$185$			148330.i			0.318640i
$186$	−208066.	−	96616.7i	−0.440979	−	0.204772i
$187$	231105.	+	231105.i	0.483288	+	0.483288i
$188$	−10797.8	+	9119.57i	−0.0222812	+	0.0188183i
$189$	192987.	−	192987.i	0.392983	−	0.392983i
$190$	−172446.	−	471438.i	−0.346552	−	0.947415i
$191$	−429992.			−0.852859			−0.426429	−	0.904521i	$-0.640229\pi$
$191$	−429992.			−0.852859			−0.426429	+	0.904521i	$0.640229\pi$
$192$	593017.	+	152799.i	1.16095	+	0.299135i
$193$	370670.			0.716298			0.358149	−	0.933664i	$-0.383408\pi$
$193$	370670.			0.716298			0.358149	+	0.933664i	$0.383408\pi$
$194$	303344.	+	829290.i	0.578669	+	1.58198i
$195$	−472180.	+	472180.i	−0.889245	+	0.889245i
$196$	−132024.	+	111505.i	−0.245479	+	0.207326i
$197$	−675759.	−	675759.i	−1.24059	−	1.24059i	−0.959759	−	0.280827i	$-0.909391\pi$
$197$	−675759.	−	675759.i	−1.24059	−	1.24059i	−0.280827	−	0.959759i	$-0.590609\pi$
$198$	−314293.	−	145944.i	−0.569733	−	0.264559i
$199$		−	286188.i		−	0.512293i	−0.966638	−	0.256147i	$-0.917547\pi$
$199$		−	286188.i		−	0.512293i	0.966638	−	0.256147i	$-0.0824530\pi$
$200$	158242.	−	277153.i	0.279734	−	0.489942i
$201$			594938.i			1.03868i
$202$	318668.	−	686257.i	0.549490	−	1.18334i
$203$	589945.	+	589945.i	1.00478	+	1.00478i
$204$	−28467.2	+	337858.i	−0.0478927	+	0.568405i
$205$	−50266.9	+	50266.9i	−0.0835406	+	0.0835406i
$206$	−121056.	+	44280.6i	−0.198755	+	0.0727019i
$207$	89146.5			0.144603
$208$	−573864.	−	808476.i	−0.919709	−	1.29571i
$209$	−1.38617e6			−2.19509
$210$	391329.	−	143143.i	0.612342	−	0.223987i
$211$	824632.	−	824632.i	1.27513	−	1.27513i	0.331767	−	0.943361i	$-0.392355\pi$
$211$	824632.	−	824632.i	1.27513	−	1.27513i	0.943361	−	0.331767i	$-0.107645\pi$
$212$	184831.	+	15573.5i	0.282446	+	0.0237983i
$213$	451409.	+	451409.i	0.681744	+	0.681744i
$214$	174193.	−	375127.i	0.260013	−	0.559943i
$215$		−	41771.9i		−	0.0616294i
$216$	121873.	+	446240.i	0.177736	+	0.650780i
$217$		−	231755.i		−	0.334102i
$218$	−445075.	−	206674.i	−0.634296	−	0.294540i
$219$	−1.02255e6	−	1.02255e6i	−1.44070	−	1.44070i
$220$	439272.	+	520108.i	0.611895	+	0.724497i
$221$	388146.	−	388146.i	0.534583	−	0.534583i
$222$	145969.	+	399054.i	0.198782	+	0.543436i
$223$	136259.			0.183486			0.0917428	−	0.995783i	$-0.470756\pi$
$223$	136259.			0.183486			0.0917428	+	0.995783i	$0.470756\pi$
$224$	112311.	+	608383.i	0.149555	+	0.810134i
$225$	−187345.			−0.246710
$226$	209420.	+	572519.i	0.272739	+	0.745622i
$227$	425671.	−	425671.i	0.548289	−	0.548289i	−0.377656	−	0.925946i	$-0.623270\pi$
$227$	425671.	−	425671.i	0.548289	−	0.548289i	0.925946	+	0.377656i	$0.123270\pi$
$228$	−927864.	−	1.09861e6i	−1.18208	−	1.39961i
$229$	576711.	+	576711.i	0.726724	+	0.726724i	0.969966	−	0.243242i	$-0.0782108\pi$
$229$	576711.	+	576711.i	0.726724	+	0.726724i	−0.243242	+	0.969966i	$0.578211\pi$
$230$	−158848.	−	73762.1i	−0.197999	−	0.0919420i
$231$		−	1.15063e6i		−	1.41875i
$232$	−1.36412e6	+	372556.i	−1.66392	+	0.454435i
$233$			563157.i			0.679578i	0.940502	+	0.339789i	$0.110356\pi$
$233$			563157.i			0.679578i	−0.940502	+	0.339789i	$0.889644\pi$
$234$	−245116.	+	527861.i	−0.292639	+	0.630202i
$235$	−11525.7	−	11525.7i	−0.0136144	−	0.0136144i
$236$	−856562.	−	72172.2i	−1.00110	−	0.0843510i
$237$	−77218.9	+	77218.9i	−0.0893002	+	0.0893002i
$238$	−321684.	+	117668.i	−0.368118	+	0.134653i
$239$	1.22493e6			1.38713			0.693565	−	0.720394i	$-0.256039\pi$
$239$	1.22493e6			1.38713			0.693565	+	0.720394i	$0.256039\pi$
$240$	−118175.	+	696290.i	−0.132433	+	0.780300i
$241$	107755.			0.119508			0.0597538	−	0.998213i	$-0.480968\pi$
$241$	107755.			0.119508			0.0597538	+	0.998213i	$0.480968\pi$
$242$	909906.	−	332832.i	0.998753	−	0.365331i
$243$	533240.	−	533240.i	0.579305	−	0.579305i
$244$	51905.6	−	616031.i	0.0558135	−	0.662412i
$245$	−140925.	−	140925.i	−0.149994	−	0.149994i
$246$	−85766.8	+	184700.i	−0.0903610	+	0.194594i
$247$			2.32811e6i			2.42807i
$248$	341118.	+	194763.i	0.352189	+	0.201084i
$249$		−	588030.i		−	0.601037i
$250$	925531.	+	429777.i	0.936572	+	0.434904i
$251$	−927180.	−	927180.i	−0.928923	−	0.928923i	0.0687135	−	0.997636i	$-0.478111\pi$
$251$	−927180.	−	927180.i	−0.928923	−	0.928923i	−0.997636	+	0.0687135i	$0.978111\pi$
$252$	277452.	−	234331.i	0.275225	−	0.232449i
$253$	−341973.	+	341973.i	−0.335885	+	0.335885i
$254$	519690.	+	1.42074e6i	0.505429	+	1.38176i
$255$	−391021.			−0.376574
$256$	−989858.	−	345965.i	−0.944003	−	0.329938i
$257$	781809.			0.738359			0.369180	−	0.929358i	$-0.379639\pi$
$257$	781809.			0.738359			0.369180	+	0.929358i	$0.379639\pi$
$258$	−41106.9	−	112379.i	−0.0384472	−	0.105108i
$259$	−303538.	+	303538.i	−0.281166	+	0.281166i
$260$	873532.	−	737767.i	0.801393	−	0.676840i
$261$	586963.	+	586963.i	0.533347	+	0.533347i
$262$	68184.2	+	31661.8i	0.0613664	+	0.0284959i
$263$			871795.i			0.777186i	0.921410	+	0.388593i	$0.127039\pi$
$263$			871795.i			0.777186i	−0.921410	+	0.388593i	$0.872961\pi$
$264$	1.69360e6	+	966970.i	1.49555	+	0.853893i
$265$			213915.i			0.187123i
$266$	611847.	−	1.31762e6i	0.530198	−	1.14179i
$267$	−553218.	−	553218.i	−0.474917	−	0.474917i
$268$	85530.5	−	1.01510e6i	0.0727418	−	0.863322i
$269$	−390591.	+	390591.i	−0.329111	+	0.329111i	−0.852248	−	0.523138i	$-0.824761\pi$
$269$	−390591.	+	390591.i	−0.329111	+	0.329111i	0.523138	+	0.852248i	$0.324761\pi$
$270$	−501017.	+	183266.i	−0.418257	+	0.152993i
$271$	−998296.			−0.825726			−0.412863	−	0.910793i	$-0.635471\pi$
$271$	−998296.			−0.825726			−0.412863	+	0.910793i	$0.635471\pi$
$272$	97143.3	−	572371.i	0.0796142	−	0.469089i
$273$	−1.93251e6			−1.56933
$274$	−156690.	+	57315.3i	−0.126086	+	0.0461205i
$275$	718672.	−	718672.i	0.573058	−	0.573058i
$276$	−499937.	−	42123.7i	−0.395042	−	0.0332854i
$277$	370354.	+	370354.i	0.290013	+	0.290013i	0.837085	−	0.547072i	$-0.184258\pi$
$277$	370354.	+	370354.i	0.290013	+	0.290013i	−0.547072	+	0.837085i	$0.684258\pi$
$278$	123582.	−	266136.i	0.0959054	−	0.206534i
$279$		−	230583.i		−	0.177344i
$280$	−688277.	+	187977.i	−0.524648	+	0.143288i
$281$		−	714854.i		−	0.540072i	−0.962850	−	0.270036i	$-0.912964\pi$
$281$		−	714854.i		−	0.540072i	0.962850	−	0.270036i	$-0.0870355\pi$
$282$	−42349.9	−	19665.5i	−0.0317125	−	0.0147259i
$283$	893188.	+	893188.i	0.662944	+	0.662944i	0.956073	−	0.293129i	$-0.0946965\pi$
$283$	893188.	+	893188.i	0.662944	+	0.662944i	−0.293129	+	0.956073i	$0.594696\pi$
$284$	−705312.	−	835104.i	−0.518902	−	0.614391i
$285$	1.17268e6	−	1.17268e6i	0.855197	−	0.855197i
$286$	−1.08463e6	−	2.96520e6i	−0.784093	−	2.14358i
$287$	−205729.			−0.147432
$288$	111743.	+	605308.i	0.0793853	+	0.430026i
$289$	−1.09843e6			−0.773617
$290$	−560227.	−	1.53156e6i	−0.391173	−	1.06940i
$291$	−2.06281e6	+	2.06281e6i	−1.42800	+	1.42800i
$292$	1.59770e6	+	1.89171e6i	1.09658	+	1.29837i
$293$	−723832.	−	723832.i	−0.492571	−	0.492571i	0.416544	−	0.909115i	$-0.363241\pi$
$293$	−723832.	−	723832.i	−0.492571	−	0.492571i	−0.909115	+	0.416544i	$0.863241\pi$
$294$	−517813.	−	240450.i	−0.349385	−	0.162239i
$295$		−	991347.i		−	0.663240i
$296$	−191687.	−	701863.i	−0.127164	−	0.465611i
$297$			1.47315e6i			0.969069i
$298$	−824012.	+	1.77452e6i	−0.537518	+	1.15755i
$299$	574351.	+	574351.i	0.371535	+	0.371535i
$300$	1.05064e6	+	88524.8i	0.673986	+	0.0567887i
$301$	85480.5	−	85480.5i	0.0543815	−	0.0543815i
$302$	−946805.	+	346329.i	−0.597369	+	0.218510i
$303$	2.49970e6			1.56416
$304$	1.42521e6	+	2.00788e6i	0.884495	+	1.24610i
$305$	712967.			0.438854
$306$	−320058.	+	117073.i	−0.195400	+	0.0714750i
$307$	1.55592e6	−	1.55592e6i	0.942196	−	0.942196i	−0.0562220	−	0.998418i	$-0.517905\pi$
$307$	1.55592e6	−	1.55592e6i	0.942196	−	0.942196i	0.998418	+	0.0562220i	$0.0179055\pi$
$308$	−165419.	+	1.96324e6i	−0.0993593	+	1.17923i
$309$	−301120.	−	301120.i	−0.179409	−	0.179409i
$310$	−190791.	+	410871.i	−0.112759	+	0.242829i
$311$			2.33899e6i			1.37128i	0.727940	+	0.685641i	$0.240478\pi$
$311$			2.33899e6i			1.37128i	−0.727940	+	0.685641i	$0.759522\pi$
$312$	1.62405e6	−	2.84444e6i	0.944522	−	1.65429i
$313$		−	1.40062e6i		−	0.808088i	−0.914740	−	0.404044i	$-0.867604\pi$
$313$		−	1.40062e6i		−	0.808088i	0.914740	−	0.404044i	$-0.132396\pi$
$314$	1.07744e6	+	500319.i	0.616696	+	0.286367i
$315$	296158.	+	296158.i	0.168169	+	0.168169i
$316$	142855.	−	120652.i	0.0804779	−	0.0679700i
$317$	1.93876e6	−	1.93876e6i	1.08362	−	1.08362i	0.0874473	−	0.996169i	$-0.472129\pi$
$317$	1.93876e6	−	1.93876e6i	1.08362	−	1.08362i	0.996169	−	0.0874473i	$-0.0278709\pi$
$318$	210510.	+	575497.i	0.116736	+	0.319136i
$319$	−4.50328e6			−2.47772
$320$	301735.	−	1.17104e6i	0.164722	−	0.639290i
$321$	1.36640e6			0.740145
$322$	−174117.	−	476005.i	−0.0935838	−	0.255842i
$323$	−963976.	+	963976.i	−0.514114	+	0.514114i
$324$	−1.79881e6	+	1.51924e6i	−0.951970	+	0.804014i
$325$	−1.20702e6	−	1.20702e6i	−0.633881	−	0.633881i
$326$	1.38481e6	+	643045.i	0.721681	+	0.335118i
$327$		−	1.62119e6i		−	0.838426i
$328$	172891.	−	302811.i	0.0887336	−	0.155413i
$329$		−	47171.7i		−	0.0240266i
$330$	−947249.	+	2.03992e6i	−0.478828	+	1.03116i
$331$	1.75185e6	+	1.75185e6i	0.878877	+	0.878877i	0.993418	−	0.114542i	$-0.0365400\pi$
$331$	1.75185e6	+	1.75185e6i	0.878877	+	0.878877i	−0.114542	+	0.993418i	$0.536540\pi$
$332$	−84537.4	+	1.00332e6i	−0.0420924	+	0.499565i
$333$	−302004.	+	302004.i	−0.149246	+	0.149246i
$334$	−560306.	+	204953.i	−0.274827	+	0.100528i
$335$	1.17483e6			0.571959
$336$	−1.66669e6	+	1.18303e6i	−0.805392	+	0.571675i
$337$	3.00166e6			1.43975			0.719875	−	0.694103i	$-0.244199\pi$
$337$	3.00166e6			1.43975			0.719875	+	0.694103i	$0.244199\pi$
$338$	−3.00759e6	+	1.10014e6i	−1.43195	+	0.523788i
$339$	−1.42411e6	+	1.42411e6i	−0.673045	+	0.673045i
$340$	667173.	+	56214.7i	0.312998	+	0.0263726i
$341$	884537.	+	884537.i	0.411936	+	0.411936i
$342$	608754.	−	1.31096e6i	0.281434	−	0.606073i
$343$		−	2.37179e6i		−	1.08853i
$344$	53981.8	+	197655.i	0.0245952	+	0.0900556i
$345$		−	578605.i		−	0.261719i
$346$	795758.	+	369516.i	0.357348	+	0.165937i
$347$	−2.05281e6	−	2.05281e6i	−0.915217	−	0.915217i	0.0814595	−	0.996677i	$-0.474042\pi$
$347$	−2.05281e6	−	2.05281e6i	−0.915217	−	0.915217i	−0.996677	+	0.0814595i	$0.974042\pi$
$348$	−3.01436e6	−	3.56907e6i	−1.33428	−	1.57982i
$349$	−2.68351e6	+	2.68351e6i	−1.17934	+	1.17934i	−0.199429	+	0.979912i	$0.563909\pi$
$349$	−2.68351e6	+	2.68351e6i	−1.17934	+	1.17934i	−0.979912	+	0.199429i	$0.936091\pi$
$350$	365914.	+	1.00035e6i	0.159665	+	0.436496i
$351$	2.47418e6			1.07192
$352$	−2.75067e6	−	1.89335e6i	−1.18326	−	0.814470i
$353$	843531.			0.360300			0.180150	−	0.983639i	$-0.442342\pi$
$353$	843531.			0.360300			0.180150	+	0.983639i	$0.442342\pi$
$354$	−975564.	−	2.66703e6i	−0.413759	−	1.13115i
$355$	891405.	−	891405.i	0.375409	−	0.375409i
$356$	864385.	+	1.02345e6i	0.361478	+	0.427998i
$357$	−800173.	−	800173.i	−0.332287	−	0.332287i
$358$	2.58129e6	+	1.19864e6i	1.06446	+	0.494290i
$359$		−	4.63130e6i		−	1.89656i	−0.317431	−	0.948281i	$-0.602820\pi$
$359$		−	4.63130e6i		−	1.89656i	0.317431	−	0.948281i	$-0.397180\pi$
$360$	−684798.	+	187026.i	−0.278488	+	0.0760583i
$361$		−	3.30584e6i		−	1.33510i
$362$	1.18670e6	−	2.55558e6i	0.475960	−	1.02499i
$363$	2.26334e6	+	2.26334e6i	0.901538	+	0.901538i
$364$	3.29731e6	+	277825.i	1.30439	+	0.109905i
$365$	−2.01925e6	+	2.01925e6i	−0.793337	+	0.793337i
$366$	1.91810e6	−	701616.i	0.748460	−	0.273777i
$367$	−571010.			−0.221298			−0.110649	−	0.993860i	$-0.535293\pi$
$367$	−571010.			−0.221298			−0.110649	+	0.993860i	$0.535293\pi$
$368$	846953.	+	143746.i	0.326017	+	0.0553319i
$369$	−204689.			−0.0782580
$370$	788018.	−	288247.i	0.299249	−	0.109461i
$371$	−437749.	+	437749.i	−0.165116	+	0.165116i
$372$	−108956.	+	1.29312e6i	−0.0408219	+	0.484487i
$373$	−860043.	−	860043.i	−0.320072	−	0.320072i	0.528722	−	0.848795i	$-0.322671\pi$
$373$	−860043.	−	860043.i	−0.320072	−	0.320072i	−0.848795	+	0.528722i	$0.822671\pi$
$374$	778667.	−	1.67687e6i	0.287854	−	0.619899i
$375$			3.37126e6i			1.23798i
$376$	69431.6	+	39642.3i	0.0253272	+	0.0144607i
$377$			7.56335e6i			2.74070i
$378$	−1.40029e6	−	650235.i	−0.504068	−	0.234067i
$379$	−2.07981e6	−	2.07981e6i	−0.743746	−	0.743746i	0.229551	−	0.973297i	$-0.426274\pi$
$379$	−2.07981e6	−	2.07981e6i	−0.743746	−	0.743746i	−0.973297	+	0.229551i	$0.926274\pi$
$380$	−2.16945e6	+	1.83227e6i	−0.770709	+	0.650924i
$381$	−3.53403e6	+	3.53403e6i	−1.24726	+	1.24726i
$382$	835595.	+	2.28437e6i	0.292980	+	0.800956i
$383$	−1.33201e6			−0.463992			−0.231996	−	0.972717i	$-0.574526\pi$
$383$	−1.33201e6			−0.463992			−0.231996	+	0.972717i	$0.574526\pi$
$384$	−340639.	−	3.44739e6i	−0.117887	−	1.19306i
$385$	−2.27217e6			−0.781248
$386$	−720315.	−	1.96922e6i	−0.246067	−	0.672706i
$387$	85048.5	−	85048.5i	0.0288662	−	0.0288662i
$388$	3.81620e6	−	3.22308e6i	1.28692	−	1.08691i
$389$	1.39805e6	+	1.39805e6i	0.468433	+	0.468433i	0.901407	−	0.432974i	$-0.142536\pi$
$389$	1.39805e6	+	1.39805e6i	0.468433	+	0.468433i	−0.432974	+	0.901407i	$0.642536\pi$
$390$	3.42608e6	+	1.59093e6i	1.14061	+	0.529649i
$391$			475631.i			0.157336i
$392$	848941.	+	484706.i	0.279037	+	0.159317i
$393$			248362.i			0.0811154i
$394$	−2.27685e6	+	4.90323e6i	−0.738913	+	1.59126i
$395$	152485.	+	152485.i	0.0491740	+	0.0491740i
$396$	−164583.	+	1.95332e6i	−0.0527408	+	0.625944i
$397$	−140895.	+	140895.i	−0.0448663	+	0.0448663i	−0.729184	−	0.684318i	$-0.760100\pi$
$397$	−140895.	+	140895.i	−0.0448663	+	0.0448663i	0.684318	+	0.729184i	$0.260100\pi$
$398$	−1.52040e6	+	556143.i	−0.481117	+	0.175986i
$399$	4.79945e6			1.50924
$400$	−1.77991e6	−	302088.i	−0.556221	−	0.0944025i
$401$	3.14262e6			0.975957			0.487978	−	0.872856i	$-0.337734\pi$
$401$	3.14262e6			0.975957			0.487978	+	0.872856i	$0.337734\pi$
$402$	3.16067e6	−	1.15613e6i	0.975469	−	0.356814i
$403$	1.48560e6	−	1.48560e6i	0.455658	−	0.455658i
$404$	−4.26507e6	−	359366.i	−1.30009	−	0.109543i
$405$	−1.92008e6	−	1.92008e6i	−0.581678	−	0.581678i
$406$	1.98771e6	−	4.28057e6i	0.598464	−	1.28880i
$407$		−	2.31702e6i		−	0.693336i
$408$	1.85022e6	−	505317.i	0.550266	−	0.150284i
$409$		−	1.50580e6i		−	0.445101i	−0.974921	−	0.222550i	$-0.928562\pi$
$409$		−	1.50580e6i		−	0.445101i	0.974921	−	0.222550i	$-0.0714382\pi$
$410$	364730.	+	169365.i	0.107155	+	0.0497582i
$411$	−389759.	−	389759.i	−0.113813	−	0.113813i
$412$	470490.	+	557071.i	0.136555	+	0.161684i
$413$	2.02866e6	−	2.02866e6i	0.585240	−	0.585240i
$414$	−173237.	−	473599.i	−0.0496751	−	0.135803i
$415$	−1.16119e6			−0.330967
$416$	−3.17993e6	+	4.61980e6i	−0.900915	+	1.30885i
$417$	969402.			0.273001
$418$	2.69372e6	+	7.36419e6i	0.754072	+	2.06150i
$419$	−3.16326e6	+	3.16326e6i	−0.880237	+	0.880237i	−0.993558	−	0.113321i	$-0.963851\pi$
$419$	−3.16326e6	+	3.16326e6i	−0.880237	+	0.880237i	0.113321	+	0.993558i	$0.463851\pi$
$420$	−1.52092e6	−	1.80081e6i	−0.420711	−	0.498131i
$421$	3.78619e6	+	3.78619e6i	1.04111	+	1.04111i	0.999118	+	0.0419924i	$0.0133705\pi$
$421$	3.78619e6	+	3.78619e6i	1.04111	+	1.04111i	0.0419924	+	0.999118i	$0.486629\pi$
$422$	−5.98342e6	−	2.77844e6i	−1.63557	−	0.759488i
$423$		−	46933.2i		−	0.0127535i
$424$	−276443.	−	1.01220e6i	−0.0746776	−	0.273432i
$425$		−	999559.i		−	0.268433i
$426$	1.52094e6	−	3.27537e6i	0.406058	−	0.874452i
$427$	1.45899e6	+	1.45899e6i	0.387243	+	0.387243i
$428$	−2.33140e6	−	196439.i	−0.615188	−	0.0518345i
$429$	7.37579e6	−	7.37579e6i	1.93493	−	1.93493i
$430$	−221917.	+	81174.4i	−0.0578788	+	0.0211713i
$431$	−4.50282e6			−1.16759			−0.583797	−	0.811900i	$-0.698433\pi$
$431$	−4.50282e6			−1.16759			−0.583797	+	0.811900i	$0.698433\pi$
$432$	2.13386e6	−	1.51463e6i	0.550118	−	0.390479i
$433$	−5.69963e6			−1.46092			−0.730460	−	0.682955i	$-0.760694\pi$
$433$	−5.69963e6			−1.46092			−0.730460	+	0.682955i	$0.760694\pi$
$434$	−1.23122e6	+	450364.i	−0.313770	+	0.114773i
$435$	3.80969e6	−	3.80969e6i	0.965308	−	0.965308i
$436$	−233069.	+	2.76613e6i	−0.0587175	+	0.696877i
$437$	−1.42642e6	−	1.42642e6i	−0.357309	−	0.357309i
$438$	−3.44529e6	+	7.41950e6i	−0.858106	+	1.84795i
$439$			316832.i			0.0784634i	0.999230	+	0.0392317i	$0.0124911\pi$
$439$			316832.i			0.0784634i	−0.999230	+	0.0392317i	$0.987509\pi$
$440$	1.90949e6	−	3.34439e6i	0.470204	−	0.823541i
$441$		−	573853.i		−	0.140509i
$442$	−2.81634e6	−	1.30779e6i	−0.685693	−	0.318406i
$443$	−797467.	−	797467.i	−0.193065	−	0.193065i	0.603954	−	0.797019i	$-0.293591\pi$
$443$	−797467.	−	797467.i	−0.193065	−	0.193065i	−0.797019	+	0.603954i	$0.793591\pi$
$444$	1.83635e6	−	1.55095e6i	0.442078	−	0.373370i
$445$	−1.09245e6	+	1.09245e6i	−0.261518	+	0.261518i
$446$	−264789.	−	723887.i	−0.0630322	−	0.172319i
$447$	−6.46372e6			−1.53008
$448$	3.01384e6	−	1.77892e6i	0.709456	−	0.418756i
$449$	−625844.			−0.146504			−0.0732521	−	0.997313i	$-0.523338\pi$
$449$	−625844.			−0.146504			−0.0732521	+	0.997313i	$0.523338\pi$
$450$	364064.	+	995289.i	0.0847513	+	0.231696i
$451$	785204.	−	785204.i	0.181778	−	0.181778i
$452$	2.63460e6	−	2.22513e6i	0.606552	−	0.512282i
$453$	−2.35513e6	−	2.35513e6i	−0.539224	−	0.539224i
$454$	−3.08862e6	−	1.43422e6i	−0.703274	−	0.326570i
$455$			3.81616e6i			0.864167i
$456$	−4.03338e6	+	7.06428e6i	−0.908357	+	1.59095i
$457$		−	3.95584e6i		−	0.886030i	−0.896514	−	0.443015i	$-0.853909\pi$
$457$		−	3.95584e6i		−	0.886030i	0.896514	−	0.443015i	$-0.146091\pi$
$458$	1.94312e6	−	4.18454e6i	0.432849	−	0.932147i
$459$	1.02446e6	+	1.02446e6i	0.226967	+	0.226967i
$460$	−83182.5	+	987235.i	−0.0183289	+	0.217533i
$461$	3.75163e6	−	3.75163e6i	0.822182	−	0.822182i	−0.164238	−	0.986421i	$-0.552517\pi$
$461$	3.75163e6	−	3.75163e6i	0.822182	−	0.822182i	0.986421	+	0.164238i	$0.0525166\pi$
$462$	−6.11283e6	+	2.23600e6i	−1.33241	+	0.487378i
$463$	6.65021e6			1.44173			0.720864	−	0.693077i	$-0.243745\pi$
$463$	6.65021e6			1.44173			0.720864	+	0.693077i	$0.243745\pi$
$464$	4.63010e6	+	6.52302e6i	0.998379	+	1.40654i
$465$	−1.49660e6			−0.320977
$466$	2.99182e6	−	1.09437e6i	0.638221	−	0.233453i
$467$	−2.08935e6	+	2.08935e6i	−0.443322	+	0.443322i	−0.893127	−	0.449805i	$-0.851494\pi$
$467$	−2.08935e6	+	2.08935e6i	−0.443322	+	0.443322i	0.449805	+	0.893127i	$0.351494\pi$
$468$	3.28064e6	+	276420.i	0.692379	+	0.0583385i
$469$	2.40414e6	+	2.40414e6i	0.504694	+	0.504694i
$470$	−38833.8	+	83629.2i	−0.00810896	+	0.0174628i
$471$			3.92461e6i			0.815162i
$472$	1.28112e6	+	4.69082e6i	0.264688	+	0.969155i
$473$			652506.i			0.134101i
$474$	560290.	+	260175.i	0.114543	+	0.0531887i
$475$	2.99769e6	+	2.99769e6i	0.609610	+	0.609610i
$476$	1.25024e6	+	1.48032e6i	0.252917	+	0.299459i
$477$	−435536.	+	435536.i	−0.0876452	+	0.0876452i
$478$	−2.38039e6	−	6.50757e6i	−0.476516	−	1.30271i
$479$	6.97076e6			1.38817			0.694083	−	0.719895i	$-0.255810\pi$
$479$	6.97076e6			1.38817			0.694083	+	0.719895i	$0.255810\pi$
$480$	3.92875e6	−	725269.i	0.778308	−	0.143680i
$481$	−3.89148e6			−0.766925
$482$	−209398.	−	572459.i	−0.0410540	−	0.112235i
$483$	1.18404e6	−	1.18404e6i	0.230939	−	0.230939i
$484$	−3.53640e6	−	4.18718e6i	−0.686196	−	0.812471i
$485$	4.07348e6	+	4.07348e6i	0.786341	+	0.786341i
$486$	−3.86912e6	−	1.79665e6i	−0.743057	−	0.345044i
$487$			5.01220e6i			0.957648i	0.877911	+	0.478824i	$0.158937\pi$
$487$			5.01220e6i			0.957648i	−0.877911	+	0.478824i	$0.841063\pi$
$488$	−3.37359e6	+	921367.i	−0.641273	+	0.175139i
$489$			5.04418e6i			0.953933i
$490$	−474821.	+	1.02253e6i	−0.0893387	+	0.192392i
$491$	−6.26073e6	−	6.26073e6i	−1.17198	−	1.17198i	−0.981737	−	0.190245i	$-0.939072\pi$
$491$	−6.26073e6	−	6.26073e6i	−1.17198	−	1.17198i	−0.190245	−	0.981737i	$-0.560928\pi$
$492$	1.14791e6	+	96720.2i	0.213793	+	0.0180138i
$493$	−3.13168e6	+	3.13168e6i	−0.580309	+	0.580309i
$494$	1.23683e7	−	4.52417e6i	2.28030	−	0.834106i
$495$	−2.26069e6			−0.414693
$496$	371808.	−	2.19070e6i	0.0678601	−	0.399833i
$497$	3.64828e6			0.662517
$498$	−3.12396e6	+	1.14271e6i	−0.564459	+	0.206472i
$499$	−47597.3	+	47597.3i	−0.00855718	+	0.00855718i	−0.711372	−	0.702815i	$-0.751926\pi$
$499$	−47597.3	+	47597.3i	−0.00855718	+	0.00855718i	0.702815	+	0.711372i	$0.251926\pi$
$500$	484665.	−	5.75215e6i	0.0866995	−	1.02898i
$501$	−1.39373e6	−	1.39373e6i	−0.248076	−	0.248076i
$502$	−3.12396e6	+	6.72750e6i	−0.553282	+	1.19150i
$503$			6.56568e6i			1.15707i	0.815657	+	0.578535i	$0.196375\pi$
$503$			6.56568e6i			1.15707i	−0.815657	+	0.578535i	$0.803625\pi$
$504$	−1.78407e6	−	1.01862e6i	−0.312850	−	0.178623i
$505$		−	4.93620e6i		−	0.861319i
$506$	2.48132e6	+	1.15222e6i	0.430830	+	0.200059i
$507$	−7.48122e6	−	7.48122e6i	−1.29257	−	1.29257i
$508$	6.53793e6	−	5.52180e6i	1.12404	−	0.949340i
$509$	−438674.	+	438674.i	−0.0750494	+	0.0750494i	−0.743635	−	0.668586i	$-0.766900\pi$
$509$	−438674.	+	438674.i	−0.0750494	+	0.0750494i	0.668586	+	0.743635i	$0.266900\pi$
$510$	759864.	+	2.07734e6i	0.129363	+	0.353657i
$511$	−8.26424e6			−1.40007
$512$	85598.9	+	5.93102e6i	0.0144309	+	0.999896i
$513$	−6.14471e6			−1.03088
$514$	−1.51927e6	−	4.15343e6i	−0.253646	−	0.693425i
$515$	−594627.	+	594627.i	−0.0987931	+	0.0987931i
$516$	−517143.	+	436768.i	−0.0855040	+	0.0722149i
$517$	180040.	+	180040.i	0.0296239	+	0.0296239i
$518$	2.20243e6	+	1.02271e6i	0.360644	+	0.167467i
$519$			2.89856e6i			0.472350i
$520$	−5.61697e6	−	3.20703e6i	−0.910949	−	0.520110i
$521$		−	4.68841e6i		−	0.756713i	−0.925660	−	0.378357i	$-0.876489\pi$
$521$		−	4.68841e6i		−	0.756713i	0.925660	−	0.378357i	$-0.123511\pi$
$522$	1.97766e6	−	4.25893e6i	0.317670	−	0.684108i
$523$	248034.	+	248034.i	0.0396513	+	0.0396513i	0.726654	−	0.687003i	$-0.241074\pi$
$523$	248034.	+	248034.i	0.0396513	+	0.0396513i	−0.687003	+	0.726654i	$0.741074\pi$
$524$	35705.4	−	423763.i	0.00568075	−	0.0674209i
$525$	−2.48831e6	+	2.48831e6i	−0.394009	+	0.394009i
$526$	4.63149e6	−	1.69414e6i	0.729889	−	0.266984i
$527$	1.23025e6			0.192960
$528$	1.84597e6	−	1.08765e7i	0.288165	−	1.69787i
$529$	5.73254e6			0.890651
$530$	1.13644e6	−	415697.i	0.175735	−	0.0642817i
$531$	2.01840e6	−	2.01840e6i	0.310650	−	0.310650i
$532$	−8.18898e6	−	689987.i	−1.25444	−	0.105697i
$533$	−1.31877e6	−	1.31877e6i	−0.201071	−	0.201071i
$534$	−1.86396e6	+	4.01408e6i	−0.282868	+	0.609162i
$535$		−	2.69826e6i		−	0.407568i
$536$	−5.55904e6	+	1.51824e6i	−0.835772	+	0.228259i
$537$			9.40239e6i			1.40703i
$538$	2.83408e6	+	1.31603e6i	0.422140	+	0.196024i
$539$	2.20135e6	+	2.20135e6i	0.326375	+	0.326375i
$540$	1.94723e6	+	2.30556e6i	0.287364	+	0.340246i
$541$	4.85712e6	−	4.85712e6i	0.713486	−	0.713486i	−0.253777	−	0.967263i	$-0.581673\pi$
$541$	4.85712e6	−	4.85712e6i	0.713486	−	0.713486i	0.967263	+	0.253777i	$0.0816730\pi$
$542$	1.93997e6	+	5.30354e6i	0.283659	+	0.775475i
$543$	9.30874e6			1.35485
$544$	−3.22955e6	+	596193.i	−0.467891	+	0.0863753i
$545$	−3.20140e6			−0.461687
$546$	3.75540e6	+	1.02666e7i	0.539107	+	1.47383i
$547$	−410716.	+	410716.i	−0.0586912	+	0.0586912i	−0.735843	−	0.677152i	$-0.763214\pi$
$547$	−410716.	+	410716.i	−0.0586912	+	0.0586912i	0.677152	+	0.735843i	$0.263214\pi$
$548$	608986.	+	721053.i	0.0866276	+	0.102569i
$549$	1.45162e6	+	1.45162e6i	0.205552	+	0.205552i
$550$	−5.21459e6	−	2.42143e6i	−0.735044	−	0.341323i
$551$		−	1.87839e7i		−	2.63576i
$552$	747732.	+	2.73782e6i	0.104447	+	0.382435i
$553$			624082.i			0.0867818i
$554$	1.24784e6	−	2.68724e6i	0.172737	−	0.371991i
$555$	1.96015e6	+	1.96015e6i	0.270121	+	0.270121i
$556$	−1.65403e6	−	139365.i	−0.226911	−	0.0191191i
$557$	−2.02585e6	+	2.02585e6i	−0.276675	+	0.276675i	−0.831780	−	0.555105i	$-0.812678\pi$
$557$	−2.02585e6	+	2.02585e6i	−0.276675	+	0.276675i	0.555105	+	0.831780i	$0.312678\pi$
$558$	−1.22500e6	+	448088.i	−0.166552	+	0.0609225i
$559$	1.09590e6			0.148334
$560$	2.33616e6	+	3.29125e6i	0.314798	+	0.443497i
$561$	6.10803e6			0.819396
$562$	−3.79773e6	+	1.38916e6i	−0.507204	+	0.185529i
$563$	1.54578e6	−	1.54578e6i	0.205530	−	0.205530i	−0.596834	−	0.802365i	$-0.703575\pi$
$563$	1.54578e6	−	1.54578e6i	0.205530	−	0.205530i	0.802365	+	0.596834i	$0.203575\pi$
$564$	−22177.0	+	263204.i	−0.00293566	+	0.0348413i
$565$	2.81222e6	+	2.81222e6i	0.370619	+	0.370619i
$566$	3.00943e6	−	6.48086e6i	0.394861	−	0.850338i
$567$		−	7.85838e6i		−	1.02654i
$568$	−3.06595e6	+	5.36988e6i	−0.398745	+	0.698383i
$569$		−	176266.i		−	0.0228238i	−0.999935	−	0.0114119i	$-0.996367\pi$
$569$		−	176266.i		−	0.0228238i	0.999935	−	0.0114119i	$-0.00363261\pi$
$570$	−8.50880e6	−	3.95112e6i	−1.09694	−	0.509370i
$571$	8.32418e6	+	8.32418e6i	1.06844	+	1.06844i	0.997479	+	0.0709630i	$0.0226072\pi$
$571$	8.32418e6	+	8.32418e6i	1.06844	+	1.06844i	0.0709630	+	0.997479i	$0.477393\pi$
$572$	−1.36452e7	+	1.15244e7i	−1.74377	+	1.47275i
$573$	−5.68226e6	+	5.68226e6i	−0.722994	+	0.722994i
$574$	399789.	+	1.09295e6i	0.0506467	+	0.138459i
$575$	1.47908e6			0.186561
$576$	2.99861e6	−	1.76993e6i	0.376585	−	0.222280i
$577$	1.72294e6			0.215442			0.107721	−	0.994181i	$-0.465645\pi$
$577$	1.72294e6			0.215442			0.107721	+	0.994181i	$0.465645\pi$
$578$	2.13455e6	+	5.83549e6i	0.265758	+	0.726537i
$579$	4.89833e6	−	4.89833e6i	0.607227	−	0.607227i
$580$	−7.04790e6	+	5.95251e6i	−0.869941	+	0.734735i
$581$	−2.37623e6	−	2.37623e6i	−0.292043	−	0.292043i
$582$	1.49675e7	+	6.95027e6i	1.83165	+	0.850539i
$583$		−	3.34150e6i		−	0.407165i
$584$	6.94513e6	−	1.21641e7i	0.842652	−	1.47587i
$585$			3.79687e6i			0.458707i
$586$	−2.43882e6	+	5.25204e6i	−0.293384	+	0.631806i
$587$	514428.	+	514428.i	0.0616211	+	0.0616211i	0.737246	−	0.675625i	$-0.236126\pi$
$587$	514428.	+	514428.i	0.0616211	+	0.0616211i	−0.675625	+	0.737246i	$0.736126\pi$
$588$	−271158.	+	3.21819e6i	−0.0323430	+	0.383856i
$589$	−3.68954e6	+	3.68954e6i	−0.438211	+	0.438211i
$590$	−5.26662e6	+	1.92646e6i	−0.622877	+	0.227840i
$591$	−1.78601e7			−2.10336
$592$	−3.35621e6	+	2.38227e6i	−0.393591	+	0.279375i
$593$	−8.60704e6			−1.00512			−0.502559	−	0.864543i	$-0.667608\pi$
$593$	−8.60704e6			−1.00512			−0.502559	+	0.864543i	$0.667608\pi$
$594$	7.82623e6	−	2.86273e6i	0.910094	−	0.332901i
$595$	−1.58012e6	+	1.58012e6i	−0.182977	+	0.182977i
$596$	1.10286e7	+	929249.i	1.27176	+	0.107156i
$597$	−3.78192e6	−	3.78192e6i	−0.434287	−	0.434287i
$598$	1.93517e6	−	4.16742e6i	0.221292	−	0.476556i
$599$		−	1.71814e6i		−	0.195655i	−0.995203	−	0.0978276i	$-0.968811\pi$
$599$		−	1.71814e6i		−	0.195655i	0.995203	−	0.0978276i	$-0.0311894\pi$
$600$	−1.57139e6	−	5.75365e6i	−0.178199	−	0.652477i
$601$			5.25547e6i			0.593506i	0.954954	+	0.296753i	$0.0959038\pi$
$601$			5.25547e6i			0.593506i	−0.954954	+	0.296753i	$0.904096\pi$
$602$	−620236.	−	288011.i	−0.0697535	−	0.0323905i
$603$	2.39199e6	+	2.39199e6i	0.267896	+	0.267896i
$604$	3.67981e6	+	4.35698e6i	0.410424	+	0.485951i
$605$	4.46947e6	−	4.46947e6i	0.496441	−	0.496441i
$606$	−4.85761e6	−	1.32799e7i	−0.537330	−	1.46897i
$607$	9.34712e6			1.02969			0.514845	−	0.857283i	$-0.327850\pi$
$607$	9.34712e6			1.02969			0.514845	+	0.857283i	$0.327850\pi$
$608$	7.89746e6	−	1.14734e7i	0.866421	−	1.25874i
$609$	1.55920e7			1.70357
$610$	−1.38549e6	−	3.78771e6i	−0.150758	−	0.412147i
$611$	302381.	−	302381.i	0.0327681	−	0.0327681i
$612$	1.24393e6	+	1.47283e6i	0.134250	+	0.158955i
$613$	−8.58082e6	−	8.58082e6i	−0.922312	−	0.922312i	0.0748805	−	0.997193i	$-0.476142\pi$
$613$	−8.58082e6	−	8.58082e6i	−0.922312	−	0.922312i	−0.997193	+	0.0748805i	$0.976142\pi$
$614$	−1.12896e7	−	5.24239e6i	−1.20853	−	0.561188i
$615$			1.32854e6i			0.141640i
$616$	1.07514e7	−	2.93632e6i	1.14159	−	0.311783i
$617$		−	809357.i		−	0.0855908i	−0.999084	−	0.0427954i	$-0.986374\pi$
$617$		−	809357.i		−	0.0855908i	0.999084	−	0.0427954i	$-0.0136264\pi$
$618$	−1.01457e6	+	2.18489e6i	−0.106859	+	0.230122i
$619$	−2.53658e6	−	2.53658e6i	−0.266086	−	0.266086i	0.561435	−	0.827521i	$-0.310250\pi$
$619$	−2.53658e6	−	2.53658e6i	−0.266086	−	0.266086i	−0.827521	+	0.561435i	$0.810250\pi$
$620$	2.55355e6	+	215157.i	0.266787	+	0.0224790i
$621$	−1.51592e6	+	1.51592e6i	−0.157742	+	0.157742i
$622$	1.24261e7	−	4.54530e6i	1.28783	−	0.471072i
$623$	−4.47110e6			−0.461524
$624$	−1.82674e7	−	3.10035e6i	−1.87808	−	0.318750i
$625$	1.14776e6			0.117530
$626$	−7.44091e6	+	2.72179e6i	−0.758910	+	0.277599i
$627$	−1.83180e7	+	1.83180e7i	−1.86084	+	1.86084i
$628$	564216.	−	6.69629e6i	0.0570882	−	0.677540i
$629$	−1.61131e6	−	1.61131e6i	−0.162387	−	0.162387i
$630$	997849.	−	2.14888e6i	0.100164	−	0.215706i
$631$			41444.9i			0.00414379i	0.999998	+	0.00207190i	$0.000659505\pi$
$631$			41444.9i			0.00414379i	−0.999998	+	0.00207190i	$0.999340\pi$
$632$	−918582.	−	524468.i	−0.0914798	−	0.0522308i
$633$		−	2.17947e7i		−	2.16193i
$634$	−1.40674e7	−	6.53229e6i	−1.38992	−	0.645420i
$635$	6.97870e6	+	6.97870e6i	0.686816	+	0.686816i
$636$	2.64831e6	−	2.23670e6i	0.259612	−	0.219263i
$637$	3.69721e6	−	3.69721e6i	0.361015	−	0.361015i
$638$	8.75113e6	+	2.39241e7i	0.851162	+	2.32693i
$639$	3.62984e6			0.351670
$640$	−6.80763e6	+	672666.i	−0.656971	+	0.0649156i
$641$	6.97921e6			0.670905			0.335453	−	0.942057i	$-0.391111\pi$
$641$	6.97921e6			0.670905			0.335453	+	0.942057i	$0.391111\pi$
$642$	−2.65531e6	−	7.25915e6i	−0.254259	−	0.695102i
$643$	−8.89601e6	+	8.89601e6i	−0.848531	+	0.848531i	−0.989950	−	0.141419i	$-0.954834\pi$
$643$	−8.89601e6	+	8.89601e6i	−0.848531	+	0.848531i	0.141419	+	0.989950i	$0.454834\pi$
$644$	−2.19047e6	+	1.85002e6i	−0.208124	+	0.175777i
$645$	−552007.	−	552007.i	−0.0522451	−	0.0522451i
$646$	6.99449e6	+	3.24794e6i	0.659439	+	0.306215i
$647$			1.63883e7i			1.53913i	0.638571	+	0.769563i	$0.279526\pi$
$647$			1.63883e7i			1.53913i	−0.638571	+	0.769563i	$0.720474\pi$
$648$	1.15667e7	+	6.60405e6i	1.08211	+	0.617836i
$649$			1.54855e7i			1.44316i
$650$	−4.06684e6	+	8.75801e6i	−0.377550	+	0.813059i
$651$	−3.06259e6	−	3.06259e6i	−0.283229	−	0.283229i
$652$	725170.	−	8.60653e6i	0.0668068	−	0.792883i
$653$	−5.42938e6	+	5.42938e6i	−0.498273	+	0.498273i	−0.910900	−	0.412627i	$-0.864611\pi$
$653$	−5.42938e6	+	5.42938e6i	−0.498273	+	0.498273i	0.412627	+	0.910900i	$0.364611\pi$
$654$	−8.61273e6	+	3.15043e6i	−0.787402	+	0.288022i
$655$	490444.			0.0446670
$656$	−1.94469e6	−	330054.i	−0.176437	−	0.0299451i
$657$	−8.22247e6			−0.743171
$658$	−250604.	+	91667.7i	−0.0225644	+	0.00825376i
$659$	57265.3	−	57265.3i	0.00513663	−	0.00513663i	−0.704534	−	0.709670i	$-0.748844\pi$
$659$	57265.3	−	57265.3i	0.00513663	−	0.00513663i	0.709670	+	0.704534i	$0.248844\pi$
$660$	1.26780e7	+	1.06822e6i	1.13290	+	0.0954559i
$661$	1.17817e7	+	1.17817e7i	1.04883	+	1.04883i	0.998745	+	0.0500855i	$0.0159494\pi$
$661$	1.17817e7	+	1.17817e7i	1.04883	+	1.04883i	0.0500855	+	0.998745i	$0.484051\pi$
$662$	5.90255e6	−	1.27112e7i	0.523473	−	1.12731i
$663$		−	1.02586e7i		−	0.906364i
$664$	5.49449e6	−	1.50061e6i	0.483623	−	0.132083i
$665$		−	9.47756e6i		−	0.831079i
$666$	2.19130e6	+	1.01755e6i	0.191433	+	0.0888931i
$667$	−4.63403e6	−	4.63403e6i	−0.403315	−	0.403315i
$668$	2.17766e6	+	2.57840e6i	0.188821	+	0.223568i
$669$	1.80063e6	−	1.80063e6i	0.155546	−	0.155546i
$670$	−2.28303e6	−	6.24142e6i	−0.196483	−	0.537151i
$671$	−1.11370e7			−0.954913
$672$	9.52383e6	+	6.55549e6i	0.813558	+	0.559993i
$673$	1.62313e7			1.38139			0.690696	−	0.723146i	$-0.257304\pi$
$673$	1.62313e7			1.38139			0.690696	+	0.723146i	$0.257304\pi$
$674$	−5.83307e6	−	1.59466e7i	−0.494593	−	1.35213i
$675$	3.18577e6	−	3.18577e6i	0.269125	−	0.269125i
$676$	1.16892e7	+	1.38402e7i	0.983823	+	1.16487i
$677$	−1.97754e6	−	1.97754e6i	−0.165827	−	0.165827i	0.619316	−	0.785142i	$-0.287410\pi$
$677$	−1.97754e6	−	1.97754e6i	−0.165827	−	0.165827i	−0.785142	+	0.619316i	$0.787410\pi$
$678$	1.03332e7	+	4.79828e6i	0.863295	+	0.400877i
$679$			1.66716e7i			1.38773i
$680$	−997858.	−	3.65366e6i	−0.0827554	−	0.303009i
$681$		−	1.12503e7i		−	0.929603i
$682$	2.98028e6	−	6.41809e6i	0.245356	−	0.528378i
$683$	1.27340e6	+	1.27340e6i	0.104451	+	0.104451i	0.757401	−	0.652950i	$-0.226469\pi$
$683$	1.27340e6	+	1.27340e6i	0.104451	+	0.104451i	−0.652950	+	0.757401i	$0.726469\pi$
$684$	−8.14759e6	−	686500.i	−0.665869	−	0.0561048i
$685$	−769664.	+	769664.i	−0.0626722	+	0.0626722i
$686$	−1.26003e7	+	4.60905e6i	−1.02229	+	0.373939i
$687$	1.52422e7			1.23213
$688$	945157.	−	670881.i	0.0761260	−	0.0540349i
$689$	−5.61213e6			−0.450380
$690$	−3.07390e6	+	1.12439e6i	−0.245791	+	0.0899073i
$691$	1.00075e7	−	1.00075e7i	0.797313	−	0.797313i	−0.185358	−	0.982671i	$-0.559344\pi$
$691$	1.00075e7	−	1.00075e7i	0.797313	−	0.797313i	0.982671	+	0.185358i	$0.0593445\pi$
$692$	416708.	−	4.94561e6i	0.0330801	−	0.392604i
$693$	−4.62619e6	−	4.62619e6i	−0.365923	−	0.365923i
$694$	−6.91655e6	+	1.48949e7i	−0.545118	+	1.17392i
$695$		−	1.91430e6i		−	0.150330i
$696$	−1.31033e7	+	2.29498e7i	−1.02531	+	1.79579i
$697$		−	1.09210e6i		−	0.0851488i
$698$	1.94712e7	+	9.04159e6i	1.51270	+	0.702435i
$699$	7.44200e6	+	7.44200e6i	0.576099	+	0.576099i
$700$	4.60336e6	−	3.88790e6i	0.355083	−	0.299896i
$701$	−1.69368e7	+	1.69368e7i	−1.30178	+	1.30178i	−0.374586	+	0.927192i	$0.622215\pi$
$701$	−1.69368e7	+	1.69368e7i	−1.30178	+	1.30178i	−0.927192	+	0.374586i	$0.877785\pi$
$702$	−4.80802e6	−	1.31443e7i	−0.368234	−	1.00669i
$703$	9.66464e6			0.737560
$704$	−4.71331e6	+	1.82925e7i	−0.358422	+	1.39105i
$705$	−304620.			−0.0230827
$706$	−1.63922e6	−	4.48134e6i	−0.123773	−	0.338373i
$707$	1.01013e7	−	1.01013e7i	0.760024	−	0.760024i
$708$	−1.22730e7	+	1.03656e7i	−0.920172	+	0.777158i
$709$	−1.71102e7	−	1.71102e7i	−1.27832	−	1.27832i	−0.941607	−	0.336713i	$-0.890685\pi$
$709$	−1.71102e7	−	1.71102e7i	−1.27832	−	1.27832i	−0.336713	−	0.941607i	$-0.609315\pi$
$710$	−6.46792e6	−	3.00343e6i	−0.481525	−	0.223600i
$711$			620928.i			0.0460646i
$712$	3.75744e6	−	6.58098e6i	0.277774	−	0.486508i
$713$			1.82044e6i			0.134107i
$714$	−2.69603e6	+	5.80595e6i	−0.197916	+	0.426214i
$715$	−1.45651e7	−	1.45651e7i	−1.06549	−	1.06549i
$716$	1.35172e6	−	1.60427e7i	0.0985384	−	1.16948i
$717$	1.61872e7	−	1.61872e7i	1.17591	−	1.17591i
$718$	−2.46042e7	+	8.99992e6i	−1.78114	+	0.651519i
$719$	−3.69511e6			−0.266566			−0.133283	−	0.991078i	$-0.542552\pi$
$719$	−3.69511e6			−0.266566			−0.133283	+	0.991078i	$0.542552\pi$
$720$	2.32435e6	+	3.27461e6i	0.167098	+	0.235412i
$721$	−2.43365e6			−0.174349
$722$	−1.75626e7	+	6.42418e6i	−1.25385	+	0.458643i
$723$	1.42396e6	−	1.42396e6i	0.101310	−	0.101310i
$724$	−1.58829e7	−	1.33826e6i	−1.12611	−	0.0948842i
$725$	9.73861e6	+	9.73861e6i	0.688101	+	0.688101i
$726$	7.62592e6	−	1.64225e7i	0.536971	−	1.15638i
$727$		−	2.47532e7i		−	1.73698i	−0.495704	−	0.868492i	$-0.665090\pi$
$727$		−	2.47532e7i		−	1.73698i	0.495704	−	0.868492i	$-0.334910\pi$
$728$	−4.93162e6	−	1.80571e7i	−0.344874	−	1.26276i
$729$			3.78638e6i			0.263879i
$730$	1.46514e7	+	6.80349e6i	1.01759	+	0.472524i
$731$	453766.	+	453766.i	0.0314079	+	0.0314079i
$732$	−7.45481e6	−	8.82665e6i	−0.514232	−	0.608861i
$733$	1.92394e7	−	1.92394e7i	1.32261	−	1.32261i	0.410954	−	0.911656i	$-0.365196\pi$
$733$	1.92394e7	−	1.92394e7i	1.32261	−	1.32261i	0.911656	−	0.410954i	$-0.134804\pi$
$734$	1.10963e6	+	3.03354e6i	0.0760219	+	0.207831i
$735$	−3.72459e6			−0.254308
$736$	−882204.	−	4.77886e6i	−0.0600308	−	0.325184i
$737$	−1.83517e7			−1.24454
$738$	397768.	+	1.08743e6i	0.0268837	+	0.0734955i
$739$	6.20086e6	−	6.20086e6i	0.417677	−	0.417677i	−0.466725	−	0.884402i	$-0.654566\pi$
$739$	6.20086e6	−	6.20086e6i	0.417677	−	0.417677i	0.884402	+	0.466725i	$0.154566\pi$
$740$	−3.06268e6	−	3.62628e6i	−0.205600	−	0.243434i
$741$	3.07655e7	+	3.07655e7i	2.05835	+	2.05835i
$742$	3.17625e6	+	1.47491e6i	0.211790	+	0.0983460i
$743$			1.51452e7i			1.00647i	0.864148	+	0.503237i	$0.167858\pi$
$743$			1.51452e7i			1.00647i	−0.864148	+	0.503237i	$0.832142\pi$
$744$	7.08156e6	−	1.93406e6i	0.469026	−	0.128096i
$745$			1.27640e7i			0.842553i
$746$	−2.89776e6	+	6.24037e6i	−0.190640	+	0.410547i
$747$	−2.36421e6	−	2.36421e6i	−0.155019	−	0.155019i
$748$	−1.04217e7	−	878113.i	−0.681059	−	0.0573847i
$749$	5.52163e6	−	5.52163e6i	0.359636	−	0.359636i
$750$	1.79101e7	−	6.55130e6i	1.16264	−	0.425279i
$751$	−2.35795e7			−1.52558			−0.762788	−	0.646648i	$-0.776170\pi$
$751$	−2.35795e7			−1.52558			−0.762788	+	0.646648i	$0.776170\pi$
$752$	75678.3	−	445898.i	0.00488008	−	0.0287535i
$753$	−2.45050e7			−1.57495
$754$	4.01810e7	−	1.46977e7i	2.57391	−	0.941502i
$755$	−4.65071e6	+	4.65071e6i	−0.296929	+	0.296929i
$756$	−733278.	+	8.70277e6i	−0.0466621	+	0.553800i
$757$	2.49220e6	+	2.49220e6i	0.158068	+	0.158068i	0.781710	−	0.623642i	$-0.214348\pi$
$757$	2.49220e6	+	2.49220e6i	0.158068	+	0.158068i	−0.623642	+	0.781710i	$0.714348\pi$
$758$	−7.00752e6	+	1.50908e7i	−0.442987	+	0.953980i
$759$			9.03822e6i			0.569480i
$760$	1.39500e7	+	7.96478e6i	0.876070	+	0.500196i
$761$			1.56133e7i			0.977314i	0.872476	+	0.488657i	$0.162513\pi$
$761$			1.56133e7i			0.977314i	−0.872476	+	0.488657i	$0.837487\pi$
$762$	2.56424e7	+	1.19072e7i	1.59982	+	0.742889i
$763$	−6.55122e6	−	6.55122e6i	−0.407391	−	0.407391i
$764$	1.05122e7	−	8.87836e6i	0.651566	−	0.550299i
$765$	−1.57213e6	+	1.57213e6i	−0.0971258	+	0.0971258i
$766$	2.58846e6	+	7.07642e6i	0.159393	+	0.435754i
$767$	2.60083e7			1.59633
$768$	−1.76526e7	+	8.50892e6i	−1.07996	+	0.520561i
$769$	−1.21956e7			−0.743680			−0.371840	−	0.928297i	$-0.621273\pi$
$769$	−1.21956e7			−0.743680			−0.371840	+	0.928297i	$0.621273\pi$
$770$	4.41546e6	+	1.20711e7i	0.268379	+	0.733704i
$771$	1.03314e7	−	1.03314e7i	0.625929	−	0.625929i
$772$	−9.06189e6	+	7.65348e6i	−0.547237	+	0.462185i
$773$	−1.15929e7	−	1.15929e7i	−0.697822	−	0.697822i	0.266119	−	0.963940i	$-0.414259\pi$
$773$	−1.15929e7	−	1.15929e7i	−0.697822	−	0.697822i	−0.963940	+	0.266119i	$0.914259\pi$
$774$	−617101.	−	286555.i	−0.0370257	−	0.0171932i
$775$		−	3.82573e6i		−	0.228802i
$776$	−2.45389e7	−	1.40106e7i	−1.46285	−	0.835221i
$777$			8.02238e6i			0.476706i
$778$	4.71046e6	−	1.01440e7i	0.279006	−	0.600844i
$779$	3.27520e6	+	3.27520e6i	0.193373	+	0.193373i
$780$	1.79411e6	−	2.12930e7i	0.105587	−	1.25314i
$781$	−1.39244e7	+	1.39244e7i	−0.816860	+	0.816860i
$782$	2.52683e6	−	924284.i	0.147761	−	0.0540491i
$783$	−1.99624e7			−1.16361
$784$	925319.	−	5.45200e6i	0.0537652	−	0.316786i
$785$	7.74999e6			0.448877
$786$	1.31945e6	−	482636.i	0.0761790	−	0.0278653i
$787$	−2.01708e7	+	2.01708e7i	−1.16088	+	1.16088i	−0.176593	+	0.984284i	$0.556508\pi$
$787$	−2.01708e7	+	2.01708e7i	−1.16088	+	1.16088i	−0.984284	+	0.176593i	$0.943492\pi$
$788$	3.04734e7	+	2.56763e6i	1.74826	+	0.147305i
$789$	1.15206e7	+	1.15206e7i	0.658844	+	0.658844i
$790$	513772.	−	1.10642e6i	0.0292889	−	0.0630740i
$791$			1.15096e7i			0.654065i
$792$	1.06970e7	−	2.92148e6i	0.605968	−	0.165497i
$793$			1.87049e7i			1.05626i
$794$	1.02232e6	+	474720.i	0.0575486	+	0.0267231i
$795$	2.82685e6	+	2.82685e6i	0.158630	+	0.158630i
$796$	5.90913e6	+	6.99653e6i	0.330553	+	0.391382i
$797$	1.10993e7	−	1.10993e7i	0.618941	−	0.618941i	−0.326319	−	0.945260i	$-0.605808\pi$
$797$	1.10993e7	−	1.10993e7i	0.618941	−	0.618941i	0.945260	+	0.326319i	$0.105808\pi$
$798$	−9.32667e6	−	2.54975e7i	−0.518465	−	1.41740i
$799$	250407.			0.0138765
$800$	1.85399e6	+	1.00430e7i	0.102419	+	0.554801i
$801$	−4.44850e6			−0.244981
$802$	−6.10698e6	−	1.66955e7i	−0.335267	−	0.916563i
$803$	3.15421e7	−	3.15421e7i	1.72624	−	1.72624i
$804$	−1.22841e7	−	1.45446e7i	−0.670199	−	0.793530i
$805$	−2.33814e6	−	2.33814e6i	−0.127169	−	0.127169i
$806$	−1.07793e7	−	5.00545e6i	−0.584458	−	0.271397i
$807$			1.03232e7i			0.557994i
$808$	6.37905e6	+	2.33569e7i	0.343738	+	1.25860i
$809$		−	5.39914e6i		−	0.290037i	−0.989429	−	0.145018i	$-0.953676\pi$
$809$		−	5.39914e6i		−	0.290037i	0.989429	−	0.145018i	$-0.0463242\pi$
$810$	−6.46937e6	+	1.39319e7i	−0.346457	+	0.746100i
$811$	−1.13884e7	−	1.13884e7i	−0.608011	−	0.608011i	0.334415	−	0.942426i	$-0.391461\pi$
$811$	−1.13884e7	−	1.13884e7i	−0.608011	−	0.608011i	−0.942426	+	0.334415i	$0.891461\pi$
$812$	−2.66036e7	−	2.24157e6i	−1.41596	−	0.119306i
$813$	−1.31923e7	+	1.31923e7i	−0.699993	+	0.699993i
$814$	−1.23094e7	+	4.50262e6i	−0.651142	+	0.238179i
$815$	9.96082e6			0.525293
$816$	−6.28004e6	−	8.84750e6i	−0.330169	−	0.465152i
$817$	−2.72170e6			−0.142654
$818$	−7.99969e6	+	2.92619e6i	−0.418013	+	0.152904i
$819$	−7.76978e6	+	7.76978e6i	−0.404761	+	0.404761i
$820$	190995.	−	2.26679e6i	0.00991946	−	0.117727i
$821$	−5.77837e6	−	5.77837e6i	−0.299190	−	0.299190i	0.541506	−	0.840697i	$-0.317854\pi$
$821$	−5.77837e6	−	5.77837e6i	−0.299190	−	0.299190i	−0.840697	+	0.541506i	$0.817854\pi$
$822$	−1.31322e6	+	2.82804e6i	−0.0677889	+	0.145984i
$823$		−	1.72231e6i		−	0.0886362i	−0.999017	−	0.0443181i	$-0.985888\pi$
$823$		−	1.72231e6i		−	0.0886362i	0.999017	−	0.0443181i	$-0.0141115\pi$
$824$	2.04520e6	−	3.58207e6i	0.104934	−	0.183787i
$825$		−	1.89942e7i		−	0.971597i
$826$	−1.47197e7	−	6.83519e6i	−0.750669	−	0.348578i
$827$	7.60095e6	+	7.60095e6i	0.386460	+	0.386460i	0.873423	−	0.486963i	$-0.161895\pi$
$827$	7.60095e6	+	7.60095e6i	0.386460	+	0.386460i	−0.486963	+	0.873423i	$0.661895\pi$
$828$	−2.17939e6	+	1.84067e6i	−0.110474	+	0.0933040i
$829$	129231.	−	129231.i	0.00653099	−	0.00653099i	−0.703834	−	0.710365i	$-0.748530\pi$
$829$	129231.	−	129231.i	0.00653099	−	0.00653099i	0.710365	+	0.703834i	$0.248530\pi$
$830$	2.25652e6	+	6.16895e6i	0.113696	+	0.310825i
$831$	9.78832e6			0.491706
$832$	3.07226e7	+	7.91611e6i	1.53869	+	0.396464i
$833$	3.06173e6			0.152881
$834$	−1.88382e6	−	5.15004e6i	−0.0937830	−	0.256387i
$835$	−2.75223e6	+	2.75223e6i	−0.136606	+	0.136606i
$836$	3.38883e7	−	2.86213e7i	1.67700	−	1.41636i
$837$	3.92103e6	+	3.92103e6i	0.193458	+	0.193458i
$838$	2.29522e7	+	1.06580e7i	1.12905	+	0.524284i
$839$		−	3.84691e6i		−	0.188672i	−0.995540	−	0.0943359i	$-0.969927\pi$
$839$		−	3.84691e6i		−	0.188672i	0.995540	−	0.0943359i	$-0.0300728\pi$
$840$	−6.61137e6	+	1.15795e7i	−0.323291	+	0.566229i
$841$		−	4.05121e7i		−	1.97513i
$842$	1.27569e7	−	2.74721e7i	0.620102	−	1.33540i
$843$	−9.44665e6	−	9.44665e6i	−0.457835	−	0.457835i
$844$	−3.13329e6	+	3.71868e7i	−0.151406	+	1.79694i
$845$	−1.47733e7	+	1.47733e7i	−0.711764	+	0.711764i
$846$	−249337.	+	91204.4i	−0.0119774	+	0.00438117i
$847$	1.82923e7			0.876113
$848$	−4.84018e6	+	3.43561e6i	−0.231138	+	0.164064i
$849$	2.36066e7			1.12400
$850$	−5.31025e6	+	1.94242e6i	−0.252097	+	0.0922139i
$851$	2.38429e6	−	2.38429e6i	0.112859	−	0.112859i
$852$	−2.03563e7	−	1.71518e6i	−0.960727	−	0.0809489i
$853$	−1.11788e7	−	1.11788e7i	−0.526042	−	0.526042i	0.393347	−	0.919390i	$-0.371317\pi$
$853$	−1.11788e7	−	1.11788e7i	−0.526042	−	0.526042i	−0.919390	+	0.393347i	$0.871317\pi$
$854$	4.91580e6	−	1.05863e7i	0.230648	−	0.496704i
$855$		−	9.42966e6i		−	0.441144i
$856$	3.48696e6	+	1.27675e7i	0.162653	+	0.595556i
$857$		−	2.33336e7i		−	1.08525i	−0.839976	−	0.542624i	$-0.817431\pi$
$857$		−	2.33336e7i		−	1.08525i	0.839976	−	0.542624i	$-0.182569\pi$
$858$	−5.35178e7	−	2.48514e7i	−2.48187	−	1.15248i
$859$	−1.27606e7	−	1.27606e7i	−0.590051	−	0.590051i	0.347594	−	0.937645i	$-0.386999\pi$
$859$	−1.27606e7	−	1.27606e7i	−0.590051	−	0.590051i	−0.937645	+	0.347594i	$0.886999\pi$
$860$	862494.	+	1.02121e6i	0.0397658	+	0.0470836i
$861$	−2.71867e6	+	2.71867e6i	−0.124982	+	0.124982i
$862$	8.75024e6	+	2.39217e7i	0.401099	+	1.09654i
$863$	−1.40892e7			−0.643959			−0.321980	−	0.946747i	$-0.604348\pi$
$863$	−1.40892e7			−0.643959			−0.321980	+	0.946747i	$0.604348\pi$
$864$	−1.21933e7	−	8.39297e6i	−0.555696	−	0.382500i
$865$	5.72383e6			0.260104
$866$	1.10760e7	+	3.02798e7i	0.501865	+	1.37201i
$867$	−1.45155e7	+	1.45155e7i	−0.655818	+	0.655818i
$868$	4.78521e6	+	5.66579e6i	0.215577	+	0.255247i
$869$	−2.38193e6	−	2.38193e6i	−0.106999	−	0.106999i
$870$	−2.76426e7	−	1.28360e7i	−1.23817	−	0.574954i
$871$			3.08221e7i			1.37663i
$872$	1.51482e7	−	4.13716e6i	0.674638	−	0.184252i
$873$			1.65874e7i			0.736618i
$874$	−4.80607e6	+	1.03499e7i	−0.212819	+	0.458310i
$875$	1.36232e7	+	1.36232e7i	0.601534	+	0.601534i
$876$	4.61119e7	+	3.88530e6i	2.03027	+	0.171066i
$877$	3.14281e7	−	3.14281e7i	1.37981	−	1.37981i	0.534887	−	0.844924i	$-0.320354\pi$
$877$	3.14281e7	−	3.14281e7i	1.37981	−	1.37981i	0.844924	−	0.534887i	$-0.179646\pi$
$878$	1.68320e6	−	615693.i	0.0736884	−	0.0269543i
$879$	−1.91306e7			−0.835135
$880$	−2.14781e7	−	3.64528e6i	−0.934950	−	0.158681i
$881$	3.09313e7			1.34264			0.671318	−	0.741169i	$-0.265728\pi$
$881$	3.09313e7			1.34264			0.671318	+	0.741169i	$0.265728\pi$
$882$	−3.04865e6	+	1.11516e6i	−0.131958	+	0.0482686i
$883$	−1.69679e7	+	1.69679e7i	−0.732364	+	0.732364i	−0.971088	−	0.238723i	$-0.923271\pi$
$883$	−1.69679e7	+	1.69679e7i	−0.732364	+	0.732364i	0.238723	+	0.971088i	$0.423271\pi$
$884$	−1.47481e6	+	1.75035e7i	−0.0634754	+	0.753345i
$885$	−1.31005e7	−	1.31005e7i	−0.562248	−	0.562248i
$886$	−2.68692e6	+	5.78632e6i	−0.114993	+	0.247638i
$887$		−	3.33974e7i		−	1.42529i	−0.701524	−	0.712646i	$-0.747497\pi$
$887$		−	3.33974e7i		−	1.42529i	0.701524	−	0.712646i	$-0.252503\pi$
$888$	−1.18081e7	−	6.74188e6i	−0.502513	−	0.286912i
$889$			2.85620e7i			1.21209i
$890$	7.92667e6	+	3.68080e6i	0.335441	+	0.155764i
$891$	2.99930e7	+	2.99930e7i	1.26569	+	1.26569i
$892$	−3.33116e6	+	2.81343e6i	−0.140179	+	0.118392i
$893$	−750973.	+	750973.i	−0.0315134	+	0.0315134i
$894$	1.25608e7	+	3.43391e7i	0.525623	+	1.43696i
$895$	1.85671e7			0.774793
$896$	−1.53074e7	−	1.25544e7i	−0.636989	−	0.522426i
$897$	1.51799e7			0.629923
$898$	1.21619e6	+	3.32486e6i	0.0503281	+	0.137588i
$899$	−1.19862e7	+	1.19862e7i	−0.494633	+	0.494633i
$900$	4.58009e6	−	3.86825e6i	0.188481	−	0.159187i
$901$	−2.32375e6	−	2.32375e6i	−0.0953626	−	0.0953626i
$902$	−5.69734e6	−	2.64560e6i	−0.233161	−	0.108270i
$903$		−	2.25922e6i		−	0.0922016i
$904$	−1.69410e7	−	9.67251e6i	−0.689472	−	0.393657i
$905$		−	1.83821e7i		−	0.746061i
$906$	−7.93517e6	+	1.70885e7i	−0.321170	+	0.691646i
$907$	−3.96669e6	−	3.96669e6i	−0.160107	−	0.160107i	0.622507	−	0.782614i	$-0.286114\pi$
$907$	−3.96669e6	−	3.96669e6i	−0.160107	−	0.160107i	−0.782614	+	0.622507i	$0.786114\pi$
$908$	−1.61739e6	+	1.91957e7i	−0.0651028	+	0.772660i
$909$	1.00502e7	−	1.00502e7i	0.403427	−	0.403427i
$910$	2.02737e7	−	7.41586e6i	0.811577	−	0.296864i
$911$	−1.66679e7			−0.665402			−0.332701	−	0.943032i	$-0.607960\pi$
$911$	−1.66679e7			−0.665402			−0.332701	+	0.943032i	$0.607960\pi$
$912$	4.53676e7	+	7.69984e6i	1.80617	+	0.306545i
$913$	1.81386e7			0.720158
$914$	−2.10158e7	+	7.68731e6i	−0.832109	+	0.304375i
$915$	9.42172e6	−	9.42172e6i	0.372030	−	0.372030i
$916$	−2.60068e7	−	2.19128e6i	−1.02411	−	0.0862898i
$917$	1.00363e6	+	1.00363e6i	0.0394139	+	0.0394139i
$918$	3.45172e6	−	7.43333e6i	0.135185	−	0.291123i
$919$			1.60909e7i			0.628481i	0.949343	+	0.314241i	$0.101750\pi$
$919$			1.60909e7i			0.628481i	−0.949343	+	0.314241i	$0.898250\pi$
$920$	5.40643e6	−	1.47656e6i	0.210591	−	0.0575150i
$921$		−	4.11224e7i		−	1.59746i
$922$	−2.72214e7	−	1.26404e7i	−1.05459	−	0.489705i
$923$	2.33863e7	+	2.33863e7i	0.903559	+	0.903559i
$924$	2.37579e7	+	2.81298e7i	0.915436	+	1.08390i
$925$	−5.01070e6	+	5.01070e6i	−0.192550	+	0.192550i
$926$	−1.29232e7	−	3.53299e7i	−0.495272	−	1.35399i
$927$	−2.42135e6			−0.0925460
$928$	2.56566e7	−	3.72739e7i	0.977977	−	1.42081i
$929$	−3.35768e7			−1.27644			−0.638219	−	0.769855i	$-0.720329\pi$
$929$	−3.35768e7			−1.27644			−0.638219	+	0.769855i	$0.720329\pi$
$930$	2.90832e6	+	7.95084e6i	0.110264	+	0.301443i
$931$	−9.18215e6	+	9.18215e6i	−0.347192	+	0.347192i
$932$	−1.16279e7	−	1.37677e7i	−0.438492	−	0.519183i
$933$	3.09092e7	+	3.09092e7i	1.16248	+	1.16248i
$934$	1.51601e7	+	7.03969e6i	0.568636	+	0.264050i
$935$		−	1.20616e7i		−	0.451208i
$936$	−4.90669e6	−	1.79659e7i	−0.183062	−	0.670284i
$937$			3.14426e7i			1.16996i	0.811049	+	0.584978i	$0.198897\pi$
$937$			3.14426e7i			1.16996i	−0.811049	+	0.584978i	$0.801103\pi$
$938$	8.10031e6	−	1.74441e7i	0.300604	−	0.647355i
$939$	−1.85089e7	−	1.85089e7i	−0.685040	−	0.685040i
$940$	519753.	+	43793.4i	0.0191857	+	0.00161655i
$941$	−2.15366e6	+	2.15366e6i	−0.0792872	+	0.0792872i	−0.745638	−	0.666351i	$-0.767855\pi$
$941$	−2.15366e6	+	2.15366e6i	−0.0792872	+	0.0792872i	0.666351	+	0.745638i	$0.267855\pi$
$942$	2.08498e7	−	7.62660e6i	0.765553	−	0.280030i
$943$	1.61600e6			0.0591784
$944$	2.24308e7	−	1.59216e7i	0.819248	−	0.581510i
$945$	−1.00722e7			−0.366898
$946$	3.46650e6	−	1.26800e6i	0.125940	−	0.0460672i
$947$	−1.36614e7	+	1.36614e7i	−0.495015	+	0.495015i	−0.909882	−	0.414867i	$-0.863828\pi$
$947$	−1.36614e7	+	1.36614e7i	−0.495015	+	0.495015i	0.414867	+	0.909882i	$0.363828\pi$
$948$	293402.	−	3.48219e6i	0.0106033	−	0.125844i
$949$	−5.29756e7	−	5.29756e7i	−1.90946	−	1.90946i
$950$	1.01002e7	−	2.17508e7i	0.363094	−	0.781928i
$951$		−	5.12406e7i		−	1.83723i
$952$	5.43475e6	−	9.51871e6i	0.194351	−	0.340397i
$953$			4.23714e7i			1.51126i	0.654996	+	0.755632i	$0.272670\pi$
$953$			4.23714e7i			1.51126i	−0.654996	+	0.755632i	$0.727330\pi$
$954$	3.16019e6	+	1.46746e6i	0.112420	+	0.0522029i
$955$	1.12209e7	+	1.12209e7i	0.398124	+	0.398124i
$956$	−2.99463e7	+	2.52921e7i	−1.05974	+	0.895034i
$957$	−5.95100e7	+	5.95100e7i	−2.10044	+	2.10044i
$958$	−1.35461e7	−	3.70328e7i	−0.476872	−	1.30369i
$959$	−3.15003e6			−0.110603
$960$	−1.14877e7	−	1.94625e7i	−0.402305	−	0.681584i
$961$	−2.39205e7			−0.835528
$962$	7.56224e6	+	2.06739e7i	0.263459	+	0.720252i
$963$	5.49372e6	−	5.49372e6i	0.190898	−	0.190898i
$964$	−2.63433e6	+	2.22490e6i	−0.0913013	+	0.0771112i
$965$	−9.67281e6	−	9.67281e6i	−0.334376	−	0.334376i
$966$	−8.59123e6	−	3.98940e6i	−0.296219	−	0.137551i
$967$		−	3.84918e7i		−	1.32374i	−0.749620	−	0.661869i	$-0.769764\pi$
$967$		−	3.84918e7i		−	1.32374i	0.749620	−	0.661869i	$-0.230236\pi$
$968$	−1.53726e7	+	2.69243e7i	−0.527300	+	0.923542i
$969$			2.54775e7i			0.871660i
$970$	1.37248e7	−	2.95566e7i	0.468358	−	1.00862i
$971$	1.28812e7	+	1.28812e7i	0.438438	+	0.438438i	0.891486	−	0.453048i	$-0.149664\pi$
$971$	1.28812e7	+	1.28812e7i	0.438438	+	0.438438i	−0.453048	+	0.891486i	$0.649664\pi$
$972$	−2.02611e6	+	2.40465e7i	−0.0687856	+	0.816368i
$973$	3.91735e6	−	3.91735e6i	0.132651	−	0.132651i
$974$	2.66278e7	−	9.74010e6i	0.899368	−	0.328977i
$975$	−3.19012e7			−1.07472
$976$	1.14507e7	+	1.61320e7i	0.384775	+	0.542082i
$977$	4.46818e6			0.149760			0.0748798	−	0.997193i	$-0.476143\pi$
$977$	4.46818e6			0.149760			0.0748798	+	0.997193i	$0.476143\pi$
$978$	2.67977e7	−	9.80224e6i	0.895880	−	0.327701i
$979$	1.70648e7	−	1.70648e7i	0.569042	−	0.569042i
$980$	6.35502e6	+	535462.i	0.211374	+	0.0178100i
$981$	−6.51811e6	−	6.51811e6i	−0.216247	−	0.216247i
$982$	−2.10944e7	+	4.54270e7i	−0.698052	+	1.50327i
$983$			3.21497e7i			1.06119i	0.847625	+	0.530595i	$0.178032\pi$
$983$			3.21497e7i			1.06119i	−0.847625	+	0.530595i	$0.821968\pi$
$984$	−1.71687e6	−	6.28631e6i	−0.0565260	−	0.206970i
$985$			3.52686e7i			1.15824i
$986$	2.27231e7	+	1.05516e7i	0.744345	+	0.345642i
$987$	−623364.	−	623364.i	−0.0203680	−	0.0203680i
$988$	−4.80701e7	−	5.69161e7i	−1.56669	−	1.85499i
$989$	−671451.	+	671451.i	−0.0218285	+	0.0218285i
$990$	4.39314e6	+	1.20101e7i	0.142458	+	0.389456i
$991$	1.46825e7			0.474915			0.237457	−	0.971398i	$-0.423686\pi$
$991$	1.46825e7			0.474915			0.237457	+	0.971398i	$0.423686\pi$
$992$	−1.23608e7	+	2.28188e6i	−0.398812	+	0.0736230i
$993$	4.63008e7			1.49010
$994$	−7.08963e6	−	1.93818e7i	−0.227592	−	0.622199i
$995$	−7.46822e6	+	7.46822e6i	−0.239144	+	0.239144i
$996$	1.21415e7	+	1.43758e7i	0.387814	+	0.459179i
$997$	2.92541e7	+	2.92541e7i	0.932071	+	0.932071i	0.997835	−	0.0657639i	$-0.0209484\pi$
$997$	2.92541e7	+	2.92541e7i	0.932071	+	0.932071i	−0.0657639	+	0.997835i	$0.520948\pi$
$998$	345360.	+	160370.i	0.0109760	+	0.00509680i
$999$		−	1.02710e7i		−	0.325612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.5.4	✓	18
3.2	odd	2		144.6.k.a.37.6		18
4.3	odd	2		64.6.e.a.49.3		18
8.3	odd	2		128.6.e.a.97.7		18
8.5	even	2		128.6.e.b.97.3		18
12.11	even	2		576.6.k.a.433.6		18
16.3	odd	4		64.6.e.a.17.3		18
16.5	even	4		128.6.e.b.33.3		18
16.11	odd	4		128.6.e.a.33.7		18
16.13	even	4	inner	16.6.e.a.13.4	yes	18
32.3	odd	8		1024.6.a.l.1.4		18
32.13	even	8		1024.6.a.k.1.4		18
32.19	odd	8		1024.6.a.l.1.15		18
32.29	even	8		1024.6.a.k.1.15		18
48.29	odd	4		144.6.k.a.109.6		18
48.35	even	4		576.6.k.a.145.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.4	✓	18	1.1	even	1	trivial
16.6.e.a.13.4	yes	18	16.13	even	4	inner
64.6.e.a.17.3		18	16.3	odd	4
64.6.e.a.49.3		18	4.3	odd	2
128.6.e.a.33.7		18	16.11	odd	4
128.6.e.a.97.7		18	8.3	odd	2
128.6.e.b.33.3		18	16.5	even	4
128.6.e.b.97.3		18	8.5	even	2
144.6.k.a.37.6		18	3.2	odd	2
144.6.k.a.109.6		18	48.29	odd	4
576.6.k.a.145.6		18	48.35	even	4
576.6.k.a.433.6		18	12.11	even	2
1024.6.a.k.1.4		18	32.13	even	8
1024.6.a.k.1.15		18	32.29	even	8
1024.6.a.l.1.4		18	32.3	odd	8
1024.6.a.l.1.15		18	32.19	odd	8

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94328 - 5.31260i) q^{2} +(13.2148 - 13.2148i) q^{3} +(-24.4473 + 20.6477i) q^{4} +(-26.0955 - 26.0955i) q^{5} +(-95.8850 - 44.5248i) q^{6} -106.802i q^{7} +(157.201 + 89.7545i) q^{8} -106.262i q^{9} +O(q^{10})\)	\(q+(-1.94328 - 5.31260i) q^{2} +(13.2148 - 13.2148i) q^{3} +(-24.4473 + 20.6477i) q^{4} +(-26.0955 - 26.0955i) q^{5} +(-95.8850 - 44.5248i) q^{6} -106.802i q^{7} +(157.201 + 89.7545i) q^{8} -106.262i q^{9} +(-87.9240 + 189.346i) q^{10} +(407.630 + 407.630i) q^{11} +(-50.2112 + 595.922i) q^{12} +(684.623 - 684.623i) q^{13} +(-567.395 + 207.546i) q^{14} -689.694 q^{15} +(171.344 - 1009.56i) q^{16} +566.949 q^{17} +(-564.527 + 206.497i) q^{18} +(-1700.29 + 1700.29i) q^{19} +(1176.78 + 99.1530i) q^{20} +(-1411.37 - 1411.37i) q^{21} +(1373.43 - 2957.71i) q^{22} +838.931i q^{23} +(3263.47 - 891.291i) q^{24} -1763.05i q^{25} +(-4967.54 - 2306.71i) q^{26} +(1806.97 + 1806.97i) q^{27} +(2205.21 + 2611.02i) q^{28} +(-5523.73 + 5523.73i) q^{29} +(1340.27 + 3664.07i) q^{30} +2169.95 q^{31} +(-5696.37 + 1051.58i) q^{32} +10773.5 q^{33} +(-1101.74 - 3011.97i) q^{34} +(-2787.05 + 2787.05i) q^{35} +(2194.07 + 2597.82i) q^{36} +(-2842.06 - 2842.06i) q^{37} +(12337.1 + 5728.80i) q^{38} -18094.3i q^{39} +(-1760.05 - 6444.43i) q^{40} -1926.27i q^{41} +(-4755.34 + 10240.7i) q^{42} +(800.365 + 800.365i) q^{43} +(-18382.1 - 1548.84i) q^{44} +(-2772.96 + 2772.96i) q^{45} +(4456.90 - 1630.28i) q^{46} +441.674 q^{47} +(-11076.9 - 15605.5i) q^{48} +5400.36 q^{49} +(-9366.36 + 3426.10i) q^{50} +(7492.12 - 7492.12i) q^{51} +(-2601.31 + 30873.1i) q^{52} +(-4098.70 - 4098.70i) q^{53} +(6088.24 - 13111.1i) q^{54} -21274.6i q^{55} +(9585.95 - 16789.4i) q^{56} +44937.9i q^{57} +(40079.5 + 18611.2i) q^{58} +(18994.6 + 18994.6i) q^{59} +(16861.2 - 14240.6i) q^{60} +(-13660.7 + 13660.7i) q^{61} +(-4216.82 - 11528.1i) q^{62} -11349.0 q^{63} +(16656.3 + 28219.0i) q^{64} -35731.2 q^{65} +(-20935.9 - 57235.2i) q^{66} +(-22510.3 + 22510.3i) q^{67} +(-13860.4 + 11706.2i) q^{68} +(11086.3 + 11086.3i) q^{69} +(20222.5 + 9390.45i) q^{70} +34159.3i q^{71} +(9537.50 - 16704.5i) q^{72} -77379.2i q^{73} +(-9575.81 + 20621.7i) q^{74} +(-23298.3 - 23298.3i) q^{75} +(6460.44 - 76674.5i) q^{76} +(43535.7 - 43535.7i) q^{77} +(-96127.8 + 35162.3i) q^{78} -5843.36 q^{79} +(-30816.4 + 21873.7i) q^{80} +73579.1 q^{81} +(-10233.5 + 3743.28i) q^{82} +(22248.9 - 22248.9i) q^{83} +(63645.6 + 5362.65i) q^{84} +(-14794.8 - 14794.8i) q^{85} +(2696.68 - 5807.35i) q^{86} +145990. i q^{87} +(27493.2 + 100666. i) q^{88} -41863.5i q^{89} +(20120.3 + 9342.99i) q^{90} +(-73119.0 - 73119.0i) q^{91} +(-17322.0 - 20509.6i) q^{92} +(28675.5 - 28675.5i) q^{93} +(-858.297 - 2346.44i) q^{94} +88739.6 q^{95} +(-61379.9 + 89172.8i) q^{96} -156099. q^{97} +(-10494.4 - 28689.9i) q^{98} +(43315.6 - 43315.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more