LMFDB - Embedded newform 300.5.c.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, 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("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.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:	$31.0109889252$
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} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 20x^14 - 108x^13 + 492x^12 - 2160x^11 + 7360x^10 - 39552x^9 + 234752x^8 - 632832x^7 + 1884160x^6 - 8847360x^5 + 32243712x^4 - 113246208x^3 + 335544320x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.2
Root			$-1.18006 - 3.82197i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.89995 + 0.889027i) q^{2} -5.19615i q^{3} +(14.4193 - 6.93433i) q^{4} +(4.61952 + 20.2647i) q^{6} +44.0991i q^{7} +(-50.0696 + 39.8627i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.89995 + 0.889027i) q^{2} -5.19615i q^{3} +(14.4193 - 6.93433i) q^{4} +(4.61952 + 20.2647i) q^{6} +44.0991i q^{7} +(-50.0696 + 39.8627i) q^{8} -27.0000 q^{9} -81.7783i q^{11} +(-36.0318 - 74.9247i) q^{12} -192.024 q^{13} +(-39.2053 - 171.984i) q^{14} +(159.830 - 199.976i) q^{16} +415.880 q^{17} +(105.299 - 24.0037i) q^{18} -23.6665i q^{19} +229.146 q^{21} +(72.7031 + 318.931i) q^{22} +525.030i q^{23} +(207.132 + 260.169i) q^{24} +(748.886 - 170.715i) q^{26} +140.296i q^{27} +(305.798 + 635.876i) q^{28} +254.717 q^{29} -1306.77i q^{31} +(-445.546 + 921.989i) q^{32} -424.932 q^{33} +(-1621.91 + 369.729i) q^{34} +(-389.320 + 187.227i) q^{36} -1228.10 q^{37} +(21.0402 + 92.2983i) q^{38} +997.787i q^{39} +1956.13 q^{41} +(-893.657 + 203.717i) q^{42} -2497.56i q^{43} +(-567.077 - 1179.18i) q^{44} +(-466.766 - 2047.59i) q^{46} +2009.43i q^{47} +(-1039.10 - 830.502i) q^{48} +456.271 q^{49} -2160.98i q^{51} +(-2768.85 + 1331.56i) q^{52} +20.8393 q^{53} +(-124.727 - 547.148i) q^{54} +(-1757.91 - 2208.02i) q^{56} -122.975 q^{57} +(-993.383 + 226.450i) q^{58} +2216.17i q^{59} +2191.60 q^{61} +(1161.75 + 5096.34i) q^{62} -1190.68i q^{63} +(917.936 - 3991.82i) q^{64} +(1657.22 - 377.776i) q^{66} -6567.99i q^{67} +(5996.68 - 2883.85i) q^{68} +2728.14 q^{69} -8342.55i q^{71} +(1351.88 - 1076.29i) q^{72} +6092.86 q^{73} +(4789.55 - 1091.82i) q^{74} +(-164.111 - 341.254i) q^{76} +3606.35 q^{77} +(-887.060 - 3891.32i) q^{78} -6129.92i q^{79} +729.000 q^{81} +(-7628.82 + 1739.05i) q^{82} -9941.10i q^{83} +(3304.11 - 1588.97i) q^{84} +(2220.40 + 9740.36i) q^{86} -1323.55i q^{87} +(3259.90 + 4094.61i) q^{88} +6746.75 q^{89} -8468.09i q^{91} +(3640.73 + 7570.55i) q^{92} -6790.17 q^{93} +(-1786.44 - 7836.69i) q^{94} +(4790.80 + 2315.13i) q^{96} -1534.23 q^{97} +(-1779.44 + 405.637i) q^{98} +2208.01i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.89995	+	0.889027i	−0.974988	+	0.222257i
$2$	−3.89995	+	0.889027i	−0.974988	+	0.222257i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	14.4193	−	6.93433i	0.901204	−	0.433396i
$5$		0			0
$5$		0			0
$6$	4.61952	+	20.2647i	0.128320	+	0.562910i
$7$			44.0991i			0.899981i	0.893033	+	0.449991i	$0.148573\pi$
$7$			44.0991i			0.899981i	−0.893033	+	0.449991i	$0.851427\pi$
$8$	−50.0696	+	39.8627i	−0.782338	+	0.622854i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	81.7783i		−	0.675853i	−0.941172	−	0.337927i	$-0.890274\pi$
$11$		−	81.7783i		−	0.675853i	0.941172	−	0.337927i	$-0.109726\pi$
$12$	−36.0318	−	74.9247i	−0.250221	−	0.520310i
$13$	−192.024			−1.13624			−0.568119	−	0.822946i	$-0.692329\pi$
$13$	−192.024			−1.13624			−0.568119	+	0.822946i	$0.692329\pi$
$14$	−39.2053	−	171.984i	−0.200027	−	0.877471i
$15$		0			0
$16$	159.830	−	199.976i	0.624337	−	0.781155i
$17$	415.880			1.43903			0.719516	−	0.694476i	$-0.244364\pi$
$17$	415.880			1.43903			0.719516	+	0.694476i	$0.244364\pi$
$18$	105.299	−	24.0037i	0.324996	−	0.0740856i
$19$		−	23.6665i		−	0.0655582i	−0.999463	−	0.0327791i	$-0.989564\pi$
$19$		−	23.6665i		−	0.0655582i	0.999463	−	0.0327791i	$-0.0104358\pi$
$20$		0			0
$21$	229.146			0.519604
$22$	72.7031	+	318.931i	0.150213	+	0.658949i
$23$			525.030i			0.992496i	0.868181	+	0.496248i	$0.165289\pi$
$23$			525.030i			0.992496i	−0.868181	+	0.496248i	$0.834711\pi$
$24$	207.132	+	260.169i	0.359605	+	0.451683i
$25$		0			0
$26$	748.886	−	170.715i	1.10782	−	0.252537i
$27$			140.296i			0.192450i
$28$	305.798	+	635.876i	0.390048	+	0.811067i
$29$	254.717			0.302873			0.151437	−	0.988467i	$-0.451610\pi$
$29$	254.717			0.302873			0.151437	+	0.988467i	$0.451610\pi$
$30$		0			0
$31$		−	1306.77i		−	1.35980i	−0.733304	−	0.679901i	$-0.762023\pi$
$31$		−	1306.77i		−	1.35980i	0.733304	−	0.679901i	$-0.237977\pi$
$32$	−445.546	+	921.989i	−0.435104	+	0.900380i
$33$	−424.932			−0.390204
$34$	−1621.91	+	369.729i	−1.40304	+	0.319835i
$35$		0			0
$36$	−389.320	+	187.227i	−0.300401	+	0.144465i
$37$	−1228.10			−0.897081			−0.448540	−	0.893763i	$-0.648056\pi$
$37$	−1228.10			−0.897081			−0.448540	+	0.893763i	$0.648056\pi$
$38$	21.0402	+	92.2983i	0.0145708	+	0.0639185i
$39$			997.787i			0.656007i
$40$		0			0
$41$	1956.13			1.16367			0.581835	−	0.813307i	$-0.302335\pi$
$41$	1956.13			1.16367			0.581835	+	0.813307i	$0.302335\pi$
$42$	−893.657	+	203.717i	−0.506608	+	0.115486i
$43$		−	2497.56i		−	1.35076i	−0.737469	−	0.675381i	$-0.763979\pi$
$43$		−	2497.56i		−	1.35076i	0.737469	−	0.675381i	$-0.236021\pi$
$44$	−567.077	−	1179.18i	−0.292912	−	0.609082i
$45$		0			0
$46$	−466.766	−	2047.59i	−0.220589	−	0.967671i
$47$			2009.43i			0.909657i	0.890579	+	0.454829i	$0.150300\pi$
$47$			2009.43i			0.909657i	−0.890579	+	0.454829i	$0.849700\pi$
$48$	−1039.10	−	830.502i	−0.451000	−	0.360461i
$49$	456.271			0.190034
$50$		0			0
$51$		−	2160.98i		−	0.830825i
$52$	−2768.85	+	1331.56i	−1.02398	+	0.492441i
$53$	20.8393			0.00741876			0.00370938	−	0.999993i	$-0.498819\pi$
$53$	20.8393			0.00741876			0.00370938	+	0.999993i	$0.498819\pi$
$54$	−124.727	−	547.148i	−0.0427733	−	0.187637i
$55$		0			0
$56$	−1757.91	−	2208.02i	−0.560557	−	0.704089i
$57$	−122.975			−0.0378501
$58$	−993.383	+	226.450i	−0.295298	+	0.0673157i
$59$			2216.17i			0.636649i	0.947982	+	0.318324i	$0.103120\pi$
$59$			2216.17i			0.636649i	−0.947982	+	0.318324i	$0.896880\pi$
$60$		0			0
$61$	2191.60			0.588981			0.294491	−	0.955654i	$-0.404850\pi$
$61$	2191.60			0.588981			0.294491	+	0.955654i	$0.404850\pi$
$62$	1161.75	+	5096.34i	0.302225	+	1.32579i
$63$		−	1190.68i		−	0.299994i
$64$	917.936	−	3991.82i	0.224105	−	0.974565i
$65$		0			0
$66$	1657.22	−	377.776i	0.380444	−	0.0867255i
$67$		−	6567.99i		−	1.46313i	−0.681772	−	0.731565i	$-0.738790\pi$
$67$		−	6567.99i		−	1.46313i	0.681772	−	0.731565i	$-0.261210\pi$
$68$	5996.68	−	2883.85i	1.29686	−	0.623670i
$69$	2728.14			0.573018
$70$		0			0
$71$		−	8342.55i		−	1.65494i	−0.561510	−	0.827470i	$-0.689780\pi$
$71$		−	8342.55i		−	1.65494i	0.561510	−	0.827470i	$-0.310220\pi$
$72$	1351.88	−	1076.29i	0.260779	−	0.207618i
$73$	6092.86			1.14334			0.571671	−	0.820483i	$-0.306296\pi$
$73$	6092.86			1.14334			0.571671	+	0.820483i	$0.306296\pi$
$74$	4789.55	−	1091.82i	0.874643	−	0.199382i
$75$		0			0
$76$	−164.111	−	341.254i	−0.0284126	−	0.0590813i
$77$	3606.35			0.608255
$78$	−887.060	−	3891.32i	−0.145802	−	0.639600i
$79$		−	6129.92i		−	0.982201i	−0.871103	−	0.491101i	$-0.836595\pi$
$79$		−	6129.92i		−	0.982201i	0.871103	−	0.491101i	$-0.163405\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−7628.82	+	1739.05i	−1.13457	+	0.258634i
$83$		−	9941.10i		−	1.44304i	−0.692394	−	0.721520i	$-0.743444\pi$
$83$		−	9941.10i		−	1.44304i	0.692394	−	0.721520i	$-0.256556\pi$
$84$	3304.11	−	1588.97i	0.468269	−	0.225194i
$85$		0			0
$86$	2220.40	+	9740.36i	0.300216	+	1.31698i
$87$		−	1323.55i		−	0.174864i
$88$	3259.90	+	4094.61i	0.420958	+	0.528746i
$89$	6746.75			0.851755			0.425877	−	0.904781i	$-0.359965\pi$
$89$	6746.75			0.851755			0.425877	+	0.904781i	$0.359965\pi$
$90$		0			0
$91$		−	8468.09i		−	1.02259i
$92$	3640.73	+	7570.55i	0.430143	+	0.894441i
$93$	−6790.17			−0.785082
$94$	−1786.44	−	7836.69i	−0.202178	−	0.886905i
$95$		0			0
$96$	4790.80	+	2315.13i	0.519835	+	0.251207i
$97$	−1534.23			−0.163060			−0.0815301	−	0.996671i	$-0.525981\pi$
$97$	−1534.23			−0.163060			−0.0815301	+	0.996671i	$0.525981\pi$
$98$	−1779.44	+	405.637i	−0.185281	+	0.0422363i
$99$			2208.01i			0.225284i
$100$		0			0
$101$	−8029.60			−0.787138			−0.393569	−	0.919295i	$-0.628760\pi$
$101$	−8029.60			−0.787138			−0.393569	+	0.919295i	$0.628760\pi$
$102$	1921.17	+	8427.71i	0.184657	+	0.810045i
$103$		−	6973.64i		−	0.657332i	−0.944446	−	0.328666i	$-0.893401\pi$
$103$		−	6973.64i		−	0.657332i	0.944446	−	0.328666i	$-0.106599\pi$
$104$	9614.58	−	7654.60i	0.888922	−	0.707711i
$105$		0			0
$106$	−81.2723	+	18.5267i	−0.00723320	+	0.00164887i
$107$		−	13213.0i		−	1.15407i	−0.816718	−	0.577036i	$-0.804209\pi$
$107$		−	13213.0i		−	1.15407i	0.816718	−	0.577036i	$-0.195791\pi$
$108$	972.859	+	2022.97i	0.0834070	+	0.173437i
$109$	−23642.6			−1.98995			−0.994976	−	0.100116i	$-0.968079\pi$
$109$	−23642.6			−1.98995			−0.994976	+	0.100116i	$0.968079\pi$
$110$		0			0
$111$			6381.41i			0.517930i
$112$	8818.75	+	7048.36i	0.703025	+	0.561891i
$113$	20927.8			1.63896			0.819478	−	0.573110i	$-0.194263\pi$
$113$	20927.8			1.63896			0.819478	+	0.573110i	$0.194263\pi$
$114$	479.596	−	109.328i	0.0369034	−	0.00841243i
$115$		0			0
$116$	3672.82	−	1766.29i	0.272951	−	0.131264i
$117$	5184.66			0.378746
$118$	−1970.24	−	8642.97i	−0.141499	−	0.620725i
$119$			18339.9i			1.29510i
$120$		0			0
$121$	7953.32			0.543222
$122$	−8547.13	+	1948.39i	−0.574250	+	0.130905i
$123$		−	10164.4i		−	0.671846i
$124$	−9061.57	−	18842.6i	−0.589332	−	1.22546i
$125$		0			0
$126$	1058.54	+	4643.58i	0.0666757	+	0.292490i
$127$		−	23012.5i		−	1.42678i	−0.700769	−	0.713388i	$-0.747160\pi$
$127$		−	23012.5i		−	1.42678i	0.700769	−	0.713388i	$-0.252840\pi$
$128$	−31.0702	+	16384.0i	−0.00189637	+	0.999998i
$129$	−12977.7			−0.779863
$130$		0			0
$131$		−	15628.0i		−	0.910669i	−0.890320	−	0.455335i	$-0.849520\pi$
$131$		−	15628.0i		−	0.910669i	0.890320	−	0.455335i	$-0.150480\pi$
$132$	−6127.21	+	2946.62i	−0.351653	+	0.169113i
$133$	1043.67			0.0590012
$134$	5839.12	+	25614.9i	0.325191	+	1.42653i
$135$		0			0
$136$	−20823.0	+	16578.1i	−1.12581	+	0.896307i
$137$	12124.8			0.645999			0.323000	−	0.946399i	$-0.395309\pi$
$137$	12124.8			0.645999			0.323000	+	0.946399i	$0.395309\pi$
$138$	−10639.6	+	2425.39i	−0.558685	+	0.127357i
$139$			21661.2i			1.12112i	0.828112	+	0.560562i	$0.189415\pi$
$139$			21661.2i			1.12112i	−0.828112	+	0.560562i	$0.810585\pi$
$140$		0			0
$141$	10441.3			0.525191
$142$	7416.75	+	32535.5i	0.367822	+	1.61355i
$143$			15703.4i			0.767930i
$144$	−4315.41	+	5399.35i	−0.208112	+	0.260385i
$145$		0			0
$146$	−23761.9	+	5416.72i	−1.11474	+	0.254115i
$147$		−	2370.85i		−	0.109716i
$148$	−17708.3	+	8516.07i	−0.808453	+	0.388791i
$149$	7153.57			0.322218			0.161109	−	0.986937i	$-0.448493\pi$
$149$	7153.57			0.322218			0.161109	+	0.986937i	$0.448493\pi$
$150$		0			0
$151$		−	6696.21i		−	0.293680i	−0.989160	−	0.146840i	$-0.953090\pi$
$151$		−	6696.21i		−	0.293680i	0.989160	−	0.146840i	$-0.0469103\pi$
$152$	943.411	+	1184.97i	0.0408332	+	0.0512887i
$153$	−11228.8			−0.479677
$154$	−14064.6	+	3206.14i	−0.593042	+	0.135189i
$155$		0			0
$156$	6918.98	+	14387.4i	0.284311	+	0.591196i
$157$	−35186.7			−1.42751			−0.713756	−	0.700394i	$-0.753007\pi$
$157$	−35186.7			−1.42751			−0.713756	+	0.700394i	$0.753007\pi$
$158$	5449.66	+	23906.4i	0.218301	+	0.957635i
$159$		−	108.284i		−	0.00428322i
$160$		0			0
$161$	−23153.3			−0.893227
$162$	−2843.07	+	648.101i	−0.108332	+	0.0246952i
$163$			37194.0i			1.39990i	0.714191	+	0.699951i	$0.246795\pi$
$163$			37194.0i			1.39990i	−0.714191	+	0.699951i	$0.753205\pi$
$164$	28206.0	−	13564.5i	1.04870	−	0.504330i
$165$		0			0
$166$	8837.91	+	38769.8i	0.320725	+	1.40695i
$167$		−	52749.4i		−	1.89140i	−0.325035	−	0.945702i	$-0.605376\pi$
$167$		−	52749.4i		−	1.89140i	0.325035	−	0.945702i	$-0.394624\pi$
$168$	−11473.2	+	9134.35i	−0.406506	+	0.323638i
$169$	8312.32			0.291037
$170$		0			0
$171$			638.996i			0.0218527i
$172$	−17318.9	−	36013.0i	−0.585414	−	1.21731i
$173$	−23695.1			−0.791711			−0.395855	−	0.918313i	$-0.629552\pi$
$173$	−23695.1			−0.791711			−0.395855	+	0.918313i	$0.629552\pi$
$174$	1176.67	+	5161.77i	0.0388647	+	0.170490i
$175$		0			0
$176$	−16353.7	−	13070.6i	−0.527946	−	0.421960i
$177$	11515.6			0.367569
$178$	−26312.0	+	5998.05i	−0.830451	+	0.189308i
$179$			39705.3i			1.23920i	0.784917	+	0.619601i	$0.212706\pi$
$179$			39705.3i			1.23920i	−0.784917	+	0.619601i	$0.787294\pi$
$180$		0			0
$181$	37853.5			1.15545			0.577723	−	0.816233i	$-0.303941\pi$
$181$	37853.5			1.15545			0.577723	+	0.816233i	$0.303941\pi$
$182$	7528.37	+	33025.2i	0.227278	+	0.997016i
$183$		−	11387.9i		−	0.340048i
$184$	−20929.1	−	26288.1i	−0.618180	−	0.776467i
$185$		0			0
$186$	26481.4	−	6036.65i	0.765446	−	0.174490i
$187$		−	34010.0i		−	0.972574i
$188$	13934.1	+	28974.5i	0.394241	+	0.819787i
$189$	−6186.93			−0.173201
$190$		0			0
$191$			9912.58i			0.271719i	0.990728	+	0.135860i	$0.0433796\pi$
$191$			9912.58i			0.271719i	−0.990728	+	0.135860i	$0.956620\pi$
$192$	−20742.1	−	4769.73i	−0.562665	−	0.129387i
$193$	−33480.7			−0.898836			−0.449418	−	0.893322i	$-0.648369\pi$
$193$	−33480.7			−0.898836			−0.449418	+	0.893322i	$0.648369\pi$
$194$	5983.44	−	1363.97i	0.158982	−	0.0362412i
$195$		0			0
$196$	6579.09	−	3163.93i	0.171259	−	0.0823598i
$197$	47603.7			1.22662			0.613308	−	0.789844i	$-0.289839\pi$
$197$	47603.7			1.22662			0.613308	+	0.789844i	$0.289839\pi$
$198$	−1962.98	−	8611.15i	−0.0500710	−	0.219650i
$199$			36097.0i			0.911518i	0.890103	+	0.455759i	$0.150632\pi$
$199$			36097.0i			0.911518i	−0.890103	+	0.455759i	$0.849368\pi$
$200$		0			0
$201$	−34128.3			−0.844738
$202$	31315.1	−	7138.53i	0.767451	−	0.174947i
$203$			11232.8i			0.272580i
$204$	−14984.9	−	31159.7i	−0.360076	−	0.748743i
$205$		0			0
$206$	6199.76	+	27196.9i	0.146097	+	0.640891i
$207$		−	14175.8i		−	0.330832i
$208$	−30691.3	+	38400.2i	−0.709395	+	0.887579i
$209$	−1935.41			−0.0443077
$210$		0			0
$211$			38188.8i			0.857770i	0.903359	+	0.428885i	$0.141093\pi$
$211$			38188.8i			0.857770i	−0.903359	+	0.428885i	$0.858907\pi$
$212$	300.487	−	144.507i	0.00668582	−	0.00321526i
$213$	−43349.2			−0.955480
$214$	11746.7	+	51530.0i	0.256501	+	1.12521i
$215$		0			0
$216$	−5592.58	−	7024.57i	−0.119868	−	0.150561i
$217$	57627.3			1.22380
$218$	92205.1	−	21018.9i	1.94018	−	0.442280i
$219$		−	31659.5i		−	0.660108i
$220$		0			0
$221$	−79859.1			−1.63508
$222$	−5673.25	−	24887.2i	−0.115113	−	0.504976i
$223$		−	57730.2i		−	1.16090i	−0.814297	−	0.580448i	$-0.802877\pi$
$223$		−	57730.2i		−	1.16090i	0.814297	−	0.580448i	$-0.197123\pi$
$224$	−40658.9	−	19648.2i	−0.810325	−	0.391585i
$225$		0			0
$226$	−81617.6	+	18605.4i	−1.59796	+	0.364269i
$227$			71760.8i			1.39263i	0.717737	+	0.696314i	$0.245178\pi$
$227$			71760.8i			1.39263i	−0.717737	+	0.696314i	$0.754822\pi$
$228$	−1773.21	+	852.748i	−0.0341106	+	0.0164040i
$229$	39466.1			0.752581			0.376290	−	0.926502i	$-0.377200\pi$
$229$	39466.1			0.752581			0.376290	+	0.926502i	$0.377200\pi$
$230$		0			0
$231$		−	18739.1i		−	0.351176i
$232$	−12753.6	+	10153.7i	−0.236949	+	0.188646i
$233$	106708.			1.96556			0.982781	−	0.184775i	$-0.0591555\pi$
$233$	106708.			1.96556			0.982781	+	0.184775i	$0.0591555\pi$
$234$	−20219.9	+	4609.30i	−0.369273	+	0.0841789i
$235$		0			0
$236$	15367.7	+	31955.6i	0.275921	+	0.573750i
$237$	−31852.0			−0.567074
$238$	−16304.7	−	71524.9i	−0.287845	−	1.26271i
$239$		−	32704.8i		−	0.572554i	−0.958147	−	0.286277i	$-0.907582\pi$
$239$		−	32704.8i		−	0.572554i	0.958147	−	0.286277i	$-0.0924177\pi$
$240$		0			0
$241$	93720.2			1.61361			0.806806	−	0.590816i	$-0.201194\pi$
$241$	93720.2			1.61361			0.806806	+	0.590816i	$0.201194\pi$
$242$	−31017.6	+	7070.72i	−0.529635	+	0.120735i
$243$		−	3788.00i		−	0.0641500i
$244$	31601.2	−	15197.3i	0.530792	−	0.255262i
$245$		0			0
$246$	9036.39	+	39640.5i	0.149322	+	0.655041i
$247$			4544.55i			0.0744898i
$248$	52091.3	+	65429.5i	0.846958	+	1.06382i
$249$	−51655.5			−0.833139
$250$		0			0
$251$		−	2858.44i		−	0.0453714i	−0.999743	−	0.0226857i	$-0.992778\pi$
$251$		−	2858.44i		−	0.0453714i	0.999743	−	0.0226857i	$-0.00722170\pi$
$252$	−8256.53	−	17168.7i	−0.130016	−	0.270356i
$253$	42936.0			0.670781
$254$	20458.7	+	89747.5i	0.317111	+	1.39109i
$255$		0			0
$256$	−14444.6	−	63924.3i	−0.220407	−	0.975408i
$257$	34273.0			0.518902			0.259451	−	0.965756i	$-0.416458\pi$
$257$	34273.0			0.518902			0.259451	+	0.965756i	$0.416458\pi$
$258$	50612.4	−	11537.5i	0.760357	−	0.173330i
$259$		−	54158.2i		−	0.807356i
$260$		0			0
$261$	−6877.35			−0.100958
$262$	13893.7	+	60948.4i	0.202402	+	0.887892i
$263$			50691.6i			0.732866i	0.930444	+	0.366433i	$0.119421\pi$
$263$			50691.6i			0.732866i	−0.930444	+	0.366433i	$0.880579\pi$
$264$	21276.2	−	16938.9i	0.305271	−	0.243040i
$265$		0			0
$266$	−4070.27	+	927.853i	−0.0575254	+	0.0131134i
$267$		−	35057.1i		−	0.491761i
$268$	−45544.6	−	94705.6i	−0.634114	−	1.31858i
$269$	42022.9			0.580740			0.290370	−	0.956914i	$-0.406222\pi$
$269$	42022.9			0.580740			0.290370	+	0.956914i	$0.406222\pi$
$270$		0			0
$271$			101170.i			1.37757i	0.724965	+	0.688786i	$0.241856\pi$
$271$			101170.i			1.37757i	−0.724965	+	0.688786i	$0.758144\pi$
$272$	66470.2	−	83166.0i	0.898440	−	1.12411i
$273$	−44001.5			−0.590394
$274$	−47286.0	+	10779.2i	−0.629841	+	0.143578i
$275$		0			0
$276$	39337.7	−	18917.8i	0.516406	−	0.248343i
$277$	−129724.			−1.69067			−0.845337	−	0.534234i	$-0.820600\pi$
$277$	−129724.			−1.69067			−0.845337	+	0.534234i	$0.820600\pi$
$278$	−19257.4	−	84477.8i	−0.249177	−	1.09308i
$279$			35282.8i			0.453267i
$280$		0			0
$281$	−10671.3			−0.135147			−0.0675733	−	0.997714i	$-0.521526\pi$
$281$	−10671.3			−0.135147			−0.0675733	+	0.997714i	$0.521526\pi$
$282$	−40720.7	+	9282.62i	−0.512055	+	0.116727i
$283$		−	98529.3i		−	1.23025i	−0.788431	−	0.615124i	$-0.789106\pi$
$283$		−	98529.3i		−	1.23025i	0.788431	−	0.615124i	$-0.210894\pi$
$284$	−57850.0	−	120293.i	−0.717243	−	1.49144i
$285$		0			0
$286$	−13960.8	−	61242.6i	−0.170678	−	0.748723i
$287$			86263.6i			1.04728i
$288$	12029.7	−	24893.7i	0.145035	−	0.300127i
$289$	89435.3			1.07081
$290$		0			0
$291$			7972.11i			0.0941428i
$292$	87854.6	−	42249.9i	1.03038	−	0.495519i
$293$	11135.2			0.129707			0.0648536	−	0.997895i	$-0.479342\pi$
$293$	11135.2			0.129707			0.0648536	+	0.997895i	$0.479342\pi$
$294$	2107.75	+	9246.22i	0.0243851	+	0.106972i
$295$		0			0
$296$	61490.7	−	48955.5i	0.701820	−	0.558751i
$297$	11473.2			0.130068
$298$	−27898.6	+	6359.72i	−0.314159	+	0.0716152i
$299$		−	100819.i		−	1.12771i
$300$		0			0
$301$	110140.			1.21566
$302$	5953.11	+	26114.9i	0.0652725	+	0.286335i
$303$			41723.0i			0.454455i
$304$	−4732.73	−	3782.62i	−0.0512112	−	0.0409304i
$305$		0			0
$306$	43791.7	−	9982.68i	0.467680	−	0.106612i
$307$			132222.i			1.40290i	0.712721	+	0.701448i	$0.247463\pi$
$307$			132222.i			1.40290i	−0.712721	+	0.701448i	$0.752537\pi$
$308$	52000.8	−	25007.6i	0.548162	−	0.263615i
$309$	−36236.1			−0.379511
$310$		0			0
$311$		−	112364.i		−	1.16173i	−0.813999	−	0.580867i	$-0.802714\pi$
$311$		−	112364.i		−	1.16173i	0.813999	−	0.580867i	$-0.197286\pi$
$312$	−39774.5	−	49958.8i	−0.408597	−	0.513220i
$313$	44150.3			0.450656			0.225328	−	0.974283i	$-0.427655\pi$
$313$	44150.3			0.450656			0.225328	+	0.974283i	$0.427655\pi$
$314$	137227.	−	31282.0i	1.39181	−	0.317274i
$315$		0			0
$316$	−42506.9	−	88388.9i	−0.425682	−	0.885164i
$317$	−48209.0			−0.479744			−0.239872	−	0.970805i	$-0.577105\pi$
$317$	−48209.0			−0.479744			−0.239872	+	0.970805i	$0.577105\pi$
$318$	96.2676	+	422.303i	0.000951976	+	0.00417609i
$319$		−	20830.3i		−	0.204698i
$320$		0			0
$321$	−68656.6			−0.666304
$322$	90297.0	−	20584.0i	0.870886	−	0.198526i
$323$		−	9842.44i		−	0.0943404i
$324$	10511.6	−	5055.13i	0.100134	−	0.0481551i
$325$		0			0
$326$	−33066.5	−	145055.i	−0.311138	−	1.36489i
$327$			122851.i			1.14890i
$328$	−97942.7	+	77976.6i	−0.910384	+	0.724797i
$329$	−88614.2			−0.818675
$330$		0			0
$331$		−	88854.4i		−	0.811004i	−0.914094	−	0.405502i	$-0.867097\pi$
$331$		−	88854.4i		−	0.811004i	0.914094	−	0.405502i	$-0.132903\pi$
$332$	−68934.8	−	143343.i	−0.625407	−	1.30047i
$333$	33158.8			0.299027
$334$	46895.6	+	205720.i	0.420377	+	1.84410i
$335$		0			0
$336$	36624.4	−	45823.6i	0.324408	−	0.405892i
$337$	−144878.			−1.27569			−0.637843	−	0.770166i	$-0.720173\pi$
$337$	−144878.			−1.27569			−0.637843	+	0.770166i	$0.720173\pi$
$338$	−32417.6	+	7389.88i	−0.283758	+	0.0646850i
$339$		−	108744.i		−	0.946252i
$340$		0			0
$341$	−106865.			−0.919026
$342$	−568.085	−	2492.05i	−0.00485692	−	0.0213062i
$343$			126003.i			1.07101i
$344$	99559.4	+	125052.i	0.841328	+	1.05675i
$345$		0			0
$346$	92409.8	−	21065.6i	0.771908	−	0.175963i
$347$			72849.3i			0.605016i	0.953147	+	0.302508i	$0.0978238\pi$
$347$			72849.3i			0.605016i	−0.953147	+	0.302508i	$0.902176\pi$
$348$	−9177.90	−	19084.6i	−0.0757853	−	0.157588i
$349$	123918.			1.01738			0.508692	−	0.860948i	$-0.330129\pi$
$349$	123918.			1.01738			0.508692	+	0.860948i	$0.330129\pi$
$350$		0			0
$351$		−	26940.3i		−	0.218669i
$352$	75398.7	+	36436.0i	0.608525	+	0.294066i
$353$	−185296.			−1.48702			−0.743508	−	0.668727i	$-0.766840\pi$
$353$	−185296.			−1.48702			−0.743508	+	0.668727i	$0.766840\pi$
$354$	−44910.2	+	10237.7i	−0.358376	+	0.0816948i
$355$		0			0
$356$	97283.2	−	46784.2i	0.767605	−	0.369147i
$357$	95297.1			0.747727
$358$	−35299.1	−	154849.i	−0.275421	−	1.20821i
$359$		−	98151.3i		−	0.761565i	−0.924665	−	0.380783i	$-0.875655\pi$
$359$		−	98151.3i		−	0.761565i	0.924665	−	0.380783i	$-0.124345\pi$
$360$		0			0
$361$	129761.			0.995702
$362$	−147627.	+	33652.8i	−1.12655	+	0.256806i
$363$		−	41326.6i		−	0.313630i
$364$	−58720.5	−	122104.i	−0.443187	−	0.921565i
$365$		0			0
$366$	10124.1	+	44412.2i	0.0755781	+	0.331543i
$367$			119078.i			0.884096i	0.896991	+	0.442048i	$0.145748\pi$
$367$			119078.i			0.884096i	−0.896991	+	0.442048i	$0.854252\pi$
$368$	104993.	+	83915.7i	0.775293	+	0.619651i
$369$	−52815.5			−0.387890
$370$		0			0
$371$			918.994i			0.00667675i
$372$	−97909.3	+	47085.3i	−0.707519	+	0.340251i
$373$	101781.			0.731558			0.365779	−	0.930702i	$-0.380803\pi$
$373$	101781.			0.731558			0.365779	+	0.930702i	$0.380803\pi$
$374$	30235.8	+	132637.i	0.216161	+	0.948249i
$375$		0			0
$376$	−80101.4	−	100612.i	−0.566584	−	0.711660i
$377$	−48911.8			−0.344136
$378$	24128.7	−	5500.35i	0.168869	−	0.0384952i
$379$		−	53693.3i		−	0.373802i	−0.982379	−	0.186901i	$-0.940156\pi$
$379$		−	53693.3i		−	0.373802i	0.982379	−	0.186901i	$-0.0598444\pi$
$380$		0			0
$381$	−119576.			−0.823749
$382$	−8812.56	−	38658.6i	−0.0603914	−	0.264923i
$383$			36473.1i			0.248642i	0.992242	+	0.124321i	$0.0396753\pi$
$383$			36473.1i			0.248642i	−0.992242	+	0.124321i	$0.960325\pi$
$384$	85133.6	+	161.445i	0.577349	+	0.00109487i
$385$		0			0
$386$	130573.	−	29765.3i	0.876355	−	0.199772i
$387$			67434.1i			0.450254i
$388$	−22122.5	+	10638.9i	−0.146950	+	0.0706695i
$389$	−95226.4			−0.629300			−0.314650	−	0.949208i	$-0.601887\pi$
$389$	−95226.4			−0.629300			−0.314650	+	0.949208i	$0.601887\pi$
$390$		0			0
$391$			218350.i			1.42823i
$392$	−22845.3	+	18188.2i	−0.148671	+	0.118363i
$393$	−81205.5			−0.525775
$394$	−185652.	+	42321.0i	−1.19594	+	0.272624i
$395$		0			0
$396$	15311.1	+	31837.9i	0.0976373	+	0.203027i
$397$	−116517.			−0.739282			−0.369641	−	0.929175i	$-0.620519\pi$
$397$	−116517.			−0.739282			−0.369641	+	0.929175i	$0.620519\pi$
$398$	−32091.2	−	140777.i	−0.202591	−	0.888719i
$399$		−	5423.08i		−	0.0340643i
$400$		0			0
$401$	13995.3			0.0870350			0.0435175	−	0.999053i	$-0.486144\pi$
$401$	13995.3			0.0870350			0.0435175	+	0.999053i	$0.486144\pi$
$402$	133099.	−	30341.0i	0.823610	−	0.187749i
$403$			250931.i			1.54506i
$404$	−115781.	+	55679.9i	−0.709372	+	0.341142i
$405$		0			0
$406$	−9986.24	−	43807.3i	−0.0605829	−	0.265763i
$407$			100432.i			0.606295i
$408$	86142.3	+	108199.i	0.517483	+	0.649986i
$409$	−213064.			−1.27369			−0.636845	−	0.770992i	$-0.719761\pi$
$409$	−213064.			−1.27369			−0.636845	+	0.770992i	$0.719761\pi$
$410$		0			0
$411$		−	63002.1i		−	0.372968i
$412$	−48357.5	−	100555.i	−0.284885	−	0.592390i
$413$	−97731.2			−0.572972
$414$	12602.7	+	55285.0i	0.0735296	+	0.322557i
$415$		0			0
$416$	85555.7	−	177044.i	0.494382	−	1.02305i
$417$	112555.			0.647281
$418$	7547.99	−	1720.63i	0.0431995	−	0.00984770i
$419$			180964.i			1.03078i	0.856957	+	0.515389i	$0.172352\pi$
$419$			180964.i			1.03078i	−0.856957	+	0.515389i	$0.827648\pi$
$420$		0			0
$421$	160722.			0.906799			0.453399	−	0.891307i	$-0.350211\pi$
$421$	160722.			0.906799			0.453399	+	0.891307i	$0.350211\pi$
$422$	−33950.9	−	148934.i	−0.190645	−	0.836315i
$423$		−	54254.7i		−	0.303219i
$424$	−1043.42	+	830.710i	−0.00580398	+	0.00462081i
$425$		0			0
$426$	169060.	−	38538.6i	0.931581	−	0.212362i
$427$			96647.5i			0.530072i
$428$	−91623.1	−	190521.i	−0.500170	−	1.04005i
$429$	81597.3			0.443365
$430$		0			0
$431$			314539.i			1.69325i	0.532193	+	0.846623i	$0.321368\pi$
$431$			314539.i			1.69325i	−0.532193	+	0.846623i	$0.678632\pi$
$432$	28055.8	+	22423.6i	0.150333	+	0.120154i
$433$	289159.			1.54227			0.771135	−	0.636671i	$-0.219689\pi$
$433$	289159.			1.54227			0.771135	+	0.636671i	$0.219689\pi$
$434$	−224744.	+	51232.3i	−1.19319	+	0.271997i
$435$		0			0
$436$	−340909.	+	163946.i	−1.79335	+	0.862436i
$437$	12425.6			0.0650662
$438$	28146.1	+	123470.i	0.146714	+	0.643598i
$439$		−	26053.1i		−	0.135185i	−0.997713	−	0.0675927i	$-0.978468\pi$
$439$		−	26053.1i		−	0.135185i	0.997713	−	0.0675927i	$-0.0215318\pi$
$440$		0			0
$441$	−12319.3			−0.0633446
$442$	311447.	−	70996.9i	1.59419	−	0.363408i
$443$		−	257150.i		−	1.31033i	−0.755487	−	0.655163i	$-0.772600\pi$
$443$		−	257150.i		−	1.31033i	0.755487	−	0.655163i	$-0.227400\pi$
$444$	44250.8	+	92015.3i	0.224468	+	0.466760i
$445$		0			0
$446$	51323.8	+	225145.i	0.258017	+	1.13186i
$447$		−	37171.0i		−	0.186033i
$448$	176036.	+	40480.1i	0.877090	+	0.201691i
$449$	134951.			0.669397			0.334698	−	0.942325i	$-0.391366\pi$
$449$	134951.			0.669397			0.334698	+	0.942325i	$0.391366\pi$
$450$		0			0
$451$		−	159969.i		−	0.786471i
$452$	301764.	−	145120.i	1.47703	−	0.710316i
$453$	−34794.5			−0.169556
$454$	−63797.3	−	279864.i	−0.309521	−	1.35780i
$455$		0			0
$456$	6157.30	−	4902.11i	0.0296115	−	0.0235751i
$457$	−57157.1			−0.273677			−0.136838	−	0.990593i	$-0.543694\pi$
$457$	−57157.1			−0.273677			−0.136838	+	0.990593i	$0.543694\pi$
$458$	−153916.	+	35086.4i	−0.733757	+	0.167266i
$459$			58346.4i			0.276942i
$460$		0			0
$461$	−255702.			−1.20319			−0.601593	−	0.798803i	$-0.705467\pi$
$461$	−255702.			−1.20319			−0.601593	+	0.798803i	$0.705467\pi$
$462$	16659.6	+	73081.7i	0.0780513	+	0.342393i
$463$			79969.9i			0.373048i	0.982450	+	0.186524i	$0.0597222\pi$
$463$			79969.9i			0.373048i	−0.982450	+	0.186524i	$0.940278\pi$
$464$	40711.4	−	50937.1i	0.189095	−	0.236591i
$465$		0			0
$466$	−416158.	+	94866.7i	−1.91640	+	0.436859i
$467$			6899.37i			0.0316356i	0.999875	+	0.0158178i	$0.00503517\pi$
$467$			6899.37i			0.0316356i	−0.999875	+	0.0158178i	$0.994965\pi$
$468$	74758.9	−	35952.1i	0.341327	−	0.164147i
$469$	289642.			1.31679
$470$		0			0
$471$			182836.i			0.824175i
$472$	−88342.6	−	110963.i	−0.396539	−	0.498074i
$473$	−204246.			−0.912917
$474$	124221.	−	28317.3i	0.552891	−	0.126036i
$475$		0			0
$476$	127175.	+	264448.i	0.561291	+	1.16715i
$477$	−562.661			−0.00247292
$478$	29075.5	+	127547.i	0.127254	+	0.558233i
$479$		−	210368.i		−	0.916870i	−0.888728	−	0.458435i	$-0.848410\pi$
$479$		−	210368.i		−	0.916870i	0.888728	−	0.458435i	$-0.151590\pi$
$480$		0			0
$481$	235826.			1.01930
$482$	−365504.	+	83319.8i	−1.57325	+	0.358636i
$483$			120308.i			0.515705i
$484$	114681.	−	55150.9i	0.489554	−	0.235430i
$485$		0			0
$486$	3367.63	+	14773.0i	0.0142578	+	0.0625455i
$487$		−	278872.i		−	1.17584i	−0.808920	−	0.587919i	$-0.799947\pi$
$487$		−	278872.i		−	1.17584i	0.808920	−	0.587919i	$-0.200053\pi$
$488$	−109733.	+	87363.0i	−0.460782	+	0.366849i
$489$	193266.			0.808234
$490$		0			0
$491$			138823.i			0.575836i	0.957655	+	0.287918i	$0.0929630\pi$
$491$			138823.i			0.575836i	−0.957655	+	0.287918i	$0.907037\pi$
$492$	−70483.0	−	146562.i	−0.291175	−	0.605470i
$493$	105932.			0.435844
$494$	−4040.23	−	17723.5i	−0.0165559	−	0.0726266i
$495$		0			0
$496$	−261322.	−	208861.i	−1.06222	−	0.848974i
$497$	367899.			1.48941
$498$	201454.	−	45923.1i	0.812301	−	0.185171i
$499$		−	95898.1i		−	0.385131i	−0.981284	−	0.192566i	$-0.938319\pi$
$499$		−	95898.1i		−	0.385131i	0.981284	−	0.192566i	$-0.0616808\pi$
$500$		0			0
$501$	−274094.			−1.09200
$502$	2541.23	+	11147.8i	0.0100841	+	0.0442365i
$503$			134868.i			0.533056i	0.963827	+	0.266528i	$0.0858766\pi$
$503$			134868.i			0.533056i	−0.963827	+	0.266528i	$0.914123\pi$
$504$	47463.5	+	59616.7i	0.186852	+	0.234696i
$505$		0			0
$506$	−167449.	+	38171.3i	−0.654004	+	0.149086i
$507$		−	43192.1i		−	0.168031i
$508$	−159576.	−	331823.i	−0.618358	−	1.28582i
$509$	−14376.3			−0.0554894			−0.0277447	−	0.999615i	$-0.508833\pi$
$509$	−14376.3			−0.0554894			−0.0277447	+	0.999615i	$0.508833\pi$
$510$		0			0
$511$			268690.i			1.02899i
$512$	113164.	+	236460.i	0.431686	+	0.902024i
$513$	3320.32			0.0126167
$514$	−133663.	+	30469.6i	−0.505923	+	0.115329i
$515$		0			0
$516$	−187129.	+	89991.6i	−0.702816	+	0.337989i
$517$	164328.			0.614795
$518$	48148.2	+	211215.i	0.179440	+	0.787163i
$519$			123123.i			0.457094i
$520$		0			0
$521$	235843.			0.868856			0.434428	−	0.900706i	$-0.356950\pi$
$521$	235843.			0.868856			0.434428	+	0.900706i	$0.356950\pi$
$522$	26821.3	−	6114.15i	0.0984327	−	0.0224386i
$523$			104237.i			0.381083i	0.981679	+	0.190541i	$0.0610243\pi$
$523$			104237.i			0.381083i	−0.981679	+	0.190541i	$0.938976\pi$
$524$	−108370.	−	225344.i	−0.394680	−	0.820699i
$525$		0			0
$526$	−45066.2	−	197695.i	−0.162885	−	0.714536i
$527$		−	543459.i		−	1.95680i
$528$	−67917.0	+	84976.2i	−0.243619	+	0.304810i
$529$	4184.37			0.0149527
$530$		0			0
$531$		−	59836.7i		−	0.212216i
$532$	15049.0	−	7237.16i	0.0531721	−	0.0255708i
$533$	−375625.			−1.32221
$534$	31166.8	+	136721.i	0.109297	+	0.479461i
$535$		0			0
$536$	261818.	+	328857.i	0.911317	+	1.14466i
$537$	206315.			0.715454
$538$	−163887.	+	37359.5i	−0.566215	+	0.129073i
$539$		−	37313.0i		−	0.128435i
$540$		0			0
$541$	−415208.			−1.41864			−0.709318	−	0.704889i	$-0.750997\pi$
$541$	−415208.			−1.41864			−0.709318	+	0.704889i	$0.750997\pi$
$542$	−89943.1	−	394559.i	−0.306175	−	1.34312i
$543$		−	196693.i		−	0.667097i
$544$	−185294.	+	383437.i	−0.626128	+	1.29568i
$545$		0			0
$546$	171604.	−	39118.5i	0.575628	−	0.131219i
$547$		−	438329.i		−	1.46496i	−0.680789	−	0.732480i	$-0.738363\pi$
$547$		−	438329.i		−	1.46496i	0.680789	−	0.732480i	$-0.261637\pi$
$548$	174830.	−	84077.0i	0.582177	−	0.279973i
$549$	−59173.2			−0.196327
$550$		0			0
$551$		−	6028.25i		−	0.0198558i
$552$	−136597.	+	108751.i	−0.448293	+	0.356906i
$553$	270324.			0.883963
$554$	505916.	−	115328.i	1.64839	−	0.375764i
$555$		0			0
$556$	150206.	+	312339.i	0.485890	+	1.01036i
$557$	−93371.4			−0.300956			−0.150478	−	0.988613i	$-0.548081\pi$
$557$	−93371.4			−0.300956			−0.150478	+	0.988613i	$0.548081\pi$
$558$	−31367.3	−	137601.i	−0.100742	−	0.441930i
$559$			479592.i			1.53479i
$560$		0			0
$561$	−176721.			−0.561516
$562$	41617.6	−	9487.08i	0.131766	−	0.0300372i
$563$		−	460554.i		−	1.45299i	−0.687170	−	0.726497i	$-0.741147\pi$
$563$		−	460554.i		−	1.45299i	0.687170	−	0.726497i	$-0.258853\pi$
$564$	150556.	−	72403.5i	0.473304	−	0.227615i
$565$		0			0
$566$	87595.2	+	384259.i	0.273431	+	1.19948i
$567$			32148.2i			0.0999979i
$568$	332556.	+	417708.i	1.03079	+	1.29472i
$569$	−451247.			−1.39376			−0.696882	−	0.717186i	$-0.745430\pi$
$569$	−451247.			−1.39376			−0.696882	+	0.717186i	$0.745430\pi$
$570$		0			0
$571$		−	5267.14i		−	0.0161548i	−0.999967	−	0.00807742i	$-0.997429\pi$
$571$		−	5267.14i		−	0.0161548i	0.999967	−	0.00807742i	$-0.00257115\pi$
$572$	108893.	+	226432.i	0.332818	+	0.692062i
$573$	51507.3			0.156877
$574$	−76690.6	−	336424.i	−0.232766	−	1.02109i
$575$		0			0
$576$	−24784.3	+	107779.i	−0.0747018	+	0.324855i
$577$	−532802.			−1.60035			−0.800174	−	0.599768i	$-0.795259\pi$
$577$	−532802.			−1.60035			−0.800174	+	0.599768i	$0.795259\pi$
$578$	−348794.	+	79510.4i	−1.04403	+	0.237995i
$579$			173971.i			0.518943i
$580$		0			0
$581$	438393.			1.29871
$582$	−7087.42	−	31090.8i	−0.0209239	−	0.0917881i
$583$		−	1704.20i		−	0.00501399i
$584$	−305067.	+	242878.i	−0.894479	+	0.712135i
$585$		0			0
$586$	−43426.9	+	9899.52i	−0.126463	+	0.0288283i
$587$			474104.i			1.37593i	0.725742	+	0.687967i	$0.241497\pi$
$587$			474104.i			1.37593i	−0.725742	+	0.687967i	$0.758503\pi$
$588$	−16440.3	−	34186.0i	−0.0475504	−	0.0988765i
$589$	−30926.7			−0.0891462
$590$		0			0
$591$		−	247356.i		−	0.708187i
$592$	−196288.	+	245591.i	−0.560080	+	0.700760i
$593$	−389837.			−1.10860			−0.554299	−	0.832318i	$-0.687013\pi$
$593$	−389837.			−1.10860			−0.554299	+	0.832318i	$0.687013\pi$
$594$	−44744.8	+	10200.0i	−0.126815	+	0.0289085i
$595$		0			0
$596$	103149.	−	49605.2i	0.290384	−	0.139648i
$597$	187566.			0.526265
$598$	89630.4	+	393187.i	0.250642	+	1.09951i
$599$			298392.i			0.831637i	0.909448	+	0.415818i	$0.136505\pi$
$599$			298392.i			0.831637i	−0.909448	+	0.415818i	$0.863495\pi$
$600$		0			0
$601$	−104029.			−0.288009			−0.144004	−	0.989577i	$-0.545998\pi$
$601$	−104029.			−0.288009			−0.144004	+	0.989577i	$0.545998\pi$
$602$	−429541.	+	97917.5i	−1.18525	+	0.270189i
$603$			177336.i			0.487710i
$604$	−46433.7	−	96554.4i	−0.127280	−	0.264666i
$605$		0			0
$606$	−37092.9	−	162718.i	−0.101006	−	0.443088i
$607$		−	335077.i		−	0.909425i	−0.890638	−	0.454712i	$-0.849742\pi$
$607$		−	335077.i		−	0.909425i	0.890638	−	0.454712i	$-0.150258\pi$
$608$	21820.3	+	10544.5i	0.0590273	+	0.0285246i
$609$	58367.2			0.157374
$610$		0			0
$611$		−	385860.i		−	1.03359i
$612$	−161910.	+	77863.9i	−0.432287	+	0.207890i
$613$	205373.			0.546539			0.273270	−	0.961937i	$-0.411895\pi$
$613$	205373.			0.546539			0.273270	+	0.961937i	$0.411895\pi$
$614$	−117549.	−	515658.i	−0.311803	−	1.36781i
$615$		0			0
$616$	−180568.	+	143759.i	−0.475861	+	0.378854i
$617$	117370.			0.308309			0.154155	−	0.988047i	$-0.450735\pi$
$617$	117370.			0.308309			0.154155	+	0.988047i	$0.450735\pi$
$618$	141319.	−	32214.9i	0.370019	−	0.0843489i
$619$			152525.i			0.398069i	0.979992	+	0.199035i	$0.0637807\pi$
$619$			152525.i			0.398069i	−0.979992	+	0.199035i	$0.936219\pi$
$620$		0			0
$621$	−73659.7			−0.191006
$622$	99894.7	+	438215.i	0.258203	+	1.13268i
$623$			297526.i			0.766563i
$624$	199533.	+	159477.i	0.512444	+	0.409570i
$625$		0			0
$626$	−172184.	+	39250.8i	−0.439384	+	0.100161i
$627$			10056.7i			0.0255811i
$628$	−507367.	+	243996.i	−1.28648	+	0.618677i
$629$	−510744.			−1.29093
$630$		0			0
$631$		−	420163.i		−	1.05526i	−0.849475	−	0.527629i	$-0.823081\pi$
$631$		−	420163.i		−	1.05526i	0.849475	−	0.527629i	$-0.176919\pi$
$632$	244355.	+	306923.i	0.611768	+	0.768413i
$633$	198435.			0.495234
$634$	188013.	−	42859.1i	0.467745	−	0.106626i
$635$		0			0
$636$	−750.878	−	1561.38i	−0.00185633	−	0.00386006i
$637$	−87615.1			−0.215924
$638$	18518.7	+	81237.1i	0.0454955	+	0.199578i
$639$			225249.i			0.551646i
$640$		0			0
$641$	−633476.			−1.54175			−0.770875	−	0.636986i	$-0.780181\pi$
$641$	−633476.			−1.54175			−0.770875	+	0.636986i	$0.780181\pi$
$642$	267758.	−	61037.6i	0.649639	−	0.148091i
$643$		−	463320.i		−	1.12062i	−0.828282	−	0.560311i	$-0.810682\pi$
$643$		−	463320.i		−	1.12062i	0.828282	−	0.560311i	$-0.189318\pi$
$644$	−333854.	+	160553.i	−0.804980	+	0.387121i
$645$		0			0
$646$	8750.19	+	38385.0i	0.0209678	+	0.0919807i
$647$		−	556505.i		−	1.32941i	−0.747104	−	0.664707i	$-0.768556\pi$
$647$		−	556505.i		−	1.32941i	0.747104	−	0.664707i	$-0.231444\pi$
$648$	−36500.8	+	29059.9i	−0.0869264	+	0.0692060i
$649$	181235.			0.430281
$650$		0			0
$651$		−	299440.i		−	0.706559i
$652$	257915.	+	536310.i	0.606711	+	1.26160i
$653$	116848.			0.274029			0.137015	−	0.990569i	$-0.456249\pi$
$653$	116848.			0.274029			0.137015	+	0.990569i	$0.456249\pi$
$654$	−109218.	−	479112.i	−0.255351	−	1.12016i
$655$		0			0
$656$	312649.	−	391179.i	0.726522	−	0.909008i
$657$	−164507.			−0.381114
$658$	345591.	−	78780.4i	0.798198	−	0.181956i
$659$			8238.25i			0.0189699i	0.999955	+	0.00948493i	$0.00301919\pi$
$659$			8238.25i			0.0189699i	−0.999955	+	0.00948493i	$0.996981\pi$
$660$		0			0
$661$	846034.			1.93635			0.968177	−	0.250265i	$-0.0805178\pi$
$661$	846034.			1.93635			0.968177	+	0.250265i	$0.0805178\pi$
$662$	78993.9	+	346528.i	0.180251	+	0.790719i
$663$			414960.i			0.944016i
$664$	396279.	+	497747.i	0.898803	+	1.12894i
$665$		0			0
$666$	−129318.	+	29479.1i	−0.291548	+	0.0664608i
$667$			133734.i			0.300601i
$668$	−365781.	−	760607.i	−0.819726	−	1.70454i
$669$	−299975.			−0.670244
$670$		0			0
$671$		−	179225.i		−	0.398065i
$672$	−102095.	+	211270.i	−0.226082	+	0.467842i
$673$	−250.046			−0.000552065			−0.000276032	−	1.00000i	$-0.500088\pi$
$673$	−250.046			−0.000552065			−0.000276032		1.00000i	$0.500088\pi$
$674$	565019.	−	128801.i	1.24378	−	0.283530i
$675$		0			0
$676$	119857.	−	57640.3i	0.262284	−	0.126134i
$677$	−241924.			−0.527838			−0.263919	−	0.964545i	$-0.585015\pi$
$677$	−241924.			−0.527838			−0.263919	+	0.964545i	$0.585015\pi$
$678$	96676.6	+	424097.i	0.210311	+	0.922584i
$679$		−	67658.3i		−	0.146751i
$680$		0			0
$681$	372880.			0.804035
$682$	416770.	−	95006.2i	0.896040	−	0.204260i
$683$		−	10868.8i		−	0.0232991i	−0.999932	−	0.0116495i	$-0.996292\pi$
$683$		−	10868.8i		−	0.0232991i	0.999932	−	0.0116495i	$-0.00370825\pi$
$684$	4431.01	+	9213.85i	0.00947088	+	0.0196938i
$685$		0			0
$686$	−112020.	−	491406.i	−0.238039	−	1.04422i
$687$		−	205072.i		−	0.434503i
$688$	−499451.	−	399185.i	−1.05516	−	0.843331i
$689$	−4001.65			−0.00842948
$690$		0			0
$691$		−	318000.i		−	0.665995i	−0.942928	−	0.332998i	$-0.891940\pi$
$691$		−	318000.i		−	0.665995i	0.942928	−	0.332998i	$-0.108060\pi$
$692$	−341666.	+	164310.i	−0.713493	+	0.343124i
$693$	−97371.3			−0.202752
$694$	−64765.0	−	284109.i	−0.134469	−	0.589883i
$695$		0			0
$696$	52760.1	+	66269.5i	0.108915	+	0.136803i
$697$	813516.			1.67456
$698$	−483276.	+	110167.i	−0.991938	+	0.226121i
$699$		−	554473.i		−	1.13482i
$700$		0			0
$701$	963668.			1.96106			0.980531	−	0.196365i	$-0.0629136\pi$
$701$	963668.			1.96106			0.980531	+	0.196365i	$0.0629136\pi$
$702$	23950.6	+	105066.i	0.0486007	+	0.213200i
$703$			29064.9i			0.0588110i
$704$	−326444.	−	75067.2i	−0.658663	−	0.151462i
$705$		0			0
$706$	722644.	−	164733.i	1.44982	−	0.330500i
$707$		−	354098.i		−	0.708410i
$708$	166046.	−	79852.8i	0.331255	−	0.159303i
$709$	−135081.			−0.268721			−0.134361	−	0.990932i	$-0.542898\pi$
$709$	−135081.			−0.268721			−0.134361	+	0.990932i	$0.542898\pi$
$710$		0			0
$711$			165508.i			0.327400i
$712$	−337807.	+	268943.i	−0.666360	+	0.530519i
$713$	686093.			1.34960
$714$	−371654.	+	84721.7i	−0.729025	+	0.166187i
$715$		0			0
$716$	275329.	+	572521.i	0.537065	+	1.11677i
$717$	−169939.			−0.330564
$718$	87259.2	+	382785.i	0.169263	+	0.742517i
$719$			471123.i			0.911332i	0.890151	+	0.455666i	$0.150599\pi$
$719$			471123.i			0.911332i	−0.890151	+	0.455666i	$0.849401\pi$
$720$		0			0
$721$	307531.			0.591587
$722$	−506061.	+	115361.i	−0.970798	+	0.221302i
$723$		−	486985.i		−	0.931620i
$724$	545820.	−	262489.i	1.04129	−	0.500765i
$725$		0			0
$726$	36740.5	+	161172.i	0.0697063	+	0.305785i
$727$		−	27020.9i		−	0.0511248i	−0.999673	−	0.0255624i	$-0.991862\pi$
$727$		−	27020.9i		−	0.0511248i	0.999673	−	0.0255624i	$-0.00813765\pi$
$728$	337561.	+	423994.i	0.636926	+	0.800013i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	1.03869e6i		−	1.94379i
$732$	−78967.3	−	164205.i	−0.147375	−	0.306453i
$733$	−203765.			−0.379246			−0.189623	−	0.981857i	$-0.560727\pi$
$733$	−203765.			−0.379246			−0.189623	+	0.981857i	$0.560727\pi$
$734$	−105864.	−	464399.i	−0.196496	−	0.861983i
$735$		0			0
$736$	−484072.	−	233925.i	−0.893623	−	0.431839i
$737$	−537119.			−0.988861
$738$	205978.	−	46954.4i	0.378188	−	0.0862112i
$739$		−	311174.i		−	0.569789i	−0.958559	−	0.284894i	$-0.908042\pi$
$739$		−	311174.i		−	0.569789i	0.958559	−	0.284894i	$-0.0919585\pi$
$740$		0			0
$741$	23614.2			0.0430067
$742$	−817.011	−	3584.03i	−0.00148395	−	0.00650975i
$743$		−	459748.i		−	0.832803i	−0.909181	−	0.416401i	$-0.863291\pi$
$743$		−	459748.i		−	0.832803i	0.909181	−	0.416401i	$-0.136709\pi$
$744$	339981.	−	270674.i	0.614199	−	0.488992i
$745$		0			0
$746$	−396941.	+	90486.0i	−0.713260	+	0.162594i
$747$			268410.i			0.481013i
$748$	−235836.	−	490398.i	−0.421509	−	0.876488i
$749$	582680.			1.03864
$750$		0			0
$751$		−	201657.i		−	0.357547i	−0.983890	−	0.178774i	$-0.942787\pi$
$751$		−	201657.i		−	0.357547i	0.983890	−	0.178774i	$-0.0572130\pi$
$752$	401838.	+	321168.i	0.710584	+	0.567932i
$753$	−14852.9			−0.0261952
$754$	190754.	−	43483.9i	0.335529	−	0.0764867i
$755$		0			0
$756$	−89211.0	+	42902.2i	−0.156090	+	0.0750647i
$757$	409395.			0.714415			0.357208	−	0.934025i	$-0.383729\pi$
$757$	409395.			0.714415			0.357208	+	0.934025i	$0.383729\pi$
$758$	47734.8	+	209401.i	0.0830801	+	0.364453i
$759$		−	223102.i		−	0.387276i
$760$		0			0
$761$	−626699.			−1.08216			−0.541078	−	0.840972i	$-0.681984\pi$
$761$	−626699.			−1.08216			−0.541078	+	0.840972i	$0.681984\pi$
$762$	466342.	−	106307.i	0.803146	−	0.183084i
$763$		−	1.04262e6i		−	1.79092i
$764$	68737.1	+	142932.i	0.117762	+	0.244874i
$765$		0			0
$766$	−32425.6	−	142243.i	−0.0552624	−	0.242423i
$767$		−	425559.i		−	0.723384i
$768$	−332161.	+	75056.5i	−0.563152	+	0.127252i
$769$	203601.			0.344292			0.172146	−	0.985071i	$-0.444930\pi$
$769$	203601.			0.344292			0.172146	+	0.985071i	$0.444930\pi$
$770$		0			0
$771$		−	178087.i		−	0.299588i
$772$	−482768.	+	232167.i	−0.810035	+	0.389552i
$773$	197131.			0.329910			0.164955	−	0.986301i	$-0.447252\pi$
$773$	197131.			0.329910			0.164955	+	0.986301i	$0.447252\pi$
$774$	−59950.8	−	262990.i	−0.100072	−	0.438992i
$775$		0			0
$776$	76818.5	−	61158.6i	0.127568	−	0.101563i
$777$	−281415.			−0.466127
$778$	371378.	−	84658.8i	0.613560	−	0.139866i
$779$		−	46294.8i		−	0.0762882i
$780$		0			0
$781$	−682239.			−1.11850
$782$	−194119.	−	851553.i	−0.317434	−	1.39251i
$783$			35735.7i			0.0582880i
$784$	72925.9	−	91243.1i	0.118645	−	0.148446i
$785$		0			0
$786$	316697.	−	72193.9i	0.512625	−	0.116857i
$787$			785688.i			1.26853i	0.773116	+	0.634265i	$0.218697\pi$
$787$			785688.i			1.26853i	−0.773116	+	0.634265i	$0.781303\pi$
$788$	686410.	−	330100.i	1.10543	−	0.531610i
$789$	263401.			0.423121
$790$		0			0
$791$			922898.i			1.47503i
$792$	−88017.3	−	110554.i	−0.140319	−	0.176249i
$793$	−420840.			−0.669223
$794$	454412.	−	103587.i	0.720791	−	0.164310i
$795$		0			0
$796$	250309.	+	520492.i	0.395048	+	0.821463i
$797$	−236487.			−0.372299			−0.186149	−	0.982521i	$-0.559601\pi$
$797$	−236487.			−0.372299			−0.186149	+	0.982521i	$0.559601\pi$
$798$	4821.26	+	21149.7i	0.00757103	+	0.0332123i
$799$			835683.i			1.30903i
$800$		0			0
$801$	−182162.			−0.283918
$802$	−54581.1	+	12442.2i	−0.0848581	+	0.0193441i
$803$		−	498264.i		−	0.772731i
$804$	−492105.	+	236657.i	−0.761282	+	0.366106i
$805$		0			0
$806$	−223085.	−	978621.i	−0.343400	−	1.50641i
$807$		−	218358.i		−	0.335290i
$808$	402039.	−	320081.i	0.615808	−	0.490272i
$809$	641882.			0.980749			0.490375	−	0.871512i	$-0.336860\pi$
$809$	641882.			0.980749			0.490375	+	0.871512i	$0.336860\pi$
$810$		0			0
$811$		−	579456.i		−	0.881006i	−0.897751	−	0.440503i	$-0.854800\pi$
$811$		−	579456.i		−	0.881006i	0.897751	−	0.440503i	$-0.145200\pi$
$812$	77891.7	+	161968.i	0.118135	+	0.245651i
$813$	525696.			0.795342
$814$	−89286.9	−	391681.i	−0.134753	−	0.591131i
$815$		0			0
$816$	−432143.	−	345389.i	−0.649004	−	0.518715i
$817$	−59108.5			−0.0885536
$818$	830940.	−	189420.i	1.24183	−	0.283086i
$819$			228639.i			0.340864i
$820$		0			0
$821$	−496893.			−0.737185			−0.368593	−	0.929591i	$-0.620160\pi$
$821$	−496893.			−0.737185			−0.368593	+	0.929591i	$0.620160\pi$
$822$	56010.6	+	245705.i	0.0828946	+	0.363639i
$823$			700154.i			1.03370i	0.856077	+	0.516849i	$0.172895\pi$
$823$			700154.i			1.03370i	−0.856077	+	0.516849i	$0.827105\pi$
$824$	277988.	+	349168.i	0.409422	+	0.514256i
$825$		0			0
$826$	381147.	−	86885.7i	0.558641	−	0.127347i
$827$			30850.5i			0.0451077i	0.999746	+	0.0225539i	$0.00717973\pi$
$827$			30850.5i			0.0451077i	−0.999746	+	0.0225539i	$0.992820\pi$
$828$	−98299.7	−	204405.i	−0.143381	−	0.298147i
$829$	−272177.			−0.396043			−0.198022	−	0.980198i	$-0.563452\pi$
$829$	−272177.			−0.396043			−0.198022	+	0.980198i	$0.563452\pi$
$830$		0			0
$831$			674064.i			0.976111i
$832$	−176266.	+	766526.i	−0.254637	+	1.10734i
$833$	189754.			0.273465
$834$	−438960.	+	100065.i	−0.631092	+	0.143863i
$835$		0			0
$836$	−27907.1	+	13420.7i	−0.0399303	+	0.0192028i
$837$	183335.			0.261694
$838$	−160882.	−	705752.i	−0.229097	−	1.00500i
$839$		−	967675.i		−	1.37469i	−0.726330	−	0.687346i	$-0.758776\pi$
$839$		−	967675.i		−	1.37469i	0.726330	−	0.687346i	$-0.241224\pi$
$840$		0			0
$841$	−642400.			−0.908268
$842$	−626808.	+	142886.i	−0.884118	+	0.201542i
$843$			55449.7i			0.0780269i
$844$	264813.	+	550654.i	0.371754	+	0.773025i
$845$		0			0
$846$	48233.9	+	211591.i	0.0673925	+	0.295635i
$847$			350734.i			0.488890i
$848$	3330.75	−	4167.36i	0.00463180	−	0.00579521i
$849$	−511973.			−0.710284
$850$		0			0
$851$		−	644791.i		−	0.890349i
$852$	−625063.	+	300597.i	−0.861082	+	0.414101i
$853$	−613978.			−0.843830			−0.421915	−	0.906635i	$-0.638642\pi$
$853$	−613978.			−0.843830			−0.421915	+	0.906635i	$0.638642\pi$
$854$	−85922.2	−	376921.i	−0.117812	−	0.516814i
$855$		0			0
$856$	526705.	+	661569.i	0.718819	+	0.902875i
$857$	553983.			0.754284			0.377142	−	0.926155i	$-0.376907\pi$
$857$	553983.			0.754284			0.377142	+	0.926155i	$0.376907\pi$
$858$	−318226.	+	72542.2i	−0.432275	+	0.0985409i
$859$		−	172159.i		−	0.233316i	−0.993172	−	0.116658i	$-0.962782\pi$
$859$		−	172159.i		−	0.233316i	0.993172	−	0.116658i	$-0.0372181\pi$
$860$		0			0
$861$	448239.			0.604648
$862$	−279634.	−	1.22669e6i	−0.376335	−	1.65089i
$863$			267304.i			0.358908i	0.983766	+	0.179454i	$0.0574331\pi$
$863$			267304.i			0.358908i	−0.983766	+	0.179454i	$0.942567\pi$
$864$	−129352.	−	62508.4i	−0.173278	−	0.0837358i
$865$		0			0
$866$	−1.12771e6	+	257070.i	−1.50370	+	0.342780i
$867$		−	464720.i		−	0.618234i
$868$	830944.	−	399607.i	1.10289	−	0.530388i
$869$	−501294.			−0.663824
$870$		0			0
$871$			1.26121e6i			1.66246i
$872$	1.18378e6	−	942458.i	1.55681	−	1.23945i
$873$	41424.3			0.0543534
$874$	−48459.4	+	11046.7i	−0.0634388	+	0.0144614i
$875$		0			0
$876$	−219537.	−	456506.i	−0.286088	−	0.594892i
$877$	354735.			0.461216			0.230608	−	0.973047i	$-0.425928\pi$
$877$	354735.			0.461216			0.230608	+	0.973047i	$0.425928\pi$
$878$	23161.9	+	101606.i	0.0300459	+	0.131804i
$879$		−	57860.3i		−	0.0748865i
$880$		0			0
$881$	699360.			0.901051			0.450525	−	0.892764i	$-0.351237\pi$
$881$	699360.			0.901051			0.450525	+	0.892764i	$0.351237\pi$
$882$	48044.8	−	10952.2i	0.0617602	−	0.0140788i
$883$		−	402106.i		−	0.515726i	−0.966182	−	0.257863i	$-0.916982\pi$
$883$		−	402106.i		−	0.515726i	0.966182	−	0.257863i	$-0.0830183\pi$
$884$	−1.15151e6	+	553769.i	−1.47354	+	0.708638i
$885$		0			0
$886$	228614.	+	1.00287e6i	0.291229	+	1.27755i
$887$			800576.i			1.01755i	0.860900	+	0.508775i	$0.169901\pi$
$887$			800576.i			1.01755i	−0.860900	+	0.508775i	$0.830099\pi$
$888$	−254380.	−	319515.i	−0.322595	−	0.405196i
$889$	1.01483e6			1.28407
$890$		0			0
$891$		−	59616.3i		−	0.0750948i
$892$	−400320.	−	832427.i	−0.503128	−	1.04620i
$893$	47556.3			0.0596355
$894$	33046.1	+	144965.i	0.0413471	+	0.181380i
$895$		0			0
$896$	−722518.	−	1370.17i	−0.899980	−	0.00170670i
$897$	−523868.			−0.651084
$898$	−526303.	+	119975.i	−0.652654	+	0.148778i
$899$		−	332856.i		−	0.411848i
$900$		0			0
$901$	8666.65			0.0106758
$902$	142217.	+	623871.i	0.174798	+	0.766800i
$903$		−	572305.i		−	0.701862i
$904$	−1.04785e6	+	834239.i	−1.28222	+	1.02083i
$905$		0			0
$906$	135697.	−	30933.3i	0.165316	−	0.0376851i
$907$		−	283313.i		−	0.344391i	−0.985063	−	0.172195i	$-0.944914\pi$
$907$		−	283313.i		−	0.344391i	0.985063	−	0.172195i	$-0.0550860\pi$
$908$	497613.	+	1.03474e6i	0.603559	+	1.25504i
$909$	216799.			0.262379
$910$		0			0
$911$			747861.i			0.901124i	0.892745	+	0.450562i	$0.148776\pi$
$911$			747861.i			0.901124i	−0.892745	+	0.450562i	$0.851224\pi$
$912$	−19655.1	+	24592.0i	−0.0236312	+	0.0295668i
$913$	−812966.			−0.975283
$914$	222910.	−	50814.3i	0.266832	−	0.0608266i
$915$		0			0
$916$	569072.	−	273671.i	0.678229	−	0.326165i
$917$	689180.			0.819585
$918$	−51871.5	−	227548.i	−0.0615522	−	0.270015i
$919$			112623.i			0.133350i	0.997775	+	0.0666752i	$0.0212391\pi$
$919$			112623.i			0.133350i	−0.997775	+	0.0666752i	$0.978761\pi$
$920$		0			0
$921$	687043.			0.809962
$922$	997227.	−	227326.i	1.17309	−	0.267416i
$923$			1.60197e6i			1.88041i
$924$	−129943.	−	270204.i	−0.152198	−	0.316481i
$925$		0			0
$926$	−71095.4	−	311879.i	−0.0829124	−	0.363717i
$927$			188288.i			0.219111i
$928$	−113488.	+	234846.i	−0.131781	+	0.272701i
$929$	531794.			0.616186			0.308093	−	0.951356i	$-0.400309\pi$
$929$	531794.			0.616186			0.308093	+	0.951356i	$0.400309\pi$
$930$		0			0
$931$		−	10798.3i		−	0.0124583i
$932$	1.53866e6	−	739951.i	1.77137	−	0.851866i
$933$	−583861.			−0.670727
$934$	−6133.73	−	26907.2i	−0.00703122	−	0.0308443i
$935$		0			0
$936$	−259594.	+	206674.i	−0.296307	+	0.235904i
$937$	146232.			0.166558			0.0832788	−	0.996526i	$-0.473461\pi$
$937$	146232.			0.166558			0.0832788	+	0.996526i	$0.473461\pi$
$938$	−1.12959e6	+	257500.i	−1.28385	+	0.292665i
$939$		−	229412.i		−	0.260186i
$940$		0			0
$941$	589980.			0.666282			0.333141	−	0.942877i	$-0.391891\pi$
$941$	589980.			0.666282			0.333141	+	0.942877i	$0.391891\pi$
$942$	−162546.	−	713051.i	−0.183178	−	0.803560i
$943$			1.02703e6i			1.15494i
$944$	443181.	+	354211.i	0.497321	+	0.397483i
$945$		0			0
$946$	796550.	−	181580.i	0.890084	−	0.202902i
$947$			1.61990e6i			1.80630i	0.429327	+	0.903149i	$0.358751\pi$
$947$			1.61990e6i			1.80630i	−0.429327	+	0.903149i	$0.641249\pi$
$948$	−459282.	+	220872.i	−0.511049	+	0.245767i
$949$	−1.16998e6			−1.29911
$950$		0			0
$951$			250501.i			0.276980i
$952$	−731079.	−	918274.i	−0.806659	−	1.01321i
$953$	1.48644e6			1.63667			0.818334	−	0.574743i	$-0.194898\pi$
$953$	1.48644e6			1.63667			0.818334	+	0.574743i	$0.194898\pi$
$954$	2194.35	−	500.221i	0.00241107	−	0.000549623i
$955$		0			0
$956$	−226786.	−	471579.i	−0.248142	−	0.515987i
$957$	−108237.			−0.118182
$958$	187023.	+	820424.i	0.203781	+	0.893938i
$959$			534691.i			0.581387i
$960$		0			0
$961$	−784125.			−0.849061
$962$	−919709.	+	209655.i	−0.993803	+	0.226546i
$963$			356750.i			0.384691i
$964$	1.35138e6	−	649887.i	1.45419	−	0.699332i
$965$		0			0
$966$	−106957.	−	469197.i	−0.114619	−	0.502806i
$967$		−	492592.i		−	0.526786i	−0.964689	−	0.263393i	$-0.915158\pi$
$967$		−	492592.i		−	0.526786i	0.964689	−	0.263393i	$-0.0848416\pi$
$968$	−398220.	+	317040.i	−0.424983	+	0.338348i
$969$	−51142.8			−0.0544674
$970$		0			0
$971$			780633.i			0.827958i	0.910286	+	0.413979i	$0.135861\pi$
$971$			780633.i			0.827958i	−0.910286	+	0.413979i	$0.864139\pi$
$972$	−26267.2	−	54620.1i	−0.0278023	−	0.0578123i
$973$	−955241.			−1.00899
$974$	247925.	+	1.08759e6i	0.261338	+	1.14643i
$975$		0			0
$976$	350284.	−	438267.i	0.367722	−	0.460086i
$977$	−552434.			−0.578751			−0.289375	−	0.957216i	$-0.593448\pi$
$977$	−552434.			−0.578751			−0.289375	+	0.957216i	$0.593448\pi$
$978$	−753727.	+	171818.i	−0.788018	+	0.179635i
$979$		−	551737.i		−	0.575661i
$980$		0			0
$981$	638351.			0.663317
$982$	−123417.	−	541403.i	−0.127983	−	0.561433i
$983$			1.05406e6i			1.09083i	0.838166	+	0.545415i	$0.183628\pi$
$983$			1.05406e6i			1.09083i	−0.838166	+	0.545415i	$0.816372\pi$
$984$	405178.	+	508925.i	0.418462	+	0.525610i
$985$		0			0
$986$	−413128.	+	94176.0i	−0.424943	+	0.0968694i
$987$			460453.i			0.472662i
$988$	31513.4	+	65529.0i	0.0322835	+	0.0671305i
$989$	1.31129e6			1.34063
$990$		0			0
$991$			1.79867e6i			1.83149i	0.401759	+	0.915745i	$0.368399\pi$
$991$			1.79867e6i			1.83149i	−0.401759	+	0.915745i	$0.631601\pi$
$992$	1.20483e6	+	582226.i	1.22434	+	0.591655i
$993$	−461701.			−0.468233
$994$	−1.43479e6	+	327072.i	−1.45216	+	0.331033i
$995$		0			0
$996$	−744834.	+	358196.i	−0.750828	+	0.361079i
$997$	−895590.			−0.900987			−0.450494	−	0.892780i	$-0.648752\pi$
$997$	−895590.			−0.900987			−0.450494	+	0.892780i	$0.648752\pi$
$998$	85256.0	+	373998.i	0.0855981	+	0.375498i
$999$		−	172298.i		−	0.172643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.c.151.2	yes	16
4.3	odd	2	inner	300.5.c.c.151.1	yes	16
5.2	odd	4		300.5.f.c.199.13		32
5.3	odd	4		300.5.f.c.199.20		32
5.4	even	2		300.5.c.b.151.15	✓	16
20.3	even	4		300.5.f.c.199.14		32
20.7	even	4		300.5.f.c.199.19		32
20.19	odd	2		300.5.c.b.151.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.15	✓	16	5.4	even	2
300.5.c.b.151.16	yes	16	20.19	odd	2
300.5.c.c.151.1	yes	16	4.3	odd	2	inner
300.5.c.c.151.2	yes	16	1.1	even	1	trivial
300.5.f.c.199.13		32	5.2	odd	4
300.5.f.c.199.14		32	20.3	even	4
300.5.f.c.199.19		32	20.7	even	4
300.5.f.c.199.20		32	5.3	odd	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.89995 + 0.889027i) q^{2} -5.19615i q^{3} +(14.4193 - 6.93433i) q^{4} +(4.61952 + 20.2647i) q^{6} +44.0991i q^{7} +(-50.0696 + 39.8627i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.89995 + 0.889027i) q^{2} -5.19615i q^{3} +(14.4193 - 6.93433i) q^{4} +(4.61952 + 20.2647i) q^{6} +44.0991i q^{7} +(-50.0696 + 39.8627i) q^{8} -27.0000 q^{9} -81.7783i q^{11} +(-36.0318 - 74.9247i) q^{12} -192.024 q^{13} +(-39.2053 - 171.984i) q^{14} +(159.830 - 199.976i) q^{16} +415.880 q^{17} +(105.299 - 24.0037i) q^{18} -23.6665i q^{19} +229.146 q^{21} +(72.7031 + 318.931i) q^{22} +525.030i q^{23} +(207.132 + 260.169i) q^{24} +(748.886 - 170.715i) q^{26} +140.296i q^{27} +(305.798 + 635.876i) q^{28} +254.717 q^{29} -1306.77i q^{31} +(-445.546 + 921.989i) q^{32} -424.932 q^{33} +(-1621.91 + 369.729i) q^{34} +(-389.320 + 187.227i) q^{36} -1228.10 q^{37} +(21.0402 + 92.2983i) q^{38} +997.787i q^{39} +1956.13 q^{41} +(-893.657 + 203.717i) q^{42} -2497.56i q^{43} +(-567.077 - 1179.18i) q^{44} +(-466.766 - 2047.59i) q^{46} +2009.43i q^{47} +(-1039.10 - 830.502i) q^{48} +456.271 q^{49} -2160.98i q^{51} +(-2768.85 + 1331.56i) q^{52} +20.8393 q^{53} +(-124.727 - 547.148i) q^{54} +(-1757.91 - 2208.02i) q^{56} -122.975 q^{57} +(-993.383 + 226.450i) q^{58} +2216.17i q^{59} +2191.60 q^{61} +(1161.75 + 5096.34i) q^{62} -1190.68i q^{63} +(917.936 - 3991.82i) q^{64} +(1657.22 - 377.776i) q^{66} -6567.99i q^{67} +(5996.68 - 2883.85i) q^{68} +2728.14 q^{69} -8342.55i q^{71} +(1351.88 - 1076.29i) q^{72} +6092.86 q^{73} +(4789.55 - 1091.82i) q^{74} +(-164.111 - 341.254i) q^{76} +3606.35 q^{77} +(-887.060 - 3891.32i) q^{78} -6129.92i q^{79} +729.000 q^{81} +(-7628.82 + 1739.05i) q^{82} -9941.10i q^{83} +(3304.11 - 1588.97i) q^{84} +(2220.40 + 9740.36i) q^{86} -1323.55i q^{87} +(3259.90 + 4094.61i) q^{88} +6746.75 q^{89} -8468.09i q^{91} +(3640.73 + 7570.55i) q^{92} -6790.17 q^{93} +(-1786.44 - 7836.69i) q^{94} +(4790.80 + 2315.13i) q^{96} -1534.23 q^{97} +(-1779.44 + 405.637i) q^{98} +2208.01i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Introduction

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