LMFDB - Embedded newform 189.6.s.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,6,Mod(17,189)]

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([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	189.s (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			17.11
Character	$\chi$	$=$	189.17
Dual form			189.6.s.a.89.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.79535 - 2.76860i) q^{2} +(-0.669744 - 1.16003i) q^{4} -79.4804 q^{5} +(-129.640 - 0.699468i) q^{7} +184.607i q^{8} +O(q^{10})$	\(q+(-4.79535 - 2.76860i) q^{2} +(-0.669744 - 1.16003i) q^{4} -79.4804 q^{5} +(-129.640 - 0.699468i) q^{7} +184.607i q^{8} +(381.136 + 220.049i) q^{10} +479.792i q^{11} +(126.577 + 73.0791i) q^{13} +(619.732 + 362.275i) q^{14} +(489.671 - 848.135i) q^{16} +(-925.298 + 1602.66i) q^{17} +(-125.438 + 72.4216i) q^{19} +(53.2315 + 92.1997i) q^{20} +(1328.35 - 2300.77i) q^{22} -3921.67i q^{23} +3192.13 q^{25} +(-404.653 - 700.880i) q^{26} +(86.0142 + 150.855i) q^{28} +(-6921.91 + 3996.37i) q^{29} +(-6207.46 + 3583.88i) q^{31} +(419.696 - 242.312i) q^{32} +(8874.26 - 5123.55i) q^{34} +(10303.8 + 55.5940i) q^{35} +(1859.07 + 3220.00i) q^{37} +802.024 q^{38} -14672.6i q^{40} +(576.073 - 997.788i) q^{41} +(2068.92 + 3583.47i) q^{43} +(556.574 - 321.338i) q^{44} +(-10857.5 + 18805.8i) q^{46} +(-1586.84 + 2748.48i) q^{47} +(16806.0 + 181.358i) q^{49} +(-15307.4 - 8837.71i) q^{50} -195.777i q^{52} +(-30894.4 - 17836.9i) q^{53} -38134.1i q^{55} +(129.127 - 23932.5i) q^{56} +44257.3 q^{58} +(-16076.9 - 27846.0i) q^{59} +(1745.82 + 1007.95i) q^{61} +39689.3 q^{62} -34022.4 q^{64} +(-10060.4 - 5808.35i) q^{65} +(-2908.68 - 5037.98i) q^{67} +2478.85 q^{68} +(-49256.5 - 28793.7i) q^{70} -36994.5i q^{71} +(-19701.9 - 11374.9i) q^{73} -20588.0i q^{74} +(168.022 + 97.0078i) q^{76} +(335.599 - 62200.2i) q^{77} +(18843.3 - 32637.5i) q^{79} +(-38919.2 + 67410.1i) q^{80} +(-5524.94 + 3189.83i) q^{82} +(36121.1 + 62563.6i) q^{83} +(73543.0 - 127380. i) q^{85} -22912.0i q^{86} -88573.1 q^{88} +(13339.1 + 23103.9i) q^{89} +(-16358.3 - 9562.51i) q^{91} +(-4549.26 + 2626.51i) q^{92} +(15218.9 - 8786.62i) q^{94} +(9969.84 - 5756.09i) q^{95} +(101416. - 58552.4i) q^{97} +(-80088.7 - 47398.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 3 q^{2} + 577 q^{4} + 6 q^{5} - 30 q^{7}+O(q^{10}) $ 76 * q + 3 * q^2 + 577 * q^4 + 6 * q^5 - 30 * q^7	$ 76 q + 3 q^{2} + 577 q^{4} + 6 q^{5} - 30 q^{7} - 6 q^{10} - 543 q^{13} + 123 q^{14} - 8223 q^{16} - 801 q^{17} - 6 q^{19} + 96 q^{20} + 62 q^{22} + 37498 q^{25} + 10128 q^{26} + 860 q^{28} - 17904 q^{29} + 3249 q^{31} - 10299 q^{32} - 96 q^{34} + 3960 q^{35} + 2577 q^{37} - 29934 q^{38} + 28230 q^{41} - 9246 q^{43} - 69885 q^{44} - 9418 q^{46} + 28281 q^{47} + 2458 q^{49} + 67509 q^{50} + 25296 q^{53} - 27288 q^{56} + 9902 q^{58} + 29538 q^{59} + 4206 q^{61} + 79536 q^{62} - 198600 q^{64} + 173388 q^{65} - 622 q^{67} - 382992 q^{68} + 14178 q^{70} - 6 q^{73} + 2880 q^{76} + 238866 q^{77} - 29992 q^{79} + 243225 q^{80} + 90 q^{82} - 246930 q^{83} + 11973 q^{85} + 69502 q^{88} - 6345 q^{89} - 120111 q^{91} + 463488 q^{92} - 3 q^{94} + 267813 q^{95} + 104037 q^{97} - 646797 q^{98}+O(q^{100}) $ 76 * q + 3 * q^2 + 577 * q^4 + 6 * q^5 - 30 * q^7 - 6 * q^10 - 543 * q^13 + 123 * q^14 - 8223 * q^16 - 801 * q^17 - 6 * q^19 + 96 * q^20 + 62 * q^22 + 37498 * q^25 + 10128 * q^26 + 860 * q^28 - 17904 * q^29 + 3249 * q^31 - 10299 * q^32 - 96 * q^34 + 3960 * q^35 + 2577 * q^37 - 29934 * q^38 + 28230 * q^41 - 9246 * q^43 - 69885 * q^44 - 9418 * q^46 + 28281 * q^47 + 2458 * q^49 + 67509 * q^50 + 25296 * q^53 - 27288 * q^56 + 9902 * q^58 + 29538 * q^59 + 4206 * q^61 + 79536 * q^62 - 198600 * q^64 + 173388 * q^65 - 622 * q^67 - 382992 * q^68 + 14178 * q^70 - 6 * q^73 + 2880 * q^76 + 238866 * q^77 - 29992 * q^79 + 243225 * q^80 + 90 * q^82 - 246930 * q^83 + 11973 * q^85 + 69502 * q^88 - 6345 * q^89 - 120111 * q^91 + 463488 * q^92 - 3 * q^94 + 267813 * q^95 + 104037 * q^97 - 646797 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.79535	−	2.76860i	−0.847706	−	0.489423i	0.0121701	−	0.999926i	$-0.496126\pi$
$2$	−4.79535	−	2.76860i	−0.847706	−	0.489423i	−0.859876	+	0.510503i	$0.829459\pi$
$3$		0			0
$3$		0			0
$4$	−0.669744	−	1.16003i	−0.0209295	−	0.0362510i
$5$	−79.4804			−1.42179			−0.710894	−	0.703299i	$-0.751709\pi$
$5$	−79.4804			−1.42179			−0.710894	+	0.703299i	$0.751709\pi$
$6$		0			0
$7$	−129.640	−	0.699468i	−0.999985	−	0.00539539i
$7$	−129.640	−	0.699468i	−0.999985	−	0.00539539i
$8$			184.607i			1.01982i
$9$		0			0
$10$	381.136	+	220.049i	1.20526	+	0.695856i
$11$			479.792i			1.19556i	0.801660	+	0.597780i	$0.203950\pi$
$11$			479.792i			1.19556i	−0.801660	+	0.597780i	$0.796050\pi$
$12$		0			0
$13$	126.577	+	73.0791i	0.207728	+	0.119932i	0.600255	−	0.799809i	$-0.295066\pi$
$13$	126.577	+	73.0791i	0.207728	+	0.119932i	−0.392527	+	0.919741i	$0.628399\pi$
$14$	619.732	+	362.275i	0.845053	+	0.493990i
$15$		0			0
$16$	489.671	−	848.135i	0.478194	−	0.828257i
$17$	−925.298	+	1602.66i	−0.776532	+	1.34499i	0.157398	+	0.987535i	$0.449690\pi$
$17$	−925.298	+	1602.66i	−0.776532	+	1.34499i	−0.933929	+	0.357457i	$0.883644\pi$
$18$		0			0
$19$	−125.438	+	72.4216i	−0.0797158	+	0.0460240i	−0.539328	−	0.842096i	$-0.681322\pi$
$19$	−125.438	+	72.4216i	−0.0797158	+	0.0460240i	0.459612	+	0.888120i	$0.347988\pi$
$20$	53.2315	+	92.1997i	0.0297573	+	0.0515412i
$21$		0			0
$22$	1328.35	−	2300.77i	0.585135	−	1.01348i
$23$		−	3921.67i		−	1.54579i	−0.634532	−	0.772896i	$-0.718807\pi$
$23$		−	3921.67i		−	1.54579i	0.634532	−	0.772896i	$-0.281193\pi$
$24$		0			0
$25$	3192.13			1.02148
$26$	−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
$31$	−6207.46	+	3583.88i	−1.16014	+	0.669806i	−0.951337	−	0.308152i	$-0.900290\pi$
$31$	−6207.46	+	3583.88i	−1.16014	+	0.669806i	−0.208801	+	0.977958i	$0.566956\pi$
$32$	419.696	−	242.312i	0.0724536	−	0.0418311i
$33$		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	0.955793	−	0.294041i	$-0.0950002\pi$
$37$	1859.07	+	3220.00i	0.223250	+	0.386680i	−0.732543	+	0.680721i	$0.761667\pi$
$38$	802.024			0.0901008
$39$		0			0
$40$		−	14672.6i		−	1.44997i
$41$	576.073	−	997.788i	0.0535202	−	0.0926997i	−0.838024	−	0.545633i	$-0.816289\pi$
$41$	576.073	−	997.788i	0.0535202	−	0.0926997i	0.891544	+	0.452934i	$0.149623\pi$
$42$		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
$47$	−1586.84	+	2748.48i	−0.104782	+	0.181488i	−0.913649	−	0.406504i	$-0.866748\pi$
$47$	−1586.84	+	2748.48i	−0.104782	+	0.181488i	0.808867	+	0.587992i	$0.200081\pi$
$48$		0			0
$49$	16806.0	+	181.358i	0.999942	+	0.0107906i
$50$	−15307.4	−	8837.71i	−0.865915	−	0.499936i
$51$		0			0
$52$		−	195.777i		−	0.0100405i
$53$	−30894.4	−	17836.9i	−1.51074	−	0.872227i	−0.999921	−	0.0125389i	$-0.996009\pi$
$53$	−30894.4	−	17836.9i	−1.51074	−	0.872227i	−0.510820	−	0.859688i	$-0.670658\pi$
$54$		0			0
$55$		−	38134.1i		−	1.69983i
$56$	129.127	−	23932.5i	0.00550233	−	1.01981i
$57$		0			0
$58$	44257.3			1.72749
$59$	−16076.9	−	27846.0i	−0.601274	−	1.04144i	−0.992628	−	0.121197i	$-0.961327\pi$
$59$	−16076.9	−	27846.0i	−0.601274	−	1.04144i	0.391354	−	0.920240i	$-0.372007\pi$
$60$		0			0
$61$	1745.82	+	1007.95i	0.0600725	+	0.0346829i	0.529735	−	0.848163i	$-0.322291\pi$
$61$	1745.82	+	1007.95i	0.0600725	+	0.0346829i	−0.469663	+	0.882846i	$0.655625\pi$
$62$	39689.3			1.31128
$63$		0			0
$64$	−34022.4			−1.03828
$65$	−10060.4	−	5808.35i	−0.295345	−	0.170518i
$66$		0			0
$67$	−2908.68	−	5037.98i	−0.0791606	−	0.137110i	0.823727	−	0.566986i	$-0.191891\pi$
$67$	−2908.68	−	5037.98i	−0.0791606	−	0.137110i	−0.902888	+	0.429876i	$0.858557\pi$
$68$	2478.85			0.0650097
$69$		0			0
$70$	−49256.5	−	28793.7i	−1.20149	−	0.702349i
$71$		−	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	0.267788	−	0.963478i	$-0.413707\pi$
$73$	−19701.9	−	11374.9i	−0.432715	−	0.249828i	−0.700503	+	0.713650i	$0.747041\pi$
$74$		−	20588.0i		−	0.437054i
$75$		0			0
$76$	168.022	+	97.0078i	0.00333683	+	0.00192652i
$77$	335.599	−	62200.2i	0.00645051	−	1.19554i
$78$		0			0
$79$	18843.3	−	32637.5i	0.339695	−	0.588368i	−0.644681	−	0.764452i	$-0.723010\pi$
$79$	18843.3	−	32637.5i	0.339695	−	0.588368i	0.984375	+	0.176084i	$0.0563430\pi$
$80$	−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	$0.0285363\pi$
$83$	36121.1	+	62563.6i	0.575527	+	0.996842i	−0.420457	+	0.907312i	$0.638130\pi$
$84$		0			0
$85$	73543.0	−	127380.i	1.10406	−	1.91229i
$86$		−	22912.0i		−	0.334054i
$87$		0			0
$88$	−88573.1			−1.21926
$89$	13339.1	+	23103.9i	0.178505	+	0.309180i	0.941369	−	0.337380i	$-0.109541\pi$
$89$	13339.1	+	23103.9i	0.178505	+	0.309180i	−0.762864	+	0.646559i	$0.776207\pi$
$90$		0			0
$91$	−16358.3	−	9562.51i	−0.207078	−	0.121051i
$92$	−4549.26	+	2626.51i	−0.0560365	+	0.0323527i
$93$		0			0
$94$	15218.9	−	8786.62i	0.177649	−	0.102566i
$95$	9969.84	−	5756.09i	0.113339	−	0.0654363i
$96$		0			0
$97$	101416.	−	58552.4i	1.09440	−	0.631852i	0.159655	−	0.987173i	$-0.448962\pi$
$97$	101416.	−	58552.4i	1.09440	−	0.631852i	0.934744	+	0.355321i	$0.115628\pi$
$98$	−80088.7	−	47398.8i	−0.842376	−	0.498542i
$99$		0			0
$100$	−2137.91	−	3702.97i	−0.0213791	−	0.0370297i
$101$	42224.5			0.411871			0.205936	−	0.978566i	$-0.433976\pi$
$101$	42224.5			0.411871			0.205936	+	0.978566i	$0.433976\pi$
$102$		0			0
$103$			53592.7i			0.497752i	0.968535	+	0.248876i	$0.0800611\pi$
$103$			53592.7i			0.497752i	−0.968535	+	0.248876i	$0.919939\pi$
$104$	−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	$-0.795250\pi$
$107$	−80626.7	+	46549.8i	−0.680800	+	0.393060i	0.119356	+	0.992851i	$0.461917\pi$
$108$		0			0
$109$	25734.7	−	44573.9i	0.207469	−	0.359347i	−0.743447	−	0.668794i	$-0.766811\pi$
$109$	25734.7	−	44573.9i	0.207469	−	0.359347i	0.950917	+	0.309447i	$0.100144\pi$
$110$	−105578.	+	182866.i	−0.831938	+	1.44096i
$111$		0			0
$112$	−64074.2	+	109610.i	−0.482656	+	0.825665i
$113$	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
$115$			311696.i			2.19779i
$116$	9271.82	+	5353.09i	0.0639765	+	0.0369368i
$117$		0			0
$118$			178042.i			1.17711i
$119$	121077.	−	207122.i	0.783777	−	1.34078i
$120$		0			0
$121$	−69149.6			−0.429364
$122$	−5581.22	−	9666.96i	−0.0339492	−	0.0588017i
$123$		0			0
$124$	8314.82	+	4800.56i	0.0485622	+	0.0280374i
$125$	−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	$0.534913\pi$
$128$	149719.	+	86440.3i	0.807704	+	0.466328i
$129$		0			0
$130$	32162.0	+	55706.2i	0.166911	+	0.289098i
$131$	104227.			0.530641			0.265320	−	0.964160i	$-0.414522\pi$
$131$	104227.			0.530641			0.265320	+	0.964160i	$0.414522\pi$
$132$		0			0
$133$	16312.4	−	9300.99i	0.0799630	−	0.0455932i
$134$			32211.9i			0.154972i
$135$		0			0
$136$	−295863.	−	170817.i	−1.37165	−	0.791923i
$137$			380936.i			1.73401i	0.498301	+	0.867004i	$0.333957\pi$
$137$			380936.i			1.73401i	−0.498301	+	0.867004i	$0.666043\pi$
$138$		0			0
$139$	−135367.	−	78154.2i	−0.594259	−	0.343096i	0.172521	−	0.985006i	$-0.444809\pi$
$139$	−135367.	−	78154.2i	−0.594259	−	0.343096i	−0.766780	+	0.641910i	$0.778142\pi$
$140$	−6836.44	−	11990.0i	−0.0294788	−	0.0517010i
$141$		0			0
$142$	−102423.	+	177402.i	−0.426262	+	0.738307i
$143$	−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
$149$		−	319682.i		−	1.17965i	−0.807531	−	0.589825i	$-0.799197\pi$
$149$		−	319682.i		−	1.17965i	0.807531	−	0.589825i	$-0.200803\pi$
$150$		0			0
$151$	339514.			1.21176			0.605879	−	0.795557i	$-0.292822\pi$
$151$	339514.			1.21176			0.605879	+	0.795557i	$0.292822\pi$
$152$	−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
$157$	−457030.	+	263866.i	−1.47977	+	0.854348i	−0.999738	−	0.0229015i	$-0.992710\pi$
$157$	−457030.	+	263866.i	−1.47977	+	0.854348i	−0.480036	+	0.877249i	$0.659376\pi$
$158$	−180720.	+	104339.i	−0.575922	+	0.332509i
$159$		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	0.995602	−	0.0936802i	$-0.0298631\pi$
$163$	141339.	+	244807.i	0.416672	+	0.721697i	−0.578931	+	0.815377i	$0.696530\pi$
$164$	−1543.29			−0.00448061
$165$		0			0
$166$		−	400019.i		−	1.12671i
$167$	−38171.9	+	66115.6i	−0.105914	+	0.183448i	−0.914111	−	0.405464i	$-0.867110\pi$
$167$	−38171.9	+	66115.6i	−0.105914	+	0.183448i	0.808197	+	0.588912i	$0.200443\pi$
$168$		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
$173$	171748.	−	297476.i	0.436291	−	0.755678i	−0.561109	−	0.827742i	$-0.689625\pi$
$173$	171748.	−	297476.i	0.436291	−	0.755678i	0.997400	+	0.0720636i	$0.0229585\pi$
$174$		0			0
$175$	−413827.	−	2232.79i	−1.02147	−	0.00551128i
$176$	406929.	+	234940.i	0.990231	+	0.571710i
$177$		0			0
$178$		−	147722.i		−	0.349458i
$179$	−231146.	−	133452.i	−0.539204	−	0.311310i	0.205552	−	0.978646i	$-0.434101\pi$
$179$	−231146.	−	133452.i	−0.539204	−	0.311310i	−0.744756	+	0.667337i	$0.767434\pi$
$180$		0			0
$181$			595254.i			1.35054i	0.737573	+	0.675268i	$0.235972\pi$
$181$			595254.i			1.35054i	−0.737573	+	0.675268i	$0.764028\pi$
$182$	51969.0	+	91145.1i	0.116296	+	0.203965i
$183$		0			0
$184$	723968.			1.57643
$185$	−147759.	−	255927.i	−0.317414	−	0.549776i
$186$		0			0
$187$	−768945.	−	443951.i	−1.60802	−	0.928391i
$188$	4251.10			0.00877216
$189$		0			0
$190$	−63745.2			−0.128104
$191$	51637.1	+	29812.7i	0.102419	+	0.0591314i	0.550334	−	0.834944i	$-0.314500\pi$
$191$	51637.1	+	29812.7i	0.102419	+	0.0591314i	−0.447916	+	0.894076i	$0.647834\pi$
$192$		0			0
$193$	249545.	+	432225.i	0.482232	+	0.835250i	0.999792	−	0.0203970i	$-0.00649301\pi$
$193$	249545.	+	432225.i	0.482232	+	0.835250i	−0.517560	+	0.855647i	$0.673160\pi$
$194$	−648432.			−1.23697
$195$		0			0
$196$	−11045.4	−	19617.0i	−0.0205371	−	0.0364747i
$197$		−	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	0.188951	−	0.981987i	$-0.439491\pi$
$199$	−316749.	−	182875.i	−0.566999	−	0.327357i	−0.755950	+	0.654629i	$0.772825\pi$
$200$			589290.i			1.04173i
$201$		0			0
$202$	−202481.	−	116903.i	−0.349146	−	0.201579i
$203$	900152.	−	513247.i	1.53312	−	0.874151i
$204$		0			0
$205$	−45786.5	+	79304.5i	−0.0760944	+	0.131799i
$206$	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	$0.00629832\pi$
$212$			47784.6i			0.0730211i
$213$		0			0
$214$	515511.			0.769491
$215$	−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
$220$	−44236.7	+	25540.1i	−0.0616206	+	0.0355767i
$221$	−234242.	+	135240.i	−0.322615	+	0.186262i
$222$		0			0
$223$	206408.	−	119169.i	0.277948	−	0.160473i	−0.354546	−	0.935039i	$-0.615365\pi$
$223$	206408.	−	119169.i	0.277948	−	0.160473i	0.632494	+	0.774565i	$0.282031\pi$
$224$	−54578.9	+	31119.7i	−0.0726782	+	0.0414396i
$225$		0			0
$226$	−398727.	−	690615.i	−0.519283	−	0.899425i
$227$	474180.			0.610771			0.305386	−	0.952229i	$-0.401215\pi$
$227$	474180.			0.610771			0.305386	+	0.952229i	$0.401215\pi$
$228$		0			0
$229$			1.05699e6i			1.33193i	0.745983	+	0.665964i	$0.231980\pi$
$229$			1.05699e6i			1.33193i	−0.745983	+	0.665964i	$0.768020\pi$
$230$	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	$-0.654469\pi$
$233$	54988.5	−	31747.6i	0.0663563	−	0.0383108i	0.532811	+	0.846234i	$0.321136\pi$
$234$		0			0
$235$	126122.	−	218450.i	0.148978	−	0.258038i
$236$	−21534.8	+	37299.4i	−0.0251687	+	0.0435935i
$237$		0			0
$238$	−1.15404e6	+	658010.i	−1.32062	+	0.752991i
$239$	−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
$241$			326623.i			0.362247i	0.983460	+	0.181123i	$0.0579734\pi$
$241$			326623.i			0.362247i	−0.983460	+	0.181123i	$0.942027\pi$
$242$	331596.	+	191447.i	0.363975	+	0.210141i
$243$		0			0
$244$		−	2700.28i		−	0.00290358i
$245$	−1.33575e6	−	14414.4i	−1.42171	−	0.0153420i
$246$		0			0
$247$	−21170.0			−0.0220790
$248$	−661610.	−	1.14594e6i	−0.683082	−	1.18313i
$249$		0			0
$250$	25584.3	+	14771.1i	0.0258895	+	0.0149473i
$251$	−275036.			−0.275554			−0.137777	−	0.990463i	$-0.543996\pi$
$251$	−275036.			−0.275554			−0.137777	+	0.990463i	$0.543996\pi$
$252$		0			0
$253$	1.88159e6			1.84809
$254$	190822.	+	110171.i	0.185586	+	0.107148i
$255$		0			0
$256$	65721.6	+	113833.i	0.0626770	+	0.108560i
$257$	545295.			0.514990			0.257495	−	0.966280i	$-0.417103\pi$
$257$	545295.			0.514990			0.257495	+	0.966280i	$0.417103\pi$
$258$		0			0
$259$	−238757.	−	418741.i	−0.221160	−	0.387879i
$260$			15560.4i			0.0142754i
$261$		0			0
$262$	−499803.	−	288562.i	−0.449828	−	0.259708i
$263$			143489.i			0.127918i	0.997953	+	0.0639588i	$0.0203726\pi$
$263$			143489.i			0.127918i	−0.997953	+	0.0639588i	$0.979627\pi$
$264$		0			0
$265$	2.45550e6	+	1.41768e6i	2.14795	+	1.24012i
$266$	−103974.	−	560.990i	−0.0900995	−	0.000486129i
$267$		0			0
$268$	−3896.15	+	6748.32i	−0.00331359	+	0.00573930i
$269$	−580604.	+	1.00564e6i	−0.489215	+	0.847345i	−0.999923	−	0.0124091i	$-0.996050\pi$
$269$	−580604.	+	1.00564e6i	−0.489215	+	0.847345i	0.510708	+	0.859754i	$0.329383\pi$
$270$		0			0
$271$	−32243.6	+	18615.8i	−0.0266698	+	0.0153978i	−0.513276	−	0.858224i	$-0.671568\pi$
$271$	−32243.6	+	18615.8i	−0.0266698	+	0.0153978i	0.486606	+	0.873622i	$0.338235\pi$
$272$	906183.	+	1.56956e6i	0.742666	+	1.28634i
$273$		0			0
$274$	1.05466e6	−	1.82672e6i	0.848664	−	1.46993i
$275$			1.53156e6i			1.22124i
$276$		0			0
$277$	591597.			0.463262			0.231631	−	0.972804i	$-0.425594\pi$
$277$	591597.			0.463262			0.231631	+	0.972804i	$0.425594\pi$
$278$	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
$283$	1.02803e6	−	593532.i	0.763025	−	0.440533i	−0.0673559	−	0.997729i	$-0.521456\pi$
$283$	1.02803e6	−	593532.i	0.763025	−	0.440533i	0.830381	+	0.557196i	$0.188123\pi$
$284$	−42914.8	+	24776.9i	−0.0315727	+	0.0182285i
$285$		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
$290$	−3.51759e6			−2.45612
$291$		0			0
$292$			30473.1i			0.0209151i
$293$	−96173.5	+	166577.i	−0.0654465	+	0.113357i	−0.896892	−	0.442250i	$-0.854180\pi$
$293$	−96173.5	+	166577.i	−0.0654465	+	0.113357i	0.831445	+	0.555606i	$0.187514\pi$
$294$		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
$299$	286592.	−	496392.i	0.185390	−	0.321105i
$300$		0			0
$301$	−265708.	−	466008.i	−0.169039	−	0.296467i
$302$	−1.62809e6	−	939978.i	−1.02721	−	0.593062i
$303$		0			0
$304$			141851.i			0.0880336i
$305$	−138759.	−	80112.3i	−0.0854103	−	0.0493117i
$306$		0			0
$307$		−	143609.i		−	0.0869634i	−0.999054	−	0.0434817i	$-0.986155\pi$
$307$		−	143609.i		−	0.0869634i	0.999054	−	0.0434817i	$-0.0138450\pi$
$308$	−72378.9	+	41268.9i	−0.0434746	+	0.0247883i
$309$		0			0
$310$	−3.15452e6			−1.86436
$311$	461364.	+	799106.i	0.270485	+	0.468494i	0.968986	−	0.247115i	$-0.0794827\pi$
$311$	461364.	+	799106.i	0.270485	+	0.468494i	−0.698501	+	0.715609i	$0.746149\pi$
$312$		0			0
$313$	−1.30000e6	−	750554.i	−0.750036	−	0.433033i	0.0756711	−	0.997133i	$-0.475890\pi$
$313$	−1.30000e6	−	750554.i	−0.750036	−	0.433033i	−0.825707	+	0.564099i	$0.809223\pi$
$314$	2.92216e6			1.67255
$315$		0			0
$316$	−50480.7			−0.0284386
$317$	−542861.	−	313421.i	−0.303418	−	0.175178i	0.340560	−	0.940223i	$-0.389384\pi$
$317$	−542861.	−	313421.i	−0.303418	−	0.175178i	−0.643977	+	0.765045i	$0.722717\pi$
$318$		0			0
$319$	−1.91743e6	−	3.32108e6i	−1.05497	−	1.82727i
$320$	2.70411e6			1.47622
$321$		0			0
$322$	1.42072e6	−	2.43038e6i	0.763606	−	1.30628i
$323$		−	268046.i		−	0.142956i
$324$		0			0
$325$	404049.	+	233278.i	0.212190	+	0.122508i
$326$		−	1.56525e6i		−	0.815716i
$327$		0			0
$328$	184199.	+	106347.i	0.0945371	+	0.0545810i
$329$	207640.	−	355203.i	0.105760	−	0.180920i
$330$		0			0
$331$	790203.	−	1.36867e6i	0.396432	−	0.686641i	−0.596851	−	0.802352i	$-0.703582\pi$
$331$	790203.	−	1.36867e6i	0.396432	−	0.686641i	0.993283	+	0.115712i	$0.0369149\pi$
$332$	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	$0.0524489\pi$
$338$			1.93763e6i			0.922529i
$339$		0			0
$340$	−197020.			−0.0924300
$341$	−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
$346$	−1.64718e6	+	951002.i	−0.739693	+	0.427062i
$347$	−2.38637e6	+	1.37777e6i	−1.06393	+	0.614261i	−0.926517	−	0.376252i	$-0.877213\pi$
$347$	−2.38637e6	+	1.37777e6i	−1.06393	+	0.614261i	−0.137415	+	0.990514i	$0.543879\pi$
$348$		0			0
$349$	−1.58554e6	+	915414.i	−0.696810	+	0.402304i	−0.806158	−	0.591700i	$-0.798457\pi$
$349$	−1.58554e6	+	915414.i	−0.696810	+	0.402304i	0.109348	+	0.994004i	$0.465124\pi$
$350$	1.97826e6	+	1.15643e6i	0.863205	+	0.504601i
$351$		0			0
$352$	116259.	+	201367.i	0.0500116	+	0.0866227i
$353$	−431303.			−0.184224			−0.0921119	−	0.995749i	$-0.529362\pi$
$353$	−431303.			−0.184224			−0.0921119	+	0.995749i	$0.529362\pi$
$354$		0			0
$355$			2.94034e6i			1.23830i
$356$	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	$-0.454540\pi$
$359$	2.61461e6	−	1.50955e6i	1.07071	−	0.618173i	0.928375	+	0.371646i	$0.121206\pi$
$360$		0			0
$361$	−1.22756e6	+	2.12620e6i	−0.495764	+	0.858688i
$362$	1.64802e6	−	2.85445e6i	0.660983	−	1.14486i
$363$		0			0
$364$	−136.940	+	25380.5i	−5.41722e−5	+	0.0100403i
$365$	1.56592e6	+	904083.i	0.615229	+	0.355202i
$366$		0			0
$367$			4.28183e6i			1.65945i	0.558172	+	0.829725i	$0.311503\pi$
$367$			4.28183e6i			1.65945i	−0.558172	+	0.829725i	$0.688497\pi$
$368$	−3.32610e6	−	1.92033e6i	−1.28031	−	0.739189i
$369$		0			0
$370$			1.63634e6i			0.621399i
$371$	3.99267e6	+	2.33398e6i	1.50601	+	0.880365i
$372$		0			0
$373$	−2.69700e6			−1.00371			−0.501856	−	0.864951i	$-0.667349\pi$
$373$	−2.69700e6			−1.00371			−0.501856	+	0.864951i	$0.667349\pi$
$374$	2.45824e6	+	4.25780e6i	0.908752	+	1.57400i
$375$		0			0
$376$	−507389.	−	292941.i	−0.185085	−	0.106859i
$377$	−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	$0.471706\pi$
$380$	−13354.5	−	7710.22i	−0.00474426	−	0.00273910i
$381$		0			0
$382$	−165079.	−	285925.i	−0.0578806	−	0.100252i
$383$	−2.96357e6			−1.03233			−0.516164	−	0.856490i	$-0.672640\pi$
$383$	−2.96357e6			−1.03233			−0.516164	+	0.856490i	$0.672640\pi$
$384$		0			0
$385$	−26673.6	+	4.94370e6i	−0.00917126	+	1.69981i
$386$		−	2.76356e6i		−	0.944062i
$387$		0			0
$388$	−135845.	−	78430.2i	−0.0458105	−	0.0264487i
$389$		−	5.52551e6i		−	1.85139i	−0.378269	−	0.925696i	$-0.623481\pi$
$389$		−	5.52551e6i		−	1.85139i	0.378269	−	0.925696i	$-0.376519\pi$
$390$		0			0
$391$	6.28511e6	+	3.62871e6i	2.07908	+	1.20036i
$392$	−33480.0	+	3.10251e6i	−0.0110045	+	1.01976i
$393$		0			0
$394$	−2.06473e6	+	3.57621e6i	−0.670073	+	1.16060i
$395$	−1.49767e6	+	2.59404e6i	−0.482974	+	0.836535i
$396$		0			0
$397$	3.36326e6	−	1.94178e6i	1.07099	−	0.618334i	0.142535	−	0.989790i	$-0.454475\pi$
$397$	3.36326e6	−	1.94178e6i	1.07099	−	0.618334i	0.928451	+	0.371456i	$0.121141\pi$
$398$	1.01261e6	+	1.75390e6i	0.320433	+	0.555005i
$399$		0			0
$400$	1.56309e6	−	2.70735e6i	0.488466	−	0.846048i
$401$			877790.i			0.272602i	0.990667	+	0.136301i	$0.0435215\pi$
$401$			877790.i			0.272602i	−0.990667	+	0.136301i	$0.956478\pi$
$402$		0			0
$403$	−1.04763e6			−0.321325
$404$	−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
$409$	−99835.5	+	57640.1i	−0.0295105	+	0.0170379i	−0.514683	−	0.857381i	$-0.672090\pi$
$409$	−99835.5	+	57640.1i	−0.0295105	+	0.0170379i	0.485172	+	0.874419i	$0.338757\pi$
$410$	439124.	−	253529.i	0.129011	−	0.0744847i
$411$		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
$416$	70831.7			0.0200675
$417$		0			0
$418$			384805.i			0.107721i
$419$	2.12049e6	−	3.67280e6i	0.590067	−	1.02203i	−0.404156	−	0.914690i	$-0.632435\pi$
$419$	2.12049e6	−	3.67280e6i	0.590067	−	1.02203i	0.994223	−	0.107336i	$-0.0342321\pi$
$420$		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
$425$	−2.95367e6	+	5.11590e6i	−0.793212	+	1.37388i
$426$		0			0
$427$	−225623.	−	131892.i	−0.0598845	−	0.0350065i
$428$	107999.	+	62353.0i	0.0284976	+	0.0164531i
$429$		0			0
$430$			1.82105e6i			0.474954i
$431$	3.72342e6	+	2.14972e6i	0.965493	+	0.557427i	0.897859	−	0.440283i	$-0.145122\pi$
$431$	3.72342e6	+	2.14972e6i	0.965493	+	0.557427i	0.0676334	+	0.997710i	$0.478455\pi$
$432$		0			0
$433$			934052.i			0.239415i	0.992809	+	0.119707i	$0.0381957\pi$
$433$			934052.i			0.239415i	−0.992809	+	0.119707i	$0.961804\pi$
$434$	−5.14531e6	−	27761.4i	−1.31126	−	0.00707484i
$435$		0			0
$436$	−68942.7			−0.0173689
$437$	284013.	+	491925.i	0.0711435	+	0.123224i
$438$		0			0
$439$	14429.3	+	8330.76i	0.00357342	+	0.00206311i	0.501786	−	0.864992i	$-0.332677\pi$
$439$	14429.3	+	8330.76i	0.00357342	+	0.00206311i	−0.498212	+	0.867055i	$0.666010\pi$
$440$	7.03982e6			1.73352
$441$		0			0
$442$	1.49770e6			0.364644
$443$	−184833.	−	106714.i	−0.0447477	−	0.0258351i	0.477459	−	0.878654i	$-0.341558\pi$
$443$	−184833.	−	106714.i	−0.0447477	−	0.0258351i	−0.522207	+	0.852819i	$0.674891\pi$
$444$		0			0
$445$	−1.06019e6	−	1.83631e6i	−0.253796	−	0.439588i
$446$	−1.31973e6			−0.314158
$447$		0			0
$448$	4.41066e6	+	23797.6i	1.03827	+	0.00560193i
$449$		−	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
$452$		−	192910.i		−	0.0444129i
$453$		0			0
$454$	−2.27386e6	−	1.31281e6i	−0.517754	−	0.298926i
$455$	1.30016e6	+	760031.i	0.294421	+	0.172109i
$456$		0			0
$457$	1.53978e6	−	2.66698e6i	0.344880	−	0.597350i	−0.640452	−	0.767998i	$-0.721253\pi$
$457$	1.53978e6	−	2.66698e6i	0.344880	−	0.597350i	0.985332	+	0.170648i	$0.0545862\pi$
$458$	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	$-0.781904\pi$
$461$	−4.26724e6	−	7.39108e6i	−0.935180	−	1.61978i	−0.160868	−	0.986976i	$-0.551429\pi$
$462$		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	$0.260750\pi$
$464$			7.82763e6i			1.68785i
$465$		0			0
$466$	−351586.			−0.0750009
$467$	4.62740e6	+	8.01489e6i	0.981849	+	1.70061i	0.655178	+	0.755475i	$0.272594\pi$
$467$	4.62740e6	+	8.01489e6i	0.981849	+	1.70061i	0.326671	+	0.945138i	$0.394073\pi$
$468$		0			0
$469$	373557.	+	655159.i	0.0784197	+	0.137535i
$470$	−1.20960e6	+	698364.i	−0.252579	+	0.145827i
$471$		0			0
$472$	5.14058e6	−	2.96791e6i	1.06208	−	0.613192i
$473$	−1.71932e6	+	992650.i	−0.353349	+	0.204006i
$474$		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
$479$	3.12554e6			0.622425			0.311212	−	0.950340i	$-0.399265\pi$
$479$	3.12554e6			0.622425			0.311212	+	0.950340i	$0.399265\pi$
$480$		0			0
$481$			543436.i			0.107099i
$482$	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	−0.660408	−	0.750907i	$-0.729617\pi$
$487$	1.67536e6	−	2.90182e6i	0.320101	−	0.554431i	0.980509	+	0.196476i	$0.0629499\pi$
$488$	−186075.	+	322291.i	−0.0353703	+	0.0612631i
$489$		0			0
$490$	6.36547e6	+	3.76727e6i	1.19768	+	0.708821i
$491$	−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
$493$		−	1.47913e7i		−	2.74088i
$494$	101518.	+	58611.2i	0.0187165	+	0.0108060i
$495$		0			0
$496$			7.01969e6i			1.28119i
$497$	−25876.5	+	4.79597e6i	−0.00469910	+	0.870934i
$498$		0			0
$499$	−6.57897e6			−1.18279			−0.591394	−	0.806383i	$-0.701422\pi$
$499$	−6.57897e6			−1.18279			−0.591394	+	0.806383i	$0.701422\pi$
$500$	3573.24	+	6189.04i	0.000639201	+	0.00110713i
$501$		0			0
$502$	1.31890e6	+	761465.i	0.233588	+	0.134862i
$503$	9.18844e6			1.61928			0.809639	−	0.586927i	$-0.199663\pi$
$503$	9.18844e6			1.61928			0.809639	+	0.586927i	$0.199663\pi$
$504$		0			0
$505$	−3.35602e6			−0.585593
$506$	−9.02286e6	−	5.20935e6i	−1.56664	−	0.904498i
$507$		0			0
$508$	26651.2	+	46161.3i	0.00458203	+	0.00793631i
$509$	−3.27484e6			−0.560268			−0.280134	−	0.959961i	$-0.590379\pi$
$509$	−3.27484e6			−0.560268			−0.280134	+	0.959961i	$0.590379\pi$
$510$		0			0
$511$	2.54620e6	+	1.48842e6i	0.431361	+	0.252159i
$512$		−	6.26001e6i		−	1.05536i
$513$		0			0
$514$	−2.61488e6	−	1.50970e6i	−0.436560	−	0.252048i
$515$		−	4.25957e6i		−	0.707697i
$516$		0			0
$517$	−1.31870e6	−	761352.i	−0.216980	−	0.125273i
$518$	−14400.7	+	2.66903e6i	−0.00235808	+	0.437048i
$519$		0			0
$520$	1.07226e6	−	1.85722e6i	0.173898	−	0.301199i
$521$	2.81270e6	−	4.87174e6i	0.453972	−	0.786303i	−0.544656	−	0.838659i	$-0.683340\pi$
$521$	2.81270e6	−	4.87174e6i	0.453972	−	0.786303i	0.998628	+	0.0523564i	$0.0166732\pi$
$522$		0			0
$523$	−713512.	+	411946.i	−0.114064	+	0.0658546i	−0.555946	−	0.831218i	$-0.687644\pi$
$523$	−713512.	+	411946.i	−0.114064	+	0.0658546i	0.441883	+	0.897073i	$0.354311\pi$
$524$	−69805.2	−	120906.i	−0.0111061	−	0.0192362i
$525$		0			0
$526$	397264.	−	688082.i	0.0626059	−	0.108437i
$527$		−	1.32646e7i		−	2.08050i
$528$		0			0
$529$	−8.94313e6			−1.38947
$530$	−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
$535$	6.40824e6	−	3.69980e6i	0.967953	−	0.558848i
$536$	930048.	−	536964.i	0.139828	−	0.0807296i
$537$		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	0.999934	−	0.0114768i	$-0.00365325\pi$
$541$	3.33591e6	+	5.77796e6i	0.490028	+	0.848753i	−0.509906	+	0.860230i	$0.670320\pi$
$542$	206159.			0.0301442
$543$		0			0
$544$			896842.i			0.129933i
$545$	−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
$551$	578847.	−	1.00259e6i	0.0812240	−	0.140684i
$552$		0			0
$553$	−2.46567e6	+	4.21794e6i	−0.342864	+	0.586527i
$554$	−2.83691e6	−	1.63789e6i	−0.392710	−	0.226731i
$555$		0			0
$556$			209373.i			0.0287233i
$557$	1.67738e6	+	968437.i	0.229084	+	0.132261i	0.610149	−	0.792287i	$-0.291109\pi$
$557$	1.67738e6	+	968437.i	0.229084	+	0.132261i	−0.381066	+	0.924548i	$0.624443\pi$
$558$		0			0
$559$			604779.i			0.0818591i
$560$	5.09264e6	−	8.71182e6i	0.686235	−	1.17392i
$561$		0			0
$562$	−1.19080e7			−1.59038
$563$	4.60297e6	+	7.97257e6i	0.612022	+	1.06005i	0.990899	+	0.134606i	$0.0429769\pi$
$563$	4.60297e6	+	7.97257e6i	0.612022	+	1.06005i	−0.378877	+	0.925447i	$0.623690\pi$
$564$		0			0
$565$	−9.91303e6	−	5.72329e6i	−1.30643	−	0.754266i
$566$	−6.57300e6			−0.862428
$567$		0			0
$568$	6.82946e6			0.888209
$569$	−2.42314e6	−	1.39900e6i	−0.313761	−	0.181150i	0.334847	−	0.942272i	$-0.391315\pi$
$569$	−2.42314e6	−	1.39900e6i	−0.313761	−	0.181150i	−0.648608	+	0.761123i	$0.724649\pi$
$570$		0			0
$571$	1.04914e6	+	1.81717e6i	0.134662	+	0.233241i	0.925468	−	0.378825i	$-0.123672\pi$
$571$	1.04914e6	+	1.81717e6i	0.134662	+	0.233241i	−0.790806	+	0.612067i	$0.790338\pi$
$572$	93932.4			0.0120040
$573$		0			0
$574$	718484.	−	409664.i	0.0910202	−	0.0518978i
$575$		−	1.25185e7i		−	1.57900i
$576$		0			0
$577$	−4.91428e6	−	2.83726e6i	−0.614498	−	0.354780i	0.160226	−	0.987080i	$-0.448778\pi$
$577$	−4.91428e6	−	2.83726e6i	−0.614498	−	0.354780i	−0.774724	+	0.632300i	$0.782111\pi$
$578$			1.11012e7i			1.38214i
$579$		0			0
$580$	−736928.	−	425465.i	−0.0909609	−	0.0525163i
$581$	−4.63897e6	−	8.13600e6i	−0.570140	−	0.999932i
$582$		0			0
$583$	8.55800e6	−	1.48229e7i	1.04280	−	1.80618i
$584$	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	$0.0620846\pi$
$587$	5.49618e6	+	9.51967e6i	0.658364	+	1.14032i	−0.322675	+	0.946510i	$0.604582\pi$
$588$		0			0
$589$	519100.	−	899108.i	0.0616543	−	0.106788i
$590$		−	1.41508e7i		−	1.67360i
$591$		0			0
$592$	3.64133e6			0.427027
$593$	1.75523e6	+	3.04015e6i	0.204974	+	0.355025i	0.950124	−	0.311871i	$-0.100956\pi$
$593$	1.75523e6	+	3.04015e6i	0.204974	+	0.355025i	−0.745151	+	0.666896i	$0.767622\pi$
$594$		0			0
$595$	−9.62321e6	+	1.64621e7i	−1.11437	+	1.90631i
$596$	−370841.	+	214105.i	−0.0427634	+	0.0246895i
$597$		0			0
$598$	−2.74862e6	+	1.58692e6i	−0.314312	+	0.181468i
$599$	8.76531e6	−	5.06065e6i	0.998160	−	0.576288i	0.0904565	−	0.995900i	$-0.471167\pi$
$599$	8.76531e6	−	5.06065e6i	0.998160	−	0.576288i	0.907703	+	0.419613i	$0.137834\pi$
$600$		0			0
$601$	−8.56347e6	+	4.94412e6i	−0.967082	+	0.558345i	−0.898346	−	0.439290i	$-0.855230\pi$
$601$	−8.56347e6	+	4.94412e6i	−0.967082	+	0.558345i	−0.0687369	+	0.997635i	$0.521897\pi$
$602$	−16026.2	+	2.97031e6i	−0.00180235	+	0.334049i
$603$		0			0
$604$	−227388.	−	393847.i	−0.0253615	−	0.0439274i
$605$	5.49603e6			0.610465
$606$		0			0
$607$		−	1.03088e7i		−	1.13563i	−0.823155	−	0.567817i	$-0.807788\pi$
$607$		−	1.03088e7i		−	1.13563i	0.823155	−	0.567817i	$-0.192212\pi$
$608$	−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	−0.584185	−	0.811621i	$-0.698586\pi$
$613$	3.82185e6	−	6.61963e6i	0.410792	−	0.711513i	0.994977	+	0.100108i	$0.0319189\pi$
$614$	−397596.	+	688656.i	−0.0425619	+	0.0737194i
$615$		0			0
$616$	1.14826e7	+	61954.1i	1.21924	+	0.00657836i
$617$	−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
$619$			3.79478e6i			0.398071i	0.979992	+	0.199035i	$0.0637808\pi$
$619$			3.79478e6i			0.398071i	−0.979992	+	0.199035i	$0.936219\pi$
$620$	−660865.	−	381551.i	−0.0690452	−	0.0398633i
$621$		0			0
$622$		−	5.10933e6i		−	0.529527i
$623$	−1.71311e6	−	3.00452e6i	−0.176834	−	0.310138i
$624$		0			0
$625$	−9.55135e6			−0.978058
$626$	4.15596e6	+	7.19834e6i	0.423873	+	0.734170i
$627$		0			0
$628$	612186.	+	353446.i	0.0619418	+	0.0357621i
$629$	−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	$0.511197\pi$
$632$	6.02512e6	+	3.47860e6i	0.600030	+	0.346427i
$633$		0			0
$634$	1.73547e6	+	3.00593e6i	0.171473	+	0.296999i
$635$	3.16277e6			0.311268
$636$		0			0
$637$	2.11400e6	+	1.25112e6i	0.206422	+	0.122166i
$638$			2.12343e7i			2.06532i
$639$		0			0
$640$	−1.18997e7	−	6.87031e6i	−1.14838	−	0.663020i
$641$		−	1.16042e7i		−	1.11550i	−0.830010	−	0.557748i	$-0.811665\pi$
$641$		−	1.16042e7i		−	1.11550i	0.830010	−	0.557748i	$-0.188335\pi$
$642$		0			0
$643$	1.76238e7	+	1.01751e7i	1.68102	+	0.970536i	0.960987	+	0.276593i	$0.0892055\pi$
$643$	1.76238e7	+	1.01751e7i	1.68102	+	0.970536i	0.720030	+	0.693942i	$0.244128\pi$
$644$	591602.	−	337319.i	0.0562102	−	0.0320499i
$645$		0			0
$646$	−742112.	+	1.28537e6i	−0.0699661	+	0.121185i
$647$	−6.92241e6	+	1.19900e7i	−0.650124	+	1.12605i	0.332968	+	0.942938i	$0.391950\pi$
$647$	−6.92241e6	+	1.19900e7i	−0.650124	+	1.12605i	−0.983092	+	0.183110i	$0.941383\pi$
$648$		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
$653$			1.56886e7i			1.43980i	0.694079	+	0.719899i	$0.255812\pi$
$653$			1.56886e7i			1.43980i	−0.694079	+	0.719899i	$0.744188\pi$
$654$		0			0
$655$	−8.28397e6			−0.754459
$656$	−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
$661$	−8.05807e6	+	4.65233e6i	−0.717344	+	0.414159i	−0.813774	−	0.581181i	$-0.802591\pi$
$661$	−8.05807e6	+	4.65233e6i	−0.717344	+	0.414159i	0.0964304	+	0.995340i	$0.469257\pi$
$662$	−7.57860e6	+	4.37551e6i	−0.672116	+	0.388046i
$663$		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
$668$	102261.			0.00886688
$669$		0			0
$670$		−	2.56021e6i		−	0.220338i
$671$	−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
$677$	−8.38482e6	+	1.45229e7i	−0.703108	+	1.21782i	0.264262	+	0.964451i	$0.414872\pi$
$677$	−8.38482e6	+	1.45229e7i	−0.703108	+	1.21782i	−0.967370	+	0.253368i	$0.918462\pi$
$678$		0			0
$679$	−1.31885e7	+	7.51979e6i	−1.09779	+	0.625938i
$680$	2.35153e7	+	1.35766e7i	1.95020	+	1.12595i
$681$		0			0
$682$			1.90426e7i			1.56771i
$683$	−1.88932e6	−	1.09080e6i	−0.154972	−	0.0894732i	0.420509	−	0.907289i	$-0.361852\pi$
$683$	−1.88932e6	−	1.09080e6i	−0.154972	−	0.0894732i	−0.575481	+	0.817815i	$0.695185\pi$
$684$		0			0
$685$		−	3.02770e7i		−	2.46539i
$686$	1.03495e7	+	6.20079e6i	0.839674	+	0.503080i
$687$		0			0
$688$	4.05236e6			0.326390
$689$	−2.60701e6	−	4.51547e6i	−0.209216	−	0.362372i
$690$		0			0
$691$	1.43225e7	+	8.26913e6i	1.14110	+	0.658817i	0.946704	−	0.322106i	$-0.104391\pi$
$691$	1.43225e7	+	8.26913e6i	1.14110	+	0.658817i	0.194400	+	0.980922i	$0.437724\pi$
$692$	−460109.			−0.0365254
$693$		0			0
$694$	1.52580e7			1.20254
$695$	1.07590e7	+	6.21172e6i	0.844910	+	0.487809i
$696$		0			0
$697$	1.06608e6	+	1.84650e6i	0.0831203	+	0.143969i
$698$	1.01376e7			0.787587
$699$		0			0
$700$	274568.	+	481548.i	0.0211790	+	0.0371445i
$701$			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
$704$		−	1.63237e7i		−	1.24133i
$705$		0			0
$706$	2.06825e6	+	1.19410e6i	0.156168	+	0.0901634i
$707$	−5.47398e6	−	29534.7i	−0.411865	−	0.00222221i
$708$		0			0
$709$	4.86400e6	−	8.42470e6i	0.363394	−	0.629417i	−0.625123	−	0.780526i	$-0.714951\pi$
$709$	4.86400e6	−	8.42470e6i	0.363394	−	0.629417i	0.988517	+	0.151109i	$0.0482845\pi$
$710$	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
$716$			357515.i			0.0260622i
$717$		0			0
$718$	−1.67173e7			−1.21019
$719$	9.35471e6	+	1.62028e7i	0.674852	+	1.16888i	0.976512	+	0.215462i	$0.0691257\pi$
$719$	9.35471e6	+	1.62028e7i	0.674852	+	1.16888i	−0.301661	+	0.953415i	$0.597541\pi$
$720$		0			0
$721$	37486.4	−	6.94776e6i	0.00268556	−	0.497745i
$722$	1.17732e7	−	6.79724e6i	0.840524	−	0.485277i
$723$		0			0
$724$	690513.	−	398668.i	0.0489582	−	0.0282660i
$725$	−2.20956e7	+	1.27569e7i	−1.56121	+	0.901365i
$726$		0			0
$727$	3.50717e6	−	2.02487e6i	0.246105	−	0.142089i	−0.371874	−	0.928283i	$-0.621285\pi$
$727$	3.50717e6	−	2.02487e6i	0.246105	−	0.142089i	0.617980	+	0.786194i	$0.287951\pi$
$728$	1.76531e6	−	3.01986e6i	0.123450	−	0.211182i
$729$		0			0
$730$	−5.00608e6	−	8.67078e6i	−0.347689	−	0.602215i
$731$	−7.65746e6			−0.530019
$732$		0			0
$733$			2.28530e7i			1.57103i	0.618846	+	0.785513i	$0.287601\pi$
$733$			2.28530e7i			1.57103i	−0.618846	+	0.785513i	$0.712399\pi$
$734$	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	0.409639	+	0.912248i	$0.365655\pi$
$739$	−8.68806e6	+	1.50482e7i	−0.585210	+	1.01361i	−0.994849	+	0.101366i	$0.967679\pi$
$740$	−197922.	+	342811.i	−0.0132866	+	0.0230131i
$741$		0			0
$742$	−1.26844e7	−	2.22464e7i	−0.845785	−	1.48337i
$743$	−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
$745$			2.54085e7i			1.67721i
$746$	1.29331e7	+	7.46691e6i	0.850852	+	0.491240i
$747$		0			0
$748$			1.18933e6i			0.0777230i
$749$	1.04850e7	−	5.97832e6i	0.682911	−	0.389381i
$750$		0			0
$751$	−6.12842e6			−0.396505			−0.198253	−	0.980151i	$-0.563527\pi$
$751$	−6.12842e6			−0.396505			−0.198253	+	0.980151i	$0.563527\pi$
$752$	1.55406e6	+	2.69170e6i	0.100213	+	0.173573i
$753$		0			0
$754$	5.60195e6	+	3.23429e6i	0.358848	+	0.207181i
$755$	−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	$0.910170\pi$
$758$	−2.38082e6	−	1.37457e6i	−0.150506	−	0.0868945i
$759$		0			0
$760$	1.06262e6	+	1.84050e6i	0.0667333	+	0.115585i
$761$	6.68961e6			0.418735			0.209367	−	0.977837i	$-0.432860\pi$
$761$	6.68961e6			0.418735			0.209367	+	0.977837i	$0.432860\pi$
$762$		0			0
$763$	−3.36743e6	+	5.76055e6i	−0.209405	+	0.358222i
$764$		−	79867.6i		−	0.00495036i
$765$		0			0
$766$	1.42113e7	+	8.20492e6i	0.875111	+	0.505245i
$767$		−	4.69954e6i		−	0.288448i
$768$		0			0
$769$	−2.00338e7	−	1.15665e7i	−1.22165	−	0.705320i	−0.256380	−	0.966576i	$-0.582530\pi$
$769$	−2.00338e7	−	1.15665e7i	−1.22165	−	0.705320i	−0.965270	+	0.261256i	$0.915863\pi$
$770$	1.38150e7	−	2.36329e7i	0.839700	−	1.43645i
$771$		0			0
$772$	334263.	−	578960.i	0.0201857	−	0.0349627i
$773$	−1.14151e7	+	1.97715e7i	−0.687117	+	1.19012i	0.285650	+	0.958334i	$0.407791\pi$
$773$	−1.14151e7	+	1.97715e7i	−0.687117	+	1.19012i	−0.972767	+	0.231787i	$0.925543\pi$
$774$		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
$779$			166880.i			0.00985285i
$780$		0			0
$781$	1.77497e7			1.04127
$782$	−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
$787$	1.41056e7	−	8.14388e6i	0.811811	−	0.468699i	−0.0357733	−	0.999360i	$-0.511389\pi$
$787$	1.41056e7	−	8.14388e6i	0.811811	−	0.468699i	0.847584	+	0.530661i	$0.178056\pi$
$788$	−865112.	+	499473.i	−0.0496314	+	0.0286547i
$789$		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
$794$	−2.15040e7			−1.21051
$795$		0			0
$796$			489918.i			0.0274057i
$797$	1.14270e7	−	1.97921e7i	0.637214	−	1.10369i	−0.348828	−	0.937187i	$-0.613420\pi$
$797$	1.14270e7	−	1.97921e7i	0.637214	−	1.10369i	0.986041	−	0.166500i	$-0.0532465\pi$
$798$		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
$803$	5.45760e6	−	9.45284e6i	0.298684	−	0.517337i
$804$		0			0
$805$	218021.	−	4.04082e7i	0.0118579	−	2.19776i
$806$	5.02374e6	+	2.90046e6i	0.272389	+	0.157264i
$807$		0			0
$808$			7.79495e6i			0.420035i
$809$	−1.49420e7	−	8.62678e6i	−0.802672	−	0.463423i	0.0417326	−	0.999129i	$-0.486712\pi$
$809$	−1.49420e7	−	8.62678e6i	−0.802672	−	0.463423i	−0.844405	+	0.535706i	$0.820046\pi$
$810$		0			0
$811$			2.87277e7i			1.53373i	0.641809	+	0.766865i	$0.278184\pi$
$811$			2.87277e7i			1.53373i	−0.641809	+	0.766865i	$0.721816\pi$
$812$	−1.19825e6	−	700459.i	−0.0637762	−	0.0372815i
$813$		0			0
$814$	9.87798e6			0.522525
$815$	−1.12337e7	−	1.94573e7i	−0.592419	−	1.02610i
$816$		0			0
$817$	−519041.	−	299668.i	−0.0272049	−	0.0157067i
$818$	638328.			0.0333550
$819$		0			0
$820$	122661.			0.00637047
$821$	1.93219e7	+	1.11555e7i	1.00044	+	0.577606i	0.908379	−	0.418148i	$-0.137321\pi$
$821$	1.93219e7	+	1.11555e7i	1.00044	+	0.577606i	0.0920631	+	0.995753i	$0.470654\pi$
$822$		0			0
$823$	1.36567e7	+	2.36540e7i	0.702821	+	1.21732i	0.967472	+	0.252978i	$0.0814099\pi$
$823$	1.36567e7	+	2.36540e7i	0.702821	+	1.21732i	−0.264651	+	0.964344i	$0.585257\pi$
$824$	−9.89360e6			−0.507617
$825$		0			0
$826$	124535.	−	2.30813e7i	0.00635097	−	1.17709i
$827$			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	0.293141	−	0.956069i	$-0.405299\pi$
$829$	−7.68278e6	−	4.43565e6i	−0.388268	−	0.224167i	−0.681410	+	0.731902i	$0.738633\pi$
$830$			3.17936e7i			1.60194i
$831$		0			0
$832$	−4.30644e6	−	2.48633e6i	−0.215680	−	0.124523i
$833$	−1.58412e7	+	2.67666e7i	−0.791000	+	1.33654i
$834$		0			0
$835$	3.03391e6	−	5.25489e6i	0.150587	−	0.260824i
$836$	−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	$-0.973228\pi$
$839$	−1.16421e7	−	2.01647e7i	−0.570986	−	0.988976i	0.425479	−	0.904968i	$-0.360106\pi$
$840$		0			0
$841$	2.16864e7	−	3.75619e7i	1.05730	−	1.83129i
$842$			9.44755e6i			0.459239i
$843$		0			0
$844$	−836398.			−0.0404163
$845$	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
$850$	2.83277e7	−	1.63550e7i	1.34482	−	0.776433i
$851$	1.26278e7	−	7.29064e6i	0.597727	−	0.345098i
$852$		0			0
$853$	−3.57837e6	+	2.06597e6i	−0.168388	+	0.0972191i	−0.581826	−	0.813314i	$-0.697661\pi$
$853$	−3.57837e6	+	2.06597e6i	−0.168388	+	0.0972191i	0.413437	+	0.910533i	$0.364328\pi$
$854$	716787.	+	1.25713e6i	0.0336315	+	0.0589841i
$855$		0			0
$856$	−8.59344e6	−	1.48843e7i	−0.400851	−	0.694294i
$857$	−1.69103e7			−0.786501			−0.393250	−	0.919431i	$-0.628649\pi$
$857$	−1.69103e7			−0.786501			−0.393250	+	0.919431i	$0.628649\pi$
$858$		0			0
$859$		−	4.12602e7i		−	1.90787i	−0.300015	−	0.953935i	$-0.596992\pi$
$859$		−	4.12602e7i		−	1.90787i	0.300015	−	0.953935i	$-0.403008\pi$
$860$	−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	$-0.528108\pi$
$863$	1.59796e7	−	9.22585e6i	0.730365	−	0.421677i	0.818556	+	0.574427i	$0.194775\pi$
$864$		0			0
$865$	−1.36506e7	+	2.36435e7i	−0.620313	+	1.07441i
$866$	2.58601e6	−	4.47911e6i	0.117175	−	0.202954i
$867$		0			0
$868$	−1.07458e6	−	628161.i	−0.0484103	−	0.0282990i
$869$	1.56592e7	+	9.04085e6i	0.703430	+	0.406125i
$870$		0			0
$871$		−	850256.i		−	0.0379756i
$872$	8.22866e6	+	4.75082e6i	0.366469	+	0.211581i
$873$		0			0
$874$		−	3.14527e6i		−	0.139277i
$875$	691660.	+	3731.83i	0.0305402	+	0.000164779i
$876$		0			0
$877$	2.26023e7			0.992324			0.496162	−	0.868230i	$-0.334742\pi$
$877$	2.26023e7			0.992324			0.496162	+	0.868230i	$0.334742\pi$
$878$	−46129.0	−	79897.8i	−0.00201947	−	0.00349783i
$879$		0			0
$880$	−3.23428e7	−	1.86731e7i	−1.40790	−	0.812851i
$881$	−3.26814e7			−1.41860			−0.709301	−	0.704906i	$-0.750989\pi$
$881$	−3.26814e7			−1.41860			−0.709301	+	0.704906i	$0.750989\pi$
$882$		0			0
$883$	−1.87005e7			−0.807145			−0.403573	−	0.914948i	$-0.632232\pi$
$883$	−1.87005e7			−0.807145			−0.403573	+	0.914948i	$0.632232\pi$
$884$	313765.	+	181152.i	0.0135044	+	0.00779674i
$885$		0			0
$886$	590894.	+	1.02346e6i	0.0252886	+	0.0438012i
$887$	1.53702e7			0.655948			0.327974	−	0.944687i	$-0.393634\pi$
$887$	1.53702e7			0.655948			0.327974	+	0.944687i	$0.393634\pi$
$888$		0			0
$889$	5.15878e6	+	27834.0i	0.218924	+	0.00118120i
$890$			1.17410e7i			0.496855i
$891$		0			0
$892$	−276480.	−	159626.i	−0.0116346	−	0.00671725i
$893$		−	459685.i		−	0.0192900i
$894$		0			0
$895$	1.83715e7	+	1.06068e7i	0.766634	+	0.442616i
$896$	−1.93491e7	−	1.13108e7i	−0.805176	−	0.470679i
$897$		0			0
$898$	−1.24342e7	+	2.15367e7i	−0.514550	+	0.891227i
$899$	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
$905$		−	4.73110e7i		−	1.92017i
$906$		0			0
$907$	1.39382e7			0.562586			0.281293	−	0.959622i	$-0.409237\pi$
$907$	1.39382e7			0.562586			0.281293	+	0.959622i	$0.409237\pi$
$908$	−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
$913$	−3.00175e7	+	1.73306e7i	−1.19178	+	0.688077i
$914$	−1.47676e7	+	8.52606e6i	−0.584714	+	0.337585i
$915$		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	0.806244	−	0.591583i	$-0.201497\pi$
$919$	−2.79593e6	−	4.84269e6i	−0.109204	−	0.189146i	−0.915448	+	0.402437i	$0.868163\pi$
$920$	−5.75412e7			−2.24135
$921$		0			0
$922$			4.72571e7i			1.83080i
$923$	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
$929$	1.24097e7	−	2.14942e7i	0.471759	−	0.817111i	−0.527719	−	0.849419i	$-0.676952\pi$
$929$	1.24097e7	−	2.14942e7i	0.471759	−	0.817111i	0.999478	+	0.0323082i	$0.0102858\pi$
$930$		0			0
$931$	−2.12125e6	+	1.19437e6i	−0.0802078	+	0.0451611i
$932$	−73656.5	−	42525.6i	−0.00277761	−	0.00160365i
$933$		0			0
$934$		−	5.12456e7i		−	1.92216i
$935$	6.11160e7	+	3.52854e7i	2.28626	+	1.31997i
$936$		0			0
$937$		−	2.89174e7i		−	1.07600i	−0.842946	−	0.537998i	$-0.819181\pi$
$937$		−	2.89174e7i		−	1.07600i	0.842946	−	0.537998i	$-0.180819\pi$
$938$	22531.2	−	4.17594e6i	0.000836136	−	0.154970i
$939$		0			0
$940$	−337879.			−0.0124721
$941$	−5.41851e6	−	9.38514e6i	−0.199483	−	0.345515i	0.748878	−	0.662708i	$-0.230593\pi$
$941$	−5.41851e6	−	9.38514e6i	−0.199483	−	0.345515i	−0.948361	+	0.317193i	$0.897260\pi$
$942$		0			0
$943$	−3.91299e6	−	2.25917e6i	−0.143295	−	0.0827311i
$944$	−3.14896e7			−1.15010
$945$		0			0
$946$	1.09930e7			0.399382
$947$	3.11682e7	+	1.79949e7i	1.12937	+	0.652042i	0.943776	−	0.330585i	$-0.107246\pi$
$947$	3.11682e7	+	1.79949e7i	1.12937	+	0.652042i	0.185594	+	0.982627i	$0.440579\pi$
$948$		0			0
$949$	−1.66254e6	−	2.87960e6i	−0.0599247	−	0.103793i
$950$	2.56016e6			0.0920362
$951$		0			0
$952$	3.82362e7	+	2.23516e7i	1.36736	+	0.799312i
$953$			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
$956$			1.90609e6i			0.0674526i
$957$		0			0
$958$	−1.49881e7	−	8.65337e6i	−0.527633	−	0.304629i
$959$	266453.	−	4.93846e7i	0.00935565	−	1.73398i
$960$		0			0
$961$	1.13738e7	−	1.97000e7i	0.397281	−	0.688111i
$962$	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	$0.100896\pi$
$968$		−	1.27655e7i		−	0.437875i
$969$		0			0
$970$	5.15376e7			1.75871
$971$	−1.88112e7	−	3.25820e7i	−0.640279	−	1.10900i	−0.985370	−	0.170427i	$-0.945485\pi$
$971$	−1.88112e7	−	3.25820e7i	−0.640279	−	1.10900i	0.345091	−	0.938569i	$-0.387848\pi$
$972$		0			0
$973$	1.74943e7	+	1.02266e7i	0.592399	+	0.346297i
$974$	−1.60679e7	+	9.27682e6i	−0.542703	+	0.313330i
$975$		0			0
$976$	1.70976e6	−	987129.i	0.0574526	−	0.0331703i
$977$	−3.79980e7	+	2.19382e7i	−1.27358	+	0.735299i	−0.975659	−	0.219293i	$-0.929625\pi$
$977$	−3.79980e7	+	2.19382e7i	−1.27358	+	0.735299i	−0.297916	+	0.954592i	$0.596292\pi$
$978$		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
$983$	2.13532e7			0.704823			0.352411	−	0.935845i	$-0.385362\pi$
$983$	2.13532e7			0.704823			0.352411	+	0.935845i	$0.385362\pi$
$984$		0			0
$985$			5.92738e7i			1.94658i
$986$	−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	−0.512506	−	0.858684i	$-0.671283\pi$
$991$	1.50682e7	−	2.60988e7i	0.487389	−	0.844183i	0.999895	+	0.0145011i	$0.00461601\pi$
$992$	−1.73683e6	+	3.00828e6i	−0.0560375	+	0.0970598i
$993$		0			0
$994$	1.34022e7	−	2.29267e7i	0.430239	−	0.735996i
$995$	2.51753e7	+	1.45350e7i	0.806153	+	0.465432i
$996$		0			0
$997$			729385.i			0.0232391i	0.999932	+	0.0116195i	$0.00369870\pi$
$997$			729385.i			0.0232391i	−0.999932	+	0.0116195i	$0.996301\pi$
$998$	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.s.a.17.11		76
3.2	odd	2		63.6.s.a.59.28	yes	76
7.5	odd	6		189.6.i.a.152.28		76
9.2	odd	6		189.6.i.a.143.11		76
9.7	even	3		63.6.i.a.38.28	yes	76
21.5	even	6		63.6.i.a.5.11	✓	76
63.47	even	6	inner	189.6.s.a.89.11		76
63.61	odd	6		63.6.s.a.47.28	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.11	✓	76	21.5	even	6
63.6.i.a.38.28	yes	76	9.7	even	3
63.6.s.a.47.28	yes	76	63.61	odd	6
63.6.s.a.59.28	yes	76	3.2	odd	2
189.6.i.a.143.11		76	9.2	odd	6
189.6.i.a.152.28		76	7.5	odd	6
189.6.s.a.17.11		76	1.1	even	1	trivial
189.6.s.a.89.11		76	63.47	even	6	inner

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.79535 - 2.76860i) q^{2} +(-0.669744 - 1.16003i) q^{4} -79.4804 q^{5} +(-129.640 - 0.699468i) q^{7} +184.607i q^{8} +O(q^{10})\)	\(q+(-4.79535 - 2.76860i) q^{2} +(-0.669744 - 1.16003i) q^{4} -79.4804 q^{5} +(-129.640 - 0.699468i) q^{7} +184.607i q^{8} +(381.136 + 220.049i) q^{10} +479.792i q^{11} +(126.577 + 73.0791i) q^{13} +(619.732 + 362.275i) q^{14} +(489.671 - 848.135i) q^{16} +(-925.298 + 1602.66i) q^{17} +(-125.438 + 72.4216i) q^{19} +(53.2315 + 92.1997i) q^{20} +(1328.35 - 2300.77i) q^{22} -3921.67i q^{23} +3192.13 q^{25} +(-404.653 - 700.880i) q^{26} +(86.0142 + 150.855i) q^{28} +(-6921.91 + 3996.37i) q^{29} +(-6207.46 + 3583.88i) q^{31} +(419.696 - 242.312i) q^{32} +(8874.26 - 5123.55i) q^{34} +(10303.8 + 55.5940i) q^{35} +(1859.07 + 3220.00i) q^{37} +802.024 q^{38} -14672.6i q^{40} +(576.073 - 997.788i) q^{41} +(2068.92 + 3583.47i) q^{43} +(556.574 - 321.338i) q^{44} +(-10857.5 + 18805.8i) q^{46} +(-1586.84 + 2748.48i) q^{47} +(16806.0 + 181.358i) q^{49} +(-15307.4 - 8837.71i) q^{50} -195.777i q^{52} +(-30894.4 - 17836.9i) q^{53} -38134.1i q^{55} +(129.127 - 23932.5i) q^{56} +44257.3 q^{58} +(-16076.9 - 27846.0i) q^{59} +(1745.82 + 1007.95i) q^{61} +39689.3 q^{62} -34022.4 q^{64} +(-10060.4 - 5808.35i) q^{65} +(-2908.68 - 5037.98i) q^{67} +2478.85 q^{68} +(-49256.5 - 28793.7i) q^{70} -36994.5i q^{71} +(-19701.9 - 11374.9i) q^{73} -20588.0i q^{74} +(168.022 + 97.0078i) q^{76} +(335.599 - 62200.2i) q^{77} +(18843.3 - 32637.5i) q^{79} +(-38919.2 + 67410.1i) q^{80} +(-5524.94 + 3189.83i) q^{82} +(36121.1 + 62563.6i) q^{83} +(73543.0 - 127380. i) q^{85} -22912.0i q^{86} -88573.1 q^{88} +(13339.1 + 23103.9i) q^{89} +(-16358.3 - 9562.51i) q^{91} +(-4549.26 + 2626.51i) q^{92} +(15218.9 - 8786.62i) q^{94} +(9969.84 - 5756.09i) q^{95} +(101416. - 58552.4i) q^{97} +(-80088.7 - 47398.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 3 q^{2} + 577 q^{4} + 6 q^{5} - 30 q^{7}+O(q^{10}) \) 76 * q + 3 * q^2 + 577 * q^4 + 6 * q^5 - 30 * q^7	\( 76 q + 3 q^{2} + 577 q^{4} + 6 q^{5} - 30 q^{7} - 6 q^{10} - 543 q^{13} + 123 q^{14} - 8223 q^{16} - 801 q^{17} - 6 q^{19} + 96 q^{20} + 62 q^{22} + 37498 q^{25} + 10128 q^{26} + 860 q^{28} - 17904 q^{29} + 3249 q^{31} - 10299 q^{32} - 96 q^{34} + 3960 q^{35} + 2577 q^{37} - 29934 q^{38} + 28230 q^{41} - 9246 q^{43} - 69885 q^{44} - 9418 q^{46} + 28281 q^{47} + 2458 q^{49} + 67509 q^{50} + 25296 q^{53} - 27288 q^{56} + 9902 q^{58} + 29538 q^{59} + 4206 q^{61} + 79536 q^{62} - 198600 q^{64} + 173388 q^{65} - 622 q^{67} - 382992 q^{68} + 14178 q^{70} - 6 q^{73} + 2880 q^{76} + 238866 q^{77} - 29992 q^{79} + 243225 q^{80} + 90 q^{82} - 246930 q^{83} + 11973 q^{85} + 69502 q^{88} - 6345 q^{89} - 120111 q^{91} + 463488 q^{92} - 3 q^{94} + 267813 q^{95} + 104037 q^{97} - 646797 q^{98}+O(q^{100}) \) 76 * q + 3 * q^2 + 577 * q^4 + 6 * q^5 - 30 * q^7 - 6 * q^10 - 543 * q^13 + 123 * q^14 - 8223 * q^16 - 801 * q^17 - 6 * q^19 + 96 * q^20 + 62 * q^22 + 37498 * q^25 + 10128 * q^26 + 860 * q^28 - 17904 * q^29 + 3249 * q^31 - 10299 * q^32 - 96 * q^34 + 3960 * q^35 + 2577 * q^37 - 29934 * q^38 + 28230 * q^41 - 9246 * q^43 - 69885 * q^44 - 9418 * q^46 + 28281 * q^47 + 2458 * q^49 + 67509 * q^50 + 25296 * q^53 - 27288 * q^56 + 9902 * q^58 + 29538 * q^59 + 4206 * q^61 + 79536 * q^62 - 198600 * q^64 + 173388 * q^65 - 622 * q^67 - 382992 * q^68 + 14178 * q^70 - 6 * q^73 + 2880 * q^76 + 238866 * q^77 - 29992 * q^79 + 243225 * q^80 + 90 * q^82 - 246930 * q^83 + 11973 * q^85 + 69502 * q^88 - 6345 * q^89 - 120111 * q^91 + 463488 * q^92 - 3 * q^94 + 267813 * q^95 + 104037 * q^97 - 646797 * q^98

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