LMFDB - Embedded newform 175.5.g.c.43.4

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			43.4
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.18640 + 3.18640i) q^{2} +(-5.77081 - 5.77081i) q^{3} -4.30624i q^{4} +36.7762 q^{6} +(13.0958 - 13.0958i) q^{7} +(-37.2610 - 37.2610i) q^{8} -14.3955i q^{9} +O(q^{10})$	\(q+(-3.18640 + 3.18640i) q^{2} +(-5.77081 - 5.77081i) q^{3} -4.30624i q^{4} +36.7762 q^{6} +(13.0958 - 13.0958i) q^{7} +(-37.2610 - 37.2610i) q^{8} -14.3955i q^{9} -82.8733 q^{11} +(-24.8505 + 24.8505i) q^{12} +(138.646 + 138.646i) q^{13} +83.4568i q^{14} +306.356 q^{16} +(322.389 - 322.389i) q^{17} +(45.8698 + 45.8698i) q^{18} +318.965i q^{19} -151.147 q^{21} +(264.067 - 264.067i) q^{22} +(-138.083 - 138.083i) q^{23} +430.052i q^{24} -883.563 q^{26} +(-550.509 + 550.509i) q^{27} +(-56.3936 - 56.3936i) q^{28} -109.237i q^{29} -1063.42 q^{31} +(-379.997 + 379.997i) q^{32} +(478.246 + 478.246i) q^{33} +2054.52i q^{34} -61.9904 q^{36} +(-1791.23 + 1791.23i) q^{37} +(-1016.35 - 1016.35i) q^{38} -1600.20i q^{39} -345.340 q^{41} +(481.613 - 481.613i) q^{42} +(-1214.03 - 1214.03i) q^{43} +356.872i q^{44} +879.973 q^{46} +(-1368.18 + 1368.18i) q^{47} +(-1767.92 - 1767.92i) q^{48} -343.000i q^{49} -3720.89 q^{51} +(597.043 - 597.043i) q^{52} +(102.370 + 102.370i) q^{53} -3508.28i q^{54} -975.924 q^{56} +(1840.69 - 1840.69i) q^{57} +(348.072 + 348.072i) q^{58} +2476.36i q^{59} -1037.52 q^{61} +(3388.47 - 3388.47i) q^{62} +(-188.521 - 188.521i) q^{63} +2480.06i q^{64} -3047.76 q^{66} +(-3421.35 + 3421.35i) q^{67} +(-1388.28 - 1388.28i) q^{68} +1593.70i q^{69} +5349.25 q^{71} +(-536.390 + 536.390i) q^{72} +(-6030.77 - 6030.77i) q^{73} -11415.1i q^{74} +1373.54 q^{76} +(-1085.29 + 1085.29i) q^{77} +(5098.87 + 5098.87i) q^{78} +9397.35i q^{79} +5187.73 q^{81} +(1100.39 - 1100.39i) q^{82} +(6842.12 + 6842.12i) q^{83} +650.874i q^{84} +7736.76 q^{86} +(-630.385 + 630.385i) q^{87} +(3087.94 + 3087.94i) q^{88} +2332.31i q^{89} +3631.36 q^{91} +(-594.617 + 594.617i) q^{92} +(6136.78 + 6136.78i) q^{93} -8719.11i q^{94} +4385.78 q^{96} +(3869.74 - 3869.74i) q^{97} +(1092.93 + 1092.93i) q^{98} +1193.00i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.18640	+	3.18640i	−0.796599	+	0.796599i	−0.982558	−	0.185959i	$-0.940461\pi$
$2$	−3.18640	+	3.18640i	−0.796599	+	0.796599i	0.185959	+	0.982558i	$0.440461\pi$
$3$	−5.77081	−	5.77081i	−0.641201	−	0.641201i	0.309650	−	0.950851i	$-0.399788\pi$
$3$	−5.77081	−	5.77081i	−0.641201	−	0.641201i	−0.950851	+	0.309650i	$0.899788\pi$
$4$		−	4.30624i		−	0.269140i
$5$		0			0
$5$		0			0
$6$	36.7762			1.02156
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	−37.2610	−	37.2610i	−0.582202	−	0.582202i
$9$		−	14.3955i		−	0.177722i
$10$		0			0
$11$	−82.8733			−0.684903			−0.342452	−	0.939535i	$-0.611257\pi$
$11$	−82.8733			−0.684903			−0.342452	+	0.939535i	$0.611257\pi$
$12$	−24.8505	+	24.8505i	−0.172573	+	0.172573i
$13$	138.646	+	138.646i	0.820391	+	0.820391i	0.986164	−	0.165773i	$-0.0530119\pi$
$13$	138.646	+	138.646i	0.820391	+	0.820391i	−0.165773	+	0.986164i	$0.553012\pi$
$14$			83.4568i			0.425800i
$15$		0			0
$16$	306.356			1.19670
$17$	322.389	−	322.389i	1.11553	−	1.11553i	0.123144	−	0.992389i	$-0.460702\pi$
$17$	322.389	−	322.389i	1.11553	−	1.11553i	0.992389	−	0.123144i	$-0.0392976\pi$
$18$	45.8698	+	45.8698i	0.141573	+	0.141573i
$19$			318.965i			0.883559i	0.897124	+	0.441780i	$0.145653\pi$
$19$			318.965i			0.883559i	−0.897124	+	0.441780i	$0.854347\pi$
$20$		0			0
$21$	−151.147			−0.342736
$22$	264.067	−	264.067i	0.545593	−	0.545593i
$23$	−138.083	−	138.083i	−0.261026	−	0.261026i	0.564445	−	0.825471i	$-0.309090\pi$
$23$	−138.083	−	138.083i	−0.261026	−	0.261026i	−0.825471	+	0.564445i	$0.809090\pi$
$24$			430.052i			0.746618i
$25$		0			0
$26$	−883.563			−1.30705
$27$	−550.509	+	550.509i	−0.755157	+	0.755157i
$28$	−56.3936	−	56.3936i	−0.0719306	−	0.0719306i
$29$		−	109.237i		−	0.129889i	−0.997889	−	0.0649446i	$-0.979313\pi$
$29$		−	109.237i		−	0.129889i	0.997889	−	0.0649446i	$-0.0206871\pi$
$30$		0			0
$31$	−1063.42			−1.10657			−0.553287	−	0.832990i	$-0.686627\pi$
$31$	−1063.42			−1.10657			−0.553287	+	0.832990i	$0.686627\pi$
$32$	−379.997	+	379.997i	−0.371090	+	0.371090i
$33$	478.246	+	478.246i	0.439161	+	0.439161i
$34$			2054.52i			1.77726i
$35$		0			0
$36$	−61.9904			−0.0478321
$37$	−1791.23	+	1791.23i	−1.30842	+	1.30842i	−0.385871	+	0.922553i	$0.626099\pi$
$37$	−1791.23	+	1791.23i	−1.30842	+	1.30842i	−0.922553	+	0.385871i	$0.873901\pi$
$38$	−1016.35	−	1016.35i	−0.703842	−	0.703842i
$39$		−	1600.20i		−	1.05207i
$40$		0			0
$41$	−345.340			−0.205437			−0.102719	−	0.994710i	$-0.532754\pi$
$41$	−345.340			−0.205437			−0.102719	+	0.994710i	$0.532754\pi$
$42$	481.613	−	481.613i	0.273023	−	0.273023i
$43$	−1214.03	−	1214.03i	−0.656587	−	0.656587i	0.297984	−	0.954571i	$-0.403686\pi$
$43$	−1214.03	−	1214.03i	−0.656587	−	0.656587i	−0.954571	+	0.297984i	$0.903686\pi$
$44$			356.872i			0.184335i
$45$		0			0
$46$	879.973			0.415866
$47$	−1368.18	+	1368.18i	−0.619365	+	0.619365i	−0.945368	−	0.326004i	$-0.894298\pi$
$47$	−1368.18	+	1368.18i	−0.619365	+	0.619365i	0.326004	+	0.945368i	$0.394298\pi$
$48$	−1767.92	−	1767.92i	−0.767328	−	0.767328i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	−3720.89			−1.43056
$52$	597.043	−	597.043i	0.220800	−	0.220800i
$53$	102.370	+	102.370i	0.0364435	+	0.0364435i	0.725094	−	0.688650i	$-0.241796\pi$
$53$	102.370	+	102.370i	0.0364435	+	0.0364435i	−0.688650	+	0.725094i	$0.741796\pi$
$54$		−	3508.28i		−	1.20311i
$55$		0			0
$56$	−975.924			−0.311200
$57$	1840.69	−	1840.69i	0.566539	−	0.566539i
$58$	348.072	+	348.072i	0.103470	+	0.103470i
$59$			2476.36i			0.711393i	0.934602	+	0.355696i	$0.115756\pi$
$59$			2476.36i			0.711393i	−0.934602	+	0.355696i	$0.884244\pi$
$60$		0			0
$61$	−1037.52			−0.278827			−0.139414	−	0.990234i	$-0.544522\pi$
$61$	−1037.52			−0.278827			−0.139414	+	0.990234i	$0.544522\pi$
$62$	3388.47	−	3388.47i	0.881496	−	0.881496i
$63$	−188.521	−	188.521i	−0.0474983	−	0.0474983i
$64$			2480.06i			0.605483i
$65$		0			0
$66$	−3047.76			−0.699670
$67$	−3421.35	+	3421.35i	−0.762162	+	0.762162i	−0.976713	−	0.214550i	$-0.931171\pi$
$67$	−3421.35	+	3421.35i	−0.762162	+	0.762162i	0.214550	+	0.976713i	$0.431171\pi$
$68$	−1388.28	−	1388.28i	−0.300234	−	0.300234i
$69$			1593.70i			0.334740i
$70$		0			0
$71$	5349.25			1.06115			0.530574	−	0.847638i	$-0.321976\pi$
$71$	5349.25			1.06115			0.530574	+	0.847638i	$0.321976\pi$
$72$	−536.390	+	536.390i	−0.103470	+	0.103470i
$73$	−6030.77	−	6030.77i	−1.13169	−	1.13169i	−0.989896	−	0.141793i	$-0.954713\pi$
$73$	−6030.77	−	6030.77i	−1.13169	−	1.13169i	−0.141793	−	0.989896i	$-0.545287\pi$
$74$		−	11415.1i		−	2.08458i
$75$		0			0
$76$	1373.54			0.237801
$77$	−1085.29	+	1085.29i	−0.183048	+	0.183048i
$78$	5098.87	+	5098.87i	0.838079	+	0.838079i
$79$			9397.35i			1.50574i	0.658167	+	0.752872i	$0.271332\pi$
$79$			9397.35i			1.50574i	−0.658167	+	0.752872i	$0.728668\pi$
$80$		0			0
$81$	5187.73			0.790693
$82$	1100.39	−	1100.39i	0.163651	−	0.163651i
$83$	6842.12	+	6842.12i	0.993195	+	0.993195i	0.999977	−	0.00678239i	$-0.00215892\pi$
$83$	6842.12	+	6842.12i	0.993195	+	0.993195i	−0.00678239	+	0.999977i	$0.502159\pi$
$84$			650.874i			0.0922440i
$85$		0			0
$86$	7736.76			1.04607
$87$	−630.385	+	630.385i	−0.0832851	+	0.0832851i
$88$	3087.94	+	3087.94i	0.398752	+	0.398752i
$89$			2332.31i			0.294446i	0.989103	+	0.147223i	$0.0470335\pi$
$89$			2332.31i			0.294446i	−0.989103	+	0.147223i	$0.952967\pi$
$90$		0			0
$91$	3631.36			0.438517
$92$	−594.617	+	594.617i	−0.0702525	+	0.0702525i
$93$	6136.78	+	6136.78i	0.709537	+	0.709537i
$94$		−	8719.11i		−	0.986771i
$95$		0			0
$96$	4385.78			0.475887
$97$	3869.74	−	3869.74i	0.411280	−	0.411280i	−0.470904	−	0.882184i	$-0.656072\pi$
$97$	3869.74	−	3869.74i	0.411280	−	0.411280i	0.882184	+	0.470904i	$0.156072\pi$
$98$	1092.93	+	1092.93i	0.113800	+	0.113800i
$99$			1193.00i			0.121723i
$100$		0			0
$101$	−9543.11			−0.935507			−0.467754	−	0.883859i	$-0.654937\pi$
$101$	−9543.11			−0.935507			−0.467754	+	0.883859i	$0.654937\pi$
$102$	11856.2	−	11856.2i	1.13958	−	1.13958i
$103$	3983.11	+	3983.11i	0.375446	+	0.375446i	0.869456	−	0.494010i	$-0.164469\pi$
$103$	3983.11	+	3983.11i	0.375446	+	0.375446i	−0.494010	+	0.869456i	$0.664469\pi$
$104$		−	10332.2i		−	0.955267i
$105$		0			0
$106$	−652.381			−0.0580617
$107$	−7833.17	+	7833.17i	−0.684179	+	0.684179i	−0.960939	−	0.276760i	$-0.910739\pi$
$107$	−7833.17	+	7833.17i	−0.684179	+	0.684179i	0.276760	+	0.960939i	$0.410739\pi$
$108$	2370.62	+	2370.62i	0.203243	+	0.203243i
$109$			6238.31i			0.525066i	0.964923	+	0.262533i	$0.0845579\pi$
$109$			6238.31i			0.525066i	−0.964923	+	0.262533i	$0.915442\pi$
$110$		0			0
$111$	20673.7			1.67793
$112$	4011.98	−	4011.98i	0.319832	−	0.319832i
$113$	10577.0	+	10577.0i	0.828335	+	0.828335i	0.987286	−	0.158952i	$-0.0508115\pi$
$113$	10577.0	+	10577.0i	0.828335	+	0.828335i	−0.158952	+	0.987286i	$0.550811\pi$
$114$			11730.3i			0.902609i
$115$		0			0
$116$	−470.400			−0.0349584
$117$	1995.88	−	1995.88i	0.145802	−	0.145802i
$118$	−7890.66	−	7890.66i	−0.566695	−	0.566695i
$119$		−	8443.88i		−	0.596277i
$120$		0			0
$121$	−7773.01			−0.530907
$122$	3305.93	−	3305.93i	0.222113	−	0.222113i
$123$	1992.89	+	1992.89i	0.131726	+	0.131726i
$124$			4579.33i			0.297823i
$125$		0			0
$126$	1201.40			0.0756741
$127$	−13759.2	+	13759.2i	−0.853070	+	0.853070i	−0.990510	−	0.137440i	$-0.956112\pi$
$127$	−13759.2	+	13759.2i	−0.853070	+	0.853070i	0.137440	+	0.990510i	$0.456112\pi$
$128$	−13982.4	−	13982.4i	−0.853418	−	0.853418i
$129$			14011.9i			0.842009i
$130$		0			0
$131$	−15675.4			−0.913432			−0.456716	−	0.889613i	$-0.650974\pi$
$131$	−15675.4			−0.913432			−0.456716	+	0.889613i	$0.650974\pi$
$132$	2059.44	−	2059.44i	0.118196	−	0.118196i
$133$	4177.10	+	4177.10i	0.236141	+	0.236141i
$134$		−	21803.5i		−	1.21428i
$135$		0			0
$136$	−24025.0			−1.29893
$137$	23960.0	−	23960.0i	1.27657	−	1.27657i	0.334003	−	0.942572i	$-0.391601\pi$
$137$	23960.0	−	23960.0i	1.27657	−	1.27657i	0.942572	−	0.334003i	$-0.108399\pi$
$138$	−5078.16	−	5078.16i	−0.266654	−	0.266654i
$139$		−	19971.2i		−	1.03365i	−0.856091	−	0.516826i	$-0.827113\pi$
$139$		−	19971.2i		−	1.03365i	0.856091	−	0.516826i	$-0.172887\pi$
$140$		0			0
$141$	15791.0			0.794275
$142$	−17044.8	+	17044.8i	−0.845310	+	0.845310i
$143$	−11490.1	−	11490.1i	−0.561889	−	0.561889i
$144$		−	4410.15i		−	0.212681i
$145$		0			0
$146$	38432.8			1.80300
$147$	−1979.39	+	1979.39i	−0.0916002	+	0.0916002i
$148$	7713.47	+	7713.47i	0.352149	+	0.352149i
$149$		−	6819.69i		−	0.307179i	−0.988135	−	0.153590i	$-0.950917\pi$
$149$		−	6819.69i		−	0.307179i	0.988135	−	0.153590i	$-0.0490834\pi$
$150$		0			0
$151$	30817.2			1.35157			0.675786	−	0.737098i	$-0.263804\pi$
$151$	30817.2			1.35157			0.675786	+	0.737098i	$0.263804\pi$
$152$	11884.9	−	11884.9i	0.514410	−	0.514410i
$153$	−4640.95	−	4640.95i	−0.198255	−	0.198255i
$154$		−	6916.34i		−	0.291632i
$155$		0			0
$156$	−6890.84			−0.283154
$157$	−28933.5	+	28933.5i	−1.17382	+	1.17382i	−0.192527	+	0.981292i	$0.561668\pi$
$157$	−28933.5	+	28933.5i	−1.17382	+	1.17382i	−0.981292	+	0.192527i	$0.938332\pi$
$158$	−29943.7	−	29943.7i	−1.19947	−	1.19947i
$159$		−	1181.51i		−	0.0467352i
$160$		0			0
$161$	−3616.61			−0.139524
$162$	−16530.2	+	16530.2i	−0.629865	+	0.629865i
$163$	10644.9	+	10644.9i	0.400652	+	0.400652i	0.878463	−	0.477811i	$-0.158570\pi$
$163$	10644.9	+	10644.9i	0.400652	+	0.400652i	−0.477811	+	0.878463i	$0.658570\pi$
$164$			1487.11i			0.0552913i
$165$		0			0
$166$	−43603.4			−1.58236
$167$	5465.46	−	5465.46i	0.195972	−	0.195972i	−0.602299	−	0.798271i	$-0.705748\pi$
$167$	5465.46	−	5465.46i	0.195972	−	0.195972i	0.798271	+	0.602299i	$0.205748\pi$
$168$	5631.87	+	5631.87i	0.199542	+	0.199542i
$169$			9884.48i			0.346083i
$170$		0			0
$171$	4591.66			0.157028
$172$	−5227.90	+	5227.90i	−0.176714	+	0.176714i
$173$	−30524.7	−	30524.7i	−1.01990	−	1.01990i	−0.999798	−	0.0201068i	$-0.993599\pi$
$173$	−30524.7	−	30524.7i	−1.01990	−	1.01990i	−0.0201068	−	0.999798i	$-0.506401\pi$
$174$		−	4017.31i		−	0.132690i
$175$		0			0
$176$	−25388.7			−0.819626
$177$	14290.6	−	14290.6i	0.456146	−	0.456146i
$178$	−7431.65	−	7431.65i	−0.234555	−	0.234555i
$179$			46636.5i			1.45553i	0.685829	+	0.727763i	$0.259440\pi$
$179$			46636.5i			1.45553i	−0.685829	+	0.727763i	$0.740560\pi$
$180$		0			0
$181$	−31065.2			−0.948238			−0.474119	−	0.880461i	$-0.657233\pi$
$181$	−31065.2			−0.948238			−0.474119	+	0.880461i	$0.657233\pi$
$182$	−11571.0	+	11571.0i	−0.349323	+	0.349323i
$183$	5987.30	+	5987.30i	0.178784	+	0.178784i
$184$			10290.2i			0.303940i
$185$		0			0
$186$	−39108.4			−1.13043
$187$	−26717.4	+	26717.4i	−0.764032	+	0.764032i
$188$	5891.69	+	5891.69i	0.166696	+	0.166696i
$189$			14418.7i			0.403648i
$190$		0			0
$191$	−65488.4			−1.79514			−0.897569	−	0.440874i	$-0.854668\pi$
$191$	−65488.4			−1.79514			−0.897569	+	0.440874i	$0.854668\pi$
$192$	14311.9	−	14311.9i	0.388236	−	0.388236i
$193$	43523.1	+	43523.1i	1.16844	+	1.16844i	0.982576	+	0.185860i	$0.0595072\pi$
$193$	43523.1	+	43523.1i	1.16844	+	1.16844i	0.185860	+	0.982576i	$0.440493\pi$
$194$			24661.0i			0.655251i
$195$		0			0
$196$	−1477.04			−0.0384485
$197$	27866.9	−	27866.9i	0.718052	−	0.718052i	−0.250154	−	0.968206i	$-0.580481\pi$
$197$	27866.9	−	27866.9i	0.718052	−	0.718052i	0.968206	+	0.250154i	$0.0804813\pi$
$198$	−3801.38	−	3801.38i	−0.0969641	−	0.0969641i
$199$			23306.9i			0.588542i	0.955722	+	0.294271i	$0.0950769\pi$
$199$			23306.9i			0.588542i	−0.955722	+	0.294271i	$0.904923\pi$
$200$		0			0
$201$	39487.9			0.977399
$202$	30408.1	−	30408.1i	0.745224	−	0.745224i
$203$	−1430.54	−	1430.54i	−0.0347144	−	0.0347144i
$204$			16023.0i			0.385021i
$205$		0			0
$206$	−25383.5			−0.598160
$207$	−1987.77	+	1987.77i	−0.0463901	+	0.0463901i
$208$	42475.1	+	42475.1i	0.981765	+	0.981765i
$209$		−	26433.7i		−	0.605153i
$210$		0			0
$211$	1800.55			0.0404426			0.0202213	−	0.999796i	$-0.493563\pi$
$211$	1800.55			0.0404426			0.0202213	+	0.999796i	$0.493563\pi$
$212$	440.829	−	440.829i	0.00980840	−	0.00980840i
$213$	−30869.5	−	30869.5i	−0.680410	−	0.680410i
$214$		−	49919.1i		−	1.09003i
$215$		0			0
$216$	41025.0			0.879308
$217$	−13926.3	+	13926.3i	−0.295745	+	0.295745i
$218$	−19877.7	−	19877.7i	−0.418267	−	0.418267i
$219$			69604.9i			1.45128i
$220$		0			0
$221$	89395.9			1.83035
$222$	−65874.7	+	65874.7i	−1.33663	+	1.33663i
$223$	−30912.7	−	30912.7i	−0.621623	−	0.621623i	0.324323	−	0.945946i	$-0.394864\pi$
$223$	−30912.7	−	30912.7i	−0.621623	−	0.621623i	−0.945946	+	0.324323i	$0.894864\pi$
$224$			9952.72i			0.198356i
$225$		0			0
$226$	−67405.0			−1.31970
$227$	−2474.87	+	2474.87i	−0.0480288	+	0.0480288i	−0.730713	−	0.682684i	$-0.760812\pi$
$227$	−2474.87	+	2474.87i	−0.0480288	+	0.0480288i	0.682684	+	0.730713i	$0.260812\pi$
$228$	−7926.43	−	7926.43i	−0.152478	−	0.152478i
$229$			45124.3i			0.860477i	0.902715	+	0.430239i	$0.141571\pi$
$229$			45124.3i			0.860477i	−0.902715	+	0.430239i	$0.858429\pi$
$230$		0			0
$231$	12526.0			0.234741
$232$	−4070.27	+	4070.27i	−0.0756219	+	0.0756219i
$233$	17537.4	+	17537.4i	0.323038	+	0.323038i	0.849931	−	0.526894i	$-0.176643\pi$
$233$	17537.4	+	17537.4i	0.323038	+	0.323038i	−0.526894	+	0.849931i	$0.676643\pi$
$234$			12719.3i			0.232291i
$235$		0			0
$236$	10663.8			0.191464
$237$	54230.3	−	54230.3i	0.965485	−	0.965485i
$238$	26905.5	+	26905.5i	0.474994	+	0.474994i
$239$		−	64631.3i		−	1.13148i	−0.824584	−	0.565740i	$-0.808591\pi$
$239$		−	64631.3i		−	1.13148i	0.824584	−	0.565740i	$-0.191409\pi$
$240$		0			0
$241$	103691.			1.78529			0.892644	−	0.450763i	$-0.148848\pi$
$241$	103691.			1.78529			0.892644	+	0.450763i	$0.148848\pi$
$242$	24767.9	−	24767.9i	0.422920	−	0.422920i
$243$	14653.8	+	14653.8i	0.248164	+	0.248164i
$244$			4467.79i			0.0750434i
$245$		0			0
$246$	−12700.3			−0.209866
$247$	−44223.2	+	44223.2i	−0.724864	+	0.724864i
$248$	39624.0	+	39624.0i	0.644250	+	0.644250i
$249$		−	78969.1i		−	1.27367i
$250$		0			0
$251$	−22110.1			−0.350949			−0.175475	−	0.984484i	$-0.556146\pi$
$251$	−22110.1			−0.350949			−0.175475	+	0.984484i	$0.556146\pi$
$252$	−811.815	+	811.815i	−0.0127837	+	0.0127837i
$253$	11443.4	+	11443.4i	0.178778	+	0.178778i
$254$		−	87684.3i		−	1.35911i
$255$		0			0
$256$	49425.9			0.754180
$257$	−6050.54	+	6050.54i	−0.0916068	+	0.0916068i	−0.751425	−	0.659818i	$-0.770633\pi$
$257$	−6050.54	+	6050.54i	−0.0916068	+	0.0916068i	0.659818	+	0.751425i	$0.270633\pi$
$258$	−44647.4	−	44647.4i	−0.670744	−	0.670744i
$259$			46915.2i			0.699382i
$260$		0			0
$261$	−1572.52			−0.0230842
$262$	49948.1	−	49948.1i	0.727639	−	0.727639i
$263$	−58737.2	−	58737.2i	−0.849183	−	0.849183i	0.140848	−	0.990031i	$-0.455017\pi$
$263$	−58737.2	−	58737.2i	−0.849183	−	0.849183i	−0.990031	+	0.140848i	$0.955017\pi$
$264$		−	35639.8i		−	0.511361i
$265$		0			0
$266$	−26619.8			−0.376220
$267$	13459.3	−	13459.3i	0.188799	−	0.188799i
$268$	14733.1	+	14733.1i	0.205128	+	0.205128i
$269$		−	43293.1i		−	0.598293i	−0.954207	−	0.299147i	$-0.903298\pi$
$269$		−	43293.1i		−	0.598293i	0.954207	−	0.299147i	$-0.0967020\pi$
$270$		0			0
$271$	−69048.3			−0.940187			−0.470093	−	0.882617i	$-0.655780\pi$
$271$	−69048.3			−0.940187			−0.470093	+	0.882617i	$0.655780\pi$
$272$	98765.8	−	98765.8i	1.33496	−	1.33496i
$273$	−20955.9	−	20955.9i	−0.281178	−	0.281178i
$274$			152692.i			2.03384i
$275$		0			0
$276$	6862.85			0.0900920
$277$	−13133.8	+	13133.8i	−0.171171	+	0.171171i	−0.787494	−	0.616323i	$-0.788622\pi$
$277$	−13133.8	+	13133.8i	−0.171171	+	0.171171i	0.616323	+	0.787494i	$0.288622\pi$
$278$	63636.1	+	63636.1i	0.823406	+	0.823406i
$279$			15308.4i			0.196663i
$280$		0			0
$281$	−75278.8			−0.953367			−0.476683	−	0.879075i	$-0.658161\pi$
$281$	−75278.8			−0.953367			−0.476683	+	0.879075i	$0.658161\pi$
$282$	−50316.3	+	50316.3i	−0.632718	+	0.632718i
$283$	−19793.7	−	19793.7i	−0.247147	−	0.247147i	0.572652	−	0.819799i	$-0.305915\pi$
$283$	−19793.7	−	19793.7i	−0.247147	−	0.247147i	−0.819799	+	0.572652i	$0.805915\pi$
$284$		−	23035.1i		−	0.285597i
$285$		0			0
$286$	73223.8			0.895200
$287$	−4522.50	+	4522.50i	−0.0549054	+	0.0549054i
$288$	5470.24	+	5470.24i	0.0659510	+	0.0659510i
$289$		−	124348.i		−	1.48883i
$290$		0			0
$291$	−44663.0			−0.527427
$292$	−25969.9	+	25969.9i	−0.304583	+	0.304583i
$293$	−94611.0	−	94611.0i	−1.10206	−	1.10206i	−0.994162	−	0.107901i	$-0.965587\pi$
$293$	−94611.0	−	94611.0i	−1.10206	−	1.10206i	−0.107901	−	0.994162i	$-0.534413\pi$
$294$		−	12614.2i		−	0.145937i
$295$		0			0
$296$	133486.			1.52354
$297$	45622.5	−	45622.5i	0.517209	−	0.517209i
$298$	21730.2	+	21730.2i	0.244699	+	0.244699i
$299$		−	38289.3i		−	0.428287i
$300$		0			0
$301$	−31797.4			−0.350961
$302$	−98195.8	+	98195.8i	−1.07666	+	1.07666i
$303$	55071.5	+	55071.5i	0.599848	+	0.599848i
$304$			97716.9i			1.05736i
$305$		0			0
$306$	29575.8			0.315859
$307$	30023.7	−	30023.7i	0.318557	−	0.318557i	−0.529655	−	0.848213i	$-0.677679\pi$
$307$	30023.7	−	30023.7i	0.318557	−	0.318557i	0.848213	+	0.529655i	$0.177679\pi$
$308$	4673.53	+	4673.53i	0.0492655	+	0.0492655i
$309$		−	45971.5i		−	0.481473i
$310$		0			0
$311$	−26989.1			−0.279040			−0.139520	−	0.990219i	$-0.544556\pi$
$311$	−26989.1			−0.279040			−0.139520	+	0.990219i	$0.544556\pi$
$312$	−59625.0	+	59625.0i	−0.612519	+	0.612519i
$313$	−2185.91	−	2185.91i	−0.0223122	−	0.0223122i	0.695863	−	0.718175i	$-0.255022\pi$
$313$	−2185.91	−	2185.91i	−0.0223122	−	0.0223122i	−0.718175	+	0.695863i	$0.755022\pi$
$314$		−	184387.i		−	1.87013i
$315$		0			0
$316$	40467.2			0.405256
$317$	10009.8	−	10009.8i	0.0996105	−	0.0996105i	−0.655545	−	0.755156i	$-0.727561\pi$
$317$	10009.8	−	10009.8i	0.0996105	−	0.0996105i	0.755156	+	0.655545i	$0.227561\pi$
$318$	3764.77	+	3764.77i	0.0372292	+	0.0372292i
$319$			9052.82i			0.0889616i
$320$		0			0
$321$	90407.4			0.877393
$322$	11524.0	−	11524.0i	0.111145	−	0.111145i
$323$	102831.	+	102831.i	0.985639	+	0.985639i
$324$		−	22339.6i		−	0.212807i
$325$		0			0
$326$	−67837.8			−0.638317
$327$	36000.1	−	36000.1i	0.336673	−	0.336673i
$328$	12867.7	+	12867.7i	0.119606	+	0.119606i
$329$			35834.7i			0.331064i
$330$		0			0
$331$	27160.9			0.247907			0.123953	−	0.992288i	$-0.460443\pi$
$331$	27160.9			0.247907			0.123953	+	0.992288i	$0.460443\pi$
$332$	29463.8	−	29463.8i	0.267308	−	0.267308i
$333$	25785.7	+	25785.7i	0.232536	+	0.232536i
$334$			34830.2i			0.312222i
$335$		0			0
$336$	−46304.7			−0.410154
$337$	−132874.	+	132874.i	−1.16999	+	1.16999i	−0.187774	+	0.982212i	$0.560127\pi$
$337$	−132874.	+	132874.i	−1.16999	+	1.16999i	−0.982212	+	0.187774i	$0.939873\pi$
$338$	−31495.9	−	31495.9i	−0.275689	−	0.275689i
$339$		−	122076.i		−	1.06226i
$340$		0			0
$341$	88129.0			0.757897
$342$	−14630.8	+	14630.8i	−0.125088	+	0.125088i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$			90471.8i			0.764534i
$345$		0			0
$346$	194528.			1.62491
$347$	15311.9	−	15311.9i	0.127165	−	0.127165i	−0.640660	−	0.767825i	$-0.721339\pi$
$347$	15311.9	−	15311.9i	0.127165	−	0.127165i	0.767825	+	0.640660i	$0.221339\pi$
$348$	2714.59	+	2714.59i	0.0224153	+	0.0224153i
$349$			37132.2i			0.304859i	0.988314	+	0.152430i	$0.0487098\pi$
$349$			37132.2i			0.304859i	−0.988314	+	0.152430i	$0.951290\pi$
$350$		0			0
$351$	−152652.			−1.23905
$352$	31491.6	−	31491.6i	0.254161	−	0.254161i
$353$	161388.	+	161388.i	1.29515	+	1.29515i	0.931556	+	0.363597i	$0.118452\pi$
$353$	161388.	+	161388.i	1.29515	+	1.29515i	0.363597	+	0.931556i	$0.381548\pi$
$354$			91070.9i			0.726730i
$355$		0			0
$356$	10043.5			0.0792471
$357$	−48728.0	+	48728.0i	−0.382334	+	0.382334i
$358$	−148602.	−	148602.i	−1.15947	−	1.15947i
$359$			125942.i			0.977196i	0.872509	+	0.488598i	$0.162492\pi$
$359$			125942.i			0.977196i	−0.872509	+	0.488598i	$0.837508\pi$
$360$		0			0
$361$	28582.4			0.219323
$362$	98986.1	−	98986.1i	0.755365	−	0.755365i
$363$	44856.6	+	44856.6i	0.340418	+	0.340418i
$364$		−	15637.5i		−	0.118023i
$365$		0			0
$366$	−38155.8			−0.284839
$367$	9247.64	−	9247.64i	0.0686592	−	0.0686592i	−0.671943	−	0.740603i	$-0.734540\pi$
$367$	9247.64	−	9247.64i	0.0686592	−	0.0686592i	0.740603	+	0.671943i	$0.234540\pi$
$368$	−42302.5	−	42302.5i	−0.312371	−	0.312371i
$369$			4971.34i			0.0365107i
$370$		0			0
$371$	2681.23			0.0194799
$372$	26426.4	−	26426.4i	0.190965	−	0.190965i
$373$	24882.0	+	24882.0i	0.178841	+	0.178841i	0.790851	−	0.612009i	$-0.209638\pi$
$373$	24882.0	+	24882.0i	0.178841	+	0.178841i	−0.612009	+	0.790851i	$0.709638\pi$
$374$		−	170265.i		−	1.21725i
$375$		0			0
$376$	101959.			0.721191
$377$	15145.3	−	15145.3i	0.106560	−	0.106560i
$378$	−45943.8	−	45943.8i	−0.321546	−	0.321546i
$379$			95296.2i			0.663433i	0.943379	+	0.331717i	$0.107628\pi$
$379$			95296.2i			0.663433i	−0.943379	+	0.331717i	$0.892372\pi$
$380$		0			0
$381$	158803.			1.09398
$382$	208672.	−	208672.i	1.43000	−	1.43000i
$383$	−53485.3	−	53485.3i	−0.364617	−	0.364617i	0.500893	−	0.865509i	$-0.333005\pi$
$383$	−53485.3	−	53485.3i	−0.364617	−	0.364617i	−0.865509	+	0.500893i	$0.833005\pi$
$384$			161379.i			1.09442i
$385$		0			0
$386$	−277364.			−1.86155
$387$	−17476.6	+	17476.6i	−0.116690	+	0.116690i
$388$	−16664.0	−	16664.0i	−0.110692	−	0.110692i
$389$			90635.5i			0.598962i	0.954102	+	0.299481i	$0.0968135\pi$
$389$			90635.5i			0.598962i	−0.954102	+	0.299481i	$0.903187\pi$
$390$		0			0
$391$	−89032.7			−0.582366
$392$	−12780.5	+	12780.5i	−0.0831718	+	0.0831718i
$393$	90459.8	+	90459.8i	0.585694	+	0.585694i
$394$			177590.i			1.14400i
$395$		0			0
$396$	5137.35			0.0327604
$397$	80322.1	−	80322.1i	0.509629	−	0.509629i	−0.404784	−	0.914412i	$-0.632653\pi$
$397$	80322.1	−	80322.1i	0.509629	−	0.509629i	0.914412	+	0.404784i	$0.132653\pi$
$398$	−74264.9	−	74264.9i	−0.468832	−	0.468832i
$399$		−	48210.5i		−	0.302828i
$400$		0			0
$401$	−218532.			−1.35902			−0.679512	−	0.733664i	$-0.737808\pi$
$401$	−218532.			−1.35902			−0.679512	+	0.733664i	$0.737808\pi$
$402$	−125824.	+	125824.i	−0.778595	+	0.778595i
$403$	−147439.	−	147439.i	−0.907824	−	0.907824i
$404$			41094.9i			0.251782i
$405$		0			0
$406$	9116.56			0.0553069
$407$	148445.	−	148445.i	0.896144	−	0.896144i
$408$	138644.	+	138644.i	0.832876	+	0.832876i
$409$		−	148940.i		−	0.890358i	−0.895442	−	0.445179i	$-0.853140\pi$
$409$		−	148940.i		−	0.890358i	0.895442	−	0.445179i	$-0.146860\pi$
$410$		0			0
$411$	−276538.			−1.63708
$412$	17152.2	−	17152.2i	0.101048	−	0.101048i
$413$	32429.9	+	32429.9i	0.190128	+	0.190128i
$414$		−	12667.7i		−	0.0739087i
$415$		0			0
$416$	−105370.			−0.608878
$417$	−115250.	+	115250.i	−0.662779	+	0.662779i
$418$	84228.2	+	84228.2i	0.482064	+	0.482064i
$419$			23757.3i			0.135322i	0.997708	+	0.0676611i	$0.0215536\pi$
$419$			23757.3i			0.135322i	−0.997708	+	0.0676611i	$0.978446\pi$
$420$		0			0
$421$	210054.			1.18513			0.592566	−	0.805522i	$-0.298115\pi$
$421$	210054.			1.18513			0.592566	+	0.805522i	$0.298115\pi$
$422$	−5737.25	+	5737.25i	−0.0322165	+	0.0322165i
$423$	19695.6	+	19695.6i	0.110075	+	0.110075i
$424$		−	7628.79i		−	0.0424350i
$425$		0			0
$426$	196725.			1.08403
$427$	−13587.1	+	13587.1i	−0.0745197	+	0.0745197i
$428$	33731.5	+	33731.5i	0.184140	+	0.184140i
$429$			132614.i			0.720567i
$430$		0			0
$431$	−214415.			−1.15425			−0.577125	−	0.816656i	$-0.695826\pi$
$431$	−214415.			−1.15425			−0.577125	+	0.816656i	$0.695826\pi$
$432$	−168652.	+	168652.i	−0.903699	+	0.903699i
$433$	9412.58	+	9412.58i	0.0502034	+	0.0502034i	0.731763	−	0.681559i	$-0.238698\pi$
$433$	9412.58	+	9412.58i	0.0502034	+	0.0502034i	−0.681559	+	0.731763i	$0.738698\pi$
$434$		−	88749.5i		−	0.471180i
$435$		0			0
$436$	26863.7			0.141316
$437$	44043.6	−	44043.6i	0.230632	−	0.230632i
$438$	−221789.	−	221789.i	−1.15609	−	1.15609i
$439$		−	202275.i		−	1.04957i	−0.851234	−	0.524787i	$-0.824145\pi$
$439$		−	202275.i		−	1.04957i	0.851234	−	0.524787i	$-0.175855\pi$
$440$		0			0
$441$	−4937.66			−0.0253889
$442$	−284851.	+	284851.i	−1.45805	+	1.45805i
$443$	−102659.	−	102659.i	−0.523103	−	0.523103i	0.395404	−	0.918507i	$-0.370605\pi$
$443$	−102659.	−	102659.i	−0.523103	−	0.523103i	−0.918507	+	0.395404i	$0.870605\pi$
$444$		−	89025.9i		−	0.451597i
$445$		0			0
$446$	197000.			0.990369
$447$	−39355.1	+	39355.1i	−0.196964	+	0.196964i
$448$	32478.4	+	32478.4i	0.161822	+	0.161822i
$449$		−	209359.i		−	1.03848i	−0.854628	−	0.519241i	$-0.826215\pi$
$449$		−	209359.i		−	1.03848i	0.854628	−	0.519241i	$-0.173785\pi$
$450$		0			0
$451$	28619.4			0.140705
$452$	45547.1	−	45547.1i	0.222938	−	0.222938i
$453$	−177840.	−	177840.i	−0.866629	−	0.866629i
$454$		−	15771.9i		−	0.0765193i
$455$		0			0
$456$	−137171.			−0.659681
$457$	−63047.3	+	63047.3i	−0.301880	+	0.301880i	−0.841749	−	0.539869i	$-0.818474\pi$
$457$	−63047.3	+	63047.3i	−0.301880	+	0.301880i	0.539869	+	0.841749i	$0.318474\pi$
$458$	−143784.	−	143784.i	−0.685455	−	0.685455i
$459$			354956.i			1.68480i
$460$		0			0
$461$	−65395.3			−0.307712			−0.153856	−	0.988093i	$-0.549169\pi$
$461$	−65395.3			−0.307712			−0.153856	+	0.988093i	$0.549169\pi$
$462$	−39912.9	+	39912.9i	−0.186995	+	0.186995i
$463$	−268394.	−	268394.i	−1.25202	−	1.25202i	−0.954814	−	0.297203i	$-0.903946\pi$
$463$	−268394.	−	268394.i	−1.25202	−	1.25202i	−0.297203	−	0.954814i	$-0.596054\pi$
$464$		−	33465.4i		−	0.155439i
$465$		0			0
$466$	−111762.			−0.514663
$467$	−119388.	+	119388.i	−0.547429	+	0.547429i	−0.925696	−	0.378268i	$-0.876520\pi$
$467$	−119388.	+	119388.i	−0.547429	+	0.547429i	0.378268	+	0.925696i	$0.376520\pi$
$468$	−8594.73	−	8594.73i	−0.0392411	−	0.0392411i
$469$			89610.6i			0.407393i
$470$		0			0
$471$	333939.			1.50531
$472$	92271.5	−	92271.5i	0.414175	−	0.414175i
$473$	100611.	+	100611.i	0.449699	+	0.449699i
$474$			345598.i			1.53821i
$475$		0			0
$476$	−36361.4			−0.160482
$477$	1473.66	−	1473.66i	0.00647682	−	0.00647682i
$478$	205941.	+	205941.i	0.901336	+	0.901336i
$479$			58396.0i			0.254514i	0.991870	+	0.127257i	$0.0406173\pi$
$479$			58396.0i			0.254514i	−0.991870	+	0.127257i	$0.959383\pi$
$480$		0			0
$481$	−496695.			−2.14684
$482$	−330401.	+	330401.i	−1.42216	+	1.42216i
$483$	20870.8	+	20870.8i	0.0894631	+	0.0894631i
$484$			33472.4i			0.142888i
$485$		0			0
$486$	−93385.8			−0.395374
$487$	136786.	−	136786.i	0.576746	−	0.576746i	−0.357259	−	0.934005i	$-0.616289\pi$
$487$	136786.	−	136786.i	0.576746	−	0.576746i	0.934005	+	0.357259i	$0.116289\pi$
$488$	38658.8	+	38658.8i	0.162334	+	0.162334i
$489$		−	122860.i		−	0.513796i
$490$		0			0
$491$	76816.5			0.318633			0.159317	−	0.987228i	$-0.449071\pi$
$491$	76816.5			0.318633			0.159317	+	0.987228i	$0.449071\pi$
$492$	8581.85	−	8581.85i	0.0354528	−	0.0354528i
$493$	−35216.8	−	35216.8i	−0.144896	−	0.144896i
$494$		−	281826.i		−	1.15485i
$495$		0			0
$496$	−325785.			−1.32424
$497$	70052.7	−	70052.7i	0.283604	−	0.283604i
$498$	251627.	+	251627.i	1.01461	+	1.01461i
$499$		−	93103.6i		−	0.373908i	−0.982369	−	0.186954i	$-0.940138\pi$
$499$		−	93103.6i		−	0.373908i	0.982369	−	0.186954i	$-0.0598616\pi$
$500$		0			0
$501$	−63080.2			−0.251315
$502$	70451.7	−	70451.7i	0.279566	−	0.279566i
$503$	−55172.2	−	55172.2i	−0.218064	−	0.218064i	0.589618	−	0.807682i	$-0.299278\pi$
$503$	−55172.2	−	55172.2i	−0.218064	−	0.218064i	−0.807682	+	0.589618i	$0.799278\pi$
$504$			14048.9i			0.0553072i
$505$		0			0
$506$	−72926.3			−0.284828
$507$	57041.5	−	57041.5i	0.221909	−	0.221909i
$508$	59250.2	+	59250.2i	0.229595	+	0.229595i
$509$		−	336340.i		−	1.29820i	−0.760702	−	0.649102i	$-0.775145\pi$
$509$		−	336340.i		−	1.29820i	0.760702	−	0.649102i	$-0.224855\pi$
$510$		0			0
$511$	−157956.			−0.604913
$512$	66227.7	−	66227.7i	0.252639	−	0.252639i
$513$	−175593.	−	175593.i	−0.667226	−	0.667226i
$514$		−	38558.8i		−	0.145948i
$515$		0			0
$516$	60338.4			0.226618
$517$	113385.	−	113385.i	0.424205	−	0.424205i
$518$	−149491.	−	149491.i	−0.557127	−	0.557127i
$519$			352305.i			1.30793i
$520$		0			0
$521$	6117.78			0.0225382			0.0112691	−	0.999937i	$-0.496413\pi$
$521$	6117.78			0.0225382			0.0112691	+	0.999937i	$0.496413\pi$
$522$	5010.67	−	5010.67i	0.0183889	−	0.0183889i
$523$	45550.4	+	45550.4i	0.166529	+	0.166529i	0.785452	−	0.618923i	$-0.212431\pi$
$523$	45550.4	+	45550.4i	0.166529	+	0.166529i	−0.618923	+	0.785452i	$0.712431\pi$
$524$			67502.0i			0.245841i
$525$		0			0
$526$	374320.			1.35292
$527$	−342834.	+	342834.i	−1.23442	+	1.23442i
$528$	146514.	+	146514.i	0.525545	+	0.525545i
$529$		−	241707.i		−	0.863731i
$530$		0			0
$531$	35648.4			0.126430
$532$	17987.6	−	17987.6i	0.0635550	−	0.0635550i
$533$	−47880.0	−	47880.0i	−0.168539	−	0.168539i
$534$			85773.3i			0.300794i
$535$		0			0
$536$	254965.			0.887466
$537$	269130.	−	269130.i	0.933285	−	0.933285i
$538$	137949.	+	137949.i	0.476600	+	0.476600i
$539$			28425.5i			0.0978433i
$540$		0			0
$541$	450261.			1.53840			0.769201	−	0.639007i	$-0.220655\pi$
$541$	450261.			1.53840			0.769201	+	0.639007i	$0.220655\pi$
$542$	220015.	−	220015.i	0.748952	−	0.748952i
$543$	179271.	+	179271.i	0.608011	+	0.608011i
$544$			245013.i			0.827927i
$545$		0			0
$546$	133548.			0.447972
$547$	244018.	−	244018.i	0.815543	−	0.815543i	−0.169916	−	0.985459i	$-0.554350\pi$
$547$	244018.	−	244018.i	0.815543	−	0.815543i	0.985459	+	0.169916i	$0.0543495\pi$
$548$	−103178.	−	103178.i	−0.343577	−	0.343577i
$549$			14935.6i			0.0495538i
$550$		0			0
$551$	34842.7			0.114765
$552$	59382.8	−	59382.8i	0.194887	−	0.194887i
$553$	123066.	+	123066.i	0.402427	+	0.402427i
$554$		−	83698.7i		−	0.272709i
$555$		0			0
$556$	−86000.7			−0.278197
$557$	48553.9	−	48553.9i	0.156500	−	0.156500i	−0.624514	−	0.781014i	$-0.714703\pi$
$557$	48553.9	−	48553.9i	0.156500	−	0.156500i	0.781014	+	0.624514i	$0.214703\pi$
$558$	−48778.8	−	48778.8i	−0.156662	−	0.156662i
$559$		−	336641.i		−	1.07732i
$560$		0			0
$561$	308362.			0.979796
$562$	239868.	−	239868.i	0.759451	−	0.759451i
$563$	−181644.	−	181644.i	−0.573065	−	0.573065i	0.359919	−	0.932984i	$-0.382804\pi$
$563$	−181644.	−	181644.i	−0.573065	−	0.573065i	−0.932984	+	0.359919i	$0.882804\pi$
$564$		−	67999.7i		−	0.213771i
$565$		0			0
$566$	126141.			0.393753
$567$	67937.5	−	67937.5i	0.211321	−	0.211321i
$568$	−199318.	−	199318.i	−0.617804	−	0.617804i
$569$		−	18687.2i		−	0.0577191i	−0.999583	−	0.0288595i	$-0.990812\pi$
$569$		−	18687.2i		−	0.0577191i	0.999583	−	0.0288595i	$-0.00918755\pi$
$570$		0			0
$571$	518058.			1.58893			0.794467	−	0.607307i	$-0.207750\pi$
$571$	518058.			1.58893			0.794467	+	0.607307i	$0.207750\pi$
$572$	−49478.9	+	49478.9i	−0.151227	+	0.151227i
$573$	377921.	+	377921.i	1.15104	+	1.15104i
$574$		−	28820.9i		−	0.0874751i
$575$		0			0
$576$	35701.7			0.107608
$577$	−151903.	+	151903.i	−0.456262	+	0.456262i	−0.897426	−	0.441164i	$-0.854566\pi$
$577$	−151903.	+	151903.i	−0.456262	+	0.456262i	0.441164	+	0.897426i	$0.354566\pi$
$578$	396222.	+	396222.i	1.18600	+	1.18600i
$579$		−	502327.i		−	1.49841i
$580$		0			0
$581$	179206.			0.530885
$582$	142314.	−	142314.i	0.420148	−	0.420148i
$583$	−8483.72	−	8483.72i	−0.0249603	−	0.0249603i
$584$			449425.i			1.31774i
$585$		0			0
$586$	602936.			1.75580
$587$	−36664.3	+	36664.3i	−0.106406	+	0.106406i	−0.758306	−	0.651899i	$-0.773972\pi$
$587$	−36664.3	+	36664.3i	−0.106406	+	0.106406i	0.651899	+	0.758306i	$0.273972\pi$
$588$	8523.71	+	8523.71i	0.0246532	+	0.0246532i
$589$		−	339193.i		−	0.977724i
$590$		0			0
$591$	−321629.			−0.920831
$592$	−548755.	+	548755.i	−1.56580	+	1.56580i
$593$	164771.	+	164771.i	0.468567	+	0.468567i	0.901450	−	0.432883i	$-0.142504\pi$
$593$	164771.	+	164771.i	0.468567	+	0.468567i	−0.432883	+	0.901450i	$0.642504\pi$
$594$			290743.i			0.824017i
$595$		0			0
$596$	−29367.2			−0.0826741
$597$	134499.	−	134499.i	0.377374	−	0.377374i
$598$	122005.	+	122005.i	0.341173	+	0.341173i
$599$		−	452258.i		−	1.26047i	−0.776405	−	0.630235i	$-0.782959\pi$
$599$		−	452258.i		−	1.26047i	0.776405	−	0.630235i	$-0.217041\pi$
$600$		0			0
$601$	−52710.0			−0.145930			−0.0729648	−	0.997335i	$-0.523246\pi$
$601$	−52710.0			−0.145930			−0.0729648	+	0.997335i	$0.523246\pi$
$602$	101319.	−	101319.i	0.279575	−	0.279575i
$603$	49252.0	+	49252.0i	0.135453	+	0.135453i
$604$		−	132706.i		−	0.363762i
$605$		0			0
$606$	−350959.			−0.955677
$607$	−89771.2	+	89771.2i	−0.243646	+	0.243646i	−0.818357	−	0.574710i	$-0.805115\pi$
$607$	−89771.2	+	89771.2i	−0.243646	+	0.243646i	0.574710	+	0.818357i	$0.305115\pi$
$608$	−121206.	−	121206.i	−0.327880	−	0.327880i
$609$			16510.8i			0.0445178i
$610$		0			0
$611$	−379385.			−1.01624
$612$	−19985.0	+	19985.0i	−0.0533583	+	0.0533583i
$613$	101979.	+	101979.i	0.271387	+	0.271387i	0.829658	−	0.558272i	$-0.188535\pi$
$613$	101979.	+	101979.i	0.271387	+	0.271387i	−0.558272	+	0.829658i	$0.688535\pi$
$614$			191335.i			0.507525i
$615$		0			0
$616$	80878.1			0.213142
$617$	265131.	−	265131.i	0.696451	−	0.696451i	−0.267192	−	0.963643i	$-0.586096\pi$
$617$	265131.	−	265131.i	0.696451	−	0.696451i	0.963643	+	0.267192i	$0.0860958\pi$
$618$	146483.	+	146483.i	0.383541	+	0.383541i
$619$			533768.i			1.39306i	0.717526	+	0.696532i	$0.245274\pi$
$619$			533768.i			1.39306i	−0.717526	+	0.696532i	$0.754726\pi$
$620$		0			0
$621$	152032.			0.394231
$622$	85997.9	−	85997.9i	0.222283	−	0.222283i
$623$	30543.4	+	30543.4i	0.0786940	+	0.0786940i
$624$		−	490231.i		−	1.25902i
$625$		0			0
$626$	13930.3			0.0355478
$627$	−152544.	+	152544.i	−0.388025	+	0.388025i
$628$	124594.	+	124594.i	0.315921	+	0.315921i
$629$			1.15495e6i			2.91918i
$630$		0			0
$631$	68287.8			0.171508			0.0857539	−	0.996316i	$-0.472670\pi$
$631$	68287.8			0.171508			0.0857539	+	0.996316i	$0.472670\pi$
$632$	350154.	−	350154.i	0.876648	−	0.876648i
$633$	−10390.6	−	10390.6i	−0.0259319	−	0.0259319i
$634$			63790.1i			0.158699i
$635$		0			0
$636$	−5087.88			−0.0125783
$637$	47555.6	−	47555.6i	0.117199	−	0.117199i
$638$	−28845.9	−	28845.9i	−0.0708667	−	0.0708667i
$639$		−	77005.2i		−	0.188590i
$640$		0			0
$641$	222733.			0.542087			0.271043	−	0.962567i	$-0.412631\pi$
$641$	222733.			0.542087			0.271043	+	0.962567i	$0.412631\pi$
$642$	−288074.	+	288074.i	−0.698930	+	0.698930i
$643$	−231245.	−	231245.i	−0.559308	−	0.559308i	0.369802	−	0.929110i	$-0.379425\pi$
$643$	−231245.	−	231245.i	−0.559308	−	0.559308i	−0.929110	+	0.369802i	$0.879425\pi$
$644$			15574.0i			0.0375515i
$645$		0			0
$646$	−655319.			−1.57032
$647$	−456819.	+	456819.i	−1.09128	+	1.09128i	−0.0958866	+	0.995392i	$0.530569\pi$
$647$	−456819.	+	456819.i	−1.09128	+	1.09128i	−0.995392	+	0.0958866i	$0.969431\pi$
$648$	−193300.	−	193300.i	−0.460343	−	0.460343i
$649$		−	205224.i		−	0.487235i
$650$		0			0
$651$	160732.			0.379263
$652$	45839.5	−	45839.5i	0.107831	−	0.107831i
$653$	−103032.	−	103032.i	−0.241627	−	0.241627i	0.575896	−	0.817523i	$-0.304653\pi$
$653$	−103032.	−	103032.i	−0.241627	−	0.241627i	−0.817523	+	0.575896i	$0.804653\pi$
$654$			229421.i			0.536387i
$655$		0			0
$656$	−105797.			−0.245847
$657$	−86816.0	+	86816.0i	−0.201126	+	0.201126i
$658$	−114184.	−	114184.i	−0.263726	−	0.263726i
$659$			121879.i			0.280645i	0.990106	+	0.140322i	$0.0448139\pi$
$659$			121879.i			0.280645i	−0.990106	+	0.140322i	$0.955186\pi$
$660$		0			0
$661$	−463772.			−1.06145			−0.530727	−	0.847543i	$-0.678081\pi$
$661$	−463772.			−1.06145			−0.530727	+	0.847543i	$0.678081\pi$
$662$	−86545.3	+	86545.3i	−0.197482	+	0.197482i
$663$	−515887.	−	515887.i	−1.17362	−	1.17362i
$664$		−	509888.i		−	1.15648i
$665$		0			0
$666$	−164327.			−0.370476
$667$	−15083.7	+	15083.7i	−0.0339045	+	0.0339045i
$668$	−23535.6	−	23535.6i	−0.0527438	−	0.0527438i
$669$			356783.i			0.797171i
$670$		0			0
$671$	85982.3			0.190970
$672$	57435.2	−	57435.2i	0.127186	−	0.127186i
$673$	507009.	+	507009.i	1.11940	+	1.11940i	0.991829	+	0.127572i	$0.0407184\pi$
$673$	507009.	+	507009.i	1.11940	+	1.11940i	0.127572	+	0.991829i	$0.459282\pi$
$674$		−	846779.i		−	1.86402i
$675$		0			0
$676$	42564.9			0.0931448
$677$	190567.	−	190567.i	0.415786	−	0.415786i	−0.467963	−	0.883748i	$-0.655012\pi$
$677$	190567.	−	190567.i	0.415786	−	0.415786i	0.883748	+	0.467963i	$0.155012\pi$
$678$	388982.	+	388982.i	0.846194	+	0.846194i
$679$		−	101355.i		−	0.219839i
$680$		0			0
$681$	28564.1			0.0615922
$682$	−280814.	+	280814.i	−0.603740	+	0.603740i
$683$	482929.	+	482929.i	1.03524	+	1.03524i	0.999356	+	0.0358871i	$0.0114257\pi$
$683$	482929.	+	482929.i	1.03524	+	1.03524i	0.0358871	+	0.999356i	$0.488574\pi$
$684$		−	19772.8i		−	0.0422625i
$685$		0			0
$686$	28625.7			0.0608286
$687$	260404.	−	260404.i	0.551739	−	0.551739i
$688$	−371926.	−	371926.i	−0.785740	−	0.785740i
$689$			28386.3i			0.0597958i
$690$		0			0
$691$	115996.			0.242933			0.121466	−	0.992596i	$-0.461240\pi$
$691$	115996.			0.242933			0.121466	+	0.992596i	$0.461240\pi$
$692$	−131447.	+	131447.i	−0.274497	+	0.274497i
$693$	15623.3	+	15623.3i	0.0325317	+	0.0325317i
$694$			97579.3i			0.202600i
$695$		0			0
$696$	46977.5			0.0969776
$697$	−111334.	+	111334.i	−0.229172	+	0.229172i
$698$	−118318.	−	118318.i	−0.242851	−	0.242851i
$699$		−	202410.i		−	0.414264i
$700$		0			0
$701$	−868.758			−0.00176792			−0.000883961	−	1.00000i	$-0.500281\pi$
$701$	−868.758			−0.00176792			−0.000883961		1.00000i	$0.500281\pi$
$702$	486410.	−	486410.i	0.987024	−	0.987024i
$703$	−571340.	−	571340.i	−1.15607	−	1.15607i
$704$		−	205531.i		−	0.414697i
$705$		0			0
$706$	−1.02849e6			−2.06344
$707$	−124975.	+	124975.i	−0.250025	+	0.250025i
$708$	−61538.7	−	61538.7i	−0.122767	−	0.122767i
$709$			339639.i			0.675654i	0.941208	+	0.337827i	$0.109692\pi$
$709$			339639.i			0.675654i	−0.941208	+	0.337827i	$0.890308\pi$
$710$		0			0
$711$	135280.			0.267604
$712$	86904.0	−	86904.0i	0.171427	−	0.171427i
$713$	146840.	+	146840.i	0.288845	+	0.288845i
$714$		−	310534.i		−	0.609133i
$715$		0			0
$716$	200828.			0.391740
$717$	−372975.	+	372975.i	−0.725506	+	0.725506i
$718$	−401301.	−	401301.i	−0.778434	−	0.778434i
$719$			479729.i			0.927979i	0.885841	+	0.463990i	$0.153582\pi$
$719$			479729.i			0.927979i	−0.885841	+	0.463990i	$0.846418\pi$
$720$		0			0
$721$	104324.			0.200684
$722$	−91074.8	+	91074.8i	−0.174712	+	0.174712i
$723$	−598383.	−	598383.i	−1.14473	−	1.14473i
$724$			133774.i			0.255209i
$725$		0			0
$726$	−285862.			−0.542354
$727$	−253324.	+	253324.i	−0.479300	+	0.479300i	−0.904908	−	0.425608i	$-0.860060\pi$
$727$	−253324.	+	253324.i	−0.479300	+	0.479300i	0.425608	+	0.904908i	$0.360060\pi$
$728$	−135308.	−	135308.i	−0.255306	−	0.255306i
$729$		−	589335.i		−	1.10894i
$730$		0			0
$731$	−782780.			−1.46489
$732$	25782.7	−	25782.7i	0.0481179	−	0.0481179i
$733$	39917.3	+	39917.3i	0.0742939	+	0.0742939i	0.743277	−	0.668983i	$-0.233270\pi$
$733$	39917.3	+	39917.3i	0.0742939	+	0.0742939i	−0.668983	+	0.743277i	$0.733270\pi$
$734$			58933.3i			0.109388i
$735$		0			0
$736$	104942.			0.193729
$737$	283538.	−	283538.i	0.522008	−	0.522008i
$738$	−15840.6	−	15840.6i	−0.0290844	−	0.0290844i
$739$			838842.i			1.53600i	0.640450	+	0.768000i	$0.278748\pi$
$739$			838842.i			1.53600i	−0.640450	+	0.768000i	$0.721252\pi$
$740$		0			0
$741$	510408.			0.929568
$742$	−8543.46	+	8543.46i	−0.0155176	+	0.0155176i
$743$	−411846.	−	411846.i	−0.746031	−	0.746031i	0.227701	−	0.973731i	$-0.426879\pi$
$743$	−411846.	−	411846.i	−0.746031	−	0.746031i	−0.973731	+	0.227701i	$0.926879\pi$
$744$		−	457325.i		−	0.826188i
$745$		0			0
$746$	−158568.			−0.284930
$747$	98495.7	−	98495.7i	0.176513	−	0.176513i
$748$	115052.	+	115052.i	0.205631	+	0.205631i
$749$			205163.i			0.365709i
$750$		0			0
$751$	223384.			0.396070			0.198035	−	0.980195i	$-0.436544\pi$
$751$	223384.			0.396070			0.198035	+	0.980195i	$0.436544\pi$
$752$	−419149.	+	419149.i	−0.741196	+	0.741196i
$753$	127593.	+	127593.i	0.225029	+	0.225029i
$754$			96517.6i			0.169771i
$755$		0			0
$756$	62090.4			0.108638
$757$	−571626.	+	571626.i	−0.997517	+	0.997517i	−0.999997	−	0.00248013i	$-0.999211\pi$
$757$	−571626.	+	571626.i	−0.997517	+	0.997517i	0.00248013	+	0.999997i	$0.499211\pi$
$758$	−303652.	−	303652.i	−0.528490	−	0.528490i
$759$		−	132075.i		−	0.229265i
$760$		0			0
$761$	−142806.			−0.246592			−0.123296	−	0.992370i	$-0.539346\pi$
$761$	−142806.			−0.246592			−0.123296	+	0.992370i	$0.539346\pi$
$762$	−506009.	+	506009.i	−0.871462	+	0.871462i
$763$	81695.7	+	81695.7i	0.140330	+	0.140330i
$764$			282009.i			0.483143i
$765$		0			0
$766$	340851.			0.580907
$767$	−343337.	+	343337.i	−0.583620	+	0.583620i
$768$	−285228.	−	285228.i	−0.483581	−	0.483581i
$769$		−	736553.i		−	1.24552i	−0.782412	−	0.622761i	$-0.786011\pi$
$769$		−	736553.i		−	1.24552i	0.782412	−	0.622761i	$-0.213989\pi$
$770$		0			0
$771$	69833.0			0.117477
$772$	187421.	−	187421.i	0.314473	−	0.314473i
$773$	17851.7	+	17851.7i	0.0298759	+	0.0298759i	0.721887	−	0.692011i	$-0.243275\pi$
$773$	17851.7	+	17851.7i	0.0298759	+	0.0298759i	−0.692011	+	0.721887i	$0.743275\pi$
$774$		−	111375.i		−	0.185911i
$775$		0			0
$776$	−288380.			−0.478897
$777$	270739.	−	270739.i	0.448444	−	0.448444i
$778$	−288801.	−	288801.i	−0.477132	−	0.477132i
$779$		−	110151.i		−	0.181516i
$780$		0			0
$781$	−443310.			−0.726785
$782$	283693.	−	283693.i	0.463912	−	0.463912i
$783$	60135.9	+	60135.9i	0.0980868	+	0.0980868i
$784$		−	105080.i		−	0.170958i
$785$		0			0
$786$	−576481.			−0.933126
$787$	406163.	−	406163.i	0.655770	−	0.655770i	−0.298607	−	0.954376i	$-0.596522\pi$
$787$	406163.	−	406163.i	0.655770	−	0.655770i	0.954376	+	0.298607i	$0.0965219\pi$
$788$	−120001.	−	120001.i	−0.193256	−	0.193256i
$789$			677922.i			1.08899i
$790$		0			0
$791$	277029.			0.442763
$792$	44452.4	−	44452.4i	0.0708672	−	0.0708672i
$793$	−143847.	−	143847.i	−0.228747	−	0.228747i
$794$			511876.i			0.811939i
$795$		0			0
$796$	100365.			0.158400
$797$	−145600.	+	145600.i	−0.229216	+	0.229216i	−0.812365	−	0.583149i	$-0.801820\pi$
$797$	−145600.	+	145600.i	−0.229216	+	0.229216i	0.583149	+	0.812365i	$0.301820\pi$
$798$	153618.	+	153618.i	0.241232	+	0.241232i
$799$			882170.i			1.38184i
$800$		0			0
$801$	33574.7			0.0523296
$802$	696331.	−	696331.i	1.08260	−	1.08260i
$803$	499790.	+	499790.i	0.775098	+	0.775098i
$804$		−	170044.i		−	0.263057i
$805$		0			0
$806$	939597.			1.44634
$807$	−249836.	+	249836.i	−0.383626	+	0.383626i
$808$	355585.	+	355585.i	0.544655	+	0.544655i
$809$			446624.i			0.682409i	0.939989	+	0.341205i	$0.110835\pi$
$809$			446624.i			0.682409i	−0.939989	+	0.341205i	$0.889165\pi$
$810$		0			0
$811$	−1.10605e6			−1.68164			−0.840821	−	0.541313i	$-0.817927\pi$
$811$	−1.10605e6			−1.68164			−0.840821	+	0.541313i	$0.817927\pi$
$812$	−6160.26	+	6160.26i	−0.00934302	+	0.00934302i
$813$	398464.	+	398464.i	0.602849	+	0.602849i
$814$			946011.i			1.42773i
$815$		0			0
$816$	−1.13992e6			−1.71196
$817$	387233.	−	387233.i	0.580134	−	0.580134i
$818$	474582.	+	474582.i	0.709258	+	0.709258i
$819$		−	52275.3i		−	0.0779343i
$820$		0			0
$821$	551335.			0.817954			0.408977	−	0.912545i	$-0.365886\pi$
$821$	551335.			0.817954			0.408977	+	0.912545i	$0.365886\pi$
$822$	881158.	−	881158.i	1.30410	−	1.30410i
$823$	435505.	+	435505.i	0.642975	+	0.642975i	0.951286	−	0.308311i	$-0.0997637\pi$
$823$	435505.	+	435505.i	0.642975	+	0.642975i	−0.308311	+	0.951286i	$0.599764\pi$
$824$		−	296829.i		−	0.437171i
$825$		0			0
$826$	−206669.			−0.302911
$827$	634581.	−	634581.i	0.927847	−	0.927847i	−0.0697197	−	0.997567i	$-0.522210\pi$
$827$	634581.	−	634581.i	0.927847	−	0.927847i	0.997567	+	0.0697197i	$0.0222105\pi$
$828$	8559.82	+	8559.82i	0.0124854	+	0.0124854i
$829$		−	471650.i		−	0.686296i	−0.939281	−	0.343148i	$-0.888507\pi$
$829$		−	471650.i		−	0.686296i	0.939281	−	0.343148i	$-0.111493\pi$
$830$		0			0
$831$	151585.			0.219510
$832$	−343851.	+	343851.i	−0.496733	+	0.496733i
$833$	−110579.	−	110579.i	−0.159362	−	0.159362i
$834$		−	734464.i		−	1.05594i
$835$		0			0
$836$	−113830.			−0.162871
$837$	585422.	−	585422.i	0.835637	−	0.835637i
$838$	−75700.1	−	75700.1i	−0.107797	−	0.107797i
$839$			476036.i			0.676263i	0.941099	+	0.338131i	$0.109795\pi$
$839$			476036.i			0.676263i	−0.941099	+	0.338131i	$0.890205\pi$
$840$		0			0
$841$	695348.			0.983129
$842$	−669316.	+	669316.i	−0.944076	+	0.944076i
$843$	434420.	+	434420.i	0.611300	+	0.611300i
$844$		−	7753.58i		−	0.0108847i
$845$		0			0
$846$	−125516.			−0.175371
$847$	−101794.	+	101794.i	−0.141891	+	0.141891i
$848$	31361.6	+	31361.6i	0.0436121	+	0.0436121i
$849$			228452.i			0.316941i
$850$		0			0
$851$	494677.			0.683065
$852$	−132931.	+	132931.i	−0.183125	+	0.183125i
$853$	305921.	+	305921.i	0.420447	+	0.420447i	0.885358	−	0.464911i	$-0.153914\pi$
$853$	305921.	+	305921.i	0.420447	+	0.420447i	−0.464911	+	0.885358i	$0.653914\pi$
$854$		−	86587.7i		−	0.118725i
$855$		0			0
$856$	583743.			0.796661
$857$	−983217.	+	983217.i	−1.33871	+	1.33871i	−0.441407	+	0.897307i	$0.645520\pi$
$857$	−983217.	+	983217.i	−1.33871	+	1.33871i	−0.897307	+	0.441407i	$0.854480\pi$
$858$	−422560.	−	422560.i	−0.574003	−	0.574003i
$859$			621201.i			0.841871i	0.907091	+	0.420936i	$0.138298\pi$
$859$			621201.i			0.841871i	−0.907091	+	0.420936i	$0.861702\pi$
$860$		0			0
$861$	52197.0			0.0704107
$862$	683210.	−	683210.i	0.919475	−	0.919475i
$863$	377282.	+	377282.i	0.506576	+	0.506576i	0.913474	−	0.406898i	$-0.133390\pi$
$863$	377282.	+	377282.i	0.506576	+	0.506576i	−0.406898	+	0.913474i	$0.633390\pi$
$864$		−	418383.i		−	0.560463i
$865$		0			0
$866$	−59984.4			−0.0799839
$867$	−717590.	+	717590.i	−0.954636	+	0.954636i
$868$	59970.0	+	59970.0i	0.0795966	+	0.0795966i
$869$		−	778789.i		−	1.03129i
$870$		0			0
$871$	−948713.			−1.25054
$872$	232446.	−	232446.i	0.305695	−	0.305695i
$873$	−55706.8	−	55706.8i	−0.0730937	−	0.0730937i
$874$			280681.i			0.367442i
$875$		0			0
$876$	299735.			0.390597
$877$	−507278.	+	507278.i	−0.659548	+	0.659548i	−0.955273	−	0.295725i	$-0.904439\pi$
$877$	−507278.	+	507278.i	−0.659548	+	0.659548i	0.295725	+	0.955273i	$0.404439\pi$
$878$	644528.	+	644528.i	0.836089	+	0.836089i
$879$			1.09196e6i			1.41329i
$880$		0			0
$881$	859437.			1.10729			0.553646	−	0.832752i	$-0.313236\pi$
$881$	859437.			1.10729			0.553646	+	0.832752i	$0.313236\pi$
$882$	15733.3	−	15733.3i	0.0202248	−	0.0202248i
$883$	95336.1	+	95336.1i	0.122275	+	0.122275i	0.765596	−	0.643322i	$-0.222444\pi$
$883$	95336.1	+	95336.1i	0.122275	+	0.122275i	−0.643322	+	0.765596i	$0.722444\pi$
$884$		−	384960.i		−	0.492619i
$885$		0			0
$886$	654221.			0.833407
$887$	−207677.	+	207677.i	−0.263962	+	0.263962i	−0.826662	−	0.562699i	$-0.809763\pi$
$887$	−207677.	+	207677.i	−0.263962	+	0.263962i	0.562699	+	0.826662i	$0.309763\pi$
$888$	−770323.	−	770323.i	−0.976892	−	0.976892i
$889$			360374.i			0.455985i
$890$		0			0
$891$	−429925.			−0.541548
$892$	−133117.	+	133117.i	−0.167304	+	0.167304i
$893$	−436400.	−	436400.i	−0.547246	−	0.547246i
$894$		−	250802.i		−	0.313802i
$895$		0			0
$896$	−366221.			−0.456171
$897$	−220960.	+	220960.i	−0.274618	+	0.274618i
$898$	667100.	+	667100.i	0.827253	+	0.827253i
$899$			116164.i			0.143732i
$900$		0			0
$901$	66005.8			0.0813078
$902$	−91192.9	+	91192.9i	−0.112085	+	0.112085i
$903$	183497.	+	183497.i	0.225036	+	0.225036i
$904$		−	788219.i		−	0.964517i
$905$		0			0
$906$	1.13334e6			1.38071
$907$	−230370.	+	230370.i	−0.280034	+	0.280034i	−0.833123	−	0.553088i	$-0.813449\pi$
$907$	−230370.	+	230370.i	−0.280034	+	0.280034i	0.553088	+	0.833123i	$0.313449\pi$
$908$	10657.4	+	10657.4i	0.0129265	+	0.0129265i
$909$			137378.i			0.166260i
$910$		0			0
$911$	−1.25046e6			−1.50672			−0.753362	−	0.657606i	$-0.771569\pi$
$911$	−1.25046e6			−1.50672			−0.753362	+	0.657606i	$0.771569\pi$
$912$	563905.	−	563905.i	0.677980	−	0.677980i
$913$	−567029.	−	567029.i	−0.680242	−	0.680242i
$914$		−	401788.i		−	0.480955i
$915$		0			0
$916$	194316.			0.231589
$917$	−205282.	+	205282.i	−0.244125	+	0.244125i
$918$	−1.13103e6	−	1.13103e6i	−1.34211	−	1.34211i
$919$		−	345006.i		−	0.408503i	−0.978918	−	0.204252i	$-0.934524\pi$
$919$		−	345006.i		−	0.408503i	0.978918	−	0.204252i	$-0.0654761\pi$
$920$		0			0
$921$	−346522.			−0.408519
$922$	208375.	−	208375.i	0.245123	−	0.245123i
$923$	741653.	+	741653.i	0.870557	+	0.870557i
$924$		−	53940.1i		−	0.0631782i
$925$		0			0
$926$	1.71042e6			1.99471
$927$	57338.9	−	57338.9i	0.0667251	−	0.0667251i
$928$	41509.6	+	41509.6i	0.0482007	+	0.0482007i
$929$		−	768509.i		−	0.890466i	−0.895415	−	0.445233i	$-0.853121\pi$
$929$		−	768509.i		−	0.890466i	0.895415	−	0.445233i	$-0.146879\pi$
$930$		0			0
$931$	109405.			0.126223
$932$	75520.2	−	75520.2i	0.0869423	−	0.0869423i
$933$	155749.	+	155749.i	0.178921	+	0.178921i
$934$		−	760836.i		−	0.872162i
$935$		0			0
$936$	−148737.			−0.169772
$937$	616858.	−	616858.i	0.702596	−	0.702596i	−0.262371	−	0.964967i	$-0.584504\pi$
$937$	616858.	−	616858.i	0.702596	−	0.702596i	0.964967	+	0.262371i	$0.0845043\pi$
$938$	−285535.	−	285535.i	−0.324529	−	0.324529i
$939$			25228.9i			0.0286132i
$940$		0			0
$941$	1.51049e6			1.70584			0.852922	−	0.522039i	$-0.174828\pi$
$941$	1.51049e6			1.70584			0.852922	+	0.522039i	$0.174828\pi$
$942$	−1.06406e6	+	1.06406e6i	−1.19913	+	1.19913i
$943$	47685.5	+	47685.5i	0.0536244	+	0.0536244i
$944$			758647.i			0.851326i
$945$		0			0
$946$	−641171.			−0.716459
$947$	1.17580e6	−	1.17580e6i	1.31109	−	1.31109i	0.390485	−	0.920609i	$-0.372307\pi$
$947$	1.17580e6	−	1.17580e6i	1.31109	−	1.31109i	0.920609	−	0.390485i	$-0.127693\pi$
$948$	−233529.	−	233529.i	−0.259850	−	0.259850i
$949$		−	1.67229e6i		−	1.85686i
$950$		0			0
$951$	−115529.			−0.127741
$952$	−314627.	+	314627.i	−0.347154	+	0.347154i
$953$	171350.	+	171350.i	0.188668	+	0.188668i	0.795120	−	0.606452i	$-0.207408\pi$
$953$	171350.	+	171350.i	0.188668	+	0.188668i	−0.606452	+	0.795120i	$0.707408\pi$
$954$			9391.36i			0.0103189i
$955$		0			0
$956$	−278318.			−0.304526
$957$	52242.1	−	52242.1i	0.0570423	−	0.0570423i
$958$	−186073.	−	186073.i	−0.202746	−	0.202746i
$959$		−	627552.i		−	0.682358i
$960$		0			0
$961$	207337.			0.224507
$962$	1.58267e6	−	1.58267e6i	1.71017	−	1.71017i
$963$	112762.	+	112762.i	0.121594	+	0.121594i
$964$		−	446519.i		−	0.480492i
$965$		0			0
$966$	−133005.			−0.142533
$967$	−330131.	+	330131.i	−0.353047	+	0.353047i	−0.861242	−	0.508195i	$-0.830313\pi$
$967$	−330131.	+	330131.i	−0.353047	+	0.353047i	0.508195	+	0.861242i	$0.330313\pi$
$968$	289630.	+	289630.i	0.309096	+	0.309096i
$969$		−	1.18683e6i		−	1.26399i
$970$		0			0
$971$	657629.			0.697497			0.348749	−	0.937216i	$-0.386607\pi$
$971$	657629.			0.697497			0.348749	+	0.937216i	$0.386607\pi$
$972$	63102.9	−	63102.9i	0.0667908	−	0.0667908i
$973$	−261539.	−	261539.i	−0.276255	−	0.276255i
$974$			871710.i			0.918870i
$975$		0			0
$976$	−317849.			−0.333673
$977$	−361872.	+	361872.i	−0.379110	+	0.379110i	−0.870781	−	0.491671i	$-0.836386\pi$
$977$	−361872.	+	361872.i	−0.379110	+	0.379110i	0.491671	+	0.870781i	$0.336386\pi$
$978$	391479.	+	391479.i	0.409290	+	0.409290i
$979$		−	193286.i		−	0.201667i
$980$		0			0
$981$	89803.7			0.0933160
$982$	−244768.	+	244768.i	−0.253823	+	0.253823i
$983$	−867909.	−	867909.i	−0.898188	−	0.898188i	0.0970877	−	0.995276i	$-0.469047\pi$
$983$	−867909.	−	867909.i	−0.898188	−	0.898188i	−0.995276	+	0.0970877i	$0.969047\pi$
$984$		−	148514.i		−	0.153383i
$985$		0			0
$986$	224429.			0.230848
$987$	206795.	−	206795.i	0.212279	−	0.212279i
$988$	190436.	+	190436.i	0.195090	+	0.195090i
$989$			335273.i			0.342773i
$990$		0			0
$991$	−1.08310e6			−1.10286			−0.551432	−	0.834220i	$-0.685918\pi$
$991$	−1.08310e6			−1.10286			−0.551432	+	0.834220i	$0.685918\pi$
$992$	404095.	−	404095.i	0.410639	−	0.410639i
$993$	−156740.	−	156740.i	−0.158958	−	0.158958i
$994$			446432.i			0.451837i
$995$		0			0
$996$	−340060.			−0.342797
$997$	−36094.4	+	36094.4i	−0.0363119	+	0.0363119i	−0.725030	−	0.688718i	$-0.758174\pi$
$997$	−36094.4	+	36094.4i	−0.0363119	+	0.0363119i	0.688718	+	0.725030i	$0.258174\pi$
$998$	296665.	+	296665.i	0.297855	+	0.297855i
$999$		−	1.97218e6i		−	1.97613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.g.c.43.4		24
5.2	odd	4	inner	175.5.g.c.57.4		24
5.3	odd	4		35.5.g.a.22.9	yes	24
5.4	even	2		35.5.g.a.8.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.9	✓	24	5.4	even	2
35.5.g.a.22.9	yes	24	5.3	odd	4
175.5.g.c.43.4		24	1.1	even	1	trivial
175.5.g.c.57.4		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)

\(f(q)\)	\(=\)	\(q+(-3.18640 + 3.18640i) q^{2} +(-5.77081 - 5.77081i) q^{3} -4.30624i q^{4} +36.7762 q^{6} +(13.0958 - 13.0958i) q^{7} +(-37.2610 - 37.2610i) q^{8} -14.3955i q^{9} +O(q^{10})\)	\(q+(-3.18640 + 3.18640i) q^{2} +(-5.77081 - 5.77081i) q^{3} -4.30624i q^{4} +36.7762 q^{6} +(13.0958 - 13.0958i) q^{7} +(-37.2610 - 37.2610i) q^{8} -14.3955i q^{9} -82.8733 q^{11} +(-24.8505 + 24.8505i) q^{12} +(138.646 + 138.646i) q^{13} +83.4568i q^{14} +306.356 q^{16} +(322.389 - 322.389i) q^{17} +(45.8698 + 45.8698i) q^{18} +318.965i q^{19} -151.147 q^{21} +(264.067 - 264.067i) q^{22} +(-138.083 - 138.083i) q^{23} +430.052i q^{24} -883.563 q^{26} +(-550.509 + 550.509i) q^{27} +(-56.3936 - 56.3936i) q^{28} -109.237i q^{29} -1063.42 q^{31} +(-379.997 + 379.997i) q^{32} +(478.246 + 478.246i) q^{33} +2054.52i q^{34} -61.9904 q^{36} +(-1791.23 + 1791.23i) q^{37} +(-1016.35 - 1016.35i) q^{38} -1600.20i q^{39} -345.340 q^{41} +(481.613 - 481.613i) q^{42} +(-1214.03 - 1214.03i) q^{43} +356.872i q^{44} +879.973 q^{46} +(-1368.18 + 1368.18i) q^{47} +(-1767.92 - 1767.92i) q^{48} -343.000i q^{49} -3720.89 q^{51} +(597.043 - 597.043i) q^{52} +(102.370 + 102.370i) q^{53} -3508.28i q^{54} -975.924 q^{56} +(1840.69 - 1840.69i) q^{57} +(348.072 + 348.072i) q^{58} +2476.36i q^{59} -1037.52 q^{61} +(3388.47 - 3388.47i) q^{62} +(-188.521 - 188.521i) q^{63} +2480.06i q^{64} -3047.76 q^{66} +(-3421.35 + 3421.35i) q^{67} +(-1388.28 - 1388.28i) q^{68} +1593.70i q^{69} +5349.25 q^{71} +(-536.390 + 536.390i) q^{72} +(-6030.77 - 6030.77i) q^{73} -11415.1i q^{74} +1373.54 q^{76} +(-1085.29 + 1085.29i) q^{77} +(5098.87 + 5098.87i) q^{78} +9397.35i q^{79} +5187.73 q^{81} +(1100.39 - 1100.39i) q^{82} +(6842.12 + 6842.12i) q^{83} +650.874i q^{84} +7736.76 q^{86} +(-630.385 + 630.385i) q^{87} +(3087.94 + 3087.94i) q^{88} +2332.31i q^{89} +3631.36 q^{91} +(-594.617 + 594.617i) q^{92} +(6136.78 + 6136.78i) q^{93} -8719.11i q^{94} +4385.78 q^{96} +(3869.74 - 3869.74i) q^{97} +(1092.93 + 1092.93i) q^{98} +1193.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 24 * q - 20 * q^3 + 72 * q^6	\( 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) \) 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Introduction

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