LMFDB - Embedded newform 198.6.e.b.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(67,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.e (of order $3$, degree $2$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Character	$\chi$	$=$	198.67
Dual form			198.6.e.b.133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-14.2828 - 6.24519i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-2.34189 + 4.05628i) q^{5} +(-6.93156 - 61.9674i) q^{6} +(-87.2715 - 151.159i) q^{7} -64.0000 q^{8} +(164.995 + 178.397i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-14.2828 - 6.24519i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-2.34189 + 4.05628i) q^{5} +(-6.93156 - 61.9674i) q^{6} +(-87.2715 - 151.159i) q^{7} -64.0000 q^{8} +(164.995 + 178.397i) q^{9} -18.7352 q^{10} +(-60.5000 - 104.789i) q^{11} +(200.798 - 147.946i) q^{12} +(177.434 - 307.325i) q^{13} +(349.086 - 604.634i) q^{14} +(58.7810 - 43.3093i) q^{15} +(-128.000 - 221.703i) q^{16} +324.260 q^{17} +(-287.996 + 928.355i) q^{18} -1142.20 q^{19} +(-37.4703 - 64.9005i) q^{20} +(302.464 + 2703.99i) q^{21} +(242.000 - 419.156i) q^{22} +(536.963 - 930.047i) q^{23} +(914.097 + 399.692i) q^{24} +(1551.53 + 2687.33i) q^{25} +1419.47 q^{26} +(-1242.46 - 3578.43i) q^{27} +2792.69 q^{28} +(2709.58 + 4693.14i) q^{29} +(267.590 + 117.005i) q^{30} +(-1542.39 + 2671.49i) q^{31} +(512.000 - 886.810i) q^{32} +(209.680 + 1874.51i) q^{33} +(648.520 + 1123.27i) q^{34} +817.522 q^{35} +(-3791.91 + 859.061i) q^{36} -11347.8 q^{37} +(-2284.40 - 3956.70i) q^{38} +(-4453.55 + 3281.34i) q^{39} +(149.881 - 259.602i) q^{40} +(-5229.95 + 9058.54i) q^{41} +(-8761.97 + 6455.75i) q^{42} +(-263.723 - 456.782i) q^{43} +1936.00 q^{44} +(-1110.03 + 251.479i) q^{45} +4295.70 q^{46} +(7487.08 + 12968.0i) q^{47} +(443.620 + 3965.91i) q^{48} +(-6829.11 + 11828.4i) q^{49} +(-6206.12 + 10749.3i) q^{50} +(-4631.33 - 2025.07i) q^{51} +(2838.94 + 4917.19i) q^{52} +10022.9 q^{53} +(9911.14 - 11460.9i) q^{54} +566.738 q^{55} +(5585.37 + 9674.15i) q^{56} +(16313.8 + 7133.26i) q^{57} +(-10838.3 + 18772.5i) q^{58} +(-24419.5 + 42295.8i) q^{59} +(129.864 + 1160.97i) q^{60} +(23859.6 + 41326.1i) q^{61} -12339.1 q^{62} +(12566.9 - 40509.4i) q^{63} +4096.00 q^{64} +(831.063 + 1439.44i) q^{65} +(-6074.14 + 4475.38i) q^{66} +(-5877.21 + 10179.6i) q^{67} +(-2594.08 + 4493.08i) q^{68} +(-13477.6 + 9930.21i) q^{69} +(1635.04 + 2831.98i) q^{70} -408.263 q^{71} +(-10559.7 - 11417.4i) q^{72} +3623.92 q^{73} +(-22695.6 - 39310.0i) q^{74} +(-5377.27 - 48072.1i) q^{75} +(9137.60 - 15826.8i) q^{76} +(-10559.8 + 18290.2i) q^{77} +(-20274.0 - 8864.87i) q^{78} +(-15292.0 - 26486.5i) q^{79} +1199.05 q^{80} +(-4602.20 + 58869.4i) q^{81} -41839.6 q^{82} +(-32781.0 - 56778.4i) q^{83} +(-39887.3 - 17440.9i) q^{84} +(-759.383 + 1315.29i) q^{85} +(1054.89 - 1827.13i) q^{86} +(-9390.82 - 83952.8i) q^{87} +(3872.00 + 6706.50i) q^{88} +89821.2 q^{89} +(-3091.21 - 3342.30i) q^{90} -61939.7 q^{91} +(8591.40 + 14880.7i) q^{92} +(38713.5 - 28523.8i) q^{93} +(-29948.3 + 51872.0i) q^{94} +(2674.91 - 4633.08i) q^{95} +(-12851.1 + 9468.57i) q^{96} +(36698.8 + 63564.2i) q^{97} -54632.9 q^{98} +(8711.88 - 28082.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) $ 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	−14.2828	−	6.24519i	−0.916240	−	0.400629i
$3$	−14.2828	−	6.24519i	−0.916240	−	0.400629i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−2.34189	+	4.05628i	−0.0418931	+	0.0725609i	−0.886212	−	0.463281i	$-0.846672\pi$
$5$	−2.34189	+	4.05628i	−0.0418931	+	0.0725609i	0.844319	+	0.535842i	$0.180006\pi$
$6$	−6.93156	−	61.9674i	−0.0786055	−	0.702724i
$7$	−87.2715	−	151.159i	−0.673174	−	1.16597i	−0.976999	−	0.213243i	$-0.931597\pi$
$7$	−87.2715	−	151.159i	−0.673174	−	1.16597i	0.303825	−	0.952728i	$-0.401736\pi$
$8$	−64.0000			−0.353553
$9$	164.995	+	178.397i	0.678992	+	0.734145i
$10$	−18.7352			−0.0592458
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$12$	200.798	−	147.946i	0.402538	−	0.296586i
$13$	177.434	−	307.325i	0.291191	−	0.504358i	−0.682900	−	0.730511i	$-0.739282\pi$
$13$	177.434	−	307.325i	0.291191	−	0.504358i	0.974092	+	0.226153i	$0.0726150\pi$
$14$	349.086	−	604.634i	0.476006	−	0.824466i
$15$	58.7810	−	43.3093i	0.0674541	−	0.0496997i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	324.260			0.272127			0.136063	−	0.990700i	$-0.456555\pi$
$17$	324.260			0.272127			0.136063	+	0.990700i	$0.456555\pi$
$18$	−287.996	+	928.355i	−0.209510	+	0.675356i
$19$	−1142.20			−0.725869			−0.362934	−	0.931815i	$-0.618225\pi$
$19$	−1142.20			−0.725869			−0.362934	+	0.931815i	$0.618225\pi$
$20$	−37.4703	−	64.9005i	−0.0209465	−	0.0362805i
$21$	302.464	+	2703.99i	0.149667	+	1.33800i
$22$	242.000	−	419.156i	0.106600	−	0.184637i
$23$	536.963	−	930.047i	0.211653	−	0.366594i	−0.740579	−	0.671969i	$-0.765449\pi$
$23$	536.963	−	930.047i	0.211653	−	0.366594i	0.952232	+	0.305376i	$0.0987820\pi$
$24$	914.097	+	399.692i	0.323940	+	0.141644i
$25$	1551.53	+	2687.33i	0.496490	+	0.859946i
$26$	1419.47			0.411807
$27$	−1242.46	−	3578.43i	−0.328000	−	0.944678i
$28$	2792.69			0.673174
$29$	2709.58	+	4693.14i	0.598284	+	1.03626i	0.993074	+	0.117487i	$0.0374839\pi$
$29$	2709.58	+	4693.14i	0.598284	+	1.03626i	−0.394790	+	0.918771i	$0.629183\pi$
$30$	267.590	+	117.005i	0.0542833	+	0.0237356i
$31$	−1542.39	+	2671.49i	−0.288263	+	0.499286i	−0.973395	−	0.229132i	$-0.926411\pi$
$31$	−1542.39	+	2671.49i	−0.288263	+	0.499286i	0.685132	+	0.728419i	$0.259744\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	209.680	+	1874.51i	0.0335175	+	0.299643i
$34$	648.520	+	1123.27i	0.0962113	+	0.166643i
$35$	817.522			0.112805
$36$	−3791.91	+	859.061i	−0.487642	+	0.110476i
$37$	−11347.8			−1.36272			−0.681362	−	0.731946i	$-0.738612\pi$
$37$	−11347.8			−1.36272			−0.681362	+	0.731946i	$0.738612\pi$
$38$	−2284.40	−	3956.70i	−0.256633	−	0.444502i
$39$	−4453.55	+	3281.34i	−0.468862	+	0.345453i
$40$	149.881	−	259.602i	0.0148114	−	0.0256542i
$41$	−5229.95	+	9058.54i	−0.485890	+	0.841587i	−0.999869	−	0.0162166i	$-0.994838\pi$
$41$	−5229.95	+	9058.54i	−0.485890	+	0.841587i	0.513978	+	0.857803i	$0.328171\pi$
$42$	−8761.97	+	6455.75i	−0.766441	+	0.564707i
$43$	−263.723	−	456.782i	−0.0217509	−	0.0376737i	0.854945	−	0.518719i	$-0.173591\pi$
$43$	−263.723	−	456.782i	−0.0217509	−	0.0376737i	−0.876696	+	0.481045i	$0.840257\pi$
$44$	1936.00			0.150756
$45$	−1110.03	+	251.479i	−0.0817153	+	0.0185127i
$46$	4295.70			0.299323
$47$	7487.08	+	12968.0i	0.494388	+	0.856305i	0.999979	−	0.00646848i	$-0.00205900\pi$
$47$	7487.08	+	12968.0i	0.494388	+	0.856305i	−0.505591	+	0.862773i	$0.668726\pi$
$48$	443.620	+	3965.91i	0.0277913	+	0.248450i
$49$	−6829.11	+	11828.4i	−0.406326	+	0.703777i
$50$	−6206.12	+	10749.3i	−0.351071	+	0.608074i
$51$	−4631.33	−	2025.07i	−0.249333	−	0.109022i
$52$	2838.94	+	4917.19i	0.145596	+	0.252179i
$53$	10022.9			0.490121			0.245060	−	0.969508i	$-0.421192\pi$
$53$	10022.9			0.490121			0.245060	+	0.969508i	$0.421192\pi$
$54$	9911.14	−	11460.9i	0.462529	−	0.534852i
$55$	566.738			0.0252625
$56$	5585.37	+	9674.15i	0.238003	+	0.412233i
$57$	16313.8	+	7133.26i	0.665070	+	0.290804i
$58$	−10838.3	+	18772.5i	−0.423051	+	0.732745i
$59$	−24419.5	+	42295.8i	−0.913286	+	1.58186i	−0.103894	+	0.994588i	$0.533130\pi$
$59$	−24419.5	+	42295.8i	−0.913286	+	1.58186i	−0.809392	+	0.587269i	$0.800203\pi$
$60$	129.864	+	1160.97i	0.00465704	+	0.0416334i
$61$	23859.6	+	41326.1i	0.820993	+	1.42200i	0.904944	+	0.425531i	$0.139913\pi$
$61$	23859.6	+	41326.1i	0.820993	+	1.42200i	−0.0839514	+	0.996470i	$0.526754\pi$
$62$	−12339.1			−0.407666
$63$	12566.9	−	40509.4i	0.398912	−	1.28589i
$64$	4096.00			0.125000
$65$	831.063	+	1439.44i	0.0243978	+	0.0422582i
$66$	−6074.14	+	4475.38i	−0.171643	+	0.126465i
$67$	−5877.21	+	10179.6i	−0.159950	+	0.277041i	−0.934850	−	0.355042i	$-0.884467\pi$
$67$	−5877.21	+	10179.6i	−0.159950	+	0.277041i	0.774901	+	0.632083i	$0.217800\pi$
$68$	−2594.08	+	4493.08i	−0.0680317	+	0.117834i
$69$	−13477.6	+	9930.21i	−0.340793	+	0.251094i
$70$	1635.04	+	2831.98i	0.0398827	+	0.0690788i
$71$	−408.263			−0.00961157			−0.00480578	−	0.999988i	$-0.501530\pi$
$71$	−408.263			−0.00961157			−0.00480578	+	0.999988i	$0.501530\pi$
$72$	−10559.7	−	11417.4i	−0.240060	−	0.259560i
$73$	3623.92			0.0795924			0.0397962	−	0.999208i	$-0.487329\pi$
$73$	3623.92			0.0795924			0.0397962	+	0.999208i	$0.487329\pi$
$74$	−22695.6	−	39310.0i	−0.481796	−	0.834495i
$75$	−5377.27	−	48072.1i	−0.110385	−	0.986825i
$76$	9137.60	−	15826.8i	0.181467	−	0.314310i
$77$	−10559.8	+	18290.2i	−0.202970	+	0.351553i
$78$	−20274.0	−	8864.87i	−0.377314	−	0.164982i
$79$	−15292.0	−	26486.5i	−0.275674	−	0.477481i	0.694631	−	0.719366i	$-0.255568\pi$
$79$	−15292.0	−	26486.5i	−0.275674	−	0.477481i	−0.970305	+	0.241885i	$0.922234\pi$
$80$	1199.05			0.0209465
$81$	−4602.20	+	58869.4i	−0.0779387	+	0.996958i
$82$	−41839.6			−0.687153
$83$	−32781.0	−	56778.4i	−0.522309	−	0.904665i	−0.999663	−	0.0259545i	$-0.991738\pi$
$83$	−32781.0	−	56778.4i	−0.522309	−	0.904665i	0.477354	−	0.878711i	$-0.341596\pi$
$84$	−39887.3	−	17440.9i	−0.616789	−	0.269693i
$85$	−759.383	+	1315.29i	−0.0114002	+	0.0197458i
$86$	1054.89	−	1827.13i	0.0153802	−	0.0266393i
$87$	−9390.82	−	83952.8i	−0.133017	−	1.18915i
$88$	3872.00	+	6706.50i	0.0533002	+	0.0923186i
$89$	89821.2			1.20200			0.600999	−	0.799250i	$-0.294769\pi$
$89$	89821.2			1.20200			0.600999	+	0.799250i	$0.294769\pi$
$90$	−3091.21	−	3342.30i	−0.0402274	−	0.0434950i
$91$	−61939.7			−0.784089
$92$	8591.40	+	14880.7i	0.105827	+	0.183297i
$93$	38713.5	−	28523.8i	0.464147	−	0.341980i
$94$	−29948.3	+	51872.0i	−0.349585	+	0.605499i
$95$	2674.91	−	4633.08i	0.0304089	−	0.0526697i
$96$	−12851.1	+	9468.57i	−0.142319	+	0.104859i
$97$	36698.8	+	63564.2i	0.396025	+	0.685936i	0.993231	−	0.116152i	$-0.0370560\pi$
$97$	36698.8	+	63564.2i	0.396025	+	0.685936i	−0.597206	+	0.802088i	$0.703723\pi$
$98$	−54632.9			−0.574631
$99$	8711.88	−	28082.7i	0.0893355	−	0.287973i
$100$	−49649.0			−0.496490
$101$	−41304.8	−	71542.0i	−0.402900	−	0.697843i	0.591175	−	0.806544i	$-0.298664\pi$
$101$	−41304.8	−	71542.0i	−0.402900	−	0.697843i	−0.994075	+	0.108700i	$0.965331\pi$
$102$	−2247.63	−	20093.5i	−0.0213907	−	0.191230i
$103$	−67706.5	+	117271.i	−0.628836	+	1.08918i	0.358950	+	0.933357i	$0.383135\pi$
$103$	−67706.5	+	117271.i	−0.628836	+	1.08918i	−0.987786	+	0.155819i	$0.950198\pi$
$104$	−11355.8	+	19668.8i	−0.102952	+	0.178318i
$105$	−11676.5	−	5105.58i	−0.103357	−	0.0451931i
$106$	20045.8	+	34720.3i	0.173284	+	0.300137i
$107$	171782.			1.45050			0.725252	−	0.688484i	$-0.241723\pi$
$107$	171782.			1.45050			0.725252	+	0.688484i	$0.241723\pi$
$108$	59523.9	+	11411.4i	0.491057	+	0.0941412i
$109$	106682.			0.860056			0.430028	−	0.902815i	$-0.358504\pi$
$109$	106682.			0.860056			0.430028	+	0.902815i	$0.358504\pi$
$110$	1133.48	+	1963.24i	0.00893163	+	0.0154700i
$111$	162078.	+	70869.3i	1.24858	+	0.545947i
$112$	−22341.5	+	38696.6i	−0.168293	+	0.291493i
$113$	24795.6	−	42947.3i	0.182675	−	0.316402i	−0.760116	−	0.649788i	$-0.774858\pi$
$113$	24795.6	−	42947.3i	0.182675	−	0.316402i	0.942791	+	0.333385i	$0.108191\pi$
$114$	7917.23	+	70779.1i	0.0570573	+	0.510085i
$115$	2515.02	+	4356.14i	0.0177336	+	0.0307155i
$116$	−86706.7			−0.598284
$117$	84101.6	−	19053.3i	0.567989	−	0.128679i
$118$	−195356.			−1.29158
$119$	−28298.6	−	49014.7i	−0.183189	−	0.317292i
$120$	−3761.98	+	2771.80i	−0.0238486	+	0.0175715i
$121$	−7320.50	+	12679.5i	−0.0454545	+	0.0787296i
$122$	−95438.5	+	165304.i	−0.580529	+	1.00551i
$123$	131271.	−	96719.1i	0.782356	−	0.576434i
$124$	−24678.2	−	42743.9i	−0.144132	−	0.249643i
$125$	−29170.9			−0.166984
$126$	165463.	−	37485.8i	0.928482	−	0.210349i
$127$	202274.			1.11283			0.556416	−	0.830904i	$-0.312176\pi$
$127$	202274.			1.11283			0.556416	+	0.830904i	$0.312176\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	914.008	+	8171.12i	0.00483588	+	0.0432322i
$130$	−3324.25	+	5757.77i	−0.0172518	+	0.0298811i
$131$	179780.	−	311388.i	0.915299	−	1.58534i	0.108836	−	0.994060i	$-0.465288\pi$
$131$	179780.	−	311388.i	0.915299	−	1.58534i	0.806463	−	0.591284i	$-0.201379\pi$
$132$	−27651.4	−	12090.7i	−0.138128	−	0.0603971i
$133$	99681.4	+	172653.i	0.488636	+	0.846342i
$134$	−47017.6			−0.226203
$135$	17424.8	+	3340.54i	0.0822876	+	0.0157755i
$136$	−20752.6			−0.0962113
$137$	−82014.0	−	142052.i	−0.373324	−	0.646617i	0.616750	−	0.787159i	$-0.288449\pi$
$137$	−82014.0	−	142052.i	−0.373324	−	0.646617i	−0.990075	+	0.140542i	$0.955115\pi$
$138$	−61354.5	−	26827.5i	−0.274251	−	0.119917i
$139$	−83679.1	+	144936.i	−0.367350	+	0.636268i	−0.989150	−	0.146907i	$-0.953068\pi$
$139$	−83679.1	+	144936.i	−0.367350	+	0.636268i	0.621801	+	0.783176i	$0.286401\pi$
$140$	−6540.18	+	11327.9i	−0.0282013	+	0.0488461i
$141$	−25948.6	−	231977.i	−0.109917	−	0.982647i
$142$	−816.526	−	1414.26i	−0.00339820	−	0.00588586i
$143$	−42939.0			−0.175595
$144$	18431.8	−	59414.7i	0.0740731	−	0.238774i
$145$	−25382.2			−0.100256
$146$	7247.84	+	12553.6i	0.0281401	+	0.0487402i
$147$	171409.	−	126293.i	0.654245	−	0.482043i
$148$	90782.5	−	157240.i	0.340681	−	0.590077i
$149$	−77961.2	+	135033.i	−0.287682	+	0.498280i	−0.973256	−	0.229723i	$-0.926218\pi$
$149$	−77961.2	+	135033.i	−0.287682	+	0.498280i	0.685574	+	0.728003i	$0.259551\pi$
$150$	155772.	−	114772.i	0.565278	−	0.416492i
$151$	155394.	+	269151.i	0.554616	+	0.960624i	0.997933	+	0.0642588i	$0.0204683\pi$
$151$	155394.	+	269151.i	0.554616	+	0.960624i	−0.443317	+	0.896365i	$0.646198\pi$
$152$	73100.8			0.256633
$153$	53501.3	+	57847.1i	0.184772	+	0.199781i
$154$	−84478.8			−0.287042
$155$	−7224.21	−	12512.7i	−0.0241525	−	0.0418333i
$156$	−9839.16	−	87960.9i	−0.0323703	−	0.289386i
$157$	−98059.3	+	169844.i	−0.317497	+	0.549921i	−0.979965	−	0.199169i	$-0.936176\pi$
$157$	−98059.3	+	169844.i	−0.317497	+	0.549921i	0.662468	+	0.749090i	$0.269509\pi$
$158$	61167.8	−	105946.i	0.194931	−	0.337630i
$159$	−143155.	−	62594.9i	−0.449068	−	0.196357i
$160$	2398.10	+	4153.63i	0.00740572	+	0.0128271i
$161$	−187446.			−0.569917
$162$	−213134.	+	101796.i	−0.638065	+	0.304750i
$163$	479260.			1.41287			0.706434	−	0.707779i	$-0.250303\pi$
$163$	479260.			1.41287			0.706434	+	0.707779i	$0.250303\pi$
$164$	−83679.3	−	144937.i	−0.242945	−	0.420793i
$165$	−8094.59	−	3539.39i	−0.0231465	−	0.0101209i
$166$	131124.	−	227114.i	0.369328	−	0.639695i
$167$	−256054.	+	443498.i	−0.710461	+	1.23055i	0.254223	+	0.967146i	$0.418180\pi$
$167$	−256054.	+	443498.i	−0.710461	+	1.23055i	−0.964684	+	0.263409i	$0.915153\pi$
$168$	−19357.7	−	173055.i	−0.0529152	−	0.473055i
$169$	122681.	+	212489.i	0.330415	+	0.572296i
$170$	−6075.06			−0.0161224
$171$	−188457.	−	203765.i	−0.492859	−	0.532893i
$172$	8439.15			0.0217509
$173$	−118050.	−	204468.i	−0.299882	−	0.519410i	0.676227	−	0.736693i	$-0.263614\pi$
$173$	−118050.	−	204468.i	−0.299882	−	0.519410i	−0.976109	+	0.217283i	$0.930281\pi$
$174$	272040.	−	200436.i	0.681175	−	0.501884i
$175$	270809.	−	469055.i	0.668448	−	1.15779i
$176$	−15488.0	+	26826.0i	−0.0376889	+	0.0652791i
$177$	612924.	−	451597.i	1.47053	−	1.08347i
$178$	179642.	+	311150.i	0.424971	+	0.736071i
$179$	−277994.			−0.648490			−0.324245	−	0.945973i	$-0.605110\pi$
$179$	−277994.			−0.648490			−0.324245	+	0.945973i	$0.605110\pi$
$180$	5395.65	−	17392.9i	0.0124126	−	0.0400120i
$181$	−114030.			−0.258716			−0.129358	−	0.991598i	$-0.541292\pi$
$181$	−114030.			−0.258716			−0.129358	+	0.991598i	$0.541292\pi$
$182$	−123879.	−	214565.i	−0.277217	−	0.480155i
$183$	−82692.3	−	739259.i	−0.182531	−	1.63181i
$184$	−34365.6	+	59523.0i	−0.0748307	+	0.129610i
$185$	26575.4	−	46029.9i	0.0570887	−	0.0988805i
$186$	176236.	+	77060.0i	0.373520	+	0.163323i
$187$	−19617.7	−	33978.9i	−0.0410246	−	0.0710568i
$188$	−239586.			−0.494388
$189$	−432480.	+	500104.i	−0.880666	+	1.01837i
$190$	21399.3			0.0430046
$191$	−259446.	−	449374.i	−0.514593	−	0.891302i	−0.999857	−	0.0169338i	$-0.994610\pi$
$191$	−259446.	−	449374.i	−0.514593	−	0.891302i	0.485263	−	0.874368i	$-0.338724\pi$
$192$	−58502.2	−	25580.3i	−0.114530	−	0.0500787i
$193$	210698.	−	364939.i	0.407161	−	0.705224i	−0.587409	−	0.809290i	$-0.699852\pi$
$193$	210698.	−	364939.i	0.407161	−	0.705224i	0.994570	+	0.104066i	$0.0331853\pi$
$194$	−146795.	+	254257.i	−0.280032	+	0.485030i
$195$	−2880.28	−	25749.4i	−0.00542436	−	0.0484932i
$196$	−109266.	−	189254.i	−0.203163	−	0.351888i
$197$	−750753.			−1.37826			−0.689131	−	0.724637i	$-0.742007\pi$
$197$	−750753.			−1.37826			−0.689131	+	0.724637i	$0.742007\pi$
$198$	114705.	−	25986.6i	0.207931	−	0.0471071i
$199$	−208841.			−0.373838			−0.186919	−	0.982375i	$-0.559850\pi$
$199$	−208841.			−0.373838			−0.186919	+	0.982375i	$0.559850\pi$
$200$	−99298.0	−	171989.i	−0.175536	−	0.304037i
$201$	147516.	−	108689.i	0.257543	−	0.189756i
$202$	165219.	−	286168.i	0.284893	−	0.493450i
$203$	472939.	−	819154.i	0.805498	−	1.39516i
$204$	65110.8	−	47973.1i	0.109541	−	0.0807091i
$205$	−24496.0	−	42428.3i	−0.0407109	−	0.0705133i
$206$	−541652.			−0.889308
$207$	254514.	−	57660.5i	0.412844	−	0.0935303i
$208$	−90846.2			−0.145596
$209$	69103.1	+	119690.i	0.109429	+	0.189536i
$210$	−5666.71	−	50659.7i	−0.00886712	−	0.0792710i
$211$	−519101.	+	899109.i	−0.802686	+	1.39029i	0.115157	+	0.993347i	$0.463263\pi$
$211$	−519101.	+	899109.i	−0.802686	+	1.39029i	−0.917842	+	0.396945i	$0.870070\pi$
$212$	−80183.1	+	138881.i	−0.122530	+	0.212229i
$213$	5831.13	+	2549.68i	0.00880650	+	0.00385067i
$214$	343565.	+	595071.i	0.512831	+	0.888249i
$215$	2470.45			0.00364485
$216$	79517.6	+	229020.i	0.115966	+	0.333994i
$217$	538425.			0.776205
$218$	213365.	+	369559.i	0.304076	+	0.526675i
$219$	−51759.6	−	22632.1i	−0.0729257	−	0.0318870i
$220$	−4533.91	+	7852.96i	−0.00631562	+	0.0109390i
$221$	57534.8	−	99653.1i	0.0792409	−	0.137249i
$222$	78658.1	+	703194.i	0.107118	+	0.957619i
$223$	−203569.	−	352593.i	−0.274126	−	0.474800i	0.695788	−	0.718247i	$-0.255055\pi$
$223$	−203569.	−	352593.i	−0.274126	−	0.474800i	−0.969914	+	0.243447i	$0.921722\pi$
$224$	−178732.			−0.238003
$225$	−223417.	+	720185.i	−0.294212	+	0.948392i
$226$	198365.			0.258341
$227$	189945.	+	328995.i	0.244661	+	0.423765i	0.962036	−	0.272922i	$-0.0879901\pi$
$227$	189945.	+	328995.i	0.244661	+	0.423765i	−0.717375	+	0.696687i	$0.754657\pi$
$228$	−229351.	+	168984.i	−0.292189	+	0.215283i
$229$	−317383.	+	549723.i	−0.399940	+	0.692716i	−0.993718	−	0.111913i	$-0.964302\pi$
$229$	−317383.	+	549723.i	−0.399940	+	0.692716i	0.593778	+	0.804629i	$0.297636\pi$
$230$	−10060.1	+	17424.6i	−0.0125395	+	0.0217191i
$231$	265050.	−	195286.i	0.326811	−	0.240792i
$232$	−173413.	−	300361.i	−0.211525	−	0.366373i
$233$	−674103.			−0.813461			−0.406730	−	0.913548i	$-0.633331\pi$
$233$	−674103.			−0.813461			−0.406730	+	0.913548i	$0.633331\pi$
$234$	234206.	+	253230.i	0.279614	+	0.302326i
$235$	−70135.8			−0.0828457
$236$	−390712.	−	676733.i	−0.456643	−	0.790929i
$237$	52998.6	+	473801.i	0.0612906	+	0.547930i
$238$	113195.	−	196059.i	0.129534	−	0.224359i
$239$	−320264.	+	554714.i	−0.362672	+	0.628166i	−0.988400	−	0.151875i	$-0.951469\pi$
$239$	−320264.	+	554714.i	−0.362672	+	0.628166i	0.625728	+	0.780041i	$0.284802\pi$
$240$	−17125.8	−	7488.30i	−0.0191921	−	0.00839180i
$241$	609061.	+	1.05493e6i	0.675489	+	1.16998i	0.976326	+	0.216306i	$0.0694008\pi$
$241$	609061.	+	1.05493e6i	0.675489	+	1.16998i	−0.300837	+	0.953676i	$0.597266\pi$
$242$	−58564.0			−0.0642824
$243$	433383.	−	812076.i	0.470821	−	0.882229i
$244$	−763508.			−0.820993
$245$	−31986.1	−	55401.6i	−0.0340445	−	0.0589667i
$246$	597586.	+	261297.i	0.629597	+	0.275293i
$247$	−202665.	+	351026.i	−0.211367	+	0.366098i
$248$	98712.8	−	170976.i	0.101916	−	0.176524i
$249$	113612.	+	1.01568e6i	0.116125	+	1.03814i
$250$	−58341.8	−	101051.i	−0.0590378	−	0.102256i
$251$	467231.			0.468110			0.234055	−	0.972223i	$-0.424800\pi$
$251$	467231.			0.468110			0.234055	+	0.972223i	$0.424800\pi$
$252$	460780.	+	498208.i	0.457080	+	0.494207i
$253$	−129945.			−0.127632
$254$	404547.	+	700696.i	0.393446	+	0.681468i
$255$	19060.3	−	14043.5i	0.0183561	−	0.0135246i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−616883.	+	1.06847e6i	−0.582600	+	1.00909i	0.412570	+	0.910926i	$0.364631\pi$
$257$	−616883.	+	1.06847e6i	−0.582600	+	1.00909i	−0.995170	+	0.0981665i	$0.968702\pi$
$258$	−26477.6	+	19508.5i	−0.0247645	+	0.0182463i
$259$	990341.	+	1.71532e6i	0.917350	+	1.58890i
$260$	−26594.0			−0.0243978
$261$	−390175.	+	1.25773e6i	−0.354534	+	1.14284i
$262$	1.43824e6			1.29443
$263$	−535454.	−	927433.i	−0.477345	−	0.826786i	0.522318	−	0.852751i	$-0.325068\pi$
$263$	−535454.	−	927433.i	−0.477345	−	0.826786i	−0.999663	+	0.0259647i	$0.991734\pi$
$264$	−13419.5	−	119969.i	−0.0118502	−	0.105940i
$265$	−23472.5	+	40655.6i	−0.0205327	+	0.0355636i
$266$	−398726.	+	690613.i	−0.345518	+	0.598454i
$267$	−1.28290e6	−	560951.i	−1.10132	−	0.481556i
$268$	−94035.3	−	162874.i	−0.0799749	−	0.138521i
$269$	148955.			0.125509			0.0627545	−	0.998029i	$-0.480012\pi$
$269$	148955.			0.125509			0.0627545	+	0.998029i	$0.480012\pi$
$270$	23277.7	+	67042.5i	0.0194326	+	0.0559681i
$271$	−1.92914e6			−1.59566			−0.797828	−	0.602885i	$-0.794018\pi$
$271$	−1.92914e6			−1.59566			−0.797828	+	0.602885i	$0.794018\pi$
$272$	−41505.3	−	71889.3i	−0.0340158	−	0.0589172i
$273$	884670.	+	386825.i	0.718414	+	0.314129i
$274$	328056.	−	568209.i	0.263980	−	0.457227i
$275$	187735.	−	325167.i	0.149697	−	0.259283i
$276$	−29775.9	−	266193.i	−0.0235284	−	0.210341i
$277$	380714.	+	659416.i	0.298126	+	0.516369i	0.975707	−	0.219079i	$-0.0703053\pi$
$277$	380714.	+	659416.i	0.298126	+	0.516369i	−0.677582	+	0.735448i	$0.736972\pi$
$278$	−669432.			−0.519511
$279$	−731073.	+	165626.i	−0.562277	+	0.127385i
$280$	−52321.4			−0.0398827
$281$	−343803.	−	595485.i	−0.259743	−	0.449889i	0.706430	−	0.707783i	$-0.250305\pi$
$281$	−343803.	−	595485.i	−0.259743	−	0.449889i	−0.966173	+	0.257895i	$0.916971\pi$
$282$	751695.	−	553843.i	0.562884	−	0.414728i
$283$	−182461.	+	316031.i	−0.135426	+	0.234565i	−0.925760	−	0.378111i	$-0.876574\pi$
$283$	−182461.	+	316031.i	−0.135426	+	0.234565i	0.790334	+	0.612676i	$0.209907\pi$
$284$	3266.10	−	5657.06i	0.00240289	−	0.00416193i
$285$	−67139.6	+	49467.9i	−0.0489628	+	0.0360754i
$286$	−85878.0	−	148745.i	−0.0620822	−	0.107530i
$287$	1.82570e6			1.30835
$288$	242682.	−	54979.9i	0.172408	−	0.0390592i
$289$	−1.31471e6			−0.925947
$290$	−50764.4	−	87926.6i	−0.0354458	−	0.0613939i
$291$	−127190.	−	1.13706e6i	−0.0880483	−	0.787141i
$292$	−28991.4	+	50214.5i	−0.0198981	+	0.0344645i
$293$	−985693.	+	1.70727e6i	−0.670768	+	1.16180i	0.306918	+	0.951736i	$0.400702\pi$
$293$	−985693.	+	1.70727e6i	−0.670768	+	1.16180i	−0.977687	+	0.210069i	$0.932631\pi$
$294$	780309.	+	341193.i	0.526500	+	0.230214i
$295$	−114376.	−	198105.i	−0.0765207	−	0.132538i
$296$	726260.			0.481796
$297$	−299812.	+	346692.i	−0.197223	+	0.228062i
$298$	−623690.			−0.406844
$299$	−190551.	−	330044.i	−0.123263	−	0.213498i
$300$	709125.	+	310068.i	0.454904	+	0.198908i
$301$	−46031.0	+	79728.1i	−0.0292843	+	0.0507219i
$302$	−621577.	+	1.07660e6i	−0.392173	+	0.679264i
$303$	143153.	+	1.27977e6i	0.0895767	+	0.800805i
$304$	146202.	+	253228.i	0.0907336	+	0.157155i
$305$	−223507.			−0.137576
$306$	−93385.6	+	301028.i	−0.0570133	+	0.183782i
$307$	1.49805e6			0.907153			0.453577	−	0.891217i	$-0.350148\pi$
$307$	1.49805e6			0.907153			0.453577	+	0.891217i	$0.350148\pi$
$308$	−168958.	−	292643.i	−0.101485	−	0.175777i
$309$	1.69942e6	−	1.25212e6i	1.01252	−	0.746017i
$310$	28896.9	−	50050.8i	0.0170784	−	0.0295806i
$311$	−641847.	+	1.11171e6i	−0.376297	+	0.651765i	−0.990520	−	0.137367i	$-0.956136\pi$
$311$	−641847.	+	1.11171e6i	−0.376297	+	0.651765i	0.614224	+	0.789132i	$0.289469\pi$
$312$	285027.	−	210006.i	0.165768	−	0.122136i
$313$	1.17399e6	+	2.03341e6i	0.677336	+	1.17318i	0.975780	+	0.218754i	$0.0701991\pi$
$313$	1.17399e6	+	2.03341e6i	0.677336	+	1.17318i	−0.298444	+	0.954427i	$0.596468\pi$
$314$	−784475.			−0.449009
$315$	134887.	+	145844.i	0.0765939	+	0.0828154i
$316$	489343.			0.275674
$317$	−1.20898e6	−	2.09401e6i	−0.675725	−	1.17039i	−0.976256	−	0.216618i	$-0.930497\pi$
$317$	−1.20898e6	−	2.09401e6i	−0.675725	−	1.17039i	0.300531	−	0.953772i	$-0.402836\pi$
$318$	−69474.3	−	621092.i	−0.0385262	−	0.344420i
$319$	327860.	−	567869.i	0.180389	−	0.312444i
$320$	−9592.40	+	16614.5i	−0.00523663	+	0.00907012i
$321$	−2.45353e6	−	1.07281e6i	−1.32901	−	0.581114i
$322$	−374892.	−	649332.i	−0.201496	−	0.349002i
$323$	−370370.			−0.197528
$324$	−778900.	−	534725.i	−0.412211	−	0.282988i
$325$	1.10118e6			0.578294
$326$	958519.	+	1.66020e6i	0.499525	+	0.865202i
$327$	−1.52372e6	−	666253.i	−0.788018	−	0.344564i
$328$	334717.	−	579747.i	0.171788	−	0.297546i
$329$	1.30682e6	−	2.26347e6i	0.665618	−	1.15288i
$330$	−3928.38	−	35119.3i	−0.00198577	−	0.0177525i
$331$	−955985.	−	1.65582e6i	−0.479602	−	0.830696i	0.520124	−	0.854091i	$-0.325886\pi$
$331$	−955985.	−	1.65582e6i	−0.479602	−	0.830696i	−0.999726	+	0.0233952i	$0.992552\pi$
$332$	1.04899e6			0.522309
$333$	−1.87233e6	−	2.02442e6i	−0.925279	−	1.00044i
$334$	−2.04843e6			−1.00474
$335$	−27527.6	−	47679.2i	−0.0134016	−	0.0232122i
$336$	560766.	−	413168.i	0.270978	−	0.199654i
$337$	412494.	−	714460.i	0.197853	−	0.342691i	−0.749979	−	0.661462i	$-0.769936\pi$
$337$	412494.	−	714460.i	0.197853	−	0.342691i	0.947832	+	0.318770i	$0.103270\pi$
$338$	−490723.	+	849958.i	−0.233639	+	0.404674i
$339$	−622364.	+	458553.i	−0.294134	+	0.216716i
$340$	−12150.1	−	21044.6i	−0.00570011	−	0.00987288i
$341$	373258.			0.173829
$342$	328949.	−	1.06037e6i	0.152077	−	0.490220i
$343$	−549596.			−0.252237
$344$	16878.3	+	29234.1i	0.00769011	+	0.0133197i
$345$	−8716.51	−	77924.6i	−0.00394271	−	0.0352474i
$346$	472199.	−	817873.i	0.212048	−	0.367279i
$347$	1.43546e6	−	2.48628e6i	0.639980	−	1.10848i	−0.345457	−	0.938435i	$-0.612276\pi$
$347$	1.43546e6	−	2.48628e6i	0.639980	−	1.10848i	0.985437	−	0.170043i	$-0.0543906\pi$
$348$	1.23841e6	+	541500.i	0.548172	+	0.239690i
$349$	−202804.	−	351267.i	−0.0891278	−	0.154374i	0.818015	−	0.575197i	$-0.195075\pi$
$349$	−202804.	−	351267.i	−0.0891278	−	0.154374i	−0.907143	+	0.420823i	$0.861741\pi$
$350$	2.16647e6			0.945328
$351$	−1.32020e6	−	253096.i	−0.571967	−	0.109652i
$352$	−123904.			−0.0533002
$353$	−33163.3	−	57440.4i	−0.0141651	−	0.0245347i	0.858856	−	0.512217i	$-0.171176\pi$
$353$	−33163.3	−	57440.4i	−0.0141651	−	0.0245347i	−0.873021	+	0.487682i	$0.837842\pi$
$354$	2.79023e6	+	1.22004e6i	1.18340	+	0.517445i
$355$	956.109	−	1656.03i	0.000402658	−	0.000697424i
$356$	−718570.	+	1.24460e6i	−0.300500	+	0.520481i
$357$	98076.9	+	876796.i	0.0407283	+	0.364106i
$358$	−555989.	−	963001.i	−0.229276	−	0.397117i
$359$	3.04823e6			1.24828			0.624139	−	0.781313i	$-0.285450\pi$
$359$	3.04823e6			1.24828			0.624139	+	0.781313i	$0.285450\pi$
$360$	71041.9	−	16094.6i	0.0288907	−	0.00654523i
$361$	−1.17148e6			−0.473115
$362$	−228060.	−	395011.i	−0.0914697	−	0.158430i
$363$	183743.	−	135380.i	0.0731887	−	0.0539248i
$364$	495518.	−	858261.i	0.196022	−	0.339521i
$365$	−8486.83	+	14699.6i	−0.00333437	+	0.00577529i
$366$	2.39548e6	−	1.76497e6i	0.934740	−	0.688708i
$367$	1.55637e6	+	2.69570e6i	0.603179	+	1.04474i	0.992336	+	0.123566i	$0.0394330\pi$
$367$	1.55637e6	+	2.69570e6i	0.603179	+	1.04474i	−0.389157	+	0.921171i	$0.627234\pi$
$368$	−274925.			−0.105827
$369$	−2.47894e6	+	561606.i	−0.947763	+	0.214717i
$370$	212603.			0.0807356
$371$	−874712.	−	1.51505e6i	−0.329936	−	0.571467i
$372$	85529.2	+	764621.i	0.0320448	+	0.286476i
$373$	−581003.	+	1.00633e6i	−0.216225	+	0.374513i	−0.953651	−	0.300915i	$-0.902708\pi$
$373$	−581003.	+	1.00633e6i	−0.216225	+	0.374513i	0.737426	+	0.675428i	$0.236041\pi$
$374$	78470.9	−	135916.i	0.0290088	−	0.0502447i
$375$	416642.	+	182178.i	0.152998	+	0.0668987i
$376$	−479173.	−	829952.i	−0.174792	−	0.302749i
$377$	1.92309e6			0.696861
$378$	−2.59737e6	−	497945.i	−0.934985	−	0.179247i
$379$	−2.03222e6			−0.726731			−0.363365	−	0.931647i	$-0.618372\pi$
$379$	−2.03222e6			−0.726731			−0.363365	+	0.931647i	$0.618372\pi$
$380$	42798.6	+	74129.3i	0.0152044	+	0.0263348i
$381$	−2.88903e6	−	1.26324e6i	−1.01962	−	0.445833i
$382$	1.03779e6	−	1.79750e6i	0.363872	−	0.630246i
$383$	1.26659e6	−	2.19379e6i	0.441202	−	0.764184i	−0.556577	−	0.830796i	$-0.687886\pi$
$383$	1.26659e6	−	2.19379e6i	0.441202	−	0.764184i	0.997779	+	0.0666117i	$0.0212189\pi$
$384$	−28391.7	−	253818.i	−0.00982569	−	0.0878405i
$385$	−49460.1	−	85667.4i	−0.0170060	−	0.0294553i
$386$	1.68558e6			0.575813
$387$	37975.7	−	122414.i	0.0128893	−	0.0415485i
$388$	−1.17436e6			−0.396025
$389$	1.36500e6	+	2.36426e6i	0.457362	+	0.792174i	0.998821	−	0.0485532i	$-0.0154610\pi$
$389$	1.36500e6	+	2.36426e6i	0.457362	+	0.792174i	−0.541459	+	0.840727i	$0.682128\pi$
$390$	83437.9	−	61476.4i	0.0277781	−	0.0204667i
$391$	174116.	−	301577.i	0.0575964	−	0.0997600i
$392$	437063.	−	757016.i	0.143658	−	0.248823i
$393$	−4.51243e6	+	3.32472e6i	−1.47377	+	1.08586i
$394$	−1.50151e6	−	2.60069e6i	−0.487289	−	0.844009i
$395$	143249.			0.0461953
$396$	319431.	+	345377.i	0.102362	+	0.110677i
$397$	−3.14248e6			−1.00068			−0.500342	−	0.865828i	$-0.666792\pi$
$397$	−3.14248e6			−1.00068			−0.500342	+	0.865828i	$0.666792\pi$
$398$	−417683.	−	723447.i	−0.132172	−	0.228928i
$399$	−345474.	−	3.08850e6i	−0.108638	−	0.971214i
$400$	397192.	−	687957.i	0.124122	−	0.214986i
$401$	318449.	−	551570.i	0.0988961	−	0.171293i	−0.812332	−	0.583195i	$-0.801802\pi$
$401$	318449.	−	551570.i	0.0988961	−	0.171293i	0.911228	+	0.411902i	$0.135136\pi$
$402$	671542.	+	293634.i	0.207257	+	0.0906237i
$403$	547344.	+	948027.i	0.167879	+	0.290776i
$404$	1.32175e6			0.402900
$405$	−228013.	−	156534.i	−0.0690751	−	0.0474209i
$406$	3.78351e6			1.13915
$407$	686543.	+	1.18913e6i	0.205438	+	0.355830i
$408$	296405.	+	129604.i	0.0881527	+	0.0385451i
$409$	775995.	−	1.34406e6i	0.229377	−	0.397293i	−0.728246	−	0.685315i	$-0.759664\pi$
$409$	775995.	−	1.34406e6i	0.229377	−	0.397293i	0.957624	+	0.288022i	$0.0929977\pi$
$410$	97984.0	−	169713.i	0.0287869	−	0.0498604i
$411$	284242.	+	2.54109e6i	0.0830012	+	0.742021i
$412$	−1.08330e6	−	1.87634e6i	−0.314418	−	0.544588i
$413$	8.52450e6			2.45920
$414$	708770.	+	766342.i	0.203238	+	0.219746i
$415$	307079.			0.0875245
$416$	−181692.	−	314700.i	−0.0514758	−	0.0891588i
$417$	2.10032e6	−	1.54750e6i	0.591488	−	0.435804i
$418$	−276412.	+	478760.i	−0.0773778	+	0.134022i
$419$	−1.59175e6	+	2.75698e6i	−0.442934	+	0.767183i	−0.997906	−	0.0646855i	$-0.979396\pi$
$419$	−1.59175e6	+	2.75698e6i	−0.442934	+	0.767183i	0.554972	+	0.831869i	$0.312729\pi$
$420$	164157.	−	120949.i	0.0454084	−	0.0334565i
$421$	−1.92335e6	−	3.33133e6i	−0.528874	−	0.916036i	−0.999433	−	0.0336678i	$-0.989281\pi$
$421$	−1.92335e6	−	3.33133e6i	−0.528874	−	0.916036i	0.470559	−	0.882368i	$-0.344052\pi$
$422$	−4.15281e6			−1.13517
$423$	−1.07812e6	+	3.47533e6i	−0.292967	+	0.944377i
$424$	−641465.			−0.173284
$425$	503100.	+	871394.i	0.135108	+	0.234014i
$426$	2829.90	+	25299.0i	0.000755522	+	0.00675428i
$427$	4.16453e6	−	7.21318e6i	1.10534	−	1.91451i
$428$	−1.37426e6	+	2.38028e6i	−0.362626	+	0.628087i
$429$	613288.	+	268162.i	0.160887	+	0.0703485i
$430$	4940.90	+	8557.88i	0.00128865	+	0.00223201i
$431$	4.60854e6			1.19501			0.597503	−	0.801866i	$-0.296159\pi$
$431$	4.60854e6			1.19501			0.597503	+	0.801866i	$0.296159\pi$
$432$	−634313.	+	733497.i	−0.163529	+	0.189099i
$433$	−2.57078e6			−0.658939			−0.329469	−	0.944166i	$-0.606870\pi$
$433$	−2.57078e6			−0.658939			−0.329469	+	0.944166i	$0.606870\pi$
$434$	1.07685e6	+	1.86516e6i	0.274430	+	0.475326i
$435$	362529.	+	158517.i	0.0918584	+	0.0401654i
$436$	−853460.	+	1.47824e6i	−0.215014	+	0.372415i
$437$	−613319.	+	1.06230e6i	−0.153632	+	0.266099i
$438$	−25119.4	−	224565.i	−0.00625640	−	0.0559315i
$439$	−3.44542e6	−	5.96764e6i	−0.853259	−	1.47789i	−0.878251	−	0.478201i	$-0.841289\pi$
$439$	−3.44542e6	−	5.96764e6i	−0.853259	−	1.47789i	0.0249912	−	0.999688i	$-0.492044\pi$
$440$	−36271.3			−0.00893163
$441$	−3.23692e6	+	733329.i	−0.792566	+	0.179557i
$442$	460278.			0.112064
$443$	369994.	+	640848.i	0.0895747	+	0.155148i	0.907331	−	0.420416i	$-0.138116\pi$
$443$	369994.	+	640848.i	0.0895747	+	0.155148i	−0.817757	+	0.575564i	$0.804783\pi$
$444$	−2.27862e6	+	1.67887e6i	−0.548548	+	0.404165i
$445$	−210352.	+	364340.i	−0.0503554	+	0.0872181i
$446$	814278.	−	1.41037e6i	0.193836	−	0.335735i
$447$	1.95681e6	−	1.44176e6i	0.463212	−	0.341290i
$448$	−357464.	−	619146.i	−0.0841467	−	0.145746i
$449$	6.76241e6			1.58302			0.791509	−	0.611158i	$-0.209296\pi$
$449$	6.76241e6			1.58302			0.791509	+	0.611158i	$0.209296\pi$
$450$	−2.94163e6	+	666430.i	−0.684789	+	0.155140i
$451$	1.26565e6			0.293003
$452$	396730.	+	687157.i	0.0913375	+	0.158201i
$453$	−538563.	−	4.81469e6i	−0.123308	−	1.10236i
$454$	−759782.	+	1.31598e6i	−0.173001	+	0.299647i
$455$	145056.	−	251245.i	0.0328479	−	0.0568942i
$456$	−1.04408e6	−	456528.i	−0.235138	−	0.102815i
$457$	1.62299e6	+	2.81110e6i	0.363517	+	0.629630i	0.988537	−	0.150979i	$-0.0482425\pi$
$457$	1.62299e6	+	2.81110e6i	0.363517	+	0.629630i	−0.625020	+	0.780609i	$0.714909\pi$
$458$	−2.53906e6			−0.565600
$459$	−402881.	−	1.16034e6i	−0.0892576	−	0.257072i
$460$	−80480.6			−0.0177336
$461$	−1.77875e6	−	3.08089e6i	−0.389819	−	0.675186i	0.602606	−	0.798039i	$-0.294129\pi$
$461$	−1.77875e6	−	3.08089e6i	−0.389819	−	0.675186i	−0.992425	+	0.122853i	$0.960796\pi$
$462$	1.20659e6	+	527586.i	0.263000	+	0.114998i
$463$	−4.26132e6	+	7.38083e6i	−0.923830	+	1.60012i	−0.130398	+	0.991462i	$0.541625\pi$
$463$	−4.26132e6	+	7.38083e6i	−0.923830	+	1.60012i	−0.793432	+	0.608659i	$0.791708\pi$
$464$	693653.	−	1.20144e6i	0.149571	−	0.259065i
$465$	25037.5	+	223833.i	0.00536982	+	0.0480055i
$466$	−1.34821e6	−	2.33516e6i	−0.287602	−	0.498141i
$467$	1.62149e6			0.344050			0.172025	−	0.985093i	$-0.444969\pi$
$467$	1.62149e6			0.344050			0.172025	+	0.985093i	$0.444969\pi$
$468$	−408802.	+	1.31777e6i	−0.0862777	+	0.278116i
$469$	2.05165e6			0.430696
$470$	−140272.	−	242957.i	−0.0292904	−	0.0507324i
$471$	2.46127e6	−	1.81344e6i	0.511218	−	0.376661i
$472$	1.56285e6	−	2.70693e6i	0.322895	−	0.559271i
$473$	−31910.5	+	55270.7i	−0.00655815	+	0.0113590i
$474$	−1.53530e6	+	1.13119e6i	−0.313868	+	0.231255i
$475$	−1.77216e6	−	3.06947e6i	−0.360386	−	0.624208i
$476$	905557.			0.183189
$477$	1.65373e6	+	1.78806e6i	0.332788	+	0.359820i
$478$	−2.56211e6			−0.512895
$479$	2.75448e6	+	4.77089e6i	0.548530	+	0.950082i	0.998376	+	0.0569754i	$0.0181457\pi$
$479$	2.75448e6	+	4.77089e6i	0.548530	+	0.950082i	−0.449846	+	0.893106i	$0.648521\pi$
$480$	−8311.29	−	74301.9i	−0.00164651	−	0.0147196i
$481$	−2.01349e6	+	3.48746e6i	−0.396813	+	0.687301i
$482$	−2.43624e6	+	4.21970e6i	−0.477643	+	0.827302i
$483$	2.67725e6	+	1.17064e6i	0.522181	+	0.228325i
$484$	−117128.	−	202872.i	−0.0227273	−	0.0393648i
$485$	−343779.			−0.0663628
$486$	3.67988e6	−	122871.i	0.706713	−	0.0235971i
$487$	8.08541e6			1.54483			0.772413	−	0.635121i	$-0.219050\pi$
$487$	8.08541e6			1.54483			0.772413	+	0.635121i	$0.219050\pi$
$488$	−1.52702e6	−	2.64487e6i	−0.290265	−	0.502753i
$489$	−6.84516e6	−	2.99307e6i	−1.29453	−	0.566037i
$490$	127944.	−	221606.i	0.0240731	−	0.0416958i
$491$	2.19415e6	−	3.80038e6i	0.410736	−	0.711415i	−0.584235	−	0.811585i	$-0.698605\pi$
$491$	2.19415e6	−	3.80038e6i	0.410736	−	0.711415i	0.994970	+	0.100169i	$0.0319385\pi$
$492$	290014.	+	2.59269e6i	0.0540140	+	0.482879i
$493$	878610.	+	1.52180e6i	0.162809	+	0.281994i
$494$	−1.62132e6			−0.298918
$495$	93509.1	+	101105.i	0.0171530	+	0.0185463i
$496$	789702.			0.144132
$497$	35629.7	+	61712.5i	0.00647025	+	0.0112068i
$498$	−3.29118e6	+	2.42492e6i	−0.594674	+	0.438151i
$499$	2.95259e6	−	5.11404e6i	0.530826	−	0.919417i	−0.468527	−	0.883449i	$-0.655215\pi$
$499$	2.95259e6	−	5.11404e6i	0.530826	−	0.919417i	0.999353	−	0.0359683i	$-0.0114515\pi$
$500$	233367.	−	404204.i	0.0417460	−	0.0723062i
$501$	6.42689e6	−	4.73528e6i	1.14395	−	0.842852i
$502$	934462.	+	1.61854e6i	0.165502	+	0.286657i
$503$	−502430.			−0.0885432			−0.0442716	−	0.999020i	$-0.514097\pi$
$503$	−502430.			−0.0885432			−0.0442716	+	0.999020i	$0.514097\pi$
$504$	−804283.	+	2.59260e6i	−0.141037	+	0.454632i
$505$	386926.			0.0675149
$506$	−259890.	−	450143.i	−0.0451246	−	0.0781581i
$507$	−425185.	−	3.80110e6i	−0.0734612	−	0.656735i
$508$	−1.61819e6	+	2.80278e6i	−0.278208	+	0.481871i
$509$	−180677.	+	312941.i	−0.0309106	+	0.0535387i	−0.881067	−	0.472992i	$-0.843174\pi$
$509$	−180677.	+	312941.i	−0.0309106	+	0.0535387i	0.850156	+	0.526530i	$0.176507\pi$
$510$	86768.7	+	37939.9i	0.0147719	+	0.00645909i
$511$	−316265.	−	547787.i	−0.0535795	−	0.0928024i
$512$	−262144.			−0.0441942
$513$	1.41914e6	+	4.08729e6i	0.238085	+	0.685712i
$514$	−4.93507e6			−0.823920
$515$	−317123.	−	549273.i	−0.0526877	−	0.0912578i
$516$	−120534.	−	52704.1i	−0.0199291	−	0.00871405i
$517$	905936.	−	1.56913e6i	0.149063	−	0.258186i
$518$	−3.96136e6	+	6.86128e6i	−0.648665	+	1.12352i
$519$	409135.	+	3.65762e6i	0.0666727	+	0.596046i
$520$	−53188.0	−	92124.4i	−0.00862592	−	0.0149405i
$521$	1.02288e6			0.165094			0.0825471	−	0.996587i	$-0.473695\pi$
$521$	1.02288e6			0.165094			0.0825471	+	0.996587i	$0.473695\pi$
$522$	−5.13724e6	+	1.16385e6i	−0.825190	+	0.186948i
$523$	1.02646e7			1.64092			0.820459	−	0.571705i	$-0.193718\pi$
$523$	1.02646e7			1.64092			0.820459	+	0.571705i	$0.193718\pi$
$524$	2.87648e6	+	4.98221e6i	0.457649	+	0.792672i
$525$	−6.79724e6	+	5.00815e6i	−1.07630	+	0.793010i
$526$	2.14182e6	−	3.70973e6i	0.337534	−	0.584626i
$527$	−500135.	+	866258.i	−0.0784441	+	0.135869i
$528$	388745.	−	286424.i	0.0606848	−	0.0447121i
$529$	2.64151e6	+	4.57524e6i	0.410406	+	0.710844i
$530$	−187780.			−0.0290376
$531$	−1.15746e7	+	2.62223e6i	−1.78143	+	0.403585i
$532$	−3.18981e6			−0.488636
$533$	1.85594e6	+	3.21459e6i	0.282974	+	0.490125i
$534$	−622602.	−	5.56598e6i	−0.0944837	−	0.844673i
$535$	−402296.	+	696797.i	−0.0607661	+	0.105250i
$536$	376141.	−	651496.i	0.0565508	−	0.0979489i
$537$	3.97053e6	+	1.73613e6i	0.594173	+	0.259804i
$538$	297910.	+	515996.i	0.0443741	+	0.0768582i
$539$	1.65265e6			0.245024
$540$	−185687.	+	214721.i	−0.0274029	+	0.0316877i
$541$	3.44164e6			0.505559			0.252780	−	0.967524i	$-0.418655\pi$
$541$	3.44164e6			0.505559			0.252780	+	0.967524i	$0.418655\pi$
$542$	−3.85827e6	−	6.68272e6i	−0.564150	−	0.977136i
$543$	1.62866e6	+	712139.i	0.237046	+	0.103649i
$544$	166021.	−	287557.i	0.0240528	−	0.0416607i
$545$	−249839.	+	432734.i	−0.0360304	+	0.0624065i
$546$	429339.	+	3.83824e6i	0.0616338	+	0.550998i
$547$	−4.39519e6	−	7.61270e6i	−0.628072	−	1.08785i	−0.987938	−	0.154849i	$-0.950511\pi$
$547$	−4.39519e6	−	7.61270e6i	−0.628072	−	1.08785i	0.359866	−	0.933004i	$-0.382822\pi$
$548$	2.62445e6			0.373324
$549$	−3.43574e6	+	1.10751e7i	−0.486507	+	1.56826i
$550$	1.50188e6			0.211704
$551$	−3.09488e6	−	5.36050e6i	−0.434276	−	0.752187i
$552$	862569.	−	635533.i	0.120489	−	0.0887750i
$553$	−2.66910e6	+	4.62302e6i	−0.371153	+	0.642855i
$554$	−1.52286e6	+	2.63766e6i	−0.210807	+	0.365128i
$555$	−667036.	+	491466.i	−0.0919214	+	0.0677269i
$556$	−1.33886e6	−	2.31898e6i	−0.183675	−	0.318134i
$557$	3.05501e6			0.417229			0.208615	−	0.977998i	$-0.433105\pi$
$557$	3.05501e6			0.417229			0.208615	+	0.977998i	$0.433105\pi$
$558$	−2.03589e6	−	2.20126e6i	−0.276802	−	0.299286i
$559$	−187174.			−0.0253347
$560$	−104643.	−	181247.i	−0.0141007	−	0.0244231i
$561$	67990.8	+	607830.i	0.00912101	+	0.0815407i
$562$	1.37521e6	−	2.38194e6i	0.183666	−	0.318119i
$563$	−4.86243e6	+	8.42198e6i	−0.646521	+	1.11981i	0.337427	+	0.941352i	$0.390443\pi$
$563$	−4.86243e6	+	8.42198e6i	−0.646521	+	1.11981i	−0.983948	+	0.178455i	$0.942890\pi$
$564$	3.42196e6	+	1.49626e6i	0.452978	+	0.198066i
$565$	116137.	+	201156.i	0.0153056	+	0.0265101i
$566$	−1.45968e6			−0.191522
$567$	9.30025e6	−	4.44195e6i	1.21489	−	0.580252i
$568$	26128.8			0.00339820
$569$	1.12676e6	+	1.95161e6i	0.145899	+	0.252704i	0.929708	−	0.368298i	$-0.120059\pi$
$569$	1.12676e6	+	1.95161e6i	0.145899	+	0.252704i	−0.783809	+	0.621002i	$0.786726\pi$
$570$	−305641.	−	133643.i	−0.0394026	−	0.0172289i
$571$	−6.65096e6	+	1.15198e7i	−0.853678	+	1.47861i	0.0241883	+	0.999707i	$0.492300\pi$
$571$	−6.65096e6	+	1.15198e7i	−0.853678	+	1.47861i	−0.877866	+	0.478906i	$0.841033\pi$
$572$	343512.	−	594981.i	0.0438987	−	0.0760349i
$573$	899185.	+	8.03860e6i	0.114410	+	1.02281i
$574$	3.65141e6	+	6.32442e6i	0.462573	+	0.801200i
$575$	3.33246e6			0.420334
$576$	675820.	+	730715.i	0.0848740	+	0.0917682i
$577$	−7.49227e6			−0.936858			−0.468429	−	0.883501i	$-0.655180\pi$
$577$	−7.49227e6			−0.936858			−0.468429	+	0.883501i	$0.655180\pi$
$578$	−2.62942e6	−	4.55430e6i	−0.327372	−	0.567024i
$579$	−5.28846e6	+	3.89649e6i	−0.655591	+	0.483034i
$580$	203058.	−	351706.i	0.0250640	−	0.0434121i
$581$	−5.72170e6	+	9.91027e6i	−0.703209	+	1.21799i
$582$	3.68453e6	−	2.71473e6i	0.450894	−	0.332215i
$583$	−606385.	−	1.05029e6i	−0.0738885	−	0.127979i
$584$	−231931.			−0.0281401
$585$	−119671.	+	385761.i	−0.0144578	+	0.0466045i
$586$	−7.88554e6			−0.948609
$587$	−6.55908e6	−	1.13607e7i	−0.785683	−	1.36084i	−0.928590	−	0.371107i	$-0.878978\pi$
$587$	−6.55908e6	−	1.13607e7i	−0.785683	−	1.36084i	0.142907	−	0.989736i	$-0.454355\pi$
$588$	378692.	+	3.38546e6i	0.0451692	+	0.403807i
$589$	1.76171e6	−	3.05138e6i	0.209241	−	0.362416i
$590$	457503.	−	792418.i	0.0541083	−	0.0937183i
$591$	1.07228e7	+	4.68860e6i	1.26282	+	0.552172i
$592$	1.45252e6	+	2.51584e6i	0.170341	+	0.295038i
$593$	−1.02678e7			−1.19906			−0.599528	−	0.800353i	$-0.704645\pi$
$593$	−1.02678e7			−1.19906			−0.599528	+	0.800353i	$0.704645\pi$
$594$	−1.80060e6	−	345195.i	−0.209388	−	0.0401420i
$595$	265090.			0.0306973
$596$	−1.24738e6	−	2.16052e6i	−0.143841	−	0.249140i
$597$	2.98283e6	+	1.30425e6i	0.342526	+	0.149771i
$598$	762203.	−	1.32018e6i	0.0871601	−	0.150966i
$599$	−1.46956e6	+	2.54535e6i	−0.167348	+	0.289855i	−0.937487	−	0.348022i	$-0.886854\pi$
$599$	−1.46956e6	+	2.54535e6i	−0.167348	+	0.289855i	0.770139	+	0.637876i	$0.220187\pi$
$600$	344145.	+	3.07662e6i	0.0390269	+	0.348895i
$601$	3.05762e6	+	5.29596e6i	0.345301	+	0.598079i	0.985408	−	0.170207i	$-0.0544436\pi$
$601$	3.05762e6	+	5.29596e6i	0.345301	+	0.598079i	−0.640108	+	0.768285i	$0.721110\pi$
$602$	−368248.			−0.0414142
$603$	−2.78573e6	+	631110.i	−0.311993	+	0.0706825i
$604$	−4.97262e6			−0.554616
$605$	−34287.7	−	59388.0i	−0.00380846	−	0.00659645i
$606$	−4.14696e6	+	3.05545e6i	−0.458721	+	0.337982i
$607$	8.15250e6	−	1.41205e7i	0.898088	−	1.55553i	0.0681521	−	0.997675i	$-0.478290\pi$
$607$	8.15250e6	−	1.41205e7i	0.898088	−	1.55553i	0.829936	−	0.557859i	$-0.188377\pi$
$608$	−584806.	+	1.01291e6i	−0.0641583	+	0.111125i
$609$	−1.18706e7	+	8.74619e6i	−1.29697	+	0.955599i
$610$	−447014.	−	774251.i	−0.0486403	−	0.0842475i
$611$	5.31385e6			0.575846
$612$	−1.22956e6	+	278559.i	−0.132701	+	0.0300635i
$613$	−7.03778e6			−0.756458			−0.378229	−	0.925712i	$-0.623467\pi$
$613$	−7.03778e6			−0.756458			−0.378229	+	0.925712i	$0.623467\pi$
$614$	2.99610e6	+	5.18940e6i	0.320727	+	0.555516i
$615$	84897.8	+	758976.i	0.00905125	+	0.0809171i
$616$	675830.	−	1.17057e6i	0.0717606	−	0.124293i
$617$	6.18382e6	−	1.07107e7i	0.653949	−	1.13267i	−0.328207	−	0.944606i	$-0.606444\pi$
$617$	6.18382e6	−	1.07107e7i	0.653949	−	1.13267i	0.982156	−	0.188067i	$-0.0602224\pi$
$618$	7.73629e6	+	3.38272e6i	0.814820	+	0.356283i
$619$	−9.03398e6	−	1.56473e7i	−0.947660	−	1.64139i	−0.750336	−	0.661057i	$-0.770108\pi$
$619$	−9.03398e6	−	1.56473e7i	−0.947660	−	1.64139i	−0.197324	−	0.980338i	$-0.563225\pi$
$620$	231175.			0.0241525
$621$	−3.99527e6	−	765938.i	−0.415735	−	0.0797011i
$622$	−5.13477e6			−0.532164
$623$	−7.83883e6	−	1.35772e7i	−0.809154	−	1.40150i
$624$	1.29754e6	+	567352.i	0.133401	+	0.0583299i
$625$	−4.78022e6	+	8.27958e6i	−0.489494	+	0.847829i
$626$	−4.69597e6	+	8.13366e6i	−0.478949	+	0.829564i
$627$	−239496.	−	2.14107e6i	−0.0243293	−	0.217501i
$628$	−1.56895e6	−	2.71750e6i	−0.158749	−	0.274961i
$629$	−3.67964e6			−0.370834
$630$	−235443.	+	758950.i	−0.0236339	+	0.0761837i
$631$	6.19317e6			0.619213			0.309606	−	0.950865i	$-0.399803\pi$
$631$	6.19317e6			0.619213			0.309606	+	0.950865i	$0.399803\pi$
$632$	978686.	+	1.69513e6i	0.0974654	+	0.168815i
$633$	1.30293e7	−	9.59988e6i	1.29244	−	0.952262i
$634$	4.83591e6	−	8.37604e6i	0.477810	−	0.827591i
$635$	−473703.	+	820478.i	−0.0466200	+	0.0807481i
$636$	2.01258e6	−	1.48285e6i	0.197292	−	0.145363i
$637$	2.42343e6	+	4.19751e6i	0.236637	+	0.409867i
$638$	2.62288e6			0.255109
$639$	−67361.4	−	72833.0i	−0.00652618	−	0.00705629i
$640$	−76739.2			−0.00740572
$641$	−5.08148e6	−	8.80139e6i	−0.488478	−	0.846069i	0.511434	−	0.859323i	$-0.329115\pi$
$641$	−5.08148e6	−	8.80139e6i	−0.488478	−	0.846069i	−0.999912	+	0.0132533i	$0.995781\pi$
$642$	−1.19072e6	−	1.06449e7i	−0.114018	−	1.01930i
$643$	−9.29169e6	+	1.60937e7i	−0.886272	+	1.53507i	−0.0420238	+	0.999117i	$0.513381\pi$
$643$	−9.29169e6	+	1.60937e7i	−0.886272	+	1.53507i	−0.844248	+	0.535952i	$0.819953\pi$
$644$	1.49957e6	−	2.59733e6i	0.142479	−	0.246781i
$645$	−35284.9	−	15428.4i	−0.00333956	−	0.00146023i
$646$	−740739.	−	1.28300e6i	−0.0698368	−	0.120961i
$647$	1.76108e7			1.65393			0.826967	−	0.562251i	$-0.190065\pi$
$647$	1.76108e7			1.65393			0.826967	+	0.562251i	$0.190065\pi$
$648$	294541.	−	3.76764e6i	0.0275555	−	0.352478i
$649$	5.90952e6			0.550732
$650$	2.20235e6	+	3.81459e6i	0.204458	+	0.354131i
$651$	−7.69021e6	−	3.36257e6i	−0.711190	−	0.310970i
$652$	−3.83408e6	+	6.64082e6i	−0.353217	+	0.611790i
$653$	−5.50178e6	+	9.52936e6i	−0.504917	+	0.874542i	0.495067	+	0.868855i	$0.335144\pi$
$653$	−5.50178e6	+	9.52936e6i	−0.504917	+	0.874542i	−0.999984	+	0.00568720i	$0.998190\pi$
$654$	−739476.	−	6.61083e6i	−0.0676052	−	0.604382i
$655$	842051.	+	1.45847e6i	0.0766894	+	0.132830i
$656$	2.67774e6			0.242945
$657$	597929.	+	646497.i	0.0540426	+	0.0584323i
$658$	1.04545e7			0.941325
$659$	−4.83490e6	−	8.37430e6i	−0.433685	−	0.751164i	0.563502	−	0.826114i	$-0.309454\pi$
$659$	−4.83490e6	−	8.37430e6i	−0.433685	−	0.751164i	−0.997187	+	0.0749501i	$0.976120\pi$
$660$	113800.	−	83846.9i	0.0101691	−	0.00749250i
$661$	2.32811e6	−	4.03241e6i	0.207253	−	0.358973i	−0.743595	−	0.668630i	$-0.766881\pi$
$661$	2.32811e6	−	4.03241e6i	0.207253	−	0.358973i	0.950848	+	0.309657i	$0.100214\pi$
$662$	3.82394e6	−	6.62326e6i	0.339130	−	0.587390i
$663$	−1.44411e6	+	1.06401e6i	−0.127590	+	0.0940071i
$664$	2.09799e6	+	3.63382e6i	0.184664	+	0.319848i
$665$	−933773.			−0.0818818
$666$	3.26813e6	−	1.05348e7i	0.285505	−	0.920324i
$667$	5.81978e6			0.506515
$668$	−4.09686e6	−	7.09597e6i	−0.355230	−	0.615277i
$669$	705527.	+	6.30733e6i	0.0609465	+	0.544854i
$670$	110110.	−	190717.i	0.00947635	−	0.0164135i
$671$	2.88702e6	−	5.00046e6i	0.247539	−	0.428749i
$672$	2.55279e6	+	1.11622e6i	0.218068	+	0.0953509i
$673$	5.79318e6	+	1.00341e7i	0.493037	+	0.853965i	0.999968	−	0.00802187i	$-0.00255347\pi$
$673$	5.79318e6	+	1.00341e7i	0.493037	+	0.853965i	−0.506931	+	0.861987i	$0.669220\pi$
$674$	3.29995e6			0.279806
$675$	7.68872e6	−	8.89096e6i	0.649523	−	0.751085i
$676$	−3.92579e6			−0.330415
$677$	4.34027e6	+	7.51757e6i	0.363953	+	0.630385i	0.988608	−	0.150516i	$-0.0480936\pi$
$677$	4.34027e6	+	7.51757e6i	0.363953	+	0.630385i	−0.624655	+	0.780901i	$0.714760\pi$
$678$	−2.83320e6	−	1.23883e6i	−0.236703	−	0.103499i
$679$	6.40552e6	−	1.10947e7i	0.533187	−	0.923508i
$680$	48600.5	−	84178.5i	0.00403059	−	0.00698118i
$681$	−658309.	−	5.88521e6i	−0.0543954	−	0.486288i
$682$	746515.	+	1.29300e6i	0.0614579	+	0.106448i
$683$	−1.56074e7			−1.28020			−0.640102	−	0.768290i	$-0.721108\pi$
$683$	−1.56074e7			−1.28020			−0.640102	+	0.768290i	$0.721108\pi$
$684$	4.33111e6	−	981220.i	0.353964	−	0.0801911i
$685$	768272.			0.0625588
$686$	−1.09919e6	−	1.90386e6i	−0.0891791	−	0.154463i
$687$	7.96623e6	−	5.86945e6i	0.643963	−	0.474467i
$688$	−67513.2	+	116936.i	−0.00543773	+	0.00941842i
$689$	1.77840e6	−	3.08028e6i	0.142719	−	0.247196i
$690$	252506.	−	186044.i	0.0201906	−	0.0148762i
$691$	−6.43886e6	−	1.11524e7i	−0.512996	−	0.888535i	−0.999886	−	0.0150718i	$-0.995202\pi$
$691$	−6.43886e6	−	1.11524e7i	−0.512996	−	0.888535i	0.486891	−	0.873463i	$-0.338131\pi$
$692$	3.77759e6			0.299882
$693$	−5.00524e6	+	1.13394e6i	−0.395906	+	0.0896930i
$694$	1.14836e7			0.905068
$695$	−391935.	−	678851.i	−0.0307788	−	0.0533105i
$696$	601013.	+	5.37298e6i	0.0470284	+	0.420429i
$697$	−1.69587e6	+	2.93732e6i	−0.132224	+	0.229018i
$698$	811216.	−	1.40507e6i	0.0630229	−	0.109159i
$699$	9.62806e6	+	4.20990e6i	0.745326	+	0.325896i
$700$	4.33294e6	+	7.50487e6i	0.334224	+	0.578893i
$701$	5.38441e6			0.413850			0.206925	−	0.978357i	$-0.433654\pi$
$701$	5.38441e6			0.413850			0.206925	+	0.978357i	$0.433654\pi$
$702$	−1.76364e6	−	5.07949e6i	−0.135073	−	0.389025i
$703$	1.29615e7			0.989159
$704$	−247808.	−	429216.i	−0.0188445	−	0.0326396i
$705$	1.00173e6	+	438011.i	0.0759065	+	0.0331904i
$706$	132653.	−	229762.i	0.0100163	−	0.0173487i
$707$	−7.20946e6	+	1.24872e7i	−0.542443	+	0.939539i
$708$	1.35412e6	+	1.21057e7i	0.101525	+	0.907625i
$709$	−6.23538e6	−	1.08000e7i	−0.465852	−	0.806879i	0.533388	−	0.845871i	$-0.320919\pi$
$709$	−6.23538e6	−	1.08000e7i	−0.465852	−	0.806879i	−0.999240	+	0.0389922i	$0.987585\pi$
$710$	7648.87			0.000569444
$711$	2.20201e6	−	7.09818e6i	0.163360	−	0.526591i
$712$	−5.74856e6			−0.424971
$713$	1.65641e6	+	2.86898e6i	0.122024	+	0.211351i
$714$	−2.84116e6	+	2.09334e6i	−0.208569	+	0.153672i
$715$	100559.	−	174173.i	0.00735621	−	0.0127413i
$716$	2.22395e6	−	3.85200e6i	0.162123	−	0.280804i
$717$	8.03856e6	−	5.92274e6i	0.583956	−	0.430254i
$718$	6.09646e6	+	1.05594e7i	0.441333	+	0.764411i
$719$	−4.67321e6			−0.337127			−0.168563	−	0.985691i	$-0.553913\pi$
$719$	−4.67321e6			−0.337127			−0.168563	+	0.985691i	$0.553913\pi$
$720$	197837.	+	213907.i	0.0142225	+	0.0153778i
$721$	2.36354e7			1.69326
$722$	−2.34296e6	−	4.05812e6i	−0.167271	−	0.289722i
$723$	−2.11087e6	−	1.88710e7i	−0.150182	−	1.34260i
$724$	912240.	−	1.58005e6i	0.0646789	−	0.112027i
$725$	−8.40800e6	+	1.45631e7i	−0.594084	+	1.02898i
$726$	836456.	+	365743.i	0.0588982	+	0.0257534i
$727$	1.15523e6	+	2.00091e6i	0.0810645	+	0.140408i	0.903707	−	0.428150i	$-0.140835\pi$
$727$	1.15523e6	+	2.00091e6i	0.0810645	+	0.140408i	−0.822643	+	0.568558i	$0.807501\pi$
$728$	3.96414e6			0.277217
$729$	−1.12615e7	+	8.89214e6i	−0.784832	+	0.619709i
$730$	−67894.7			−0.00471551
$731$	−85515.0	−	148116.i	−0.00591900	−	0.0102520i
$732$	1.09050e7	+	4.76826e6i	0.752226	+	0.328914i
$733$	4.31998e6	−	7.48243e6i	0.296976	−	0.514378i	−0.678466	−	0.734632i	$-0.737355\pi$
$733$	4.31998e6	−	7.48243e6i	0.296976	−	0.514378i	0.975443	+	0.220253i	$0.0706884\pi$
$734$	−6.22546e6	+	1.07828e7i	−0.426512	+	0.738741i
$735$	110857.	+	991048.i	0.00756910	+	0.0676669i
$736$	−549850.	−	952368.i	−0.0374153	−	0.0648052i
$737$	1.42228e6			0.0964534
$738$	−6.90334e6	−	7.46408e6i	−0.466571	−	0.504470i
$739$	−2.31846e6			−0.156167			−0.0780833	−	0.996947i	$-0.524880\pi$
$739$	−2.31846e6			−0.156167			−0.0780833	+	0.996947i	$0.524880\pi$
$740$	425206.	+	736479.i	0.0285444	+	0.0494403i
$741$	5.08684e6	−	3.74794e6i	0.340332	−	0.250754i
$742$	3.49885e6	−	6.06018e6i	0.233300	−	0.404088i
$743$	−9.23356e6	+	1.59930e7i	−0.613617	+	1.06282i	0.377008	+	0.926210i	$0.376953\pi$
$743$	−9.23356e6	+	1.59930e7i	−0.613617	+	1.06282i	−0.990625	+	0.136606i	$0.956381\pi$
$744$	−2.47767e6	+	1.82552e6i	−0.164101	+	0.120908i
$745$	−365154.	−	632465.i	−0.0241038	−	0.0417490i
$746$	−4.64802e6			−0.305789
$747$	4.72040e6	−	1.52162e7i	0.309512	−	0.997711i
$748$	627767.			0.0410246
$749$	−1.49917e7	−	2.59664e7i	−0.976441	−	1.69125i
$750$	202200.	+	1.80764e6i	0.0131259	+	0.117344i
$751$	−1.40167e7	+	2.42776e7i	−0.906871	+	1.57075i	−0.0884857	+	0.996077i	$0.528203\pi$
$751$	−1.40167e7	+	2.42776e7i	−0.906871	+	1.57075i	−0.818386	+	0.574670i	$0.805131\pi$
$752$	1.91669e6	−	3.31981e6i	0.123597	−	0.214076i
$753$	−6.67336e6	−	2.91795e6i	−0.428901	−	0.187538i
$754$	3.84618e6	+	6.66177e6i	0.246377	+	0.426738i
$755$	−1.45567e6			−0.0929383
$756$	−3.46981e6	−	9.99345e6i	−0.220801	−	0.635932i
$757$	1.35453e7			0.859107			0.429554	−	0.903041i	$-0.358671\pi$
$757$	1.35453e7			0.859107			0.429554	+	0.903041i	$0.358671\pi$
$758$	−4.06445e6	−	7.03983e6i	−0.256938	−	0.445030i
$759$	1.85597e6	+	811531.i	0.116941	+	0.0511330i
$760$	−171194.	+	296517.i	−0.0107512	+	0.0186215i
$761$	−3.60889e6	+	6.25078e6i	−0.225898	+	0.391267i	−0.956588	−	0.291442i	$-0.905865\pi$
$761$	−3.60889e6	+	6.25078e6i	−0.225898	+	0.391267i	0.730691	+	0.682709i	$0.239198\pi$
$762$	−1.40207e6	−	1.25344e7i	−0.0874748	−	0.782014i
$763$	−9.31034e6	−	1.61260e7i	−0.578967	−	1.00280i
$764$	8.30228e6			0.514593
$765$	−359939.	+	81544.5i	−0.0222369	+	0.00503780i
$766$	1.01327e7			0.623954
$767$	8.66570e6	+	1.50094e7i	0.531882	+	0.921246i
$768$	822469.	−	605988.i	0.0503172	−	0.0370733i
$769$	−1.18528e7	+	2.05296e7i	−0.722778	+	1.25189i	0.237104	+	0.971484i	$0.423802\pi$
$769$	−1.18528e7	+	2.05296e7i	−0.722778	+	1.25189i	−0.959882	+	0.280404i	$0.909532\pi$
$770$	197840.	−	342669.i	0.0120251	−	0.0208281i
$771$	1.54836e7	−	1.14082e7i	0.938073	−	0.691164i
$772$	3.37116e6	+	5.83903e6i	0.203581	+	0.352612i
$773$	−2.59811e7			−1.56390			−0.781948	−	0.623343i	$-0.785774\pi$
$773$	−2.59811e7			−1.56390			−0.781948	+	0.623343i	$0.785774\pi$
$774$	500007.	−	113277.i	0.0300002	−	0.00679658i
$775$	−9.57225e6			−0.572479
$776$	−2.34872e6	−	4.06811e6i	−0.140016	−	0.242515i
$777$	−3.43230e6	−	3.06844e7i	−0.203954	−	1.82333i
$778$	−5.46002e6	+	9.45703e6i	−0.323404	+	0.560152i
$779$	5.97365e6	−	1.03467e7i	0.352692	−	0.610881i
$780$	379836.	+	166085.i	0.0223542	+	0.00977447i
$781$	24699.9	+	42781.5i	0.00144900	+	0.00250974i
$782$	1.39292e6			0.0814537
$783$	1.34275e7	−	1.55271e7i	0.782693	−	0.905078i
$784$	3.49651e6			0.203163
$785$	−459289.	−	795512.i	−0.0266019	−	0.0460758i
$786$	−2.05420e7	−	8.98208e6i	−1.18601	−	0.518586i
$787$	−1.16029e7	+	2.00968e7i	−0.667775	+	1.15662i	0.310750	+	0.950492i	$0.399420\pi$
$787$	−1.16029e7	+	2.00968e7i	−0.667775	+	1.15662i	−0.978525	+	0.206128i	$0.933914\pi$
$788$	6.00603e6	−	1.04027e7i	0.344565	−	0.596805i
$789$	1.85577e6	+	1.65903e7i	0.106128	+	0.948773i
$790$	286497.	+	496228.i	0.0163325	+	0.0282887i
$791$	−8.65580e6			−0.491888
$792$	−557560.	+	1.79729e6i	−0.0315849	+	0.101814i
$793$	1.69340e7			0.956264
$794$	−6.28497e6	−	1.08859e7i	−0.353795	−	0.612791i
$795$	589155.	−	434085.i	0.0330607	−	0.0243588i
$796$	1.67073e6	−	2.89379e6i	0.0934595	−	0.161877i
$797$	−2.37444e6	+	4.11265e6i	−0.132408	+	0.229338i	−0.924604	−	0.380929i	$-0.875604\pi$
$797$	−2.37444e6	+	4.11265e6i	−0.132408	+	0.229338i	0.792196	+	0.610266i	$0.208938\pi$
$798$	1.00079e7	−	7.37375e6i	0.556335	−	0.409903i
$799$	2.42776e6	+	4.20500e6i	0.134536	+	0.233023i
$800$	3.17754e6			0.175536
$801$	1.48201e7	+	1.60239e7i	0.816148	+	0.882442i
$802$	2.54759e6			0.139860
$803$	−219247.	−	379747.i	−0.0119990	−	0.0207829i
$804$	325906.	+	2.91356e6i	0.0177808	+	0.158958i
$805$	438979.	−	760334.i	0.0238756	−	0.0413537i
$806$	−2.18937e6	+	3.79211e6i	−0.118709	+	0.205609i
$807$	−2.12749e6	−	930253.i	−0.114996	−	0.0502825i
$808$	2.64351e6	+	4.57869e6i	0.142447	+	0.246725i
$809$	1.83243e7			0.984363			0.492182	−	0.870493i	$-0.336200\pi$
$809$	1.83243e7			0.984363			0.492182	+	0.870493i	$0.336200\pi$
$810$	86222.9	−	1.10293e6i	0.00461753	−	0.0590655i
$811$	−2.13080e7			−1.13760			−0.568801	−	0.822476i	$-0.692592\pi$
$811$	−2.13080e7			−1.13760			−0.568801	+	0.822476i	$0.692592\pi$
$812$	7.56702e6	+	1.31065e7i	0.402749	+	0.697582i
$813$	2.75534e7	+	1.20478e7i	1.46201	+	0.639267i
$814$	−2.74617e6	+	4.75651e6i	−0.145267	+	0.251610i
$815$	−1.12238e6	+	1.94401e6i	−0.0591894	+	0.102519i
$816$	143848.	+	1.28599e6i	0.00756274	+	0.0676100i
$817$	301225.	+	521736.i	0.0157883	+	0.0273461i
$818$	6.20796e6			0.324389
$819$	−1.02197e7	−	1.10499e7i	−0.532391	−	0.575635i
$820$	783872.			0.0407109
$821$	−1.79098e7	−	3.10207e7i	−0.927328	−	1.60618i	−0.787774	−	0.615964i	$-0.788767\pi$
$821$	−1.79098e7	−	3.10207e7i	−0.927328	−	1.60618i	−0.139553	−	0.990215i	$-0.544567\pi$
$822$	−8.23412e6	+	6.06683e6i	−0.425048	+	0.313172i
$823$	6.98131e6	−	1.20920e7i	0.359284	−	0.622298i	−0.628558	−	0.777763i	$-0.716354\pi$
$823$	6.98131e6	−	1.20920e7i	0.359284	−	0.622298i	0.987841	+	0.155465i	$0.0496877\pi$
$824$	4.33322e6	−	7.50535e6i	0.222327	−	0.385082i
$825$	−4.71211e6	+	3.47184e6i	−0.241035	+	0.177593i
$826$	1.70490e7	+	2.95297e7i	0.869458	+	1.50595i
$827$	7.59380e6			0.386096			0.193048	−	0.981189i	$-0.438163\pi$
$827$	7.59380e6			0.386096			0.193048	+	0.981189i	$0.438163\pi$
$828$	−1.23715e6	+	3.98793e6i	−0.0627112	+	0.202149i
$829$	−2.63661e7			−1.33247			−0.666237	−	0.745740i	$-0.732096\pi$
$829$	−2.63661e7			−1.33247			−0.666237	+	0.745740i	$0.732096\pi$
$830$	614158.	+	1.06375e6i	0.0309446	+	0.0535976i
$831$	−1.31947e6	−	1.17959e7i	−0.0662823	−	0.592555i
$832$	726770.	−	1.25880e6i	0.0363989	−	0.0630448i
$833$	−2.21441e6	+	3.83547e6i	−0.110572	+	0.191516i
$834$	9.56135e6	+	4.18073e6i	0.475997	+	0.208131i
$835$	−1.19930e6	−	2.07725e6i	−0.0595268	−	0.103103i
$836$	−2.21130e6			−0.109429
$837$	1.14761e7	+	2.20010e6i	0.566215	+	0.108550i
$838$	−1.27340e7			−0.626403
$839$	2.60631e6	+	4.51426e6i	0.127827	+	0.221402i	0.922834	−	0.385197i	$-0.125867\pi$
$839$	2.60631e6	+	4.51426e6i	0.127827	+	0.221402i	−0.795008	+	0.606599i	$0.792533\pi$
$840$	747295.	+	326757.i	0.0365421	+	0.0159782i
$841$	−4.42811e6	+	7.66970e6i	−0.215888	+	0.373929i
$842$	7.69338e6	−	1.33253e7i	0.373970	−	0.647735i
$843$	1.19155e6	+	1.06523e7i	0.0577487	+	0.516267i
$844$	−8.30561e6	−	1.43857e7i	−0.401343	−	0.695146i
$845$	−1.14922e6			−0.0553684
$846$	−1.41951e7	+	3.21593e6i	−0.681890	+	0.154483i
$847$	2.55548e6			0.122395
$848$	−1.28293e6	−	2.22210e6i	−0.0612651	−	0.106114i
$849$	4.57972e6	−	3.37430e6i	0.218057	−	0.160662i
$850$	−2.01240e6	+	3.48558e6i	−0.0955359	+	0.165473i
$851$	−6.09335e6	+	1.05540e7i	−0.288425	+	0.499566i
$852$	−81978.4	+	60401.0i	−0.00386902	+	0.00285066i
$853$	−875768.	−	1.51687e6i	−0.0412113	−	0.0713801i	0.844684	−	0.535265i	$-0.179788\pi$
$853$	−875768.	−	1.51687e6i	−0.0412113	−	0.0713801i	−0.885895	+	0.463885i	$0.846455\pi$
$854$	3.33162e7			1.56319
$855$	1.26788e6	−	287239.i	0.0593146	−	0.0134378i
$856$	−1.09941e7			−0.512831
$857$	5.84955e6	+	1.01317e7i	0.272064	+	0.471228i	0.969390	−	0.245525i	$-0.0789605\pi$
$857$	5.84955e6	+	1.01317e7i	0.272064	+	0.471228i	−0.697326	+	0.716754i	$0.745627\pi$
$858$	297635.	+	2.66082e6i	0.0138027	+	0.123395i
$859$	−1.43507e7	+	2.48562e7i	−0.663577	+	1.14935i	0.316092	+	0.948728i	$0.397629\pi$
$859$	−1.43507e7	+	2.48562e7i	−0.663577	+	1.14935i	−0.979669	+	0.200620i	$0.935704\pi$
$860$	−19763.6	+	34231.5i	−0.000911213	+	0.00157827i
$861$	−2.60761e7	−	1.14019e7i	−1.19877	−	0.524165i
$862$	9.21708e6	+	1.59645e7i	0.422499	+	0.731789i
$863$	7.99505e6			0.365422			0.182711	−	0.983167i	$-0.441513\pi$
$863$	7.99505e6			0.365422			0.182711	+	0.983167i	$0.441513\pi$
$864$	−3.80953e6	−	730330.i	−0.173615	−	0.0332839i
$865$	1.10584e6			0.0502519
$866$	−5.14156e6	−	8.90544e6i	−0.232970	−	0.403516i
$867$	1.87777e7	+	8.21063e6i	0.848390	+	0.370961i
$868$	−4.30740e6	+	7.46064e6i	−0.194051	+	0.336106i
$869$	−1.85033e6	+	3.20486e6i	−0.0831188	+	0.143966i
$870$	175939.	+	1.57287e6i	0.00788066	+	0.0704522i
$871$	2.08563e6	+	3.61242e6i	0.0931520	+	0.161344i
$872$	−6.82768e6			−0.304076
$873$	−5.28456e6	+	1.70348e7i	−0.234678	+	0.756485i
$874$	−4.90655e6			−0.217269
$875$	2.54579e6	+	4.40944e6i	0.112409	+	0.194699i
$876$	727676.	−	536146.i	0.0320389	−	0.0236060i
$877$	5.63637e6	−	9.76248e6i	0.247458	−	0.428609i	−0.715362	−	0.698754i	$-0.753738\pi$
$877$	5.63637e6	−	9.76248e6i	0.247458	−	0.428609i	0.962820	+	0.270145i	$0.0870716\pi$
$878$	1.37817e7	−	2.38706e7i	0.603345	−	1.04502i
$879$	2.47407e7	−	1.82287e7i	1.08004	−	0.795763i
$880$	−72542.5	−	125647.i	−0.00315781	−	0.00546949i
$881$	−1.28426e7			−0.557460			−0.278730	−	0.960369i	$-0.589913\pi$
$881$	−1.28426e7			−0.557460			−0.278730	+	0.960369i	$0.589913\pi$
$882$	−9.01417e6	−	9.74637e6i	−0.390170	−	0.421863i
$883$	−2.67013e7			−1.15247			−0.576237	−	0.817283i	$-0.695479\pi$
$883$	−2.67013e7			−1.15247			−0.576237	+	0.817283i	$0.695479\pi$
$884$	920556.	+	1.59445e6i	0.0396205	+	0.0686247i
$885$	396401.	+	3.54378e6i	0.0170128	+	0.152093i
$886$	−1.47998e6	+	2.56339e6i	−0.0633389	+	0.109706i
$887$	1.15053e7	−	1.99278e7i	0.491008	−	0.850451i	−0.508938	−	0.860803i	$-0.669962\pi$
$887$	1.15053e7	−	1.99278e7i	0.491008	−	0.850451i	0.999946	+	0.0103519i	$0.00329517\pi$
$888$	−1.03730e7	−	4.53563e6i	−0.441441	−	0.193021i
$889$	−1.76527e7	−	3.05754e7i	−0.749129	−	1.29753i
$890$	−1.68281e6			−0.0712133
$891$	6.44730e6	−	3.07934e6i	0.272072	−	0.129946i
$892$	6.51422e6			0.274126
$893$	−8.55174e6	−	1.48120e7i	−0.358860	−	0.621565i
$894$	8.90802e6	+	3.89506e6i	0.372767	+	0.162994i
$895$	651033.	−	1.12762e6i	0.0271672	−	0.0470550i
$896$	1.42986e6	−	2.47658e6i	0.0595007	−	0.103058i
$897$	660408.	+	5.90397e6i	0.0274051	+	0.244998i
$898$	1.35248e7	+	2.34257e7i	0.559681	+	0.969396i
$899$	−1.67169e7			−0.689853
$900$	−8.19184e6	−	8.85725e6i	−0.337113	−	0.364496i
$901$	3.25002e6			0.133375
$902$	2.53130e6	+	4.38434e6i	0.103592	+	0.179427i
$903$	1.15537e6	−	851266.i	0.0471521	−	0.0347413i
$904$	−1.58692e6	+	2.74863e6i	−0.0645854	+	0.111865i
$905$	267046.	−	462537.i	0.0108384	−	0.0187726i
$906$	1.56014e7	−	1.14950e7i	0.631458	−	0.465253i
$907$	8.31073e6	+	1.43946e7i	0.335445	+	0.581007i	0.983570	−	0.180526i	$-0.0577802\pi$
$907$	8.31073e6	+	1.43946e7i	0.335445	+	0.581007i	−0.648126	+	0.761533i	$0.724447\pi$
$908$	−6.07825e6			−0.244661
$909$	5.94781e6	−	1.91728e7i	0.238752	−	0.769617i
$910$	1.16045e6			0.0464540
$911$	1.97004e7	+	3.41222e7i	0.786466	+	1.36220i	0.928119	+	0.372282i	$0.121425\pi$
$911$	1.97004e7	+	3.41222e7i	0.786466	+	1.36220i	−0.141654	+	0.989916i	$0.545242\pi$
$912$	−506703.	−	4.52986e6i	−0.0201728	−	0.180342i
$913$	−3.96650e6	+	6.87019e6i	−0.157482	+	0.272767i
$914$	−6.49195e6	+	1.12444e7i	−0.257045	+	0.445216i
$915$	3.19230e6	+	1.39584e6i	0.126052	+	0.0551168i
$916$	−5.07813e6	−	8.79557e6i	−0.199970	−	0.346358i
$917$	−6.27586e7			−2.46462
$918$	3.21379e6	−	3.71631e6i	0.125867	−	0.145548i
$919$	−2.77428e7			−1.08358			−0.541791	−	0.840513i	$-0.682254\pi$
$919$	−2.77428e7			−1.08358			−0.541791	+	0.840513i	$0.682254\pi$
$920$	−160961.	−	278793.i	−0.00626977	−	0.0108596i
$921$	−2.13963e7	−	9.35562e6i	−0.831170	−	0.363432i
$922$	7.11501e6	−	1.23236e7i	0.275644	−	0.477429i
$923$	−72439.7	+	125469.i	−0.00279880	+	0.00484767i
$924$	585570.	+	5.23493e6i	0.0225631	+	0.201711i
$925$	−1.76065e7	−	3.04953e7i	−0.676579	−	1.17187i
$926$	−3.40906e7			−1.30649
$927$	−3.20921e7	+	7.27051e6i	−1.22659	+	0.277885i
$928$	5.54923e6			0.211525
$929$	−3.86220e6	−	6.68953e6i	−0.146824	−	0.254306i	0.783228	−	0.621734i	$-0.213572\pi$
$929$	−3.86220e6	−	6.68953e6i	−0.146824	−	0.254306i	−0.930052	+	0.367428i	$0.880238\pi$
$930$	−725304.	+	534398.i	−0.0274987	+	0.0202608i
$931$	7.80021e6	−	1.35104e7i	0.294939	−	0.510849i
$932$	5.39283e6	−	9.34065e6i	0.203365	−	0.352239i
$933$	1.61102e7	−	1.18699e7i	0.605894	−	0.446418i
$934$	3.24298e6	+	5.61700e6i	0.121640	+	0.210687i
$935$	183771.			0.00687459
$936$	−5.38250e6	+	1.21941e6i	−0.200814	+	0.0454948i
$937$	5.92823e6			0.220585			0.110293	−	0.993899i	$-0.464821\pi$
$937$	5.92823e6			0.220585			0.110293	+	0.993899i	$0.464821\pi$
$938$	4.10330e6	+	7.10712e6i	0.152274	+	0.263746i
$939$	−4.06880e6	−	3.63746e7i	−0.150592	−	1.34628i
$940$	561086.	−	971830.i	0.0207114	−	0.0358732i
$941$	7.33425e6	−	1.27033e7i	0.270011	−	0.467673i	−0.698853	−	0.715265i	$-0.746306\pi$
$941$	7.33425e6	−	1.27033e7i	0.270011	−	0.467673i	0.968864	+	0.247592i	$0.0796393\pi$
$942$	1.12045e7	+	4.89919e6i	0.411400	+	0.179886i
$943$	5.61658e6	+	9.72820e6i	0.205680	+	0.356249i
$944$	1.25028e7			0.456643
$945$	−1.01574e6	−	2.92545e6i	−0.0370001	−	0.106565i
$946$	−255284.			−0.00927462
$947$	8.88896e6	+	1.53961e7i	0.322089	+	0.557875i	0.980919	−	0.194417i	$-0.0622816\pi$
$947$	8.88896e6	+	1.53961e7i	0.322089	+	0.557875i	−0.658830	+	0.752292i	$0.728948\pi$
$948$	−6.98917e6	−	3.05604e6i	−0.252583	−	0.110443i
$949$	643006.	−	1.11372e6i	0.0231766	−	0.0401431i
$950$	7.08863e6	−	1.22779e7i	0.254832	−	0.441381i
$951$	4.19005e6	+	3.74586e7i	0.150234	+	1.34307i
$952$	1.81111e6	+	3.13694e6i	0.0647669	+	0.112180i
$953$	2.64927e7			0.944919			0.472459	−	0.881352i	$-0.343366\pi$
$953$	2.64927e7			0.944919			0.472459	+	0.881352i	$0.343366\pi$
$954$	−2.88655e6	+	9.30479e6i	−0.102685	+	0.331006i
$955$	2.43038e6			0.0862316
$956$	−5.12423e6	−	8.87543e6i	−0.181336	−	0.314083i
$957$	−8.22920e6	+	6.06320e6i	−0.290454	+	0.214004i
$958$	−1.10179e7	+	1.90836e7i	−0.387869	+	0.671809i
$959$	−1.43150e7	+	2.47942e7i	−0.502624	+	0.870571i
$960$	240767.	−	177395.i	0.00843177	−	0.00621246i
$961$	9.55666e6	+	1.65526e7i	0.333809	+	0.578174i
$962$	−1.61079e7			−0.561179
$963$	2.83432e7	+	3.06455e7i	0.984881	+	1.06488i
$964$	−1.94900e7			−0.675489
$965$	986863.	+	1.70930e6i	0.0341145	+	0.0590880i
$966$	1.29929e6	+	1.16155e7i	0.0447986	+	0.400494i
$967$	−1.78298e7	+	3.08822e7i	−0.613170	+	1.06204i	0.377532	+	0.925996i	$0.376773\pi$
$967$	−1.78298e7	+	3.08822e7i	−0.613170	+	1.06204i	−0.990703	+	0.136046i	$0.956561\pi$
$968$	468512.	−	811487.i	0.0160706	−	0.0278351i
$969$	5.28991e6	+	2.31303e6i	0.180983	+	0.0791356i
$970$	−687558.	−	1.19089e6i	−0.0234628	−	0.0406388i
$971$	−4.35808e7			−1.48336			−0.741681	−	0.670752i	$-0.765971\pi$
$971$	−4.35808e7			−1.48336			−0.741681	+	0.670752i	$0.765971\pi$
$972$	7.78540e6	+	1.25017e7i	0.264311	+	0.424429i
$973$	2.92112e7			0.989161
$974$	1.61708e7	+	2.80087e7i	0.546178	+	0.946009i
$975$	−1.57279e7	−	6.87706e6i	−0.529856	−	0.231682i
$976$	6.10807e6	−	1.05795e7i	0.205248	−	0.355500i
$977$	−3.60582e6	+	6.24546e6i	−0.120856	+	0.209328i	−0.920105	−	0.391671i	$-0.871897\pi$
$977$	−3.60582e6	+	6.24546e6i	−0.120856	+	0.209328i	0.799250	+	0.600999i	$0.205231\pi$
$978$	−3.32202e6	−	2.96985e7i	−0.111059	−	0.992857i
$979$	−5.43418e6	−	9.41228e6i	−0.181208	−	0.313862i
$980$	1.02356e6			0.0340445
$981$	1.76021e7	+	1.90319e7i	0.583972	+	0.631406i
$982$	1.75532e7			0.580868
$983$	2.18807e7	+	3.78984e7i	0.722232	+	1.25094i	0.960103	+	0.279646i	$0.0902170\pi$
$983$	2.18807e7	+	3.78984e7i	0.722232	+	1.25094i	−0.237871	+	0.971297i	$0.576450\pi$
$984$	−8.40132e6	+	6.19002e6i	−0.276605	+	0.203800i
$985$	1.75818e6	−	3.04526e6i	0.0577396	−	0.100008i
$986$	−3.51444e6	+	6.08719e6i	−0.115123	+	0.199400i
$987$	−3.28008e7	+	2.41673e7i	−1.07174	+	0.789652i
$988$	−3.24264e6	−	5.61642e6i	−0.105683	−	0.183049i
$989$	−566438.			−0.0184146
$990$	−163218.	+	526134.i	−0.00529275	+	0.0170612i
$991$	1.01431e7			0.328085			0.164042	−	0.986453i	$-0.447547\pi$
$991$	1.01431e7			0.328085			0.164042	+	0.986453i	$0.447547\pi$
$992$	1.57940e6	+	2.73561e6i	0.0509582	+	0.0882622i
$993$	3.31324e6	+	2.96199e7i	0.106630	+	0.953259i
$994$	−142519.	+	246850.i	−0.00457516	+	0.00792441i
$995$	489084.	−	847119.i	0.0156612	−	0.0271260i
$996$	−1.49825e7	−	6.55116e6i	−0.478560	−	0.209252i
$997$	2.30893e7	+	3.99918e7i	0.735652	+	1.27419i	0.954437	+	0.298414i	$0.0964576\pi$
$997$	2.30893e7	+	3.99918e7i	0.735652	+	1.27419i	−0.218784	+	0.975773i	$0.570209\pi$
$998$	2.36207e7			0.750701
$999$	1.40992e7	+	4.06074e7i	0.446974	+	1.28734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.e.b.67.2	✓	24
3.2	odd	2		594.6.e.a.199.7		24
9.2	odd	6		594.6.e.a.397.7		24
9.7	even	3	inner	198.6.e.b.133.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.e.b.67.2	✓	24	1.1	even	1	trivial
198.6.e.b.133.2	yes	24	9.7	even	3	inner
594.6.e.a.199.7		24	3.2	odd	2
594.6.e.a.397.7		24	9.2	odd	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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-14.2828 - 6.24519i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-2.34189 + 4.05628i) q^{5} +(-6.93156 - 61.9674i) q^{6} +(-87.2715 - 151.159i) q^{7} -64.0000 q^{8} +(164.995 + 178.397i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-14.2828 - 6.24519i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-2.34189 + 4.05628i) q^{5} +(-6.93156 - 61.9674i) q^{6} +(-87.2715 - 151.159i) q^{7} -64.0000 q^{8} +(164.995 + 178.397i) q^{9} -18.7352 q^{10} +(-60.5000 - 104.789i) q^{11} +(200.798 - 147.946i) q^{12} +(177.434 - 307.325i) q^{13} +(349.086 - 604.634i) q^{14} +(58.7810 - 43.3093i) q^{15} +(-128.000 - 221.703i) q^{16} +324.260 q^{17} +(-287.996 + 928.355i) q^{18} -1142.20 q^{19} +(-37.4703 - 64.9005i) q^{20} +(302.464 + 2703.99i) q^{21} +(242.000 - 419.156i) q^{22} +(536.963 - 930.047i) q^{23} +(914.097 + 399.692i) q^{24} +(1551.53 + 2687.33i) q^{25} +1419.47 q^{26} +(-1242.46 - 3578.43i) q^{27} +2792.69 q^{28} +(2709.58 + 4693.14i) q^{29} +(267.590 + 117.005i) q^{30} +(-1542.39 + 2671.49i) q^{31} +(512.000 - 886.810i) q^{32} +(209.680 + 1874.51i) q^{33} +(648.520 + 1123.27i) q^{34} +817.522 q^{35} +(-3791.91 + 859.061i) q^{36} -11347.8 q^{37} +(-2284.40 - 3956.70i) q^{38} +(-4453.55 + 3281.34i) q^{39} +(149.881 - 259.602i) q^{40} +(-5229.95 + 9058.54i) q^{41} +(-8761.97 + 6455.75i) q^{42} +(-263.723 - 456.782i) q^{43} +1936.00 q^{44} +(-1110.03 + 251.479i) q^{45} +4295.70 q^{46} +(7487.08 + 12968.0i) q^{47} +(443.620 + 3965.91i) q^{48} +(-6829.11 + 11828.4i) q^{49} +(-6206.12 + 10749.3i) q^{50} +(-4631.33 - 2025.07i) q^{51} +(2838.94 + 4917.19i) q^{52} +10022.9 q^{53} +(9911.14 - 11460.9i) q^{54} +566.738 q^{55} +(5585.37 + 9674.15i) q^{56} +(16313.8 + 7133.26i) q^{57} +(-10838.3 + 18772.5i) q^{58} +(-24419.5 + 42295.8i) q^{59} +(129.864 + 1160.97i) q^{60} +(23859.6 + 41326.1i) q^{61} -12339.1 q^{62} +(12566.9 - 40509.4i) q^{63} +4096.00 q^{64} +(831.063 + 1439.44i) q^{65} +(-6074.14 + 4475.38i) q^{66} +(-5877.21 + 10179.6i) q^{67} +(-2594.08 + 4493.08i) q^{68} +(-13477.6 + 9930.21i) q^{69} +(1635.04 + 2831.98i) q^{70} -408.263 q^{71} +(-10559.7 - 11417.4i) q^{72} +3623.92 q^{73} +(-22695.6 - 39310.0i) q^{74} +(-5377.27 - 48072.1i) q^{75} +(9137.60 - 15826.8i) q^{76} +(-10559.8 + 18290.2i) q^{77} +(-20274.0 - 8864.87i) q^{78} +(-15292.0 - 26486.5i) q^{79} +1199.05 q^{80} +(-4602.20 + 58869.4i) q^{81} -41839.6 q^{82} +(-32781.0 - 56778.4i) q^{83} +(-39887.3 - 17440.9i) q^{84} +(-759.383 + 1315.29i) q^{85} +(1054.89 - 1827.13i) q^{86} +(-9390.82 - 83952.8i) q^{87} +(3872.00 + 6706.50i) q^{88} +89821.2 q^{89} +(-3091.21 - 3342.30i) q^{90} -61939.7 q^{91} +(8591.40 + 14880.7i) q^{92} +(38713.5 - 28523.8i) q^{93} +(-29948.3 + 51872.0i) q^{94} +(2674.91 - 4633.08i) q^{95} +(-12851.1 + 9468.57i) q^{96} +(36698.8 + 63564.2i) q^{97} -54632.9 q^{98} +(8711.88 - 28082.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

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