LMFDB - Embedded newform 175.5.g.c.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(43,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("175.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.g (of order $4$, degree $2$, 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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.88957 - 2.88957i) q^{2} +(-11.3498 - 11.3498i) q^{3} -0.699277i q^{4} -65.5923 q^{6} +(-13.0958 + 13.0958i) q^{7} +(44.2126 + 44.2126i) q^{8} +176.637i q^{9} +O(q^{10})$	\(q+(2.88957 - 2.88957i) q^{2} +(-11.3498 - 11.3498i) q^{3} -0.699277i q^{4} -65.5923 q^{6} +(-13.0958 + 13.0958i) q^{7} +(44.2126 + 44.2126i) q^{8} +176.637i q^{9} -15.6486 q^{11} +(-7.93668 + 7.93668i) q^{12} +(137.742 + 137.742i) q^{13} +75.6826i q^{14} +266.699 q^{16} +(-108.806 + 108.806i) q^{17} +(510.406 + 510.406i) q^{18} -375.111i q^{19} +297.270 q^{21} +(-45.2177 + 45.2177i) q^{22} +(-153.121 - 153.121i) q^{23} -1003.61i q^{24} +796.034 q^{26} +(1085.46 - 1085.46i) q^{27} +(9.15760 + 9.15760i) q^{28} +1530.33i q^{29} -201.870 q^{31} +(63.2467 - 63.2467i) q^{32} +(177.608 + 177.608i) q^{33} +628.807i q^{34} +123.518 q^{36} +(186.081 - 186.081i) q^{37} +(-1083.91 - 1083.91i) q^{38} -3126.70i q^{39} +3013.33 q^{41} +(858.984 - 858.984i) q^{42} +(2337.57 + 2337.57i) q^{43} +10.9427i q^{44} -884.909 q^{46} +(922.323 - 922.323i) q^{47} +(-3026.99 - 3026.99i) q^{48} -343.000i q^{49} +2469.86 q^{51} +(96.3201 - 96.3201i) q^{52} +(700.207 + 700.207i) q^{53} -6273.06i q^{54} -1158.00 q^{56} +(-4257.44 + 4257.44i) q^{57} +(4421.99 + 4421.99i) q^{58} +760.617i q^{59} -2823.65 q^{61} +(-583.320 + 583.320i) q^{62} +(-2313.20 - 2313.20i) q^{63} +3901.68i q^{64} +1026.43 q^{66} +(-2588.42 + 2588.42i) q^{67} +(76.0857 + 76.0857i) q^{68} +3475.79i q^{69} -5878.41 q^{71} +(-7809.58 + 7809.58i) q^{72} +(3613.01 + 3613.01i) q^{73} -1075.39i q^{74} -262.306 q^{76} +(204.930 - 204.930i) q^{77} +(-9034.84 - 9034.84i) q^{78} +7492.79i q^{79} -10332.1 q^{81} +(8707.24 - 8707.24i) q^{82} +(2538.32 + 2538.32i) q^{83} -207.874i q^{84} +13509.2 q^{86} +(17368.9 - 17368.9i) q^{87} +(-691.863 - 691.863i) q^{88} +2545.52i q^{89} -3607.69 q^{91} +(-107.074 + 107.074i) q^{92} +(2291.19 + 2291.19i) q^{93} -5330.24i q^{94} -1435.68 q^{96} +(-7253.08 + 7253.08i) q^{97} +(-991.124 - 991.124i) q^{98} -2764.12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) $ 24 * q - 20 * q^3 + 72 * q^6	$ 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) $ 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	2.88957	−	2.88957i	0.722394	−	0.722394i	−0.246699	−	0.969092i	$-0.579346\pi$
$2$	2.88957	−	2.88957i	0.722394	−	0.722394i	0.969092	+	0.246699i	$0.0793458\pi$
$3$	−11.3498	−	11.3498i	−1.26109	−	1.26109i	−0.950564	−	0.310527i	$-0.899494\pi$
$3$	−11.3498	−	11.3498i	−1.26109	−	1.26109i	−0.310527	−	0.950564i	$-0.600506\pi$
$4$		−	0.699277i		−	0.0437048i
$5$		0			0
$5$		0			0
$6$	−65.5923			−1.82201
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$8$	44.2126	+	44.2126i	0.690821	+	0.690821i
$9$			176.637i			2.18070i
$10$		0			0
$11$	−15.6486			−0.129327			−0.0646635	−	0.997907i	$-0.520597\pi$
$11$	−15.6486			−0.129327			−0.0646635	+	0.997907i	$0.520597\pi$
$12$	−7.93668	+	7.93668i	−0.0551158	+	0.0551158i
$13$	137.742	+	137.742i	0.815044	+	0.815044i	0.985385	−	0.170342i	$-0.0544871\pi$
$13$	137.742	+	137.742i	0.815044	+	0.815044i	−0.170342	+	0.985385i	$0.554487\pi$
$14$			75.6826i			0.386136i
$15$		0			0
$16$	266.699			1.04179
$17$	−108.806	+	108.806i	−0.376492	+	0.376492i	−0.869835	−	0.493343i	$-0.835775\pi$
$17$	−108.806	+	108.806i	−0.376492	+	0.376492i	0.493343	+	0.869835i	$0.335775\pi$
$18$	510.406	+	510.406i	1.57533	+	1.57533i
$19$		−	375.111i		−	1.03909i	−0.854444	−	0.519544i	$-0.826102\pi$
$19$		−	375.111i		−	1.03909i	0.854444	−	0.519544i	$-0.173898\pi$
$20$		0			0
$21$	297.270			0.674082
$22$	−45.2177	+	45.2177i	−0.0934250	+	0.0934250i
$23$	−153.121	−	153.121i	−0.289454	−	0.289454i	0.547411	−	0.836864i	$-0.315614\pi$
$23$	−153.121	−	153.121i	−0.289454	−	0.289454i	−0.836864	+	0.547411i	$0.815614\pi$
$24$		−	1003.61i		−	1.74238i
$25$		0			0
$26$	796.034			1.17756
$27$	1085.46	−	1085.46i	1.48898	−	1.48898i
$28$	9.15760	+	9.15760i	0.0116806	+	0.0116806i
$29$			1530.33i			1.81965i	0.414992	+	0.909825i	$0.363784\pi$
$29$			1530.33i			1.81965i	−0.414992	+	0.909825i	$0.636216\pi$
$30$		0			0
$31$	−201.870			−0.210063			−0.105031	−	0.994469i	$-0.533494\pi$
$31$	−201.870			−0.210063			−0.105031	+	0.994469i	$0.533494\pi$
$32$	63.2467	−	63.2467i	0.0617643	−	0.0617643i
$33$	177.608	+	177.608i	0.163093	+	0.163093i
$34$			628.807i			0.543951i
$35$		0			0
$36$	123.518			0.0953073
$37$	186.081	−	186.081i	0.135924	−	0.135924i	−0.635871	−	0.771795i	$-0.719359\pi$
$37$	186.081	−	186.081i	0.135924	−	0.135924i	0.771795	+	0.635871i	$0.219359\pi$
$38$	−1083.91	−	1083.91i	−0.750630	−	0.750630i
$39$		−	3126.70i		−	2.05569i
$40$		0			0
$41$	3013.33			1.79258			0.896291	−	0.443467i	$-0.146252\pi$
$41$	3013.33			1.79258			0.896291	+	0.443467i	$0.146252\pi$
$42$	858.984	−	858.984i	0.486952	−	0.486952i
$43$	2337.57	+	2337.57i	1.26424	+	1.26424i	0.949020	+	0.315217i	$0.102077\pi$
$43$	2337.57	+	2337.57i	1.26424	+	1.26424i	0.315217	+	0.949020i	$0.397923\pi$
$44$			10.9427i			0.00565221i
$45$		0			0
$46$	−884.909			−0.418199
$47$	922.323	−	922.323i	0.417530	−	0.417530i	−0.466822	−	0.884351i	$-0.654601\pi$
$47$	922.323	−	922.323i	0.417530	−	0.417530i	0.884351	+	0.466822i	$0.154601\pi$
$48$	−3026.99	−	3026.99i	−1.31380	−	1.31380i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	2469.86			0.949582
$52$	96.3201	−	96.3201i	0.0356213	−	0.0356213i
$53$	700.207	+	700.207i	0.249273	+	0.249273i	0.820672	−	0.571399i	$-0.193599\pi$
$53$	700.207	+	700.207i	0.249273	+	0.249273i	−0.571399	+	0.820672i	$0.693599\pi$
$54$		−	6273.06i		−	2.15126i
$55$		0			0
$56$	−1158.00			−0.369260
$57$	−4257.44	+	4257.44i	−1.31038	+	1.31038i
$58$	4421.99	+	4421.99i	1.31450	+	1.31450i
$59$			760.617i			0.218505i	0.994014	+	0.109253i	$0.0348458\pi$
$59$			760.617i			0.218505i	−0.994014	+	0.109253i	$0.965154\pi$
$60$		0			0
$61$	−2823.65			−0.758842			−0.379421	−	0.925224i	$-0.623877\pi$
$61$	−2823.65			−0.758842			−0.379421	+	0.925224i	$0.623877\pi$
$62$	−583.320	+	583.320i	−0.151748	+	0.151748i
$63$	−2313.20	−	2313.20i	−0.582818	−	0.582818i
$64$			3901.68i			0.952558i
$65$		0			0
$66$	1026.43			0.235635
$67$	−2588.42	+	2588.42i	−0.576613	+	0.576613i	−0.933969	−	0.357355i	$-0.883679\pi$
$67$	−2588.42	+	2588.42i	−0.576613	+	0.576613i	0.357355	+	0.933969i	$0.383679\pi$
$68$	76.0857	+	76.0857i	0.0164545	+	0.0164545i
$69$			3475.79i			0.730055i
$70$		0			0
$71$	−5878.41			−1.16612			−0.583060	−	0.812429i	$-0.698145\pi$
$71$	−5878.41			−1.16612			−0.583060	+	0.812429i	$0.698145\pi$
$72$	−7809.58	+	7809.58i	−1.50648	+	1.50648i
$73$	3613.01	+	3613.01i	0.677989	+	0.677989i	0.959545	−	0.281556i	$-0.0908504\pi$
$73$	3613.01	+	3613.01i	0.677989	+	0.677989i	−0.281556	+	0.959545i	$0.590850\pi$
$74$		−	1075.39i		−	0.196382i
$75$		0			0
$76$	−262.306			−0.0454131
$77$	204.930	−	204.930i	0.0345641	−	0.0345641i
$78$	−9034.84	−	9034.84i	−1.48502	−	1.48502i
$79$			7492.79i			1.20058i	0.799784	+	0.600288i	$0.204947\pi$
$79$			7492.79i			1.20058i	−0.799784	+	0.600288i	$0.795053\pi$
$80$		0			0
$81$	−10332.1			−1.57477
$82$	8707.24	−	8707.24i	1.29495	−	1.29495i
$83$	2538.32	+	2538.32i	0.368459	+	0.368459i	0.866915	−	0.498456i	$-0.166099\pi$
$83$	2538.32	+	2538.32i	0.368459	+	0.368459i	−0.498456	+	0.866915i	$0.666099\pi$
$84$		−	207.874i		−	0.0294606i
$85$		0			0
$86$	13509.2			1.82655
$87$	17368.9	−	17368.9i	2.29475	−	2.29475i
$88$	−691.863	−	691.863i	−0.0893418	−	0.0893418i
$89$			2545.52i			0.321364i	0.987006	+	0.160682i	$0.0513693\pi$
$89$			2545.52i			0.321364i	−0.987006	+	0.160682i	$0.948631\pi$
$90$		0			0
$91$	−3607.69			−0.435659
$92$	−107.074	+	107.074i	−0.0126505	+	0.0126505i
$93$	2291.19	+	2291.19i	0.264909	+	0.264909i
$94$		−	5330.24i		−	0.603241i
$95$		0			0
$96$	−1435.68			−0.155781
$97$	−7253.08	+	7253.08i	−0.770867	+	0.770867i	−0.978258	−	0.207391i	$-0.933503\pi$
$97$	−7253.08	+	7253.08i	−0.770867	+	0.770867i	0.207391	+	0.978258i	$0.433503\pi$
$98$	−991.124	−	991.124i	−0.103199	−	0.103199i
$99$		−	2764.12i		−	0.282024i
$100$		0			0
$101$	10863.6			1.06495			0.532476	−	0.846445i	$-0.321262\pi$
$101$	10863.6			1.06495			0.532476	+	0.846445i	$0.321262\pi$
$102$	7136.85	−	7136.85i	0.685972	−	0.685972i
$103$	−1576.66	−	1576.66i	−0.148616	−	0.148616i	0.628884	−	0.777499i	$-0.283512\pi$
$103$	−1576.66	−	1576.66i	−0.148616	−	0.148616i	−0.777499	+	0.628884i	$0.783512\pi$
$104$			12179.9i			1.12610i
$105$		0			0
$106$	4046.60			0.360146
$107$	−105.592	+	105.592i	−0.00922278	+	0.00922278i	−0.711703	−	0.702480i	$-0.752076\pi$
$107$	−105.592	+	105.592i	−0.00922278	+	0.00922278i	0.702480	+	0.711703i	$0.252076\pi$
$108$	−759.041	−	759.041i	−0.0650755	−	0.0650755i
$109$		−	7733.07i		−	0.650877i	−0.945563	−	0.325438i	$-0.894488\pi$
$109$		−	7733.07i		−	0.650877i	0.945563	−	0.325438i	$-0.105512\pi$
$110$		0			0
$111$	−4223.96			−0.342826
$112$	−3492.64	+	3492.64i	−0.278431	+	0.278431i
$113$	2964.43	+	2964.43i	0.232159	+	0.232159i	0.813593	−	0.581435i	$-0.197508\pi$
$113$	2964.43	+	2964.43i	0.232159	+	0.232159i	−0.581435	+	0.813593i	$0.697508\pi$
$114$			24604.4i			1.89323i
$115$		0			0
$116$	1070.12			0.0795275
$117$	−24330.4	+	24330.4i	−1.77737	+	1.77737i
$118$	2197.86	+	2197.86i	0.157847	+	0.157847i
$119$		−	2849.81i		−	0.201243i
$120$		0			0
$121$	−14396.1			−0.983275
$122$	−8159.15	+	8159.15i	−0.548183	+	0.548183i
$123$	−34200.8	−	34200.8i	−2.26061	−	2.26061i
$124$			141.163i			0.00918076i
$125$		0			0
$126$	−13368.4			−0.842048
$127$	9715.36	−	9715.36i	0.602353	−	0.602353i	−0.338583	−	0.940936i	$-0.609948\pi$
$127$	9715.36	−	9715.36i	0.602353	−	0.602353i	0.940936	+	0.338583i	$0.109948\pi$
$128$	12286.1	+	12286.1i	0.749886	+	0.749886i
$129$		−	53062.1i		−	3.18864i
$130$		0			0
$131$	−20298.4			−1.18282			−0.591412	−	0.806370i	$-0.701429\pi$
$131$	−20298.4			−1.18282			−0.591412	+	0.806370i	$0.701429\pi$
$132$	124.198	−	124.198i	0.00712796	−	0.00712796i
$133$	4912.37	+	4912.37i	0.277708	+	0.277708i
$134$			14958.8i			0.833083i
$135$		0			0
$136$	−9621.20			−0.520178
$137$	9485.96	−	9485.96i	0.505406	−	0.505406i	−0.407707	−	0.913113i	$-0.633671\pi$
$137$	9485.96	−	9485.96i	0.505406	−	0.505406i	0.913113	+	0.407707i	$0.133671\pi$
$138$	10043.6	+	10043.6i	0.527387	+	0.527387i
$139$			11313.5i			0.585554i	0.956181	+	0.292777i	$0.0945794\pi$
$139$			11313.5i			0.585554i	−0.956181	+	0.292777i	$0.905421\pi$
$140$		0			0
$141$	−20936.4			−1.05309
$142$	−16986.1	+	16986.1i	−0.842397	+	0.842397i
$143$	−2155.47	−	2155.47i	−0.105407	−	0.105407i
$144$			47109.0i			2.27185i
$145$		0			0
$146$	20880.1			0.979550
$147$	−3892.99	+	3892.99i	−0.180156	+	0.180156i
$148$	−130.122	−	130.122i	−0.00594055	−	0.00594055i
$149$		−	6205.16i		−	0.279499i	−0.990187	−	0.139750i	$-0.955370\pi$
$149$		−	6205.16i		−	0.279499i	0.990187	−	0.139750i	$-0.0446298\pi$
$150$		0			0
$151$	14726.0			0.645849			0.322925	−	0.946425i	$-0.395334\pi$
$151$	14726.0			0.645849			0.322925	+	0.946425i	$0.395334\pi$
$152$	16584.6	−	16584.6i	0.717824	−	0.717824i
$153$	−19219.2	−	19219.2i	−0.821018	−	0.821018i
$154$		−	1184.32i		−	0.0499377i
$155$		0			0
$156$	−2186.43			−0.0898436
$157$	−8949.34	+	8949.34i	−0.363071	+	0.363071i	−0.864942	−	0.501871i	$-0.832645\pi$
$157$	−8949.34	+	8949.34i	−0.363071	+	0.363071i	0.501871	+	0.864942i	$0.332645\pi$
$158$	21651.0	+	21651.0i	0.867288	+	0.867288i
$159$		−	15894.5i		−	0.628712i
$160$		0			0
$161$	4010.48			0.154719
$162$	−29855.3	+	29855.3i	−1.13760	+	1.13760i
$163$	−3110.33	−	3110.33i	−0.117066	−	0.117066i	0.646147	−	0.763213i	$-0.276379\pi$
$163$	−3110.33	−	3110.33i	−0.117066	−	0.117066i	−0.763213	+	0.646147i	$0.776379\pi$
$164$		−	2107.15i		−	0.0783445i
$165$		0			0
$166$	14669.3			0.532345
$167$	31251.0	−	31251.0i	1.12055	−	1.12055i	0.128891	−	0.991659i	$-0.458858\pi$
$167$	31251.0	−	31251.0i	1.12055	−	1.12055i	0.991659	−	0.128891i	$-0.0411417\pi$
$168$	13143.1	+	13143.1i	0.465670	+	0.465670i
$169$			9384.92i			0.328592i
$170$		0			0
$171$	66258.5			2.26594
$172$	1634.61	−	1634.61i	0.0552532	−	0.0552532i
$173$	−21670.1	−	21670.1i	−0.724049	−	0.724049i	0.245378	−	0.969427i	$-0.421088\pi$
$173$	−21670.1	−	21670.1i	−0.724049	−	0.724049i	−0.969427	+	0.245378i	$0.921088\pi$
$174$		−	100378.i		−	3.31542i
$175$		0			0
$176$	−4173.46			−0.134732
$177$	8632.87	−	8632.87i	0.275555	−	0.275555i
$178$	7355.47	+	7355.47i	0.232151	+	0.232151i
$179$		−	19194.6i		−	0.599063i	−0.954086	−	0.299531i	$-0.903170\pi$
$179$		−	19194.6i		−	0.599063i	0.954086	−	0.299531i	$-0.0968303\pi$
$180$		0			0
$181$	−45031.1			−1.37453			−0.687267	−	0.726405i	$-0.741190\pi$
$181$	−45031.1			−1.37453			−0.687267	+	0.726405i	$0.741190\pi$
$182$	−10424.7	+	10424.7i	−0.314717	+	0.314717i
$183$	32048.0	+	32048.0i	0.956970	+	0.956970i
$184$		−	13539.7i		−	0.399921i
$185$		0			0
$186$	13241.1			0.382736
$187$	1702.66	−	1702.66i	0.0486906	−	0.0486906i
$188$	−644.959	−	644.959i	−0.0182481	−	0.0182481i
$189$			28430.1i			0.795892i
$190$		0			0
$191$	25510.8			0.699289			0.349645	−	0.936882i	$-0.386302\pi$
$191$	25510.8			0.699289			0.349645	+	0.936882i	$0.386302\pi$
$192$	44283.4	−	44283.4i	1.20126	−	1.20126i
$193$	−24294.0	−	24294.0i	−0.652207	−	0.652207i	0.301317	−	0.953524i	$-0.402574\pi$
$193$	−24294.0	−	24294.0i	−0.652207	−	0.652207i	−0.953524	+	0.301317i	$0.902574\pi$
$194$			41916.7i			1.11374i
$195$		0			0
$196$	−239.852			−0.00624355
$197$	−10584.7	+	10584.7i	−0.272738	+	0.272738i	−0.830202	−	0.557463i	$-0.811775\pi$
$197$	−10584.7	+	10584.7i	−0.272738	+	0.272738i	0.557463	+	0.830202i	$0.311775\pi$
$198$	−7987.12	−	7987.12i	−0.203732	−	0.203732i
$199$			1923.05i			0.0485606i	0.999705	+	0.0242803i	$0.00772942\pi$
$199$			1923.05i			0.0485606i	−0.999705	+	0.0242803i	$0.992271\pi$
$200$		0			0
$201$	58756.2			1.45432
$202$	31391.1	−	31391.1i	0.769315	−	0.769315i
$203$	−20040.8	−	20040.8i	−0.486322	−	0.486322i
$204$		−	1727.12i		−	0.0415013i
$205$		0			0
$206$	−9111.78			−0.214718
$207$	27046.8	−	27046.8i	0.631213	−	0.631213i
$208$	36735.8	+	36735.8i	0.849108	+	0.849108i
$209$			5869.94i			0.134382i
$210$		0			0
$211$	2828.45			0.0635308			0.0317654	−	0.999495i	$-0.489887\pi$
$211$	2828.45			0.0635308			0.0317654	+	0.999495i	$0.489887\pi$
$212$	489.639	−	489.639i	0.0108944	−	0.0108944i
$213$	66718.9	+	66718.9i	1.47058	+	1.47058i
$214$			610.230i			0.0133250i
$215$		0			0
$216$	95982.4			2.05723
$217$	2643.65	−	2643.65i	0.0561417	−	0.0561417i
$218$	−22345.3	−	22345.3i	−0.470189	−	0.470189i
$219$		−	82014.0i		−	1.71001i
$220$		0			0
$221$	−29974.4			−0.613715
$222$	−12205.5	+	12205.5i	−0.247656	+	0.247656i
$223$	2804.72	+	2804.72i	0.0564002	+	0.0564002i	0.734744	−	0.678344i	$-0.237302\pi$
$223$	2804.72	+	2804.72i	0.0564002	+	0.0564002i	−0.678344	+	0.734744i	$0.737302\pi$
$224$			1656.53i			0.0330144i
$225$		0			0
$226$	17131.9			0.335420
$227$	−5898.38	+	5898.38i	−0.114467	+	0.114467i	−0.762020	−	0.647553i	$-0.775792\pi$
$227$	−5898.38	+	5898.38i	−0.114467	+	0.114467i	0.647553	+	0.762020i	$0.275792\pi$
$228$	2977.13	+	2977.13i	0.0572701	+	0.0572701i
$229$			38635.6i			0.736744i	0.929679	+	0.368372i	$0.120085\pi$
$229$			38635.6i			0.736744i	−0.929679	+	0.368372i	$0.879915\pi$
$230$		0			0
$231$	−4651.85			−0.0871770
$232$	−67659.6	+	67659.6i	−1.25705	+	1.25705i
$233$	48330.7	+	48330.7i	0.890249	+	0.890249i	0.994546	−	0.104297i	$-0.0332592\pi$
$233$	48330.7	+	48330.7i	0.890249	+	0.890249i	−0.104297	+	0.994546i	$0.533259\pi$
$234$			140609.i			2.56792i
$235$		0			0
$236$	531.882			0.00954974
$237$	85041.9	−	85041.9i	1.51404	−	1.51404i
$238$	−8234.73	−	8234.73i	−0.145377	−	0.145377i
$239$			13241.8i			0.231819i	0.993260	+	0.115910i	$0.0369783\pi$
$239$			13241.8i			0.231819i	−0.993260	+	0.115910i	$0.963022\pi$
$240$		0			0
$241$	35305.5			0.607867			0.303933	−	0.952693i	$-0.401700\pi$
$241$	35305.5			0.607867			0.303933	+	0.952693i	$0.401700\pi$
$242$	−41598.7	+	41598.7i	−0.710311	+	0.710311i
$243$	29344.5	+	29344.5i	0.496951	+	0.496951i
$244$			1974.52i			0.0331651i
$245$		0			0
$246$	−197651.			−3.26610
$247$	51668.6	−	51668.6i	0.846902	−	0.846902i
$248$	−8925.21	−	8925.21i	−0.145116	−	0.145116i
$249$		−	57618.9i		−	0.929322i
$250$		0			0
$251$	73633.3			1.16876			0.584382	−	0.811479i	$-0.301337\pi$
$251$	73633.3			1.16876			0.584382	+	0.811479i	$0.301337\pi$
$252$	−1617.57	+	1617.57i	−0.0254720	+	0.0254720i
$253$	2396.12	+	2396.12i	0.0374342	+	0.0374342i
$254$		−	56146.5i		−	0.870272i
$255$		0			0
$256$	8576.55			0.130868
$257$	−60051.8	+	60051.8i	−0.909201	+	0.909201i	−0.996208	−	0.0870065i	$-0.972270\pi$
$257$	−60051.8	+	60051.8i	−0.909201	+	0.909201i	0.0870065	+	0.996208i	$0.472270\pi$
$258$	−153327.	−	153327.i	−2.30345	−	2.30345i
$259$			4873.75i			0.0726547i
$260$		0			0
$261$	−270312.			−3.96812
$262$	−58653.9	+	58653.9i	−0.854464	+	0.854464i
$263$	57887.7	+	57887.7i	0.836902	+	0.836902i	0.988450	−	0.151548i	$-0.0484258\pi$
$263$	57887.7	+	57887.7i	0.836902	+	0.836902i	−0.151548	+	0.988450i	$0.548426\pi$
$264$			15705.1i			0.225337i
$265$		0			0
$266$	28389.3			0.401229
$267$	28891.2	−	28891.2i	0.405269	−	0.405269i
$268$	1810.02	+	1810.02i	0.0252008	+	0.0252008i
$269$			92538.2i			1.27884i	0.768857	+	0.639420i	$0.220826\pi$
$269$			92538.2i			1.27884i	−0.768857	+	0.639420i	$0.779174\pi$
$270$		0			0
$271$	−71744.3			−0.976897			−0.488449	−	0.872593i	$-0.662437\pi$
$271$	−71744.3			−0.976897			−0.488449	+	0.872593i	$0.662437\pi$
$272$	−29018.6	+	29018.6i	−0.392227	+	0.392227i
$273$	40946.7	+	40946.7i	0.549406	+	0.549406i
$274$		−	54820.8i		−	0.730204i
$275$		0			0
$276$	2430.54			0.0319069
$277$	−82433.8	+	82433.8i	−1.07435	+	1.07435i	−0.0773456	+	0.997004i	$0.524644\pi$
$277$	−82433.8	+	82433.8i	−1.07435	+	1.07435i	−0.997004	+	0.0773456i	$0.975356\pi$
$278$	32691.2	+	32691.2i	0.423001	+	0.423001i
$279$		−	35657.8i		−	0.458085i
$280$		0			0
$281$	94587.5			1.19790			0.598951	−	0.800786i	$-0.295585\pi$
$281$	94587.5			1.19790			0.598951	+	0.800786i	$0.295585\pi$
$282$	−60497.3	+	60497.3i	−0.760743	+	0.760743i
$283$	−109370.	−	109370.i	−1.36560	−	1.36560i	−0.866599	−	0.499005i	$-0.833699\pi$
$283$	−109370.	−	109370.i	−1.36560	−	1.36560i	−0.499005	−	0.866599i	$-0.666301\pi$
$284$			4110.64i			0.0509651i
$285$		0			0
$286$	−12456.8			−0.152291
$287$	−39462.0	+	39462.0i	−0.479088	+	0.479088i
$288$	11171.7	+	11171.7i	0.134690	+	0.134690i
$289$			59843.4i			0.716508i
$290$		0			0
$291$	164642.			1.94427
$292$	2526.49	−	2526.49i	0.0296314	−	0.0296314i
$293$	−84378.2	−	84378.2i	−0.982868	−	0.982868i	0.0169882	−	0.999856i	$-0.494592\pi$
$293$	−84378.2	−	84378.2i	−0.982868	−	0.982868i	−0.999856	+	0.0169882i	$0.994592\pi$
$294$			22498.2i			0.260287i
$295$		0			0
$296$	16454.2			0.187799
$297$	−16986.0	+	16986.0i	−0.192565	+	0.192565i
$298$	−17930.3	−	17930.3i	−0.201908	−	0.201908i
$299$		−	42182.5i		−	0.471835i
$300$		0			0
$301$	−61224.8			−0.675763
$302$	42551.9	−	42551.9i	0.466557	−	0.466557i
$303$	−123300.	−	123300.i	−1.34300	−	1.34300i
$304$		−	100042.i		−	1.08252i
$305$		0			0
$306$	−111071.			−1.18620
$307$	87611.2	−	87611.2i	0.929572	−	0.929572i	−0.0681062	−	0.997678i	$-0.521696\pi$
$307$	87611.2	−	87611.2i	0.929572	−	0.929572i	0.997678	+	0.0681062i	$0.0216957\pi$
$308$	−143.303	−	143.303i	−0.00151062	−	0.00151062i
$309$			35789.7i			0.374836i
$310$		0			0
$311$	−6128.69			−0.0633647			−0.0316823	−	0.999498i	$-0.510086\pi$
$311$	−6128.69			−0.0633647			−0.0316823	+	0.999498i	$0.510086\pi$
$312$	138240.	−	138240.i	1.42011	−	1.42011i
$313$	−51652.1	−	51652.1i	−0.527229	−	0.527229i	0.392516	−	0.919745i	$-0.371605\pi$
$313$	−51652.1	−	51652.1i	−0.527229	−	0.527229i	−0.919745	+	0.392516i	$0.871605\pi$
$314$			51719.6i			0.524561i
$315$		0			0
$316$	5239.54			0.0524709
$317$	−14665.0	+	14665.0i	−0.145937	+	0.145937i	−0.776300	−	0.630363i	$-0.782906\pi$
$317$	−14665.0	+	14665.0i	−0.145937	+	0.145937i	0.630363	+	0.776300i	$0.282906\pi$
$318$	−45928.2	−	45928.2i	−0.454177	−	0.454177i
$319$		−	23947.4i		−	0.235330i
$320$		0			0
$321$	2396.89			0.0232616
$322$	11588.6	−	11588.6i	0.111768	−	0.111768i
$323$	40814.4	+	40814.4i	0.391208	+	0.391208i
$324$			7224.98i			0.0688250i
$325$		0			0
$326$	−17975.1			−0.169136
$327$	−87769.0	+	87769.0i	−0.820816	+	0.820816i
$328$	133227.	+	133227.i	1.23835	+	1.23835i
$329$			24157.1i			0.223179i
$330$		0			0
$331$	−185767.			−1.69555			−0.847777	−	0.530352i	$-0.822060\pi$
$331$	−185767.			−1.69555			−0.847777	+	0.530352i	$0.822060\pi$
$332$	1774.99	−	1774.99i	0.0161035	−	0.0161035i
$333$	32868.7	+	32868.7i	0.296411	+	0.296411i
$334$		−	180604.i		−	1.61896i
$335$		0			0
$336$	79281.8			0.702255
$337$	15311.6	−	15311.6i	0.134822	−	0.134822i	−0.636475	−	0.771297i	$-0.719608\pi$
$337$	15311.6	−	15311.6i	0.134822	−	0.134822i	0.771297	+	0.636475i	$0.219608\pi$
$338$	27118.4	+	27118.4i	0.237373	+	0.237373i
$339$		−	67291.6i		−	0.585547i
$340$		0			0
$341$	3158.98			0.0271668
$342$	191459.	−	191459.i	1.63690	−	1.63690i
$343$	4491.86	+	4491.86i	0.0381802	+	0.0381802i
$344$			206700.i			1.74672i
$345$		0			0
$346$	−125235.			−1.04610
$347$	73106.7	−	73106.7i	0.607153	−	0.607153i	−0.335048	−	0.942201i	$-0.608753\pi$
$347$	73106.7	−	73106.7i	0.607153	−	0.607153i	0.942201	+	0.335048i	$0.108753\pi$
$348$	−12145.7	−	12145.7i	−0.100291	−	0.100291i
$349$		−	30531.6i		−	0.250668i	−0.992115	−	0.125334i	$-0.960000\pi$
$349$		−	30531.6i		−	0.250668i	0.992115	−	0.125334i	$-0.0400002\pi$
$350$		0			0
$351$	299029.			2.42716
$352$	−989.719	+	989.719i	−0.00798779	+	0.00798779i
$353$	−145186.	−	145186.i	−1.16513	−	1.16513i	−0.983337	−	0.181792i	$-0.941810\pi$
$353$	−145186.	−	145186.i	−1.16513	−	1.16513i	−0.181792	−	0.983337i	$-0.558190\pi$
$354$		−	49890.6i		−	0.398119i
$355$		0			0
$356$	1780.03			0.0140451
$357$	−32344.8	+	32344.8i	−0.253786	+	0.253786i
$358$	−55464.1	−	55464.1i	−0.432759	−	0.432759i
$359$			231453.i			1.79587i	0.440128	+	0.897935i	$0.354933\pi$
$359$			231453.i			1.79587i	−0.440128	+	0.897935i	$0.645067\pi$
$360$		0			0
$361$	−10387.0			−0.0797031
$362$	−130121.	+	130121.i	−0.992954	+	0.992954i
$363$	163393.	+	163393.i	1.24000	+	1.24000i
$364$			2522.78i			0.0190404i
$365$		0			0
$366$	185210.			1.38262
$367$	23938.0	−	23938.0i	0.177728	−	0.177728i	−0.612637	−	0.790365i	$-0.709891\pi$
$367$	23938.0	−	23938.0i	0.177728	−	0.177728i	0.790365	+	0.612637i	$0.209891\pi$
$368$	−40837.3	−	40837.3i	−0.301551	−	0.301551i
$369$			532266.i			3.90909i
$370$		0			0
$371$	−18339.6			−0.133242
$372$	1602.18	−	1602.18i	0.0115778	−	0.0115778i
$373$	74646.5	+	74646.5i	0.536527	+	0.536527i	0.922507	−	0.385980i	$-0.126137\pi$
$373$	74646.5	+	74646.5i	0.536527	+	0.536527i	−0.385980	+	0.922507i	$0.626137\pi$
$374$		−	9839.93i		−	0.0703475i
$375$		0			0
$376$	81556.5			0.576877
$377$	−210791.	+	210791.i	−1.48309	+	1.48309i
$378$	82150.7	+	82150.7i	0.574947	+	0.574947i
$379$		−	216518.i		−	1.50736i	−0.657244	−	0.753678i	$-0.728278\pi$
$379$		−	216518.i		−	1.50736i	0.657244	−	0.753678i	$-0.271722\pi$
$380$		0			0
$381$	−220535.			−1.51925
$382$	73715.3	−	73715.3i	0.505162	−	0.505162i
$383$	60012.3	+	60012.3i	0.409112	+	0.409112i	0.881429	−	0.472317i	$-0.156582\pi$
$383$	60012.3	+	60012.3i	0.409112	+	0.409112i	−0.472317	+	0.881429i	$0.656582\pi$
$384$		−	278891.i		−	1.89135i
$385$		0			0
$386$	−140399.			−0.942300
$387$	−412902.	+	412902.i	−2.75693	+	2.75693i
$388$	5071.92	+	5071.92i	0.0336906	+	0.0336906i
$389$		−	81329.9i		−	0.537466i	−0.963215	−	0.268733i	$-0.913395\pi$
$389$		−	81329.9i		−	0.537466i	0.963215	−	0.268733i	$-0.0866050\pi$
$390$		0			0
$391$	33321.0			0.217954
$392$	15164.9	−	15164.9i	0.0986888	−	0.0986888i
$393$	230384.	+	230384.i	1.49165	+	1.49165i
$394$			61170.6i			0.394049i
$395$		0			0
$396$	−1932.88			−0.0123258
$397$	123071.	−	123071.i	0.780862	−	0.780862i	−0.199115	−	0.979976i	$-0.563807\pi$
$397$	123071.	−	123071.i	0.780862	−	0.780862i	0.979976	+	0.199115i	$0.0638066\pi$
$398$	5556.79	+	5556.79i	0.0350799	+	0.0350799i
$399$		−	111509.i		−	0.700430i
$400$		0			0
$401$	115445.			0.717937			0.358969	−	0.933350i	$-0.383128\pi$
$401$	115445.			0.717937			0.358969	+	0.933350i	$0.383128\pi$
$402$	169780.	−	169780.i	1.05059	−	1.05059i
$403$	−27806.1	−	27806.1i	−0.171210	−	0.171210i
$404$		−	7596.66i		−	0.0465436i
$405$		0			0
$406$	−115819.			−0.702632
$407$	−2911.89	+	2911.89i	−0.0175787	+	0.0175787i
$408$	109199.	+	109199.i	0.655992	+	0.655992i
$409$		−	34541.9i		−	0.206490i	−0.994656	−	0.103245i	$-0.967077\pi$
$409$		−	34541.9i		−	0.206490i	0.994656	−	0.103245i	$-0.0329226\pi$
$410$		0			0
$411$	−215328.			−1.27473
$412$	−1102.53	+	1102.53i	−0.00649522	+	0.00649522i
$413$	−9960.89	−	9960.89i	−0.0583980	−	0.0583980i
$414$		−	156308.i		−	0.911968i
$415$		0			0
$416$	17423.5			0.100681
$417$	128406.	−	128406.i	0.738438	−	0.738438i
$418$	16961.6	+	16961.6i	0.0970767	+	0.0970767i
$419$			64910.6i			0.369732i	0.982764	+	0.184866i	$0.0591852\pi$
$419$			64910.6i			0.369732i	−0.982764	+	0.184866i	$0.940815\pi$
$420$		0			0
$421$	275775.			1.55593			0.777966	−	0.628307i	$-0.216252\pi$
$421$	275775.			1.55593			0.777966	+	0.628307i	$0.216252\pi$
$422$	8173.03	−	8173.03i	0.0458942	−	0.0458942i
$423$	162916.	+	162916.i	0.910509	+	0.910509i
$424$			61915.9i			0.344406i
$425$		0			0
$426$	385579.			2.12468
$427$	36978.0	−	36978.0i	0.202809	−	0.202809i
$428$	73.8378	+	73.8378i	0.000403080	+	0.000403080i
$429$			48928.4i			0.265856i
$430$		0			0
$431$	260995.			1.40500			0.702501	−	0.711683i	$-0.252067\pi$
$431$	260995.			1.40500			0.702501	+	0.711683i	$0.252067\pi$
$432$	289493.	−	289493.i	1.55121	−	1.55121i
$433$	−216699.	−	216699.i	−1.15579	−	1.15579i	−0.985371	−	0.170423i	$-0.945486\pi$
$433$	−216699.	−	216699.i	−1.15579	−	1.15579i	−0.170423	−	0.985371i	$-0.554514\pi$
$434$		−	15278.1i		−	0.0811127i
$435$		0			0
$436$	−5407.56			−0.0284465
$437$	−57437.3	+	57437.3i	−0.300768	+	0.300768i
$438$	−236985.	−	236985.i	−1.23530	−	1.23530i
$439$		−	295240.i		−	1.53196i	−0.642867	−	0.765978i	$-0.722255\pi$
$439$		−	295240.i		−	1.53196i	0.642867	−	0.765978i	$-0.277745\pi$
$440$		0			0
$441$	60586.5			0.311529
$442$	−86613.4	+	86613.4i	−0.443344	+	0.443344i
$443$	140162.	+	140162.i	0.714207	+	0.714207i	0.967413	−	0.253205i	$-0.0814848\pi$
$443$	140162.	+	140162.i	0.714207	+	0.714207i	−0.253205	+	0.967413i	$0.581485\pi$
$444$			2953.72i			0.0149832i
$445$		0			0
$446$	16208.9			0.0814862
$447$	−70427.5	+	70427.5i	−0.352474	+	0.352474i
$448$	−51095.6	−	51095.6i	−0.254582	−	0.254582i
$449$		−	125616.i		−	0.623094i	−0.950231	−	0.311547i	$-0.899153\pi$
$449$		−	125616.i		−	0.623094i	0.950231	−	0.311547i	$-0.100847\pi$
$450$		0			0
$451$	−47154.3			−0.231829
$452$	2072.96	−	2072.96i	0.0101465	−	0.0101465i
$453$	−167138.	−	167138.i	−0.814475	−	0.814475i
$454$			34087.6i			0.165381i
$455$		0			0
$456$	−376465.			−1.81048
$457$	231172.	−	231172.i	1.10689	−	1.10689i	0.113328	−	0.993558i	$-0.463849\pi$
$457$	231172.	−	231172.i	1.10689	−	1.10689i	0.993558	−	0.113328i	$-0.0361511\pi$
$458$	111640.	+	111640.i	0.532219	+	0.532219i
$459$			236211.i			1.12118i
$460$		0			0
$461$	86474.0			0.406896			0.203448	−	0.979086i	$-0.434785\pi$
$461$	86474.0			0.406896			0.203448	+	0.979086i	$0.434785\pi$
$462$	−13441.9	+	13441.9i	−0.0629761	+	0.0629761i
$463$	−8481.44	−	8481.44i	−0.0395647	−	0.0395647i	0.687048	−	0.726612i	$-0.258906\pi$
$463$	−8481.44	−	8481.44i	−0.0395647	−	0.0395647i	−0.726612	+	0.687048i	$0.758906\pi$
$464$			408137.i			1.89570i
$465$		0			0
$466$	279311.			1.28622
$467$	−59451.7	+	59451.7i	−0.272603	+	0.272603i	−0.830147	−	0.557544i	$-0.811744\pi$
$467$	−59451.7	+	59451.7i	−0.272603	+	0.272603i	0.557544	+	0.830147i	$0.311744\pi$
$468$	17013.7	+	17013.7i	0.0776796	+	0.0776796i
$469$		−	67794.8i		−	0.308213i
$470$		0			0
$471$	203147.			0.915733
$472$	−33628.8	+	33628.8i	−0.150948	+	0.150948i
$473$	−36579.7	−	36579.7i	−0.163500	−	0.163500i
$474$		−	491470.i		−	2.18746i
$475$		0			0
$476$	−1992.81			−0.00879531
$477$	−123683.	+	123683.i	−0.543590	+	0.543590i
$478$	38263.0	+	38263.0i	0.167465	+	0.167465i
$479$		−	214582.i		−	0.935239i	−0.883930	−	0.467619i	$-0.845112\pi$
$479$		−	214582.i		−	0.935239i	0.883930	−	0.467619i	$-0.154888\pi$
$480$		0			0
$481$	51262.4			0.221569
$482$	102018.	−	102018.i	0.439119	−	0.439119i
$483$	−45518.3	−	45518.3i	−0.195115	−	0.195115i
$484$			10066.9i			0.0429738i
$485$		0			0
$486$	169586.			0.717988
$487$	105943.	−	105943.i	0.446699	−	0.446699i	−0.447556	−	0.894256i	$-0.647706\pi$
$487$	105943.	−	105943.i	0.446699	−	0.446699i	0.894256	+	0.447556i	$0.147706\pi$
$488$	−124841.	−	124841.i	−0.524224	−	0.524224i
$489$			70603.5i			0.295263i
$490$		0			0
$491$	−269002.			−1.11581			−0.557907	−	0.829903i	$-0.688395\pi$
$491$	−269002.			−1.11581			−0.557907	+	0.829903i	$0.688395\pi$
$492$	−23915.8	+	23915.8i	−0.0987996	+	0.0987996i
$493$	−166509.	−	166509.i	−0.685084	−	0.685084i
$494$		−	298601.i		−	1.22359i
$495$		0			0
$496$	−53838.7			−0.218842
$497$	76982.5	−	76982.5i	0.311659	−	0.311659i
$498$	−166494.	−	166494.i	−0.671336	−	0.671336i
$499$		−	35396.7i		−	0.142155i	−0.997471	−	0.0710774i	$-0.977356\pi$
$499$		−	35396.7i		−	0.142155i	0.997471	−	0.0710774i	$-0.0226437\pi$
$500$		0			0
$501$	−709387.			−2.82623
$502$	212769.	−	212769.i	0.844307	−	0.844307i
$503$	125202.	+	125202.i	0.494850	+	0.494850i	0.909830	−	0.414980i	$-0.136211\pi$
$503$	125202.	+	125202.i	0.494850	+	0.494850i	−0.414980	+	0.909830i	$0.636211\pi$
$504$		−	204545.i		−	0.805246i
$505$		0			0
$506$	13847.5			0.0540844
$507$	106517.	−	106517.i	0.414385	−	0.414385i
$508$	−6793.73	−	6793.73i	−0.0263258	−	0.0263258i
$509$			43090.7i			0.166321i	0.996536	+	0.0831607i	$0.0265015\pi$
$509$			43090.7i			0.166321i	−0.996536	+	0.0831607i	$0.973499\pi$
$510$		0			0
$511$	−94630.4			−0.362401
$512$	−171796.	+	171796.i	−0.655348	+	0.655348i
$513$	−407169.	−	407169.i	−1.54718	−	1.54718i
$514$			347048.i			1.31360i
$515$		0			0
$516$	−37105.1			−0.139359
$517$	−14433.0	+	14433.0i	−0.0539978	+	0.0539978i
$518$	14083.1	+	14083.1i	0.0524853	+	0.0524853i
$519$			491903.i			1.82618i
$520$		0			0
$521$	−253399.			−0.933532			−0.466766	−	0.884381i	$-0.654581\pi$
$521$	−253399.			−0.933532			−0.466766	+	0.884381i	$0.654581\pi$
$522$	−781087.	+	781087.i	−2.86654	+	2.86654i
$523$	53364.3	+	53364.3i	0.195096	+	0.195096i	0.797894	−	0.602798i	$-0.205948\pi$
$523$	53364.3	+	53364.3i	0.195096	+	0.195096i	−0.602798	+	0.797894i	$0.705948\pi$
$524$			14194.2i			0.0516951i
$525$		0			0
$526$	334541.			1.20915
$527$	21964.8	−	21964.8i	0.0790870	−	0.0790870i
$528$	47368.1	+	47368.1i	0.169910	+	0.169910i
$529$		−	232949.i		−	0.832433i
$530$		0			0
$531$	−134353.			−0.476496
$532$	3435.11	−	3435.11i	0.0121372	−	0.0121372i
$533$	415063.	+	415063.i	1.46103	+	1.46103i
$534$		−	166967.i		−	0.585528i
$535$		0			0
$536$	−228881.			−0.796674
$537$	−217855.	+	217855.i	−0.755473	+	0.755473i
$538$	267396.	+	267396.i	0.923826	+	0.923826i
$539$			5367.46i			0.0184753i
$540$		0			0
$541$	285411.			0.975161			0.487580	−	0.873078i	$-0.337880\pi$
$541$	285411.			0.975161			0.487580	+	0.873078i	$0.337880\pi$
$542$	−207311.	+	207311.i	−0.705704	+	0.705704i
$543$	511095.	+	511095.i	1.73341	+	1.73341i
$544$			13763.3i			0.0465076i
$545$		0			0
$546$	236637.			0.793775
$547$	−139965.	+	139965.i	−0.467784	+	0.467784i	−0.901196	−	0.433412i	$-0.857309\pi$
$547$	−139965.	+	139965.i	−0.467784	+	0.467784i	0.433412	+	0.901196i	$0.357309\pi$
$548$	−6633.32	−	6633.32i	−0.0220887	−	0.0220887i
$549$		−	498762.i		−	1.65481i
$550$		0			0
$551$	574041.			1.89078
$552$	−153674.	+	153674.i	−0.504338	+	0.504338i
$553$	−98124.1	−	98124.1i	−0.320867	−	0.320867i
$554$			476397.i			1.55221i
$555$		0			0
$556$	7911.27			0.0255916
$557$	333543.	−	333543.i	1.07508	−	1.07508i	0.0781386	−	0.996943i	$-0.475102\pi$
$557$	333543.	−	333543.i	1.07508	−	1.07508i	0.996943	−	0.0781386i	$-0.0248977\pi$
$558$	−103036.	−	103036.i	−0.330918	−	0.330918i
$559$			643966.i			2.06082i
$560$		0			0
$561$	−38649.8			−0.122807
$562$	273318.	−	273318.i	0.865356	−	0.865356i
$563$	28193.8	+	28193.8i	0.0889480	+	0.0889480i	0.750181	−	0.661233i	$-0.229966\pi$
$563$	28193.8	+	28193.8i	0.0889480	+	0.0889480i	−0.661233	+	0.750181i	$0.729966\pi$
$564$			14640.4i			0.0460250i
$565$		0			0
$566$	−632065.			−1.97301
$567$	135307.	−	135307.i	0.420875	−	0.420875i
$568$	−259900.	−	259900.i	−0.805581	−	0.805581i
$569$		−	171092.i		−	0.528453i	−0.964461	−	0.264226i	$-0.914883\pi$
$569$		−	171092.i		−	0.528453i	0.964461	−	0.264226i	$-0.0851166\pi$
$570$		0			0
$571$	268834.			0.824540			0.412270	−	0.911062i	$-0.364736\pi$
$571$	268834.			0.824540			0.412270	+	0.911062i	$0.364736\pi$
$572$	−1507.27	+	1507.27i	−0.00460680	+	0.00460680i
$573$	−289543.	−	289543.i	−0.881868	−	0.881868i
$574$			228057.i			0.692180i
$575$		0			0
$576$	−689181.			−2.07725
$577$	−186519.	+	186519.i	−0.560235	+	0.560235i	−0.929374	−	0.369139i	$-0.879653\pi$
$577$	−186519.	+	186519.i	−0.560235	+	0.560235i	0.369139	+	0.929374i	$0.379653\pi$
$578$	172922.	+	172922.i	0.517600	+	0.517600i
$579$			551466.i			1.64499i
$580$		0			0
$581$	−66482.6			−0.196950
$582$	475747.	−	475747.i	1.40453	−	1.40453i
$583$	−10957.2	−	10957.2i	−0.0322377	−	0.0322377i
$584$			319481.i			0.936739i
$585$		0			0
$586$	−487634.			−1.42003
$587$	65684.5	−	65684.5i	0.190628	−	0.190628i	−0.605339	−	0.795967i	$-0.706963\pi$
$587$	65684.5	−	65684.5i	0.190628	−	0.190628i	0.795967	+	0.605339i	$0.206963\pi$
$588$	2722.28	+	2722.28i	0.00787369	+	0.00787369i
$589$			75723.7i			0.218274i
$590$		0			0
$591$	240269.			0.687896
$592$	49627.6	−	49627.6i	0.141605	−	0.141605i
$593$	240851.	+	240851.i	0.684917	+	0.684917i	0.961104	−	0.276187i	$-0.0890708\pi$
$593$	240851.	+	240851.i	0.684917	+	0.684917i	−0.276187	+	0.961104i	$0.589071\pi$
$594$			98164.4i			0.278215i
$595$		0			0
$596$	−4339.13			−0.0122155
$597$	21826.3	−	21826.3i	0.0612394	−	0.0612394i
$598$	−121889.	−	121889.i	−0.340850	−	0.340850i
$599$			560503.i			1.56216i	0.624433	+	0.781078i	$0.285330\pi$
$599$			560503.i			1.56216i	−0.624433	+	0.781078i	$0.714670\pi$
$600$		0			0
$601$	−34723.1			−0.0961324			−0.0480662	−	0.998844i	$-0.515306\pi$
$601$	−34723.1			−0.0961324			−0.0480662	+	0.998844i	$0.515306\pi$
$602$	−176914.	+	176914.i	−0.488167	+	0.488167i
$603$	−457210.	−	457210.i	−1.25742	−	1.25742i
$604$		−	10297.6i		−	0.0282267i
$605$		0			0
$606$	−712568.			−1.94035
$607$	−205346.	+	205346.i	−0.557327	+	0.557327i	−0.928545	−	0.371219i	$-0.878940\pi$
$607$	−205346.	+	205346.i	−0.557327	+	0.557327i	0.371219	+	0.928545i	$0.378940\pi$
$608$	−23724.5	−	23724.5i	−0.0641785	−	0.0641785i
$609$			454920.i			1.22659i
$610$		0			0
$611$	254086.			0.680610
$612$	−13439.6	+	13439.6i	−0.0358825	+	0.0358825i
$613$	130834.	+	130834.i	0.348177	+	0.348177i	0.859430	−	0.511253i	$-0.170819\pi$
$613$	130834.	+	130834.i	0.348177	+	0.348177i	−0.511253	+	0.859430i	$0.670819\pi$
$614$		−	506318.i		−	1.34303i
$615$		0			0
$616$	18121.0			0.0477552
$617$	424045.	−	424045.i	1.11389	−	1.11389i	0.121270	−	0.992620i	$-0.461303\pi$
$617$	424045.	−	424045.i	1.11389	−	1.11389i	0.992620	−	0.121270i	$-0.0386965\pi$
$618$	103417.	+	103417.i	0.270779	+	0.270779i
$619$		−	184571.i		−	0.481707i	−0.970562	−	0.240853i	$-0.922573\pi$
$619$		−	184571.i		−	0.481707i	0.970562	−	0.240853i	$-0.0774273\pi$
$620$		0			0
$621$	−332415.			−0.861980
$622$	−17709.3	+	17709.3i	−0.0457742	+	0.0457742i
$623$	−33335.6	−	33335.6i	−0.0858881	−	0.0858881i
$624$		−	833890.i		−	2.14161i
$625$		0			0
$626$	−298505.			−0.761733
$627$	66622.8	−	66622.8i	0.169468	−	0.169468i
$628$	6258.07	+	6258.07i	0.0158680	+	0.0158680i
$629$			40493.4i			0.102349i
$630$		0			0
$631$	−57625.9			−0.144730			−0.0723651	−	0.997378i	$-0.523055\pi$
$631$	−57625.9			−0.144730			−0.0723651	+	0.997378i	$0.523055\pi$
$632$	−331276.	+	331276.i	−0.829383	+	0.829383i
$633$	−32102.5	−	32102.5i	−0.0801181	−	0.0801181i
$634$			84751.4i			0.210848i
$635$		0			0
$636$	−11114.6			−0.0274777
$637$	47245.6	−	47245.6i	0.116435	−	0.116435i
$638$	−69197.8	−	69197.8i	−0.170001	−	0.170001i
$639$		−	1.03835e6i		−	2.54296i
$640$		0			0
$641$	727896.			1.77155			0.885775	−	0.464115i	$-0.153627\pi$
$641$	727896.			1.77155			0.885775	+	0.464115i	$0.153627\pi$
$642$	6926.00	−	6926.00i	0.0168040	−	0.0168040i
$643$	21671.5	+	21671.5i	0.0524163	+	0.0524163i	0.732829	−	0.680413i	$-0.238199\pi$
$643$	21671.5	+	21671.5i	0.0524163	+	0.0524163i	−0.680413	+	0.732829i	$0.738199\pi$
$644$		−	2804.44i		−	0.00676199i
$645$		0			0
$646$	235872.			0.565213
$647$	364642.	−	364642.i	0.871081	−	0.871081i	−0.121510	−	0.992590i	$-0.538774\pi$
$647$	364642.	−	364642.i	0.871081	−	0.871081i	0.992590	+	0.121510i	$0.0387736\pi$
$648$	−456807.	−	456807.i	−1.08788	−	1.08788i
$649$		−	11902.6i		−	0.0282586i
$650$		0			0
$651$	−60010.0			−0.141600
$652$	−2174.99	+	2174.99i	−0.00511636	+	0.00511636i
$653$	−159295.	−	159295.i	−0.373574	−	0.373574i	0.495203	−	0.868777i	$-0.335094\pi$
$653$	−159295.	−	159295.i	−0.373574	−	0.373574i	−0.868777	+	0.495203i	$0.835094\pi$
$654$			507230.i			1.18590i
$655$		0			0
$656$	803653.			1.86750
$657$	−638191.	+	638191.i	−1.47849	+	1.47849i
$658$	69803.8	+	69803.8i	0.161223	+	0.161223i
$659$		−	76560.3i		−	0.176292i	−0.996108	−	0.0881460i	$-0.971906\pi$
$659$		−	76560.3i		−	0.176292i	0.996108	−	0.0881460i	$-0.0280942\pi$
$660$		0			0
$661$	692129.			1.58410			0.792052	−	0.610453i	$-0.209013\pi$
$661$	692129.			1.58410			0.792052	+	0.610453i	$0.209013\pi$
$662$	−536787.	+	536787.i	−1.22486	+	1.22486i
$663$	340205.	+	340205.i	0.773951	+	0.773951i
$664$			224451.i			0.509079i
$665$		0			0
$666$	189953.			0.428251
$667$	234325.	−	234325.i	0.526704	−	0.526704i
$668$	−21853.1	−	21853.1i	−0.0489734	−	0.0489734i
$669$		−	63666.3i		−	0.142252i
$670$		0			0
$671$	44186.1			0.0981388
$672$	18801.3	−	18801.3i	0.0416342	−	0.0416342i
$673$	−253100.	−	253100.i	−0.558808	−	0.558808i	0.370160	−	0.928968i	$-0.379303\pi$
$673$	−253100.	−	253100.i	−0.558808	−	0.558808i	−0.928968	+	0.370160i	$0.879303\pi$
$674$		−	88488.2i		−	0.194789i
$675$		0			0
$676$	6562.66			0.0143611
$677$	305692.	−	305692.i	0.666970	−	0.666970i	−0.290043	−	0.957014i	$-0.593670\pi$
$677$	305692.	−	305692.i	0.666970	−	0.666970i	0.957014	+	0.290043i	$0.0936697\pi$
$678$	−194444.	−	194444.i	−0.422995	−	0.422995i
$679$		−	189970.i		−	0.412046i
$680$		0			0
$681$	133891.			0.288707
$682$	9128.11	−	9128.11i	0.0196251	−	0.0196251i
$683$	−209466.	−	209466.i	−0.449026	−	0.449026i	0.446004	−	0.895031i	$-0.352847\pi$
$683$	−209466.	−	209466.i	−0.449026	−	0.449026i	−0.895031	+	0.446004i	$0.852847\pi$
$684$		−	46333.0i		−	0.0990327i
$685$		0			0
$686$	25959.1			0.0551622
$687$	438507.	−	438507.i	0.929101	−	0.929101i
$688$	623430.	+	623430.i	1.31707	+	1.31707i
$689$			192896.i			0.406336i
$690$		0			0
$691$	−423474.			−0.886892			−0.443446	−	0.896301i	$-0.646244\pi$
$691$	−423474.			−0.886892			−0.443446	+	0.896301i	$0.646244\pi$
$692$	−15153.4	+	15153.4i	−0.0316444	+	0.0316444i
$693$	36198.3	+	36198.3i	0.0753741	+	0.0753741i
$694$		−	422494.i		−	0.877207i
$695$		0			0
$696$	1.53585e6			3.17052
$697$	−327869.	+	327869.i	−0.674893	+	0.674893i
$698$	−88223.2	−	88223.2i	−0.181081	−	0.181081i
$699$		−	1.09709e6i		−	2.24537i
$700$		0			0
$701$	−273872.			−0.557328			−0.278664	−	0.960389i	$-0.589892\pi$
$701$	−273872.			−0.557328			−0.278664	+	0.960389i	$0.589892\pi$
$702$	864066.	−	864066.i	1.75337	−	1.75337i
$703$	−69800.8	−	69800.8i	−0.141237	−	0.141237i
$704$		−	61055.7i		−	0.123191i
$705$		0			0
$706$	−839049.			−1.68336
$707$	−142267.	+	142267.i	−0.284621	+	0.284621i
$708$	−6036.77	−	6036.77i	−0.0120431	−	0.0120431i
$709$		−	694645.i		−	1.38188i	−0.722912	−	0.690940i	$-0.757197\pi$
$709$		−	694645.i		−	1.38188i	0.722912	−	0.690940i	$-0.242803\pi$
$710$		0			0
$711$	−1.32350e6			−2.61810
$712$	−112544.	+	112544.i	−0.222005	+	0.222005i
$713$	30910.6	+	30910.6i	0.0608034	+	0.0608034i
$714$			186926.i			0.366667i
$715$		0			0
$716$	−13422.3			−0.0261819
$717$	150292.	−	150292.i	0.292345	−	0.292345i
$718$	668802.	+	668802.i	1.29732	+	1.29732i
$719$			798522.i			1.54465i	0.635230	+	0.772323i	$0.280905\pi$
$719$			798522.i			1.54465i	−0.635230	+	0.772323i	$0.719095\pi$
$720$		0			0
$721$	41295.4			0.0794384
$722$	−30014.0	+	30014.0i	−0.0575770	+	0.0575770i
$723$	−400712.	−	400712.i	−0.766576	−	0.766576i
$724$			31489.2i			0.0600738i
$725$		0			0
$726$	944275.			1.79154
$727$	−213500.	+	213500.i	−0.403951	+	0.403951i	−0.879623	−	0.475672i	$-0.842205\pi$
$727$	−213500.	+	213500.i	−0.403951	+	0.403951i	0.475672	+	0.879623i	$0.342205\pi$
$728$	−159505.	−	159505.i	−0.300963	−	0.300963i
$729$			170788.i			0.321367i
$730$		0			0
$731$	−508685.			−0.951950
$732$	22410.4	−	22410.4i	0.0418242	−	0.0418242i
$733$	67650.5	+	67650.5i	0.125911	+	0.125911i	0.767254	−	0.641343i	$-0.221623\pi$
$733$	67650.5	+	67650.5i	0.125911	+	0.125911i	−0.641343	+	0.767254i	$0.721623\pi$
$734$		−	138341.i		−	0.256779i
$735$		0			0
$736$	−19368.8			−0.0357558
$737$	40505.0	−	40505.0i	0.0745716	−	0.0745716i
$738$	1.53802e6	+	1.53802e6i	2.82390	+	2.82390i
$739$		−	619888.i		−	1.13507i	−0.823348	−	0.567537i	$-0.807896\pi$
$739$		−	619888.i		−	1.13507i	0.823348	−	0.567537i	$-0.192104\pi$
$740$		0			0
$741$	−1.17286e6			−2.13604
$742$	−52993.5	+	52993.5i	−0.0962531	+	0.0962531i
$743$	−515480.	−	515480.i	−0.933758	−	0.933758i	0.0641808	−	0.997938i	$-0.479557\pi$
$743$	−515480.	−	515480.i	−0.933758	−	0.933758i	−0.997938	+	0.0641808i	$0.979557\pi$
$744$			202599.i			0.366009i
$745$		0			0
$746$	431393.			0.775167
$747$	−448361.	+	448361.i	−0.803501	+	0.803501i
$748$	−1190.63	−	1190.63i	−0.00212801	−	0.00212801i
$749$		−	2765.61i		−	0.00492978i
$750$		0			0
$751$	−678013.			−1.20215			−0.601075	−	0.799193i	$-0.705261\pi$
$751$	−678013.			−1.20215			−0.601075	+	0.799193i	$0.705261\pi$
$752$	245983.	−	245983.i	0.434980	−	0.434980i
$753$	−835725.	−	835725.i	−1.47392	−	1.47392i
$754$			1.21819e6i			2.14276i
$755$		0			0
$756$	19880.5			0.0347843
$757$	−567306.	+	567306.i	−0.989978	+	0.989978i	−0.999950	−	0.00997241i	$-0.996826\pi$
$757$	−567306.	+	567306.i	−0.989978	+	0.989978i	0.00997241	+	0.999950i	$0.496826\pi$
$758$	−625645.	−	625645.i	−1.08890	−	1.08890i
$759$		−	54391.2i		−	0.0944158i
$760$		0			0
$761$	−2140.48			−0.00369608			−0.00184804	−	0.999998i	$-0.500588\pi$
$761$	−2140.48			−0.00369608			−0.00184804	+	0.999998i	$0.500588\pi$
$762$	−637253.	+	637253.i	−1.09749	+	1.09749i
$763$	101271.	+	101271.i	0.173954	+	0.173954i
$764$		−	17839.1i		−	0.0305623i
$765$		0			0
$766$	346820.			0.591080
$767$	−104769.	+	104769.i	−0.178091	+	0.178091i
$768$	−97342.3	−	97342.3i	−0.165036	−	0.165036i
$769$			832779.i			1.40824i	0.710081	+	0.704120i	$0.248659\pi$
$769$			832779.i			1.40824i	−0.710081	+	0.704120i	$0.751341\pi$
$770$		0			0
$771$	1.36316e6			2.29317
$772$	−16988.3	+	16988.3i	−0.0285046	+	0.0285046i
$773$	488655.	+	488655.i	0.817792	+	0.817792i	0.985788	−	0.167996i	$-0.0537294\pi$
$773$	488655.	+	488655.i	0.817792	+	0.817792i	−0.167996	+	0.985788i	$0.553729\pi$
$774$			2.38622e6i			3.98317i
$775$		0			0
$776$	−641355.			−1.06506
$777$	55316.2	−	55316.2i	0.0916242	−	0.0916242i
$778$	−235009.	−	235009.i	−0.388262	−	0.388262i
$779$		−	1.13033e6i		−	1.86265i
$780$		0			0
$781$	91988.7			0.150811
$782$	96283.5	−	96283.5i	0.157449	−	0.157449i
$783$	1.66111e6	+	1.66111e6i	2.70942	+	2.70942i
$784$		−	91477.9i		−	0.148828i
$785$		0			0
$786$	1.33142e6			2.15512
$787$	−525759.	+	525759.i	−0.848863	+	0.848863i	−0.989991	−	0.141129i	$-0.954927\pi$
$787$	−525759.	+	525759.i	−0.848863	+	0.848863i	0.141129	+	0.989991i	$0.454927\pi$
$788$	7401.64	+	7401.64i	0.0119200	+	0.0119200i
$789$		−	1.31403e6i		−	2.11082i
$790$		0			0
$791$	−77643.3			−0.124094
$792$	122209.	−	122209.i	0.194828	−	0.194828i
$793$	−388936.	−	388936.i	−0.618489	−	0.618489i
$794$		−	711245.i		−	1.12818i
$795$		0			0
$796$	1344.74			0.00212233
$797$	515738.	−	515738.i	0.811918	−	0.811918i	−0.173003	−	0.984921i	$-0.555347\pi$
$797$	515738.	−	515738.i	0.811918	−	0.811918i	0.984921	+	0.173003i	$0.0553471\pi$
$798$	−322214.	−	322214.i	−0.505986	−	0.505986i
$799$			200709.i			0.314393i
$800$		0			0
$801$	−449634.			−0.700799
$802$	333587.	−	333587.i	0.518633	−	0.518633i
$803$	−56538.3	−	56538.3i	−0.0876823	−	0.0876823i
$804$		−	41086.8i		−	0.0635610i
$805$		0			0
$806$	−160696.			−0.247363
$807$	1.05029e6	−	1.05029e6i	1.61274	−	1.61274i
$808$	480307.	+	480307.i	0.735692	+	0.735692i
$809$		−	870048.i		−	1.32937i	−0.747123	−	0.664685i	$-0.768566\pi$
$809$		−	870048.i		−	1.32937i	0.747123	−	0.664685i	$-0.231434\pi$
$810$		0			0
$811$	496320.			0.754606			0.377303	−	0.926090i	$-0.376852\pi$
$811$	496320.			0.754606			0.377303	+	0.926090i	$0.376852\pi$
$812$	−14014.1	+	14014.1i	−0.0212546	+	0.0212546i
$813$	814286.	+	814286.i	1.23196	+	1.23196i
$814$			16828.3i			0.0253975i
$815$		0			0
$816$	658711.			0.989270
$817$	876849.	−	876849.i	1.31365	−	1.31365i
$818$	−99811.4	−	99811.4i	−0.149167	−	0.149167i
$819$		−	637252.i		−	0.950044i
$820$		0			0
$821$	−11775.0			−0.0174692			−0.00873462	−	0.999962i	$-0.502780\pi$
$821$	−11775.0			−0.0174692			−0.00873462	+	0.999962i	$0.502780\pi$
$822$	−622206.	+	622206.i	−0.920854	+	0.920854i
$823$	517110.	+	517110.i	0.763455	+	0.763455i	0.976945	−	0.213490i	$-0.0684831\pi$
$823$	517110.	+	517110.i	0.763455	+	0.763455i	−0.213490	+	0.976945i	$0.568483\pi$
$824$		−	139417.i		−	0.205334i
$825$		0			0
$826$	−57565.5			−0.0843727
$827$	20348.5	−	20348.5i	0.0297524	−	0.0297524i	−0.692074	−	0.721826i	$-0.743303\pi$
$827$	20348.5	−	20348.5i	0.0297524	−	0.0297524i	0.721826	+	0.692074i	$0.243303\pi$
$828$	−18913.2	−	18913.2i	−0.0275871	−	0.0275871i
$829$			325196.i			0.473190i	0.971608	+	0.236595i	$0.0760315\pi$
$829$			325196.i			0.473190i	−0.971608	+	0.236595i	$0.923968\pi$
$830$		0			0
$831$	1.87122e6			2.70971
$832$	−537427.	+	537427.i	−0.776377	+	0.776377i
$833$	37320.5	+	37320.5i	0.0537846	+	0.0537846i
$834$		−	742079.i		−	1.06689i
$835$		0			0
$836$	4104.72			0.00587314
$837$	−219123.	+	219123.i	−0.312779	+	0.312779i
$838$	187564.	+	187564.i	0.267092	+	0.267092i
$839$		−	853915.i		−	1.21308i	−0.795052	−	0.606542i	$-0.792556\pi$
$839$		−	853915.i		−	1.21308i	0.795052	−	0.606542i	$-0.207444\pi$
$840$		0			0
$841$	−1.63462e6			−2.31113
$842$	796872.	−	796872.i	1.12399	−	1.12399i
$843$	−1.07355e6	−	1.07355e6i	−1.51066	−	1.51066i
$844$		−	1977.87i		−	0.00277660i
$845$		0			0
$846$	941518.			1.31549
$847$	188529.	−	188529.i	0.262791	−	0.262791i
$848$	186745.	+	186745.i	0.259691	+	0.259691i
$849$			2.48266e6i			3.44430i
$850$		0			0
$851$	−56985.7			−0.0786876
$852$	46655.0	−	46655.0i	0.0642716	−	0.0642716i
$853$	−85442.8	−	85442.8i	−0.117429	−	0.117429i	0.645950	−	0.763380i	$-0.276461\pi$
$853$	−85442.8	−	85442.8i	−0.117429	−	0.117429i	−0.763380	+	0.645950i	$0.776461\pi$
$854$		−	213701.i		−	0.293016i
$855$		0			0
$856$	−9336.96			−0.0127426
$857$	−612597.	+	612597.i	−0.834091	+	0.834091i	−0.988074	−	0.153983i	$-0.950790\pi$
$857$	−612597.	+	612597.i	−0.834091	+	0.834091i	0.153983	+	0.988074i	$0.450790\pi$
$858$	141382.	+	141382.i	0.192053	+	0.192053i
$859$		−	1.25212e6i		−	1.69691i	−0.529264	−	0.848457i	$-0.677532\pi$
$859$		−	1.25212e6i		−	1.69691i	0.529264	−	0.848457i	$-0.322468\pi$
$860$		0			0
$861$	895773.			1.20835
$862$	754163.	−	754163.i	1.01496	−	1.01496i
$863$	640507.	+	640507.i	0.860008	+	0.860008i	0.991339	−	0.131330i	$-0.0419249\pi$
$863$	640507.	+	640507.i	0.860008	+	0.860008i	−0.131330	+	0.991339i	$0.541925\pi$
$864$		−	137304.i		−	0.183931i
$865$		0			0
$866$	−1.25233e6			−1.66988
$867$	679212.	−	679212.i	0.903582	−	0.903582i
$868$	−1848.65	−	1848.65i	−0.00245366	−	0.00245366i
$869$		−	117251.i		−	0.155267i
$870$		0			0
$871$	−713069.			−0.939930
$872$	341899.	−	341899.i	0.449640	−	0.449640i
$873$	−1.28116e6	−	1.28116e6i	−1.68103	−	1.68103i
$874$			331939.i			0.434545i
$875$		0			0
$876$	−57350.5			−0.0747359
$877$	−366024.	+	366024.i	−0.475895	+	0.475895i	−0.903816	−	0.427921i	$-0.859246\pi$
$877$	−366024.	+	366024.i	−0.475895	+	0.475895i	0.427921	+	0.903816i	$0.359246\pi$
$878$	−853118.	−	853118.i	−1.10667	−	1.10667i
$879$			1.91536e6i			2.47897i
$880$		0			0
$881$	634454.			0.817425			0.408713	−	0.912663i	$-0.365978\pi$
$881$	634454.			0.817425			0.408713	+	0.912663i	$0.365978\pi$
$882$	175069.	−	175069.i	0.225047	−	0.225047i
$883$	−15889.4	−	15889.4i	−0.0203791	−	0.0203791i	0.696844	−	0.717223i	$-0.254587\pi$
$883$	−15889.4	−	15889.4i	−0.0203791	−	0.0203791i	−0.717223	+	0.696844i	$0.754587\pi$
$884$			20960.4i			0.0268223i
$885$		0			0
$886$	810020.			1.03188
$887$	526509.	−	526509.i	0.669204	−	0.669204i	−0.288328	−	0.957532i	$-0.593099\pi$
$887$	526509.	−	526509.i	0.669204	−	0.669204i	0.957532	+	0.288328i	$0.0930992\pi$
$888$	−186752.	−	186752.i	−0.236832	−	0.236832i
$889$			254461.i			0.321971i
$890$		0			0
$891$	161682.			0.203660
$892$	1961.28	−	1961.28i	0.00246496	−	0.00246496i
$893$	−345973.	−	345973.i	−0.433850	−	0.433850i
$894$			407011.i			0.509250i
$895$		0			0
$896$	−321794.			−0.400831
$897$	−478764.	+	478764.i	−0.595027	+	0.595027i
$898$	−362978.	−	362978.i	−0.450119	−	0.450119i
$899$		−	308927.i		−	0.382241i
$900$		0			0
$901$	−152374.			−0.187698
$902$	−136256.	+	136256.i	−0.167472	+	0.167472i
$903$	694891.	+	694891.i	0.852199	+	0.852199i
$904$			262131.i			0.320760i
$905$		0			0
$906$	−965913.			−1.17674
$907$	−891273.	+	891273.i	−1.08342	+	1.08342i	−0.0872297	+	0.996188i	$0.527801\pi$
$907$	−891273.	+	891273.i	−1.08342	+	1.08342i	−0.996188	+	0.0872297i	$0.972199\pi$
$908$	4124.60	+	4124.60i	0.00500277	+	0.00500277i
$909$			1.91891e6i			2.32235i
$910$		0			0
$911$	222639.			0.268265			0.134133	−	0.990963i	$-0.457175\pi$
$911$	222639.			0.268265			0.134133	+	0.990963i	$0.457175\pi$
$912$	−1.13546e6	+	1.13546e6i	−1.36515	+	1.36515i
$913$	−39721.0	−	39721.0i	−0.0476517	−	0.0476517i
$914$		−	1.33598e6i		−	1.59921i
$915$		0			0
$916$	27017.0			0.0321993
$917$	265824.	−	265824.i	0.316123	−	0.316123i
$918$	682548.	+	682548.i	0.809930	+	0.809930i
$919$		−	1.11569e6i		−	1.32103i	−0.750811	−	0.660517i	$-0.770337\pi$
$919$		−	1.11569e6i		−	1.32103i	0.750811	−	0.660517i	$-0.229663\pi$
$920$		0			0
$921$	−1.98874e6			−2.34455
$922$	249873.	−	249873.i	0.293939	−	0.293939i
$923$	−809706.	−	809706.i	−0.950439	−	0.950439i
$924$			3252.93i			0.00381005i
$925$		0			0
$926$	−49015.5			−0.0571625
$927$	278497.	−	278497.i	0.324087	−	0.324087i
$928$	96788.0	+	96788.0i	0.112389	+	0.112389i
$929$			371623.i			0.430597i	0.976548	+	0.215298i	$0.0690724\pi$
$929$			371623.i			0.430597i	−0.976548	+	0.215298i	$0.930928\pi$
$930$		0			0
$931$	−128663.			−0.148441
$932$	33796.6	−	33796.6i	0.0389082	−	0.0389082i
$933$	69559.6	+	69559.6i	0.0799086	+	0.0799086i
$934$			343580.i			0.393853i
$935$		0			0
$936$	−2.15142e6			−2.45569
$937$	−1.15042e6	+	1.15042e6i	−1.31032	+	1.31032i	−0.389140	+	0.921178i	$0.627228\pi$
$937$	−1.15042e6	+	1.15042e6i	−1.31032	+	1.31032i	−0.921178	+	0.389140i	$0.872772\pi$
$938$	−195898.	−	195898.i	−0.222651	−	0.222651i
$939$			1.17248e6i			1.32977i
$940$		0			0
$941$	−1.30963e6			−1.47900			−0.739500	−	0.673156i	$-0.764938\pi$
$941$	−1.30963e6			−1.47900			−0.739500	+	0.673156i	$0.764938\pi$
$942$	587008.	−	587008.i	0.661519	−	0.661519i
$943$	−461404.	−	461404.i	−0.518869	−	0.518869i
$944$			202856.i			0.227638i
$945$		0			0
$946$	−211399.			−0.236223
$947$	−1.14832e6	+	1.14832e6i	−1.28045	+	1.28045i	−0.340039	+	0.940411i	$0.610440\pi$
$947$	−1.14832e6	+	1.14832e6i	−1.28045	+	1.28045i	−0.940411	+	0.340039i	$0.889560\pi$
$948$	−59467.8	−	59467.8i	−0.0661707	−	0.0661707i
$949$			995328.i			1.10518i
$950$		0			0
$951$	332891.			0.368079
$952$	125997.	−	125997.i	0.139023	−	0.139023i
$953$	160332.	+	160332.i	0.176536	+	0.176536i	0.789844	−	0.613308i	$-0.210161\pi$
$953$	160332.	+	160332.i	0.176536	+	0.176536i	−0.613308	+	0.789844i	$0.710161\pi$
$954$			714780.i			0.785372i
$955$		0			0
$956$	9259.66			0.0101316
$957$	−271799.	+	271799.i	−0.296773	+	0.296773i
$958$	−620051.	−	620051.i	−0.675610	−	0.675610i
$959$			248453.i			0.270151i
$960$		0			0
$961$	−882769.			−0.955874
$962$	148126.	−	148126.i	0.160060	−	0.160060i
$963$	−18651.4	−	18651.4i	−0.0201122	−	0.0201122i
$964$		−	24688.4i		−	0.0265667i
$965$		0			0
$966$	−263057.			−0.281900
$967$	407790.	−	407790.i	0.436097	−	0.436097i	−0.454599	−	0.890696i	$-0.650217\pi$
$967$	407790.	−	407790.i	0.436097	−	0.436097i	0.890696	+	0.454599i	$0.150217\pi$
$968$	−636490.	−	636490.i	−0.679267	−	0.679267i
$969$		−	926472.i		−	0.986699i
$970$		0			0
$971$	615632.			0.652954			0.326477	−	0.945205i	$-0.394138\pi$
$971$	615632.			0.652954			0.326477	+	0.945205i	$0.394138\pi$
$972$	20519.9	−	20519.9i	0.0217192	−	0.0217192i
$973$	−148159.	−	148159.i	−0.156496	−	0.156496i
$974$		−	612262.i		−	0.645385i
$975$		0			0
$976$	−753066.			−0.790558
$977$	474542.	−	474542.i	0.497147	−	0.497147i	−0.413401	−	0.910549i	$-0.635659\pi$
$977$	474542.	−	474542.i	0.497147	−	0.497147i	0.910549	+	0.413401i	$0.135659\pi$
$978$	204014.	+	204014.i	0.213296	+	0.213296i
$979$		−	39833.8i		−	0.0415610i
$980$		0			0
$981$	1.36595e6			1.41937
$982$	−777300.	+	777300.i	−0.806057	+	0.806057i
$983$	−1.08591e6	−	1.08591e6i	−1.12379	−	1.12379i	−0.991166	−	0.132628i	$-0.957658\pi$
$983$	−1.08591e6	−	1.08591e6i	−1.12379	−	1.12379i	−0.132628	−	0.991166i	$-0.542342\pi$
$984$		−	3.02421e6i		−	3.12336i
$985$		0			0
$986$	−962280.			−0.989800
$987$	274179.	−	274179.i	0.281449	−	0.281449i
$988$	−36130.7	−	36130.7i	−0.0370137	−	0.0370137i
$989$		−	715863.i		−	0.731876i
$990$		0			0
$991$	1.88433e6			1.91871			0.959354	−	0.282207i	$-0.0910665\pi$
$991$	1.88433e6			1.91871			0.959354	+	0.282207i	$0.0910665\pi$
$992$	−12767.6	+	12767.6i	−0.0129744	+	0.0129744i
$993$	2.10842e6	+	2.10842e6i	2.13825	+	2.13825i
$994$		−	444893.i		−	0.450280i
$995$		0			0
$996$	−40291.6			−0.0406159
$997$	−685157.	+	685157.i	−0.689286	+	0.689286i	−0.962074	−	0.272788i	$-0.912054\pi$
$997$	−685157.	+	685157.i	−0.689286	+	0.689286i	0.272788	+	0.962074i	$0.412054\pi$
$998$	−102281.	−	102281.i	−0.102692	−	0.102692i
$999$		−	403968.i		−	0.404777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.43.8		24
5.2	odd	4	inner	175.5.g.c.57.8		24
5.3	odd	4		35.5.g.a.22.5	yes	24
5.4	even	2		35.5.g.a.8.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.5	✓	24	5.4	even	2
35.5.g.a.22.5	yes	24	5.3	odd	4
175.5.g.c.43.8		24	1.1	even	1	trivial
175.5.g.c.57.8		24	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.88957 - 2.88957i) q^{2} +(-11.3498 - 11.3498i) q^{3} -0.699277i q^{4} -65.5923 q^{6} +(-13.0958 + 13.0958i) q^{7} +(44.2126 + 44.2126i) q^{8} +176.637i q^{9} +O(q^{10})\)	\(q+(2.88957 - 2.88957i) q^{2} +(-11.3498 - 11.3498i) q^{3} -0.699277i q^{4} -65.5923 q^{6} +(-13.0958 + 13.0958i) q^{7} +(44.2126 + 44.2126i) q^{8} +176.637i q^{9} -15.6486 q^{11} +(-7.93668 + 7.93668i) q^{12} +(137.742 + 137.742i) q^{13} +75.6826i q^{14} +266.699 q^{16} +(-108.806 + 108.806i) q^{17} +(510.406 + 510.406i) q^{18} -375.111i q^{19} +297.270 q^{21} +(-45.2177 + 45.2177i) q^{22} +(-153.121 - 153.121i) q^{23} -1003.61i q^{24} +796.034 q^{26} +(1085.46 - 1085.46i) q^{27} +(9.15760 + 9.15760i) q^{28} +1530.33i q^{29} -201.870 q^{31} +(63.2467 - 63.2467i) q^{32} +(177.608 + 177.608i) q^{33} +628.807i q^{34} +123.518 q^{36} +(186.081 - 186.081i) q^{37} +(-1083.91 - 1083.91i) q^{38} -3126.70i q^{39} +3013.33 q^{41} +(858.984 - 858.984i) q^{42} +(2337.57 + 2337.57i) q^{43} +10.9427i q^{44} -884.909 q^{46} +(922.323 - 922.323i) q^{47} +(-3026.99 - 3026.99i) q^{48} -343.000i q^{49} +2469.86 q^{51} +(96.3201 - 96.3201i) q^{52} +(700.207 + 700.207i) q^{53} -6273.06i q^{54} -1158.00 q^{56} +(-4257.44 + 4257.44i) q^{57} +(4421.99 + 4421.99i) q^{58} +760.617i q^{59} -2823.65 q^{61} +(-583.320 + 583.320i) q^{62} +(-2313.20 - 2313.20i) q^{63} +3901.68i q^{64} +1026.43 q^{66} +(-2588.42 + 2588.42i) q^{67} +(76.0857 + 76.0857i) q^{68} +3475.79i q^{69} -5878.41 q^{71} +(-7809.58 + 7809.58i) q^{72} +(3613.01 + 3613.01i) q^{73} -1075.39i q^{74} -262.306 q^{76} +(204.930 - 204.930i) q^{77} +(-9034.84 - 9034.84i) q^{78} +7492.79i q^{79} -10332.1 q^{81} +(8707.24 - 8707.24i) q^{82} +(2538.32 + 2538.32i) q^{83} -207.874i q^{84} +13509.2 q^{86} +(17368.9 - 17368.9i) q^{87} +(-691.863 - 691.863i) q^{88} +2545.52i q^{89} -3607.69 q^{91} +(-107.074 + 107.074i) q^{92} +(2291.19 + 2291.19i) q^{93} -5330.24i q^{94} -1435.68 q^{96} +(-7253.08 + 7253.08i) q^{97} +(-991.124 - 991.124i) q^{98} -2764.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 24 * q - 20 * q^3 + 72 * q^6	\( 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) \) 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Introduction

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