LMFDB - Embedded newform 162.3.f.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, 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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	162.35
Dual form			162.3.f.a.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-2.71293 + 7.45370i) q^{5} +(0.0787775 - 0.446769i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-2.71293 + 7.45370i) q^{5} +(0.0787775 - 0.446769i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-5.60882 - 9.71475i) q^{10} +(-4.82381 - 13.2533i) q^{11} +(-9.80599 + 8.22820i) q^{13} +(0.412396 + 0.491475i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(-28.5583 + 16.4882i) q^{17} +(0.202792 - 0.351246i) q^{19} +(15.6231 + 2.75478i) q^{20} +(18.7430 + 6.82189i) q^{22} +(-14.2603 + 2.51448i) q^{23} +(-29.0466 - 24.3730i) q^{25} -18.1031i q^{26} -0.907323 q^{28} +(16.8547 - 20.0866i) q^{29} +(4.33881 + 24.6066i) q^{31} +(1.93476 - 5.31570i) q^{32} +(8.09818 - 45.9270i) q^{34} +(3.11637 + 1.79924i) q^{35} +(3.84477 + 6.65933i) q^{37} +(0.196177 + 0.538991i) q^{38} +(-17.1864 + 14.4211i) q^{40} +(15.9304 + 18.9851i) q^{41} +(-16.8662 + 6.13880i) q^{43} +(-24.4286 + 14.1039i) q^{44} +(10.2391 - 17.7347i) q^{46} +(46.7491 + 8.24313i) q^{47} +(45.8515 + 16.6886i) q^{49} +(52.8090 - 9.31165i) q^{50} +(19.6120 + 16.4564i) q^{52} -0.261457i q^{53} +111.873 q^{55} +(0.824792 - 0.982949i) q^{56} +(6.43929 + 36.5190i) q^{58} +(-18.8461 + 51.7793i) q^{59} +(-18.1761 + 103.082i) q^{61} +(-30.6018 - 17.6679i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-34.7276 - 95.4134i) q^{65} +(-49.4929 + 41.5295i) q^{67} +(42.3935 + 50.5226i) q^{68} +(-4.78210 + 1.74054i) q^{70} +(94.6180 - 54.6277i) q^{71} +(31.4705 - 54.5085i) q^{73} +(-10.7094 - 1.88836i) q^{74} +(-0.762248 - 0.277436i) q^{76} +(-6.30118 + 1.11107i) q^{77} +(-14.7532 - 12.3794i) q^{79} -31.7283i q^{80} -35.0489 q^{82} +(-36.7220 + 43.7636i) q^{83} +(-45.4212 - 257.596i) q^{85} +(8.68158 - 23.8524i) q^{86} +(6.92713 - 39.2857i) q^{88} +(-89.7902 - 51.8404i) q^{89} +(2.90362 + 5.02921i) q^{91} +(9.90511 + 27.2141i) q^{92} +(-51.4269 + 43.1523i) q^{94} +(2.06792 + 2.46445i) q^{95} +(-52.8231 + 19.2260i) q^{97} +(-59.7604 + 34.5027i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$3$		0			0
$3$		0			0
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	−2.71293	+	7.45370i	−0.542585	+	1.49074i	0.300936	+	0.953644i	$0.402701\pi$
$5$	−2.71293	+	7.45370i	−0.542585	+	1.49074i	−0.843521	+	0.537096i	$0.819521\pi$
$6$		0			0
$7$	0.0787775	−	0.446769i	0.0112539	−	0.0638242i	−0.978664	−	0.205469i	$-0.934128\pi$
$7$	0.0787775	−	0.446769i	0.0112539	−	0.0638242i	0.989918	+	0.141645i	$0.0452391\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$		0			0
$10$	−5.60882	−	9.71475i	−0.560882	−	0.971475i
$11$	−4.82381	−	13.2533i	−0.438528	−	1.20485i	−0.940450	−	0.339933i	$-0.889596\pi$
$11$	−4.82381	−	13.2533i	−0.438528	−	1.20485i	0.501922	−	0.864913i	$-0.332627\pi$
$12$		0			0
$13$	−9.80599	+	8.22820i	−0.754307	+	0.632939i	−0.936638	−	0.350299i	$-0.886080\pi$
$13$	−9.80599	+	8.22820i	−0.754307	+	0.632939i	0.182331	+	0.983237i	$0.441636\pi$
$14$	0.412396	+	0.491475i	0.0294569	+	0.0351053i
$15$		0			0
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−28.5583	+	16.4882i	−1.67990	+	0.969891i	−0.718182	+	0.695856i	$0.755025\pi$
$17$	−28.5583	+	16.4882i	−1.67990	+	0.969891i	−0.961720	+	0.274036i	$0.911641\pi$
$18$		0			0
$19$	0.202792	−	0.351246i	0.0106733	−	0.0184866i	−0.860639	−	0.509215i	$-0.829936\pi$
$19$	0.202792	−	0.351246i	0.0106733	−	0.0184866i	0.871313	+	0.490728i	$0.163269\pi$
$20$	15.6231	+	2.75478i	0.781156	+	0.137739i
$21$		0			0
$22$	18.7430	+	6.82189i	0.851955	+	0.310086i
$23$	−14.2603	+	2.51448i	−0.620013	+	0.109325i	−0.474827	−	0.880079i	$-0.657489\pi$
$23$	−14.2603	+	2.51448i	−0.620013	+	0.109325i	−0.145187	+	0.989404i	$0.546378\pi$
$24$		0			0
$25$	−29.0466	−	24.3730i	−1.16186	−	0.974920i
$26$		−	18.1031i		−	0.696272i
$27$		0			0
$28$	−0.907323			−0.0324044
$29$	16.8547	−	20.0866i	0.581195	−	0.692642i	−0.392693	−	0.919670i	$-0.628456\pi$
$29$	16.8547	−	20.0866i	0.581195	−	0.692642i	0.973888	+	0.227028i	$0.0729009\pi$
$30$		0			0
$31$	4.33881	+	24.6066i	0.139962	+	0.793762i	0.971275	+	0.237959i	$0.0764783\pi$
$31$	4.33881	+	24.6066i	0.139962	+	0.793762i	−0.831314	+	0.555804i	$0.812411\pi$
$32$	1.93476	−	5.31570i	0.0604612	−	0.166116i
$33$		0			0
$34$	8.09818	−	45.9270i	0.238182	−	1.35080i
$35$	3.11637	+	1.79924i	0.0890391	+	0.0514068i
$36$		0			0
$37$	3.84477	+	6.65933i	0.103913	+	0.179982i	0.913293	−	0.407302i	$-0.133530\pi$
$37$	3.84477	+	6.65933i	0.103913	+	0.179982i	−0.809381	+	0.587284i	$0.800197\pi$
$38$	0.196177	+	0.538991i	0.00516254	+	0.0141840i
$39$		0			0
$40$	−17.1864	+	14.4211i	−0.429660	+	0.360528i
$41$	15.9304	+	18.9851i	0.388547	+	0.463052i	0.924492	−	0.381200i	$-0.124489\pi$
$41$	15.9304	+	18.9851i	0.388547	+	0.463052i	−0.535946	+	0.844253i	$0.680045\pi$
$42$		0			0
$43$	−16.8662	+	6.13880i	−0.392238	+	0.142763i	−0.530607	−	0.847618i	$-0.678036\pi$
$43$	−16.8662	+	6.13880i	−0.392238	+	0.142763i	0.138369	+	0.990381i	$0.455814\pi$
$44$	−24.4286	+	14.1039i	−0.555196	+	0.320543i
$45$		0			0
$46$	10.2391	−	17.7347i	0.222589	−	0.385536i
$47$	46.7491	+	8.24313i	0.994662	+	0.175386i	0.647210	−	0.762312i	$-0.275936\pi$
$47$	46.7491	+	8.24313i	0.994662	+	0.175386i	0.347452	+	0.937698i	$0.387047\pi$
$48$		0			0
$49$	45.8515	+	16.6886i	0.935746	+	0.340584i
$50$	52.8090	−	9.31165i	1.05618	−	0.186233i
$51$		0			0
$52$	19.6120	+	16.4564i	0.377153	+	0.316469i
$53$		−	0.261457i		−	0.00493315i	−0.999997	−	0.00246657i	$-0.999215\pi$
$53$		−	0.261457i		−	0.00493315i	0.999997	−	0.00246657i	$-0.000785136\pi$
$54$		0			0
$55$	111.873			2.03405
$56$	0.824792	−	0.982949i	0.0147284	−	0.0175527i
$57$		0			0
$58$	6.43929	+	36.5190i	0.111022	+	0.629638i
$59$	−18.8461	+	51.7793i	−0.319426	+	0.877615i	0.671232	+	0.741247i	$0.265765\pi$
$59$	−18.8461	+	51.7793i	−0.319426	+	0.877615i	−0.990658	+	0.136368i	$0.956457\pi$
$60$		0			0
$61$	−18.1761	+	103.082i	−0.297969	+	1.68987i	0.356916	+	0.934137i	$0.383828\pi$
$61$	−18.1761	+	103.082i	−0.297969	+	1.68987i	−0.654885	+	0.755729i	$0.727283\pi$
$62$	−30.6018	−	17.6679i	−0.493577	−	0.284967i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−34.7276	−	95.4134i	−0.534271	−	1.46790i
$66$		0			0
$67$	−49.4929	+	41.5295i	−0.738700	+	0.619843i	−0.932488	−	0.361200i	$-0.882367\pi$
$67$	−49.4929	+	41.5295i	−0.738700	+	0.619843i	0.193788	+	0.981043i	$0.437923\pi$
$68$	42.3935	+	50.5226i	0.623434	+	0.742980i
$69$		0			0
$70$	−4.78210	+	1.74054i	−0.0683158	+	0.0248649i
$71$	94.6180	−	54.6277i	1.33265	−	0.769405i	0.346943	−	0.937886i	$-0.387220\pi$
$71$	94.6180	−	54.6277i	1.33265	−	0.769405i	0.985705	+	0.168481i	$0.0538862\pi$
$72$		0			0
$73$	31.4705	−	54.5085i	0.431103	−	0.746692i	−0.565866	−	0.824497i	$-0.691458\pi$
$73$	31.4705	−	54.5085i	0.431103	−	0.746692i	0.996969	+	0.0778057i	$0.0247914\pi$
$74$	−10.7094	−	1.88836i	−0.144722	−	0.0255184i
$75$		0			0
$76$	−0.762248	−	0.277436i	−0.0100296	−	0.00365047i
$77$	−6.30118	+	1.11107i	−0.0818335	+	0.0144295i
$78$		0			0
$79$	−14.7532	−	12.3794i	−0.186750	−	0.156702i	0.544620	−	0.838683i	$-0.316674\pi$
$79$	−14.7532	−	12.3794i	−0.186750	−	0.156702i	−0.731369	+	0.681981i	$0.761118\pi$
$80$		−	31.7283i		−	0.396603i
$81$		0			0
$82$	−35.0489			−0.427426
$83$	−36.7220	+	43.7636i	−0.442434	+	0.527273i	−0.940467	−	0.339886i	$-0.889612\pi$
$83$	−36.7220	+	43.7636i	−0.442434	+	0.527273i	0.498033	+	0.867158i	$0.334056\pi$
$84$		0			0
$85$	−45.4212	−	257.596i	−0.534367	−	3.03055i
$86$	8.68158	−	23.8524i	0.100949	−	0.277354i
$87$		0			0
$88$	6.92713	−	39.2857i	0.0787174	−	0.446429i
$89$	−89.7902	−	51.8404i	−1.00888	−	0.582476i	−0.0980154	−	0.995185i	$-0.531249\pi$
$89$	−89.7902	−	51.8404i	−1.00888	−	0.582476i	−0.910863	+	0.412709i	$0.864583\pi$
$90$		0			0
$91$	2.90362	+	5.02921i	0.0319079	+	0.0552661i
$92$	9.90511	+	27.2141i	0.107664	+	0.295805i
$93$		0			0
$94$	−51.4269	+	43.1523i	−0.547095	+	0.459067i
$95$	2.06792	+	2.46445i	0.0217676	+	0.0259416i
$96$		0			0
$97$	−52.8231	+	19.2260i	−0.544568	+	0.198207i	−0.599631	−	0.800276i	$-0.704686\pi$
$97$	−52.8231	+	19.2260i	−0.544568	+	0.198207i	0.0550633	+	0.998483i	$0.482464\pi$
$98$	−59.7604	+	34.5027i	−0.609800	+	0.352068i
$99$		0			0
$100$	−37.9176	+	65.6753i	−0.379176	+	0.656753i
$101$	44.2921	+	7.80990i	0.438536	+	0.0773258i	0.388557	−	0.921425i	$-0.372974\pi$
$101$	44.2921	+	7.80990i	0.438536	+	0.0773258i	0.0499788	+	0.998750i	$0.484085\pi$
$102$		0			0
$103$	85.6429	+	31.1715i	0.831485	+	0.302636i	0.722468	−	0.691404i	$-0.243008\pi$
$103$	85.6429	+	31.1715i	0.831485	+	0.302636i	0.109017	+	0.994040i	$0.465230\pi$
$104$	−35.6561	+	6.28713i	−0.342847	+	0.0604532i
$105$		0			0
$106$	0.283249	+	0.237674i	0.00267216	+	0.00224221i
$107$			206.049i			1.92569i	0.270046	+	0.962847i	$0.412961\pi$
$107$			206.049i			1.92569i	−0.270046	+	0.962847i	$0.587039\pi$
$108$		0			0
$109$	−140.161			−1.28588			−0.642942	−	0.765915i	$-0.722286\pi$
$109$	−140.161			−1.28588			−0.642942	+	0.765915i	$0.722286\pi$
$110$	−101.697	+	121.197i	−0.924516	+	1.10180i
$111$		0			0
$112$	0.315110	+	1.78708i	0.00281348	+	0.0159561i
$113$	24.9375	−	68.5153i	0.220686	−	0.606330i	−0.779102	−	0.626897i	$-0.784325\pi$
$113$	24.9375	−	68.5153i	0.220686	−	0.606330i	0.999788	+	0.0205666i	$0.00654701\pi$
$114$		0			0
$115$	19.9450	−	113.114i	0.173435	−	0.983597i
$116$	−45.4165	−	26.2212i	−0.391521	−	0.226045i
$117$		0			0
$118$	−38.9633	−	67.4864i	−0.330197	−	0.571918i
$119$	5.11665	+	14.0579i	0.0429971	+	0.118133i
$120$		0			0
$121$	−59.6896	+	50.0855i	−0.493302	+	0.413930i
$122$	−95.1509	−	113.396i	−0.779925	−	0.929479i
$123$		0			0
$124$	46.9588	−	17.0916i	0.378700	−	0.137835i
$125$	88.7360	−	51.2318i	0.709888	−	0.409854i
$126$		0			0
$127$	−5.49347	+	9.51497i	−0.0432557	+	0.0749210i	−0.886843	−	0.462072i	$-0.847106\pi$
$127$	−5.49347	+	9.51497i	−0.0432557	+	0.0749210i	0.843587	+	0.536993i	$0.180440\pi$
$128$	−11.1418	−	1.96460i	−0.0870455	−	0.0153485i
$129$		0			0
$130$	134.935	+	49.1123i	1.03796	+	0.377787i
$131$	−36.9106	+	6.50833i	−0.281760	+	0.0496819i	−0.312742	−	0.949838i	$-0.601248\pi$
$131$	−36.9106	+	6.50833i	−0.281760	+	0.0496819i	0.0309820	+	0.999520i	$0.490137\pi$
$132$		0			0
$133$	−0.140951	−	0.118272i	−0.00105978	−	0.000889260i
$134$		−	91.3701i		−	0.681866i
$135$		0			0
$136$	−93.2711			−0.685817
$137$	27.2090	−	32.4264i	0.198606	−	0.236689i	−0.657545	−	0.753415i	$-0.728405\pi$
$137$	27.2090	−	32.4264i	0.198606	−	0.236689i	0.856151	+	0.516726i	$0.172850\pi$
$138$		0			0
$139$	−28.2955	−	160.472i	−0.203565	−	1.15447i	−0.899682	−	0.436545i	$-0.856202\pi$
$139$	−28.2955	−	160.472i	−0.203565	−	1.15447i	0.696117	−	0.717928i	$-0.254909\pi$
$140$	2.46150	−	6.76292i	0.0175821	−	0.0483066i
$141$		0			0
$142$	−26.8305	+	152.163i	−0.188947	+	1.07157i
$143$	156.353	+	90.2705i	1.09338	+	0.631262i
$144$		0			0
$145$	103.994	+	180.123i	0.717201	+	1.24223i
$146$	30.4439	+	83.6439i	0.208520	+	0.572903i
$147$		0			0
$148$	11.7810	−	9.88547i	0.0796017	−	0.0667937i
$149$	−115.419	−	137.551i	−0.774624	−	0.923161i	0.224054	−	0.974577i	$-0.428071\pi$
$149$	−115.419	−	137.551i	−0.774624	−	0.923161i	−0.998677	+	0.0514163i	$0.983626\pi$
$150$		0			0
$151$	151.225	−	55.0415i	1.00149	−	0.364514i	0.211333	−	0.977414i	$-0.432220\pi$
$151$	151.225	−	55.0415i	1.00149	−	0.364514i	0.790160	+	0.612901i	$0.209997\pi$
$152$	0.993473	−	0.573582i	0.00653601	−	0.00377357i
$153$		0			0
$154$	4.52434	−	7.83639i	0.0293788	−	0.0508856i
$155$	−195.181	−	34.4157i	−1.25923	−	0.222037i
$156$		0			0
$157$	−72.6336	−	26.4365i	−0.462635	−	0.168385i	0.100178	−	0.994969i	$-0.468059\pi$
$157$	−72.6336	−	26.4365i	−0.462635	−	0.168385i	−0.562813	+	0.826584i	$0.690281\pi$
$158$	26.8225	−	4.72954i	0.169763	−	0.0299338i
$159$		0			0
$160$	34.3728	+	28.8422i	0.214830	+	0.180264i
$161$			6.56915i			0.0408022i
$162$		0			0
$163$	−2.14092			−0.0131345			−0.00656723	−	0.999978i	$-0.502090\pi$
$163$	−2.14092			−0.0131345			−0.00656723	+	0.999978i	$0.502090\pi$
$164$	31.8608	−	37.9703i	0.194273	−	0.231526i
$165$		0			0
$166$	−14.0296	−	79.5657i	−0.0845155	−	0.479311i
$167$	−30.6994	+	84.3460i	−0.183829	+	0.505066i	−0.997038	−	0.0769052i	$-0.975496\pi$
$167$	−30.6994	+	84.3460i	−0.183829	+	0.505066i	0.813209	+	0.581971i	$0.197718\pi$
$168$		0			0
$169$	−0.892424	+	5.06119i	−0.00528061	+	0.0299479i
$170$	320.357	+	184.958i	1.88445	+	1.08799i
$171$		0			0
$172$	17.9487	+	31.0880i	0.104353	+	0.180744i
$173$	62.3682	+	171.355i	0.360510	+	0.990492i	0.978850	+	0.204581i	$0.0655832\pi$
$173$	62.3682	+	171.355i	0.360510	+	0.990492i	−0.618340	+	0.785911i	$0.712195\pi$
$174$		0			0
$175$	−13.1773	+	11.0571i	−0.0752990	+	0.0631834i
$176$	36.2632	+	43.2168i	0.206041	+	0.245550i
$177$		0			0
$178$	137.784	−	50.1493i	0.774068	−	0.281738i
$179$	104.032	−	60.0628i	0.581183	−	0.335546i	−0.180420	−	0.983590i	$-0.557746\pi$
$179$	104.032	−	60.0628i	0.581183	−	0.335546i	0.761604	+	0.648043i	$0.224412\pi$
$180$		0			0
$181$	−79.9928	+	138.552i	−0.441949	+	0.765478i	−0.997834	−	0.0657809i	$-0.979046\pi$
$181$	−79.9928	+	138.552i	−0.441949	+	0.765478i	0.555885	+	0.831259i	$0.312380\pi$
$182$	−8.08790	−	1.42612i	−0.0444390	−	0.00783580i
$183$		0			0
$184$	−38.4865	−	14.0079i	−0.209166	−	0.0761301i
$185$	−60.0672	+	10.5915i	−0.324688	+	0.0572512i
$186$		0			0
$187$	356.282	+	298.956i	1.90525	+	1.59870i
$188$		−	94.9406i		−	0.505003i
$189$		0			0
$190$	−4.54969			−0.0239457
$191$	82.0805	−	97.8197i	0.429741	−	0.512145i	−0.507107	−	0.861883i	$-0.669285\pi$
$191$	82.0805	−	97.8197i	0.429741	−	0.512145i	0.936847	+	0.349738i	$0.113729\pi$
$192$		0			0
$193$	17.3129	+	98.1865i	0.0897043	+	0.508738i	0.996242	+	0.0866135i	$0.0276045\pi$
$193$	17.3129	+	98.1865i	0.0897043	+	0.508738i	−0.906538	+	0.422125i	$0.861284\pi$
$194$	27.1897	−	74.7032i	0.140153	−	0.385068i
$195$		0			0
$196$	16.9460	−	96.1058i	0.0864594	−	0.490336i
$197$	32.9869	+	19.0450i	0.167446	+	0.0966751i	0.581381	−	0.813631i	$-0.302513\pi$
$197$	32.9869	+	19.0450i	0.167446	+	0.0966751i	−0.413935	+	0.910306i	$0.635846\pi$
$198$		0			0
$199$	−192.718	−	333.797i	−0.968430	−	1.67737i	−0.700102	−	0.714043i	$-0.746862\pi$
$199$	−192.718	−	333.797i	−0.968430	−	1.67737i	−0.268329	−	0.963327i	$-0.586471\pi$
$200$	−36.6807	−	100.779i	−0.183404	−	0.503897i
$201$		0			0
$202$	−48.7241	+	40.8844i	−0.241209	+	0.202398i
$203$	−7.64631	−	9.11252i	−0.0376666	−	0.0448893i
$204$		0			0
$205$	−184.728	+	67.2354i	−0.901110	+	0.327977i
$206$	−111.622	+	64.4452i	−0.541856	+	0.312841i
$207$		0			0
$208$	25.6016	−	44.3433i	0.123085	−	0.213189i
$209$	−5.63340	−	0.993320i	−0.0269541	−	0.00475273i
$210$		0			0
$211$	320.622	+	116.697i	1.51953	+	0.553065i	0.961032	−	0.276439i	$-0.0891542\pi$
$211$	320.622	+	116.697i	1.51953	+	0.553065i	0.558502	+	0.829503i	$0.311376\pi$
$212$	−0.514970	+	0.0908030i	−0.00242910	+	0.000428316i
$213$		0			0
$214$	−223.224	−	187.307i	−1.04310	−	0.875266i
$215$		−	142.370i		−	0.662186i
$216$		0			0
$217$	11.3353			0.0522364
$218$	127.412	−	151.844i	0.584459	−	0.696532i
$219$		0			0
$220$	−38.8530	−	220.346i	−0.176605	−	1.00157i
$221$	144.375	−	396.666i	0.653279	−	1.79487i
$222$		0			0
$223$	−10.1542	+	57.5872i	−0.0455344	+	0.258238i	−0.999074	−	0.0430300i	$-0.986299\pi$
$223$	−10.1542	+	57.5872i	−0.0455344	+	0.258238i	0.953539	+	0.301268i	$0.0974100\pi$
$224$	−2.22248	−	1.28315i	−0.00992178	−	0.00572834i
$225$		0			0
$226$	51.5569	+	89.2992i	0.228128	+	0.395129i
$227$	−14.3644	−	39.4658i	−0.0632792	−	0.173858i	0.904024	−	0.427483i	$-0.140600\pi$
$227$	−14.3644	−	39.4658i	−0.0632792	−	0.173858i	−0.967303	+	0.253624i	$0.918377\pi$
$228$		0			0
$229$	68.1857	−	57.2146i	0.297754	−	0.249845i	−0.481655	−	0.876361i	$-0.659964\pi$
$229$	68.1857	−	57.2146i	0.297754	−	0.249845i	0.779409	+	0.626516i	$0.215520\pi$
$230$	104.411	+	124.432i	0.453961	+	0.541009i
$231$		0			0
$232$	69.6921	−	25.3658i	0.300397	−	0.109336i
$233$	−121.622	+	70.2184i	−0.521982	+	0.301367i	−0.737745	−	0.675079i	$-0.764109\pi$
$233$	−121.622	+	70.2184i	−0.521982	+	0.301367i	0.215763	+	0.976446i	$0.430776\pi$
$234$		0			0
$235$	−188.269	+	326.091i	−0.801143	+	1.38762i
$236$	108.530	+	19.1369i	0.459875	+	0.0810884i
$237$		0			0
$238$	−19.8808	−	7.23604i	−0.0835330	−	0.0304035i
$239$	28.6122	−	5.04510i	0.119716	−	0.0211092i	−0.113469	−	0.993542i	$-0.536196\pi$
$239$	28.6122	−	5.04510i	0.119716	−	0.0211092i	0.233185	+	0.972432i	$0.425085\pi$
$240$		0			0
$241$	−113.719	−	95.4212i	−0.471861	−	0.395938i	0.375612	−	0.926777i	$-0.377433\pi$
$241$	−113.719	−	95.4212i	−0.471861	−	0.395938i	−0.847473	+	0.530839i	$0.821877\pi$
$242$		−	110.194i		−	0.455349i
$243$		0			0
$244$	209.344			0.857967
$245$	−248.784	+	296.489i	−1.01544	+	1.21016i
$246$		0			0
$247$	0.901547	+	5.11293i	0.00364999	+	0.0207001i
$248$	−24.1712	+	66.4097i	−0.0974643	+	0.267781i
$249$		0			0
$250$	−25.1625	+	142.704i	−0.100650	+	0.570816i
$251$	−270.246	−	156.027i	−1.07668	−	0.621621i	−0.146680	−	0.989184i	$-0.546859\pi$
$251$	−270.246	−	156.027i	−1.07668	−	0.621621i	−0.929999	+	0.367563i	$0.880192\pi$
$252$		0			0
$253$	102.114	+	176.867i	0.403613	+	0.699078i
$254$	−5.31427	−	14.6008i	−0.0209223	−	0.0574836i
$255$		0			0
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	33.8555	+	40.3474i	0.131733	+	0.156994i	0.827879	−	0.560907i	$-0.189548\pi$
$257$	33.8555	+	40.3474i	0.131733	+	0.156994i	−0.696145	+	0.717901i	$0.745103\pi$
$258$		0			0
$259$	3.27807	−	1.19312i	0.0126566	−	0.00460664i
$260$	−175.867	+	101.537i	−0.676411	+	0.390526i
$261$		0			0
$262$	26.5024	−	45.9034i	0.101154	−	0.175204i
$263$	15.7913	+	2.78443i	0.0600429	+	0.0105872i	0.203589	−	0.979056i	$-0.434739\pi$
$263$	15.7913	+	2.78443i	0.0600429	+	0.0105872i	−0.143546	+	0.989644i	$0.545851\pi$
$264$		0			0
$265$	1.94882	+	0.709313i	0.00735404	+	0.00267665i
$266$	0.256259	−	0.0451854i	0.000963380	−	0.000169870i
$267$		0			0
$268$	98.9858	+	83.0590i	0.369350	+	0.309922i
$269$			233.865i			0.869388i	0.900578	+	0.434694i	$0.143143\pi$
$269$			233.865i			0.869388i	−0.900578	+	0.434694i	$0.856857\pi$
$270$		0			0
$271$	−229.874			−0.848243			−0.424122	−	0.905605i	$-0.639417\pi$
$271$	−229.874			−0.848243			−0.424122	+	0.905605i	$0.639417\pi$
$272$	84.7870	−	101.045i	0.311717	−	0.371490i
$273$		0			0
$274$	10.3951	+	58.9537i	0.0379384	+	0.215159i
$275$	−182.907	+	502.534i	−0.665118	+	1.82740i
$276$		0			0
$277$	45.6767	−	259.046i	0.164898	−	0.935183i	−0.784272	−	0.620418i	$-0.786963\pi$
$277$	45.6767	−	259.046i	0.164898	−	0.935183i	0.949170	−	0.314765i	$-0.101926\pi$
$278$	199.569	+	115.221i	0.717874	+	0.414465i
$279$		0			0
$280$	5.08901	+	8.81442i	0.0181750	+	0.0314801i
$281$	168.471	+	462.870i	0.599540	+	1.64722i	0.752193	+	0.658943i	$0.228996\pi$
$281$	168.471	+	462.870i	0.599540	+	1.64722i	−0.152653	+	0.988280i	$0.548782\pi$
$282$		0			0
$283$	−375.336	+	314.944i	−1.32628	+	1.11288i	−0.341343	+	0.939939i	$0.610882\pi$
$283$	−375.336	+	314.944i	−1.32628	+	1.11288i	−0.984933	+	0.172938i	$0.944674\pi$
$284$	−140.456	−	167.389i	−0.494564	−	0.589398i
$285$		0			0
$286$	−239.926	+	87.3258i	−0.838901	+	0.305335i
$287$	9.73694	−	5.62162i	0.0339266	−	0.0195875i
$288$		0			0
$289$	399.218	−	691.467i	1.38138	−	2.39262i
$290$	−289.671	−	51.0768i	−0.998866	−	0.176127i
$291$		0			0
$292$	−118.290	−	43.0542i	−0.405104	−	0.147446i
$293$	149.954	−	26.4409i	0.511788	−	0.0902420i	0.0882105	−	0.996102i	$-0.471885\pi$
$293$	149.954	−	26.4409i	0.511788	−	0.0902420i	0.423578	+	0.905860i	$0.360774\pi$
$294$		0			0
$295$	−334.819	−	280.947i	−1.13498	−	0.952362i
$296$			21.7493i			0.0734773i
$297$		0			0
$298$	253.936			0.852135
$299$	119.147	−	141.994i	0.398484	−	0.474895i
$300$		0			0
$301$	1.41395	+	8.01892i	0.00469751	+	0.0266409i
$302$	−77.8405	+	213.865i	−0.257750	+	0.708162i
$303$		0			0
$304$	−0.281716	+	1.59769i	−0.000926696	+	0.00525555i
$305$	−719.030	−	415.132i	−2.35748	−	1.36109i
$306$		0			0
$307$	−152.701	−	264.487i	−0.497399	−	0.861520i	0.502597	−	0.864521i	$-0.332378\pi$
$307$	−152.701	−	264.487i	−0.497399	−	0.861520i	−0.999995	+	0.00300104i	$0.999045\pi$
$308$	4.37675	+	12.0250i	0.0142102	+	0.0390423i
$309$		0			0
$310$	214.712	−	180.165i	0.692619	−	0.581176i
$311$	227.448	+	271.062i	0.731344	+	0.871582i	0.995680	−	0.0928489i	$-0.0295973\pi$
$311$	227.448	+	271.062i	0.731344	+	0.871582i	−0.264336	+	0.964431i	$0.585153\pi$
$312$		0			0
$313$	−109.151	+	39.7277i	−0.348725	+	0.126926i	−0.510443	−	0.859911i	$-0.670519\pi$
$313$	−109.151	+	39.7277i	−0.348725	+	0.126926i	0.161718	+	0.986837i	$0.448297\pi$
$314$	94.6668	−	54.6559i	0.301487	−	0.174063i
$315$		0			0
$316$	−19.2590	+	33.3575i	−0.0609462	+	0.105562i
$317$	−223.759	−	39.4548i	−0.705866	−	0.124463i	−0.190819	−	0.981625i	$-0.561114\pi$
$317$	−223.759	−	39.4548i	−0.705866	−	0.124463i	−0.515047	+	0.857162i	$0.672225\pi$
$318$		0			0
$319$	−347.518	−	126.486i	−1.08940	−	0.396508i
$320$	−62.4925	+	11.0191i	−0.195289	+	0.0344347i
$321$		0			0
$322$	−7.11670	−	5.97162i	−0.0221015	−	0.0185454i
$323$			13.3747i			0.0414076i
$324$		0			0
$325$	485.376			1.49347
$326$	1.94618	−	2.31936i	0.00596987	−	0.00711461i
$327$		0			0
$328$	12.1724	+	69.0329i	0.0371109	+	0.210466i
$329$	7.36556	−	20.2367i	0.0223877	−	0.0615097i
$330$		0			0
$331$	−16.3581	+	92.7715i	−0.0494203	+	0.280276i	−0.999496	−	0.0317429i	$-0.989894\pi$
$331$	−16.3581	+	92.7715i	−0.0494203	+	0.280276i	0.950076	+	0.312019i	$0.101005\pi$
$332$	98.9509	+	57.1293i	0.298045	+	0.172076i
$333$		0			0
$334$	−63.4693	−	109.932i	−0.190028	−	0.329138i
$335$	−175.278	−	481.572i	−0.523217	−	1.43753i
$336$		0			0
$337$	55.5042	−	46.5735i	0.164701	−	0.138200i	−0.556712	−	0.830705i	$-0.687937\pi$
$337$	55.5042	−	46.5735i	0.164701	−	0.138200i	0.721413	+	0.692505i	$0.243493\pi$
$338$	−4.67179	−	5.56762i	−0.0138219	−	0.0164723i
$339$		0			0
$340$	−491.591	+	178.925i	−1.44586	+	0.526249i
$341$	305.190	−	176.201i	0.894984	−	0.516719i
$342$		0			0
$343$	22.1827	−	38.4216i	0.0646727	−	0.112016i
$344$	−49.9952	−	8.81551i	−0.145335	−	0.0256265i
$345$		0			0
$346$	−242.333	−	88.2019i	−0.700384	−	0.254919i
$347$	407.086	−	71.7802i	1.17316	−	0.206859i	0.447094	−	0.894487i	$-0.352459\pi$
$347$	407.086	−	71.7802i	1.17316	−	0.206859i	0.726063	+	0.687628i	$0.241348\pi$
$348$		0			0
$349$	−53.8823	−	45.2127i	−0.154391	−	0.129549i	0.562320	−	0.826920i	$-0.309909\pi$
$349$	−53.8823	−	45.2127i	−0.154391	−	0.129549i	−0.716711	+	0.697370i	$0.754353\pi$
$350$		−	24.3270i		−	0.0695057i
$351$		0			0
$352$	−79.7835			−0.226658
$353$	318.904	−	380.055i	0.903411	−	1.07664i	−0.0933029	−	0.995638i	$-0.529743\pi$
$353$	318.904	−	380.055i	0.903411	−	1.07664i	0.996714	−	0.0810052i	$-0.0258131\pi$
$354$		0			0
$355$	150.487	+	853.456i	0.423908	+	2.40410i
$356$	−70.9218	+	194.856i	−0.199219	+	0.547349i
$357$		0			0
$358$	−29.4999	+	167.302i	−0.0824020	+	0.467325i
$359$	−251.693	−	145.315i	−0.701094	−	0.404777i	0.106661	−	0.994295i	$-0.465984\pi$
$359$	−251.693	−	145.315i	−0.701094	−	0.404777i	−0.807755	+	0.589519i	$0.799317\pi$
$360$		0			0
$361$	180.418	+	312.493i	0.499772	+	0.865631i
$362$	−77.3834	−	212.609i	−0.213766	−	0.587318i
$363$		0			0
$364$	8.89720	−	7.46564i	0.0244429	−	0.0205100i
$365$	320.913	+	382.449i	0.879213	+	1.04781i
$366$		0			0
$367$	536.255	−	195.181i	1.46119	−	0.531828i	0.515495	−	0.856893i	$-0.327608\pi$
$367$	536.255	−	195.181i	1.46119	−	0.531828i	0.945692	+	0.325065i	$0.105386\pi$
$368$	50.1612	−	28.9606i	0.136308	−	0.0786973i
$369$		0			0
$370$	43.1292	−	74.7019i	0.116565	−	0.201897i
$371$	−0.116811	−	0.0205969i	−0.000314854	−	5.55173e-5i
$372$		0			0
$373$	18.7449	+	6.82259i	0.0502545	+	0.0182911i	0.367025	−	0.930211i	$-0.380376\pi$
$373$	18.7449	+	6.82259i	0.0502545	+	0.0182911i	−0.316771	+	0.948502i	$0.602599\pi$
$374$	−647.749	+	114.216i	−1.73195	+	0.305389i
$375$		0			0
$376$	102.854	+	86.3047i	0.273548	+	0.229534i
$377$			335.653i			0.890325i
$378$		0			0
$379$	−37.0647			−0.0977961			−0.0488981	−	0.998804i	$-0.515571\pi$
$379$	−37.0647			−0.0977961			−0.0488981	+	0.998804i	$0.515571\pi$
$380$	4.13585	−	4.92891i	0.0108838	−	0.0129708i
$381$		0			0
$382$	31.3587	+	177.844i	0.0820908	+	0.465560i
$383$	139.086	−	382.135i	0.363148	−	0.997740i	−0.614762	−	0.788713i	$-0.710748\pi$
$383$	139.086	−	382.135i	0.363148	−	0.997740i	0.977910	−	0.209028i	$-0.0670298\pi$
$384$		0			0
$385$	8.81306	−	49.9814i	0.0228911	−	0.129822i
$386$	−122.109	−	70.4994i	−0.316343	−	0.182641i
$387$		0			0
$388$	56.2132	+	97.3641i	0.144879	+	0.250938i
$389$	53.2715	+	146.362i	0.136945	+	0.376253i	0.989141	−	0.146970i	$-0.0469519\pi$
$389$	53.2715	+	146.362i	0.136945	+	0.376253i	−0.852196	+	0.523222i	$0.824730\pi$
$390$		0			0
$391$	365.791	−	306.935i	0.935528	−	0.785001i
$392$	88.7116	+	105.722i	0.226305	+	0.269700i
$393$		0			0
$394$	−50.6188	+	18.4237i	−0.128474	+	0.0467607i
$395$	132.297	−	76.3818i	0.334929	−	0.193372i
$396$		0			0
$397$	−203.720	+	352.853i	−0.513147	+	0.888797i	0.486736	+	0.873549i	$0.338187\pi$
$397$	−203.720	+	352.853i	−0.513147	+	0.888797i	−0.999884	+	0.0152485i	$0.995146\pi$
$398$	536.807	+	94.6535i	1.34876	+	0.237823i
$399$		0			0
$400$	142.524	+	51.8744i	0.356309	+	0.129686i
$401$	57.1810	−	10.0826i	0.142596	−	0.0251435i	−0.101894	−	0.994795i	$-0.532490\pi$
$401$	57.1810	−	10.0826i	0.142596	−	0.0251435i	0.244491	+	0.969652i	$0.421379\pi$
$402$		0			0
$403$	−245.015	−	205.592i	−0.607977	−	0.510153i
$404$		−	89.9509i		−	0.222651i
$405$		0			0
$406$	16.8229			0.0414356
$407$	69.7117	−	83.0792i	0.171282	−	0.204126i
$408$		0			0
$409$	50.2599	+	285.038i	0.122885	+	0.696915i	0.982542	+	0.186043i	$0.0595664\pi$
$409$	50.2599	+	285.038i	0.122885	+	0.696915i	−0.859657	+	0.510872i	$0.829323\pi$
$410$	95.0851	−	261.244i	0.231915	−	0.637181i
$411$		0			0
$412$	31.6524	−	179.509i	0.0768261	−	0.435702i
$413$	21.6488	+	12.4989i	0.0524183	+	0.0302637i
$414$		0			0
$415$	−226.577	−	392.443i	−0.545968	−	0.945645i
$416$	24.7665	+	68.0453i	0.0595348	+	0.163570i
$417$		0			0
$418$	6.19709	−	5.19998i	0.0148256	−	0.0124401i
$419$	−432.059	−	514.908i	−1.03117	−	1.22890i	−0.973052	−	0.230587i	$-0.925935\pi$
$419$	−432.059	−	514.908i	−1.03117	−	1.22890i	−0.0581156	−	0.998310i	$-0.518509\pi$
$420$		0			0
$421$	211.095	−	76.8324i	0.501414	−	0.182500i	−0.0789157	−	0.996881i	$-0.525146\pi$
$421$	211.095	−	76.8324i	0.501414	−	0.182500i	0.580330	+	0.814381i	$0.302924\pi$
$422$	−417.881	+	241.264i	−0.990239	+	0.571715i
$423$		0			0
$424$	0.369756	−	0.640436i	0.000872066	−	0.00151046i
$425$	1231.39	+	217.127i	2.89738	+	0.510887i
$426$		0			0
$427$	44.6219	+	16.2411i	0.104501	+	0.0380353i
$428$	405.838	−	71.5602i	0.948220	−	0.167197i
$429$		0			0
$430$	154.237	+	129.420i	0.358690	+	0.300976i
$431$			189.283i			0.439171i	0.975593	+	0.219585i	$0.0704705\pi$
$431$			189.283i			0.439171i	−0.975593	+	0.219585i	$0.929530\pi$
$432$		0			0
$433$	−364.876			−0.842669			−0.421334	−	0.906905i	$-0.638438\pi$
$433$	−364.876			−0.842669			−0.421334	+	0.906905i	$0.638438\pi$
$434$	−10.3042	+	12.2801i	−0.0237425	+	0.0282952i
$435$		0			0
$436$	48.6775	+	276.064i	0.111646	+	0.633174i
$437$	−2.00868	+	5.51879i	−0.00459651	+	0.0126288i
$438$		0			0
$439$	73.6423	−	417.646i	0.167750	−	0.951358i	−0.778433	−	0.627727i	$-0.783985\pi$
$439$	73.6423	−	417.646i	0.167750	−	0.951358i	0.946183	−	0.323631i	$-0.104904\pi$
$440$	274.031	+	158.212i	0.622798	+	0.359573i
$441$		0			0
$442$	298.486	+	516.994i	0.675308	+	1.16967i
$443$	−61.4880	−	168.937i	−0.138799	−	0.381348i	0.850745	−	0.525579i	$-0.176151\pi$
$443$	−61.4880	−	168.937i	−0.138799	−	0.381348i	−0.989544	+	0.144231i	$0.953929\pi$
$444$		0			0
$445$	629.997	−	528.630i	1.41572	−	1.18793i
$446$	−53.1565	−	63.3495i	−0.119185	−	0.142039i
$447$		0			0
$448$	3.41042	−	1.24129i	0.00761254	−	0.00277074i
$449$	−558.134	+	322.239i	−1.24306	+	0.717681i	−0.969716	−	0.244236i	$-0.921463\pi$
$449$	−558.134	+	322.239i	−1.24306	+	0.717681i	−0.273343	+	0.961917i	$0.588129\pi$
$450$		0			0
$451$	174.770	−	302.711i	0.387518	−	0.671200i
$452$	−143.610	−	25.3222i	−0.317720	−	0.0560226i
$453$		0			0
$454$	55.8131	+	20.3143i	0.122936	+	0.0447452i
$455$	−45.3636	+	7.99882i	−0.0997001	+	0.0175798i
$456$		0			0
$457$	198.907	+	166.903i	0.435246	+	0.365215i	0.833927	−	0.551875i	$-0.186088\pi$
$457$	198.907	+	166.903i	0.435246	+	0.365215i	−0.398681	+	0.917090i	$0.630532\pi$
$458$			125.879i			0.274846i
$459$		0			0
$460$	−229.717			−0.499385
$461$	−313.010	+	373.031i	−0.678981	+	0.809178i	−0.989976	−	0.141234i	$-0.954893\pi$
$461$	−313.010	+	373.031i	−0.678981	+	0.809178i	0.310996	+	0.950411i	$0.399338\pi$
$462$		0			0
$463$	104.106	+	590.412i	0.224850	+	1.27519i	0.862972	+	0.505252i	$0.168601\pi$
$463$	104.106	+	590.412i	0.224850	+	1.27519i	−0.638121	+	0.769936i	$0.720288\pi$
$464$	−35.8727	+	98.5595i	−0.0773119	+	0.212413i
$465$		0			0
$466$	34.4879	−	195.590i	0.0740083	−	0.419722i
$467$	551.534	+	318.428i	1.18102	+	0.681860i	0.956249	−	0.292553i	$-0.0945049\pi$
$467$	551.534	+	318.428i	1.18102	+	0.681860i	0.224766	+	0.974413i	$0.427838\pi$
$468$		0			0
$469$	14.6552	+	25.3835i	0.0312477	+	0.0541226i
$470$	−182.127	−	500.390i	−0.387505	−	1.06466i
$471$		0			0
$472$	−119.390	+	100.180i	−0.252946	+	0.212247i
$473$	162.719	+	193.921i	0.344015	+	0.409981i
$474$		0			0
$475$	−14.4513	+	5.25985i	−0.0304238	+	0.0110734i
$476$	25.9116	−	14.9601i	0.0544362	−	0.0314288i
$477$		0			0
$478$	−20.5440	+	35.5832i	−0.0429790	+	0.0744419i
$479$	−393.091	−	69.3125i	−0.820649	−	0.144703i	−0.252467	−	0.967605i	$-0.581242\pi$
$479$	−393.091	−	69.3125i	−0.820649	−	0.144703i	−0.568182	+	0.822903i	$0.692353\pi$
$480$		0			0
$481$	−92.4960	−	33.6658i	−0.192299	−	0.0699913i
$482$	206.749	−	36.4555i	0.428940	−	0.0756337i
$483$		0			0
$484$	119.379	+	100.171i	0.246651	+	0.206965i
$485$		−	445.886i		−	0.919354i
$486$		0			0
$487$	−379.619			−0.779505			−0.389753	−	0.920920i	$-0.627440\pi$
$487$	−379.619			−0.779505			−0.389753	+	0.920920i	$0.627440\pi$
$488$	−190.302	+	226.793i	−0.389963	+	0.464740i
$489$		0			0
$490$	−95.0473	−	539.040i	−0.193974	−	1.10008i
$491$	−204.694	+	562.393i	−0.416893	+	1.14540i	0.536561	+	0.843862i	$0.319723\pi$
$491$	−204.694	+	562.393i	−0.416893	+	1.14540i	−0.953453	+	0.301541i	$0.902499\pi$
$492$		0			0
$493$	−150.150	+	851.542i	−0.304564	+	1.72727i
$494$	−6.35863	−	3.67116i	−0.0128717	−	0.00743149i
$495$		0			0
$496$	−49.9725	−	86.5549i	−0.100751	−	0.174506i
$497$	−16.9522	−	46.5759i	−0.0341091	−	0.0937141i
$498$		0			0
$499$	−35.4771	+	29.7688i	−0.0710964	+	0.0596569i	−0.677643	−	0.735391i	$-0.736999\pi$
$499$	−35.4771	+	29.7688i	−0.0710964	+	0.0596569i	0.606547	+	0.795048i	$0.292554\pi$
$500$	−131.725	−	156.983i	−0.263449	−	0.313966i
$501$		0			0
$502$	414.696	−	150.937i	0.826088	−	0.300672i
$503$	728.991	−	420.883i	1.44929	−	0.836745i	0.450847	−	0.892601i	$-0.351122\pi$
$503$	728.991	−	420.883i	1.44929	−	0.836745i	0.998439	+	0.0558562i	$0.0177888\pi$
$504$		0			0
$505$	−178.374	+	308.953i	−0.353216	+	0.611788i
$506$	−284.434	−	50.1535i	−0.562123	−	0.0991175i
$507$		0			0
$508$	20.6487	+	7.51551i	0.0406470	+	0.0147943i
$509$	−503.035	+	88.6986i	−0.988281	+	0.174261i	−0.644347	−	0.764733i	$-0.722871\pi$
$509$	−503.035	+	88.6986i	−0.988281	+	0.174261i	−0.343934	+	0.938994i	$0.611760\pi$
$510$		0			0
$511$	−21.8736	−	18.3541i	−0.0428054	−	0.0359180i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−74.4863			−0.144915
$515$	−464.686	+	553.791i	−0.902303	+	1.07532i
$516$		0			0
$517$	−116.260	−	659.343i	−0.224874	−	1.27533i
$518$	−1.68732	+	4.63589i	−0.00325738	+	0.00894959i
$519$		0			0
$520$	49.8699	−	282.827i	0.0959037	−	0.543897i
$521$	496.828	+	286.844i	0.953604	+	0.550563i	0.894199	−	0.447670i	$-0.147746\pi$
$521$	496.828	+	286.844i	0.953604	+	0.550563i	0.0594053	+	0.998234i	$0.481080\pi$
$522$		0			0
$523$	257.403	+	445.835i	0.492166	+	0.852457i	0.999959	−	0.00902213i	$-0.00287187\pi$
$523$	257.403	+	445.835i	0.492166	+	0.852457i	−0.507793	+	0.861479i	$0.669539\pi$
$524$	25.6378	+	70.4394i	0.0489272	+	0.134426i
$525$		0			0
$526$	−17.3714	+	14.5763i	−0.0330255	+	0.0277117i
$527$	−529.627	−	631.185i	−1.00499	−	1.19769i
$528$		0			0
$529$	−300.064	+	109.214i	−0.567228	+	0.206454i
$530$	−2.53999	+	1.46646i	−0.00479243	+	0.00276691i
$531$		0			0
$532$	−0.183998	+	0.318694i	−0.000345861	+	0.000599048i
$533$	−312.427	−	55.0893i	−0.586167	−	0.103357i
$534$		0			0
$535$	−1535.83	−	558.997i	−2.87071	−	1.04485i
$536$	−179.964	+	31.7325i	−0.335754	+	0.0592024i
$537$		0			0
$538$	−253.358	−	212.593i	−0.470926	−	0.395154i
$539$		−	688.187i		−	1.27678i
$540$		0			0
$541$	104.119			0.192457			0.0962284	−	0.995359i	$-0.469322\pi$
$541$	104.119			0.192457			0.0962284	+	0.995359i	$0.469322\pi$
$542$	208.964	−	249.034i	0.385543	−	0.459472i
$543$		0			0
$544$	32.3927	+	183.708i	0.0595454	+	0.337699i
$545$	380.247	−	1044.72i	0.697702	−	1.91692i
$546$		0			0
$547$	−34.7198	+	196.906i	−0.0634732	+	0.359974i	0.936484	+	0.350711i	$0.114060\pi$
$547$	−34.7198	+	196.906i	−0.0634732	+	0.359974i	−0.999957	+	0.00926380i	$0.997051\pi$
$548$	−73.3171	−	42.3296i	−0.133790	−	0.0772439i
$549$		0			0
$550$	−378.150	−	654.976i	−0.687546	−	1.19087i
$551$	−3.63735	−	9.99353i	−0.00660136	−	0.0181371i
$552$		0			0
$553$	−6.69298	+	5.61608i	−0.0121030	+	0.0101557i
$554$	239.115	+	284.966i	0.431616	+	0.514380i
$555$		0			0
$556$	−306.241	+	111.463i	−0.550793	+	0.200472i
$557$	−289.044	+	166.880i	−0.518930	+	0.299604i	−0.736497	−	0.676441i	$-0.763521\pi$
$557$	−289.044	+	166.880i	−0.518930	+	0.299604i	0.217567	+	0.976045i	$0.430188\pi$
$558$		0			0
$559$	114.879	−	198.976i	0.205508	−	0.355950i
$560$	−14.1752	−	2.49947i	−0.0253129	−	0.00446334i
$561$		0			0
$562$	−654.597	−	238.254i	−1.16476	−	0.423939i
$563$	−989.177	+	174.419i	−1.75697	+	0.309802i	−0.956969	−	0.290190i	$-0.906281\pi$
$563$	−989.177	+	174.419i	−1.75697	+	0.309802i	−0.800006	+	0.599992i	$0.795170\pi$
$564$		0			0
$565$	443.039	+	371.754i	0.784140	+	0.657971i
$566$		−	692.917i		−	1.22423i
$567$		0			0
$568$	309.021			0.544051
$569$	−441.594	+	526.272i	−0.776089	+	0.924906i	−0.998750	−	0.0499895i	$-0.984081\pi$
$569$	−441.594	+	526.272i	−0.776089	+	0.924906i	0.222661	+	0.974896i	$0.428526\pi$
$570$		0			0
$571$	−67.2813	−	381.571i	−0.117831	−	0.668251i	−0.985310	−	0.170777i	$-0.945372\pi$
$571$	−67.2813	−	381.571i	−0.117831	−	0.668251i	0.867479	−	0.497474i	$-0.165739\pi$
$572$	123.497	−	339.306i	0.215904	−	0.593192i
$573$		0			0
$574$	−2.76107	+	15.6588i	−0.00481022	+	0.0272801i
$575$	475.499	+	274.529i	0.826954	+	0.477442i
$576$		0			0
$577$	−279.632	−	484.337i	−0.484631	−	0.839406i	0.515213	−	0.857062i	$-0.327713\pi$
$577$	−279.632	−	484.337i	−0.484631	−	0.839406i	−0.999844	+	0.0176564i	$0.994379\pi$
$578$	386.196	+	1061.06i	0.668158	+	1.83575i
$579$		0			0
$580$	318.656	−	267.385i	0.549408	−	0.461008i
$581$	16.6594	+	19.8539i	0.0286736	+	0.0341719i
$582$		0			0
$583$	−3.46517	+	1.26122i	−0.00594368	+	0.00216332i
$584$	154.173	−	89.0120i	0.263995	−	0.152418i
$585$		0			0
$586$	−107.669	+	186.488i	−0.183736	+	0.318240i
$587$	−499.131	−	88.0103i	−0.850309	−	0.149932i	−0.268522	−	0.963274i	$-0.586535\pi$
$587$	−499.131	−	88.0103i	−0.850309	−	0.149932i	−0.581787	+	0.813341i	$0.697646\pi$
$588$		0			0
$589$	9.52286	+	3.46604i	0.0161678	+	0.00588461i
$590$	608.728	−	107.335i	1.03174	−	0.181924i
$591$		0			0
$592$	−23.5621	−	19.7709i	−0.0398008	−	0.0333969i
$593$			598.516i			1.00930i	0.863324	+	0.504651i	$0.168379\pi$
$593$			598.516i			1.00930i	−0.863324	+	0.504651i	$0.831621\pi$
$594$		0			0
$595$	−118.664			−0.199436
$596$	−230.838	+	275.102i	−0.387312	+	0.461580i
$597$		0			0
$598$	45.5198	+	258.155i	0.0761200	+	0.431698i
$599$	−264.288	+	726.125i	−0.441215	+	1.21223i	0.497478	+	0.867477i	$0.334259\pi$
$599$	−264.288	+	726.125i	−0.441215	+	1.21223i	−0.938694	+	0.344753i	$0.887963\pi$
$600$		0			0
$601$	−22.6179	+	128.272i	−0.0376337	+	0.213431i	−0.997826	−	0.0659100i	$-0.979005\pi$
$601$	−22.6179	+	128.272i	−0.0376337	+	0.213431i	0.960192	+	0.279341i	$0.0901161\pi$
$602$	−9.97263	−	5.75770i	−0.0165658	−	0.00956429i
$603$		0			0
$604$	−160.931	−	278.740i	−0.266442	−	0.461490i
$605$	−211.389	−	580.786i	−0.349403	−	0.959978i
$606$		0			0
$607$	485.221	−	407.149i	0.799376	−	0.670756i	−0.148671	−	0.988887i	$-0.547500\pi$
$607$	485.221	−	407.149i	0.799376	−	0.670756i	0.948047	+	0.318131i	$0.103055\pi$
$608$	−1.47477	−	1.75756i	−0.00242560	−	0.00289072i
$609$		0			0
$610$	1103.36	−	401.590i	1.80879	−	0.658345i
$611$	−526.247	+	303.829i	−0.861288	+	0.497265i
$612$		0			0
$613$	−388.396	+	672.722i	−0.633599	+	1.09743i	0.353211	+	0.935544i	$0.385090\pi$
$613$	−388.396	+	672.722i	−0.633599	+	1.09743i	−0.986810	+	0.161883i	$0.948243\pi$
$614$	425.343	+	74.9995i	0.692741	+	0.122149i
$615$		0			0
$616$	−17.0060	−	6.18966i	−0.0276071	−	0.0100482i
$617$	360.546	−	63.5740i	0.584353	−	0.103037i	0.126347	−	0.991986i	$-0.459675\pi$
$617$	360.546	−	63.5740i	0.584353	−	0.103037i	0.458006	+	0.888949i	$0.348564\pi$
$618$		0			0
$619$	341.806	+	286.809i	0.552190	+	0.463343i	0.875682	−	0.482888i	$-0.160412\pi$
$619$	341.806	+	286.809i	0.552190	+	0.463343i	−0.323492	+	0.946231i	$0.604857\pi$
$620$			396.385i			0.639330i
$621$		0			0
$622$	−500.414			−0.804524
$623$	−30.2342	+	36.0317i	−0.0485299	+	0.0578357i
$624$		0			0
$625$	−23.4761	−	133.140i	−0.0375618	−	0.213024i
$626$	56.1835	−	154.363i	0.0897500	−	0.246586i
$627$		0			0
$628$	−26.8443	+	152.242i	−0.0427457	+	0.242423i
$629$	−219.600	−	126.786i	−0.349126	−	0.201568i
$630$		0			0
$631$	444.799	+	770.415i	0.704911	+	1.22094i	0.966723	+	0.255824i	$0.0823466\pi$
$631$	444.799	+	770.415i	0.704911	+	1.22094i	−0.261812	+	0.965119i	$0.584320\pi$
$632$	−18.6307	−	51.1875i	−0.0294790	−	0.0809929i
$633$		0			0
$634$	246.150	−	206.544i	0.388248	−	0.325779i
$635$	−56.0184	−	66.7601i	−0.0882179	−	0.105134i
$636$		0			0
$637$	−586.937	+	213.628i	−0.921408	+	0.335365i
$638$	452.936	−	261.503i	0.709931	−	0.409879i
$639$		0			0
$640$	44.8705	−	77.7180i	0.0701102	−	0.121434i
$641$	−460.754	−	81.2433i	−0.718805	−	0.126745i	−0.197731	−	0.980256i	$-0.563357\pi$
$641$	−460.754	−	81.2433i	−0.718805	−	0.126745i	−0.521074	+	0.853512i	$0.674468\pi$
$642$		0			0
$643$	367.369	+	133.711i	0.571336	+	0.207949i	0.611501	−	0.791244i	$-0.290566\pi$
$643$	367.369	+	133.711i	0.571336	+	0.207949i	−0.0401649	+	0.999193i	$0.512788\pi$
$644$	12.9387	−	2.28144i	0.0200912	−	0.00354261i
$645$		0			0
$646$	−14.4894	−	12.1581i	−0.0224295	−	0.0188206i
$647$			343.874i			0.531490i	0.964043	+	0.265745i	$0.0856180\pi$
$647$			343.874i			0.531490i	−0.964043	+	0.265745i	$0.914382\pi$
$648$		0			0
$649$	777.157			1.19747
$650$	−441.226	+	525.833i	−0.678809	+	0.808974i
$651$		0			0
$652$	0.743533	+	4.21678i	0.00114039	+	0.00646746i
$653$	−40.4063	+	111.015i	−0.0618779	+	0.170008i	−0.966779	−	0.255614i	$-0.917722\pi$
$653$	−40.4063	+	111.015i	−0.0618779	+	0.170008i	0.904901	+	0.425622i	$0.139945\pi$
$654$		0			0
$655$	51.6245	−	292.777i	0.0788161	−	0.446988i
$656$	−85.8520	−	49.5667i	−0.130872	−	0.0755590i
$657$		0			0
$658$	15.2279	+	26.3754i	0.0231426	+	0.0400842i
$659$	236.242	+	649.069i	0.358485	+	0.984930i	0.979555	+	0.201175i	$0.0644760\pi$
$659$	236.242	+	649.069i	0.358485	+	0.984930i	−0.621070	+	0.783755i	$0.713302\pi$
$660$		0			0
$661$	767.161	−	643.724i	1.16061	−	0.973864i	0.160692	−	0.987005i	$-0.448627\pi$
$661$	767.161	−	643.724i	1.16061	−	0.973864i	0.999914	+	0.0131403i	$0.00418282\pi$
$662$	−85.6338	−	102.054i	−0.129356	−	0.154161i
$663$		0			0
$664$	−151.841	+	55.2657i	−0.228677	+	0.0832315i
$665$	1.26395	−	0.729741i	0.00190068	−	0.00109736i
$666$		0			0
$667$	−189.845	+	328.822i	−0.284626	+	0.492986i
$668$	176.791	+	31.1730i	0.264657	+	0.0466662i
$669$		0			0
$670$	681.045	+	247.880i	1.01649	+	0.369971i
$671$	1453.85	−	256.353i	2.16669	−	0.382047i
$672$		0			0
$673$	−122.061	−	102.421i	−0.181368	−	0.152186i	0.547584	−	0.836751i	$-0.315548\pi$
$673$	−122.061	−	102.421i	−0.181368	−	0.152186i	−0.728952	+	0.684565i	$0.759992\pi$
$674$			102.468i			0.152029i
$675$		0			0
$676$	10.2785			0.0152049
$677$	657.379	−	783.434i	0.971018	−	1.15721i	−0.0165244	−	0.999863i	$-0.505260\pi$
$677$	657.379	−	783.434i	0.971018	−	1.15721i	0.987543	−	0.157351i	$-0.0502954\pi$
$678$		0			0
$679$	4.42833	+	25.1143i	0.00652185	+	0.0369872i
$680$	253.038	−	695.215i	0.372114	−	1.02237i
$681$		0			0
$682$	−86.5415	+	490.801i	−0.126894	+	0.719650i
$683$	−376.428	−	217.331i	−0.551139	−	0.318200i	0.198442	−	0.980113i	$-0.436412\pi$
$683$	−376.428	−	217.331i	−0.551139	−	0.318200i	−0.749581	+	0.661912i	$0.769745\pi$
$684$		0			0
$685$	167.881	+	290.778i	0.245081	+	0.424493i
$686$	21.4591	+	58.9584i	0.0312815	+	0.0859452i
$687$		0			0
$688$	54.9979	−	46.1487i	0.0799388	−	0.0670766i
$689$	2.15132	+	2.56384i	0.00312238	+	0.00372111i
$690$		0			0
$691$	−576.062	+	209.669i	−0.833664	+	0.303429i	−0.723362	−	0.690469i	$-0.757404\pi$
$691$	−576.062	+	209.669i	−0.833664	+	0.303429i	−0.110302	+	0.993898i	$0.535182\pi$
$692$	315.843	−	182.352i	0.456421	−	0.263515i
$693$		0			0
$694$	−292.294	+	506.267i	−0.421172	+	0.729492i
$695$	1272.87	+	224.442i	1.83147	+	0.322938i
$696$		0			0
$697$	−767.976	−	279.520i	−1.10183	−	0.401034i
$698$	97.9623	−	17.2734i	0.140347	−	0.0247470i
$699$		0			0
$700$	26.3547	+	22.1142i	0.0376495	+	0.0315917i
$701$		−	644.120i		−	0.918859i	−0.888214	−	0.459430i	$-0.848054\pi$
$701$		−	644.120i		−	0.918859i	0.888214	−	0.459430i	$-0.151946\pi$
$702$		0			0
$703$	3.11875			0.00443634
$704$	72.5264	−	86.4335i	0.103020	−	0.122775i
$705$		0			0
$706$	121.837	+	690.970i	0.172573	+	0.978710i
$707$	6.97845	−	19.1731i	0.00987051	−	0.0271190i
$708$		0			0
$709$	54.3773	−	308.389i	0.0766958	−	0.434963i	−0.922146	−	0.386843i	$-0.873566\pi$
$709$	54.3773	−	308.389i	0.0766958	−	0.434963i	0.998842	−	0.0481207i	$-0.0153232\pi$
$710$	−1061.39	−	612.794i	−1.49492	−	0.863090i
$711$		0			0
$712$	−146.627	−	253.965i	−0.205936	−	0.356692i
$713$	−123.746	−	339.988i	−0.173556	−	0.476842i
$714$		0			0
$715$	−1097.02	+	920.512i	−1.53430	+	1.28743i
$716$	−154.431	−	184.043i	−0.215685	−	0.257043i
$717$		0			0
$718$	386.226	−	140.575i	0.537919	−	0.195786i
$719$	1134.61	−	655.066i	1.57804	−	0.911079i	0.582902	−	0.812543i	$-0.301917\pi$
$719$	1134.61	−	655.066i	1.57804	−	0.911079i	0.995133	−	0.0985362i	$-0.0314160\pi$
$720$		0			0
$721$	20.6732	−	35.8070i	0.0286730	−	0.0496630i
$722$	−502.546	−	88.6124i	−0.696047	−	0.122732i
$723$		0			0
$724$	300.675	+	109.437i	0.415296	+	0.151156i
$725$	−979.141	+	172.649i	−1.35054	+	0.238137i
$726$		0			0
$727$	965.609	+	810.242i	1.32821	+	1.11450i	0.984492	+	0.175428i	$0.0561308\pi$
$727$	965.609	+	810.242i	1.32821	+	1.11450i	0.343718	+	0.939073i	$0.388314\pi$
$728$			16.4253i			0.0225623i
$729$		0			0
$730$	−706.049			−0.967190
$731$	380.454	−	453.407i	0.520456	−	0.620256i
$732$		0			0
$733$	36.7966	+	208.684i	0.0502000	+	0.284698i	0.999566	−	0.0294754i	$-0.00938366\pi$
$733$	36.7966	+	208.684i	0.0502000	+	0.284698i	−0.949365	+	0.314174i	$0.898273\pi$
$734$	−276.028	+	758.380i	−0.376059	+	1.03321i
$735$		0			0
$736$	−14.2240	+	80.6685i	−0.0193261	+	0.109604i
$737$	789.147	+	455.614i	1.07076	+	0.618201i
$738$		0			0
$739$	26.2115	+	45.3996i	0.0354688	+	0.0614338i	0.883215	−	0.468968i	$-0.155374\pi$
$739$	26.2115	+	45.3996i	0.0354688	+	0.0614338i	−0.847746	+	0.530402i	$0.822041\pi$
$740$	41.7223	+	114.631i	0.0563814	+	0.154907i
$741$		0			0
$742$	0.128499	−	0.107824i	0.000173180	−	0.000145315i
$743$	12.7448	+	15.1886i	0.0171531	+	0.0204423i	0.774553	−	0.632509i	$-0.217975\pi$
$743$	12.7448	+	15.1886i	0.0171531	+	0.0204423i	−0.757400	+	0.652952i	$0.773531\pi$
$744$		0			0
$745$	1338.39	−	487.133i	1.79649	−	0.653870i
$746$	−24.4311	+	14.1053i	−0.0327495	+	0.0189079i
$747$		0			0
$748$	465.094	−	805.566i	0.621783	−	1.07696i
$749$	92.0566	+	16.2321i	0.122906	+	0.0216716i
$750$		0			0
$751$	1260.89	+	458.927i	1.67895	+	0.611088i	0.993165	−	0.116716i	$-0.0372368\pi$
$751$	1260.89	+	458.927i	1.67895	+	0.611088i	0.685785	+	0.727804i	$0.259459\pi$
$752$	−186.996	+	32.9725i	−0.248665	+	0.0438464i
$753$		0			0
$754$	−363.629	−	305.121i	−0.482267	−	0.404670i
$755$			1276.51i			1.69075i
$756$		0			0
$757$	1369.68			1.80935			0.904675	−	0.426102i	$-0.140114\pi$
$757$	1369.68			1.80935			0.904675	+	0.426102i	$0.140114\pi$
$758$	33.6933	−	40.1541i	0.0444503	−	0.0529738i
$759$		0			0
$760$	1.58009	+	8.96114i	0.00207907	+	0.0117910i
$761$	18.9789	−	52.1440i	0.0249394	−	0.0685204i	−0.926598	−	0.376053i	$-0.877281\pi$
$761$	18.9789	−	52.1440i	0.0249394	−	0.0685204i	0.951538	+	0.307533i	$0.0995033\pi$
$762$		0			0
$763$	−11.0416	+	62.6198i	−0.0144712	+	0.0820705i
$764$	−221.174	−	127.695i	−0.289494	−	0.167140i
$765$		0			0
$766$	287.551	+	498.054i	0.375393	+	0.650200i
$767$	−241.246	−	662.817i	−0.314531	−	0.864168i
$768$		0			0
$769$	−859.169	+	720.928i	−1.11725	+	0.937488i	−0.998463	−	0.0554311i	$-0.982347\pi$
$769$	−859.169	+	720.928i	−1.11725	+	0.937488i	−0.118792	+	0.992919i	$0.537902\pi$
$770$	46.1359	+	54.9826i	0.0599168	+	0.0714060i
$771$		0			0
$772$	187.377	−	68.1996i	0.242716	−	0.0883415i
$773$	126.972	−	73.3074i	0.164259	−	0.0948349i	−0.415617	−	0.909540i	$-0.636434\pi$
$773$	126.972	−	73.3074i	0.164259	−	0.0948349i	0.579876	+	0.814705i	$0.303101\pi$
$774$		0			0
$775$	473.709	−	820.489i	0.611238	−	1.05870i
$776$	−156.579	−	27.6092i	−0.201778	−	0.0355788i
$777$		0			0
$778$	−206.988	−	75.3373i	−0.266051	−	0.0968346i
$779$	9.89901	−	1.74546i	0.0127073	−	0.00224065i
$780$		0			0
$781$	−1180.42	−	990.488i	−1.51142	−	1.26823i
$782$			675.296i			0.863550i
$783$		0			0
$784$	−195.177			−0.248950
$785$	394.099	−	469.669i	0.502037	−	0.598305i
$786$		0			0
$787$	−249.810	−	1416.74i	−0.317420	−	1.80018i	−0.558317	−	0.829628i	$-0.688553\pi$
$787$	−249.810	−	1416.74i	−0.317420	−	1.80018i	0.240896	−	0.970551i	$-0.422559\pi$
$788$	26.0551	−	71.5857i	0.0330648	−	0.0908448i
$789$		0			0
$790$	−37.5150	+	212.758i	−0.0474873	+	0.269314i
$791$	−28.6460	−	16.5388i	−0.0362150	−	0.0209087i
$792$		0			0
$793$	−669.943	−	1160.38i	−0.844821	−	1.46327i
$794$	−197.074	−	541.456i	−0.248204	−	0.681935i
$795$		0			0
$796$	−590.521	+	495.506i	−0.741861	+	0.622495i
$797$	866.974	+	1033.22i	1.08780	+	1.29639i	0.952151	+	0.305629i	$0.0988667\pi$
$797$	866.974	+	1033.22i	1.08780	+	1.29639i	0.135646	+	0.990757i	$0.456689\pi$
$798$		0			0
$799$	−1470.99	+	535.396i	−1.84104	+	0.670083i
$800$	−185.758	+	107.247i	−0.232197	+	0.134059i
$801$		0			0
$802$	−41.0568	+	71.1125i	−0.0511931	+	0.0886690i
$803$	−874.225	−	154.149i	−1.08870	−	0.191967i
$804$		0			0
$805$	−48.9645	−	17.8216i	−0.0608255	−	0.0221387i
$806$	445.456	−	78.5459i	0.552675	−	0.0974515i
$807$		0			0
$808$	97.4483	+	81.7688i	0.120604	+	0.101199i
$809$		−	596.082i		−	0.736813i	−0.929665	−	0.368407i	$-0.879903\pi$
$809$		−	596.082i		−	0.736813i	0.929665	−	0.368407i	$-0.120097\pi$
$810$		0			0
$811$	−304.801			−0.375833			−0.187917	−	0.982185i	$-0.560173\pi$
$811$	−304.801			−0.375833			−0.187917	+	0.982185i	$0.560173\pi$
$812$	−15.2926	+	18.2250i	−0.0188333	+	0.0224446i
$813$		0			0
$814$	26.6332	+	151.044i	0.0327189	+	0.185558i
$815$	5.80815	−	15.9578i	0.00712656	−	0.0195801i
$816$		0			0
$817$	−1.26410	+	7.16909i	−0.00154725	+	0.00877490i
$818$	−354.485	−	204.662i	−0.433355	−	0.250198i
$819$		0			0
$820$	196.583	+	340.492i	0.239735	+	0.415234i
$821$	226.613	+	622.615i	0.276021	+	0.758362i	0.997804	+	0.0662419i	$0.0211009\pi$
$821$	226.613	+	622.615i	0.276021	+	0.758362i	−0.721782	+	0.692120i	$0.756677\pi$
$822$		0			0
$823$	837.373	−	702.639i	1.01746	−	0.853753i	0.0281569	−	0.999604i	$-0.491036\pi$
$823$	837.373	−	702.639i	1.01746	−	0.853753i	0.989307	+	0.145850i	$0.0465918\pi$
$824$	165.698	+	197.472i	0.201090	+	0.239650i
$825$		0			0
$826$	−33.2203	+	12.0912i	−0.0402182	+	0.0146382i
$827$	−876.396	+	505.987i	−1.05973	+	0.611835i	−0.925357	−	0.379096i	$-0.876235\pi$
$827$	−876.396	+	505.987i	−1.05973	+	0.611835i	−0.134372	+	0.990931i	$0.542902\pi$
$828$		0			0
$829$	482.406	−	835.551i	0.581913	−	1.00790i	−0.413340	−	0.910577i	$-0.635638\pi$
$829$	482.406	−	835.551i	0.581913	−	1.00790i	0.995253	−	0.0973256i	$-0.0310288\pi$
$830$	631.120	+	111.283i	0.760385	+	0.134076i
$831$		0			0
$832$	−96.2306	−	35.0251i	−0.115662	−	0.0420975i
$833$	−1584.61	+	279.409i	−1.90229	+	0.335425i
$834$		0			0
$835$	−545.405	−	457.649i	−0.653179	−	0.548083i
$836$			11.4406i			0.0136849i
$837$		0			0
$838$	950.584			1.13435
$839$	641.845	−	764.921i	0.765012	−	0.911705i	−0.233142	−	0.972443i	$-0.574901\pi$
$839$	641.845	−	764.921i	0.765012	−	0.911705i	0.998154	+	0.0607373i	$0.0193452\pi$
$840$		0			0
$841$	26.6461	+	151.117i	0.0316838	+	0.179688i
$842$	−108.657	+	298.534i	−0.129047	+	0.354553i
$843$		0			0
$844$	118.497	−	672.029i	0.140399	−	0.796243i
$845$	−35.3035	−	20.3825i	−0.0417793	−	0.0241213i
$846$		0			0
$847$	17.6745	+	30.6131i	0.0208671	+	0.0361430i
$848$	0.357694	+	0.982756i	0.000421809	+	0.00115891i
$849$		0			0
$850$	−1354.60	+	1136.65i	−1.59365	+	1.33723i
$851$	−71.5723	−	85.2965i	−0.0841037	−	0.100231i
$852$		0			0
$853$	−1055.33	+	384.107i	−1.23719	+	0.450301i	−0.876055	−	0.482211i	$-0.839834\pi$
$853$	−1055.33	+	384.107i	−1.23719	+	0.450301i	−0.361138	+	0.932513i	$0.617612\pi$
$854$	−58.1578	+	33.5774i	−0.0681005	+	0.0393178i
$855$		0			0
$856$	−291.398	+	504.716i	−0.340418	+	0.589621i
$857$	−385.076	−	67.8994i	−0.449331	−	0.0792291i	−0.0555962	−	0.998453i	$-0.517706\pi$
$857$	−385.076	−	67.8994i	−0.449331	−	0.0792291i	−0.393735	+	0.919224i	$0.628817\pi$
$858$		0			0
$859$	1362.58	+	495.937i	1.58624	+	0.577343i	0.976548	−	0.215299i	$-0.0690726\pi$
$859$	1362.58	+	495.937i	1.58624	+	0.577343i	0.609688	+	0.792642i	$0.291295\pi$
$860$	−280.414	+	49.4446i	−0.326063	+	0.0574937i
$861$		0			0
$862$	−205.059	−	172.065i	−0.237888	−	0.199612i
$863$		−	953.368i		−	1.10471i	−0.833608	−	0.552357i	$-0.813729\pi$
$863$		−	953.368i		−	1.10471i	0.833608	−	0.552357i	$-0.186271\pi$
$864$		0			0
$865$	−1446.43			−1.67217
$866$	331.686	−	395.288i	0.383009	−	0.456453i
$867$		0			0
$868$	−3.93671	−	22.3262i	−0.00453538	−	0.0257214i
$869$	−92.9017	+	255.245i	−0.106906	+	0.293723i
$870$		0			0
$871$	143.614	−	814.475i	0.164884	−	0.935104i
$872$	−343.324	−	198.218i	−0.393720	−	0.227314i
$873$		0			0
$874$	−4.15282	−	7.19290i	−0.00475151	−	0.00822986i
$875$	−15.8984	−	43.6805i	−0.0181696	−	0.0499205i
$876$		0			0
$877$	−949.180	+	796.456i	−1.08230	+	0.908160i	−0.996110	−	0.0881183i	$-0.971915\pi$
$877$	−949.180	+	796.456i	−1.08230	+	0.908160i	−0.0861931	+	0.996278i	$0.527470\pi$
$878$	385.513	+	459.437i	0.439081	+	0.523277i
$879$		0			0
$880$	−420.504	+	153.051i	−0.477846	+	0.173922i
$881$	43.1058	−	24.8871i	0.0489282	−	0.0282487i	−0.475336	−	0.879804i	$-0.657674\pi$
$881$	43.1058	−	24.8871i	0.0489282	−	0.0282487i	0.524265	+	0.851555i	$0.324340\pi$
$882$		0			0
$883$	214.961	−	372.324i	0.243444	−	0.421658i	−0.718249	−	0.695787i	$-0.755056\pi$
$883$	214.961	−	372.324i	0.243444	−	0.421658i	0.961693	+	0.274128i	$0.0883893\pi$
$884$	−831.421	−	146.602i	−0.940521	−	0.165839i
$885$		0			0
$886$	238.913	+	86.9572i	0.269653	+	0.0981458i
$887$	611.223	−	107.775i	0.689091	−	0.121505i	0.181871	−	0.983322i	$-0.441785\pi$
$887$	611.223	−	107.775i	0.689091	−	0.121505i	0.507219	+	0.861817i	$0.330673\pi$
$888$		0			0
$889$	3.81824	+	3.20388i	0.00429498	+	0.00360391i
$890$			1163.05i			1.30680i
$891$		0			0
$892$	116.951			0.131111
$893$	12.3757	−	14.7488i	0.0138586	−	0.0165160i
$894$		0			0
$895$	165.460	+	938.368i	0.184871	+	1.04846i
$896$	−1.75545	+	4.82306i	−0.00195921	+	0.00538288i
$897$		0			0
$898$	158.268	−	897.582i	0.176245	−	0.999534i
$899$	567.393	+	327.585i	0.631138	+	0.364388i
$900$		0			0
$901$	4.31094	+	7.46677i	0.00478462	+	0.00828720i
$902$	169.069	+	464.514i	0.187438	+	0.514982i
$903$		0			0
$904$	157.980	−	132.561i	0.174756	−	0.146638i
$905$	−815.708	−	972.123i	−0.901334	−	1.07417i
$906$		0			0
$907$	1623.70	−	590.977i	1.79018	−	0.651573i	0.790972	−	0.611852i	$-0.209575\pi$
$907$	1623.70	−	590.977i	1.79018	−	0.651573i	0.999211	−	0.0397211i	$-0.0126470\pi$
$908$	−72.7438	+	41.9987i	−0.0801143	+	0.0462540i
$909$		0			0
$910$	32.5717	−	56.4159i	0.0357931	−	0.0619955i
$911$	633.504	+	111.704i	0.695394	+	0.122617i	0.510162	−	0.860078i	$-0.329585\pi$
$911$	633.504	+	111.704i	0.695394	+	0.122617i	0.185231	+	0.982695i	$0.440697\pi$
$912$		0			0
$913$	757.153	+	275.581i	0.829302	+	0.301841i
$914$	−361.629	+	63.7649i	−0.395655	+	0.0697647i
$915$		0			0
$916$	−136.371	−	114.429i	−0.148877	−	0.124923i
$917$			17.0032i			0.0185422i
$918$		0			0
$919$	436.696			0.475186			0.237593	−	0.971365i	$-0.423642\pi$
$919$	436.696			0.475186			0.237593	+	0.971365i	$0.423642\pi$
$920$	208.822	−	248.864i	0.226980	−	0.270505i
$921$		0			0
$922$	−119.585	−	678.199i	−0.129702	−	0.735574i
$923$	−478.335	+	1314.22i	−0.518240	+	1.42385i
$924$		0			0
$925$	50.6304	−	287.139i	0.0547356	−	0.310421i
$926$	−734.259	−	423.925i	−0.792937	−	0.457802i
$927$		0			0
$928$	−74.1648	−	128.457i	−0.0799189	−	0.138424i
$929$	537.202	+	1475.95i	0.578258	+	1.58875i	0.791115	+	0.611668i	$0.209501\pi$
$929$	537.202	+	1475.95i	0.578258	+	1.58875i	−0.212856	+	0.977084i	$0.568277\pi$
$930$		0			0
$931$	15.1601	−	12.7209i	0.0162837	−	0.0136636i
$932$	180.542	+	215.162i	0.193715	+	0.230860i
$933$		0			0
$934$	−846.336	+	308.041i	−0.906141	+	0.329808i
$935$	−3194.90	+	1844.58i	−3.41700	+	1.97281i
$936$		0			0
$937$	−492.267	+	852.632i	−0.525366	+	0.909960i	0.474198	+	0.880418i	$0.342738\pi$
$937$	−492.267	+	852.632i	−0.525366	+	0.909960i	−0.999564	+	0.0295416i	$0.990595\pi$
$938$	−40.8214	−	7.19791i	−0.0435196	−	0.00767368i
$939$		0			0
$940$	707.659	+	257.567i	0.752828	+	0.274007i
$941$	202.540	−	35.7132i	0.215239	−	0.0379524i	−0.0649887	−	0.997886i	$-0.520701\pi$
$941$	202.540	−	35.7132i	0.215239	−	0.0379524i	0.280228	+	0.959934i	$0.409590\pi$
$942$		0			0
$943$	−274.910	−	230.677i	−0.291527	−	0.244621i
$944$		−	220.410i		−	0.233485i
$945$		0			0
$946$	−358.002			−0.378438
$947$	401.343	−	478.302i	0.423804	−	0.505070i	−0.511320	−	0.859391i	$-0.670843\pi$
$947$	401.343	−	478.302i	0.423804	−	0.505070i	0.935124	+	0.354320i	$0.115288\pi$
$948$		0			0
$949$	139.908	+	793.455i	0.147426	+	0.836096i
$950$	7.43856	−	20.4373i	0.00783006	−	0.0215129i
$951$		0			0
$952$	−7.34766	+	41.6707i	−0.00771813	+	0.0437717i
$953$	−593.317	−	342.552i	−0.622578	−	0.359445i	0.155294	−	0.987868i	$-0.450367\pi$
$953$	−593.317	−	342.552i	−0.622578	−	0.359445i	−0.777872	+	0.628423i	$0.783701\pi$
$954$		0			0
$955$	506.441	+	877.181i	0.530304	+	0.918514i
$956$	−19.8738	−	54.6029i	−0.0207885	−	0.0571160i
$957$		0			0
$958$	432.425	−	362.847i	0.451383	−	0.378755i
$959$	−12.3437	−	14.7106i	−0.0128714	−	0.0153395i
$960$		0			0
$961$	316.383	−	115.154i	0.329223	−	0.119827i
$962$	120.554	−	69.6021i	0.125316	−	0.0723515i
$963$		0			0
$964$	−148.449	+	257.121i	−0.153993	+	0.266723i
$965$	−778.822	−	137.327i	−0.807069	−	0.142308i
$966$		0			0
$967$	−665.140	−	242.091i	−0.687839	−	0.250353i	−0.0256294	−	0.999672i	$-0.508159\pi$
$967$	−665.140	−	242.091i	−0.687839	−	0.250353i	−0.662210	+	0.749319i	$0.730381\pi$
$968$	−217.041	+	38.2701i	−0.224215	+	0.0395352i
$969$		0			0
$970$	483.051	+	405.328i	0.497991	+	0.417864i
$971$		−	1276.82i		−	1.31496i	−0.753473	−	0.657479i	$-0.771623\pi$
$971$		−	1276.82i		−	1.31496i	0.753473	−	0.657479i	$-0.228377\pi$
$972$		0			0
$973$	−73.9230			−0.0759743
$974$	345.089	−	411.261i	0.354300	−	0.422239i
$975$		0			0
$976$	−72.7044	−	412.327i	−0.0744922	−	0.422466i
$977$	552.252	−	1517.30i	0.565252	−	1.55302i	−0.246577	−	0.969123i	$-0.579306\pi$
$977$	552.252	−	1517.30i	0.565252	−	1.55302i	0.811829	−	0.583895i	$-0.198472\pi$
$978$		0			0
$979$	−253.926	+	1440.08i	−0.259373	+	1.47098i
$980$	670.371	+	387.039i	0.684052	+	0.394937i
$981$		0			0
$982$	−423.193	−	732.993i	−0.430951	−	0.746428i
$983$	308.388	+	847.290i	0.313721	+	0.861943i	0.991897	+	0.127043i	$0.0405486\pi$
$983$	308.388	+	847.290i	0.313721	+	0.861943i	−0.678176	+	0.734900i	$0.737229\pi$
$984$		0			0
$985$	−231.447	+	194.207i	−0.234971	+	0.197164i
$986$	−786.026	−	936.750i	−0.797187	−	0.950050i
$987$		0			0
$988$	9.75740	−	3.55140i	0.00987591	−	0.00359454i
$989$	225.082	−	129.951i	0.227585	−	0.131396i
$990$		0			0
$991$	442.929	−	767.176i	0.446952	−	0.774143i	−0.551234	−	0.834350i	$-0.685843\pi$
$991$	442.929	−	767.176i	0.446952	−	0.774143i	0.998186	+	0.0602077i	$0.0191763\pi$
$992$	139.196	+	24.5440i	0.140319	+	0.0247420i
$993$		0			0
$994$	65.8683	+	23.9741i	0.0662658	+	0.0241188i
$995$	3010.85	−	530.894i	3.02598	−	0.533562i
$996$		0			0
$997$	−962.201	−	807.383i	−0.965097	−	0.809812i	0.0166779	−	0.999861i	$-0.494691\pi$
$997$	−962.201	−	807.383i	−0.965097	−	0.809812i	−0.981775	+	0.190049i	$0.939135\pi$
$998$		−	65.4951i		−	0.0656264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.35.1		36
3.2	odd	2		54.3.f.a.11.4	yes	36
12.11	even	2		432.3.bc.c.65.6		36
27.5	odd	18	inner	162.3.f.a.125.1		36
27.7	even	9		1458.3.b.c.1457.20		36
27.20	odd	18		1458.3.b.c.1457.17		36
27.22	even	9		54.3.f.a.5.4	✓	36
108.103	odd	18		432.3.bc.c.113.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.5.4	✓	36	27.22	even	9
54.3.f.a.11.4	yes	36	3.2	odd	2
162.3.f.a.35.1		36	1.1	even	1	trivial
162.3.f.a.125.1		36	27.5	odd	18	inner
432.3.bc.c.65.6		36	12.11	even	2
432.3.bc.c.113.6		36	108.103	odd	18
1458.3.b.c.1457.17		36	27.20	odd	18
1458.3.b.c.1457.20		36	27.7	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-2.71293 + 7.45370i) q^{5} +(0.0787775 - 0.446769i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-2.71293 + 7.45370i) q^{5} +(0.0787775 - 0.446769i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-5.60882 - 9.71475i) q^{10} +(-4.82381 - 13.2533i) q^{11} +(-9.80599 + 8.22820i) q^{13} +(0.412396 + 0.491475i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(-28.5583 + 16.4882i) q^{17} +(0.202792 - 0.351246i) q^{19} +(15.6231 + 2.75478i) q^{20} +(18.7430 + 6.82189i) q^{22} +(-14.2603 + 2.51448i) q^{23} +(-29.0466 - 24.3730i) q^{25} -18.1031i q^{26} -0.907323 q^{28} +(16.8547 - 20.0866i) q^{29} +(4.33881 + 24.6066i) q^{31} +(1.93476 - 5.31570i) q^{32} +(8.09818 - 45.9270i) q^{34} +(3.11637 + 1.79924i) q^{35} +(3.84477 + 6.65933i) q^{37} +(0.196177 + 0.538991i) q^{38} +(-17.1864 + 14.4211i) q^{40} +(15.9304 + 18.9851i) q^{41} +(-16.8662 + 6.13880i) q^{43} +(-24.4286 + 14.1039i) q^{44} +(10.2391 - 17.7347i) q^{46} +(46.7491 + 8.24313i) q^{47} +(45.8515 + 16.6886i) q^{49} +(52.8090 - 9.31165i) q^{50} +(19.6120 + 16.4564i) q^{52} -0.261457i q^{53} +111.873 q^{55} +(0.824792 - 0.982949i) q^{56} +(6.43929 + 36.5190i) q^{58} +(-18.8461 + 51.7793i) q^{59} +(-18.1761 + 103.082i) q^{61} +(-30.6018 - 17.6679i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-34.7276 - 95.4134i) q^{65} +(-49.4929 + 41.5295i) q^{67} +(42.3935 + 50.5226i) q^{68} +(-4.78210 + 1.74054i) q^{70} +(94.6180 - 54.6277i) q^{71} +(31.4705 - 54.5085i) q^{73} +(-10.7094 - 1.88836i) q^{74} +(-0.762248 - 0.277436i) q^{76} +(-6.30118 + 1.11107i) q^{77} +(-14.7532 - 12.3794i) q^{79} -31.7283i q^{80} -35.0489 q^{82} +(-36.7220 + 43.7636i) q^{83} +(-45.4212 - 257.596i) q^{85} +(8.68158 - 23.8524i) q^{86} +(6.92713 - 39.2857i) q^{88} +(-89.7902 - 51.8404i) q^{89} +(2.90362 + 5.02921i) q^{91} +(9.90511 + 27.2141i) q^{92} +(-51.4269 + 43.1523i) q^{94} +(2.06792 + 2.46445i) q^{95} +(-52.8231 + 19.2260i) q^{97} +(-59.7604 + 34.5027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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