LMFDB - Embedded newform 16.6.e.a.5.6

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			5.6
Root			$-2.63220 - 3.01190i$ of defining polynomial
Character	$\chi$	$=$	16.5
Dual form			16.6.e.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.379698 - 5.64410i) q^{2} +(-20.6438 + 20.6438i) q^{3} +(-31.7117 - 4.28611i) q^{4} +(-28.3274 - 28.3274i) q^{5} +(108.677 + 124.354i) q^{6} +55.5494i q^{7} +(-36.2321 + 177.356i) q^{8} -609.330i q^{9} +O(q^{10})$	\(q+(0.379698 - 5.64410i) q^{2} +(-20.6438 + 20.6438i) q^{3} +(-31.7117 - 4.28611i) q^{4} +(-28.3274 - 28.3274i) q^{5} +(108.677 + 124.354i) q^{6} +55.5494i q^{7} +(-36.2321 + 177.356i) q^{8} -609.330i q^{9} +(-170.638 + 149.127i) q^{10} +(-137.411 - 137.411i) q^{11} +(743.129 - 566.167i) q^{12} +(-574.133 + 574.133i) q^{13} +(313.526 + 21.0920i) q^{14} +1169.57 q^{15} +(987.259 + 271.839i) q^{16} +320.902 q^{17} +(-3439.12 - 231.362i) q^{18} +(-858.068 + 858.068i) q^{19} +(776.894 + 1019.72i) q^{20} +(-1146.75 - 1146.75i) q^{21} +(-827.733 + 723.384i) q^{22} +825.465i q^{23} +(-2913.33 - 4409.27i) q^{24} -1520.12i q^{25} +(3022.47 + 3458.46i) q^{26} +(7562.43 + 7562.43i) q^{27} +(238.091 - 1761.56i) q^{28} +(333.912 - 333.912i) q^{29} +(444.083 - 6601.16i) q^{30} -8904.00 q^{31} +(1909.15 - 5468.97i) q^{32} +5673.34 q^{33} +(121.846 - 1811.20i) q^{34} +(1573.57 - 1573.57i) q^{35} +(-2611.66 + 19322.9i) q^{36} +(-3878.91 - 3878.91i) q^{37} +(4517.21 + 5168.83i) q^{38} -23704.5i q^{39} +(6050.40 - 3997.68i) q^{40} +6546.26i q^{41} +(-6907.77 + 6036.94i) q^{42} +(-5620.33 - 5620.33i) q^{43} +(3768.56 + 4946.47i) q^{44} +(-17260.7 + 17260.7i) q^{45} +(4659.00 + 313.428i) q^{46} -3122.27 q^{47} +(-25992.5 + 14768.9i) q^{48} +13721.3 q^{49} +(-8579.69 - 577.186i) q^{50} +(-6624.62 + 6624.62i) q^{51} +(20667.5 - 15745.9i) q^{52} +(18167.5 + 18167.5i) q^{53} +(45554.5 - 39811.6i) q^{54} +7784.97i q^{55} +(-9852.03 - 2012.67i) q^{56} -35427.5i q^{57} +(-1757.85 - 2011.42i) q^{58} +(-5538.91 - 5538.91i) q^{59} +(-37088.9 - 5012.90i) q^{60} +(-701.393 + 701.393i) q^{61} +(-3380.83 + 50255.0i) q^{62} +33847.9 q^{63} +(-30142.5 - 12852.0i) q^{64} +32527.4 q^{65} +(2154.16 - 32020.9i) q^{66} +(-14453.4 + 14453.4i) q^{67} +(-10176.3 - 1375.42i) q^{68} +(-17040.7 - 17040.7i) q^{69} +(-8283.89 - 9478.86i) q^{70} +23608.4i q^{71} +(108068. + 22077.3i) q^{72} +57755.7i q^{73} +(-23365.8 + 20420.1i) q^{74} +(31380.9 + 31380.9i) q^{75} +(30888.5 - 23533.0i) q^{76} +(7633.07 - 7633.07i) q^{77} +(-133791. - 9000.58i) q^{78} -57871.5 q^{79} +(-20266.0 - 35667.0i) q^{80} -164167. q^{81} +(36947.7 + 2485.60i) q^{82} +(78955.3 - 78955.3i) q^{83} +(31450.2 + 41280.4i) q^{84} +(-9090.32 - 9090.32i) q^{85} +(-33855.7 + 29587.6i) q^{86} +13786.4i q^{87} +(29349.3 - 19391.9i) q^{88} -25908.3i q^{89} +(90867.4 + 103975. i) q^{90} +(-31892.7 - 31892.7i) q^{91} +(3538.03 - 26176.9i) q^{92} +(183812. - 183812. i) q^{93} +(-1185.52 + 17622.4i) q^{94} +48613.7 q^{95} +(73488.0 + 152312. i) q^{96} +39197.0 q^{97} +(5209.95 - 77444.2i) q^{98} +(-83728.4 + 83728.4i) 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 $

$2$	0.379698	−	5.64410i	0.0671218	−	0.997745i
$2$	0.379698	−	5.64410i	0.0671218	−	0.997745i
$3$	−20.6438	+	20.6438i	−1.32430	+	1.32430i	−0.414039	+	0.910259i	$0.635882\pi$
$3$	−20.6438	+	20.6438i	−1.32430	+	1.32430i	−0.910259	+	0.414039i	$0.864118\pi$
$4$	−31.7117	−	4.28611i	−0.990989	−	0.133941i
$5$	−28.3274	−	28.3274i	−0.506736	−	0.506736i	0.406787	−	0.913523i	$-0.366649\pi$
$5$	−28.3274	−	28.3274i	−0.506736	−	0.506736i	−0.913523	+	0.406787i	$0.866649\pi$
$6$	108.677	+	124.354i	1.23242	+	1.41020i
$7$			55.5494i			0.428483i	0.976781	+	0.214242i	$0.0687280\pi$
$7$			55.5494i			0.428483i	−0.976781	+	0.214242i	$0.931272\pi$
$8$	−36.2321	+	177.356i	−0.200156	+	0.979764i
$9$		−	609.330i		−	2.50753i
$10$	−170.638	+	149.127i	−0.539606	+	0.471580i
$11$	−137.411	−	137.411i	−0.342404	−	0.342404i	0.514867	−	0.857270i	$-0.327841\pi$
$11$	−137.411	−	137.411i	−0.342404	−	0.342404i	−0.857270	+	0.514867i	$0.827841\pi$
$12$	743.129	−	566.167i	1.48974	−	1.13499i
$13$	−574.133	+	574.133i	−0.942225	+	0.942225i	−0.998420	−	0.0561952i	$-0.982103\pi$
$13$	−574.133	+	574.133i	−0.942225	+	0.942225i	0.0561952	+	0.998420i	$0.482103\pi$
$14$	313.526	+	21.0920i	0.427517	+	0.0287606i
$15$	1169.57			1.34214
$16$	987.259	+	271.839i	0.964120	+	0.265468i
$17$	320.902			0.269308			0.134654	−	0.990893i	$-0.457008\pi$
$17$	320.902			0.269308			0.134654	+	0.990893i	$0.457008\pi$
$18$	−3439.12	−	231.362i	−2.50188	−	0.168310i
$19$	−858.068	+	858.068i	−0.545303	+	0.545303i	−0.925079	−	0.379776i	$-0.876001\pi$
$19$	−858.068	+	858.068i	−0.545303	+	0.545303i	0.379776	+	0.925079i	$0.376001\pi$
$20$	776.894	+	1019.72i	0.434297	+	0.570042i
$21$	−1146.75	−	1146.75i	−0.567440	−	0.567440i
$22$	−827.733	+	723.384i	−0.364614	+	0.318649i
$23$			825.465i			0.325371i	0.986678	+	0.162686i	$0.0520156\pi$
$23$			825.465i			0.325371i	−0.986678	+	0.162686i	$0.947984\pi$
$24$	−2913.33	−	4409.27i	−1.03243	−	1.56257i
$25$		−	1520.12i		−	0.486438i
$26$	3022.47	+	3458.46i	0.876856	+	1.00334i
$27$	7562.43	+	7562.43i	1.99642	+	1.99642i
$28$	238.091	−	1761.56i	0.0573915	−	0.424622i
$29$	333.912	−	333.912i	0.0737288	−	0.0737288i	−0.669281	−	0.743010i	$-0.733398\pi$
$29$	333.912	−	333.912i	0.0737288	−	0.0737288i	0.743010	+	0.669281i	$0.233398\pi$
$30$	444.083	−	6601.16i	0.0900868	−	1.33911i
$31$	−8904.00			−1.66411			−0.832053	−	0.554697i	$-0.812834\pi$
$31$	−8904.00			−1.66411			−0.832053	+	0.554697i	$0.812834\pi$
$32$	1909.15	−	5468.97i	0.329583	−	0.944127i
$33$	5673.34			0.906889
$34$	121.846	−	1811.20i	0.0180765	−	0.268701i
$35$	1573.57	−	1573.57i	0.217128	−	0.217128i
$36$	−2611.66	+	19322.9i	−0.335861	+	2.48494i
$37$	−3878.91	−	3878.91i	−0.465806	−	0.465806i	0.434746	−	0.900553i	$-0.356838\pi$
$37$	−3878.91	−	3878.91i	−0.465806	−	0.465806i	−0.900553	+	0.434746i	$0.856838\pi$
$38$	4517.21	+	5168.83i	0.507472	+	0.580675i
$39$		−	23704.5i		−	2.49557i
$40$	6050.40	−	3997.68i	0.597908	−	0.395055i
$41$			6546.26i			0.608182i	0.952643	+	0.304091i	$0.0983527\pi$
$41$			6546.26i			0.608182i	−0.952643	+	0.304091i	$0.901647\pi$
$42$	−6907.77	+	6036.94i	−0.604248	+	0.528072i
$43$	−5620.33	−	5620.33i	−0.463544	−	0.463544i	0.436272	−	0.899815i	$-0.356299\pi$
$43$	−5620.33	−	5620.33i	−0.463544	−	0.463544i	−0.899815	+	0.436272i	$0.856299\pi$
$44$	3768.56	+	4946.47i	0.293457	+	0.385180i
$45$	−17260.7	+	17260.7i	−1.27066	+	1.27066i
$46$	4659.00	+	313.428i	0.324637	+	0.0218395i
$47$	−3122.27			−0.206170			−0.103085	−	0.994673i	$-0.532871\pi$
$47$	−3122.27			−0.206170			−0.103085	+	0.994673i	$0.532871\pi$
$48$	−25992.5	+	14768.9i	−1.62834	+	0.925223i
$49$	13721.3			0.816402
$50$	−8579.69	−	577.186i	−0.485341	−	0.0326506i
$51$	−6624.62	+	6624.62i	−0.356645	+	0.356645i
$52$	20667.5	−	15745.9i	1.05994	−	0.807532i
$53$	18167.5	+	18167.5i	0.888395	+	0.888395i	0.994369	−	0.105974i	$-0.0337961\pi$
$53$	18167.5	+	18167.5i	0.888395	+	0.888395i	−0.105974	+	0.994369i	$0.533796\pi$
$54$	45554.5	−	39811.6i	2.12592	−	1.85791i
$55$			7784.97i			0.347016i
$56$	−9852.03	−	2012.67i	−0.419813	−	0.0857635i
$57$		−	35427.5i		−	1.44429i
$58$	−1757.85	−	2011.42i	−0.0686137	−	0.0785114i
$59$	−5538.91	−	5538.91i	−0.207154	−	0.207154i	0.595902	−	0.803057i	$-0.296794\pi$
$59$	−5538.91	−	5538.91i	−0.207154	−	0.207154i	−0.803057	+	0.595902i	$0.796794\pi$
$60$	−37088.9	−	5012.90i	−1.33004	−	0.179767i
$61$	−701.393	+	701.393i	−0.0241344	+	0.0241344i	−0.719071	−	0.694937i	$-0.755432\pi$
$61$	−701.393	+	701.393i	−0.0241344	+	0.0241344i	0.694937	+	0.719071i	$0.255432\pi$
$62$	−3380.83	+	50255.0i	−0.111698	+	1.66035i
$63$	33847.9			1.07444
$64$	−30142.5	−	12852.0i	−0.919875	−	0.392211i
$65$	32527.4			0.954918
$66$	2154.16	−	32020.9i	0.0608721	−	0.904844i
$67$	−14453.4	+	14453.4i	−0.393354	+	0.393354i	−0.875881	−	0.482527i	$-0.839719\pi$
$67$	−14453.4	+	14453.4i	−0.393354	+	0.393354i	0.482527	+	0.875881i	$0.339719\pi$
$68$	−10176.3	−	1375.42i	−0.266882	−	0.0360714i
$69$	−17040.7	−	17040.7i	−0.430888	−	0.430888i
$70$	−8283.89	−	9478.86i	−0.202064	−	0.231212i
$71$			23608.4i			0.555802i	0.960610	+	0.277901i	$0.0896388\pi$
$71$			23608.4i			0.555802i	−0.960610	+	0.277901i	$0.910361\pi$
$72$	108068.	+	22077.3i	2.45679	+	0.501897i
$73$			57755.7i			1.26849i	0.773131	+	0.634246i	$0.218689\pi$
$73$			57755.7i			1.26849i	−0.773131	+	0.634246i	$0.781311\pi$
$74$	−23365.8	+	20420.1i	−0.496022	+	0.433490i
$75$	31380.9	+	31380.9i	0.644188	+	0.644188i
$76$	30888.5	−	23533.0i	0.613428	−	0.467351i
$77$	7633.07	−	7633.07i	0.146714	−	0.146714i
$78$	−133791.	−	9000.58i	−2.48994	−	0.167507i
$79$	−57871.5			−1.04327			−0.521635	−	0.853169i	$-0.674678\pi$
$79$	−57871.5			−1.04327			−0.521635	+	0.853169i	$0.674678\pi$
$80$	−20266.0	−	35667.0i	−0.354032	−	0.623076i
$81$	−164167.			−2.78018
$82$	36947.7	+	2485.60i	0.606810	+	0.0408223i
$83$	78955.3	−	78955.3i	1.25802	−	1.25802i	0.305976	−	0.952039i	$-0.401017\pi$
$83$	78955.3	−	78955.3i	1.25802	−	1.25802i	0.952039	−	0.305976i	$-0.0989827\pi$
$84$	31450.2	+	41280.4i	0.486323	+	0.638330i
$85$	−9090.32	−	9090.32i	−0.136468	−	0.136468i
$86$	−33855.7	+	29587.6i	−0.493612	+	0.431384i
$87$			13786.4i			0.195278i
$88$	29349.3	−	19391.9i	0.404009	−	0.266941i
$89$		−	25908.3i		−	0.346708i	−0.984860	−	0.173354i	$-0.944540\pi$
$89$		−	25908.3i		−	0.346708i	0.984860	−	0.173354i	$-0.0554605\pi$
$90$	90867.4	+	103975.i	1.18250	+	1.35308i
$91$	−31892.7	−	31892.7i	−0.403728	−	0.403728i
$92$	3538.03	−	26176.9i	0.0435805	−	0.322439i
$93$	183812.	−	183812.i	2.20377	−	2.20377i
$94$	−1185.52	+	17622.4i	−0.0138385	+	0.205705i
$95$	48613.7			0.552649
$96$	73488.0	+	152312.i	0.813839	+	1.68677i
$97$	39197.0			0.422983			0.211492	−	0.977380i	$-0.432168\pi$
$97$	39197.0			0.422983			0.211492	+	0.977380i	$0.432168\pi$
$98$	5209.95	−	77444.2i	0.0547984	−	0.814561i
$99$	−83728.4	+	83728.4i	−0.858588	+	0.858588i
$100$	−6515.39	+	48205.4i	−0.0651539	+	0.482054i
$101$	−99841.8	−	99841.8i	−0.973887	−	0.973887i	0.0257802	−	0.999668i	$-0.491793\pi$
$101$	−99841.8	−	99841.8i	−0.973887	−	0.973887i	−0.999668	+	0.0257802i	$0.991793\pi$
$102$	34874.7	+	39905.4i	0.331902	+	0.379779i
$103$			154754.i			1.43731i	0.695368	+	0.718654i	$0.255241\pi$
$103$			154754.i			1.43731i	−0.695368	+	0.718654i	$0.744759\pi$
$104$	−81024.1	−	122628.i	−0.734566	−	1.11175i
$105$			64968.8i			0.575084i
$106$	109437.	−	95641.1i	0.946022	−	0.826760i
$107$	−73018.1	−	73018.1i	−0.616554	−	0.616554i	0.328092	−	0.944646i	$-0.393594\pi$
$107$	−73018.1	−	73018.1i	−0.616554	−	0.616554i	−0.944646	+	0.328092i	$0.893594\pi$
$108$	−207404.	−	272231.i	−1.71103	−	2.24583i
$109$	−135654.	+	135654.i	−1.09362	+	1.09362i	−0.0984792	+	0.995139i	$0.531398\pi$
$109$	−135654.	+	135654.i	−1.09362	+	1.09362i	−0.995139	+	0.0984792i	$0.968602\pi$
$110$	43939.1	+	2955.94i	0.346234	+	0.0232924i
$111$	160151.			1.23373
$112$	−15100.5	+	54841.6i	−0.113749	+	0.413109i
$113$	−74503.6			−0.548885			−0.274442	−	0.961604i	$-0.588493\pi$
$113$	−74503.6			−0.548885			−0.274442	+	0.961604i	$0.588493\pi$
$114$	−199956.	−	13451.8i	−1.44103	−	0.0969432i
$115$	23383.3	−	23383.3i	0.164877	−	0.164877i
$116$	−12020.1	+	9157.73i	−0.0829398	+	0.0631892i
$117$	349837.	+	349837.i	2.36266	+	2.36266i
$118$	−33365.3	+	29159.0i	−0.220592	+	0.192783i
$119$			17825.9i			0.115394i
$120$	−42375.9	+	207430.i	−0.268637	+	1.31498i
$121$		−	123288.i		−	0.765519i
$122$	3692.41	+	4225.05i	0.0224600	+	0.0256999i
$123$	−135139.	−	135139.i	−0.805414	−	0.805414i
$124$	282361.	+	38163.5i	1.64911	+	0.222892i
$125$	−131584.	+	131584.i	−0.753231	+	0.753231i
$126$	12852.0	−	191041.i	0.0721181	−	1.07201i
$127$	−162314.			−0.892988			−0.446494	−	0.894787i	$-0.647328\pi$
$127$	−162314.			−0.892988			−0.446494	+	0.894787i	$0.647328\pi$
$128$	−83982.8	+	165247.i	−0.453070	+	0.891475i
$129$	232049.			1.22774
$130$	12350.6	−	183588.i	0.0640959	−	0.952764i
$131$	142911.	−	142911.i	0.727589	−	0.727589i	−0.242550	−	0.970139i	$-0.577984\pi$
$131$	142911.	−	142911.i	0.727589	−	0.727589i	0.970139	+	0.242550i	$0.0779839\pi$
$132$	−179911.	−	24316.6i	−0.898717	−	0.121470i
$133$	−47665.2	−	47665.2i	−0.233653	−	0.233653i
$134$	76088.5	+	87064.3i	0.366064	+	0.418869i
$135$		−	428448.i		−	2.02331i
$136$	−11626.9	+	56914.0i	−0.0539037	+	0.263859i
$137$			286655.i			1.30484i	0.757856	+	0.652422i	$0.226247\pi$
$137$			286655.i			1.30484i	−0.757856	+	0.652422i	$0.773753\pi$
$138$	−102650.	+	89709.0i	−0.458839	+	0.400995i
$139$	56704.6	+	56704.6i	0.248932	+	0.248932i	0.820532	−	0.571600i	$-0.193677\pi$
$139$	56704.6	+	56704.6i	0.248932	+	0.248932i	−0.571600	+	0.820532i	$0.693677\pi$
$140$	−56645.0	+	43156.0i	−0.244254	+	0.186089i
$141$	64455.5	−	64455.5i	0.273031	−	0.273031i
$142$	133248.	+	8964.07i	0.554549	+	0.0373065i
$143$	157784.			0.645242
$144$	165640.	−	601566.i	0.665669	−	2.41756i
$145$	−18917.7			−0.0747221
$146$	325979.	+	21929.8i	1.26563	+	0.0851436i
$147$	−283259.	+	283259.i	−1.08116	+	1.08116i
$148$	106381.	+	139632.i	0.399219	+	0.524000i
$149$	−329942.	−	329942.i	−1.21751	−	1.21751i	−0.968502	−	0.249006i	$-0.919896\pi$
$149$	−329942.	−	329942.i	−1.21751	−	1.21751i	−0.249006	−	0.968502i	$-0.580104\pi$
$150$	189032.	−	165202.i	0.685975	−	0.599496i
$151$			200506.i			0.715625i	0.933794	+	0.357812i	$0.116477\pi$
$151$			200506.i			0.715625i	−0.933794	+	0.357812i	$0.883523\pi$
$152$	−121094.	−	183273.i	−0.425123	−	0.643414i
$153$		−	195535.i		−	0.675299i
$154$	−40183.5	−	45980.0i	−0.136536	−	0.156231i
$155$	252227.	+	252227.i	0.843262	+	0.843262i
$156$	−101600.	+	751711.i	−0.334259	+	2.47309i
$157$	236335.	−	236335.i	0.765206	−	0.765206i	−0.212053	−	0.977258i	$-0.568015\pi$
$157$	236335.	−	236335.i	0.765206	−	0.765206i	0.977258	+	0.212053i	$0.0680148\pi$
$158$	−21973.7	+	326632.i	−0.0700262	+	1.04092i
$159$	−750092.			−2.35300
$160$	−209003.	+	100840.i	−0.645434	+	0.311411i
$161$	−45854.0			−0.139416
$162$	−62333.9	+	926573.i	−0.186611	+	2.77391i
$163$	137842.	−	137842.i	0.406363	−	0.406363i	−0.474105	−	0.880468i	$-0.657228\pi$
$163$	137842.	−	137842.i	0.406363	−	0.406363i	0.880468	+	0.474105i	$0.157228\pi$
$164$	28058.0	−	207593.i	0.0814604	−	0.602702i
$165$	−160711.	−	160711.i	−0.459553	−	0.459553i
$166$	−415652.	−	475610.i	−1.17074	−	1.33962i
$167$		−	324357.i		−	0.899978i	−0.893034	−	0.449989i	$-0.851428\pi$
$167$		−	324357.i		−	0.899978i	0.893034	−	0.449989i	$-0.148572\pi$
$168$	244932.	−	161834.i	0.669533	−	0.442381i
$169$		−	287965.i		−	0.775574i
$170$	−54758.2	+	47855.0i	−0.145320	+	0.127000i
$171$	522847.	+	522847.i	1.36736	+	1.36736i
$172$	154141.	+	202319.i	0.397279	+	0.521454i
$173$	−376606.	+	376606.i	−0.956691	+	0.956691i	−0.999100	−	0.0424095i	$-0.986497\pi$
$173$	−376606.	+	376606.i	−0.956691	+	0.956691i	0.0424095	+	0.999100i	$0.486497\pi$
$174$	77811.8	+	5234.68i	0.194837	+	0.0131074i
$175$	84441.6			0.208430
$176$	−98306.2	−	173013.i	−0.239221	−	0.421015i
$177$	228688.			0.548668
$178$	−146229.	−	9837.35i	−0.345926	−	0.0232717i
$179$	166781.	−	166781.i	0.389058	−	0.389058i	−0.485293	−	0.874351i	$-0.661287\pi$
$179$	166781.	−	166781.i	0.389058	−	0.389058i	0.874351	+	0.485293i	$0.161287\pi$
$180$	621348.	−	473385.i	1.42940	−	1.08901i
$181$	85411.9	+	85411.9i	0.193786	+	0.193786i	0.797330	−	0.603544i	$-0.206245\pi$
$181$	85411.9	+	85411.9i	0.193786	+	0.193786i	−0.603544	+	0.797330i	$0.706245\pi$
$182$	−192115.	+	167896.i	−0.429916	+	0.375718i
$183$		−	28958.8i		−	0.0639223i
$184$	−146401.	−	29908.3i	−0.318787	−	0.0651249i
$185$			219759.i			0.472082i
$186$	−967660.	−	1.10725e6i	−2.05088	−	2.34672i
$187$	−44095.3	−	44095.3i	−0.0922122	−	0.0922122i
$188$	99012.5	+	13382.4i	0.204313	+	0.0276147i
$189$	−420088.	+	420088.i	−0.855433	+	0.855433i
$190$	18458.5	−	274380.i	0.0370948	−	0.551403i
$191$	804534.			1.59574			0.797868	−	0.602832i	$-0.205961\pi$
$191$	804534.			1.59574			0.797868	+	0.602832i	$0.205961\pi$
$192$	887567.	−	356941.i	1.73759	−	0.698785i
$193$	247122.			0.477550			0.238775	−	0.971075i	$-0.423254\pi$
$193$	247122.			0.477550			0.238775	+	0.971075i	$0.423254\pi$
$194$	14883.0	−	221231.i	0.0283914	−	0.422029i
$195$	−671488.	+	671488.i	−1.26460	+	1.26460i
$196$	−435124.	−	58810.9i	−0.809046	−	0.109350i
$197$	295923.	+	295923.i	0.543267	+	0.543267i	0.924485	−	0.381218i	$-0.124495\pi$
$197$	295923.	+	295923.i	0.543267	+	0.543267i	−0.381218	+	0.924485i	$0.624495\pi$
$198$	440779.	+	504363.i	0.799021	+	0.914281i
$199$			252267.i			0.451572i	0.974177	+	0.225786i	$0.0724950\pi$
$199$			252267.i			0.451572i	−0.974177	+	0.225786i	$0.927505\pi$
$200$	269602.	+	55077.0i	0.476594	+	0.0973634i
$201$		−	596745.i		−	1.04183i
$202$	−601426.	+	525607.i	−1.03706	+	0.906322i
$203$	18548.6	+	18548.6i	0.0315916	+	0.0315916i
$204$	238472.	−	181684.i	0.401200	−	0.305662i
$205$	185438.	−	185438.i	0.308188	−	0.308188i
$206$	873448.	+	58760.0i	1.43407	+	0.0964747i
$207$	502980.			0.815878
$208$	−722890.	+	410746.i	−1.15855	+	0.658287i
$209$	235815.			0.373428
$210$	366690.	+	24668.5i	0.573787	+	0.0386007i
$211$	517797.	−	517797.i	0.800670	−	0.800670i	−0.182530	−	0.983200i	$-0.558429\pi$
$211$	517797.	−	517797.i	0.800670	−	0.800670i	0.983200	+	0.182530i	$0.0584287\pi$
$212$	−498254.	−	653990.i	−0.761397	−	0.999382i
$213$	−487366.	−	487366.i	−0.736048	−	0.736048i
$214$	−439846.	+	384396.i	−0.656548	+	0.573779i
$215$			318419.i			0.469788i
$216$	−1.61525e6	+	1.06724e6i	−2.35562	+	1.55643i
$217$		−	494611.i		−	0.713041i
$218$	714136.	+	817151.i	1.01775	+	1.16456i
$219$	−1.19230e6	−	1.19230e6i	−1.67986	−	1.67986i
$220$	33367.2	−	246874.i	0.0464797	−	0.343890i
$221$	−184241.	+	184241.i	−0.253749	+	0.253749i
$222$	60808.9	−	903906.i	0.0828104	−	1.23095i
$223$	−1.09445e6			−1.47379			−0.736895	−	0.676007i	$-0.763709\pi$
$223$	−1.09445e6			−1.47379			−0.736895	+	0.676007i	$0.763709\pi$
$224$	303798.	+	106052.i	0.404543	+	0.141221i
$225$	−926253.			−1.21976
$226$	−28288.9	+	420506.i	−0.0368422	+	0.547647i
$227$	−775097.	+	775097.i	−0.998370	+	0.998370i	−0.999999	−	0.00162838i	$-0.999482\pi$
$227$	−775097.	+	775097.i	−0.998370	+	0.998370i	0.00162838	+	0.999999i	$0.499482\pi$
$228$	−151846.	+	1.12347e6i	−0.193449	+	1.43127i
$229$	951518.	+	951518.i	1.19903	+	1.19903i	0.974459	+	0.224567i	$0.0720968\pi$
$229$	951518.	+	951518.i	1.19903	+	1.19903i	0.224567	+	0.974459i	$0.427903\pi$
$230$	−123099.	−	140856.i	−0.153438	−	0.175572i
$231$			315151.i			0.388587i
$232$	47123.1	+	71319.7i	0.0574796	+	0.0869941i
$233$			652629.i			0.787547i	0.919207	+	0.393774i	$0.128831\pi$
$233$			652629.i			0.787547i	−0.919207	+	0.393774i	$0.871169\pi$
$234$	2.10734e6	−	1.84168e6i	2.51591	−	2.19874i
$235$	88445.9	+	88445.9i	0.104474	+	0.104474i
$236$	151908.	+	199388.i	0.177541	+	0.233034i
$237$	1.19468e6	−	1.19468e6i	1.38160	−	1.38160i
$238$	100611.	+	6768.47i	0.115134	+	0.00774547i
$239$	−99764.8			−0.112975			−0.0564875	−	0.998403i	$-0.517990\pi$
$239$	−99764.8			−0.112975			−0.0564875	+	0.998403i	$0.517990\pi$
$240$	1.15467e6	+	317935.i	1.29398	+	0.356295i
$241$	274915.			0.304899			0.152449	−	0.988311i	$-0.451284\pi$
$241$	274915.			0.304899			0.152449	+	0.988311i	$0.451284\pi$
$242$	−695848.	−	46812.1i	−0.763793	−	0.0513831i
$243$	1.55135e6	−	1.55135e6i	1.68537	−	1.68537i
$244$	25248.6	−	19236.1i	0.0271495	−	0.0206844i
$245$	−388688.	−	388688.i	−0.413700	−	0.413700i
$246$	−814052.	+	711428.i	−0.857658	+	0.749537i
$247$		−	985292.i		−	1.02760i
$248$	322610.	−	1.57918e6i	0.333081	−	1.63043i
$249$			3.25987e6i			3.33197i
$250$	692711.	+	792636.i	0.700974	+	0.802091i
$251$	−509257.	−	509257.i	−0.510214	−	0.510214i	0.404378	−	0.914592i	$-0.367488\pi$
$251$	−509257.	−	509257.i	−0.510214	−	0.510214i	−0.914592	+	0.404378i	$0.867488\pi$
$252$	−1.07337e6	−	145076.i	−1.06475	−	0.143911i
$253$	113428.	−	113428.i	0.111408	−	0.111408i
$254$	−61630.2	+	916114.i	−0.0599390	+	0.890974i
$255$	375317.			0.361449
$256$	900783.	+	536751.i	0.859053	+	0.511886i
$257$	−1.81164e6			−1.71096			−0.855480	−	0.517835i	$-0.826738\pi$
$257$	−1.81164e6			−1.71096			−0.855480	+	0.517835i	$0.826738\pi$
$258$	88108.8	−	1.30971e6i	0.0824081	−	1.22497i
$259$	215471.	−	215471.i	0.199590	−	0.199590i
$260$	−1.03150e6	−	139416.i	−0.946313	−	0.127903i
$261$	−203463.	−	203463.i	−0.184877	−	0.184877i
$262$	−752338.	−	860864.i	−0.677111	−	0.774785i
$263$		−	1.76822e6i		−	1.57633i	−0.615465	−	0.788164i	$-0.711032\pi$
$263$		−	1.76822e6i		−	1.57633i	0.615465	−	0.788164i	$-0.288968\pi$
$264$	−205557.	+	1.00620e6i	−0.181519	+	0.888537i
$265$		−	1.02928e6i		−	0.900363i
$266$	−287125.	+	250928.i	−0.248810	+	0.217443i
$267$	534845.	+	534845.i	0.459145	+	0.459145i
$268$	520290.	−	396392.i	0.442495	−	0.337123i
$269$	864877.	−	864877.i	0.728742	−	0.728742i	−0.241627	−	0.970369i	$-0.577681\pi$
$269$	864877.	−	864877.i	0.728742	−	0.728742i	0.970369	+	0.241627i	$0.0776811\pi$
$270$	−2.41820e6	−	162681.i	−2.01875	−	0.135809i
$271$	−597062.			−0.493851			−0.246926	−	0.969034i	$-0.579420\pi$
$271$	−597062.			−0.493851			−0.246926	+	0.969034i	$0.579420\pi$
$272$	316813.	+	87233.8i	0.259646	+	0.0714928i
$273$	1.31677e6			1.06931
$274$	1.61791e6	+	108843.i	1.30190	+	0.0875836i
$275$	−208880.	+	208880.i	−0.166558	+	0.166558i
$276$	467351.	+	613427.i	0.369292	+	0.484719i
$277$	1.20879e6	+	1.20879e6i	0.946564	+	0.946564i	0.998643	−	0.0520791i	$-0.0165848\pi$
$277$	1.20879e6	+	1.20879e6i	0.946564	+	0.946564i	−0.0520791	+	0.998643i	$0.516585\pi$
$278$	341577.	−	298516.i	0.265080	−	0.231662i
$279$			5.42547e6i			4.17279i
$280$	222069.	+	336096.i	0.169275	+	0.256194i
$281$		−	174043.i		−	0.131489i	−0.997836	−	0.0657446i	$-0.979058\pi$
$281$		−	174043.i		−	0.131489i	0.997836	−	0.0657446i	$-0.0209423\pi$
$282$	−339319.	−	388267.i	−0.254089	−	0.290742i
$283$	483416.	+	483416.i	0.358802	+	0.358802i	0.863371	−	0.504569i	$-0.168349\pi$
$283$	483416.	+	483416.i	0.358802	+	0.358802i	−0.504569	+	0.863371i	$0.668349\pi$
$284$	101188.	−	748661.i	0.0744447	−	0.550794i
$285$	−1.00357e6	+	1.00357e6i	−0.731872	+	0.731872i
$286$	59910.3	−	890548.i	0.0433099	−	0.643787i
$287$	−363640.			−0.260596
$288$	−3.33240e6	−	1.16330e6i	−2.36743	−	0.826439i
$289$	−1.31688e6			−0.927473
$290$	−7183.03	+	106773.i	−0.00501548	+	0.0745536i
$291$	−809173.	+	809173.i	−0.560156	+	0.560156i
$292$	247547.	−	1.83153e6i	0.169903	−	1.25706i
$293$	146105.	+	146105.i	0.0994252	+	0.0994252i	0.755070	−	0.655644i	$-0.227603\pi$
$293$	146105.	+	146105.i	0.0994252	+	0.0994252i	−0.655644	+	0.755070i	$0.727603\pi$
$294$	1.49119e6	+	1.70629e6i	1.00615	+	1.15129i
$295$			313806.i			0.209945i
$296$	828490.	−	547408.i	0.549614	−	0.363146i
$297$		−	2.07832e6i		−	1.36716i
$298$	−1.98750e6	+	1.73695e6i	−1.29648	+	1.13304i
$299$	−473927.	−	473927.i	−0.306573	−	0.306573i
$300$	−860640.	−	1.12964e6i	−0.552101	−	0.724667i
$301$	312206.	−	312206.i	0.198621	−	0.198621i
$302$	1.13168e6	+	76131.9i	0.714011	+	0.0480341i
$303$	4.12222e6			2.57943
$304$	−1.08039e6	+	613879.i	−0.670498	+	0.380977i
$305$	39737.3			0.0244596
$306$	−1.10362e6	−	74244.4i	−0.673776	−	0.0453273i
$307$	−887303.	+	887303.i	−0.537311	+	0.537311i	−0.922738	−	0.385427i	$-0.874054\pi$
$307$	−887303.	+	887303.i	−0.537311	+	0.537311i	0.385427	+	0.922738i	$0.374054\pi$
$308$	−274773.	+	209341.i	−0.165043	+	0.125741i
$309$	−3.19471e6	−	3.19471e6i	−1.90342	−	1.90342i
$310$	1.51936e6	−	1.32782e6i	0.897961	−	0.784759i
$311$		−	273571.i		−	0.160387i	−0.996779	−	0.0801935i	$-0.974446\pi$
$311$		−	273571.i		−	0.160387i	0.996779	−	0.0801935i	$-0.0255538\pi$
$312$	4.20415e6	+	858865.i	2.44507	+	0.499504i
$313$		−	1.86824e6i		−	1.07788i	−0.842343	−	0.538942i	$-0.818824\pi$
$313$		−	1.86824e6i		−	1.07788i	0.842343	−	0.538942i	$-0.181176\pi$
$314$	−1.24416e6	−	1.42363e6i	−0.712118	−	0.814842i
$315$	−958822.	−	958822.i	−0.544455	−	0.544455i
$316$	1.83520e6	+	248043.i	1.03387	+	0.139737i
$317$	202652.	−	202652.i	0.113267	−	0.113267i	−0.648202	−	0.761469i	$-0.724479\pi$
$317$	202652.	−	202652.i	0.113267	−	0.113267i	0.761469	+	0.648202i	$0.224479\pi$
$318$	−284809.	+	4.23359e6i	−0.157938	+	2.34769i
$319$	−91766.1			−0.0504900
$320$	489795.	+	1.21792e6i	0.267386	+	0.664881i
$321$	3.01474e6			1.63300
$322$	−17410.7	+	258805.i	−0.00935787	+	0.139102i
$323$	−275356.	+	275356.i	−0.146855	+	0.146855i
$324$	5.20600e6	+	703637.i	2.75513	+	0.372380i
$325$	872750.	+	872750.i	0.458333	+	0.458333i
$326$	−725658.	−	830335.i	−0.378171	−	0.432722i
$327$		−	5.60081e6i		−	2.89655i
$328$	−1.16102e6	−	237185.i	−0.595875	−	0.121731i
$329$		−	173440.i		−	0.0883406i
$330$	−968090.	+	846047.i	−0.489363	+	0.427671i
$331$	895762.	+	895762.i	0.449389	+	0.449389i	0.895151	−	0.445762i	$-0.147067\pi$
$331$	895762.	+	895762.i	0.449389	+	0.449389i	−0.445762	+	0.895151i	$0.647067\pi$
$332$	−2.84221e6	+	2.16539e6i	−1.41518	+	1.07818i
$333$	−2.36354e6	+	2.36354e6i	−1.16802	+	1.16802i
$334$	−1.83070e6	−	123158.i	−0.897949	−	0.0604082i
$335$	818854.			0.398653
$336$	−820405.	−	1.44387e6i	−0.396443	−	0.697717i
$337$	−2.99915e6			−1.43855			−0.719274	−	0.694727i	$-0.755525\pi$
$337$	−2.99915e6			−1.43855			−0.719274	+	0.694727i	$0.755525\pi$
$338$	−1.62530e6	−	109340.i	−0.773825	−	0.0520580i
$339$	1.53804e6	−	1.53804e6i	0.726887	−	0.726887i
$340$	249307.	+	327231.i	0.116960	+	0.153517i
$341$	1.22350e6	+	1.22350e6i	0.569796	+	0.569796i
$342$	3.14952e6	−	2.75247e6i	1.45606	−	1.27250i
$343$			1.69583e6i			0.778298i
$344$	1.20044e6	−	793164.i	0.546944	−	0.361382i
$345$			965437.i			0.436693i
$346$	1.98260e6	+	2.26860e6i	0.890318	+	1.01875i
$347$	1.04197e6	+	1.04197e6i	0.464548	+	0.464548i	0.900143	−	0.435595i	$-0.143462\pi$
$347$	1.04197e6	+	1.04197e6i	0.464548	+	0.464548i	−0.435595	+	0.900143i	$0.643462\pi$
$348$	59090.1	−	437190.i	0.0261557	−	0.193518i
$349$	−2.07045e6	+	2.07045e6i	−0.909918	+	0.909918i	−0.996265	−	0.0863472i	$-0.972481\pi$
$349$	−2.07045e6	+	2.07045e6i	−0.909918	+	0.909918i	0.0863472	+	0.996265i	$0.472481\pi$
$350$	32062.3	−	476596.i	0.0139902	−	0.207960i
$351$	−8.68369e6			−3.76215
$352$	−1.01383e6	+	489157.i	−0.436123	+	0.210422i
$353$	1.99154e6			0.850655			0.425327	−	0.905040i	$-0.360159\pi$
$353$	1.99154e6			0.850655			0.425327	+	0.905040i	$0.360159\pi$
$354$	86832.4	−	1.29074e6i	0.0368276	−	0.547431i
$355$	668764.	−	668764.i	0.281645	−	0.281645i
$356$	−111046.	+	821595.i	−0.0464384	+	0.343584i
$357$	−367994.	−	367994.i	−0.152816	−	0.152816i
$358$	−878002.	−	1.00466e6i	−0.362066	−	0.414295i
$359$			603261.i			0.247041i	0.992342	+	0.123520i	$0.0394184\pi$
$359$			603261.i			0.247041i	−0.992342	+	0.123520i	$0.960582\pi$
$360$	−2.43591e6	−	3.68669e6i	−0.990613	−	1.49927i
$361$			1.00354e6i			0.405289i
$362$	514504.	−	449642.i	0.206356	−	0.180342i
$363$	2.54512e6	+	2.54512e6i	1.01378	+	1.01378i
$364$	874676.	+	1.14807e6i	0.346014	+	0.454165i
$365$	1.63607e6	−	1.63607e6i	0.642791	−	0.642791i
$366$	−163446.	−	10995.6i	−0.0637782	−	0.00429059i
$367$	−946062.			−0.366652			−0.183326	−	0.983052i	$-0.558686\pi$
$367$	−946062.			−0.366652			−0.183326	+	0.983052i	$0.558686\pi$
$368$	−224394.	+	814947.i	−0.0863756	+	0.313697i
$369$	3.98883e6			1.52503
$370$	1.24034e6	+	83442.1i	0.471017	+	0.0316870i
$371$	−1.00919e6	+	1.00919e6i	−0.380662	+	0.380662i
$372$	−6.61682e6	+	5.04115e6i	−2.47909	+	1.88874i
$373$	21095.1	+	21095.1i	0.00785070	+	0.00785070i	0.711021	−	0.703171i	$-0.248233\pi$
$373$	21095.1	+	21095.1i	0.00785070	+	0.00785070i	−0.703171	+	0.711021i	$0.748233\pi$
$374$	−265621.	+	232135.i	−0.0981937	+	0.0858148i
$375$		−	5.43278e6i		−	1.99501i
$376$	113127.	−	553755.i	0.0412662	−	0.201998i
$377$			383420.i			0.138938i
$378$	2.21151e6	+	2.53052e6i	0.796085	+	0.910922i
$379$	576840.	+	576840.i	0.206280	+	0.206280i	0.802684	−	0.596404i	$-0.203404\pi$
$379$	576840.	+	576840.i	0.206280	+	0.206280i	−0.596404	+	0.802684i	$0.703404\pi$
$380$	−1.54162e6	−	208364.i	−0.547669	−	0.0740224i
$381$	3.35076e6	−	3.35076e6i	1.18258	−	1.18258i
$382$	305481.	−	4.54087e6i	0.107109	−	1.59214i
$383$	3.61983e6			1.26093			0.630466	−	0.776217i	$-0.282864\pi$
$383$	3.61983e6			1.26093			0.630466	+	0.776217i	$0.282864\pi$
$384$	−1.67760e6	−	5.14504e6i	−0.580578	−	1.78058i
$385$	−432450.			−0.148691
$386$	93832.0	−	1.39478e6i	0.0320540	−	0.476473i
$387$	−3.42463e6	+	3.42463e6i	−1.16235	+	1.16235i
$388$	−1.24300e6	−	168002.i	−0.419172	−	0.0566548i
$389$	−2.88292e6	−	2.88292e6i	−0.965958	−	0.965958i	0.0334816	−	0.999439i	$-0.489340\pi$
$389$	−2.88292e6	−	2.88292e6i	−0.965958	−	0.965958i	−0.999439	+	0.0334816i	$0.989340\pi$
$390$	3.53498e6	+	4.04491e6i	1.17686	+	1.34663i
$391$			264893.i			0.0876252i
$392$	−497150.	+	2.43355e6i	−0.163408	+	0.799881i
$393$			5.90042e6i			1.92709i
$394$	1.78258e6	−	1.55786e6i	0.578507	−	0.505577i
$395$	1.63935e6	+	1.63935e6i	0.528662	+	0.528662i
$396$	3.01403e6	−	2.29630e6i	0.965851	−	0.735851i
$397$	−2.91477e6	+	2.91477e6i	−0.928172	+	0.928172i	−0.997588	−	0.0694156i	$-0.977887\pi$
$397$	−2.91477e6	+	2.91477e6i	−0.928172	+	0.928172i	0.0694156	+	0.997588i	$0.477887\pi$
$398$	1.42382e6	+	95785.3i	0.450554	+	0.0303104i
$399$	1.96798e6			0.618853
$400$	413228.	−	1.50075e6i	0.129134	−	0.468984i
$401$	2.02162e6			0.627824			0.313912	−	0.949452i	$-0.398360\pi$
$401$	2.02162e6			0.627824			0.313912	+	0.949452i	$0.398360\pi$
$402$	−3.36809e6	−	226583.i	−1.03949	−	0.0699299i
$403$	5.11208e6	−	5.11208e6i	1.56796	−	1.56796i
$404$	2.73821e6	+	3.59408e6i	0.834669	+	1.09556i
$405$	4.65042e6	+	4.65042e6i	1.40882	+	1.40882i
$406$	111733.	−	97647.3i	0.0336408	−	0.0293998i
$407$			1.06601e6i			0.318988i
$408$	−934894.	−	1.41494e6i	−0.278043	−	0.420812i
$409$		−	3.30579e6i		−	0.977162i	−0.872519	−	0.488581i	$-0.837515\pi$
$409$		−	3.30579e6i		−	0.977162i	0.872519	−	0.488581i	$-0.162485\pi$
$410$	−976222.	−	1.11704e6i	−0.286806	−	0.328179i
$411$	−5.91765e6	−	5.91765e6i	−1.72800	−	1.72800i
$412$	663294.	−	4.90752e6i	0.192514	−	1.42436i
$413$	307683.	−	307683.i	0.0887622	−	0.0887622i
$414$	190981.	−	2.83887e6i	0.0547632	−	0.814038i
$415$	−4.47319e6			−1.27496
$416$	2.04381e6	+	4.23602e6i	0.579038	+	1.20012i
$417$	−2.34119e6			−0.659321
$418$	89538.7	−	1.33096e6i	0.0250651	−	0.372585i
$419$	−1.85951e6	+	1.85951e6i	−0.517445	+	0.517445i	−0.916797	−	0.399353i	$-0.869235\pi$
$419$	−1.85951e6	+	1.85951e6i	−0.517445	+	0.517445i	0.399353	+	0.916797i	$0.369235\pi$
$420$	278463.	−	2.06027e6i	0.0770273	−	0.569902i
$421$	1.25469e6	+	1.25469e6i	0.345010	+	0.345010i	0.858247	−	0.513237i	$-0.171554\pi$
$421$	1.25469e6	+	1.25469e6i	0.345010	+	0.345010i	−0.513237	+	0.858247i	$0.671554\pi$
$422$	−2.72589e6	−	3.11911e6i	−0.745122	−	0.852607i
$423$			1.90250e6i			0.516979i
$424$	−3.88037e6	+	2.56388e6i	−1.04823	+	0.692600i
$425$		−	487809.i		−	0.131002i
$426$	−2.93579e6	+	2.56569e6i	−0.783793	+	0.684983i
$427$	−38961.9	−	38961.9i	−0.0103412	−	0.0103412i
$428$	2.00256e6	+	2.62849e6i	0.528417	+	0.693580i
$429$	−3.25726e6	+	3.25726e6i	−0.854493	+	0.854493i
$430$	1.79718e6	+	120903.i	0.468729	+	0.0315331i
$431$	−129266.			−0.0335191			−0.0167596	−	0.999860i	$-0.505335\pi$
$431$	−129266.			−0.0335191			−0.0167596	+	0.999860i	$0.505335\pi$
$432$	5.41031e6	+	9.52184e6i	1.39480	+	2.45477i
$433$	−6.66800e6			−1.70913			−0.854567	−	0.519342i	$-0.826177\pi$
$433$	−6.66800e6			−1.70913			−0.854567	+	0.519342i	$0.826177\pi$
$434$	−2.79163e6	−	187803.i	−0.711433	−	0.0478607i
$435$	390533.	−	390533.i	0.0989543	−	0.0989543i
$436$	4.88323e6	−	3.72038e6i	1.23024	−	0.937284i
$437$	−708305.	−	708305.i	−0.177426	−	0.177426i
$438$	−7.18214e6	+	6.27672e6i	−1.78883	+	1.56332i
$439$		−	378688.i		−	0.0937823i	−0.998900	−	0.0468911i	$-0.985069\pi$
$439$		−	378688.i		−	0.0937823i	0.998900	−	0.0468911i	$-0.0149314\pi$
$440$	−1.38071e6	−	282066.i	−0.339994	−	0.0694574i
$441$		−	8.36078e6i		−	2.04715i
$442$	969915.	+	1.10983e6i	0.236145	+	0.270209i
$443$	−4.52584e6	−	4.52584e6i	−1.09570	−	1.09570i	−0.994908	−	0.100788i	$-0.967864\pi$
$443$	−4.52584e6	−	4.52584e6i	−1.09570	−	1.09570i	−0.100788	−	0.994908i	$-0.532136\pi$
$444$	−5.07864e6	−	686423.i	−1.22262	−	0.165247i
$445$	−733915.	+	733915.i	−0.175689	+	0.175689i
$446$	−415563.	+	6.17721e6i	−0.0989235	+	1.47047i
$447$	1.36225e7			3.22469
$448$	713919.	−	1.67439e6i	0.168056	−	0.394151i
$449$	6.64190e6			1.55481			0.777404	−	0.629002i	$-0.216536\pi$
$449$	6.64190e6			1.55481			0.777404	+	0.629002i	$0.216536\pi$
$450$	−351697.	+	5.22786e6i	−0.0818723	+	1.21701i
$451$	899525.	−	899525.i	0.208244	−	0.208244i
$452$	2.36263e6	+	319331.i	0.543939	+	0.0735182i
$453$	−4.13920e6	−	4.13920e6i	−0.947700	−	0.947700i
$454$	4.08042e6	+	4.66903e6i	0.929106	+	1.06313i
$455$			1.80688e6i			0.409166i
$456$	6.28329e6	+	1.28361e6i	1.41506	+	0.289083i
$457$		−	1.35265e6i		−	0.302966i	−0.988460	−	0.151483i	$-0.951595\pi$
$457$		−	1.35265e6i		−	0.302966i	0.988460	−	0.151483i	$-0.0484048\pi$
$458$	5.73175e6	−	5.00917e6i	1.27680	−	1.11584i
$459$	2.42680e6	+	2.42680e6i	0.537653	+	0.537653i
$460$	−841745.	+	641299.i	−0.185475	+	0.141308i
$461$	2.17241e6	−	2.17241e6i	0.476090	−	0.476090i	−0.427789	−	0.903879i	$-0.640707\pi$
$461$	2.17241e6	−	2.17241e6i	0.476090	−	0.476090i	0.903879	+	0.427789i	$0.140707\pi$
$462$	1.77874e6	+	119662.i	0.387711	+	0.0260827i
$463$	−484327.			−0.104999			−0.0524996	−	0.998621i	$-0.516719\pi$
$463$	−484327.			−0.104999			−0.0524996	+	0.998621i	$0.516719\pi$
$464$	420428.	−	238887.i	0.0906561	−	0.0515108i
$465$	−1.04138e7			−2.23346
$466$	3.68350e6	+	247802.i	0.785771	+	0.0528616i
$467$	−4.84130e6	+	4.84130e6i	−1.02724	+	1.02724i	−0.0276165	+	0.999619i	$0.508792\pi$
$467$	−4.84130e6	+	4.84130e6i	−1.02724	+	1.02724i	−0.999619	+	0.0276165i	$0.991208\pi$
$468$	−9.59446e6	−	1.25933e7i	−2.02491	−	2.65782i
$469$	−802877.	−	802877.i	−0.168545	−	0.168545i
$470$	532780.	−	465614.i	0.111251	−	0.0972259i
$471$			9.75767e6i			2.02672i
$472$	1.18305e6	−	781674.i	0.244426	−	0.161499i
$473$			1.54458e6i			0.317438i
$474$	−6.28930e6	−	7.19654e6i	−1.28575	−	1.47122i
$475$	1.30436e6	+	1.30436e6i	0.265256	+	0.265256i
$476$	76403.8	−	565289.i	0.0154560	−	0.114354i
$477$	1.10700e7	−	1.10700e7i	2.22768	−	2.22768i
$478$	−37880.5	+	563082.i	−0.00758309	+	0.112720i
$479$	−8.10148e6			−1.61334			−0.806670	−	0.591002i	$-0.798732\pi$
$479$	−8.10148e6			−1.61334			−0.806670	+	0.591002i	$0.798732\pi$
$480$	2.23288e6	−	6.39633e6i	0.442346	−	1.26715i
$481$	4.45402e6			0.877788
$482$	104385.	−	1.55165e6i	0.0204654	−	0.304211i
$483$	946600.	−	946600.i	0.184628	−	0.184628i
$484$	−528425.	+	3.90966e6i	−0.102534	+	0.758622i
$485$	−1.11035e6	−	1.11035e6i	−0.214341	−	0.214341i
$486$	−8.16692e6	−	9.34501e6i	−1.56844	−	1.79469i
$487$			6.33460e6i			1.21031i	0.796108	+	0.605155i	$0.206889\pi$
$487$			6.33460e6i			1.21031i	−0.796108	+	0.605155i	$0.793111\pi$
$488$	−98983.5	−	149809.i	−0.0188154	−	0.0284767i
$489$			5.69117e6i			1.07629i
$490$	−2.34138e6	+	2.04621e6i	−0.440535	+	0.384999i
$491$	662865.	+	662865.i	0.124086	+	0.124086i	0.766422	−	0.642337i	$-0.222035\pi$
$491$	662865.	+	662865.i	0.124086	+	0.124086i	−0.642337	+	0.766422i	$0.722035\pi$
$492$	3.70627e6	+	4.86472e6i	0.690279	+	0.906035i
$493$	107153.	−	107153.i	0.0198558	−	0.0198558i
$494$	−5.56108e6	−	374114.i	−1.02528	−	0.0689741i
$495$	4.74361e6			0.870154
$496$	−8.79055e6	−	2.42046e6i	−1.60440	−	0.441767i
$497$	−1.31143e6			−0.238152
$498$	1.83990e7	+	1.23777e6i	3.32446	+	0.223648i
$499$	5.01189e6	−	5.01189e6i	0.901052	−	0.901052i	−0.0944754	−	0.995527i	$-0.530117\pi$
$499$	5.01189e6	−	5.01189e6i	0.901052	−	0.901052i	0.995527	+	0.0944754i	$0.0301174\pi$
$500$	4.73673e6	−	3.60877e6i	0.847333	−	0.645556i
$501$	6.69595e6	+	6.69595e6i	1.19184	+	1.19184i
$502$	−3.06766e6	+	2.68093e6i	−0.543310	+	0.474817i
$503$		−	752594.i		−	0.132630i	−0.997799	−	0.0663149i	$-0.978876\pi$
$503$		−	752594.i		−	0.132630i	0.997799	−	0.0663149i	$-0.0211242\pi$
$504$	−1.22638e6	+	6.00313e6i	−0.215055	+	1.05269i
$505$			5.65651e6i			0.987007i
$506$	−597128.	−	683265.i	−0.103679	−	0.118635i
$507$	5.94469e6	+	5.94469e6i	1.02709	+	1.02709i
$508$	5.14723e6	+	695694.i	0.884942	+	0.119608i
$509$	−649015.	+	649015.i	−0.111035	+	0.111035i	−0.760442	−	0.649406i	$-0.775017\pi$
$509$	−649015.	+	649015.i	−0.111035	+	0.111035i	0.649406	+	0.760442i	$0.275017\pi$
$510$	142507.	−	2.11832e6i	0.0242611	−	0.360634i
$511$	−3.20829e6			−0.543528
$512$	3.37150e6	−	4.88030e6i	0.568393	−	0.822757i
$513$	−1.29782e7			−2.17731
$514$	−687879.	+	1.02251e7i	−0.114843	+	1.70710i
$515$	4.38379e6	−	4.38379e6i	0.728335	−	0.728335i
$516$	−7.35867e6	−	994590.i	−1.21668	−	0.164445i
$517$	429033.	+	429033.i	0.0705935	+	0.0705935i
$518$	−1.13433e6	−	1.29795e6i	−0.185743	−	0.212537i
$519$		−	1.55491e7i		−	2.53389i
$520$	−1.17854e6	+	5.76894e6i	−0.191132	+	0.935594i
$521$			5.88783e6i			0.950300i	0.879905	+	0.475150i	$0.157606\pi$
$521$			5.88783e6i			0.950300i	−0.879905	+	0.475150i	$0.842394\pi$
$522$	−1.22562e6	+	1.07111e6i	−0.196870	+	0.172051i
$523$	−6.82221e6	−	6.82221e6i	−1.09061	−	1.09061i	−0.995463	−	0.0951505i	$-0.969667\pi$
$523$	−6.82221e6	−	6.82221e6i	−1.09061	−	1.09061i	−0.0951505	−	0.995463i	$-0.530333\pi$
$524$	−5.14446e6	+	3.91940e6i	−0.818487	+	0.623579i
$525$	−1.74319e6	+	1.74319e6i	−0.276024	+	0.276024i
$526$	−9.98000e6	−	671390.i	−1.57277	−	0.105806i
$527$	−2.85731e6			−0.448158
$528$	5.60106e6	+	1.54224e6i	0.874350	+	0.240750i
$529$	5.75495e6			0.894134
$530$	−5.80934e6	−	390815.i	−0.898332	−	0.0604340i
$531$	−3.37502e6	+	3.37502e6i	−0.519446	+	0.519446i
$532$	1.30724e6	+	1.71584e6i	0.200252	+	0.262844i
$533$	−3.75842e6	−	3.75842e6i	−0.573044	−	0.573044i
$534$	3.22180e6	−	2.81564e6i	0.488928	−	0.427291i
$535$			4.13683e6i			0.624860i
$536$	−2.03972e6	−	3.08708e6i	−0.306662	−	0.464126i
$537$			6.88598e6i			1.03046i
$538$	−4.55306e6	−	5.20984e6i	−0.678184	−	0.776013i
$539$	−1.88545e6	−	1.88545e6i	−0.279539	−	0.279539i
$540$	−1.83637e6	+	1.35868e7i	−0.271005	+	2.00508i
$541$	1.05152e6	−	1.05152e6i	0.154463	−	0.154463i	−0.625645	−	0.780108i	$-0.715164\pi$
$541$	1.05152e6	−	1.05152e6i	0.154463	−	0.154463i	0.780108	+	0.625645i	$0.215164\pi$
$542$	−226704.	+	3.36988e6i	−0.0331482	+	0.492738i
$543$	−3.52645e6			−0.513260
$544$	612649.	−	1.75500e6i	0.0887595	−	0.254261i
$545$	7.68544e6			1.10835
$546$	499977.	−	7.43199e6i	0.0717741	−	1.06690i
$547$	210027.	−	210027.i	0.0300128	−	0.0300128i	−0.691941	−	0.721954i	$-0.743244\pi$
$547$	210027.	−	210027.i	0.0300128	−	0.0300128i	0.721954	+	0.691941i	$0.243244\pi$
$548$	1.22864e6	−	9.09032e6i	0.174772	−	1.29309i
$549$	427380.	+	427380.i	0.0605178	+	0.0605178i
$550$	1.09963e6	+	1.25825e6i	0.155003	+	0.177362i
$551$			573039.i			0.0804091i
$552$	3.63969e6	−	2.40485e6i	0.508414	−	0.335924i
$553$		−	3.21472e6i		−	0.447024i
$554$	7.28148e6	−	6.36353e6i	1.00796	−	0.880894i
$555$	−4.53665e6	−	4.53665e6i	−0.625177	−	0.625177i
$556$	−1.55515e6	−	2.04124e6i	−0.213347	−	0.280032i
$557$	−644791.	+	644791.i	−0.0880604	+	0.0880604i	−0.749765	−	0.661704i	$-0.769833\pi$
$557$	−644791.	+	644791.i	−0.0880604	+	0.0880604i	0.661704	+	0.749765i	$0.269833\pi$
$558$	3.06219e7	+	2.06004e6i	4.16338	+	0.280086i
$559$	6.45364e6			0.873524
$560$	1.98128e6	−	1.12576e6i	0.266978	−	0.151697i
$561$	1.82059e6			0.244233
$562$	−982314.	−	66083.8i	−0.131193	−	0.00882580i
$563$	−1.51267e6	+	1.51267e6i	−0.201128	+	0.201128i	−0.800483	−	0.599355i	$-0.795424\pi$
$563$	−1.51267e6	+	1.51267e6i	−0.201128	+	0.201128i	0.599355	+	0.800483i	$0.295424\pi$
$564$	−2.32025e6	+	1.76773e6i	−0.307141	+	0.234001i
$565$	2.11049e6	+	2.11049e6i	0.278140	+	0.278140i
$566$	2.91200e6	−	2.54489e6i	0.382076	−	0.333909i
$567$		−	9.11936e6i		−	1.19126i
$568$	−4.18709e6	−	855381.i	−0.544555	−	0.111247i
$569$		−	1.27829e7i		−	1.65520i	−0.561321	−	0.827598i	$-0.689707\pi$
$569$		−	1.27829e7i		−	1.65520i	0.561321	−	0.827598i	$-0.310293\pi$
$570$	5.28319e6	+	6.04530e6i	0.681097	+	0.779346i
$571$	4.54358e6	+	4.54358e6i	0.583187	+	0.583187i	0.935778	−	0.352591i	$-0.114699\pi$
$571$	4.54358e6	+	4.54358e6i	0.583187	+	0.583187i	−0.352591	+	0.935778i	$0.614699\pi$
$572$	−5.00359e6	−	676280.i	−0.639428	−	0.0864244i
$573$	−1.66086e7	+	1.66086e7i	−2.11323	+	2.11323i
$574$	−138074.	+	2.05242e6i	−0.0174917	+	0.260008i
$575$	1.25480e6			0.158273
$576$	−7.83109e6	+	1.83667e7i	−0.983481	+	2.30662i
$577$	9.65395e6			1.20716			0.603581	−	0.797302i	$-0.293740\pi$
$577$	9.65395e6			1.20716			0.603581	+	0.797302i	$0.293740\pi$
$578$	−500017.	+	7.43259e6i	−0.0622537	+	0.925381i
$579$	−5.10153e6	+	5.10153e6i	−0.632418	+	0.632418i
$580$	599912.	+	81083.5i	0.0740488	+	0.0100083i
$581$	4.38591e6	+	4.38591e6i	0.539039	+	0.539039i
$582$	4.25981e6	+	4.87429e6i	0.521294	+	0.596491i
$583$		−	4.99282e6i		−	0.608379i
$584$	−1.02433e7	−	2.09261e6i	−1.24282	−	0.253896i
$585$		−	1.98199e7i		−	2.39449i
$586$	880108.	−	769156.i	0.105875	−	0.0925274i
$587$	−6.86328e6	−	6.86328e6i	−0.822122	−	0.822122i	0.164290	−	0.986412i	$-0.447467\pi$
$587$	−6.86328e6	−	6.86328e6i	−0.822122	−	0.822122i	−0.986412	+	0.164290i	$0.947467\pi$
$588$	1.01967e7	−	7.76852e6i	1.21623	−	0.926606i
$589$	7.64024e6	−	7.64024e6i	0.907442	−	0.907442i
$590$	1.77115e6	+	119152.i	0.209472	+	0.0140919i
$591$	−1.22179e7			−1.43890
$592$	−2.77505e6	−	4.88393e6i	−0.325436	−	0.572750i
$593$	3.03066e6			0.353916			0.176958	−	0.984218i	$-0.443374\pi$
$593$	3.03066e6			0.353916			0.176958	+	0.984218i	$0.443374\pi$
$594$	−1.17302e7	−	789133.i	−1.36408	−	0.0917665i
$595$	504961.	−	504961.i	0.0584744	−	0.0584744i
$596$	9.04883e6	+	1.18772e7i	1.04346	+	1.36961i
$597$	−5.20773e6	−	5.20773e6i	−0.598016	−	0.598016i
$598$	−2.85484e6	+	2.49494e6i	−0.326459	+	0.285304i
$599$			2.59781e6i			0.295829i	0.989000	+	0.147915i	$0.0472561\pi$
$599$			2.59781e6i			0.295829i	−0.989000	+	0.147915i	$0.952744\pi$
$600$	−6.70260e6	+	4.42861e6i	−0.760091	+	0.502214i
$601$		−	6.77065e6i		−	0.764618i	−0.924035	−	0.382309i	$-0.875129\pi$
$601$		−	6.77065e6i		−	0.764618i	0.924035	−	0.382309i	$-0.124871\pi$
$602$	−1.64357e6	−	1.88066e6i	−0.184841	−	0.211505i
$603$	8.80689e6	+	8.80689e6i	0.986346	+	0.986346i
$604$	859391.	−	6.35838e6i	0.0958514	−	0.709176i
$605$	−3.49242e6	+	3.49242e6i	−0.387916	+	0.387916i
$606$	1.56520e6	−	2.32662e7i	0.173136	−	2.57362i
$607$	5.58620e6			0.615382			0.307691	−	0.951486i	$-0.400444\pi$
$607$	5.58620e6			0.615382			0.307691	+	0.951486i	$0.400444\pi$
$608$	3.05457e6	+	6.33093e6i	0.335113	+	0.694558i
$609$	−765826.			−0.0836733
$610$	15088.2	−	224281.i	0.00164177	−	0.0244044i
$611$	1.79260e6	−	1.79260e6i	0.194259	−	0.194259i
$612$	−838085.	+	6.20074e6i	−0.0904502	+	0.669214i
$613$	3.01179e6	+	3.01179e6i	0.323723	+	0.323723i	0.850193	−	0.526470i	$-0.176485\pi$
$613$	3.01179e6	+	3.01179e6i	0.323723	+	0.323723i	−0.526470	+	0.850193i	$0.676485\pi$
$614$	4.67112e6	+	5.34493e6i	0.500034	+	0.572165i
$615$			7.65629e6i			0.816264i
$616$	1.07721e6	+	1.63033e6i	0.114380	+	0.173111i
$617$			1.20095e7i			1.27003i	0.772502	+	0.635013i	$0.219005\pi$
$617$			1.20095e7i			1.27003i	−0.772502	+	0.635013i	$0.780995\pi$
$618$	−1.92443e7	+	1.68182e7i	−2.02689	+	1.77137i
$619$	3.23215e6	+	3.23215e6i	0.339051	+	0.339051i	0.856010	−	0.516959i	$-0.172936\pi$
$619$	3.23215e6	+	3.23215e6i	0.339051	+	0.339051i	−0.516959	+	0.856010i	$0.672936\pi$
$620$	−6.91747e6	−	9.07961e6i	−0.722716	−	0.948611i
$621$	−6.24252e6	+	6.24252e6i	−0.649577	+	0.649577i
$622$	−1.54406e6	−	103875.i	−0.160025	−	0.0107655i
$623$	1.43919e6			0.148559
$624$	6.44383e6	−	2.34025e7i	0.662495	−	2.40603i
$625$	2.70450e6			0.276941
$626$	−1.05445e7	−	709368.i	−1.07545	−	0.0723496i
$627$	−4.86812e6	+	4.86812e6i	−0.494529	+	0.494529i
$628$	−8.50752e6	+	6.48161e6i	−0.860803	+	0.655818i
$629$	−1.24475e6	−	1.24475e6i	−0.125446	−	0.125446i
$630$	−5.77575e6	+	5.04762e6i	−0.579772	+	0.506682i
$631$		−	1.24972e7i		−	1.24951i	−0.780821	−	0.624755i	$-0.785199\pi$
$631$		−	1.24972e7i		−	1.24951i	0.780821	−	0.624755i	$-0.214801\pi$
$632$	2.09680e6	−	1.02639e7i	0.208817	−	1.02216i
$633$			2.13786e7i			2.12065i
$634$	−1.06684e6	−	1.22073e6i	−0.105409	−	0.120614i
$635$	4.59792e6	+	4.59792e6i	0.452509	+	0.452509i
$636$	2.37867e7	+	3.21498e6i	2.33180	+	0.315163i
$637$	−7.87784e6	+	7.87784e6i	−0.769234	+	0.769234i
$638$	−34843.5	+	517937.i	−0.00338898	+	0.0503762i
$639$	1.43853e7			1.39369
$640$	7.06004e6	−	2.30201e6i	0.681329	−	0.222155i
$641$	−1.96793e7			−1.89176			−0.945879	−	0.324520i	$-0.894797\pi$
$641$	−1.96793e7			−1.89176			−0.945879	+	0.324520i	$0.894797\pi$
$642$	1.14469e6	−	1.70155e7i	0.109610	−	1.62932i
$643$	−3.25875e6	+	3.25875e6i	−0.310831	+	0.310831i	−0.845231	−	0.534401i	$-0.820537\pi$
$643$	−3.25875e6	+	3.25875e6i	−0.310831	+	0.310831i	0.534401	+	0.845231i	$0.320537\pi$
$644$	1.45411e6	+	196535.i	0.138160	+	0.0186735i
$645$	−6.57336e6	−	6.57336e6i	−0.622140	−	0.622140i
$646$	1.44958e6	+	1.65869e6i	0.136666	+	0.156381i
$647$			7.75349e6i			0.728177i	0.931364	+	0.364088i	$0.118619\pi$
$647$			7.75349e6i			0.728177i	−0.931364	+	0.364088i	$0.881381\pi$
$648$	5.94811e6	−	2.91160e7i	0.556469	−	2.72392i
$649$			1.52221e6i			0.141861i
$650$	5.25727e6	−	4.59450e6i	0.488064	−	0.426536i
$651$	1.02106e7	+	1.02106e7i	0.944279	+	0.944279i
$652$	−4.96202e6	+	3.78041e6i	−0.457130	+	0.348273i
$653$	3.26906e6	−	3.26906e6i	0.300013	−	0.300013i	−0.541006	−	0.841019i	$-0.681956\pi$
$653$	3.26906e6	−	3.26906e6i	0.300013	−	0.300013i	0.841019	+	0.541006i	$0.181956\pi$
$654$	−3.16115e7	−	2.12662e6i	−2.89002	−	0.194422i
$655$	−8.09657e6			−0.737391
$656$	−1.77953e6	+	6.46285e6i	−0.161453	+	0.586360i
$657$	3.51923e7			3.18078
$658$	−978914.	−	65855.0i	−0.0881414	−	0.00592958i
$659$	3.61551e6	−	3.61551e6i	0.324307	−	0.324307i	−0.526110	−	0.850417i	$-0.676350\pi$
$659$	3.61551e6	−	3.61551e6i	0.324307	−	0.324307i	0.850417	+	0.526110i	$0.176350\pi$
$660$	4.40759e6	+	5.78524e6i	0.393859	+	0.516965i
$661$	−1.10992e7	−	1.10992e7i	−0.988068	−	0.988068i	0.0118621	−	0.999930i	$-0.496224\pi$
$661$	−1.10992e7	−	1.10992e7i	−0.988068	−	0.988068i	−0.999930	+	0.0118621i	$0.996224\pi$
$662$	5.39589e6	−	4.71565e6i	0.478540	−	0.418212i
$663$		−	7.60684e6i		−	0.672079i
$664$	1.11425e7	+	1.68639e7i	0.980759	+	1.48436i
$665$			2.70046e6i			0.236801i
$666$	1.24426e7	+	1.42375e7i	1.08699	+	1.24379i
$667$	275633.	+	275633.i	0.0239892	+	0.0239892i
$668$	−1.39023e6	+	1.02859e7i	−0.120544	+	0.891869i
$669$	2.25937e7	−	2.25937e7i	1.95174	−	1.95174i
$670$	310918.	−	4.62169e6i	0.0267583	−	0.397754i
$671$	192758.			0.0165274
$672$	−8.46084e6	+	4.08221e6i	−0.722753	+	0.348716i
$673$	−1.15752e7			−0.985122			−0.492561	−	0.870278i	$-0.663939\pi$
$673$	−1.15752e7			−0.985122			−0.492561	+	0.870278i	$0.663939\pi$
$674$	−1.13877e6	+	1.69275e7i	−0.0965579	+	1.43530i
$675$	1.14958e7	−	1.14958e7i	0.971134	−	0.971134i
$676$	−1.23425e6	+	9.13186e6i	−0.103881	+	0.768586i
$677$	6.16288e6	+	6.16288e6i	0.516788	+	0.516788i	0.916598	−	0.399810i	$-0.130924\pi$
$677$	6.16288e6	+	6.16288e6i	0.516788	+	0.516788i	−0.399810	+	0.916598i	$0.630924\pi$
$678$	−8.09683e6	−	9.26481e6i	−0.676458	−	0.774038i
$679$			2.17737e6i			0.181241i
$680$	1.94159e6	−	1.28286e6i	0.161022	−	0.106392i
$681$		−	3.20019e7i		−	2.64428i
$682$	7.37013e6	−	6.44101e6i	0.606757	−	0.530265i
$683$	1.61758e7	+	1.61758e7i	1.32683	+	1.32683i	0.908124	+	0.418701i	$0.137514\pi$
$683$	1.61758e7	+	1.61758e7i	1.32683	+	1.32683i	0.418701	+	0.908124i	$0.362486\pi$
$684$	−1.43394e7	−	1.88213e7i	−1.17190	−	1.53819i
$685$	8.12020e6	−	8.12020e6i	0.661212	−	0.661212i
$686$	9.57140e6	+	643902.i	0.776543	+	0.0522408i
$687$	−3.92858e7			−3.17573
$688$	−4.02089e6	−	7.07654e6i	−0.323855	−	0.569967i
$689$	−2.08612e7			−1.67413
$690$	5.44902e6	+	366575.i	0.435708	+	0.0293116i
$691$	−5.55329e6	+	5.55329e6i	−0.442441	+	0.442441i	−0.892832	−	0.450391i	$-0.851285\pi$
$691$	−5.55329e6	+	5.55329e6i	−0.442441	+	0.442441i	0.450391	+	0.892832i	$0.351285\pi$
$692$	1.35570e7	−	1.03286e7i	1.07621	−	0.819930i
$693$	−4.65106e6	−	4.65106e6i	−0.367891	−	0.367891i
$694$	6.27659e6	−	5.48533e6i	0.494681	−	0.432319i
$695$		−	3.21259e6i		−	0.252286i
$696$	−2.44511e6	−	499510.i	−0.191326	−	0.0390860i
$697$			2.10071e6i			0.163789i
$698$	1.08997e7	+	1.24720e7i	0.846790	+	0.968941i
$699$	−1.34727e7	−	1.34727e7i	−1.04295	−	1.04295i
$700$	−2.67778e6	−	361926.i	−0.206552	−	0.0279174i
$701$	−1.27706e7	+	1.27706e7i	−0.981556	+	0.981556i	−0.999833	−	0.0182770i	$-0.994182\pi$
$701$	−1.27706e7	+	1.27706e7i	−0.981556	+	0.981556i	0.0182770	+	0.999833i	$0.494182\pi$
$702$	−3.29718e6	+	4.90116e7i	−0.252523	+	3.75367i
$703$	6.65674e6			0.508011
$704$	2.37590e6	+	5.90789e6i	0.180674	+	0.449263i
$705$	−3.65171e6			−0.276709
$706$	756187.	−	1.12405e7i	0.0570975	−	0.848736i
$707$	5.54615e6	−	5.54615e6i	0.417295	−	0.417295i
$708$	−7.25207e6	−	980181.i	−0.543724	−	0.0734892i
$709$	3.14350e6	+	3.14350e6i	0.234854	+	0.234854i	0.814715	−	0.579861i	$-0.196893\pi$
$709$	3.14350e6	+	3.14350e6i	0.234854	+	0.234854i	−0.579861	+	0.814715i	$0.696893\pi$
$710$	−3.52064e6	−	4.02850e6i	−0.262105	−	0.299914i
$711$			3.52628e7i			2.61603i
$712$	4.59500e6	+	938712.i	0.339692	+	0.0693957i
$713$		−	7.34994e6i		−	0.541452i
$714$	−2.21672e6	+	1.93726e6i	−0.162729	+	0.142214i
$715$	−4.46961e6	−	4.46961e6i	−0.326967	−	0.326967i
$716$	−6.00375e6	+	4.57406e6i	−0.437663	+	0.333441i
$717$	2.05952e6	−	2.05952e6i	0.149613	−	0.149613i
$718$	3.40486e6	+	229057.i	0.246484	+	0.0165818i
$719$	1.75922e7			1.26911			0.634553	−	0.772879i	$-0.281184\pi$
$719$	1.75922e7			1.26911			0.634553	+	0.772879i	$0.281184\pi$
$720$	−2.17329e7	+	1.23487e7i	−1.56238	+	0.887745i
$721$	−8.59650e6			−0.615862
$722$	5.66405e6	+	381041.i	0.404375	+	0.0272038i
$723$	−5.67527e6	+	5.67527e6i	−0.403777	+	0.403777i
$724$	−2.34247e6	−	3.07464e6i	−0.166084	−	0.217996i
$725$	−507586.	−	507586.i	−0.0358645	−	0.0358645i
$726$	1.53313e7	−	1.33985e7i	1.07954	−	0.943443i
$727$		−	1.28421e7i		−	0.901153i	−0.892738	−	0.450576i	$-0.851219\pi$
$727$		−	1.28421e7i		−	0.901153i	0.892738	−	0.450576i	$-0.148781\pi$
$728$	6.81192e6	−	4.50084e6i	0.476366	−	0.314749i
$729$			2.41589e7i			1.68367i
$730$	−8.61292e6	−	9.85535e6i	−0.598196	−	0.684486i
$731$	−1.80357e6	−	1.80357e6i	−0.124836	−	0.124836i
$732$	−124121.	+	918331.i	−0.00856182	+	0.0633464i
$733$	−4.54419e6	+	4.54419e6i	−0.312389	+	0.312389i	−0.845835	−	0.533445i	$-0.820897\pi$
$733$	−4.54419e6	+	4.54419e6i	−0.312389	+	0.312389i	0.533445	+	0.845835i	$0.320897\pi$
$734$	−359218.	+	5.33966e6i	−0.0246104	+	0.365825i
$735$	1.60480e7			1.09572
$736$	4.51444e6	+	1.57593e6i	0.307192	+	0.107237i
$737$	3.97210e6			0.269371
$738$	1.51455e6	−	2.25133e7i	0.102363	−	1.52160i
$739$	−1.76573e7	+	1.76573e7i	−1.18936	+	1.18936i	−0.212114	+	0.977245i	$0.568035\pi$
$739$	−1.76573e7	+	1.76573e7i	−1.18936	+	1.18936i	−0.977245	+	0.212114i	$0.931965\pi$
$740$	941911.	−	6.96892e6i	0.0632311	−	0.467828i
$741$	2.03401e7	+	2.03401e7i	1.36084	+	1.36084i
$742$	5.31280e6	+	6.07918e6i	0.354253	+	0.405355i
$743$		−	1.87092e7i		−	1.24332i	−0.783286	−	0.621662i	$-0.786458\pi$
$743$		−	1.87092e7i		−	1.24332i	0.783286	−	0.621662i	$-0.213542\pi$
$744$	2.59403e7	+	3.92601e7i	1.71808	+	2.60027i
$745$			1.86928e7i			1.23391i
$746$	127072.	−	111053.i	0.00835995	−	0.00730605i
$747$	−4.81098e7	−	4.81098e7i	−3.15451	−	3.15451i
$748$	1.20934e6	+	1.58733e6i	0.0790303	+	0.103732i
$749$	4.05611e6	−	4.05611e6i	0.264183	−	0.264183i
$750$	−3.06631e7	−	2.06282e6i	−1.99051	−	0.133908i
$751$	1.38400e7			0.895441			0.447721	−	0.894174i	$-0.352236\pi$
$751$	1.38400e7			0.895441			0.447721	+	0.894174i	$0.352236\pi$
$752$	−3.08249e6	−	848757.i	−0.198773	−	0.0547317i
$753$	2.10259e7			1.35135
$754$	2.16406e6	+	145584.i	0.138625	+	0.00932579i
$755$	5.67982e6	−	5.67982e6i	0.362633	−	0.362633i
$756$	1.51222e7	−	1.15211e7i	0.962302	−	0.733147i
$757$	−1.49710e7	−	1.49710e7i	−0.949535	−	0.949535i	0.0492513	−	0.998786i	$-0.484316\pi$
$757$	−1.49710e7	−	1.49710e7i	−0.949535	−	0.949535i	−0.998786	+	0.0492513i	$0.984316\pi$
$758$	3.47477e6	−	3.03672e6i	0.219661	−	0.191969i
$759$			4.68314e6i			0.295075i
$760$	−1.76138e6	+	8.62194e6i	−0.110616	+	0.541466i
$761$		−	1.28130e7i		−	0.802030i	−0.916072	−	0.401015i	$-0.868658\pi$
$761$		−	1.28130e7i		−	0.802030i	0.916072	−	0.401015i	$-0.131342\pi$
$762$	−1.76398e7	−	2.01843e7i	−1.10054	−	1.25929i
$763$	−7.53548e6	−	7.53548e6i	−0.468597	−	0.468597i
$764$	−2.55131e7	−	3.44832e6i	−1.58136	−	0.213734i
$765$	−5.53900e6	+	5.53900e6i	−0.342198	+	0.342198i
$766$	1.37445e6	−	2.04307e7i	0.0846361	−	1.25809i
$767$	6.36015e6			0.390372
$768$	−2.96761e7	+	7.51498e6i	−1.81553	+	0.459753i
$769$	−4.01336e6			−0.244733			−0.122366	−	0.992485i	$-0.539048\pi$
$769$	−4.01336e6			−0.244733			−0.122366	+	0.992485i	$0.539048\pi$
$770$	−164201.	+	2.44079e6i	−0.00998040	+	0.148355i
$771$	3.73992e7	−	3.73992e7i	2.26582	−	2.26582i
$772$	−7.83666e6	−	1.05919e6i	−0.473247	−	0.0639635i
$773$	1.37735e7	+	1.37735e7i	0.829081	+	0.829081i	0.987390	−	0.158309i	$-0.0506041\pi$
$773$	1.37735e7	+	1.37735e7i	0.829081	+	0.829081i	−0.158309	+	0.987390i	$0.550604\pi$
$774$	1.80286e7	+	2.06293e7i	1.08171	+	1.23775i
$775$			1.35351e7i			0.809483i
$776$	−1.42019e6	+	6.95183e6i	−0.0846626	+	0.414424i
$777$			8.89626e6i			0.528634i
$778$	−1.73661e7	+	1.51768e7i	−1.02862	+	0.898942i
$779$	−5.61714e6	−	5.61714e6i	−0.331643	−	0.331643i
$780$	2.41721e7	−	1.84159e7i	1.42258	−	1.08382i
$781$	3.24404e6	−	3.24404e6i	0.190309	−	0.190309i
$782$	1.49508e6	+	100580.i	0.0874276	+	0.00588156i
$783$	5.05037e6			0.294387
$784$	1.35464e7	+	3.72998e6i	0.787109	+	0.216729i
$785$	−1.33895e7			−0.775514
$786$	3.33026e7	+	2.24038e6i	1.92274	+	0.129350i
$787$	−1.67606e7	+	1.67606e7i	−0.964612	+	0.964612i	−0.999395	−	0.0347829i	$-0.988926\pi$
$787$	−1.67606e7	+	1.67606e7i	−0.964612	+	0.964612i	0.0347829	+	0.999395i	$0.488926\pi$
$788$	−8.11586e6	−	1.06526e7i	−0.465606	−	0.611138i
$789$	3.65027e7	+	3.65027e7i	2.08753	+	2.08753i
$790$	9.87510e6	−	8.63018e6i	0.562955	−	0.491985i
$791$		−	4.13863e6i		−	0.235188i
$792$	−1.18161e7	−	1.78834e7i	−0.669362	−	1.01306i
$793$		−	805387.i		−	0.0454801i
$794$	1.53445e7	+	1.75580e7i	0.863778	+	0.988380i
$795$	2.12481e7	+	2.12481e7i	1.19235	+	1.19235i
$796$	1.08124e6	−	7.99979e6i	0.0604840	−	0.447503i
$797$	−1.27890e6	+	1.27890e6i	−0.0713165	+	0.0713165i	−0.741865	−	0.670549i	$-0.766059\pi$
$797$	−1.27890e6	+	1.27890e6i	−0.0713165	+	0.0713165i	0.670549	+	0.741865i	$0.266059\pi$
$798$	747238.	−	1.11074e7i	0.0415386	−	0.617458i
$799$	−1.00194e6			−0.0555234
$800$	−8.31347e6	−	2.90213e6i	−0.459259	−	0.160322i
$801$	−1.57867e7			−0.869381
$802$	767605.	−	1.14102e7i	0.0421407	−	0.626408i
$803$	7.93625e6	−	7.93625e6i	0.434336	−	0.434336i
$804$	−2.55772e6	+	1.89238e7i	−0.139544	+	1.03245i
$805$	1.29893e6	+	1.29893e6i	0.0706471	+	0.0706471i
$806$	−2.69120e7	−	3.07941e7i	−1.45918	−	1.66967i
$807$			3.57086e7i			1.93014i
$808$	2.13250e7	−	1.40901e7i	1.14911	−	0.759251i
$809$			2.13057e6i			0.114452i	0.998361	+	0.0572260i	$0.0182256\pi$
$809$			2.13057e6i			0.114452i	−0.998361	+	0.0572260i	$0.981774\pi$
$810$	2.80132e7	−	2.44816e7i	1.50020	−	1.31108i
$811$	3.29628e6	+	3.29628e6i	0.175983	+	0.175983i	0.789602	−	0.613619i	$-0.210287\pi$
$811$	3.29628e6	+	3.29628e6i	0.175983	+	0.175983i	−0.613619	+	0.789602i	$0.710287\pi$
$812$	−508706.	−	667709.i	−0.0270755	−	0.0355383i
$813$	1.23256e7	−	1.23256e7i	0.654006	−	0.654006i
$814$	6.01664e6	+	404761.i	0.318268	+	0.0214110i
$815$	−7.80944e6			−0.411837
$816$	−8.34105e6	+	4.73938e6i	−0.438526	+	0.249170i
$817$	9.64525e6			0.505543
$818$	−1.86582e7	−	1.25520e6i	−0.974958	−	0.0655889i
$819$	−1.94332e7	+	1.94332e7i	−1.01236	+	1.01236i
$820$	−6.67537e6	+	5.08575e6i	−0.346689	+	0.264132i
$821$	−1.10250e7	−	1.10250e7i	−0.570847	−	0.570847i	0.361518	−	0.932365i	$-0.382258\pi$
$821$	−1.10250e7	−	1.10250e7i	−0.570847	−	0.570847i	−0.932365	+	0.361518i	$0.882258\pi$
$822$	−3.56467e7	+	3.11529e7i	−1.84009	+	1.60812i
$823$			1.19996e7i			0.617545i	0.951136	+	0.308773i	$0.0999182\pi$
$823$			1.19996e7i			0.617545i	−0.951136	+	0.308773i	$0.900082\pi$
$824$	−2.74466e7	−	5.60707e6i	−1.40822	−	0.287686i
$825$		−	8.62415e6i		−	0.441145i
$826$	−1.61977e6	−	1.85342e6i	−0.0826042	−	0.0945199i
$827$	2.02039e7	+	2.02039e7i	1.02724	+	1.02724i	0.999618	+	0.0276211i	$0.00879319\pi$
$827$	2.02039e7	+	2.02039e7i	1.02724	+	1.02724i	0.0276211	+	0.999618i	$0.491207\pi$
$828$	−1.59503e7	−	2.15583e6i	−0.808526	−	0.109279i
$829$	1.63964e7	−	1.63964e7i	0.828633	−	0.828633i	−0.158695	−	0.987328i	$-0.550729\pi$
$829$	1.63964e7	−	1.63964e7i	0.828633	−	0.828633i	0.987328	+	0.158695i	$0.0507285\pi$
$830$	−1.69847e6	+	2.52471e7i	−0.0855779	+	1.27209i
$831$	−4.99078e7			−2.50707
$832$	2.46845e7	−	9.92705e6i	1.23628	−	0.497178i
$833$	4.40318e6			0.219864
$834$	−888947.	+	1.32139e7i	−0.0442549	+	0.657834i
$835$	−9.18819e6	+	9.18819e6i	−0.456051	+	0.456051i
$836$	−7.47810e6	−	1.01073e6i	−0.370063	−	0.0500172i
$837$	−6.73358e7	−	6.73358e7i	−3.32225	−	3.32225i
$838$	9.78921e6	+	1.12013e7i	0.481546	+	0.551010i
$839$		−	2.67951e7i		−	1.31417i	−0.753819	−	0.657083i	$-0.771790\pi$
$839$		−	2.67951e7i		−	1.31417i	0.753819	−	0.657083i	$-0.228210\pi$
$840$	−1.15226e7	−	2.35395e6i	−0.563447	−	0.115106i
$841$			2.02882e7i			0.989128i
$842$	7.55800e6	−	6.60519e6i	0.367389	−	0.321074i
$843$	3.59290e6	+	3.59290e6i	0.174131	+	0.174131i
$844$	−1.86396e7	+	1.42009e7i	−0.900698	+	0.686213i
$845$	−8.15731e6	+	8.15731e6i	−0.393011	+	0.393011i
$846$	1.07379e7	+	722375.i	0.515813	+	0.0347006i
$847$	6.84855e6			0.328012
$848$	1.29974e7	+	2.28747e7i	0.620678	+	1.09236i
$849$	−1.99590e7			−0.950321
$850$	−2.75324e6	−	185220.i	−0.130706	−	0.00879308i
$851$	3.20190e6	−	3.20190e6i	0.151560	−	0.151560i
$852$	1.33663e7	+	1.75441e7i	0.630829	+	0.828002i
$853$	9.90761e6	+	9.90761e6i	0.466226	+	0.466226i	0.900689	−	0.434463i	$-0.143062\pi$
$853$	9.90761e6	+	9.90761e6i	0.466226	+	0.466226i	−0.434463	+	0.900689i	$0.643062\pi$
$854$	−234699.	+	205111.i	−0.0110120	+	0.00962376i
$855$		−	2.96218e7i		−	1.38578i
$856$	1.55958e7	−	1.03046e7i	0.727485	−	0.480671i
$857$			1.79738e6i			0.0835963i	0.999126	+	0.0417982i	$0.0133086\pi$
$857$			1.79738e6i			0.0835963i	−0.999126	+	0.0417982i	$0.986691\pi$
$858$	1.71475e7	+	1.96210e7i	0.795211	+	0.909921i
$859$	8.93866e6	+	8.93866e6i	0.413323	+	0.413323i	0.882894	−	0.469572i	$-0.155592\pi$
$859$	8.93866e6	+	8.93866e6i	0.413323	+	0.413323i	−0.469572	+	0.882894i	$0.655592\pi$
$860$	1.36478e6	−	1.00976e7i	0.0629239	−	0.465555i
$861$	7.50691e6	−	7.50691e6i	0.345106	−	0.345106i
$862$	−49082.2	+	729592.i	−0.00224986	+	0.0334435i
$863$	1.94832e7			0.890498			0.445249	−	0.895407i	$-0.353115\pi$
$863$	1.94832e7			0.890498			0.445249	+	0.895407i	$0.353115\pi$
$864$	5.57965e7	−	2.69209e7i	2.54286	−	1.22689i
$865$	2.13365e7			0.969579
$866$	−2.53183e6	+	3.76348e7i	−0.114720	+	1.70528i
$867$	2.71853e7	−	2.71853e7i	1.22825	−	1.22825i
$868$	−2.11996e6	+	1.56849e7i	−0.0955054	+	0.706616i
$869$	7.95215e6	+	7.95215e6i	0.357220	+	0.357220i
$870$	−2.05592e6	−	2.35249e6i	−0.0920891	−	0.105373i
$871$		−	1.65964e7i		−	0.741255i
$872$	−1.91440e7	−	2.89741e7i	−0.852594	−	1.29038i
$873$		−	2.38839e7i		−	1.06064i
$874$	−4.26669e6	+	3.72880e6i	−0.188935	+	0.165117i
$875$	−7.30941e6	−	7.30941e6i	−0.322747	−	0.322747i
$876$	3.26994e7	+	4.29200e7i	1.43972	+	1.88973i
$877$	3.95987e6	−	3.95987e6i	0.173853	−	0.173853i	−0.614817	−	0.788670i	$-0.710770\pi$
$877$	3.95987e6	−	3.95987e6i	0.173853	−	0.173853i	0.788670	+	0.614817i	$0.210770\pi$
$878$	−2.13735e6	−	143787.i	−0.0935708	−	0.00629484i
$879$	−6.03232e6			−0.263337
$880$	−2.11626e6	+	7.68577e6i	−0.0921218	+	0.334565i
$881$	−1.91087e7			−0.829453			−0.414727	−	0.909946i	$-0.636123\pi$
$881$	−1.91087e7			−0.829453			−0.414727	+	0.909946i	$0.636123\pi$
$882$	−4.71890e7	−	3.17458e6i	−2.04254	−	0.137409i
$883$	−4.24231e6	+	4.24231e6i	−0.183105	+	0.183105i	−0.792707	−	0.609602i	$-0.791329\pi$
$883$	−4.24231e6	+	4.24231e6i	−0.183105	+	0.183105i	0.609602	+	0.792707i	$0.291329\pi$
$884$	6.63225e6	−	5.05290e6i	0.285450	−	0.217475i
$885$	−6.47813e6	−	6.47813e6i	−0.278030	−	0.278030i
$886$	−2.72627e7	+	2.38258e7i	−1.16677	+	1.01968i
$887$			1.89345e7i			0.808061i	0.914746	+	0.404030i	$0.132391\pi$
$887$			1.89345e7i			0.808061i	−0.914746	+	0.404030i	$0.867609\pi$
$888$	−5.80259e6	+	2.84037e7i	−0.246939	+	1.20877i
$889$		−	9.01642e6i		−	0.382631i
$890$	3.86362e6	+	4.42095e6i	0.163501	+	0.187086i
$891$	2.25582e7	+	2.25582e7i	0.951943	+	0.951943i
$892$	3.47070e7	+	4.69095e6i	1.46051	+	0.197401i
$893$	2.67912e6	−	2.67912e6i	0.112425	−	0.112425i
$894$	5.17244e6	−	7.68866e7i	0.216447	−	3.21741i
$895$	−9.44895e6			−0.394299
$896$	−9.17937e6	−	4.66519e6i	−0.381982	−	0.194133i
$897$	1.95673e7			0.811987
$898$	2.52192e6	−	3.74875e7i	0.104362	−	1.55130i
$899$	−2.97315e6	+	2.97315e6i	−0.122693	+	0.122693i
$900$	2.93730e7	+	3.97002e6i	1.20877	+	0.163375i
$901$	5.82999e6	+	5.82999e6i	0.239252	+	0.239252i
$902$	−4.73546e6	−	5.41855e6i	−0.193796	−	0.221752i
$903$			1.28902e7i			0.526066i
$904$	2.69942e6	−	1.32137e7i	0.109863	−	0.537778i
$905$		−	4.83899e6i		−	0.196396i
$906$	−2.49337e7	+	2.17904e7i	−1.00917	+	0.881952i
$907$	−5.57532e6	−	5.57532e6i	−0.225036	−	0.225036i	0.585579	−	0.810615i	$-0.300867\pi$
$907$	−5.57532e6	−	5.57532e6i	−0.225036	−	0.225036i	−0.810615	+	0.585579i	$0.800867\pi$
$908$	2.79018e7	−	2.12575e7i	1.12310	−	0.855652i
$909$	−6.08366e7	+	6.08366e7i	−2.44205	+	2.44205i
$910$	1.01982e7	+	686068.i	0.408244	+	0.0274640i
$911$	−3.30115e7			−1.31786			−0.658929	−	0.752205i	$-0.728990\pi$
$911$	−3.30115e7			−1.31786			−0.658929	+	0.752205i	$0.728990\pi$
$912$	9.63059e6	−	3.49761e7i	0.383412	−	1.39247i
$913$	−2.16986e7			−0.861498
$914$	−7.63446e6	−	513597.i	−0.302282	−	0.0203356i
$915$	−820327.	+	820327.i	−0.0323917	+	0.0323917i
$916$	−2.60959e7	−	3.42525e7i	−1.02762	−	1.34882i
$917$	7.93859e6	+	7.93859e6i	0.311760	+	0.311760i
$918$	1.46185e7	−	1.27756e7i	0.572528	−	0.500352i
$919$		−	2.94518e7i		−	1.15033i	−0.818037	−	0.575166i	$-0.804938\pi$
$919$		−	2.94518e7i		−	1.15033i	0.818037	−	0.575166i	$-0.195062\pi$
$920$	3.29994e6	+	4.99439e6i	0.128540	+	0.194542i
$921$		−	3.66346e7i		−	1.42312i
$922$	−1.14364e7	−	1.30861e7i	−0.443060	−	0.506973i
$923$	−1.35544e7	−	1.35544e7i	−0.523691	−	0.523691i
$924$	1.35077e6	−	9.99395e6i	0.0520477	−	0.385085i
$925$	−5.89640e6	+	5.89640e6i	−0.226586	+	0.226586i
$926$	−183898.	+	2.73359e6i	−0.00704774	+	0.104762i
$927$	9.42964e7			3.60409
$928$	−1.18867e6	−	2.46364e6i	−0.0453096	−	0.0939091i
$929$	3.47221e7			1.31998			0.659989	−	0.751275i	$-0.270561\pi$
$929$	3.47221e7			1.31998			0.659989	+	0.751275i	$0.270561\pi$
$930$	−3.95412e6	+	5.87767e7i	−0.149914	+	2.22842i
$931$	−1.17738e7	+	1.17738e7i	−0.445187	+	0.445187i
$932$	2.79724e6	−	2.06959e7i	0.105485	−	0.780451i
$933$	5.64754e6	+	5.64754e6i	0.212400	+	0.212400i
$934$	2.54865e7	+	2.91630e7i	0.955969	+	1.09387i
$935$			2.49821e6i			0.0934545i
$936$	−7.47210e7	+	4.93704e7i	−2.78775	+	1.84195i
$937$			3.02876e7i			1.12698i	0.826123	+	0.563490i	$0.190542\pi$
$937$			3.02876e7i			1.12698i	−0.826123	+	0.563490i	$0.809458\pi$
$938$	−4.83637e6	+	4.22667e6i	−0.179478	+	0.156852i
$939$	3.85675e7	+	3.85675e7i	1.42744	+	1.42744i
$940$	−2.42568e6	−	3.18385e6i	−0.0895392	−	0.117526i
$941$	−529526.	+	529526.i	−0.0194945	+	0.0194945i	−0.716787	−	0.697292i	$-0.754388\pi$
$941$	−529526.	+	529526.i	−0.0194945	+	0.0194945i	0.697292	+	0.716787i	$0.254388\pi$
$942$	5.50732e7	+	3.70497e6i	2.02215	+	0.136037i
$943$	−5.40370e6			−0.197885
$944$	−3.96264e6	−	6.97403e6i	−0.144729	−	0.254715i
$945$	2.38000e7			0.866957
$946$	8.71779e6	+	586477.i	0.316722	+	0.0213070i
$947$	−9.98574e6	+	9.98574e6i	−0.361831	+	0.361831i	−0.864487	−	0.502656i	$-0.832356\pi$
$947$	−9.98574e6	+	9.98574e6i	−0.361831	+	0.361831i	0.502656	+	0.864487i	$0.332356\pi$
$948$	−4.30060e7	+	3.27649e7i	−1.55420	+	1.18410i
$949$	−3.31595e7	−	3.31595e7i	−1.19520	−	1.19520i
$950$	7.85723e6	−	6.86670e6i	0.282462	−	0.246853i
$951$			8.36698e6i			0.299997i
$952$	−3.16153e6	−	645869.i	−0.113059	−	0.0230968i
$953$		−	1.77547e7i		−	0.633258i	−0.948549	−	0.316629i	$-0.897449\pi$
$953$		−	1.77547e7i		−	0.633258i	0.948549	−	0.316629i	$-0.102551\pi$
$954$	−5.82770e7	−	6.66835e7i	−2.07313	−	2.37218i
$955$	−2.27904e7	−	2.27904e7i	−0.808617	−	0.808617i
$956$	3.16371e6	+	427603.i	0.111957	+	0.0151320i
$957$	1.89440e6	−	1.89440e6i	0.0668639	−	0.0668639i
$958$	−3.07612e6	+	4.57256e7i	−0.108290	+	1.60970i
$959$	−1.59235e7			−0.559104
$960$	−3.52537e7	−	1.50313e7i	−1.23460	−	0.526402i
$961$	5.06520e7			1.76925
$962$	1.69119e6	−	2.51389e7i	0.0589188	−	0.875809i
$963$	−4.44921e7	+	4.44921e7i	−1.54603	+	1.54603i
$964$	−8.71800e6	−	1.17831e6i	−0.302151	−	0.0408384i
$965$	−7.00033e6	−	7.00033e6i	−0.241992	−	0.241992i
$966$	−4.98328e6	−	5.70212e6i	−0.171819	−	0.196605i
$967$			1.67748e7i			0.576888i	0.957497	+	0.288444i	$0.0931378\pi$
$967$			1.67748e7i			0.576888i	−0.957497	+	0.288444i	$0.906862\pi$
$968$	2.18658e7	+	4.46697e6i	0.750028	+	0.153223i
$969$		−	1.13688e7i		−	0.388959i
$970$	−6.68851e6	+	5.84531e6i	−0.228244	+	0.199470i
$971$	−1.02779e7	−	1.02779e7i	−0.349829	−	0.349829i	0.510217	−	0.860046i	$-0.329565\pi$
$971$	−1.02779e7	−	1.02779e7i	−0.349829	−	0.349829i	−0.860046	+	0.510217i	$0.829565\pi$
$972$	−5.58451e7	+	4.25466e7i	−1.89592	+	1.44444i
$973$	−3.14990e6	+	3.14990e6i	−0.106663	+	0.106663i
$974$	3.57531e7	+	2.40524e6i	1.20758	+	0.0812382i
$975$	−3.60337e7			−1.21394
$976$	−883123.	+	501790.i	−0.0296754	+	0.0168616i
$977$	8.61733e6			0.288826			0.144413	−	0.989518i	$-0.453871\pi$
$977$	8.61733e6			0.288826			0.144413	+	0.989518i	$0.453871\pi$
$978$	3.21215e7	+	2.16093e6i	1.07386	+	0.0722426i
$979$	−3.56008e6	+	3.56008e6i	−0.118714	+	0.118714i
$980$	1.06600e7	+	1.39919e7i	0.354561	+	0.465384i
$981$	8.26579e7	+	8.26579e7i	2.74228	+	2.74228i
$982$	3.99296e6	−	3.48958e6i	0.132135	−	0.115477i
$983$		−	9.65214e6i		−	0.318596i	−0.987231	−	0.159298i	$-0.949077\pi$
$983$		−	9.65214e6i		−	0.318596i	0.987231	−	0.159298i	$-0.0509230\pi$
$984$	2.88642e7	−	1.90714e7i	0.950324	−	0.627907i
$985$		−	1.67655e7i		−	0.550586i
$986$	−564096.	−	645468.i	−0.0184783	−	0.0211438i
$987$	3.58046e6	+	3.58046e6i	0.116989	+	0.116989i
$988$	−4.22307e6	+	3.12452e7i	−0.137637	+	1.01834i
$989$	4.63938e6	−	4.63938e6i	0.150824	−	0.150824i
$990$	1.80114e6	−	2.67734e7i	0.0584064	−	0.868192i
$991$	3.34127e7			1.08075			0.540377	−	0.841423i	$-0.318282\pi$
$991$	3.34127e7			1.08075			0.540377	+	0.841423i	$0.318282\pi$
$992$	−1.69991e7	+	4.86957e7i	−0.548461	+	1.57113i
$993$	−3.69838e7			−1.19025
$994$	−497948.	+	7.40184e6i	−0.0159852	+	0.237615i
$995$	7.14606e6	−	7.14606e6i	0.228828	−	0.228828i
$996$	1.39722e7	−	1.03376e8i	0.446288	−	3.30195i
$997$	−9.62270e6	−	9.62270e6i	−0.306591	−	0.306591i	0.536995	−	0.843586i	$-0.319559\pi$
$997$	−9.62270e6	−	9.62270e6i	−0.306591	−	0.306591i	−0.843586	+	0.536995i	$0.819559\pi$
$998$	−2.63846e7	−	3.01906e7i	−0.838539	−	0.959500i
$999$		−	5.86680e7i		−	1.85989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.5.6	✓	18
3.2	odd	2		144.6.k.a.37.4		18
4.3	odd	2		64.6.e.a.49.9		18
8.3	odd	2		128.6.e.a.97.1		18
8.5	even	2		128.6.e.b.97.9		18
12.11	even	2		576.6.k.a.433.7		18
16.3	odd	4		64.6.e.a.17.9		18
16.5	even	4		128.6.e.b.33.9		18
16.11	odd	4		128.6.e.a.33.1		18
16.13	even	4	inner	16.6.e.a.13.6	yes	18
32.3	odd	8		1024.6.a.l.1.18		18
32.13	even	8		1024.6.a.k.1.18		18
32.19	odd	8		1024.6.a.l.1.1		18
32.29	even	8		1024.6.a.k.1.1		18
48.29	odd	4		144.6.k.a.109.4		18
48.35	even	4		576.6.k.a.145.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.6	✓	18	1.1	even	1	trivial
16.6.e.a.13.6	yes	18	16.13	even	4	inner
64.6.e.a.17.9		18	16.3	odd	4
64.6.e.a.49.9		18	4.3	odd	2
128.6.e.a.33.1		18	16.11	odd	4
128.6.e.a.97.1		18	8.3	odd	2
128.6.e.b.33.9		18	16.5	even	4
128.6.e.b.97.9		18	8.5	even	2
144.6.k.a.37.4		18	3.2	odd	2
144.6.k.a.109.4		18	48.29	odd	4
576.6.k.a.145.7		18	48.35	even	4
576.6.k.a.433.7		18	12.11	even	2
1024.6.a.k.1.1		18	32.29	even	8
1024.6.a.k.1.18		18	32.13	even	8
1024.6.a.l.1.1		18	32.19	odd	8
1024.6.a.l.1.18		18	32.3	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)

\(f(q)\)	\(=\)	\(q+(0.379698 - 5.64410i) q^{2} +(-20.6438 + 20.6438i) q^{3} +(-31.7117 - 4.28611i) q^{4} +(-28.3274 - 28.3274i) q^{5} +(108.677 + 124.354i) q^{6} +55.5494i q^{7} +(-36.2321 + 177.356i) q^{8} -609.330i q^{9} +O(q^{10})\)	\(q+(0.379698 - 5.64410i) q^{2} +(-20.6438 + 20.6438i) q^{3} +(-31.7117 - 4.28611i) q^{4} +(-28.3274 - 28.3274i) q^{5} +(108.677 + 124.354i) q^{6} +55.5494i q^{7} +(-36.2321 + 177.356i) q^{8} -609.330i q^{9} +(-170.638 + 149.127i) q^{10} +(-137.411 - 137.411i) q^{11} +(743.129 - 566.167i) q^{12} +(-574.133 + 574.133i) q^{13} +(313.526 + 21.0920i) q^{14} +1169.57 q^{15} +(987.259 + 271.839i) q^{16} +320.902 q^{17} +(-3439.12 - 231.362i) q^{18} +(-858.068 + 858.068i) q^{19} +(776.894 + 1019.72i) q^{20} +(-1146.75 - 1146.75i) q^{21} +(-827.733 + 723.384i) q^{22} +825.465i q^{23} +(-2913.33 - 4409.27i) q^{24} -1520.12i q^{25} +(3022.47 + 3458.46i) q^{26} +(7562.43 + 7562.43i) q^{27} +(238.091 - 1761.56i) q^{28} +(333.912 - 333.912i) q^{29} +(444.083 - 6601.16i) q^{30} -8904.00 q^{31} +(1909.15 - 5468.97i) q^{32} +5673.34 q^{33} +(121.846 - 1811.20i) q^{34} +(1573.57 - 1573.57i) q^{35} +(-2611.66 + 19322.9i) q^{36} +(-3878.91 - 3878.91i) q^{37} +(4517.21 + 5168.83i) q^{38} -23704.5i q^{39} +(6050.40 - 3997.68i) q^{40} +6546.26i q^{41} +(-6907.77 + 6036.94i) q^{42} +(-5620.33 - 5620.33i) q^{43} +(3768.56 + 4946.47i) q^{44} +(-17260.7 + 17260.7i) q^{45} +(4659.00 + 313.428i) q^{46} -3122.27 q^{47} +(-25992.5 + 14768.9i) q^{48} +13721.3 q^{49} +(-8579.69 - 577.186i) q^{50} +(-6624.62 + 6624.62i) q^{51} +(20667.5 - 15745.9i) q^{52} +(18167.5 + 18167.5i) q^{53} +(45554.5 - 39811.6i) q^{54} +7784.97i q^{55} +(-9852.03 - 2012.67i) q^{56} -35427.5i q^{57} +(-1757.85 - 2011.42i) q^{58} +(-5538.91 - 5538.91i) q^{59} +(-37088.9 - 5012.90i) q^{60} +(-701.393 + 701.393i) q^{61} +(-3380.83 + 50255.0i) q^{62} +33847.9 q^{63} +(-30142.5 - 12852.0i) q^{64} +32527.4 q^{65} +(2154.16 - 32020.9i) q^{66} +(-14453.4 + 14453.4i) q^{67} +(-10176.3 - 1375.42i) q^{68} +(-17040.7 - 17040.7i) q^{69} +(-8283.89 - 9478.86i) q^{70} +23608.4i q^{71} +(108068. + 22077.3i) q^{72} +57755.7i q^{73} +(-23365.8 + 20420.1i) q^{74} +(31380.9 + 31380.9i) q^{75} +(30888.5 - 23533.0i) q^{76} +(7633.07 - 7633.07i) q^{77} +(-133791. - 9000.58i) q^{78} -57871.5 q^{79} +(-20266.0 - 35667.0i) q^{80} -164167. q^{81} +(36947.7 + 2485.60i) q^{82} +(78955.3 - 78955.3i) q^{83} +(31450.2 + 41280.4i) q^{84} +(-9090.32 - 9090.32i) q^{85} +(-33855.7 + 29587.6i) q^{86} +13786.4i q^{87} +(29349.3 - 19391.9i) q^{88} -25908.3i q^{89} +(90867.4 + 103975. i) q^{90} +(-31892.7 - 31892.7i) q^{91} +(3538.03 - 26176.9i) q^{92} +(183812. - 183812. i) q^{93} +(-1185.52 + 17622.4i) q^{94} +48613.7 q^{95} +(73488.0 + 152312. i) q^{96} +39197.0 q^{97} +(5209.95 - 77444.2i) q^{98} +(-83728.4 + 83728.4i) 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