LMFDB - Embedded newform 38.5.d.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, 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:	$3.92805859719$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Root			$0.500000 - 6.86019i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.5.d.a.27.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{2} +(-7.91584 + 4.57021i) q^{3} +(4.00000 - 6.92820i) q^{4} +(19.7357 + 34.1832i) q^{5} +(-12.9265 + 22.3894i) q^{6} +91.5785 q^{7} -22.6274i q^{8} +(1.27372 - 2.20614i) q^{9} +O(q^{10})$	\(q+(2.44949 - 1.41421i) q^{2} +(-7.91584 + 4.57021i) q^{3} +(4.00000 - 6.92820i) q^{4} +(19.7357 + 34.1832i) q^{5} +(-12.9265 + 22.3894i) q^{6} +91.5785 q^{7} -22.6274i q^{8} +(1.27372 - 2.20614i) q^{9} +(96.6847 + 55.8209i) q^{10} -154.274 q^{11} +73.1234i q^{12} +(-5.46159 - 3.15325i) q^{13} +(224.321 - 129.512i) q^{14} +(-312.449 - 180.393i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-35.4376 - 61.3797i) q^{17} -7.20523i q^{18} +(338.973 + 124.170i) q^{19} +315.771 q^{20} +(-724.921 + 418.533i) q^{21} +(-377.894 + 218.177i) q^{22} +(328.524 - 569.020i) q^{23} +(103.412 + 179.115i) q^{24} +(-466.494 + 807.991i) q^{25} -17.8375 q^{26} -717.090i q^{27} +(366.314 - 634.475i) q^{28} +(-756.663 - 436.859i) q^{29} -1020.45 q^{30} -1356.82i q^{31} +(-156.767 - 90.5097i) q^{32} +(1221.21 - 705.067i) q^{33} +(-173.608 - 100.233i) q^{34} +(1807.36 + 3130.45i) q^{35} +(-10.1897 - 17.6491i) q^{36} +204.056i q^{37} +(1005.91 - 175.227i) q^{38} +57.6441 q^{39} +(773.477 - 446.567i) q^{40} +(-1254.28 + 724.157i) q^{41} +(-1183.79 + 2050.39i) q^{42} +(694.511 + 1202.93i) q^{43} +(-617.098 + 1068.84i) q^{44} +100.551 q^{45} -1858.41i q^{46} +(396.636 - 686.994i) q^{47} +(506.614 + 292.494i) q^{48} +5985.63 q^{49} +2638.89i q^{50} +(561.037 + 323.915i) q^{51} +(-43.6927 + 25.2260i) q^{52} +(-427.719 - 246.944i) q^{53} +(-1014.12 - 1756.50i) q^{54} +(-3044.71 - 5273.59i) q^{55} -2072.19i q^{56} +(-3250.74 + 566.268i) q^{57} -2471.25 q^{58} +(414.766 - 239.465i) q^{59} +(-2499.59 + 1443.14i) q^{60} +(-1244.82 + 2156.08i) q^{61} +(-1918.83 - 3323.51i) q^{62} +(116.645 - 202.035i) q^{63} -512.000 q^{64} -248.926i q^{65} +(1994.23 - 3454.11i) q^{66} +(-3155.80 - 1822.00i) q^{67} -567.002 q^{68} +6005.69i q^{69} +(8854.24 + 5112.00i) q^{70} +(408.962 - 236.114i) q^{71} +(-49.9193 - 28.8209i) q^{72} +(656.228 + 1136.62i) q^{73} +(288.579 + 499.833i) q^{74} -8527.91i q^{75} +(2216.17 - 1851.79i) q^{76} -14128.2 q^{77} +(141.199 - 81.5211i) q^{78} +(6824.92 - 3940.37i) q^{79} +(1263.08 - 2187.72i) q^{80} +(3380.43 + 5855.07i) q^{81} +(-2048.23 + 3547.63i) q^{82} -7247.57 q^{83} +6696.54i q^{84} +(1398.77 - 2422.74i) q^{85} +(3402.40 + 1964.37i) q^{86} +7986.16 q^{87} +3490.83i q^{88} +(-2753.52 - 1589.75i) q^{89} +(246.298 - 142.200i) q^{90} +(-500.164 - 288.770i) q^{91} +(-2628.19 - 4552.16i) q^{92} +(6200.94 + 10740.3i) q^{93} -2243.71i q^{94} +(2445.33 + 14037.8i) q^{95} +1654.59 q^{96} +(4303.37 - 2484.55i) q^{97} +(14661.7 - 8464.95i) q^{98} +(-196.502 + 340.351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.44949	−	1.41421i	0.612372	−	0.353553i
$2$	2.44949	−	1.41421i	0.612372	−	0.353553i
$3$	−7.91584	+	4.57021i	−0.879538	+	0.507802i	−0.870506	−	0.492158i	$-0.836208\pi$
$3$	−7.91584	+	4.57021i	−0.879538	+	0.507802i	−0.00903204	+	0.999959i	$0.502875\pi$
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	19.7357	+	34.1832i	0.789427	+	1.36733i	0.926318	+	0.376742i	$0.122956\pi$
$5$	19.7357	+	34.1832i	0.789427	+	1.36733i	−0.136891	+	0.990586i	$0.543711\pi$
$6$	−12.9265	+	22.3894i	−0.359070	+	0.621927i
$7$	91.5785			1.86895			0.934475	−	0.356029i	$-0.115870\pi$
$7$	91.5785			1.86895			0.934475	+	0.356029i	$0.115870\pi$
$8$		−	22.6274i		−	0.353553i
$9$	1.27372	−	2.20614i	0.0157249	−	0.0272363i
$10$	96.6847	+	55.8209i	0.966847	+	0.558209i
$11$	−154.274			−1.27500			−0.637498	−	0.770452i	$-0.720030\pi$
$11$	−154.274			−1.27500			−0.637498	+	0.770452i	$0.720030\pi$
$12$			73.1234i			0.507802i
$13$	−5.46159	−	3.15325i	−0.0323171	−	0.0186583i	0.483754	−	0.875204i	$-0.339273\pi$
$13$	−5.46159	−	3.15325i	−0.0323171	−	0.0186583i	−0.516072	+	0.856545i	$0.672606\pi$
$14$	224.321	−	129.512i	1.14449	−	0.660773i
$15$	−312.449	−	180.393i	−1.38866	−	0.801745i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−35.4376	−	61.3797i	−0.122622	−	0.212387i	0.798179	−	0.602420i	$-0.205797\pi$
$17$	−35.4376	−	61.3797i	−0.122622	−	0.212387i	−0.920801	+	0.390033i	$0.872463\pi$
$18$		−	7.20523i		−	0.0222384i
$19$	338.973	+	124.170i	0.938984	+	0.343962i
$19$	338.973	+	124.170i	0.938984	+	0.343962i
$20$	315.771			0.789427
$21$	−724.921	+	418.533i	−1.64381	+	0.949056i
$22$	−377.894	+	218.177i	−0.780772	+	0.450779i
$23$	328.524	−	569.020i	0.621028	−	1.07565i	−0.368267	−	0.929720i	$-0.620049\pi$
$23$	328.524	−	569.020i	0.621028	−	1.07565i	0.989295	−	0.145932i	$-0.0466179\pi$
$24$	103.412	+	179.115i	0.179535	+	0.310964i
$25$	−466.494	+	807.991i	−0.746390	+	1.29279i
$26$	−17.8375			−0.0263868
$27$		−	717.090i		−	0.983663i
$28$	366.314	−	634.475i	0.467237	−	0.809279i
$29$	−756.663	−	436.859i	−0.899718	−	0.519452i	−0.0226091	−	0.999744i	$-0.507197\pi$
$29$	−756.663	−	436.859i	−0.899718	−	0.519452i	−0.877109	+	0.480292i	$0.840531\pi$
$30$	−1020.45			−1.13384
$31$		−	1356.82i		−	1.41188i	−0.708272	−	0.705940i	$-0.750525\pi$
$31$		−	1356.82i		−	1.41188i	0.708272	−	0.705940i	$-0.249475\pi$
$32$	−156.767	−	90.5097i	−0.153093	−	0.0883883i
$33$	1221.21	−	705.067i	1.12141	−	0.647445i
$34$	−173.608	−	100.233i	−0.150180	−	0.0867065i
$35$	1807.36	+	3130.45i	1.47540	+	2.55547i
$36$	−10.1897	−	17.6491i	−0.00786245	−	0.0136182i
$37$			204.056i			0.149055i	0.997219	+	0.0745273i	$0.0237448\pi$
$37$			204.056i			0.149055i	−0.997219	+	0.0745273i	$0.976255\pi$
$38$	1005.91	−	175.227i	0.696617	−	0.121348i
$39$	57.6441			0.0378988
$40$	773.477	−	446.567i	0.483423	−	0.279105i
$41$	−1254.28	+	724.157i	−0.746150	+	0.430790i	−0.824301	−	0.566152i	$-0.808432\pi$
$41$	−1254.28	+	724.157i	−0.746150	+	0.430790i	0.0781513	+	0.996942i	$0.475098\pi$
$42$	−1183.79	+	2050.39i	−0.671084	+	1.16235i
$43$	694.511	+	1202.93i	0.375614	+	0.650583i	0.990419	−	0.138096i	$-0.0440984\pi$
$43$	694.511	+	1202.93i	0.375614	+	0.650583i	−0.614804	+	0.788680i	$0.710765\pi$
$44$	−617.098	+	1068.84i	−0.318749	+	0.552089i
$45$	100.551			0.0496546
$46$		−	1858.41i		−	0.878266i
$47$	396.636	−	686.994i	0.179555	−	0.310998i	−0.762174	−	0.647373i	$-0.775868\pi$
$47$	396.636	−	686.994i	0.179555	−	0.310998i	0.941728	+	0.336375i	$0.109201\pi$
$48$	506.614	+	292.494i	0.219885	+	0.126950i
$49$	5985.63			2.49297
$50$			2638.89i			1.05555i
$51$	561.037	+	323.915i	0.215701	+	0.124535i
$52$	−43.6927	+	25.2260i	−0.0161586	+	0.00932915i
$53$	−427.719	−	246.944i	−0.152267	−	0.0879116i	0.421930	−	0.906628i	$-0.361353\pi$
$53$	−427.719	−	246.944i	−0.152267	−	0.0879116i	−0.574198	+	0.818717i	$0.694686\pi$
$54$	−1014.12	−	1756.50i	−0.347777	−	0.602368i
$55$	−3044.71	−	5273.59i	−1.00652	−	1.74334i
$56$		−	2072.19i		−	0.660773i
$57$	−3250.74	+	566.268i	−1.00054	+	0.174290i
$58$	−2471.25			−0.734616
$59$	414.766	−	239.465i	0.119151	−	0.0687920i	−0.439240	−	0.898370i	$-0.644752\pi$
$59$	414.766	−	239.465i	0.119151	−	0.0687920i	0.558391	+	0.829578i	$0.311419\pi$
$60$	−2499.59	+	1443.14i	−0.694331	+	0.400872i
$61$	−1244.82	+	2156.08i	−0.334538	+	0.579437i	−0.983396	−	0.181473i	$-0.941914\pi$
$61$	−1244.82	+	2156.08i	−0.334538	+	0.579437i	0.648858	+	0.760909i	$0.275247\pi$
$62$	−1918.83	−	3323.51i	−0.499175	−	0.864596i
$63$	116.645	−	202.035i	0.0293890	−	0.0509033i
$64$	−512.000			−0.125000
$65$		−	248.926i		−	0.0589174i
$66$	1994.23	−	3454.11i	0.457813	−	0.792955i
$67$	−3155.80	−	1822.00i	−0.703008	−	0.405882i	0.105459	−	0.994424i	$-0.466369\pi$
$67$	−3155.80	−	1822.00i	−0.703008	−	0.405882i	−0.808467	+	0.588542i	$0.799702\pi$
$68$	−567.002			−0.122622
$69$			6005.69i			1.26144i
$70$	8854.24	+	5112.00i	1.80699	+	1.04326i
$71$	408.962	−	236.114i	0.0811272	−	0.0468388i	−0.458888	−	0.888494i	$-0.651752\pi$
$71$	408.962	−	236.114i	0.0811272	−	0.0468388i	0.540015	+	0.841656i	$0.318419\pi$
$72$	−49.9193	−	28.8209i	−0.00962949	−	0.00555959i
$73$	656.228	+	1136.62i	0.123143	+	0.213290i	0.921005	−	0.389550i	$-0.127369\pi$
$73$	656.228	+	1136.62i	0.123143	+	0.213290i	−0.797863	+	0.602839i	$0.794036\pi$
$74$	288.579	+	499.833i	0.0526988	+	0.0912770i
$75$		−	8527.91i		−	1.51607i
$76$	2216.17	−	1851.79i	0.383686	−	0.320601i
$77$	−14128.2			−2.38290
$78$	141.199	−	81.5211i	0.0232082	−	0.0133993i
$79$	6824.92	−	3940.37i	1.09356	−	0.631368i	0.159039	−	0.987272i	$-0.449160\pi$
$79$	6824.92	−	3940.37i	1.09356	−	0.631368i	0.934523	+	0.355904i	$0.115827\pi$
$80$	1263.08	−	2187.72i	0.197357	−	0.341832i
$81$	3380.43	+	5855.07i	0.515230	+	0.892405i
$82$	−2048.23	+	3547.63i	−0.304614	+	0.527607i
$83$	−7247.57			−1.05205			−0.526025	−	0.850469i	$-0.676318\pi$
$83$	−7247.57			−1.05205			−0.526025	+	0.850469i	$0.676318\pi$
$84$			6696.54i			0.949056i
$85$	1398.77	−	2422.74i	0.193601	−	0.335328i
$86$	3402.40	+	1964.37i	0.460032	+	0.265600i
$87$	7986.16			1.05511
$88$			3490.83i			0.450779i
$89$	−2753.52	−	1589.75i	−0.347623	−	0.200700i	0.316015	−	0.948754i	$-0.397655\pi$
$89$	−2753.52	−	1589.75i	−0.347623	−	0.200700i	−0.663638	+	0.748054i	$0.730988\pi$
$90$	246.298	−	142.200i	0.0304071	−	0.0175556i
$91$	−500.164	−	288.770i	−0.0603990	−	0.0348714i
$92$	−2628.19	−	4552.16i	−0.310514	−	0.537826i
$93$	6200.94	+	10740.3i	0.716955	+	1.24180i
$94$		−	2243.71i		−	0.253928i
$95$	2445.33	+	14037.8i	0.270950	+	1.55543i
$96$	1654.59			0.179535
$97$	4303.37	−	2484.55i	0.457367	−	0.264061i	−0.253569	−	0.967317i	$-0.581605\pi$
$97$	4303.37	−	2484.55i	0.457367	−	0.264061i	0.710936	+	0.703256i	$0.248271\pi$
$98$	14661.7	−	8464.95i	1.52663	−	0.881399i
$99$	−196.502	+	340.351i	−0.0200492	+	0.0347262i
$100$	3731.95	+	6463.93i	0.373195	+	0.646393i
$101$	3533.50	−	6120.21i	0.346388	−	0.599961i	−0.639217	−	0.769026i	$-0.720741\pi$
$101$	3533.50	−	6120.21i	0.346388	−	0.599961i	0.985605	+	0.169065i	$0.0540748\pi$
$102$	1832.34			0.176119
$103$		−	4182.70i		−	0.394260i	−0.980377	−	0.197130i	$-0.936838\pi$
$103$		−	4182.70i		−	0.394260i	0.980377	−	0.197130i	$-0.0631621\pi$
$104$	−71.3499	+	123.582i	−0.00659670	+	0.0114258i
$105$	−28613.6	−	16520.1i	−2.59534	−	1.49842i
$106$	−1396.92			−0.124326
$107$			19195.8i			1.67664i	0.545180	+	0.838319i	$0.316461\pi$
$107$			19195.8i			1.67664i	−0.545180	+	0.838319i	$0.683539\pi$
$108$	−4968.15	−	2868.36i	−0.425938	−	0.245916i
$109$	8924.98	−	5152.84i	0.751198	−	0.433704i	−0.0749286	−	0.997189i	$-0.523873\pi$
$109$	8924.98	−	5152.84i	0.751198	−	0.433704i	0.826127	+	0.563485i	$0.190540\pi$
$110$	−14916.0	−	8611.74i	−1.23273	−	0.711714i
$111$	−932.579	−	1615.27i	−0.0756902	−	0.131099i
$112$	−2930.51	−	5075.80i	−0.233619	−	0.404639i
$113$			10459.9i			0.819167i	0.912273	+	0.409584i	$0.134326\pi$
$113$			10459.9i			0.819167i	−0.912273	+	0.409584i	$0.865674\pi$
$114$	−7161.84	+	5984.31i	−0.551080	+	0.460473i
$115$	25934.5			1.96102
$116$	−6053.30	+	3494.87i	−0.449859	+	0.259726i
$117$	−13.9130	+	8.03270i	−0.00101637	+	0.000586799i
$118$	677.309	−	1173.13i	0.0486433	−	0.0842527i
$119$	−3245.32	−	5621.07i	−0.229173	−	0.396940i
$120$	−4081.82	+	7069.91i	−0.283460	+	0.490966i
$121$	9159.60			0.625613
$122$			7041.74i			0.473108i
$123$	6619.11	−	11464.6i	0.437511	−	0.757792i
$124$	−9400.30	−	5427.26i	−0.611362	−	0.352970i
$125$	−12156.7			−0.778028
$126$		−	659.844i		−	0.0415624i
$127$	−26131.5	−	15087.0i	−1.62016	−	0.935398i	−0.986877	−	0.161475i	$-0.948375\pi$
$127$	−26131.5	−	15087.0i	−1.62016	−	0.935398i	−0.633280	−	0.773923i	$-0.718292\pi$
$128$	−1254.14	+	724.077i	−0.0765466	+	0.0441942i
$129$	−10995.3	−	6348.13i	−0.660734	−	0.381475i
$130$	−352.035	−	609.742i	−0.0208305	−	0.0360794i
$131$	−3772.02	−	6533.34i	−0.219802	−	0.380708i	0.734945	−	0.678126i	$-0.237208\pi$
$131$	−3772.02	−	6533.34i	−0.219802	−	0.380708i	−0.954747	+	0.297418i	$0.903874\pi$
$132$		−	11281.1i		−	0.647445i
$133$	31042.7	+	11371.3i	1.75491	+	0.642847i
$134$	−10306.8			−0.574004
$135$	24512.4	−	14152.3i	1.34499	−	0.776530i
$136$	−1388.87	+	801.862i	−0.0750900	+	0.0433532i
$137$	−13701.7	+	23732.1i	−0.730019	+	1.26443i	0.226855	+	0.973929i	$0.427156\pi$
$137$	−13701.7	+	23732.1i	−0.730019	+	1.26443i	−0.956874	+	0.290502i	$0.906178\pi$
$138$	8493.33	+	14710.9i	0.445985	+	0.772468i
$139$	−9868.94	+	17093.5i	−0.510788	+	0.884711i	0.489134	+	0.872209i	$0.337313\pi$
$139$	−9868.94	+	17093.5i	−0.510788	+	0.884711i	−0.999922	+	0.0125021i	$0.996020\pi$
$140$	28917.8			1.47540
$141$			7250.84i			0.364712i
$142$	667.832	−	1156.72i	0.0331200	−	0.0573656i
$143$	842.584	+	486.466i	0.0412042	+	0.0237892i
$144$	−163.036			−0.00786245
$145$		−	34486.9i		−	1.64028i
$146$	3214.85	+	1856.09i	0.150819	+	0.0870752i
$147$	−47381.3	+	27355.6i	−2.19266	+	1.26594i
$148$	1413.74	+	816.223i	0.0645426	+	0.0372637i
$149$	3705.52	+	6418.15i	0.166908	+	0.289093i	0.937331	−	0.348440i	$-0.113288\pi$
$149$	3705.52	+	6418.15i	0.166908	+	0.289093i	−0.770423	+	0.637533i	$0.779955\pi$
$150$	−12060.3	−	20889.0i	−0.536012	−	0.928401i
$151$			8534.29i			0.374295i	0.982332	+	0.187147i	$0.0599242\pi$
$151$			8534.29i			0.374295i	−0.982332	+	0.187147i	$0.940076\pi$
$152$	2809.65	−	7670.09i	0.121609	−	0.331981i
$153$	−180.550			−0.00771284
$154$	−34606.9	+	19980.3i	−1.45922	+	0.842483i
$155$	46380.3	−	26777.7i	1.93050	−	1.11458i
$156$	230.577	−	399.370i	0.00947471	−	0.0164107i
$157$	14757.3	+	25560.4i	0.598699	+	1.03698i	0.993013	+	0.118001i	$0.0376487\pi$
$157$	14757.3	+	25560.4i	0.598699	+	1.03698i	−0.394315	+	0.918975i	$0.629018\pi$
$158$	11145.0	−	19303.8i	0.446445	−	0.773265i
$159$	4514.34			0.178567
$160$		−	7145.08i		−	0.279105i
$161$	30085.7	−	52110.0i	1.16067	−	2.01034i
$162$	16560.6	+	9561.29i	0.631026	+	0.364323i
$163$	−27593.4			−1.03856			−0.519279	−	0.854605i	$-0.673799\pi$
$163$	−27593.4			−1.03856			−0.519279	+	0.854605i	$0.673799\pi$
$164$			11586.5i			0.430790i
$165$	48202.9	+	27830.0i	1.77054	+	1.02222i
$166$	−17752.8	+	10249.6i	−0.644246	+	0.371956i
$167$	−702.182	−	405.405i	−0.0251777	−	0.0145364i	0.487358	−	0.873202i	$-0.337961\pi$
$167$	−702.182	−	405.405i	−0.0251777	−	0.0145364i	−0.512536	+	0.858666i	$0.671294\pi$
$168$	9470.33	+	16403.1i	0.335542	+	0.581175i
$169$	−14260.6	−	24700.1i	−0.499304	−	0.864819i
$170$		−	7912.64i		−	0.273794i
$171$	705.693	−	589.665i	0.0241337	−	0.0201657i
$172$	11112.2			0.375614
$173$	11940.9	−	6894.09i	0.398975	−	0.230348i	−0.287067	−	0.957911i	$-0.592680\pi$
$173$	11940.9	−	6894.09i	0.398975	−	0.230348i	0.686041	+	0.727562i	$0.259347\pi$
$174$	19562.0	−	11294.1i	0.646123	−	0.373039i
$175$	−42720.8	+	73994.6i	−1.39497	+	2.41615i
$176$	4936.78	+	8550.76i	0.159374	+	0.276045i
$177$	−2188.81	+	3791.13i	−0.0698654	+	0.121010i
$178$	−8992.97			−0.283833
$179$			49715.3i			1.55162i	0.630969	+	0.775808i	$0.282658\pi$
$179$			49715.3i			1.55162i	−0.630969	+	0.775808i	$0.717342\pi$
$180$	402.203	−	696.635i	0.0124137	−	0.0215011i
$181$	−21871.1	−	12627.3i	−0.667595	−	0.385436i	0.127570	−	0.991830i	$-0.459282\pi$
$181$	−21871.1	−	12627.3i	−0.667595	−	0.385436i	−0.795165	+	0.606394i	$0.792616\pi$
$182$	−1633.53			−0.0493156
$183$		−	22756.3i		−	0.679516i
$184$	−12875.4	−	7433.64i	−0.380300	−	0.219566i
$185$	−6975.28	+	4027.18i	−0.203807	+	0.117668i
$186$	30378.3	+	17538.9i	0.878086	+	0.506963i
$187$	5467.12	+	9469.33i	0.156342	+	0.270792i
$188$	−3173.09	−	5495.95i	−0.0897773	−	0.155499i
$189$		−	65670.1i		−	1.83842i
$190$	25842.2	+	30927.1i	0.715851	+	0.856708i
$191$	−32047.2			−0.878463			−0.439232	−	0.898374i	$-0.644749\pi$
$191$	−32047.2			−0.878463			−0.439232	+	0.898374i	$0.644749\pi$
$192$	4052.91	−	2339.95i	0.109942	−	0.0634752i
$193$	−38641.8	+	22309.9i	−1.03739	+	0.598938i	−0.919093	−	0.394040i	$-0.871077\pi$
$193$	−38641.8	+	22309.9i	−1.03739	+	0.598938i	−0.118298	+	0.992978i	$0.537744\pi$
$194$	7027.37	−	12171.8i	0.186719	−	0.323407i
$195$	1137.65	+	1970.46i	0.0299184	+	0.0518201i
$196$	23942.5	−	41469.6i	0.623243	−	1.07949i
$197$	49921.4			1.28634			0.643168	−	0.765725i	$-0.277620\pi$
$197$	49921.4			1.28634			0.643168	+	0.765725i	$0.277620\pi$
$198$			1111.58i			0.0283538i
$199$	−14042.5	+	24322.3i	−0.354599	+	0.614183i	−0.987049	−	0.160418i	$-0.948716\pi$
$199$	−14042.5	+	24322.3i	−0.354599	+	0.614183i	0.632451	+	0.774601i	$0.282049\pi$
$200$	18282.7	+	10555.5i	0.457069	+	0.263889i
$201$	33307.8			0.824430
$202$		−	19988.5i		−	0.489866i
$203$	−69294.0	−	40006.9i	−1.68153	−	0.970830i
$204$	4488.30	−	2591.32i	0.107850	−	0.0622674i
$205$	−49508.0	−	28583.5i	−1.17806	−	0.680154i
$206$	−5915.23	−	10245.5i	−0.139392	−	0.241434i
$207$	−836.892	−	1449.54i	−0.0195312	−	0.0338290i
$208$			403.616i			0.00932915i
$209$	−52294.9	−	19156.3i	−1.19720	−	0.438550i
$210$	−93451.7			−2.11909
$211$	48943.0	−	28257.2i	1.09932	−	0.634694i	0.163280	−	0.986580i	$-0.447793\pi$
$211$	48943.0	−	28257.2i	1.09932	−	0.634694i	0.936043	+	0.351885i	$0.114459\pi$
$212$	−3421.75	+	1975.55i	−0.0761337	+	0.0439558i
$213$	−2158.19	+	3738.09i	−0.0475696	+	0.0823930i
$214$	27147.0	+	47020.0i	0.592781	+	1.02673i
$215$	−27413.3	+	47481.2i	−0.593040	+	1.02718i
$216$	−16225.9			−0.347777
$217$		−	124255.i		−	2.63873i
$218$	14574.4	−	25243.7i	0.306675	−	0.531177i
$219$	−10389.2	−	5998.21i	−0.216618	−	0.125064i
$220$	−48715.4			−1.00652
$221$			446.975i			0.00915163i
$222$	−4568.69	−	2637.73i	−0.0927012	−	0.0535211i
$223$	−2486.15	+	1435.38i	−0.0499941	+	0.0288641i	−0.524789	−	0.851233i	$-0.675856\pi$
$223$	−2486.15	+	1435.38i	−0.0499941	+	0.0288641i	0.474795	+	0.880097i	$0.342522\pi$
$224$	−14356.5	−	8288.74i	−0.286123	−	0.165193i
$225$	1188.36	+	2058.30i	0.0234738	+	0.0406578i
$226$	14792.6	+	25621.5i	0.289619	+	0.501635i
$227$			65962.5i			1.28010i	0.768331	+	0.640052i	$0.221087\pi$
$227$			65962.5i			1.28010i	−0.768331	+	0.640052i	$0.778913\pi$
$228$	−9079.75	+	24786.9i	−0.174664	+	0.476817i
$229$	−29460.5			−0.561784			−0.280892	−	0.959739i	$-0.590630\pi$
$229$	−29460.5			−0.561784			−0.280892	+	0.959739i	$0.590630\pi$
$230$	63526.4	−	36677.0i	1.20088	−	0.693327i
$231$	111837.	−	64569.0i	2.09585	−	1.21004i
$232$	−9885.00	+	17121.3i	−0.183654	+	0.318098i
$233$	23522.7	+	40742.5i	0.433286	+	0.750474i	0.997154	−	0.0753912i	$-0.0240205\pi$
$233$	23522.7	+	40742.5i	0.433286	+	0.750474i	−0.563868	+	0.825865i	$0.690687\pi$
$234$	−22.7199	+	39.3520i	−0.000414930	+	0.000718680i
$235$	31311.5			0.566981
$236$		−	3831.44i		−	0.0687920i
$237$	−36016.7	+	62382.7i	−0.641220	+	1.11062i
$238$	−15898.8	−	9179.16i	−0.280679	−	0.162050i
$239$	50217.8			0.879147			0.439574	−	0.898207i	$-0.355130\pi$
$239$	50217.8			0.879147			0.439574	+	0.898207i	$0.355130\pi$
$240$			23090.2i			0.400872i
$241$	60000.5	+	34641.3i	1.03305	+	0.596431i	0.917856	−	0.396913i	$-0.129918\pi$
$241$	60000.5	+	34641.3i	1.03305	+	0.596431i	0.115192	+	0.993343i	$0.463252\pi$
$242$	22436.4	−	12953.6i	0.383108	−	0.221188i
$243$	−3215.37	−	1856.40i	−0.0544527	−	0.0314383i
$244$	9958.52	+	17248.7i	0.167269	+	0.289718i
$245$	118130.	+	204608.i	1.96802	+	3.40871i
$246$		−	37443.3i		−	0.618735i
$247$	−1459.79	−	1747.03i	−0.0239275	−	0.0286357i
$248$	−30701.2			−0.499175
$249$	57370.6	−	33122.9i	0.925318	−	0.534232i
$250$	−29777.7	+	17192.1i	−0.476443	+	0.275074i
$251$	47640.3	−	82515.4i	0.756183	−	1.30975i	−0.188601	−	0.982054i	$-0.560395\pi$
$251$	47640.3	−	82515.4i	0.756183	−	1.30975i	0.944784	−	0.327694i	$-0.106271\pi$
$252$	−933.161	−	1616.28i	−0.0146945	−	0.0254517i
$253$	−50682.8	+	87785.2i	−0.791808	+	1.37145i
$254$	−85345.2			−1.32285
$255$			25570.7i			0.393245i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−70302.9	−	40589.4i	−1.06440	−	0.614534i	−0.137757	−	0.990466i	$-0.543989\pi$
$257$	−70302.9	−	40589.4i	−1.06440	−	0.614534i	−0.926647	+	0.375932i	$0.877323\pi$
$258$	−35910.4			−0.539487
$259$			18687.1i			0.278576i
$260$	−1724.61	−	995.705i	−0.0255120	−	0.0147294i
$261$	−1927.55	+	1112.87i	−0.0282959	+	0.0163367i
$262$	−18479.1	−	10668.9i	−0.269201	−	0.155424i
$263$	−36206.1	−	62710.8i	−0.523444	−	0.906632i	−0.999628	−	0.0272860i	$-0.991314\pi$
$263$	−36206.1	−	62710.8i	−0.523444	−	0.906632i	0.476184	−	0.879346i	$-0.342020\pi$
$264$	−15953.9	−	27632.9i	−0.228906	−	0.396477i
$265$		−	19494.4i		−	0.277599i
$266$	92120.1	−	16047.0i	1.30194	−	0.226793i
$267$	29061.9			0.407664
$268$	−25246.4	+	14576.0i	−0.351504	+	0.202941i
$269$	1546.82	−	893.058i	0.0213765	−	0.0123417i	−0.489274	−	0.872130i	$-0.662738\pi$
$269$	1546.82	−	893.058i	0.0213765	−	0.0123417i	0.510650	+	0.859789i	$0.329405\pi$
$270$	40028.6	−	69331.6i	0.549090	−	0.951051i
$271$	25581.7	+	44308.7i	0.348329	+	0.603324i	0.985953	−	0.167024i	$-0.0534157\pi$
$271$	25581.7	+	44308.7i	0.348329	+	0.603324i	−0.637623	+	0.770348i	$0.720082\pi$
$272$	−2268.01	+	3928.30i	−0.0306554	+	0.0530967i
$273$	5278.96			0.0708310
$274$			77508.7i			1.03240i
$275$	71968.1	−	124652.i	0.951644	−	1.64830i
$276$	41608.7	+	24022.8i	0.546218	+	0.315359i
$277$	−46030.2			−0.599906			−0.299953	−	0.953954i	$-0.596971\pi$
$277$	−46030.2			−0.599906			−0.299953	+	0.953954i	$0.596971\pi$
$278$			55827.1i			0.722363i
$279$	−2993.33	−	1728.20i	−0.0384544	−	0.0222017i
$280$	70833.9	−	40896.0i	0.903494	−	0.521632i
$281$	21812.2	+	12593.3i	0.276240	+	0.159487i	0.631720	−	0.775197i	$-0.282349\pi$
$281$	21812.2	+	12593.3i	0.276240	+	0.159487i	−0.355480	+	0.934684i	$0.615683\pi$
$282$	10254.2	+	17760.9i	0.128945	+	0.223340i
$283$	−61381.5	−	106316.i	−0.766417	−	1.32747i	−0.939494	−	0.342564i	$-0.888705\pi$
$283$	−61381.5	−	106316.i	−0.766417	−	1.32747i	0.173078	−	0.984908i	$-0.444629\pi$
$284$		−	3777.83i		−	0.0468388i
$285$	−83512.4	−	99945.1i	−1.02816	−	1.23047i
$286$	2751.87			0.0336431
$287$	−114865.	+	66317.3i	−1.39452	+	0.805124i
$288$	−399.354	+	230.567i	−0.00481475	+	0.00277980i
$289$	39248.9	−	67981.0i	0.469928	−	0.813939i
$290$	−48771.8	−	84475.2i	−0.579926	−	1.00446i
$291$	−22709.8	+	39334.6i	−0.268181	+	0.464503i
$292$	10499.7			0.123143
$293$		−	123220.i		−	1.43531i	−0.696397	−	0.717657i	$-0.745215\pi$
$293$		−	123220.i		−	1.43531i	0.696397	−	0.717657i	$-0.254785\pi$
$294$	−77373.3	+	134014.i	−0.895151	+	1.55045i
$295$	16371.4	+	9452.01i	0.188122	+	0.108613i
$296$	4617.26			0.0526988
$297$			110629.i			1.25417i
$298$	18153.3	+	10480.8i	0.204419	+	0.118022i
$299$	−3588.52	+	2071.84i	−0.0401396	+	0.0231746i
$300$	−59083.1	−	34111.6i	−0.656478	−	0.379018i
$301$	63602.3	+	110162.i	0.702004	+	1.21591i
$302$	12069.3	+	20904.7i	0.132333	+	0.229208i
$303$			64595.4i			0.703585i
$304$	−3964.93	−	22761.2i	−0.0429030	−	0.246291i
$305$	−98269.1			−1.05637
$306$	−442.255	+	255.336i	−0.00472313	+	0.00272690i
$307$	−58068.1	+	33525.7i	−0.616114	+	0.355714i	−0.775355	−	0.631526i	$-0.782429\pi$
$307$	−58068.1	+	33525.7i	−0.616114	+	0.355714i	0.159240	+	0.987240i	$0.449095\pi$
$308$	−56512.9	+	97883.2i	−0.595725	+	1.03183i
$309$	19115.8	+	33109.6i	0.200206	+	0.346766i
$310$	75738.7	−	131183.i	0.788124	−	1.36507i
$311$	−101780.			−1.05230			−0.526152	−	0.850391i	$-0.676366\pi$
$311$	−101780.			−1.05230			−0.526152	+	0.850391i	$0.676366\pi$
$312$		−	1304.34i		−	0.0133993i
$313$	20271.4	−	35111.1i	0.206916	−	0.358389i	−0.743825	−	0.668374i	$-0.766991\pi$
$313$	20271.4	−	35111.1i	0.206916	−	0.358389i	0.950742	+	0.309985i	$0.100324\pi$
$314$	72295.8	+	41740.0i	0.733253	+	0.423344i
$315$	9208.28			0.0928020
$316$		−	63045.9i		−	0.631368i
$317$	−23876.6	−	13785.2i	−0.237604	−	0.137181i	0.376471	−	0.926428i	$-0.377137\pi$
$317$	−23876.6	−	13785.2i	−0.237604	−	0.137181i	−0.614075	+	0.789248i	$0.710471\pi$
$318$	11057.8	−	6384.24i	0.109349	−	0.0631328i
$319$	116734.	+	67396.2i	1.14714	+	0.662299i
$320$	−10104.7	−	17501.8i	−0.0986784	−	0.170916i
$321$	−87729.1	−	151951.i	−0.851400	−	1.47467i
$322$		−	170190.i		−	1.64143i
$323$	−4390.86	−	25206.4i	−0.0420867	−	0.241605i
$324$	54086.8			0.515230
$325$	5095.60	−	2941.94i	0.0482423	−	0.0278527i
$326$	−67589.9	+	39023.0i	−0.635984	+	0.367186i
$327$	−47099.2	+	81578.2i	−0.440472	+	0.762919i
$328$	16385.8	+	28381.1i	0.152307	+	0.263804i
$329$	36323.3	−	62913.9i	0.335578	−	0.581239i
$330$	157430.			1.44564
$331$		−	51678.7i		−	0.471689i	−0.971791	−	0.235844i	$-0.924214\pi$
$331$		−	51678.7i		−	0.471689i	0.971791	−	0.235844i	$-0.0757856\pi$
$332$	−28990.3	+	50212.6i	−0.263012	+	0.455551i
$333$	450.176	+	259.909i	0.00405970	+	0.00234387i
$334$	−2293.32			−0.0205575
$335$		−	143834.i		−	1.28166i
$336$	46395.0	+	26786.1i	0.410953	+	0.237264i
$337$	−136060.	+	78554.5i	−1.19804	+	0.691689i	−0.960118	−	0.279595i	$-0.909800\pi$
$337$	−136060.	+	78554.5i	−1.19804	+	0.691689i	−0.237923	+	0.971284i	$0.576467\pi$
$338$	−69862.5	−	40335.1i	−0.611520	−	0.353061i
$339$	−47804.2	−	82799.3i	−0.415974	−	0.720489i
$340$	−11190.2	−	19381.9i	−0.0968007	−	0.167664i
$341$			209322.i			1.80014i
$342$	894.675	−	2442.38i	0.00764915	−	0.0208815i
$343$	328275.			2.79029
$344$	27219.2	−	15715.0i	0.230016	−	0.132800i
$345$	−205294.	+	118526.i	−1.72480	+	0.995811i
$346$	19499.4	−	33774.0i	0.162881	−	0.282118i
$347$	−25867.2	−	44803.3i	−0.214828	−	0.372092i	0.738392	−	0.674372i	$-0.235586\pi$
$347$	−25867.2	−	44803.3i	−0.214828	−	0.372092i	−0.953219	+	0.302280i	$0.902252\pi$
$348$	31944.7	−	55329.8i	0.263779	−	0.456878i
$349$	−75431.6			−0.619302			−0.309651	−	0.950850i	$-0.600212\pi$
$349$	−75431.6			−0.619302			−0.309651	+	0.950850i	$0.600212\pi$
$350$			241665.i			1.97278i
$351$	−2261.17	+	3916.45i	−0.0183535	+	0.0317891i
$352$	24185.2	+	13963.3i	0.195193	+	0.112695i
$353$	221690.			1.77909			0.889544	−	0.456850i	$-0.151023\pi$
$353$	221690.			1.77909			0.889544	+	0.456850i	$0.151023\pi$
$354$			12381.8i			0.0988046i
$355$	16142.3	+	9319.75i	0.128088	+	0.0739516i
$356$	−22028.2	+	12718.0i	−0.173812	+	0.100350i
$357$	51379.0	+	29663.7i	0.403133	+	0.232749i
$358$	70308.1	+	121777.i	0.548579	+	0.950167i
$359$	−30200.4	−	52308.6i	−0.234328	−	0.405868i	0.724749	−	0.689013i	$-0.241956\pi$
$359$	−30200.4	−	52308.6i	−0.234328	−	0.405868i	−0.959077	+	0.283145i	$0.908622\pi$
$360$		−	2275.20i		−	0.0175556i
$361$	99484.5	+	84180.7i	0.763381	+	0.645949i
$362$	−71430.6			−0.545089
$363$	−72506.0	+	41861.3i	−0.550251	+	0.317687i
$364$	−4001.32	+	2310.16i	−0.0301995	+	0.0174357i
$365$	−25902.2	+	44864.0i	−0.194425	+	0.336753i
$366$	−32182.3	−	55741.3i	−0.240245	−	0.416117i
$367$	93007.4	−	161093.i	0.690534	−	1.19604i	−0.281129	−	0.959670i	$-0.590709\pi$
$367$	93007.4	−	161093.i	0.690534	−	1.19604i	0.971663	−	0.236370i	$-0.0759578\pi$
$368$	−42051.0			−0.310514
$369$			3689.49i			0.0270965i
$370$	−11390.6	+	19729.1i	−0.0832037	+	0.144113i
$371$	−39169.9	−	22614.7i	−0.284580	−	0.164302i
$372$	99215.0			0.716955
$373$			36978.4i			0.265785i	0.991130	+	0.132893i	$0.0424266\pi$
$373$			36978.4i			0.265785i	−0.991130	+	0.132893i	$0.957573\pi$
$374$	26783.3	+	15463.3i	0.191479	+	0.110550i
$375$	96230.4	−	55558.6i	0.684305	−	0.395084i
$376$	−15544.9	−	8974.85i	−0.109954	−	0.0634821i
$377$	2755.05	+	4771.89i	0.0193842	+	0.0335744i
$378$	−92871.5	−	160858.i	−0.649978	−	1.12580i
$379$			202054.i			1.40666i	0.710864	+	0.703330i	$0.248304\pi$
$379$			202054.i			1.40666i	−0.710864	+	0.703330i	$0.751696\pi$
$380$	107038.	+	39209.3i	0.741259	+	0.271533i
$381$	275804.			1.89999
$382$	−78499.4	+	45321.6i	−0.537947	+	0.310584i
$383$	−54335.3	+	31370.5i	−0.370412	+	0.213857i	−0.673638	−	0.739061i	$-0.735269\pi$
$383$	−54335.3	+	31370.5i	−0.370412	+	0.213857i	0.303227	+	0.952918i	$0.401936\pi$
$384$	6618.38	−	11463.4i	0.0448837	−	0.0777409i
$385$	−278830.	−	482948.i	−1.88113	−	3.25821i
$386$	−63101.8	+	109296.i	−0.423513	+	0.733547i
$387$	3538.44			0.0236260
$388$		−	39752.8i		−	0.264061i
$389$	58638.1	−	101564.i	0.387508	−	0.671184i	−0.604606	−	0.796525i	$-0.706669\pi$
$389$	58638.1	−	101564.i	0.387508	−	0.671184i	0.992114	+	0.125341i	$0.0400026\pi$
$390$	5573.30	+	3217.75i	0.0366424	+	0.0211555i
$391$	−46568.4			−0.304605
$392$		−	135439.i		−	0.881399i
$393$	59717.5	+	34477.9i	0.386649	+	0.223232i
$394$	122282.	−	70599.6i	0.787717	−	0.454789i
$395$	269389.	+	155532.i	1.72657	+	0.996838i
$396$	1572.02	+	2722.81i	0.0100246	+	0.0173631i
$397$	154251.	+	267171.i	0.978695	+	1.69515i	0.667159	+	0.744915i	$0.267510\pi$
$397$	154251.	+	267171.i	0.978695	+	1.69515i	0.311536	+	0.950234i	$0.399156\pi$
$398$			79436.2i			0.501478i
$399$	−297698.	+	51858.0i	−1.86995	+	0.325739i
$400$	59711.2			0.373195
$401$	−246024.	+	142042.i	−1.52999	+	0.883339i	−0.530627	+	0.847606i	$0.678043\pi$
$401$	−246024.	+	142042.i	−1.52999	+	0.883339i	−0.999361	+	0.0357332i	$0.988623\pi$
$402$	81587.1	−	47104.3i	0.504858	−	0.291480i
$403$	−4278.38	+	7410.38i	−0.0263433	+	0.0456279i
$404$	−28268.0	−	48961.6i	−0.173194	−	0.299981i
$405$	−133430.	+	231108.i	−0.813474	+	1.40898i
$406$	−226313.			−1.37296
$407$		−	31480.6i		−	0.190044i
$408$	7329.36	−	12694.8i	0.0440297	−	0.0762617i
$409$	104932.	+	60582.4i	0.627279	+	0.362159i	0.779697	−	0.626157i	$-0.215373\pi$
$409$	104932.	+	60582.4i	0.627279	+	0.362159i	−0.152419	+	0.988316i	$0.548706\pi$
$410$	−161693.			−0.961883
$411$		−	250479.i		−	1.48282i
$412$	−28978.6	−	16730.8i	−0.170719	−	0.0985649i
$413$	37983.6	−	21929.8i	0.222688	−	0.128569i
$414$	−4099.92	−	2367.09i	−0.0239207	−	0.0138106i
$415$	−143036.	−	247745.i	−0.830516	−	1.43850i
$416$	570.799	+	988.654i	0.00329835	+	0.00571291i
$417$		−	180413.i		−	1.03752i
$418$	−155187.	+	27033.0i	−0.888183	+	0.154718i
$419$	137920.			0.785597			0.392799	−	0.919624i	$-0.371507\pi$
$419$	137920.			0.785597			0.392799	+	0.919624i	$0.371507\pi$
$420$	−228909.	+	132161.i	−1.29767	+	0.749210i
$421$	110340.	−	63704.5i	0.622539	−	0.359423i	−0.155318	−	0.987865i	$-0.549640\pi$
$421$	110340.	−	63704.5i	0.622539	−	0.359423i	0.777857	+	0.628441i	$0.216307\pi$
$422$	79923.5	−	138432.i	0.448797	−	0.777339i
$423$	−1010.40	−	1750.07i	−0.00564695	−	0.00978081i
$424$	−5587.70	+	9678.17i	−0.0310814	+	0.0538346i
$425$	66125.7			0.366094
$426$			12208.5i			0.0672736i
$427$	−113998.	+	197451.i	−0.625234	+	1.08294i
$428$	132993.	+	76783.3i	0.726006	+	0.419160i
$429$	−8893.02			−0.0483208
$430$			155073.i			0.838686i
$431$	−123022.	−	71026.5i	−0.662257	−	0.382354i	0.130879	−	0.991398i	$-0.458220\pi$
$431$	−123022.	−	71026.5i	−0.662257	−	0.382354i	−0.793136	+	0.609044i	$0.791553\pi$
$432$	−39745.2	+	22946.9i	−0.212969	+	0.122958i
$433$	−87079.8	−	50275.6i	−0.464453	−	0.268152i	0.249462	−	0.968385i	$-0.419746\pi$
$433$	−87079.8	−	50275.6i	−0.464453	−	0.268152i	−0.713915	+	0.700233i	$0.753080\pi$
$434$	−175723.	−	304362.i	−0.932932	−	1.61589i
$435$	157612.	+	272993.i	0.832936	+	1.44269i
$436$		−	82445.5i		−	0.433704i
$437$	182016.	−	152090.i	0.953118	−	0.796409i
$438$	−33931.0			−0.176868
$439$	268003.	−	154731.i	1.39062	−	0.802878i	0.397240	−	0.917715i	$-0.369968\pi$
$439$	268003.	−	154731.i	1.39062	−	0.802878i	0.993384	+	0.114837i	$0.0366346\pi$
$440$	−119328.	+	68893.9i	−0.616363	+	0.355857i
$441$	7623.99	−	13205.1i	0.0392017	−	0.0678994i
$442$	632.118	+	1094.86i	0.00323559	+	0.00560421i
$443$	−25678.9	+	44477.2i	−0.130849	+	0.226637i	−0.924004	−	0.382383i	$-0.875104\pi$
$443$	−25678.9	+	44477.2i	−0.130849	+	0.226637i	0.793155	+	0.609020i	$0.208437\pi$
$444$	−14921.3			−0.0756902
$445$		−	125499.i		−	0.633753i
$446$	−4059.87	+	7031.91i	−0.0204100	+	0.0353511i
$447$	−58664.6	−	33870.0i	−0.293604	−	0.169512i
$448$	−46888.2			−0.233619
$449$			220983.i			1.09614i	0.836433	+	0.548069i	$0.184637\pi$
$449$			220983.i			1.09614i	−0.836433	+	0.548069i	$0.815363\pi$
$450$	5821.76	+	3361.19i	0.0287494	+	0.0165985i
$451$	193503.	−	111719.i	0.951337	−	0.549255i
$452$	72468.6	+	41839.8i	0.354710	+	0.204792i
$453$	−39003.5	−	67556.1i	−0.190067	−	0.329206i
$454$	93285.1	+	161574.i	0.452585	+	0.783901i
$455$		−	22796.3i		−	0.110114i
$456$	12813.2	+	73555.9i	0.0616208	+	0.353743i
$457$	−43888.6			−0.210145			−0.105073	−	0.994465i	$-0.533507\pi$
$457$	−43888.6			−0.210145			−0.105073	+	0.994465i	$0.533507\pi$
$458$	−72163.2	+	41663.4i	−0.344021	+	0.198621i
$459$	−44014.8	+	25412.0i	−0.208917	+	0.120618i
$460$	103738.	−	179680.i	0.490256	−	0.849148i
$461$	−111284.	−	192750.i	−0.523640	−	0.906971i	−0.999621	−	0.0275157i	$-0.991240\pi$
$461$	−111284.	−	192750.i	−0.523640	−	0.906971i	0.475981	−	0.879455i	$-0.342093\pi$
$462$	182629.	−	316322.i	0.855628	−	1.48199i
$463$	91798.8			0.428228			0.214114	−	0.976809i	$-0.431314\pi$
$463$	91798.8			0.428228			0.214114	+	0.976809i	$0.431314\pi$
$464$			55918.0i			0.259726i
$465$	−244759.	+	423936.i	−1.13197	+	1.96062i
$466$	115237.	+	66532.2i	0.530665	+	0.306380i
$467$	−58856.8			−0.269875			−0.134938	−	0.990854i	$-0.543083\pi$
$467$	−58856.8			−0.269875			−0.134938	+	0.990854i	$0.543083\pi$
$468$			128.523i			0.000586799i
$469$	−289004.	−	166856.i	−1.31389	−	0.758573i
$470$	76697.2	−	44281.2i	0.347203	−	0.200458i
$471$	−233633.	−	134888.i	−1.05316	−	0.608040i
$472$	−5418.47	−	9385.07i	−0.0243216	−	0.0421263i
$473$	−107145.	−	185581.i	−0.478907	−	0.829491i
$474$			203741.i			0.906821i
$475$	−258457.	+	215963.i	−1.14552	+	0.957175i
$476$	−51925.2			−0.229173
$477$	−1089.59	+	629.073i	−0.00478878	+	0.00276480i
$478$	123008.	−	71018.6i	0.538365	−	0.310825i
$479$	210351.	−	364338.i	0.916796	−	1.58794i	0.112547	−	0.993646i	$-0.464099\pi$
$479$	210351.	−	364338.i	0.916796	−	1.58794i	0.804250	−	0.594292i	$-0.202567\pi$
$480$	32654.5	+	56559.3i	0.141730	+	0.245483i
$481$	643.439	−	1114.47i	0.00278111	−	0.00481702i
$482$	195961.			0.843480
$483$			549993.i			2.35756i
$484$	36638.4	−	63459.6i	0.156403	−	0.270898i
$485$	169860.	+	98068.5i	0.722116	+	0.416914i
$486$	−10501.4			−0.0444604
$487$			439469.i			1.85298i	0.376323	+	0.926488i	$0.377188\pi$
$487$			439469.i			1.85298i	−0.376323	+	0.926488i	$0.622812\pi$
$488$	48786.6	+	28167.0i	0.204862	+	0.118277i
$489$	218425.	−	126108.i	0.913451	−	0.527381i
$490$	578718.	+	334123.i	2.41032	+	1.39160i
$491$	129517.	+	224331.i	0.537236	+	0.930519i	0.999052	+	0.0435437i	$0.0138648\pi$
$491$	129517.	+	224331.i	0.537236	+	0.930519i	−0.461816	+	0.886976i	$0.652802\pi$
$492$	−52952.9	−	91717.1i	−0.218756	−	0.378896i
$493$			61925.0i			0.254784i
$494$	−6046.43	−	2214.88i	−0.0247768	−	0.00907606i
$495$	−15512.4			−0.0633094
$496$	−75202.4	+	43418.1i	−0.305681	+	0.176485i
$497$	37452.1	−	21623.0i	0.151623	−	0.0875393i
$498$	93685.8	−	162269.i	0.377759	−	0.654298i
$499$	−75250.9	−	130338.i	−0.302211	−	0.523445i	0.674425	−	0.738343i	$-0.264391\pi$
$499$	−75250.9	−	130338.i	−0.302211	−	0.523445i	−0.976637	+	0.214898i	$0.931058\pi$
$500$	−48626.7	+	84224.0i	−0.194507	+	0.336896i
$501$	7411.15			0.0295264
$502$		−	269494.i		−	1.06940i
$503$	64403.8	−	111551.i	0.254551	−	0.440896i	−0.710222	−	0.703978i	$-0.751406\pi$
$503$	64403.8	−	111551.i	0.254551	−	0.440896i	0.964774	+	0.263082i	$0.0847389\pi$
$504$	−4571.54	−	2639.38i	−0.0179970	−	0.0103906i
$505$	278944.			1.09379
$506$			286705.i			1.11978i
$507$	225770.	+	130348.i	0.878313	+	0.507094i
$508$	−209052.	+	120696.i	−0.810078	+	0.467699i
$509$	181168.	+	104598.i	0.699273	+	0.403726i	0.807077	−	0.590447i	$-0.201048\pi$
$509$	181168.	+	104598.i	0.699273	+	0.403726i	−0.107804	+	0.994172i	$0.534382\pi$
$510$	36162.5	+	62635.2i	0.139033	+	0.240812i
$511$	60096.4	+	104090.i	0.230148	+	0.398628i
$512$			11585.2i			0.0441942i
$513$	89041.2	−	243074.i	0.338342	−	0.923643i
$514$	−229608.			−0.869083
$515$	142978.	−	82548.4i	0.539082	−	0.311239i
$516$	−87962.3	+	50785.0i	−0.330367	+	0.190738i
$517$	−61190.8	+	105986.i	−0.228931	+	0.396520i
$518$	26427.6	+	45773.9i	0.0984914	+	0.170592i
$519$	−63014.9	+	109145.i	−0.233942	+	0.405200i
$520$	−5632.56			−0.0208305
$521$			151066.i			0.556535i	0.960504	+	0.278268i	$0.0897602\pi$
$521$			151066.i			0.556535i	−0.960504	+	0.278268i	$0.910240\pi$
$522$	−3147.67	+	5451.93i	−0.0115518	+	0.0200083i
$523$	−224920.	−	129857.i	−0.822288	−	0.474748i	0.0289168	−	0.999582i	$-0.490794\pi$
$523$	−224920.	−	129857.i	−0.822288	−	0.474748i	−0.851205	+	0.524834i	$0.824128\pi$
$524$	−60352.4			−0.219802
$525$		−	780973.i		−	2.83346i
$526$	−177373.	−	102406.i	−0.641086	−	0.370131i
$527$	−83281.0	+	48082.3i	−0.299864	+	0.173127i
$528$	−78157.6	−	45124.3i	−0.280352	−	0.161861i
$529$	−75935.1	−	131523.i	−0.271351	−	0.469994i
$530$	−27569.2	−	47751.3i	−0.0981461	−	0.169994i
$531$		−	1220.04i		−	0.00432699i
$532$	202953.	−	169585.i	0.717089	−	0.599188i
$533$	9133.80			0.0321512
$534$	71186.9	−	41099.8i	0.249642	−	0.144131i
$535$	−656175.	+	378843.i	−2.29251	+	1.32358i
$536$	−41227.3	+	71407.7i	−0.143501	+	0.248551i
$537$	−227210.	−	393539.i	−0.787913	−	1.36471i
$538$	2525.95	−	4375.07i	0.00872690	−	0.0151154i
$539$	−923429.			−3.17853
$540$		−	226436.i		−	0.776530i
$541$	−258891.	+	448413.i	−0.884551	+	1.53209i	−0.0383234	+	0.999265i	$0.512202\pi$
$541$	−258891.	+	448413.i	−0.884551	+	1.53209i	−0.846227	+	0.532822i	$0.821132\pi$
$542$	125324.	+	72355.9i	0.426615	+	0.246306i
$543$	230837.			0.782900
$544$			12829.8i			0.0433532i
$545$	352281.	+	203390.i	1.18603	+	0.684756i
$546$	12930.8	−	7465.58i	0.0433750	−	0.0250425i
$547$	−4516.32	−	2607.50i	−0.0150942	−	0.00871463i	0.492434	−	0.870350i	$-0.336107\pi$
$547$	−4516.32	−	2607.50i	−0.0150942	−	0.00871463i	−0.507528	+	0.861635i	$0.669441\pi$
$548$	109614.	+	189857.i	0.365010	+	0.632215i
$549$	3171.09	+	5492.48i	0.0105211	+	0.0182232i
$550$		−	407113.i		−	1.34583i
$551$	−202243.	−	242039.i	−0.666148	−	0.797226i
$552$	135893.			0.445985
$553$	625016.	−	360853.i	2.04381	−	1.18000i
$554$	−112751.	+	65096.5i	−0.367366	+	0.212099i
$555$	36810.2	−	63757.1i	0.119504	−	0.206987i
$556$	78951.5	+	136748.i	0.255394	+	0.442355i
$557$	195505.	−	338624.i	0.630155	−	1.09146i	−0.357365	−	0.933965i	$-0.616325\pi$
$557$	195505.	−	338624.i	0.630155	−	1.09146i	0.987520	−	0.157495i	$-0.0503418\pi$
$558$	−9776.17			−0.0313979
$559$		−	8759.87i		−	0.0280333i
$560$	115671.	−	200349.i	0.368850	−	0.638867i
$561$	−86553.7	−	49971.8i	−0.275017	−	0.158781i
$562$	71238.4			0.225549
$563$		−	599322.i		−	1.89079i	−0.325924	−	0.945396i	$-0.605675\pi$
$563$		−	599322.i		−	1.89079i	0.325924	−	0.945396i	$-0.394325\pi$
$564$	50235.3	+	29003.4i	0.157925	+	0.0911781i
$565$	−357554.	+	206434.i	−1.12007	+	0.646673i
$566$	−300707.	−	173613.i	−0.938665	−	0.541938i
$567$	309574.	+	536199.i	0.962939	+	1.66786i
$568$	−5342.66	−	9253.75i	−0.0165600	−	0.0286828i
$569$			257309.i			0.794750i	0.917656	+	0.397375i	$0.130079\pi$
$569$			257309.i			0.794750i	−0.917656	+	0.397375i	$0.869921\pi$
$570$	−345907.	−	126710.i	−1.06466	−	0.389997i
$571$	−624235.			−1.91459			−0.957296	−	0.289110i	$-0.906641\pi$
$571$	−624235.			−1.91459			−0.957296	+	0.289110i	$0.906641\pi$
$572$	6740.67	−	3891.73i	0.0206021	−	0.0118946i
$573$	253681.	−	146463.i	0.772642	−	0.446085i
$574$	−187574.	+	324887.i	−0.569309	+	0.986072i
$575$	306508.	+	530888.i	0.927058	+	1.60571i
$576$	−652.143	+	1129.54i	−0.00196561	+	0.00340454i
$577$	442248.			1.32835			0.664177	−	0.747575i	$-0.268782\pi$
$577$	442248.			1.32835			0.664177	+	0.747575i	$0.268782\pi$
$578$		−	222025.i		−	0.664578i
$579$	203922.	−	353203.i	0.608284	−	1.05358i
$580$	−238932.	−	137947.i	−0.710261	−	0.410070i
$581$	−663722.			−1.96623
$582$			128466.i			0.379265i
$583$	65986.1	+	38097.1i	0.194140	+	0.112087i
$584$	25718.8	−	14848.8i	0.0754093	−	0.0435376i
$585$	−549.167	−	317.061i	−0.00160469	−	0.000926471i
$586$	−174260.	−	301827.i	−0.507460	−	0.878947i
$587$	−102866.	−	178169.i	−0.298535	−	0.517078i	0.677266	−	0.735738i	$-0.263165\pi$
$587$	−102866.	−	178169.i	−0.298535	−	0.517078i	−0.975801	+	0.218661i	$0.929831\pi$
$588$			437690.i			1.26594i
$589$	168476.	−	459924.i	0.485633	−	1.32573i
$590$	53468.6			0.153601
$591$	−395170.	+	228152.i	−1.13138	+	0.653204i
$592$	11309.9	−	6529.79i	0.0322713	−	0.0186318i
$593$	−217809.	+	377256.i	−0.619392	+	1.07282i	0.370204	+	0.928950i	$0.379288\pi$
$593$	−217809.	+	377256.i	−0.619392	+	1.07282i	−0.989597	+	0.143869i	$0.954046\pi$
$594$	156453.	+	270984.i	0.443414	+	0.768016i
$595$	128097.	−	221871.i	0.361831	−	0.626710i
$596$	59288.3			0.166908
$597$		−	256708.i		−	0.720263i
$598$	−5860.04	+	10149.9i	−0.0163869	+	0.0283830i
$599$	371458.	+	214461.i	1.03528	+	0.597717i	0.918492	−	0.395440i	$-0.129408\pi$
$599$	371458.	+	214461.i	1.03528	+	0.597717i	0.116785	+	0.993157i	$0.462741\pi$
$600$	−192964.			−0.536012
$601$			564476.i			1.56277i	0.624047	+	0.781387i	$0.285488\pi$
$601$			564476.i			1.56277i	−0.624047	+	0.781387i	$0.714512\pi$
$602$	311586.	+	179894.i	0.859776	+	0.496392i
$603$	−8039.20	+	4641.44i	−0.0221095	+	0.0127649i
$604$	59127.3	+	34137.2i	0.162074	+	0.0935736i
$605$	180771.	+	313104.i	0.493876	+	0.855418i
$606$	91351.8	+	158226.i	0.248755	+	0.430856i
$607$			34058.1i			0.0924365i	0.998931	+	0.0462182i	$0.0147170\pi$
$607$			34058.1i			0.0924365i	−0.998931	+	0.0462182i	$0.985283\pi$
$608$	−41901.3	−	50146.2i	−0.113350	−	0.135653i
$609$	731361.			1.97196
$610$	−240709.	+	138973.i	−0.646894	+	0.373484i
$611$	−4332.53	+	2501.39i	−0.0116054	+	0.00670036i
$612$	−722.200	+	1250.89i	−0.00192821	+	0.00333976i
$613$	200437.	+	347166.i	0.533404	+	0.923882i	0.999239	+	0.0390107i	$0.0124207\pi$
$613$	200437.	+	347166.i	0.533404	+	0.923882i	−0.465835	+	0.884872i	$0.654246\pi$
$614$	−94824.9	+	164241.i	−0.251528	+	0.435658i
$615$	522530.			1.38153
$616$			319685.i			0.842483i
$617$	42818.9	−	74164.5i	0.112477	−	0.194817i	−0.804291	−	0.594235i	$-0.797455\pi$
$617$	42818.9	−	74164.5i	0.112477	−	0.194817i	0.916769	+	0.399419i	$0.130788\pi$
$618$	93648.1	+	54067.8i	0.245201	+	0.141567i
$619$	289791.			0.756316			0.378158	−	0.925741i	$-0.376558\pi$
$619$	289791.			0.756316			0.378158	+	0.925741i	$0.376558\pi$
$620$		−	428443.i		−	1.11458i
$621$	−408038.	−	235581.i	−1.05808	−	0.610882i
$622$	−249309.	+	143939.i	−0.644402	+	0.372046i
$623$	−252164.	−	145587.i	−0.649690	−	0.375099i
$624$	−1844.61	−	3194.96i	−0.00473735	−	0.00820534i
$625$	51638.3	+	89440.1i	0.132194	+	0.228967i
$626$		−	114672.i		−	0.292624i
$627$	501506.	−	87360.6i	1.27568	−	0.222219i
$628$	236117.			0.598699
$629$	12524.9	−	7231.25i	0.0316572	−	0.0182773i
$630$	22555.6	−	13022.5i	0.0568294	−	0.0328105i
$631$	−38693.7	+	67019.5i	−0.0971811	+	0.168323i	−0.910517	−	0.413472i	$-0.864316\pi$
$631$	−38693.7	+	67019.5i	−0.0971811	+	0.168323i	0.813336	+	0.581795i	$0.197649\pi$
$632$	−89160.4	−	154430.i	−0.223222	−	0.386632i
$633$	−258283.	+	447360.i	−0.644598	+	1.11648i
$634$	−77980.6			−0.194003
$635$		−	1.19101e6i		−	2.95371i
$636$	18057.4	−	31276.3i	0.0446416	−	0.0773216i
$637$	−32691.0	−	18874.2i	−0.0805657	−	0.0465146i
$638$	381251.			0.936632
$639$		−	1202.97i		−	0.00294614i
$640$	−49502.5	−	28580.3i	−0.120856	−	0.0697761i
$641$	−18429.5	+	10640.3i	−0.0448536	+	0.0258962i	−0.522259	−	0.852787i	$-0.674911\pi$
$641$	−18429.5	+	10640.3i	−0.0448536	+	0.0258962i	0.477406	+	0.878683i	$0.341577\pi$
$642$	−429783.	−	248135.i	−1.04275	−	0.602030i
$643$	−49010.6	−	84888.8i	−0.118541	−	0.205319i	0.800649	−	0.599134i	$-0.204488\pi$
$643$	−49010.6	−	84888.8i	−0.118541	−	0.205319i	−0.919190	+	0.393815i	$0.871155\pi$
$644$	−240686.	−	416880.i	−0.580335	−	1.00517i
$645$		−	501138.i		−	1.20459i
$646$	−46402.6	−	55533.2i	−0.111193	−	0.133072i
$647$	−177251.			−0.423429			−0.211714	−	0.977332i	$-0.567905\pi$
$647$	−177251.			−0.423429			−0.211714	+	0.977332i	$0.567905\pi$
$648$	132485.	−	76490.3i	0.315513	−	0.182161i
$649$	−63987.7	+	36943.3i	−0.151917	+	0.0877095i
$650$	8321.07	−	14412.5i	0.0196948	−	0.0341125i
$651$	567873.	+	983585.i	1.33995	+	2.32086i
$652$	−110374.	+	191173.i	−0.259639	+	0.449709i
$653$	−273207.			−0.640716			−0.320358	−	0.947297i	$-0.603803\pi$
$653$	−273207.			−0.640716			−0.320358	+	0.947297i	$0.603803\pi$
$654$			266433.i			0.622921i
$655$	148887.	−	257880.i	0.347035	−	0.601083i
$656$	80273.8	+	46346.1i	0.186537	+	0.107697i
$657$	3343.40			0.00774564
$658$		−	205476.i		−	0.474579i
$659$	259815.	+	150004.i	0.598264	+	0.345408i	0.768358	−	0.640020i	$-0.221074\pi$
$659$	259815.	+	150004.i	0.598264	+	0.345408i	−0.170094	+	0.985428i	$0.554407\pi$
$660$	385623.	−	222640.i	0.885269	−	0.511110i
$661$	−256196.	−	147915.i	−0.586366	−	0.338539i	0.177293	−	0.984158i	$-0.443266\pi$
$661$	−256196.	−	147915.i	−0.586366	−	0.338539i	−0.763659	+	0.645619i	$0.776599\pi$
$662$	−73084.7	−	126586.i	−0.166767	−	0.288849i
$663$	−2042.77	−	3538.18i	−0.00464721	−	0.00804921i
$664$			163994.i			0.371956i
$665$	223940.	+	1.28556e6i	0.506393	+	2.90702i
$666$	1470.27			0.00331473
$667$	−497163.	+	287037.i	−1.11750	+	0.645189i
$668$	−5617.45	+	3243.24i	−0.0125889	+	0.00726818i
$669$	13120.0	−	22724.5i	0.0293145	−	0.0507741i
$670$	−203412.	−	352320.i	−0.453134	−	0.784851i
$671$	192043.	−	332629.i	0.426534	−	0.738779i
$672$	151525.			0.335542
$673$		−	83113.9i		−	0.183503i	−0.995782	−	0.0917516i	$-0.970753\pi$
$673$		−	83113.9i		−	0.183503i	0.995782	−	0.0917516i	$-0.0292466\pi$
$674$	−222186.	+	384837.i	−0.489098	+	0.847143i
$675$	579402.	+	334518.i	1.27166	+	0.734196i
$676$	−228170.			−0.499304
$677$		−	23926.5i		−	0.0522037i	−0.999659	−	0.0261018i	$-0.991691\pi$
$677$		−	23926.5i		−	0.0522037i	0.999659	−	0.0261018i	$-0.00830941\pi$
$678$	−234192.	−	135211.i	−0.509463	−	0.294138i
$679$	394096.	−	227531.i	0.854796	−	0.493517i
$680$	−54820.4	−	31650.6i	−0.118556	−	0.0684485i
$681$	−301463.	−	522149.i	−0.650039	−	1.12590i
$682$	296026.	+	512732.i	0.636445	+	1.10236i
$683$			438631.i			0.940281i	0.882592	+	0.470140i	$0.155797\pi$
$683$			438631.i			0.940281i	−0.882592	+	0.470140i	$0.844203\pi$
$684$	−1262.55	−	7247.84i	−0.00269858	−	0.0154916i
$685$	−1.08165e6			−2.30519
$686$	804106.	−	464251.i	1.70870	−	0.986516i
$687$	233205.	−	134641.i	0.494110	−	0.285275i
$688$	44448.7	−	76987.4i	0.0939036	−	0.162646i
$689$	1557.35	+	2697.41i	0.00328056	+	0.00568210i
$690$	−335243.	+	580659.i	−0.704145	+	1.21961i
$691$	137539.			0.288050			0.144025	−	0.989574i	$-0.453995\pi$
$691$	137539.			0.288050			0.144025	+	0.989574i	$0.453995\pi$
$692$		−	110305.i		−	0.230348i
$693$	−17995.4	+	31168.9i	−0.0374709	+	0.0649015i
$694$	−126723.	−	73163.4i	−0.263109	−	0.151906i
$695$	−779080.			−1.61292
$696$		−	180706.i		−	0.373039i
$697$	88897.2	+	51324.8i	0.182988	+	0.105648i
$698$	−184769.	+	106676.i	−0.379244	+	0.218956i
$699$	−372404.	−	215007.i	−0.762184	−	0.440047i
$700$	341766.	+	591957.i	0.697483	+	1.20808i
$701$	45346.4	+	78542.3i	0.0922798	+	0.159833i	0.908470	−	0.417950i	$-0.137251\pi$
$701$	45346.4	+	78542.3i	0.0922798	+	0.159833i	−0.816190	+	0.577783i	$0.803918\pi$
$702$			12791.1i			0.0259557i
$703$	−25337.7	+	69169.4i	−0.0512691	+	0.139960i
$704$	78988.5			0.159374
$705$	−247857.	+	143100.i	−0.498681	+	0.287914i
$706$	543028.	−	313517.i	1.08946	−	0.629002i
$707$	323593.	−	560479.i	0.647381	−	1.12130i
$708$	17510.5	+	30329.1i	0.0349327	+	0.0605052i
$709$	389004.	−	673774.i	0.773858	−	1.34036i	−0.161576	−	0.986860i	$-0.551658\pi$
$709$	389004.	−	673774.i	0.773858	−	1.34036i	0.935434	−	0.353501i	$-0.115009\pi$
$710$	52720.5			0.104583
$711$		−	20075.7i		−	0.0397128i
$712$	−35971.9	+	62305.1i	−0.0709583	+	0.122903i
$713$	−772055.	−	445746.i	−1.51869	−	0.876816i
$714$	167803.			0.329157
$715$			38402.9i			0.0751195i
$716$	344438.	+	198861.i	0.671870	+	0.387904i
$717$	−397516.	+	229506.i	−0.773243	+	0.446432i
$718$	−147951.	−	85419.6i	−0.286992	−	0.165695i
$719$	235283.	+	407522.i	0.455127	+	0.788304i	0.998696	−	0.0510614i	$-0.0162604\pi$
$719$	235283.	+	407522.i	0.455127	+	0.788304i	−0.543568	+	0.839365i	$0.682927\pi$
$720$	−3217.62	−	5573.08i	−0.00620683	−	0.0107505i
$721$		−	383046.i		−	0.736851i
$722$	362736.	+	65507.5i	0.695851	+	0.125666i
$723$	−633272.			−1.21147
$724$	−174969.	+	101018.i	−0.333797	+	0.192718i
$725$	705957.	−	407584.i	1.34308	−	0.775428i
$726$	−118402.	+	205078.i	−0.224639	+	0.389086i
$727$	109552.	+	189750.i	0.207278	+	0.359016i	0.950856	−	0.309633i	$-0.100206\pi$
$727$	109552.	+	189750.i	0.207278	+	0.359016i	−0.743578	+	0.668649i	$0.766873\pi$
$728$	−6534.12	+	11317.4i	−0.0123289	+	0.0213543i
$729$	−513693.			−0.966603
$730$			146525.i			0.274958i
$731$	49223.6	−	85257.8i	0.0921168	−	0.159551i
$732$	−157660.	−	91025.2i	−0.294239	−	0.169879i
$733$	−707123.			−1.31609			−0.658047	−	0.752977i	$-0.728617\pi$
$733$	−707123.			−1.31609			−0.658047	+	0.752977i	$0.728617\pi$
$734$		−	526129.i		−	0.976563i
$735$	−1.87020e6	−	1.07976e6i	−3.46190	−	1.99873i
$736$	−103004.	+	59469.1i	−0.190150	+	0.109783i
$737$	486860.	+	281089.i	0.896332	+	0.517498i
$738$	5217.72	+	9037.36i	0.00958006	+	0.0165931i
$739$	−150067.	−	259924.i	−0.274788	−	0.475946i	0.695294	−	0.718726i	$-0.255274\pi$
$739$	−150067.	−	259924.i	−0.274788	−	0.475946i	−0.970082	+	0.242779i	$0.921941\pi$
$740$			64434.9i			0.117668i
$741$	19539.8	+	7157.69i	0.0355864	+	0.0130358i
$742$	−127928.			−0.232359
$743$	575271.	−	332133.i	1.04206	−	0.601636i	0.121647	−	0.992573i	$-0.461182\pi$
$743$	575271.	−	332133.i	1.04206	−	0.601636i	0.920417	+	0.390937i	$0.127849\pi$
$744$	243026.	−	140311.i	0.439043	−	0.253482i
$745$	−146262.	+	253333.i	−0.263523	+	0.456435i
$746$	52295.4	+	90578.3i	0.0939693	+	0.162760i
$747$	−9231.35	+	15989.2i	−0.0165434	+	0.0286540i
$748$	87473.9			0.156342
$749$			1.75793e6i			3.13355i
$750$	157144.	−	272181.i	0.279366	−	0.483877i
$751$	−254570.	−	146976.i	−0.451365	−	0.260596i	0.257042	−	0.966400i	$-0.417252\pi$
$751$	−254570.	−	146976.i	−0.451365	−	0.260596i	−0.708406	+	0.705805i	$0.750586\pi$
$752$	−50769.4			−0.0897773
$753$			870906.i			1.53596i
$754$	13497.0	+	7792.47i	0.0237407	+	0.0137067i
$755$	−291729.	+	168430.i	−0.511783	+	0.295478i
$756$	−454975.	−	262680.i	−0.796057	−	0.459604i
$757$	−436923.	−	756773.i	−0.762453	−	1.32061i	−0.941583	−	0.336782i	$-0.890661\pi$
$757$	−436923.	−	756773.i	−0.762453	−	1.32061i	0.179129	−	0.983826i	$-0.442672\pi$
$758$	285748.	+	494929.i	0.497329	+	0.861400i
$759$		−	926525.i		−	1.60832i
$760$	317638.	−	55331.5i	0.549928	−	0.0957955i
$761$	676281.			1.16777			0.583886	−	0.811836i	$-0.301532\pi$
$761$	676281.			1.16777			0.583886	+	0.811836i	$0.301532\pi$
$762$	675579.	−	390046.i	1.16350	−	0.671747i
$763$	817337.	−	471890.i	1.40395	−	0.810572i
$764$	−128189.	+	222030.i	−0.219616	+	0.380386i
$765$	−3563.28	−	6171.77i	−0.00608873	−	0.0105460i
$766$	−88729.2	+	153683.i	−0.151220	+	0.261921i
$767$	−3020.37			−0.00513417
$768$		−	37439.2i		−	0.0634752i
$769$	295116.	−	511157.i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$769$	295116.	−	511157.i	0.499046	−	0.864373i	0.999999	+	0.00110121i	$0.000350527\pi$
$770$	−1.36598e6	−	788651.i	−2.30390	−	1.33016i
$771$	742009.			1.24825
$772$			356958.i			0.598938i
$773$	553601.	+	319622.i	0.926484	+	0.534906i	0.885698	−	0.464262i	$-0.153680\pi$
$773$	553601.	+	319622.i	0.926484	+	0.534906i	0.0407864	+	0.999168i	$0.487014\pi$
$774$	8667.38	−	5004.11i	0.0144679	−	0.00835305i
$775$	1.09630e6	+	632946.i	1.82526	+	1.05381i
$776$	−56218.9	−	97374.1i	−0.0933596	−	0.161704i
$777$	−85404.2	−	147924.i	−0.141461	−	0.245018i
$778$		−	331707.i		−	0.548019i
$779$	−515085.	+	89726.0i	−0.848798	+	0.147857i
$780$	18202.3			0.0299184
$781$	−63092.4	+	36426.4i	−0.103437	+	0.0597192i
$782$	−114069.	+	65857.6i	−0.186532	+	0.107694i
$783$	−313267.	+	542595.i	−0.510966	+	0.885019i
$784$	−191540.	−	331757.i	−0.311622	−	0.539744i
$785$	−582492.	+	1.00891e6i	−0.945258	+	1.63723i
$786$	195037.			0.315697
$787$		−	129013.i		−	0.208297i	−0.994562	−	0.104149i	$-0.966788\pi$
$787$		−	129013.i		−	0.208297i	0.994562	−	0.104149i	$-0.0332118\pi$
$788$	199686.	−	345866.i	0.321584	−	0.557000i
$789$	573204.	+	330939.i	0.920778	+	0.531612i
$790$	879820.			1.40974
$791$			957906.i			1.53098i
$792$	7701.27	+	4446.33i	0.0122776	+	0.00708845i
$793$	13597.3	−	7850.43i	0.0216226	−	0.0124838i
$794$	755673.	+	436288.i	1.19865	+	0.692042i
$795$	89093.6	+	154315.i	0.140965	+	0.244159i
$796$	112340.	+	194578.i	0.177299	+	0.307091i
$797$		−	540582.i		−	0.851030i	−0.904951	−	0.425515i	$-0.860093\pi$
$797$		−	540582.i		−	0.851030i	0.904951	−	0.425515i	$-0.139907\pi$
$798$	−655870.	+	548034.i	−1.02994	+	0.860601i
$799$	−56223.3			−0.0880690
$800$	146262.	−	84444.4i	0.228534	−	0.131944i
$801$	−7014.42	+	4049.78i	−0.0109327	+	0.00631199i
$802$	−401755.	+	695860.i	−0.624615	+	1.08186i
$803$	−101239.	−	175352.i	−0.157007	−	0.271943i
$804$	133231.	−	230763.i	0.206108	−	0.356989i
$805$	2.37505e6			3.66506
$806$			24202.2i			0.0372550i
$807$	−8162.93	+	14138.6i	−0.0125343	+	0.0217100i
$808$	−138484.	−	79954.0i	−0.212118	−	0.122467i
$809$	−304565.			−0.465354			−0.232677	−	0.972554i	$-0.574749\pi$
$809$	−304565.			−0.465354			−0.232677	+	0.972554i	$0.574749\pi$
$810$			754794.i			1.15043i
$811$	773795.	+	446750.i	1.17648	+	0.679240i	0.955197	−	0.295970i	$-0.0956428\pi$
$811$	773795.	+	446750.i	1.17648	+	0.679240i	0.221281	+	0.975210i	$0.428976\pi$
$812$	−554352.	+	320055.i	−0.840763	+	0.485415i
$813$	−405001.	−	233827.i	−0.612738	−	0.353765i
$814$	−44520.3	−	77111.4i	−0.0671907	−	0.116378i
$815$	−544575.	−	943232.i	−0.819866	−	1.42005i
$816$		−	41461.1i		−	0.0622674i
$817$	86052.7	+	493998.i	0.128920	+	0.740084i
$818$	342706.			0.512171
$819$	−1274.14	+	735.623i	−0.00189954	+	0.00109670i
$820$	−396064.	+	228668.i	−0.589031	+	0.340077i
$821$	−102914.	+	178253.i	−0.152683	+	0.264454i	−0.932213	−	0.361911i	$-0.882125\pi$
$821$	−102914.	+	178253.i	−0.152683	+	0.264454i	0.779530	+	0.626365i	$0.215458\pi$
$822$	−354231.	−	613547.i	−0.524256	−	0.908038i
$823$	39049.5	−	67635.8i	0.0576522	−	0.0998566i	−0.835759	−	0.549097i	$-0.814972\pi$
$823$	39049.5	−	67635.8i	0.0576522	−	0.0998566i	0.893411	+	0.449240i	$0.148305\pi$
$824$	−94643.7			−0.139392
$825$			1.31564e6i			1.93298i
$826$	62027.0	−	107434.i	0.0909119	−	0.157464i
$827$	−691422.	−	399193.i	−1.01096	−	0.583676i	−0.0994844	−	0.995039i	$-0.531719\pi$
$827$	−691422.	−	399193.i	−1.01096	−	0.583676i	−0.911471	+	0.411364i	$0.865053\pi$
$828$	−13390.3			−0.0195312
$829$		−	643855.i		−	0.936870i	−0.883498	−	0.468435i	$-0.844818\pi$
$829$		−	643855.i		−	0.936870i	0.883498	−	0.468435i	$-0.155182\pi$
$830$	−700729.	−	404566.i	−1.01717	−	0.587264i
$831$	364368.	−	210368.i	0.527640	−	0.304633i
$832$	2796.33	+	1614.46i	0.00403964	+	0.00233229i
$833$	−212116.	−	367396.i	−0.305692	−	0.529474i
$834$	−255142.	−	441919.i	−0.366817	−	0.635346i
$835$		−	32003.7i		−	0.0459016i
$836$	−341898.	+	285684.i	−0.489198	+	0.408765i
$837$	−972959.			−1.38881
$838$	337834.	−	195049.i	0.481078	−	0.277751i
$839$	551512.	−	318416.i	0.783486	−	0.452346i	−0.0541786	−	0.998531i	$-0.517254\pi$
$839$	551512.	−	318416.i	0.783486	−	0.452346i	0.837664	+	0.546186i	$0.183921\pi$
$840$	−373807.	+	647452.i	−0.529772	+	0.917591i
$841$	28051.7	+	48586.9i	0.0396613	+	0.0686953i
$842$	180184.	−	312087.i	0.254151	−	0.440202i
$843$	−230216.			−0.323952
$844$		−	452116.i		−	0.634694i
$845$	562886.	−	974947.i	0.788328	−	1.36542i
$846$	−4949.95	−	2857.85i	−0.00691608	−	0.00399300i
$847$	838823.			1.16924
$848$			31608.8i			0.0439558i
$849$	971773.	+	561054.i	1.34819	+	0.778375i
$850$	161974.	−	93515.9i	0.224186	−	0.129434i
$851$	116112.	+	67037.2i	0.160331	+	0.0925671i
$852$	17265.5	+	29904.7i	0.0237848	+	0.0411965i
$853$	18130.8	+	31403.5i	0.0249184	+	0.0431599i	0.878216	−	0.478265i	$-0.158734\pi$
$853$	18130.8	+	31403.5i	0.0249184	+	0.0431599i	−0.853297	+	0.521425i	$0.825401\pi$
$854$			644872.i			0.884215i
$855$	34084.0	+	12485.4i	0.0466249	+	0.0170793i
$856$	434352.			0.592781
$857$	−78544.1	+	45347.4i	−0.106943	+	0.0617435i	−0.552517	−	0.833501i	$-0.686333\pi$
$857$	−78544.1	+	45347.4i	−0.106943	+	0.0617435i	0.445575	+	0.895245i	$0.352999\pi$
$858$	−21783.4	+	12576.6i	−0.0295904	+	0.0170840i
$859$	401667.	−	695707.i	0.544351	−	0.942844i	−0.454296	−	0.890851i	$-0.650109\pi$
$859$	401667.	−	695707.i	0.544351	−	0.942844i	0.998647	−	0.0519934i	$-0.0165575\pi$
$860$	219306.	+	379850.i	0.296520	+	0.513588i
$861$	606168.	−	1.04991e6i	0.817687	−	1.41627i
$862$	−401787.			−0.540731
$863$			34074.8i			0.0457521i	0.999738	+	0.0228761i	$0.00728231\pi$
$863$			34074.8i			0.0457521i	−0.999738	+	0.0228761i	$0.992718\pi$
$864$	−64903.6	+	112416.i	−0.0869443	+	0.150592i
$865$	471324.	+	272119.i	0.629923	+	0.363686i
$866$	−284402.			−0.379224
$867$			717503.i			0.954521i
$868$	−860865.	−	497021.i	−1.14260	−	0.659683i
$869$	−1.05291e6	+	607898.i	−1.39429	+	0.804992i
$870$	772140.	+	445795.i	1.02013	+	0.588975i
$871$	11490.5	+	19902.1i	0.0151461	+	0.0262339i
$872$	−116595.	−	201949.i	−0.153338	−	0.265589i
$873$		−	12658.5i		−	0.0166093i
$874$	230759.	−	629951.i	0.302090	−	0.824677i
$875$	−1.11329e6			−1.45409
$876$	−83113.6	+	47985.7i	−0.108309	+	0.0625321i
$877$	−395994.	+	228627.i	−0.514860	+	0.297254i	−0.734829	−	0.678252i	$-0.762738\pi$
$877$	−395994.	+	228627.i	−0.514860	+	0.297254i	0.219969	+	0.975507i	$0.429404\pi$
$878$	437646.	−	758026.i	0.567720	−	0.983320i
$879$	563143.	+	975393.i	0.728855	+	1.26241i
$880$	−194861.	+	337510.i	−0.251629	+	0.435834i
$881$	−599177.			−0.771975			−0.385987	−	0.922504i	$-0.626139\pi$
$881$	−599177.			−0.771975			−0.385987	+	0.922504i	$0.626139\pi$
$882$		−	43127.8i		−	0.0554396i
$883$	5620.23	−	9734.53i	0.00720830	−	0.0124851i	−0.862399	−	0.506230i	$-0.831039\pi$
$883$	5620.23	−	9734.53i	0.00720830	−	0.0124851i	0.869607	+	0.493744i	$0.164372\pi$
$884$	3096.73	+	1787.90i	0.00396277	+	0.00228791i
$885$	−172791.			−0.220614
$886$			145262.i			0.185048i
$887$	821694.	+	474406.i	1.04439	+	0.602979i	0.921074	−	0.389388i	$-0.127313\pi$
$887$	821694.	+	474406.i	1.04439	+	0.602979i	0.123317	+	0.992367i	$0.460647\pi$
$888$	−36549.5	+	21101.9i	−0.0463506	+	0.0267605i
$889$	−2.39309e6	−	1.38165e6i	−3.02799	−	1.74821i
$890$	−177482.	−	307408.i	−0.224066	−	0.388093i
$891$	−521513.	−	903288.i	−0.656916	−	1.13781i
$892$			22966.1i			0.0288641i
$893$	219753.	−	183622.i	0.275570	−	0.230262i
$894$	−191598.			−0.239726
$895$	−1.69943e6	+	981166.i	−2.12157	+	1.22489i
$896$	−114852.	+	66309.9i	−0.143062	+	0.0825967i
$897$	18937.5	−	32800.6i	0.0235362	−	0.0407659i
$898$	312517.	+	541294.i	0.387543	+	0.671245i
$899$	−592738.	+	1.02665e6i	−0.733404	+	1.27029i
$900$	19013.8			0.0234738
$901$			35004.4i			0.0431194i
$902$	315989.	−	547309.i	0.388382	−	0.672697i
$903$	−1.00693e6	−	581352.i	−1.23488	−	0.712958i
$904$	236682.			0.289619
$905$		−	996831.i		−	1.21709i
$906$	−191078.	−	110319.i	−0.232784	−	0.134398i
$907$	−925379.	+	534268.i	−1.12488	+	0.649448i	−0.942642	−	0.333807i	$-0.891667\pi$
$907$	−925379.	+	534268.i	−1.12488	+	0.649448i	−0.182236	+	0.983255i	$0.558333\pi$
$908$	457002.	+	263850.i	0.554301	+	0.320026i
$909$	−9001.36	−	15590.8i	−0.0108938	−	0.0188687i
$910$	−32238.8	−	55839.3i	−0.0389311	−	0.0674306i
$911$		−	1.33286e6i		−	1.60601i	−0.595972	−	0.803005i	$-0.703233\pi$
$911$		−	1.33286e6i		−	1.60601i	0.595972	−	0.803005i	$-0.296767\pi$
$912$	135409.	+	162054.i	0.162802	+	0.194836i
$913$	1.11811e6			1.34136
$914$	−107505.	+	62067.8i	−0.128687	+	0.0742975i
$915$	777883.	−	449111.i	0.929120	−	0.536428i
$916$	−117842.	+	204108.i	−0.140446	+	0.243260i
$917$	−345436.	−	598313.i	−0.410799	−	0.711525i
$918$	−71875.9	+	124493.i	−0.0852899	+	0.147727i
$919$	780374.			0.923999			0.462000	−	0.886880i	$-0.347132\pi$
$919$	780374.			0.923999			0.462000	+	0.886880i	$0.347132\pi$
$920$		−	586832.i		−	0.693327i
$921$	306439.	−	530768.i	0.361264	−	0.625727i
$922$	−545180.	−	314760.i	−0.641325	−	0.370269i
$923$	−2978.11			−0.00349573
$924$		−	1.03310e6i		−	1.21004i
$925$	−164875.	−	95190.8i	−0.192696	−	0.111253i
$926$	224860.	−	129823.i	0.262235	−	0.151401i
$927$	−9227.63	−	5327.58i	−0.0107382	−	0.00619969i
$928$	79080.0	+	136971.i	0.0918271	+	0.159049i
$929$	9446.97	+	16362.6i	0.0109461	+	0.0189593i	0.871447	−	0.490490i	$-0.163182\pi$
$929$	9446.97	+	16362.6i	0.0109461	+	0.0189593i	−0.860500	+	0.509450i	$0.829849\pi$
$930$			1.38457e6i			1.60084i
$931$	2.02897e6	+	743237.i	2.34086	+	0.857487i
$932$	376363.			0.433286
$933$	805674.	−	465156.i	0.925541	−	0.534362i
$934$	−144169.	+	83236.1i	−0.165264	+	0.0954153i
$935$	−215795.	+	373767.i	−0.246841	+	0.427541i
$936$	181.759	+	314.816i	0.000207465	+	0.000359340i
$937$	234557.	−	406265.i	0.267159	−	0.462732i	−0.700968	−	0.713192i	$-0.747249\pi$
$937$	234557.	−	406265.i	0.267159	−	0.462732i	0.968127	+	0.250460i	$0.0805819\pi$
$938$	−943883.			−1.07278
$939$			370578.i			0.420290i
$940$	125246.	−	216933.i	0.141745	−	0.245510i
$941$	1.12237e6	+	648002.i	1.26753	+	0.731808i	0.974520	−	0.224301i	$-0.0720100\pi$
$941$	1.12237e6	+	648002.i	1.26753	+	0.731808i	0.293009	+	0.956110i	$0.405343\pi$
$942$	−763043.			−0.859899
$943$			951612.i			1.07013i
$944$	−26545.0	−	15325.8i	−0.0297878	−	0.0171980i
$945$	2.24481e6	−	1.29604e6i	2.51372	−	1.45130i
$946$	−524903.	−	303053.i	−0.586538	−	0.338638i
$947$	327123.	+	566594.i	0.364764	+	0.631789i	0.988738	−	0.149656i	$-0.0478165\pi$
$947$	327123.	+	566594.i	0.364764	+	0.631789i	−0.623975	+	0.781445i	$0.714483\pi$
$948$	288133.	+	499061.i	0.320610	+	0.555312i
$949$		−	8277.01i		−	0.00919054i
$950$	−327671.	+	894512.i	−0.363071	+	0.991149i
$951$	252004.			0.278642
$952$	−127190.	+	73433.3i	−0.140339	+	0.0810250i
$953$	−190421.	+	109940.i	−0.209667	+	0.121051i	−0.601157	−	0.799131i	$-0.705293\pi$
$953$	−190421.	+	109940.i	−0.209667	+	0.121051i	0.391490	+	0.920182i	$0.371960\pi$
$954$	−1779.29	+	3081.81i	−0.00195501	+	0.00338618i
$955$	−632474.	−	1.09548e6i	−0.693483	−	1.20115i
$956$	200871.	−	347919.i	0.219787	−	0.380682i
$957$	−1.23206e6			−1.34527
$958$		−	1.18992e6i		−	1.29655i
$959$	−1.25478e6	+	2.17335e6i	−1.36437	+	2.36316i
$960$	159974.	+	92361.0i	0.173583	+	0.100218i
$961$	−917429.			−0.993404
$962$		−	3639.84i		−	0.00393308i
$963$	42348.7	+	24450.1i	0.0456655	+	0.0263650i
$964$	480004.	−	277130.i	0.516524	−	0.298215i
$965$	−1.52524e6	−	880600.i	−1.63789	−	0.945636i
$966$	777807.	+	1.34720e6i	0.833523	+	1.44370i
$967$	−109124.	−	189008.i	−0.116699	−	0.202129i	0.801759	−	0.597648i	$-0.203898\pi$
$967$	−109124.	−	189008.i	−0.116699	−	0.202129i	−0.918458	+	0.395519i	$0.870565\pi$
$968$		−	207258.i		−	0.221188i
$969$	149956.	+	179463.i	0.159704	+	0.191129i
$970$	554759.			0.589605
$971$	−643947.	+	371783.i	−0.682986	+	0.394322i	−0.800979	−	0.598692i	$-0.795687\pi$
$971$	−643947.	+	371783.i	−0.682986	+	0.394322i	0.117993	+	0.993014i	$0.462354\pi$
$972$	−25723.0	+	14851.2i	−0.0272263	+	0.0157191i
$973$	−903783.	+	1.56540e6i	−0.954637	+	1.65348i
$974$	621503.	+	1.07647e6i	0.655126	+	1.13471i
$975$	−26890.6	+	46575.9i	−0.0282873	+	0.0489951i
$976$	159336.			0.167269
$977$			496951.i			0.520624i	0.965525	+	0.260312i	$0.0838254\pi$
$977$			496951.i			0.520624i	−0.965525	+	0.260312i	$0.916175\pi$
$978$	356687.	−	617800.i	0.372915	−	0.645908i
$979$	424798.	+	245257.i	0.443218	+	0.255892i
$980$	1.89009e6			1.96802
$981$		−	26253.0i		−	0.0272798i
$982$	634503.	+	366330.i	0.657977	+	0.379883i
$983$	1.24870e6	−	720937.i	1.29226	−	0.746088i	0.313207	−	0.949685i	$-0.398597\pi$
$983$	1.24870e6	−	720937.i	1.29226	−	0.746088i	0.979055	+	0.203597i	$0.0652632\pi$
$984$	−259415.	−	149773.i	−0.267920	−	0.154684i
$985$	985233.	+	1.70647e6i	1.01547	+	1.75884i
$986$	87575.2	+	151685.i	0.0900798	+	0.156023i
$987$			664022.i			0.681629i
$988$	−17943.0	+	3125.60i	−0.0183815	+	0.00320199i
$989$	912653.			0.933068
$990$	−37997.4	+	21937.8i	−0.0387690	+	0.0223833i
$991$	−139194.	+	80364.0i	−0.141734	+	0.0818303i	−0.569190	−	0.822206i	$-0.692743\pi$
$991$	−139194.	+	80364.0i	−0.141734	+	0.0818303i	0.427456	+	0.904036i	$0.359410\pi$
$992$	−122805.	+	212704.i	−0.124794	+	0.216149i
$993$	236183.	+	409081.i	0.239524	+	0.414868i
$994$	61159.1	−	105931.i	0.0618996	−	0.107213i
$995$	−1.10855e6			−1.11972
$996$		−	529967.i		−	0.534232i
$997$	93355.2	−	161696.i	0.0939178	−	0.162670i	−0.815239	−	0.579125i	$-0.803394\pi$
$997$	93355.2	−	161696.i	0.0939178	−	0.162670i	0.909156	+	0.416455i	$0.136728\pi$
$998$	−368653.	−	212842.i	−0.370132	−	0.213696i
$999$	146326.			0.146620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.d.a.31.6	yes	16
3.2	odd	2		342.5.m.c.145.1		16
4.3	odd	2		304.5.r.c.145.6		16
19.8	odd	6	inner	38.5.d.a.27.6	✓	16
57.8	even	6		342.5.m.c.217.1		16
76.27	even	6		304.5.r.c.65.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.6	✓	16	19.8	odd	6	inner
38.5.d.a.31.6	yes	16	1.1	even	1	trivial
304.5.r.c.65.6		16	76.27	even	6
304.5.r.c.145.6		16	4.3	odd	2
342.5.m.c.145.1		16	3.2	odd	2
342.5.m.c.217.1		16	57.8	even	6

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{2} +(-7.91584 + 4.57021i) q^{3} +(4.00000 - 6.92820i) q^{4} +(19.7357 + 34.1832i) q^{5} +(-12.9265 + 22.3894i) q^{6} +91.5785 q^{7} -22.6274i q^{8} +(1.27372 - 2.20614i) q^{9} +O(q^{10})\)	\(q+(2.44949 - 1.41421i) q^{2} +(-7.91584 + 4.57021i) q^{3} +(4.00000 - 6.92820i) q^{4} +(19.7357 + 34.1832i) q^{5} +(-12.9265 + 22.3894i) q^{6} +91.5785 q^{7} -22.6274i q^{8} +(1.27372 - 2.20614i) q^{9} +(96.6847 + 55.8209i) q^{10} -154.274 q^{11} +73.1234i q^{12} +(-5.46159 - 3.15325i) q^{13} +(224.321 - 129.512i) q^{14} +(-312.449 - 180.393i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-35.4376 - 61.3797i) q^{17} -7.20523i q^{18} +(338.973 + 124.170i) q^{19} +315.771 q^{20} +(-724.921 + 418.533i) q^{21} +(-377.894 + 218.177i) q^{22} +(328.524 - 569.020i) q^{23} +(103.412 + 179.115i) q^{24} +(-466.494 + 807.991i) q^{25} -17.8375 q^{26} -717.090i q^{27} +(366.314 - 634.475i) q^{28} +(-756.663 - 436.859i) q^{29} -1020.45 q^{30} -1356.82i q^{31} +(-156.767 - 90.5097i) q^{32} +(1221.21 - 705.067i) q^{33} +(-173.608 - 100.233i) q^{34} +(1807.36 + 3130.45i) q^{35} +(-10.1897 - 17.6491i) q^{36} +204.056i q^{37} +(1005.91 - 175.227i) q^{38} +57.6441 q^{39} +(773.477 - 446.567i) q^{40} +(-1254.28 + 724.157i) q^{41} +(-1183.79 + 2050.39i) q^{42} +(694.511 + 1202.93i) q^{43} +(-617.098 + 1068.84i) q^{44} +100.551 q^{45} -1858.41i q^{46} +(396.636 - 686.994i) q^{47} +(506.614 + 292.494i) q^{48} +5985.63 q^{49} +2638.89i q^{50} +(561.037 + 323.915i) q^{51} +(-43.6927 + 25.2260i) q^{52} +(-427.719 - 246.944i) q^{53} +(-1014.12 - 1756.50i) q^{54} +(-3044.71 - 5273.59i) q^{55} -2072.19i q^{56} +(-3250.74 + 566.268i) q^{57} -2471.25 q^{58} +(414.766 - 239.465i) q^{59} +(-2499.59 + 1443.14i) q^{60} +(-1244.82 + 2156.08i) q^{61} +(-1918.83 - 3323.51i) q^{62} +(116.645 - 202.035i) q^{63} -512.000 q^{64} -248.926i q^{65} +(1994.23 - 3454.11i) q^{66} +(-3155.80 - 1822.00i) q^{67} -567.002 q^{68} +6005.69i q^{69} +(8854.24 + 5112.00i) q^{70} +(408.962 - 236.114i) q^{71} +(-49.9193 - 28.8209i) q^{72} +(656.228 + 1136.62i) q^{73} +(288.579 + 499.833i) q^{74} -8527.91i q^{75} +(2216.17 - 1851.79i) q^{76} -14128.2 q^{77} +(141.199 - 81.5211i) q^{78} +(6824.92 - 3940.37i) q^{79} +(1263.08 - 2187.72i) q^{80} +(3380.43 + 5855.07i) q^{81} +(-2048.23 + 3547.63i) q^{82} -7247.57 q^{83} +6696.54i q^{84} +(1398.77 - 2422.74i) q^{85} +(3402.40 + 1964.37i) q^{86} +7986.16 q^{87} +3490.83i q^{88} +(-2753.52 - 1589.75i) q^{89} +(246.298 - 142.200i) q^{90} +(-500.164 - 288.770i) q^{91} +(-2628.19 - 4552.16i) q^{92} +(6200.94 + 10740.3i) q^{93} -2243.71i q^{94} +(2445.33 + 14037.8i) q^{95} +1654.59 q^{96} +(4303.37 - 2484.55i) q^{97} +(14661.7 - 8464.95i) q^{98} +(-196.502 + 340.351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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