LMFDB - Embedded newform 108.3.f.c.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.f (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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.8
Root			$1.93353 - 0.511345i$ of defining polynomial
Character	$\chi$	$=$	108.19
Dual form			108.3.f.c.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93353 - 0.511345i) q^{2} +(3.47705 - 1.97740i) q^{4} +(4.03104 + 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(5.71184 - 5.60133i) q^{8} +O(q^{10})$	\(q+(1.93353 - 0.511345i) q^{2} +(3.47705 - 1.97740i) q^{4} +(4.03104 + 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(5.71184 - 5.60133i) q^{8} +(11.3643 + 11.4386i) q^{10} +(-3.25842 - 1.88125i) q^{11} +(-3.52605 - 6.10730i) q^{13} +(-8.69780 - 2.36095i) q^{14} +(8.17979 - 13.7510i) q^{16} -0.517890 q^{17} -16.4164i q^{19} +(27.8223 + 16.3057i) q^{20} +(-7.26222 - 1.97127i) q^{22} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(-9.94065 - 10.0056i) q^{26} +(-18.0247 - 0.117384i) q^{28} +(-9.48394 + 16.4267i) q^{29} +(-13.1355 + 7.58377i) q^{31} +(8.78432 - 30.7707i) q^{32} +(-1.00135 + 0.264820i) q^{34} -36.3299i q^{35} +0.592061 q^{37} +(-8.39446 - 31.7416i) q^{38} +(62.1330 + 17.3007i) q^{40} +(-12.3766 - 21.4369i) q^{41} +(27.8686 + 16.0900i) q^{43} +(-15.0497 - 0.0980099i) q^{44} +(-45.3890 + 45.0944i) q^{46} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} +(-20.9556 + 77.2010i) q^{50} +(-24.3368 - 14.2630i) q^{52} +0.664765 q^{53} -30.3336i q^{55} +(-34.9113 + 8.98987i) q^{56} +(-9.93776 + 36.6110i) q^{58} +(30.5921 - 17.6623i) q^{59} +(33.7750 - 58.5000i) q^{61} +(-21.5199 + 21.3802i) q^{62} +(1.25029 - 63.9878i) q^{64} +(28.4273 - 49.2376i) q^{65} +(-74.4692 + 42.9948i) q^{67} +(-1.80073 + 1.02407i) q^{68} +(-18.5771 - 70.2449i) q^{70} +56.4434i q^{71} +131.921 q^{73} +(1.14477 - 0.302748i) q^{74} +(-32.4618 - 57.0808i) q^{76} +(8.47743 + 14.6833i) q^{77} +(126.869 + 73.2481i) q^{79} +(128.982 + 1.68005i) q^{80} +(-34.8921 - 35.1201i) q^{82} +(-87.1029 - 50.2889i) q^{83} +(-2.08764 - 3.61589i) q^{85} +(62.1122 + 16.8599i) q^{86} +(-29.1491 + 7.50608i) q^{88} +25.8362 q^{89} +31.7786i q^{91} +(-64.7021 + 110.401i) q^{92} +(116.939 + 31.7420i) q^{94} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +(-40.4465 - 40.7107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.93353	−	0.511345i	0.966763	−	0.255672i
$2$	1.93353	−	0.511345i	0.966763	−	0.255672i
$3$		0			0
$3$		0			0
$4$	3.47705	−	1.97740i	0.869263	−	0.494350i
$5$	4.03104	+	6.98197i	0.806209	+	1.39639i	0.915472	+	0.402382i	$0.131818\pi$
$5$	4.03104	+	6.98197i	0.806209	+	1.39639i	−0.109263	+	0.994013i	$0.534849\pi$
$6$		0			0
$7$	−3.90254	−	2.25313i	−0.557506	−	0.321876i	0.194638	−	0.980875i	$-0.437647\pi$
$7$	−3.90254	−	2.25313i	−0.557506	−	0.321876i	−0.752144	+	0.658999i	$0.770980\pi$
$8$	5.71184	−	5.60133i	0.713980	−	0.700166i
$9$		0			0
$10$	11.3643	+	11.4386i	1.13643	+	1.14386i
$11$	−3.25842	−	1.88125i	−0.296220	−	0.171023i	0.344523	−	0.938778i	$-0.388041\pi$
$11$	−3.25842	−	1.88125i	−0.296220	−	0.171023i	−0.640744	+	0.767755i	$0.721374\pi$
$12$		0			0
$13$	−3.52605	−	6.10730i	−0.271235	−	0.469792i	0.697944	−	0.716153i	$-0.254099\pi$
$13$	−3.52605	−	6.10730i	−0.271235	−	0.469792i	−0.969178	+	0.246361i	$0.920765\pi$
$14$	−8.69780	−	2.36095i	−0.621271	−	0.168639i
$15$		0			0
$16$	8.17979	−	13.7510i	0.511237	−	0.859440i
$17$	−0.517890			−0.0304641			−0.0152321	−	0.999884i	$-0.504849\pi$
$17$	−0.517890			−0.0304641			−0.0152321	+	0.999884i	$0.504849\pi$
$18$		0			0
$19$		−	16.4164i		−	0.864023i	−0.901868	−	0.432012i	$-0.857804\pi$
$19$		−	16.4164i		−	0.864023i	0.901868	−	0.432012i	$-0.142196\pi$
$20$	27.8223	+	16.3057i	1.39111	+	0.815286i
$21$		0			0
$22$	−7.26222	−	1.97127i	−0.330101	−	0.0896033i
$23$	−27.7049	+	15.9954i	−1.20456	+	0.695454i	−0.961566	−	0.274573i	$-0.911463\pi$
$23$	−27.7049	+	15.9954i	−1.20456	+	0.695454i	−0.242996	+	0.970027i	$0.578130\pi$
$24$		0			0
$25$	−19.9986	+	34.6387i	−0.799946	+	1.38555i
$26$	−9.94065	−	10.0056i	−0.382333	−	0.384831i
$27$		0			0
$28$	−18.0247	−	0.117384i	−0.643739	−	0.00419230i
$29$	−9.48394	+	16.4267i	−0.327032	+	0.566437i	−0.981922	−	0.189288i	$-0.939382\pi$
$29$	−9.48394	+	16.4267i	−0.327032	+	0.566437i	0.654889	+	0.755725i	$0.272715\pi$
$30$		0			0
$31$	−13.1355	+	7.58377i	−0.423725	+	0.244638i	−0.696670	−	0.717392i	$-0.745336\pi$
$31$	−13.1355	+	7.58377i	−0.423725	+	0.244638i	0.272945	+	0.962030i	$0.412002\pi$
$32$	8.78432	−	30.7707i	0.274510	−	0.961584i
$33$		0			0
$34$	−1.00135	+	0.264820i	−0.0294516	+	0.00778884i
$35$		−	36.3299i		−	1.03800i
$36$		0			0
$37$	0.592061			0.0160017			0.00800083	−	0.999968i	$-0.497453\pi$
$37$	0.592061			0.0160017			0.00800083	+	0.999968i	$0.497453\pi$
$38$	−8.39446	−	31.7416i	−0.220907	−	0.835306i
$39$		0			0
$40$	62.1330	+	17.3007i	1.55333	+	0.432518i
$41$	−12.3766	−	21.4369i	−0.301868	−	0.522850i	0.674691	−	0.738100i	$-0.264277\pi$
$41$	−12.3766	−	21.4369i	−0.301868	−	0.522850i	−0.976559	+	0.215250i	$0.930943\pi$
$42$		0			0
$43$	27.8686	+	16.0900i	0.648107	+	0.374185i	0.787731	−	0.616020i	$-0.211256\pi$
$43$	27.8686	+	16.0900i	0.648107	+	0.374185i	−0.139623	+	0.990205i	$0.544589\pi$
$44$	−15.0497	−	0.0980099i	−0.342039	−	0.00222750i
$45$		0			0
$46$	−45.3890	+	45.0944i	−0.986718	+	0.980313i
$47$	52.4682	+	30.2925i	1.11634	+	0.644521i	0.940465	−	0.339890i	$-0.110390\pi$
$47$	52.4682	+	30.2925i	1.11634	+	0.644521i	0.175879	+	0.984412i	$0.443723\pi$
$48$		0			0
$49$	−14.3468	−	24.8493i	−0.292791	−	0.507129i
$50$	−20.9556	+	77.2010i	−0.419112	+	1.54402i
$51$		0			0
$52$	−24.3368	−	14.2630i	−0.468016	−	0.274288i
$53$	0.664765			0.0125427			0.00627137	−	0.999980i	$-0.498004\pi$
$53$	0.664765			0.0125427			0.00627137	+	0.999980i	$0.498004\pi$
$54$		0			0
$55$		−	30.3336i		−	0.551521i
$56$	−34.9113	+	8.98987i	−0.623415	+	0.160533i
$57$		0			0
$58$	−9.93776	+	36.6110i	−0.171341	+	0.631224i
$59$	30.5921	−	17.6623i	0.518510	−	0.299362i	−0.217815	−	0.975990i	$-0.569893\pi$
$59$	30.5921	−	17.6623i	0.518510	−	0.299362i	0.736325	+	0.676628i	$0.236560\pi$
$60$		0			0
$61$	33.7750	−	58.5000i	0.553688	−	0.959016i	−0.444316	−	0.895870i	$-0.646553\pi$
$61$	33.7750	−	58.5000i	0.553688	−	0.959016i	0.998004	−	0.0631460i	$-0.0201134\pi$
$62$	−21.5199	+	21.3802i	−0.347095	+	0.344842i
$63$		0			0
$64$	1.25029	−	63.9878i	0.0195357	−	0.999809i
$65$	28.4273	−	49.2376i	0.437343	−	0.757501i
$66$		0			0
$67$	−74.4692	+	42.9948i	−1.11148	+	0.641714i	−0.939213	−	0.343336i	$-0.888443\pi$
$67$	−74.4692	+	42.9948i	−1.11148	+	0.641714i	−0.172269	+	0.985050i	$0.555110\pi$
$68$	−1.80073	+	1.02407i	−0.0264813	+	0.0150599i
$69$		0			0
$70$	−18.5771	−	70.2449i	−0.265388	−	1.00350i
$71$			56.4434i			0.794977i	0.917607	+	0.397489i	$0.130118\pi$
$71$			56.4434i			0.794977i	−0.917607	+	0.397489i	$0.869882\pi$
$72$		0			0
$73$	131.921			1.80713			0.903567	−	0.428447i	$-0.140939\pi$
$73$	131.921			1.80713			0.903567	+	0.428447i	$0.140939\pi$
$74$	1.14477	−	0.302748i	0.0154698	−	0.00409118i
$75$		0			0
$76$	−32.4618	−	57.0808i	−0.427129	−	0.751063i
$77$	8.47743	+	14.6833i	0.110096	+	0.190693i
$78$		0			0
$79$	126.869	+	73.2481i	1.60594	+	0.927191i	0.990265	+	0.139192i	$0.0444505\pi$
$79$	126.869	+	73.2481i	1.60594	+	0.927191i	0.615677	+	0.787999i	$0.288883\pi$
$80$	128.982	+	1.68005i	1.61228	+	0.0210006i
$81$		0			0
$82$	−34.8921	−	35.1201i	−0.425513	−	0.428293i
$83$	−87.1029	−	50.2889i	−1.04943	−	0.605890i	−0.126942	−	0.991910i	$-0.540516\pi$
$83$	−87.1029	−	50.2889i	−1.04943	−	0.605890i	−0.922491	+	0.386020i	$0.873850\pi$
$84$		0			0
$85$	−2.08764	−	3.61589i	−0.0245604	−	0.0425399i
$86$	62.1122	+	16.8599i	0.722235	+	0.196045i
$87$		0			0
$88$	−29.1491	+	7.50608i	−0.331240	+	0.0852964i
$89$	25.8362			0.290295			0.145147	−	0.989410i	$-0.453634\pi$
$89$	25.8362			0.290295			0.145147	+	0.989410i	$0.453634\pi$
$90$		0			0
$91$			31.7786i			0.349216i
$92$	−64.7021	+	110.401i	−0.703284	+	1.20001i
$93$		0			0
$94$	116.939	+	31.7420i	1.24403	+	0.337681i
$95$	114.619	−	66.1754i	1.20652	−	0.696583i
$96$		0			0
$97$	−48.2534	+	83.5773i	−0.497457	+	0.861621i	−0.999996	−	0.00293363i	$-0.999066\pi$
$97$	−48.2534	+	83.5773i	−0.497457	+	0.861621i	0.502538	+	0.864555i	$0.332400\pi$
$98$	−40.4465	−	40.7107i	−0.412719	−	0.415415i
$99$		0			0
$100$	−1.04189	+	159.986i	−0.0104189	+	1.59986i
$101$	21.6600	−	37.5163i	0.214456	−	0.371448i	−0.738648	−	0.674091i	$-0.764536\pi$
$101$	21.6600	−	37.5163i	0.214456	−	0.371448i	0.953104	+	0.302643i	$0.0978689\pi$
$102$		0			0
$103$	125.439	−	72.4223i	1.21786	−	0.703129i	0.253397	−	0.967362i	$-0.418452\pi$
$103$	125.439	−	72.4223i	1.21786	−	0.703129i	0.964459	+	0.264233i	$0.0851189\pi$
$104$	−54.3492	−	15.1334i	−0.522588	−	0.145513i
$105$		0			0
$106$	1.28534	−	0.339924i	0.0121259	−	0.00320683i
$107$			54.9861i			0.513889i	0.966426	+	0.256944i	$0.0827158\pi$
$107$			54.9861i			0.513889i	−0.966426	+	0.256944i	$0.917284\pi$
$108$		0			0
$109$	−63.9235			−0.586454			−0.293227	−	0.956043i	$-0.594729\pi$
$109$	−63.9235			−0.586454			−0.293227	+	0.956043i	$0.594729\pi$
$110$	−15.5110	−	58.6509i	−0.141009	−	0.533190i
$111$		0			0
$112$	−62.9049	+	35.2338i	−0.561651	+	0.314588i
$113$	−17.8239	−	30.8720i	−0.157734	−	0.273203i	0.776317	−	0.630342i	$-0.217086\pi$
$113$	−17.8239	−	30.8720i	−0.157734	−	0.273203i	−0.934051	+	0.357139i	$0.883752\pi$
$114$		0			0
$115$	−223.360	−	128.957i	−1.94226	−	1.12136i
$116$	−0.494097	+	75.8699i	−0.00425945	+	0.654051i
$117$		0			0
$118$	50.1190	−	49.7937i	0.424738	−	0.421981i
$119$	2.02109	+	1.16688i	0.0169839	+	0.00980568i
$120$		0			0
$121$	−53.4218	−	92.5292i	−0.441502	−	0.764704i
$122$	35.3912	−	130.382i	0.290091	−	1.06870i
$123$		0			0
$124$	−30.6766	+	52.3432i	−0.247392	+	0.422123i
$125$	−120.909			−0.967276
$126$		0			0
$127$			9.81219i			0.0772613i	0.999254	+	0.0386307i	$0.0122996\pi$
$127$			9.81219i			0.0772613i	−0.999254	+	0.0386307i	$0.987700\pi$
$128$	−30.3024	−	124.361i	−0.236737	−	0.971574i
$129$		0			0
$130$	29.7876	−	109.738i	0.229135	−	0.844141i
$131$	−101.561	+	58.6365i	−0.775278	+	0.447607i	−0.834754	−	0.550623i	$-0.814390\pi$
$131$	−101.561	+	58.6365i	−0.775278	+	0.447607i	0.0594761	+	0.998230i	$0.481057\pi$
$132$		0			0
$133$	−36.9884	+	64.0659i	−0.278109	+	0.481698i
$134$	−122.003	+	121.211i	−0.910471	+	0.904561i
$135$		0			0
$136$	−2.95811	+	2.90087i	−0.0217508	+	0.0213299i
$137$	−125.606	+	217.556i	−0.916831	+	1.58800i	−0.112634	+	0.993637i	$0.535929\pi$
$137$	−125.606	+	217.556i	−0.916831	+	1.58800i	−0.804198	+	0.594362i	$0.797405\pi$
$138$		0			0
$139$	−133.073	+	76.8298i	−0.957361	+	0.552732i	−0.895360	−	0.445344i	$-0.853081\pi$
$139$	−133.073	+	76.8298i	−0.957361	+	0.552732i	−0.0620009	+	0.998076i	$0.519748\pi$
$140$	−71.8388	−	126.321i	−0.513134	−	0.902294i
$141$		0			0
$142$	28.8620	+	109.135i	0.203254	+	0.768555i
$143$			26.5335i			0.185549i
$144$		0			0
$145$	−152.921			−1.05463
$146$	255.072	−	67.4570i	1.74707	−	0.462034i
$147$		0			0
$148$	2.05863	−	1.17074i	0.0139097	−	0.00791041i
$149$	45.8643	+	79.4393i	0.307814	+	0.533150i	0.977884	−	0.209148i	$-0.0670691\pi$
$149$	45.8643	+	79.4393i	0.307814	+	0.533150i	−0.670070	+	0.742298i	$0.733736\pi$
$150$		0			0
$151$	36.0215	+	20.7970i	0.238553	+	0.137729i	0.614512	−	0.788908i	$-0.289353\pi$
$151$	36.0215	+	20.7970i	0.238553	+	0.137729i	−0.375958	+	0.926637i	$0.622686\pi$
$152$	−91.9538	−	93.7681i	−0.604959	−	0.616895i
$153$		0			0
$154$	23.8996	+	24.0557i	0.155192	+	0.156206i
$155$	−105.899	−	61.1410i	−0.683222	−	0.394458i
$156$		0			0
$157$	112.909	+	195.565i	0.719167	+	1.24563i	0.961330	+	0.275399i	$0.0888099\pi$
$157$	112.909	+	195.565i	0.719167	+	1.24563i	−0.242163	+	0.970236i	$0.577857\pi$
$158$	282.760	+	76.7531i	1.78962	+	0.485779i
$159$		0			0
$160$	250.250	−	62.7061i	1.56406	−	0.391913i
$161$	144.160			0.895401
$162$		0			0
$163$		−	125.175i		−	0.767945i	−0.923344	−	0.383973i	$-0.874556\pi$
$163$		−	125.175i		−	0.767945i	0.923344	−	0.383973i	$-0.125444\pi$
$164$	−85.4233	−	50.0637i	−0.520874	−	0.305266i
$165$		0			0
$166$	−194.131	−	52.6953i	−1.16946	−	0.317442i
$167$	−154.373	+	89.1274i	−0.924390	+	0.533697i	−0.885033	−	0.465528i	$-0.845864\pi$
$167$	−154.373	+	89.1274i	−0.924390	+	0.533697i	−0.0393573	+	0.999225i	$0.512531\pi$
$168$		0			0
$169$	59.6340	−	103.289i	0.352864	−	0.611178i
$170$	−5.88547	−	5.92393i	−0.0346204	−	0.0348466i
$171$		0			0
$172$	128.717	+	0.838258i	0.748354	+	0.00487359i
$173$	75.5904	−	130.926i	0.436939	−	0.756800i	−0.560513	−	0.828146i	$-0.689396\pi$
$173$	75.5904	−	130.926i	0.436939	−	0.756800i	0.997452	+	0.0713455i	$0.0227293\pi$
$174$		0			0
$175$	156.091	−	90.1193i	0.891949	−	0.514967i
$176$	−52.5224	+	29.4185i	−0.298423	+	0.167150i
$177$		0			0
$178$	49.9551	−	13.2112i	0.280646	−	0.0742204i
$179$		−	276.827i		−	1.54652i	−0.634088	−	0.773261i	$-0.718624\pi$
$179$		−	276.827i		−	1.54652i	0.634088	−	0.773261i	$-0.281376\pi$
$180$		0			0
$181$	−104.729			−0.578612			−0.289306	−	0.957237i	$-0.593425\pi$
$181$	−104.729			−0.578612			−0.289306	+	0.957237i	$0.593425\pi$
$182$	16.2499	+	61.4449i	0.0892849	+	0.337609i
$183$		0			0
$184$	−68.6504	+	246.548i	−0.373100	+	1.33993i
$185$	2.38663	+	4.13376i	0.0129007	+	0.0223446i
$186$		0			0
$187$	1.68751	+	0.974282i	0.00902409	+	0.00521006i
$188$	242.335	+	1.57819i	1.28902	+	0.00839461i
$189$		0			0
$190$	187.781	−	186.562i	0.988320	−	0.981904i
$191$	192.972	+	111.413i	1.01033	+	0.583312i	0.911287	−	0.411772i	$-0.135090\pi$
$191$	192.972	+	111.413i	1.01033	+	0.583312i	0.0990389	+	0.995084i	$0.468423\pi$
$192$		0			0
$193$	56.6790	+	98.1709i	0.293674	+	0.508657i	0.974675	−	0.223624i	$-0.0717888\pi$
$193$	56.6790	+	98.1709i	0.293674	+	0.508657i	−0.681002	+	0.732282i	$0.738455\pi$
$194$	−50.5623	+	186.273i	−0.260631	+	0.960170i
$195$		0			0
$196$	−99.0215	−	58.0332i	−0.505212	−	0.296088i
$197$	120.998			0.614201			0.307100	−	0.951677i	$-0.400641\pi$
$197$	120.998			0.614201			0.307100	+	0.951677i	$0.400641\pi$
$198$		0			0
$199$			82.2364i			0.413248i	0.978420	+	0.206624i	$0.0662477\pi$
$199$			82.2364i			0.413248i	−0.978420	+	0.206624i	$0.933752\pi$
$200$	79.7934	+	309.870i	0.398967	+	1.54935i
$201$		0			0
$202$	22.6965	−	83.6145i	0.112359	−	0.413933i
$203$	74.0230	−	42.7372i	0.364645	−	0.210528i
$204$		0			0
$205$	99.7811	−	172.826i	0.486737	−	0.843053i
$206$	205.507	−	204.173i	0.997607	−	0.991132i
$207$		0			0
$208$	−112.824	−	1.46958i	−0.542423	−	0.00706527i
$209$	−30.8835	+	53.4917i	−0.147768	+	0.255941i
$210$		0			0
$211$	93.5819	−	54.0295i	0.443516	−	0.256064i	−0.261572	−	0.965184i	$-0.584241\pi$
$211$	93.5819	−	54.0295i	0.443516	−	0.256064i	0.705088	+	0.709120i	$0.250907\pi$
$212$	2.31142	−	1.31451i	0.0109029	−	0.00620050i
$213$		0			0
$214$	28.1169	+	106.317i	0.131387	+	0.496809i
$215$			259.437i			1.20668i
$216$		0			0
$217$	68.3490			0.314972
$218$	−123.598	+	32.6870i	−0.566962	+	0.149940i
$219$		0			0
$220$	−59.9817	−	105.472i	−0.272644	−	0.479417i
$221$	1.82611	+	3.16291i	0.00826292	+	0.0143118i
$222$		0			0
$223$	−141.400	−	81.6371i	−0.634079	−	0.366086i	0.148251	−	0.988950i	$-0.452636\pi$
$223$	−141.400	−	81.6371i	−0.634079	−	0.366086i	−0.782330	+	0.622864i	$0.785969\pi$
$224$	−103.612	+	100.292i	−0.462552	+	0.447731i
$225$		0			0
$226$	−50.2493	−	50.5776i	−0.222342	−	0.223795i
$227$	−9.56722	−	5.52364i	−0.0421463	−	0.0243332i	0.478779	−	0.877936i	$-0.341080\pi$
$227$	−9.56722	−	5.52364i	−0.0421463	−	0.0243332i	−0.520925	+	0.853602i	$0.674413\pi$
$228$		0			0
$229$	−16.1725	−	28.0116i	−0.0706222	−	0.122321i	0.828552	−	0.559912i	$-0.189165\pi$
$229$	−16.1725	−	28.0116i	−0.0706222	−	0.122321i	−0.899174	+	0.437591i	$0.855832\pi$
$230$	−497.813	−	135.127i	−2.16440	−	0.587511i
$231$		0			0
$232$	37.8404	+	146.949i	0.163105	+	0.633402i
$233$	−181.049			−0.777036			−0.388518	−	0.921441i	$-0.627013\pi$
$233$	−181.049			−0.777036			−0.388518	+	0.921441i	$0.627013\pi$
$234$		0			0
$235$			488.442i			2.07848i
$236$	71.4448	−	121.906i	0.302732	−	0.516549i
$237$		0			0
$238$	4.50450	+	1.22271i	0.0189265	+	0.00513745i
$239$	39.6432	−	22.8880i	0.165871	−	0.0957658i	−0.414766	−	0.909928i	$-0.636137\pi$
$239$	39.6432	−	22.8880i	0.165871	−	0.0957658i	0.580638	+	0.814162i	$0.302803\pi$
$240$		0			0
$241$	169.216	−	293.090i	0.702140	−	1.21614i	−0.265573	−	0.964091i	$-0.585561\pi$
$241$	169.216	−	293.090i	0.702140	−	1.21614i	0.967714	−	0.252052i	$-0.0811054\pi$
$242$	−150.607	−	151.591i	−0.622342	−	0.626408i
$243$		0			0
$244$	1.75962	−	270.194i	0.00721154	−	1.10735i
$245$	115.665	−	200.338i	0.472102	−	0.817704i
$246$		0			0
$247$	−100.260	+	57.8852i	−0.405911	+	0.234353i
$248$	−32.5486	+	116.893i	−0.131244	+	0.471344i
$249$		0			0
$250$	−233.782	+	61.8264i	−0.935127	+	0.247306i
$251$		−	282.587i		−	1.12585i	−0.826510	−	0.562923i	$-0.809677\pi$
$251$		−	282.587i		−	1.12585i	0.826510	−	0.562923i	$-0.190323\pi$
$252$		0			0
$253$	120.366			0.475754
$254$	5.01741	+	18.9721i	0.0197536	+	0.0746934i
$255$		0			0
$256$	−122.182	−	224.961i	−0.477274	−	0.878755i
$257$	−38.8897	−	67.3589i	−0.151322	−	0.262097i	0.780392	−	0.625291i	$-0.215020\pi$
$257$	−38.8897	−	67.3589i	−0.151322	−	0.262097i	−0.931714	+	0.363194i	$0.881686\pi$
$258$		0			0
$259$	−2.31055	−	1.33399i	−0.00892102	−	0.00515056i
$260$	1.48101	−	227.414i	0.00569620	−	0.874668i
$261$		0			0
$262$	−166.388	+	165.308i	−0.635070	+	0.630947i
$263$	195.201	+	112.700i	0.742211	+	0.428516i	0.822873	−	0.568226i	$-0.192370\pi$
$263$	195.201	+	112.700i	0.742211	+	0.428516i	−0.0806619	+	0.996742i	$0.525703\pi$
$264$		0			0
$265$	2.67970	+	4.64138i	0.0101121	+	0.0175146i
$266$	−38.7584	+	142.787i	−0.145708	+	0.536793i
$267$		0			0
$268$	−173.916	+	296.751i	−0.648939	+	1.10728i
$269$	−425.808			−1.58293			−0.791465	−	0.611214i	$-0.790681\pi$
$269$	−425.808			−1.58293			−0.791465	+	0.611214i	$0.790681\pi$
$270$		0			0
$271$		−	56.3665i		−	0.207995i	−0.994578	−	0.103997i	$-0.966837\pi$
$271$		−	56.3665i		−	0.207995i	0.994578	−	0.103997i	$-0.0331633\pi$
$272$	−4.23623	+	7.12152i	−0.0155744	+	0.0261821i
$273$		0			0
$274$	−131.616	+	484.878i	−0.480352	+	1.76963i
$275$	130.328	−	75.2450i	0.473920	−	0.273618i
$276$		0			0
$277$	−209.641	+	363.109i	−0.756828	+	1.31086i	0.187633	+	0.982239i	$0.439918\pi$
$277$	−209.641	+	363.109i	−0.756828	+	1.31086i	−0.944461	+	0.328625i	$0.893415\pi$
$278$	−218.014	+	216.599i	−0.784223	+	0.779132i
$279$		0			0
$280$	−203.496	−	207.511i	−0.726771	−	0.741110i
$281$	73.9638	−	128.109i	0.263216	−	0.455904i	−0.703878	−	0.710320i	$-0.748550\pi$
$281$	73.9638	−	128.109i	0.263216	−	0.455904i	0.967095	+	0.254416i	$0.0818833\pi$
$282$		0			0
$283$	229.852	−	132.705i	0.812198	−	0.468923i	−0.0355207	−	0.999369i	$-0.511309\pi$
$283$	229.852	−	132.705i	0.812198	−	0.468923i	0.847719	+	0.530446i	$0.177976\pi$
$284$	111.611	+	196.257i	0.392997	+	0.691045i
$285$		0			0
$286$	13.5678	+	51.3033i	0.0474398	+	0.179382i
$287$			111.544i			0.388656i
$288$		0			0
$289$	−288.732			−0.999072
$290$	−295.676	+	78.1953i	−1.01957	+	0.269639i
$291$		0			0
$292$	458.695	−	260.860i	1.57087	−	0.893356i
$293$	−124.844	−	216.236i	−0.426088	−	0.738006i	0.570433	−	0.821344i	$-0.306775\pi$
$293$	−124.844	−	216.236i	−0.426088	−	0.738006i	−0.996521	+	0.0833379i	$0.973442\pi$
$294$		0			0
$295$	246.636	+	142.395i	0.836054	+	0.482696i
$296$	3.38176	−	3.31633i	0.0114249	−	0.0112038i
$297$		0			0
$298$	129.301	+	130.146i	0.433895	+	0.436730i
$299$	195.378	+	112.801i	0.653438	+	0.377262i
$300$		0			0
$301$	−72.5056	−	125.583i	−0.240883	−	0.417221i
$302$	80.2830	+	21.7922i	0.265838	+	0.0721596i
$303$		0			0
$304$	−225.743	−	134.283i	−0.742576	−	0.441721i
$305$	544.594			1.78555
$306$		0			0
$307$		−	259.968i		−	0.846801i	−0.905943	−	0.423401i	$-0.860836\pi$
$307$		−	259.968i		−	0.846801i	0.905943	−	0.423401i	$-0.139164\pi$
$308$	58.5113	+	34.2915i	0.189972	+	0.111336i
$309$		0			0
$310$	−236.023	−	64.0667i	−0.761366	−	0.206667i
$311$	16.5959	−	9.58164i	0.0533630	−	0.0308091i	−0.473081	−	0.881019i	$-0.656858\pi$
$311$	16.5959	−	9.58164i	0.0533630	−	0.0308091i	0.526444	+	0.850210i	$0.323525\pi$
$312$		0			0
$313$	−21.9358	+	37.9939i	−0.0700823	+	0.121386i	−0.898937	−	0.438078i	$-0.855660\pi$
$313$	−21.9358	+	37.9939i	−0.0700823	+	0.121386i	0.828855	+	0.559464i	$0.188993\pi$
$314$	318.314	+	320.394i	1.01374	+	1.02036i
$315$		0			0
$316$	585.972	+	3.81610i	1.85434	+	0.0120763i
$317$	−68.9690	+	119.458i	−0.217568	+	0.376838i	−0.954064	−	0.299603i	$-0.903146\pi$
$317$	−68.9690	+	119.458i	−0.217568	+	0.376838i	0.736496	+	0.676442i	$0.236479\pi$
$318$		0			0
$319$	61.8054	−	35.6834i	0.193747	−	0.111860i
$320$	451.801	−	249.208i	1.41188	−	0.778775i
$321$		0			0
$322$	278.736	−	73.7152i	0.865641	−	0.228929i
$323$			8.50191i			0.0263217i
$324$		0			0
$325$	282.065			0.867892
$326$	−64.0076	−	242.029i	−0.196342	−	0.742421i
$327$		0			0
$328$	−190.768	−	53.1187i	−0.581610	−	0.161947i
$329$	−136.506	−	236.436i	−0.414912	−	0.718649i
$330$		0			0
$331$	−51.7490	−	29.8773i	−0.156341	−	0.0902638i	0.419788	−	0.907622i	$-0.362104\pi$
$331$	−51.7490	−	29.8773i	−0.156341	−	0.0902638i	−0.576130	+	0.817358i	$0.695438\pi$
$332$	−402.303	−	2.61996i	−1.21176	−	0.00789145i
$333$		0			0
$334$	−252.910	+	251.268i	−0.757215	+	0.752300i
$335$	−600.378	−	346.628i	−1.79217	−	1.03471i
$336$		0			0
$337$	224.356	+	388.595i	0.665743	+	1.15310i	0.979083	+	0.203460i	$0.0652188\pi$
$337$	224.356	+	388.595i	0.665743	+	1.15310i	−0.313340	+	0.949641i	$0.601448\pi$
$338$	62.4875	−	230.206i	0.184874	−	0.681082i
$339$		0			0
$340$	−14.4089	−	8.44457i	−0.0423791	−	0.0248370i
$341$	57.0679			0.167355
$342$		0			0
$343$			350.108i			1.02072i
$344$	249.306	−	64.1979i	0.724727	−	0.186622i
$345$		0			0
$346$	79.2075	−	291.803i	0.228924	−	0.843360i
$347$	−500.441	+	288.930i	−1.44219	+	0.832651i	−0.997996	−	0.0632779i	$-0.979845\pi$
$347$	−500.441	+	288.930i	−1.44219	+	0.832651i	−0.444198	+	0.895929i	$0.646511\pi$
$348$		0			0
$349$	66.1311	−	114.542i	0.189487	−	0.328202i	−0.755592	−	0.655042i	$-0.772651\pi$
$349$	66.1311	−	114.542i	0.189487	−	0.328202i	0.945079	+	0.326841i	$0.105984\pi$
$350$	255.724	−	254.064i	0.730641	−	0.725898i
$351$		0			0
$352$	−86.5105	+	83.7384i	−0.245768	+	0.237893i
$353$	−270.562	+	468.628i	−0.766465	+	1.32756i	0.173003	+	0.984921i	$0.444653\pi$
$353$	−270.562	+	468.628i	−0.766465	+	1.32756i	−0.939468	+	0.342636i	$0.888680\pi$
$354$		0			0
$355$	−394.086	+	227.526i	−1.11010	+	0.640918i
$356$	89.8339	−	51.0885i	0.252343	−	0.143507i
$357$		0			0
$358$	−141.554	−	535.253i	−0.395403	−	1.49512i
$359$		−	292.754i		−	0.815470i	−0.913100	−	0.407735i	$-0.866319\pi$
$359$		−	292.754i		−	0.815470i	0.913100	−	0.407735i	$-0.133681\pi$
$360$		0			0
$361$	91.5006			0.253464
$362$	−202.496	+	53.5525i	−0.559381	+	0.147935i
$363$		0			0
$364$	62.8390	+	110.496i	0.172635	+	0.303561i
$365$	531.779	+	921.067i	1.45693	+	2.52347i
$366$		0			0
$367$	−378.870	−	218.741i	−1.03234	−	0.596024i	−0.114689	−	0.993401i	$-0.536587\pi$
$367$	−378.870	−	218.741i	−1.03234	−	0.596024i	−0.917655	+	0.397377i	$0.869920\pi$
$368$	−6.66653	+	511.811i	−0.0181156	+	1.39079i
$369$		0			0
$370$	6.72838	+	6.77234i	0.0181848	+	0.0183036i
$371$	−2.59428	−	1.49781i	−0.00699266	−	0.00403721i
$372$		0			0
$373$	−352.979	−	611.377i	−0.946323	−	1.63908i	−0.753080	−	0.657929i	$-0.771433\pi$
$373$	−352.979	−	611.377i	−0.946323	−	1.63908i	−0.193243	−	0.981151i	$-0.561901\pi$
$374$	3.76103	+	1.02090i	0.0100562	+	0.00272969i
$375$		0			0
$376$	469.368	−	120.865i	1.24832	−	0.321450i
$377$	133.763			0.354810
$378$		0			0
$379$		−	541.432i		−	1.42858i	−0.699850	−	0.714290i	$-0.746750\pi$
$379$		−	541.432i		−	1.42858i	0.699850	−	0.714290i	$-0.253250\pi$
$380$	267.682	−	456.743i	0.704426	−	1.20196i
$381$		0			0
$382$	430.087	+	116.744i	1.12588	+	0.305612i
$383$	311.941	−	180.099i	0.814467	−	0.470233i	−0.0340377	−	0.999421i	$-0.510837\pi$
$383$	311.941	−	180.099i	0.814467	−	0.470233i	0.848505	+	0.529188i	$0.177503\pi$
$384$		0			0
$385$	−68.3458	+	118.378i	−0.177521	+	0.307476i
$386$	159.790	+	160.834i	0.413963	+	0.416667i
$387$		0			0
$388$	−2.51391	+	386.019i	−0.00647916	+	0.994893i
$389$	43.9057	−	76.0468i	0.112868	−	0.195493i	−0.804057	−	0.594552i	$-0.797330\pi$
$389$	43.9057	−	76.0468i	0.112868	−	0.195493i	0.916926	+	0.399058i	$0.130663\pi$
$390$		0			0
$391$	14.3481	−	8.28388i	0.0366959	−	0.0211864i
$392$	−221.136	−	61.5745i	−0.564122	−	0.157078i
$393$		0			0
$394$	233.952	−	61.8715i	0.593787	−	0.157034i
$395$			1181.07i			2.99004i
$396$		0			0
$397$	−48.4128			−0.121947			−0.0609733	−	0.998139i	$-0.519420\pi$
$397$	−48.4128			−0.121947			−0.0609733	+	0.998139i	$0.519420\pi$
$398$	42.0512	+	159.006i	0.105656	+	0.399513i
$399$		0			0
$400$	312.733	+	558.339i	0.781832	+	1.39585i
$401$	−217.859	−	377.343i	−0.543290	−	0.941005i	−0.998712	−	0.0507299i	$-0.983845\pi$
$401$	−217.859	−	377.343i	−0.543290	−	0.941005i	0.455423	−	0.890275i	$-0.349488\pi$
$402$		0			0
$403$	92.6326	+	53.4815i	0.229858	+	0.132708i
$404$	1.12845	−	173.277i	0.00279319	−	0.428902i
$405$		0			0
$406$	121.272	−	120.485i	0.298699	−	0.296761i
$407$	−1.92919	−	1.11382i	−0.00474002	−	0.00273665i
$408$		0			0
$409$	−27.1145	−	46.9636i	−0.0662945	−	0.114825i	0.830973	−	0.556313i	$-0.187784\pi$
$409$	−27.1145	−	46.9636i	−0.0662945	−	0.114825i	−0.897267	+	0.441487i	$0.854451\pi$
$410$	104.556	−	385.186i	0.255014	−	0.939479i
$411$		0			0
$412$	292.951	−	499.859i	0.711045	−	1.21325i
$413$	−159.182			−0.385430
$414$		0			0
$415$		−	810.867i		−	1.95390i
$416$	−218.900	+	54.8505i	−0.526201	+	0.131852i
$417$		0			0
$418$	−32.3613	+	119.220i	−0.0774193	+	0.285215i
$419$	552.029	−	318.714i	1.31749	−	0.760655i	0.334168	−	0.942514i	$-0.391545\pi$
$419$	552.029	−	318.714i	1.31749	−	0.760655i	0.983325	+	0.181859i	$0.0582114\pi$
$420$		0			0
$421$	−95.7757	+	165.888i	−0.227496	+	0.394034i	−0.957065	−	0.289873i	$-0.906387\pi$
$421$	−95.7757	+	165.888i	−0.227496	+	0.394034i	0.729570	+	0.683907i	$0.239720\pi$
$422$	153.315	−	152.320i	0.363307	−	0.360948i
$423$		0			0
$424$	3.79704	−	3.72357i	0.00895527	−	0.00878200i
$425$	10.3571	−	17.9390i	0.0243696	−	0.0422095i
$426$		0			0
$427$	−263.617	+	152.199i	−0.617369	+	0.356438i
$428$	108.729	+	191.190i	0.254041	+	0.446705i
$429$		0			0
$430$	132.662	+	501.629i	0.308516	+	1.16658i
$431$		−	481.190i		−	1.11645i	−0.829689	−	0.558225i	$-0.811482\pi$
$431$		−	481.190i		−	1.11645i	0.829689	−	0.558225i	$-0.188518\pi$
$432$		0			0
$433$	−360.347			−0.832209			−0.416105	−	0.909317i	$-0.636605\pi$
$433$	−360.347			−0.832209			−0.416105	+	0.909317i	$0.636605\pi$
$434$	132.155	−	34.9499i	0.304504	−	0.0805297i
$435$		0			0
$436$	−222.265	+	126.402i	−0.509783	+	0.289913i
$437$	262.588	+	454.816i	0.600888	+	1.04077i
$438$		0			0
$439$	488.267	+	281.901i	1.11223	+	0.642144i	0.939405	−	0.342809i	$-0.111378\pi$
$439$	488.267	+	281.901i	1.11223	+	0.642144i	0.172821	+	0.984953i	$0.444712\pi$
$440$	−169.909	−	173.261i	−0.386156	−	0.393775i
$441$		0			0
$442$	5.14816	+	5.18180i	0.0116474	+	0.0117235i
$443$	−569.917	−	329.042i	−1.28649	−	0.742757i	−0.308467	−	0.951235i	$-0.599816\pi$
$443$	−569.917	−	329.042i	−1.28649	−	0.742757i	−0.978027	+	0.208478i	$0.933149\pi$
$444$		0			0
$445$	104.147	+	180.388i	0.234038	+	0.405366i
$446$	−315.145	−	85.5436i	−0.706603	−	0.191802i
$447$		0			0
$448$	−149.052	+	246.898i	−0.332706	+	0.551112i
$449$	−227.569			−0.506836			−0.253418	−	0.967357i	$-0.581555\pi$
$449$	−227.569			−0.506836			−0.253418	+	0.967357i	$0.581555\pi$
$450$		0			0
$451$			93.1339i			0.206505i
$452$	−123.021	−	72.0984i	−0.272170	−	0.159510i
$453$		0			0
$454$	−21.3230	−	5.78795i	−0.0469669	−	0.0127488i
$455$	−221.878	+	128.101i	−0.487643	+	0.281541i
$456$		0			0
$457$	−358.879	+	621.596i	−0.785292	+	1.36017i	0.143532	+	0.989646i	$0.454154\pi$
$457$	−358.879	+	621.596i	−0.785292	+	1.36017i	−0.928824	+	0.370520i	$0.879179\pi$
$458$	−45.5935	−	45.8914i	−0.0995492	−	0.100200i
$459$		0			0
$460$	−1031.63	−	6.71842i	−2.24268	−	0.0146053i
$461$	200.873	−	347.922i	0.435733	−	0.754712i	−0.561622	−	0.827394i	$-0.689822\pi$
$461$	200.873	−	347.922i	0.435733	−	0.754712i	0.997355	+	0.0726819i	$0.0231558\pi$
$462$		0			0
$463$	−396.754	+	229.066i	−0.856920	+	0.494743i	−0.862980	−	0.505239i	$-0.831405\pi$
$463$	−396.754	+	229.066i	−0.856920	+	0.494743i	0.00605956	+	0.999982i	$0.498071\pi$
$464$	148.307	+	264.781i	0.319627	+	0.570648i
$465$		0			0
$466$	−350.064	+	92.5787i	−0.751210	+	0.198667i
$467$		−	204.395i		−	0.437677i	−0.975761	−	0.218838i	$-0.929773\pi$
$467$		−	204.395i		−	0.437677i	0.975761	−	0.218838i	$-0.0702267\pi$
$468$		0			0
$469$	387.493			0.826210
$470$	249.762	+	944.415i	0.531409	+	2.00939i
$471$		0			0
$472$	75.8045	−	272.241i	0.160603	−	0.576781i
$473$	−60.5385	−	104.856i	−0.127988	−	0.221682i
$474$		0			0
$475$	568.643	+	328.306i	1.19714	+	0.691172i
$476$	9.33481	+	0.0607922i	0.0196109	+	0.000127715i
$477$		0			0
$478$	64.9475	−	64.5259i	0.135874	−	0.134992i
$479$	−78.4548	−	45.2959i	−0.163789	−	0.0945634i	0.415865	−	0.909426i	$-0.363479\pi$
$479$	−78.4548	−	45.2959i	−0.163789	−	0.0945634i	−0.579654	+	0.814863i	$0.696812\pi$
$480$		0			0
$481$	−2.08764	−	3.61589i	−0.00434020	−	0.00751745i
$482$	177.313	−	653.226i	0.367869	−	1.35524i
$483$		0			0
$484$	−368.718	−	216.093i	−0.761813	−	0.446473i
$485$	−778.046			−1.60422
$486$		0			0
$487$			301.289i			0.618663i	0.950954	+	0.309332i	$0.100105\pi$
$487$			301.289i			0.618663i	−0.950954	+	0.309332i	$0.899895\pi$
$488$	−134.760	−	523.327i	−0.276148	−	1.07239i
$489$		0			0
$490$	121.200	−	446.503i	0.247346	−	0.911230i
$491$	−389.556	+	224.911i	−0.793394	+	0.458066i	−0.841156	−	0.540792i	$-0.818124\pi$
$491$	−389.556	+	224.911i	−0.793394	+	0.458066i	0.0477620	+	0.998859i	$0.484791\pi$
$492$		0			0
$493$	4.91164	−	8.50721i	0.00996276	−	0.0172560i
$494$	−164.256	+	163.190i	−0.332502	+	0.330344i
$495$		0			0
$496$	−3.16074	+	242.660i	−0.00637246	+	0.489234i
$497$	127.175	−	220.273i	0.255884	−	0.443205i
$498$		0			0
$499$	552.630	−	319.061i	1.10748	−	0.639401i	0.169301	−	0.985564i	$-0.445849\pi$
$499$	552.630	−	319.061i	1.10748	−	0.639401i	0.938174	+	0.346163i	$0.112516\pi$
$500$	−420.409	+	239.086i	−0.840817	+	0.478172i
$501$		0			0
$502$	−144.500	−	546.390i	−0.287848	−	1.08843i
$503$			182.179i			0.362185i	0.983466	+	0.181093i	$0.0579634\pi$
$503$			182.179i			0.362185i	−0.983466	+	0.181093i	$0.942037\pi$
$504$		0			0
$505$	349.250			0.691585
$506$	232.731	−	61.5485i	0.459942	−	0.121637i
$507$		0			0
$508$	19.4026	+	34.1175i	0.0381941	+	0.0671604i
$509$	−471.123	−	816.009i	−0.925585	−	1.60316i	−0.790617	−	0.612311i	$-0.790240\pi$
$509$	−471.123	−	816.009i	−0.925585	−	1.60316i	−0.134968	−	0.990850i	$-0.543093\pi$
$510$		0			0
$511$	−514.827	−	297.235i	−1.00749	−	0.581674i
$512$	−351.275	−	372.491i	−0.686084	−	0.727522i
$513$		0			0
$514$	−109.638	−	110.354i	−0.213303	−	0.214697i
$515$	1011.30	+	583.875i	1.96369	+	1.13374i
$516$		0			0
$517$	−113.976	−	197.412i	−0.220456	−	0.381841i
$518$	−5.14963	−	1.39783i	−0.00994138	−	0.00269851i
$519$		0			0
$520$	−113.423	−	440.468i	−0.218122	−	0.847054i
$521$	634.330			1.21752			0.608762	−	0.793353i	$-0.291666\pi$
$521$	634.330			1.21752			0.608762	+	0.793353i	$0.291666\pi$
$522$		0			0
$523$			534.777i			1.02252i	0.859426	+	0.511259i	$0.170821\pi$
$523$			534.777i			1.02252i	−0.859426	+	0.511259i	$0.829179\pi$
$524$	−237.187	+	404.710i	−0.452646	+	0.772347i
$525$		0			0
$526$	435.056	+	118.092i	0.827102	+	0.224510i
$527$	6.80273	−	3.92756i	0.0129084	−	0.00745267i
$528$		0			0
$529$	247.208	−	428.178i	0.467313	−	0.809409i
$530$	7.55461	+	7.60397i	0.0142540	+	0.0143471i
$531$		0			0
$532$	−1.92703	+	295.901i	−0.00362224	+	0.556205i
$533$	−87.2809	+	151.175i	−0.163754	+	0.283630i
$534$		0			0
$535$	−383.912	+	221.652i	−0.717592	+	0.414302i
$536$	−184.528	+	662.706i	−0.344270	+	1.23639i
$537$		0			0
$538$	−823.312	+	217.735i	−1.53032	+	0.404712i
$539$			107.960i			0.200296i
$540$		0			0
$541$	−61.0097			−0.112772			−0.0563860	−	0.998409i	$-0.517958\pi$
$541$	−61.0097			−0.112772			−0.0563860	+	0.998409i	$0.517958\pi$
$542$	−28.8227	−	108.986i	−0.0531785	−	0.201082i
$543$		0			0
$544$	−4.54931	+	15.9358i	−0.00836271	+	0.0292938i
$545$	−257.678	−	446.312i	−0.472805	−	0.818921i
$546$		0			0
$547$	104.430	+	60.2925i	0.190914	+	0.110224i	0.592410	−	0.805637i	$-0.298177\pi$
$547$	104.430	+	60.2925i	0.190914	+	0.110224i	−0.401497	+	0.915861i	$0.631510\pi$
$548$	−6.54385	+	1004.83i	−0.0119413	+	1.83362i
$549$		0			0
$550$	213.517	−	212.131i	0.388212	−	0.385692i
$551$	269.667	+	155.693i	0.489415	+	0.282564i
$552$		0			0
$553$	−330.076	−	571.708i	−0.596882	−	1.03383i
$554$	−219.673	+	809.281i	−0.396521	+	1.46080i
$555$		0			0
$556$	−310.779	+	530.280i	−0.558955	+	0.953741i
$557$	527.461			0.946968			0.473484	−	0.880802i	$-0.342996\pi$
$557$	527.461			0.946968			0.473484	+	0.880802i	$0.342996\pi$
$558$		0			0
$559$		−	226.936i		−	0.405967i
$560$	−499.574	−	297.171i	−0.892097	−	0.530663i
$561$		0			0
$562$	77.5031	−	285.523i	0.137906	−	0.508049i
$563$	595.478	−	343.800i	1.05769	−	0.610656i	0.132896	−	0.991130i	$-0.457572\pi$
$563$	595.478	−	343.800i	1.05769	−	0.610656i	0.924792	+	0.380474i	$0.124239\pi$
$564$		0			0
$565$	143.698	−	248.893i	0.254333	−	0.440518i
$566$	376.567	−	374.123i	0.665313	−	0.660994i
$567$		0			0
$568$	316.158	+	322.396i	0.556616	+	0.567598i
$569$	−293.677	+	508.664i	−0.516128	+	0.893961i	0.483696	+	0.875236i	$0.339294\pi$
$569$	−293.677	+	508.664i	−0.516128	+	0.893961i	−0.999825	+	0.0187248i	$0.994039\pi$
$570$		0			0
$571$	742.245	−	428.535i	1.29990	−	0.750500i	0.319517	−	0.947581i	$-0.396479\pi$
$571$	742.245	−	428.535i	1.29990	−	0.750500i	0.980387	+	0.197081i	$0.0631461\pi$
$572$	52.4674	+	92.2585i	0.0917262	+	0.161291i
$573$		0			0
$574$	57.0377	+	215.674i	0.0993688	+	0.375739i
$575$		−	1279.55i		−	2.22530i
$576$		0			0
$577$	871.732			1.51080			0.755401	−	0.655263i	$-0.227442\pi$
$577$	871.732			1.51080			0.755401	+	0.655263i	$0.227442\pi$
$578$	−558.271	+	147.642i	−0.965866	+	0.255435i
$579$		0			0
$580$	−531.714	+	302.385i	−0.916748	+	0.521354i
$581$	226.615	+	392.509i	0.390044	+	0.675575i
$582$		0			0
$583$	−2.16609	−	1.25059i	−0.00371542	−	0.00214510i
$584$	753.511	−	738.931i	1.29026	−	1.26529i
$585$		0			0
$586$	−351.960	−	354.259i	−0.600614	−	0.604538i
$587$	700.071	+	404.186i	1.19263	+	0.688563i	0.958901	−	0.283740i	$-0.0915753\pi$
$587$	700.071	+	404.186i	1.19263	+	0.688563i	0.233725	+	0.972303i	$0.424909\pi$
$588$		0			0
$589$	124.498	+	215.638i	0.211373	+	0.366108i
$590$	549.690	+	149.209i	0.931679	+	0.252897i
$591$		0			0
$592$	4.84294	−	8.14146i	0.00818064	−	0.0137525i
$593$	445.123			0.750628			0.375314	−	0.926898i	$-0.377535\pi$
$593$	445.123			0.750628			0.375314	+	0.926898i	$0.377535\pi$
$594$		0			0
$595$			18.8149i			0.0316217i
$596$	316.556	+	185.523i	0.531134	+	0.311280i
$597$		0			0
$598$	435.449	+	118.199i	0.728175	+	0.197657i
$599$	−684.932	+	395.445i	−1.14346	+	0.660176i	−0.947285	−	0.320393i	$-0.896185\pi$
$599$	−684.932	+	395.445i	−1.14346	+	0.660176i	−0.196174	+	0.980569i	$0.562852\pi$
$600$		0			0
$601$	193.532	−	335.208i	0.322017	−	0.557750i	−0.658887	−	0.752242i	$-0.728972\pi$
$601$	193.532	−	335.208i	0.322017	−	0.557750i	0.980904	+	0.194492i	$0.0623057\pi$
$602$	−204.408	−	205.744i	−0.339548	−	0.341767i
$603$		0			0
$604$	166.373	+	1.08349i	0.275451	+	0.00179385i
$605$	430.691	−	745.979i	0.711886	−	1.23302i
$606$		0			0
$607$	−902.512	+	521.066i	−1.48684	+	0.858428i	−0.999887	−	0.0150003i	$-0.995225\pi$
$607$	−902.512	+	521.066i	−1.48684	+	0.858428i	−0.486953	+	0.873428i	$0.661892\pi$
$608$	−505.145	−	144.207i	−0.830831	−	0.237183i
$609$		0			0
$610$	1052.99	−	278.475i	1.72621	−	0.456517i
$611$		−	427.251i		−	0.699266i
$612$		0			0
$613$	256.336			0.418166			0.209083	−	0.977898i	$-0.432952\pi$
$613$	256.336			0.418166			0.209083	+	0.977898i	$0.432952\pi$
$614$	−132.933	−	502.655i	−0.216504	−	0.818657i
$615$		0			0
$616$	130.668	+	36.3841i	0.212123	+	0.0590650i
$617$	253.519	+	439.108i	0.410890	+	0.711683i	0.994987	−	0.100001i	$-0.0318846\pi$
$617$	253.519	+	439.108i	0.410890	+	0.711683i	−0.584097	+	0.811684i	$0.698551\pi$
$618$		0			0
$619$	662.787	+	382.660i	1.07074	+	0.618191i	0.928383	−	0.371624i	$-0.121199\pi$
$619$	662.787	+	382.660i	1.07074	+	0.618191i	0.142355	+	0.989816i	$0.454532\pi$
$620$	−489.118	−	3.18534i	−0.788900	−	0.00513764i
$621$		0			0
$622$	27.1891	−	27.0126i	0.0437123	−	0.0434286i
$623$	−100.827	−	58.2125i	−0.161841	−	0.0934390i
$624$		0			0
$625$	12.5746	+	21.7799i	0.0201194	+	0.0348479i
$626$	−22.9854	+	84.6789i	−0.0367179	+	0.135270i
$627$		0			0
$628$	779.301	+	456.722i	1.24092	+	0.727264i
$629$	−0.306623			−0.000487477
$630$		0			0
$631$			719.756i			1.14066i	0.821416	+	0.570330i	$0.193185\pi$
$631$			719.756i			1.14066i	−0.821416	+	0.570330i	$0.806815\pi$
$632$	1134.94	−	292.255i	1.79580	−	0.462429i
$633$		0			0
$634$	−72.2692	+	266.242i	−0.113989	+	0.419940i
$635$	−68.5084	+	39.5534i	−0.107887	+	0.0622888i
$636$		0			0
$637$	−101.175	+	175.240i	−0.158830	+	0.275102i
$638$	101.256	−	100.599i	0.158708	−	0.157678i
$639$		0			0
$640$	746.138	−	712.877i	1.16584	−	1.11387i
$641$	−351.516	+	608.844i	−0.548388	+	0.949835i	0.449998	+	0.893030i	$0.351425\pi$
$641$	−351.516	+	608.844i	−0.548388	+	0.949835i	−0.998385	+	0.0568054i	$0.981909\pi$
$642$		0			0
$643$	507.224	−	292.846i	0.788841	−	0.455437i	−0.0507136	−	0.998713i	$-0.516150\pi$
$643$	507.224	−	292.846i	0.788841	−	0.455437i	0.839554	+	0.543276i	$0.182816\pi$
$644$	501.250	−	285.061i	0.778339	−	0.442641i
$645$		0			0
$646$	4.34741	+	16.4387i	0.00672973	+	0.0254469i
$647$			791.553i			1.22342i	0.791082	+	0.611710i	$0.209518\pi$
$647$			791.553i			1.22342i	−0.791082	+	0.611710i	$0.790482\pi$
$648$		0			0
$649$	−132.909			−0.204791
$650$	545.380	−	144.232i	0.839046	−	0.221896i
$651$		0			0
$652$	−247.521	−	435.240i	−0.379633	−	0.667547i
$653$	196.385	+	340.148i	0.300742	+	0.520901i	0.976304	−	0.216402i	$-0.0694323\pi$
$653$	196.385	+	340.148i	0.300742	+	0.520901i	−0.675562	+	0.737303i	$0.736099\pi$
$654$		0			0
$655$	−818.797	−	472.733i	−1.25007	−	0.721730i
$656$	−396.017	−	5.15827i	−0.603685	−	0.00786322i
$657$		0			0
$658$	−384.838	−	387.353i	−0.584861	−	0.588682i
$659$	−372.557	−	215.096i	−0.565337	−	0.326398i	0.189948	−	0.981794i	$-0.439168\pi$
$659$	−372.557	−	215.096i	−0.565337	−	0.326398i	−0.755285	+	0.655397i	$0.772501\pi$
$660$		0			0
$661$	453.865	+	786.117i	0.686633	+	1.18928i	0.972920	+	0.231140i	$0.0742456\pi$
$661$	453.865	+	786.117i	0.686633	+	1.18928i	−0.286287	+	0.958144i	$0.592421\pi$
$662$	−115.336	−	31.3070i	−0.174223	−	0.0472915i
$663$		0			0
$664$	−779.203	+	200.650i	−1.17350	+	0.302183i
$665$	−596.408			−0.896854
$666$		0			0
$667$		−	606.799i		−	0.909744i
$668$	−360.523	+	615.158i	−0.539706	+	0.920895i
$669$		0			0
$670$	−1338.09	−	363.215i	−1.99715	−	0.542112i
$671$	−220.106	+	127.078i	−0.328027	+	0.189387i
$672$		0			0
$673$	−34.8528	+	60.3668i	−0.0517872	+	0.0896980i	−0.890757	−	0.454480i	$-0.849825\pi$
$673$	−34.8528	+	60.3668i	−0.0517872	+	0.0896980i	0.838970	+	0.544178i	$0.183158\pi$
$674$	632.504	+	636.636i	0.938433	+	0.944564i
$675$		0			0
$676$	3.10682	−	477.062i	0.00459589	−	0.705712i
$677$	144.502	−	250.285i	0.213444	−	0.369697i	−0.739346	−	0.673326i	$-0.764865\pi$
$677$	144.502	−	250.285i	0.213444	−	0.369697i	0.952790	+	0.303629i	$0.0981984\pi$
$678$		0			0
$679$	376.622	−	217.443i	0.554671	−	0.320239i
$680$	−32.1781	−	8.95988i	−0.0473207	−	0.0131763i
$681$		0			0
$682$	110.342	−	29.1814i	0.161792	−	0.0427880i
$683$			522.729i			0.765343i	0.923884	+	0.382672i	$0.124996\pi$
$683$			522.729i			0.765343i	−0.923884	+	0.382672i	$0.875004\pi$
$684$		0			0
$685$	−2025.29			−2.95663
$686$	179.026	+	676.943i	0.260971	+	0.986798i
$687$		0			0
$688$	449.213	−	251.610i	0.652926	−	0.365712i
$689$	−2.34400	−	4.05992i	−0.00340203	−	0.00589248i
$690$		0			0
$691$	−485.917	−	280.544i	−0.703208	−	0.405997i	0.105333	−	0.994437i	$-0.466409\pi$
$691$	−485.917	−	280.544i	−0.703208	−	0.405997i	−0.808541	+	0.588440i	$0.799742\pi$
$692$	3.93813	−	604.711i	0.00569093	−	0.873859i
$693$		0			0
$694$	−819.874	+	814.552i	−1.18137	+	1.17371i
$695$	−1072.85	−	619.409i	−1.54367	−	0.891236i
$696$		0			0
$697$	6.40971	+	11.1019i	0.00919614	+	0.0159282i
$698$	69.2956	−	255.287i	0.0992773	−	0.365740i
$699$		0			0
$700$	364.535	−	622.004i	0.520765	−	0.888577i
$701$	−1203.11			−1.71627			−0.858137	−	0.513421i	$-0.828378\pi$
$701$	−1203.11			−1.71627			−0.858137	+	0.513421i	$0.828378\pi$
$702$		0			0
$703$		−	9.71954i		−	0.0138258i
$704$	−124.451	+	206.147i	−0.176777	+	0.292823i
$705$		0			0
$706$	−283.509	+	1044.45i	−0.401571	+	1.47940i
$707$	−169.058	+	97.6059i	−0.239121	+	0.138056i
$708$		0			0
$709$	89.2724	−	154.624i	0.125913	−	0.218088i	−0.796176	−	0.605065i	$-0.793147\pi$
$709$	89.2724	−	154.624i	0.125913	−	0.218088i	0.922090	+	0.386977i	$0.126481\pi$
$710$	−645.632	+	641.441i	−0.909341	+	0.903439i
$711$		0			0
$712$	147.572	−	144.717i	0.207265	−	0.203254i
$713$	242.611	−	420.215i	0.340269	−	0.589362i
$714$		0			0
$715$	−185.257	+	106.958i	−0.259100	+	0.149591i
$716$	−547.398	−	962.543i	−0.764522	−	1.34433i
$717$		0			0
$718$	−149.698	−	566.048i	−0.208493	−	0.788367i
$719$		−	53.0278i		−	0.0737521i	−0.999320	−	0.0368760i	$-0.988259\pi$
$719$		−	53.0278i		−	0.0737521i	0.999320	−	0.0368760i	$-0.0117407\pi$
$720$		0			0
$721$	−652.709			−0.905282
$722$	176.919	−	46.7884i	0.245040	−	0.0648038i
$723$		0			0
$724$	−364.148	+	207.091i	−0.502966	+	0.286037i
$725$	−379.332	−	657.022i	−0.523216	−	0.906238i
$726$		0			0
$727$	−436.956	−	252.277i	−0.601041	−	0.347011i	0.168410	−	0.985717i	$-0.446137\pi$
$727$	−436.956	−	252.277i	−0.601041	−	0.347011i	−0.769451	+	0.638706i	$0.779470\pi$
$728$	178.003	+	181.515i	0.244509	+	0.249333i
$729$		0			0
$730$	1499.19	+	1508.99i	2.05369	+	2.06710i
$731$	−14.4329	−	8.33283i	−0.0197440	−	0.0113992i
$732$		0			0
$733$	410.964	+	711.811i	0.560660	+	0.971092i	0.997439	+	0.0715233i	$0.0227860\pi$
$733$	410.964	+	711.811i	0.560660	+	0.971092i	−0.436779	+	0.899569i	$0.643881\pi$
$734$	−844.408	−	229.208i	−1.15042	−	0.312272i
$735$		0			0
$736$	248.822	+	993.009i	0.338073	+	1.34920i
$737$	323.536			0.438991
$738$		0			0
$739$		−	190.298i		−	0.257507i	−0.991677	−	0.128754i	$-0.958902\pi$
$739$		−	190.298i		−	0.257507i	0.991677	−	0.128754i	$-0.0410977\pi$
$740$	16.4725	+	9.65398i	0.0222602	+	0.0130459i
$741$		0			0
$742$	−5.78200	−	1.56948i	−0.00779245	−	0.00211520i
$743$	664.128	−	383.435i	0.893847	−	0.516063i	0.0186481	−	0.999826i	$-0.494064\pi$
$743$	664.128	−	383.435i	0.893847	−	0.516063i	0.875199	+	0.483763i	$0.160730\pi$
$744$		0			0
$745$	−369.762	+	640.447i	−0.496325	+	0.859660i
$746$	−995.118	−	1001.62i	−1.33394	−	1.34265i
$747$		0			0
$748$	7.79409	+	0.0507583i	0.0104199	+	6.78587e-5i
$749$	123.891	−	214.586i	0.165409	−	0.286496i
$750$		0			0
$751$	519.601	−	299.992i	0.691879	−	0.399456i	−0.112437	−	0.993659i	$-0.535866\pi$
$751$	519.601	−	299.992i	0.691879	−	0.399456i	0.804315	+	0.594202i	$0.202532\pi$
$752$	845.732	−	473.705i	1.12464	−	0.629927i
$753$		0			0
$754$	258.635	−	68.3992i	0.343017	−	0.0907152i
$755$			335.335i			0.444152i
$756$		0			0
$757$	−343.082			−0.453213			−0.226606	−	0.973986i	$-0.572763\pi$
$757$	−343.082			−0.453213			−0.226606	+	0.973986i	$0.572763\pi$
$758$	−276.858	−	1046.87i	−0.365249	−	1.38110i
$759$		0			0
$760$	284.017	−	1020.00i	0.373706	−	1.34211i
$761$	149.365	+	258.708i	0.196275	+	0.339958i	0.947318	−	0.320295i	$-0.103782\pi$
$761$	149.365	+	258.708i	0.196275	+	0.339958i	−0.751043	+	0.660253i	$0.770449\pi$
$762$		0			0
$763$	249.464	+	144.028i	0.326952	+	0.188766i
$764$	891.282	+	5.80440i	1.16660	+	0.00759738i
$765$		0			0
$766$	511.053	−	507.736i	0.667171	−	0.662841i
$767$	−215.738	−	124.557i	−0.281275	−	0.162394i
$768$		0			0
$769$	−466.241	−	807.553i	−0.606295	−	1.05013i	−0.991845	−	0.127447i	$-0.959322\pi$
$769$	−466.241	−	807.553i	−0.606295	−	1.05013i	0.385550	−	0.922687i	$-0.374012\pi$
$770$	−71.6162	+	263.836i	−0.0930081	+	0.342644i
$771$		0			0
$772$	391.199	+	229.268i	0.506734	+	0.296980i
$773$	173.239			0.224113			0.112056	−	0.993702i	$-0.464256\pi$
$773$	173.239			0.224113			0.112056	+	0.993702i	$0.464256\pi$
$774$		0			0
$775$		−	606.660i		−	0.782787i
$776$	192.528	+	747.663i	0.248103	+	0.963483i
$777$		0			0
$778$	46.0066	−	169.490i	0.0591345	−	0.217853i
$779$	−351.917	+	203.179i	−0.451755	+	0.260821i
$780$		0			0
$781$	106.184	−	183.916i	0.135959	−	0.235488i
$782$	23.5065	−	23.3539i	0.0300595	−	0.0298644i
$783$		0			0
$784$	−459.058	−	5.97940i	−0.585533	−	0.00762679i
$785$	−910.285	+	1576.66i	−1.15960	+	2.00848i
$786$		0			0
$787$	−43.1896	+	24.9355i	−0.0548788	+	0.0316843i	−0.527188	−	0.849748i	$-0.676754\pi$
$787$	−43.1896	+	24.9355i	−0.0548788	+	0.0316843i	0.472310	+	0.881433i	$0.343420\pi$
$788$	420.715	−	239.260i	0.533902	−	0.303630i
$789$		0			0
$790$	603.932	+	2283.62i	0.764471	+	2.89066i
$791$			160.639i			0.203083i
$792$		0			0
$793$	−476.369			−0.600717
$794$	−93.6075	+	24.7557i	−0.117894	+	0.0311784i
$795$		0			0
$796$	162.614	+	285.940i	0.204289	+	0.359221i
$797$	513.753	+	889.846i	0.644608	+	1.11649i	0.984392	+	0.175991i	$0.0563129\pi$
$797$	513.753	+	889.846i	0.644608	+	1.11649i	−0.339784	+	0.940504i	$0.610354\pi$
$798$		0			0
$799$	−27.1727	−	15.6882i	−0.0340084	−	0.0196348i
$800$	890.181	+	919.649i	1.11273	+	1.14956i
$801$		0			0
$802$	−614.189	−	618.202i	−0.765822	−	0.770825i
$803$	−429.854	−	248.176i	−0.535310	−	0.309061i
$804$		0			0
$805$	581.114	+	1006.52i	0.721880	+	1.25033i
$806$	206.455	+	56.0406i	0.256148	+	0.0695293i
$807$		0			0
$808$	−86.4222	−	335.612i	−0.106958	−	0.415361i
$809$	637.363			0.787841			0.393920	−	0.919145i	$-0.371119\pi$
$809$	637.363			0.787841			0.393920	+	0.919145i	$0.371119\pi$
$810$		0			0
$811$			1486.54i			1.83298i	0.400061	+	0.916489i	$0.368989\pi$
$811$			1486.54i			1.83298i	−0.400061	+	0.916489i	$0.631011\pi$
$812$	172.873	−	294.972i	0.212898	−	0.363266i
$813$		0			0
$814$	−4.29968	−	1.16711i	−0.00528216	−	0.00143380i
$815$	873.969	−	504.586i	1.07235	−	0.619124i
$816$		0			0
$817$	264.140	−	457.503i	0.323304	−	0.559980i
$818$	−76.4412	−	76.9406i	−0.0934488	−	0.0940594i
$819$		0			0
$820$	5.19842	−	798.232i	0.00633954	−	0.973454i
$821$	−517.865	+	896.969i	−0.630773	+	1.09253i	0.356620	+	0.934249i	$0.383929\pi$
$821$	−517.865	+	896.969i	−0.630773	+	1.09253i	−0.987394	+	0.158282i	$0.949404\pi$
$822$		0			0
$823$	−278.230	+	160.636i	−0.338068	+	0.195184i	−0.659417	−	0.751777i	$-0.729197\pi$
$823$	−278.230	+	160.636i	−0.338068	+	0.195184i	0.321349	+	0.946961i	$0.395864\pi$
$824$	310.827	−	1116.29i	0.377218	−	1.35472i
$825$		0			0
$826$	−307.784	+	81.3972i	−0.372619	+	0.0985438i
$827$			119.865i			0.144939i	0.997371	+	0.0724695i	$0.0230880\pi$
$827$			119.865i			0.144939i	−0.997371	+	0.0724695i	$0.976912\pi$
$828$		0			0
$829$	810.947			0.978223			0.489112	−	0.872221i	$-0.337321\pi$
$829$	810.947			0.978223			0.489112	+	0.872221i	$0.337321\pi$
$830$	−414.633	−	1567.83i	−0.499558	−	1.88896i
$831$		0			0
$832$	−395.201	+	217.988i	−0.475001	+	0.262005i
$833$	7.43005	+	12.8692i	0.00891963	+	0.0154492i
$834$		0			0
$835$	−1244.57	−	718.553i	−1.49050	−	0.860543i
$836$	−1.60897	+	247.062i	−0.00192461	+	0.295529i
$837$		0			0
$838$	904.391	−	898.520i	1.07923	−	1.07222i
$839$	51.3491	+	29.6464i	0.0612027	+	0.0353354i	0.530289	−	0.847817i	$-0.322083\pi$
$839$	51.3491	+	29.6464i	0.0612027	+	0.0353354i	−0.469086	+	0.883152i	$0.655417\pi$
$840$		0			0
$841$	240.610	+	416.748i	0.286100	+	0.495539i
$842$	−100.359	+	369.724i	−0.119191	+	0.439102i
$843$		0			0
$844$	218.551	−	372.912i	0.258947	−	0.441839i
$845$	961.549			1.13793
$846$		0			0
$847$			481.466i			0.568437i
$848$	5.43764	−	9.14121i	0.00641231	−	0.0107797i
$849$		0			0
$850$	10.8527	−	39.9816i	0.0127679	−	0.0470372i
$851$	−16.4030	+	9.47029i	−0.0192750	+	0.0111284i
$852$		0			0
$853$	547.729	−	948.694i	0.642121	−	1.11219i	−0.342838	−	0.939395i	$-0.611388\pi$
$853$	547.729	−	948.694i	0.642121	−	1.11219i	0.984959	−	0.172791i	$-0.0552785\pi$
$854$	−431.884	+	429.080i	−0.505718	+	0.502436i
$855$		0			0
$856$	307.995	+	314.072i	0.359807	+	0.366907i
$857$	692.162	−	1198.86i	0.807658	−	1.39890i	−0.106825	−	0.994278i	$-0.534068\pi$
$857$	692.162	−	1198.86i	0.807658	−	1.39890i	0.914482	−	0.404626i	$-0.132598\pi$
$858$		0			0
$859$	−414.983	+	239.591i	−0.483101	+	0.278918i	−0.721708	−	0.692198i	$-0.756643\pi$
$859$	−414.983	+	239.591i	−0.483101	+	0.278918i	0.238607	+	0.971116i	$0.423309\pi$
$860$	513.011	+	902.077i	0.596524	+	1.04893i
$861$		0			0
$862$	−246.054	−	930.394i	−0.285446	−	1.07934i
$863$			4.93230i			0.00571530i	0.999996	+	0.00285765i	$0.000909619\pi$
$863$			4.93230i			0.00571530i	−0.999996	+	0.00285765i	$0.999090\pi$
$864$		0			0
$865$	1218.83			1.40906
$866$	−696.740	+	184.261i	−0.804550	+	0.212773i
$867$		0			0
$868$	237.653	−	135.153i	0.273794	−	0.155706i
$869$	−275.596	−	477.347i	−0.317142	−	0.549306i
$870$		0			0
$871$	525.164	+	303.204i	0.602944	+	0.348110i
$872$	−365.121	+	358.056i	−0.418717	+	0.410615i
$873$		0			0
$874$	740.289	+	745.126i	0.847013	+	0.852547i
$875$	471.854	+	272.425i	0.539262	+	0.311343i
$876$		0			0
$877$	−839.494	−	1454.05i	−0.957234	−	1.65798i	−0.729172	−	0.684331i	$-0.760095\pi$
$877$	−839.494	−	1454.05i	−0.957234	−	1.65798i	−0.228062	−	0.973647i	$-0.573239\pi$
$878$	1088.23	+	295.391i	1.23944	+	0.336436i
$879$		0			0
$880$	−417.119	−	248.123i	−0.473999	−	0.281958i
$881$	−830.879			−0.943109			−0.471555	−	0.881837i	$-0.656307\pi$
$881$	−830.879			−0.943109			−0.471555	+	0.881837i	$0.656307\pi$
$882$		0			0
$883$		−	1228.46i		−	1.39123i	−0.718414	−	0.695615i	$-0.755132\pi$
$883$		−	1228.46i		−	1.39123i	0.718414	−	0.695615i	$-0.244868\pi$
$884$	12.6038	+	7.38666i	0.0142577	+	0.00835595i
$885$		0			0
$886$	−1270.20	−	344.787i	−1.43364	−	0.389150i
$887$	−660.079	+	381.097i	−0.744170	+	0.429647i	−0.823584	−	0.567195i	$-0.808029\pi$
$887$	−660.079	+	381.097i	−0.744170	+	0.429647i	0.0794134	+	0.996842i	$0.474695\pi$
$888$		0			0
$889$	22.1082	−	38.2925i	0.0248686	−	0.0430737i
$890$	293.612	+	295.530i	0.329901	+	0.332056i
$891$		0			0
$892$	−653.083	−	4.25315i	−0.732156	−	0.00476810i
$893$	497.295	−	861.340i	0.556881	−	0.964547i
$894$		0			0
$895$	1932.80	−	1115.90i	2.15955	−	1.24682i
$896$	−161.947	+	553.601i	−0.180744	+	0.617858i
$897$		0			0
$898$	−440.011	+	116.366i	−0.489990	+	0.129584i
$899$		−	287.696i		−	0.320018i
$900$		0			0
$901$	−0.344275			−0.000382104
$902$	47.6235	+	180.077i	0.0527977	+	0.199642i
$903$		0			0
$904$	−274.731	−	76.4981i	−0.303907	−	0.0846218i
$905$	−422.166	−	731.214i	−0.466482	−	0.807971i
$906$		0			0
$907$	324.076	+	187.106i	0.357306	+	0.206291i	0.667898	−	0.744253i	$-0.267194\pi$
$907$	324.076	+	187.106i	0.357306	+	0.206291i	−0.310592	+	0.950543i	$0.600527\pi$
$908$	−44.1882	−	0.287772i	−0.0486654	−	0.000316929i
$909$		0			0
$910$	−363.503	+	361.143i	−0.399453	+	0.396861i
$911$	1265.50	+	730.639i	1.38914	+	0.802018i	0.993218	−	0.116268i	$-0.0370930\pi$
$911$	1265.50	+	730.639i	1.38914	+	0.802018i	0.395918	+	0.918286i	$0.370426\pi$
$912$		0			0
$913$	189.212	+	327.725i	0.207242	+	0.358954i
$914$	−376.051	+	1385.38i	−0.411435	+	1.51574i
$915$		0			0
$916$	−111.623	−	65.4183i	−0.121859	−	0.0714173i
$917$	528.464			0.576296
$918$		0			0
$919$			1112.72i			1.21080i	0.795923	+	0.605398i	$0.206986\pi$
$919$			1112.72i			1.21080i	−0.795923	+	0.605398i	$0.793014\pi$
$920$	−1998.12	+	514.529i	−2.17187	+	0.559271i
$921$		0			0
$922$	210.485	−	775.432i	0.228292	−	0.841033i
$923$	344.717	−	199.022i	0.373474	−	0.215625i
$924$		0			0
$925$	−11.8404	+	20.5082i	−0.0128005	+	0.0221710i
$926$	−650.003	+	645.784i	−0.701947	+	0.697390i
$927$		0			0
$928$	422.150	+	436.125i	0.454903	+	0.469962i
$929$	508.204	−	880.234i	0.547044	−	0.947507i	−0.451432	−	0.892306i	$-0.649086\pi$
$929$	508.204	−	880.234i	0.547044	−	0.947507i	0.998475	−	0.0552017i	$-0.0175802\pi$
$930$		0			0
$931$	−407.938	+	235.523i	−0.438171	+	0.252978i
$932$	−629.518	+	358.007i	−0.675449	+	0.384127i
$933$		0			0
$934$	−104.516	−	395.203i	−0.111902	−	0.423130i
$935$			15.7095i			0.0168016i
$936$		0			0
$937$	170.282			0.181731			0.0908654	−	0.995863i	$-0.471037\pi$
$937$	170.282			0.181731			0.0908654	+	0.995863i	$0.471037\pi$
$938$	749.227	−	198.142i	0.798750	−	0.211239i
$939$		0			0
$940$	965.844	+	1698.34i	1.02749	+	1.80674i
$941$	150.929	+	261.417i	0.160392	+	0.277808i	0.935009	−	0.354623i	$-0.115391\pi$
$941$	150.929	+	261.417i	0.160392	+	0.277808i	−0.774617	+	0.632430i	$0.782057\pi$
$942$		0			0
$943$	685.784	+	395.938i	0.727237	+	0.419870i
$944$	7.36126	−	565.147i	0.00779794	−	0.598673i
$945$		0			0
$946$	−170.670	−	171.785i	−0.180413	−	0.181591i
$947$	−730.155	−	421.555i	−0.771019	−	0.445148i	0.0622189	−	0.998063i	$-0.480182\pi$
$947$	−730.155	−	421.555i	−0.771019	−	0.445148i	−0.833238	+	0.552914i	$0.813516\pi$
$948$		0			0
$949$	−465.159	−	805.679i	−0.490157	−	0.848977i
$950$	1267.37	+	344.016i	1.33407	+	0.362123i
$951$		0			0
$952$	18.0802	−	4.65576i	0.0189918	−	0.00489051i
$953$	−306.171			−0.321270			−0.160635	−	0.987014i	$-0.551354\pi$
$953$	−306.171			−0.321270			−0.160635	+	0.987014i	$0.551354\pi$
$954$		0			0
$955$			1796.44i			1.88109i
$956$	92.5828	−	157.973i	0.0968439	−	0.165244i
$957$		0			0
$958$	−174.856	−	47.4634i	−0.182522	−	0.0495442i
$959$	980.365	−	566.014i	1.02228	−	0.590213i
$960$		0			0
$961$	−365.473	+	633.018i	−0.380305	+	0.658707i
$962$	−5.88547	−	5.92393i	−0.00611796	−	0.00615793i
$963$		0			0
$964$	8.81584	−	1353.70i	0.00914507	−	1.40425i
$965$	−456.951	+	791.462i	−0.473524	+	0.820168i
$966$		0			0
$967$	−103.822	+	59.9417i	−0.107365	+	0.0619873i	−0.552721	−	0.833366i	$-0.686410\pi$
$967$	−103.822	+	59.9417i	−0.107365	+	0.0619873i	0.445356	+	0.895354i	$0.353077\pi$
$968$	−823.423	−	229.280i	−0.850644	−	0.236859i
$969$		0			0
$970$	−1504.37	+	397.850i	−1.55090	+	0.410154i
$971$		−	62.7602i		−	0.0646346i	−0.999478	−	0.0323173i	$-0.989711\pi$
$971$		−	62.7602i		−	0.0646346i	0.999478	−	0.0323173i	$-0.0102887\pi$
$972$		0			0
$973$	692.431			0.711646
$974$	154.063	+	582.551i	0.158175	+	0.598101i
$975$		0			0
$976$	−528.163	−	942.959i	−0.541151	−	0.966146i
$977$	−618.115	−	1070.61i	−0.632666	−	1.09581i	−0.987004	−	0.160693i	$-0.948627\pi$
$977$	−618.115	−	1070.61i	−0.632666	−	1.09581i	0.354338	−	0.935117i	$-0.384706\pi$
$978$		0			0
$979$	−84.1854	−	48.6045i	−0.0859912	−	0.0496471i
$980$	6.02594	−	925.300i	0.00614892	−	0.944184i
$981$		0			0
$982$	−638.211	+	634.068i	−0.649909	+	0.645691i
$983$	−490.618	−	283.258i	−0.499103	−	0.288157i	0.229240	−	0.973370i	$-0.426376\pi$
$983$	−490.618	−	283.258i	−0.499103	−	0.288157i	−0.728343	+	0.685213i	$0.759709\pi$
$984$		0			0
$985$	487.746	+	844.801i	0.495174	+	0.857666i
$986$	5.14667	−	18.9605i	0.00521974	−	0.0192297i
$987$		0			0
$988$	−234.147	+	399.524i	−0.236991	+	0.404376i
$989$	−1029.46			−1.04091
$990$		0			0
$991$		−	457.774i		−	0.461931i	−0.972962	−	0.230966i	$-0.925812\pi$
$991$		−	457.774i		−	0.461931i	0.972962	−	0.230966i	$-0.0741885\pi$
$992$	117.972	+	470.806i	0.118923	+	0.474603i
$993$		0			0
$994$	133.260	−	490.933i	0.134064	−	0.493897i
$995$	−574.172	+	331.498i	−0.577057	+	0.333164i
$996$		0			0
$997$	19.3798	−	33.5667i	0.0194381	−	0.0336677i	−0.856143	−	0.516739i	$-0.827146\pi$
$997$	19.3798	−	33.5667i	0.0194381	−	0.0336677i	0.875581	+	0.483072i	$0.160479\pi$
$998$	905.375	−	899.498i	0.907190	−	0.901301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.f.c.19.8		16
3.2	odd	2		36.3.f.c.7.1	✓	16
4.3	odd	2	inner	108.3.f.c.19.4		16
8.3	odd	2		1728.3.o.g.127.2		16
8.5	even	2		1728.3.o.g.127.1		16
9.2	odd	6		324.3.d.i.163.6		8
9.4	even	3	inner	108.3.f.c.91.4		16
9.5	odd	6		36.3.f.c.31.5	yes	16
9.7	even	3		324.3.d.g.163.3		8
12.11	even	2		36.3.f.c.7.5	yes	16
24.5	odd	2		576.3.o.g.511.8		16
24.11	even	2		576.3.o.g.511.1		16
36.7	odd	6		324.3.d.g.163.4		8
36.11	even	6		324.3.d.i.163.5		8
36.23	even	6		36.3.f.c.31.1	yes	16
36.31	odd	6	inner	108.3.f.c.91.8		16
72.5	odd	6		576.3.o.g.319.1		16
72.13	even	6		1728.3.o.g.1279.2		16
72.59	even	6		576.3.o.g.319.8		16
72.67	odd	6		1728.3.o.g.1279.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.1	✓	16	3.2	odd	2
36.3.f.c.7.5	yes	16	12.11	even	2
36.3.f.c.31.1	yes	16	36.23	even	6
36.3.f.c.31.5	yes	16	9.5	odd	6
108.3.f.c.19.4		16	4.3	odd	2	inner
108.3.f.c.19.8		16	1.1	even	1	trivial
108.3.f.c.91.4		16	9.4	even	3	inner
108.3.f.c.91.8		16	36.31	odd	6	inner
324.3.d.g.163.3		8	9.7	even	3
324.3.d.g.163.4		8	36.7	odd	6
324.3.d.i.163.5		8	36.11	even	6
324.3.d.i.163.6		8	9.2	odd	6
576.3.o.g.319.1		16	72.5	odd	6
576.3.o.g.319.8		16	72.59	even	6
576.3.o.g.511.1		16	24.11	even	2
576.3.o.g.511.8		16	24.5	odd	2
1728.3.o.g.127.1		16	8.5	even	2
1728.3.o.g.127.2		16	8.3	odd	2
1728.3.o.g.1279.1		16	72.67	odd	6
1728.3.o.g.1279.2		16	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93353 - 0.511345i) q^{2} +(3.47705 - 1.97740i) q^{4} +(4.03104 + 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(5.71184 - 5.60133i) q^{8} +O(q^{10})\)	\(q+(1.93353 - 0.511345i) q^{2} +(3.47705 - 1.97740i) q^{4} +(4.03104 + 6.98197i) q^{5} +(-3.90254 - 2.25313i) q^{7} +(5.71184 - 5.60133i) q^{8} +(11.3643 + 11.4386i) q^{10} +(-3.25842 - 1.88125i) q^{11} +(-3.52605 - 6.10730i) q^{13} +(-8.69780 - 2.36095i) q^{14} +(8.17979 - 13.7510i) q^{16} -0.517890 q^{17} -16.4164i q^{19} +(27.8223 + 16.3057i) q^{20} +(-7.26222 - 1.97127i) q^{22} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(-9.94065 - 10.0056i) q^{26} +(-18.0247 - 0.117384i) q^{28} +(-9.48394 + 16.4267i) q^{29} +(-13.1355 + 7.58377i) q^{31} +(8.78432 - 30.7707i) q^{32} +(-1.00135 + 0.264820i) q^{34} -36.3299i q^{35} +0.592061 q^{37} +(-8.39446 - 31.7416i) q^{38} +(62.1330 + 17.3007i) q^{40} +(-12.3766 - 21.4369i) q^{41} +(27.8686 + 16.0900i) q^{43} +(-15.0497 - 0.0980099i) q^{44} +(-45.3890 + 45.0944i) q^{46} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} +(-20.9556 + 77.2010i) q^{50} +(-24.3368 - 14.2630i) q^{52} +0.664765 q^{53} -30.3336i q^{55} +(-34.9113 + 8.98987i) q^{56} +(-9.93776 + 36.6110i) q^{58} +(30.5921 - 17.6623i) q^{59} +(33.7750 - 58.5000i) q^{61} +(-21.5199 + 21.3802i) q^{62} +(1.25029 - 63.9878i) q^{64} +(28.4273 - 49.2376i) q^{65} +(-74.4692 + 42.9948i) q^{67} +(-1.80073 + 1.02407i) q^{68} +(-18.5771 - 70.2449i) q^{70} +56.4434i q^{71} +131.921 q^{73} +(1.14477 - 0.302748i) q^{74} +(-32.4618 - 57.0808i) q^{76} +(8.47743 + 14.6833i) q^{77} +(126.869 + 73.2481i) q^{79} +(128.982 + 1.68005i) q^{80} +(-34.8921 - 35.1201i) q^{82} +(-87.1029 - 50.2889i) q^{83} +(-2.08764 - 3.61589i) q^{85} +(62.1122 + 16.8599i) q^{86} +(-29.1491 + 7.50608i) q^{88} +25.8362 q^{89} +31.7786i q^{91} +(-64.7021 + 110.401i) q^{92} +(116.939 + 31.7420i) q^{94} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +(-40.4465 - 40.7107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

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