LMFDB - Embedded newform 60.5.c.a.31.3

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			31.3
Root			$-1.14149 + 2.58786i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.5.c.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.40825 - 2.09376i) q^{2} -5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} -11.1803 q^{5} +(-10.8795 + 17.7098i) q^{6} +61.3317i q^{7} +(5.23271 - 63.7857i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.40825 - 2.09376i) q^{2} -5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} -11.1803 q^{5} +(-10.8795 + 17.7098i) q^{6} +61.3317i q^{7} +(5.23271 - 63.7857i) q^{8} -27.0000 q^{9} +(38.1054 + 23.4089i) q^{10} +74.1525i q^{11} +(74.1601 - 37.5804i) q^{12} +181.358 q^{13} +(128.414 - 209.034i) q^{14} +58.0948i q^{15} +(-151.386 + 206.442i) q^{16} +516.182 q^{17} +(92.0228 + 56.5315i) q^{18} +407.870i q^{19} +(-80.8601 - 159.567i) q^{20} +318.689 q^{21} +(155.258 - 252.730i) q^{22} -7.48405i q^{23} +(-331.440 - 27.1900i) q^{24} +125.000 q^{25} +(-618.114 - 379.720i) q^{26} +140.296i q^{27} +(-875.333 + 443.572i) q^{28} -1473.47 q^{29} +(121.636 - 198.001i) q^{30} +1041.01i q^{31} +(948.202 - 386.639i) q^{32} +385.308 q^{33} +(-1759.28 - 1080.76i) q^{34} -685.709i q^{35} +(-195.273 - 385.347i) q^{36} -667.800 q^{37} +(853.982 - 1390.12i) q^{38} -942.365i q^{39} +(-58.5035 + 713.146i) q^{40} +1215.10 q^{41} +(-1086.17 - 667.258i) q^{42} +987.639i q^{43} +(-1058.31 + 536.297i) q^{44} +301.869 q^{45} +(-15.6698 + 25.5075i) q^{46} +2943.18i q^{47} +(1072.70 + 786.626i) q^{48} -1360.58 q^{49} +(-426.031 - 261.720i) q^{50} -2682.16i q^{51} +(1311.64 + 2588.36i) q^{52} -2287.61 q^{53} +(293.746 - 478.164i) q^{54} -829.051i q^{55} +(3912.09 + 320.931i) q^{56} +2119.36 q^{57} +(5021.96 + 3085.09i) q^{58} -390.685i q^{59} +(-829.135 + 420.161i) q^{60} +4108.86 q^{61} +(2179.63 - 3548.03i) q^{62} -1655.96i q^{63} +(-4041.24 - 667.545i) q^{64} -2027.65 q^{65} +(-1313.23 - 806.742i) q^{66} -6166.96i q^{67} +(3733.20 + 7367.00i) q^{68} -38.8883 q^{69} +(-1435.71 + 2337.07i) q^{70} +4462.68i q^{71} +(-141.283 + 1722.21i) q^{72} +3369.06 q^{73} +(2276.03 + 1398.21i) q^{74} -649.519i q^{75} +(-5821.17 + 2949.86i) q^{76} -4547.90 q^{77} +(-1973.08 + 3211.81i) q^{78} -7060.25i q^{79} +(1692.55 - 2308.09i) q^{80} +729.000 q^{81} +(-4141.36 - 2544.12i) q^{82} -4972.33i q^{83} +(2304.87 + 4548.36i) q^{84} -5771.09 q^{85} +(2067.88 - 3366.12i) q^{86} +7656.38i q^{87} +(4729.87 + 388.019i) q^{88} -12370.7 q^{89} +(-1028.85 - 632.041i) q^{90} +11123.0i q^{91} +(106.813 - 54.1273i) q^{92} +5409.26 q^{93} +(6162.30 - 10031.1i) q^{94} -4560.13i q^{95} +(-2009.03 - 4927.00i) q^{96} +2516.32 q^{97} +(4637.19 + 2848.72i) q^{98} -2002.12i 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 $

$2$	−3.40825	−	2.09376i	−0.852063	−	0.523440i
$2$	−3.40825	−	2.09376i	−0.852063	−	0.523440i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	7.23235	+	14.2721i	0.452022	+	0.892007i
$5$	−11.1803			−0.447214
$5$	−11.1803			−0.447214
$6$	−10.8795	+	17.7098i	−0.302208	+	0.491939i
$7$			61.3317i			1.25167i	0.779956	+	0.625834i	$0.215241\pi$
$7$			61.3317i			1.25167i	−0.779956	+	0.625834i	$0.784759\pi$
$8$	5.23271	−	63.7857i	0.0817612	−	0.996652i
$9$	−27.0000			−0.333333
$10$	38.1054	+	23.4089i	0.381054	+	0.234089i
$11$			74.1525i			0.612831i	0.951898	+	0.306415i	$0.0991297\pi$
$11$			74.1525i			0.612831i	−0.951898	+	0.306415i	$0.900870\pi$
$12$	74.1601	−	37.5804i	0.515000	−	0.260975i
$13$	181.358			1.07313			0.536563	−	0.843861i	$-0.319723\pi$
$13$	181.358			1.07313			0.536563	+	0.843861i	$0.319723\pi$
$14$	128.414	−	209.034i	0.655173	−	1.06650i
$15$			58.0948i			0.258199i
$16$	−151.386	+	206.442i	−0.591353	+	0.806413i
$17$	516.182			1.78610			0.893048	−	0.449962i	$-0.148562\pi$
$17$	516.182			1.78610			0.893048	+	0.449962i	$0.148562\pi$
$18$	92.0228	+	56.5315i	0.284021	+	0.174480i
$19$			407.870i			1.12983i	0.825147	+	0.564917i	$0.191092\pi$
$19$			407.870i			1.12983i	−0.825147	+	0.564917i	$0.808908\pi$
$20$	−80.8601	−	159.567i	−0.202150	−	0.398918i
$21$	318.689			0.722651
$22$	155.258	−	252.730i	0.320780	−	0.522170i
$23$		−	7.48405i		−	0.0141475i	−0.999975	−	0.00707377i	$-0.997748\pi$
$23$		−	7.48405i		−	0.0141475i	0.999975	−	0.00707377i	$-0.00225167\pi$
$24$	−331.440	−	27.1900i	−0.575417	−	0.0472048i
$25$	125.000			0.200000
$26$	−618.114	−	379.720i	−0.914370	−	0.561716i
$27$			140.296i			0.192450i
$28$	−875.333	+	443.572i	−1.11650	+	0.565781i
$29$	−1473.47			−1.75205			−0.876023	−	0.482270i	$-0.839812\pi$
$29$	−1473.47			−1.75205			−0.876023	+	0.482270i	$0.839812\pi$
$30$	121.636	−	198.001i	0.135152	−	0.220002i
$31$			1041.01i			1.08326i	0.840617	+	0.541630i	$0.182192\pi$
$31$			1041.01i			1.08326i	−0.840617	+	0.541630i	$0.817808\pi$
$32$	948.202	−	386.639i	0.925978	−	0.377577i
$33$	385.308			0.353818
$34$	−1759.28	−	1080.76i	−1.52187	−	0.934913i
$35$		−	685.709i		−	0.559763i
$36$	−195.273	−	385.347i	−0.150674	−	0.297336i
$37$	−667.800			−0.487802			−0.243901	−	0.969800i	$-0.578427\pi$
$37$	−667.800			−0.487802			−0.243901	+	0.969800i	$0.578427\pi$
$38$	853.982	−	1390.12i	0.591400	−	0.962690i
$39$		−	942.365i		−	0.619569i
$40$	−58.5035	+	713.146i	−0.0365647	+	0.445716i
$41$	1215.10			0.722842			0.361421	−	0.932403i	$-0.382292\pi$
$41$	1215.10			0.722842			0.361421	+	0.932403i	$0.382292\pi$
$42$	−1086.17	−	667.258i	−0.615744	−	0.378264i
$43$			987.639i			0.534148i	0.963676	+	0.267074i	$0.0860568\pi$
$43$			987.639i			0.534148i	−0.963676	+	0.267074i	$0.913943\pi$
$44$	−1058.31	+	536.297i	−0.546649	+	0.277013i
$45$	301.869			0.149071
$46$	−15.6698	+	25.5075i	−0.00740539	+	0.0120546i
$47$			2943.18i			1.33236i	0.745792	+	0.666178i	$0.232071\pi$
$47$			2943.18i			1.33236i	−0.745792	+	0.666178i	$0.767929\pi$
$48$	1072.70	+	786.626i	0.465583	+	0.341418i
$49$	−1360.58			−0.566672
$50$	−426.031	−	261.720i	−0.170413	−	0.104688i
$51$		−	2682.16i		−	1.03120i
$52$	1311.64	+	2588.36i	0.485076	+	0.957235i
$53$	−2287.61			−0.814384			−0.407192	−	0.913343i	$-0.633492\pi$
$53$	−2287.61			−0.814384			−0.407192	+	0.913343i	$0.633492\pi$
$54$	293.746	−	478.164i	0.100736	−	0.163980i
$55$		−	829.051i		−	0.274066i
$56$	3912.09	+	320.931i	1.24748	+	0.102338i
$57$	2119.36			0.652310
$58$	5021.96	+	3085.09i	1.49285	+	0.917090i
$59$		−	390.685i		−	0.112234i	−0.998424	−	0.0561168i	$-0.982128\pi$
$59$		−	390.685i		−	0.112234i	0.998424	−	0.0561168i	$-0.0178719\pi$
$60$	−829.135	+	420.161i	−0.230315	+	0.116711i
$61$	4108.86			1.10424			0.552118	−	0.833766i	$-0.313820\pi$
$61$	4108.86			1.10424			0.552118	+	0.833766i	$0.313820\pi$
$62$	2179.63	−	3548.03i	0.567021	−	0.923005i
$63$		−	1655.96i		−	0.417223i
$64$	−4041.24	−	667.545i	−0.986630	−	0.162975i
$65$	−2027.65			−0.479916
$66$	−1313.23	−	806.742i	−0.301475	−	0.185202i
$67$		−	6166.96i		−	1.37379i	−0.726755	−	0.686897i	$-0.758972\pi$
$67$		−	6166.96i		−	1.37379i	0.726755	−	0.686897i	$-0.241028\pi$
$68$	3733.20	+	7367.00i	0.807354	+	1.59321i
$69$	−38.8883			−0.00816809
$70$	−1435.71	+	2337.07i	−0.293002	+	0.476953i
$71$			4462.68i			0.885276i	0.896700	+	0.442638i	$0.145957\pi$
$71$			4462.68i			0.885276i	−0.896700	+	0.442638i	$0.854043\pi$
$72$	−141.283	+	1722.21i	−0.0272537	+	0.332217i
$73$	3369.06			0.632213			0.316106	−	0.948724i	$-0.397624\pi$
$73$	3369.06			0.632213			0.316106	+	0.948724i	$0.397624\pi$
$74$	2276.03	+	1398.21i	0.415638	+	0.255335i
$75$		−	649.519i		−	0.115470i
$76$	−5821.17	+	2949.86i	−1.00782	+	0.510710i
$77$	−4547.90			−0.767061
$78$	−1973.08	+	3211.81i	−0.324307	+	0.527912i
$79$		−	7060.25i		−	1.13127i	−0.824656	−	0.565635i	$-0.808631\pi$
$79$		−	7060.25i		−	1.13127i	0.824656	−	0.565635i	$-0.191369\pi$
$80$	1692.55	−	2308.09i	0.264461	−	0.360639i
$81$	729.000			0.111111
$82$	−4141.36	−	2544.12i	−0.615907	−	0.378364i
$83$		−	4972.33i		−	0.721777i	−0.932609	−	0.360889i	$-0.882473\pi$
$83$		−	4972.33i		−	0.721777i	0.932609	−	0.360889i	$-0.117527\pi$
$84$	2304.87	+	4548.36i	0.326654	+	0.644609i
$85$	−5771.09			−0.798766
$86$	2067.88	−	3366.12i	0.279594	−	0.455127i
$87$			7656.38i			1.01154i
$88$	4729.87	+	388.019i	0.610779	+	0.0501058i
$89$	−12370.7			−1.56175			−0.780877	−	0.624685i	$-0.785227\pi$
$89$	−12370.7			−1.56175			−0.780877	+	0.624685i	$0.785227\pi$
$90$	−1028.85	−	632.041i	−0.127018	−	0.0780298i
$91$			11123.0i			1.34320i
$92$	106.813	−	54.1273i	0.0126197	−	0.00639500i
$93$	5409.26			0.625420
$94$	6162.30	−	10031.1i	0.697408	−	1.13525i
$95$		−	4560.13i		−	0.505277i
$96$	−2009.03	−	4927.00i	−0.217994	−	0.534614i
$97$	2516.32			0.267438			0.133719	−	0.991019i	$-0.457308\pi$
$97$	2516.32			0.267438			0.133719	+	0.991019i	$0.457308\pi$
$98$	4637.19	+	2848.72i	0.482840	+	0.296619i
$99$		−	2002.12i		−	0.204277i
$100$	904.043	+	1784.01i	0.0904043	+	0.178401i
$101$	−2974.94			−0.291632			−0.145816	−	0.989312i	$-0.546581\pi$
$101$	−2974.94			−0.291632			−0.145816	+	0.989312i	$0.546581\pi$
$102$	−5615.79	+	9141.47i	−0.539773	+	0.878649i
$103$		−	17963.5i		−	1.69323i	−0.532202	−	0.846617i	$-0.678635\pi$
$103$		−	17963.5i		−	1.69323i	0.532202	−	0.846617i	$-0.321365\pi$
$104$	948.995	−	11568.1i	0.0877399	−	1.06953i
$105$	−3563.05			−0.323179
$106$	7796.73	+	4789.69i	0.693906	+	0.426281i
$107$		−	1200.48i		−	0.104854i	−0.998625	−	0.0524272i	$-0.983304\pi$
$107$		−	1200.48i		−	0.104854i	0.998625	−	0.0524272i	$-0.0166958\pi$
$108$	−2002.32	+	1014.67i	−0.171667	+	0.0869916i
$109$	16500.9			1.38884			0.694422	−	0.719568i	$-0.255660\pi$
$109$	16500.9			1.38884			0.694422	+	0.719568i	$0.255660\pi$
$110$	−1735.83	+	2825.61i	−0.143457	+	0.233522i
$111$			3469.99i			0.281632i
$112$	−12661.4	−	9284.78i	−1.00936	−	0.740177i
$113$	−6037.80			−0.472849			−0.236424	−	0.971650i	$-0.575976\pi$
$113$	−6037.80			−0.472849			−0.236424	+	0.971650i	$0.575976\pi$
$114$	−7223.30	−	4437.42i	−0.555809	−	0.341445i
$115$			83.6742i			0.00632697i
$116$	−10656.6	−	21029.5i	−0.791962	−	1.56284i
$117$	−4896.67			−0.357708
$118$	−818.000	+	1331.55i	−0.0587475	+	0.0956300i
$119$			31658.3i			2.23560i
$120$	3705.62	+	303.993i	0.257334	+	0.0211106i
$121$	9142.40			0.624438
$122$	−14004.0	−	8602.97i	−0.940878	−	0.578001i
$123$		−	6313.83i		−	0.417333i
$124$	−14857.4	+	7528.96i	−0.966275	+	0.489657i
$125$	−1397.54			−0.0894427
$126$	−3467.17	+	5643.91i	−0.218391	+	0.355500i
$127$			17483.7i			1.08399i	0.840382	+	0.541995i	$0.182331\pi$
$127$			17483.7i			1.08399i	−0.840382	+	0.541995i	$0.817669\pi$
$128$	12375.9	+	10736.5i	0.755363	+	0.655306i
$129$	5131.92			0.308390
$130$	6910.72	+	4245.40i	0.408919	+	0.251207i
$131$			10698.3i			0.623408i	0.950179	+	0.311704i	$0.100900\pi$
$131$			10698.3i			0.623408i	−0.950179	+	0.311704i	$0.899100\pi$
$132$	2786.68	+	5499.16i	0.159933	+	0.315608i
$133$	−25015.4			−1.41418
$134$	−12912.1	+	21018.6i	−0.719099	+	1.17056i
$135$		−	1568.56i		−	0.0860663i
$136$	2701.03	−	32925.0i	0.146033	−	1.78012i
$137$	31259.4			1.66548			0.832740	−	0.553665i	$-0.186771\pi$
$137$	31259.4			1.66548			0.832740	+	0.553665i	$0.186771\pi$
$138$	132.541	+	81.4227i	0.00695972	+	0.00427550i
$139$		−	22483.1i		−	1.16366i	−0.813310	−	0.581831i	$-0.802337\pi$
$139$		−	22483.1i		−	1.16366i	0.813310	−	0.581831i	$-0.197663\pi$
$140$	9786.52	−	4959.29i	0.499312	−	0.253025i
$141$	15293.2			0.769236
$142$	9343.77	−	15209.9i	0.463389	−	0.754311i
$143$			13448.2i			0.657644i
$144$	4087.43	−	5573.93i	0.197118	−	0.268804i
$145$	16473.9			0.783539
$146$	−11482.6	−	7054.01i	−0.538685	−	0.330925i
$147$			7069.78i			0.327168i
$148$	−4829.76	−	9530.92i	−0.220497	−	0.435122i
$149$	19244.0			0.866808			0.433404	−	0.901200i	$-0.357312\pi$
$149$	19244.0			0.866808			0.433404	+	0.901200i	$0.357312\pi$
$150$	−1359.94	+	2213.72i	−0.0604416	+	0.0983877i
$151$			42406.7i			1.85986i	0.367735	+	0.929931i	$0.380133\pi$
$151$			42406.7i			1.85986i	−0.367735	+	0.929931i	$0.619867\pi$
$152$	26016.3	+	2134.27i	1.12605	+	0.0923766i
$153$	−13936.9			−0.595365
$154$	15500.4	+	9522.21i	0.653584	+	0.401510i
$155$		−	11638.9i		−	0.484448i
$156$	13449.5	−	6815.51i	0.552660	−	0.280059i
$157$	13979.2			0.567129			0.283565	−	0.958953i	$-0.408483\pi$
$157$	13979.2			0.567129			0.283565	+	0.958953i	$0.408483\pi$
$158$	−14782.5	+	24063.1i	−0.592151	+	0.963913i
$159$			11886.7i			0.470185i
$160$	−10601.2	+	4322.75i	−0.414110	+	0.168857i
$161$	459.010			0.0177080
$162$	−2484.61	−	1526.35i	−0.0946736	−	0.0581600i
$163$		−	31094.2i		−	1.17032i	−0.810919	−	0.585159i	$-0.801032\pi$
$163$		−	31094.2i		−	1.17032i	0.810919	−	0.585159i	$-0.198968\pi$
$164$	8788.00	+	17342.0i	0.326740	+	0.644780i
$165$	−4307.87			−0.158232
$166$	−10410.9	+	16946.9i	−0.377807	+	0.615000i
$167$		−	30204.9i		−	1.08304i	−0.840687	−	0.541521i	$-0.817849\pi$
$167$		−	30204.9i		−	1.08304i	0.840687	−	0.541521i	$-0.182151\pi$
$168$	1667.61	−	20327.8i	0.0590847	−	0.720231i
$169$	4329.78			0.151598
$170$	19669.3	+	12083.3i	0.680599	+	0.418106i
$171$		−	11012.5i		−	0.376612i
$172$	−14095.7	+	7142.95i	−0.476463	+	0.241446i
$173$	−22061.5			−0.737128			−0.368564	−	0.929602i	$-0.620150\pi$
$173$	−22061.5			−0.737128			−0.368564	+	0.929602i	$0.620150\pi$
$174$	16030.6	−	26094.8i	0.529482	−	0.861899i
$175$			7666.46i			0.250334i
$176$	−15308.2	−	11225.7i	−0.494195	−	0.362399i
$177$	−2030.06			−0.0647981
$178$	42162.3	+	25901.2i	1.33071	+	0.817484i
$179$			4300.24i			0.134210i	0.997746	+	0.0671052i	$0.0213763\pi$
$179$			4300.24i			0.134210i	−0.997746	+	0.0671052i	$0.978624\pi$
$180$	2183.22	+	4308.31i	0.0673834	+	0.132973i
$181$	−32288.1			−0.985566			−0.492783	−	0.870152i	$-0.664020\pi$
$181$	−32288.1			−0.985566			−0.492783	+	0.870152i	$0.664020\pi$
$182$	23288.9	−	37910.0i	0.703082	−	1.14449i
$183$		−	21350.3i		−	0.637531i
$184$	−477.376	−	39.1619i	−0.0141002	−	0.00115672i
$185$	7466.24			0.218152
$186$	−18436.1	−	11325.7i	−0.532897	−	0.327370i
$187$			38276.2i			1.09457i
$188$	−42005.3	+	21286.1i	−1.18847	+	0.602254i
$189$	−8604.60			−0.240884
$190$	−9547.81	+	15542.1i	−0.264482	+	0.430528i
$191$		−	23139.2i		−	0.634279i	−0.948379	−	0.317140i	$-0.897278\pi$
$191$		−	23139.2i		−	0.634279i	0.948379	−	0.317140i	$-0.102722\pi$
$192$	−3468.66	+	20998.9i	−0.0940936	+	0.569631i
$193$	−64774.6			−1.73896			−0.869481	−	0.493966i	$-0.835547\pi$
$193$	−64774.6			−1.73896			−0.869481	+	0.493966i	$0.835547\pi$
$194$	−8576.25	−	5268.57i	−0.227874	−	0.139988i
$195$			10536.0i			0.277080i
$196$	−9840.18	−	19418.3i	−0.256148	−	0.505475i
$197$	317.341			0.00817699			0.00408850	−	0.999992i	$-0.498699\pi$
$197$	317.341			0.00817699			0.00408850	+	0.999992i	$0.498699\pi$
$198$	−4191.95	+	6823.72i	−0.106927	+	0.174057i
$199$			18051.2i			0.455828i	0.973681	+	0.227914i	$0.0731905\pi$
$199$			18051.2i			0.455828i	−0.973681	+	0.227914i	$0.926810\pi$
$200$	654.089	−	7973.22i	0.0163522	−	0.199330i
$201$	−32044.5			−0.793161
$202$	10139.3	+	6228.80i	0.248489	+	0.152652i
$203$		−	90370.5i		−	2.19298i
$204$	38280.1	−	19398.3i	0.919840	−	0.466126i
$205$	−13585.2			−0.323265
$206$	−37611.3	+	61224.2i	−0.886306	+	1.44274i
$207$			202.069i			0.00471585i
$208$	−27455.1	+	37439.9i	−0.634596	+	0.865382i
$209$	−30244.6			−0.692398
$210$	12143.8	+	7460.17i	0.275369	+	0.169165i
$211$		−	62848.8i		−	1.41167i	−0.708378	−	0.705833i	$-0.750573\pi$
$211$		−	62848.8i		−	1.41167i	0.708378	−	0.705833i	$-0.249427\pi$
$212$	−16544.8	−	32649.0i	−0.368119	−	0.726436i
$213$	23188.8			0.511115
$214$	−2513.51	+	4091.53i	−0.0548850	+	0.0893426i
$215$		−	11042.1i		−	0.238878i
$216$	8948.89	+	734.129i	0.191806	+	0.0157349i
$217$	−63847.1			−1.35588
$218$	−56239.1	−	34548.8i	−1.18338	−	0.726976i
$219$		−	17506.2i		−	0.365008i
$220$	11832.3	−	5995.98i	0.244469	−	0.123884i
$221$	93613.7			1.91670
$222$	7265.33	−	11826.6i	0.147418	−	0.239968i
$223$			60726.4i			1.22115i	0.791960	+	0.610573i	$0.209061\pi$
$223$			60726.4i			1.22115i	−0.791960	+	0.610573i	$0.790939\pi$
$224$	23713.2	+	58154.8i	0.472601	+	1.15902i
$225$	−3375.00			−0.0666667
$226$	20578.4	+	12641.7i	0.402897	+	0.247508i
$227$		−	98629.1i		−	1.91405i	−0.290006	−	0.957025i	$-0.593657\pi$
$227$		−	98629.1i		−	1.91405i	0.290006	−	0.957025i	$-0.406343\pi$
$228$	15327.9	+	30247.7i	0.294858	+	0.581865i
$229$	56329.9			1.07416			0.537079	−	0.843532i	$-0.319528\pi$
$229$	56329.9			1.07416			0.537079	+	0.843532i	$0.319528\pi$
$230$	175.194	−	285.183i	0.00331179	−	0.00539098i
$231$			23631.6i			0.442863i
$232$	−7710.25	+	93986.4i	−0.143249	+	1.74618i
$233$	52509.1			0.967215			0.483608	−	0.875285i	$-0.339326\pi$
$233$	52509.1			0.967215			0.483608	+	0.875285i	$0.339326\pi$
$234$	16689.1	+	10252.4i	0.304790	+	0.187239i
$235$		−	32905.7i		−	0.595848i
$236$	5575.90	−	2825.57i	0.100113	−	0.0507320i
$237$	−36686.2			−0.653139
$238$	66284.9	−	107899.i	1.17020	−	1.90487i
$239$			51142.5i			0.895336i	0.894200	+	0.447668i	$0.147745\pi$
$239$			51142.5i			0.895336i	−0.894200	+	0.447668i	$0.852255\pi$
$240$	−11993.2	−	8794.75i	−0.208215	−	0.152687i
$241$	7.06147			0.000121580			6.07899e−5	−	1.00000i	$-0.499981\pi$
$241$	7.06147			0.000121580			6.07899e−5		1.00000i	$0.499981\pi$
$242$	−31159.6	−	19142.0i	−0.532061	−	0.326856i
$243$		−	3788.00i		−	0.0641500i
$244$	29716.7	+	58642.1i	0.499139	+	0.984986i
$245$	15211.7			0.253423
$246$	−13219.6	+	21519.1i	−0.218449	+	0.355594i
$247$			73970.6i			1.21245i
$248$	66401.7	+	5447.32i	1.07963	+	0.0885685i
$249$	−25837.0			−0.416718
$250$	4763.18	+	2926.12i	0.0762108	+	0.0468179i
$251$			60466.9i			0.959776i	0.877330	+	0.479888i	$0.159323\pi$
$251$			60466.9i			0.959776i	−0.877330	+	0.479888i	$0.840677\pi$
$252$	23634.0	−	11976.4i	0.372165	−	0.188594i
$253$	554.961			0.00867005
$254$	36606.6	−	59588.7i	0.567403	−	0.923627i
$255$			29987.4i			0.461168i
$256$	−19700.4	−	62504.9i	−0.300604	−	0.953749i
$257$	38335.4			0.580408			0.290204	−	0.956965i	$-0.406277\pi$
$257$	38335.4			0.580408			0.290204	+	0.956965i	$0.406277\pi$
$258$	−17490.9	−	10745.0i	−0.262768	−	0.161424i
$259$		−	40957.3i		−	0.610566i
$260$	−14664.6	−	28938.8i	−0.216932	−	0.428089i
$261$	39783.7			0.584015
$262$	22399.7	−	36462.5i	0.326316	−	0.531183i
$263$			38851.9i			0.561696i	0.959752	+	0.280848i	$0.0906156\pi$
$263$			38851.9i			0.561696i	−0.959752	+	0.280848i	$0.909384\pi$
$264$	2016.21	−	24577.1i	0.0289286	−	0.352634i
$265$	25576.2			0.364204
$266$	85258.7	+	52376.2i	1.20497	+	0.740237i
$267$			64279.8i			0.901679i
$268$	88015.6	−	44601.6i	1.22543	−	0.620985i
$269$	−18724.5			−0.258765			−0.129382	−	0.991595i	$-0.541299\pi$
$269$	−18724.5			−0.258765			−0.129382	+	0.991595i	$0.541299\pi$
$270$	−3284.18	+	5346.04i	−0.0450505	+	0.0733339i
$271$		−	25639.5i		−	0.349117i	−0.984647	−	0.174559i	$-0.944150\pi$
$271$		−	25639.5i		−	0.349117i	0.984647	−	0.174559i	$-0.0558499\pi$
$272$	−78142.8	+	106561.i	−1.05621	+	1.44033i
$273$	57796.8			0.775495
$274$	−106540.	−	65449.6i	−1.41909	−	0.871778i
$275$			9269.07i			0.122566i
$276$	−281.253	−	555.018i	−0.00369215	−	0.00728599i
$277$	−69695.7			−0.908335			−0.454168	−	0.890916i	$-0.650063\pi$
$277$	−69695.7			−0.908335			−0.454168	+	0.890916i	$0.650063\pi$
$278$	−47074.2	+	76628.1i	−0.609107	+	0.991513i
$279$		−	28107.3i		−	0.361086i
$280$	−43738.5	−	3588.12i	−0.557889	−	0.0457668i
$281$	−69900.0			−0.885248			−0.442624	−	0.896707i	$-0.645952\pi$
$281$	−69900.0			−0.885248			−0.442624	+	0.896707i	$0.645952\pi$
$282$	−52123.0	−	32020.3i	−0.655438	−	0.402649i
$283$			107624.i			1.34381i	0.740637	+	0.671905i	$0.234524\pi$
$283$			107624.i			1.34381i	−0.740637	+	0.671905i	$0.765476\pi$
$284$	−63691.8	+	32275.6i	−0.789673	+	0.400164i
$285$	−23695.1			−0.291722
$286$	28157.2	−	45834.7i	0.344237	−	0.560354i
$287$			74524.0i			0.904758i
$288$	−25601.4	+	10439.2i	−0.308659	+	0.125859i
$289$	182922.			2.19014
$290$	−56147.2	−	34492.4i	−0.667624	−	0.410135i
$291$		−	13075.2i		−	0.154405i
$292$	24366.2	+	48083.6i	0.285774	+	0.563938i
$293$	21779.0			0.253689			0.126845	−	0.991923i	$-0.459515\pi$
$293$	21779.0			0.253689			0.126845	+	0.991923i	$0.459515\pi$
$294$	14802.4	−	24095.6i	0.171253	−	0.278768i
$295$			4367.99i			0.0501924i
$296$	−3494.41	+	42596.1i	−0.0398832	+	0.486168i
$297$	−10403.3			−0.117939
$298$	−65588.4	−	40292.3i	−0.738574	−	0.453722i
$299$		−	1357.29i		−	0.0151821i
$300$	9270.01	−	4697.55i	0.103000	−	0.0521950i
$301$	−60573.6			−0.668575
$302$	88789.4	−	144533.i	0.973525	−	1.58472i
$303$			15458.2i			0.168374i
$304$	−84201.5	−	61746.0i	−0.911113	−	0.668131i
$305$	−45938.5			−0.493829
$306$	47500.5	+	29180.5i	0.507288	+	0.311638i
$307$		−	129208.i		−	1.37092i	−0.728111	−	0.685460i	$-0.759601\pi$
$307$		−	129208.i		−	1.37092i	0.728111	−	0.685460i	$-0.240399\pi$
$308$	−32892.0	−	64908.2i	−0.346728	−	0.684223i
$309$	−93341.2			−0.977590
$310$	−24369.0	+	39668.2i	−0.253580	+	0.412780i
$311$		−	39962.2i		−	0.413170i	−0.978429	−	0.206585i	$-0.933765\pi$
$311$		−	39962.2i		−	0.413170i	0.978429	−	0.206585i	$-0.0662351\pi$
$312$	−60109.4	−	4931.12i	−0.617495	−	0.0506567i
$313$	99259.1			1.01317			0.506584	−	0.862191i	$-0.330908\pi$
$313$	99259.1			1.01317			0.506584	+	0.862191i	$0.330908\pi$
$314$	−47644.5	−	29269.0i	−0.483230	−	0.296858i
$315$			18514.2i			0.186588i
$316$	100765.	−	51062.2i	1.00910	−	0.511358i
$317$	92350.2			0.919008			0.459504	−	0.888176i	$-0.348027\pi$
$317$	92350.2			0.919008			0.459504	+	0.888176i	$0.348027\pi$
$318$	24888.0	−	40513.0i	0.246114	−	0.400627i
$319$		−	109262.i		−	1.07371i
$320$	45182.4	+	7463.38i	0.441234	+	0.0728846i
$321$	−6237.87			−0.0605378
$322$	−1564.42	−	961.056i	−0.0150883	−	0.00926908i
$323$			210535.i			2.01799i
$324$	5272.38	+	10404.4i	0.0502246	+	0.0991119i
$325$	22669.8			0.214625
$326$	−65103.7	+	105977.i	−0.612591	+	0.997184i
$327$		−	85741.0i		−	0.801850i
$328$	6358.25	−	77505.8i	0.0591004	−	0.720422i
$329$	−180510.			−1.66767
$330$	14682.3	+	9019.65i	0.134824	+	0.0828251i
$331$		−	37376.0i		−	0.341143i	−0.985345	−	0.170572i	$-0.945439\pi$
$331$		−	37376.0i		−	0.341143i	0.985345	−	0.170572i	$-0.0545614\pi$
$332$	70965.6	−	35961.6i	0.643831	−	0.326259i
$333$	18030.6			0.162601
$334$	−63241.9	+	102946.i	−0.566907	+	0.922819i
$335$			68948.7i			0.614380i
$336$	−48245.2	+	65790.7i	−0.427342	+	0.582755i
$337$	119047.			1.04824			0.524118	−	0.851645i	$-0.324395\pi$
$337$	119047.			1.04824			0.524118	+	0.851645i	$0.324395\pi$
$338$	−14757.0	−	9065.51i	−0.129171	−	0.0793522i
$339$			31373.4i			0.272999i
$340$	−41738.5	−	82365.6i	−0.361060	−	0.712505i
$341$	−77193.7			−0.663855
$342$	−23057.5	+	37533.4i	−0.197133	+	0.320897i
$343$			63810.8i			0.542383i
$344$	62997.3	+	5168.03i	0.532359	+	0.0436725i
$345$	434.784			0.00365288
$346$	75191.1	+	46191.5i	0.628079	+	0.385842i
$347$		−	84780.6i		−	0.704105i	−0.935980	−	0.352052i	$-0.885484\pi$
$347$		−	84780.6i		−	0.704105i	0.935980	−	0.352052i	$-0.114516\pi$
$348$	−109273.	+	55373.6i	−0.902304	+	0.457240i
$349$	−171629.			−1.40909			−0.704545	−	0.709659i	$-0.748849\pi$
$349$	−171629.			−1.40909			−0.704545	+	0.709659i	$0.748849\pi$
$350$	16051.7	−	26129.2i	0.131035	−	0.213300i
$351$			25443.8i			0.206523i
$352$	28670.2	+	70311.6i	0.231391	+	0.567468i
$353$	195140.			1.56602			0.783010	−	0.622009i	$-0.213683\pi$
$353$	195140.			1.56602			0.783010	+	0.622009i	$0.213683\pi$
$354$	6918.95	+	4250.45i	0.0552120	+	0.0339179i
$355$		−	49894.3i		−	0.395908i
$356$	−89468.9	−	176555.i	−0.705947	−	1.39310i
$357$	164501.			1.29072
$358$	9003.66	−	14656.3i	0.0702511	−	0.114356i
$359$			50318.4i			0.390426i	0.980761	+	0.195213i	$0.0625398\pi$
$359$			50318.4i			0.390426i	−0.980761	+	0.195213i	$0.937460\pi$
$360$	1579.59	−	19254.9i	0.0121882	−	0.148572i
$361$	−36037.2			−0.276527
$362$	110046.	+	67603.6i	0.839764	+	0.515884i
$363$		−	47505.3i		−	0.360520i
$364$	−158749.	+	80445.4i	−1.19814	+	0.607154i
$365$	−37667.3			−0.282734
$366$	−44702.3	+	72767.1i	−0.333709	+	0.543216i
$367$		−	50718.2i		−	0.376558i	−0.982116	−	0.188279i	$-0.939709\pi$
$367$		−	50718.2i		−	0.376558i	0.982116	−	0.188279i	$-0.0602909\pi$
$368$	1545.02	+	1132.98i	0.0114088	+	0.00836619i
$369$	−32807.6			−0.240947
$370$	−25446.8	−	15632.5i	−0.185879	−	0.114189i
$371$		−	140303.i		−	1.01934i
$372$	39121.6	+	77201.5i	0.282703	+	0.557879i
$373$	−119570.			−0.859417			−0.429709	−	0.902968i	$-0.641384\pi$
$373$	−119570.			−0.859417			−0.429709	+	0.902968i	$0.641384\pi$
$374$	80141.1	−	130455.i	0.572944	−	0.932646i
$375$			7261.84i			0.0516398i
$376$	187733.	+	15400.8i	1.32790	+	0.108935i
$377$	−267226.			−1.88016
$378$	29326.6	+	18016.0i	0.205248	+	0.126088i
$379$		−	104060.i		−	0.724447i	−0.932091	−	0.362223i	$-0.882018\pi$
$379$		−	104060.i		−	0.724447i	0.932091	−	0.362223i	$-0.117982\pi$
$380$	65082.7	−	32980.4i	0.450711	−	0.228396i
$381$	90847.8			0.625842
$382$	−48447.8	+	78864.0i	−0.332007	+	0.540446i
$383$		−	72442.8i		−	0.493853i	−0.969034	−	0.246926i	$-0.920579\pi$
$383$		−	72442.8i		−	0.493853i	0.969034	−	0.246926i	$-0.0794206\pi$
$384$	55788.7	−	64306.9i	0.378341	−	0.436109i
$385$	50847.1			0.343040
$386$	220768.	+	135622.i	1.48171	+	0.910242i
$387$		−	26666.3i		−	0.178049i
$388$	18198.9	+	35913.2i	0.120888	+	0.238556i
$389$	−162511.			−1.07395			−0.536975	−	0.843598i	$-0.680433\pi$
$389$	−162511.			−1.07395			−0.536975	+	0.843598i	$0.680433\pi$
$390$	22059.8	−	35909.2i	0.145035	−	0.236089i
$391$		−	3863.13i		−	0.0252689i
$392$	−7119.52	+	86785.5i	−0.0463317	+	0.564775i
$393$	55590.0			0.359925
$394$	−1081.58	−	664.435i	−0.00696731	−	0.00428016i
$395$			78936.0i			0.505919i
$396$	28574.5	−	14480.0i	0.182216	−	0.0923376i
$397$	53291.6			0.338125			0.169063	−	0.985605i	$-0.445926\pi$
$397$	53291.6			0.338125			0.169063	+	0.985605i	$0.445926\pi$
$398$	37794.9	−	61523.1i	0.238598	−	0.388394i
$399$			129984.i			0.816476i
$400$	−18923.3	+	25805.2i	−0.118271	+	0.161283i
$401$	−33793.7			−0.210159			−0.105079	−	0.994464i	$-0.533510\pi$
$401$	−33793.7			−0.210159			−0.105079	+	0.994464i	$0.533510\pi$
$402$	109216.	+	67093.4i	0.675823	+	0.415172i
$403$			188796.i			1.16247i
$404$	−21515.8	−	42458.6i	−0.131824	−	0.260138i
$405$	−8150.47			−0.0496904
$406$	−189214.	+	308005.i	−1.14789	+	1.86856i
$407$		−	49519.1i		−	0.298940i
$408$	−171083.	−	14035.0i	−1.02775	−	0.0843123i
$409$	192978.			1.15361			0.576807	−	0.816881i	$-0.304299\pi$
$409$	192978.			1.15361			0.576807	+	0.816881i	$0.304299\pi$
$410$	46301.8	+	28444.1i	0.275442	+	0.169210i
$411$		−	162429.i		−	0.961565i
$412$	256377.	−	129918.i	1.51038	−	0.765379i
$413$	23961.4			0.140479
$414$	423.085	−	688.703i	0.00246846	−	0.00401820i
$415$			55592.3i			0.322789i
$416$	171964.	−	70120.1i	0.993691	−	0.405187i
$417$	−116826.			−0.671840
$418$	103081.	+	63325.0i	0.589966	+	0.362428i
$419$		−	207731.i		−	1.18324i	−0.806216	−	0.591621i	$-0.798488\pi$
$419$		−	207731.i		−	1.18324i	0.806216	−	0.591621i	$-0.201512\pi$
$420$	−25769.2	−	50852.3i	−0.146084	−	0.288278i
$421$	−135957.			−0.767075			−0.383538	−	0.923525i	$-0.625294\pi$
$421$	−135957.			−0.767075			−0.383538	+	0.923525i	$0.625294\pi$
$422$	−131590.	+	214204.i	−0.738922	+	1.20283i
$423$		−	79465.8i		−	0.444119i
$424$	−11970.4	+	145917.i	−0.0665850	+	0.811658i
$425$	64522.7			0.357219
$426$	−79033.1	−	48551.7i	−0.435502	−	0.267538i
$427$			252004.i			1.38214i
$428$	17133.4	−	8682.28i	0.0935309	−	0.0473965i
$429$	69878.7			0.379691
$430$	−23119.6	+	37634.4i	−0.125038	+	0.203539i
$431$		−	151994.i		−	0.818222i	−0.912485	−	0.409111i	$-0.865839\pi$
$431$		−	151994.i		−	0.818222i	0.912485	−	0.409111i	$-0.134161\pi$
$432$	−28963.0	−	21238.9i	−0.155194	−	0.113806i
$433$	−36457.2			−0.194450			−0.0972249	−	0.995262i	$-0.530997\pi$
$433$	−36457.2			−0.194450			−0.0972249	+	0.995262i	$0.530997\pi$
$434$	217607.	+	133680.i	1.15530	+	0.709722i
$435$		−	85600.9i		−	0.452376i
$436$	119340.	+	235502.i	0.627788	+	1.23886i
$437$	3052.52			0.0159844
$438$	−36653.7	+	59665.4i	−0.191060	+	0.311010i
$439$		−	118065.i		−	0.612620i	−0.951932	−	0.306310i	$-0.900906\pi$
$439$		−	118065.i		−	0.612620i	0.951932	−	0.306310i	$-0.0990944\pi$
$440$	−52881.6	−	4338.18i	−0.273149	−	0.0224080i
$441$	36735.6			0.188891
$442$	−319059.	−	196005.i	−1.63315	−	1.00328i
$443$			113592.i			0.578817i	0.957206	+	0.289409i	$0.0934587\pi$
$443$			113592.i			0.578817i	−0.957206	+	0.289409i	$0.906541\pi$
$444$	−49524.1	+	25096.2i	−0.251218	+	0.127304i
$445$	138308.			0.698438
$446$	127146.	−	206971.i	0.639196	−	1.04049i
$447$		−	99994.7i		−	0.500452i
$448$	40941.7	−	247856.i	0.203990	−	1.23493i
$449$	−1745.18			−0.00865662			−0.00432831	−	0.999991i	$-0.501378\pi$
$449$	−1745.18			−0.00865662			−0.00432831	+	0.999991i	$0.501378\pi$
$450$	11502.8	+	7066.44i	0.0568042	+	0.0348960i
$451$			90102.5i			0.442980i
$452$	−43667.5	−	86172.2i	−0.213738	−	0.421784i
$453$	220352.			1.07379
$454$	−206506.	+	336153.i	−1.00189	+	1.63089i
$455$		−	124359.i		−	0.600696i
$456$	11090.0	−	135185.i	0.0533337	−	0.650126i
$457$	−74606.1			−0.357225			−0.178613	−	0.983919i	$-0.557161\pi$
$457$	−74606.1			−0.357225			−0.178613	+	0.983919i	$0.557161\pi$
$458$	−191987.	−	117941.i	−0.915250	−	0.562257i
$459$			72418.3i			0.343734i
$460$	−1194.21	+	605.161i	−0.00564371	+	0.00285993i
$461$	17305.9			0.0814314			0.0407157	−	0.999171i	$-0.487036\pi$
$461$	17305.9			0.0814314			0.0407157	+	0.999171i	$0.487036\pi$
$462$	49478.9	−	80542.4i	0.231812	−	0.377347i
$463$		−	124639.i		−	0.581422i	−0.956811	−	0.290711i	$-0.906108\pi$
$463$		−	124639.i		−	0.581422i	0.956811	−	0.290711i	$-0.0938918\pi$
$464$	223063.	−	304186.i	1.03608	−	1.41287i
$465$	−60477.3			−0.279696
$466$	−178964.	−	109941.i	−0.824128	−	0.506279i
$467$			208541.i			0.956219i	0.878300	+	0.478110i	$0.158678\pi$
$467$			208541.i			0.956219i	−0.878300	+	0.478110i	$0.841322\pi$
$468$	−35414.4	−	69885.8i	−0.161692	−	0.319078i
$469$	378230.			1.71953
$470$	−68896.6	+	112151.i	−0.311891	+	0.507700i
$471$		−	72637.9i		−	0.327432i
$472$	−24920.1	−	2044.34i	−0.111858	−	0.00917634i
$473$	−73235.9			−0.327342
$474$	125036.	+	76812.0i	0.556515	+	0.341879i
$475$			50983.8i			0.225967i
$476$	−451831.	+	228964.i	−1.99417	+	1.01054i
$477$	61765.3			0.271461
$478$	107080.	−	174306.i	0.468654	−	0.762882i
$479$			399291.i			1.74028i	0.492805	+	0.870140i	$0.335972\pi$
$479$			399291.i			1.74028i	−0.492805	+	0.870140i	$0.664028\pi$
$480$	22461.7	+	55085.5i	0.0974899	+	0.239087i
$481$	−121111.			−0.523472
$482$	−24.0673	−	14.7850i	−0.000103594	−	6.36397e-5i
$483$		−	2385.08i		−	0.0102237i
$484$	66121.0	+	130481.i	0.282260	+	0.557003i
$485$	−28133.3			−0.119602
$486$	−7931.15	+	12910.4i	−0.0335787	+	0.0546598i
$487$		−	432403.i		−	1.82318i	−0.411097	−	0.911592i	$-0.634854\pi$
$487$		−	432403.i		−	1.82318i	0.411097	−	0.911592i	$-0.365146\pi$
$488$	21500.5	−	262087.i	0.0902836	−	1.10054i
$489$	−161570.			−0.675683
$490$	−51845.4	−	31849.7i	−0.215933	−	0.132652i
$491$			266902.i			1.10710i	0.832814	+	0.553552i	$0.186728\pi$
$491$			266902.i			1.10710i	−0.832814	+	0.553552i	$0.813272\pi$
$492$	90111.7	−	45663.8i	0.372264	−	0.188643i
$493$	−760578.			−3.12932
$494$	154877.	−	252110.i	0.634647	−	1.03309i
$495$			22384.4i			0.0913554i
$496$	−214908.	−	157595.i	−0.873554	−	0.640589i
$497$	−273704.			−1.10807
$498$	88058.8	+	54096.4i	0.355070	+	0.218127i
$499$		−	21287.2i		−	0.0854905i	−0.999086	−	0.0427452i	$-0.986390\pi$
$499$		−	21287.2i		−	0.0854905i	0.999086	−	0.0427452i	$-0.0136104\pi$
$500$	−10107.5	−	19945.9i	−0.0404300	−	0.0797835i
$501$	−156949.			−0.625294
$502$	126603.	−	206086.i	0.502385	−	0.817790i
$503$		−	267207.i		−	1.05612i	−0.849208	−	0.528058i	$-0.822920\pi$
$503$		−	267207.i		−	1.05612i	0.849208	−	0.528058i	$-0.177080\pi$
$504$	−105626.	−	8665.15i	−0.415826	−	0.0341126i
$505$	33260.8			0.130422
$506$	−1891.45	−	1161.96i	−0.00738743	−	0.00453825i
$507$		−	22498.2i		−	0.0875249i
$508$	−249529.	+	126448.i	−0.966926	+	0.489987i
$509$	449991.			1.73687			0.868437	−	0.495800i	$-0.165125\pi$
$509$	449991.			1.73687			0.868437	+	0.495800i	$0.165125\pi$
$510$	62786.5	−	102205.i	0.241394	−	0.392944i
$511$			206630.i			0.791320i
$512$	−63726.5	+	254280.i	−0.243097	+	0.970002i
$513$	−57222.6			−0.217437
$514$	−130657.	−	80265.0i	−0.494544	−	0.303809i
$515$			200838.i			0.757238i
$516$	37115.8	+	73243.4i	0.139399	+	0.275086i
$517$	−218244.			−0.816509
$518$	−85754.8	+	139593.i	−0.319594	+	0.520240i
$519$			114635.i			0.425581i
$520$	−10610.1	+	129335.i	−0.0392385	+	0.478309i
$521$	147922.			0.544951			0.272475	−	0.962163i	$-0.412158\pi$
$521$	147922.			0.544951			0.272475	+	0.962163i	$0.412158\pi$
$522$	−135593.	−	83297.5i	−0.497618	−	0.305697i
$523$			329638.i			1.20513i	0.798070	+	0.602565i	$0.205855\pi$
$523$			329638.i			1.20513i	−0.798070	+	0.602565i	$0.794145\pi$
$524$	−152687.	+	77373.8i	−0.556084	+	0.281794i
$525$	39836.1			0.144530
$526$	81346.6	−	132417.i	0.294014	−	0.478600i
$527$			537351.i			1.93480i
$528$	−58330.4	+	79543.6i	−0.209231	+	0.285323i
$529$	279785.			0.999800
$530$	−87170.1	−	53550.4i	−0.310324	−	0.190639i
$531$			10548.5i			0.0374112i
$532$	−180920.	−	357022.i	−0.639239	−	1.26146i
$533$	220368.			0.775700
$534$	134586.	−	219082.i	0.471975	−	0.768287i
$535$			13421.8i			0.0468923i
$536$	−393364.	−	32270.0i	−1.36919	−	0.112323i
$537$	22344.7			0.0774865
$538$	63817.7	+	39204.6i	0.220484	+	0.135448i
$539$		−	100890.i		−	0.347274i
$540$	22386.6	−	11344.4i	0.0767717	−	0.0389038i
$541$	412276.			1.40862			0.704309	−	0.709894i	$-0.251257\pi$
$541$	412276.			1.40862			0.704309	+	0.709894i	$0.251257\pi$
$542$	−53683.0	+	87385.9i	−0.182742	+	0.297470i
$543$			167774.i			0.569017i
$544$	489444.	−	199576.i	1.65389	−	0.674388i
$545$	−184485.			−0.621110
$546$	−196986.	−	121013.i	−0.660770	−	0.405925i
$547$		−	37918.1i		−	0.126728i	−0.997990	−	0.0633638i	$-0.979817\pi$
$547$		−	37918.1i		−	0.126728i	0.997990	−	0.0633638i	$-0.0201829\pi$
$548$	226079.	+	446137.i	0.752833	+	1.48562i
$549$	−110939.			−0.368079
$550$	19407.2	−	31591.3i	0.0641560	−	0.104434i
$551$		−	600985.i		−	1.97952i
$552$	−203.491	+	2480.52i	−0.000667832	+	0.00814074i
$553$	433017.			1.41597
$554$	237540.	+	145926.i	0.773959	+	0.475459i
$555$		−	38795.7i		−	0.125950i
$556$	320881.	−	162606.i	1.03799	−	0.526000i
$557$	229026.			0.738200			0.369100	−	0.929390i	$-0.379666\pi$
$557$	229026.			0.738200			0.369100	+	0.929390i	$0.379666\pi$
$558$	−58850.0	+	95796.8i	−0.189007	+	0.307668i
$559$			179116.i			0.573207i
$560$	141559.	+	103807.i	0.451400	+	0.331017i
$561$	198889.			0.631953
$562$	238237.	+	146354.i	0.754286	+	0.463374i
$563$		−	529561.i		−	1.67070i	−0.549717	−	0.835351i	$-0.685265\pi$
$563$		−	529561.i		−	1.67070i	0.549717	−	0.835351i	$-0.314735\pi$
$564$	110606.	+	218266.i	0.347712	+	0.686164i
$565$	67504.7			0.211464
$566$	225340.	−	366811.i	0.703403	−	1.14501i
$567$			44710.8i			0.139074i
$568$	284655.	+	23351.9i	0.882312	+	0.0723812i
$569$	273177.			0.843760			0.421880	−	0.906652i	$-0.361370\pi$
$569$	273177.			0.843760			0.421880	+	0.906652i	$0.361370\pi$
$570$	80758.9	+	49611.9i	0.248566	+	0.152699i
$571$			465596.i			1.42803i	0.700132	+	0.714014i	$0.253125\pi$
$571$			465596.i			1.42803i	−0.700132	+	0.714014i	$0.746875\pi$
$572$	−191934.	+	97261.8i	−0.586623	+	0.297269i
$573$	−120235.			−0.366201
$574$	156035.	−	253996.i	0.473586	−	0.770910i
$575$		−	935.506i		−	0.00282951i
$576$	109113.	+	18023.7i	0.328877	+	0.0543249i
$577$	292168.			0.877570			0.438785	−	0.898592i	$-0.355409\pi$
$577$	292168.			0.877570			0.438785	+	0.898592i	$0.355409\pi$
$578$	−623446.	−	382996.i	−1.86613	−	1.14641i
$579$			336579.i			1.00399i
$580$	119145.	+	235117.i	0.354176	+	0.698922i
$581$	304961.			0.903426
$582$	−27376.3	+	44563.5i	−0.0808218	+	0.131563i
$583$		−	169632.i		−	0.499080i
$584$	17629.3	−	214898.i	0.0516905	−	0.630096i
$585$	54746.4			0.159972
$586$	−74228.2	−	45599.9i	−0.216159	−	0.132791i
$587$			184222.i			0.534644i	0.963607	+	0.267322i	$0.0861387\pi$
$587$			184222.i			0.534644i	−0.963607	+	0.267322i	$0.913861\pi$
$588$	−100901.	+	51131.1i	−0.291836	+	0.147887i
$589$	−424598.			−1.22390
$590$	9145.52	−	14887.2i	0.0262727	−	0.0427670i
$591$		−	1648.95i		−	0.00472099i
$592$	101096.	−	137862.i	0.288463	−	0.393370i
$593$	−385641.			−1.09666			−0.548332	−	0.836261i	$-0.684737\pi$
$593$	−385641.			−1.09666			−0.548332	+	0.836261i	$0.684737\pi$
$594$	35457.1	+	21782.0i	0.100492	+	0.0617342i
$595$		−	353951.i		−	0.999790i
$596$	139179.	+	274652.i	0.391816	+	0.773198i
$597$	93797.0			0.263172
$598$	−2841.85	+	4626.00i	−0.00794691	+	0.0129361i
$599$		−	316862.i		−	0.883115i	−0.897233	−	0.441557i	$-0.854426\pi$
$599$		−	316862.i		−	0.883115i	0.897233	−	0.441557i	$-0.145574\pi$
$600$	−41430.0	−	3398.75i	−0.115083	−	0.00944096i
$601$	−388882.			−1.07663			−0.538317	−	0.842742i	$-0.680940\pi$
$601$	−388882.			−1.07663			−0.538317	+	0.842742i	$0.680940\pi$
$602$	206450.	+	126827.i	0.569668	+	0.349959i
$603$			166508.i			0.457931i
$604$	−605233.	+	306700.i	−1.65901	+	0.840698i
$605$	−102215.			−0.279257
$606$	32365.8	−	52685.5i	0.0881335	−	0.143465i
$607$		−	235572.i		−	0.639362i	−0.947525	−	0.319681i	$-0.896424\pi$
$607$		−	235572.i		−	0.639362i	0.947525	−	0.319681i	$-0.103576\pi$
$608$	157698.	+	386743.i	0.426599	+	1.04620i
$609$	−469579.			−1.26612
$610$	156570.	+	96184.1i	0.420774	+	0.258490i
$611$			533769.i			1.42979i
$612$	−100797.	−	198909.i	−0.269118	−	0.531070i
$613$	−74819.9			−0.199111			−0.0995557	−	0.995032i	$-0.531742\pi$
$613$	−74819.9			−0.199111			−0.0995557	+	0.995032i	$0.531742\pi$
$614$	−270530.	+	440372.i	−0.717594	+	1.16811i
$615$			70590.8i			0.186637i
$616$	−23797.9	+	290091.i	−0.0627158	+	0.764493i
$617$	476184.			1.25085			0.625424	−	0.780285i	$-0.284926\pi$
$617$	476184.			1.25085			0.625424	+	0.780285i	$0.284926\pi$
$618$	318130.	+	195434.i	0.832968	+	0.511709i
$619$			95751.1i			0.249898i	0.992163	+	0.124949i	$0.0398767\pi$
$619$			95751.1i			0.249898i	−0.992163	+	0.124949i	$0.960123\pi$
$620$	166111.	−	84176.3i	0.432131	−	0.218981i
$621$	1049.98			0.00272270
$622$	−83671.3	+	136201.i	−0.216270	+	0.352047i
$623$		−	758713.i		−	1.95480i
$624$	194543.	+	142661.i	0.499628	+	0.366384i
$625$	15625.0			0.0400000
$626$	−338300.	−	207825.i	−0.863283	−	0.530332i
$627$			157156.i			0.399756i
$628$	101102.	+	199512.i	0.256355	+	0.505883i
$629$	−344706.			−0.871260
$630$	38764.2	−	63100.9i	0.0976674	−	0.158984i
$631$		−	363696.i		−	0.913439i	−0.889611	−	0.456720i	$-0.849024\pi$
$631$		−	363696.i		−	0.913439i	0.889611	−	0.456720i	$-0.150976\pi$
$632$	−450343.	−	36944.3i	−1.12748	−	0.0924939i
$633$	−326572.			−0.815026
$634$	−314753.	−	193359.i	−0.783053	−	0.481045i
$635$		−	195473.i		−	0.484775i
$636$	−169649.	+	85969.1i	−0.419408	+	0.212534i
$637$	−246752.			−0.608110
$638$	−228767.	+	372391.i	−0.562021	+	0.914866i
$639$		−	120492.i		−	0.295092i
$640$	−138366.	−	120038.i	−0.337809	−	0.293062i
$641$	11650.4			0.0283547			0.0141773	−	0.999899i	$-0.495487\pi$
$641$	11650.4			0.0283547			0.0141773	+	0.999899i	$0.495487\pi$
$642$	21260.2	+	13060.6i	0.0515820	+	0.0316879i
$643$		−	477647.i		−	1.15527i	−0.816294	−	0.577637i	$-0.803975\pi$
$643$		−	477647.i		−	1.15527i	0.816294	−	0.577637i	$-0.196025\pi$
$644$	3319.72	+	6551.04i	0.00800441	+	0.0157957i
$645$	−57376.6			−0.137916
$646$	440810.	−	717557.i	1.05630	−	1.71946i
$647$		−	184457.i		−	0.440642i	−0.975427	−	0.220321i	$-0.929289\pi$
$647$		−	184457.i		−	0.440642i	0.975427	−	0.220321i	$-0.0707105\pi$
$648$	3814.65	−	46499.8i	0.00908457	−	0.110739i
$649$	28970.3			0.0687802
$650$	−77264.3	−	47465.0i	−0.182874	−	0.112343i
$651$			331759.i			0.782818i
$652$	443779.	−	224884.i	1.04393	−	0.529009i
$653$	105463.			0.247329			0.123664	−	0.992324i	$-0.460535\pi$
$653$	105463.			0.247329			0.123664	+	0.992324i	$0.460535\pi$
$654$	−179521.	+	292227.i	−0.419720	+	0.683226i
$655$		−	119611.i		−	0.278796i
$656$	−183949.	+	250847.i	−0.427455	+	0.582909i
$657$	−90964.7			−0.210738
$658$	615223.	+	377944.i	1.42096	+	0.872924i
$659$		−	434371.i		−	1.00021i	−0.865966	−	0.500103i	$-0.833295\pi$
$659$		−	434371.i		−	1.00021i	0.865966	−	0.500103i	$-0.166705\pi$
$660$	−31156.0	−	61482.5i	−0.0715244	−	0.141144i
$661$	−474718.			−1.08651			−0.543254	−	0.839568i	$-0.682808\pi$
$661$	−474718.			−1.08651			−0.543254	+	0.839568i	$0.682808\pi$
$662$	−78256.3	+	127387.i	−0.178568	+	0.290675i
$663$		−	486431.i		−	1.10661i
$664$	−317163.	−	26018.8i	−0.719361	−	0.0590134i
$665$	279681.			0.632439
$666$	−61452.8	−	37751.8i	−0.138546	−	0.0851116i
$667$			11027.5i			0.0247871i
$668$	431088.	−	218453.i	0.966080	−	0.489558i
$669$	315544.			0.705029
$670$	144362.	−	234995.i	0.321591	−	0.523490i
$671$			304683.i			0.676710i
$672$	302181.	−	123217.i	0.669159	−	0.272856i
$673$	−701401.			−1.54859			−0.774295	−	0.632825i	$-0.781895\pi$
$673$	−701401.			−1.54859			−0.774295	+	0.632825i	$0.781895\pi$
$674$	−405743.	−	249256.i	−0.893164	−	0.548689i
$675$			17537.0i			0.0384900i
$676$	31314.4	+	61795.1i	0.0685254	+	0.135226i
$677$	−284255.			−0.620199			−0.310100	−	0.950704i	$-0.600362\pi$
$677$	−284255.			−0.620199			−0.310100	+	0.950704i	$0.600362\pi$
$678$	65688.2	−	106928.i	0.142899	−	0.232613i
$679$			154330.i			0.334743i
$680$	−30198.4	+	368113.i	−0.0653080	+	0.796092i
$681$	−512492.			−1.10508
$682$	263096.	+	161625.i	0.565646	+	0.347488i
$683$			659478.i			1.41371i	0.707361	+	0.706853i	$0.249886\pi$
$683$			659478.i			1.41371i	−0.707361	+	0.706853i	$0.750114\pi$
$684$	157172.	−	79646.2i	0.335940	−	0.170237i
$685$	−349491.			−0.744825
$686$	133604.	−	217483.i	0.283905	−	0.462144i
$687$		−	292699.i		−	0.620166i
$688$	−203890.	−	149515.i	−0.430744	−	0.315870i
$689$	−414876.			−0.873936
$690$	−1481.85	−	910.333i	−0.00311248	−	0.00191206i
$691$			163007.i			0.341390i	0.985324	+	0.170695i	$0.0546012\pi$
$691$			163007.i			0.341390i	−0.985324	+	0.170695i	$0.945399\pi$
$692$	−159556.	−	314864.i	−0.333198	−	0.657523i
$693$	122793.			0.255687
$694$	−177510.	+	288953.i	−0.368556	+	0.599941i
$695$			251369.i			0.520405i
$696$	488367.	+	40063.6i	1.00816	+	0.0827050i
$697$	627211.			1.29106
$698$	584953.	+	359349.i	1.20063	+	0.737574i
$699$		−	272846.i		−	0.558422i
$700$	−109417.	+	55446.5i	−0.223299	+	0.113156i
$701$	270195.			0.549847			0.274924	−	0.961466i	$-0.411347\pi$
$701$	270195.			0.549847			0.274924	+	0.961466i	$0.411347\pi$
$702$	53273.3	−	86719.0i	0.108102	−	0.175971i
$703$		−	272376.i		−	0.551135i
$704$	49500.2	−	299668.i	0.0998760	−	0.604638i
$705$	−170983.			−0.344013
$706$	−665087.	−	408577.i	−1.33435	−	0.819717i
$707$		−	182458.i		−	0.365026i
$708$	−14682.1	−	28973.2i	−0.0292901	−	0.0578003i
$709$	40040.3			0.0796534			0.0398267	−	0.999207i	$-0.487319\pi$
$709$	40040.3			0.0796534			0.0398267	+	0.999207i	$0.487319\pi$
$710$	−104467.	+	170052.i	−0.207234	+	0.337338i
$711$			190627.i			0.377090i
$712$	−64732.1	+	789071.i	−0.127691	+	1.55653i
$713$	7790.99			0.0153255
$714$	−560662.	−	344426.i	−1.09978	−	0.675616i
$715$		−	150355.i		−	0.294107i
$716$	−61373.5	+	31100.8i	−0.119717	+	0.0606660i
$717$	265744.			0.516922
$718$	105355.	−	171498.i	0.204364	−	0.332667i
$719$		−	388789.i		−	0.752066i	−0.926606	−	0.376033i	$-0.877288\pi$
$719$		−	388789.i		−	0.752066i	0.926606	−	0.376033i	$-0.122712\pi$
$720$	−45698.9	+	62318.4i	−0.0881537	+	0.120213i
$721$	1.10173e6			2.11937
$722$	122824.	+	75453.3i	0.235618	+	0.144745i
$723$		−	36.6925i		−	7.01941e-5i
$724$	−233519.	−	460820.i	−0.445497	−	0.879132i
$725$	−184184.			−0.350409
$726$	−99464.7	+	161910.i	−0.188710	+	0.307185i
$727$			569739.i			1.07797i	0.842315	+	0.538985i	$0.181192\pi$
$727$			569739.i			1.07797i	−0.842315	+	0.538985i	$0.818808\pi$
$728$	709489.	+	58203.5i	1.33870	+	0.109821i
$729$	−19683.0			−0.0370370
$730$	128379.	+	78866.2i	0.240907	+	0.147994i
$731$			509801.i			0.954039i
$732$	304714.	−	154413.i	0.568682	−	0.288178i
$733$	119853.			0.223070			0.111535	−	0.993760i	$-0.464423\pi$
$733$	119853.			0.223070			0.111535	+	0.993760i	$0.464423\pi$
$734$	−106192.	+	172860.i	−0.197105	+	0.320851i
$735$		−	79042.5i		−	0.146314i
$736$	−2893.62	−	7096.39i	−0.00534178	−	0.0131003i
$737$	457296.			0.841904
$738$	111817.	+	68691.3i	0.205302	+	0.126121i
$739$		−	543414.i		−	0.995044i	−0.867451	−	0.497522i	$-0.834243\pi$
$739$		−	543414.i		−	0.995044i	0.867451	−	0.497522i	$-0.165757\pi$
$740$	53998.4	+	106559.i	0.0986092	+	0.194593i
$741$	384363.			0.700011
$742$	−293760.	+	478187.i	−0.533562	+	0.868540i
$743$			33513.7i			0.0607078i	0.999539	+	0.0303539i	$0.00966343\pi$
$743$			33513.7i			0.0607078i	−0.999539	+	0.0303539i	$0.990337\pi$
$744$	28305.1	−	345033.i	0.0511351	−	0.623326i
$745$	−215154.			−0.387648
$746$	407524.	+	250351.i	0.732277	+	0.449853i
$747$			134253.i			0.240592i
$748$	−546282.	+	276827.i	−0.976368	+	0.494771i
$749$	73627.4			0.131243
$750$	15204.6	−	24750.2i	0.0270303	−	0.0440003i
$751$			483614.i			0.857471i	0.903430	+	0.428735i	$0.141041\pi$
$751$			483614.i			0.857471i	−0.903430	+	0.428735i	$0.858959\pi$
$752$	−607594.	−	445557.i	−1.07443	−	0.787893i
$753$	314195.			0.554127
$754$	910773.	+	559506.i	1.60202	+	0.984153i
$755$		−	474121.i		−	0.831755i
$756$	−62231.5	−	122806.i	−0.108885	−	0.214870i
$757$	−154021.			−0.268774			−0.134387	−	0.990929i	$-0.542906\pi$
$757$	−154021.			−0.268774			−0.134387	+	0.990929i	$0.542906\pi$
$758$	−217877.	+	354663.i	−0.379204	+	0.617274i
$759$		−	2883.66i		−	0.00500566i
$760$	−290871.	−	23861.9i	−0.503586	−	0.0413121i
$761$	−242974.			−0.419557			−0.209779	−	0.977749i	$-0.567274\pi$
$761$	−242974.			−0.419557			−0.209779	+	0.977749i	$0.567274\pi$
$762$	−309632.	−	190213.i	−0.533256	−	0.327590i
$763$			1.01203e6i			1.73837i
$764$	330245.	−	167350.i	0.565782	−	0.286708i
$765$	155819.			0.266255
$766$	−151678.	+	246903.i	−0.258502	+	0.420794i
$767$		−	70853.9i		−	0.120441i
$768$	−324785.	+	102366.i	−0.550647	+	0.173554i
$769$	−86574.7			−0.146399			−0.0731995	−	0.997317i	$-0.523321\pi$
$769$	−86574.7			−0.146399			−0.0731995	+	0.997317i	$0.523321\pi$
$770$	−173300.	−	106462.i	−0.292292	−	0.179561i
$771$		−	199196.i		−	0.335099i
$772$	−468473.	−	924471.i	−0.786049	−	1.55117i
$773$	1.07093e6			1.79227			0.896133	−	0.443785i	$-0.146365\pi$
$773$	1.07093e6			1.79227			0.896133	+	0.443785i	$0.146365\pi$
$774$	−55832.7	+	90885.3i	−0.0931980	+	0.151709i
$775$			130127.i			0.216652i
$776$	13167.2	−	160505.i	0.0218660	−	0.266542i
$777$	−212821.			−0.352510
$778$	553879.	+	340259.i	0.915073	+	0.562148i
$779$			495602.i			0.816692i
$780$	−150370.	+	76199.7i	−0.247157	+	0.125246i
$781$	−330919.			−0.542525
$782$	−8088.46	+	13166.5i	−0.0132267	+	0.0215307i
$783$		−	206722.i		−	0.337181i
$784$	205973.	−	280880.i	0.335103	−	0.456972i
$785$	−156292.			−0.253628
$786$	−189465.	−	116392.i	−0.306678	−	0.188399i
$787$			751269.i			1.21296i	0.795099	+	0.606479i	$0.207419\pi$
$787$			751269.i			1.21296i	−0.795099	+	0.606479i	$0.792581\pi$
$788$	2295.12	+	4529.12i	0.00369618	+	0.00729393i
$789$	201881.			0.324295
$790$	165273.	−	269034.i	0.264818	−	0.431075i
$791$		−	370309.i		−	0.591849i
$792$	−127707.	−	10476.5i	−0.203593	−	0.0167019i
$793$	745176.			1.18498
$794$	−181631.	−	111580.i	−0.288104	−	0.176988i
$795$		−	132898.i		−	0.210273i
$796$	−257629.	+	130553.i	−0.406601	+	0.206044i
$797$	−410930.			−0.646921			−0.323461	−	0.946242i	$-0.604846\pi$
$797$	−410930.			−0.646921			−0.323461	+	0.946242i	$0.604846\pi$
$798$	272155.	−	443017.i	0.427376	−	0.695689i
$799$			1.51921e6i			2.37972i
$800$	118525.	−	48329.8i	0.185196	−	0.0755153i
$801$	334008.			0.520585
$802$	115177.	+	70755.9i	0.179068	+	0.110005i
$803$			249825.i			0.387440i
$804$	−231757.	−	457342.i	−0.358526	−	0.707505i
$805$	−5131.88			−0.00791927
$806$	395293.	−	643464.i	0.608484	−	0.990500i
$807$			97295.3i			0.149398i
$808$	−15567.0	+	189758.i	−0.0238442	+	0.290655i
$809$	−81222.3			−0.124102			−0.0620510	−	0.998073i	$-0.519764\pi$
$809$	−81222.3			−0.124102			−0.0620510	+	0.998073i	$0.519764\pi$
$810$	27778.8	+	17065.1i	0.0423393	+	0.0260099i
$811$		−	665948.i		−	1.01251i	−0.862384	−	0.506254i	$-0.831030\pi$
$811$		−	665948.i		−	1.01251i	0.862384	−	0.506254i	$-0.168970\pi$
$812$	1.28978e6	−	653590.i	1.95615	−	0.991274i
$813$	−133227.			−0.201563
$814$	−103681.	+	168774.i	−0.156477	+	0.254716i
$815$			347643.i			0.523382i
$816$	553709.	+	406042.i	0.831575	+	0.609805i
$817$	−402829.			−0.603499
$818$	−657716.	−	404049.i	−0.982951	−	0.603847i
$819$		−	300321.i		−	0.447732i
$820$	−98252.9	−	193889.i	−0.146123	−	0.288354i
$821$	175974.			0.261074			0.130537	−	0.991443i	$-0.458330\pi$
$821$	175974.			0.261074			0.130537	+	0.991443i	$0.458330\pi$
$822$	−340086.	+	553597.i	−0.503321	+	0.819314i
$823$		−	825656.i		−	1.21899i	−0.792790	−	0.609494i	$-0.791373\pi$
$823$		−	825656.i		−	1.21899i	0.792790	−	0.609494i	$-0.208627\pi$
$824$	−1.14582e6	−	93998.0i	−1.68757	−	0.138441i
$825$	48163.5			0.0707636
$826$	−81666.4	−	50169.4i	−0.119697	−	0.0735324i
$827$		−	184129.i		−	0.269222i	−0.990899	−	0.134611i	$-0.957022\pi$
$827$		−	184129.i		−	0.269222i	0.990899	−	0.134611i	$-0.0429785\pi$
$828$	−2883.96	+	1461.44i	−0.00420657	+	0.00213167i
$829$	−713518.			−1.03824			−0.519118	−	0.854703i	$-0.673739\pi$
$829$	−713518.			−1.03824			−0.519118	+	0.854703i	$0.673739\pi$
$830$	116397.	−	189472.i	0.168960	−	0.275036i
$831$			362149.i			0.524428i
$832$	−732911.	−	121065.i	−1.05878	−	0.174892i
$833$	−702306.			−1.01213
$834$	398171.	+	244605.i	0.572450	+	0.351668i
$835$			337701.i			0.484351i
$836$	−218740.	−	431655.i	−0.312979	−	0.617624i
$837$	−146050.			−0.208473
$838$	−434939.	+	708000.i	−0.619356	+	1.00820i
$839$			1.30678e6i			1.85643i	0.372047	+	0.928214i	$0.378656\pi$
$839$			1.30678e6i			1.85643i	−0.372047	+	0.928214i	$0.621344\pi$
$840$	−18644.4	+	227272.i	−0.0264235	+	0.322097i
$841$	1.46383e6			2.06966
$842$	463376.	+	284662.i	0.653596	+	0.401518i
$843$			363211.i			0.511098i
$844$	896985.	−	454544.i	1.25922	−	0.638104i
$845$	−48408.4			−0.0677965
$846$	−166382.	+	270839.i	−0.232469	+	0.378417i
$847$			560719.i			0.781589i
$848$	346312.	−	472257.i	0.481589	−	0.656730i
$849$	559233.			0.775849
$850$	−219910.	−	135095.i	−0.304373	−	0.186983i
$851$			4997.85i			0.00690120i
$852$	167709.	+	330952.i	0.231035	+	0.455918i
$853$	590922.			0.812143			0.406071	−	0.913841i	$-0.366898\pi$
$853$	590922.			0.812143			0.406071	+	0.913841i	$0.366898\pi$
$854$	527635.	−	858891.i	0.723465	−	1.17767i
$855$			123123.i			0.168426i
$856$	−76573.4	−	6281.76i	−0.104503	−	0.00857302i
$857$	−756073.			−1.02944			−0.514721	−	0.857358i	$-0.672105\pi$
$857$	−756073.			−1.02944			−0.514721	+	0.857358i	$0.672105\pi$
$858$	−238164.	−	146309.i	−0.323521	−	0.198745i
$859$		−	1.02880e6i		−	1.39426i	−0.716945	−	0.697130i	$-0.754460\pi$
$859$		−	1.02880e6i		−	1.39426i	0.716945	−	0.697130i	$-0.245540\pi$
$860$	157595.	−	79860.6i	0.213081	−	0.107978i
$861$	387238.			0.522362
$862$	−318238.	+	518033.i	−0.428290	+	0.697176i
$863$			520287.i			0.698589i	0.937013	+	0.349294i	$0.113579\pi$
$863$			520287.i			0.698589i	−0.937013	+	0.349294i	$0.886421\pi$
$864$	54243.9	+	133029.i	0.0726647	+	0.178205i
$865$	246655.			0.329654
$866$	124255.	+	76332.6i	0.165683	+	0.101783i
$867$		−	950493.i		−	1.26448i
$868$	−461764.	−	911232.i	−0.612887	−	1.20946i
$869$	523536.			0.693277
$870$	−179228.	+	291749.i	−0.236792	+	0.385453i
$871$		−	1.11843e6i		−	1.47425i
$872$	86344.3	−	1.05252e6i	0.113554	−	1.38419i
$873$	−67940.7			−0.0891459
$874$	−10403.8	−	6391.25i	−0.0136197	−	0.00836686i
$875$		−	85713.7i		−	0.111953i
$876$	249850.	−	126611.i	0.325590	−	0.164992i
$877$	−132059.			−0.171699			−0.0858496	−	0.996308i	$-0.527360\pi$
$877$	−132059.			−0.171699			−0.0858496	+	0.996308i	$0.527360\pi$
$878$	−247199.	+	402394.i	−0.320670	+	0.521990i
$879$		−	113167.i		−	0.146468i
$880$	171151.	+	125507.i	0.221011	+	0.162070i
$881$	−485203.			−0.625132			−0.312566	−	0.949896i	$-0.601189\pi$
$881$	−485203.			−0.625132			−0.312566	+	0.949896i	$0.601189\pi$
$882$	−125204.	−	76915.6i	−0.160947	−	0.0988729i
$883$		−	454909.i		−	0.583449i	−0.956502	−	0.291725i	$-0.905771\pi$
$883$		−	454909.i		−	0.583449i	0.956502	−	0.291725i	$-0.0942291\pi$
$884$	677047.	+	1.33607e6i	0.866392	+	1.70971i
$885$	22696.7			0.0289786
$886$	237835.	−	387151.i	0.302976	−	0.493189i
$887$		−	372656.i		−	0.473654i	−0.971552	−	0.236827i	$-0.923893\pi$
$887$		−	372656.i		−	0.473654i	0.971552	−	0.236827i	$-0.0761075\pi$
$888$	221336.	+	18157.5i	0.280689	+	0.0230266i
$889$	−1.07230e6			−1.35679
$890$	−471389.	−	289584.i	−0.595113	−	0.365590i
$891$			54057.2i			0.0680923i
$892$	−866694.	+	439194.i	−1.08927	+	0.551985i
$893$	−1.20043e6			−1.50534
$894$	−209365.	+	340807.i	−0.261956	+	0.426416i
$895$		−	48078.1i		−	0.0600207i
$896$	−658490.	+	759033.i	−0.820226	+	0.945464i
$897$	−7052.71			−0.00876538
$898$	5948.02	+	3653.99i	0.00737598	+	0.00453122i
$899$		−	1.53390e6i		−	1.89792i
$900$	−24409.2	−	48168.4i	−0.0301348	−	0.0594671i
$901$	−1.18082e6			−1.45457
$902$	188653.	−	307092.i	0.231873	−	0.377447i
$903$			314750.i			0.386002i
$904$	−31594.1	+	385126.i	−0.0386607	+	0.471266i
$905$	360992.			0.440759
$906$	−751014.	−	461363.i	−0.914938	−	0.562065i
$907$			354962.i			0.431487i	0.976450	+	0.215743i	$0.0692175\pi$
$907$			354962.i			0.431487i	−0.976450	+	0.215743i	$0.930783\pi$
$908$	1.40765e6	−	713320.i	1.70735	−	0.865192i
$909$	80323.3			0.0972106
$910$	−260378.	+	423847.i	−0.314428	+	0.511830i
$911$			108935.i			0.131260i	0.997844	+	0.0656298i	$0.0209056\pi$
$911$			108935.i			0.131260i	−0.997844	+	0.0656298i	$0.979094\pi$
$912$	−320842.	+	437524.i	−0.385746	+	0.526032i
$913$	368711.			0.442328
$914$	254276.	+	156207.i	0.304378	+	0.186986i
$915$			238703.i			0.285113i
$916$	407398.	+	803947.i	0.485543	+	0.958157i
$917$	−656145.			−0.780299
$918$	151626.	−	246820.i	0.179924	−	0.292883i
$919$		−	306482.i		−	0.362889i	−0.983401	−	0.181444i	$-0.941923\pi$
$919$		−	306482.i		−	0.362889i	0.983401	−	0.181444i	$-0.0580772\pi$
$920$	5337.22	+	437.843i	0.00630579	+	0.000517301i
$921$	−671383.			−0.791500
$922$	−58982.8	−	36234.3i	−0.0693846	−	0.0426244i
$923$			809343.i			0.950012i
$924$	−337273.	+	170912.i	−0.395037	+	0.200184i
$925$	−83475.1			−0.0975603
$926$	−260964.	+	424800.i	−0.304339	+	0.495408i
$927$			485015.i			0.564412i
$928$	−1.39715e6	+	569700.i	−1.62236	+	0.661532i
$929$	230175.			0.266702			0.133351	−	0.991069i	$-0.457426\pi$
$929$	230175.			0.266702			0.133351	+	0.991069i	$0.457426\pi$
$930$	206122.	+	126625.i	0.238319	+	0.146404i
$931$		−	554940.i		−	0.640246i
$932$	379764.	+	749416.i	0.437202	+	0.862763i
$933$	−207650.			−0.238544
$934$	436634.	−	710760.i	0.500523	−	0.814759i
$935$		−	427941.i		−	0.489509i
$936$	−25622.9	+	312338.i	−0.0292466	+	0.356511i
$937$	1.06117e6			1.20867			0.604333	−	0.796732i	$-0.293440\pi$
$937$	1.06117e6			1.20867			0.604333	+	0.796732i	$0.293440\pi$
$938$	−1.28910e6	−	791923.i	−1.46515	−	0.900073i
$939$		−	515765.i		−	0.584953i
$940$	469634.	−	237985.i	0.531501	−	0.269336i
$941$	−1.17032e6			−1.32168			−0.660838	−	0.750529i	$-0.729799\pi$
$941$	−1.17032e6			−1.32168			−0.660838	+	0.750529i	$0.729799\pi$
$942$	−152086.	+	247568.i	−0.171391	+	0.278993i
$943$		−	9093.85i		−	0.0102264i
$944$	80653.7	+	59144.4i	0.0905066	+	0.0663696i
$945$	96202.4			0.107726
$946$	249606.	+	153338.i	0.278916	+	0.171344i
$947$		−	605186.i		−	0.674822i	−0.941357	−	0.337411i	$-0.890449\pi$
$947$		−	605186.i		−	0.674822i	0.941357	−	0.337411i	$-0.109551\pi$
$948$	−265327.	−	523589.i	−0.295233	−	0.582604i
$949$	611007.			0.678444
$950$	106748.	−	173766.i	0.118280	−	0.192538i
$951$		−	479866.i		−	0.530590i
$952$	2.01935e6	+	165659.i	2.22811	+	0.182785i
$953$	−1.26323e6			−1.39090			−0.695452	−	0.718572i	$-0.744796\pi$
$953$	−1.26323e6			−1.39090			−0.695452	+	0.718572i	$0.744796\pi$
$954$	−210512.	−	129322.i	−0.231302	−	0.142094i
$955$			258704.i			0.283658i
$956$	−729911.	+	369880.i	−0.798646	+	0.404711i
$957$	−567740.			−0.619905
$958$	836020.	−	1.36089e6i	0.910931	−	1.48283i
$959$			1.91719e6i			2.08463i
$960$	38780.9	−	234775.i	0.0420799	−	0.254747i
$961$	−160185.			−0.173451
$962$	412777.	+	253577.i	0.446031	+	0.274006i
$963$			32412.9i			0.0349515i
$964$	51.0710	+	100.782i	5.49567e−5	+	0.000108450i
$965$	724202.			0.777688
$966$	−4993.79	+	8128.97i	−0.00535151	+	0.00871126i
$967$		−	1.65602e6i		−	1.77098i	−0.464657	−	0.885491i	$-0.653823\pi$
$967$		−	1.65602e6i		−	1.77098i	0.464657	−	0.885491i	$-0.346177\pi$
$968$	47839.6	−	583155.i	0.0510548	−	0.622348i
$969$	1.09397e6			1.16509
$970$	95885.4	+	58904.4i	0.101908	+	0.0626043i
$971$		−	538842.i		−	0.571508i	−0.958303	−	0.285754i	$-0.907756\pi$
$971$		−	538842.i		−	0.571508i	0.958303	−	0.285754i	$-0.0922441\pi$
$972$	54062.7	−	27396.1i	0.0572223	−	0.0289972i
$973$	1.37893e6			1.45652
$974$	−905347.	+	1.47374e6i	−0.954327	+	1.55347i
$975$		−	117796.i		−	0.123914i
$976$	−622026.	+	848241.i	−0.652993	+	0.890470i
$977$	962571.			1.00843			0.504213	−	0.863579i	$-0.331783\pi$
$977$	962571.			1.00843			0.504213	+	0.863579i	$0.331783\pi$
$978$	550671.	+	338289.i	0.575724	+	0.353679i
$979$		−	917315.i		−	0.957091i
$980$	110017.	+	217104.i	0.114553	+	0.226055i
$981$	−445523.			−0.462948
$982$	558828.	−	909669.i	0.579503	−	0.943323i
$983$		−	386329.i		−	0.399807i	−0.979816	−	0.199903i	$-0.935937\pi$
$983$		−	386329.i		−	0.399807i	0.979816	−	0.199903i	$-0.0640628\pi$
$984$	−402732.	−	33038.5i	−0.415936	−	0.0341216i
$985$	−3547.98			−0.00365686
$986$	2.59224e6	+	1.59247e6i	2.66638	+	1.63801i
$987$			937958.i			0.962828i
$988$	−1.05572e6	+	534981.i	−1.08152	+	0.548055i
$989$	7391.54			0.00755688
$990$	46867.5	−	76291.5i	0.0478191	−	0.0778406i
$991$		−	18475.3i		−	0.0188124i	−0.999956	−	0.00940620i	$-0.997006\pi$
$991$		−	18475.3i		−	0.0188124i	0.999956	−	0.00940620i	$-0.00299413\pi$
$992$	402495.	+	987090.i	0.409014	+	1.00307i
$993$	−194211.			−0.196959
$994$	932851.	+	573070.i	0.944147	+	0.580009i
$995$		−	201819.i		−	0.203852i
$996$	−186862.	−	368748.i	−0.188366	−	0.371716i
$997$	177630.			0.178701			0.0893503	−	0.996000i	$-0.471521\pi$
$997$	177630.			0.178701			0.0893503	+	0.996000i	$0.471521\pi$
$998$	−44570.3	+	72552.1i	−0.0447491	+	0.0728432i
$999$		−	93689.8i		−	0.0938775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.c.a.31.3	✓	16
3.2	odd	2		180.5.c.c.91.14		16
4.3	odd	2	inner	60.5.c.a.31.4	yes	16
5.2	odd	4		300.5.f.b.199.21		32
5.3	odd	4		300.5.f.b.199.12		32
5.4	even	2		300.5.c.d.151.14		16
8.3	odd	2		960.5.e.f.511.5		16
8.5	even	2		960.5.e.f.511.16		16
12.11	even	2		180.5.c.c.91.13		16
20.3	even	4		300.5.f.b.199.22		32
20.7	even	4		300.5.f.b.199.11		32
20.19	odd	2		300.5.c.d.151.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.3	✓	16	1.1	even	1	trivial
60.5.c.a.31.4	yes	16	4.3	odd	2	inner
180.5.c.c.91.13		16	12.11	even	2
180.5.c.c.91.14		16	3.2	odd	2
300.5.c.d.151.13		16	20.19	odd	2
300.5.c.d.151.14		16	5.4	even	2
300.5.f.b.199.11		32	20.7	even	4
300.5.f.b.199.12		32	5.3	odd	4
300.5.f.b.199.21		32	5.2	odd	4
300.5.f.b.199.22		32	20.3	even	4
960.5.e.f.511.5		16	8.3	odd	2
960.5.e.f.511.16		16	8.5	even	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)

\(f(q)\)	\(=\)	\(q+(-3.40825 - 2.09376i) q^{2} -5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} -11.1803 q^{5} +(-10.8795 + 17.7098i) q^{6} +61.3317i q^{7} +(5.23271 - 63.7857i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.40825 - 2.09376i) q^{2} -5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} -11.1803 q^{5} +(-10.8795 + 17.7098i) q^{6} +61.3317i q^{7} +(5.23271 - 63.7857i) q^{8} -27.0000 q^{9} +(38.1054 + 23.4089i) q^{10} +74.1525i q^{11} +(74.1601 - 37.5804i) q^{12} +181.358 q^{13} +(128.414 - 209.034i) q^{14} +58.0948i q^{15} +(-151.386 + 206.442i) q^{16} +516.182 q^{17} +(92.0228 + 56.5315i) q^{18} +407.870i q^{19} +(-80.8601 - 159.567i) q^{20} +318.689 q^{21} +(155.258 - 252.730i) q^{22} -7.48405i q^{23} +(-331.440 - 27.1900i) q^{24} +125.000 q^{25} +(-618.114 - 379.720i) q^{26} +140.296i q^{27} +(-875.333 + 443.572i) q^{28} -1473.47 q^{29} +(121.636 - 198.001i) q^{30} +1041.01i q^{31} +(948.202 - 386.639i) q^{32} +385.308 q^{33} +(-1759.28 - 1080.76i) q^{34} -685.709i q^{35} +(-195.273 - 385.347i) q^{36} -667.800 q^{37} +(853.982 - 1390.12i) q^{38} -942.365i q^{39} +(-58.5035 + 713.146i) q^{40} +1215.10 q^{41} +(-1086.17 - 667.258i) q^{42} +987.639i q^{43} +(-1058.31 + 536.297i) q^{44} +301.869 q^{45} +(-15.6698 + 25.5075i) q^{46} +2943.18i q^{47} +(1072.70 + 786.626i) q^{48} -1360.58 q^{49} +(-426.031 - 261.720i) q^{50} -2682.16i q^{51} +(1311.64 + 2588.36i) q^{52} -2287.61 q^{53} +(293.746 - 478.164i) q^{54} -829.051i q^{55} +(3912.09 + 320.931i) q^{56} +2119.36 q^{57} +(5021.96 + 3085.09i) q^{58} -390.685i q^{59} +(-829.135 + 420.161i) q^{60} +4108.86 q^{61} +(2179.63 - 3548.03i) q^{62} -1655.96i q^{63} +(-4041.24 - 667.545i) q^{64} -2027.65 q^{65} +(-1313.23 - 806.742i) q^{66} -6166.96i q^{67} +(3733.20 + 7367.00i) q^{68} -38.8883 q^{69} +(-1435.71 + 2337.07i) q^{70} +4462.68i q^{71} +(-141.283 + 1722.21i) q^{72} +3369.06 q^{73} +(2276.03 + 1398.21i) q^{74} -649.519i q^{75} +(-5821.17 + 2949.86i) q^{76} -4547.90 q^{77} +(-1973.08 + 3211.81i) q^{78} -7060.25i q^{79} +(1692.55 - 2308.09i) q^{80} +729.000 q^{81} +(-4141.36 - 2544.12i) q^{82} -4972.33i q^{83} +(2304.87 + 4548.36i) q^{84} -5771.09 q^{85} +(2067.88 - 3366.12i) q^{86} +7656.38i q^{87} +(4729.87 + 388.019i) q^{88} -12370.7 q^{89} +(-1028.85 - 632.041i) q^{90} +11123.0i q^{91} +(106.813 - 54.1273i) q^{92} +5409.26 q^{93} +(6162.30 - 10031.1i) q^{94} -4560.13i q^{95} +(-2009.03 - 4927.00i) q^{96} +2516.32 q^{97} +(4637.19 + 2848.72i) q^{98} -2002.12i 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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