LMFDB - Embedded newform 38.6.e.b.25.3

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			25.3
Character	$\chi$	$=$	38.25
Dual form			38.6.e.b.35.3

$q$-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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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	0.276798	−	0.960928i	$-0.410727\pi$
$3$	−2.00835	−	0.730979i	−0.128836	−	0.0468924i	−0.405633	+	0.914036i	$0.632949\pi$
$4$	2.77837	−	15.7569i	0.0868241	−	0.492404i
$5$	−1.87444	−	10.6305i	−0.0335310	−	0.190164i	0.963441	−	0.267919i	$-0.0863359\pi$
$5$	−1.87444	−	10.6305i	−0.0335310	−	0.190164i	−0.996972	+	0.0777550i	$0.975225\pi$
$6$	−8.03340	+	2.92392i	−0.0911006	+	0.0331579i
$7$	97.5540	−	168.968i	0.752488	−	1.30335i	−0.194125	−	0.980977i	$-0.562187\pi$
$7$	97.5540	−	168.968i	0.752488	−	1.30335i	0.946613	−	0.322371i	$-0.104480\pi$
$8$	−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	0.876476	−	0.481446i	$-0.159888\pi$
$11$	8.54534	+	14.8010i	0.0212935	+	0.0368815i	−0.855182	+	0.518327i	$0.826555\pi$
$12$	−17.0979	+	29.6145i	−0.0342760	+	0.0593678i
$13$	247.314	−	90.0149i	0.405873	−	0.147726i	−0.131013	−	0.991381i	$-0.541823\pi$
$13$	247.314	−	90.0149i	0.405873	−	0.147726i	0.536886	+	0.843655i	$0.319601\pi$
$14$	−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	−0.809319	−	0.587370i	$-0.800163\pi$
$17$	−442.563	+	371.354i	−0.371409	+	0.311649i	0.437910	+	0.899019i	$0.355719\pi$
$18$	−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	−0.998026	−	0.0628072i	$-0.979995\pi$
$23$	−98.1994	+	556.917i	−0.0387070	+	0.219518i	0.959319	+	0.282325i	$0.0911058\pi$
$24$	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	0.999277	−	0.0380192i	$-0.0121048\pi$
$29$	5141.95	+	4314.61i	1.13536	+	0.952678i	0.136081	+	0.990698i	$0.456549\pi$
$30$	46.1408	+	79.9182i	0.00936013	+	0.0162122i
$31$	−4640.48	+	8037.55i	−0.867279	+	1.50217i	−0.00251180	+	0.999997i	$0.500800\pi$
$31$	−4640.48	+	8037.55i	−0.867279	+	1.50217i	−0.864767	+	0.502174i	$0.832534\pi$
$32$	−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	0.288261	−	0.957552i	$-0.406923\pi$
$41$	−1145.49	−	416.922i	−0.106422	−	0.0387343i	−0.394682	+	0.918818i	$0.629145\pi$
$42$	−289.640	+	1642.63i	−0.0253358	+	0.143687i
$43$	−2686.78	−	15237.5i	−0.221595	−	1.25673i	−0.869088	−	0.494658i	$-0.835293\pi$
$43$	−2686.78	−	15237.5i	−0.221595	−	1.25673i	0.647492	−	0.762072i	$-0.275818\pi$
$44$	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	0.679759	−	0.733435i	$-0.262084\pi$
$47$	1143.47	+	959.485i	0.0755057	+	0.0633568i	−0.604254	+	0.796792i	$0.706529\pi$
$48$	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	−0.657783	−	0.753207i	$-0.728506\pi$
$53$	4456.89	−	25276.3i	0.217943	−	1.23602i	0.875726	−	0.482808i	$-0.160383\pi$
$54$	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	−0.599233	−	0.800575i	$-0.704528\pi$
$59$	2276.05	−	1909.83i	0.0851239	−	0.0714274i	0.684357	+	0.729147i	$0.260083\pi$
$60$	346.865	+	126.249i	0.0124389	+	0.00452740i
$61$	1991.63	−	11295.1i	0.0685305	−	0.388656i	−0.931179	−	0.364562i	$-0.881219\pi$
$61$	1991.63	−	11295.1i	0.0685305	−	0.388656i	0.999710	−	0.0240939i	$-0.00767008\pi$
$62$	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	0.597993	−	0.801501i	$-0.295965\pi$
$67$	−3214.75	−	2697.50i	−0.0874904	−	0.0734132i	−0.685484	+	0.728088i	$0.740409\pi$
$68$	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	0.737112	+	0.675771i	$0.236189\pi$
$71$	11705.6	+	66385.9i	0.275581	+	1.56290i	−0.461531	+	0.887124i	$0.652700\pi$
$72$	−2649.81	+	15027.8i	−0.0602398	+	0.341637i
$73$	42873.9	+	15604.8i	0.941643	+	0.342730i	0.766814	−	0.641869i	$-0.221841\pi$
$73$	42873.9	+	15604.8i	0.941643	+	0.342730i	0.174829	+	0.984599i	$0.444063\pi$
$74$	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	0.0429285	−	0.999078i	$-0.486331\pi$
$79$	−31417.9	−	11435.2i	−0.566381	−	0.206146i	−0.609310	+	0.792932i	$0.708553\pi$
$80$	−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	0.466494	+	0.884524i	$0.345517\pi$
$83$	−33437.8	+	57916.0i	−0.532773	+	0.922790i	−0.999268	+	0.0382662i	$0.987817\pi$
$84$	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	0.261645	−	0.965164i	$-0.415735\pi$
$89$	80889.4	−	29441.3i	1.08247	−	0.393988i	0.820827	+	0.571176i	$0.193513\pi$
$90$	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	0.0844881	−	0.996424i	$-0.473075\pi$
$97$	100123.	−	84012.9i	1.08045	−	0.906602i	0.995958	+	0.0898228i	$0.0286301\pi$
$98$	−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	−0.257073	−	0.966392i	$-0.582758\pi$
$101$	17139.4	−	6238.24i	0.167183	−	0.0608497i	0.424256	+	0.905542i	$0.360536\pi$
$102$	2469.47	−	4277.25i	0.0235020	−	0.0407066i
$103$	−13400.0	−	23209.5i	−0.124455	−	0.215562i	0.797065	−	0.603894i	$-0.206385\pi$
$103$	−13400.0	−	23209.5i	−0.124455	−	0.215562i	−0.921520	+	0.388332i	$0.873052\pi$
$104$	−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	0.254407	+	0.967097i	$0.418120\pi$
$107$	−84123.6	+	145706.i	−0.710327	+	1.23032i	−0.964734	+	0.263225i	$0.915214\pi$
$108$	15470.1	−	5630.67i	0.127625	−	0.0464516i
$109$	−2794.75	−	15849.8i	−0.0225308	−	0.127778i	0.971468	−	0.237172i	$-0.0762204\pi$
$109$	−2794.75	−	15849.8i	−0.0225308	−	0.127778i	−0.993999	+	0.109393i	$0.965109\pi$
$110$	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	0.274253	−	0.961658i	$-0.411570\pi$
$127$	200393.	−	72936.9i	1.10248	−	0.401271i	0.828231	+	0.560386i	$0.189347\pi$
$128$	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	−0.263580	+	0.964637i	$0.584903\pi$
$131$	−247354.	+	207555.i	−1.25933	+	1.05671i	−0.995753	+	0.0920683i	$0.970652\pi$
$132$	−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	0.606865	+	0.794805i	$0.292427\pi$
$137$	−51679.0	+	293086.i	−0.235241	+	1.33412i	−0.842106	+	0.539312i	$0.818684\pi$
$138$	−839.503	−	4761.06i	−0.00375253	−	0.0212817i
$139$	39962.3	−	14545.1i	0.175434	−	0.0638527i	−0.252810	−	0.967516i	$-0.581355\pi$
$139$	39962.3	−	14545.1i	0.175434	−	0.0638527i	0.428244	+	0.903663i	$0.359132\pi$
$140$	−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	−0.457800	−	0.889055i	$-0.651362\pi$
$149$	−373968.	−	136113.i	−1.37997	−	0.502268i	−0.922169	+	0.386788i	$0.873585\pi$
$150$	−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	0.798392	+	0.602138i	$0.205684\pi$
$157$	78476.6	+	445063.i	0.254092	+	1.44103i	−0.544300	+	0.838891i	$0.683205\pi$
$158$	−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	−0.983445	−	0.181206i	$-0.942000\pi$
$163$	−220029.	−	381102.i	−0.648652	−	1.12350i	0.334793	−	0.942292i	$-0.391333\pi$
$164$	−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	−0.941632	−	0.336644i	$-0.890708\pi$
$167$	21030.3	−	119269.i	0.0583517	−	0.330929i	0.999984	+	0.00571507i	$0.00181917\pi$
$168$	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	0.0983581	−	0.995151i	$-0.468641\pi$
$173$	431237.	−	361851.i	1.09547	−	0.919209i	0.997112	+	0.0759423i	$0.0241965\pi$
$174$	−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	0.982188	+	0.187902i	$0.0601689\pi$
$179$	280280.	+	485459.i	0.653822	+	1.13245i	−0.328366	+	0.944551i	$0.606498\pi$
$180$	31545.7	+	26470.0i	0.0725703	+	0.0608937i
$181$	−358213.	−	300577.i	−0.812728	−	0.681960i	0.138529	−	0.990358i	$-0.455763\pi$
$181$	−358213.	−	300577.i	−0.812728	−	0.681960i	−0.951257	+	0.308398i	$0.900207\pi$
$182$	−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	−0.532538	−	0.846406i	$-0.678762\pi$
$193$	−768222.	−	279610.i	−1.48455	−	0.540330i	−0.952007	+	0.306076i	$0.900984\pi$
$194$	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	−0.995784	−	0.0917287i	$-0.970761\pi$
$197$	−227935.	+	394796.i	−0.418453	+	0.724781i	0.577331	+	0.816510i	$0.304094\pi$
$198$	−8149.93	−	14116.1i	−0.0147738	−	0.0255889i
$199$	419129.	+	351691.i	0.750266	+	0.629548i	0.935573	−	0.353132i	$-0.114884\pi$
$199$	419129.	+	351691.i	0.750266	+	0.629548i	−0.185307	+	0.982681i	$0.559328\pi$
$200$	−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	−0.623699	−	0.781664i	$-0.714371\pi$
$211$	24435.9	−	20504.1i	0.0377852	−	0.0317056i	0.661485	+	0.749959i	$0.269927\pi$
$212$	−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	0.698255	+	0.715849i	$0.253960\pi$
$223$	213089.	+	1.20849e6i	0.286945	+	1.62734i	−0.411311	+	0.911495i	$0.634929\pi$
$224$	−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	0.787570	+	0.616226i	$0.211339\pi$
$233$	214015.	+	1.21374e6i	0.258258	+	1.46465i	−0.529312	+	0.848427i	$0.677550\pi$
$234$	−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	0.938314	−	0.345786i	$-0.112388\pi$
$239$	149855.	+	259556.i	0.169698	+	0.293925i	−0.768616	+	0.639711i	$0.779054\pi$
$240$	2953.01	−	5114.76i	0.00330931	−	0.00573189i
$241$	313971.	−	114276.i	0.348215	−	0.126740i	−0.161991	−	0.986792i	$-0.551791\pi$
$241$	313971.	−	114276.i	0.348215	−	0.126740i	0.510206	+	0.860052i	$0.329569\pi$
$242$	−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	−0.283251	−	0.959046i	$-0.591413\pi$
$251$	310347.	−	1.76007e6i	0.310931	−	1.76338i	0.594182	−	0.804331i	$-0.297476\pi$
$252$	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	0.978478	−	0.206349i	$-0.0661583\pi$
$257$	1.00079e6	+	839767.i	0.945175	+	0.793096i	−0.0333033	+	0.999445i	$0.510603\pi$
$258$	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	−0.980452	−	0.196759i	$-0.936958\pi$
$263$	−2.08417e6	−	758578.i	−1.85800	−	0.676255i	−0.877544	−	0.479496i	$-0.840820\pi$
$264$	−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	0.164665	−	0.986349i	$-0.447346\pi$
$269$	−407321.	−	148253.i	−0.343207	−	0.124917i	−0.507872	+	0.861432i	$0.669568\pi$
$270$	7714.72	−	43752.4i	0.00644037	−	0.0365252i
$271$	−251241.	−	1.42486e6i	−0.207810	−	1.17855i	−0.892956	−	0.450144i	$-0.851373\pi$
$271$	−251241.	−	1.42486e6i	−0.207810	−	1.17855i	0.685146	−	0.728406i	$-0.259739\pi$
$272$	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	−0.984429	−	0.175782i	$-0.943755\pi$
$277$	−822974.	−	1.42543e6i	−0.644446	−	1.11621i	0.339983	−	0.940431i	$-0.389579\pi$
$278$	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	−0.861945	−	0.507002i	$-0.830754\pi$
$281$	160719.	−	911484.i	0.121423	−	0.688626i	0.983368	−	0.181624i	$-0.0581353\pi$
$282$	−11991.4	−	4364.51i	−0.00897940	−	0.00326823i
$283$	−1.62408e6	+	1.36276e6i	−1.20543	+	1.01147i	−0.205968	+	0.978559i	$0.566034\pi$
$283$	−1.62408e6	+	1.36276e6i	−1.20543	+	1.01147i	−0.999458	+	0.0329140i	$0.989521\pi$
$284$	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	0.980676	−	0.195638i	$-0.0626778\pi$
$293$	471577.	+	816796.i	0.320910	+	0.555833i	−0.659766	+	0.751471i	$0.729344\pi$
$294$	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	0.860480	−	0.509485i	$-0.170164\pi$
$307$	1.96870e6	+	716547.i	1.19216	+	0.433909i	0.331675	+	0.943394i	$0.392386\pi$
$308$	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	−0.944340	−	0.328970i	$-0.893298\pi$
$311$	−319431.	+	553271.i	−0.187273	+	0.324367i	0.757067	+	0.653337i	$0.226632\pi$
$312$	17999.7	+	31176.4i	0.0104684	+	0.0181318i
$313$	866797.	+	727329.i	0.500099	+	0.419633i	0.857629	−	0.514268i	$-0.171937\pi$
$313$	866797.	+	727329.i	0.500099	+	0.419633i	−0.357530	+	0.933902i	$0.616381\pi$
$314$	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	−0.0152493	−	0.999884i	$-0.504854\pi$
$317$	1.10173e6	−	400997.i	0.615782	−	0.224126i	0.631031	+	0.775757i	$0.282632\pi$
$318$	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	0.943649	−	0.330947i	$-0.107368\pi$
$331$	369189.	+	639453.i	0.185216	+	0.320803i	−0.758433	+	0.651751i	$0.774035\pi$
$332$	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	0.950132	+	0.311848i	$0.100948\pi$
$337$	341828.	+	1.93860e6i	0.163958	+	0.929853i	−0.786174	+	0.618005i	$0.787941\pi$
$338$	−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	0.898790	+	0.438379i	$0.144447\pi$
$347$	457876.	+	2.59675e6i	0.204138	+	1.15773i	−0.694652	+	0.719346i	$0.744442\pi$
$348$	−215692.	+	78505.3i	−0.0954740	+	0.0347497i
$349$	248301.	−	430070.i	0.109123	−	0.189006i	−0.806292	−	0.591517i	$-0.798529\pi$
$349$	248301.	−	430070.i	0.109123	−	0.189006i	0.915415	+	0.402511i	$0.131863\pi$
$350$	−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	0.999173	−	0.0406569i	$-0.0129451\pi$
$353$	1.08719e6	+	1.88308e6i	0.464377	+	0.804324i	−0.534797	+	0.844981i	$0.679612\pi$
$354$	−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	−0.682342	−	0.731033i	$-0.739038\pi$
$359$	−197557.	+	165770.i	−0.0809016	+	0.0678845i	0.601440	+	0.798918i	$0.294594\pi$
$360$	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	0.182606	−	0.983186i	$-0.441547\pi$
$367$	2.46279e6	−	896383.i	0.954470	−	0.347399i	0.771864	+	0.635787i	$0.219324\pi$
$368$	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	−0.343013	−	0.939331i	$-0.611447\pi$
$373$	1.72501e6	−	2.98781e6i	0.641978	−	1.11194i	0.984991	−	0.172608i	$-0.0552192\pi$
$374$	−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	0.237678	−	0.971344i	$-0.423614\pi$
$383$	−587411.	−	213800.i	−0.204619	−	0.0744751i	−0.442296	+	0.896869i	$0.645836\pi$
$384$	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	0.145570	−	0.989348i	$-0.453499\pi$
$389$	−2.39797e6	−	2.01214e6i	−0.803470	−	0.674192i	−0.949040	+	0.315156i	$0.897943\pi$
$390$	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	0.00263866	−	0.999997i	$-0.499160\pi$
$397$	3.10234e6	−	2.60317e6i	0.987901	−	0.828948i	0.985263	+	0.171049i	$0.0547156\pi$
$398$	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	−0.000225032	−	1.00000i	$-0.500072\pi$
$401$	3.17027e6	−	2.66017e6i	0.984544	−	0.826130i	0.984769	+	0.173870i	$0.0556272\pi$
$402$	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	0.189484	−	0.981884i	$-0.439319\pi$
$409$	−2.51895e6	−	2.11365e6i	−0.744579	−	0.624776i	−0.934063	+	0.357108i	$0.883763\pi$
$410$	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	0.392195	−	0.919882i	$-0.371716\pi$
$421$	368560.	+	134145.i	0.101345	+	0.0368867i	−0.290850	+	0.956769i	$0.593938\pi$
$422$	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	−0.945809	−	0.324725i	$-0.894728\pi$
$431$	−5.63670e6	+	2.05159e6i	−1.46161	+	0.531983i	−0.515802	+	0.856708i	$0.672506\pi$
$432$	−45740.3	−	259406.i	−0.0117921	−	0.0668761i
$433$	397918.	−	2.25671e6i	0.101994	−	0.578436i	−0.890385	−	0.455209i	$-0.849565\pi$
$433$	397918.	−	2.25671e6i	0.101994	−	0.578436i	0.992379	−	0.123227i	$-0.0393243\pi$
$434$	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	−0.626633	−	0.779315i	$-0.715567\pi$
$439$	129329.	−	108520.i	0.0320284	−	0.0268750i	0.658661	+	0.752440i	$0.271123\pi$
$440$	−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	0.0369262	−	0.999318i	$-0.488243\pi$
$443$	2.92263e6	−	1.06375e6i	0.707563	−	0.257532i	0.670636	+	0.741786i	$0.266021\pi$
$444$	−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	0.402641	+	0.915358i	$0.368092\pi$
$449$	−2.52638e6	+	4.37583e6i	−0.591403	+	1.02434i	−0.994044	+	0.108982i	$0.965241\pi$
$450$	−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	−0.650263	−	0.759710i	$-0.725341\pi$
$461$	−1.36458e6	−	7.73891e6i	−0.299052	−	1.69601i	0.351211	−	0.936296i	$-0.385770\pi$
$462$	−26787.6	+	9749.88i	−0.00583887	+	0.00212517i
$463$	−2.43458e6	+	4.21681e6i	−0.527802	+	0.914180i	0.471673	+	0.881774i	$0.343650\pi$
$463$	−2.43458e6	+	4.21681e6i	−0.527802	+	0.914180i	−0.999475	+	0.0324062i	$0.989683\pi$
$464$	−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	0.756166	−	0.654380i	$-0.227070\pi$
$467$	−888988.	−	1.53977e6i	−0.188627	−	0.326711i	−0.944793	+	0.327669i	$0.893737\pi$
$468$	−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	−0.0427305	+	0.999087i	$0.513606\pi$
$479$	−1.72885e6	+	9.80478e6i	−0.344285	+	1.95254i	−0.301554	+	0.953449i	$0.597505\pi$
$480$	−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	−0.827497	−	0.561470i	$-0.810236\pi$
$487$	379449.	−	657225.i	0.0724988	−	0.125572i	0.899996	+	0.435898i	$0.143569\pi$
$488$	−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	0.173358	−	0.984859i	$-0.444538\pi$
$491$	−1.74628e6	−	635595.i	−0.326897	−	0.118981i	−0.500255	+	0.865878i	$0.666760\pi$
$492$	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	−0.830401	−	0.557167i	$-0.811888\pi$
$499$	−1.33851e6	−	7.59107e6i	−0.240642	−	1.36475i	0.589759	−	0.807579i	$-0.299223\pi$
$500$	−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	0.0739799	−	0.997260i	$-0.476430\pi$
$503$	−5.08019e6	−	4.26279e6i	−0.895283	−	0.751231i	−0.969263	+	0.246028i	$0.920874\pi$
$504$	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	−0.159149	−	0.987255i	$-0.550875\pi$
$509$	1.91757e6	−	1.08751e7i	0.328063	−	1.86054i	0.487212	−	0.873284i	$-0.338014\pi$
$510$	−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	0.567971	−	0.823048i	$-0.307728\pi$
$521$	−2.65671e6	−	4.60156e6i	−0.428795	−	0.742695i	−0.996766	+	0.0803533i	$0.974395\pi$
$522$	−4.90403e6	−	4.11497e6i	−0.787728	−	0.660983i
$523$	143090.	+	120066.i	0.0228746	+	0.0191941i	0.654153	−	0.756362i	$-0.273025\pi$
$523$	143090.	+	120066.i	0.0228746	+	0.0191941i	−0.631279	+	0.775556i	$0.717470\pi$
$524$	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	0.614981	−	0.788542i	$-0.289164\pi$
$541$	−372996.	−	312981.i	−0.0547912	−	0.0459753i	−0.669772	+	0.742567i	$0.733608\pi$
$542$	−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	0.845173	+	0.534493i	$0.179498\pi$
$547$	−922585.	+	5.23224e6i	−0.131837	+	0.747686i	−0.977010	+	0.213193i	$0.931614\pi$
$548$	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	−0.100399	−	0.994947i	$-0.532012\pi$
$557$	3.38452e6	−	1.23187e6i	0.462232	−	0.168239i	0.562630	+	0.826709i	$0.309790\pi$
$558$	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	−0.791951	−	0.610585i	$-0.790934\pi$
$563$	998831.	−	1.73003e6i	0.132807	−	0.230029i	0.924758	+	0.380557i	$0.124268\pi$
$564$	−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	−0.143376	+	0.989668i	$0.545796\pi$
$577$	−7.42755e6	+	1.28649e7i	−0.928766	+	1.60867i	−0.785390	+	0.619001i	$0.787538\pi$
$578$	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	−0.123659	−	0.992325i	$-0.539463\pi$
$587$	6.94671e6	−	5.82898e6i	0.832116	−	0.698229i	0.955776	+	0.294096i	$0.0950186\pi$
$588$	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	−0.970837	−	0.239742i	$-0.922937\pi$
$593$	200790.	−	1.13874e6i	0.0234480	−	0.132980i	0.994285	+	0.106762i	$0.0340483\pi$
$594$	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	0.254558	−	0.967058i	$-0.418070\pi$
$599$	−5.73961e6	−	4.81610e6i	−0.653605	−	0.548440i	−0.908162	+	0.418618i	$0.862515\pi$
$600$	205755.	+	356378.i	0.0233331	+	0.0404141i
$601$	−1.23287e6	+	2.13539e6i	−0.139229	+	0.241152i	−0.927205	−	0.374554i	$-0.877796\pi$
$601$	−1.23287e6	+	2.13539e6i	−0.139229	+	0.241152i	0.787976	+	0.615706i	$0.211129\pi$
$602$	−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	−0.999248	−	0.0387827i	$-0.987652\pi$
$613$	−684061.	−	3.87950e6i	−0.0735265	−	0.416989i	0.925721	−	0.378207i	$-0.123459\pi$
$614$	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	0.283074	−	0.959098i	$-0.408646\pi$
$617$	−5.78997e6	−	4.85836e6i	−0.612299	−	0.513779i	−0.895372	+	0.445319i	$0.853090\pi$
$618$	175510.	+	147270.i	0.0184855	+	0.0155112i
$619$	3.56314e6	+	6.17154e6i	0.373772	+	0.647392i	0.990142	−	0.140065i	$-0.0447310\pi$
$619$	3.56314e6	+	6.17154e6i	0.373772	+	0.647392i	−0.616371	+	0.787456i	$0.711398\pi$
$620$	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	0.812672	+	0.582722i	$0.198012\pi$
$631$	−1.50318e6	+	8.52495e6i	−0.150292	+	0.852350i	−0.962964	+	0.269629i	$0.913099\pi$
$632$	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	0.853974	+	0.520316i	$0.174186\pi$
$641$	2.38699e6	+	1.35373e7i	0.229460	+	1.30133i	−0.624514	+	0.781014i	$0.714703\pi$
$642$	249765.	−	1.41649e6i	0.0239163	−	0.135636i
$643$	−5.00006e6	−	1.81987e6i	−0.476922	−	0.173586i	0.0923632	−	0.995725i	$-0.470558\pi$
$643$	−5.00006e6	−	1.81987e6i	−0.476922	−	0.173586i	−0.569286	+	0.822140i	$0.692780\pi$
$644$	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	−0.527656	−	0.849458i	$-0.676929\pi$
$653$	5.14118e6	−	8.90479e6i	0.471824	−	0.817223i	0.999480	+	0.0322348i	$0.0102624\pi$
$654$	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	−0.732737	−	0.680512i	$-0.761758\pi$
$659$	−9.54999e6	+	3.47591e6i	−0.856622	+	0.311785i	−0.123885	+	0.992297i	$0.539535\pi$
$660$	1095.48	+	6212.78i	9.78914e−5	+	0.000555170i
$661$	−3.09838e6	+	1.75718e7i	−0.275824	+	1.56427i	0.460510	+	0.887655i	$0.347667\pi$
$661$	−3.09838e6	+	1.75718e7i	−0.275824	+	1.56427i	−0.736333	+	0.676619i	$0.763444\pi$
$662$	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	0.583523	−	0.812096i	$-0.301674\pi$
$673$	−4.83553e6	−	8.37538e6i	−0.411535	−	0.712799i	−0.995058	+	0.0992977i	$0.968340\pi$
$674$	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	−0.533566	−	0.845759i	$-0.679148\pi$
$677$	5.55323e6	−	9.61848e6i	0.465665	−	0.806556i	0.999231	+	0.0392023i	$0.0124817\pi$
$678$	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	−0.972616	−	0.232418i	$-0.925336\pi$
$691$	−3.57752e6	+	6.19645e6i	−0.285028	+	0.493683i	0.687588	+	0.726101i	$0.258670\pi$
$692$	−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	−0.984676	−	0.174396i	$-0.944203\pi$
$701$	−1.28013e7	+	1.07415e7i	−0.983917	+	0.825604i	0.000759093		1.00000i	$0.499758\pi$
$702$	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	−0.180470	−	0.983580i	$-0.557762\pi$
$709$	4.19636e6	−	1.52735e6i	0.313514	−	0.114110i	0.493985	+	0.869470i	$0.335540\pi$
$710$	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	0.0519692	−	0.998649i	$-0.483450\pi$
$719$	−7.62596e6	−	2.77562e6i	−0.550139	−	0.200234i	−0.602108	+	0.798414i	$0.705672\pi$
$720$	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	0.989452	+	0.144860i	$0.0462733\pi$
$727$	1.55641e6	+	8.82684e6i	0.109216	+	0.619397i	−0.880236	+	0.474537i	$0.842616\pi$
$728$	−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	0.984138	−	0.177405i	$-0.0567702\pi$
$733$	4.92301e6	+	8.52691e6i	0.338432	+	0.586181i	−0.645706	+	0.763586i	$0.723437\pi$
$734$	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	−0.901353	−	0.433085i	$-0.857425\pi$
$739$	−9.37329e6	+	7.86512e6i	−0.631365	+	0.529778i	0.269988	+	0.962864i	$0.412980\pi$
$740$	−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	−0.586500	−	0.809949i	$-0.699495\pi$
$743$	1.64471e6	−	1.38008e6i	0.109300	−	0.0917132i	0.695800	+	0.718236i	$0.255050\pi$
$744$	−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	0.983699	−	0.179824i	$-0.0575528\pi$
$751$	1.51072e7	+	1.26764e7i	0.977424	+	0.820156i	−0.00627458	+	0.999980i	$0.501997\pi$
$752$	−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	−0.591331	−	0.806429i	$-0.701397\pi$
$757$	−2.46382e7	−	8.96758e6i	−1.56268	−	0.568769i	−0.971348	+	0.237661i	$0.923619\pi$
$758$	−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	0.269568	−	0.962981i	$-0.413119\pi$
$769$	−1.03637e7	−	8.69617e6i	−0.631973	−	0.530288i	−0.901541	+	0.432693i	$0.857563\pi$
$770$	−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	−0.679560	−	0.733619i	$-0.737829\pi$
$773$	−1.21038e7	+	4.40542e6i	−0.728572	+	0.265179i	−0.0490120	+	0.998798i	$0.515607\pi$
$774$	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	0.861204	−	0.508260i	$-0.169711\pi$
$787$	−166178.	−	287829.i	−0.00956395	−	0.0165653i	−0.870768	+	0.491695i	$0.836378\pi$
$788$	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	0.940816	−	0.338919i	$-0.110061\pi$
$809$	3.29297e6	+	5.70359e6i	0.176895	+	0.306391i	−0.763920	+	0.645311i	$0.776728\pi$
$810$	1.20337e6	−	2.08429e6i	0.0644444	−	0.111621i
$811$	2.50115e7	−	9.10345e6i	1.33533	−	0.486020i	0.426991	−	0.904256i	$-0.359574\pi$
$811$	2.50115e7	−	9.10345e6i	1.33533	−	0.486020i	0.908338	+	0.418236i	$0.137352\pi$
$812$	−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	−0.369672	−	0.929162i	$-0.620530\pi$
$821$	5.70707e6	−	3.23664e7i	0.295498	−	1.67585i	0.665170	−	0.746692i	$-0.268359\pi$
$822$	−441802.	−	2.50558e6i	−0.0228059	−	0.129339i
$823$	−8.40935e6	+	3.06075e6i	−0.432776	+	0.157517i	−0.549216	−	0.835680i	$-0.685074\pi$
$823$	−8.40935e6	+	3.06075e6i	−0.432776	+	0.157517i	0.116441	+	0.993198i	$0.462852\pi$
$824$	−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	0.349756	−	0.936841i	$-0.386265\pi$
$827$	−1.00724e7	−	8.45177e6i	−0.512118	−	0.429718i	−0.861874	+	0.507123i	$0.830709\pi$
$828$	−1.07868e6	−	1.86833e6i	−0.0546786	−	0.0947062i
$829$	536322.	−	928938.i	0.0271044	−	0.0469462i	−0.852155	−	0.523289i	$-0.824705\pi$
$829$	536322.	−	928938.i	0.0271044	−	0.0469462i	0.879259	+	0.476343i	$0.158038\pi$
$830$	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	−0.627044	−	0.778984i	$-0.715735\pi$
$839$	−3.27884e7	−	1.19340e7i	−1.60811	−	0.585304i	−0.981065	+	0.193681i	$0.937957\pi$
$840$	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	−0.253108	−	0.967438i	$-0.581453\pi$
$853$	1.39337e7	−	1.16917e7i	0.655681	−	0.550182i	0.908789	+	0.417256i	$0.137008\pi$
$854$	−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	0.199014	−	0.979997i	$-0.436226\pi$
$857$	2.57724e7	−	2.16256e7i	1.19868	−	1.00581i	0.999667	−	0.0258156i	$-0.00821828\pi$
$858$	−36134.4	−	13151.9i	−0.00167573	−	0.000609914i
$859$	5.46694e6	−	3.10045e7i	0.252791	−	1.43365i	−0.548889	−	0.835895i	$-0.684949\pi$
$859$	5.46694e6	−	3.10045e7i	0.252791	−	1.43365i	0.801680	−	0.597753i	$-0.203940\pi$
$860$	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	0.916397	−	0.400271i	$-0.131084\pi$
$863$	2.44068e6	+	4.22739e6i	0.111554	+	0.193217i	−0.804843	+	0.593488i	$0.797751\pi$
$864$	−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	0.461707	−	0.887032i	$-0.347237\pi$
$877$	5.58544e6	+	2.03294e6i	0.245222	+	0.0892534i	−0.216485	+	0.976286i	$0.569459\pi$
$878$	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	−0.572043	−	0.820224i	$-0.693849\pi$
$881$	9.77522e6	−	1.69312e7i	0.424313	−	0.734932i	0.996356	+	0.0852917i	$0.0271822\pi$
$882$	1.01382e7	+	1.75598e7i	0.438822	+	0.760062i
$883$	1.68331e7	+	1.41247e7i	0.726546	+	0.609645i	0.929188	−	0.369608i	$-0.120508\pi$
$883$	1.68331e7	+	1.41247e7i	0.726546	+	0.609645i	−0.202641	+	0.979253i	$0.564953\pi$
$884$	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	−0.388983	−	0.921245i	$-0.627174\pi$
$887$	−2.22127e6	+	808475.i	−0.0947963	+	0.0345030i	0.294187	+	0.955748i	$0.404951\pi$
$888$	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	0.927517	+	0.373780i	$0.121938\pi$
$907$	4.55311e6	+	2.58220e7i	0.183776	+	1.04225i	−0.743741	+	0.668468i	$0.766950\pi$
$908$	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	−0.873524	−	0.486781i	$-0.838171\pi$
$919$	−389089.	+	673922.i	−0.0151971	+	0.0263221i	0.858327	+	0.513103i	$0.171504\pi$
$920$	−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	−0.973622	−	0.228166i	$-0.926727\pi$
$929$	−2.41478e7	+	2.02624e7i	−0.917990	+	0.770285i	0.0556320	+	0.998451i	$0.482283\pi$
$930$	−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	−0.790424	−	0.612560i	$-0.790140\pi$
$937$	−2.69336e7	+	9.80302e6i	−1.00218	+	0.364763i	−0.211754	+	0.977323i	$0.567918\pi$
$938$	−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	0.999487	−	0.0320426i	$-0.0102012\pi$
$941$	3.10060e7	+	2.60171e7i	1.14149	+	0.957824i	0.142003	+	0.989866i	$0.454646\pi$
$942$	−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	0.541521	−	0.840687i	$-0.317849\pi$
$947$	1.14798e7	+	4.17830e6i	0.415967	+	0.151400i	−0.125554	+	0.992087i	$0.540071\pi$
$948$	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	−0.341294	−	0.939957i	$-0.610865\pi$
$953$	−3.38388e7	−	1.23163e7i	−1.20693	−	0.439287i	−0.865639	+	0.500669i	$0.833087\pi$
$954$	−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	−0.566165	−	0.824292i	$-0.691574\pi$
$967$	4.28291e6	−	3.59379e6i	0.147290	−	0.123591i	0.713455	+	0.700701i	$0.247129\pi$
$968$	−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	−0.785714	−	0.618590i	$-0.787704\pi$
$971$	−9.19466e6	+	7.71524e6i	−0.312959	+	0.262604i	0.472755	+	0.881194i	$0.343260\pi$
$972$	−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	−0.999006	−	0.0445811i	$-0.985805\pi$
$977$	−1.60549e7	−	2.78080e7i	−0.538111	−	0.932036i	0.460895	−	0.887455i	$-0.347529\pi$
$978$	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	0.995952	−	0.0898901i	$-0.0286516\pi$
$983$	888246.	+	5.03749e6i	0.0293190	+	0.166276i	−0.966633	+	0.256167i	$0.917540\pi$
$984$	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	0.269655	−	0.962957i	$-0.413090\pi$
$991$	−4.41340e6	−	1.60635e6i	−0.142754	−	0.0519583i	−0.412409	+	0.910999i	$0.635313\pi$
$992$	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	0.565346	−	0.824854i	$-0.308743\pi$
$997$	−4.67044e6	−	3.91897e6i	−0.148806	−	0.124863i	−0.714152	+	0.699991i	$0.753187\pi$
$998$	−2.36192e7	−	1.98189e7i	−0.750653	−	0.629873i
$999$	881620.	+	1.52701e6i	0.0279491	+	0.0484092i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.25.3	✓	30	1.1	even	1	trivial
38.6.e.b.35.3	yes	30	19.16	even	9	inner
722.6.a.q.1.7		15	19.15	odd	18
722.6.a.r.1.9		15	19.4	even	9

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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