LMFDB - Embedded newform 147.6.e.p.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 $ x^12 - 2x^11 + 63x^10 - 126x^9 + 2784x^8 - 5290x^7 + 62015x^6 - 99530x^5 + 973971x^4 - 1176024x^3 + 5644794x^2 + 4339328*x + 5466244
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.5
Root			$-0.455061 + 0.788188i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.p.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.65908 + 4.60566i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(1.85862 - 3.21922i) q^{4} +(-51.7353 - 89.6081i) q^{5} -47.8634 q^{6} +189.950 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(2.65908 + 4.60566i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(1.85862 - 3.21922i) q^{4} +(-51.7353 - 89.6081i) q^{5} -47.8634 q^{6} +189.950 q^{8} +(-40.5000 - 70.1481i) q^{9} +(275.136 - 476.550i) q^{10} +(-326.654 + 565.781i) q^{11} +(16.7276 + 28.9730i) q^{12} -138.055 q^{13} +931.235 q^{15} +(445.615 + 771.828i) q^{16} +(-587.188 + 1017.04i) q^{17} +(215.385 - 373.058i) q^{18} +(855.386 + 1481.57i) q^{19} -384.625 q^{20} -3474.39 q^{22} +(2010.14 + 3481.67i) q^{23} +(-854.774 + 1480.51i) q^{24} +(-3790.57 + 6565.47i) q^{25} +(-367.098 - 635.832i) q^{26} +729.000 q^{27} +2649.46 q^{29} +(2476.22 + 4288.95i) q^{30} +(1437.32 - 2489.52i) q^{31} +(669.346 - 1159.34i) q^{32} +(-2939.89 - 5092.03i) q^{33} -6245.51 q^{34} -301.096 q^{36} +(-1428.43 - 2474.12i) q^{37} +(-4549.08 + 7879.23i) q^{38} +(621.246 - 1076.03i) q^{39} +(-9827.10 - 17021.0i) q^{40} +216.487 q^{41} +2928.29 q^{43} +(1214.25 + 2103.14i) q^{44} +(-4190.56 + 7258.26i) q^{45} +(-10690.2 + 18516.0i) q^{46} +(-7408.41 - 12831.7i) q^{47} -8021.07 q^{48} -40317.7 q^{50} +(-5284.69 - 9153.35i) q^{51} +(-256.591 + 444.429i) q^{52} +(-10583.9 + 18331.8i) q^{53} +(1938.47 + 3357.52i) q^{54} +67598.1 q^{55} -15397.0 q^{57} +(7045.13 + 12202.5i) q^{58} +(-17344.6 + 30041.7i) q^{59} +(1730.81 - 2997.85i) q^{60} +(4376.56 + 7580.43i) q^{61} +15287.8 q^{62} +35638.7 q^{64} +(7142.29 + 12370.8i) q^{65} +(15634.8 - 27080.2i) q^{66} +(6034.26 - 10451.6i) q^{67} +(2182.72 + 3780.58i) q^{68} -36182.5 q^{69} -35541.5 q^{71} +(-7692.97 - 13324.6i) q^{72} +(-16742.9 + 28999.5i) q^{73} +(7596.63 - 13157.8i) q^{74} +(-34115.2 - 59089.2i) q^{75} +6359.35 q^{76} +6607.76 q^{78} +(-21567.4 - 37355.9i) q^{79} +(46108.0 - 79861.5i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(575.656 + 997.066i) q^{82} -43338.8 q^{83} +121513. q^{85} +(7786.54 + 13486.7i) q^{86} +(-11922.6 + 20650.5i) q^{87} +(-62047.9 + 107470. i) q^{88} +(51766.7 + 89662.5i) q^{89} -44572.0 q^{90} +14944.3 q^{92} +(12935.9 + 22405.7i) q^{93} +(39399.1 - 68241.2i) q^{94} +(88507.3 - 153299. i) q^{95} +(6024.11 + 10434.1i) q^{96} -86294.4 q^{97} +52918.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	2.65908	+	4.60566i	0.470063	+	0.814173i	0.999414	−	0.0342301i	$-0.0108979\pi$
$2$	2.65908	+	4.60566i	0.470063	+	0.814173i	−0.529351	+	0.848403i	$0.677565\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	1.85862	−	3.21922i	0.0580818	−	0.100601i
$5$	−51.7353	−	89.6081i	−0.925468	−	1.60296i	−0.790806	−	0.612067i	$-0.790338\pi$
$5$	−51.7353	−	89.6081i	−0.925468	−	1.60296i	−0.134662	−	0.990892i	$-0.542995\pi$
$6$	−47.8634			−0.542782
$7$		0			0
$7$		0			0
$8$	189.950			1.04933
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	275.136	−	476.550i	0.870057	−	1.50698i
$11$	−326.654	+	565.781i	−0.813966	+	1.40983i	0.0961016	+	0.995372i	$0.469363\pi$
$11$	−326.654	+	565.781i	−0.813966	+	1.40983i	−0.910068	+	0.414459i	$0.863971\pi$
$12$	16.7276	+	28.9730i	0.0335336	+	0.0580818i
$13$	−138.055			−0.226565			−0.113282	−	0.993563i	$-0.536137\pi$
$13$	−138.055			−0.226565			−0.113282	+	0.993563i	$0.536137\pi$
$14$		0			0
$15$	931.235			1.06864
$16$	445.615	+	771.828i	0.435171	+	0.753739i
$17$	−587.188	+	1017.04i	−0.492782	+	0.853523i	−0.999965	−	0.00831489i	$-0.997353\pi$
$17$	−587.188	+	1017.04i	−0.492782	+	0.853523i	0.507184	+	0.861838i	$0.330687\pi$
$18$	215.385	−	373.058i	0.156688	−	0.271391i
$19$	855.386	+	1481.57i	0.543599	+	0.941541i	0.998694	+	0.0510976i	$0.0162720\pi$
$19$	855.386	+	1481.57i	0.543599	+	0.941541i	−0.455095	+	0.890443i	$0.650395\pi$
$20$	−384.625			−0.215012
$21$		0			0
$22$	−3474.39			−1.53046
$23$	2010.14	+	3481.67i	0.792332	+	1.37236i	0.924520	+	0.381134i	$0.124466\pi$
$23$	2010.14	+	3481.67i	0.792332	+	1.37236i	−0.132188	+	0.991225i	$0.542200\pi$
$24$	−854.774	+	1480.51i	−0.302917	+	0.524667i
$25$	−3790.57	+	6565.47i	−1.21298	+	2.10095i
$26$	−367.098	−	635.832i	−0.106500	−	0.184463i
$27$	729.000			0.192450
$28$		0			0
$29$	2649.46			0.585009			0.292505	−	0.956264i	$-0.405511\pi$
$29$	2649.46			0.585009			0.292505	+	0.956264i	$0.405511\pi$
$30$	2476.22	+	4288.95i	0.502327	+	0.870057i
$31$	1437.32	−	2489.52i	0.268628	−	0.465277i	−0.699880	−	0.714260i	$-0.746763\pi$
$31$	1437.32	−	2489.52i	0.268628	−	0.465277i	0.968508	+	0.248984i	$0.0800966\pi$
$32$	669.346	−	1159.34i	0.115551	−	0.200141i
$33$	−2939.89	−	5092.03i	−0.469944	−	0.813966i
$34$	−6245.51			−0.926554
$35$		0			0
$36$	−301.096			−0.0387212
$37$	−1428.43	−	2474.12i	−0.171536	−	0.297110i	0.767421	−	0.641144i	$-0.221540\pi$
$37$	−1428.43	−	2474.12i	−0.171536	−	0.297110i	−0.938957	+	0.344034i	$0.888206\pi$
$38$	−4549.08	+	7879.23i	−0.511051	+	0.885166i
$39$	621.246	−	1076.03i	0.0654037	−	0.113282i
$40$	−9827.10	−	17021.0i	−0.971126	−	1.68204i
$41$	216.487			0.0201128			0.0100564	−	0.999949i	$-0.496799\pi$
$41$	216.487			0.0201128			0.0100564	+	0.999949i	$0.496799\pi$
$42$		0			0
$43$	2928.29			0.241514			0.120757	−	0.992682i	$-0.461468\pi$
$43$	2928.29			0.241514			0.120757	+	0.992682i	$0.461468\pi$
$44$	1214.25	+	2103.14i	0.0945533	+	0.163771i
$45$	−4190.56	+	7258.26i	−0.308489	+	0.534319i
$46$	−10690.2	+	18516.0i	−0.744891	+	1.29019i
$47$	−7408.41	−	12831.7i	−0.489193	−	0.847307i	0.510730	−	0.859741i	$-0.329375\pi$
$47$	−7408.41	−	12831.7i	−0.489193	−	0.847307i	−0.999923	+	0.0124342i	$0.996042\pi$
$48$	−8021.07			−0.502492
$49$		0			0
$50$	−40317.7			−2.28071
$51$	−5284.69	−	9153.35i	−0.284508	−	0.492782i
$52$	−256.591	+	444.429i	−0.0131593	+	0.0227926i
$53$	−10583.9	+	18331.8i	−0.517552	+	0.896427i	0.482240	+	0.876039i	$0.339823\pi$
$53$	−10583.9	+	18331.8i	−0.517552	+	0.896427i	−0.999792	+	0.0203878i	$0.993510\pi$
$54$	1938.47	+	3357.52i	0.0904636	+	0.156688i
$55$	67598.1			3.01320
$56$		0			0
$57$	−15397.0			−0.627694
$58$	7045.13	+	12202.5i	0.274991	+	0.476299i
$59$	−17344.6	+	30041.7i	−0.648684	+	1.12355i	0.334753	+	0.942306i	$0.391347\pi$
$59$	−17344.6	+	30041.7i	−0.648684	+	1.12355i	−0.983437	+	0.181248i	$0.941986\pi$
$60$	1730.81	−	2997.85i	0.0620685	−	0.107506i
$61$	4376.56	+	7580.43i	0.150594	+	0.260837i	0.931446	−	0.363879i	$-0.118548\pi$
$61$	4376.56	+	7580.43i	0.150594	+	0.260837i	−0.780852	+	0.624716i	$0.785215\pi$
$62$	15287.8			0.505087
$63$		0			0
$64$	35638.7			1.08761
$65$	7142.29	+	12370.8i	0.209679	+	0.363174i
$66$	15634.8	−	27080.2i	0.441806	−	0.765231i
$67$	6034.26	−	10451.6i	0.164224	−	0.284444i	−0.772155	−	0.635434i	$-0.780821\pi$
$67$	6034.26	−	10451.6i	0.164224	−	0.284444i	0.936379	+	0.350989i	$0.114155\pi$
$68$	2182.72	+	3780.58i	0.0572433	+	0.0991484i
$69$	−36182.5			−0.914906
$70$		0			0
$71$	−35541.5			−0.836738			−0.418369	−	0.908277i	$-0.637398\pi$
$71$	−35541.5			−0.836738			−0.418369	+	0.908277i	$0.637398\pi$
$72$	−7692.97	−	13324.6i	−0.174889	−	0.302917i
$73$	−16742.9	+	28999.5i	−0.367725	+	0.636918i	−0.989209	−	0.146508i	$-0.953197\pi$
$73$	−16742.9	+	28999.5i	−0.367725	+	0.636918i	0.621484	+	0.783426i	$0.286530\pi$
$74$	7596.63	−	13157.8i	0.161266	−	0.279320i
$75$	−34115.2	−	59089.2i	−0.700316	−	1.21298i
$76$	6359.35			0.126293
$77$		0			0
$78$	6607.76			0.122975
$79$	−21567.4	−	37355.9i	−0.388804	−	0.673428i	0.603485	−	0.797374i	$-0.293778\pi$
$79$	−21567.4	−	37355.9i	−0.388804	−	0.673428i	−0.992289	+	0.123946i	$0.960445\pi$
$80$	46108.0	−	79861.5i	0.805474	−	1.39512i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	575.656	+	997.066i	0.00945428	+	0.0163753i
$83$	−43338.8			−0.690529			−0.345265	−	0.938505i	$-0.612211\pi$
$83$	−43338.8			−0.690529			−0.345265	+	0.938505i	$0.612211\pi$
$84$		0			0
$85$	121513.			1.82422
$86$	7786.54	+	13486.7i	0.113527	+	0.196634i
$87$	−11922.6	+	20650.5i	−0.168878	+	0.292505i
$88$	−62047.9	+	107470.i	−0.854123	+	1.47938i
$89$	51766.7	+	89662.5i	0.692748	+	1.19987i	0.970934	+	0.239347i	$0.0769334\pi$
$89$	51766.7	+	89662.5i	0.692748	+	1.19987i	−0.278186	+	0.960527i	$0.589733\pi$
$90$	−44572.0			−0.580038
$91$		0			0
$92$	14944.3			0.184080
$93$	12935.9	+	22405.7i	0.155092	+	0.268628i
$94$	39399.1	−	68241.2i	0.459903	−	0.796575i
$95$	88507.3	−	153299.i	1.00617	−	1.74273i
$96$	6024.11	+	10434.1i	0.0667137	+	0.115551i
$97$	−86294.4			−0.931223			−0.465611	−	0.884989i	$-0.654165\pi$
$97$	−86294.4			−0.931223			−0.465611	+	0.884989i	$0.654165\pi$
$98$		0			0
$99$	52918.0			0.542644
$100$	14090.5	+	24405.4i	0.140905	+	0.244054i
$101$	−91338.5	+	158203.i	−0.890944	+	1.54316i	−0.0521977	+	0.998637i	$0.516623\pi$
$101$	−91338.5	+	158203.i	−0.890944	+	1.54316i	−0.838746	+	0.544523i	$0.816711\pi$
$102$	28104.8	−	48678.9i	0.267473	−	0.463277i
$103$	20044.1	+	34717.4i	0.186163	+	0.322444i	0.943968	−	0.330038i	$-0.107061\pi$
$103$	20044.1	+	34717.4i	0.186163	+	0.322444i	−0.757805	+	0.652481i	$0.773728\pi$
$104$	−26223.5			−0.237742
$105$		0			0
$106$	−112573.			−0.973129
$107$	55103.7	+	95442.4i	0.465287	+	0.805901i	0.999214	−	0.0396292i	$-0.0126177\pi$
$107$	55103.7	+	95442.4i	0.465287	+	0.805901i	−0.533927	+	0.845531i	$0.679284\pi$
$108$	1354.93	−	2346.81i	0.0111779	−	0.0193606i
$109$	111177.	−	192564.i	0.896289	−	1.55242i	0.0640869	−	0.997944i	$-0.479587\pi$
$109$	111177.	−	192564.i	0.896289	−	1.55242i	0.832202	−	0.554473i	$-0.187080\pi$
$110$	179749.	+	311334.i	1.41639	+	2.45327i
$111$	25711.8			0.198073
$112$		0			0
$113$	−153473.			−1.13067			−0.565335	−	0.824861i	$-0.691253\pi$
$113$	−153473.			−1.13067			−0.565335	+	0.824861i	$0.691253\pi$
$114$	−40941.7	−	70913.1i	−0.295055	−	0.511051i
$115$	207990.	−	360250.i	1.46656	−	2.54015i
$116$	4924.34	−	8529.21i	0.0339784	−	0.0588524i
$117$	5591.21	+	9684.27i	0.0377608	+	0.0654037i
$118$	−184482.			−1.21969
$119$		0			0
$120$	176888.			1.12136
$121$	−132880.	−	230155.i	−0.825082	−	1.42908i
$122$	−23275.2	+	40313.9i	−0.141578	+	0.245219i
$123$	−974.193	+	1687.35i	−0.00580607	+	0.0100564i
$124$	−5342.88	−	9254.14i	−0.0312048	−	0.0540483i
$125$	461080.			2.63938
$126$		0			0
$127$	142247.			0.782591			0.391296	−	0.920265i	$-0.372027\pi$
$127$	142247.			0.782591			0.391296	+	0.920265i	$0.372027\pi$
$128$	73347.1	+	127041.i	0.395693	+	0.685360i
$129$	−13177.3	+	22823.7i	−0.0697191	+	0.120757i
$130$	−37983.8	+	65789.9i	−0.197124	+	0.341429i
$131$	−63500.2	−	109986.i	−0.323293	−	0.559961i	0.657872	−	0.753130i	$-0.271457\pi$
$131$	−63500.2	−	109986.i	−0.323293	−	0.559961i	−0.981165	+	0.193169i	$0.938123\pi$
$132$	−21856.5			−0.109181
$133$		0			0
$134$	64182.2			0.308782
$135$	−37715.0	−	65324.3i	−0.178106	−	0.308489i
$136$	−111536.	+	193186.i	−0.517093	+	0.895631i
$137$	−49827.4	+	86303.6i	−0.226812	+	0.392851i	−0.956862	−	0.290544i	$-0.906164\pi$
$137$	−49827.4	+	86303.6i	−0.226812	+	0.392851i	0.730049	+	0.683395i	$0.239497\pi$
$138$	−96212.2	−	166644.i	−0.430063	−	0.744891i
$139$	23441.9			0.102909			0.0514547	−	0.998675i	$-0.483614\pi$
$139$	23441.9			0.102909			0.0514547	+	0.998675i	$0.483614\pi$
$140$		0			0
$141$	133351.			0.564871
$142$	−94507.5	−	163692.i	−0.393319	−	0.681249i
$143$	45096.1	−	78108.8i	0.184416	−	0.319418i
$144$	36094.8	−	62518.1i	0.145057	−	0.251246i
$145$	−137071.	−	237413.i	−0.541408	−	0.937746i
$146$	−178082.			−0.691415
$147$		0			0
$148$	−10619.7			−0.0398526
$149$	−249352.	−	431891.i	−0.920127	−	1.59371i	−0.799216	−	0.601043i	$-0.794752\pi$
$149$	−249352.	−	431891.i	−0.920127	−	1.59371i	−0.120911	−	0.992663i	$-0.538581\pi$
$150$	181430.	−	314245.i	0.658386	−	1.14036i
$151$	108169.	−	187354.i	0.386065	−	0.668684i	−0.605851	−	0.795578i	$-0.707167\pi$
$151$	108169.	−	187354.i	0.386065	−	0.668684i	0.991916	+	0.126894i	$0.0405007\pi$
$152$	162480.	+	281424.i	0.570417	+	0.987991i
$153$	95124.4			0.328521
$154$		0			0
$155$	−297441.			−0.994426
$156$	−2309.32	−	3999.86i	−0.00759753	−	0.0131593i
$157$	−213418.	+	369651.i	−0.691007	+	1.19686i	0.280501	+	0.959854i	$0.409499\pi$
$157$	−213418.	+	369651.i	−0.691007	+	1.19686i	−0.971508	+	0.237006i	$0.923834\pi$
$158$	114699.	−	198664.i	0.365524	−	0.633107i
$159$	−95254.7	−	164986.i	−0.298809	−	0.517552i
$160$	−138515.			−0.427757
$161$		0			0
$162$	−34892.4			−0.104458
$163$	136598.	+	236594.i	0.402694	+	0.697486i	0.994050	−	0.108925i	$-0.0347407\pi$
$163$	136598.	+	236594.i	0.402694	+	0.697486i	−0.591356	+	0.806410i	$0.701407\pi$
$164$	402.367	−	696.921i	0.00116819	−	0.00202336i
$165$	−304192.	+	526875.i	−0.869836	+	1.50660i
$166$	−115241.	−	199604.i	−0.324592	−	0.562210i
$167$	600365.			1.66581			0.832903	−	0.553420i	$-0.186677\pi$
$167$	600365.			1.66581			0.832903	+	0.553420i	$0.186677\pi$
$168$		0			0
$169$	−352234.			−0.948668
$170$	323113.	+	559648.i	0.857496	+	1.48523i
$171$	69286.3	−	120007.i	0.181200	−	0.313847i
$172$	5442.57	−	9426.81i	0.0140276	−	0.0242965i
$173$	250094.	+	433176.i	0.635313	+	1.10040i	0.986449	+	0.164070i	$0.0524624\pi$
$173$	250094.	+	433176.i	0.635313	+	1.10040i	−0.351135	+	0.936325i	$0.614204\pi$
$174$	−126812.			−0.317532
$175$		0			0
$176$	−582248.			−1.41686
$177$	−156101.	−	270375.i	−0.374518	−	0.648684i
$178$	−275303.	+	476839.i	−0.651270	+	1.12803i
$179$	−144782.	+	250769.i	−0.337739	+	0.584981i	−0.984007	−	0.178130i	$-0.942995\pi$
$179$	−144782.	+	250769.i	−0.337739	+	0.584981i	0.646268	+	0.763110i	$0.276329\pi$
$180$	15577.3	+	26980.7i	0.0358353	+	0.0620685i
$181$	168243.			0.381715			0.190858	−	0.981618i	$-0.438873\pi$
$181$	168243.			0.381715			0.190858	+	0.981618i	$0.438873\pi$
$182$		0			0
$183$	−78778.1			−0.173891
$184$	381826.	+	661342.i	0.831421	+	1.44006i
$185$	−147801.	+	255999.i	−0.317503	+	0.549931i
$186$	−68795.2	+	119157.i	−0.145806	+	0.252544i
$187$	−383615.	−	664440.i	−0.802216	−	1.38948i
$188$	−55077.6			−0.113653
$189$		0			0
$190$	941391.			1.89185
$191$	193055.	+	334381.i	0.382911	+	0.663222i	0.991477	−	0.130282i	$-0.0415882\pi$
$191$	193055.	+	334381.i	0.382911	+	0.663222i	−0.608566	+	0.793503i	$0.708255\pi$
$192$	−160374.	+	277777.i	−0.313965	+	0.543804i
$193$	169841.	−	294173.i	0.328208	−	0.568473i	−0.653948	−	0.756539i	$-0.726889\pi$
$193$	169841.	−	294173.i	0.328208	−	0.568473i	0.982156	+	0.188066i	$0.0602220\pi$
$194$	−229464.	−	397443.i	−0.437733	−	0.758176i
$195$	−128561.			−0.242116
$196$		0			0
$197$	−460915.			−0.846166			−0.423083	−	0.906091i	$-0.639052\pi$
$197$	−460915.			−0.846166			−0.423083	+	0.906091i	$0.639052\pi$
$198$	140713.	+	243722.i	0.255077	+	0.441806i
$199$	196444.	−	340251.i	0.351646	−	0.609069i	−0.634892	−	0.772601i	$-0.718955\pi$
$199$	196444.	−	340251.i	0.351646	−	0.609069i	0.986538	+	0.163532i	$0.0522887\pi$
$200$	−720019.	+	1.24711e6i	−1.27283	+	2.20460i
$201$	54308.3	+	94064.7i	0.0948148	+	0.164224i
$202$	−971504.			−1.67520
$203$		0			0
$204$	−39288.9			−0.0660989
$205$	−11200.0	−	19399.0i	−0.0186138	−	0.0322400i
$206$	−106598.	+	184632.i	−0.175017	+	0.303138i
$207$	162821.	−	282015.i	0.264111	−	0.457453i
$208$	−61519.3	−	106554.i	−0.0985945	−	0.170771i
$209$	−1.11766e6			−1.76988
$210$		0			0
$211$	−469348.			−0.725752			−0.362876	−	0.931837i	$-0.618205\pi$
$211$	−469348.			−0.725752			−0.362876	+	0.931837i	$0.618205\pi$
$212$	39342.7	+	68143.6i	0.0601208	+	0.104132i
$213$	159937.	−	277018.i	0.241545	−	0.418369i
$214$	−293050.	+	507577.i	−0.437429	+	0.757649i
$215$	−151496.	−	262398.i	−0.223514	−	0.387137i
$216$	138473.			0.201944
$217$		0			0
$218$	1.18251e6			1.68525
$219$	−150686.	−	260996.i	−0.212306	−	0.367725i
$220$	125639.	−	217613.i	0.175012	−	0.303130i
$221$	81064.0	−	140407.i	0.111647	−	0.193378i
$222$	68369.7	+	118420.i	0.0931068	+	0.161266i
$223$	83059.4			0.111848			0.0559238	−	0.998435i	$-0.482190\pi$
$223$	83059.4			0.111848			0.0559238	+	0.998435i	$0.482190\pi$
$224$		0			0
$225$	614073.			0.808656
$226$	−408097.	−	706844.i	−0.531486	−	0.920561i
$227$	−69884.4	+	121043.i	−0.0900152	+	0.155911i	−0.907517	−	0.420015i	$-0.862025\pi$
$227$	−69884.4	+	121043.i	−0.0900152	+	0.155911i	0.817502	+	0.575926i	$0.195358\pi$
$228$	−28617.1	+	49566.2i	−0.0364576	+	0.0631464i
$229$	−71923.5	−	124575.i	−0.0906321	−	0.156979i	0.817145	−	0.576432i	$-0.195555\pi$
$229$	−71923.5	−	124575.i	−0.0906321	−	0.156979i	−0.907777	+	0.419453i	$0.862222\pi$
$230$	2.21225e6			2.75749
$231$		0			0
$232$	503265.			0.613870
$233$	186246.	+	322588.i	0.224749	+	0.389276i	0.956244	−	0.292570i	$-0.0945105\pi$
$233$	186246.	+	322588.i	0.224749	+	0.389276i	−0.731495	+	0.681847i	$0.761177\pi$
$234$	−29734.9	+	51502.4i	−0.0354999	+	0.0614877i
$235$	−766552.	+	1.32771e6i	−0.905465	+	1.56831i
$236$	64473.9	+	111672.i	0.0753535	+	0.130516i
$237$	388213.			0.448952
$238$		0			0
$239$	−201182.			−0.227822			−0.113911	−	0.993491i	$-0.536338\pi$
$239$	−201182.			−0.227822			−0.113911	+	0.993491i	$0.536338\pi$
$240$	414972.	+	718753.i	0.465041	+	0.805474i
$241$	21010.3	−	36390.9i	0.0233018	−	0.0403599i	−0.854139	−	0.520044i	$-0.825915\pi$
$241$	21010.3	−	36390.9i	0.0233018	−	0.0403599i	0.877441	+	0.479684i	$0.159249\pi$
$242$	706678.	−	1.22400e6i	0.775681	−	1.34352i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	32537.4			0.0349872
$245$		0			0
$246$	−10361.8			−0.0109169
$247$	−118090.	−	204538.i	−0.123160	−	0.213320i
$248$	273019.	−	472884.i	0.281880	−	0.488231i
$249$	195025.	−	337793.i	0.199339	−	0.345265i
$250$	1.22605e6	+	2.12358e6i	1.24067	+	2.14891i
$251$	−1.23330e6			−1.23562			−0.617809	−	0.786329i	$-0.711979\pi$
$251$	−1.23330e6			−1.23562			−0.617809	+	0.786329i	$0.711979\pi$
$252$		0			0
$253$	−2.62648e6			−2.57972
$254$	378247.	+	655143.i	0.367867	+	0.637164i
$255$	−546810.	+	947102.i	−0.526606	+	0.912108i
$256$	180149.	−	312027.i	0.171803	−	0.297572i
$257$	−280344.	−	485570.i	−0.264764	−	0.458584i	0.702738	−	0.711449i	$-0.251961\pi$
$257$	−280344.	−	485570.i	−0.264764	−	0.458584i	−0.967502	+	0.252865i	$0.918627\pi$
$258$	−140158.			−0.131089
$259$		0			0
$260$	53099.2			0.0487141
$261$	−107303.	−	185855.i	−0.0975016	−	0.168878i
$262$	337704.	−	584920.i	0.303936	−	0.526433i
$263$	722618.	−	1.25161e6i	0.644198	−	1.11578i	−0.340288	−	0.940321i	$-0.610525\pi$
$263$	722618.	−	1.25161e6i	0.644198	−	1.11578i	0.984486	−	0.175462i	$-0.0561420\pi$
$264$	−558431.	−	967231.i	−0.493128	−	0.854123i
$265$	2.19023e6			1.91591
$266$		0			0
$267$	−931800.			−0.799916
$268$	−22430.8	−	38851.2i	−0.0190769	−	0.0330421i
$269$	−208771.	+	361602.i	−0.175910	+	0.304685i	−0.940476	−	0.339861i	$-0.889620\pi$
$269$	−208771.	+	361602.i	−0.175910	+	0.304685i	0.764566	+	0.644545i	$0.222953\pi$
$270$	200574.	−	347405.i	0.167442	−	0.290019i
$271$	214256.	+	371102.i	0.177219	+	0.306952i	0.940927	−	0.338610i	$-0.109957\pi$
$271$	214256.	+	371102.i	0.177219	+	0.306952i	−0.763708	+	0.645562i	$0.776623\pi$
$272$	−1.04664e6			−0.857778
$273$		0			0
$274$	−529980.			−0.426465
$275$	−2.47641e6	−	4.28927e6i	−1.97466	−	3.42020i
$276$	−67249.6	+	116480.i	−0.0531394	+	0.0920402i
$277$	345444.	−	598326.i	0.270506	−	0.468531i	−0.698485	−	0.715625i	$-0.746142\pi$
$277$	345444.	−	598326.i	0.270506	−	0.468531i	0.968992	+	0.247094i	$0.0794755\pi$
$278$	62333.7	+	107965.i	0.0483739	+	0.0837860i
$279$	−232847.			−0.179085
$280$		0			0
$281$	1.91606e6			1.44758			0.723792	−	0.690018i	$-0.242397\pi$
$281$	1.91606e6			1.44758			0.723792	+	0.690018i	$0.242397\pi$
$282$	354592.	+	614171.i	0.265525	+	0.459903i
$283$	812086.	−	1.40657e6i	0.602748	−	1.04399i	−0.389655	−	0.920961i	$-0.627406\pi$
$283$	812086.	−	1.40657e6i	0.602748	−	1.04399i	0.992403	−	0.123030i	$-0.0392610\pi$
$284$	−66058.0	+	114416.i	−0.0485993	+	0.0841764i
$285$	796566.	+	1.37969e6i	0.580911	+	1.00617i
$286$	479656.			0.346749
$287$		0			0
$288$	−108434.			−0.0770343
$289$	20349.6	+	35246.6i	0.0143322	+	0.0248241i
$290$	728963.	−	1.26260e6i	0.508991	−	0.881599i
$291$	388325.	−	672599.i	0.268821	−	0.465611i
$292$	62237.3	+	107798.i	0.0427163	+	0.0739868i
$293$	−531272.			−0.361533			−0.180767	−	0.983526i	$-0.557858\pi$
$293$	−531272.			−0.361533			−0.180767	+	0.983526i	$0.557858\pi$
$294$		0			0
$295$	3.58930e6			2.40135
$296$	−271331.	−	469959.i	−0.179999	−	0.311767i
$297$	−238131.	+	412455.i	−0.156648	+	0.271322i
$298$	1.32609e6	−	2.29686e6i	0.865035	−	1.49828i
$299$	−277509.	−	480660.i	−0.179515	−	0.310928i
$300$	−253628.			−0.162703
$301$		0			0
$302$	1.15052e6			0.725899
$303$	−822046.	−	1.42383e6i	−0.514387	−	0.890944i
$304$	−762347.	+	1.32042e6i	−0.473117	+	0.819463i
$305$	452845.	−	784351.i	0.278740	−	0.482793i
$306$	252943.	+	438110.i	0.154426	+	0.267473i
$307$	409059.			0.247708			0.123854	−	0.992300i	$-0.460475\pi$
$307$	409059.			0.247708			0.123854	+	0.992300i	$0.460475\pi$
$308$		0			0
$309$	−360794.			−0.214963
$310$	−790920.	−	1.36991e6i	−0.467442	−	0.809634i
$311$	154352.	−	267345.i	0.0904922	−	0.156737i	−0.817226	−	0.576317i	$-0.804489\pi$
$311$	154352.	−	267345.i	0.0904922	−	0.156737i	0.907718	+	0.419580i	$0.137823\pi$
$312$	118006.	−	204392.i	0.0686303	−	0.118871i
$313$	−318866.	−	552293.i	−0.183970	−	0.318646i	0.759259	−	0.650789i	$-0.225562\pi$
$313$	−318866.	−	552293.i	−0.183970	−	0.318646i	−0.943229	+	0.332143i	$0.892228\pi$
$314$	−2.26998e6			−1.29927
$315$		0			0
$316$	−160342.			−0.0903297
$317$	1.47162e6	+	2.54893e6i	0.822525	+	1.42465i	0.903796	+	0.427963i	$0.140768\pi$
$317$	1.47162e6	+	2.54893e6i	0.822525	+	1.42465i	−0.0812718	+	0.996692i	$0.525898\pi$
$318$	506579.	−	877421.i	0.280918	−	0.486564i
$319$	−865458.	+	1.49902e6i	−0.476178	+	0.824764i
$320$	−1.84378e6	−	3.19352e6i	−1.00655	−	1.74339i
$321$	−991866.			−0.537268
$322$		0			0
$323$	−2.00909e6			−1.07150
$324$	12194.4	+	21121.3i	0.00645354	+	0.0111779i
$325$	523306.	−	906393.i	0.274820	−	0.476002i
$326$	−726448.	+	1.25824e6i	−0.378583	+	0.655724i
$327$	1.00059e6	+	1.73307e6i	0.517472	+	0.896289i
$328$	41121.7			0.0211051
$329$		0			0
$330$	−3.23548e6			−1.63551
$331$	1.42496e6	+	2.46810e6i	0.714878	+	1.23820i	0.963007	+	0.269478i	$0.0868510\pi$
$331$	1.42496e6	+	2.46810e6i	0.714878	+	1.23820i	−0.248129	+	0.968727i	$0.579816\pi$
$332$	−80550.4	+	139517.i	−0.0401072	+	0.0694677i
$333$	−115703.	+	200404.i	−0.0571788	+	0.0990365i
$334$	1.59642e6	+	2.76507e6i	0.783033	+	1.35625i
$335$	−1.24874e6			−0.607937
$336$		0			0
$337$	3.46617e6			1.66255			0.831277	−	0.555859i	$-0.187611\pi$
$337$	3.46617e6			1.66255			0.831277	+	0.555859i	$0.187611\pi$
$338$	−936617.	−	1.62227e6i	−0.445934	−	0.772380i
$339$	690629.	−	1.19620e6i	0.326397	−	0.565335i
$340$	225847.	−	391178.i	0.105954	−	0.183517i
$341$	939016.	+	1.62642e6i	0.437308	+	0.757439i
$342$	736950.			0.340701
$343$		0			0
$344$	556228.			0.253429
$345$	1.87191e6	+	3.24225e6i	0.846716	+	1.46656i
$346$	−1.33004e6	+	2.30369e6i	−0.597274	+	1.03451i
$347$	−7557.66	+	13090.3i	−0.00336949	+	0.00583612i	−0.867705	−	0.497079i	$-0.834406\pi$
$347$	−7557.66	+	13090.3i	−0.00336949	+	0.00583612i	0.864336	+	0.502915i	$0.167739\pi$
$348$	44319.1	+	76762.9i	0.0196175	+	0.0339784i
$349$	3.24698e6			1.42698			0.713488	−	0.700667i	$-0.247114\pi$
$349$	3.24698e6			1.42698			0.713488	+	0.700667i	$0.247114\pi$
$350$		0			0
$351$	−100642.			−0.0436024
$352$	437289.	+	757407.i	0.188110	+	0.325816i
$353$	883929.	−	1.53101e6i	0.377555	−	0.653945i	−0.613151	−	0.789966i	$-0.710098\pi$
$353$	883929.	−	1.53101e6i	0.377555	−	0.653945i	0.990706	+	0.136021i	$0.0434315\pi$
$354$	830169.	−	1.43790e6i	0.352094	−	0.609845i
$355$	1.83875e6	+	3.18480e6i	0.774374	+	1.34126i
$356$	384858.			0.160944
$357$		0			0
$358$	−1.53994e6			−0.635034
$359$	60790.4	+	105292.i	0.0248942	+	0.0431181i	0.878204	−	0.478286i	$-0.158742\pi$
$359$	60790.4	+	105292.i	0.0248942	+	0.0431181i	−0.853310	+	0.521404i	$0.825408\pi$
$360$	−795995.	+	1.37870e6i	−0.323709	+	0.560680i
$361$	−225323.	+	390270.i	−0.0909990	+	0.157615i
$362$	447370.	+	774868.i	0.179430	+	0.310782i
$363$	2.39185e6			0.952723
$364$		0			0
$365$	3.46479e6			1.36127
$366$	−209477.	−	362825.i	−0.0817398	−	0.141578i
$367$	−1.04421e6	+	1.80862e6i	−0.404689	+	0.700942i	−0.994285	−	0.106756i	$-0.965954\pi$
$367$	−1.04421e6	+	1.80862e6i	−0.404689	+	0.700942i	0.589596	+	0.807698i	$0.299287\pi$
$368$	−1.79150e6	+	3.10297e6i	−0.689600	+	1.19442i
$369$	−8767.73	−	15186.2i	−0.00335213	−	0.00580607i
$370$	−1.57206e6			−0.596985
$371$		0			0
$372$	96171.8			0.0360322
$373$	1.14677e6	+	1.98627e6i	0.426782	+	0.739208i	0.996585	−	0.0825735i	$-0.0263139\pi$
$373$	1.14677e6	+	1.98627e6i	0.426782	+	0.739208i	−0.569803	+	0.821781i	$0.692981\pi$
$374$	2.04012e6	−	3.53359e6i	0.754183	−	1.30628i
$375$	−2.07486e6	+	3.59376e6i	−0.761922	+	1.31969i
$376$	−1.40723e6	−	2.43739e6i	−0.513327	−	0.889108i
$377$	−365771.			−0.132543
$378$		0			0
$379$	−2.93812e6			−1.05068			−0.525341	−	0.850892i	$-0.676062\pi$
$379$	−2.93812e6			−1.05068			−0.525341	+	0.850892i	$0.676062\pi$
$380$	−329003.	−	569849.i	−0.116880	−	0.202442i
$381$	−640113.	+	1.10871e6i	−0.225915	+	0.391296i
$382$	−1.02670e6	+	1.77829e6i	−0.359985	+	0.623512i
$383$	−2.52303e6	−	4.37001e6i	−0.878871	−	1.52225i	−0.852581	−	0.522594i	$-0.824964\pi$
$383$	−2.52303e6	−	4.37001e6i	−0.878871	−	1.52225i	−0.0262892	−	0.999654i	$-0.508369\pi$
$384$	−1.32025e6			−0.456907
$385$		0			0
$386$	1.80648e6			0.617113
$387$	−118596.	−	205414.i	−0.0402524	−	0.0697191i
$388$	−160388.	+	277801.i	−0.0540871	+	0.0936816i
$389$	538107.	−	932029.i	0.180300	−	0.312288i	−0.761683	−	0.647950i	$-0.775627\pi$
$389$	538107.	−	932029.i	0.180300	−	0.312288i	0.941983	+	0.335662i	$0.108960\pi$
$390$	−341854.	−	592109.i	−0.113810	−	0.197124i
$391$	−4.72132e6			−1.56179
$392$		0			0
$393$	1.14300e6			0.373307
$394$	−1.22561e6	−	2.12282e6i	−0.397751	−	0.688925i
$395$	−2.23159e6	+	3.86523e6i	−0.719651	+	1.24647i
$396$	98354.3	−	170355.i	0.0315178	−	0.0545904i
$397$	−2.17173e6	−	3.76154e6i	−0.691559	−	1.19781i	−0.971327	−	0.237747i	$-0.923591\pi$
$397$	−2.17173e6	−	3.76154e6i	−0.691559	−	1.19781i	0.279769	−	0.960067i	$-0.409742\pi$
$398$	2.08944e6			0.661183
$399$		0			0
$400$	−6.75655e6			−2.11142
$401$	352042.	+	609754.i	0.109328	+	0.189362i	0.915498	−	0.402322i	$-0.131797\pi$
$401$	352042.	+	609754.i	0.109328	+	0.189362i	−0.806170	+	0.591684i	$0.798463\pi$
$402$	−288820.	+	500251.i	−0.0891378	+	0.154391i
$403$	−198429.	+	343690.i	−0.0608616	+	0.105415i
$404$	339527.	+	588078.i	0.103495	+	0.179259i
$405$	678870.			0.205660
$406$		0			0
$407$	1.86642e6			0.558499
$408$	−1.00383e6	−	1.73868e6i	−0.298544	−	0.517093i
$409$	817500.	−	1.41595e6i	0.241646	−	0.418543i	−0.719537	−	0.694454i	$-0.755646\pi$
$409$	817500.	−	1.41595e6i	0.241646	−	0.418543i	0.961183	+	0.275911i	$0.0889794\pi$
$410$	59563.4	−	103167.i	0.0174993	−	0.0303096i
$411$	−448447.	−	776733.i	−0.130950	−	0.226812i
$412$	149017.			0.0432508
$413$		0			0
$414$	1.73182e6			0.496594
$415$	2.24215e6	+	3.88351e6i	0.639063	+	1.10689i
$416$	−92406.3	+	160052.i	−0.0261799	+	0.0453449i
$417$	−105488.	+	182711.i	−0.0297074	+	0.0514547i
$418$	−2.97195e6	−	5.14757e6i	−0.831957	−	1.44099i
$419$	−5.92839e6			−1.64969			−0.824844	−	0.565360i	$-0.808737\pi$
$419$	−5.92839e6			−1.64969			−0.824844	+	0.565360i	$0.808737\pi$
$420$		0			0
$421$	−5.46170e6			−1.50184			−0.750918	−	0.660395i	$-0.770389\pi$
$421$	−5.46170e6			−1.50184			−0.750918	+	0.660395i	$0.770389\pi$
$422$	−1.24803e6	−	2.16165e6i	−0.341149	−	0.590888i
$423$	−600081.	+	1.03937e6i	−0.163064	+	0.282436i
$424$	−2.01040e6	+	3.48212e6i	−0.543085	+	0.940651i
$425$	−4.45156e6	−	7.71032e6i	−1.19547	−	2.07062i
$426$	1.70113e6			0.454166
$427$		0			0
$428$	409667.			0.108099
$429$	405865.	+	702979.i	0.106473	+	0.184416i
$430$	805678.	−	1.39547e6i	0.210131	−	0.363958i
$431$	−1.72263e6	+	2.98369e6i	−0.446683	+	0.773677i	−0.998168	−	0.0605075i	$-0.980728\pi$
$431$	−1.72263e6	+	2.98369e6i	−0.446683	+	0.773677i	0.551485	+	0.834185i	$0.314061\pi$
$432$	324854.	+	562663.i	0.0837487	+	0.145057i
$433$	2.46833e6			0.632680			0.316340	−	0.948646i	$-0.397546\pi$
$433$	2.46833e6			0.632680			0.316340	+	0.948646i	$0.397546\pi$
$434$		0			0
$435$	2.46727e6			0.625164
$436$	−413271.	−	715806.i	−0.104116	−	0.180335i
$437$	−3.43890e6	+	5.95634e6i	−0.861421	+	1.49202i
$438$	801371.	−	1.38802e6i	0.199594	−	0.345708i
$439$	3.06890e6	+	5.31549e6i	0.760014	+	1.31638i	0.942843	+	0.333238i	$0.108141\pi$
$439$	3.06890e6	+	5.31549e6i	0.760014	+	1.31638i	−0.182829	+	0.983145i	$0.558526\pi$
$440$	1.28403e7			3.16185
$441$		0			0
$442$	862222.			0.209925
$443$	896094.	+	1.55208e6i	0.216942	+	0.375755i	0.953872	−	0.300215i	$-0.0970583\pi$
$443$	896094.	+	1.55208e6i	0.216942	+	0.375755i	−0.736929	+	0.675970i	$0.763725\pi$
$444$	47788.5	−	82772.0i	0.0115044	−	0.0199263i
$445$	5.35632e6	−	9.27742e6i	1.28223	−	2.22089i
$446$	220861.	+	382543.i	0.0525754	+	0.0910633i
$447$	4.48834e6			1.06247
$448$		0			0
$449$	−3.76014e6			−0.880213			−0.440107	−	0.897945i	$-0.645059\pi$
$449$	−3.76014e6			−0.880213			−0.440107	+	0.897945i	$0.645059\pi$
$450$	1.63287e6	+	2.82821e6i	0.380119	+	0.658386i
$451$	−70716.4	+	122484.i	−0.0163711	+	0.0283557i
$452$	−285248.	+	494064.i	−0.0656714	+	0.113746i
$453$	973521.	+	1.68619e6i	0.222895	+	0.386065i
$454$	−743312.			−0.169251
$455$		0			0
$456$	−2.92465e6			−0.658660
$457$	−3.77251e6	−	6.53418e6i	−0.844968	−	1.46353i	−0.885649	−	0.464355i	$-0.846286\pi$
$457$	−3.77251e6	−	6.53418e6i	−0.844968	−	1.46353i	0.0406817	−	0.999172i	$-0.487047\pi$
$458$	382500.	−	662510.i	0.0852056	−	0.147580i
$459$	−428060.	+	741421.i	−0.0948359	+	0.164261i
$460$	−773150.	−	1.33913e6i	−0.170361	−	0.295073i
$461$	359098.			0.0786975			0.0393487	−	0.999226i	$-0.487472\pi$
$461$	359098.			0.0786975			0.0393487	+	0.999226i	$0.487472\pi$
$462$		0			0
$463$	−890950.			−0.193153			−0.0965764	−	0.995326i	$-0.530789\pi$
$463$	−890950.			−0.193153			−0.0965764	+	0.995326i	$0.530789\pi$
$464$	1.18064e6	+	2.04493e6i	0.254579	+	0.440944i
$465$	1.33849e6	−	2.31833e6i	0.287066	−	0.497213i
$466$	−990486.	+	1.71557e6i	−0.211292	+	0.365969i
$467$	3.80660e6	+	6.59322e6i	0.807690	+	1.39896i	0.914460	+	0.404676i	$0.132616\pi$
$467$	3.80660e6	+	6.59322e6i	0.807690	+	1.39896i	−0.106770	+	0.994284i	$0.534051\pi$
$468$	41567.7			0.00877287
$469$		0			0
$470$	−8.15328e6			−1.70250
$471$	−1.92076e6	−	3.32686e6i	−0.398953	−	0.691007i
$472$	−3.29459e6	+	5.70641e6i	−0.680686	+	1.17898i
$473$	−956537.	+	1.65677e6i	−0.196584	+	0.340494i
$474$	1.03229e6	+	1.78798e6i	0.211036	+	0.365524i
$475$	−1.29696e7			−2.63751
$476$		0			0
$477$	1.71458e6			0.345035
$478$	−534960.	−	926577.i	−0.107091	−	0.185486i
$479$	2.98004e6	−	5.16158e6i	0.593448	−	1.02788i	−0.400316	−	0.916377i	$-0.631100\pi$
$479$	2.98004e6	−	5.16158e6i	0.593448	−	1.02788i	0.993764	−	0.111505i	$-0.0355672\pi$
$480$	623318.	−	1.07962e6i	0.123483	−	0.213879i
$481$	197202.	+	341564.i	0.0388641	+	0.0673146i
$482$	223472.			0.0438132
$483$		0			0
$484$	−987895.			−0.191689
$485$	4.46447e6	+	7.73268e6i	0.861817	+	1.49271i
$486$	157016.	−	271959.i	0.0301545	−	0.0522292i
$487$	128913.	−	223284.i	0.0246306	−	0.0426615i	−0.853447	−	0.521179i	$-0.825492\pi$
$487$	128913.	−	223284.i	0.0246306	−	0.0426615i	0.878078	+	0.478518i	$0.158826\pi$
$488$	831327.	+	1.43990e6i	0.158024	+	0.273705i
$489$	−2.45876e6			−0.464990
$490$		0			0
$491$	592660.			0.110944			0.0554718	−	0.998460i	$-0.482334\pi$
$491$	592660.			0.110944			0.0554718	+	0.998460i	$0.482334\pi$
$492$	3621.31	+	6272.28i	0.000674454	+	0.00116819i
$493$	−1.55573e6	+	2.69461e6i	−0.288282	+	0.499319i
$494$	628021.	−	1.08776e6i	0.115786	−	0.200548i
$495$	−2.73772e6	−	4.74188e6i	−0.502200	−	0.869836i
$496$	2.56198e6			0.467596
$497$		0			0
$498$	2.07434e6			0.374807
$499$	1.21121e6	+	2.09788e6i	0.217755	+	0.377163i	0.954121	−	0.299420i	$-0.0967932\pi$
$499$	1.21121e6	+	2.09788e6i	0.217755	+	0.377163i	−0.736366	+	0.676583i	$0.763460\pi$
$500$	856972.	−	1.48432e6i	0.153300	−	0.265523i
$501$	−2.70164e6	+	4.67938e6i	−0.480876	+	0.832903i
$502$	−3.27944e6	−	5.68015e6i	−0.580818	−	1.00601i
$503$	2.31849e6			0.408588			0.204294	−	0.978910i	$-0.434510\pi$
$503$	2.31849e6			0.408588			0.204294	+	0.978910i	$0.434510\pi$
$504$		0			0
$505$	1.89017e7			3.29816
$506$	−6.98402e6	−	1.20967e7i	−1.21263	−	2.10034i
$507$	1.58505e6	−	2.74539e6i	0.273857	−	0.474334i
$508$	264384.	−	457926.i	0.0454543	−	0.0787292i
$509$	4.24943e6	+	7.36023e6i	0.727003	+	1.25921i	0.958144	+	0.286286i	$0.0924208\pi$
$509$	4.24943e6	+	7.36023e6i	0.727003	+	1.25921i	−0.231141	+	0.972920i	$0.574246\pi$
$510$	−5.81604e6			−0.990151
$511$		0			0
$512$	6.61033e6			1.11442
$513$	623577.	+	1.08007e6i	0.104616	+	0.181200i
$514$	1.49091e6	−	2.58234e6i	0.248911	−	0.431127i
$515$	2.07397e6	−	3.59223e6i	0.344576	−	0.596823i
$516$	48983.1	+	84841.3i	0.00809883	+	0.0140276i
$517$	9.67995e6			1.59275
$518$		0			0
$519$	−4.50169e6			−0.733597
$520$	1.35668e6	+	2.34983e6i	0.220023	+	0.381091i
$521$	580461.	−	1.00539e6i	0.0936868	−	0.162270i	−0.815373	−	0.578936i	$-0.803468\pi$
$521$	580461.	−	1.00539e6i	0.0936868	−	0.162270i	0.909060	+	0.416666i	$0.136801\pi$
$522$	570655.	−	988404.i	0.0916637	−	0.158766i
$523$	−614536.	−	1.06441e6i	−0.0982411	−	0.170159i	0.812716	−	0.582661i	$-0.197988\pi$
$523$	−614536.	−	1.06441e6i	−0.0982411	−	0.170159i	−0.910957	+	0.412502i	$0.864655\pi$
$524$	−472091.			−0.0751099
$525$		0			0
$526$	7.68598e6			1.21125
$527$	1.68796e6	+	2.92363e6i	0.264750	+	0.458560i
$528$	2.62012e6	−	4.53818e6i	0.409012	−	0.708429i
$529$	−4.86316e6	+	8.42325e6i	−0.755579	+	1.30870i
$530$	5.82400e6	+	1.00875e7i	0.900600	+	1.55988i
$531$	2.80982e6			0.432456
$532$		0			0
$533$	−29887.1			−0.00455686
$534$	−2.47773e6	−	4.29155e6i	−0.376011	−	0.651270i
$535$	5.70161e6	−	9.87547e6i	0.861218	−	1.49167i
$536$	1.14621e6	−	1.98529e6i	0.172326	−	0.298477i
$537$	−1.30303e6	−	2.25692e6i	−0.194994	−	0.337739i
$538$	−2.22055e6			−0.330754
$539$		0			0
$540$	−280391.			−0.0413790
$541$	395140.	+	684402.i	0.0580440	+	0.100535i	0.893587	−	0.448889i	$-0.148180\pi$
$541$	395140.	+	684402.i	0.0580440	+	0.100535i	−0.835543	+	0.549425i	$0.814847\pi$
$542$	−1.13945e6	+	1.97358e6i	−0.166608	+	0.288573i
$543$	−757092.	+	1.31132e6i	−0.110192	+	0.190858i
$544$	786063.	+	1.36150e6i	0.113883	+	0.197252i
$545$	−2.30070e7			−3.31795
$546$		0			0
$547$	1.74335e6			0.249124			0.124562	−	0.992212i	$-0.460247\pi$
$547$	1.74335e6			0.249124			0.124562	+	0.992212i	$0.460247\pi$
$548$	185220.	+	320811.i	0.0263474	+	0.0456350i
$549$	354501.	−	614015.i	0.0501981	−	0.0869456i
$550$	1.31699e7	−	2.28110e7i	1.85642	−	3.21542i
$551$	2.26631e6	+	3.92537e6i	0.318010	+	0.550810i
$552$	−6.87287e6			−0.960042
$553$		0			0
$554$	3.67424e6			0.508620
$555$	−1.33021e6	−	2.30399e6i	−0.183310	−	0.317503i
$556$	43569.5	−	75464.5i	0.00597717	−	0.0103528i
$557$	5.09171e6	−	8.81910e6i	0.695385	−	1.20444i	−0.274665	−	0.961540i	$-0.588567\pi$
$557$	5.09171e6	−	8.81910e6i	0.695385	−	1.20444i	0.970051	−	0.242903i	$-0.0780996\pi$
$558$	−619157.	−	1.07241e6i	−0.0841812	−	0.145806i
$559$	−404264.			−0.0547186
$560$		0			0
$561$	6.90506e6			0.926319
$562$	5.09496e6	+	8.82473e6i	0.680456	+	1.17858i
$563$	4.28710e6	−	7.42547e6i	0.570023	−	0.987309i	−0.426540	−	0.904469i	$-0.640268\pi$
$563$	4.28710e6	−	7.42547e6i	0.570023	−	0.987309i	0.996563	−	0.0828400i	$-0.0263991\pi$
$564$	247849.	−	429288.i	0.0328088	−	0.0568265i
$565$	7.93997e6	+	1.37524e7i	1.04640	+	1.81242i
$566$	8.63760e6			1.13332
$567$		0			0
$568$	−6.75109e6			−0.878018
$569$	−1.33980e6	−	2.32060e6i	−0.173484	−	0.300483i	0.766152	−	0.642660i	$-0.222169\pi$
$569$	−1.33980e6	−	2.32060e6i	−0.173484	−	0.300483i	−0.939636	+	0.342177i	$0.888836\pi$
$570$	−4.23626e6	+	7.33741e6i	−0.546129	+	0.945923i
$571$	−3.72509e6	+	6.45204e6i	−0.478130	+	0.828145i	−0.999686	−	0.0250718i	$-0.992019\pi$
$571$	−3.72509e6	+	6.45204e6i	−0.478130	+	0.828145i	0.521556	+	0.853217i	$0.325352\pi$
$572$	−167633.	−	290349.i	−0.0214225	−	0.0371048i
$573$	−3.47499e6			−0.442148
$574$		0			0
$575$	−3.04784e7			−3.84434
$576$	−1.44337e6	−	2.49999e6i	−0.181268	−	0.313965i
$577$	−2.86445e6	+	4.96138e6i	−0.358181	+	0.620387i	−0.987657	−	0.156632i	$-0.949936\pi$
$577$	−2.86445e6	+	4.96138e6i	−0.358181	+	0.620387i	0.629476	+	0.777020i	$0.283270\pi$
$578$	−108223.	+	187447.i	−0.0134741	+	0.0233377i
$579$	1.52857e6	+	2.64756e6i	0.189491	+	0.328208i
$580$	−1.01905e6			−0.125784
$581$		0			0
$582$	4.13034e6			0.505451
$583$	−6.91452e6	−	1.19763e7i	−0.842540	−	1.45932i
$584$	−3.18031e6	+	5.50845e6i	−0.385866	+	0.668340i
$585$	578526.	−	1.00204e6i	0.0698929	−	0.121058i
$586$	−1.41269e6	−	2.44686e6i	−0.169943	−	0.294350i
$587$	1.41744e7			1.69788			0.848942	−	0.528486i	$-0.177240\pi$
$587$	1.41744e7			1.69788			0.848942	+	0.528486i	$0.177240\pi$
$588$		0			0
$589$	4.91787e6			0.584102
$590$	9.54423e6	+	1.65311e7i	1.12878	+	1.95511i
$591$	2.07412e6	−	3.59248e6i	0.244267	−	0.423083i
$592$	1.27306e6	−	2.20501e6i	0.149295	−	0.258587i
$593$	3.04747e6	+	5.27837e6i	0.355879	+	0.616401i	0.987268	−	0.159066i	$-0.0508482\pi$
$593$	3.04747e6	+	5.27837e6i	0.355879	+	0.616401i	−0.631389	+	0.775466i	$0.717515\pi$
$594$	−2.53283e6			−0.294537
$595$		0			0
$596$	−1.85380e6			−0.213771
$597$	1.76799e6	+	3.06226e6i	0.203023	+	0.351646i
$598$	1.47584e6	−	2.55623e6i	0.168766	−	0.292312i
$599$	−987321.	+	1.71009e6i	−0.112432	+	0.194738i	−0.916750	−	0.399460i	$-0.869197\pi$
$599$	−987321.	+	1.71009e6i	−0.112432	+	0.194738i	0.804318	+	0.594199i	$0.202531\pi$
$600$	−6.48017e6	−	1.12240e7i	−0.734866	−	1.27283i
$601$	5.14078e6			0.580554			0.290277	−	0.956943i	$-0.406253\pi$
$601$	5.14078e6			0.580554			0.290277	+	0.956943i	$0.406253\pi$
$602$		0			0
$603$	−977549.			−0.109483
$604$	−402090.	−	696440.i	−0.0448467	−	0.0776768i
$605$	−1.37492e7	+	2.38143e7i	−1.52717	+	2.64514i
$606$	4.37177e6	−	7.57212e6i	0.483588	−	0.837599i
$607$	657412.	+	1.13867e6i	0.0724213	+	0.125437i	0.899962	−	0.435968i	$-0.143594\pi$
$607$	657412.	+	1.13867e6i	0.0724213	+	0.125437i	−0.827541	+	0.561406i	$0.810261\pi$
$608$	2.29020e6			0.251255
$609$		0			0
$610$	4.81660e6			0.524102
$611$	1.02277e6	+	1.77148e6i	0.110834	+	0.191970i
$612$	176800.	−	306227.i	0.0190811	−	0.0330495i
$613$	−6.70903e6	+	1.16204e7i	−0.721122	+	1.24902i	0.239429	+	0.970914i	$0.423040\pi$
$613$	−6.70903e6	+	1.16204e7i	−0.721122	+	1.24902i	−0.960551	+	0.278106i	$0.910293\pi$
$614$	1.08772e6	+	1.88399e6i	0.116438	+	0.201677i
$615$	201600.			0.0214933
$616$		0			0
$617$	1.48394e7			1.56929			0.784646	−	0.619944i	$-0.212845\pi$
$617$	1.48394e7			1.56929			0.784646	+	0.619944i	$0.212845\pi$
$618$	−959378.	−	1.66169e6i	−0.101046	−	0.175017i
$619$	5.72341e6	−	9.91324e6i	0.600383	−	1.03989i	−0.392380	−	0.919803i	$-0.628348\pi$
$619$	5.72341e6	−	9.91324e6i	0.600383	−	1.03989i	0.992763	−	0.120091i	$-0.0383186\pi$
$620$	−552830.	+	957530.i	−0.0577581	+	0.100040i
$621$	1.46539e6	+	2.53814e6i	0.152484	+	0.264111i
$622$	1.64173e6			0.170148
$623$		0			0
$624$	1.10735e6			0.113847
$625$	−1.20085e7	−	2.07994e7i	−1.22968	−	2.12986i
$626$	1.69578e6	−	2.93718e6i	0.172955	−	0.299567i
$627$	5.02948e6	−	8.71131e6i	0.510921	−	0.884942i
$628$	793327.	+	1.37408e6i	0.0802699	+	0.139032i
$629$	3.35504e6			0.338120
$630$		0			0
$631$	−1.11608e7			−1.11589			−0.557944	−	0.829878i	$-0.688410\pi$
$631$	−1.11608e7			−1.11589			−0.557944	+	0.829878i	$0.688410\pi$
$632$	−4.09673e6	−	7.09574e6i	−0.407985	−	0.706651i
$633$	2.11206e6	−	3.65820e6i	0.209507	−	0.362876i
$634$	−7.82633e6	+	1.35556e7i	−0.773277	+	1.33935i
$635$	−7.35921e6	−	1.27465e7i	−0.724263	−	1.25446i
$636$	−708169.			−0.0694215
$637$		0			0
$638$	−9.20528e6			−0.895334
$639$	1.43943e6	+	2.49316e6i	0.139456	+	0.241545i
$640$	7.58926e6	−	1.31450e7i	0.732402	−	1.26856i
$641$	8.60750e6	−	1.49086e7i	0.827431	−	1.43315i	−0.0726153	−	0.997360i	$-0.523135\pi$
$641$	8.60750e6	−	1.49086e7i	0.827431	−	1.43315i	0.900047	−	0.435793i	$-0.143532\pi$
$642$	−2.63745e6	−	4.56820e6i	−0.252550	−	0.437429i
$643$	−2.73062e6			−0.260456			−0.130228	−	0.991484i	$-0.541571\pi$
$643$	−2.73062e6			−0.260456			−0.130228	+	0.991484i	$0.541571\pi$
$644$		0			0
$645$	2.72692e6			0.258091
$646$	−5.34232e6	−	9.25318e6i	−0.503673	−	0.872388i
$647$	2.19984e6	−	3.81024e6i	0.206600	−	0.357843i	−0.744041	−	0.668134i	$-0.767093\pi$
$647$	2.19984e6	−	3.81024e6i	0.206600	−	0.357843i	0.950641	+	0.310291i	$0.100427\pi$
$648$	−623130.	+	1.07929e6i	−0.0582963	+	0.100972i
$649$	−1.13313e7	−	1.96265e7i	−1.05601	−	1.82907i
$650$	5.56605e6			0.516730
$651$		0			0
$652$	1.01553e6			0.0935567
$653$	−2.80250e6	−	4.85407e6i	−0.257195	−	0.445475i	0.708294	−	0.705917i	$-0.249465\pi$
$653$	−2.80250e6	−	4.85407e6i	−0.257195	−	0.445475i	−0.965489	+	0.260442i	$0.916132\pi$
$654$	−5.32130e6	+	9.21676e6i	−0.486489	+	0.842624i
$655$	−6.57040e6	+	1.13803e7i	−0.598396	+	1.03645i
$656$	96470.0	+	167091.i	0.00875251	+	0.0151598i
$657$	2.71235e6			0.245150
$658$		0			0
$659$	−1.33959e7			−1.20159			−0.600796	−	0.799402i	$-0.705150\pi$
$659$	−1.33959e7			−1.20159			−0.600796	+	0.799402i	$0.705150\pi$
$660$	1.13075e6	+	1.95852e6i	0.101043	+	0.175012i
$661$	−938286.	+	1.62516e6i	−0.0835279	+	0.144675i	−0.904763	−	0.425915i	$-0.859952\pi$
$661$	−938286.	+	1.62516e6i	−0.0835279	+	0.144675i	0.821235	+	0.570590i	$0.193285\pi$
$662$	−7.57814e6	+	1.31257e7i	−0.672075	+	1.16407i
$663$	729576.	+	1.26366e6i	0.0644595	+	0.111647i
$664$	−8.23220e6			−0.724596
$665$		0			0
$666$	−1.23065e6			−0.107510
$667$	5.32579e6	+	9.22455e6i	0.463521	+	0.802843i
$668$	1.11585e6	−	1.93271e6i	0.0967530	−	0.167581i
$669$	−373767.	+	647384.i	−0.0322876	+	0.0559238i
$670$	−3.32048e6	−	5.75124e6i	−0.285768	−	0.494965i
$671$	−5.71849e6			−0.490315
$672$		0			0
$673$	2.82367e6			0.240313			0.120156	−	0.992755i	$-0.461660\pi$
$673$	2.82367e6			0.240313			0.120156	+	0.992755i	$0.461660\pi$
$674$	9.21682e6	+	1.59640e7i	0.781505	+	1.35361i
$675$	−2.76333e6	+	4.78623e6i	−0.233439	+	0.404328i
$676$	−654669.	+	1.13392e6i	−0.0551004	+	0.0954367i
$677$	−4.65924e6	−	8.07005e6i	−0.390700	−	0.676713i	0.601842	−	0.798615i	$-0.294434\pi$
$677$	−4.65924e6	−	8.07005e6i	−0.390700	−	0.676713i	−0.992542	+	0.121902i	$0.961100\pi$
$678$	7.34574e6			0.613708
$679$		0			0
$680$	2.30814e7			1.91421
$681$	−628960.	−	1.08939e6i	−0.0519703	−	0.0900152i
$682$	−4.99383e6	+	8.64957e6i	−0.411124	+	0.712088i
$683$	1.06809e7	−	1.84999e7i	0.876108	−	1.51746i	0.0205308	−	0.999789i	$-0.493464\pi$
$683$	1.06809e7	−	1.84999e7i	0.876108	−	1.51746i	0.855577	−	0.517675i	$-0.173202\pi$
$684$	−257554.	−	446096.i	−0.0210488	−	0.0364576i
$685$	1.03113e7			0.839631
$686$		0			0
$687$	1.29462e6			0.104653
$688$	1.30489e6	+	2.26014e6i	0.105100	+	0.182039i
$689$	1.46115e6	−	2.53079e6i	0.117259	−	0.203099i
$690$	−9.95512e6	+	1.72428e7i	−0.796020	+	1.37875i
$691$	−5.54424e6	−	9.60290e6i	−0.441720	−	0.765081i	0.556098	−	0.831117i	$-0.312298\pi$
$691$	−5.54424e6	−	9.60290e6i	−0.441720	−	0.765081i	−0.997817	+	0.0660361i	$0.978965\pi$
$692$	1.85932e6			0.147601
$693$		0			0
$694$	−80385.6			−0.00633548
$695$	−1.21277e6	−	2.10058e6i	−0.0952394	−	0.164959i
$696$	−2.26469e6	+	3.92256e6i	−0.177209	+	0.306935i
$697$	−127119.	+	220176.i	−0.00991122	+	0.0171667i
$698$	8.63398e6	+	1.49545e7i	0.670768	+	1.16180i
$699$	−3.35243e6			−0.259518
$700$		0			0
$701$	−2.02256e7			−1.55456			−0.777279	−	0.629156i	$-0.783401\pi$
$701$	−2.02256e7			−1.55456			−0.777279	+	0.629156i	$0.783401\pi$
$702$	−267614.	−	463522.i	−0.0204959	−	0.0354999i
$703$	2.44373e6	−	4.23266e6i	0.186494	−	0.323017i
$704$	−1.16415e7	+	2.01637e7i	−0.885276	+	1.53334i
$705$	−6.89897e6	−	1.19494e7i	−0.522771	−	0.905465i
$706$	9.40174e6			0.709899
$707$		0			0
$708$	−1.16053e6			−0.0870108
$709$	1.05417e7	+	1.82587e7i	0.787580	+	1.36413i	0.927446	+	0.373957i	$0.121999\pi$
$709$	1.05417e7	+	1.82587e7i	0.787580	+	1.36413i	−0.139866	+	0.990170i	$0.544667\pi$
$710$	−9.77874e6	+	1.69373e7i	−0.728009	+	1.26095i
$711$	−1.74696e6	+	3.02582e6i	−0.129601	+	0.224476i
$712$	9.83306e6	+	1.70314e7i	0.726924	+	1.25907i
$713$	1.15569e7			0.851369
$714$		0			0
$715$	−9.33224e6			−0.682686
$716$	538188.	+	932168.i	0.0392330	+	0.0679535i
$717$	905321.	−	1.56806e6i	0.0657665	−	0.113911i
$718$	−323293.	+	559959.i	−0.0234037	+	0.0405364i
$719$	2.94030e6	+	5.09275e6i	0.212114	+	0.367392i	0.952376	−	0.304926i	$-0.0986319\pi$
$719$	2.94030e6	+	5.09275e6i	0.212114	+	0.367392i	−0.740262	+	0.672319i	$0.765299\pi$
$720$	−7.46950e6			−0.536983
$721$		0			0
$722$	−2.39660e6			−0.171101
$723$	189093.	+	327518.i	0.0134533	+	0.0233018i
$724$	312699.	−	541610.i	0.0221707	−	0.0384008i
$725$	−1.00430e7	+	1.73950e7i	−0.709607	+	1.22908i
$726$	6.36010e6	+	1.10160e7i	0.447840	+	0.775681i
$727$	9.23778e6			0.648233			0.324117	−	0.946017i	$-0.394933\pi$
$727$	9.23778e6			0.648233			0.324117	+	0.946017i	$0.394933\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	9.21314e6	+	1.59576e7i	0.639883	+	1.10831i
$731$	−1.71945e6	+	2.97818e6i	−0.119014	+	0.206138i
$732$	−146418.	+	253604.i	−0.0100999	+	0.0174936i
$733$	−3.87556e6	−	6.71267e6i	−0.266425	−	0.461462i	0.701511	−	0.712659i	$-0.252509\pi$
$733$	−3.87556e6	−	6.71267e6i	−0.266425	−	0.461462i	−0.967936	+	0.251197i	$0.919176\pi$
$734$	−1.11065e7			−0.760917
$735$		0			0
$736$	5.38192e6			0.366220
$737$	3.94223e6	+	6.82814e6i	0.267346	+	0.463056i
$738$	46628.2	−	80762.3i	0.00315143	−	0.00545843i
$739$	−5.14509e6	+	8.91155e6i	−0.346563	+	0.600264i	−0.985636	−	0.168881i	$-0.945985\pi$
$739$	−5.14509e6	+	8.91155e6i	−0.346563	+	0.600264i	0.639074	+	0.769145i	$0.279318\pi$
$740$	549411.	+	951607.i	0.0368823	+	0.0638820i
$741$	2.12562e6			0.142213
$742$		0			0
$743$	−2.04494e6			−0.135897			−0.0679483	−	0.997689i	$-0.521645\pi$
$743$	−2.04494e6			−0.135897			−0.0679483	+	0.997689i	$0.521645\pi$
$744$	2.45718e6	+	4.25595e6i	0.162744	+	0.281880i
$745$	−2.58006e7	+	4.46880e7i	−1.70310	+	2.94985i
$746$	−6.09872e6	+	1.05633e7i	−0.401228	+	0.694948i
$747$	1.75522e6	+	3.04014e6i	0.115088	+	0.199339i
$748$	−2.85197e6			−0.186377
$749$		0			0
$750$	−2.20688e7			−1.43261
$751$	5.93708e6	+	1.02833e7i	0.384125	+	0.665325i	0.991647	−	0.128978i	$-0.0411697\pi$
$751$	5.93708e6	+	1.02833e7i	0.384125	+	0.665325i	−0.607522	+	0.794303i	$0.707836\pi$
$752$	6.60260e6	−	1.14360e7i	0.425765	−	0.737447i
$753$	5.54984e6	−	9.61261e6i	0.356692	−	0.617809i
$754$	−972613.	−	1.68461e6i	−0.0623034	−	0.107913i
$755$	−2.23846e7			−1.42916
$756$		0			0
$757$	−8.48702e6			−0.538289			−0.269145	−	0.963100i	$-0.586741\pi$
$757$	−8.48702e6			−0.538289			−0.269145	+	0.963100i	$0.586741\pi$
$758$	−7.81268e6	−	1.35320e7i	−0.493886	−	0.855436i
$759$	1.18192e7	−	2.04714e7i	0.744702	−	1.28986i
$760$	1.68119e7	−	2.91191e7i	1.05581	−	1.82871i
$761$	−1.19966e7	−	2.07787e7i	−0.750925	−	1.30064i	−0.947375	−	0.320126i	$-0.896275\pi$
$761$	−1.19966e7	−	2.07787e7i	−0.750925	−	1.30064i	0.196450	−	0.980514i	$-0.437059\pi$
$762$	−6.80844e6			−0.424776
$763$		0			0
$764$	1.43526e6			0.0889607
$765$	−4.92129e6	−	8.52392e6i	−0.304036	−	0.526606i
$766$	1.34178e7	−	2.32404e7i	0.826249	−	1.43111i
$767$	2.39450e6	−	4.14739e6i	0.146969	−	0.254558i
$768$	1.62134e6	+	2.80824e6i	0.0991906	+	0.171803i
$769$	−2.43194e7			−1.48299			−0.741494	−	0.670959i	$-0.765883\pi$
$769$	−2.43194e7			−1.48299			−0.741494	+	0.670959i	$0.765883\pi$
$770$		0			0
$771$	5.04619e6			0.305723
$772$	−631339.	−	1.09351e6i	−0.0381258	−	0.0660359i
$773$	2.69075e6	−	4.66051e6i	0.161966	−	0.280534i	−0.773608	−	0.633665i	$-0.781550\pi$
$773$	2.69075e6	−	4.66051e6i	0.161966	−	0.280534i	0.935574	+	0.353131i	$0.114883\pi$
$774$	630710.	−	1.09242e6i	0.0378423	−	0.0655447i
$775$	1.08966e7	+	1.88734e7i	0.651682	+	1.12875i
$776$	−1.63916e7			−0.977164
$777$		0			0
$778$	5.72347e6			0.339009
$779$	185180.	+	320742.i	0.0109333	+	0.0189370i
$780$	−238946.	+	413867.i	−0.0140626	+	0.0243571i
$781$	1.16098e7	−	2.01087e7i	0.681076	−	1.17966i
$782$	−1.25544e7	−	2.17448e7i	−0.734138	−	1.27156i
$783$	1.93146e6			0.112585
$784$		0			0
$785$	4.41650e7			2.55802
$786$	3.03933e6	+	5.26428e6i	0.175478	+	0.303936i
$787$	−1.40359e7	+	2.43109e7i	−0.807800	+	1.39915i	0.106584	+	0.994304i	$0.466009\pi$
$787$	−1.40359e7	+	2.43109e7i	−0.807800	+	1.39915i	−0.914384	+	0.404848i	$0.867325\pi$
$788$	−856666.	+	1.48379e6i	−0.0491469	+	0.0851249i
$789$	6.50356e6	+	1.12645e7i	0.371928	+	0.644198i
$790$	−2.37359e7			−1.35312
$791$		0			0
$792$	1.00518e7			0.569415
$793$	−604205.	−	1.04651e6i	−0.0341194	−	0.0590965i
$794$	1.15496e7	−	2.00045e7i	0.650152	−	1.12610i
$795$	−9.85606e6	+	1.70712e7i	−0.553077	+	0.957957i
$796$	−730228.	−	1.26479e6i	−0.0408485	−	0.0707517i
$797$	1.97055e7			1.09886			0.549428	−	0.835541i	$-0.314846\pi$
$797$	1.97055e7			1.09886			0.549428	+	0.835541i	$0.314846\pi$
$798$		0			0
$799$	1.74005e7			0.964262
$800$	5.07441e6	+	8.78913e6i	0.280324	+	0.485536i
$801$	4.19310e6	−	7.26266e6i	0.230916	−	0.399958i
$802$	−1.87221e6	+	3.24276e6i	−0.102782	+	0.178024i
$803$	−1.09383e7	−	1.89456e7i	−0.598631	−	1.03686i
$804$	403754.			0.0220281
$805$		0			0
$806$	−2.11056e6			−0.114435
$807$	−1.87894e6	−	3.25442e6i	−0.101562	−	0.175910i
$808$	−1.73497e7	+	3.00506e7i	−0.934898	+	1.61929i
$809$	1.69704e6	−	2.93936e6i	0.0911633	−	0.157900i	−0.816838	−	0.576868i	$-0.804275\pi$
$809$	1.69704e6	−	2.93936e6i	0.0911633	−	0.157900i	0.908001	+	0.418968i	$0.137608\pi$
$810$	1.80517e6	+	3.12664e6i	0.0966730	+	0.167442i
$811$	1.78837e7			0.954786			0.477393	−	0.878690i	$-0.341582\pi$
$811$	1.78837e7			0.954786			0.477393	+	0.878690i	$0.341582\pi$
$812$		0			0
$813$	−3.85661e6			−0.204634
$814$	4.96294e6	+	8.59607e6i	0.262530	+	0.454715i
$815$	1.41338e7	−	2.44805e7i	0.745360	−	1.29100i
$816$	4.70988e6	−	8.15775e6i	0.247619	−	0.428889i
$817$	2.50482e6	+	4.33847e6i	0.131287	+	0.227395i
$818$	8.69518e6			0.454355
$819$		0			0
$820$	−83266.3			−0.00432449
$821$	−4.63474e6	−	8.02761e6i	−0.239976	−	0.415651i	0.720731	−	0.693215i	$-0.243806\pi$
$821$	−4.63474e6	−	8.02761e6i	−0.239976	−	0.415651i	−0.960707	+	0.277564i	$0.910473\pi$
$822$	2.38491e6	−	4.13078e6i	0.123110	−	0.213232i
$823$	762896.	−	1.32137e6i	0.0392614	−	0.0680027i	−0.845727	−	0.533616i	$-0.820833\pi$
$823$	762896.	−	1.32137e6i	0.0392614	−	0.0680027i	0.884988	+	0.465613i	$0.154166\pi$
$824$	3.80737e6	+	6.59456e6i	0.195347	+	0.338351i
$825$	4.45754e7			2.28014
$826$		0			0
$827$	806595.			0.0410102			0.0205051	−	0.999790i	$-0.493473\pi$
$827$	806595.			0.0410102			0.0205051	+	0.999790i	$0.493473\pi$
$828$	−605246.	−	1.04832e6i	−0.0306801	−	0.0531394i
$829$	1.09637e7	−	1.89898e7i	0.554080	−	0.959695i	−0.443894	−	0.896079i	$-0.646403\pi$
$829$	1.09637e7	−	1.89898e7i	0.554080	−	0.959695i	0.997974	−	0.0636160i	$-0.0202633\pi$
$830$	−1.19241e7	+	2.06531e7i	−0.600800	+	1.04062i
$831$	3.10899e6	+	5.38493e6i	0.156177	+	0.270506i
$832$	−4.92010e6			−0.246414
$833$		0			0
$834$	−1.12201e6			−0.0558573
$835$	−3.10600e7	−	5.37976e7i	−1.54165	−	2.67022i
$836$	−2.07731e6	+	3.59800e6i	−0.102798	+	0.178052i
$837$	1.04781e6	−	1.81486e6i	0.0516974	−	0.0895425i
$838$	−1.57641e7	−	2.73041e7i	−0.775457	−	1.34313i
$839$	−2.40115e7			−1.17765			−0.588823	−	0.808262i	$-0.700409\pi$
$839$	−2.40115e7			−1.17765			−0.588823	+	0.808262i	$0.700409\pi$
$840$		0			0
$841$	−1.34915e7			−0.657764
$842$	−1.45231e7	−	2.51547e7i	−0.705958	−	1.22275i
$843$	−8.62228e6	+	1.49342e7i	−0.417882	+	0.723792i
$844$	−872338.	+	1.51093e6i	−0.0421530	+	0.0730112i
$845$	1.82229e7	+	3.15630e7i	0.877963	+	1.52068i
$846$	−6.38265e6			−0.306602
$847$		0			0
$848$	−1.88653e7			−0.900895
$849$	7.30877e6	+	1.26592e7i	0.347997	+	0.602748i
$850$	2.36741e7	−	4.10047e7i	1.12389	−	1.94664i
$851$	5.74271e6	−	9.94666e6i	0.271827	−	0.470819i
$852$	−594522.	−	1.02974e6i	−0.0280588	−	0.0485993i
$853$	2.26785e7			1.06719			0.533594	−	0.845741i	$-0.320841\pi$
$853$	2.26785e7			1.06719			0.533594	+	0.845741i	$0.320841\pi$
$854$		0			0
$855$	−1.43382e7			−0.670778
$856$	1.04669e7	+	1.81293e7i	0.488242	+	0.845660i
$857$	−2.53759e6	+	4.39524e6i	−0.118024	+	0.204423i	−0.918984	−	0.394294i	$-0.870989\pi$
$857$	−2.53759e6	+	4.39524e6i	−0.118024	+	0.204423i	0.800961	+	0.598717i	$0.204323\pi$
$858$	−2.15845e6	+	3.73855e6i	−0.100098	+	0.173374i
$859$	8.57027e6	+	1.48441e7i	0.396289	+	0.686392i	0.993265	−	0.115867i	$-0.0369646\pi$
$859$	8.57027e6	+	1.48441e7i	0.396289	+	0.686392i	−0.596976	+	0.802259i	$0.703631\pi$
$860$	−1.12629e6			−0.0519284
$861$		0			0
$862$	−1.83224e7			−0.839876
$863$	−1.92343e7	−	3.33148e7i	−0.879122	−	1.52268i	−0.852306	−	0.523044i	$-0.824796\pi$
$863$	−1.92343e7	−	3.33148e7i	−0.879122	−	1.52268i	−0.0268162	−	0.999640i	$-0.508537\pi$
$864$	487953.	−	845159.i	0.0222379	−	0.0385172i
$865$	2.58774e7	−	4.48209e7i	1.17593	−	2.03676i
$866$	6.56349e6	+	1.13683e7i	0.297399	+	0.515111i
$867$	−366294.			−0.0165494
$868$		0			0
$869$	2.81803e7			1.26589
$870$	6.56067e6	+	1.13634e7i	0.293866	+	0.508991i
$871$	−833057.	+	1.44290e6i	−0.0372074	+	0.0644451i
$872$	2.11180e7	−	3.65775e7i	0.940506	−	1.62900i
$873$	3.49492e6	+	6.05339e6i	0.155204	+	0.268821i
$874$	−3.65772e7			−1.61969
$875$		0			0
$876$	−1.12027e6			−0.0493245
$877$	9.58353e6	+	1.65992e7i	0.420752	+	0.728764i	0.996013	−	0.0892057i	$-0.0284329\pi$
$877$	9.58353e6	+	1.65992e7i	0.420752	+	0.728764i	−0.575261	+	0.817970i	$0.695100\pi$
$878$	−1.63209e7	+	2.82686e7i	−0.714508	+	1.23756i
$879$	2.39073e6	−	4.14086e6i	0.104366	−	0.180767i
$880$	3.01228e7	+	5.21742e7i	1.31126	+	2.27117i
$881$	4.15340e7			1.80287			0.901434	−	0.432916i	$-0.142515\pi$
$881$	4.15340e7			1.80287			0.901434	+	0.432916i	$0.142515\pi$
$882$		0			0
$883$	−4.31950e7			−1.86437			−0.932183	−	0.361987i	$-0.882099\pi$
$883$	−4.31950e7			−1.86437			−0.932183	+	0.361987i	$0.882099\pi$
$884$	−301334.	−	521926.i	−0.0129693	−	0.0224635i
$885$	−1.61519e7	+	2.79758e7i	−0.693209	+	1.20067i
$886$	−4.76557e6	+	8.25420e6i	−0.203953	+	0.353257i
$887$	−3.43754e6	−	5.95399e6i	−0.146703	−	0.254097i	0.783304	−	0.621639i	$-0.213533\pi$
$887$	−3.43754e6	−	5.95399e6i	−0.146703	−	0.254097i	−0.930007	+	0.367542i	$0.880199\pi$
$888$	4.88395e6			0.207845
$889$		0			0
$890$	5.69715e7			2.41092
$891$	−2.14318e6	−	3.71209e6i	−0.0904407	−	0.156648i
$892$	154376.	−	267387.i	0.00649631	−	0.0112519i
$893$	1.26741e7	−	2.19522e7i	0.531849	−	0.921190i
$894$	1.19348e7	+	2.06718e7i	0.499428	+	0.865035i
$895$	2.99613e7			1.25027
$896$		0			0
$897$	4.99517e6			0.207286
$898$	−9.99850e6	−	1.73179e7i	−0.413756	−	0.716646i
$899$	3.80814e6	−	6.59589e6i	0.157150	−	0.272191i
$900$	1.14133e6	−	1.97684e6i	0.0469682	−	0.0813513i
$901$	−1.24294e7	−	2.15284e7i	−0.510081	−	0.883486i
$902$	−752162.			−0.0307819
$903$		0			0
$904$	−2.91522e7			−1.18645
$905$	−8.70407e6	−	1.50759e7i	−0.353265	−	0.611874i
$906$	−5.17733e6	+	8.96741e6i	−0.209549	+	0.362950i
$907$	−7.48737e6	+	1.29685e7i	−0.302212	+	0.523446i	−0.976637	−	0.214897i	$-0.931058\pi$
$907$	−7.48737e6	+	1.29685e7i	−0.302212	+	0.523446i	0.674425	+	0.738343i	$0.264392\pi$
$908$	259777.	+	449947.i	0.0104565	+	0.0181112i
$909$	1.47968e7			0.593962
$910$		0			0
$911$	3.13061e7			1.24978			0.624889	−	0.780714i	$-0.285144\pi$
$911$	3.13061e7			1.24978			0.624889	+	0.780714i	$0.285144\pi$
$912$	−6.86112e6	−	1.18838e7i	−0.273154	−	0.473117i
$913$	1.41568e7	−	2.45203e7i	0.562068	−	0.973530i
$914$	2.00628e7	−	3.47498e7i	0.794376	−	1.37590i
$915$	4.07561e6	+	7.05916e6i	0.160931	+	0.278740i
$916$	−534713.			−0.0210563
$917$		0			0
$918$	−4.55298e6			−0.178315
$919$	−7.34952e6	−	1.27297e7i	−0.287058	−	0.497200i	0.686048	−	0.727556i	$-0.259344\pi$
$919$	−7.34952e6	−	1.27297e7i	−0.287058	−	0.497200i	−0.973106	+	0.230357i	$0.926011\pi$
$920$	3.95077e7	−	6.84294e7i	1.53891	−	2.66547i
$921$	−1.84077e6	+	3.18830e6i	−0.0715072	+	0.123854i
$922$	954870.	+	1.65388e6i	0.0369928	+	0.0640733i
$923$	4.90666e6			0.189575
$924$		0			0
$925$	2.16583e7			0.832283
$926$	−2.36910e6	−	4.10341e6i	−0.0907939	−	0.157260i
$927$	1.62357e6	−	2.81211e6i	0.0620543	−	0.107481i
$928$	1.77341e6	−	3.07163e6i	0.0675987	−	0.117084i
$929$	−8.42099e6	−	1.45856e7i	−0.320128	−	0.554478i	0.660386	−	0.750926i	$-0.270393\pi$
$929$	−8.42099e6	−	1.45856e7i	−0.320128	−	0.554478i	−0.980514	+	0.196448i	$0.937059\pi$
$930$	1.42366e7			0.539756
$931$		0			0
$932$	1.38464e6			0.0522153
$933$	1.38917e6	+	2.40611e6i	0.0522457	+	0.0904922i
$934$	−2.02441e7	+	3.50637e7i	−0.759330	+	1.31520i
$935$	−3.96928e7	+	6.87499e7i	−1.48485	+	2.57184i
$936$	1.06205e6	+	1.83952e6i	0.0396237	+	0.0686303i
$937$	−3.22026e7			−1.19824			−0.599118	−	0.800661i	$-0.704482\pi$
$937$	−3.22026e7			−1.19824			−0.599118	+	0.800661i	$0.704482\pi$
$938$		0			0
$939$	5.73959e6			0.212431
$940$	2.84946e6	+	4.93540e6i	0.105182	+	0.182181i
$941$	−1.32532e7	+	2.29553e7i	−0.487919	+	0.845100i	−0.999903	−	0.0138946i	$-0.995577\pi$
$941$	−1.32532e7	+	2.29553e7i	−0.487919	+	0.845100i	0.511985	+	0.858994i	$0.328910\pi$
$942$	1.02149e7	−	1.76928e7i	0.375066	−	0.649634i
$943$	435170.	+	753736.i	0.0159360	+	0.0276020i
$944$	−3.09160e7			−1.12915
$945$		0			0
$946$	−1.01740e7			−0.369628
$947$	2.49341e7	+	4.31871e7i	0.903481	+	1.56487i	0.822944	+	0.568123i	$0.192330\pi$
$947$	2.49341e7	+	4.31871e7i	0.903481	+	1.56487i	0.0805371	+	0.996752i	$0.474336\pi$
$948$	721541.	−	1.24975e6i	0.0260759	−	0.0451649i
$949$	2.31143e6	−	4.00352e6i	0.0833136	−	0.144303i
$950$	−3.44872e7	−	5.97336e7i	−1.23979	−	2.14738i
$951$	−2.64892e7			−0.949770
$952$		0			0
$953$	−2.46027e7			−0.877508			−0.438754	−	0.898607i	$-0.644580\pi$
$953$	−2.46027e7			−0.877508			−0.438754	+	0.898607i	$0.644580\pi$
$954$	4.55921e6	+	7.89679e6i	0.162188	+	0.280918i
$955$	1.99755e7	−	3.45986e7i	0.708744	−	1.22758i
$956$	−373922.	+	647651.i	−0.0132323	+	0.0229190i
$957$	−7.78912e6	−	1.34912e7i	−0.274921	−	0.476178i
$958$	3.16966e7			1.11583
$959$		0			0
$960$	3.31880e7			1.16226
$961$	1.01828e7	+	1.76371e7i	0.355678	+	0.616053i
$962$	−1.04875e6	+	1.81649e6i	−0.0365371	+	0.0632842i
$963$	4.46340e6	−	7.73083e6i	0.155096	−	0.268634i
$964$	−78100.2	−	135274.i	−0.00270682	−	0.00468835i
$965$	−3.51471e7			−1.21498
$966$		0			0
$967$	1.59962e7			0.550111			0.275056	−	0.961428i	$-0.411304\pi$
$967$	1.59962e7			0.550111			0.275056	+	0.961428i	$0.411304\pi$
$968$	−2.52406e7	−	4.37180e7i	−0.865787	−	1.49959i
$969$	9.04090e6	−	1.56593e7i	0.309316	−	0.535751i
$970$	−2.37427e7	+	4.11236e7i	−0.810216	+	1.40334i
$971$	−4.97212e6	−	8.61197e6i	−0.169236	−	0.293126i	0.768915	−	0.639351i	$-0.220797\pi$
$971$	−4.97212e6	−	8.61197e6i	−0.169236	−	0.293126i	−0.938152	+	0.346225i	$0.887463\pi$
$972$	−219499.			−0.00745190
$973$		0			0
$974$	1.37116e6			0.0463118
$975$	4.70976e6	+	8.15754e6i	0.158667	+	0.274820i
$976$	−3.90053e6	+	6.75591e6i	−0.131069	+	0.227017i
$977$	6.04354e6	−	1.04677e7i	0.202561	−	0.350845i	−0.746792	−	0.665058i	$-0.768407\pi$
$977$	6.04354e6	−	1.04677e7i	0.202561	−	0.350845i	0.949353	+	0.314212i	$0.101740\pi$
$978$	−6.53803e6	−	1.13242e7i	−0.218575	−	0.378583i
$979$	−6.76392e7			−2.25549
$980$		0			0
$981$	−1.80106e7			−0.597526
$982$	1.57593e6	+	2.72959e6i	0.0521505	+	0.0903273i
$983$	−1.71388e7	+	2.96853e7i	−0.565714	+	0.979846i	0.431269	+	0.902224i	$0.358066\pi$
$983$	−1.71388e7	+	2.96853e7i	−0.565714	+	0.979846i	−0.996983	+	0.0776222i	$0.975267\pi$
$984$	−185048.	+	320512.i	−0.00609250	+	0.0105525i
$985$	2.38456e7	+	4.13017e7i	0.783100	+	1.35637i
$986$	−1.65472e7			−0.542043
$987$		0			0
$988$	−877938.			−0.0286135
$989$	5.88627e6	+	1.01953e7i	0.191359	+	0.331444i
$990$	1.45596e7	−	2.52180e7i	0.472131	−	0.817755i
$991$	1.75049e7	−	3.03195e7i	0.566209	−	0.980703i	−0.430727	−	0.902482i	$-0.641743\pi$
$991$	1.75049e7	−	3.03195e7i	0.566209	−	0.980703i	0.996936	−	0.0782204i	$-0.0249238\pi$
$992$	−1.92413e6	−	3.33270e6i	−0.0620806	−	0.107527i
$993$	−2.56492e7			−0.825470
$994$		0			0
$995$	−4.06523e7			−1.30175
$996$	−724954.	−	1.25566e6i	−0.0231559	−	0.0401072i
$997$	−4.99615e6	+	8.65359e6i	−0.159183	+	0.275714i	−0.934574	−	0.355768i	$-0.884219\pi$
$997$	−4.99615e6	+	8.65359e6i	−0.159183	+	0.275714i	0.775391	+	0.631481i	$0.217553\pi$
$998$	−6.44141e6	+	1.11569e7i	−0.204717	+	0.354581i
$999$	−1.04133e6	−	1.80363e6i	−0.0330122	−	0.0571788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.p.67.5		12
7.2	even	3	inner	147.6.e.p.79.5		12
7.3	odd	6		147.6.a.n.1.2	✓	6
7.4	even	3		147.6.a.o.1.2	yes	6
7.5	odd	6		147.6.e.q.79.5		12
7.6	odd	2		147.6.e.q.67.5		12
21.11	odd	6		441.6.a.ba.1.5		6
21.17	even	6		441.6.a.bb.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.2	✓	6	7.3	odd	6
147.6.a.o.1.2	yes	6	7.4	even	3
147.6.e.p.67.5		12	1.1	even	1	trivial
147.6.e.p.79.5		12	7.2	even	3	inner
147.6.e.q.67.5		12	7.6	odd	2
147.6.e.q.79.5		12	7.5	odd	6
441.6.a.ba.1.5		6	21.11	odd	6
441.6.a.bb.1.5		6	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.65908 + 4.60566i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(1.85862 - 3.21922i) q^{4} +(-51.7353 - 89.6081i) q^{5} -47.8634 q^{6} +189.950 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(2.65908 + 4.60566i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(1.85862 - 3.21922i) q^{4} +(-51.7353 - 89.6081i) q^{5} -47.8634 q^{6} +189.950 q^{8} +(-40.5000 - 70.1481i) q^{9} +(275.136 - 476.550i) q^{10} +(-326.654 + 565.781i) q^{11} +(16.7276 + 28.9730i) q^{12} -138.055 q^{13} +931.235 q^{15} +(445.615 + 771.828i) q^{16} +(-587.188 + 1017.04i) q^{17} +(215.385 - 373.058i) q^{18} +(855.386 + 1481.57i) q^{19} -384.625 q^{20} -3474.39 q^{22} +(2010.14 + 3481.67i) q^{23} +(-854.774 + 1480.51i) q^{24} +(-3790.57 + 6565.47i) q^{25} +(-367.098 - 635.832i) q^{26} +729.000 q^{27} +2649.46 q^{29} +(2476.22 + 4288.95i) q^{30} +(1437.32 - 2489.52i) q^{31} +(669.346 - 1159.34i) q^{32} +(-2939.89 - 5092.03i) q^{33} -6245.51 q^{34} -301.096 q^{36} +(-1428.43 - 2474.12i) q^{37} +(-4549.08 + 7879.23i) q^{38} +(621.246 - 1076.03i) q^{39} +(-9827.10 - 17021.0i) q^{40} +216.487 q^{41} +2928.29 q^{43} +(1214.25 + 2103.14i) q^{44} +(-4190.56 + 7258.26i) q^{45} +(-10690.2 + 18516.0i) q^{46} +(-7408.41 - 12831.7i) q^{47} -8021.07 q^{48} -40317.7 q^{50} +(-5284.69 - 9153.35i) q^{51} +(-256.591 + 444.429i) q^{52} +(-10583.9 + 18331.8i) q^{53} +(1938.47 + 3357.52i) q^{54} +67598.1 q^{55} -15397.0 q^{57} +(7045.13 + 12202.5i) q^{58} +(-17344.6 + 30041.7i) q^{59} +(1730.81 - 2997.85i) q^{60} +(4376.56 + 7580.43i) q^{61} +15287.8 q^{62} +35638.7 q^{64} +(7142.29 + 12370.8i) q^{65} +(15634.8 - 27080.2i) q^{66} +(6034.26 - 10451.6i) q^{67} +(2182.72 + 3780.58i) q^{68} -36182.5 q^{69} -35541.5 q^{71} +(-7692.97 - 13324.6i) q^{72} +(-16742.9 + 28999.5i) q^{73} +(7596.63 - 13157.8i) q^{74} +(-34115.2 - 59089.2i) q^{75} +6359.35 q^{76} +6607.76 q^{78} +(-21567.4 - 37355.9i) q^{79} +(46108.0 - 79861.5i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(575.656 + 997.066i) q^{82} -43338.8 q^{83} +121513. q^{85} +(7786.54 + 13486.7i) q^{86} +(-11922.6 + 20650.5i) q^{87} +(-62047.9 + 107470. i) q^{88} +(51766.7 + 89662.5i) q^{89} -44572.0 q^{90} +14944.3 q^{92} +(12935.9 + 22405.7i) q^{93} +(39399.1 - 68241.2i) q^{94} +(88507.3 - 153299. i) q^{95} +(6024.11 + 10434.1i) q^{96} -86294.4 q^{97} +52918.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more