LMFDB - Embedded newform 189.6.s.a.89.20

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			89.20
Character	$\chi$	$=$	189.89
Dual form			189.6.s.a.17.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0316775 + 0.0182890i) q^{2} +(-15.9993 + 27.7117i) q^{4} -62.5776 q^{5} +(87.2452 - 95.8920i) q^{7} -2.34094i q^{8} +O(q^{10})$	\(q+(-0.0316775 + 0.0182890i) q^{2} +(-15.9993 + 27.7117i) q^{4} -62.5776 q^{5} +(87.2452 - 95.8920i) q^{7} -2.34094i q^{8} +(1.98230 - 1.14448i) q^{10} -208.840i q^{11} +(-447.217 + 258.201i) q^{13} +(-1.00994 + 4.63325i) q^{14} +(-511.936 - 886.699i) q^{16} +(-558.291 - 966.988i) q^{17} +(819.372 + 473.065i) q^{19} +(1001.20 - 1734.13i) q^{20} +(3.81948 + 6.61553i) q^{22} +1022.14i q^{23} +790.950 q^{25} +(9.44447 - 16.3583i) q^{26} +(1261.46 + 3951.92i) q^{28} +(4524.33 + 2612.13i) q^{29} +(8025.88 + 4633.74i) q^{31} +(97.3078 + 56.1807i) q^{32} +(35.3705 + 20.4212i) q^{34} +(-5459.59 + 6000.69i) q^{35} +(1499.33 - 2596.91i) q^{37} -34.6075 q^{38} +146.491i q^{40} +(6210.55 + 10757.0i) q^{41} +(6478.23 - 11220.6i) q^{43} +(5787.31 + 3341.30i) q^{44} +(-18.6939 - 32.3788i) q^{46} +(9979.25 + 17284.6i) q^{47} +(-1583.56 - 16732.2i) q^{49} +(-25.0553 + 14.4657i) q^{50} -16524.2i q^{52} +(-21892.1 + 12639.4i) q^{53} +13068.7i q^{55} +(-224.478 - 204.236i) q^{56} -191.093 q^{58} +(16653.4 - 28844.5i) q^{59} +(10462.0 - 6040.26i) q^{61} -338.986 q^{62} +32759.8 q^{64} +(27985.7 - 16157.6i) q^{65} +(-11858.5 + 20539.5i) q^{67} +35729.1 q^{68} +(63.1994 - 289.937i) q^{70} +53406.7i q^{71} +(67780.6 - 39133.2i) q^{73} +109.685i q^{74} +(-26218.8 + 15137.4i) q^{76} +(-20026.1 - 18220.3i) q^{77} +(24665.4 + 42721.6i) q^{79} +(32035.7 + 55487.4i) q^{80} +(-393.469 - 227.170i) q^{82} +(-28362.0 + 49124.5i) q^{83} +(34936.5 + 60511.8i) q^{85} +473.921i q^{86} -488.883 q^{88} +(57629.5 - 99817.2i) q^{89} +(-14258.1 + 65411.3i) q^{91} +(-28325.2 - 16353.6i) q^{92} +(-632.235 - 365.021i) q^{94} +(-51274.3 - 29603.2i) q^{95} +(17070.5 + 9855.67i) q^{97} +(356.179 + 501.073i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0316775	+	0.0182890i	−0.00559984	+	0.00323307i	−0.502797	−	0.864404i	$-0.667696\pi$
$2$	−0.0316775	+	0.0182890i	−0.00559984	+	0.00323307i	0.497197	+	0.867637i	$0.334362\pi$
$3$		0			0
$3$		0			0
$4$	−15.9993	+	27.7117i	−0.499979	+	0.865989i
$5$	−62.5776			−1.11942			−0.559711	−	0.828688i	$-0.689088\pi$
$5$	−62.5776			−1.11942			−0.559711	+	0.828688i	$0.689088\pi$
$6$		0			0
$7$	87.2452	−	95.8920i	0.672971	−	0.739669i
$7$	87.2452	−	95.8920i	0.672971	−	0.739669i
$8$		−	2.34094i		−	0.0129320i
$9$		0			0
$10$	1.98230	−	1.14448i	0.00626858	−	0.00361917i
$11$		−	208.840i		−	0.520394i	−0.965556	−	0.260197i	$-0.916212\pi$
$11$		−	208.840i		−	0.520394i	0.965556	−	0.260197i	$-0.0837875\pi$
$12$		0			0
$13$	−447.217	+	258.201i	−0.733939	+	0.423740i	−0.819861	−	0.572562i	$-0.805950\pi$
$13$	−447.217	+	258.201i	−0.733939	+	0.423740i	0.0859226	+	0.996302i	$0.472616\pi$
$14$	−1.00994	+	4.63325i	−0.00137713	+	0.00631779i
$15$		0			0
$16$	−511.936	−	886.699i	−0.499937	−	0.865917i
$17$	−558.291	−	966.988i	−0.468531	−	0.811519i	0.530822	−	0.847483i	$-0.321883\pi$
$17$	−558.291	−	966.988i	−0.468531	−	0.811519i	−0.999353	+	0.0359638i	$0.988550\pi$
$18$		0			0
$19$	819.372	+	473.065i	0.520712	+	0.300633i	0.737226	−	0.675646i	$-0.236135\pi$
$19$	819.372	+	473.065i	0.520712	+	0.300633i	−0.216514	+	0.976279i	$0.569469\pi$
$20$	1001.20	−	1734.13i	0.559687	−	0.969407i
$21$		0			0
$22$	3.81948	+	6.61553i	0.00168247	+	0.00291412i
$23$			1022.14i			0.402894i	0.979499	+	0.201447i	$0.0645644\pi$
$23$			1022.14i			0.402894i	−0.979499	+	0.201447i	$0.935436\pi$
$24$		0			0
$25$	790.950			0.253104
$26$	9.44447	−	16.3583i	0.00273996	−	0.00474575i
$27$		0			0
$28$	1261.46	+	3951.92i	0.304074	+	0.952605i
$29$	4524.33	+	2612.13i	0.998987	+	0.576765i	0.907948	−	0.419082i	$-0.137648\pi$
$29$	4524.33	+	2612.13i	0.998987	+	0.576765i	0.0910383	+	0.995847i	$0.470981\pi$
$30$		0			0
$31$	8025.88	+	4633.74i	1.49999	+	0.866020i	1.00000		1.13515e-5i	$-3.61330e-6\pi$
$31$	8025.88	+	4633.74i	1.49999	+	0.866020i	0.499990	+	0.866031i	$0.333337\pi$
$32$	97.3078	+	56.1807i	0.0167986	+	0.00969867i
$33$		0			0
$34$	35.3705	+	20.4212i	0.00524740	+	0.00302959i
$35$	−5459.59	+	6000.69i	−0.753338	+	0.828001i
$36$		0			0
$37$	1499.33	−	2596.91i	0.180050	−	0.311855i	−0.761848	−	0.647756i	$-0.775708\pi$
$37$	1499.33	−	2596.91i	0.180050	−	0.311855i	0.941897	+	0.335901i	$0.109041\pi$
$38$	−34.6075			−0.00388787
$39$		0			0
$40$			146.491i			0.0144764i
$41$	6210.55	+	10757.0i	0.576993	+	0.999381i	0.995822	+	0.0913162i	$0.0291074\pi$
$41$	6210.55	+	10757.0i	0.576993	+	0.999381i	−0.418829	+	0.908065i	$0.637559\pi$
$42$		0			0
$43$	6478.23	−	11220.6i	0.534300	−	0.925434i	−0.464897	−	0.885365i	$-0.653909\pi$
$43$	6478.23	−	11220.6i	0.534300	−	0.925434i	0.999197	−	0.0400696i	$-0.0127580\pi$
$44$	5787.31	+	3341.30i	0.450656	+	0.260186i
$45$		0			0
$46$	−18.6939	−	32.3788i	−0.00130259	−	0.00225614i
$47$	9979.25	+	17284.6i	0.658951	+	1.14134i	0.980888	+	0.194576i	$0.0623329\pi$
$47$	9979.25	+	17284.6i	0.658951	+	1.14134i	−0.321936	+	0.946761i	$0.604334\pi$
$48$		0			0
$49$	−1583.56	−	16732.2i	−0.0942203	−	0.995551i
$50$	−25.0553	+	14.4657i	−0.00141734	+	0.000818303i
$51$		0			0
$52$		−	16524.2i		−	0.847444i
$53$	−21892.1	+	12639.4i	−1.07053	+	0.618069i	−0.928326	−	0.371768i	$-0.878752\pi$
$53$	−21892.1	+	12639.4i	−1.07053	+	0.618069i	−0.142202	+	0.989838i	$0.545418\pi$
$54$		0			0
$55$			13068.7i			0.582540i
$56$	−224.478	−	204.236i	−0.00956540	−	0.00870287i
$57$		0			0
$58$	−191.093			−0.00745889
$59$	16653.4	−	28844.5i	0.622833	−	1.07878i	−0.366122	−	0.930567i	$-0.619315\pi$
$59$	16653.4	−	28844.5i	0.622833	−	1.07878i	0.988956	−	0.148212i	$-0.0473518\pi$
$60$		0			0
$61$	10462.0	−	6040.26i	0.359991	−	0.207841i	−0.309086	−	0.951034i	$-0.600023\pi$
$61$	10462.0	−	6040.26i	0.359991	−	0.207841i	0.669077	+	0.743193i	$0.266690\pi$
$62$	−338.986			−0.0111996
$63$		0			0
$64$	32759.8			0.999749
$65$	27985.7	−	16157.6i	0.821587	−	0.474343i
$66$		0			0
$67$	−11858.5	+	20539.5i	−0.322732	+	0.558988i	−0.981051	−	0.193751i	$-0.937935\pi$
$67$	−11858.5	+	20539.5i	−0.322732	+	0.558988i	0.658319	+	0.752739i	$0.271268\pi$
$68$	35729.1			0.937023
$69$		0			0
$70$	63.1994	−	289.937i	0.00154159	−	0.00707227i
$71$			53406.7i			1.25733i	0.777675	+	0.628666i	$0.216399\pi$
$71$			53406.7i			1.25733i	−0.777675	+	0.628666i	$0.783601\pi$
$72$		0			0
$73$	67780.6	−	39133.2i	1.48867	−	0.859484i	0.488754	−	0.872422i	$-0.337452\pi$
$73$	67780.6	−	39133.2i	1.48867	−	0.859484i	0.999916	+	0.0129379i	$0.00411838\pi$
$74$			109.685i			0.00232845i
$75$		0			0
$76$	−26218.8	+	15137.4i	−0.520690	+	0.300620i
$77$	−20026.1	−	18220.3i	−0.384919	−	0.350210i
$78$		0			0
$79$	24665.4	+	42721.6i	0.444651	+	0.770159i	0.998028	−	0.0627725i	$-0.0199942\pi$
$79$	24665.4	+	42721.6i	0.444651	+	0.770159i	−0.553376	+	0.832931i	$0.686661\pi$
$80$	32035.7	+	55487.4i	0.559640	+	0.969326i
$81$		0			0
$82$	−393.469	−	227.170i	−0.00646214	−	0.00373092i
$83$	−28362.0	+	49124.5i	−0.451899	+	0.782713i	−0.998504	−	0.0546780i	$-0.982587\pi$
$83$	−28362.0	+	49124.5i	−0.451899	+	0.782713i	0.546605	+	0.837391i	$0.315920\pi$
$84$		0			0
$85$	34936.5	+	60511.8i	0.524484	+	0.908432i
$86$			473.921i			0.00690971i
$87$		0			0
$88$	−488.883			−0.00672974
$89$	57629.5	−	99817.2i	0.771205	−	1.33577i	−0.165698	−	0.986177i	$-0.552988\pi$
$89$	57629.5	−	99817.2i	0.771205	−	1.33577i	0.936903	−	0.349589i	$-0.113679\pi$
$90$		0			0
$91$	−14258.1	+	65411.3i	−0.180492	+	0.828036i
$92$	−28325.2	−	16353.6i	−0.348902	−	0.201439i
$93$		0			0
$94$	−632.235	−	365.021i	−0.00738004	−	0.00426087i
$95$	−51274.3	−	29603.2i	−0.582896	−	0.336535i
$96$		0			0
$97$	17070.5	+	9855.67i	0.184212	+	0.106355i	0.589270	−	0.807936i	$-0.299415\pi$
$97$	17070.5	+	9855.67i	0.184212	+	0.106355i	−0.405058	+	0.914291i	$0.632749\pi$
$98$	356.179	+	501.073i	0.00374631	+	0.00527031i
$99$		0			0
$100$	−12654.7	+	21918.5i	−0.126547	+	0.219185i
$101$	−90419.0			−0.881975			−0.440988	−	0.897513i	$-0.645372\pi$
$101$	−90419.0			−0.881975			−0.440988	+	0.897513i	$0.645372\pi$
$102$		0			0
$103$		−	136880.i		−	1.27130i	−0.771978	−	0.635649i	$-0.780733\pi$
$103$		−	136880.i		−	1.27130i	0.771978	−	0.635649i	$-0.219267\pi$
$104$	604.434	+	1046.91i	0.00547981	+	0.00949130i
$105$		0			0
$106$	462.325	−	800.770i	0.00399652	−	0.00692218i
$107$	42006.7	+	24252.6i	0.354698	+	0.204785i	0.666752	−	0.745279i	$-0.267684\pi$
$107$	42006.7	+	24252.6i	0.354698	+	0.204785i	−0.312055	+	0.950064i	$0.601017\pi$
$108$		0			0
$109$	−62765.7	−	108713.i	−0.506007	−	0.876429i	−0.999976	−	0.00695000i	$-0.997788\pi$
$109$	−62765.7	−	108713.i	−0.506007	−	0.876429i	0.493969	−	0.869479i	$-0.335546\pi$
$110$	−239.014	−	413.984i	−0.00188339	−	0.00326213i
$111$		0			0
$112$	−129691.	−	28269.6i	−0.976935	−	0.212949i
$113$	31167.2	−	17994.4i	0.229616	−	0.132569i	−0.380779	−	0.924666i	$-0.624344\pi$
$113$	31167.2	−	17994.4i	0.229616	−	0.132569i	0.610395	+	0.792097i	$0.291011\pi$
$114$		0			0
$115$		−	63963.1i		−	0.451008i
$116$	−144773.	+	83584.5i	−0.998945	+	0.576741i
$117$		0			0
$118$			1218.29i			0.00805465i
$119$	−141435.	−	30829.4i	−0.915563	−	0.199571i
$120$		0			0
$121$	117437.			0.729190
$122$	−220.941	+	382.681i	−0.00134393	+	0.00232775i
$123$		0			0
$124$	−256817.	+	148274.i	−1.49993	+	0.865984i
$125$	146059.			0.836091
$126$		0			0
$127$	−155648.			−0.856315			−0.428157	−	0.903704i	$-0.640837\pi$
$127$	−155648.			−0.856315			−0.428157	+	0.903704i	$0.640837\pi$
$128$	−4151.60	+	2396.93i	−0.0223970	+	0.0129309i
$129$		0			0
$130$	−591.012	+	1023.66i	−0.00306717	+	0.00531249i
$131$	239391.			1.21879			0.609395	−	0.792866i	$-0.291412\pi$
$131$	239391.			1.21879			0.609395	+	0.792866i	$0.291412\pi$
$132$		0			0
$133$	116849.	−	37298.6i	0.572793	−	0.182837i
$134$		−	867.519i		−	0.00417366i
$135$		0			0
$136$	−2263.66	+	1306.93i	−0.0104946	+	0.00605905i
$137$		−	47378.4i		−	0.215665i	−0.994169	−	0.107832i	$-0.965609\pi$
$137$		−	47378.4i		−	0.215665i	0.994169	−	0.107832i	$-0.0343910\pi$
$138$		0			0
$139$	40845.5	−	23582.1i	0.179311	−	0.103525i	−0.407658	−	0.913135i	$-0.633654\pi$
$139$	40845.5	−	23582.1i	0.179311	−	0.103525i	0.586969	+	0.809609i	$0.300321\pi$
$140$	−78939.2	−	247301.i	−0.340387	−	1.06637i
$141$		0			0
$142$	−976.756	−	1691.79i	−0.00406504	−	0.00704086i
$143$	53922.7	+	93396.9i	0.220512	+	0.381937i
$144$		0			0
$145$	−283122.	−	163460.i	−1.11829	−	0.645643i
$146$	−1431.41	+	2479.28i	−0.00555754	+	0.00962595i
$147$		0			0
$148$	47976.5	+	83097.7i	0.180042	+	0.311842i
$149$		−	385237.i		−	1.42155i	−0.703418	−	0.710776i	$-0.748344\pi$
$149$		−	385237.i		−	1.42155i	0.703418	−	0.710776i	$-0.251656\pi$
$150$		0			0
$151$	−115125.			−0.410892			−0.205446	−	0.978668i	$-0.565864\pi$
$151$	−115125.			−0.410892			−0.205446	+	0.978668i	$0.565864\pi$
$152$	1107.42	−	1918.10i	0.00388779	−	0.00673385i
$153$		0			0
$154$	967.608	+	210.916i	0.00328774	+	0.000716650i
$155$	−502240.	−	289968.i	−1.67912	−	0.969441i
$156$		0			0
$157$	22976.9	+	13265.7i	0.0743946	+	0.0429518i	0.536736	−	0.843750i	$-0.319657\pi$
$157$	22976.9	+	13265.7i	0.0743946	+	0.0429518i	−0.462341	+	0.886702i	$0.652990\pi$
$158$	−1562.67	−	902.210i	−0.00497995	−	0.00287518i
$159$		0			0
$160$	−6089.28	−	3515.65i	−0.0188047	−	0.0108569i
$161$	98015.1	+	89176.8i	0.298008	+	0.271136i
$162$		0			0
$163$	−224228.	+	388374.i	−0.661030	+	1.14494i	0.319316	+	0.947648i	$0.396547\pi$
$163$	−224228.	+	388374.i	−0.661030	+	1.14494i	−0.980345	+	0.197289i	$0.936786\pi$
$164$	−397459.			−1.15394
$165$		0			0
$166$		−	2074.85i		−	0.00584409i
$167$	222908.	+	386089.i	0.618494	+	1.07126i	0.989761	+	0.142737i	$0.0455902\pi$
$167$	222908.	+	386089.i	0.618494	+	1.07126i	−0.371267	+	0.928526i	$0.621077\pi$
$168$		0			0
$169$	−52311.2	+	90605.6i	−0.140889	+	0.244027i
$170$	−2213.40	−	1277.91i	−0.00587405	−	0.00339138i
$171$		0			0
$172$	207295.	+	359045.i	0.534277	+	0.925396i
$173$	−189463.	−	328159.i	−0.481292	−	0.833623i	0.518477	−	0.855092i	$-0.326499\pi$
$173$	−189463.	−	328159.i	−0.481292	−	0.833623i	−0.999770	+	0.0214686i	$0.993166\pi$
$174$		0			0
$175$	69006.6	−	75845.8i	0.170332	−	0.187213i
$176$	−185178.	+	106913.i	−0.450618	+	0.260164i
$177$		0			0
$178$			4215.94i			0.00997344i
$179$	571478.	−	329943.i	1.33311	−	0.769673i	0.347337	−	0.937740i	$-0.387086\pi$
$179$	571478.	−	329943.i	1.33311	−	0.769673i	0.985775	+	0.168068i	$0.0537528\pi$
$180$		0			0
$181$		−	551804.i		−	1.25195i	−0.779842	−	0.625977i	$-0.784701\pi$
$181$		−	551804.i		−	1.25195i	0.779842	−	0.625977i	$-0.215299\pi$
$182$	−744.646	−	2332.83i	−0.00166637	−	0.00522042i
$183$		0			0
$184$	2392.77			0.00521023
$185$	−93824.2	+	162508.i	−0.201551	+	0.349097i
$186$		0			0
$187$	−201946.	+	116594.i	−0.422310	+	0.243821i
$188$	−638645.			−1.31785
$189$		0			0
$190$	2165.66			0.00435216
$191$	35637.9	−	20575.6i	0.0706853	−	0.0408102i	−0.464241	−	0.885709i	$-0.653673\pi$
$191$	35637.9	−	20575.6i	0.0706853	−	0.0408102i	0.534926	+	0.844899i	$0.320339\pi$
$192$		0			0
$193$	−162000.	+	280592.i	−0.313056	+	0.542228i	−0.979022	−	0.203753i	$-0.934686\pi$
$193$	−162000.	+	280592.i	−0.313056	+	0.542228i	0.665967	+	0.745982i	$0.268019\pi$
$194$	−721.002			−0.00137541
$195$		0			0
$196$	489014.	+	223821.i	0.909245	+	0.416161i
$197$			898843.i			1.65013i	0.565038	+	0.825065i	$0.308862\pi$
$197$			898843.i			1.65013i	−0.565038	+	0.825065i	$0.691138\pi$
$198$		0			0
$199$	−185743.	+	107239.i	−0.332491	+	0.191964i	−0.656947	−	0.753937i	$-0.728152\pi$
$199$	−185743.	+	107239.i	−0.332491	+	0.191964i	0.324455	+	0.945901i	$0.394819\pi$
$200$		−	1851.57i		−	0.00327314i
$201$		0			0
$202$	2864.25	−	1653.67i	0.00493892	−	0.00285149i
$203$	645208.	−	205952.i	1.09890	−	0.350773i
$204$		0			0
$205$	−388641.	−	673146.i	−0.645898	−	1.11873i
$206$	2503.40	+	4336.02i	0.00411019	+	0.00711906i
$207$		0			0
$208$	457893.	+	264364.i	0.733847	+	0.423687i
$209$	98794.9	−	171118.i	0.156448	−	0.270975i
$210$		0			0
$211$	77523.0	+	134274.i	0.119874	+	0.207628i	0.919718	−	0.392581i	$-0.128418\pi$
$211$	77523.0	+	134274.i	0.119874	+	0.207628i	−0.799844	+	0.600208i	$0.795084\pi$
$212$		−	808889.i		−	1.23609i
$213$		0			0
$214$	−1774.22			−0.00264834
$215$	−405392.	+	702159.i	−0.598107	+	1.03595i
$216$		0			0
$217$	1.14456e6	−	365346.i	1.65002	−	0.526690i
$218$	3976.52	+	2295.85i	0.00566712	+	0.00327191i
$219$		0			0
$220$	−362155.	−	209091.i	−0.504473	−	0.291258i
$221$	499354.	+	288302.i	0.687746	+	0.397070i
$222$		0			0
$223$	906052.	+	523109.i	1.22009	+	0.704418i	0.964937	−	0.262483i	$-0.0845415\pi$
$223$	906052.	+	523109.i	1.22009	+	0.704418i	0.255151	+	0.966901i	$0.417875\pi$
$224$	13876.9	−	4429.55i	0.0184788	−	0.00589847i
$225$		0			0
$226$	−658.200	+	1140.04i	−0.000857209	+	0.00148473i
$227$	903374.			1.16360			0.581799	−	0.813333i	$-0.302349\pi$
$227$	903374.			1.16360			0.581799	+	0.813333i	$0.302349\pi$
$228$		0			0
$229$		−	604327.i		−	0.761524i	−0.924673	−	0.380762i	$-0.875662\pi$
$229$		−	604327.i		−	0.761524i	0.924673	−	0.380762i	$-0.124338\pi$
$230$	1169.82	+	2026.19i	0.00145814	+	0.00252557i
$231$		0			0
$232$	6114.84	−	10591.2i	0.00745873	−	0.0129189i
$233$	−238586.	−	137747.i	−0.287908	−	0.166224i	0.349090	−	0.937089i	$-0.386491\pi$
$233$	−238586.	−	137747.i	−0.287908	−	0.166224i	−0.636998	+	0.770865i	$0.719824\pi$
$234$		0			0
$235$	−624477.	−	1.08163e6i	−0.737644	−	1.27764i
$236$	532885.	+	922984.i	0.622807	+	1.07873i
$237$		0			0
$238$	5044.13	−	1610.10i	0.00577224	−	0.00184251i
$239$	916492.	−	529137.i	1.03785	−	0.599202i	0.118625	−	0.992939i	$-0.462151\pi$
$239$	916492.	−	529137.i	1.03785	−	0.599202i	0.919223	+	0.393737i	$0.128818\pi$
$240$		0			0
$241$		−	495513.i		−	0.549557i	−0.961508	−	0.274778i	$-0.911396\pi$
$241$		−	495513.i		−	0.549557i	0.961508	−	0.274778i	$-0.0886045\pi$
$242$	−3720.10	+	2147.80i	−0.00408335	+	0.00235752i
$243$		0			0
$244$			386561.i			0.415665i
$245$	99095.3	+	1.04706e6i	0.105472	+	1.11444i
$246$		0			0
$247$	−488583.			−0.509561
$248$	10847.3	−	18788.1i	0.0111994	−	0.0193979i
$249$		0			0
$250$	−4626.79	+	2671.28i	−0.00468198	+	0.00270314i
$251$	773459.			0.774913			0.387456	−	0.921888i	$-0.373354\pi$
$251$	773459.			0.774913			0.387456	+	0.921888i	$0.373354\pi$
$252$		0			0
$253$	213464.			0.209664
$254$	4930.53	−	2846.64i	0.00479523	−	0.00276853i
$255$		0			0
$256$	−524069.	+	907714.i	−0.499791	+	0.865663i
$257$	−1.09138e6			−1.03073			−0.515364	−	0.856972i	$-0.672343\pi$
$257$	−1.09138e6			−1.03073			−0.515364	+	0.856972i	$0.672343\pi$
$258$		0			0
$259$	−118214.	−	370341.i	−0.109501	−	0.343046i
$260$			1.03404e6i			0.948647i
$261$		0			0
$262$	−7583.30	+	4378.22i	−0.00682503	+	0.00394044i
$263$			363851.i			0.324365i	0.986761	+	0.162183i	$0.0518533\pi$
$263$			363851.i			0.324365i	−0.986761	+	0.162183i	$0.948147\pi$
$264$		0			0
$265$	1.36995e6	−	790944.i	1.19837	−	0.691880i
$266$	−3019.34	+	3318.59i	−0.00261642	+	0.00287574i
$267$		0			0
$268$	−379455.	−	657236.i	−0.322718	−	0.558965i
$269$	189727.	+	328617.i	0.159863	+	0.276891i	0.934819	−	0.355124i	$-0.115561\pi$
$269$	189727.	+	328617.i	0.159863	+	0.276891i	−0.774956	+	0.632015i	$0.782228\pi$
$270$		0			0
$271$	1.70719e6	+	985645.i	1.41208	+	0.815262i	0.995584	−	0.0938771i	$-0.0299261\pi$
$271$	1.70719e6	+	985645.i	1.41208	+	0.815262i	0.416492	+	0.909139i	$0.363259\pi$
$272$	−571618.	+	990072.i	−0.468472	+	0.811418i
$273$		0			0
$274$	866.504	+	1500.83i	0.000697259	+	0.00120769i
$275$		−	165182.i		−	0.131714i
$276$		0			0
$277$	2.00010e6			1.56622			0.783109	−	0.621884i	$-0.213633\pi$
$277$	2.00010e6			1.56622			0.783109	+	0.621884i	$0.213633\pi$
$278$	−862.588	+	1494.05i	−0.000669408	+	0.00115945i
$279$		0			0
$280$	14047.3	+	12780.6i	0.0107077	+	0.00974217i
$281$	−2.15849e6	−	1.24620e6i	−1.63074	−	0.941506i	−0.983866	−	0.178906i	$-0.942744\pi$
$281$	−2.15849e6	−	1.24620e6i	−1.63074	−	0.941506i	−0.646870	−	0.762600i	$-0.723922\pi$
$282$		0			0
$283$	362849.	+	209491.i	0.269314	+	0.155489i	0.628576	−	0.777748i	$-0.283638\pi$
$283$	362849.	+	209491.i	0.269314	+	0.155489i	−0.359262	+	0.933237i	$0.616971\pi$
$284$	−1.47999e6	−	854472.i	−1.08884	−	0.628640i
$285$		0			0
$286$	−3416.27	−	1972.38i	−0.00246966	−	0.00142586i
$287$	1.57335e6	+	342953.i	1.12751	+	0.245771i
$288$		0			0
$289$	86550.9	−	149911.i	0.0609575	−	0.105581i
$290$	11958.1			0.00834964
$291$		0			0
$292$			2.50442e6i			1.71890i
$293$	1.04949e6	+	1.81777e6i	0.714182	+	1.23700i	0.963274	+	0.268520i	$0.0865344\pi$
$293$	1.04949e6	+	1.81777e6i	0.714182	+	1.23700i	−0.249092	+	0.968480i	$0.580132\pi$
$294$		0			0
$295$	−1.04213e6	+	1.80502e6i	−0.697213	+	1.20761i
$296$	−6079.22	−	3509.84i	−0.00403291	−	0.00232840i
$297$		0			0
$298$	7045.61	+	12203.4i	0.00459598	+	0.00796047i
$299$	−263918.	−	457119.i	−0.170722	−	0.295700i
$300$		0			0
$301$	−510774.	−	1.60015e6i	−0.324947	−	1.01800i
$302$	3646.87	−	2105.52i	0.00230093	−	0.00132844i
$303$		0			0
$304$		−	968715.i		−	0.601191i
$305$	−654689.	+	377985.i	−0.402982	+	0.232662i
$306$		0			0
$307$			1.64040e6i			0.993356i	0.867935	+	0.496678i	$0.165447\pi$
$307$			1.64040e6i			0.993356i	−0.867935	+	0.496678i	$0.834553\pi$
$308$	825319.	−	263444.i	0.495730	−	0.158238i
$309$		0			0
$310$	21212.9			0.0125371
$311$	1.42933e6	−	2.47567e6i	0.837977	−	1.45142i	−0.0536068	−	0.998562i	$-0.517072\pi$
$311$	1.42933e6	−	2.47567e6i	0.837977	−	1.45142i	0.891584	−	0.452856i	$-0.149595\pi$
$312$		0			0
$313$	−362882.	+	209510.i	−0.209365	+	0.120877i	−0.601016	−	0.799237i	$-0.705237\pi$
$313$	−362882.	+	209510.i	−0.209365	+	0.120877i	0.391651	+	0.920114i	$0.371904\pi$
$314$	−970.465			−0.000555464
$315$		0			0
$316$	−1.57852e6			−0.889266
$317$	402273.	−	232252.i	0.224839	−	0.129811i	−0.383350	−	0.923603i	$-0.625230\pi$
$317$	402273.	−	232252.i	0.224839	−	0.129811i	0.608189	+	0.793792i	$0.291896\pi$
$318$		0			0
$319$	545517.	−	944863.i	0.300145	−	0.519867i
$320$	−2.05003e6			−1.11914
$321$		0			0
$322$	−4735.83	−	1032.30i	−0.00254540	−	0.000554837i
$323$		−	1.05643e6i		−	0.563424i
$324$		0			0
$325$	−353726.	+	204224.i	−0.185763	+	0.107250i
$326$		−	16403.6i		−	0.00854862i
$327$		0			0
$328$	25181.5	−	14538.6i	0.0129240	−	0.00746168i
$329$	2.52809e6	+	551065.i	1.28767	+	0.280681i
$330$		0			0
$331$	−1.71251e6	−	2.96615e6i	−0.859138	−	1.48807i	−0.872752	−	0.488164i	$-0.837667\pi$
$331$	−1.71251e6	−	2.96615e6i	−0.859138	−	1.48807i	0.0136135	−	0.999907i	$-0.495667\pi$
$332$	−907547.	−	1.57192e6i	−0.451881	−	0.782680i
$333$		0			0
$334$	−14122.4	−	8153.55i	−0.00692693	−	0.00399927i
$335$	742075.	−	1.28531e6i	0.361273	−	0.625743i
$336$		0			0
$337$	1.98556e6	+	3.43909e6i	0.952376	+	1.64956i	0.740262	+	0.672318i	$0.234701\pi$
$337$	1.98556e6	+	3.43909e6i	0.952376	+	1.64956i	0.212114	+	0.977245i	$0.431965\pi$
$338$		−	3826.88i		−	0.00182202i
$339$		0			0
$340$	−2.23584e6			−1.04892
$341$	967712.	−	1.67613e6i	0.450671	−	0.780586i
$342$		0			0
$343$	−1.74265e6	−	1.30796e6i	−0.799786	−	0.600285i
$344$	−26266.8	−	15165.2i	−0.0119677	−	0.00690957i
$345$		0			0
$346$	12003.4	+	6930.18i	0.00539032	+	0.00311210i
$347$	−2.72569e6	−	1.57368e6i	−1.21521	−	0.701603i	−0.251323	−	0.967903i	$-0.580865\pi$
$347$	−2.72569e6	−	1.57368e6i	−1.21521	−	0.701603i	−0.963890	+	0.266300i	$0.914199\pi$
$348$		0			0
$349$	2.32028e6	+	1.33961e6i	1.01971	+	0.588730i	0.914020	−	0.405669i	$-0.132962\pi$
$349$	2.32028e6	+	1.33961e6i	1.01971	+	0.588730i	0.105690	+	0.994399i	$0.466295\pi$
$350$	−798.810	+	3664.67i	−0.000348557	+	0.00159906i
$351$		0			0
$352$	11732.8	−	20321.8i	0.00504713	−	0.00874188i
$353$	1.27492e6			0.544559			0.272280	−	0.962218i	$-0.412222\pi$
$353$	1.27492e6			0.544559			0.272280	+	0.962218i	$0.412222\pi$
$354$		0			0
$355$		−	3.34206e6i		−	1.40749i
$356$	1.84407e6	+	3.19402e6i	0.771173	+	1.33571i
$357$		0			0
$358$	−12068.6	+	20903.5i	−0.00497681	+	0.00862009i
$359$	−1.66089e6	−	958913.i	−0.680148	−	0.392684i	0.119763	−	0.992803i	$-0.461787\pi$
$359$	−1.66089e6	−	958913.i	−0.680148	−	0.392684i	−0.799911	+	0.600119i	$0.795120\pi$
$360$		0			0
$361$	−790469.	−	1.36913e6i	−0.319240	−	0.552939i
$362$	10091.9	+	17479.8i	0.00404765	+	0.00701074i
$363$		0			0
$364$	−1.58454e6	−	1.44165e6i	−0.626828	−	0.570305i
$365$	−4.24155e6	+	2.44886e6i	−1.66645	+	0.962125i
$366$		0			0
$367$			2.45946e6i			0.953180i	0.879126	+	0.476590i	$0.158127\pi$
$367$			2.45946e6i			0.953180i	−0.879126	+	0.476590i	$0.841873\pi$
$368$	906331.	−	523270.i	0.348873	−	0.201422i
$369$		0			0
$370$		−	6863.81i		−	0.00260652i
$371$	−697962.	+	3.20201e6i	−0.263267	+	1.20778i
$372$		0			0
$373$	−2.66049e6			−0.990123			−0.495061	−	0.868858i	$-0.664854\pi$
$373$	−2.66049e6			−0.990123			−0.495061	+	0.868858i	$0.664854\pi$
$374$	4264.76	−	7386.78i	0.00157658	−	0.00273071i
$375$		0			0
$376$	40462.2	−	23360.9i	0.0147598	−	0.00852156i
$377$	−2.69781e6			−0.977593
$378$		0			0
$379$	−1.62518e6			−0.581172			−0.290586	−	0.956849i	$-0.593850\pi$
$379$	−1.62518e6			−0.581172			−0.290586	+	0.956849i	$0.593850\pi$
$380$	1.64071e6	−	947264.i	0.582871	−	0.336521i
$381$		0			0
$382$	−752.614	+	1303.57i	−0.000263884	+	0.000457061i
$383$	−1.65754e6			−0.577388			−0.288694	−	0.957421i	$-0.593221\pi$
$383$	−1.65754e6			−0.577388			−0.288694	+	0.957421i	$0.593221\pi$
$384$		0			0
$385$	1.25318e6	+	1.14018e6i	0.430887	+	0.392033i
$386$		−	11851.3i		−	0.00404852i
$387$		0			0
$388$	−546234.	+	315368.i	−0.184204	+	0.106350i
$389$		−	3.16936e6i		−	1.06193i	−0.847393	−	0.530966i	$-0.821829\pi$
$389$		−	3.16936e6i		−	1.06193i	0.847393	−	0.530966i	$-0.178171\pi$
$390$		0			0
$391$	988398.	−	570652.i	0.326956	−	0.188768i
$392$	−39169.2	+	3707.02i	−0.0128745	+	0.00121846i
$393$		0			0
$394$	−16438.9	−	28473.1i	−0.00533499	−	0.00924047i
$395$	−1.54350e6	−	2.67342e6i	−0.497752	−	0.862132i
$396$		0			0
$397$	−2.14283e6	−	1.23716e6i	−0.682357	−	0.393959i	0.118386	−	0.992968i	$-0.462228\pi$
$397$	−2.14283e6	−	1.23716e6i	−0.682357	−	0.393959i	−0.800742	+	0.599009i	$0.795561\pi$
$398$	3922.59	−	6794.12i	0.00124127	−	0.00214994i
$399$		0			0
$400$	−404916.	−	701334.i	−0.126536	−	0.219167i
$401$			5.85321e6i			1.81775i	0.417072	+	0.908874i	$0.363056\pi$
$401$			5.85321e6i			1.81775i	−0.417072	+	0.908874i	$0.636944\pi$
$402$		0			0
$403$	−4.78575e6			−1.46787
$404$	1.44664e6	−	2.50566e6i	0.440969	−	0.763781i
$405$		0			0
$406$	−16671.9	+	18324.3i	−0.00501962	+	0.00551711i
$407$	−542339.	−	313120.i	−0.162287	−	0.0936967i
$408$		0			0
$409$	−1.16694e6	−	673731.i	−0.344936	−	0.199149i	0.317517	−	0.948253i	$-0.397151\pi$
$409$	−1.16694e6	−	673731.i	−0.344936	−	0.199149i	−0.662453	+	0.749104i	$0.730484\pi$
$410$	24622.3	+	14215.7i	0.00723386	+	0.00417647i
$411$		0			0
$412$	3.79317e6	+	2.18999e6i	1.10093	+	0.635622i
$413$	−1.31303e6	−	4.11346e6i	−0.378790	−	1.18668i
$414$		0			0
$415$	1.77483e6	−	3.07409e6i	0.505866	−	0.876185i
$416$	−58023.6			−0.0164388
$417$		0			0
$418$			7227.44i			0.00202322i
$419$	1.81560e6	+	3.14471e6i	0.505225	+	0.875076i	0.999982	+	0.00604403i	$0.00192389\pi$
$419$	1.81560e6	+	3.14471e6i	0.505225	+	0.875076i	−0.494757	+	0.869032i	$0.664743\pi$
$420$		0			0
$421$	−2.21059e6	+	3.82885e6i	−0.607858	+	1.05284i	0.383735	+	0.923443i	$0.374638\pi$
$421$	−2.21059e6	+	3.82885e6i	−0.607858	+	1.05284i	−0.991593	+	0.129397i	$0.958696\pi$
$422$	−4911.47	−	2835.64i	−0.00134255	−	0.000775121i
$423$		0			0
$424$	29588.2	+	51248.2i	0.00799288	+	0.0138441i
$425$	−441580.	−	764839.i	−0.118587	−	0.205399i
$426$		0			0
$427$	333550.	−	1.53021e6i	0.0885301	−	0.406145i
$428$	−1.34416e6	+	776049.i	−0.354683	+	0.204776i
$429$		0			0
$430$		−	29656.8i		−	0.00773488i
$431$	−911427.	+	526213.i	−0.236335	+	0.136448i	−0.613491	−	0.789701i	$-0.710235\pi$
$431$	−911427.	+	526213.i	−0.236335	+	0.136448i	0.377156	+	0.926150i	$0.376902\pi$
$432$		0			0
$433$			3.23100e6i			0.828166i	0.910239	+	0.414083i	$0.135898\pi$
$433$			3.23100e6i			0.828166i	−0.910239	+	0.414083i	$0.864102\pi$
$434$	−29574.9	+	32506.1i	−0.00753701	+	0.00828400i
$435$		0			0
$436$	4.01684e6			1.01197
$437$	−483539.	+	837514.i	−0.121123	+	0.209792i
$438$		0			0
$439$	338800.	−	195606.i	0.0839038	−	0.0484419i	−0.457461	−	0.889230i	$-0.651241\pi$
$439$	338800.	−	195606.i	0.0839038	−	0.0484419i	0.541365	+	0.840788i	$0.317908\pi$
$440$	30593.1			0.00753341
$441$		0			0
$442$	−21091.1			−0.00513503
$443$	5.81377e6	−	3.35658e6i	1.40750	−	0.812621i	0.412355	−	0.911023i	$-0.364706\pi$
$443$	5.81377e6	−	3.35658e6i	1.40750	−	0.812621i	0.995147	+	0.0984019i	$0.0313731\pi$
$444$		0			0
$445$	−3.60631e6	+	6.24632e6i	−0.863303	+	1.49528i
$446$	−38268.6			−0.00910973
$447$		0			0
$448$	2.85813e6	−	3.14140e6i	0.672802	−	0.739483i
$449$			2.96589e6i			0.694288i	0.937812	+	0.347144i	$0.112848\pi$
$449$			2.96589e6i			0.694288i	−0.937812	+	0.347144i	$0.887152\pi$
$450$		0			0
$451$	2.24649e6	−	1.29701e6i	0.520072	−	0.300264i
$452$			1.15159e6i			0.265127i
$453$		0			0
$454$	−28616.6	+	16521.8i	−0.00651596	+	0.00376199i
$455$	892238.	−	4.09328e6i	0.202047	−	0.926921i
$456$		0			0
$457$	−855264.	−	1.48136e6i	−0.191562	−	0.331795i	0.754206	−	0.656638i	$-0.228022\pi$
$457$	−855264.	−	1.48136e6i	−0.191562	−	0.331795i	−0.945768	+	0.324843i	$0.894689\pi$
$458$	11052.5	+	19143.6i	0.00246206	+	0.00426441i
$459$		0			0
$460$	1.77252e6	+	1.02337e6i	0.390568	+	0.225495i
$461$	−242995.	+	420880.i	−0.0532532	+	0.0922372i	−0.891423	−	0.453172i	$-0.850292\pi$
$461$	−242995.	+	420880.i	−0.0532532	+	0.0922372i	0.838170	+	0.545409i	$0.183626\pi$
$462$		0			0
$463$	1.37552e6	+	2.38247e6i	0.298205	+	0.516507i	0.975725	−	0.218998i	$-0.0702787\pi$
$463$	1.37552e6	+	2.38247e6i	0.298205	+	0.516507i	−0.677520	+	0.735504i	$0.736945\pi$
$464$		−	5.34896e6i		−	1.15339i
$465$		0			0
$466$	10077.1			0.00214966
$467$	−653915.	+	1.13261e6i	−0.138749	+	0.240320i	−0.927023	−	0.375004i	$-0.877641\pi$
$467$	−653915.	+	1.13261e6i	−0.138749	+	0.240320i	0.788274	+	0.615324i	$0.210975\pi$
$468$		0			0
$469$	934978.	+	2.92910e6i	0.196277	+	0.614898i
$470$	39563.7	+	22842.1i	0.00826138	+	0.00476971i
$471$		0			0
$472$	−67523.3	−	38984.6i	−0.0139508	−	0.00805448i
$473$	−2.34332e6	−	1.35291e6i	−0.481590	−	0.278046i
$474$		0			0
$475$	648083.	+	374171.i	0.131794	+	0.0760914i
$476$	3.11719e6	−	3.42614e6i	0.630589	−	0.693087i
$477$		0			0
$478$	−19354.8	+	33523.5i	−0.00387452	+	0.00671087i
$479$	3.83472e6			0.763651			0.381825	−	0.924235i	$-0.375296\pi$
$479$	3.83472e6			0.763651			0.381825	+	0.924235i	$0.375296\pi$
$480$		0			0
$481$			1.54851e6i			0.305177i
$482$	9062.44	+	15696.6i	0.00177676	+	0.00307743i
$483$		0			0
$484$	−1.87891e6	+	3.25437e6i	−0.364580	+	0.631471i
$485$	−1.06823e6	−	616744.i	−0.206211	−	0.119056i
$486$		0			0
$487$	4.09145e6	+	7.08661e6i	0.781727	+	1.35399i	0.930935	+	0.365186i	$0.118994\pi$
$487$	4.09145e6	+	7.08661e6i	0.781727	+	1.35399i	−0.149207	+	0.988806i	$0.547672\pi$
$488$	−14139.9	−	24491.0i	−0.00268780	−	0.00465541i
$489$		0			0
$490$	−22288.8	−	31355.9i	−0.00419369	−	0.00589970i
$491$	−4.69323e6	+	2.70964e6i	−0.878554	+	0.507233i	−0.870181	−	0.492731i	$-0.835998\pi$
$491$	−4.69323e6	+	2.70964e6i	−0.878554	+	0.507233i	−0.00837272	+	0.999965i	$0.502665\pi$
$492$		0			0
$493$		−	5.83330e6i		−	1.08093i
$494$	15477.1	−	8935.70i	0.00285346	−	0.00164745i
$495$		0			0
$496$		−	9.48872e6i		−	1.73182i
$497$	5.12128e6	+	4.65948e6i	0.930010	+	0.846148i
$498$		0			0
$499$	−6.40906e6			−1.15224			−0.576120	−	0.817365i	$-0.695434\pi$
$499$	−6.40906e6			−1.15224			−0.576120	+	0.817365i	$0.695434\pi$
$500$	−2.33685e6	+	4.04754e6i	−0.418028	+	0.724046i
$501$		0			0
$502$	−24501.2	+	14145.8i	−0.00433939	+	0.00250535i
$503$	350628.			0.0617912			0.0308956	−	0.999523i	$-0.490164\pi$
$503$	350628.			0.0617912			0.0308956	+	0.999523i	$0.490164\pi$
$504$		0			0
$505$	5.65820e6			0.987302
$506$	−6762.00	+	3904.04i	−0.00117408	+	0.000677857i
$507$		0			0
$508$	2.49026e6	−	4.31326e6i	0.428140	−	0.741559i
$509$	6.08531e6			1.04109			0.520545	−	0.853834i	$-0.325729\pi$
$509$	6.08531e6			1.04109			0.520545	+	0.853834i	$0.325729\pi$
$510$		0			0
$511$	2.16097e6	−	9.91380e6i	0.366098	−	1.67953i
$512$		−	191742.i		−	0.0323253i
$513$		0			0
$514$	34572.2	−	19960.3i	0.00577191	−	0.00333241i
$515$			8.56562e6i			1.42312i
$516$		0			0
$517$	3.60971e6	−	2.08407e6i	0.593945	−	0.342914i
$518$	10517.9	+	9569.47i	0.00172228	+	0.00156698i
$519$		0			0
$520$	−37824.0	−	65513.0i	−0.00613421	−	0.0106248i
$521$	4.61410e6	+	7.99185e6i	0.744719	+	1.28989i	0.950326	+	0.311256i	$0.100750\pi$
$521$	4.61410e6	+	7.99185e6i	0.744719	+	1.28989i	−0.205607	+	0.978635i	$0.565917\pi$
$522$		0			0
$523$	−6.25767e6	−	3.61287e6i	−1.00037	−	0.577561i	−0.0920089	−	0.995758i	$-0.529329\pi$
$523$	−6.25767e6	−	3.61287e6i	−1.00037	−	0.577561i	−0.908356	+	0.418197i	$0.862662\pi$
$524$	−3.83009e6	+	6.63391e6i	−0.609370	+	1.05546i
$525$		0			0
$526$	−6654.47	−	11525.9i	−0.00104869	−	0.00181639i
$527$		−	1.03479e7i		−	1.62303i
$528$		0			0
$529$	5.39157e6			0.837676
$530$	−28931.1	+	50110.2i	−0.00447379	+	0.00774884i
$531$		0			0
$532$	−835905.	+	3.83484e6i	−0.128050	+	0.587447i
$533$	−5.55493e6	−	3.20714e6i	−0.846955	−	0.488990i
$534$		0			0
$535$	−2.62867e6	−	1.51767e6i	−0.397056	−	0.229241i
$536$	48081.8	+	27760.0i	0.00722884	+	0.00417357i
$537$		0			0
$538$	−12020.1	−	6939.83i	−0.00179042	−	0.00103370i
$539$	−3.49436e6	+	330711.i	−0.518079	+	0.0490317i
$540$		0			0
$541$	−649951.	+	1.12575e6i	−0.0954746	+	0.165367i	−0.909807	−	0.415033i	$-0.863770\pi$
$541$	−649951.	+	1.12575e6i	−0.0954746	+	0.165367i	0.814332	+	0.580399i	$0.197104\pi$
$542$	−72105.9			−0.0105432
$543$		0			0
$544$		−	125461.i		−	0.0181765i
$545$	3.92773e6	+	6.80302e6i	0.566435	+	0.981094i
$546$		0			0
$547$	1.06154e6	−	1.83864e6i	0.151694	−	0.262742i	−0.780156	−	0.625585i	$-0.784861\pi$
$547$	1.06154e6	−	1.83864e6i	0.151694	−	0.262742i	0.931850	+	0.362843i	$0.118194\pi$
$548$	1.31293e6	+	758023.i	0.186763	+	0.107828i
$549$		0			0
$550$	3021.02	+	5232.55i	0.000425840	+	0.000737576i
$551$	2.47141e6	+	4.28061e6i	0.346789	+	0.600657i
$552$		0			0
$553$	6.24860e6	+	1.36205e6i	0.868900	+	0.189400i
$554$	−63358.1	+	36579.8i	−0.00877057	+	0.00506369i
$555$		0			0
$556$			1.50919e6i			0.207042i
$557$	−616805.	+	356112.i	−0.0842383	+	0.0486350i	−0.541527	−	0.840683i	$-0.682154\pi$
$557$	−616805.	+	356112.i	−0.0842383	+	0.0486350i	0.457289	+	0.889318i	$0.348820\pi$
$558$		0			0
$559$			6.69073e6i			0.905616i
$560$	8.11576e6	+	1.76904e6i	1.09360	+	0.238379i
$561$		0			0
$562$	91167.3			0.0121758
$563$	1.53945e6	−	2.66640e6i	0.204689	−	0.354532i	−0.745345	−	0.666679i	$-0.767715\pi$
$563$	1.53945e6	−	2.66640e6i	0.204689	−	0.354532i	0.950034	+	0.312148i	$0.101048\pi$
$564$		0			0
$565$	−1.95037e6	+	1.12605e6i	−0.257037	+	0.148400i
$566$	−15325.5			−0.00201082
$567$		0			0
$568$	125022.			0.0162598
$569$	257274.	−	148537.i	0.0333131	−	0.0192333i	−0.483251	−	0.875482i	$-0.660544\pi$
$569$	257274.	−	148537.i	0.0333131	−	0.0192333i	0.516564	+	0.856249i	$0.327211\pi$
$570$		0			0
$571$	48109.5	−	83328.1i	0.00617505	−	0.0106955i	−0.862921	−	0.505338i	$-0.831368\pi$
$571$	48109.5	−	83328.1i	0.00617505	−	0.0106955i	0.869096	+	0.494643i	$0.164701\pi$
$572$	−3.45091e6			−0.441005
$573$		0			0
$574$	−56112.1	+	17911.1i	−0.00710848	+	0.00226904i
$575$			808462.i			0.101974i
$576$		0			0
$577$	695339.	−	401454.i	0.0869475	−	0.0501991i	−0.455896	−	0.890033i	$-0.650681\pi$
$577$	695339.	−	401454.i	0.0869475	−	0.0501991i	0.542843	+	0.839834i	$0.317348\pi$
$578$			6331.72i			0.000788319i
$579$		0			0
$580$	9.05952e6	−	5.23051e6i	1.11824	−	0.645616i
$581$	2.23619e6	+	7.00556e6i	0.274833	+	0.860999i
$582$		0			0
$583$	2.63962e6	+	4.57195e6i	0.321640	+	0.557096i
$584$	−91608.5	−	158671.i	−0.0111149	−	0.0192515i
$585$		0			0
$586$	−66490.4	−	38388.2i	−0.00799861	−	0.00461800i
$587$	3.17488e6	−	5.49905e6i	0.380305	−	0.658707i	−0.610801	−	0.791784i	$-0.709152\pi$
$587$	3.17488e6	−	5.49905e6i	0.380305	−	0.658707i	0.991106	+	0.133077i	$0.0424857\pi$
$588$		0			0
$589$	4.38412e6	+	7.59352e6i	0.520708	+	0.901893i
$590$		−	76237.8i		−	0.00901655i
$591$		0			0
$592$	−3.07024e6			−0.360054
$593$	−6.03938e6	+	1.04605e7i	−0.705271	+	1.22156i	0.261323	+	0.965251i	$0.415841\pi$
$593$	−6.03938e6	+	1.04605e7i	−0.705271	+	1.22156i	−0.966594	+	0.256313i	$0.917492\pi$
$594$		0			0
$595$	8.85063e6	+	1.92923e6i	1.02490	+	0.223404i
$596$	1.06756e7	+	6.16354e6i	1.23105	+	0.710746i
$597$		0			0
$598$	16720.5	+	9653.58i	0.00191204	+	0.00110391i
$599$	−1.65969e6	−	958221.i	−0.188999	−	0.109119i	0.402515	−	0.915413i	$-0.368136\pi$
$599$	−1.65969e6	−	958221.i	−0.188999	−	0.109119i	−0.591514	+	0.806295i	$0.701469\pi$
$600$		0			0
$601$	−198299.	−	114488.i	−0.0223941	−	0.0129292i	0.488761	−	0.872418i	$-0.337449\pi$
$601$	−198299.	−	114488.i	−0.0223941	−	0.0129292i	−0.511155	+	0.859488i	$0.670782\pi$
$602$	45445.3	+	41347.3i	0.00511090	+	0.00465004i
$603$		0			0
$604$	1.84192e6	−	3.19030e6i	0.205437	−	0.355828i
$605$	−7.34891e6			−0.816271
$606$		0			0
$607$			9.39692e6i			1.03518i	0.855630	+	0.517588i	$0.173170\pi$
$607$			9.39692e6i			1.03518i	−0.855630	+	0.517588i	$0.826830\pi$
$608$	53154.2	+	92065.8i	0.00583148	+	0.0101004i
$609$		0			0
$610$	13825.9	−	23947.2i	0.00150442	−	0.00260574i
$611$	−8.92578e6	−	5.15330e6i	−0.967260	−	0.558448i
$612$		0			0
$613$	−2.24094e6	−	3.88142e6i	−0.240868	−	0.417195i	0.720094	−	0.693877i	$-0.244099\pi$
$613$	−2.24094e6	−	3.88142e6i	−0.240868	−	0.417195i	−0.960962	+	0.276681i	$0.910765\pi$
$614$	−30001.4	−	51963.9i	−0.00321159	−	0.00556264i
$615$		0			0
$616$	−42652.7	+	46880.0i	−0.00452892	+	0.00497778i
$617$	−2.69919e6	+	1.55838e6i	−0.285444	+	0.164801i	−0.635885	−	0.771783i	$-0.719365\pi$
$617$	−2.69919e6	+	1.55838e6i	−0.285444	+	0.164801i	0.350441	+	0.936585i	$0.386032\pi$
$618$		0			0
$619$		−	8.07242e6i		−	0.846793i	−0.905944	−	0.423397i	$-0.860838\pi$
$619$		−	8.07242e6i		−	0.846793i	0.905944	−	0.423397i	$-0.139162\pi$
$620$	1.60710e7	−	9.27860e6i	1.67905	−	0.969400i
$621$		0			0
$622$			104564.i			0.0108369i
$623$	−4.54378e6	−	1.42348e7i	−0.469026	−	1.46937i
$624$		0			0
$625$	−1.16117e7			−1.18904
$626$	7663.46	−	13273.5i	0.000781608	−	0.00135379i
$627$		0			0
$628$	−735229.	+	424485.i	−0.0743915	+	0.0429500i
$629$	−3.34824e6			−0.337435
$630$		0			0
$631$	−2.90946e6			−0.290897			−0.145448	−	0.989366i	$-0.546463\pi$
$631$	−2.90946e6			−0.290897			−0.145448	+	0.989366i	$0.546463\pi$
$632$	100009.	−	57740.2i	0.00995970	−	0.00575024i
$633$		0			0
$634$	−8495.32	+	14714.3i	−0.000839377	+	0.00145384i
$635$	9.74005e6			0.958577
$636$		0			0
$637$	5.02847e6	+	7.07406e6i	0.491007	+	0.690749i
$638$			39907.8i			0.00388156i
$639$		0			0
$640$	259797.	−	149994.i	0.0250717	−	0.0144752i
$641$		−	4.28928e6i		−	0.412325i	−0.978518	−	0.206162i	$-0.933902\pi$
$641$		−	4.28928e6i		−	0.412325i	0.978518	−	0.206162i	$-0.0660975\pi$
$642$		0			0
$643$	−7.44581e6	+	4.29884e6i	−0.710206	+	0.410038i	−0.811137	−	0.584856i	$-0.801151\pi$
$643$	−7.44581e6	+	4.29884e6i	−0.710206	+	0.410038i	0.100931	+	0.994893i	$0.467818\pi$
$644$	−4.03941e6	+	1.28939e6i	−0.383799	+	0.122510i
$645$		0			0
$646$	19321.1	+	33465.1i	0.00182159	+	0.00315508i
$647$	2.55765e6	+	4.42997e6i	0.240204	+	0.416045i	0.960772	−	0.277339i	$-0.0894524\pi$
$647$	2.55765e6	+	4.42997e6i	0.240204	+	0.416045i	−0.720568	+	0.693384i	$0.756119\pi$
$648$		0			0
$649$	−6.02388e6	−	3.47789e6i	−0.561390	−	0.324119i
$650$	7470.11	−	12938.6i	0.000693495	−	0.00120117i
$651$		0			0
$652$	−7.17500e6	−	1.24275e7i	−0.661002	−	1.14489i
$653$		−	1.65599e7i		−	1.51976i	−0.650063	−	0.759880i	$-0.725257\pi$
$653$		−	1.65599e7i		−	1.51976i	0.650063	−	0.759880i	$-0.274743\pi$
$654$		0			0
$655$	−1.49805e7			−1.36434
$656$	6.35881e6	−	1.10138e7i	0.576921	−	0.999256i
$657$		0			0
$658$	−90162.1	+	28780.0i	−0.00811819	+	0.00259135i
$659$	−1.63291e7	−	9.42759e6i	−1.46470	−	0.845644i	−0.465475	−	0.885061i	$-0.654116\pi$
$659$	−1.63291e7	−	9.42759e6i	−1.46470	−	0.845644i	−0.999223	+	0.0394175i	$0.987450\pi$
$660$		0			0
$661$	−4.60955e6	−	2.66132e6i	−0.410350	−	0.236916i	0.280590	−	0.959828i	$-0.409470\pi$
$661$	−4.60955e6	−	2.66132e6i	−0.410350	−	0.236916i	−0.690940	+	0.722912i	$0.742803\pi$
$662$	108496.	+	62640.2i	0.00962208	+	0.00555531i
$663$		0			0
$664$	114998.	+	66393.9i	0.0101220	+	0.00584397i
$665$	−7.31215e6	+	2.33406e6i	−0.641196	+	0.204672i
$666$		0			0
$667$	−2.66996e6	+	4.62451e6i	−0.232375	+	0.402486i
$668$	−1.42655e7			−1.23694
$669$		0			0
$670$			54287.2i			0.00467208i
$671$	−1.26145e6	−	2.18489e6i	−0.108159	−	0.187337i
$672$		0			0
$673$	−3.88232e6	+	6.72437e6i	−0.330410	+	0.572287i	−0.982592	−	0.185775i	$-0.940520\pi$
$673$	−3.88232e6	+	6.72437e6i	−0.330410	+	0.572287i	0.652182	+	0.758062i	$0.273854\pi$
$674$	−125795.	−	72627.8i	−0.0106663	−	0.00615819i
$675$		0			0
$676$	−1.67389e6	−	2.89926e6i	−0.140883	−	0.244017i
$677$	−7.37106e6	−	1.27671e7i	−0.618100	−	1.07058i	−0.989832	−	0.142240i	$-0.954569\pi$
$677$	−7.37106e6	−	1.27671e7i	−0.618100	−	1.07058i	0.371732	−	0.928340i	$-0.378764\pi$
$678$		0			0
$679$	2.43440e6	−	777067.i	0.202637	−	0.0646821i
$680$	141655.	−	81784.3i	0.0117479	−	0.00678263i
$681$		0			0
$682$			70793.9i			0.00582821i
$683$	−3.30879e6	+	1.91033e6i	−0.271404	+	0.156695i	−0.629526	−	0.776980i	$-0.716751\pi$
$683$	−3.30879e6	+	1.91033e6i	−0.271404	+	0.156695i	0.358121	+	0.933675i	$0.383417\pi$
$684$		0			0
$685$			2.96482e6i			0.241420i
$686$	79123.8	+	9561.50i	0.00641944	+	0.000775739i
$687$		0			0
$688$	−1.32657e7			−1.06847
$689$	6.52701e6	−	1.13051e7i	0.523801	−	0.907250i
$690$		0			0
$691$	3.71352e6	−	2.14400e6i	0.295863	−	0.170817i	−0.344720	−	0.938706i	$-0.612026\pi$
$691$	3.71352e6	−	2.14400e6i	0.295863	−	0.170817i	0.640583	+	0.767889i	$0.278693\pi$
$692$	1.21251e7			0.962545
$693$		0			0
$694$	115124.			0.00907333
$695$	−2.55601e6	+	1.47571e6i	−0.200724	+	0.115888i
$696$		0			0
$697$	6.93459e6	−	1.20111e7i	0.540678	−	0.936482i
$698$	−98000.8			−0.00761362
$699$		0			0
$700$	997754.	+	3.12577e6i	0.0769623	+	0.241108i
$701$		−	3.30925e6i		−	0.254351i	−0.991880	−	0.127176i	$-0.959409\pi$
$701$		−	3.30925e6i		−	0.254351i	0.991880	−	0.127176i	$-0.0405912\pi$
$702$		0			0
$703$	2.45701e6	−	1.41856e6i	0.187508	−	0.108258i
$704$		−	6.84156e6i		−	0.520263i
$705$		0			0
$706$	−40386.2	+	23317.0i	−0.00304945	+	0.00176060i
$707$	−7.88862e6	+	8.67046e6i	−0.593544	+	0.652370i
$708$		0			0
$709$	1.05888e7	+	1.83403e7i	0.791099	+	1.37022i	0.925287	+	0.379267i	$0.123824\pi$
$709$	1.05888e7	+	1.83403e7i	0.791099	+	1.37022i	−0.134188	+	0.990956i	$0.542843\pi$
$710$	61123.0	+	105868.i	0.00455050	+	0.00788169i
$711$		0			0
$712$	−233666.	−	134907.i	−0.0172741	−	0.00997323i
$713$	−4.73634e6	+	8.20358e6i	−0.348914	+	0.604337i
$714$		0			0
$715$	−3.37435e6	−	5.84455e6i	−0.246845	−	0.427549i
$716$			2.11155e7i			1.53928i
$717$		0			0
$718$	70150.2			0.00507830
$719$	−1.36318e7	+	2.36110e7i	−0.983401	+	1.70330i	−0.334564	+	0.942373i	$0.608589\pi$
$719$	−1.36318e7	+	2.36110e7i	−0.983401	+	1.70330i	−0.648837	+	0.760927i	$0.724744\pi$
$720$		0			0
$721$	−1.31257e7	−	1.19421e7i	−0.940339	−	0.855546i
$722$	50080.1	+	28913.8i	0.00357538	+	0.00206425i
$723$		0			0
$724$	1.52914e7	+	8.82849e6i	1.08418	+	0.625950i
$725$	3.57852e6	+	2.06606e6i	0.252848	+	0.145982i
$726$		0			0
$727$	−9.28331e6	−	5.35972e6i	−0.651429	−	0.376103i	0.137575	−	0.990491i	$-0.456069\pi$
$727$	−9.28331e6	−	5.35972e6i	−0.651429	−	0.376103i	−0.789003	+	0.614389i	$0.789403\pi$
$728$	153124.	+	33377.5i	0.0107082	+	0.00233413i
$729$		0			0
$730$	89574.3	−	155147.i	0.00622123	−	0.0107755i
$731$	−1.44669e7			−1.00134
$732$		0			0
$733$			1.35789e7i			0.933477i	0.884395	+	0.466739i	$0.154571\pi$
$733$			1.35789e7i			0.933477i	−0.884395	+	0.466739i	$0.845429\pi$
$734$	−44981.1	−	77909.6i	−0.00308170	−	0.00533766i
$735$		0			0
$736$	−57424.6	+	99462.3i	−0.00390754	+	0.00676805i
$737$	4.28947e6	+	2.47653e6i	0.290894	+	0.167948i
$738$		0			0
$739$	−3.64402e6	−	6.31163e6i	−0.245454	−	0.425139i	0.716805	−	0.697274i	$-0.245604\pi$
$739$	−3.64402e6	−	6.31163e6i	−0.245454	−	0.425139i	−0.962259	+	0.272135i	$0.912270\pi$
$740$	−3.00225e6	−	5.20005e6i	−0.201543	−	0.349083i
$741$		0			0
$742$	−36451.8	−	114197.i	−0.00243058	−	0.00761453i
$743$	1.67522e7	−	9.67187e6i	1.11327	−	0.642744i	0.173593	−	0.984818i	$-0.444462\pi$
$743$	1.67522e7	−	9.67187e6i	1.11327	−	0.642744i	0.939673	+	0.342073i	$0.111129\pi$
$744$		0			0
$745$			2.41072e7i			1.59132i
$746$	84277.5	−	48657.7i	0.00554453	−	0.00320114i
$747$		0			0
$748$		−	7.46168e6i		−	0.487621i
$749$	5.99050e6	−	1.91218e6i	0.390174	−	0.124545i
$750$		0			0
$751$	1.51858e7			0.982512			0.491256	−	0.871015i	$-0.336538\pi$
$751$	1.51858e7			0.982512			0.491256	+	0.871015i	$0.336538\pi$
$752$	1.02175e7	−	1.76972e7i	0.658868	−	1.14119i
$753$		0			0
$754$	85459.9	−	49340.3i	0.00547437	−	0.00316063i
$755$	7.20424e6			0.459961
$756$		0			0
$757$	−1.74980e7			−1.10981			−0.554906	−	0.831913i	$-0.687246\pi$
$757$	−1.74980e7			−1.10981			−0.554906	+	0.831913i	$0.687246\pi$
$758$	51481.8	−	29723.0i	0.00325447	−	0.00187897i
$759$		0			0
$760$	−69299.5	+	120030.i	−0.00435207	+	0.00753801i
$761$	1.07783e7			0.674666			0.337333	−	0.941385i	$-0.390475\pi$
$761$	1.07783e7			0.674666			0.337333	+	0.941385i	$0.390475\pi$
$762$		0			0
$763$	−1.59008e7	−	3.46599e6i	−0.988796	−	0.215534i
$764$			1.31678e6i			0.0816170i
$765$		0			0
$766$	52506.8	−	30314.8i	0.00323328	−	0.00186674i
$767$			1.71996e7i			1.05568i
$768$		0			0
$769$	8.07648e6	−	4.66296e6i	0.492500	−	0.284345i	−0.233111	−	0.972450i	$-0.574891\pi$
$769$	8.07648e6	−	4.66296e6i	0.492500	−	0.284345i	0.725611	+	0.688105i	$0.241557\pi$
$770$	−60550.5	−	13198.6i	−0.00368037	−	0.000802233i
$771$		0			0
$772$	−5.18378e6	−	8.97857e6i	−0.313043	−	0.542206i
$773$	5.87761e6	+	1.01803e7i	0.353795	+	0.612792i	0.986911	−	0.161266i	$-0.0515576\pi$
$773$	5.87761e6	+	1.01803e7i	0.353795	+	0.612792i	−0.633116	+	0.774057i	$0.718224\pi$
$774$		0			0
$775$	6.34807e6	+	3.66506e6i	0.379654	+	0.219193i
$776$	23071.6	−	39961.1i	0.00137538	−	0.00238223i
$777$		0			0
$778$	57964.4	+	100397.i	0.00343330	+	0.00594665i
$779$			1.17520e7i			0.693853i
$780$		0			0
$781$	1.11535e7			0.654308
$782$	−20873.3	+	36153.6i	−0.00122060	+	0.00211415i
$783$		0			0
$784$	−1.40258e7	+	9.96997e6i	−0.814960	+	0.579300i
$785$	−1.43784e6	−	830135.i	−0.0832789	−	0.0480811i
$786$		0			0
$787$	−7.84640e6	−	4.53012e6i	−0.451579	−	0.260719i	0.256918	−	0.966433i	$-0.417293\pi$
$787$	−7.84640e6	−	4.53012e6i	−0.451579	−	0.260719i	−0.708497	+	0.705714i	$0.750626\pi$
$788$	−2.49084e7	−	1.43809e7i	−1.42899	−	0.825030i
$789$		0			0
$790$	97788.2	+	56458.1i	0.00557467	+	0.00321854i
$791$	993670.	−	4.55861e6i	0.0564678	−	0.259055i
$792$		0			0
$793$	−3.11920e6	+	5.40262e6i	−0.176141	+	0.305085i
$794$	90506.0			0.00509479
$795$		0			0
$796$		−	6.86300e6i		−	0.383912i
$797$	−588634.	−	1.01954e6i	−0.0328246	−	0.0568538i	0.849146	−	0.528157i	$-0.177117\pi$
$797$	−588634.	−	1.01954e6i	−0.0328246	−	0.0568538i	−0.881971	+	0.471304i	$0.843784\pi$
$798$		0			0
$799$	1.11426e7	−	1.92996e7i	0.617478	−	1.06950i
$800$	76965.6	+	44436.1i	0.00425179	+	0.00245477i
$801$		0			0
$802$	−107049.	−	185415.i	−0.00587690	−	0.0101791i
$803$	−8.17258e6	−	1.41553e7i	−0.447270	−	0.774695i
$804$		0			0
$805$	−6.13355e6	−	5.58047e6i	−0.333597	−	0.303516i
$806$	151600.	−	87526.5i	0.00821983	−	0.00474572i
$807$		0			0
$808$			211666.i			0.0114057i
$809$	−2.15920e6	+	1.24662e6i	−0.115990	+	0.0669671i	−0.556873	−	0.830598i	$-0.687999\pi$
$809$	−2.15920e6	+	1.24662e6i	−0.115990	+	0.0669671i	0.440882	+	0.897565i	$0.354666\pi$
$810$		0			0
$811$			2.14197e7i			1.14357i	0.820405	+	0.571783i	$0.193748\pi$
$811$			2.14197e7i			1.14357i	−0.820405	+	0.571783i	$0.806252\pi$
$812$	−4.61563e6	+	2.11749e7i	−0.245663	+	1.12702i
$813$		0			0
$814$	22906.6			0.00121171
$815$	1.40316e7	−	2.43035e7i	0.739971	−	1.28167i
$816$		0			0
$817$	1.06162e7	−	6.12924e6i	0.556432	−	0.321256i
$818$	49287.5			0.00257545
$819$		0			0
$820$	2.48720e7			1.29174
$821$	−1.12322e7	+	6.48492e6i	−0.581577	+	0.335774i	−0.761760	−	0.647859i	$-0.775664\pi$
$821$	−1.12322e7	+	6.48492e6i	−0.581577	+	0.335774i	0.180183	+	0.983633i	$0.442331\pi$
$822$		0			0
$823$	3.07468e6	−	5.32550e6i	0.158234	−	0.274070i	−0.775998	−	0.630736i	$-0.782753\pi$
$823$	3.07468e6	−	5.32550e6i	0.158234	−	0.274070i	0.934232	+	0.356666i	$0.116087\pi$
$824$	−320429.			−0.0164404
$825$		0			0
$826$	116825.	+	106290.i	0.00595778	+	0.00542055i
$827$		−	8.96370e6i		−	0.455747i	−0.973691	−	0.227873i	$-0.926823\pi$
$827$		−	8.96370e6i		−	0.455747i	0.973691	−	0.227873i	$-0.0731772\pi$
$828$		0			0
$829$	9.22718e6	−	5.32732e6i	0.466319	−	0.269229i	−0.248379	−	0.968663i	$-0.579898\pi$
$829$	9.22718e6	−	5.32732e6i	0.466319	−	0.269229i	0.714697	+	0.699434i	$0.246564\pi$
$830$			129839.i			0.00654200i
$831$		0			0
$832$	−1.46507e7	+	8.45860e6i	−0.733755	+	0.423633i
$833$	−1.52958e7	+	1.08727e7i	−0.763764	+	0.542908i
$834$		0			0
$835$	−1.39491e7	−	2.41605e7i	−0.692355	−	1.19919i
$836$	3.16131e6	+	5.47554e6i	0.156441	+	0.270964i
$837$		0			0
$838$	−115027.	−	66411.0i	−0.00565836	−	0.00326686i
$839$	1.54509e7	−	2.67618e7i	0.757791	−	1.31253i	−0.186184	−	0.982515i	$-0.559612\pi$
$839$	1.54509e7	−	2.67618e7i	0.757791	−	1.31253i	0.943975	−	0.330017i	$-0.107054\pi$
$840$		0			0
$841$	3.39083e6	+	5.87308e6i	0.165316	+	0.286336i
$842$		−	161718.i		−	0.00786099i
$843$		0			0
$844$	−4.96127e6			−0.239738
$845$	3.27351e6	−	5.66988e6i	0.157714	−	0.273169i
$846$		0			0
$847$	1.02458e7	−	1.12613e7i	0.490724	−	0.539359i
$848$	2.24147e7	+	1.29411e7i	1.07039	+	0.617992i
$849$		0			0
$850$	27976.3	+	16152.1i	0.00132814	+	0.000766800i
$851$	2.65441e6	+	1.53252e6i	0.125645	+	0.0725409i
$852$		0			0
$853$	−1.38828e7	−	8.01527e6i	−0.653290	−	0.377177i	0.136426	−	0.990650i	$-0.456439\pi$
$853$	−1.38828e7	−	8.01527e6i	−0.653290	−	0.377177i	−0.789716	+	0.613473i	$0.789772\pi$
$854$	17420.0	+	54573.5i	0.000817342	+	0.00256057i
$855$		0			0
$856$	56773.9	−	98335.2i	0.00264828	−	0.00458696i
$857$	−1.99838e7			−0.929450			−0.464725	−	0.885455i	$-0.653847\pi$
$857$	−1.99838e7			−0.929450			−0.464725	+	0.885455i	$0.653847\pi$
$858$		0			0
$859$		−	1.65184e7i		−	0.763808i	−0.924202	−	0.381904i	$-0.875268\pi$
$859$		−	1.65184e7i		−	0.763808i	0.924202	−	0.381904i	$-0.124732\pi$
$860$	−1.29720e7	−	2.24681e7i	−0.598082	−	1.03591i
$861$		0			0
$862$	19247.8	−	33338.2i	0.000882294	−	0.00152818i
$863$	2.59300e7	+	1.49707e7i	1.18516	+	0.684251i	0.957202	−	0.289420i	$-0.0934625\pi$
$863$	2.59300e7	+	1.49707e7i	1.18516	+	0.684251i	0.227956	+	0.973672i	$0.426796\pi$
$864$		0			0
$865$	1.18561e7	+	2.05354e7i	0.538769	+	0.933175i
$866$	−59091.8	−	102350.i	−0.00267752	−	0.00463760i
$867$		0			0
$868$	−8.18782e6	+	3.75629e7i	−0.368866	+	1.69223i
$869$	8.92200e6	−	5.15112e6i	0.400786	−	0.231394i
$870$		0			0
$871$		−	1.22475e7i		−	0.547017i
$872$	−254492.	+	146931.i	−0.0113340	+	0.00654368i
$873$		0			0
$874$		−	35373.8i		−	0.00156640i
$875$	1.27430e7	−	1.40059e7i	0.562665	−	0.618431i
$876$		0			0
$877$	4.23314e7			1.85850			0.929252	−	0.369447i	$-0.120453\pi$
$877$	4.23314e7			1.85850			0.929252	+	0.369447i	$0.120453\pi$
$878$	−7154.88	+	12392.6i	−0.000313232	+	0.000542534i
$879$		0			0
$880$	1.15880e7	−	6.69034e6i	0.504431	−	0.291234i
$881$	−3.17552e7			−1.37840			−0.689201	−	0.724571i	$-0.742038\pi$
$881$	−3.17552e7			−1.37840			−0.689201	+	0.724571i	$0.742038\pi$
$882$		0			0
$883$	1.71883e7			0.741874			0.370937	−	0.928658i	$-0.379037\pi$
$883$	1.71883e7			0.741874			0.370937	+	0.928658i	$0.379037\pi$
$884$	−1.59787e7	+	9.22529e6i	−0.687717	+	0.397054i
$885$		0			0
$886$	−122777.	+	212656.i	−0.00525452	+	0.00910110i
$887$	2.36859e7			1.01084			0.505419	−	0.862874i	$-0.331338\pi$
$887$	2.36859e7			1.01084			0.505419	+	0.862874i	$0.331338\pi$
$888$		0			0
$889$	−1.35795e7	+	1.49254e7i	−0.576275	+	0.633390i
$890$		−	263823.i		−	0.0111645i
$891$		0			0
$892$	−2.89925e7	+	1.67388e7i	−1.22004	+	0.704388i
$893$			1.88833e7i			0.792410i
$894$		0			0
$895$	−3.57617e7	+	2.06470e7i	−1.49231	+	0.861588i
$896$	−132361.	+	607225.i	−0.00550794	+	0.0252685i
$897$		0			0
$898$	−54243.2	−	93952.0i	−0.00224468	−	0.00388790i
$899$	2.42078e7	+	4.19292e7i	0.998980	+	1.73028i
$900$		0			0
$901$	2.44443e7	+	1.41129e7i	1.00315	+	0.579169i
$902$	−47442.1	+	82172.2i	−0.00194155	+	0.00336286i
$903$		0			0
$904$	−42123.9	−	72960.7i	−0.00171438	−	0.00296940i
$905$			3.45305e7i			1.40146i
$906$		0			0
$907$	4.91466e7			1.98370			0.991849	−	0.127420i	$-0.0406697\pi$
$907$	4.91466e7			1.98370			0.991849	+	0.127420i	$0.0406697\pi$
$908$	−1.44534e7	+	2.50340e7i	−0.581775	+	1.00766i
$909$		0			0
$910$	46598.1	+	145983.i	0.00186537	+	0.00584384i
$911$	3.73255e7	+	2.15499e7i	1.49008	+	0.860298i	0.999936	−	0.0113430i	$-0.00361066\pi$
$911$	3.73255e7	+	2.15499e7i	1.49008	+	0.860298i	0.490145	+	0.871641i	$0.336944\pi$
$912$		0			0
$913$	1.02592e7	+	5.92313e6i	0.407319	+	0.235166i
$914$	54185.2	+	31283.9i	0.00214543	+	0.00123867i
$915$		0			0
$916$	1.67469e7	+	9.66883e6i	0.659472	+	0.380746i
$917$	2.08857e7	−	2.29557e7i	0.820211	−	0.901502i
$918$		0			0
$919$	1.93863e7	−	3.35781e7i	0.757193	−	1.31150i	−0.187084	−	0.982344i	$-0.559904\pi$
$919$	1.93863e7	−	3.35781e7i	0.757193	−	1.31150i	0.944277	−	0.329152i	$-0.106763\pi$
$920$	−149734.			−0.00583244
$921$		0			0
$922$		−	17776.6i		−	0.000688685i
$923$	−1.37897e7	−	2.38844e7i	−0.532782	−	0.922805i
$924$		0			0
$925$	1.18589e6	−	2.05403e6i	0.0455713	−	0.0789317i
$926$	−87146.2	−	50313.9i	−0.00333980	−	0.00192824i
$927$		0			0
$928$	293502.	+	508360.i	0.0111877	+	0.0193777i
$929$	−68816.6	−	119194.i	−0.00261610	−	0.00453121i	0.864714	−	0.502264i	$-0.167499\pi$
$929$	−68816.6	−	119194.i	−0.00261610	−	0.00453121i	−0.867330	+	0.497733i	$0.834166\pi$
$930$		0			0
$931$	6.61791e6	−	1.44591e7i	0.250234	−	0.546721i
$932$	7.63442e6	−	4.40773e6i	0.287896	−	0.166217i
$933$		0			0
$934$		−	47837.8i		−	0.00179434i
$935$	1.26373e7	−	7.29614e6i	0.472743	−	0.272938i
$936$		0			0
$937$		−	3.30702e7i		−	1.23052i	−0.788325	−	0.615259i	$-0.789052\pi$
$937$		−	3.30702e7i		−	1.23052i	0.788325	−	0.615259i	$-0.210948\pi$
$938$	−83188.2	−	75686.9i	−0.00308713	−	0.00280875i
$939$		0			0
$940$	3.99649e7			1.47523
$941$	−3.37537e6	+	5.84631e6i	−0.124265	+	0.215233i	−0.921445	−	0.388508i	$-0.872990\pi$
$941$	−3.37537e6	+	5.84631e6i	−0.124265	+	0.215233i	0.797181	+	0.603741i	$0.206324\pi$
$942$		0			0
$943$	−1.09952e7	+	6.34806e6i	−0.402645	+	0.232467i
$944$	−3.41018e7			−1.24551
$945$		0			0
$946$	98973.8			0.00359577
$947$	−184943.	+	106777.i	−0.00670137	+	0.00386904i	−0.503347	−	0.864084i	$-0.667898\pi$
$947$	−184943.	+	106777.i	−0.00670137	+	0.00386904i	0.496646	+	0.867953i	$0.334565\pi$
$948$		0			0
$949$	−2.02084e7	+	3.50020e7i	−0.728395	+	1.26162i
$950$	−27372.8			−0.000984036
$951$		0			0
$952$	−72169.9	+	331091.i	−0.00258086	+	0.0118401i
$953$			5.03164e6i			0.179464i	0.995966	+	0.0897320i	$0.0286011\pi$
$953$			5.03164e6i			0.179464i	−0.995966	+	0.0897320i	$0.971399\pi$
$954$		0			0
$955$	−2.23014e6	+	1.28757e6i	−0.0791267	+	0.0456838i
$956$			3.38634e7i			1.19835i
$957$		0			0
$958$	−121474.	+	70133.2i	−0.00427632	+	0.00246894i
$959$	−4.54321e6	−	4.13354e6i	−0.159520	−	0.145136i
$960$		0			0
$961$	2.86286e7	+	4.95862e7i	0.999980	+	1.73202i
$962$	−28320.7	−	49052.9i	−0.000986657	−	0.00170894i
$963$		0			0
$964$	1.37315e7	+	7.92788e6i	0.475910	+	0.274767i
$965$	1.01376e7	−	1.75588e7i	0.350441	−	0.606982i
$966$		0			0
$967$	−1.93524e7	−	3.35193e7i	−0.665531	−	1.15273i	−0.979141	−	0.203182i	$-0.934872\pi$
$967$	−1.93524e7	−	3.35193e7i	−0.665531	−	1.15273i	0.313610	−	0.949552i	$-0.398462\pi$
$968$		−	274913.i		−	0.00942989i
$969$		0			0
$970$	45118.5			0.00153966
$971$	2.76587e6	−	4.79062e6i	0.0941419	−	0.163059i	−0.815108	−	0.579309i	$-0.803323\pi$
$971$	2.76587e6	−	4.79062e6i	0.0941419	−	0.163059i	0.909250	+	0.416250i	$0.136656\pi$
$972$		0			0
$973$	1.30223e6	−	5.97418e6i	0.0440967	−	0.202300i
$974$	−259214.	−	149657.i	−0.00875510	−	0.00505476i
$975$		0			0
$976$	−1.07118e7	−	6.18445e6i	−0.359946	−	0.207815i
$977$	3.58671e7	+	2.07079e7i	1.20215	+	0.694064i	0.961034	−	0.276431i	$-0.0891519\pi$
$977$	3.58671e7	+	2.07079e7i	1.20215	+	0.694064i	0.241120	+	0.970495i	$0.422485\pi$
$978$		0			0
$979$	−2.08458e7	−	1.20354e7i	−0.695125	−	0.401330i
$980$	−3.06013e7	−	1.40062e7i	−1.01783	−	0.465860i
$981$		0			0
$982$	99113.2	−	171669.i	0.00327984	−	0.00568085i
$983$	7.15134e6			0.236050			0.118025	−	0.993011i	$-0.462344\pi$
$983$	7.15134e6			0.236050			0.118025	+	0.993011i	$0.462344\pi$
$984$		0			0
$985$		−	5.62474e7i		−	1.84719i
$986$	106685.	+	184784.i	0.00349472	+	0.00605303i
$987$		0			0
$988$	7.81700e6	−	1.35394e7i	0.254770	−	0.441274i
$989$	1.14690e7	+	6.62166e6i	0.372852	+	0.215266i
$990$		0			0
$991$	6.45962e6	+	1.11884e7i	0.208941	+	0.361896i	0.951381	−	0.308016i	$-0.0996651\pi$
$991$	6.45962e6	+	1.11884e7i	0.208941	+	0.361896i	−0.742440	+	0.669912i	$0.766332\pi$
$992$	520654.	+	901799.i	0.0167985	+	0.0290958i
$993$		0			0
$994$	−247447.	−	53937.5i	−0.00794357	−	0.00173151i
$995$	1.16234e7	−	6.71075e6i	0.372198	−	0.214889i
$996$		0			0
$997$		−	7.20160e6i		−	0.229452i	−0.993397	−	0.114726i	$-0.963401\pi$
$997$		−	7.20160e6i		−	0.229452i	0.993397	−	0.114726i	$-0.0365990\pi$
$998$	203023.	−	117215.i	0.00645236	−	0.00372527i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.6.s.a.89.20		76
3.2	odd	2		63.6.s.a.47.19	yes	76
7.3	odd	6		189.6.i.a.143.20		76
9.4	even	3		63.6.i.a.5.20	✓	76
9.5	odd	6		189.6.i.a.152.19		76
21.17	even	6		63.6.i.a.38.19	yes	76
63.31	odd	6		63.6.s.a.59.19	yes	76
63.59	even	6	inner	189.6.s.a.17.20		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.20	✓	76	9.4	even	3
63.6.i.a.38.19	yes	76	21.17	even	6
63.6.s.a.47.19	yes	76	3.2	odd	2
63.6.s.a.59.19	yes	76	63.31	odd	6
189.6.i.a.143.20		76	7.3	odd	6
189.6.i.a.152.19		76	9.5	odd	6
189.6.s.a.17.20		76	63.59	even	6	inner
189.6.s.a.89.20		76	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.0316775 + 0.0182890i) q^{2} +(-15.9993 + 27.7117i) q^{4} -62.5776 q^{5} +(87.2452 - 95.8920i) q^{7} -2.34094i q^{8} +O(q^{10})\)	\(q+(-0.0316775 + 0.0182890i) q^{2} +(-15.9993 + 27.7117i) q^{4} -62.5776 q^{5} +(87.2452 - 95.8920i) q^{7} -2.34094i q^{8} +(1.98230 - 1.14448i) q^{10} -208.840i q^{11} +(-447.217 + 258.201i) q^{13} +(-1.00994 + 4.63325i) q^{14} +(-511.936 - 886.699i) q^{16} +(-558.291 - 966.988i) q^{17} +(819.372 + 473.065i) q^{19} +(1001.20 - 1734.13i) q^{20} +(3.81948 + 6.61553i) q^{22} +1022.14i q^{23} +790.950 q^{25} +(9.44447 - 16.3583i) q^{26} +(1261.46 + 3951.92i) q^{28} +(4524.33 + 2612.13i) q^{29} +(8025.88 + 4633.74i) q^{31} +(97.3078 + 56.1807i) q^{32} +(35.3705 + 20.4212i) q^{34} +(-5459.59 + 6000.69i) q^{35} +(1499.33 - 2596.91i) q^{37} -34.6075 q^{38} +146.491i q^{40} +(6210.55 + 10757.0i) q^{41} +(6478.23 - 11220.6i) q^{43} +(5787.31 + 3341.30i) q^{44} +(-18.6939 - 32.3788i) q^{46} +(9979.25 + 17284.6i) q^{47} +(-1583.56 - 16732.2i) q^{49} +(-25.0553 + 14.4657i) q^{50} -16524.2i q^{52} +(-21892.1 + 12639.4i) q^{53} +13068.7i q^{55} +(-224.478 - 204.236i) q^{56} -191.093 q^{58} +(16653.4 - 28844.5i) q^{59} +(10462.0 - 6040.26i) q^{61} -338.986 q^{62} +32759.8 q^{64} +(27985.7 - 16157.6i) q^{65} +(-11858.5 + 20539.5i) q^{67} +35729.1 q^{68} +(63.1994 - 289.937i) q^{70} +53406.7i q^{71} +(67780.6 - 39133.2i) q^{73} +109.685i q^{74} +(-26218.8 + 15137.4i) q^{76} +(-20026.1 - 18220.3i) q^{77} +(24665.4 + 42721.6i) q^{79} +(32035.7 + 55487.4i) q^{80} +(-393.469 - 227.170i) q^{82} +(-28362.0 + 49124.5i) q^{83} +(34936.5 + 60511.8i) q^{85} +473.921i q^{86} -488.883 q^{88} +(57629.5 - 99817.2i) q^{89} +(-14258.1 + 65411.3i) q^{91} +(-28325.2 - 16353.6i) q^{92} +(-632.235 - 365.021i) q^{94} +(-51274.3 - 29603.2i) q^{95} +(17070.5 + 9855.67i) q^{97} +(356.179 + 501.073i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 3 q^{2} + 577 q^{4} + 6 q^{5} - 30 q^{7}+O(q^{10}) \) 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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