LMFDB - Embedded newform 300.5.c.c.151.1

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

$q$-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	$-0.851427\pi$
$7$		−	44.0991i		−	0.899981i	0.893033	−	0.449991i	$-0.148573\pi$
$8$	−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	$0.109726\pi$
$11$			81.7783i			0.675853i	−0.941172	+	0.337927i	$0.890274\pi$
$12$	−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	$0.0104358\pi$
$19$			23.6665i			0.0655582i	−0.999463	+	0.0327791i	$0.989564\pi$
$20$		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	$-0.834711\pi$
$23$		−	525.030i		−	0.992496i	0.868181	−	0.496248i	$-0.165289\pi$
$24$	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	$0.237977\pi$
$31$			1306.77i			1.35980i	−0.733304	+	0.679901i	$0.762023\pi$
$32$	−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	$0.236021\pi$
$43$			2497.56i			1.35076i	−0.737469	+	0.675381i	$0.763979\pi$
$44$	−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	$-0.849700\pi$
$47$		−	2009.43i		−	0.909657i	0.890579	−	0.454829i	$-0.150300\pi$
$48$	−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	$-0.896880\pi$
$59$		−	2216.17i		−	0.636649i	0.947982	−	0.318324i	$-0.103120\pi$
$60$		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	$0.261210\pi$
$67$			6567.99i			1.46313i	−0.681772	+	0.731565i	$0.738790\pi$
$68$	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	$0.310220\pi$
$71$			8342.55i			1.65494i	−0.561510	+	0.827470i	$0.689780\pi$
$72$	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	$0.163405\pi$
$79$			6129.92i			0.982201i	−0.871103	+	0.491101i	$0.836595\pi$
$80$		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	$0.256556\pi$
$83$			9941.10i			1.44304i	−0.692394	+	0.721520i	$0.743444\pi$
$84$	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	$0.106599\pi$
$103$			6973.64i			0.657332i	−0.944446	+	0.328666i	$0.893401\pi$
$104$	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	$0.195791\pi$
$107$			13213.0i			1.15407i	−0.816718	+	0.577036i	$0.804209\pi$
$108$	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	$0.252840\pi$
$127$			23012.5i			1.42678i	−0.700769	+	0.713388i	$0.747160\pi$
$128$	−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	$0.150480\pi$
$131$			15628.0i			0.910669i	−0.890320	+	0.455335i	$0.849520\pi$
$132$	−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	$-0.810585\pi$
$139$		−	21661.2i		−	1.12112i	0.828112	−	0.560562i	$-0.189415\pi$
$140$		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	$0.0469103\pi$
$151$			6696.21i			0.293680i	−0.989160	+	0.146840i	$0.953090\pi$
$152$	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	$-0.753205\pi$
$163$		−	37194.0i		−	1.39990i	0.714191	−	0.699951i	$-0.246795\pi$
$164$	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	$0.394624\pi$
$167$			52749.4i			1.89140i	−0.325035	+	0.945702i	$0.605376\pi$
$168$	−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	$-0.787294\pi$
$179$		−	39705.3i		−	1.23920i	0.784917	−	0.619601i	$-0.212706\pi$
$180$		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	$-0.956620\pi$
$191$		−	9912.58i		−	0.271719i	0.990728	−	0.135860i	$-0.0433796\pi$
$192$	−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	$-0.849368\pi$
$199$		−	36097.0i		−	0.911518i	0.890103	−	0.455759i	$-0.150632\pi$
$200$		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	$-0.858907\pi$
$211$		−	38188.8i		−	0.857770i	0.903359	−	0.428885i	$-0.141093\pi$
$212$	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	$0.197123\pi$
$223$			57730.2i			1.16090i	−0.814297	+	0.580448i	$0.802877\pi$
$224$	−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	$-0.754822\pi$
$227$		−	71760.8i		−	1.39263i	0.717737	−	0.696314i	$-0.245178\pi$
$228$	−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	$0.0924177\pi$
$239$			32704.8i			0.572554i	−0.958147	+	0.286277i	$0.907582\pi$
$240$		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	$0.00722170\pi$
$251$			2858.44i			0.0453714i	−0.999743	+	0.0226857i	$0.992778\pi$
$252$	−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	$-0.880579\pi$
$263$		−	50691.6i		−	0.732866i	0.930444	−	0.366433i	$-0.119421\pi$
$264$	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	$-0.758144\pi$
$271$		−	101170.i		−	1.37757i	0.724965	−	0.688786i	$-0.241856\pi$
$272$	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	$0.210894\pi$
$283$			98529.3i			1.23025i	−0.788431	+	0.615124i	$0.789106\pi$
$284$	−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	$-0.752537\pi$
$307$		−	132222.i		−	1.40290i	0.712721	−	0.701448i	$-0.247463\pi$
$308$	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	$0.197286\pi$
$311$			112364.i			1.16173i	−0.813999	+	0.580867i	$0.802714\pi$
$312$	−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	$0.132903\pi$
$331$			88854.4i			0.811004i	−0.914094	+	0.405502i	$0.867097\pi$
$332$	−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	$-0.902176\pi$
$347$		−	72849.3i		−	0.605016i	0.953147	−	0.302508i	$-0.0978238\pi$
$348$	−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	$0.124345\pi$
$359$			98151.3i			0.761565i	−0.924665	+	0.380783i	$0.875655\pi$
$360$		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	$-0.854252\pi$
$367$		−	119078.i		−	0.884096i	0.896991	−	0.442048i	$-0.145748\pi$
$368$	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	$0.0598444\pi$
$379$			53693.3i			0.373802i	−0.982379	+	0.186901i	$0.940156\pi$
$380$		0			0
$381$	−119576.			−0.823749
$382$	−8812.56	+	38658.6i	−0.0603914	+	0.264923i
$383$		−	36473.1i		−	0.248642i	−0.992242	−	0.124321i	$-0.960325\pi$
$383$		−	36473.1i		−	0.248642i	0.992242	−	0.124321i	$-0.0396753\pi$
$384$	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	$-0.827648\pi$
$419$		−	180964.i		−	1.03078i	0.856957	−	0.515389i	$-0.172352\pi$
$420$		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	$-0.678632\pi$
$431$		−	314539.i		−	1.69325i	0.532193	−	0.846623i	$-0.321368\pi$
$432$	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	$0.0215318\pi$
$439$			26053.1i			0.135185i	−0.997713	+	0.0675927i	$0.978468\pi$
$440$		0			0
$441$	−12319.3			−0.0633446
$442$	311447.	+	70996.9i	1.59419	+	0.363408i
$443$			257150.i			1.31033i	0.755487	+	0.655163i	$0.227400\pi$
$443$			257150.i			1.31033i	−0.755487	+	0.655163i	$0.772600\pi$
$444$	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	$-0.940278\pi$
$463$		−	79969.9i		−	0.373048i	0.982450	−	0.186524i	$-0.0597222\pi$
$464$	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	$-0.994965\pi$
$467$		−	6899.37i		−	0.0316356i	0.999875	−	0.0158178i	$-0.00503517\pi$
$468$	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	$0.151590\pi$
$479$			210368.i			0.916870i	−0.888728	+	0.458435i	$0.848410\pi$
$480$		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	$0.200053\pi$
$487$			278872.i			1.17584i	−0.808920	+	0.587919i	$0.799947\pi$
$488$	−109733.	−	87363.0i	−0.460782	−	0.366849i
$489$	193266.			0.808234
$490$		0			0
$491$		−	138823.i		−	0.575836i	−0.957655	−	0.287918i	$-0.907037\pi$
$491$		−	138823.i		−	0.575836i	0.957655	−	0.287918i	$-0.0929630\pi$
$492$	−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	$0.0616808\pi$
$499$			95898.1i			0.385131i	−0.981284	+	0.192566i	$0.938319\pi$
$500$		0			0
$501$	−274094.			−1.09200
$502$	2541.23	−	11147.8i	0.0100841	−	0.0442365i
$503$		−	134868.i		−	0.533056i	−0.963827	−	0.266528i	$-0.914123\pi$
$503$		−	134868.i		−	0.533056i	0.963827	−	0.266528i	$-0.0858766\pi$
$504$	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	$-0.938976\pi$
$523$		−	104237.i		−	0.381083i	0.981679	−	0.190541i	$-0.0610243\pi$
$524$	−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	$0.261637\pi$
$547$			438329.i			1.46496i	−0.680789	+	0.732480i	$0.738363\pi$
$548$	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	$0.258853\pi$
$563$			460554.i			1.45299i	−0.687170	+	0.726497i	$0.741147\pi$
$564$	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	$0.00257115\pi$
$571$			5267.14i			0.0161548i	−0.999967	+	0.00807742i	$0.997429\pi$
$572$	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	$-0.758503\pi$
$587$		−	474104.i		−	1.37593i	0.725742	−	0.687967i	$-0.241497\pi$
$588$	−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	$-0.863495\pi$
$599$		−	298392.i		−	0.831637i	0.909448	−	0.415818i	$-0.136505\pi$
$600$		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	$0.150258\pi$
$607$			335077.i			0.909425i	−0.890638	+	0.454712i	$0.849742\pi$
$608$	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	$-0.936219\pi$
$619$		−	152525.i		−	0.398069i	0.979992	−	0.199035i	$-0.0637807\pi$
$620$		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	$0.176919\pi$
$631$			420163.i			1.05526i	−0.849475	+	0.527629i	$0.823081\pi$
$632$	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	$0.189318\pi$
$643$			463320.i			1.12062i	−0.828282	+	0.560311i	$0.810682\pi$
$644$	−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	$0.231444\pi$
$647$			556505.i			1.32941i	−0.747104	+	0.664707i	$0.768556\pi$
$648$	−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	$-0.996981\pi$
$659$		−	8238.25i		−	0.0189699i	0.999955	−	0.00948493i	$-0.00301919\pi$
$660$		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	$0.00370825\pi$
$683$			10868.8i			0.0232991i	−0.999932	+	0.0116495i	$0.996292\pi$
$684$	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	$0.108060\pi$
$691$			318000.i			0.665995i	−0.942928	+	0.332998i	$0.891940\pi$
$692$	−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	$-0.849401\pi$
$719$		−	471123.i		−	0.911332i	0.890151	−	0.455666i	$-0.150599\pi$
$720$		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	$0.00813765\pi$
$727$			27020.9i			0.0511248i	−0.999673	+	0.0255624i	$0.991862\pi$
$728$	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	$0.0919585\pi$
$739$			311174.i			0.569789i	−0.958559	+	0.284894i	$0.908042\pi$
$740$		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	$0.136709\pi$
$743$			459748.i			0.832803i	−0.909181	+	0.416401i	$0.863291\pi$
$744$	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	$0.0572130\pi$
$751$			201657.i			0.357547i	−0.983890	+	0.178774i	$0.942787\pi$
$752$	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	$-0.781303\pi$
$787$		−	785688.i		−	1.26853i	0.773116	−	0.634265i	$-0.218697\pi$
$788$	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	$0.145200\pi$
$811$			579456.i			0.881006i	−0.897751	+	0.440503i	$0.854800\pi$
$812$	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	$-0.827105\pi$
$823$		−	700154.i		−	1.03370i	0.856077	−	0.516849i	$-0.172895\pi$
$824$	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	$-0.992820\pi$
$827$		−	30850.5i		−	0.0451077i	0.999746	−	0.0225539i	$-0.00717973\pi$
$828$	−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	$0.241224\pi$
$839$			967675.i			1.37469i	−0.726330	+	0.687346i	$0.758776\pi$
$840$		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	$0.0372181\pi$
$859$			172159.i			0.233316i	−0.993172	+	0.116658i	$0.962782\pi$
$860$		0			0
$861$	448239.			0.604648
$862$	−279634.	+	1.22669e6i	−0.376335	+	1.65089i
$863$		−	267304.i		−	0.358908i	−0.983766	−	0.179454i	$-0.942567\pi$
$863$		−	267304.i		−	0.358908i	0.983766	−	0.179454i	$-0.0574331\pi$
$864$	−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	$0.0830183\pi$
$883$			402106.i			0.515726i	−0.966182	+	0.257863i	$0.916982\pi$
$884$	−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	$-0.830099\pi$
$887$		−	800576.i		−	1.01755i	0.860900	−	0.508775i	$-0.169901\pi$
$888$	−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	$0.0550860\pi$
$907$			283313.i			0.344391i	−0.985063	+	0.172195i	$0.944914\pi$
$908$	497613.	−	1.03474e6i	0.603559	−	1.25504i
$909$	216799.			0.262379
$910$		0			0
$911$		−	747861.i		−	0.901124i	−0.892745	−	0.450562i	$-0.851224\pi$
$911$		−	747861.i		−	0.901124i	0.892745	−	0.450562i	$-0.148776\pi$
$912$	−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	$-0.978761\pi$
$919$		−	112623.i		−	0.133350i	0.997775	−	0.0666752i	$-0.0212391\pi$
$920$		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	$-0.641249\pi$
$947$		−	1.61990e6i		−	1.80630i	0.429327	−	0.903149i	$-0.358751\pi$
$948$	−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	$0.0848416\pi$
$967$			492592.i			0.526786i	−0.964689	+	0.263393i	$0.915158\pi$
$968$	−398220.	−	317040.i	−0.424983	−	0.338348i
$969$	−51142.8			−0.0544674
$970$		0			0
$971$		−	780633.i		−	0.827958i	−0.910286	−	0.413979i	$-0.864139\pi$
$971$		−	780633.i		−	0.827958i	0.910286	−	0.413979i	$-0.135861\pi$
$972$	−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	$-0.816372\pi$
$983$		−	1.05406e6i		−	1.09083i	0.838166	−	0.545415i	$-0.183628\pi$
$984$	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	$-0.631601\pi$
$991$		−	1.79867e6i		−	1.83149i	0.401759	−	0.915745i	$-0.368399\pi$
$992$	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.151.1	yes	16
4.3	odd	2	inner	300.5.c.c.151.2	yes	16
5.2	odd	4		300.5.f.c.199.19		32
5.3	odd	4		300.5.f.c.199.14		32
5.4	even	2		300.5.c.b.151.16	yes	16
20.3	even	4		300.5.f.c.199.20		32
20.7	even	4		300.5.f.c.199.13		32
20.19	odd	2		300.5.c.b.151.15	✓	16

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