LMFDB - Embedded newform 38.6.e.b.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$38 = 2 \cdot 19$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	38.e (of order $9$ , degree $6$ , 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			35.3
Character	$\chi$	$=$	38.35
Dual form			38.6.e.b.25.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.06418 + 2.57115i) q^{2} +(-2.00835 + 0.730979i) q^{3} +(2.77837 + 15.7569i) q^{4} +(-1.87444 + 10.6305i) q^{5} +(-8.03340 - 2.92392i) q^{6} +(97.5540 + 168.968i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-182.650 + 153.261i) q^{9} +(-33.0762 + 27.7542i) q^{10} +(8.54534 - 14.8010i) q^{11} +(-17.0979 - 29.6145i) q^{12} +(247.314 + 90.0149i) q^{13} +(-135.521 + 768.575i) q^{14} +(-4.00613 - 22.7199i) q^{15} +(-240.561 + 87.5572i) q^{16} +(-442.563 - 371.354i) q^{17} -953.729 q^{18} +(1492.25 - 499.286i) q^{19} -172.712 q^{20} +(-319.435 - 268.038i) q^{21} +(64.2399 - 23.3814i) q^{22} +(-98.1994 - 556.917i) q^{23} +(23.7522 - 134.705i) q^{24} +(2827.05 + 1028.96i) q^{25} +(526.372 + 911.703i) q^{26} +(514.468 - 891.085i) q^{27} +(-2391.38 + 2006.61i) q^{28} +(5141.95 - 4314.61i) q^{29} +(46.1408 - 79.9182i) q^{30} +(-4640.48 - 8037.55i) q^{31} +(-962.245 - 350.229i) q^{32} +(-6.34283 + 35.9720i) q^{33} +(-401.283 - 2275.79i) q^{34} +(-1979.07 + 720.324i) q^{35} +(-2922.39 - 2452.18i) q^{36} +1713.65 q^{37} +(5856.26 + 2306.90i) q^{38} -562.492 q^{39} +(-529.219 - 444.067i) q^{40} +(-1145.49 + 416.922i) q^{41} +(-289.640 - 1642.63i) q^{42} +(-2686.78 + 15237.5i) q^{43} +(256.960 + 93.5257i) q^{44} +(-1286.88 - 2228.93i) q^{45} +(1131.02 - 1958.98i) q^{46} +(1143.47 - 959.485i) q^{47} +(419.129 - 351.691i) q^{48} +(-10630.0 + 18411.8i) q^{49} +(6016.96 + 10421.7i) q^{50} +(1160.27 + 422.305i) q^{51} +(-731.228 + 4147.00i) q^{52} +(4456.89 + 25276.3i) q^{53} +(3867.54 - 1407.67i) q^{54} +(141.324 + 118.585i) q^{55} -12486.9 q^{56} +(-2631.99 + 2093.55i) q^{57} +26849.4 q^{58} +(2276.05 + 1909.83i) q^{59} +(346.865 - 126.249i) q^{60} +(1991.63 + 11295.1i) q^{61} +(6446.49 - 36559.8i) q^{62} +(-43714.5 - 15910.8i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-1420.48 + 2460.34i) q^{65} +(-111.925 + 93.9161i) q^{66} +(-3214.75 + 2697.50i) q^{67} +(4621.80 - 8005.19i) q^{68} +(604.313 + 1046.70i) q^{69} +(-7916.30 - 2881.30i) q^{70} +(11705.6 - 66385.9i) q^{71} +(-2649.81 - 15027.8i) q^{72} +(42873.9 - 15604.8i) q^{73} +(5250.93 + 4406.06i) q^{74} -6429.85 q^{75} +(12013.2 + 22126.1i) q^{76} +3334.53 q^{77} +(-1723.57 - 1446.25i) q^{78} +(-31417.9 + 11435.2i) q^{79} +(-479.857 - 2721.40i) q^{80} +(9679.14 - 54893.1i) q^{81} +(-4581.94 - 1667.69i) q^{82} +(-33437.8 - 57916.0i) q^{83} +(3335.94 - 5778.02i) q^{84} +(4777.23 - 4008.57i) q^{85} +(-47410.6 + 39782.2i) q^{86} +(-7172.94 + 12423.9i) q^{87} +(546.902 + 947.261i) q^{88} +(80889.4 + 29441.3i) q^{89} +(1787.71 - 10138.6i) q^{90} +(8916.77 + 50569.5i) q^{91} +(8502.46 - 3094.64i) q^{92} +(15195.0 + 12750.1i) q^{93} +5970.77 q^{94} +(2510.51 + 16799.2i) q^{95} +2188.53 q^{96} +(100123. + 84012.9i) q^{97} +(-79911.8 + 29085.5i) q^{98} +(707.611 + 4013.06i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23}+ \cdots - 1068531 q^{99}+O(q^{100})$ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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

)

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

$2$	3.06418	+	2.57115i	0.541675	+	0.454519i
$2$	3.06418	+	2.57115i	0.541675	+	0.454519i
$3$	−2.00835	+	0.730979i	−0.128836	+	0.0468924i	−0.405633	−	0.914036i	$-0.632949\pi$
$3$	−2.00835	+	0.730979i	−0.128836	+	0.0468924i	0.276798	+	0.960928i	$0.410727\pi$
$4$	2.77837	+	15.7569i	0.0868241	+	0.492404i
$5$	−1.87444	+	10.6305i	−0.0335310	+	0.190164i	−0.996972	−	0.0777550i	$-0.975225\pi$
$5$	−1.87444	+	10.6305i	−0.0335310	+	0.190164i	0.963441	+	0.267919i	$0.0863359\pi$
$6$	−8.03340	−	2.92392i	−0.0911006	−	0.0331579i
$7$	97.5540	+	168.968i	0.752488	+	1.30335i	0.946613	+	0.322371i	$0.104480\pi$
$7$	97.5540	+	168.968i	0.752488	+	1.30335i	−0.194125	+	0.980977i	$0.562187\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	−182.650	+	153.261i	−0.751645	+	0.630705i
$10$	−33.0762	+	27.7542i	−0.104596	+	0.0877665i
$11$	8.54534	−	14.8010i	0.0212935	−	0.0368815i	−0.855182	−	0.518327i	$-0.826555\pi$
$11$	8.54534	−	14.8010i	0.0212935	−	0.0368815i	0.876476	+	0.481446i	$0.159888\pi$
$12$	−17.0979	−	29.6145i	−0.0342760	−	0.0593678i
$13$	247.314	+	90.0149i	0.405873	+	0.147726i	0.536886	−	0.843655i	$-0.319601\pi$
$13$	247.314	+	90.0149i	0.405873	+	0.147726i	−0.131013	+	0.991381i	$0.541823\pi$
$14$	−135.521	+	768.575i	−0.184793	+	1.04801i
$15$	−4.00613	−	22.7199i	−0.00459724	−	0.0260722i
$16$	−240.561	+	87.5572i	−0.234923	+	0.0855050i
$17$	−442.563	−	371.354i	−0.371409	−	0.311649i	0.437910	−	0.899019i	$-0.355719\pi$
$17$	−442.563	−	371.354i	−0.371409	−	0.311649i	−0.809319	+	0.587370i	$0.800163\pi$
$18$	−953.729			−0.693815
$19$	1492.25	−	499.286i	0.948326	−	0.317296i
$19$	1492.25	−	499.286i	0.948326	−	0.317296i
$20$	−172.712			−0.0965487
$21$	−319.435	−	268.038i	−0.158064	−	0.132632i
$22$	64.2399	−	23.3814i	0.0282975	−	0.0102995i
$23$	−98.1994	−	556.917i	−0.0387070	−	0.219518i	0.959319	−	0.282325i	$-0.0911058\pi$
$23$	−98.1994	−	556.917i	−0.0387070	−	0.219518i	−0.998026	+	0.0628072i	$0.979995\pi$
$24$	23.7522	−	134.705i	0.00841735	−	0.0477372i
$25$	2827.05	+	1028.96i	0.904655	+	0.329267i
$26$	526.372	+	911.703i	0.152707	+	0.264496i
$27$	514.468	−	891.085i	0.135815	−	0.235239i
$28$	−2391.38	+	2006.61i	−0.576439	+	0.483690i
$29$	5141.95	−	4314.61i	1.13536	−	0.952678i	0.136081	−	0.990698i	$-0.456549\pi$
$29$	5141.95	−	4314.61i	1.13536	−	0.952678i	0.999277	+	0.0380192i	$0.0121048\pi$
$30$	46.1408	−	79.9182i	0.00936013	−	0.0162122i
$31$	−4640.48	−	8037.55i	−0.867279	−	1.50217i	−0.864767	−	0.502174i	$-0.832534\pi$
$31$	−4640.48	−	8037.55i	−0.867279	−	1.50217i	−0.00251180	−	0.999997i	$-0.500800\pi$
$32$	−962.245	−	350.229i	−0.166116	−	0.0604612i
$33$	−6.34283	+	35.9720i	−0.00101391	+	0.00575015i
$34$	−401.283	−	2275.79i	−0.0595325	−	0.337625i
$35$	−1979.07	+	720.324i	−0.273081	+	0.0993935i
$36$	−2922.39	−	2452.18i	−0.375822	−	0.315352i
$37$	1713.65			0.205787			0.102894	−	0.994692i	$-0.467190\pi$
$37$	1713.65			0.205787			0.102894	+	0.994692i	$0.467190\pi$
$38$	5856.26	+	2306.90i	0.657902	+	0.259161i
$39$	−562.492			−0.0592181
$40$	−529.219	−	444.067i	−0.0522980	−	0.0438833i
$41$	−1145.49	+	416.922i	−0.106422	+	0.0387343i	−0.394682	−	0.918818i	$-0.629145\pi$
$41$	−1145.49	+	416.922i	−0.106422	+	0.0387343i	0.288261	+	0.957552i	$0.406923\pi$
$42$	−289.640	−	1642.63i	−0.0253358	−	0.143687i
$43$	−2686.78	+	15237.5i	−0.221595	+	1.25673i	0.647492	+	0.762072i	$0.275818\pi$
$43$	−2686.78	+	15237.5i	−0.221595	+	1.25673i	−0.869088	+	0.494658i	$0.835293\pi$
$44$	256.960	+	93.5257i	0.0200094	+	0.00728281i
$45$	−1286.88	−	2228.93i	−0.0947338	−	0.164084i
$46$	1131.02	−	1958.98i	0.0788087	−	0.136501i
$47$	1143.47	−	959.485i	0.0755057	−	0.0633568i	−0.604254	−	0.796792i	$-0.706529\pi$
$47$	1143.47	−	959.485i	0.0755057	−	0.0633568i	0.679759	+	0.733435i	$0.262084\pi$
$48$	419.129	−	351.691i	0.0262570	−	0.0220322i
$49$	−10630.0	+	18411.8i	−0.632477	+	1.09548i
$50$	6016.96	+	10421.7i	0.340371	+	0.589539i
$51$	1160.27	+	422.305i	0.0624647	+	0.0227353i
$52$	−731.228	+	4147.00i	−0.0375011	+	0.212679i
$53$	4456.89	+	25276.3i	0.217943	+	1.23602i	0.875726	+	0.482808i	$0.160383\pi$
$53$	4456.89	+	25276.3i	0.217943	+	1.23602i	−0.657783	+	0.753207i	$0.728506\pi$
$54$	3867.54	−	1407.67i	0.180489	−	0.0656925i
$55$	141.324	+	118.585i	0.00629953	+	0.00528593i
$56$	−12486.9			−0.532090
$57$	−2631.99	+	2093.55i	−0.107300	+	0.0853484i
$58$	26849.4			1.04801
$59$	2276.05	+	1909.83i	0.0851239	+	0.0714274i	0.684357	−	0.729147i	$-0.260083\pi$
$59$	2276.05	+	1909.83i	0.0851239	+	0.0714274i	−0.599233	+	0.800575i	$0.704528\pi$
$60$	346.865	−	126.249i	0.0124389	−	0.00452740i
$61$	1991.63	+	11295.1i	0.0685305	+	0.388656i	0.999710	+	0.0240939i	$0.00767008\pi$
$61$	1991.63	+	11295.1i	0.0685305	+	0.388656i	−0.931179	+	0.364562i	$0.881219\pi$
$62$	6446.49	−	36559.8i	0.212982	−	1.20788i
$63$	−43714.5	−	15910.8i	−1.38763	−	0.505057i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−1420.48	+	2460.34i	−0.0417014	+	0.0722289i
$66$	−111.925	+	93.9161i	−0.00316276	+	0.00265387i
$67$	−3214.75	+	2697.50i	−0.0874904	+	0.0734132i	−0.685484	−	0.728088i	$-0.740409\pi$
$67$	−3214.75	+	2697.50i	−0.0874904	+	0.0734132i	0.597993	+	0.801501i	$0.295965\pi$
$68$	4621.80	−	8005.19i	0.121210	−	0.209942i
$69$	604.313	+	1046.70i	0.0152806	+	0.0264667i
$70$	−7916.30	−	2881.30i	−0.193098	−	0.0702818i
$71$	11705.6	−	66385.9i	0.275581	−	1.56290i	−0.461531	−	0.887124i	$-0.652700\pi$
$71$	11705.6	−	66385.9i	0.275581	−	1.56290i	0.737112	−	0.675771i	$-0.236189\pi$
$72$	−2649.81	−	15027.8i	−0.0602398	−	0.341637i
$73$	42873.9	−	15604.8i	0.941643	−	0.342730i	0.174829	−	0.984599i	$-0.444063\pi$
$73$	42873.9	−	15604.8i	0.941643	−	0.342730i	0.766814	+	0.641869i	$0.221841\pi$
$74$	5250.93	+	4406.06i	0.111470	+	0.0935343i
$75$	−6429.85			−0.131992
$76$	12013.2	+	22126.1i	0.238576	+	0.439411i
$77$	3334.53			0.0640925
$78$	−1723.57	−	1446.25i	−0.0320770	−	0.0269158i
$79$	−31417.9	+	11435.2i	−0.566381	+	0.206146i	−0.609310	−	0.792932i	$-0.708553\pi$
$79$	−31417.9	+	11435.2i	−0.566381	+	0.206146i	0.0429285	+	0.999078i	$0.486331\pi$
$80$	−479.857	−	2721.40i	−0.00838275	−	0.0475410i
$81$	9679.14	−	54893.1i	0.163917	−	0.929620i
$82$	−4581.94	−	1667.69i	−0.0752514	−	0.0273893i
$83$	−33437.8	−	57916.0i	−0.532773	−	0.922790i	−0.999268	−	0.0382662i	$-0.987817\pi$
$83$	−33437.8	−	57916.0i	−0.532773	−	0.922790i	0.466494	−	0.884524i	$-0.345517\pi$
$84$	3335.94	−	5778.02i	0.0515846	−	0.0893472i
$85$	4777.23	−	4008.57i	0.0717182	−	0.0601787i
$86$	−47410.6	+	39782.2i	−0.691241	+	0.580020i
$87$	−7172.94	+	12423.9i	−0.101601	+	0.175979i
$88$	546.902	+	947.261i	0.00752840	+	0.0130396i
$89$	80889.4	+	29441.3i	1.08247	+	0.393988i	0.820827	−	0.571176i	$-0.193513\pi$
$89$	80889.4	+	29441.3i	1.08247	+	0.393988i	0.261645	+	0.965164i	$0.415735\pi$
$90$	1787.71	−	10138.6i	0.0232643	−	0.131939i
$91$	8916.77	+	50569.5i	0.112877	+	0.640155i
$92$	8502.46	−	3094.64i	0.104731	−	0.0381189i
$93$	15195.0	+	12750.1i	0.182177	+	0.152864i
$94$	5970.77			0.0696965
$95$	2510.51	+	16799.2i	0.0285400	+	0.190977i
$96$	2188.53			0.0242368
$97$	100123.	+	84012.9i	1.08045	+	0.906602i	0.995958	−	0.0898228i	$-0.0286301\pi$
$97$	100123.	+	84012.9i	1.08045	+	0.906602i	0.0844881	+	0.996424i	$0.473075\pi$
$98$	−79911.8	+	29085.5i	−0.840516	+	0.305923i
$99$	707.611	+	4013.06i	0.00725615	+	0.0411517i
$100$	−8358.67	+	47404.4i	−0.0835867	+	0.474044i
$101$	17139.4	+	6238.24i	0.167183	+	0.0608497i	0.424256	−	0.905542i	$-0.360536\pi$
$101$	17139.4	+	6238.24i	0.167183	+	0.0608497i	−0.257073	+	0.966392i	$0.582758\pi$
$102$	2469.47	+	4277.25i	0.0235020	+	0.0407066i
$103$	−13400.0	+	23209.5i	−0.124455	+	0.215562i	−0.921520	−	0.388332i	$-0.873052\pi$
$103$	−13400.0	+	23209.5i	−0.124455	+	0.215562i	0.797065	+	0.603894i	$0.206385\pi$
$104$	−12903.2	+	10827.0i	−0.116980	+	0.0981582i
$105$	3448.13	−	2893.33i	0.0305218	−	0.0256109i
$106$	−51332.5	+	88910.4i	−0.443739	+	0.768578i
$107$	−84123.6	−	145706.i	−0.710327	−	1.23032i	−0.964734	−	0.263225i	$-0.915214\pi$
$107$	−84123.6	−	145706.i	−0.710327	−	1.23032i	0.254407	−	0.967097i	$-0.418120\pi$
$108$	15470.1	+	5630.67i	0.127625	+	0.0464516i
$109$	−2794.75	+	15849.8i	−0.0225308	+	0.127778i	−0.993999	−	0.109393i	$-0.965109\pi$
$109$	−2794.75	+	15849.8i	−0.0225308	+	0.127778i	0.971468	+	0.237172i	$0.0762204\pi$
$110$	128.142	+	726.728i	0.00100974	+	0.00572652i
$111$	−3441.61	+	1252.64i	−0.0265127	+	0.00964985i
$112$	−38262.1	−	32105.7i	−0.288220	−	0.241845i
$113$	−103218.			−0.760427			−0.380213	−	0.924899i	$-0.624149\pi$
$113$	−103218.			−0.760427			−0.380213	+	0.924899i	$0.624149\pi$
$114$	−13447.7	−	352.258i	−0.0969140	−	0.00253863i
$115$	6104.36			0.0430423
$116$	82271.2	+	69033.7i	0.567679	+	0.476339i
$117$	−58967.6	+	21462.4i	−0.398243	+	0.144949i
$118$	2063.75	+	11704.1i	0.0136443	+	0.0773809i
$119$	19573.4	−	111006.i	0.126706	−	0.718588i
$120$	1387.46	+	504.995i	0.00879565	+	0.00320135i
$121$	80379.5	+	139221.i	0.499093	+	0.864455i
$122$	−22938.7	+	39730.9i	−0.139530	+	0.241674i
$123$	1995.77	−	1674.65i	0.0118946	−	0.00998072i
$124$	113754.	−	95451.0i	0.664374	−	0.557476i
$125$	−33103.8	+	57337.5i	−0.189497	+	0.328219i
$126$	−93040.0	−	161150.i	−0.522088	−	0.904282i
$127$	200393.	+	72936.9i	1.10248	+	0.401271i	0.828231	−	0.560386i	$-0.189347\pi$
$127$	200393.	+	72936.9i	1.10248	+	0.401271i	0.274253	+	0.961658i	$0.411570\pi$
$128$	2845.05	−	16135.1i	0.0153485	−	0.0870455i
$129$	−5742.29	−	32566.2i	−0.0303816	−	0.172303i
$130$	−10678.5	+	3886.65i	−0.0554181	+	0.0201705i
$131$	−247354.	−	207555.i	−1.25933	−	1.05671i	−0.995753	−	0.0920683i	$-0.970652\pi$
$131$	−247354.	−	207555.i	−1.25933	−	1.05671i	−0.263580	−	0.964637i	$-0.584903\pi$
$132$	−584.430			−0.00291943
$133$	229938.	+	203436.i	1.12715	+	0.997238i
$134$	−16786.2			−0.0807591
$135$	8508.33	+	7139.33i	0.0401800	+	0.0337150i
$136$	34744.6	−	12646.0i	0.161079	−	0.0586280i
$137$	−51679.0	−	293086.i	−0.235241	−	1.33412i	−0.842106	−	0.539312i	$-0.818684\pi$
$137$	−51679.0	−	293086.i	−0.235241	−	1.33412i	0.606865	−	0.794805i	$-0.292427\pi$
$138$	−839.503	+	4761.06i	−0.00375253	+	0.0212817i
$139$	39962.3	+	14545.1i	0.175434	+	0.0638527i	0.428244	−	0.903663i	$-0.359132\pi$
$139$	39962.3	+	14545.1i	0.175434	+	0.0638527i	−0.252810	+	0.967516i	$0.581355\pi$
$140$	−16848.7	−	29182.8i	−0.0726518	−	0.125837i
$141$	−1595.12	+	2762.83i	−0.00675688	+	0.0117033i
$142$	206556.	−	173321.i	0.859642	−	0.721325i
$143$	3445.69	−	2891.27i	0.0140908	−	0.0118236i
$144$	30519.3	−	52861.0i	0.122650	−	0.212437i
$145$	36228.1	+	62748.9i	0.143095	+	0.247848i
$146$	171496.	+	62419.4i	0.665842	+	0.242347i
$147$	7890.22	−	44747.6i	0.0301159	−	0.170796i
$148$	4761.16	+	27001.9i	0.0178673	+	0.101330i
$149$	−373968.	+	136113.i	−1.37997	+	0.502268i	−0.922169	−	0.386788i	$-0.873585\pi$
$149$	−373968.	+	136113.i	−1.37997	+	0.502268i	−0.457800	+	0.889055i	$0.651362\pi$
$150$	−19702.2	−	16532.1i	−0.0714968	−	0.0599929i
$151$	−312906.			−1.11679			−0.558394	−	0.829576i	$-0.688582\pi$
$151$	−312906.			−1.11679			−0.558394	+	0.829576i	$0.688582\pi$
$152$	−20078.8	+	98686.1i	−0.0704902	+	0.346455i
$153$	137748.			0.475726
$154$	10217.6	+	8573.57i	0.0347173	+	0.0291313i
$155$	94141.3	−	34264.6i	0.314739	−	0.114556i
$156$	−1562.81	−	8863.14i	−0.00514156	−	0.0291592i
$157$	78476.6	−	445063.i	0.254092	−	1.44103i	−0.544300	−	0.838891i	$-0.683205\pi$
$157$	78476.6	−	445063.i	0.254092	−	1.44103i	0.798392	−	0.602138i	$-0.205684\pi$
$158$	−125671.	−	45740.7i	−0.400492	−	0.145767i
$159$	−27427.5	−	47505.7i	−0.0860385	−	0.149023i
$160$	5526.77	−	9572.65i	0.0170676	−	0.0295619i
$161$	84521.6	−	70922.0i	0.256982	−	0.215634i
$162$	170797.	−	143316.i	0.511320	−	0.429049i
$163$	−220029.	+	381102.i	−0.648652	+	1.12350i	0.334793	+	0.942292i	$0.391333\pi$
$163$	−220029.	+	381102.i	−0.648652	+	1.12350i	−0.983445	+	0.181206i	$0.942000\pi$
$164$	−9752.00	−	16891.0i	−0.0283129	−	0.0490393i
$165$	−370.510	−	134.855i	−0.00105947	−	0.000385617i
$166$	46451.3	−	263438.i	0.130836	−	0.742008i
$167$	21030.3	+	119269.i	0.0583517	+	0.330929i	0.999984	−	0.00571507i	$-0.00181917\pi$
$167$	21030.3	+	119269.i	0.0583517	+	0.330929i	−0.941632	+	0.336644i	$0.890708\pi$
$168$	25078.1	−	9127.67i	0.0685521	−	0.0249509i
$169$	−231366.	−	194139.i	−0.623135	−	0.522872i
$170$	24944.9			0.0662003
$171$	−196038.	+	319899.i	−0.512684	+	0.836608i
$172$	−247561.			−0.638058
$173$	431237.	+	361851.i	1.09547	+	0.919209i	0.997112	−	0.0759423i	$-0.0241965\pi$
$173$	431237.	+	361851.i	1.09547	+	0.919209i	0.0983581	+	0.995151i	$0.468641\pi$
$174$	−53922.9	+	19626.3i	−0.135021	+	0.0491435i
$175$	101928.	+	578061.i	0.251592	+	1.42685i
$176$	−759.748	+	4308.74i	−0.00184879	+	0.0104850i
$177$	−5967.15	−	2171.86i	−0.0143164	−	0.00521074i
$178$	172161.	+	298192.i	0.407273	+	0.705418i
$179$	280280.	−	485459.i	0.653822	−	1.13245i	−0.328366	−	0.944551i	$-0.606498\pi$
$179$	280280.	−	485459.i	0.653822	−	1.13245i	0.982188	−	0.187902i	$-0.0601689\pi$
$180$	31545.7	−	26470.0i	0.0725703	−	0.0608937i
$181$	−358213.	+	300577.i	−0.812728	+	0.681960i	−0.951257	−	0.308398i	$-0.900207\pi$
$181$	−358213.	+	300577.i	−0.812728	+	0.681960i	0.138529	+	0.990358i	$0.455763\pi$
$182$	−102699.	+	177880.i	−0.229821	+	0.398061i
$183$	−12256.4	−	21228.6i	−0.0270542	−	0.0468592i
$184$	34009.8	+	12378.6i	0.0740559	+	0.0269542i
$185$	−3212.14	+	18216.9i	−0.00690025	+	0.0391333i
$186$	13777.7	+	78137.2i	0.0292008	+	0.165606i
$187$	−9278.25	+	3377.01i	−0.0194027	+	0.00706200i
$188$	18295.5	+	15351.8i	0.0377529	+	0.0316784i
$189$	200754.			0.408798
$190$	−35500.7	+	57930.7i	−0.0713432	+	0.116419i
$191$	50390.1			0.0999452			0.0499726	−	0.998751i	$-0.484087\pi$
$191$	50390.1			0.0999452			0.0499726	+	0.998751i	$0.484087\pi$
$192$	6706.06	+	5627.05i	0.0131285	+	0.0110161i
$193$	−768222.	+	279610.i	−1.48455	+	0.540330i	−0.952007	−	0.306076i	$-0.900984\pi$
$193$	−768222.	+	279610.i	−1.48455	+	0.540330i	−0.532538	+	0.846406i	$0.678762\pi$
$194$	90783.9	+	514861.i	0.173183	+	0.982167i
$195$	1054.36	−	5979.56i	0.00198564	−	0.0112611i
$196$	−319647.	−	116342.i	−0.594334	−	0.216320i
$197$	−227935.	−	394796.i	−0.418453	−	0.724781i	0.577331	−	0.816510i	$-0.304094\pi$
$197$	−227935.	−	394796.i	−0.418453	−	0.724781i	−0.995784	+	0.0917287i	$0.970761\pi$
$198$	−8149.93	+	14116.1i	−0.0147738	+	0.0255889i
$199$	419129.	−	351691.i	0.750266	−	0.629548i	−0.185307	−	0.982681i	$-0.559328\pi$
$199$	419129.	−	351691.i	0.750266	−	0.629548i	0.935573	+	0.353132i	$0.114884\pi$
$200$	−147496.	+	123764.i	−0.260739	+	0.218786i
$201$	4484.53	−	7767.44i	0.00782937	−	0.0135609i
$202$	36478.8	+	63183.1i	0.0629016	+	0.108949i
$203$	1.23065e6	+	447920.i	2.09602	+	0.762887i
$204$	−3430.56	+	19455.7i	−0.00577151	+	0.0327318i
$205$	−2284.94	−	12958.6i	−0.00379744	−	0.0215363i
$206$	−100735.	+	36664.5i	−0.165391	+	0.0601975i
$207$	103290.	+	86670.5i	0.167545	+	0.140587i
$208$	−67375.6			−0.107980
$209$	5361.88	−	26353.3i	0.00849085	−	0.0417320i
$210$	18004.9			0.0281736
$211$	24435.9	+	20504.1i	0.0377852	+	0.0317056i	0.661485	−	0.749959i	$-0.269927\pi$
$211$	24435.9	+	20504.1i	0.0377852	+	0.0317056i	−0.623699	+	0.781664i	$0.714371\pi$
$212$	−385894.	+	140454.i	−0.589696	+	0.214632i
$213$	25017.7	+	141883.i	0.0377832	+	0.214279i
$214$	116863.	−	662764.i	0.174439	−	0.989293i
$215$	−156945.	−	57123.5i	−0.231554	−	0.0842788i
$216$	32926.0	+	57029.5i	0.0480180	+	0.0831696i
$217$	905394.	−	1.56819e6i	1.30523	−	2.26073i
$218$	−49315.8	+	41380.9i	−0.0702822	+	0.0589737i
$219$	−74699.1	+	62680.0i	−0.105246	+	0.0883117i
$220$	−1475.88	+	2556.30i	−0.00205586	+	0.00356086i
$221$	−76024.5	−	131678.i	−0.104706	−	0.181357i
$222$	−13766.4	−	5010.58i	−0.0187473	−	0.00682347i
$223$	213089.	−	1.20849e6i	0.286945	−	1.62734i	−0.411311	−	0.911495i	$-0.634929\pi$
$223$	213089.	−	1.20849e6i	0.286945	−	1.62734i	0.698255	−	0.715849i	$-0.253960\pi$
$224$	−34693.3	−	196755.i	−0.0461982	−	0.262003i
$225$	−674059.	+	245337.i	−0.887649	+	0.323078i
$226$	−316277.	−	265388.i	−0.411904	−	0.345629i
$227$	243999.			0.314285			0.157143	−	0.987576i	$-0.449772\pi$
$227$	243999.			0.314285			0.157143	+	0.987576i	$0.449772\pi$
$228$	−40300.5	−	35655.5i	−0.0513420	−	0.0454244i
$229$	−1.29079e6			−1.62654			−0.813272	−	0.581884i	$-0.802316\pi$
$229$	−1.29079e6			−1.62654			−0.813272	+	0.581884i	$0.802316\pi$
$230$	18704.8	+	15695.2i	0.0233150	+	0.0195636i
$231$	−6696.89	+	2437.47i	−0.00825740	+	0.00300545i
$232$	74597.5	+	423063.i	0.0909922	+	0.516042i
$233$	214015.	−	1.21374e6i	0.258258	−	1.46465i	−0.529312	−	0.848427i	$-0.677550\pi$
$233$	214015.	−	1.21374e6i	0.258258	−	1.46465i	0.787570	−	0.616226i	$-0.211339\pi$
$234$	−235870.	−	85849.8i	−0.281601	−	0.102494i
$235$	8056.42	+	13954.1i	0.00951640	+	0.0164829i
$236$	−23769.4	+	41169.7i	−0.0277803	+	0.0481170i
$237$	54739.2	−	45931.6i	0.0633035	−	0.0531179i
$238$	345390.	−	289817.i	0.395246	−	0.331651i
$239$	149855.	−	259556.i	0.169698	−	0.293925i	−0.768616	−	0.639711i	$-0.779054\pi$
$239$	149855.	−	259556.i	0.169698	−	0.293925i	0.938314	+	0.345786i	$0.112388\pi$
$240$	2953.01	+	5114.76i	0.00330931	+	0.00573189i
$241$	313971.	+	114276.i	0.348215	+	0.126740i	0.510206	−	0.860052i	$-0.329569\pi$
$241$	313971.	+	114276.i	0.348215	+	0.126740i	−0.161991	+	0.986792i	$0.551791\pi$
$242$	−111662.	+	633266.i	−0.122565	+	0.695101i
$243$	64104.2	+	363553.i	0.0696419	+	0.394959i
$244$	−172442.	+	62763.9i	−0.185425	+	0.0674893i
$245$	−175801.	−	147514.i	−0.187114	−	0.157007i
$246$	10421.2			0.0109794
$247$	413997.	+	10844.5i	0.431773	+	0.0113101i
$248$	593981.			0.613259
$249$	109490.	+	91873.2i	0.111912	+	0.0939053i
$250$	−248860.	+	90577.5i	−0.251828	+	0.0916579i
$251$	310347.	+	1.76007e6i	0.310931	+	1.76338i	0.594182	+	0.804331i	$0.297476\pi$
$251$	310347.	+	1.76007e6i	0.310931	+	1.76338i	−0.283251	+	0.959046i	$0.591413\pi$
$252$	129250.	−	733012.i	0.128212	−	0.727126i
$253$	−9082.05	−	3305.59i	−0.00892036	−	0.00324675i
$254$	426507.	+	738731.i	0.414803	+	0.718459i
$255$	−6664.17	+	11542.7i	−0.00641794	+	0.0111162i
$256$	50203.5	−	42125.7i	0.0478778	−	0.0401742i
$257$	1.00079e6	−	839767.i	0.945175	−	0.793096i	−0.0333033	−	0.999445i	$-0.510603\pi$
$257$	1.00079e6	−	839767.i	0.945175	−	0.793096i	0.978478	+	0.206349i	$0.0661583\pi$
$258$	66137.1	−	114553.i	0.0618580	−	0.107141i
$259$	167174.	+	289553.i	0.154852	+	0.268212i
$260$	−42714.0	−	15546.6i	−0.0391865	−	0.0142627i
$261$	−277913.	+	1.57612e6i	−0.252527	+	1.43215i
$262$	−224282.	−	1.27197e6i	−0.201856	−	1.14478i
$263$	−2.08417e6	+	758578.i	−1.85800	+	0.676255i	−0.877544	+	0.479496i	$0.840820\pi$
$263$	−2.08417e6	+	758578.i	−1.85800	+	0.676255i	−0.980452	+	0.196759i	$0.936958\pi$
$264$	−1790.80	−	1502.66i	−0.00158138	−	0.00132694i
$265$	−277053.			−0.242353
$266$	181508.	+	1.21457e6i	0.157287	+	1.05249i
$267$	−183975.			−0.157936
$268$	−51436.0	−	43160.0i	−0.0437452	−	0.0367066i
$269$	−407321.	+	148253.i	−0.343207	+	0.124917i	−0.507872	−	0.861432i	$-0.669568\pi$
$269$	−407321.	+	148253.i	−0.343207	+	0.124917i	0.164665	+	0.986349i	$0.447346\pi$
$270$	7714.72	+	43752.4i	0.00644037	+	0.0365252i
$271$	−251241.	+	1.42486e6i	−0.207810	+	1.17855i	0.685146	+	0.728406i	$0.259739\pi$
$271$	−251241.	+	1.42486e6i	−0.207810	+	1.17855i	−0.892956	+	0.450144i	$0.851373\pi$
$272$	138978.	+	50583.9i	0.113900	+	0.0414563i
$273$	−54873.3	−	95043.3i	−0.0445609	−	0.0771818i
$274$	595215.	−	1.03094e6i	0.478958	−	0.829580i
$275$	39387.7	−	33050.2i	0.0314071	−	0.0263537i
$276$	−14813.8	+	12430.2i	−0.0117056	+	0.00982216i
$277$	−822974.	+	1.42543e6i	−0.644446	+	1.11621i	0.339983	+	0.940431i	$0.389579\pi$
$277$	−822974.	+	1.42543e6i	−0.644446	+	1.11621i	−0.984429	+	0.175782i	$0.943755\pi$
$278$	85054.0	+	147318.i	0.0660059	+	0.114326i
$279$	2.07943e6	+	756849.i	1.59931	+	0.582102i
$280$	23406.0	−	132742.i	0.0178415	−	0.101184i
$281$	160719.	+	911484.i	0.121423	+	0.688626i	0.983368	+	0.181624i	$0.0581353\pi$
$281$	160719.	+	911484.i	0.121423	+	0.688626i	−0.861945	+	0.507002i	$0.830754\pi$
$282$	−11991.4	+	4364.51i	−0.00897940	+	0.00326823i
$283$	−1.62408e6	−	1.36276e6i	−1.20543	−	1.01147i	−0.999458	−	0.0329140i	$-0.989521\pi$
$283$	−1.62408e6	−	1.36276e6i	−1.20543	−	1.01147i	−0.205968	−	0.978559i	$-0.566034\pi$
$284$	1.07856e6			0.793503
$285$	−17321.9	−	31903.6i	−0.0126323	−	0.0232663i
$286$	17992.1			0.0130067
$287$	−182193.	−	152878.i	−0.130565	−	0.109557i
$288$	229430.	−	83505.8i	0.162993	−	0.0593247i
$289$	−188598.	−	1.06959e6i	−0.132829	−	0.753309i
$290$	−50327.5	+	285422.i	−0.0351407	+	0.199293i
$291$	−262493.	−	95539.6i	−0.181713	−	0.0661380i
$292$	365004.	+	632205.i	0.250519	+	0.433911i
$293$	471577.	−	816796.i	0.320910	−	0.555833i	−0.659766	−	0.751471i	$-0.729344\pi$
$293$	471577.	−	816796.i	0.320910	−	0.555833i	0.980676	+	0.195638i	$0.0626778\pi$
$294$	139230.	−	116828.i	0.0939430	−	0.0788275i
$295$	−24568.7	+	20615.6i	−0.0164372	+	0.0137925i
$296$	−54836.9	+	94980.2i	−0.0363784	+	0.0630092i
$297$	−8792.61	−	15229.2i	−0.00578398	−	0.0100181i
$298$	−1.49587e6	−	544453.i	−0.975785	−	0.355157i
$299$	25844.7	−	146573.i	0.0167184	−	0.0948145i
$300$	−17864.5	−	101315.i	−0.0114601	−	0.0649933i
$301$	−2.83676e6	+	1.03250e6i	−1.80470	+	0.656859i
$302$	−958798.	−	804527.i	−0.604937	−	0.507602i
$303$	−38982.0			−0.0243926
$304$	−315262.	+	250766.i	−0.195653	+	0.155627i
$305$	−123805.			−0.0762062
$306$	422085.	+	354171.i	0.257689	+	0.216227i
$307$	1.96870e6	−	716547.i	1.19216	−	0.433909i	0.331675	−	0.943394i	$-0.392386\pi$
$307$	1.96870e6	−	716547.i	1.19216	−	0.433909i	0.860480	+	0.509485i	$0.170164\pi$
$308$	9264.55	+	52541.9i	0.00556477	+	0.0315594i
$309$	9946.23	−	56407.8i	0.00592601	−	0.0336081i
$310$	376565.	+	137059.i	0.222554	+	0.0810031i
$311$	−319431.	−	553271.i	−0.187273	−	0.324367i	0.757067	−	0.653337i	$-0.226632\pi$
$311$	−319431.	−	553271.i	−0.187273	−	0.324367i	−0.944340	+	0.328970i	$0.893298\pi$
$312$	17999.7	−	31176.4i	0.0104684	−	0.0181318i
$313$	866797.	−	727329.i	0.500099	−	0.419633i	−0.357530	−	0.933902i	$-0.616381\pi$
$313$	866797.	−	727329.i	0.500099	−	0.419633i	0.857629	+	0.514268i	$0.171937\pi$
$314$	1.38479e6	−	1.16198e6i	0.792611	−	0.665079i
$315$	251080.	−	434882.i	0.142572	−	0.246942i
$316$	−267474.	−	463278.i	−0.150683	−	0.260990i
$317$	1.10173e6	+	400997.i	0.615782	+	0.224126i	0.631031	−	0.775757i	$-0.282632\pi$
$317$	1.10173e6	+	400997.i	0.615782	+	0.224126i	−0.0152493	+	0.999884i	$0.504854\pi$
$318$	38101.8	−	216086.i	0.0211290	−	0.119828i
$319$	−19920.6	−	112976.i	−0.0109604	−	0.0621595i
$320$	41547.7	−	15122.1i	0.0226815	−	0.00825540i
$321$	275458.	+	231137.i	0.149208	+	0.125201i
$322$	441340.			0.237210
$323$	−845827.	−	333188.i	−0.451102	−	0.177698i
$324$	891839.			0.471980
$325$	606546.	+	508952.i	0.318534	+	0.267281i
$326$	−1.65408e6	+	602036.i	−0.862010	+	0.313746i
$327$	−5973.05	−	33874.8i	−0.00308906	−	0.0175189i
$328$	13547.3	−	76830.7i	0.00695295	−	0.0394321i
$329$	273673.	+	99608.7i	0.139393	+	0.0507350i
$330$	−788.577	−	1365.86i	−0.000398620	−	0.000690431i
$331$	369189.	−	639453.i	0.185216	−	0.320803i	−0.758433	−	0.651751i	$-0.774035\pi$
$331$	369189.	−	639453.i	0.185216	−	0.320803i	0.943649	+	0.330947i	$0.107368\pi$
$332$	819675.	−	687789.i	0.408128	−	0.342460i
$333$	−312998.	+	262636.i	−0.154679	+	0.129791i
$334$	−242217.	+	419532.i	−0.118806	+	0.205778i
$335$	−22649.8	−	39230.7i	−0.0110269	−	0.0190991i
$336$	100312.	+	36510.7i	0.0484737	+	0.0176430i
$337$	341828.	−	1.93860e6i	0.163958	−	0.929853i	−0.786174	−	0.618005i	$-0.787941\pi$
$337$	341828.	−	1.93860e6i	0.163958	−	0.929853i	0.950132	−	0.311848i	$-0.100948\pi$
$338$	−209785.	−	1.18975e6i	−0.0998811	−	0.566454i
$339$	207297.	−	75449.9i	0.0979701	−	0.0356582i
$340$	76435.7	+	64137.2i	0.0358591	+	0.0300893i
$341$	−158618.			−0.0738697
$342$	−1.42320e6	+	476183.i	−0.657963	+	0.220145i
$343$	−868834.			−0.398751
$344$	−758570.	−	636516.i	−0.345620	−	0.290010i
$345$	−12259.7	+	4462.16i	−0.00554539	+	0.00201836i
$346$	391014.	+	2.21755e6i	0.175591	+	0.995825i
$347$	457876.	−	2.59675e6i	0.204138	−	1.15773i	−0.694652	−	0.719346i	$-0.744442\pi$
$347$	457876.	−	2.59675e6i	0.204138	−	1.15773i	0.898790	−	0.438379i	$-0.144447\pi$
$348$	−215692.	−	78505.3i	−0.0954740	−	0.0347497i
$349$	248301.	+	430070.i	0.109123	+	0.189006i	0.915415	−	0.402511i	$-0.131863\pi$
$349$	248301.	+	430070.i	0.109123	+	0.189006i	−0.806292	+	0.591517i	$0.798529\pi$
$350$	−1.17396e6	+	2.03335e6i	−0.512250	+	0.887243i
$351$	207446.	−	174068.i	0.0898747	−	0.0754138i
$352$	−13406.4	+	11249.3i	−0.00576709	+	0.00483916i
$353$	1.08719e6	−	1.88308e6i	0.464377	−	0.804324i	−0.534797	−	0.844981i	$-0.679612\pi$
$353$	1.08719e6	−	1.88308e6i	0.464377	−	0.804324i	0.999173	+	0.0406569i	$0.0129451\pi$
$354$	−12700.2	−	21997.4i	−0.00538645	−	0.00932961i
$355$	683772.	+	248873.i	0.287966	+	0.104811i
$356$	−239164.	+	1.35637e6i	−0.100016	+	0.567221i
$357$	41833.1	+	237247.i	0.0173720	+	0.0985213i
$358$	2.10702e6	−	766891.i	0.868881	−	0.316247i
$359$	−197557.	−	165770.i	−0.0809016	−	0.0678845i	0.601440	−	0.798918i	$-0.294594\pi$
$359$	−197557.	−	165770.i	−0.0809016	−	0.0678845i	−0.682342	+	0.731033i	$0.739038\pi$
$360$	164720.			0.0669869
$361$	1.97753e6	−	1.49012e6i	0.798646	−	0.601801i
$362$	−1.87046e6			−0.750199
$363$	−263198.	−	220849.i	−0.104837	−	0.0879690i
$364$	−772046.	+	281002.i	−0.305415	+	0.111162i
$365$	85522.3	+	485021.i	0.0336006	+	0.190559i
$366$	17026.4	−	96561.3i	0.00664384	−	0.0376791i
$367$	2.46279e6	+	896383.i	0.954470	+	0.347399i	0.771864	−	0.635787i	$-0.219324\pi$
$367$	2.46279e6	+	896383.i	0.954470	+	0.347399i	0.182606	+	0.983186i	$0.441547\pi$
$368$	72385.0	+	125375.i	0.0278631	+	0.0482603i
$369$	145324.	−	251709.i	0.0555613	−	0.0962350i
$370$	−56681.1	+	47561.1i	−0.0215245	+	0.0180612i
$371$	−3.83611e6	+	3.21888e6i	−1.44696	+	1.21414i
$372$	−158685.	+	274851.i	−0.0594537	+	0.102977i
$373$	1.72501e6	+	2.98781e6i	0.641978	+	1.11194i	0.984991	+	0.172608i	$0.0552192\pi$
$373$	1.72501e6	+	2.98781e6i	0.641978	+	1.11194i	−0.343013	+	0.939331i	$0.611447\pi$
$374$	−37113.0	−	13508.0i	−0.0137198	−	0.00499359i
$375$	24571.5	−	139352.i	0.00902306	−	0.0511723i
$376$	16589.0	+	94081.0i	0.00605134	+	0.0343188i
$377$	1.66005e6	−	604210.i	0.601546	−	0.218945i
$378$	615145.	+	516168.i	0.221436	+	0.185807i
$379$	−3.09133e6			−1.10547			−0.552736	−	0.833356i	$-0.686416\pi$
$379$	−3.09133e6			−1.10547			−0.552736	+	0.833356i	$0.686416\pi$
$380$	−257729.	+	86232.4i	−0.0915597	+	0.0306346i
$381$	−455774.			−0.160856
$382$	154404.	+	129561.i	0.0541378	+	0.0454270i
$383$	−587411.	+	213800.i	−0.204619	+	0.0744751i	−0.442296	−	0.896869i	$-0.645836\pi$
$383$	−587411.	+	213800.i	−0.204619	+	0.0744751i	0.237678	+	0.971344i	$0.423614\pi$
$384$	6080.56	+	34484.6i	0.00210434	+	0.0119343i
$385$	−6250.37	+	35447.6i	−0.00214909	+	0.0121881i
$386$	−3.07289e6	−	1.11844e6i	−1.04973	−	0.382071i
$387$	−1.84458e6	−	3.19490e6i	−0.626064	−	1.08438i
$388$	−1.04561e6	+	1.81104e6i	−0.352605	+	0.610731i
$389$	−2.39797e6	+	2.01214e6i	−0.803470	+	0.674192i	−0.949040	−	0.315156i	$-0.897943\pi$
$389$	−2.39797e6	+	2.01214e6i	−0.803470	+	0.674192i	0.145570	+	0.989348i	$0.453499\pi$
$390$	18605.1	−	15611.5i	0.00619398	−	0.00519737i
$391$	−163354.	+	282937.i	−0.0540366	+	0.0935941i
$392$	−680323.	−	1.17835e6i	−0.223615	−	0.387312i
$393$	648491.	+	236032.i	0.211798	+	0.0770883i
$394$	316645.	−	1.79578e6i	0.102762	−	0.582791i
$395$	−62670.4	−	355422.i	−0.0202102	−	0.114618i
$396$	−61267.5	+	22299.5i	−0.0196332	+	0.00714591i
$397$	3.10234e6	+	2.60317e6i	0.987901	+	0.828948i	0.985263	−	0.171049i	$-0.0547156\pi$
$397$	3.10234e6	+	2.60317e6i	0.987901	+	0.828948i	0.00263866	+	0.999997i	$0.499160\pi$
$398$	2.18854e6			0.692543
$399$	−610504.	−	240490.i	−0.191980	−	0.0756250i
$400$	−770171.			−0.240678
$401$	3.17027e6	+	2.66017e6i	0.984544	+	0.826130i	0.984769	−	0.173870i	$-0.0556272\pi$
$401$	3.17027e6	+	2.66017e6i	0.984544	+	0.826130i	−0.000225032		1.00000i	$0.500072\pi$
$402$	33712.7	−	12270.4i	0.0104047	−	0.00378699i
$403$	−424156.	−	2.40551e6i	−0.130096	−	0.737809i
$404$	−50675.8	+	287397.i	−0.0154471	+	0.0876049i
$405$	565397.	+	205788.i	0.171284	+	0.0623422i
$406$	2.61926e6	+	4.53669e6i	0.788612	+	1.36592i
$407$	14643.7	−	25363.7i	0.00438193	−	0.00758973i
$408$	−60535.3	+	50795.1i	−0.0180035	+	0.0151068i
$409$	−2.51895e6	+	2.11365e6i	−0.744579	+	0.624776i	−0.934063	−	0.357108i	$-0.883763\pi$
$409$	−2.51895e6	+	2.11365e6i	−0.744579	+	0.624776i	0.189484	+	0.981884i	$0.439319\pi$
$410$	26316.9	−	45582.2i	0.00773171	−	0.0133917i
$411$	318030.	+	550843.i	0.0928673	+	0.160851i
$412$	−402940.	−	146658.i	−0.116949	−	0.0425660i
$413$	−100664.	+	570892.i	−0.0290401	+	0.164694i
$414$	93655.6	+	531147.i	0.0268555	+	0.152305i
$415$	678352.	−	246900.i	0.193346	−	0.0703721i
$416$	−206451.	−	173233.i	−0.0584902	−	0.0490791i
$417$	−90890.4			−0.0255964
$418$	84188.1	−	66965.0i	0.0235673	−	0.0187459i
$419$	3.77322e6			1.04997			0.524985	−	0.851111i	$-0.324071\pi$
$419$	3.77322e6			1.04997			0.524985	+	0.851111i	$0.324071\pi$
$420$	55170.1	+	46293.2i	0.0152609	+	0.0128054i
$421$	368560.	−	134145.i	0.101345	−	0.0368867i	−0.290850	−	0.956769i	$-0.593938\pi$
$421$	368560.	−	134145.i	0.101345	−	0.0368867i	0.392195	+	0.919882i	$0.371716\pi$
$422$	22156.7	+	125657.i	0.00605652	+	0.0343482i
$423$	−61802.5	+	350499.i	−0.0167940	+	0.0952437i
$424$	−1.54358e6	−	561815.i	−0.416978	−	0.151768i
$425$	−869036.	−	1.50522e6i	−0.233381	−	0.404228i
$426$	−288143.	+	499078.i	−0.0769279	+	0.133243i
$427$	−1.71422e6	+	1.43840e6i	−0.454985	+	0.381778i
$428$	2.06216e6	−	1.73035e6i	0.544142	−	0.456589i
$429$	−4806.68	+	8325.41i	−0.00126096	+	0.00218405i
$430$	−334036.	−	578567.i	−0.0871208	−	0.150898i
$431$	−5.63670e6	−	2.05159e6i	−1.46161	−	0.531983i	−0.515802	−	0.856708i	$-0.672506\pi$
$431$	−5.63670e6	−	2.05159e6i	−1.46161	−	0.531983i	−0.945809	+	0.324725i	$0.894728\pi$
$432$	−45740.3	+	259406.i	−0.0117921	+	0.0668761i
$433$	397918.	+	2.25671e6i	0.101994	+	0.578436i	0.992379	+	0.123227i	$0.0393243\pi$
$433$	397918.	+	2.25671e6i	0.101994	+	0.578436i	−0.890385	+	0.455209i	$0.849565\pi$
$434$	6.80634e6	−	2.47730e6i	1.73456	−	0.631328i
$435$	−118627.	−	99539.7i	−0.0300580	−	0.0252216i
$436$	−257509.			−0.0648748
$437$	−424599.	−	782030.i	−0.106359	−	0.195893i
$438$	−390051.			−0.0971484
$439$	129329.	+	108520.i	0.0320284	+	0.0268750i	0.658661	−	0.752440i	$-0.271123\pi$
$439$	129329.	+	108520.i	0.0320284	+	0.0268750i	−0.626633	+	0.779315i	$0.715567\pi$
$440$	−11095.0	+	4038.24i	−0.00273209	+	0.000994399i
$441$	−880238.	−	4.99208e6i	−0.215528	−	1.22232i
$442$	105612.	−	598956.i	0.0257133	−	0.145827i
$443$	2.92263e6	+	1.06375e6i	0.707563	+	0.257532i	0.670636	−	0.741786i	$-0.266021\pi$
$443$	2.92263e6	+	1.06375e6i	0.707563	+	0.257532i	0.0369262	+	0.999318i	$0.488243\pi$
$444$	−29299.9	−	50748.9i	−0.00705357	−	0.0122171i
$445$	−464598.	+	804708.i	−0.111219	+	0.192636i
$446$	3.76014e6	−	3.15513e6i	0.895090	−	0.751070i
$447$	651563.	−	546726.i	0.154237	−	0.129420i
$448$	399581.	−	692095.i	0.0940610	−	0.162919i
$449$	−2.52638e6	−	4.37583e6i	−0.591403	−	1.02434i	−0.994044	−	0.108982i	$-0.965241\pi$
$449$	−2.52638e6	−	4.37583e6i	−0.591403	−	1.02434i	0.402641	−	0.915358i	$-0.368092\pi$
$450$	−2.69624e6	−	981349.i	−0.627663	−	0.228451i
$451$	−3617.70	+	20517.0i	−0.000837513	+	0.00474977i
$452$	−286777.	−	1.62639e6i	−0.0660233	−	0.374437i
$453$	628424.	−	228728.i	0.143882	−	0.0523688i
$454$	747657.	+	627359.i	0.170240	+	0.142849i
$455$	−554292.			−0.125519
$456$	−31812.2	−	212873.i	−0.00716444	−	0.0479412i
$457$	2.57909e6			0.577665			0.288832	−	0.957380i	$-0.406733\pi$
$457$	2.57909e6			0.577665			0.288832	+	0.957380i	$0.406733\pi$
$458$	−3.95520e6	−	3.31881e6i	−0.881058	−	0.739296i
$459$	−558593.	+	203311.i	−0.123755	+	0.0450432i
$460$	16960.2	+	96185.9i	0.00373711	+	0.0211942i
$461$	−1.36458e6	+	7.73891e6i	−0.299052	+	1.69601i	0.351211	+	0.936296i	$0.385770\pi$
$461$	−1.36458e6	+	7.73891e6i	−0.299052	+	1.69601i	−0.650263	+	0.759710i	$0.725341\pi$
$462$	−26787.6	−	9749.88i	−0.00583887	−	0.00212517i
$463$	−2.43458e6	−	4.21681e6i	−0.527802	−	0.914180i	−0.999475	−	0.0324062i	$-0.989683\pi$
$463$	−2.43458e6	−	4.21681e6i	−0.527802	−	0.914180i	0.471673	−	0.881774i	$-0.343650\pi$
$464$	−859179.	+	1.48814e6i	−0.185263	+	0.320885i
$465$	−164022.	+	137631.i	−0.0351779	+	0.0295177i
$466$	3.77648e6	−	3.16884e6i	0.805605	−	0.675983i
$467$	−888988.	+	1.53977e6i	−0.188627	+	0.326711i	−0.944793	−	0.327669i	$-0.893737\pi$
$467$	−888988.	+	1.53977e6i	−0.188627	+	0.326711i	0.756166	+	0.654380i	$0.227070\pi$
$468$	−502016.	−	869517.i	−0.105950	−	0.183512i
$469$	−769404.	−	280040.i	−0.161518	−	0.0587879i
$470$	−11191.9	+	63472.2i	−0.00233699	+	0.0132538i
$471$	167723.	+	951207.i	0.0348371	+	0.197571i
$472$	−178687.	+	65036.8i	−0.0369180	+	0.0134371i
$473$	202570.	+	169976.i	0.0416315	+	0.0349330i
$474$	285828.			0.0584330
$475$	4.73241e6	+	123964.i	0.962383	+	0.0252093i
$476$	1.80350e6			0.364837
$477$	−4.68793e6	−	3.93364e6i	−0.943376	−	0.791587i
$478$	1.12654e6	−	410027.i	0.225516	−	0.0820810i
$479$	−1.72885e6	−	9.80478e6i	−0.344285	−	1.95254i	−0.301554	−	0.953449i	$-0.597505\pi$
$479$	−1.72885e6	−	9.80478e6i	−0.344285	−	1.95254i	−0.0427305	−	0.999087i	$-0.513606\pi$
$480$	−4102.28	+	23265.2i	−0.000812685	+	0.00460896i
$481$	423810.	+	154254.i	0.0835234	+	0.0304000i
$482$	668243.	+	1.15743e6i	0.131014	+	0.226922i
$483$	−117906.	+	204220.i	−0.0229969	+	0.0398318i
$484$	−1.97038e6	+	1.65334e6i	−0.382328	+	0.320811i
$485$	−1.08077e6	+	906875.i	−0.208631	+	0.175062i
$486$	−738323.	+	1.27881e6i	−0.141793	+	0.245593i
$487$	379449.	+	657225.i	0.0724988	+	0.125572i	0.899996	−	0.435898i	$-0.143569\pi$
$487$	379449.	+	657225.i	0.0724988	+	0.125572i	−0.827497	+	0.561470i	$0.810236\pi$
$488$	−689769.	−	251056.i	−0.131116	−	0.0477222i
$489$	163318.	−	926223.i	0.0308860	−	0.175163i
$490$	−159403.	−	904020.i	−0.0299921	−	0.170094i
$491$	−1.74628e6	+	635595.i	−0.326897	+	0.118981i	−0.500255	−	0.865878i	$-0.666760\pi$
$491$	−1.74628e6	+	635595.i	−0.326897	+	0.118981i	0.173358	+	0.984859i	$0.444538\pi$
$492$	31932.4	+	26794.4i	0.00594728	+	0.00499036i
$493$	−3.87788e6			−0.718584
$494$	1.24068e6	+	1.09768e6i	0.228740	+	0.202376i
$495$	−43987.1			−0.00806887
$496$	1.82006e6	+	1.52722e6i	0.332187	+	0.278738i
$497$	1.23590e7	−	4.49832e6i	2.24437	−	0.816883i
$498$	99277.6	+	563031.i	0.0179382	+	0.101732i
$499$	−1.33851e6	+	7.59107e6i	−0.240642	+	1.36475i	0.589759	+	0.807579i	$0.299223\pi$
$499$	−1.33851e6	+	7.59107e6i	−0.240642	+	1.36475i	−0.830401	+	0.557167i	$0.811888\pi$
$500$	−995438.	−	362310.i	−0.178069	−	0.0648119i
$501$	−129419.	−	224160.i	−0.0230358	−	0.0398992i
$502$	−3.57444e6	+	6.19111e6i	−0.633065	+	1.09650i
$503$	−5.08019e6	+	4.26279e6i	−0.895283	+	0.751231i	−0.969263	−	0.246028i	$-0.920874\pi$
$503$	−5.08019e6	+	4.26279e6i	−0.895283	+	0.751231i	0.0739799	+	0.997260i	$0.476430\pi$
$504$	2.28073e6	−	1.91376e6i	0.399942	−	0.335591i
$505$	−98442.4	+	170507.i	−0.0171772	+	0.0297519i
$506$	−19329.8	−	33480.2i	−0.00335623	−	0.00581316i
$507$	606574.	+	220775.i	0.104801	+	0.0381443i
$508$	−592497.	+	3.36022e6i	−0.101865	+	0.577707i
$509$	1.91757e6	+	1.08751e7i	0.328063	+	1.86054i	0.487212	+	0.873284i	$0.338014\pi$
$509$	1.91757e6	+	1.08751e7i	0.328063	+	1.86054i	−0.159149	+	0.987255i	$0.550875\pi$
$510$	−50098.2	+	18234.2i	−0.00852897	+	0.00310429i
$511$	6.81925e6	+	5.72203e6i	1.15527	+	0.969388i
$512$	262144.			0.0441942
$513$	322810.	−	1.58659e6i	0.0541568	−	0.266177i
$514$	5.22578e6			0.872456
$515$	−221610.	−	185953.i	−0.0368190	−	0.0308948i
$516$	497188.	−	180962.i	0.0822047	−	0.0299201i
$517$	−4429.96	−	25123.6i	−0.000728910	−	0.00413385i
$518$	−232235.	+	1.31707e6i	−0.0380280	+	0.215667i
$519$	−1.13058e6	−	411497.i	−0.184240	−	0.0670577i
$520$	−90910.5	−	157462.i	−0.0147437	−	0.0255368i
$521$	−2.65671e6	+	4.60156e6i	−0.428795	+	0.742695i	−0.996766	−	0.0803533i	$-0.974395\pi$
$521$	−2.65671e6	+	4.60156e6i	−0.428795	+	0.742695i	0.567971	+	0.823048i	$0.307728\pi$
$522$	−4.90403e6	+	4.11497e6i	−0.787728	+	0.660983i
$523$	143090.	−	120066.i	0.0228746	−	0.0191941i	−0.631279	−	0.775556i	$-0.717470\pi$
$523$	143090.	−	120066.i	0.0228746	−	0.0191941i	0.654153	+	0.756362i	$0.273025\pi$
$524$	2.58318e6	−	4.47420e6i	0.410986	−	0.711848i
$525$	−627257.	−	1.08644e6i	−0.0993224	−	0.172031i
$526$	−8.33670e6	−	3.03431e6i	−1.31380	−	0.478185i
$527$	−931074.	+	5.28038e6i	−0.146035	+	0.828207i
$528$	−1623.76	−	9208.82i	−0.000253477	−	0.00143754i
$529$	5.74767e6	−	2.09198e6i	0.893003	−	0.325026i
$530$	−848941.	−	712346.i	−0.131277	−	0.110154i
$531$	−708423.			−0.109033
$532$	−2.56667e6	+	4.18834e6i	−0.393180	+	0.641598i
$533$	−320823.			−0.0489157
$534$	−563733.	−	473028.i	−0.0855501	−	0.0717850i
$535$	1.70661e6	−	621156.i	0.257781	−	0.0938245i
$536$	−46638.4	−	264500.i	−0.00701184	−	0.0397661i
$537$	−208040.	+	1.17985e6i	−0.0311322	+	0.176560i
$538$	−1.62928e6	−	593010.i	−0.242684	−	0.0883297i
$539$	181675.	+	314670.i	0.0269353	+	0.0466534i
$540$	−88854.6	+	153901.i	−0.0131128	+	0.0227121i
$541$	−372996.	+	312981.i	−0.0547912	+	0.0459753i	−0.669772	−	0.742567i	$-0.733608\pi$
$541$	−372996.	+	312981.i	−0.0547912	+	0.0459753i	0.614981	+	0.788542i	$0.289164\pi$
$542$	−4.43337e6	+	3.72004e6i	−0.648240	+	0.543938i
$543$	499702.	−	865510.i	0.0727297	−	0.125972i
$544$	295795.	+	512332.i	0.0428542	+	0.0742257i
$545$	−163252.	−	59419.0i	−0.0235434	−	0.00856908i
$546$	76229.2	−	432317.i	0.0109431	−	0.0620613i
$547$	−922585.	−	5.23224e6i	−0.131837	−	0.747686i	−0.977010	−	0.213193i	$-0.931614\pi$
$547$	−922585.	−	5.23224e6i	−0.131837	−	0.747686i	0.845173	−	0.534493i	$-0.179498\pi$
$548$	4.47455e6	−	1.62860e6i	0.636500	−	0.231667i
$549$	−2.09487e6	−	1.75780e6i	−0.296638	−	0.248908i
$550$	205668.			0.0289908
$551$	5.51886e6	−	9.00578e6i	0.774409	−	1.26370i
$552$	−77352.1			−0.0108050
$553$	−4.99712e6	−	4.19308e6i	−0.694875	−	0.583070i
$554$	−6.18674e6	+	2.25179e6i	−0.856421	+	0.311712i
$555$	−6865.12	−	38934.0i	−0.000946053	−	0.00536533i
$556$	−118156.	+	670095.i	−0.0162094	+	0.0919283i
$557$	3.38452e6	+	1.23187e6i	0.462232	+	0.168239i	0.562630	−	0.826709i	$-0.309790\pi$
$557$	3.38452e6	+	1.23187e6i	0.462232	+	0.168239i	−0.100399	+	0.994947i	$0.532012\pi$
$558$	4.42576e6	+	7.66564e6i	0.601731	+	1.04223i
$559$	−2.03608e6	+	3.52659e6i	−0.275591	+	0.477337i
$560$	413019.	−	346564.i	0.0556545	−	0.0466997i
$561$	16165.4	−	13564.4i	0.00216861	−	0.00181968i
$562$	−1.85109e6	+	3.20618e6i	−0.247222	+	0.428201i
$563$	998831.	+	1.73003e6i	0.132807	+	0.230029i	0.924758	−	0.380557i	$-0.124268\pi$
$563$	998831.	+	1.73003e6i	0.132807	+	0.230029i	−0.791951	+	0.610585i	$0.790934\pi$
$564$	−47965.6	−	17458.1i	−0.00634939	−	0.00231099i
$565$	193475.	−	1.09725e6i	0.0254979	−	0.144606i
$566$	−1.47259e6	−	8.35149e6i	−0.193215	−	1.09578i
$567$	1.02194e7	−	3.71957e6i	1.33496	−	0.485887i
$568$	3.30490e6	+	2.77314e6i	0.429821	+	0.360662i
$569$	−5.80414e6			−0.751549			−0.375775	−	0.926711i	$-0.622623\pi$
$569$	−5.80414e6			−0.751549			−0.375775	+	0.926711i	$0.622623\pi$
$570$	28951.6	−	142295.i	0.00373238	−	0.0183444i
$571$	2.27354e6			0.291818			0.145909	−	0.989298i	$-0.453389\pi$
$571$	2.27354e6			0.291818			0.145909	+	0.989298i	$0.453389\pi$
$572$	55131.0	+	46260.4i	0.00704540	+	0.00591179i
$573$	−101201.	+	36834.1i	−0.0128765	+	0.00468666i
$574$	−165199.	−	936893.i	−0.0209281	−	0.118689i
$575$	295431.	−	1.67547e6i	0.0372637	−	0.211333i
$576$	917721.	+	334023.i	0.115254	+	0.0419489i
$577$	−7.42755e6	−	1.28649e7i	−0.928766	−	1.60867i	−0.785390	−	0.619001i	$-0.787538\pi$
$577$	−7.42755e6	−	1.28649e7i	−0.928766	−	1.60867i	−0.143376	−	0.989668i	$-0.545796\pi$
$578$	2.17218e6	−	3.76233e6i	0.270444	−	0.468422i
$579$	1.33847e6	−	1.12311e6i	0.165925	−	0.139228i
$580$	−888074.	+	745183.i	−0.109617	+	0.0919799i
$581$	6.52398e6	−	1.12999e7i	0.801811	−	1.38878i
$582$	−558678.	−	967659.i	−0.0683682	−	0.118417i
$583$	412199.	+	150028.i	0.0502268	+	0.0182811i
$584$	−507058.	+	2.87567e6i	−0.0615213	+	0.348905i
$585$	−117625.	−	667084.i	−0.0142105	−	0.0805918i
$586$	3.54510e6	−	1.29031e6i	0.426466	−	0.155221i
$587$	6.94671e6	+	5.82898e6i	0.832116	+	0.698229i	0.955776	−	0.294096i	$-0.0950186\pi$
$587$	6.94671e6	+	5.82898e6i	0.832116	+	0.698229i	−0.123659	+	0.992325i	$0.539463\pi$
$588$	727007.			0.0867152
$589$	−1.09378e7	−	9.67711e6i	−1.29910	−	1.14936i
$590$	−128289.			−0.0151726
$591$	746362.	+	626272.i	0.0878983	+	0.0737555i
$592$	−412238.	+	150042.i	−0.0483442	+	0.0175958i
$593$	200790.	+	1.13874e6i	0.0234480	+	0.132980i	0.994285	−	0.106762i	$-0.0340483\pi$
$593$	200790.	+	1.13874e6i	0.0234480	+	0.132980i	−0.970837	+	0.239742i	$0.922937\pi$
$594$	12214.6	−	69272.2i	0.00142040	−	0.00805551i
$595$	1.14336e6	+	416149.i	0.132401	+	0.0481900i
$596$	−3.18375e6	−	5.51442e6i	−0.367133	−	0.635893i
$597$	−584679.	+	1.01269e6i	−0.0671401	+	0.116290i
$598$	456053.	−	382674.i	0.0521509	−	0.0437598i
$599$	−5.73961e6	+	4.81610e6i	−0.653605	+	0.548440i	−0.908162	−	0.418618i	$-0.862515\pi$
$599$	−5.73961e6	+	4.81610e6i	−0.653605	+	0.548440i	0.254558	+	0.967058i	$0.418070\pi$
$600$	205755.	−	356378.i	0.0233331	−	0.0404141i
$601$	−1.23287e6	−	2.13539e6i	−0.139229	−	0.241152i	0.787976	−	0.615706i	$-0.211129\pi$
$601$	−1.23287e6	−	2.13539e6i	−0.139229	−	0.241152i	−0.927205	+	0.374554i	$0.877796\pi$
$602$	−1.13470e7	−	4.12998e6i	−1.27612	−	0.464469i
$603$	173752.	−	985394.i	0.0194597	−	0.110361i
$604$	−869368.	−	4.93043e6i	−0.0969641	−	0.549911i
$605$	−1.63066e6	+	593510.i	−0.181123	+	0.0659234i
$606$	−119448.	−	100229.i	−0.0132128	−	0.0110869i
$607$	1.30412e7			1.43663			0.718316	−	0.695717i	$-0.244913\pi$
$607$	1.30412e7			1.43663			0.718316	+	0.695717i	$0.244913\pi$
$608$	−1.61078e6	−	42193.7i	−0.176716	−	0.00462901i
$609$	−2.79900e6			−0.305815
$610$	−379362.	−	318322.i	−0.0412790	−	0.0346372i
$611$	369164.	−	134365.i	0.0400052	−	0.0145607i
$612$	382716.	+	2.17049e6i	0.0413045	+	0.234250i
$613$	−684061.	+	3.87950e6i	−0.0735265	+	0.416989i	0.925721	+	0.378207i	$0.123459\pi$
$613$	−684061.	+	3.87950e6i	−0.0735265	+	0.416989i	−0.999248	+	0.0387827i	$0.987652\pi$
$614$	7.87479e6	+	2.86619e6i	0.842981	+	0.306820i
$615$	14061.4	+	24355.1i	0.00149914	+	0.00259658i
$616$	−106705.	+	184818.i	−0.0113301	+	0.0196242i
$617$	−5.78997e6	+	4.85836e6i	−0.612299	+	0.513779i	−0.895372	−	0.445319i	$-0.853090\pi$
$617$	−5.78997e6	+	4.85836e6i	−0.612299	+	0.513779i	0.283074	+	0.959098i	$0.408646\pi$
$618$	175510.	−	147270.i	0.0184855	−	0.0155112i
$619$	3.56314e6	−	6.17154e6i	0.373772	−	0.647392i	−0.616371	−	0.787456i	$-0.711398\pi$
$619$	3.56314e6	−	6.17154e6i	0.373772	−	0.647392i	0.990142	+	0.140065i	$0.0447310\pi$
$620$	801465.	+	1.38818e6i	0.0837346	+	0.145033i
$621$	−546781.	−	199012.i	−0.0568963	−	0.0207086i
$622$	443749.	−	2.51663e6i	0.0459898	−	0.260821i
$623$	2.91643e6	+	1.65399e7i	0.301045	+	1.70731i
$624$	135314.	−	49250.2i	0.0139117	−	0.00506345i
$625$	6.65449e6	+	5.58378e6i	0.681420	+	0.571779i
$626$	4.52609e6			0.461623
$627$	8495.20	+	56846.1i	0.000862988	+	0.00577473i
$628$	7.23086e6			0.731629
$629$	−758399.	−	636372.i	−0.0764312	−	0.0641334i
$630$	1.88750e6	−	686994.i	0.189468	−	0.0689607i
$631$	−1.50318e6	−	8.52495e6i	−0.150292	−	0.852350i	−0.962964	−	0.269629i	$-0.913099\pi$
$631$	−1.50318e6	−	8.52495e6i	−0.150292	−	0.852350i	0.812672	−	0.582722i	$-0.198012\pi$
$632$	371570.	−	2.10728e6i	0.0370040	−	0.209860i
$633$	−64063.9	−	23317.4i	−0.00635483	−	0.00231297i
$634$	2.34487e6	+	4.06144e6i	0.231684	+	0.401289i
$635$	−1.15098e6	+	1.99355e6i	−0.113275	+	0.196198i
$636$	672341.	−	564161.i	0.0659093	−	0.0553045i
$637$	−4.28629e6	+	3.59663e6i	−0.418536	+	0.351194i
$638$	229437.	−	397396.i	0.0223157	−	0.0386520i
$639$	8.03636e6	+	1.39194e7i	0.778587	+	1.34855i
$640$	166191.	+	60488.5i	0.0160383	+	0.00583745i
$641$	2.38699e6	−	1.35373e7i	0.229460	−	1.30133i	−0.624514	−	0.781014i	$-0.714703\pi$
$641$	2.38699e6	−	1.35373e7i	0.229460	−	1.30133i	0.853974	−	0.520316i	$-0.174186\pi$
$642$	249765.	+	1.41649e6i	0.0239163	+	0.135636i
$643$	−5.00006e6	+	1.81987e6i	−0.476922	+	0.173586i	−0.569286	−	0.822140i	$-0.692780\pi$
$643$	−5.00006e6	+	1.81987e6i	−0.476922	+	0.173586i	0.0923632	+	0.995725i	$0.470558\pi$
$644$	1.35234e6	+	1.13475e6i	0.128491	+	0.107817i
$645$	356958.			0.0337845
$646$	−1.73509e6	−	3.19570e6i	−0.163584	−	0.301290i
$647$	−1.91181e7			−1.79549			−0.897747	−	0.440512i	$-0.854797\pi$
$647$	−1.91181e7			−1.79549			−0.897747	+	0.440512i	$0.854797\pi$
$648$	2.73275e6	+	2.29305e6i	0.255660	+	0.214524i
$649$	47716.9	−	17367.5i	0.00444694	−	0.00161855i
$650$	549971.	+	3.11904e6i	0.0510571	+	0.289559i
$651$	−672034.	+	3.81130e6i	−0.0621497	+	0.352468i
$652$	−6.61632e6	−	2.40814e6i	−0.609533	−	0.221852i
$653$	5.14118e6	+	8.90479e6i	0.471824	+	0.817223i	0.999480	−	0.0322348i	$-0.0102624\pi$
$653$	5.14118e6	+	8.90479e6i	0.471824	+	0.817223i	−0.527656	+	0.849458i	$0.676929\pi$
$654$	68794.8	−	119156.i	0.00628943	−	0.0108936i
$655$	2.67006e6	−	2.24044e6i	0.243174	−	0.204047i
$656$	239055.	−	200591.i	0.0216889	−	0.0181992i
$657$	−5.43929e6	+	9.42113e6i	−0.491620	+	0.851510i
$658$	582473.	+	1.00887e6i	0.0524458	+	0.0908388i
$659$	−9.54999e6	−	3.47591e6i	−0.856622	−	0.311785i	−0.123885	−	0.992297i	$-0.539535\pi$
$659$	−9.54999e6	−	3.47591e6i	−0.856622	−	0.311785i	−0.732737	+	0.680512i	$0.761758\pi$
$660$	1095.48	−	6212.78i	9.78914e−5	−	0.000555170i
$661$	−3.09838e6	−	1.75718e7i	−0.275824	−	1.56427i	−0.736333	−	0.676619i	$-0.763444\pi$
$661$	−3.09838e6	−	1.75718e7i	−0.275824	−	1.56427i	0.460510	−	0.887655i	$-0.347667\pi$
$662$	2.77539e6	−	1.01016e6i	0.246138	−	0.0895870i
$663$	248938.	+	208884.i	0.0219941	+	0.0184553i
$664$	4.28004e6			0.376728
$665$	−2.59363e6	+	2.06303e6i	−0.227433	+	0.180905i
$666$	−1.63436e6			−0.142778
$667$	−2.90781e6	−	2.43994e6i	−0.253077	−	0.212356i
$668$	−1.82088e6	+	662745.i	−0.157884	+	0.0574652i
$669$	455422.	+	2.58283e6i	0.0393413	+	0.223116i
$670$	31464.8	−	178446.i	0.00270794	−	0.0153575i
$671$	184197.	+	67042.3i	0.0157934	+	0.00574834i
$672$	213500.	+	369793.i	0.0182379	+	0.0315890i
$673$	−4.83553e6	+	8.37538e6i	−0.411535	+	0.712799i	−0.995058	−	0.0992977i	$-0.968340\pi$
$673$	−4.83553e6	+	8.37538e6i	−0.411535	+	0.712799i	0.583523	+	0.812096i	$0.301674\pi$
$674$	6.03186e6	−	5.06133e6i	0.511448	−	0.429156i
$675$	2.37132e6	−	1.98977e6i	0.200323	−	0.168091i
$676$	2.41621e6	−	4.18500e6i	0.203361	−	0.352232i
$677$	5.55323e6	+	9.61848e6i	0.465665	+	0.806556i	0.999231	−	0.0392023i	$-0.0124817\pi$
$677$	5.55323e6	+	9.61848e6i	0.465665	+	0.806556i	−0.533566	+	0.845759i	$0.679148\pi$
$678$	829187.	+	301800.i	0.0692753	+	0.0252142i
$679$	−4.42816e6	+	2.51134e7i	−0.368595	+	2.09040i
$680$	69306.3	+	393056.i	0.00574778	+	0.0325973i
$681$	−490036.	+	178358.i	−0.0404911	+	0.0147376i
$682$	−486033.	−	407830.i	−0.0400134	−	0.0335752i
$683$	323437.			0.0265301			0.0132650	−	0.999912i	$-0.495777\pi$
$683$	323437.			0.0265301			0.0132650	+	0.999912i	$0.495777\pi$
$684$	−5.58528e6	−	2.20016e6i	−0.456462	−	0.179810i
$685$	3.21252e6			0.261589
$686$	−2.66226e6	−	2.23390e6i	−0.215993	−	0.181240i
$687$	2.59235e6	−	943538.i	0.209557	−	0.0762725i
$688$	−687815.	−	3.90079e6i	−0.0553988	−	0.314182i
$689$	−1.17299e6	+	6.65236e6i	−0.0941340	+	0.533861i
$690$	−49038.8	−	17848.6i	−0.00392118	−	0.00142719i
$691$	−3.57752e6	−	6.19645e6i	−0.285028	−	0.493683i	0.687588	−	0.726101i	$-0.258670\pi$
$691$	−3.57752e6	−	6.19645e6i	−0.285028	−	0.493683i	−0.972616	+	0.232418i	$0.925336\pi$
$692$	−4.50352e6	+	7.80032e6i	−0.357509	+	0.619223i
$693$	−609050.	+	511054.i	−0.0481748	+	0.0404235i
$694$	8.07964e6	−	6.77962e6i	0.636786	−	0.534326i
$695$	−229528.	+	397555.i	−0.0180250	+	0.0312201i
$696$	−459068.	−	795130.i	−0.0359215	−	0.0622178i
$697$	661775.	+	240866.i	0.0515975	+	0.0187799i
$698$	−344936.	+	1.95623e6i	−0.0267979	+	0.151978i
$699$	457401.	+	2.59405e6i	0.0354082	+	0.200810i
$700$	−8.82526e6	+	3.21213e6i	−0.680742	+	0.247770i
$701$	−1.28013e7	−	1.07415e7i	−0.983917	−	0.825604i	0.000759093	−	1.00000i	$-0.499758\pi$
$701$	−1.28013e7	−	1.07415e7i	−0.983917	−	0.825604i	−0.984676	+	0.174396i	$0.944203\pi$
$702$	1.08321e6			0.0829599
$703$	2.55720e6	−	855602.i	0.195153	−	0.0652955i
$704$	−70003.4			−0.00532338
$705$	−26380.3	−	22135.7i	−0.00199897	−	0.00167734i
$706$	8.17303e6	−	2.97474e6i	0.617122	−	0.224614i
$707$	617953.	+	3.50459e6i	0.0464951	+	0.263687i
$708$	17643.0	−	100058.i	0.00132278	−	0.00750187i
$709$	4.19636e6	+	1.52735e6i	0.313514	+	0.114110i	0.493985	−	0.869470i	$-0.335540\pi$
$709$	4.19636e6	+	1.52735e6i	0.313514	+	0.114110i	−0.180470	+	0.983580i	$0.557762\pi$
$710$	1.45531e6	+	2.52067e6i	0.108345	+	0.187659i
$711$	3.98589e6	−	6.90377e6i	0.295700	−	0.512168i
$712$	−4.22027e6	+	3.54122e6i	−0.311989	+	0.261790i
$713$	−4.02055e6	+	3.37364e6i	−0.296184	+	0.248528i
$714$	−481814.	+	834526.i	−0.0353699	+	0.0612625i
$715$	24276.9	+	42048.8i	0.00177594	+	0.00307602i
$716$	8.42807e6	+	3.06757e6i	0.614392	+	0.223620i
$717$	−111231.	+	630820.i	−0.00808028	+	0.0458255i
$718$	−179131.	−	1.01590e6i	−0.0129676	−	0.0735427i
$719$	−7.62596e6	+	2.77562e6i	−0.550139	+	0.200234i	−0.602108	−	0.798414i	$-0.705672\pi$
$719$	−7.62596e6	+	2.77562e6i	−0.550139	+	0.200234i	0.0519692	+	0.998649i	$0.483450\pi$
$720$	504731.	+	423520.i	0.0362852	+	0.0304469i
$721$	−5.22889e6			−0.374603
$722$	9.89081e6	+	518528.i	0.706137	+	0.0370194i
$723$	−714098.			−0.0508056
$724$	−5.73141e6	−	4.80923e6i	−0.406364	−	0.340980i
$725$	1.89761e7	−	6.90673e6i	1.34079	−	0.488009i
$726$	−238649.	−	1.35344e6i	−0.0168042	−	0.0953012i
$727$	1.55641e6	−	8.82684e6i	0.109216	−	0.619397i	−0.880236	−	0.474537i	$-0.842616\pi$
$727$	1.55641e6	−	8.82684e6i	0.109216	−	0.619397i	0.989452	−	0.144860i	$-0.0462733\pi$
$728$	−3.08818e6	−	1.12401e6i	−0.215961	−	0.0786033i
$729$	6.37791e6	+	1.10469e7i	0.444487	+	0.769875i
$730$	−985007.	+	1.70608e6i	−0.0684120	+	0.118493i
$731$	6.84757e6	−	5.74579e6i	0.473961	−	0.397701i
$732$	300445.	−	252104.i	0.0207247	−	0.0173901i
$733$	4.92301e6	−	8.52691e6i	0.338432	−	0.586181i	−0.645706	−	0.763586i	$-0.723437\pi$
$733$	4.92301e6	−	8.52691e6i	0.338432	−	0.586181i	0.984138	+	0.177405i	$0.0567702\pi$
$734$	5.24170e6	+	9.07888e6i	0.359113	+	0.622003i
$735$	460899.	+	167754.i	0.0314693	+	0.0114539i
$736$	−100556.	+	570283.i	−0.00684249	+	0.0388057i
$737$	12454.4	+	70632.4i	0.000844606	+	0.00479000i
$738$	1.09248e6	−	397631.i	0.0738369	−	0.0268744i
$739$	−9.37329e6	−	7.86512e6i	−0.631365	−	0.529778i	0.269988	−	0.962864i	$-0.412980\pi$
$739$	−9.37329e6	−	7.86512e6i	−0.631365	−	0.529778i	−0.901353	+	0.433085i	$0.857425\pi$
$740$	−295968.			−0.0198685
$741$	−839379.	+	280844.i	−0.0561581	+	0.0187897i
$742$	−2.00307e7			−1.33563
$743$	1.64471e6	+	1.38008e6i	0.109300	+	0.0917132i	0.695800	−	0.718236i	$-0.255050\pi$
$743$	1.64471e6	+	1.38008e6i	0.109300	+	0.0917132i	−0.586500	+	0.809949i	$0.699495\pi$
$744$	−1.19292e6	+	434188.i	−0.0790096	+	0.0287571i
$745$	−745969.	−	4.23060e6i	−0.0492414	−	0.279262i
$746$	−2.39636e6	+	1.35904e7i	−0.157654	+	0.894101i
$747$	1.49837e7	+	5.45361e6i	0.982465	+	0.357588i
$748$	−78989.6	−	136814.i	−0.00516198	−	0.00894081i
$749$	1.64132e7	−	2.84285e7i	1.06903	−	1.85161i
$750$	433587.	−	363822.i	0.0281464	−	0.0236176i
$751$	1.51072e7	−	1.26764e7i	0.977424	−	0.820156i	−0.00627458	−	0.999980i	$-0.501997\pi$
$751$	1.51072e7	−	1.26764e7i	0.977424	−	0.820156i	0.983699	+	0.179824i	$0.0575528\pi$
$752$	−191065.	+	330934.i	−0.0123207	+	0.0213401i
$753$	−1.90986e6	−	3.30797e6i	−0.122748	−	0.212606i
$754$	6.64022e6	+	2.41684e6i	0.425357	+	0.154817i
$755$	586523.	−	3.32634e6i	0.0374471	−	0.212373i
$756$	557768.	+	3.16326e6i	0.0354935	+	0.201294i
$757$	−2.46382e7	+	8.96758e6i	−1.56268	+	0.568769i	−0.971348	−	0.237661i	$-0.923619\pi$
$757$	−2.46382e7	+	8.96758e6i	−1.56268	+	0.568769i	−0.591331	+	0.806429i	$0.701397\pi$
$758$	−9.47239e6	−	7.94828e6i	−0.598807	−	0.502459i
$759$	20656.2			0.00130151
$760$	−1.01144e6	−	398429.i	−0.0635196	−	0.0250217i
$761$	2.89872e7			1.81445			0.907225	−	0.420645i	$-0.138196\pi$
$761$	2.89872e7			1.81445			0.907225	+	0.420645i	$0.138196\pi$
$762$	−1.39657e6	−	1.17186e6i	−0.0871316	−	0.0731121i
$763$	−2.95075e6	+	1.07399e6i	−0.183494	+	0.0667863i
$764$	140002.	+	793993.i	0.00867765	+	0.0492134i
$765$	−258201.	+	1.46433e6i	−0.0159516	+	0.0904660i
$766$	−2.34964e6	−	855200.i	−0.144687	−	0.0526618i
$767$	390985.	+	677206.i	0.0239978	+	0.0415654i
$768$	−70033.1	+	121301.i	−0.00428450	+	0.00742098i
$769$	−1.03637e7	+	8.69617e6i	−0.631973	+	0.530288i	−0.901541	−	0.432693i	$-0.857563\pi$
$769$	−1.03637e7	+	8.69617e6i	−0.631973	+	0.530288i	0.269568	+	0.962981i	$0.413119\pi$
$770$	−110293.	+	92547.2i	−0.00670383	+	0.00562518i
$771$	−1.39609e6	+	2.41811e6i	−0.0845821	+	0.146501i
$772$	−6.54020e6	−	1.13280e7i	−0.394955	−	0.684082i
$773$	−1.21038e7	−	4.40542e6i	−0.728572	−	0.265179i	−0.0490120	−	0.998798i	$-0.515607\pi$
$773$	−1.21038e7	−	4.40542e6i	−0.728572	−	0.265179i	−0.679560	+	0.733619i	$0.737829\pi$
$774$	2.56246e6	−	1.45324e7i	0.153746	−	0.871938i
$775$	−4.84853e6	−	2.74974e7i	−0.289972	−	1.64451i
$776$	−7.86039e6	+	2.86095e6i	−0.468587	+	0.170552i
$777$	−547400.	−	459323.i	−0.0325276	−	0.0272939i
$778$	−1.25213e7			−0.741653
$779$	−1.50119e6	+	1.19408e6i	−0.0886322	+	0.0704999i
$780$	97148.8			0.00571743
$781$	−882546.	−	740544.i	−0.0517738	−	0.0434434i
$782$	−1.22802e6	+	446963.i	−0.0718106	+	0.0261369i
$783$	−1.19931e6	−	6.80164e6i	−0.0699082	−	0.396469i
$784$	945095.	−	5.35990e6i	0.0549143	−	0.311434i
$785$	4.58414e6	+	1.66849e6i	0.265511	+	0.0966383i
$786$	1.38022e6	+	2.39061e6i	0.0796878	+	0.138023i
$787$	−166178.	+	287829.i	−0.00956395	+	0.0165653i	−0.870768	−	0.491695i	$-0.836378\pi$
$787$	−166178.	+	287829.i	−0.00956395	+	0.0165653i	0.861204	+	0.508260i	$0.169711\pi$
$788$	5.58748e6	−	4.68845e6i	0.320553	−	0.268976i
$789$	3.63125e6	−	3.04698e6i	0.207665	−	0.174252i
$790$	721809.	−	1.25021e6i	0.0411486	−	0.0712714i
$791$	−1.00693e7	−	1.74405e7i	−0.572212	−	0.991101i
$792$	−245070.	−	89198.1i	−0.0138828	−	0.00505292i
$793$	−524168.	+	2.97271e6i	−0.0295997	+	0.167868i
$794$	2.81298e6	+	1.59532e7i	0.158349	+	0.898041i
$795$	556420.	−	202520.i	0.0312237	−	0.0113645i
$796$	6.70607e6	+	5.62706e6i	0.375133	+	0.314774i
$797$	3.13377e7			1.74752			0.873760	−	0.486358i	$-0.161675\pi$
$797$	3.13377e7			1.74752			0.873760	+	0.486358i	$0.161675\pi$
$798$	−1.25236e6	−	2.30660e6i	−0.0696179	−	0.128223i
$799$	−862366.			−0.0477886
$800$	−2.35994e6	−	1.98022e6i	−0.130369	−	0.109393i
$801$	−1.92866e7	+	7.01977e6i	−1.06212	+	0.386582i
$802$	2.87457e6	+	1.63025e7i	0.157811	+	0.894989i
$803$	135406.	−	767924.i	0.00741051	−	0.0420271i
$804$	134851.	+	49081.6i	0.00735720	+	0.00267780i
$805$	595504.	+	1.03144e6i	0.0323888	+	0.0560991i
$806$	4.88523e6	−	8.46147e6i	0.264879	−	0.458784i
$807$	709673.	−	595486.i	0.0383596	−	0.0321875i
$808$	−894220.	+	750340.i	−0.0481855	+	0.0404324i
$809$	3.29297e6	−	5.70359e6i	0.176895	−	0.306391i	−0.763920	−	0.645311i	$-0.776728\pi$
$809$	3.29297e6	−	5.70359e6i	0.176895	−	0.306391i	0.940816	+	0.338919i	$0.110061\pi$
$810$	1.20337e6	+	2.08429e6i	0.0644444	+	0.111621i
$811$	2.50115e7	+	9.10345e6i	1.33533	+	0.486020i	0.908338	−	0.418236i	$-0.137352\pi$
$811$	2.50115e7	+	9.10345e6i	1.33533	+	0.486020i	0.426991	+	0.904256i	$0.359574\pi$
$812$	−3.63864e6	+	2.06357e7i	−0.193664	+	1.09832i
$813$	−536962.	−	3.04526e6i	−0.0284916	−	0.161584i
$814$	110085.	−	40067.6i	0.00582327	−	0.00211950i
$815$	−3.63887e6	−	3.05337e6i	−0.191899	−	0.161022i
$816$	−316093.			−0.0166184
$817$	3.59851e6	+	2.40796e7i	0.188611	+	1.26210i
$818$	−1.31530e7			−0.687293
$819$	−9.37899e6	−	7.86991e6i	−0.488592	−	0.409978i
$820$	197839.	−	72007.3i	0.0102749	−	0.00373975i
$821$	5.70707e6	+	3.23664e7i	0.295498	+	1.67585i	0.665170	+	0.746692i	$0.268359\pi$
$821$	5.70707e6	+	3.23664e7i	0.295498	+	1.67585i	−0.369672	+	0.929162i	$0.620530\pi$
$822$	−441802.	+	2.50558e6i	−0.0228059	+	0.129339i
$823$	−8.40935e6	−	3.06075e6i	−0.432776	−	0.157517i	0.116441	−	0.993198i	$-0.462852\pi$
$823$	−8.40935e6	−	3.06075e6i	−0.432776	−	0.157517i	−0.549216	+	0.835680i	$0.685074\pi$
$824$	−857600.	−	1.48541e6i	−0.0440014	−	0.0762127i
$825$	−54945.2	+	95167.9i	−0.00281057	+	0.00486806i
$826$	−1.77630e6	+	1.49049e6i	−0.0905871	+	0.0760116i
$827$	−1.00724e7	+	8.45177e6i	−0.512118	+	0.429718i	−0.861874	−	0.507123i	$-0.830709\pi$
$827$	−1.00724e7	+	8.45177e6i	−0.512118	+	0.429718i	0.349756	+	0.936841i	$0.386265\pi$
$828$	−1.07868e6	+	1.86833e6i	−0.0546786	+	0.0947062i
$829$	536322.	+	928938.i	0.0271044	+	0.0469462i	0.879259	−	0.476343i	$-0.158038\pi$
$829$	536322.	+	928938.i	0.0271044	+	0.0469462i	−0.852155	+	0.523289i	$0.824705\pi$
$830$	2.71341e6	+	987599.i	0.136716	+	0.0497606i
$831$	610857.	−	3.46434e6i	0.0306858	−	0.174028i
$832$	−187194.	−	1.06163e6i	−0.00937528	−	0.0531699i
$833$	1.15418e7	−	4.20086e6i	0.576314	−	0.209761i
$834$	−278504.	−	233693.i	−0.0138649	−	0.0116340i
$835$	−1.30730e6			−0.0648873
$836$	430144.	+	11267.5i	0.0212862	+	0.000557585i
$837$	−9.54952e6			−0.471159
$838$	1.15618e7	+	9.70152e6i	0.568743	+	0.477232i
$839$	−3.27884e7	+	1.19340e7i	−1.60811	+	0.585304i	−0.981065	−	0.193681i	$-0.937957\pi$
$839$	−3.27884e7	+	1.19340e7i	−1.60811	+	0.585304i	−0.627044	+	0.778984i	$0.715735\pi$
$840$	50024.2	+	283701.i	0.00244614	+	0.0138728i
$841$	4.26208e6	−	2.41715e7i	0.207793	−	1.17845i
$842$	1.47424e6	+	536580.i	0.0716619	+	0.0260828i
$843$	−989057.	−	1.71310e6i	−0.0479350	−	0.0830258i
$844$	−255190.	+	442002.i	−0.0123313	+	0.0213584i
$845$	2.49747e6	−	2.09563e6i	0.120326	−	0.100965i
$846$	−1.09056e6	+	915088.i	−0.0523870	+	0.0439579i
$847$	−1.56827e7	+	2.71632e7i	−0.751124	+	1.30098i
$848$	−3.28528e6	−	5.69027e6i	−0.156885	−	0.271733i
$849$	4.25787e6	+	1.54974e6i	0.202732	+	0.0737885i
$850$	1.20725e6	−	6.84667e6i	0.0573127	−	0.325036i
$851$	−168280.	−	954361.i	−0.00796540	−	0.0451740i
$852$	−2.16613e6	+	788405.i	−0.102231	+	0.0372092i
$853$	1.39337e7	+	1.16917e7i	0.655681	+	0.550182i	0.908789	−	0.417256i	$-0.137008\pi$
$853$	1.39337e7	+	1.16917e7i	0.655681	+	0.550182i	−0.253108	+	0.967438i	$0.581453\pi$
$854$	−8.95103e6			−0.419980
$855$	−3.03322e6	−	2.68361e6i	−0.141902	−	0.125546i
$856$	1.07678e7			0.502277
$857$	2.57724e7	+	2.16256e7i	1.19868	+	1.00581i	0.999667	+	0.0258156i	$0.00821828\pi$
$857$	2.57724e7	+	2.16256e7i	1.19868	+	1.00581i	0.199014	+	0.979997i	$0.436226\pi$
$858$	−36134.4	+	13151.9i	−0.00167573	+	0.000609914i
$859$	5.46694e6	+	3.10045e7i	0.252791	+	1.43365i	0.801680	+	0.597753i	$0.203940\pi$
$859$	5.46694e6	+	3.10045e7i	0.252791	+	1.43365i	−0.548889	+	0.835895i	$0.684949\pi$
$860$	464038.	−	2.63169e6i	0.0213947	−	0.121336i
$861$	477659.	+	173854.i	0.0219589	+	0.00799237i
$862$	−1.19969e7	−	2.07792e7i	−0.549922	−	0.952492i
$863$	2.44068e6	−	4.22739e6i	0.111554	−	0.193217i	−0.804843	−	0.593488i	$-0.797751\pi$
$863$	2.44068e6	−	4.22739e6i	0.111554	−	0.193217i	0.916397	+	0.400271i	$0.131084\pi$
$864$	−807128.	+	677261.i	−0.0367839	+	0.0308654i
$865$	−4.65498e6	+	3.90599e6i	−0.211533	+	0.177497i
$866$	−4.58304e6	+	7.93805e6i	−0.207663	+	0.359682i
$867$	1.16062e6	+	2.01025e6i	0.0524375	+	0.0908244i
$868$	2.72254e7	+	9.90922e6i	1.22652	+	0.446416i
$869$	−99224.8	+	562732.i	−0.00445729	+	0.0252785i
$870$	−107562.	−	610015.i	−0.00481794	−	0.0273239i
$871$	−1.03787e6	+	377753.i	−0.0463550	+	0.0168718i
$872$	−789053.	−	662094.i	−0.0351411	−	0.0294869i
$873$	−3.11633e7			−1.38391
$874$	709670.	−	3.48798e6i	0.0314252	−	0.154453i
$875$	−1.29176e7			−0.570379
$876$	−1.19518e6	−	1.00288e6i	−0.0526229	−	0.0441559i
$877$	5.58544e6	−	2.03294e6i	0.245222	−	0.0892534i	−0.216485	−	0.976286i	$-0.569459\pi$
$877$	5.58544e6	−	2.03294e6i	0.245222	−	0.0892534i	0.461707	+	0.887032i	$0.347237\pi$
$878$	117266.	+	665049.i	0.00513376	+	0.0291150i
$879$	−350031.	+	1.98513e6i	−0.0152804	+	0.0866594i
$880$	−44379.9	−	16153.0i	−0.00193188	−	0.000703146i
$881$	9.77522e6	+	1.69312e7i	0.424313	+	0.734932i	0.996356	−	0.0852917i	$-0.0271822\pi$
$881$	9.77522e6	+	1.69312e7i	0.424313	+	0.734932i	−0.572043	+	0.820224i	$0.693849\pi$
$882$	1.01382e7	−	1.75598e7i	0.438822	−	0.760062i
$883$	1.68331e7	−	1.41247e7i	0.726546	−	0.609645i	−0.202641	−	0.979253i	$-0.564953\pi$
$883$	1.68331e7	−	1.41247e7i	0.726546	−	0.609645i	0.929188	+	0.369608i	$0.120508\pi$
$884$	1.86362e6	−	1.56376e6i	0.0802097	−	0.0673039i
$885$	34273.0	−	59362.6i	0.00147094	−	0.00254774i
$886$	6.22040e6	+	1.07741e7i	0.266216	+	0.461100i
$887$	−2.22127e6	−	808475.i	−0.0947963	−	0.0345030i	0.294187	−	0.955748i	$-0.404951\pi$
$887$	−2.22127e6	−	808475.i	−0.0947963	−	0.0345030i	−0.388983	+	0.921245i	$0.627174\pi$
$888$	40703.0	−	230838.i	0.00173218	−	0.00982370i
$889$	7.22505e6	+	4.09753e7i	0.306610	+	1.73887i
$890$	−3.49264e6	+	1.27122e6i	−0.147801	+	0.0537953i
$891$	−729759.	−	612341.i	−0.0307954	−	0.0258404i
$892$	1.96341e7			0.826224
$893$	1.22729e6	−	2.00271e6i	0.0515012	−	0.0840407i
$894$	3.40222e6			0.142370
$895$	4.63530e6	+	3.88948e6i	0.193428	+	0.162306i
$896$	3.00387e6	−	1.09332e6i	0.125000	−	0.0454963i
$897$	55236.3	+	313261.i	0.00229215	+	0.0129995i
$898$	3.50962e6	−	1.99040e7i	0.145234	−	0.823664i
$899$	−5.85400e7	−	2.13068e7i	−2.41576	−	0.879264i
$900$	−5.73855e6	−	9.93945e6i	−0.236154	−	0.409031i
$901$	7.41401e6	−	1.28414e7i	0.304257	−	0.526989i
$902$	−63837.6	+	53566.1i	−0.00261252	+	0.00219217i
$903$	4.94247e6	−	4.14722e6i	0.201709	−	0.169254i
$904$	3.30296e6	−	5.72090e6i	0.134426	−	0.232832i
$905$	−2.52383e6	−	4.37139e6i	−0.102433	−	0.177418i
$906$	2.51370e6	+	914910.i	0.101740	+	0.0370304i
$907$	4.55311e6	−	2.58220e7i	0.183776	−	1.04225i	−0.743741	−	0.668468i	$-0.766950\pi$
$907$	4.55311e6	−	2.58220e7i	0.183776	−	1.04225i	0.927517	−	0.373780i	$-0.121938\pi$
$908$	677920.	+	3.84468e6i	0.0272875	+	0.154755i
$909$	−4.08659e6	+	1.48740e6i	−0.164041	+	0.0597059i
$910$	−1.69845e6	−	1.42517e6i	−0.0679907	−	0.0570510i
$911$	−1.31649e7			−0.525558			−0.262779	−	0.964856i	$-0.584639\pi$
$911$	−1.31649e7			−0.525558			−0.262779	+	0.964856i	$0.584639\pi$
$912$	449851.	−	734076.i	0.0179094	−	0.0292250i
$913$	−1.14295e6			−0.0453785
$914$	7.90279e6	+	6.63123e6i	0.312907	+	0.262560i
$915$	248645.	−	90499.2i	0.00981807	−	0.00357349i
$916$	−3.58628e6	−	2.03388e7i	−0.141223	−	0.800916i
$917$	1.09398e7	−	6.20428e7i	0.429622	−	2.43651i
$918$	−2.23437e6	−	813245.i	−0.0875082	−	0.0318504i
$919$	−389089.	−	673922.i	−0.0151971	−	0.0263221i	0.858327	−	0.513103i	$-0.171504\pi$
$919$	−389089.	−	673922.i	−0.0151971	−	0.0263221i	−0.873524	+	0.486781i	$0.838171\pi$
$920$	−195340.	+	338338.i	−0.00760888	+	0.0131790i
$921$	−3.43005e6	+	2.87815e6i	−0.133245	+	0.111806i
$922$	−2.40792e7	+	2.02049e7i	−0.932857	+	0.782760i
$923$	8.87068e6	−	1.53645e7i	0.342730	−	0.593626i
$924$	−57013.5	−	98750.2i	−0.00219684	−	0.00380503i
$925$	4.84457e6	+	1.76328e6i	0.186166	+	0.0677590i
$926$	3.38208e6	−	1.91807e7i	0.129615	−	0.735085i
$927$	−1.10961e6	−	6.29290e6i	−0.0424102	−	0.240520i
$928$	−6.45892e6	+	2.35085e6i	−0.246201	+	0.0896098i
$929$	−2.41478e7	−	2.02624e7i	−0.917990	−	0.770285i	0.0556320	−	0.998451i	$-0.482283\pi$
$929$	−2.41478e7	−	2.02624e7i	−0.917990	−	0.770285i	−0.973622	+	0.228166i	$0.926727\pi$
$930$	−856462.			−0.0324714
$931$	−6.66996e6	+	3.27824e7i	−0.252202	+	1.23956i
$932$	1.97194e7			0.743624
$933$	1.04596e6	+	877664.i	0.0393378	+	0.0330084i
$934$	−6.68300e6	+	2.43241e6i	−0.250671	+	0.0912368i
$935$	−18507.7	−	104962.i	−0.000692345	−	0.00392649i
$936$	697393.	−	3.95511e6i	0.0260188	−	0.147560i
$937$	−2.69336e7	−	9.80302e6i	−1.00218	−	0.364763i	−0.211754	−	0.977323i	$-0.567918\pi$
$937$	−2.69336e7	−	9.80302e6i	−1.00218	−	0.364763i	−0.790424	+	0.612560i	$0.790140\pi$
$938$	−1.63756e6	−	2.83635e6i	−0.0607703	−	0.105257i
$939$	−1.20917e6	+	2.09434e6i	−0.0447531	+	0.0775146i
$940$	−197490.	+	165714.i	−0.00728998	+	0.00611702i
$941$	3.10060e7	−	2.60171e7i	1.14149	−	0.957824i	0.142003	−	0.989866i	$-0.454646\pi$
$941$	3.10060e7	−	2.60171e7i	1.14149	−	0.957824i	0.999487	+	0.0320426i	$0.0102012\pi$
$942$	−1.93176e6	+	3.34591e6i	−0.0709294	+	0.122853i
$943$	344677.	+	596998.i	0.0126221	+	0.0218622i
$944$	−714749.	−	260147.i	−0.0261050	−	0.00950144i
$945$	−376301.	+	2.13411e6i	−0.0137074	+	0.0777386i
$946$	183675.	+	1.04167e6i	0.00667303	+	0.0378446i
$947$	1.14798e7	−	4.17830e6i	0.415967	−	0.151400i	−0.125554	−	0.992087i	$-0.540071\pi$
$947$	1.14798e7	−	4.17830e6i	0.415967	−	0.151400i	0.541521	+	0.840687i	$0.317849\pi$
$948$	875827.	+	734906.i	0.0316517	+	0.0265590i
$949$	1.20080e7			0.432817
$950$	1.41822e7	+	1.25476e7i	0.509841	+	0.451077i
$951$	−2.50578e6			−0.0898445
$952$	5.52624e6	+	4.63707e6i	0.197623	+	0.165825i
$953$	−3.38388e7	+	1.23163e7i	−1.20693	+	0.439287i	−0.865639	−	0.500669i	$-0.833087\pi$
$953$	−3.38388e7	+	1.23163e7i	−1.20693	+	0.439287i	−0.341294	+	0.939957i	$0.610865\pi$
$954$	−4.25067e6	−	2.41067e7i	−0.151212	−	0.857566i
$955$	−94453.3	+	535671.i	−0.00335126	+	0.0190060i
$956$	4.50616e6	+	1.64011e6i	0.159464	+	0.0580400i
$957$	122590.	+	212333.i	0.00432690	+	0.00749441i
$958$	1.99121e7	−	3.44887e7i	0.700975	−	1.21412i
$959$	4.44808e7	−	3.73238e7i	1.56180	−	1.31051i
$960$	−72388.4	+	60741.1i	−0.00253508	+	0.00212718i
$961$	−2.87535e7	+	4.98026e7i	−1.00434	+	1.73958i
$962$	902018.	+	1.56234e6i	0.0314252	+	0.0544300i
$963$	3.76963e7	+	1.37203e7i	1.30988	+	0.476759i
$964$	−928313.	+	5.26472e6i	−0.0321738	+	0.182466i
$965$	−1.53240e6	−	8.69068e6i	−0.0529730	−	0.300425i
$966$	−886365.	+	322611.i	−0.0305612	+	0.0111234i
$967$	4.28291e6	+	3.59379e6i	0.147290	+	0.123591i	0.713455	−	0.700701i	$-0.247129\pi$
$967$	4.28291e6	+	3.59379e6i	0.147290	+	0.123591i	−0.566165	+	0.824292i	$0.691574\pi$
$968$	−1.02886e7			−0.352912
$969$	1.94227e6	+	50877.0i	0.0664508	+	0.00174065i
$970$	−5.64339e6			−0.192580
$971$	−9.19466e6	−	7.71524e6i	−0.312959	−	0.262604i	0.472755	−	0.881194i	$-0.343260\pi$
$971$	−9.19466e6	−	7.71524e6i	−0.312959	−	0.262604i	−0.785714	+	0.618590i	$0.787704\pi$
$972$	−5.55037e6	+	2.02017e6i	−0.188433	+	0.0685839i
$973$	1.44082e6	+	8.17130e6i	0.0487896	+	0.276700i
$974$	−527125.	+	2.98947e6i	−0.0178039	+	0.100971i
$975$	−1.59019e6	−	578782.i	−0.0535719	−	0.0194986i
$976$	−1.46807e6	−	2.54278e6i	−0.0493314	−	0.0854445i
$977$	−1.60549e7	+	2.78080e7i	−0.538111	+	0.932036i	0.460895	+	0.887455i	$0.347529\pi$
$977$	−1.60549e7	+	2.78080e7i	−0.538111	+	0.932036i	−0.999006	+	0.0445811i	$0.985805\pi$
$978$	2.88189e6	−	2.41820e6i	0.0963454	−	0.0808434i
$979$	1.12699e6	−	945655.i	0.0375805	−	0.0315338i
$980$	1.83593e6	−	3.17993e6i	0.0610649	−	0.105767i
$981$	−1.91870e6	−	3.32329e6i	−0.0636553	−	0.110254i
$982$	−6.98513e6	−	2.54238e6i	−0.231151	−	0.0841321i
$983$	888246.	−	5.03749e6i	0.0293190	−	0.166276i	−0.966633	−	0.256167i	$-0.917540\pi$
$983$	888246.	−	5.03749e6i	0.0293190	−	0.166276i	0.995952	+	0.0898901i	$0.0286516\pi$
$984$	28953.9	+	164206.i	0.000953278	+	0.00540631i
$985$	4.62412e6	−	1.68304e6i	0.151858	−	0.0552719i
$986$	−1.18825e7	−	9.97062e6i	−0.389239	−	0.326610i
$987$	−622442.			−0.0203379
$988$	979362.	+	6.55346e6i	0.0319191	+	0.213589i
$989$	8.74984e6			0.284452
$990$	−134784.	−	113098.i	−0.00437071	−	0.00366746i
$991$	−4.41340e6	+	1.60635e6i	−0.142754	+	0.0519583i	−0.412409	−	0.910999i	$-0.635313\pi$
$991$	−4.41340e6	+	1.60635e6i	−0.142754	+	0.0519583i	0.269655	+	0.962957i	$0.413090\pi$
$992$	1.65030e6	+	9.35932e6i	0.0532456	+	0.301971i
$993$	−274032.	+	1.55412e6i	−0.00881919	+	0.0500161i
$994$	4.94362e7	+	1.79933e7i	1.58701	+	0.577624i
$995$	2.95302e6	+	5.11477e6i	0.0945601	+	0.163783i
$996$	−1.14343e6	+	1.98049e6i	−0.0365227	+	0.0632592i
$997$	−4.67044e6	+	3.91897e6i	−0.148806	+	0.124863i	−0.714152	−	0.699991i	$-0.753187\pi$
$997$	−4.67044e6	+	3.91897e6i	−0.148806	+	0.124863i	0.565346	+	0.824854i	$0.308743\pi$
$998$	−2.36192e7	+	1.98189e7i	−0.750653	+	0.629873i
$999$	881620.	−	1.52701e6i	0.0279491	−	0.0484092i

Display

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.35.3	yes	30
19.5	even	9		722.6.a.r.1.9		15
19.6	even	9	inner	38.6.e.b.25.3	✓	30
19.14	odd	18		722.6.a.q.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.25.3	✓	30	19.6	even	9	inner
38.6.e.b.35.3	yes	30	1.1	even	1	trivial
722.6.a.q.1.7		15	19.14	odd	18
722.6.a.r.1.9		15	19.5	even	9

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	38.6.e.b.35.3

Level	$38$
Weight	$6$
Character	38.35
Analytic conductor	$6.095$
Analytic rank	$0$
Dimension	$30$
Inner twists	$2$