LMFDB - Embedded newform 12.6.b.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,6,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	12.b (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:	$1.92460583776$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 6x^{5} - 11x^{4} - 73x^{3} + 223x^{2} - 768x + 912 $ x^8 - x^7 + 7x^6 + 6x^5 - 11x^4 - 73x^3 + 223x^2 - 768x + 912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{18}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.6
Root			$1.67284 - 0.274906i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.6.b.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91937 + 5.32128i) q^{2} +(14.9174 - 4.52459i) q^{3} +(-24.6320 + 20.4270i) q^{4} +35.2908i q^{5} +(52.7086 + 70.6951i) q^{6} -190.564i q^{7} +(-155.976 - 91.8667i) q^{8} +(202.056 - 134.990i) q^{9} +O(q^{10})$	\(q+(1.91937 + 5.32128i) q^{2} +(14.9174 - 4.52459i) q^{3} +(-24.6320 + 20.4270i) q^{4} +35.2908i q^{5} +(52.7086 + 70.6951i) q^{6} -190.564i q^{7} +(-155.976 - 91.8667i) q^{8} +(202.056 - 134.990i) q^{9} +(-187.792 + 67.7362i) q^{10} -33.3357 q^{11} +(-275.021 + 416.168i) q^{12} -396.112 q^{13} +(1014.04 - 365.763i) q^{14} +(159.676 + 526.446i) q^{15} +(189.472 - 1006.32i) q^{16} +1279.32i q^{17} +(1106.14 + 816.100i) q^{18} +1333.42i q^{19} +(-720.886 - 869.283i) q^{20} +(-862.224 - 2842.71i) q^{21} +(-63.9836 - 177.388i) q^{22} -2235.78 q^{23} +(-2742.41 - 664.681i) q^{24} +1879.56 q^{25} +(-760.287 - 2107.82i) q^{26} +(2403.37 - 2927.92i) q^{27} +(3892.66 + 4693.97i) q^{28} +3984.36i q^{29} +(-2494.89 + 1860.13i) q^{30} -3670.76i q^{31} +(5718.57 - 923.267i) q^{32} +(-497.280 + 150.830i) q^{33} +(-6807.62 + 2455.49i) q^{34} +6725.15 q^{35} +(-2219.60 + 7452.49i) q^{36} +1216.11 q^{37} +(-7095.48 + 2559.32i) q^{38} +(-5908.95 + 1792.25i) q^{39} +(3242.05 - 5504.51i) q^{40} -9048.65i q^{41} +(13471.9 - 10044.4i) q^{42} +5349.13i q^{43} +(821.124 - 680.949i) q^{44} +(4763.91 + 7130.72i) q^{45} +(-4291.29 - 11897.2i) q^{46} -16413.1 q^{47} +(-1726.76 - 15868.9i) q^{48} -19507.6 q^{49} +(3607.58 + 10001.7i) q^{50} +(5788.40 + 19084.1i) q^{51} +(9757.04 - 8091.40i) q^{52} -11568.5i q^{53} +(20193.2 + 7169.23i) q^{54} -1176.44i q^{55} +(-17506.5 + 29723.4i) q^{56} +(6033.17 + 19891.1i) q^{57} +(-21201.9 + 7647.48i) q^{58} +42636.9 q^{59} +(-14686.9 - 9705.70i) q^{60} +24268.6 q^{61} +(19533.1 - 7045.56i) q^{62} +(-25724.2 - 38504.6i) q^{63} +(15889.0 + 28658.0i) q^{64} -13979.1i q^{65} +(-1757.08 - 2356.67i) q^{66} -19925.6i q^{67} +(-26132.7 - 31512.2i) q^{68} +(-33351.9 + 10116.0i) q^{69} +(12908.1 + 35786.4i) q^{70} -33389.6 q^{71} +(-43917.0 + 2493.00i) q^{72} +29782.6 q^{73} +(2334.17 + 6471.27i) q^{74} +(28038.1 - 8504.25i) q^{75} +(-27237.8 - 32844.7i) q^{76} +6352.57i q^{77} +(-20878.5 - 28003.2i) q^{78} +26206.1i q^{79} +(35513.8 + 6686.61i) q^{80} +(22604.3 - 54551.2i) q^{81} +(48150.4 - 17367.7i) q^{82} +1851.74 q^{83} +(79306.5 + 52409.0i) q^{84} -45148.2 q^{85} +(-28464.2 + 10267.0i) q^{86} +(18027.6 + 59436.2i) q^{87} +(5199.56 + 3062.44i) q^{88} +120134. i q^{89} +(-28800.8 + 39036.6i) q^{90} +75484.7i q^{91} +(55071.7 - 45670.3i) q^{92} +(-16608.7 - 54758.1i) q^{93} +(-31502.8 - 87338.5i) q^{94} -47057.3 q^{95} +(81128.6 - 39646.9i) q^{96} -75663.3 q^{97} +(-37442.4 - 103805. i) q^{98} +(-6735.67 + 4499.98i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 + 24 * q^6 - 24 * q^9	$ 8 q + 8 q^{4} + 24 q^{6} - 24 q^{9} - 272 q^{10} - 696 q^{12} + 112 q^{13} + 2336 q^{16} + 3696 q^{18} - 336 q^{21} - 8304 q^{22} - 11232 q^{24} - 1368 q^{25} + 19248 q^{28} + 25008 q^{30} + 4224 q^{33} - 36416 q^{34} - 42072 q^{36} + 6448 q^{37} + 53824 q^{40} + 59088 q^{42} - 17664 q^{45} - 69600 q^{46} - 74976 q^{48} - 21544 q^{49} + 84208 q^{52} + 78120 q^{54} + 43344 q^{57} - 62576 q^{58} - 64704 q^{60} + 59632 q^{61} + 38528 q^{64} + 33360 q^{66} - 92928 q^{69} - 30432 q^{70} + 20544 q^{72} - 129200 q^{73} - 86256 q^{76} - 83760 q^{78} + 200520 q^{81} + 154720 q^{82} + 167856 q^{84} + 229376 q^{85} - 150336 q^{88} - 251472 q^{90} - 346128 q^{93} + 386112 q^{94} + 331392 q^{96} - 392048 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 + 24 * q^6 - 24 * q^9 - 272 * q^10 - 696 * q^12 + 112 * q^13 + 2336 * q^16 + 3696 * q^18 - 336 * q^21 - 8304 * q^22 - 11232 * q^24 - 1368 * q^25 + 19248 * q^28 + 25008 * q^30 + 4224 * q^33 - 36416 * q^34 - 42072 * q^36 + 6448 * q^37 + 53824 * q^40 + 59088 * q^42 - 17664 * q^45 - 69600 * q^46 - 74976 * q^48 - 21544 * q^49 + 84208 * q^52 + 78120 * q^54 + 43344 * q^57 - 62576 * q^58 - 64704 * q^60 + 59632 * q^61 + 38528 * q^64 + 33360 * q^66 - 92928 * q^69 - 30432 * q^70 + 20544 * q^72 - 129200 * q^73 - 86256 * q^76 - 83760 * q^78 + 200520 * q^81 + 154720 * q^82 + 167856 * q^84 + 229376 * q^85 - 150336 * q^88 - 251472 * q^90 - 346128 * q^93 + 386112 * q^94 + 331392 * q^96 - 392048 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.91937	+	5.32128i	0.339300	+	0.940678i
$2$	1.91937	+	5.32128i	0.339300	+	0.940678i
$3$	14.9174	−	4.52459i	0.956950	−	0.290253i
$3$	14.9174	−	4.52459i	0.956950	−	0.290253i
$4$	−24.6320	+	20.4270i	−0.769750	+	0.638345i
$5$			35.2908i			0.631301i	0.948876	+	0.315650i	$0.102223\pi$
$5$			35.2908i			0.631301i	−0.948876	+	0.315650i	$0.897777\pi$
$6$	52.7086	+	70.6951i	0.597728	+	0.801699i
$7$		−	190.564i		−	1.46993i	−0.678107	−	0.734963i	$-0.737199\pi$
$7$		−	190.564i		−	1.46993i	0.678107	−	0.734963i	$-0.262801\pi$
$8$	−155.976	−	91.8667i	−0.861654	−	0.507496i
$9$	202.056	−	134.990i	0.831507	−	0.555515i
$10$	−187.792	+	67.7362i	−0.593851	+	0.214201i
$11$	−33.3357			−0.0830668			−0.0415334	−	0.999137i	$-0.513224\pi$
$11$	−33.3357			−0.0830668			−0.0415334	+	0.999137i	$0.513224\pi$
$12$	−275.021	+	416.168i	−0.551331	+	0.834287i
$13$	−396.112			−0.650070			−0.325035	−	0.945702i	$-0.605376\pi$
$13$	−396.112			−0.650070			−0.325035	+	0.945702i	$0.605376\pi$
$14$	1014.04	−	365.763i	1.38273	−	0.498747i
$15$	159.676	+	526.446i	0.183237	+	0.604123i
$16$	189.472	−	1006.32i	0.185031	−	0.982733i
$17$			1279.32i			1.07364i	0.843698	+	0.536818i	$0.180374\pi$
$17$			1279.32i			1.07364i	−0.843698	+	0.536818i	$0.819626\pi$
$18$	1106.14	+	816.100i	0.804691	+	0.593693i
$19$			1333.42i			0.847387i	0.905806	+	0.423693i	$0.139267\pi$
$19$			1333.42i			0.847387i	−0.905806	+	0.423693i	$0.860733\pi$
$20$	−720.886	−	869.283i	−0.402988	−	0.485944i
$21$	−862.224	−	2842.71i	−0.426650	−	1.40665i
$22$	−63.9836	−	177.388i	−0.0281846	−	0.0781391i
$23$	−2235.78			−0.881270			−0.440635	−	0.897686i	$-0.645247\pi$
$23$	−2235.78			−0.881270			−0.440635	+	0.897686i	$0.645247\pi$
$24$	−2742.41	−	664.681i	−0.971862	−	0.235551i
$25$	1879.56			0.601459
$26$	−760.287	−	2107.82i	−0.220569	−	0.611506i
$27$	2403.37	−	2927.92i	0.634470	−	0.772947i
$28$	3892.66	+	4693.97i	0.938320	+	1.13148i
$29$			3984.36i			0.879760i	0.898057	+	0.439880i	$0.144979\pi$
$29$			3984.36i			0.879760i	−0.898057	+	0.439880i	$0.855021\pi$
$30$	−2494.89	+	1860.13i	−0.506113	+	0.377346i
$31$		−	3670.76i		−	0.686044i	−0.939327	−	0.343022i	$-0.888549\pi$
$31$		−	3670.76i		−	0.686044i	0.939327	−	0.343022i	$-0.111451\pi$
$32$	5718.57	−	923.267i	0.987216	−	0.159387i
$33$	−497.280	+	150.830i	−0.0794907	+	0.0241104i
$34$	−6807.62	+	2455.49i	−1.00995	+	0.364285i
$35$	6725.15			0.927965
$36$	−2219.60	+	7452.49i	−0.285442	+	0.958396i
$37$	1216.11			0.146039			0.0730196	−	0.997331i	$-0.476736\pi$
$37$	1216.11			0.146039			0.0730196	+	0.997331i	$0.476736\pi$
$38$	−7095.48	+	2559.32i	−0.797118	+	0.287519i
$39$	−5908.95	+	1792.25i	−0.622084	+	0.188685i
$40$	3242.05	−	5504.51i	0.320383	−	0.543963i
$41$		−	9048.65i		−	0.840667i	−0.907370	−	0.420334i	$-0.861913\pi$
$41$		−	9048.65i		−	0.840667i	0.907370	−	0.420334i	$-0.138087\pi$
$42$	13471.9	−	10044.4i	1.17844	−	0.878616i
$43$			5349.13i			0.441176i	0.975367	+	0.220588i	$0.0707977\pi$
$43$			5349.13i			0.441176i	−0.975367	+	0.220588i	$0.929202\pi$
$44$	821.124	−	680.949i	0.0639407	−	0.0530253i
$45$	4763.91	+	7130.72i	0.350697	+	0.524931i
$46$	−4291.29	−	11897.2i	−0.299015	−	0.828992i
$47$	−16413.1			−1.08379			−0.541895	−	0.840446i	$-0.682293\pi$
$47$	−16413.1			−1.08379			−0.541895	+	0.840446i	$0.682293\pi$
$48$	−1726.76	−	15868.9i	−0.108175	−	0.994132i
$49$	−19507.6			−1.16068
$50$	3607.58	+	10001.7i	0.204076	+	0.565780i
$51$	5788.40	+	19084.1i	0.311626	+	1.02742i
$52$	9757.04	−	8091.40i	0.500391	−	0.414969i
$53$		−	11568.5i		−	0.565702i	−0.959164	−	0.282851i	$-0.908720\pi$
$53$		−	11568.5i		−	0.565702i	0.959164	−	0.282851i	$-0.0912801\pi$
$54$	20193.2	+	7169.23i	0.942371	+	0.334571i
$55$		−	1176.44i		−	0.0524401i
$56$	−17506.5	+	29723.4i	−0.745982	+	1.26657i
$57$	6033.17	+	19891.1i	0.245956	+	0.810907i
$58$	−21201.9	+	7647.48i	−0.827570	+	0.298503i
$59$	42636.9			1.59461			0.797307	−	0.603574i	$-0.206257\pi$
$59$	42636.9			1.59461			0.797307	+	0.603574i	$0.206257\pi$
$60$	−14686.9	−	9705.70i	−0.526686	−	0.348056i
$61$	24268.6			0.835065			0.417532	−	0.908662i	$-0.362895\pi$
$61$	24268.6			0.835065			0.417532	+	0.908662i	$0.362895\pi$
$62$	19533.1	−	7045.56i	0.645347	−	0.232775i
$63$	−25724.2	−	38504.6i	−0.816566	−	1.22225i
$64$	15889.0	+	28658.0i	0.484895	+	0.874573i
$65$		−	13979.1i		−	0.410389i
$66$	−1757.08	−	2356.67i	−0.0496513	−	0.0665945i
$67$		−	19925.6i		−	0.542280i	−0.962540	−	0.271140i	$-0.912599\pi$
$67$		−	19925.6i		−	0.542280i	0.962540	−	0.271140i	$-0.0874007\pi$
$68$	−26132.7	−	31512.2i	−0.685350	−	0.826431i
$69$	−33351.9	+	10116.0i	−0.843332	+	0.255791i
$70$	12908.1	+	35786.4i	0.314859	+	0.872917i
$71$	−33389.6			−0.786078			−0.393039	−	0.919522i	$-0.628576\pi$
$71$	−33389.6			−0.786078			−0.393039	+	0.919522i	$0.628576\pi$
$72$	−43917.0	+	2493.00i	−0.998393	+	0.0566750i
$73$	29782.6			0.654116			0.327058	−	0.945004i	$-0.393943\pi$
$73$	29782.6			0.654116			0.327058	+	0.945004i	$0.393943\pi$
$74$	2334.17	+	6471.27i	0.0495512	+	0.137376i
$75$	28038.1	−	8504.25i	0.575567	−	0.174575i
$76$	−27237.8	−	32844.7i	−0.540925	−	0.652276i
$77$			6352.57i			0.122102i
$78$	−20878.5	−	28003.2i	−0.388565	−	0.521160i
$79$			26206.1i			0.472428i	0.971701	+	0.236214i	$0.0759066\pi$
$79$			26206.1i			0.472428i	−0.971701	+	0.236214i	$0.924093\pi$
$80$	35513.8	+	6686.61i	0.620400	+	0.116810i
$81$	22604.3	−	54551.2i	0.382806	−	0.923829i
$82$	48150.4	−	17367.7i	0.790797	−	0.285239i
$83$	1851.74			0.0295042			0.0147521	−	0.999891i	$-0.495304\pi$
$83$	1851.74			0.0295042			0.0147521	+	0.999891i	$0.495304\pi$
$84$	79306.5	+	52409.0i	1.22634	+	0.810416i
$85$	−45148.2			−0.677787
$86$	−28464.2	+	10267.0i	−0.415005	+	0.149691i
$87$	18027.6	+	59436.2i	0.255353	+	0.841886i
$88$	5199.56	+	3062.44i	0.0715748	+	0.0421561i
$89$			120134.i			1.60764i	0.594869	+	0.803822i	$0.297204\pi$
$89$			120134.i			1.60764i	−0.594869	+	0.803822i	$0.702796\pi$
$90$	−28800.8	+	39036.6i	−0.374799	+	0.508002i
$91$			75484.7i			0.955554i
$92$	55071.7	−	45670.3i	0.678358	−	0.562555i
$93$	−16608.7	−	54758.1i	−0.199126	−	0.656510i
$94$	−31502.8	−	87338.5i	−0.367731	−	1.01950i
$95$	−47057.3			−0.534956
$96$	81128.6	−	39646.9i	0.898454	−	0.439068i
$97$	−75663.3			−0.816499			−0.408250	−	0.912870i	$-0.633861\pi$
$97$	−75663.3			−0.816499			−0.408250	+	0.912870i	$0.633861\pi$
$98$	−37442.4	−	103805.i	−0.393820	−	1.09183i
$99$	−6735.67	+	4499.98i	−0.0690706	+	0.0461448i
$100$	−46297.4	+	38393.9i	−0.462974	+	0.383939i
$101$		−	36670.8i		−	0.357699i	−0.983876	−	0.178849i	$-0.942763\pi$
$101$		−	36670.8i		−	0.357699i	0.983876	−	0.178849i	$-0.0572375\pi$
$102$	−90441.7	+	67431.2i	−0.860732	+	0.641742i
$103$		−	148155.i		−	1.37602i	−0.725702	−	0.688009i	$-0.758485\pi$
$103$		−	148155.i		−	1.37602i	0.725702	−	0.688009i	$-0.241515\pi$
$104$	61784.0	+	36389.5i	0.560135	+	0.329908i
$105$	100322.	−	30428.6i	0.888016	−	0.269345i
$106$	61559.2	−	22204.3i	0.532143	−	0.191943i
$107$	−35855.5			−0.302759			−0.151379	−	0.988476i	$-0.548372\pi$
$107$	−35855.5			−0.302759			−0.151379	+	0.988476i	$0.548372\pi$
$108$	608.895	+	121214.i	0.00502323	+	0.999987i
$109$	149700.			1.20686			0.603429	−	0.797416i	$-0.293801\pi$
$109$	149700.			1.20686			0.603429	+	0.797416i	$0.293801\pi$
$110$	6260.17	−	2258.03i	0.0493293	−	0.0177930i
$111$	18141.2	−	5502.41i	0.139752	−	0.0423883i
$112$	−191768.	−	36106.5i	−1.44454	−	0.271982i
$113$		−	29981.1i		−	0.220877i	−0.993883	−	0.110439i	$-0.964774\pi$
$113$		−	29981.1i		−	0.220877i	0.993883	−	0.110439i	$-0.0352256\pi$
$114$	−94266.0	+	70282.6i	−0.679349	+	0.506507i
$115$		−	78902.4i		−	0.556347i
$116$	−81388.8	−	98142.9i	−0.561590	−	0.677195i
$117$	−80036.9	+	53471.2i	−0.540537	+	0.361123i
$118$	81836.1	+	226883.i	0.541053	+	1.50002i
$119$	243792.			1.57816
$120$	23457.1	−	96781.9i	0.148704	−	0.613537i
$121$	−159940.			−0.993100
$122$	46580.5	+	129140.i	0.283338	+	0.785527i
$123$	−40941.5	−	134982.i	−0.244006	−	0.804476i
$124$	74982.8	+	90418.2i	0.437933	+	0.528083i
$125$			176615.i			1.01100i
$126$	155519.	−	210791.i	0.872686	−	1.18284i
$127$			162916.i			0.896303i	0.893958	+	0.448152i	$0.147918\pi$
$127$			162916.i			0.896303i	−0.893958	+	0.448152i	$0.852082\pi$
$128$	−122000.	+	139555.i	−0.658166	+	0.752873i
$129$	24202.7	+	79795.0i	0.128053	+	0.422184i
$130$	74386.7	−	26831.1i	0.386044	−	0.139245i
$131$	−244446.			−1.24453			−0.622265	−	0.782807i	$-0.713787\pi$
$131$	−244446.			−1.24453			−0.622265	+	0.782807i	$0.713787\pi$
$132$	9168.00	−	13873.2i	0.0457973	−	0.0693015i
$133$	254101.			1.24560
$134$	106030.	−	38244.6i	0.510111	−	0.183996i
$135$	103329.	+	84816.8i	0.487962	+	0.400542i
$136$	117527.	−	199543.i	0.544866	−	0.925102i
$137$		−	432998.i		−	1.97099i	−0.169700	−	0.985496i	$-0.554280\pi$
$137$		−	432998.i		−	1.97099i	0.169700	−	0.985496i	$-0.445720\pi$
$138$	−117845.	−	158059.i	−0.526760	−	0.706514i
$139$			102633.i			0.450559i	0.974294	+	0.225280i	$0.0723296\pi$
$139$			102633.i			0.450559i	−0.974294	+	0.225280i	$0.927670\pi$
$140$	−165654.	+	137375.i	−0.714302	+	0.592362i
$141$	−244840.	+	74262.5i	−1.03713	+	0.314573i
$142$	−64087.2	−	177676.i	−0.266717	−	0.739447i
$143$	13204.7			0.0539992
$144$	−97559.1	−	228910.i	−0.392068	−	0.919936i
$145$	−140611.			−0.555393
$146$	57163.9	+	158481.i	0.221942	+	0.615313i
$147$	−291002.	+	88264.0i	−1.11072	+	0.336892i
$148$	−29955.3	+	24841.6i	−0.112414	+	0.0932234i
$149$		−	247074.i		−	0.911721i	−0.890051	−	0.455860i	$-0.849332\pi$
$149$		−	247074.i		−	0.911721i	0.890051	−	0.455860i	$-0.150668\pi$
$150$	99069.1	+	132876.i	0.359509	+	0.482189i
$151$			276688.i			0.987525i	0.869597	+	0.493762i	$0.164379\pi$
$151$			276688.i			0.987525i	−0.869597	+	0.493762i	$0.835621\pi$
$152$	122497.	−	207981.i	0.430046	−	0.730154i
$153$	172696.	+	258494.i	0.596421	+	0.892735i
$154$	−33803.8	+	12193.0i	−0.114859	+	0.0414293i
$155$	129544.			0.433100
$156$	108939.	−	164849.i	0.358404	−	0.542344i
$157$	10102.0			0.0327082			0.0163541	−	0.999866i	$-0.494794\pi$
$157$	10102.0			0.0327082			0.0163541	+	0.999866i	$0.494794\pi$
$158$	−139450.	+	50299.4i	−0.444402	+	0.160295i
$159$	−52342.8	−	172572.i	−0.164197	−	0.541348i
$160$	32582.8	+	201813.i	0.100621	+	0.623230i
$161$			426059.i			1.29540i
$162$	333668.	+	15579.9i	0.998912	+	0.0466419i
$163$		−	523136.i		−	1.54222i	−0.636704	−	0.771108i	$-0.719703\pi$
$163$		−	523136.i		−	1.54222i	0.636704	−	0.771108i	$-0.280297\pi$
$164$	184837.	+	222886.i	0.536636	+	0.647104i
$165$	−5322.92	−	17549.4i	−0.0152209	−	0.0501826i
$166$	3554.17	+	9853.60i	0.0100108	+	0.0277540i
$167$	525626.			1.45843			0.729214	−	0.684285i	$-0.239886\pi$
$167$	525626.			1.45843			0.729214	+	0.684285i	$0.239886\pi$
$168$	−126664.	+	522605.i	−0.346243	+	1.42857i
$169$	−214388.			−0.577410
$170$	−86656.2	−	240246.i	−0.229973	−	0.637579i
$171$	179998.	+	269425.i	0.470736	+	0.704608i
$172$	−109267.	−	131760.i	−0.281623	−	0.339596i
$173$		−	168521.i		−	0.428094i	−0.976823	−	0.214047i	$-0.931335\pi$
$173$		−	168521.i		−	0.428094i	0.976823	−	0.214047i	$-0.0686646\pi$
$174$	−281675.	+	210010.i	−0.705302	+	0.525857i
$175$		−	358176.i		−	0.884101i
$176$	−6316.17	+	33546.3i	−0.0153699	+	0.0816324i
$177$	636030.	−	192915.i	1.52597	−	0.462841i
$178$	−639265.	+	230582.i	−1.51228	+	0.545475i
$179$	−688174.			−1.60534			−0.802668	−	0.596427i	$-0.796587\pi$
$179$	−688174.			−1.60534			−0.802668	+	0.596427i	$0.796587\pi$
$180$	−263004.	−	78331.4i	−0.605036	−	0.180200i
$181$	96556.0			0.219070			0.109535	−	0.993983i	$-0.465064\pi$
$181$	96556.0			0.219070			0.109535	+	0.993983i	$0.465064\pi$
$182$	−401675.	+	144883.i	−0.898869	+	0.324220i
$183$	362024.	−	109806.i	0.799115	−	0.242380i
$184$	348728.	+	205394.i	0.759350	+	0.447242i
$185$			42917.5i			0.0921946i
$186$	259505.	−	193481.i	0.550001	−	0.410068i
$187$		−	42647.0i		−	0.0891834i
$188$	404287.	−	335271.i	0.834248	−	0.691832i
$189$	−557956.	−	457996.i	−1.13618	−	0.932625i
$190$	−90320.5	−	250405.i	−0.181511	−	0.503221i
$191$	−525163.			−1.04162			−0.520811	−	0.853672i	$-0.674370\pi$
$191$	−525163.			−1.04162			−0.520811	+	0.853672i	$0.674370\pi$
$192$	366688.	+	355611.i	0.717867	+	0.696180i
$193$	36606.6			0.0707402			0.0353701	−	0.999374i	$-0.488739\pi$
$193$	36606.6			0.0707402			0.0353701	+	0.999374i	$0.488739\pi$
$194$	−145226.	−	402625.i	−0.277039	−	0.768063i
$195$	−63249.8	−	208532.i	−0.119117	−	0.392722i
$196$	480511.	−	398483.i	0.893436	−	0.740916i
$197$			904110.i			1.65980i	0.557912	+	0.829900i	$0.311603\pi$
$197$			904110.i			1.65980i	−0.557912	+	0.829900i	$0.688397\pi$
$198$	−36873.9	−	27205.2i	−0.0668431	−	0.0493162i
$199$			520039.i			0.930900i	0.885074	+	0.465450i	$0.154108\pi$
$199$			520039.i			0.930900i	−0.885074	+	0.465450i	$0.845892\pi$
$200$	−293166.	−	172669.i	−0.518250	−	0.305239i
$201$	−90155.1	−	297237.i	−0.157398	−	0.518935i
$202$	195136.	−	70385.0i	0.336479	−	0.121367i
$203$	759276.			1.29318
$204$	−532412.	−	351840.i	−0.895720	−	0.591929i
$205$	319334.			0.530714
$206$	788375.	−	284365.i	1.29439	−	0.466883i
$207$	−451753.	+	301808.i	−0.732782	+	0.489559i
$208$	−75052.1	+	398615.i	−0.120283	+	0.638845i
$209$		−	44450.3i		−	0.0703897i
$210$	354473.	+	475435.i	0.554671	+	0.743949i
$211$			1.25354e6i			1.93835i	0.246372	+	0.969175i	$0.420762\pi$
$211$			1.25354e6i			1.93835i	−0.246372	+	0.969175i	$0.579238\pi$
$212$	236310.	+	284956.i	0.361113	+	0.435449i
$213$	−498086.	+	151075.i	−0.752238	+	0.228162i
$214$	−68820.2	−	190797.i	−0.102726	−	0.284799i
$215$	−188775.			−0.278515
$216$	−643846.	+	235896.i	−0.938962	+	0.344021i
$217$	−699515.			−1.00843
$218$	287331.	+	796597.i	0.409488	+	1.13527i
$219$	444278.	−	134754.i	0.625957	−	0.189859i
$220$	24031.2	+	28978.1i	0.0334749	+	0.0403658i
$221$		−	506754.i		−	0.697938i
$222$	64099.6	+	85973.2i	0.0872917	+	0.117079i
$223$		−	785292.i		−	1.05747i	−0.848786	−	0.528736i	$-0.822666\pi$
$223$		−	785292.i		−	1.05747i	0.848786	−	0.528736i	$-0.177334\pi$
$224$	−175941.	−	1.08975e6i	−0.234287	−	1.45113i
$225$	379777.	−	253722.i	0.500117	−	0.334120i
$226$	159538.	−	57544.9i	0.207775	−	0.0749438i
$227$	79311.0			0.102157			0.0510786	−	0.998695i	$-0.483734\pi$
$227$	79311.0			0.102157			0.0510786	+	0.998695i	$0.483734\pi$
$228$	−554925.	−	366717.i	−0.706964	−	0.467191i
$229$	1.19706e6			1.50844			0.754221	−	0.656621i	$-0.228015\pi$
$229$	1.19706e6			1.50844			0.754221	+	0.656621i	$0.228015\pi$
$230$	419861.	−	151443.i	0.523343	−	0.188769i
$231$	28742.8	+	94763.7i	0.0354405	+	0.116846i
$232$	366030.	−	621465.i	0.446475	−	0.758048i
$233$			683524.i			0.824829i	0.910996	+	0.412415i	$0.135314\pi$
$233$			683524.i			0.824829i	−0.910996	+	0.412415i	$0.864686\pi$
$234$	−438156.	−	323267.i	−0.523105	−	0.385942i
$235$		−	579230.i		−	0.684198i
$236$	−1.05023e6	+	870946.i	−1.22745	+	1.01791i
$237$	118572.	+	390927.i	0.137124	+	0.452090i
$238$	467928.	+	1.29729e6i	0.535472	+	1.48454i
$239$	−1.17006e6			−1.32500			−0.662498	−	0.749064i	$-0.730504\pi$
$239$	−1.17006e6			−1.32500			−0.662498	+	0.749064i	$0.730504\pi$
$240$	560026.	−	60938.6i	0.627596	−	0.0682912i
$241$	−790728.			−0.876969			−0.438485	−	0.898739i	$-0.644485\pi$
$241$	−790728.			−0.876969			−0.438485	+	0.898739i	$0.644485\pi$
$242$	−306984.	−	851084.i	−0.336959	−	0.934187i
$243$	90375.3	−	916035.i	0.0981825	−	0.995168i
$244$	−597784.	+	495736.i	−0.642791	+	0.533059i
$245$		−	688438.i		−	0.732740i
$246$	639695.	−	476942.i	0.673962	−	0.502490i
$247$		−	528182.i		−	0.550860i
$248$	−337221.	+	572551.i	−0.348165	+	0.591132i
$249$	27623.0	−	8378.35i	0.0282340	−	0.00856368i
$250$	−939817.	+	338990.i	−0.951028	+	0.343034i
$251$	1.41649e6			1.41915			0.709574	−	0.704631i	$-0.248887\pi$
$251$	1.41649e6			1.41915			0.709574	+	0.704631i	$0.248887\pi$
$252$	1.42017e6	+	422975.i	1.40877	+	0.419579i
$253$	74531.1			0.0732043
$254$	−866923.	+	312697.i	−0.843133	+	0.304116i
$255$	−673492.	+	204277.i	−0.648608	+	0.196730i
$256$	−976777.	−	381338.i	−0.931527	−	0.363672i
$257$		−	808032.i		−	0.763125i	−0.924343	−	0.381562i	$-0.875386\pi$
$257$		−	808032.i		−	0.763125i	0.924343	−	0.381562i	$-0.124614\pi$
$258$	−378158.	+	281945.i	−0.353691	+	0.263703i
$259$		−	231747.i		−	0.214667i
$260$	285552.	+	344334.i	0.261970	+	0.315897i
$261$	537850.	+	805065.i	0.488720	+	0.731526i
$262$	−469184.	−	1.30077e6i	−0.422269	−	1.17070i
$263$	804766.			0.717431			0.358716	−	0.933447i	$-0.383215\pi$
$263$	804766.			0.717431			0.358716	+	0.933447i	$0.383215\pi$
$264$	91420.1	+	22157.6i	0.0807294	+	0.0195665i
$265$	408261.			0.357128
$266$	487715.	+	1.35214e6i	0.422631	+	1.17171i
$267$	543557.	+	1.79208e6i	0.466623	+	1.53844i
$268$	407021.	+	490807.i	0.346162	+	0.417420i
$269$			432855.i			0.364722i	0.983232	+	0.182361i	$0.0583739\pi$
$269$			432855.i			0.364722i	−0.983232	+	0.182361i	$0.941626\pi$
$270$	−253008.	+	712635.i	−0.211215	+	0.594919i
$271$		−	207740.i		−	0.171829i	−0.996302	−	0.0859147i	$-0.972619\pi$
$271$		−	207740.i		−	0.171829i	0.996302	−	0.0859147i	$-0.0273813\pi$
$272$	1.28740e6	+	242395.i	1.05510	+	0.198656i
$273$	341538.	+	1.12603e6i	0.277352	+	0.914418i
$274$	2.30410e6	−	831085.i	1.85407	−	0.668758i
$275$	−62656.4			−0.0499613
$276$	614886.	−	930459.i	0.485872	−	0.735232i
$277$	−1.69477e6			−1.32712			−0.663560	−	0.748123i	$-0.730955\pi$
$277$	−1.69477e6			−1.32712			−0.663560	+	0.748123i	$0.730955\pi$
$278$	−546141.	+	196992.i	−0.423831	+	0.152875i
$279$	−495517.	−	741700.i	−0.381108	−	0.570450i
$280$	−1.04896e6	−	617817.i	−0.799585	−	0.470939i
$281$		−	1.50990e6i		−	1.14073i	−0.821392	−	0.570364i	$-0.806802\pi$
$281$		−	1.50990e6i		−	1.14073i	0.821392	−	0.570364i	$-0.193198\pi$
$282$	−865111.	−	1.16032e6i	−0.647812	−	0.868874i
$283$			1.48985e6i			1.10580i	0.833247	+	0.552901i	$0.186479\pi$
$283$			1.48985e6i			1.10580i	−0.833247	+	0.552901i	$0.813521\pi$
$284$	822454.	−	682052.i	0.605084	−	0.501789i
$285$	−701971.	+	212915.i	−0.511926	+	0.155272i
$286$	25344.7	+	70265.7i	0.0183219	+	0.0507958i
$287$	−1.72435e6			−1.23572
$288$	1.03084e6	−	958502.i	0.732335	−	0.680945i
$289$	−216802.			−0.152693
$290$	−269886.	−	748232.i	−0.188445	−	0.522446i
$291$	−1.12870e6	+	342346.i	−0.781349	+	0.236991i
$292$	−733604.	+	608370.i	−0.503506	+	0.417552i
$293$		−	759752.i		−	0.517015i	−0.966009	−	0.258507i	$-0.916769\pi$
$293$		−	759752.i		−	0.517015i	0.966009	−	0.258507i	$-0.0832306\pi$
$294$	−1.02822e6	−	1.37909e6i	−0.693773	−	0.930518i
$295$			1.50469e6i			1.00668i
$296$	−189684.	−	111720.i	−0.125835	−	0.0741144i
$297$	−80117.9	+	97604.1i	−0.0527034	+	0.0642062i
$298$	1.31475e6	−	474228.i	0.857636	−	0.309347i
$299$	885619.			0.572887
$300$	−516918.	+	782212.i	−0.331603	+	0.501790i
$301$	1.01935e6			0.648497
$302$	−1.47233e6	+	531068.i	−0.928943	+	0.335068i
$303$	−165921.	−	547033.i	−0.103823	−	0.342300i
$304$	1.34184e6	+	252645.i	0.832755	+	0.156793i
$305$			856458.i			0.527177i
$306$	−1.04405e6	+	1.41511e6i	−0.637410	+	0.863945i
$307$		−	1.26088e6i		−	0.763532i	−0.924259	−	0.381766i	$-0.875316\pi$
$307$		−	1.26088e6i		−	0.763532i	0.924259	−	0.381766i	$-0.124684\pi$
$308$	−129764.	−	156477.i	−0.0779432	−	0.0939881i
$309$	−670342.	−	2.21009e6i	−0.399393	−	1.31678i
$310$	248643.	+	689340.i	0.146951	+	0.407408i
$311$	932334.			0.546601			0.273300	−	0.961929i	$-0.411885\pi$
$311$	932334.			0.546601			0.273300	+	0.961929i	$0.411885\pi$
$312$	1.08630e6	+	263288.i	0.631778	+	0.153125i
$313$	2.60743e6			1.50436			0.752179	−	0.658959i	$-0.229003\pi$
$313$	2.60743e6			1.50436			0.752179	+	0.658959i	$0.229003\pi$
$314$	19389.4	+	53755.4i	0.0110979	+	0.0307679i
$315$	1.35886e6	−	907829.i	0.771609	−	0.515499i
$316$	−535314.	−	645510.i	−0.301572	−	0.363651i
$317$			1.08779e6i			0.607992i	0.952673	+	0.303996i	$0.0983210\pi$
$317$			1.08779e6i			0.607992i	−0.952673	+	0.303996i	$0.901679\pi$
$318$	817837.	−	609760.i	0.453522	−	0.338136i
$319$		−	132821.i		−	0.0730788i
$320$	−1.01136e6	+	560736.i	−0.552118	+	0.306114i
$321$	−534870.	+	162232.i	−0.289725	+	0.0878766i
$322$	−2.26718e6	+	817766.i	−1.21856	+	0.439531i
$323$	−1.70587e6			−0.909785
$324$	557529.	+	1.80544e6i	0.295056	+	0.955480i
$325$	−744517.			−0.390990
$326$	2.78375e6	−	1.00409e6i	1.45073	−	0.523275i
$327$	2.23314e6	−	677333.i	1.15490	−	0.350294i
$328$	−831269.	+	1.41137e6i	−0.426636	+	0.724364i
$329$			3.12774e6i			1.59309i
$330$	83168.7	−	62008.6i	0.0420412	−	0.0313449i
$331$		−	1.54918e6i		−	0.777200i	−0.921406	−	0.388600i	$-0.872959\pi$
$331$		−	1.54918e6i		−	0.777200i	0.921406	−	0.388600i	$-0.127041\pi$
$332$	−45612.0	+	37825.5i	−0.0227109	+	0.0188339i
$333$	245723.	−	164163.i	0.121433	−	0.0811269i
$334$	1.00887e6	+	2.79700e6i	0.494846	+	1.37191i
$335$	703189.			0.342342
$336$	−3.02404e6	+	329058.i	−1.46130	+	0.159010i
$337$	−1.23639e6			−0.593035			−0.296518	−	0.955027i	$-0.595825\pi$
$337$	−1.23639e6			−0.593035			−0.296518	+	0.955027i	$0.595825\pi$
$338$	−411491.	−	1.14082e6i	−0.195915	−	0.543157i
$339$	−135652.	−	447239.i	−0.0641103	−	0.211369i
$340$	1.11209e6	−	922244.i	0.521727	−	0.432662i
$341$			122367.i			0.0569875i
$342$	−1.08820e6	+	1.47495e6i	−0.503088	+	0.681885i
$343$			514637.i			0.236192i
$344$	491407.	−	834336.i	0.223895	−	0.380141i
$345$	−357001.	−	1.17702e6i	−0.161481	−	0.532396i
$346$	896748.	−	323455.i	0.402699	−	0.145253i
$347$	−1.35733e6			−0.605150			−0.302575	−	0.953126i	$-0.597846\pi$
$347$	−1.35733e6			−0.605150			−0.302575	+	0.953126i	$0.597846\pi$
$348$	−1.65816e6	−	1.09578e6i	−0.733972	−	0.485039i
$349$	506931.			0.222785			0.111392	−	0.993777i	$-0.464469\pi$
$349$	506931.			0.222785			0.111392	+	0.993777i	$0.464469\pi$
$350$	1.90596e6	−	687474.i	0.831654	−	0.299976i
$351$	−952004.	+	1.15978e6i	−0.412450	+	0.502469i
$352$	−190632.	+	30777.7i	−0.0820049	+	0.0132398i
$353$		−	1.78557e6i		−	0.762674i	−0.924436	−	0.381337i	$-0.875464\pi$
$353$		−	1.78557e6i		−	0.762674i	0.924436	−	0.381337i	$-0.124536\pi$
$354$	2.24733e6	+	3.01422e6i	0.953145	+	1.27840i
$355$		−	1.17835e6i		−	0.496252i
$356$	−2.45398e6	−	2.95914e6i	−1.02623	−	1.23749i
$357$	3.63674e6	−	1.10306e6i	1.51022	−	0.458067i
$358$	−1.32086e6	−	3.66197e6i	−0.544691	−	1.51010i
$359$	1.79260e6			0.734087			0.367044	−	0.930204i	$-0.380370\pi$
$359$	1.79260e6			0.734087			0.367044	+	0.930204i	$0.380370\pi$
$360$	−87980.0	−	1.54987e6i	−0.0357789	−	0.630286i
$361$	698100.			0.281935
$362$	185327.	+	513801.i	0.0743305	+	0.206074i
$363$	−2.38588e6	+	723662.i	−0.950347	+	0.288250i
$364$	−1.54193e6	−	1.85934e6i	−0.609973	−	0.735538i
$365$			1.05105e6i			0.412944i
$366$	1.27916e6	+	1.71567e6i	0.499142	+	0.669470i
$367$			721697.i			0.279698i	0.990173	+	0.139849i	$0.0446617\pi$
$367$			721697.i			0.279698i	−0.990173	+	0.139849i	$0.955338\pi$
$368$	−423617.	+	2.24990e6i	−0.163063	+	0.866053i
$369$	−1.22148e6	−	1.82833e6i	−0.467003	−	0.699020i
$370$	−228376.	+	82374.8i	−0.0867255	+	0.0312817i
$371$	−2.20454e6			−0.831540
$372$	1.52765e6	+	1.00954e6i	0.572357	+	0.378237i
$373$	−4.93336e6			−1.83599			−0.917996	−	0.396591i	$-0.870193\pi$
$373$	−4.93336e6			−1.83599			−0.917996	+	0.396591i	$0.870193\pi$
$374$	226936.	−	81855.5i	0.0838929	−	0.0302600i
$375$	799111.	+	2.63463e6i	0.293446	+	0.967479i
$376$	2.56005e6	+	1.50781e6i	0.933852	+	0.550020i
$377$		−	1.57826e6i		−	0.571905i
$378$	1.36620e6	−	3.84810e6i	0.491795	−	1.38522i
$379$			3.76403e6i			1.34603i	0.739629	+	0.673015i	$0.235001\pi$
$379$			3.76403e6i			1.34603i	−0.739629	+	0.673015i	$0.764999\pi$
$380$	1.15912e6	−	961241.i	0.411783	−	0.341486i
$381$	737130.	+	2.43028e6i	0.260155	+	0.857717i
$382$	−1.00798e6	−	2.79454e6i	−0.353423	−	0.979831i
$383$	1.15231e6			0.401394			0.200697	−	0.979653i	$-0.435679\pi$
$383$	1.15231e6			0.401394			0.200697	+	0.979653i	$0.435679\pi$
$384$	−1.18849e6	+	2.63380e6i	−0.411309	+	0.911496i
$385$	−224187.			−0.0770831
$386$	70261.7	+	194794.i	0.0240022	+	0.0665437i
$387$	722080.	+	1.08082e6i	0.245080	+	0.366841i
$388$	1.86374e6	−	1.54558e6i	0.628501	−	0.521208i
$389$			4.29070e6i			1.43765i	0.695189	+	0.718827i	$0.255321\pi$
$389$			4.29070e6i			1.43765i	−0.695189	+	0.718827i	$0.744679\pi$
$390$	988255.	−	736820.i	0.329009	−	0.245301i
$391$		−	2.86028e6i		−	0.946163i
$392$	3.04272e6	+	1.79210e6i	1.00011	+	0.589043i
$393$	−3.64650e6	+	1.10602e6i	−1.19095	+	0.361228i
$394$	−4.81102e6	+	1.73532e6i	−1.56134	+	0.563171i
$395$	−924835.			−0.298244
$396$	73991.8	−	248434.i	0.0237108	−	0.0796108i
$397$	2.49061e6			0.793102			0.396551	−	0.918013i	$-0.370207\pi$
$397$	2.49061e6			0.793102			0.396551	+	0.918013i	$0.370207\pi$
$398$	−2.76727e6	+	998149.i	−0.875678	+	0.315855i
$399$	3.79052e6	−	1.14970e6i	1.19197	−	0.361538i
$400$	356124.	−	1.89144e6i	0.111289	−	0.591074i
$401$		−	1.01615e6i		−	0.315569i	−0.987474	−	0.157785i	$-0.949565\pi$
$401$		−	1.01615e6i		−	0.315569i	0.987474	−	0.157785i	$-0.0504352\pi$
$402$	1.40864e6	−	1.05025e6i	0.434745	−	0.324136i
$403$			1.45403e6i			0.445976i
$404$	749077.	+	903277.i	0.228335	+	0.275339i
$405$	1.92515e6	+	797724.i	0.583214	+	0.241666i
$406$	1.45733e6	+	4.04032e6i	0.438777	+	1.21647i
$407$	−40539.9			−0.0121310
$408$	850340.	−	3.50842e6i	0.252896	−	1.04343i
$409$	2.55994e6			0.756697			0.378349	−	0.925663i	$-0.376492\pi$
$409$	2.55994e6			0.756697			0.378349	+	0.925663i	$0.376492\pi$
$410$	612921.	+	1.69926e6i	0.180071	+	0.499231i
$411$	−1.95914e6	−	6.45920e6i	−0.572086	−	1.88614i
$412$	3.02637e6	+	3.64936e6i	0.878374	+	1.05919i
$413$		−	8.12505e6i		−	2.34396i
$414$	−2.47309e6	−	1.82462e6i	−0.709151	−	0.523204i
$415$			65349.2i			0.0186260i
$416$	−2.26519e6	+	365717.i	−0.641759	+	0.103613i
$417$	464375.	+	1.53102e6i	0.130776	+	0.431163i
$418$	236532.	−	85316.7i	0.0662140	−	0.0238833i
$419$	140154.			0.0390006			0.0195003	−	0.999810i	$-0.493792\pi$
$419$	140154.			0.0390006			0.0195003	+	0.999810i	$0.493792\pi$
$420$	−1.84956e6	+	2.79879e6i	−0.511616	+	0.774189i
$421$	−143774.			−0.0395344			−0.0197672	−	0.999805i	$-0.506292\pi$
$421$	−143774.			−0.0395344			−0.0197672	+	0.999805i	$0.506292\pi$
$422$	−6.67044e6	+	2.40601e6i	−1.82336	+	0.657683i
$423$	−3.31636e6	+	2.21560e6i	−0.901179	+	0.602062i
$424$	−1.06276e6	+	1.80441e6i	−0.287092	+	0.487439i
$425$			2.40456e6i			0.645748i
$426$	−1.75992e6	−	2.36048e6i	−0.469861	−	0.630198i
$427$		−	4.62472e6i		−	1.22748i
$428$	883194.	−	732422.i	0.233049	−	0.193265i
$429$	196979.	−	59745.7i	0.0516745	−	0.0156734i
$430$	−362330.	−	1.00452e6i	−0.0945002	−	0.261993i
$431$	6.33735e6			1.64329			0.821646	−	0.569998i	$-0.193056\pi$
$431$	6.33735e6			1.64329			0.821646	+	0.569998i	$0.193056\pi$
$432$	−2.49105e6	−	2.97331e6i	−0.642204	−	0.766534i
$433$	3.23311e6			0.828707			0.414353	−	0.910116i	$-0.364008\pi$
$433$	3.23311e6			0.828707			0.414353	+	0.910116i	$0.364008\pi$
$434$	−1.34263e6	−	3.72231e6i	−0.342162	−	0.948612i
$435$	−2.09755e6	+	636209.i	−0.531483	+	0.161204i
$436$	−3.68742e6	+	3.05793e6i	−0.928980	+	0.770392i
$437$		−	2.98122e6i		−	0.746777i
$438$	1.56980e6	+	2.10548e6i	0.390984	+	0.524404i
$439$		−	431210.i		−	0.106789i	−0.998573	−	0.0533947i	$-0.982996\pi$
$439$		−	431210.i		−	0.106789i	0.998573	−	0.0533947i	$-0.0170041\pi$
$440$	−108076.	+	183497.i	−0.0266132	+	0.0451852i
$441$	−3.94163e6	+	2.63333e6i	−0.965116	+	0.644777i
$442$	2.69658e6	−	972650.i	0.656535	−	0.236811i
$443$	−1.62011e6			−0.392225			−0.196112	−	0.980581i	$-0.562832\pi$
$443$	−1.62011e6			−0.392225			−0.196112	+	0.980581i	$0.562832\pi$
$444$	−334456.	+	506107.i	−0.0805159	+	0.121839i
$445$	−4.23961e6			−1.01491
$446$	4.17876e6	−	1.50727e6i	0.994741	−	0.358801i
$447$	−1.11791e6	−	3.68570e6i	−0.264630	−	0.872471i
$448$	5.46118e6	−	3.02788e6i	1.28556	−	0.712759i
$449$		−	782536.i		−	0.183184i	−0.995797	−	0.0915922i	$-0.970804\pi$
$449$		−	782536.i		−	0.183184i	0.995797	−	0.0915922i	$-0.0291956\pi$
$450$	2.07906e6	+	1.53391e6i	0.483989	+	0.357083i
$451$			301643.i			0.0698315i
$452$	612425.	+	738494.i	0.140996	+	0.170020i
$453$	1.25190e6	+	4.12746e6i	0.286632	+	0.945012i
$454$	152227.	+	422036.i	0.0346620	+	0.0960970i
$455$	−2.66391e6			−0.603242
$456$	886297.	−	3.65678e6i	0.199603	−	0.823543i
$457$	3.85018e6			0.862365			0.431182	−	0.902265i	$-0.358097\pi$
$457$	3.85018e6			0.862365			0.431182	+	0.902265i	$0.358097\pi$
$458$	2.29761e6	+	6.36991e6i	0.511815	+	1.41896i
$459$	3.74575e6	+	3.07468e6i	0.829863	+	0.681190i
$460$	1.61174e6	+	1.94352e6i	0.355141	+	0.428248i
$461$			2.26341e6i			0.496032i	0.968756	+	0.248016i	$0.0797786\pi$
$461$			2.26341e6i			0.496032i	−0.968756	+	0.248016i	$0.920221\pi$
$462$	−449096.	+	334835.i	−0.0978890	+	0.0729838i
$463$			7.51046e6i			1.62822i	0.580708	+	0.814112i	$0.302776\pi$
$463$			7.51046e6i			1.62822i	−0.580708	+	0.814112i	$0.697224\pi$
$464$	4.00954e6	+	754925.i	0.864568	+	0.162783i
$465$	1.93246e6	−	586134.i	0.414455	−	0.125709i
$466$	−3.63722e6	+	1.31194e6i	−0.775899	+	0.279865i
$467$	5.74296e6			1.21855			0.609275	−	0.792959i	$-0.291461\pi$
$467$	5.74296e6			1.21855			0.609275	+	0.792959i	$0.291461\pi$
$468$	879210.	−	2.95202e6i	0.185557	−	0.623024i
$469$	−3.79709e6			−0.797112
$470$	3.08225e6	−	1.11176e6i	0.643610	−	0.232149i
$471$	150695.	−	45707.3i	0.0313001	−	0.00949365i
$472$	−6.65033e6	−	3.91691e6i	−1.37401	−	0.809261i
$473$		−	178317.i		−	0.0366471i
$474$	−1.85265e6	+	1.38129e6i	−0.378745	+	0.282383i
$475$			2.50624e6i			0.509669i
$476$	−6.00509e6	+	4.97995e6i	−1.21479	+	1.00741i
$477$	−1.56163e6	−	2.33749e6i	−0.314256	−	0.470385i
$478$	−2.24579e6	−	6.22623e6i	−0.449572	−	1.24639i
$479$	−6.71306e6			−1.33685			−0.668424	−	0.743781i	$-0.733031\pi$
$479$	−6.71306e6			−1.33685			−0.668424	+	0.743781i	$0.733031\pi$
$480$	1.39917e6	+	2.86309e6i	0.277184	+	0.567195i
$481$	−481717.			−0.0949356
$482$	−1.51770e6	−	4.20768e6i	−0.297556	−	0.824945i
$483$	1.92774e6	+	6.35568e6i	0.375994	+	1.23964i
$484$	3.93964e6	−	3.26710e6i	0.764439	−	0.633940i
$485$		−	2.67022e6i		−	0.515457i
$486$	5.04794e6	−	1.27730e6i	0.969446	−	0.245303i
$487$		−	1.39245e6i		−	0.266047i	−0.991113	−	0.133024i	$-0.957531\pi$
$487$		−	1.39245e6i		−	0.266047i	0.991113	−	0.133024i	$-0.0424686\pi$
$488$	−3.78532e6	−	2.22948e6i	−0.719537	−	0.423792i
$489$	−2.36698e6	−	7.80381e6i	−0.447633	−	1.47582i
$490$	3.66337e6	−	1.32137e6i	0.689272	−	0.248619i
$491$	−1.82030e6			−0.340753			−0.170376	−	0.985379i	$-0.554498\pi$
$491$	−1.82030e6			−0.340753			−0.170376	+	0.985379i	$0.554498\pi$
$492$	3.76576e6	+	2.48857e6i	0.701357	+	0.463486i
$493$	−5.09728e6			−0.944541
$494$	2.81061e6	−	1.01378e6i	0.518182	−	0.186907i
$495$	−158808.	−	237707.i	−0.0291313	−	0.0436043i
$496$	−3.69395e6	−	695506.i	−0.674198	−	0.126940i
$497$			6.36286e6i			1.15548i
$498$	97602.5	+	130909.i	0.0176355	+	0.0236535i
$499$		−	5.00674e6i		−	0.900126i	−0.892997	−	0.450063i	$-0.851401\pi$
$499$		−	5.00674e6i		−	0.900126i	0.892997	−	0.450063i	$-0.148599\pi$
$500$	−3.60772e6	−	4.35038e6i	−0.645368	−	0.778219i
$501$	7.84095e6	−	2.37824e6i	1.39564	−	0.423313i
$502$	2.71876e6	+	7.53751e6i	0.481518	+	1.33496i
$503$	−6.04240e6			−1.06485			−0.532426	−	0.846477i	$-0.678720\pi$
$503$	−6.04240e6			−1.06485			−0.532426	+	0.846477i	$0.678720\pi$
$504$	475076.	+	8.36899e6i	0.0833080	+	1.46756i
$505$	1.29414e6			0.225815
$506$	143053.	+	396601.i	0.0248382	+	0.0688617i
$507$	−3.19811e6	+	970019.i	−0.552552	+	0.167595i
$508$	−3.32790e6	−	4.01295e6i	−0.572151	−	0.689930i
$509$			9.24427e6i			1.58153i	0.612118	+	0.790767i	$0.290318\pi$
$509$			9.24427e6i			1.58153i	−0.612118	+	0.790767i	$0.709682\pi$
$510$	−2.37970e6	−	3.19176e6i	−0.405132	−	0.543381i
$511$		−	5.67548e6i		−	0.961503i
$512$	154407.	−	5.92963e6i	0.0260311	−	0.999661i
$513$	3.90414e6	+	3.20469e6i	0.654985	+	0.537642i
$514$	4.29976e6	−	1.55091e6i	0.717855	−	0.258929i
$515$	5.22851e6			0.868681
$516$	−2.22614e6	−	1.47112e6i	−0.368067	−	0.243234i
$517$	547141.			0.0900270
$518$	1.23319e6	−	444809.i	0.201932	−	0.0728365i
$519$	−762490.	−	2.51389e6i	−0.124256	−	0.409665i
$520$	−1.28421e6	+	2.18041e6i	−0.208271	+	0.353614i
$521$		−	7.94882e6i		−	1.28295i	−0.767146	−	0.641473i	$-0.778324\pi$
$521$		−	7.94882e6i		−	1.28295i	0.767146	−	0.641473i	$-0.221676\pi$
$522$	−3.25164e6	+	4.40727e6i	−0.522307	+	0.707935i
$523$		−	182966.i		−	0.0292494i	−0.999893	−	0.0146247i	$-0.995345\pi$
$523$		−	182966.i		−	0.0292494i	0.999893	−	0.0146247i	$-0.00465535\pi$
$524$	6.02120e6	−	4.99331e6i	0.957977	−	0.794439i
$525$	−1.62060e6	−	5.34305e6i	−0.256613	−	0.846040i
$526$	1.54465e6	+	4.28238e6i	0.243425	+	0.674872i
$527$	4.69608e6			0.736561
$528$	57562.6	+	529000.i	0.00898578	+	0.0825793i
$529$	−1.43764e6			−0.223362
$530$	783606.	+	2.17247e6i	0.121174	+	0.335942i
$531$	8.61504e6	−	5.75556e6i	1.32593	−	0.885832i
$532$	−6.25902e6	+	5.19053e6i	−0.958798	+	0.795120i
$533$			3.58428e6i			0.546492i
$534$	−8.49287e6	+	6.33209e6i	−1.28885	+	0.960934i
$535$		−	1.26537e6i		−	0.191132i
$536$	−1.83050e6	+	3.10791e6i	−0.275205	+	0.467258i
$537$	−1.02658e7	+	3.11371e6i	−1.53623	+	0.465953i
$538$	−2.30334e6	+	830811.i	−0.343086	+	0.123750i
$539$	650299.			0.0964142
$540$	−4.27775e6	+	21488.4i	−0.631293	+	0.00317117i
$541$	7.40533e6			1.08781			0.543903	−	0.839148i	$-0.316946\pi$
$541$	7.40533e6			1.08781			0.543903	+	0.839148i	$0.316946\pi$
$542$	1.10544e6	−	398731.i	0.161636	−	0.0583018i
$543$	1.44036e6	−	436877.i	0.209639	−	0.0635857i
$544$	1.18115e6	+	7.31588e6i	0.171123	+	1.05991i
$545$			5.28304e6i			0.761891i
$546$	−5.33640e6	+	3.97869e6i	−0.766067	+	0.571162i
$547$			5.88557e6i			0.841047i	0.907282	+	0.420523i	$0.138154\pi$
$547$			5.88557e6i			0.841047i	−0.907282	+	0.420523i	$0.861846\pi$
$548$	8.84487e6	+	1.06656e7i	1.25817	+	1.51717i
$549$	4.90362e6	−	3.27602e6i	0.694362	−	0.463891i
$550$	−120261.	−	333412.i	−0.0169519	−	0.0469975i
$551$	−5.31282e6			−0.745497
$552$	6.13143e6	+	1.48608e6i	0.856473	+	0.207584i
$553$	4.99395e6			0.694434
$554$	−3.25289e6	−	9.01832e6i	−0.450293	−	1.24839i
$555$	194184.	+	640217.i	0.0267598	+	0.0882256i
$556$	−2.09650e6	−	2.52807e6i	−0.287612	−	0.346818i
$557$		−	730413.i		−	0.0997540i	−0.998755	−	0.0498770i	$-0.984117\pi$
$557$		−	730413.i		−	0.0997540i	0.998755	−	0.0498770i	$-0.0158829\pi$
$558$	2.99571e6	−	4.06038e6i	0.407300	−	0.552054i
$559$		−	2.11886e6i		−	0.286795i
$560$	1.27423e6	−	6.76764e6i	0.171703	−	0.911942i
$561$	−192960.	−	636181.i	−0.0258857	−	0.0853441i
$562$	8.03460e6	−	2.89806e6i	1.07306	−	0.387050i
$563$	7.31154e6			0.972160			0.486080	−	0.873914i	$-0.338426\pi$
$563$	7.31154e6			0.972160			0.486080	+	0.873914i	$0.338426\pi$
$564$	4.51394e6	−	6.83059e6i	0.597527	−	0.904192i
$565$	1.05806e6			0.139440
$566$	−7.92793e6	+	2.85959e6i	−1.04020	+	0.375199i
$567$	−1.03955e7	−	4.30757e6i	−1.35796	−	0.562697i
$568$	5.20798e6	+	3.06740e6i	0.677327	+	0.398932i
$569$		−	363173.i		−	0.0470254i	−0.999724	−	0.0235127i	$-0.992515\pi$
$569$		−	363173.i		−	0.0470254i	0.999724	−	0.0235127i	$-0.00748502\pi$
$570$	−2.48033e6	−	3.32672e6i	−0.319758	−	0.428874i
$571$			4.63421e6i			0.594820i	0.954750	+	0.297410i	$0.0961228\pi$
$571$			4.63421e6i			0.594820i	−0.954750	+	0.297410i	$0.903877\pi$
$572$	−325257.	+	269732.i	−0.0415659	+	0.0344701i
$573$	−7.83405e6	+	2.37615e6i	−0.996781	+	0.302334i
$574$	−3.30966e6	−	9.17572e6i	−0.419280	−	1.16241i
$575$	−4.20228e6			−0.530048
$576$	7.07902e6	+	3.64566e6i	0.889031	+	0.457847i
$577$	−9.36102e6			−1.17053			−0.585267	−	0.810841i	$-0.699010\pi$
$577$	−9.36102e6			−1.17053			−0.585267	+	0.810841i	$0.699010\pi$
$578$	−416124.	−	1.15366e6i	−0.0518088	−	0.143635i
$579$	546074.	−	165630.i	0.0676948	−	0.0205325i
$580$	3.46354e6	−	2.87227e6i	0.427514	−	0.354532i
$581$		−	352874.i		−	0.0433690i
$582$	−3.98811e6	−	5.34903e6i	−0.488045	−	0.654587i
$583$			385644.i			0.0469910i
$584$	−4.64537e6	−	2.73603e6i	−0.563622	−	0.331962i
$585$	−1.88704e6	−	2.82456e6i	−0.227977	−	0.341241i
$586$	4.04285e6	−	1.45825e6i	0.486344	−	0.175423i
$587$	−4.07722e6			−0.488393			−0.244196	−	0.969726i	$-0.578524\pi$
$587$	−4.07722e6			−0.488393			−0.244196	+	0.969726i	$0.578524\pi$
$588$	5.36500e6	−	8.11843e6i	0.639921	−	0.968342i
$589$	4.89465e6			0.581345
$590$	−8.00687e6	+	2.88806e6i	−0.946962	+	0.341567i
$591$	4.09073e6	+	1.34869e7i	0.481762	+	1.58835i
$592$	230419.	−	1.22380e6i	0.0270218	−	0.143517i
$593$		−	9.55091e6i		−	1.11534i	−0.830062	−	0.557671i	$-0.811695\pi$
$593$		−	9.55091e6i		−	1.11534i	0.830062	−	0.557671i	$-0.188305\pi$
$594$	−673155.	−	238991.i	−0.0782797	−	0.0277917i
$595$			8.60362e6i			0.996296i
$596$	5.04700e6	+	6.08594e6i	0.581992	+	0.701797i
$597$	2.35297e6	+	7.75762e6i	0.270196	+	0.890825i
$598$	1.69983e6	+	4.71263e6i	0.194381	+	0.538902i
$599$	−1.32333e7			−1.50695			−0.753477	−	0.657475i	$-0.771625\pi$
$599$	−1.32333e7			−1.50695			−0.753477	+	0.657475i	$0.771625\pi$
$600$	−5.15453e6	−	1.24931e6i	−0.584536	−	0.141675i
$601$	275735.			0.0311391			0.0155696	−	0.999879i	$-0.495044\pi$
$601$	275735.			0.0311391			0.0155696	+	0.999879i	$0.495044\pi$
$602$	1.95652e6	+	5.42425e6i	0.220035	+	0.610027i
$603$	−2.68976e6	−	4.02608e6i	−0.301245	−	0.450910i
$604$	−5.65192e6	−	6.81538e6i	−0.630382	−	0.760147i
$605$		−	5.64440e6i		−	0.626945i
$606$	2.59245e6	−	1.93287e6i	0.286767	−	0.213807i
$607$			7.63408e6i			0.840978i	0.907298	+	0.420489i	$0.138141\pi$
$607$			7.63408e6i			0.840978i	−0.907298	+	0.420489i	$0.861859\pi$
$608$	1.23110e6	+	7.62523e6i	0.135062	+	0.836554i
$609$	1.13264e7	−	3.43542e6i	1.23751	−	0.375350i
$610$	−4.55745e6	+	1.64386e6i	−0.495904	+	0.178871i
$611$	6.50142e6			0.704539
$612$	−9.53411e6	−	2.83958e6i	−1.02897	−	0.306461i
$613$	−1.16844e7			−1.25590			−0.627952	−	0.778252i	$-0.716107\pi$
$613$	−1.16844e7			−1.25590			−0.627952	+	0.778252i	$0.716107\pi$
$614$	6.70948e6	−	2.42010e6i	0.718237	−	0.259067i
$615$	4.76362e6	−	1.44486e6i	0.507866	−	0.154041i
$616$	583590.	−	990849.i	0.0619663	−	0.105210i
$617$		−	1.81938e6i		−	0.192402i	−0.995362	−	0.0962011i	$-0.969331\pi$
$617$		−	1.81938e6i		−	0.192402i	0.995362	−	0.0962011i	$-0.0306692\pi$
$618$	1.04739e7	−	7.80906e6i	1.10315	−	0.822484i
$619$		−	1.02220e7i		−	1.07228i	−0.844129	−	0.536140i	$-0.819882\pi$
$619$		−	1.02220e7i		−	1.07228i	0.844129	−	0.536140i	$-0.180118\pi$
$620$	−3.19093e6	+	2.64620e6i	−0.333379	+	0.276467i
$621$	−5.37340e6	+	6.54618e6i	−0.559140	+	0.681176i
$622$	1.78950e6	+	4.96121e6i	0.185462	+	0.514176i
$623$	2.28932e7			2.36312
$624$	683990.	+	6.28587e6i	0.0703215	+	0.646255i
$625$	−359248.			−0.0367870
$626$	5.00462e6	+	1.38748e7i	0.510429	+	1.41512i
$627$	−201120.	−	663082.i	−0.0204308	−	0.0673594i
$628$	−248832.	+	206353.i	−0.0251772	+	0.0208791i
$629$			1.55580e6i			0.156793i
$630$	7.43896e6	+	5.48840e6i	0.746726	+	0.550927i
$631$		−	1.08527e7i		−	1.08509i	−0.840027	−	0.542545i	$-0.817461\pi$
$631$		−	1.08527e7i		−	1.08509i	0.840027	−	0.542545i	$-0.182539\pi$
$632$	2.40747e6	−	4.08753e6i	0.239755	−	0.407069i
$633$	5.67176e6	+	1.86995e7i	0.562612	+	1.85490i
$634$	−5.78845e6	+	2.08788e6i	−0.571925	+	0.206292i
$635$	−5.74944e6			−0.565837
$636$	4.81444e6	+	3.18158e6i	0.471957	+	0.311889i
$637$	7.72720e6			0.754525
$638$	706780.	−	254934.i	0.0687436	−	0.0247957i
$639$	−6.74658e6	+	4.50727e6i	−0.653629	+	0.436678i
$640$	−4.92502e6	−	4.30548e6i	−0.475289	−	0.415501i
$641$			397330.i			0.0381949i	0.999818	+	0.0190975i	$0.00607928\pi$
$641$			397330.i			0.0381949i	−0.999818	+	0.0190975i	$0.993921\pi$
$642$	−1.88990e6	−	2.53481e6i	−0.180967	−	0.242721i
$643$		−	5.25770e6i		−	0.501497i	−0.968052	−	0.250748i	$-0.919323\pi$
$643$		−	5.25770e6i		−	0.501497i	0.968052	−	0.250748i	$-0.0806767\pi$
$644$	−8.70312e6	−	1.04947e7i	−0.826914	−	0.997137i
$645$	−2.81603e6	+	854131.i	−0.266525	+	0.0808398i
$646$	−3.27419e6	−	9.07739e6i	−0.308690	−	0.855814i
$647$	7.78890e6			0.731502			0.365751	−	0.930713i	$-0.380812\pi$
$647$	7.78890e6			0.731502			0.365751	+	0.930713i	$0.380812\pi$
$648$	−8.53717e6	+	6.43209e6i	−0.798686	+	0.601748i
$649$	−1.42133e6			−0.132459
$650$	−1.42901e6	−	3.96178e6i	−0.132663	−	0.367796i
$651$	−1.04349e7	+	3.16502e6i	−0.965021	+	0.292701i
$652$	1.06861e7	+	1.28859e7i	0.984466	+	1.18712i
$653$		−	1.12506e7i		−	1.03251i	−0.856435	−	0.516255i	$-0.827326\pi$
$653$		−	1.12506e7i		−	1.03251i	0.856435	−	0.516255i	$-0.172674\pi$
$654$	7.89050e6	+	1.05831e7i	0.721373	+	0.967537i
$655$		−	8.62670e6i		−	0.785672i
$656$	−9.10582e6	−	1.71447e6i	−0.826151	−	0.155550i
$657$	6.01775e6	−	4.02035e6i	0.543902	−	0.363371i
$658$	−1.66436e7	+	6.00330e6i	−1.49859	+	0.540537i
$659$	−437221.			−0.0392182			−0.0196091	−	0.999808i	$-0.506242\pi$
$659$	−437221.			−0.0392182			−0.0196091	+	0.999808i	$0.506242\pi$
$660$	489597.	+	323546.i	0.0437501	+	0.0289119i
$661$	−2.76418e6			−0.246072			−0.123036	−	0.992402i	$-0.539263\pi$
$661$	−2.76418e6			−0.246072			−0.123036	+	0.992402i	$0.539263\pi$
$662$	8.24364e6	−	2.97346e6i	0.731095	−	0.263704i
$663$	−2.29286e6	−	7.55944e6i	−0.202578	−	0.667891i
$664$	−288826.	−	170113.i	−0.0254224	−	0.0149733i
$665$			8.96742e6i			0.786346i
$666$	1.34519e6	+	992469.i	0.117516	+	0.0867025i
$667$		−	8.90816e6i		−	0.775306i
$668$	−1.29472e7	+	1.07370e7i	−1.12263	+	0.930981i
$669$	−3.55313e6	−	1.17145e7i	−0.306934	−	1.01195i
$670$	1.34968e6	+	3.74186e6i	0.116157	+	0.322033i
$671$	−809010.			−0.0693661
$672$	−7.55527e6	−	1.54602e7i	−0.645397	−	1.32066i
$673$	−4.40364e6			−0.374778			−0.187389	−	0.982286i	$-0.560003\pi$
$673$	−4.40364e6			−0.374778			−0.187389	+	0.982286i	$0.560003\pi$
$674$	−2.37309e6	−	6.57917e6i	−0.201217	−	0.557855i
$675$	4.51728e6	−	5.50320e6i	0.381608	−	0.464896i
$676$	5.28081e6	−	4.37932e6i	0.444461	−	0.368587i
$677$		−	1.33389e7i		−	1.11853i	−0.828988	−	0.559267i	$-0.811083\pi$
$677$		−	1.33389e7i		−	1.11853i	0.828988	−	0.559267i	$-0.188917\pi$
$678$	2.11952e6	−	1.58026e6i	0.177077	−	0.132025i
$679$			1.44187e7i			1.20019i
$680$	7.04203e6	+	4.14761e6i	0.584018	+	0.343974i
$681$	1.18311e6	−	358850.i	0.0977593	−	0.0296514i
$682$	−651150.	+	234868.i	−0.0536068	+	0.0193359i
$683$	−1.54515e7			−1.26742			−0.633709	−	0.773571i	$-0.718468\pi$
$683$	−1.54515e7			−1.26742			−0.633709	+	0.773571i	$0.718468\pi$
$684$	−9.93727e6	−	2.95965e6i	−0.812132	−	0.241880i
$685$	1.52808e7			1.24429
$686$	−2.73853e6	+	987780.i	−0.222181	+	0.0801401i
$687$	1.78571e7	−	5.41623e6i	1.44350	−	0.437830i
$688$	5.38293e6	+	1.01351e6i	0.433558	+	0.0816314i
$689$			4.58243e6i			0.367745i
$690$	5.57801e6	−	4.15884e6i	0.446022	−	0.332544i
$691$			1.41207e7i			1.12503i	0.826789	+	0.562513i	$0.190165\pi$
$691$			1.41207e7i			1.12503i	−0.826789	+	0.562513i	$0.809835\pi$
$692$	3.44239e6	+	4.15101e6i	0.273272	+	0.329525i
$693$	857535.	+	1.28358e6i	0.0678295	+	0.101529i
$694$	−2.60523e6	−	7.22276e6i	−0.205328	−	0.569252i
$695$	−3.62202e6			−0.284438
$696$	2.64833e6	−	1.09268e7i	0.207228	−	0.855005i
$697$	1.15761e7			0.902570
$698$	972990.	+	2.69752e6i	0.0755909	+	0.209569i
$699$	3.09267e6	+	1.01964e7i	0.239409	+	0.789320i
$700$	7.31649e6	+	8.82261e6i	0.564362	+	0.680537i
$701$			1.80511e7i			1.38743i	0.720252	+	0.693713i	$0.244026\pi$
$701$			1.80511e7i			1.38743i	−0.720252	+	0.693713i	$0.755974\pi$
$702$	−7.99879e6	−	2.83982e6i	−0.612606	−	0.217494i
$703$			1.62158e6i			0.123752i
$704$	−529671.	−	955333.i	−0.0402786	−	0.0726479i
$705$	−2.62078e6	−	8.64059e6i	−0.198590	−	0.654743i
$706$	9.50150e6	−	3.42717e6i	0.717431	−	0.258776i
$707$	−6.98814e6			−0.525791
$708$	−1.17260e7	+	1.77441e7i	−0.879160	+	1.33036i
$709$	−1.76046e7			−1.31526			−0.657628	−	0.753343i	$-0.728440\pi$
$709$	−1.76046e7			−1.31526			−0.657628	+	0.753343i	$0.728440\pi$
$710$	6.27031e6	−	2.26169e6i	0.466813	−	0.168378i
$711$	3.53757e6	+	5.29511e6i	0.262441	+	0.392827i
$712$	1.10363e7	−	1.87380e7i	0.815874	−	1.38523i
$713$			8.20701e6i			0.604590i
$714$	1.28500e7	+	1.72349e7i	0.943313	+	1.26521i
$715$			466003.i			0.0340897i
$716$	1.69511e7	−	1.40574e7i	1.23571	−	1.02476i
$717$	−1.74543e7	+	5.29406e6i	−1.26795	+	0.384584i
$718$	3.44067e6	+	9.53893e6i	0.249076	+	0.690540i
$719$	1.00812e7			0.727259			0.363630	−	0.931544i	$-0.381537\pi$
$719$	1.00812e7			0.727259			0.363630	+	0.931544i	$0.381537\pi$
$720$	8.07840e6	−	3.44294e6i	0.580756	−	0.247513i
$721$	−2.82330e7			−2.02264
$722$	1.33991e6	+	3.71478e6i	0.0956608	+	0.265210i
$723$	−1.17956e7	+	3.57772e6i	−0.839215	+	0.254543i
$724$	−2.37837e6	+	1.97235e6i	−0.168629	+	0.139842i
$725$			7.48885e6i			0.529140i
$726$	−8.43021e6	−	1.13070e7i	−0.593604	−	0.796167i
$727$			2.32781e7i			1.63347i	0.577013	+	0.816735i	$0.304218\pi$
$727$			2.32781e7i			1.63347i	−0.577013	+	0.816735i	$0.695782\pi$
$728$	6.93453e6	−	1.17738e7i	0.484940	−	0.823357i
$729$	−2.79653e6	−	1.40738e7i	−0.194895	−	0.980824i
$730$	−5.59293e6	+	2.01736e6i	−0.388447	+	0.140112i
$731$	−6.84325e6			−0.473663
$732$	−6.67437e6	+	1.00998e7i	−0.460397	+	0.696683i
$733$	2.69297e7			1.85128			0.925640	−	0.378405i	$-0.123527\pi$
$733$	2.69297e7			1.85128			0.925640	+	0.378405i	$0.123527\pi$
$734$	−3.84035e6	+	1.38521e6i	−0.263106	+	0.0949017i
$735$	−3.11490e6	−	1.02697e7i	−0.212680	−	0.701195i
$736$	−1.27854e7	+	2.06422e6i	−0.870004	+	0.140463i
$737$			664232.i			0.0450455i
$738$	7.38460e6	−	1.00091e7i	0.499099	−	0.676478i
$739$		−	6.71268e6i		−	0.452152i	−0.974110	−	0.226076i	$-0.927410\pi$
$739$		−	6.71268e6i		−	0.452152i	0.974110	−	0.226076i	$-0.0725898\pi$
$740$	−876679.	−	1.05715e6i	−0.0588520	−	0.0709668i
$741$	−2.38981e6	−	7.87910e6i	−0.159889	−	0.527146i
$742$	−4.23133e6	−	1.17310e7i	−0.282142	−	0.782211i
$743$	1.95647e7			1.30017			0.650087	−	0.759860i	$-0.274732\pi$
$743$	1.95647e7			1.30017			0.650087	+	0.759860i	$0.274732\pi$
$744$	−2.43989e6	+	1.00667e7i	−0.161599	+	0.666740i
$745$	8.71944e6			0.575570
$746$	−9.46896e6	−	2.62518e7i	−0.622953	−	1.72708i
$747$	374155.	−	249966.i	0.0245329	−	0.0163900i
$748$	871151.	+	1.05048e6i	0.0569298	+	0.0686490i
$749$			6.83277e6i			0.445033i
$750$	−1.24858e7	+	9.30913e6i	−0.810520	+	0.604305i
$751$			6.08953e6i			0.393989i	0.980405	+	0.196994i	$0.0631180\pi$
$751$			6.08953e6i			0.393989i	−0.980405	+	0.196994i	$0.936882\pi$
$752$	−3.10982e6	+	1.65168e7i	−0.200535	+	1.06508i
$753$	2.11302e7	−	6.40902e6i	1.35805	−	0.411912i
$754$	8.39833e6	−	3.02926e6i	0.537978	−	0.194048i
$755$	−9.76454e6			−0.623425
$756$	2.30991e7	−	116033.i	1.46991	−	0.00738377i
$757$	2.24957e7			1.42679			0.713396	−	0.700761i	$-0.247156\pi$
$757$	2.24957e7			1.42679			0.713396	+	0.700761i	$0.247156\pi$
$758$	−2.00294e7	+	7.22457e6i	−1.26618	+	0.456708i
$759$	1.11181e6	−	337223.i	0.0700528	−	0.0212478i
$760$	7.33981e6	+	4.32300e6i	0.460947	+	0.271488i
$761$		−	1.94840e7i		−	1.21960i	−0.792555	−	0.609800i	$-0.791250\pi$
$761$		−	1.94840e7i		−	1.21960i	0.792555	−	0.609800i	$-0.208750\pi$
$762$	−1.15174e7	+	8.58709e6i	−0.718565	+	0.535746i
$763$		−	2.85275e7i		−	1.77399i
$764$	1.29358e7	−	1.07275e7i	0.801789	−	0.664915i
$765$	−9.12247e6	+	6.09456e6i	−0.563584	+	0.376521i
$766$	2.21171e6	+	6.13175e6i	0.136193	+	0.377583i
$767$	−1.68890e7			−1.03661
$768$	−1.62963e7	−	1.26905e6i	−0.996982	−	0.0776380i
$769$	−2.49302e7			−1.52023			−0.760117	−	0.649786i	$-0.774858\pi$
$769$	−2.49302e7			−1.52023			−0.760117	+	0.649786i	$0.774858\pi$
$770$	−430299.	−	1.19296e6i	−0.0261543	−	0.0725104i
$771$	−3.65602e6	−	1.20537e7i	−0.221499	−	0.730272i
$772$	−901694.	+	747764.i	−0.0544523	+	0.0451566i
$773$			3.44505e6i			0.207370i	0.994610	+	0.103685i	$0.0330634\pi$
$773$			3.44505e6i			0.207370i	−0.994610	+	0.103685i	$0.966937\pi$
$774$	−4.36543e6	+	5.91690e6i	−0.261924	+	0.355011i
$775$		−	6.89942e6i		−	0.412628i
$776$	1.18017e7	+	6.95093e6i	0.703540	+	0.414371i
$777$	−1.04856e6	−	3.45706e6i	−0.0623077	−	0.205425i
$778$	−2.28320e7	+	8.23546e6i	−1.35237	+	0.487797i
$779$	1.20656e7			0.712370
$780$	5.81765e6	+	3.84455e6i	0.342382	+	0.226260i
$781$	1.11307e6			0.0652970
$782$	1.52203e7	−	5.48994e6i	0.890035	−	0.321034i
$783$	1.16659e7	+	9.57590e6i	0.680008	+	0.558181i
$784$	−3.69614e6	+	1.96309e7i	−0.214763	+	1.14064i
$785$			356506.i			0.0206487i
$786$	−1.28844e7	−	1.72812e7i	−0.743890	−	0.997738i
$787$		−	9.04481e6i		−	0.520550i	−0.965534	−	0.260275i	$-0.916187\pi$
$787$		−	9.04481e6i		−	0.520550i	0.965534	−	0.260275i	$-0.0838133\pi$
$788$	−1.84683e7	−	2.22700e7i	−1.05952	−	1.27763i
$789$	1.20050e7	−	3.64124e6i	0.686546	−	0.208236i
$790$	−1.77510e6	−	4.92131e6i	−0.101194	−	0.280552i
$791$	−5.71331e6			−0.324673
$792$	1.46400e6	−	83105.8i	0.0829333	−	0.00470781i
$793$	−9.61309e6			−0.542850
$794$	4.78041e6	+	1.32532e7i	0.269100	+	0.746054i
$795$	6.09019e6	−	1.84722e6i	0.341754	−	0.103657i
$796$	−1.06229e7	−	1.28096e7i	−0.594236	−	0.716561i
$797$			8.73525e6i			0.487113i	0.969887	+	0.243556i	$0.0783141\pi$
$797$			8.73525e6i			0.487113i	−0.969887	+	0.243556i	$0.921686\pi$
$798$	1.33933e7	+	1.79637e7i	0.744528	+	0.998593i
$799$		−	2.09976e7i		−	1.16360i
$800$	1.07484e7	−	1.73534e6i	0.593771	−	0.0958648i
$801$	1.62169e7	+	2.42738e7i	0.893071	+	1.33677i
$802$	5.40719e6	−	1.95036e6i	0.296849	−	0.107073i
$803$	−992821.			−0.0543353
$804$	8.29238e6	+	5.47995e6i	0.452417	+	0.298976i
$805$	−1.50359e7			−0.817788
$806$	−7.73732e6	+	2.79083e6i	−0.419520	+	0.151320i
$807$	1.95849e6	+	6.45706e6i	0.105862	+	0.349021i
$808$	−3.36883e6	+	5.71977e6i	−0.181531	+	0.308213i
$809$			2.81254e7i			1.51087i	0.655222	+	0.755437i	$0.272575\pi$
$809$			2.81254e7i			1.51087i	−0.655222	+	0.755437i	$0.727425\pi$
$810$	−549826.	+	1.17754e7i	−0.0294451	+	0.630614i
$811$			3.13595e7i			1.67424i	0.547020	+	0.837119i	$0.315762\pi$
$811$			3.13595e7i			1.67424i	−0.547020	+	0.837119i	$0.684238\pi$
$812$	−1.87025e7	+	1.55098e7i	−0.995427	+	0.825496i
$813$	−939941.	−	3.09894e6i	−0.0498740	−	0.164432i
$814$	−77811.2	−	215724.i	−0.00411605	−	0.0114114i
$815$	1.84619e7			0.973602
$816$	2.03014e7	−	2.20908e6i	1.06734	−	0.116141i
$817$	−7.13262e6			−0.373847
$818$	4.91349e6	+	1.36222e7i	0.256748	+	0.711809i
$819$	1.01897e7	+	1.52521e7i	0.530825	+	0.794550i
$820$	−7.86584e6	+	6.52305e6i	−0.408517	+	0.338778i
$821$		−	2.15360e7i		−	1.11508i	−0.830149	−	0.557541i	$-0.811745\pi$
$821$		−	2.15360e7i		−	1.11508i	0.830149	−	0.557541i	$-0.188255\pi$
$822$	3.06109e7	−	2.28227e7i	1.58014	−	1.17812i
$823$		−	3.44819e7i		−	1.77456i	−0.461228	−	0.887282i	$-0.652591\pi$
$823$		−	3.44819e7i		−	1.77456i	0.461228	−	0.887282i	$-0.347409\pi$
$824$	−1.36105e7	+	2.31087e7i	−0.698324	+	1.18565i
$825$	−934669.	+	283495.i	−0.0478105	+	0.0145014i
$826$	4.32357e7	−	1.55950e7i	2.20492	−	0.795308i
$827$	4.02453e6			0.204622			0.102311	−	0.994752i	$-0.467376\pi$
$827$	4.02453e6			0.204622			0.102311	+	0.994752i	$0.467376\pi$
$828$	4.96253e6	−	1.66621e7i	0.251552	−	0.844606i
$829$	2.00981e7			1.01571			0.507855	−	0.861443i	$-0.330439\pi$
$829$	2.00981e7			1.01571			0.507855	+	0.861443i	$0.330439\pi$
$830$	−347741.	+	125430.i	−0.0175211	+	0.00631982i
$831$	−2.52815e7	+	7.66813e6i	−1.26999	+	0.385201i
$832$	−6.29384e6	−	1.13518e7i	−0.315215	−	0.568533i
$833$		−	2.49565e7i		−	1.24615i
$834$	−7.25569e6	+	5.40967e6i	−0.361213	+	0.269312i
$835$			1.85497e7i			0.920707i
$836$	907988.	+	1.09490e6i	0.0449329	+	0.0541825i
$837$	−1.07477e7	−	8.82220e6i	−0.530276	−	0.435275i
$838$	269008.	+	745800.i	0.0132329	+	0.0366870i
$839$	870459.			0.0426917			0.0213458	−	0.999772i	$-0.493205\pi$
$839$	870459.			0.0426917			0.0213458	+	0.999772i	$0.493205\pi$
$840$	−1.84431e7	−	4.47008e6i	−0.901854	−	0.218583i
$841$	4.63599e6			0.226023
$842$	−275956.	−	765061.i	−0.0134140	−	0.0371891i
$843$	−6.83168e6	−	2.25237e7i	−0.331100	−	1.09162i
$844$	−2.56061e7	−	3.08772e7i	−1.23734	−	1.49205i
$845$		−	7.56592e6i		−	0.364519i
$846$	−1.81552e7	−	1.33947e7i	−0.872117	−	0.643439i
$847$			3.04787e7i			1.45978i
$848$	−1.16416e7	−	2.19191e6i	−0.555934	−	0.104672i
$849$	6.74098e6	+	2.22247e7i	0.320962	+	1.05820i
$850$	−1.27953e7	+	4.61525e6i	−0.607441	+	0.219103i
$851$	−2.71896e6			−0.128700
$852$	9.18285e6	−	1.38957e7i	0.433389	−	0.655815i
$853$	−2.81846e6			−0.132629			−0.0663145	−	0.997799i	$-0.521124\pi$
$853$	−2.81846e6			−0.132629			−0.0663145	+	0.997799i	$0.521124\pi$
$854$	2.46094e7	−	8.87656e6i	1.15467	−	0.416486i
$855$	−9.50821e6	+	6.35227e6i	−0.444819	+	0.297176i
$856$	5.59260e6	+	3.29393e6i	0.260873	+	0.153649i
$857$		−	3.15864e7i		−	1.46909i	−0.678559	−	0.734545i	$-0.737395\pi$
$857$		−	3.15864e7i		−	1.46909i	0.678559	−	0.734545i	$-0.262605\pi$
$858$	696000.	+	933505.i	0.0322768	+	0.0432911i
$859$			3.28617e7i			1.51952i	0.650202	+	0.759762i	$0.274684\pi$
$859$			3.28617e7i			1.51952i	−0.650202	+	0.759762i	$0.725316\pi$
$860$	4.64991e6	−	3.85612e6i	0.214387	−	0.177789i
$861$	−2.57227e7	+	7.80197e6i	−1.18252	+	0.358671i
$862$	1.21638e7	+	3.37228e7i	0.557570	+	1.54581i
$863$	−3.88977e7			−1.77786			−0.888928	−	0.458047i	$-0.848549\pi$
$863$	−3.88977e7			−1.77786			−0.888928	+	0.458047i	$0.848549\pi$
$864$	1.10406e7	−	1.89625e7i	0.503162	−	0.864192i
$865$	5.94724e6			0.270256
$866$	6.20555e6	+	1.72043e7i	0.281181	+	0.779546i
$867$	−3.23412e6	+	980942.i	−0.146119	+	0.0443196i
$868$	1.72305e7	−	1.42890e7i	0.776242	−	0.643729i
$869$		−	873599.i		−	0.0392430i
$870$	−7.41143e6	−	9.94053e6i	−0.331974	−	0.445258i
$871$			7.89276e6i			0.352520i
$872$	−2.33497e7	−	1.37525e7i	−1.03989	−	0.612477i
$873$	−1.52882e7	+	1.02138e7i	−0.678925	+	0.453578i
$874$	1.58639e7	−	5.72208e6i	0.702477	−	0.253382i
$875$	3.36564e7			1.48610
$876$	−8.19083e6	+	1.23945e7i	−0.360635	+	0.545720i
$877$	−2.60310e7			−1.14286			−0.571428	−	0.820652i	$-0.693610\pi$
$877$	−2.60310e7			−1.14286			−0.571428	+	0.820652i	$0.693610\pi$
$878$	2.29459e6	−	827654.i	0.100454	−	0.0362337i
$879$	−3.43757e6	−	1.13335e7i	−0.150065	−	0.494757i
$880$	−1.18387e6	−	222903.i	−0.0515346	−	0.00970306i
$881$			1.20174e7i			0.521638i	0.965388	+	0.260819i	$0.0839926\pi$
$881$			1.20174e7i			0.521638i	−0.965388	+	0.260819i	$0.916007\pi$
$882$	−2.15782e7	−	1.59202e7i	−0.933992	−	0.689090i
$883$		−	2.58606e7i		−	1.11619i	−0.829778	−	0.558094i	$-0.811533\pi$
$883$		−	2.58606e7i		−	1.11619i	0.829778	−	0.558094i	$-0.188467\pi$
$884$	1.03515e7	+	1.24824e7i	0.445525	+	0.537238i
$885$	6.80811e6	+	2.24460e7i	0.292192	+	0.963343i
$886$	−3.10960e6	−	8.62106e6i	−0.133082	−	0.368957i
$887$	−7.77528e6			−0.331824			−0.165912	−	0.986141i	$-0.553057\pi$
$887$	−7.77528e6			−0.331824			−0.165912	+	0.986141i	$0.553057\pi$
$888$	−3.33508e6	−	808327.i	−0.141930	−	0.0343997i
$889$	3.10459e7			1.31750
$890$	−8.13740e6	−	2.25602e7i	−0.344358	−	0.954701i
$891$	−753530.	+	1.81850e6i	−0.0317985	+	0.0767395i
$892$	1.60412e7	+	1.93433e7i	0.675032	+	0.813990i
$893$		−	2.18855e7i		−	0.918390i
$894$	1.74669e7	−	1.30229e7i	0.730925	−	0.544961i
$895$		−	2.42862e7i		−	1.01345i
$896$	2.65942e7	+	2.32488e7i	1.10667	+	0.967456i
$897$	1.32111e7	−	4.00707e6i	0.548224	−	0.166282i
$898$	4.16409e6	−	1.50198e6i	0.172318	−	0.0621546i
$899$	1.46257e7			0.603554
$900$	−4.17187e6	+	1.40074e7i	−0.171682	+	0.576436i
$901$	1.47998e7			0.607357
$902$	−1.60512e6	+	578965.i	−0.0656890	+	0.0236939i
$903$	1.52060e7	−	4.61215e6i	0.620579	−	0.188228i
$904$	−2.75426e6	+	4.67633e6i	−0.112094	+	0.190320i
$905$			3.40753e6i			0.138299i
$906$	−1.95605e7	+	1.45838e7i	−0.791697	+	0.590271i
$907$			7.84270e6i			0.316554i	0.987395	+	0.158277i	$0.0505938\pi$
$907$			7.84270e6i			0.316554i	−0.987395	+	0.158277i	$0.949406\pi$
$908$	−1.95359e6	+	1.62009e6i	−0.0786355	+	0.0652115i
$909$	−4.95020e6	−	7.40957e6i	−0.198707	−	0.297429i
$910$	−5.11304e6	−	1.41754e7i	−0.204680	−	0.567457i
$911$	1.38954e7			0.554721			0.277360	−	0.960766i	$-0.410540\pi$
$911$	1.38954e7			0.554721			0.277360	+	0.960766i	$0.410540\pi$
$912$	2.11599e7	−	2.30249e6i	0.842414	−	0.0916664i
$913$	−61728.8			−0.00245082
$914$	7.38994e6	+	2.04879e7i	0.292601	+	0.811208i
$915$	3.87512e6	+	1.27761e7i	0.153015	+	0.504482i
$916$	−2.94861e7	+	2.44525e7i	−1.16112	+	0.962907i
$917$			4.65826e7i			1.82937i
$918$	−9.17174e6	+	2.58336e7i	−0.359207	+	1.01176i
$919$			1.73363e6i			0.0677124i	0.999427	+	0.0338562i	$0.0107788\pi$
$919$			1.73363e6i			0.0677124i	−0.999427	+	0.0338562i	$0.989221\pi$
$920$	−7.24850e6	+	1.23069e7i	−0.282344	+	0.479378i
$921$	−5.70496e6	−	1.88090e7i	−0.221617	−	0.730662i
$922$	−1.20442e7	+	4.34432e6i	−0.466607	+	0.168304i
$923$	1.32260e7			0.511006
$924$	−2.64374e6	−	1.74709e6i	−0.101868	−	0.0673186i
$925$	2.28576e6			0.0878366
$926$	−3.99652e7	+	1.44154e7i	−1.53163	+	0.552457i
$927$	−1.99995e7	−	2.99357e7i	−0.764398	−	1.14417i
$928$	3.67863e6	+	2.27849e7i	0.140222	+	0.868513i
$929$			2.75393e6i			0.104692i	0.998629	+	0.0523460i	$0.0166699\pi$
$929$			2.75393e6i			0.104692i	−0.998629	+	0.0523460i	$0.983330\pi$
$930$	6.82809e6	+	9.15813e6i	0.258876	+	0.347216i
$931$		−	2.60118e7i		−	0.983548i
$932$	−1.39624e7	−	1.68366e7i	−0.526526	−	0.634913i
$933$	1.39080e7	−	4.21843e6i	0.523070	−	0.158653i
$934$	1.10229e7	+	3.05599e7i	0.413455	+	1.14626i
$935$	1.50504e6			0.0563015
$936$	1.73961e7	−	987508.i	0.649025	−	0.0368427i
$937$	−2.15099e7			−0.800367			−0.400183	−	0.916435i	$-0.631054\pi$
$937$	−2.15099e7			−0.800367			−0.400183	+	0.916435i	$0.631054\pi$
$938$	−7.28804e6	−	2.02054e7i	−0.270460	−	0.749826i
$939$	3.88960e7	−	1.17975e7i	1.43960	−	0.436644i
$940$	1.18320e7	+	1.42676e7i	0.436754	+	0.526661i
$941$		−	2.36563e7i		−	0.870907i	−0.900211	−	0.435454i	$-0.856588\pi$
$941$		−	2.36563e7i		−	0.870907i	0.900211	−	0.435454i	$-0.143412\pi$
$942$	532461.	+	714160.i	0.0195506	+	0.0262221i
$943$			2.02308e7i			0.740855i
$944$	8.07850e6	−	4.29063e7i	0.295053	−	1.56708i
$945$	1.61630e7	−	1.96907e7i	0.588767	−	0.717268i
$946$	948874.	−	342257.i	0.0344731	−	0.0124344i
$947$	−3.42431e6			−0.124079			−0.0620396	−	0.998074i	$-0.519760\pi$
$947$	−3.42431e6			−0.124079			−0.0620396	+	0.998074i	$0.519760\pi$
$948$	−1.09062e7	−	7.20724e6i	−0.394140	−	0.260464i
$949$	−1.17972e7			−0.425221
$950$	−1.33364e7	+	4.81041e6i	−0.479434	+	0.172931i
$951$	4.92182e6	+	1.62270e7i	0.176471	+	0.581818i
$952$	−3.80257e7	−	2.23964e7i	−1.35983	−	0.800913i
$953$			3.22434e7i			1.15003i	0.818143	+	0.575014i	$0.195004\pi$
$953$			3.22434e7i			1.15003i	−0.818143	+	0.575014i	$0.804996\pi$
$954$	9.44106e6	−	1.27964e7i	0.335853	−	0.455215i
$955$		−	1.85334e7i		−	0.657577i
$956$	2.88210e7	−	2.39009e7i	1.01992	−	0.845804i
$957$	−600963.	−	1.98135e6i	−0.0212113	−	0.0699327i
$958$	−1.28849e7	−	3.57221e7i	−0.453593	−	1.25754i
$959$	−8.25138e7			−2.89721
$960$	−1.25498e7	+	1.29407e7i	−0.439499	+	0.453190i
$961$	1.51547e7			0.529344
$962$	−924595.	−	2.56335e6i	−0.0322117	−	0.0893038i
$963$	−7.24483e6	+	4.84014e6i	−0.251746	+	0.168187i
$964$	1.94772e7	−	1.61522e7i	0.675047	−	0.559809i
$965$			1.29188e6i			0.0446583i
$966$	−3.01203e7	+	2.24570e7i	−1.03852	+	0.774298i
$967$		−	2.68972e7i		−	0.924998i	−0.886620	−	0.462499i	$-0.846953\pi$
$967$		−	2.68972e7i		−	0.924998i	0.886620	−	0.462499i	$-0.153047\pi$
$968$	2.49468e7	+	1.46931e7i	0.855708	+	0.503995i
$969$	−2.54470e7	+	7.71835e6i	−0.870618	+	0.264068i
$970$	1.42090e7	−	5.12514e6i	0.484879	−	0.174895i
$971$	4.53191e6			0.154253			0.0771264	−	0.997021i	$-0.475426\pi$
$971$	4.53191e6			0.154253			0.0771264	+	0.997021i	$0.475426\pi$
$972$	1.64858e7	+	2.44099e7i	0.559685	+	0.828706i
$973$	1.95582e7			0.662289
$974$	7.40964e6	−	2.67264e6i	0.250265	−	0.0902699i
$975$	−1.11062e7	+	3.36864e6i	−0.374158	+	0.113486i
$976$	4.59822e6	−	2.44219e7i	0.154513	−	0.820645i
$977$			1.54207e7i			0.516853i	0.966031	+	0.258426i	$0.0832039\pi$
$977$			1.54207e7i			0.516853i	−0.966031	+	0.258426i	$0.916796\pi$
$978$	3.69831e7	−	2.75738e7i	1.23639	−	0.921826i
$979$		−	4.00474e6i		−	0.133542i
$980$	1.40628e7	+	1.69576e7i	0.467741	+	0.564027i
$981$	3.02479e7	−	2.02081e7i	1.00351	−	0.670428i
$982$	−3.49384e6	−	9.68632e6i	−0.115618	−	0.320539i
$983$	2.15180e7			0.710263			0.355131	−	0.934816i	$-0.384436\pi$
$983$	2.15180e7			0.710263			0.355131	+	0.934816i	$0.384436\pi$
$984$	−6.01447e6	+	2.48151e7i	−0.198020	+	0.817012i
$985$	−3.19067e7			−1.04783
$986$	−9.78358e6	−	2.71240e7i	−0.320483	−	0.888509i
$987$	1.41518e7	+	4.66577e7i	0.462399	+	1.52451i
$988$	1.07892e7	+	1.30102e7i	0.351639	+	0.424025i
$989$		−	1.19595e7i		−	0.388796i
$990$	960094.	−	1.30131e6i	0.0311333	−	0.0421981i
$991$			1.65100e7i			0.534028i	0.963693	+	0.267014i	$0.0860370\pi$
$991$			1.65100e7i			0.534028i	−0.963693	+	0.267014i	$0.913963\pi$
$992$	−3.38909e6	−	2.09915e7i	−0.109346	−	0.677274i
$993$	−7.00943e6	−	2.31098e7i	−0.225585	−	0.743742i
$994$	−3.38586e7	+	1.22127e7i	−1.08693	+	0.392054i
$995$	−1.83526e7			−0.587678
$996$	−509266.	+	770633.i	−0.0162666	+	0.0246150i
$997$	−1.65409e7			−0.527012			−0.263506	−	0.964658i	$-0.584879\pi$
$997$	−1.65409e7			−0.527012			−0.263506	+	0.964658i	$0.584879\pi$
$998$	2.66422e7	−	9.60980e6i	0.846729	−	0.305413i
$999$	2.92277e6	−	3.56068e6i	0.0926575	−	0.112881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.6.b.a.11.6	yes	8
3.2	odd	2	inner	12.6.b.a.11.3	✓	8
4.3	odd	2	inner	12.6.b.a.11.4	yes	8
8.3	odd	2		192.6.c.e.191.7		8
8.5	even	2		192.6.c.e.191.2		8
12.11	even	2	inner	12.6.b.a.11.5	yes	8
24.5	odd	2		192.6.c.e.191.8		8
24.11	even	2		192.6.c.e.191.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.6.b.a.11.3	✓	8	3.2	odd	2	inner
12.6.b.a.11.4	yes	8	4.3	odd	2	inner
12.6.b.a.11.5	yes	8	12.11	even	2	inner
12.6.b.a.11.6	yes	8	1.1	even	1	trivial
192.6.c.e.191.1		8	24.11	even	2
192.6.c.e.191.2		8	8.5	even	2
192.6.c.e.191.7		8	8.3	odd	2
192.6.c.e.191.8		8	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91937 + 5.32128i) q^{2} +(14.9174 - 4.52459i) q^{3} +(-24.6320 + 20.4270i) q^{4} +35.2908i q^{5} +(52.7086 + 70.6951i) q^{6} -190.564i q^{7} +(-155.976 - 91.8667i) q^{8} +(202.056 - 134.990i) q^{9} +O(q^{10})\)	\(q+(1.91937 + 5.32128i) q^{2} +(14.9174 - 4.52459i) q^{3} +(-24.6320 + 20.4270i) q^{4} +35.2908i q^{5} +(52.7086 + 70.6951i) q^{6} -190.564i q^{7} +(-155.976 - 91.8667i) q^{8} +(202.056 - 134.990i) q^{9} +(-187.792 + 67.7362i) q^{10} -33.3357 q^{11} +(-275.021 + 416.168i) q^{12} -396.112 q^{13} +(1014.04 - 365.763i) q^{14} +(159.676 + 526.446i) q^{15} +(189.472 - 1006.32i) q^{16} +1279.32i q^{17} +(1106.14 + 816.100i) q^{18} +1333.42i q^{19} +(-720.886 - 869.283i) q^{20} +(-862.224 - 2842.71i) q^{21} +(-63.9836 - 177.388i) q^{22} -2235.78 q^{23} +(-2742.41 - 664.681i) q^{24} +1879.56 q^{25} +(-760.287 - 2107.82i) q^{26} +(2403.37 - 2927.92i) q^{27} +(3892.66 + 4693.97i) q^{28} +3984.36i q^{29} +(-2494.89 + 1860.13i) q^{30} -3670.76i q^{31} +(5718.57 - 923.267i) q^{32} +(-497.280 + 150.830i) q^{33} +(-6807.62 + 2455.49i) q^{34} +6725.15 q^{35} +(-2219.60 + 7452.49i) q^{36} +1216.11 q^{37} +(-7095.48 + 2559.32i) q^{38} +(-5908.95 + 1792.25i) q^{39} +(3242.05 - 5504.51i) q^{40} -9048.65i q^{41} +(13471.9 - 10044.4i) q^{42} +5349.13i q^{43} +(821.124 - 680.949i) q^{44} +(4763.91 + 7130.72i) q^{45} +(-4291.29 - 11897.2i) q^{46} -16413.1 q^{47} +(-1726.76 - 15868.9i) q^{48} -19507.6 q^{49} +(3607.58 + 10001.7i) q^{50} +(5788.40 + 19084.1i) q^{51} +(9757.04 - 8091.40i) q^{52} -11568.5i q^{53} +(20193.2 + 7169.23i) q^{54} -1176.44i q^{55} +(-17506.5 + 29723.4i) q^{56} +(6033.17 + 19891.1i) q^{57} +(-21201.9 + 7647.48i) q^{58} +42636.9 q^{59} +(-14686.9 - 9705.70i) q^{60} +24268.6 q^{61} +(19533.1 - 7045.56i) q^{62} +(-25724.2 - 38504.6i) q^{63} +(15889.0 + 28658.0i) q^{64} -13979.1i q^{65} +(-1757.08 - 2356.67i) q^{66} -19925.6i q^{67} +(-26132.7 - 31512.2i) q^{68} +(-33351.9 + 10116.0i) q^{69} +(12908.1 + 35786.4i) q^{70} -33389.6 q^{71} +(-43917.0 + 2493.00i) q^{72} +29782.6 q^{73} +(2334.17 + 6471.27i) q^{74} +(28038.1 - 8504.25i) q^{75} +(-27237.8 - 32844.7i) q^{76} +6352.57i q^{77} +(-20878.5 - 28003.2i) q^{78} +26206.1i q^{79} +(35513.8 + 6686.61i) q^{80} +(22604.3 - 54551.2i) q^{81} +(48150.4 - 17367.7i) q^{82} +1851.74 q^{83} +(79306.5 + 52409.0i) q^{84} -45148.2 q^{85} +(-28464.2 + 10267.0i) q^{86} +(18027.6 + 59436.2i) q^{87} +(5199.56 + 3062.44i) q^{88} +120134. i q^{89} +(-28800.8 + 39036.6i) q^{90} +75484.7i q^{91} +(55071.7 - 45670.3i) q^{92} +(-16608.7 - 54758.1i) q^{93} +(-31502.8 - 87338.5i) q^{94} -47057.3 q^{95} +(81128.6 - 39646.9i) q^{96} -75663.3 q^{97} +(-37442.4 - 103805. i) q^{98} +(-6735.67 + 4499.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 + 24 * q^6 - 24 * q^9	\( 8 q + 8 q^{4} + 24 q^{6} - 24 q^{9} - 272 q^{10} - 696 q^{12} + 112 q^{13} + 2336 q^{16} + 3696 q^{18} - 336 q^{21} - 8304 q^{22} - 11232 q^{24} - 1368 q^{25} + 19248 q^{28} + 25008 q^{30} + 4224 q^{33} - 36416 q^{34} - 42072 q^{36} + 6448 q^{37} + 53824 q^{40} + 59088 q^{42} - 17664 q^{45} - 69600 q^{46} - 74976 q^{48} - 21544 q^{49} + 84208 q^{52} + 78120 q^{54} + 43344 q^{57} - 62576 q^{58} - 64704 q^{60} + 59632 q^{61} + 38528 q^{64} + 33360 q^{66} - 92928 q^{69} - 30432 q^{70} + 20544 q^{72} - 129200 q^{73} - 86256 q^{76} - 83760 q^{78} + 200520 q^{81} + 154720 q^{82} + 167856 q^{84} + 229376 q^{85} - 150336 q^{88} - 251472 q^{90} - 346128 q^{93} + 386112 q^{94} + 331392 q^{96} - 392048 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 + 24 * q^6 - 24 * q^9 - 272 * q^10 - 696 * q^12 + 112 * q^13 + 2336 * q^16 + 3696 * q^18 - 336 * q^21 - 8304 * q^22 - 11232 * q^24 - 1368 * q^25 + 19248 * q^28 + 25008 * q^30 + 4224 * q^33 - 36416 * q^34 - 42072 * q^36 + 6448 * q^37 + 53824 * q^40 + 59088 * q^42 - 17664 * q^45 - 69600 * q^46 - 74976 * q^48 - 21544 * q^49 + 84208 * q^52 + 78120 * q^54 + 43344 * q^57 - 62576 * q^58 - 64704 * q^60 + 59632 * q^61 + 38528 * q^64 + 33360 * q^66 - 92928 * q^69 - 30432 * q^70 + 20544 * q^72 - 129200 * q^73 - 86256 * q^76 - 83760 * q^78 + 200520 * q^81 + 154720 * q^82 + 167856 * q^84 + 229376 * q^85 - 150336 * q^88 - 251472 * q^90 - 346128 * q^93 + 386112 * q^94 + 331392 * q^96 - 392048 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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