LMFDB - Embedded newform 99.3.k.c.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 77x^12 + 88x^11 - 577x^10 + 578x^9 + 1520x^8 + 1868x^7 - 1619x^6 - 16804x^5 + 32427x^4 + 43316x^3 - 71672x^2 + 83521
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.3
Root			$-1.29715 + 0.104262i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.3.k.c.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.40785 + 0.782357i) q^{2} +(1.94958 + 1.41645i) q^{4} +(2.61024 + 8.03348i) q^{5} +(1.43445 - 1.97435i) q^{7} +(-2.36641 - 3.25708i) q^{8} +O(q^{10})$	\(q+(2.40785 + 0.782357i) q^{2} +(1.94958 + 1.41645i) q^{4} +(2.61024 + 8.03348i) q^{5} +(1.43445 - 1.97435i) q^{7} +(-2.36641 - 3.25708i) q^{8} +21.3855i q^{10} +(-2.51703 - 10.7082i) q^{11} +(11.1993 + 3.63888i) q^{13} +(4.99858 - 3.63168i) q^{14} +(-6.12844 - 18.8614i) q^{16} +(1.93053 - 0.627268i) q^{17} +(-4.97861 - 6.85246i) q^{19} +(-6.29019 + 19.3592i) q^{20} +(2.31697 - 27.7528i) q^{22} -41.9571 q^{23} +(-37.4981 + 27.2440i) q^{25} +(24.1193 + 17.5237i) q^{26} +(5.59314 - 1.81732i) q^{28} +(14.4679 - 19.9133i) q^{29} +(6.74074 - 20.7459i) q^{31} -34.1061i q^{32} +5.13918 q^{34} +(19.6051 + 6.37010i) q^{35} +(12.9478 + 9.40714i) q^{37} +(-6.62665 - 20.3947i) q^{38} +(19.9888 - 27.5122i) q^{40} +(30.9272 + 42.5677i) q^{41} +42.3507i q^{43} +(10.2604 - 24.4417i) q^{44} +(-101.026 - 32.8254i) q^{46} +(-13.0910 + 9.51117i) q^{47} +(13.3014 + 40.9376i) q^{49} +(-111.604 + 36.2624i) q^{50} +(16.6797 + 22.9576i) q^{52} +(15.3065 - 47.1085i) q^{53} +(79.4537 - 48.1714i) q^{55} -9.82509 q^{56} +(50.4158 - 36.6292i) q^{58} +(16.1257 + 11.7160i) q^{59} +(-113.086 + 36.7440i) q^{61} +(32.4614 - 44.6792i) q^{62} +(2.16942 - 6.67679i) q^{64} +99.4678i q^{65} -4.41442 q^{67} +(4.65223 + 1.51160i) q^{68} +(42.2225 + 30.6764i) q^{70} +(-1.86520 - 5.74049i) q^{71} +(-3.57399 + 4.91917i) q^{73} +(23.8166 + 32.7808i) q^{74} -20.4114i q^{76} +(-24.7522 - 10.3908i) q^{77} +(98.3988 + 31.9717i) q^{79} +(135.526 - 98.4655i) q^{80} +(41.1649 + 126.693i) q^{82} +(-28.6898 + 9.32189i) q^{83} +(10.0783 + 13.8716i) q^{85} +(-33.1334 + 101.974i) q^{86} +(-28.9210 + 33.5380i) q^{88} +60.4650 q^{89} +(23.2492 - 16.8916i) q^{91} +(-81.7987 - 59.4302i) q^{92} +(-38.9623 + 12.6596i) q^{94} +(42.0538 - 57.8821i) q^{95} +(11.3376 - 34.8935i) q^{97} +108.978i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	2.40785	+	0.782357i	1.20392	+	0.391179i	0.841203	−	0.540719i	$-0.181848\pi$
$2$	2.40785	+	0.782357i	1.20392	+	0.391179i	0.362721	+	0.931898i	$0.381848\pi$
$3$		0			0
$3$		0			0
$4$	1.94958	+	1.41645i	0.487395	+	0.354113i
$5$	2.61024	+	8.03348i	0.522047	+	1.60670i	0.770082	+	0.637945i	$0.220215\pi$
$5$	2.61024	+	8.03348i	0.522047	+	1.60670i	−0.248034	+	0.968751i	$0.579785\pi$
$6$		0			0
$7$	1.43445	−	1.97435i	0.204921	−	0.282050i	−0.694170	−	0.719811i	$-0.744228\pi$
$7$	1.43445	−	1.97435i	0.204921	−	0.282050i	0.899091	+	0.437761i	$0.144228\pi$
$8$	−2.36641	−	3.25708i	−0.295801	−	0.407135i
$9$		0			0
$10$			21.3855i			2.13855i
$11$	−2.51703	−	10.7082i	−0.228821	−	0.973469i
$11$	−2.51703	−	10.7082i	−0.228821	−	0.973469i
$12$		0			0
$13$	11.1993	+	3.63888i	0.861485	+	0.279914i	0.706249	−	0.707964i	$-0.250386\pi$
$13$	11.1993	+	3.63888i	0.861485	+	0.279914i	0.155236	+	0.987877i	$0.450386\pi$
$14$	4.99858	−	3.63168i	0.357041	−	0.259406i
$15$		0			0
$16$	−6.12844	−	18.8614i	−0.383028	−	1.17884i
$17$	1.93053	−	0.627268i	0.113561	−	0.0368981i	−0.251685	−	0.967809i	$-0.580985\pi$
$17$	1.93053	−	0.627268i	0.113561	−	0.0368981i	0.365246	+	0.930911i	$0.380985\pi$
$18$		0			0
$19$	−4.97861	−	6.85246i	−0.262032	−	0.360656i	0.657648	−	0.753326i	$-0.271552\pi$
$19$	−4.97861	−	6.85246i	−0.262032	−	0.360656i	−0.919680	+	0.392670i	$0.871552\pi$
$20$	−6.29019	+	19.3592i	−0.314509	+	0.967960i
$21$		0			0
$22$	2.31697	−	27.7528i	0.105317	−	1.26149i
$23$	−41.9571			−1.82422			−0.912110	−	0.409946i	$-0.865548\pi$
$23$	−41.9571			−1.82422			−0.912110	+	0.409946i	$0.865548\pi$
$24$		0			0
$25$	−37.4981	+	27.2440i	−1.49992	+	1.08976i
$26$	24.1193	+	17.5237i	0.927667	+	0.673989i
$27$		0			0
$28$	5.59314	−	1.81732i	0.199755	−	0.0649044i
$29$	14.4679	−	19.9133i	0.498893	−	0.686667i	−0.483105	−	0.875563i	$-0.660491\pi$
$29$	14.4679	−	19.9133i	0.498893	−	0.686667i	0.981997	+	0.188896i	$0.0604909\pi$
$30$		0			0
$31$	6.74074	−	20.7459i	0.217443	−	0.669222i	−0.781528	−	0.623870i	$-0.785559\pi$
$31$	6.74074	−	20.7459i	0.217443	−	0.669222i	0.998971	−	0.0453514i	$-0.0144407\pi$
$32$		−	34.1061i		−	1.06582i
$33$		0			0
$34$	5.13918			0.151152
$35$	19.6051	+	6.37010i	0.560147	+	0.182003i
$36$		0			0
$37$	12.9478	+	9.40714i	0.349941	+	0.254247i	0.748844	−	0.662746i	$-0.230609\pi$
$37$	12.9478	+	9.40714i	0.349941	+	0.254247i	−0.398903	+	0.916993i	$0.630609\pi$
$38$	−6.62665	−	20.3947i	−0.174386	−	0.536704i
$39$		0			0
$40$	19.9888	−	27.5122i	0.499720	−	0.687806i
$41$	30.9272	+	42.5677i	0.754323	+	1.03824i	0.997665	+	0.0682958i	$0.0217562\pi$
$41$	30.9272	+	42.5677i	0.754323	+	1.03824i	−0.243342	+	0.969940i	$0.578244\pi$
$42$		0			0
$43$			42.3507i			0.984900i	0.870341	+	0.492450i	$0.163899\pi$
$43$			42.3507i			0.984900i	−0.870341	+	0.492450i	$0.836101\pi$
$44$	10.2604	−	24.4417i	0.233192	−	0.555493i
$45$		0			0
$46$	−101.026	−	32.8254i	−2.19622	−	0.713596i
$47$	−13.0910	+	9.51117i	−0.278532	+	0.202365i	−0.718277	−	0.695757i	$-0.755069\pi$
$47$	−13.0910	+	9.51117i	−0.278532	+	0.202365i	0.439745	+	0.898123i	$0.355069\pi$
$48$		0			0
$49$	13.3014	+	40.9376i	0.271458	+	0.835461i
$50$	−111.604	+	36.2624i	−2.23208	+	0.725248i
$51$		0			0
$52$	16.6797	+	22.9576i	0.320763	+	0.441492i
$53$	15.3065	−	47.1085i	0.288802	−	0.888840i	−0.696432	−	0.717623i	$-0.745230\pi$
$53$	15.3065	−	47.1085i	0.288802	−	0.888840i	0.985233	−	0.171217i	$-0.0547700\pi$
$54$		0			0
$55$	79.4537	−	48.1714i	1.44461	−	0.875843i
$56$	−9.82509			−0.175448
$57$		0			0
$58$	50.4158	−	36.6292i	0.869238	−	0.631538i
$59$	16.1257	+	11.7160i	0.273317	+	0.198576i	0.715997	−	0.698103i	$-0.245972\pi$
$59$	16.1257	+	11.7160i	0.273317	+	0.198576i	−0.442680	+	0.896679i	$0.645972\pi$
$60$		0			0
$61$	−113.086	+	36.7440i	−1.85387	+	0.602360i	−0.857784	+	0.514011i	$0.828159\pi$
$61$	−113.086	+	36.7440i	−1.85387	+	0.602360i	−0.996090	+	0.0883491i	$0.971841\pi$
$62$	32.4614	−	44.6792i	0.523571	−	0.720633i
$63$		0			0
$64$	2.16942	−	6.67679i	0.0338972	−	0.104325i
$65$			99.4678i			1.53027i
$66$		0			0
$67$	−4.41442			−0.0658869			−0.0329434	−	0.999457i	$-0.510488\pi$
$67$	−4.41442			−0.0658869			−0.0329434	+	0.999457i	$0.510488\pi$
$68$	4.65223	+	1.51160i	0.0684151	+	0.0222294i
$69$		0			0
$70$	42.2225	+	30.6764i	0.603179	+	0.438235i
$71$	−1.86520	−	5.74049i	−0.0262704	−	0.0808520i	0.937062	−	0.349164i	$-0.113534\pi$
$71$	−1.86520	−	5.74049i	−0.0262704	−	0.0808520i	−0.963332	+	0.268312i	$0.913534\pi$
$72$		0			0
$73$	−3.57399	+	4.91917i	−0.0489588	+	0.0673859i	−0.832794	−	0.553582i	$-0.813260\pi$
$73$	−3.57399	+	4.91917i	−0.0489588	+	0.0673859i	0.783836	+	0.620968i	$0.213260\pi$
$74$	23.8166	+	32.7808i	0.321847	+	0.442984i
$75$		0			0
$76$		−	20.4114i		−	0.268571i
$77$	−24.7522	−	10.3908i	−0.321457	−	0.134945i
$78$		0			0
$79$	98.3988	+	31.9717i	1.24555	+	0.404705i	0.856326	−	0.516436i	$-0.172742\pi$
$79$	98.3988	+	31.9717i	1.24555	+	0.404705i	0.389229	+	0.921141i	$0.372742\pi$
$80$	135.526	−	98.4655i	1.69408	−	1.23082i
$81$		0			0
$82$	41.1649	+	126.693i	0.502011	+	1.54503i
$83$	−28.6898	+	9.32189i	−0.345660	+	0.112312i	−0.476702	−	0.879065i	$-0.658168\pi$
$83$	−28.6898	+	9.32189i	−0.345660	+	0.112312i	0.131041	+	0.991377i	$0.458168\pi$
$84$		0			0
$85$	10.0783	+	13.8716i	0.118568	+	0.163195i
$86$	−33.1334	+	101.974i	−0.385272	+	1.18574i
$87$		0			0
$88$	−28.9210	+	33.5380i	−0.328647	+	0.381114i
$89$	60.4650			0.679382			0.339691	−	0.940537i	$-0.389677\pi$
$89$	60.4650			0.679382			0.339691	+	0.940537i	$0.389677\pi$
$90$		0			0
$91$	23.2492	−	16.8916i	0.255486	−	0.185621i
$92$	−81.7987	−	59.4302i	−0.889116	−	0.645981i
$93$		0			0
$94$	−38.9623	+	12.6596i	−0.414492	+	0.134677i
$95$	42.0538	−	57.8821i	0.442672	−	0.609285i
$96$		0			0
$97$	11.3376	−	34.8935i	0.116882	−	0.359727i	−0.875453	−	0.483304i	$-0.839437\pi$
$97$	11.3376	−	34.8935i	0.116882	−	0.359727i	0.992335	+	0.123577i	$0.0394366\pi$
$98$			108.978i			1.11202i
$99$		0			0
$100$	−111.695			−1.11695
$101$	−134.816	−	43.8043i	−1.33481	−	0.433706i	−0.447255	−	0.894406i	$-0.647598\pi$
$101$	−134.816	−	43.8043i	−1.33481	−	0.433706i	−0.887556	+	0.460700i	$0.847598\pi$
$102$		0			0
$103$	−31.5689	−	22.9361i	−0.306494	−	0.222681i	0.423897	−	0.905711i	$-0.360662\pi$
$103$	−31.5689	−	22.9361i	−0.306494	−	0.222681i	−0.730391	+	0.683030i	$0.760662\pi$
$104$	−14.6500	−	45.0881i	−0.140865	−	0.433539i
$105$		0			0
$106$	73.7114	−	101.455i	0.695391	−	0.957123i
$107$	68.5495	+	94.3503i	0.640650	+	0.881779i	0.998650	−	0.0519427i	$-0.0165413\pi$
$107$	68.5495	+	94.3503i	0.640650	+	0.881779i	−0.358000	+	0.933721i	$0.616541\pi$
$108$		0			0
$109$		−	81.2670i		−	0.745569i	−0.927918	−	0.372784i	$-0.878403\pi$
$109$		−	81.2670i		−	0.745569i	0.927918	−	0.372784i	$-0.121597\pi$
$110$	229.000	−	53.8281i	2.08182	−	0.489346i
$111$		0			0
$112$	−46.0299	−	14.9560i	−0.410981	−	0.133536i
$113$	−61.8457	+	44.9335i	−0.547307	+	0.397642i	−0.826791	−	0.562509i	$-0.809836\pi$
$113$	−61.8457	+	44.9335i	−0.547307	+	0.397642i	0.279485	+	0.960150i	$0.409836\pi$
$114$		0			0
$115$	−109.518	−	337.061i	−0.952329	−	2.93097i
$116$	56.4126	−	18.3296i	0.486316	−	0.158014i
$117$		0			0
$118$	29.6621	+	40.8264i	0.251374	+	0.345986i
$119$	1.53080	−	4.71133i	0.0128639	−	0.0395910i
$120$		0			0
$121$	−108.329	+	53.9055i	−0.895282	+	0.445500i
$122$	−301.041			−2.46755
$123$		0			0
$124$	42.5272	−	30.8978i	0.342961	−	0.249176i
$125$	−145.901	−	106.003i	−1.16720	−	0.848024i
$126$		0			0
$127$	−20.0314	+	6.50861i	−0.157728	+	0.0512489i	−0.386817	−	0.922157i	$-0.626425\pi$
$127$	−20.0314	+	6.50861i	−0.157728	+	0.0512489i	0.229089	+	0.973406i	$0.426425\pi$
$128$	−69.7411	+	95.9903i	−0.544852	+	0.749925i
$129$		0			0
$130$	−77.8193	+	239.503i	−0.598610	+	1.84233i
$131$		−	106.847i		−	0.815628i	−0.913065	−	0.407814i	$-0.866291\pi$
$131$		−	106.847i		−	0.815628i	0.913065	−	0.407814i	$-0.133709\pi$
$132$		0			0
$133$	−20.6707			−0.155419
$134$	−10.6293	−	3.45365i	−0.0793228	−	0.0257735i
$135$		0			0
$136$	−6.61148	−	4.80352i	−0.0486138	−	0.0353200i
$137$	−36.8295	−	113.349i	−0.268828	−	0.827368i	−0.990787	−	0.135432i	$-0.956758\pi$
$137$	−36.8295	−	113.349i	−0.268828	−	0.827368i	0.721959	−	0.691936i	$-0.243242\pi$
$138$		0			0
$139$	−4.36390	+	6.00639i	−0.0313950	+	0.0432115i	−0.824426	−	0.565970i	$-0.808502\pi$
$139$	−4.36390	+	6.00639i	−0.0313950	+	0.0432115i	0.793031	+	0.609181i	$0.208502\pi$
$140$	29.1989	+	40.1888i	0.208563	+	0.287063i
$141$		0			0
$142$		−	15.2815i		−	0.107616i
$143$	10.7766	−	129.083i	0.0753610	−	0.902679i
$144$		0			0
$145$	197.738	+	64.2490i	1.36371	+	0.443096i
$146$	−12.4542	+	9.04849i	−0.0853026	+	0.0619759i
$147$		0			0
$148$	11.9180	+	36.6800i	0.0805274	+	0.247838i
$149$	134.349	−	43.6527i	0.901673	−	0.292971i	0.178746	−	0.983895i	$-0.442796\pi$
$149$	134.349	−	43.6527i	0.901673	−	0.292971i	0.722927	+	0.690924i	$0.242796\pi$
$150$		0			0
$151$	37.4614	+	51.5612i	0.248089	+	0.341465i	0.914841	−	0.403815i	$-0.132316\pi$
$151$	37.4614	+	51.5612i	0.248089	+	0.341465i	−0.666752	+	0.745280i	$0.732316\pi$
$152$	−10.5376	+	32.4314i	−0.0693264	+	0.213365i
$153$		0			0
$154$	−51.4702	−	44.3845i	−0.334222	−	0.288211i
$155$	184.257			1.18875
$156$		0			0
$157$	−29.8448	+	21.6835i	−0.190094	+	0.138111i	−0.678762	−	0.734359i	$-0.737483\pi$
$157$	−29.8448	+	21.6835i	−0.190094	+	0.138111i	0.488668	+	0.872470i	$0.337483\pi$
$158$	211.916	+	153.966i	1.34124	+	0.974469i
$159$		0			0
$160$	273.991	−	89.0251i	1.71244	−	0.556407i
$161$	−60.1852	+	82.8378i	−0.373821	+	0.514521i
$162$		0			0
$163$	−16.5744	+	51.0109i	−0.101684	+	0.312950i	−0.988938	−	0.148331i	$-0.952610\pi$
$163$	−16.5744	+	51.0109i	−0.101684	+	0.312950i	0.887254	+	0.461281i	$0.152610\pi$
$164$			126.796i			0.773147i
$165$		0			0
$166$	−76.3738			−0.460083
$167$	125.534	+	40.7886i	0.751703	+	0.244243i	0.659714	−	0.751517i	$-0.270677\pi$
$167$	125.534	+	40.7886i	0.751703	+	0.244243i	0.0919892	+	0.995760i	$0.470677\pi$
$168$		0			0
$169$	−24.5408	−	17.8299i	−0.145212	−	0.105503i
$170$	13.4145	+	41.2855i	0.0789086	+	0.242856i
$171$		0			0
$172$	−59.9878	+	82.5661i	−0.348766	+	0.480036i
$173$	39.1282	+	53.8553i	0.226174	+	0.311302i	0.906990	−	0.421153i	$-0.138374\pi$
$173$	39.1282	+	53.8553i	0.226174	+	0.311302i	−0.680815	+	0.732455i	$0.738374\pi$
$174$		0			0
$175$			113.114i			0.646368i
$176$	−186.545	+	113.099i	−1.05992	+	0.642608i
$177$		0			0
$178$	145.591	+	47.3052i	0.817925	+	0.265760i
$179$	144.418	−	104.926i	0.806807	−	0.586179i	−0.106096	−	0.994356i	$-0.533835\pi$
$179$	144.418	−	104.926i	0.806807	−	0.586179i	0.912903	+	0.408177i	$0.133835\pi$
$180$		0			0
$181$	−16.1042	−	49.5637i	−0.0889736	−	0.273833i	0.896663	−	0.442714i	$-0.145984\pi$
$181$	−16.1042	−	49.5637i	−0.0889736	−	0.273833i	−0.985636	+	0.168882i	$0.945984\pi$
$182$	69.1958	−	22.4831i	0.380197	−	0.123533i
$183$		0			0
$184$	99.2874	+	136.657i	0.539605	+	0.742703i
$185$	−41.7753	+	128.571i	−0.225812	+	0.694978i
$186$		0			0
$187$	−11.5761	−	19.0936i	−0.0619042	−	0.102105i
$188$	−38.9941			−0.207415
$189$		0			0
$190$	146.544	−	106.470i	0.771282	−	0.560370i
$191$	−289.898	−	210.623i	−1.51779	−	1.10274i	−0.962569	−	0.271035i	$-0.912634\pi$
$191$	−289.898	−	210.623i	−1.51779	−	1.10274i	−0.555220	−	0.831703i	$-0.687366\pi$
$192$		0			0
$193$	203.430	−	66.0985i	1.05404	−	0.342479i	0.269789	−	0.962920i	$-0.413046\pi$
$193$	203.430	−	66.0985i	1.05404	−	0.342479i	0.784254	+	0.620440i	$0.213046\pi$
$194$	54.5984	−	75.1482i	0.281435	−	0.387362i
$195$		0			0
$196$	−32.0540	+	98.6520i	−0.163541	+	0.503326i
$197$			276.568i			1.40390i	0.712227	+	0.701949i	$0.247687\pi$
$197$			276.568i			1.40390i	−0.712227	+	0.701949i	$0.752313\pi$
$198$		0			0
$199$	78.8085			0.396022			0.198011	−	0.980200i	$-0.436552\pi$
$199$	78.8085			0.396022			0.198011	+	0.980200i	$0.436552\pi$
$200$	177.471	+	57.6640i	0.887357	+	0.288320i
$201$		0			0
$202$	−290.346	−	210.948i	−1.43735	−	1.04430i
$203$	−18.5624	−	57.1293i	−0.0914405	−	0.281425i
$204$		0			0
$205$	−261.239	+	359.565i	−1.27434	+	1.75398i
$206$	−58.0688	−	79.9249i	−0.281888	−	0.387985i
$207$		0			0
$208$		−	233.535i		−	1.12277i
$209$	−60.8459	+	70.5595i	−0.291129	+	0.337605i
$210$		0			0
$211$	−208.249	−	67.6643i	−0.986964	−	0.320684i	−0.229319	−	0.973351i	$-0.573650\pi$
$211$	−208.249	−	67.6643i	−0.986964	−	0.320684i	−0.757645	+	0.652667i	$0.773650\pi$
$212$	96.5683	−	70.1610i	0.455511	−	0.330948i
$213$		0			0
$214$	91.2412	+	280.811i	0.426361	+	1.31220i
$215$	−340.224	+	110.545i	−1.58244	+	0.514165i
$216$		0			0
$217$	−31.2903	−	43.0675i	−0.144195	−	0.198468i
$218$	63.5798	−	195.679i	0.291650	−	0.897608i
$219$		0			0
$220$	223.134	+	18.6286i	1.01425	+	0.0846753i
$221$	23.9032			0.108159
$222$		0			0
$223$	169.528	−	123.169i	0.760216	−	0.552329i	−0.138761	−	0.990326i	$-0.544312\pi$
$223$	169.528	−	123.169i	0.760216	−	0.552329i	0.898977	+	0.437997i	$0.144312\pi$
$224$	−67.3374	−	48.9235i	−0.300613	−	0.218408i
$225$		0			0
$226$	−184.069	+	59.8076i	−0.814465	+	0.264636i
$227$	48.9868	−	67.4246i	0.215801	−	0.297025i	−0.687368	−	0.726309i	$-0.741234\pi$
$227$	48.9868	−	67.4246i	0.215801	−	0.297025i	0.903169	+	0.429284i	$0.141234\pi$
$228$		0			0
$229$	102.180	−	314.478i	0.446201	−	1.37327i	−0.434959	−	0.900450i	$-0.643237\pi$
$229$	102.180	−	314.478i	0.446201	−	1.37327i	0.881161	−	0.472817i	$-0.156763\pi$
$230$		−	897.274i		−	3.90119i
$231$		0			0
$232$	−99.0962			−0.427139
$233$	157.314	+	51.1146i	0.675169	+	0.219376i	0.626479	−	0.779438i	$-0.284495\pi$
$233$	157.314	+	51.1146i	0.675169	+	0.219376i	0.0486901	+	0.998814i	$0.484495\pi$
$234$		0			0
$235$	−110.578	−	80.3400i	−0.470547	−	0.341872i
$236$	14.8432	+	45.6826i	0.0628948	+	0.193570i
$237$		0			0
$238$	7.37188	−	10.1465i	0.0309743	−	0.0426324i
$239$	105.769	+	145.579i	0.442550	+	0.609117i	0.970776	−	0.239986i	$-0.0771429\pi$
$239$	105.769	+	145.579i	0.442550	+	0.609117i	−0.528227	+	0.849103i	$0.677143\pi$
$240$		0			0
$241$			226.632i			0.940380i	0.882565	+	0.470190i	$0.155815\pi$
$241$			226.632i			0.940380i	−0.882565	+	0.470190i	$0.844185\pi$
$242$	−303.013	+	45.0442i	−1.25212	+	0.186133i
$243$		0			0
$244$	−272.517	−	88.5461i	−1.11687	−	0.362894i
$245$	−294.151	+	213.714i	−1.20062	+	0.872300i
$246$		0			0
$247$	−30.8217	−	94.8594i	−0.124784	−	0.384046i
$248$	−83.5223	+	27.1380i	−0.336783	+	0.109428i
$249$		0			0
$250$	−268.374	−	369.385i	−1.07350	−	1.47754i
$251$	24.4520	−	75.2554i	0.0974181	−	0.299822i	−0.890458	−	0.455065i	$-0.849616\pi$
$251$	24.4520	−	75.2554i	0.0974181	−	0.299822i	0.987876	+	0.155243i	$0.0496160\pi$
$252$		0			0
$253$	105.607	+	449.283i	0.417420	+	1.77582i
$254$	−53.3247			−0.209940
$255$		0			0
$256$	−265.743	+	193.074i	−1.03806	+	0.754194i
$257$	241.518	+	175.473i	0.939758	+	0.682774i	0.948362	−	0.317189i	$-0.102739\pi$
$257$	241.518	+	175.473i	0.939758	+	0.682774i	−0.00860422	+	0.999963i	$0.502739\pi$
$258$		0			0
$259$	37.1460	−	12.0695i	0.143421	−	0.0466002i
$260$	−140.891	+	193.920i	−0.541890	+	0.745848i
$261$		0			0
$262$	83.5928	−	257.272i	0.319056	−	0.981955i
$263$			60.3285i			0.229386i	0.993401	+	0.114693i	$0.0365884\pi$
$263$			60.3285i			0.229386i	−0.993401	+	0.114693i	$0.963412\pi$
$264$		0			0
$265$	418.399			1.57887
$266$	−49.7719	−	16.1719i	−0.187112	−	0.0607965i
$267$		0			0
$268$	−8.60627	−	6.25282i	−0.0321130	−	0.0233314i
$269$	60.5588	+	186.381i	0.225126	+	0.692866i	0.998279	+	0.0586463i	$0.0186784\pi$
$269$	60.5588	+	186.381i	0.225126	+	0.692866i	−0.773153	+	0.634219i	$0.781322\pi$
$270$		0			0
$271$	200.141	−	275.470i	0.738527	−	1.01650i	−0.260175	−	0.965561i	$-0.583780\pi$
$271$	200.141	−	275.470i	0.738527	−	1.01650i	0.998702	−	0.0509339i	$-0.0162198\pi$
$272$	−23.6623	−	32.5684i	−0.0869938	−	0.119737i
$273$		0			0
$274$		−	301.742i		−	1.10125i
$275$	386.116	+	332.961i	1.40406	+	1.21077i
$276$		0			0
$277$	−333.579	−	108.386i	−1.20426	−	0.391287i	−0.362932	−	0.931816i	$-0.618224\pi$
$277$	−333.579	−	108.386i	−1.20426	−	0.391287i	−0.841326	+	0.540529i	$0.818224\pi$
$278$	−15.2067	+	11.0483i	−0.0547005	+	0.0397423i
$279$		0			0
$280$	−25.6458	−	78.9297i	−0.0915922	−	0.281892i
$281$	388.450	−	126.215i	1.38238	−	0.449164i	0.478931	−	0.877853i	$-0.341024\pi$
$281$	388.450	−	126.215i	1.38238	−	0.449164i	0.903452	+	0.428689i	$0.141024\pi$
$282$		0			0
$283$	188.772	+	259.822i	0.667039	+	0.918100i	0.999689	−	0.0249503i	$-0.00794275\pi$
$283$	188.772	+	259.822i	0.667039	+	0.918100i	−0.332650	+	0.943050i	$0.607943\pi$
$284$	4.49478	−	13.8335i	0.0158267	−	0.0487096i
$285$		0			0
$286$	126.938	−	302.381i	0.443838	−	1.05728i
$287$	128.407			0.447411
$288$		0			0
$289$	−230.472	+	167.448i	−0.797482	+	0.579405i
$290$	425.858	+	309.404i	1.46847	+	1.06691i
$291$		0			0
$292$	−13.9356	+	4.52794i	−0.0477245	+	0.0155066i
$293$	221.635	−	305.055i	0.756435	−	1.04114i	−0.241067	−	0.970508i	$-0.577497\pi$
$293$	221.635	−	305.055i	0.756435	−	1.04114i	0.997502	−	0.0706350i	$-0.0225026\pi$
$294$		0			0
$295$	−52.0284	+	160.127i	−0.176367	+	0.542803i
$296$		−	64.4332i		−	0.217680i
$297$		0			0
$298$	357.645			1.20015
$299$	−469.890	−	152.677i	−1.57154	−	0.510624i
$300$		0			0
$301$	83.6150	+	60.7499i	0.277791	+	0.201827i
$302$	49.8621	+	153.460i	0.165106	+	0.508144i
$303$		0			0
$304$	−98.7360	+	135.898i	−0.324789	+	0.447034i
$305$	−590.364	−	812.566i	−1.93562	−	2.66415i
$306$		0			0
$307$			505.973i			1.64812i	0.566502	+	0.824060i	$0.308296\pi$
$307$			505.973i			1.64812i	−0.566502	+	0.824060i	$0.691704\pi$
$308$	−33.5383	−	55.3180i	−0.108891	−	0.179604i
$309$		0			0
$310$	443.662	+	144.154i	1.43117	+	0.465014i
$311$	−134.356	+	97.6152i	−0.432012	+	0.313875i	−0.782453	−	0.622710i	$-0.786032\pi$
$311$	−134.356	+	97.6152i	−0.432012	+	0.313875i	0.350441	+	0.936585i	$0.386032\pi$
$312$		0			0
$313$	28.9379	+	89.0616i	0.0924533	+	0.284542i	0.986582	−	0.163269i	$-0.0522038\pi$
$313$	28.9379	+	89.0616i	0.0924533	+	0.284542i	−0.894128	+	0.447811i	$0.852204\pi$
$314$	−88.8259	+	28.8613i	−0.282885	+	0.0919149i
$315$		0			0
$316$	146.550	+	201.709i	0.463766	+	0.638319i
$317$	−46.2133	+	142.230i	−0.145783	+	0.448675i	−0.997111	−	0.0759598i	$-0.975798\pi$
$317$	−46.2133	+	142.230i	−0.145783	+	0.448675i	0.851328	+	0.524634i	$0.175798\pi$
$318$		0			0
$319$	−249.651	−	104.802i	−0.782606	−	0.328532i
$320$	59.3006			0.185314
$321$		0			0
$322$	−209.726	+	152.375i	−0.651322	+	0.473213i
$323$	−13.9097	−	10.1060i	−0.0430641	−	0.0312879i
$324$		0			0
$325$	−519.090	+	168.663i	−1.59720	+	0.518962i
$326$	−79.8175	+	109.859i	−0.244839	+	0.336992i
$327$		0			0
$328$	65.4599	−	201.465i	0.199573	−	0.614222i
$329$			39.4895i			0.120029i
$330$		0			0
$331$	−271.711			−0.820880			−0.410440	−	0.911888i	$-0.634625\pi$
$331$	−271.711			−0.820880			−0.410440	+	0.911888i	$0.634625\pi$
$332$	−69.1371	−	22.4640i	−0.208244	−	0.0676627i
$333$		0			0
$334$	270.357	+	196.426i	0.809451	+	0.588100i
$335$	−11.5227	−	35.4632i	−0.0343961	−	0.105860i
$336$		0			0
$337$	294.136	−	404.843i	0.872807	−	1.20132i	−0.105555	−	0.994413i	$-0.533662\pi$
$337$	294.136	−	404.843i	0.872807	−	1.20132i	0.978362	−	0.206902i	$-0.0663380\pi$
$338$	−45.1411	−	62.1314i	−0.133554	−	0.183821i
$339$		0			0
$340$			41.3192i			0.121527i
$341$	−239.117	−	19.9629i	−0.701222	−	0.0585422i
$342$		0			0
$343$	213.633	+	69.4137i	0.622838	+	0.202372i
$344$	137.940	−	100.219i	0.400987	−	0.291334i
$345$		0			0
$346$	52.0806	+	160.288i	0.150522	+	0.463259i
$347$	230.849	−	75.0075i	0.665272	−	0.216160i	0.0431362	−	0.999069i	$-0.486265\pi$
$347$	230.849	−	75.0075i	0.665272	−	0.216160i	0.622136	+	0.782909i	$0.286265\pi$
$348$		0			0
$349$	−262.931	−	361.893i	−0.753383	−	1.03694i	−0.997736	−	0.0672560i	$-0.978576\pi$
$349$	−262.931	−	361.893i	−0.753383	−	1.03694i	0.244353	−	0.969686i	$-0.421424\pi$
$350$	−88.4958	+	272.362i	−0.252845	+	0.778178i
$351$		0			0
$352$	−365.214	+	85.8462i	−1.03754	+	0.243881i
$353$	226.910			0.642805			0.321403	−	0.946943i	$-0.395846\pi$
$353$	226.910			0.642805			0.321403	+	0.946943i	$0.395846\pi$
$354$		0			0
$355$	41.2475	−	29.9681i	0.116190	−	0.0844171i
$356$	117.881	+	85.6459i	0.331128	+	0.240578i
$357$		0			0
$358$	429.827	−	139.659i	1.20063	−	0.390110i
$359$	−377.742	+	519.917i	−1.05221	+	1.44824i	−0.165324	+	0.986239i	$0.552867\pi$
$359$	−377.742	+	519.917i	−1.05221	+	1.44824i	−0.886881	+	0.461997i	$0.847133\pi$
$360$		0			0
$361$	89.3854	−	275.100i	0.247605	−	0.762050i
$362$		−	131.941i		−	0.364478i
$363$		0			0
$364$	69.2524			0.190254
$365$	−48.8471	−	15.8714i	−0.133828	−	0.0434832i
$366$		0			0
$367$	580.779	+	421.960i	1.58250	+	1.14976i	0.913755	+	0.406267i	$0.133170\pi$
$367$	580.779	+	421.960i	1.58250	+	1.14976i	0.668748	+	0.743489i	$0.266830\pi$
$368$	257.131	+	791.369i	0.698726	+	2.15046i
$369$		0			0
$370$	−201.177	+	276.896i	−0.543721	+	0.748368i
$371$	−71.0523	−	97.7951i	−0.191516	−	0.263599i
$372$		0			0
$373$			18.1857i			0.0487552i	0.999703	+	0.0243776i	$0.00776040\pi$
$373$			18.1857i			0.0487552i	−0.999703	+	0.0243776i	$0.992240\pi$
$374$	−12.9355	−	55.0311i	−0.0345868	−	0.147142i
$375$		0			0
$376$	61.9572	+	20.1311i	0.164780	+	0.0535402i
$377$	234.492	−	170.369i	0.621996	−	0.451906i
$378$		0			0
$379$	−48.1193	−	148.096i	−0.126964	−	0.390755i	0.867290	−	0.497803i	$-0.165860\pi$
$379$	−48.1193	−	148.096i	−0.126964	−	0.390755i	−0.994254	+	0.107049i	$0.965860\pi$
$380$	163.975	−	53.2786i	0.431512	−	0.140207i
$381$		0			0
$382$	−533.247	−	733.952i	−1.39594	−	1.92134i
$383$	222.614	−	685.137i	0.581239	−	1.78887i	−0.0326387	−	0.999467i	$-0.510391\pi$
$383$	222.614	−	685.137i	0.581239	−	1.78887i	0.613877	−	0.789401i	$-0.289609\pi$
$384$		0			0
$385$	18.8652	−	225.969i	0.0490005	−	0.586931i
$386$	541.542			1.40296
$387$		0			0
$388$	71.5286	−	51.9685i	0.184352	−	0.133940i
$389$	7.19093	+	5.22452i	0.0184857	+	0.0134306i	0.596990	−	0.802249i	$-0.296363\pi$
$389$	7.19093	+	5.22452i	0.0184857	+	0.0134306i	−0.578504	+	0.815680i	$0.696363\pi$
$390$		0			0
$391$	−80.9995	+	26.3183i	−0.207160	+	0.0673103i
$392$	101.860	−	140.199i	0.259848	−	0.357650i
$393$		0			0
$394$	−216.375	+	665.933i	−0.549175	+	1.69019i
$395$			873.939i			2.21250i
$396$		0			0
$397$	513.254			1.29283			0.646416	−	0.762985i	$-0.276267\pi$
$397$	513.254			1.29283			0.646416	+	0.762985i	$0.276267\pi$
$398$	189.759	+	61.6564i	0.476781	+	0.154915i
$399$		0			0
$400$	743.664	+	540.304i	1.85916	+	1.35076i
$401$	−169.595	−	521.961i	−0.422931	−	1.30165i	−0.904961	−	0.425494i	$-0.860100\pi$
$401$	−169.595	−	521.961i	−0.422931	−	1.30165i	0.482030	−	0.876155i	$-0.339900\pi$
$402$		0			0
$403$	150.983	−	207.811i	0.374648	−	0.515659i
$404$	−200.788	−	276.361i	−0.496999	−	0.684061i
$405$		0			0
$406$		−	152.081i		−	0.374584i
$407$	68.1431	−	162.325i	0.167428	−	0.398834i
$408$		0			0
$409$	−481.308	−	156.386i	−1.17679	−	0.382363i	−0.345618	−	0.938375i	$-0.612331\pi$
$409$	−481.308	−	156.386i	−1.17679	−	0.382363i	−0.831174	+	0.556013i	$0.812331\pi$
$410$	−910.333	+	661.396i	−2.22032	+	1.61316i
$411$		0			0
$412$	−29.0581	−	89.4317i	−0.0705294	−	0.217067i
$413$	46.2629	−	15.0317i	0.112017	−	0.0363964i
$414$		0			0
$415$	−149.774	−	206.147i	−0.360902	−	0.496739i
$416$	124.108	−	381.965i	0.298337	−	0.918185i
$417$		0			0
$418$	−201.711	+	122.293i	−0.482561	+	0.292568i
$419$	111.580			0.266300			0.133150	−	0.991096i	$-0.457491\pi$
$419$	111.580			0.266300			0.133150	+	0.991096i	$0.457491\pi$
$420$		0			0
$421$	−302.005	+	219.420i	−0.717352	+	0.521187i	−0.885537	−	0.464569i	$-0.846209\pi$
$421$	−302.005	+	219.420i	−0.717352	+	0.521187i	0.168185	+	0.985755i	$0.446209\pi$
$422$	−448.495	−	325.851i	−1.06278	−	0.772158i
$423$		0			0
$424$	−189.658	+	61.6235i	−0.447306	+	0.145338i
$425$	−55.3020	+	76.1167i	−0.130122	+	0.179098i
$426$		0			0
$427$	−89.6710	+	275.979i	−0.210002	+	0.646321i
$428$			281.041i			0.656637i
$429$		0			0
$430$	−905.693			−2.10626
$431$	74.2514	+	24.1257i	0.172277	+	0.0559762i	0.393885	−	0.919160i	$-0.371131\pi$
$431$	74.2514	+	24.1257i	0.172277	+	0.0559762i	−0.221608	+	0.975136i	$0.571131\pi$
$432$		0			0
$433$	−575.600	−	418.198i	−1.32933	−	0.965816i	−0.999765	−	0.0216834i	$-0.993097\pi$
$433$	−575.600	−	418.198i	−1.32933	−	0.965816i	−0.329567	−	0.944132i	$-0.606903\pi$
$434$	−41.6482	−	128.180i	−0.0959637	−	0.295346i
$435$		0			0
$436$	115.111	−	158.437i	0.264016	−	0.363387i
$437$	208.888	+	287.509i	0.478004	+	0.657916i
$438$		0			0
$439$		−	262.674i		−	0.598347i	−0.954199	−	0.299173i	$-0.903289\pi$
$439$		−	262.674i		−	0.598347i	0.954199	−	0.299173i	$-0.0967109\pi$
$440$	−344.918	−	144.794i	−0.783904	−	0.329077i
$441$		0			0
$442$	57.5552	+	18.7008i	0.130215	+	0.0423096i
$443$	−427.731	+	310.765i	−0.965533	+	0.701501i	−0.954429	−	0.298438i	$-0.903534\pi$
$443$	−427.731	+	310.765i	−0.965533	+	0.701501i	−0.0111036	+	0.999938i	$0.503534\pi$
$444$		0			0
$445$	157.828	+	485.745i	0.354670	+	1.09156i
$446$	504.560	−	163.942i	1.13130	−	0.367582i
$447$		0			0
$448$	−10.0704	−	13.8607i	−0.0224786	−	0.0309391i
$449$	88.9372	−	273.721i	0.198078	−	0.609623i	−0.801848	−	0.597528i	$-0.796150\pi$
$449$	88.9372	−	273.721i	0.198078	−	0.609623i	0.999927	−	0.0120953i	$-0.00385015\pi$
$450$		0			0
$451$	377.976	−	438.318i	0.838085	−	0.971880i
$452$	−184.219			−0.407565
$453$		0			0
$454$	170.703	−	124.023i	0.375998	−	0.273178i
$455$	196.384	+	142.681i	0.431613	+	0.313585i
$456$		0			0
$457$	786.473	−	255.540i	1.72095	−	0.559169i	0.728853	−	0.684670i	$-0.240054\pi$
$457$	786.473	−	255.540i	1.72095	−	0.559169i	0.992094	+	0.125501i	$0.0400537\pi$
$458$	492.068	−	677.274i	1.07439	−	1.47876i
$459$		0			0
$460$	263.918	−	812.255i	0.573734	−	1.76577i
$461$		−	325.354i		−	0.705756i	−0.935669	−	0.352878i	$-0.885203\pi$
$461$		−	325.354i		−	0.705756i	0.935669	−	0.352878i	$-0.114797\pi$
$462$		0			0
$463$	−711.656			−1.53705			−0.768527	−	0.639818i	$-0.779010\pi$
$463$	−711.656			−1.53705			−0.768527	+	0.639818i	$0.779010\pi$
$464$	−464.259	−	150.847i	−1.00056	−	0.325101i
$465$		0			0
$466$	338.799	+	246.152i	0.727037	+	0.528224i
$467$	−141.566	−	435.697i	−0.303140	−	0.932970i	−0.980365	−	0.197193i	$-0.936817\pi$
$467$	−141.566	−	435.697i	−0.303140	−	0.932970i	0.677225	−	0.735776i	$-0.263183\pi$
$468$		0			0
$469$	−6.33226	+	8.71560i	−0.0135016	+	0.0185834i
$470$	−203.402	−	279.958i	−0.432769	−	0.595656i
$471$		0			0
$472$		−	80.2474i		−	0.170016i
$473$	453.498	−	106.598i	0.958769	−	0.225366i
$474$		0			0
$475$	373.377	+	121.317i	0.786056	+	0.255405i
$476$	9.65780	−	7.01680i	0.0202895	−	0.0147412i
$477$		0			0
$478$	140.782	+	433.282i	0.294523	+	0.906447i
$479$	−563.437	+	183.072i	−1.17628	+	0.382196i	−0.830983	−	0.556298i	$-0.812221\pi$
$479$	−563.437	+	183.072i	−1.17628	+	0.382196i	−0.345295	+	0.938494i	$0.612221\pi$
$480$		0			0
$481$	110.775	+	152.469i	0.230302	+	0.316983i
$482$	−177.307	+	545.694i	−0.367857	+	1.13215i
$483$		0			0
$484$	−287.551	−	48.3500i	−0.594114	−	0.0998966i
$485$	309.910			0.638990
$486$		0			0
$487$	−354.198	+	257.340i	−0.727307	+	0.528419i	−0.888710	−	0.458469i	$-0.848398\pi$
$487$	−354.198	+	257.340i	−0.727307	+	0.528419i	0.161403	+	0.986889i	$0.448398\pi$
$488$	387.286	+	281.380i	0.793619	+	0.576598i
$489$		0			0
$490$	−875.472	+	284.458i	−1.78668	+	0.580527i
$491$	−455.377	+	626.773i	−0.927449	+	1.27652i	0.0333976	+	0.999442i	$0.489367\pi$
$491$	−455.377	+	626.773i	−0.927449	+	1.27652i	−0.960846	+	0.277082i	$0.910633\pi$
$492$		0			0
$493$	15.4397	−	47.5186i	0.0313179	−	0.0963866i
$494$		−	252.521i		−	0.511175i
$495$		0			0
$496$	−432.607			−0.872191
$497$	−14.0093	−	4.55188i	−0.0281876	−	0.00915872i
$498$		0			0
$499$	−212.052	−	154.065i	−0.424953	−	0.308747i	0.354674	−	0.934990i	$-0.384592\pi$
$499$	−212.052	−	154.065i	−0.424953	−	0.308747i	−0.779628	+	0.626243i	$0.784592\pi$
$500$	−134.297	−	413.323i	−0.268593	−	0.826646i
$501$		0			0
$502$	117.753	−	162.073i	0.234568	−	0.322855i
$503$	90.2264	+	124.186i	0.179377	+	0.246891i	0.889232	−	0.457457i	$-0.151240\pi$
$503$	90.2264	+	124.186i	0.179377	+	0.246891i	−0.709855	+	0.704348i	$0.751240\pi$
$504$		0			0
$505$		−	1197.38i		−	2.37105i
$506$	−97.2133	+	1164.43i	−0.192121	+	2.30124i
$507$		0			0
$508$	−48.2720	−	15.6845i	−0.0950237	−	0.0308751i
$509$	−633.283	+	460.107i	−1.24417	+	0.903943i	−0.997869	−	0.0652505i	$-0.979215\pi$
$509$	−633.283	+	460.107i	−1.24417	+	0.903943i	−0.246302	+	0.969193i	$0.579215\pi$
$510$		0			0
$511$	4.58546	+	14.1126i	0.00897350	+	0.0276176i
$512$	−339.548	+	110.326i	−0.663180	+	0.215480i
$513$		0			0
$514$	444.256	+	611.466i	0.864311	+	1.18962i
$515$	101.855	−	313.477i	0.197776	−	0.608693i
$516$		0			0
$517$	134.798	+	116.241i	0.260730	+	0.224837i
$518$	98.8844			0.190897
$519$		0			0
$520$	323.974	−	235.381i	0.623027	−	0.452656i
$521$	−146.048	−	106.110i	−0.280323	−	0.203667i	0.438735	−	0.898616i	$-0.355427\pi$
$521$	−146.048	−	106.110i	−0.280323	−	0.203667i	−0.719058	+	0.694950i	$0.755427\pi$
$522$		0			0
$523$	144.402	−	46.9189i	0.276103	−	0.0897112i	−0.167693	−	0.985839i	$-0.553632\pi$
$523$	144.402	−	46.9189i	0.276103	−	0.0897112i	0.443795	+	0.896128i	$0.353632\pi$
$524$	151.344	−	208.308i	0.288825	−	0.397533i
$525$		0			0
$526$	−47.1985	+	145.262i	−0.0897309	+	0.276163i
$527$		−	44.2788i		−	0.0840206i
$528$		0			0
$529$	1231.39			2.32778
$530$	1007.44	+	327.338i	1.90083	+	0.617618i
$531$		0			0
$532$	−40.2992	−	29.2791i	−0.0757504	−	0.0550359i
$533$	191.465	+	589.269i	0.359222	+	1.10557i
$534$		0			0
$535$	−579.031	+	796.968i	−1.08230	+	1.48966i
$536$	10.4463	+	14.3781i	0.0194894	+	0.0268248i
$537$		0			0
$538$			496.155i			0.922222i
$539$	404.886	−	245.475i	0.751179	−	0.455426i
$540$		0			0
$541$	−273.764	−	88.9514i	−0.506034	−	0.164420i	0.0448639	−	0.998993i	$-0.485715\pi$
$541$	−273.764	−	88.9514i	−0.506034	−	0.164420i	−0.550898	+	0.834573i	$0.685715\pi$
$542$	697.425	−	506.709i	1.28676	−	0.934887i
$543$		0			0
$544$	−21.3937	−	65.8430i	−0.0393266	−	0.121035i
$545$	652.857	−	212.126i	1.19790	−	0.389222i
$546$		0			0
$547$	71.9684	+	99.0560i	0.131569	+	0.181090i	0.869719	−	0.493548i	$-0.164300\pi$
$547$	71.9684	+	99.0560i	0.131569	+	0.181090i	−0.738150	+	0.674637i	$0.764300\pi$
$548$	88.7522	−	273.151i	0.161956	−	0.498451i
$549$		0			0
$550$	669.215	+	1103.80i	1.21675	+	2.00691i
$551$	−208.485			−0.378376
$552$		0			0
$553$	204.271	−	148.412i	0.369387	−	0.268376i
$554$	−718.411	−	521.956i	−1.29677	−	0.942159i
$555$		0			0
$556$	−17.0155	+	5.52869i	−0.0306035	+	0.00994368i
$557$	−329.379	+	453.352i	−0.591345	+	0.813917i	−0.994882	−	0.101047i	$-0.967781\pi$
$557$	−329.379	+	453.352i	−0.591345	+	0.813917i	0.403536	+	0.914964i	$0.367781\pi$
$558$		0			0
$559$	−154.109	+	474.299i	−0.275687	+	0.848477i
$560$		−	408.819i		−	0.730034i
$561$		0			0
$562$	1034.07			1.83999
$563$	−438.838	−	142.587i	−0.779464	−	0.253263i	−0.107853	−	0.994167i	$-0.534397\pi$
$563$	−438.838	−	142.587i	−0.779464	−	0.253263i	−0.671611	+	0.740904i	$0.734397\pi$
$564$		0			0
$565$	−522.404	−	379.549i	−0.924609	−	0.671768i
$566$	251.260	+	773.300i	0.443923	+	1.36625i
$567$		0			0
$568$	−14.2834	+	19.6594i	−0.0251468	+	0.0346117i
$569$	500.191	+	688.453i	0.879070	+	1.20994i	0.976678	+	0.214711i	$0.0688808\pi$
$569$	500.191	+	688.453i	0.879070	+	1.20994i	−0.0976081	+	0.995225i	$0.531119\pi$
$570$		0			0
$571$			558.153i			0.977500i	0.872424	+	0.488750i	$0.162547\pi$
$571$			558.153i			0.977500i	−0.872424	+	0.488750i	$0.837453\pi$
$572$	203.850	−	236.393i	0.356381	−	0.413275i
$573$		0			0
$574$	309.184	+	100.460i	0.538649	+	0.175018i
$575$	1573.31	−	1143.08i	2.73619	−	1.98796i
$576$		0			0
$577$	328.715	+	1011.68i	0.569697	+	1.75335i	0.653565	+	0.756870i	$0.273272\pi$
$577$	328.715	+	1011.68i	0.569697	+	1.75335i	−0.0838684	+	0.996477i	$0.526728\pi$
$578$	−685.947	+	222.878i	−1.18676	+	0.385601i
$579$		0			0
$580$	294.501	+	405.345i	0.507760	+	0.698871i
$581$	−22.7494	+	70.0154i	−0.0391556	+	0.120509i
$582$		0			0
$583$	−542.972	−	45.3306i	−0.931342	−	0.0777540i
$584$	24.4796			0.0419172
$585$		0			0
$586$	772.326	−	561.128i	1.31796	−	0.957556i
$587$	−111.426	−	80.9556i	−0.189822	−	0.137914i	0.488815	−	0.872387i	$-0.337429\pi$
$587$	−111.426	−	80.9556i	−0.189822	−	0.137914i	−0.678638	+	0.734473i	$0.737429\pi$
$588$		0			0
$589$	−175.720	+	57.0948i	−0.298336	+	0.0969352i
$590$	−250.553	+	344.857i	−0.424666	+	0.584503i
$591$		0			0
$592$	98.0820	−	301.865i	0.165679	−	0.509908i
$593$		−	42.1576i		−	0.0710921i	−0.999368	−	0.0355461i	$-0.988683\pi$
$593$		−	42.1576i		−	0.0710921i	0.999368	−	0.0355461i	$-0.0113170\pi$
$594$		0			0
$595$	41.8441			0.0703263
$596$	323.757	+	105.195i	0.543216	+	0.176502i
$597$		0			0
$598$	−1011.98	−	735.244i	−1.69227	−	1.22950i
$599$	99.8140	+	307.196i	0.166634	+	0.512848i	0.999153	−	0.0411491i	$-0.0131019\pi$
$599$	99.8140	+	307.196i	0.166634	+	0.512848i	−0.832519	+	0.553997i	$0.813102\pi$
$600$		0			0
$601$	401.291	−	552.330i	0.667706	−	0.919018i	−0.332000	−	0.943279i	$-0.607723\pi$
$601$	401.291	−	552.330i	0.667706	−	0.919018i	0.999706	+	0.0242612i	$0.00772333\pi$
$602$	153.804	+	211.693i	0.255489	+	0.351650i
$603$		0			0
$604$			153.585i			0.254280i
$605$	−715.814	−	729.554i	−1.18316	−	1.20587i
$606$		0			0
$607$	209.112	+	67.9445i	0.344500	+	0.111935i	0.476157	−	0.879361i	$-0.342030\pi$
$607$	209.112	+	67.9445i	0.344500	+	0.111935i	−0.131656	+	0.991295i	$0.542030\pi$
$608$	−233.711	+	169.801i	−0.384393	+	0.279278i
$609$		0			0
$610$	−785.790	−	2418.41i	−1.28818	−	3.96461i
$611$	−181.220	+	58.8820i	−0.296596	+	0.0963699i
$612$		0			0
$613$	116.415	+	160.231i	0.189910	+	0.261389i	0.893346	−	0.449370i	$-0.148352\pi$
$613$	116.415	+	160.231i	0.189910	+	0.261389i	−0.703436	+	0.710759i	$0.748352\pi$
$614$	−395.852	+	1218.31i	−0.644709	+	1.98421i
$615$		0			0
$616$	24.7301	+	105.209i	0.0401462	+	0.170793i
$617$	−666.299			−1.07990			−0.539951	−	0.841697i	$-0.681557\pi$
$617$	−666.299			−1.07990			−0.539951	+	0.841697i	$0.681557\pi$
$618$		0			0
$619$	−409.934	+	297.834i	−0.662252	+	0.481154i	−0.867423	−	0.497572i	$-0.834225\pi$
$619$	−409.934	+	297.834i	−0.662252	+	0.481154i	0.205171	+	0.978726i	$0.434225\pi$
$620$	359.223	+	260.991i	0.579392	+	0.420953i
$621$		0			0
$622$	−399.878	+	129.928i	−0.642891	+	0.208888i
$623$	86.7339	−	119.379i	0.139220	−	0.191620i
$624$		0			0
$625$	112.663	−	346.742i	0.180261	−	0.554787i
$626$			237.087i			0.378733i
$627$		0			0
$628$	−88.8984			−0.141558
$629$	30.8970	+	10.0390i	0.0491208	+	0.0159603i
$630$		0			0
$631$	−615.691	−	447.325i	−0.975738	−	0.708915i	−0.0189857	−	0.999820i	$-0.506044\pi$
$631$	−615.691	−	447.325i	−0.975738	−	0.708915i	−0.956752	+	0.290905i	$0.906044\pi$
$632$	−128.717	−	396.151i	−0.203666	−	0.626821i
$633$		0			0
$634$	−222.549	+	306.313i	−0.351024	+	0.483143i
$635$	−104.574	−	143.933i	−0.164683	−	0.226666i
$636$		0			0
$637$			506.875i			0.795722i
$638$	−519.130	−	447.663i	−0.813683	−	0.701667i
$639$		0			0
$640$	−953.178	−	309.706i	−1.48934	−	0.483916i
$641$	164.241	−	119.328i	0.256227	−	0.186160i	−0.452255	−	0.891889i	$-0.649380\pi$
$641$	164.241	−	119.328i	0.256227	−	0.186160i	0.708482	+	0.705729i	$0.249380\pi$
$642$		0			0
$643$	−140.650	−	432.877i	−0.218741	−	0.673215i	−0.998867	−	0.0475925i	$-0.984845\pi$
$643$	−140.650	−	432.877i	−0.218741	−	0.673215i	0.780126	−	0.625622i	$-0.215155\pi$
$644$	−234.672	+	76.2495i	−0.364397	+	0.118400i
$645$		0			0
$646$	−25.5859	−	35.2160i	−0.0396067	−	0.0545140i
$647$	−165.477	+	509.287i	−0.255761	+	0.787151i	0.737918	+	0.674890i	$0.235809\pi$
$647$	−165.477	+	509.287i	−0.255761	+	0.787151i	−0.993679	+	0.112260i	$0.964191\pi$
$648$		0			0
$649$	84.8678	−	202.166i	0.130767	−	0.311504i
$650$	−1381.84			−2.12591
$651$		0			0
$652$	−104.568	+	75.9730i	−0.160380	+	0.116523i
$653$	−670.730	−	487.314i	−1.02715	−	0.746269i	−0.0594144	−	0.998233i	$-0.518923\pi$
$653$	−670.730	−	487.314i	−1.02715	−	0.746269i	−0.967736	+	0.251965i	$0.918923\pi$
$654$		0			0
$655$	858.356	−	278.897i	1.31047	−	0.425797i
$656$	613.351	−	844.205i	0.934986	−	1.28690i
$657$		0			0
$658$	−30.8949	+	95.0847i	−0.0469527	+	0.144506i
$659$		−	1089.67i		−	1.65353i	−0.562551	−	0.826763i	$-0.690180\pi$
$659$		−	1089.67i		−	1.65353i	0.562551	−	0.826763i	$-0.309820\pi$
$660$		0			0
$661$	−920.151			−1.39206			−0.696029	−	0.718013i	$-0.745052\pi$
$661$	−920.151			−1.39206			−0.696029	+	0.718013i	$0.745052\pi$
$662$	−654.239	−	212.575i	−0.988277	−	0.321111i
$663$		0			0
$664$	98.2538	+	71.3856i	0.147973	+	0.107508i
$665$	−53.9554	−	166.058i	−0.0811360	−	0.249711i
$666$		0			0
$667$	−607.030	+	835.505i	−0.910090	+	1.25263i
$668$	186.964	+	257.334i	0.279887	+	0.385231i
$669$		0			0
$670$		−	94.4048i		−	0.140903i
$671$	678.102	+	1118.46i	1.01058	+	1.66685i
$672$		0			0
$673$	614.204	+	199.567i	0.912636	+	0.296533i	0.727442	−	0.686169i	$-0.240709\pi$
$673$	614.204	+	199.567i	0.912636	+	0.296533i	0.185193	+	0.982702i	$0.440709\pi$
$674$	1024.97	−	744.682i	1.52072	−	1.10487i
$675$		0			0
$676$	−22.5890	−	69.5218i	−0.0334157	−	0.102843i
$677$	701.518	−	227.937i	1.03622	−	0.336687i	0.258971	−	0.965885i	$-0.416617\pi$
$677$	701.518	−	227.937i	1.03622	−	0.336687i	0.777245	+	0.629198i	$0.216617\pi$
$678$		0			0
$679$	−52.6287	−	72.4372i	−0.0775092	−	0.106682i
$680$	21.3315	−	65.6516i	0.0313698	−	0.0965464i
$681$		0			0
$682$	−560.139	−	235.142i	−0.821318	−	0.344783i
$683$	−527.576			−0.772440			−0.386220	−	0.922407i	$-0.626219\pi$
$683$	−527.576			−0.772440			−0.386220	+	0.922407i	$0.626219\pi$
$684$		0			0
$685$	814.457	−	591.738i	1.18899	−	0.863851i
$686$	460.091	+	334.275i	0.670686	+	0.487282i
$687$		0			0
$688$	798.794	−	259.544i	1.16104	−	0.377244i
$689$	342.844	−	471.885i	0.497597	−	0.684883i
$690$		0			0
$691$	−159.667	+	491.405i	−0.231067	+	0.711151i	0.766552	+	0.642182i	$0.221971\pi$
$691$	−159.667	+	491.405i	−0.231067	+	0.711151i	−0.997619	+	0.0689685i	$0.978029\pi$
$692$			160.419i			0.231819i
$693$		0			0
$694$	614.533			0.885494
$695$	−59.6431	−	19.3792i	−0.0858174	−	0.0278837i
$696$		0			0
$697$	86.4074	+	62.7786i	0.123970	+	0.0900698i
$698$	−349.967	−	1077.09i	−0.501386	−	1.54311i
$699$		0			0
$700$	−160.221	+	220.526i	−0.228887	+	0.315037i
$701$	−411.442	−	566.302i	−0.586936	−	0.807848i	0.407498	−	0.913206i	$-0.366401\pi$
$701$	−411.442	−	566.302i	−0.586936	−	0.807848i	−0.994434	+	0.105358i	$0.966401\pi$
$702$		0			0
$703$		−	135.559i		−	0.192829i
$704$	−76.9566	−	6.42480i	−0.109313	−	0.00912614i
$705$		0			0
$706$	546.365	+	177.525i	0.773888	+	0.251452i
$707$	−279.871	+	203.338i	−0.395858	+	0.287607i
$708$		0			0
$709$	−200.757	−	617.867i	−0.283155	−	0.871463i	−0.986945	−	0.161055i	$-0.948510\pi$
$709$	−200.757	−	617.867i	−0.283155	−	0.871463i	0.703790	−	0.710408i	$-0.251490\pi$
$710$	122.763	−	39.8883i	0.172906	−	0.0561807i
$711$		0			0
$712$	−143.085	−	196.939i	−0.200962	−	0.276600i
$713$	−282.822	+	870.436i	−0.396664	+	1.22081i
$714$		0			0
$715$	1065.12	−	250.364i	1.48967	−	0.350159i
$716$	430.178			0.600808
$717$		0			0
$718$	−1316.31	+	956.352i	−1.83329	+	1.33197i
$719$	561.880	+	408.230i	0.781474	+	0.567774i	0.905421	−	0.424515i	$-0.139555\pi$
$719$	561.880	+	408.230i	0.781474	+	0.567774i	−0.123947	+	0.992289i	$0.539555\pi$
$720$		0			0
$721$	−90.5678	+	29.4273i	−0.125614	+	0.0408145i
$722$	430.453	−	592.468i	0.596195	−	0.820592i
$723$		0			0
$724$	38.8082	−	119.439i	0.0536025	−	0.164972i
$725$			1140.87i			1.57362i
$726$		0			0
$727$	−970.108			−1.33440			−0.667200	−	0.744879i	$-0.732507\pi$
$727$	−970.108			−1.33440			−0.667200	+	0.744879i	$0.732507\pi$
$728$	−110.034	−	35.7523i	−0.151146	−	0.0491103i
$729$		0			0
$730$	−105.199	−	76.4317i	−0.144109	−	0.104701i
$731$	26.5652	+	81.7594i	0.0363410	+	0.111846i
$732$		0			0
$733$	−92.6359	+	127.502i	−0.126379	+	0.173946i	−0.867518	−	0.497406i	$-0.834286\pi$
$733$	−92.6359	+	127.502i	−0.126379	+	0.173946i	0.741139	+	0.671352i	$0.234286\pi$
$734$	1068.30	+	1470.39i	1.45545	+	2.00326i
$735$		0			0
$736$			1430.99i			1.94428i
$737$	11.1112	+	47.2703i	0.0150763	+	0.0641388i
$738$		0			0
$739$	−651.979	−	211.841i	−0.882244	−	0.286659i	−0.167355	−	0.985897i	$-0.553523\pi$
$739$	−651.979	−	211.841i	−0.882244	−	0.286659i	−0.714889	+	0.699238i	$0.753523\pi$
$740$	−263.559	+	191.487i	−0.356161	+	0.258766i
$741$		0			0
$742$	−94.5724	−	291.064i	−0.127456	−	0.392270i
$743$	−490.820	+	159.477i	−0.660592	+	0.214639i	−0.620079	−	0.784540i	$-0.712899\pi$
$743$	−490.820	+	159.477i	−0.660592	+	0.214639i	−0.0405134	+	0.999179i	$0.512899\pi$
$744$		0			0
$745$	701.367	+	965.349i	0.941432	+	1.29577i
$746$	−14.2277	+	43.7884i	−0.0190720	+	0.0586976i
$747$		0			0
$748$	4.47664	−	53.6215i	0.00598482	−	0.0716865i
$749$	284.611			0.379988
$750$		0			0
$751$	690.649	−	501.786i	0.919640	−	0.668157i	−0.0237947	−	0.999717i	$-0.507575\pi$
$751$	690.649	−	501.786i	0.919640	−	0.668157i	0.943434	+	0.331560i	$0.107575\pi$
$752$	259.621	+	188.626i	0.345241	+	0.250832i
$753$		0			0
$754$	697.911	−	226.765i	0.925612	−	0.300750i
$755$	−316.433	+	435.532i	−0.419116	+	0.576864i
$756$		0			0
$757$	−153.287	+	471.770i	−0.202493	+	0.623210i	0.797314	+	0.603565i	$0.206254\pi$
$757$	−153.287	+	471.770i	−0.202493	+	0.623210i	−0.999807	+	0.0196452i	$0.993746\pi$
$758$		−	394.239i		−	0.520104i
$759$		0			0
$760$	−288.043			−0.379004
$761$	1.23010	+	0.399683i	0.00161642	+	0.000525208i	0.309825	−	0.950794i	$-0.399729\pi$
$761$	1.23010	+	0.399683i	0.00161642	+	0.000525208i	−0.308209	+	0.951319i	$0.599729\pi$
$762$		0			0
$763$	−160.449	−	116.573i	−0.210287	−	0.152783i
$764$	−266.841	−	821.254i	−0.349269	−	1.07494i
$765$		0			0
$766$	1072.04	−	1475.54i	1.39953	−	1.92629i
$767$	137.963	+	189.890i	0.179874	+	0.247576i
$768$		0			0
$769$		−	398.342i		−	0.518000i	−0.965877	−	0.259000i	$-0.916607\pi$
$769$		−	398.342i		−	0.518000i	0.965877	−	0.259000i	$-0.0833929\pi$
$770$	222.213	−	529.339i	0.288588	−	0.687453i
$771$		0			0
$772$	490.229	+	159.285i	0.635012	+	0.206328i
$773$	−515.743	+	374.709i	−0.667196	+	0.484747i	−0.869086	−	0.494662i	$-0.835292\pi$
$773$	−515.743	+	374.709i	−0.667196	+	0.484747i	0.201889	+	0.979408i	$0.435292\pi$
$774$		0			0
$775$	312.435	+	961.575i	0.403142	+	1.24074i
$776$	−140.480	+	45.6448i	−0.181031	+	0.0588206i
$777$		0			0
$778$	13.2272	+	18.2057i	0.0170016	+	0.0234007i
$779$	137.719	−	423.855i	0.176789	−	0.544102i
$780$		0			0
$781$	−56.7753	+	34.4218i	−0.0726956	+	0.0440740i
$782$	−215.625			−0.275735
$783$		0			0
$784$	690.623	−	501.767i	0.880897	−	0.640009i
$785$	−252.096	−	183.158i	−0.321141	−	0.233323i
$786$		0			0
$787$	1018.20	−	330.835i	1.29378	−	0.420375i	0.420367	−	0.907354i	$-0.361901\pi$
$787$	1018.20	−	330.835i	1.29378	−	0.420375i	0.873413	+	0.486980i	$0.161901\pi$
$788$	−391.746	+	539.191i	−0.497139	+	0.684253i
$789$		0			0
$790$	−683.733	+	2104.31i	−0.865484	+	2.66369i
$791$			186.560i			0.235853i
$792$		0			0
$793$	−1400.19			−1.76569
$794$	1235.84	+	401.548i	1.55647	+	0.505728i
$795$		0			0
$796$	153.643	+	111.629i	0.193019	+	0.140237i
$797$	−113.056	−	347.952i	−0.141852	−	0.436577i	0.854740	−	0.519056i	$-0.173716\pi$
$797$	−113.056	−	347.952i	−0.141852	−	0.436577i	−0.996593	+	0.0824789i	$0.973716\pi$
$798$		0			0
$799$	−19.3066	+	26.5732i	−0.0241634	+	0.0332581i
$800$	929.186	+	1278.92i	1.16148	+	1.59864i
$801$		0			0
$802$		−	1389.49i		−	1.73253i
$803$	61.6711	+	25.8891i	0.0768009	+	0.0322405i
$804$		0			0
$805$	−822.574	−	267.271i	−1.02183	−	0.332013i
$806$	526.127	−	382.254i	0.652763	−	0.474260i
$807$		0			0
$808$	176.355	+	542.765i	0.218261	+	0.671739i
$809$	−168.019	+	54.5926i	−0.207687	+	0.0674816i	−0.411013	−	0.911629i	$-0.634825\pi$
$809$	−168.019	+	54.5926i	−0.207687	+	0.0674816i	0.203326	+	0.979111i	$0.434825\pi$
$810$		0			0
$811$	150.709	+	207.434i	0.185832	+	0.255775i	0.891761	−	0.452507i	$-0.149470\pi$
$811$	150.709	+	207.434i	0.185832	+	0.255775i	−0.705929	+	0.708282i	$0.749470\pi$
$812$	44.7320	−	137.671i	0.0550887	−	0.169546i
$813$		0			0
$814$	291.075	−	337.543i	0.357585	−	0.414671i
$815$	−453.058			−0.555900
$816$		0			0
$817$	290.207	−	210.847i	0.355210	−	0.258075i
$818$	−1036.57	−	753.109i	−1.26720	−	0.920672i
$819$		0			0
$820$	−1018.61	+	330.968i	−1.24221	+	0.403620i
$821$	551.722	−	759.381i	0.672013	−	0.924946i	−0.327791	−	0.944750i	$-0.606304\pi$
$821$	551.722	−	759.381i	0.672013	−	0.924946i	0.999804	+	0.0198041i	$0.00630424\pi$
$822$		0			0
$823$	172.552	−	531.062i	0.209663	−	0.645275i	−0.789827	−	0.613330i	$-0.789830\pi$
$823$	172.552	−	531.062i	0.209663	−	0.645275i	0.999490	−	0.0319455i	$-0.0101703\pi$
$824$			157.099i			0.190654i
$825$		0			0
$826$	123.154			0.149097
$827$	1261.70	+	409.950i	1.52563	+	0.495708i	0.947369	−	0.320144i	$-0.103731\pi$
$827$	1261.70	+	409.950i	1.52563	+	0.495708i	0.578262	+	0.815851i	$0.303731\pi$
$828$		0			0
$829$	727.620	+	528.647i	0.877709	+	0.637693i	0.932644	−	0.360797i	$-0.117495\pi$
$829$	727.620	+	528.647i	0.877709	+	0.637693i	−0.0549356	+	0.998490i	$0.517495\pi$
$830$	−199.354	−	613.547i	−0.240185	−	0.739214i
$831$		0			0
$832$	48.5920	−	66.8812i	0.0584039	−	0.0803861i
$833$	51.3577	+	70.6877i	0.0616538	+	0.0848592i
$834$		0			0
$835$			1114.95i			1.33527i
$836$	−218.568	+	51.3761i	−0.261445	+	0.0614547i
$837$		0			0
$838$	268.667	+	87.2953i	0.320605	+	0.104171i
$839$	229.444	−	166.701i	0.273473	−	0.198690i	−0.442592	−	0.896723i	$-0.645941\pi$
$839$	229.444	−	166.701i	0.273473	−	0.198690i	0.716066	+	0.698033i	$0.245941\pi$
$840$		0			0
$841$	72.6621	+	223.631i	0.0863996	+	0.265911i
$842$	−898.847	+	292.053i	−1.06751	+	0.346856i
$843$		0			0
$844$	−310.156	−	426.893i	−0.367483	−	0.505797i
$845$	79.1792	−	243.688i	0.0937032	−	0.288389i
$846$		0			0
$847$	−48.9642	+	291.204i	−0.0578090	+	0.343806i
$848$	−982.338			−1.15842
$849$		0			0
$850$	−192.709	+	140.012i	−0.226717	+	0.164719i
$851$	−543.253	−	394.696i	−0.638370	−	0.463803i
$852$		0			0
$853$	−419.377	+	136.264i	−0.491650	+	0.159747i	−0.544341	−	0.838864i	$-0.683220\pi$
$853$	−419.377	+	136.264i	−0.491650	+	0.159747i	0.0526910	+	0.998611i	$0.483220\pi$
$854$	−431.828	+	594.361i	−0.505654	+	0.695973i
$855$		0			0
$856$	145.090	−	446.542i	0.169498	−	0.521662i
$857$			1378.52i			1.60854i	0.594264	+	0.804270i	$0.297443\pi$
$857$			1378.52i			1.60854i	−0.594264	+	0.804270i	$0.702557\pi$
$858$		0			0
$859$	1387.60			1.61537			0.807685	−	0.589614i	$-0.200720\pi$
$859$	1387.60			1.61537			0.807685	+	0.589614i	$0.200720\pi$
$860$	−819.876	−	266.394i	−0.953344	−	0.309760i
$861$		0			0
$862$	159.911	+	116.182i	0.185512	+	0.134782i
$863$	159.131	+	489.755i	0.184393	+	0.567503i	0.999937	−	0.0111912i	$-0.00356233\pi$
$863$	159.131	+	489.755i	0.184393	+	0.567503i	−0.815544	+	0.578695i	$0.803562\pi$
$864$		0			0
$865$	−330.512	+	454.911i	−0.382095	+	0.525908i
$866$	−1058.78	−	1457.28i	−1.22261	−	1.68277i
$867$		0			0
$868$		−	128.285i		−	0.147794i
$869$	94.6851	−	1134.14i	0.108959	−	1.30511i
$870$		0			0
$871$	−49.4385	−	16.0635i	−0.0567606	−	0.0184426i
$872$	−264.693	+	192.311i	−0.303547	+	0.220540i
$873$		0			0
$874$	278.035	+	855.703i	0.318118	+	0.979065i
$875$	−418.574	+	136.003i	−0.478370	+	0.155432i
$876$		0			0
$877$	−436.200	−	600.377i	−0.497377	−	0.684581i	0.484350	−	0.874874i	$-0.339056\pi$
$877$	−436.200	−	600.377i	−0.497377	−	0.684581i	−0.981727	+	0.190293i	$0.939056\pi$
$878$	205.505	−	632.479i	0.234060	−	0.720364i
$879$		0			0
$880$	−1395.51	−	1203.39i	−1.58580	−	1.36749i
$881$	620.478			0.704288			0.352144	−	0.935946i	$-0.385453\pi$
$881$	620.478			0.704288			0.352144	+	0.935946i	$0.385453\pi$
$882$		0			0
$883$	−545.414	+	396.266i	−0.617683	+	0.448773i	−0.852111	−	0.523361i	$-0.824678\pi$
$883$	−545.414	+	396.266i	−0.617683	+	0.448773i	0.234429	+	0.972133i	$0.424678\pi$
$884$	46.6012	+	33.8577i	0.0527163	+	0.0383006i
$885$		0			0
$886$	−1273.04	+	413.636i	−1.43684	+	0.466858i
$887$	645.643	−	888.652i	0.727895	−	1.00186i	−0.271329	−	0.962487i	$-0.587463\pi$
$887$	645.643	−	888.652i	0.727895	−	1.00186i	0.999224	−	0.0393755i	$-0.0125368\pi$
$888$		0			0
$889$	−15.8838	+	48.8853i	−0.0178670	+	0.0549891i
$890$			1293.08i			1.45290i
$891$		0			0
$892$	504.973			0.566113
$893$	130.350	+	42.3533i	0.145969	+	0.0474281i
$894$		0			0
$895$	1219.89	+	886.301i	1.36300	+	0.990280i
$896$	89.4784	+	275.386i	0.0998643	+	0.307351i
$897$		0			0
$898$	428.295	−	589.497i	0.476943	−	0.656456i
$899$	−315.595	−	434.380i	−0.351051	−	0.483181i
$900$		0			0
$901$		−	100.546i		−	0.111594i
$902$	1253.03	−	759.690i	1.38917	−	0.842228i
$903$		0			0
$904$	292.704	+	95.1052i	0.323787	+	0.105205i
$905$	356.133	−	258.746i	0.393518	−	0.285907i
$906$		0			0
$907$	76.3752	+	235.059i	0.0842064	+	0.259161i	0.984291	−	0.176555i	$-0.0564953\pi$
$907$	76.3752	+	235.059i	0.0842064	+	0.259161i	−0.900084	+	0.435716i	$0.856495\pi$
$908$	191.008	−	62.0621i	0.210361	−	0.0683504i
$909$		0			0
$910$	361.235	+	497.197i	0.396962	+	0.546371i
$911$	−212.218	+	653.140i	−0.232951	+	0.716948i	0.764436	+	0.644700i	$0.223018\pi$
$911$	−212.218	+	653.140i	−0.232951	+	0.716948i	−0.997387	+	0.0722488i	$0.976982\pi$
$912$		0			0
$913$	172.033	+	283.751i	0.188426	+	0.310790i
$914$	2093.63			2.29062
$915$		0			0
$916$	644.652	−	468.367i	0.703769	−	0.511318i
$917$	−210.954	−	153.267i	−0.230048	−	0.167140i
$918$		0			0
$919$	−1412.55	+	458.966i	−1.53705	+	0.499419i	−0.950562	−	0.310536i	$-0.899491\pi$
$919$	−1412.55	+	458.966i	−1.53705	+	0.499419i	−0.586492	+	0.809955i	$0.699491\pi$
$920$	−838.671	+	1154.33i	−0.911599	+	1.25471i
$921$		0			0
$922$	254.543	−	783.402i	0.276077	−	0.849677i
$923$		−	71.0767i		−	0.0770062i
$924$		0			0
$925$	−741.807			−0.801953
$926$	−1713.56	−	556.769i	−1.85050	−	0.601262i
$927$		0			0
$928$	−679.167	−	493.444i	−0.731861	−	0.531728i
$929$	210.565	+	648.052i	0.226658	+	0.697580i	0.998119	+	0.0613042i	$0.0195260\pi$
$929$	210.565	+	648.052i	0.226658	+	0.697580i	−0.771462	+	0.636276i	$0.780474\pi$
$930$		0			0
$931$	214.301	−	294.960i	0.230183	−	0.316820i
$932$	234.296	+	322.481i	0.251390	+	0.346009i
$933$		0			0
$934$		−	1159.85i		−	1.24181i
$935$	123.172	−	142.835i	0.131734	−	0.152765i
$936$		0			0
$937$	84.2017	+	27.3588i	0.0898630	+	0.0291983i	0.353603	−	0.935395i	$-0.384956\pi$
$937$	84.2017	+	27.3588i	0.0898630	+	0.0291983i	−0.263740	+	0.964594i	$0.584956\pi$
$938$	−22.0658	+	16.0318i	−0.0235243	+	0.0170914i
$939$		0			0
$940$	−101.784	−	313.258i	−0.108281	−	0.333254i
$941$	553.577	−	179.868i	0.588286	−	0.191146i	0.000276616	−	1.00000i	$-0.499912\pi$
$941$	553.577	−	179.868i	0.588286	−	0.191146i	0.588009	+	0.808854i	$0.299912\pi$
$942$		0			0
$943$	−1297.62	−	1786.01i	−1.37605	−	1.89397i
$944$	122.155	−	375.954i	0.129401	−	0.398256i
$945$		0			0
$946$	1175.35	+	98.1254i	1.24244	+	0.103727i
$947$	912.836			0.963924			0.481962	−	0.876192i	$-0.339924\pi$
$947$	912.836			0.963924			0.481962	+	0.876192i	$0.339924\pi$
$948$		0			0
$949$	−57.9265	+	42.0860i	−0.0610395	+	0.0443478i
$950$	804.120	+	584.228i	0.846442	+	0.614976i
$951$		0			0
$952$	−18.9677	+	6.16296i	−0.0199240	+	0.00647370i
$953$	326.027	−	448.738i	0.342106	−	0.470869i	−0.602949	−	0.797780i	$-0.706008\pi$
$953$	326.027	−	448.738i	0.342106	−	0.470869i	0.945055	+	0.326911i	$0.106008\pi$
$954$		0			0
$955$	935.335	−	2878.67i	0.979409	−	3.01431i
$956$			433.636i			0.453594i
$957$		0			0
$958$	−1499.90			−1.56566
$959$	−276.621	−	89.8796i	−0.288447	−	0.0937223i
$960$		0			0
$961$	392.512	+	285.176i	0.408441	+	0.296750i
$962$	147.445	+	453.788i	0.153269	+	0.471713i
$963$		0			0
$964$	−321.013	+	441.837i	−0.333001	+	0.458337i
$965$	1062.00	+	1461.72i	1.10052	+	1.51474i
$966$		0			0
$967$		−	1781.13i		−	1.84191i	−0.389667	−	0.920956i	$-0.627410\pi$
$967$		−	1781.13i		−	1.84191i	0.389667	−	0.920956i	$-0.372590\pi$
$968$	431.925	+	225.274i	0.446204	+	0.232721i
$969$		0			0
$970$	746.216	+	242.460i	0.769295	+	0.249959i
$971$	−801.707	+	582.474i	−0.825651	+	0.599870i	−0.918325	−	0.395826i	$-0.870458\pi$
$971$	−801.707	+	582.474i	−0.825651	+	0.599870i	0.0926749	+	0.995696i	$0.470458\pi$
$972$		0			0
$973$	5.59892	+	17.2317i	0.00575429	+	0.0177099i
$974$	−1054.19	+	342.526i	−1.08233	+	0.351670i
$975$		0			0
$976$	1386.09	+	1907.78i	1.42017	+	1.95470i
$977$	−233.282	+	717.969i	−0.238774	+	0.734871i	0.757824	+	0.652459i	$0.226262\pi$
$977$	−233.282	+	717.969i	−0.238774	+	0.734871i	−0.996598	+	0.0824121i	$0.973738\pi$
$978$		0			0
$979$	−152.192	−	647.469i	−0.155457	−	0.661357i
$980$	−876.187			−0.894069
$981$		0			0
$982$	−1586.84	+	1152.91i	−1.61593	+	1.17404i
$983$	−167.072	−	121.385i	−0.169961	−	0.123484i	0.499553	−	0.866283i	$-0.333498\pi$
$983$	−167.072	−	121.385i	−0.169961	−	0.123484i	−0.669514	+	0.742799i	$0.733498\pi$
$984$		0			0
$985$	−2221.80	+	721.908i	−2.25564	+	0.732901i
$986$	74.3530	−	102.338i	0.0754087	−	0.103791i
$987$		0			0
$988$	74.2745	−	228.594i	0.0751767	−	0.231370i
$989$		−	1776.91i		−	1.79667i
$990$		0			0
$991$	852.133			0.859872			0.429936	−	0.902859i	$-0.358536\pi$
$991$	852.133			0.859872			0.429936	+	0.902859i	$0.358536\pi$
$992$	−707.562	−	229.901i	−0.713268	−	0.231755i
$993$		0			0
$994$	−30.1710	−	21.9205i	−0.0303531	−	0.0220528i
$995$	205.709	+	633.106i	0.206742	+	0.636288i
$996$		0			0
$997$	686.595	−	945.017i	0.688661	−	0.947861i	−0.311336	−	0.950300i	$-0.600776\pi$
$997$	686.595	−	945.017i	0.688661	−	0.947861i	0.999997	+	0.00243927i	$0.000776445\pi$
$998$	−390.055	−	536.864i	−0.390836	−	0.537940i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.c.46.3		16
3.2	odd	2		33.3.g.a.13.2	✓	16
11.4	even	5		1089.3.c.m.604.14		16
11.6	odd	10	inner	99.3.k.c.28.3		16
11.7	odd	10		1089.3.c.m.604.3		16
12.11	even	2		528.3.bf.b.145.1		16
33.2	even	10		363.3.g.a.118.2		16
33.5	odd	10		363.3.g.f.94.3		16
33.8	even	10		363.3.g.g.40.3		16
33.14	odd	10		363.3.g.a.40.2		16
33.17	even	10		33.3.g.a.28.2	yes	16
33.20	odd	10		363.3.g.g.118.3		16
33.26	odd	10		363.3.c.e.241.3		16
33.29	even	10		363.3.c.e.241.14		16
33.32	even	2		363.3.g.f.112.3		16
132.83	odd	10		528.3.bf.b.193.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.13.2	✓	16	3.2	odd	2
33.3.g.a.28.2	yes	16	33.17	even	10
99.3.k.c.28.3		16	11.6	odd	10	inner
99.3.k.c.46.3		16	1.1	even	1	trivial
363.3.c.e.241.3		16	33.26	odd	10
363.3.c.e.241.14		16	33.29	even	10
363.3.g.a.40.2		16	33.14	odd	10
363.3.g.a.118.2		16	33.2	even	10
363.3.g.f.94.3		16	33.5	odd	10
363.3.g.f.112.3		16	33.32	even	2
363.3.g.g.40.3		16	33.8	even	10
363.3.g.g.118.3		16	33.20	odd	10
528.3.bf.b.145.1		16	12.11	even	2
528.3.bf.b.193.1		16	132.83	odd	10
1089.3.c.m.604.3		16	11.7	odd	10
1089.3.c.m.604.14		16	11.4	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.40785 + 0.782357i) q^{2} +(1.94958 + 1.41645i) q^{4} +(2.61024 + 8.03348i) q^{5} +(1.43445 - 1.97435i) q^{7} +(-2.36641 - 3.25708i) q^{8} +O(q^{10})\)	\(q+(2.40785 + 0.782357i) q^{2} +(1.94958 + 1.41645i) q^{4} +(2.61024 + 8.03348i) q^{5} +(1.43445 - 1.97435i) q^{7} +(-2.36641 - 3.25708i) q^{8} +21.3855i q^{10} +(-2.51703 - 10.7082i) q^{11} +(11.1993 + 3.63888i) q^{13} +(4.99858 - 3.63168i) q^{14} +(-6.12844 - 18.8614i) q^{16} +(1.93053 - 0.627268i) q^{17} +(-4.97861 - 6.85246i) q^{19} +(-6.29019 + 19.3592i) q^{20} +(2.31697 - 27.7528i) q^{22} -41.9571 q^{23} +(-37.4981 + 27.2440i) q^{25} +(24.1193 + 17.5237i) q^{26} +(5.59314 - 1.81732i) q^{28} +(14.4679 - 19.9133i) q^{29} +(6.74074 - 20.7459i) q^{31} -34.1061i q^{32} +5.13918 q^{34} +(19.6051 + 6.37010i) q^{35} +(12.9478 + 9.40714i) q^{37} +(-6.62665 - 20.3947i) q^{38} +(19.9888 - 27.5122i) q^{40} +(30.9272 + 42.5677i) q^{41} +42.3507i q^{43} +(10.2604 - 24.4417i) q^{44} +(-101.026 - 32.8254i) q^{46} +(-13.0910 + 9.51117i) q^{47} +(13.3014 + 40.9376i) q^{49} +(-111.604 + 36.2624i) q^{50} +(16.6797 + 22.9576i) q^{52} +(15.3065 - 47.1085i) q^{53} +(79.4537 - 48.1714i) q^{55} -9.82509 q^{56} +(50.4158 - 36.6292i) q^{58} +(16.1257 + 11.7160i) q^{59} +(-113.086 + 36.7440i) q^{61} +(32.4614 - 44.6792i) q^{62} +(2.16942 - 6.67679i) q^{64} +99.4678i q^{65} -4.41442 q^{67} +(4.65223 + 1.51160i) q^{68} +(42.2225 + 30.6764i) q^{70} +(-1.86520 - 5.74049i) q^{71} +(-3.57399 + 4.91917i) q^{73} +(23.8166 + 32.7808i) q^{74} -20.4114i q^{76} +(-24.7522 - 10.3908i) q^{77} +(98.3988 + 31.9717i) q^{79} +(135.526 - 98.4655i) q^{80} +(41.1649 + 126.693i) q^{82} +(-28.6898 + 9.32189i) q^{83} +(10.0783 + 13.8716i) q^{85} +(-33.1334 + 101.974i) q^{86} +(-28.9210 + 33.5380i) q^{88} +60.4650 q^{89} +(23.2492 - 16.8916i) q^{91} +(-81.7987 - 59.4302i) q^{92} +(-38.9623 + 12.6596i) q^{94} +(42.0538 - 57.8821i) q^{95} +(11.3376 - 34.8935i) q^{97} +108.978i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

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