LMFDB - Embedded newform 175.5.g.c.43.11

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			43.11
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.43769 - 4.43769i) q^{2} +(10.8098 + 10.8098i) q^{3} -23.3862i q^{4} +95.9409 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-32.7776 - 32.7776i) q^{8} +152.703i q^{9} +O(q^{10})$	\(q+(4.43769 - 4.43769i) q^{2} +(10.8098 + 10.8098i) q^{3} -23.3862i q^{4} +95.9409 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-32.7776 - 32.7776i) q^{8} +152.703i q^{9} +208.255 q^{11} +(252.800 - 252.800i) q^{12} +(1.92052 + 1.92052i) q^{13} +116.230i q^{14} +83.2655 q^{16} +(-164.913 + 164.913i) q^{17} +(677.648 + 677.648i) q^{18} -212.136i q^{19} -283.126 q^{21} +(924.172 - 924.172i) q^{22} +(-391.446 - 391.446i) q^{23} -708.637i q^{24} +17.0453 q^{26} +(-775.093 + 775.093i) q^{27} +(306.261 + 306.261i) q^{28} -36.5090i q^{29} +349.238 q^{31} +(893.948 - 893.948i) q^{32} +(2251.19 + 2251.19i) q^{33} +1463.66i q^{34} +3571.14 q^{36} +(-479.357 + 479.357i) q^{37} +(-941.393 - 941.393i) q^{38} +41.5207i q^{39} +959.088 q^{41} +(-1256.42 + 1256.42i) q^{42} +(-1355.39 - 1355.39i) q^{43} -4870.29i q^{44} -3474.23 q^{46} +(-1898.85 + 1898.85i) q^{47} +(900.082 + 900.082i) q^{48} -343.000i q^{49} -3565.34 q^{51} +(44.9135 - 44.9135i) q^{52} +(-2839.10 - 2839.10i) q^{53} +6879.24i q^{54} +858.497 q^{56} +(2293.14 - 2293.14i) q^{57} +(-162.016 - 162.016i) q^{58} -3146.30i q^{59} -1735.34 q^{61} +(1549.81 - 1549.81i) q^{62} +(-1999.77 - 1999.77i) q^{63} -6601.88i q^{64} +19980.2 q^{66} +(245.525 - 245.525i) q^{67} +(3856.67 + 3856.67i) q^{68} -8462.88i q^{69} -6002.50 q^{71} +(5005.23 - 5005.23i) q^{72} +(2330.88 + 2330.88i) q^{73} +4254.48i q^{74} -4961.05 q^{76} +(-2727.27 + 2727.27i) q^{77} +(184.256 + 184.256i) q^{78} -6606.13i q^{79} -4388.24 q^{81} +(4256.14 - 4256.14i) q^{82} +(-5773.38 - 5773.38i) q^{83} +6621.23i q^{84} -12029.6 q^{86} +(394.655 - 394.655i) q^{87} +(-6826.10 - 6826.10i) q^{88} +10776.1i q^{89} -50.3014 q^{91} +(-9154.42 + 9154.42i) q^{92} +(3775.19 + 3775.19i) q^{93} +16853.0i q^{94} +19326.8 q^{96} +(-3200.07 + 3200.07i) q^{97} +(-1522.13 - 1522.13i) q^{98} +31801.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.43769	−	4.43769i	1.10942	−	1.10942i	0.116196	−	0.993226i	$-0.462930\pi$
$2$	4.43769	−	4.43769i	1.10942	−	1.10942i	0.993226	−	0.116196i	$-0.0370701\pi$
$3$	10.8098	+	10.8098i	1.20109	+	1.20109i	0.973836	+	0.227251i	$0.0729738\pi$
$3$	10.8098	+	10.8098i	1.20109	+	1.20109i	0.227251	+	0.973836i	$0.427026\pi$
$4$		−	23.3862i		−	1.46164i
$5$		0			0
$5$		0			0
$6$	95.9409			2.66503
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$8$	−32.7776	−	32.7776i	−0.512150	−	0.512150i
$9$			152.703i			1.88522i
$10$		0			0
$11$	208.255			1.72112			0.860559	−	0.509351i	$-0.170114\pi$
$11$	208.255			1.72112			0.860559	+	0.509351i	$0.170114\pi$
$12$	252.800	−	252.800i	1.75555	−	1.75555i
$13$	1.92052	+	1.92052i	0.0113640	+	0.0113640i	0.712766	−	0.701402i	$-0.247442\pi$
$13$	1.92052	+	1.92052i	0.0113640	+	0.0113640i	−0.701402	+	0.712766i	$0.747442\pi$
$14$			116.230i			0.593011i
$15$		0			0
$16$	83.2655			0.325256
$17$	−164.913	+	164.913i	−0.570632	+	0.570632i	−0.932305	−	0.361673i	$-0.882206\pi$
$17$	−164.913	+	164.913i	−0.570632	+	0.570632i	0.361673	+	0.932305i	$0.382206\pi$
$18$	677.648	+	677.648i	2.09151	+	2.09151i
$19$		−	212.136i		−	0.587634i	−0.955862	−	0.293817i	$-0.905074\pi$
$19$		−	212.136i		−	0.587634i	0.955862	−	0.293817i	$-0.0949257\pi$
$20$		0			0
$21$	−283.126			−0.642008
$22$	924.172	−	924.172i	1.90945	−	1.90945i
$23$	−391.446	−	391.446i	−0.739973	−	0.739973i	0.232600	−	0.972573i	$-0.425277\pi$
$23$	−391.446	−	391.446i	−0.739973	−	0.739973i	−0.972573	+	0.232600i	$0.925277\pi$
$24$		−	708.637i		−	1.23027i
$25$		0			0
$26$	17.0453			0.0252150
$27$	−775.093	+	775.093i	−1.06323	+	1.06323i
$28$	306.261	+	306.261i	0.390639	+	0.390639i
$29$		−	36.5090i		−	0.0434115i	−0.999764	−	0.0217057i	$-0.993090\pi$
$29$		−	36.5090i		−	0.0434115i	0.999764	−	0.0217057i	$-0.00690969\pi$
$30$		0			0
$31$	349.238			0.363411			0.181706	−	0.983353i	$-0.441838\pi$
$31$	349.238			0.363411			0.181706	+	0.983353i	$0.441838\pi$
$32$	893.948	−	893.948i	0.872996	−	0.872996i
$33$	2251.19	+	2251.19i	2.06721	+	2.06721i
$34$			1463.66i			1.26614i
$35$		0			0
$36$	3571.14			2.75551
$37$	−479.357	+	479.357i	−0.350151	+	0.350151i	−0.860166	−	0.510014i	$-0.829640\pi$
$37$	−479.357	+	479.357i	−0.350151	+	0.350151i	0.510014	+	0.860166i	$0.329640\pi$
$38$	−941.393	−	941.393i	−0.651935	−	0.651935i
$39$			41.5207i			0.0272983i
$40$		0			0
$41$	959.088			0.570546			0.285273	−	0.958446i	$-0.407916\pi$
$41$	959.088			0.570546			0.285273	+	0.958446i	$0.407916\pi$
$42$	−1256.42	+	1256.42i	−0.712258	+	0.712258i
$43$	−1355.39	−	1355.39i	−0.733038	−	0.733038i	0.238183	−	0.971220i	$-0.423448\pi$
$43$	−1355.39	−	1355.39i	−0.733038	−	0.733038i	−0.971220	+	0.238183i	$0.923448\pi$
$44$		−	4870.29i		−	2.51565i
$45$		0			0
$46$	−3474.23			−1.64188
$47$	−1898.85	+	1898.85i	−0.859596	+	0.859596i	−0.991290	−	0.131694i	$-0.957958\pi$
$47$	−1898.85	+	1898.85i	−0.859596	+	0.859596i	0.131694	+	0.991290i	$0.457958\pi$
$48$	900.082	+	900.082i	0.390661	+	0.390661i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	−3565.34			−1.37076
$52$	44.9135	−	44.9135i	0.0166100	−	0.0166100i
$53$	−2839.10	−	2839.10i	−1.01071	−	1.01071i	−0.999942	−	0.0107728i	$-0.996571\pi$
$53$	−2839.10	−	2839.10i	−1.01071	−	1.01071i	−0.0107728	−	0.999942i	$-0.503429\pi$
$54$			6879.24i			2.35914i
$55$		0			0
$56$	858.497			0.273755
$57$	2293.14	−	2293.14i	0.705800	−	0.705800i
$58$	−162.016	−	162.016i	−0.0481616	−	0.0481616i
$59$		−	3146.30i		−	0.903849i	−0.892056	−	0.451924i	$-0.850738\pi$
$59$		−	3146.30i		−	0.903849i	0.892056	−	0.451924i	$-0.149262\pi$
$60$		0			0
$61$	−1735.34			−0.466363			−0.233181	−	0.972433i	$-0.574914\pi$
$61$	−1735.34			−0.466363			−0.233181	+	0.972433i	$0.574914\pi$
$62$	1549.81	−	1549.81i	0.403177	−	0.403177i
$63$	−1999.77	−	1999.77i	−0.503846	−	0.503846i
$64$		−	6601.88i		−	1.61179i
$65$		0			0
$66$	19980.2			4.58682
$67$	245.525	−	245.525i	0.0546949	−	0.0546949i	−0.679230	−	0.733925i	$-0.737686\pi$
$67$	245.525	−	245.525i	0.0546949	−	0.0546949i	0.733925	+	0.679230i	$0.237686\pi$
$68$	3856.67	+	3856.67i	0.834056	+	0.834056i
$69$		−	8462.88i		−	1.77754i
$70$		0			0
$71$	−6002.50			−1.19074			−0.595368	−	0.803453i	$-0.702994\pi$
$71$	−6002.50			−1.19074			−0.595368	+	0.803453i	$0.702994\pi$
$72$	5005.23	−	5005.23i	0.965515	−	0.965515i
$73$	2330.88	+	2330.88i	0.437395	+	0.437395i	0.891134	−	0.453739i	$-0.149910\pi$
$73$	2330.88	+	2330.88i	0.437395	+	0.437395i	−0.453739	+	0.891134i	$0.649910\pi$
$74$			4254.48i			0.776932i
$75$		0			0
$76$	−4961.05			−0.858907
$77$	−2727.27	+	2727.27i	−0.459988	+	0.459988i
$78$	184.256	+	184.256i	0.0302854	+	0.0302854i
$79$		−	6606.13i		−	1.05850i	−0.848465	−	0.529252i	$-0.822473\pi$
$79$		−	6606.13i		−	1.05850i	0.848465	−	0.529252i	$-0.177527\pi$
$80$		0			0
$81$	−4388.24			−0.668836
$82$	4256.14	−	4256.14i	0.632977	−	0.632977i
$83$	−5773.38	−	5773.38i	−0.838058	−	0.838058i	0.150546	−	0.988603i	$-0.451897\pi$
$83$	−5773.38	−	5773.38i	−0.838058	−	0.838058i	−0.988603	+	0.150546i	$0.951897\pi$
$84$			6621.23i			0.938382i
$85$		0			0
$86$	−12029.6			−1.62650
$87$	394.655	−	394.655i	0.0521409	−	0.0521409i
$88$	−6826.10	−	6826.10i	−0.881470	−	0.881470i
$89$			10776.1i			1.36045i	0.733002	+	0.680227i	$0.238119\pi$
$89$			10776.1i			1.36045i	−0.733002	+	0.680227i	$0.761881\pi$
$90$		0			0
$91$	−50.3014			−0.00607431
$92$	−9154.42	+	9154.42i	−1.08157	+	1.08157i
$93$	3775.19	+	3775.19i	0.436489	+	0.436489i
$94$			16853.0i			1.90731i
$95$		0			0
$96$	19326.8			2.09709
$97$	−3200.07	+	3200.07i	−0.340107	+	0.340107i	−0.856408	−	0.516300i	$-0.827309\pi$
$97$	−3200.07	+	3200.07i	−0.340107	+	0.340107i	0.516300	+	0.856408i	$0.327309\pi$
$98$	−1522.13	−	1522.13i	−0.158489	−	0.158489i
$99$			31801.2i			3.24469i
$100$		0			0
$101$	−9248.33			−0.906610			−0.453305	−	0.891356i	$-0.649755\pi$
$101$	−9248.33			−0.906610			−0.453305	+	0.891356i	$0.649755\pi$
$102$	−15821.9	+	15821.9i	−1.52075	+	1.52075i
$103$	13265.8	+	13265.8i	1.25043	+	1.25043i	0.955529	+	0.294898i	$0.0952858\pi$
$103$	13265.8	+	13265.8i	1.25043	+	1.25043i	0.294898	+	0.955529i	$0.404714\pi$
$104$		−	125.900i		−	0.0116401i
$105$		0			0
$106$	−25198.1			−2.24262
$107$	10621.5	−	10621.5i	0.927719	−	0.927719i	−0.0698394	−	0.997558i	$-0.522249\pi$
$107$	10621.5	−	10621.5i	0.927719	−	0.927719i	0.997558	+	0.0698394i	$0.0222487\pi$
$108$	18126.5	+	18126.5i	1.55405	+	1.55405i
$109$			910.444i			0.0766303i	0.999266	+	0.0383151i	$0.0121991\pi$
$109$			910.444i			0.0766303i	−0.999266	+	0.0383151i	$0.987801\pi$
$110$		0			0
$111$	−10363.5			−0.841125
$112$	−1090.43	+	1090.43i	−0.0869283	+	0.0869283i
$113$	−3472.90	−	3472.90i	−0.271979	−	0.271979i	0.557917	−	0.829897i	$-0.311601\pi$
$113$	−3472.90	−	3472.90i	−0.271979	−	0.271979i	−0.829897	+	0.557917i	$0.811601\pi$
$114$		−	20352.5i		−	1.56606i
$115$		0			0
$116$	−853.807			−0.0634517
$117$	−293.268	+	293.268i	−0.0214237	+	0.0214237i
$118$	−13962.3	−	13962.3i	−1.00275	−	1.00275i
$119$		−	4319.32i		−	0.305015i
$120$		0			0
$121$	28729.2			1.96225
$122$	−7700.89	+	7700.89i	−0.517394	+	0.517394i
$123$	10367.5	+	10367.5i	0.685276	+	0.685276i
$124$		−	8167.35i		−	0.531175i
$125$		0			0
$126$	−17748.7			−1.11796
$127$	−15544.6	+	15544.6i	−0.963770	+	0.963770i	−0.999366	−	0.0355963i	$-0.988667\pi$
$127$	−15544.6	+	15544.6i	−0.963770	+	0.963770i	0.0355963	+	0.999366i	$0.488667\pi$
$128$	−14993.9	−	14993.9i	−0.915156	−	0.915156i
$129$		−	29302.9i		−	1.76088i
$130$		0			0
$131$	18977.2			1.10583			0.552915	−	0.833238i	$-0.313515\pi$
$131$	18977.2			1.10583			0.552915	+	0.833238i	$0.313515\pi$
$132$	52646.8	−	52646.8i	3.02151	−	3.02151i
$133$	2778.09	+	2778.09i	0.157052	+	0.157052i
$134$		−	2179.13i		−	0.121359i
$135$		0			0
$136$	10810.9			0.584497
$137$	12478.0	−	12478.0i	0.664822	−	0.664822i	−0.291691	−	0.956513i	$-0.594218\pi$
$137$	12478.0	−	12478.0i	0.664822	−	0.664822i	0.956513	+	0.291691i	$0.0942178\pi$
$138$	−37555.7	−	37555.7i	−1.97205	−	1.97205i
$139$			6825.04i			0.353244i	0.984279	+	0.176622i	$0.0565171\pi$
$139$			6825.04i			0.353244i	−0.984279	+	0.176622i	$0.943483\pi$
$140$		0			0
$141$	−41052.3			−2.06490
$142$	−26637.2	+	26637.2i	−1.32103	+	1.32103i
$143$	399.958	+	399.958i	0.0195588	+	0.0195588i
$144$			12714.9i			0.613179i
$145$		0			0
$146$	20687.4			0.970512
$147$	3707.76	−	3707.76i	0.171584	−	0.171584i
$148$	11210.3	+	11210.3i	0.511794	+	0.511794i
$149$			2580.25i			0.116222i	0.998310	+	0.0581111i	$0.0185078\pi$
$149$			2580.25i			0.116222i	−0.998310	+	0.0581111i	$0.981492\pi$
$150$		0			0
$151$	6139.31			0.269256			0.134628	−	0.990896i	$-0.457016\pi$
$151$	6139.31			0.269256			0.134628	+	0.990896i	$0.457016\pi$
$152$	−6953.30	+	6953.30i	−0.300957	+	0.300957i
$153$	−25182.6	−	25182.6i	−1.07577	−	1.07577i
$154$			24205.5i			1.02064i
$155$		0			0
$156$	971.011			0.0399002
$157$	17290.7	−	17290.7i	0.701476	−	0.701476i	−0.263251	−	0.964727i	$-0.584795\pi$
$157$	17290.7	−	17290.7i	0.701476	−	0.701476i	0.964727	+	0.263251i	$0.0847948\pi$
$158$	−29315.9	−	29315.9i	−1.17433	−	1.17433i
$159$		−	61380.1i		−	2.42791i
$160$		0			0
$161$	10252.6			0.395532
$162$	−19473.6	+	19473.6i	−0.742022	+	0.742022i
$163$	−8983.55	−	8983.55i	−0.338121	−	0.338121i	0.517538	−	0.855660i	$-0.326848\pi$
$163$	−8983.55	−	8983.55i	−0.338121	−	0.338121i	−0.855660	+	0.517538i	$0.826848\pi$
$164$		−	22429.4i		−	0.833931i
$165$		0			0
$166$	−51240.9			−1.85952
$167$	−20379.6	+	20379.6i	−0.730739	+	0.730739i	−0.970766	−	0.240027i	$-0.922844\pi$
$167$	−20379.6	+	20379.6i	−0.730739	+	0.730739i	0.240027	+	0.970766i	$0.422844\pi$
$168$	9280.17	+	9280.17i	0.328804	+	0.328804i
$169$		−	28553.6i		−	0.999742i
$170$		0			0
$171$	32393.8			1.10782
$172$	−31697.3	+	31697.3i	−1.07143	+	1.07143i
$173$	17274.7	+	17274.7i	0.577189	+	0.577189i	0.934128	−	0.356939i	$-0.116179\pi$
$173$	17274.7	+	17274.7i	0.577189	+	0.577189i	−0.356939	+	0.934128i	$0.616179\pi$
$174$		−	3502.71i		−	0.115693i
$175$		0			0
$176$	17340.5			0.559804
$177$	34010.8	−	34010.8i	1.08560	−	1.08560i
$178$	47821.2	+	47821.2i	1.50932	+	1.50932i
$179$			54531.6i			1.70193i	0.525220	+	0.850967i	$0.323983\pi$
$179$			54531.6i			1.70193i	−0.525220	+	0.850967i	$0.676017\pi$
$180$		0			0
$181$	−14323.8			−0.437221			−0.218610	−	0.975812i	$-0.570152\pi$
$181$	−14323.8			−0.437221			−0.218610	+	0.975812i	$0.570152\pi$
$182$	−223.222	+	223.222i	−0.00673898	+	0.00673898i
$183$	−18758.6	−	18758.6i	−0.560143	−	0.560143i
$184$			25661.3i			0.757953i
$185$		0			0
$186$	33506.3			0.968501
$187$	−34343.9	+	34343.9i	−0.982124	+	0.982124i
$188$	44406.8	+	44406.8i	1.25642	+	1.25642i
$189$		−	20300.9i		−	0.568319i
$190$		0			0
$191$	9760.68			0.267555			0.133778	−	0.991011i	$-0.457289\pi$
$191$	9760.68			0.267555			0.133778	+	0.991011i	$0.457289\pi$
$192$	71364.9	−	71364.9i	1.93590	−	1.93590i
$193$	11883.5	+	11883.5i	0.319028	+	0.319028i	0.848394	−	0.529365i	$-0.177570\pi$
$193$	11883.5	+	11883.5i	0.319028	+	0.319028i	−0.529365	+	0.848394i	$0.677570\pi$
$194$			28401.8i			0.754645i
$195$		0			0
$196$	−8021.46			−0.208805
$197$	36747.1	−	36747.1i	0.946870	−	0.946870i	−0.0517883	−	0.998658i	$-0.516492\pi$
$197$	36747.1	−	36747.1i	0.946870	−	0.946870i	0.998658	+	0.0517883i	$0.0164921\pi$
$198$	141124.	+	141124.i	3.59973	+	3.59973i
$199$		−	25164.8i		−	0.635458i	−0.948182	−	0.317729i	$-0.897080\pi$
$199$		−	25164.8i		−	0.635458i	0.948182	−	0.317729i	$-0.102920\pi$
$200$		0			0
$201$	5308.15			0.131387
$202$	−41041.2	+	41041.2i	−1.00581	+	1.00581i
$203$	478.115	+	478.115i	0.0116022	+	0.0116022i
$204$			83379.6i			2.00355i
$205$		0			0
$206$	117739.			2.77450
$207$	59774.9	−	59774.9i	1.39501	−	1.39501i
$208$	159.913	+	159.913i	0.00369621	+	0.00369621i
$209$		−	44178.4i		−	1.01139i
$210$		0			0
$211$	−36722.5			−0.824836			−0.412418	−	0.910995i	$-0.635316\pi$
$211$	−36722.5			−0.824836			−0.412418	+	0.910995i	$0.635316\pi$
$212$	−66395.7	+	66395.7i	−1.47730	+	1.47730i
$213$	−64885.7	−	64885.7i	−1.43018	−	1.43018i
$214$		−	94269.4i		−	2.05846i
$215$		0			0
$216$	50811.3			1.08906
$217$	−4573.56	+	4573.56i	−0.0971258	+	0.0971258i
$218$	4040.27	+	4040.27i	0.0850153	+	0.0850153i
$219$			50392.6i			1.05070i
$220$		0			0
$221$	−633.434			−0.0129693
$222$	−45990.0	+	45990.0i	−0.933163	+	0.933163i
$223$	5579.99	+	5579.99i	0.112208	+	0.112208i	0.760982	−	0.648774i	$-0.224718\pi$
$223$	5579.99	+	5579.99i	0.112208	+	0.112208i	−0.648774	+	0.760982i	$0.724718\pi$
$224$			23413.9i			0.466636i
$225$		0			0
$226$	−30823.3			−0.603480
$227$	−10643.9	+	10643.9i	−0.206561	+	0.206561i	−0.802804	−	0.596243i	$-0.796660\pi$
$227$	−10643.9	+	10643.9i	−0.206561	+	0.206561i	0.596243	+	0.802804i	$0.296660\pi$
$228$	−53627.9	−	53627.9i	−1.03162	−	1.03162i
$229$			75976.4i			1.44880i	0.689381	+	0.724399i	$0.257883\pi$
$229$			75976.4i			1.44880i	−0.689381	+	0.724399i	$0.742117\pi$
$230$		0			0
$231$	−58962.4			−1.10497
$232$	−1196.68	+	1196.68i	−0.0222332	+	0.0222332i
$233$	13214.9	+	13214.9i	0.243418	+	0.243418i	0.818262	−	0.574845i	$-0.194938\pi$
$233$	13214.9	+	13214.9i	0.243418	+	0.243418i	−0.574845	+	0.818262i	$0.694938\pi$
$234$			2602.87i			0.0475358i
$235$		0			0
$236$	−73579.9			−1.32110
$237$	71410.8	−	71410.8i	1.27136	−	1.27136i
$238$	−19167.8	−	19167.8i	−0.338391	−	0.338391i
$239$		−	66987.7i		−	1.17273i	−0.810046	−	0.586367i	$-0.800558\pi$
$239$		−	66987.7i		−	1.17273i	0.810046	−	0.586367i	$-0.199442\pi$
$240$		0			0
$241$	−22572.7			−0.388641			−0.194321	−	0.980938i	$-0.562250\pi$
$241$	−22572.7			−0.388641			−0.194321	+	0.980938i	$0.562250\pi$
$242$	127491.	−	127491.i	2.17696	−	2.17696i
$243$	15346.6	+	15346.6i	0.259896	+	0.259896i
$244$			40582.9i			0.681653i
$245$		0			0
$246$	92015.8			1.52052
$247$	407.411	−	407.411i	0.00667788	−	0.00667788i
$248$	−11447.2	−	11447.2i	−0.186121	−	0.186121i
$249$		−	124818.i		−	2.01316i
$250$		0			0
$251$	53386.2			0.847386			0.423693	−	0.905806i	$-0.360733\pi$
$251$	53386.2			0.847386			0.423693	+	0.905806i	$0.360733\pi$
$252$	−46766.9	+	46766.9i	−0.736440	+	0.736440i
$253$	−81520.6	−	81520.6i	−1.27358	−	1.27358i
$254$			137965.i			2.13846i
$255$		0			0
$256$	−27446.7			−0.418803
$257$	76886.0	−	76886.0i	1.16408	−	1.16408i	0.180501	−	0.983575i	$-0.442228\pi$
$257$	76886.0	−	76886.0i	1.16408	−	1.16408i	0.983575	−	0.180501i	$-0.0577719\pi$
$258$	−130037.	−	130037.i	−1.95356	−	1.95356i
$259$		−	12555.1i		−	0.187164i
$260$		0			0
$261$	5575.03			0.0818402
$262$	84214.7	−	84214.7i	1.22683	−	1.22683i
$263$	66114.9	+	66114.9i	0.955846	+	0.955846i	0.999066	−	0.0432196i	$-0.0137615\pi$
$263$	66114.9	+	66114.9i	0.955846	+	0.955846i	−0.0432196	+	0.999066i	$0.513762\pi$
$264$		−	147577.i		−	2.11744i
$265$		0			0
$266$	24656.6			0.348474
$267$	−116488.	+	116488.i	−1.63402	+	1.63402i
$268$	−5741.90	−	5741.90i	−0.0799440	−	0.0799440i
$269$		−	21550.7i		−	0.297822i	−0.988851	−	0.148911i	$-0.952423\pi$
$269$		−	21550.7i		−	0.297822i	0.988851	−	0.148911i	$-0.0475768\pi$
$270$		0			0
$271$	39252.7			0.534480			0.267240	−	0.963630i	$-0.413888\pi$
$271$	39252.7			0.534480			0.267240	+	0.963630i	$0.413888\pi$
$272$	−13731.5	+	13731.5i	−0.185601	+	0.185601i
$273$	−543.747	−	543.747i	−0.00729578	−	0.00729578i
$274$		−	110747.i		−	1.47514i
$275$		0			0
$276$	−197915.			−2.59812
$277$	−46061.9	+	46061.9i	−0.600319	+	0.600319i	−0.940397	−	0.340078i	$-0.889547\pi$
$277$	−46061.9	+	46061.9i	−0.600319	+	0.600319i	0.340078	+	0.940397i	$0.389547\pi$
$278$	30287.4	+	30287.4i	0.391897	+	0.391897i
$279$			53329.7i			0.685111i
$280$		0			0
$281$	67069.9			0.849405			0.424703	−	0.905333i	$-0.360379\pi$
$281$	67069.9			0.849405			0.424703	+	0.905333i	$0.360379\pi$
$282$	−182177.	+	182177.i	−2.29085	+	2.29085i
$283$	17122.7	+	17122.7i	0.213796	+	0.213796i	0.805878	−	0.592082i	$-0.201694\pi$
$283$	17122.7	+	17122.7i	0.213796	+	0.213796i	−0.592082	+	0.805878i	$0.701694\pi$
$284$			140375.i			1.74042i
$285$		0			0
$286$	3549.78			0.0433979
$287$	−12560.0	+	12560.0i	−0.152485	+	0.152485i
$288$	136508.	+	136508.i	1.64579	+	1.64579i
$289$			29128.7i			0.348759i
$290$		0			0
$291$	−69184.1			−0.816997
$292$	54510.3	−	54510.3i	0.639312	−	0.639312i
$293$	−36819.7	−	36819.7i	−0.428889	−	0.428889i	0.459361	−	0.888250i	$-0.348079\pi$
$293$	−36819.7	−	36819.7i	−0.428889	−	0.428889i	−0.888250	+	0.459361i	$0.848079\pi$
$294$		−	32907.7i		−	0.380718i
$295$		0			0
$296$	31424.3			0.358660
$297$	−161417.	+	161417.i	−1.82994	+	1.82994i
$298$	11450.3	+	11450.3i	0.128939	+	0.128939i
$299$		−	1503.56i		−	0.0168181i
$300$		0			0
$301$	35499.7			0.391825
$302$	27244.4	−	27244.4i	0.298719	−	0.298719i
$303$	−99972.4	−	99972.4i	−1.08892	−	1.08892i
$304$		−	17663.6i		−	0.191131i
$305$		0			0
$306$	−223505.			−2.38696
$307$	76665.7	−	76665.7i	0.813438	−	0.813438i	−0.171710	−	0.985148i	$-0.554929\pi$
$307$	76665.7	−	76665.7i	0.813438	−	0.813438i	0.985148	+	0.171710i	$0.0549291\pi$
$308$	63780.4	+	63780.4i	0.672335	+	0.672335i
$309$			286800.i			3.00374i
$310$		0			0
$311$	−162834.			−1.68354			−0.841772	−	0.539833i	$-0.818488\pi$
$311$	−162834.			−1.68354			−0.841772	+	0.539833i	$0.818488\pi$
$312$	1360.95	−	1360.95i	0.0139808	−	0.0139808i
$313$	−6882.26	−	6882.26i	−0.0702493	−	0.0702493i	0.671109	−	0.741359i	$-0.265818\pi$
$313$	−6882.26	−	6882.26i	−0.0702493	−	0.0702493i	−0.741359	+	0.671109i	$0.765818\pi$
$314$		−	153461.i		−	1.55647i
$315$		0			0
$316$	−154492.			−1.54715
$317$	−104475.	+	104475.i	−1.03967	+	1.03967i	−0.0404883	+	0.999180i	$0.512891\pi$
$317$	−104475.	+	104475.i	−1.03967	+	1.03967i	−0.999180	+	0.0404883i	$0.987109\pi$
$318$	−272386.	−	272386.i	−2.69358	−	2.69358i
$319$		−	7603.20i		−	0.0747162i
$320$		0			0
$321$	229631.			2.22854
$322$	45497.8	−	45497.8i	0.438812	−	0.438812i
$323$	34983.9	+	34983.9i	0.335323	+	0.335323i
$324$			102624.i			0.977595i
$325$		0			0
$326$	−79732.4			−0.750239
$327$	−9841.70	+	9841.70i	−0.0920396	+	0.0920396i
$328$	−31436.6	−	31436.6i	−0.292205	−	0.292205i
$329$		−	49733.9i		−	0.459474i
$330$		0			0
$331$	−183623.			−1.67599			−0.837993	−	0.545681i	$-0.816271\pi$
$331$	−183623.			−1.67599			−0.837993	+	0.545681i	$0.816271\pi$
$332$	−135017.	+	135017.i	−1.22494	+	1.22494i
$333$	−73199.2	−	73199.2i	−0.660113	−	0.660113i
$334$			180876.i			1.62140i
$335$		0			0
$336$	−23574.6			−0.208817
$337$	−71038.3	+	71038.3i	−0.625507	+	0.625507i	−0.946934	−	0.321427i	$-0.895838\pi$
$337$	−71038.3	+	71038.3i	−0.625507	+	0.625507i	0.321427	+	0.946934i	$0.395838\pi$
$338$	−126712.	−	126712.i	−1.10914	−	1.10914i
$339$		−	75082.7i		−	0.653341i
$340$		0			0
$341$	72730.7			0.625474
$342$	143753.	−	143753.i	1.22904	−	1.22904i
$343$	4491.86	+	4491.86i	0.0381802	+	0.0381802i
$344$			88852.5i			0.750850i
$345$		0			0
$346$	153319.			1.28069
$347$	−21455.0	+	21455.0i	−0.178184	+	0.178184i	−0.790564	−	0.612380i	$-0.790212\pi$
$347$	−21455.0	+	21455.0i	−0.178184	+	0.178184i	0.612380	+	0.790564i	$0.290212\pi$
$348$	−9229.47	−	9229.47i	−0.0762111	−	0.0762111i
$349$			26283.6i			0.215791i	0.994162	+	0.107895i	$0.0344112\pi$
$349$			26283.6i			0.215791i	−0.994162	+	0.107895i	$0.965589\pi$
$350$		0			0
$351$	−2977.16			−0.0241650
$352$	186169.	−	186169.i	1.50253	−	1.50253i
$353$	98327.5	+	98327.5i	0.789088	+	0.789088i	0.981345	−	0.192257i	$-0.0615806\pi$
$353$	98327.5	+	98327.5i	0.789088	+	0.789088i	−0.192257	+	0.981345i	$0.561581\pi$
$354$		−	301859.i		−	2.40878i
$355$		0			0
$356$	252013.			1.98849
$357$	46691.0	−	46691.0i	0.366350	−	0.366350i
$358$	241995.	+	241995.i	1.88816	+	1.88816i
$359$		−	169257.i		−	1.31328i	−0.754205	−	0.656639i	$-0.771978\pi$
$359$		−	169257.i		−	1.31328i	0.754205	−	0.656639i	$-0.228022\pi$
$360$		0			0
$361$	85319.3			0.654686
$362$	−63564.6	+	63564.6i	−0.485063	+	0.485063i
$363$	310557.	+	310557.i	2.35683	+	2.35683i
$364$			1176.36i			0.00887844i
$365$		0			0
$366$	−166490.			−1.24287
$367$	88641.1	−	88641.1i	0.658117	−	0.658117i	−0.296817	−	0.954934i	$-0.595925\pi$
$367$	88641.1	−	88641.1i	0.658117	−	0.658117i	0.954934	+	0.296817i	$0.0959252\pi$
$368$	−32593.9	−	32593.9i	−0.240680	−	0.240680i
$369$			146456.i			1.07561i
$370$		0			0
$371$	74360.5			0.540250
$372$	88287.3	−	88287.3i	0.637988	−	0.637988i
$373$	−56848.8	−	56848.8i	−0.408605	−	0.408605i	0.472647	−	0.881252i	$-0.343299\pi$
$373$	−56848.8	−	56848.8i	−0.408605	−	0.408605i	−0.881252	+	0.472647i	$0.843299\pi$
$374$			304815.i			2.17918i
$375$		0			0
$376$	124479.			0.880484
$377$	70.1162	−	70.1162i	0.000493328	−	0.000493328i
$378$	−90089.2	−	90089.2i	−0.630506	−	0.630506i
$379$		−	15626.1i		−	0.108786i	−0.998520	−	0.0543929i	$-0.982678\pi$
$379$		−	15626.1i		−	0.108786i	0.998520	−	0.0543929i	$-0.0173224\pi$
$380$		0			0
$381$	−336069.			−2.31514
$382$	43314.9	−	43314.9i	0.296832	−	0.296832i
$383$	150354.	+	150354.i	1.02499	+	1.02499i	0.999680	+	0.0253062i	$0.00805608\pi$
$383$	150354.	+	150354.i	1.02499	+	1.02499i	0.0253062	+	0.999680i	$0.491944\pi$
$384$		−	324162.i		−	2.19836i
$385$		0			0
$386$	105470.			0.707875
$387$	206971.	−	206971.i	1.38194	−	1.38194i
$388$	74837.4	+	74837.4i	0.497113	+	0.497113i
$389$			110195.i			0.728222i	0.931356	+	0.364111i	$0.118627\pi$
$389$			110195.i			0.728222i	−0.931356	+	0.364111i	$0.881373\pi$
$390$		0			0
$391$	129109.			0.844504
$392$	−11242.7	+	11242.7i	−0.0731642	+	0.0731642i
$393$	205139.	+	205139.i	1.32820	+	1.32820i
$394$		−	326144.i		−	2.10096i
$395$		0			0
$396$	743708.			4.74255
$397$	−13919.8	+	13919.8i	−0.0883183	+	0.0883183i	−0.749886	−	0.661567i	$-0.769892\pi$
$397$	−13919.8	+	13919.8i	−0.0883183	+	0.0883183i	0.661567	+	0.749886i	$0.269892\pi$
$398$	−111674.	−	111674.i	−0.704992	−	0.704992i
$399$			60061.1i			0.377266i
$400$		0			0
$401$	−154994.			−0.963886			−0.481943	−	0.876202i	$-0.660069\pi$
$401$	−154994.			−0.963886			−0.481943	+	0.876202i	$0.660069\pi$
$402$	23555.9	−	23555.9i	0.145763	−	0.145763i
$403$	670.718	+	670.718i	0.00412981	+	0.00412981i
$404$			216283.i			1.32513i
$405$		0			0
$406$	4243.45			0.0257435
$407$	−99828.7	+	99828.7i	−0.602652	+	0.602652i
$408$	116863.	+	116863.i	0.702032	+	0.702032i
$409$			150201.i			0.897894i	0.893558	+	0.448947i	$0.148201\pi$
$409$			150201.i			0.897894i	−0.893558	+	0.448947i	$0.851799\pi$
$410$		0			0
$411$	269770.			1.59702
$412$	310236.	−	310236.i	1.82767	−	1.82767i
$413$	41203.3	+	41203.3i	0.241564	+	0.241564i
$414$		−	530525.i		−	3.09531i
$415$		0			0
$416$	3433.68			0.0198414
$417$	−73777.2	+	73777.2i	−0.424277	+	0.424277i
$418$	−196050.	−	196050.i	−1.12206	−	1.12206i
$419$			150030.i			0.854573i	0.904116	+	0.427286i	$0.140530\pi$
$419$			150030.i			0.854573i	−0.904116	+	0.427286i	$0.859470\pi$
$420$		0			0
$421$	−110889.			−0.625639			−0.312820	−	0.949813i	$-0.601274\pi$
$421$	−110889.			−0.625639			−0.312820	+	0.949813i	$0.601274\pi$
$422$	−162963.	+	162963.i	−0.915091	+	0.915091i
$423$	−289960.	−	289960.i	−1.62053	−	1.62053i
$424$			186117.i			1.03527i
$425$		0			0
$426$	−575885.			−3.17334
$427$	22725.6	−	22725.6i	0.124641	−	0.124641i
$428$	−248395.	−	248395.i	−1.35599	−	1.35599i
$429$			8646.91i			0.0469836i
$430$		0			0
$431$	51534.2			0.277422			0.138711	−	0.990333i	$-0.455704\pi$
$431$	51534.2			0.277422			0.138711	+	0.990333i	$0.455704\pi$
$432$	−64538.5	+	64538.5i	−0.345821	+	0.345821i
$433$	−200913.	−	200913.i	−1.07160	−	1.07160i	−0.997231	−	0.0743657i	$-0.976307\pi$
$433$	−200913.	−	200913.i	−1.07160	−	1.07160i	−0.0743657	−	0.997231i	$-0.523693\pi$
$434$			40592.0i			0.215507i
$435$		0			0
$436$	21291.8			0.112006
$437$	−83039.7	+	83039.7i	−0.434833	+	0.434833i
$438$	223627.	+	223627.i	1.16567	+	1.16567i
$439$		−	124611.i		−	0.646589i	−0.946298	−	0.323294i	$-0.895210\pi$
$439$		−	124611.i		−	0.646589i	0.946298	−	0.323294i	$-0.104790\pi$
$440$		0			0
$441$	52377.1			0.269317
$442$	−2810.99	+	2810.99i	−0.0143885	+	0.0143885i
$443$	274465.	+	274465.i	1.39855	+	1.39855i	0.804213	+	0.594341i	$0.202587\pi$
$443$	274465.	+	274465.i	1.39855	+	1.39855i	0.594341	+	0.804213i	$0.297413\pi$
$444$			242363.i			1.22942i
$445$		0			0
$446$	49524.6			0.248972
$447$	−27891.9	+	27891.9i	−0.139593	+	0.139593i
$448$	86456.8	+	86456.8i	0.430768	+	0.430768i
$449$			204661.i			1.01518i	0.861599	+	0.507589i	$0.169463\pi$
$449$			204661.i			1.01518i	−0.861599	+	0.507589i	$0.830537\pi$
$450$		0			0
$451$	199735.			0.981977
$452$	−81217.9	+	81217.9i	−0.397535	+	0.397535i
$453$	66364.6	+	66364.6i	0.323400	+	0.323400i
$454$			94468.6i			0.458327i
$455$		0			0
$456$	−150327.			−0.722950
$457$	−191543.	+	191543.i	−0.917135	+	0.917135i	−0.996820	−	0.0796854i	$-0.974608\pi$
$457$	−191543.	+	191543.i	−0.917135	+	0.917135i	0.0796854	+	0.996820i	$0.474608\pi$
$458$	337160.	+	337160.i	1.60733	+	1.60733i
$459$		−	255645.i		−	1.21342i
$460$		0			0
$461$	−390266.			−1.83636			−0.918181	−	0.396160i	$-0.870342\pi$
$461$	−390266.			−1.83636			−0.918181	+	0.396160i	$0.870342\pi$
$462$	−261657.	+	261657.i	−1.22588	+	1.22588i
$463$	−73034.9	−	73034.9i	−0.340697	−	0.340697i	0.515932	−	0.856629i	$-0.327446\pi$
$463$	−73034.9	−	73034.9i	−0.340697	−	0.340697i	−0.856629	+	0.515932i	$0.827446\pi$
$464$		−	3039.94i		−	0.0141198i
$465$		0			0
$466$	117287.			0.540106
$467$	−247955.	+	247955.i	−1.13694	+	1.13694i	−0.147946	+	0.988995i	$0.547266\pi$
$467$	−247955.	+	247955.i	−1.13694	+	1.13694i	−0.988995	+	0.147946i	$0.952734\pi$
$468$	6858.43	+	6858.43i	0.0313136	+	0.0313136i
$469$			6430.70i			0.0292356i
$470$		0			0
$471$	373817.			1.68507
$472$	−103128.	+	103128.i	−0.462906	+	0.462906i
$473$	−282266.	−	282266.i	−1.26164	−	1.26164i
$474$		−	633798.i		−	2.82094i
$475$		0			0
$476$	−101012.			−0.445822
$477$	433538.	−	433538.i	1.90542	−	1.90542i
$478$	−297271.	−	297271.i	−1.30106	−	1.30106i
$479$			413109.i			1.80050i	0.435373	+	0.900250i	$0.356616\pi$
$479$			413109.i			1.80050i	−0.435373	+	0.900250i	$0.643384\pi$
$480$		0			0
$481$	−1841.23			−0.00795824
$482$	−100171.	+	100171.i	−0.431167	+	0.431167i
$483$	110828.	+	110828.i	0.475068	+	0.475068i
$484$		−	671867.i		−	2.86809i
$485$		0			0
$486$	136207.			0.576670
$487$	7417.37	−	7417.37i	0.0312746	−	0.0312746i	−0.691297	−	0.722571i	$-0.742960\pi$
$487$	7417.37	−	7417.37i	0.0312746	−	0.0312746i	0.722571	+	0.691297i	$0.242960\pi$
$488$	56880.1	+	56880.1i	0.238848	+	0.238848i
$489$		−	194220.i		−	0.812227i
$490$		0			0
$491$	430752.			1.78675			0.893376	−	0.449309i	$-0.148330\pi$
$491$	430752.			1.78675			0.893376	+	0.449309i	$0.148330\pi$
$492$	242457.	−	242457.i	1.00162	−	1.00162i
$493$	6020.80	+	6020.80i	0.0247719	+	0.0247719i
$494$		−	3615.92i		−	0.0148172i
$495$		0			0
$496$	29079.5			0.118202
$497$	78607.5	−	78607.5i	0.318237	−	0.318237i
$498$	−553903.	−	553903.i	−2.23345	−	2.23345i
$499$		−	265534.i		−	1.06640i	−0.845990	−	0.533199i	$-0.820990\pi$
$499$		−	265534.i		−	1.06640i	0.845990	−	0.533199i	$-0.179010\pi$
$500$		0			0
$501$	−440598.			−1.75536
$502$	236911.	−	236911.i	0.940109	−	0.940109i
$503$	154343.	+	154343.i	0.610031	+	0.610031i	0.942954	−	0.332923i	$-0.108035\pi$
$503$	154343.	+	154343.i	0.610031	+	0.610031i	−0.332923	+	0.942954i	$0.608035\pi$
$504$			131095.i			0.516089i
$505$		0			0
$506$	−723526.			−2.82588
$507$	308659.	−	308659.i	1.20078	−	1.20078i
$508$	363530.	+	363530.i	1.40868	+	1.40868i
$509$			414048.i			1.59814i	0.601237	+	0.799071i	$0.294675\pi$
$509$			414048.i			1.59814i	−0.601237	+	0.799071i	$0.705325\pi$
$510$		0			0
$511$	−61049.4			−0.233797
$512$	118103.	−	118103.i	0.450527	−	0.450527i
$513$	164425.	+	164425.i	0.624789	+	0.624789i
$514$		−	682393.i		−	2.58290i
$515$		0			0
$516$	−685282.			−2.57377
$517$	−395445.	+	395445.i	−1.47947	+	1.47947i
$518$	−55715.8	−	55715.8i	−0.207644	−	0.207644i
$519$			373471.i			1.38651i
$520$		0			0
$521$	−141292.			−0.520524			−0.260262	−	0.965538i	$-0.583809\pi$
$521$	−141292.			−0.520524			−0.260262	+	0.965538i	$0.583809\pi$
$522$	24740.3	−	24740.3i	0.0907953	−	0.0907953i
$523$	−258549.	−	258549.i	−0.945233	−	0.945233i	0.0533430	−	0.998576i	$-0.483012\pi$
$523$	−258549.	−	258549.i	−0.945233	−	0.945233i	−0.998576	+	0.0533430i	$0.983012\pi$
$524$		−	443803.i		−	1.61632i
$525$		0			0
$526$	586795.			2.12087
$527$	−57593.8	+	57593.8i	−0.207374	+	0.207374i
$528$	187447.	+	187447.i	0.672373	+	0.672373i
$529$			26618.3i			0.0951193i
$530$		0			0
$531$	480449.			1.70395
$532$	64968.9	−	64968.9i	0.229553	−	0.229553i
$533$	1841.94	+	1841.94i	0.00648369	+	0.00648369i
$534$			1.03387e6i			3.62564i
$535$		0			0
$536$	−16095.4			−0.0560239
$537$	−589475.	+	589475.i	−2.04417	+	2.04417i
$538$	−95635.2	−	95635.2i	−0.330410	−	0.330410i
$539$		−	71431.5i		−	0.245874i
$540$		0			0
$541$	35978.6			0.122928			0.0614639	−	0.998109i	$-0.480423\pi$
$541$	35978.6			0.122928			0.0614639	+	0.998109i	$0.480423\pi$
$542$	174191.	−	174191.i	0.592964	−	0.592964i
$543$	−154837.	−	154837.i	−0.525141	−	0.525141i
$544$			294846.i			0.996318i
$545$		0			0
$546$	−4825.96			−0.0161882
$547$	−84541.2	+	84541.2i	−0.282549	+	0.282549i	−0.834125	−	0.551576i	$-0.814027\pi$
$547$	−84541.2	+	84541.2i	−0.282549	+	0.282549i	0.551576	+	0.834125i	$0.314027\pi$
$548$	−291814.	−	291814.i	−0.971728	−	0.971728i
$549$		−	264991.i		−	0.879197i
$550$		0			0
$551$	−7744.88			−0.0255101
$552$	−277393.	+	277393.i	−0.910368	+	0.910368i
$553$	86512.5	+	86512.5i	0.282897	+	0.282897i
$554$			408817.i			1.33202i
$555$		0			0
$556$	159612.			0.516315
$557$	231346.	−	231346.i	0.745679	−	0.745679i	−0.227986	−	0.973664i	$-0.573214\pi$
$557$	231346.	−	231346.i	0.745679	−	0.745679i	0.973664	+	0.227986i	$0.0732140\pi$
$558$	236661.	+	236661.i	0.760077	+	0.760077i
$559$		−	5206.08i		−	0.0166605i
$560$		0			0
$561$	−742500.			−2.35923
$562$	297635.	−	297635.i	0.942349	−	0.942349i
$563$	−55650.4	−	55650.4i	−0.175570	−	0.175570i	0.613851	−	0.789422i	$-0.289619\pi$
$563$	−55650.4	−	55650.4i	−0.175570	−	0.175570i	−0.789422	+	0.613851i	$0.789619\pi$
$564$			960056.i			3.01813i
$565$		0			0
$566$	151970.			0.474380
$567$	57467.5	−	57467.5i	0.178754	−	0.178754i
$568$	196747.	+	196747.i	0.609835	+	0.609835i
$569$		−	339008.i		−	1.04709i	−0.851997	−	0.523546i	$-0.824609\pi$
$569$		−	339008.i		−	1.04709i	0.851997	−	0.523546i	$-0.175391\pi$
$570$		0			0
$571$	−450122.			−1.38057			−0.690284	−	0.723539i	$-0.742514\pi$
$571$	−450122.			−1.38057			−0.690284	+	0.723539i	$0.742514\pi$
$572$	9353.48	−	9353.48i	0.0285878	−	0.0285878i
$573$	105511.	+	105511.i	0.321357	+	0.321357i
$574$			111475.i			0.338340i
$575$		0			0
$576$	1.00813e6			3.03857
$577$	−36276.0	+	36276.0i	−0.108960	+	0.108960i	−0.759485	−	0.650525i	$-0.774549\pi$
$577$	−36276.0	+	36276.0i	−0.108960	+	0.108960i	0.650525	+	0.759485i	$0.274549\pi$
$578$	129264.	+	129264.i	0.386921	+	0.386921i
$579$			256916.i			0.766362i
$580$		0			0
$581$	151214.			0.447961
$582$	−307018.	+	307018.i	−0.906395	+	0.906395i
$583$	−591257.	−	591257.i	−1.73956	−	1.73956i
$584$		−	152801.i		−	0.448023i
$585$		0			0
$586$	−326789.			−0.951639
$587$	401647.	−	401647.i	1.16565	−	1.16565i	0.182433	−	0.983218i	$-0.441603\pi$
$587$	401647.	−	401647.i	1.16565	−	1.16565i	0.983218	−	0.182433i	$-0.0583973\pi$
$588$	−86710.2	−	86710.2i	−0.250793	−	0.250793i
$589$		−	74086.0i		−	0.213553i
$590$		0			0
$591$	794456.			2.27455
$592$	−39913.9	+	39913.9i	−0.113889	+	0.113889i
$593$	−54743.8	−	54743.8i	−0.155677	−	0.155677i	0.624971	−	0.780648i	$-0.285111\pi$
$593$	−54743.8	−	54743.8i	−0.155677	−	0.155677i	−0.780648	+	0.624971i	$0.785111\pi$
$594$			1.43264e6i			4.06035i
$595$		0			0
$596$	60342.2			0.169875
$597$	272026.	−	272026.i	0.763241	−	0.763241i
$598$	−6672.31	−	6672.31i	−0.0186584	−	0.0186584i
$599$		−	598286.i		−	1.66746i	−0.552174	−	0.833729i	$-0.686202\pi$
$599$		−	598286.i		−	1.66746i	0.552174	−	0.833729i	$-0.313798\pi$
$600$		0			0
$601$	89584.5			0.248018			0.124009	−	0.992281i	$-0.460425\pi$
$601$	89584.5			0.248018			0.124009	+	0.992281i	$0.460425\pi$
$602$	157537.	−	157537.i	0.434699	−	0.434699i
$603$	37492.4	+	37492.4i	0.103112	+	0.103112i
$604$		−	143575.i		−	0.393555i
$605$		0			0
$606$	−887293.			−2.41614
$607$	441509.	−	441509.i	1.19829	−	1.19829i	0.223612	−	0.974678i	$-0.428215\pi$
$607$	441509.	−	441509.i	1.19829	−	1.19829i	0.974678	−	0.223612i	$-0.0717847\pi$
$608$	−189638.	−	189638.i	−0.513002	−	0.513002i
$609$			10336.6i			0.0278705i
$610$		0			0
$611$	−7293.54			−0.0195369
$612$	−588925.	+	588925.i	−1.57238	+	1.57238i
$613$	94009.2	+	94009.2i	0.250178	+	0.250178i	0.821044	−	0.570865i	$-0.193392\pi$
$613$	94009.2	+	94009.2i	0.250178	+	0.250178i	−0.570865	+	0.821044i	$0.693392\pi$
$614$		−	680437.i		−	1.80489i
$615$		0			0
$616$	178787.			0.471165
$617$	71831.6	−	71831.6i	0.188688	−	0.188688i	−0.606440	−	0.795129i	$-0.707403\pi$
$617$	71831.6	−	71831.6i	0.188688	−	0.188688i	0.795129	+	0.606440i	$0.207403\pi$
$618$	1.27273e6	+	1.27273e6i	3.33242	+	3.33242i
$619$		−	251115.i		−	0.655378i	−0.944786	−	0.327689i	$-0.893730\pi$
$619$		−	251115.i		−	0.655378i	0.944786	−	0.327689i	$-0.106270\pi$
$620$		0			0
$621$	606813.			1.57352
$622$	−722607.	+	722607.i	−1.86776	+	1.86776i
$623$	−141122.	−	141122.i	−0.363596	−	0.363596i
$624$			3457.25i			0.00887894i
$625$		0			0
$626$	−61082.6			−0.155872
$627$	477559.	−	477559.i	1.21476	−	1.21476i
$628$	−404363.	−	404363.i	−1.02530	−	1.02530i
$629$		−	158104.i		−	0.399615i
$630$		0			0
$631$	−115449.			−0.289957			−0.144978	−	0.989435i	$-0.546311\pi$
$631$	−115449.			−0.289957			−0.144978	+	0.989435i	$0.546311\pi$
$632$	−216533.	+	216533.i	−0.542113	+	0.542113i
$633$	−396962.	−	396962.i	−0.990700	−	0.990700i
$634$			927257.i			2.30686i
$635$		0			0
$636$	−1.43545e6			−3.54873
$637$	658.737	−	658.737i	0.00162343	−	0.00162343i
$638$	−33740.6	−	33740.6i	−0.0828918	−	0.0828918i
$639$		−	916599.i		−	2.24480i
$640$		0			0
$641$	214800.			0.522780			0.261390	−	0.965233i	$-0.415819\pi$
$641$	214800.			0.522780			0.261390	+	0.965233i	$0.415819\pi$
$642$	1.01903e6	−	1.01903e6i	2.47239	−	2.47239i
$643$	455613.	+	455613.i	1.10198	+	1.10198i	0.994172	+	0.107810i	$0.0343838\pi$
$643$	455613.	+	455613.i	1.10198	+	1.10198i	0.107810	+	0.994172i	$0.465616\pi$
$644$		−	239769.i		−	0.578124i
$645$		0			0
$646$	310495.			0.744029
$647$	−110254.	+	110254.i	−0.263382	+	0.263382i	−0.826427	−	0.563044i	$-0.809630\pi$
$647$	−110254.	+	110254.i	−0.263382	+	0.263382i	0.563044	+	0.826427i	$0.309630\pi$
$648$	143836.	+	143836.i	0.342544	+	0.342544i
$649$		−	655233.i		−	1.55563i
$650$		0			0
$651$	−98878.3			−0.233313
$652$	−210091.	+	210091.i	−0.494211	+	0.494211i
$653$	59503.0	+	59503.0i	0.139544	+	0.139544i	0.773428	−	0.633884i	$-0.218540\pi$
$653$	59503.0	+	59503.0i	0.139544	+	0.139544i	−0.633884	+	0.773428i	$0.718540\pi$
$654$			87348.9i			0.204222i
$655$		0			0
$656$	79859.0			0.185574
$657$	−355932.	+	355932.i	−0.824586	+	0.824586i
$658$	−220704.	−	220704.i	−0.509750	−	0.509750i
$659$			232511.i			0.535394i	0.963503	+	0.267697i	$0.0862626\pi$
$659$			232511.i			0.535394i	−0.963503	+	0.267697i	$0.913737\pi$
$660$		0			0
$661$	−456788.			−1.04547			−0.522736	−	0.852495i	$-0.675089\pi$
$661$	−456788.			−1.04547			−0.522736	+	0.852495i	$0.675089\pi$
$662$	−814861.	+	814861.i	−1.85938	+	1.85938i
$663$	−6847.29	−	6847.29i	−0.0155773	−	0.0155773i
$664$			378475.i			0.858421i
$665$		0			0
$666$	−649671.			−1.46469
$667$	−14291.3	+	14291.3i	−0.0321233	+	0.0321233i
$668$	476600.	+	476600.i	1.06807	+	1.06807i
$669$			120637.i			0.269543i
$670$		0			0
$671$	−361393.			−0.802666
$672$	−253099.	+	253099.i	−0.560470	+	0.560470i
$673$	238249.	+	238249.i	0.526018	+	0.526018i	0.919382	−	0.393365i	$-0.128689\pi$
$673$	238249.	+	238249.i	0.526018	+	0.526018i	−0.393365	+	0.919382i	$0.628689\pi$
$674$			630492.i			1.38790i
$675$		0			0
$676$	−667760.			−1.46126
$677$	−426610.	+	426610.i	−0.930793	+	0.930793i	−0.997756	−	0.0669621i	$-0.978669\pi$
$677$	−426610.	+	426610.i	−0.930793	+	0.930793i	0.0669621	+	0.997756i	$0.478669\pi$
$678$	−333194.	−	333194.i	−0.724832	−	0.724832i
$679$		−	83814.9i		−	0.181795i
$680$		0			0
$681$	−230116.			−0.496196
$682$	322756.	−	322756.i	0.693915	−	0.693915i
$683$	−268129.	−	268129.i	−0.574781	−	0.574781i	0.358680	−	0.933461i	$-0.383227\pi$
$683$	−268129.	−	268129.i	−0.574781	−	0.574781i	−0.933461	+	0.358680i	$0.883227\pi$
$684$		−	757566.i		−	1.61923i
$685$		0			0
$686$	39867.0			0.0847159
$687$	−821289.	+	821289.i	−1.74013	+	1.74013i
$688$	−112857.	−	112857.i	−0.238425	−	0.238425i
$689$		−	10905.1i		−	0.0229715i
$690$		0			0
$691$	−595267.			−1.24668			−0.623341	−	0.781950i	$-0.714225\pi$
$691$	−595267.			−1.24668			−0.623341	+	0.781950i	$0.714225\pi$
$692$	403989.	−	403989.i	0.843641	−	0.843641i
$693$	−416462.	−	416462.i	−0.867179	−	0.867179i
$694$			190421.i			0.395363i
$695$		0			0
$696$	−25871.6			−0.0534079
$697$	−158166.	+	158166.i	−0.325572	+	0.325572i
$698$	116638.	+	116638.i	0.239403	+	0.239403i
$699$			285700.i			0.584731i
$700$		0			0
$701$	−219310.			−0.446296			−0.223148	−	0.974785i	$-0.571633\pi$
$701$	−219310.			−0.446296			−0.223148	+	0.974785i	$0.571633\pi$
$702$	−13211.7	+	13211.7i	−0.0268092	+	0.0268092i
$703$	101689.	+	101689.i	0.205761	+	0.205761i
$704$		−	1.37488e6i		−	2.77407i
$705$		0			0
$706$	872694.			1.75086
$707$	121114.	−	121114.i	0.242302	−	0.242302i
$708$	−795382.	−	795382.i	−1.58675	−	1.58675i
$709$			136829.i			0.272199i	0.990695	+	0.136099i	$0.0434567\pi$
$709$			136829.i			0.272199i	−0.990695	+	0.136099i	$0.956543\pi$
$710$		0			0
$711$	1.00877e6			1.99551
$712$	353216.	−	353216.i	0.696755	−	0.696755i
$713$	−136708.	−	136708.i	−0.268915	−	0.268915i
$714$		−	414400.i		−	0.812874i
$715$		0			0
$716$	1.27529e6			2.48761
$717$	724123.	−	724123.i	1.40856	−	1.40856i
$718$	−751108.	−	751108.i	−1.45698	−	1.45698i
$719$			402863.i			0.779291i	0.920965	+	0.389646i	$0.127403\pi$
$719$			402863.i			0.779291i	−0.920965	+	0.389646i	$0.872597\pi$
$720$		0			0
$721$	−347452.			−0.668381
$722$	378621.	−	378621.i	0.726323	−	0.726323i
$723$	−244006.	−	244006.i	−0.466792	−	0.466792i
$724$			334979.i			0.639058i
$725$		0			0
$726$	2.75631e6			5.22944
$727$	188424.	−	188424.i	0.356506	−	0.356506i	−0.506017	−	0.862523i	$-0.668883\pi$
$727$	188424.	−	188424.i	0.356506	−	0.356506i	0.862523	+	0.506017i	$0.168883\pi$
$728$	1648.76	+	1648.76i	0.00311096	+	0.00311096i
$729$			687234.i			1.29315i
$730$		0			0
$731$	447040.			0.836589
$732$	−438692.	+	438692.i	−0.818725	+	0.818725i
$733$	313496.	+	313496.i	0.583478	+	0.583478i	0.935857	−	0.352380i	$-0.114627\pi$
$733$	313496.	+	313496.i	0.583478	+	0.583478i	−0.352380	+	0.935857i	$0.614627\pi$
$734$		−	786724.i		−	1.46026i
$735$		0			0
$736$	−699864.			−1.29199
$737$	51131.9	−	51131.9i	0.0941363	−	0.0941363i
$738$	649924.	+	649924.i	1.19330	+	1.19330i
$739$			548480.i			1.00432i	0.864775	+	0.502160i	$0.167461\pi$
$739$			548480.i			1.00432i	−0.864775	+	0.502160i	$0.832539\pi$
$740$		0			0
$741$	8808.04			0.0160414
$742$	329989.	−	329989.i	0.599365	−	0.599365i
$743$	−11348.8	−	11348.8i	−0.0205576	−	0.0205576i	0.696753	−	0.717311i	$-0.254627\pi$
$743$	−11348.8	−	11348.8i	−0.0205576	−	0.0205576i	−0.717311	+	0.696753i	$0.754627\pi$
$744$		−	247483.i		−	0.447095i
$745$		0			0
$746$	−504554.			−0.906630
$747$	881611.	−	881611.i	1.57992	−	1.57992i
$748$	803173.	+	803173.i	1.43551	+	1.43551i
$749$			278193.i			0.495887i
$750$		0			0
$751$	−625714.			−1.10942			−0.554710	−	0.832044i	$-0.687171\pi$
$751$	−625714.			−1.10942			−0.554710	+	0.832044i	$0.687171\pi$
$752$	−158109.	+	158109.i	−0.279589	+	0.279589i
$753$	577093.	+	577093.i	1.01778	+	1.01778i
$754$		−	622.308i		−	0.00109462i
$755$		0			0
$756$	−474761.			−0.830675
$757$	−19192.0	+	19192.0i	−0.0334909	+	0.0334909i	−0.723654	−	0.690163i	$-0.757539\pi$
$757$	−19192.0	+	19192.0i	−0.0334909	+	0.0334909i	0.690163	+	0.723654i	$0.257539\pi$
$758$	−69343.8	−	69343.8i	−0.120689	−	0.120689i
$759$		−	1.76244e6i		−	3.05936i
$760$		0			0
$761$	313327.			0.541039			0.270520	−	0.962714i	$-0.412805\pi$
$761$	313327.			0.541039			0.270520	+	0.962714i	$0.412805\pi$
$762$	−1.49137e6	+	1.49137e6i	−2.56847	+	2.56847i
$763$	−11923.0	−	11923.0i	−0.0204803	−	0.0204803i
$764$		−	228265.i		−	0.391068i
$765$		0			0
$766$	1.33445e6			2.27428
$767$	6042.51	−	6042.51i	0.0102713	−	0.0102713i
$768$	−296692.	−	296692.i	−0.503019	−	0.503019i
$769$			825244.i			1.39550i	0.716342	+	0.697750i	$0.245815\pi$
$769$			825244.i			1.39550i	−0.716342	+	0.697750i	$0.754185\pi$
$770$		0			0
$771$	1.66224e6			2.79631
$772$	277909.	−	277909.i	0.466304	−	0.466304i
$773$	−108078.	−	108078.i	−0.180875	−	0.180875i	0.610862	−	0.791737i	$-0.290823\pi$
$773$	−108078.	−	108078.i	−0.180875	−	0.180875i	−0.791737	+	0.610862i	$0.790823\pi$
$774$		−	1.83695e6i		−	3.06630i
$775$		0			0
$776$	209781.			0.348372
$777$	135718.	−	135718.i	0.224800	−	0.224800i
$778$	489012.	+	489012.i	0.807906	+	0.807906i
$779$		−	203457.i		−	0.335273i
$780$		0			0
$781$	−1.25005e6			−2.04940
$782$	572944.	−	572944.i	0.936911	−	0.936911i
$783$	28297.9	+	28297.9i	0.0461562	+	0.0461562i
$784$		−	28560.1i		−	0.0464651i
$785$		0			0
$786$	1.82069e6			2.94707
$787$	−694016.	+	694016.i	−1.12052	+	1.12052i	−0.128858	+	0.991663i	$0.541131\pi$
$787$	−694016.	+	694016.i	−1.12052	+	1.12052i	−0.991663	+	0.128858i	$0.958869\pi$
$788$	−859374.	−	859374.i	−1.38398	−	1.38398i
$789$			1.42938e6i			2.29611i
$790$		0			0
$791$	90960.9			0.145379
$792$	1.04237e6	−	1.04237e6i	1.66176	−	1.66176i
$793$	−3332.74	−	3332.74i	−0.00529975	−	0.00529975i
$794$			123543.i			0.195965i
$795$		0			0
$796$	−588508.			−0.928809
$797$	468926.	−	468926.i	0.738223	−	0.738223i	−0.234011	−	0.972234i	$-0.575185\pi$
$797$	468926.	−	468926.i	0.738223	−	0.738223i	0.972234	+	0.234011i	$0.0751852\pi$
$798$	266533.	+	266533.i	0.418547	+	0.418547i
$799$		−	626288.i		−	0.981026i
$800$		0			0
$801$	−1.64555e6			−2.56475
$802$	−687815.	+	687815.i	−1.06936	+	1.06936i
$803$	485418.	+	485418.i	0.752808	+	0.752808i
$804$		−	124137.i		−	0.192039i
$805$		0			0
$806$	5952.88			0.00916340
$807$	232958.	−	232958.i	0.357710	−	0.357710i
$808$	303138.	+	303138.i	0.464320	+	0.464320i
$809$			1.16441e6i			1.77913i	0.456807	+	0.889566i	$0.348993\pi$
$809$			1.16441e6i			1.77913i	−0.456807	+	0.889566i	$0.651007\pi$
$810$		0			0
$811$	68693.3			0.104441			0.0522207	−	0.998636i	$-0.483370\pi$
$811$	68693.3			0.104441			0.0522207	+	0.998636i	$0.483370\pi$
$812$	11181.3	−	11181.3i	0.0169582	−	0.0169582i
$813$	424313.	+	424313.i	0.641957	+	0.641957i
$814$			886017.i			1.33719i
$815$		0			0
$816$	−296870.			−0.445847
$817$	−287526.	+	287526.i	−0.430758	+	0.430758i
$818$	666544.	+	666544.i	0.996144	+	0.996144i
$819$		−	7681.17i		−	0.0114514i
$820$		0			0
$821$	478746.			0.710262			0.355131	−	0.934817i	$-0.384436\pi$
$821$	478746.			0.710262			0.355131	+	0.934817i	$0.384436\pi$
$822$	1.19716e6	−	1.19716e6i	1.77177	−	1.77177i
$823$	154554.	+	154554.i	0.228181	+	0.228181i	0.811933	−	0.583751i	$-0.198416\pi$
$823$	154554.	+	154554.i	0.228181	+	0.228181i	−0.583751	+	0.811933i	$0.698416\pi$
$824$		−	869640.i		−	1.28081i
$825$		0			0
$826$	365695.			0.535992
$827$	886177.	−	886177.i	1.29571	−	1.29571i	0.364519	−	0.931196i	$-0.381234\pi$
$827$	886177.	−	886177.i	1.29571	−	1.29571i	0.931196	−	0.364519i	$-0.118766\pi$
$828$	−1.39791e6	−	1.39791e6i	−2.03900	−	2.03900i
$829$		−	907552.i		−	1.32057i	−0.751014	−	0.660286i	$-0.770435\pi$
$829$		−	907552.i		−	1.32057i	0.751014	−	0.660286i	$-0.229565\pi$
$830$		0			0
$831$	−995838.			−1.44207
$832$	12679.0	−	12679.0i	0.0183163	−	0.0183163i
$833$	56565.0	+	56565.0i	0.0815188	+	0.0815188i
$834$			654800.i			0.941406i
$835$		0			0
$836$	−1.03316e6			−1.47828
$837$	−270692.	+	270692.i	−0.386389	+	0.386389i
$838$	665785.	+	665785.i	0.948082	+	0.948082i
$839$			646487.i			0.918408i	0.888331	+	0.459204i	$0.151865\pi$
$839$			646487.i			0.918408i	−0.888331	+	0.459204i	$0.848135\pi$
$840$		0			0
$841$	705948.			0.998115
$842$	−492090.	+	492090.i	−0.694098	+	0.694098i
$843$	725011.	+	725011.i	1.02021	+	1.02021i
$844$			858799.i			1.20561i
$845$		0			0
$846$	−2.57350e6			−3.59570
$847$	−376233.	+	376233.i	−0.524432	+	0.524432i
$848$	−236399.	−	236399.i	−0.328741	−	0.328741i
$849$			370185.i			0.513575i
$850$		0			0
$851$	375285.			0.518205
$852$	−1.51743e6	+	1.51743e6i	−2.09040	+	2.09040i
$853$	−369587.	−	369587.i	−0.507947	−	0.507947i	0.405949	−	0.913896i	$-0.366941\pi$
$853$	−369587.	−	369587.i	−0.507947	−	0.507947i	−0.913896	+	0.405949i	$0.866941\pi$
$854$		−	201699.i		−	0.276558i
$855$		0			0
$856$	−696291.			−0.950261
$857$	267926.	−	267926.i	0.364798	−	0.364798i	−0.500778	−	0.865576i	$-0.666953\pi$
$857$	267926.	−	267926.i	0.364798	−	0.364798i	0.865576	+	0.500778i	$0.166953\pi$
$858$	38372.3	+	38372.3i	0.0521247	+	0.0521247i
$859$			267374.i			0.362354i	0.983450	+	0.181177i	$0.0579907\pi$
$859$			267374.i			0.362354i	−0.983450	+	0.181177i	$0.942009\pi$
$860$		0			0
$861$	−271542.			−0.366295
$862$	228693.	−	228693.i	0.307778	−	0.307778i
$863$	968841.	+	968841.i	1.30086	+	1.30086i	0.927812	+	0.373049i	$0.121688\pi$
$863$	968841.	+	968841.i	1.30086	+	1.30086i	0.373049	+	0.927812i	$0.378312\pi$
$864$			1.38578e6i			1.85639i
$865$		0			0
$866$	−1.78318e6			−2.37771
$867$	−314875.	+	314875.i	−0.418890	+	0.418890i
$868$	106958.	+	106958.i	0.141963	+	0.141963i
$869$		−	1.37576e6i		−	1.82181i
$870$		0			0
$871$	943.071			0.00124311
$872$	29842.1	−	29842.1i	0.0392462	−	0.0392462i
$873$	−488660.	−	488660.i	−0.641177	−	0.641177i
$874$			737009.i			0.964828i
$875$		0			0
$876$	1.17849e6			1.53574
$877$	−552371.	+	552371.i	−0.718177	+	0.718177i	−0.968232	−	0.250055i	$-0.919551\pi$
$877$	−552371.	+	552371.i	−0.718177	+	0.718177i	0.250055	+	0.968232i	$0.419551\pi$
$878$	−552986.	−	552986.i	−0.717340	−	0.717340i
$879$		−	796026.i		−	1.03027i
$880$		0			0
$881$	−392723.			−0.505981			−0.252990	−	0.967469i	$-0.581414\pi$
$881$	−392723.			−0.505981			−0.252990	+	0.967469i	$0.581414\pi$
$882$	232433.	−	232433.i	0.298787	−	0.298787i
$883$	−423959.	−	423959.i	−0.543755	−	0.543755i	0.380873	−	0.924627i	$-0.375624\pi$
$883$	−423959.	−	423959.i	−0.543755	−	0.543755i	−0.924627	+	0.380873i	$0.875624\pi$
$884$			14813.6i			0.0189564i
$885$		0			0
$886$	2.43598e6			3.10317
$887$	−74353.8	+	74353.8i	−0.0945052	+	0.0945052i	−0.752779	−	0.658274i	$-0.771287\pi$
$887$	−74353.8	+	74353.8i	−0.0945052	+	0.0945052i	0.658274	+	0.752779i	$0.271287\pi$
$888$	339690.	+	339690.i	0.430782	+	0.430782i
$889$		−	407139.i		−	0.515157i
$890$		0			0
$891$	−913873.			−1.15115
$892$	130495.	−	130495.i	0.164007	−	0.164007i
$893$	402814.	+	402814.i	0.505128	+	0.505128i
$894$			247551.i			0.309735i
$895$		0			0
$896$	392715.			0.489171
$897$	16253.1	−	16253.1i	0.0202000	−	0.0202000i
$898$	908221.	+	908221.i	1.12626	+	1.12626i
$899$		−	12750.4i		−	0.0157762i
$900$		0			0
$901$	936406.			1.15349
$902$	886363.	−	886363.i	1.08943	−	1.08943i
$903$	383745.	+	383745.i	0.470616	+	0.470616i
$904$			227667.i			0.278588i
$905$		0			0
$906$	589011.			0.717575
$907$	387876.	−	387876.i	0.471496	−	0.471496i	−0.430902	−	0.902399i	$-0.641805\pi$
$907$	387876.	−	387876.i	0.471496	−	0.471496i	0.902399	+	0.430902i	$0.141805\pi$
$908$	248920.	+	248920.i	0.301917	+	0.301917i
$909$		−	1.41225e6i		−	1.70916i
$910$		0			0
$911$	621927.			0.749380			0.374690	−	0.927150i	$-0.377749\pi$
$911$	621927.			0.749380			0.374690	+	0.927150i	$0.377749\pi$
$912$	190940.	−	190940.i	0.229566	−	0.229566i
$913$	−1.20234e6	−	1.20234e6i	−1.44240	−	1.44240i
$914$			1.70001e6i			2.03498i
$915$		0			0
$916$	1.77680e6			2.11762
$917$	−248521.	+	248521.i	−0.295546	+	0.295546i
$918$	−1.13447e6	−	1.13447e6i	−1.34620	−	1.34620i
$919$		−	191177.i		−	0.226363i	−0.993574	−	0.113181i	$-0.963896\pi$
$919$		−	191177.i		−	0.226363i	0.993574	−	0.113181i	$-0.0361041\pi$
$920$		0			0
$921$	1.65748e6			1.95402
$922$	−1.73188e6	+	1.73188e6i	−2.03730	+	2.03730i
$923$	−11527.9	−	11527.9i	−0.0135315	−	0.0135315i
$924$			1.37890e6i			1.61507i
$925$		0			0
$926$	−648213.			−0.755954
$927$	−2.02572e6	+	2.02572e6i	−2.35733	+	2.35733i
$928$	−32637.2	−	32637.2i	−0.0378980	−	0.0378980i
$929$		−	577221.i		−	0.668822i	−0.942427	−	0.334411i	$-0.891463\pi$
$929$		−	577221.i		−	0.668822i	0.942427	−	0.334411i	$-0.108537\pi$
$930$		0			0
$931$	−72762.6			−0.0839477
$932$	309046.	−	309046.i	0.355788	−	0.355788i
$933$	−1.76020e6	−	1.76020e6i	−2.02208	−	2.02208i
$934$			2.20069e6i			2.52270i
$935$		0			0
$936$	19225.2			0.0219442
$937$	−901445.	+	901445.i	−1.02674	+	1.02674i	−0.0271065	+	0.999633i	$0.508629\pi$
$937$	−901445.	+	901445.i	−1.02674	+	1.02674i	−0.999633	+	0.0271065i	$0.991371\pi$
$938$	28537.5	+	28537.5i	0.0324347	+	0.0324347i
$939$		−	148791.i		−	0.168751i
$940$		0			0
$941$	612137.			0.691304			0.345652	−	0.938363i	$-0.387658\pi$
$941$	612137.			0.691304			0.345652	+	0.938363i	$0.387658\pi$
$942$	1.65888e6	−	1.65888e6i	1.86945	−	1.86945i
$943$	−375431.	−	375431.i	−0.422189	−	0.422189i
$944$		−	261978.i		−	0.293982i
$945$		0			0
$946$	−2.50522e6			−2.79939
$947$	−516439.	+	516439.i	−0.575862	+	0.575862i	−0.933761	−	0.357898i	$-0.883493\pi$
$947$	−516439.	+	516439.i	−0.575862	+	0.575862i	0.357898	+	0.933761i	$0.383493\pi$
$948$	−1.67003e6	−	1.67003e6i	−1.85826	−	1.85826i
$949$			8952.98i			0.00994112i
$950$		0			0
$951$	−2.25871e6			−2.49746
$952$	−141577.	+	141577.i	−0.156213	+	0.156213i
$953$	424134.	+	424134.i	0.467000	+	0.467000i	0.900941	−	0.433941i	$-0.142877\pi$
$953$	424134.	+	424134.i	0.467000	+	0.467000i	−0.433941	+	0.900941i	$0.642877\pi$
$954$		−	3.84782e6i		−	4.22783i
$955$		0			0
$956$	−1.56659e6			−1.71411
$957$	82188.9	−	82188.9i	0.0897407	−	0.0897407i
$958$	1.83325e6	+	1.83325e6i	1.99752	+	1.99752i
$959$			326820.i			0.355362i
$960$		0			0
$961$	−801554.			−0.867932
$962$	−8170.79	+	8170.79i	−0.00882905	+	0.00882905i
$963$	1.62193e6	+	1.62193e6i	1.74895	+	1.74895i
$964$			527889.i			0.568052i
$965$		0			0
$966$	983643.			1.05410
$967$	587318.	−	587318.i	0.628088	−	0.628088i	−0.319499	−	0.947587i	$-0.603515\pi$
$967$	587318.	−	587318.i	0.628088	−	0.628088i	0.947587	+	0.319499i	$0.103515\pi$
$968$	−941675.	−	941675.i	−1.00496	−	1.00496i
$969$			756336.i			0.805503i
$970$		0			0
$971$	−135351.			−0.143556			−0.0717781	−	0.997421i	$-0.522867\pi$
$971$	−135351.			−0.143556			−0.0717781	+	0.997421i	$0.522867\pi$
$972$	358899.	−	358899.i	0.379874	−	0.379874i
$973$	−89379.3	−	89379.3i	−0.0944086	−	0.0944086i
$974$		−	65831.9i		−	0.0693935i
$975$		0			0
$976$	−144494.			−0.151687
$977$	1.08598e6	−	1.08598e6i	1.13772	−	1.13772i	0.148859	−	0.988858i	$-0.452440\pi$
$977$	1.08598e6	−	1.08598e6i	1.13772	−	1.13772i	0.988858	−	0.148859i	$-0.0475599\pi$
$978$	−861890.	−	861890.i	−0.901103	−	0.901103i
$979$			2.24419e6i			2.34150i
$980$		0			0
$981$	−139027.			−0.144465
$982$	1.91154e6	−	1.91154e6i	1.98226	−	1.98226i
$983$	−1.07181e6	−	1.07181e6i	−1.10920	−	1.10920i	−0.993256	−	0.115946i	$-0.963010\pi$
$983$	−1.07181e6	−	1.07181e6i	−1.10920	−	1.10920i	−0.115946	−	0.993256i	$-0.536990\pi$
$984$		−	679645.i		−	0.701927i
$985$		0			0
$986$	53436.9			0.0549651
$987$	537612.	−	537612.i	0.551868	−	0.551868i
$988$	−9527.78	−	9527.78i	−0.00976063	−	0.00976063i
$989$			1.06112e6i			1.08486i
$990$		0			0
$991$	−1.09775e6			−1.11778			−0.558890	−	0.829241i	$-0.688773\pi$
$991$	−1.09775e6			−1.11778			−0.558890	+	0.829241i	$0.688773\pi$
$992$	312201.	−	312201.i	0.317257	−	0.317257i
$993$	−1.98492e6	−	1.98492e6i	−2.01301	−	2.01301i
$994$		−	697671.i		−	0.706120i
$995$		0			0
$996$	−2.91901e6			−2.94251
$997$	−115323.	+	115323.i	−0.116018	+	0.116018i	−0.762732	−	0.646714i	$-0.776143\pi$
$997$	−115323.	+	115323.i	−0.116018	+	0.116018i	0.646714	+	0.762732i	$0.276143\pi$
$998$	−1.17836e6	−	1.17836e6i	−1.18309	−	1.18309i
$999$		−	743093.i		−	0.744581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.43.11		24
5.2	odd	4	inner	175.5.g.c.57.11		24
5.3	odd	4		35.5.g.a.22.2	yes	24
5.4	even	2		35.5.g.a.8.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.2	✓	24	5.4	even	2
35.5.g.a.22.2	yes	24	5.3	odd	4
175.5.g.c.43.11		24	1.1	even	1	trivial
175.5.g.c.57.11		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)

\(f(q)\)	\(=\)	\(q+(4.43769 - 4.43769i) q^{2} +(10.8098 + 10.8098i) q^{3} -23.3862i q^{4} +95.9409 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-32.7776 - 32.7776i) q^{8} +152.703i q^{9} +O(q^{10})\)	\(q+(4.43769 - 4.43769i) q^{2} +(10.8098 + 10.8098i) q^{3} -23.3862i q^{4} +95.9409 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-32.7776 - 32.7776i) q^{8} +152.703i q^{9} +208.255 q^{11} +(252.800 - 252.800i) q^{12} +(1.92052 + 1.92052i) q^{13} +116.230i q^{14} +83.2655 q^{16} +(-164.913 + 164.913i) q^{17} +(677.648 + 677.648i) q^{18} -212.136i q^{19} -283.126 q^{21} +(924.172 - 924.172i) q^{22} +(-391.446 - 391.446i) q^{23} -708.637i q^{24} +17.0453 q^{26} +(-775.093 + 775.093i) q^{27} +(306.261 + 306.261i) q^{28} -36.5090i q^{29} +349.238 q^{31} +(893.948 - 893.948i) q^{32} +(2251.19 + 2251.19i) q^{33} +1463.66i q^{34} +3571.14 q^{36} +(-479.357 + 479.357i) q^{37} +(-941.393 - 941.393i) q^{38} +41.5207i q^{39} +959.088 q^{41} +(-1256.42 + 1256.42i) q^{42} +(-1355.39 - 1355.39i) q^{43} -4870.29i q^{44} -3474.23 q^{46} +(-1898.85 + 1898.85i) q^{47} +(900.082 + 900.082i) q^{48} -343.000i q^{49} -3565.34 q^{51} +(44.9135 - 44.9135i) q^{52} +(-2839.10 - 2839.10i) q^{53} +6879.24i q^{54} +858.497 q^{56} +(2293.14 - 2293.14i) q^{57} +(-162.016 - 162.016i) q^{58} -3146.30i q^{59} -1735.34 q^{61} +(1549.81 - 1549.81i) q^{62} +(-1999.77 - 1999.77i) q^{63} -6601.88i q^{64} +19980.2 q^{66} +(245.525 - 245.525i) q^{67} +(3856.67 + 3856.67i) q^{68} -8462.88i q^{69} -6002.50 q^{71} +(5005.23 - 5005.23i) q^{72} +(2330.88 + 2330.88i) q^{73} +4254.48i q^{74} -4961.05 q^{76} +(-2727.27 + 2727.27i) q^{77} +(184.256 + 184.256i) q^{78} -6606.13i q^{79} -4388.24 q^{81} +(4256.14 - 4256.14i) q^{82} +(-5773.38 - 5773.38i) q^{83} +6621.23i q^{84} -12029.6 q^{86} +(394.655 - 394.655i) q^{87} +(-6826.10 - 6826.10i) q^{88} +10776.1i q^{89} -50.3014 q^{91} +(-9154.42 + 9154.42i) q^{92} +(3775.19 + 3775.19i) q^{93} +16853.0i q^{94} +19326.8 q^{96} +(-3200.07 + 3200.07i) q^{97} +(-1522.13 - 1522.13i) q^{98} +31801.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 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

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