LMFDB - Embedded newform 38.5.d.a.27.3

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			27.3
Root			$0.500000 - 0.961202i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.5.d.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 - 1.41421i) q^{2} +(1.30717 + 0.754695i) q^{3} +(4.00000 + 6.92820i) q^{4} +(1.35492 - 2.34679i) q^{5} +(-2.13460 - 3.69723i) q^{6} +79.4947 q^{7} -22.6274i q^{8} +(-39.3609 - 68.1750i) q^{9} +O(q^{10})$	\(q+(-2.44949 - 1.41421i) q^{2} +(1.30717 + 0.754695i) q^{3} +(4.00000 + 6.92820i) q^{4} +(1.35492 - 2.34679i) q^{5} +(-2.13460 - 3.69723i) q^{6} +79.4947 q^{7} -22.6274i q^{8} +(-39.3609 - 68.1750i) q^{9} +(-6.63772 + 3.83229i) q^{10} +109.030 q^{11} +12.0751i q^{12} +(269.920 - 155.839i) q^{13} +(-194.722 - 112.423i) q^{14} +(3.54222 - 2.04510i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(-212.438 + 367.953i) q^{17} +222.659i q^{18} +(-333.675 + 137.776i) q^{19} +21.6787 q^{20} +(103.913 + 59.9943i) q^{21} +(-267.068 - 154.192i) q^{22} +(-132.097 - 228.798i) q^{23} +(17.0768 - 29.5779i) q^{24} +(308.828 + 534.906i) q^{25} -881.556 q^{26} -241.082i q^{27} +(317.979 + 550.756i) q^{28} +(-203.478 + 117.478i) q^{29} -11.5688 q^{30} -648.147i q^{31} +(156.767 - 90.5097i) q^{32} +(142.521 + 82.2843i) q^{33} +(1040.73 - 600.864i) q^{34} +(107.709 - 186.557i) q^{35} +(314.887 - 545.400i) q^{36} -626.819i q^{37} +(1012.18 + 134.408i) q^{38} +470.442 q^{39} +(-53.1017 - 30.6583i) q^{40} +(-415.611 - 239.953i) q^{41} +(-169.689 - 293.911i) q^{42} +(-622.065 + 1077.45i) q^{43} +(436.119 + 755.381i) q^{44} -213.323 q^{45} +747.251i q^{46} +(-822.028 - 1423.79i) q^{47} +(-83.6589 + 48.3005i) q^{48} +3918.41 q^{49} -1747.00i q^{50} +(-555.384 + 320.651i) q^{51} +(2159.36 + 1246.71i) q^{52} +(-4118.24 + 2377.67i) q^{53} +(-340.942 + 590.529i) q^{54} +(147.727 - 255.870i) q^{55} -1798.76i q^{56} +(-540.148 - 71.7266i) q^{57} +664.555 q^{58} +(-4227.83 - 2440.94i) q^{59} +(28.3377 + 16.3608i) q^{60} +(3545.36 + 6140.74i) q^{61} +(-916.619 + 1587.63i) q^{62} +(-3128.98 - 5419.56i) q^{63} -512.000 q^{64} -844.594i q^{65} +(-232.735 - 403.109i) q^{66} +(51.8915 - 29.9596i) q^{67} -3399.00 q^{68} -398.771i q^{69} +(-527.664 + 304.647i) q^{70} +(5416.15 + 3127.02i) q^{71} +(-1542.62 + 890.635i) q^{72} +(-1209.33 + 2094.62i) q^{73} +(-886.456 + 1535.39i) q^{74} +932.285i q^{75} +(-2289.24 - 1760.66i) q^{76} +8667.30 q^{77} +(-1152.34 - 665.306i) q^{78} +(-3684.36 - 2127.16i) q^{79} +(86.7148 + 150.194i) q^{80} +(-3006.29 + 5207.04i) q^{81} +(678.690 + 1175.53i) q^{82} -6643.06 q^{83} +959.908i q^{84} +(575.671 + 997.091i) q^{85} +(3047.48 - 1759.47i) q^{86} -354.640 q^{87} -2467.06i q^{88} +(8489.61 - 4901.48i) q^{89} +(522.533 + 301.684i) q^{90} +(21457.2 - 12388.3i) q^{91} +(1056.77 - 1830.38i) q^{92} +(489.153 - 847.239i) q^{93} +4650.09i q^{94} +(-128.772 + 969.738i) q^{95} +273.229 q^{96} +(-4066.41 - 2347.74i) q^{97} +(-9598.12 - 5541.48i) q^{98} +(-4291.51 - 7433.11i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	1.30717	+	0.754695i	0.145241	+	0.0838550i	0.570860	−	0.821048i	$-0.306610\pi$
$3$	1.30717	+	0.754695i	0.145241	+	0.0838550i	−0.425618	+	0.904903i	$0.639943\pi$
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	1.35492	−	2.34679i	0.0541967	−	0.0938715i	−0.837654	−	0.546201i	$-0.816074\pi$
$5$	1.35492	−	2.34679i	0.0541967	−	0.0938715i	0.891851	+	0.452329i	$0.149407\pi$
$6$	−2.13460	−	3.69723i	−0.0592944	−	0.102701i
$7$	79.4947			1.62234			0.811171	−	0.584809i	$-0.198831\pi$
$7$	79.4947			1.62234			0.811171	+	0.584809i	$0.198831\pi$
$8$		−	22.6274i		−	0.353553i
$9$	−39.3609	−	68.1750i	−0.485937	−	0.841667i
$10$	−6.63772	+	3.83229i	−0.0663772	+	0.0383229i
$11$	109.030			0.901073			0.450537	−	0.892758i	$-0.351233\pi$
$11$	109.030			0.901073			0.450537	+	0.892758i	$0.351233\pi$
$12$			12.0751i			0.0838550i
$13$	269.920	−	155.839i	1.59716	−	0.922121i	0.605130	−	0.796126i	$-0.293121\pi$
$13$	269.920	−	155.839i	1.59716	−	0.922121i	0.992031	−	0.125995i	$-0.0402123\pi$
$14$	−194.722	−	112.423i	−0.993477	−	0.573584i
$15$	3.54222	−	2.04510i	0.0157432	−	0.00908933i
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	−212.438	+	367.953i	−0.735078	+	1.27319i	0.219611	+	0.975587i	$0.429521\pi$
$17$	−212.438	+	367.953i	−0.735078	+	1.27319i	−0.954689	+	0.297605i	$0.903812\pi$
$18$			222.659i			0.687218i
$19$	−333.675	+	137.776i	−0.924307	+	0.381650i
$19$	−333.675	+	137.776i	−0.924307	+	0.381650i
$20$	21.6787			0.0541967
$21$	103.913	+	59.9943i	0.235631	+	0.136041i
$22$	−267.068	−	154.192i	−0.551792	−	0.318578i
$23$	−132.097	−	228.798i	−0.249710	−	0.432510i	0.713735	−	0.700416i	$-0.247002\pi$
$23$	−132.097	−	228.798i	−0.249710	−	0.432510i	−0.963445	+	0.267905i	$0.913669\pi$
$24$	17.0768	−	29.5779i	0.0296472	−	0.0513505i
$25$	308.828	+	534.906i	0.494125	+	0.855850i
$26$	−881.556			−1.30408
$27$		−	241.082i		−	0.330703i
$28$	317.979	+	550.756i	0.405585	+	0.702495i
$29$	−203.478	+	117.478i	−0.241947	+	0.139688i	−0.616071	−	0.787690i	$-0.711277\pi$
$29$	−203.478	+	117.478i	−0.241947	+	0.139688i	0.374124	+	0.927379i	$0.377943\pi$
$30$	−11.5688			−0.0128543
$31$		−	648.147i		−	0.674451i	−0.941424	−	0.337225i	$-0.890512\pi$
$31$		−	648.147i		−	0.674451i	0.941424	−	0.337225i	$-0.109488\pi$
$32$	156.767	−	90.5097i	0.153093	−	0.0883883i
$33$	142.521	+	82.2843i	0.130873	+	0.0755595i
$34$	1040.73	−	600.864i	0.900283	−	0.519779i
$35$	107.709	−	186.557i	0.0879256	−	0.152292i
$36$	314.887	−	545.400i	0.242968	−	0.420834i
$37$		−	626.819i		−	0.457866i	−0.973442	−	0.228933i	$-0.926476\pi$
$37$		−	626.819i		−	0.457866i	0.973442	−	0.228933i	$-0.0735237\pi$
$38$	1012.18	+	134.408i	0.700954	+	0.0930800i
$39$	470.442			0.309298
$40$	−53.1017	−	30.6583i	−0.0331886	−	0.0191614i
$41$	−415.611	−	239.953i	−0.247240	−	0.142744i	0.371260	−	0.928529i	$-0.378926\pi$
$41$	−415.611	−	239.953i	−0.247240	−	0.142744i	−0.618500	+	0.785785i	$0.712259\pi$
$42$	−169.689	−	293.911i	−0.0961958	−	0.166616i
$43$	−622.065	+	1077.45i	−0.336433	+	0.582720i	−0.983759	−	0.179494i	$-0.942554\pi$
$43$	−622.065	+	1077.45i	−0.336433	+	0.582720i	0.647326	+	0.762213i	$0.275887\pi$
$44$	436.119	+	755.381i	0.225268	+	0.390176i
$45$	−213.323			−0.105345
$46$			747.251i			0.353143i
$47$	−822.028	−	1423.79i	−0.372127	−	0.644542i	0.617766	−	0.786362i	$-0.288038\pi$
$47$	−822.028	−	1423.79i	−0.372127	−	0.644542i	−0.989892	+	0.141820i	$0.954705\pi$
$48$	−83.6589	+	48.3005i	−0.0363103	+	0.0209637i
$49$	3918.41			1.63199
$50$		−	1747.00i		−	0.698799i
$51$	−555.384	+	320.651i	−0.213527	+	0.123280i
$52$	2159.36	+	1246.71i	0.798581	+	0.461061i
$53$	−4118.24	+	2377.67i	−1.46609	+	0.846447i	−0.999281	−	0.0379118i	$-0.987929\pi$
$53$	−4118.24	+	2377.67i	−1.46609	+	0.846447i	−0.466808	+	0.884359i	$0.654596\pi$
$54$	−340.942	+	590.529i	−0.116921	+	0.202513i
$55$	147.727	−	255.870i	0.0488352	−	0.0845851i
$56$		−	1798.76i		−	0.573584i
$57$	−540.148	−	71.7266i	−0.166251	−	0.0220765i
$58$	664.555			0.197549
$59$	−4227.83	−	2440.94i	−1.21455	−	0.701219i	−0.250800	−	0.968039i	$-0.580694\pi$
$59$	−4227.83	−	2440.94i	−1.21455	−	0.701219i	−0.963746	+	0.266820i	$0.914027\pi$
$60$	28.3377	+	16.3608i	0.00787159	+	0.00454467i
$61$	3545.36	+	6140.74i	0.952797	+	1.65029i	0.739330	+	0.673343i	$0.235142\pi$
$61$	3545.36	+	6140.74i	0.952797	+	1.65029i	0.213467	+	0.976950i	$0.431524\pi$
$62$	−916.619	+	1587.63i	−0.238454	+	0.413015i
$63$	−3128.98	−	5419.56i	−0.788355	−	1.36547i
$64$	−512.000			−0.125000
$65$		−	844.594i		−	0.199904i
$66$	−232.735	−	403.109i	−0.0534286	−	0.0925411i
$67$	51.8915	−	29.9596i	0.0115597	−	0.00667400i	−0.494209	−	0.869343i	$-0.664542\pi$
$67$	51.8915	−	29.9596i	0.0115597	−	0.00667400i	0.505769	+	0.862669i	$0.331209\pi$
$68$	−3399.00			−0.735078
$69$		−	398.771i		−	0.0837577i
$70$	−527.664	+	304.647i	−0.107686	+	0.0621728i
$71$	5416.15	+	3127.02i	1.07442	+	0.620317i	0.929386	−	0.369110i	$-0.120337\pi$
$71$	5416.15	+	3127.02i	1.07442	+	0.620317i	0.145035	+	0.989427i	$0.453671\pi$
$72$	−1542.62	+	890.635i	−0.297574	+	0.171805i
$73$	−1209.33	+	2094.62i	−0.226934	+	0.393061i	−0.956898	−	0.290424i	$-0.906204\pi$
$73$	−1209.33	+	2094.62i	−0.226934	+	0.393061i	0.729964	+	0.683486i	$0.239537\pi$
$74$	−886.456	+	1535.39i	−0.161880	+	0.280385i
$75$			932.285i			0.165740i
$76$	−2289.24	−	1760.66i	−0.396336	−	0.304824i
$77$	8667.30			1.46185
$78$	−1152.34	−	665.306i	−0.189406	−	0.109353i
$79$	−3684.36	−	2127.16i	−0.590347	−	0.340837i	0.174888	−	0.984588i	$-0.444044\pi$
$79$	−3684.36	−	2127.16i	−0.590347	−	0.340837i	−0.765235	+	0.643751i	$0.777377\pi$
$80$	86.7148	+	150.194i	0.0135492	+	0.0234679i
$81$	−3006.29	+	5207.04i	−0.458206	+	0.793635i
$82$	678.690	+	1175.53i	0.100935	+	0.174825i
$83$	−6643.06			−0.964299			−0.482150	−	0.876089i	$-0.660144\pi$
$83$	−6643.06			−0.964299			−0.482150	+	0.876089i	$0.660144\pi$
$84$			959.908i			0.136041i
$85$	575.671	+	997.091i	0.0796776	+	0.138006i
$86$	3047.48	−	1759.47i	0.412045	−	0.237894i
$87$	−354.640			−0.0468542
$88$		−	2467.06i		−	0.318578i
$89$	8489.61	−	4901.48i	1.07179	−	0.618796i	0.143117	−	0.989706i	$-0.454288\pi$
$89$	8489.61	−	4901.48i	1.07179	−	0.618796i	0.928669	+	0.370910i	$0.120954\pi$
$90$	522.533	+	301.684i	0.0645102	+	0.0372450i
$91$	21457.2	−	12388.3i	2.59114	−	1.49600i
$92$	1056.77	−	1830.38i	0.124855	−	0.216255i
$93$	489.153	−	847.239i	0.0565561	−	0.0979580i
$94$			4650.09i			0.526266i
$95$	−128.772	+	969.738i	−0.0142684	+	0.107450i
$96$	273.229			0.0296472
$97$	−4066.41	−	2347.74i	−0.432183	−	0.249521i	0.268093	−	0.963393i	$-0.413606\pi$
$97$	−4066.41	−	2347.74i	−0.432183	−	0.249521i	−0.700276	+	0.713872i	$0.746940\pi$
$98$	−9598.12	−	5541.48i	−0.999387	−	0.576997i
$99$	−4291.51	−	7433.11i	−0.437865	−	0.758404i
$100$	−2470.63	+	4279.25i	−0.247063	+	0.427925i
$101$	6044.15	+	10468.8i	0.592506	+	1.02625i	0.993894	+	0.110342i	$0.0351947\pi$
$101$	6044.15	+	10468.8i	0.592506	+	1.02625i	−0.401388	+	0.915908i	$0.631472\pi$
$102$	1813.88			0.174344
$103$			5955.85i			0.561396i	0.959796	+	0.280698i	$0.0905660\pi$
$103$			5955.85i			0.561396i	−0.959796	+	0.280698i	$0.909434\pi$
$104$	−3526.22	−	6107.60i	−0.326019	−	0.564682i
$105$	281.588	−	162.575i	0.0255408	−	0.0147460i
$106$	13450.1			1.19706
$107$		−	565.173i		−	0.0493644i	−0.999695	−	0.0246822i	$-0.992143\pi$
$107$		−	565.173i		−	0.0493644i	0.999695	−	0.0246822i	$-0.00785738\pi$
$108$	1670.27	−	964.329i	0.143199	−	0.0826757i
$109$	1522.49	+	879.012i	0.128145	+	0.0739847i	0.562702	−	0.826660i	$-0.309762\pi$
$109$	1522.49	+	879.012i	0.128145	+	0.0739847i	−0.434557	+	0.900644i	$0.643095\pi$
$110$	−723.709	+	417.834i	−0.0598107	+	0.0345317i
$111$	473.057	−	819.359i	0.0383944	−	0.0665010i
$112$	−2543.83	+	4406.05i	−0.202793	+	0.351247i
$113$		−	9913.95i		−	0.776408i	−0.921574	−	0.388204i	$-0.873096\pi$
$113$		−	9913.95i		−	0.776408i	0.921574	−	0.388204i	$-0.126904\pi$
$114$	1221.65	+	939.578i	0.0940021	+	0.0722975i
$115$	−715.920			−0.0541339
$116$	−1627.82	−	939.823i	−0.120974	−	0.0698441i
$117$	−21248.6	−	12267.9i	−1.55224	−	0.896185i
$118$	6904.03	+	11958.1i	0.495836	+	0.858814i
$119$	−16887.7	+	29250.3i	−1.19255	+	2.06555i
$120$	−46.2753	−	80.1512i	−0.00321356	−	0.00556606i
$121$	−2753.49			−0.188067
$122$		−	20055.6i		−	1.34746i
$123$	−362.183	−	627.319i	−0.0239396	−	0.0414647i
$124$	4490.50	−	2592.59i	0.292046	−	0.168613i
$125$	3367.40			0.215513
$126$			17700.2i			1.11490i
$127$	−12784.5	+	7381.12i	−0.792639	+	0.457630i	−0.840891	−	0.541205i	$-0.817968\pi$
$127$	−12784.5	+	7381.12i	−0.792639	+	0.457630i	0.0482521	+	0.998835i	$0.484635\pi$
$128$	1254.14	+	724.077i	0.0765466	+	0.0441942i
$129$	−1626.29	+	938.939i	−0.0977279	+	0.0564232i
$130$	−1194.44	+	2068.82i	−0.0706767	+	0.122416i
$131$	−3378.16	+	5851.14i	−0.196851	+	0.340956i	−0.947506	−	0.319739i	$-0.896405\pi$
$131$	−3378.16	+	5851.14i	−0.196851	+	0.340956i	0.750655	+	0.660695i	$0.229738\pi$
$132$			1316.55i			0.0755595i
$133$	−26525.4	+	10952.4i	−1.49954	+	0.619167i
$134$	−169.477			−0.00943846
$135$	−565.769	−	326.647i	−0.0310436	−	0.0179230i
$136$	8325.82	+	4806.91i	0.450141	+	0.259889i
$137$	4112.96	+	7123.85i	0.219136	+	0.379554i	0.954544	−	0.298070i	$-0.0963429\pi$
$137$	4112.96	+	7123.85i	0.219136	+	0.379554i	−0.735408	+	0.677624i	$0.763010\pi$
$138$	−563.947	+	976.784i	−0.0296128	+	0.0512909i
$139$	−3781.52	−	6549.79i	−0.195721	−	0.338999i	0.751416	−	0.659829i	$-0.229371\pi$
$139$	−3781.52	−	6549.79i	−0.195721	−	0.338999i	−0.947137	+	0.320831i	$0.896038\pi$
$140$	1723.34			0.0879256
$141$		−	2481.52i		−	0.124819i
$142$	−8844.54	−	15319.2i	−0.438630	−	0.759730i
$143$	29429.4	−	16991.1i	1.43916	−	0.830899i
$144$	5038.19			0.242968
$145$			636.691i			0.0302826i
$146$	5924.49	−	3420.51i	0.277936	−	0.160467i
$147$	5122.03	+	2957.21i	0.237032	+	0.136851i
$148$	4342.73	−	2507.28i	0.198262	−	0.114467i
$149$	−5962.37	+	10327.1i	−0.268563	+	0.465165i	−0.968491	−	0.249048i	$-0.919882\pi$
$149$	−5962.37	+	10327.1i	−0.268563	+	0.465165i	0.699928	+	0.714214i	$0.253215\pi$
$150$	1318.45	−	2283.62i	0.0585978	−	0.101494i
$151$		−	28967.0i		−	1.27043i	−0.772336	−	0.635214i	$-0.780912\pi$
$151$		−	28967.0i		−	1.27043i	0.772336	−	0.635214i	$-0.219088\pi$
$152$	3117.51	+	7550.20i	0.134934	+	0.326792i
$153$	33446.9			1.42881
$154$	−21230.5	−	12257.4i	−0.895196	−	0.516842i
$155$	−1521.06	−	878.187i	−0.0633117	−	0.0365530i
$156$	1881.77	+	3259.32i	0.0773245	+	0.133930i
$157$	−3199.97	+	5542.52i	−0.129822	+	0.224858i	−0.923607	−	0.383340i	$-0.874774\pi$
$157$	−3199.97	+	5542.52i	−0.129822	+	0.224858i	0.793786	+	0.608198i	$0.208107\pi$
$158$	6016.53	+	10420.9i	0.241008	+	0.417439i
$159$	−7177.66			−0.283915
$160$		−	490.533i		−	0.0191614i
$161$	−10501.0	−	18188.2i	−0.405115	−	0.701680i
$162$	14727.7	−	8503.06i	0.561185	−	0.324000i
$163$	−5001.30			−0.188238			−0.0941191	−	0.995561i	$-0.530003\pi$
$163$	−5001.30			−0.188238			−0.0941191	+	0.995561i	$0.530003\pi$
$164$		−	3839.25i		−	0.142744i
$165$	386.207	−	222.977i	0.0141858	−	0.00819015i
$166$	16272.1	+	9394.70i	0.590510	+	0.340931i
$167$	21896.3	−	12641.8i	0.785122	−	0.453290i	−0.0531207	−	0.998588i	$-0.516917\pi$
$167$	21896.3	−	12641.8i	0.785122	−	0.453290i	0.838242	+	0.545298i	$0.183583\pi$
$168$	1357.52	−	2351.29i	0.0480979	−	0.0833080i
$169$	34290.8	−	59393.4i	1.20062	−	2.07953i
$170$		−	3256.49i		−	0.112681i
$171$	22526.6	+	17325.3i	0.770377	+	0.592501i
$172$	−9953.04			−0.336433
$173$	−8946.68	−	5165.37i	−0.298930	−	0.172587i	0.343032	−	0.939324i	$-0.388546\pi$
$173$	−8946.68	−	5165.37i	−0.298930	−	0.172587i	−0.641962	+	0.766736i	$0.721879\pi$
$174$	868.686	+	501.536i	0.0286922	+	0.0165655i
$175$	24550.2	+	42522.3i	0.801640	+	1.38848i
$176$	−3488.96	+	6043.05i	−0.112634	+	0.195088i
$177$	−3684.33	−	6381.45i	−0.117601	−	0.203691i
$178$	−27727.0			−0.875109
$179$			51529.9i			1.60825i	0.594460	+	0.804125i	$0.297366\pi$
$179$			51529.9i			1.60825i	−0.594460	+	0.804125i	$0.702634\pi$
$180$	−853.292	−	1477.95i	−0.0263362	−	0.0456156i
$181$	−6016.05	+	3473.37i	−0.183635	+	0.106022i	−0.588999	−	0.808134i	$-0.700478\pi$
$181$	−6016.05	+	3473.37i	−0.183635	+	0.106022i	0.405365	+	0.914155i	$0.367145\pi$
$182$	−70079.1			−2.11566
$183$			10702.7i			0.319587i
$184$	−5177.11	+	2989.00i	−0.152916	+	0.0882858i
$185$	−1471.01	−	849.289i	−0.0429806	−	0.0248149i
$186$	−2396.35	+	1383.53i	−0.0692668	+	0.0399912i
$187$	−23162.0	+	40117.8i	−0.662359	+	1.14724i
$188$	6576.22	−	11390.3i	0.186063	−	0.322271i
$189$		−	19164.8i		−	0.536513i
$190$	1686.84	−	2193.25i	0.0467270	−	0.0607549i
$191$	51066.6			1.39981			0.699906	−	0.714235i	$-0.253225\pi$
$191$	51066.6			1.39981			0.699906	+	0.714235i	$0.253225\pi$
$192$	−669.271	−	386.404i	−0.0181551	−	0.0104819i
$193$	−32396.3	−	18704.0i	−0.869723	−	0.502135i	−0.00246664	−	0.999997i	$-0.500785\pi$
$193$	−32396.3	−	18704.0i	−0.869723	−	0.502135i	−0.867256	+	0.497862i	$0.834118\pi$
$194$	6640.42	+	11501.5i	0.176438	+	0.305599i
$195$	637.411	−	1104.03i	0.0167629	−	0.0290343i
$196$	15673.7	+	27147.6i	0.407998	+	0.706674i
$197$	717.559			0.0184895			0.00924475	−	0.999957i	$-0.497057\pi$
$197$	717.559			0.0184895			0.00924475	+	0.999957i	$0.497057\pi$
$198$			24276.5i			0.619234i
$199$	−36697.8	−	63562.4i	−0.926688	−	1.60507i	−0.788824	−	0.614619i	$-0.789310\pi$
$199$	−36697.8	−	63562.4i	−0.926688	−	1.60507i	−0.137863	−	0.990451i	$-0.544023\pi$
$200$	12103.6	−	6987.99i	0.302589	−	0.174700i
$201$	90.4414			0.00223859
$202$		−	34190.9i		−	0.837930i
$203$	−16175.4	+	9338.87i	−0.392521	+	0.226622i
$204$	−4443.07	−	2565.21i	−0.106764	−	0.0616399i
$205$	−1126.24	+	650.234i	−0.0267992	+	0.0154725i
$206$	8422.85	−	14588.8i	0.198484	−	0.343784i
$207$	−10398.9	+	18011.4i	−0.242687	+	0.420345i
$208$			19947.3i			0.461061i
$209$	−36380.5	+	15021.7i	−0.832868	+	0.343895i
$210$	−919.661			−0.0208540
$211$	47735.6	+	27560.2i	1.07221	+	0.619038i	0.928783	−	0.370624i	$-0.120856\pi$
$211$	47735.6	+	27560.2i	1.07221	+	0.619038i	0.143422	+	0.989662i	$0.454189\pi$
$212$	−32946.0	−	19021.4i	−0.733045	−	0.423223i
$213$	4719.89	+	8175.09i	0.104033	+	0.180191i
$214$	−799.275	+	1384.38i	−0.0174529	+	0.0302294i
$215$	1685.70	+	2919.71i	0.0364672	+	0.0631630i
$216$	−5455.07			−0.116921
$217$		−	51524.3i		−	1.09419i
$218$	−2486.22	−	4306.26i	−0.0523151	−	0.0906124i
$219$	−3161.60	+	1825.35i	−0.0659203	+	0.0380591i
$220$	2363.62			0.0488352
$221$			132424.i			2.71132i
$222$	−2317.50	+	1338.01i	−0.0470233	+	0.0271489i
$223$	−46662.3	−	26940.5i	−0.938333	−	0.541747i	−0.0488954	−	0.998804i	$-0.515570\pi$
$223$	−46662.3	−	26940.5i	−0.938333	−	0.541747i	−0.889437	+	0.457057i	$0.848903\pi$
$224$	12462.2	−	7195.04i	0.248369	−	0.143396i
$225$	24311.5	−	42108.8i	0.480227	−	0.831778i
$226$	−14020.4	+	24284.1i	−0.274502	+	0.475451i
$227$		−	68480.7i		−	1.32897i	−0.747300	−	0.664487i	$-0.768650\pi$
$227$		−	68480.7i		−	1.32897i	0.747300	−	0.664487i	$-0.231350\pi$
$228$	−1663.66	−	4029.16i	−0.0320032	−	0.0775077i
$229$	−31051.4			−0.592120			−0.296060	−	0.955169i	$-0.595673\pi$
$229$	−31051.4			−0.592120			−0.296060	+	0.955169i	$0.595673\pi$
$230$	1753.64	+	1012.46i	0.0331501	+	0.0191392i
$231$	11329.6	+	6541.17i	0.212321	+	0.122583i
$232$	2658.22	+	4604.17i	0.0493873	+	0.0855412i
$233$	−8921.34	+	15452.2i	−0.164330	+	0.284629i	−0.936417	−	0.350888i	$-0.885880\pi$
$233$	−8921.34	+	15452.2i	−0.164330	+	0.284629i	0.772087	+	0.635517i	$0.219213\pi$
$234$	34698.8	+	60100.1i	0.633699	+	1.09760i
$235$	−4455.12			−0.0806722
$236$		−	39055.1i		−	0.701219i
$237$	−3210.72	−	5561.13i	−0.0571618	−	0.0990071i
$238$	82732.3	−	47765.5i	1.46057	−	0.843258i
$239$	76980.4			1.34767			0.673837	−	0.738880i	$-0.264645\pi$
$239$	76980.4			1.34767			0.673837	+	0.738880i	$0.264645\pi$
$240$			261.773i			0.00454467i
$241$	52604.0	−	30371.0i	0.905701	−	0.522907i	0.0266557	−	0.999645i	$-0.491514\pi$
$241$	52604.0	−	30371.0i	0.905701	−	0.522907i	0.879046	+	0.476738i	$0.158181\pi$
$242$	6744.64	+	3894.02i	0.115167	+	0.0664917i
$243$	−24770.9	+	14301.5i	−0.419498	+	0.242197i
$244$	−28362.9	+	49125.9i	−0.476399	+	0.825147i
$245$	5309.13	−	9195.69i	0.0884487	−	0.153198i
$246$			2048.82i			0.0338558i
$247$	−68594.8	+	89187.8i	−1.12434	+	1.46188i
$248$	−14665.9			−0.238454
$249$	−8683.60	−	5013.48i	−0.140056	−	0.0808613i
$250$	−8248.40	−	4762.22i	−0.131974	−	0.0761955i
$251$	−19773.1	−	34248.0i	−0.313853	−	0.543610i	0.665340	−	0.746541i	$-0.268287\pi$
$251$	−19773.1	−	34248.0i	−0.313853	−	0.543610i	−0.979193	+	0.202931i	$0.934953\pi$
$252$	25031.9	−	43356.5i	0.394178	−	0.682736i
$253$	−14402.5	−	24945.8i	−0.225007	−	0.389724i
$254$	41753.9			0.647187
$255$			1737.82i			0.0267255i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−29307.4	+	16920.7i	−0.443723	+	0.256183i	−0.705175	−	0.709033i	$-0.749132\pi$
$257$	−29307.4	+	16920.7i	−0.443723	+	0.256183i	0.261453	+	0.965216i	$0.415798\pi$
$258$	5311.44			0.0797945
$259$		−	49828.8i		−	0.742816i
$260$	5851.52	−	3378.38i	0.0865609	−	0.0499760i
$261$	16018.1	+	9248.06i	0.235142	+	0.135759i
$262$	16549.5	−	9554.88i	0.241092	−	0.139195i
$263$	48919.2	−	84730.5i	0.707241	−	1.22498i	−0.258635	−	0.965975i	$-0.583273\pi$
$263$	48919.2	−	84730.5i	0.707241	−	1.22498i	0.965877	−	0.259003i	$-0.0833939\pi$
$264$	1861.88	−	3224.87i	0.0267143	−	0.0462706i
$265$			12886.2i			0.183499i
$266$	80462.8	+	10684.7i	1.13719	+	0.151008i
$267$	14796.5			0.207556
$268$	415.132	+	239.677i	0.00577985	+	0.00333700i
$269$	540.509	+	312.063i	0.00746962	+	0.00431259i	0.503730	−	0.863861i	$-0.331961\pi$
$269$	540.509	+	312.063i	0.00746962	+	0.00431259i	−0.496261	+	0.868174i	$0.665294\pi$
$270$	923.897	+	1600.24i	0.0126735	+	0.0219511i
$271$	−27056.1	+	46862.5i	−0.368406	+	0.638097i	−0.989316	−	0.145784i	$-0.953430\pi$
$271$	−27056.1	+	46862.5i	−0.368406	+	0.638097i	0.620911	+	0.783881i	$0.286763\pi$
$272$	−13596.0	−	23549.0i	−0.183769	−	0.318298i
$273$	37397.7			0.501787
$274$		−	23266.4i		−	0.309905i
$275$	33671.5	+	58320.8i	0.445243	+	0.771184i
$276$	2762.76	−	1595.08i	0.0362682	−	0.0209394i
$277$	−56774.7			−0.739938			−0.369969	−	0.929044i	$-0.620632\pi$
$277$	−56774.7			−0.739938			−0.369969	+	0.929044i	$0.620632\pi$
$278$			21391.5i			0.276791i
$279$	−44187.5	+	25511.6i	−0.567663	+	0.327740i
$280$	−4221.31	−	2437.17i	−0.0538432	−	0.0310864i
$281$	97544.0	−	56317.0i	1.23534	−	0.713226i	0.267205	−	0.963640i	$-0.413900\pi$
$281$	97544.0	−	56317.0i	1.23534	−	0.713226i	0.968139	+	0.250414i	$0.0805667\pi$
$282$	−3509.40	+	6078.46i	−0.0441301	+	0.0764355i
$283$	30039.8	−	52030.4i	0.375080	−	0.649658i	−0.615259	−	0.788325i	$-0.710949\pi$
$283$	30039.8	−	52030.4i	0.375080	−	0.649658i	0.990339	+	0.138667i	$0.0442819\pi$
$284$			50032.3i			0.620317i
$285$	−900.184	+	1170.43i	−0.0110826	+	0.0144097i
$286$	−96115.9			−1.17507
$287$	−33038.9	−	19075.0i	−0.401108	−	0.231580i
$288$	−12341.0	−	7125.08i	−0.148787	−	0.0859023i
$289$	−48498.9	−	84002.5i	−0.580679	−	1.00577i
$290$	900.418	−	1559.57i	0.0107065	−	0.0185442i
$291$	−3543.66	−	6137.79i	−0.0418471	−	0.0724814i
$292$	−19349.3			−0.226934
$293$			143559.i			1.67223i	0.548555	+	0.836115i	$0.315178\pi$
$293$			143559.i			1.67223i	−0.548555	+	0.836115i	$0.684822\pi$
$294$	−8364.25	−	14487.3i	−0.0967681	−	0.167607i
$295$	−11456.7	+	6614.55i	−0.131649	+	0.0760075i
$296$	−14183.3			−0.161880
$297$		−	26285.2i		−	0.297988i
$298$	29209.5	−	16864.1i	0.328921	−	0.189903i
$299$	−71311.1	−	41171.5i	−0.797654	−	0.460526i
$300$	−6459.06	+	3729.14i	−0.0717673	+	0.0414349i
$301$	−49450.9	+	85651.5i	−0.545810	+	0.945370i
$302$	−40965.6	+	70954.4i	−0.449164	+	0.777975i
$303$			18246.0i			0.198738i
$304$	3041.29	−	22903.0i	0.0329087	−	0.247825i
$305$	19214.7			0.206554
$306$	−81927.8	−	47301.1i	−0.874961	−	0.505159i
$307$	46012.3	+	26565.2i	0.488200	+	0.281862i	0.723827	−	0.689981i	$-0.242381\pi$
$307$	46012.3	+	26565.2i	0.488200	+	0.281862i	−0.235628	+	0.971843i	$0.575715\pi$
$308$	34669.2	+	60048.8i	0.365462	+	0.632999i
$309$	−4494.85	+	7785.31i	−0.0470759	+	0.0815378i
$310$	2483.89	+	4302.22i	0.0258469	+	0.0447681i
$311$	−74095.4			−0.766074			−0.383037	−	0.923733i	$-0.625122\pi$
$311$	−74095.4			−0.766074			−0.383037	+	0.923733i	$0.625122\pi$
$312$		−	10644.9i		−	0.109353i
$313$	70166.3	+	121532.i	0.716209	+	1.24051i	0.962491	+	0.271313i	$0.0874577\pi$
$313$	70166.3	+	121532.i	0.716209	+	1.24051i	−0.246282	+	0.969198i	$0.579209\pi$
$314$	15676.6	−	9050.89i	0.158998	−	0.0917978i
$315$	−16958.1			−0.170905
$316$		−	34034.6i		−	0.340837i
$317$	−88820.2	+	51280.4i	−0.883880	+	0.510308i	−0.871936	−	0.489620i	$-0.837135\pi$
$317$	−88820.2	+	51280.4i	−0.883880	+	0.510308i	−0.0119442	+	0.999929i	$0.503802\pi$
$318$	17581.6	+	10150.7i	0.173862	+	0.100379i
$319$	−22185.1	+	12808.6i	−0.218012	+	0.125869i
$320$	−693.718	+	1201.56i	−0.00677459	+	0.0117339i
$321$	426.533	−	738.777i	0.00413945	−	0.00716974i
$322$			59402.5i			0.572919i
$323$	20190.2	−	152045.i	0.193524	−	1.45736i
$324$	−48100.6			−0.458206
$325$	166718.	+	96254.7i	1.57840	+	0.911287i
$326$	12250.6	+	7072.91i	0.115272	+	0.0665522i
$327$	1326.77	+	2298.04i	0.0124080	+	0.0214912i
$328$	−5429.52	+	9404.20i	−0.0504677	+	0.0874127i
$329$	−65346.9	−	113184.i	−0.603717	−	1.04567i
$330$	−1261.35			−0.0115826
$331$			34528.3i			0.315152i	0.987507	+	0.157576i	$0.0503679\pi$
$331$			34528.3i			0.315152i	−0.987507	+	0.157576i	$0.949632\pi$
$332$	−26572.2	−	46024.5i	−0.241075	−	0.417554i
$333$	−42733.4	+	24672.1i	−0.385371	+	0.222494i
$334$	−71512.9			−0.641049
$335$		−	162.371i		−	0.00144684i
$336$	−6650.44	+	3839.63i	−0.0589077	+	0.0340104i
$337$	155389.	+	89714.0i	1.36824	+	0.789951i	0.990703	−	0.136045i	$-0.0434392\pi$
$337$	155389.	+	89714.0i	1.36824	+	0.789951i	0.377533	+	0.925996i	$0.376773\pi$
$338$	−167990.	+	96989.0i	−1.47045	+	0.848964i
$339$	7482.01	−	12959.2i	0.0651057	−	0.112766i
$340$	−4605.37	+	7976.73i	−0.0398388	+	0.0690029i
$341$		−	70667.4i		−	0.607730i
$342$	−30676.9	−	74295.6i	−0.262277	−	0.635201i
$343$	120626.			1.02531
$344$	24379.9	+	14075.7i	0.206023	+	0.118947i
$345$	−935.829	−	540.301i	−0.00786246	−	0.00453939i
$346$	14609.9	+	25305.0i	0.122038	+	0.211376i
$347$	96226.4	−	166669.i	0.799163	−	1.38419i	−0.120999	−	0.992653i	$-0.538610\pi$
$347$	96226.4	−	166669.i	0.799163	−	1.38419i	0.920162	−	0.391538i	$-0.128057\pi$
$348$	−1418.56	−	2457.02i	−0.0117136	−	0.0202885i
$349$	91163.6			0.748463			0.374232	−	0.927335i	$-0.377906\pi$
$349$	91163.6			0.748463			0.374232	+	0.927335i	$0.377906\pi$
$350$		−	138877.i		−	1.13369i
$351$	−37569.9	−	65073.0i	−0.304948	−	0.528186i
$352$	17092.3	−	9868.26i	0.137948	−	0.0796444i
$353$	126024.			1.01136			0.505678	−	0.862722i	$-0.331242\pi$
$353$	126024.			1.01136			0.505678	+	0.862722i	$0.331242\pi$
$354$			20841.7i			0.166313i
$355$	14676.9	−	8473.71i	0.116460	−	0.0672383i
$356$	67916.9	+	39211.8i	0.535893	+	0.309398i
$357$	−44150.1	+	25490.1i	−0.346414	+	0.200002i
$358$	72874.3	−	126222.i	0.568602	−	0.984848i
$359$	32340.5	−	56015.4i	0.250933	−	0.434629i	−0.712850	−	0.701317i	$-0.752596\pi$
$359$	32340.5	−	56015.4i	0.250933	−	0.434629i	0.963783	+	0.266688i	$0.0859293\pi$
$360$			4826.95i			0.0372450i
$361$	92356.8	−	91944.5i	0.708687	−	0.705523i
$362$	19648.4			0.149937
$363$	−3599.28	−	2078.04i	−0.0273150	−	0.0157703i
$364$	171658.	+	99106.7i	1.29557	+	0.747998i
$365$	3277.09	+	5676.09i	0.0245982	+	0.0426053i
$366$	15135.8	−	26216.1i	0.112991	−	0.195706i
$367$	−83548.4	−	144710.i	−0.620306	−	1.07440i	−0.989429	−	0.145021i	$-0.953675\pi$
$367$	−83548.4	−	144710.i	−0.620306	−	1.07440i	0.369123	−	0.929381i	$-0.379658\pi$
$368$	16908.4			0.124855
$369$			37779.1i			0.277459i
$370$	2402.15	+	4160.65i	0.0175468	+	0.0303919i
$371$	−327379.	+	189012.i	−2.37850	+	1.37323i
$372$	7826.45			0.0565561
$373$		−	115820.i		−	0.832467i	−0.909258	−	0.416234i	$-0.863350\pi$
$373$		−	115820.i		−	0.832467i	0.909258	−	0.416234i	$-0.136650\pi$
$374$	113470.	−	65512.1i	0.811221	−	0.468359i
$375$	4401.76	+	2541.36i	0.0313014	+	0.0180719i
$376$	−32216.8	+	18600.4i	−0.227880	+	0.131567i
$377$	−36615.1	+	63419.3i	−0.257619	+	0.446209i
$378$	−27103.1	+	46943.9i	−0.189686	+	0.328546i
$379$			90727.2i			0.631624i	0.948822	+	0.315812i	$0.102277\pi$
$379$			90727.2i			0.631624i	−0.948822	+	0.315812i	$0.897723\pi$
$380$	−7233.63	+	2986.79i	−0.0500944	+	0.0206842i
$381$	−22282.0			−0.153498
$382$	−125087.	−	72219.0i	−0.857207	−	0.494908i
$383$	26744.8	+	15441.1i	0.182323	+	0.105264i	0.588384	−	0.808582i	$-0.299764\pi$
$383$	26744.8	+	15441.1i	0.182323	+	0.105264i	−0.406061	+	0.913846i	$0.633098\pi$
$384$	1092.91	+	1892.98i	0.00741180	+	0.0128376i
$385$	11743.5	−	20340.3i	0.0792274	−	0.137226i
$386$	52902.9	+	91630.6i	0.355063	+	0.614987i
$387$	97940.1			0.653941
$388$		−	37563.9i		−	0.249521i
$389$	55857.2	+	96747.4i	0.369130	+	0.639352i	0.989430	−	0.145013i	$-0.0463223\pi$
$389$	55857.2	+	96747.4i	0.369130	+	0.639352i	−0.620300	+	0.784365i	$0.712989\pi$
$390$	−3122.66	+	1802.87i	−0.0205303	+	0.0118532i
$391$	112249.			0.734225
$392$		−	88663.6i		−	0.576997i
$393$	−8831.66	+	5098.96i	−0.0571817	+	0.0330139i
$394$	−1757.65	−	1014.78i	−0.0113225	−	0.00653703i
$395$	−9984.00	+	5764.27i	−0.0639898	+	0.0369445i
$396$	34332.1	−	59464.9i	0.218932	−	0.379202i
$397$	−96824.6	+	167705.i	−0.614334	+	1.06406i	0.376167	+	0.926552i	$0.377242\pi$
$397$	−96824.6	+	167705.i	−0.614334	+	1.06406i	−0.990501	+	0.137506i	$0.956091\pi$
$398$			207594.i			1.31053i
$399$	−42938.9	−	5701.88i	−0.269715	−	0.0358156i
$400$	−39530.0			−0.247063
$401$	35967.6	+	20765.9i	0.223678	+	0.129140i	0.607652	−	0.794203i	$-0.292112\pi$
$401$	35967.6	+	20765.9i	0.223678	+	0.129140i	−0.383974	+	0.923344i	$0.625445\pi$
$402$	−221.535	−	127.903i	−0.00137085	−	0.000791462i
$403$	−101006.	−	174948.i	−0.621926	−	1.07721i
$404$	−48353.2	+	83750.3i	−0.296253	+	0.513125i
$405$	8146.55	+	14110.2i	0.0496665	+	0.0860249i
$406$	52828.6			0.320492
$407$		−	68342.0i		−	0.412571i
$408$	7255.50	+	12566.9i	0.0435860	+	0.0754932i
$409$	−120340.	+	69478.3i	−0.719388	+	0.415339i	−0.814527	−	0.580125i	$-0.803004\pi$
$409$	−120340.	+	69478.3i	−0.719388	+	0.415339i	0.0951394	+	0.995464i	$0.469670\pi$
$410$	3678.28			0.0218815
$411$			12416.1i			0.0735025i
$412$	−41263.4	+	23823.4i	−0.243092	+	0.140349i
$413$	−336091.	−	194042.i	−1.97041	−	1.13762i
$414$	50943.9	−	29412.5i	0.297229	−	0.171605i
$415$	−9000.80	+	15589.8i	−0.0522619	+	0.0905202i
$416$	28209.8	−	48860.8i	0.163010	−	0.282341i
$417$		−	11415.6i		−	0.0656487i
$418$	110358.	+	14654.4i	0.631611	+	0.0838719i
$419$	−265295.			−1.51113			−0.755563	−	0.655075i	$-0.772637\pi$
$419$	−265295.			−1.51113			−0.755563	+	0.655075i	$0.772637\pi$
$420$	2252.70	+	1300.60i	0.0127704	+	0.00737300i
$421$	78399.4	+	45263.9i	0.442332	+	0.255381i	0.704586	−	0.709618i	$-0.251133\pi$
$421$	78399.4	+	45263.9i	0.442332	+	0.255381i	−0.262254	+	0.964999i	$0.584466\pi$
$422$	−77952.0	−	135017.i	−0.437726	−	0.758164i
$423$	−64711.4	+	112084.i	−0.361660	+	0.626413i
$424$	53800.5	+	93185.2i	0.299264	+	0.518341i
$425$	−262427.			−1.45288
$426$		−	26699.7i		−	0.147125i
$427$	281837.	+	488157.i	1.54576	+	2.67734i
$428$	3915.63	−	2260.69i	0.0213754	−	0.0123411i
$429$	51292.2			0.278700
$430$		−	9535.73i		−	0.0515724i
$431$	102698.	−	59292.7i	0.552850	−	0.319188i	−0.197421	−	0.980319i	$-0.563257\pi$
$431$	102698.	−	59292.7i	0.552850	−	0.319188i	0.750271	+	0.661131i	$0.229923\pi$
$432$	13362.1	+	7714.64i	0.0715993	+	0.0413379i
$433$	−134033.	+	77384.1i	−0.714885	+	0.412739i	−0.812867	−	0.582449i	$-0.802095\pi$
$433$	−134033.	+	77384.1i	−0.714885	+	0.412739i	0.0979820	+	0.995188i	$0.468761\pi$
$434$	−72866.4	+	126208.i	−0.386855	+	0.670052i
$435$	−480.508	+	832.264i	−0.00253935	+	0.00439828i
$436$			14064.2i			0.0739847i
$437$	75600.1	+	58144.4i	0.395876	+	0.304471i
$438$	10325.8			0.0538237
$439$	−104458.	−	60308.7i	−0.542015	−	0.312933i	0.203880	−	0.978996i	$-0.434645\pi$
$439$	−104458.	−	60308.7i	−0.542015	−	0.312933i	−0.745895	+	0.666063i	$0.767978\pi$
$440$	−5789.67	−	3342.67i	−0.0299053	−	0.0172659i
$441$	−154232.	−	267138.i	−0.793045	−	1.37359i
$442$	187276.	−	324371.i	0.958598	−	1.66034i
$443$	59838.7	+	103644.i	0.304912	+	0.528123i	0.977242	−	0.212129i	$-0.0680396\pi$
$443$	59838.7	+	103644.i	0.304912	+	0.528123i	−0.672330	+	0.740252i	$0.734706\pi$
$444$	7568.92			0.0383944
$445$		−	26564.4i		−	0.134147i
$446$	76199.3	+	131981.i	0.383073	+	0.663501i
$447$	−15587.7	+	8999.54i	−0.0780128	+	0.0450407i
$448$	−40701.3			−0.202793
$449$		−	361353.i		−	1.79242i	−0.443632	−	0.896209i	$-0.646310\pi$
$449$		−	361353.i		−	1.79242i	0.443632	−	0.896209i	$-0.353690\pi$
$450$	−119102.	+	68763.3i	−0.588156	+	0.339572i
$451$	−45314.0	−	26162.1i	−0.222782	−	0.128623i
$452$	68685.9	−	39655.8i	0.336194	−	0.194102i
$453$	21861.3	−	37864.8i	0.106532	−	0.184518i
$454$	−96846.3	+	167743.i	−0.469863	+	0.813827i
$455$		−	67140.8i		−	0.324312i
$456$	−1622.99	+	12222.2i	−0.00780522	+	0.0587785i
$457$	247568.			1.18539			0.592695	−	0.805427i	$-0.298064\pi$
$457$	247568.			1.18539			0.592695	+	0.805427i	$0.298064\pi$
$458$	76060.1	+	43913.3i	0.362598	+	0.209346i
$459$	88706.9	+	51214.9i	0.421048	+	0.243092i
$460$	−2863.68	−	4960.04i	−0.0135335	−	0.0234406i
$461$	34100.9	−	59064.5i	0.160459	−	0.277923i	−0.774574	−	0.632483i	$-0.782036\pi$
$461$	34100.9	−	59064.5i	0.160459	−	0.277923i	0.935033	+	0.354560i	$0.115369\pi$
$462$	−18501.2	−	32045.1i	−0.0866795	−	0.150133i
$463$	265413.			1.23811			0.619057	−	0.785346i	$-0.287515\pi$
$463$	265413.			1.23811			0.619057	+	0.785346i	$0.287515\pi$
$464$		−	15037.2i		−	0.0698441i
$465$	−1325.53	−	2295.88i	−0.00613031	−	0.0106180i
$466$	43705.4	−	25233.4i	0.201263	−	0.116199i
$467$	44511.7			0.204099			0.102049	−	0.994779i	$-0.467460\pi$
$467$	44511.7			0.204099			0.102049	+	0.994779i	$0.467460\pi$
$468$		−	196286.i		−	0.896185i
$469$	4125.10	−	2381.63i	0.0187538	−	0.0108275i
$470$	10912.8	+	6300.49i	0.0494014	+	0.0285219i
$471$	−8365.82	+	4830.01i	−0.0377109	+	0.0217724i
$472$	−55232.2	+	95665.0i	−0.247918	+	0.429407i
$473$	−67823.7	+	117474.i	−0.303151	+	0.525073i
$474$			18162.6i			0.0808390i
$475$	−176745.	−	135936.i	−0.783359	−	0.602486i
$476$	−270203.			−1.19255
$477$	324195.	+	187174.i	1.42485	+	0.822639i
$478$	−188563.	−	108867.i	−0.825278	−	0.476474i
$479$	110281.	+	191012.i	0.480650	+	0.832511i	0.999754	−	0.0222009i	$-0.00706733\pi$
$479$	110281.	+	191012.i	0.480650	+	0.832511i	−0.519103	+	0.854712i	$0.673734\pi$
$480$	370.203	−	641.210i	0.00160678	−	0.00278303i
$481$	−97682.6	−	169191.i	−0.422208	−	0.731286i
$482$	−171804.			−0.739502
$483$		−	31700.2i		−	0.135884i
$484$	−11013.9	−	19076.7i	−0.0470167	−	0.0814353i
$485$	−11019.3	+	6361.99i	−0.0468458	+	0.0270464i
$486$	80901.5			0.342518
$487$			291672.i			1.22981i	0.788602	+	0.614904i	$0.210805\pi$
$487$			291672.i			1.22981i	−0.788602	+	0.614904i	$0.789195\pi$
$488$	138949.	−	80222.3i	0.583467	−	0.336865i
$489$	−6537.55	−	3774.46i	−0.0273399	−	0.0157847i
$490$	−26009.3	+	15016.5i	−0.108327	+	0.0625427i
$491$	155315.	−	269013.i	0.644243	−	1.11586i	−0.340233	−	0.940341i	$-0.610506\pi$
$491$	155315.	−	269013.i	0.644243	−	1.11586i	0.984476	−	0.175521i	$-0.0561609\pi$
$492$	2897.46	−	5018.55i	0.0119698	−	0.0207323i
$493$		−	99826.8i		−	0.410727i
$494$	294153.	−	121457.i	1.20537	−	0.497701i
$495$	−23258.6			−0.0949233
$496$	35924.0	+	20740.7i	0.146023	+	0.0843064i
$497$	430556.	+	248581.i	1.74308	+	1.00637i
$498$	14180.3	+	24560.9i	0.0571776	+	0.0990345i
$499$	184973.	−	320383.i	0.742862	−	1.28667i	−0.208325	−	0.978060i	$-0.566801\pi$
$499$	184973.	−	320383.i	0.742862	−	1.28667i	0.951187	−	0.308615i	$-0.0998655\pi$
$500$	13469.6	+	23330.0i	0.0538783	+	0.0933200i
$501$	38162.8			0.152043
$502$			111853.i			0.443856i
$503$	−109000.	−	188793.i	−0.430814	−	0.746192i	0.566130	−	0.824316i	$-0.308440\pi$
$503$	−109000.	−	188793.i	−0.430814	−	0.746192i	−0.996944	+	0.0781244i	$0.975107\pi$
$504$	−122631.	+	70800.8i	−0.482767	+	0.278726i
$505$	32757.3			0.128448
$506$			81472.7i			0.318208i
$507$	89647.8	−	51758.2i	0.348758	−	0.201355i
$508$	−102276.	−	59048.9i	−0.396319	−	0.228815i
$509$	−217588.	+	125625.i	−0.839847	+	0.484886i	−0.857212	−	0.514964i	$-0.827805\pi$
$509$	−217588.	+	125625.i	−0.839847	+	0.484886i	0.0173655	+	0.999849i	$0.494472\pi$
$510$	2457.65	−	4256.78i	0.00944888	−	0.0163659i
$511$	−96135.5	+	166512.i	−0.368165	+	0.637680i
$512$			11585.2i			0.0441942i
$513$	33215.3	+	80443.1i	0.126213	+	0.305671i
$514$	95717.7			0.362298
$515$	13977.1	+	8069.69i	0.0526991	+	0.0304258i
$516$	−13010.3	−	7511.51i	−0.0488639	−	0.0282116i
$517$	−89625.6	−	155236.i	−0.335313	−	0.580780i
$518$	−70468.6	+	122055.i	−0.262625	+	0.454880i
$519$	−7796.55	−	13504.0i	−0.0289446	−	0.0501336i
$520$	−19111.0			−0.0706767
$521$		−	102324.i		−	0.376968i	−0.982076	−	0.188484i	$-0.939643\pi$
$521$		−	102324.i		−	0.376968i	0.982076	−	0.188484i	$-0.0603573\pi$
$522$	−26157.5	−	45306.1i	−0.0959963	−	0.166271i
$523$	−190819.	+	110169.i	−0.697618	+	0.402770i	−0.806460	−	0.591289i	$-0.798619\pi$
$523$	−190819.	+	110169.i	−0.697618	+	0.402770i	0.108841	+	0.994059i	$0.465286\pi$
$524$	−54050.6			−0.196851
$525$			74111.7i			0.268886i
$526$	−239654.	+	138364.i	−0.866190	+	0.500095i
$527$	238487.	+	137691.i	0.858706	+	0.495774i
$528$	−9121.32	+	5266.19i	−0.0327182	+	0.0188899i
$529$	105021.	−	181903.i	0.375290	−	0.650021i
$530$	18223.8	−	31564.6i	0.0648766	−	0.112369i
$531$			384310.i			1.36299i
$532$	−181982.	−	139964.i	−0.642992	−	0.494529i
$533$	−149576.			−0.526510
$534$	−36243.9	−	20925.4i	−0.127102	−	0.0733823i
$535$	−1326.34	−	765.763i	−0.00463391	−	0.00267539i
$536$	−677.908	−	1174.17i	−0.00235962	−	0.00408697i
$537$	−38889.4	+	67358.4i	−0.134860	+	0.233584i
$538$	−882.648	−	1528.79i	−0.00304946	−	0.00528182i
$539$	427224.			1.47055
$540$		−	5226.35i		−	0.0179230i
$541$	−203815.	−	353017.i	−0.696372	−	1.20615i	−0.969716	−	0.244235i	$-0.921463\pi$
$541$	−203815.	−	353017.i	−0.696372	−	1.20615i	0.273344	−	0.961916i	$-0.411870\pi$
$542$	132547.	−	76526.2i	0.451203	−	0.260502i
$543$	−10485.3			−0.0355617
$544$			76910.6i			0.259889i
$545$	4125.71	−	2381.98i	0.0138901	−	0.00801946i
$546$	−91605.2	−	52888.3i	−0.307280	−	0.177408i
$547$	−96394.7	+	55653.5i	−0.322165	+	0.186002i	−0.652357	−	0.757912i	$-0.726220\pi$
$547$	−96394.7	+	55653.5i	−0.322165	+	0.186002i	0.330192	+	0.943914i	$0.392886\pi$
$548$	−32903.7	+	56990.8i	−0.109568	+	0.189777i
$549$	279097.	−	483410.i	0.925998	−	1.60388i
$550$		−	190475.i		−	0.629669i
$551$	51709.8	−	67233.6i	0.170321	−	0.221454i
$552$	−9023.15			−0.0296128
$553$	−292887.	−	169098.i	−0.957745	−	0.552954i
$554$	139069.	+	80291.5i	0.453117	+	0.261607i
$555$	−1281.91	−	2220.33i	−0.00416170	−	0.00720828i
$556$	30252.2	−	52398.3i	0.0978604	−	0.169499i
$557$	−175783.	−	304466.i	−0.566588	−	0.981360i	−0.996900	−	0.0786795i	$-0.974930\pi$
$557$	−175783.	−	304466.i	−0.566588	−	0.981360i	0.430312	−	0.902680i	$-0.358404\pi$
$558$	144316.			0.463495
$559$			387767.i			1.24093i
$560$	6893.37	+	11939.7i	0.0219814	+	0.0380729i
$561$	−60553.4	+	34960.5i	−0.192404	+	0.111084i
$562$	−318577.			−1.00865
$563$			328649.i			1.03685i	0.855124	+	0.518424i	$0.173481\pi$
$563$			328649.i			1.03685i	−0.855124	+	0.518424i	$0.826519\pi$
$564$	17192.5	−	9926.08i	0.0540481	−	0.0312047i
$565$	−23265.9	−	13432.6i	−0.0728825	−	0.0420788i
$566$	−147164.	+	84965.4i	−0.459377	+	0.265222i
$567$	−238984.	+	413932.i	−0.743366	+	1.28755i
$568$	70756.3	−	122554.i	0.219315	−	0.379865i
$569$			388285.i			1.19929i	0.800264	+	0.599647i	$0.204692\pi$
$569$			388285.i			1.19929i	−0.800264	+	0.599647i	$0.795308\pi$
$570$	3860.23	−	1593.90i	0.0118813	−	0.00490583i
$571$	16892.4			0.0518107			0.0259054	−	0.999664i	$-0.491753\pi$
$571$	16892.4			0.0518107			0.0259054	+	0.999664i	$0.491753\pi$
$572$	235435.	+	135928.i	0.719580	+	0.415450i
$573$	66752.7	+	38539.7i	0.203310	+	0.117381i
$574$	53952.3	+	93448.1i	0.163752	+	0.283626i
$575$	81590.4	−	141319.i	0.246776	−	0.427429i
$576$	20152.8	+	34905.6i	0.0607421	+	0.105208i
$577$	−522045.			−1.56804			−0.784018	−	0.620738i	$-0.786833\pi$
$577$	−522045.			−1.56804			−0.784018	+	0.620738i	$0.786833\pi$
$578$			274351.i			0.821204i
$579$	−28231.6	−	48898.6i	−0.0842130	−	0.145861i
$580$	−4411.13	+	2546.77i	−0.0131127	+	0.00757065i
$581$	−528088.			−1.56442
$582$			20045.9i			0.0591808i
$583$	−449012.	+	259237.i	−1.32105	+	0.762711i
$584$	47395.9	+	27364.1i	0.138968	+	0.0802333i
$585$	−57580.2	+	33243.9i	−0.168252	+	0.0971406i
$586$	203023.	−	351647.i	0.591222	−	1.02403i
$587$	200724.	−	347665.i	0.582538	−	1.00898i	−0.412640	−	0.910894i	$-0.635393\pi$
$587$	200724.	−	347665.i	0.582538	−	1.00898i	0.995177	−	0.0980906i	$-0.0312735\pi$
$588$			47315.3i			0.136851i
$589$	89298.9	+	216270.i	0.257404	+	0.623400i
$590$	37417.6			0.107491
$591$	937.972	+	541.538i	0.00268544	+	0.00155044i
$592$	34741.8	+	20058.2i	0.0991310	+	0.0572333i
$593$	171949.	+	297824.i	0.488979	+	0.846936i	0.999920	−	0.0126797i	$-0.00403619\pi$
$593$	171949.	+	297824.i	0.488979	+	0.846936i	−0.510941	+	0.859616i	$0.670703\pi$
$594$	−37172.9	+	64385.3i	−0.105354	+	0.182479i
$595$	45762.8	+	79263.5i	0.129264	+	0.223892i
$596$	−95398.0			−0.268563
$597$		−	110782.i		−	0.310830i
$598$	116451.	+	201698.i	0.325641	+	0.564027i
$599$	73567.3	−	42474.1i	0.205036	−	0.118378i	−0.393966	−	0.919125i	$-0.628897\pi$
$599$	73567.3	−	42474.1i	0.205036	−	0.118378i	0.599003	+	0.800747i	$0.295564\pi$
$600$	21095.2			0.0585978
$601$			40436.4i			0.111950i	0.998432	+	0.0559749i	$0.0178267\pi$
$601$			40436.4i			0.111950i	−0.998432	+	0.0559749i	$0.982173\pi$
$602$	242259.	−	139868.i	0.668478	−	0.385946i
$603$	−4084.99	−	2358.47i	−0.0112346	−	0.00648628i
$604$	200689.	−	115868.i	0.550111	−	0.317607i
$605$	−3730.75	+	6461.85i	−0.0101926	+	0.0176541i
$606$	25803.7	−	44693.3i	0.0702646	−	0.121702i
$607$		−	484179.i		−	1.31410i	−0.753847	−	0.657050i	$-0.771804\pi$
$607$		−	484179.i		−	1.31410i	0.753847	−	0.657050i	$-0.228196\pi$
$608$	−39839.3	+	51799.5i	−0.107772	+	0.140126i
$609$	−28192.0			−0.0760136
$610$	−47066.2	−	27173.7i	−0.126488	−	0.0730279i
$611$	−443764.	−	256207.i	−1.18869	−	0.686292i
$612$	133788.	+	231727.i	0.357201	+	0.618691i
$613$	154104.	−	266916.i	0.410102	−	0.710318i	−0.584798	−	0.811179i	$-0.698826\pi$
$613$	154104.	−	266916.i	0.410102	−	0.710318i	0.994901	+	0.100861i	$0.0321596\pi$
$614$	−75137.8	−	130142.i	−0.199307	−	0.345209i
$615$	−1962.91			−0.00518980
$616$		−	196119.i		−	0.516842i
$617$	290312.	+	502835.i	0.762596	+	1.32086i	0.941508	+	0.336990i	$0.109409\pi$
$617$	290312.	+	502835.i	0.762596	+	1.32086i	−0.178912	+	0.983865i	$0.557258\pi$
$618$	22020.2	−	12713.4i	0.0576559	−	0.0332877i
$619$	−137052.			−0.357688			−0.178844	−	0.983877i	$-0.557236\pi$
$619$	−137052.			−0.357688			−0.178844	+	0.983877i	$0.557236\pi$
$620$		−	14051.0i		−	0.0365530i
$621$	−55159.2	+	31846.2i	−0.143032	+	0.0825798i
$622$	181496.	+	104787.i	0.469122	+	0.270848i
$623$	674880.	−	389642.i	1.73880	−	1.00390i
$624$	−15054.1	+	26074.5i	−0.0386622	+	0.0669650i
$625$	−188455.	+	326414.i	−0.482445	+	0.835620i
$626$		−	396921.i		−	1.01287i
$627$	−58892.3	−	7820.34i	−0.149804	−	0.0198925i
$628$	−51199.6			−0.129822
$629$	230640.	+	133160.i	0.582952	+	0.336567i
$630$	41538.6	+	23982.3i	0.104658	+	0.0604241i
$631$	−78369.0	−	135739.i	−0.196827	−	0.340915i	0.750671	−	0.660677i	$-0.229730\pi$
$631$	−78369.0	−	135739.i	−0.196827	−	0.340915i	−0.947498	+	0.319762i	$0.896397\pi$
$632$	−48132.2	+	83367.5i	−0.120504	+	0.208719i
$633$	41599.1	+	72051.7i	0.103819	+	0.179820i
$634$	290086.			0.721685
$635$			40003.2i			0.0992082i
$636$	−28710.6	−	49728.3i	−0.0709788	−	0.122939i
$637$	1.05766e6	−	610640.i	2.60656	−	1.50490i
$638$	72456.3			0.178006
$639$		−	492329.i		−	1.20574i
$640$	3398.51	−	1962.13i	0.00829715	−	0.00479036i
$641$	−158874.	−	91726.2i	−0.386668	−	0.223243i	0.294047	−	0.955791i	$-0.404998\pi$
$641$	−158874.	−	91726.2i	−0.386668	−	0.223243i	−0.680715	+	0.732548i	$0.738331\pi$
$642$	−2089.58	+	1206.42i	−0.00506977	+	0.00292703i
$643$	−176524.	+	305749.i	−0.426955	+	0.739508i	−0.996601	−	0.0823825i	$-0.973747\pi$
$643$	−176524.	+	305749.i	−0.426955	+	0.739508i	0.569646	+	0.821890i	$0.307080\pi$
$644$	84007.9	−	145506.i	0.202557	−	0.350840i
$645$			5088.74i			0.0122318i
$646$	−264480.	+	343880.i	−0.633764	+	0.824028i
$647$	−523782.			−1.25124			−0.625622	−	0.780126i	$-0.715155\pi$
$647$	−523782.			−1.25124			−0.625622	+	0.780126i	$0.715155\pi$
$648$	117822.	+	68024.5i	0.280592	+	0.162000i
$649$	−460960.	−	266136.i	−1.09440	−	0.631849i
$650$	−272249.	−	471550.i	−0.644377	−	1.11609i
$651$	38885.1	−	67351.0i	0.0917533	−	0.158921i
$652$	−20005.2	−	34650.0i	−0.0470595	−	0.0815095i
$653$	522720.			1.22587			0.612933	−	0.790135i	$-0.289990\pi$
$653$	522720.			1.22587			0.612933	+	0.790135i	$0.289990\pi$
$654$		−	7505.36i		−	0.0175475i
$655$	9154.26	+	15855.6i	0.0213374	+	0.0369574i
$656$	26599.1	−	15357.0i	0.0618101	−	0.0356861i
$657$	190401.			0.441102
$658$			369658.i			0.853784i
$659$	209686.	−	121062.i	0.482834	−	0.278764i	−0.238763	−	0.971078i	$-0.576742\pi$
$659$	209686.	−	121062.i	0.482834	−	0.278764i	0.721597	+	0.692314i	$0.243408\pi$
$660$	3089.66	+	1783.82i	0.00709288	+	0.00409508i
$661$	114420.	−	66060.4i	0.261878	−	0.151195i	−0.363313	−	0.931667i	$-0.618354\pi$
$661$	114420.	−	66060.4i	0.261878	−	0.151195i	0.625191	+	0.780472i	$0.285021\pi$
$662$	48830.4	−	84576.8i	0.111423	−	0.192990i
$663$	−99939.6	+	173100.i	−0.227358	+	0.393796i
$664$			150315.i			0.340931i
$665$	−10236.7	+	77089.1i	−0.0231482	+	0.174321i
$666$	139567.			0.314654
$667$	53757.4	+	31036.8i	0.120833	+	0.0697631i
$668$	175170.	+	101134.i	0.392561	+	0.226645i
$669$	−40663.7	−	70431.7i	−0.0908563	−	0.157368i
$670$	−229.627	+	397.726i	−0.000511534	+	0.000886002i
$671$	386550.	+	669524.i	0.858540	+	1.48704i
$672$	21720.2			0.0480979
$673$		−	427834.i		−	0.944594i	−0.881440	−	0.472297i	$-0.843425\pi$
$673$		−	427834.i		−	0.944594i	0.881440	−	0.472297i	$-0.156575\pi$
$674$	−253749.	−	439507.i	−0.558580	−	0.967489i
$675$	128957.	−	74453.1i	0.283032	−	0.163409i
$676$	548653.			1.20062
$677$			605243.i			1.32054i	0.751027	+	0.660272i	$0.229559\pi$
$677$			605243.i			1.32054i	−0.751027	+	0.660272i	$0.770441\pi$
$678$	−36654.2	+	21162.3i	−0.0797378	+	0.0460367i
$679$	−323258.	−	186633.i	−0.701148	−	0.404808i
$680$	22561.6	−	13025.9i	0.0487924	−	0.0281703i
$681$	51682.0	−	89515.9i	0.111441	−	0.193022i
$682$	−99938.8	+	173099.i	−0.214865	+	0.372157i
$683$		−	638680.i		−	1.36912i	−0.728956	−	0.684561i	$-0.759994\pi$
$683$		−	638680.i		−	1.36912i	0.728956	−	0.684561i	$-0.240006\pi$
$684$	−29927.0	+	225370.i	−0.0639663	+	0.481708i
$685$	22290.9			0.0475058
$686$	−295473.	−	170592.i	−0.627871	−	0.362501i
$687$	−40589.4	−	23434.3i	−0.0860002	−	0.0496523i
$688$	−39812.2	−	68956.7i	−0.0841083	−	0.145680i
$689$	−741065.	+	1.28356e6i	−1.56105	+	2.70382i
$690$	1528.20	+	2646.93i	0.00320984	+	0.00555960i
$691$	−586931.			−1.22922			−0.614612	−	0.788829i	$-0.710688\pi$
$691$	−586931.			−1.22922			−0.614612	+	0.788829i	$0.710688\pi$
$692$		−	82645.9i		−	0.172587i
$693$	−341153.	−	590894.i	−0.710366	−	1.23039i
$694$	−471411.	+	272169.i	−0.978770	+	0.565093i
$695$	−20494.6			−0.0424297
$696$			8024.58i			0.0165655i
$697$	176583.	−	101950.i	0.363482	−	0.209856i
$698$	−223304.	−	128925.i	−0.458338	−	0.264622i
$699$	−23323.4	+	13465.8i	−0.0477351	+	0.0275599i
$700$	−196402.	+	340178.i	−0.400820	+	0.694241i
$701$	16565.6	−	28692.4i	0.0337109	−	0.0583890i	−0.848678	−	0.528910i	$-0.822601\pi$
$701$	16565.6	−	28692.4i	0.0337109	−	0.0583890i	0.882389	+	0.470521i	$0.155934\pi$
$702$			212528.i			0.431262i
$703$	86360.4	+	209154.i	0.174745	+	0.423209i
$704$	−55823.3			−0.112634
$705$	−5823.60	−	3362.26i	−0.0117169	−	0.00676476i
$706$	−308695.	−	178225.i	−0.619327	−	0.357569i
$707$	480478.	+	832213.i	0.961247	+	1.66493i
$708$	29474.7	−	51051.6i	0.0588007	−	0.101846i
$709$	209345.	+	362596.i	0.416457	+	0.721324i	0.995580	−	0.0939159i	$-0.0299385\pi$
$709$	209345.	+	362596.i	0.416457	+	0.721324i	−0.579124	+	0.815240i	$0.696605\pi$
$710$	−47934.5			−0.0950893
$711$			334908.i			0.662501i
$712$	−110908.	−	192098.i	−0.218777	−	0.378933i
$713$	−148295.	+	85618.0i	−0.291707	+	0.168417i
$714$	144194.			0.282846
$715$		−	92086.0i		−	0.180128i
$716$	−357010.	+	206120.i	−0.696393	+	0.402063i
$717$	100627.	+	58096.7i	0.195738	+	0.113009i
$718$	−158435.	+	91472.7i	−0.307329	+	0.177436i
$719$	408717.	−	707919.i	0.790616	−	1.36939i	−0.134971	−	0.990850i	$-0.543094\pi$
$719$	408717.	−	707919.i	0.790616	−	1.36939i	0.925586	−	0.378537i	$-0.123573\pi$
$720$	6826.34	−	11823.6i	0.0131681	−	0.0228078i
$721$			473459.i			0.910777i
$722$	−356256.	+	94604.9i	−0.683420	+	0.181484i
$723$	91683.2			0.175393
$724$	−48128.4	−	27787.0i	−0.0918173	−	0.0530108i
$725$	−125679.	−	72561.0i	−0.239105	−	0.138047i
$726$	5877.59	+	10180.3i	0.0111513	+	0.0193146i
$727$	118045.	−	204459.i	0.223346	−	0.386846i	−0.732476	−	0.680793i	$-0.761635\pi$
$727$	118045.	−	204459.i	0.223346	−	0.386846i	0.955822	+	0.293947i	$0.0949688\pi$
$728$	−280316.	−	485522.i	−0.528914	−	0.916107i
$729$	443845.			0.835173
$730$		−	18538.0i		−	0.0347871i
$731$	−264300.	−	457781.i	−0.494609	−	0.856689i
$732$	−74150.2	+	42810.6i	−0.138385	+	0.0798968i
$733$	−388188.			−0.722494			−0.361247	−	0.932470i	$-0.617649\pi$
$733$	−388188.			−0.722494			−0.361247	+	0.932470i	$0.617649\pi$
$734$			472621.i			0.877245i
$735$	13879.9	−	8013.55i	0.0256928	−	0.0148337i
$736$	−41416.9	−	23912.0i	−0.0764578	−	0.0441429i
$737$	5657.73	−	3266.49i	0.0104161	−	0.00601376i
$738$	53427.6	−	92539.4i	0.0980965	−	0.169908i
$739$	−119148.	+	206371.i	−0.218172	+	0.377886i	−0.954249	−	0.299012i	$-0.903343\pi$
$739$	−119148.	+	206371.i	−0.218172	+	0.377886i	0.736077	+	0.676898i	$0.236676\pi$
$740$		−	13588.6i		−	0.0248149i
$741$	−156975.	+	64815.5i	−0.285886	+	0.118044i
$742$	1.06921e6			1.94204
$743$	−531342.	−	306771.i	−0.962491	−	0.555694i	−0.0655522	−	0.997849i	$-0.520881\pi$
$743$	−531342.	−	306771.i	−0.962491	−	0.555694i	−0.896939	+	0.442155i	$0.854214\pi$
$744$	−19170.8	−	11068.3i	−0.0346334	−	0.0199956i
$745$	16157.1	+	27984.8i	0.0291105	+	0.0504209i
$746$	−163795.	+	283701.i	−0.294322	+	0.509780i
$747$	261477.	+	452891.i	0.468588	+	0.811619i
$748$	−370593.			−0.662359
$749$		−	44928.3i		−	0.0800859i
$750$	−7188.04	−	12450.1i	−0.0127787	−	0.0221334i
$751$	640541.	−	369816.i	1.13571	−	0.655701i	0.190344	−	0.981717i	$-0.439040\pi$
$751$	640541.	−	369816.i	1.13571	−	0.655701i	0.945364	+	0.326016i	$0.105706\pi$
$752$	105220.			0.186063
$753$		−	59690.6i		−	0.105273i
$754$	179377.	−	103563.i	0.315518	−	0.182164i
$755$	−67979.4	−	39247.9i	−0.119257	−	0.0688530i
$756$	132778.	−	76659.1i	0.232317	−	0.134128i
$757$	−166628.	+	288609.i	−0.290775	+	0.503637i	−0.973993	−	0.226577i	$-0.927246\pi$
$757$	−166628.	+	288609.i	−0.290775	+	0.503637i	0.683218	+	0.730214i	$0.260580\pi$
$758$	128308.	−	222235.i	0.223313	−	0.386789i
$759$		−	43477.9i		−	0.0754718i
$760$	21942.7	+	2913.78i	0.0379894	+	0.00504463i
$761$	502308.			0.867362			0.433681	−	0.901066i	$-0.357214\pi$
$761$	502308.			0.867362			0.433681	+	0.901066i	$0.357214\pi$
$762$	54579.4	+	31511.5i	0.0939981	+	0.0542698i
$763$	121030.	+	69876.9i	0.207895	+	0.120028i
$764$	204266.	+	353799.i	0.349953	+	0.606137i
$765$	45317.8	−	78492.8i	0.0774366	−	0.134124i
$766$	−43674.1	−	75645.7i	−0.0744331	−	0.128922i
$767$	−1.52157e6			−2.58643
$768$		−	6182.46i		−	0.0104819i
$769$	−227459.	−	393970.i	−0.384636	−	0.666210i	0.607082	−	0.794639i	$-0.292340\pi$
$769$	−227459.	−	393970.i	−0.384636	−	0.666210i	−0.991719	+	0.128429i	$0.959006\pi$
$770$	−57531.1	+	33215.6i	−0.0970334	+	0.0560222i
$771$	−51079.7			−0.0859290
$772$		−	299264.i		−	0.502135i
$773$	618605.	−	357152.i	1.03527	−	0.597714i	0.116781	−	0.993158i	$-0.462742\pi$
$773$	618605.	−	357152.i	1.03527	−	0.597714i	0.918490	+	0.395443i	$0.129409\pi$
$774$	−239903.	−	138508.i	−0.400456	−	0.231203i
$775$	346698.	−	200166.i	0.577229	−	0.333263i
$776$	−53123.3	+	92012.3i	−0.0882189	+	0.152800i
$777$	37605.6	−	65134.7i	0.0622888	−	0.107887i
$778$		−	315976.i		−	0.522029i
$779$	171739.	+	22805.3i	0.283004	+	0.0375803i
$780$	10198.6			0.0167629
$781$	590523.	+	340938.i	0.968132	+	0.558951i
$782$	−274953.	−	158744.i	−0.449619	−	0.259588i
$783$	28321.8	+	49054.9i	0.0461953	+	0.0800126i
$784$	−125389.	+	217181.i	−0.203999	+	0.353337i
$785$	8671.41	+	15019.3i	0.0140718	+	0.0243731i
$786$	28844.1			0.0466887
$787$		−	414479.i		−	0.669196i	−0.942361	−	0.334598i	$-0.891399\pi$
$787$		−	414479.i		−	0.669196i	0.942361	−	0.334598i	$-0.108601\pi$
$788$	2870.24	+	4971.40i	0.00462238	+	0.00800619i
$789$	127891.	−	73838.1i	0.205441	−	0.118611i
$790$	32607.6			0.0522474
$791$		−	788107.i		−	1.25960i
$792$	−168192.	+	97105.8i	−0.268136	+	0.154809i
$793$	1.91393e6	+	1.10501e6i	3.04354	+	1.75719i
$794$	474342.	−	273861.i	0.752403	−	0.434400i
$795$	−9725.14	+	16844.4i	−0.0153873	+	0.0266515i
$796$	293582.	−	508499.i	0.463344	−	0.802535i
$797$		−	444827.i		−	0.700285i	−0.936696	−	0.350143i	$-0.886133\pi$
$797$		−	444827.i		−	0.700285i	0.936696	−	0.350143i	$-0.113867\pi$
$798$	97114.8	+	74691.5i	0.152503	+	0.117291i
$799$	698518.			1.09417
$800$	96828.4	+	55903.9i	0.151294	+	0.0873499i
$801$	−668317.	−	385853.i	−1.04164	−	0.601391i
$802$	−58734.8	−	101732.i	−0.0913160	−	0.158164i
$803$	−131853.	+	228377.i	−0.204484	+	0.354177i
$804$	361.766	+	626.596i	0.000559648	+	0.000969339i
$805$	−56911.9			−0.0878236
$806$			571378.i			0.879536i
$807$	471.025	+	815.839i	0.000723264	+	0.00125273i
$808$	236881.	−	136764.i	0.362834	−	0.209483i
$809$	−23210.9			−0.0354646			−0.0177323	−	0.999843i	$-0.505645\pi$
$809$	−23210.9			−0.0354646			−0.0177323	+	0.999843i	$0.505645\pi$
$810$		−	46083.8i		−	0.0702390i
$811$	−397137.	+	229287.i	−0.603808	+	0.348609i	−0.770538	−	0.637394i	$-0.780012\pi$
$811$	−397137.	+	229287.i	−0.603808	+	0.348609i	0.166730	+	0.986003i	$0.446679\pi$
$812$	−129403.	−	74711.0i	−0.196261	−	0.113311i
$813$	−70733.8	+	40838.2i	−0.107015	+	0.0617853i
$814$	−96650.2	+	167403.i	−0.145866	+	0.252647i
$815$	−6776.35	+	11737.0i	−0.0102019	+	0.0176702i
$816$		−	41043.3i		−	0.0616399i
$817$	59121.4	−	445223.i	0.0885728	−	0.667012i
$818$	393029.			0.587378
$819$	−1.68915e6	−	975232.i	−2.51826	−	1.45392i
$820$	−9009.90	−	5201.87i	−0.0133996	−	0.00773627i
$821$	153601.	+	266045.i	0.227881	+	0.394702i	0.957180	−	0.289493i	$-0.0934868\pi$
$821$	153601.	+	266045.i	0.227881	+	0.394702i	−0.729299	+	0.684196i	$0.760153\pi$
$822$	17559.0	−	30413.2i	0.0259871	−	0.0450109i
$823$	−18258.2	−	31624.2i	−0.0269562	−	0.0466895i	0.852233	−	0.523163i	$-0.175248\pi$
$823$	−18258.2	−	31624.2i	−0.0269562	−	0.0466895i	−0.879189	+	0.476474i	$0.841915\pi$
$824$	134766.			0.198484
$825$			101647.i			0.149343i
$826$	548834.	+	950608.i	0.804416	+	1.39329i
$827$	310653.	−	179355.i	0.454218	−	0.262243i	−0.255392	−	0.966838i	$-0.582205\pi$
$827$	310653.	−	179355.i	0.454218	−	0.262243i	0.709610	+	0.704595i	$0.248871\pi$
$828$	−166382.			−0.242687
$829$			468345.i			0.681485i	0.940157	+	0.340743i	$0.110678\pi$
$829$			468345.i			0.681485i	−0.940157	+	0.340743i	$0.889322\pi$
$830$	44094.7	−	25458.1i	0.0640074	−	0.0369547i
$831$	−74214.2	−	42847.6i	−0.107469	−	0.0620475i
$832$	−138199.	+	79789.3i	−0.199645	+	0.115265i
$833$	−832418.	+	1.44179e6i	−1.19964	+	2.07784i
$834$	−16144.1	+	27962.4i	−0.0232103	+	0.0402015i
$835$		−	68514.5i		−	0.0982674i
$836$	−249595.	−	191965.i	−0.357128	−	0.274669i
$837$	−156257.			−0.223043
$838$	649837.	+	375184.i	0.925372	+	0.534264i
$839$	269666.	+	155692.i	0.383091	+	0.221178i	0.679162	−	0.733988i	$-0.262343\pi$
$839$	269666.	+	155692.i	0.383091	+	0.221178i	−0.296071	+	0.955166i	$0.595677\pi$
$840$	−3678.64	−	6371.60i	−0.00521350	−	0.00903005i
$841$	−326038.	+	564715.i	−0.460974	+	0.798431i
$842$	−128026.	−	221747.i	−0.180581	−	0.312776i
$843$	170009.			0.239230
$844$			440963.i			0.619038i
$845$	−92922.4	−	160946.i	−0.130139	−	0.225407i
$846$	317020.	−	183032.i	0.442941	−	0.255732i
$847$	−218888.			−0.305109
$848$		−	304342.i		−	0.423223i
$849$	78534.2	−	45341.8i	0.108954	−	0.0629047i
$850$	642812.	+	371128.i	0.889705	+	0.513672i
$851$	−143415.	+	82800.7i	−0.198032	+	0.114334i
$852$	−37759.1	+	65400.7i	−0.0520167	+	0.0900955i
$853$	301187.	−	521671.i	0.413940	−	0.716966i	−0.581376	−	0.813635i	$-0.697485\pi$
$853$	301187.	−	521671.i	0.413940	−	0.716966i	0.995317	+	0.0966690i	$0.0308188\pi$
$854$		−	1.59431e6i		−	2.18604i
$855$	71180.5	−	29390.7i	0.0973708	−	0.0402048i
$856$	−12788.4			−0.0174529
$857$	−1.06472e6	−	614717.i	−1.44969	−	0.836977i	−0.451225	−	0.892410i	$-0.649013\pi$
$857$	−1.06472e6	−	614717.i	−1.44969	−	0.836977i	−0.998462	+	0.0554328i	$0.982346\pi$
$858$	−125640.	−	72538.2i	−0.170668	−	0.0985354i
$859$	580962.	+	1.00626e6i	0.787338	+	1.36371i	0.927592	+	0.373595i	$0.121875\pi$
$859$	580962.	+	1.00626e6i	0.787338	+	1.36371i	−0.140254	+	0.990116i	$0.544792\pi$
$860$	−13485.6	+	23357.7i	−0.0182336	+	0.0315815i
$861$	−28791.6	−	49868.6i	−0.0388383	−	0.0672699i
$862$	−335410.			−0.451400
$863$			23780.8i			0.0319304i	0.999873	+	0.0159652i	$0.00508210\pi$
$863$			23780.8i			0.0319304i	−0.999873	+	0.0159652i	$0.994918\pi$
$864$	−21820.3	−	37793.8i	−0.0292303	−	0.0506283i
$865$	−24244.0	+	13997.3i	−0.0324021	+	0.0187073i
$866$	437750.			0.583701
$867$		−	146407.i		−	0.194771i
$868$	356971.	−	206097.i	0.473798	−	0.273547i
$869$	−401705.	−	231924.i	−0.531946	−	0.307119i
$870$	2354.00	−	1359.08i	0.00311005	−	0.00179559i
$871$	9337.71	−	16173.4i	0.0123085	−	0.0213189i
$872$	19889.8	−	34450.1i	0.0261575	−	0.0453062i
$873$			369637.i			0.485005i
$874$	−102953.	−	249339.i	−0.134777	−	0.326413i
$875$	267690.			0.349636
$876$	−25292.8	−	14602.8i	−0.0329602	−	0.0190296i
$877$	−731385.	−	422265.i	−0.950927	−	0.549018i	−0.0575579	−	0.998342i	$-0.518331\pi$
$877$	−731385.	−	422265.i	−0.950927	−	0.549018i	−0.893369	+	0.449324i	$0.851665\pi$
$878$	170579.	+	295451.i	0.221277	+	0.383263i
$879$	−108343.	+	187656.i	−0.140225	+	0.242876i
$880$	9454.50	+	16375.7i	0.0122088	+	0.0211463i
$881$	519810.			0.669719			0.334860	−	0.942268i	$-0.391311\pi$
$881$	519810.			0.669719			0.334860	+	0.942268i	$0.391311\pi$
$882$			872469.i			1.12154i
$883$	−576930.	−	999273.i	−0.739949	−	1.28163i	−0.952518	−	0.304484i	$-0.901516\pi$
$883$	−576930.	−	999273.i	−0.739949	−	1.28163i	0.212568	−	0.977146i	$-0.431817\pi$
$884$	−917459.	+	529695.i	−1.17404	+	0.677831i
$885$	−19967.9			−0.0254944
$886$		−	338499.i		−	0.431211i
$887$	−631174.	+	364409.i	−0.802236	+	0.463171i	−0.844252	−	0.535946i	$-0.819955\pi$
$887$	−631174.	+	364409.i	−0.802236	+	0.463171i	0.0420166	+	0.999117i	$0.486622\pi$
$888$	−18540.0	−	10704.1i	−0.0235117	−	0.0135745i
$889$	−1.01630e6	+	586760.i	−1.28593	+	0.742432i
$890$	−37567.8	+	65069.3i	−0.0474281	+	0.0821478i
$891$	−327775.	+	567723.i	−0.412877	+	0.715124i
$892$		−	431048.i		−	0.541747i
$893$	470454.	+	361829.i	0.589949	+	0.453733i
$894$	50909.1			0.0636972
$895$	120930.	+	69818.9i	0.150969	+	0.0871619i
$896$	99697.4	+	57560.3i	0.124185	+	0.0716981i
$897$	−62143.8	−	107636.i	−0.0772348	−	0.133775i
$898$	−511031.	+	885131.i	−0.633715	+	1.09763i
$899$	76142.9	+	131883.i	0.0942129	+	0.163181i
$900$	388984.			0.480227
$901$		−	2.02042e6i		−	2.48882i
$902$	73997.5	+	128167.i	0.0909502	+	0.157530i
$903$	−129282.	+	74640.7i	−0.158548	+	0.0915378i
$904$	−224327.			−0.274502
$905$			18824.5i			0.0229841i
$906$	−107098.	+	61833.0i	−0.130474	+	0.0753293i
$907$	800625.	+	462241.i	0.973228	+	0.561893i	0.900219	−	0.435438i	$-0.143406\pi$
$907$	800625.	+	462241.i	0.973228	+	0.561893i	0.0730091	+	0.997331i	$0.476740\pi$
$908$	474448.	−	273923.i	0.575463	−	0.332244i
$909$	475806.	−	824121.i	0.575841	−	0.997386i
$910$	−94951.4	+	164461.i	−0.114662	+	0.198600i
$911$			1.60442e6i			1.93322i	0.256257	+	0.966609i	$0.417511\pi$
$911$			1.60442e6i			1.93322i	−0.256257	+	0.966609i	$0.582489\pi$
$912$	21260.2	−	27642.8i	0.0255610	−	0.0332347i
$913$	−724292.			−0.868904
$914$	−606414.	−	350113.i	−0.725900	−	0.419099i
$915$	25116.9	+	14501.2i	0.0300001	+	0.0173206i
$916$	−124206.	−	215130.i	−0.148030	−	0.256396i
$917$	−268546.	+	465135.i	−0.319360	+	0.553147i
$918$	−144858.	−	250901.i	−0.171892	−	0.297726i
$919$	−126222.			−0.149453			−0.0747264	−	0.997204i	$-0.523808\pi$
$919$	−126222.			−0.149453			−0.0747264	+	0.997204i	$0.523808\pi$
$920$			16199.4i			0.0191392i
$921$	40097.3	+	69450.5i	0.0472711	+	0.0818759i
$922$	−167060.	+	96452.0i	−0.196521	+	0.113462i
$923$	1.94924e6			2.28803
$924$			104659.i			0.122583i
$925$	335290.	−	193580.i	0.391865	−	0.226243i
$926$	−650127.	−	375351.i	−0.758186	−	0.437739i
$927$	406041.	−	234428.i	0.472509	−	0.272803i
$928$	−21265.8	+	36833.4i	−0.0246936	+	0.0427706i
$929$	109861.	−	190286.i	0.127296	−	0.220483i	−0.795332	−	0.606174i	$-0.792704\pi$
$929$	109861.	−	190286.i	0.127296	−	0.220483i	0.922628	+	0.385691i	$0.126037\pi$
$930$			7498.31i			0.00866956i
$931$	−1.30748e6	+	539862.i	−1.50846	+	0.622850i
$932$	−142741.			−0.164330
$933$	−96855.3	−	55919.4i	−0.111265	−	0.0642391i
$934$	−109031.	−	62949.0i	−0.124984	−	0.0721597i
$935$	62765.3	+	108713.i	0.0717954	+	0.124353i
$936$	−277590.	+	480801.i	−0.316849	+	0.548799i
$937$	63546.7	+	110066.i	0.0723792	+	0.125365i	0.899944	−	0.436006i	$-0.143607\pi$
$937$	63546.7	+	110066.i	0.0723792	+	0.125365i	−0.827564	+	0.561371i	$0.810274\pi$
$938$	−13472.5			−0.0153124
$939$			211817.i			0.240231i
$940$	−17820.5	−	30866.0i	−0.0201680	−	0.0349321i
$941$	677172.	−	390965.i	0.764751	−	0.441529i	−0.0662482	−	0.997803i	$-0.521103\pi$
$941$	677172.	−	390965.i	0.764751	−	0.441529i	0.830999	+	0.556274i	$0.187770\pi$
$942$	27322.7			0.0307908
$943$			126788.i			0.142579i
$944$	270581.	−	156220.i	0.303637	−	0.175305i
$945$	−44975.7	−	25966.7i	−0.0503633	−	0.0290772i
$946$	332267.	−	191834.i	0.371283	−	0.214360i
$947$	778015.	−	1.34756e6i	0.867537	−	1.50262i	0.00303020	−	0.999995i	$-0.499035\pi$
$947$	778015.	−	1.34756e6i	0.867537	−	1.50262i	0.864506	−	0.502622i	$-0.167631\pi$
$948$	25685.8	−	44489.0i	0.0285809	−	0.0495036i
$949$			753842.i			0.837043i
$950$	240694.	+	582929.i	0.266697	+	0.645905i
$951$	−154804.			−0.171168
$952$	661859.	+	382124.i	0.730283	+	0.421629i
$953$	−651018.	−	375865.i	−0.716815	−	0.413853i	0.0967642	−	0.995307i	$-0.469151\pi$
$953$	−651018.	−	375865.i	−0.716815	−	0.413853i	−0.813579	+	0.581454i	$0.802484\pi$
$954$	−529409.	−	916963.i	−0.581694	−	1.00752i
$955$	69191.0	−	119842.i	0.0758652	−	0.131402i
$956$	307922.	+	533336.i	0.336918	+	0.583560i
$957$	−38666.3			−0.0422191
$958$		−	623843.i		−	0.679742i
$959$	326959.	+	566309.i	0.355513	+	0.615767i
$960$	−1813.61	+	1047.09i	−0.00196790	+	0.00113617i
$961$	503426.			0.545116
$962$			552576.i			0.597093i
$963$	−38530.7	+	22245.7i	−0.0415484	+	0.0239880i
$964$	420832.	+	242968.i	0.452851	+	0.261453i
$965$	−87788.7	+	50684.8i	−0.0942723	+	0.0544281i
$966$	−44830.8	+	77649.2i	−0.0480421	+	0.0832114i
$967$	−609402.	+	1.05552e6i	−0.651705	+	1.12879i	0.331004	+	0.943629i	$0.392613\pi$
$967$	−609402.	+	1.05552e6i	−0.651705	+	1.12879i	−0.982709	+	0.185157i	$0.940721\pi$
$968$			62304.3i			0.0664917i
$969$	141140.	−	183512.i	0.150315	−	0.195441i
$970$	35988.9			0.0382494
$971$	−47714.5	−	27548.0i	−0.0506072	−	0.0292181i	0.474483	−	0.880265i	$-0.342635\pi$
$971$	−47714.5	−	27548.0i	−0.0506072	−	0.0292181i	−0.525090	+	0.851047i	$0.675968\pi$
$972$	−198167.	−	114412.i	−0.209749	−	0.121099i
$973$	−300611.	−	520674.i	−0.317526	−	0.549971i
$974$	412487.	−	714448.i	0.434803	−	0.753100i
$975$	145286.	+	251643.i	0.152832	+	0.264713i
$976$	−453806.			−0.476399
$977$		−	722803.i		−	0.757236i	−0.925553	−	0.378618i	$-0.876399\pi$
$977$		−	722803.i		−	0.757236i	0.925553	−	0.378618i	$-0.123601\pi$
$978$	10675.8	+	18491.0i	0.0111615	+	0.0193322i
$979$	925622.	−	534408.i	0.965758	−	0.557580i
$980$	84946.1			0.0884487
$981$		−	138395.i		−	0.143808i
$982$	−760884.	+	439297.i	−0.789034	+	0.455549i
$983$	−345011.	−	199192.i	−0.357048	−	0.206142i	0.310737	−	0.950496i	$-0.399424\pi$
$983$	−345011.	−	199192.i	−0.357048	−	0.206142i	−0.667785	+	0.744354i	$0.732757\pi$
$984$	−14194.6	+	8195.26i	−0.0146600	+	0.00846394i
$985$	972.234	−	1683.96i	0.00100207	−	0.00173564i
$986$	−141176.	+	244525.i	−0.145214	+	0.251518i
$987$		−	197268.i		−	0.202499i
$988$	−892291.	−	118488.i	−0.914097	−	0.121383i
$989$	328691.			0.336043
$990$	56971.7	+	32892.6i	0.0581284	+	0.0335605i
$991$	1.00784e6	+	581876.i	1.02623	+	0.592493i	0.915902	−	0.401402i	$-0.131477\pi$
$991$	1.00784e6	+	581876.i	1.02623	+	0.592493i	0.110327	+	0.993895i	$0.464810\pi$
$992$	−58663.6	−	101608.i	−0.0596136	−	0.103254i
$993$	−26058.4	+	45134.4i	−0.0264270	+	0.0457730i
$994$	−703095.	−	1.21780e6i	−0.711608	−	1.23254i
$995$	−198890.			−0.200894
$996$		−	80215.7i		−	0.0808613i
$997$	152584.	+	264284.i	0.153504	+	0.265877i	0.932513	−	0.361136i	$-0.117611\pi$
$997$	152584.	+	264284.i	0.153504	+	0.265877i	−0.779009	+	0.627012i	$0.784278\pi$
$998$	−906181.	+	523184.i	−0.909817	+	0.525283i
$999$	−151115.			−0.151418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.d.a.27.3	✓	16
3.2	odd	2		342.5.m.c.217.6		16
4.3	odd	2		304.5.r.c.65.4		16
19.12	odd	6	inner	38.5.d.a.31.3	yes	16
57.50	even	6		342.5.m.c.145.6		16
76.31	even	6		304.5.r.c.145.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.3	✓	16	1.1	even	1	trivial
38.5.d.a.31.3	yes	16	19.12	odd	6	inner
304.5.r.c.65.4		16	4.3	odd	2
304.5.r.c.145.4		16	76.31	even	6
342.5.m.c.145.6		16	57.50	even	6
342.5.m.c.217.6		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.44949 - 1.41421i) q^{2} +(1.30717 + 0.754695i) q^{3} +(4.00000 + 6.92820i) q^{4} +(1.35492 - 2.34679i) q^{5} +(-2.13460 - 3.69723i) q^{6} +79.4947 q^{7} -22.6274i q^{8} +(-39.3609 - 68.1750i) q^{9} +O(q^{10})\)	\(q+(-2.44949 - 1.41421i) q^{2} +(1.30717 + 0.754695i) q^{3} +(4.00000 + 6.92820i) q^{4} +(1.35492 - 2.34679i) q^{5} +(-2.13460 - 3.69723i) q^{6} +79.4947 q^{7} -22.6274i q^{8} +(-39.3609 - 68.1750i) q^{9} +(-6.63772 + 3.83229i) q^{10} +109.030 q^{11} +12.0751i q^{12} +(269.920 - 155.839i) q^{13} +(-194.722 - 112.423i) q^{14} +(3.54222 - 2.04510i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(-212.438 + 367.953i) q^{17} +222.659i q^{18} +(-333.675 + 137.776i) q^{19} +21.6787 q^{20} +(103.913 + 59.9943i) q^{21} +(-267.068 - 154.192i) q^{22} +(-132.097 - 228.798i) q^{23} +(17.0768 - 29.5779i) q^{24} +(308.828 + 534.906i) q^{25} -881.556 q^{26} -241.082i q^{27} +(317.979 + 550.756i) q^{28} +(-203.478 + 117.478i) q^{29} -11.5688 q^{30} -648.147i q^{31} +(156.767 - 90.5097i) q^{32} +(142.521 + 82.2843i) q^{33} +(1040.73 - 600.864i) q^{34} +(107.709 - 186.557i) q^{35} +(314.887 - 545.400i) q^{36} -626.819i q^{37} +(1012.18 + 134.408i) q^{38} +470.442 q^{39} +(-53.1017 - 30.6583i) q^{40} +(-415.611 - 239.953i) q^{41} +(-169.689 - 293.911i) q^{42} +(-622.065 + 1077.45i) q^{43} +(436.119 + 755.381i) q^{44} -213.323 q^{45} +747.251i q^{46} +(-822.028 - 1423.79i) q^{47} +(-83.6589 + 48.3005i) q^{48} +3918.41 q^{49} -1747.00i q^{50} +(-555.384 + 320.651i) q^{51} +(2159.36 + 1246.71i) q^{52} +(-4118.24 + 2377.67i) q^{53} +(-340.942 + 590.529i) q^{54} +(147.727 - 255.870i) q^{55} -1798.76i q^{56} +(-540.148 - 71.7266i) q^{57} +664.555 q^{58} +(-4227.83 - 2440.94i) q^{59} +(28.3377 + 16.3608i) q^{60} +(3545.36 + 6140.74i) q^{61} +(-916.619 + 1587.63i) q^{62} +(-3128.98 - 5419.56i) q^{63} -512.000 q^{64} -844.594i q^{65} +(-232.735 - 403.109i) q^{66} +(51.8915 - 29.9596i) q^{67} -3399.00 q^{68} -398.771i q^{69} +(-527.664 + 304.647i) q^{70} +(5416.15 + 3127.02i) q^{71} +(-1542.62 + 890.635i) q^{72} +(-1209.33 + 2094.62i) q^{73} +(-886.456 + 1535.39i) q^{74} +932.285i q^{75} +(-2289.24 - 1760.66i) q^{76} +8667.30 q^{77} +(-1152.34 - 665.306i) q^{78} +(-3684.36 - 2127.16i) q^{79} +(86.7148 + 150.194i) q^{80} +(-3006.29 + 5207.04i) q^{81} +(678.690 + 1175.53i) q^{82} -6643.06 q^{83} +959.908i q^{84} +(575.671 + 997.091i) q^{85} +(3047.48 - 1759.47i) q^{86} -354.640 q^{87} -2467.06i q^{88} +(8489.61 - 4901.48i) q^{89} +(522.533 + 301.684i) q^{90} +(21457.2 - 12388.3i) q^{91} +(1056.77 - 1830.38i) q^{92} +(489.153 - 847.239i) q^{93} +4650.09i q^{94} +(-128.772 + 969.738i) q^{95} +273.229 q^{96} +(-4066.41 - 2347.74i) q^{97} +(-9598.12 - 5541.48i) q^{98} +(-4291.51 - 7433.11i) 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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