LMFDB - Embedded newform 165.6.c.a.34.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, 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:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.4
Character	$\chi$	$=$	165.34
Dual form			165.6.c.a.34.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.30687i q^{2} +9.00000i q^{3} -37.0041 q^{4} +(41.8926 + 37.0137i) q^{5} +74.7618 q^{6} +54.6353i q^{7} +41.5686i q^{8} -81.0000 q^{9} +(307.468 - 347.996i) q^{10} -121.000 q^{11} -333.037i q^{12} -175.063i q^{13} +453.849 q^{14} +(-333.123 + 377.033i) q^{15} -838.827 q^{16} +1248.20i q^{17} +672.857i q^{18} -1248.23 q^{19} +(-1550.20 - 1369.66i) q^{20} -491.718 q^{21} +1005.13i q^{22} +2563.30i q^{23} -374.117 q^{24} +(384.972 + 3101.20i) q^{25} -1454.23 q^{26} -729.000i q^{27} -2021.73i q^{28} -3450.78 q^{29} +(3131.96 + 2767.21i) q^{30} +3171.29 q^{31} +8298.22i q^{32} -1089.00i q^{33} +10368.6 q^{34} +(-2022.26 + 2288.81i) q^{35} +2997.33 q^{36} +15357.2i q^{37} +10368.9i q^{38} +1575.57 q^{39} +(-1538.61 + 1741.41i) q^{40} -14538.0 q^{41} +4084.64i q^{42} -7671.37i q^{43} +4477.50 q^{44} +(-3393.30 - 2998.11i) q^{45} +21293.0 q^{46} +21772.6i q^{47} -7549.44i q^{48} +13822.0 q^{49} +(25761.2 - 3197.92i) q^{50} -11233.8 q^{51} +6478.06i q^{52} -38910.5i q^{53} -6055.71 q^{54} +(-5069.00 - 4478.66i) q^{55} -2271.11 q^{56} -11234.1i q^{57} +28665.2i q^{58} +4608.63 q^{59} +(12326.9 - 13951.8i) q^{60} -5627.67 q^{61} -26343.5i q^{62} -4425.46i q^{63} +42089.8 q^{64} +(6479.73 - 7333.84i) q^{65} -9046.18 q^{66} +35573.8i q^{67} -46188.5i q^{68} -23069.7 q^{69} +(19012.9 + 16798.6i) q^{70} +33448.0 q^{71} -3367.05i q^{72} +18523.8i q^{73} +127571. q^{74} +(-27910.8 + 3464.75i) q^{75} +46189.6 q^{76} -6610.88i q^{77} -13088.0i q^{78} -15606.1 q^{79} +(-35140.6 - 31048.1i) q^{80} +6561.00 q^{81} +120765. i q^{82} +76298.1i q^{83} +18195.6 q^{84} +(-46200.4 + 52290.2i) q^{85} -63725.1 q^{86} -31057.0i q^{87} -5029.80i q^{88} +59295.1 q^{89} +(-24904.9 + 28187.7i) q^{90} +9564.63 q^{91} -94852.8i q^{92} +28541.6i q^{93} +180863. q^{94} +(-52291.5 - 46201.6i) q^{95} -74684.0 q^{96} +77264.9i q^{97} -114817. i q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 458 q^{4} - 98 q^{5} - 54 q^{6} - 2106 q^{9} - 1944 q^{10} - 3146 q^{11} + 5516 q^{14} + 8282 q^{16} + 620 q^{19} + 1594 q^{20} - 5112 q^{21} + 6642 q^{24} + 10778 q^{25} + 4560 q^{26} + 9696 q^{29}+ \cdots + 254826 q^{99}+O(q^{100}) $ 26 * q - 458 * q^4 - 98 * q^5 - 54 * q^6 - 2106 * q^9 - 1944 * q^10 - 3146 * q^11 + 5516 * q^14 + 8282 * q^16 + 620 * q^19 + 1594 * q^20 - 5112 * q^21 + 6642 * q^24 + 10778 * q^25 + 4560 * q^26 + 9696 * q^29 - 9378 * q^30 - 48 * q^31 - 11036 * q^34 + 17748 * q^35 + 37098 * q^36 + 6588 * q^39 + 46308 * q^40 - 30240 * q^41 + 55418 * q^44 + 7938 * q^45 - 40560 * q^46 - 163674 * q^49 + 81164 * q^50 - 37008 * q^51 + 4374 * q^54 + 11858 * q^55 - 393204 * q^56 + 131184 * q^59 + 127260 * q^60 - 104084 * q^61 - 371954 * q^64 + 43108 * q^65 + 6534 * q^66 + 65016 * q^69 + 228364 * q^70 - 155640 * q^71 + 480056 * q^74 + 74232 * q^75 - 542348 * q^76 + 224516 * q^79 + 428642 * q^80 + 170586 * q^81 + 142128 * q^84 - 124796 * q^85 - 638500 * q^86 + 591620 * q^89 + 157464 * q^90 - 48400 * q^91 + 716288 * q^94 - 35124 * q^95 - 685998 * q^96 + 254826 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	8.30687i		−	1.46846i	−0.678900	−	0.734231i	$-0.737543\pi$
$2$		−	8.30687i		−	1.46846i	0.678900	−	0.734231i	$-0.262457\pi$
$3$			9.00000i			0.577350i
$3$			9.00000i			0.577350i
$4$	−37.0041			−1.15638
$5$	41.8926	+	37.0137i	0.749397	+	0.662121i
$5$	41.8926	+	37.0137i	0.749397	+	0.662121i
$6$	74.7618			0.847817
$7$			54.6353i			0.421433i	0.977547	+	0.210717i	$0.0675797\pi$
$7$			54.6353i			0.421433i	−0.977547	+	0.210717i	$0.932420\pi$
$8$			41.5686i			0.229636i
$9$	−81.0000			−0.333333
$10$	307.468	−	347.996i	0.972299	−	1.10046i
$11$	−121.000			−0.301511
$11$	−121.000			−0.301511
$12$		−	333.037i		−	0.667636i
$13$		−	175.063i		−	0.287300i	−0.989629	−	0.143650i	$-0.954116\pi$
$13$		−	175.063i		−	0.287300i	0.989629	−	0.143650i	$-0.0458840\pi$
$14$	453.849			0.618858
$15$	−333.123	+	377.033i	−0.382276	+	0.432664i
$16$	−838.827			−0.819167
$17$			1248.20i			1.04752i	0.851867	+	0.523758i	$0.175471\pi$
$17$			1248.20i			1.04752i	−0.851867	+	0.523758i	$0.824529\pi$
$18$			672.857i			0.489487i
$19$	−1248.23			−0.793251			−0.396625	−	0.917981i	$-0.629819\pi$
$19$	−1248.23			−0.793251			−0.396625	+	0.917981i	$0.629819\pi$
$20$	−1550.20	−	1369.66i	−0.866587	−	0.765663i
$21$	−491.718			−0.243314
$22$			1005.13i			0.442758i
$23$			2563.30i			1.01037i	0.863011	+	0.505185i	$0.168576\pi$
$23$			2563.30i			1.01037i	−0.863011	+	0.505185i	$0.831424\pi$
$24$	−374.117			−0.132580
$25$	384.972	+	3101.20i	0.123191	+	0.992383i
$26$	−1454.23			−0.421890
$27$		−	729.000i		−	0.192450i
$28$		−	2021.73i		−	0.487336i
$29$	−3450.78			−0.761943			−0.380972	−	0.924587i	$-0.624410\pi$
$29$	−3450.78			−0.761943			−0.380972	+	0.924587i	$0.624410\pi$
$30$	3131.96	+	2767.21i	0.635351	+	0.561357i
$31$	3171.29			0.592695			0.296348	−	0.955080i	$-0.404231\pi$
$31$	3171.29			0.592695			0.296348	+	0.955080i	$0.404231\pi$
$32$			8298.22i			1.43255i
$33$		−	1089.00i		−	0.174078i
$34$	10368.6			1.53824
$35$	−2022.26	+	2288.81i	−0.279040	+	0.315821i
$36$	2997.33			0.385460
$37$			15357.2i			1.84420i	0.386947	+	0.922102i	$0.373530\pi$
$37$			15357.2i			1.84420i	−0.386947	+	0.922102i	$0.626470\pi$
$38$			10368.9i			1.16486i
$39$	1575.57			0.165873
$40$	−1538.61	+	1741.41i	−0.152047	+	0.172089i
$41$	−14538.0			−1.35066			−0.675329	−	0.737517i	$-0.735998\pi$
$41$	−14538.0			−1.35066			−0.675329	+	0.737517i	$0.735998\pi$
$42$			4084.64i			0.357298i
$43$		−	7671.37i		−	0.632706i	−0.948642	−	0.316353i	$-0.897542\pi$
$43$		−	7671.37i		−	0.632706i	0.948642	−	0.316353i	$-0.102458\pi$
$44$	4477.50			0.348661
$45$	−3393.30	−	2998.11i	−0.249799	−	0.220707i
$46$	21293.0			1.48369
$47$			21772.6i			1.43769i	0.695168	+	0.718847i	$0.255330\pi$
$47$			21772.6i			1.43769i	−0.695168	+	0.718847i	$0.744670\pi$
$48$		−	7549.44i		−	0.472946i
$49$	13822.0			0.822394
$50$	25761.2	−	3197.92i	1.45728	−	0.180901i
$51$	−11233.8			−0.604784
$52$			6478.06i			0.332228i
$53$		−	38910.5i		−	1.90273i	−0.308070	−	0.951364i	$-0.599683\pi$
$53$		−	38910.5i		−	1.90273i	0.308070	−	0.951364i	$-0.400317\pi$
$54$	−6055.71			−0.282606
$55$	−5069.00	−	4478.66i	−0.225952	−	0.199637i
$56$	−2271.11			−0.0967762
$57$		−	11234.1i		−	0.457984i
$58$			28665.2i			1.11888i
$59$	4608.63			0.172362			0.0861810	−	0.996279i	$-0.472534\pi$
$59$	4608.63			0.172362			0.0861810	+	0.996279i	$0.472534\pi$
$60$	12326.9	−	13951.8i	0.442056	−	0.500324i
$61$	−5627.67			−0.193644			−0.0968220	−	0.995302i	$-0.530868\pi$
$61$	−5627.67			−0.193644			−0.0968220	+	0.995302i	$0.530868\pi$
$62$		−	26343.5i		−	0.870350i
$63$		−	4425.46i		−	0.140478i
$64$	42089.8			1.28448
$65$	6479.73	−	7333.84i	0.190228	−	0.215302i
$66$	−9046.18			−0.255626
$67$			35573.8i			0.968150i	0.875026	+	0.484075i	$0.160844\pi$
$67$			35573.8i			0.968150i	−0.875026	+	0.484075i	$0.839156\pi$
$68$		−	46188.5i		−	1.21133i
$69$	−23069.7			−0.583338
$70$	19012.9	+	16798.6i	0.463770	+	0.409759i
$71$	33448.0			0.787453			0.393727	−	0.919228i	$-0.371186\pi$
$71$	33448.0			0.787453			0.393727	+	0.919228i	$0.371186\pi$
$72$		−	3367.05i		−	0.0765454i
$73$			18523.8i			0.406839i	0.979092	+	0.203420i	$0.0652056\pi$
$73$			18523.8i			0.406839i	−0.979092	+	0.203420i	$0.934794\pi$
$74$	127571.			2.70814
$75$	−27910.8	+	3464.75i	−0.572953	+	0.0711245i
$76$	46189.6			0.917298
$77$		−	6610.88i		−	0.127067i
$78$		−	13088.0i		−	0.243578i
$79$	−15606.1			−0.281336			−0.140668	−	0.990057i	$-0.544925\pi$
$79$	−15606.1			−0.281336			−0.140668	+	0.990057i	$0.544925\pi$
$80$	−35140.6	−	31048.1i	−0.613881	−	0.542388i
$81$	6561.00			0.111111
$82$			120765.i			1.98339i
$83$			76298.1i			1.21568i	0.794060	+	0.607839i	$0.207963\pi$
$83$			76298.1i			1.21568i	−0.794060	+	0.607839i	$0.792037\pi$
$84$	18195.6			0.281364
$85$	−46200.4	+	52290.2i	−0.693583	+	0.785006i
$86$	−63725.1			−0.929104
$87$		−	31057.0i		−	0.439908i
$88$		−	5029.80i		−	0.0692379i
$89$	59295.1			0.793494			0.396747	−	0.917928i	$-0.370139\pi$
$89$	59295.1			0.793494			0.396747	+	0.917928i	$0.370139\pi$
$90$	−24904.9	+	28187.7i	−0.324100	+	0.366820i
$91$	9564.63			0.121078
$92$		−	94852.8i		−	1.16837i
$93$			28541.6i			0.342193i
$94$	180863.			2.11120
$95$	−52291.5	−	46201.6i	−0.594460	−	0.525228i
$96$	−74684.0			−0.827084
$97$			77264.9i			0.833783i	0.908956	+	0.416891i	$0.136880\pi$
$97$			77264.9i			0.833783i	−0.908956	+	0.416891i	$0.863120\pi$
$98$		−	114817.i		−	1.20765i
$99$	9801.00			0.100504
$100$	−14245.6	−	114757.i	−0.142456	−	1.14757i
$101$	−143856.			−1.40322			−0.701609	−	0.712562i	$-0.747535\pi$
$101$	−143856.			−1.40322			−0.701609	+	0.712562i	$0.747535\pi$
$102$			93317.6i			0.888102i
$103$			84193.3i			0.781960i	0.920399	+	0.390980i	$0.127864\pi$
$103$			84193.3i			0.781960i	−0.920399	+	0.390980i	$0.872136\pi$
$104$	7277.12			0.0659746
$105$	−20599.3	−	18200.3i	−0.182339	−	0.161104i
$106$	−323224.			−2.79408
$107$		−	148939.i		−	1.25762i	−0.777560	−	0.628808i	$-0.783543\pi$
$107$		−	148939.i		−	1.25762i	0.777560	−	0.628808i	$-0.216457\pi$
$108$			26976.0i			0.222545i
$109$	−88621.2			−0.714449			−0.357225	−	0.934018i	$-0.616277\pi$
$109$	−88621.2			−0.714449			−0.357225	+	0.934018i	$0.616277\pi$
$110$	−37203.6	+	42107.5i	−0.293159	+	0.331801i
$111$	−138215.			−1.06475
$112$		−	45829.6i		−	0.345224i
$113$		−	76122.3i		−	0.560810i	−0.959882	−	0.280405i	$-0.909531\pi$
$113$		−	76122.3i		−	0.560810i	0.959882	−	0.280405i	$-0.0904687\pi$
$114$	−93320.0			−0.672531
$115$	−94877.4	+	107383.i	−0.668987	+	0.757168i
$116$	127693.			0.881095
$117$			14180.1i			0.0957668i
$118$		−	38283.3i		−	0.253107i
$119$	−68195.7			−0.441458
$120$	−15672.7	−	13847.5i	−0.0993554	−	0.0877843i
$121$	14641.0			0.0909091
$122$			46748.3i			0.284359i
$123$		−	130842.i		−	0.779803i
$124$	−117351.			−0.685380
$125$	−98659.3	+	144166.i	−0.564759	+	0.825256i
$126$	−36761.8			−0.206286
$127$			133153.i			0.732559i	0.930505	+	0.366280i	$0.119369\pi$
$127$			133153.i			0.732559i	−0.930505	+	0.366280i	$0.880631\pi$
$128$		−	84091.5i		−	0.453657i
$129$	69042.3			0.365293
$130$	−60921.3	−	53826.3i	−0.316163	−	0.279342i
$131$	−128189.			−0.652639			−0.326319	−	0.945260i	$-0.605808\pi$
$131$	−128189.			−0.652639			−0.326319	+	0.945260i	$0.605808\pi$
$132$			40297.5i			0.201300i
$133$		−	68197.5i		−	0.334302i
$134$	295507.			1.42169
$135$	26983.0	−	30539.7i	0.127425	−	0.144221i
$136$	−51885.8			−0.240548
$137$		−	221707.i		−	1.00920i	−0.863353	−	0.504601i	$-0.831640\pi$
$137$		−	221707.i		−	1.00920i	0.863353	−	0.504601i	$-0.168360\pi$
$138$			191637.i			0.856609i
$139$	−105276.			−0.462160			−0.231080	−	0.972935i	$-0.574226\pi$
$139$	−105276.			−0.462160			−0.231080	+	0.972935i	$0.574226\pi$
$140$	74831.8	−	84695.5i	0.322676	−	0.365208i
$141$	−195954.			−0.830053
$142$		−	277849.i		−	1.15634i
$143$			21182.6i			0.0866243i
$144$	67945.0			0.273056
$145$	−144562.	−	127726.i	−0.570998	−	0.504499i
$146$	153875.			0.597428
$147$			124398.i			0.474810i
$148$		−	568281.i		−	2.13260i
$149$	408871.			1.50876			0.754381	−	0.656437i	$-0.227937\pi$
$149$	408871.			1.50876			0.754381	+	0.656437i	$0.227937\pi$
$150$	28781.2	+	231851.i	0.104444	+	0.841359i
$151$	382934.			1.36673			0.683364	−	0.730078i	$-0.260516\pi$
$151$	382934.			1.36673			0.683364	+	0.730078i	$0.260516\pi$
$152$		−	51887.1i		−	0.182159i
$153$		−	101104.i		−	0.349172i
$154$	−54915.7			−0.186593
$155$	132853.	+	117381.i	0.444164	+	0.392436i
$156$	−58302.5			−0.191812
$157$		−	367155.i		−	1.18878i	−0.804178	−	0.594389i	$-0.797394\pi$
$157$		−	367155.i		−	1.18878i	0.804178	−	0.594389i	$-0.202606\pi$
$158$			129637.i			0.413131i
$159$	350194.			1.09854
$160$	−307148.	+	347634.i	−0.948522	+	1.07355i
$161$	−140047.			−0.425803
$162$		−	54501.4i		−	0.163162i
$163$			32509.1i			0.0958377i	0.998851	+	0.0479188i	$0.0152589\pi$
$163$			32509.1i			0.0958377i	−0.998851	+	0.0479188i	$0.984741\pi$
$164$	537966.			1.56187
$165$	40307.9	−	45621.0i	0.115260	−	0.130453i
$166$	633799.			1.78518
$167$		−	526634.i		−	1.46123i	−0.682791	−	0.730613i	$-0.739234\pi$
$167$		−	526634.i		−	1.46123i	0.682791	−	0.730613i	$-0.260766\pi$
$168$		−	20440.0i		−	0.0558738i
$169$	340646.			0.917458
$170$	434368.	+	383781.i	1.15275	+	1.01850i
$171$	101107.			0.264417
$172$			283872.i			0.731648i
$173$		−	162431.i		−	0.412623i	−0.978486	−	0.206312i	$-0.933854\pi$
$173$		−	162431.i		−	0.412623i	0.978486	−	0.206312i	$-0.0661461\pi$
$174$	−257987.			−0.645988
$175$	−169435.	+	21033.1i	−0.418223	+	0.0519168i
$176$	101498.			0.246988
$177$			41477.6i			0.0995132i
$178$		−	492557.i		−	1.16522i
$179$	−632163.			−1.47468			−0.737338	−	0.675524i	$-0.763918\pi$
$179$	−632163.			−1.47468			−0.737338	+	0.675524i	$0.763918\pi$
$180$	125566.	+	110942.i	0.288862	+	0.255221i
$181$	−447428.			−1.01514			−0.507571	−	0.861610i	$-0.669456\pi$
$181$	−447428.			−1.01514			−0.507571	+	0.861610i	$0.669456\pi$
$182$		−	79452.2i		−	0.177798i
$183$		−	50649.0i		−	0.111800i
$184$	−106553.			−0.232017
$185$	−568428.	+	643354.i	−1.22109	+	1.38204i
$186$	237091.			0.502497
$187$		−	151032.i		−	0.315838i
$188$		−	805677.i		−	1.66252i
$189$	39829.2			0.0811048
$190$	−383791.	+	434379.i	−0.771277	+	0.872941i
$191$	−79686.3			−0.158052			−0.0790261	−	0.996873i	$-0.525181\pi$
$191$	−79686.3			−0.158052			−0.0790261	+	0.996873i	$0.525181\pi$
$192$			378808.i			0.741594i
$193$		−	115133.i		−	0.222488i	−0.993793	−	0.111244i	$-0.964516\pi$
$193$		−	115133.i		−	0.222488i	0.993793	−	0.111244i	$-0.0354835\pi$
$194$	641830.			1.22438
$195$	66004.6	+	58317.6i	0.124305	+	0.109828i
$196$	−511470.			−0.950999
$197$		−	359835.i		−	0.660600i	−0.943876	−	0.330300i	$-0.892850\pi$
$197$		−	359835.i		−	0.660600i	0.943876	−	0.330300i	$-0.107150\pi$
$198$		−	81415.7i		−	0.147586i
$199$	281811.			0.504459			0.252229	−	0.967667i	$-0.418836\pi$
$199$	281811.			0.504459			0.252229	+	0.967667i	$0.418836\pi$
$200$	−128912.	+	16002.8i	−0.227887	+	0.0282891i
$201$	−320164.			−0.558962
$202$			1.19500e6i			2.06057i
$203$		−	188535.i		−	0.321108i
$204$	415696.			0.699360
$205$	−609034.	−	538105.i	−1.01218	−	0.894299i
$206$	699383.			1.14828
$207$		−	207628.i		−	0.336790i
$208$			146848.i			0.235347i
$209$	151036.			0.239174
$210$	−151188.	+	171116.i	−0.236574	+	0.267758i
$211$	791279.			1.22356			0.611778	−	0.791030i	$-0.290455\pi$
$211$	791279.			1.22356			0.611778	+	0.791030i	$0.290455\pi$
$212$			1.43985e6i			2.20027i
$213$			301032.i			0.454636i
$214$	−1.23722e6			−1.84676
$215$	283946.	−	321373.i	0.418928	−	0.474148i
$216$	30303.5			0.0441935
$217$			173264.i			0.249781i
$218$			736165.i			1.04914i
$219$	−166714.			−0.234889
$220$	187574.	+	165729.i	0.261286	+	0.230856i
$221$	218513.			0.300952
$222$			1.14814e6i			1.56355i
$223$			80187.6i			0.107980i	0.998541	+	0.0539902i	$0.0171940\pi$
$223$			80187.6i			0.107980i	−0.998541	+	0.0539902i	$0.982806\pi$
$224$	−453376.			−0.603724
$225$	−31182.8	−	251197.i	−0.0410637	−	0.330794i
$226$	−632338.			−0.823528
$227$			538847.i			0.694066i	0.937853	+	0.347033i	$0.112811\pi$
$227$			538847.i			0.694066i	−0.937853	+	0.347033i	$0.887189\pi$
$228$			415707.i			0.529602i
$229$	−431400.			−0.543616			−0.271808	−	0.962352i	$-0.587621\pi$
$229$	−431400.			−0.543616			−0.271808	+	0.962352i	$0.587621\pi$
$230$	892020.	+	788134.i	1.11187	+	0.982382i
$231$	59497.9			0.0733621
$232$		−	143444.i		−	0.174970i
$233$		−	1.56748e6i		−	1.89152i	−0.324866	−	0.945760i	$-0.605319\pi$
$233$		−	1.56748e6i		−	1.89152i	0.324866	−	0.945760i	$-0.394681\pi$
$234$	117792.			0.140630
$235$	−805886.	+	912111.i	−0.951927	+	1.07740i
$236$	−170538.			−0.199316
$237$		−	140454.i		−	0.162429i
$238$			566493.i			0.648264i
$239$	402820.			0.456159			0.228079	−	0.973643i	$-0.426755\pi$
$239$	402820.			0.456159			0.228079	+	0.973643i	$0.426755\pi$
$240$	279433.	−	316265.i	0.313148	−	0.354424i
$241$	1.08492e6			1.20325			0.601625	−	0.798779i	$-0.294520\pi$
$241$	1.08492e6			1.20325			0.601625	+	0.798779i	$0.294520\pi$
$242$		−	121621.i		−	0.133496i
$243$			59049.0i			0.0641500i
$244$	208247.			0.223926
$245$	579038.	+	511603.i	0.616300	+	0.544525i
$246$	−1.08689e6			−1.14511
$247$			218519.i			0.227901i
$248$			131826.i			0.136104i
$249$	−686683.			−0.701872
$250$	1.19757e6	+	819550.i	1.21186	+	0.829326i
$251$	705007.			0.706332			0.353166	−	0.935561i	$-0.385105\pi$
$251$	705007.			0.706332			0.353166	+	0.935561i	$0.385105\pi$
$252$			163760.i			0.162445i
$253$		−	310160.i		−	0.304638i
$254$	1.10609e6			1.07573
$255$	−470612.	−	415804.i	−0.453223	−	0.400440i
$256$	648336.			0.618302
$257$		−	247273.i		−	0.233530i	−0.993160	−	0.116765i	$-0.962748\pi$
$257$		−	247273.i		−	0.233530i	0.993160	−	0.116765i	$-0.0372525\pi$
$258$		−	573526.i		−	0.536418i
$259$	−839048.			−0.777209
$260$	−239777.	+	271382.i	−0.219975	+	0.248971i
$261$	279513.			0.253981
$262$			1.06485e6i			0.958375i
$263$		−	270166.i		−	0.240847i	−0.992723	−	0.120423i	$-0.961575\pi$
$263$		−	270166.i		−	0.240847i	0.992723	−	0.120423i	$-0.0384252\pi$
$264$	45268.2			0.0399745
$265$	1.44022e6	−	1.63006e6i	1.25984	−	1.42590i
$266$	−566507.			−0.490910
$267$			533656.i			0.458124i
$268$		−	1.31638e6i		−	1.11955i
$269$	−838616.			−0.706614			−0.353307	−	0.935507i	$-0.614943\pi$
$269$	−838616.			−0.706614			−0.353307	+	0.935507i	$0.614943\pi$
$270$	−253689.	−	224144.i	−0.211784	−	0.187119i
$271$	1.01547e6			0.839930			0.419965	−	0.907540i	$-0.362042\pi$
$271$	1.01547e6			0.839930			0.419965	+	0.907540i	$0.362042\pi$
$272$		−	1.04702e6i		−	0.858091i
$273$			86081.7i			0.0699044i
$274$	−1.84169e6			−1.48197
$275$	−46581.7	−	375245.i	−0.0371435	−	0.299215i
$276$	853675.			0.674559
$277$			688627.i			0.539243i	0.962966	+	0.269622i	$0.0868986\pi$
$277$			688627.i			0.539243i	−0.962966	+	0.269622i	$0.913101\pi$
$278$			874514.i			0.678664i
$279$	−256874.			−0.197565
$280$	−95142.7	−	84062.3i	−0.0725238	−	0.0640776i
$281$	−14371.5			−0.0108577			−0.00542885	−	0.999985i	$-0.501728\pi$
$281$	−14371.5			−0.0108577			−0.00542885	+	0.999985i	$0.501728\pi$
$282$			1.62776e6i			1.21890i
$283$		−	1.23554e6i		−	0.917044i	−0.888683	−	0.458522i	$-0.848379\pi$
$283$		−	1.23554e6i		−	0.917044i	0.888683	−	0.458522i	$-0.151621\pi$
$284$	−1.23772e6			−0.910594
$285$	415814.	−	470624.i	0.303241	−	0.343211i
$286$	175961.			0.127205
$287$		−	794289.i		−	0.569212i
$288$		−	672156.i		−	0.477517i
$289$	−138140.			−0.0972918
$290$	−1.06101e6	+	1.20086e6i	−0.740837	+	0.838488i
$291$	−695384.			−0.481385
$292$		−	685457.i		−	0.470460i
$293$			794280.i			0.540511i	0.962789	+	0.270256i	$0.0871082\pi$
$293$			794280.i			0.540511i	−0.962789	+	0.270256i	$0.912892\pi$
$294$	1.03336e6			0.697239
$295$	193067.	+	170582.i	0.129168	+	0.114125i
$296$	−638379.			−0.423496
$297$			88209.0i			0.0580259i
$298$		−	3.39644e6i		−	2.21556i
$299$	448740.			0.290280
$300$	1.03281e6	−	128210.i	0.662550	−	0.0822468i
$301$	419128.			0.266643
$302$		−	3.18099e6i		−	2.00699i
$303$		−	1.29471e6i		−	0.810148i
$304$	1.04705e6			0.649805
$305$	−235758.	−	208301.i	−0.145116	−	0.128216i
$306$	−839858.			−0.512746
$307$			2.78716e6i			1.68778i	0.536516	+	0.843890i	$0.319740\pi$
$307$			2.78716e6i			1.68778i	−0.536516	+	0.843890i	$0.680260\pi$
$308$			244630.i			0.146937i
$309$	−757740.			−0.451465
$310$	975069.	−	1.10360e6i	0.576277	−	0.652237i
$311$	−2.91123e6			−1.70677			−0.853386	−	0.521280i	$-0.825455\pi$
$311$	−2.91123e6			−1.70677			−0.853386	+	0.521280i	$0.825455\pi$
$312$			65494.1i			0.0380904i
$313$		−	563042.i		−	0.324848i	−0.986721	−	0.162424i	$-0.948069\pi$
$313$		−	563042.i		−	0.324848i	0.986721	−	0.162424i	$-0.0519312\pi$
$314$	−3.04991e6			−1.74567
$315$	163803.	−	185394.i	0.0930132	−	0.105274i
$316$	577488.			0.325331
$317$		−	442425.i		−	0.247282i	−0.992327	−	0.123641i	$-0.960543\pi$
$317$		−	442425.i		−	0.247282i	0.992327	−	0.123641i	$-0.0394571\pi$
$318$		−	2.90902e6i		−	1.61316i
$319$	417545.			0.229735
$320$	1.76325e6	+	1.55790e6i	0.962584	+	0.850481i
$321$	1.34045e6			0.726085
$322$			1.16335e6i			0.625276i
$323$		−	1.55804e6i		−	0.830944i
$324$	−242784.			−0.128487
$325$	542905.	−	67394.5i	0.285112	−	0.0353929i
$326$	270049.			0.140734
$327$		−	797591.i		−	0.412487i
$328$		−	604324.i		−	0.310160i
$329$	−1.18956e6			−0.605892
$330$	−378968.	−	334833.i	−0.191566	−	0.169256i
$331$	3.35851e6			1.68491			0.842454	−	0.538768i	$-0.181110\pi$
$331$	3.35851e6			1.68491			0.842454	+	0.538768i	$0.181110\pi$
$332$		−	2.82335e6i		−	1.40578i
$333$		−	1.24394e6i		−	0.614735i
$334$	−4.37468e6			−2.14576
$335$	−1.31672e6	+	1.49028e6i	−0.641033	+	0.725529i
$336$	412466.			0.199315
$337$			460497.i			0.220878i	0.993883	+	0.110439i	$0.0352256\pi$
$337$			460497.i			0.220878i	−0.993883	+	0.110439i	$0.964774\pi$
$338$		−	2.82970e6i		−	1.34725i
$339$	685100.			0.323784
$340$	1.70961e6	−	1.93495e6i	0.802045	−	0.907764i
$341$	−383726.			−0.178704
$342$		−	839880.i		−	0.388286i
$343$			1.67342e6i			0.768017i
$344$	318888.			0.145292
$345$	−966450.	−	853896.i	−0.437151	−	0.386240i
$346$	−1.34929e6			−0.605922
$347$			115478.i			0.0514846i	0.999669	+	0.0257423i	$0.00819493\pi$
$347$			115478.i			0.0514846i	−0.999669	+	0.0257423i	$0.991805\pi$
$348$			1.14924e6i			0.508700i
$349$	3.65056e6			1.60434			0.802168	−	0.597098i	$-0.203680\pi$
$349$	3.65056e6			1.60434			0.802168	+	0.597098i	$0.203680\pi$
$350$	174719.	+	1.40747e6i	0.0762379	+	0.614144i
$351$	−127621.			−0.0552910
$352$		−	1.00408e6i		−	0.431930i
$353$			2.90387e6i			1.24034i	0.784467	+	0.620170i	$0.212936\pi$
$353$			2.90387e6i			1.24034i	−0.784467	+	0.620170i	$0.787064\pi$
$354$	344549.			0.146131
$355$	1.40122e6	+	1.23804e6i	0.590115	+	0.521390i
$356$	−2.19416e6			−0.917580
$357$		−	613761.i		−	0.254876i
$358$			5.25130e6i			2.16551i
$359$	−4.14381e6			−1.69693			−0.848464	−	0.529254i	$-0.822472\pi$
$359$	−4.14381e6			−1.69693			−0.848464	+	0.529254i	$0.822472\pi$
$360$	124627.	−	141055.i	0.0506823	−	0.0573628i
$361$	−918022.			−0.370753
$362$			3.71673e6i			1.49070i
$363$			131769.i			0.0524864i
$364$	−353931.			−0.140012
$365$	−685634.	+	776009.i	−0.269377	+	0.304884i
$366$	−420735.			−0.164175
$367$			527417.i			0.204404i	0.994764	+	0.102202i	$0.0325888\pi$
$367$			527417.i			0.204404i	−0.994764	+	0.102202i	$0.967411\pi$
$368$		−	2.15017e6i		−	0.827662i
$369$	1.17758e6			0.450219
$370$	5.34426e6	+	4.72186e6i	2.02947	+	1.79312i
$371$	2.12589e6			0.801872
$372$		−	1.05616e6i		−	0.395704i
$373$		−	2.76612e6i		−	1.02944i	−0.857360	−	0.514718i	$-0.827897\pi$
$373$		−	2.76612e6i		−	1.02944i	0.857360	−	0.514718i	$-0.172103\pi$
$374$	−1.25460e6			−0.463796
$375$	−1.29750e6	−	887934.i	−0.476462	−	0.326064i
$376$	−905057.			−0.330146
$377$			604105.i			0.218907i
$378$		−	330856.i		−	0.119099i
$379$	−2.05750e6			−0.735769			−0.367884	−	0.929872i	$-0.619918\pi$
$379$	−2.05750e6			−0.735769			−0.367884	+	0.929872i	$0.619918\pi$
$380$	1.93500e6	+	1.70965e6i	0.687420	+	0.607363i
$381$	−1.19838e6			−0.422943
$382$			661944.i			0.232093i
$383$			4.97186e6i			1.73190i	0.500133	+	0.865949i	$0.333285\pi$
$383$			4.97186e6i			1.73190i	−0.500133	+	0.865949i	$0.666715\pi$
$384$	756824.			0.261919
$385$	244693.	−	276947.i	0.0841336	−	0.0952235i
$386$	−956396.			−0.326715
$387$			621381.i			0.210902i
$388$		−	2.85912e6i		−	0.964169i
$389$	−4.75117e6			−1.59194			−0.795970	−	0.605336i	$-0.793039\pi$
$389$	−4.75117e6			−1.59194			−0.795970	+	0.605336i	$0.793039\pi$
$390$	484437.	−	548292.i	0.161278	−	0.182537i
$391$	−3.19951e6			−1.05838
$392$			574560.i			0.188851i
$393$		−	1.15370e6i		−	0.376801i
$394$	−2.98911e6			−0.970065
$395$	−653777.	−	577638.i	−0.210832	−	0.186279i
$396$	−362677.			−0.116220
$397$			405.982i			0.000129280i	1.00000		6.46398e-5i	$2.05755e-5\pi$
$397$			405.982i			0.000129280i	−1.00000		6.46398e-5i	$0.999979\pi$
$398$		−	2.34097e6i		−	0.740778i
$399$	613777.			0.193009
$400$	−322925.	−	2.60137e6i	−0.100914	−	0.812927i
$401$	21666.1			0.00672851			0.00336426	−	0.999994i	$-0.498929\pi$
$401$	21666.1			0.00672851			0.00336426	+	0.999994i	$0.498929\pi$
$402$			2.65956e6i			0.820814i
$403$		−	555175.i		−	0.170282i
$404$	5.32327e6			1.62265
$405$	274857.	+	242847.i	0.0832663	+	0.0735690i
$406$	−1.56613e6			−0.471535
$407$		−	1.85823e6i		−	0.556049i
$408$		−	466972.i		−	0.138880i
$409$	−142989.			−0.0422664			−0.0211332	−	0.999777i	$-0.506727\pi$
$409$	−142989.			−0.0422664			−0.0211332	+	0.999777i	$0.506727\pi$
$410$	−4.46997e6	+	5.05917e6i	−1.31324	+	1.48635i
$411$	1.99536e6			0.582663
$412$		−	3.11550e6i		−	0.904242i
$413$			251794.i			0.0726390i
$414$	−1.72474e6			−0.494563
$415$	−2.82408e6	+	3.19632e6i	−0.804926	+	0.911026i
$416$	1.45271e6			0.411573
$417$		−	947484.i		−	0.266828i
$418$		−	1.25463e6i		−	0.351218i
$419$	454799.			0.126557			0.0632783	−	0.997996i	$-0.479844\pi$
$419$	454799.			0.126557			0.0632783	+	0.997996i	$0.479844\pi$
$420$	762260.	+	673486.i	0.210853	+	0.186297i
$421$	3.37870e6			0.929062			0.464531	−	0.885557i	$-0.346223\pi$
$421$	3.37870e6			0.929062			0.464531	+	0.885557i	$0.346223\pi$
$422$		−	6.57305e6i		−	1.79674i
$423$		−	1.76358e6i		−	0.479231i
$424$	1.61745e6			0.436935
$425$	−3.87091e6	+	480522.i	−1.03954	+	0.129045i
$426$	2.50064e6			0.667616
$427$		−	307470.i		−	0.0816080i
$428$			5.51135e6i			1.45428i
$429$	−190644.			−0.0500126
$430$	−2.66961e6	−	2.35870e6i	−0.696268	−	0.615179i
$431$	−5.68143e6			−1.47321			−0.736604	−	0.676324i	$-0.763572\pi$
$431$	−5.68143e6			−1.47321			−0.736604	+	0.676324i	$0.763572\pi$
$432$			611505.i			0.157649i
$433$			1.86171e6i			0.477191i	0.971119	+	0.238596i	$0.0766870\pi$
$433$			1.86171e6i			0.477191i	−0.971119	+	0.238596i	$0.923313\pi$
$434$	1.43928e6			0.366794
$435$	1.14954e6	−	1.30106e6i	0.291272	−	0.329666i
$436$	3.27935e6			0.826174
$437$		−	3.19959e6i		−	0.801477i
$438$			1.38487e6i			0.344925i
$439$	801463.			0.198482			0.0992412	−	0.995063i	$-0.468358\pi$
$439$	801463.			0.198482			0.0992412	+	0.995063i	$0.468358\pi$
$440$	186171.	−	210711.i	0.0458439	−	0.0518866i
$441$	−1.11958e6			−0.274131
$442$		−	1.81516e6i		−	0.441937i
$443$			2.24766e6i			0.544154i	0.962275	+	0.272077i	$0.0877106\pi$
$443$			2.24766e6i			0.544154i	−0.962275	+	0.272077i	$0.912289\pi$
$444$	5.11453e6			1.23126
$445$	2.48402e6	+	2.19473e6i	0.594642	+	0.525389i
$446$	666108.			0.158565
$447$			3.67984e6i			0.871084i
$448$			2.29959e6i			0.541322i
$449$	4.10754e6			0.961537			0.480769	−	0.876848i	$-0.340358\pi$
$449$	4.10754e6			0.961537			0.480769	+	0.876848i	$0.340358\pi$
$450$	−2.08666e6	+	259031.i	−0.485759	+	0.0603005i
$451$	1.75910e6			0.407239
$452$			2.81684e6i			0.648509i
$453$			3.44641e6i			0.789081i
$454$	4.47613e6			1.01921
$455$	400687.	+	354022.i	0.0907354	+	0.0801682i
$456$	466984.			0.105170
$457$			7.14569e6i			1.60049i	0.599672	+	0.800246i	$0.295298\pi$
$457$			7.14569e6i			1.60049i	−0.599672	+	0.800246i	$0.704702\pi$
$458$			3.58359e6i			0.798278i
$459$	909936.			0.201595
$460$	3.51085e6	−	3.97363e6i	0.773603	−	0.875573i
$461$	4.42326e6			0.969372			0.484686	−	0.874688i	$-0.338934\pi$
$461$	4.42326e6			0.969372			0.484686	+	0.874688i	$0.338934\pi$
$462$		−	494241.i		−	0.107729i
$463$		−	2.72107e6i		−	0.589912i	−0.955511	−	0.294956i	$-0.904695\pi$
$463$		−	2.72107e6i		−	0.589912i	0.955511	−	0.294956i	$-0.0953050\pi$
$464$	2.89461e6			0.624159
$465$	−1.05643e6	+	1.19568e6i	−0.226573	+	0.256438i
$466$	−1.30208e7			−2.77762
$467$			2.07874e6i			0.441070i	0.975379	+	0.220535i	$0.0707803\pi$
$467$			2.07874e6i			0.441070i	−0.975379	+	0.220535i	$0.929220\pi$
$468$		−	524723.i		−	0.110743i
$469$	−1.94358e6			−0.408010
$470$	7.57679e6	+	6.69439e6i	1.58212	+	1.39787i
$471$	3.30440e6			0.686341
$472$			191574.i			0.0395805i
$473$			928236.i			0.190768i
$474$	−1.16674e6			−0.238521
$475$	−480534.	−	3.87101e6i	−0.0977215	−	0.787209i
$476$	2.52352e6			0.510493
$477$			3.15175e6i			0.634243i
$478$		−	3.34617e6i		−	0.669851i
$479$	7.38214e6			1.47009			0.735044	−	0.678019i	$-0.237161\pi$
$479$	7.38214e6			1.47009			0.735044	+	0.678019i	$0.237161\pi$
$480$	−3.12870e6	−	2.76433e6i	−0.619814	−	0.547630i
$481$	2.68849e6			0.529841
$482$		−	9.01230e6i		−	1.76693i
$483$		−	1.26042e6i		−	0.245838i
$484$	−541777.			−0.105125
$485$	−2.85986e6	+	3.23682e6i	−0.552065	+	0.624834i
$486$	490512.			0.0942018
$487$			4.25158e6i			0.812321i	0.913802	+	0.406161i	$0.133133\pi$
$487$			4.25158e6i			0.812321i	−0.913802	+	0.406161i	$0.866867\pi$
$488$		−	233934.i		−	0.0444677i
$489$	−292582.			−0.0553319
$490$	4.24982e6	−	4.80999e6i	0.799613	−	0.905012i
$491$	5.75275e6			1.07689			0.538446	−	0.842660i	$-0.319012\pi$
$491$	5.75275e6			1.07689			0.538446	+	0.842660i	$0.319012\pi$
$492$			4.84170e6i			0.901747i
$493$		−	4.30726e6i		−	0.798148i
$494$	1.81521e6			0.334664
$495$	410589.	+	362771.i	0.0753172	+	0.0665457i
$496$	−2.66016e6			−0.485516
$497$			1.82745e6i			0.331859i
$498$			5.70419e6i			1.03067i
$499$	7.53164e6			1.35406			0.677031	−	0.735955i	$-0.263266\pi$
$499$	7.53164e6			1.35406			0.677031	+	0.735955i	$0.263266\pi$
$500$	3.65080e6	−	5.33475e6i	0.653075	−	0.954309i
$501$	4.73971e6			0.843640
$502$		−	5.85640e6i		−	1.03722i
$503$			6.85977e6i			1.20890i	0.796644	+	0.604449i	$0.206607\pi$
$503$			6.85977e6i			1.20890i	−0.796644	+	0.604449i	$0.793393\pi$
$504$	183960.			0.0322587
$505$	−6.02651e6	−	5.32465e6i	−1.05157	−	0.929101i
$506$	−2.57646e6			−0.447349
$507$			3.06581e6i			0.529695i
$508$		−	4.92722e6i		−	0.847116i
$509$	3.43084e6			0.586956			0.293478	−	0.955966i	$-0.405187\pi$
$509$	3.43084e6			0.586956			0.293478	+	0.955966i	$0.405187\pi$
$510$	−3.45403e6	+	3.90931e6i	−0.588031	+	0.665541i
$511$	−1.01205e6			−0.171455
$512$		−	8.07658e6i		−	1.36161i
$513$			909959.i			0.152661i
$514$	−2.05406e6			−0.342930
$515$	−3.11631e6	+	3.52707e6i	−0.517752	+	0.585998i
$516$	−2.55485e6			−0.422417
$517$		−	2.63449e6i		−	0.433481i
$518$			6.96987e6i			1.14130i
$519$	1.46188e6			0.238228
$520$	304857.	+	269353.i	0.0494411	+	0.0436831i
$521$	7.81233e6			1.26092			0.630458	−	0.776223i	$-0.282867\pi$
$521$	7.81233e6			1.26092			0.630458	+	0.776223i	$0.282867\pi$
$522$		−	2.32188e6i		−	0.372961i
$523$			9.26985e6i			1.48190i	0.671561	+	0.740949i	$0.265624\pi$
$523$			9.26985e6i			1.48190i	−0.671561	+	0.740949i	$0.734376\pi$
$524$	4.74352e6			0.754698
$525$	−189298.	−	1.52491e6i	−0.0299742	−	0.241461i
$526$	−2.24423e6			−0.353674
$527$			3.95839e6i			0.620858i
$528$			913483.i			0.142599i
$529$	−134185.			−0.0208480
$530$	−1.35407e7	−	1.19637e7i	−2.09388	−	1.85002i
$531$	−373299.			−0.0574540
$532$			2.52359e6i			0.386580i
$533$			2.54507e6i			0.388045i
$534$	4.43301e6			0.672737
$535$	5.51277e6	−	6.23943e6i	0.832695	−	0.942454i
$536$	−1.47875e6			−0.222322
$537$		−	5.68947e6i		−	0.851405i
$538$			6.96627e6i			1.03764i
$539$	−1.67246e6			−0.247961
$540$	−998482.	+	1.13009e6i	−0.147352	+	0.166775i
$541$	−8.86597e6			−1.30237			−0.651183	−	0.758921i	$-0.725727\pi$
$541$	−8.86597e6			−1.30237			−0.651183	+	0.758921i	$0.725727\pi$
$542$		−	8.43537e6i		−	1.23341i
$543$		−	4.02685e6i		−	0.586092i
$544$	−1.03578e7			−1.50062
$545$	−3.71257e6	−	3.28020e6i	−0.535406	−	0.473052i
$546$	715070.			0.102652
$547$			9.18782e6i			1.31294i	0.754353	+	0.656469i	$0.227951\pi$
$547$			9.18782e6i			1.31294i	−0.754353	+	0.656469i	$0.772049\pi$
$548$			8.20407e6i			1.16702i
$549$	455841.			0.0645480
$550$	−3.11711e6	+	386948.i	−0.439385	+	0.0545438i
$551$	4.30737e6			0.604412
$552$		−	958976.i		−	0.133955i
$553$		−	852642.i		−	0.118564i
$554$	5.72034e6			0.791858
$555$	−5.79019e6	−	5.11586e6i	−0.797922	−	0.704995i
$556$	3.89565e6			0.534432
$557$		−	5.08584e6i		−	0.694584i	−0.937757	−	0.347292i	$-0.887101\pi$
$557$		−	5.08584e6i		−	0.694584i	0.937757	−	0.347292i	$-0.112899\pi$
$558$			2.13382e6i			0.290117i
$559$	−1.34297e6			−0.181777
$560$	1.69632e6	−	1.91992e6i	0.228580	−	0.258710i
$561$	1.35929e6			0.182349
$562$			119383.i			0.0159441i
$563$		−	9.69174e6i		−	1.28864i	−0.764757	−	0.644319i	$-0.777141\pi$
$563$		−	9.69174e6i		−	1.28864i	0.764757	−	0.644319i	$-0.222859\pi$
$564$	7.25110e6			0.959855
$565$	2.81757e6	−	3.18896e6i	0.371324	−	0.420269i
$566$	−1.02635e7			−1.34664
$567$			358462.i			0.0468259i
$568$			1.39039e6i			0.180828i
$569$	−1.19915e6			−0.155271			−0.0776357	−	0.996982i	$-0.524737\pi$
$569$	−1.19915e6			−0.155271			−0.0776357	+	0.996982i	$0.524737\pi$
$570$	−3.90941e6	−	3.45412e6i	−0.503993	−	0.445297i
$571$	2.76815e6			0.355303			0.177652	−	0.984093i	$-0.443150\pi$
$571$	2.76815e6			0.355303			0.177652	+	0.984093i	$0.443150\pi$
$572$		−	783845.i		−	0.100171i
$573$		−	717177.i		−	0.0912515i
$574$	−6.59806e6			−0.835865
$575$	−7.94931e6	+	986801.i	−1.00267	+	0.124469i
$576$	−3.40927e6			−0.428160
$577$		−	1.52867e7i		−	1.91150i	−0.294186	−	0.955748i	$-0.595049\pi$
$577$		−	1.52867e7i		−	1.91150i	0.294186	−	0.955748i	$-0.404951\pi$
$578$			1.14751e6i			0.142869i
$579$	1.03620e6			0.128454
$580$	5.34939e6	+	4.72640e6i	0.660290	+	0.583392i
$581$	−4.16857e6			−0.512327
$582$			5.77647e6i			0.706895i
$583$			4.70817e6i			0.573694i
$584$	−770008.			−0.0934250
$585$	−524858.	+	594041.i	−0.0634092	+	0.0717674i
$586$	6.59798e6			0.793720
$587$			1.19628e7i			1.43298i	0.697599	+	0.716489i	$0.254252\pi$
$587$			1.19628e7i			1.43298i	−0.697599	+	0.716489i	$0.745748\pi$
$588$		−	4.60323e6i		−	0.549060i
$589$	−3.95849e6			−0.470156
$590$	1.41701e6	−	1.60378e6i	0.167587	−	0.189677i
$591$	3.23852e6			0.381397
$592$		−	1.28821e7i		−	1.51071i
$593$		−	5.73684e6i		−	0.669940i	−0.942229	−	0.334970i	$-0.891274\pi$
$593$		−	5.73684e6i		−	0.669940i	0.942229	−	0.334970i	$-0.108726\pi$
$594$	732741.			0.0852088
$595$	−2.85689e6	−	2.52418e6i	−0.330827	−	0.292299i
$596$	−1.51299e7			−1.74470
$597$			2.53630e6i			0.291249i
$598$		−	3.72763e6i		−	0.426265i
$599$	−3.70905e6			−0.422373			−0.211186	−	0.977446i	$-0.567733\pi$
$599$	−3.70905e6			−0.422373			−0.211186	+	0.977446i	$0.567733\pi$
$600$	−144025.	−	1.16021e6i	−0.0163327	−	0.131571i
$601$	−128805.			−0.0145461			−0.00727306	−	0.999974i	$-0.502315\pi$
$601$	−128805.			−0.0145461			−0.00727306	+	0.999974i	$0.502315\pi$
$602$		−	3.48164e6i		−	0.391555i
$603$		−	2.88147e6i		−	0.322717i
$604$	−1.41702e7			−1.58046
$605$	613349.	+	541918.i	0.0681270	+	0.0601928i
$606$	−1.07550e7			−1.18967
$607$			1.63065e7i			1.79635i	0.439642	+	0.898173i	$0.355105\pi$
$607$			1.63065e7i			1.79635i	−0.439642	+	0.898173i	$0.644895\pi$
$608$		−	1.03581e7i		−	1.13637i
$609$	1.69681e6			0.185392
$610$	−1.73033e6	+	1.95841e6i	−0.188280	+	0.213098i
$611$	3.81159e6			0.413050
$612$			3.74126e6i			0.403775i
$613$			1.05148e6i			0.113019i	0.998402	+	0.0565094i	$0.0179971\pi$
$613$			1.05148e6i			0.113019i	−0.998402	+	0.0565094i	$0.982003\pi$
$614$	2.31526e7			2.47844
$615$	4.84295e6	−	5.48131e6i	0.516324	−	0.584382i
$616$	274805.			0.0291791
$617$			1.47566e7i			1.56053i	0.625449	+	0.780265i	$0.284916\pi$
$617$			1.47566e7i			1.56053i	−0.625449	+	0.780265i	$0.715084\pi$
$618$			6.29445e6i			0.662959i
$619$	3.16617e6			0.332130			0.166065	−	0.986115i	$-0.446894\pi$
$619$	3.16617e6			0.332130			0.166065	+	0.986115i	$0.446894\pi$
$620$	−4.91612e6	−	4.34358e6i	−0.513622	−	0.453805i
$621$	1.86865e6			0.194446
$622$			2.41832e7i			2.50633i
$623$			3.23961e6i			0.334405i
$624$	−1.32163e6			−0.135878
$625$	−9.46922e6	+	2.38775e6i	−0.969648	+	0.244506i
$626$	−4.67712e6			−0.477027
$627$			1.35932e6i			0.138087i
$628$			1.35863e7i			1.37468i
$629$	−1.91689e7			−1.93184
$630$	−1.54004e6	−	1.36069e6i	−0.154590	−	0.136586i
$631$	1.74306e7			1.74276			0.871382	−	0.490605i	$-0.163224\pi$
$631$	1.74306e7			1.74276			0.871382	+	0.490605i	$0.163224\pi$
$632$		−	648721.i		−	0.0646049i
$633$			7.12151e6i			0.706420i
$634$	−3.67517e6			−0.363123
$635$	−4.92850e6	+	5.57813e6i	−0.485043	+	0.548977i
$636$	−1.29586e7			−1.27033
$637$		−	2.41972e6i		−	0.236274i
$638$		−	3.46849e6i		−	0.337356i
$639$	−2.70929e6			−0.262484
$640$	3.11254e6	−	3.52281e6i	0.300376	−	0.339969i
$641$	1.80105e6			0.173134			0.0865669	−	0.996246i	$-0.472410\pi$
$641$	1.80105e6			0.173134			0.0865669	+	0.996246i	$0.472410\pi$
$642$		−	1.11349e7i		−	1.06623i
$643$			4.35963e6i			0.415836i	0.978146	+	0.207918i	$0.0666687\pi$
$643$			4.35963e6i			0.415836i	−0.978146	+	0.207918i	$0.933331\pi$
$644$	5.18232e6			0.492390
$645$	2.89236e6	+	2.55551e6i	0.273749	+	0.241868i
$646$	−1.29424e7			−1.22021
$647$		−	1.51638e7i		−	1.42412i	−0.702117	−	0.712061i	$-0.747762\pi$
$647$		−	1.51638e7i		−	1.42412i	0.702117	−	0.712061i	$-0.252238\pi$
$648$			272731.i			0.0255151i
$649$	−557644.			−0.0519691
$650$	−559837.	−	4.50984e6i	−0.0519731	−	0.418676i
$651$	−1.55938e6			−0.144211
$652$		−	1.20297e6i		−	0.110825i
$653$		−	9.42837e6i		−	0.865274i	−0.901568	−	0.432637i	$-0.857583\pi$
$653$		−	9.42837e6i		−	0.865274i	0.901568	−	0.432637i	$-0.142417\pi$
$654$	−6.62548e6			−0.605722
$655$	−5.37017e6	−	4.74475e6i	−0.489085	−	0.432126i
$656$	1.21949e7			1.10641
$657$		−	1.50043e6i		−	0.135613i
$658$			9.88149e6i			0.889728i
$659$	1.78022e7			1.59683			0.798415	−	0.602107i	$-0.205672\pi$
$659$	1.78022e7			1.59683			0.798415	+	0.602107i	$0.205672\pi$
$660$	−1.49156e6	+	1.68816e6i	−0.133285	+	0.150853i
$661$	−1.63561e6			−0.145605			−0.0728027	−	0.997346i	$-0.523194\pi$
$661$	−1.63561e6			−0.145605			−0.0728027	+	0.997346i	$0.523194\pi$
$662$		−	2.78987e7i		−	2.47422i
$663$			1.96662e6i			0.173755i
$664$	−3.17160e6			−0.279164
$665$	2.52424e6	−	2.85697e6i	0.221348	−	0.250525i
$666$	−1.03332e7			−0.902714
$667$		−	8.84541e6i		−	0.769845i
$668$			1.94876e7i			1.68973i
$669$	−721688.			−0.0623425
$670$	1.23795e7	+	1.09378e7i	1.06541	+	0.941332i
$671$	680948.			0.0583859
$672$		−	4.08039e6i		−	0.348560i
$673$		−	9.45334e6i		−	0.804540i	−0.915521	−	0.402270i	$-0.868221\pi$
$673$		−	9.45334e6i		−	0.804540i	0.915521	−	0.402270i	$-0.131779\pi$
$674$	3.82529e6			0.324350
$675$	2.26077e6	−	280645.i	0.190984	−	0.0237082i
$676$	−1.26053e7			−1.06093
$677$			1.41485e7i			1.18642i	0.805047	+	0.593212i	$0.202140\pi$
$677$			1.41485e7i			1.18642i	−0.805047	+	0.593212i	$0.797860\pi$
$678$		−	5.69104e6i		−	0.475464i
$679$	−4.22139e6			−0.351384
$680$	−2.17363e6	−	1.92049e6i	−0.180266	−	0.159272i
$681$	−4.84962e6			−0.400719
$682$			3.18756e6i			0.262420i
$683$		−	1.45731e6i		−	0.119536i	−0.998212	−	0.0597681i	$-0.980964\pi$
$683$		−	1.45731e6i		−	0.119536i	0.998212	−	0.0597681i	$-0.0190361\pi$
$684$	−3.74136e6			−0.305766
$685$	8.20619e6	−	9.28787e6i	0.668214	−	0.756292i
$686$	1.39009e7			1.12780
$687$		−	3.88260e6i		−	0.313857i
$688$			6.43495e6i			0.518292i
$689$	−6.81179e6			−0.546655
$690$	−7.09321e6	+	8.02818e6i	−0.567179	+	0.641940i
$691$	1.64861e7			1.31348			0.656740	−	0.754117i	$-0.271935\pi$
$691$	1.64861e7			1.31348			0.656740	+	0.754117i	$0.271935\pi$
$692$			6.01062e6i			0.477149i
$693$			535481.i			0.0423556i
$694$	959264.			0.0756031
$695$	−4.41028e6	−	3.89665e6i	−0.346341	−	0.306006i
$696$	1.29100e6			0.101019
$697$		−	1.81463e7i		−	1.41484i
$698$		−	3.03247e7i		−	2.35591i
$699$	1.41073e7			1.09207
$700$	6.26979e6	−	778311.i	0.483624	−	0.0600355i
$701$	−1.82652e7			−1.40388			−0.701939	−	0.712237i	$-0.747682\pi$
$701$	−1.82652e7			−1.40388			−0.701939	+	0.712237i	$0.747682\pi$
$702$			1.06013e6i			0.0811927i
$703$		−	1.91694e7i		−	1.46292i
$704$	−5.09287e6			−0.387285
$705$	−8.20900e6	−	7.25297e6i	−0.622039	−	0.549596i
$706$	2.41221e7			1.82139
$707$		−	7.85963e6i		−	0.591363i
$708$		−	1.53484e6i		−	0.115075i
$709$	−2.53273e7			−1.89223			−0.946115	−	0.323830i	$-0.895030\pi$
$709$	−2.53273e7			−1.89223			−0.946115	+	0.323830i	$0.895030\pi$
$710$	1.02842e7	−	1.16398e7i	0.765640	−	0.866561i
$711$	1.26409e6			0.0937787
$712$			2.46481e6i			0.182215i
$713$			8.12897e6i			0.598841i
$714$	−5.09844e6			−0.374276
$715$	−784048.	+	887395.i	−0.0573558	+	0.0649160i
$716$	2.33926e7			1.70528
$717$			3.62538e6i			0.263363i
$718$			3.44221e7i			2.49187i
$719$	1.50245e7			1.08387			0.541937	−	0.840419i	$-0.317691\pi$
$719$	1.50245e7			1.08387			0.541937	+	0.840419i	$0.317691\pi$
$720$	2.84639e6	+	2.51490e6i	0.204627	+	0.180796i
$721$	−4.59993e6			−0.329544
$722$			7.62589e6i			0.544437i
$723$			9.76429e6i			0.694697i
$724$	1.65567e7			1.17389
$725$	−1.32846e6	−	1.07016e7i	−0.0938647	−	0.756139i
$726$	1.09459e6			0.0770742
$727$			1.17483e7i			0.824401i	0.911093	+	0.412200i	$0.135240\pi$
$727$			1.17483e7i			0.824401i	−0.911093	+	0.412200i	$0.864760\pi$
$728$			397588.i			0.0278039i
$729$	−531441.			−0.0370370
$730$	6.44621e6	+	5.69547e6i	0.447710	+	0.395569i
$731$	9.57539e6			0.662770
$732$			1.87422e6i			0.129284i
$733$			9.57778e6i			0.658423i	0.944256	+	0.329211i	$0.106783\pi$
$733$			9.57778e6i			0.658423i	−0.944256	+	0.329211i	$0.893217\pi$
$734$	4.38119e6			0.300159
$735$	−4.60442e6	+	5.21134e6i	−0.314381	+	0.355821i
$736$	−2.12709e7			−1.44741
$737$		−	4.30442e6i		−	0.291908i
$738$		−	9.78200e6i		−	0.661130i
$739$	1.95084e7			1.31405			0.657023	−	0.753871i	$-0.271816\pi$
$739$	1.95084e7			1.31405			0.657023	+	0.753871i	$0.271816\pi$
$740$	2.10342e7	−	2.38068e7i	1.41204	−	1.59816i
$741$	−1.96667e6			−0.131579
$742$		−	1.76595e7i		−	1.17752i
$743$			1.16476e6i			0.0774039i	0.999251	+	0.0387019i	$0.0123223\pi$
$743$			1.16476e6i			0.0774039i	−0.999251	+	0.0387019i	$0.987678\pi$
$744$	−1.18643e6			−0.0785798
$745$	1.71287e7	+	1.51338e7i	1.13066	+	0.998983i
$746$	−2.29778e7			−1.51169
$747$		−	6.18015e6i		−	0.405226i
$748$			5.58880e6i			0.365229i
$749$	8.13732e6			0.530001
$750$	−7.37595e6	+	1.07781e7i	−0.478812	+	0.699666i
$751$	2.66259e7			1.72268			0.861340	−	0.508029i	$-0.169626\pi$
$751$	2.66259e7			1.72268			0.861340	+	0.508029i	$0.169626\pi$
$752$		−	1.82635e7i		−	1.17771i
$753$			6.34506e6i			0.407801i
$754$	5.01822e6			0.321456
$755$	1.60421e7	+	1.41738e7i	1.02422	+	0.904939i
$756$	−1.47384e6			−0.0937879
$757$		−	2.27792e7i		−	1.44477i	−0.691491	−	0.722385i	$-0.743046\pi$
$757$		−	2.27792e7i		−	1.44477i	0.691491	−	0.722385i	$-0.256954\pi$
$758$			1.70914e7i			1.08045i
$759$	2.79144e6			0.175883
$760$	1.92053e6	−	2.17368e6i	0.120611	−	0.136509i
$761$	−2.05310e7			−1.28513			−0.642567	−	0.766229i	$-0.722131\pi$
$761$	−2.05310e7			−1.28513			−0.642567	+	0.766229i	$0.722131\pi$
$762$			9.95479e6i			0.621076i
$763$		−	4.84185e6i		−	0.301093i
$764$	2.94872e6			0.182768
$765$	3.74223e6	−	4.23551e6i	0.231194	−	0.261669i
$766$	4.13006e7			2.54322
$767$		−	806801.i		−	0.0495197i
$768$			5.83503e6i			0.356977i
$769$	−2.16009e7			−1.31721			−0.658606	−	0.752488i	$-0.728854\pi$
$769$	−2.16009e7			−1.31721			−0.658606	+	0.752488i	$0.728854\pi$
$770$	−2.30056e6	−	2.03263e6i	−0.139832	−	0.123547i
$771$	2.22545e6			0.134829
$772$			4.26040e6i			0.257281i
$773$		−	2.83324e7i		−	1.70543i	−0.522373	−	0.852717i	$-0.674953\pi$
$773$		−	2.83324e7i		−	1.70543i	0.522373	−	0.852717i	$-0.325047\pi$
$774$	5.16173e6			0.309701
$775$	1.22086e6	+	9.83478e6i	0.0730148	+	0.588180i
$776$	−3.21179e6			−0.191467
$777$		−	7.55144e6i		−	0.448722i
$778$			3.94674e7i			2.33770i
$779$	1.81468e7			1.07141
$780$	−2.44244e6	−	2.15799e6i	−0.143743	−	0.127003i
$781$	−4.04721e6			−0.237426
$782$			2.65779e7i			1.55419i
$783$			2.51562e6i			0.146636i
$784$	−1.15942e7			−0.673678
$785$	1.35898e7	−	1.53811e7i	0.787115	−	0.890866i
$786$	−9.58365e6			−0.553318
$787$		−	1.78605e7i		−	1.02791i	−0.857816	−	0.513956i	$-0.828179\pi$
$787$		−	1.78605e7i		−	1.02791i	0.857816	−	0.513956i	$-0.171821\pi$
$788$			1.33154e7i			0.763903i
$789$	2.43149e6			0.139053
$790$	−4.79836e6	+	5.43085e6i	−0.273543	+	0.309599i
$791$	4.15897e6			0.236344
$792$			407414.i			0.0230793i
$793$			985198.i			0.0556340i
$794$	3372.44			0.000189842
$795$	1.46705e7	+	1.29620e7i	0.823243	+	0.727367i
$796$	−1.04282e7			−0.583345
$797$			2.12249e7i			1.18359i	0.806090	+	0.591793i	$0.201580\pi$
$797$			2.12249e7i			1.18359i	−0.806090	+	0.591793i	$0.798420\pi$
$798$		−	5.09857e6i		−	0.283427i
$799$	−2.71766e7			−1.50601
$800$	−2.57344e7	+	3.19459e6i	−1.42164	+	0.176478i
$801$	−4.80290e6			−0.264498
$802$		−	179977.i		−	0.00988056i
$803$		−	2.24138e6i		−	0.122667i
$804$	1.18474e7			0.646371
$805$	−5.86693e6	−	5.18366e6i	−0.319096	−	0.281933i
$806$	−4.61177e6			−0.250052
$807$		−	7.54754e6i		−	0.407964i
$808$		−	5.97990e6i		−	0.322230i
$809$	−2.98029e7			−1.60098			−0.800492	−	0.599343i	$-0.795428\pi$
$809$	−2.98029e7			−1.60098			−0.800492	+	0.599343i	$0.795428\pi$
$810$	2.01730e6	−	2.28320e6i	0.108033	−	0.122273i
$811$	2.84229e6			0.151745			0.0758727	−	0.997118i	$-0.475826\pi$
$811$	2.84229e6			0.151745			0.0758727	+	0.997118i	$0.475826\pi$
$812$			6.97656e6i			0.371323i
$813$			9.13922e6i			0.484934i
$814$	−1.54361e7			−0.816536
$815$	−1.20328e6	+	1.36189e6i	−0.0634561	+	0.0718204i
$816$	9.42320e6			0.495419
$817$			9.57563e6i			0.501894i
$818$			1.18779e6i			0.0620665i
$819$	−774735.			−0.0403593
$820$	2.25368e7	+	1.99121e7i	1.17046	+	1.03415i
$821$	3.04342e7			1.57581			0.787906	−	0.615795i	$-0.211165\pi$
$821$	3.04342e7			1.57581			0.787906	+	0.615795i	$0.211165\pi$
$822$		−	1.65752e7i		−	0.855618i
$823$			8.37626e6i			0.431073i	0.976496	+	0.215536i	$0.0691500\pi$
$823$			8.37626e6i			0.431073i	−0.976496	+	0.215536i	$0.930850\pi$
$824$	−3.49980e6			−0.179566
$825$	3.37720e6	−	419235.i	0.172752	−	0.0214448i
$826$	2.09162e6			0.106668
$827$			1.58227e7i			0.804482i	0.915534	+	0.402241i	$0.131769\pi$
$827$			1.58227e7i			0.804482i	−0.915534	+	0.402241i	$0.868231\pi$
$828$			7.68308e6i			0.389457i
$829$	−1.41878e7			−0.717016			−0.358508	−	0.933527i	$-0.616714\pi$
$829$	−1.41878e7			−0.717016			−0.358508	+	0.933527i	$0.616714\pi$
$830$	2.65515e7	+	2.34592e7i	1.33781	+	1.18200i
$831$	−6.19765e6			−0.311332
$832$		−	7.36837e6i		−	0.369031i
$833$			1.72526e7i			0.861472i
$834$	−7.87063e6			−0.391827
$835$	1.94927e7	−	2.20620e7i	0.967509	−	1.09504i
$836$	−5.58895e6			−0.276576
$837$		−	2.31187e6i		−	0.114064i
$838$		−	3.77796e6i		−	0.185843i
$839$	−3.30757e7			−1.62220			−0.811099	−	0.584908i	$-0.801131\pi$
$839$	−3.30757e7			−1.62220			−0.811099	+	0.584908i	$0.801131\pi$
$840$	756561.	−	856285.i	0.0369952	−	0.0418716i
$841$	−8.60325e6			−0.419442
$842$		−	2.80665e7i		−	1.36429i
$843$		−	129344.i		−	0.00626869i
$844$	−2.92806e7			−1.41489
$845$	1.42705e7	+	1.26086e7i	0.687540	+	0.607469i
$846$	−1.46499e7			−0.703733
$847$			799916.i			0.0383121i
$848$			3.26391e7i			1.55865i
$849$	1.11198e7			0.529456
$850$	3.99163e6	+	3.21551e7i	0.189497	+	1.52652i
$851$	−3.93653e7			−1.86333
$852$		−	1.11394e7i		−	0.525732i
$853$		−	1.36981e7i		−	0.644596i	−0.946638	−	0.322298i	$-0.895545\pi$
$853$		−	1.36981e7i		−	0.644596i	0.946638	−	0.322298i	$-0.104455\pi$
$854$	−2.55411e6			−0.119838
$855$	4.23561e6	+	3.74233e6i	0.198153	+	0.175076i
$856$	6.19117e6			0.288794
$857$			3.02670e7i			1.40773i	0.710336	+	0.703863i	$0.248543\pi$
$857$			3.02670e7i			1.40773i	−0.710336	+	0.703863i	$0.751457\pi$
$858$			1.58365e6i			0.0734416i
$859$	−3.84178e7			−1.77643			−0.888217	−	0.459424i	$-0.848056\pi$
$859$	−3.84178e7			−1.77643			−0.888217	+	0.459424i	$0.848056\pi$
$860$	−1.05072e7	+	1.18921e7i	−0.484439	+	0.548294i
$861$	7.14860e6			0.328635
$862$			4.71949e7i			2.16335i
$863$			4.21231e7i			1.92528i	0.270793	+	0.962638i	$0.412714\pi$
$863$			4.21231e7i			1.92528i	−0.270793	+	0.962638i	$0.587286\pi$
$864$	6.04940e6			0.275695
$865$	6.01217e6	−	6.80465e6i	0.273207	−	0.309219i
$866$	1.54650e7			0.700737
$867$		−	1.24326e6i		−	0.0561714i
$868$		−	6.41149e6i		−	0.288842i
$869$	1.88833e6			0.0848260
$870$	−1.08077e7	−	9.54905e6i	−0.484101	−	0.427722i
$871$	6.22765e6			0.278150
$872$		−	3.68386e6i		−	0.164063i
$873$		−	6.25846e6i		−	0.277928i
$874$	−2.65786e7			−1.17694
$875$	−7.87658e6	−	5.39028e6i	−0.347790	−	0.238008i
$876$	6.16911e6			0.271620
$877$		−	2.52548e7i		−	1.10878i	−0.832257	−	0.554391i	$-0.812951\pi$
$877$		−	2.52548e7i		−	1.10878i	0.832257	−	0.554391i	$-0.187049\pi$
$878$		−	6.65765e6i		−	0.291464i
$879$	−7.14852e6			−0.312064
$880$	4.25201e6	+	3.75682e6i	0.185092	+	0.163536i
$881$	−1.22164e7			−0.530279			−0.265139	−	0.964210i	$-0.585418\pi$
$881$	−1.22164e7			−0.530279			−0.265139	+	0.964210i	$0.585418\pi$
$882$			9.30021e6i			0.402551i
$883$			1.53042e7i			0.660554i	0.943884	+	0.330277i	$0.107142\pi$
$883$			1.53042e7i			0.660554i	−0.943884	+	0.330277i	$0.892858\pi$
$884$	−8.08590e6			−0.348015
$885$	−1.53524e6	+	1.73760e6i	−0.0658898	+	0.0745749i
$886$	1.86711e7			0.799070
$887$			4.48803e7i			1.91534i	0.287861	+	0.957672i	$0.407056\pi$
$887$			4.48803e7i			1.91534i	−0.287861	+	0.957672i	$0.592944\pi$
$888$		−	5.74541e6i		−	0.244505i
$889$	−7.27488e6			−0.308725
$890$	1.82313e7	−	2.06345e7i	0.771514	−	0.873209i
$891$	−793881.			−0.0335013
$892$		−	2.96727e6i		−	0.124866i
$893$		−	2.71773e7i		−	1.14045i
$894$	3.05680e7			1.27915
$895$	−2.64829e7	−	2.33987e7i	−1.10512	−	0.976414i
$896$	4.59437e6			0.191186
$897$			4.03866e6i			0.167593i
$898$		−	3.41208e7i		−	1.41198i
$899$	−1.09434e7			−0.451600
$900$	1.15389e6	+	9.29532e6i	0.0474852	+	0.382524i
$901$	4.85679e7			1.99314
$902$		−	1.46126e7i		−	0.598014i
$903$			3.77215e6i			0.153946i
$904$	3.16429e6			0.128782
$905$	−1.87439e7	−	1.65610e7i	−0.760744	−	0.672147i
$906$	2.86289e7			1.15873
$907$			898531.i			0.0362673i	0.999836	+	0.0181336i	$0.00577243\pi$
$907$			898531.i			0.0362673i	−0.999836	+	0.0181336i	$0.994228\pi$
$908$		−	1.99396e7i		−	0.802604i
$909$	1.16524e7			0.467739
$910$	2.94082e6	−	3.32846e6i	0.117724	−	0.133241i
$911$	1.67133e7			0.667217			0.333609	−	0.942712i	$-0.391734\pi$
$911$	1.67133e7			0.667217			0.333609	+	0.942712i	$0.391734\pi$
$912$			9.42344e6i			0.375165i
$913$		−	9.23207e6i		−	0.366541i
$914$	5.93583e7			2.35026
$915$	1.87471e6	−	2.12182e6i	0.0740254	−	0.0837829i
$916$	1.59636e7			0.628625
$917$		−	7.00366e6i		−	0.275044i
$918$		−	7.55872e6i		−	0.296034i
$919$	−1.70008e7			−0.664019			−0.332009	−	0.943276i	$-0.607727\pi$
$919$	−1.70008e7			−0.664019			−0.332009	+	0.943276i	$0.607727\pi$
$920$	−4.46377e6	−	3.94392e6i	−0.173873	−	0.153624i
$921$	−2.50844e7			−0.974440
$922$		−	3.67435e7i		−	1.42349i
$923$		−	5.85552e6i		−	0.226236i
$924$	−2.20167e6			−0.0848343
$925$	−4.76258e7	+	5.91212e6i	−1.83016	+	0.227190i
$926$	−2.26036e7			−0.866263
$927$		−	6.81966e6i		−	0.260653i
$928$		−	2.86354e7i		−	1.09152i
$929$	−4.86778e7			−1.85051			−0.925255	−	0.379345i	$-0.876149\pi$
$929$	−4.86778e7			−1.85051			−0.925255	+	0.379345i	$0.876149\pi$
$930$	9.93236e6	+	8.77562e6i	0.376569	+	0.332714i
$931$	−1.72530e7			−0.652365
$932$			5.80030e7i			2.18731i
$933$		−	2.62011e7i		−	0.985405i
$934$	1.72678e7			0.647694
$935$	5.59025e6	−	6.32711e6i	0.209123	−	0.236688i
$936$	−589447.			−0.0219915
$937$		−	2.95283e6i		−	0.109873i	−0.998490	−	0.0549363i	$-0.982504\pi$
$937$		−	2.95283e6i		−	0.109873i	0.998490	−	0.0549363i	$-0.0174956\pi$
$938$			1.61451e7i			0.599148i
$939$	5.06738e6			0.187551
$940$	2.98211e7	−	3.37519e7i	1.10079	−	1.24589i
$941$	−2.28430e7			−0.840969			−0.420484	−	0.907300i	$-0.638140\pi$
$941$	−2.28430e7			−0.840969			−0.420484	+	0.907300i	$0.638140\pi$
$942$		−	2.74492e7i		−	1.00787i
$943$		−	3.72653e7i		−	1.36466i
$944$	−3.86584e6			−0.141193
$945$	1.66855e6	+	1.47422e6i	0.0607797	+	0.0537012i
$946$	7.71074e6			0.280135
$947$			2.08580e7i			0.755783i	0.925850	+	0.377892i	$0.123351\pi$
$947$			2.08580e7i			0.755783i	−0.925850	+	0.377892i	$0.876649\pi$
$948$			5.19739e6i			0.187830i
$949$	3.24283e6			0.116885
$950$	−3.21559e7	+	3.99173e6i	−1.15599	+	0.143500i
$951$	3.98183e6			0.142768
$952$		−	2.83480e6i		−	0.101375i
$953$		−	4.73251e7i		−	1.68795i	−0.536384	−	0.843974i	$-0.680210\pi$
$953$		−	4.73251e7i		−	1.68795i	0.536384	−	0.843974i	$-0.319790\pi$
$954$	2.61812e7			0.931361
$955$	−3.33826e6	−	2.94949e6i	−0.118444	−	0.104650i
$956$	−1.49060e7			−0.527492
$957$			3.75790e6i			0.132637i
$958$		−	6.13225e7i		−	2.15877i
$959$	1.21130e7			0.425311
$960$	−1.40211e7	+	1.58692e7i	−0.491025	+	0.555748i
$961$	−1.85721e7			−0.648713
$962$		−	2.23329e7i		−	0.778051i
$963$			1.20640e7i			0.419206i
$964$	−4.01466e7			−1.39141
$965$	4.26150e6	−	4.82322e6i	0.147314	−	0.166732i
$966$	−1.04702e7			−0.361003
$967$		−	2.72981e6i		−	0.0938785i	−0.998898	−	0.0469393i	$-0.985053\pi$
$967$		−	2.72981e6i		−	0.0938785i	0.998898	−	0.0469393i	$-0.0149467\pi$
$968$			608605.i			0.0208760i
$969$	1.40223e7			0.479746
$970$	2.68879e7	+	2.37565e7i	0.917545	+	0.810686i
$971$	−1.09369e6			−0.0372260			−0.0186130	−	0.999827i	$-0.505925\pi$
$971$	−1.09369e6			−0.0372260			−0.0186130	+	0.999827i	$0.505925\pi$
$972$		−	2.18506e6i		−	0.0741817i
$973$		−	5.75179e6i		−	0.194770i
$974$	3.53173e7			1.19286
$975$	606550.	+	4.88615e6i	0.0204341	+	0.164610i
$976$	4.72064e6			0.158627
$977$			5.19943e7i			1.74269i	0.490675	+	0.871343i	$0.336750\pi$
$977$			5.19943e7i			1.74269i	−0.490675	+	0.871343i	$0.663250\pi$
$978$			2.43044e6i			0.0812528i
$979$	−7.17471e6			−0.239247
$980$	−2.14268e7	−	1.89314e7i	−0.712676	−	0.629677i
$981$	7.17832e6			0.238150
$982$		−	4.77874e7i		−	1.58137i
$983$		−	3.13653e7i		−	1.03530i	−0.855593	−	0.517649i	$-0.826807\pi$
$983$		−	3.13653e7i		−	1.03530i	0.855593	−	0.517649i	$-0.173193\pi$
$984$	5.43892e6			0.179071
$985$	1.33188e7	−	1.50744e7i	0.437397	−	0.495051i
$986$	−3.57798e7			−1.17205
$987$		−	1.07060e7i		−	0.349812i
$988$		−	8.08610e6i		−	0.263540i
$989$	1.96641e7			0.639267
$990$	3.01349e6	−	3.41071e6i	0.0977198	−	0.110600i
$991$	−2.56995e7			−0.831266			−0.415633	−	0.909532i	$-0.636440\pi$
$991$	−2.56995e7			−0.831266			−0.415633	+	0.909532i	$0.636440\pi$
$992$			2.63160e7i			0.849066i
$993$			3.02266e7i			0.972782i
$994$	1.51804e7			0.487322
$995$	1.18058e7	+	1.04309e7i	0.378040	+	0.334013i
$996$	2.54101e7			0.811630
$997$			3.33461e7i			1.06245i	0.847231	+	0.531224i	$0.178268\pi$
$997$			3.33461e7i			1.06245i	−0.847231	+	0.531224i	$0.821732\pi$
$998$		−	6.25644e7i		−	1.98839i
$999$	1.11954e7			0.354917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.a.34.4	✓	26
5.2	odd	4		825.6.a.w.1.12		13
5.3	odd	4		825.6.a.x.1.2		13
5.4	even	2	inner	165.6.c.a.34.23	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.a.34.4	✓	26	1.1	even	1	trivial
165.6.c.a.34.23	yes	26	5.4	even	2	inner
825.6.a.w.1.12		13	5.2	odd	4
825.6.a.x.1.2		13	5.3	odd	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.30687i q^{2} +9.00000i q^{3} -37.0041 q^{4} +(41.8926 + 37.0137i) q^{5} +74.7618 q^{6} +54.6353i q^{7} +41.5686i q^{8} -81.0000 q^{9} +(307.468 - 347.996i) q^{10} -121.000 q^{11} -333.037i q^{12} -175.063i q^{13} +453.849 q^{14} +(-333.123 + 377.033i) q^{15} -838.827 q^{16} +1248.20i q^{17} +672.857i q^{18} -1248.23 q^{19} +(-1550.20 - 1369.66i) q^{20} -491.718 q^{21} +1005.13i q^{22} +2563.30i q^{23} -374.117 q^{24} +(384.972 + 3101.20i) q^{25} -1454.23 q^{26} -729.000i q^{27} -2021.73i q^{28} -3450.78 q^{29} +(3131.96 + 2767.21i) q^{30} +3171.29 q^{31} +8298.22i q^{32} -1089.00i q^{33} +10368.6 q^{34} +(-2022.26 + 2288.81i) q^{35} +2997.33 q^{36} +15357.2i q^{37} +10368.9i q^{38} +1575.57 q^{39} +(-1538.61 + 1741.41i) q^{40} -14538.0 q^{41} +4084.64i q^{42} -7671.37i q^{43} +4477.50 q^{44} +(-3393.30 - 2998.11i) q^{45} +21293.0 q^{46} +21772.6i q^{47} -7549.44i q^{48} +13822.0 q^{49} +(25761.2 - 3197.92i) q^{50} -11233.8 q^{51} +6478.06i q^{52} -38910.5i q^{53} -6055.71 q^{54} +(-5069.00 - 4478.66i) q^{55} -2271.11 q^{56} -11234.1i q^{57} +28665.2i q^{58} +4608.63 q^{59} +(12326.9 - 13951.8i) q^{60} -5627.67 q^{61} -26343.5i q^{62} -4425.46i q^{63} +42089.8 q^{64} +(6479.73 - 7333.84i) q^{65} -9046.18 q^{66} +35573.8i q^{67} -46188.5i q^{68} -23069.7 q^{69} +(19012.9 + 16798.6i) q^{70} +33448.0 q^{71} -3367.05i q^{72} +18523.8i q^{73} +127571. q^{74} +(-27910.8 + 3464.75i) q^{75} +46189.6 q^{76} -6610.88i q^{77} -13088.0i q^{78} -15606.1 q^{79} +(-35140.6 - 31048.1i) q^{80} +6561.00 q^{81} +120765. i q^{82} +76298.1i q^{83} +18195.6 q^{84} +(-46200.4 + 52290.2i) q^{85} -63725.1 q^{86} -31057.0i q^{87} -5029.80i q^{88} +59295.1 q^{89} +(-24904.9 + 28187.7i) q^{90} +9564.63 q^{91} -94852.8i q^{92} +28541.6i q^{93} +180863. q^{94} +(-52291.5 - 46201.6i) q^{95} -74684.0 q^{96} +77264.9i q^{97} -114817. i q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 458 q^{4} - 98 q^{5} - 54 q^{6} - 2106 q^{9} - 1944 q^{10} - 3146 q^{11} + 5516 q^{14} + 8282 q^{16} + 620 q^{19} + 1594 q^{20} - 5112 q^{21} + 6642 q^{24} + 10778 q^{25} + 4560 q^{26} + 9696 q^{29}+ \cdots + 254826 q^{99}+O(q^{100}) \) 26 * q - 458 * q^4 - 98 * q^5 - 54 * q^6 - 2106 * q^9 - 1944 * q^10 - 3146 * q^11 + 5516 * q^14 + 8282 * q^16 + 620 * q^19 + 1594 * q^20 - 5112 * q^21 + 6642 * q^24 + 10778 * q^25 + 4560 * q^26 + 9696 * q^29 - 9378 * q^30 - 48 * q^31 - 11036 * q^34 + 17748 * q^35 + 37098 * q^36 + 6588 * q^39 + 46308 * q^40 - 30240 * q^41 + 55418 * q^44 + 7938 * q^45 - 40560 * q^46 - 163674 * q^49 + 81164 * q^50 - 37008 * q^51 + 4374 * q^54 + 11858 * q^55 - 393204 * q^56 + 131184 * q^59 + 127260 * q^60 - 104084 * q^61 - 371954 * q^64 + 43108 * q^65 + 6534 * q^66 + 65016 * q^69 + 228364 * q^70 - 155640 * q^71 + 480056 * q^74 + 74232 * q^75 - 542348 * q^76 + 224516 * q^79 + 428642 * q^80 + 170586 * q^81 + 142128 * q^84 - 124796 * q^85 - 638500 * q^86 + 591620 * q^89 + 157464 * q^90 - 48400 * q^91 + 716288 * q^94 - 35124 * q^95 - 685998 * q^96 + 254826 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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