LMFDB - Embedded newform 19.5.f.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,5,Mod(2,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.96402929859$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	19.2
Dual form			19.5.f.a.10.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.43376 + 0.781791i) q^{2} +(6.29743 - 7.50499i) q^{3} +(4.01191 + 1.46022i) q^{4} +(-26.3200 + 9.57971i) q^{5} +(33.7886 - 28.3520i) q^{6} +(37.8762 + 65.6035i) q^{7} +(-45.7374 - 26.4065i) q^{8} +(-2.60170 - 14.7550i) q^{9} +O(q^{10})$	\(q+(4.43376 + 0.781791i) q^{2} +(6.29743 - 7.50499i) q^{3} +(4.01191 + 1.46022i) q^{4} +(-26.3200 + 9.57971i) q^{5} +(33.7886 - 28.3520i) q^{6} +(37.8762 + 65.6035i) q^{7} +(-45.7374 - 26.4065i) q^{8} +(-2.60170 - 14.7550i) q^{9} +(-124.186 + 21.8973i) q^{10} +(46.3196 - 80.2278i) q^{11} +(36.2236 - 20.9137i) q^{12} +(-105.304 - 125.496i) q^{13} +(116.646 + 320.481i) q^{14} +(-93.8531 + 257.859i) q^{15} +(-234.473 - 196.746i) q^{16} +(27.7313 - 157.272i) q^{17} -67.4538i q^{18} +(360.786 - 12.4226i) q^{19} -119.582 q^{20} +(730.876 + 128.873i) q^{21} +(268.091 - 319.498i) q^{22} +(57.4137 + 20.8969i) q^{23} +(-486.209 + 176.966i) q^{24} +(122.196 - 102.535i) q^{25} +(-368.779 - 638.744i) q^{26} +(560.126 + 323.389i) q^{27} +(56.1606 + 318.503i) q^{28} +(257.731 - 45.4449i) q^{29} +(-617.714 + 1069.91i) q^{30} +(-1554.50 + 897.490i) q^{31} +(-342.620 - 408.319i) q^{32} +(-310.415 - 852.858i) q^{33} +(245.907 - 675.624i) q^{34} +(-1625.37 - 1363.84i) q^{35} +(11.1076 - 62.9946i) q^{36} +1743.86i q^{37} +(1609.35 + 226.980i) q^{38} -1604.99 q^{39} +(1456.78 + 256.869i) q^{40} +(407.163 - 485.238i) q^{41} +(3139.78 + 1142.78i) q^{42} +(2489.00 - 905.922i) q^{43} +(302.980 - 254.230i) q^{44} +(209.825 + 363.428i) q^{45} +(238.221 + 137.537i) q^{46} +(-700.829 - 3974.60i) q^{47} +(-2953.15 + 520.721i) q^{48} +(-1668.71 + 2890.29i) q^{49} +(621.948 - 359.082i) q^{50} +(-1005.69 - 1198.53i) q^{51} +(-239.217 - 657.244i) q^{52} +(-929.916 + 2554.92i) q^{53} +(2230.64 + 1871.73i) q^{54} +(-450.573 + 2555.33i) q^{55} -4000.71i q^{56} +(2178.80 - 2785.93i) q^{57} +1178.24 q^{58} +(-3146.82 - 554.869i) q^{59} +(-753.060 + 897.462i) q^{60} +(2403.35 + 874.750i) q^{61} +(-7593.91 + 2763.96i) q^{62} +(869.434 - 729.542i) q^{63} +(1248.79 + 2162.96i) q^{64} +(3973.81 + 2294.28i) q^{65} +(-709.547 - 4024.04i) q^{66} +(3.17299 - 0.559484i) q^{67} +(340.906 - 590.466i) q^{68} +(518.390 - 299.293i) q^{69} +(-6140.23 - 7317.64i) q^{70} +(775.375 + 2130.33i) q^{71} +(-270.632 + 743.555i) q^{72} +(-2431.28 - 2040.09i) q^{73} +(-1363.34 + 7731.86i) q^{74} -1562.79i q^{75} +(1465.58 + 476.987i) q^{76} +7017.63 q^{77} +(-7116.13 - 1254.76i) q^{78} +(-3534.31 + 4212.03i) q^{79} +(8056.11 + 2932.18i) q^{80} +(7094.78 - 2582.29i) q^{81} +(2184.61 - 1833.11i) q^{82} +(-2877.77 - 4984.45i) q^{83} +(2744.03 + 1584.26i) q^{84} +(776.730 + 4405.06i) q^{85} +(11743.9 - 2070.76i) q^{86} +(1281.98 - 2220.46i) q^{87} +(-4237.08 + 2446.28i) q^{88} +(-2045.12 - 2437.28i) q^{89} +(646.188 + 1775.39i) q^{90} +(4244.47 - 11661.6i) q^{91} +(199.825 + 167.673i) q^{92} +(-3053.70 + 17318.4i) q^{93} -18170.3i q^{94} +(-9376.90 + 3783.19i) q^{95} -5222.05 q^{96} +(-1301.49 - 229.488i) q^{97} +(-9658.26 + 11510.3i) q^{98} +(-1304.27 - 474.715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9	\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9} - 153 q^{10} - 48 q^{11} + 855 q^{12} + 555 q^{13} - 399 q^{14} - 1647 q^{15} - 2112 q^{16} + 39 q^{17} - 12 q^{19} + 2886 q^{20} + 912 q^{21} + 1386 q^{22} + 1074 q^{23} + 168 q^{24} + 2448 q^{25} - 3675 q^{26} + 1215 q^{27} + 2316 q^{28} - 1743 q^{29} + 2580 q^{30} - 2817 q^{31} - 6039 q^{32} - 7368 q^{33} - 8460 q^{34} - 1326 q^{35} - 4581 q^{36} + 2892 q^{38} + 7164 q^{39} + 4482 q^{40} + 6150 q^{41} + 22299 q^{42} + 2091 q^{43} + 34053 q^{44} + 3165 q^{45} + 7326 q^{46} + 4539 q^{47} - 44943 q^{48} + 102 q^{49} - 51876 q^{50} - 25836 q^{51} - 3279 q^{52} - 11607 q^{53} + 6069 q^{54} - 7044 q^{55} + 2532 q^{57} + 13644 q^{58} - 681 q^{59} + 63654 q^{60} + 44346 q^{61} + 14796 q^{62} + 53388 q^{63} + 939 q^{64} + 3636 q^{65} + 11148 q^{66} - 52089 q^{67} + 5262 q^{68} - 54954 q^{69} - 69999 q^{70} - 24504 q^{71} - 101118 q^{72} - 6666 q^{73} - 9675 q^{74} - 6462 q^{76} + 48918 q^{77} + 56871 q^{78} + 41043 q^{79} + 65649 q^{80} + 2919 q^{81} + 114711 q^{82} - 17598 q^{83} + 11115 q^{84} + 52344 q^{85} - 55716 q^{86} + 2121 q^{87} - 69057 q^{88} - 11706 q^{89} - 41394 q^{90} - 84249 q^{91} - 88668 q^{92} - 60321 q^{93} + 93405 q^{95} + 167166 q^{96} + 4401 q^{97} + 69381 q^{98} + 58386 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9 - 153 * q^10 - 48 * q^11 + 855 * q^12 + 555 * q^13 - 399 * q^14 - 1647 * q^15 - 2112 * q^16 + 39 * q^17 - 12 * q^19 + 2886 * q^20 + 912 * q^21 + 1386 * q^22 + 1074 * q^23 + 168 * q^24 + 2448 * q^25 - 3675 * q^26 + 1215 * q^27 + 2316 * q^28 - 1743 * q^29 + 2580 * q^30 - 2817 * q^31 - 6039 * q^32 - 7368 * q^33 - 8460 * q^34 - 1326 * q^35 - 4581 * q^36 + 2892 * q^38 + 7164 * q^39 + 4482 * q^40 + 6150 * q^41 + 22299 * q^42 + 2091 * q^43 + 34053 * q^44 + 3165 * q^45 + 7326 * q^46 + 4539 * q^47 - 44943 * q^48 + 102 * q^49 - 51876 * q^50 - 25836 * q^51 - 3279 * q^52 - 11607 * q^53 + 6069 * q^54 - 7044 * q^55 + 2532 * q^57 + 13644 * q^58 - 681 * q^59 + 63654 * q^60 + 44346 * q^61 + 14796 * q^62 + 53388 * q^63 + 939 * q^64 + 3636 * q^65 + 11148 * q^66 - 52089 * q^67 + 5262 * q^68 - 54954 * q^69 - 69999 * q^70 - 24504 * q^71 - 101118 * q^72 - 6666 * q^73 - 9675 * q^74 - 6462 * q^76 + 48918 * q^77 + 56871 * q^78 + 41043 * q^79 + 65649 * q^80 + 2919 * q^81 + 114711 * q^82 - 17598 * q^83 + 11115 * q^84 + 52344 * q^85 - 55716 * q^86 + 2121 * q^87 - 69057 * q^88 - 11706 * q^89 - 41394 * q^90 - 84249 * q^91 - 88668 * q^92 - 60321 * q^93 + 93405 * q^95 + 167166 * q^96 + 4401 * q^97 + 69381 * q^98 + 58386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.43376	+	0.781791i	1.10844	+	0.195448i	0.697759	−	0.716332i	$-0.254180\pi$
$2$	4.43376	+	0.781791i	1.10844	+	0.195448i	0.410679	+	0.911780i	$0.365292\pi$
$3$	6.29743	−	7.50499i	0.699715	−	0.833888i	−0.292779	−	0.956180i	$-0.594580\pi$
$3$	6.29743	−	7.50499i	0.699715	−	0.833888i	0.992494	+	0.122292i	$0.0390245\pi$
$4$	4.01191	+	1.46022i	0.250744	+	0.0912635i
$5$	−26.3200	+	9.57971i	−1.05280	+	0.383189i	−0.809719	−	0.586817i	$-0.800381\pi$
$5$	−26.3200	+	9.57971i	−1.05280	+	0.383189i	−0.243082	+	0.970006i	$0.578159\pi$
$6$	33.7886	−	28.3520i	0.938573	−	0.787556i
$7$	37.8762	+	65.6035i	0.772983	+	1.33885i	0.935921	+	0.352210i	$0.114570\pi$
$7$	37.8762	+	65.6035i	0.772983	+	1.33885i	−0.162938	+	0.986636i	$0.552097\pi$
$8$	−45.7374	−	26.4065i	−0.714647	−	0.412602i
$9$	−2.60170	−	14.7550i	−0.0321197	−	0.182160i
$10$	−124.186	+	21.8973i	−1.24186	+	0.218973i
$11$	46.3196	−	80.2278i	0.382806	−	0.663040i	−0.608656	−	0.793434i	$-0.708291\pi$
$11$	46.3196	−	80.2278i	0.382806	−	0.663040i	0.991462	+	0.130394i	$0.0416243\pi$
$12$	36.2236	−	20.9137i	0.251553	−	0.145234i
$13$	−105.304	−	125.496i	−0.623098	−	0.742579i	0.358502	−	0.933529i	$-0.383288\pi$
$13$	−105.304	−	125.496i	−0.623098	−	0.742579i	−0.981600	+	0.190950i	$0.938843\pi$
$14$	116.646	+	320.481i	0.595130	+	1.63511i
$15$	−93.8531	+	257.859i	−0.417125	+	1.14604i
$16$	−234.473	−	196.746i	−0.915909	−	0.768539i
$17$	27.7313	−	157.272i	0.0959559	−	0.544193i	−0.898494	−	0.438985i	$-0.855338\pi$
$17$	27.7313	−	157.272i	0.0959559	−	0.544193i	0.994450	−	0.105208i	$-0.0335508\pi$
$18$		−	67.4538i		−	0.208191i
$19$	360.786	−	12.4226i	0.999408	−	0.0344118i
$19$	360.786	−	12.4226i	0.999408	−	0.0344118i
$20$	−119.582			−0.298955
$21$	730.876	+	128.873i	1.65732	+	0.292230i
$22$	268.091	−	319.498i	0.553907	−	0.660121i
$23$	57.4137	+	20.8969i	0.108533	+	0.0395026i	0.395716	−	0.918373i	$-0.370497\pi$
$23$	57.4137	+	20.8969i	0.108533	+	0.0395026i	−0.287183	+	0.957876i	$0.592719\pi$
$24$	−486.209	+	176.966i	−0.844113	+	0.307232i
$25$	122.196	−	102.535i	0.195514	−	0.164055i
$26$	−368.779	−	638.744i	−0.545531	−	0.944887i
$27$	560.126	+	323.389i	0.768348	+	0.443606i
$28$	56.1606	+	318.503i	0.0716334	+	0.406253i
$29$	257.731	−	45.4449i	0.306458	−	0.0540368i	−0.0183045	−	0.999832i	$-0.505827\pi$
$29$	257.731	−	45.4449i	0.306458	−	0.0540368i	0.324762	+	0.945796i	$0.394716\pi$
$30$	−617.714	+	1069.91i	−0.686349	+	1.18879i
$31$	−1554.50	+	897.490i	−1.61758	+	0.933912i	−0.630041	+	0.776562i	$0.716962\pi$
$31$	−1554.50	+	897.490i	−1.61758	+	0.933912i	−0.987543	+	0.157350i	$0.949705\pi$
$32$	−342.620	−	408.319i	−0.334590	−	0.398749i
$33$	−310.415	−	852.858i	−0.285046	−	0.783157i
$34$	245.907	−	675.624i	0.212722	−	0.584450i
$35$	−1625.37	−	1363.84i	−1.32683	−	1.11334i
$36$	11.1076	−	62.9946i	0.00857071	−	0.0486069i
$37$			1743.86i			1.27382i	0.770937	+	0.636911i	$0.219788\pi$
$37$			1743.86i			1.27382i	−0.770937	+	0.636911i	$0.780212\pi$
$38$	1609.35	+	226.980i	1.11451	+	0.157189i
$39$	−1604.99			−1.05522
$40$	1456.78	+	256.869i	0.910486	+	0.160543i
$41$	407.163	−	485.238i	0.242215	−	0.288660i	−0.631218	−	0.775606i	$-0.717445\pi$
$41$	407.163	−	485.238i	0.242215	−	0.288660i	0.873432	+	0.486946i	$0.161889\pi$
$42$	3139.78	+	1142.78i	1.77992	+	0.647837i
$43$	2489.00	−	905.922i	1.34613	−	0.489952i	0.434394	−	0.900723i	$-0.356962\pi$
$43$	2489.00	−	905.922i	1.34613	−	0.489952i	0.911739	+	0.410770i	$0.134740\pi$
$44$	302.980	−	254.230i	0.156498	−	0.131317i
$45$	209.825	+	363.428i	0.103617	+	0.179470i
$46$	238.221	+	137.537i	0.112581	+	0.0649987i
$47$	−700.829	−	3974.60i	−0.317261	−	1.79928i	−0.559253	−	0.828997i	$-0.688912\pi$
$47$	−700.829	−	3974.60i	−0.317261	−	1.79928i	0.241992	−	0.970278i	$-0.422199\pi$
$48$	−2953.15	+	520.721i	−1.28175	+	0.226007i
$49$	−1668.71	+	2890.29i	−0.695007	+	1.20379i
$50$	621.948	−	359.082i	0.248779	−	0.143633i
$51$	−1005.69	−	1198.53i	−0.386654	−	0.460796i
$52$	−239.217	−	657.244i	−0.0884680	−	0.243064i
$53$	−929.916	+	2554.92i	−0.331049	+	0.909549i	0.656791	+	0.754073i	$0.271913\pi$
$53$	−929.916	+	2554.92i	−0.331049	+	0.909549i	−0.987840	+	0.155476i	$0.950309\pi$
$54$	2230.64	+	1871.73i	0.764965	+	0.641882i
$55$	−450.573	+	2555.33i	−0.148950	+	0.844737i
$56$		−	4000.71i		−	1.27574i
$57$	2178.80	−	2785.93i	0.670605	−	0.857472i
$58$	1178.24			0.350251
$59$	−3146.82	−	554.869i	−0.903999	−	0.159399i	−0.297722	−	0.954653i	$-0.596227\pi$
$59$	−3146.82	−	554.869i	−0.903999	−	0.159399i	−0.606277	+	0.795253i	$0.707338\pi$
$60$	−753.060	+	897.462i	−0.209183	+	0.249295i
$61$	2403.35	+	874.750i	0.645890	+	0.235085i	0.644133	−	0.764914i	$-0.277219\pi$
$61$	2403.35	+	874.750i	0.645890	+	0.235085i	0.00175698	+	0.999998i	$0.499441\pi$
$62$	−7593.91	+	2763.96i	−1.97552	+	0.719032i
$63$	869.434	−	729.542i	0.219056	−	0.183810i
$64$	1248.79	+	2162.96i	0.304880	+	0.528067i
$65$	3973.81	+	2294.28i	0.940547	+	0.543025i
$66$	−709.547	−	4024.04i	−0.162890	−	0.923793i
$67$	3.17299	−	0.559484i	0.000706837	−	0.000124634i	−0.173295	−	0.984870i	$-0.555441\pi$
$67$	3.17299	−	0.559484i	0.000706837	−	0.000124634i	0.174002	+	0.984745i	$0.444330\pi$
$68$	340.906	−	590.466i	0.0737253	−	0.127696i
$69$	518.390	−	299.293i	0.108883	−	0.0628634i
$70$	−6140.23	−	7317.64i	−1.25311	−	1.49340i
$71$	775.375	+	2130.33i	0.153814	+	0.422600i	0.992535	−	0.121961i	$-0.0389184\pi$
$71$	775.375	+	2130.33i	0.153814	+	0.422600i	−0.838721	+	0.544561i	$0.816696\pi$
$72$	−270.632	+	743.555i	−0.0522052	+	0.143433i
$73$	−2431.28	−	2040.09i	−0.456237	−	0.382828i	0.385507	−	0.922705i	$-0.374026\pi$
$73$	−2431.28	−	2040.09i	−0.456237	−	0.382828i	−0.841744	+	0.539877i	$0.818471\pi$
$74$	−1363.34	+	7731.86i	−0.248965	+	1.41195i
$75$		−	1562.79i		−	0.277829i
$76$	1465.58	+	476.987i	0.253736	+	0.0825809i
$77$	7017.63			1.18361
$78$	−7116.13	−	1254.76i	−1.16965	−	0.206240i
$79$	−3534.31	+	4212.03i	−0.566305	+	0.674896i	−0.970868	−	0.239614i	$-0.922979\pi$
$79$	−3534.31	+	4212.03i	−0.566305	+	0.674896i	0.404563	+	0.914510i	$0.367424\pi$
$80$	8056.11	+	2932.18i	1.25877	+	0.458154i
$81$	7094.78	−	2582.29i	1.08136	−	0.393582i
$82$	2184.61	−	1833.11i	0.324898	−	0.272622i
$83$	−2877.77	−	4984.45i	−0.417734	−	0.723537i	0.577977	−	0.816053i	$-0.303842\pi$
$83$	−2877.77	−	4984.45i	−0.417734	−	0.723537i	−0.995711	+	0.0925159i	$0.970509\pi$
$84$	2744.03	+	1584.26i	0.388893	+	0.224527i
$85$	776.730	+	4405.06i	0.107506	+	0.609696i
$86$	11743.9	−	2070.76i	1.58787	−	0.279984i
$87$	1281.98	−	2220.46i	0.169372	−	0.293362i
$88$	−4237.08	+	2446.28i	−0.547143	+	0.315893i
$89$	−2045.12	−	2437.28i	−0.258189	−	0.307698i	0.621342	−	0.783540i	$-0.286588\pi$
$89$	−2045.12	−	2437.28i	−0.258189	−	0.307698i	−0.879531	+	0.475842i	$0.842143\pi$
$90$	646.188	+	1775.39i	0.0797763	+	0.219184i
$91$	4244.47	−	11661.6i	0.512555	−	1.40823i
$92$	199.825	+	167.673i	0.0236088	+	0.0198101i
$93$	−3053.70	+	17318.4i	−0.353069	+	2.00236i
$94$		−	18170.3i		−	2.05639i
$95$	−9376.90	+	3783.19i	−1.03899	+	0.419190i
$96$	−5222.05			−0.566629
$97$	−1301.49	−	229.488i	−0.138324	−	0.0243902i	0.104058	−	0.994571i	$-0.466817\pi$
$97$	−1301.49	−	229.488i	−0.138324	−	0.0243902i	−0.242381	+	0.970181i	$0.577929\pi$
$98$	−9658.26	+	11510.3i	−1.00565	+	1.19849i
$99$	−1304.27	−	474.715i	−0.133075	−	0.0484353i
$100$	639.962	−	232.927i	0.0639962	−	0.0232927i
$101$	13994.4	−	11742.7i	1.37186	−	1.15113i	0.399747	−	0.916626i	$-0.369098\pi$
$101$	13994.4	−	11742.7i	1.37186	−	1.15113i	0.972115	−	0.234504i	$-0.0753464\pi$
$102$	−3521.97	−	6100.23i	−0.338521	−	0.586335i
$103$	5152.15	+	2974.59i	0.485639	+	0.280384i	0.722764	−	0.691095i	$-0.242872\pi$
$103$	5152.15	+	2974.59i	0.485639	+	0.280384i	−0.237124	+	0.971479i	$0.576205\pi$
$104$	1502.40	+	8520.56i	0.138906	+	0.787774i
$105$	−20471.3	+	3609.64i	−1.85680	+	0.327405i
$106$	−6120.43	+	10600.9i	−0.544716	+	0.943477i
$107$	−12416.4	+	7168.64i	−1.08450	+	0.626136i	−0.932107	−	0.362184i	$-0.882031\pi$
$107$	−12416.4	+	7168.64i	−1.08450	+	0.626136i	−0.152393	+	0.988320i	$0.548698\pi$
$108$	1774.96	+	2115.31i	0.152174	+	0.181354i
$109$	−3832.83	−	10530.6i	−0.322601	−	0.886340i	−0.989928	−	0.141575i	$-0.954784\pi$
$109$	−3832.83	−	10530.6i	−0.322601	−	0.886340i	0.667326	−	0.744766i	$-0.267439\pi$
$110$	−3995.46	+	10977.4i	−0.330204	+	0.907227i
$111$	13087.7	+	10981.9i	1.06222	+	0.891312i
$112$	4026.29	−	22834.2i	0.320973	−	1.82033i
$113$			4052.00i			0.317331i	0.987332	+	0.158665i	$0.0507191\pi$
$113$			4052.00i			0.317331i	−0.987332	+	0.158665i	$0.949281\pi$
$114$	11838.3	−	10648.8i	0.910916	−	0.819388i
$115$	−1711.32			−0.129400
$116$	1100.35	+	194.022i	0.0817741	+	0.0144190i
$117$	−1577.72	+	1880.25i	−0.115254	+	0.137355i
$118$	−13518.4	−	4920.31i	−0.970873	−	0.353369i
$119$	11367.9	−	4137.59i	0.802763	−	0.292182i
$120$	11101.8	−	9315.49i	0.770956	−	0.646909i
$121$	3029.50	+	5247.24i	0.206919	+	0.358394i
$122$	9972.02	+	5757.35i	0.669982	+	0.386814i
$123$	−1077.62	−	6111.50i	−0.0712290	−	0.403960i
$124$	−7547.03	+	1330.75i	−0.490832	+	0.0865469i
$125$	6518.92	−	11291.1i	0.417211	−	0.722631i
$126$	4425.21	−	2554.89i	0.278736	−	0.160928i
$127$	2822.64	+	3363.89i	0.175004	+	0.208561i	0.846415	−	0.532523i	$-0.178756\pi$
$127$	2822.64	+	3363.89i	0.175004	+	0.208561i	−0.671412	+	0.741085i	$0.734312\pi$
$128$	6762.70	+	18580.4i	0.412762	+	1.13406i
$129$	8875.38	−	24384.9i	0.533344	−	1.46535i
$130$	15825.3	+	13279.0i	0.936406	+	0.785738i
$131$	−54.3381	+	308.167i	−0.00316637	+	0.0179574i	−0.986350	−	0.164662i	$-0.947347\pi$
$131$	−54.3381	+	308.167i	−0.00316637	+	0.0179574i	0.983184	+	0.182620i	$0.0584577\pi$
$132$		−	3874.86i		−	0.222386i
$133$	14480.2	+	23198.3i	0.818598	+	1.31145i
$134$	14.5057			0.000807845
$135$	−17840.5	−	3145.76i	−0.978903	−	0.172607i
$136$	−5421.35	+	6460.92i	−0.293110	+	0.349314i
$137$	−1083.74	−	394.449i	−0.0577409	−	0.0210160i	0.312988	−	0.949757i	$-0.398670\pi$
$137$	−1083.74	−	394.449i	−0.0577409	−	0.0210160i	−0.370729	+	0.928741i	$0.620892\pi$
$138$	2532.40	−	921.718i	0.132976	−	0.0483994i
$139$	−3942.26	+	3307.95i	−0.204040	+	0.171210i	−0.739082	−	0.673616i	$-0.764740\pi$
$139$	−3942.26	+	3307.95i	−0.204040	+	0.171210i	0.535042	+	0.844826i	$0.320296\pi$
$140$	−4529.31	−	7845.00i	−0.231087	−	0.400255i
$141$	−34242.8	−	19770.1i	−1.72239	−	0.994420i
$142$	1772.35	+	10051.5i	0.0878970	+	0.498489i
$143$	−14945.9	+	2635.36i	−0.730886	+	0.128875i
$144$	−2292.95	+	3971.51i	−0.110578	+	0.191527i
$145$	−6348.14	+	3665.10i	−0.301933	+	0.174321i
$146$	−9184.80	−	10946.0i	−0.430888	−	0.513512i
$147$	11183.0	+	30725.1i	0.517517	+	1.42187i
$148$	−2546.41	+	6996.22i	−0.116253	+	0.319404i
$149$	−21907.0	−	18382.2i	−0.986758	−	0.827988i	−0.00166273	−	0.999999i	$-0.500529\pi$
$149$	−21907.0	−	18382.2i	−0.986758	−	0.827988i	−0.985095	+	0.172010i	$0.944974\pi$
$150$	1221.77	−	6929.01i	0.0543010	−	0.307956i
$151$		−	7058.91i		−	0.309588i	−0.987947	−	0.154794i	$-0.950529\pi$
$151$		−	7058.91i		−	0.309588i	0.987947	−	0.154794i	$-0.0494713\pi$
$152$	−16829.5	−	8958.93i	−0.728422	−	0.387765i
$153$	−2392.69			−0.102212
$154$	31114.5	+	5486.32i	1.31196	+	0.231334i
$155$	32316.8	−	38513.6i	1.34513	−	1.60306i
$156$	−6439.07	−	2343.63i	−0.264590	−	0.0963030i
$157$	−20578.9	+	7490.10i	−0.834877	+	0.303870i	−0.723859	−	0.689948i	$-0.757633\pi$
$157$	−20578.9	+	7490.10i	−0.834877	+	0.303870i	−0.111018	+	0.993818i	$0.535411\pi$
$158$	−18963.2	+	15912.0i	−0.759621	+	0.637398i
$159$	13318.6	+	23068.5i	0.526822	+	0.912482i
$160$	12929.3	+	7464.76i	0.505053	+	0.291592i
$161$	803.704	+	4558.03i	0.0310059	+	0.175843i
$162$	33475.3	−	5902.61i	1.27554	−	0.224913i
$163$	−10384.2	+	17985.9i	−0.390838	+	0.676952i	−0.992560	−	0.121754i	$-0.961148\pi$
$163$	−10384.2	+	17985.9i	−0.390838	+	0.676952i	0.601722	+	0.798706i	$0.294482\pi$
$164$	2342.05	−	1352.18i	0.0870781	−	0.0502745i
$165$	16340.3	+	19473.6i	0.600193	+	0.715282i
$166$	−8862.54	−	24349.6i	−0.321619	−	0.883642i
$167$	2980.83	−	8189.76i	0.106882	−	0.293655i	−0.874710	−	0.484647i	$-0.838948\pi$
$167$	2980.83	−	8189.76i	0.106882	−	0.293655i	0.981592	+	0.190992i	$0.0611703\pi$
$168$	−30025.3	−	25194.2i	−1.06382	−	0.892653i
$169$	299.183	−	1696.75i	0.0104752	−	0.0594080i
$170$			20138.2i			0.696823i
$171$	−1121.95	−	5291.06i	−0.0383691	−	0.180947i
$172$	11308.5			0.382250
$173$	396.109	+	69.8447i	0.0132349	+	0.00233368i	0.180262	−	0.983619i	$-0.442306\pi$
$173$	396.109	+	69.8447i	0.0132349	+	0.00233368i	−0.167027	+	0.985952i	$0.553417\pi$
$174$	7419.92	−	8842.71i	0.245076	−	0.292070i
$175$	11355.0	+	4132.86i	0.370774	+	0.134951i
$176$	−26645.2	+	9698.06i	−0.860188	+	0.313083i
$177$	−23981.2	+	20122.6i	−0.765463	+	0.642300i
$178$	−7162.11	−	12405.1i	−0.226048	−	0.391527i
$179$	21293.2	+	12293.6i	0.664560	+	0.383684i	0.794012	−	0.607902i	$-0.207989\pi$
$179$	21293.2	+	12293.6i	0.664560	+	0.383684i	−0.129453	+	0.991586i	$0.541322\pi$
$180$	311.116	+	1764.43i	0.00960235	+	0.0544577i
$181$	49214.8	−	8677.90i	1.50224	−	0.264885i	0.638813	−	0.769362i	$-0.279426\pi$
$181$	49214.8	−	8677.90i	1.50224	−	0.264885i	0.863425	+	0.504477i	$0.168315\pi$
$182$	27935.9	−	48386.3i	0.843372	−	1.46076i
$183$	21700.0	−	12528.5i	0.647973	−	0.374107i
$184$	−2074.14	−	2471.87i	−0.0612636	−	0.0730111i
$185$	−16705.7	−	45898.5i	−0.488114	−	1.34108i
$186$	−27078.7	+	74398.1i	−0.782712	+	2.15048i
$187$	−11333.1	−	9509.58i	−0.324089	−	0.271943i
$188$	2992.11	−	16969.1i	0.0846568	−	0.480112i
$189$			48994.9i			1.37160i
$190$	−44532.6	+	9442.98i	−1.23359	+	0.261578i
$191$	4566.04			0.125162			0.0625811	−	0.998040i	$-0.480067\pi$
$191$	4566.04			0.125162			0.0625811	+	0.998040i	$0.480067\pi$
$192$	24097.2	+	4248.98i	0.653677	+	0.115261i
$193$	−4423.96	+	5272.27i	−0.118767	+	0.141541i	−0.822152	−	0.569268i	$-0.807227\pi$
$193$	−4423.96	+	5272.27i	−0.118767	+	0.141541i	0.703385	+	0.710809i	$0.251671\pi$
$194$	−5591.07	−	2034.98i	−0.148556	−	0.0540701i
$195$	42243.4	−	15375.3i	1.11094	−	0.404348i
$196$	−10915.2	+	9158.91i	−0.284131	+	0.238414i
$197$	5586.45	+	9676.02i	0.143947	+	0.249324i	0.928980	−	0.370131i	$-0.120687\pi$
$197$	5586.45	+	9676.02i	0.143947	+	0.249324i	−0.785032	+	0.619455i	$0.787354\pi$
$198$	−5411.68	−	3124.43i	−0.138039	−	0.0796968i
$199$	−7406.79	−	42006.0i	−0.187035	−	1.06073i	−0.923312	−	0.384050i	$-0.874529\pi$
$199$	−7406.79	−	42006.0i	−0.187035	−	1.06073i	0.736277	−	0.676680i	$-0.236582\pi$
$200$	−8296.52	+	1462.90i	−0.207413	+	0.0365725i
$201$	15.7828	−	27.3366i	0.000390653	−	0.000676631i
$202$	71227.9	−	41123.5i	1.74561	−	1.00783i
$203$	12743.2	+	15186.8i	0.309234	+	0.368530i
$204$	−2284.61	−	6276.92i	−0.0548974	−	0.150829i
$205$	−6068.10	+	16672.0i	−0.144393	+	0.396716i
$206$	20517.8	+	17216.5i	0.483501	+	0.405705i
$207$	158.959	−	901.504i	0.00370976	−	0.0210391i
$208$			50143.4i			1.15901i
$209$	15714.8	−	29520.5i	0.359763	−	0.675820i
$210$	−93586.6			−2.12214
$211$	36983.5	+	6521.18i	0.830697	+	0.146474i	0.572797	−	0.819697i	$-0.305858\pi$
$211$	36983.5	+	6521.18i	0.830697	+	0.146474i	0.257900	+	0.966172i	$0.416969\pi$
$212$	−7461.48	+	8892.24i	−0.166017	+	0.197852i
$213$	20870.9	+	7596.40i	0.460027	+	0.167436i
$214$	−60655.8	+	22076.9i	−1.32448	+	0.482071i
$215$	−56832.1	+	47687.8i	−1.22947	+	1.03165i
$216$	−17079.1	−	29581.9i	−0.366065	−	0.634043i
$217$	−117757.	−	67987.0i	−2.50073	−	1.44380i
$218$	−8761.09	−	49686.6i	−0.184351	−	1.04551i
$219$	−30621.7	+	5399.43i	−0.638471	+	0.112580i
$220$	−5538.99	+	9593.81i	−0.114442	+	0.198219i
$221$	−22657.2	+	13081.1i	−0.463896	+	0.267831i
$222$	49442.0	+	58922.7i	1.00321	+	1.19557i
$223$	−16417.5	−	45106.6i	−0.330139	−	0.907049i	−0.988075	−	0.153975i	$-0.950793\pi$
$223$	−16417.5	−	45106.6i	−0.330139	−	0.907049i	0.657936	−	0.753074i	$-0.271430\pi$
$224$	13810.0	−	37942.6i	0.275231	−	0.756190i
$225$	−1830.81	−	1536.23i	−0.0361642	−	0.0303453i
$226$	−3167.81	+	17965.6i	−0.0620216	+	0.351742i
$227$			65214.6i			1.26559i	0.774319	+	0.632796i	$0.218093\pi$
$227$			65214.6i			1.26559i	−0.774319	+	0.632796i	$0.781907\pi$
$228$	12809.2	−	7995.38i	0.246406	−	0.153805i
$229$	69793.3			1.33089			0.665446	−	0.746446i	$-0.268241\pi$
$229$	69793.3			1.33089			0.665446	+	0.746446i	$0.268241\pi$
$230$	−7587.56	−	1337.89i	−0.143432	−	0.0252910i
$231$	44193.1	−	52667.3i	0.828191	−	0.987000i
$232$	−12988.0	−	4727.24i	−0.241305	−	0.0878278i
$233$	49673.1	−	18079.5i	0.914976	−	0.333024i	0.158738	−	0.987321i	$-0.449257\pi$
$233$	49673.1	−	18079.5i	0.914976	−	0.333024i	0.756238	+	0.654297i	$0.227035\pi$
$234$	−8465.18	+	7103.13i	−0.154598	+	0.129723i
$235$	56521.4	+	97897.9i	1.02347	+	1.77271i
$236$	−11814.5	−	6821.12i	−0.212125	−	0.122471i
$237$	9354.13	+	53049.9i	0.166536	+	0.944470i
$238$	53637.3	−	9457.71i	0.946920	−	0.166968i
$239$	−24811.7	+	42975.0i	−0.434370	+	0.752351i	−0.997244	−	0.0741917i	$-0.976362\pi$
$239$	−24811.7	+	42975.0i	−0.434370	+	0.752351i	0.562874	+	0.826543i	$0.309696\pi$
$240$	72738.8	−	41995.8i	1.26283	−	0.729093i
$241$	340.622	+	405.937i	0.00586460	+	0.00698916i	0.768969	−	0.639286i	$-0.220770\pi$
$241$	340.622	+	405.937i	0.00586460	+	0.00698916i	−0.763104	+	0.646276i	$0.776326\pi$
$242$	9329.80	+	25633.4i	0.159309	+	0.437699i
$243$	7380.79	−	20278.6i	0.124994	−	0.343419i
$244$	8364.72	+	7018.83i	0.140499	+	0.117892i
$245$	16232.4	−	92058.4i	0.270427	−	1.53367i
$246$		−	27939.4i		−	0.461686i
$247$	−39551.1	−	43969.0i	−0.648283	−	0.720698i
$248$	94798.3			1.54134
$249$	−55530.8	−	9791.58i	−0.895644	−	0.157926i
$250$	37730.6	−	44965.6i	0.603690	−	0.719449i
$251$	−87230.8	−	31749.4i	−1.38459	−	0.503951i	−0.461026	−	0.887387i	$-0.652519\pi$
$251$	−87230.8	−	31749.4i	−1.38459	−	0.503951i	−0.923568	+	0.383436i	$0.874741\pi$
$252$	4553.38	−	1657.29i	0.0717022	−	0.0260975i
$253$	4335.89	−	3638.24i	0.0677388	−	0.0568396i
$254$	9885.03	+	17121.4i	0.153218	+	0.265382i
$255$	37951.3	+	21911.2i	0.583642	+	0.336966i
$256$	8519.01	+	48313.7i	0.129990	+	0.737209i
$257$	−61243.2	+	10798.8i	−0.927239	+	0.163497i	−0.616822	−	0.787103i	$-0.711580\pi$
$257$	−61243.2	+	10798.8i	−0.927239	+	0.163497i	−0.310418	+	0.950600i	$0.600469\pi$
$258$	58415.2	−	101178.i	0.877579	−	1.52001i
$259$	−114403.	+	66050.8i	−1.70545	+	0.984643i
$260$	12592.4	+	15007.1i	0.186278	+	0.221998i
$261$	−1341.08	−	3684.57i	−0.0196867	−	0.0540887i
$262$	−481.844	+	1323.85i	−0.00701946	+	0.0192858i
$263$	59520.0	+	49943.2i	0.860501	+	0.722046i	0.962076	−	0.272782i	$-0.0879437\pi$
$263$	59520.0	+	49943.2i	0.860501	+	0.722046i	−0.101575	+	0.994828i	$0.532388\pi$
$264$	−8323.42	+	47204.5i	−0.119425	+	0.677291i
$265$		−	76154.0i		−	1.08443i
$266$	46065.3	+	114176.i	0.651045	+	1.61366i
$267$	−31170.7			−0.437244
$268$	13.5467	+	2.38865i	0.000188610	+	3.32570e-5i
$269$	−34965.1	+	41669.8i	−0.483204	+	0.575860i	−0.951476	−	0.307724i	$-0.900433\pi$
$269$	−34965.1	+	41669.8i	−0.483204	+	0.575860i	0.468271	+	0.883585i	$0.344877\pi$
$270$	−76641.1	−	27895.1i	−1.05132	−	0.382649i
$271$	−1371.52	+	499.192i	−0.0186751	+	0.00679718i	−0.351341	−	0.936248i	$-0.614274\pi$
$271$	−1371.52	+	499.192i	−0.0186751	+	0.00679718i	0.332666	+	0.943045i	$0.392052\pi$
$272$	−37444.8	+	31419.9i	−0.506121	+	0.424686i
$273$	−60790.8	−	105293.i	−0.815667	−	1.41278i
$274$	−4496.66	−	2596.15i	−0.0598947	−	0.0345802i
$275$	−2566.07	−	14552.9i	−0.0339315	−	0.192435i
$276$	2516.77	−	443.774i	0.0330388	−	0.00582564i
$277$	−23404.6	+	40538.0i	−0.305030	+	0.528327i	−0.977268	−	0.212008i	$-0.932000\pi$
$277$	−23404.6	+	40538.0i	−0.305030	+	0.528327i	0.672238	+	0.740335i	$0.265333\pi$
$278$	−20065.1	+	11584.6i	−0.259629	+	0.149897i
$279$	17286.8	+	20601.5i	0.222078	+	0.264662i
$280$	38325.7	+	105299.i	0.488848	+	1.34310i
$281$	8844.80	−	24300.9i	0.112015	−	0.307758i	−0.871000	−	0.491282i	$-0.836528\pi$
$281$	8844.80	−	24300.9i	0.112015	−	0.307758i	0.983015	+	0.183524i	$0.0587506\pi$
$282$	−136368.	−	114426.i	−1.71480	−	1.43889i
$283$	21117.1	−	119761.i	0.263671	−	1.49535i	−0.509122	−	0.860694i	$-0.670030\pi$
$283$	21117.1	−	119761.i	0.263671	−	1.49535i	0.772793	−	0.634658i	$-0.218859\pi$
$284$			9678.89i			0.120002i
$285$	−30657.6	+	94198.0i	−0.377441	+	1.15972i
$286$	−68326.7			−0.835331
$287$	47255.0	+	8332.34i	0.573699	+	0.101159i
$288$	−5133.33	+	6117.66i	−0.0618891	+	0.0737565i
$289$	54518.7	+	19843.2i	0.652754	+	0.237583i
$290$	−31011.4	+	11287.2i	−0.368745	+	0.134212i
$291$	−9918.34	+	8322.48i	−0.117126	+	0.0982803i
$292$	−6775.12	−	11734.9i	−0.0794605	−	0.137630i
$293$	42170.3	+	24347.0i	0.491215	+	0.283603i	0.725078	−	0.688666i	$-0.241803\pi$
$293$	42170.3	+	24347.0i	0.491215	+	0.283603i	−0.233863	+	0.972269i	$0.575137\pi$
$294$	25562.2	+	144970.i	0.295735	+	1.67720i
$295$	88139.9	−	15541.5i	1.01281	−	0.178586i
$296$	46049.3	−	79759.8i	0.525581	−	0.910333i
$297$	51889.6	−	29958.4i	0.588257	−	0.339630i
$298$	−82759.3	−	98628.7i	−0.931932	−	1.11063i
$299$	−3423.40	−	9405.70i	−0.0382926	−	0.105208i
$300$	2282.00	−	6269.76i	0.0253556	−	0.0696640i
$301$	153705.	+	128974.i	1.69651	+	1.42354i
$302$	5518.59	−	31297.5i	0.0605082	−	0.343159i
$303$		−	178976.i		−	1.94944i
$304$	−87038.7	−	68070.5i	−0.941814	−	0.736566i
$305$	−71636.3			−0.770075
$306$	−10608.6	−	1870.58i	−0.113296	−	0.0199771i
$307$	−60716.6	+	72359.3i	−0.644215	+	0.767746i	−0.985030	−	0.172385i	$-0.944853\pi$
$307$	−60716.6	+	72359.3i	−0.644215	+	0.767746i	0.340815	+	0.940131i	$0.389297\pi$
$308$	28154.1	+	10247.3i	0.296784	+	0.108021i
$309$	54769.6	−	19934.5i	0.573618	−	0.208780i
$310$	173394.	−	145495.i	1.80431	−	1.51400i
$311$	−23770.8	−	41172.2i	−0.245767	−	0.425680i	0.716580	−	0.697505i	$-0.245706\pi$
$311$	−23770.8	−	41172.2i	−0.245767	−	0.425680i	−0.962347	+	0.271824i	$0.912373\pi$
$312$	73408.0	+	42382.1i	0.754109	+	0.435385i
$313$	11306.4	+	64121.7i	0.115408	+	0.654510i	0.986548	+	0.163475i	$0.0522702\pi$
$313$	11306.4	+	64121.7i	0.115408	+	0.654510i	−0.871140	+	0.491035i	$0.836619\pi$
$314$	−97097.4	+	17120.9i	−0.984800	+	0.173647i
$315$	−15894.7	+	27530.5i	−0.160189	+	0.277455i
$316$	−20329.8	+	11737.4i	−0.203591	+	0.117543i
$317$	121738.	+	145082.i	1.21146	+	1.44376i	0.862078	+	0.506776i	$0.169163\pi$
$317$	121738.	+	145082.i	1.21146	+	1.44376i	0.349379	+	0.936982i	$0.386393\pi$
$318$	41016.6	+	112692.i	0.405607	+	1.11440i
$319$	8292.04	−	22782.2i	0.0814854	−	0.223879i
$320$	−53588.7	−	44966.2i	−0.523327	−	0.439123i
$321$	−24391.2	+	138329.i	−0.236713	+	1.34247i
$322$			20837.5i			0.200972i
$323$	8051.32	−	57086.0i	0.0771724	−	0.547173i
$324$	32234.3			0.307064
$325$	−25735.4	−	4537.84i	−0.243648	−	0.0429618i
$326$	−60102.2	+	71627.0i	−0.565529	+	0.673972i
$327$	−103169.	−	37550.5i	−0.964837	−	0.351172i
$328$	−31436.0	+	11441.8i	−0.292200	+	0.106352i
$329$	234203.	−	196519.i	2.16372	−	1.81557i
$330$	57224.5	+	99115.7i	0.525477	+	0.910153i
$331$	−49364.1	−	28500.4i	−0.450563	−	0.260133i	0.257505	−	0.966277i	$-0.417100\pi$
$331$	−49364.1	−	28500.4i	−0.450563	−	0.260133i	−0.708068	+	0.706144i	$0.750433\pi$
$332$	−4266.99	−	24199.3i	−0.0387120	−	0.219547i
$333$	25730.6	−	4537.00i	0.232039	−	0.0409148i
$334$	19618.9	−	33981.0i	0.175866	−	0.304609i
$335$	−78.1536	+	45.1220i	−0.000696401	+	0.000402067i
$336$	−146015.	−	174014.i	−1.29336	−	1.54137i
$337$	−6606.85	−	18152.2i	−0.0581748	−	0.159834i	0.907201	−	0.420698i	$-0.138215\pi$
$337$	−6606.85	−	18152.2i	−0.0581748	−	0.159834i	−0.965376	+	0.260864i	$0.915993\pi$
$338$	2653.01	−	7289.09i	0.0232223	−	0.0638028i
$339$	30410.2	+	25517.2i	0.264618	+	0.222041i
$340$	−3316.16	+	18806.9i	−0.0286865	+	0.162689i
$341$			166285.i			1.43003i
$342$	−837.955	−	24336.4i	−0.00716421	−	0.208068i
$343$	−70936.2			−0.602948
$344$	−137763.	−	24291.3i	−1.16417	−	0.205274i
$345$	−10776.9	+	12843.4i	−0.0905432	+	0.107905i
$346$	1701.65	+	619.348i	0.0142140	+	0.00517348i
$347$	60701.5	−	22093.6i	0.504128	−	0.183488i	−0.0774218	−	0.996998i	$-0.524669\pi$
$347$	60701.5	−	22093.6i	0.504128	−	0.183488i	0.581550	+	0.813511i	$0.302447\pi$
$348$	8385.53	−	7036.30i	0.0692424	−	0.0581013i
$349$	−35450.4	−	61401.9i	−0.291052	−	0.504117i	0.683007	−	0.730412i	$-0.260672\pi$
$349$	−35450.4	−	61401.9i	−0.291052	−	0.504117i	−0.974059	+	0.226295i	$0.927339\pi$
$350$	47114.0	+	27201.3i	0.384604	+	0.222052i
$351$	−18399.3	−	104347.i	−0.149344	−	0.846969i
$352$	−48628.5	+	8574.52i	−0.392469	+	0.0692029i
$353$	−73973.5	+	128126.i	−0.593645	+	1.02822i	0.400092	+	0.916475i	$0.368978\pi$
$353$	−73973.5	+	128126.i	−0.593645	+	1.02822i	−0.993737	+	0.111748i	$0.964355\pi$
$354$	−122058.	+	70470.4i	−0.974005	+	0.562342i
$355$	−40815.8	−	48642.4i	−0.323871	−	0.385974i
$356$	−4645.88	−	12764.4i	−0.0366579	−	0.100717i
$357$	40536.2	−	111372.i	0.318058	−	0.873858i
$358$	84797.6	+	71153.6i	0.661634	+	0.555176i
$359$	−24127.2	+	136832.i	−0.187205	+	1.06169i	0.735885	+	0.677107i	$0.236767\pi$
$359$	−24127.2	+	136832.i	−0.187205	+	1.06169i	−0.923090	+	0.384585i	$0.874345\pi$
$360$		−	22163.0i		−	0.171011i
$361$	130012.	−	8963.84i	0.997632	−	0.0687828i
$362$	224991.			1.71691
$363$	58458.5	+	10307.8i	0.443644	+	0.0782264i
$364$	34056.9	−	40587.4i	0.257041	−	0.306329i
$365$	83535.0	+	30404.3i	0.627022	+	0.228217i
$366$	106007.	−	38583.4i	0.791357	−	0.288030i
$367$	−187339.	+	157196.i	−1.39090	+	1.16710i	−0.425927	+	0.904757i	$0.640052\pi$
$367$	−187339.	+	157196.i	−1.39090	+	1.16710i	−0.964974	+	0.262347i	$0.915503\pi$
$368$	−9350.57	−	16195.7i	−0.0690467	−	0.119592i
$369$	−8218.97	−	4745.23i	−0.0603622	−	0.0348501i
$370$	−38185.9	−	216563.i	−0.278933	−	1.58191i
$371$	−202833.	+	35765.0i	−1.47364	+	0.259843i
$372$	−37539.7	+	65020.7i	−0.271272	+	0.469857i
$373$	−45644.6	+	26352.9i	−0.328074	+	0.189414i	−0.654986	−	0.755641i	$-0.727325\pi$
$373$	−45644.6	+	26352.9i	−0.328074	+	0.189414i	0.326912	+	0.945055i	$0.393992\pi$
$374$	−42813.6	−	51023.2i	−0.306082	−	0.364775i
$375$	−43687.2	−	120029.i	−0.310664	−	0.853543i
$376$	−72901.2	+	200294.i	−0.515655	+	1.41675i
$377$	−32843.1	−	27558.7i	−0.231080	−	0.193899i
$378$	−38303.8	+	217231.i	−0.268076	+	1.52033i
$379$		−	239026.i		−	1.66405i	−0.554738	−	0.832025i	$-0.687181\pi$
$379$		−	239026.i		−	1.66405i	0.554738	−	0.832025i	$-0.312819\pi$
$380$	−43143.6	+	1485.53i	−0.298778	+	0.0102876i
$381$	43021.3			0.296370
$382$	20244.7	+	3569.69i	0.138735	+	0.0244627i
$383$	−126305.	+	150524.i	−0.861037	+	1.02614i	0.138324	+	0.990387i	$0.455829\pi$
$383$	−126305.	+	150524.i	−0.861037	+	1.02614i	−0.999361	+	0.0357567i	$0.988616\pi$
$384$	182033.	+	66254.6i	1.23449	+	0.449318i
$385$	−184704.	+	67226.9i	−1.24611	+	0.453546i
$386$	−23736.6	+	19917.4i	−0.159310	+	0.133677i
$387$	−19842.5	−	34368.2i	−0.132487	−	0.229474i
$388$	−4886.35	−	2821.14i	−0.0324580	−	0.0187396i
$389$	−19028.9	−	107918.i	−0.125752	−	0.713175i	−0.980858	−	0.194722i	$-0.937619\pi$
$389$	−19028.9	−	107918.i	−0.125752	−	0.713175i	0.855106	−	0.518452i	$-0.173492\pi$
$390$	199317.	−	35145.0i	1.31043	−	0.231065i
$391$	4878.64	−	8450.06i	0.0319114	−	0.0552721i
$392$	152645.	−	88129.7i	0.993369	−	0.573522i
$393$	1970.60	+	2348.47i	0.0127589	+	0.0152054i
$394$	17204.3	+	47268.5i	0.110827	+	0.304495i
$395$	52673.2	−	144718.i	0.337595	−	0.927533i
$396$	−4539.42	−	3809.02i	−0.0289474	−	0.0242898i
$397$	27122.3	−	153818.i	0.172086	−	0.975948i	−0.769368	−	0.638806i	$-0.779429\pi$
$397$	27122.3	−	153818.i	0.172086	−	0.975948i	0.941454	−	0.337142i	$-0.109460\pi$
$398$		−	192035.i		−	1.21231i
$399$	265291.	+	37416.3i	1.66639	+	0.235025i
$400$	−48824.9			−0.305156
$401$	−192070.	−	33867.1i	−1.19446	−	0.210615i	−0.459155	−	0.888356i	$-0.651848\pi$
$401$	−192070.	−	33867.1i	−1.19446	−	0.210615i	−0.735301	+	0.677741i	$0.762959\pi$
$402$	91.3485	−	108.865i	0.000565261	−	0.000673652i
$403$	276326.	+	100574.i	1.70142	+	0.619265i
$404$	73291.0	−	26675.7i	0.449043	−	0.163438i
$405$	−161997.	+	135932.i	−0.987639	+	0.828727i
$406$	44627.4	+	77296.9i	0.270738	+	0.468932i
$407$	139906.	+	80774.9i	0.844595	+	0.487627i
$408$	14348.5	+	81374.4i	0.0861959	+	0.488841i
$409$	84313.9	−	14866.8i	0.504026	−	0.0888733i	0.0841466	−	0.996453i	$-0.473184\pi$
$409$	84313.9	−	14866.8i	0.504026	−	0.0888733i	0.419879	+	0.907580i	$0.362072\pi$
$410$	−39938.5	+	69175.5i	−0.237588	+	0.411514i
$411$	−9785.11	+	5649.43i	−0.0579271	+	0.0334442i
$412$	16326.4	+	19457.0i	0.0961825	+	0.114626i
$413$	−82788.2	−	227459.i	−0.485365	−	1.33353i
$414$	1409.57	−	3872.77i	0.00822408	−	0.0225955i
$415$	123493.	+	103623.i	0.717043	+	0.601670i
$416$	−15163.2	+	85994.8i	−0.0876202	+	0.496919i
$417$			50418.2i			0.289945i
$418$	92754.5	−	118601.i	0.530863	−	0.678791i
$419$	121992.			0.694872			0.347436	−	0.937704i	$-0.387052\pi$
$419$	121992.			0.694872			0.347436	+	0.937704i	$0.387052\pi$
$420$	−87399.7	−	15410.9i	−0.495463	−	0.0873635i
$421$	122903.	−	146470.i	0.693425	−	0.826392i	−0.298341	−	0.954459i	$-0.596433\pi$
$421$	122903.	−	146470.i	0.693425	−	0.826392i	0.991765	+	0.128068i	$0.0408776\pi$
$422$	158877.	+	57826.7i	0.892149	+	0.324716i
$423$	−56821.7	+	20681.4i	−0.317566	+	0.115584i
$424$	109999.	−	92299.7i	0.611865	−	0.513415i
$425$	−12737.2	−	22061.4i	−0.0705171	−	0.122139i
$426$	86597.9	+	49997.3i	0.477186	+	0.275504i
$427$	33643.3	+	190801.i	0.184520	+	1.04646i
$428$	−60281.4	+	10629.2i	−0.329076	+	0.0580249i
$429$	−74342.4	+	128765.i	−0.403945	+	0.699653i
$430$	−289262.	+	167005.i	−1.56442	+	0.903220i
$431$	−188991.	−	225231.i	−1.01739	−	1.21248i	−0.976988	−	0.213295i	$-0.931580\pi$
$431$	−188991.	−	225231.i	−1.01739	−	1.21248i	−0.0404026	−	0.999183i	$-0.512864\pi$
$432$	−67708.8	−	186028.i	−0.362809	−	0.996808i
$433$	−83467.2	+	229324.i	−0.445185	+	1.22313i	0.490855	+	0.871241i	$0.336684\pi$
$433$	−83467.2	+	229324.i	−0.445185	+	1.22313i	−0.936040	+	0.351894i	$0.885538\pi$
$434$	−468954.	−	393499.i	−2.48972	−	2.08912i
$435$	−12470.5	+	70723.5i	−0.0659028	+	0.373753i
$436$		−	47844.6i		−	0.251686i
$437$	20973.7	+	6826.08i	0.109828	+	0.0357444i
$438$	−139990.			−0.729710
$439$	60808.9	+	10722.2i	0.315528	+	0.0556361i	0.329170	−	0.944271i	$-0.393231\pi$
$439$	60808.9	+	10722.2i	0.315528	+	0.0556361i	−0.0136415	+	0.999907i	$0.504342\pi$
$440$	88085.4	−	104976.i	0.454987	−	0.542232i
$441$	46987.6	+	17102.1i	0.241605	+	0.0879371i
$442$	−110683.	+	40285.3i	−0.566548	+	0.206207i
$443$	−135472.	+	113674.i	−0.690306	+	0.579236i	−0.918998	−	0.394263i	$-0.871000\pi$
$443$	−135472.	+	113674.i	−0.690306	+	0.579236i	0.228691	+	0.973499i	$0.426555\pi$
$444$	36470.7	+	63169.0i	0.185003	+	0.320434i
$445$	77176.0	+	44557.6i	0.389728	+	0.225010i
$446$	−37527.1	−	212827.i	−0.188658	−	1.06993i
$447$	−275916.	+	48651.4i	−1.38090	+	0.243490i
$448$	−94598.6	+	163850.i	−0.471334	+	0.816374i
$449$	136756.	−	78956.1i	0.678349	−	0.391645i	−0.120884	−	0.992667i	$-0.538573\pi$
$449$	136756.	−	78956.1i	0.678349	−	0.391645i	0.799233	+	0.601022i	$0.205239\pi$
$450$	−6916.36	−	8242.59i	−0.0341549	−	0.0407042i
$451$	−20070.0	−	55141.8i	−0.0986719	−	0.271099i
$452$	−5916.79	+	16256.2i	−0.0289607	+	0.0795689i
$453$	−52977.0	−	44453.0i	−0.258161	−	0.216623i
$454$	−50984.2	+	289146.i	−0.247357	+	1.40283i
$455$			347594.i			1.67900i
$456$	−173219.	+	69886.8i	−0.833041	+	0.336097i
$457$	−203549.			−0.974623			−0.487311	−	0.873228i	$-0.662022\pi$
$457$	−203549.			−0.974623			−0.487311	+	0.873228i	$0.662022\pi$
$458$	309446.	+	54563.8i	1.47521	+	0.260120i
$459$	66392.9	−	79124.0i	0.315135	−	0.375563i
$460$	−6865.65	−	2498.89i	−0.0324464	−	0.0118095i
$461$	−73629.6	+	26799.0i	−0.346458	+	0.126100i	−0.509387	−	0.860537i	$-0.670128\pi$
$461$	−73629.6	+	26799.0i	−0.346458	+	0.126100i	0.162929	+	0.986638i	$0.447906\pi$
$462$	237116.	−	198964.i	1.11091	−	0.932161i
$463$	−34464.2	−	59693.8i	−0.160771	−	0.278463i	0.774375	−	0.632727i	$-0.218065\pi$
$463$	−34464.2	−	59693.8i	−0.160771	−	0.278463i	−0.935145	+	0.354264i	$0.884731\pi$
$464$	−69372.0	−	40052.0i	−0.322217	−	0.186032i
$465$	−85531.6	−	485074.i	−0.395568	−	2.24338i
$466$	234373.	−	41326.3i	1.07928	−	0.190307i
$467$	169356.	−	293333.i	0.776544	−	1.34501i	−0.157378	−	0.987538i	$-0.550304\pi$
$467$	169356.	−	293333.i	0.776544	−	1.34501i	0.933922	−	0.357476i	$-0.116363\pi$
$468$	−9075.24	+	5239.59i	−0.0414349	+	0.0239225i
$469$	156.885	+	186.968i	0.000713240	+	0.000850006i
$470$	174066.	+	478243.i	0.787987	+	2.16498i
$471$	−73381.0	+	201613.i	−0.330782	+	0.908816i
$472$	129275.	+	108475.i	0.580272	+	0.486906i
$473$	42609.3	−	241649.i	0.190450	−	1.08010i
$474$			242523.i			1.07944i
$475$	42812.9	−	38511.1i	0.189752	−	0.170686i
$476$	51648.9			0.227954
$477$	40117.1	+	7073.73i	0.176317	+	0.0310894i
$478$	−143606.	+	171143.i	−0.628518	+	0.749039i
$479$	56150.2	+	20437.0i	0.244726	+	0.0890730i	0.461471	−	0.887155i	$-0.347322\pi$
$479$	56150.2	+	20437.0i	0.244726	+	0.0890730i	−0.216745	+	0.976228i	$0.569544\pi$
$480$	137445.	−	50025.8i	0.596548	−	0.217126i
$481$	218848.	−	183635.i	0.945914	−	0.793716i
$482$	1192.88	+	2066.12i	0.00513454	+	0.00889328i
$483$	39269.3	+	22672.1i	0.168329	+	0.0971847i
$484$	4491.96	+	25475.2i	0.0191754	+	0.108749i
$485$	36453.7	−	6427.77i	0.154974	−	0.0273260i
$486$	48578.2	−	84140.0i	0.205669	−	0.356229i
$487$	16046.7	−	9264.56i	0.0676593	−	0.0390631i	−0.465789	−	0.884896i	$-0.654229\pi$
$487$	16046.7	−	9264.56i	0.0676593	−	0.0390631i	0.533448	+	0.845833i	$0.320896\pi$
$488$	−86824.2	−	103473.i	−0.364587	−	0.434498i
$489$	69590.6	+	191199.i	0.291027	+	0.799589i
$490$	143941.	−	395474.i	0.599503	−	1.64712i
$491$	−62659.9	−	52577.9i	−0.259912	−	0.218092i	0.503514	−	0.863987i	$-0.332040\pi$
$491$	−62659.9	−	52577.9i	−0.259912	−	0.218092i	−0.763427	+	0.645895i	$0.776485\pi$
$492$	4600.79	−	26092.4i	0.0190065	−	0.107791i
$493$		−	41794.0i		−	0.171957i
$494$	−140985.	−	225869.i	−0.577723	−	0.925555i
$495$	38876.0			0.158661
$496$	541065.	+	95404.4i	2.19931	+	0.387797i
$497$	−110389.	+	131556.i	−0.446901	+	0.532596i
$498$	−238555.	−	86827.0i	−0.961900	−	0.350103i
$499$	289217.	−	105266.i	1.16151	−	0.422755i	0.311874	−	0.950124i	$-0.399043\pi$
$499$	289217.	−	105266.i	1.16151	−	0.422755i	0.849637	+	0.527368i	$0.176821\pi$
$500$	42640.8	−	35779.9i	0.170563	−	0.143119i
$501$	−42692.5	−	73945.5i	−0.170089	−	0.294603i
$502$	−361939.	−	208965.i	−1.43624	−	0.829214i
$503$	73990.8	+	419623.i	0.292443	+	1.65853i	0.677416	+	0.735600i	$0.263100\pi$
$503$	73990.8	+	419623.i	0.292443	+	1.65853i	−0.384973	+	0.922928i	$0.625789\pi$
$504$	−59030.3	+	10408.6i	−0.232388	+	0.0409763i
$505$	−255841.	+	443130.i	−1.00320	+	1.73759i
$506$	22068.6	−	12741.3i	0.0861934	−	0.0497638i
$507$	−10850.0	−	12930.6i	−0.0422100	−	0.0503039i
$508$	6412.16	+	17617.3i	0.0248472	+	0.0682671i
$509$	−34735.9	+	95436.2i	−0.134074	+	0.368364i	−0.988503	−	0.151204i	$-0.951685\pi$
$509$	−34735.9	+	95436.2i	−0.134074	+	0.368364i	0.854429	+	0.519568i	$0.173907\pi$
$510$	151137.	+	126819.i	0.581072	+	0.487578i
$511$	41749.2	−	236772.i	0.159885	−	0.906750i
$512$		−	95493.6i		−	0.364279i
$513$	206103.	+	109716.i	0.783158	+	0.416903i
$514$	−279980.			−1.05974
$515$	−164100.	−	28935.3i	−0.618722	−	0.109097i
$516$	71214.5	−	84870.1i	0.267466	−	0.318754i
$517$	−351336.	−	127876.i	−1.31444	−	0.478417i
$518$	−558875.	+	203414.i	−2.08284	+	0.758090i
$519$	3018.65	−	2532.95i	0.0112067	−	0.00940355i
$520$	−121168.	−	209869.i	−0.448106	−	0.776143i
$521$	394890.	+	227990.i	1.45479	+	0.839925i	0.998748	−	0.0500320i	$-0.0159323\pi$
$521$	394890.	+	227990.i	1.45479	+	0.839925i	0.456045	+	0.889957i	$0.349266\pi$
$522$	−3065.43	−	17384.9i	−0.0112500	−	0.0638017i
$523$	1907.54	−	336.351i	0.00697382	−	0.00122967i	−0.170160	−	0.985416i	$-0.554429\pi$
$523$	1907.54	−	336.351i	0.00697382	−	0.00122967i	0.177134	+	0.984187i	$0.443317\pi$
$524$	−667.989	+	1156.99i	−0.00243280	+	0.00421374i
$525$	102524.	−	59192.4i	0.371970	−	0.214757i
$526$	224852.	+	267968.i	0.812691	+	0.968527i
$527$	98041.6	+	269367.i	0.353012	+	0.969892i
$528$	−95012.5	+	261045.i	−0.340811	+	0.936369i
$529$	−211511.	−	177479.i	−0.755826	−	0.634213i
$530$	59536.5	−	337648.i	0.211949	−	1.20202i
$531$			47874.8i			0.169792i
$532$	24218.6	+	114214.i	0.0855709	+	0.403548i
$533$	−103771.			−0.365276
$534$	−138203.	−	24369.0i	−0.484659	−	0.0854584i
$535$	258128.	−	307625.i	0.901835	−	1.07477i
$536$	−159.898	−	58.1983i	−0.000556564	−	0.000202573i
$537$	226356.	−	82386.7i	0.784951	−	0.285699i
$538$	−187604.	+	157418.i	−0.648153	+	0.543865i
$539$	154588.	+	267754.i	0.532106	+	0.921634i
$540$	−66981.0	−	38671.5i	−0.229702	−	0.132618i
$541$	31613.8	+	179291.i	0.108014	+	0.612581i	0.989973	+	0.141254i	$0.0451135\pi$
$541$	31613.8	+	179291.i	0.108014	+	0.612581i	−0.881959	+	0.471326i	$0.843775\pi$
$542$	−6471.24	+	1141.05i	−0.0220287	+	0.00388425i
$543$	244800.	−	424005.i	0.830254	−	1.43804i
$544$	−73718.3	+	42561.3i	−0.249102	+	0.143819i
$545$	201760.	+	240449.i	0.679271	+	0.809523i
$546$	−187215.	−	514368.i	−0.627993	−	1.72540i
$547$	31846.5	−	87497.5i	0.106436	−	0.292429i	−0.875030	−	0.484069i	$-0.839158\pi$
$547$	31846.5	−	87497.5i	0.106436	−	0.292429i	0.981465	+	0.191640i	$0.0613805\pi$
$548$	−3771.88	−	3164.98i	−0.0125602	−	0.0105393i
$549$	6654.09	−	37737.2i	0.0220772	−	0.125206i
$550$		−	66530.1i		−	0.219934i
$551$	92421.2	−	19597.6i	0.304417	−	0.0645505i
$552$	−31613.1			−0.103750
$553$	−410190.	−	72327.5i	−1.34133	−	0.236512i
$554$	−135463.	+	161438.i	−0.441367	+	0.526001i
$555$	−449671.	−	163667.i	−1.45985	−	0.531343i
$556$	−20646.3	+	7514.64i	−0.0667872	+	0.0243085i
$557$	−246675.	+	206985.i	−0.795086	+	0.667156i	−0.946999	−	0.321238i	$-0.895901\pi$
$557$	−246675.	+	206985.i	−0.795086	+	0.667156i	0.151913	+	0.988394i	$0.451457\pi$
$558$	60539.1	+	104857.i	0.194432	+	0.336766i
$559$	−375790.	−	216963.i	−1.20260	−	0.694322i
$560$	112773.	+	639568.i	0.359608	+	2.03944i
$561$	−142739.	+	25168.7i	−0.453540	+	0.0799714i
$562$	58213.9	−	100829.i	0.184312	−	0.319238i
$563$	16306.3	−	9414.46i	0.0514446	−	0.0297015i	−0.474057	−	0.880494i	$-0.657211\pi$
$563$	16306.3	−	9414.46i	0.0514446	−	0.0297015i	0.525502	+	0.850793i	$0.323878\pi$
$564$	−108510.	−	129318.i	−0.341124	−	0.406536i
$565$	−38817.0	−	106649.i	−0.121598	−	0.334086i
$566$	187257.	−	514483.i	0.584526	−	1.60597i
$567$	438131.	+	367635.i	1.36282	+	1.14354i
$568$	20790.8	−	117911.i	0.0644429	−	0.365474i
$569$		−	242523.i		−	0.749082i	−0.927210	−	0.374541i	$-0.877800\pi$
$569$		−	242523.i		−	0.749082i	0.927210	−	0.374541i	$-0.122200\pi$
$570$	−209571.	+	393683.i	−0.645034	+	1.21171i
$571$	476042.			1.46007			0.730034	−	0.683411i	$-0.239504\pi$
$571$	476042.			1.46007			0.730034	+	0.683411i	$0.239504\pi$
$572$	−63809.7	−	11251.4i	−0.195027	−	0.0343885i
$573$	28754.4	−	34268.1i	0.0875779	−	0.104371i
$574$	203003.	+	73887.1i	0.616139	+	0.224256i
$575$	9158.38	−	3333.38i	0.0277002	−	0.0100821i
$576$	28665.4	−	24053.2i	0.0864000	−	0.0724982i
$577$	−60313.8	−	104467.i	−0.181161	−	0.313780i	0.761115	−	0.648617i	$-0.224652\pi$
$577$	−60313.8	−	104467.i	−0.181161	−	0.313780i	−0.942276	+	0.334837i	$0.891319\pi$
$578$	226209.	+	130602.i	0.677103	+	0.390926i
$579$	11708.7	+	66403.6i	0.0349263	+	0.198077i
$580$	−30820.0	+	5434.40i	−0.0916171	+	0.0161546i
$581$	217998.	−	377584.i	0.645804	−	1.11856i
$582$	−50481.9	+	29145.8i	−0.149036	+	0.0860458i
$583$	161903.	+	192948.i	0.476340	+	0.567680i
$584$	57329.0	+	157510.i	0.168093	+	0.461831i
$585$	23513.4	−	64602.4i	0.0687073	−	0.188772i
$586$	167939.	+	140917.i	0.489052	+	0.410364i
$587$	−48664.3	+	275989.i	−0.141232	+	0.800969i	0.829083	+	0.559126i	$0.188863\pi$
$587$	−48664.3	+	275989.i	−0.141232	+	0.800969i	−0.970315	+	0.241843i	$0.922248\pi$
$588$			139596.i			0.403755i
$589$	−549692.	+	343113.i	−1.58449	+	0.989023i
$590$	402941.			1.15754
$591$	107799.	+	19007.8i	0.308630	+	0.0544199i
$592$	343098.	−	408888.i	0.978982	−	1.16671i
$593$	−150461.	−	54763.4i	−0.427873	−	0.155733i	0.119102	−	0.992882i	$-0.461999\pi$
$593$	−150461.	−	54763.4i	−0.427873	−	0.155733i	−0.546975	+	0.837149i	$0.684221\pi$
$594$	253487.	−	92261.7i	0.718427	−	0.261486i
$595$	−259567.	+	217803.i	−0.733190	+	0.615219i
$596$	−61047.0	−	105737.i	−0.171859	−	0.297668i
$597$	−361898.	−	208942.i	−1.01540	−	0.586242i
$598$	−7825.21	−	44379.0i	−0.0218823	−	0.124101i
$599$	47631.9	−	8398.80i	0.132753	−	0.0234080i	−0.106877	−	0.994272i	$-0.534085\pi$
$599$	47631.9	−	8398.80i	0.132753	−	0.0234080i	0.239630	+	0.970864i	$0.422974\pi$
$600$	−41267.7	+	71477.8i	−0.114633	+	0.198549i
$601$	−167304.	+	96593.3i	−0.463189	+	0.267423i	−0.713384	−	0.700773i	$-0.752839\pi$
$601$	−167304.	+	96593.3i	−0.463189	+	0.267423i	0.250195	+	0.968195i	$0.419505\pi$
$602$	580662.	+	692006.i	1.60225	+	1.90949i
$603$	−16.5103	−	45.3617i	−4.54068e−5	−	0.000124754i
$604$	10307.5	−	28319.7i	0.0282540	−	0.0776273i
$605$	−130003.	−	109086.i	−0.355177	−	0.298029i
$606$	139922.	−	793537.i	0.381014	−	2.16084i
$607$		−	613391.i		−	1.66479i	−0.554181	−	0.832396i	$-0.686969\pi$
$607$		−	613391.i		−	1.66479i	0.554181	−	0.832396i	$-0.313031\pi$
$608$	−128685.	−	143059.i	−0.348113	−	0.386999i
$609$	194226.			0.523688
$610$	−317618.	−	56004.6i	−0.853581	−	0.150509i
$611$	−424996.	+	506491.i	−1.13842	+	1.35672i
$612$	−9599.24	−	3493.84i	−0.0256291	−	0.00932824i
$613$	510842.	−	185931.i	1.35946	−	0.494802i	0.443571	−	0.896239i	$-0.353712\pi$
$613$	510842.	−	185931.i	1.35946	−	0.494802i	0.915886	+	0.401437i	$0.131489\pi$
$614$	−325773.	+	273356.i	−0.864127	+	0.725089i
$615$	86909.5	+	150532.i	0.229783	+	0.397995i
$616$	−320969.	−	185311.i	−0.845865	−	0.488360i
$617$	−48149.3	−	273068.i	−0.126479	−	0.717300i	−0.980418	−	0.196927i	$-0.936904\pi$
$617$	−48149.3	−	273068.i	−0.126479	−	0.717300i	0.853939	−	0.520373i	$-0.174207\pi$
$618$	258420.	−	45566.3i	0.676626	−	0.119307i
$619$	106483.	−	184434.i	0.277906	−	0.481347i	−0.692958	−	0.720978i	$-0.743693\pi$
$619$	106483.	−	184434.i	0.277906	−	0.481347i	0.970864	+	0.239630i	$0.0770263\pi$
$620$	185890.	−	107324.i	0.483585	−	0.279198i
$621$	25401.1	+	30271.8i	0.0658671	+	0.0784974i
$622$	−73205.9	−	201131.i	−0.189219	−	0.519875i
$623$	82432.5	−	226481.i	0.212384	−	0.583521i
$624$	376326.	+	315775.i	0.966485	+	0.810977i
$625$	−80725.1	+	457815.i	−0.206656	+	1.17201i
$626$			293139.i			0.748040i
$627$	−122588.	−	303843.i	−0.311827	−	0.772884i
$628$	−93497.7			−0.237073
$629$	274260.	+	48359.5i	0.693205	+	0.122231i
$630$	−91996.5	+	109637.i	−0.231788	+	0.276234i
$631$	−329756.	−	120022.i	−0.828199	−	0.301440i	−0.107079	−	0.994250i	$-0.534150\pi$
$631$	−329756.	−	120022.i	−0.828199	−	0.301440i	−0.721119	+	0.692811i	$0.756372\pi$
$632$	272875.	−	99318.4i	0.683172	−	0.248654i
$633$	281842.	−	236494.i	0.703395	−	0.590218i
$634$	426333.	+	738431.i	1.06065	+	1.83709i
$635$	−106517.	−	61497.6i	−0.264163	−	0.152514i
$636$	19748.0	+	111997.i	0.0488213	+	0.276879i
$637$	538441.	−	94941.7i	1.32696	−	0.233980i
$638$	54575.8	−	94528.0i	0.134078	−	0.232230i
$639$	29415.6	−	16983.1i	0.0720403	−	0.0415925i
$640$	−355989.	−	424251.i	−0.869114	−	1.03577i
$641$	−17040.6	−	46818.6i	−0.0414733	−	0.113947i	0.917227	−	0.398364i	$-0.130422\pi$
$641$	−17040.6	−	46818.6i	−0.0414733	−	0.113947i	−0.958701	+	0.284417i	$0.908200\pi$
$642$	−216289.	+	594249.i	−0.524765	+	1.44178i
$643$	−86644.8	−	72703.6i	−0.209566	−	0.175847i	0.531963	−	0.846768i	$-0.321455\pi$
$643$	−86644.8	−	72703.6i	−0.209566	−	0.175847i	−0.741529	+	0.670921i	$0.765899\pi$
$644$	−3431.32	+	19460.0i	−0.00827351	+	0.0469214i
$645$			726836.i			1.74710i
$646$	80326.9	−	246811.i	0.192485	−	0.591424i
$647$	−624970.			−1.49297			−0.746484	−	0.665403i	$-0.768260\pi$
$647$	−624970.			−1.49297			−0.746484	+	0.665403i	$0.768260\pi$
$648$	−392686.	−	69241.2i	−0.935181	−	0.164898i
$649$	−190275.	+	226761.i	−0.451745	+	0.538368i
$650$	−110557.	−	40239.3i	−0.261673	−	0.0952411i
$651$	−1.25181e6	+	455621.i	−2.95376	+	1.07508i
$652$	−67923.8	+	56994.8i	−0.159782	+	0.134073i
$653$	−292946.	−	507397.i	−0.687007	−	1.18993i	−0.972801	−	0.231640i	$-0.925591\pi$
$653$	−292946.	−	507397.i	−0.687007	−	1.18993i	0.285794	−	0.958291i	$-0.407743\pi$
$654$	−428070.	−	247146.i	−1.00083	−	0.577828i
$655$	−1521.97	−	8631.50i	−0.00354750	−	0.0201189i
$656$	−190937.	+	33667.4i	−0.443693	+	0.0782351i
$657$	−23776.0	+	41181.2i	−0.0550817	+	0.0954043i
$658$	1.19204e6	−	688222.i	2.75320	−	1.58956i
$659$	234617.	+	279605.i	0.540241	+	0.643835i	0.965242	−	0.261359i	$-0.0841705\pi$
$659$	234617.	+	279605.i	0.540241	+	0.643835i	−0.425000	+	0.905193i	$0.639726\pi$
$660$	37120.0	+	101986.i	0.0852159	+	0.234129i
$661$	−150990.	+	414842.i	−0.345578	+	0.949467i	0.638168	+	0.769898i	$0.279693\pi$
$661$	−150990.	+	414842.i	−0.345578	+	0.949467i	−0.983745	+	0.179570i	$0.942530\pi$
$662$	−196587.	−	164956.i	−0.448579	−	0.376402i
$663$	−44508.3	+	252419.i	−0.101254	+	0.574243i
$664$			303968.i			0.689432i
$665$	−603352.	−	471865.i	−1.36436	−	1.06702i
$666$	117630.			0.265198
$667$	15746.9	+	2776.61i	0.0353952	+	0.00624113i
$668$	23917.6	−	28503.9i	0.0536000	−	0.0638780i
$669$	−441913.	−	160843.i	−0.987380	−	0.359377i
$670$	−381.790	+	138.960i	−0.000850501	+	0.000309557i
$671$	181502.	−	152298.i	0.403121	−	0.338259i
$672$	−197791.	−	342585.i	−0.437995	−	0.758629i
$673$	683643.	+	394701.i	1.50938	+	0.871442i	0.999940	+	0.0109371i	$0.00348145\pi$
$673$	683643.	+	394701.i	1.50938	+	0.871442i	0.509442	+	0.860505i	$0.329852\pi$
$674$	−15102.0	−	85647.5i	−0.0332440	−	0.188536i
$675$	101604.	−	17915.5i	0.222999	−	0.0393207i
$676$	3677.92	−	6370.35i	0.00804839	−	0.0139402i
$677$	298127.	−	172124.i	0.650466	−	0.375547i	−0.138169	−	0.990409i	$-0.544122\pi$
$677$	298127.	−	172124.i	0.650466	−	0.375547i	0.788635	+	0.614862i	$0.210788\pi$
$678$	114882.	+	136911.i	0.249916	+	0.297838i
$679$	−34240.2	−	94074.3i	−0.0742672	−	0.204048i
$680$	80796.6	−	221987.i	0.174733	−	0.480075i
$681$	489435.	+	410685.i	1.05536	+	0.885553i
$682$	−130000.	+	737269.i	−0.279496	+	1.58510i
$683$			402244.i			0.862281i	0.902285	+	0.431140i	$0.141889\pi$
$683$			402244.i			0.862281i	−0.902285	+	0.431140i	$0.858111\pi$
$684$	3224.93	−	22865.6i	0.00689299	−	0.0488731i
$685$	32302.8			0.0688428
$686$	−314514.	−	55457.2i	−0.668330	−	0.117845i
$687$	439519.	−	523798.i	0.931245	−	1.10981i
$688$	−761840.	−	277287.i	−1.60948	−	0.585804i
$689$	418556.	−	152342.i	0.881688	−	0.320908i
$690$	−57823.1	+	48519.3i	−0.121451	+	0.101910i
$691$	103401.	+	179096.i	0.216555	+	0.375085i	0.953753	−	0.300593i	$-0.0971845\pi$
$691$	103401.	+	179096.i	0.216555	+	0.375085i	−0.737197	+	0.675678i	$0.763851\pi$
$692$	1487.16	+	858.615i	0.00310561	+	0.00179302i
$693$	−18257.8	−	103545.i	−0.0380173	−	0.215607i
$694$	286408.	−	50501.5i	0.594657	−	0.104854i
$695$	72071.3	−	124831.i	0.149208	−	0.258436i
$696$	−117269.	+	67705.3i	−0.242083	+	0.139767i
$697$	−65023.0	−	77491.4i	−0.133845	−	0.159510i
$698$	−109175.	−	299956.i	−0.224085	−	0.615668i
$699$	177127.	−	486651.i	0.362518	−	0.996010i
$700$	39520.2	+	33161.4i	0.0806534	+	0.0676762i
$701$	149181.	−	846049.i	0.303584	−	1.72171i	−0.326514	−	0.945192i	$-0.605874\pi$
$701$	149181.	−	846049.i	0.303584	−	1.72171i	0.630098	−	0.776516i	$-0.283015\pi$
$702$		−	477036.i		−	0.968003i
$703$	21663.4	+	629161.i	0.0438344	+	1.27307i
$704$	231373.			0.466839
$705$	1.09066e6	+	192313.i	2.19438	+	0.386929i
$706$	−428148.	+	510247.i	−0.858983	+	1.02370i
$707$	1.30041e6	+	473312.i	2.60161	+	0.946909i
$708$	−125594.	+	45712.4i	−0.250554	+	0.0911942i
$709$	187022.	−	156930.i	0.372048	−	0.312185i	−0.437523	−	0.899207i	$-0.644144\pi$
$709$	187022.	−	156930.i	0.372048	−	0.312185i	0.809571	+	0.587022i	$0.199700\pi$
$710$	−142939.	−	247578.i	−0.283553	−	0.491129i
$711$	71343.5	+	41190.2i	0.141129	+	0.0814806i
$712$	29178.4	+	165479.i	0.0575575	+	0.326425i
$713$	−108004.	+	19044.1i	−0.212452	+	0.0374611i
$714$	266798.	−	462107.i	0.523342	−	0.906455i
$715$	368130.	−	212540.i	0.720095	−	0.415747i
$716$	67474.9	+	80413.4i	0.131618	+	0.156857i
$717$	166278.	+	456844.i	0.323441	+	0.888647i
$718$	−213948.	+	587817.i	−0.415010	+	1.14023i
$719$	−736562.	−	618049.i	−1.42479	−	1.19554i	−0.948713	−	0.316140i	$-0.897613\pi$
$719$	−736562.	−	618049.i	−1.42479	−	1.19554i	−0.476079	−	0.879402i	$-0.657943\pi$
$720$	22304.7	−	126496.i	0.0430260	−	0.244013i
$721$			450665.i			0.866928i
$722$	583451.	+	61899.0i	1.11926	+	0.118743i
$723$	5191.60			0.00993172
$724$	210117.	+	37049.3i	0.400852	+	0.0706810i
$725$	26834.0	−	31979.6i	0.0510517	−	0.0608410i
$726$	251132.	+	91404.7i	0.476463	+	0.173418i
$727$	−308877.	+	112422.i	−0.584409	+	0.212708i	−0.617269	−	0.786752i	$-0.711761\pi$
$727$	−308877.	+	112422.i	−0.584409	+	0.212708i	0.0328595	+	0.999460i	$0.489539\pi$
$728$	−502073.	+	421289.i	−0.947336	+	0.794910i
$729$	200069.	+	346530.i	0.376465	+	0.652057i
$730$	346604.	+	200112.i	0.650411	+	0.375515i
$731$	−73452.9	−	416572.i	−0.137459	−	0.779570i
$732$	105353.	−	18576.5i	0.196618	−	0.0346690i
$733$	−49208.4	+	85231.4i	−0.0915865	+	0.158632i	−0.908179	−	0.418582i	$-0.862527\pi$
$733$	−49208.4	+	85231.4i	−0.0915865	+	0.158632i	0.816592	+	0.577215i	$0.195860\pi$
$734$	−953510.	+	550509.i	−1.76984	+	1.02182i
$735$	−588675.	−	701556.i	−1.08968	−	1.29864i
$736$	−11138.5	−	30602.8i	−0.0205623	−	0.0564944i
$737$	102.085	−	280.477i	0.000187944	−	0.000516372i
$738$	−32731.1	−	27464.7i	−0.0600964	−	0.0504269i
$739$	8480.69	−	48096.4i	0.0155290	−	0.0880691i	−0.976058	−	0.217509i	$-0.930207\pi$
$739$	8480.69	−	48096.4i	0.0155290	−	0.0880691i	0.991587	+	0.129440i	$0.0413179\pi$
$740$		−	208535.i		−	0.380816i
$741$	−579058.	+	19938.2i	−1.05459	+	0.0363119i
$742$	−927275.			−1.68423
$743$	−313679.	−	55310.0i	−0.568208	−	0.100190i	−0.117839	−	0.993033i	$-0.537597\pi$
$743$	−313679.	−	55310.0i	−0.568208	−	0.100190i	−0.450369	+	0.892842i	$0.648708\pi$
$744$	596986.	−	711460.i	1.07850	−	1.28530i
$745$	752689.	+	273957.i	1.35614	+	0.493593i
$746$	−222980.	+	81157.9i	−0.400671	+	0.145832i
$747$	−66058.2	+	55429.4i	−0.118382	+	0.0993343i
$748$	−31581.2	−	54700.3i	−0.0564451	−	0.0977657i
$749$	−940575.	−	543041.i	−1.67660	−	0.967986i
$750$	−99860.2	−	566336.i	−0.177529	−	1.00682i
$751$	2798.51	−	493.453i	0.00496189	−	0.000874916i	−0.171167	−	0.985242i	$-0.554754\pi$
$751$	2798.51	−	493.453i	0.00496189	−	0.000874916i	0.176129	+	0.984367i	$0.443643\pi$
$752$	−617661.	+	1.06982e6i	−1.09223	+	1.89180i
$753$	−787609.	+	454726.i	−1.38906	+	0.801974i
$754$	−124073.	−	147865.i	−0.218241	−	0.260089i
$755$	67622.3	+	185791.i	0.118630	+	0.325934i
$756$	−71543.1	+	196563.i	−0.125177	+	0.343921i
$757$	−828041.	−	694809.i	−1.44497	−	1.21248i	−0.936148	−	0.351607i	$-0.885635\pi$
$757$	−828041.	−	694809.i	−1.44497	−	1.21248i	−0.508826	−	0.860869i	$-0.669920\pi$
$758$	186868.	−	1.05978e6i	0.325235	−	1.84450i
$759$		−	55452.4i		−	0.0962580i
$760$	528776.	+	74577.8i	0.915471	+	0.129117i
$761$	667048.			1.15183			0.575914	−	0.817510i	$-0.304646\pi$
$761$	667048.			1.15183			0.575914	+	0.817510i	$0.304646\pi$
$762$	190746.	+	33633.7i	0.328508	+	0.0579248i
$763$	545672.	−	650306.i	0.937308	−	1.11704i
$764$	18318.6	+	6667.41i	0.0313837	+	0.0114227i
$765$	62975.6	−	22921.2i	0.107609	−	0.0391665i
$766$	−677682.	+	568643.i	−1.15496	+	0.969130i
$767$	261738.	+	453343.i	0.444913	+	0.770613i
$768$	416242.	+	240317.i	0.705706	+	0.407439i
$769$	111277.	+	631082.i	0.188171	+	1.06717i	0.921813	+	0.387634i	$0.126708\pi$
$769$	111277.	+	631082.i	0.188171	+	1.06717i	−0.733643	+	0.679535i	$0.762181\pi$
$770$	−871492.	+	153668.i	−1.46988	+	0.259179i
$771$	−304630.	+	527635.i	−0.512465	+	0.887615i
$772$	−25447.2	+	14691.9i	−0.0426978	+	0.0246516i
$773$	381065.	+	454135.i	0.637735	+	0.760022i	0.984011	−	0.178110i	$-0.0569984\pi$
$773$	381065.	+	454135.i	0.637735	+	0.760022i	−0.346276	+	0.938133i	$0.612554\pi$
$774$	−61107.9	−	167893.i	−0.102004	−	0.280253i
$775$	−97929.7	+	269060.i	−0.163046	+	0.447966i
$776$	53466.8	+	44864.0i	0.0887893	+	0.0745031i
$777$	−224737.	+	1.27455e6i	−0.372248	+	2.11112i
$778$		−	493360.i		−	0.815088i
$779$	140871.	−	180125.i	0.232138	−	0.296824i
$780$	191928.			0.315463
$781$	206826.	+	36469.1i	0.339081	+	0.0597892i
$782$	28236.9	−	33651.4i	0.0461746	−	0.0550288i
$783$	159058.	+	57892.4i	0.259437	+	0.0944274i
$784$	959921.	−	349383.i	1.56172	−	0.568420i
$785$	469884.	−	394279.i	0.762520	−	0.639830i
$786$	6901.14	+	11953.1i	0.0111706	+	0.0193480i
$787$	−83625.4	−	48281.1i	−0.135017	−	0.0779521i	0.430970	−	0.902366i	$-0.358171\pi$
$787$	−83625.4	−	48281.1i	−0.135017	−	0.0779521i	−0.565987	+	0.824414i	$0.691505\pi$
$788$	8283.26	+	46976.7i	0.0133398	+	0.0756537i
$789$	749647.	−	132183.i	1.20421	−	0.212335i
$790$	346680.	−	600467.i	0.555487	−	0.962132i
$791$	−265825.	+	153474.i	−0.424857	+	0.245291i
$792$	47118.3	+	56153.4i	0.0751171	+	0.0895211i
$793$	−143304.	−	393726.i	−0.227884	−	0.626105i
$794$	240507.	−	660788.i	0.381493	−	1.04814i
$795$	−571535.	−	479575.i	−0.904292	−	0.758791i
$796$	31622.4	−	179340.i	0.0499079	−	0.283042i
$797$		−	827116.i		−	1.30212i	−0.759028	−	0.651058i	$-0.774326\pi$
$797$		−	827116.i		−	1.30212i	0.759028	−	0.651058i	$-0.225674\pi$
$798$	1.14698e6	+	373297.i	1.80116	+	0.586203i
$799$	−644527.			−1.00960
$800$	−83733.6	−	14764.5i	−0.130834	−	0.0230695i
$801$	−30641.1	+	36516.7i	−0.0477573	+	0.0569149i
$802$	−825113.	−	300317.i	−1.28282	−	0.466907i
$803$	−276288.	+	100561.i	−0.428481	+	0.155954i
$804$	103.236	−	86.6256i	0.000159706	−	0.000134009i
$805$	−64818.2	−	112268.i	−0.100024	−	0.173247i
$806$	1.14653e6	+	661950.i	1.76488	+	1.01896i
$807$	92541.0	+	524826.i	0.142098	+	0.805876i
$808$	−950149.	+	167537.i	−1.45536	+	0.256618i
$809$	−358056.	+	620171.i	−0.547084	+	0.947577i	0.451388	+	0.892328i	$0.350929\pi$
$809$	−358056.	+	620171.i	−0.547084	+	0.947577i	−0.998473	+	0.0552499i	$0.982404\pi$
$810$	−824527.	+	476041.i	−1.25671	+	0.725562i
$811$	−434884.	−	518275.i	−0.661199	−	0.787986i	0.326358	−	0.945246i	$-0.394178\pi$
$811$	−434884.	−	518275.i	−0.661199	−	0.787986i	−0.987557	+	0.157260i	$0.949734\pi$
$812$	28948.7	+	79535.8i	0.0439052	+	0.120629i
$813$	−4890.62	+	13436.9i	−0.00739916	+	0.0203290i
$814$	557161.	+	467514.i	0.840876	+	0.705579i
$815$	101012.	−	572868.i	0.152075	−	0.862461i
$816$			478888.i			0.719207i
$817$	886743.	−	357764.i	1.32848	−	0.535985i
$818$	385450.			0.576052
$819$	−183109.	−	32287.1i	−0.272987	−	0.0481350i
$820$	−48689.4	+	58025.7i	−0.0724113	+	0.0862964i
$821$	238399.	+	86770.0i	0.353686	+	0.128731i	0.512752	−	0.858537i	$-0.328626\pi$
$821$	238399.	+	86770.0i	0.353686	+	0.128731i	−0.159066	+	0.987268i	$0.550848\pi$
$822$	−47801.5	+	17398.3i	−0.0707453	+	0.0257492i
$823$	407180.	−	341665.i	0.601156	−	0.504430i	−0.290661	−	0.956826i	$-0.593875\pi$
$823$	407180.	−	341665.i	0.601156	−	0.504430i	0.891817	+	0.452396i	$0.149431\pi$
$824$	−157097.	−	272100.i	−0.231374	−	0.400751i
$825$	−125379.	−	72387.6i	−0.184211	−	0.106355i
$826$	−189238.	−	1.07322e6i	−0.277362	−	1.57300i
$827$	−895196.	+	157847.i	−1.30890	+	0.230795i	−0.784209	−	0.620497i	$-0.786931\pi$
$827$	−895196.	+	157847.i	−1.30890	+	0.230795i	−0.524693	+	0.851292i	$0.675820\pi$
$828$	1954.12	−	3384.64i	0.00285030	−	0.00493687i
$829$	279758.	−	161518.i	0.407074	−	0.235024i	−0.282458	−	0.959280i	$-0.591150\pi$
$829$	279758.	−	161518.i	0.407074	−	0.235024i	0.689532	+	0.724255i	$0.257816\pi$
$830$	466525.	+	555983.i	0.677203	+	0.807059i
$831$	156848.	+	430937.i	0.227131	+	0.624039i
$832$	139941.	−	384485.i	0.202162	−	0.555435i
$833$	408286.	+	342593.i	0.588402	+	0.493728i
$834$	−39416.5	+	223542.i	−0.0566691	+	0.321386i
$835$			244110.i			0.350117i
$836$	106153.	−	95486.6i	0.151886	−	0.136625i
$837$	−1.16095e6			−1.65716
$838$	540884.	+	95372.5i	0.770223	+	0.135811i
$839$	143752.	−	171316.i	0.204215	−	0.243374i	−0.654210	−	0.756313i	$-0.726999\pi$
$839$	143752.	−	171316.i	0.204215	−	0.243374i	0.858425	+	0.512939i	$0.171443\pi$
$840$	1.03162e6	+	375479.i	1.46205	+	0.532142i
$841$	−600267.	+	218479.i	−0.848696	+	0.308900i
$842$	659432.	−	553330.i	0.930135	−	0.780476i
$843$	−126678.	−	219413.i	−0.178257	−	0.308751i
$844$	138852.	+	80166.3i	0.194925	+	0.112540i
$845$	8379.89	+	47524.7i	0.0117361	+	0.0665589i
$846$	−268102.	+	47273.6i	−0.374593	+	0.0660508i
$847$	−229491.	+	397491.i	−0.319889	+	0.554064i
$848$	720711.	−	416103.i	1.00223	−	0.578640i
$849$	−765824.	−	912673.i	−1.06246	−	1.26619i
$850$	−39226.0	−	107773.i	−0.0542921	−	0.149166i
$851$	−36441.3	+	100122.i	−0.0503193	+	0.138251i
$852$	72640.0	+	60952.2i	0.100068	+	0.0839673i
$853$	−98304.2	+	557511.i	−0.135106	+	0.766223i	0.839680	+	0.543081i	$0.182742\pi$
$853$	−98304.2	+	557511.i	−0.135106	+	0.766223i	−0.974786	+	0.223142i	$0.928369\pi$
$854$			872265.i			1.19600i
$855$	80216.7	+	128513.i	0.109732	+	0.175798i
$856$	757195.			1.03338
$857$	876496.	+	154550.i	1.19341	+	0.210430i	0.734846	−	0.678234i	$-0.237254\pi$
$857$	876496.	+	154550.i	1.19341	+	0.210430i	0.458560	+	0.888663i	$0.348365\pi$
$858$	−430283.	+	512791.i	−0.584493	+	0.696572i
$859$	−181103.	−	65916.0i	−0.245436	−	0.0893315i	0.216373	−	0.976311i	$-0.430577\pi$
$859$	−181103.	−	65916.0i	−0.245436	−	0.0893315i	−0.461809	+	0.886979i	$0.652800\pi$
$860$	−297640.	+	108332.i	−0.402434	+	0.146474i
$861$	360120.	−	302176.i	0.485781	−	0.407619i
$862$	−661858.	−	1.14637e6i	−0.890739	−	1.54281i
$863$	−628385.	−	362798.i	−0.843732	−	0.487129i	0.0147992	−	0.999890i	$-0.495289\pi$
$863$	−628385.	−	362798.i	−0.843732	−	0.487129i	−0.858531	+	0.512762i	$0.828622\pi$
$864$	−59864.6	−	339509.i	−0.0801941	−	0.454804i
$865$	−11094.7	+	1956.29i	−0.0148280	+	0.00261458i
$866$	−549357.	+	951514.i	−0.732519	+	1.26876i
$867$	492251.	−	284201.i	0.654860	−	0.378083i
$868$	−373154.	−	444708.i	−0.495278	−	0.590249i
$869$	174214.	+	478649.i	0.230698	+	0.633837i
$870$	−110582.	+	303821.i	−0.146098	+	0.401402i
$871$	−404.340	−	339.282i	−0.000532980	−	0.000447223i
$872$	−102773.	+	582854.i	−0.135159	+	0.766526i
$873$			19800.5i			0.0259805i
$874$	87655.5	+	46662.2i	0.114751	+	0.0610861i
$875$	987648.			1.28999
$876$	−130736.	−	23052.3i	−0.170367	−	0.0300404i
$877$	−804377.	+	958619.i	−1.04583	+	1.24637i	−0.0774200	+	0.996999i	$0.524668\pi$
$877$	−804377.	+	958619.i	−1.04583	+	1.24637i	−0.968408	+	0.249371i	$0.919776\pi$
$878$	261229.	+	95079.6i	0.338870	+	0.123338i
$879$	448289.	−	163164.i	0.580204	−	0.211177i
$880$	608398.	−	510507.i	0.785638	−	0.659229i
$881$	79204.7	+	137187.i	0.102047	+	0.176750i	0.912528	−	0.409015i	$-0.134128\pi$
$881$	79204.7	+	137187.i	0.102047	+	0.176750i	−0.810481	+	0.585765i	$0.800794\pi$
$882$	194961.	+	112561.i	0.250617	+	0.144694i
$883$	−92710.0	−	525784.i	−0.118906	−	0.674351i	−0.984742	−	0.174022i	$-0.944324\pi$
$883$	−92710.0	−	525784.i	−0.118906	−	0.674351i	0.865835	−	0.500329i	$-0.166788\pi$
$884$	−110000.	+	19395.9i	−0.140763	+	0.0248202i
$885$	438417.	−	759361.i	0.559759	−	0.969531i
$886$	−689519.	+	398094.i	−0.878373	+	0.507129i
$887$	−727236.	−	866686.i	−0.924332	−	1.10158i	−0.994572	−	0.104046i	$-0.966821\pi$
$887$	−727236.	−	866686.i	−0.924332	−	1.10158i	0.0702404	−	0.997530i	$-0.477623\pi$
$888$	−308604.	−	847882.i	−0.391359	−	1.07525i
$889$	−113772.	+	312586.i	−0.143957	+	0.395518i
$890$	307345.	+	257893.i	0.388012	+	0.325581i
$891$	121456.	−	688810.i	0.152990	−	0.867649i
$892$		−	204937.i		−	0.257567i
$893$	−302225.	−	1.42527e6i	−0.378989	−	1.78729i
$894$	−1.26138e6			−1.57823
$895$	−678206.	−	119586.i	−0.846673	−	0.149291i
$896$	−962791.	+	1.14741e6i	−1.19927	+	1.42923i
$897$	−92148.3	−	33539.2i	−0.114526	−	0.0416839i
$898$	668069.	−	243157.i	0.828455	−	0.301533i
$899$	−359856.	+	301955.i	−0.445255	+	0.373614i
$900$	−5101.82	−	8836.61i	−0.00629854	−	0.0109094i
$901$	376029.	+	217101.i	0.463204	+	0.267431i
$902$	−45876.0	−	260176.i	−0.0563861	−	0.319782i
$903$	1.93590e6	−	341352.i	2.37415	−	0.418626i
$904$	106999.	−	185328.i	0.130931	−	0.226780i
$905$	−1.21220e6	+	699867.i	−1.48006	+	0.854512i
$906$	−200134.	−	238511.i	−0.243818	−	0.290570i
$907$	498858.	+	1.37060e6i	0.606404	+	1.66608i	0.738018	+	0.674781i	$0.235762\pi$
$907$	498858.	+	1.37060e6i	0.606404	+	1.66608i	−0.131613	+	0.991301i	$0.542016\pi$
$908$	−95227.4	+	261635.i	−0.115502	+	0.317340i
$909$	−209672.	−	175935.i	−0.253753	−	0.212924i
$910$	−271746.	+	1.54115e6i	−0.328156	+	1.86107i
$911$		−	721630.i		−	0.869517i	−0.900547	−	0.434758i	$-0.856834\pi$
$911$		−	721630.i		−	0.869517i	0.900547	−	0.434758i	$-0.143166\pi$
$912$	−1.05899e6	+	224555.i	−1.27321	+	0.269981i
$913$	−533189.			−0.639646
$914$	−902486.	−	159133.i	−1.08031	−	0.190488i
$915$	−451125.	+	537629.i	−0.538833	+	0.642156i
$916$	280004.	+	101913.i	0.333714	+	0.121462i
$917$	−22274.9	+	8107.41i	−0.0264897	+	0.00964147i
$918$	356228.	−	298911.i	0.422710	−	0.354696i
$919$	645335.	+	1.11775e6i	0.764107	+	1.32347i	0.940718	+	0.339191i	$0.110153\pi$
$919$	645335.	+	1.11775e6i	0.764107	+	1.32347i	−0.176611	+	0.984281i	$0.556513\pi$
$920$	78271.2	+	45189.9i	0.0924755	+	0.0533907i
$921$	160697.	+	911356.i	0.189447	+	1.07441i
$922$	−347407.	+	61257.2i	−0.408674	+	0.0720602i
$923$	185697.	−	321637.i	0.217973	−	0.377540i
$924$	254204.	−	146765.i	0.297741	−	0.171901i
$925$	178806.	+	213093.i	0.208977	+	0.249050i
$926$	−106138.	−	291612.i	−0.123779	−	0.340081i
$927$	30485.7	−	83758.6i	0.0354761	−	0.0974698i
$928$	−106860.	−	89666.0i	−0.124085	−	0.104119i
$929$	−107932.	+	612112.i	−0.125060	+	0.709251i	0.856212	+	0.516624i	$0.172812\pi$
$929$	−107932.	+	612112.i	−0.125060	+	0.709251i	−0.981272	+	0.192626i	$0.938299\pi$
$930$		−	2.21757e6i		−	2.56396i
$931$	−566143.	+	1.06351e6i	−0.653171	+	1.22699i
$932$	225684.			0.259818
$933$	−458692.	−	80879.8i	−0.526936	−	0.0929131i
$934$	980207.	−	1.16817e6i	1.12363	−	1.33909i
$935$	389386.	+	141725.i	0.445407	+	0.162115i
$936$	121812.	−	44335.8i	0.139039	−	0.0506061i
$937$	1.25451e6	−	1.05266e6i	1.42888	−	1.19897i	0.482504	−	0.875894i	$-0.339727\pi$
$937$	1.25451e6	−	1.05266e6i	1.42888	−	1.19897i	0.946373	−	0.323076i	$-0.104717\pi$
$938$	549.419	+	951.622i	0.000624451	+	0.00108158i
$939$	552434.	+	318948.i	0.626540	+	0.361733i
$940$	83806.6	+	475291.i	0.0948468	+	0.537903i
$941$	196915.	−	34721.5i	0.222382	−	0.0392120i	−0.0613466	−	0.998117i	$-0.519540\pi$
$941$	196915.	−	34721.5i	0.222382	−	0.0392120i	0.283729	+	0.958905i	$0.408428\pi$
$942$	−482972.	+	836533.i	−0.544278	+	0.942716i
$943$	33516.7	−	19350.9i	0.0376910	−	0.0217609i
$944$	628676.	+	749226.i	0.705477	+	0.840754i
$945$	−469357.	−	1.28955e6i	−0.525581	−	1.44402i
$946$	377838.	−	1.03810e6i	0.422205	−	1.16000i
$947$	204631.	+	171706.i	0.228177	+	0.191463i	0.749707	−	0.661769i	$-0.230194\pi$
$947$	204631.	+	171706.i	0.228177	+	0.191463i	−0.521530	+	0.853233i	$0.674639\pi$
$948$	−39936.4	+	226491.i	−0.0444378	+	0.252019i
$949$			519945.i			0.577331i
$950$	219930.	−	137278.i	0.243689	−	0.152109i
$951$	1.85547e6			2.05161
$952$	−629199.	−	110945.i	−0.694247	−	0.122415i
$953$	−285665.	+	340442.i	−0.314537	+	0.374850i	−0.900031	−	0.435827i	$-0.856456\pi$
$953$	−285665.	+	340442.i	−0.314537	+	0.374850i	0.585494	+	0.810677i	$0.300901\pi$
$954$	172339.	+	62726.4i	0.189360	+	0.0689213i
$955$	−120178.	+	43741.4i	−0.131771	+	0.0479607i
$956$	−162295.	+	136182.i	−0.177578	+	0.149006i
$957$	−118762.	−	205701.i	−0.129674	−	0.224601i
$958$	232979.	+	134510.i	0.253855	+	0.146563i
$959$	−15170.7	−	86037.2i	−0.0164956	−	0.0935512i
$960$	−674942.	+	119011.i	−0.732359	+	0.129135i
$961$	1.14922e6	−	1.99050e6i	1.24438	−	2.15534i
$962$	1.11388e6	−	643099.i	1.20362	−	0.694909i
$963$	138077.	+	164553.i	0.148891	+	0.177441i
$964$	773.788	+	2125.97i	0.000832660	+	0.00228772i
$965$	65932.0	−	181147.i	0.0708014	−	0.194525i
$966$	156385.	+	131223.i	0.167588	+	0.140623i
$967$	−302510.	+	1.71562e6i	−0.323510	+	1.83471i	0.196438	+	0.980516i	$0.437062\pi$
$967$	−302510.	+	1.71562e6i	−0.323510	+	1.83471i	−0.519948	+	0.854198i	$0.674049\pi$
$968$		−	319994.i		−	0.341500i
$969$	−377727.	−	419920.i	−0.402282	−	0.447218i
$970$	166652.			0.177120
$971$	−987299.	−	174087.i	−1.04715	−	0.184641i	−0.376503	−	0.926415i	$-0.622874\pi$
$971$	−987299.	−	174087.i	−1.04715	−	0.184641i	−0.670650	+	0.741774i	$0.733985\pi$
$972$	59222.2	−	70578.2i	0.0626833	−	0.0747030i
$973$	−366331.	−	133334.i	−0.386944	−	0.140836i
$974$	78390.0	−	28531.6i	0.0826310	−	0.0300752i
$975$	−196123.	+	164567.i	−0.206310	+	0.173114i
$976$	−391418.	−	677956.i	−0.410905	−	0.711708i
$977$	1.57853e6	+	911364.i	1.65373	+	0.954779i	0.975521	+	0.219905i	$0.0705748\pi$
$977$	1.57853e6	+	911364.i	1.65373	+	0.954779i	0.678204	+	0.734874i	$0.262758\pi$
$978$	159070.	+	902133.i	0.166307	+	0.943176i
$979$	−290266.	+	51181.8i	−0.302853	+	0.0534011i
$980$	199548.	−	345627.i	0.207776	−	0.359878i
$981$	−145407.	+	83950.6i	−0.151094	+	0.0872340i
$982$	−236714.	−	282105.i	−0.245471	−	0.292541i
$983$	593685.	+	1.63114e6i	0.614397	+	1.68804i	0.720299	+	0.693664i	$0.244005\pi$
$983$	593685.	+	1.63114e6i	0.614397	+	1.68804i	−0.105902	+	0.994377i	$0.533773\pi$
$984$	−112096.	+	307981.i	−0.115771	+	0.318078i
$985$	−239729.	−	201157.i	−0.247086	−	0.207330i
$986$	32674.2	−	185305.i	0.0336087	−	0.190604i
$987$		−	2.99526e6i		−	3.07468i
$988$	−94471.0	−	234153.i	−0.0967798	−	0.239875i
$989$	161834.			0.165454
$990$	172367.	+	30392.9i	0.175866	+	0.0310100i
$991$	814108.	−	970216.i	0.828962	−	0.987918i	−0.171034	−	0.985265i	$-0.554711\pi$
$991$	814108.	−	970216.i	0.828962	−	0.987918i	0.999996	−	0.00265344i	$-0.000844616\pi$
$992$	899064.	+	327232.i	0.913623	+	0.332532i
$993$	−524762.	+	190998.i	−0.532187	+	0.193700i
$994$	−592285.	+	496986.i	−0.599457	+	0.503004i
$995$	597352.	+	1.03464e6i	0.603371	+	1.04507i
$996$	−208487.	−	120370.i	−0.210165	−	0.121339i
$997$	−217880.	−	1.23566e6i	−0.219193	−	1.24311i	−0.873480	−	0.486860i	$-0.838142\pi$
$997$	−217880.	−	1.23566e6i	−0.219193	−	1.24311i	0.654286	−	0.756247i	$-0.272969\pi$
$998$	1.36461e6	−	240618.i	1.37009	−	0.241584i
$999$	−563945.	+	976782.i	−0.565075	+	0.978738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.5.f.a.2.5	✓	36
19.10	odd	18	inner	19.5.f.a.10.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.f.a.2.5	✓	36	1.1	even	1	trivial
19.5.f.a.10.5	yes	36	19.10	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(4.43376 + 0.781791i) q^{2} +(6.29743 - 7.50499i) q^{3} +(4.01191 + 1.46022i) q^{4} +(-26.3200 + 9.57971i) q^{5} +(33.7886 - 28.3520i) q^{6} +(37.8762 + 65.6035i) q^{7} +(-45.7374 - 26.4065i) q^{8} +(-2.60170 - 14.7550i) q^{9} +O(q^{10})\)	\(q+(4.43376 + 0.781791i) q^{2} +(6.29743 - 7.50499i) q^{3} +(4.01191 + 1.46022i) q^{4} +(-26.3200 + 9.57971i) q^{5} +(33.7886 - 28.3520i) q^{6} +(37.8762 + 65.6035i) q^{7} +(-45.7374 - 26.4065i) q^{8} +(-2.60170 - 14.7550i) q^{9} +(-124.186 + 21.8973i) q^{10} +(46.3196 - 80.2278i) q^{11} +(36.2236 - 20.9137i) q^{12} +(-105.304 - 125.496i) q^{13} +(116.646 + 320.481i) q^{14} +(-93.8531 + 257.859i) q^{15} +(-234.473 - 196.746i) q^{16} +(27.7313 - 157.272i) q^{17} -67.4538i q^{18} +(360.786 - 12.4226i) q^{19} -119.582 q^{20} +(730.876 + 128.873i) q^{21} +(268.091 - 319.498i) q^{22} +(57.4137 + 20.8969i) q^{23} +(-486.209 + 176.966i) q^{24} +(122.196 - 102.535i) q^{25} +(-368.779 - 638.744i) q^{26} +(560.126 + 323.389i) q^{27} +(56.1606 + 318.503i) q^{28} +(257.731 - 45.4449i) q^{29} +(-617.714 + 1069.91i) q^{30} +(-1554.50 + 897.490i) q^{31} +(-342.620 - 408.319i) q^{32} +(-310.415 - 852.858i) q^{33} +(245.907 - 675.624i) q^{34} +(-1625.37 - 1363.84i) q^{35} +(11.1076 - 62.9946i) q^{36} +1743.86i q^{37} +(1609.35 + 226.980i) q^{38} -1604.99 q^{39} +(1456.78 + 256.869i) q^{40} +(407.163 - 485.238i) q^{41} +(3139.78 + 1142.78i) q^{42} +(2489.00 - 905.922i) q^{43} +(302.980 - 254.230i) q^{44} +(209.825 + 363.428i) q^{45} +(238.221 + 137.537i) q^{46} +(-700.829 - 3974.60i) q^{47} +(-2953.15 + 520.721i) q^{48} +(-1668.71 + 2890.29i) q^{49} +(621.948 - 359.082i) q^{50} +(-1005.69 - 1198.53i) q^{51} +(-239.217 - 657.244i) q^{52} +(-929.916 + 2554.92i) q^{53} +(2230.64 + 1871.73i) q^{54} +(-450.573 + 2555.33i) q^{55} -4000.71i q^{56} +(2178.80 - 2785.93i) q^{57} +1178.24 q^{58} +(-3146.82 - 554.869i) q^{59} +(-753.060 + 897.462i) q^{60} +(2403.35 + 874.750i) q^{61} +(-7593.91 + 2763.96i) q^{62} +(869.434 - 729.542i) q^{63} +(1248.79 + 2162.96i) q^{64} +(3973.81 + 2294.28i) q^{65} +(-709.547 - 4024.04i) q^{66} +(3.17299 - 0.559484i) q^{67} +(340.906 - 590.466i) q^{68} +(518.390 - 299.293i) q^{69} +(-6140.23 - 7317.64i) q^{70} +(775.375 + 2130.33i) q^{71} +(-270.632 + 743.555i) q^{72} +(-2431.28 - 2040.09i) q^{73} +(-1363.34 + 7731.86i) q^{74} -1562.79i q^{75} +(1465.58 + 476.987i) q^{76} +7017.63 q^{77} +(-7116.13 - 1254.76i) q^{78} +(-3534.31 + 4212.03i) q^{79} +(8056.11 + 2932.18i) q^{80} +(7094.78 - 2582.29i) q^{81} +(2184.61 - 1833.11i) q^{82} +(-2877.77 - 4984.45i) q^{83} +(2744.03 + 1584.26i) q^{84} +(776.730 + 4405.06i) q^{85} +(11743.9 - 2070.76i) q^{86} +(1281.98 - 2220.46i) q^{87} +(-4237.08 + 2446.28i) q^{88} +(-2045.12 - 2437.28i) q^{89} +(646.188 + 1775.39i) q^{90} +(4244.47 - 11661.6i) q^{91} +(199.825 + 167.673i) q^{92} +(-3053.70 + 17318.4i) q^{93} -18170.3i q^{94} +(-9376.90 + 3783.19i) q^{95} -5222.05 q^{96} +(-1301.49 - 229.488i) q^{97} +(-9658.26 + 11510.3i) q^{98} +(-1304.27 - 474.715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9	\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9} - 153 q^{10} - 48 q^{11} + 855 q^{12} + 555 q^{13} - 399 q^{14} - 1647 q^{15} - 2112 q^{16} + 39 q^{17} - 12 q^{19} + 2886 q^{20} + 912 q^{21} + 1386 q^{22} + 1074 q^{23} + 168 q^{24} + 2448 q^{25} - 3675 q^{26} + 1215 q^{27} + 2316 q^{28} - 1743 q^{29} + 2580 q^{30} - 2817 q^{31} - 6039 q^{32} - 7368 q^{33} - 8460 q^{34} - 1326 q^{35} - 4581 q^{36} + 2892 q^{38} + 7164 q^{39} + 4482 q^{40} + 6150 q^{41} + 22299 q^{42} + 2091 q^{43} + 34053 q^{44} + 3165 q^{45} + 7326 q^{46} + 4539 q^{47} - 44943 q^{48} + 102 q^{49} - 51876 q^{50} - 25836 q^{51} - 3279 q^{52} - 11607 q^{53} + 6069 q^{54} - 7044 q^{55} + 2532 q^{57} + 13644 q^{58} - 681 q^{59} + 63654 q^{60} + 44346 q^{61} + 14796 q^{62} + 53388 q^{63} + 939 q^{64} + 3636 q^{65} + 11148 q^{66} - 52089 q^{67} + 5262 q^{68} - 54954 q^{69} - 69999 q^{70} - 24504 q^{71} - 101118 q^{72} - 6666 q^{73} - 9675 q^{74} - 6462 q^{76} + 48918 q^{77} + 56871 q^{78} + 41043 q^{79} + 65649 q^{80} + 2919 q^{81} + 114711 q^{82} - 17598 q^{83} + 11115 q^{84} + 52344 q^{85} - 55716 q^{86} + 2121 q^{87} - 69057 q^{88} - 11706 q^{89} - 41394 q^{90} - 84249 q^{91} - 88668 q^{92} - 60321 q^{93} + 93405 q^{95} + 167166 q^{96} + 4401 q^{97} + 69381 q^{98} + 58386 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9 - 153 * q^10 - 48 * q^11 + 855 * q^12 + 555 * q^13 - 399 * q^14 - 1647 * q^15 - 2112 * q^16 + 39 * q^17 - 12 * q^19 + 2886 * q^20 + 912 * q^21 + 1386 * q^22 + 1074 * q^23 + 168 * q^24 + 2448 * q^25 - 3675 * q^26 + 1215 * q^27 + 2316 * q^28 - 1743 * q^29 + 2580 * q^30 - 2817 * q^31 - 6039 * q^32 - 7368 * q^33 - 8460 * q^34 - 1326 * q^35 - 4581 * q^36 + 2892 * q^38 + 7164 * q^39 + 4482 * q^40 + 6150 * q^41 + 22299 * q^42 + 2091 * q^43 + 34053 * q^44 + 3165 * q^45 + 7326 * q^46 + 4539 * q^47 - 44943 * q^48 + 102 * q^49 - 51876 * q^50 - 25836 * q^51 - 3279 * q^52 - 11607 * q^53 + 6069 * q^54 - 7044 * q^55 + 2532 * q^57 + 13644 * q^58 - 681 * q^59 + 63654 * q^60 + 44346 * q^61 + 14796 * q^62 + 53388 * q^63 + 939 * q^64 + 3636 * q^65 + 11148 * q^66 - 52089 * q^67 + 5262 * q^68 - 54954 * q^69 - 69999 * q^70 - 24504 * q^71 - 101118 * q^72 - 6666 * q^73 - 9675 * q^74 - 6462 * q^76 + 48918 * q^77 + 56871 * q^78 + 41043 * q^79 + 65649 * q^80 + 2919 * q^81 + 114711 * q^82 - 17598 * q^83 + 11115 * q^84 + 52344 * q^85 - 55716 * q^86 + 2121 * q^87 - 69057 * q^88 - 11706 * q^89 - 41394 * q^90 - 84249 * q^91 - 88668 * q^92 - 60321 * q^93 + 93405 * q^95 + 167166 * q^96 + 4401 * q^97 + 69381 * q^98 + 58386 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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