LMFDB - Embedded newform 35.5.g.a.8.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, 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("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.6
Character	$\chi$	$=$	35.8
Dual form			35.5.g.a.22.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0151985 + 0.0151985i) q^{2} +(8.40408 + 8.40408i) q^{3} +15.9995i q^{4} +(-24.2998 - 5.87527i) q^{5} -0.255459 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-0.486345 - 0.486345i) q^{8} +60.2572i q^{9} +O(q^{10})$	\(q+(-0.0151985 + 0.0151985i) q^{2} +(8.40408 + 8.40408i) q^{3} +15.9995i q^{4} +(-24.2998 - 5.87527i) q^{5} -0.255459 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-0.486345 - 0.486345i) q^{8} +60.2572i q^{9} +(0.458616 - 0.280025i) q^{10} +178.541 q^{11} +(-134.461 + 134.461i) q^{12} +(130.151 + 130.151i) q^{13} -0.398073i q^{14} +(-154.841 - 253.594i) q^{15} -255.978 q^{16} +(219.300 - 219.300i) q^{17} +(-0.915819 - 0.915819i) q^{18} -255.173i q^{19} +(94.0016 - 388.786i) q^{20} -220.116 q^{21} +(-2.71356 + 2.71356i) q^{22} +(-54.1585 - 54.1585i) q^{23} -8.17456i q^{24} +(555.962 + 285.536i) q^{25} -3.95620 q^{26} +(174.324 - 174.324i) q^{27} +(-209.527 - 209.527i) q^{28} +438.959i q^{29} +(6.20760 + 1.50089i) q^{30} -1449.39 q^{31} +(11.6720 - 11.6720i) q^{32} +(1500.48 + 1500.48i) q^{33} +6.66605i q^{34} +(395.167 - 241.284i) q^{35} -964.087 q^{36} +(914.326 - 914.326i) q^{37} +(3.87825 + 3.87825i) q^{38} +2187.60i q^{39} +(8.96069 + 14.6755i) q^{40} -1734.82 q^{41} +(3.34544 - 3.34544i) q^{42} +(-103.893 - 103.893i) q^{43} +2856.58i q^{44} +(354.027 - 1464.24i) q^{45} +1.64625 q^{46} +(1422.27 - 1422.27i) q^{47} +(-2151.26 - 2151.26i) q^{48} -343.000i q^{49} +(-12.7895 + 4.11008i) q^{50} +3686.03 q^{51} +(-2082.36 + 2082.36i) q^{52} +(3305.54 + 3305.54i) q^{53} +5.29893i q^{54} +(-4338.52 - 1048.98i) q^{55} +12.7381 q^{56} +(2144.50 - 2144.50i) q^{57} +(-6.67152 - 6.67152i) q^{58} -4661.12i q^{59} +(4057.39 - 2477.39i) q^{60} -3974.31 q^{61} +(22.0285 - 22.0285i) q^{62} +(-789.116 - 789.116i) q^{63} -4095.29i q^{64} +(-2397.97 - 3927.32i) q^{65} -45.6100 q^{66} +(-3729.40 + 3729.40i) q^{67} +(3508.69 + 3508.69i) q^{68} -910.305i q^{69} +(-2.33878 + 9.67310i) q^{70} -1249.55 q^{71} +(29.3058 - 29.3058i) q^{72} +(-3437.16 - 3437.16i) q^{73} +27.7928i q^{74} +(2272.69 + 7072.02i) q^{75} +4082.66 q^{76} +(-2338.14 + 2338.14i) q^{77} +(-33.2482 - 33.2482i) q^{78} +11135.9i q^{79} +(6220.21 + 1503.94i) q^{80} +7810.90 q^{81} +(26.3666 - 26.3666i) q^{82} +(3632.77 + 3632.77i) q^{83} -3521.76i q^{84} +(-6617.39 + 4040.50i) q^{85} +3.15802 q^{86} +(-3689.05 + 3689.05i) q^{87} +(-86.8327 - 86.8327i) q^{88} -8157.71i q^{89} +(16.8736 + 27.6349i) q^{90} -3408.86 q^{91} +(866.511 - 866.511i) q^{92} +(-12180.8 - 12180.8i) q^{93} +43.2326i q^{94} +(-1499.21 + 6200.67i) q^{95} +196.185 q^{96} +(4381.16 - 4381.16i) q^{97} +(5.21308 + 5.21308i) q^{98} +10758.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.0151985	+	0.0151985i	−0.00379962	+	0.00379962i	−0.709004	−	0.705204i	$-0.750855\pi$
$2$	−0.0151985	+	0.0151985i	−0.00379962	+	0.00379962i	0.705204	+	0.709004i	$0.250855\pi$
$3$	8.40408	+	8.40408i	0.933787	+	0.933787i	0.997940	−	0.0641531i	$-0.0204346\pi$
$3$	8.40408	+	8.40408i	0.933787	+	0.933787i	−0.0641531	+	0.997940i	$0.520435\pi$
$4$			15.9995i			0.999971i
$5$	−24.2998	−	5.87527i	−0.971993	−	0.235011i
$5$	−24.2998	−	5.87527i	−0.971993	−	0.235011i
$6$	−0.255459			−0.00709608
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$8$	−0.486345	−	0.486345i	−0.00759914	−	0.00759914i
$9$			60.2572i			0.743916i
$10$	0.458616	−	0.280025i	0.00458616	−	0.00280025i
$11$	178.541			1.47555			0.737774	−	0.675048i	$-0.235877\pi$
$11$	178.541			1.47555			0.737774	+	0.675048i	$0.235877\pi$
$12$	−134.461	+	134.461i	−0.933760	+	0.933760i
$13$	130.151	+	130.151i	0.770125	+	0.770125i	0.978128	−	0.208004i	$-0.0666965\pi$
$13$	130.151	+	130.151i	0.770125	+	0.770125i	−0.208004	+	0.978128i	$0.566697\pi$
$14$		−	0.398073i		−	0.00203098i
$15$	−154.841	−	253.594i	−0.688184	−	1.12708i
$16$	−255.978			−0.999913
$17$	219.300	−	219.300i	0.758823	−	0.758823i	−0.217285	−	0.976108i	$-0.569720\pi$
$17$	219.300	−	219.300i	0.758823	−	0.758823i	0.976108	+	0.217285i	$0.0697203\pi$
$18$	−0.915819	−	0.915819i	−0.00282660	−	0.00282660i
$19$		−	255.173i		−	0.706851i	−0.935463	−	0.353426i	$-0.885017\pi$
$19$		−	255.173i		−	0.706851i	0.935463	−	0.353426i	$-0.114983\pi$
$20$	94.0016	−	388.786i	0.235004	−	0.971965i
$21$	−220.116			−0.499130
$22$	−2.71356	+	2.71356i	−0.00560653	+	0.00560653i
$23$	−54.1585	−	54.1585i	−0.102379	−	0.102379i	0.654062	−	0.756441i	$-0.273064\pi$
$23$	−54.1585	−	54.1585i	−0.102379	−	0.102379i	−0.756441	+	0.654062i	$0.773064\pi$
$24$		−	8.17456i		−	0.0141920i
$25$	555.962	+	285.536i	0.889540	+	0.456857i
$26$	−3.95620			−0.00585237
$27$	174.324	−	174.324i	0.239128	−	0.239128i
$28$	−209.527	−	209.527i	−0.267254	−	0.267254i
$29$			438.959i			0.521949i	0.965346	+	0.260975i	$0.0840439\pi$
$29$			438.959i			0.521949i	−0.965346	+	0.260975i	$0.915956\pi$
$30$	6.20760	+	1.50089i	0.00689734	+	0.00166765i
$31$	−1449.39			−1.50821			−0.754103	−	0.656757i	$-0.771928\pi$
$31$	−1449.39			−1.50821			−0.754103	+	0.656757i	$0.771928\pi$
$32$	11.6720	−	11.6720i	0.0113984	−	0.0113984i
$33$	1500.48	+	1500.48i	1.37785	+	1.37785i
$34$			6.66605i			0.00576648i
$35$	395.167	−	241.284i	0.322585	−	0.196967i
$36$	−964.087			−0.743895
$37$	914.326	−	914.326i	0.667879	−	0.667879i	−0.289346	−	0.957225i	$-0.593438\pi$
$37$	914.326	−	914.326i	0.667879	−	0.667879i	0.957225	+	0.289346i	$0.0934377\pi$
$38$	3.87825	+	3.87825i	0.00268577	+	0.00268577i
$39$			2187.60i			1.43826i
$40$	8.96069	+	14.6755i	0.00560043	+	0.00917219i
$41$	−1734.82			−1.03202			−0.516008	−	0.856584i	$-0.672582\pi$
$41$	−1734.82			−1.03202			−0.516008	+	0.856584i	$0.672582\pi$
$42$	3.34544	−	3.34544i	0.00189651	−	0.00189651i
$43$	−103.893	−	103.893i	−0.0561885	−	0.0561885i	0.678454	−	0.734643i	$-0.262650\pi$
$43$	−103.893	−	103.893i	−0.0561885	−	0.0561885i	−0.734643	+	0.678454i	$0.762650\pi$
$44$			2856.58i			1.47551i
$45$	354.027	−	1464.24i	0.174828	−	0.723081i
$46$	1.64625			0.000778003
$47$	1422.27	−	1422.27i	0.643851	−	0.643851i	−0.307649	−	0.951500i	$-0.599542\pi$
$47$	1422.27	−	1422.27i	0.643851	−	0.643851i	0.951500	+	0.307649i	$0.0995423\pi$
$48$	−2151.26	−	2151.26i	−0.933706	−	0.933706i
$49$		−	343.000i		−	0.142857i
$50$	−12.7895	+	4.11008i	−0.00511580	+	0.00164403i
$51$	3686.03			1.41716
$52$	−2082.36	+	2082.36i	−0.770102	+	0.770102i
$53$	3305.54	+	3305.54i	1.17677	+	1.17677i	0.980563	+	0.196204i	$0.0628614\pi$
$53$	3305.54	+	3305.54i	1.17677	+	1.17677i	0.196204	+	0.980563i	$0.437139\pi$
$54$			5.29893i			0.00181719i
$55$	−4338.52	−	1048.98i	−1.43422	−	0.346770i
$56$	12.7381			0.00406191
$57$	2144.50	−	2144.50i	0.660049	−	0.660049i
$58$	−6.67152	−	6.67152i	−0.00198321	−	0.00198321i
$59$		−	4661.12i		−	1.33902i	−0.742804	−	0.669509i	$-0.766505\pi$
$59$		−	4661.12i		−	1.33902i	0.742804	−	0.669509i	$-0.233495\pi$
$60$	4057.39	−	2477.39i	1.12705	−	0.688164i
$61$	−3974.31			−1.06808			−0.534038	−	0.845460i	$-0.679326\pi$
$61$	−3974.31			−1.06808			−0.534038	+	0.845460i	$0.679326\pi$
$62$	22.0285	−	22.0285i	0.00573061	−	0.00573061i
$63$	−789.116	−	789.116i	−0.198820	−	0.198820i
$64$		−	4095.29i		−	0.999827i
$65$	−2397.97	−	3927.32i	−0.567568	−	0.929543i
$66$	−45.6100			−0.0104706
$67$	−3729.40	+	3729.40i	−0.830786	+	0.830786i	−0.987624	−	0.156838i	$-0.949870\pi$
$67$	−3729.40	+	3729.40i	−0.830786	+	0.830786i	0.156838	+	0.987624i	$0.449870\pi$
$68$	3508.69	+	3508.69i	0.758801	+	0.758801i
$69$		−	910.305i		−	0.191200i
$70$	−2.33878	+	9.67310i	−0.000477303	+	0.00197410i
$71$	−1249.55			−0.247877			−0.123938	−	0.992290i	$-0.539553\pi$
$71$	−1249.55			−0.247877			−0.123938	+	0.992290i	$0.539553\pi$
$72$	29.3058	−	29.3058i	0.00565312	−	0.00565312i
$73$	−3437.16	−	3437.16i	−0.644992	−	0.644992i	0.306786	−	0.951779i	$-0.400746\pi$
$73$	−3437.16	−	3437.16i	−0.644992	−	0.644992i	−0.951779	+	0.306786i	$0.900746\pi$
$74$			27.7928i			0.00507538i
$75$	2272.69	+	7072.02i	0.404033	+	1.25725i
$76$	4082.66			0.706831
$77$	−2338.14	+	2338.14i	−0.394357	+	0.394357i
$78$	−33.2482	−	33.2482i	−0.00546486	−	0.00546486i
$79$			11135.9i			1.78431i	0.451731	+	0.892154i	$0.350807\pi$
$79$			11135.9i			1.78431i	−0.451731	+	0.892154i	$0.649193\pi$
$80$	6220.21	+	1503.94i	0.971909	+	0.234990i
$81$	7810.90			1.19050
$82$	26.3666	−	26.3666i	0.00392127	−	0.00392127i
$83$	3632.77	+	3632.77i	0.527329	+	0.527329i	0.919775	−	0.392446i	$-0.128371\pi$
$83$	3632.77	+	3632.77i	0.527329	+	0.527329i	−0.392446	+	0.919775i	$0.628371\pi$
$84$		−	3521.76i		−	0.499116i
$85$	−6617.39	+	4040.50i	−0.915902	+	0.559239i
$86$	3.15802			0.000426990
$87$	−3689.05	+	3689.05i	−0.487389	+	0.487389i
$88$	−86.8327	−	86.8327i	−0.0112129	−	0.0112129i
$89$		−	8157.71i		−	1.02988i	−0.857225	−	0.514942i	$-0.827814\pi$
$89$		−	8157.71i		−	1.02988i	0.857225	−	0.514942i	$-0.172186\pi$
$90$	16.8736	+	27.6349i	0.00208315	+	0.00341172i
$91$	−3408.86			−0.411649
$92$	866.511	−	866.511i	0.102376	−	0.102376i
$93$	−12180.8	−	12180.8i	−1.40834	−	1.40834i
$94$			43.2326i			0.00489278i
$95$	−1499.21	+	6200.67i	−0.166118	+	0.687054i
$96$	196.185			0.0212874
$97$	4381.16	−	4381.16i	0.465635	−	0.465635i	−0.434862	−	0.900497i	$-0.643203\pi$
$97$	4381.16	−	4381.16i	0.465635	−	0.465635i	0.900497	+	0.434862i	$0.143203\pi$
$98$	5.21308	+	5.21308i	0.000542803	+	0.000542803i
$99$			10758.4i			1.09768i
$100$	−4568.44	+	8895.14i	−0.456844	+	0.889514i
$101$	410.097			0.0402016			0.0201008	−	0.999798i	$-0.493601\pi$
$101$	410.097			0.0402016			0.0201008	+	0.999798i	$0.493601\pi$
$102$	−56.0221	+	56.0221i	−0.00538466	+	0.00538466i
$103$	−3073.57	−	3073.57i	−0.289713	−	0.289713i	0.547254	−	0.836967i	$-0.315673\pi$
$103$	−3073.57	−	3073.57i	−0.289713	−	0.289713i	−0.836967	+	0.547254i	$0.815673\pi$
$104$		−	126.597i		−	0.0117046i
$105$	5348.79	+	1293.24i	0.485151	+	0.117301i
$106$	−100.478			−0.00894254
$107$	11506.0	−	11506.0i	1.00498	−	1.00498i	0.00499151	−	0.999988i	$-0.498411\pi$
$107$	11506.0	−	11506.0i	1.00498	−	1.00498i	0.999988	−	0.00499151i	$-0.00158885\pi$
$108$	2789.11	+	2789.11i	0.239121	+	0.239121i
$109$		−	13007.3i		−	1.09480i	−0.836871	−	0.547400i	$-0.815618\pi$
$109$		−	13007.3i		−	1.09480i	0.836871	−	0.547400i	$-0.184382\pi$
$110$	81.8819	−	49.9961i	0.00676710	−	0.00413191i
$111$	15368.1			1.24731
$112$	3352.23	−	3352.23i	0.267238	−	0.267238i
$113$	−6514.25	−	6514.25i	−0.510162	−	0.510162i	0.404414	−	0.914576i	$-0.367475\pi$
$113$	−6514.25	−	6514.25i	−0.510162	−	0.510162i	−0.914576	+	0.404414i	$0.867475\pi$
$114$			65.1863i			0.00501587i
$115$	997.846	+	1634.24i	0.0754515	+	0.123572i
$116$	−7023.15			−0.521934
$117$	−7842.54	+	7842.54i	−0.572908	+	0.572908i
$118$	70.8420	+	70.8420i	0.00508777	+	0.00508777i
$119$			5743.81i			0.405608i
$120$	−48.0277	+	198.640i	−0.00333526	+	0.0137945i
$121$	17236.0			1.17724
$122$	60.4036	−	60.4036i	0.00405829	−	0.00405829i
$123$	−14579.6	−	14579.6i	−0.963683	−	0.963683i
$124$		−	23189.5i		−	1.50816i
$125$	−11832.2	−	10204.9i	−0.757260	−	0.653113i
$126$	23.9868			0.00151088
$127$	5300.60	−	5300.60i	0.328638	−	0.328638i	−0.523430	−	0.852068i	$-0.675348\pi$
$127$	5300.60	−	5300.60i	0.328638	−	0.328638i	0.852068	+	0.523430i	$0.175348\pi$
$128$	248.994	+	248.994i	0.0151974	+	0.0151974i
$129$		−	1746.24i		−	0.104936i
$130$	96.1350	+	23.2437i	0.00568846	+	0.00137537i
$131$	−3216.78			−0.187447			−0.0937234	−	0.995598i	$-0.529877\pi$
$131$	−3216.78			−0.187447			−0.0937234	+	0.995598i	$0.529877\pi$
$132$	−24006.9	+	24006.9i	−1.37781	+	1.37781i
$133$	3341.70	+	3341.70i	0.188914	+	0.188914i
$134$		−	113.362i		−	0.00631335i
$135$	−5260.25	+	3211.84i	−0.288628	+	0.176233i
$136$	−213.311			−0.0115328
$137$	−9320.99	+	9320.99i	−0.496616	+	0.496616i	−0.910383	−	0.413767i	$-0.864213\pi$
$137$	−9320.99	+	9320.99i	−0.496616	+	0.496616i	0.413767	+	0.910383i	$0.364213\pi$
$138$	13.8353	+	13.8353i	0.000726489	+	0.000726489i
$139$			10358.2i			0.536111i	0.963404	+	0.268055i	$0.0863810\pi$
$139$			10358.2i			0.536111i	−0.963404	+	0.268055i	$0.913619\pi$
$140$	3860.44	+	6322.49i	0.196961	+	0.322576i
$141$	23905.7			1.20244
$142$	18.9912	−	18.9912i	0.000941838	−	0.000941838i
$143$	23237.3	+	23237.3i	1.13636	+	1.13636i
$144$		−	15424.5i		−	0.743852i
$145$	2579.00	−	10666.6i	0.122664	−	0.507331i
$146$	104.479			0.00490146
$147$	2882.60	−	2882.60i	0.133398	−	0.133398i
$148$	14628.8	+	14628.8i	0.667860	+	0.667860i
$149$			3719.04i			0.167517i	0.996486	+	0.0837584i	$0.0266924\pi$
$149$			3719.04i			0.167517i	−0.996486	+	0.0837584i	$0.973308\pi$
$150$	−142.026	−	72.9427i	−0.00631225	−	0.00324190i
$151$	−22024.4			−0.965940			−0.482970	−	0.875637i	$-0.660442\pi$
$151$	−22024.4			−0.965940			−0.482970	+	0.875637i	$0.660442\pi$
$152$	−124.102	+	124.102i	−0.00537146	+	0.00537146i
$153$	13214.4	+	13214.4i	0.564500	+	0.564500i
$154$		−	71.0725i		−	0.00299682i
$155$	35219.8	+	8515.53i	1.46596	+	0.354444i
$156$	−35000.6			−1.43822
$157$	−11748.5	+	11748.5i	−0.476634	+	0.476634i	−0.904053	−	0.427420i	$-0.859423\pi$
$157$	−11748.5	+	11748.5i	−0.476634	+	0.476634i	0.427420	+	0.904053i	$0.359423\pi$
$158$	−169.248	−	169.248i	−0.00677970	−	0.00677970i
$159$			55560.0i			2.19770i
$160$	−352.203	+	215.051i	−0.0137579	+	0.00840044i
$161$	1418.50			0.0547239
$162$	−118.714	+	118.714i	−0.00452347	+	0.00452347i
$163$	5346.78	+	5346.78i	0.201241	+	0.201241i	0.800532	−	0.599290i	$-0.204550\pi$
$163$	5346.78	+	5346.78i	0.201241	+	0.201241i	−0.599290	+	0.800532i	$0.704550\pi$
$164$		−	27756.3i		−	1.03199i
$165$	−27645.6	−	45277.0i	−1.01545	−	1.66307i
$166$	−110.425			−0.00400731
$167$	−6998.41	+	6998.41i	−0.250938	+	0.250938i	−0.821355	−	0.570417i	$-0.806782\pi$
$167$	−6998.41	+	6998.41i	−0.250938	+	0.250938i	0.570417	+	0.821355i	$0.306782\pi$
$168$	107.052	+	107.052i	0.00379296	+	0.00379296i
$169$			5317.59i			0.186184i
$170$	39.1648	−	161.984i	0.00135518	−	0.00560498i
$171$	15376.0			0.525838
$172$	1662.23	−	1662.23i	0.0561869	−	0.0561869i
$173$	−32836.2	−	32836.2i	−1.09714	−	1.09714i	−0.994744	−	0.102392i	$-0.967350\pi$
$173$	−32836.2	−	32836.2i	−1.09714	−	1.09714i	−0.102392	−	0.994744i	$-0.532650\pi$
$174$		−	112.136i		−	0.00370379i
$175$	−11020.1	+	3541.45i	−0.359840	+	0.115639i
$176$	−45702.6			−1.47542
$177$	39172.5	−	39172.5i	1.25036	−	1.25036i
$178$	123.985	+	123.985i	0.00391317	+	0.00391317i
$179$		−	4157.69i		−	0.129761i	−0.997893	−	0.0648807i	$-0.979333\pi$
$179$		−	4157.69i		−	0.129761i	0.997893	−	0.0648807i	$-0.0206667\pi$
$180$	23427.2	+	5664.27i	0.723060	+	0.174823i
$181$	48603.7			1.48359			0.741793	−	0.670629i	$-0.233976\pi$
$181$	48603.7			1.48359			0.741793	+	0.670629i	$0.233976\pi$
$182$	51.8096	−	51.8096i	0.00156411	−	0.00156411i
$183$	−33400.5	−	33400.5i	−0.997356	−	0.997356i
$184$			52.6794i			0.00155598i
$185$	−27589.9	+	16846.1i	−0.806132	+	0.492215i
$186$	370.258			0.0107023
$187$	39154.1	−	39154.1i	1.11968	−	1.11968i
$188$	22755.6	+	22755.6i	0.643832	+	0.643832i
$189$			4565.83i			0.127819i
$190$	−71.4550	−	117.027i	−0.00197936	−	0.00324173i
$191$	−59079.1			−1.61945			−0.809724	−	0.586811i	$-0.800383\pi$
$191$	−59079.1			−1.61945			−0.809724	+	0.586811i	$0.800383\pi$
$192$	34417.2	−	34417.2i	0.933625	−	0.933625i
$193$	41523.8	+	41523.8i	1.11476	+	1.11476i	0.992498	+	0.122264i	$0.0390156\pi$
$193$	41523.8	+	41523.8i	1.11476	+	1.11476i	0.122264	+	0.992498i	$0.460984\pi$
$194$			133.174i			0.00353848i
$195$	12852.7	−	53158.3i	0.338008	−	1.39798i
$196$	5487.84			0.142853
$197$	14556.7	−	14556.7i	0.375085	−	0.375085i	−0.494240	−	0.869325i	$-0.664554\pi$
$197$	14556.7	−	14556.7i	0.375085	−	0.375085i	0.869325	+	0.494240i	$0.164554\pi$
$198$	−163.512	−	163.512i	−0.00417079	−	0.00417079i
$199$			68770.5i			1.73658i	0.496053	+	0.868292i	$0.334782\pi$
$199$			68770.5i			1.73658i	−0.496053	+	0.868292i	$0.665218\pi$
$200$	−131.521	−	409.258i	−0.00328801	−	0.0102315i
$201$	−62684.3			−1.55155
$202$	−6.23286	+	6.23286i	−0.000152751	+	0.000152751i
$203$	−5748.52	−	5748.52i	−0.139497	−	0.139497i
$204$			58974.7i			1.41712i
$205$	42155.8	+	10192.5i	1.00311	+	0.242535i
$206$	93.4271			0.00220160
$207$	3263.44	−	3263.44i	0.0761614	−	0.0761614i
$208$	−33315.8	−	33315.8i	−0.770058	−	0.770058i
$209$		−	45559.0i		−	1.04299i
$210$	−100.949	+	61.6382i	−0.00228909	+	0.00139769i
$211$	−40600.3			−0.911935			−0.455968	−	0.889996i	$-0.650707\pi$
$211$	−40600.3			−0.911935			−0.455968	+	0.889996i	$0.650707\pi$
$212$	−52887.1	+	52887.1i	−1.17673	+	1.17673i
$213$	−10501.3	−	10501.3i	−0.231464	−	0.231464i
$214$			349.748i			0.00763708i
$215$	1914.17	+	3134.97i	0.0414099	+	0.0678197i
$216$	−169.563			−0.00363433
$217$	18980.9	−	18980.9i	0.403085	−	0.403085i
$218$	197.692	+	197.692i	0.00415983	+	0.00415983i
$219$		−	57772.4i		−	1.20457i
$220$	16783.2	−	69414.4i	0.346760	−	1.43418i
$221$	57084.2			1.16878
$222$	−233.573	+	233.573i	−0.00473932	+	0.00473932i
$223$	21915.3	+	21915.3i	0.440695	+	0.440695i	0.892246	−	0.451550i	$-0.149129\pi$
$223$	21915.3	+	21915.3i	0.440695	+	0.440695i	−0.451550	+	0.892246i	$0.649129\pi$
$224$			305.708i			0.00609272i
$225$	−17205.6	+	33500.7i	−0.339864	+	0.661743i
$226$	198.014			0.00387685
$227$	−30850.1	+	30850.1i	−0.598694	+	0.598694i	−0.939965	−	0.341271i	$-0.889143\pi$
$227$	−30850.1	+	30850.1i	−0.598694	+	0.598694i	0.341271	+	0.939965i	$0.389143\pi$
$228$	34311.0	+	34311.0i	0.660029	+	0.660029i
$229$			63623.5i			1.21324i	0.794992	+	0.606620i	$0.207475\pi$
$229$			63623.5i			1.21324i	−0.794992	+	0.606620i	$0.792525\pi$
$230$	−40.0037	−	9.67219i	−0.000756214	−	0.000182839i
$231$	−39299.9			−0.736491
$232$	213.486	−	213.486i	0.00396636	−	0.00396636i
$233$	29781.5	+	29781.5i	0.548574	+	0.548574i	0.926028	−	0.377454i	$-0.123200\pi$
$233$	29781.5	+	29781.5i	0.548574	+	0.548574i	−0.377454	+	0.926028i	$0.623200\pi$
$234$		−	238.390i		−	0.00435367i
$235$	−42917.0	+	26204.6i	−0.777130	+	0.474506i
$236$	74575.8			1.33898
$237$	−93586.8	+	93586.8i	−1.66616	+	1.66616i
$238$	−87.2973	−	87.2973i	−0.00154116	−	0.00154116i
$239$		−	70756.8i		−	1.23872i	−0.785108	−	0.619359i	$-0.787392\pi$
$239$		−	70756.8i		−	1.23872i	0.785108	−	0.619359i	$-0.212608\pi$
$240$	39636.0	+	64914.4i	0.688125	+	1.12699i
$241$	12911.9			0.222308			0.111154	−	0.993803i	$-0.464545\pi$
$241$	12911.9			0.222308			0.111154	+	0.993803i	$0.464545\pi$
$242$	−261.962	+	261.962i	−0.00447308	+	0.00447308i
$243$	51523.2	+	51523.2i	0.872550	+	0.872550i
$244$		−	63587.2i		−	1.06805i
$245$	−2015.22	+	8334.84i	−0.0335730	+	0.138856i
$246$	443.175			0.00732326
$247$	33211.1	−	33211.1i	0.544364	−	0.544364i
$248$	704.901	+	704.901i	0.0114611	+	0.0114611i
$249$			61060.2i			0.984826i
$250$	334.931	−	24.7324i	0.00535889	−	0.000395718i
$251$	−45510.3			−0.722374			−0.361187	−	0.932494i	$-0.617628\pi$
$251$	−45510.3			−0.722374			−0.361187	+	0.932494i	$0.617628\pi$
$252$	12625.5	−	12625.5i	0.198814	−	0.198814i
$253$	−9669.53	−	9669.53i	−0.151065	−	0.151065i
$254$			161.122i			0.00249740i
$255$	−89569.8	−	21656.4i	−1.37747	−	0.333047i
$256$	65517.1			0.999711
$257$	−28510.9	+	28510.9i	−0.431663	+	0.431663i	−0.889194	−	0.457530i	$-0.848734\pi$
$257$	−28510.9	+	28510.9i	−0.431663	+	0.431663i	0.457530	+	0.889194i	$0.348734\pi$
$258$	26.5403	+	26.5403i	0.000398718	+	0.000398718i
$259$			23947.7i			0.356996i
$260$	62835.3	−	38366.5i	0.929516	−	0.567552i
$261$	−26450.5			−0.388287
$262$	48.8902	−	48.8902i	0.000712228	−	0.000712228i
$263$	−28724.4	−	28724.4i	−0.415279	−	0.415279i	0.468294	−	0.883573i	$-0.344869\pi$
$263$	−28724.4	−	28724.4i	−0.415279	−	0.415279i	−0.883573	+	0.468294i	$0.844869\pi$
$264$		−	1459.50i		−	0.0209409i
$265$	−60903.1	−	99744.9i	−0.867256	−	1.42036i
$266$	−101.578			−0.00143560
$267$	68558.1	−	68558.1i	0.961692	−	0.961692i
$268$	−59668.6	−	59668.6i	−0.830762	−	0.830762i
$269$		−	56575.8i		−	0.781855i	−0.920422	−	0.390927i	$-0.872154\pi$
$269$		−	56575.8i		−	0.781855i	0.920422	−	0.390927i	$-0.127846\pi$
$270$	31.1326	−	128.763i	0.000427059	−	0.00176630i
$271$	85972.1			1.17063			0.585314	−	0.810807i	$-0.300971\pi$
$271$	85972.1			1.17063			0.585314	+	0.810807i	$0.300971\pi$
$272$	−56135.9	+	56135.9i	−0.758757	+	0.758757i
$273$	−28648.4	−	28648.4i	−0.384392	−	0.384392i
$274$		−	283.330i		−	0.00377391i
$275$	99262.3	+	50980.0i	1.31256	+	0.674115i
$276$	14564.5			0.191195
$277$	−52002.6	+	52002.6i	−0.677743	+	0.677743i	−0.959489	−	0.281746i	$-0.909087\pi$
$277$	−52002.6	+	52002.6i	−0.677743	+	0.677743i	0.281746	+	0.959489i	$0.409087\pi$
$278$	−157.429	−	157.429i	−0.00203702	−	0.00203702i
$279$		−	87335.9i		−	1.12198i
$280$	−309.535	−	74.8400i	−0.00394815	−	0.000954592i
$281$	48758.7			0.617503			0.308752	−	0.951143i	$-0.400089\pi$
$281$	48758.7			0.617503			0.308752	+	0.951143i	$0.400089\pi$
$282$	−363.330	+	363.330i	−0.00456881	+	0.00456881i
$283$	−80206.3	−	80206.3i	−1.00146	−	1.00146i	−0.999999	−	0.00146510i	$-0.999534\pi$
$283$	−80206.3	−	80206.3i	−1.00146	−	1.00146i	−0.00146510	−	0.999999i	$-0.500466\pi$
$284$		−	19992.2i		−	0.247870i
$285$	−64710.4	+	39511.4i	−0.796681	+	0.486444i
$286$	−706.345			−0.00863545
$287$	22718.8	−	22718.8i	0.275818	−	0.275818i
$288$	703.322	+	703.322i	0.00847948	+	0.00847948i
$289$		−	12663.7i		−	0.151623i
$290$	122.920	+	201.314i	0.00146159	+	0.00239374i
$291$	73639.3			0.869608
$292$	54993.1	−	54993.1i	0.644974	−	0.644974i
$293$	−4087.77	−	4087.77i	−0.0476159	−	0.0476159i	0.682898	−	0.730514i	$-0.260719\pi$
$293$	−4087.77	−	4087.77i	−0.0476159	−	0.0476159i	−0.730514	+	0.682898i	$0.760719\pi$
$294$			87.6224i			0.00101373i
$295$	−27385.3	+	113264.i	−0.314684	+	1.30152i
$296$	−889.356			−0.0101506
$297$	31124.1	−	31124.1i	0.352845	−	0.352845i
$298$	−56.5238	−	56.5238i	−0.000636501	−	0.000636501i
$299$		−	14097.6i		−	0.157689i
$300$	−113149.	+	36361.9i	−1.25721	+	0.404022i
$301$	2721.11			0.0300340
$302$	334.738	−	334.738i	0.00367021	−	0.00367021i
$303$	3446.49	+	3446.49i	0.0375398	+	0.0375398i
$304$			65318.7i			0.706790i
$305$	96575.1	+	23350.2i	1.03816	+	0.251009i
$306$	−401.678			−0.00428978
$307$	−23151.2	+	23151.2i	−0.245639	+	0.245639i	−0.819178	−	0.573539i	$-0.805570\pi$
$307$	−23151.2	+	23151.2i	−0.245639	+	0.245639i	0.573539	+	0.819178i	$0.305570\pi$
$308$	−37409.2	−	37409.2i	−0.394346	−	0.394346i
$309$		−	51661.0i		−	0.541060i
$310$	−664.711	+	405.865i	−0.00691687	+	0.00422336i
$311$	30470.3			0.315033			0.157517	−	0.987516i	$-0.449651\pi$
$311$	30470.3			0.315033			0.157517	+	0.987516i	$0.449651\pi$
$312$	1063.93	−	1063.93i	0.0109296	−	0.0109296i
$313$	12110.0	+	12110.0i	0.123610	+	0.123610i	0.766206	−	0.642595i	$-0.222142\pi$
$313$	12110.0	+	12110.0i	0.123610	+	0.123610i	−0.642595	+	0.766206i	$0.722142\pi$
$314$		−	357.120i		−	0.00362206i
$315$	14539.1	+	23811.7i	0.146527	+	0.239976i
$316$	−178169.			−1.78426
$317$	52830.9	−	52830.9i	0.525738	−	0.525738i	−0.393561	−	0.919299i	$-0.628757\pi$
$317$	52830.9	−	52830.9i	0.525738	−	0.525738i	0.919299	+	0.393561i	$0.128757\pi$
$318$	−844.429	−	844.429i	−0.00835043	−	0.00835043i
$319$			78372.4i			0.770161i
$320$	−24060.9	+	99514.8i	−0.234970	+	0.971824i
$321$	193395.			1.87687
$322$	−21.5590	+	21.5590i	−0.000207930	+	0.000207930i
$323$	−55959.4	−	55959.4i	−0.536375	−	0.536375i
$324$			124971.i			1.19047i
$325$	35196.3	+	109522.i	0.333219	+	1.03689i
$326$	−162.526			−0.00152928
$327$	109315.	−	109315.i	1.02231	−	1.02231i
$328$	843.720	+	843.720i	0.00784243	+	0.00784243i
$329$			37251.4i			0.344153i
$330$	1108.31	+	267.971i	0.0101774	+	0.00246070i
$331$	−67516.0			−0.616241			−0.308121	−	0.951347i	$-0.599700\pi$
$331$	−67516.0			−0.616241			−0.308121	+	0.951347i	$0.599700\pi$
$332$	−58122.7	+	58122.7i	−0.527314	+	0.527314i
$333$	55094.8	+	55094.8i	0.496846	+	0.496846i
$334$		−	212.730i		−	0.00190694i
$335$	112535.	−	68712.5i	1.00276	−	0.612274i
$336$	56344.9			0.499087
$337$	−135510.	+	135510.i	−1.19320	+	1.19320i	−0.217033	+	0.976164i	$0.569638\pi$
$337$	−135510.	+	135510.i	−1.19320	+	1.19320i	−0.976164	+	0.217033i	$0.930362\pi$
$338$	−80.8194	−	80.8194i	−0.000707428	−	0.000707428i
$339$		−	109493.i		−	0.952765i
$340$	−64646.1	−	105875.i	−0.559223	−	0.915875i
$341$	−258775.			−2.22543
$342$	−233.693	+	233.693i	−0.00199799	+	0.00199799i
$343$	4491.86	+	4491.86i	0.0381802	+	0.0381802i
$344$			101.055i			0.000853968i
$345$	−5348.28	+	22120.2i	−0.0449341	+	0.185845i
$346$	998.121			0.00833741
$347$	−82622.8	+	82622.8i	−0.686185	+	0.686185i	−0.961387	−	0.275202i	$-0.911255\pi$
$347$	−82622.8	+	82622.8i	−0.686185	+	0.686185i	0.275202	+	0.961387i	$0.411255\pi$
$348$	−59023.1	−	59023.1i	−0.487375	−	0.487375i
$349$		−	41675.4i		−	0.342160i	−0.985257	−	0.171080i	$-0.945274\pi$
$349$		−	41675.4i		−	0.342160i	0.985257	−	0.171080i	$-0.0547256\pi$
$350$	113.664	−	221.314i	0.000927870	−	0.00180664i
$351$	45376.9			0.368316
$352$	2083.93	−	2083.93i	0.0168189	−	0.0168189i
$353$	76506.9	+	76506.9i	0.613976	+	0.613976i	0.943980	−	0.330004i	$-0.107050\pi$
$353$	76506.9	+	76506.9i	0.613976	+	0.613976i	−0.330004	+	0.943980i	$0.607050\pi$
$354$			1190.72i			0.00950178i
$355$	30363.8	+	7341.42i	0.240934	+	0.0582537i
$356$	130520.			1.02985
$357$	−48271.5	+	48271.5i	−0.378751	+	0.378751i
$358$	63.1906	+	63.1906i	0.000493045	+	0.000493045i
$359$		−	39385.8i		−	0.305598i	−0.988257	−	0.152799i	$-0.951171\pi$
$359$		−	39385.8i		−	0.305598i	0.988257	−	0.152799i	$-0.0488287\pi$
$360$	−884.304	+	539.946i	−0.00682334	+	0.00416625i
$361$	65207.6			0.500361
$362$	−738.704	+	738.704i	−0.00563707	+	0.00563707i
$363$	144853.	+	144853.i	1.09929	+	1.09929i
$364$		−	54540.3i		−	0.411637i
$365$	63328.2	+	103717.i	0.475348	+	0.778508i
$366$	1015.27			0.00757916
$367$	−59666.2	+	59666.2i	−0.442992	+	0.442992i	−0.893016	−	0.450024i	$-0.851415\pi$
$367$	−59666.2	+	59666.2i	−0.442992	+	0.442992i	0.450024	+	0.893016i	$0.351415\pi$
$368$	13863.4	+	13863.4i	0.102370	+	0.102370i
$369$		−	104535.i		−	0.767733i
$370$	163.290	−	675.359i	0.00119277	−	0.00493323i
$371$	−86577.3			−0.629008
$372$	194886.	−	194886.i	1.40830	−	1.40830i
$373$	−151950.	−	151950.i	−1.09215	−	1.09215i	−0.995299	−	0.0968525i	$-0.969122\pi$
$373$	−151950.	−	151950.i	−1.09215	−	1.09215i	−0.0968525	−	0.995299i	$-0.530878\pi$
$374$			1190.17i			0.00850872i
$375$	−13675.9	−	185201.i	−0.0972507	−	1.31699i
$376$	−1383.42			−0.00978542
$377$	−57131.0	+	57131.0i	−0.401966	+	0.401966i
$378$	−69.3937	−	69.3937i	−0.000485665	−	0.000485665i
$379$			200208.i			1.39381i	0.717165	+	0.696904i	$0.245439\pi$
$379$			200208.i			1.39381i	−0.717165	+	0.696904i	$0.754561\pi$
$380$	−99207.8	−	23986.7i	−0.687035	−	0.166113i
$381$	89093.4			0.613756
$382$	897.913	−	897.913i	0.00615330	−	0.00615330i
$383$	108161.	+	108161.i	0.737351	+	0.737351i	0.972065	−	0.234714i	$-0.0754153\pi$
$383$	108161.	+	108161.i	0.737351	+	0.737351i	−0.234714	+	0.972065i	$0.575415\pi$
$384$			4185.14i			0.0283823i
$385$	70553.6	−	43079.2i	0.475990	−	0.290634i
$386$	−1262.20			−0.00847135
$387$	6260.27	−	6260.27i	0.0417995	−	0.0417995i
$388$	70096.6	+	70096.6i	0.465622	+	0.465622i
$389$		−	287702.i		−	1.90127i	−0.310317	−	0.950633i	$-0.600435\pi$
$389$		−	287702.i		−	1.90127i	0.310317	−	0.950633i	$-0.399565\pi$
$390$	612.584	+	1003.27i	0.00402751	+	0.00659611i
$391$	−23753.9			−0.155375
$392$	−166.816	+	166.816i	−0.00108559	+	0.00108559i
$393$	−27034.0	−	27034.0i	−0.175035	−	0.175035i
$394$			442.480i			0.00285037i
$395$	65426.2	−	270600.i	0.419332	−	1.73433i
$396$	−172129.			−1.09765
$397$	−15821.3	+	15821.3i	−0.100383	+	0.100383i	−0.755515	−	0.655132i	$-0.772613\pi$
$397$	−15821.3	+	15821.3i	−0.100383	+	0.100383i	0.655132	+	0.755515i	$0.272613\pi$
$398$	−1045.21	−	1045.21i	−0.00659837	−	0.00659837i
$399$			56167.8i			0.352811i
$400$	−142314.	−	73090.9i	−0.889463	−	0.456818i
$401$	37856.9			0.235427			0.117714	−	0.993048i	$-0.462444\pi$
$401$	37856.9			0.235427			0.117714	+	0.993048i	$0.462444\pi$
$402$	952.707	−	952.707i	0.00589532	−	0.00589532i
$403$	−188639.	−	188639.i	−1.16151	−	1.16151i
$404$			6561.36i			0.0402005i
$405$	−189804.	−	45891.1i	−1.15716	−	0.279781i
$406$	174.738			0.00106007
$407$	163245.	−	163245.i	0.985488	−	0.985488i
$408$	−1792.68	−	1792.68i	−0.0107692	−	0.0107692i
$409$			16990.5i			0.101569i	0.998710	+	0.0507844i	$0.0161721\pi$
$409$			16990.5i			0.101569i	−0.998710	+	0.0507844i	$0.983828\pi$
$410$	−795.615	+	485.793i	−0.00473299	+	0.00288991i
$411$	−156669.			−0.927467
$412$	49175.6	−	49175.6i	0.289705	−	0.289705i
$413$	61041.1	+	61041.1i	0.357868	+	0.357868i
$414$			99.1987i			0.000578769i
$415$	−66932.2	−	109619.i	−0.388632	−	0.636488i
$416$	3038.24			0.0175564
$417$	−87051.1	+	87051.1i	−0.500613	+	0.500613i
$418$	692.428	+	692.428i	0.00396298	+	0.00396298i
$419$			291749.i			1.66181i	0.556413	+	0.830906i	$0.312177\pi$
$419$			291749.i			1.66181i	−0.556413	+	0.830906i	$0.687823\pi$
$420$	−20691.3	+	85578.1i	−0.117298	+	0.485137i
$421$	105749.			0.596637			0.298319	−	0.954466i	$-0.403574\pi$
$421$	105749.			0.596637			0.298319	+	0.954466i	$0.403574\pi$
$422$	617.063	−	617.063i	0.00346501	−	0.00346501i
$423$	85701.8	+	85701.8i	0.478971	+	0.478971i
$424$		−	3215.26i		−	0.0178848i
$425$	184540.	−	59304.5i	1.02168	−	0.328329i
$426$	319.208			0.00175895
$427$	52046.8	−	52046.8i	0.285456	−	0.285456i
$428$	184091.	+	184091.i	1.00495	+	1.00495i
$429$			390577.i			2.12223i
$430$	−76.7393	−	18.5542i	−0.000415031	−	0.000100347i
$431$	−193428.			−1.04127			−0.520637	−	0.853778i	$-0.674305\pi$
$431$	−193428.			−1.04127			−0.520637	+	0.853778i	$0.674305\pi$
$432$	−44623.1	+	44623.1i	−0.239107	+	0.239107i
$433$	123647.	+	123647.i	0.659488	+	0.659488i	0.955259	−	0.295771i	$-0.0955765\pi$
$433$	123647.	+	123647.i	0.659488	+	0.659488i	−0.295771	+	0.955259i	$0.595576\pi$
$434$			576.961i			0.00306314i
$435$	111317.	−	67969.1i	0.588281	−	0.359197i
$436$	208111.			1.09477
$437$	−13819.8	+	13819.8i	−0.0723667	+	0.0723667i
$438$	878.054	+	878.054i	0.00457692	+	0.00457692i
$439$		−	120323.i		−	0.624337i	−0.950027	−	0.312168i	$-0.898945\pi$
$439$		−	120323.i		−	0.624337i	0.950027	−	0.312168i	$-0.101055\pi$
$440$	1599.85	+	2620.18i	0.00826370	+	0.0135340i
$441$	20668.2			0.106274
$442$	−867.594	+	867.594i	−0.00444091	+	0.00444091i
$443$	42476.7	+	42476.7i	0.216443	+	0.216443i	0.806998	−	0.590555i	$-0.201091\pi$
$443$	42476.7	+	42476.7i	0.216443	+	0.216443i	−0.590555	+	0.806998i	$0.701091\pi$
$444$			245883.i			1.24728i
$445$	−47928.7	+	198231.i	−0.242034	+	1.00104i
$446$	−666.160			−0.00334895
$447$	−31255.1	+	31255.1i	−0.156425	+	0.156425i
$448$	53631.1	+	53631.1i	0.267215	+	0.267215i
$449$			58862.3i			0.291974i	0.989286	+	0.145987i	$0.0466358\pi$
$449$			58862.3i			0.291974i	−0.989286	+	0.145987i	$0.953364\pi$
$450$	−247.662	−	770.660i	−0.00122302	−	0.00380573i
$451$	−309737.			−1.52279
$452$	104225.	−	104225.i	0.510147	−	0.510147i
$453$	−185095.	−	185095.i	−0.901983	−	0.901983i
$454$		−	937.751i		−	0.00454963i
$455$	82834.8	+	20028.0i	0.400120	+	0.0967419i
$456$	−2085.93			−0.0100316
$457$	273815.	−	273815.i	1.31107	−	1.31107i	0.390438	−	0.920629i	$-0.372324\pi$
$457$	273815.	−	273815.i	1.31107	−	1.31107i	0.920629	−	0.390438i	$-0.127676\pi$
$458$	−966.981	−	966.981i	−0.00460985	−	0.00460985i
$459$		−	76458.5i		−	0.362911i
$460$	−26147.0	+	15965.1i	−0.123568	+	0.0754493i
$461$	−361733.			−1.70210			−0.851052	−	0.525082i	$-0.824035\pi$
$461$	−361733.			−1.70210			−0.851052	+	0.525082i	$0.824035\pi$
$462$	597.299	−	597.299i	0.00279839	−	0.00279839i
$463$	−16249.5	−	16249.5i	−0.0758014	−	0.0758014i	0.668190	−	0.743991i	$-0.267069\pi$
$463$	−16249.5	−	16249.5i	−0.0758014	−	0.0758014i	−0.743991	+	0.668190i	$0.767069\pi$
$464$		−	112364.i		−	0.521904i
$465$	224425.	+	367555.i	1.03792	+	1.69987i
$466$	−905.269			−0.00416875
$467$	−188589.	+	188589.i	−0.864735	+	0.864735i	−0.991884	−	0.127148i	$-0.959418\pi$
$467$	−188589.	+	188589.i	−0.864735	+	0.864735i	0.127148	+	0.991884i	$0.459418\pi$
$468$	−125477.	−	125477.i	−0.572892	−	0.572892i
$469$		−	97678.9i		−	0.444074i
$470$	254.003	−	1050.54i	0.00114986	−	0.00475575i
$471$	−197471.			−0.890149
$472$	−2266.91	+	2266.91i	−0.0101754	+	0.0101754i
$473$	−18549.1	−	18549.1i	−0.0829088	−	0.0829088i
$474$		−	2844.76i		−	0.0126616i
$475$	72861.1	−	141867.i	0.322930	−	0.628772i
$476$	−91898.3			−0.405596
$477$	−199183.	+	199183.i	−0.875416	+	0.875416i
$478$	1075.40	+	1075.40i	0.00470666	+	0.00470666i
$479$		−	347260.i		−	1.51351i	−0.653701	−	0.756753i	$-0.726785\pi$
$479$		−	347260.i		−	1.51351i	0.653701	−	0.756753i	$-0.273215\pi$
$480$	−4767.26	−	1152.64i	−0.0206912	−	0.00500277i
$481$	238001.			1.02870
$482$	−196.241	+	196.241i	−0.000844689	+	0.000844689i
$483$	11921.2	+	11921.2i	0.0511004	+	0.0511004i
$484$			275768.i			1.17721i
$485$	−132202.	+	80721.0i	−0.562023	+	0.343165i
$486$	−1566.15			−0.00663072
$487$	35396.5	−	35396.5i	0.149246	−	0.149246i	−0.628535	−	0.777781i	$-0.716345\pi$
$487$	35396.5	−	35396.5i	0.149246	−	0.149246i	0.777781	+	0.628535i	$0.216345\pi$
$488$	1932.89	+	1932.89i	0.00811646	+	0.00811646i
$489$			89869.6i			0.375833i
$490$	−96.0487	−	157.305i	−0.000400036	−	0.000655166i
$491$	−180759.			−0.749785			−0.374893	−	0.927068i	$-0.622320\pi$
$491$	−180759.			−0.749785			−0.374893	+	0.927068i	$0.622320\pi$
$492$	233266.	−	233266.i	0.963655	−	0.963655i
$493$	96263.7	+	96263.7i	0.396067	+	0.396067i
$494$			1009.52i			0.00413675i
$495$	63208.5	−	261427.i	0.257968	−	1.06694i
$496$	371010.			1.50807
$497$	16363.8	−	16363.8i	0.0662479	−	0.0662479i
$498$	−928.023	−	928.023i	−0.00374197	−	0.00374197i
$499$			186215.i			0.747847i	0.927460	+	0.373923i	$0.121988\pi$
$499$			186215.i			0.747847i	−0.927460	+	0.373923i	$0.878012\pi$
$500$	163274.	−	189310.i	0.653095	−	0.757238i
$501$	−117630.			−0.468645
$502$	691.687	−	691.687i	0.00274475	−	0.00274475i
$503$	−28470.2	−	28470.2i	−0.112526	−	0.112526i	0.648602	−	0.761128i	$-0.275354\pi$
$503$	−28470.2	−	28470.2i	−0.112526	−	0.112526i	−0.761128	+	0.648602i	$0.775354\pi$
$504$			767.565i			0.00302172i
$505$	−9965.28	−	2409.43i	−0.0390757	−	0.00944782i
$506$	293.925			0.00114798
$507$	−44689.5	+	44689.5i	−0.173856	+	0.173856i
$508$	84807.2	+	84807.2i	0.328629	+	0.328629i
$509$		−	9013.98i		−	0.0347921i	−0.999849	−	0.0173961i	$-0.994462\pi$
$509$		−	9013.98i		−	0.0347921i	0.999849	−	0.0173961i	$-0.00553762\pi$
$510$	1690.47	−	1032.18i	0.00649931	−	0.00396840i
$511$	90024.9			0.344763
$512$	−4979.67	+	4979.67i	−0.0189959	+	0.0189959i
$513$	−44482.9	−	44482.9i	−0.169028	−	0.169028i
$514$		−	866.647i		−	0.00328032i
$515$	56629.1	+	92745.1i	0.213513	+	0.349685i
$516$	27939.1			0.104933
$517$	253933.	−	253933.i	0.950033	−	0.950033i
$518$	−363.969	−	363.969i	−0.00135645	−	0.00135645i
$519$		−	551916.i		−	2.04898i
$520$	−743.789	+	3076.27i	−0.00275070	+	0.0113768i
$521$	123697.			0.455704			0.227852	−	0.973696i	$-0.426830\pi$
$521$	123697.			0.455704			0.227852	+	0.973696i	$0.426830\pi$
$522$	402.007	−	402.007i	0.00147534	−	0.00147534i
$523$	82201.1	+	82201.1i	0.300521	+	0.300521i	0.841218	−	0.540697i	$-0.181839\pi$
$523$	82201.1	+	82201.1i	0.300521	+	0.300521i	−0.540697	+	0.841218i	$0.681839\pi$
$524$		−	51466.9i		−	0.187441i
$525$	−122376.	−	62851.1i	−0.443996	−	0.228031i
$526$	873.135			0.00315580
$527$	−317850.	+	317850.i	−1.14446	+	1.14446i
$528$	−384089.	−	384089.i	−1.37773	−	1.37773i
$529$		−	273975.i		−	0.979037i
$530$	2441.61	+	590.338i	0.00869209	+	0.00210159i
$531$	280866.			0.996117
$532$	−53465.6	+	53465.6i	−0.188909	+	0.188909i
$533$	−225788.	−	225788.i	−0.794780	−	0.794780i
$534$			2083.96i			0.00730814i
$535$	−347195.	+	211993.i	−1.21301	+	0.740652i
$536$	3627.55			0.0126265
$537$	34941.5	−	34941.5i	0.121170	−	0.121170i
$538$	859.867	+	859.867i	0.00297075	+	0.00297075i
$539$		−	61239.7i		−	0.210793i
$540$	−51388.0	−	84161.5i	−0.176228	−	0.288620i
$541$	17926.3			0.0612484			0.0306242	−	0.999531i	$-0.490250\pi$
$541$	17926.3			0.0612484			0.0306242	+	0.999531i	$0.490250\pi$
$542$	−1306.65	+	1306.65i	−0.00444795	+	0.00444795i
$543$	408470.	+	408470.i	1.38535	+	1.38535i
$544$		−	5119.33i		−	0.0172988i
$545$	−76421.4	+	316075.i	−0.257290	+	1.06414i
$546$	870.825			0.00292109
$547$	−336131.	+	336131.i	−1.12340	+	1.12340i	−0.132173	+	0.991227i	$0.542196\pi$
$547$	−336131.	+	336131.i	−1.12340	+	1.12340i	−0.991227	+	0.132173i	$0.957804\pi$
$548$	−149132.	−	149132.i	−0.496602	−	0.496602i
$549$		−	239481.i		−	0.794560i
$550$	−2283.46	+	733.819i	−0.00754862	+	0.00242585i
$551$	112011.			0.368941
$552$	−442.722	+	442.722i	−0.00145296	+	0.00145296i
$553$	−145833.	−	145833.i	−0.476876	−	0.476876i
$554$		−	1580.72i		−	0.00515034i
$555$	−373443.	−	90292.0i	−1.21238	−	0.293132i
$556$	−165726.			−0.536095
$557$	178158.	−	178158.i	0.574241	−	0.574241i	−0.359070	−	0.933311i	$-0.616906\pi$
$557$	178158.	−	178158.i	0.574241	−	0.574241i	0.933311	+	0.359070i	$0.116906\pi$
$558$	1327.37	+	1327.37i	0.00426309	+	0.00426309i
$559$		−	27043.4i		−	0.0865443i
$560$	−101154.	+	61763.4i	−0.322557	+	0.196950i
$561$	658108.			2.09108
$562$	−741.058	+	741.058i	−0.00234628	+	0.00234628i
$563$	289503.	+	289503.i	0.913348	+	0.913348i	0.996534	−	0.0831863i	$-0.0265097\pi$
$563$	289503.	+	289503.i	0.913348	+	0.913348i	−0.0831863	+	0.996534i	$0.526510\pi$
$564$			382480.i			1.20240i
$565$	120022.	+	196568.i	0.375980	+	0.615767i
$566$	2438.03			0.00761037
$567$	−102290.	+	102290.i	−0.318176	+	0.318176i
$568$	607.711	+	607.711i	0.00188365	+	0.00188365i
$569$		−	448419.i		−	1.38503i	−0.721403	−	0.692516i	$-0.756502\pi$
$569$		−	448419.i		−	1.38503i	0.721403	−	0.692516i	$-0.243498\pi$
$570$	382.987	−	1584.01i	0.00117878	−	0.00487539i
$571$	403775.			1.23842			0.619209	−	0.785226i	$-0.287453\pi$
$571$	403775.			1.23842			0.619209	+	0.785226i	$0.287453\pi$
$572$	−371787.	+	371787.i	−1.13632	+	1.13632i
$573$	−496506.	−	496506.i	−1.51222	−	1.51222i
$574$			690.584i			0.00209601i
$575$	−14645.9	−	45574.3i	−0.0442976	−	0.137843i
$576$	246771.			0.743787
$577$	314392.	−	314392.i	0.944321	−	0.944321i	−0.0542087	−	0.998530i	$-0.517264\pi$
$577$	314392.	−	314392.i	0.944321	−	0.944321i	0.998530	+	0.0542087i	$0.0172636\pi$
$578$	192.470	+	192.470i	0.000576112	+	0.000576112i
$579$			697938.i			2.08190i
$580$	170661.	+	41262.9i	0.507316	+	0.122660i
$581$	−95148.1			−0.281869
$582$	−1119.21	+	1119.21i	−0.00330418	+	0.00330418i
$583$	590175.	+	590175.i	1.73638	+	1.73638i
$584$			3343.29i			0.00980277i
$585$	236649.	−	144495.i	0.691502	−	0.422223i
$586$	124.256			0.000361845
$587$	−56100.9	+	56100.9i	−0.162815	+	0.162815i	−0.783812	−	0.620998i	$-0.786728\pi$
$587$	−56100.9	+	56100.9i	−0.162815	+	0.162815i	0.620998	+	0.783812i	$0.286728\pi$
$588$	46120.3	+	46120.3i	0.133394	+	0.133394i
$589$			369844.i			1.06608i
$590$	−1305.23	−	2137.66i	−0.00374959	−	0.00614095i
$591$	244671.			0.700500
$592$	−234047.	+	234047.i	−0.667821	+	0.667821i
$593$	−65402.5	−	65402.5i	−0.185988	−	0.185988i	0.607971	−	0.793959i	$-0.291984\pi$
$593$	−65402.5	−	65402.5i	−0.185988	−	0.185988i	−0.793959	+	0.607971i	$0.791984\pi$
$594$			946.078i			0.00268135i
$595$	33746.4	−	139574.i	0.0953222	−	0.394248i
$596$	−59502.9			−0.167512
$597$	−577953.	+	577953.i	−1.62160	+	1.62160i
$598$	214.262	+	214.262i	0.000599159	+	0.000599159i
$599$			519621.i			1.44822i	0.689687	+	0.724108i	$0.257748\pi$
$599$			519621.i			1.44822i	−0.689687	+	0.724108i	$0.742252\pi$
$600$	2334.13	−	4544.75i	0.00648370	−	0.0126243i
$601$	−433485.			−1.20012			−0.600060	−	0.799955i	$-0.704857\pi$
$601$	−433485.			−1.20012			−0.600060	+	0.799955i	$0.704857\pi$
$602$	−41.3568	+	41.3568i	−0.000114118	+	0.000114118i
$603$	−224723.	−	224723.i	−0.618035	−	0.618035i
$604$		−	352380.i		−	0.965913i
$605$	−418832.	−	101266.i	−1.14427	−	0.276665i
$606$	−104.763			−0.000285274
$607$	374141.	−	374141.i	1.01545	−	1.01545i	0.0155710	−	0.999879i	$-0.495043\pi$
$607$	374141.	−	374141.i	1.01545	−	1.01545i	0.999879	−	0.0155710i	$-0.00495661\pi$
$608$	−2978.38	−	2978.38i	−0.00805700	−	0.00805700i
$609$		−	96622.1i		−	0.260521i
$610$	−1822.68	+	1112.91i	−0.00489837	+	0.00299089i
$611$	370219.			0.991690
$612$	−211424.	+	211424.i	−0.564484	+	0.564484i
$613$	−152256.	−	152256.i	−0.405186	−	0.405186i	0.474870	−	0.880056i	$-0.342495\pi$
$613$	−152256.	−	152256.i	−0.405186	−	0.405186i	−0.880056	+	0.474870i	$0.842495\pi$
$614$		−	703.727i		−	0.00186667i
$615$	268622.	+	439939.i	0.710217	+	1.16317i
$616$	2274.29			0.00599355
$617$	408731.	−	408731.i	1.07366	−	1.07366i	0.0766005	−	0.997062i	$-0.475593\pi$
$617$	408731.	−	408731.i	1.07366	−	1.07366i	0.997062	−	0.0766005i	$-0.0244066\pi$
$618$	785.169	+	785.169i	0.00205583	+	0.00205583i
$619$		−	72206.4i		−	0.188449i	−0.995551	−	0.0942247i	$-0.969963\pi$
$619$		−	72206.4i		−	0.188449i	0.995551	−	0.0942247i	$-0.0300372\pi$
$620$	−136244.	+	563500.i	−0.354434	+	1.46592i
$621$	−18882.3			−0.0489633
$622$	−463.103	+	463.103i	−0.00119701	+	0.00119701i
$623$	106832.	+	106832.i	0.275248	+	0.275248i
$624$		−	559977.i		−	1.43814i
$625$	227564.	+	317494.i	0.582563	+	0.812786i
$626$	−368.107			−0.000939345
$627$	382882.	−	382882.i	0.973934	−	0.973934i
$628$	−187971.	−	187971.i	−0.476620	−	0.476620i
$629$		−	401023.i		−	1.01360i
$630$	−582.874	−	140.929i	−0.00146857	−	0.000355073i
$631$	−453999.			−1.14024			−0.570120	−	0.821561i	$-0.693103\pi$
$631$	−453999.			−1.14024			−0.570120	+	0.821561i	$0.693103\pi$
$632$	5415.87	−	5415.87i	0.0135592	−	0.0135592i
$633$	−341208.	−	341208.i	−0.851553	−	0.851553i
$634$			1605.90i			0.00399521i
$635$	−159946.	+	97661.2i	−0.396667	+	0.242200i
$636$	−888935.			−2.19764
$637$	44641.8	−	44641.8i	0.110018	−	0.110018i
$638$	−1191.14	−	1191.14i	−0.00292632	−	0.00292632i
$639$		−	75294.2i		−	0.184400i
$640$	−4587.61	−	7513.42i	−0.0112002	−	0.0183433i
$641$	419719.			1.02151			0.510755	−	0.859727i	$-0.329366\pi$
$641$	419719.			1.02151			0.510755	+	0.859727i	$0.329366\pi$
$642$	−2939.31	+	2939.31i	−0.00713141	+	0.00713141i
$643$	−291772.	−	291772.i	−0.705703	−	0.705703i	0.259926	−	0.965629i	$-0.416302\pi$
$643$	−291772.	−	291772.i	−0.705703	−	0.705703i	−0.965629	+	0.259926i	$0.916302\pi$
$644$			22695.3i			0.0547223i
$645$	−10259.6	+	42433.4i	−0.0246611	+	0.101997i
$646$	1701.00			0.00407604
$647$	123334.	−	123334.i	0.294628	−	0.294628i	−0.544278	−	0.838905i	$-0.683196\pi$
$647$	123334.	−	123334.i	0.294628	−	0.294628i	0.838905	+	0.544278i	$0.183196\pi$
$648$	−3798.79	−	3798.79i	−0.00904681	−	0.00904681i
$649$		−	832203.i		−	1.97579i
$650$	−2199.50	−	1129.64i	−0.00520591	−	0.00267370i
$651$	319033.			0.752791
$652$	−85546.1	+	85546.1i	−0.201236	+	0.201236i
$653$	140737.	+	140737.i	0.330052	+	0.330052i	0.852606	−	0.522554i	$-0.175021\pi$
$653$	140737.	+	140737.i	0.330052	+	0.330052i	−0.522554	+	0.852606i	$0.675021\pi$
$654$			3322.83i			0.00776878i
$655$	78167.1	+	18899.4i	0.182197	+	0.0440520i
$656$	444075.			1.03193
$657$	207114.	−	207114.i	0.479820	−	0.479820i
$658$	−566.166	−	566.166i	−0.00130765	−	0.00130765i
$659$			38660.5i			0.0890218i	0.999009	+	0.0445109i	$0.0141729\pi$
$659$			38660.5i			0.0890218i	−0.999009	+	0.0445109i	$0.985827\pi$
$660$	724411.	−	442317.i	1.66302	−	1.01542i
$661$	−252816.			−0.578631			−0.289315	−	0.957234i	$-0.593428\pi$
$661$	−252816.			−0.578631			−0.289315	+	0.957234i	$0.593428\pi$
$662$	1026.14	−	1026.14i	0.00234148	−	0.00234148i
$663$	479740.	+	479740.i	1.09139	+	1.09139i
$664$		−	3533.56i		−	0.00801449i
$665$	−61569.3	−	100836.i	−0.139226	−	0.228020i
$666$	−1674.71			−0.00377566
$667$	23773.4	−	23773.4i	0.0534366	−	0.0534366i
$668$	−111971.	−	111971.i	−0.250931	−	0.250931i
$669$			368356.i			0.823031i
$670$	−666.035	+	2754.69i	−0.00148370	+	0.00613653i
$671$	−709579.			−1.57600
$672$	−2569.20	+	2569.20i	−0.00568930	+	0.00568930i
$673$	322576.	+	322576.i	0.712199	+	0.712199i	0.966995	−	0.254796i	$-0.0820083\pi$
$673$	322576.	+	322576.i	0.712199	+	0.712199i	−0.254796	+	0.966995i	$0.582008\pi$
$674$		−	4119.10i		−	0.00906740i
$675$	146693.	−	47141.9i	0.321961	−	0.103466i
$676$	−85079.0			−0.186178
$677$	105500.	−	105500.i	0.230184	−	0.230184i	−0.582586	−	0.812769i	$-0.697959\pi$
$677$	105500.	−	105500.i	0.230184	−	0.230184i	0.812769	+	0.582586i	$0.197959\pi$
$678$	1664.12	+	1664.12i	0.00362015	+	0.00362015i
$679$			114750.i			0.248893i
$680$	5183.41	+	1253.26i	0.0112098	+	0.00271033i
$681$	−518534.			−1.11811
$682$	3932.99	−	3932.99i	0.00845580	−	0.00845580i
$683$	−424431.	−	424431.i	−0.909841	−	0.909841i	0.0864179	−	0.996259i	$-0.472458\pi$
$683$	−424431.	−	424431.i	−0.909841	−	0.909841i	−0.996259	+	0.0864179i	$0.972458\pi$
$684$			246009.i			0.525823i
$685$	281262.	−	171735.i	0.599417	−	0.365997i
$686$	−136.539			−0.000290141
$687$	−534697.	+	534697.i	−1.13291	+	1.13291i
$688$	26594.2	+	26594.2i	0.0561836	+	0.0561836i
$689$			860439.i			1.81251i
$690$	−254.909	−	417.480i	−0.000535410	−	0.000876875i
$691$	240516.			0.503718			0.251859	−	0.967764i	$-0.418958\pi$
$691$	240516.			0.503718			0.251859	+	0.967764i	$0.418958\pi$
$692$	525364.	−	525364.i	1.09710	−	1.09710i
$693$	−140890.	−	140890.i	−0.293368	−	0.293368i
$694$		−	2511.49i		−	0.00521449i
$695$	60857.1	−	251702.i	0.125992	−	0.521096i
$696$	3588.30			0.00740748
$697$	−380445.	+	380445.i	−0.783117	+	0.783117i
$698$	633.403	+	633.403i	0.00130008	+	0.00130008i
$699$			500573.i			1.02450i
$700$	−56661.6	−	176316.i	−0.115636	−	0.359829i
$701$	451921.			0.919658			0.459829	−	0.888008i	$-0.347911\pi$
$701$	451921.			0.919658			0.459829	+	0.888008i	$0.347911\pi$
$702$	−689.661	+	689.661i	−0.00139946	+	0.00139946i
$703$	−233312.	−	233312.i	−0.472091	−	0.472091i
$704$		−	731179.i		−	1.47529i
$705$	−580904.	−	140452.i	−1.16876	−	0.282586i
$706$	−2325.58			−0.00466576
$707$	−5370.55	+	5370.55i	−0.0107443	+	0.0107443i
$708$	626741.	+	626741.i	1.25032	+	1.25032i
$709$		−	567115.i		−	1.12818i	−0.825713	−	0.564091i	$-0.809227\pi$
$709$		−	567115.i		−	1.12818i	0.825713	−	0.564091i	$-0.190773\pi$
$710$	−573.062	+	349.905i	−0.00113680	+	0.000694118i
$711$	−671016.			−1.32738
$712$	−3967.46	+	3967.46i	−0.00782623	+	0.00782623i
$713$	78496.5	+	78496.5i	0.154409	+	0.154409i
$714$		−	1467.31i		−	0.00287822i
$715$	−428138.	−	701189.i	−0.837474	−	1.37159i
$716$	66521.1			0.129758
$717$	594646.	−	594646.i	1.15670	−	1.15670i
$718$	598.605	+	598.605i	0.00116116	+	0.00116116i
$719$			316359.i			0.611959i	0.952038	+	0.305979i	$0.0989838\pi$
$719$			316359.i			0.611959i	−0.952038	+	0.305979i	$0.901016\pi$
$720$	−90623.1	+	374813.i	−0.174813	+	0.723018i
$721$	80501.6			0.154858
$722$	−991.057	+	991.057i	−0.00190118	+	0.00190118i
$723$	108513.	+	108513.i	0.207589	+	0.207589i
$724$			777637.i			1.48354i
$725$	−125339.	+	244045.i	−0.238456	+	0.464295i
$726$	−4403.09			−0.00835381
$727$	9776.49	−	9776.49i	0.0184975	−	0.0184975i	−0.697798	−	0.716295i	$-0.745836\pi$
$727$	9776.49	−	9776.49i	0.0184975	−	0.0184975i	0.716295	+	0.697798i	$0.245836\pi$
$728$	1657.88	+	1657.88i	0.00312818	+	0.00312818i
$729$			233328.i			0.439047i
$730$	−2538.83	−	613.845i	−0.00476418	−	0.00115189i
$731$	−45567.2			−0.0852742
$732$	534392.	−	534392.i	0.997327	−	0.997327i
$733$	160398.	+	160398.i	0.298533	+	0.298533i	0.840439	−	0.541906i	$-0.182297\pi$
$733$	160398.	+	160398.i	0.298533	+	0.298533i	−0.541906	+	0.840439i	$0.682297\pi$
$734$		−	1813.67i		−	0.00336641i
$735$	−86982.7	+	53110.6i	−0.161012	+	0.0983120i
$736$	−1264.28			−0.00233392
$737$	−665852.	+	665852.i	−1.22586	+	1.22586i
$738$	1588.78	+	1588.78i	0.00291710	+	0.00291710i
$739$			754750.i			1.38202i	0.722845	+	0.691010i	$0.242834\pi$
$739$			754750.i			1.38202i	−0.722845	+	0.691010i	$0.757166\pi$
$740$	−269529.	−	441425.i	−0.492201	−	0.806109i
$741$	558217.			1.01664
$742$	1315.85	−	1315.85i	0.00239000	−	0.00239000i
$743$	212897.	+	212897.i	0.385649	+	0.385649i	0.873132	−	0.487483i	$-0.162085\pi$
$743$	212897.	+	212897.i	0.385649	+	0.385649i	−0.487483	+	0.873132i	$0.662085\pi$
$744$			11848.1i			0.0214044i
$745$	21850.4	−	90372.0i	0.0393682	−	0.162825i
$746$	4618.82			0.00829953
$747$	−218901.	+	218901.i	−0.392289	+	0.392289i
$748$	626447.	+	626447.i	1.11965	+	1.11965i
$749$			301361.i			0.537184i
$750$	3022.64	+	2606.93i	0.00537358	+	0.00463454i
$751$	−177487.			−0.314693			−0.157347	−	0.987543i	$-0.550294\pi$
$751$	−177487.			−0.314693			−0.157347	+	0.987543i	$0.550294\pi$
$752$	−364069.	+	364069.i	−0.643795	+	0.643795i
$753$	−382472.	−	382472.i	−0.674543	−	0.674543i
$754$		−	1736.61i		−	0.00305464i
$755$	535189.	+	129399.i	0.938887	+	0.227006i
$756$	−73051.1			−0.127815
$757$	−402096.	+	402096.i	−0.701678	+	0.701678i	−0.964771	−	0.263093i	$-0.915258\pi$
$757$	−402096.	+	402096.i	−0.701678	+	0.701678i	0.263093	+	0.964771i	$0.415258\pi$
$758$	−3042.86	−	3042.86i	−0.00529594	−	0.00529594i
$759$		−	162527.i		−	0.282125i
$760$	3744.80	−	2286.53i	0.00648337	−	0.00395867i
$761$	374461.			0.646603			0.323301	−	0.946296i	$-0.395207\pi$
$761$	374461.			0.646603			0.323301	+	0.946296i	$0.395207\pi$
$762$	−1354.09	+	1354.09i	−0.00233204	+	0.00233204i
$763$	170341.	+	170341.i	0.292597	+	0.292597i
$764$		−	945238.i		−	1.61940i
$765$	−243469.	−	398745.i	−0.416027	−	0.681354i
$766$	−3287.78			−0.00560331
$767$	606650.	−	606650.i	1.03121	−	1.03121i
$768$	550611.	+	550611.i	0.933517	+	0.933517i
$769$			660539.i			1.11698i	0.829511	+	0.558490i	$0.188619\pi$
$769$			660539.i			1.11698i	−0.829511	+	0.558490i	$0.811381\pi$
$770$	−417.570	+	1727.05i	−0.000704284	+	0.00291288i
$771$	−479217.			−0.806163
$772$	−664361.	+	664361.i	−1.11473	+	1.11473i
$773$	166751.	+	166751.i	0.279067	+	0.279067i	0.832737	−	0.553669i	$-0.186773\pi$
$773$	166751.	+	166751.i	0.279067	+	0.279067i	−0.553669	+	0.832737i	$0.686773\pi$
$774$			190.293i			0.000317645i
$775$	−805804.	−	413851.i	−1.34161	−	0.689035i
$776$	−4261.51			−0.00707685
$777$	−201258.	+	201258.i	−0.333359	+	0.333359i
$778$	4372.63	+	4372.63i	0.00722410	+	0.00722410i
$779$			442679.i			0.729481i
$780$	850508.	+	205638.i	1.39794	+	0.337998i
$781$	−223096.			−0.365754
$782$	361.023	−	361.023i	0.000590366	−	0.000590366i
$783$	76521.2	+	76521.2i	0.124813	+	0.124813i
$784$			87800.4i			0.142845i
$785$	354513.	−	216462.i	0.575299	−	0.351271i
$786$	821.754			0.00133014
$787$	334297.	−	334297.i	0.539738	−	0.539738i	−0.383714	−	0.923452i	$-0.625355\pi$
$787$	334297.	−	334297.i	0.539738	−	0.539738i	0.923452	+	0.383714i	$0.125355\pi$
$788$	232900.	+	232900.i	0.375075	+	0.375075i
$789$		−	482804.i		−	0.775563i
$790$	3118.33	+	5107.09i	0.00499652	+	0.00818312i
$791$	170619.			0.272693
$792$	5232.29	−	5232.29i	0.00834145	−	0.00834145i
$793$	−517261.	−	517261.i	−0.822552	−	0.822552i
$794$		−	480.919i		−	0.000762836i
$795$	326430.	−	1.35010e6i	0.516483	−	2.13615i
$796$	−1.10030e6			−1.73653
$797$	316482.	−	316482.i	0.498232	−	0.498232i	−0.412655	−	0.910887i	$-0.635398\pi$
$797$	316482.	−	316482.i	0.498232	−	0.498232i	0.910887	+	0.412655i	$0.135398\pi$
$798$	−853.666	−	853.666i	−0.00134055	−	0.00134055i
$799$		−	623805.i		−	0.977137i
$800$	9821.96	−	3156.42i	0.0153468	−	0.00493190i
$801$	491561.			0.766147
$802$	−575.368	+	575.368i	−0.000894535	+	0.000894535i
$803$	−613676.	−	613676.i	−0.951718	−	0.951718i
$804$		−	1.00292e6i		−	1.55151i
$805$	−34469.2	−	8334.05i	−0.0531912	−	0.0128607i
$806$	5734.06			0.00882657
$807$	475468.	−	475468.i	0.730086	−	0.730086i
$808$	−199.449	−	199.449i	−0.000305498	−	0.000305498i
$809$			287899.i			0.439889i	0.975512	+	0.219945i	$0.0705877\pi$
$809$			287899.i			0.439889i	−0.975512	+	0.219945i	$0.929412\pi$
$810$	3582.20	−	2187.25i	0.00545985	−	0.00333372i
$811$	−265302.			−0.403366			−0.201683	−	0.979451i	$-0.564641\pi$
$811$	−265302.			−0.403366			−0.201683	+	0.979451i	$0.564641\pi$
$812$	91973.7	−	91973.7i	0.139493	−	0.139493i
$813$	722517.	+	722517.i	1.09312	+	1.09312i
$814$			4962.16i			0.00748897i
$815$	−98512.1	−	161340.i	−0.148311	−	0.242899i
$816$	−943541.			−1.41703
$817$	−26510.6	+	26510.6i	−0.0397169	+	0.0397169i
$818$	−258.230	−	258.230i	−0.000385923	−	0.000385923i
$819$		−	205409.i		−	0.306232i
$820$	−163076.	+	674473.i	−0.242528	+	1.00308i
$821$	−61802.8			−0.0916899			−0.0458450	−	0.998949i	$-0.514598\pi$
$821$	−61802.8			−0.0916899			−0.0458450	+	0.998949i	$0.514598\pi$
$822$	2381.13	−	2381.13i	0.00352403	−	0.00352403i
$823$	−729615.	−	729615.i	−1.07719	−	1.07719i	−0.996760	−	0.0804343i	$-0.974369\pi$
$823$	−729615.	−	729615.i	−1.07719	−	1.07719i	−0.0804343	−	0.996760i	$-0.525631\pi$
$824$			2989.63i			0.00440314i
$825$	405769.	+	1.26265e6i	0.596171	+	1.85513i
$826$	−1855.47			−0.00271952
$827$	341394.	−	341394.i	0.499165	−	0.499165i	−0.412013	−	0.911178i	$-0.635174\pi$
$827$	341394.	−	341394.i	0.499165	−	0.499165i	0.911178	+	0.412013i	$0.135174\pi$
$828$	52213.5	+	52213.5i	0.0761592	+	0.0761592i
$829$			83296.0i			0.121203i	0.998162	+	0.0606017i	$0.0193019\pi$
$829$			83296.0i			0.121203i	−0.998162	+	0.0606017i	$0.980698\pi$
$830$	2683.31	+	648.778i	0.00389507	+	0.000941760i
$831$	−874068.			−1.26574
$832$	533006.	−	533006.i	0.769991	−	0.769991i
$833$	−75219.8	−	75219.8i	−0.108403	−	0.108403i
$834$		−	2646.09i		−	0.00380428i
$835$	211178.	−	128942.i	0.302883	−	0.184937i
$836$	728923.			1.04296
$837$	−252663.	+	252663.i	−0.360654	+	0.360654i
$838$	−4434.15	−	4434.15i	−0.00631426	−	0.00631426i
$839$			1.16611e6i			1.65659i	0.560296	+	0.828293i	$0.310688\pi$
$839$			1.16611e6i			1.65659i	−0.560296	+	0.828293i	$0.689312\pi$
$840$	−1972.39	−	3230.32i	−0.00279534	−	0.00457811i
$841$	514596.			0.727569
$842$	−1607.22	+	1607.22i	−0.00226700	+	0.00226700i
$843$	409772.	+	409772.i	0.576616	+	0.576616i
$844$		−	649586.i		−	0.911909i
$845$	31242.3	−	129217.i	0.0437552	−	0.180969i
$846$	−2605.08			−0.00363982
$847$	−225719.	+	225719.i	−0.314632	+	0.314632i
$848$	−846144.	−	846144.i	−1.17666	−	1.17666i
$849$		−	1.34812e6i		−	1.87031i
$850$	−1903.40	+	3706.07i	−0.00263446	+	0.00512952i
$851$	−99037.1			−0.136754
$852$	168016.	−	168016.i	0.231457	−	0.231457i
$853$	−904459.	−	904459.i	−1.24306	−	1.24306i	−0.958726	−	0.284330i	$-0.908229\pi$
$853$	−904459.	−	904459.i	−1.24306	−	1.24306i	−0.284330	−	0.958726i	$-0.591771\pi$
$854$			1582.07i			0.00216925i
$855$	−373635.	−	90338.3i	−0.511111	−	0.123578i
$856$	−11191.8			−0.0152739
$857$	−206785.	+	206785.i	−0.281552	+	0.281552i	−0.833728	−	0.552176i	$-0.813798\pi$
$857$	−206785.	+	206785.i	−0.281552	+	0.281552i	0.552176	+	0.833728i	$0.313798\pi$
$858$	−5936.19	−	5936.19i	−0.00806367	−	0.00806367i
$859$		−	428256.i		−	0.580386i	−0.956968	−	0.290193i	$-0.906280\pi$
$859$		−	428256.i		−	0.580386i	0.956968	−	0.290193i	$-0.0937195\pi$
$860$	−50158.0	+	30625.9i	−0.0678178	+	0.0414087i
$861$	381862.			0.515110
$862$	2939.81	−	2939.81i	0.00395645	−	0.00395645i
$863$	572263.	+	572263.i	0.768376	+	0.768376i	0.977821	−	0.209444i	$-0.0671655\pi$
$863$	572263.	+	572263.i	0.768376	+	0.768376i	−0.209444	+	0.977821i	$0.567165\pi$
$864$		−	4069.42i		−	0.00545136i
$865$	604992.	+	990835.i	0.808570	+	1.32425i
$866$	−3758.49			−0.00501161
$867$	106427.	−	106427.i	0.141584	−	0.141584i
$868$	303685.	+	303685.i	0.403073	+	0.403073i
$869$			1.98821e6i			2.63283i
$870$	−658.829	+	2724.89i	−0.000870431	+	0.00360006i
$871$	−970770.			−1.27962
$872$	−6326.04	+	6326.04i	−0.00831953	+	0.00831953i
$873$	263997.	+	263997.i	0.346394	+	0.346394i
$874$		−	420.080i		−	0.000549933i
$875$	288593.	−	21310.7i	0.376938	−	0.0278343i
$876$	924332.			1.20454
$877$	45559.5	−	45559.5i	0.0592352	−	0.0592352i	−0.676869	−	0.736104i	$-0.736664\pi$
$877$	45559.5	−	45559.5i	0.0592352	−	0.0592352i	0.736104	+	0.676869i	$0.236664\pi$
$878$	1828.73	+	1828.73i	0.00237225	+	0.00237225i
$879$		−	68708.0i		−	0.0889261i
$880$	1.11057e6	+	268515.i	1.43410	+	0.346740i
$881$	−85914.1			−0.110691			−0.0553455	−	0.998467i	$-0.517626\pi$
$881$	−85914.1			−0.110691			−0.0553455	+	0.998467i	$0.517626\pi$
$882$	−314.126	+	314.126i	−0.000403800	+	0.000403800i
$883$	−340402.	−	340402.i	−0.436586	−	0.436586i	0.454275	−	0.890861i	$-0.349898\pi$
$883$	−340402.	−	340402.i	−0.436586	−	0.436586i	−0.890861	+	0.454275i	$0.849898\pi$
$884$			913321.i			1.16874i
$885$	−1.18203e6	+	721735.i	−1.50919	+	0.921491i
$886$	−1291.16			−0.00164480
$887$	97903.9	−	97903.9i	0.124438	−	0.124438i	−0.642145	−	0.766583i	$-0.721955\pi$
$887$	97903.9	−	97903.9i	0.124438	−	0.124438i	0.766583	+	0.642145i	$0.221955\pi$
$888$	−7474.22	−	7474.22i	−0.00947851	−	0.00947851i
$889$			138831.i			0.175664i
$890$	−2284.37	−	3741.26i	−0.00288394	−	0.00472321i
$891$	1.39457e6			1.75665
$892$	−350635.	+	350635.i	−0.440682	+	0.440682i
$893$	−362924.	−	362924.i	−0.455107	−	0.455107i
$894$		−	950.062i		−	0.00118871i
$895$	−24427.5	+	101031.i	−0.0304953	+	0.126127i
$896$	−6521.56			−0.00812335
$897$	118477.	−	118477.i	0.147248	−	0.147248i
$898$	−894.619	−	894.619i	−0.00110939	−	0.00110939i
$899$		−	636221.i		−	0.787207i
$900$	−535996.	−	275282.i	−0.661724	−	0.339854i
$901$	1.44981e6			1.78591
$902$	4707.53	−	4707.53i	0.00578602	−	0.00578602i
$903$	22868.4	+	22868.4i	0.0280454	+	0.0280454i
$904$			6336.35i			0.00775358i
$905$	−1.18106e6	−	285560.i	−1.44203	−	0.348658i
$906$	5626.33			0.00685439
$907$	−398218.	+	398218.i	−0.484068	+	0.484068i	−0.906428	−	0.422360i	$-0.861202\pi$
$907$	−398218.	+	398218.i	−0.484068	+	0.484068i	0.422360	+	0.906428i	$0.361202\pi$
$908$	−493588.	−	493588.i	−0.598677	−	0.598677i
$909$			24711.3i			0.0299067i
$910$	−1563.36	+	954.569i	−0.00188789	+	0.00115272i
$911$	−250366.			−0.301674			−0.150837	−	0.988559i	$-0.548197\pi$
$911$	−250366.			−0.301674			−0.150837	+	0.988559i	$0.548197\pi$
$912$	−548944.	+	548944.i	−0.659991	+	0.659991i
$913$	648600.	+	648600.i	0.778100	+	0.778100i
$914$			8323.15i			0.00996312i
$915$	615389.	+	1.00786e6i	0.735034	+	1.20381i
$916$	−1.01795e6			−1.21320
$917$	42126.3	−	42126.3i	0.0500973	−	0.0500973i
$918$	1162.05	+	1162.05i	0.00137893	+	0.00137893i
$919$			319536.i			0.378345i	0.981944	+	0.189173i	$0.0605806\pi$
$919$			319536.i			0.378345i	−0.981944	+	0.189173i	$0.939419\pi$
$920$	309.506	−	1280.10i	0.000365673	−	0.00151241i
$921$	−389129.			−0.458748
$922$	5497.79	−	5497.79i	0.00646735	−	0.00646735i
$923$	−162630.	−	162630.i	−0.190896	−	0.190896i
$924$		−	628780.i		−	0.736469i
$925$	769404.	−	247258.i	0.899231	−	0.288980i
$926$	493.935			0.000576034
$927$	185204.	−	185204.i	0.215522	−	0.215522i
$928$	5123.53	+	5123.53i	0.00594940	+	0.00594940i
$929$		−	318241.i		−	0.368744i	−0.982857	−	0.184372i	$-0.940975\pi$
$929$		−	318241.i		−	0.368744i	0.982857	−	0.184372i	$-0.0590251\pi$
$930$	−8997.21	−	2175.37i	−0.0104026	−	0.00251516i
$931$	−87524.4			−0.100979
$932$	−476491.	+	476491.i	−0.548558	+	0.548558i
$933$	256075.	+	256075.i	0.294174	+	0.294174i
$934$		−	5732.55i		−	0.00657134i
$935$	−1.18148e6	+	721396.i	−1.35146	+	0.825184i
$936$	7628.36			0.00870722
$937$	−201589.	+	201589.i	−0.229608	+	0.229608i	−0.812529	−	0.582921i	$-0.801910\pi$
$937$	−201589.	+	201589.i	−0.229608	+	0.229608i	0.582921	+	0.812529i	$0.301910\pi$
$938$	1484.57	+	1484.57i	0.00168731	+	0.00168731i
$939$			203547.i			0.230851i
$940$	−419262.	−	686652.i	−0.474493	−	0.777107i
$941$	−438035.			−0.494686			−0.247343	−	0.968928i	$-0.579557\pi$
$941$	−438035.			−0.494686			−0.247343	+	0.968928i	$0.579557\pi$
$942$	3001.27	−	3001.27i	0.00338223	−	0.00338223i
$943$	93955.1	+	93955.1i	0.105657	+	0.105657i
$944$			1.19314e6i			1.33890i
$945$	26825.5	−	110949.i	0.0300389	−	0.124239i
$946$	563.837			0.000630045
$947$	1.20314e6	−	1.20314e6i	1.34158	−	1.34158i	0.447098	−	0.894485i	$-0.352457\pi$
$947$	1.20314e6	−	1.20314e6i	1.34158	−	1.34158i	0.894485	−	0.447098i	$-0.147543\pi$
$948$	−1.49734e6	−	1.49734e6i	−1.66612	−	1.66612i
$949$		−	894701.i		−	0.993449i
$950$	1048.78	+	3263.54i	0.00116209	+	0.00361611i
$951$	887990.			0.981855
$952$	2793.47	−	2793.47i	0.00308227	−	0.00308227i
$953$	323897.	+	323897.i	0.356633	+	0.356633i	0.862570	−	0.505937i	$-0.168853\pi$
$953$	323897.	+	323897.i	0.356633	+	0.356633i	−0.505937	+	0.862570i	$0.668853\pi$
$954$		−	6054.55i		−	0.00665250i
$955$	1.43561e6	+	347106.i	1.57409	+	0.380588i
$956$	1.13208e6			1.23868
$957$	−658648.	+	658648.i	−0.719167	+	0.719167i
$958$	5277.83	+	5277.83i	0.00575075	+	0.00575075i
$959$		−	244132.i		−	0.265453i
$960$	−1.03854e6	+	634121.i	−1.12689	+	0.688065i
$961$	1.17720e6			1.27468
$962$	−3617.26	+	3617.26i	−0.00390867	+	0.00390867i
$963$	693320.	+	693320.i	0.747620	+	0.747620i
$964$			206584.i			0.222302i
$965$	−765057.	−	1.25298e6i	−0.821560	−	1.34552i
$966$	−362.368			−0.000388325
$967$	206662.	−	206662.i	0.221008	−	0.221008i	−0.587915	−	0.808923i	$-0.700051\pi$
$967$	206662.	−	206662.i	0.221008	−	0.221008i	0.808923	+	0.587915i	$0.200051\pi$
$968$	−8382.65	−	8382.65i	−0.00894603	−	0.00894603i
$969$		−	940576.i		−	1.00172i
$970$	782.434	−	3236.11i	0.000831580	−	0.00343937i
$971$	772001.			0.818803			0.409402	−	0.912354i	$-0.365737\pi$
$971$	772001.			0.818803			0.409402	+	0.912354i	$0.365737\pi$
$972$	−824348.	+	824348.i	−0.872525	+	0.872525i
$973$	−135649.	−	135649.i	−0.143282	−	0.143282i
$974$			1075.95i			0.00113416i
$975$	−624638.	+	1.21622e6i	−0.657082	+	1.27939i
$976$	1.01734e6			1.06798
$977$	−433267.	+	433267.i	−0.453907	+	0.453907i	−0.896649	−	0.442742i	$-0.854006\pi$
$977$	−433267.	+	433267.i	−0.453907	+	0.453907i	0.442742	+	0.896649i	$0.354006\pi$
$978$	−1365.88	−	1365.88i	−0.00142802	−	0.00142802i
$979$		−	1.45649e6i		−	1.51964i
$980$	−133354.	−	32242.5i	−0.138852	−	0.0335720i
$981$	783784.			0.814439
$982$	2747.26	−	2747.26i	0.00284890	−	0.00284890i
$983$	697281.	+	697281.i	0.721607	+	0.721607i	0.968933	−	0.247325i	$-0.0795516\pi$
$983$	697281.	+	697281.i	0.721607	+	0.721607i	−0.247325	+	0.968933i	$0.579552\pi$
$984$			14181.4i			0.0146463i
$985$	−439249.	+	268200.i	−0.452729	+	0.276431i
$986$	−2926.13			−0.00300981
$987$	−313064.	+	313064.i	−0.321365	+	0.321365i
$988$	531362.	+	531362.i	0.544348	+	0.544348i
$989$			11253.3i			0.0115050i
$990$	3012.63	+	4933.98i	0.00307380	+	0.00503416i
$991$	1.67220e6			1.70271			0.851354	−	0.524591i	$-0.175782\pi$
$991$	1.67220e6			1.70271			0.851354	+	0.524591i	$0.175782\pi$
$992$	−16917.2	+	16917.2i	−0.0171912	+	0.0171912i
$993$	−567410.	−	567410.i	−0.575438	−	0.575438i
$994$			497.411i			0.000503434i
$995$	404045.	−	1.67111e6i	0.408116	−	1.68795i
$996$	−976935.			−0.984798
$997$	−387338.	+	387338.i	−0.389672	+	0.389672i	−0.874571	−	0.484898i	$-0.838857\pi$
$997$	−387338.	+	387338.i	−0.389672	+	0.389672i	0.484898	+	0.874571i	$0.338857\pi$
$998$	−2830.18	−	2830.18i	−0.00284154	−	0.00284154i
$999$		−	318778.i		−	0.319417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.8.6	✓	24
5.2	odd	4	inner	35.5.g.a.22.6	yes	24
5.3	odd	4		175.5.g.c.57.7		24
5.4	even	2		175.5.g.c.43.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.6	✓	24	1.1	even	1	trivial
35.5.g.a.22.6	yes	24	5.2	odd	4	inner
175.5.g.c.43.7		24	5.4	even	2
175.5.g.c.57.7		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0151985 + 0.0151985i) q^{2} +(8.40408 + 8.40408i) q^{3} +15.9995i q^{4} +(-24.2998 - 5.87527i) q^{5} -0.255459 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-0.486345 - 0.486345i) q^{8} +60.2572i q^{9} +O(q^{10})\)	\(q+(-0.0151985 + 0.0151985i) q^{2} +(8.40408 + 8.40408i) q^{3} +15.9995i q^{4} +(-24.2998 - 5.87527i) q^{5} -0.255459 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-0.486345 - 0.486345i) q^{8} +60.2572i q^{9} +(0.458616 - 0.280025i) q^{10} +178.541 q^{11} +(-134.461 + 134.461i) q^{12} +(130.151 + 130.151i) q^{13} -0.398073i q^{14} +(-154.841 - 253.594i) q^{15} -255.978 q^{16} +(219.300 - 219.300i) q^{17} +(-0.915819 - 0.915819i) q^{18} -255.173i q^{19} +(94.0016 - 388.786i) q^{20} -220.116 q^{21} +(-2.71356 + 2.71356i) q^{22} +(-54.1585 - 54.1585i) q^{23} -8.17456i q^{24} +(555.962 + 285.536i) q^{25} -3.95620 q^{26} +(174.324 - 174.324i) q^{27} +(-209.527 - 209.527i) q^{28} +438.959i q^{29} +(6.20760 + 1.50089i) q^{30} -1449.39 q^{31} +(11.6720 - 11.6720i) q^{32} +(1500.48 + 1500.48i) q^{33} +6.66605i q^{34} +(395.167 - 241.284i) q^{35} -964.087 q^{36} +(914.326 - 914.326i) q^{37} +(3.87825 + 3.87825i) q^{38} +2187.60i q^{39} +(8.96069 + 14.6755i) q^{40} -1734.82 q^{41} +(3.34544 - 3.34544i) q^{42} +(-103.893 - 103.893i) q^{43} +2856.58i q^{44} +(354.027 - 1464.24i) q^{45} +1.64625 q^{46} +(1422.27 - 1422.27i) q^{47} +(-2151.26 - 2151.26i) q^{48} -343.000i q^{49} +(-12.7895 + 4.11008i) q^{50} +3686.03 q^{51} +(-2082.36 + 2082.36i) q^{52} +(3305.54 + 3305.54i) q^{53} +5.29893i q^{54} +(-4338.52 - 1048.98i) q^{55} +12.7381 q^{56} +(2144.50 - 2144.50i) q^{57} +(-6.67152 - 6.67152i) q^{58} -4661.12i q^{59} +(4057.39 - 2477.39i) q^{60} -3974.31 q^{61} +(22.0285 - 22.0285i) q^{62} +(-789.116 - 789.116i) q^{63} -4095.29i q^{64} +(-2397.97 - 3927.32i) q^{65} -45.6100 q^{66} +(-3729.40 + 3729.40i) q^{67} +(3508.69 + 3508.69i) q^{68} -910.305i q^{69} +(-2.33878 + 9.67310i) q^{70} -1249.55 q^{71} +(29.3058 - 29.3058i) q^{72} +(-3437.16 - 3437.16i) q^{73} +27.7928i q^{74} +(2272.69 + 7072.02i) q^{75} +4082.66 q^{76} +(-2338.14 + 2338.14i) q^{77} +(-33.2482 - 33.2482i) q^{78} +11135.9i q^{79} +(6220.21 + 1503.94i) q^{80} +7810.90 q^{81} +(26.3666 - 26.3666i) q^{82} +(3632.77 + 3632.77i) q^{83} -3521.76i q^{84} +(-6617.39 + 4040.50i) q^{85} +3.15802 q^{86} +(-3689.05 + 3689.05i) q^{87} +(-86.8327 - 86.8327i) q^{88} -8157.71i q^{89} +(16.8736 + 27.6349i) q^{90} -3408.86 q^{91} +(866.511 - 866.511i) q^{92} +(-12180.8 - 12180.8i) q^{93} +43.2326i q^{94} +(-1499.21 + 6200.67i) q^{95} +196.185 q^{96} +(4381.16 - 4381.16i) q^{97} +(5.21308 + 5.21308i) q^{98} +10758.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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