LMFDB - Embedded newform 189.6.i.a.152.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,6,Mod(143,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	189.i (of order $6$, 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:	$30.3125419447$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.28
Character	$\chi$	$=$	189.152
Dual form			189.6.i.a.143.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.53719i q^{2} +1.33949 q^{4} +(-39.7402 - 68.8320i) q^{5} +(64.2142 - 112.621i) q^{7} +184.607i q^{8} +O(q^{10})$	\(q+5.53719i q^{2} +1.33949 q^{4} +(-39.7402 - 68.8320i) q^{5} +(64.2142 - 112.621i) q^{7} +184.607i q^{8} +(381.136 - 220.049i) q^{10} +(-415.512 - 239.896i) q^{11} +(-126.577 - 73.0791i) q^{13} +(623.605 + 355.566i) q^{14} -979.342 q^{16} +(925.298 + 1602.66i) q^{17} +(-125.438 - 72.4216i) q^{19} +(-53.2315 - 92.1997i) q^{20} +(1328.35 - 2300.77i) q^{22} +(-3396.26 + 1960.83i) q^{23} +(-1596.06 + 2764.46i) q^{25} +(404.653 - 700.880i) q^{26} +(86.0142 - 150.855i) q^{28} +(-6921.91 + 3996.37i) q^{29} +7167.76i q^{31} +484.623i q^{32} +(-8874.26 + 5123.55i) q^{34} +(-10303.8 + 55.5940i) q^{35} +(1859.07 - 3220.00i) q^{37} +(401.012 - 694.574i) q^{38} +(12706.9 - 7336.32i) q^{40} +(-576.073 + 997.788i) q^{41} +(2068.92 + 3583.47i) q^{43} +(-556.574 - 321.338i) q^{44} +(-10857.5 - 18805.8i) q^{46} -3173.67 q^{47} +(-8560.07 - 14463.8i) q^{49} +(-15307.4 - 8837.71i) q^{50} +(-169.548 - 97.8886i) q^{52} +(30894.4 - 17836.9i) q^{53} +38134.1i q^{55} +(20790.7 + 11854.4i) q^{56} +(-22128.7 - 38328.0i) q^{58} -32153.8 q^{59} +2015.90i q^{61} -39689.3 q^{62} -34022.4 q^{64} +11616.7i q^{65} +5817.36 q^{67} +(1239.43 + 2146.75i) q^{68} +(-307.835 - 57054.3i) q^{70} -36994.5i q^{71} +(-19701.9 + 11374.9i) q^{73} +(17829.8 + 10294.0i) q^{74} +(-168.022 - 97.0078i) q^{76} +(-53699.2 + 31390.8i) q^{77} -37686.5 q^{79} +(38919.2 + 67410.1i) q^{80} +(-5524.94 - 3189.83i) q^{82} +(-36121.1 - 62563.6i) q^{83} +(73543.0 - 127380. i) q^{85} +(-19842.4 + 11456.0i) q^{86} +(44286.5 - 76706.6i) q^{88} +(-13339.1 + 23103.9i) q^{89} +(-16358.3 + 9562.51i) q^{91} +(-4549.26 + 2626.51i) q^{92} -17573.2i q^{94} +11512.2i q^{95} +(-101416. + 58552.4i) q^{97} +(80088.7 - 47398.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 1154 q^{4} + 3 q^{5} - 30 q^{7}+O(q^{10}) $ 76 * q - 1154 * q^4 + 3 * q^5 - 30 * q^7	$ 76 q - 1154 q^{4} + 3 q^{5} - 30 q^{7} - 6 q^{10} - 567 q^{11} + 543 q^{13} + 1638 q^{14} + 16446 q^{16} + 801 q^{17} - 6 q^{19} - 96 q^{20} + 62 q^{22} - 7806 q^{23} - 18749 q^{25} - 10128 q^{26} + 860 q^{28} - 17904 q^{29} + 96 q^{34} - 3960 q^{35} + 2577 q^{37} - 14967 q^{38} + 9564 q^{40} - 28230 q^{41} - 9246 q^{43} + 69885 q^{44} - 9418 q^{46} + 56562 q^{47} + 7948 q^{49} + 67509 q^{50} - 40899 q^{52} - 25296 q^{53} - 104754 q^{56} - 4951 q^{58} + 59076 q^{59} - 79536 q^{62} - 198600 q^{64} + 1244 q^{67} - 191496 q^{68} - 127197 q^{70} - 6 q^{73} + 45681 q^{74} - 2880 q^{76} - 13854 q^{77} + 59984 q^{79} - 243225 q^{80} + 90 q^{82} + 246930 q^{83} + 11973 q^{85} - 291801 q^{86} - 34751 q^{88} + 6345 q^{89} - 120111 q^{91} + 463488 q^{92} - 104037 q^{97} + 646797 q^{98}+O(q^{100}) $ 76 * q - 1154 * q^4 + 3 * q^5 - 30 * q^7 - 6 * q^10 - 567 * q^11 + 543 * q^13 + 1638 * q^14 + 16446 * q^16 + 801 * q^17 - 6 * q^19 - 96 * q^20 + 62 * q^22 - 7806 * q^23 - 18749 * q^25 - 10128 * q^26 + 860 * q^28 - 17904 * q^29 + 96 * q^34 - 3960 * q^35 + 2577 * q^37 - 14967 * q^38 + 9564 * q^40 - 28230 * q^41 - 9246 * q^43 + 69885 * q^44 - 9418 * q^46 + 56562 * q^47 + 7948 * q^49 + 67509 * q^50 - 40899 * q^52 - 25296 * q^53 - 104754 * q^56 - 4951 * q^58 + 59076 * q^59 - 79536 * q^62 - 198600 * q^64 + 1244 * q^67 - 191496 * q^68 - 127197 * q^70 - 6 * q^73 + 45681 * q^74 - 2880 * q^76 - 13854 * q^77 + 59984 * q^79 - 243225 * q^80 + 90 * q^82 + 246930 * q^83 + 11973 * q^85 - 291801 * q^86 - 34751 * q^88 + 6345 * q^89 - 120111 * q^91 + 463488 * q^92 - 104037 * q^97 + 646797 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			5.53719i			0.978847i	0.872046	+	0.489423i	$0.162793\pi$
$2$			5.53719i			0.978847i	−0.872046	+	0.489423i	$0.837207\pi$
$3$		0			0
$3$		0			0
$4$	1.33949			0.0418590
$5$	−39.7402	−	68.8320i	−0.710894	−	1.23130i	−0.964522	−	0.264003i	$-0.914957\pi$
$5$	−39.7402	−	68.8320i	−0.710894	−	1.23130i	0.253628	−	0.967302i	$-0.418376\pi$
$6$		0			0
$7$	64.2142	−	112.621i	0.495320	−	0.868710i
$7$	64.2142	−	112.621i	0.495320	−	0.868710i
$8$			184.607i			1.01982i
$9$		0			0
$10$	381.136	−	220.049i	1.20526	−	0.695856i
$11$	−415.512	−	239.896i	−1.03539	−	0.597780i	−0.116863	−	0.993148i	$-0.537284\pi$
$11$	−415.512	−	239.896i	−1.03539	−	0.597780i	−0.918523	+	0.395368i	$0.870617\pi$
$12$		0			0
$13$	−126.577	−	73.0791i	−0.207728	−	0.119932i	0.392527	−	0.919741i	$-0.371601\pi$
$13$	−126.577	−	73.0791i	−0.207728	−	0.119932i	−0.600255	+	0.799809i	$0.704934\pi$
$14$	623.605	+	355.566i	0.850334	+	0.484843i
$15$		0			0
$16$	−979.342			−0.956389
$17$	925.298	+	1602.66i	0.776532	+	1.34499i	0.933929	+	0.357457i	$0.116356\pi$
$17$	925.298	+	1602.66i	0.776532	+	1.34499i	−0.157398	+	0.987535i	$0.550310\pi$
$18$		0			0
$19$	−125.438	−	72.4216i	−0.0797158	−	0.0460240i	0.459612	−	0.888120i	$-0.347988\pi$
$19$	−125.438	−	72.4216i	−0.0797158	−	0.0460240i	−0.539328	+	0.842096i	$0.681322\pi$
$20$	−53.2315	−	92.1997i	−0.0297573	−	0.0515412i
$21$		0			0
$22$	1328.35	−	2300.77i	0.585135	−	1.01348i
$23$	−3396.26	+	1960.83i	−1.33870	+	0.772896i	−0.986614	−	0.163073i	$-0.947859\pi$
$23$	−3396.26	+	1960.83i	−1.33870	+	0.772896i	−0.352082	+	0.935969i	$0.614526\pi$
$24$		0			0
$25$	−1596.06	+	2764.46i	−0.510740	+	0.884628i
$26$	404.653	−	700.880i	0.117395	−	0.203334i
$27$		0			0
$28$	86.0142	−	150.855i	0.0207336	−	0.0363634i
$29$	−6921.91	+	3996.37i	−1.52838	+	0.882410i	−0.528949	+	0.848653i	$0.677414\pi$
$29$	−6921.91	+	3996.37i	−1.52838	+	0.882410i	−0.999430	+	0.0337571i	$0.989253\pi$
$30$		0			0
$31$			7167.76i			1.33961i	0.742536	+	0.669806i	$0.233623\pi$
$31$			7167.76i			1.33961i	−0.742536	+	0.669806i	$0.766377\pi$
$32$			484.623i			0.0836622i
$33$		0			0
$34$	−8874.26	+	5123.55i	−1.31654	+	0.760106i
$35$	−10303.8	+	55.5940i	−1.42177	+	0.00767110i
$36$		0			0
$37$	1859.07	−	3220.00i	0.223250	−	0.386680i	−0.732543	−	0.680721i	$-0.761667\pi$
$37$	1859.07	−	3220.00i	0.223250	−	0.386680i	0.955793	+	0.294041i	$0.0950002\pi$
$38$	401.012	−	694.574i	0.0450504	−	0.0780296i
$39$		0			0
$40$	12706.9	−	7336.32i	1.25571	−	0.724984i
$41$	−576.073	+	997.788i	−0.0535202	+	0.0926997i	−0.891544	−	0.452934i	$-0.850377\pi$
$41$	−576.073	+	997.788i	−0.0535202	+	0.0926997i	0.838024	+	0.545633i	$0.183711\pi$
$42$		0			0
$43$	2068.92	+	3583.47i	0.170637	+	0.295551i	0.938643	−	0.344891i	$-0.112084\pi$
$43$	2068.92	+	3583.47i	0.170637	+	0.295551i	−0.768006	+	0.640443i	$0.778751\pi$
$44$	−556.574	−	321.338i	−0.0433402	−	0.0250225i
$45$		0			0
$46$	−10857.5	−	18805.8i	−0.756547	−	1.31038i
$47$	−3173.67			−0.209564			−0.104782	−	0.994495i	$-0.533415\pi$
$47$	−3173.67			−0.209564			−0.104782	+	0.994495i	$0.533415\pi$
$48$		0			0
$49$	−8560.07	−	14463.8i	−0.509316	−	0.860580i
$50$	−15307.4	−	8837.71i	−0.865915	−	0.499936i
$51$		0			0
$52$	−169.548	−	97.8886i	−0.00869530	−	0.00502023i
$53$	30894.4	−	17836.9i	1.51074	−	0.872227i	0.510820	−	0.859688i	$-0.329342\pi$
$53$	30894.4	−	17836.9i	1.51074	−	0.872227i	0.999921	−	0.0125389i	$-0.00399135\pi$
$54$		0			0
$55$			38134.1i			1.69983i
$56$	20790.7	+	11854.4i	0.885929	+	0.505138i
$57$		0			0
$58$	−22128.7	−	38328.0i	−0.863745	−	1.49605i
$59$	−32153.8			−1.20255			−0.601274	−	0.799043i	$-0.705340\pi$
$59$	−32153.8			−1.20255			−0.601274	+	0.799043i	$0.705340\pi$
$60$		0			0
$61$			2015.90i			0.0693657i	0.999398	+	0.0346829i	$0.0110421\pi$
$61$			2015.90i			0.0693657i	−0.999398	+	0.0346829i	$0.988958\pi$
$62$	−39689.3			−1.31128
$63$		0			0
$64$	−34022.4			−1.03828
$65$			11616.7i			0.341036i
$66$		0			0
$67$	5817.36			0.158321			0.0791606	−	0.996862i	$-0.474776\pi$
$67$	5817.36			0.158321			0.0791606	+	0.996862i	$0.474776\pi$
$68$	1239.43	+	2146.75i	0.0325049	+	0.0563001i
$69$		0			0
$70$	−307.835	−	57054.3i	−0.00750883	−	1.39169i
$71$		−	36994.5i		−	0.870947i	−0.900202	−	0.435473i	$-0.856581\pi$
$71$		−	36994.5i		−	0.870947i	0.900202	−	0.435473i	$-0.143419\pi$
$72$		0			0
$73$	−19701.9	+	11374.9i	−0.432715	+	0.249828i	−0.700503	−	0.713650i	$-0.747041\pi$
$73$	−19701.9	+	11374.9i	−0.432715	+	0.249828i	0.267788	+	0.963478i	$0.413707\pi$
$74$	17829.8	+	10294.0i	0.378500	+	0.218527i
$75$		0			0
$76$	−168.022	−	97.0078i	−0.00333683	−	0.00192652i
$77$	−53699.2	+	31390.8i	−1.03215	+	0.603358i
$78$		0			0
$79$	−37686.5			−0.679389			−0.339695	−	0.940536i	$-0.610324\pi$
$79$	−37686.5			−0.679389			−0.339695	+	0.940536i	$0.610324\pi$
$80$	38919.2	+	67410.1i	0.679891	+	1.17761i
$81$		0			0
$82$	−5524.94	−	3189.83i	−0.0907388	−	0.0523881i
$83$	−36121.1	−	62563.6i	−0.575527	−	0.996842i	−0.995984	−	0.0895293i	$-0.971464\pi$
$83$	−36121.1	−	62563.6i	−0.575527	−	0.996842i	0.420457	−	0.907312i	$-0.361870\pi$
$84$		0			0
$85$	73543.0	−	127380.i	1.10406	−	1.91229i
$86$	−19842.4	+	11456.0i	−0.289299	+	0.167027i
$87$		0			0
$88$	44286.5	−	76706.6i	0.609628	−	1.05591i
$89$	−13339.1	+	23103.9i	−0.178505	+	0.309180i	−0.941369	−	0.337380i	$-0.890459\pi$
$89$	−13339.1	+	23103.9i	−0.178505	+	0.309180i	0.762864	+	0.646559i	$0.223793\pi$
$90$		0			0
$91$	−16358.3	+	9562.51i	−0.207078	+	0.121051i
$92$	−4549.26	+	2626.51i	−0.0560365	+	0.0323527i
$93$		0			0
$94$		−	17573.2i		−	0.205131i
$95$			11512.2i			0.130873i
$96$		0			0
$97$	−101416.	+	58552.4i	−1.09440	+	0.631852i	−0.934744	−	0.355321i	$-0.884372\pi$
$97$	−101416.	+	58552.4i	−1.09440	+	0.631852i	−0.159655	+	0.987173i	$0.551038\pi$
$98$	80088.7	−	47398.8i	0.842376	−	0.498542i
$99$		0			0
$100$	−2137.91	+	3702.97i	−0.0213791	+	0.0370297i
$101$	21112.3	−	36567.5i	0.205936	−	0.356691i	−0.744495	−	0.667628i	$-0.767310\pi$
$101$	21112.3	−	36567.5i	0.205936	−	0.356691i	0.950430	+	0.310937i	$0.100643\pi$
$102$		0			0
$103$	−46412.7	+	26796.4i	−0.431066	+	0.248876i	−0.699801	−	0.714338i	$-0.746728\pi$
$103$	−46412.7	+	26796.4i	−0.431066	+	0.248876i	0.268735	+	0.963214i	$0.413394\pi$
$104$	13490.9	−	23367.0i	0.122309	−	0.211845i
$105$		0			0
$106$	98766.3	+	171068.i	0.853776	+	1.47878i
$107$	80626.7	+	46549.8i	0.680800	+	0.393060i	0.800156	−	0.599791i	$-0.204750\pi$
$107$	80626.7	+	46549.8i	0.680800	+	0.393060i	−0.119356	+	0.992851i	$0.538083\pi$
$108$		0			0
$109$	25734.7	+	44573.9i	0.207469	+	0.359347i	0.950917	−	0.309447i	$-0.100144\pi$
$109$	25734.7	+	44573.9i	0.207469	+	0.359347i	−0.743447	+	0.668794i	$0.766811\pi$
$110$	−211156.			−1.66388
$111$		0			0
$112$	−62887.7	+	110295.i	−0.473719	+	0.830825i
$113$	124723.	+	72008.8i	0.918862	+	0.530505i	0.883272	−	0.468861i	$-0.155336\pi$
$113$	124723.	+	72008.8i	0.918862	+	0.530505i	0.0355903	+	0.999366i	$0.488669\pi$
$114$		0			0
$115$	269936.	+	155848.i	1.90334	+	1.09889i
$116$	−9271.82	+	5353.09i	−0.0639765	+	0.0369368i
$117$		0			0
$118$		−	178042.i		−	1.17711i
$119$	239911.	−	1294.43i	1.55304	−	0.00837938i
$120$		0			0
$121$	34574.8	+	59885.3i	0.214682	+	0.371841i
$122$	−11162.4			−0.0678984
$123$		0			0
$124$			9601.13i			0.0560749i
$125$	5335.24			0.0305407
$126$		0			0
$127$	−39793.2			−0.218927			−0.109463	−	0.993991i	$-0.534913\pi$
$127$	−39793.2			−0.218927			−0.109463	+	0.993991i	$0.534913\pi$
$128$		−	172881.i		−	0.932656i
$129$		0			0
$130$	−64324.0			−0.333822
$131$	52113.3	+	90263.0i	0.265320	+	0.459548i	0.967648	−	0.252306i	$-0.0811889\pi$
$131$	52113.3	+	90263.0i	0.265320	+	0.459548i	−0.702327	+	0.711854i	$0.747856\pi$
$132$		0			0
$133$	−16211.1	+	9476.47i	−0.0794663	+	0.0464534i
$134$			32211.9i			0.154972i
$135$		0			0
$136$	−295863.	+	170817.i	−1.37165	+	0.791923i
$137$	−329901.	−	190468.i	−1.50170	−	0.867004i	−0.999998	−	0.00196065i	$-0.999376\pi$
$137$	−329901.	−	190468.i	−1.50170	−	0.867004i	−0.501697	−	0.865043i	$-0.667291\pi$
$138$		0			0
$139$	135367.	+	78154.2i	0.594259	+	0.343096i	0.766780	−	0.641910i	$-0.221858\pi$
$139$	135367.	+	78154.2i	0.594259	+	0.343096i	−0.172521	+	0.985006i	$0.555191\pi$
$140$	−13801.9	+	74.4675i	−0.0595138	+	0.000321105i
$141$		0			0
$142$	204846.			0.852524
$143$	35062.8	+	60730.5i	0.143386	+	0.248352i
$144$		0			0
$145$	550156.	+	317633.i	2.17303	+	1.25460i
$146$	−62985.1	−	109093.i	−0.244543	−	0.423562i
$147$		0			0
$148$	2490.20	−	4313.15i	0.00934501	−	0.0161860i
$149$	−276853.	+	159841.i	−1.02161	+	0.589825i	−0.914569	−	0.404430i	$-0.867470\pi$
$149$	−276853.	+	159841.i	−1.02161	+	0.589825i	−0.107037	+	0.994255i	$0.534136\pi$
$150$		0			0
$151$	−169757.	+	294028.i	−0.605879	+	1.04941i	0.386033	+	0.922485i	$0.373845\pi$
$151$	−169757.	+	294028.i	−0.605879	+	1.04941i	−0.991912	+	0.126928i	$0.959488\pi$
$152$	13369.5	−	23156.7i	0.0469362	−	0.0812958i
$153$		0			0
$154$	−173817.	−	297343.i	−0.590595	−	1.01031i
$155$	493371.	−	284848.i	1.64947	−	0.952322i
$156$		0			0
$157$			527732.i			1.70870i	0.519702	+	0.854348i	$0.326043\pi$
$157$			527732.i			1.70870i	−0.519702	+	0.854348i	$0.673957\pi$
$158$		−	208678.i		−	0.665018i
$159$		0			0
$160$	33357.6	−	19259.0i	0.103014	−	0.0594750i
$161$	2743.08	+	508405.i	0.00834015	+	1.54577i
$162$		0			0
$163$	141339.	−	244807.i	0.416672	−	0.721697i	−0.578931	−	0.815377i	$-0.696530\pi$
$163$	141339.	−	244807.i	0.416672	−	0.721697i	0.995602	+	0.0936802i	$0.0298631\pi$
$164$	−771.643	+	1336.52i	−0.00224030	+	0.00388032i
$165$		0			0
$166$	346426.	−	200009.i	0.975755	−	0.563353i
$167$	38171.9	−	66115.6i	0.105914	−	0.183448i	−0.808197	−	0.588912i	$-0.799557\pi$
$167$	38171.9	−	66115.6i	0.105914	−	0.183448i	0.914111	+	0.405464i	$0.132890\pi$
$168$		0			0
$169$	−174965.	−	303049.i	−0.471233	−	0.816199i
$170$	705329.	+	407222.i	1.87184	+	1.08071i
$171$		0			0
$172$	2771.29	+	4800.02i	0.00714268	+	0.0123715i
$173$	343496.			0.872582			0.436291	−	0.899806i	$-0.356292\pi$
$173$	343496.			0.872582			0.436291	+	0.899806i	$0.356292\pi$
$174$		0			0
$175$	208847.	+	357268.i	0.515506	+	0.881860i
$176$	406929.	+	234940.i	0.990231	+	0.571710i
$177$		0			0
$178$	−127931.	−	73860.9i	−0.302639	−	0.174729i
$179$	231146.	−	133452.i	0.539204	−	0.311310i	−0.205552	−	0.978646i	$-0.565899\pi$
$179$	231146.	−	133452.i	0.539204	−	0.311310i	0.744756	+	0.667337i	$0.232566\pi$
$180$		0			0
$181$		−	595254.i		−	1.35054i	−0.737573	−	0.675268i	$-0.764028\pi$
$181$		−	595254.i		−	1.35054i	0.737573	−	0.675268i	$-0.235972\pi$
$182$	−52949.5	−	90579.0i	−0.118490	−	0.202698i
$183$		0			0
$184$	−361984.	−	626975.i	−0.788215	−	1.36523i
$185$	−295519.			−0.634827
$186$		0			0
$187$		−	887901.i		−	1.85678i
$188$	−4251.10			−0.00877216
$189$		0			0
$190$	−63745.2			−0.128104
$191$		−	59625.4i		−	0.118263i	−0.998250	−	0.0591314i	$-0.981167\pi$
$191$		−	59625.4i		−	0.118263i	0.998250	−	0.0591314i	$-0.0188331\pi$
$192$		0			0
$193$	−499090.			−0.964463			−0.482232	−	0.876044i	$-0.660174\pi$
$193$	−499090.			−0.964463			−0.482232	+	0.876044i	$0.660174\pi$
$194$	−324216.	−	561558.i	−0.618486	−	1.07125i
$195$		0			0
$196$	−11466.1	−	19374.0i	−0.0213195	−	0.0360230i
$197$		−	745766.i		−	1.36911i	−0.728963	−	0.684553i	$-0.759997\pi$
$197$		−	745766.i		−	1.36911i	0.728963	−	0.684553i	$-0.240003\pi$
$198$		0			0
$199$	−316749.	+	182875.i	−0.566999	+	0.327357i	−0.755950	−	0.654629i	$-0.772825\pi$
$199$	−316749.	+	182875.i	−0.566999	+	0.327357i	0.188951	+	0.981987i	$0.439491\pi$
$200$	−510340.	−	294645.i	−0.902162	−	0.520863i
$201$		0			0
$202$	202481.	+	116903.i	0.349146	+	0.201579i
$203$	5590.67	+	1.03618e6i	0.00952189	+	1.76480i
$204$		0			0
$205$	91573.0			0.152189
$206$	−148377.	−	256996.i	−0.243611	−	0.421947i
$207$		0			0
$208$	123962.	+	71569.5i	0.198669	+	0.114702i
$209$	34747.3	+	60184.1i	0.0550244	+	0.0953051i
$210$		0			0
$211$	312208.	−	540760.i	0.482767	−	0.836178i	−0.517037	−	0.855963i	$-0.672965\pi$
$211$	312208.	−	540760.i	0.482767	−	0.836178i	0.999804	+	0.0197855i	$0.00629832\pi$
$212$	41382.7	−	23892.3i	0.0632381	−	0.0365105i
$213$		0			0
$214$	−257756.	+	446446.i	−0.384746	+	0.666399i
$215$	164438.	−	284815.i	0.242609	−	0.420211i
$216$		0			0
$217$	807242.	+	460272.i	1.16374	+	0.663537i
$218$	−246814.	+	142498.i	−0.351746	+	0.203080i
$219$		0			0
$220$			51080.1i			0.0711533i
$221$		−	270480.i		−	0.372524i
$222$		0			0
$223$	−206408.	+	119169.i	−0.277948	+	0.160473i	−0.632494	−	0.774565i	$-0.717969\pi$
$223$	−206408.	+	119169.i	−0.277948	+	0.160473i	0.354546	+	0.935039i	$0.384635\pi$
$224$	54578.9	+	31119.7i	0.0726782	+	0.0414396i
$225$		0			0
$226$	−398727.	+	690615.i	−0.519283	+	0.899425i
$227$	237090.	−	410652.i	0.305386	−	0.528943i	−0.671962	−	0.740586i	$-0.734548\pi$
$227$	237090.	−	410652.i	0.305386	−	0.528943i	0.977347	+	0.211643i	$0.0678813\pi$
$228$		0			0
$229$	−915378.	+	528494.i	−1.15348	+	0.665964i	−0.949734	−	0.313058i	$-0.898646\pi$
$229$	−915378.	+	528494.i	−1.15348	+	0.665964i	−0.203750	+	0.979023i	$0.565313\pi$
$230$	−862959.	+	1.49469e6i	−1.07565	+	1.86308i
$231$		0			0
$232$	−737758.	−	1.27784e6i	−0.899900	−	1.55867i
$233$	−54988.5	−	31747.6i	−0.0663563	−	0.0383108i	0.466455	−	0.884545i	$-0.345531\pi$
$233$	−54988.5	−	31747.6i	−0.0663563	−	0.0383108i	−0.532811	+	0.846234i	$0.678864\pi$
$234$		0			0
$235$	126122.	+	218450.i	0.148978	+	0.258038i
$236$	−43069.7			−0.0503375
$237$		0			0
$238$	7167.52	+	1.32843e6i	0.00820213	+	1.52019i
$239$	−1.23235e6	−	711499.i	−1.39553	−	0.805712i	−0.401613	−	0.915810i	$-0.631550\pi$
$239$	−1.23235e6	−	711499.i	−1.39553	−	0.805712i	−0.993921	+	0.110098i	$0.964884\pi$
$240$		0			0
$241$	282864.	+	163312.i	0.313715	+	0.181123i	0.648588	−	0.761140i	$-0.275360\pi$
$241$	282864.	+	163312.i	0.313715	+	0.181123i	−0.334873	+	0.942263i	$0.608693\pi$
$242$	−331596.	+	191447.i	−0.363975	+	0.210141i
$243$		0			0
$244$			2700.28i			0.00290358i
$245$	−655391.	+	1.16400e6i	−0.697566	+	1.23890i
$246$		0			0
$247$	10585.0	+	18333.8i	0.0110395	+	0.0191209i
$248$	−1.32322e6			−1.36616
$249$		0			0
$250$			29542.2i			0.0298947i
$251$	275036.			0.275554			0.137777	−	0.990463i	$-0.456004\pi$
$251$	275036.			0.275554			0.137777	+	0.990463i	$0.456004\pi$
$252$		0			0
$253$	1.88159e6			1.84809
$254$		−	220342.i		−	0.214296i
$255$		0			0
$256$	−131443.			−0.125354
$257$	272648.	+	472239.i	0.257495	+	0.445994i	0.965570	−	0.260143i	$-0.0837696\pi$
$257$	272648.	+	472239.i	0.257495	+	0.445994i	−0.708075	+	0.706137i	$0.750436\pi$
$258$		0			0
$259$	−243262.	−	416140.i	−0.225333	−	0.385470i
$260$			15560.4i			0.0142754i
$261$		0			0
$262$	−499803.	+	288562.i	−0.449828	+	0.259708i
$263$	−124265.	−	71744.7i	−0.110780	−	0.0639588i	0.443586	−	0.896232i	$-0.353706\pi$
$263$	−124265.	−	71744.7i	−0.110780	−	0.0639588i	−0.554366	+	0.832273i	$0.687039\pi$
$264$		0			0
$265$	−2.45550e6	−	1.41768e6i	−2.14795	−	1.24012i
$266$	−52473.0	−	89764.0i	−0.0454707	−	0.0777854i
$267$		0			0
$268$	7792.29			0.00662717
$269$	580604.	+	1.00564e6i	0.489215	+	0.847345i	0.999923	−	0.0124091i	$-0.00395005\pi$
$269$	580604.	+	1.00564e6i	0.489215	+	0.847345i	−0.510708	+	0.859754i	$0.670617\pi$
$270$		0			0
$271$	−32243.6	−	18615.8i	−0.0266698	−	0.0153978i	0.486606	−	0.873622i	$-0.338235\pi$
$271$	−32243.6	−	18615.8i	−0.0266698	−	0.0153978i	−0.513276	+	0.858224i	$0.671568\pi$
$272$	−906183.	−	1.56956e6i	−0.742666	−	1.28634i
$273$		0			0
$274$	1.05466e6	−	1.82672e6i	0.848664	−	1.46993i
$275$	1.32637e6	−	765779.i	1.05763	−	0.610621i
$276$		0			0
$277$	−295798.	+	512338.i	−0.231631	+	0.401197i	−0.958288	−	0.285804i	$-0.907740\pi$
$277$	−295798.	+	512338.i	−0.231631	+	0.401197i	0.726657	+	0.687000i	$0.241073\pi$
$278$	−432755.	+	749553.i	−0.335838	+	0.581689i
$279$		0			0
$280$	−10263.0	−	1.90216e6i	−0.00782314	−	1.44995i
$281$	1.86244e6	−	1.07528e6i	1.40707	−	0.812372i	0.411965	−	0.911200i	$-0.364842\pi$
$281$	1.86244e6	−	1.07528e6i	1.40707	−	0.812372i	0.995105	+	0.0988274i	$0.0315092\pi$
$282$		0			0
$283$		−	1.18706e6i		−	0.881065i	−0.897737	−	0.440533i	$-0.854790\pi$
$283$		−	1.18706e6i		−	0.881065i	0.897737	−	0.440533i	$-0.145210\pi$
$284$		−	49553.7i		−	0.0364570i
$285$		0			0
$286$	−336277.	+	194149.i	−0.243098	+	0.140353i
$287$	75380.0	+	128950.i	0.0540196	+	0.0924096i
$288$		0			0
$289$	−1.00242e6	+	1.73625e6i	−0.706003	+	1.22283i
$290$	−1.75879e6	+	3.04632e6i	−1.22806	+	2.12706i
$291$		0			0
$292$	−26390.5	+	15236.6i	−0.0181130	+	0.0104576i
$293$	96173.5	−	166577.i	0.0654465	−	0.113357i	−0.831445	−	0.555606i	$-0.812486\pi$
$293$	96173.5	−	166577.i	0.0654465	−	0.113357i	0.896892	+	0.442250i	$0.145820\pi$
$294$		0			0
$295$	1.27780e6	+	2.21321e6i	0.854884	+	1.48070i
$296$	594435.	+	343197.i	0.394344	+	0.227675i
$297$		0			0
$298$	−885071.	−	1.53299e6i	−0.577348	−	0.999996i
$299$	573184.			0.370780
$300$		0			0
$301$	536429.	−	2894.28i	0.341268	−	0.00184130i
$302$	−1.62809e6	−	939978.i	−1.02721	−	0.593062i
$303$		0			0
$304$	122847.	+	70925.5i	0.0762393	+	0.0440168i
$305$	138759.	−	80112.3i	0.0854103	−	0.0493117i
$306$		0			0
$307$			143609.i			0.0869634i	0.999054	+	0.0434817i	$0.0138450\pi$
$307$			143609.i			0.0869634i	−0.999054	+	0.0434817i	$0.986155\pi$
$308$	−71929.4	+	42047.5i	−0.0432046	+	0.0252560i
$309$		0			0
$310$	1.57726e6	+	2.73189e6i	0.932178	+	1.61458i
$311$	922729.			0.540970			0.270485	−	0.962724i	$-0.412816\pi$
$311$	922729.			0.540970			0.270485	+	0.962724i	$0.412816\pi$
$312$		0			0
$313$		−	1.50111e6i		−	0.866067i	−0.901378	−	0.433033i	$-0.857443\pi$
$313$		−	1.50111e6i		−	0.866067i	0.901378	−	0.433033i	$-0.142557\pi$
$314$	−2.92216e6			−1.67255
$315$		0			0
$316$	−50480.7			−0.0284386
$317$			626842.i			0.350356i	0.984537	+	0.175178i	$0.0560502\pi$
$317$			626842.i			0.350356i	−0.984537	+	0.175178i	$0.943950\pi$
$318$		0			0
$319$	3.83485e6			2.10995
$320$	1.35206e6	+	2.34183e6i	0.738108	+	1.27844i
$321$		0			0
$322$	−2.81514e6	+	15189.0i	−1.51307	+	0.00816373i
$323$		−	268046.i		−	0.142956i
$324$		0			0
$325$	404049.	−	233278.i	0.212190	−	0.122508i
$326$	1.35554e6	+	782623.i	0.706430	+	0.407858i
$327$		0			0
$328$	−184199.	−	106347.i	−0.0945371	−	0.0545810i
$329$	−203795.	+	357423.i	−0.103801	+	0.182051i
$330$		0			0
$331$	−1.58041e6			−0.792864			−0.396432	−	0.918064i	$-0.629752\pi$
$331$	−1.58041e6			−0.792864			−0.396432	+	0.918064i	$0.629752\pi$
$332$	−48383.8	−	83803.1i	−0.0240910	−	0.0417268i
$333$		0			0
$334$	366095.	+	211365.i	0.179567	+	0.103673i
$335$	−231183.	−	400421.i	−0.112550	−	0.194942i
$336$		0			0
$337$	732147.	−	1.26812e6i	0.351175	−	0.608253i	−0.635281	−	0.772281i	$-0.719116\pi$
$337$	732147.	−	1.26812e6i	0.351175	−	0.608253i	0.986456	+	0.164029i	$0.0524489\pi$
$338$	1.67804e6	−	968817.i	0.798934	−	0.461265i
$339$		0			0
$340$	98510.0	−	170624.i	0.0462150	−	0.0800467i
$341$	1.71952e6	−	2.97829e6i	0.800794	−	1.38702i
$342$		0			0
$343$	−2.17860e6	+	35266.5i	−0.999869	+	0.0161855i
$344$	−661534.	+	381937.i	−0.301409	+	0.174019i
$345$		0			0
$346$			1.90200e6i			0.854124i
$347$		−	2.75554e6i		−	1.22852i	−0.789103	−	0.614261i	$-0.789454\pi$
$347$		−	2.75554e6i		−	1.22852i	0.789103	−	0.614261i	$-0.210546\pi$
$348$		0			0
$349$	1.58554e6	−	915414.i	0.696810	−	0.402304i	−0.109348	−	0.994004i	$-0.534876\pi$
$349$	1.58554e6	−	915414.i	0.696810	−	0.402304i	0.806158	+	0.591700i	$0.201543\pi$
$350$	−1.97826e6	+	1.15643e6i	−0.863205	+	0.504601i
$351$		0			0
$352$	116259.	−	201367.i	0.0500116	−	0.0866227i
$353$	−215652.	+	373519.i	−0.0921119	+	0.159542i	−0.908400	−	0.418103i	$-0.862695\pi$
$353$	−215652.	+	373519.i	−0.0921119	+	0.159542i	0.816288	+	0.577646i	$0.196028\pi$
$354$		0			0
$355$	−2.54641e6	+	1.47017e6i	−1.07240	+	0.619151i
$356$	−17867.5	+	30947.4i	−0.00747204	+	0.0129419i
$357$		0			0
$358$	738949.	+	1.27990e6i	0.304724	+	0.527798i
$359$	−2.61461e6	−	1.50955e6i	−1.07071	−	0.618173i	−0.142332	−	0.989819i	$-0.545460\pi$
$359$	−2.61461e6	−	1.50955e6i	−1.07071	−	0.618173i	−0.928375	+	0.371646i	$0.878794\pi$
$360$		0			0
$361$	−1.22756e6	−	2.12620e6i	−0.495764	−	0.858688i
$362$	3.29604e6			1.32197
$363$		0			0
$364$	−21911.7	+	12808.9i	−0.00866809	+	0.00506707i
$365$	1.56592e6	+	904083.i	0.615229	+	0.355202i
$366$		0			0
$367$	3.70817e6	+	2.14092e6i	1.43713	+	0.829725i	0.997649	−	0.0685287i	$-0.0218305\pi$
$367$	3.70817e6	+	2.14092e6i	1.43713	+	0.829725i	0.439477	+	0.898254i	$0.355164\pi$
$368$	3.32610e6	−	1.92033e6i	1.28031	−	0.739189i
$369$		0			0
$370$		−	1.63634e6i		−	0.621399i
$371$	−24952.7	−	4.62475e6i	−0.00941201	−	1.74443i
$372$		0			0
$373$	1.34850e6	+	2.33567e6i	0.501856	+	0.869240i	0.999998	+	0.00214417i	$0.000682510\pi$
$373$	1.34850e6	+	2.33567e6i	0.501856	+	0.869240i	−0.498142	+	0.867095i	$0.665984\pi$
$374$	4.91648e6			1.81750
$375$		0			0
$376$		−	585883.i		−	0.213718i
$377$	1.16820e6			0.423317
$378$		0			0
$379$	496485.			0.177545			0.0887724	−	0.996052i	$-0.471706\pi$
$379$	496485.			0.177545			0.0887724	+	0.996052i	$0.471706\pi$
$380$			15420.4i			0.00547820i
$381$		0			0
$382$	330158.			0.115761
$383$	−1.48178e6	−	2.56652e6i	−0.516164	−	0.894022i	−0.999824	−	0.0187662i	$-0.994026\pi$
$383$	−1.48178e6	−	2.56652e6i	−0.516164	−	0.894022i	0.483660	−	0.875256i	$-0.339307\pi$
$384$		0			0
$385$	4.29470e6	+	2.44875e6i	1.47666	+	0.841962i
$386$		−	2.76356e6i		−	0.944062i
$387$		0			0
$388$	−135845.	+	78430.2i	−0.0458105	+	0.0264487i
$389$	4.78523e6	+	2.76275e6i	1.60335	+	0.925696i	0.990811	+	0.135257i	$0.0431860\pi$
$389$	4.78523e6	+	2.76275e6i	1.60335	+	0.925696i	0.612541	+	0.790439i	$0.290147\pi$
$390$		0			0
$391$	−6.28511e6	−	3.62871e6i	−2.07908	−	1.20036i
$392$	2.67011e6	−	1.58025e6i	0.877637	−	0.519411i
$393$		0			0
$394$	4.12945e6			1.34015
$395$	1.49767e6	+	2.59404e6i	0.482974	+	0.836535i
$396$		0			0
$397$	3.36326e6	+	1.94178e6i	1.07099	+	0.618334i	0.928451	−	0.371456i	$-0.121141\pi$
$397$	3.36326e6	+	1.94178e6i	1.07099	+	0.618334i	0.142535	+	0.989790i	$0.454475\pi$
$398$	−1.01261e6	−	1.75390e6i	−0.320433	−	0.555005i
$399$		0			0
$400$	1.56309e6	−	2.70735e6i	0.488466	−	0.846048i
$401$	760189.	−	438895.i	0.236081	−	0.136301i	−0.377293	−	0.926094i	$-0.623145\pi$
$401$	760189.	−	438895.i	0.236081	−	0.136301i	0.613374	+	0.789793i	$0.289812\pi$
$402$		0			0
$403$	523814.	−	907272.i	0.160662	−	0.278275i
$404$	28279.6	−	48981.8i	0.00862026	−	0.0149307i
$405$		0			0
$406$	−5.73752e6	+	30956.6i	−1.72746	+	0.00932048i
$407$	−1.54493e6	+	891966.i	−0.462299	+	0.266908i
$408$		0			0
$409$			115280.i			0.0340758i	0.999855	+	0.0170379i	$0.00542360\pi$
$409$			115280.i			0.0340758i	−0.999855	+	0.0170379i	$0.994576\pi$
$410$			507057.i			0.148969i
$411$		0			0
$412$	−62169.2	+	35893.4i	−0.0180440	+	0.0104177i
$413$	−2.06473e6	+	3.62120e6i	−0.595646	+	1.04467i
$414$		0			0
$415$	−2.87092e6	+	4.97257e6i	−0.818277	+	1.41730i
$416$	35415.8	−	61342.0i	0.0100338	−	0.0173790i
$417$		0			0
$418$	−333251.	+	192403.i	−0.0932891	+	0.0538605i
$419$	−2.12049e6	+	3.67280e6i	−0.590067	+	1.02203i	0.404156	+	0.914690i	$0.367565\pi$
$419$	−2.12049e6	+	3.67280e6i	−0.590067	+	1.02203i	−0.994223	+	0.107336i	$0.965768\pi$
$420$		0			0
$421$	−853099.	−	1.47761e6i	−0.234582	−	0.406307i	0.724569	−	0.689202i	$-0.242039\pi$
$421$	−853099.	−	1.47761e6i	−0.234582	−	0.406307i	−0.959151	+	0.282895i	$0.908705\pi$
$422$	2.99429e6	+	1.72876e6i	0.818490	+	0.472555i
$423$		0			0
$424$	3.29282e6	+	5.70333e6i	0.889515	+	1.54068i
$425$	−5.90734e6			−1.58642
$426$		0			0
$427$	227033.	+	129450.i	0.0602587	+	0.0343582i
$428$	107999.	+	62353.0i	0.0284976	+	0.0164531i
$429$		0			0
$430$	1.57708e6	+	910527.i	0.411322	+	0.237477i
$431$	−3.72342e6	+	2.14972e6i	−0.965493	+	0.557427i	−0.897859	−	0.440283i	$-0.854878\pi$
$431$	−3.72342e6	+	2.14972e6i	−0.965493	+	0.557427i	−0.0676334	+	0.997710i	$0.521545\pi$
$432$		0			0
$433$		−	934052.i		−	0.239415i	−0.992809	−	0.119707i	$-0.961804\pi$
$433$		−	934052.i		−	0.239415i	0.992809	−	0.119707i	$-0.0381957\pi$
$434$	−2.54862e6	+	4.46985e6i	−0.649501	+	1.13912i
$435$		0			0
$436$	34471.4	+	59706.2i	0.00868445	+	0.0150419i
$437$	568027.			0.142287
$438$		0			0
$439$			16661.5i			0.00412623i	0.999998	+	0.00206311i	$0.000656710\pi$
$439$			16661.5i			0.00412623i	−0.999998	+	0.00206311i	$0.999343\pi$
$440$	−7.03982e6			−1.73352
$441$		0			0
$442$	1.49770e6			0.364644
$443$			213427.i			0.0516702i	0.999666	+	0.0258351i	$0.00822449\pi$
$443$			213427.i			0.0516702i	−0.999666	+	0.0258351i	$0.991776\pi$
$444$		0			0
$445$	2.12039e6			0.507592
$446$	−659864.	−	1.14292e6i	−0.157079	−	0.272068i
$447$		0			0
$448$	−2.18472e6	+	3.83164e6i	−0.514282	+	0.901966i
$449$		−	4.49117e6i		−	1.05134i	−0.850689	−	0.525670i	$-0.823815\pi$
$449$		−	4.49117e6i		−	1.05134i	0.850689	−	0.525670i	$-0.176185\pi$
$450$		0			0
$451$	478731.	−	276395.i	0.110828	−	0.0639866i
$452$	167065.	+	96455.0i	0.0384627	+	0.0222064i
$453$		0			0
$454$	2.27386e6	+	1.31281e6i	0.517754	+	0.298926i
$455$	1.30829e6	+	745958.i	0.296261	+	0.168922i
$456$		0			0
$457$	−3.07956e6			−0.689760			−0.344880	−	0.938647i	$-0.612080\pi$
$457$	−3.07956e6			−0.689760			−0.344880	+	0.938647i	$0.612080\pi$
$458$	−2.92637e6	−	5.06862e6i	−0.651877	−	1.12908i
$459$		0			0
$460$	361576.	+	208756.i	0.0796720	+	0.0459986i
$461$	4.26724e6	+	7.39108e6i	0.935180	+	1.61978i	0.774312	+	0.632803i	$0.218096\pi$
$461$	4.26724e6	+	7.39108e6i	0.935180	+	1.61978i	0.160868	+	0.986976i	$0.448571\pi$
$462$		0			0
$463$	−1.34361e6	+	2.32719e6i	−0.291286	+	0.504522i	−0.974114	−	0.226057i	$-0.927416\pi$
$463$	−1.34361e6	+	2.32719e6i	−0.291286	+	0.504522i	0.682828	+	0.730579i	$0.260750\pi$
$464$	6.77892e6	−	3.91381e6i	1.46173	−	0.843927i
$465$		0			0
$466$	175793.	−	304482.i	0.0375004	−	0.0649527i
$467$	−4.62740e6	+	8.01489e6i	−0.981849	+	1.70061i	−0.326671	+	0.945138i	$0.605927\pi$
$467$	−4.62740e6	+	8.01489e6i	−0.981849	+	1.70061i	−0.655178	+	0.755475i	$0.727406\pi$
$468$		0			0
$469$	373557.	−	655159.i	0.0784197	−	0.137535i
$470$	−1.20960e6	+	698364.i	−0.252579	+	0.145827i
$471$		0			0
$472$		−	5.93583e6i		−	1.22638i
$473$		−	1.98530e6i		−	0.408013i
$474$		0			0
$475$	400413.	−	231179.i	0.0814282	−	0.0470126i
$476$	321358.	−	1733.88i	0.0650088	−	0.000350753i
$477$		0			0
$478$	3.93971e6	−	6.82378e6i	0.788668	−	1.36601i
$479$	1.56277e6	−	2.70680e6i	0.311212	−	0.539035i	−0.667413	−	0.744688i	$-0.732598\pi$
$479$	1.56277e6	−	2.70680e6i	0.311212	−	0.539035i	0.978625	+	0.205652i	$0.0659316\pi$
$480$		0			0
$481$	−470629.	+	271718.i	−0.0927505	+	0.0535495i
$482$	−904288.	+	1.56627e6i	−0.177292	+	0.307079i
$483$		0			0
$484$	46312.5	+	80215.6i	0.00898638	+	0.0155649i
$485$	8.06056e6	+	4.65376e6i	1.55600	+	0.898359i
$486$		0			0
$487$	1.67536e6	+	2.90182e6i	0.320101	+	0.554431i	0.980509	−	0.196476i	$-0.0629499\pi$
$487$	1.67536e6	+	2.90182e6i	0.320101	+	0.554431i	−0.660408	+	0.750907i	$0.729617\pi$
$488$	−372150.			−0.0707406
$489$		0			0
$490$	−6.44529e6	−	3.62903e6i	−1.21270	−	0.682810i
$491$	−4.67851e6	−	2.70114e6i	−0.875797	−	0.505642i	−0.00652663	−	0.999979i	$-0.502078\pi$
$491$	−4.67851e6	−	2.70114e6i	−0.875797	−	0.505642i	−0.869270	+	0.494337i	$0.835411\pi$
$492$		0			0
$493$	−1.28097e7	−	7.39566e6i	−2.37367	−	1.37044i
$494$	−101518.	+	58611.2i	−0.0187165	+	0.0108060i
$495$		0			0
$496$		−	7.01969e6i		−	1.28119i
$497$	−4.16637e6	−	2.37557e6i	−0.756601	−	0.431398i
$498$		0			0
$499$	3.28949e6	+	5.69756e6i	0.591394	+	1.02432i	0.994045	+	0.108970i	$0.0347553\pi$
$499$	3.28949e6	+	5.69756e6i	0.591394	+	1.02432i	−0.402651	+	0.915353i	$0.631911\pi$
$500$	7146.49			0.00127840
$501$		0			0
$502$			1.52293e6i			0.269725i
$503$	−9.18844e6			−1.61928			−0.809639	−	0.586927i	$-0.800337\pi$
$503$	−9.18844e6			−1.61928			−0.809639	+	0.586927i	$0.800337\pi$
$504$		0			0
$505$	−3.35602e6			−0.585593
$506$			1.04187e7i			1.80900i
$507$		0			0
$508$	−53302.5			−0.00916406
$509$	−1.63742e6	−	2.83609e6i	−0.280134	−	0.485206i	0.691284	−	0.722583i	$-0.257046\pi$
$509$	−1.63742e6	−	2.83609e6i	−0.280134	−	0.485206i	−0.971417	+	0.237377i	$0.923712\pi$
$510$		0			0
$511$	15912.8	+	2.94929e6i	0.00269584	+	0.499649i
$512$		−	6.26001e6i		−	1.05536i
$513$		0			0
$514$	−2.61488e6	+	1.50970e6i	−0.436560	+	0.252048i
$515$	3.68889e6	+	2.12978e6i	0.612884	+	0.353849i
$516$		0			0
$517$	1.31870e6	+	761352.i	0.216980	+	0.125273i
$518$	2.30425e6	−	1.34699e6i	0.377316	−	0.220566i
$519$		0			0
$520$	−2.14453e6			−0.347795
$521$	−2.81270e6	−	4.87174e6i	−0.453972	−	0.786303i	0.544656	−	0.838659i	$-0.316660\pi$
$521$	−2.81270e6	−	4.87174e6i	−0.453972	−	0.786303i	−0.998628	+	0.0523564i	$0.983327\pi$
$522$		0			0
$523$	−713512.	−	411946.i	−0.114064	−	0.0658546i	0.441883	−	0.897073i	$-0.354311\pi$
$523$	−713512.	−	411946.i	−0.114064	−	0.0658546i	−0.555946	+	0.831218i	$0.687644\pi$
$524$	69805.2	+	120906.i	0.0111061	+	0.0192362i
$525$		0			0
$526$	397264.	−	688082.i	0.0626059	−	0.108437i
$527$	−1.14875e7	+	6.63231e6i	−1.80177	+	1.04025i
$528$		0			0
$529$	4.47157e6	−	7.74498e6i	0.694737	−	1.20332i
$530$	7.84998e6	−	1.35966e7i	1.21389	−	2.10252i
$531$		0			0
$532$	−21714.6	+	12693.6i	−0.00332638	+	0.00194449i
$533$	145835.	−	84197.8i	0.0222353	−	0.0128376i
$534$		0			0
$535$		−	7.39960e6i		−	1.11770i
$536$			1.07393e6i			0.161459i
$537$		0			0
$538$	−5.56840e6	+	3.21492e6i	−0.829421	+	0.478866i
$539$	87014.1	+	8.06340e6i	0.0129008	+	1.19549i
$540$		0			0
$541$	3.33591e6	−	5.77796e6i	0.490028	−	0.848753i	−0.509906	−	0.860230i	$-0.670320\pi$
$541$	3.33591e6	−	5.77796e6i	0.490028	−	0.848753i	0.999934	+	0.0114768i	$0.00365325\pi$
$542$	103079.	−	178539.i	0.0150721	−	0.0261057i
$543$		0			0
$544$	−776688.	+	448421.i	−0.112525	+	0.0649664i
$545$	2.04541e6	−	3.54275e6i	0.294977	−	0.510915i
$546$		0			0
$547$	−1.09337e6	−	1.89377e6i	−0.156242	−	0.270620i	0.777268	−	0.629169i	$-0.216605\pi$
$547$	−1.09337e6	−	1.89377e6i	−0.156242	−	0.270620i	−0.933511	+	0.358549i	$0.883271\pi$
$548$	−441898.	−	255130.i	−0.0628595	−	0.0362919i
$549$		0			0
$550$	4.24026e6	+	7.34435e6i	0.597704	+	1.03525i
$551$	1.15769e6			0.162448
$552$		0			0
$553$	−2.42001e6	+	4.24430e6i	−0.336515	+	0.590192i
$554$	−2.83691e6	−	1.63789e6i	−0.392710	−	0.226731i
$555$		0			0
$556$	181323.	+	104687.i	0.0248751	+	0.0143616i
$557$	−1.67738e6	+	968437.i	−0.229084	+	0.132261i	−0.610149	−	0.792287i	$-0.708891\pi$
$557$	−1.67738e6	+	968437.i	−0.229084	+	0.132261i	0.381066	+	0.924548i	$0.375557\pi$
$558$		0			0
$559$		−	604779.i		−	0.0818591i
$560$	1.00910e7	−	54445.5i	1.35976	−	0.00733655i
$561$		0			0
$562$	5.95402e6	+	1.03127e7i	0.795188	+	1.37731i
$563$	9.20594e6			1.22404			0.612022	−	0.790841i	$-0.290356\pi$
$563$	9.20594e6			1.22404			0.612022	+	0.790841i	$0.290356\pi$
$564$		0			0
$565$		−	1.14466e7i		−	1.50853i
$566$	6.57300e6			0.862428
$567$		0			0
$568$	6.82946e6			0.888209
$569$			2.79801e6i			0.362300i	0.983456	+	0.181150i	$0.0579819\pi$
$569$			2.79801e6i			0.362300i	−0.983456	+	0.181150i	$0.942018\pi$
$570$		0			0
$571$	−2.09829e6			−0.269324			−0.134662	−	0.990892i	$-0.542995\pi$
$571$	−2.09829e6			−0.269324			−0.134662	+	0.990892i	$0.542995\pi$
$572$	46966.2	+	81347.8i	0.00600199	+	0.0103958i
$573$		0			0
$574$	−714022.	+	417394.i	−0.0904549	+	0.0528769i
$575$		−	1.25185e7i		−	1.57900i
$576$		0			0
$577$	−4.91428e6	+	2.83726e6i	−0.614498	+	0.354780i	−0.774724	−	0.632300i	$-0.782111\pi$
$577$	−4.91428e6	+	2.83726e6i	−0.614498	+	0.354780i	0.160226	+	0.987080i	$0.448778\pi$
$578$	−9.61395e6	−	5.55062e6i	−1.19697	−	0.691069i
$579$		0			0
$580$	736928.	+	425465.i	0.0909609	+	0.0525163i
$581$	−9.36547e6	+	50531.1i	−1.15104	+	0.00621038i
$582$		0			0
$583$	−1.71160e7			−2.08560
$584$	−2.09989e6	−	3.63712e6i	−0.254780	−	0.441291i
$585$		0			0
$586$	922371.	+	532531.i	0.110959	+	0.0640621i
$587$	−5.49618e6	−	9.51967e6i	−0.658364	−	1.14032i	−0.981039	−	0.193810i	$-0.937915\pi$
$587$	−5.49618e6	−	9.51967e6i	−0.658364	−	1.14032i	0.322675	−	0.946510i	$-0.395418\pi$
$588$		0			0
$589$	519100.	−	899108.i	0.0616543	−	0.106788i
$590$	−1.22550e7	+	7.07542e6i	−1.44938	+	0.836801i
$591$		0			0
$592$	−1.82066e6	+	3.15348e6i	−0.213513	+	0.369816i
$593$	−1.75523e6	+	3.04015e6i	−0.204974	+	0.355025i	−0.950124	−	0.311871i	$-0.899044\pi$
$593$	−1.75523e6	+	3.04015e6i	−0.204974	+	0.355025i	0.745151	+	0.666896i	$0.232378\pi$
$594$		0			0
$595$	−9.62321e6	−	1.64621e7i	−1.11437	−	1.90631i
$596$	−370841.	+	214105.i	−0.0427634	+	0.0246895i
$597$		0			0
$598$			3.17383e6i			0.362937i
$599$			1.01213e7i			1.15258i	0.817247	+	0.576288i	$0.195499\pi$
$599$			1.01213e7i			1.15258i	−0.817247	+	0.576288i	$0.804501\pi$
$600$		0			0
$601$	8.56347e6	−	4.94412e6i	0.967082	−	0.558345i	0.0687369	−	0.997635i	$-0.478103\pi$
$601$	8.56347e6	−	4.94412e6i	0.967082	−	0.558345i	0.898346	+	0.439290i	$0.144770\pi$
$602$	16026.2	+	2.97031e6i	0.00180235	+	0.334049i
$603$		0			0
$604$	−227388.	+	393847.i	−0.0253615	+	0.0439274i
$605$	2.74802e6	−	4.75970e6i	0.305233	−	0.528678i
$606$		0			0
$607$	8.92772e6	−	5.15442e6i	0.983488	−	0.567817i	0.0801666	−	0.996781i	$-0.474455\pi$
$607$	8.92772e6	−	5.15442e6i	0.983488	−	0.567817i	0.903321	+	0.428964i	$0.141121\pi$
$608$	35097.2	−	60790.1i	0.00385047	−	0.00666920i
$609$		0			0
$610$	443597.	+	768333.i	0.0482686	+	0.0836036i
$611$	401713.	+	231929.i	0.0435324	+	0.0251335i
$612$		0			0
$613$	3.82185e6	+	6.61963e6i	0.410792	+	0.711513i	0.994977	−	0.100108i	$-0.0319189\pi$
$613$	3.82185e6	+	6.61963e6i	0.410792	+	0.711513i	−0.584185	+	0.811621i	$0.698586\pi$
$614$	−795192.			−0.0851238
$615$		0			0
$616$	−5.79496e6	−	9.91325e6i	−0.615317	−	1.05260i
$617$	−5.92682e6	−	3.42185e6i	−0.626771	−	0.361866i	0.152729	−	0.988268i	$-0.451194\pi$
$617$	−5.92682e6	−	3.42185e6i	−0.626771	−	0.361866i	−0.779501	+	0.626402i	$0.784527\pi$
$618$		0			0
$619$	3.28638e6	+	1.89739e6i	0.344739	+	0.199035i	0.662366	−	0.749181i	$-0.269553\pi$
$619$	3.28638e6	+	1.89739e6i	0.344739	+	0.199035i	−0.317627	+	0.948216i	$0.602886\pi$
$620$	660865.	−	381551.i	0.0690452	−	0.0398633i
$621$		0			0
$622$			5.10933e6i			0.529527i
$623$	1.74543e6	+	2.98586e6i	0.180170	+	0.308212i
$624$		0			0
$625$	4.77567e6	+	8.27171e6i	0.489029	+	0.847023i
$626$	8.31193e6			0.847747
$627$		0			0
$628$			706891.i			0.0715243i
$629$	6.88076e6			0.693442
$630$		0			0
$631$	−703499.			−0.0703380			−0.0351690	−	0.999381i	$-0.511197\pi$
$631$	−703499.			−0.0703380			−0.0351690	+	0.999381i	$0.511197\pi$
$632$		−	6.95721e6i		−	0.692855i
$633$		0			0
$634$	−3.47095e6			−0.342945
$635$	1.58139e6	+	2.73904e6i	0.155634	+	0.269566i
$636$		0			0
$637$	26507.0	+	2.45634e6i	0.00258828	+	0.239850i
$638$			2.12343e7i			2.06532i
$639$		0			0
$640$	−1.18997e7	+	6.87031e6i	−1.14838	+	0.663020i
$641$	1.00495e7	+	5.80208e6i	0.966049	+	0.557748i	0.898029	−	0.439936i	$-0.144999\pi$
$641$	1.00495e7	+	5.80208e6i	0.966049	+	0.557748i	0.0680193	+	0.997684i	$0.478332\pi$
$642$		0			0
$643$	−1.76238e7	−	1.01751e7i	−1.68102	−	0.970536i	−0.960987	−	0.276593i	$-0.910794\pi$
$643$	−1.76238e7	−	1.01751e7i	−1.68102	−	0.970536i	−0.720030	−	0.693942i	$-0.755872\pi$
$644$	3674.33	+	681002.i	0.000349110	+	0.0647044i
$645$		0			0
$646$	1.48422e6			0.139932
$647$	6.92241e6	+	1.19900e7i	0.650124	+	1.12605i	0.983092	+	0.183110i	$0.0586165\pi$
$647$	6.92241e6	+	1.19900e7i	0.650124	+	1.12605i	−0.332968	+	0.942938i	$0.608050\pi$
$648$		0			0
$649$	1.33603e7	+	7.71358e6i	1.24510	+	0.718859i
$650$	1.29170e6	+	2.23730e6i	0.119917	+	0.207702i
$651$		0			0
$652$	189322.	−	327916.i	0.0174415	−	0.0302095i
$653$	1.35867e7	−	7.84430e6i	1.24690	−	0.719899i	0.276411	−	0.961040i	$-0.410855\pi$
$653$	1.35867e7	−	7.84430e6i	1.24690	−	0.719899i	0.970490	+	0.241141i	$0.0775216\pi$
$654$		0			0
$655$	4.14199e6	−	7.17413e6i	0.377229	−	0.653380i
$656$	564173.	−	977175.i	0.0511861	−	0.0886570i
$657$		0			0
$658$	−1.97912e6	−	1.12845e6i	−0.178200	−	0.101606i
$659$	−1.05074e7	+	6.06642e6i	−0.942497	+	0.544151i	−0.890742	−	0.454509i	$-0.849815\pi$
$659$	−1.05074e7	+	6.06642e6i	−0.942497	+	0.544151i	−0.0517546	+	0.998660i	$0.516481\pi$
$660$		0			0
$661$			9.30466e6i			0.828317i	0.910205	+	0.414159i	$0.135924\pi$
$661$			9.30466e6i			0.828317i	−0.910205	+	0.414159i	$0.864076\pi$
$662$		−	8.75102e6i		−	0.776093i
$663$		0			0
$664$	1.15497e7	−	6.66821e6i	1.01660	−	0.586934i
$665$	1.29652e6	+	739246.i	0.113690	+	0.0648238i
$666$		0			0
$667$	1.56724e7	−	2.71454e7i	1.36402	−	2.36256i
$668$	51130.7	−	88561.1i	0.00443344	−	0.00767895i
$669$		0			0
$670$	2.21721e6	−	1.28011e6i	0.190818	−	0.110169i
$671$	483607.	−	837632.i	0.0414655	−	0.0718203i
$672$		0			0
$673$	5.48762e6	+	9.50484e6i	0.467032	+	0.808923i	0.999291	−	0.0376590i	$-0.0119901\pi$
$673$	5.48762e6	+	9.50484e6i	0.467032	+	0.808923i	−0.532259	+	0.846582i	$0.678657\pi$
$674$	7.02180e6	+	4.05404e6i	0.595386	+	0.343746i
$675$		0			0
$676$	−234364.	−	405930.i	−0.0197253	−	0.0341653i
$677$	−1.67696e7			−1.40622			−0.703108	−	0.711083i	$-0.748205\pi$
$677$	−1.67696e7			−1.40622			−0.703108	+	0.711083i	$0.748205\pi$
$678$		0			0
$679$	81911.0	+	1.51815e7i	0.00681817	+	1.26369i
$680$	2.35153e7	+	1.35766e7i	1.95020	+	1.12595i
$681$		0			0
$682$	1.64914e7	+	9.52130e6i	1.35768	+	0.783854i
$683$	1.88932e6	−	1.09080e6i	0.154972	−	0.0894732i	−0.420509	−	0.907289i	$-0.638148\pi$
$683$	1.88932e6	−	1.09080e6i	0.154972	−	0.0894732i	0.575481	+	0.817815i	$0.304815\pi$
$684$		0			0
$685$			3.02770e7i			2.46539i
$686$	−195277.	−	1.20634e7i	−0.0158432	−	0.978719i
$687$		0			0
$688$	−2.02618e6	−	3.50944e6i	−0.163195	−	0.282662i
$689$	−5.21402e6			−0.418431
$690$		0			0
$691$			1.65383e7i			1.31763i	0.752304	+	0.658817i	$0.228943\pi$
$691$			1.65383e7i			1.31763i	−0.752304	+	0.658817i	$0.771057\pi$
$692$	460109.			0.0365254
$693$		0			0
$694$	1.52580e7			1.20254
$695$		−	1.24234e7i		−	0.975619i
$696$		0			0
$697$	−2.13216e6			−0.166241
$698$	5.06882e6	+	8.77946e6i	0.393794	+	0.682071i
$699$		0			0
$700$	279748.	+	478557.i	0.0215786	+	0.0369138i
$701$			5.57862e6i			0.428777i	0.976748	+	0.214389i	$0.0687759\pi$
$701$			5.57862e6i			0.428777i	−0.976748	+	0.214389i	$0.931224\pi$
$702$		0			0
$703$	−466395.	+	269273.i	−0.0355931	+	0.0205497i
$704$	1.41367e7	+	8.16184e6i	1.07502	+	0.620664i
$705$		0			0
$706$	−2.06825e6	−	1.19410e6i	−0.156168	−	0.0901634i
$707$	−2.76257e6	−	4.72584e6i	−0.207857	−	0.355575i
$708$		0			0
$709$	−9.72800e6			−0.726788			−0.363394	−	0.931635i	$-0.618382\pi$
$709$	−9.72800e6			−0.726788			−0.363394	+	0.931635i	$0.618382\pi$
$710$	−8.14061e6	−	1.41000e7i	−0.606054	−	1.04972i
$711$		0			0
$712$	−4.26515e6	−	2.46249e6i	−0.315308	−	0.182043i
$713$	−1.40548e7	−	2.43436e7i	−1.03538	−	1.79333i
$714$		0			0
$715$	2.78680e6	−	4.82688e6i	0.203864	−	0.353103i
$716$	309617.	−	178757.i	0.0225705	−	0.0130311i
$717$		0			0
$718$	8.35864e6	−	1.44776e7i	0.605097	−	1.04806i
$719$	−9.35471e6	+	1.62028e7i	−0.674852	+	1.16888i	0.301661	+	0.953415i	$0.402459\pi$
$719$	−9.35471e6	+	1.62028e7i	−0.674852	+	1.16888i	−0.976512	+	0.215462i	$0.930874\pi$
$720$		0			0
$721$	37486.4	+	6.94776e6i	0.00268556	+	0.497745i
$722$	1.17732e7	−	6.79724e6i	0.840524	−	0.485277i
$723$		0			0
$724$		−	797336.i		−	0.0565321i
$725$		−	2.55138e7i		−	1.80273i
$726$		0			0
$727$	−3.50717e6	+	2.02487e6i	−0.246105	+	0.142089i	−0.617980	−	0.786194i	$-0.712049\pi$
$727$	−3.50717e6	+	2.02487e6i	−0.246105	+	0.142089i	0.371874	+	0.928283i	$0.378715\pi$
$728$	−1.76531e6	−	3.01986e6i	−0.123450	−	0.211182i
$729$		0			0
$730$	−5.00608e6	+	8.67078e6i	−0.347689	+	0.602215i
$731$	−3.82873e6	+	6.63155e6i	−0.265009	+	0.459010i
$732$		0			0
$733$	−1.97913e7	+	1.14265e7i	−1.36055	+	0.785513i	−0.989697	−	0.143180i	$-0.954267\pi$
$733$	−1.97913e7	+	1.14265e7i	−1.36055	+	0.785513i	−0.370851	+	0.928692i	$0.620934\pi$
$734$	−1.18547e7	+	2.05329e7i	−0.812174	+	1.40673i
$735$		0			0
$736$	−950266.	−	1.64591e6i	−0.0646622	−	0.111998i
$737$	−2.41719e6	−	1.39556e6i	−0.163924	−	0.0946413i
$738$		0			0
$739$	−8.68806e6	−	1.50482e7i	−0.585210	−	1.01361i	−0.994849	−	0.101366i	$-0.967679\pi$
$739$	−8.68806e6	−	1.50482e7i	−0.585210	−	1.01361i	0.409639	−	0.912248i	$-0.365655\pi$
$740$	−395844.			−0.0265732
$741$		0			0
$742$	2.56081e7	−	138168.i	1.70753	−	0.00921291i
$743$	−1.87215e7	−	1.08088e7i	−1.24414	−	0.718302i	−0.274202	−	0.961672i	$-0.588414\pi$
$743$	−1.87215e7	−	1.08088e7i	−1.24414	−	0.718302i	−0.969934	+	0.243370i	$0.921747\pi$
$744$		0			0
$745$	2.20044e7	+	1.27042e7i	1.45251	+	0.838605i
$746$	−1.29331e7	+	7.46691e6i	−0.850852	+	0.491240i
$747$		0			0
$748$		−	1.18933e6i		−	0.0777230i
$749$	1.04199e7	−	6.09111e6i	0.678669	−	0.396727i
$750$		0			0
$751$	3.06421e6	+	5.30737e6i	0.198253	+	0.343384i	0.947962	−	0.318384i	$-0.103140\pi$
$751$	3.06421e6	+	5.30737e6i	0.198253	+	0.343384i	−0.749709	+	0.661767i	$0.769807\pi$
$752$	3.10811e6			0.200425
$753$		0			0
$754$			6.46857e6i			0.414362i
$755$	2.69847e7			1.72286
$756$		0			0
$757$	−3.02859e7			−1.92089			−0.960443	−	0.278478i	$-0.910170\pi$
$757$	−3.02859e7			−1.92089			−0.960443	+	0.278478i	$0.910170\pi$
$758$			2.74913e6i			0.173789i
$759$		0			0
$760$	−2.12523e6			−0.133467
$761$	3.34481e6	+	5.79337e6i	0.209367	+	0.362635i	0.951515	−	0.307601i	$-0.0995262\pi$
$761$	3.34481e6	+	5.79337e6i	0.209367	+	0.362635i	−0.742148	+	0.670236i	$0.766193\pi$
$762$		0			0
$763$	6.67250e6	−	36001.2i	0.414932	−	0.00223875i
$764$		−	79867.6i		−	0.00495036i
$765$		0			0
$766$	1.42113e7	−	8.20492e6i	0.875111	−	0.505245i
$767$	4.06993e6	+	2.34977e6i	0.249803	+	0.144224i
$768$		0			0
$769$	2.00338e7	+	1.15665e7i	1.22165	+	0.705320i	0.965270	−	0.261256i	$-0.0841367\pi$
$769$	2.00338e7	+	1.15665e7i	1.22165	+	0.705320i	0.256380	+	0.966576i	$0.417470\pi$
$770$	−1.35592e7	+	2.37806e7i	−0.824151	+	1.44543i
$771$		0			0
$772$	−668525.			−0.0403715
$773$	1.14151e7	+	1.97715e7i	0.687117	+	1.19012i	0.972767	+	0.231787i	$0.0744573\pi$
$773$	1.14151e7	+	1.97715e7i	0.687117	+	1.19012i	−0.285650	+	0.958334i	$0.592209\pi$
$774$		0			0
$775$	−1.98150e7	−	1.14402e7i	−1.18506	−	0.684194i
$776$	−1.08092e7	−	1.87221e7i	−0.644375	−	1.11609i
$777$		0			0
$778$	−1.52979e7	+	2.64967e7i	−0.906114	+	1.56944i
$779$	144523.	−	83440.2i	0.00853282	−	0.00492642i
$780$		0			0
$781$	−8.87484e6	+	1.53717e7i	−0.520635	+	0.901766i
$782$	2.00929e7	−	3.48019e7i	1.17497	−	2.03510i
$783$		0			0
$784$	8.38324e6	+	1.41650e7i	0.487104	+	0.823049i
$785$	3.63249e7	−	2.09722e7i	2.10392	−	1.21470i
$786$		0			0
$787$		−	1.62878e7i		−	0.937399i	−0.883358	−	0.468699i	$-0.844723\pi$
$787$		−	1.62878e7i		−	0.937399i	0.883358	−	0.468699i	$-0.155277\pi$
$788$		−	998945.i		−	0.0573094i
$789$		0			0
$790$	−1.43637e7	+	8.29289e6i	−0.818839	+	0.472757i
$791$	1.61187e7	−	9.42246e6i	0.915987	−	0.535455i
$792$		0			0
$793$	147320.	−	255166.i	0.00831917	−	0.0144092i
$794$	−1.07520e7	+	1.86230e7i	−0.605254	+	1.04833i
$795$		0			0
$796$	−424282.	+	244959.i	−0.0237340	+	0.0137028i
$797$	−1.14270e7	+	1.97921e7i	−0.637214	+	1.10369i	0.348828	+	0.937187i	$0.386580\pi$
$797$	−1.14270e7	+	1.97921e7i	−0.637214	+	1.10369i	−0.986041	+	0.166500i	$0.946753\pi$
$798$		0			0
$799$	−2.93659e6	−	5.08633e6i	−0.162733	−	0.281863i
$800$	−1.33972e6	−	773490.i	−0.0740099	−	0.0427297i
$801$		0			0
$802$	2.43025e6	+	4.20931e6i	0.133418	+	0.231087i
$803$	1.09152e7			0.597369
$804$		0			0
$805$	3.48855e7	−	2.03929e7i	1.89738	−	1.10915i
$806$	5.02374e6	+	2.90046e6i	0.272389	+	0.157264i
$807$		0			0
$808$	6.75063e6	+	3.89748e6i	0.363761	+	0.210017i
$809$	1.49420e7	−	8.62678e6i	0.802672	−	0.463423i	−0.0417326	−	0.999129i	$-0.513288\pi$
$809$	1.49420e7	−	8.62678e6i	0.802672	−	0.463423i	0.844405	+	0.535706i	$0.179954\pi$
$810$		0			0
$811$		−	2.87277e7i		−	1.53373i	−0.641809	−	0.766865i	$-0.721816\pi$
$811$		−	2.87277e7i		−	1.53373i	0.641809	−	0.766865i	$-0.278184\pi$
$812$	7488.63	+	1.38795e6i	0.000398577	+	0.0738726i
$813$		0			0
$814$	−4.93899e6	−	8.55458e6i	−0.261262	−	0.452520i
$815$	−2.24674e7			−1.18484
$816$		0			0
$817$		−	599337.i		−	0.0314135i
$818$	−638328.			−0.0333550
$819$		0			0
$820$	122661.			0.00637047
$821$		−	2.23110e7i		−	1.15521i	−0.816316	−	0.577606i	$-0.803987\pi$
$821$		−	2.23110e7i		−	1.15521i	0.816316	−	0.577606i	$-0.196013\pi$
$822$		0			0
$823$	−2.73133e7			−1.40564			−0.702821	−	0.711367i	$-0.748077\pi$
$823$	−2.73133e7			−1.40564			−0.702821	+	0.711367i	$0.748077\pi$
$824$	−4.94680e6	−	8.56811e6i	−0.253809	−	0.439610i
$825$		0			0
$826$	−2.00513e7	−	1.14328e7i	−1.02257	−	0.583047i
$827$			3.74634e6i			0.190478i	0.995454	+	0.0952388i	$0.0303615\pi$
$827$			3.74634e6i			0.190478i	−0.995454	+	0.0952388i	$0.969639\pi$
$828$		0			0
$829$	−7.68278e6	+	4.43565e6i	−0.388268	+	0.224167i	−0.681410	−	0.731902i	$-0.738633\pi$
$829$	−7.68278e6	+	4.43565e6i	−0.388268	+	0.224167i	0.293141	+	0.956069i	$0.405299\pi$
$830$	−2.75341e7	−	1.58968e7i	−1.38732	−	0.800968i
$831$		0			0
$832$	4.30644e6	+	2.48633e6i	0.215680	+	0.124523i
$833$	1.52599e7	−	2.71022e7i	0.761973	−	1.35329i
$834$		0			0
$835$	−6.06782e6			−0.301174
$836$	46543.6	+	80615.9i	0.00230327	+	0.00398938i
$837$		0			0
$838$	−2.03370e7	−	1.17416e7i	−1.00041	−	0.577585i
$839$	1.16421e7	+	2.01647e7i	0.570986	+	0.988976i	0.996465	+	0.0840083i	$0.0267722\pi$
$839$	1.16421e7	+	2.01647e7i	0.570986	+	0.988976i	−0.425479	+	0.904968i	$0.639894\pi$
$840$		0			0
$841$	2.16864e7	−	3.75619e7i	1.05730	−	1.83129i
$842$	8.18181e6	−	4.72377e6i	0.397713	−	0.229619i
$843$		0			0
$844$	418199.	−	724342.i	0.0202082	−	0.0350016i
$845$	−1.39063e7	+	2.40864e7i	−0.669993	+	1.16046i
$846$		0			0
$847$	8.96455e6	−	48367.9i	0.429358	−	0.00231659i
$848$	−3.02562e7	+	1.74684e7i	−1.44486	+	0.834188i
$849$		0			0
$850$		−	3.27101e7i		−	1.55287i
$851$			1.45813e7i			0.690195i
$852$		0			0
$853$	3.57837e6	−	2.06597e6i	0.168388	−	0.0972191i	−0.413437	−	0.910533i	$-0.635672\pi$
$853$	3.57837e6	−	2.06597e6i	0.168388	−	0.0972191i	0.581826	+	0.813314i	$0.302339\pi$
$854$	−716787.	+	1.25713e6i	−0.0336315	+	0.0589841i
$855$		0			0
$856$	−8.59344e6	+	1.48843e7i	−0.400851	+	0.694294i
$857$	−8.45515e6	+	1.46447e7i	−0.393250	+	0.681129i	−0.992876	−	0.119151i	$-0.961983\pi$
$857$	−8.45515e6	+	1.46447e7i	−0.393250	+	0.681129i	0.599626	+	0.800280i	$0.295316\pi$
$858$		0			0
$859$	3.57324e7	−	2.06301e7i	1.65226	−	0.953935i	0.676124	−	0.736788i	$-0.263658\pi$
$859$	3.57324e7	−	2.06301e7i	1.65226	−	0.953935i	0.976139	−	0.217147i	$-0.0696750\pi$
$860$	220263.	−	381507.i	0.0101554	−	0.0175896i
$861$		0			0
$862$	−1.19034e7	−	2.06173e7i	−0.545636	−	0.945069i
$863$	−1.59796e7	−	9.22585e6i	−0.730365	−	0.421677i	0.0881904	−	0.996104i	$-0.471892\pi$
$863$	−1.59796e7	−	9.22585e6i	−0.730365	−	0.421677i	−0.818556	+	0.574427i	$0.805225\pi$
$864$		0			0
$865$	−1.36506e7	−	2.36435e7i	−0.620313	−	1.07441i
$866$	5.17203e6			0.234351
$867$		0			0
$868$	1.08129e6	+	616529.i	0.0487128	+	0.0277750i
$869$	1.56592e7	+	9.04085e6i	0.703430	+	0.406125i
$870$		0			0
$871$	−736343.	−	425128.i	−0.0328878	−	0.0189878i
$872$	−8.22866e6	+	4.75082e6i	−0.366469	+	0.211581i
$873$		0			0
$874$			3.14527e6i			0.139277i
$875$	342598.	−	600861.i	0.0151274	−	0.0265310i
$876$		0			0
$877$	−1.13011e7	−	1.95742e7i	−0.496162	−	0.859378i	0.503828	−	0.863804i	$-0.331924\pi$
$877$	−1.13011e7	−	1.95742e7i	−0.496162	−	0.859378i	−0.999990	+	0.00442628i	$0.998591\pi$
$878$	−92258.1			−0.00403895
$879$		0			0
$880$		−	3.73463e7i		−	1.62570i
$881$	3.26814e7			1.41860			0.709301	−	0.704906i	$-0.249011\pi$
$881$	3.26814e7			1.41860			0.709301	+	0.704906i	$0.249011\pi$
$882$		0			0
$883$	−1.87005e7			−0.807145			−0.403573	−	0.914948i	$-0.632232\pi$
$883$	−1.87005e7			−0.807145			−0.403573	+	0.914948i	$0.632232\pi$
$884$		−	362305.i		−	0.0155935i
$885$		0			0
$886$	−1.18179e6			−0.0505772
$887$	7.68508e6	+	1.33109e7i	0.327974	+	0.568067i	0.982110	−	0.188310i	$-0.0603009\pi$
$887$	7.68508e6	+	1.33109e7i	0.327974	+	0.568067i	−0.654136	+	0.756377i	$0.726968\pi$
$888$		0			0
$889$	−2.55529e6	+	4.48155e6i	−0.108439	+	0.190184i
$890$			1.17410e7i			0.496855i
$891$		0			0
$892$	−276480.	+	159626.i	−0.0116346	+	0.00671725i
$893$	398099.	+	229842.i	0.0167056	+	0.00964498i
$894$		0			0
$895$	−1.83715e7	−	1.06068e7i	−0.766634	−	0.442616i
$896$	−1.94700e7	−	1.11014e7i	−0.810208	−	0.461963i
$897$		0			0
$898$	2.48685e7			1.02910
$899$	−2.86450e7	−	4.96146e7i	−1.18209	−	2.04744i
$900$		0			0
$901$	5.71730e7	+	3.30089e7i	2.34628	+	1.35462i
$902$	1.53045e6	+	2.65082e6i	0.0626331	+	0.108484i
$903$		0			0
$904$	−1.32934e7	+	2.30248e7i	−0.541020	+	0.937074i
$905$	−4.09725e7	+	2.36555e7i	−1.66292	+	0.960087i
$906$		0			0
$907$	−6.96911e6	+	1.20708e7i	−0.281293	+	0.487214i	−0.971703	−	0.236204i	$-0.924097\pi$
$907$	−6.96911e6	+	1.20708e7i	−0.281293	+	0.487214i	0.690411	+	0.723418i	$0.257430\pi$
$908$	317579.	−	550063.i	0.0127831	−	0.0221410i
$909$		0			0
$910$	−4.13051e6	+	7.24424e6i	−0.165349	+	0.289994i
$911$	−5.07823e6	+	2.93192e6i	−0.202729	+	0.117046i	−0.597928	−	0.801550i	$-0.704009\pi$
$911$	−5.07823e6	+	2.93192e6i	−0.202729	+	0.117046i	0.395199	+	0.918596i	$0.370676\pi$
$912$		0			0
$913$			3.46612e7i			1.37615i
$914$		−	1.70521e7i		−	0.675170i
$915$		0			0
$916$	−1.22614e6	+	707911.i	−0.0482837	+	0.0278766i
$917$	1.35119e7	−	72903.2i	0.530633	−	0.00286301i
$918$		0			0
$919$	−2.79593e6	+	4.84269e6i	−0.109204	+	0.189146i	−0.915448	−	0.402437i	$-0.868163\pi$
$919$	−2.79593e6	+	4.84269e6i	−0.109204	+	0.189146i	0.806244	+	0.591583i	$0.201497\pi$
$920$	−2.87706e7	+	4.98322e7i	−1.12067	+	1.94107i
$921$		0			0
$922$	−4.09259e7	+	2.36286e7i	−1.58552	+	0.915398i
$923$	−2.70353e6	+	4.68265e6i	−0.104454	+	0.180920i
$924$		0			0
$925$	5.93438e6	+	1.02786e7i	0.228045	+	0.394986i
$926$	−1.28861e7	−	7.43980e6i	−0.493849	−	0.285124i
$927$		0			0
$928$	−1.93673e6	−	3.35452e6i	−0.0738244	−	0.127868i
$929$	2.48193e7			0.943519			0.471759	−	0.881727i	$-0.343619\pi$
$929$	2.48193e7			0.943519			0.471759	+	0.881727i	$0.343619\pi$
$930$		0			0
$931$	26268.5	+	2.43424e6i	0.000993254	+	0.0920425i
$932$	−73656.5	−	42525.6i	−0.00277761	−	0.00160365i
$933$		0			0
$934$	−4.43800e7	−	2.56228e7i	−1.66464	−	0.961080i
$935$	−6.11160e7	+	3.52854e7i	−2.28626	+	1.31997i
$936$		0			0
$937$			2.89174e7i			1.07600i	0.842946	+	0.537998i	$0.180819\pi$
$937$			2.89174e7i			1.07600i	−0.842946	+	0.537998i	$0.819181\pi$
$938$	3.62774e6	+	2.06846e6i	0.134626	+	0.0767609i
$939$		0			0
$940$	168939.	+	292612.i	0.00623607	+	0.0108012i
$941$	−1.08370e7			−0.398966			−0.199483	−	0.979901i	$-0.563926\pi$
$941$	−1.08370e7			−0.398966			−0.199483	+	0.979901i	$0.563926\pi$
$942$		0			0
$943$		−	4.51833e6i		−	0.165462i
$944$	3.14896e7			1.15010
$945$		0			0
$946$	1.09930e7			0.399382
$947$		−	3.59899e7i		−	1.30408i	−0.758183	−	0.652042i	$-0.773913\pi$
$947$		−	3.59899e7i		−	1.30408i	0.758183	−	0.652042i	$-0.226087\pi$
$948$		0			0
$949$	3.32508e6			0.119849
$950$	1.28008e6	+	2.21717e6i	0.0460181	+	0.0797057i
$951$		0			0
$952$	238962.	+	4.42893e7i	0.00854547	+	1.58382i
$953$			2.42272e7i			0.864113i	0.901847	+	0.432057i	$0.142212\pi$
$953$			2.42272e7i			0.864113i	−0.901847	+	0.432057i	$0.857788\pi$
$954$		0			0
$955$	−4.10414e6	+	2.36952e6i	−0.145617	+	0.0840723i
$956$	−1.65072e6	−	953045.i	−0.0584157	−	0.0337263i
$957$		0			0
$958$	1.49881e7	+	8.65337e6i	0.527633	+	0.304629i
$959$	−4.26351e7	+	2.49230e7i	−1.49700	+	0.875094i
$960$		0			0
$961$	−2.27476e7			−0.794562
$962$	−1.50455e6	−	2.60597e6i	−0.0524168	−	0.0907885i
$963$		0			0
$964$	378893.	+	218754.i	0.0131318	+	0.00758165i
$965$	1.98339e7	+	3.43534e7i	0.685631	+	1.18755i
$966$		0			0
$967$	5.96563e6	−	1.03328e7i	0.205159	−	0.355346i	−0.745024	−	0.667037i	$-0.767562\pi$
$967$	5.96563e6	−	1.03328e7i	0.205159	−	0.355346i	0.950183	+	0.311691i	$0.100896\pi$
$968$	−1.10553e7	+	6.38275e6i	−0.379211	+	0.218937i
$969$		0			0
$970$	−2.57688e7	+	4.46329e7i	−0.879356	+	1.52309i
$971$	1.88112e7	−	3.25820e7i	0.640279	−	1.10900i	−0.345091	−	0.938569i	$-0.612152\pi$
$971$	1.88112e7	−	3.25820e7i	0.640279	−	1.10900i	0.985370	−	0.170427i	$-0.0545147\pi$
$972$		0			0
$973$	1.74943e7	−	1.02266e7i	0.592399	−	0.346297i
$974$	−1.60679e7	+	9.27682e6i	−0.542703	+	0.313330i
$975$		0			0
$976$		−	1.97426e6i		−	0.0663406i
$977$		−	4.38763e7i		−	1.47060i	−0.677743	−	0.735299i	$-0.737042\pi$
$977$		−	4.38763e7i		−	1.47060i	0.677743	−	0.735299i	$-0.262958\pi$
$978$		0			0
$979$	1.10851e7	−	6.39998e6i	0.369643	−	0.213413i
$980$	−877889.	+	1.55916e6i	−0.0291994	+	0.0518593i
$981$		0			0
$982$	1.49567e7	−	2.59058e7i	0.494946	−	0.857271i
$983$	1.06766e7	−	1.84924e7i	0.352411	−	0.610395i	−0.634260	−	0.773120i	$-0.718695\pi$
$983$	1.06766e7	−	1.84924e7i	0.352411	−	0.610395i	0.986671	+	0.162725i	$0.0520284\pi$
$984$		0			0
$985$	−5.13326e7	+	2.96369e7i	−1.68579	+	0.973290i
$986$	4.09512e7	−	7.09296e7i	1.34145	−	2.32346i
$987$		0			0
$988$	14178.5	+	24557.9i	0.000462102	+	0.000800384i
$989$	−1.40532e7	−	8.11361e6i	−0.456861	−	0.263769i
$990$		0			0
$991$	1.50682e7	+	2.60988e7i	0.487389	+	0.844183i	0.999895	−	0.0145011i	$-0.00461601\pi$
$991$	1.50682e7	+	2.60988e7i	0.487389	+	0.844183i	−0.512506	+	0.858684i	$0.671283\pi$
$992$	−3.47366e6			−0.112075
$993$		0			0
$994$	1.31540e7	−	2.30700e7i	0.422272	−	0.740596i
$995$	2.51753e7	+	1.45350e7i	0.806153	+	0.465432i
$996$		0			0
$997$	631666.	+	364692.i	0.0201256	+	0.0116195i	0.510029	−	0.860157i	$-0.329635\pi$
$997$	631666.	+	364692.i	0.0201256	+	0.0116195i	−0.489903	+	0.871777i	$0.662968\pi$
$998$	−3.15485e7	+	1.82145e7i	−1.00266	+	0.578884i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.6.i.a.152.28		76
3.2	odd	2		63.6.i.a.5.11	✓	76
7.3	odd	6		189.6.s.a.17.11		76
9.2	odd	6		189.6.s.a.89.11		76
9.7	even	3		63.6.s.a.47.28	yes	76
21.17	even	6		63.6.s.a.59.28	yes	76
63.38	even	6	inner	189.6.i.a.143.11		76
63.52	odd	6		63.6.i.a.38.28	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.11	✓	76	3.2	odd	2
63.6.i.a.38.28	yes	76	63.52	odd	6
63.6.s.a.47.28	yes	76	9.7	even	3
63.6.s.a.59.28	yes	76	21.17	even	6
189.6.i.a.143.11		76	63.38	even	6	inner
189.6.i.a.152.28		76	1.1	even	1	trivial
189.6.s.a.17.11		76	7.3	odd	6
189.6.s.a.89.11		76	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	189.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+5.53719i q^{2} +1.33949 q^{4} +(-39.7402 - 68.8320i) q^{5} +(64.2142 - 112.621i) q^{7} +184.607i q^{8} +O(q^{10})\)	\(q+5.53719i q^{2} +1.33949 q^{4} +(-39.7402 - 68.8320i) q^{5} +(64.2142 - 112.621i) q^{7} +184.607i q^{8} +(381.136 - 220.049i) q^{10} +(-415.512 - 239.896i) q^{11} +(-126.577 - 73.0791i) q^{13} +(623.605 + 355.566i) q^{14} -979.342 q^{16} +(925.298 + 1602.66i) q^{17} +(-125.438 - 72.4216i) q^{19} +(-53.2315 - 92.1997i) q^{20} +(1328.35 - 2300.77i) q^{22} +(-3396.26 + 1960.83i) q^{23} +(-1596.06 + 2764.46i) q^{25} +(404.653 - 700.880i) q^{26} +(86.0142 - 150.855i) q^{28} +(-6921.91 + 3996.37i) q^{29} +7167.76i q^{31} +484.623i q^{32} +(-8874.26 + 5123.55i) q^{34} +(-10303.8 + 55.5940i) q^{35} +(1859.07 - 3220.00i) q^{37} +(401.012 - 694.574i) q^{38} +(12706.9 - 7336.32i) q^{40} +(-576.073 + 997.788i) q^{41} +(2068.92 + 3583.47i) q^{43} +(-556.574 - 321.338i) q^{44} +(-10857.5 - 18805.8i) q^{46} -3173.67 q^{47} +(-8560.07 - 14463.8i) q^{49} +(-15307.4 - 8837.71i) q^{50} +(-169.548 - 97.8886i) q^{52} +(30894.4 - 17836.9i) q^{53} +38134.1i q^{55} +(20790.7 + 11854.4i) q^{56} +(-22128.7 - 38328.0i) q^{58} -32153.8 q^{59} +2015.90i q^{61} -39689.3 q^{62} -34022.4 q^{64} +11616.7i q^{65} +5817.36 q^{67} +(1239.43 + 2146.75i) q^{68} +(-307.835 - 57054.3i) q^{70} -36994.5i q^{71} +(-19701.9 + 11374.9i) q^{73} +(17829.8 + 10294.0i) q^{74} +(-168.022 - 97.0078i) q^{76} +(-53699.2 + 31390.8i) q^{77} -37686.5 q^{79} +(38919.2 + 67410.1i) q^{80} +(-5524.94 - 3189.83i) q^{82} +(-36121.1 - 62563.6i) q^{83} +(73543.0 - 127380. i) q^{85} +(-19842.4 + 11456.0i) q^{86} +(44286.5 - 76706.6i) q^{88} +(-13339.1 + 23103.9i) q^{89} +(-16358.3 + 9562.51i) q^{91} +(-4549.26 + 2626.51i) q^{92} -17573.2i q^{94} +11512.2i q^{95} +(-101416. + 58552.4i) q^{97} +(80088.7 - 47398.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 1154 q^{4} + 3 q^{5} - 30 q^{7}+O(q^{10}) \) 76 * q - 1154 * q^4 + 3 * q^5 - 30 * q^7	\( 76 q - 1154 q^{4} + 3 q^{5} - 30 q^{7} - 6 q^{10} - 567 q^{11} + 543 q^{13} + 1638 q^{14} + 16446 q^{16} + 801 q^{17} - 6 q^{19} - 96 q^{20} + 62 q^{22} - 7806 q^{23} - 18749 q^{25} - 10128 q^{26} + 860 q^{28} - 17904 q^{29} + 96 q^{34} - 3960 q^{35} + 2577 q^{37} - 14967 q^{38} + 9564 q^{40} - 28230 q^{41} - 9246 q^{43} + 69885 q^{44} - 9418 q^{46} + 56562 q^{47} + 7948 q^{49} + 67509 q^{50} - 40899 q^{52} - 25296 q^{53} - 104754 q^{56} - 4951 q^{58} + 59076 q^{59} - 79536 q^{62} - 198600 q^{64} + 1244 q^{67} - 191496 q^{68} - 127197 q^{70} - 6 q^{73} + 45681 q^{74} - 2880 q^{76} - 13854 q^{77} + 59984 q^{79} - 243225 q^{80} + 90 q^{82} + 246930 q^{83} + 11973 q^{85} - 291801 q^{86} - 34751 q^{88} + 6345 q^{89} - 120111 q^{91} + 463488 q^{92} - 104037 q^{97} + 646797 q^{98}+O(q^{100}) \) 76 * q - 1154 * q^4 + 3 * q^5 - 30 * q^7 - 6 * q^10 - 567 * q^11 + 543 * q^13 + 1638 * q^14 + 16446 * q^16 + 801 * q^17 - 6 * q^19 - 96 * q^20 + 62 * q^22 - 7806 * q^23 - 18749 * q^25 - 10128 * q^26 + 860 * q^28 - 17904 * q^29 + 96 * q^34 - 3960 * q^35 + 2577 * q^37 - 14967 * q^38 + 9564 * q^40 - 28230 * q^41 - 9246 * q^43 + 69885 * q^44 - 9418 * q^46 + 56562 * q^47 + 7948 * q^49 + 67509 * q^50 - 40899 * q^52 - 25296 * q^53 - 104754 * q^56 - 4951 * q^58 + 59076 * q^59 - 79536 * q^62 - 198600 * q^64 + 1244 * q^67 - 191496 * q^68 - 127197 * q^70 - 6 * q^73 + 45681 * q^74 - 2880 * q^76 - 13854 * q^77 + 59984 * q^79 - 243225 * q^80 + 90 * q^82 + 246930 * q^83 + 11973 * q^85 - 291801 * q^86 - 34751 * q^88 + 6345 * q^89 - 120111 * q^91 + 463488 * q^92 - 104037 * q^97 + 646797 * q^98

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