LMFDB - Embedded newform 60.5.c.a.31.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.16
Root			$-2.28990 - 1.66022i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.5.c.a.31.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.88613 + 0.947630i) q^{2} +5.19615i q^{3} +(14.2040 + 7.36522i) q^{4} +11.1803 q^{5} +(-4.92403 + 20.1929i) q^{6} +12.7755i q^{7} +(48.2191 + 42.0823i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(3.88613 + 0.947630i) q^{2} +5.19615i q^{3} +(14.2040 + 7.36522i) q^{4} +11.1803 q^{5} +(-4.92403 + 20.1929i) q^{6} +12.7755i q^{7} +(48.2191 + 42.0823i) q^{8} -27.0000 q^{9} +(43.4482 + 10.5948i) q^{10} +45.0527i q^{11} +(-38.2708 + 73.8061i) q^{12} +1.08514 q^{13} +(-12.1064 + 49.6471i) q^{14} +58.0948i q^{15} +(147.507 + 209.231i) q^{16} +40.6771 q^{17} +(-104.925 - 25.5860i) q^{18} -290.566i q^{19} +(158.805 + 82.3457i) q^{20} -66.3833 q^{21} +(-42.6933 + 175.081i) q^{22} -949.332i q^{23} +(-218.666 + 250.554i) q^{24} +125.000 q^{25} +(4.21700 + 1.02831i) q^{26} -140.296i q^{27} +(-94.0942 + 181.463i) q^{28} -402.995 q^{29} +(-55.0523 + 225.764i) q^{30} -762.034i q^{31} +(374.957 + 952.881i) q^{32} -234.101 q^{33} +(158.077 + 38.5469i) q^{34} +142.834i q^{35} +(-383.508 - 198.861i) q^{36} +1322.44 q^{37} +(275.349 - 1129.18i) q^{38} +5.63857i q^{39} +(539.105 + 470.495i) q^{40} -3204.44 q^{41} +(-257.974 - 62.9068i) q^{42} -2387.72i q^{43} +(-331.823 + 639.928i) q^{44} -301.869 q^{45} +(899.615 - 3689.22i) q^{46} +730.161i q^{47} +(-1087.20 + 766.469i) q^{48} +2237.79 q^{49} +(485.766 + 118.454i) q^{50} +211.365i q^{51} +(15.4134 + 7.99232i) q^{52} -3353.34 q^{53} +(132.949 - 545.209i) q^{54} +503.704i q^{55} +(-537.622 + 616.021i) q^{56} +1509.82 q^{57} +(-1566.09 - 381.890i) q^{58} +5216.42i q^{59} +(-427.881 + 825.178i) q^{60} +4693.09 q^{61} +(722.126 - 2961.36i) q^{62} -344.938i q^{63} +(554.154 + 4058.34i) q^{64} +12.1323 q^{65} +(-909.745 - 221.841i) q^{66} +3350.15i q^{67} +(577.778 + 299.596i) q^{68} +4932.87 q^{69} +(-135.354 + 555.072i) q^{70} +8480.62i q^{71} +(-1301.91 - 1136.22i) q^{72} -174.622 q^{73} +(5139.18 + 1253.18i) q^{74} +649.519i q^{75} +(2140.08 - 4127.20i) q^{76} -575.569 q^{77} +(-5.34327 + 21.9122i) q^{78} +10190.1i q^{79} +(1649.18 + 2339.28i) q^{80} +729.000 q^{81} +(-12452.9 - 3036.63i) q^{82} -8834.98i q^{83} +(-942.908 - 488.928i) q^{84} +454.784 q^{85} +(2262.67 - 9278.99i) q^{86} -2094.02i q^{87} +(-1895.92 + 2172.40i) q^{88} -1931.20 q^{89} +(-1173.10 - 286.060i) q^{90} +13.8632i q^{91} +(6992.04 - 13484.3i) q^{92} +3959.65 q^{93} +(-691.923 + 2837.50i) q^{94} -3248.62i q^{95} +(-4951.32 + 1948.34i) q^{96} -14299.1 q^{97} +(8696.33 + 2120.59i) q^{98} -1216.42i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	3.88613	+	0.947630i	0.971532	+	0.236907i
$2$	3.88613	+	0.947630i	0.971532	+	0.236907i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	14.2040	+	7.36522i	0.887750	+	0.460326i
$5$	11.1803			0.447214
$5$	11.1803			0.447214
$6$	−4.92403	+	20.1929i	−0.136779	+	0.560914i
$7$			12.7755i			0.260724i	0.991466	+	0.130362i	$0.0416139\pi$
$7$			12.7755i			0.260724i	−0.991466	+	0.130362i	$0.958386\pi$
$8$	48.2191	+	42.0823i	0.753423	+	0.657536i
$9$	−27.0000			−0.333333
$10$	43.4482	+	10.5948i	0.434482	+	0.105948i
$11$			45.0527i			0.372336i	0.982518	+	0.186168i	$0.0596069\pi$
$11$			45.0527i			0.372336i	−0.982518	+	0.186168i	$0.940393\pi$
$12$	−38.2708	+	73.8061i	−0.265770	+	0.512543i
$13$	1.08514			0.00642096			0.00321048	−	0.999995i	$-0.498978\pi$
$13$	1.08514			0.00642096			0.00321048	+	0.999995i	$0.498978\pi$
$14$	−12.1064	+	49.6471i	−0.0617674	+	0.253302i
$15$			58.0948i			0.258199i
$16$	147.507	+	209.231i	0.576199	+	0.817309i
$17$	40.6771			0.140751			0.0703757	−	0.997521i	$-0.477580\pi$
$17$	40.6771			0.140751			0.0703757	+	0.997521i	$0.477580\pi$
$18$	−104.925	−	25.5860i	−0.323844	−	0.0789691i
$19$		−	290.566i		−	0.804892i	−0.915444	−	0.402446i	$-0.868160\pi$
$19$		−	290.566i		−	0.804892i	0.915444	−	0.402446i	$-0.131840\pi$
$20$	158.805	+	82.3457i	0.397014	+	0.205864i
$21$	−66.3833			−0.150529
$22$	−42.6933	+	175.081i	−0.0882092	+	0.361737i
$23$		−	949.332i		−	1.79458i	−0.441444	−	0.897289i	$-0.645534\pi$
$23$		−	949.332i		−	1.79458i	0.441444	−	0.897289i	$-0.354466\pi$
$24$	−218.666	+	250.554i	−0.379629	+	0.434989i
$25$	125.000			0.200000
$26$	4.21700	+	1.02831i	0.00623817	+	0.00152117i
$27$		−	140.296i		−	0.192450i
$28$	−94.0942	+	181.463i	−0.120018	+	0.231458i
$29$	−402.995			−0.479186			−0.239593	−	0.970873i	$-0.577014\pi$
$29$	−402.995			−0.479186			−0.239593	+	0.970873i	$0.577014\pi$
$30$	−55.0523	+	225.764i	−0.0611692	+	0.250849i
$31$		−	762.034i		−	0.792960i	−0.918043	−	0.396480i	$-0.870232\pi$
$31$		−	762.034i		−	0.792960i	0.918043	−	0.396480i	$-0.129768\pi$
$32$	374.957	+	952.881i	0.366169	+	0.930548i
$33$	−234.101			−0.214968
$34$	158.077	+	38.5469i	0.136744	+	0.0333450i
$35$			142.834i			0.116599i
$36$	−383.508	−	198.861i	−0.295917	−	0.153442i
$37$	1322.44			0.965991			0.482995	−	0.875623i	$-0.339549\pi$
$37$	1322.44			0.965991			0.482995	+	0.875623i	$0.339549\pi$
$38$	275.349	−	1129.18i	0.190685	−	0.781978i
$39$			5.63857i			0.00370714i
$40$	539.105	+	470.495i	0.336941	+	0.294059i
$41$	−3204.44			−1.90627			−0.953136	−	0.302541i	$-0.902165\pi$
$41$	−3204.44			−1.90627			−0.953136	+	0.302541i	$0.902165\pi$
$42$	−257.974	−	62.9068i	−0.146244	−	0.0356614i
$43$		−	2387.72i		−	1.29136i	−0.763609	−	0.645679i	$-0.776575\pi$
$43$		−	2387.72i		−	1.29136i	0.763609	−	0.645679i	$-0.223425\pi$
$44$	−331.823	+	639.928i	−0.171396	+	0.330541i
$45$	−301.869			−0.149071
$46$	899.615	−	3689.22i	0.425149	−	1.74349i
$47$			730.161i			0.330539i	0.986248	+	0.165270i	$0.0528495\pi$
$47$			730.161i			0.330539i	−0.986248	+	0.165270i	$0.947151\pi$
$48$	−1087.20	+	766.469i	−0.471874	+	0.332669i
$49$	2237.79			0.932023
$50$	485.766	+	118.454i	0.194306	+	0.0473815i
$51$			211.365i			0.0812628i
$52$	15.4134	+	7.99232i	0.00570021	+	0.00295574i
$53$	−3353.34			−1.19378			−0.596892	−	0.802322i	$-0.703598\pi$
$53$	−3353.34			−1.19378			−0.596892	+	0.802322i	$0.703598\pi$
$54$	132.949	−	545.209i	0.0455929	−	0.186971i
$55$			503.704i			0.166514i
$56$	−537.622	+	616.021i	−0.171435	+	0.196435i
$57$	1509.82			0.464704
$58$	−1566.09	−	381.890i	−0.465544	−	0.113523i
$59$			5216.42i			1.49854i	0.662264	+	0.749270i	$0.269596\pi$
$59$			5216.42i			1.49854i	−0.662264	+	0.749270i	$0.730404\pi$
$60$	−427.881	+	825.178i	−0.118856	+	0.229216i
$61$	4693.09			1.26124			0.630622	−	0.776090i	$-0.282800\pi$
$61$	4693.09			1.26124			0.630622	+	0.776090i	$0.282800\pi$
$62$	722.126	−	2961.36i	0.187858	−	0.770386i
$63$		−	344.938i		−	0.0869080i
$64$	554.154	+	4058.34i	0.135292	+	0.990806i
$65$	12.1323			0.00287154
$66$	−909.745	−	221.841i	−0.208849	−	0.0509276i
$67$			3350.15i			0.746302i	0.927771	+	0.373151i	$0.121723\pi$
$67$			3350.15i			0.746302i	−0.927771	+	0.373151i	$0.878277\pi$
$68$	577.778	+	299.596i	0.124952	+	0.0647916i
$69$	4932.87			1.03610
$70$	−135.354	+	555.072i	−0.0276232	+	0.113280i
$71$			8480.62i			1.68233i	0.540780	+	0.841164i	$0.318129\pi$
$71$			8480.62i			1.68233i	−0.540780	+	0.841164i	$0.681871\pi$
$72$	−1301.91	−	1136.22i	−0.251141	−	0.219179i
$73$	−174.622			−0.0327683			−0.0163842	−	0.999866i	$-0.505215\pi$
$73$	−174.622			−0.0327683			−0.0163842	+	0.999866i	$0.505215\pi$
$74$	5139.18	+	1253.18i	0.938491	+	0.228850i
$75$			649.519i			0.115470i
$76$	2140.08	−	4127.20i	0.370513	−	0.714542i
$77$	−575.569			−0.0970770
$78$	−5.34327	+	21.9122i	−0.000878250	+	0.00360161i
$79$			10190.1i			1.63277i	0.577510	+	0.816384i	$0.304024\pi$
$79$			10190.1i			1.63277i	−0.577510	+	0.816384i	$0.695976\pi$
$80$	1649.18	+	2339.28i	0.257684	+	0.365512i
$81$	729.000			0.111111
$82$	−12452.9	−	3036.63i	−1.85201	−	0.451610i
$83$		−	8834.98i		−	1.28248i	−0.767342	−	0.641238i	$-0.778421\pi$
$83$		−	8834.98i		−	1.28248i	0.767342	−	0.641238i	$-0.221579\pi$
$84$	−942.908	−	488.928i	−0.133632	−	0.0692925i
$85$	454.784			0.0629459
$86$	2262.67	−	9278.99i	0.305932	−	1.25460i
$87$		−	2094.02i		−	0.276658i
$88$	−1895.92	+	2172.40i	−0.244825	+	0.280527i
$89$	−1931.20			−0.243807			−0.121904	−	0.992542i	$-0.538900\pi$
$89$	−1931.20			−0.243807			−0.121904	+	0.992542i	$0.538900\pi$
$90$	−1173.10	−	286.060i	−0.144827	−	0.0353161i
$91$			13.8632i			0.00167410i
$92$	6992.04	−	13484.3i	0.826092	−	1.59314i
$93$	3959.65			0.457816
$94$	−691.923	+	2837.50i	−0.0783072	+	0.321130i
$95$		−	3248.62i		−	0.359958i
$96$	−4951.32	+	1948.34i	−0.537252	+	0.211408i
$97$	−14299.1			−1.51973			−0.759865	−	0.650081i	$-0.774735\pi$
$97$	−14299.1			−1.51973			−0.759865	+	0.650081i	$0.774735\pi$
$98$	8696.33	+	2120.59i	0.905490	+	0.220803i
$99$		−	1216.42i		−	0.124112i
$100$	1775.50	+	920.653i	0.177550	+	0.0920653i
$101$	−2580.80			−0.252995			−0.126498	−	0.991967i	$-0.540374\pi$
$101$	−2580.80			−0.252995			−0.126498	+	0.991967i	$0.540374\pi$
$102$	−200.295	+	821.390i	−0.0192518	+	0.0789495i
$103$		−	15113.1i		−	1.42455i	−0.701900	−	0.712276i	$-0.747664\pi$
$103$		−	15113.1i		−	1.42455i	0.701900	−	0.712276i	$-0.252336\pi$
$104$	52.3246	+	45.6653i	0.00483770	+	0.00422202i
$105$	−742.188			−0.0673186
$106$	−13031.5	−	3177.72i	−1.15980	−	0.282816i
$107$		−	8409.89i		−	0.734552i	−0.930112	−	0.367276i	$-0.880290\pi$
$107$		−	8409.89i		−	0.734552i	0.930112	−	0.367276i	$-0.119710\pi$
$108$	1033.31	−	1992.77i	0.0885899	−	0.170848i
$109$	−3681.26			−0.309845			−0.154922	−	0.987927i	$-0.549513\pi$
$109$	−3681.26			−0.309845			−0.154922	+	0.987927i	$0.549513\pi$
$110$	−477.325	+	1957.46i	−0.0394484	+	0.161774i
$111$			6871.61i			0.557715i
$112$	−2673.03	+	1884.47i	−0.213092	+	0.150229i
$113$	−13035.1			−1.02084			−0.510421	−	0.859925i	$-0.670510\pi$
$113$	−13035.1			−1.02084			−0.510421	+	0.859925i	$0.670510\pi$
$114$	5867.37	+	1430.75i	0.451475	+	0.110092i
$115$		−	10613.8i		−	0.802560i
$116$	−5724.14	−	2968.15i	−0.425397	−	0.220582i
$117$	−29.2989			−0.00214032
$118$	−4943.23	+	20271.7i	−0.355015	+	1.45588i
$119$			519.670i			0.0366972i
$120$	−2444.76	+	2801.27i	−0.169775	+	0.194533i
$121$	12611.3			0.861366
$122$	18238.0	+	4447.31i	1.22534	+	0.298798i
$123$		−	16650.8i		−	1.10059i
$124$	5612.55	−	10823.9i	0.365020	−	0.703950i
$125$	1397.54			0.0894427
$126$	326.873	−	1340.47i	0.0205891	−	0.0844339i
$127$			19550.9i			1.21216i	0.795403	+	0.606080i	$0.207259\pi$
$127$			19550.9i			1.21216i	−0.795403	+	0.606080i	$0.792741\pi$
$128$	−1692.29	+	16296.4i	−0.103289	+	0.994651i
$129$	12407.0			0.745566
$130$	47.1475	+	11.4969i	0.00278980	+	0.000680290i
$131$			1887.90i			0.110011i	0.998486	+	0.0550055i	$0.0175176\pi$
$131$			1887.90i			0.110011i	−0.998486	+	0.0550055i	$0.982482\pi$
$132$	−3325.16	−	1724.20i	−0.190838	−	0.0989557i
$133$	3712.12			0.209854
$134$	−3174.70	+	13019.1i	−0.176805	+	0.725057i
$135$		−	1568.56i		−	0.0860663i
$136$	1961.41	+	1711.79i	0.106045	+	0.0925491i
$137$	25161.2			1.34057			0.670286	−	0.742102i	$-0.266171\pi$
$137$	25161.2			1.34057			0.670286	+	0.742102i	$0.266171\pi$
$138$	19169.8	+	4674.54i	1.00660	+	0.245460i
$139$		−	18985.8i		−	0.982652i	−0.870976	−	0.491326i	$-0.836512\pi$
$139$		−	18985.8i		−	0.982652i	0.870976	−	0.491326i	$-0.163488\pi$
$140$	−1052.01	+	2028.82i	−0.0536737	+	0.103511i
$141$	−3794.03			−0.190837
$142$	−8036.48	+	32956.8i	−0.398556	+	1.63444i
$143$			48.8886i			0.00239076i
$144$	−3982.69	−	5649.24i	−0.192066	−	0.272436i
$145$	−4505.62			−0.214298
$146$	−678.605	−	165.477i	−0.0318355	−	0.00776306i
$147$			11627.9i			0.538104i
$148$	18784.0	+	9740.08i	0.857558	+	0.444671i
$149$	−21626.8			−0.974137			−0.487069	−	0.873364i	$-0.661934\pi$
$149$	−21626.8			−0.974137			−0.487069	+	0.873364i	$0.661934\pi$
$150$	−615.504	+	2524.11i	−0.0273557	+	0.112183i
$151$			23313.1i			1.02246i	0.859445	+	0.511229i	$0.170810\pi$
$151$			23313.1i			1.02246i	−0.859445	+	0.511229i	$0.829190\pi$
$152$	12227.7	−	14010.8i	0.529246	−	0.606424i
$153$	−1098.28			−0.0469171
$154$	−2236.74	−	545.427i	−0.0943134	−	0.0229983i
$155$		−	8519.80i		−	0.354622i
$156$	−41.5293	+	80.0902i	−0.00170650	+	0.00329102i
$157$	−927.181			−0.0376154			−0.0188077	−	0.999823i	$-0.505987\pi$
$157$	−927.181			−0.0376154			−0.0188077	+	0.999823i	$0.505987\pi$
$158$	−9656.44	+	39600.0i	−0.386815	+	1.58629i
$159$		−	17424.5i		−	0.689231i
$160$	4192.15	+	10653.5i	0.163756	+	0.416154i
$161$	12128.2			0.467889
$162$	2832.99	+	690.822i	0.107948	+	0.0263230i
$163$		−	22278.6i		−	0.838517i	−0.907867	−	0.419258i	$-0.862290\pi$
$163$		−	22278.6i		−	0.838517i	0.907867	−	0.419258i	$-0.137710\pi$
$164$	−45515.9	−	23601.4i	−1.69229	−	0.877508i
$165$	−2617.33			−0.0961368
$166$	8372.29	−	34333.9i	0.303828	−	1.24597i
$167$			17349.7i			0.622097i	0.950394	+	0.311048i	$0.100680\pi$
$167$			17349.7i			0.622097i	−0.950394	+	0.311048i	$0.899320\pi$
$168$	−3200.94	−	2793.56i	−0.113412	−	0.0989783i
$169$	−28559.8			−0.999959
$170$	1767.35	+	430.967i	0.0611540	+	0.0149124i
$171$			7845.28i			0.268297i
$172$	17586.1	−	33915.2i	0.594446	−	1.14640i
$173$	−24129.5			−0.806224			−0.403112	−	0.915151i	$-0.632072\pi$
$173$	−24129.5			−0.806224			−0.403112	+	0.915151i	$0.632072\pi$
$174$	1984.36	−	8137.65i	0.0655424	−	0.268782i
$175$			1596.93i			0.0521448i
$176$	−9426.43	+	6645.59i	−0.304314	+	0.214540i
$177$	−27105.3			−0.865183
$178$	−7504.88	−	1830.06i	−0.236867	−	0.0577597i
$179$		−	20100.0i		−	0.627321i	−0.949535	−	0.313661i	$-0.898445\pi$
$179$		−	20100.0i		−	0.627321i	0.949535	−	0.313661i	$-0.101555\pi$
$180$	−4287.75	−	2223.33i	−0.132338	−	0.0686214i
$181$	22998.4			0.702004			0.351002	−	0.936375i	$-0.385841\pi$
$181$	22998.4			0.702004			0.351002	+	0.936375i	$0.385841\pi$
$182$	−13.1372	+	53.8742i	−0.000396606	+	0.00162644i
$183$			24386.0i			0.728180i
$184$	39950.1	−	45775.9i	1.18000	−	1.35208i
$185$	14785.3			0.432004
$186$	15387.7	+	3752.28i	0.444783	+	0.108460i
$187$			1832.61i			0.0524068i
$188$	−5377.80	+	10371.2i	−0.152156	+	0.293436i
$189$	1792.35			0.0501763
$190$	3078.49	−	12624.6i	0.0852768	−	0.349711i
$191$			54858.4i			1.50375i	0.659304	+	0.751877i	$0.270851\pi$
$191$			54858.4i			1.50375i	−0.659304	+	0.751877i	$0.729149\pi$
$192$	−21087.8	+	2879.47i	−0.572042	+	0.0781106i
$193$	46044.5			1.23613			0.618064	−	0.786128i	$-0.287917\pi$
$193$	46044.5			1.23613			0.618064	+	0.786128i	$0.287917\pi$
$194$	−55568.3	−	13550.3i	−1.47647	−	0.360035i
$195$			63.0411i			0.00165789i
$196$	31785.5	+	16481.8i	0.827403	+	0.429035i
$197$	65186.1			1.67966			0.839832	−	0.542846i	$-0.182653\pi$
$197$	65186.1			1.67966			0.839832	+	0.542846i	$0.182653\pi$
$198$	1152.72	−	4727.18i	0.0294031	−	0.120579i
$199$		−	2331.77i		−	0.0588816i	−0.999567	−	0.0294408i	$-0.990627\pi$
$199$		−	2331.77i		−	0.0588816i	0.999567	−	0.0294408i	$-0.00937265\pi$
$200$	6027.38	+	5260.29i	0.150685	+	0.131507i
$201$	−17407.9			−0.430878
$202$	−10029.3	−	2445.65i	−0.245793	−	0.0599365i
$203$		−	5148.45i		−	0.124935i
$204$	−1556.75	+	3002.22i	−0.0374074	+	0.0721411i
$205$	−35826.8			−0.852511
$206$	14321.6	−	58731.3i	0.337487	−	1.38400i
$207$			25632.0i			0.598193i
$208$	160.066	+	227.046i	0.00369975	+	0.00524791i
$209$	13090.8			0.299690
$210$	−2884.24	−	703.319i	−0.0654022	−	0.0159483i
$211$			11895.7i			0.267193i	0.991036	+	0.133596i	$0.0426526\pi$
$211$			11895.7i			0.267193i	−0.991036	+	0.133596i	$0.957347\pi$
$212$	−47630.8	−	24698.1i	−1.05978	−	0.549530i
$213$	−44066.6			−0.971293
$214$	7969.46	−	32681.9i	0.174021	−	0.713641i
$215$		−	26695.5i		−	0.577513i
$216$	5903.99	−	6764.95i	0.126543	−	0.144996i
$217$	9735.35			0.206744
$218$	−14305.9	−	3488.48i	−0.301024	−	0.0734045i
$219$		−	907.365i		−	0.0189188i
$220$	−3709.90	+	7154.62i	−0.0766507	+	0.147823i
$221$	44.1405			0.000903759
$222$	−6511.74	+	26703.9i	−0.132127	+	0.541838i
$223$			33260.6i			0.668838i	0.942425	+	0.334419i	$0.108540\pi$
$223$			33260.6i			0.668838i	−0.942425	+	0.334419i	$0.891460\pi$
$224$	−12173.5	+	4790.26i	−0.242616	+	0.0954691i
$225$	−3375.00			−0.0666667
$226$	−50656.2	−	12352.5i	−0.991781	−	0.241845i
$227$		−	43187.7i		−	0.838124i	−0.907958	−	0.419062i	$-0.862359\pi$
$227$		−	43187.7i		−	0.838124i	0.907958	−	0.419062i	$-0.137641\pi$
$228$	21445.5	+	11120.2i	0.412541	+	0.213916i
$229$	3712.09			0.0707860			0.0353930	−	0.999373i	$-0.488732\pi$
$229$	3712.09			0.0707860			0.0353930	+	0.999373i	$0.488732\pi$
$230$	10058.0	−	41246.8i	0.190132	−	0.779712i
$231$		−	2990.75i		−	0.0560474i
$232$	−19432.1	−	16959.0i	−0.361029	−	0.315082i
$233$	58034.1			1.06898			0.534492	−	0.845174i	$-0.320503\pi$
$233$	58034.1			1.06898			0.534492	+	0.845174i	$0.320503\pi$
$234$	−113.859	−	27.7645i	−0.00207939	−	0.000507058i
$235$			8163.45i			0.147822i
$236$	−38420.1	+	74094.0i	−0.689818	+	1.33033i
$237$	−52949.3			−0.942679
$238$	−492.454	+	2019.50i	−0.00869385	+	0.0356526i
$239$			51784.2i			0.906571i	0.891365	+	0.453285i	$0.149748\pi$
$239$			51784.2i			0.906571i	−0.891365	+	0.453285i	$0.850252\pi$
$240$	−12155.2	+	8569.38i	−0.211028	+	0.148774i
$241$	−67110.2			−1.15546			−0.577730	−	0.816228i	$-0.696061\pi$
$241$	−67110.2			−1.15546			−0.577730	+	0.816228i	$0.696061\pi$
$242$	49009.0	+	11950.8i	0.836844	+	0.204064i
$243$			3788.00i			0.0641500i
$244$	66660.6	+	34565.7i	1.11967	+	0.580584i
$245$	25019.2			0.416813
$246$	15778.8	−	64707.1i	0.260737	−	1.06926i
$247$		−	315.305i		−	0.00516818i
$248$	32068.2	−	36744.6i	0.521400	−	0.597434i
$249$	45907.9			0.740438
$250$	5431.03	+	1324.35i	0.0868965	+	0.0211896i
$251$		−	48057.4i		−	0.762804i	−0.924409	−	0.381402i	$-0.875441\pi$
$251$		−	48057.4i		−	0.762804i	0.924409	−	0.381402i	$-0.124559\pi$
$252$	2540.54	−	4899.49i	0.0400060	−	0.0771525i
$253$	42769.9			0.668186
$254$	−18527.1	+	75977.5i	−0.287170	+	1.17765i
$255$			2363.13i			0.0363418i
$256$	−22019.4	+	61726.1i	−0.335989	+	0.941866i
$257$	−6448.35			−0.0976298			−0.0488149	−	0.998808i	$-0.515544\pi$
$257$	−6448.35			−0.0976298			−0.0488149	+	0.998808i	$0.515544\pi$
$258$	48215.0	+	11757.2i	0.724341	+	0.176630i
$259$			16894.8i			0.251857i
$260$	172.327	+	89.3568i	0.00254921	+	0.00132185i
$261$	10880.9			0.159729
$262$	−1789.03	+	7336.61i	−0.0260624	+	0.106879i
$263$			39962.0i			0.577744i	0.957368	+	0.288872i	$0.0932802\pi$
$263$			39962.0i			0.577744i	−0.957368	+	0.288872i	$0.906720\pi$
$264$	−11288.1	−	9851.50i	−0.161962	−	0.141350i
$265$	−37491.4			−0.533876
$266$	14425.8	+	3517.71i	0.203880	+	0.0497161i
$267$		−	10034.8i		−	0.140762i
$268$	−24674.6	+	47585.5i	−0.343543	+	0.662529i
$269$	44075.5			0.609105			0.304553	−	0.952496i	$-0.401493\pi$
$269$	44075.5			0.609105			0.304553	+	0.952496i	$0.401493\pi$
$270$	1486.41	−	6095.62i	0.0203897	−	0.0836162i
$271$		−	6304.42i		−	0.0858433i	−0.999078	−	0.0429216i	$-0.986333\pi$
$271$		−	6304.42i		−	0.0858433i	0.999078	−	0.0429216i	$-0.0136666\pi$
$272$	6000.16	+	8510.93i	0.0811008	+	0.115037i
$273$	−72.0354			−0.000966541
$274$	97779.7	+	23843.5i	1.30241	+	0.317592i
$275$			5631.59i			0.0744673i
$276$	70066.5	+	36331.7i	0.919797	+	0.476944i
$277$	−9193.62			−0.119819			−0.0599097	−	0.998204i	$-0.519081\pi$
$277$	−9193.62			−0.119819			−0.0599097	+	0.998204i	$0.519081\pi$
$278$	17991.5	−	73781.4i	0.232798	−	0.954679i
$279$			20574.9i			0.264320i
$280$	−6010.79	+	6887.33i	−0.0766683	+	0.0878485i
$281$	−35394.6			−0.448254			−0.224127	−	0.974560i	$-0.571953\pi$
$281$	−35394.6			−0.448254			−0.224127	+	0.974560i	$0.571953\pi$
$282$	−14744.1	−	3595.34i	−0.185404	−	0.0452107i
$283$		−	45365.6i		−	0.566439i	−0.959055	−	0.283220i	$-0.908597\pi$
$283$		−	45365.6i		−	0.566439i	0.959055	−	0.283220i	$-0.0914026\pi$
$284$	−62461.6	+	120459.i	−0.774420	+	1.49349i
$285$	16880.3			0.207822
$286$	−46.3283	+	189.987i	−0.000566388	+	0.00232270i
$287$		−	40938.3i		−	0.497011i
$288$	−10123.9	−	25727.8i	−0.122056	−	0.310183i
$289$	−81866.4			−0.980189
$290$	−17509.4	−	4269.66i	−0.208198	−	0.0507689i
$291$		−	74300.5i		−	0.877416i
$292$	−2480.34	−	1286.13i	−0.0290901	−	0.0150841i
$293$	−105959.			−1.23425			−0.617123	−	0.786867i	$-0.711702\pi$
$293$	−105959.			−1.23425			−0.617123	+	0.786867i	$0.711702\pi$
$294$	−11018.9	+	45187.5i	−0.127481	+	0.522785i
$295$			58321.3i			0.670168i
$296$	63766.9	+	55651.4i	0.727799	+	0.635174i
$297$	6320.72			0.0716562
$298$	−84044.6	−	20494.2i	−0.946405	−	0.230780i
$299$		−	1030.16i		−	0.0115229i
$300$	−4783.85	+	9225.77i	−0.0531539	+	0.102509i
$301$	30504.2			0.336688
$302$	−22092.1	+	90597.5i	−0.242228	+	0.993351i
$303$		−	13410.3i		−	0.146067i
$304$	60795.4	−	42860.5i	0.657845	−	0.463778i
$305$	52470.3			0.564046
$306$	−4268.07	−	1040.77i	−0.0455815	−	0.0111150i
$307$		−	135901.i		−	1.44194i	−0.692968	−	0.720968i	$-0.743697\pi$
$307$		−	135901.i		−	1.44194i	0.692968	−	0.720968i	$-0.256303\pi$
$308$	−8175.39	−	4239.20i	−0.0861801	−	0.0446871i
$309$	78529.8			0.822465
$310$	8073.62	−	33109.1i	0.0840127	−	0.344527i
$311$		−	129107.i		−	1.33484i	−0.744682	−	0.667420i	$-0.767399\pi$
$311$		−	129107.i		−	1.33484i	0.744682	−	0.667420i	$-0.232601\pi$
$312$	−237.284	+	271.886i	−0.00243758	+	0.00279305i
$313$	18229.0			0.186069			0.0930344	−	0.995663i	$-0.470343\pi$
$313$	18229.0			0.186069			0.0930344	+	0.995663i	$0.470343\pi$
$314$	−3603.15	−	878.625i	−0.0365446	−	0.00891136i
$315$		−	3856.52i		−	0.0388664i
$316$	−75052.4	+	144740.i	−0.751606	+	1.44949i
$317$	−56111.6			−0.558385			−0.279193	−	0.960235i	$-0.590067\pi$
$317$	−56111.6			−0.558385			−0.279193	+	0.960235i	$0.590067\pi$
$318$	16511.9	−	67713.7i	0.163284	−	0.669610i
$319$		−	18156.0i		−	0.178418i
$320$	6195.63	+	45373.6i	0.0605042	+	0.443102i
$321$	43699.0			0.424094
$322$	47131.6	+	11493.0i	0.454570	+	0.110846i
$323$		−	11819.4i		−	0.113290i
$324$	10354.7	+	5369.25i	0.0986389	+	0.0511474i
$325$	135.643			0.00128419
$326$	21111.8	−	86577.3i	0.198651	−	0.814646i
$327$		−	19128.4i		−	0.178889i
$328$	−154515.	−	134851.i	−1.43623	−	1.25344i
$329$	−9328.16			−0.0861795
$330$	−10171.3	−	2480.26i	−0.0934000	−	0.0227755i
$331$		−	139482.i		−	1.27310i	−0.771237	−	0.636548i	$-0.780362\pi$
$331$		−	139482.i		−	1.27310i	0.771237	−	0.636548i	$-0.219638\pi$
$332$	65071.6	−	125492.i	0.590358	−	1.13852i
$333$	−35705.9			−0.321997
$334$	−16441.1	+	67423.0i	−0.147379	+	0.604387i
$335$			37455.8i			0.333756i
$336$	−9792.00	−	13889.5i	−0.0867347	−	0.123029i
$337$	−73535.8			−0.647499			−0.323749	−	0.946143i	$-0.604943\pi$
$337$	−73535.8			−0.647499			−0.323749	+	0.946143i	$0.604943\pi$
$338$	−110987.	−	27064.1i	−0.971492	−	0.236898i
$339$		−	67732.5i		−	0.589384i
$340$	6459.75	+	3349.59i	0.0558802	+	0.0289757i
$341$	34331.7			0.295248
$342$	−7434.42	+	30487.8i	−0.0635616	+	0.260659i
$343$			59262.7i			0.503725i
$344$	100481.	−	115134.i	0.849115	−	0.972938i
$345$	55151.2			0.463358
$346$	−93770.3	−	22865.8i	−0.783273	−	0.191001i
$347$			16756.7i			0.139165i	0.997576	+	0.0695825i	$0.0221667\pi$
$347$			16756.7i			0.139165i	−0.997576	+	0.0695825i	$0.977833\pi$
$348$	15423.0	−	29743.5i	0.127353	−	0.245603i
$349$	−132485.			−1.08772			−0.543858	−	0.839177i	$-0.683037\pi$
$349$	−132485.			−1.08772			−0.543858	+	0.839177i	$0.683037\pi$
$350$	−1513.30	+	6205.89i	−0.0123535	+	0.0506603i
$351$		−	152.241i		−	0.00123571i
$352$	−42929.9	+	16892.8i	−0.346477	+	0.136338i
$353$	−139862.			−1.12241			−0.561204	−	0.827678i	$-0.689662\pi$
$353$	−139862.			−1.12241			−0.561204	+	0.827678i	$0.689662\pi$
$354$	−105335.	−	25685.8i	−0.840553	−	0.204968i
$355$			94816.2i			0.752360i
$356$	−27430.7	−	14223.7i	−0.216440	−	0.112231i
$357$	−2700.28			−0.0211872
$358$	19047.4	−	78111.2i	0.148617	−	0.609463i
$359$			7657.52i			0.0594155i	0.999559	+	0.0297077i	$0.00945766\pi$
$359$			7657.52i			0.0594155i	−0.999559	+	0.0297077i	$0.990542\pi$
$360$	−14555.8	−	12703.4i	−0.112314	−	0.0980198i
$361$	45892.5			0.352150
$362$	89374.6	+	21793.9i	0.682020	+	0.166310i
$363$			65530.0i			0.497310i
$364$	−102.106	+	196.913i	−0.000770632	+	0.00148618i
$365$	−1952.34			−0.0146544
$366$	−23108.9	+	94767.2i	−0.172511	+	0.707450i
$367$			107072.i			0.794957i	0.917611	+	0.397479i	$0.130115\pi$
$367$			107072.i			0.794957i	−0.917611	+	0.397479i	$0.869885\pi$
$368$	198630.	−	140033.i	1.46673	−	1.03403i
$369$	86520.0			0.635424
$370$	57457.8	+	14011.0i	0.419706	+	0.102345i
$371$		−	42840.5i		−	0.311248i
$372$	56242.8	+	29163.7i	0.406426	+	0.210745i
$373$	236050.			1.69662			0.848312	−	0.529496i	$-0.177619\pi$
$373$	236050.			1.69662			0.848312	+	0.529496i	$0.177619\pi$
$374$	−1736.64	+	7121.78i	−0.0124156	+	0.0509149i
$375$			7261.84i			0.0516398i
$376$	−30726.9	+	35207.7i	−0.217342	+	0.249036i
$377$	−437.307			−0.00307683
$378$	6965.30	+	1698.48i	0.0487479	+	0.0118871i
$379$			260543.i			1.81385i	0.421291	+	0.906925i	$0.361577\pi$
$379$			260543.i			1.81385i	−0.421291	+	0.906925i	$0.638423\pi$
$380$	23926.8	−	46143.5i	0.165698	−	0.319553i
$381$	−101590.			−0.699841
$382$	−51985.5	+	213187.i	−0.356250	+	1.46094i
$383$			265752.i			1.81167i	0.423633	+	0.905834i	$0.360755\pi$
$383$			265752.i			1.81167i	−0.423633	+	0.905834i	$0.639245\pi$
$384$	−84678.4	−	8793.40i	−0.574262	−	0.0596340i
$385$	−6435.06			−0.0434141
$386$	178935.	+	43633.1i	1.20094	+	0.292848i
$387$			64468.4i			0.430453i
$388$	−203105.	−	105316.i	−1.34914	−	0.699572i
$389$	84750.8			0.560073			0.280036	−	0.959989i	$-0.409653\pi$
$389$	84750.8			0.560073			0.280036	+	0.959989i	$0.409653\pi$
$390$	−59.7396	+	244.986i	−0.000392765	+	0.00161069i
$391$		−	38616.1i		−	0.252589i
$392$	107904.	+	94171.3i	0.702207	+	0.612839i
$393$	−9809.80			−0.0635148
$394$	253322.	+	61772.3i	1.63185	+	0.397925i
$395$			113929.i			0.730196i
$396$	8959.23	−	17278.1i	0.0571321	−	0.110180i
$397$	301506.			1.91300			0.956500	−	0.291733i	$-0.0942317\pi$
$397$	301506.			1.91300			0.956500	+	0.291733i	$0.0942317\pi$
$398$	2209.65	−	9061.56i	0.0139495	−	0.0572054i
$399$			19288.7i			0.121160i
$400$	18438.4	+	26153.9i	0.115240	+	0.163462i
$401$	−185990.			−1.15665			−0.578324	−	0.815807i	$-0.696293\pi$
$401$	−185990.			−1.15665			−0.578324	+	0.815807i	$0.696293\pi$
$402$	−67649.3	−	16496.2i	−0.418612	−	0.102078i
$403$		−	826.916i		−	0.00509156i
$404$	−36657.7	−	19008.2i	−0.224596	−	0.116460i
$405$	8150.47			0.0496904
$406$	4878.83	−	20007.6i	0.0295981	−	0.121379i
$407$			59579.5i			0.359673i
$408$	−8894.72	+	10191.8i	−0.0534333	+	0.0612253i
$409$	−178037.			−1.06430			−0.532151	−	0.846650i	$-0.678616\pi$
$409$	−178037.			−1.06430			−0.532151	+	0.846650i	$0.678616\pi$
$410$	−139227.	−	33950.5i	−0.828242	−	0.201966i
$411$			130741.i			0.773980i
$412$	111311.	−	214666.i	0.655759	−	1.26465i
$413$	−66642.2			−0.390705
$414$	−24289.6	+	99609.1i	−0.141716	+	0.581163i
$415$		−	98778.1i		−	0.573541i
$416$	406.882	+	1034.01i	0.00235116	+	0.00597502i
$417$	98653.3			0.567335
$418$	50872.4	+	12405.2i	0.291159	+	0.0709989i
$419$			4609.81i			0.0262576i	0.999914	+	0.0131288i	$0.00417914\pi$
$419$			4609.81i			0.0262576i	−0.999914	+	0.0131288i	$0.995821\pi$
$420$	−10542.0	−	5466.38i	−0.0597621	−	0.0309885i
$421$	215594.			1.21639			0.608196	−	0.793787i	$-0.291894\pi$
$421$	215594.			1.21639			0.608196	+	0.793787i	$0.291894\pi$
$422$	−11272.7	+	46228.2i	−0.0632999	+	0.259586i
$423$		−	19714.4i		−	0.110180i
$424$	−161695.	−	141116.i	−0.899423	−	0.784956i
$425$	5084.64			0.0281503
$426$	−171248.	−	41758.8i	−0.943642	−	0.230106i
$427$			59956.4i			0.328837i
$428$	61940.7	−	119454.i	0.338134	−	0.652098i
$429$	−254.033			−0.00138030
$430$	25297.5	−	103742.i	0.136817	−	0.561072i
$431$		−	49330.6i		−	0.265560i	−0.991146	−	0.132780i	$-0.957610\pi$
$431$		−	49330.6i		−	0.265560i	0.991146	−	0.132780i	$-0.0423903\pi$
$432$	29354.3	−	20694.7i	0.157291	−	0.110890i
$433$	291687.			1.55576			0.777879	−	0.628414i	$-0.216296\pi$
$433$	291687.			1.55576			0.777879	+	0.628414i	$0.216296\pi$
$434$	37832.8	+	9225.50i	0.200858	+	0.0489791i
$435$		−	23411.9i		−	0.123725i
$436$	−52288.7	−	27113.3i	−0.275065	−	0.142630i
$437$	−275843.			−1.44444
$438$	859.846	−	3526.14i	0.00448201	−	0.0183802i
$439$		−	190491.i		−	0.988427i	−0.869341	−	0.494213i	$-0.835456\pi$
$439$		−	190491.i		−	0.988427i	0.869341	−	0.494213i	$-0.164544\pi$
$440$	−21197.1	+	24288.2i	−0.109489	+	0.125455i
$441$	−60420.3			−0.310674
$442$	171.536	+	41.8289i	0.000878031	+	0.000214107i
$443$			125997.i			0.642026i	0.947075	+	0.321013i	$0.104023\pi$
$443$			125997.i			0.642026i	−0.947075	+	0.321013i	$0.895977\pi$
$444$	−50610.9	+	97604.3i	−0.256731	+	0.495111i
$445$	−21591.4			−0.109034
$446$	−31518.8	+	129255.i	−0.158453	+	0.649798i
$447$		−	112376.i		−	0.562418i
$448$	−51847.2	+	7079.58i	−0.258327	+	0.0352737i
$449$	151547.			0.751719			0.375860	−	0.926677i	$-0.377347\pi$
$449$	151547.			0.751719			0.375860	+	0.926677i	$0.377347\pi$
$450$	−13115.7	−	3198.25i	−0.0647688	−	0.0157938i
$451$		−	144369.i		−	0.709775i
$452$	−185151.	−	96006.7i	−0.906252	−	0.469921i
$453$	−121138.			−0.590316
$454$	40925.9	−	167833.i	0.198558	−	0.814265i
$455$			154.995i			0.000748680i
$456$	72802.3	+	63536.9i	0.350119	+	0.305560i
$457$	−132643.			−0.635115			−0.317557	−	0.948239i	$-0.602863\pi$
$457$	−132643.			−0.635115			−0.317557	+	0.948239i	$0.602863\pi$
$458$	14425.7	+	3517.69i	0.0687709	+	0.0167697i
$459$		−	5706.84i		−	0.0270876i
$460$	78173.4	−	150759.i	0.369439	−	0.712472i
$461$	−216287.			−1.01772			−0.508860	−	0.860849i	$-0.669933\pi$
$461$	−216287.			−1.01772			−0.508860	+	0.860849i	$0.669933\pi$
$462$	2834.12	−	11622.4i	0.0132781	−	0.0544519i
$463$			92938.0i			0.433542i	0.976222	+	0.216771i	$0.0695525\pi$
$463$			92938.0i			0.433542i	−0.976222	+	0.216771i	$0.930447\pi$
$464$	−59444.6	−	84319.2i	−0.276106	−	0.391643i
$465$	44270.2			0.204741
$466$	225528.	+	54994.8i	1.03855	+	0.253250i
$467$		−	28501.5i		−	0.130688i	−0.997863	−	0.0653438i	$-0.979186\pi$
$467$		−	28501.5i		−	0.130688i	0.997863	−	0.0653438i	$-0.0208144\pi$
$468$	−416.161	−	215.793i	−0.00190007	−	0.000985246i
$469$	−42799.7			−0.194579
$470$	−7735.93	+	31724.2i	−0.0350201	+	0.143614i
$471$		−	4817.78i		−	0.0217172i
$472$	−219519.	+	251531.i	−0.985345	+	1.12903i
$473$	107573.			0.480819
$474$	−205768.	−	50176.3i	−0.915843	−	0.223328i
$475$		−	36320.7i		−	0.160978i
$476$	−3827.48	+	7381.39i	−0.0168927	+	0.0325780i
$477$	90540.1			0.397928
$478$	−49072.3	+	201240.i	−0.214773	+	0.880763i
$479$		−	405064.i		−	1.76544i	−0.469901	−	0.882719i	$-0.655710\pi$
$479$		−	405064.i		−	1.76544i	0.469901	−	0.882719i	$-0.344290\pi$
$480$	−55357.4	+	21783.1i	−0.240267	+	0.0945445i
$481$	1435.04			0.00620259
$482$	−260799.	−	63595.6i	−1.12257	−	0.273737i
$483$			63019.8i			0.270136i
$484$	179130.	+	92884.7i	0.764677	+	0.396509i
$485$	−159869.			−0.679644
$486$	−3589.62	+	14720.6i	−0.0151976	+	0.0623238i
$487$		−	423164.i		−	1.78423i	−0.451809	−	0.892115i	$-0.649221\pi$
$487$		−	423164.i		−	1.78423i	0.451809	−	0.892115i	$-0.350779\pi$
$488$	226296.	+	197496.i	0.950250	+	0.829314i
$489$	115763.			0.484118
$490$	97227.9	+	23709.0i	0.404948	+	0.0987462i
$491$			323161.i			1.34047i	0.742150	+	0.670234i	$0.233806\pi$
$491$			323161.i			1.34047i	−0.742150	+	0.670234i	$0.766194\pi$
$492$	122637.	−	236508.i	0.506629	−	0.977046i
$493$	−16392.7			−0.0674460
$494$	298.793	−	1225.32i	0.00122438	−	0.00502105i
$495$		−	13600.0i		−	0.0555046i
$496$	159441.	−	112405.i	0.648093	−	0.456903i
$497$	−108344.			−0.438623
$498$	178404.	+	43503.7i	0.719360	+	0.175415i
$499$			13711.2i			0.0550648i	0.999621	+	0.0275324i	$0.00876495\pi$
$499$			13711.2i			0.0550648i	−0.999621	+	0.0275324i	$0.991235\pi$
$500$	19850.7	+	10293.2i	0.0794027	+	0.0411728i
$501$	−90151.5			−0.359168
$502$	45540.6	−	186757.i	0.180714	−	0.741088i
$503$		−	247715.i		−	0.979077i	−0.871982	−	0.489538i	$-0.837165\pi$
$503$		−	247715.i		−	0.979077i	0.871982	−	0.489538i	$-0.162835\pi$
$504$	14515.8	−	16632.6i	0.0571452	−	0.0654784i
$505$	−28854.3			−0.113143
$506$	166210.	+	40530.1i	0.649165	+	0.158298i
$507$		−	148401.i		−	0.577326i
$508$	−143997.	+	277702.i	−0.557990	+	1.07610i
$509$	109435.			0.422398			0.211199	−	0.977443i	$-0.432263\pi$
$509$	109435.			0.422398			0.211199	+	0.977443i	$0.432263\pi$
$510$	−2239.37	+	9183.42i	−0.00860965	+	0.0353073i
$511$		−	2230.88i		−	0.00854349i
$512$	−144064.	+	219009.i	−0.549559	+	0.835455i
$513$	−40765.3			−0.154901
$514$	−25059.1	−	6110.65i	−0.0948505	−	0.0231292i
$515$		−	168969.i		−	0.637079i
$516$	176228.	+	91380.0i	0.661876	+	0.343204i
$517$	−32895.7			−0.123072
$518$	−16010.0	+	65655.4i	−0.0596668	+	0.244687i
$519$		−	125380.i		−	0.465474i
$520$	585.006	+	510.554i	0.00216348	+	0.00188814i
$521$	143958.			0.530346			0.265173	−	0.964201i	$-0.414571\pi$
$521$	143958.			0.530346			0.265173	+	0.964201i	$0.414571\pi$
$522$	42284.5	+	10311.0i	0.155181	+	0.0378409i
$523$			106750.i			0.390270i	0.980776	+	0.195135i	$0.0625145\pi$
$523$			106750.i			0.390270i	−0.980776	+	0.195135i	$0.937485\pi$
$524$	−13904.8	+	26815.7i	−0.0506409	+	0.0976622i
$525$	−8297.91			−0.0301058
$526$	−37869.2	+	155297.i	−0.136872	+	0.561297i
$527$		−	30997.4i		−	0.111610i
$528$	−34531.5	−	48981.2i	−0.123865	−	0.175696i
$529$	−621389.			−2.22051
$530$	−145697.	−	35528.0i	−0.518678	−	0.126479i
$531$		−	140843.i		−	0.499514i
$532$	52726.9	+	27340.6i	0.186298	+	0.0966016i
$533$	−3477.28			−0.0122401
$534$	9509.27	−	38996.5i	0.0333476	−	0.136755i
$535$		−	94025.4i		−	0.328502i
$536$	−140982.	+	161541.i	−0.490721	+	0.562281i
$537$	104443.			0.362184
$538$	171283.	+	41767.2i	0.591765	+	0.144302i
$539$			100818.i			0.347026i
$540$	11552.8	−	22279.8i	0.0396186	−	0.0764053i
$541$	433836.			1.48228			0.741142	−	0.671348i	$-0.234285\pi$
$541$	433836.			1.48228			0.741142	+	0.671348i	$0.234285\pi$
$542$	5974.25	−	24499.8i	0.0203369	−	0.0833995i
$543$			119503.i			0.405302i
$544$	15252.2	+	38760.5i	0.0515388	+	0.130976i
$545$	−41157.8			−0.138567
$546$	−279.939	−	68.2628i	−0.000939026	−	0.000228981i
$547$			191917.i			0.641414i	0.947178	+	0.320707i	$0.103921\pi$
$547$			191917.i			0.641414i	−0.947178	+	0.320707i	$0.896079\pi$
$548$	357390.	+	185318.i	1.19009	+	0.617101i
$549$	−126713.			−0.420415
$550$	−5336.66	+	21885.1i	−0.0176418	+	0.0723473i
$551$			117097.i			0.385693i
$552$	237858.	+	207587.i	0.780621	+	0.681273i
$553$	−130183.			−0.425701
$554$	−35727.6	−	8712.15i	−0.116408	−	0.0283861i
$555$			76826.9i			0.249418i
$556$	139835.	−	269675.i	0.452341	−	0.872349i
$557$	75812.5			0.244360			0.122180	−	0.992508i	$-0.461011\pi$
$557$	75812.5			0.244360			0.122180	+	0.992508i	$0.461011\pi$
$558$	−19497.4	+	79956.8i	−0.0626194	+	0.256795i
$559$		−	2591.02i		−	0.00829176i
$560$	−29885.4	+	21069.0i	−0.0952977	+	0.0671844i
$561$	−9522.55			−0.0302571
$562$	−137548.	−	33540.9i	−0.435493	−	0.106195i
$563$		−	287479.i		−	0.906964i	−0.891265	−	0.453482i	$-0.850182\pi$
$563$		−	287479.i		−	0.906964i	0.891265	−	0.453482i	$-0.149818\pi$
$564$	−53890.4	−	27943.9i	−0.169415	−	0.0878473i
$565$	−145737.			−0.456535
$566$	42989.8	−	176296.i	0.134194	−	0.550314i
$567$			9313.32i			0.0289693i
$568$	−356884.	+	408927.i	−1.10619	+	1.26750i
$569$	627396.			1.93784			0.968919	−	0.247380i	$-0.0795695\pi$
$569$	627396.			1.93784			0.968919	+	0.247380i	$0.0795695\pi$
$570$	65599.2	+	15996.3i	0.201906	+	0.0492346i
$571$			191617.i			0.587709i	0.955850	+	0.293855i	$0.0949381\pi$
$571$			191617.i			0.587709i	−0.955850	+	0.293855i	$0.905062\pi$
$572$	−360.075	+	694.414i	−0.00110053	+	0.00212239i
$573$	−285053.			−0.868192
$574$	38794.3	−	159091.i	0.117746	−	0.482862i
$575$		−	118666.i		−	0.358916i
$576$	−14962.2	−	109575.i	−0.0450972	−	0.330269i
$577$	143680.			0.431565			0.215782	−	0.976441i	$-0.430770\pi$
$577$	143680.			0.431565			0.215782	+	0.976441i	$0.430770\pi$
$578$	−318143.	−	77579.0i	−0.952285	−	0.232214i
$579$			239254.i			0.713678i
$580$	−63997.9	−	33184.9i	−0.190243	−	0.0986472i
$581$	112871.			0.334372
$582$	70409.3	−	288741.i	0.207866	−	0.852438i
$583$		−	151077.i		−	0.444489i
$584$	−8420.13	−	7348.52i	−0.0246884	−	0.0215464i
$585$	−327.571			−0.000957181
$586$	−411770.	−	100410.i	−1.19911	−	0.292402i
$587$			386493.i			1.12167i	0.827927	+	0.560836i	$0.189520\pi$
$587$			386493.i			1.12167i	−0.827927	+	0.560836i	$0.810480\pi$
$588$	−85642.0	+	165162.i	−0.247703	+	0.477701i
$589$	−221421.			−0.638247
$590$	−55267.0	+	226644.i	−0.158768	+	0.651090i
$591$			338717.i			0.969755i
$592$	195069.	+	276696.i	0.556603	+	0.789513i
$593$	535525.			1.52290			0.761449	−	0.648225i	$-0.224488\pi$
$593$	535525.			1.52290			0.761449	+	0.648225i	$0.224488\pi$
$594$	24563.1	+	5989.70i	0.0696163	+	0.0169759i
$595$			5810.08i			0.0164115i
$596$	−307187.	−	159286.i	−0.864790	−	0.448421i
$597$	12116.2			0.0339953
$598$	976.211	−	4003.34i	0.00272986	−	0.0111949i
$599$		−	569817.i		−	1.58812i	−0.607842	−	0.794058i	$-0.707965\pi$
$599$		−	569817.i		−	1.58812i	0.607842	−	0.794058i	$-0.292035\pi$
$600$	−27333.3	+	31319.2i	−0.0759258	+	0.0869978i
$601$	−466168.			−1.29060			−0.645302	−	0.763927i	$-0.723269\pi$
$601$	−466168.			−1.29060			−0.645302	+	0.763927i	$0.723269\pi$
$602$	118543.	+	28906.7i	0.327103	+	0.0797638i
$603$		−	90454.1i		−	0.248767i
$604$	−171706.	+	331139.i	−0.470664	+	0.907686i
$605$	140998.			0.385214
$606$	12708.0	−	52114.0i	0.0346043	−	0.141909i
$607$			500743.i			1.35906i	0.733650	+	0.679528i	$0.237815\pi$
$607$			500743.i			1.35906i	−0.733650	+	0.679528i	$0.762185\pi$
$608$	276875.	−	108950.i	0.748990	−	0.294727i
$609$	26752.2			0.0721314
$610$	203907.	+	49722.5i	0.547989	+	0.133627i
$611$			792.329i			0.00212238i
$612$	−15600.0	−	8089.10i	−0.0416507	−	0.0215972i
$613$	77559.7			0.206403			0.103201	−	0.994660i	$-0.467091\pi$
$613$	77559.7			0.206403			0.103201	+	0.994660i	$0.467091\pi$
$614$	128784.	−	528129.i	0.341605	−	1.40089i
$615$		−	186161.i		−	0.492198i
$616$	−27753.4	−	24221.3i	−0.0731400	−	0.0638317i
$617$	217815.			0.572160			0.286080	−	0.958206i	$-0.407648\pi$
$617$	217815.			0.572160			0.286080	+	0.958206i	$0.407648\pi$
$618$	305177.	+	74417.2i	0.799052	+	0.194848i
$619$			594385.i			1.55127i	0.631183	+	0.775634i	$0.282570\pi$
$619$			594385.i			1.55127i	−0.631183	+	0.775634i	$0.717430\pi$
$620$	62750.2	−	121015.i	0.163242	−	0.314816i
$621$	−133188.			−0.345367
$622$	122346.	−	501727.i	0.316233	−	1.29684i
$623$		−	24671.9i		−	0.0635664i
$624$	−1179.76	+	831.728i	−0.00302988	+	0.00213605i
$625$	15625.0			0.0400000
$626$	70840.2	+	17274.3i	0.180772	+	0.0440811i
$627$			68021.7i			0.173026i
$628$	−13169.7	−	6828.90i	−0.0333930	−	0.0173154i
$629$	53793.1			0.135965
$630$	3654.55	−	14986.9i	0.00920775	−	0.0377600i
$631$			219540.i			0.551384i	0.961246	+	0.275692i	$0.0889070\pi$
$631$			219540.i			0.551384i	−0.961246	+	0.275692i	$0.911093\pi$
$632$	−428823.	+	491357.i	−1.07360	+	1.23016i
$633$	−61811.8			−0.154264
$634$	−218057.	−	53173.0i	−0.542489	−	0.132286i
$635$			218586.i			0.542095i
$636$	128335.	−	247497.i	0.317271	−	0.611865i
$637$	2428.32			0.00598449
$638$	17205.2	−	70556.6i	0.0422686	−	0.173339i
$639$		−	228977.i		−	0.560776i
$640$	−18920.4	+	182199.i	−0.0461923	+	0.444822i
$641$	487576.			1.18666			0.593330	−	0.804959i	$-0.297813\pi$
$641$	487576.			1.18666			0.593330	+	0.804959i	$0.297813\pi$
$642$	169820.	+	41410.5i	0.412021	+	0.100471i
$643$		−	605387.i		−	1.46424i	−0.681177	−	0.732118i	$-0.738532\pi$
$643$		−	605387.i		−	1.46424i	0.681177	−	0.732118i	$-0.261468\pi$
$644$	172268.	+	89326.6i	0.415369	+	0.215382i
$645$	138714.			0.333427
$646$	11200.4	−	45931.7i	0.0268391	−	0.110064i
$647$			227775.i			0.544124i	0.962280	+	0.272062i	$0.0877055\pi$
$647$			227775.i			0.544124i	−0.962280	+	0.272062i	$0.912294\pi$
$648$	35151.7	+	30678.0i	0.0837136	+	0.0730596i
$649$	−235014.			−0.557961
$650$	527.126	+	128.539i	0.00124763	+	0.000304235i
$651$			50586.3i			0.119363i
$652$	164087.	−	316445.i	0.385992	−	0.744393i
$653$	−106837.			−0.250551			−0.125276	−	0.992122i	$-0.539982\pi$
$653$	−106837.			−0.250551			−0.125276	+	0.992122i	$0.539982\pi$
$654$	18126.7	−	74335.5i	0.0423801	−	0.173796i
$655$			21107.3i			0.0491984i
$656$	−472678.	−	670470.i	−1.09839	−	1.55801i
$657$	4714.81			0.0109228
$658$	−36250.4	−	8839.64i	−0.0837262	−	0.0204166i
$659$			427598.i			0.984611i	0.870423	+	0.492305i	$0.163846\pi$
$659$			427598.i			0.984611i	−0.870423	+	0.492305i	$0.836154\pi$
$660$	−37176.5	−	19277.2i	−0.0853454	−	0.0442543i
$661$	−42462.2			−0.0971852			−0.0485926	−	0.998819i	$-0.515474\pi$
$661$	−42462.2			−0.0971852			−0.0485926	+	0.998819i	$0.515474\pi$
$662$	132177.	−	542044.i	0.301606	−	1.23685i
$663$			229.361i			0.000521786i
$664$	371797.	−	426014.i	0.843275	−	0.966247i
$665$	41502.7			0.0938498
$666$	−138758.	−	33836.0i	−0.312830	−	0.0762835i
$667$			382576.i			0.859936i
$668$	−127784.	+	246434.i	−0.286368	+	0.552266i
$669$	−172827.			−0.386154
$670$	−35494.2	+	145558.i	−0.0790694	+	0.324255i
$671$			211436.i			0.469607i
$672$	−24890.9	−	63255.4i	−0.0551191	−	0.140075i
$673$	−850306.			−1.87735			−0.938675	−	0.344804i	$-0.887945\pi$
$673$	−850306.			−1.87735			−0.938675	+	0.344804i	$0.887945\pi$
$674$	−285770.	−	69684.7i	−0.629066	−	0.153397i
$675$		−	17537.0i		−	0.0384900i
$676$	−405664.	−	210349.i	−0.887713	−	0.460307i
$677$	−310498.			−0.677456			−0.338728	−	0.940884i	$-0.609997\pi$
$677$	−310498.			−0.677456			−0.338728	+	0.940884i	$0.609997\pi$
$678$	64185.4	−	263217.i	0.139629	−	0.572605i
$679$		−	182678.i		−	0.396230i
$680$	21929.3	+	19138.4i	0.0474249	+	0.0413892i
$681$	224410.			0.483891
$682$	133417.	+	32533.7i	0.286843	+	0.0699464i
$683$		−	681014.i		−	1.45987i	−0.683515	−	0.729936i	$-0.739550\pi$
$683$		−	681014.i		−	1.45987i	0.683515	−	0.729936i	$-0.260450\pi$
$684$	−57782.2	+	111434.i	−0.123504	+	0.238181i
$685$	281311.			0.599522
$686$	−56159.1	+	230302.i	−0.119336	+	0.489385i
$687$			19288.6i			0.0408683i
$688$	499586.	−	352205.i	1.05544	−	0.744079i
$689$	−3638.85			−0.00766524
$690$	214325.	+	52262.9i	0.450167	+	0.109773i
$691$			474459.i			0.993671i	0.867845	+	0.496836i	$0.165505\pi$
$691$			474459.i			0.993671i	−0.867845	+	0.496836i	$0.834495\pi$
$692$	−342735.	−	177719.i	−0.715725	−	0.371126i
$693$	15540.4			0.0323590
$694$	−15879.2	+	65118.8i	−0.0329692	+	0.135203i
$695$		−	212268.i		−	0.439456i
$696$	88121.5	−	100972.i	0.181913	−	0.208440i
$697$	−130348.			−0.268310
$698$	−514854.	−	125547.i	−1.05675	−	0.257688i
$699$			301554.i			0.617178i
$700$	−11761.8	+	22682.8i	−0.0240036	+	0.0462915i
$701$	6142.38			0.0124997			0.00624986	−	0.999980i	$-0.498011\pi$
$701$	6142.38			0.0124997			0.00624986	+	0.999980i	$0.498011\pi$
$702$	144.268	−	591.629i	0.000292750	−	0.00120054i
$703$		−	384256.i		−	0.777518i
$704$	−182839.	+	24966.1i	−0.368913	+	0.0503740i
$705$	−42418.5			−0.0853449
$706$	−543522.	−	132537.i	−1.09046	−	0.265907i
$707$		−	32971.0i		−	0.0659619i
$708$	−385004.	−	199637.i	−0.768066	−	0.398267i
$709$	325611.			0.647750			0.323875	−	0.946100i	$-0.395014\pi$
$709$	325611.			0.647750			0.323875	+	0.946100i	$0.395014\pi$
$710$	−89850.6	+	368468.i	−0.178240	+	0.730942i
$711$		−	275133.i		−	0.544256i
$712$	−93120.5	−	81269.3i	−0.183690	−	0.160312i
$713$	−723423.			−1.42303
$714$	−10493.6	−	2558.87i	−0.0205840	−	0.00501940i
$715$			546.591i			0.00106918i
$716$	148041.	−	285500.i	0.288773	−	0.556904i
$717$	−269079.			−0.523409
$718$	−7256.50	+	29758.1i	−0.0140760	+	0.0577240i
$719$			511874.i			0.990159i	0.868848	+	0.495080i	$0.164861\pi$
$719$			511874.i			0.990159i	−0.868848	+	0.495080i	$0.835139\pi$
$720$	−44527.8	−	63160.4i	−0.0858947	−	0.121837i
$721$	193077.			0.371415
$722$	178344.	+	43489.1i	0.342125	+	0.0834269i
$723$		−	348715.i		−	0.667105i
$724$	326669.	+	169388.i	0.623204	+	0.323151i
$725$	−50374.4			−0.0958372
$726$	−62098.2	+	254658.i	−0.117816	+	0.483152i
$727$		−	734055.i		−	1.38886i	−0.719558	−	0.694432i	$-0.755656\pi$
$727$		−	734055.i		−	1.38886i	0.719558	−	0.694432i	$-0.244344\pi$
$728$	−583.396	+	668.471i	−0.00110078	+	0.00126130i
$729$	−19683.0			−0.0370370
$730$	−7587.04	−	1850.09i	−0.0142373	−	0.00347175i
$731$		−	97125.6i		−	0.181760i
$732$	−179608.	+	346379.i	−0.335200	+	0.646441i
$733$	788853.			1.46821			0.734105	−	0.679036i	$-0.237602\pi$
$733$	788853.			1.46821			0.734105	+	0.679036i	$0.237602\pi$
$734$	−101465.	+	416095.i	−0.188331	+	0.772326i
$735$			130004.i			0.240647i
$736$	904600.	−	355959.i	1.66994	−	0.657119i
$737$	−150933.			−0.277875
$738$	336228.	+	81988.9i	0.617335	+	0.150537i
$739$		−	277987.i		−	0.509020i	−0.967070	−	0.254510i	$-0.918086\pi$
$739$		−	277987.i		−	0.509020i	0.967070	−	0.254510i	$-0.0819142\pi$
$740$	210011.	+	108897.i	0.383512	+	0.198863i
$741$	1638.37			0.00298385
$742$	40596.9	−	166484.i	0.0737369	−	0.302387i
$743$		−	132497.i		−	0.240009i	−0.992773	−	0.120004i	$-0.961709\pi$
$743$		−	132497.i		−	0.240009i	0.992773	−	0.120004i	$-0.0382909\pi$
$744$	190930.	+	166631.i	0.344929	+	0.301030i
$745$	−241795.			−0.435647
$746$	917319.	+	223688.i	1.64833	+	0.401943i
$747$			238545.i			0.427492i
$748$	−13497.6	+	26030.5i	−0.0241243	+	0.0465242i
$749$	107440.			0.191515
$750$	−6881.54	+	28220.5i	−0.0122338	+	0.0501697i
$751$			185265.i			0.328483i	0.986420	+	0.164241i	$0.0525176\pi$
$751$			185265.i			0.328483i	−0.986420	+	0.164241i	$0.947482\pi$
$752$	−152773.	+	107704.i	−0.270153	+	0.190456i
$753$	249714.			0.440405
$754$	−1699.43	−	414.406i	−0.00298924	−	0.000728925i
$755$			260648.i			0.457257i
$756$	25458.5	+	13201.0i	0.0445440	+	0.0230975i
$757$	857946.			1.49716			0.748580	−	0.663044i	$-0.230736\pi$
$757$	857946.			1.49716			0.748580	+	0.663044i	$0.230736\pi$
$758$	−246899.	+	1.01251e6i	−0.429715	+	1.76221i
$759$			222239.i			0.385778i
$760$	136710.	−	156646.i	0.236686	−	0.271201i
$761$	320114.			0.552759			0.276380	−	0.961049i	$-0.410865\pi$
$761$	320114.			0.552759			0.276380	+	0.961049i	$0.410865\pi$
$762$	−394791.	−	96269.4i	−0.679919	−	0.165798i
$763$		−	47029.9i		−	0.0807839i
$764$	−404045.	+	779209.i	−0.692217	+	1.33496i
$765$	−12279.2			−0.0209820
$766$	−251834.	+	1.03275e6i	−0.429198	+	1.76009i
$767$			5660.56i			0.00962207i
$768$	−320738.	−	114416.i	−0.543787	−	0.193983i
$769$	1.08393e6			1.83293			0.916467	−	0.400110i	$-0.131028\pi$
$769$	1.08393e6			1.83293			0.916467	+	0.400110i	$0.131028\pi$
$770$	−25007.5	−	6098.06i	−0.0421782	−	0.0102851i
$771$		−	33506.6i		−	0.0563666i
$772$	654016.	+	339128.i	1.09737	+	0.569022i
$773$	−225062.			−0.376654			−0.188327	−	0.982106i	$-0.560306\pi$
$773$	−225062.			−0.376654			−0.188327	+	0.982106i	$0.560306\pi$
$774$	−61092.2	+	250533.i	−0.101977	+	0.418198i
$775$		−	95254.3i		−	0.158592i
$776$	−689491.	−	601741.i	−1.14500	−	0.999277i
$777$	−87788.0			−0.145410
$778$	329352.	+	80312.3i	0.544129	+	0.132685i
$779$			931102.i			1.53434i
$780$	−464.312	+	895.435i	−0.000763169	+	0.00147179i
$781$	−382075.			−0.626392
$782$	36593.8	−	150067.i	0.0598403	−	0.245399i
$783$			56538.7i			0.0922194i
$784$	330089.	+	468215.i	0.537031	+	0.761751i
$785$	−10366.2			−0.0168221
$786$	−38122.2	−	9296.06i	−0.0617067	−	0.0150471i
$787$		−	746646.i		−	1.20550i	−0.797932	−	0.602748i	$-0.794073\pi$
$787$		−	746646.i		−	1.20550i	0.797932	−	0.602748i	$-0.205927\pi$
$788$	925903.	+	480110.i	1.49112	+	0.773194i
$789$	−207649.			−0.333561
$790$	−107962.	+	442742.i	−0.172989	+	0.709409i
$791$		−	166530.i		−	0.266158i
$792$	51189.9	−	58654.8i	0.0816082	−	0.0935089i
$793$	5092.67			0.00809840
$794$	1.17169e6	+	285716.i	1.85854	+	0.453204i
$795$		−	194811.i		−	0.308234i
$796$	17174.0	−	33120.5i	0.0271048	−	0.0522721i
$797$	−192600.			−0.303207			−0.151604	−	0.988441i	$-0.548444\pi$
$797$	−192600.			−0.303207			−0.151604	+	0.988441i	$0.548444\pi$
$798$	−18278.6	+	74958.4i	−0.0287036	+	0.117710i
$799$			29700.9i			0.0465239i
$800$	46869.7	+	119110.i	0.0732339	+	0.186110i
$801$	52142.3			0.0812691
$802$	−722782.	−	176250.i	−1.12372	−	0.274018i
$803$		−	7867.21i		−	0.0122008i
$804$	−247262.	−	128213.i	−0.382512	−	0.198344i
$805$	135597.			0.209246
$806$	783.610	−	3213.50i	0.00120623	−	0.00494662i
$807$			229023.i			0.351667i
$808$	−124444.	−	108606.i	−0.190612	−	0.166354i
$809$	−1.12614e6			−1.72066			−0.860330	−	0.509738i	$-0.829742\pi$
$809$	−1.12614e6			−1.72066			−0.860330	+	0.509738i	$0.829742\pi$
$810$	31673.8	+	7723.63i	0.0482758	+	0.0117720i
$811$		−	235548.i		−	0.358127i	−0.983838	−	0.179063i	$-0.942693\pi$
$811$		−	235548.i		−	0.358127i	0.983838	−	0.179063i	$-0.0573067\pi$
$812$	37919.5	−	73128.6i	0.0575110	−	0.110911i
$813$	32758.7			0.0495616
$814$	−56459.4	+	231534.i	−0.0852093	+	0.349434i
$815$		−	249082.i		−	0.374996i
$816$	−44224.1	+	31177.8i	−0.0664169	+	0.0468236i
$817$	−693790.			−1.03940
$818$	−691876.	−	168714.i	−1.03400	−	0.252141i
$819$		−	374.307i		−	0.000558033i
$820$	−508883.	−	263872.i	−0.756817	−	0.392433i
$821$	−596397.			−0.884808			−0.442404	−	0.896816i	$-0.645874\pi$
$821$	−596397.			−0.884808			−0.442404	+	0.896816i	$0.645874\pi$
$822$	−123895.	+	508078.i	−0.183362	+	0.751947i
$823$		−	14906.2i		−	0.0220074i	−0.999939	−	0.0110037i	$-0.996497\pi$
$823$		−	14906.2i		−	0.0220074i	0.999939	−	0.0110037i	$-0.00350265\pi$
$824$	635993.	−	728738.i	0.936695	−	1.07329i
$825$	−29262.6			−0.0429937
$826$	−258980.	−	63152.2i	−0.379583	−	0.0925610i
$827$		−	505013.i		−	0.738400i	−0.929350	−	0.369200i	$-0.879632\pi$
$827$		−	505013.i		−	0.738400i	0.929350	−	0.369200i	$-0.120368\pi$
$828$	−188785.	+	364076.i	−0.275364	+	0.531045i
$829$	1.30007e6			1.89173			0.945864	−	0.324564i	$-0.105217\pi$
$829$	1.30007e6			1.89173			0.945864	+	0.324564i	$0.105217\pi$
$830$	93605.1	−	383864.i	0.135876	−	0.557214i
$831$		−	47771.5i		−	0.0691777i
$832$	601.336	+	4403.88i	0.000868702	+	0.00636193i
$833$	91026.8			0.131184
$834$	383379.	+	93486.8i	0.551184	+	0.134406i
$835$			193975.i			0.278210i
$836$	185941.	+	96416.5i	0.266050	+	0.137955i
$837$	−106910.			−0.152605
$838$	−4368.39	+	17914.3i	−0.00622062	+	0.0255101i
$839$		−	1.14596e6i		−	1.62796i	−0.580890	−	0.813982i	$-0.697295\pi$
$839$		−	1.14596e6i		−	1.62796i	0.580890	−	0.813982i	$-0.302705\pi$
$840$	−35787.6	−	31233.0i	−0.0507194	−	0.0442645i
$841$	−544876.			−0.770381
$842$	837828.	+	204304.i	1.18176	+	0.288172i
$843$		−	183916.i		−	0.258799i
$844$	−87614.4	+	168966.i	−0.122996	+	0.237200i
$845$	−319309.			−0.447195
$846$	18681.9	−	76612.5i	0.0261024	−	0.107043i
$847$			161115.i			0.224579i
$848$	−494641.	−	701623.i	−0.687857	−	0.975690i
$849$	235726.			0.327034
$850$	19759.6	+	4818.36i	0.0273489	+	0.00666901i
$851$		−	1.25544e6i		−	1.73355i
$852$	−625921.	−	324560.i	−0.862265	−	0.447112i
$853$	−892592.			−1.22675			−0.613373	−	0.789793i	$-0.710188\pi$
$853$	−892592.			−1.22675			−0.613373	+	0.789793i	$0.710188\pi$
$854$	−56816.5	+	232998.i	−0.0779038	+	0.319475i
$855$			87712.9i			0.119986i
$856$	353908.	−	405517.i	0.482995	−	0.553428i
$857$	715733.			0.974518			0.487259	−	0.873258i	$-0.337997\pi$
$857$	715733.			0.974518			0.487259	+	0.873258i	$0.337997\pi$
$858$	−987.204	−	240.729i	−0.00134101	−	0.000327004i
$859$			366306.i			0.496429i	0.968705	+	0.248215i	$0.0798438\pi$
$859$			366306.i			0.496429i	−0.968705	+	0.248215i	$0.920156\pi$
$860$	196618.	−	379183.i	0.265844	−	0.512687i
$861$	212722.			0.286949
$862$	46747.2	−	191705.i	0.0629130	−	0.258000i
$863$			1.16920e6i			1.56988i	0.619569	+	0.784942i	$0.287307\pi$
$863$			1.16920e6i			1.56988i	−0.619569	+	0.784942i	$0.712693\pi$
$864$	133686.	−	52605.1i	0.179084	−	0.0704693i
$865$	−269776.			−0.360554
$866$	1.13354e6	+	276412.i	1.51147	+	0.368571i
$867$		−	425390.i		−	0.565912i
$868$	138281.	+	71703.0i	0.183537	+	0.0951695i
$869$	−459091.			−0.607939
$870$	22185.8	−	90981.7i	0.0293114	−	0.120203i
$871$			3635.39i			0.00479198i
$872$	−177507.	−	154916.i	−0.233444	−	0.203734i
$873$	386077.			0.506576
$874$	−1.07196e6	−	261397.i	−1.40332	−	0.342199i
$875$			17854.3i			0.0233199i
$876$	6682.94	−	12888.2i	0.00870883	−	0.0167952i
$877$	481774.			0.626390			0.313195	−	0.949689i	$-0.398601\pi$
$877$	481774.			0.626390			0.313195	+	0.949689i	$0.398601\pi$
$878$	180515.	−	740271.i	0.234166	−	0.960288i
$879$		−	550578.i		−	0.712593i
$880$	−105391.	+	74299.9i	−0.136093	+	0.0959451i
$881$	−868503.			−1.11897			−0.559486	−	0.828840i	$-0.689001\pi$
$881$	−868503.			−1.11897			−0.559486	+	0.828840i	$0.689001\pi$
$882$	−234801.	−	57256.0i	−0.301830	−	0.0736011i
$883$		−	554009.i		−	0.710551i	−0.934762	−	0.355276i	$-0.884387\pi$
$883$		−	554009.i		−	0.710551i	0.934762	−	0.355276i	$-0.115613\pi$
$884$	626.972	+	325.105i	0.000802312	+	0.000416024i
$885$	−303047.			−0.386922
$886$	−119398.	+	489640.i	−0.152101	+	0.623749i
$887$		−	174815.i		−	0.222194i	−0.993810	−	0.111097i	$-0.964564\pi$
$887$		−	174815.i		−	0.222194i	0.993810	−	0.111097i	$-0.0354364\pi$
$888$	−289173.	+	331342.i	−0.366718	+	0.420195i
$889$	−249773.			−0.316039
$890$	−83907.1	−	20460.7i	−0.105930	−	0.0258309i
$891$			32843.4i			0.0413707i
$892$	−244972.	+	472434.i	−0.307884	+	0.593761i
$893$	212160.			0.266048
$894$	106491.	−	436709.i	0.133241	−	0.546407i
$895$		−	224725.i		−	0.280547i
$896$	−208194.	−	21619.8i	−0.259329	−	0.0269300i
$897$	5352.87			0.00665276
$898$	588933.	+	143611.i	0.730320	+	0.178088i
$899$			307096.i			0.379975i
$900$	−47938.5	−	24857.6i	−0.0591833	−	0.0306884i
$901$	−136404.			−0.168027
$902$	136808.	−	561036.i	0.168151	−	0.689569i
$903$			158505.i			0.194387i
$904$	−628542.	−	548549.i	−0.769126	−	0.671241i
$905$	257130.			0.313946
$906$	−470759.	−	114794.i	−0.573511	−	0.139850i
$907$			152131.i			0.184929i	0.995716	+	0.0924644i	$0.0294744\pi$
$907$			152131.i			0.184929i	−0.995716	+	0.0924644i	$0.970526\pi$
$908$	318087.	−	613438.i	0.385811	−	0.744044i
$909$	69681.7			0.0843318
$910$	−146.878	+	602.332i	−0.000177368	+	0.000727366i
$911$			1.22718e6i			1.47867i	0.673339	+	0.739333i	$0.264859\pi$
$911$			1.22718e6i			1.47867i	−0.673339	+	0.739333i	$0.735141\pi$
$912$	222710.	+	315902.i	0.267762	+	0.379807i
$913$	398040.			0.477513
$914$	−515468.	−	125697.i	−0.617034	−	0.150463i
$915$			272644.i			0.325652i
$916$	52726.5	+	27340.4i	0.0628403	+	0.0325847i
$917$	−24118.8			−0.0286825
$918$	5407.98	−	22177.5i	0.00641726	−	0.0263165i
$919$		−	1.07341e6i		−	1.27096i	−0.772115	−	0.635482i	$-0.780801\pi$
$919$		−	1.07341e6i		−	1.27096i	0.772115	−	0.635482i	$-0.219199\pi$
$920$	446656.	−	511790.i	0.527712	−	0.604667i
$921$	706162.			0.832502
$922$	−840519.	−	204960.i	−0.988748	−	0.241106i
$923$			9202.68i			0.0108022i
$924$	22027.5	−	42480.5i	0.0258001	−	0.0497561i
$925$	165305.			0.193198
$926$	−88070.8	+	361169.i	−0.102709	+	0.421200i
$927$			408053.i			0.474851i
$928$	−151106.	−	384007.i	−0.175463	−	0.445906i
$929$	−383223.			−0.444038			−0.222019	−	0.975042i	$-0.571265\pi$
$929$	−383223.			−0.444038			−0.222019	+	0.975042i	$0.571265\pi$
$930$	172040.	+	41951.8i	0.198913	+	0.0485047i
$931$		−	650225.i		−	0.750177i
$932$	824316.	+	427434.i	0.948990	+	0.492082i
$933$	670860.			0.770670
$934$	27008.9	−	110761.i	0.0309609	−	0.126967i
$935$			20489.3i			0.0234371i
$936$	−1412.76	−	1232.96i	−0.00161257	−	0.00140734i
$937$	−457379.			−0.520952			−0.260476	−	0.965480i	$-0.583879\pi$
$937$	−457379.			−0.520952			−0.260476	+	0.965480i	$0.583879\pi$
$938$	−166325.	−	40558.3i	−0.189040	−	0.0460972i
$939$			94720.6i			0.107427i
$940$	−60125.7	+	115954.i	−0.0680462	+	0.131229i
$941$	423781.			0.478589			0.239294	−	0.970947i	$-0.423084\pi$
$941$	423781.			0.478589			0.239294	+	0.970947i	$0.423084\pi$
$942$	4565.47	−	18722.5i	0.00514498	−	0.0210990i
$943$			3.04208e6i			3.42095i
$944$	−1.09144e6	+	769458.i	−1.22477	+	0.863458i
$945$	20039.1			0.0224395
$946$	418043.	+	101940.i	0.467131	+	0.113910i
$947$		−	443751.i		−	0.494811i	−0.968912	−	0.247406i	$-0.920422\pi$
$947$		−	443751.i		−	0.494811i	0.968912	−	0.247406i	$-0.0795780\pi$
$948$	−752092.	−	389984.i	−0.836863	−	0.433940i
$949$	−189.490			−0.000210404
$950$	34418.6	−	141147.i	0.0381370	−	0.156396i
$951$		−	291564.i		−	0.322384i
$952$	−21868.9	+	25058.0i	−0.0241298	+	0.0276485i
$953$	226241.			0.249107			0.124553	−	0.992213i	$-0.460250\pi$
$953$	226241.			0.249107			0.124553	+	0.992213i	$0.460250\pi$
$954$	351851.	+	85798.5i	0.386600	+	0.0942720i
$955$			613336.i			0.672499i
$956$	−381402.	+	735543.i	−0.417318	+	0.804808i
$957$	94341.5			0.103010
$958$	383851.	−	1.57413e6i	0.418246	−	1.71518i
$959$			321446.i			0.349519i
$960$	−235768.	+	32193.4i	−0.255825	+	0.0349321i
$961$	342825.			0.371215
$962$	5576.74	+	1359.88i	0.00602602	+	0.00146944i
$963$			227067.i			0.244851i
$964$	−953233.	−	494282.i	−1.02576	−	0.531888i
$965$	514793.			0.552813
$966$	−59719.4	+	244903.i	−0.0639972	+	0.262446i
$967$			938781.i			1.00395i	0.864883	+	0.501974i	$0.167393\pi$
$967$			938781.i			1.00395i	−0.864883	+	0.501974i	$0.832607\pi$
$968$	608103.	+	530711.i	0.648972	+	0.566379i
$969$	61415.3			0.0654078
$970$	−621272.	−	151497.i	−0.660296	−	0.161013i
$971$			789216.i			0.837062i	0.908203	+	0.418531i	$0.137455\pi$
$971$			789216.i			0.837062i	−0.908203	+	0.418531i	$0.862545\pi$
$972$	−27899.4	+	53804.7i	−0.0295300	+	0.0569492i
$973$	242553.			0.256201
$974$	401003.	−	1.64447e6i	0.422697	−	1.73344i
$975$			704.821i			0.000741429i
$976$	692264.	+	981941.i	0.726728	+	1.03083i
$977$	842022.			0.882133			0.441067	−	0.897474i	$-0.354600\pi$
$977$	842022.			0.882133			0.441067	+	0.897474i	$0.354600\pi$
$978$	449869.	+	109700.i	0.470336	+	0.114691i
$979$		−	87005.6i		−	0.0907783i
$980$	355373.	+	184272.i	0.370026	+	0.191870i
$981$	99394.2			0.103282
$982$	−306237.	+	1.25585e6i	−0.317567	+	1.30231i
$983$			1.21978e6i			1.26233i	0.775649	+	0.631165i	$0.217423\pi$
$983$			1.21978e6i			1.26233i	−0.775649	+	0.631165i	$0.782577\pi$
$984$	700704.	−	802885.i	0.723676	−	0.829207i
$985$	728803.			0.751169
$986$	−63704.1	−	15534.2i	−0.0655260	−	0.0159785i
$987$		−	48470.5i		−	0.0497558i
$988$	2322.29	−	4478.60i	0.00237905	−	0.00458805i
$989$	−2.26674e6			−2.31744
$990$	12887.8	−	52851.4i	0.0131495	−	0.0539245i
$991$			392087.i			0.399241i	0.979873	+	0.199621i	$0.0639710\pi$
$991$			392087.i			0.399241i	−0.979873	+	0.199621i	$0.936029\pi$
$992$	726128.	−	285730.i	0.737887	−	0.290358i
$993$	724768.			0.735022
$994$	−421038.	−	102670.i	−0.426136	−	0.103913i
$995$		−	26070.0i		−	0.0263327i
$996$	652076.	+	338122.i	0.657324	+	0.340843i
$997$	−1.15182e6			−1.15876			−0.579381	−	0.815057i	$-0.696706\pi$
$997$	−1.15182e6			−1.15876			−0.579381	+	0.815057i	$0.696706\pi$
$998$	−12993.1	+	53283.5i	−0.0130453	+	0.0534973i
$999$		−	185533.i		−	0.185905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.c.a.31.16	yes	16
3.2	odd	2		180.5.c.c.91.1		16
4.3	odd	2	inner	60.5.c.a.31.15	✓	16
5.2	odd	4		300.5.f.b.199.14		32
5.3	odd	4		300.5.f.b.199.19		32
5.4	even	2		300.5.c.d.151.1		16
8.3	odd	2		960.5.e.f.511.10		16
8.5	even	2		960.5.e.f.511.3		16
12.11	even	2		180.5.c.c.91.2		16
20.3	even	4		300.5.f.b.199.13		32
20.7	even	4		300.5.f.b.199.20		32
20.19	odd	2		300.5.c.d.151.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.15	✓	16	4.3	odd	2	inner
60.5.c.a.31.16	yes	16	1.1	even	1	trivial
180.5.c.c.91.1		16	3.2	odd	2
180.5.c.c.91.2		16	12.11	even	2
300.5.c.d.151.1		16	5.4	even	2
300.5.c.d.151.2		16	20.19	odd	2
300.5.f.b.199.13		32	20.3	even	4
300.5.f.b.199.14		32	5.2	odd	4
300.5.f.b.199.19		32	5.3	odd	4
300.5.f.b.199.20		32	20.7	even	4
960.5.e.f.511.3		16	8.5	even	2
960.5.e.f.511.10		16	8.3	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.88613 + 0.947630i) q^{2} +5.19615i q^{3} +(14.2040 + 7.36522i) q^{4} +11.1803 q^{5} +(-4.92403 + 20.1929i) q^{6} +12.7755i q^{7} +(48.2191 + 42.0823i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(3.88613 + 0.947630i) q^{2} +5.19615i q^{3} +(14.2040 + 7.36522i) q^{4} +11.1803 q^{5} +(-4.92403 + 20.1929i) q^{6} +12.7755i q^{7} +(48.2191 + 42.0823i) q^{8} -27.0000 q^{9} +(43.4482 + 10.5948i) q^{10} +45.0527i q^{11} +(-38.2708 + 73.8061i) q^{12} +1.08514 q^{13} +(-12.1064 + 49.6471i) q^{14} +58.0948i q^{15} +(147.507 + 209.231i) q^{16} +40.6771 q^{17} +(-104.925 - 25.5860i) q^{18} -290.566i q^{19} +(158.805 + 82.3457i) q^{20} -66.3833 q^{21} +(-42.6933 + 175.081i) q^{22} -949.332i q^{23} +(-218.666 + 250.554i) q^{24} +125.000 q^{25} +(4.21700 + 1.02831i) q^{26} -140.296i q^{27} +(-94.0942 + 181.463i) q^{28} -402.995 q^{29} +(-55.0523 + 225.764i) q^{30} -762.034i q^{31} +(374.957 + 952.881i) q^{32} -234.101 q^{33} +(158.077 + 38.5469i) q^{34} +142.834i q^{35} +(-383.508 - 198.861i) q^{36} +1322.44 q^{37} +(275.349 - 1129.18i) q^{38} +5.63857i q^{39} +(539.105 + 470.495i) q^{40} -3204.44 q^{41} +(-257.974 - 62.9068i) q^{42} -2387.72i q^{43} +(-331.823 + 639.928i) q^{44} -301.869 q^{45} +(899.615 - 3689.22i) q^{46} +730.161i q^{47} +(-1087.20 + 766.469i) q^{48} +2237.79 q^{49} +(485.766 + 118.454i) q^{50} +211.365i q^{51} +(15.4134 + 7.99232i) q^{52} -3353.34 q^{53} +(132.949 - 545.209i) q^{54} +503.704i q^{55} +(-537.622 + 616.021i) q^{56} +1509.82 q^{57} +(-1566.09 - 381.890i) q^{58} +5216.42i q^{59} +(-427.881 + 825.178i) q^{60} +4693.09 q^{61} +(722.126 - 2961.36i) q^{62} -344.938i q^{63} +(554.154 + 4058.34i) q^{64} +12.1323 q^{65} +(-909.745 - 221.841i) q^{66} +3350.15i q^{67} +(577.778 + 299.596i) q^{68} +4932.87 q^{69} +(-135.354 + 555.072i) q^{70} +8480.62i q^{71} +(-1301.91 - 1136.22i) q^{72} -174.622 q^{73} +(5139.18 + 1253.18i) q^{74} +649.519i q^{75} +(2140.08 - 4127.20i) q^{76} -575.569 q^{77} +(-5.34327 + 21.9122i) q^{78} +10190.1i q^{79} +(1649.18 + 2339.28i) q^{80} +729.000 q^{81} +(-12452.9 - 3036.63i) q^{82} -8834.98i q^{83} +(-942.908 - 488.928i) q^{84} +454.784 q^{85} +(2262.67 - 9278.99i) q^{86} -2094.02i q^{87} +(-1895.92 + 2172.40i) q^{88} -1931.20 q^{89} +(-1173.10 - 286.060i) q^{90} +13.8632i q^{91} +(6992.04 - 13484.3i) q^{92} +3959.65 q^{93} +(-691.923 + 2837.50i) q^{94} -3248.62i q^{95} +(-4951.32 + 1948.34i) q^{96} -14299.1 q^{97} +(8696.33 + 2120.59i) q^{98} -1216.42i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Introduction

L-functions

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