LMFDB - Embedded newform 38.5.d.a.31.5

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			31.5
Root			$0.500000 - 11.2515i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.5.d.a.27.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{2} +(-11.7188 + 6.76588i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-15.6059 - 27.0302i) q^{5} +(-19.1368 + 33.1459i) q^{6} -61.1277 q^{7} -22.6274i q^{8} +(51.0542 - 88.4285i) q^{9} +O(q^{10})$	\(q+(2.44949 - 1.41421i) q^{2} +(-11.7188 + 6.76588i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-15.6059 - 27.0302i) q^{5} +(-19.1368 + 33.1459i) q^{6} -61.1277 q^{7} -22.6274i q^{8} +(51.0542 - 88.4285i) q^{9} +(-76.4529 - 44.1401i) q^{10} -130.170 q^{11} +108.254i q^{12} +(252.926 + 146.027i) q^{13} +(-149.732 + 86.4476i) q^{14} +(365.766 + 211.175i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-27.4834 - 47.6027i) q^{17} -288.806i q^{18} +(-276.362 - 232.261i) q^{19} -249.694 q^{20} +(716.346 - 413.583i) q^{21} +(-318.850 + 184.088i) q^{22} +(96.8702 - 167.784i) q^{23} +(153.094 + 265.167i) q^{24} +(-174.587 + 302.393i) q^{25} +826.052 q^{26} +285.634i q^{27} +(-244.511 + 423.505i) q^{28} +(-856.000 - 494.212i) q^{29} +1194.59 q^{30} +1409.47i q^{31} +(-156.767 - 90.5097i) q^{32} +(1525.44 - 880.714i) q^{33} +(-134.641 - 77.7348i) q^{34} +(953.951 + 1652.29i) q^{35} +(-408.434 - 707.428i) q^{36} -1682.62i q^{37} +(-1005.41 - 178.087i) q^{38} -3952.00 q^{39} +(-611.623 + 353.121i) q^{40} +(-1386.48 + 800.482i) q^{41} +(1169.79 - 2026.13i) q^{42} +(-428.068 - 741.435i) q^{43} +(-520.680 + 901.844i) q^{44} -3186.98 q^{45} -547.981i q^{46} +(1106.62 - 1916.72i) q^{47} +(750.006 + 433.016i) q^{48} +1335.59 q^{49} +987.611i q^{50} +(644.148 + 371.899i) q^{51} +(2023.41 - 1168.21i) q^{52} +(-2033.02 - 1173.76i) q^{53} +(403.948 + 699.659i) q^{54} +(2031.42 + 3518.51i) q^{55} +1383.16i q^{56} +(4810.09 + 852.001i) q^{57} -2795.68 q^{58} +(2054.40 - 1186.11i) q^{59} +(2926.13 - 1689.40i) q^{60} +(-2489.61 + 4312.14i) q^{61} +(1993.30 + 3452.49i) q^{62} +(-3120.83 + 5405.43i) q^{63} -512.000 q^{64} -9115.50i q^{65} +(2491.03 - 4314.60i) q^{66} +(-1337.28 - 772.081i) q^{67} -439.735 q^{68} +2621.65i q^{69} +(4673.39 + 2698.18i) q^{70} +(6857.15 - 3958.98i) q^{71} +(-2000.91 - 1155.23i) q^{72} +(430.026 + 744.828i) q^{73} +(-2379.58 - 4121.55i) q^{74} -4724.93i q^{75} +(-2714.60 + 985.646i) q^{76} +7956.99 q^{77} +(-9680.38 + 5588.97i) q^{78} +(-6478.02 + 3740.09i) q^{79} +(-998.776 + 1729.93i) q^{80} +(2202.82 + 3815.40i) q^{81} +(-2264.11 + 3921.55i) q^{82} +629.303 q^{83} -6617.32i q^{84} +(-857.806 + 1485.76i) q^{85} +(-2097.09 - 1210.76i) q^{86} +13375.1 q^{87} +2945.41i q^{88} +(2407.21 + 1389.81i) q^{89} +(-7806.48 + 4507.08i) q^{90} +(-15460.8 - 8926.28i) q^{91} +(-774.962 - 1342.27i) q^{92} +(-9536.32 - 16517.4i) q^{93} -6259.97i q^{94} +(-1965.19 + 11094.7i) q^{95} +2449.51 q^{96} +(10670.3 - 6160.52i) q^{97} +(3271.52 - 1888.82i) q^{98} +(-6645.72 + 11510.7i) 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
$3$	−11.7188	+	6.76588i	−1.30209	+	0.751764i	−0.980763	−	0.195203i	$-0.937464\pi$
$3$	−11.7188	+	6.76588i	−1.30209	+	0.751764i	−0.321331	+	0.946967i	$0.604130\pi$
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	−15.6059	−	27.0302i	−0.624235	−	1.08121i	−0.988688	−	0.149985i	$-0.952077\pi$
$5$	−15.6059	−	27.0302i	−0.624235	−	1.08121i	0.364453	−	0.931222i	$-0.381256\pi$
$6$	−19.1368	+	33.1459i	−0.531578	+	0.920719i
$7$	−61.1277			−1.24750			−0.623752	−	0.781622i	$-0.714392\pi$
$7$	−61.1277			−1.24750			−0.623752	+	0.781622i	$0.714392\pi$
$8$		−	22.6274i		−	0.353553i
$9$	51.0542	−	88.4285i	0.630299	−	1.09171i
$10$	−76.4529	−	44.1401i	−0.764529	−	0.441401i
$11$	−130.170			−1.07578			−0.537892	−	0.843014i	$-0.680779\pi$
$11$	−130.170			−1.07578			−0.537892	+	0.843014i	$0.680779\pi$
$12$			108.254i			0.751764i
$13$	252.926	+	146.027i	1.49660	+	0.864064i	0.999992	−	0.00391025i	$-0.00124467\pi$
$13$	252.926	+	146.027i	1.49660	+	0.864064i	0.496610	+	0.867974i	$0.334578\pi$
$14$	−149.732	+	86.4476i	−0.763937	+	0.441059i
$15$	365.766	+	211.175i	1.62563	+	0.938555i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−27.4834	−	47.6027i	−0.0950983	−	0.164715i	0.814551	−	0.580092i	$-0.196983\pi$
$17$	−27.4834	−	47.6027i	−0.0950983	−	0.164715i	−0.909650	+	0.415376i	$0.863650\pi$
$18$		−	288.806i		−	0.891378i
$19$	−276.362	−	232.261i	−0.765545	−	0.643382i
$19$	−276.362	−	232.261i	−0.765545	−	0.643382i
$20$	−249.694			−0.624235
$21$	716.346	−	413.583i	1.62437	−	0.937829i
$22$	−318.850	+	184.088i	−0.658781	+	0.380347i
$23$	96.8702	−	167.784i	0.183120	−	0.317172i	−0.759822	−	0.650131i	$-0.774714\pi$
$23$	96.8702	−	167.784i	0.183120	−	0.317172i	0.942941	+	0.332959i	$0.108047\pi$
$24$	153.094	+	265.167i	0.265789	+	0.460360i
$25$	−174.587	+	302.393i	−0.279339	+	0.483829i
$26$	826.052			1.22197
$27$			285.634i			0.391817i
$28$	−244.511	+	423.505i	−0.311876	+	0.540185i
$29$	−856.000	−	494.212i	−1.01784	−	0.587648i	−0.104360	−	0.994540i	$-0.533279\pi$
$29$	−856.000	−	494.212i	−1.01784	−	0.587648i	−0.913476	+	0.406892i	$0.866613\pi$
$30$	1194.59			1.32732
$31$			1409.47i			1.46667i	0.679866	+	0.733337i	$0.262038\pi$
$31$			1409.47i			1.46667i	−0.679866	+	0.733337i	$0.737962\pi$
$32$	−156.767	−	90.5097i	−0.153093	−	0.0883883i
$33$	1525.44	−	880.714i	1.40077	−	0.808736i
$34$	−134.641	−	77.7348i	−0.116471	−	0.0672447i
$35$	953.951	+	1652.29i	0.778736	+	1.34881i
$36$	−408.434	−	707.428i	−0.315150	−	0.545855i
$37$		−	1682.62i		−	1.22909i	−0.788884	−	0.614543i	$-0.789341\pi$
$37$		−	1682.62i		−	1.22909i	0.788884	−	0.614543i	$-0.210659\pi$
$38$	−1005.41	−	178.087i	−0.696269	−	0.123329i
$39$	−3952.00			−2.59829
$40$	−611.623	+	353.121i	−0.382264	+	0.220700i
$41$	−1386.48	+	800.482i	−0.824792	+	0.476194i	−0.852066	−	0.523434i	$-0.824651\pi$
$41$	−1386.48	+	800.482i	−0.824792	+	0.476194i	0.0272740	+	0.999628i	$0.491317\pi$
$42$	1169.79	−	2026.13i	0.663145	−	1.14860i
$43$	−428.068	−	741.435i	−0.231513	−	0.400992i	0.726740	−	0.686912i	$-0.241034\pi$
$43$	−428.068	−	741.435i	−0.231513	−	0.400992i	−0.958254	+	0.285920i	$0.907701\pi$
$44$	−520.680	+	901.844i	−0.268946	+	0.465828i
$45$	−3186.98			−1.57382
$46$		−	547.981i		−	0.258970i
$47$	1106.62	−	1916.72i	0.500958	−	0.867685i	−0.499041	−	0.866578i	$-0.666314\pi$
$47$	1106.62	−	1916.72i	0.500958	−	0.867685i	0.999999	−	0.00110706i	$-0.000352387\pi$
$48$	750.006	+	433.016i	0.325523	+	0.187941i
$49$	1335.59			0.556266
$50$			987.611i			0.395044i
$51$	644.148	+	371.899i	0.247654	+	0.142983i
$52$	2023.41	−	1168.21i	0.748301	−	0.432032i
$53$	−2033.02	−	1173.76i	−0.723751	−	0.417858i	0.0923809	−	0.995724i	$-0.470552\pi$
$53$	−2033.02	−	1173.76i	−0.723751	−	0.417858i	−0.816132	+	0.577866i	$0.803886\pi$
$54$	403.948	+	699.659i	0.138528	+	0.239938i
$55$	2031.42	+	3518.51i	0.671542	+	1.16315i
$56$			1383.16i			0.441059i
$57$	4810.09	+	852.001i	1.48048	+	0.262235i
$58$	−2795.68			−0.831060
$59$	2054.40	−	1186.11i	0.590174	−	0.340737i	−0.174992	−	0.984570i	$-0.555990\pi$
$59$	2054.40	−	1186.11i	0.590174	−	0.340737i	0.765166	+	0.643832i	$0.222657\pi$
$60$	2926.13	−	1689.40i	0.812813	−	0.469278i
$61$	−2489.61	+	4312.14i	−0.669071	+	1.15887i	0.309093	+	0.951032i	$0.399975\pi$
$61$	−2489.61	+	4312.14i	−0.669071	+	1.15887i	−0.978164	+	0.207834i	$0.933359\pi$
$62$	1993.30	+	3452.49i	0.518547	+	0.898150i
$63$	−3120.83	+	5405.43i	−0.786301	+	1.36191i
$64$	−512.000			−0.125000
$65$		−	9115.50i		−	2.15752i
$66$	2491.03	−	4314.60i	0.571863	−	0.990496i
$67$	−1337.28	−	772.081i	−0.297902	−	0.171994i	0.343598	−	0.939117i	$-0.388354\pi$
$67$	−1337.28	−	772.081i	−0.297902	−	0.171994i	−0.641500	+	0.767123i	$0.721688\pi$
$68$	−439.735			−0.0950983
$69$			2621.65i			0.550651i
$70$	4673.39	+	2698.18i	0.953752	+	0.550649i
$71$	6857.15	−	3958.98i	1.36028	−	0.785355i	0.370615	−	0.928787i	$-0.379147\pi$
$71$	6857.15	−	3958.98i	1.36028	−	0.785355i	0.989660	+	0.143431i	$0.0458136\pi$
$72$	−2000.91	−	1155.23i	−0.385978	−	0.222844i
$73$	430.026	+	744.828i	0.0806955	+	0.139769i	0.903549	−	0.428485i	$-0.140953\pi$
$73$	430.026	+	744.828i	0.0806955	+	0.139769i	−0.822853	+	0.568254i	$0.807619\pi$
$74$	−2379.58	−	4121.55i	−0.434547	−	0.752658i
$75$		−	4724.93i		−	0.839987i
$76$	−2714.60	+	985.646i	−0.469979	+	0.170645i
$77$	7956.99			1.34205
$78$	−9680.38	+	5588.97i	−1.59112	+	0.918634i
$79$	−6478.02	+	3740.09i	−1.03798	+	0.599277i	−0.919260	−	0.393651i	$-0.871212\pi$
$79$	−6478.02	+	3740.09i	−1.03798	+	0.599277i	−0.118718	+	0.992928i	$0.537878\pi$
$80$	−998.776	+	1729.93i	−0.156059	+	0.270302i
$81$	2202.82	+	3815.40i	0.335745	+	0.581528i
$82$	−2264.11	+	3921.55i	−0.336720	+	0.583216i
$83$	629.303			0.0913489			0.0456745	−	0.998956i	$-0.485456\pi$
$83$	629.303			0.0913489			0.0456745	+	0.998956i	$0.485456\pi$
$84$		−	6617.32i		−	0.937829i
$85$	−857.806	+	1485.76i	−0.118727	+	0.205642i
$86$	−2097.09	−	1210.76i	−0.283544	−	0.163704i
$87$	13375.1			1.76709
$88$			2945.41i			0.380347i
$89$	2407.21	+	1389.81i	0.303903	+	0.175458i	0.644195	−	0.764861i	$-0.277193\pi$
$89$	2407.21	+	1389.81i	0.303903	+	0.175458i	−0.340292	+	0.940320i	$0.610526\pi$
$90$	−7806.48	+	4507.08i	−0.963763	+	0.556429i
$91$	−15460.8	−	8926.28i	−1.86702	−	1.07792i
$92$	−774.962	−	1342.27i	−0.0915598	−	0.158586i
$93$	−9536.32	−	16517.4i	−1.10259	−	1.90975i
$94$		−	6259.97i		−	0.708462i
$95$	−1965.19	+	11094.7i	−0.217749	+	1.22933i
$96$	2449.51			0.265789
$97$	10670.3	−	6160.52i	1.13406	−	0.654748i	0.189104	−	0.981957i	$-0.439442\pi$
$97$	10670.3	−	6160.52i	1.13406	−	0.654748i	0.944952	+	0.327209i	$0.106108\pi$
$98$	3271.52	−	1888.82i	0.340642	−	0.196670i
$99$	−6645.72	+	11510.7i	−0.678066	+	1.17444i
$100$	1396.69	+	2419.14i	0.139669	+	0.241914i
$101$	6064.33	−	10503.7i	0.594484	−	1.02968i	−0.399136	−	0.916892i	$-0.630690\pi$
$101$	6064.33	−	10503.7i	0.594484	−	1.02968i	0.993620	−	0.112784i	$-0.0359768\pi$
$102$	2103.78			0.202209
$103$			20294.1i			1.91292i	0.291870	+	0.956458i	$0.405722\pi$
$103$			20294.1i			1.91292i	−0.291870	+	0.956458i	$0.594278\pi$
$104$	3304.21	−	5723.06i	0.305493	−	0.529129i
$105$	−22358.4	−	12908.6i	−2.02797	−	1.17085i
$106$	−6639.80			−0.590940
$107$		−	9253.68i		−	0.808253i	−0.914703	−	0.404126i	$-0.867576\pi$
$107$		−	9253.68i		−	0.808253i	0.914703	−	0.404126i	$-0.132424\pi$
$108$	1978.93	+	1142.54i	0.169662	+	0.0979542i
$109$	−11549.7	+	6668.22i	−0.972114	+	0.561250i	−0.899880	−	0.436137i	$-0.856346\pi$
$109$	−11549.7	+	6668.22i	−0.972114	+	0.561250i	−0.0722341	+	0.997388i	$0.523013\pi$
$110$	9951.86	+	5745.71i	0.822468	+	0.474852i
$111$	11384.4	+	19718.3i	0.923982	+	1.60038i
$112$	1956.09	+	3388.04i	0.155938	+	0.270093i
$113$			10358.4i			0.811217i	0.914047	+	0.405608i	$0.132940\pi$
$113$			10358.4i			0.811217i	−0.914047	+	0.405608i	$0.867060\pi$
$114$	12987.2	−	4715.53i	0.999321	−	0.362844i
$115$	−6046.98			−0.457238
$116$	−6848.00	+	3953.69i	−0.508918	+	0.293824i
$117$	25825.9	−	14910.6i	1.88661	−	1.08924i
$118$	3354.82	−	5810.71i	0.240938	−	0.417316i
$119$	1680.00	+	2909.84i	0.118636	+	0.205483i
$120$	4778.34	−	8276.33i	0.331829	−	0.574745i
$121$	2303.21			0.157312
$122$			14083.4i			0.946210i
$123$	10831.9	−	18761.5i	0.715971	−	1.24010i
$124$	9765.11	+	5637.89i	0.635088	+	0.366668i
$125$	−8609.03			−0.550978
$126$			17654.1i			1.11200i
$127$	−17402.7	−	10047.5i	−1.07897	−	0.622944i	−0.148352	−	0.988935i	$-0.547397\pi$
$127$	−17402.7	−	10047.5i	−1.07897	−	0.622944i	−0.930618	+	0.365991i	$0.880730\pi$
$128$	−1254.14	+	724.077i	−0.0765466	+	0.0441942i
$129$	10032.9	+	5792.51i	0.602904	+	0.348087i
$130$	−12891.3	−	22328.3i	−0.762797	−	1.32120i
$131$	−470.086	−	814.213i	−0.0273927	−	0.0474455i	0.852004	−	0.523535i	$-0.175387\pi$
$131$	−470.086	−	814.213i	−0.0273927	−	0.0474455i	−0.879397	+	0.476090i	$0.842054\pi$
$132$		−	14091.4i		−	0.808736i
$133$	16893.4	+	14197.6i	0.955020	+	0.802622i
$134$	−4367.55			−0.243236
$135$	7720.75	−	4457.58i	0.423635	−	0.244586i
$136$	−1077.13	+	621.879i	−0.0582356	+	0.0336223i
$137$	−6477.43	+	11219.2i	−0.345113	+	0.597754i	−0.985374	−	0.170404i	$-0.945493\pi$
$137$	−6477.43	+	11219.2i	−0.345113	+	0.597754i	0.640261	+	0.768157i	$0.278826\pi$
$138$	3707.57	+	6421.70i	0.194684	+	0.337203i
$139$	1596.89	−	2765.89i	0.0826503	−	0.143154i	−0.821737	−	0.569867i	$-0.806995\pi$
$139$	1596.89	−	2765.89i	0.0826503	−	0.143154i	0.904388	+	0.426712i	$0.140328\pi$
$140$	15263.2			0.778736
$141$			29948.9i			1.50641i
$142$	11197.7	−	19394.9i	0.555330	−	0.961860i
$143$	−32923.3	−	19008.3i	−1.61002	−	0.929546i
$144$	−6534.94			−0.315150
$145$			30850.4i			1.46732i
$146$	2106.69	+	1216.30i	0.0988314	+	0.0570604i
$147$	−15651.6	+	9036.47i	−0.724310	+	0.418181i
$148$	−11657.5	−	6730.47i	−0.532209	−	0.307271i
$149$	−12167.1	−	21074.1i	−0.548045	−	0.949241i	−0.998408	−	0.0563960i	$-0.982039\pi$
$149$	−12167.1	−	21074.1i	−0.548045	−	0.949241i	0.450364	−	0.892845i	$-0.351294\pi$
$150$	−6682.06	−	11573.7i	−0.296980	−	0.514385i
$151$		−	10896.5i		−	0.477895i	−0.971032	−	0.238948i	$-0.923198\pi$
$151$		−	10896.5i		−	0.477895i	0.971032	−	0.238948i	$-0.0768024\pi$
$152$	−5255.47	+	6253.35i	−0.227470	+	0.270661i
$153$	−5612.58			−0.239762
$154$	19490.6	−	11252.9i	0.821832	−	0.474485i
$155$	38098.3	−	21996.1i	1.58578	−	0.915549i
$156$	−15808.0	+	27380.2i	−0.649572	+	1.12509i
$157$	−6370.70	−	11034.4i	−0.258457	−	0.447660i	0.707372	−	0.706842i	$-0.249881\pi$
$157$	−6370.70	−	11034.4i	−0.258457	−	0.447660i	−0.965829	+	0.259181i	$0.916547\pi$
$158$	−10578.6	+	18322.6i	−0.423753	+	0.733961i
$159$	31766.1			1.25652
$160$			5649.93i			0.220700i
$161$	−5921.45	+	10256.3i	−0.228442	+	0.395674i
$162$	10791.6	+	6230.53i	0.411202	+	0.237408i
$163$	5410.19			0.203628			0.101814	−	0.994803i	$-0.467535\pi$
$163$	5410.19			0.203628			0.101814	+	0.994803i	$0.467535\pi$
$164$			12807.7i			0.476194i
$165$	−47611.7	−	27488.6i	−1.74882	−	1.00968i
$166$	1541.47	−	889.969i	0.0559396	−	0.0322967i
$167$	−5776.01	−	3334.78i	−0.207107	−	0.119573i	0.392859	−	0.919599i	$-0.371486\pi$
$167$	−5776.01	−	3334.78i	−0.207107	−	0.119573i	−0.599966	+	0.800025i	$0.704819\pi$
$168$	−9358.30	−	16209.1i	−0.331573	−	0.574301i
$169$	28367.1	+	49133.3i	0.993212	+	1.72029i
$170$			4852.48i			0.167906i
$171$	−34647.9	+	12580.4i	−1.18491	+	0.430230i
$172$	−6849.08			−0.231513
$173$	4454.90	−	2572.04i	0.148849	−	0.0859379i	−0.423726	−	0.905791i	$-0.639278\pi$
$173$	4454.90	−	2572.04i	0.148849	−	0.0859379i	0.572575	+	0.819853i	$0.305945\pi$
$174$	32762.2	−	18915.3i	1.08212	−	0.624761i
$175$	10672.1	−	18484.6i	0.348476	−	0.603578i
$176$	4165.44	+	7214.75i	0.134473	+	0.232914i
$177$	−16050.1	+	27799.6i	−0.512308	+	0.887344i
$178$	7861.93			0.248136
$179$		−	48218.6i		−	1.50490i	−0.658647	−	0.752452i	$-0.728871\pi$
$179$		−	48218.6i		−	1.50490i	0.658647	−	0.752452i	$-0.271129\pi$
$180$	−12747.9	+	22080.1i	−0.393455	+	0.681484i
$181$	−17375.9	−	10032.0i	−0.530385	−	0.306218i	0.210788	−	0.977532i	$-0.432397\pi$
$181$	−17375.9	−	10032.0i	−0.530385	−	0.306218i	−0.741173	+	0.671314i	$0.765730\pi$
$182$	−50494.7			−1.52441
$183$		−	67377.7i		−	2.01194i
$184$	−3796.52	−	2191.92i	−0.112137	−	0.0647425i
$185$	−45481.4	+	26258.7i	−1.32890	+	0.767238i
$186$	−46718.2	−	26972.8i	−1.35039	−	0.779651i
$187$	3577.51	+	6196.44i	0.102305	+	0.177198i
$188$	−8852.94	−	15333.7i	−0.250479	−	0.433843i
$189$		−	17460.2i		−	0.488793i
$190$	10876.6	+	29955.6i	0.301292	+	0.829796i
$191$	8158.58			0.223639			0.111820	−	0.993729i	$-0.464332\pi$
$191$	8158.58			0.223639			0.111820	+	0.993729i	$0.464332\pi$
$192$	6000.05	−	3464.13i	0.162762	−	0.0939705i
$193$	59295.1	−	34234.0i	1.59186	−	0.919059i	0.598869	−	0.800847i	$-0.295617\pi$
$193$	59295.1	−	34234.0i	1.59186	−	0.919059i	0.992988	−	0.118212i	$-0.0377164\pi$
$194$	17424.6	−	30180.3i	0.462977	−	0.801899i
$195$	61674.4	+	106823.i	1.62194	+	2.80929i
$196$	5342.38	−	9253.27i	0.139066	−	0.240870i
$197$	2962.66			0.0763394			0.0381697	−	0.999271i	$-0.487847\pi$
$197$	2962.66			0.0763394			0.0381697	+	0.999271i	$0.487847\pi$
$198$			37593.9i			0.958930i
$199$	17370.4	−	30086.5i	0.438636	−	0.759740i	−0.558949	−	0.829202i	$-0.688795\pi$
$199$	17370.4	−	30086.5i	0.438636	−	0.759740i	0.997585	+	0.0694626i	$0.0221284\pi$
$200$	6842.37	+	3950.44i	0.171059	+	0.0987611i
$201$	20895.2			0.517195
$202$		−	34305.0i		−	0.840727i
$203$	52325.3	+	30210.0i	1.26975	+	0.733093i
$204$	5153.18	−	2975.19i	0.123827	−	0.0714915i
$205$	43274.3	+	24984.4i	1.02973	+	0.594514i
$206$	28700.2	+	49710.2i	0.676318	+	1.17142i
$207$	−9891.27	−	17132.2i	−0.230840	−	0.399827i
$208$		−	18691.4i		−	0.432032i
$209$	35974.0	+	30233.4i	0.823561	+	0.692141i
$210$	−73022.3			−1.65583
$211$	43647.5	−	25199.9i	0.980379	−	0.566022i	0.0779946	−	0.996954i	$-0.475148\pi$
$211$	43647.5	−	25199.9i	0.980379	−	0.566022i	0.902385	+	0.430932i	$0.141815\pi$
$212$	−16264.1	+	9390.10i	−0.361875	+	0.208929i
$213$	−53571.9	+	92789.3i	−1.18080	+	2.04521i
$214$	−13086.7	−	22666.8i	−0.285760	−	0.494952i
$215$	−13360.7	+	23141.5i	−0.289037	+	0.500627i
$216$	6463.17			0.138528
$217$		−	86157.8i		−	1.82968i
$218$	−18860.6	+	32667.5i	−0.396864	+	0.687389i
$219$	−10078.8	−	5819.01i	−0.210146	−	0.121328i
$220$	32502.6			0.671542
$221$		−	16053.3i		−	0.328684i
$222$	55771.9	+	32199.9i	1.13164	+	0.653354i
$223$	41419.3	−	23913.5i	0.832901	−	0.480875i	−0.0219441	−	0.999759i	$-0.506986\pi$
$223$	41419.3	−	23913.5i	0.832901	−	0.480875i	0.854845	+	0.518884i	$0.173652\pi$
$224$	9582.83	+	5532.65i	0.190984	+	0.110265i
$225$	17826.8	+	30876.9i	0.352134	+	0.609914i
$226$	14649.0	+	25372.9i	0.286809	+	0.496767i
$227$			10170.7i			0.197378i	0.995118	+	0.0986890i	$0.0314649\pi$
$227$			10170.7i			0.197378i	−0.995118	+	0.0986890i	$0.968535\pi$
$228$	25143.2	−	29917.3i	0.483672	−	0.575509i
$229$	−53760.3			−1.02516			−0.512579	−	0.858640i	$-0.671310\pi$
$229$	−53760.3			−1.02516			−0.512579	+	0.858640i	$0.671310\pi$
$230$	−14812.0	+	8551.72i	−0.280000	+	0.161658i
$231$	−93246.7	+	53836.0i	−1.74747	+	1.00890i
$232$	−11182.7	+	19369.1i	−0.207765	+	0.359859i
$233$	3153.22	+	5461.54i	0.0580822	+	0.100601i	0.893604	−	0.448855i	$-0.148168\pi$
$233$	3153.22	+	5461.54i	0.0580822	+	0.100601i	−0.835522	+	0.549457i	$0.814835\pi$
$234$	42173.4	−	73046.6i	0.770207	−	1.33404i
$235$	−69078.9			−1.25086
$236$		−	18977.7i		−	0.340737i
$237$	50609.9	−	87659.0i	0.901029	−	1.56063i
$238$	8230.27	+	4751.75i	0.145298	+	0.0838880i
$239$	−72360.8			−1.26680			−0.633399	−	0.773825i	$-0.718341\pi$
$239$	−72360.8			−1.26680			−0.633399	+	0.773825i	$0.718341\pi$
$240$		−	27030.4i		−	0.469278i
$241$	−60019.9	−	34652.5i	−1.03338	−	0.596623i	−0.115430	−	0.993316i	$-0.536825\pi$
$241$	−60019.9	−	34652.5i	−1.03338	−	0.596623i	−0.917952	+	0.396692i	$0.870158\pi$
$242$	5641.68	−	3257.23i	0.0963336	−	0.0556183i
$243$	−71665.8	−	41376.3i	−1.21367	−	0.700711i
$244$	19916.9	+	34497.1i	0.334536	+	0.579433i
$245$	−20843.1	−	36101.3i	−0.347241	−	0.601438i
$246$		−	61274.6i		−	1.01254i
$247$	−35982.7	−	99101.0i	−0.589793	−	1.62437i
$248$	31892.7			0.518547
$249$	−7374.70	+	4257.79i	−0.118945	+	0.0686729i
$250$	−21087.7	+	12175.0i	−0.337404	+	0.194800i
$251$	−19859.1	+	34397.0i	−0.315219	+	0.545975i	−0.979484	−	0.201522i	$-0.935411\pi$
$251$	−19859.1	+	34397.0i	−0.315219	+	0.545975i	0.664265	+	0.747497i	$0.268745\pi$
$252$	24966.6	+	43243.4i	0.393150	+	0.680956i
$253$	−12609.6	+	21840.4i	−0.196997	+	0.341209i
$254$	−56837.0			−0.880976
$255$		−	23215.2i		−	0.357020i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	69562.4	+	40161.8i	1.05319	+	0.608061i	0.923542	−	0.383498i	$-0.125281\pi$
$257$	69562.4	+	40161.8i	1.05319	+	0.608061i	0.129652	+	0.991560i	$0.458614\pi$
$258$	32767.4			0.492269
$259$			102855.i			1.53329i
$260$	−63154.0	−	36462.0i	−0.934231	−	0.539379i
$261$	−87404.8	+	50463.2i	−1.28308	+	0.740788i
$262$	−2302.94	−	1329.60i	−0.0335491	−	0.0193696i
$263$	−17122.9	−	29657.8i	−0.247552	−	0.428772i	0.715294	−	0.698823i	$-0.246293\pi$
$263$	−17122.9	−	29657.8i	−0.247552	−	0.428772i	−0.962846	+	0.270051i	$0.912959\pi$
$264$	−19928.3	−	34516.8i	−0.285931	−	0.495248i
$265$			73270.3i			1.04337i
$266$	61458.5	+	10886.0i	0.868598	+	0.153853i
$267$	−37613.0			−0.527613
$268$	−10698.3	+	6176.64i	−0.148951	+	0.0859969i
$269$	−46338.3	+	26753.4i	−0.640377	+	0.369722i	−0.784760	−	0.619800i	$-0.787214\pi$
$269$	−46338.3	+	26753.4i	−0.640377	+	0.369722i	0.144383	+	0.989522i	$0.453880\pi$
$270$	12607.9	−	21837.6i	0.172948	−	0.299555i
$271$	42893.0	+	74292.8i	0.584047	+	1.01160i	0.994994	+	0.0999396i	$0.0318650\pi$
$271$	42893.0	+	74292.8i	0.584047	+	1.01160i	−0.410947	+	0.911659i	$0.634802\pi$
$272$	−1758.94	+	3046.57i	−0.0237746	+	0.0411788i
$273$	241576.			3.24138
$274$			36641.9i			0.488064i
$275$	22725.9	−	39362.5i	0.300508	−	0.520495i
$276$	18163.3	+	10486.6i	0.238439	+	0.137663i
$277$	5684.12			0.0740805			0.0370402	−	0.999314i	$-0.488207\pi$
$277$	5684.12			0.0740805			0.0370402	+	0.999314i	$0.488207\pi$
$278$		−	9033.35i		−	0.116885i
$279$	124638.	+	71959.5i	1.60118	+	0.924443i
$280$	37387.1	−	21585.4i	0.476876	−	0.275325i
$281$	−62546.9	−	36111.4i	−0.792123	−	0.457333i	0.0485861	−	0.998819i	$-0.484528\pi$
$281$	−62546.9	−	36111.4i	−0.792123	−	0.457333i	−0.840710	+	0.541486i	$0.817862\pi$
$282$	42354.2	+	73359.6i	0.532597	+	0.922484i
$283$	−2472.15	−	4281.89i	−0.0308675	−	0.0534641i	0.850179	−	0.526494i	$-0.176494\pi$
$283$	−2472.15	−	4281.89i	−0.0308675	−	0.0534641i	−0.881046	+	0.473030i	$0.843160\pi$
$284$		−	63343.6i		−	0.785355i
$285$	−52035.9	−	143314.i	−0.640639	−	1.76440i
$286$	−107527.			−1.31458
$287$	84752.1	−	48931.6i	1.02893	−	0.594054i
$288$	−16007.3	+	9241.80i	−0.192989	+	0.111422i
$289$	40249.8	−	69714.7i	0.481913	−	0.834697i
$290$	43629.1	+	75567.8i	0.518776	+	0.898547i
$291$	−83362.7	+	144388.i	−0.984432	+	1.70509i
$292$	6880.42			0.0806955
$293$		−	80851.3i		−	0.941785i	−0.882191	−	0.470893i	$-0.843932\pi$
$293$		−	80851.3i		−	0.941785i	0.882191	−	0.470893i	$-0.156068\pi$
$294$	−25559.0	+	44269.5i	−0.295698	+	0.512165i
$295$	−64121.3	−	37020.5i	−0.736815	−	0.425400i
$296$	−38073.3			−0.434547
$297$		−	37181.0i		−	0.421510i
$298$	−59606.6	−	34413.9i	−0.671215	−	0.387526i
$299$	49001.9	−	28291.3i	0.548114	−	0.316454i
$300$	−32735.3	−	18899.7i	−0.363725	−	0.209997i
$301$	26166.8	+	45322.2i	0.288813	+	0.500240i
$302$	−15410.0	−	26690.8i	−0.168962	−	0.292650i
$303$			164122.i			1.78765i
$304$	−4029.64	+	22749.9i	−0.0436032	+	0.246168i
$305$	155410.			1.67063
$306$	−13748.0	+	7937.38i	−0.146823	+	0.0847685i
$307$	41898.8	−	24190.3i	0.444554	−	0.256664i	−0.260973	−	0.965346i	$-0.584043\pi$
$307$	41898.8	−	24190.3i	0.444554	−	0.256664i	0.705528	+	0.708682i	$0.250710\pi$
$308$	31827.9	−	55127.6i	0.335511	−	0.581123i
$309$	−137308.	−	237824.i	−1.43806	−	2.49080i
$310$	62214.2	−	107758.i	0.647391	−	1.12131i
$311$	−186768.			−1.93100			−0.965499	−	0.260408i	$-0.916143\pi$
$311$	−186768.			−1.93100			−0.965499	+	0.260408i	$0.916143\pi$
$312$			89423.5i			0.918634i
$313$	−48058.2	+	83239.3i	−0.490545	+	0.849650i	−0.999941	−	0.0108830i	$-0.996536\pi$
$313$	−48058.2	+	83239.3i	−0.490545	+	0.849650i	0.509395	+	0.860533i	$0.329869\pi$
$314$	−31209.9	−	18019.1i	−0.316544	−	0.182757i
$315$	194813.			1.96335
$316$			59841.4i			0.599277i
$317$	168238.	+	97132.1i	1.67419	+	0.966595i	0.965251	+	0.261326i	$0.0841598\pi$
$317$	168238.	+	97132.1i	1.67419	+	0.966595i	0.708940	+	0.705268i	$0.249174\pi$
$318$	77810.8	−	44924.1i	0.769459	−	0.444248i
$319$	111425.	+	64331.5i	1.09497	+	0.632182i
$320$	7990.21	+	13839.4i	0.0780294	+	0.135151i
$321$	62609.3	+	108443.i	0.607615	+	1.05242i
$322$			33496.8i			0.323066i
$323$	−3460.88	+	19538.9i	−0.0331728	+	0.187281i
$324$	35245.2			0.335745
$325$	−88314.9	+	50988.6i	−0.836118	+	0.482733i
$326$	13252.2	−	7651.17i	0.124696	−	0.0719934i
$327$	90232.7	−	156288.i	0.843856	−	1.46160i
$328$	18112.8	+	31372.4i	0.168360	+	0.291608i
$329$	−67645.0	+	117164.i	−0.624948	+	1.08244i
$330$	−155499.			−1.42791
$331$		−	27030.5i		−	0.246717i	−0.992362	−	0.123358i	$-0.960634\pi$
$331$		−	27030.5i		−	0.246717i	0.992362	−	0.123358i	$-0.0393664\pi$
$332$	2517.21	−	4359.94i	0.0228372	−	0.0395552i
$333$	−148791.	−	85904.7i	−1.34180	−	0.774691i
$334$	−18864.4			−0.169102
$335$			48196.0i			0.429458i
$336$	−45846.1	−	26469.3i	−0.406092	−	0.234457i
$337$	−23678.7	+	13670.9i	−0.208496	+	0.120375i	−0.600612	−	0.799540i	$-0.705076\pi$
$337$	−23678.7	+	13670.9i	−0.208496	+	0.120375i	0.392116	+	0.919916i	$0.371743\pi$
$338$	138970.	+	80234.4i	1.21643	+	0.702307i
$339$	−70083.9	−	121389.i	−0.609844	−	1.05628i
$340$	6862.44	+	11886.1i	0.0593637	+	0.102821i
$341$		−	183471.i		−	1.57782i
$342$	−67078.5	+	79815.0i	−0.573497	+	0.682390i
$343$	65125.8			0.553560
$344$	−16776.8	+	9686.07i	−0.141772	+	0.0818522i
$345$	70863.6	−	40913.1i	0.595367	−	0.343736i
$346$	7274.82	−	12600.4i	0.0607673	−	0.105252i
$347$	10130.9	+	17547.3i	0.0841377	+	0.145731i	0.905023	−	0.425362i	$-0.139853\pi$
$347$	10130.9	+	17547.3i	0.0841377	+	0.145731i	−0.820886	+	0.571092i	$0.806520\pi$
$348$	53500.4	−	92665.5i	0.441773	−	0.765173i
$349$	6241.93			0.0512470			0.0256235	−	0.999672i	$-0.491843\pi$
$349$	6241.93			0.0512470			0.0256235	+	0.999672i	$0.491843\pi$
$350$		−	60370.4i		−	0.492820i
$351$	−41710.3	+	72244.3i	−0.338555	+	0.586394i
$352$	20406.4	+	11781.6i	0.164695	+	0.0950868i
$353$	−93892.4			−0.753496			−0.376748	−	0.926316i	$-0.622958\pi$
$353$	−93892.4			−0.753496			−0.376748	+	0.926316i	$0.622958\pi$
$354$			90793.1i			0.724513i
$355$	−214024.	−	123567.i	−1.69826	−	0.980493i
$356$	19257.7	−	11118.4i	0.151951	−	0.0877292i
$357$	−39375.3	−	22733.3i	−0.308949	−	0.178372i
$358$	−68191.4	−	118111.i	−0.532064	−	0.921562i
$359$	55244.0	+	95685.4i	0.428644	+	0.742432i	0.996753	−	0.0805207i	$-0.0256583\pi$
$359$	55244.0	+	95685.4i	0.428644	+	0.742432i	−0.568109	+	0.822953i	$0.692325\pi$
$360$			72113.2i			0.556429i
$361$	22430.6	+	128376.i	0.172118	+	0.985076i
$362$	−56749.6			−0.433057
$363$	−26990.9	+	15583.2i	−0.204835	+	0.118262i
$364$	−123686.	+	71410.2i	−0.933508	+	0.538961i
$365$	13421.9	−	23247.4i	0.100746	−	0.174497i
$366$	−95286.5	−	165041.i	−0.711327	−	1.23205i
$367$	39424.4	−	68285.1i	0.292707	−	0.506984i	−0.681742	−	0.731593i	$-0.738777\pi$
$367$	39424.4	−	68285.1i	0.292707	−	0.506984i	0.974449	+	0.224609i	$0.0721106\pi$
$368$	−12399.4			−0.0915598
$369$			163472.i			1.20058i
$370$	−74270.9	+	128641.i	−0.542519	+	0.939671i
$371$	124274.	+	71749.4i	0.902882	+	0.521279i
$372$	−152581.			−1.10259
$373$			14398.0i			0.103486i	0.998660	+	0.0517432i	$0.0164777\pi$
$373$			14398.0i			0.103486i	−0.998660	+	0.0517432i	$0.983522\pi$
$374$	17526.2	+	10118.7i	0.125298	+	0.0723408i
$375$	100888.	−	58247.7i	0.717425	−	0.414206i
$376$	−43370.4	−	25039.9i	−0.306773	−	0.177116i
$377$	−144336.	−	249998.i	−1.01553	−	1.75895i
$378$	−24692.4	−	42768.5i	−0.172814	−	0.299323i
$379$			40098.1i			0.279155i	0.990211	+	0.139577i	$0.0445744\pi$
$379$			40098.1i			0.279155i	−0.990211	+	0.139577i	$0.955426\pi$
$380$	69005.9	+	57994.2i	0.477880	+	0.401622i
$381$	271920.			1.87323
$382$	19984.4	−	11538.0i	0.136950	−	0.0790684i
$383$	−77195.6	+	44568.9i	−0.526253	+	0.303833i	−0.739489	−	0.673168i	$-0.764933\pi$
$383$	−77195.6	+	44568.9i	−0.526253	+	0.303833i	0.213236	+	0.977001i	$0.431600\pi$
$384$	9798.04	−	16970.7i	0.0664472	−	0.115090i
$385$	−124176.	−	215079.i	−0.837752	−	1.45103i
$386$	96828.5	−	167712.i	0.649873	−	1.12561i
$387$	−87418.7			−0.583690
$388$		−	98568.3i		−	0.654748i
$389$	−39465.0	+	68355.4i	−0.260803	+	0.451724i	−0.966456	−	0.256834i	$-0.917321\pi$
$389$	−39465.0	+	68355.4i	−0.260803	+	0.451724i	0.705652	+	0.708558i	$0.250654\pi$
$390$	302141.	+	174441.i	1.98647	+	1.14689i
$391$	−10649.3			−0.0696574
$392$		−	30221.1i		−	0.196670i
$393$	11017.7	+	6361.09i	0.0713357	+	0.0411857i
$394$	7256.99	−	4189.83i	0.0467481	−	0.0269901i
$395$	202190.	+	116735.i	1.29588	+	0.748179i
$396$	53165.8	+	92085.9i	0.339033	+	0.587222i
$397$	74599.2	+	129210.i	0.473318	+	0.819811i	0.999534	−	0.0305403i	$-0.00972278\pi$
$397$	74599.2	+	129210.i	0.473318	+	0.819811i	−0.526215	+	0.850351i	$0.676389\pi$
$398$		−	98261.9i		−	0.620325i
$399$	−294030.	−	52080.9i	−1.84691	−	0.327139i
$400$	22347.1			0.139669
$401$	2615.21	−	1509.89i	0.0162636	−	0.00938980i	−0.491846	−	0.870682i	$-0.663678\pi$
$401$	2615.21	−	1509.89i	0.0162636	−	0.00938980i	0.508110	+	0.861292i	$0.330344\pi$
$402$	51182.6	−	29550.3i	0.316716	−	0.182856i
$403$	−205821.	+	356492.i	−1.26730	+	2.19503i
$404$	−48514.6	−	84029.8i	−0.297242	−	0.514838i
$405$	68754.0	−	119085.i	0.419168	−	0.726020i
$406$	170894.			1.03675
$407$			219026.i			1.32223i
$408$	8415.11	−	14575.4i	0.0505521	−	0.0875589i
$409$	−16103.8	−	9297.50i	−0.0962677	−	0.0555802i	0.451093	−	0.892477i	$-0.351034\pi$
$409$	−16103.8	−	9297.50i	−0.0962677	−	0.0555802i	−0.547361	+	0.836897i	$0.684368\pi$
$410$	141333.			0.840770
$411$		−	175302.i		−	1.03778i
$412$	140602.	+	81176.5i	0.828317	+	0.478229i
$413$	−125581.	+	72504.0i	−0.736245	+	0.425071i
$414$	−48457.1	−	27976.7i	−0.282720	−	0.163229i
$415$	−9820.82	−	17010.2i	−0.0570232	−	0.0987671i
$416$	−26433.7	−	45784.5i	−0.152746	−	0.264564i
$417$			43217.3i			0.248534i
$418$	130874.	+	23181.5i	0.749035	+	0.132675i
$419$	84423.4			0.480878			0.240439	−	0.970664i	$-0.422709\pi$
$419$	84423.4			0.480878			0.240439	+	0.970664i	$0.422709\pi$
$420$	−178867.	+	103269.i	−1.01399	+	0.585426i
$421$	−91985.6	+	53107.9i	−0.518986	+	0.299637i	−0.736520	−	0.676416i	$-0.763532\pi$
$421$	−91985.6	+	53107.9i	−0.518986	+	0.299637i	0.217534	+	0.976053i	$0.430199\pi$
$422$	71276.0	−	123454.i	0.400238	−	0.693233i
$423$	−112995.	−	195713.i	−0.631507	−	1.09380i
$424$	−26559.2	+	46001.9i	−0.147735	+	0.255885i
$425$	19193.0			0.106259
$426$			303048.i			1.66991i
$427$	152184.	−	263591.i	0.834669	−	1.44569i
$428$	−64111.4	−	37014.7i	−0.349984	−	0.202063i
$429$	514431.			2.79520
$430$			75579.8i			0.408760i
$431$	−93550.3	−	54011.3i	−0.503606	−	0.290757i	0.226596	−	0.973989i	$-0.427240\pi$
$431$	−93550.3	−	54011.3i	−0.503606	−	0.290757i	−0.730201	+	0.683232i	$0.760574\pi$
$432$	15831.5	−	9140.30i	0.0848308	−	0.0489771i
$433$	120901.	+	69802.0i	0.644841	+	0.372299i	0.786477	−	0.617620i	$-0.211903\pi$
$433$	120901.	+	69802.0i	0.644841	+	0.372299i	−0.141636	+	0.989919i	$0.545236\pi$
$434$	−121846.	−	211043.i	−0.646890	−	1.12045i
$435$	−208730.	−	361531.i	−1.10308	−	1.91059i
$436$			106691.i			0.561250i
$437$	−65740.9	+	23869.9i	−0.344249	+	0.124994i
$438$	−32917.3			−0.171584
$439$	−288739.	+	166703.i	−1.49822	+	0.864999i	−0.999998	−	0.00204890i	$-0.999348\pi$
$439$	−288739.	+	166703.i	−1.49822	+	0.864999i	−0.498225	+	0.867048i	$0.666014\pi$
$440$	79614.9	−	45965.7i	0.411234	−	0.237426i
$441$	68187.7	−	118105.i	0.350614	−	0.607281i
$442$	−22702.7	−	39322.3i	−0.116207	−	0.201277i
$443$	−69224.5	+	119900.i	−0.352738	+	0.610960i	−0.986728	−	0.162381i	$-0.948083\pi$
$443$	−69224.5	+	119900.i	−0.352738	+	0.610960i	0.633990	+	0.773341i	$0.281416\pi$
$444$	182150.			0.923982
$445$		−	86756.6i		−	0.438109i
$446$	67637.5	−	117152.i	0.340030	−	0.588950i
$447$	285170.	+	164643.i	1.42721	+	0.824001i
$448$	31297.4			0.155938
$449$		−	108309.i		−	0.537245i	−0.963245	−	0.268623i	$-0.913432\pi$
$449$		−	108309.i		−	0.537245i	0.963245	−	0.268623i	$-0.0865685\pi$
$450$	87333.0	+	50421.7i	0.431274	+	0.248996i
$451$	180477.	−	104199.i	0.887299	−	0.512282i
$452$	71765.3	+	41433.7i	0.351267	+	0.202804i
$453$	73724.3	+	127694.i	0.359265	+	0.622265i
$454$	14383.5	+	24913.0i	0.0697837	+	0.120869i
$455$			557210.i			2.69151i
$456$	19278.6	−	108840.i	0.0927140	−	0.523430i
$457$	176180.			0.843578			0.421789	−	0.906694i	$-0.361402\pi$
$457$	176180.			0.843578			0.421789	+	0.906694i	$0.361402\pi$
$458$	−131685.	+	76028.6i	−0.627779	+	0.362448i
$459$	13597.0	−	7850.21i	0.0645382	−	0.0372611i
$460$	−24187.9	+	41894.7i	−0.114310	+	0.197990i
$461$	−168037.	−	291049.i	−0.790685	−	1.36951i	−0.925544	−	0.378641i	$-0.876391\pi$
$461$	−168037.	−	291049.i	−0.790685	−	1.36951i	0.134859	−	0.990865i	$-0.456942\pi$
$462$	−152271.	+	263741.i	−0.713401	+	1.23565i
$463$	−86990.1			−0.405796			−0.202898	−	0.979200i	$-0.565036\pi$
$463$	−86990.1			−0.405796			−0.202898	+	0.979200i	$0.565036\pi$
$464$			63259.1i			0.293824i
$465$	−297645.	+	515537.i	−1.37655	+	2.38426i
$466$	15447.6	+	8918.66i	0.0711358	+	0.0410703i
$467$	−212435.			−0.974074			−0.487037	−	0.873381i	$-0.661922\pi$
$467$	−212435.			−0.974074			−0.487037	+	0.873381i	$0.661922\pi$
$468$		−	238569.i		−	1.08924i
$469$	81745.0	+	47195.5i	0.371634	+	0.214563i
$470$	−169208.	+	97692.3i	−0.765994	+	0.442247i
$471$	149315.	+	86206.8i	0.673070	+	0.388597i
$472$	−26838.5	−	46485.7i	−0.120469	−	0.208658i
$473$	55721.5	+	96512.5i	0.249058	+	0.431381i
$474$		−	286293.i		−	1.27425i
$475$	118483.	−	43020.2i	0.525133	−	0.190671i
$476$	26880.0			0.118636
$477$	−207588.	+	119851.i	−0.912359	+	0.526751i
$478$	−177247.	+	102334.i	−0.775752	+	0.447881i
$479$	153890.	−	266545.i	0.670717	−	1.16172i	−0.306984	−	0.951715i	$-0.599320\pi$
$479$	153890.	−	266545.i	0.670717	−	1.16172i	0.977701	−	0.210002i	$-0.0673470\pi$
$480$	−38226.7	−	66210.7i	−0.165915	−	0.287373i
$481$	245707.	−	425577.i	1.06201	−	1.83945i
$482$	−196024.			−0.843753
$483$		−	160255.i		−	0.686939i
$484$	9212.83	−	15957.1i	0.0393280	−	0.0681182i
$485$	−333040.	−	192281.i	−1.41584	−	0.817433i
$486$	−234060.			−0.990955
$487$		−	275108.i		−	1.15996i	−0.814629	−	0.579982i	$-0.803059\pi$
$487$		−	275108.i		−	1.15996i	0.814629	−	0.579982i	$-0.196941\pi$
$488$	97572.6	+	56333.6i	0.409721	+	0.236552i
$489$	−63401.2	+	36604.7i	−0.265143	+	0.153080i
$490$	−102110.	−	58953.2i	−0.425281	−	0.245536i
$491$	236932.	+	410379.i	0.982792	+	1.70225i	0.651365	+	0.758764i	$0.274197\pi$
$491$	236932.	+	410379.i	0.982792	+	1.70225i	0.331427	+	0.943481i	$0.392470\pi$
$492$	−86655.4	−	150092.i	−0.357986	−	0.620049i
$493$			54330.5i			0.223537i
$494$	−228289.	−	191860.i	−0.935473	−	0.786194i
$495$	414849.			1.69309
$496$	78120.9	−	45103.1i	0.317544	−	0.183334i
$497$	−419162.	+	242003.i	−1.69695	+	0.979734i
$498$	−12042.8	+	20858.8i	−0.0485590	+	0.0841067i
$499$	−29927.0	−	51835.0i	−0.120188	−	0.208172i	0.799654	−	0.600462i	$-0.205016\pi$
$499$	−29927.0	−	51835.0i	−0.120188	−	0.208172i	−0.919842	+	0.392290i	$0.871683\pi$
$500$	−34436.1	+	59645.1i	−0.137745	+	0.238581i
$501$	90250.8			0.359564
$502$			112340.i			0.445787i
$503$	183801.	−	318352.i	0.726460	−	1.25826i	−0.231911	−	0.972737i	$-0.574498\pi$
$503$	183801.	−	318352.i	0.726460	−	1.25826i	0.958370	−	0.285528i	$-0.0921689\pi$
$504$	122311.	+	70616.2i	0.481509	+	0.277999i
$505$	−378557.			−1.48439
$506$			71330.6i			0.278596i
$507$	−664860.	−	383857.i	−2.58651	−	1.49332i
$508$	−139222.	+	80379.7i	−0.539485	+	0.311472i
$509$	191568.	+	110602.i	0.739415	+	0.426901i	0.821857	−	0.569694i	$-0.192938\pi$
$509$	191568.	+	110602.i	0.739415	+	0.426901i	−0.0824416	+	0.996596i	$0.526272\pi$
$510$	−32831.3	−	56865.5i	−0.126226	−	0.218629i
$511$	−26286.5	−	45529.6i	−0.100668	−	0.174362i
$512$			11585.2i			0.0441942i
$513$	66341.7	−	78938.4i	0.252088	−	0.299953i
$514$	227190.			0.859929
$515$	548554.	−	316708.i	2.06826	−	1.19411i
$516$	80263.3	−	46340.1i	0.301452	−	0.174043i
$517$	−144048.	+	249499.i	−0.538923	+	0.933443i
$518$	145458.	+	251941.i	0.542099	+	0.938944i
$519$	−34804.2	+	60282.6i	−0.129210	+	0.223799i
$520$	−206260.			−0.762797
$521$		−	537023.i		−	1.97841i	−0.146524	−	0.989207i	$-0.546809\pi$
$521$		−	537023.i		−	1.97841i	0.146524	−	0.989207i	$-0.453191\pi$
$522$	−142732.	+	247218.i	−0.523816	+	0.907276i
$523$	−35036.1	−	20228.1i	−0.128089	−	0.0739523i	0.434586	−	0.900630i	$-0.356895\pi$
$523$	−35036.1	−	20228.1i	−0.128089	−	0.0739523i	−0.562675	+	0.826678i	$0.690228\pi$
$524$	−7521.37			−0.0273927
$525$			288824.i			1.04789i
$526$	−83884.8	−	48430.9i	−0.303188	−	0.175046i
$527$	67094.7	−	38737.1i	0.241583	−	0.139478i
$528$	−97628.2	−	56365.7i	−0.350193	−	0.202184i
$529$	121153.	+	209843.i	0.432934	+	0.749865i
$530$	103620.	+	179475.i	0.368885	+	0.638928i
$531$		−	242223.i		−	0.859066i
$532$	165937.	−	60250.3i	0.586301	−	0.212880i
$533$	−467567.			−1.64585
$534$	−92132.7	+	53192.9i	−0.323096	+	0.186540i
$535$	−250129.	+	144412.i	−0.873888	+	0.504540i
$536$	−17470.2	+	30259.3i	−0.0608090	+	0.105324i
$537$	326241.	+	565067.i	1.13133	+	1.95953i
$538$	−75670.2	+	131065.i	−0.261433	+	0.452815i
$539$	−173854.			−0.598422
$540$		−	71321.2i		−	0.244586i
$541$	−69891.5	+	121056.i	−0.238798	+	0.413610i	−0.960370	−	0.278730i	$-0.910087\pi$
$541$	−69891.5	+	121056.i	−0.238798	+	0.413610i	0.721572	+	0.692339i	$0.243420\pi$
$542$	210132.	+	121320.i	0.715309	+	0.412984i
$543$	271501.			0.920814
$544$			9950.06i			0.0336223i
$545$	360486.	+	208127.i	1.21366	+	0.700704i
$546$	591739.	−	341641.i	1.98493	−	1.14600i
$547$	105235.	+	60757.5i	0.351711	+	0.203060i	0.665439	−	0.746453i	$-0.268245\pi$
$547$	105235.	+	60757.5i	0.351711	+	0.203060i	−0.313728	+	0.949513i	$0.601578\pi$
$548$	51819.4	+	89753.9i	0.172557	+	0.298877i
$549$	254211.	+	440306.i	0.843430	+	1.46086i
$550$		−	128557.i		−	0.424983i
$551$	121780.	+	335397.i	0.401117	+	1.10473i
$552$	59321.1			0.194684
$553$	395986.	−	228623.i	1.29488	−	0.747600i
$554$	13923.2	−	8038.56i	0.0453648	−	0.0261914i
$555$	355327.	−	615444.i	1.15356	−	1.99803i
$556$	−12775.1	−	22127.1i	−0.0413251	−	0.0715772i
$557$	4738.98	−	8208.16i	0.0152748	−	0.0264567i	−0.858287	−	0.513170i	$-0.828471\pi$
$557$	4738.98	−	8208.16i	0.0152748	−	0.0264567i	0.873562	+	0.486713i	$0.161804\pi$
$558$	407065.			1.30736
$559$		−	250037.i		−	0.800168i
$560$	61052.9	−	105747.i	0.194684	−	0.337202i
$561$	−83848.7	−	48410.1i	−0.266422	−	0.153819i
$562$	−204277.			−0.646766
$563$			229461.i			0.723921i	0.932193	+	0.361961i	$0.117893\pi$
$563$			229461.i			0.723921i	−0.932193	+	0.361961i	$0.882107\pi$
$564$	207492.	+	119796.i	0.652295	+	0.376603i
$565$	279990.	−	161652.i	0.877093	−	0.506390i
$566$	−12111.0	−	6992.29i	−0.0378048	−	0.0218266i
$567$	−134654.	−	233227.i	−0.418843	−	0.725458i
$568$	−89581.4	−	155160.i	−0.277665	−	0.480930i
$569$			359455.i			1.11025i	0.831768	+	0.555123i	$0.187329\pi$
$569$			359455.i			1.11025i	−0.831768	+	0.555123i	$0.812671\pi$
$570$	−330138.	−	277456.i	−1.01612	−	0.853973i
$571$	−173264.			−0.531417			−0.265708	−	0.964053i	$-0.585606\pi$
$571$	−173264.			−0.531417			−0.265708	+	0.964053i	$0.585606\pi$
$572$	−263387.	+	152066.i	−0.805011	+	0.464773i
$573$	−95609.1	+	55200.0i	−0.291199	+	0.168124i
$574$	138400.	−	239715.i	0.420060	−	0.727564i
$575$	33824.5	+	58585.7i	0.102305	+	0.177197i
$576$	−26139.8	+	45275.4i	−0.0787874	+	0.136464i
$577$	−8989.74			−0.0270020			−0.0135010	−	0.999909i	$-0.504298\pi$
$577$	−8989.74			−0.0270020			−0.0135010	+	0.999909i	$0.504298\pi$
$578$		−	227687.i		−	0.681527i
$579$	−463247.	+	802367.i	−1.38183	+	2.39340i
$580$	213738.	+	123402.i	0.635369	+	0.366830i
$581$	−38467.8			−0.113958
$582$			471570.i			1.39220i
$583$	264638.	+	152789.i	0.778600	+	0.449525i
$584$	16853.5	−	9730.39i	0.0494157	−	0.0285302i
$585$	−806070.	−	465385.i	−2.35538	−	1.35988i
$586$	−114341.	−	198044.i	−0.332971	−	0.576723i
$587$	−130557.	−	226131.i	−0.378899	−	0.656272i	0.612004	−	0.790855i	$-0.290364\pi$
$587$	−130557.	−	226131.i	−0.378899	−	0.656272i	−0.990902	+	0.134583i	$0.957030\pi$
$588$			144584.i			0.418181i
$589$	327366.	−	389524.i	0.943632	−	1.12280i
$590$	−209419.			−0.601607
$591$	−34718.9	+	20045.0i	−0.0994011	+	0.0573892i
$592$	−93260.1	+	53843.8i	−0.266105	+	0.153636i
$593$	61040.0	−	105724.i	0.173582	−	0.300653i	−0.766088	−	0.642736i	$-0.777799\pi$
$593$	61040.0	−	105724.i	0.173582	−	0.300653i	0.939670	+	0.342083i	$0.111132\pi$
$594$	−52581.9	−	91074.5i	−0.149026	−	0.258121i
$595$	52435.7	−	90821.2i	0.148113	−	0.256539i
$596$	−194674.			−0.548045
$597$			470105.i			1.31900i
$598$	80019.8	−	138598.i	0.223767	−	0.387575i
$599$	178506.	+	103061.i	0.497508	+	0.287236i	0.727684	−	0.685913i	$-0.240597\pi$
$599$	178506.	+	103061.i	0.497508	+	0.287236i	−0.230176	+	0.973149i	$0.573930\pi$
$600$	−106913.			−0.296980
$601$		−	212842.i		−	0.589262i	−0.955611	−	0.294631i	$-0.904803\pi$
$601$		−	212842.i		−	0.589262i	0.955611	−	0.294631i	$-0.0951967\pi$
$602$	128191.	+	74010.9i	0.353723	+	0.204222i
$603$	−136548.	+	78836.0i	−0.375535	+	0.216815i
$604$	−75493.1	−	43586.0i	−0.206935	−	0.119474i
$605$	−35943.6	−	62256.1i	−0.0981998	−	0.170087i
$606$	232104.	+	402015.i	0.632028	+	1.09471i
$607$		−	402247.i		−	1.09173i	−0.837873	−	0.545865i	$-0.816201\pi$
$607$		−	402247.i		−	1.09173i	0.837873	−	0.545865i	$-0.183799\pi$
$608$	22302.6	+	61424.4i	0.0603322	+	0.166163i
$609$	−817590.			−2.20445
$610$	380676.	−	219784.i	1.02305	−	0.590657i
$611$	559784.	−	323191.i	1.49947	−	0.865720i
$612$	−22450.3	+	38885.1i	−0.0599404	+	0.103820i
$613$	−55742.6	−	96549.0i	−0.148343	−	0.256937i	0.782272	−	0.622937i	$-0.214061\pi$
$613$	−55742.6	−	96549.0i	−0.148343	−	0.256937i	−0.930615	+	0.366000i	$0.880727\pi$
$614$	68420.5	−	118508.i	0.181489	−	0.314347i
$615$	−676167.			−1.78774
$616$		−	180046.i		−	0.474485i
$617$	223001.	−	386249.i	0.585783	−	1.01461i	−0.408995	−	0.912537i	$-0.634121\pi$
$617$	223001.	−	386249.i	0.585783	−	1.01461i	0.994777	−	0.102068i	$-0.0325461\pi$
$618$	−672667.	−	388364.i	−1.76126	−	1.01686i
$619$	205626.			0.536657			0.268329	−	0.963327i	$-0.413529\pi$
$619$	205626.			0.536657			0.268329	+	0.963327i	$0.413529\pi$
$620$		−	351937.i		−	0.915549i
$621$	47924.9	+	27669.5i	0.124273	+	0.0717493i
$622$	−457486.	+	264130.i	−1.18249	+	0.682711i
$623$	−147147.	−	84955.6i	−0.379120	−	0.218885i
$624$	126464.	+	219042.i	0.324786	+	0.562546i
$625$	243468.	+	421699.i	0.623278	+	1.07955i
$626$			271858.i			0.693736i
$627$	−626129.	−	110905.i	−1.59268	−	0.282108i
$628$	−101931.			−0.258457
$629$	−80097.1	+	46244.1i	−0.202449	+	0.116884i
$630$	477192.	−	275507.i	1.20230	−	0.694147i
$631$	−34645.1	+	60007.1i	−0.0870128	+	0.150711i	−0.906247	−	0.422748i	$-0.861065\pi$
$631$	−34645.1	+	60007.1i	−0.0870128	+	0.150711i	0.819234	+	0.573459i	$0.194399\pi$
$632$	84628.5	+	146581.i	0.211876	+	0.366980i
$633$	−340999.	+	590627.i	−0.851031	+	1.47403i
$634$	549462.			1.36697
$635$			627198.i			1.55545i
$636$	127065.	−	220082.i	0.314130	−	0.544090i
$637$	337806.	+	195033.i	0.832509	+	0.480649i
$638$	363914.			0.894041
$639$		−	808490.i		−	1.98004i
$640$	39143.9	+	22599.7i	0.0955661	+	0.0551751i
$641$	5876.16	−	3392.60i	0.0143014	−	0.00825689i	−0.492832	−	0.870124i	$-0.664038\pi$
$641$	5876.16	−	3392.60i	0.0143014	−	0.00825689i	0.507134	+	0.861867i	$0.330705\pi$
$642$	306722.	+	177086.i	0.744174	+	0.429649i
$643$	123257.	+	213487.i	0.298119	+	0.516357i	0.975706	−	0.219086i	$-0.0703075\pi$
$643$	123257.	+	213487.i	0.298119	+	0.516357i	−0.677587	+	0.735443i	$0.736974\pi$
$644$	47371.6	+	82050.1i	0.114221	+	0.197837i
$645$		−	361589.i		−	0.869151i
$646$	19154.8	+	52754.7i	0.0458999	+	0.126414i
$647$	−738254.			−1.76359			−0.881794	−	0.471635i	$-0.843664\pi$
$647$	−738254.			−1.76359			−0.881794	+	0.471635i	$0.843664\pi$
$648$	86332.7	−	49844.2i	0.205601	−	0.118704i
$649$	−267421.	+	154395.i	−0.634900	+	0.366560i
$650$	−144218.	+	249792.i	−0.341344	+	0.591224i
$651$	582933.	+	1.00967e6i	1.37549	+	2.38242i
$652$	21640.8	−	37482.9i	0.0509070	−	0.0881735i
$653$	−123958.			−0.290701			−0.145351	−	0.989380i	$-0.546431\pi$
$653$	−123958.			−0.290701			−0.145351	+	0.989380i	$0.546431\pi$
$654$		−	510433.i		−	1.19339i
$655$	−14672.2	+	25413.0i	−0.0341989	+	0.0592343i
$656$	88734.4	+	51230.9i	0.206198	+	0.119049i
$657$	87818.7			0.203449
$658$			382658.i			0.883809i
$659$	−198891.	−	114830.i	−0.457977	−	0.264413i	0.253216	−	0.967410i	$-0.418512\pi$
$659$	−198891.	−	114830.i	−0.457977	−	0.264413i	−0.711193	+	0.702996i	$0.751845\pi$
$660$	−380893.	+	219909.i	−0.874411	+	0.504842i
$661$	63898.7	+	36891.9i	0.146248	+	0.0844362i	0.571338	−	0.820715i	$-0.306424\pi$
$661$	63898.7	+	36891.9i	0.146248	+	0.0844362i	−0.425091	+	0.905151i	$0.639758\pi$
$662$	−38226.9	−	66211.0i	−0.0872275	−	0.151082i
$663$	108614.	+	188126.i	0.247093	+	0.427978i
$664$		−	14239.5i		−	0.0322967i
$665$	120127.	−	678196.i	0.271643	−	1.53360i
$666$	−485951.			−1.09558
$667$	−165842.	+	95748.8i	−0.372771	+	0.215220i
$668$	−46208.1	+	26678.2i	−0.103554	+	0.0597866i
$669$	−323591.	+	560476.i	−0.723010	+	1.25229i
$670$	68159.4	+	118056.i	0.151836	+	0.262988i
$671$	324073.	−	561311.i	0.719777	−	1.24669i
$672$	−149733.			−0.331573
$673$		−	857144.i		−	1.89245i	−0.323515	−	0.946223i	$-0.604864\pi$
$673$		−	857144.i		−	1.89245i	0.323515	−	0.946223i	$-0.395136\pi$
$674$	−38667.2	+	66973.5i	−0.0851182	+	0.147429i
$675$	−86373.8	−	49868.0i	−0.189572	−	0.109450i
$676$	453874.			0.993212
$677$			395500.i			0.862918i	0.902133	+	0.431459i	$0.142001\pi$
$677$			395500.i			0.862918i	−0.902133	+	0.431459i	$0.857999\pi$
$678$	−343339.	−	198227.i	−0.746903	−	0.431225i
$679$	−652253.	+	376578.i	−1.41474	+	0.816800i
$680$	33619.0	+	19409.9i	0.0727054	+	0.0419765i
$681$	−68813.7	−	119189.i	−0.148382	−	0.257005i
$682$	−259467.	−	449410.i	−0.557845	−	0.966216i
$683$			187801.i			0.402585i	0.979531	+	0.201292i	$0.0645141\pi$
$683$			187801.i			0.402585i	−0.979531	+	0.201292i	$0.935486\pi$
$684$	−51432.5	+	290369.i	−0.109932	+	0.620638i
$685$	404344.			0.861727
$686$	159525.	−	92101.8i	0.338985	−	0.195713i
$687$	630009.	−	363736.i	1.33485	−	0.770678i
$688$	−27396.3	+	47451.8i	−0.0578783	+	0.100248i
$689$	−342801.	−	593749.i	−0.722111	−	1.25073i
$690$	115720.	−	200433.i	0.243058	−	0.420988i
$691$	703371.			1.47309			0.736543	−	0.676391i	$-0.236457\pi$
$691$	703371.			1.47309			0.736543	+	0.676391i	$0.236457\pi$
$692$		−	41152.6i		−	0.0859379i
$693$	406238.	−	703624.i	0.845890	−	1.46512i
$694$	49631.3	+	28654.6i	0.103047	+	0.0594943i
$695$	−99683.2			−0.206373
$696$		−	302644.i		−	0.624761i
$697$	76210.2	+	44000.0i	0.156873	+	0.0905705i
$698$	15289.5	−	8827.42i	0.0313822	−	0.0181185i
$699$	−73904.3	−	42668.7i	−0.151257	−	0.0873282i
$700$	−85376.6	−	147877.i	−0.174238	−	0.301789i
$701$	−241585.	−	418438.i	−0.491626	−	0.851521i	0.508328	−	0.861164i	$-0.330264\pi$
$701$	−241585.	−	418438.i	−0.491626	−	0.851521i	−0.999954	+	0.00964296i	$0.996931\pi$
$702$			235949.i			0.478789i
$703$	−390806.	+	465011.i	−0.790772	+	0.940920i
$704$	66647.0			0.134473
$705$	809525.	−	467380.i	1.62874	−	0.940354i
$706$	−229988.	+	132784.i	−0.461420	+	0.266401i
$707$	−370698.	+	642068.i	−0.741621	+	1.28452i
$708$	128401.	+	222397.i	0.256154	+	0.443672i
$709$	48922.0	−	84735.4i	0.0973222	−	0.168567i	−0.813253	−	0.581910i	$-0.802306\pi$
$709$	48922.0	−	84735.4i	0.0973222	−	0.168567i	0.910575	+	0.413343i	$0.135639\pi$
$710$	−698998.			−1.38663
$711$			763789.i			1.51089i
$712$	31447.7	−	54469.0i	0.0620339	−	0.107446i
$713$	236487.	+	136536.i	0.465188	+	0.268576i
$714$	−128599.			−0.252256
$715$			1.18656e6i			2.32102i
$716$	−334068.	−	192874.i	−0.651642	−	0.376226i
$717$	847984.	−	489584.i	1.64949	−	0.952333i
$718$	270639.	+	156254.i	0.524979	+	0.303097i
$719$	50793.5	+	87977.0i	0.0982541	+	0.170181i	0.910962	−	0.412490i	$-0.135341\pi$
$719$	50793.5	+	87977.0i	0.0982541	+	0.170181i	−0.812708	+	0.582671i	$0.802008\pi$
$720$	101983.	+	176641.i	0.196727	+	0.340742i
$721$		−	1.24053e6i		−	2.38637i
$722$	236495.	+	282734.i	0.453678	+	0.542381i
$723$	937818.			1.79408
$724$	−139007.	+	80256.0i	−0.265192	+	0.153109i
$725$	298892.	−	172566.i	0.568642	−	0.328305i
$726$	−44076.0	+	76341.9i	−0.0836236	+	0.144840i
$727$	85668.0	+	148381.i	0.162088	+	0.280744i	0.935617	−	0.353016i	$-0.114844\pi$
$727$	85668.0	+	148381.i	0.162088	+	0.280744i	−0.773530	+	0.633760i	$0.781511\pi$
$728$	−201979.	+	349837.i	−0.381103	+	0.660090i
$729$	762930.			1.43559
$730$		−	75925.6i		−	0.142476i
$731$	−23529.5	+	40754.3i	−0.0440330	+	0.0762674i
$732$	−466807.	−	269511.i	−0.871194	−	0.502984i
$733$	−518592.			−0.965202			−0.482601	−	0.875840i	$-0.660308\pi$
$733$	−518592.			−0.965202			−0.482601	+	0.875840i	$0.660308\pi$
$734$		−	223018.i		−	0.413950i
$735$	488515.	+	282044.i	0.904280	+	0.522086i
$736$	−30372.2	+	17535.4i	−0.0560687	+	0.0323713i
$737$	174074.	+	100502.i	0.320479	+	0.185028i
$738$	231184.	+	400423.i	0.424469	+	0.735201i
$739$	−233486.	−	404410.i	−0.427536	−	0.740514i	0.569118	−	0.822256i	$-0.307285\pi$
$739$	−233486.	−	404410.i	−0.427536	−	0.740514i	−0.996653	+	0.0817425i	$0.973951\pi$
$740$			420139.i			0.767238i
$741$	1.09218e6	+	917895.i	1.98911	+	1.67169i
$742$	405876.			0.737200
$743$	−36347.6	+	20985.3i	−0.0658413	+	0.0380135i	−0.532559	−	0.846393i	$-0.678770\pi$
$743$	−36347.6	+	20985.3i	−0.0658413	+	0.0380135i	0.466718	+	0.884406i	$0.345436\pi$
$744$	−373746.	+	215782.i	−0.675197	+	0.389825i
$745$	−379758.	+	657760.i	−0.684217	+	1.18510i
$746$	20361.8	+	35267.7i	0.0365880	+	0.0633722i
$747$	32128.6	−	55648.3i	0.0575771	−	0.0997265i
$748$	57240.2			0.102305
$749$			565656.i			1.00830i
$750$	164749.	−	285354.i	0.292888	−	0.507296i
$751$	−770130.	−	444635.i	−1.36548	−	0.788358i	−0.375130	−	0.926972i	$-0.622402\pi$
$751$	−770130.	−	444635.i	−1.36548	−	0.788358i	−0.990346	+	0.138614i	$0.955735\pi$
$752$	−141647.			−0.250479
$753$		−	537458.i		−	0.947882i
$754$	−707101.	−	408245.i	−1.24377	−	0.718088i
$755$	−294534.	+	170049.i	−0.516704	+	0.298319i
$756$	−120968.	−	69840.7i	−0.211654	−	0.122198i
$757$	159938.	+	277020.i	0.279099	+	0.483414i	0.971161	−	0.238424i	$-0.0766308\pi$
$757$	159938.	+	277020.i	0.279099	+	0.483414i	−0.692062	+	0.721838i	$0.743297\pi$
$758$	56707.2	+	98219.8i	0.0986961	+	0.170947i
$759$		−	341260.i		−	0.592382i
$760$	251045.	+	44467.1i	0.434635	+	0.0769860i
$761$	−446363.			−0.770760			−0.385380	−	0.922758i	$-0.625930\pi$
$761$	−446363.			−0.770760			−0.385380	+	0.922758i	$0.625930\pi$
$762$	666064.	−	384552.i	1.14711	−	0.662286i
$763$	706006.	−	407613.i	1.21272	−	0.700162i
$764$	32634.3	−	56524.3i	0.0559098	−	0.0968386i
$765$	87589.2	+	151709.i	0.149668	+	0.259232i
$766$	−126060.	+	218342.i	−0.214842	+	0.372117i
$767$	692813.			1.17768
$768$		−	55426.1i		−	0.0939705i
$769$	−258951.	+	448516.i	−0.437890	+	0.758448i	−0.997527	−	0.0702905i	$-0.977607\pi$
$769$	−258951.	+	448516.i	−0.437890	+	0.758448i	0.559637	+	0.828738i	$0.310941\pi$
$770$	−608334.	−	351222.i	−1.02603	−	0.592380i
$771$	−1.08692e6			−1.82848
$772$		−	547745.i		−	0.919059i
$773$	−152632.	−	88122.0i	−0.255438	−	0.147477i	0.366814	−	0.930294i	$-0.380449\pi$
$773$	−152632.	−	88122.0i	−0.255438	−	0.147477i	−0.622252	+	0.782817i	$0.713782\pi$
$774$	−214131.	+	123629.i	−0.357436	+	0.206366i
$775$	−426215.	−	246075.i	−0.709619	−	0.409698i
$776$	−139397.	−	241442.i	−0.231488	−	0.400949i
$777$	−695901.	−	1.20534e6i	−1.15267	−	1.99649i
$778$			223248.i			0.368831i
$779$	569090.	+	100802.i	0.937790	+	0.166109i
$780$	986790.			1.62194
$781$	−892594.	+	515340.i	−1.46336	+	0.844873i
$782$	−26085.3	+	15060.4i	−0.0426563	+	0.0246276i
$783$	141164.	−	244503.i	0.230250	−	0.398805i
$784$	−42739.0	−	74026.2i	−0.0695332	−	0.120435i
$785$	−198841.	+	344402.i	−0.322676	+	0.558890i
$786$	35983.7			0.0582454
$787$		−	93070.1i		−	0.150266i	−0.997174	−	0.0751330i	$-0.976062\pi$
$787$		−	93070.1i		−	0.150266i	0.997174	−	0.0751330i	$-0.0239381\pi$
$788$	11850.6	−	20525.9i	0.0190848	−	0.0330559i
$789$	401322.	+	231703.i	0.644671	+	0.372201i
$790$	660351.			1.05808
$791$		−	633187.i		−	1.01200i
$792$	260458.	+	150376.i	0.415229	+	0.239733i
$793$	−1.25938e6	+	727101.i	−2.00267	+	1.15624i
$794$	365460.	+	210998.i	0.579694	+	0.334686i
$795$	−495738.	−	858644.i	−0.784365	−	1.35856i
$796$	−138963.	−	240692.i	−0.219318	−	0.379870i
$797$			268248.i			0.422298i	0.977454	+	0.211149i	$0.0677206\pi$
$797$			268248.i			0.422298i	−0.977454	+	0.211149i	$0.932279\pi$
$798$	−793876.	+	288249.i	−1.24666	+	0.452650i
$799$	−121654.			−0.190561
$800$	54739.0	−	31603.6i	0.0855296	−	0.0493806i
$801$	245797.	−	141911.i	0.383099	−	0.221183i
$802$	4270.61	−	7396.92i	0.00663959	−	0.0115001i
$803$	−55976.5	−	96954.2i	−0.0868110	−	0.150361i
$804$	83580.9	−	144766.i	0.129299	−	0.223952i
$805$	369638.			0.570407
$806$			1.16430e6i			1.79223i
$807$	362021.	−	627039.i	0.555887	−	0.962825i
$808$	−237672.	−	137220.i	−0.364045	−	0.210182i
$809$	−1.04971e6			−1.60388			−0.801939	−	0.597406i	$-0.796198\pi$
$809$	−1.04971e6			−1.60388			−0.801939	+	0.597406i	$0.796198\pi$
$810$		−	388931.i		−	0.592793i
$811$	57904.0	+	33430.9i	0.0880373	+	0.0508284i	0.543372	−	0.839492i	$-0.317147\pi$
$811$	57904.0	+	33430.9i	0.0880373	+	0.0508284i	−0.455335	+	0.890320i	$0.650481\pi$
$812$	418602.	−	241680.i	0.634877	−	0.366546i
$813$	−1.00531e6	−	580418.i	−1.52097	−	0.878131i
$814$	309750.	+	536502.i	0.467479	+	0.809698i
$815$	−84430.8	−	146238.i	−0.127112	−	0.220164i
$816$		−	47603.1i		−	0.0714915i
$817$	−53904.9	+	304328.i	−0.0807578	+	0.455929i
$818$	−52594.6			−0.0786022
$819$	−1.57868e6	+	911448.i	−2.35356	+	1.35883i
$820$	346195.	−	199876.i	0.514864	−	0.297257i
$821$	533810.	−	924586.i	0.791954	−	1.37171i	−0.132801	−	0.991143i	$-0.542397\pi$
$821$	533810.	−	924586.i	0.791954	−	1.37171i	0.924755	−	0.380563i	$-0.124270\pi$
$822$	−247914.	−	429400.i	−0.366909	−	0.635505i
$823$	−94457.1	+	163604.i	−0.139455	+	0.241544i	−0.927291	−	0.374342i	$-0.877868\pi$
$823$	−94457.1	+	163604.i	−0.139455	+	0.241544i	0.787835	+	0.615886i	$0.211202\pi$
$824$	459204.			0.676318
$825$			615044.i			0.903645i
$826$	−205072.	+	355195.i	−0.300571	+	0.520604i
$827$	174892.	+	100974.i	0.255716	+	0.147638i	0.622379	−	0.782716i	$-0.286166\pi$
$827$	174892.	+	100974.i	0.255716	+	0.147638i	−0.366662	+	0.930354i	$0.619500\pi$
$828$	−158260.			−0.230840
$829$			796457.i			1.15892i	0.815001	+	0.579459i	$0.196736\pi$
$829$			796457.i			1.15892i	−0.815001	+	0.579459i	$0.803264\pi$
$830$	−48112.0	−	27777.5i	−0.0698389	−	0.0403215i
$831$	−66611.3	+	38458.1i	−0.0964597	+	0.0556910i
$832$	−129498.	−	74765.7i	−0.187075	−	0.108008i
$833$	−36706.7	−	63577.9i	−0.0529000	−	0.0916254i
$834$	61118.6	+	105860.i	0.0878701	+	0.152195i
$835$			208169.i			0.298567i
$836$	353359.	−	128301.i	0.505596	−	0.183577i
$837$	−402594.			−0.574667
$838$	206794.	−	119393.i	0.294477	−	0.170016i
$839$	320631.	−	185117.i	0.455493	−	0.262979i	−0.254654	−	0.967032i	$-0.581962\pi$
$839$	320631.	−	185117.i	0.455493	−	0.262979i	0.710147	+	0.704053i	$0.248628\pi$
$840$	−292089.	+	505913.i	−0.413958	+	0.716997i
$841$	134850.	+	233567.i	0.190660	+	0.330233i
$842$	−150212.	+	260174.i	−0.211875	+	0.366978i
$843$	977303.			1.37523
$844$		−	403198.i		−	0.566022i
$845$	885388.	−	1.53354e6i	1.24000	−	2.14773i
$846$	−553560.	−	319598.i	−0.773435	−	0.446543i
$847$	−140790.			−0.196248
$848$			150242.i			0.208929i
$849$	57941.5	+	33452.5i	0.0803848	+	0.0464102i
$850$	47012.9	−	27142.9i	0.0650698	−	0.0375681i
$851$	−282317.	−	162996.i	−0.389832	−	0.225069i
$852$	428575.	+	742314.i	0.590402	+	1.02261i
$853$	436985.	+	756880.i	0.600577	+	1.04023i	0.992734	+	0.120331i	$0.0383957\pi$
$853$	436985.	+	756880.i	0.600577	+	1.04023i	−0.392157	+	0.919898i	$0.628271\pi$
$854$		−	860885.i		−	1.18040i
$855$	880760.	+	740212.i	1.20483	+	1.01257i
$856$	−209387.			−0.285760
$857$	437523.	−	252604.i	0.595716	−	0.343937i	−0.171638	−	0.985160i	$-0.554906\pi$
$857$	437523.	−	252604.i	0.595716	−	0.343937i	0.767354	+	0.641223i	$0.221573\pi$
$858$	1.26009e6	−	727516.i	1.71170	−	0.988252i
$859$	275661.	−	477459.i	0.373585	−	0.647068i	−0.616529	−	0.787332i	$-0.711462\pi$
$859$	275661.	−	477459.i	0.373585	−	0.647068i	0.990114	+	0.140264i	$0.0447952\pi$
$860$	106886.	+	185132.i	0.144519	+	0.250314i
$861$	−662131.	+	1.14684e6i	−0.893177	+	1.54703i
$862$	−305534.			−0.411192
$863$			541763.i			0.727424i	0.931511	+	0.363712i	$0.118491\pi$
$863$			541763.i			0.727424i	−0.931511	+	0.363712i	$0.881509\pi$
$864$	25852.7	−	44778.1i	0.0346320	−	0.0599844i
$865$	−139045.	−	80277.8i	−0.185833	−	0.107291i
$866$	394860.			0.526511
$867$			1.08930e6i			1.44914i
$868$	−596919.	−	344631.i	−0.792275	−	0.457420i
$869$	843243.	−	486847.i	1.11664	−	0.644692i
$870$	−1.02257e6	−	590378.i	−1.35099	−	0.779995i
$871$	−225489.	−	390558.i	−0.297227	−	0.514813i
$872$	150885.	+	261340.i	0.198432	+	0.343694i
$873$		−	1.25808e6i		−	1.65075i
$874$	−127275.	+	151441.i	−0.166617	+	0.198253i
$875$	526250.			0.687347
$876$	−80630.6	+	46552.1i	−0.105073	+	0.0606640i
$877$	221090.	−	127647.i	0.287456	−	0.165963i	−0.349338	−	0.936997i	$-0.613594\pi$
$877$	221090.	−	127647.i	0.287456	−	0.165963i	0.636794	+	0.771034i	$0.280260\pi$
$878$	−471509.	+	816677.i	−0.611647	+	1.05940i
$879$	547030.	+	947484.i	0.708001	+	1.22629i
$880$	130011.	−	225185.i	0.167886	−	0.290786i
$881$	−1.45518e6			−1.87484			−0.937420	−	0.348202i	$-0.886792\pi$
$881$	−1.45518e6			−1.87484			−0.937420	+	0.348202i	$0.886792\pi$
$882$		−	385728.i		−	0.495843i
$883$	304905.	−	528112.i	0.391060	−	0.677336i	−0.601529	−	0.798851i	$-0.705442\pi$
$883$	304905.	−	528112.i	0.391060	−	0.677336i	0.992590	+	0.121514i	$0.0387750\pi$
$884$	−111220.	−	64213.0i	−0.142324	−	0.0821710i
$885$	1.00190e6			1.27920
$886$			391593.i			0.498847i
$887$	−576568.	−	332882.i	−0.732830	−	0.423100i	0.0866264	−	0.996241i	$-0.472391\pi$
$887$	−576568.	−	332882.i	−0.732830	−	0.423100i	−0.819457	+	0.573141i	$0.805725\pi$
$888$	446175.	−	257599.i	0.565821	−	0.326677i
$889$	1.06379e6	+	614178.i	1.34602	+	0.777125i
$890$	−122692.	−	212509.i	−0.154895	−	0.268286i
$891$	−286741.	−	496651.i	−0.361189	−	0.625599i
$892$		−	382615.i		−	0.480875i
$893$	−751005.	+	272683.i	−0.941760	+	0.341944i
$894$	931360.			1.16531
$895$	−1.30336e6	+	752494.i	−1.62711	+	0.939414i
$896$	76662.6	−	44261.2i	0.0954921	−	0.0551324i
$897$	−382831.	+	663082.i	−0.475797	+	0.824105i
$898$	−153172.	−	265302.i	−0.189945	−	0.328994i
$899$	696578.	−	1.20651e6i	0.861887	−	1.49283i
$900$	285228.			0.352134
$901$			129036.i			0.158950i
$902$	294718.	−	510467.i	0.362238	−	0.627415i
$903$	−613289.	−	354083.i	−0.752125	−	0.434239i
$904$	234385.			0.286809
$905$			626232.i			0.764607i
$906$	361174.	+	208524.i	0.440008	+	0.254038i
$907$	619322.	−	357566.i	0.752838	−	0.434651i	−0.0738801	−	0.997267i	$-0.523538\pi$
$907$	619322.	−	357566.i	0.752838	−	0.434651i	0.826719	+	0.562616i	$0.190205\pi$
$908$	70464.6	+	40682.8i	0.0854672	+	0.0493445i
$909$	−619219.	−	1.07252e6i	−0.749405	−	1.29801i
$910$	788013.	+	1.36488e6i	0.951592	+	1.64821i
$911$			1.19913e6i			1.44488i	0.691435	+	0.722438i	$0.256979\pi$
$911$			1.19913e6i			1.44488i	−0.691435	+	0.722438i	$0.743021\pi$
$912$	−106700.	−	293866.i	−0.128285	−	0.353313i
$913$	−81916.3			−0.0982718
$914$	431552.	−	249157.i	0.516584	−	0.298250i
$915$	−1.82123e6	+	1.05149e6i	−2.17532	+	1.25592i
$916$	−215041.	+	372463.i	−0.256290	+	0.443907i
$917$	28735.3	+	49770.9i	0.0341725	+	0.0591885i
$918$	22203.7	−	38458.0i	0.0263476	−	0.0456354i
$919$	290768.			0.344283			0.172142	−	0.985072i	$-0.444931\pi$
$919$	290768.			0.344283			0.172142	+	0.985072i	$0.444931\pi$
$920$			136827.i			0.161658i
$921$	−327337.	+	566964.i	−0.385901	+	0.668400i
$922$	−823210.	−	475281.i	−0.968387	−	0.559099i
$923$	2.31247e6			2.71439
$924$			861376.i			1.00890i
$925$	508812.	+	293763.i	0.594667	+	0.343331i
$926$	−213081.	+	123023.i	−0.248498	+	0.143471i
$927$	1.79458e6	+	1.03610e6i	2.08835	+	1.20571i
$928$	89461.9	+	154953.i	0.103882	+	0.179930i
$929$	−446462.	−	773294.i	−0.517312	−	0.896011i	−0.999798	−	0.0201073i	$-0.993599\pi$
$929$	−446462.	−	773294.i	−0.517312	−	0.896011i	0.482486	−	0.875904i	$-0.339734\pi$
$930$			1.68374e6i			1.94674i
$931$	−369107.	−	310207.i	−0.425847	−	0.357892i
$932$	50451.6			0.0580822
$933$	2.18871e6	−	1.26365e6i	2.51434	−	1.45165i
$934$	−520357.	+	300428.i	−0.596496	+	0.344387i
$935$	111660.	−	193402.i	0.127725	−	0.221226i
$936$	−337388.	−	584372.i	−0.385103	−	0.667019i
$937$	541062.	−	937146.i	0.616265	−	1.06740i	−0.373896	−	0.927471i	$-0.621978\pi$
$937$	541062.	−	937146.i	0.616265	−	1.06740i	0.990161	−	0.139932i	$-0.0446883\pi$
$938$	266978.			0.303438
$939$		−	1.30062e6i		−	1.47510i
$940$	−276316.	+	478593.i	−0.312716	+	0.541640i
$941$	1.41506e6	+	816988.i	1.59807	+	0.922649i	0.991858	+	0.127349i	$0.0406468\pi$
$941$	1.41506e6	+	816988.i	1.59807	+	0.922649i	0.606217	+	0.795300i	$0.292686\pi$
$942$	487659.			0.549559
$943$			310172.i			0.348802i
$944$	−131481.	−	75910.8i	−0.147544	−	0.0851843i
$945$	−471951.	+	272481.i	−0.528486	+	0.305122i
$946$	272979.	+	157604.i	0.305033	+	0.176111i
$947$	143451.	+	248464.i	0.159957	+	0.277053i	0.934853	−	0.355035i	$-0.115531\pi$
$947$	143451.	+	248464.i	0.159957	+	0.277053i	−0.774896	+	0.632089i	$0.782198\pi$
$948$	−404879.	−	701272.i	−0.450515	−	0.780314i
$949$			251182.i			0.278904i
$950$	229384.	−	272938.i	0.254165	−	0.302424i
$951$	−2.62874e6			−2.90661
$952$	65842.2	−	38014.0i	0.0726491	−	0.0419440i
$953$	1.03209e6	−	595880.i	1.13641	−	0.656105i	0.190868	−	0.981616i	$-0.438870\pi$
$953$	1.03209e6	−	595880.i	1.13641	−	0.656105i	0.945538	+	0.325511i	$0.105536\pi$
$954$	−338990.	+	587148.i	−0.372469	+	0.645135i
$955$	−127322.	−	220528.i	−0.139603	−	0.241800i
$956$	−289443.	+	501330.i	−0.316699	+	0.548540i
$957$	−1.74104e6			−1.90101
$958$		−	870534.i		−	0.948538i
$959$	395950.	−	685806.i	0.430530	−	0.745700i
$960$	−187272.	−	108122.i	−0.203203	−	0.117319i
$961$	−1.06309e6			−1.15113
$962$		−	1.38993e6i		−	1.50191i
$963$	−818290.	−	472440.i	−0.882378	−	0.509441i
$964$	−480159.	+	277220.i	−0.516691	+	0.298312i
$965$	−1.85070e6	−	1.06850e6i	−1.98739	−	1.14742i
$966$	−226635.	−	392544.i	−0.242870	−	0.420663i
$967$	186405.	+	322862.i	0.199344	+	0.345274i	0.948316	−	0.317328i	$-0.102785\pi$
$967$	186405.	+	322862.i	0.199344	+	0.345274i	−0.748972	+	0.662602i	$0.769452\pi$
$968$		−	52115.6i		−	0.0556183i
$969$	−91640.2	−	252389.i	−0.0975974	−	0.268796i
$970$	−1.08770e6			−1.15602
$971$	−803785.	+	464065.i	−0.852514	+	0.492199i	−0.861498	−	0.507761i	$-0.830473\pi$
$971$	−803785.	+	464065.i	−0.852514	+	0.492199i	0.00898453	+	0.999960i	$0.497140\pi$
$972$	−573327.	+	331010.i	−0.606833	+	0.350355i
$973$	−97614.0	+	169072.i	−0.103107	+	0.178586i
$974$	−389061.	−	673874.i	−0.410110	−	0.710331i
$975$	689966.	−	1.19506e6i	0.725802	−	1.25713i
$976$	318671.			0.334536
$977$			636929.i			0.667271i	0.942702	+	0.333635i	$0.108275\pi$
$977$			636929.i			0.667271i	−0.942702	+	0.333635i	$0.891725\pi$
$978$	−103534.	+	179326.i	−0.108244	+	0.187484i
$979$	−313347.	−	180911.i	−0.326934	−	0.188755i
$980$	−333490.			−0.347241
$981$			1.36176e6i			1.41502i
$982$	1.16073e6	+	670146.i	1.20367	+	0.694939i
$983$	−761402.	+	439596.i	−0.787965	+	0.454932i	−0.839246	−	0.543752i	$-0.817003\pi$
$983$	−761402.	+	439596.i	−0.787965	+	0.454932i	0.0512804	+	0.998684i	$0.483670\pi$
$984$	−424523.	−	245099.i	−0.438441	−	0.253134i
$985$	−46234.8	−	80081.1i	−0.0476537	−	0.0825387i
$986$	76835.0	+	133082.i	0.0790324	+	0.136888i
$987$		−	1.83071e6i		−	1.87925i
$988$	−830523.	−	147109.i	−0.850820	−	0.150704i
$989$	−165868.			−0.169578
$990$	1.01617e6	−	586686.i	1.03680	−	0.598598i
$991$	1.22906e6	−	709601.i	1.25149	−	0.722548i	0.280084	−	0.959975i	$-0.409638\pi$
$991$	1.22906e6	−	709601.i	1.25149	−	0.722548i	0.971405	+	0.237427i	$0.0763042\pi$
$992$	127571.	−	220959.i	0.129637	−	0.224538i
$993$	182885.	+	316766.i	0.185473	+	0.321248i
$994$	−684488.	+	1.18557e6i	−0.692776	+	1.19992i
$995$	−1.08432e6			−1.09525
$996$			68124.6i			0.0686729i
$997$	−851833.	+	1.47542e6i	−0.856967	+	1.48431i	0.0178418	+	0.999841i	$0.494320\pi$
$997$	−851833.	+	1.47542e6i	−0.856967	+	1.48431i	−0.874808	+	0.484469i	$0.839013\pi$
$998$	−146612.	−	84646.2i	−0.147200	−	0.0849858i
$999$	480613.			0.481576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.d.a.31.5	yes	16
3.2	odd	2		342.5.m.c.145.3		16
4.3	odd	2		304.5.r.c.145.7		16
19.8	odd	6	inner	38.5.d.a.27.5	✓	16
57.8	even	6		342.5.m.c.217.3		16
76.27	even	6		304.5.r.c.65.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.5	✓	16	19.8	odd	6	inner
38.5.d.a.31.5	yes	16	1.1	even	1	trivial
304.5.r.c.65.7		16	76.27	even	6
304.5.r.c.145.7		16	4.3	odd	2
342.5.m.c.145.3		16	3.2	odd	2
342.5.m.c.217.3		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)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{2} +(-11.7188 + 6.76588i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-15.6059 - 27.0302i) q^{5} +(-19.1368 + 33.1459i) q^{6} -61.1277 q^{7} -22.6274i q^{8} +(51.0542 - 88.4285i) q^{9} +O(q^{10})\)	\(q+(2.44949 - 1.41421i) q^{2} +(-11.7188 + 6.76588i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-15.6059 - 27.0302i) q^{5} +(-19.1368 + 33.1459i) q^{6} -61.1277 q^{7} -22.6274i q^{8} +(51.0542 - 88.4285i) q^{9} +(-76.4529 - 44.1401i) q^{10} -130.170 q^{11} +108.254i q^{12} +(252.926 + 146.027i) q^{13} +(-149.732 + 86.4476i) q^{14} +(365.766 + 211.175i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-27.4834 - 47.6027i) q^{17} -288.806i q^{18} +(-276.362 - 232.261i) q^{19} -249.694 q^{20} +(716.346 - 413.583i) q^{21} +(-318.850 + 184.088i) q^{22} +(96.8702 - 167.784i) q^{23} +(153.094 + 265.167i) q^{24} +(-174.587 + 302.393i) q^{25} +826.052 q^{26} +285.634i q^{27} +(-244.511 + 423.505i) q^{28} +(-856.000 - 494.212i) q^{29} +1194.59 q^{30} +1409.47i q^{31} +(-156.767 - 90.5097i) q^{32} +(1525.44 - 880.714i) q^{33} +(-134.641 - 77.7348i) q^{34} +(953.951 + 1652.29i) q^{35} +(-408.434 - 707.428i) q^{36} -1682.62i q^{37} +(-1005.41 - 178.087i) q^{38} -3952.00 q^{39} +(-611.623 + 353.121i) q^{40} +(-1386.48 + 800.482i) q^{41} +(1169.79 - 2026.13i) q^{42} +(-428.068 - 741.435i) q^{43} +(-520.680 + 901.844i) q^{44} -3186.98 q^{45} -547.981i q^{46} +(1106.62 - 1916.72i) q^{47} +(750.006 + 433.016i) q^{48} +1335.59 q^{49} +987.611i q^{50} +(644.148 + 371.899i) q^{51} +(2023.41 - 1168.21i) q^{52} +(-2033.02 - 1173.76i) q^{53} +(403.948 + 699.659i) q^{54} +(2031.42 + 3518.51i) q^{55} +1383.16i q^{56} +(4810.09 + 852.001i) q^{57} -2795.68 q^{58} +(2054.40 - 1186.11i) q^{59} +(2926.13 - 1689.40i) q^{60} +(-2489.61 + 4312.14i) q^{61} +(1993.30 + 3452.49i) q^{62} +(-3120.83 + 5405.43i) q^{63} -512.000 q^{64} -9115.50i q^{65} +(2491.03 - 4314.60i) q^{66} +(-1337.28 - 772.081i) q^{67} -439.735 q^{68} +2621.65i q^{69} +(4673.39 + 2698.18i) q^{70} +(6857.15 - 3958.98i) q^{71} +(-2000.91 - 1155.23i) q^{72} +(430.026 + 744.828i) q^{73} +(-2379.58 - 4121.55i) q^{74} -4724.93i q^{75} +(-2714.60 + 985.646i) q^{76} +7956.99 q^{77} +(-9680.38 + 5588.97i) q^{78} +(-6478.02 + 3740.09i) q^{79} +(-998.776 + 1729.93i) q^{80} +(2202.82 + 3815.40i) q^{81} +(-2264.11 + 3921.55i) q^{82} +629.303 q^{83} -6617.32i q^{84} +(-857.806 + 1485.76i) q^{85} +(-2097.09 - 1210.76i) q^{86} +13375.1 q^{87} +2945.41i q^{88} +(2407.21 + 1389.81i) q^{89} +(-7806.48 + 4507.08i) q^{90} +(-15460.8 - 8926.28i) q^{91} +(-774.962 - 1342.27i) q^{92} +(-9536.32 - 16517.4i) q^{93} -6259.97i q^{94} +(-1965.19 + 11094.7i) q^{95} +2449.51 q^{96} +(10670.3 - 6160.52i) q^{97} +(3271.52 - 1888.82i) q^{98} +(-6645.72 + 11510.7i) 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

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