LMFDB - Embedded newform 99.4.f.b.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, 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:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.2
Root			$0.581882 + 1.79085i$ of defining polynomial
Character	$\chi$	$=$	99.37
Dual form			99.4.f.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.02339 + 1.47008i) q^{2} +(-0.539165 - 1.65938i) q^{4} +(8.44146 - 6.13308i) q^{5} +(-10.1220 - 31.1524i) q^{7} +(7.53140 - 23.1793i) q^{8} +O(q^{10})$	\(q+(2.02339 + 1.47008i) q^{2} +(-0.539165 - 1.65938i) q^{4} +(8.44146 - 6.13308i) q^{5} +(-10.1220 - 31.1524i) q^{7} +(7.53140 - 23.1793i) q^{8} +26.0964 q^{10} +(-12.6666 + 34.2134i) q^{11} +(59.2672 + 43.0601i) q^{13} +(25.3157 - 77.9137i) q^{14} +(38.0218 - 27.6245i) q^{16} +(-44.7200 + 32.4909i) q^{17} +(27.9834 - 86.1240i) q^{19} +(-14.7284 - 10.7008i) q^{20} +(-75.9259 + 50.6060i) q^{22} +91.1987 q^{23} +(-4.98357 + 15.3379i) q^{25} +(56.6188 + 174.255i) q^{26} +(-46.2362 + 33.5926i) q^{28} +(23.7073 + 72.9635i) q^{29} +(-18.6296 - 13.5352i) q^{31} -77.4339 q^{32} -138.250 q^{34} +(-276.505 - 200.893i) q^{35} +(38.8841 + 119.673i) q^{37} +(183.230 - 133.124i) q^{38} +(-78.5842 - 241.857i) q^{40} +(-43.2807 + 133.204i) q^{41} +146.015 q^{43} +(63.6024 + 2.57208i) q^{44} +(184.530 + 134.069i) q^{46} +(68.4490 - 210.664i) q^{47} +(-590.526 + 429.042i) q^{49} +(-32.6315 + 23.7082i) q^{50} +(39.4983 - 121.563i) q^{52} +(-35.5597 - 25.8356i) q^{53} +(102.909 + 366.496i) q^{55} -798.324 q^{56} +(-59.2930 + 182.485i) q^{58} +(124.159 + 382.121i) q^{59} +(328.861 - 238.932i) q^{61} +(-17.7972 - 54.7740i) q^{62} +(-460.853 - 334.830i) q^{64} +764.393 q^{65} +221.234 q^{67} +(78.0262 + 56.6893i) q^{68} +(-264.149 - 812.968i) q^{70} +(-606.376 + 440.558i) q^{71} +(-68.6023 - 211.136i) q^{73} +(-97.2508 + 299.307i) q^{74} -158.000 q^{76} +(1194.04 + 48.2871i) q^{77} +(954.850 + 693.739i) q^{79} +(151.537 - 466.382i) q^{80} +(-283.394 + 205.898i) q^{82} +(547.425 - 397.728i) q^{83} +(-178.232 + 548.542i) q^{85} +(295.444 + 214.653i) q^{86} +(697.644 + 551.278i) q^{88} -1054.06 q^{89} +(741.524 - 2282.17i) q^{91} +(-49.1711 - 151.333i) q^{92} +(448.192 - 325.630i) q^{94} +(-291.985 - 898.636i) q^{95} +(198.573 + 144.272i) q^{97} -1825.59 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8}+O(q^{10}) $ 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8	$ 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8} + 8 q^{10} + 87 q^{11} + 171 q^{13} - 12 q^{14} + 44 q^{16} - 36 q^{17} + 324 q^{19} + 87 q^{20} - 521 q^{22} + 84 q^{23} + 263 q^{25} + 774 q^{26} + 387 q^{28} - 393 q^{29} + 15 q^{31} - 102 q^{32} - 712 q^{34} - 1002 q^{35} - 747 q^{37} + 36 q^{38} + 41 q^{40} - 159 q^{41} - 644 q^{43} - 219 q^{44} + 753 q^{46} + 351 q^{47} - 1967 q^{49} - 330 q^{50} + 2871 q^{52} + 531 q^{53} - 716 q^{55} - 1470 q^{56} - 1205 q^{58} + 1002 q^{59} + 1449 q^{61} - 99 q^{62} - 1118 q^{64} + 954 q^{65} - 518 q^{67} - 873 q^{68} + 26 q^{70} - 429 q^{71} + 2547 q^{73} - 468 q^{74} - 2276 q^{76} + 2697 q^{77} + 2805 q^{79} + 1620 q^{80} - 1631 q^{82} + 2553 q^{83} - 197 q^{85} + 1713 q^{86} + 2866 q^{88} - 1788 q^{89} + 2885 q^{91} - 423 q^{92} + 1159 q^{94} - 3009 q^{95} + 9 q^{97} - 5550 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8 + 8 * q^10 + 87 * q^11 + 171 * q^13 - 12 * q^14 + 44 * q^16 - 36 * q^17 + 324 * q^19 + 87 * q^20 - 521 * q^22 + 84 * q^23 + 263 * q^25 + 774 * q^26 + 387 * q^28 - 393 * q^29 + 15 * q^31 - 102 * q^32 - 712 * q^34 - 1002 * q^35 - 747 * q^37 + 36 * q^38 + 41 * q^40 - 159 * q^41 - 644 * q^43 - 219 * q^44 + 753 * q^46 + 351 * q^47 - 1967 * q^49 - 330 * q^50 + 2871 * q^52 + 531 * q^53 - 716 * q^55 - 1470 * q^56 - 1205 * q^58 + 1002 * q^59 + 1449 * q^61 - 99 * q^62 - 1118 * q^64 + 954 * q^65 - 518 * q^67 - 873 * q^68 + 26 * q^70 - 429 * q^71 + 2547 * q^73 - 468 * q^74 - 2276 * q^76 + 2697 * q^77 + 2805 * q^79 + 1620 * q^80 - 1631 * q^82 + 2553 * q^83 - 197 * q^85 + 1713 * q^86 + 2866 * q^88 - 1788 * q^89 + 2885 * q^91 - 423 * q^92 + 1159 * q^94 - 3009 * q^95 + 9 * q^97 - 5550 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	2.02339	+	1.47008i	0.715376	+	0.519751i	0.884903	−	0.465775i	$-0.154224\pi$
$2$	2.02339	+	1.47008i	0.715376	+	0.519751i	−0.169528	+	0.985525i	$0.554224\pi$
$3$		0			0
$3$		0			0
$4$	−0.539165	−	1.65938i	−0.0673956	−	0.207422i
$5$	8.44146	−	6.13308i	0.755027	−	0.548559i	−0.142354	−	0.989816i	$-0.545467\pi$
$5$	8.44146	−	6.13308i	0.755027	−	0.548559i	0.897381	+	0.441257i	$0.145467\pi$
$6$		0			0
$7$	−10.1220	−	31.1524i	−0.546539	−	1.68207i	−0.717302	−	0.696762i	$-0.754623\pi$
$7$	−10.1220	−	31.1524i	−0.546539	−	1.68207i	0.170763	−	0.985312i	$-0.445377\pi$
$8$	7.53140	−	23.1793i	0.332844	−	1.02439i
$9$		0			0
$10$	26.0964			0.825242
$11$	−12.6666	+	34.2134i	−0.347194	+	0.937793i
$11$	−12.6666	+	34.2134i	−0.347194	+	0.937793i
$12$		0			0
$13$	59.2672	+	43.0601i	1.26444	+	0.918672i	0.998967	−	0.0454454i	$-0.0144707\pi$
$13$	59.2672	+	43.0601i	1.26444	+	0.918672i	0.265477	+	0.964117i	$0.414471\pi$
$14$	25.3157	−	77.9137i	0.483279	−	1.48738i
$15$		0			0
$16$	38.0218	−	27.6245i	0.594091	−	0.431633i
$17$	−44.7200	+	32.4909i	−0.638011	+	0.463542i	−0.859166	−	0.511697i	$-0.829017\pi$
$17$	−44.7200	+	32.4909i	−0.638011	+	0.463542i	0.221155	+	0.975239i	$0.429017\pi$
$18$		0			0
$19$	27.9834	−	86.1240i	0.337886	−	1.03990i	−0.627398	−	0.778699i	$-0.715880\pi$
$19$	27.9834	−	86.1240i	0.337886	−	1.03990i	0.965283	−	0.261206i	$-0.0841201\pi$
$20$	−14.7284	−	10.7008i	−0.164669	−	0.119639i
$21$		0			0
$22$	−75.9259	+	50.6060i	−0.735793	+	0.490420i
$23$	91.1987			0.826793			0.413397	−	0.910551i	$-0.364342\pi$
$23$	91.1987			0.826793			0.413397	+	0.910551i	$0.364342\pi$
$24$		0			0
$25$	−4.98357	+	15.3379i	−0.0398686	+	0.122703i
$26$	56.6188	+	174.255i	0.427072	+	1.31439i
$27$		0			0
$28$	−46.2362	+	33.5926i	−0.312065	+	0.226729i
$29$	23.7073	+	72.9635i	0.151805	+	0.467206i	0.997823	−	0.0659470i	$-0.0210068\pi$
$29$	23.7073	+	72.9635i	0.151805	+	0.467206i	−0.846019	+	0.533153i	$0.821007\pi$
$30$		0			0
$31$	−18.6296	−	13.5352i	−0.107935	−	0.0784193i	0.532509	−	0.846425i	$-0.321249\pi$
$31$	−18.6296	−	13.5352i	−0.107935	−	0.0784193i	−0.640443	+	0.768005i	$0.721249\pi$
$32$	−77.4339			−0.427766
$33$		0			0
$34$	−138.250			−0.697344
$35$	−276.505	−	200.893i	−1.33537	−	0.970202i
$36$		0			0
$37$	38.8841	+	119.673i	0.172770	+	0.531732i	0.999525	−	0.0308308i	$-0.00981532\pi$
$37$	38.8841	+	119.673i	0.172770	+	0.531732i	−0.826754	+	0.562563i	$0.809815\pi$
$38$	183.230	−	133.124i	0.782207	−	0.568306i
$39$		0			0
$40$	−78.5842	−	241.857i	−0.310631	−	0.956025i
$41$	−43.2807	+	133.204i	−0.164861	+	0.507391i	−0.999026	−	0.0441244i	$-0.985950\pi$
$41$	−43.2807	+	133.204i	−0.164861	+	0.507391i	0.834165	+	0.551515i	$0.185950\pi$
$42$		0			0
$43$	146.015			0.517838			0.258919	−	0.965899i	$-0.416634\pi$
$43$	146.015			0.517838			0.258919	+	0.965899i	$0.416634\pi$
$44$	63.6024	+	2.57208i	0.217919	+	0.00881262i
$45$		0			0
$46$	184.530	+	134.069i	0.591468	+	0.429727i
$47$	68.4490	−	210.664i	0.212432	−	0.653799i	−0.786894	−	0.617088i	$-0.788312\pi$
$47$	68.4490	−	210.664i	0.212432	−	0.653799i	0.999326	−	0.0367105i	$-0.0116879\pi$
$48$		0			0
$49$	−590.526	+	429.042i	−1.72165	+	1.25085i
$50$	−32.6315	+	23.7082i	−0.0922959	+	0.0670569i
$51$		0			0
$52$	39.4983	−	121.563i	0.105335	−	0.324188i
$53$	−35.5597	−	25.8356i	−0.0921604	−	0.0669585i	0.540751	−	0.841183i	$-0.318140\pi$
$53$	−35.5597	−	25.8356i	−0.0921604	−	0.0669585i	−0.632911	+	0.774224i	$0.718140\pi$
$54$		0			0
$55$	102.909	+	366.496i	0.252294	+	0.898516i
$56$	−798.324			−1.90501
$57$		0			0
$58$	−59.2930	+	182.485i	−0.134234	+	0.413129i
$59$	124.159	+	382.121i	0.273967	+	0.843184i	0.989491	+	0.144596i	$0.0461882\pi$
$59$	124.159	+	382.121i	0.273967	+	0.843184i	−0.715524	+	0.698589i	$0.753812\pi$
$60$		0			0
$61$	328.861	−	238.932i	0.690269	−	0.501509i	−0.186480	−	0.982459i	$-0.559708\pi$
$61$	328.861	−	238.932i	0.690269	−	0.501509i	0.876748	+	0.480949i	$0.159708\pi$
$62$	−17.7972	−	54.7740i	−0.0364555	−	0.112199i
$63$		0			0
$64$	−460.853	−	334.830i	−0.900104	−	0.653964i
$65$	764.393			1.45863
$66$		0			0
$67$	221.234			0.403404			0.201702	−	0.979447i	$-0.435353\pi$
$67$	221.234			0.403404			0.201702	+	0.979447i	$0.435353\pi$
$68$	78.0262	+	56.6893i	0.139148	+	0.101097i
$69$		0			0
$70$	−264.149	−	812.968i	−0.451027	−	1.38812i
$71$	−606.376	+	440.558i	−1.01357	+	0.736403i	−0.964955	−	0.262415i	$-0.915481\pi$
$71$	−606.376	+	440.558i	−1.01357	+	0.736403i	−0.0486165	+	0.998818i	$0.515481\pi$
$72$		0			0
$73$	−68.6023	−	211.136i	−0.109990	−	0.338516i	0.880879	−	0.473342i	$-0.156952\pi$
$73$	−68.6023	−	211.136i	−0.109990	−	0.338516i	−0.990869	+	0.134826i	$0.956952\pi$
$74$	−97.2508	+	299.307i	−0.152773	+	0.470186i
$75$		0			0
$76$	−158.000			−0.238471
$77$	1194.04	+	48.2871i	1.76719	+	0.0714652i
$78$		0			0
$79$	954.850	+	693.739i	1.35986	+	0.987997i	0.998454	+	0.0555887i	$0.0177036\pi$
$79$	954.850	+	693.739i	1.35986	+	0.987997i	0.361407	+	0.932408i	$0.382296\pi$
$80$	151.537	−	466.382i	0.211779	−	0.651788i
$81$		0			0
$82$	−283.394	+	205.898i	−0.381655	+	0.277288i
$83$	547.425	−	397.728i	0.723948	−	0.525979i	−0.163695	−	0.986511i	$-0.552341\pi$
$83$	547.425	−	397.728i	0.723948	−	0.525979i	0.887643	+	0.460532i	$0.152341\pi$
$84$		0			0
$85$	−178.232	+	548.542i	−0.227435	+	0.699973i
$86$	295.444	+	214.653i	0.370449	+	0.269147i
$87$		0			0
$88$	697.644	+	551.278i	0.845103	+	0.667800i
$89$	−1054.06			−1.25539			−0.627695	−	0.778460i	$-0.716001\pi$
$89$	−1054.06			−1.25539			−0.627695	+	0.778460i	$0.716001\pi$
$90$		0			0
$91$	741.524	−	2282.17i	0.854207	−	2.62898i
$92$	−49.1711	−	151.333i	−0.0557222	−	0.171495i
$93$		0			0
$94$	448.192	−	325.630i	0.491781	−	0.357300i
$95$	−291.985	−	898.636i	−0.315337	−	0.970506i
$96$		0			0
$97$	198.573	+	144.272i	0.207857	+	0.151017i	0.686843	−	0.726805i	$-0.258996\pi$
$97$	198.573	+	144.272i	0.207857	+	0.151017i	−0.478987	+	0.877822i	$0.658996\pi$
$98$	−1825.59			−1.88176
$99$		0			0
$100$	28.1383			0.0281383
$101$	18.3580	+	13.3379i	0.0180860	+	0.0131403i	0.596792	−	0.802396i	$-0.296442\pi$
$101$	18.3580	+	13.3379i	0.0180860	+	0.0131403i	−0.578706	+	0.815537i	$0.696442\pi$
$102$		0			0
$103$	303.269	+	933.366i	0.290116	+	0.892886i	0.984818	+	0.173588i	$0.0555363\pi$
$103$	303.269	+	933.366i	0.290116	+	0.892886i	−0.694702	+	0.719298i	$0.744464\pi$
$104$	1444.47	−	1049.47i	1.36194	−	0.989507i
$105$		0			0
$106$	−33.9707	−	104.551i	−0.0311276	−	0.0958009i
$107$	205.796	−	633.375i	0.185935	−	0.572249i	−0.814028	−	0.580825i	$-0.802730\pi$
$107$	205.796	−	633.375i	0.185935	−	0.572249i	0.999963	+	0.00857617i	$0.00272991\pi$
$108$		0			0
$109$	85.6516			0.0752654			0.0376327	−	0.999292i	$-0.488018\pi$
$109$	85.6516			0.0752654			0.0376327	+	0.999292i	$0.488018\pi$
$110$	−330.554	+	892.848i	−0.286519	+	0.773906i
$111$		0			0
$112$	−1245.43	−	904.857i	−1.05073	−	0.763401i
$113$	136.056	−	418.736i	0.113266	−	0.348597i	−0.878315	−	0.478081i	$-0.841332\pi$
$113$	136.056	−	418.736i	0.113266	−	0.348597i	0.991581	+	0.129485i	$0.0413324\pi$
$114$		0			0
$115$	769.850	−	559.329i	0.624251	−	0.453545i
$116$	108.292	−	78.6787i	0.0866780	−	0.0629753i
$117$		0			0
$118$	−310.526	+	955.701i	−0.242256	+	0.745588i
$119$	1464.83	+	1064.26i	1.12841	+	0.819838i
$120$		0			0
$121$	−1010.11	−	866.737i	−0.758913	−	0.651192i
$122$	1016.66			0.754461
$123$		0			0
$124$	−12.4156	+	38.2113i	−0.00899157	+	0.0276732i
$125$	455.043	+	1400.48i	0.325603	+	1.00210i
$126$		0			0
$127$	−1314.97	+	955.382i	−0.918778	+	0.667531i	−0.943219	−	0.332170i	$-0.892219\pi$
$127$	−1314.97	+	955.382i	−0.918778	+	0.667531i	0.0244418	+	0.999701i	$0.492219\pi$
$128$	−248.833	−	765.829i	−0.171828	−	0.528831i
$129$		0			0
$130$	1546.66	+	1123.72i	1.04347	+	0.758127i
$131$	−1049.60			−0.700030			−0.350015	−	0.936744i	$-0.613823\pi$
$131$	−1049.60			−0.700030			−0.350015	+	0.936744i	$0.613823\pi$
$132$		0			0
$133$	−2966.22			−1.93386
$134$	447.642	+	325.231i	0.288585	+	0.209669i
$135$		0			0
$136$	416.312	+	1281.28i	0.262489	+	0.807858i
$137$	−2486.37	+	1806.45i	−1.55055	+	1.12654i	−0.607287	+	0.794483i	$0.707742\pi$
$137$	−2486.37	+	1806.45i	−1.55055	+	1.12654i	−0.943260	+	0.332055i	$0.892258\pi$
$138$		0			0
$139$	−329.681	−	1014.65i	−0.201174	−	0.619149i	−0.999849	−	0.0173866i	$-0.994465\pi$
$139$	−329.681	−	1014.65i	−0.201174	−	0.619149i	0.798675	−	0.601762i	$-0.205535\pi$
$140$	−184.275	+	567.141i	−0.111244	+	0.342372i
$141$		0			0
$142$	−1874.59			−1.10783
$143$	−2223.95	+	1482.31i	−1.30053	+	0.866829i
$144$		0			0
$145$	647.615	+	470.520i	0.370907	+	0.269480i
$146$	171.578	−	528.061i	0.0972593	−	0.299333i
$147$		0			0
$148$	177.618	−	129.047i	0.0986492	−	0.0716728i
$149$	1706.92	−	1240.15i	0.938501	−	0.681861i	−0.00955863	−	0.999954i	$-0.503043\pi$
$149$	1706.92	−	1240.15i	0.938501	−	0.681861i	0.948059	+	0.318094i	$0.103043\pi$
$150$		0			0
$151$	366.835	−	1129.00i	0.197699	−	0.608456i	−0.802235	−	0.597008i	$-0.796356\pi$
$151$	366.835	−	1129.00i	0.197699	−	0.608456i	0.999934	−	0.0114476i	$-0.00364398\pi$
$152$	−1785.54	−	1297.27i	−0.952803	−	0.692252i
$153$		0			0
$154$	2345.03	+	1853.04i	1.22706	+	0.969624i
$155$	−240.274			−0.124511
$156$		0			0
$157$	−571.355	+	1758.45i	−0.290440	+	0.893882i	0.694275	+	0.719710i	$0.255725\pi$
$157$	−571.355	+	1758.45i	−0.290440	+	0.893882i	−0.984715	+	0.174173i	$0.944275\pi$
$158$	912.182	+	2807.41i	0.459299	+	1.41358i
$159$		0			0
$160$	−653.655	+	474.908i	−0.322975	+	0.234655i
$161$	−923.117	−	2841.06i	−0.451875	−	1.39073i
$162$		0			0
$163$	−1466.71	−	1065.63i	−0.704796	−	0.512064i	0.176695	−	0.984266i	$-0.443459\pi$
$163$	−1466.71	−	1065.63i	−0.704796	−	0.512064i	−0.881491	+	0.472202i	$0.843459\pi$
$164$	244.372			0.116355
$165$		0			0
$166$	1692.34			0.791273
$167$	213.891	+	155.401i	0.0991100	+	0.0720076i	0.636237	−	0.771494i	$-0.280490\pi$
$167$	213.891	+	155.401i	0.0991100	+	0.0720076i	−0.537127	+	0.843502i	$0.680490\pi$
$168$		0			0
$169$	979.515	+	3014.64i	0.445842	+	1.37216i
$170$	−1167.03	+	847.898i	−0.526513	+	0.382534i
$171$		0			0
$172$	−78.7260	−	242.294i	−0.0349000	−	0.107411i
$173$	205.545	−	632.602i	0.0903311	−	0.278011i	−0.895678	−	0.444704i	$-0.853309\pi$
$173$	205.545	−	632.602i	0.0903311	−	0.278011i	0.986009	+	0.166693i	$0.0533089\pi$
$174$		0			0
$175$	528.256			0.228185
$176$	463.519	+	1650.77i	0.198517	+	0.706995i
$177$		0			0
$178$	−2132.76	−	1549.54i	−0.898075	−	0.652490i
$179$	20.1093	−	61.8901i	0.00839688	−	0.0258429i	−0.946770	−	0.321910i	$-0.895675\pi$
$179$	20.1093	−	61.8901i	0.00839688	−	0.0258429i	0.955167	+	0.296067i	$0.0956752\pi$
$180$		0			0
$181$	33.1354	−	24.0743i	0.0136074	−	0.00988634i	−0.580961	−	0.813932i	$-0.697323\pi$
$181$	33.1354	−	24.0743i	0.0136074	−	0.00988634i	0.594568	+	0.804045i	$0.297323\pi$
$182$	4855.36	−	3527.63i	1.97749	−	1.43673i
$183$		0			0
$184$	686.854	−	2113.92i	0.275193	−	0.846958i
$185$	1062.20	+	771.734i	0.422133	+	0.306697i
$186$		0			0
$187$	−545.175	−	1941.57i	−0.213193	−	0.759261i
$188$	−386.477			−0.149929
$189$		0			0
$190$	730.266	−	2247.53i	0.278837	−	0.858173i
$191$	−1415.27	−	4355.76i	−0.536155	−	1.65012i	−0.741140	−	0.671351i	$-0.765715\pi$
$191$	−1415.27	−	4355.76i	−0.536155	−	1.65012i	0.204985	−	0.978765i	$-0.434285\pi$
$192$		0			0
$193$	4081.18	−	2965.15i	1.52212	−	1.10589i	0.561703	−	0.827339i	$-0.310146\pi$
$193$	4081.18	−	2965.15i	1.52212	−	1.10589i	0.960422	−	0.278550i	$-0.0898536\pi$
$194$	189.700	+	583.837i	0.0702045	+	0.216067i
$195$		0			0
$196$	1030.33	+	748.582i	0.375486	+	0.272807i
$197$	−1703.26			−0.616001			−0.308000	−	0.951386i	$-0.599660\pi$
$197$	−1703.26			−0.616001			−0.308000	+	0.951386i	$0.599660\pi$
$198$		0			0
$199$	−3326.11			−1.18483			−0.592416	−	0.805632i	$-0.701826\pi$
$199$	−3326.11			−1.18483			−0.592416	+	0.805632i	$0.701826\pi$
$200$	317.987	+	231.031i	0.112425	+	0.0816818i
$201$		0			0
$202$	17.5376	+	53.9753i	0.00610863	+	0.0188004i
$203$	2033.03	−	1477.08i	0.702909	−	0.510693i
$204$		0			0
$205$	451.600	+	1389.88i	0.153859	+	0.473530i
$206$	−758.489	+	2334.39i	−0.256536	+	0.789537i
$207$		0			0
$208$	3442.96			1.14772
$209$	2592.14	+	2048.31i	0.857904	+	0.677915i
$210$		0			0
$211$	−4013.48	−	2915.96i	−1.30947	−	0.951389i	−1.00000		0.000481181i	$-0.999847\pi$
$211$	−4013.48	−	2915.96i	−1.30947	−	0.951389i	−0.309475	−	0.950908i	$-0.600153\pi$
$212$	−23.6986	+	72.9367i	−0.00767747	+	0.0236288i
$213$		0			0
$214$	1347.52	−	979.027i	0.430440	−	0.312733i
$215$	1232.58	−	895.520i	0.390982	−	0.284065i
$216$		0			0
$217$	−233.085	+	717.363i	−0.0729164	+	0.224414i
$218$	173.306	+	125.914i	0.0538431	+	0.0391193i
$219$		0			0
$220$	552.671	−	368.366i	0.169369	−	0.112887i
$221$	−4049.49			−1.23257
$222$		0			0
$223$	−1136.92	+	3499.07i	−0.341406	+	1.05074i	0.622074	+	0.782959i	$0.286290\pi$
$223$	−1136.92	+	3499.07i	−0.341406	+	1.05074i	−0.963480	+	0.267781i	$0.913710\pi$
$224$	783.789	+	2412.25i	0.233791	+	0.719534i
$225$		0			0
$226$	890.869	−	647.254i	0.262211	−	0.190507i
$227$	−124.139	−	382.062i	−0.0362970	−	0.111711i	0.931266	−	0.364339i	$-0.118705\pi$
$227$	−124.139	−	382.062i	−0.0362970	−	0.111711i	−0.967563	+	0.252628i	$0.918705\pi$
$228$		0			0
$229$	2388.11	+	1735.06i	0.689129	+	0.500681i	0.876374	−	0.481632i	$-0.159956\pi$
$229$	2388.11	+	1735.06i	0.689129	+	0.500681i	−0.187245	+	0.982313i	$0.559956\pi$
$230$	2379.96			0.682305
$231$		0			0
$232$	1869.79			0.529128
$233$	−1994.88	−	1449.36i	−0.560896	−	0.407515i	0.270891	−	0.962610i	$-0.412682\pi$
$233$	−1994.88	−	1449.36i	−0.560896	−	0.407515i	−0.831787	+	0.555095i	$0.812682\pi$
$234$		0			0
$235$	−714.211	−	2198.12i	−0.198255	−	0.610167i
$236$	567.141	−	412.052i	0.156431	−	0.113654i
$237$		0			0
$238$	1399.37	+	4306.83i	0.381125	+	1.17298i
$239$	1311.91	−	4037.64i	0.355064	−	1.09278i	−0.600908	−	0.799318i	$-0.705194\pi$
$239$	1311.91	−	4037.64i	0.355064	−	1.09278i	0.955972	−	0.293457i	$-0.0948059\pi$
$240$		0			0
$241$	−2686.25			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$241$	−2686.25			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$242$	−769.680	−	3238.69i	−0.204450	−	0.860293i
$243$		0			0
$244$	−573.789	−	416.882i	−0.150545	−	0.109378i
$245$	−2353.55	+	7243.49i	−0.613726	+	1.88885i
$246$		0			0
$247$	5367.01	−	3899.36i	1.38257	−	1.00449i
$248$	−454.044	+	329.882i	−0.116257	+	0.0844659i
$249$		0			0
$250$	−1138.08	+	3502.66i	−0.287915	+	0.886111i
$251$	5951.11	+	4323.74i	1.49654	+	1.08730i	0.971735	+	0.236074i	$0.0758607\pi$
$251$	5951.11	+	4323.74i	1.49654	+	1.08730i	0.524802	+	0.851224i	$0.324139\pi$
$252$		0			0
$253$	−1155.18	+	3120.22i	−0.287058	+	0.775361i
$254$	−4065.18			−1.00422
$255$		0			0
$256$	−785.901	+	2418.75i	−0.191870	+	0.590516i
$257$	147.792	+	454.856i	0.0358716	+	0.110401i	0.967389	−	0.253295i	$-0.0815144\pi$
$257$	147.792	+	454.856i	0.0358716	+	0.110401i	−0.931517	+	0.363697i	$0.881514\pi$
$258$		0			0
$259$	3334.52	−	2422.67i	0.799987	−	0.581225i
$260$	−412.133	−	1268.42i	−0.0983055	−	0.302553i
$261$		0			0
$262$	−2123.75	−	1542.99i	−0.500784	−	0.363841i
$263$	−3955.38			−0.927373			−0.463686	−	0.885999i	$-0.653474\pi$
$263$	−3955.38			−0.927373			−0.463686	+	0.885999i	$0.653474\pi$
$264$		0			0
$265$	−458.628			−0.106314
$266$	−6001.82	−	4360.57i	−1.38344	−	1.00513i
$267$		0			0
$268$	−119.282	−	367.111i	−0.0271876	−	0.0836749i
$269$	−1059.90	+	770.065i	−0.240236	+	0.174542i	−0.701388	−	0.712779i	$-0.747436\pi$
$269$	−1059.90	+	770.065i	−0.240236	+	0.174542i	0.461153	+	0.887321i	$0.347436\pi$
$270$		0			0
$271$	−1685.61	−	5187.78i	−0.377836	−	1.16286i	−0.941545	−	0.336887i	$-0.890626\pi$
$271$	−1685.61	−	5187.78i	−0.377836	−	1.16286i	0.563709	−	0.825974i	$-0.309374\pi$
$272$	−802.789	+	2470.73i	−0.178957	+	0.550772i
$273$		0			0
$274$	−7686.52			−1.69474
$275$	−461.635	−	364.784i	−0.101228	−	0.0799901i
$276$		0			0
$277$	3852.71	+	2799.16i	0.835693	+	0.607167i	0.921164	−	0.389174i	$-0.127240\pi$
$277$	3852.71	+	2799.16i	0.835693	+	0.607167i	−0.0854711	+	0.996341i	$0.527240\pi$
$278$	824.546	−	2537.69i	0.177888	−	0.547484i
$279$		0			0
$280$	−6739.02	+	4896.18i	−1.43833	+	1.04501i
$281$	−451.960	+	328.368i	−0.0959490	+	0.0697110i	−0.634725	−	0.772738i	$-0.718887\pi$
$281$	−451.960	+	328.368i	−0.0959490	+	0.0697110i	0.538776	+	0.842449i	$0.318887\pi$
$282$		0			0
$283$	−638.145	+	1964.01i	−0.134042	+	0.412538i	−0.995440	−	0.0953928i	$-0.969589\pi$
$283$	−638.145	+	1964.01i	−0.134042	+	0.412538i	0.861398	+	0.507930i	$0.169589\pi$
$284$	1057.99	+	768.674i	0.221057	+	0.160607i
$285$		0			0
$286$	−6679.02	−	270.099i	−1.38090	−	0.0558437i
$287$	4587.73			0.943572
$288$		0			0
$289$	−573.988	+	1766.55i	−0.116830	+	0.359567i
$290$	618.676	+	1904.09i	0.125275	+	0.385558i
$291$		0			0
$292$	−313.367	+	227.674i	−0.0628028	+	0.0456289i
$293$	2316.44	+	7129.26i	0.461869	+	1.42149i	0.862877	+	0.505413i	$0.168660\pi$
$293$	2316.44	+	7129.26i	0.461869	+	1.42149i	−0.401008	+	0.916074i	$0.631340\pi$
$294$		0			0
$295$	3391.65	+	2464.18i	0.669389	+	0.486340i
$296$	3066.78			0.602206
$297$		0			0
$298$	5276.89			1.02578
$299$	5405.09	+	3927.03i	1.04543	+	0.759552i
$300$		0			0
$301$	−1477.97	−	4548.72i	−0.283019	−	0.871042i
$302$	2401.97	−	1745.13i	0.457675	−	0.332520i
$303$		0			0
$304$	−1315.15	−	4047.62i	−0.248122	−	0.763641i
$305$	1310.68	−	4033.86i	0.246064	−	0.757306i
$306$		0			0
$307$	1036.23			0.192640			0.0963201	−	0.995350i	$-0.469293\pi$
$307$	1036.23			0.192640			0.0963201	+	0.995350i	$0.469293\pi$
$308$	−563.659	−	2007.40i	−0.104277	−	0.371372i
$309$		0			0
$310$	−486.167	−	353.221i	−0.0890724	−	0.0647149i
$311$	3193.59	−	9828.85i	0.582288	−	1.79210i	−0.0276089	−	0.999619i	$-0.508789\pi$
$311$	3193.59	−	9828.85i	0.582288	−	1.79210i	0.609897	−	0.792481i	$-0.291211\pi$
$312$		0			0
$313$	−5769.05	+	4191.46i	−1.04181	+	0.756918i	−0.970638	−	0.240546i	$-0.922674\pi$
$313$	−5769.05	+	4191.46i	−1.04181	+	0.756918i	−0.0711707	+	0.997464i	$0.522674\pi$
$314$	−3741.13	+	2718.09i	−0.672370	+	0.488505i
$315$		0			0
$316$	636.354	−	1958.50i	0.113284	−	0.348652i
$317$	−5215.16	−	3789.04i	−0.924014	−	0.671336i	0.0205056	−	0.999790i	$-0.493472\pi$
$317$	−5215.16	−	3789.04i	−0.924014	−	0.671336i	−0.944520	+	0.328454i	$0.893472\pi$
$318$		0			0
$319$	−2796.62	−	113.095i	−0.490849	−	0.0198499i
$320$	−5943.81			−1.03834
$321$		0			0
$322$	2308.76	−	7105.63i	0.399572	−	1.22976i
$323$	1546.83	+	4760.67i	0.266465	+	0.820095i
$324$		0			0
$325$	−955.812	+	694.438i	−0.163135	+	0.118525i
$326$	−1401.17	−	4312.36i	−0.238048	−	0.732636i
$327$		0			0
$328$	2761.61	+	2006.43i	0.464892	+	0.337764i
$329$	−7255.55			−1.21584
$330$		0			0
$331$	5634.51			0.935652			0.467826	−	0.883821i	$-0.345037\pi$
$331$	5634.51			0.935652			0.467826	+	0.883821i	$0.345037\pi$
$332$	−955.133	−	693.945i	−0.157891	−	0.114714i
$333$		0			0
$334$	204.333	+	628.872i	0.0334749	+	0.103025i
$335$	1867.54	−	1356.85i	0.304580	−	0.221291i
$336$		0			0
$337$	945.112	+	2908.76i	0.152770	+	0.470178i	0.997928	−	0.0643383i	$-0.0204937\pi$
$337$	945.112	+	2908.76i	0.152770	+	0.470178i	−0.845158	+	0.534517i	$0.820494\pi$
$338$	−2449.81	+	7539.74i	−0.394237	+	1.21334i
$339$		0			0
$340$	1006.33			0.160518
$341$	699.061	−	465.937i	0.111015	−	0.0739939i
$342$		0			0
$343$	10253.6	+	7449.68i	1.61412	+	1.17273i
$344$	1099.70	−	3384.51i	0.172359	−	0.530467i
$345$		0			0
$346$	1345.87	−	977.832i	0.209117	−	0.151932i
$347$	−8507.85	+	6181.32i	−1.31621	+	0.956284i	−0.316241	+	0.948679i	$0.602421\pi$
$347$	−8507.85	+	6181.32i	−1.31621	+	0.956284i	−0.999971	+	0.00760501i	$0.997579\pi$
$348$		0			0
$349$	465.051	−	1431.28i	0.0713283	−	0.219526i	−0.909037	−	0.416715i	$-0.863181\pi$
$349$	465.051	−	1431.28i	0.0713283	−	0.219526i	0.980365	+	0.197189i	$0.0631813\pi$
$350$	1068.87	+	776.577i	0.163238	+	0.118599i
$351$		0			0
$352$	980.826	−	2649.28i	0.148518	−	0.401156i
$353$	11810.2			1.78071			0.890356	−	0.455264i	$-0.150455\pi$
$353$	11810.2			1.78071			0.890356	+	0.455264i	$0.150455\pi$
$354$		0			0
$355$	−2416.72	+	7437.90i	−0.361313	+	1.11201i
$356$	568.309	+	1749.08i	0.0846077	+	0.260396i
$357$		0			0
$358$	131.672	−	95.6655i	0.0194388	−	0.0141231i
$359$	−1021.81	−	3144.82i	−0.150221	−	0.462332i	0.847424	−	0.530916i	$-0.178152\pi$
$359$	−1021.81	−	3144.82i	−0.150221	−	0.462332i	−0.997645	+	0.0685836i	$0.978152\pi$
$360$		0			0
$361$	−1085.22	−	788.459i	−0.158218	−	0.114952i
$362$	102.437			0.0148728
$363$		0			0
$364$	−4186.79			−0.602878
$365$	−1874.02	−	1361.55i	−0.268741	−	0.195252i
$366$		0			0
$367$	−1108.64	−	3412.03i	−0.157685	−	0.485304i	0.840738	−	0.541442i	$-0.182121\pi$
$367$	−1108.64	−	3412.03i	−0.157685	−	0.485304i	−0.998423	+	0.0561380i	$0.982121\pi$
$368$	3467.54	−	2519.32i	0.491191	−	0.356871i
$369$		0			0
$370$	1014.74	+	3123.04i	0.142577	+	0.438808i
$371$	−444.906	+	1369.28i	−0.0622598	+	0.191616i
$372$		0			0
$373$	−2022.36			−0.280734			−0.140367	−	0.990100i	$-0.544828\pi$
$373$	−2022.36			−0.280734			−0.140367	+	0.990100i	$0.544828\pi$
$374$	1751.16	−	4730.00i	0.242113	−	0.653964i
$375$		0			0
$376$	−4367.53	−	3173.19i	−0.599037	−	0.435226i
$377$	−1736.76	+	5345.18i	−0.237261	+	0.730215i
$378$		0			0
$379$	4696.18	−	3411.97i	0.636482	−	0.462431i	−0.222158	−	0.975011i	$-0.571310\pi$
$379$	4696.18	−	3411.97i	0.636482	−	0.462431i	0.858640	+	0.512580i	$0.171310\pi$
$380$	−1333.75	+	969.025i	−0.180052	+	0.130816i
$381$		0			0
$382$	3539.66	−	10894.0i	0.474097	−	1.45912i
$383$	−4237.83	−	3078.96i	−0.565387	−	0.410777i	0.268040	−	0.963408i	$-0.413624\pi$
$383$	−4237.83	−	3078.96i	−0.565387	−	0.410777i	−0.833426	+	0.552630i	$0.813624\pi$
$384$		0			0
$385$	10375.6	−	6915.55i	1.37348	−	0.915452i
$386$	12616.8			1.66368
$387$		0			0
$388$	132.338	−	407.295i	0.0173156	−	0.0532919i
$389$	26.2617	+	80.8251i	0.00342293	+	0.0105347i	0.952753	−	0.303745i	$-0.0982371\pi$
$389$	26.2617	+	80.8251i	0.00342293	+	0.0105347i	−0.949330	+	0.314280i	$0.898237\pi$
$390$		0			0
$391$	−4078.40	+	2963.13i	−0.527503	+	0.383253i
$392$	5497.40	+	16919.3i	0.708318	+	2.17998i
$393$		0			0
$394$	−3446.35	−	2503.92i	−0.440672	−	0.320167i
$395$	12315.1			1.56871
$396$		0			0
$397$	−7187.71			−0.908667			−0.454334	−	0.890832i	$-0.650123\pi$
$397$	−7187.71			−0.908667			−0.454334	+	0.890832i	$0.650123\pi$
$398$	−6730.01	−	4889.64i	−0.847600	−	0.615818i
$399$		0			0
$400$	234.216	+	720.842i	0.0292770	+	0.0901052i
$401$	1839.76	−	1336.66i	0.229110	−	0.166458i	−0.467308	−	0.884095i	$-0.654776\pi$
$401$	1839.76	−	1336.66i	0.229110	−	0.166458i	0.696418	+	0.717636i	$0.254776\pi$
$402$		0			0
$403$	−521.298	−	1604.39i	−0.0644360	−	0.198314i
$404$	12.2346	−	37.6541i	0.00150666	−	0.00463704i
$405$		0			0
$406$	6285.02			0.768277
$407$	−4586.94	−	185.496i	−0.558640	−	0.0225914i
$408$		0			0
$409$	7772.40	+	5646.98i	0.939659	+	0.682702i	0.948339	−	0.317260i	$-0.102763\pi$
$409$	7772.40	+	5646.98i	0.939659	+	0.682702i	−0.00867953	+	0.999962i	$0.502763\pi$
$410$	−1129.47	+	3476.16i	−0.136050	+	0.418720i
$411$		0			0
$412$	1385.30	−	1006.48i	0.165652	−	0.120353i
$413$	10647.3	−	7735.68i	1.26856	−	0.921666i
$414$		0			0
$415$	2181.77	−	6714.80i	0.258070	−	0.794257i
$416$	−4589.29	−	3334.31i	−0.540886	−	0.392976i
$417$		0			0
$418$	2233.73	+	7955.16i	0.261377	+	0.930861i
$419$	−10777.3			−1.25658			−0.628291	−	0.777979i	$-0.716245\pi$
$419$	−10777.3			−1.25658			−0.628291	+	0.777979i	$0.716245\pi$
$420$		0			0
$421$	380.512	−	1171.10i	0.0440500	−	0.135572i	−0.926613	−	0.376017i	$-0.877293\pi$
$421$	380.512	−	1171.10i	0.0440500	−	0.135572i	0.970663	+	0.240445i	$0.0772934\pi$
$422$	−3834.13	−	11800.2i	−0.442281	−	1.36120i
$423$		0			0
$424$	−866.665	+	629.669i	−0.0992665	+	0.0721213i
$425$	−275.476	−	847.829i	−0.0314413	−	0.0967665i
$426$		0			0
$427$	−10772.1	−	7826.36i	−1.22083	−	0.886988i
$428$	−1161.97			−0.131228
$429$		0			0
$430$	3810.46			0.427342
$431$	7047.38	+	5120.22i	0.787611	+	0.572233i	0.907253	−	0.420584i	$-0.138175\pi$
$431$	7047.38	+	5120.22i	0.787611	+	0.572233i	−0.119643	+	0.992817i	$0.538175\pi$
$432$		0			0
$433$	2313.66	+	7120.71i	0.256784	+	0.790299i	0.993473	+	0.114068i	$0.0363880\pi$
$433$	2313.66	+	7120.71i	0.256784	+	0.790299i	−0.736689	+	0.676231i	$0.763612\pi$
$434$	−1526.20	+	1108.85i	−0.168802	+	0.122642i
$435$		0			0
$436$	−46.1803	−	142.128i	−0.00507256	−	0.0156117i
$437$	2552.05	−	7854.40i	0.279362	−	0.859787i
$438$		0			0
$439$	9595.95			1.04326			0.521628	−	0.853173i	$-0.325325\pi$
$439$	9595.95			1.04326			0.521628	+	0.853173i	$0.325325\pi$
$440$	9270.16	+	374.885i	1.00440	+	0.0406180i
$441$		0			0
$442$	−8193.69	−	5953.07i	−0.881752	−	0.640630i
$443$	−2871.05	+	8836.18i	−0.307918	+	0.947674i	0.670654	+	0.741770i	$0.266013\pi$
$443$	−2871.05	+	8836.18i	−0.307918	+	0.947674i	−0.978572	+	0.205904i	$0.933987\pi$
$444$		0			0
$445$	−8897.76	+	6464.60i	−0.947853	+	0.688655i
$446$	−7444.32	+	5408.62i	−0.790356	+	0.574227i
$447$		0			0
$448$	−5765.98	+	17745.9i	−0.608074	+	1.87146i
$449$	−5550.31	−	4032.54i	−0.583375	−	0.423847i	0.256564	−	0.966527i	$-0.417409\pi$
$449$	−5550.31	−	4032.54i	−0.583375	−	0.423847i	−0.839939	+	0.542680i	$0.817409\pi$
$450$		0			0
$451$	−4009.15	−	3168.03i	−0.418589	−	0.330769i
$452$	−768.199			−0.0799403
$453$		0			0
$454$	310.478	−	955.553i	0.0320957	−	0.0987805i
$455$	−7737.22	−	23812.7i	−0.797201	−	2.45353i
$456$		0			0
$457$	−935.459	+	679.650i	−0.0957525	+	0.0695683i	−0.634631	−	0.772815i	$-0.718848\pi$
$457$	−935.459	+	679.650i	−0.0957525	+	0.0695683i	0.538879	+	0.842383i	$0.318848\pi$
$458$	2281.39	+	7021.40i	0.232756	+	0.716351i
$459$		0			0
$460$	−1343.21	−	975.902i	−0.136147	−	0.0989167i
$461$	8394.87			0.848131			0.424065	−	0.905632i	$-0.360603\pi$
$461$	8394.87			0.848131			0.424065	+	0.905632i	$0.360603\pi$
$462$		0			0
$463$	1801.45			0.180822			0.0904108	−	0.995905i	$-0.471182\pi$
$463$	1801.45			0.180822			0.0904108	+	0.995905i	$0.471182\pi$
$464$	2916.97	+	2119.31i	0.291847	+	0.212039i
$465$		0			0
$466$	−1905.73	−	5865.25i	−0.189445	−	0.583052i
$467$	−15389.4	+	11181.0i	−1.52492	+	1.10792i	−0.565934	+	0.824451i	$0.691484\pi$
$467$	−15389.4	+	11181.0i	−1.52492	+	1.10792i	−0.958982	+	0.283466i	$0.908516\pi$
$468$		0			0
$469$	−2239.34	−	6891.98i	−0.220476	−	0.678555i
$470$	1786.27	−	5497.59i	0.175308	−	0.539542i
$471$		0			0
$472$	9792.36			0.954936
$473$	−1849.51	+	4995.66i	−0.179790	+	0.485625i
$474$		0			0
$475$	1181.50	+	858.410i	0.114128	+	0.0829190i
$476$	976.227	−	3004.52i	0.0940027	−	0.289311i
$477$		0			0
$478$	8590.15	−	6241.11i	0.821976	−	0.597200i
$479$	−13686.9	+	9944.13i	−1.30558	+	0.948557i	−0.999993	−	0.00360855i	$-0.998851\pi$
$479$	−13686.9	+	9944.13i	−1.30558	+	0.948557i	−0.305583	+	0.952165i	$0.598851\pi$
$480$		0			0
$481$	−2848.58	+	8767.03i	−0.270029	+	0.831065i
$482$	−5435.33	−	3949.00i	−0.513636	−	0.373178i
$483$		0			0
$484$	−893.627	+	2143.47i	−0.0839244	+	0.201303i
$485$	2561.08			0.239779
$486$		0			0
$487$	−2844.77	+	8755.32i	−0.264700	+	0.814664i	0.727062	+	0.686572i	$0.240885\pi$
$487$	−2844.77	+	8755.32i	−0.264700	+	0.814664i	−0.991762	+	0.128092i	$0.959115\pi$
$488$	−3061.48	−	9422.25i	−0.283989	−	0.874027i
$489$		0			0
$490$	−15410.6	+	11196.5i	−1.42078	+	1.03226i
$491$	−5069.27	−	15601.6i	−0.465933	−	1.43399i	−0.857805	−	0.513975i	$-0.828173\pi$
$491$	−5069.27	−	15601.6i	−0.465933	−	1.43399i	0.391872	−	0.920020i	$-0.371827\pi$
$492$		0			0
$493$	−3430.84	−	2492.65i	−0.313423	−	0.227715i
$494$	16591.9			1.51114
$495$		0			0
$496$	−1082.24			−0.0979715
$497$	19862.2	+	14430.7i	1.79264	+	1.30243i
$498$		0			0
$499$	−1431.17	−	4404.69i	−0.128393	−	0.395152i	0.866111	−	0.499851i	$-0.166612\pi$
$499$	−1431.17	−	4404.69i	−0.128393	−	0.395152i	−0.994504	+	0.104699i	$0.966612\pi$
$500$	2078.58	−	1510.18i	0.185914	−	0.135074i
$501$		0			0
$502$	5685.18	+	17497.2i	0.505462	+	1.55565i
$503$	−6057.33	+	18642.5i	−0.536944	+	1.65255i	0.202465	+	0.979289i	$0.435105\pi$
$503$	−6057.33	+	18642.5i	−0.536944	+	1.65255i	−0.739410	+	0.673256i	$0.764895\pi$
$504$		0			0
$505$	236.770			0.0208636
$506$	−6924.34	+	4615.21i	−0.608349	+	0.405476i
$507$		0			0
$508$	2294.33	+	1666.93i	0.200382	+	0.145586i
$509$	−5031.84	+	15486.4i	−0.438178	+	1.34857i	0.451617	+	0.892212i	$0.350847\pi$
$509$	−5031.84	+	15486.4i	−0.438178	+	1.34857i	−0.889795	+	0.456360i	$0.849153\pi$
$510$		0			0
$511$	−5883.02	+	4274.26i	−0.509294	+	0.370024i
$512$	−10357.6	+	7525.21i	−0.894031	+	0.649551i
$513$		0			0
$514$	−369.634	+	1137.62i	−0.0317196	+	0.0976227i
$515$	8284.44	+	6019.00i	0.708846	+	0.515007i
$516$		0			0
$517$	6340.52	+	5010.28i	0.539373	+	0.426212i
$518$	10308.5			0.874384
$519$		0			0
$520$	5756.95	−	17718.1i	0.485498	−	1.49421i
$521$	3170.21	+	9756.91i	0.266583	+	0.820457i	0.991325	+	0.131436i	$0.0419589\pi$
$521$	3170.21	+	9756.91i	0.266583	+	0.820457i	−0.724742	+	0.689020i	$0.758041\pi$
$522$		0			0
$523$	−17290.3	+	12562.2i	−1.44561	+	1.05030i	−0.458776	+	0.888552i	$0.651712\pi$
$523$	−17290.3	+	12562.2i	−1.44561	+	1.05030i	−0.986833	+	0.161744i	$0.948288\pi$
$524$	565.907	+	1741.68i	0.0471789	+	0.145202i
$525$		0			0
$526$	−8003.27	−	5814.71i	−0.663420	−	0.482003i
$527$	1272.89			0.105214
$528$		0			0
$529$	−3849.79			−0.316413
$530$	−927.982	−	674.218i	−0.0760546	−	0.0552569i
$531$		0			0
$532$	1599.28	+	4922.08i	0.130334	+	0.401127i
$533$	−8300.93	+	6030.98i	−0.674584	+	0.490114i
$534$		0			0
$535$	−2147.32	−	6608.77i	−0.173527	−	0.534060i
$536$	1666.20	−	5128.04i	0.134270	−	0.413242i
$537$		0			0
$538$	−3276.65			−0.262577
$539$	−7199.02	−	25638.4i	−0.575295	−	2.04884i
$540$		0			0
$541$	−17097.0	−	12421.7i	−1.35870	−	0.987157i	−0.998526	−	0.0542736i	$-0.982716\pi$
$541$	−17097.0	−	12421.7i	−1.35870	−	0.987157i	−0.360179	−	0.932883i	$-0.617284\pi$
$542$	4215.79	−	12974.9i	0.334103	−	1.02826i
$543$		0			0
$544$	3462.84	−	2515.90i	0.272919	−	0.198287i
$545$	723.024	−	525.308i	0.0568274	−	0.0412875i
$546$		0			0
$547$	214.684	−	660.729i	0.0167810	−	0.0516467i	−0.942315	−	0.334726i	$-0.891356\pi$
$547$	214.684	−	660.729i	0.0167810	−	0.0516467i	0.959096	+	0.283080i	$0.0913561\pi$
$548$	4338.15	+	3151.85i	0.338169	+	0.245694i
$549$		0			0
$550$	−397.806	−	1416.74i	−0.0308409	−	0.109836i
$551$	6947.32			0.537143
$552$		0			0
$553$	11946.6	−	36768.0i	0.918667	−	2.82737i
$554$	3680.55	+	11327.6i	0.282259	+	0.868704i
$555$		0			0
$556$	−1505.94	+	1094.13i	−0.114867	+	0.0834558i
$557$	−5531.72	−	17024.9i	−0.420801	−	1.29509i	−0.906958	−	0.421222i	$-0.861601\pi$
$557$	−5531.72	−	17024.9i	−0.420801	−	1.29509i	0.486156	−	0.873872i	$-0.338399\pi$
$558$		0			0
$559$	8653.88	+	6287.42i	0.654777	+	0.475723i
$560$	−16062.8			−1.21210
$561$		0			0
$562$	−1397.22			−0.104872
$563$	12328.2	+	8956.97i	0.922864	+	0.670500i	0.944235	−	0.329272i	$-0.106803\pi$
$563$	12328.2	+	8956.97i	0.922864	+	0.670500i	−0.0213713	+	0.999772i	$0.506803\pi$
$564$		0			0
$565$	−1419.63	−	4369.19i	−0.105707	−	0.325333i
$566$	−4178.46	+	3035.83i	−0.310307	+	0.225451i
$567$		0			0
$568$	5644.95	+	17373.4i	0.417001	+	1.28340i
$569$	7618.38	−	23447.0i	0.561299	−	1.72750i	−0.117401	−	0.993085i	$-0.537456\pi$
$569$	7618.38	−	23447.0i	0.561299	−	1.72750i	0.678700	−	0.734416i	$-0.262544\pi$
$570$		0			0
$571$	20893.8			1.53131			0.765656	−	0.643250i	$-0.222415\pi$
$571$	20893.8			1.53131			0.765656	+	0.643250i	$0.222415\pi$
$572$	3658.78	+	2891.17i	0.267450	+	0.211339i
$573$		0			0
$574$	9282.76	+	6744.32i	0.675009	+	0.490422i
$575$	−454.495	+	1398.79i	−0.0329631	+	0.101450i
$576$		0			0
$577$	11720.4	−	8515.35i	0.845624	−	0.614382i	−0.0783117	−	0.996929i	$-0.524953\pi$
$577$	11720.4	−	8515.35i	0.845624	−	0.614382i	0.923936	+	0.382547i	$0.124953\pi$
$578$	−3758.37	+	2730.62i	−0.270463	+	0.196503i
$579$		0			0
$580$	431.599	−	1328.33i	0.0308986	−	0.0950961i
$581$	−17931.2	−	13027.8i	−1.28040	−	0.930266i
$582$		0			0
$583$	1334.35	−	889.368i	0.0947907	−	0.0631798i
$584$	−5410.65			−0.383381
$585$		0			0
$586$	−5793.51	+	17830.6i	−0.408409	+	1.25695i
$587$	−2950.00	−	9079.16i	−0.207427	−	0.638394i	−0.999605	−	0.0281041i	$-0.991053\pi$
$587$	−2950.00	−	9079.16i	−0.207427	−	0.638394i	0.792178	−	0.610290i	$-0.208947\pi$
$588$		0			0
$589$	−1687.03	+	1225.70i	−0.118018	+	0.0857453i
$590$	3240.10	+	9971.99i	0.226089	+	0.695831i
$591$		0			0
$592$	4784.34	+	3476.03i	0.332154	+	0.241324i
$593$	15771.0			1.09213			0.546067	−	0.837741i	$-0.316124\pi$
$593$	15771.0			1.09213			0.546067	+	0.837741i	$0.316124\pi$
$594$		0			0
$595$	18892.5			1.30171
$596$	−2978.19	−	2163.78i	−0.204684	−	0.148712i
$597$		0			0
$598$	5163.56	+	15891.8i	0.353100	+	1.08673i
$599$	15970.3	−	11603.1i	1.08936	−	0.791469i	0.110072	−	0.993924i	$-0.464892\pi$
$599$	15970.3	−	11603.1i	1.08936	−	0.791469i	0.979292	+	0.202455i	$0.0648918\pi$
$600$		0			0
$601$	667.170	+	2053.34i	0.0452819	+	0.139363i	0.971141	−	0.238505i	$-0.0766573\pi$
$601$	667.170	+	2053.34i	0.0452819	+	0.139363i	−0.925859	+	0.377868i	$0.876657\pi$
$602$	3696.46	−	11376.5i	0.250260	−	0.770221i
$603$		0			0
$604$	−2071.22			−0.139531
$605$	−13842.6	−	1121.42i	−0.930217	−	0.0753591i
$606$		0			0
$607$	−4096.74	−	2976.46i	−0.273940	−	0.199029i	0.442330	−	0.896852i	$-0.354152\pi$
$607$	−4096.74	−	2976.46i	−0.273940	−	0.199029i	−0.716270	+	0.697823i	$0.754152\pi$
$608$	−2166.86	+	6668.91i	−0.144536	+	0.444836i
$609$		0			0
$610$	8582.11	−	6235.27i	0.569639	−	0.413867i
$611$	13128.0	−	9538.06i	0.869235	−	0.631536i
$612$		0			0
$613$	7547.95	−	23230.2i	0.497323	−	1.53060i	−0.315982	−	0.948765i	$-0.602334\pi$
$613$	7547.95	−	23230.2i	0.497323	−	1.53060i	0.813305	−	0.581837i	$-0.197666\pi$
$614$	2096.69	+	1523.33i	0.137810	+	0.100125i
$615$		0			0
$616$	10112.1	−	27313.4i	0.661408	−	1.78650i
$617$	13814.4			0.901369			0.450685	−	0.892683i	$-0.351180\pi$
$617$	13814.4			0.901369			0.450685	+	0.892683i	$0.351180\pi$
$618$		0			0
$619$	−1351.02	+	4158.01i	−0.0877255	+	0.269991i	−0.985290	−	0.170892i	$-0.945335\pi$
$619$	−1351.02	+	4158.01i	−0.0877255	+	0.269991i	0.897564	+	0.440884i	$0.145335\pi$
$620$	129.547	+	398.705i	0.00839151	+	0.0258264i
$621$		0			0
$622$	20911.0	−	15192.8i	1.34800	−	0.979379i
$623$	10669.2	+	32836.4i	0.686119	+	2.11166i
$624$		0			0
$625$	10799.6	+	7846.36i	0.691173	+	0.502167i
$626$	−17834.8			−1.13869
$627$		0			0
$628$	3225.99			0.204985
$629$	−5627.18	−	4088.38i	−0.356710	−	0.259165i
$630$		0			0
$631$	−714.402	−	2198.70i	−0.0450711	−	0.138715i	0.925989	−	0.377552i	$-0.123234\pi$
$631$	−714.402	−	2198.70i	−0.0450711	−	0.138715i	−0.971060	+	0.238837i	$0.923234\pi$
$632$	23271.7	−	16907.9i	1.46471	−	1.06418i
$633$		0			0
$634$	−4982.12	−	15333.4i	−0.312090	−	0.960514i
$635$	−5240.84	+	16129.6i	−0.327522	+	1.00801i
$636$		0			0
$637$	−53473.5			−3.32605
$638$	−5492.39	−	4340.09i	−0.340824	−	0.269319i
$639$		0			0
$640$	−6797.40	−	4938.60i	−0.419829	−	0.305024i
$641$	5704.03	−	17555.2i	0.351475	−	1.08173i	−0.606550	−	0.795045i	$-0.707447\pi$
$641$	5704.03	−	17555.2i	0.351475	−	1.08173i	0.958025	−	0.286684i	$-0.0925529\pi$
$642$		0			0
$643$	−23792.8	+	17286.4i	−1.45925	+	1.06020i	−0.475686	+	0.879615i	$0.657800\pi$
$643$	−23792.8	+	17286.4i	−1.45925	+	1.06020i	−0.983559	+	0.180589i	$0.942200\pi$
$644$	−4216.69	+	3063.60i	−0.258014	+	0.187458i
$645$		0			0
$646$	−3868.70	+	11906.6i	−0.235622	+	0.725171i
$647$	−1793.76	−	1303.24i	−0.108995	−	0.0791897i	0.531953	−	0.846774i	$-0.321458\pi$
$647$	−1793.76	−	1303.24i	−0.108995	−	0.0791897i	−0.640948	+	0.767585i	$0.721458\pi$
$648$		0			0
$649$	−14646.3	−	592.297i	−0.885852	−	0.0358238i
$650$	−2954.86			−0.178306
$651$		0			0
$652$	−977.481	+	3008.38i	−0.0587134	+	0.180701i
$653$	−6953.29	−	21400.0i	−0.416697	−	1.28246i	−0.910724	−	0.413015i	$-0.864476\pi$
$653$	−6953.29	−	21400.0i	−0.416697	−	1.28246i	0.494027	−	0.869447i	$-0.335524\pi$
$654$		0			0
$655$	−8860.14	+	6437.27i	−0.528541	+	0.384008i
$656$	2034.09	+	6260.28i	0.121064	+	0.372596i
$657$		0			0
$658$	−14680.8	−	10666.2i	−0.869783	−	0.631934i
$659$	−5908.12			−0.349238			−0.174619	−	0.984636i	$-0.555869\pi$
$659$	−5908.12			−0.349238			−0.174619	+	0.984636i	$0.555869\pi$
$660$		0			0
$661$	22387.2			1.31734			0.658670	−	0.752432i	$-0.271120\pi$
$661$	22387.2			1.31734			0.658670	+	0.752432i	$0.271120\pi$
$662$	11400.8	+	8283.17i	0.669343	+	0.486306i
$663$		0			0
$664$	−5096.16	−	15684.4i	−0.297845	−	0.916673i
$665$	−25039.2	+	18192.1i	−1.46012	+	1.06084i
$666$		0			0
$667$	2162.07	+	6654.18i	0.125511	+	0.386283i
$668$	142.546	−	438.712i	0.00825641	−	0.0254106i
$669$		0			0
$670$	5773.42			0.332906
$671$	4009.10	+	14277.9i	0.230655	+	0.821450i
$672$		0			0
$673$	25692.3	+	18666.6i	1.47157	+	1.06916i	0.980155	+	0.198233i	$0.0635204\pi$
$673$	25692.3	+	18666.6i	1.47157	+	1.06916i	0.491416	+	0.870925i	$0.336480\pi$
$674$	−2363.77	+	7274.93i	−0.135087	+	0.415757i
$675$		0			0
$676$	4474.30	−	3250.77i	0.254569	−	0.184955i
$677$	−2970.62	+	2158.28i	−0.168641	+	0.122525i	−0.668905	−	0.743348i	$-0.733237\pi$
$677$	−2970.62	+	2158.28i	−0.168641	+	0.122525i	0.500263	+	0.865873i	$0.333237\pi$
$678$		0			0
$679$	2484.46	−	7646.38i	0.140419	−	0.432166i
$680$	11372.5	+	8262.58i	0.641344	+	0.465964i
$681$		0			0
$682$	2099.44	+	84.9011i	0.117876	+	0.00476691i
$683$	11719.2			0.656549			0.328274	−	0.944582i	$-0.393533\pi$
$683$	11719.2			0.656549			0.328274	+	0.944582i	$0.393533\pi$
$684$		0			0
$685$	−9909.46	+	30498.2i	−0.552732	+	1.70113i
$686$	9795.42	+	30147.2i	0.545176	+	1.67788i
$687$		0			0
$688$	5551.75	−	4033.58i	0.307643	−	0.223516i
$689$	−995.038	−	3062.41i	−0.0550188	−	0.169330i
$690$		0			0
$691$	−495.853	−	360.259i	−0.0272983	−	0.0198334i	0.574052	−	0.818819i	$-0.305371\pi$
$691$	−495.853	−	360.259i	−0.0272983	−	0.0198334i	−0.601351	+	0.798985i	$0.705371\pi$
$692$	−1160.55			−0.0637535
$693$		0			0
$694$	−26301.7			−1.43862
$695$	−9005.93	−	6543.19i	−0.491531	−	0.357119i
$696$		0			0
$697$	−2392.42	−	7363.13i	−0.130014	−	0.400141i
$698$	3045.07	−	2212.37i	0.165125	−	0.119971i
$699$		0			0
$700$	−284.817	−	876.576i	−0.0153787	−	0.0473306i
$701$	−8657.42	+	26644.8i	−0.466457	+	1.43561i	0.390684	+	0.920525i	$0.372238\pi$
$701$	−8657.42	+	26644.8i	−0.466457	+	1.43561i	−0.857141	+	0.515082i	$0.827762\pi$
$702$		0			0
$703$	11394.8			0.611328
$704$	17293.1	−	11526.2i	0.925794	−	0.617060i
$705$		0			0
$706$	23896.5	+	17361.9i	1.27388	+	0.925527i
$707$	229.686	−	706.902i	0.0122182	−	0.0376037i
$708$		0			0
$709$	−9146.28	+	6645.16i	−0.484479	+	0.351995i	−0.803057	−	0.595902i	$-0.796795\pi$
$709$	−9146.28	+	6645.16i	−0.484479	+	0.351995i	0.318578	+	0.947897i	$0.396795\pi$
$710$	−15824.3	+	11497.0i	−0.836442	+	0.607711i
$711$		0			0
$712$	−7938.51	+	24432.2i	−0.417849	+	1.28601i
$713$	−1699.00	−	1234.40i	−0.0892399	−	0.0648366i
$714$		0			0
$715$	−9682.28	+	26152.5i	−0.506429	+	1.36790i
$716$	−113.541			−0.00592631
$717$		0			0
$718$	2555.60	−	7865.34i	0.132833	−	0.408819i
$719$	−3455.04	−	10633.5i	−0.179209	−	0.551549i	0.820592	−	0.571515i	$-0.193644\pi$
$719$	−3455.04	−	10633.5i	−0.179209	−	0.551549i	−0.999801	+	0.0199662i	$0.993644\pi$
$720$		0			0
$721$	26006.9	−	18895.1i	1.34334	−	0.975994i
$722$	−1036.73	−	3190.72i	−0.0534390	−	0.164468i
$723$		0			0
$724$	−57.8138	−	42.0042i	−0.00296772	−	0.00215618i
$725$	−1237.25			−0.0633798
$726$		0			0
$727$	−31428.7			−1.60334			−0.801669	−	0.597769i	$-0.796054\pi$
$727$	−31428.7			−1.60334			−0.801669	+	0.597769i	$0.796054\pi$
$728$	−47314.4	−	34375.9i	−2.40878	−	1.75008i
$729$		0			0
$730$	−1790.28	−	5509.91i	−0.0907687	−	0.279357i
$731$	−6529.77	+	4744.16i	−0.330386	+	0.240040i
$732$		0			0
$733$	392.631	+	1208.39i	0.0197847	+	0.0608910i	0.960461	−	0.278413i	$-0.0898084\pi$
$733$	392.631	+	1208.39i	0.0197847	+	0.0608910i	−0.940677	+	0.339304i	$0.889808\pi$
$734$	2772.75	−	8533.64i	0.139433	−	0.429131i
$735$		0			0
$736$	−7061.87			−0.353674
$737$	−2802.29	+	7569.17i	−0.140059	+	0.378309i
$738$		0			0
$739$	−10929.8	−	7940.95i	−0.544057	−	0.395281i	0.281532	−	0.959552i	$-0.409157\pi$
$739$	−10929.8	−	7940.95i	−0.544057	−	0.395281i	−0.825590	+	0.564271i	$0.809157\pi$
$740$	707.898	−	2178.68i	0.0351660	−	0.108230i
$741$		0			0
$742$	−2913.17	+	2116.54i	−0.144132	+	0.104718i
$743$	25972.0	−	18869.8i	1.28240	−	0.931716i	0.282775	−	0.959186i	$-0.408745\pi$
$743$	25972.0	−	18869.8i	1.28240	−	0.931716i	0.999623	+	0.0274700i	$0.00874508\pi$
$744$		0			0
$745$	6802.97	−	20937.4i	0.334552	−	1.02965i
$746$	−4092.02	−	2973.03i	−0.200830	−	0.145912i
$747$		0			0
$748$	−2927.86	+	1951.48i	−0.143119	+	0.0953918i
$749$	−21814.3			−1.06419
$750$		0			0
$751$	−7329.02	+	22556.4i	−0.356111	+	1.09600i	0.599251	+	0.800561i	$0.295465\pi$
$751$	−7329.02	+	22556.4i	−0.356111	+	1.09600i	−0.955362	+	0.295437i	$0.904535\pi$
$752$	−3216.94	−	9900.71i	−0.155997	−	0.480109i
$753$		0			0
$754$	−11372.0	+	8262.21i	−0.549260	+	0.399061i
$755$	−3827.63	−	11780.2i	−0.184506	−	0.567850i
$756$		0			0
$757$	18715.6	+	13597.7i	0.898589	+	0.652863i	0.938103	−	0.346356i	$-0.112581\pi$
$757$	18715.6	+	13597.7i	0.898589	+	0.652863i	−0.0395142	+	0.999219i	$0.512581\pi$
$758$	14518.1			0.695672
$759$		0			0
$760$	−23028.8			−1.09913
$761$	667.872	+	485.238i	0.0318139	+	0.0231141i	0.603579	−	0.797304i	$-0.293741\pi$
$761$	667.872	+	485.238i	0.0318139	+	0.0231141i	−0.571765	+	0.820418i	$0.693741\pi$
$762$		0			0
$763$	−866.969	−	2668.26i	−0.0411355	−	0.126602i
$764$	−6464.80	+	4696.95i	−0.306136	+	0.222421i
$765$		0			0
$766$	−4048.46	−	12459.9i	−0.190962	−	0.587720i
$767$	−9095.64	+	27993.5i	−0.428194	+	1.31784i
$768$		0			0
$769$	9591.21			0.449763			0.224882	−	0.974386i	$-0.427800\pi$
$769$	9591.21			0.449763			0.224882	+	0.974386i	$0.427800\pi$
$770$	31160.3	+	1260.12i	1.45836	+	0.0589761i
$771$		0			0
$772$	−7120.74	−	5173.52i	−0.331970	−	0.241191i
$773$	−724.297	+	2229.16i	−0.0337014	+	0.103722i	−0.966492	−	0.256696i	$-0.917366\pi$
$773$	−724.297	+	2229.16i	−0.0337014	+	0.103722i	0.932791	+	0.360418i	$0.117366\pi$
$774$		0			0
$775$	300.443	−	218.285i	0.0139255	−	0.0101175i
$776$	4839.66	−	3516.22i	0.223883	−	0.162661i
$777$		0			0
$778$	−65.6816	+	202.147i	−0.00302674	+	0.00931533i
$779$	10260.9	+	7455.02i	0.471934	+	0.342880i
$780$		0			0
$781$	−7392.24	−	26326.6i	−0.338688	−	1.20620i
$782$	−12608.2			−0.576559
$783$		0			0
$784$	−10600.8	+	32626.0i	−0.482909	+	1.48624i
$785$	5961.64	+	18348.0i	0.271057	+	0.834229i
$786$		0			0
$787$	21078.8	−	15314.6i	0.954736	−	0.693656i	0.00281375	−	0.999996i	$-0.499104\pi$
$787$	21078.8	−	15314.6i	0.954736	−	0.693656i	0.951922	+	0.306340i	$0.0991044\pi$
$788$	918.337	+	2826.35i	0.0415157	+	0.127772i
$789$		0			0
$790$	24918.2	+	18104.1i	1.12221	+	0.815336i
$791$	−14421.8			−0.648269
$792$		0			0
$793$	29779.1			1.33353
$794$	−14543.5	−	10566.5i	−0.650039	−	0.472281i
$795$		0			0
$796$	1793.32	+	5519.27i	0.0798525	+	0.245761i
$797$	35109.5	−	25508.5i	1.56040	−	1.13370i	0.624727	−	0.780844i	$-0.285210\pi$
$797$	35109.5	−	25508.5i	1.56040	−	1.13370i	0.935677	−	0.352856i	$-0.114790\pi$
$798$		0			0
$799$	3783.65	+	11644.9i	0.167529	+	0.515602i
$800$	385.897	−	1187.67i	0.0170544	−	0.0524881i
$801$		0			0
$802$	5687.54			0.250417
$803$	8092.65	+	327.267i	0.355646	+	0.0143823i
$804$		0			0
$805$	−25216.9	−	18321.2i	−1.10407	−	0.802157i
$806$	1303.79	−	4012.65i	0.0569777	−	0.175359i
$807$		0			0
$808$	447.423	−	325.072i	0.0194805	−	0.0141534i
$809$	−6863.36	+	4986.53i	−0.298273	+	0.216708i	−0.726848	−	0.686798i	$-0.759016\pi$
$809$	−6863.36	+	4986.53i	−0.298273	+	0.216708i	0.428575	+	0.903506i	$0.359016\pi$
$810$		0			0
$811$	1715.59	−	5280.06i	0.0742820	−	0.228616i	−0.907021	−	0.421085i	$-0.861649\pi$
$811$	1715.59	−	5280.06i	0.0742820	−	0.228616i	0.981303	+	0.192469i	$0.0616494\pi$
$812$	−3547.17	−	2577.17i	−0.153302	−	0.111380i
$813$		0			0
$814$	−9008.48	−	7118.49i	−0.387895	−	0.306515i
$815$	−18916.8			−0.813037
$816$		0			0
$817$	4085.98	−	12575.4i	0.174970	−	0.538502i
$818$	7425.09	+	22852.1i	0.317374	+	0.976777i
$819$		0			0
$820$	2062.85	−	1498.75i	0.0878512	−	0.0638276i
$821$	32.7348	+	100.748i	0.00139154	+	0.00428272i	0.951750	−	0.306875i	$-0.0992833\pi$
$821$	32.7348	+	100.748i	0.00139154	+	0.00428272i	−0.950358	+	0.311158i	$0.899283\pi$
$822$		0			0
$823$	−30200.5	−	21941.9i	−1.27913	−	0.929341i	−0.279602	−	0.960116i	$-0.590202\pi$
$823$	−30200.5	−	21941.9i	−1.27913	−	0.929341i	−0.999526	+	0.0307751i	$0.990202\pi$
$824$	23918.8			1.01123
$825$		0			0
$826$	32915.6			1.38654
$827$	−1408.83	−	1023.58i	−0.0592380	−	0.0430389i	0.557772	−	0.829994i	$-0.311656\pi$
$827$	−1408.83	−	1023.58i	−0.0592380	−	0.0430389i	−0.617010	+	0.786955i	$0.711656\pi$
$828$		0			0
$829$	−1629.09	−	5013.82i	−0.0682516	−	0.210057i	0.911114	−	0.412155i	$-0.135224\pi$
$829$	−1629.09	−	5013.82i	−0.0682516	−	0.210057i	−0.979365	+	0.202098i	$0.935224\pi$
$830$	14285.8	−	10379.3i	0.597432	−	0.434060i
$831$		0			0
$832$	−12895.7	−	39688.8i	−0.537353	−	1.65380i
$833$	12468.3	−	38373.5i	0.518609	−	1.59611i
$834$		0			0
$835$	2758.64			0.114331
$836$	2001.33	−	5405.71i	0.0827958	−	0.223637i
$837$		0			0
$838$	−21806.7	−	15843.5i	−0.898928	−	0.653109i
$839$	−7446.81	+	22918.9i	−0.306427	+	0.943086i	0.672714	+	0.739903i	$0.265129\pi$
$839$	−7446.81	+	22918.9i	−0.306427	+	0.943086i	−0.979141	+	0.203183i	$0.934871\pi$
$840$		0			0
$841$	14969.5	−	10876.0i	0.613780	−	0.445937i
$842$	2491.53	−	1810.20i	0.101976	−	0.0740898i
$843$		0			0
$844$	−2674.76	+	8232.06i	−0.109086	+	0.335734i
$845$	26757.5	+	19440.5i	1.08933	+	0.791447i
$846$		0			0
$847$	−16776.6	+	40240.6i	−0.680578	+	1.63245i
$848$	−2065.74			−0.0836531
$849$		0			0
$850$	688.979	−	2120.46i	0.0278021	−	0.0855660i
$851$	3546.18	+	10914.0i	0.142845	+	0.439633i
$852$		0			0
$853$	22983.5	−	16698.5i	0.922555	−	0.670275i	−0.0216040	−	0.999767i	$-0.506877\pi$
$853$	22983.5	−	16698.5i	0.922555	−	0.670275i	0.944159	+	0.329491i	$0.106877\pi$
$854$	−10290.7	−	31671.5i	−0.412343	−	1.26906i
$855$		0			0
$856$	−13131.2	−	9540.40i	−0.524318	−	0.380939i
$857$	6941.16			0.276669			0.138335	−	0.990386i	$-0.455825\pi$
$857$	6941.16			0.276669			0.138335	+	0.990386i	$0.455825\pi$
$858$		0			0
$859$	21637.2			0.859430			0.429715	−	0.902965i	$-0.358614\pi$
$859$	21637.2			0.859430			0.429715	+	0.902965i	$0.358614\pi$
$860$	−2150.57	−	1562.48i	−0.0852718	−	0.0619536i
$861$		0			0
$862$	6732.46	+	20720.4i	0.266019	+	0.818723i
$863$	6019.83	−	4373.67i	0.237448	−	0.172516i	−0.462698	−	0.886516i	$-0.653118\pi$
$863$	6019.83	−	4373.67i	0.237448	−	0.172516i	0.700146	+	0.714000i	$0.253118\pi$
$864$		0			0
$865$	−2144.70	−	6600.70i	−0.0843028	−	0.259457i
$866$	−5786.56	+	17809.2i	−0.227062	+	0.698824i
$867$		0			0
$868$	1316.05			0.0514626
$869$	−35829.9	+	23881.3i	−1.39867	+	0.932242i
$870$		0			0
$871$	13111.9	+	9526.37i	0.510081	+	0.370595i
$872$	645.076	−	1985.34i	0.0250516	−	0.0771010i
$873$		0			0
$874$	16710.4	−	12140.8i	0.646723	−	0.469872i
$875$	39022.4	−	28351.4i	1.50765	−	1.09537i
$876$		0			0
$877$	−9984.83	+	30730.2i	−0.384451	+	1.18322i	0.552426	+	0.833562i	$0.313702\pi$
$877$	−9984.83	+	30730.2i	−0.384451	+	1.18322i	−0.936877	+	0.349658i	$0.886298\pi$
$878$	19416.3	+	14106.8i	0.746320	+	0.542233i
$879$		0			0
$880$	14037.0	+	11092.1i	0.537714	+	0.424902i
$881$	−21907.4			−0.837774			−0.418887	−	0.908038i	$-0.637580\pi$
$881$	−21907.4			−0.837774			−0.418887	+	0.908038i	$0.637580\pi$
$882$		0			0
$883$	−370.914	+	1141.56i	−0.0141362	+	0.0435067i	−0.957876	−	0.287183i	$-0.907281\pi$
$883$	−370.914	+	1141.56i	−0.0141362	+	0.0435067i	0.943740	+	0.330689i	$0.107281\pi$
$884$	2183.34	+	6719.64i	0.0830699	+	0.255663i
$885$		0			0
$886$	−18799.1	+	13658.3i	−0.712831	+	0.517902i
$887$	7342.41	+	22597.6i	0.277941	+	0.855415i	0.988426	+	0.151703i	$0.0484757\pi$
$887$	7342.41	+	22597.6i	0.277941	+	0.855415i	−0.710485	+	0.703712i	$0.751524\pi$
$888$		0			0
$889$	43072.7	+	31294.1i	1.62498	+	1.18062i
$890$	−27507.1			−1.03600
$891$		0			0
$892$	6419.26			0.240956
$893$	−16227.8	−	11790.2i	−0.608111	−	0.441818i
$894$		0			0
$895$	−209.825	−	645.775i	−0.00783651	−	0.0241183i
$896$	−21338.7	+	15503.5i	−0.795622	+	0.578053i
$897$		0			0
$898$	−5302.29	−	16318.8i	−0.197038	−	0.606419i
$899$	545.919	−	1680.17i	0.0202530	−	0.0623323i
$900$		0			0
$901$	2429.65			0.0898374
$902$	−3454.82	−	12303.9i	−0.127531	−	0.454186i
$903$		0			0
$904$	−8681.31	−	6307.34i	−0.319398	−	0.232057i
$905$	132.062	−	406.444i	0.00485069	−	0.0149289i
$906$		0			0
$907$	10232.4	−	7434.24i	0.374597	−	0.272161i	−0.384517	−	0.923118i	$-0.625632\pi$
$907$	10232.4	−	7434.24i	0.374597	−	0.272161i	0.759115	+	0.650957i	$0.225632\pi$
$908$	−567.053	+	411.988i	−0.0207250	+	0.0150576i
$909$		0			0
$910$	19351.1	−	59556.6i	0.704927	−	2.16954i
$911$	−10814.5	−	7857.18i	−0.393304	−	0.285752i	0.373504	−	0.927628i	$-0.378156\pi$
$911$	−10814.5	−	7857.18i	−0.393304	−	0.285752i	−0.766808	+	0.641877i	$0.778156\pi$
$912$		0			0
$913$	6673.58	+	23767.1i	0.241909	+	0.861531i
$914$	−2891.93			−0.104657
$915$		0			0
$916$	1591.54	−	4898.26i	0.0574082	−	0.176684i
$917$	10624.1	+	32697.6i	0.382593	+	1.17750i
$918$		0			0
$919$	14994.8	−	10894.4i	0.538230	−	0.391047i	−0.285197	−	0.958469i	$-0.592059\pi$
$919$	14994.8	−	10894.4i	0.538230	−	0.391047i	0.823427	+	0.567422i	$0.192059\pi$
$920$	−7166.78	−	22057.1i	−0.256828	−	0.790435i
$921$		0			0
$922$	16986.1	+	12341.1i	0.606732	+	0.440817i
$923$	−54908.7			−1.95812
$924$		0			0
$925$	−2029.31			−0.0721332
$926$	3645.03	+	2648.27i	0.129355	+	0.0939822i
$927$		0			0
$928$	−1835.75	−	5649.85i	−0.0649368	−	0.199855i
$929$	21222.9	−	15419.3i	0.749517	−	0.544556i	−0.146160	−	0.989261i	$-0.546691\pi$
$929$	21222.9	−	15419.3i	0.749517	−	0.544556i	0.895677	+	0.444705i	$0.146691\pi$
$930$		0			0
$931$	20425.9	+	62864.5i	0.719047	+	2.21300i
$932$	−1329.47	+	4091.70i	−0.0467257	+	0.143807i
$933$		0			0
$934$	−47575.7			−1.66673
$935$	−16509.9	−	13046.1i	−0.577466	−	0.456314i
$936$		0			0
$937$	11249.4	+	8173.17i	0.392212	+	0.284958i	0.766361	−	0.642410i	$-0.222065\pi$
$937$	11249.4	+	8173.17i	0.392212	+	0.284958i	−0.374150	+	0.927368i	$0.622065\pi$
$938$	5600.69	−	17237.2i	0.194956	−	0.600014i
$939$		0			0
$940$	−3262.43	+	2370.29i	−0.113201	+	0.0822452i
$941$	29656.0	−	21546.4i	1.02737	−	0.746431i	0.0595926	−	0.998223i	$-0.481020\pi$
$941$	29656.0	−	21546.4i	1.02737	−	0.746431i	0.967781	+	0.251792i	$0.0810199\pi$
$942$		0			0
$943$	−3947.15	+	12148.1i	−0.136306	+	0.419508i
$944$	15276.6	+	11099.1i	0.526707	+	0.382675i
$945$		0			0
$946$	−11086.3	+	7389.23i	−0.381022	+	0.253958i
$947$	9454.30			0.324417			0.162209	−	0.986756i	$-0.448138\pi$
$947$	9454.30			0.324417			0.162209	+	0.986756i	$0.448138\pi$
$948$		0			0
$949$	5025.69	−	15467.5i	0.171908	−	0.529079i
$950$	1128.70	+	3473.79i	0.0385473	+	0.118637i
$951$		0			0
$952$	35701.0	−	25938.3i	1.21542	−	0.883052i
$953$	−9444.38	−	29066.8i	−0.321022	−	0.988003i	−0.973204	−	0.229941i	$-0.926147\pi$
$953$	−9444.38	−	29066.8i	−0.321022	−	0.988003i	0.652183	−	0.758062i	$-0.273853\pi$
$954$		0			0
$955$	−38661.2	−	28089.0i	−1.31000	−	0.951769i
$956$	−7407.31			−0.250596
$957$		0			0
$958$	−42312.6			−1.42699
$959$	81442.6	+	59171.5i	2.74235	+	1.99244i
$960$		0			0
$961$	−9042.06	−	27828.6i	−0.303517	−	0.934128i
$962$	−18652.0	+	13551.5i	−0.625119	+	0.454175i
$963$		0			0
$964$	1448.33	+	4457.51i	0.0483897	+	0.148928i
$965$	16265.6	−	50060.4i	0.542600	−	1.66995i
$966$		0			0
$967$	−30119.6			−1.00164			−0.500818	−	0.865553i	$-0.666967\pi$
$967$	−30119.6			−1.00164			−0.500818	+	0.865553i	$0.666967\pi$
$968$	−27697.9	+	16885.9i	−0.919673	+	0.560676i
$969$		0			0
$970$	5182.06	+	3764.99i	0.171532	+	0.124625i
$971$	9953.51	−	30633.7i	0.328963	−	1.01244i	−0.640657	−	0.767828i	$-0.721338\pi$
$971$	9953.51	−	30633.7i	0.328963	−	1.01244i	0.969620	−	0.244617i	$-0.0786622\pi$
$972$		0			0
$973$	−28271.9	+	20540.7i	−0.931505	+	0.676778i
$974$	−18627.1	+	13533.4i	−0.612782	+	0.445212i
$975$		0			0
$976$	5903.55	−	18169.3i	0.193615	−	0.595885i
$977$	−6868.82	−	4990.49i	−0.224926	−	0.163419i	0.469615	−	0.882871i	$-0.344393\pi$
$977$	−6868.82	−	4990.49i	−0.224926	−	0.163419i	−0.694541	+	0.719453i	$0.744393\pi$
$978$		0			0
$979$	13351.3	−	36062.8i	0.435864	−	1.17730i
$980$	13288.6			0.433153
$981$		0			0
$982$	12678.5	−	39020.3i	0.412003	−	1.26801i
$983$	1043.50	+	3211.55i	0.0338580	+	0.104204i	0.966557	−	0.256451i	$-0.0825532\pi$
$983$	1043.50	+	3211.55i	0.0338580	+	0.104204i	−0.932699	+	0.360655i	$0.882553\pi$
$984$		0			0
$985$	−14378.0	+	10446.2i	−0.465097	+	0.337913i
$986$	−3277.53	−	10087.2i	−0.105860	−	0.325803i
$987$		0			0
$988$	−9364.21	−	6803.50i	−0.301534	−	0.219077i
$989$	13316.4			0.428145
$990$		0			0
$991$	−20081.5			−0.643703			−0.321851	−	0.946790i	$-0.604305\pi$
$991$	−20081.5			−0.643703			−0.321851	+	0.946790i	$0.604305\pi$
$992$	1442.57	+	1048.08i	0.0461709	+	0.0335451i
$993$		0			0
$994$	18974.7	+	58398.0i	0.605473	+	1.86345i
$995$	−28077.2	+	20399.3i	−0.894580	+	0.649951i
$996$		0			0
$997$	−10625.0	−	32700.4i	−0.337510	−	1.03875i	−0.965472	−	0.260506i	$-0.916111\pi$
$997$	−10625.0	−	32700.4i	−0.337510	−	1.03875i	0.627962	−	0.778244i	$-0.283889\pi$
$998$	3579.42	−	11016.3i	0.113532	−	0.349414i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.b.37.2		8
3.2	odd	2		33.4.e.b.4.1	✓	8
11.3	even	5	inner	99.4.f.b.91.2		8
11.5	even	5		1089.4.a.bg.1.1		4
11.6	odd	10		1089.4.a.z.1.4		4
33.5	odd	10		363.4.a.p.1.4		4
33.14	odd	10		33.4.e.b.25.1	yes	8
33.17	even	10		363.4.a.t.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.4.1	✓	8	3.2	odd	2
33.4.e.b.25.1	yes	8	33.14	odd	10
99.4.f.b.37.2		8	1.1	even	1	trivial
99.4.f.b.91.2		8	11.3	even	5	inner
363.4.a.p.1.4		4	33.5	odd	10
363.4.a.t.1.1		4	33.17	even	10
1089.4.a.z.1.4		4	11.6	odd	10
1089.4.a.bg.1.1		4	11.5	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02339 + 1.47008i) q^{2} +(-0.539165 - 1.65938i) q^{4} +(8.44146 - 6.13308i) q^{5} +(-10.1220 - 31.1524i) q^{7} +(7.53140 - 23.1793i) q^{8} +O(q^{10})\)	\(q+(2.02339 + 1.47008i) q^{2} +(-0.539165 - 1.65938i) q^{4} +(8.44146 - 6.13308i) q^{5} +(-10.1220 - 31.1524i) q^{7} +(7.53140 - 23.1793i) q^{8} +26.0964 q^{10} +(-12.6666 + 34.2134i) q^{11} +(59.2672 + 43.0601i) q^{13} +(25.3157 - 77.9137i) q^{14} +(38.0218 - 27.6245i) q^{16} +(-44.7200 + 32.4909i) q^{17} +(27.9834 - 86.1240i) q^{19} +(-14.7284 - 10.7008i) q^{20} +(-75.9259 + 50.6060i) q^{22} +91.1987 q^{23} +(-4.98357 + 15.3379i) q^{25} +(56.6188 + 174.255i) q^{26} +(-46.2362 + 33.5926i) q^{28} +(23.7073 + 72.9635i) q^{29} +(-18.6296 - 13.5352i) q^{31} -77.4339 q^{32} -138.250 q^{34} +(-276.505 - 200.893i) q^{35} +(38.8841 + 119.673i) q^{37} +(183.230 - 133.124i) q^{38} +(-78.5842 - 241.857i) q^{40} +(-43.2807 + 133.204i) q^{41} +146.015 q^{43} +(63.6024 + 2.57208i) q^{44} +(184.530 + 134.069i) q^{46} +(68.4490 - 210.664i) q^{47} +(-590.526 + 429.042i) q^{49} +(-32.6315 + 23.7082i) q^{50} +(39.4983 - 121.563i) q^{52} +(-35.5597 - 25.8356i) q^{53} +(102.909 + 366.496i) q^{55} -798.324 q^{56} +(-59.2930 + 182.485i) q^{58} +(124.159 + 382.121i) q^{59} +(328.861 - 238.932i) q^{61} +(-17.7972 - 54.7740i) q^{62} +(-460.853 - 334.830i) q^{64} +764.393 q^{65} +221.234 q^{67} +(78.0262 + 56.6893i) q^{68} +(-264.149 - 812.968i) q^{70} +(-606.376 + 440.558i) q^{71} +(-68.6023 - 211.136i) q^{73} +(-97.2508 + 299.307i) q^{74} -158.000 q^{76} +(1194.04 + 48.2871i) q^{77} +(954.850 + 693.739i) q^{79} +(151.537 - 466.382i) q^{80} +(-283.394 + 205.898i) q^{82} +(547.425 - 397.728i) q^{83} +(-178.232 + 548.542i) q^{85} +(295.444 + 214.653i) q^{86} +(697.644 + 551.278i) q^{88} -1054.06 q^{89} +(741.524 - 2282.17i) q^{91} +(-49.1711 - 151.333i) q^{92} +(448.192 - 325.630i) q^{94} +(-291.985 - 898.636i) q^{95} +(198.573 + 144.272i) q^{97} -1825.59 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8}+O(q^{10}) \) 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8	\( 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8} + 8 q^{10} + 87 q^{11} + 171 q^{13} - 12 q^{14} + 44 q^{16} - 36 q^{17} + 324 q^{19} + 87 q^{20} - 521 q^{22} + 84 q^{23} + 263 q^{25} + 774 q^{26} + 387 q^{28} - 393 q^{29} + 15 q^{31} - 102 q^{32} - 712 q^{34} - 1002 q^{35} - 747 q^{37} + 36 q^{38} + 41 q^{40} - 159 q^{41} - 644 q^{43} - 219 q^{44} + 753 q^{46} + 351 q^{47} - 1967 q^{49} - 330 q^{50} + 2871 q^{52} + 531 q^{53} - 716 q^{55} - 1470 q^{56} - 1205 q^{58} + 1002 q^{59} + 1449 q^{61} - 99 q^{62} - 1118 q^{64} + 954 q^{65} - 518 q^{67} - 873 q^{68} + 26 q^{70} - 429 q^{71} + 2547 q^{73} - 468 q^{74} - 2276 q^{76} + 2697 q^{77} + 2805 q^{79} + 1620 q^{80} - 1631 q^{82} + 2553 q^{83} - 197 q^{85} + 1713 q^{86} + 2866 q^{88} - 1788 q^{89} + 2885 q^{91} - 423 q^{92} + 1159 q^{94} - 3009 q^{95} + 9 q^{97} - 5550 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8 + 8 * q^10 + 87 * q^11 + 171 * q^13 - 12 * q^14 + 44 * q^16 - 36 * q^17 + 324 * q^19 + 87 * q^20 - 521 * q^22 + 84 * q^23 + 263 * q^25 + 774 * q^26 + 387 * q^28 - 393 * q^29 + 15 * q^31 - 102 * q^32 - 712 * q^34 - 1002 * q^35 - 747 * q^37 + 36 * q^38 + 41 * q^40 - 159 * q^41 - 644 * q^43 - 219 * q^44 + 753 * q^46 + 351 * q^47 - 1967 * q^49 - 330 * q^50 + 2871 * q^52 + 531 * q^53 - 716 * q^55 - 1470 * q^56 - 1205 * q^58 + 1002 * q^59 + 1449 * q^61 - 99 * q^62 - 1118 * q^64 + 954 * q^65 - 518 * q^67 - 873 * q^68 + 26 * q^70 - 429 * q^71 + 2547 * q^73 - 468 * q^74 - 2276 * q^76 + 2697 * q^77 + 2805 * q^79 + 1620 * q^80 - 1631 * q^82 + 2553 * q^83 - 197 * q^85 + 1713 * q^86 + 2866 * q^88 - 1788 * q^89 + 2885 * q^91 - 423 * q^92 + 1159 * q^94 - 3009 * q^95 + 9 * q^97 - 5550 * q^98

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