LMFDB - Embedded newform 175.5.g.c.57.2

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			57.2
Character	$\chi$	$=$	175.57
Dual form			175.5.g.c.43.2

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

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

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	−0.954032	−	0.299705i	$-0.903112\pi$
$2$	−5.01495	−	5.01495i	−1.25374	−	1.25374i	−0.299705	−	0.954032i	$-0.596888\pi$
$3$	5.80055	−	5.80055i	0.644506	−	0.644506i	−0.307154	−	0.951660i	$-0.599377\pi$
$3$	5.80055	−	5.80055i	0.644506	−	0.644506i	0.951660	+	0.307154i	$0.0993767\pi$
$4$			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	−0.917086	−	0.398690i	$-0.869465\pi$
$13$	−87.6088	+	87.6088i	−0.518395	+	0.518395i	0.398690	+	0.917086i	$0.369465\pi$
$14$		−	131.350i		−	0.670151i
$15$		0			0
$16$	−371.660			−1.45180
$17$	−230.654	−	230.654i	−0.798111	−	0.798111i	0.184686	−	0.982798i	$-0.440873\pi$
$17$	−230.654	−	230.654i	−0.798111	−	0.798111i	−0.982798	+	0.184686i	$0.940873\pi$
$18$	68.7410	−	68.7410i	0.212163	−	0.212163i
$19$		−	527.538i		−	1.46132i	−0.682739	−	0.730662i	$-0.739211\pi$
$19$		−	527.538i		−	1.46132i	0.682739	−	0.730662i	$-0.260789\pi$
$20$		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	0.117728	−	0.993046i	$-0.462439\pi$
$23$	587.599	−	587.599i	1.11077	−	1.11077i	0.993046	−	0.117728i	$-0.0375611\pi$
$24$		−	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	$-0.610504\pi$
$29$		−	1581.66i		−	1.88069i	0.340226	−	0.940344i	$-0.389496\pi$
$30$		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	0.438690	−	0.898639i	$-0.355443\pi$
$37$	−629.670	−	629.670i	−0.459949	−	0.459949i	−0.898639	+	0.438690i	$0.855443\pi$
$38$	−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	−0.235485	−	0.971878i	$-0.575668\pi$
$43$	1361.59	−	1361.59i	0.736393	−	0.736393i	0.971878	+	0.235485i	$0.0756678\pi$
$44$			2605.06i			1.34559i
$45$		0			0
$46$	−5893.56			−2.78524
$47$	1625.74	+	1625.74i	0.735963	+	0.735963i	0.971794	−	0.235831i	$-0.0757811\pi$
$47$	1625.74	+	1625.74i	0.735963	+	0.735963i	−0.235831	+	0.971794i	$0.575781\pi$
$48$	−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	−0.841462	−	0.540316i	$-0.818305\pi$
$53$	−845.919	+	845.919i	−0.301146	+	0.301146i	0.540316	+	0.841462i	$0.318305\pi$
$54$		−	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	$0.0741485\pi$
$59$			1607.13i			0.461686i	−0.972991	+	0.230843i	$0.925852\pi$
$60$		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	0.167881	−	0.985807i	$-0.446308\pi$
$67$	−3671.67	−	3671.67i	−0.817926	−	0.817926i	−0.985807	+	0.167881i	$0.946308\pi$
$68$	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	−0.540830	−	0.841132i	$-0.681890\pi$
$73$	1600.31	−	1600.31i	0.300302	−	0.300302i	0.841132	+	0.540830i	$0.181890\pi$
$74$			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	$-0.900940\pi$
$79$		−	3822.06i		−	0.612412i	0.951965	−	0.306206i	$-0.0990596\pi$
$80$		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	−0.341437	−	0.939905i	$-0.610914\pi$
$83$	4122.84	−	4122.84i	0.598467	−	0.598467i	0.939905	+	0.341437i	$0.110914\pi$
$84$			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	$-0.977062\pi$
$89$		−	1140.60i		−	0.143997i	0.997405	−	0.0719984i	$-0.0229377\pi$
$90$		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	0.620637	−	0.784098i	$-0.286874\pi$
$97$	−1538.00	−	1538.00i	−0.163460	−	0.163460i	−0.784098	+	0.620637i	$0.786874\pi$
$98$	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	−0.133625	−	0.991032i	$-0.542662\pi$
$103$	9096.24	−	9096.24i	0.857407	−	0.857407i	0.991032	+	0.133625i	$0.0426616\pi$
$104$			16079.8i			1.48667i
$105$		0			0
$106$	8484.48			0.755116
$107$	2177.73	+	2177.73i	0.190211	+	0.190211i	0.795787	−	0.605576i	$-0.207057\pi$
$107$	2177.73	+	2177.73i	0.190211	+	0.190211i	−0.605576	+	0.795787i	$0.707057\pi$
$108$	−18842.5	+	18842.5i	−1.61544	+	1.61544i
$109$			2560.05i			0.215474i	0.994179	+	0.107737i	$0.0343605\pi$
$109$			2560.05i			0.215474i	−0.994179	+	0.107737i	$0.965640\pi$
$110$		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	−0.687616	−	0.726075i	$-0.741343\pi$
$113$	491.079	−	491.079i	0.0384587	−	0.0384587i	0.726075	+	0.687616i	$0.241343\pi$
$114$			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	0.493417	−	0.869793i	$-0.335748\pi$
$127$	−6070.58	−	6070.58i	−0.376377	−	0.376377i	−0.869793	+	0.493417i	$0.835748\pi$
$128$	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	0.117528	−	0.993070i	$-0.462503\pi$
$137$	−16433.0	−	16433.0i	−0.875541	−	0.875541i	−0.993070	+	0.117528i	$0.962503\pi$
$138$	−34185.9	+	34185.9i	−1.79510	+	1.79510i
$139$			2459.25i			0.127284i	0.997973	+	0.0636419i	$0.0202715\pi$
$139$			2459.25i			0.127284i	−0.997973	+	0.0636419i	$0.979728\pi$
$140$		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	$-0.642889\pi$
$149$		−	40002.9i		−	1.80185i	0.433973	−	0.900926i	$-0.357111\pi$
$150$		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	0.504205	−	0.863584i	$-0.331786\pi$
$157$	−8858.33	−	8858.33i	−0.359379	−	0.359379i	−0.863584	+	0.504205i	$0.831786\pi$
$158$	−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	−0.784862	−	0.619670i	$-0.787266\pi$
$163$	−4388.99	+	4388.99i	−0.165192	+	0.165192i	0.619670	+	0.784862i	$0.287266\pi$
$164$		−	8074.90i		−	0.300227i
$165$		0			0
$166$	−41351.7			−1.50064
$167$	36986.7	+	36986.7i	1.32621	+	1.32621i	0.908649	+	0.417560i	$0.137115\pi$
$167$	36986.7	+	36986.7i	1.32621	+	1.32621i	0.417560	+	0.908649i	$0.362885\pi$
$168$	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	−0.201528	+	0.979483i	$0.564591\pi$
$173$	−35346.5	+	35346.5i	−1.18101	+	1.18101i	−0.979483	+	0.201528i	$0.935409\pi$
$174$			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	$0.156042\pi$
$179$			30171.1i			0.941640i	−0.882229	+	0.470820i	$0.843958\pi$
$180$		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	−0.625857	−	0.779938i	$-0.715251\pi$
$193$	5739.33	−	5739.33i	0.154080	−	0.154080i	0.779938	+	0.625857i	$0.215251\pi$
$194$			15426.0i			0.409873i
$195$		0			0
$196$	−11764.7			−0.306245
$197$	33650.6	+	33650.6i	0.867082	+	0.867082i	0.992148	−	0.125066i	$-0.0399144\pi$
$197$	33650.6	+	33650.6i	0.867082	+	0.867082i	−0.125066	+	0.992148i	$0.539914\pi$
$198$	5220.90	−	5220.90i	0.133173	−	0.133173i
$199$		−	8221.91i		−	0.207619i	−0.994597	−	0.103809i	$-0.966897\pi$
$199$		−	8221.91i		−	0.207619i	0.994597	−	0.103809i	$-0.0331032\pi$
$200$		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	−0.695419	−	0.718604i	$-0.744781\pi$
$223$	1152.95	−	1152.95i	0.0231846	−	0.0231846i	0.718604	+	0.695419i	$0.244781\pi$
$224$			10359.4i			0.206462i
$225$		0			0
$226$	−4925.47			−0.0964341
$227$	−5784.04	−	5784.04i	−0.112248	−	0.112248i	0.648752	−	0.761000i	$-0.275291\pi$
$227$	−5784.04	−	5784.04i	−0.112248	−	0.112248i	−0.761000	+	0.648752i	$0.775291\pi$
$228$	104957.	−	104957.i	2.01902	−	2.01902i
$229$			102632.i			1.95710i	0.206001	+	0.978552i	$0.433955\pi$
$229$			102632.i			1.95710i	−0.206001	+	0.978552i	$0.566045\pi$
$230$		0			0
$231$	11538.8			0.216241
$232$	−145150.	−	145150.i	−2.69675	−	2.69675i
$233$	−16734.1	+	16734.1i	−0.308241	+	0.308241i	−0.844227	−	0.535986i	$-0.819940\pi$
$233$	−16734.1	+	16734.1i	−0.308241	+	0.308241i	0.535986	+	0.844227i	$0.319940\pi$
$234$			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	$-0.884890\pi$
$239$		−	40418.5i		−	0.707594i	0.935322	−	0.353797i	$-0.115110\pi$
$240$		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	0.809558	−	0.587040i	$-0.199707\pi$
$257$	14697.1	+	14697.1i	0.222518	+	0.222518i	−0.587040	+	0.809558i	$0.699707\pi$
$258$	−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	−0.823906	−	0.566727i	$-0.808209\pi$
$263$	−17788.8	+	17788.8i	−0.257179	+	0.257179i	0.566727	+	0.823906i	$0.308209\pi$
$264$		−	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	$0.00636755\pi$
$269$			2894.86i			0.0400058i	−0.999800	+	0.0200029i	$0.993632\pi$
$270$		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	0.262644	−	0.964893i	$-0.415406\pi$
$277$	−53882.9	−	53882.9i	−0.702249	−	0.702249i	−0.964893	+	0.262644i	$0.915406\pi$
$278$	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	−0.977335	−	0.211697i	$-0.932101\pi$
$283$	−61319.2	+	61319.2i	−0.765639	+	0.765639i	0.211697	+	0.977335i	$0.432101\pi$
$284$			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	−0.200539	−	0.979686i	$-0.564269\pi$
$293$	66889.0	−	66889.0i	0.779147	−	0.779147i	0.979686	+	0.200539i	$0.0642693\pi$
$294$		−	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	0.634346	−	0.773049i	$-0.281269\pi$
$307$	−13072.6	−	13072.6i	−0.138703	−	0.138703i	−0.773049	+	0.634346i	$0.781269\pi$
$308$	−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	−0.275016	−	0.961440i	$-0.588683\pi$
$313$	67248.3	−	67248.3i	0.686424	−	0.686424i	0.961440	+	0.275016i	$0.0886830\pi$
$314$			88848.1i			0.901133i
$315$		0			0
$316$	131095.			1.31284
$317$	−126470.	−	126470.i	−1.25854	−	1.25854i	−0.951790	−	0.306752i	$-0.900758\pi$
$317$	−126470.	−	126470.i	−1.25854	−	1.25854i	−0.306752	−	0.951790i	$-0.599242\pi$
$318$	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	0.999817	−	0.0191559i	$-0.00609788\pi$
$337$	111373.	+	111373.i	0.980661	+	0.980661i	−0.0191559	+	0.999817i	$0.506098\pi$
$338$	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	0.666533	−	0.745476i	$-0.267778\pi$
$347$	−9505.40	−	9505.40i	−0.0789426	−	0.0789426i	−0.745476	+	0.666533i	$0.767778\pi$
$348$	314680.	−	314680.i	2.59843	−	2.59843i
$349$			187256.i			1.53739i	0.639615	+	0.768696i	$0.279094\pi$
$349$			187256.i			1.53739i	−0.639615	+	0.768696i	$0.720906\pi$
$350$		0			0
$351$	−96256.5			−0.781296
$352$	30040.2	+	30040.2i	0.242448	+	0.242448i
$353$	109193.	−	109193.i	0.876284	−	0.876284i	−0.116864	−	0.993148i	$-0.537284\pi$
$353$	109193.	−	109193.i	0.876284	−	0.876284i	0.993148	+	0.116864i	$0.0372841\pi$
$354$		−	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	$-0.929690\pi$
$359$		−	56473.7i		−	0.438185i	0.975704	−	0.219092i	$-0.0703096\pi$
$360$		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	0.527177	−	0.849756i	$-0.323251\pi$
$367$	−43447.8	−	43447.8i	−0.322579	−	0.322579i	−0.849756	+	0.527177i	$0.823251\pi$
$368$	−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	−0.585641	−	0.810570i	$-0.699157\pi$
$373$	31294.2	−	31294.2i	0.224929	−	0.224929i	0.810570	+	0.585641i	$0.199157\pi$
$374$			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	$-0.958285\pi$
$379$		−	37541.2i		−	0.261354i	0.991425	−	0.130677i	$-0.0417151\pi$
$380$		0			0
$381$	−70425.4			−0.485154
$382$	−184024.	−	184024.i	−1.26109	−	1.26109i
$383$	40494.9	−	40494.9i	0.276060	−	0.276060i	−0.555474	−	0.831534i	$-0.687463\pi$
$383$	40494.9	−	40494.9i	0.276060	−	0.276060i	0.831534	+	0.555474i	$0.187463\pi$
$384$		−	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	$0.0834565\pi$
$389$			78442.6i			0.518386i	−0.965826	+	0.259193i	$0.916543\pi$
$390$		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	0.988438	−	0.151623i	$-0.0484500\pi$
$397$	131890.	+	131890.i	0.836815	+	0.836815i	−0.151623	+	0.988438i	$0.548450\pi$
$398$	−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	$0.273693\pi$
$409$			253509.i			1.51547i	−0.652564	+	0.757734i	$0.726307\pi$
$410$		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	$-0.944745\pi$
$419$		−	60645.6i		−	0.345439i	0.984971	−	0.172719i	$-0.0552554\pi$
$420$		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	−0.999569	−	0.0293680i	$-0.990651\pi$
$433$	−181902.	+	181902.i	−0.970201	+	0.970201i	0.0293680	+	0.999569i	$0.490651\pi$
$434$			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	$0.272907\pi$
$439$			291440.i			1.51224i	−0.654435	+	0.756118i	$0.727093\pi$
$440$		0			0
$441$	−4701.57			−0.0241750
$442$	−202677.	−	202677.i	−1.03744	−	1.03744i
$443$	75828.2	−	75828.2i	0.386388	−	0.386388i	−0.487009	−	0.873397i	$-0.661912\pi$
$443$	75828.2	−	75828.2i	0.386388	−	0.386388i	0.873397	+	0.487009i	$0.161912\pi$
$444$		−	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	$0.202067\pi$
$449$			239109.i			1.18605i	−0.805184	+	0.593025i	$0.797933\pi$
$450$		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	0.620614	−	0.784117i	$-0.286884\pi$
$457$	−34147.5	−	34147.5i	−0.163503	−	0.163503i	−0.784117	+	0.620614i	$0.786884\pi$
$458$	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	−0.936498	−	0.350672i	$-0.885953\pi$
$463$	−125583.	+	125583.i	−0.585826	+	0.585826i	0.350672	+	0.936498i	$0.385953\pi$
$464$			587839.i			2.73038i
$465$		0			0
$466$	167841.			0.772907
$467$	126812.	+	126812.i	0.581469	+	0.581469i	0.935307	−	0.353838i	$-0.115124\pi$
$467$	126812.	+	126812.i	0.581469	+	0.581469i	−0.353838	+	0.935307i	$0.615124\pi$
$468$	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	$-0.717043\pi$
$479$		−	356277.i		−	1.55280i	0.630239	−	0.776401i	$-0.282957\pi$
$480$		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	0.580986	−	0.813914i	$-0.302667\pi$
$487$	−55243.2	−	55243.2i	−0.232927	−	0.232927i	−0.813914	+	0.580986i	$0.802667\pi$
$488$	−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	$0.0202536\pi$
$499$			31665.7i			0.127171i	−0.997976	+	0.0635855i	$0.979746\pi$
$500$		0			0
$501$	429086.			1.70950
$502$	−160916.	−	160916.i	−0.638543	−	0.638543i
$503$	84275.0	−	84275.0i	0.333091	−	0.333091i	−0.520668	−	0.853759i	$-0.674317\pi$
$503$	84275.0	−	84275.0i	0.333091	−	0.333091i	0.853759	+	0.520668i	$0.174317\pi$
$504$			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	$0.115827\pi$
$509$			184416.i			0.711807i	−0.934523	+	0.355903i	$0.884173\pi$
$510$		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	−0.198895	+	0.980021i	$0.563735\pi$
$523$	−322468.	+	322468.i	−1.17892	+	1.17892i	−0.980021	+	0.198895i	$0.936265\pi$
$524$			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	−0.839508	−	0.543348i	$-0.817157\pi$
$547$	−413763.	−	413763.i	−1.38286	−	1.38286i	−0.543348	−	0.839508i	$-0.682843\pi$
$548$	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	0.999286	−	0.0377744i	$-0.0120268\pi$
$557$	298308.	+	298308.i	0.961512	+	0.961512i	−0.0377744	+	0.999286i	$0.512027\pi$
$558$	−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	−0.826226	−	0.563338i	$-0.809517\pi$
$563$	−83327.3	+	83327.3i	−0.262888	+	0.262888i	0.563338	+	0.826226i	$0.309517\pi$
$564$			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	$-0.868257\pi$
$569$		−	260413.i		−	0.804336i	0.915566	−	0.402168i	$-0.131743\pi$
$570$		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	0.982961	+	0.183816i	$0.0588449\pi$
$577$	388454.	+	388454.i	1.16678	+	1.16678i	0.183816	+	0.982961i	$0.441155\pi$
$578$	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	0.984961	−	0.172774i	$-0.0552731\pi$
$587$	279855.	+	279855.i	0.812187	+	0.812187i	−0.172774	+	0.984961i	$0.555273\pi$
$588$	−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	−0.829021	−	0.559218i	$-0.811102\pi$
$593$	−94876.0	+	94876.0i	−0.269803	+	0.269803i	0.559218	+	0.829021i	$0.311102\pi$
$594$		−	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	$-0.845065\pi$
$599$		−	335657.i		−	0.935496i	0.883862	−	0.467748i	$-0.154935\pi$
$600$		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	0.997782	+	0.0665679i	$0.0212049\pi$
$607$	392159.	+	392159.i	1.06435	+	1.06435i	0.0665679	+	0.997782i	$0.478795\pi$
$608$	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	−0.162135	−	0.986769i	$-0.551838\pi$
$613$	309872.	−	309872.i	0.824634	−	0.824634i	0.986769	+	0.162135i	$0.0518380\pi$
$614$			131117.i			0.347794i
$615$		0			0
$616$	182556.			0.481099
$617$	343853.	+	343853.i	0.903238	+	0.903238i	0.995715	−	0.0924768i	$-0.0294784\pi$
$617$	343853.	+	343853.i	0.903238	+	0.903238i	−0.0924768	+	0.995715i	$0.529478\pi$
$618$	−529209.	+	529209.i	−1.38564	+	1.38564i
$619$			166876.i			0.435524i	0.976002	+	0.217762i	$0.0698757\pi$
$619$			166876.i			0.435524i	−0.976002	+	0.217762i	$0.930124\pi$
$620$		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	−0.694024	−	0.719952i	$-0.744164\pi$
$643$	10719.7	−	10719.7i	0.0259276	−	0.0259276i	0.719952	+	0.694024i	$0.244164\pi$
$644$			527874.i			1.27280i
$645$		0			0
$646$	1.22043e6			2.92447
$647$	−437318.	−	437318.i	−1.04469	−	1.04469i	−0.998953	−	0.0457394i	$-0.985436\pi$
$647$	−437318.	−	437318.i	−1.04469	−	1.04469i	−0.0457394	−	0.998953i	$-0.514564\pi$
$648$	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	−0.999769	−	0.0214948i	$-0.993157\pi$
$653$	−417145.	+	417145.i	−0.978274	+	0.978274i	0.0214948	+	0.999769i	$0.493157\pi$
$654$		−	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	$-0.663164\pi$
$659$		−	756930.i		−	1.74295i	0.490440	−	0.871475i	$-0.336836\pi$
$660$		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	−0.660057	−	0.751216i	$-0.729468\pi$
$673$	41288.5	−	41288.5i	0.0911588	−	0.0911588i	0.751216	+	0.660057i	$0.229468\pi$
$674$		−	1.11706e6i		−	2.45898i
$675$		0			0
$676$	−453109.			−0.991539
$677$	14140.5	+	14140.5i	0.0308523	+	0.0308523i	0.722365	−	0.691512i	$-0.243055\pi$
$677$	14140.5	+	14140.5i	0.0308523	+	0.0308523i	−0.691512	+	0.722365i	$0.743055\pi$
$678$	−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	−0.969175	−	0.246375i	$-0.920761\pi$
$683$	−337178.	+	337178.i	−0.722800	+	0.722800i	0.246375	+	0.969175i	$0.420761\pi$
$684$			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	$-0.967240\pi$
$709$		−	103288.i		−	0.205475i	0.994709	−	0.102737i	$-0.0327602\pi$
$710$		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	$-0.994467\pi$
$719$		−	17971.7i		−	0.0347641i	0.999849	−	0.0173820i	$-0.00553316\pi$
$720$		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	0.686725	−	0.726917i	$-0.259048\pi$
$727$	−21242.5	−	21242.5i	−0.0401918	−	0.0401918i	−0.726917	+	0.686725i	$0.759048\pi$
$728$	−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	−0.999903	−	0.0139530i	$-0.995558\pi$
$733$	−529740.	+	529740.i	−0.985950	+	0.985950i	0.0139530	+	0.999903i	$0.495558\pi$
$734$			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	$0.184006\pi$
$739$			596812.i			1.09282i	−0.837518	+	0.546410i	$0.815994\pi$
$740$		0			0
$741$	536168.			0.976482
$742$	111111.	+	111111.i	0.201813	+	0.201813i
$743$	431072.	−	431072.i	0.780859	−	0.780859i	−0.199117	−	0.979976i	$-0.563807\pi$
$743$	431072.	−	431072.i	0.780859	−	0.780859i	0.979976	+	0.199117i	$0.0638074\pi$
$744$			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	0.673062	−	0.739586i	$-0.264979\pi$
$757$	−38121.2	−	38121.2i	−0.0665234	−	0.0665234i	−0.739586	+	0.673062i	$0.764979\pi$
$758$	−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	$-0.877268\pi$
$769$		−	444810.i		−	0.752179i	0.926583	−	0.376090i	$-0.122732\pi$
$770$		0			0
$771$	170502.			0.286828
$772$	196856.	+	196856.i	0.330304	+	0.330304i
$773$	810826.	−	810826.i	1.35696	−	1.35696i	0.479329	−	0.877635i	$-0.340880\pi$
$773$	810826.	−	810826.i	1.35696	−	1.35696i	0.877635	−	0.479329i	$-0.159120\pi$
$774$		−	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	−0.997727	−	0.0673806i	$-0.978536\pi$
$787$	−659695.	−	659695.i	−1.06511	−	1.06511i	−0.0673806	−	0.997727i	$-0.521464\pi$
$788$	−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	0.349287	−	0.937016i	$-0.386424\pi$
$797$	−373331.	−	373331.i	−0.587729	−	0.587729i	−0.937016	+	0.349287i	$0.886424\pi$
$798$	−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	$-0.783074\pi$
$809$		−	824584.i		−	1.25990i	0.776634	−	0.629952i	$-0.216926\pi$
$810$		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	−0.996609	−	0.0822833i	$-0.973779\pi$
$823$	−619299.	+	619299.i	−0.914326	+	0.914326i	0.0822833	+	0.996609i	$0.473779\pi$
$824$		−	1.66954e6i		−	2.45890i
$825$		0			0
$826$	211096.			0.309400
$827$	44733.2	+	44733.2i	0.0654062	+	0.0654062i	0.739053	−	0.673647i	$-0.235273\pi$
$827$	44733.2	+	44733.2i	0.0654062	+	0.0654062i	−0.673647	+	0.739053i	$0.735273\pi$
$828$	−276259.	+	276259.i	−0.402955	+	0.402955i
$829$		−	264797.i		−	0.385305i	−0.981267	−	0.192653i	$-0.938291\pi$
$829$		−	264797.i		−	0.385305i	0.981267	−	0.192653i	$-0.0617090\pi$
$830$		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	$-0.585739\pi$
$839$		−	1.35708e6i		−	1.92789i	0.266110	−	0.963943i	$-0.414261\pi$
$840$		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	−0.523320	−	0.852136i	$-0.675307\pi$
$853$	239249.	−	239249.i	0.328816	−	0.328816i	0.852136	+	0.523320i	$0.175307\pi$
$854$			330968.i			0.453806i
$855$		0			0
$856$	399703.			0.545494
$857$	397948.	+	397948.i	0.541832	+	0.541832i	0.924066	−	0.382234i	$-0.124845\pi$
$857$	397948.	+	397948.i	0.541832	+	0.541832i	−0.382234	+	0.924066i	$0.624845\pi$
$858$	387118.	−	387118.i	0.525859	−	0.525859i
$859$			352827.i			0.478163i	0.971000	+	0.239081i	$0.0768462\pi$
$859$			352827.i			0.478163i	−0.971000	+	0.239081i	$0.923154\pi$
$860$		0			0
$861$	−35766.9			−0.0482475
$862$	−696012.	−	696012.i	−0.936704	−	0.936704i
$863$	−697837.	+	697837.i	−0.936984	+	0.936984i	−0.998129	−	0.0611447i	$-0.980525\pi$
$863$	−697837.	+	697837.i	−0.936984	+	0.936984i	0.0611447	+	0.998129i	$0.480525\pi$
$864$			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	0.855233	−	0.518243i	$-0.173414\pi$
$877$	259189.	+	259189.i	0.336990	+	0.336990i	−0.518243	+	0.855233i	$0.673414\pi$
$878$	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	−0.938122	−	0.346306i	$-0.887436\pi$
$883$	−461432.	+	461432.i	−0.591816	+	0.591816i	0.346306	+	0.938122i	$0.387436\pi$
$884$			1.38620e6i			1.77387i
$885$		0			0
$886$	−760550.			−0.968858
$887$	−474502.	−	474502.i	−0.603102	−	0.603102i	0.338033	−	0.941134i	$-0.390239\pi$
$887$	−474502.	−	474502.i	−0.603102	−	0.603102i	−0.941134	+	0.338033i	$0.890239\pi$
$888$	−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	0.916646	−	0.399701i	$-0.130886\pi$
$907$	425264.	+	425264.i	0.516945	+	0.516945i	−0.399701	+	0.916646i	$0.630886\pi$
$908$	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	$-0.999768\pi$
$919$		−	1231.53i		−	0.00145819i	1.00000		0.000729096i	$-0.000232078\pi$
$920$		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	$0.311821\pi$
$929$			1.43314e6i			1.66057i	−0.557342	+	0.830283i	$0.688179\pi$
$930$		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	0.727649	−	0.685950i	$-0.240613\pi$
$937$	36611.0	+	36611.0i	0.0416996	+	0.0416996i	−0.685950	+	0.727649i	$0.740613\pi$
$938$	−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	0.817111	−	0.576481i	$-0.195574\pi$
$947$	215799.	+	215799.i	0.240630	+	0.240630i	−0.576481	+	0.817111i	$0.695574\pi$
$948$	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	−0.229233	−	0.973372i	$-0.573622\pi$
$953$	675833.	−	675833.i	0.744139	−	0.744139i	0.973372	+	0.229233i	$0.0736218\pi$
$954$			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	0.611886	−	0.790946i	$-0.290411\pi$
$967$	−167436.	−	167436.i	−0.179059	−	0.179059i	−0.790946	+	0.611886i	$0.790411\pi$
$968$	−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	0.135644	−	0.990758i	$-0.456690\pi$
$977$	−816231.	−	816231.i	−0.855114	−	0.855114i	−0.990758	+	0.135644i	$0.956690\pi$
$978$	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	−0.385447	−	0.922730i	$-0.625953\pi$
$983$	519170.	−	519170.i	0.537283	−	0.537283i	0.922730	+	0.385447i	$0.125953\pi$
$984$			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	0.889419	−	0.457093i	$-0.151110\pi$
$997$	429735.	+	429735.i	0.432325	+	0.432325i	−0.457093	+	0.889419i	$0.651110\pi$
$998$	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.57.2		24
5.2	odd	4		35.5.g.a.8.11	✓	24
5.3	odd	4	inner	175.5.g.c.43.2		24
5.4	even	2		35.5.g.a.22.11	yes	24

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

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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