LMFDB - Embedded newform 175.5.g.c.57.3

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			57.3
Character	$\chi$	$=$	175.57
Dual form			175.5.g.c.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.68989 - 3.68989i) q^{2} +(5.41571 - 5.41571i) q^{3} +11.2306i q^{4} -39.9667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-17.5987 + 17.5987i) q^{8} +22.3403i q^{9} +O(q^{10})$	\(q+(-3.68989 - 3.68989i) q^{2} +(5.41571 - 5.41571i) q^{3} +11.2306i q^{4} -39.9667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-17.5987 + 17.5987i) q^{8} +22.3403i q^{9} +58.8300 q^{11} +(60.8214 + 60.8214i) q^{12} +(-90.6864 + 90.6864i) q^{13} +96.6441i q^{14} +309.563 q^{16} +(-18.7384 - 18.7384i) q^{17} +(82.4331 - 82.4331i) q^{18} +466.090i q^{19} -141.846 q^{21} +(-217.076 - 217.076i) q^{22} +(-617.449 + 617.449i) q^{23} +190.619i q^{24} +669.245 q^{26} +(559.660 + 559.660i) q^{27} +(147.073 - 147.073i) q^{28} -33.4645i q^{29} -1029.34 q^{31} +(-860.676 - 860.676i) q^{32} +(318.606 - 318.606i) q^{33} +138.285i q^{34} -250.894 q^{36} +(495.185 + 495.185i) q^{37} +(1719.82 - 1719.82i) q^{38} +982.261i q^{39} +1437.24 q^{41} +(523.396 + 523.396i) q^{42} +(2157.18 - 2157.18i) q^{43} +660.695i q^{44} +4556.64 q^{46} +(722.273 + 722.273i) q^{47} +(1676.50 - 1676.50i) q^{48} +343.000i q^{49} -202.964 q^{51} +(-1018.46 - 1018.46i) q^{52} +(-2101.64 + 2101.64i) q^{53} -4130.17i q^{54} +460.938 q^{56} +(2524.21 + 2524.21i) q^{57} +(-123.480 + 123.480i) q^{58} -3852.92i q^{59} +5498.61 q^{61} +(3798.15 + 3798.15i) q^{62} +(292.564 - 292.564i) q^{63} +1398.58i q^{64} -2351.24 q^{66} +(-1180.08 - 1180.08i) q^{67} +(210.443 - 210.443i) q^{68} +6687.84i q^{69} -2609.74 q^{71} +(-393.159 - 393.159i) q^{72} +(-6998.11 + 6998.11i) q^{73} -3654.36i q^{74} -5234.45 q^{76} +(-770.426 - 770.426i) q^{77} +(3624.44 - 3624.44i) q^{78} +10261.0i q^{79} +4252.35 q^{81} +(-5303.26 - 5303.26i) q^{82} +(1422.61 - 1422.61i) q^{83} -1593.01i q^{84} -15919.5 q^{86} +(-181.234 - 181.234i) q^{87} +(-1035.33 + 1035.33i) q^{88} -5359.08i q^{89} +2375.22 q^{91} +(-6934.30 - 6934.30i) q^{92} +(-5574.60 + 5574.60i) q^{93} -5330.22i q^{94} -9322.33 q^{96} +(3093.79 + 3093.79i) q^{97} +(1265.63 - 1265.63i) q^{98} +1314.28i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.68989	−	3.68989i	−0.922472	−	0.922472i	0.0747314	−	0.997204i	$-0.476190\pi$
$2$	−3.68989	−	3.68989i	−0.922472	−	0.922472i	−0.997204	+	0.0747314i	$0.976190\pi$
$3$	5.41571	−	5.41571i	0.601745	−	0.601745i	−0.339030	−	0.940775i	$-0.610099\pi$
$3$	5.41571	−	5.41571i	0.601745	−	0.601745i	0.940775	+	0.339030i	$0.110099\pi$
$4$			11.2306i			0.701910i
$5$		0			0
$5$		0			0
$6$	−39.9667			−1.11019
$7$	−13.0958	−	13.0958i	−0.267261	−	0.267261i
$7$	−13.0958	−	13.0958i	−0.267261	−	0.267261i
$8$	−17.5987	+	17.5987i	−0.274980	+	0.274980i
$9$			22.3403i			0.275806i
$10$		0			0
$11$	58.8300			0.486199			0.243099	−	0.970001i	$-0.421836\pi$
$11$	58.8300			0.486199			0.243099	+	0.970001i	$0.421836\pi$
$12$	60.8214	+	60.8214i	0.422371	+	0.422371i
$13$	−90.6864	+	90.6864i	−0.536606	+	0.536606i	−0.922530	−	0.385925i	$-0.873882\pi$
$13$	−90.6864	+	90.6864i	−0.536606	+	0.536606i	0.385925	+	0.922530i	$0.373882\pi$
$14$			96.6441i			0.493082i
$15$		0			0
$16$	309.563			1.20923
$17$	−18.7384	−	18.7384i	−0.0648388	−	0.0648388i	0.673944	−	0.738783i	$-0.264599\pi$
$17$	−18.7384	−	18.7384i	−0.0648388	−	0.0648388i	−0.738783	+	0.673944i	$0.764599\pi$
$18$	82.4331	−	82.4331i	0.254423	−	0.254423i
$19$			466.090i			1.29111i	0.763715	+	0.645554i	$0.223373\pi$
$19$			466.090i			1.29111i	−0.763715	+	0.645554i	$0.776627\pi$
$20$		0			0
$21$	−141.846			−0.321646
$22$	−217.076	−	217.076i	−0.448505	−	0.448505i
$23$	−617.449	+	617.449i	−1.16720	+	1.16720i	−0.184337	+	0.982863i	$0.559014\pi$
$23$	−617.449	+	617.449i	−1.16720	+	1.16720i	−0.982863	+	0.184337i	$0.940986\pi$
$24$			190.619i			0.330935i
$25$		0			0
$26$	669.245			0.990008
$27$	559.660	+	559.660i	0.767710	+	0.767710i
$28$	147.073	−	147.073i	0.187593	−	0.187593i
$29$		−	33.4645i		−	0.0397913i	−0.999802	−	0.0198957i	$-0.993667\pi$
$29$		−	33.4645i		−	0.0397913i	0.999802	−	0.0198957i	$-0.00633341\pi$
$30$		0			0
$31$	−1029.34			−1.07111			−0.535556	−	0.844500i	$-0.679898\pi$
$31$	−1029.34			−1.07111			−0.535556	+	0.844500i	$0.679898\pi$
$32$	−860.676	−	860.676i	−0.840504	−	0.840504i
$33$	318.606	−	318.606i	0.292568	−	0.292568i
$34$			138.285i			0.119624i
$35$		0			0
$36$	−250.894			−0.193591
$37$	495.185	+	495.185i	0.361713	+	0.361713i	0.864443	−	0.502730i	$-0.167671\pi$
$37$	495.185	+	495.185i	0.361713	+	0.361713i	−0.502730	+	0.864443i	$0.667671\pi$
$38$	1719.82	−	1719.82i	1.19101	−	1.19101i
$39$			982.261i			0.645800i
$40$		0			0
$41$	1437.24			0.854992			0.427496	−	0.904017i	$-0.359396\pi$
$41$	1437.24			0.854992			0.427496	+	0.904017i	$0.359396\pi$
$42$	523.396	+	523.396i	0.296710	+	0.296710i
$43$	2157.18	−	2157.18i	1.16667	−	1.16667i	0.183687	−	0.982985i	$-0.441197\pi$
$43$	2157.18	−	2157.18i	1.16667	−	1.16667i	0.982985	−	0.183687i	$-0.0588032\pi$
$44$			660.695i			0.341268i
$45$		0			0
$46$	4556.64			2.15342
$47$	722.273	+	722.273i	0.326968	+	0.326968i	0.851433	−	0.524464i	$-0.175734\pi$
$47$	722.273	+	722.273i	0.326968	+	0.326968i	−0.524464	+	0.851433i	$0.675734\pi$
$48$	1676.50	−	1676.50i	0.727650	−	0.727650i
$49$			343.000i			0.142857i
$50$		0			0
$51$	−202.964			−0.0780329
$52$	−1018.46	−	1018.46i	−0.376649	−	0.376649i
$53$	−2101.64	+	2101.64i	−0.748180	+	0.748180i	−0.974137	−	0.225957i	$-0.927449\pi$
$53$	−2101.64	+	2101.64i	−0.748180	+	0.748180i	0.225957	+	0.974137i	$0.427449\pi$
$54$		−	4130.17i		−	1.41638i
$55$		0			0
$56$	460.938			0.146983
$57$	2524.21	+	2524.21i	0.776918	+	0.776918i
$58$	−123.480	+	123.480i	−0.0367064	+	0.0367064i
$59$		−	3852.92i		−	1.10684i	−0.832902	−	0.553421i	$-0.813322\pi$
$59$		−	3852.92i		−	1.10684i	0.832902	−	0.553421i	$-0.186678\pi$
$60$		0			0
$61$	5498.61			1.47772			0.738862	−	0.673857i	$-0.235363\pi$
$61$	5498.61			1.47772			0.738862	+	0.673857i	$0.235363\pi$
$62$	3798.15	+	3798.15i	0.988071	+	0.988071i
$63$	292.564	−	292.564i	0.0737122	−	0.0737122i
$64$			1398.58i			0.341451i
$65$		0			0
$66$	−2351.24			−0.539771
$67$	−1180.08	−	1180.08i	−0.262883	−	0.262883i	0.563341	−	0.826224i	$-0.309516\pi$
$67$	−1180.08	−	1180.08i	−0.262883	−	0.262883i	−0.826224	+	0.563341i	$0.809516\pi$
$68$	210.443	−	210.443i	0.0455111	−	0.0455111i
$69$			6687.84i			1.40471i
$70$		0			0
$71$	−2609.74			−0.517702			−0.258851	−	0.965917i	$-0.583344\pi$
$71$	−2609.74			−0.517702			−0.258851	+	0.965917i	$0.583344\pi$
$72$	−393.159	−	393.159i	−0.0758409	−	0.0758409i
$73$	−6998.11	+	6998.11i	−1.31321	+	1.31321i	−0.394178	+	0.919034i	$0.628971\pi$
$73$	−6998.11	+	6998.11i	−1.31321	+	1.31321i	−0.919034	+	0.394178i	$0.871029\pi$
$74$		−	3654.36i		−	0.667341i
$75$		0			0
$76$	−5234.45			−0.906242
$77$	−770.426	−	770.426i	−0.129942	−	0.129942i
$78$	3624.44	−	3624.44i	0.595732	−	0.595732i
$79$			10261.0i			1.64413i	0.569391	+	0.822067i	$0.307179\pi$
$79$			10261.0i			1.64413i	−0.569391	+	0.822067i	$0.692821\pi$
$80$		0			0
$81$	4252.35			0.648125
$82$	−5303.26	−	5303.26i	−0.788706	−	0.788706i
$83$	1422.61	−	1422.61i	0.206504	−	0.206504i	−0.596276	−	0.802780i	$-0.703353\pi$
$83$	1422.61	−	1422.61i	0.206504	−	0.206504i	0.802780	+	0.596276i	$0.203353\pi$
$84$		−	1593.01i		−	0.225767i
$85$		0			0
$86$	−15919.5			−2.15244
$87$	−181.234	−	181.234i	−0.0239442	−	0.0239442i
$88$	−1035.33	+	1035.33i	−0.133695	+	0.133695i
$89$		−	5359.08i		−	0.676566i	−0.941044	−	0.338283i	$-0.890154\pi$
$89$		−	5359.08i		−	0.676566i	0.941044	−	0.338283i	$-0.109846\pi$
$90$		0			0
$91$	2375.22			0.286828
$92$	−6934.30	−	6934.30i	−0.819270	−	0.819270i
$93$	−5574.60	+	5574.60i	−0.644537	+	0.644537i
$94$		−	5330.22i		−	0.603239i
$95$		0			0
$96$	−9322.33			−1.01154
$97$	3093.79	+	3093.79i	0.328812	+	0.328812i	0.852135	−	0.523323i	$-0.175308\pi$
$97$	3093.79	+	3093.79i	0.328812	+	0.328812i	−0.523323	+	0.852135i	$0.675308\pi$
$98$	1265.63	−	1265.63i	0.131782	−	0.131782i
$99$			1314.28i			0.134096i
$100$		0			0
$101$	−15070.6			−1.47736			−0.738681	−	0.674056i	$-0.764551\pi$
$101$	−15070.6			−1.47736			−0.738681	+	0.674056i	$0.764551\pi$
$102$	748.913	+	748.913i	0.0719832	+	0.0719832i
$103$	−3480.59	+	3480.59i	−0.328079	+	0.328079i	−0.851856	−	0.523777i	$-0.824523\pi$
$103$	−3480.59	+	3480.59i	−0.328079	+	0.328079i	0.523777	+	0.851856i	$0.324523\pi$
$104$		−	3191.92i		−	0.295111i
$105$		0			0
$106$	15509.6			1.38035
$107$	−9084.98	−	9084.98i	−0.793518	−	0.793518i	0.188547	−	0.982064i	$-0.439622\pi$
$107$	−9084.98	−	9084.98i	−0.793518	−	0.793518i	−0.982064	+	0.188547i	$0.939622\pi$
$108$	−6285.30	+	6285.30i	−0.538863	+	0.538863i
$109$			14035.8i			1.18136i	0.806905	+	0.590681i	$0.201141\pi$
$109$			14035.8i			1.18136i	−0.806905	+	0.590681i	$0.798859\pi$
$110$		0			0
$111$	5363.56			0.435318
$112$	−4053.98	−	4053.98i	−0.323181	−	0.323181i
$113$	−2840.13	+	2840.13i	−0.222424	+	0.222424i	−0.809518	−	0.587095i	$-0.800272\pi$
$113$	−2840.13	+	2840.13i	−0.222424	+	0.222424i	0.587095	+	0.809518i	$0.300272\pi$
$114$		−	18628.1i		−	1.43337i
$115$		0			0
$116$	375.825			0.0279300
$117$	−2025.96	−	2025.96i	−0.147999	−	0.147999i
$118$	−14216.8	+	14216.8i	−1.02103	+	1.02103i
$119$			490.789i			0.0346578i
$120$		0			0
$121$	−11180.0			−0.763611
$122$	−20289.3	−	20289.3i	−1.36316	−	1.36316i
$123$	7783.68	−	7783.68i	0.514487	−	0.514487i
$124$		−	11560.1i		−	0.751825i
$125$		0			0
$126$	−2159.05			−0.135995
$127$	22225.8	+	22225.8i	1.37800	+	1.37800i	0.847993	+	0.530008i	$0.177811\pi$
$127$	22225.8	+	22225.8i	1.37800	+	1.37800i	0.530008	+	0.847993i	$0.322189\pi$
$128$	−8610.20	+	8610.20i	−0.525525	+	0.525525i
$129$		−	23365.3i		−	1.40408i
$130$		0			0
$131$	−21851.6			−1.27333			−0.636664	−	0.771141i	$-0.719686\pi$
$131$	−21851.6			−1.27333			−0.636664	+	0.771141i	$0.719686\pi$
$132$	3578.13	+	3578.13i	0.205356	+	0.205356i
$133$	6103.82	−	6103.82i	0.345063	−	0.345063i
$134$			8708.74i			0.485004i
$135$		0			0
$136$	659.544			0.0356587
$137$	22705.8	+	22705.8i	1.20975	+	1.20975i	0.971107	+	0.238645i	$0.0767032\pi$
$137$	22705.8	+	22705.8i	1.20975	+	1.20975i	0.238645	+	0.971107i	$0.423297\pi$
$138$	24677.4	−	24677.4i	1.29581	−	1.29581i
$139$			18608.8i			0.963138i	0.876408	+	0.481569i	$0.159933\pi$
$139$			18608.8i			0.963138i	−0.876408	+	0.481569i	$0.840067\pi$
$140$		0			0
$141$	7823.24			0.393503
$142$	9629.63	+	9629.63i	0.477566	+	0.477566i
$143$	−5335.08	+	5335.08i	−0.260897	+	0.260897i
$144$			6915.73i			0.333513i
$145$		0			0
$146$	51644.5			2.42280
$147$	1857.59	+	1857.59i	0.0859636	+	0.0859636i
$148$	−5561.21	+	5561.21i	−0.253890	+	0.253890i
$149$		−	14411.1i		−	0.649117i	−0.945866	−	0.324559i	$-0.894784\pi$
$149$		−	14411.1i		−	0.649117i	0.945866	−	0.324559i	$-0.105216\pi$
$150$		0			0
$151$	−2652.53			−0.116334			−0.0581671	−	0.998307i	$-0.518526\pi$
$151$	−2652.53			−0.116334			−0.0581671	+	0.998307i	$0.518526\pi$
$152$	−8202.57	−	8202.57i	−0.355028	−	0.355028i
$153$	418.621	−	418.621i	0.0178829	−	0.0178829i
$154$			5685.58i			0.239736i
$155$		0			0
$156$	−11031.3			−0.453293
$157$	18983.9	+	18983.9i	0.770170	+	0.770170i	0.978136	−	0.207966i	$-0.0666843\pi$
$157$	18983.9	+	18983.9i	0.770170	+	0.770170i	−0.207966	+	0.978136i	$0.566684\pi$
$158$	37862.1	−	37862.1i	1.51667	−	1.51667i
$159$			22763.7i			0.900427i
$160$		0			0
$161$	16172.0			0.623895
$162$	−15690.7	−	15690.7i	−0.597878	−	0.597878i
$163$	26111.6	−	26111.6i	0.982785	−	0.982785i	−0.0170698	−	0.999854i	$-0.505434\pi$
$163$	26111.6	−	26111.6i	0.982785	−	0.982785i	0.999854	+	0.0170698i	$0.00543374\pi$
$164$			16141.0i			0.600128i
$165$		0			0
$166$	−10498.5			−0.380989
$167$	47.7040	+	47.7040i	0.00171049	+	0.00171049i	0.707962	−	0.706251i	$-0.249615\pi$
$167$	47.7040	+	47.7040i	0.00171049	+	0.00171049i	−0.706251	+	0.707962i	$0.749615\pi$
$168$	2496.30	−	2496.30i	0.0884461	−	0.0884461i
$169$			12113.0i			0.424109i
$170$		0			0
$171$	−10412.6			−0.356095
$172$	24226.3	+	24226.3i	0.818899	+	0.818899i
$173$	−20794.9	+	20794.9i	−0.694806	+	0.694806i	−0.963286	−	0.268479i	$-0.913479\pi$
$173$	−20794.9	+	20794.9i	−0.694806	+	0.694806i	0.268479	+	0.963286i	$0.413479\pi$
$174$			1337.47i			0.0441758i
$175$		0			0
$176$	18211.6			0.587927
$177$	−20866.3	−	20866.3i	−0.666037	−	0.666037i
$178$	−19774.4	+	19774.4i	−0.624113	+	0.624113i
$179$		−	18069.2i		−	0.563939i	−0.959423	−	0.281970i	$-0.909012\pi$
$179$		−	18069.2i		−	0.563939i	0.959423	−	0.281970i	$-0.0909877\pi$
$180$		0			0
$181$	35446.6			1.08198			0.540988	−	0.841030i	$-0.318050\pi$
$181$	35446.6			1.08198			0.540988	+	0.841030i	$0.318050\pi$
$182$	−8764.30	−	8764.30i	−0.264591	−	0.264591i
$183$	29778.9	−	29778.9i	0.889213	−	0.889213i
$184$		−	21732.6i		−	0.641912i
$185$		0			0
$186$	41139.3			1.18913
$187$	−1102.38	−	1102.38i	−0.0315246	−	0.0315246i
$188$	−8111.54	+	8111.54i	−0.229503	+	0.229503i
$189$		−	14658.4i		−	0.410358i
$190$		0			0
$191$	−18088.9			−0.495845			−0.247922	−	0.968780i	$-0.579748\pi$
$191$	−18088.9			−0.495845			−0.247922	+	0.968780i	$0.579748\pi$
$192$	7574.31	+	7574.31i	0.205466	+	0.205466i
$193$	−28809.2	+	28809.2i	−0.773423	+	0.773423i	−0.978703	−	0.205280i	$-0.934189\pi$
$193$	−28809.2	+	28809.2i	−0.773423	+	0.773423i	0.205280	+	0.978703i	$0.434189\pi$
$194$		−	22831.5i		−	0.606640i
$195$		0			0
$196$	−3852.08			−0.100273
$197$	−51897.3	−	51897.3i	−1.33725	−	1.33725i	−0.898715	−	0.438534i	$-0.855498\pi$
$197$	−51897.3	−	51897.3i	−1.33725	−	1.33725i	−0.438534	−	0.898715i	$-0.644502\pi$
$198$	4849.54	−	4849.54i	0.123700	−	0.123700i
$199$		−	21817.7i		−	0.550939i	−0.961310	−	0.275469i	$-0.911167\pi$
$199$		−	21817.7i		−	0.550939i	0.961310	−	0.275469i	$-0.0888333\pi$
$200$		0			0
$201$	−12781.9			−0.316377
$202$	55608.7	+	55608.7i	1.36282	+	1.36282i
$203$	−438.245	+	438.245i	−0.0106347	+	0.0106347i
$204$		−	2279.40i		−	0.0547721i
$205$		0			0
$206$	25686.0			0.605288
$207$	−13794.0	−	13794.0i	−0.321920	−	0.321920i
$208$	−28073.2	+	28073.2i	−0.648881	+	0.648881i
$209$			27420.1i			0.627735i
$210$		0			0
$211$	−43403.1			−0.974891			−0.487445	−	0.873154i	$-0.662071\pi$
$211$	−43403.1			−0.974891			−0.487445	+	0.873154i	$0.662071\pi$
$212$	−23602.6	−	23602.6i	−0.525155	−	0.525155i
$213$	−14133.6	+	14133.6i	−0.311525	+	0.311525i
$214$			67045.2i			1.46400i
$215$		0			0
$216$	−19698.6			−0.422209
$217$	13480.0	+	13480.0i	0.286267	+	0.286267i
$218$	51790.4	−	51790.4i	1.08977	−	1.08977i
$219$			75799.4i			1.58044i
$220$		0			0
$221$	3398.64			0.0695858
$222$	−19790.9	−	19790.9i	−0.401569	−	0.401569i
$223$	15100.3	−	15100.3i	0.303652	−	0.303652i	−0.538789	−	0.842441i	$-0.681118\pi$
$223$	15100.3	−	15100.3i	0.303652	−	0.303652i	0.842441	+	0.538789i	$0.181118\pi$
$224$			22542.5i			0.449268i
$225$		0			0
$226$	20959.5			0.410359
$227$	−31349.3	−	31349.3i	−0.608381	−	0.608381i	0.334142	−	0.942523i	$-0.391553\pi$
$227$	−31349.3	−	31349.3i	−0.608381	−	0.608381i	−0.942523	+	0.334142i	$0.891553\pi$
$228$	−28348.3	+	28348.3i	−0.545327	+	0.545327i
$229$			54019.7i			1.03010i	0.857159	+	0.515052i	$0.172227\pi$
$229$			54019.7i			1.03010i	−0.857159	+	0.515052i	$0.827773\pi$
$230$		0			0
$231$	−8344.81			−0.156384
$232$	588.932	+	588.932i	0.0109418	+	0.0109418i
$233$	43078.3	−	43078.3i	0.793500	−	0.793500i	−0.188562	−	0.982061i	$-0.560383\pi$
$233$	43078.3	−	43078.3i	0.793500	−	0.793500i	0.982061	+	0.188562i	$0.0603825\pi$
$234$			14951.1i			0.273050i
$235$		0			0
$236$	43270.4			0.776904
$237$	55570.7	+	55570.7i	0.989349	+	0.989349i
$238$	1810.96	−	1810.96i	0.0319709	−	0.0319709i
$239$		−	13420.6i		−	0.234951i	−0.993076	−	0.117475i	$-0.962520\pi$
$239$		−	13420.6i		−	0.234951i	0.993076	−	0.117475i	$-0.0374801\pi$
$240$		0			0
$241$	−56201.9			−0.967648			−0.483824	−	0.875165i	$-0.660752\pi$
$241$	−56201.9			−0.967648			−0.483824	+	0.875165i	$0.660752\pi$
$242$	41253.1	+	41253.1i	0.704410	+	0.704410i
$243$	−22303.0	+	22303.0i	−0.377704	+	0.377704i
$244$			61752.5i			1.03723i
$245$		0			0
$246$	−57441.8			−0.949200
$247$	−42268.0	−	42268.0i	−0.692816	−	0.692816i
$248$	18115.0	−	18115.0i	0.294534	−	0.294534i
$249$		−	15408.8i		−	0.248526i
$250$		0			0
$251$	51757.5			0.821534			0.410767	−	0.911740i	$-0.365261\pi$
$251$	51757.5			0.821534			0.410767	+	0.911740i	$0.365261\pi$
$252$	3285.65	+	3285.65i	0.0517393	+	0.0517393i
$253$	−36324.5	+	36324.5i	−0.567491	+	0.567491i
$254$		−	164021.i		−	2.54233i
$255$		0			0
$256$	85918.7			1.31102
$257$	35425.6	+	35425.6i	0.536353	+	0.536353i	0.922456	−	0.386103i	$-0.126179\pi$
$257$	35425.6	+	35425.6i	0.536353	+	0.536353i	−0.386103	+	0.922456i	$0.626179\pi$
$258$	−86215.2	+	86215.2i	−1.29522	+	1.29522i
$259$		−	12969.7i		−	0.193344i
$260$		0			0
$261$	747.606			0.0109747
$262$	80630.0	+	80630.0i	1.17461	+	1.17461i
$263$	−33455.5	+	33455.5i	−0.483678	+	0.483678i	−0.906304	−	0.422626i	$-0.861108\pi$
$263$	−33455.5	+	33455.5i	−0.483678	+	0.483678i	0.422626	+	0.906304i	$0.361108\pi$
$264$			11214.1i			0.160900i
$265$		0			0
$266$	−45044.8			−0.636622
$267$	−29023.2	−	29023.2i	−0.407120	−	0.407120i
$268$	13253.0	−	13253.0i	0.184520	−	0.184520i
$269$			37095.3i			0.512642i	0.966592	+	0.256321i	$0.0825105\pi$
$269$			37095.3i			0.512642i	−0.966592	+	0.256321i	$0.917490\pi$
$270$		0			0
$271$	−33530.1			−0.456559			−0.228279	−	0.973596i	$-0.573310\pi$
$271$	−33530.1			−0.456559			−0.228279	+	0.973596i	$0.573310\pi$
$272$	−5800.73	−	5800.73i	−0.0784052	−	0.0784052i
$273$	12863.5	−	12863.5i	0.172597	−	0.172597i
$274$		−	167564.i		−	2.23193i
$275$		0			0
$276$	−75108.2			−0.985983
$277$	−44691.5	−	44691.5i	−0.582459	−	0.582459i	0.353120	−	0.935578i	$-0.385121\pi$
$277$	−44691.5	−	44691.5i	−0.582459	−	0.582459i	−0.935578	+	0.353120i	$0.885121\pi$
$278$	68664.3	−	68664.3i	0.888468	−	0.888468i
$279$		−	22995.7i		−	0.295419i
$280$		0			0
$281$	−10609.2			−0.134359			−0.0671797	−	0.997741i	$-0.521400\pi$
$281$	−10609.2			−0.134359			−0.0671797	+	0.997741i	$0.521400\pi$
$282$	−28866.9	−	28866.9i	−0.362996	−	0.362996i
$283$	21964.5	−	21964.5i	0.274251	−	0.274251i	−0.556558	−	0.830809i	$-0.687878\pi$
$283$	21964.5	−	21964.5i	0.274251	−	0.274251i	0.830809	+	0.556558i	$0.187878\pi$
$284$		−	29308.8i		−	0.363380i
$285$		0			0
$286$	39371.7			0.481340
$287$	−18821.8	−	18821.8i	−0.228506	−	0.228506i
$288$	19227.7	−	19227.7i	0.231816	−	0.231816i
$289$		−	82818.7i		−	0.991592i
$290$		0			0
$291$	33510.1			0.395722
$292$	−78592.7	−	78592.7i	−0.921757	−	0.921757i
$293$	18838.8	−	18838.8i	0.219441	−	0.219441i	−0.588822	−	0.808263i	$-0.700408\pi$
$293$	18838.8	−	18838.8i	0.219441	−	0.219441i	0.808263	+	0.588822i	$0.200408\pi$
$294$		−	13708.6i		−	0.158598i
$295$		0			0
$296$	−17429.2			−0.198927
$297$	32924.8	+	32924.8i	0.373260	+	0.373260i
$298$	−53175.2	+	53175.2i	−0.598793	+	0.598793i
$299$		−	111988.i		−	1.25265i
$300$		0			0
$301$	−56499.9			−0.623612
$302$	9787.56	+	9787.56i	0.107315	+	0.107315i
$303$	−81617.7	+	81617.7i	−0.888995	+	0.888995i
$304$			144284.i			1.56125i
$305$		0			0
$306$	−3089.33			−0.0329930
$307$	53554.6	+	53554.6i	0.568225	+	0.568225i	0.931631	−	0.363406i	$-0.118386\pi$
$307$	53554.6	+	53554.6i	0.568225	+	0.568225i	−0.363406	+	0.931631i	$0.618386\pi$
$308$	8652.32	−	8652.32i	0.0912077	−	0.0912077i
$309$			37699.7i			0.394840i
$310$		0			0
$311$	141225.			1.46012			0.730062	−	0.683381i	$-0.239491\pi$
$311$	141225.			1.46012			0.730062	+	0.683381i	$0.239491\pi$
$312$	−17286.5	−	17286.5i	−0.177582	−	0.177582i
$313$	60441.2	−	60441.2i	0.616942	−	0.616942i	−0.327804	−	0.944746i	$-0.606309\pi$
$313$	60441.2	−	60441.2i	0.616942	−	0.616942i	0.944746	+	0.327804i	$0.106309\pi$
$314$		−	140097.i		−	1.42092i
$315$		0			0
$316$	−115237.			−1.15403
$317$	−42023.3	−	42023.3i	−0.418188	−	0.418188i	0.466391	−	0.884579i	$-0.345554\pi$
$317$	−42023.3	−	42023.3i	−0.418188	−	0.418188i	−0.884579	+	0.466391i	$0.845554\pi$
$318$	83995.5	−	83995.5i	0.830619	−	0.830619i
$319$		−	1968.72i		−	0.0193465i
$320$		0			0
$321$	−98403.2			−0.954991
$322$	−59672.8	−	59672.8i	−0.575526	−	0.575526i
$323$	8733.79	−	8733.79i	0.0837139	−	0.0837139i
$324$			47756.3i			0.454926i
$325$		0			0
$326$	−192698.			−1.81318
$327$	76013.6	+	76013.6i	0.710879	+	0.710879i
$328$	−25293.6	+	25293.6i	−0.235105	+	0.235105i
$329$		−	18917.5i		−	0.174772i
$330$		0			0
$331$	138028.			1.25983			0.629913	−	0.776666i	$-0.283091\pi$
$331$	138028.			1.25983			0.629913	+	0.776666i	$0.283091\pi$
$332$	15976.7	+	15976.7i	0.144947	+	0.144947i
$333$	−11062.6	+	11062.6i	−0.0997626	+	0.0997626i
$334$		−	352.045i		−	0.00315577i
$335$		0			0
$336$	−43910.3			−0.388945
$337$	−27775.7	−	27775.7i	−0.244571	−	0.244571i	0.574167	−	0.818738i	$-0.305326\pi$
$337$	−27775.7	−	27775.7i	−0.244571	−	0.244571i	−0.818738	+	0.574167i	$0.805326\pi$
$338$	44695.5	−	44695.5i	0.391228	−	0.391228i
$339$			30762.6i			0.267685i
$340$		0			0
$341$	−60556.1			−0.520773
$342$	38421.2	+	38421.2i	0.328488	+	0.328488i
$343$	4491.86	−	4491.86i	0.0381802	−	0.0381802i
$344$			75926.9i			0.641622i
$345$		0			0
$346$	153461.			1.28188
$347$	12498.3	+	12498.3i	0.103798	+	0.103798i	0.757099	−	0.653300i	$-0.226616\pi$
$347$	12498.3	+	12498.3i	0.103798	+	0.103798i	−0.653300	+	0.757099i	$0.726616\pi$
$348$	2035.36	−	2035.36i	0.0168067	−	0.0168067i
$349$			45819.8i			0.376185i	0.982151	+	0.188093i	$0.0602306\pi$
$349$			45819.8i			0.376185i	−0.982151	+	0.188093i	$0.939769\pi$
$350$		0			0
$351$	−101507.			−0.823915
$352$	−50633.6	−	50633.6i	−0.408652	−	0.408652i
$353$	−50727.5	+	50727.5i	−0.407094	+	0.407094i	−0.880724	−	0.473630i	$-0.842943\pi$
$353$	−50727.5	+	50727.5i	−0.407094	+	0.407094i	0.473630	+	0.880724i	$0.342943\pi$
$354$			153988.i			1.22880i
$355$		0			0
$356$	60185.5			0.474888
$357$	2657.97	+	2657.97i	0.0208552	+	0.0208552i
$358$	−66673.3	+	66673.3i	−0.520218	+	0.520218i
$359$			39847.8i			0.309183i	0.987979	+	0.154591i	$0.0494061\pi$
$359$			39847.8i			0.309183i	−0.987979	+	0.154591i	$0.950594\pi$
$360$		0			0
$361$	−86918.8			−0.666960
$362$	−130794.	−	130794.i	−0.998093	−	0.998093i
$363$	−60547.7	+	60547.7i	−0.459499	+	0.459499i
$364$			26675.1i			0.201327i
$365$		0			0
$366$	−219761.			−1.64055
$367$	72997.2	+	72997.2i	0.541969	+	0.541969i	0.924106	−	0.382137i	$-0.124812\pi$
$367$	72997.2	+	72997.2i	0.541969	+	0.541969i	−0.382137	+	0.924106i	$0.624812\pi$
$368$	−191140.	+	191140.i	−1.41142	+	1.41142i
$369$			32108.4i			0.235812i
$370$		0			0
$371$	55045.2			0.399919
$372$	−62605.9	−	62605.9i	−0.452407	−	0.452407i
$373$	126446.	−	126446.i	0.908840	−	0.908840i	−0.0873385	−	0.996179i	$-0.527836\pi$
$373$	126446.	−	126446.i	0.908840	−	0.908840i	0.996179	+	0.0873385i	$0.0278362\pi$
$374$			8135.34i			0.0581611i
$375$		0			0
$376$	−25422.1			−0.179819
$377$	3034.78	+	3034.78i	0.0213523	+	0.0213523i
$378$	−54087.9	+	54087.9i	−0.378544	+	0.378544i
$379$		−	150298.i		−	1.04635i	−0.852226	−	0.523173i	$-0.824748\pi$
$379$		−	150298.i		−	1.04635i	0.852226	−	0.523173i	$-0.175252\pi$
$380$		0			0
$381$	240736.			1.65841
$382$	66746.1	+	66746.1i	0.457403	+	0.457403i
$383$	48516.0	−	48516.0i	0.330740	−	0.330740i	−0.522127	−	0.852868i	$-0.674861\pi$
$383$	48516.0	−	48516.0i	0.330740	−	0.330740i	0.852868	+	0.522127i	$0.174861\pi$
$384$			93260.6i			0.632464i
$385$		0			0
$386$	212606.			1.42692
$387$	48191.9	+	48191.9i	0.321775	+	0.321775i
$388$	−34745.0	+	34745.0i	−0.230797	+	0.230797i
$389$		−	209327.i		−	1.38333i	−0.722218	−	0.691665i	$-0.756877\pi$
$389$		−	209327.i		−	1.38333i	0.722218	−	0.691665i	$-0.243123\pi$
$390$		0			0
$391$	23140.0			0.151360
$392$	−6036.35	−	6036.35i	−0.0392828	−	0.0392828i
$393$	−118342.	+	118342.i	−0.766219	+	0.766219i
$394$			382990.i			2.46715i
$395$		0			0
$396$	−14760.1			−0.0941236
$397$	−26149.0	−	26149.0i	−0.165911	−	0.165911i	0.619269	−	0.785179i	$-0.287429\pi$
$397$	−26149.0	−	26149.0i	−0.165911	−	0.165911i	−0.785179	+	0.619269i	$0.787429\pi$
$398$	−80505.0	+	80505.0i	−0.508226	+	0.508226i
$399$		−	66113.0i		−	0.415280i
$400$		0			0
$401$	−30989.9			−0.192722			−0.0963609	−	0.995346i	$-0.530720\pi$
$401$	−30989.9			−0.192722			−0.0963609	+	0.995346i	$0.530720\pi$
$402$	47163.9	+	47163.9i	0.291849	+	0.291849i
$403$	93347.0	−	93347.0i	0.574765	−	0.574765i
$404$		−	169251.i		−	1.03698i
$405$		0			0
$406$	3234.15			0.0196204
$407$	29131.8	+	29131.8i	0.175865	+	0.175865i
$408$	3571.89	−	3571.89i	0.0214575	−	0.0214575i
$409$		−	70714.6i		−	0.422730i	−0.977407	−	0.211365i	$-0.932209\pi$
$409$		−	70714.6i		−	0.422730i	0.977407	−	0.211365i	$-0.0677908\pi$
$410$		0			0
$411$	245936.			1.45592
$412$	−39089.0	−	39089.0i	−0.230282	−	0.230282i
$413$	−50457.0	+	50457.0i	−0.295816	+	0.295816i
$414$			101796.i			0.593925i
$415$		0			0
$416$	156103.			0.902038
$417$	100780.	+	100780.i	0.579563	+	0.579563i
$418$	101177.	−	101177.i	0.579068	−	0.579068i
$419$			94930.1i			0.540724i	0.962759	+	0.270362i	$0.0871434\pi$
$419$			94930.1i			0.540724i	−0.962759	+	0.270362i	$0.912857\pi$
$420$		0			0
$421$	−111250.			−0.627676			−0.313838	−	0.949477i	$-0.601615\pi$
$421$	−111250.			−0.627676			−0.313838	+	0.949477i	$0.601615\pi$
$422$	160153.	+	160153.i	0.899309	+	0.899309i
$423$	−16135.8	+	16135.8i	−0.0901798	+	0.0901798i
$424$		−	73972.1i		−	0.411468i
$425$		0			0
$426$	104303.			0.574746
$427$	−72008.7	−	72008.7i	−0.394938	−	0.394938i
$428$	102030.	−	102030.i	0.556978	−	0.556978i
$429$			57786.5i			0.313987i
$430$		0			0
$431$	247126.			1.33035			0.665173	−	0.746689i	$-0.268358\pi$
$431$	247126.			1.33035			0.665173	+	0.746689i	$0.268358\pi$
$432$	173250.	+	173250.i	0.928339	+	0.928339i
$433$	2688.79	−	2688.79i	0.0143410	−	0.0143410i	−0.699900	−	0.714241i	$-0.746772\pi$
$433$	2688.79	−	2688.79i	0.0143410	−	0.0143410i	0.714241	+	0.699900i	$0.246772\pi$
$434$		−	99479.5i		−	0.528146i
$435$		0			0
$436$	−157630.			−0.829210
$437$	−287787.	−	287787.i	−1.50698	−	1.50698i
$438$	279691.	−	279691.i	1.45791	−	1.45791i
$439$			324182.i			1.68213i	0.540934	+	0.841065i	$0.318071\pi$
$439$			324182.i			1.68213i	−0.540934	+	0.841065i	$0.681929\pi$
$440$		0			0
$441$	−7662.71			−0.0394008
$442$	−12540.6	−	12540.6i	−0.0641910	−	0.0641910i
$443$	180535.	−	180535.i	0.919928	−	0.919928i	−0.0770961	−	0.997024i	$-0.524565\pi$
$443$	180535.	−	180535.i	0.919928	−	0.919928i	0.997024	+	0.0770961i	$0.0245648\pi$
$444$			60235.8i			0.305554i
$445$		0			0
$446$	−111437.			−0.560222
$447$	−78046.0	−	78046.0i	−0.390603	−	0.390603i
$448$	18315.5	−	18315.5i	0.0912565	−	0.0912565i
$449$		−	98163.0i		−	0.486917i	−0.969911	−	0.243459i	$-0.921718\pi$
$449$		−	98163.0i		−	0.486917i	0.969911	−	0.243459i	$-0.0782820\pi$
$450$		0			0
$451$	84553.0			0.415696
$452$	−31896.2	−	31896.2i	−0.156121	−	0.156121i
$453$	−14365.3	+	14365.3i	−0.0700035	+	0.0700035i
$454$			231351.i			1.12243i
$455$		0			0
$456$	−88845.4			−0.427273
$457$	8778.56	+	8778.56i	0.0420331	+	0.0420331i	0.727811	−	0.685778i	$-0.240538\pi$
$457$	8778.56	+	8778.56i	0.0420331	+	0.0420331i	−0.685778	+	0.727811i	$0.740538\pi$
$458$	199327.	−	199327.i	0.950243	−	0.950243i
$459$		−	20974.3i		−	0.0995548i
$460$		0			0
$461$	190575.			0.896737			0.448368	−	0.893849i	$-0.352005\pi$
$461$	190575.			0.896737			0.448368	+	0.893849i	$0.352005\pi$
$462$	30791.4	+	30791.4i	0.144260	+	0.144260i
$463$	96817.3	−	96817.3i	0.451638	−	0.451638i	−0.444260	−	0.895898i	$-0.646533\pi$
$463$	96817.3	−	96817.3i	0.451638	−	0.451638i	0.895898	+	0.444260i	$0.146533\pi$
$464$		−	10359.4i		−	0.0481170i
$465$		0			0
$466$	−317908.			−1.46396
$467$	133875.	+	133875.i	0.613853	+	0.613853i	0.943948	−	0.330094i	$-0.107081\pi$
$467$	133875.	+	133875.i	0.613853	+	0.613853i	−0.330094	+	0.943948i	$0.607081\pi$
$468$	22752.6	−	22752.6i	0.103882	−	0.103882i
$469$			30908.2i			0.140517i
$470$		0			0
$471$	205623.			0.926892
$472$	67806.3	+	67806.3i	0.304359	+	0.304359i
$473$	126907.	−	126907.i	0.567234	−	0.567234i
$474$		−	410100.i		−	1.82529i
$475$		0			0
$476$	−5511.84			−0.0243267
$477$	−46951.1	−	46951.1i	−0.206352	−	0.206352i
$478$	−49520.6	+	49520.6i	−0.216736	+	0.216736i
$479$			19912.2i			0.0867856i	0.999058	+	0.0433928i	$0.0138167\pi$
$479$			19912.2i			0.0867856i	−0.999058	+	0.0433928i	$0.986183\pi$
$480$		0			0
$481$	−89813.1			−0.388195
$482$	207379.	+	207379.i	0.892628	+	0.892628i
$483$	87582.6	−	87582.6i	0.375426	−	0.375426i
$484$		−	125558.i		−	0.535986i
$485$		0			0
$486$	164591.			0.696842
$487$	−42819.4	−	42819.4i	−0.180544	−	0.180544i	0.611049	−	0.791593i	$-0.290748\pi$
$487$	−42819.4	−	42819.4i	−0.180544	−	0.180544i	−0.791593	+	0.611049i	$0.790748\pi$
$488$	−96768.4	+	96768.4i	−0.406344	+	0.406344i
$489$		−	282825.i		−	1.18277i
$490$		0			0
$491$	−210345.			−0.872509			−0.436254	−	0.899823i	$-0.643695\pi$
$491$	−210345.			−0.872509			−0.436254	+	0.899823i	$0.643695\pi$
$492$	87415.1	+	87415.1i	0.361124	+	0.361124i
$493$	−627.073	+	627.073i	−0.00258003	+	0.00258003i
$494$			311928.i			1.27821i
$495$		0			0
$496$	−318646.			−1.29522
$497$	34176.6	+	34176.6i	0.138362	+	0.138362i
$498$	−56856.9	+	56856.9i	−0.229258	+	0.229258i
$499$		−	397649.i		−	1.59698i	−0.602011	−	0.798488i	$-0.705634\pi$
$499$		−	397649.i		−	1.59698i	0.602011	−	0.798488i	$-0.294366\pi$
$500$		0			0
$501$	516.701			0.00205856
$502$	−190979.	−	190979.i	−0.757842	−	0.757842i
$503$	−147414.	+	147414.i	−0.582644	+	0.582644i	−0.935629	−	0.352985i	$-0.885167\pi$
$503$	−147414.	+	147414.i	−0.582644	+	0.582644i	0.352985	+	0.935629i	$0.385167\pi$
$504$			10297.5i			0.0405387i
$505$		0			0
$506$	268067.			1.04699
$507$	65600.3	+	65600.3i	0.255205	+	0.255205i
$508$	−249608.	+	249608.i	−0.967233	+	0.967233i
$509$			343629.i			1.32634i	0.748470	+	0.663168i	$0.230789\pi$
$509$			343629.i			1.32634i	−0.748470	+	0.663168i	$0.769211\pi$
$510$		0			0
$511$	183292.			0.701941
$512$	−179267.	−	179267.i	−0.683850	−	0.683850i
$513$	−260852.	+	260852.i	−0.991196	+	0.991196i
$514$		−	261433.i		−	0.989542i
$515$		0			0
$516$	262405.			0.985537
$517$	42491.4	+	42491.4i	0.158972	+	0.158972i
$518$	−47856.8	+	47856.8i	−0.178354	+	0.178354i
$519$			225238.i			0.836193i
$520$		0			0
$521$	−539599.			−1.98790			−0.993952	−	0.109811i	$-0.964975\pi$
$521$	−539599.			−1.98790			−0.993952	+	0.109811i	$0.964975\pi$
$522$	−2758.58	−	2758.58i	−0.0101238	−	0.0101238i
$523$	−60008.9	+	60008.9i	−0.219388	+	0.219388i	−0.808240	−	0.588853i	$-0.799580\pi$
$523$	−60008.9	+	60008.9i	−0.219388	+	0.219388i	0.588853	+	0.808240i	$0.299580\pi$
$524$		−	245406.i		−	0.893763i
$525$		0			0
$526$	246894.			0.892359
$527$	19288.2	+	19288.2i	0.0694497	+	0.0694497i
$528$	98628.8	−	98628.8i	0.353782	−	0.353782i
$529$		−	482645.i		−	1.72471i
$530$		0			0
$531$	86075.2			0.305273
$532$	68549.4	+	68549.4i	0.242203	+	0.242203i
$533$	−130338.	+	130338.i	−0.458794	+	0.458794i
$534$			214185.i			0.751114i
$535$		0			0
$536$	41535.8			0.144575
$537$	−97857.4	−	97857.4i	−0.339348	−	0.339348i
$538$	136878.	−	136878.i	0.472898	−	0.472898i
$539$			20178.7i			0.0694570i
$540$		0			0
$541$	−21605.5			−0.0738193			−0.0369096	−	0.999319i	$-0.511751\pi$
$541$	−21605.5			−0.0738193			−0.0369096	+	0.999319i	$0.511751\pi$
$542$	123723.	+	123723.i	0.421163	+	0.421163i
$543$	191968.	−	191968.i	0.651074	−	0.651074i
$544$			32255.4i			0.108995i
$545$		0			0
$546$	−94929.8			−0.318432
$547$	225012.	+	225012.i	0.752023	+	0.752023i	0.974857	−	0.222833i	$-0.0715306\pi$
$547$	225012.	+	225012.i	0.752023	+	0.752023i	−0.222833	+	0.974857i	$0.571531\pi$
$548$	−254999.	+	254999.i	−0.849137	+	0.849137i
$549$			122840.i			0.407565i
$550$		0			0
$551$	15597.5			0.0513749
$552$	−117697.	−	117697.i	−0.386268	−	0.386268i
$553$	134376.	−	134376.i	0.439413	−	0.439413i
$554$			329813.i			1.07460i
$555$		0			0
$556$	−208987.			−0.676036
$557$	−360189.	−	360189.i	−1.16097	−	1.16097i	−0.984264	−	0.176705i	$-0.943456\pi$
$557$	−360189.	−	360189.i	−1.16097	−	1.16097i	−0.176705	−	0.984264i	$-0.556544\pi$
$558$	−84851.6	+	84851.6i	−0.272516	+	0.272516i
$559$			391253.i			1.25209i
$560$		0			0
$561$	−11940.4			−0.0379395
$562$	39146.6	+	39146.6i	0.123943	+	0.123943i
$563$	115815.	−	115815.i	0.365383	−	0.365383i	−0.500407	−	0.865790i	$-0.666816\pi$
$563$	115815.	−	115815.i	0.365383	−	0.365383i	0.865790	+	0.500407i	$0.166816\pi$
$564$			87859.4i			0.276204i
$565$		0			0
$566$	−162093.			−0.505978
$567$	−55687.9	−	55687.9i	−0.173219	−	0.173219i
$568$	45927.9	−	45927.9i	0.142357	−	0.142357i
$569$		−	190399.i		−	0.588085i	−0.955792	−	0.294043i	$-0.904999\pi$
$569$		−	190399.i		−	0.588085i	0.955792	−	0.294043i	$-0.0950008\pi$
$570$		0			0
$571$	−148108.			−0.454262			−0.227131	−	0.973864i	$-0.572935\pi$
$571$	−148108.			−0.454262			−0.227131	+	0.973864i	$0.572935\pi$
$572$	−59916.0	−	59916.0i	−0.183126	−	0.183126i
$573$	−97964.2	+	97964.2i	−0.298372	+	0.298372i
$574$			138901.i			0.421581i
$575$		0			0
$576$	−31244.7			−0.0941740
$577$	−259813.	−	259813.i	−0.780384	−	0.780384i	0.199511	−	0.979896i	$-0.436065\pi$
$577$	−259813.	−	259813.i	−0.780384	−	0.780384i	−0.979896	+	0.199511i	$0.936065\pi$
$578$	−305592.	+	305592.i	−0.914716	+	0.914716i
$579$			312045.i			0.930807i
$580$		0			0
$581$	−37260.4			−0.110381
$582$	−123649.	−	123649.i	−0.365043	−	0.365043i
$583$	−123639.	+	123639.i	−0.363764	+	0.363764i
$584$		−	246315.i		−	0.722213i
$585$		0			0
$586$	−139026.			−0.404857
$587$	3256.15	+	3256.15i	0.00944991	+	0.00944991i	0.711816	−	0.702366i	$-0.247873\pi$
$587$	3256.15	+	3256.15i	0.00944991	+	0.00944991i	−0.702366	+	0.711816i	$0.747873\pi$
$588$	−20861.8	+	20861.8i	−0.0603387	+	0.0603387i
$589$		−	479765.i		−	1.38292i
$590$		0			0
$591$	−562121.			−1.60937
$592$	153291.	+	153291.i	0.437395	+	0.437395i
$593$	−270954.	+	270954.i	−0.770524	+	0.770524i	−0.978198	−	0.207674i	$-0.933411\pi$
$593$	−270954.	+	270954.i	−0.770524	+	0.770524i	0.207674	+	0.978198i	$0.433411\pi$
$594$		−	242978.i		−	0.688643i
$595$		0			0
$596$	161844.			0.455622
$597$	−118158.	−	118158.i	−0.331525	−	0.331525i
$598$	−413225.	+	413225.i	−1.15554	+	1.15554i
$599$			22355.2i			0.0623053i	0.999515	+	0.0311526i	$0.00991780\pi$
$599$			22355.2i			0.0623053i	−0.999515	+	0.0311526i	$0.990082\pi$
$600$		0			0
$601$	−599464.			−1.65964			−0.829820	−	0.558031i	$-0.811557\pi$
$601$	−599464.			−1.65964			−0.829820	+	0.558031i	$0.811557\pi$
$602$	208478.	+	208478.i	0.575265	+	0.575265i
$603$	26363.3	−	26363.3i	0.0725046	−	0.0725046i
$604$		−	29789.5i		−	0.0816561i
$605$		0			0
$606$	602321.			1.64015
$607$	−221901.	−	221901.i	−0.602258	−	0.602258i	0.338653	−	0.940911i	$-0.390029\pi$
$607$	−221901.	−	221901.i	−0.602258	−	0.602258i	−0.940911	+	0.338653i	$0.890029\pi$
$608$	401152.	−	401152.i	1.08518	−	1.08518i
$609$			4746.81i			0.0127987i
$610$		0			0
$611$	−131001.			−0.350906
$612$	4701.35	+	4701.35i	0.0125522	+	0.0125522i
$613$	56020.3	−	56020.3i	0.149082	−	0.149082i	−0.628626	−	0.777708i	$-0.716382\pi$
$613$	56020.3	−	56020.3i	0.149082	−	0.149082i	0.777708	+	0.628626i	$0.216382\pi$
$614$		−	395221.i		−	1.04834i
$615$		0			0
$616$	27117.0			0.0714628
$617$	376138.	+	376138.i	0.988045	+	0.988045i	0.999929	−	0.0118843i	$-0.00378297\pi$
$617$	376138.	+	376138.i	0.988045	+	0.988045i	−0.0118843	+	0.999929i	$0.503783\pi$
$618$	139108.	−	139108.i	0.364229	−	0.364229i
$619$			133682.i			0.348891i	0.984667	+	0.174446i	$0.0558134\pi$
$619$			133682.i			0.348891i	−0.984667	+	0.174446i	$0.944187\pi$
$620$		0			0
$621$	−691123.			−1.79214
$622$	−521103.	−	521103.i	−1.34692	−	1.34692i
$623$	−70181.4	+	70181.4i	−0.180820	+	0.180820i
$624$			304072.i			0.780922i
$625$		0			0
$626$	−446042.			−1.13822
$627$	148499.	+	148499.i	0.377736	+	0.377736i
$628$	−213200.	+	213200.i	−0.540590	+	0.540590i
$629$		−	18558.0i		−	0.0469061i
$630$		0			0
$631$	74938.8			0.188212			0.0941061	−	0.995562i	$-0.470001\pi$
$631$	74938.8			0.188212			0.0941061	+	0.995562i	$0.470001\pi$
$632$	−180581.	−	180581.i	−0.452103	−	0.452103i
$633$	−235058.	+	235058.i	−0.586636	+	0.586636i
$634$			310123.i			0.771534i
$635$		0			0
$636$	−255649.			−0.632019
$637$	−31105.4	−	31105.4i	−0.0766580	−	0.0766580i
$638$	−7264.36	+	7264.36i	−0.0178466	+	0.0178466i
$639$		−	58302.2i		−	0.142785i
$640$		0			0
$641$	772221.			1.87943			0.939714	−	0.341961i	$-0.111091\pi$
$641$	772221.			1.87943			0.939714	+	0.341961i	$0.111091\pi$
$642$	363097.	+	363097.i	0.880953	+	0.880953i
$643$	397464.	−	397464.i	0.961336	−	0.961336i	−0.0379437	−	0.999280i	$-0.512081\pi$
$643$	397464.	−	397464.i	0.961336	−	0.961336i	0.999280	+	0.0379437i	$0.0120807\pi$
$644$			181620.i			0.437918i
$645$		0			0
$646$	−64453.5			−0.154448
$647$	−289594.	−	289594.i	−0.691800	−	0.691800i	0.270828	−	0.962628i	$-0.412703\pi$
$647$	−289594.	−	289594.i	−0.691800	−	0.691800i	−0.962628	+	0.270828i	$0.912703\pi$
$648$	−74835.8	+	74835.8i	−0.178221	+	0.178221i
$649$		−	226667.i		−	0.538145i
$650$		0			0
$651$	146008.			0.344519
$652$	293248.	+	293248.i	0.689827	+	0.689827i
$653$	−98311.6	+	98311.6i	−0.230557	+	0.230557i	−0.812925	−	0.582368i	$-0.802126\pi$
$653$	−98311.6	+	98311.6i	−0.230557	+	0.230557i	0.582368	+	0.812925i	$0.302126\pi$
$654$		−	560963.i		−	1.31153i
$655$		0			0
$656$	444917.			1.03388
$657$	−156340.	−	156340.i	−0.362191	−	0.362191i
$658$	−69803.5	+	69803.5i	−0.161222	+	0.161222i
$659$			462521.i			1.06503i	0.846422	+	0.532513i	$0.178752\pi$
$659$			462521.i			1.06503i	−0.846422	+	0.532513i	$0.821248\pi$
$660$		0			0
$661$	751.874			0.00172085			0.000860423	−	1.00000i	$-0.499726\pi$
$661$	751.874			0.00172085			0.000860423		1.00000i	$0.499726\pi$
$662$	−509307.	−	509307.i	−1.16215	−	1.16215i
$663$	18406.0	−	18406.0i	0.0418729	−	0.0418729i
$664$			50072.0i			0.113569i
$665$		0			0
$666$	81639.3			0.184056
$667$	20662.6	+	20662.6i	0.0464445	+	0.0464445i
$668$	−535.743	+	535.743i	−0.00120061	+	0.00120061i
$669$		−	163558.i		−	0.365442i
$670$		0			0
$671$	323484.			0.718468
$672$	122083.	+	122083.i	0.270345	+	0.270345i
$673$	−47103.9	+	47103.9i	−0.103999	+	0.103999i	−0.757191	−	0.653193i	$-0.773429\pi$
$673$	−47103.9	+	47103.9i	−0.103999	+	0.103999i	0.653193	+	0.757191i	$0.273429\pi$
$674$			204978.i			0.451220i
$675$		0			0
$676$	−136035.			−0.297686
$677$	261543.	+	261543.i	0.570645	+	0.570645i	0.932309	−	0.361663i	$-0.117791\pi$
$677$	261543.	+	261543.i	0.570645	+	0.570645i	−0.361663	+	0.932309i	$0.617791\pi$
$678$	113511.	−	113511.i	0.246932	−	0.246932i
$679$		−	81031.4i		−	0.175757i
$680$		0			0
$681$	−339557.			−0.732180
$682$	223445.	+	223445.i	0.480399	+	0.480399i
$683$	210280.	−	210280.i	0.450772	−	0.450772i	−0.444838	−	0.895611i	$-0.646739\pi$
$683$	210280.	−	210280.i	0.450772	−	0.450772i	0.895611	+	0.444838i	$0.146739\pi$
$684$		−	116939.i		−	0.249947i
$685$		0			0
$686$	−33148.9			−0.0704403
$687$	292555.	+	292555.i	0.619860	+	0.619860i
$688$	667783.	−	667783.i	1.41078	−	1.41078i
$689$		−	381180.i		−	0.802955i
$690$		0			0
$691$	405248.			0.848721			0.424361	−	0.905493i	$-0.360499\pi$
$691$	405248.			0.848721			0.424361	+	0.905493i	$0.360499\pi$
$692$	−233538.	−	233538.i	−0.487692	−	0.487692i
$693$	17211.5	−	17211.5i	0.0358388	−	0.0358388i
$694$		−	92234.5i		−	0.191502i
$695$		0			0
$696$	6378.96			0.0131684
$697$	−26931.6	−	26931.6i	−0.0554367	−	0.0554367i
$698$	169070.	−	169070.i	0.347021	−	0.347021i
$699$		−	466599.i		−	0.954969i
$700$		0			0
$701$	776018.			1.57920			0.789598	−	0.613625i	$-0.210289\pi$
$701$	776018.			1.57920			0.789598	+	0.613625i	$0.210289\pi$
$702$	374550.	+	374550.i	0.760039	+	0.760039i
$703$	−230801.	+	230801.i	−0.467011	+	0.467011i
$704$			82278.6i			0.166013i
$705$		0			0
$706$	374358.			0.751065
$707$	197361.	+	197361.i	0.394841	+	0.394841i
$708$	234340.	−	234340.i	0.467498	−	0.467498i
$709$		−	411451.i		−	0.818513i	−0.912419	−	0.409257i	$-0.865788\pi$
$709$		−	411451.i		−	0.818513i	0.912419	−	0.409257i	$-0.134212\pi$
$710$		0			0
$711$	−229234.			−0.453461
$712$	94312.7	+	94312.7i	0.186042	+	0.186042i
$713$	635564.	−	635564.i	1.25020	−	1.25020i
$714$		−	19615.2i		−	0.0384766i
$715$		0			0
$716$	202927.			0.395835
$717$	−72682.2	−	72682.2i	−0.141380	−	0.141380i
$718$	147034.	−	147034.i	0.285212	−	0.285212i
$719$			471072.i			0.911233i	0.890176	+	0.455617i	$0.150581\pi$
$719$			471072.i			0.911233i	−0.890176	+	0.455617i	$0.849419\pi$
$720$		0			0
$721$	91162.2			0.175366
$722$	320721.	+	320721.i	0.615252	+	0.615252i
$723$	−304373.	+	304373.i	−0.582277	+	0.582277i
$724$			398086.i			0.759450i
$725$		0			0
$726$	446829.			0.847750
$727$	179969.	+	179969.i	0.340510	+	0.340510i	0.856559	−	0.516049i	$-0.172598\pi$
$727$	179969.	+	179969.i	0.340510	+	0.340510i	−0.516049	+	0.856559i	$0.672598\pi$
$728$	−41800.8	+	41800.8i	−0.0788718	+	0.0788718i
$729$			586014.i			1.10269i
$730$		0			0
$731$	−80844.2			−0.151291
$732$	334433.	+	334433.i	0.624148	+	0.624148i
$733$	96617.9	−	96617.9i	0.179825	−	0.179825i	−0.611455	−	0.791279i	$-0.709415\pi$
$733$	96617.9	−	96617.9i	0.179825	−	0.179825i	0.791279	+	0.611455i	$0.209415\pi$
$734$		−	538703.i		−	0.999902i
$735$		0			0
$736$	1.06285e6			1.96207
$737$	−69424.2	−	69424.2i	−0.127813	−	0.127813i
$738$	118476.	−	118476.i	0.217530	−	0.217530i
$739$			571596.i			1.04665i	0.852134	+	0.523324i	$0.175308\pi$
$739$			571596.i			1.04665i	−0.852134	+	0.523324i	$0.824692\pi$
$740$		0			0
$741$	−457822.			−0.833797
$742$	−203111.	−	203111.i	−0.368914	−	0.368914i
$743$	647230.	−	647230.i	1.17241	−	1.17241i	0.190782	−	0.981632i	$-0.438898\pi$
$743$	647230.	−	647230.i	1.17241	−	1.17241i	0.981632	−	0.190782i	$-0.0611024\pi$
$744$		−	196211.i		−	0.354469i
$745$		0			0
$746$	−933144.			−1.67676
$747$	31781.4	+	31781.4i	0.0569550	+	0.0569550i
$748$	12380.4	−	12380.4i	0.0221274	−	0.0221274i
$749$			237950.i			0.424153i
$750$		0			0
$751$	716592.			1.27055			0.635275	−	0.772286i	$-0.280887\pi$
$751$	716592.			1.27055			0.635275	+	0.772286i	$0.280887\pi$
$752$	223589.	+	223589.i	0.395381	+	0.395381i
$753$	280303.	−	280303.i	0.494354	−	0.494354i
$754$		−	22396.0i		−	0.0393937i
$755$		0			0
$756$	164622.			0.288035
$757$	−38892.4	−	38892.4i	−0.0678693	−	0.0678693i	0.672357	−	0.740227i	$-0.265282\pi$
$757$	−38892.4	−	38892.4i	−0.0678693	−	0.0678693i	−0.740227	+	0.672357i	$0.765282\pi$
$758$	−554584.	+	554584.i	−0.965226	+	0.965226i
$759$			393446.i			0.682970i
$760$		0			0
$761$	−673905.			−1.16367			−0.581835	−	0.813307i	$-0.697665\pi$
$761$	−673905.			−1.16367			−0.581835	+	0.813307i	$0.697665\pi$
$762$	−888291.	−	888291.i	−1.52984	−	1.52984i
$763$	183810.	−	183810.i	0.315732	−	0.315732i
$764$		−	203149.i		−	0.348039i
$765$		0			0
$766$	−358037.			−0.610198
$767$	349407.	+	349407.i	0.593938	+	0.593938i
$768$	465310.	−	465310.i	0.788897	−	0.788897i
$769$			182164.i			0.308043i	0.988068	+	0.154021i	$0.0492225\pi$
$769$			182164.i			0.308043i	−0.988068	+	0.154021i	$0.950778\pi$
$770$		0			0
$771$	383709.			0.645496
$772$	−323544.	−	323544.i	−0.542873	−	0.542873i
$773$	−618979.	+	618979.i	−1.03590	+	1.03590i	−0.0365671	+	0.999331i	$0.511642\pi$
$773$	−618979.	+	618979.i	−1.03590	+	1.03590i	−0.999331	+	0.0365671i	$0.988358\pi$
$774$		−	355645.i		−	0.593657i
$775$		0			0
$776$	−108893.			−0.180833
$777$	−70240.1	−	70240.1i	−0.116344	−	0.116344i
$778$	−772393.	+	772393.i	−1.27608	+	1.27608i
$779$			669884.i			1.10389i
$780$		0			0
$781$	−153531.			−0.251706
$782$	−85384.2	−	85384.2i	−0.139625	−	0.139625i
$783$	18728.8	−	18728.8i	0.0305482	−	0.0305482i
$784$			106180.i			0.172747i
$785$		0			0
$786$	873336.			1.41363
$787$	−41089.9	−	41089.9i	−0.0663415	−	0.0663415i	0.673158	−	0.739499i	$-0.264938\pi$
$787$	−41089.9	−	41089.9i	−0.0663415	−	0.0663415i	−0.739499	+	0.673158i	$0.764938\pi$
$788$	582836.	−	582836.i	0.938629	−	0.938629i
$789$			362370.i			0.582101i
$790$		0			0
$791$	74387.5			0.118890
$792$	−23129.6	−	23129.6i	−0.0368738	−	0.0368738i
$793$	−498649.	+	498649.i	−0.792955	+	0.792955i
$794$			192974.i			0.306096i
$795$		0			0
$796$	245025.			0.386710
$797$	418332.	+	418332.i	0.658574	+	0.658574i	0.955043	−	0.296469i	$-0.0958091\pi$
$797$	418332.	+	418332.i	0.658574	+	0.658574i	−0.296469	+	0.955043i	$0.595809\pi$
$798$	−243950.	+	243950.i	−0.383084	+	0.383084i
$799$		−	27068.5i		−	0.0424005i
$800$		0			0
$801$	119723.			0.186601
$802$	114349.	+	114349.i	0.177781	+	0.177781i
$803$	−411699.	+	411699.i	−0.638482	+	0.638482i
$804$		−	143548.i		−	0.222068i
$805$		0			0
$806$	−688880.			−1.06041
$807$	200897.	+	200897.i	0.308480	+	0.308480i
$808$	265222.	−	265222.i	0.406244	−	0.406244i
$809$			717373.i			1.09609i	0.836447	+	0.548047i	$0.184629\pi$
$809$			717373.i			1.09609i	−0.836447	+	0.548047i	$0.815371\pi$
$810$		0			0
$811$	1.04158e6			1.58362			0.791812	−	0.610765i	$-0.209138\pi$
$811$	1.04158e6			1.58362			0.791812	+	0.610765i	$0.209138\pi$
$812$	−4921.74	−	4921.74i	−0.00746459	−	0.00746459i
$813$	−181589.	+	181589.i	−0.274732	+	0.274732i
$814$		−	214986.i		−	0.324460i
$815$		0			0
$816$	−62830.1			−0.0943599
$817$	1.00544e6	+	1.00544e6i	1.50630	+	1.50630i
$818$	−260929.	+	260929.i	−0.389956	+	0.389956i
$819$			53063.1i			0.0791088i
$820$		0			0
$821$	−892265.			−1.32375			−0.661877	−	0.749612i	$-0.730240\pi$
$821$	−892265.			−1.32375			−0.661877	+	0.749612i	$0.730240\pi$
$822$	−907477.	−	907477.i	−1.34305	−	1.34305i
$823$	−126260.	+	126260.i	−0.186409	+	0.186409i	−0.794142	−	0.607733i	$-0.792079\pi$
$823$	−126260.	+	126260.i	−0.186409	+	0.186409i	0.607733	+	0.794142i	$0.292079\pi$
$824$		−	122508.i		−	0.180430i
$825$		0			0
$826$	372362.			0.545764
$827$	298491.	+	298491.i	0.436435	+	0.436435i	0.890810	−	0.454375i	$-0.150137\pi$
$827$	298491.	+	298491.i	0.436435	+	0.436435i	−0.454375	+	0.890810i	$0.650137\pi$
$828$	154914.	−	154914.i	0.225959	−	0.225959i
$829$			624542.i			0.908767i	0.890806	+	0.454384i	$0.150140\pi$
$829$			624542.i			0.908767i	−0.890806	+	0.454384i	$0.849860\pi$
$830$		0			0
$831$	−484072.			−0.700983
$832$	−126832.	−	126832.i	−0.183224	−	0.183224i
$833$	6427.28	−	6427.28i	0.00926269	−	0.00926269i
$834$		−	743732.i		−	1.06926i
$835$		0			0
$836$	−307943.			−0.440614
$837$	−576080.	−	576080.i	−0.822303	−	0.822303i
$838$	350282.	−	350282.i	0.498803	−	0.498803i
$839$		−	778116.i		−	1.10540i	−0.833380	−	0.552701i	$-0.813597\pi$
$839$		−	778116.i		−	1.10540i	0.833380	−	0.552701i	$-0.186403\pi$
$840$		0			0
$841$	706161.			0.998417
$842$	410500.	+	410500.i	0.579013	+	0.579013i
$843$	−57456.0	+	57456.0i	−0.0808501	+	0.0808501i
$844$		−	487441.i		−	0.684286i
$845$		0			0
$846$	119078.			0.166377
$847$	146411.	+	146411.i	0.204084	+	0.204084i
$848$	−650590.	+	650590.i	−0.904723	+	0.904723i
$849$		−	237906.i		−	0.330058i
$850$		0			0
$851$	−611503.			−0.844383
$852$	−158728.	−	158728.i	−0.218662	−	0.218662i
$853$	−756967.	+	756967.i	−1.04035	+	1.04035i	−0.0411974	+	0.999151i	$0.513117\pi$
$853$	−756967.	+	756967.i	−1.04035	+	1.04035i	−0.999151	+	0.0411974i	$0.986883\pi$
$854$			531408.i			0.728640i
$855$		0			0
$856$	319768.			0.436402
$857$	−393557.	−	393557.i	−0.535853	−	0.535853i	0.386455	−	0.922308i	$-0.373699\pi$
$857$	−393557.	−	393557.i	−0.535853	−	0.535853i	−0.922308	+	0.386455i	$0.873699\pi$
$858$	213226.	−	213226.i	0.289644	−	0.289644i
$859$		−	45899.9i		−	0.0622051i	−0.999516	−	0.0311025i	$-0.990098\pi$
$859$		−	45899.9i		−	0.0622051i	0.999516	−	0.0311025i	$-0.00990184\pi$
$860$		0			0
$861$	−203867.			−0.275005
$862$	−911869.	−	911869.i	−1.22721	−	1.22721i
$863$	−101268.	+	101268.i	−0.135972	+	0.135972i	−0.771817	−	0.635845i	$-0.780652\pi$
$863$	−101268.	+	101268.i	−0.135972	+	0.135972i	0.635845	+	0.771817i	$0.280652\pi$
$864$		−	963372.i		−	1.29053i
$865$		0			0
$866$	−19842.6			−0.0264584
$867$	−448522.	−	448522.i	−0.596686	−	0.596686i
$868$	−151388.	+	151388.i	−0.200934	+	0.200934i
$869$			603657.i			0.799375i
$870$		0			0
$871$	214034.			0.282129
$872$	−247011.	−	247011.i	−0.324850	−	0.324850i
$873$	−69116.2	+	69116.2i	−0.0906883	+	0.0906883i
$874$			2.12380e6i			2.78030i
$875$		0			0
$876$	−851270.			−1.10933
$877$	44909.1	+	44909.1i	0.0583895	+	0.0583895i	0.735699	−	0.677309i	$-0.236854\pi$
$877$	44909.1	+	44909.1i	0.0583895	+	0.0583895i	−0.677309	+	0.735699i	$0.736854\pi$
$878$	1.19620e6	−	1.19620e6i	1.55172	−	1.55172i
$879$		−	204051.i		−	0.264095i
$880$		0			0
$881$	−954666.			−1.22998			−0.614992	−	0.788533i	$-0.710841\pi$
$881$	−954666.			−1.22998			−0.614992	+	0.788533i	$0.710841\pi$
$882$	28274.6	+	28274.6i	0.0363462	+	0.0363462i
$883$	708672.	−	708672.i	0.908916	−	0.908916i	−0.0872691	−	0.996185i	$-0.527814\pi$
$883$	708672.	−	708672.i	0.908916	−	0.908916i	0.996185	+	0.0872691i	$0.0278140\pi$
$884$			38168.6i			0.0488430i
$885$		0			0
$886$	−1.33231e6			−1.69722
$887$	−20953.6	−	20953.6i	−0.0266325	−	0.0266325i	0.693665	−	0.720298i	$-0.255995\pi$
$887$	−20953.6	−	20953.6i	−0.0266325	−	0.0266325i	−0.720298	+	0.693665i	$0.755995\pi$
$888$	−94391.6	+	94391.6i	−0.119704	+	0.119704i
$889$		−	582129.i		−	0.736572i
$890$		0			0
$891$	250166.			0.315118
$892$	169585.	+	169585.i	0.213137	+	0.213137i
$893$	−336644.	+	336644.i	−0.422152	+	0.422152i
$894$			575963.i			0.720641i
$895$		0			0
$896$	225515.			0.280905
$897$	−606496.	−	606496.i	−0.753777	−	0.753777i
$898$	−362211.	+	362211.i	−0.449168	+	0.449168i
$899$			34446.3i			0.0426210i
$900$		0			0
$901$	78762.8			0.0970222
$902$	−311991.	−	311991.i	−0.383468	−	0.383468i
$903$	−305987.	+	305987.i	−0.375256	+	0.375256i
$904$		−	99965.1i		−	0.122324i
$905$		0			0
$906$	106013.			0.129153
$907$	388490.	+	388490.i	0.472242	+	0.472242i	0.902640	−	0.430397i	$-0.141626\pi$
$907$	388490.	+	388490.i	0.472242	+	0.472242i	−0.430397	+	0.902640i	$0.641626\pi$
$908$	352070.	−	352070.i	0.427029	−	0.427029i
$909$		−	336680.i		−	0.407465i
$910$		0			0
$911$	−511824.			−0.616714			−0.308357	−	0.951271i	$-0.599779\pi$
$911$	−511824.			−0.616714			−0.308357	+	0.951271i	$0.599779\pi$
$912$	781402.	+	781402.i	0.939474	+	0.939474i
$913$	83692.0	−	83692.0i	0.100402	−	0.100402i
$914$		−	64783.9i		−	0.0775487i
$915$		0			0
$916$	−606672.			−0.723041
$917$	286164.	+	286164.i	0.340311	+	0.340311i
$918$	−77392.9	+	77392.9i	−0.0918366	+	0.0918366i
$919$			96227.2i			0.113938i	0.998376	+	0.0569688i	$0.0181436\pi$
$919$			96227.2i			0.113938i	−0.998376	+	0.0569688i	$0.981856\pi$
$920$		0			0
$921$	580072.			0.683853
$922$	−703202.	−	703202.i	−0.827215	−	0.827215i
$923$	236667.	−	236667.i	0.277802	−	0.277802i
$924$		−	93716.9i		−	0.109768i
$925$		0			0
$926$	−714490.			−0.833248
$927$	−77757.3	−	77757.3i	−0.0904861	−	0.0904861i
$928$	−28802.1	+	28802.1i	−0.0334448	+	0.0334448i
$929$		−	600335.i		−	0.695604i	−0.937568	−	0.347802i	$-0.886928\pi$
$929$		−	600335.i		−	0.695604i	0.937568	−	0.347802i	$-0.113072\pi$
$930$		0			0
$931$	−159869.			−0.184444
$932$	483794.	+	483794.i	0.556966	+	0.556966i
$933$	764831.	−	764831.i	0.878622	−	0.878622i
$934$		−	987965.i		−	1.13253i
$935$		0			0
$936$	71308.4			0.0813933
$937$	641234.	+	641234.i	0.730360	+	0.730360i	0.970691	−	0.240331i	$-0.0772559\pi$
$937$	641234.	+	641234.i	0.730360	+	0.730360i	−0.240331	+	0.970691i	$0.577256\pi$
$938$	114048.	−	114048.i	0.129623	−	0.129623i
$939$		−	654663.i		−	0.742483i
$940$		0			0
$941$	1.07984e6			1.21950			0.609749	−	0.792595i	$-0.291270\pi$
$941$	1.07984e6			1.21950			0.609749	+	0.792595i	$0.291270\pi$
$942$	−758725.	−	758725.i	−0.855032	−	0.855032i
$943$	−887423.	+	887423.i	−0.997947	+	0.997947i
$944$		−	1.19272e6i		−	1.33843i
$945$		0			0
$946$	−936544.			−1.04652
$947$	−24749.7	−	24749.7i	−0.0275975	−	0.0275975i	0.693173	−	0.720771i	$-0.256212\pi$
$947$	−24749.7	−	24749.7i	−0.0275975	−	0.0275975i	−0.720771	+	0.693173i	$0.756212\pi$
$948$	−624091.	+	624091.i	−0.694434	+	0.694434i
$949$		−	1.26927e6i		−	1.40935i
$950$		0			0
$951$	−455172.			−0.503286
$952$	−8637.25	−	8637.25i	−0.00953019	−	0.00953019i
$953$	−289360.	+	289360.i	−0.318605	+	0.318605i	−0.848231	−	0.529626i	$-0.822332\pi$
$953$	−289360.	+	289360.i	−0.318605	+	0.318605i	0.529626	+	0.848231i	$0.322332\pi$
$954$			346489.i			0.380709i
$955$		0			0
$956$	150721.			0.164914
$957$	−10662.0	−	10662.0i	−0.0116417	−	0.0116417i
$958$	73473.7	−	73473.7i	0.0800573	−	0.0800573i
$959$		−	594702.i		−	0.646640i
$960$		0			0
$961$	136018.			0.147282
$962$	331401.	+	331401.i	0.358099	+	0.358099i
$963$	202961.	−	202961.i	0.218857	−	0.218857i
$964$		−	631180.i		−	0.679202i
$965$		0			0
$966$	−646341.			−0.692639
$967$	254563.	+	254563.i	0.272234	+	0.272234i	0.829999	−	0.557765i	$-0.188341\pi$
$967$	254563.	+	254563.i	0.272234	+	0.272234i	−0.557765	+	0.829999i	$0.688341\pi$
$968$	196754.	−	196754.i	0.209977	−	0.209977i
$969$		−	94599.3i		−	0.100749i
$970$		0			0
$971$	861405.			0.913627			0.456813	−	0.889563i	$-0.348991\pi$
$971$	861405.			0.913627			0.456813	+	0.889563i	$0.348991\pi$
$972$	−250475.	−	250475.i	−0.265114	−	0.265114i
$973$	243697.	−	243697.i	0.257409	−	0.257409i
$974$			315998.i			0.333093i
$975$		0			0
$976$	1.70217e6			1.78691
$977$	−37416.1	−	37416.1i	−0.0391984	−	0.0391984i	0.687236	−	0.726434i	$-0.258824\pi$
$977$	−37416.1	−	37416.1i	−0.0391984	−	0.0391984i	−0.726434	+	0.687236i	$0.758824\pi$
$978$	−1.04359e6	+	1.04359e6i	−1.09107	+	1.09107i
$979$		−	315275.i		−	0.328945i
$980$		0			0
$981$	−313563.			−0.325826
$982$	776151.	+	776151.i	0.804865	+	0.804865i
$983$	194549.	−	194549.i	0.201336	−	0.201336i	−0.599236	−	0.800572i	$-0.704529\pi$
$983$	194549.	−	194549.i	0.201336	−	0.201336i	0.800572	+	0.599236i	$0.204529\pi$
$984$			273965.i			0.282947i
$985$		0			0
$986$	4627.66			0.00476000
$987$	−102452.	−	102452.i	−0.105168	−	0.105168i
$988$	474694.	−	474694.i	0.486295	−	0.486295i
$989$			2.66389e6i			2.72348i
$990$		0			0
$991$	814684.			0.829548			0.414774	−	0.909924i	$-0.363861\pi$
$991$	814684.			0.829548			0.414774	+	0.909924i	$0.363861\pi$
$992$	885927.	+	885927.i	0.900274	+	0.900274i
$993$	747517.	−	747517.i	0.758094	−	0.758094i
$994$		−	252216.i		−	0.255270i
$995$		0			0
$996$	173050.			0.174443
$997$	1.24250e6	+	1.24250e6i	1.24999	+	1.24999i	0.955724	+	0.294266i	$0.0950751\pi$
$997$	1.24250e6	+	1.24250e6i	1.24999	+	1.24999i	0.294266	+	0.955724i	$0.404925\pi$
$998$	−1.46728e6	+	1.46728e6i	−1.47317	+	1.47317i
$999$			554271.i			0.555382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.57.3		24
5.2	odd	4		35.5.g.a.8.10	✓	24
5.3	odd	4	inner	175.5.g.c.43.3		24
5.4	even	2		35.5.g.a.22.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.10	✓	24	5.2	odd	4
35.5.g.a.22.10	yes	24	5.4	even	2
175.5.g.c.43.3		24	5.3	odd	4	inner
175.5.g.c.57.3		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)

\(f(q)\)	\(=\)	\(q+(-3.68989 - 3.68989i) q^{2} +(5.41571 - 5.41571i) q^{3} +11.2306i q^{4} -39.9667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-17.5987 + 17.5987i) q^{8} +22.3403i q^{9} +O(q^{10})\)	\(q+(-3.68989 - 3.68989i) q^{2} +(5.41571 - 5.41571i) q^{3} +11.2306i q^{4} -39.9667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-17.5987 + 17.5987i) q^{8} +22.3403i q^{9} +58.8300 q^{11} +(60.8214 + 60.8214i) q^{12} +(-90.6864 + 90.6864i) q^{13} +96.6441i q^{14} +309.563 q^{16} +(-18.7384 - 18.7384i) q^{17} +(82.4331 - 82.4331i) q^{18} +466.090i q^{19} -141.846 q^{21} +(-217.076 - 217.076i) q^{22} +(-617.449 + 617.449i) q^{23} +190.619i q^{24} +669.245 q^{26} +(559.660 + 559.660i) q^{27} +(147.073 - 147.073i) q^{28} -33.4645i q^{29} -1029.34 q^{31} +(-860.676 - 860.676i) q^{32} +(318.606 - 318.606i) q^{33} +138.285i q^{34} -250.894 q^{36} +(495.185 + 495.185i) q^{37} +(1719.82 - 1719.82i) q^{38} +982.261i q^{39} +1437.24 q^{41} +(523.396 + 523.396i) q^{42} +(2157.18 - 2157.18i) q^{43} +660.695i q^{44} +4556.64 q^{46} +(722.273 + 722.273i) q^{47} +(1676.50 - 1676.50i) q^{48} +343.000i q^{49} -202.964 q^{51} +(-1018.46 - 1018.46i) q^{52} +(-2101.64 + 2101.64i) q^{53} -4130.17i q^{54} +460.938 q^{56} +(2524.21 + 2524.21i) q^{57} +(-123.480 + 123.480i) q^{58} -3852.92i q^{59} +5498.61 q^{61} +(3798.15 + 3798.15i) q^{62} +(292.564 - 292.564i) q^{63} +1398.58i q^{64} -2351.24 q^{66} +(-1180.08 - 1180.08i) q^{67} +(210.443 - 210.443i) q^{68} +6687.84i q^{69} -2609.74 q^{71} +(-393.159 - 393.159i) q^{72} +(-6998.11 + 6998.11i) q^{73} -3654.36i q^{74} -5234.45 q^{76} +(-770.426 - 770.426i) q^{77} +(3624.44 - 3624.44i) q^{78} +10261.0i q^{79} +4252.35 q^{81} +(-5303.26 - 5303.26i) q^{82} +(1422.61 - 1422.61i) q^{83} -1593.01i q^{84} -15919.5 q^{86} +(-181.234 - 181.234i) q^{87} +(-1035.33 + 1035.33i) q^{88} -5359.08i q^{89} +2375.22 q^{91} +(-6934.30 - 6934.30i) q^{92} +(-5574.60 + 5574.60i) q^{93} -5330.22i q^{94} -9322.33 q^{96} +(3093.79 + 3093.79i) q^{97} +(1265.63 - 1265.63i) q^{98} +1314.28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more