LMFDB - Embedded newform 38.5.d.a.31.8

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			31.8
Root			$0.500000 + 14.3823i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.5.d.a.27.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{2} +(10.4807 - 6.05105i) q^{3} +(4.00000 - 6.92820i) q^{4} +(9.13314 + 15.8191i) q^{5} +(17.1150 - 29.6440i) q^{6} -40.6944 q^{7} -22.6274i q^{8} +(32.7305 - 56.6909i) q^{9} +O(q^{10})$	\(q+(2.44949 - 1.41421i) q^{2} +(10.4807 - 6.05105i) q^{3} +(4.00000 - 6.92820i) q^{4} +(9.13314 + 15.8191i) q^{5} +(17.1150 - 29.6440i) q^{6} -40.6944 q^{7} -22.6274i q^{8} +(32.7305 - 56.6909i) q^{9} +(44.7431 + 25.8324i) q^{10} -52.4698 q^{11} -96.8168i q^{12} +(133.461 + 77.0538i) q^{13} +(-99.6805 + 57.5506i) q^{14} +(191.444 + 110.530i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-137.797 - 238.671i) q^{17} -185.152i q^{18} +(-70.6137 + 354.026i) q^{19} +146.130 q^{20} +(-426.507 + 246.244i) q^{21} +(-128.524 + 74.2034i) q^{22} +(-448.573 + 776.951i) q^{23} +(-136.920 - 237.152i) q^{24} +(145.671 - 252.310i) q^{25} +435.882 q^{26} +188.055i q^{27} +(-162.778 + 281.939i) q^{28} +(268.560 + 155.053i) q^{29} +625.253 q^{30} -904.934i q^{31} +(-156.767 - 90.5097i) q^{32} +(-549.921 + 317.497i) q^{33} +(-675.063 - 389.748i) q^{34} +(-371.668 - 643.747i) q^{35} +(-261.844 - 453.527i) q^{36} +115.035i q^{37} +(327.702 + 967.047i) q^{38} +1865.03 q^{39} +(357.945 - 206.659i) q^{40} +(1836.56 - 1060.34i) q^{41} +(-696.483 + 1206.34i) q^{42} +(-1000.64 - 1733.16i) q^{43} +(-209.879 + 363.521i) q^{44} +1195.73 q^{45} +2537.51i q^{46} +(2012.65 - 3486.01i) q^{47} +(-670.767 - 387.267i) q^{48} -744.965 q^{49} -824.042i q^{50} +(-2888.42 - 1667.63i) q^{51} +(1067.69 - 616.430i) q^{52} +(2557.89 + 1476.80i) q^{53} +(265.950 + 460.639i) q^{54} +(-479.214 - 830.022i) q^{55} +920.809i q^{56} +(1402.15 + 4137.74i) q^{57} +877.113 q^{58} +(-5202.69 + 3003.77i) q^{59} +(1531.55 - 884.242i) q^{60} +(606.668 - 1050.78i) q^{61} +(-1279.77 - 2216.63i) q^{62} +(-1331.95 + 2307.00i) q^{63} -512.000 q^{64} +2814.97i q^{65} +(-898.018 + 1555.41i) q^{66} +(-5554.61 - 3206.96i) q^{67} -2204.75 q^{68} +10857.4i q^{69} +(-1820.79 - 1051.24i) q^{70} +(-2812.41 + 1623.75i) q^{71} +(-1282.77 - 740.606i) q^{72} +(-3824.61 - 6624.43i) q^{73} +(162.683 + 281.776i) q^{74} -3525.86i q^{75} +(2170.31 + 1905.33i) q^{76} +2135.23 q^{77} +(4568.36 - 2637.55i) q^{78} +(5809.97 - 3354.39i) q^{79} +(584.521 - 1012.42i) q^{80} +(3789.10 + 6562.91i) q^{81} +(2999.09 - 5194.57i) q^{82} +8748.10 q^{83} +3939.90i q^{84} +(2517.03 - 4359.63i) q^{85} +(-4902.12 - 2830.24i) q^{86} +3752.94 q^{87} +1187.26i q^{88} +(6846.92 + 3953.07i) q^{89} +(2928.92 - 1691.02i) q^{90} +(-5431.12 - 3135.66i) q^{91} +(3588.58 + 6215.61i) q^{92} +(-5475.80 - 9484.37i) q^{93} -11385.3i q^{94} +(-6245.29 + 2116.33i) q^{95} -2190.72 q^{96} +(6081.56 - 3511.19i) q^{97} +(-1824.78 + 1053.54i) q^{98} +(-1717.36 + 2974.56i) 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
$3$	10.4807	−	6.05105i	1.16453	−	0.672339i	0.212141	−	0.977239i	$-0.431956\pi$
$3$	10.4807	−	6.05105i	1.16453	−	0.672339i	0.952384	+	0.304900i	$0.0986230\pi$
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	9.13314	+	15.8191i	0.365326	+	0.632763i	0.988828	−	0.149059i	$-0.0476243\pi$
$5$	9.13314	+	15.8191i	0.365326	+	0.632763i	−0.623503	+	0.781821i	$0.714291\pi$
$6$	17.1150	−	29.6440i	0.475416	−	0.823444i
$7$	−40.6944			−0.830498			−0.415249	−	0.909708i	$-0.636306\pi$
$7$	−40.6944			−0.830498			−0.415249	+	0.909708i	$0.636306\pi$
$8$		−	22.6274i		−	0.353553i
$9$	32.7305	−	56.6909i	0.404080	−	0.699887i
$10$	44.7431	+	25.8324i	0.447431	+	0.258324i
$11$	−52.4698			−0.433634			−0.216817	−	0.976212i	$-0.569568\pi$
$11$	−52.4698			−0.433634			−0.216817	+	0.976212i	$0.569568\pi$
$12$		−	96.8168i		−	0.672339i
$13$	133.461	+	77.0538i	0.789711	+	0.455940i	0.839861	−	0.542802i	$-0.182637\pi$
$13$	133.461	+	77.0538i	0.789711	+	0.455940i	−0.0501501	+	0.998742i	$0.515970\pi$
$14$	−99.6805	+	57.5506i	−0.508574	+	0.293625i
$15$	191.444	+	110.530i	0.850862	+	0.491245i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−137.797	−	238.671i	−0.476805	−	0.825850i	0.522842	−	0.852430i	$-0.324872\pi$
$17$	−137.797	−	238.671i	−0.476805	−	0.825850i	−0.999647	+	0.0265796i	$0.991538\pi$
$18$		−	185.152i		−	0.571455i
$19$	−70.6137	+	354.026i	−0.195606	+	0.980683i
$19$	−70.6137	+	354.026i	−0.195606	+	0.980683i
$20$	146.130			0.365326
$21$	−426.507	+	246.244i	−0.967136	+	0.558376i
$22$	−128.524	+	74.2034i	−0.265546	+	0.153313i
$23$	−448.573	+	776.951i	−0.847964	+	1.46872i	0.0350577	+	0.999385i	$0.488838\pi$
$23$	−448.573	+	776.951i	−0.847964	+	1.46872i	−0.883022	+	0.469332i	$0.844495\pi$
$24$	−136.920	−	237.152i	−0.237708	−	0.411722i
$25$	145.671	−	252.310i	0.233074	−	0.403697i
$26$	435.882			0.644796
$27$			188.055i			0.257963i
$28$	−162.778	+	281.939i	−0.207625	+	0.359616i
$29$	268.560	+	155.053i	0.319334	+	0.184368i	0.651096	−	0.758996i	$-0.274310\pi$
$29$	268.560	+	155.053i	0.319334	+	0.184368i	−0.331762	+	0.943363i	$0.607643\pi$
$30$	625.253			0.694726
$31$		−	904.934i		−	0.941659i	−0.882224	−	0.470829i	$-0.843955\pi$
$31$		−	904.934i		−	0.941659i	0.882224	−	0.470829i	$-0.156045\pi$
$32$	−156.767	−	90.5097i	−0.153093	−	0.0883883i
$33$	−549.921	+	317.497i	−0.504978	+	0.291549i
$34$	−675.063	−	389.748i	−0.583964	−	0.337152i
$35$	−371.668	−	643.747i	−0.303402	−	0.525508i
$36$	−261.844	−	453.527i	−0.202040	−	0.349944i
$37$			115.035i			0.0840282i	0.999117	+	0.0420141i	$0.0133774\pi$
$37$			115.035i			0.0840282i	−0.999117	+	0.0420141i	$0.986623\pi$
$38$	327.702	+	967.047i	0.226940	+	0.669700i
$39$	1865.03			1.22618
$40$	357.945	−	206.659i	0.223715	−	0.129162i
$41$	1836.56	−	1060.34i	1.09254	−	0.630778i	0.158288	−	0.987393i	$-0.449402\pi$
$41$	1836.56	−	1060.34i	1.09254	−	0.630778i	0.934251	+	0.356615i	$0.116069\pi$
$42$	−696.483	+	1206.34i	−0.394832	+	0.683869i
$43$	−1000.64	−	1733.16i	−0.541179	−	0.937350i	−0.998837	−	0.0482214i	$-0.984645\pi$
$43$	−1000.64	−	1733.16i	−0.541179	−	0.937350i	0.457657	−	0.889129i	$-0.348689\pi$
$44$	−209.879	+	363.521i	−0.108409	+	0.187769i
$45$	1195.73			0.590483
$46$			2537.51i			1.19920i
$47$	2012.65	−	3486.01i	0.911113	−	1.57809i	0.0986174	−	0.995125i	$-0.468558\pi$
$47$	2012.65	−	3486.01i	0.911113	−	1.57809i	0.812495	−	0.582968i	$-0.198109\pi$
$48$	−670.767	−	387.267i	−0.291131	−	0.168085i
$49$	−744.965			−0.310273
$50$		−	824.042i		−	0.329617i
$51$	−2888.42	−	1667.63i	−1.11050	−	0.641149i
$52$	1067.69	−	616.430i	0.394855	−	0.227970i
$53$	2557.89	+	1476.80i	0.910607	+	0.525739i	0.880626	−	0.473811i	$-0.157122\pi$
$53$	2557.89	+	1476.80i	0.910607	+	0.525739i	0.0299806	+	0.999550i	$0.490455\pi$
$54$	265.950	+	460.639i	0.0912037	+	0.157970i
$55$	−479.214	−	830.022i	−0.158418	−	0.274388i
$56$			920.809i			0.293625i
$57$	1402.15	+	4137.74i	0.431563	+	1.27354i
$58$	877.113			0.260735
$59$	−5202.69	+	3003.77i	−1.49460	+	0.862905i	−0.999981	−	0.00620675i	$-0.998024\pi$
$59$	−5202.69	+	3003.77i	−1.49460	+	0.862905i	−0.494615	+	0.869112i	$0.664691\pi$
$60$	1531.55	−	884.242i	0.425431	−	0.245623i
$61$	606.668	−	1050.78i	0.163039	−	0.282392i	−0.772918	−	0.634506i	$-0.781204\pi$
$61$	606.668	−	1050.78i	0.163039	−	0.282392i	0.935957	+	0.352114i	$0.114537\pi$
$62$	−1279.77	−	2216.63i	−0.332927	−	0.576646i
$63$	−1331.95	+	2307.00i	−0.335588	+	0.581255i
$64$	−512.000			−0.125000
$65$			2814.97i			0.666266i
$66$	−898.018	+	1555.41i	−0.206157	+	0.357074i
$67$	−5554.61	−	3206.96i	−1.23738	−	0.714404i	−0.268825	−	0.963189i	$-0.586635\pi$
$67$	−5554.61	−	3206.96i	−1.23738	−	0.714404i	−0.968559	+	0.248785i	$0.919969\pi$
$68$	−2204.75			−0.476805
$69$			10857.4i			2.28048i
$70$	−1820.79	−	1051.24i	−0.371590	−	0.214538i
$71$	−2812.41	+	1623.75i	−0.557907	+	0.322108i	−0.752305	−	0.658815i	$-0.771058\pi$
$71$	−2812.41	+	1623.75i	−0.557907	+	0.322108i	0.194398	+	0.980923i	$0.437725\pi$
$72$	−1282.77	−	740.606i	−0.247447	−	0.142864i
$73$	−3824.61	−	6624.43i	−0.717698	−	1.24309i	−0.961910	−	0.273368i	$-0.911862\pi$
$73$	−3824.61	−	6624.43i	−0.717698	−	1.24309i	0.244211	−	0.969722i	$-0.421471\pi$
$74$	162.683	+	281.776i	0.0297085	+	0.0514565i
$75$		−	3525.86i		−	0.626820i
$76$	2170.31	+	1905.33i	0.375747	+	0.329870i
$77$	2135.23			0.360133
$78$	4568.36	−	2637.55i	0.750881	−	0.433522i
$79$	5809.97	−	3354.39i	0.930936	−	0.537476i	0.0438282	−	0.999039i	$-0.486045\pi$
$79$	5809.97	−	3354.39i	0.930936	−	0.537476i	0.887107	+	0.461563i	$0.152711\pi$
$80$	584.521	−	1012.42i	0.0913314	−	0.158191i
$81$	3789.10	+	6562.91i	0.577519	+	1.00029i
$82$	2999.09	−	5194.57i	0.446027	−	0.772542i
$83$	8748.10			1.26986			0.634932	−	0.772568i	$-0.281028\pi$
$83$	8748.10			1.26986			0.634932	+	0.772568i	$0.281028\pi$
$84$			3939.90i			0.558376i
$85$	2517.03	−	4359.63i	0.348378	−	0.603408i
$86$	−4902.12	−	2830.24i	−0.662807	−	0.382672i
$87$	3752.94			0.495830
$88$			1187.26i			0.153313i
$89$	6846.92	+	3953.07i	0.864401	+	0.499062i	0.865483	−	0.500938i	$-0.167011\pi$
$89$	6846.92	+	3953.07i	0.864401	+	0.499062i	−0.00108292	+	0.999999i	$0.500345\pi$
$90$	2928.92	−	1691.02i	0.361596	−	0.208767i
$91$	−5431.12	−	3135.66i	−0.655853	−	0.378657i
$92$	3588.58	+	6215.61i	0.423982	+	0.734359i
$93$	−5475.80	−	9484.37i	−0.633114	−	1.09659i
$94$		−	11385.3i		−	1.28851i
$95$	−6245.29	+	2116.33i	−0.691999	+	0.234497i
$96$	−2190.72			−0.237708
$97$	6081.56	−	3511.19i	0.646356	−	0.373174i	−0.140703	−	0.990052i	$-0.544936\pi$
$97$	6081.56	−	3511.19i	0.646356	−	0.373174i	0.787059	+	0.616878i	$0.211603\pi$
$98$	−1824.78	+	1053.54i	−0.190003	+	0.109698i
$99$	−1717.36	+	2974.56i	−0.175223	+	0.303495i
$100$	−1165.37	−	2018.48i	−0.116537	−	0.201848i
$101$	−4727.68	+	8188.57i	−0.463452	+	0.802723i	−0.999130	−	0.0416997i	$-0.986723\pi$
$101$	−4727.68	+	8188.57i	−0.463452	+	0.802723i	0.535678	+	0.844422i	$0.320056\pi$
$102$	−9433.53			−0.906722
$103$			1584.35i			0.149340i	0.997208	+	0.0746699i	$0.0237903\pi$
$103$			1584.35i			0.149340i	−0.997208	+	0.0746699i	$0.976210\pi$
$104$	1743.53	−	3019.88i	0.161199	−	0.279205i
$105$	−7790.70	−	4497.96i	−0.706639	−	0.407978i
$106$	8354.05			0.743507
$107$			5489.78i			0.479498i	0.970835	+	0.239749i	$0.0770652\pi$
$107$			5489.78i			0.479498i	−0.970835	+	0.239749i	$0.922935\pi$
$108$	1302.88	+	752.221i	0.111701	+	0.0644908i
$109$	−1219.92	+	704.320i	−0.102678	+	0.0592812i	−0.550460	−	0.834862i	$-0.685548\pi$
$109$	−1219.92	+	704.320i	−0.102678	+	0.0592812i	0.447782	+	0.894143i	$0.352214\pi$
$110$	−2347.66	−	1355.42i	−0.194021	−	0.112018i
$111$	696.080	+	1205.65i	0.0564954	+	0.0978530i
$112$	1302.22	+	2255.51i	0.103812	+	0.179808i
$113$			2362.53i			0.185021i	0.995712	+	0.0925105i	$0.0294892\pi$
$113$			2362.53i			0.185021i	−0.995712	+	0.0925105i	$0.970511\pi$
$114$	9286.20	+	8152.42i	0.714543	+	0.627302i
$115$	−16387.5			−1.23913
$116$	2148.48	−	1240.43i	0.159667	−	0.0921838i
$117$	8736.49	−	5044.02i	0.638212	−	0.368472i
$118$	−8495.95	+	14715.4i	−0.610166	+	1.05684i
$119$	5607.55	+	9712.56i	0.395985	+	0.685867i
$120$	2501.01	−	4331.88i	0.173682	−	0.300825i
$121$	−11887.9			−0.811961
$122$		−	3431.83i		−	0.230572i
$123$	12832.3	−	22226.2i	0.848194	−	1.46911i
$124$	−6269.57	−	3619.74i	−0.407750	−	0.235415i
$125$	16738.2			1.07124
$126$			7534.63i			0.474593i
$127$	20297.0	+	11718.5i	1.25842	+	0.726547i	0.972767	−	0.231786i	$-0.0744570\pi$
$127$	20297.0	+	11718.5i	1.25842	+	0.726547i	0.285650	+	0.958334i	$0.407790\pi$
$128$	−1254.14	+	724.077i	−0.0765466	+	0.0441942i
$129$	−20974.9	−	12109.9i	−1.26043	−	0.727712i
$130$	3980.97	+	6895.25i	0.235560	+	0.408003i
$131$	1960.23	+	3395.22i	0.114226	+	0.197845i	0.917470	−	0.397805i	$-0.130228\pi$
$131$	1960.23	+	3395.22i	0.114226	+	0.197845i	−0.803244	+	0.595650i	$0.796895\pi$
$132$			5079.96i			0.291549i
$133$	2873.58	−	14406.9i	0.162450	−	0.814455i
$134$	−18141.3			−1.01032
$135$	−2974.86	+	1717.53i	−0.163229	+	0.0942405i
$136$	−5400.50	+	3117.98i	−0.291982	+	0.168576i
$137$	−13070.8	+	22639.4i	−0.696406	+	1.20621i	0.273298	+	0.961929i	$0.411885\pi$
$137$	−13070.8	+	22639.4i	−0.696406	+	1.20621i	−0.969704	+	0.244281i	$0.921448\pi$
$138$	15354.6	+	26595.0i	0.806271	+	1.39650i
$139$	−9845.46	+	17052.8i	−0.509573	+	0.882606i	0.490366	+	0.871517i	$0.336863\pi$
$139$	−9845.46	+	17052.8i	−0.509573	+	0.882606i	−0.999939	+	0.0110893i	$0.996470\pi$
$140$	−5946.68			−0.303402
$141$		−	48714.5i		−	2.45031i
$142$	−4592.64	+	7954.69i	−0.227765	+	0.394500i
$143$	−7002.67	−	4042.99i	−0.342446	−	0.197711i
$144$	−4189.50			−0.202040
$145$			5664.49i			0.269417i
$146$	−18736.7	−	10817.6i	−0.878997	−	0.507489i
$147$	−7807.78	+	4507.82i	−0.361321	+	0.208609i
$148$	796.983	+	460.138i	0.0363853	+	0.0210070i
$149$	10988.5	+	19032.6i	0.494953	+	0.857284i	0.999983	−	0.00581763i	$-0.00185182\pi$
$149$	10988.5	+	19032.6i	0.494953	+	0.857284i	−0.505030	+	0.863102i	$0.668518\pi$
$150$	−4986.32	−	8636.57i	−0.221614	−	0.383847i
$151$		−	22987.8i		−	1.00819i	−0.863647	−	0.504096i	$-0.831826\pi$
$151$		−	22987.8i		−	1.00819i	0.863647	−	0.504096i	$-0.168174\pi$
$152$	8010.70	+	1597.80i	0.346724	+	0.0691571i
$153$	−18040.6			−0.770669
$154$	5230.21	−	3019.67i	0.220535	−	0.127326i
$155$	14315.2	−	8264.89i	0.595846	−	0.344012i
$156$	7460.11	−	12921.3i	0.306546	−	0.530953i
$157$	20607.3	+	35692.9i	0.836029	+	1.44804i	0.893190	+	0.449680i	$0.148462\pi$
$157$	20607.3	+	35692.9i	0.836029	+	1.44804i	−0.0571609	+	0.998365i	$0.518205\pi$
$158$	9487.64	−	16433.1i	0.380053	−	0.658271i
$159$	35744.8			1.41390
$160$		−	3306.55i		−	0.129162i
$161$	18254.4	−	31617.6i	0.704233	−	1.21977i
$162$	18562.7	+	10717.2i	0.707313	+	0.408367i
$163$	−3003.65			−0.113051			−0.0565254	−	0.998401i	$-0.518002\pi$
$163$	−3003.65			−0.113051			−0.0565254	+	0.998401i	$0.518002\pi$
$164$		−	16965.4i		−	0.630778i
$165$	−10045.0	−	5799.49i	−0.368963	−	0.213021i
$166$	21428.4	−	12371.7i	0.777630	−	0.448965i
$167$	−28990.2	−	16737.5i	−1.03949	−	0.600147i	−0.119798	−	0.992798i	$-0.538225\pi$
$167$	−28990.2	−	16737.5i	−1.03949	−	0.600147i	−0.919688	+	0.392651i	$0.871558\pi$
$168$	5571.87	+	9650.75i	0.197416	+	0.341934i
$169$	−2405.93	−	4167.19i	−0.0842381	−	0.145905i
$170$		−	14238.5i		−	0.492681i
$171$	17758.8	+	15590.6i	0.607327	+	0.533176i
$172$	−16010.2			−0.541179
$173$	24129.7	−	13931.3i	0.806231	−	0.465478i	−0.0394143	−	0.999223i	$-0.512549\pi$
$173$	24129.7	−	13931.3i	0.806231	−	0.465478i	0.845645	+	0.533745i	$0.179216\pi$
$174$	9192.79	−	5307.46i	0.303633	−	0.175303i
$175$	−5928.01	+	10267.6i	−0.193568	+	0.335269i
$176$	1679.03	+	2908.17i	0.0542043	+	0.0938846i
$177$	−36352.0	+	62963.5i	−1.16033	+	2.00975i
$178$	22361.9			0.705780
$179$			9775.14i			0.305082i	0.988297	+	0.152541i	$0.0487457\pi$
$179$			9775.14i			0.305082i	−0.988297	+	0.152541i	$0.951254\pi$
$180$	4782.91	−	8284.25i	0.147621	−	0.255687i
$181$	−20831.3	−	12027.0i	−0.635858	−	0.367113i	0.147159	−	0.989113i	$-0.452987\pi$
$181$	−20831.3	−	12027.0i	−0.635858	−	0.367113i	−0.783017	+	0.622000i	$0.786320\pi$
$182$	−17738.0			−0.535502
$183$		−	14683.9i		−	0.438470i
$184$	17580.4	+	10150.0i	0.519270	+	0.299801i
$185$	−1819.74	+	1050.63i	−0.0531699	+	0.0306977i
$186$	−26825.8	−	15487.9i	−0.775403	−	0.447679i
$187$	7230.15	+	12523.0i	0.206759	+	0.358117i
$188$	−16101.2	−	27888.1i	−0.455556	−	0.789047i
$189$		−	7652.79i		−	0.214238i
$190$	−12304.8	+	14016.1i	−0.340854	+	0.388258i
$191$	6591.39			0.180680			0.0903400	−	0.995911i	$-0.471205\pi$
$191$	6591.39			0.180680			0.0903400	+	0.995911i	$0.471205\pi$
$192$	−5366.13	+	3098.14i	−0.145566	+	0.0840424i
$193$	11519.8	−	6650.95i	0.309264	−	0.178554i	−0.337333	−	0.941385i	$-0.609525\pi$
$193$	11519.8	−	6650.95i	0.309264	−	0.178554i	0.646597	+	0.762832i	$0.276192\pi$
$194$	9931.15	−	17201.3i	0.263874	−	0.457043i
$195$	17033.5	+	29503.0i	0.447957	+	0.775883i
$196$	−2979.86	+	5161.27i	−0.0775682	+	0.134352i
$197$	−8607.77			−0.221798			−0.110899	−	0.993832i	$-0.535373\pi$
$197$	−8607.77			−0.221798			−0.110899	+	0.993832i	$0.535373\pi$
$198$			9714.86i			0.247803i
$199$	−18628.0	+	32264.6i	−0.470391	+	0.814742i	−0.999427	−	0.0338581i	$-0.989221\pi$
$199$	−18628.0	+	32264.6i	−0.470391	+	0.814742i	0.529035	+	0.848600i	$0.322554\pi$
$200$	−5709.13	−	3296.17i	−0.142728	−	0.0824042i
$201$	−77621.9			−1.92129
$202$			26743.8i			0.655420i
$203$	−10928.9	−	6309.80i	−0.265206	−	0.153117i
$204$	−23107.3	+	13341.0i	−0.555251	+	0.320575i
$205$	33547.1	+	19368.4i	0.798266	+	0.460879i
$206$	2240.60	+	3880.84i	0.0527996	+	0.0914515i
$207$	29364.0	+	50860.0i	0.685291	+	1.18696i
$208$		−	9862.89i		−	0.227970i
$209$	3705.08	−	18575.7i	0.0848214	−	0.425258i
$210$	−25444.3			−0.576969
$211$	64223.3	−	37079.3i	1.44254	−	0.832850i	0.444520	−	0.895769i	$-0.353374\pi$
$211$	64223.3	−	37079.3i	1.44254	−	0.832850i	0.998019	+	0.0629190i	$0.0200410\pi$
$212$	20463.2	−	11814.4i	0.455303	−	0.262870i
$213$	−19650.7	+	34036.1i	−0.433131	+	0.750205i
$214$	7763.71	+	13447.1i	0.169528	+	0.293631i
$215$	18278.0	−	31658.4i	0.395413	−	0.684876i
$216$	4255.20			0.0912037
$217$			36825.8i			0.782046i
$218$	−1992.12	+	3450.45i	−0.0419181	+	0.0726043i
$219$	−80169.5	−	46285.9i	−1.67156	−	0.965073i
$220$	−7667.42			−0.158418
$221$		−	42471.0i		−	0.869577i
$222$	3410.08	+	1968.81i	0.0691925	+	0.0399483i
$223$	−73682.3	+	42540.5i	−1.48168	+	0.855447i	−0.999784	−	0.0207829i	$-0.993384\pi$
$223$	−73682.3	+	42540.5i	−1.48168	+	0.855447i	−0.481894	+	0.876230i	$0.660051\pi$
$224$	6379.55	+	3683.24i	0.127144	+	0.0734064i
$225$	−9535.79	−	16516.5i	−0.188361	−	0.326251i
$226$	3341.13	+	5787.00i	0.0654148	+	0.113302i
$227$			34377.0i			0.667140i	0.942725	+	0.333570i	$0.108253\pi$
$227$			34377.0i			0.667140i	−0.942725	+	0.333570i	$0.891747\pi$
$228$	34275.7	+	6836.59i	0.659351	+	0.131513i
$229$	−16889.2			−0.322062			−0.161031	−	0.986949i	$-0.551482\pi$
$229$	−16889.2			−0.322062			−0.161031	+	0.986949i	$0.551482\pi$
$230$	−40141.1	+	23175.5i	−0.758810	+	0.438099i
$231$	22378.7	−	12920.4i	0.419384	−	0.242131i
$232$	3508.45	−	6076.82i	0.0651838	−	0.112902i
$233$	−7596.98	−	13158.4i	−0.139936	−	0.242376i	0.787536	−	0.616268i	$-0.211356\pi$
$233$	−7596.98	−	13158.4i	−0.139936	−	0.242376i	−0.927472	+	0.373892i	$0.878023\pi$
$234$	14266.6	−	24710.5i	0.260549	−	0.451284i
$235$	73527.2			1.33141
$236$			48060.4i			0.862905i
$237$	40595.1	−	70312.9i	0.722732	−	1.25181i
$238$	27471.3	+	15860.5i	0.484981	+	0.280004i
$239$	35768.6			0.626190			0.313095	−	0.949722i	$-0.398634\pi$
$239$	35768.6			0.626190			0.313095	+	0.949722i	$0.398634\pi$
$240$		−	14147.9i		−	0.245623i
$241$	−91819.3	−	53011.9i	−1.58088	−	0.912723i	−0.994731	−	0.102523i	$-0.967309\pi$
$241$	−91819.3	−	53011.9i	−1.58088	−	0.912723i	−0.586153	−	0.810201i	$-0.699358\pi$
$242$	−29119.3	+	16812.1i	−0.497223	+	0.287072i
$243$	66233.4	+	38239.9i	1.12167	+	0.647595i
$244$	−4853.34	−	8406.24i	−0.0815195	−	0.141196i
$245$	−6803.87	−	11784.7i	−0.113351	−	0.196329i
$246$		−	72590.6i		−	1.19953i
$247$	−36703.3	+	41807.7i	−0.601604	+	0.685271i
$248$	−20476.3			−0.332927
$249$	91686.4	−	52935.2i	1.47879	−	0.853780i
$250$	41000.0	−	23671.4i	0.656000	−	0.378742i
$251$	−27632.2	+	47860.4i	−0.438600	+	0.759678i	−0.997582	−	0.0695024i	$-0.977859\pi$
$251$	−27632.2	+	47860.4i	−0.438600	+	0.759678i	0.558982	+	0.829180i	$0.311192\pi$
$252$	10655.6	+	18456.0i	0.167794	+	0.290627i
$253$	23536.5	−	40766.4i	0.367706	−	0.636886i
$254$	66289.8			1.02749
$255$		−	60922.7i		−	0.936913i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	38690.0	+	22337.7i	0.585778	+	0.338199i	0.763426	−	0.645895i	$-0.223516\pi$
$257$	38690.0	+	22337.7i	0.585778	+	0.338199i	−0.177649	+	0.984094i	$0.556849\pi$
$258$	−68503.7			−1.02914
$259$		−	4681.26i		−	0.0697853i
$260$	19502.7	+	11259.9i	0.288502	+	0.166566i
$261$	17580.2	−	10149.9i	0.258073	−	0.148999i
$262$	9603.13	+	5544.37i	0.139898	+	0.0807699i
$263$	−29030.4	−	50282.2i	−0.419703	−	0.726947i	0.576206	−	0.817304i	$-0.304532\pi$
$263$	−29030.4	−	50282.2i	−0.419703	−	0.726947i	−0.995909	+	0.0903572i	$0.971199\pi$
$264$	7184.14	+	12443.3i	0.103078	+	0.178537i
$265$			53951.3i			0.768264i
$266$	−13335.6	−	39353.4i	−0.188473	−	0.556185i
$267$	95680.9			1.34216
$268$	−44436.9	+	25655.7i	−0.618692	+	0.357202i
$269$	62637.7	−	36163.9i	0.865627	−	0.499770i	−0.000265353	−	1.00000i	$-0.500084\pi$
$269$	62637.7	−	36163.9i	0.865627	−	0.499770i	0.865893	+	0.500230i	$0.166751\pi$
$270$	−4857.92	+	8414.16i	−0.0666381	+	0.115421i
$271$	−43116.8	−	74680.5i	−0.587094	−	1.01688i	−0.994611	−	0.103680i	$-0.966938\pi$
$271$	−43116.8	−	74680.5i	−0.587094	−	1.01688i	0.407516	−	0.913198i	$-0.366395\pi$
$272$	−8818.98	+	15274.9i	−0.119201	+	0.206463i
$273$	−75896.1			−1.01834
$274$			73939.9i			0.984867i
$275$	−7643.35	+	13238.7i	−0.101069	+	0.175057i
$276$	75222.0	+	43429.4i	0.987476	+	0.570120i
$277$	133588.			1.74103			0.870516	−	0.492139i	$-0.163785\pi$
$277$	133588.			1.74103			0.870516	+	0.492139i	$0.163785\pi$
$278$			55694.3i			0.720645i
$279$	−51301.5	−	29618.9i	−0.659055	−	0.380505i
$280$	−14566.3	+	8409.88i	−0.185795	+	0.107269i
$281$	−67741.3	−	39110.5i	−0.857908	−	0.495314i	0.00540286	−	0.999985i	$-0.498280\pi$
$281$	−67741.3	−	39110.5i	−0.857908	−	0.495314i	−0.863311	+	0.504672i	$0.831614\pi$
$282$	−68892.8	−	119326.i	−0.866314	−	1.50050i
$283$	1941.73	+	3363.17i	0.0242446	+	0.0419929i	0.877893	−	0.478857i	$-0.158949\pi$
$283$	1941.73	+	3363.17i	0.0242446	+	0.0419929i	−0.853649	+	0.520849i	$0.825615\pi$
$284$			25979.9i			0.322108i
$285$	−52649.2	+	59971.3i	−0.648189	+	0.738335i
$286$	−22870.6			−0.279606
$287$	−74737.7	+	43149.8i	−0.907352	+	0.523860i
$288$	−10262.1	+	5924.85i	−0.123724	+	0.0714319i
$289$	3784.71	−	6555.31i	0.0453145	−	0.0784870i
$290$	8010.80	+	13875.1i	0.0952533	+	0.164984i
$291$	42492.8	−	73599.7i	0.501799	−	0.869141i
$292$	−61193.8			−0.717698
$293$			115090.i			1.34061i	0.742087	+	0.670304i	$0.233836\pi$
$293$			115090.i			1.34061i	−0.742087	+	0.670304i	$0.766164\pi$
$294$	−12750.1	+	22083.7i	−0.147509	+	0.255492i
$295$	−95033.8	−	54867.8i	−1.09203	−	0.630483i
$296$	2602.94			0.0297085
$297$		−	9867.21i		−	0.111862i
$298$	53832.2	+	31080.1i	0.606192	+	0.349985i
$299$	−119734.	+	69128.5i	−1.33929	+	0.773241i
$300$	−24427.9	−	14103.5i	−0.271421	−	0.156705i
$301$	40720.5	+	70529.9i	0.449448	+	0.778467i
$302$	−32509.7	−	56308.4i	−0.356450	−	0.617389i
$303$			114430.i			1.24639i
$304$	21881.8	−	7415.04i	0.236775	−	0.0802354i
$305$	22163.1			0.238249
$306$	−44190.2	+	25513.2i	−0.471936	+	0.272473i
$307$	24719.2	−	14271.7i	0.262276	−	0.151425i	−0.363096	−	0.931752i	$-0.618280\pi$
$307$	24719.2	−	14271.7i	0.262276	−	0.151425i	0.625372	+	0.780327i	$0.284947\pi$
$308$	8540.90	−	14793.3i	0.0900331	−	0.155942i
$309$	9586.96	+	16605.1i	0.100407	+	0.173910i
$310$	23376.6	−	40489.5i	0.243253	−	0.421327i
$311$	−13146.5			−0.135921			−0.0679607	−	0.997688i	$-0.521649\pi$
$311$	−13146.5			−0.135921			−0.0679607	+	0.997688i	$0.521649\pi$
$312$		−	42200.7i		−	0.433522i
$313$	−87731.9	+	151956.i	−0.895507	+	1.55106i	−0.0623313	+	0.998056i	$0.519854\pi$
$313$	−87731.9	+	151956.i	−0.895507	+	1.55106i	−0.833176	+	0.553008i	$0.813480\pi$
$314$	100955.	+	58286.2i	1.02392	+	0.591162i
$315$	−48659.5			−0.490395
$316$		−	53670.2i		−	0.537476i
$317$	75547.7	+	43617.5i	0.751801	+	0.434052i	0.826344	−	0.563165i	$-0.190417\pi$
$317$	75547.7	+	43617.5i	0.751801	+	0.434052i	−0.0745435	+	0.997218i	$0.523750\pi$
$318$	87556.5	−	50550.8i	0.865834	−	0.499889i
$319$	−14091.3	−	8135.60i	−0.138474	−	0.0799482i
$320$	−4676.17	−	8099.36i	−0.0456657	−	0.0790953i
$321$	33218.9	+	57536.9i	0.322385	+	0.558388i
$322$		−	103263.i		−	0.995935i
$323$	94226.0	−	31930.2i	0.903162	−	0.306053i
$324$	60625.6			0.577519
$325$	38882.9	−	22449.1i	0.368123	−	0.212536i
$326$	−7357.40	+	4247.80i	−0.0692292	+	0.0399695i
$327$	−8523.75	+	14763.6i	−0.0797141	+	0.138069i
$328$	−23992.7	−	41556.6i	−0.223014	−	0.386271i
$329$	−81903.5	+	141861.i	−0.756677	+	1.31060i
$330$	−32806.9			−0.301257
$331$		−	161860.i		−	1.47735i	−0.674060	−	0.738677i	$-0.735451\pi$
$331$		−	161860.i		−	1.47735i	0.674060	−	0.738677i	$-0.264549\pi$
$332$	34992.4	−	60608.6i	0.317466	−	0.549867i
$333$	6521.41	+	3765.14i	0.0588102	+	0.0339541i
$334$	−94681.7			−0.848737
$335$		−	117158.i		−	1.04396i
$336$	27296.5	+	15759.6i	0.241784	+	0.139594i
$337$	110393.	−	63735.2i	0.972031	−	0.561203i	0.0721764	−	0.997392i	$-0.477006\pi$
$337$	110393.	−	63735.2i	0.972031	−	0.561203i	0.899855	+	0.436189i	$0.143672\pi$
$338$	−11786.6	−	6804.99i	−0.103170	−	0.0595654i
$339$	14295.8	+	24761.1i	0.124397	+	0.215462i
$340$	−20136.2	−	34877.0i	−0.174189	−	0.301704i
$341$			47481.7i			0.408336i
$342$	65548.5	+	13074.2i	0.560416	+	0.111780i
$343$	128023.			1.08818
$344$	−39216.9	+	22641.9i	−0.331403	+	0.191336i
$345$	−171753.	+	99161.8i	−1.44300	+	0.833117i
$346$	39403.6	−	68249.1i	0.329142	−	0.570091i
$347$	−71952.7	−	124626.i	−0.597569	−	1.03502i	−0.993179	−	0.116602i	$-0.962800\pi$
$347$	−71952.7	−	124626.i	−0.597569	−	1.03502i	0.395609	−	0.918419i	$-0.370533\pi$
$348$	15011.8	−	26001.1i	0.123958	−	0.214701i
$349$	−66908.7			−0.549328			−0.274664	−	0.961540i	$-0.588567\pi$
$349$	−66908.7			−0.549328			−0.274664	+	0.961540i	$0.588567\pi$
$350$			33533.9i			0.273746i
$351$	−14490.4	+	25098.0i	−0.117616	+	0.203716i
$352$	8225.54	+	4749.02i	0.0663864	+	0.0383282i
$353$	116126.			0.931921			0.465961	−	0.884806i	$-0.345709\pi$
$353$	116126.			0.931921			0.465961	+	0.884806i	$0.345709\pi$
$354$			205638.i			1.64095i
$355$	−51372.3	−	29659.8i	−0.407635	−	0.235348i
$356$	54775.3	−	31624.6i	0.432200	−	0.249531i
$357$	117542.	+	67863.2i	0.922270	+	0.532473i
$358$	13824.1	+	23944.1i	0.107863	+	0.186824i
$359$	46490.7	+	80524.3i	0.360726	+	0.624795i	0.988080	−	0.153938i	$-0.0491957\pi$
$359$	46490.7	+	80524.3i	0.360726	+	0.624795i	−0.627355	+	0.778734i	$0.715862\pi$
$360$		−	27056.2i		−	0.208767i
$361$	−120348.	−	49998.2i	−0.923477	−	0.383654i
$362$	−68034.9			−0.519176
$363$	−124594.	+	71934.5i	−0.945550	+	0.545913i
$364$	−43449.0	+	25085.3i	−0.327927	+	0.189328i
$365$	69861.5	−	121004.i	0.524387	−	0.908265i
$366$	−20766.2	−	35968.1i	−0.155023	−	0.268507i
$367$	5846.49	−	10126.4i	0.0434073	−	0.0751837i	−0.843505	−	0.537121i	$-0.819512\pi$
$367$	5846.49	−	10126.4i	0.0434073	−	0.0751837i	0.886913	+	0.461937i	$0.152845\pi$
$368$	57417.4			0.423982
$369$		−	138821.i		−	1.01954i
$370$	−2971.62	+	5147.00i	−0.0217065	+	0.0375968i
$371$	−104092.	−	60097.6i	−0.756257	−	0.436625i
$372$	−87612.9			−0.633114
$373$		−	56159.4i		−	0.403650i	−0.979422	−	0.201825i	$-0.935313\pi$
$373$		−	56159.4i		−	0.403650i	0.979422	−	0.201825i	$-0.0646872\pi$
$374$	35420.4	+	20450.0i	0.253227	+	0.146201i
$375$	175428.	−	101284.i	1.24749	−	0.720239i
$376$	−78879.4	−	45541.0i	−0.557940	−	0.322127i
$377$	23894.9	+	41387.1i	0.168121	+	0.291194i
$378$	−10822.7	−	18745.4i	−0.0757445	−	0.131193i
$379$		−	77613.7i		−	0.540331i	−0.962814	−	0.270165i	$-0.912922\pi$
$379$		−	77613.7i		−	0.540331i	0.962814	−	0.270165i	$-0.0870784\pi$
$380$	−10318.8	+	51734.0i	−0.0714598	+	0.358268i
$381$	283637.			1.95395
$382$	16145.5	−	9321.63i	0.110643	−	0.0638800i
$383$	−203087.	+	117252.i	−1.38447	+	0.799327i	−0.992686	−	0.120728i	$-0.961477\pi$
$383$	−203087.	+	117252.i	−1.38447	+	0.799327i	−0.391789	+	0.920055i	$0.628144\pi$
$384$	−8762.86	+	15177.7i	−0.0594270	+	0.102930i
$385$	19501.3	+	33777.3i	0.131566	+	0.227878i
$386$	18811.7	−	32582.8i	0.126257	−	0.218683i
$387$	−131006.			−0.874719
$388$		−	56179.1i		−	0.373174i
$389$	60585.7	−	104938.i	0.400379	−	0.693476i	−0.593393	−	0.804913i	$-0.702212\pi$
$389$	60585.7	−	104938.i	0.400379	−	0.693476i	0.993772	+	0.111437i	$0.0355453\pi$
$390$	83447.0	+	48178.1i	0.548632	+	0.316753i
$391$	247247.			1.61725
$392$			16856.6i			0.109698i
$393$	41089.3	+	23722.9i	0.266038	+	0.153597i
$394$	−21084.6	+	12173.2i	−0.135823	+	0.0784175i
$395$	106127.	+	61272.2i	0.680189	+	0.392707i
$396$	13738.9	+	23796.4i	0.0876115	+	0.151748i
$397$	−84743.0	−	146779.i	−0.537679	−	0.931287i	−0.999029	−	0.0440685i	$-0.985968\pi$
$397$	−84743.0	−	146779.i	−0.537679	−	0.931287i	0.461350	−	0.887218i	$-0.347365\pi$
$398$			105376.i			0.665234i
$399$	−57059.7	−	168383.i	−0.358413	−	1.05768i
$400$	−18646.0			−0.116537
$401$	53887.1	−	31111.8i	0.335117	−	0.193480i	−0.322994	−	0.946401i	$-0.604689\pi$
$401$	53887.1	−	31111.8i	0.335117	−	0.193480i	0.658111	+	0.752921i	$0.271356\pi$
$402$	−190134.	+	109774.i	−1.17654	+	0.679277i
$403$	69728.6	−	120773.i	0.429339	−	0.743638i
$404$	37821.4	+	65508.6i	0.231726	+	0.401361i
$405$	−69212.8	+	119880.i	−0.421965	+	0.730864i
$406$	−35693.6			−0.216540
$407$		−	6035.84i		−	0.0364375i
$408$	−37734.1	+	65357.4i	−0.226680	+	0.392622i
$409$	−19314.6	−	11151.3i	−0.115462	−	0.0666621i	0.441157	−	0.897430i	$-0.354568\pi$
$409$	−19314.6	−	11151.3i	−0.115462	−	0.0666621i	−0.556619	+	0.830768i	$0.687902\pi$
$410$	109564.			0.651781
$411$			316369.i			1.87288i
$412$	10976.7	+	6337.38i	0.0646660	+	0.0373349i
$413$	211720.	−	122237.i	1.24126	−	0.716641i
$414$	143854.	+	83054.0i	0.839306	+	0.484574i
$415$	79897.6	+	138387.i	0.463914	+	0.803523i
$416$	−13948.2	−	24159.0i	−0.0805995	−	0.139602i
$417$			238302.i			1.37042i
$418$	−17194.4	−	50740.7i	−0.0984090	−	0.290405i
$419$	−276136.			−1.57288			−0.786438	−	0.617669i	$-0.788077\pi$
$419$	−276136.			−1.57288			−0.786438	+	0.617669i	$0.788077\pi$
$420$	−62325.6	+	35983.7i	−0.353320	+	0.203989i
$421$	−245912.	+	141977.i	−1.38744	+	0.801041i	−0.993027	−	0.117890i	$-0.962387\pi$
$421$	−245912.	+	141977.i	−1.38744	+	0.801041i	−0.394417	+	0.918931i	$0.629054\pi$
$422$	104876.	−	181651.i	0.588914	−	1.02003i
$423$	−131750.	−	228197.i	−0.736325	−	1.27535i
$424$	33416.2	−	57878.6i	0.185877	−	0.321948i
$425$	−80292.1			−0.444524
$426$			111161.i			0.612540i
$427$	−24688.0	+	42760.9i	−0.135404	+	0.234526i
$428$	38034.3	+	21959.1i	0.207629	+	0.119875i
$429$	−97857.5			−0.531716
$430$		−	103396.i		−	0.559199i
$431$	91869.3	+	53040.8i	0.494557	+	0.285532i	0.726463	−	0.687206i	$-0.241163\pi$
$431$	91869.3	+	53040.8i	0.494557	+	0.285532i	−0.231906	+	0.972738i	$0.574496\pi$
$432$	10423.1	−	6017.76i	0.0558507	−	0.0322454i
$433$	−154599.	−	89257.9i	−0.824577	−	0.476070i	0.0274149	−	0.999624i	$-0.491272\pi$
$433$	−154599.	−	89257.9i	−0.824577	−	0.476070i	−0.851992	+	0.523554i	$0.824606\pi$
$434$	52079.5	+	90204.3i	0.276495	+	0.478903i
$435$	34276.1	+	59368.0i	0.181140	+	0.313743i
$436$			11269.1i			0.0592812i
$437$	−243386.	−	213670.i	−1.27448	−	1.11887i
$438$	−261833.			−1.36482
$439$	−156345.	+	90265.9i	−0.811252	+	0.468376i	−0.847390	−	0.530970i	$-0.821827\pi$
$439$	−156345.	+	90265.9i	−0.811252	+	0.468376i	0.0361388	+	0.999347i	$0.488494\pi$
$440$	−18781.3	+	10843.4i	−0.0970107	+	0.0560091i
$441$	−24383.1	+	42232.7i	−0.125375	+	0.217156i
$442$	−60063.1	−	104032.i	−0.307442	−	0.532505i
$443$	−116330.	+	201489.i	−0.592766	+	1.02670i	0.401092	+	0.916038i	$0.368631\pi$
$443$	−116330.	+	201489.i	−0.592766	+	1.02670i	−0.993858	+	0.110663i	$0.964702\pi$
$444$	11137.3			0.0564954
$445$			144416.i			0.729280i
$446$	−120323.	+	208405.i	−0.604892	+	1.04770i
$447$	230334.	+	132983.i	1.15277	+	0.665553i
$448$	20835.5			0.103812
$449$		−	182552.i		−	0.905510i	−0.891635	−	0.452755i	$-0.850441\pi$
$449$		−	182552.i		−	0.905510i	0.891635	−	0.452755i	$-0.149559\pi$
$450$	−46715.7	−	26971.3i	−0.230695	−	0.133192i
$451$	−96363.8	+	55635.7i	−0.473763	+	0.273527i
$452$	16368.1	+	9450.13i	0.0801164	+	0.0462553i
$453$	−139100.	−	240929.i	−0.677848	−	1.17407i
$454$	48616.5	+	84206.2i	0.235869	+	0.408538i
$455$		−	114554.i		−	0.553332i
$456$	93626.4	−	31727.0i	0.450266	−	0.152581i
$457$	78140.6			0.374149			0.187074	−	0.982346i	$-0.440099\pi$
$457$	78140.6			0.374149			0.187074	+	0.982346i	$0.440099\pi$
$458$	−41370.0	+	23885.0i	−0.197222	+	0.113866i
$459$	44883.2	−	25913.4i	0.213039	−	0.122998i
$460$	−65550.1	+	113536.i	−0.309783	+	0.536560i
$461$	−110657.	−	191663.i	−0.520687	−	0.901856i	−0.999711	−	0.0240539i	$-0.992343\pi$
$461$	−110657.	−	191663.i	−0.520687	−	0.901856i	0.479024	−	0.877802i	$-0.340991\pi$
$462$	36544.3	−	63296.6i	0.171213	−	0.296549i
$463$	330182.			1.54025			0.770126	−	0.637891i	$-0.220193\pi$
$463$	330182.			1.54025			0.770126	+	0.637891i	$0.220193\pi$
$464$		−	19846.8i		−	0.0921838i
$465$	100023.	−	173244.i	0.462586	−	0.801222i
$466$	−37217.5	−	21487.5i	−0.171386	−	0.0989496i
$467$	123478.			0.566183			0.283092	−	0.959093i	$-0.408640\pi$
$467$	123478.			0.566183			0.283092	+	0.959093i	$0.408640\pi$
$468$		−	80704.2i		−	0.368472i
$469$	226042.	+	130505.i	1.02764	+	0.593311i
$470$	180104.	−	103983.i	0.815319	−	0.470725i
$471$	431959.	+	249391.i	1.94715	+	1.12419i
$472$	67967.6	+	117723.i	0.305083	+	0.528419i
$473$	52503.4	+	90938.5i	0.234674	+	0.406467i
$474$		−	229641.i		−	1.02210i
$475$	79038.2	+	69388.1i	0.350308	+	0.307537i
$476$	89720.8			0.395985
$477$	167442.	−	96672.8i	0.735916	−	0.424881i
$478$	87614.8	−	50584.4i	0.383461	−	0.221391i
$479$	70014.4	−	121269.i	0.305152	−	0.528539i	−0.672143	−	0.740421i	$-0.734626\pi$
$479$	70014.4	−	121269.i	0.305152	−	0.528539i	0.977295	+	0.211882i	$0.0679593\pi$
$480$	−20008.1	−	34655.1i	−0.0868408	−	0.150413i
$481$	−8863.85	+	15352.6i	−0.0383118	+	0.0663579i
$482$	−299881.			−1.29079
$483$		−	441834.i		−	1.89393i
$484$	−47551.7	+	82362.0i	−0.202990	+	0.351590i
$485$	111088.	+	64136.4i	0.472261	+	0.272660i
$486$	216317.			0.915838
$487$			141943.i			0.598489i	0.954176	+	0.299245i	$0.0967347\pi$
$487$			141943.i			0.598489i	−0.954176	+	0.299245i	$0.903265\pi$
$488$	−23776.4	−	13727.3i	−0.0998406	−	0.0576430i
$489$	−31480.4	+	18175.2i	−0.131650	+	0.0760084i
$490$	−33332.0	−	19244.3i	−0.138826	−	0.0801510i
$491$	−1364.05	−	2362.60i	−0.00565804	−	0.00980001i	0.863183	−	0.504892i	$-0.168468\pi$
$491$	−1364.05	−	2362.60i	−0.00565804	−	0.00980001i	−0.868841	+	0.495092i	$0.835134\pi$
$492$	−102659.	−	177810.i	−0.424097	−	0.734557i
$493$		−	85463.2i		−	0.351630i
$494$	−30779.2	+	154314.i	−0.126126	+	0.632340i
$495$	−62739.6			−0.256054
$496$	−50156.5	+	28957.9i	−0.203875	+	0.117707i
$497$	114449.	−	66077.3i	0.463341	−	0.267510i
$498$	149723.	−	259328.i	0.603713	−	1.04566i
$499$	−105201.	−	182214.i	−0.422494	−	0.731780i	0.573689	−	0.819073i	$-0.305512\pi$
$499$	−105201.	−	182214.i	−0.422494	−	0.731780i	−0.996183	+	0.0872927i	$0.972178\pi$
$500$	66952.7	−	115966.i	0.267811	−	0.463862i
$501$	−405118.			−1.61401
$502$			156312.i			0.620274i
$503$	−159932.	+	277011.i	−0.632121	+	1.09486i	0.354997	+	0.934867i	$0.384482\pi$
$503$	−159932.	+	277011.i	−0.632121	+	1.09486i	−0.987117	+	0.159997i	$0.948851\pi$
$504$	52201.5	+	30138.5i	0.205505	+	0.118648i
$505$	−172714.			−0.677244
$506$		−	133143.i		−	0.520015i
$507$	−50431.7	−	29116.8i	−0.196195	−	0.113273i
$508$	162376.	−	93747.9i	0.629209	−	0.363274i
$509$	−116894.	−	67488.9i	−0.451188	−	0.260493i	0.257144	−	0.966373i	$-0.417219\pi$
$509$	−116894.	−	67488.9i	−0.451188	−	0.260493i	−0.708332	+	0.705880i	$0.750552\pi$
$510$	−86157.8	−	149230.i	−0.331249	−	0.573739i
$511$	155640.	+	269577.i	0.596047	+	1.03238i
$512$			11585.2i			0.0441942i
$513$	−66576.5	−	13279.3i	−0.252980	−	0.0504591i
$514$	126361.			0.478285
$515$	−25062.9	+	14470.0i	−0.0944966	+	0.0545576i
$516$	−167799.	+	96878.9i	−0.630217	+	0.363856i
$517$	−105603.	+	182910.i	−0.395090	+	0.684315i
$518$	−6620.31	−	11466.7i	−0.0246728	−	0.0427346i
$519$	168598.	−	292020.i	0.625918	−	1.08412i
$520$	63695.6			0.235560
$521$			253689.i			0.934601i	0.884099	+	0.467300i	$0.154773\pi$
$521$			253689.i			0.934601i	−0.884099	+	0.467300i	$0.845227\pi$
$522$	28708.3	−	49724.3i	0.105358	−	0.182485i
$523$	287975.	+	166262.i	1.05281	+	0.607841i	0.923435	−	0.383754i	$-0.125369\pi$
$523$	287975.	+	166262.i	1.05281	+	0.607841i	0.129377	+	0.991596i	$0.458702\pi$
$524$	31363.7			0.114226
$525$			143483.i			0.520573i
$526$	−142220.	−	82110.5i	−0.514029	−	0.296775i
$527$	−215981.	+	124697.i	−0.777669	+	0.448987i
$528$	35195.0	+	20319.8i	0.126245	+	0.0728873i
$529$	−262515.	−	454689.i	−0.938087	−	1.62481i
$530$	76298.7	+	132153.i	0.271622	+	0.470464i
$531$			393260.i			1.39473i
$532$	−88319.6	−	77536.3i	−0.312057	−	0.273957i
$533$	326812.			1.15039
$534$	234369.	−	135313.i	0.821899	−	0.474524i
$535$	−86843.1	+	50138.9i	−0.303409	+	0.175173i
$536$	−72565.2	+	125687.i	−0.252580	+	0.437481i
$537$	59149.9	+	102451.i	0.205119	+	0.355276i
$538$	102287.	−	177166.i	0.353391	−	0.612091i
$539$	39088.1			0.134545
$540$			27480.5i			0.0942405i
$541$	−156555.	+	271161.i	−0.534899	+	0.926473i	0.464269	+	0.885694i	$0.346317\pi$
$541$	−156555.	+	271161.i	−0.534899	+	0.926473i	−0.999168	+	0.0407784i	$0.987016\pi$
$542$	−211228.	−	121953.i	−0.719041	−	0.415138i
$543$	−291104.			−0.987297
$544$			49887.7i			0.168576i
$545$	−22283.4	−	12865.3i	−0.0750218	−	0.0433139i
$546$	−185907.	+	107333.i	−0.623606	+	0.360039i
$547$	−54608.4	−	31528.2i	−0.182509	−	0.105372i	0.405962	−	0.913890i	$-0.366937\pi$
$547$	−54608.4	−	31528.2i	−0.182509	−	0.105372i	−0.588471	+	0.808518i	$0.700270\pi$
$548$	104567.	+	181115.i	0.348203	+	0.603105i
$549$	−39713.1	−	68785.0i	−0.131762	−	0.228218i
$550$			43237.3i			0.142933i
$551$	−73856.9	+	84128.5i	−0.243270	+	0.277102i
$552$	245674.			0.806271
$553$	−236433.	+	136505.i	−0.773140	+	0.446373i
$554$	327222.	−	188922.i	1.06616	−	0.615548i
$555$	−12714.8	+	22022.7i	−0.0412785	+	0.0714964i
$556$	78763.7	+	136423.i	0.254786	+	0.441303i
$557$	−98461.3	+	170540.i	−0.317362	+	0.549688i	−0.979937	−	0.199308i	$-0.936130\pi$
$557$	−98461.3	+	170540.i	−0.317362	+	0.549688i	0.662575	+	0.748996i	$0.269464\pi$
$558$	−167550.			−0.538116
$559$		−	308413.i		−	0.986980i
$560$	−23786.7	+	41199.8i	−0.0758506	+	0.131377i
$561$	151555.	+	87500.1i	0.481552	+	0.278024i
$562$	−221242.			−0.700479
$563$		−	307676.i		−	0.970681i	−0.874325	−	0.485341i	$-0.838696\pi$
$563$		−	307676.i		−	0.970681i	0.874325	−	0.485341i	$-0.161304\pi$
$564$	−337504.	−	194858.i	−1.06101	−	0.612577i
$565$	−37373.1	+	21577.3i	−0.117074	+	0.0675929i
$566$	9512.48	+	5492.03i	0.0296935	+	0.0171435i
$567$	−154195.	−	267074.i	−0.479628	−	0.830740i
$568$	36741.2	+	63637.6i	0.113882	+	0.197250i
$569$			249874.i			0.771785i	0.922544	+	0.385892i	$0.126106\pi$
$569$			249874.i			0.771785i	−0.922544	+	0.385892i	$0.873894\pi$
$570$	−44151.4	+	221356.i	−0.135892	+	0.681306i
$571$	333305.			1.02228			0.511140	−	0.859498i	$-0.329223\pi$
$571$	333305.			1.02228			0.511140	+	0.859498i	$0.329223\pi$
$572$	−56021.4	+	32344.0i	−0.171223	+	0.0988555i
$573$	69082.6	−	39884.8i	0.210407	−	0.121478i
$574$	−122046.	+	211390.i	−0.370425	+	0.641595i
$575$	130689.	+	226359.i	0.395277	+	0.684641i
$576$	−16758.0	+	29025.7i	−0.0505100	+	0.0874859i
$577$	452372.			1.35876			0.679382	−	0.733785i	$-0.262248\pi$
$577$	452372.			1.35876			0.679382	+	0.733785i	$0.262248\pi$
$578$		−	21409.6i		−	0.0640844i
$579$	80490.4	−	139414.i	0.240097	−	0.415861i
$580$	39244.7	+	22658.0i	0.116661	+	0.0673542i
$581$	−355999.			−1.05462
$582$		−	240376.i		−	0.709651i
$583$	−134212.	−	77487.4i	−0.394870	−	0.227979i
$584$	−149894.	+	86541.1i	−0.439499	+	0.253745i
$585$	159583.	+	92135.4i	0.466311	+	0.269225i
$586$	162762.	+	281911.i	0.473976	+	0.820951i
$587$	−112606.	−	195040.i	−0.326803	−	0.566040i	0.655072	−	0.755566i	$-0.272638\pi$
$587$	−112606.	−	195040.i	−0.326803	−	0.566040i	−0.981876	+	0.189526i	$0.939305\pi$
$588$			72125.2i			0.208609i
$589$	320371.	+	63900.7i	0.923468	+	0.184194i
$590$	−310379.			−0.891637
$591$	−90215.7	+	52086.1i	−0.258290	+	0.149124i
$592$	6375.86	−	3681.11i	0.0181926	−	0.0105035i
$593$	225542.	−	390650.i	0.641384	−	1.11091i	−0.343740	−	0.939065i	$-0.611694\pi$
$593$	225542.	−	390650.i	0.641384	−	1.11091i	0.985124	−	0.171844i	$-0.0549726\pi$
$594$	−13954.3	−	24169.6i	−0.0395491	−	0.0685010i
$595$	−102429.	+	177412.i	−0.289327	+	0.501129i
$596$	175815.			0.494953
$597$			450875.i			1.26505i
$598$	−195525.	+	338659.i	−0.546764	+	0.947023i
$599$	−376004.	−	217086.i	−1.04795	−	0.605032i	−0.125873	−	0.992046i	$-0.540173\pi$
$599$	−376004.	−	217086.i	−1.04795	−	0.605032i	−0.922074	+	0.387014i	$0.873506\pi$
$600$	−79781.2			−0.221614
$601$		−	545183.i		−	1.50936i	−0.656091	−	0.754681i	$-0.727791\pi$
$601$		−	545183.i		−	1.50936i	0.656091	−	0.754681i	$-0.272209\pi$
$602$	199489.	+	115175.i	0.550460	+	0.317808i
$603$	−363610.	+	209931.i	−1.00000	+	0.577352i
$604$	−159264.	−	91951.2i	−0.436560	−	0.252048i
$605$	−108574.	−	188056.i	−0.296630	−	0.513779i
$606$	161828.	+	280294.i	0.440665	+	0.763254i
$607$		−	2996.79i		−	0.00813352i	−0.999992	−	0.00406676i	$-0.998706\pi$
$607$		−	2996.79i		−	0.00813352i	0.999992	−	0.00406676i	$-0.00129449\pi$
$608$	43112.7	−	49108.6i	0.116627	−	0.132846i
$609$	−152724.			−0.411786
$610$	54288.4	−	31343.4i	0.145897	−	0.0842338i
$611$	537220.	−	310164.i	1.43903	−	0.830825i
$612$	−72162.4	+	124989.i	−0.192667	+	0.333709i
$613$	−42295.9	−	73258.7i	−0.112558	−	0.194957i	0.804243	−	0.594301i	$-0.202571\pi$
$613$	−42295.9	−	73258.7i	−0.112558	−	0.194957i	−0.916801	+	0.399344i	$0.869238\pi$
$614$	40366.3	−	69916.6i	0.107074	−	0.185457i
$615$	468798.			1.23947
$616$		−	48314.6i		−	0.127326i
$617$	276736.	−	479321.i	0.726935	−	1.25909i	−0.231238	−	0.972897i	$-0.574278\pi$
$617$	276736.	−	479321.i	0.726935	−	1.25909i	0.958173	−	0.286191i	$-0.0923891\pi$
$618$	46966.3	+	27116.0i	0.122973	+	0.0709984i
$619$	434064.			1.13285			0.566426	−	0.824113i	$-0.308326\pi$
$619$	434064.			1.13285			0.566426	+	0.824113i	$0.308326\pi$
$620$		−	132238.i		−	0.344012i
$621$	−146110.	−	84356.5i	−0.378875	−	0.218744i
$622$	−32202.1	+	18591.9i	−0.0832345	+	0.0480555i
$623$	−278631.	−	160868.i	−0.717883	−	0.414470i
$624$	−59680.8	−	103370.i	−0.153273	−	0.265477i
$625$	61827.5	+	107088.i	0.158278	+	0.274146i
$626$			496287.i			1.26644i
$627$	−73570.5	−	217106.i	−0.187141	−	0.552252i
$628$	329716.			0.836029
$629$	27455.4	−	15851.4i	0.0693947	−	0.0400650i
$630$	−119191.	+	68814.9i	−0.300304	+	0.173381i
$631$	94963.7	−	164482.i	0.238506	−	0.413104i	−0.721780	−	0.692123i	$-0.756676\pi$
$631$	94963.7	−	164482.i	0.238506	−	0.413104i	0.960286	+	0.279018i	$0.0900091\pi$
$632$	−75901.1	−	131465.i	−0.190026	−	0.329135i
$633$	448738.	−	777237.i	1.11992	−	1.93975i
$634$	246738.			0.613843
$635$			428106.i			1.06171i
$636$	142979.	−	247647.i	0.353475	−	0.612237i
$637$	−99423.9	−	57402.4i	−0.245026	−	0.141466i
$638$	−46021.9			−0.113064
$639$			212584.i			0.520629i
$640$	−22908.5	−	13226.2i	−0.0559288	−	0.0322905i
$641$	−176029.	+	101631.i	−0.428419	+	0.247348i	−0.698673	−	0.715441i	$-0.746226\pi$
$641$	−176029.	+	101631.i	−0.428419	+	0.247348i	0.270254	+	0.962789i	$0.412892\pi$
$642$	162739.	+	93957.3i	0.394840	+	0.227961i
$643$	262304.	+	454324.i	0.634430	+	1.09886i	0.986636	+	0.162942i	$0.0520984\pi$
$643$	262304.	+	454324.i	0.634430	+	1.09886i	−0.352206	+	0.935923i	$0.614568\pi$
$644$	−146035.	−	252941.i	−0.352116	−	0.609883i
$645$		−	442404.i		−	1.06341i
$646$	185650.	−	211468.i	0.444866	−	0.506735i
$647$	223408.			0.533690			0.266845	−	0.963739i	$-0.414019\pi$
$647$	223408.			0.533690			0.266845	+	0.963739i	$0.414019\pi$
$648$	148502.	−	85737.6i	0.353657	−	0.204184i
$649$	272984.	−	157607.i	0.648108	−	0.374185i
$650$	63495.6	−	109978.i	0.150285	−	0.260302i
$651$	222835.	+	385961.i	0.525800	+	0.910712i
$652$	−12014.6	+	20809.9i	−0.0282627	+	0.0489524i
$653$	−333259.			−0.781548			−0.390774	−	0.920487i	$-0.627793\pi$
$653$	−333259.			−0.781548			−0.390774	+	0.920487i	$0.627793\pi$
$654$			48217.6i			0.112733i
$655$	−35806.1	+	62018.0i	−0.0834593	+	0.144556i
$656$	−117540.	−	67861.6i	−0.273135	−	0.157695i
$657$	−500726.			−1.16003
$658$			463316.i			1.07010i
$659$	143860.	+	83057.9i	0.331261	+	0.191254i	0.656401	−	0.754412i	$-0.272078\pi$
$659$	143860.	+	83057.9i	0.331261	+	0.191254i	−0.325140	+	0.945666i	$0.605411\pi$
$660$	−80360.2	+	46396.0i	−0.184482	+	0.106510i
$661$	−177769.	−	102635.i	−0.406867	−	0.234905i	0.282576	−	0.959245i	$-0.408811\pi$
$661$	−177769.	−	102635.i	−0.406867	−	0.234905i	−0.689443	+	0.724340i	$0.742144\pi$
$662$	−228905.	−	396475.i	−0.522323	−	0.904690i
$663$	−256994.	−	445127.i	−0.584650	−	1.01264i
$664$		−	197947.i		−	0.448965i
$665$	254148.	−	86122.8i	0.574704	−	0.194749i
$666$	21298.8			0.0480184
$667$	−240938.	+	139105.i	−0.541568	+	0.312674i
$668$	−231922.	+	133900.i	−0.519743	+	0.300074i
$669$	−514830.	+	891711.i	−1.15030	+	1.99238i
$670$	−165687.	−	286978.i	−0.369096	−	0.639292i
$671$	−31831.7	+	55134.2i	−0.0706993	+	0.122455i
$672$	89149.9			0.197416
$673$			589468.i			1.30146i	0.759310	+	0.650729i	$0.225537\pi$
$673$			589468.i			1.30146i	−0.759310	+	0.650729i	$0.774463\pi$
$674$	180270.	−	312238.i	0.396830	−	0.687330i
$675$	47448.3	+	27394.3i	0.104139	+	0.0601246i
$676$	−38494.8			−0.0842381
$677$			197706.i			0.431362i	0.976464	+	0.215681i	$0.0691971\pi$
$677$			197706.i			0.431362i	−0.976464	+	0.215681i	$0.930803\pi$
$678$	70034.9	+	40434.7i	0.152354	+	0.0879619i
$679$	−247486.	+	142886.i	−0.536797	+	0.309920i
$680$	−98647.1	−	56953.9i	−0.213337	−	0.123170i
$681$	208017.	+	360296.i	0.448544	+	0.776901i
$682$	67149.2	+	116306.i	0.144368	+	0.250053i
$683$		−	450800.i		−	0.966368i	−0.875519	−	0.483184i	$-0.839480\pi$
$683$		−	450800.i		−	0.966368i	0.875519	−	0.483184i	$-0.160520\pi$
$684$	179050.	−	60674.4i	0.382704	−	0.129686i
$685$	−477511.			−1.01766
$686$	313591.	−	181052.i	0.666371	−	0.384729i
$687$	−177012.	+	102198.i	−0.375049	+	0.216535i
$688$	−64041.0	+	110922.i	−0.135295	+	0.234338i
$689$	227586.	+	394191.i	0.479411	+	0.830364i
$690$	−280472.	+	485791.i	−0.589103	+	1.02036i
$691$	90174.6			0.188855			0.0944274	−	0.995532i	$-0.469898\pi$
$691$	90174.6			0.188855			0.0944274	+	0.995532i	$0.469898\pi$
$692$		−	222901.i		−	0.465478i
$693$	69887.0	−	121048.i	0.145522	−	0.252052i
$694$	−352495.	−	203513.i	−0.731870	−	0.422545i
$695$	−359680.			−0.744640
$696$		−	84919.4i		−	0.175303i
$697$	−506143.	−	292222.i	−1.04186	−	0.601516i
$698$	−163892.	+	94623.3i	−0.336394	+	0.194217i
$699$	−159244.	−	91939.5i	−0.325918	−	0.188169i
$700$	47424.1	+	82141.0i	0.0967839	+	0.167635i
$701$	52451.2	+	90848.2i	0.106738	+	0.184876i	0.914447	−	0.404706i	$-0.132626\pi$
$701$	52451.2	+	90848.2i	0.106738	+	0.184876i	−0.807709	+	0.589582i	$0.799293\pi$
$702$			81969.9i			0.166334i
$703$	−40725.3	−	8123.01i	−0.0824050	−	0.0164364i
$704$	26864.5			0.0542043
$705$	770619.	−	444917.i	1.55046	−	0.895160i
$706$	284449.	−	164227.i	0.570683	−	0.329484i
$707$	192390.	−	333229.i	0.384896	−	0.666660i
$708$	290816.	+	503708.i	0.580165	+	1.00488i
$709$	−163355.	+	282939.i	−0.324968	+	0.562860i	−0.981506	−	0.191432i	$-0.938687\pi$
$709$	−163355.	+	282939.i	−0.324968	+	0.562860i	0.656538	+	0.754293i	$0.272020\pi$
$710$	−167781.			−0.332833
$711$		−	439163.i		−	0.868733i
$712$	89447.7	−	154928.i	0.176445	−	0.305612i
$713$	703090.	+	405929.i	1.38303	+	0.798493i
$714$	383892.			0.753031
$715$		−	147701.i		−	0.288916i
$716$	67724.2	+	39100.6i	0.132105	+	0.0762706i
$717$	374881.	−	216438.i	0.729214	−	0.421012i
$718$	227757.	+	131496.i	0.441797	+	0.255072i
$719$	395433.	+	684910.i	0.764919	+	1.32488i	0.940289	+	0.340376i	$0.110554\pi$
$719$	395433.	+	684910.i	0.764919	+	1.32488i	−0.175371	+	0.984502i	$0.556112\pi$
$720$	−38263.3	−	66274.0i	−0.0738104	−	0.127843i
$721$		−	64474.0i		−	0.124026i
$722$	−365500.	+	47728.3i	−0.701154	+	0.0915591i
$723$	−1.28311e6			−2.45464
$724$	−166651.	+	96215.8i	−0.317929	+	0.183556i
$725$	78243.1	−	45173.7i	0.148857	−	0.0859428i
$726$	−203461.	+	352405.i	−0.386019	+	0.668605i
$727$	466495.	+	807992.i	0.882628	+	1.52876i	0.848408	+	0.529342i	$0.177561\pi$
$727$	466495.	+	807992.i	0.882628	+	1.52876i	0.0342199	+	0.999414i	$0.489105\pi$
$728$	−70951.8	+	122892.i	−0.133875	+	0.231879i
$729$	311731.			0.586578
$730$		−	395196.i		−	0.741595i
$731$	−275770.	+	477647.i	−0.516074	+	0.893866i
$732$	−101733.	−	58735.7i	−0.189863	−	0.109617i
$733$	27589.8			0.0513500			0.0256750	−	0.999670i	$-0.491826\pi$
$733$	27589.8			0.0513500			0.0256750	+	0.999670i	$0.491826\pi$
$734$		−	33072.7i		−	0.0613872i
$735$	−142619.	−	82341.2i	−0.263999	−	0.152420i
$736$	140643.	−	81200.4i	0.259635	−	0.149900i
$737$	291449.	+	168268.i	0.536572	+	0.309790i
$738$	−196323.	−	340042.i	−0.360462	−	0.624338i
$739$	−86704.5	−	150177.i	−0.158764	−	0.274988i	0.775659	−	0.631152i	$-0.217418\pi$
$739$	−86704.5	−	150177.i	−0.158764	−	0.274988i	−0.934423	+	0.356164i	$0.884084\pi$
$740$			16810.0i			0.0306977i
$741$	−131696.	+	660269.i	−0.239849	+	1.20250i
$742$	−339963.			−0.617482
$743$	−84623.8	+	48857.6i	−0.153290	+	0.0885022i	−0.574683	−	0.818376i	$-0.694875\pi$
$743$	−84623.8	+	48857.6i	−0.153290	+	0.0885022i	0.421393	+	0.906878i	$0.361541\pi$
$744$	−214607.	+	123903.i	−0.387702	+	0.223840i
$745$	−200718.	+	347654.i	−0.361638	+	0.626376i
$746$	−79421.4	−	137562.i	−0.142712	−	0.247184i
$747$	286329.	−	495937.i	0.513127	−	0.888762i
$748$	115682.			0.206759
$749$		−	223403.i		−	0.398222i
$750$	286473.	−	496186.i	0.509286	−	0.882109i
$751$	−878645.	−	507286.i	−1.55788	−	0.899442i	−0.997460	−	0.0712325i	$-0.977307\pi$
$751$	−878645.	−	507286.i	−1.55788	−	0.899442i	−0.560419	−	0.828209i	$-0.689360\pi$
$752$	−257619.			−0.455556
$753$			668817.i			1.17955i
$754$	117061.	+	67584.9i	0.205905	+	0.118880i
$755$	363646.	−	209951.i	0.637947	−	0.368319i
$756$	−53020.1	−	30611.2i	−0.0927677	−	0.0535595i
$757$	−35978.1	−	62315.9i	−0.0627836	−	0.108744i	0.832925	−	0.553386i	$-0.186664\pi$
$757$	−35978.1	−	62315.9i	−0.0627836	−	0.108744i	−0.895709	+	0.444641i	$0.853331\pi$
$758$	−109762.	−	190114.i	−0.191036	−	0.330884i
$759$		−	569683.i		−	0.988894i
$760$	47887.1	+	141315.i	0.0829070	+	0.244659i
$761$	−376652.			−0.650386			−0.325193	−	0.945648i	$-0.605429\pi$
$761$	−376652.			−0.650386			−0.325193	+	0.945648i	$0.605429\pi$
$762$	694765.	−	401123.i	1.19654	−	0.690824i
$763$	49643.8	−	28661.9i	0.0852739	−	0.0492329i
$764$	26365.6	−	45666.5i	0.0451700	−	0.0782368i
$765$	−164767.	−	285385.i	−0.281545	−	0.487650i
$766$	−331640.	+	574417.i	−0.565209	+	0.978972i
$767$	−925809.			−1.57373
$768$			49570.2i			0.0840424i
$769$	−148128.	+	256565.i	−0.250486	+	0.433855i	−0.963660	−	0.267132i	$-0.913924\pi$
$769$	−148128.	+	256565.i	−0.250486	+	0.433855i	0.713173	+	0.700988i	$0.247257\pi$
$770$	95536.5	+	55158.1i	0.161134	+	0.0930310i
$771$	540666.			0.909537
$772$		−	106415.i		−	0.178554i
$773$	876530.	+	506065.i	1.46693	+	0.846930i	0.999315	−	0.0370049i	$-0.0117817\pi$
$773$	876530.	+	506065.i	1.46693	+	0.846930i	0.467610	+	0.883935i	$0.345115\pi$
$774$	−320897.	+	185270.i	−0.535654	+	0.309260i
$775$	−228324.	−	131823.i	−0.380144	−	0.219477i
$776$	−79449.2	−	137610.i	−0.131937	−	0.228521i
$777$	−28326.6	−	49063.1i	−0.0469194	−	0.0812667i
$778$		−	342724.i		−	0.566221i
$779$	245701.	+	725065.i	0.404886	+	1.19482i
$780$	272537.			0.447957
$781$	147566.	−	85197.5i	0.241928	−	0.139677i
$782$	605630.	−	349661.i	0.990361	−	0.571785i
$783$	−29158.6	+	50504.1i	−0.0475601	+	0.0823764i
$784$	23838.9	+	41290.2i	0.0387841	+	0.0671761i
$785$	−376418.	+	651976.i	−0.610846	+	1.05802i
$786$	134197.			0.217219
$787$		−	1.06296e6i		−	1.71620i	−0.513486	−	0.858098i	$-0.671646\pi$
$787$		−	1.06296e6i		−	1.71620i	0.513486	−	0.858098i	$-0.328354\pi$
$788$	−34431.1	+	59636.4i	−0.0554496	+	0.0960415i
$789$	−608521.	−	351329.i	−0.977510	−	0.564366i
$790$	346608.			0.555372
$791$		−	96141.9i		−	0.153660i
$792$	67306.5	+	38859.4i	0.107302	+	0.0619507i
$793$	161933.	−	93492.1i	0.257507	−	0.148672i
$794$	−415154.	−	239689.i	−0.658519	−	0.380196i
$795$	326462.	+	565449.i	0.516534	+	0.894663i
$796$	149024.	+	258117.i	0.235196	+	0.407371i
$797$		−	492593.i		−	0.775482i	−0.921768	−	0.387741i	$-0.873255\pi$
$797$		−	492593.i		−	0.775482i	0.921768	−	0.387741i	$-0.126745\pi$
$798$	−377897.	−	331758.i	−0.593427	−	0.520973i
$799$	−1.10934e6			−1.73769
$800$	−45673.1	+	26369.4i	−0.0713642	+	0.0412021i
$801$	448206.	−	258772.i	0.698574	−	0.403322i
$802$	87997.3	−	152416.i	0.136811	−	0.236964i
$803$	200677.	+	347582.i	0.311219	+	0.539046i
$804$	−310488.	+	537780.i	−0.480322	+	0.831941i
$805$	666881.			1.02910
$806$		−	394445.i		−	0.607178i
$807$	437659.	−	758048.i	0.672030	−	1.16399i
$808$	185286.	+	106975.i	0.283805	+	0.163855i
$809$	955780.			1.46036			0.730181	−	0.683253i	$-0.239436\pi$
$809$	955780.			1.46036			0.730181	+	0.683253i	$0.239436\pi$
$810$			391527.i			0.596748i
$811$	159358.	+	92005.2i	0.242288	+	0.139885i	0.616228	−	0.787568i	$-0.288660\pi$
$811$	159358.	+	92005.2i	0.242288	+	0.139885i	−0.373940	+	0.927453i	$0.621993\pi$
$812$	−87431.1	+	50478.4i	−0.132603	+	0.0765585i
$813$	−903791.	−	521804.i	−1.36737	−	0.789453i
$814$	−8535.96	−	14784.7i	−0.0128826	−	0.0223133i
$815$	−27432.7	−	47514.9i	−0.0413003	−	0.0715343i
$816$			213456.i			0.320575i
$817$	684243.	−	231868.i	1.02510	−	0.347374i
$818$	−63081.3			−0.0942744
$819$	−355526.	+	205263.i	−0.530034	+	0.306015i
$820$	268377.	−	154947.i	0.399133	−	0.230439i
$821$	241392.	−	418103.i	0.358126	−	0.620293i	−0.629522	−	0.776983i	$-0.716749\pi$
$821$	241392.	−	418103.i	0.358126	−	0.620293i	0.987648	+	0.156690i	$0.0500824\pi$
$822$	447414.	+	774944.i	0.662165	+	1.14690i
$823$	525182.	−	909641.i	0.775372	−	1.34298i	−0.159214	−	0.987244i	$-0.550896\pi$
$823$	525182.	−	909641.i	0.775372	−	1.34298i	0.934585	−	0.355739i	$-0.115771\pi$
$824$	35849.6			0.0527996
$825$			185001.i			0.271811i
$826$	345738.	−	598835.i	0.506742	−	0.877703i
$827$	−297865.	−	171973.i	−0.435521	−	0.251448i	0.266175	−	0.963925i	$-0.414240\pi$
$827$	−297865.	−	171973.i	−0.435521	−	0.251448i	−0.701696	+	0.712477i	$0.747573\pi$
$828$	469824.			0.685291
$829$			655153.i			0.953309i	0.879091	+	0.476654i	$0.158151\pi$
$829$			655153.i			0.953309i	−0.879091	+	0.476654i	$0.841849\pi$
$830$	391417.	+	225985.i	0.568176	+	0.328037i
$831$	1.40010e6	−	808346.i	2.02748	−	1.17056i
$832$	−68332.1	−	39451.5i	−0.0987138	−	0.0569925i
$833$	102654.	+	177801.i	0.147940	+	0.256239i
$834$	337009.	+	583717.i	0.484518	+	0.839209i
$835$		−	611464.i		−	0.876997i
$836$	−113876.	−	99972.3i	−0.162937	−	0.143043i
$837$	170177.			0.242913
$838$	−676391.	+	390515.i	−0.963186	+	0.556096i
$839$	4544.02	−	2623.49i	0.00645529	−	0.00372697i	−0.496769	−	0.867883i	$-0.665480\pi$
$839$	4544.02	−	2623.49i	0.00645529	−	0.00372697i	0.503224	+	0.864156i	$0.332147\pi$
$840$	−101777.	+	176283.i	−0.144242	+	0.249835i
$841$	−305558.	−	529241.i	−0.432017	−	0.748276i
$842$	−401573.	+	695544.i	−0.566422	+	0.981071i
$843$	−946638.			−1.33208
$844$		−	593269.i		−	0.832850i
$845$	43947.3	−	76119.0i	0.0615487	−	0.106605i
$846$	−645440.	−	372645.i	−0.901810	−	0.520660i
$847$	483772.			0.674332
$848$		−	189031.i		−	0.262870i
$849$	40701.4	+	23499.0i	0.0564669	+	0.0326012i
$850$	−196675.	+	113550.i	−0.272214	+	0.157163i
$851$	−89376.3	−	51601.4i	−0.123414	−	0.0712529i
$852$	157206.	+	272289.i	0.216566	+	0.375103i
$853$	263.952	+	457.177i	0.000362766	+	0.000628328i	0.866207	−	0.499686i	$-0.166551\pi$
$853$	263.952	+	457.177i	0.000362766	+	0.000628328i	−0.865844	+	0.500314i	$0.833218\pi$
$854$			139656.i			0.191490i
$855$	−84434.7	+	423319.i	−0.115502	+	0.579077i
$856$	124219.			0.169528
$857$	891345.	−	514618.i	1.21362	−	0.700686i	0.250078	−	0.968226i	$-0.419544\pi$
$857$	891345.	−	514618.i	1.21362	−	0.700686i	0.963547	+	0.267539i	$0.0862105\pi$
$858$	−239701.	+	138391.i	−0.325608	+	0.187990i
$859$	145913.	−	252730.i	0.197747	−	0.342507i	−0.750051	−	0.661380i	$-0.769971\pi$
$859$	145913.	−	252730.i	0.197747	−	0.342507i	0.947797	+	0.318873i	$0.103304\pi$
$860$	−146224.	−	253267.i	−0.197707	−	0.342438i
$861$	−522204.	+	904483.i	−0.704423	+	1.22010i
$862$	300044.			0.403804
$863$			1.24371e6i			1.66993i	0.550307	+	0.834963i	$0.314511\pi$
$863$			1.24371e6i			1.66993i	−0.550307	+	0.834963i	$0.685489\pi$
$864$	17020.8	−	29480.9i	0.0228009	−	0.0394924i
$865$	440760.	+	254473.i	0.589074	+	0.340102i
$866$	−504919.			−0.673265
$867$		−	91606.0i		−	0.121867i
$868$	255136.	+	147303.i	0.338636	+	0.195511i
$869$	−304848.	+	176004.i	−0.403686	+	0.233068i
$870$	167918.	+	96947.5i	0.221850	+	0.128085i
$871$	−494217.	−	856008.i	−0.651450	−	1.12834i
$872$	15936.9	+	27603.6i	0.0209591	+	0.0363022i
$873$		−	459692.i		−	0.603168i
$874$	−898346.	−	179183.i	−1.17604	−	0.234571i
$875$	−681150.			−0.889666
$876$	−641356.	+	370287.i	−0.835778	+	0.482537i
$877$	−806389.	+	465569.i	−1.04844	+	0.605320i	−0.922214	−	0.386681i	$-0.873621\pi$
$877$	−806389.	+	465569.i	−1.04844	+	0.605320i	−0.126231	+	0.992001i	$0.540288\pi$
$878$	−255311.	+	442211.i	−0.331192	+	0.573641i
$879$	696415.	+	1.20623e6i	0.901343	+	1.56117i
$880$	−30669.7	+	53121.4i	−0.0396044	+	0.0685969i
$881$	−465283.			−0.599467			−0.299734	−	0.954023i	$-0.596898\pi$
$881$	−465283.			−0.599467			−0.299734	+	0.954023i	$0.596898\pi$
$882$			137931.i			0.177307i
$883$	208028.	−	360315.i	0.266809	−	0.462126i	−0.701227	−	0.712938i	$-0.747364\pi$
$883$	208028.	−	360315.i	0.266809	−	0.462126i	0.968036	+	0.250812i	$0.0806975\pi$
$884$	−294248.	−	169884.i	−0.376538	−	0.217394i
$885$	−1.32803e6			−1.69559
$886$			658061.i			0.838298i
$887$	−833217.	−	481058.i	−1.05904	−	0.611435i	−0.133871	−	0.990999i	$-0.542741\pi$
$887$	−833217.	−	481058.i	−1.05904	−	0.611435i	−0.925166	+	0.379564i	$0.876074\pi$
$888$	27280.7	−	15750.5i	0.0345963	−	0.0199742i
$889$	−825975.	−	476877.i	−1.04511	−	0.603396i
$890$	204235.	+	353745.i	0.257840	+	0.446591i
$891$	−198813.	−	344355.i	−0.250432	−	0.433761i
$892$			680648.i			0.855447i
$893$	1.09202e6	+	958690.i	1.36939	+	1.20220i
$894$	752268.			0.941234
$895$	−154634.	+	89277.7i	−0.193045	+	0.111454i
$896$	51036.4	−	29465.9i	0.0635718	−	0.0367032i
$897$	−836601.	+	1.44903e6i	−1.03976	+	1.80092i
$898$	−258167.	−	447159.i	−0.320146	−	0.554509i
$899$	140313.	−	243029.i	0.173611	−	0.300704i
$900$	−152573.			−0.188361
$901$		−	813993.i		−	1.00270i
$902$	−157361.	+	272558.i	−0.193413	+	0.335001i
$903$	853561.	+	492803.i	1.04679	+	0.604364i
$904$	53458.0			0.0654148
$905$		−	439376.i		−	0.536463i
$906$	−681450.	−	393435.i	−0.830190	−	0.479311i
$907$	−214782.	+	124005.i	−0.261086	+	0.150738i	−0.624830	−	0.780761i	$-0.714832\pi$
$907$	−214782.	+	124005.i	−0.261086	+	0.150738i	0.363744	+	0.931499i	$0.381498\pi$
$908$	238171.	+	137508.i	0.288880	+	0.166785i
$909$	309478.	+	536032.i	0.374543	+	0.648728i
$910$	−162003.	−	280598.i	−0.195633	−	0.338845i
$911$			598290.i			0.720900i	0.932779	+	0.360450i	$0.117377\pi$
$911$			598290.i			0.720900i	−0.932779	+	0.360450i	$0.882623\pi$
$912$	184468.	−	210123.i	0.221785	−	0.252629i
$913$	−459010.			−0.550657
$914$	191405.	−	110507.i	0.229118	−	0.132282i
$915$	232286.	−	134110.i	0.277447	−	0.160184i
$916$	−67556.9	+	117012.i	−0.0805154	+	0.139457i
$917$	−79770.4	−	138166.i	−0.0948644	−	0.164310i
$918$	73294.0	−	126949.i	0.0869728	−	0.150641i
$919$	1.03278e6			1.22286			0.611432	−	0.791297i	$-0.290594\pi$
$919$	1.03278e6			1.22286			0.611432	+	0.791297i	$0.290594\pi$
$920$			370807.i			0.438099i
$921$	172717.	−	299155.i	0.203618	−	0.352677i
$922$	−542106.	−	312985.i	−0.637708	−	0.368181i
$923$	−500463.			−0.587447
$924$		−	206726.i		−	0.242131i
$925$	29024.4	+	16757.3i	0.0339219	+	0.0195848i
$926$	808779.	−	466949.i	0.943208	−	0.544562i
$927$	89817.9	+	51856.4i	0.104521	+	0.0603452i
$928$	−28067.6	−	48614.6i	−0.0325919	−	0.0564508i
$929$	−388831.	−	673475.i	−0.450536	−	0.780351i	0.547883	−	0.836555i	$-0.315434\pi$
$929$	−388831.	−	673475.i	−0.450536	−	0.780351i	−0.998419	+	0.0562037i	$0.982100\pi$
$930$		−	565813.i		−	0.654195i
$931$	52604.7	−	263737.i	0.0606912	−	0.304279i
$932$	−121552.			−0.139936
$933$	−137784.	+	79549.9i	−0.158284	+	0.0913853i
$934$	302459.	−	174625.i	0.346715	−	0.200176i
$935$	−132068.	+	228748.i	−0.151069	+	0.261659i
$936$	−114133.	−	197684.i	−0.130275	−	0.225642i
$937$	587086.	−	1.01686e6i	0.668686	−	1.15820i	−0.309585	−	0.950872i	$-0.600190\pi$
$937$	587086.	−	1.01686e6i	0.668686	−	1.15820i	0.978272	−	0.207327i	$-0.0664764\pi$
$938$	738249.			0.839068
$939$			2.12348e6i			2.40834i
$940$	294109.	−	509411.i	0.332853	−	0.576518i
$941$	−698093.	−	403044.i	−0.788378	−	0.455170i	0.0510135	−	0.998698i	$-0.483755\pi$
$941$	−698093.	−	403044.i	−0.788378	−	0.455170i	−0.839391	+	0.543528i	$0.817088\pi$
$942$	1.41077e6			1.58984
$943$			1.90256e6i			2.13951i
$944$	332972.	+	192242.i	0.373649	+	0.215726i
$945$	121060.	−	69894.0i	0.135562	−	0.0782666i
$946$	257213.	+	148502.i	0.287416	+	0.165940i
$947$	91047.7	+	157699.i	0.101524	+	0.175845i	0.912313	−	0.409494i	$-0.134295\pi$
$947$	91047.7	+	157699.i	0.101524	+	0.175845i	−0.810789	+	0.585339i	$0.800961\pi$
$948$	−324761.	−	562503.i	−0.361366	−	0.625904i
$949$		−	1.17880e6i		−	1.30891i
$950$	291733.	+	58188.6i	0.323250	+	0.0644750i
$951$	1.05573e6			1.16732
$952$	219770.	−	126884.i	0.242491	−	0.140002i
$953$	−665244.	+	384079.i	−0.732479	+	0.422897i	−0.819328	−	0.573325i	$-0.805653\pi$
$953$	−665244.	+	384079.i	−0.732479	+	0.422897i	0.0868497	+	0.996221i	$0.472320\pi$
$954$	273432.	−	473598.i	0.300436	−	0.520371i
$955$	60200.1	+	104270.i	0.0660071	+	0.114328i
$956$	143074.	−	247812.i	0.156547	−	0.271148i
$957$	−196916.			−0.215009
$958$		−	396061.i		−	0.431550i
$959$	531910.	−	921296.i	0.578364	−	1.00176i
$960$	−98019.3	−	56591.5i	−0.106358	−	0.0614057i
$961$	104615.			0.113279
$962$			50141.5i			0.0541810i
$963$	311220.	+	179683.i	0.335595	+	0.193756i
$964$	−734554.	+	424095.i	−0.790442	+	0.456362i
$965$	210423.	+	121488.i	0.225964	+	0.130460i
$966$	−624847.	−	1.08227e6i	−0.669606	−	1.15979i
$967$	42211.1	+	73111.7i	0.0451412	+	0.0781869i	0.887713	−	0.460397i	$-0.152293\pi$
$967$	42211.1	+	73111.7i	0.0451412	+	0.0781869i	−0.842572	+	0.538584i	$0.818960\pi$
$968$			268993.i			0.287072i
$969$	794346.	−	904819.i	0.845984	−	0.963638i
$970$	362810.			0.385599
$971$	−36053.5	+	20815.5i	−0.0382392	+	0.0220774i	−0.518998	−	0.854776i	$-0.673695\pi$
$971$	−36053.5	+	20815.5i	−0.0382392	+	0.0220774i	0.480759	+	0.876853i	$0.340361\pi$
$972$	529867.	−	305919.i	0.560834	−	0.323798i
$973$	400655.	−	693955.i	0.423199	−	0.733003i
$974$	200738.	+	347688.i	0.211598	+	0.366498i
$975$	271681.	−	470566.i	0.285792	−	0.495006i
$976$	−77653.5			−0.0815195
$977$			586443.i			0.614380i	0.951648	+	0.307190i	$0.0993887\pi$
$977$			586443.i			0.614380i	−0.951648	+	0.307190i	$0.900611\pi$
$978$	−51407.3	+	89040.0i	−0.0537461	+	0.0930910i
$979$	−359256.	−	207417.i	−0.374834	−	0.216410i
$980$	−108862.			−0.113351
$981$			92210.9i			0.0958173i
$982$	−6682.43	−	3858.10i	−0.00692965	−	0.00400084i
$983$	−516678.	+	298304.i	−0.534703	+	0.308711i	−0.742930	−	0.669370i	$-0.766564\pi$
$983$	−516678.	+	298304.i	−0.534703	+	0.308711i	0.208226	+	0.978081i	$0.433231\pi$
$984$	−502922.	−	290362.i	−0.519410	−	0.299882i
$985$	−78616.0	−	136167.i	−0.0810286	−	0.140346i
$986$	−120863.	−	209341.i	−0.124320	−	0.215328i
$987$			1.98241e6i			2.03498i
$988$	142839.	+	421518.i	0.146330	+	0.431820i
$989$	1.79544e6			1.83560
$990$	−153680.	+	88727.2i	−0.156800	+	0.0905287i
$991$	125022.	−	72181.2i	0.127303	−	0.0734982i	−0.434996	−	0.900432i	$-0.643250\pi$
$991$	125022.	−	72181.2i	0.127303	−	0.0734982i	0.562299	+	0.826934i	$0.309917\pi$
$992$	−81905.3	+	141864.i	−0.0832317	+	0.144161i
$993$	−979425.	−	1.69641e6i	−0.993282	−	1.72042i
$994$	186895.	−	323712.i	0.189158	−	0.327631i
$995$	−680527.			−0.687384
$996$		−	846963.i		−	0.853780i
$997$	−975015.	+	1.68878e6i	−0.980892	+	1.69895i	−0.321958	+	0.946754i	$0.604341\pi$
$997$	−975015.	+	1.68878e6i	−0.980892	+	1.69895i	−0.658934	+	0.752201i	$0.728992\pi$
$998$	−515379.	−	297554.i	−0.517447	−	0.298748i
$999$	−21632.8			−0.0216762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.d.a.31.8	yes	16
3.2	odd	2		342.5.m.c.145.2		16
4.3	odd	2		304.5.r.c.145.2		16
19.8	odd	6	inner	38.5.d.a.27.8	✓	16
57.8	even	6		342.5.m.c.217.2		16
76.27	even	6		304.5.r.c.65.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.8	✓	16	19.8	odd	6	inner
38.5.d.a.31.8	yes	16	1.1	even	1	trivial
304.5.r.c.65.2		16	76.27	even	6
304.5.r.c.145.2		16	4.3	odd	2
342.5.m.c.145.2		16	3.2	odd	2
342.5.m.c.217.2		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)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{2} +(10.4807 - 6.05105i) q^{3} +(4.00000 - 6.92820i) q^{4} +(9.13314 + 15.8191i) q^{5} +(17.1150 - 29.6440i) q^{6} -40.6944 q^{7} -22.6274i q^{8} +(32.7305 - 56.6909i) q^{9} +O(q^{10})\)	\(q+(2.44949 - 1.41421i) q^{2} +(10.4807 - 6.05105i) q^{3} +(4.00000 - 6.92820i) q^{4} +(9.13314 + 15.8191i) q^{5} +(17.1150 - 29.6440i) q^{6} -40.6944 q^{7} -22.6274i q^{8} +(32.7305 - 56.6909i) q^{9} +(44.7431 + 25.8324i) q^{10} -52.4698 q^{11} -96.8168i q^{12} +(133.461 + 77.0538i) q^{13} +(-99.6805 + 57.5506i) q^{14} +(191.444 + 110.530i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(-137.797 - 238.671i) q^{17} -185.152i q^{18} +(-70.6137 + 354.026i) q^{19} +146.130 q^{20} +(-426.507 + 246.244i) q^{21} +(-128.524 + 74.2034i) q^{22} +(-448.573 + 776.951i) q^{23} +(-136.920 - 237.152i) q^{24} +(145.671 - 252.310i) q^{25} +435.882 q^{26} +188.055i q^{27} +(-162.778 + 281.939i) q^{28} +(268.560 + 155.053i) q^{29} +625.253 q^{30} -904.934i q^{31} +(-156.767 - 90.5097i) q^{32} +(-549.921 + 317.497i) q^{33} +(-675.063 - 389.748i) q^{34} +(-371.668 - 643.747i) q^{35} +(-261.844 - 453.527i) q^{36} +115.035i q^{37} +(327.702 + 967.047i) q^{38} +1865.03 q^{39} +(357.945 - 206.659i) q^{40} +(1836.56 - 1060.34i) q^{41} +(-696.483 + 1206.34i) q^{42} +(-1000.64 - 1733.16i) q^{43} +(-209.879 + 363.521i) q^{44} +1195.73 q^{45} +2537.51i q^{46} +(2012.65 - 3486.01i) q^{47} +(-670.767 - 387.267i) q^{48} -744.965 q^{49} -824.042i q^{50} +(-2888.42 - 1667.63i) q^{51} +(1067.69 - 616.430i) q^{52} +(2557.89 + 1476.80i) q^{53} +(265.950 + 460.639i) q^{54} +(-479.214 - 830.022i) q^{55} +920.809i q^{56} +(1402.15 + 4137.74i) q^{57} +877.113 q^{58} +(-5202.69 + 3003.77i) q^{59} +(1531.55 - 884.242i) q^{60} +(606.668 - 1050.78i) q^{61} +(-1279.77 - 2216.63i) q^{62} +(-1331.95 + 2307.00i) q^{63} -512.000 q^{64} +2814.97i q^{65} +(-898.018 + 1555.41i) q^{66} +(-5554.61 - 3206.96i) q^{67} -2204.75 q^{68} +10857.4i q^{69} +(-1820.79 - 1051.24i) q^{70} +(-2812.41 + 1623.75i) q^{71} +(-1282.77 - 740.606i) q^{72} +(-3824.61 - 6624.43i) q^{73} +(162.683 + 281.776i) q^{74} -3525.86i q^{75} +(2170.31 + 1905.33i) q^{76} +2135.23 q^{77} +(4568.36 - 2637.55i) q^{78} +(5809.97 - 3354.39i) q^{79} +(584.521 - 1012.42i) q^{80} +(3789.10 + 6562.91i) q^{81} +(2999.09 - 5194.57i) q^{82} +8748.10 q^{83} +3939.90i q^{84} +(2517.03 - 4359.63i) q^{85} +(-4902.12 - 2830.24i) q^{86} +3752.94 q^{87} +1187.26i q^{88} +(6846.92 + 3953.07i) q^{89} +(2928.92 - 1691.02i) q^{90} +(-5431.12 - 3135.66i) q^{91} +(3588.58 + 6215.61i) q^{92} +(-5475.80 - 9484.37i) q^{93} -11385.3i q^{94} +(-6245.29 + 2116.33i) q^{95} -2190.72 q^{96} +(6081.56 - 3511.19i) q^{97} +(-1824.78 + 1053.54i) q^{98} +(-1717.36 + 2974.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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