LMFDB - Embedded newform 15.5.f.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,5,Mod(7,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("15.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	15.f (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:	$1.55054944626$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 $ x^8 - 60x^5 + 1973x^4 - 3300x^3 + 1800x^2 + 31560*x + 276676
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$3.30519 - 3.30519i$ of defining polynomial
Character	$\chi$	$=$	15.13
Dual form			15.5.f.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.30519 - 3.30519i) q^{2} +(3.67423 + 3.67423i) q^{3} -5.84858i q^{4} +(-16.2403 - 19.0066i) q^{5} +24.2881 q^{6} +(-33.1649 + 33.1649i) q^{7} +(33.5524 + 33.5524i) q^{8} +27.0000i q^{9} +O(q^{10})$	\(q+(3.30519 - 3.30519i) q^{2} +(3.67423 + 3.67423i) q^{3} -5.84858i q^{4} +(-16.2403 - 19.0066i) q^{5} +24.2881 q^{6} +(-33.1649 + 33.1649i) q^{7} +(33.5524 + 33.5524i) q^{8} +27.0000i q^{9} +(-116.498 - 9.14312i) q^{10} +55.3118 q^{11} +(21.4891 - 21.4891i) q^{12} +(-161.918 - 161.918i) q^{13} +219.233i q^{14} +(10.1640 - 129.506i) q^{15} +315.371 q^{16} +(278.961 - 278.961i) q^{17} +(89.2402 + 89.2402i) q^{18} +179.871i q^{19} +(-111.162 + 94.9829i) q^{20} -243.711 q^{21} +(182.816 - 182.816i) q^{22} +(-398.080 - 398.080i) q^{23} +246.559i q^{24} +(-97.5033 + 617.348i) q^{25} -1070.34 q^{26} +(-99.2043 + 99.2043i) q^{27} +(193.968 + 193.968i) q^{28} +547.472i q^{29} +(-394.447 - 461.635i) q^{30} +1538.11 q^{31} +(505.525 - 505.525i) q^{32} +(203.229 + 203.229i) q^{33} -1844.04i q^{34} +(1168.96 + 91.7437i) q^{35} +157.912 q^{36} +(-1660.74 + 1660.74i) q^{37} +(594.509 + 594.509i) q^{38} -1189.85i q^{39} +(92.8156 - 1182.62i) q^{40} -307.601 q^{41} +(-805.512 + 805.512i) q^{42} +(104.254 + 104.254i) q^{43} -323.496i q^{44} +(513.179 - 438.489i) q^{45} -2631.46 q^{46} +(-346.159 + 346.159i) q^{47} +(1158.75 + 1158.75i) q^{48} +201.180i q^{49} +(1718.19 + 2362.72i) q^{50} +2049.94 q^{51} +(-946.991 + 946.991i) q^{52} +(-2025.02 - 2025.02i) q^{53} +655.779i q^{54} +(-898.282 - 1051.29i) q^{55} -2225.52 q^{56} +(-660.889 + 660.889i) q^{57} +(1809.50 + 1809.50i) q^{58} -2854.49i q^{59} +(-757.424 - 59.4450i) q^{60} -1057.37 q^{61} +(5083.73 - 5083.73i) q^{62} +(-895.452 - 895.452i) q^{63} +1704.23i q^{64} +(-447.912 + 5707.12i) q^{65} +1343.42 q^{66} +(3756.53 - 3756.53i) q^{67} +(-1631.53 - 1631.53i) q^{68} -2925.28i q^{69} +(4166.87 - 3560.41i) q^{70} +1429.24 q^{71} +(-905.914 + 905.914i) q^{72} +(813.690 + 813.690i) q^{73} +10978.2i q^{74} +(-2626.53 + 1910.03i) q^{75} +1051.99 q^{76} +(-1834.41 + 1834.41i) q^{77} +(-3932.68 - 3932.68i) q^{78} +4854.69i q^{79} +(-5121.74 - 5994.14i) q^{80} -729.000 q^{81} +(-1016.68 + 1016.68i) q^{82} +(-1316.57 - 1316.57i) q^{83} +1425.37i q^{84} +(-9832.53 - 771.687i) q^{85} +689.160 q^{86} +(-2011.54 + 2011.54i) q^{87} +(1855.84 + 1855.84i) q^{88} -5185.49i q^{89} +(246.864 - 3145.44i) q^{90} +10740.0 q^{91} +(-2328.20 + 2328.20i) q^{92} +(5651.36 + 5651.36i) q^{93} +2288.24i q^{94} +(3418.74 - 2921.17i) q^{95} +3714.83 q^{96} +(3495.32 - 3495.32i) q^{97} +(664.940 + 664.940i) q^{98} +1493.42i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8}+O(q^{10}) $ 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8} + 104 q^{10} - 288 q^{11} - 360 q^{12} - 340 q^{13} + 144 q^{15} + 620 q^{16} + 900 q^{17} + 564 q^{20} + 792 q^{21} - 1100 q^{22} - 1560 q^{23} - 1204 q^{25} - 3024 q^{26} + 3580 q^{28} - 2664 q^{30} - 512 q^{31} + 4980 q^{32} + 2700 q^{33} + 6600 q^{35} + 2484 q^{36} - 3820 q^{37} - 7680 q^{38} - 2952 q^{40} - 2712 q^{41} - 7380 q^{42} - 1240 q^{43} - 1944 q^{45} + 13528 q^{46} + 4800 q^{47} + 3600 q^{48} + 3744 q^{50} + 6264 q^{51} - 1240 q^{52} + 1020 q^{53} - 3644 q^{55} - 30720 q^{56} - 5400 q^{57} + 2340 q^{58} - 1044 q^{60} - 4760 q^{61} + 28680 q^{62} + 540 q^{63} - 1212 q^{65} + 10008 q^{66} - 8920 q^{67} - 1920 q^{68} + 7380 q^{70} + 7536 q^{71} - 4860 q^{72} + 11600 q^{73} - 5976 q^{75} + 4344 q^{76} - 360 q^{77} - 4680 q^{78} + 10644 q^{80} - 5832 q^{81} - 27200 q^{82} - 32400 q^{83} - 15628 q^{85} + 14592 q^{86} + 10620 q^{87} - 14340 q^{88} + 8964 q^{90} + 16528 q^{91} - 31800 q^{92} + 14040 q^{93} + 18864 q^{95} - 4068 q^{96} + 58640 q^{97} + 46440 q^{98}+O(q^{100}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	3.30519	−	3.30519i	0.826298	−	0.826298i	−0.160705	−	0.987003i	$-0.551377\pi$
$2$	3.30519	−	3.30519i	0.826298	−	0.826298i	0.987003	+	0.160705i	$0.0513767\pi$
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$4$		−	5.84858i		−	0.365537i
$5$	−16.2403	−	19.0066i	−0.649613	−	0.760265i
$5$	−16.2403	−	19.0066i	−0.649613	−	0.760265i
$6$	24.2881			0.674669
$7$	−33.1649	+	33.1649i	−0.676834	+	0.676834i	−0.959283	−	0.282448i	$-0.908853\pi$
$7$	−33.1649	+	33.1649i	−0.676834	+	0.676834i	0.282448	+	0.959283i	$0.408853\pi$
$8$	33.5524	+	33.5524i	0.524256	+	0.524256i
$9$			27.0000i			0.333333i
$10$	−116.498	−	9.14312i	−1.16498	−	0.0914312i
$11$	55.3118			0.457122			0.228561	−	0.973530i	$-0.426598\pi$
$11$	55.3118			0.457122			0.228561	+	0.973530i	$0.426598\pi$
$12$	21.4891	−	21.4891i	0.149230	−	0.149230i
$13$	−161.918	−	161.918i	−0.958095	−	0.958095i	0.0410619	−	0.999157i	$-0.486926\pi$
$13$	−161.918	−	161.918i	−0.958095	−	0.958095i	−0.999157	+	0.0410619i	$0.986926\pi$
$14$			219.233i			1.11853i
$15$	10.1640	−	129.506i	0.0451733	−	0.575580i
$16$	315.371			1.23192
$17$	278.961	−	278.961i	0.965264	−	0.965264i	−0.0341531	−	0.999417i	$-0.510873\pi$
$17$	278.961	−	278.961i	0.965264	−	0.965264i	0.999417	+	0.0341531i	$0.0108734\pi$
$18$	89.2402	+	89.2402i	0.275433	+	0.275433i
$19$			179.871i			0.498258i	0.968470	+	0.249129i	$0.0801443\pi$
$19$			179.871i			0.498258i	−0.968470	+	0.249129i	$0.919856\pi$
$20$	−111.162	+	94.9829i	−0.277905	+	0.237457i
$21$	−243.711			−0.552633
$22$	182.816	−	182.816i	0.377719	−	0.377719i
$23$	−398.080	−	398.080i	−0.752514	−	0.752514i	0.222434	−	0.974948i	$-0.428600\pi$
$23$	−398.080	−	398.080i	−0.752514	−	0.752514i	−0.974948	+	0.222434i	$0.928600\pi$
$24$			246.559i			0.428053i
$25$	−97.5033	+	617.348i	−0.156005	+	0.987756i
$26$	−1070.34			−1.58334
$27$	−99.2043	+	99.2043i	−0.136083	+	0.136083i
$28$	193.968	+	193.968i	0.247408	+	0.247408i
$29$			547.472i			0.650977i	0.945546	+	0.325488i	$0.105529\pi$
$29$			547.472i			0.650977i	−0.945546	+	0.325488i	$0.894471\pi$
$30$	−394.447	−	461.635i	−0.438274	−	0.512927i
$31$	1538.11			1.60053			0.800263	−	0.599649i	$-0.204693\pi$
$31$	1538.11			1.60053			0.800263	+	0.599649i	$0.204693\pi$
$32$	505.525	−	505.525i	0.493677	−	0.493677i
$33$	203.229	+	203.229i	0.186619	+	0.186619i
$34$		−	1844.04i		−	1.59519i
$35$	1168.96	+	91.7437i	0.954254	+	0.0748928i
$36$	157.912			0.121846
$37$	−1660.74	+	1660.74i	−1.21311	+	1.21311i	−0.243109	+	0.969999i	$0.578167\pi$
$37$	−1660.74	+	1660.74i	−1.21311	+	1.21311i	−0.969999	+	0.243109i	$0.921833\pi$
$38$	594.509	+	594.509i	0.411710	+	0.411710i
$39$		−	1189.85i		−	0.782281i
$40$	92.8156	−	1182.62i	0.0580097	−	0.739137i
$41$	−307.601			−0.182987			−0.0914933	−	0.995806i	$-0.529164\pi$
$41$	−307.601			−0.182987			−0.0914933	+	0.995806i	$0.529164\pi$
$42$	−805.512	+	805.512i	−0.456640	+	0.456640i
$43$	104.254	+	104.254i	0.0563841	+	0.0563841i	0.734737	−	0.678353i	$-0.237306\pi$
$43$	104.254	+	104.254i	0.0563841	+	0.0563841i	−0.678353	+	0.734737i	$0.737306\pi$
$44$		−	323.496i		−	0.167095i
$45$	513.179	−	438.489i	0.253422	−	0.216538i
$46$	−2631.46			−1.24360
$47$	−346.159	+	346.159i	−0.156704	+	0.156704i	−0.781104	−	0.624400i	$-0.785343\pi$
$47$	−346.159	+	346.159i	−0.156704	+	0.156704i	0.624400	+	0.781104i	$0.285343\pi$
$48$	1158.75	+	1158.75i	0.502929	+	0.502929i
$49$			201.180i			0.0837903i
$50$	1718.19	+	2362.72i	0.687274	+	0.945088i
$51$	2049.94			0.788134
$52$	−946.991	+	946.991i	−0.350219	+	0.350219i
$53$	−2025.02	−	2025.02i	−0.720906	−	0.720906i	0.247884	−	0.968790i	$-0.420265\pi$
$53$	−2025.02	−	2025.02i	−0.720906	−	0.720906i	−0.968790	+	0.247884i	$0.920265\pi$
$54$			655.779i			0.224890i
$55$	−898.282	−	1051.29i	−0.296953	−	0.347534i
$56$	−2225.52			−0.709669
$57$	−660.889	+	660.889i	−0.203413	+	0.203413i
$58$	1809.50	+	1809.50i	0.537901	+	0.537901i
$59$		−	2854.49i		−	0.820020i	−0.912081	−	0.410010i	$-0.865525\pi$
$59$		−	2854.49i		−	0.820020i	0.912081	−	0.410010i	$-0.134475\pi$
$60$	−757.424	−	59.4450i	−0.210396	−	0.0165125i
$61$	−1057.37			−0.284163			−0.142082	−	0.989855i	$-0.545380\pi$
$61$	−1057.37			−0.284163			−0.142082	+	0.989855i	$0.545380\pi$
$62$	5083.73	−	5083.73i	1.32251	−	1.32251i
$63$	−895.452	−	895.452i	−0.225611	−	0.225611i
$64$			1704.23i			0.416071i
$65$	−447.912	+	5707.12i	−0.106015	+	1.35080i
$66$	1343.42			0.308406
$67$	3756.53	−	3756.53i	0.836830	−	0.836830i	−0.151611	−	0.988440i	$-0.548446\pi$
$67$	3756.53	−	3756.53i	0.836830	−	0.836830i	0.988440	+	0.151611i	$0.0484460\pi$
$68$	−1631.53	−	1631.53i	−0.352839	−	0.352839i
$69$		−	2925.28i		−	0.614425i
$70$	4166.87	−	3560.41i	0.850382	−	0.726614i
$71$	1429.24			0.283523			0.141761	−	0.989901i	$-0.454723\pi$
$71$	1429.24			0.283523			0.141761	+	0.989901i	$0.454723\pi$
$72$	−905.914	+	905.914i	−0.174752	+	0.174752i
$73$	813.690	+	813.690i	0.152691	+	0.152691i	0.779319	−	0.626628i	$-0.215565\pi$
$73$	813.690	+	813.690i	0.152691	+	0.152691i	−0.626628	+	0.779319i	$0.715565\pi$
$74$			10978.2i			2.00478i
$75$	−2626.53	+	1910.03i	−0.466939	+	0.339561i
$76$	1051.99			0.182132
$77$	−1834.41	+	1834.41i	−0.309396	+	0.309396i
$78$	−3932.68	−	3932.68i	−0.646397	−	0.646397i
$79$			4854.69i			0.777871i	0.921265	+	0.388936i	$0.127157\pi$
$79$			4854.69i			0.777871i	−0.921265	+	0.388936i	$0.872843\pi$
$80$	−5121.74	−	5994.14i	−0.800271	−	0.936585i
$81$	−729.000			−0.111111
$82$	−1016.68	+	1016.68i	−0.151201	+	0.151201i
$83$	−1316.57	−	1316.57i	−0.191111	−	0.191111i	0.605065	−	0.796176i	$-0.293147\pi$
$83$	−1316.57	−	1316.57i	−0.191111	−	0.191111i	−0.796176	+	0.605065i	$0.793147\pi$
$84$			1425.37i			0.202008i
$85$	−9832.53	−	771.687i	−1.36090	−	0.106808i
$86$	689.160			0.0931801
$87$	−2011.54	+	2011.54i	−0.265760	+	0.265760i
$88$	1855.84	+	1855.84i	0.239649	+	0.239649i
$89$		−	5185.49i		−	0.654651i	−0.944912	−	0.327326i	$-0.893853\pi$
$89$		−	5185.49i		−	0.654651i	0.944912	−	0.327326i	$-0.106147\pi$
$90$	246.864	−	3145.44i	0.0304771	−	0.388326i
$91$	10740.0			1.29694
$92$	−2328.20	+	2328.20i	−0.275071	+	0.275071i
$93$	5651.36	+	5651.36i	0.653412	+	0.653412i
$94$			2288.24i			0.258968i
$95$	3418.74	−	2921.17i	0.378808	−	0.323675i
$96$	3714.83			0.403085
$97$	3495.32	−	3495.32i	0.371487	−	0.371487i	−0.496532	−	0.868018i	$-0.665393\pi$
$97$	3495.32	−	3495.32i	0.371487	−	0.371487i	0.868018	+	0.496532i	$0.165393\pi$
$98$	664.940	+	664.940i	0.0692357	+	0.0692357i
$99$			1493.42i			0.152374i
$100$	3610.61	+	570.256i	0.361061	+	0.0570256i
$101$	7708.86			0.755697			0.377848	−	0.925867i	$-0.376664\pi$
$101$	7708.86			0.755697			0.377848	+	0.925867i	$0.376664\pi$
$102$	6775.44	−	6775.44i	0.651234	−	0.651234i
$103$	−5098.51	−	5098.51i	−0.480583	−	0.480583i	0.424735	−	0.905318i	$-0.360367\pi$
$103$	−5098.51	−	5098.51i	−0.480583	−	0.480583i	−0.905318	+	0.424735i	$0.860367\pi$
$104$		−	10865.5i		−	1.00457i
$105$	3957.95	+	4632.13i	0.358998	+	0.420147i
$106$	−13386.2			−1.19137
$107$	−2041.19	+	2041.19i	−0.178285	+	0.178285i	−0.790608	−	0.612323i	$-0.790235\pi$
$107$	−2041.19	+	2041.19i	−0.178285	+	0.178285i	0.612323	+	0.790608i	$0.290235\pi$
$108$	580.205	+	580.205i	0.0497432	+	0.0497432i
$109$		−	11999.0i		−	1.00993i	−0.863139	−	0.504966i	$-0.831505\pi$
$109$		−	11999.0i		−	1.00993i	0.863139	−	0.504966i	$-0.168495\pi$
$110$	−6443.71	−	505.722i	−0.532538	−	0.0417952i
$111$	−12203.9			−0.990498
$112$	−10459.3	+	10459.3i	−0.833806	+	0.833806i
$113$	8953.64	+	8953.64i	0.701202	+	0.701202i	0.964668	−	0.263467i	$-0.0848659\pi$
$113$	8953.64	+	8953.64i	0.701202	+	0.701202i	−0.263467	+	0.964668i	$0.584866\pi$
$114$			4368.73i			0.336160i
$115$	−1101.20	+	14031.1i	−0.0832669	+	1.06095i
$116$	3201.93			0.237956
$117$	4371.79	−	4371.79i	0.319365	−	0.319365i
$118$	−9434.64	−	9434.64i	−0.677581	−	0.677581i
$119$			18503.4i			1.30665i
$120$	4686.25	−	4004.19i	0.325434	−	0.278069i
$121$	−11581.6			−0.791039
$122$	−3494.82	+	3494.82i	−0.234804	+	0.234804i
$123$	−1130.20	−	1130.20i	−0.0747040	−	0.0747040i
$124$		−	8995.74i		−	0.585051i
$125$	13317.2	−	8172.72i	0.852299	−	0.523054i
$126$	−5919.28			−0.372845
$127$	6051.36	−	6051.36i	0.375185	−	0.375185i	−0.494177	−	0.869361i	$-0.664530\pi$
$127$	6051.36	−	6051.36i	0.375185	−	0.375185i	0.869361	+	0.494177i	$0.164530\pi$
$128$	13721.2	+	13721.2i	0.837476	+	0.837476i
$129$			766.109i			0.0460374i
$130$	17382.7	+	20343.5i	1.02856	+	1.20376i
$131$	−22015.7			−1.28289			−0.641446	−	0.767168i	$-0.721665\pi$
$131$	−22015.7			−1.28289			−0.641446	+	0.767168i	$0.721665\pi$
$132$	1188.60	−	1188.60i	0.0682162	−	0.0682162i
$133$	−5965.41	−	5965.41i	−0.337238	−	0.337238i
$134$		−	24832.1i		−	1.38294i
$135$	3496.65	+	274.428i	0.191860	+	0.0150578i
$136$	18719.6			1.01209
$137$	−11424.0	+	11424.0i	−0.608661	+	0.608661i	−0.942596	−	0.333935i	$-0.891623\pi$
$137$	−11424.0	+	11424.0i	−0.608661	+	0.608661i	0.333935	+	0.942596i	$0.391623\pi$
$138$	−9668.61	−	9668.61i	−0.507698	−	0.507698i
$139$		−	432.165i		−	0.0223676i	−0.999937	−	0.0111838i	$-0.996440\pi$
$139$		−	432.165i		−	0.0223676i	0.999937	−	0.0111838i	$-0.00356000\pi$
$140$	536.571	−	6836.77i	0.0273761	−	0.348815i
$141$	−2543.74			−0.127948
$142$	4723.90	−	4723.90i	0.234274	−	0.234274i
$143$	−8955.98	−	8955.98i	−0.437967	−	0.437967i
$144$			8515.03i			0.410640i
$145$	10405.6	−	8891.12i	0.494915	−	0.422883i
$146$	5378.81			0.252337
$147$	−739.184	+	739.184i	−0.0342072	+	0.0342072i
$148$	9713.00	+	9713.00i	0.443435	+	0.443435i
$149$		−	17370.9i		−	0.782438i	−0.920298	−	0.391219i	$-0.872053\pi$
$149$		−	17370.9i		−	0.782438i	0.920298	−	0.391219i	$-0.127947\pi$
$150$	−2368.17	+	14994.2i	−0.105252	+	0.666409i
$151$	20493.6			0.898805			0.449402	−	0.893329i	$-0.351637\pi$
$151$	20493.6			0.898805			0.449402	+	0.893329i	$0.351637\pi$
$152$	−6035.10	+	6035.10i	−0.261215	+	0.261215i
$153$	7531.95	+	7531.95i	0.321755	+	0.321755i
$154$			12126.2i			0.511307i
$155$	−24979.3	−	29234.2i	−1.03972	−	1.21682i
$156$	−6958.94			−0.285952
$157$	2340.31	−	2340.31i	0.0949456	−	0.0949456i	−0.658039	−	0.752984i	$-0.728614\pi$
$157$	2340.31	−	2340.31i	0.0949456	−	0.0949456i	0.752984	+	0.658039i	$0.228614\pi$
$158$	16045.7	+	16045.7i	0.642753	+	0.642753i
$159$		−	14880.8i		−	0.588617i
$160$	−17818.2	−	1398.43i	−0.696024	−	0.0546261i
$161$	26404.6			1.01866
$162$	−2409.48	+	2409.48i	−0.0918109	+	0.0918109i
$163$	15303.1	+	15303.1i	0.575977	+	0.575977i	0.933792	−	0.357815i	$-0.116478\pi$
$163$	15303.1	+	15303.1i	0.575977	+	0.575977i	−0.357815	+	0.933792i	$0.616478\pi$
$164$			1799.03i			0.0668883i
$165$	562.189	−	7163.19i	0.0206497	−	0.263111i
$166$	−8703.01			−0.315830
$167$	−23457.8	+	23457.8i	−0.841113	+	0.841113i	−0.989004	−	0.147891i	$-0.952752\pi$
$167$	−23457.8	+	23457.8i	−0.841113	+	0.841113i	0.147891	+	0.989004i	$0.452752\pi$
$168$	−8177.09	−	8177.09i	−0.289721	−	0.289721i
$169$			23873.9i			0.835891i
$170$	−35049.0	+	29947.8i	−1.21277	+	1.03626i
$171$	−4856.52			−0.166086
$172$	609.739	−	609.739i	0.0206104	−	0.0206104i
$173$	−20512.3	−	20512.3i	−0.685366	−	0.685366i	0.275838	−	0.961204i	$-0.411045\pi$
$173$	−20512.3	−	20512.3i	−0.685366	−	0.685366i	−0.961204	+	0.275838i	$0.911045\pi$
$174$			13297.0i			0.439194i
$175$	−17240.6	−	23708.0i	−0.562958	−	0.774137i
$176$	17443.8			0.563138
$177$	10488.1	−	10488.1i	0.334772	−	0.334772i
$178$	−17139.0	−	17139.0i	−0.540937	−	0.540937i
$179$			52460.9i			1.63731i	0.574288	+	0.818653i	$0.305279\pi$
$179$			52460.9i			1.63731i	−0.574288	+	0.818653i	$0.694721\pi$
$180$	−2564.54	−	3001.37i	−0.0791525	−	0.0926349i
$181$	−60242.8			−1.83886			−0.919428	−	0.393258i	$-0.871348\pi$
$181$	−60242.8			−1.83886			−0.919428	+	0.393258i	$0.871348\pi$
$182$	35497.7	−	35497.7i	1.07166	−	1.07166i
$183$	−3885.03	−	3885.03i	−0.116009	−	0.116009i
$184$		−	26713.1i		−	0.789020i
$185$	58536.2	+	4594.10i	1.71033	+	0.134232i
$186$	37357.7			1.07983
$187$	15429.8	−	15429.8i	0.441244	−	0.441244i
$188$	2024.54	+	2024.54i	0.0572810	+	0.0572810i
$189$		−	6580.20i		−	0.184211i
$190$	1644.58	−	20954.6i	0.0455563	−	0.580460i
$191$	44243.4			1.21278			0.606390	−	0.795167i	$-0.292617\pi$
$191$	44243.4			1.21278			0.606390	+	0.795167i	$0.292617\pi$
$192$	−6261.74	+	6261.74i	−0.169860	+	0.169860i
$193$	18449.5	+	18449.5i	0.495303	+	0.495303i	0.909972	−	0.414669i	$-0.136103\pi$
$193$	18449.5	+	18449.5i	0.495303	+	0.495303i	−0.414669	+	0.909972i	$0.636103\pi$
$194$		−	23105.4i		−	0.613917i
$195$	−22615.0	+	19323.5i	−0.594741	+	0.508180i
$196$	1176.62			0.0306284
$197$	18454.6	−	18454.6i	0.475524	−	0.475524i	−0.428173	−	0.903697i	$-0.640843\pi$
$197$	18454.6	−	18454.6i	0.475524	−	0.475524i	0.903697	+	0.428173i	$0.140843\pi$
$198$	4936.04	+	4936.04i	0.125906	+	0.125906i
$199$			69350.3i			1.75123i	0.483013	+	0.875613i	$0.339542\pi$
$199$			69350.3i			1.75123i	−0.483013	+	0.875613i	$0.660458\pi$
$200$	−23984.9	+	17442.0i	−0.599624	+	0.436050i
$201$	27604.7			0.683269
$202$	25479.3	−	25479.3i	0.624431	−	0.624431i
$203$	−18156.8	−	18156.8i	−0.440604	−	0.440604i
$204$		−	11989.2i		−	0.288092i
$205$	4995.53	+	5846.45i	0.118871	+	0.139118i
$206$	−33703.1			−0.794210
$207$	10748.2	−	10748.2i	0.250838	−	0.250838i
$208$	−51064.3	−	51064.3i	−1.18030	−	1.18030i
$209$			9949.00i			0.227765i
$210$	28391.8	+	2228.28i	0.643806	+	0.0505279i
$211$	−19458.0			−0.437052			−0.218526	−	0.975831i	$-0.570125\pi$
$211$	−19458.0			−0.437052			−0.218526	+	0.975831i	$0.570125\pi$
$212$	−11843.5	+	11843.5i	−0.263517	+	0.263517i
$213$	5251.35	+	5251.35i	0.115748	+	0.115748i
$214$			13493.0i			0.294633i
$215$	288.397	−	3674.64i	0.00623899	−	0.0794947i
$216$	−6657.08			−0.142684
$217$	−51011.1	+	51011.1i	−1.08329	+	1.08329i
$218$	−39659.0	−	39659.0i	−0.834505	−	0.834505i
$219$			5979.38i			0.124672i
$220$	−6148.56	+	5253.68i	−0.127036	+	0.108547i
$221$	−90337.7			−1.84963
$222$	−40336.3	+	40336.3i	−0.818447	+	0.818447i
$223$	52732.0	+	52732.0i	1.06039	+	1.06039i	0.998056	+	0.0623311i	$0.0198535\pi$
$223$	52732.0	+	52732.0i	1.06039	+	1.06039i	0.0623311	+	0.998056i	$0.480147\pi$
$224$			33531.4i			0.668275i
$225$	−16668.4	−	2632.59i	−0.329252	−	0.0520018i
$226$	59187.0			1.15880
$227$	61436.6	−	61436.6i	1.19227	−	1.19227i	0.215844	−	0.976428i	$-0.430750\pi$
$227$	61436.6	−	61436.6i	1.19227	−	1.19227i	0.976428	−	0.215844i	$-0.0692503\pi$
$228$	3865.26	+	3865.26i	0.0743549	+	0.0743549i
$229$		−	98741.9i		−	1.88292i	−0.337132	−	0.941458i	$-0.609457\pi$
$229$		−	98741.9i		−	1.88292i	0.337132	−	0.941458i	$-0.390543\pi$
$230$	42735.8	+	50015.2i	0.807860	+	0.945467i
$231$	−13480.1			−0.252621
$232$	−18369.0	+	18369.0i	−0.341278	+	0.341278i
$233$	26861.4	+	26861.4i	0.494785	+	0.494785i	0.909810	−	0.415025i	$-0.136227\pi$
$233$	26861.4	+	26861.4i	0.494785	+	0.494785i	−0.415025	+	0.909810i	$0.636227\pi$
$234$		−	28899.2i		−	0.527781i
$235$	12201.1	+	957.576i	0.220934	+	0.0173395i
$236$	−16694.7			−0.299747
$237$	−17837.3	+	17837.3i	−0.317565	+	0.317565i
$238$	61157.4	+	61157.4i	1.07968	+	1.07968i
$239$		−	64860.8i		−	1.13550i	−0.823202	−	0.567749i	$-0.807814\pi$
$239$		−	64860.8i		−	1.13550i	0.823202	−	0.567749i	$-0.192186\pi$
$240$	3205.43	−	40842.4i	0.0556499	−	0.709069i
$241$	11766.6			0.202590			0.101295	−	0.994856i	$-0.467701\pi$
$241$	11766.6			0.202590			0.101295	+	0.994856i	$0.467701\pi$
$242$	−38279.4	+	38279.4i	−0.653634	+	0.653634i
$243$	−2678.52	−	2678.52i	−0.0453609	−	0.0453609i
$244$			6184.13i			0.103872i
$245$	3823.76	−	3267.24i	0.0637028	−	0.0544313i
$246$	−7471.03			−0.123455
$247$	29124.4	−	29124.4i	0.477378	−	0.477378i
$248$	51607.1	+	51607.1i	0.839085	+	0.839085i
$249$		−	9674.75i		−	0.156042i
$250$	17003.4	−	71028.2i	0.272055	−	1.13645i
$251$	14659.6			0.232688			0.116344	−	0.993209i	$-0.462882\pi$
$251$	14659.6			0.232688			0.116344	+	0.993209i	$0.462882\pi$
$252$	−5237.13	+	5237.13i	−0.0824692	+	0.0824692i
$253$	−22018.5	−	22018.5i	−0.343991	−	0.343991i
$254$		−	40001.8i		−	0.620029i
$255$	−33291.7	−	38962.4i	−0.511983	−	0.599191i
$256$	63434.7			0.967937
$257$	−47816.3	+	47816.3i	−0.723951	+	0.723951i	−0.969408	−	0.245456i	$-0.921062\pi$
$257$	−47816.3	+	47816.3i	−0.723951	+	0.723951i	0.245456	+	0.969408i	$0.421062\pi$
$258$	2532.14	+	2532.14i	0.0380406	+	0.0380406i
$259$		−	110157.i		−	1.64215i
$260$	33378.6	+	2619.65i	0.493766	+	0.0387522i
$261$	−14781.7			−0.216992
$262$	−72766.2	+	72766.2i	−1.06005	+	1.06005i
$263$	−45872.6	−	45872.6i	−0.663197	−	0.663197i	0.292936	−	0.956132i	$-0.405368\pi$
$263$	−45872.6	−	45872.6i	−0.663197	−	0.663197i	−0.956132	+	0.292936i	$0.905368\pi$
$264$			13637.6i			0.195673i
$265$	−5601.80	+	71375.9i	−0.0797694	+	1.01639i
$266$	−39433.6			−0.557319
$267$	19052.7	−	19052.7i	0.267260	−	0.267260i
$268$	−21970.4	−	21970.4i	−0.305892	−	0.305892i
$269$			80295.1i			1.10965i	0.831968	+	0.554823i	$0.187214\pi$
$269$			80295.1i			1.10965i	−0.831968	+	0.554823i	$0.812786\pi$
$270$	12464.1	−	10650.1i	0.170976	−	0.146091i
$271$	40047.7			0.545304			0.272652	−	0.962113i	$-0.412099\pi$
$271$	40047.7			0.545304			0.272652	+	0.962113i	$0.412099\pi$
$272$	87976.4	−	87976.4i	1.18913	−	1.18913i
$273$	39461.2	+	39461.2i	0.529475	+	0.529475i
$274$			75516.8i			1.00587i
$275$	−5393.08	+	34146.6i	−0.0713135	+	0.451525i
$276$	−17108.7			−0.224595
$277$	−49870.0	+	49870.0i	−0.649950	+	0.649950i	−0.952981	−	0.303031i	$-0.902001\pi$
$277$	−49870.0	+	49870.0i	−0.649950	+	0.649950i	0.303031	+	0.952981i	$0.402001\pi$
$278$	−1428.39	−	1428.39i	−0.0184823	−	0.0184823i
$279$			41528.9i			0.533509i
$280$	36143.2	+	42299.6i	0.461010	+	0.539536i
$281$	−12842.2			−0.162639			−0.0813196	−	0.996688i	$-0.525913\pi$
$281$	−12842.2			−0.162639			−0.0813196	+	0.996688i	$0.525913\pi$
$282$	−8407.55	+	8407.55i	−0.105723	+	0.105723i
$283$	−35925.4	−	35925.4i	−0.448568	−	0.448568i	0.446310	−	0.894878i	$-0.352738\pi$
$283$	−35925.4	−	35925.4i	−0.448568	−	0.448568i	−0.894878	+	0.446310i	$0.852738\pi$
$284$		−	8359.02i		−	0.103638i
$285$	23294.3	+	1828.21i	0.286788	+	0.0225080i
$286$	−59202.4			−0.723782
$287$	10201.5	−	10201.5i	0.123852	−	0.123852i
$288$	13649.2	+	13649.2i	0.164559	+	0.164559i
$289$		−	72117.7i		−	0.863467i
$290$	5005.60	−	63779.3i	0.0595196	−	0.758375i
$291$	25685.2			0.303318
$292$	4758.94	−	4758.94i	0.0558141	−	0.0558141i
$293$	−50366.0	−	50366.0i	−0.586681	−	0.586681i	0.350050	−	0.936731i	$-0.386165\pi$
$293$	−50366.0	−	50366.0i	−0.586681	−	0.586681i	−0.936731	+	0.350050i	$0.886165\pi$
$294$			4886.29i			0.0565307i
$295$	−54254.2	+	46357.9i	−0.623432	+	0.532696i
$296$	−111444.			−1.27196
$297$	−5487.17	+	5487.17i	−0.0622065	+	0.0622065i
$298$	−57414.2	−	57414.2i	−0.646527	−	0.646527i
$299$			128913.i			1.44196i
$300$	11171.0	+	15361.5i	0.124122	+	0.170683i
$301$	−6915.16			−0.0763254
$302$	67735.4	−	67735.4i	0.742680	−	0.742680i
$303$	28324.2	+	28324.2i	0.308512	+	0.308512i
$304$			56726.2i			0.613814i
$305$	17172.1	+	20097.1i	0.184596	+	0.216039i
$306$	49789.1			0.531730
$307$	75581.6	−	75581.6i	0.801936	−	0.801936i	−0.181462	−	0.983398i	$-0.558083\pi$
$307$	75581.6	−	75581.6i	0.801936	−	0.801936i	0.983398	+	0.181462i	$0.0580830\pi$
$308$	10728.7	+	10728.7i	0.113096	+	0.113096i
$309$		−	37466.2i		−	0.392395i
$310$	−179186.	−	14063.1i	−1.86458	−	0.146338i
$311$	107241.			1.10877			0.554384	−	0.832261i	$-0.312954\pi$
$311$	107241.			1.10877			0.554384	+	0.832261i	$0.312954\pi$
$312$	39922.3	−	39922.3i	0.410115	−	0.410115i
$313$	24848.0	+	24848.0i	0.253631	+	0.253631i	0.822458	−	0.568826i	$-0.192602\pi$
$313$	24848.0	+	24848.0i	0.253631	+	0.253631i	−0.568826	+	0.822458i	$0.692602\pi$
$314$		−	15470.4i		−	0.156907i
$315$	−2477.08	+	31562.0i	−0.0249643	+	0.318085i
$316$	28393.1			0.284340
$317$	−7619.16	+	7619.16i	−0.0758209	+	0.0758209i	−0.744000	−	0.668179i	$-0.767074\pi$
$317$	−7619.16	+	7619.16i	−0.0758209	+	0.0758209i	0.668179	+	0.744000i	$0.267074\pi$
$318$	−49184.0	−	49184.0i	−0.486373	−	0.486373i
$319$			30281.6i			0.297576i
$320$	32391.6	−	27677.2i	0.316324	−	0.270286i
$321$	−14999.6			−0.145569
$322$	87272.1	−	87272.1i	0.841713	−	0.841713i
$323$	50177.1	+	50177.1i	0.480950	+	0.480950i
$324$			4263.62i			0.0406152i
$325$	115747.	−	84172.2i	1.09583	−	0.796896i
$326$	101160.			0.951857
$327$	44087.2	−	44087.2i	0.412303	−	0.412303i
$328$	−10320.7	−	10320.7i	−0.0959318	−	0.0959318i
$329$		−	22960.7i		−	0.212125i
$330$	−21817.6	−	25533.8i	−0.200345	−	0.234471i
$331$	28518.2			0.260295			0.130148	−	0.991495i	$-0.458455\pi$
$331$	28518.2			0.260295			0.130148	+	0.991495i	$0.458455\pi$
$332$	−7700.05	+	7700.05i	−0.0698582	+	0.0698582i
$333$	−44840.1	−	44840.1i	−0.404369	−	0.404369i
$334$			155065.i			1.39002i
$335$	−132406.	−	10391.6i	−1.17983	−	0.0925965i
$336$	−76859.5			−0.680799
$337$	−22519.8	+	22519.8i	−0.198292	+	0.198292i	−0.799267	−	0.600976i	$-0.794779\pi$
$337$	−22519.8	+	22519.8i	−0.198292	+	0.198292i	0.600976	+	0.799267i	$0.294779\pi$
$338$	78907.8	+	78907.8i	0.690695	+	0.690695i
$339$			65795.6i			0.572529i
$340$	−4513.28	+	57506.4i	−0.0390422	+	0.497460i
$341$	85075.4			0.731636
$342$	−16051.7	+	16051.7i	−0.137237	+	0.137237i
$343$	−86301.0	−	86301.0i	−0.733547	−	0.733547i
$344$			6995.95i			0.0591194i
$345$	−55599.7	+	47507.5i	−0.467126	+	0.399139i
$346$	−135594.			−1.13263
$347$	−123818.	+	123818.i	−1.02831	+	1.02831i	−0.0287203	+	0.999587i	$0.509143\pi$
$347$	−123818.	+	123818.i	−1.02831	+	1.02831i	−0.999587	+	0.0287203i	$0.990857\pi$
$348$	11764.7	+	11764.7i	0.0971451	+	0.0971451i
$349$		−	53357.0i		−	0.438067i	−0.975717	−	0.219034i	$-0.929710\pi$
$349$		−	53357.0i		−	0.438067i	0.975717	−	0.219034i	$-0.0702905\pi$
$350$	−135343.	−	21375.9i	−1.10484	−	0.174497i
$351$	32125.9			0.260760
$352$	27961.5	−	27961.5i	0.225671	−	0.225671i
$353$	−48279.2	−	48279.2i	−0.387445	−	0.387445i	0.486330	−	0.873775i	$-0.338335\pi$
$353$	−48279.2	−	48279.2i	−0.387445	−	0.387445i	−0.873775	+	0.486330i	$0.838335\pi$
$354$		−	69330.1i		−	0.553242i
$355$	−23211.3	−	27165.0i	−0.184180	−	0.215552i
$356$	−30327.8			−0.239299
$357$	−67985.9	+	67985.9i	−0.533436	+	0.533436i
$358$	173393.	+	173393.i	1.35290	+	1.35290i
$359$		−	91012.9i		−	0.706178i	−0.935590	−	0.353089i	$-0.885131\pi$
$359$		−	91012.9i		−	0.706178i	0.935590	−	0.353089i	$-0.114869\pi$
$360$	31930.7	+	2506.02i	0.246379	+	0.0193366i
$361$	97967.4			0.751739
$362$	−199114.	+	199114.i	−1.51944	+	1.51944i
$363$	−42553.5	−	42553.5i	−0.322940	−	0.322940i
$364$		−	62813.7i		−	0.474080i
$365$	2250.90	−	28680.1i	0.0168955	−	0.215276i
$366$	−25681.6			−0.191716
$367$	−94731.0	+	94731.0i	−0.703331	+	0.703331i	−0.965124	−	0.261793i	$-0.915686\pi$
$367$	−94731.0	+	94731.0i	−0.703331	+	0.703331i	0.261793	+	0.965124i	$0.415686\pi$
$368$	−125543.	−	125543.i	−0.927037	−	0.927037i
$369$		−	8305.21i		−	0.0609955i
$370$	208658.	−	178289.i	1.52416	−	1.30233i
$371$	134319.			0.975868
$372$	33052.5	−	33052.5i	0.238846	−	0.238846i
$373$	174691.	+	174691.i	1.25560	+	1.25560i	0.953172	+	0.302430i	$0.0977978\pi$
$373$	174691.	+	174691.i	1.25560	+	1.25560i	0.302430	+	0.953172i	$0.402202\pi$
$374$		−	101997.i		−	0.729197i
$375$	78958.9	+	18901.9i	0.561486	+	0.134414i
$376$	−23228.9			−0.164306
$377$	88645.5	−	88645.5i	0.623697	−	0.623697i
$378$	−21748.8	−	21748.8i	−0.152213	−	0.152213i
$379$			216082.i			1.50432i	0.658981	+	0.752159i	$0.270988\pi$
$379$			216082.i			1.50432i	−0.658981	+	0.752159i	$0.729012\pi$
$380$	−17084.7	−	19994.8i	−0.118315	−	0.138468i
$381$	44468.2			0.306337
$382$	146233.	−	146233.i	1.00212	−	1.00212i
$383$	−6943.25	−	6943.25i	−0.0473331	−	0.0473331i	0.683044	−	0.730377i	$-0.260656\pi$
$383$	−6943.25	−	6943.25i	−0.0473331	−	0.0473331i	−0.730377	+	0.683044i	$0.760656\pi$
$384$			100830.i			0.683796i
$385$	64657.4	+	5074.51i	0.436211	+	0.0342352i
$386$	121959.			0.818536
$387$	−2814.86	+	2814.86i	−0.0187947	+	0.0187947i
$388$	−20442.7	−	20442.7i	−0.135792	−	0.135792i
$389$		−	171993.i		−	1.13661i	−0.822817	−	0.568306i	$-0.807599\pi$
$389$		−	171993.i		−	1.13661i	0.822817	−	0.568306i	$-0.192401\pi$
$390$	−10878.9	+	138615.i	−0.0715249	+	0.911341i
$391$	−222098.			−1.45275
$392$	−6750.08	+	6750.08i	−0.0439275	+	0.0439275i
$393$	−80890.9	−	80890.9i	−0.523739	−	0.523739i
$394$		−	121992.i		−	0.785849i
$395$	92271.3	−	78841.8i	0.591388	−	0.505315i
$396$	8734.39			0.0556983
$397$	47564.4	−	47564.4i	0.301787	−	0.301787i	−0.539925	−	0.841713i	$-0.681548\pi$
$397$	47564.4	−	47564.4i	0.301787	−	0.301787i	0.841713	+	0.539925i	$0.181548\pi$
$398$	229216.	+	229216.i	1.44703	+	1.44703i
$399$		−	43836.6i		−	0.275354i
$400$	−30749.7	+	194694.i	−0.192186	+	1.21684i
$401$	−193768.			−1.20502			−0.602508	−	0.798113i	$-0.705832\pi$
$401$	−193768.			−1.20502			−0.602508	+	0.798113i	$0.705832\pi$
$402$	91238.9	−	91238.9i	0.564583	−	0.564583i
$403$	−249047.	−	249047.i	−1.53346	−	1.53346i
$404$		−	45085.9i		−	0.276235i
$405$	11839.2	+	13855.8i	0.0721792	+	0.0844739i
$406$	−120024.			−0.728140
$407$	−91858.8	+	91858.8i	−0.554539	+	0.554539i
$408$	68780.3	+	68780.3i	0.413184	+	0.413184i
$409$			265.258i			0.00158570i	1.00000		0.000792852i	$0.000252373\pi$
$409$			265.258i			0.00158570i	−1.00000		0.000792852i	$0.999748\pi$
$410$	35834.8	+	2812.43i	0.213176	+	0.0167307i
$411$	−83948.6			−0.496970
$412$	−29819.0	+	29819.0i	−0.175671	+	0.175671i
$413$	94668.8	+	94668.8i	0.555018	+	0.555018i
$414$		−	71049.5i		−	0.414534i
$415$	−3642.00	+	46405.0i	−0.0211468	+	0.269444i
$416$	−163707.			−0.945978
$417$	1587.88	−	1587.88i	0.00913155	−	0.00913155i
$418$	32883.3	+	32883.3i	0.188202	+	0.188202i
$419$		−	30926.0i		−	0.176155i	−0.996114	−	0.0880775i	$-0.971928\pi$
$419$		−	30926.0i		−	0.176155i	0.996114	−	0.0880775i	$-0.0280723\pi$
$420$	27091.4	−	23148.4i	0.153579	−	0.131227i
$421$	−62470.0			−0.352458			−0.176229	−	0.984349i	$-0.556390\pi$
$421$	−62470.0			−0.352458			−0.176229	+	0.984349i	$0.556390\pi$
$422$	−64312.3	+	64312.3i	−0.361135	+	0.361135i
$423$	−9346.30	−	9346.30i	−0.0522347	−	0.0522347i
$424$		−	135889.i		−	0.755878i
$425$	145016.	+	199416.i	0.802859	+	1.10403i
$426$	34713.5			0.191284
$427$	35067.6	−	35067.6i	0.192332	−	0.192332i
$428$	11938.1	+	11938.1i	0.0651698	+	0.0651698i
$429$		−	65812.7i		−	0.357598i
$430$	−11192.2	−	13098.6i	−0.0605310	−	0.0708416i
$431$	69270.8			0.372903			0.186451	−	0.982464i	$-0.440301\pi$
$431$	69270.8			0.372903			0.186451	+	0.982464i	$0.440301\pi$
$432$	−31286.2	+	31286.2i	−0.167643	+	0.167643i
$433$	−110961.	−	110961.i	−0.591829	−	0.591829i	0.346296	−	0.938125i	$-0.387439\pi$
$433$	−110961.	−	110961.i	−0.591829	−	0.591829i	−0.938125	+	0.346296i	$0.887439\pi$
$434$			337203.i			1.79024i
$435$	70900.6	+	5564.50i	0.374689	+	0.0294068i
$436$	−70177.2			−0.369167
$437$	71603.1	−	71603.1i	0.374946	−	0.374946i
$438$	19763.0	+	19763.0i	0.103016	+	0.103016i
$439$			167998.i			0.871716i	0.900016	+	0.435858i	$0.143555\pi$
$439$			167998.i			0.871716i	−0.900016	+	0.435858i	$0.856445\pi$
$440$	5133.80	−	65412.8i	0.0265176	−	0.337876i
$441$	−5431.87			−0.0279301
$442$	−298583.	+	298583.i	−1.52834	+	1.52834i
$443$	66278.3	+	66278.3i	0.337726	+	0.337726i	0.855511	−	0.517785i	$-0.173243\pi$
$443$	66278.3	+	66278.3i	0.337726	+	0.337726i	−0.517785	+	0.855511i	$0.673243\pi$
$444$			71375.7i			0.362063i
$445$	−98558.7	+	84214.1i	−0.497708	+	0.425270i
$446$	348579.			1.75239
$447$	63824.8	−	63824.8i	0.319429	−	0.319429i
$448$	−56520.6	−	56520.6i	−0.281611	−	0.281611i
$449$		−	212689.i		−	1.05500i	−0.849556	−	0.527499i	$-0.823130\pi$
$449$		−	212689.i		−	1.05500i	0.849556	−	0.527499i	$-0.176870\pi$
$450$	−63793.4	+	46391.0i	−0.315029	+	0.229091i
$451$	−17013.9			−0.0836473
$452$	52366.1	−	52366.1i	0.256315	−	0.256315i
$453$	75298.5	+	75298.5i	0.366935	+	0.366935i
$454$		−	406119.i		−	1.97034i
$455$	−174421.	−	204131.i	−0.842511	−	0.986020i
$456$	−44348.8			−0.213281
$457$	188980.	−	188980.i	0.904864	−	0.904864i	−0.0909883	−	0.995852i	$-0.529003\pi$
$457$	188980.	−	188980.i	0.904864	−	0.904864i	0.995852	+	0.0909883i	$0.0290026\pi$
$458$	−326361.	−	326361.i	−1.55585	−	1.55585i
$459$			55348.3i			0.262711i
$460$	82062.1	+	6440.49i	0.387817	+	0.0304371i
$461$	−203463.			−0.957379			−0.478690	−	0.877984i	$-0.658888\pi$
$461$	−203463.			−0.957379			−0.478690	+	0.877984i	$0.658888\pi$
$462$	−44554.3	+	44554.3i	−0.208740	+	0.208740i
$463$	280217.	+	280217.i	1.30717	+	1.30717i	0.923448	+	0.383724i	$0.125359\pi$
$463$	280217.	+	280217.i	1.30717	+	1.30717i	0.383724	+	0.923448i	$0.374641\pi$
$464$			172657.i			0.801951i
$465$	15633.3	−	199193.i	0.0723011	−	0.921231i
$466$	177564.			0.817679
$467$	25143.8	−	25143.8i	0.115291	−	0.115291i	−0.647107	−	0.762399i	$-0.724021\pi$
$467$	25143.8	−	25143.8i	0.115291	−	0.115291i	0.762399	+	0.647107i	$0.224021\pi$
$468$	−25568.8	−	25568.8i	−0.116740	−	0.116740i
$469$			249170.i			1.13279i
$470$	43491.8	−	37161.8i	0.196885	−	0.168229i
$471$	17197.7			0.0775227
$472$	95774.9	−	95774.9i	0.429900	−	0.429900i
$473$	5766.49	+	5766.49i	0.0257744	+	0.0257744i
$474$			117911.i			0.524806i
$475$	−111043.	−	17538.0i	−0.492158	−	0.0777309i
$476$	108219.			0.477627
$477$	54675.7	−	54675.7i	0.240302	−	0.240302i
$478$	−214377.	−	214377.i	−0.938260	−	0.938260i
$479$			17282.5i			0.0753246i	0.999291	+	0.0376623i	$0.0119911\pi$
$479$			17282.5i			0.0753246i	−0.999291	+	0.0376623i	$0.988009\pi$
$480$	−60330.1	−	70606.5i	−0.261850	−	0.306452i
$481$	537809.			2.32454
$482$	38891.0	−	38891.0i	0.167400	−	0.167400i
$483$	97016.5	+	97016.5i	0.415864	+	0.415864i
$484$			67736.0i			0.289154i
$485$	−123199.	−	9669.06i	−0.523751	−	0.0411056i
$486$	−17706.0			−0.0749633
$487$	−250914.	+	250914.i	−1.05795	+	1.05795i	−0.0597410	+	0.998214i	$0.519027\pi$
$487$	−250914.	+	250914.i	−1.05795	+	1.05795i	−0.998214	+	0.0597410i	$0.980973\pi$
$488$	−35477.4	−	35477.4i	−0.148974	−	0.148974i
$489$			112455.i			0.470283i
$490$	1839.42	−	23437.1i	0.00766104	−	0.0976139i
$491$	−175178.			−0.726634			−0.363317	−	0.931666i	$-0.618356\pi$
$491$	−175178.			−0.726634			−0.363317	+	0.931666i	$0.618356\pi$
$492$	−6610.05	+	6610.05i	−0.0273070	+	0.0273070i
$493$	152723.	+	152723.i	0.628364	+	0.628364i
$494$		−	192523.i		−	0.788914i
$495$	28384.8	−	24253.6i	0.115845	−	0.0989842i
$496$	485075.			1.97172
$497$	−47400.5	+	47400.5i	−0.191898	+	0.191898i
$498$	−31976.9	−	31976.9i	−0.128937	−	0.128937i
$499$		−	219732.i		−	0.882454i	−0.897396	−	0.441227i	$-0.854543\pi$
$499$		−	219732.i		−	0.882454i	0.897396	−	0.441227i	$-0.145457\pi$
$500$	−47798.9	−	77886.6i	−0.191195	−	0.311547i
$501$	−172379.			−0.686766
$502$	48452.8	−	48452.8i	0.192270	−	0.192270i
$503$	298149.	+	298149.i	1.17841	+	1.17841i	0.980148	+	0.198266i	$0.0635311\pi$
$503$	298149.	+	298149.i	1.17841	+	1.17841i	0.198266	+	0.980148i	$0.436469\pi$
$504$		−	60089.1i		−	0.236556i
$505$	−125194.	−	146519.i	−0.490911	−	0.574530i
$506$	−145551.			−0.568478
$507$	−87718.2	+	87718.2i	−0.341251	+	0.341251i
$508$	−35391.9	−	35391.9i	−0.137144	−	0.137144i
$509$			476403.i			1.83882i	0.393303	+	0.919409i	$0.371332\pi$
$509$			476403.i			1.83882i	−0.393303	+	0.919409i	$0.628668\pi$
$510$	−238813.	−	18742.8i	−0.918160	−	0.0720601i
$511$	−53971.9			−0.206693
$512$	−9875.23	+	9875.23i	−0.0376710	+	0.0376710i
$513$	−17844.0	−	17844.0i	−0.0678043	−	0.0678043i
$514$			316084.i			1.19640i
$515$	−14103.9	+	179707.i	−0.0531773	+	0.677564i
$516$	4480.65			0.0168284
$517$	−19146.7	+	19146.7i	−0.0716329	+	0.0716329i
$518$	−364089.	−	364089.i	−1.35690	−	1.35690i
$519$		−	150734.i		−	0.559599i
$520$	−206516.	+	176459.i	−0.763742	+	0.652584i
$521$	−366162.			−1.34896			−0.674479	−	0.738294i	$-0.735632\pi$
$521$	−366162.			−1.34896			−0.674479	+	0.738294i	$0.735632\pi$
$522$	−48856.5	+	48856.5i	−0.179300	+	0.179300i
$523$	−236853.	−	236853.i	−0.865916	−	0.865916i	0.126101	−	0.992017i	$-0.459754\pi$
$523$	−236853.	−	236853.i	−0.865916	−	0.865916i	−0.992017	+	0.126101i	$0.959754\pi$
$524$			128761.i			0.468944i
$525$	23762.6	−	150455.i	0.0862137	−	0.545867i
$526$	−303236.			−1.09600
$527$	429072.	−	429072.i	1.54493	−	1.54493i
$528$	64092.5	+	64092.5i	0.229900	+	0.229900i
$529$			37094.3i			0.132555i
$530$	217396.	+	254426.i	0.773927	+	0.905754i
$531$	77071.2			0.273340
$532$	−34889.2	+	34889.2i	−0.123273	+	0.123273i
$533$	49806.1	+	49806.1i	0.175319	+	0.175319i
$534$		−	125946.i		−	0.441673i
$535$	71945.6	+	5646.52i	0.251360	+	0.0197275i
$536$	252081.			0.877426
$537$	−192754.	+	192754.i	−0.668428	+	0.668428i
$538$	265391.	+	265391.i	0.916898	+	0.916898i
$539$			11127.7i			0.0383024i
$540$	1605.01	−	20450.5i	0.00550417	−	0.0701319i
$541$	70441.7			0.240678			0.120339	−	0.992733i	$-0.461602\pi$
$541$	70441.7			0.240678			0.120339	+	0.992733i	$0.461602\pi$
$542$	132365.	−	132365.i	0.450584	−	0.450584i
$543$	−221346.	−	221346.i	−0.750710	−	0.750710i
$544$		−	282044.i		−	0.953056i
$545$	−228061.	+	194868.i	−0.767816	+	0.656065i
$546$	260854.			0.875008
$547$	347520.	−	347520.i	1.16146	−	1.16146i	0.177308	−	0.984155i	$-0.443261\pi$
$547$	347520.	−	347520.i	1.16146	−	1.16146i	0.984155	−	0.177308i	$-0.0567387\pi$
$548$	66814.0	+	66814.0i	0.222488	+	0.222488i
$549$		−	28549.1i		−	0.0947212i
$550$	95035.9	+	130686.i	0.314168	+	0.432021i
$551$	−98474.3			−0.324354
$552$	98150.0	−	98150.0i	0.322116	−	0.322116i
$553$	−161005.	−	161005.i	−0.526490	−	0.526490i
$554$			329660.i			1.07410i
$555$	198196.	+	231955.i	0.643441	+	0.753041i
$556$	−2527.56			−0.00817619
$557$	254820.	−	254820.i	0.821340	−	0.821340i	−0.164960	−	0.986300i	$-0.552749\pi$
$557$	254820.	−	254820.i	0.821340	−	0.821340i	0.986300	+	0.164960i	$0.0527495\pi$
$558$	137261.	+	137261.i	0.440837	+	0.440837i
$559$		−	33761.3i		−	0.108043i
$560$	368657.	+	28933.3i	1.17556	+	0.0922619i
$561$	113386.			0.360274
$562$	−42445.8	+	42445.8i	−0.134389	+	0.134389i
$563$	31884.1	+	31884.1i	0.100591	+	0.100591i	0.755611	−	0.655021i	$-0.227340\pi$
$563$	31884.1	+	31884.1i	0.100591	+	0.100591i	−0.655021	+	0.755611i	$0.727340\pi$
$564$			14877.3i			0.0467698i
$565$	24768.4	−	315589.i	0.0775891	−	0.988609i
$566$	−237480.			−0.741302
$567$	24177.2	−	24177.2i	0.0752038	−	0.0752038i
$568$	47954.3	+	47954.3i	0.148638	+	0.148638i
$569$		−	609312.i		−	1.88198i	−0.338431	−	0.940991i	$-0.609896\pi$
$569$		−	609312.i		−	1.88198i	0.338431	−	0.940991i	$-0.390104\pi$
$570$	83034.8	−	70949.6i	0.255570	−	0.218374i
$571$	−233321.			−0.715618			−0.357809	−	0.933795i	$-0.616476\pi$
$571$	−233321.			−0.715618			−0.357809	+	0.933795i	$0.616476\pi$
$572$	−52379.8	+	52379.8i	−0.160093	+	0.160093i
$573$	162561.	+	162561.i	0.495115	+	0.495115i
$574$		−	67436.1i		−	0.204677i
$575$	284568.	−	206940.i	0.860697	−	0.625904i
$576$	−46014.2			−0.138690
$577$	−324793.	+	324793.i	−0.975562	+	0.975562i	−0.999708	−	0.0241466i	$-0.992313\pi$
$577$	−324793.	+	324793.i	−0.975562	+	0.975562i	0.0241466	+	0.999708i	$0.492313\pi$
$578$	−238363.	−	238363.i	−0.713481	−	0.713481i
$579$			135576.i			0.404413i
$580$	−52000.5	−	60857.9i	−0.154579	−	0.180909i
$581$	87327.6			0.258702
$582$	84894.6	−	84894.6i	0.250631	−	0.250631i
$583$	−112008.	−	112008.i	−0.329542	−	0.329542i
$584$			54602.5i			0.160098i
$585$	−154092.	−	12093.6i	−0.450266	−	0.0353382i
$586$	−332939.			−0.969547
$587$	−369440.	+	369440.i	−1.07218	+	1.07218i	−0.0749961	+	0.997184i	$0.523894\pi$
$587$	−369440.	+	369440.i	−1.07218	+	1.07218i	−0.997184	+	0.0749961i	$0.976106\pi$
$588$	4323.18	+	4323.18i	0.0125040	+	0.0125040i
$589$			276661.i			0.797475i
$590$	−26098.9	+	332542.i	−0.0749754	+	0.955306i
$591$	135613.			0.388263
$592$	−523751.	+	523751.i	−1.49445	+	1.49445i
$593$	−263575.	−	263575.i	−0.749541	−	0.749541i	0.224852	−	0.974393i	$-0.427810\pi$
$593$	−263575.	−	263575.i	−0.749541	−	0.749541i	−0.974393	+	0.224852i	$0.927810\pi$
$594$			36272.3i			0.102802i
$595$	351688.	−	300502.i	0.993398	−	0.848815i
$596$	−101595.			−0.286010
$597$	−254809.	+	254809.i	−0.714935	+	0.714935i
$598$	426081.	+	426081.i	1.19149	+	1.19149i
$599$		−	319604.i		−	0.890756i	−0.895343	−	0.445378i	$-0.853069\pi$
$599$		−	319604.i		−	0.890756i	0.895343	−	0.445378i	$-0.146931\pi$
$600$	−152212.	−	24040.3i	−0.422812	−	0.0667785i
$601$	−558724.			−1.54685			−0.773425	−	0.633887i	$-0.781458\pi$
$601$	−558724.			−1.54685			−0.773425	+	0.633887i	$0.781458\pi$
$602$	−22855.9	+	22855.9i	−0.0630675	+	0.0630675i
$603$	101426.	+	101426.i	0.278943	+	0.278943i
$604$		−	119859.i		−	0.328546i
$605$	188089.	+	220127.i	0.513870	+	0.601399i
$606$	187234.			0.509845
$607$	31979.5	−	31979.5i	0.0867950	−	0.0867950i	−0.662376	−	0.749171i	$-0.730452\pi$
$607$	31979.5	−	31979.5i	0.0867950	−	0.0867950i	0.749171	+	0.662376i	$0.230452\pi$
$608$	90929.4	+	90929.4i	0.245978	+	0.245978i
$609$		−	133425.i		−	0.359751i
$610$	123182.	+	9667.68i	0.331045	+	0.0259814i
$611$	112099.			0.300275
$612$	44051.3	−	44051.3i	0.117613	−	0.117613i
$613$	181360.	+	181360.i	0.482636	+	0.482636i	0.905973	−	0.423336i	$-0.139141\pi$
$613$	181360.	+	181360.i	0.482636	+	0.482636i	−0.423336	+	0.905973i	$0.639141\pi$
$614$		−	499624.i		−	1.32528i
$615$	−3126.45	+	39836.0i	−0.00826611	+	0.105323i
$616$	−123098.			−0.324405
$617$	58514.8	−	58514.8i	0.153708	−	0.153708i	−0.626064	−	0.779772i	$-0.715335\pi$
$617$	58514.8	−	58514.8i	0.153708	−	0.153708i	0.779772	+	0.626064i	$0.215335\pi$
$618$	−123833.	−	123833.i	−0.324235	−	0.324235i
$619$		−	193773.i		−	0.505722i	−0.967503	−	0.252861i	$-0.918628\pi$
$619$		−	193773.i		−	0.505722i	0.967503	−	0.252861i	$-0.0813716\pi$
$620$	−170979.	+	146094.i	−0.444794	+	0.380057i
$621$	78982.5			0.204808
$622$	354452.	−	354452.i	0.916172	−	0.916172i
$623$	171976.	+	171976.i	0.443090	+	0.443090i
$624$		−	375245.i		−	0.963707i
$625$	−371611.	−	120387.i	−0.951325	−	0.308190i
$626$	164255.			0.419150
$627$	−36555.0	+	36555.0i	−0.0929846	+	0.0929846i
$628$	−13687.5	−	13687.5i	−0.0347061	−	0.0347061i
$629$			926566.i			2.34194i
$630$	96131.1	+	112506.i	0.242205	+	0.283461i
$631$	276166.			0.693604			0.346802	−	0.937938i	$-0.387268\pi$
$631$	276166.			0.693604			0.346802	+	0.937938i	$0.387268\pi$
$632$	−162886.	+	162886.i	−0.407803	+	0.407803i
$633$	−71493.2	−	71493.2i	−0.178426	−	0.178426i
$634$			50365.6i			0.125301i
$635$	−213292.	−	16739.8i	−0.528965	−	0.0415148i
$636$	−87031.8			−0.215161
$637$	32574.7	−	32574.7i	0.0802790	−	0.0802790i
$638$	100087.	+	100087.i	0.245886	+	0.245886i
$639$			38589.4i			0.0945075i
$640$	37956.8	−	483631.i	0.0926680	−	1.18074i
$641$	556595.			1.35464			0.677319	−	0.735689i	$-0.263142\pi$
$641$	556595.			1.35464			0.677319	+	0.735689i	$0.263142\pi$
$642$	−49576.6	+	49576.6i	−0.120284	+	0.120284i
$643$	288950.	+	288950.i	0.698878	+	0.698878i	0.964169	−	0.265291i	$-0.0854679\pi$
$643$	288950.	+	288950.i	0.698878	+	0.698878i	−0.265291	+	0.964169i	$0.585468\pi$
$644$		−	154429.i		−	0.372356i
$645$	14561.1	−	12441.9i	0.0350006	−	0.0299065i
$646$	331690.			0.794817
$647$	−435693.	+	435693.i	−1.04081	+	1.04081i	−0.0416796	+	0.999131i	$0.513271\pi$
$647$	−435693.	+	435693.i	−1.04081	+	1.04081i	−0.999131	+	0.0416796i	$0.986729\pi$
$648$	−24459.7	−	24459.7i	−0.0582507	−	0.0582507i
$649$		−	157887.i		−	0.374849i
$650$	104362.	−	660772.i	0.247010	−	1.56396i
$651$	−374854.			−0.884504
$652$	89501.7	−	89501.7i	0.210541	−	0.210541i
$653$	−96648.2	−	96648.2i	−0.226656	−	0.226656i	0.584638	−	0.811294i	$-0.301237\pi$
$653$	−96648.2	−	96648.2i	−0.226656	−	0.226656i	−0.811294	+	0.584638i	$0.801237\pi$
$654$		−	291433.i		−	0.681370i
$655$	357543.	+	418444.i	0.833384	+	0.975338i
$656$	−97008.4			−0.225425
$657$	−21969.6	+	21969.6i	−0.0508970	+	0.0508970i
$658$	−75889.4	−	75889.4i	−0.175279	−	0.175279i
$659$		−	693374.i		−	1.59660i	−0.602259	−	0.798301i	$-0.705733\pi$
$659$		−	693374.i		−	1.59660i	0.602259	−	0.798301i	$-0.294267\pi$
$660$	−41894.5	−	3288.01i	−0.0961765	−	0.00754823i
$661$	102052.			0.233572			0.116786	−	0.993157i	$-0.462741\pi$
$661$	102052.			0.233572			0.116786	+	0.993157i	$0.462741\pi$
$662$	94258.1	−	94258.1i	0.215081	−	0.215081i
$663$	−331922.	−	331922.i	−0.755107	−	0.755107i
$664$		−	88347.9i		−	0.200383i
$665$	−16502.0	+	210262.i	−0.0373159	+	0.475465i
$666$	−296410.			−0.668259
$667$	217937.	−	217937.i	0.489869	−	0.489869i
$668$	137195.	+	137195.i	0.307457	+	0.307457i
$669$			387499.i			0.865802i
$670$	−471974.	+	403281.i	−1.05140	+	0.898377i
$671$	−58485.2			−0.129897
$672$	−123202.	+	123202.i	−0.272822	+	0.272822i
$673$	−222583.	−	222583.i	−0.491431	−	0.491431i	0.417326	−	0.908757i	$-0.362967\pi$
$673$	−222583.	−	222583.i	−0.491431	−	0.491431i	−0.908757	+	0.417326i	$0.862967\pi$
$674$			148865.i			0.327696i
$675$	−51570.8	−	70916.3i	−0.113187	−	0.155646i
$676$	139628.			0.305549
$677$	423786.	−	423786.i	0.924633	−	0.924633i	−0.0727193	−	0.997352i	$-0.523168\pi$
$677$	423786.	−	423786.i	0.924633	−	0.924633i	0.997352	+	0.0727193i	$0.0231677\pi$
$678$	217467.	+	217467.i	0.473079	+	0.473079i
$679$			231844.i			0.502870i
$680$	−304013.	−	355797.i	−0.657467	−	0.769457i
$681$	451465.			0.973486
$682$	281191.	−	281191.i	0.604550	−	0.604550i
$683$	215197.	+	215197.i	0.461313	+	0.461313i	0.899086	−	0.437773i	$-0.144233\pi$
$683$	215197.	+	215197.i	0.461313	+	0.461313i	−0.437773	+	0.899086i	$0.644233\pi$
$684$			28403.8i			0.0607105i
$685$	402660.	+	31602.0i	0.858138	+	0.0673493i
$686$	−570483.			−1.21226
$687$	362801.	−	362801.i	0.768697	−	0.768697i
$688$	32878.8	+	32878.8i	0.0694607	+	0.0694607i
$689$			655776.i			1.38139i
$690$	−26746.2	+	340789.i	−0.0561776	+	0.715793i
$691$	322148.			0.674683			0.337341	−	0.941382i	$-0.390472\pi$
$691$	322148.			0.674683			0.337341	+	0.941382i	$0.390472\pi$
$692$	−119968.	+	119968.i	−0.250526	+	0.250526i
$693$	−49529.1	−	49529.1i	−0.103132	−	0.103132i
$694$			818481.i			1.69938i
$695$	−8214.00	+	7018.51i	−0.0170053	+	0.0145303i
$696$	−134984.			−0.278653
$697$	−85808.6	+	85808.6i	−0.176630	+	0.176630i
$698$	−176355.	−	176355.i	−0.361974	−	0.361974i
$699$			197390.i			0.403990i
$700$	−138658.	+	100833.i	−0.282975	+	0.205782i
$701$	−324568.			−0.660495			−0.330248	−	0.943894i	$-0.607132\pi$
$701$	−324568.			−0.660495			−0.330248	+	0.943894i	$0.607132\pi$
$702$	106182.	−	106182.i	0.215466	−	0.215466i
$703$	−298720.	−	298720.i	−0.604441	−	0.604441i
$704$			94264.0i			0.190196i
$705$	41311.2	+	48347.9i	0.0831169	+	0.0972746i
$706$	−319144.			−0.640291
$707$	−255664.	+	255664.i	−0.511482	+	0.511482i
$708$	−61340.3	−	61340.3i	−0.122371	−	0.122371i
$709$			248026.i			0.493406i	0.969091	+	0.246703i	$0.0793472\pi$
$709$			248026.i			0.493406i	−0.969091	+	0.246703i	$0.920653\pi$
$710$	−166503.	−	13067.7i	−0.330298	−	0.0259228i
$711$	−131077.			−0.259290
$712$	173986.	−	173986.i	0.343205	−	0.343205i
$713$	−612289.	−	612289.i	−1.20442	−	1.20442i
$714$			449413.i			0.881555i
$715$	−24774.8	+	315671.i	−0.0484617	+	0.617479i
$716$	306822.			0.598495
$717$	238314.	−	238314.i	0.463565	−	0.463565i
$718$	−300815.	−	300815.i	−0.583514	−	0.583514i
$719$		−	406907.i		−	0.787113i	−0.919300	−	0.393557i	$-0.871244\pi$
$719$		−	406907.i		−	0.787113i	0.919300	−	0.393557i	$-0.128756\pi$
$720$	161842.	−	138287.i	0.312195	−	0.266757i
$721$	338183.			0.650550
$722$	323801.	−	323801.i	0.621160	−	0.621160i
$723$	43233.4	+	43233.4i	0.0827070	+	0.0827070i
$724$			352335.i			0.672169i
$725$	−337980.	−	53380.3i	−0.643006	−	0.101556i
$726$	−281295.			−0.533690
$727$	−465457.	+	465457.i	−0.880664	+	0.880664i	−0.993602	−	0.112938i	$-0.963974\pi$
$727$	−465457.	+	465457.i	−0.880664	+	0.880664i	0.112938	+	0.993602i	$0.463974\pi$
$728$	360352.	+	360352.i	0.679930	+	0.679930i
$729$		−	19683.0i		−	0.0370370i
$730$	−87353.6	−	102233.i	−0.163921	−	0.191843i
$731$	58165.7			0.108851
$732$	−22721.9	+	22721.9i	−0.0424056	+	0.0424056i
$733$	−596415.	−	596415.i	−1.11004	−	1.11004i	−0.993144	−	0.116901i	$-0.962704\pi$
$733$	−596415.	−	596415.i	−1.11004	−	1.11004i	−0.116901	−	0.993144i	$-0.537296\pi$
$734$			626208.i			1.16232i
$735$	26054.0	+	2044.80i	0.0482280	+	0.00378508i
$736$	−402479.			−0.742997
$737$	207780.	−	207780.i	0.382534	−	0.382534i
$738$	−27450.3	−	27450.3i	−0.0504005	−	0.0504005i
$739$		−	672211.i		−	1.23088i	−0.788182	−	0.615442i	$-0.788978\pi$
$739$		−	672211.i		−	1.23088i	0.788182	−	0.615442i	$-0.211022\pi$
$740$	26869.0	−	342354.i	0.0490668	−	0.625190i
$741$	214020.			0.389778
$742$	443951.	−	443951.i	0.806358	−	0.806358i
$743$	251951.	+	251951.i	0.456393	+	0.456393i	0.897470	−	0.441076i	$-0.145403\pi$
$743$	251951.	+	251951.i	0.456393	+	0.456393i	−0.441076	+	0.897470i	$0.645403\pi$
$744$			379233.i			0.685110i
$745$	−330162.	+	282109.i	−0.594860	+	0.508282i
$746$	1.15477e6			2.07500
$747$	35547.3	−	35547.3i	0.0637038	−	0.0637038i
$748$	−90242.8	−	90242.8i	−0.161291	−	0.161291i
$749$		−	135392.i		−	0.241339i
$750$	323449.	−	198500.i	0.575020	−	0.352889i
$751$	−37245.9			−0.0660387			−0.0330194	−	0.999455i	$-0.510512\pi$
$751$	−37245.9			−0.0660387			−0.0330194	+	0.999455i	$0.510512\pi$
$752$	−109169.	+	109169.i	−0.193047	+	0.193047i
$753$	53862.8	+	53862.8i	0.0949946	+	0.0949946i
$754$		−	585981.i		−	1.03072i
$755$	−332824.	−	389515.i	−0.583875	−	0.683330i
$756$	−38484.9			−0.0673359
$757$	−133738.	+	133738.i	−0.233380	+	0.233380i	−0.814102	−	0.580722i	$-0.802770\pi$
$757$	−133738.	+	133738.i	−0.233380	+	0.233380i	0.580722	+	0.814102i	$0.302770\pi$
$758$	714192.	+	714192.i	1.24302	+	1.24302i
$759$		−	161802.i		−	0.280868i
$760$	212719.	+	16694.8i	0.368281	+	0.0289038i
$761$	969173.			1.67352			0.836762	−	0.547567i	$-0.184446\pi$
$761$	969173.			1.67352			0.836762	+	0.547567i	$0.184446\pi$
$762$	146976.	−	146976.i	0.253126	−	0.253126i
$763$	397946.	+	397946.i	0.683557	+	0.683557i
$764$		−	258761.i		−	0.443315i
$765$	20835.6	−	265478.i	0.0356026	−	0.453635i
$766$	−45897.5			−0.0782225
$767$	−462193.	+	462193.i	−0.785657	+	0.785657i
$768$	233074.	+	233074.i	0.395159	+	0.395159i
$769$		−	572412.i		−	0.967956i	−0.875080	−	0.483978i	$-0.839191\pi$
$769$		−	572412.i		−	0.967956i	0.875080	−	0.483978i	$-0.160809\pi$
$770$	230477.	−	196933.i	0.388729	−	0.332152i
$771$	−351376.			−0.591104
$772$	107904.	−	107904.i	0.181051	−	0.181051i
$773$	345426.	+	345426.i	0.578090	+	0.578090i	0.934377	−	0.356287i	$-0.115957\pi$
$773$	345426.	+	345426.i	0.578090	+	0.578090i	−0.356287	+	0.934377i	$0.615957\pi$
$774$			18607.3i			0.0310600i
$775$	−149970.	+	949546.i	−0.249691	+	1.58093i
$776$	234552.			0.389508
$777$	404742.	−	404742.i	0.670403	−	0.670403i
$778$	−568471.	−	568471.i	−0.939180	−	0.939180i
$779$		−	55328.5i		−	0.0911746i
$780$	113015.	+	132266.i	0.185758	+	0.217399i
$781$	79053.7			0.129605
$782$	−734076.	+	734076.i	−1.20040	+	1.20040i
$783$	−54311.5	−	54311.5i	−0.0885867	−	0.0885867i
$784$			63446.5i			0.103223i
$785$	−82488.9	−	6473.99i	−0.133862	−	0.0105059i
$786$	−534720.			−0.865528
$787$	−172088.	+	172088.i	−0.277843	+	0.277843i	−0.832248	−	0.554404i	$-0.812946\pi$
$787$	−172088.	+	172088.i	−0.277843	+	0.277843i	0.554404	+	0.832248i	$0.312946\pi$
$788$	−107933.	−	107933.i	−0.173821	−	0.173821i
$789$		−	337094.i		−	0.541498i
$790$	44387.0	−	565562.i	0.0711217	−	0.906204i
$791$	−593893.			−0.949195
$792$	−50107.7	+	50107.7i	−0.0798830	+	0.0798830i
$793$	171208.	+	171208.i	0.272256	+	0.272256i
$794$		−	314419.i		−	0.498733i
$795$	−282834.	+	241670.i	−0.447505	+	0.382374i
$796$	405601.			0.640137
$797$	296648.	−	296648.i	0.467009	−	0.467009i	−0.433935	−	0.900944i	$-0.642875\pi$
$797$	296648.	−	296648.i	0.467009	−	0.467009i	0.900944	+	0.433935i	$0.142875\pi$
$798$	−144888.	−	144888.i	−0.227524	−	0.227524i
$799$			193130.i			0.302521i
$800$	262794.	+	361375.i	0.410616	+	0.564648i
$801$	140008.			0.218217
$802$	−640440.	+	640440.i	−0.995703	+	0.995703i
$803$	45006.7	+	45006.7i	0.0697985	+	0.0697985i
$804$		−	161449.i		−	0.249760i
$805$	−428819.	−	501861.i	−0.661732	−	0.774448i
$806$	−1.64630e6			−2.53418
$807$	−295023.	+	295023.i	−0.453011	+	0.453011i
$808$	258651.	+	258651.i	0.396178	+	0.396178i
$809$		−	286471.i		−	0.437707i	−0.975758	−	0.218854i	$-0.929768\pi$
$809$		−	286471.i		−	0.437707i	0.975758	−	0.218854i	$-0.0702317\pi$
$810$	84927.0	+	6665.33i	0.129442	+	0.0101590i
$811$	−672778.			−1.02289			−0.511447	−	0.859315i	$-0.670890\pi$
$811$	−672778.			−1.02289			−0.511447	+	0.859315i	$0.670890\pi$
$812$	−106192.	+	106192.i	−0.161057	+	0.161057i
$813$	147145.	+	147145.i	0.222619	+	0.222619i
$814$			607222.i			0.916428i
$815$	42332.9	−	539389.i	0.0637328	−	0.812058i
$816$	646492.			0.970918
$817$	−18752.3	+	18752.3i	−0.0280938	+	0.0280938i
$818$	876.729	+	876.729i	0.00131026	+	0.00131026i
$819$			289980.i			0.432314i
$820$	34193.4	−	29216.8i	0.0508528	−	0.0434515i
$821$	−270459.			−0.401251			−0.200625	−	0.979668i	$-0.564297\pi$
$821$	−270459.			−0.401251			−0.200625	+	0.979668i	$0.564297\pi$
$822$	−277466.	+	277466.i	−0.410645	+	0.410645i
$823$	445888.	+	445888.i	0.658304	+	0.658304i	0.954979	−	0.296675i	$-0.0958777\pi$
$823$	445888.	+	445888.i	0.658304	+	0.658304i	−0.296675	+	0.954979i	$0.595878\pi$
$824$		−	342134.i		−	0.503897i
$825$	−145278.	+	105647.i	−0.213448	+	0.155221i
$826$	625797.			0.917220
$827$	−505149.	+	505149.i	−0.738599	+	0.738599i	−0.972307	−	0.233708i	$-0.924914\pi$
$827$	−505149.	+	505149.i	−0.738599	+	0.738599i	0.233708	+	0.972307i	$0.424914\pi$
$828$	−62861.5	−	62861.5i	−0.0916905	−	0.0916905i
$829$		−	176611.i		−	0.256986i	−0.991710	−	0.128493i	$-0.958986\pi$
$829$		−	176611.i		−	0.256986i	0.991710	−	0.128493i	$-0.0410139\pi$
$830$	141340.	+	165415.i	0.205167	+	0.240114i
$831$	−366468.			−0.530682
$832$	275945.	−	275945.i	0.398636	−	0.398636i
$833$	56121.5	+	56121.5i	0.0808797	+	0.0808797i
$834$		−	10496.5i		−	0.0150908i
$835$	826816.	+	64891.1i	1.18587	+	0.0930705i
$836$	58187.6			0.0832564
$837$	−152587.	+	152587.i	−0.217804	+	0.217804i
$838$	−102216.	−	102216.i	−0.145557	−	0.145557i
$839$		−	153954.i		−	0.218709i	−0.994003	−	0.109354i	$-0.965122\pi$
$839$		−	153954.i		−	0.218709i	0.994003	−	0.109354i	$-0.0348783\pi$
$840$	−22620.2	+	288217.i	−0.0320581	+	0.408471i
$841$	407556.			0.576229
$842$	−206475.	+	206475.i	−0.291235	+	0.291235i
$843$	−47185.1	−	47185.1i	−0.0663972	−	0.0663972i
$844$			113802.i			0.159758i
$845$	453762.	−	387720.i	0.635498	−	0.543006i
$846$	−61782.6			−0.0863228
$847$	384103.	−	384103.i	0.535403	−	0.535403i
$848$	−638635.	−	638635.i	−0.888098	−	0.888098i
$849$		−	263996.i		−	0.366254i
$850$	1.13841e6	+	179800.i	1.57566	+	0.248858i
$851$	1.32222e6			1.82576
$852$	30713.0	−	30713.0i	0.0423100	−	0.0423100i
$853$	601023.	+	601023.i	0.826025	+	0.826025i	0.986964	−	0.160940i	$-0.0514524\pi$
$853$	601023.	+	601023.i	0.826025	+	0.826025i	−0.160940	+	0.986964i	$0.551452\pi$
$854$		−	231811.i		−	0.317846i
$855$	78871.5	+	92306.1i	0.107892	+	0.126269i
$856$	−136973.			−0.186934
$857$	479752.	−	479752.i	0.653214	−	0.653214i	−0.300552	−	0.953766i	$-0.597171\pi$
$857$	479752.	−	479752.i	0.653214	−	0.653214i	0.953766	+	0.300552i	$0.0971708\pi$
$858$	−217524.	−	217524.i	−0.295483	−	0.295483i
$859$		−	925363.i		−	1.25408i	−0.778987	−	0.627041i	$-0.784266\pi$
$859$		−	925363.i		−	1.25408i	0.778987	−	0.627041i	$-0.215734\pi$
$860$	−21491.5	−	1686.72i	−0.0290582	−	0.00228058i
$861$	74965.7			0.101124
$862$	228953.	−	228953.i	0.308129	−	0.308129i
$863$	−882185.	−	882185.i	−1.18451	−	1.18451i	−0.978564	−	0.205944i	$-0.933974\pi$
$863$	−882185.	−	882185.i	−1.18451	−	1.18451i	−0.205944	−	0.978564i	$-0.566026\pi$
$864$			100301.i			0.134362i
$865$	−56743.0	+	722997.i	−0.0758368	+	0.966282i
$866$	−733498.			−0.978054
$867$	264977.	−	264977.i	0.352509	−	0.352509i
$868$	298343.	+	298343.i	0.395983	+	0.395983i
$869$			268522.i			0.355582i
$870$	252732.	−	215948.i	0.333904	−	0.285306i
$871$	−1.21650e6			−1.60352
$872$	402595.	−	402595.i	0.529463	−	0.529463i
$873$	94373.6	+	94373.6i	0.123829	+	0.123829i
$874$		−	473324.i		−	0.619635i
$875$	−170615.	+	712710.i	−0.222844	+	0.930887i
$876$	34970.9			0.0455721
$877$	−272599.	+	272599.i	−0.354426	+	0.354426i	−0.861753	−	0.507328i	$-0.830633\pi$
$877$	−272599.	+	272599.i	−0.354426	+	0.354426i	0.507328	+	0.861753i	$0.330633\pi$
$878$	555265.	+	555265.i	0.720297	+	0.720297i
$879$		−	370113.i		−	0.479023i
$880$	−283292.	−	331547.i	−0.365822	−	0.428134i
$881$	−557598.			−0.718405			−0.359202	−	0.933260i	$-0.616951\pi$
$881$	−557598.			−0.718405			−0.359202	+	0.933260i	$0.616951\pi$
$882$	−17953.4	+	17953.4i	−0.0230786	+	0.0230786i
$883$	180236.	+	180236.i	0.231164	+	0.231164i	0.813179	−	0.582014i	$-0.197735\pi$
$883$	180236.	+	180236.i	0.231164	+	0.231164i	−0.582014	+	0.813179i	$0.697735\pi$
$884$			528347.i			0.676107i
$885$	−369672.	−	29013.0i	−0.471987	−	0.0370430i
$886$	438125.			0.558124
$887$	170589.	−	170589.i	0.216822	−	0.216822i	−0.590336	−	0.807158i	$-0.701005\pi$
$887$	170589.	−	170589.i	0.216822	−	0.216822i	0.807158	+	0.590336i	$0.201005\pi$
$888$	−409471.	−	409471.i	−0.519274	−	0.519274i
$889$			401385.i			0.507876i
$890$	−47411.6	+	604099.i	−0.0598555	+	0.762655i
$891$	−40322.3			−0.0507914
$892$	308407.	−	308407.i	0.387610	−	0.387610i
$893$	−62264.0	−	62264.0i	−0.0780790	−	0.0780790i
$894$		−	421907.i		−	0.527887i
$895$	997105.	−	851983.i	1.24479	−	1.06362i
$896$	−910124.			−1.13366
$897$	−473655.	+	473655.i	−0.588678	+	0.588678i
$898$	−702977.	−	702977.i	−0.871743	−	0.871743i
$899$			842069.i			1.04191i
$900$	−15396.9	+	97486.5i	−0.0190085	+	0.120354i
$901$	−1.12981e6			−1.39173
$902$	−56234.3	+	56234.3i	−0.0691176	+	0.0691176i
$903$	−25407.9	−	25407.9i	−0.0311597	−	0.0311597i
$904$			600832.i			0.735218i
$905$	978362.	+	1.14501e6i	1.19455	+	1.39802i
$906$	497752.			0.606396
$907$	399726.	−	399726.i	0.485901	−	0.485901i	−0.421109	−	0.907010i	$-0.638359\pi$
$907$	399726.	−	399726.i	0.485901	−	0.485901i	0.907010	+	0.421109i	$0.138359\pi$
$908$	−359317.	−	359317.i	−0.435819	−	0.435819i
$909$			208139.i			0.251899i
$910$	−1.25119e6	−	98196.9i	−1.51091	−	0.118581i
$911$	1.58194e6			1.90614			0.953068	−	0.302757i	$-0.0979071\pi$
$911$	1.58194e6			1.90614			0.953068	+	0.302757i	$0.0979071\pi$
$912$	−208425.	+	208425.i	−0.250588	+	0.250588i
$913$	−72821.7	−	72821.7i	−0.0873613	−	0.0873613i
$914$		−	1.24923e6i		−	1.49537i
$915$	−10747.1	+	136936.i	−0.0128366	+	0.163559i
$916$	−577501.			−0.688274
$917$	730149.	−	730149.i	0.868306	−	0.868306i
$918$	182937.	+	182937.i	0.217078	+	0.217078i
$919$			1.60006e6i			1.89455i	0.320420	+	0.947276i	$0.396176\pi$
$919$			1.60006e6i			1.89455i	−0.320420	+	0.947276i	$0.603824\pi$
$920$	−507725.	+	433829.i	−0.599864	+	0.512558i
$921$	555409.			0.654778
$922$	−672485.	+	672485.i	−0.791081	+	0.791081i
$923$	−231419.	−	231419.i	−0.271641	−	0.271641i
$924$			78839.5i			0.0923422i
$925$	−863329.	−	1.18718e6i	−1.00900	−	1.38751i
$926$	1.85234e6			2.16023
$927$	137660.	−	137660.i	0.160194	−	0.160194i
$928$	276761.	+	276761.i	0.321372	+	0.321372i
$929$			1.50251e6i			1.74095i	0.492209	+	0.870477i	$0.336189\pi$
$929$			1.50251e6i			1.74095i	−0.492209	+	0.870477i	$0.663811\pi$
$930$	−606701.	−	710043.i	−0.701469	−	0.820954i
$931$	−36186.6			−0.0417492
$932$	157101.	−	157101.i	0.180862	−	0.180862i
$933$	394029.	+	394029.i	0.452652	+	0.452652i
$934$		−	166210.i		−	0.190530i
$935$	−543855.	−	42683.4i	−0.622100	−	0.0488243i
$936$	293368.			0.334858
$937$	45116.6	−	45116.6i	0.0513874	−	0.0513874i	−0.680946	−	0.732334i	$-0.738431\pi$
$937$	45116.6	−	45116.6i	0.0513874	−	0.0513874i	0.732334	+	0.680946i	$0.238431\pi$
$938$	823554.	+	823554.i	0.936022	+	0.936022i
$939$			182595.i			0.207089i
$940$	5600.47	−	71358.9i	0.00633824	−	0.0807593i
$941$	−1.62275e6			−1.83262			−0.916312	−	0.400466i	$-0.868848\pi$
$941$	−1.62275e6			−1.83262			−0.916312	+	0.400466i	$0.868848\pi$
$942$	56841.8	−	56841.8i	0.0640569	−	0.0640569i
$943$	122450.	+	122450.i	0.137700	+	0.137700i
$944$		−	900224.i		−	1.01020i
$945$	−125067.	+	106865.i	−0.140049	+	0.119666i
$946$	38118.7			0.0425947
$947$	−868195.	+	868195.i	−0.968094	+	0.968094i	−0.999506	−	0.0314128i	$-0.989999\pi$
$947$	−868195.	+	868195.i	−0.968094	+	0.968094i	0.0314128	+	0.999506i	$0.489999\pi$
$948$	104323.	+	104323.i	0.116081	+	0.116081i
$949$		−	263502.i		−	0.292585i
$950$	−424985.	+	309052.i	−0.470898	+	0.342440i
$951$	−55989.2			−0.0619075
$952$	−620834.	+	620834.i	−0.685017	+	0.685017i
$953$	−221674.	−	221674.i	−0.244078	−	0.244078i	0.574457	−	0.818535i	$-0.305213\pi$
$953$	−221674.	−	221674.i	−0.244078	−	0.244078i	−0.818535	+	0.574457i	$0.805213\pi$
$954$		−	361427.i		−	0.397122i
$955$	−718528.	−	840918.i	−0.787838	−	0.922034i
$956$	−379344.			−0.415066
$957$	−111262.	+	111262.i	−0.121485	+	0.121485i
$958$	57122.1	+	57122.1i	0.0622406	+	0.0622406i
$959$		−	757749.i		−	0.823926i
$960$	220707.	+	17321.8i	0.239483	+	0.0187953i
$961$	1.44225e6			1.56168
$962$	1.77756e6	−	1.77756e6i	1.92077	−	1.92077i
$963$	−55112.1	−	55112.1i	−0.0594284	−	0.0594284i
$964$		−	68818.1i		−	0.0740540i
$965$	51036.8	−	650290.i	0.0548061	−	0.698317i
$966$	641316.			0.687255
$967$	310704.	−	310704.i	0.332272	−	0.332272i	−0.521176	−	0.853449i	$-0.674507\pi$
$967$	310704.	−	310704.i	0.332272	−	0.332272i	0.853449	+	0.521176i	$0.174507\pi$
$968$	−388590.	−	388590.i	−0.414707	−	0.414707i
$969$			368725.i			0.392694i
$970$	−439155.	+	375239.i	−0.466740	+	0.398809i
$971$	−993419.			−1.05364			−0.526822	−	0.849976i	$-0.676617\pi$
$971$	−993419.			−1.05364			−0.526822	+	0.849976i	$0.676617\pi$
$972$	−15665.5	+	15665.5i	−0.0165811	+	0.0165811i
$973$	14332.7	+	14332.7i	0.0151392	+	0.0151392i
$974$			1.65864e6i			1.74837i
$975$	734551.	+	116014.i	0.772703	+	0.122040i
$976$	−333465.			−0.350067
$977$	−575998.	+	575998.i	−0.603437	+	0.603437i	−0.941223	−	0.337786i	$-0.890322\pi$
$977$	−575998.	+	575998.i	−0.603437	+	0.603437i	0.337786	+	0.941223i	$0.390322\pi$
$978$	371684.	+	371684.i	0.388594	+	0.388594i
$979$		−	286819.i		−	0.299256i
$980$	−19108.7	−	22363.6i	−0.0198966	−	0.0232857i
$981$	323973.			0.336644
$982$	−578996.	+	578996.i	−0.600416	+	0.600416i
$983$	−164785.	−	164785.i	−0.170533	−	0.170533i	0.616680	−	0.787214i	$-0.288477\pi$
$983$	−164785.	−	164785.i	−0.170533	−	0.170533i	−0.787214	+	0.616680i	$0.788477\pi$
$984$		−	75841.5i		−	0.0783280i
$985$	−650468.	−	51050.8i	−0.670430	−	0.0526175i
$986$	1.00956e6			1.03843
$987$	84362.8	−	84362.8i	0.0865998	−	0.0865998i
$988$	−170336.	−	170336.i	−0.174499	−	0.174499i
$989$		−	83003.0i		−	0.0848596i
$990$	13654.5	−	173980.i	0.0139317	−	0.177513i
$991$	1.06880e6			1.08830			0.544148	−	0.838989i	$-0.316853\pi$
$991$	1.06880e6			1.08830			0.544148	+	0.838989i	$0.316853\pi$
$992$	777551.	−	777551.i	0.790143	−	0.790143i
$993$	104782.	+	104782.i	0.106265	+	0.106265i
$994$			313335.i			0.317130i
$995$	1.31811e6	−	1.12627e6i	1.33140	−	1.13762i
$996$	−56583.6			−0.0570390
$997$	205698.	−	205698.i	0.206938	−	0.206938i	−0.596027	−	0.802965i	$-0.703255\pi$
$997$	205698.	−	205698.i	0.206938	−	0.206938i	0.802965	+	0.596027i	$0.203255\pi$
$998$	−726256.	−	726256.i	−0.729170	−	0.729170i
$999$		−	329506.i		−	0.330166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.5.f.a.13.3	yes	8
3.2	odd	2		45.5.g.e.28.2		8
4.3	odd	2		240.5.bg.c.193.1		8
5.2	odd	4	inner	15.5.f.a.7.3	✓	8
5.3	odd	4		75.5.f.e.7.2		8
5.4	even	2		75.5.f.e.43.2		8
15.2	even	4		45.5.g.e.37.2		8
15.8	even	4		225.5.g.m.82.3		8
15.14	odd	2		225.5.g.m.118.3		8
20.7	even	4		240.5.bg.c.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.3	✓	8	5.2	odd	4	inner
15.5.f.a.13.3	yes	8	1.1	even	1	trivial
45.5.g.e.28.2		8	3.2	odd	2
45.5.g.e.37.2		8	15.2	even	4
75.5.f.e.7.2		8	5.3	odd	4
75.5.f.e.43.2		8	5.4	even	2
225.5.g.m.82.3		8	15.8	even	4
225.5.g.m.118.3		8	15.14	odd	2
240.5.bg.c.97.1		8	20.7	even	4
240.5.bg.c.193.1		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.30519 - 3.30519i) q^{2} +(3.67423 + 3.67423i) q^{3} -5.84858i q^{4} +(-16.2403 - 19.0066i) q^{5} +24.2881 q^{6} +(-33.1649 + 33.1649i) q^{7} +(33.5524 + 33.5524i) q^{8} +27.0000i q^{9} +O(q^{10})\)	\(q+(3.30519 - 3.30519i) q^{2} +(3.67423 + 3.67423i) q^{3} -5.84858i q^{4} +(-16.2403 - 19.0066i) q^{5} +24.2881 q^{6} +(-33.1649 + 33.1649i) q^{7} +(33.5524 + 33.5524i) q^{8} +27.0000i q^{9} +(-116.498 - 9.14312i) q^{10} +55.3118 q^{11} +(21.4891 - 21.4891i) q^{12} +(-161.918 - 161.918i) q^{13} +219.233i q^{14} +(10.1640 - 129.506i) q^{15} +315.371 q^{16} +(278.961 - 278.961i) q^{17} +(89.2402 + 89.2402i) q^{18} +179.871i q^{19} +(-111.162 + 94.9829i) q^{20} -243.711 q^{21} +(182.816 - 182.816i) q^{22} +(-398.080 - 398.080i) q^{23} +246.559i q^{24} +(-97.5033 + 617.348i) q^{25} -1070.34 q^{26} +(-99.2043 + 99.2043i) q^{27} +(193.968 + 193.968i) q^{28} +547.472i q^{29} +(-394.447 - 461.635i) q^{30} +1538.11 q^{31} +(505.525 - 505.525i) q^{32} +(203.229 + 203.229i) q^{33} -1844.04i q^{34} +(1168.96 + 91.7437i) q^{35} +157.912 q^{36} +(-1660.74 + 1660.74i) q^{37} +(594.509 + 594.509i) q^{38} -1189.85i q^{39} +(92.8156 - 1182.62i) q^{40} -307.601 q^{41} +(-805.512 + 805.512i) q^{42} +(104.254 + 104.254i) q^{43} -323.496i q^{44} +(513.179 - 438.489i) q^{45} -2631.46 q^{46} +(-346.159 + 346.159i) q^{47} +(1158.75 + 1158.75i) q^{48} +201.180i q^{49} +(1718.19 + 2362.72i) q^{50} +2049.94 q^{51} +(-946.991 + 946.991i) q^{52} +(-2025.02 - 2025.02i) q^{53} +655.779i q^{54} +(-898.282 - 1051.29i) q^{55} -2225.52 q^{56} +(-660.889 + 660.889i) q^{57} +(1809.50 + 1809.50i) q^{58} -2854.49i q^{59} +(-757.424 - 59.4450i) q^{60} -1057.37 q^{61} +(5083.73 - 5083.73i) q^{62} +(-895.452 - 895.452i) q^{63} +1704.23i q^{64} +(-447.912 + 5707.12i) q^{65} +1343.42 q^{66} +(3756.53 - 3756.53i) q^{67} +(-1631.53 - 1631.53i) q^{68} -2925.28i q^{69} +(4166.87 - 3560.41i) q^{70} +1429.24 q^{71} +(-905.914 + 905.914i) q^{72} +(813.690 + 813.690i) q^{73} +10978.2i q^{74} +(-2626.53 + 1910.03i) q^{75} +1051.99 q^{76} +(-1834.41 + 1834.41i) q^{77} +(-3932.68 - 3932.68i) q^{78} +4854.69i q^{79} +(-5121.74 - 5994.14i) q^{80} -729.000 q^{81} +(-1016.68 + 1016.68i) q^{82} +(-1316.57 - 1316.57i) q^{83} +1425.37i q^{84} +(-9832.53 - 771.687i) q^{85} +689.160 q^{86} +(-2011.54 + 2011.54i) q^{87} +(1855.84 + 1855.84i) q^{88} -5185.49i q^{89} +(246.864 - 3145.44i) q^{90} +10740.0 q^{91} +(-2328.20 + 2328.20i) q^{92} +(5651.36 + 5651.36i) q^{93} +2288.24i q^{94} +(3418.74 - 2921.17i) q^{95} +3714.83 q^{96} +(3495.32 - 3495.32i) q^{97} +(664.940 + 664.940i) q^{98} +1493.42i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8}+O(q^{10}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8} + 104 q^{10} - 288 q^{11} - 360 q^{12} - 340 q^{13} + 144 q^{15} + 620 q^{16} + 900 q^{17} + 564 q^{20} + 792 q^{21} - 1100 q^{22} - 1560 q^{23} - 1204 q^{25} - 3024 q^{26} + 3580 q^{28} - 2664 q^{30} - 512 q^{31} + 4980 q^{32} + 2700 q^{33} + 6600 q^{35} + 2484 q^{36} - 3820 q^{37} - 7680 q^{38} - 2952 q^{40} - 2712 q^{41} - 7380 q^{42} - 1240 q^{43} - 1944 q^{45} + 13528 q^{46} + 4800 q^{47} + 3600 q^{48} + 3744 q^{50} + 6264 q^{51} - 1240 q^{52} + 1020 q^{53} - 3644 q^{55} - 30720 q^{56} - 5400 q^{57} + 2340 q^{58} - 1044 q^{60} - 4760 q^{61} + 28680 q^{62} + 540 q^{63} - 1212 q^{65} + 10008 q^{66} - 8920 q^{67} - 1920 q^{68} + 7380 q^{70} + 7536 q^{71} - 4860 q^{72} + 11600 q^{73} - 5976 q^{75} + 4344 q^{76} - 360 q^{77} - 4680 q^{78} + 10644 q^{80} - 5832 q^{81} - 27200 q^{82} - 32400 q^{83} - 15628 q^{85} + 14592 q^{86} + 10620 q^{87} - 14340 q^{88} + 8964 q^{90} + 16528 q^{91} - 31800 q^{92} + 14040 q^{93} + 18864 q^{95} - 4068 q^{96} + 58640 q^{97} + 46440 q^{98}+O(q^{100}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Introduction

L-functions

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