LMFDB - Embedded newform 175.5.g.c.43.2

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			43.2
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.01495 + 5.01495i) q^{2} +(5.80055 + 5.80055i) q^{3} -34.2994i q^{4} -58.1789 q^{6} +(13.0958 - 13.0958i) q^{7} +(91.7707 + 91.7707i) q^{8} -13.7072i q^{9} +O(q^{10})$	\(q+(-5.01495 + 5.01495i) q^{2} +(5.80055 + 5.80055i) q^{3} -34.2994i q^{4} -58.1789 q^{6} +(13.0958 - 13.0958i) q^{7} +(91.7707 + 91.7707i) q^{8} -13.7072i q^{9} +75.9504 q^{11} +(198.956 - 198.956i) q^{12} +(-87.6088 - 87.6088i) q^{13} +131.350i q^{14} -371.660 q^{16} +(-230.654 + 230.654i) q^{17} +(68.7410 + 68.7410i) q^{18} +527.538i q^{19} +151.926 q^{21} +(-380.888 + 380.888i) q^{22} +(587.599 + 587.599i) q^{23} +1064.64i q^{24} +878.707 q^{26} +(549.354 - 549.354i) q^{27} +(-449.178 - 449.178i) q^{28} +1581.66i q^{29} -588.270 q^{31} +(395.524 - 395.524i) q^{32} +(440.554 + 440.554i) q^{33} -2313.44i q^{34} -470.149 q^{36} +(-629.670 + 629.670i) q^{37} +(-2645.58 - 2645.58i) q^{38} -1016.36i q^{39} -235.424 q^{41} +(-761.900 + 761.900i) q^{42} +(1361.59 + 1361.59i) q^{43} -2605.06i q^{44} -5893.56 q^{46} +(1625.74 - 1625.74i) q^{47} +(-2155.83 - 2155.83i) q^{48} -343.000i q^{49} -2675.84 q^{51} +(-3004.93 + 3004.93i) q^{52} +(-845.919 - 845.919i) q^{53} +5509.96i q^{54} +2403.62 q^{56} +(-3060.01 + 3060.01i) q^{57} +(-7931.94 - 7931.94i) q^{58} -1607.13i q^{59} -2519.75 q^{61} +(2950.14 - 2950.14i) q^{62} +(-179.507 - 179.507i) q^{63} -1979.49i q^{64} -4418.72 q^{66} +(-3671.67 + 3671.67i) q^{67} +(7911.31 + 7911.31i) q^{68} +6816.80i q^{69} +6830.43 q^{71} +(1257.92 - 1257.92i) q^{72} +(1600.31 + 1600.31i) q^{73} -6315.53i q^{74} +18094.3 q^{76} +(994.632 - 994.632i) q^{77} +(5096.99 + 5096.99i) q^{78} +3822.06i q^{79} +5262.83 q^{81} +(1180.64 - 1180.64i) q^{82} +(4122.84 + 4122.84i) q^{83} -5210.97i q^{84} -13656.6 q^{86} +(-9174.49 + 9174.49i) q^{87} +(6970.02 + 6970.02i) q^{88} +1140.60i q^{89} -2294.61 q^{91} +(20154.3 - 20154.3i) q^{92} +(-3412.29 - 3412.29i) q^{93} +16306.0i q^{94} +4588.52 q^{96} +(-1538.00 + 1538.00i) q^{97} +(1720.13 + 1720.13i) q^{98} -1041.07i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.01495	+	5.01495i	−1.25374	+	1.25374i	−0.299705	+	0.954032i	$0.596888\pi$
$2$	−5.01495	+	5.01495i	−1.25374	+	1.25374i	−0.954032	+	0.299705i	$0.903112\pi$
$3$	5.80055	+	5.80055i	0.644506	+	0.644506i	0.951660	−	0.307154i	$-0.0993767\pi$
$3$	5.80055	+	5.80055i	0.644506	+	0.644506i	−0.307154	+	0.951660i	$0.599377\pi$
$4$		−	34.2994i		−	2.14371i
$5$		0			0
$5$		0			0
$6$	−58.1789			−1.61608
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	91.7707	+	91.7707i	1.43392	+	1.43392i
$9$		−	13.7072i		−	0.169225i
$10$		0			0
$11$	75.9504			0.627689			0.313845	−	0.949474i	$-0.398383\pi$
$11$	75.9504			0.627689			0.313845	+	0.949474i	$0.398383\pi$
$12$	198.956	−	198.956i	1.38164	−	1.38164i
$13$	−87.6088	−	87.6088i	−0.518395	−	0.518395i	0.398690	−	0.917086i	$-0.369465\pi$
$13$	−87.6088	−	87.6088i	−0.518395	−	0.518395i	−0.917086	+	0.398690i	$0.869465\pi$
$14$			131.350i			0.670151i
$15$		0			0
$16$	−371.660			−1.45180
$17$	−230.654	+	230.654i	−0.798111	+	0.798111i	−0.982798	−	0.184686i	$-0.940873\pi$
$17$	−230.654	+	230.654i	−0.798111	+	0.798111i	0.184686	+	0.982798i	$0.440873\pi$
$18$	68.7410	+	68.7410i	0.212163	+	0.212163i
$19$			527.538i			1.46132i	0.682739	+	0.730662i	$0.260789\pi$
$19$			527.538i			1.46132i	−0.682739	+	0.730662i	$0.739211\pi$
$20$		0			0
$21$	151.926			0.344503
$22$	−380.888	+	380.888i	−0.786958	+	0.786958i
$23$	587.599	+	587.599i	1.11077	+	1.11077i	0.993046	+	0.117728i	$0.0375611\pi$
$23$	587.599	+	587.599i	1.11077	+	1.11077i	0.117728	+	0.993046i	$0.462439\pi$
$24$			1064.64i			1.84834i
$25$		0			0
$26$	878.707			1.29986
$27$	549.354	−	549.354i	0.753572	−	0.753572i
$28$	−449.178	−	449.178i	−0.572932	−	0.572932i
$29$			1581.66i			1.88069i	0.340226	+	0.940344i	$0.389496\pi$
$29$			1581.66i			1.88069i	−0.340226	+	0.940344i	$0.610504\pi$
$30$		0			0
$31$	−588.270			−0.612144			−0.306072	−	0.952008i	$-0.599015\pi$
$31$	−588.270			−0.612144			−0.306072	+	0.952008i	$0.599015\pi$
$32$	395.524	−	395.524i	0.386254	−	0.386254i
$33$	440.554	+	440.554i	0.404549	+	0.404549i
$34$		−	2313.44i		−	2.00124i
$35$		0			0
$36$	−470.149			−0.362770
$37$	−629.670	+	629.670i	−0.459949	+	0.459949i	−0.898639	−	0.438690i	$-0.855443\pi$
$37$	−629.670	+	629.670i	−0.459949	+	0.459949i	0.438690	+	0.898639i	$0.355443\pi$
$38$	−2645.58	−	2645.58i	−1.83212	−	1.83212i
$39$		−	1016.36i		−	0.668217i
$40$		0			0
$41$	−235.424			−0.140050			−0.0700249	−	0.997545i	$-0.522308\pi$
$41$	−235.424			−0.140050			−0.0700249	+	0.997545i	$0.522308\pi$
$42$	−761.900	+	761.900i	−0.431916	+	0.431916i
$43$	1361.59	+	1361.59i	0.736393	+	0.736393i	0.971878	−	0.235485i	$-0.0756678\pi$
$43$	1361.59	+	1361.59i	0.736393	+	0.736393i	−0.235485	+	0.971878i	$0.575668\pi$
$44$		−	2605.06i		−	1.34559i
$45$		0			0
$46$	−5893.56			−2.78524
$47$	1625.74	−	1625.74i	0.735963	−	0.735963i	−0.235831	−	0.971794i	$-0.575781\pi$
$47$	1625.74	−	1625.74i	0.735963	−	0.735963i	0.971794	+	0.235831i	$0.0757811\pi$
$48$	−2155.83	−	2155.83i	−0.935691	−	0.935691i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	−2675.84			−1.02877
$52$	−3004.93	+	3004.93i	−1.11129	+	1.11129i
$53$	−845.919	−	845.919i	−0.301146	−	0.301146i	0.540316	−	0.841462i	$-0.318305\pi$
$53$	−845.919	−	845.919i	−0.301146	−	0.301146i	−0.841462	+	0.540316i	$0.818305\pi$
$54$			5509.96i			1.88956i
$55$		0			0
$56$	2403.62			0.766461
$57$	−3060.01	+	3060.01i	−0.941832	+	0.941832i
$58$	−7931.94	−	7931.94i	−2.35789	−	2.35789i
$59$		−	1607.13i		−	0.461686i	−0.972991	−	0.230843i	$-0.925852\pi$
$59$		−	1607.13i		−	0.461686i	0.972991	−	0.230843i	$-0.0741485\pi$
$60$		0			0
$61$	−2519.75			−0.677170			−0.338585	−	0.940936i	$-0.609948\pi$
$61$	−2519.75			−0.677170			−0.338585	+	0.940936i	$0.609948\pi$
$62$	2950.14	−	2950.14i	0.767467	−	0.767467i
$63$	−179.507	−	179.507i	−0.0452272	−	0.0452272i
$64$		−	1979.49i		−	0.483274i
$65$		0			0
$66$	−4418.72			−1.01440
$67$	−3671.67	+	3671.67i	−0.817926	+	0.817926i	−0.985807	−	0.167881i	$-0.946308\pi$
$67$	−3671.67	+	3671.67i	−0.817926	+	0.817926i	0.167881	+	0.985807i	$0.446308\pi$
$68$	7911.31	+	7911.31i	1.71092	+	1.71092i
$69$			6816.80i			1.43180i
$70$		0			0
$71$	6830.43			1.35498			0.677488	−	0.735534i	$-0.263069\pi$
$71$	6830.43			1.35498			0.677488	+	0.735534i	$0.263069\pi$
$72$	1257.92	−	1257.92i	0.242654	−	0.242654i
$73$	1600.31	+	1600.31i	0.300302	+	0.300302i	0.841132	−	0.540830i	$-0.181890\pi$
$73$	1600.31	+	1600.31i	0.300302	+	0.300302i	−0.540830	+	0.841132i	$0.681890\pi$
$74$		−	6315.53i		−	1.15331i
$75$		0			0
$76$	18094.3			3.13266
$77$	994.632	−	994.632i	0.167757	−	0.167757i
$78$	5096.99	+	5096.99i	0.837769	+	0.837769i
$79$			3822.06i			0.612412i	0.951965	+	0.306206i	$0.0990596\pi$
$79$			3822.06i			0.612412i	−0.951965	+	0.306206i	$0.900940\pi$
$80$		0			0
$81$	5262.83			0.802138
$82$	1180.64	−	1180.64i	0.175586	−	0.175586i
$83$	4122.84	+	4122.84i	0.598467	+	0.598467i	0.939905	−	0.341437i	$-0.110914\pi$
$83$	4122.84	+	4122.84i	0.598467	+	0.598467i	−0.341437	+	0.939905i	$0.610914\pi$
$84$		−	5210.97i		−	0.738516i
$85$		0			0
$86$	−13656.6			−1.84649
$87$	−9174.49	+	9174.49i	−1.21211	+	1.21211i
$88$	6970.02	+	6970.02i	0.900055	+	0.900055i
$89$			1140.60i			0.143997i	0.997405	+	0.0719984i	$0.0229377\pi$
$89$			1140.60i			0.143997i	−0.997405	+	0.0719984i	$0.977062\pi$
$90$		0			0
$91$	−2294.61			−0.277094
$92$	20154.3	−	20154.3i	2.38118	−	2.38118i
$93$	−3412.29	−	3412.29i	−0.394530	−	0.394530i
$94$			16306.0i			1.84541i
$95$		0			0
$96$	4588.52			0.497886
$97$	−1538.00	+	1538.00i	−0.163460	+	0.163460i	−0.784098	−	0.620637i	$-0.786874\pi$
$97$	−1538.00	+	1538.00i	−0.163460	+	0.163460i	0.620637	+	0.784098i	$0.286874\pi$
$98$	1720.13	+	1720.13i	0.179105	+	0.179105i
$99$		−	1041.07i		−	0.106221i
$100$		0			0
$101$	−3238.10			−0.317430			−0.158715	−	0.987324i	$-0.550735\pi$
$101$	−3238.10			−0.317430			−0.158715	+	0.987324i	$0.550735\pi$
$102$	13419.2	−	13419.2i	1.28981	−	1.28981i
$103$	9096.24	+	9096.24i	0.857407	+	0.857407i	0.991032	−	0.133625i	$-0.0426616\pi$
$103$	9096.24	+	9096.24i	0.857407	+	0.857407i	−0.133625	+	0.991032i	$0.542662\pi$
$104$		−	16079.8i		−	1.48667i
$105$		0			0
$106$	8484.48			0.755116
$107$	2177.73	−	2177.73i	0.190211	−	0.190211i	−0.605576	−	0.795787i	$-0.707057\pi$
$107$	2177.73	−	2177.73i	0.190211	−	0.190211i	0.795787	+	0.605576i	$0.207057\pi$
$108$	−18842.5	−	18842.5i	−1.61544	−	1.61544i
$109$		−	2560.05i		−	0.215474i	−0.994179	−	0.107737i	$-0.965640\pi$
$109$		−	2560.05i		−	0.215474i	0.994179	−	0.107737i	$-0.0343605\pi$
$110$		0			0
$111$	−7304.87			−0.592880
$112$	−4867.18	+	4867.18i	−0.388009	+	0.388009i
$113$	491.079	+	491.079i	0.0384587	+	0.0384587i	0.726075	−	0.687616i	$-0.241343\pi$
$113$	491.079	+	491.079i	0.0384587	+	0.0384587i	−0.687616	+	0.726075i	$0.741343\pi$
$114$		−	30691.6i		−	2.36162i
$115$		0			0
$116$	54250.0			4.03166
$117$	−1200.87	+	1200.87i	−0.0877253	+	0.0877253i
$118$	8059.68	+	8059.68i	0.578834	+	0.578834i
$119$			6041.20i			0.426608i
$120$		0			0
$121$	−8872.53			−0.606006
$122$	12636.4	−	12636.4i	0.848993	−	0.848993i
$123$	−1365.59	−	1365.59i	−0.0902629	−	0.0902629i
$124$			20177.3i			1.31226i
$125$		0			0
$126$	1800.44			0.113406
$127$	−6070.58	+	6070.58i	−0.376377	+	0.376377i	−0.869793	−	0.493417i	$-0.835748\pi$
$127$	−6070.58	+	6070.58i	−0.376377	+	0.376377i	0.493417	+	0.869793i	$0.335748\pi$
$128$	16255.4	+	16255.4i	0.992153	+	0.992153i
$129$			15796.0i			0.949219i
$130$		0			0
$131$	2199.94			0.128194			0.0640970	−	0.997944i	$-0.479583\pi$
$131$	2199.94			0.128194			0.0640970	+	0.997944i	$0.479583\pi$
$132$	15110.8	−	15110.8i	0.867238	−	0.867238i
$133$	6908.53	+	6908.53i	0.390555	+	0.390555i
$134$		−	36826.5i		−	2.05093i
$135$		0			0
$136$	−42334.6			−2.28885
$137$	−16433.0	+	16433.0i	−0.875541	+	0.875541i	−0.993070	−	0.117528i	$-0.962503\pi$
$137$	−16433.0	+	16433.0i	−0.875541	+	0.875541i	0.117528	+	0.993070i	$0.462503\pi$
$138$	−34185.9	−	34185.9i	−1.79510	−	1.79510i
$139$		−	2459.25i		−	0.127284i	−0.997973	−	0.0636419i	$-0.979728\pi$
$139$		−	2459.25i		−	0.127284i	0.997973	−	0.0636419i	$-0.0202715\pi$
$140$		0			0
$141$	18860.4			0.948665
$142$	−34254.3	+	34254.3i	−1.69878	+	1.69878i
$143$	−6653.92	−	6653.92i	−0.325391	−	0.325391i
$144$			5094.42i			0.245680i
$145$		0			0
$146$	−16050.9			−0.753000
$147$	1989.59	−	1989.59i	0.0920722	−	0.0920722i
$148$	21597.3	+	21597.3i	0.986000	+	0.986000i
$149$			40002.9i			1.80185i	0.433973	+	0.900926i	$0.357111\pi$
$149$			40002.9i			1.80185i	−0.433973	+	0.900926i	$0.642889\pi$
$150$		0			0
$151$	−11343.6			−0.497503			−0.248751	−	0.968567i	$-0.580020\pi$
$151$	−11343.6			−0.497503			−0.248751	+	0.968567i	$0.580020\pi$
$152$	−48412.5	+	48412.5i	−2.09542	+	2.09542i
$153$	3161.63	+	3161.63i	0.135060	+	0.135060i
$154$			9976.05i			0.420647i
$155$		0			0
$156$	−34860.5			−1.43247
$157$	−8858.33	+	8858.33i	−0.359379	+	0.359379i	−0.863584	−	0.504205i	$-0.831786\pi$
$157$	−8858.33	+	8858.33i	−0.359379	+	0.359379i	0.504205	+	0.863584i	$0.331786\pi$
$158$	−19167.4	−	19167.4i	−0.767804	−	0.767804i
$159$		−	9813.59i		−	0.388181i
$160$		0			0
$161$	15390.2			0.593734
$162$	−26392.8	+	26392.8i	−1.00567	+	1.00567i
$163$	−4388.99	−	4388.99i	−0.165192	−	0.165192i	0.619670	−	0.784862i	$-0.287266\pi$
$163$	−4388.99	−	4388.99i	−0.165192	−	0.165192i	−0.784862	+	0.619670i	$0.787266\pi$
$164$			8074.90i			0.300227i
$165$		0			0
$166$	−41351.7			−1.50064
$167$	36986.7	−	36986.7i	1.32621	−	1.32621i	0.417560	−	0.908649i	$-0.362885\pi$
$167$	36986.7	−	36986.7i	1.32621	−	1.32621i	0.908649	−	0.417560i	$-0.137115\pi$
$168$	13942.3	+	13942.3i	0.493988	+	0.493988i
$169$		−	13210.4i		−	0.462533i
$170$		0			0
$171$	7231.08			0.247292
$172$	46701.8	−	46701.8i	1.57862	−	1.57862i
$173$	−35346.5	−	35346.5i	−1.18101	−	1.18101i	−0.979483	−	0.201528i	$-0.935409\pi$
$173$	−35346.5	−	35346.5i	−1.18101	−	1.18101i	−0.201528	−	0.979483i	$-0.564591\pi$
$174$		−	92019.2i		−	3.03934i
$175$		0			0
$176$	−28227.7			−0.911277
$177$	9322.24	−	9322.24i	0.297560	−	0.297560i
$178$	−5720.05	−	5720.05i	−0.180534	−	0.180534i
$179$		−	30171.1i		−	0.941640i	−0.882229	−	0.470820i	$-0.843958\pi$
$179$		−	30171.1i		−	0.941640i	0.882229	−	0.470820i	$-0.156042\pi$
$180$		0			0
$181$	35744.0			1.09105			0.545526	−	0.838094i	$-0.316330\pi$
$181$	35744.0			1.09105			0.545526	+	0.838094i	$0.316330\pi$
$182$	11507.4	−	11507.4i	0.347403	−	0.347403i
$183$	−14615.9	−	14615.9i	−0.436440	−	0.436440i
$184$			107849.i			3.18552i
$185$		0			0
$186$	34224.9			0.989274
$187$	−17518.3	+	17518.3i	−0.500966	+	0.500966i
$188$	−55762.0	−	55762.0i	−1.57769	−	1.57769i
$189$		−	14388.5i		−	0.402801i
$190$		0			0
$191$	36695.0			1.00587			0.502933	−	0.864325i	$-0.332254\pi$
$191$	36695.0			1.00587			0.502933	+	0.864325i	$0.332254\pi$
$192$	11482.1	−	11482.1i	0.311473	−	0.311473i
$193$	5739.33	+	5739.33i	0.154080	+	0.154080i	0.779938	−	0.625857i	$-0.215251\pi$
$193$	5739.33	+	5739.33i	0.154080	+	0.154080i	−0.625857	+	0.779938i	$0.715251\pi$
$194$		−	15426.0i		−	0.409873i
$195$		0			0
$196$	−11764.7			−0.306245
$197$	33650.6	−	33650.6i	0.867082	−	0.867082i	−0.125066	−	0.992148i	$-0.539914\pi$
$197$	33650.6	−	33650.6i	0.867082	−	0.867082i	0.992148	+	0.125066i	$0.0399144\pi$
$198$	5220.90	+	5220.90i	0.133173	+	0.133173i
$199$			8221.91i			0.207619i	0.994597	+	0.103809i	$0.0331032\pi$
$199$			8221.91i			0.207619i	−0.994597	+	0.103809i	$0.966897\pi$
$200$		0			0
$201$	−42595.4			−1.05432
$202$	16238.9	−	16238.9i	0.397974	−	0.397974i
$203$	20713.1	+	20713.1i	0.502635	+	0.502635i
$204$			91779.9i			2.20540i
$205$		0			0
$206$	−91234.3			−2.14993
$207$	8054.35	−	8054.35i	0.187970	−	0.187970i
$208$	32560.7	+	32560.7i	0.752604	+	0.752604i
$209$			40066.7i			0.917258i
$210$		0			0
$211$	−30204.5			−0.678432			−0.339216	−	0.940708i	$-0.610162\pi$
$211$	−30204.5			−0.678432			−0.339216	+	0.940708i	$0.610162\pi$
$212$	−29014.5	+	29014.5i	−0.645571	+	0.645571i
$213$	39620.3	+	39620.3i	0.873289	+	0.873289i
$214$			21842.4i			0.476950i
$215$		0			0
$216$	100829.			2.16112
$217$	−7703.87	+	7703.87i	−0.163602	+	0.163602i
$218$	12838.5	+	12838.5i	0.270148	+	0.270148i
$219$			18565.4i			0.387093i
$220$		0			0
$221$	40414.7			0.827474
$222$	36633.6	−	36633.6i	0.743315	−	0.743315i
$223$	1152.95	+	1152.95i	0.0231846	+	0.0231846i	0.718604	−	0.695419i	$-0.244781\pi$
$223$	1152.95	+	1152.95i	0.0231846	+	0.0231846i	−0.695419	+	0.718604i	$0.744781\pi$
$224$		−	10359.4i		−	0.206462i
$225$		0			0
$226$	−4925.47			−0.0964341
$227$	−5784.04	+	5784.04i	−0.112248	+	0.112248i	−0.761000	−	0.648752i	$-0.775291\pi$
$227$	−5784.04	+	5784.04i	−0.112248	+	0.112248i	0.648752	+	0.761000i	$0.275291\pi$
$228$	104957.	+	104957.i	2.01902	+	2.01902i
$229$		−	102632.i		−	1.95710i	−0.206001	−	0.978552i	$-0.566045\pi$
$229$		−	102632.i		−	1.95710i	0.206001	−	0.978552i	$-0.433955\pi$
$230$		0			0
$231$	11538.8			0.216241
$232$	−145150.	+	145150.i	−2.69675	+	2.69675i
$233$	−16734.1	−	16734.1i	−0.308241	−	0.308241i	0.535986	−	0.844227i	$-0.319940\pi$
$233$	−16734.1	−	16734.1i	−0.308241	−	0.308241i	−0.844227	+	0.535986i	$0.819940\pi$
$234$		−	12044.6i		−	0.219969i
$235$		0			0
$236$	−55123.7			−0.989724
$237$	−22170.1	+	22170.1i	−0.394703	+	0.394703i
$238$	−30296.3	−	30296.3i	−0.534855	−	0.534855i
$239$			40418.5i			0.707594i	0.935322	+	0.353797i	$0.115110\pi$
$239$			40418.5i			0.707594i	−0.935322	+	0.353797i	$0.884890\pi$
$240$		0			0
$241$	27952.5			0.481268			0.240634	−	0.970616i	$-0.422645\pi$
$241$	27952.5			0.481268			0.240634	+	0.970616i	$0.422645\pi$
$242$	44495.3	−	44495.3i	0.759772	−	0.759772i
$243$	−13970.4	−	13970.4i	−0.236589	−	0.236589i
$244$			86425.9i			1.45166i
$245$		0			0
$246$	13696.7			0.226332
$247$	46217.0	−	46217.0i	0.757543	−	0.757543i
$248$	−53986.0	−	53986.0i	−0.877763	−	0.877763i
$249$			47829.5i			0.771431i
$250$		0			0
$251$	32087.2			0.509312			0.254656	−	0.967032i	$-0.418038\pi$
$251$	32087.2			0.509312			0.254656	+	0.967032i	$0.418038\pi$
$252$	−6156.98	+	6156.98i	−0.0969543	+	0.0969543i
$253$	44628.4	+	44628.4i	0.697221	+	0.697221i
$254$		−	60887.3i		−	0.943755i
$255$		0			0
$256$	−131368.			−2.00452
$257$	14697.1	−	14697.1i	0.222518	−	0.222518i	−0.587040	−	0.809558i	$-0.699707\pi$
$257$	14697.1	−	14697.1i	0.222518	−	0.222518i	0.809558	+	0.587040i	$0.199707\pi$
$258$	−79215.9	−	79215.9i	−1.19007	−	1.19007i
$259$			16492.1i			0.245853i
$260$		0			0
$261$	21680.1			0.318259
$262$	−11032.6	+	11032.6i	−0.160722	+	0.160722i
$263$	−17788.8	−	17788.8i	−0.257179	−	0.257179i	0.566727	−	0.823906i	$-0.308209\pi$
$263$	−17788.8	−	17788.8i	−0.257179	−	0.257179i	−0.823906	+	0.566727i	$0.808209\pi$
$264$			80860.0i			1.16018i
$265$		0			0
$266$	−69291.9			−0.979308
$267$	−6616.10	+	6616.10i	−0.0928068	+	0.0928068i
$268$	125936.	+	125936.i	1.75340	+	1.75340i
$269$		−	2894.86i		−	0.0400058i	−0.999800	−	0.0200029i	$-0.993632\pi$
$269$		−	2894.86i		−	0.0400058i	0.999800	−	0.0200029i	$-0.00636755\pi$
$270$		0			0
$271$	120397.			1.63937			0.819685	−	0.572814i	$-0.194148\pi$
$271$	120397.			1.63937			0.819685	+	0.572814i	$0.194148\pi$
$272$	85724.9	−	85724.9i	1.15870	−	1.15870i
$273$	−13310.0	−	13310.0i	−0.178589	−	0.178589i
$274$		−	164822.i		−	2.19540i
$275$		0			0
$276$	233812.			3.06937
$277$	−53882.9	+	53882.9i	−0.702249	+	0.702249i	−0.964893	−	0.262644i	$-0.915406\pi$
$277$	−53882.9	+	53882.9i	−0.702249	+	0.702249i	0.262644	+	0.964893i	$0.415406\pi$
$278$	12333.0	+	12333.0i	0.159580	+	0.159580i
$279$			8063.54i			0.103590i
$280$		0			0
$281$	−131983.			−1.67150			−0.835748	−	0.549113i	$-0.814966\pi$
$281$	−131983.			−1.67150			−0.835748	+	0.549113i	$0.814966\pi$
$282$	−94584.0	+	94584.0i	−1.18938	+	1.18938i
$283$	−61319.2	−	61319.2i	−0.765639	−	0.765639i	0.211697	−	0.977335i	$-0.432101\pi$
$283$	−61319.2	−	61319.2i	−0.765639	−	0.765639i	−0.977335	+	0.211697i	$0.932101\pi$
$284$		−	234280.i		−	2.90468i
$285$		0			0
$286$	66738.2			0.815910
$287$	−3083.06	+	3083.06i	−0.0374299	+	0.0374299i
$288$	−5421.53	−	5421.53i	−0.0653638	−	0.0653638i
$289$		−	22881.7i		−	0.273964i
$290$		0			0
$291$	−17842.5			−0.210702
$292$	54889.7	−	54889.7i	0.643762	−	0.643762i
$293$	66889.0	+	66889.0i	0.779147	+	0.779147i	0.979686	−	0.200539i	$-0.0642693\pi$
$293$	66889.0	+	66889.0i	0.779147	+	0.779147i	−0.200539	+	0.979686i	$0.564269\pi$
$294$			19955.4i			0.230869i
$295$		0			0
$296$	−115571.			−1.31906
$297$	41723.7	−	41723.7i	0.473009	−	0.473009i
$298$	−200613.	−	200613.i	−2.25905	−	2.25905i
$299$		−	102958.i		−	1.15164i
$300$		0			0
$301$	35662.3			0.393619
$302$	56887.4	−	56887.4i	0.623737	−	0.623737i
$303$	−18782.8	−	18782.8i	−0.204585	−	0.204585i
$304$		−	196065.i		−	2.12155i
$305$		0			0
$306$	−31710.8			−0.338660
$307$	−13072.6	+	13072.6i	−0.138703	+	0.138703i	−0.773049	−	0.634346i	$-0.781269\pi$
$307$	−13072.6	+	13072.6i	−0.138703	+	0.138703i	0.634346	+	0.773049i	$0.281269\pi$
$308$	−34115.3	−	34115.3i	−0.359623	−	0.359623i
$309$			105526.i			1.10521i
$310$		0			0
$311$	−34805.2			−0.359851			−0.179926	−	0.983680i	$-0.557586\pi$
$311$	−34805.2			−0.359851			−0.179926	+	0.983680i	$0.557586\pi$
$312$	93271.9	−	93271.9i	0.958168	−	0.958168i
$313$	67248.3	+	67248.3i	0.686424	+	0.686424i	0.961440	−	0.275016i	$-0.0886830\pi$
$313$	67248.3	+	67248.3i	0.686424	+	0.686424i	−0.275016	+	0.961440i	$0.588683\pi$
$314$		−	88848.1i		−	0.901133i
$315$		0			0
$316$	131095.			1.31284
$317$	−126470.	+	126470.i	−1.25854	+	1.25854i	−0.306752	+	0.951790i	$0.599242\pi$
$317$	−126470.	+	126470.i	−1.25854	+	1.25854i	−0.951790	+	0.306752i	$0.900758\pi$
$318$	49214.7	+	49214.7i	0.486676	+	0.486676i
$319$			120128.i			1.18049i
$320$		0			0
$321$	25264.0			0.245184
$322$	−77180.9	+	77180.9i	−0.744386	+	0.744386i
$323$	−121679.	−	121679.i	−1.16630	−	1.16630i
$324$		−	180512.i		−	1.71955i
$325$		0			0
$326$	44021.1			0.414215
$327$	14849.7	−	14849.7i	0.138874	−	0.138874i
$328$	−21605.0	−	21605.0i	−0.200820	−	0.200820i
$329$		−	42580.8i		−	0.393389i
$330$		0			0
$331$	−81352.0			−0.742527			−0.371264	−	0.928527i	$-0.621075\pi$
$331$	−81352.0			−0.742527			−0.371264	+	0.928527i	$0.621075\pi$
$332$	141411.	−	141411.i	1.28294	−	1.28294i
$333$	8631.02	+	8631.02i	0.0778348	+	0.0778348i
$334$			370972.i			3.32544i
$335$		0			0
$336$	−56464.7			−0.500148
$337$	111373.	−	111373.i	0.980661	−	0.980661i	−0.0191559	−	0.999817i	$-0.506098\pi$
$337$	111373.	−	111373.i	0.980661	−	0.980661i	0.999817	+	0.0191559i	$0.00609788\pi$
$338$	66249.5	+	66249.5i	0.579895	+	0.579895i
$339$			5697.05i			0.0495736i
$340$		0			0
$341$	−44679.4			−0.384236
$342$	−36263.5	+	36263.5i	−0.310040	+	0.310040i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$			249908.i			2.11185i
$345$		0			0
$346$	354522.			2.96135
$347$	−9505.40	+	9505.40i	−0.0789426	+	0.0789426i	−0.745476	−	0.666533i	$-0.767778\pi$
$347$	−9505.40	+	9505.40i	−0.0789426	+	0.0789426i	0.666533	+	0.745476i	$0.267778\pi$
$348$	314680.	+	314680.i	2.59843	+	2.59843i
$349$		−	187256.i		−	1.53739i	−0.639615	−	0.768696i	$-0.720906\pi$
$349$		−	187256.i		−	1.53739i	0.639615	−	0.768696i	$-0.279094\pi$
$350$		0			0
$351$	−96256.5			−0.781296
$352$	30040.2	−	30040.2i	0.242448	−	0.242448i
$353$	109193.	+	109193.i	0.876284	+	0.876284i	0.993148	−	0.116864i	$-0.0372841\pi$
$353$	109193.	+	109193.i	0.876284	+	0.876284i	−0.116864	+	0.993148i	$0.537284\pi$
$354$			93501.2i			0.746123i
$355$		0			0
$356$	39121.9			0.308688
$357$	−35042.3	+	35042.3i	−0.274952	+	0.274952i
$358$	151307.	+	151307.i	1.18057	+	1.18057i
$359$			56473.7i			0.438185i	0.975704	+	0.219092i	$0.0703096\pi$
$359$			56473.7i			0.438185i	−0.975704	+	0.219092i	$0.929690\pi$
$360$		0			0
$361$	−147976.			−1.13547
$362$	−179254.	+	179254.i	−1.36789	+	1.36789i
$363$	−51465.6	−	51465.6i	−0.390574	−	0.390574i
$364$			78704.0i			0.594010i
$365$		0			0
$366$	146596.			1.09436
$367$	−43447.8	+	43447.8i	−0.322579	+	0.322579i	−0.849756	−	0.527177i	$-0.823251\pi$
$367$	−43447.8	+	43447.8i	−0.322579	+	0.322579i	0.527177	+	0.849756i	$0.323251\pi$
$368$	−218387.	−	218387.i	−1.61262	−	1.61262i
$369$			3227.00i			0.0236999i
$370$		0			0
$371$	−22156.0			−0.160969
$372$	−117040.	+	117040.i	−0.845760	+	0.845760i
$373$	31294.2	+	31294.2i	0.224929	+	0.224929i	0.810570	−	0.585641i	$-0.199157\pi$
$373$	31294.2	+	31294.2i	0.224929	+	0.224929i	−0.585641	+	0.810570i	$0.699157\pi$
$374$		−	175707.i		−	1.25616i
$375$		0			0
$376$	298391.			2.11062
$377$	138567.	−	138567.i	0.974939	−	0.974939i
$378$	72157.4	+	72157.4i	0.505007	+	0.505007i
$379$			37541.2i			0.261354i	0.991425	+	0.130677i	$0.0417151\pi$
$379$			37541.2i			0.261354i	−0.991425	+	0.130677i	$0.958285\pi$
$380$		0			0
$381$	−70425.4			−0.485154
$382$	−184024.	+	184024.i	−1.26109	+	1.26109i
$383$	40494.9	+	40494.9i	0.276060	+	0.276060i	0.831534	−	0.555474i	$-0.187463\pi$
$383$	40494.9	+	40494.9i	0.276060	+	0.276060i	−0.555474	+	0.831534i	$0.687463\pi$
$384$			188581.i			1.27890i
$385$		0			0
$386$	−57564.9			−0.386352
$387$	18663.6	−	18663.6i	0.124616	−	0.124616i
$388$	52752.5	+	52752.5i	0.350412	+	0.350412i
$389$		−	78442.6i		−	0.518386i	−0.965826	−	0.259193i	$-0.916543\pi$
$389$		−	78442.6i		−	0.518386i	0.965826	−	0.259193i	$-0.0834565\pi$
$390$		0			0
$391$	−271064.			−1.77304
$392$	31477.3	−	31477.3i	0.204845	−	0.204845i
$393$	12760.8	+	12760.8i	0.0826218	+	0.0826218i
$394$			337512.i			2.17419i
$395$		0			0
$396$	−35708.0			−0.227707
$397$	131890.	−	131890.i	0.836815	−	0.836815i	−0.151623	−	0.988438i	$-0.548450\pi$
$397$	131890.	−	131890.i	0.836815	−	0.836815i	0.988438	+	0.151623i	$0.0484500\pi$
$398$	−41232.5	−	41232.5i	−0.260299	−	0.260299i
$399$			80146.6i			0.503430i
$400$		0			0
$401$	260765.			1.62166			0.810832	−	0.585280i	$-0.199015\pi$
$401$	260765.			1.62166			0.810832	+	0.585280i	$0.199015\pi$
$402$	213614.	−	213614.i	1.32184	−	1.32184i
$403$	51537.6	+	51537.6i	0.317332	+	0.317332i
$404$			111065.i			0.680479i
$405$		0			0
$406$	−207750.			−1.26034
$407$	−47823.7	+	47823.7i	−0.288705	+	0.288705i
$408$	−245564.	−	245564.i	−1.47518	−	1.47518i
$409$		−	253509.i		−	1.51547i	−0.652564	−	0.757734i	$-0.726307\pi$
$409$		−	253509.i		−	1.51547i	0.652564	−	0.757734i	$-0.273693\pi$
$410$		0			0
$411$	−190641.			−1.12858
$412$	311996.	−	311996.i	1.83804	−	1.83804i
$413$	−21046.7	−	21046.7i	−0.123391	−	0.123391i
$414$			80784.3i			0.471331i
$415$		0			0
$416$	−69302.8			−0.400465
$417$	14265.0	−	14265.0i	0.0820351	−	0.0820351i
$418$	−200933.	−	200933.i	−1.15000	−	1.15000i
$419$			60645.6i			0.345439i	0.984971	+	0.172719i	$0.0552554\pi$
$419$			60645.6i			0.345439i	−0.984971	+	0.172719i	$0.944745\pi$
$420$		0			0
$421$	−63976.9			−0.360960			−0.180480	−	0.983579i	$-0.557765\pi$
$421$	−63976.9			−0.360960			−0.180480	+	0.983579i	$0.557765\pi$
$422$	151474.	−	151474.i	0.850576	−	0.850576i
$423$	−22284.4	−	22284.4i	−0.124543	−	0.124543i
$424$		−	155261.i		−	0.863637i
$425$		0			0
$426$	−397387.			−2.18975
$427$	−32998.1	+	32998.1i	−0.180981	+	0.180981i
$428$	−74694.8	−	74694.8i	−0.407758	−	0.407758i
$429$		−	77192.8i		−	0.419433i
$430$		0			0
$431$	138787.			0.747129			0.373565	−	0.927604i	$-0.378135\pi$
$431$	138787.			0.747129			0.373565	+	0.927604i	$0.378135\pi$
$432$	−204173.	+	204173.i	−1.09403	+	1.09403i
$433$	−181902.	−	181902.i	−0.970201	−	0.970201i	0.0293680	−	0.999569i	$-0.490651\pi$
$433$	−181902.	−	181902.i	−0.970201	−	0.970201i	−0.999569	+	0.0293680i	$0.990651\pi$
$434$		−	77269.0i		−	0.410229i
$435$		0			0
$436$	−87808.3			−0.461915
$437$	−309981.	+	309981.i	−1.62320	+	1.62320i
$438$	−93104.3	−	93104.3i	−0.485313	−	0.485313i
$439$		−	291440.i		−	1.51224i	−0.654435	−	0.756118i	$-0.727093\pi$
$439$		−	291440.i		−	1.51224i	0.654435	−	0.756118i	$-0.272907\pi$
$440$		0			0
$441$	−4701.57			−0.0241750
$442$	−202677.	+	202677.i	−1.03744	+	1.03744i
$443$	75828.2	+	75828.2i	0.386388	+	0.386388i	0.873397	−	0.487009i	$-0.161912\pi$
$443$	75828.2	+	75828.2i	0.386388	+	0.386388i	−0.487009	+	0.873397i	$0.661912\pi$
$444$			250553.i			1.27096i
$445$		0			0
$446$	−11564.0			−0.0581349
$447$	−232039.	+	232039.i	−1.16130	+	1.16130i
$448$	−25923.0	−	25923.0i	−0.129160	−	0.129160i
$449$		−	239109.i		−	1.18605i	−0.805184	−	0.593025i	$-0.797933\pi$
$449$		−	239109.i		−	1.18605i	0.805184	−	0.593025i	$-0.202067\pi$
$450$		0			0
$451$	−17880.5			−0.0879078
$452$	16843.7	−	16843.7i	0.0824444	−	0.0824444i
$453$	−65798.9	−	65798.9i	−0.320643	−	0.320643i
$454$		−	58013.3i		−	0.281459i
$455$		0			0
$456$	−561639.			−2.70102
$457$	−34147.5	+	34147.5i	−0.163503	+	0.163503i	−0.784117	−	0.620614i	$-0.786884\pi$
$457$	−34147.5	+	34147.5i	−0.163503	+	0.163503i	0.620614	+	0.784117i	$0.286884\pi$
$458$	514697.	+	514697.i	2.45369	+	2.45369i
$459$			253422.i			1.20287i
$460$		0			0
$461$	171075.			0.804981			0.402491	−	0.915424i	$-0.368145\pi$
$461$	171075.			0.804981			0.402491	+	0.915424i	$0.368145\pi$
$462$	−57866.6	+	57866.6i	−0.271109	+	0.271109i
$463$	−125583.	−	125583.i	−0.585826	−	0.585826i	0.350672	−	0.936498i	$-0.385953\pi$
$463$	−125583.	−	125583.i	−0.585826	−	0.585826i	−0.936498	+	0.350672i	$0.885953\pi$
$464$		−	587839.i		−	2.73038i
$465$		0			0
$466$	167841.			0.772907
$467$	126812.	−	126812.i	0.581469	−	0.581469i	−0.353838	−	0.935307i	$-0.615124\pi$
$467$	126812.	−	126812.i	0.581469	−	0.581469i	0.935307	+	0.353838i	$0.115124\pi$
$468$	41189.2	+	41189.2i	0.188058	+	0.188058i
$469$			96167.0i			0.437200i
$470$		0			0
$471$	−102766.			−0.463243
$472$	147487.	−	147487.i	0.662020	−	0.662020i
$473$	103413.	+	103413.i	0.462226	+	0.462226i
$474$		−	222364.i		−	0.989707i
$475$		0			0
$476$	207210.			0.914527
$477$	−11595.2	+	11595.2i	−0.0509614	+	0.0509614i
$478$	−202697.	−	202697.i	−0.887137	−	0.887137i
$479$			356277.i			1.55280i	0.630239	+	0.776401i	$0.282957\pi$
$479$			356277.i			1.55280i	−0.630239	+	0.776401i	$0.717043\pi$
$480$		0			0
$481$	110329.			0.476871
$482$	−140181.	+	140181.i	−0.603384	+	0.603384i
$483$	89271.5	+	89271.5i	0.382665	+	0.382665i
$484$			304323.i			1.29910i
$485$		0			0
$486$	140121.			0.593242
$487$	−55243.2	+	55243.2i	−0.232927	+	0.232927i	−0.813914	−	0.580986i	$-0.802667\pi$
$487$	−55243.2	+	55243.2i	−0.232927	+	0.232927i	0.580986	+	0.813914i	$0.302667\pi$
$488$	−231239.	−	231239.i	−0.971005	−	0.971005i
$489$		−	50917.1i		−	0.212934i
$490$		0			0
$491$	−22553.0			−0.0935495			−0.0467747	−	0.998905i	$-0.514894\pi$
$491$	−22553.0			−0.0935495			−0.0467747	+	0.998905i	$0.514894\pi$
$492$	−46838.9	+	46838.9i	−0.193498	+	0.193498i
$493$	−364816.	−	364816.i	−1.50100	−	1.50100i
$494$			463552.i			1.89952i
$495$		0			0
$496$	218636.			0.888708
$497$	89450.0	−	89450.0i	0.362132	−	0.362132i
$498$	−239862.	−	239862.i	−0.967172	−	0.967172i
$499$		−	31665.7i		−	0.127171i	−0.997976	−	0.0635855i	$-0.979746\pi$
$499$		−	31665.7i		−	0.127171i	0.997976	−	0.0635855i	$-0.0202536\pi$
$500$		0			0
$501$	429086.			1.70950
$502$	−160916.	+	160916.i	−0.638543	+	0.638543i
$503$	84275.0	+	84275.0i	0.333091	+	0.333091i	0.853759	−	0.520668i	$-0.174317\pi$
$503$	84275.0	+	84275.0i	0.333091	+	0.333091i	−0.520668	+	0.853759i	$0.674317\pi$
$504$		−	32946.9i		−	0.129704i
$505$		0			0
$506$	−447618.			−1.74826
$507$	76627.6	−	76627.6i	0.298105	−	0.298105i
$508$	208217.	+	208217.i	0.806844	+	0.806844i
$509$		−	184416.i		−	0.711807i	−0.934523	−	0.355903i	$-0.884173\pi$
$509$		−	184416.i		−	0.711807i	0.934523	−	0.355903i	$-0.115827\pi$
$510$		0			0
$511$	41914.7			0.160518
$512$	398719.	−	398719.i	1.52099	−	1.52099i
$513$	289805.	+	289805.i	1.10121	+	1.10121i
$514$			147410.i			0.557957i
$515$		0			0
$516$	541792.			2.03486
$517$	123476.	−	123476.i	0.461956	−	0.461956i
$518$	−82706.9	−	82706.9i	−0.308235	−	0.308235i
$519$		−	410058.i		−	1.52234i
$520$		0			0
$521$	−37375.8			−0.137694			−0.0688470	−	0.997627i	$-0.521932\pi$
$521$	−37375.8			−0.137694			−0.0688470	+	0.997627i	$0.521932\pi$
$522$	−108725.	+	108725.i	−0.399013	+	0.399013i
$523$	−322468.	−	322468.i	−1.17892	−	1.17892i	−0.980021	−	0.198895i	$-0.936265\pi$
$523$	−322468.	−	322468.i	−1.17892	−	1.17892i	−0.198895	−	0.980021i	$-0.563735\pi$
$524$		−	75456.6i		−	0.274811i
$525$		0			0
$526$	178420.			0.644869
$527$	135687.	−	135687.i	0.488559	−	0.488559i
$528$	−163736.	−	163736.i	−0.587323	−	0.587323i
$529$			410705.i			1.46764i
$530$		0			0
$531$	−22029.3			−0.0781288
$532$	236959.	−	236959.i	0.837239	−	0.837239i
$533$	20625.2	+	20625.2i	0.0726011	+	0.0726011i
$534$		−	66358.9i		−	0.232711i
$535$		0			0
$536$	−673904.			−2.34568
$537$	175009.	−	175009.i	0.606893	−	0.606893i
$538$	14517.6	+	14517.6i	0.0501568	+	0.0501568i
$539$		−	26051.0i		−	0.0896699i
$540$		0			0
$541$	372458.			1.27257			0.636287	−	0.771452i	$-0.280469\pi$
$541$	372458.			1.27257			0.636287	+	0.771452i	$0.280469\pi$
$542$	−603785.	+	603785.i	−2.05534	+	2.05534i
$543$	207335.	+	207335.i	0.703189	+	0.703189i
$544$			182459.i			0.616548i
$545$		0			0
$546$	133498.			0.447806
$547$	−413763.	+	413763.i	−1.38286	+	1.38286i	−0.543348	+	0.839508i	$0.682843\pi$
$547$	−413763.	+	413763.i	−1.38286	+	1.38286i	−0.839508	+	0.543348i	$0.817157\pi$
$548$	563644.	+	563644.i	1.87691	+	1.87691i
$549$			34538.7i			0.114594i
$550$		0			0
$551$	−834385.			−2.74829
$552$	−625583.	+	625583.i	−2.05308	+	2.05308i
$553$	50053.0	+	50053.0i	0.163674	+	0.163674i
$554$		−	540440.i		−	1.76087i
$555$		0			0
$556$	−84350.9			−0.272860
$557$	298308.	−	298308.i	0.961512	−	0.961512i	−0.0377744	−	0.999286i	$-0.512027\pi$
$557$	298308.	−	298308.i	0.961512	−	0.961512i	0.999286	+	0.0377744i	$0.0120268\pi$
$558$	−40438.2	−	40438.2i	−0.129875	−	0.129875i
$559$		−	238575.i		−	0.763485i
$560$		0			0
$561$	−203231.			−0.645751
$562$	661888.	−	661888.i	2.09562	−	2.09562i
$563$	−83327.3	−	83327.3i	−0.262888	−	0.262888i	0.563338	−	0.826226i	$-0.309517\pi$
$563$	−83327.3	−	83327.3i	−0.262888	−	0.262888i	−0.826226	+	0.563338i	$0.809517\pi$
$564$		−	646901.i		−	2.03367i
$565$		0			0
$566$	615026.			1.91982
$567$	68921.0	−	68921.0i	0.214380	−	0.214380i
$568$	626833.	+	626833.i	1.94292	+	1.94292i
$569$			260413.i			0.804336i	0.915566	+	0.402168i	$0.131743\pi$
$569$			260413.i			0.804336i	−0.915566	+	0.402168i	$0.868257\pi$
$570$		0			0
$571$	−94163.6			−0.288809			−0.144405	−	0.989519i	$-0.546127\pi$
$571$	−94163.6			−0.288809			−0.144405	+	0.989519i	$0.546127\pi$
$572$	−228226.	+	228226.i	−0.697546	+	0.697546i
$573$	212851.	+	212851.i	0.648287	+	0.648287i
$574$		−	30922.8i		−	0.0938545i
$575$		0			0
$576$	−27133.3			−0.0817819
$577$	388454.	−	388454.i	1.16678	−	1.16678i	0.183816	−	0.982961i	$-0.441155\pi$
$577$	388454.	−	388454.i	1.16678	−	1.16678i	0.982961	−	0.183816i	$-0.0588449\pi$
$578$	114751.	+	114751.i	0.343478	+	0.343478i
$579$			66582.6i			0.198611i
$580$		0			0
$581$	107984.			0.319894
$582$	89479.1	−	89479.1i	0.264165	−	0.264165i
$583$	−64247.9	−	64247.9i	−0.189026	−	0.189026i
$584$			293723.i			0.861217i
$585$		0			0
$586$	−670890.			−1.95369
$587$	279855.	−	279855.i	0.812187	−	0.812187i	−0.172774	−	0.984961i	$-0.555273\pi$
$587$	279855.	−	279855.i	0.812187	−	0.812187i	0.984961	+	0.172774i	$0.0552731\pi$
$588$	−68241.8	−	68241.8i	−0.197377	−	0.197377i
$589$		−	310335.i		−	0.894540i
$590$		0			0
$591$	390384.			1.11768
$592$	234023.	−	234023.i	0.667753	−	0.667753i
$593$	−94876.0	−	94876.0i	−0.269803	−	0.269803i	0.559218	−	0.829021i	$-0.311102\pi$
$593$	−94876.0	−	94876.0i	−0.269803	−	0.269803i	−0.829021	+	0.559218i	$0.811102\pi$
$594$			418484.i			1.18606i
$595$		0			0
$596$	1.37208e6			3.86265
$597$	−47691.6	+	47691.6i	−0.133811	+	0.133811i
$598$	516328.	+	516328.i	1.44385	+	1.44385i
$599$			335657.i			0.935496i	0.883862	+	0.467748i	$0.154935\pi$
$599$			335657.i			0.935496i	−0.883862	+	0.467748i	$0.845065\pi$
$600$		0			0
$601$	−78337.0			−0.216879			−0.108440	−	0.994103i	$-0.534585\pi$
$601$	−78337.0			−0.216879			−0.108440	+	0.994103i	$0.534585\pi$
$602$	−178844.	+	178844.i	−0.493495	+	0.493495i
$603$	50328.4	+	50328.4i	0.138413	+	0.138413i
$604$			389077.i			1.06650i
$605$		0			0
$606$	188389.			0.512992
$607$	392159.	−	392159.i	1.06435	−	1.06435i	0.0665679	−	0.997782i	$-0.478795\pi$
$607$	392159.	−	392159.i	1.06435	−	1.06435i	0.997782	−	0.0665679i	$-0.0212049\pi$
$608$	208654.	+	208654.i	0.564443	+	0.564443i
$609$			240295.i			0.647902i
$610$		0			0
$611$	−284859.			−0.763039
$612$	108442.	−	108442.i	0.289531	−	0.289531i
$613$	309872.	+	309872.i	0.824634	+	0.824634i	0.986769	−	0.162135i	$-0.0518380\pi$
$613$	309872.	+	309872.i	0.824634	+	0.824634i	−0.162135	+	0.986769i	$0.551838\pi$
$614$		−	131117.i		−	0.347794i
$615$		0			0
$616$	182556.			0.481099
$617$	343853.	−	343853.i	0.903238	−	0.903238i	−0.0924768	−	0.995715i	$-0.529478\pi$
$617$	343853.	−	343853.i	0.903238	−	0.903238i	0.995715	+	0.0924768i	$0.0294784\pi$
$618$	−529209.	−	529209.i	−1.38564	−	1.38564i
$619$		−	166876.i		−	0.435524i	−0.976002	−	0.217762i	$-0.930124\pi$
$619$		−	166876.i		−	0.435524i	0.976002	−	0.217762i	$-0.0698757\pi$
$620$		0			0
$621$	645600.			1.67410
$622$	174546.	−	174546.i	0.451159	−	0.451159i
$623$	14937.1	+	14937.1i	0.0384848	+	0.0384848i
$624$			377740.i			0.970115i
$625$		0			0
$626$	−674493.			−1.72119
$627$	−232409.	+	232409.i	−0.591178	+	0.591178i
$628$	303836.	+	303836.i	0.770405	+	0.770405i
$629$		−	290472.i		−	0.734181i
$630$		0			0
$631$	586336.			1.47261			0.736305	−	0.676650i	$-0.236569\pi$
$631$	586336.			1.47261			0.736305	+	0.676650i	$0.236569\pi$
$632$	−350753.	+	350753.i	−0.878148	+	0.878148i
$633$	−175203.	−	175203.i	−0.437253	−	0.437253i
$634$		−	1.26848e6i		−	3.15576i
$635$		0			0
$636$	−336601.			−0.832148
$637$	−30049.8	+	30049.8i	−0.0740564	+	0.0740564i
$638$	−602434.	−	602434.i	−1.48002	−	1.48002i
$639$		−	93626.2i		−	0.229295i
$640$		0			0
$641$	285959.			0.695966			0.347983	−	0.937501i	$-0.386867\pi$
$641$	285959.			0.695966			0.347983	+	0.937501i	$0.386867\pi$
$642$	−126698.	+	126698.i	−0.307397	+	0.307397i
$643$	10719.7	+	10719.7i	0.0259276	+	0.0259276i	0.719952	−	0.694024i	$-0.244164\pi$
$643$	10719.7	+	10719.7i	0.0259276	+	0.0259276i	−0.694024	+	0.719952i	$0.744164\pi$
$644$		−	527874.i		−	1.27280i
$645$		0			0
$646$	1.22043e6			2.92447
$647$	−437318.	+	437318.i	−1.04469	+	1.04469i	−0.0457394	+	0.998953i	$0.514564\pi$
$647$	−437318.	+	437318.i	−1.04469	+	1.04469i	−0.998953	+	0.0457394i	$0.985436\pi$
$648$	482973.	+	482973.i	1.15020	+	1.15020i
$649$		−	122062.i		−	0.289796i
$650$		0			0
$651$	−89373.4			−0.210885
$652$	−150540.	+	150540.i	−0.354125	+	0.354125i
$653$	−417145.	−	417145.i	−0.978274	−	0.978274i	0.0214948	−	0.999769i	$-0.493157\pi$
$653$	−417145.	−	417145.i	−0.978274	−	0.978274i	−0.999769	+	0.0214948i	$0.993157\pi$
$654$			148941.i			0.348224i
$655$		0			0
$656$	87497.6			0.203324
$657$	21935.8	−	21935.8i	0.0508186	−	0.0508186i
$658$	213541.	+	213541.i	0.493206	+	0.493206i
$659$			756930.i			1.74295i	0.490440	+	0.871475i	$0.336836\pi$
$659$			756930.i			1.74295i	−0.490440	+	0.871475i	$0.663164\pi$
$660$		0			0
$661$	−260817.			−0.596943			−0.298472	−	0.954418i	$-0.596477\pi$
$661$	−260817.			−0.596943			−0.298472	+	0.954418i	$0.596477\pi$
$662$	407976.	−	407976.i	0.930934	−	0.930934i
$663$	234427.	+	234427.i	0.533312	+	0.533312i
$664$			756712.i			1.71630i
$665$		0			0
$666$	−86568.3			−0.195169
$667$	−929381.	+	929381.i	−2.08902	+	2.08902i
$668$	−1.26862e6	−	1.26862e6i	−2.84301	−	2.84301i
$669$			13375.5i			0.0298852i
$670$		0			0
$671$	−191376.			−0.425052
$672$	60090.3	−	60090.3i	0.133066	−	0.133066i
$673$	41288.5	+	41288.5i	0.0911588	+	0.0911588i	0.751216	−	0.660057i	$-0.229468\pi$
$673$	41288.5	+	41288.5i	0.0911588	+	0.0911588i	−0.660057	+	0.751216i	$0.729468\pi$
$674$			1.11706e6i			2.45898i
$675$		0			0
$676$	−453109.			−0.991539
$677$	14140.5	−	14140.5i	0.0308523	−	0.0308523i	−0.691512	−	0.722365i	$-0.743055\pi$
$677$	14140.5	−	14140.5i	0.0308523	−	0.0308523i	0.722365	+	0.691512i	$0.243055\pi$
$678$	−28570.4	−	28570.4i	−0.0621523	−	0.0621523i
$679$			40282.7i			0.0873733i
$680$		0			0
$681$	−67101.2			−0.144689
$682$	224065.	−	224065.i	0.481731	−	0.481731i
$683$	−337178.	−	337178.i	−0.722800	−	0.722800i	0.246375	−	0.969175i	$-0.420761\pi$
$683$	−337178.	−	337178.i	−0.722800	−	0.722800i	−0.969175	+	0.246375i	$0.920761\pi$
$684$		−	248022.i		−	0.530124i
$685$		0			0
$686$	45052.9			0.0957358
$687$	595325.	−	595325.i	1.26136	−	1.26136i
$688$	−506049.	−	506049.i	−1.06909	−	1.06909i
$689$			148220.i			0.312225i
$690$		0			0
$691$	−565385.			−1.18410			−0.592049	−	0.805902i	$-0.701681\pi$
$691$	−565385.			−1.18410			−0.592049	+	0.805902i	$0.701681\pi$
$692$	−1.21236e6	+	1.21236e6i	−2.53175	+	2.53175i
$693$	−13633.6	−	13633.6i	−0.0283887	−	0.0283887i
$694$		−	95338.2i		−	0.197947i
$695$		0			0
$696$	−1.68390e6			−3.47614
$697$	54301.5	−	54301.5i	0.111775	−	0.111775i
$698$	939078.	+	939078.i	1.92748	+	1.92748i
$699$		−	194134.i		−	0.397326i
$700$		0			0
$701$	564548.			1.14885			0.574427	−	0.818556i	$-0.305225\pi$
$701$	564548.			1.14885			0.574427	+	0.818556i	$0.305225\pi$
$702$	482721.	−	482721.i	0.979540	−	0.979540i
$703$	−332175.	−	332175.i	−0.672135	−	0.672135i
$704$		−	150343.i		−	0.303346i
$705$		0			0
$706$	−1.09519e6			−2.19726
$707$	−42405.5	+	42405.5i	−0.0848367	+	0.0848367i
$708$	−319748.	−	319748.i	−0.637883	−	0.637883i
$709$			103288.i			0.205475i	0.994709	+	0.102737i	$0.0327602\pi$
$709$			103288.i			0.205475i	−0.994709	+	0.102737i	$0.967240\pi$
$710$		0			0
$711$	52389.8			0.103635
$712$	−104674.	+	104674.i	−0.206480	+	0.206480i
$713$	−345667.	−	345667.i	−0.679953	−	0.679953i
$714$		−	351471.i		−	0.689434i
$715$		0			0
$716$	−1.03485e6			−2.01861
$717$	−234450.	+	234450.i	−0.456049	+	0.456049i
$718$	−283213.	−	283213.i	−0.549369	−	0.549369i
$719$			17971.7i			0.0347641i	0.999849	+	0.0173820i	$0.00553316\pi$
$719$			17971.7i			0.0347641i	−0.999849	+	0.0173820i	$0.994467\pi$
$720$		0			0
$721$	238245.			0.458304
$722$	742090.	−	742090.i	1.42358	−	1.42358i
$723$	162140.	+	162140.i	0.310180	+	0.310180i
$724$		−	1.22600e6i		−	2.33890i
$725$		0			0
$726$	516195.			0.979355
$727$	−21242.5	+	21242.5i	−0.0401918	+	0.0401918i	−0.726917	−	0.686725i	$-0.759048\pi$
$727$	−21242.5	+	21242.5i	−0.0401918	+	0.0401918i	0.686725	+	0.726917i	$0.259048\pi$
$728$	−210578.	−	210578.i	−0.397330	−	0.397330i
$729$		−	588361.i		−	1.10710i
$730$		0			0
$731$	−628113.			−1.17545
$732$	−501318.	+	501318.i	−0.935602	+	0.935602i
$733$	−529740.	−	529740.i	−0.985950	−	0.985950i	0.0139530	−	0.999903i	$-0.495558\pi$
$733$	−529740.	−	529740.i	−0.985950	−	0.985950i	−0.999903	+	0.0139530i	$0.995558\pi$
$734$		−	435777.i		−	0.808858i
$735$		0			0
$736$	464820.			0.858082
$737$	−278865.	+	278865.i	−0.513404	+	0.513404i
$738$	−16183.3	−	16183.3i	−0.0297134	−	0.0297134i
$739$		−	596812.i		−	1.09282i	−0.837518	−	0.546410i	$-0.815994\pi$
$739$		−	596812.i		−	1.09282i	0.837518	−	0.546410i	$-0.184006\pi$
$740$		0			0
$741$	536168.			0.976482
$742$	111111.	−	111111.i	0.201813	−	0.201813i
$743$	431072.	+	431072.i	0.780859	+	0.780859i	0.979976	−	0.199117i	$-0.0638074\pi$
$743$	431072.	+	431072.i	0.780859	+	0.780859i	−0.199117	+	0.979976i	$0.563807\pi$
$744$		−	626297.i		−	1.13145i
$745$		0			0
$746$	−313877.			−0.564004
$747$	56512.6	−	56512.6i	0.101275	−	0.101275i
$748$	600867.	+	600867.i	1.07393	+	1.07393i
$749$		−	57038.2i		−	0.101672i
$750$		0			0
$751$	−173893.			−0.308320			−0.154160	−	0.988046i	$-0.549267\pi$
$751$	−173893.			−0.308320			−0.154160	+	0.988046i	$0.549267\pi$
$752$	−604223.	+	604223.i	−1.06847	+	1.06847i
$753$	186123.	+	186123.i	0.328254	+	0.328254i
$754$			1.38981e6i			2.44464i
$755$		0			0
$756$	−493516.			−0.863491
$757$	−38121.2	+	38121.2i	−0.0665234	+	0.0665234i	−0.739586	−	0.673062i	$-0.764979\pi$
$757$	−38121.2	+	38121.2i	−0.0665234	+	0.0665234i	0.673062	+	0.739586i	$0.264979\pi$
$758$	−188267.	−	188267.i	−0.327669	−	0.327669i
$759$			517739.i			0.898726i
$760$		0			0
$761$	189381.			0.327014			0.163507	−	0.986542i	$-0.447719\pi$
$761$	189381.			0.327014			0.163507	+	0.986542i	$0.447719\pi$
$762$	353180.	−	353180.i	0.608255	−	0.608255i
$763$	−33525.9	−	33525.9i	−0.0575879	−	0.0575879i
$764$		−	1.25862e6i		−	2.15629i
$765$		0			0
$766$	−406160.			−0.692213
$767$	−140799.	+	140799.i	−0.239336	+	0.239336i
$768$	−762010.	−	762010.i	−1.29193	−	1.29193i
$769$			444810.i			0.752179i	0.926583	+	0.376090i	$0.122732\pi$
$769$			444810.i			0.752179i	−0.926583	+	0.376090i	$0.877268\pi$
$770$		0			0
$771$	170502.			0.286828
$772$	196856.	−	196856.i	0.330304	−	0.330304i
$773$	810826.	+	810826.i	1.35696	+	1.35696i	0.877635	+	0.479329i	$0.159120\pi$
$773$	810826.	+	810826.i	1.35696	+	1.35696i	0.479329	+	0.877635i	$0.340880\pi$
$774$			187194.i			0.312471i
$775$		0			0
$776$	−282286.			−0.468777
$777$	−95663.1	+	95663.1i	−0.158454	+	0.158454i
$778$	393386.	+	393386.i	0.649919	+	0.649919i
$779$		−	124195.i		−	0.204658i
$780$		0			0
$781$	518774.			0.850504
$782$	1.35937e6	−	1.35937e6i	2.22293	−	2.22293i
$783$	868890.	+	868890.i	1.41723	+	1.41723i
$784$			127479.i			0.207399i
$785$		0			0
$786$	−127990.			−0.207172
$787$	−659695.	+	659695.i	−1.06511	+	1.06511i	−0.0673806	+	0.997727i	$0.521464\pi$
$787$	−659695.	+	659695.i	−1.06511	+	1.06511i	−0.997727	+	0.0673806i	$0.978536\pi$
$788$	−1.15420e6	−	1.15420e6i	−1.85878	−	1.85878i
$789$		−	206370.i		−	0.331506i
$790$		0			0
$791$	12862.1			0.0205570
$792$	95539.6	−	95539.6i	0.152312	−	0.152312i
$793$	220752.	+	220752.i	0.351041	+	0.351041i
$794$			1.32284e6i			2.09829i
$795$		0			0
$796$	282007.			0.445075
$797$	−373331.	+	373331.i	−0.587729	+	0.587729i	−0.937016	−	0.349287i	$-0.886424\pi$
$797$	−373331.	+	373331.i	−0.587729	+	0.587729i	0.349287	+	0.937016i	$0.386424\pi$
$798$	−401931.	−	401931.i	−0.631169	−	0.631169i
$799$			749969.i			1.17476i
$800$		0			0
$801$	15634.4			0.0243678
$802$	−1.30772e6	+	1.30772e6i	−2.03314	+	2.03314i
$803$	121544.	+	121544.i	0.188496	+	0.188496i
$804$			1.46100e6i			2.26015i
$805$		0			0
$806$	−516917.			−0.795703
$807$	16791.8	−	16791.8i	0.0257840	−	0.0257840i
$808$	−297163.	−	297163.i	−0.455168	−	0.455168i
$809$			824584.i			1.25990i	0.776634	+	0.629952i	$0.216926\pi$
$809$			824584.i			1.25990i	−0.776634	+	0.629952i	$0.783074\pi$
$810$		0			0
$811$	469009.			0.713081			0.356541	−	0.934280i	$-0.383956\pi$
$811$	469009.			0.713081			0.356541	+	0.934280i	$0.383956\pi$
$812$	710447.	−	710447.i	1.07751	−	1.07751i
$813$	698369.	+	698369.i	1.05658	+	1.05658i
$814$		−	479667.i		−	0.723921i
$815$		0			0
$816$	994504.			1.49357
$817$	−718291.	+	718291.i	−1.07611	+	1.07611i
$818$	1.27133e6	+	1.27133e6i	1.90000	+	1.90000i
$819$			31452.8i			0.0468912i
$820$		0			0
$821$	88089.6			0.130689			0.0653444	−	0.997863i	$-0.479185\pi$
$821$	88089.6			0.130689			0.0653444	+	0.997863i	$0.479185\pi$
$822$	956057.	−	956057.i	1.41495	−	1.41495i
$823$	−619299.	−	619299.i	−0.914326	−	0.914326i	0.0822833	−	0.996609i	$-0.473779\pi$
$823$	−619299.	−	619299.i	−0.914326	−	0.914326i	−0.996609	+	0.0822833i	$0.973779\pi$
$824$			1.66954e6i			2.45890i
$825$		0			0
$826$	211096.			0.309400
$827$	44733.2	−	44733.2i	0.0654062	−	0.0654062i	−0.673647	−	0.739053i	$-0.735273\pi$
$827$	44733.2	−	44733.2i	0.0654062	−	0.0654062i	0.739053	+	0.673647i	$0.235273\pi$
$828$	−276259.	−	276259.i	−0.402955	−	0.402955i
$829$			264797.i			0.385305i	0.981267	+	0.192653i	$0.0617090\pi$
$829$			264797.i			0.385305i	−0.981267	+	0.192653i	$0.938291\pi$
$830$		0			0
$831$	−625101.			−0.905207
$832$	−173421.	+	173421.i	−0.250527	+	0.250527i
$833$	79114.4	+	79114.4i	0.114016	+	0.114016i
$834$			143077.i			0.205701i
$835$		0			0
$836$	1.37427e6			1.96634
$837$	−323169.	+	323169.i	−0.461294	+	0.461294i
$838$	−304135.	−	304135.i	−0.433090	−	0.433090i
$839$			1.35708e6i			1.92789i	0.266110	+	0.963943i	$0.414261\pi$
$839$			1.35708e6i			1.92789i	−0.266110	+	0.963943i	$0.585739\pi$
$840$		0			0
$841$	−1.79436e6			−2.53699
$842$	320841.	−	320841.i	0.452549	−	0.452549i
$843$	−765574.	−	765574.i	−1.07729	−	1.07729i
$844$			1.03600e6i			1.45436i
$845$		0			0
$846$	223510.			0.312289
$847$	−116193.	+	116193.i	−0.161962	+	0.161962i
$848$	314394.	+	314394.i	0.437203	+	0.437203i
$849$		−	711371.i		−	0.986917i
$850$		0			0
$851$	−739988.			−1.02180
$852$	1.35895e6	−	1.35895e6i	1.87208	−	1.87208i
$853$	239249.	+	239249.i	0.328816	+	0.328816i	0.852136	−	0.523320i	$-0.175307\pi$
$853$	239249.	+	239249.i	0.328816	+	0.328816i	−0.523320	+	0.852136i	$0.675307\pi$
$854$		−	330968.i		−	0.453806i
$855$		0			0
$856$	399703.			0.545494
$857$	397948.	−	397948.i	0.541832	−	0.541832i	−0.382234	−	0.924066i	$-0.624845\pi$
$857$	397948.	−	397948.i	0.541832	−	0.541832i	0.924066	+	0.382234i	$0.124845\pi$
$858$	387118.	+	387118.i	0.525859	+	0.525859i
$859$		−	352827.i		−	0.478163i	−0.971000	−	0.239081i	$-0.923154\pi$
$859$		−	352827.i		−	0.478163i	0.971000	−	0.239081i	$-0.0768462\pi$
$860$		0			0
$861$	−35766.9			−0.0482475
$862$	−696012.	+	696012.i	−0.936704	+	0.936704i
$863$	−697837.	−	697837.i	−0.936984	−	0.936984i	0.0611447	−	0.998129i	$-0.480525\pi$
$863$	−697837.	−	697837.i	−0.936984	−	0.936984i	−0.998129	+	0.0611447i	$0.980525\pi$
$864$		−	434566.i		−	0.582141i
$865$		0			0
$866$	1.82446e6			2.43275
$867$	132727.	−	132727.i	0.176571	−	0.176571i
$868$	264238.	+	264238.i	0.350717	+	0.350717i
$869$			290287.i			0.384404i
$870$		0			0
$871$	643341.			0.848018
$872$	234938.	−	234938.i	0.308972	−	0.308972i
$873$	21081.7	+	21081.7i	0.0276616	+	0.0276616i
$874$		−	3.10908e6i		−	4.07014i
$875$		0			0
$876$	636781.			0.829816
$877$	259189.	−	259189.i	0.336990	−	0.336990i	−0.518243	−	0.855233i	$-0.673414\pi$
$877$	259189.	−	259189.i	0.336990	−	0.336990i	0.855233	+	0.518243i	$0.173414\pi$
$878$	1.46156e6	+	1.46156e6i	1.89595	+	1.89595i
$879$			775986.i			1.00433i
$880$		0			0
$881$	978078.			1.26015			0.630074	−	0.776535i	$-0.283024\pi$
$881$	978078.			1.26015			0.630074	+	0.776535i	$0.283024\pi$
$882$	23578.1	−	23578.1i	0.0303091	−	0.0303091i
$883$	−461432.	−	461432.i	−0.591816	−	0.591816i	0.346306	−	0.938122i	$-0.387436\pi$
$883$	−461432.	−	461432.i	−0.591816	−	0.591816i	−0.938122	+	0.346306i	$0.887436\pi$
$884$		−	1.38620e6i		−	1.77387i
$885$		0			0
$886$	−760550.			−0.968858
$887$	−474502.	+	474502.i	−0.603102	+	0.603102i	−0.941134	−	0.338033i	$-0.890239\pi$
$887$	−474502.	+	474502.i	−0.603102	+	0.603102i	0.338033	+	0.941134i	$0.390239\pi$
$888$	−670373.	−	670373.i	−0.850140	−	0.850140i
$889$			158998.i			0.201182i
$890$		0			0
$891$	399714.			0.503494
$892$	39545.5	−	39545.5i	0.0497012	−	0.0497012i
$893$	857641.	+	857641.i	1.07548	+	1.07548i
$894$		−	2.32733e6i		−	2.91194i
$895$		0			0
$896$	425756.			0.530328
$897$	597211.	−	597211.i	0.742238	−	0.742238i
$898$	1.19912e6	+	1.19912e6i	1.48700	+	1.48700i
$899$		−	930442.i		−	1.15125i
$900$		0			0
$901$	390230.			0.480696
$902$	89669.9	−	89669.9i	0.110213	−	0.110213i
$903$	206861.	+	206861.i	0.253690	+	0.253690i
$904$			90133.3i			0.110293i
$905$		0			0
$906$	659956.			0.804005
$907$	425264.	−	425264.i	0.516945	−	0.516945i	−0.399701	−	0.916646i	$-0.630886\pi$
$907$	425264.	−	425264.i	0.516945	−	0.516945i	0.916646	+	0.399701i	$0.130886\pi$
$908$	198389.	+	198389.i	0.240628	+	0.240628i
$909$			44385.3i			0.0537170i
$910$		0			0
$911$	482049.			0.580837			0.290419	−	0.956900i	$-0.406205\pi$
$911$	482049.			0.580837			0.290419	+	0.956900i	$0.406205\pi$
$912$	1.13728e6	−	1.13728e6i	1.36735	−	1.36735i
$913$	313131.	+	313131.i	0.375651	+	0.375651i
$914$		−	342495.i		−	0.409980i
$915$		0			0
$916$	−3.52023e6			−4.19547
$917$	28809.9	−	28809.9i	0.0342613	−	0.0342613i
$918$	−1.27090e6	−	1.27090e6i	−1.50808	−	1.50808i
$919$			1231.53i			0.00145819i	1.00000		0.000729096i	$0.000232078\pi$
$919$			1231.53i			0.00145819i	−1.00000		0.000729096i	$0.999768\pi$
$920$		0			0
$921$	−151657.			−0.178789
$922$	−857934.	+	857934.i	−1.00923	+	1.00923i
$923$	−598406.	−	598406.i	−0.702413	−	0.702413i
$924$		−	395775.i		−	0.463558i
$925$		0			0
$926$	1.25958e6			1.46894
$927$	124684.	−	124684.i	0.145095	−	0.145095i
$928$	625584.	+	625584.i	0.726423	+	0.726423i
$929$		−	1.43314e6i		−	1.66057i	−0.557342	−	0.830283i	$-0.688179\pi$
$929$		−	1.43314e6i		−	1.66057i	0.557342	−	0.830283i	$-0.311821\pi$
$930$		0			0
$931$	180946.			0.208761
$932$	−573970.	+	573970.i	−0.660781	+	0.660781i
$933$	−201889.	−	201889.i	−0.231926	−	0.231926i
$934$			1.27191e6i			1.45802i
$935$		0			0
$936$	−220410.			−0.251582
$937$	36611.0	−	36611.0i	0.0416996	−	0.0416996i	−0.685950	−	0.727649i	$-0.740613\pi$
$937$	36611.0	−	36611.0i	0.0416996	−	0.0416996i	0.727649	+	0.685950i	$0.240613\pi$
$938$	−482272.	−	482272.i	−0.548134	−	0.548134i
$939$			780154.i			0.884808i
$940$		0			0
$941$	−1.64250e6			−1.85492			−0.927462	−	0.373918i	$-0.878014\pi$
$941$	−1.64250e6			−1.85492			−0.927462	+	0.373918i	$0.878014\pi$
$942$	515368.	−	515368.i	0.580785	−	0.580785i
$943$	−138335.	−	138335.i	−0.155564	−	0.155564i
$944$			597306.i			0.670275i
$945$		0			0
$946$	−1.03723e6			−1.15902
$947$	215799.	−	215799.i	0.240630	−	0.240630i	−0.576481	−	0.817111i	$-0.695574\pi$
$947$	215799.	−	215799.i	0.240630	−	0.240630i	0.817111	+	0.576481i	$0.195574\pi$
$948$	760421.	+	760421.i	0.846130	+	0.846130i
$949$		−	280402.i		−	0.311350i
$950$		0			0
$951$	−1.46719e6			−1.62227
$952$	−554405.	+	554405.i	−0.611721	+	0.611721i
$953$	675833.	+	675833.i	0.744139	+	0.744139i	0.973372	−	0.229233i	$-0.0736218\pi$
$953$	675833.	+	675833.i	0.744139	+	0.744139i	−0.229233	+	0.973372i	$0.573622\pi$
$954$		−	116299.i		−	0.127784i
$955$		0			0
$956$	1.38633e6			1.51688
$957$	−696806.	+	696806.i	−0.760831	+	0.760831i
$958$	−1.78671e6	−	1.78671e6i	−1.94681	−	1.94681i
$959$			430408.i			0.467997i
$960$		0			0
$961$	−577459.			−0.625280
$962$	−553296.	+	553296.i	−0.597871	+	0.597871i
$963$	−29850.6	−	29850.6i	−0.0321884	−	0.0321884i
$964$		−	958756.i		−	1.03170i
$965$		0			0
$966$	−895384.			−0.959522
$967$	−167436.	+	167436.i	−0.179059	+	0.179059i	−0.790946	−	0.611886i	$-0.790411\pi$
$967$	−167436.	+	167436.i	−0.179059	+	0.179059i	0.611886	+	0.790946i	$0.290411\pi$
$968$	−814239.	−	814239.i	−0.868962	−	0.868962i
$969$		−	1.41161e6i		−	1.50337i
$970$		0			0
$971$	−406368.			−0.431004			−0.215502	−	0.976503i	$-0.569139\pi$
$971$	−406368.			−0.431004			−0.215502	+	0.976503i	$0.569139\pi$
$972$	−479176.	+	479176.i	−0.507180	+	0.507180i
$973$	−32205.8	−	32205.8i	−0.0340180	−	0.0340180i
$974$		−	554083.i		−	0.584060i
$975$		0			0
$976$	936489.			0.983113
$977$	−816231.	+	816231.i	−0.855114	+	0.855114i	−0.990758	−	0.135644i	$-0.956690\pi$
$977$	−816231.	+	816231.i	−0.855114	+	0.855114i	0.135644	+	0.990758i	$0.456690\pi$
$978$	255347.	+	255347.i	0.266964	+	0.266964i
$979$			86629.0i			0.0903853i
$980$		0			0
$981$	−35091.1			−0.0364636
$982$	113102.	−	113102.i	0.117286	−	0.117286i
$983$	519170.	+	519170.i	0.537283	+	0.537283i	0.922730	−	0.385447i	$-0.125953\pi$
$983$	519170.	+	519170.i	0.537283	+	0.537283i	−0.385447	+	0.922730i	$0.625953\pi$
$984$		−	250642.i		−	0.258859i
$985$		0			0
$986$	3.65907e6			3.76371
$987$	246992.	−	246992.i	0.253541	−	0.253541i
$988$	−1.58522e6	−	1.58522e6i	−1.62396	−	1.62396i
$989$			1.60014e6i			1.63593i
$990$		0			0
$991$	382417.			0.389395			0.194697	−	0.980863i	$-0.437627\pi$
$991$	382417.			0.389395			0.194697	+	0.980863i	$0.437627\pi$
$992$	−232675.	+	232675.i	−0.236443	+	0.236443i
$993$	−471887.	−	471887.i	−0.478563	−	0.478563i
$994$			897174.i			0.908038i
$995$		0			0
$996$	1.64052e6			1.65373
$997$	429735.	−	429735.i	0.432325	−	0.432325i	−0.457093	−	0.889419i	$-0.651110\pi$
$997$	429735.	−	429735.i	0.432325	−	0.432325i	0.889419	+	0.457093i	$0.151110\pi$
$998$	158802.	+	158802.i	0.159439	+	0.159439i
$999$			691824.i			0.693210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.43.2		24
5.2	odd	4	inner	175.5.g.c.57.2		24
5.3	odd	4		35.5.g.a.22.11	yes	24
5.4	even	2		35.5.g.a.8.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.11	✓	24	5.4	even	2
35.5.g.a.22.11	yes	24	5.3	odd	4
175.5.g.c.43.2		24	1.1	even	1	trivial
175.5.g.c.57.2		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)

\(f(q)\)	\(=\)	\(q+(-5.01495 + 5.01495i) q^{2} +(5.80055 + 5.80055i) q^{3} -34.2994i q^{4} -58.1789 q^{6} +(13.0958 - 13.0958i) q^{7} +(91.7707 + 91.7707i) q^{8} -13.7072i q^{9} +O(q^{10})\)	\(q+(-5.01495 + 5.01495i) q^{2} +(5.80055 + 5.80055i) q^{3} -34.2994i q^{4} -58.1789 q^{6} +(13.0958 - 13.0958i) q^{7} +(91.7707 + 91.7707i) q^{8} -13.7072i q^{9} +75.9504 q^{11} +(198.956 - 198.956i) q^{12} +(-87.6088 - 87.6088i) q^{13} +131.350i q^{14} -371.660 q^{16} +(-230.654 + 230.654i) q^{17} +(68.7410 + 68.7410i) q^{18} +527.538i q^{19} +151.926 q^{21} +(-380.888 + 380.888i) q^{22} +(587.599 + 587.599i) q^{23} +1064.64i q^{24} +878.707 q^{26} +(549.354 - 549.354i) q^{27} +(-449.178 - 449.178i) q^{28} +1581.66i q^{29} -588.270 q^{31} +(395.524 - 395.524i) q^{32} +(440.554 + 440.554i) q^{33} -2313.44i q^{34} -470.149 q^{36} +(-629.670 + 629.670i) q^{37} +(-2645.58 - 2645.58i) q^{38} -1016.36i q^{39} -235.424 q^{41} +(-761.900 + 761.900i) q^{42} +(1361.59 + 1361.59i) q^{43} -2605.06i q^{44} -5893.56 q^{46} +(1625.74 - 1625.74i) q^{47} +(-2155.83 - 2155.83i) q^{48} -343.000i q^{49} -2675.84 q^{51} +(-3004.93 + 3004.93i) q^{52} +(-845.919 - 845.919i) q^{53} +5509.96i q^{54} +2403.62 q^{56} +(-3060.01 + 3060.01i) q^{57} +(-7931.94 - 7931.94i) q^{58} -1607.13i q^{59} -2519.75 q^{61} +(2950.14 - 2950.14i) q^{62} +(-179.507 - 179.507i) q^{63} -1979.49i q^{64} -4418.72 q^{66} +(-3671.67 + 3671.67i) q^{67} +(7911.31 + 7911.31i) q^{68} +6816.80i q^{69} +6830.43 q^{71} +(1257.92 - 1257.92i) q^{72} +(1600.31 + 1600.31i) q^{73} -6315.53i q^{74} +18094.3 q^{76} +(994.632 - 994.632i) q^{77} +(5096.99 + 5096.99i) q^{78} +3822.06i q^{79} +5262.83 q^{81} +(1180.64 - 1180.64i) q^{82} +(4122.84 + 4122.84i) q^{83} -5210.97i q^{84} -13656.6 q^{86} +(-9174.49 + 9174.49i) q^{87} +(6970.02 + 6970.02i) q^{88} +1140.60i q^{89} -2294.61 q^{91} +(20154.3 - 20154.3i) q^{92} +(-3412.29 - 3412.29i) q^{93} +16306.0i q^{94} +4588.52 q^{96} +(-1538.00 + 1538.00i) q^{97} +(1720.13 + 1720.13i) q^{98} -1041.07i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 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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