LMFDB - Embedded newform 99.4.f.b.82.1

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			82.1
Root			$-1.20316 + 0.874145i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.4.f.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0404346 + 0.124445i) q^{2} +(6.45828 - 4.69222i) q^{4} +(-2.06705 + 6.36172i) q^{5} +(11.6029 - 8.43002i) q^{7} +(1.69194 + 1.22926i) q^{8} +O(q^{10})$	\(q+(0.0404346 + 0.124445i) q^{2} +(6.45828 - 4.69222i) q^{4} +(-2.06705 + 6.36172i) q^{5} +(11.6029 - 8.43002i) q^{7} +(1.69194 + 1.22926i) q^{8} -0.875265 q^{10} +(28.3816 - 22.9234i) q^{11} +(10.8178 + 33.2938i) q^{13} +(1.51823 + 1.10306i) q^{14} +(19.6502 - 60.4771i) q^{16} +(21.6244 - 66.5530i) q^{17} +(45.0187 + 32.7080i) q^{19} +(16.5010 + 50.7849i) q^{20} +(4.00030 + 2.60506i) q^{22} +43.4430 q^{23} +(64.9283 + 47.1732i) q^{25} +(-3.70583 + 2.69244i) q^{26} +(35.3795 - 108.887i) q^{28} +(-168.156 + 122.172i) q^{29} +(-38.3253 - 117.953i) q^{31} +25.0514 q^{32} +9.15657 q^{34} +(29.6457 + 91.2399i) q^{35} +(-316.639 + 230.052i) q^{37} +(-2.25003 + 6.92488i) q^{38} +(-11.3175 + 8.22268i) q^{40} +(-340.499 - 247.387i) q^{41} -410.216 q^{43} +(75.7352 - 281.219i) q^{44} +(1.75660 + 5.40626i) q^{46} +(177.304 + 128.819i) q^{47} +(-42.4301 + 130.586i) q^{49} +(-3.24511 + 9.98743i) q^{50} +(226.086 + 164.261i) q^{52} +(109.401 + 336.701i) q^{53} +(87.1660 + 227.940i) q^{55} +29.9941 q^{56} +(-22.0031 - 15.9862i) q^{58} +(2.98246 - 2.16688i) q^{59} +(37.7322 - 116.128i) q^{61} +(13.1290 - 9.53880i) q^{62} +(-156.189 - 480.699i) q^{64} -234.167 q^{65} -219.635 q^{67} +(-172.625 - 531.285i) q^{68} +(-10.1556 + 7.37851i) q^{70} +(-332.200 + 1022.41i) q^{71} +(592.358 - 430.373i) q^{73} +(-41.4320 - 30.1021i) q^{74} +444.216 q^{76} +(136.066 - 505.237i) q^{77} +(-85.3301 - 262.619i) q^{79} +(344.121 + 250.018i) q^{80} +(17.0181 - 52.3764i) q^{82} +(117.512 - 361.666i) q^{83} +(378.693 + 275.137i) q^{85} +(-16.5869 - 51.0493i) q^{86} +(76.1988 - 3.89639i) q^{88} +1309.41 q^{89} +(406.185 + 295.111i) q^{91} +(280.567 - 203.844i) q^{92} +(-8.86164 + 27.2733i) q^{94} +(-301.135 + 218.787i) q^{95} +(242.603 + 746.654i) q^{97} -17.9665 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.0404346	+	0.124445i	0.0142958	+	0.0439980i	0.957950	−	0.286935i	$-0.0926365\pi$
$2$	0.0404346	+	0.124445i	0.0142958	+	0.0439980i	−0.943654	+	0.330933i	$0.892636\pi$
$3$		0			0
$3$		0			0
$4$	6.45828	−	4.69222i	0.807286	−	0.586527i
$5$	−2.06705	+	6.36172i	−0.184883	+	0.569010i	−0.999946	−	0.0103613i	$-0.996702\pi$
$5$	−2.06705	+	6.36172i	−0.184883	+	0.569010i	0.815064	+	0.579371i	$0.196702\pi$
$6$		0			0
$7$	11.6029	−	8.43002i	0.626500	−	0.455179i	−0.228686	−	0.973500i	$-0.573443\pi$
$7$	11.6029	−	8.43002i	0.626500	−	0.455179i	0.855186	+	0.518322i	$0.173443\pi$
$8$	1.69194	+	1.22926i	0.0747737	+	0.0543263i
$9$		0			0
$10$	−0.875265			−0.0276783
$11$	28.3816	−	22.9234i	0.777944	−	0.628333i
$11$	28.3816	−	22.9234i	0.777944	−	0.628333i
$12$		0			0
$13$	10.8178	+	33.2938i	0.230794	+	0.710310i	0.997652	+	0.0684930i	$0.0218191\pi$
$13$	10.8178	+	33.2938i	0.230794	+	0.710310i	−0.766858	+	0.641817i	$0.778181\pi$
$14$	1.51823	+	1.10306i	0.0289832	+	0.0210576i
$15$		0			0
$16$	19.6502	−	60.4771i	0.307034	−	0.944955i
$17$	21.6244	−	66.5530i	0.308511	−	0.949499i	−0.669833	−	0.742512i	$-0.733634\pi$
$17$	21.6244	−	66.5530i	0.308511	−	0.949499i	0.978344	−	0.206987i	$-0.0663657\pi$
$18$		0			0
$19$	45.0187	+	32.7080i	0.543578	+	0.394933i	0.825412	−	0.564530i	$-0.190943\pi$
$19$	45.0187	+	32.7080i	0.543578	+	0.394933i	−0.281834	+	0.959463i	$0.590943\pi$
$20$	16.5010	+	50.7849i	0.184487	+	0.567792i
$21$		0			0
$22$	4.00030	+	2.60506i	0.0387667	+	0.0252454i
$23$	43.4430			0.393847			0.196924	−	0.980419i	$-0.436905\pi$
$23$	43.4430			0.393847			0.196924	+	0.980419i	$0.436905\pi$
$24$		0			0
$25$	64.9283	+	47.1732i	0.519426	+	0.377385i
$26$	−3.70583	+	2.69244i	−0.0279528	+	0.0203089i
$27$		0			0
$28$	35.3795	−	108.887i	0.238789	−	0.734918i
$29$	−168.156	+	122.172i	−1.07675	+	0.782306i	−0.977114	−	0.212718i	$-0.931768\pi$
$29$	−168.156	+	122.172i	−1.07675	+	0.782306i	−0.0996377	+	0.995024i	$0.531768\pi$
$30$		0			0
$31$	−38.3253	−	117.953i	−0.222046	−	0.683388i	−0.998578	−	0.0533101i	$-0.983023\pi$
$31$	−38.3253	−	117.953i	−0.222046	−	0.683388i	0.776532	−	0.630078i	$-0.216977\pi$
$32$	25.0514			0.138391
$33$		0			0
$34$	9.15657			0.0461864
$35$	29.6457	+	91.2399i	0.143172	+	0.440639i
$36$		0			0
$37$	−316.639	+	230.052i	−1.40690	+	1.02217i	−0.413133	+	0.910671i	$0.635566\pi$
$37$	−316.639	+	230.052i	−1.40690	+	1.02217i	−0.993764	+	0.111500i	$0.964434\pi$
$38$	−2.25003	+	6.92488i	−0.00960535	+	0.0295622i
$39$		0			0
$40$	−11.3175	+	8.22268i	−0.0447365	+	0.0325030i
$41$	−340.499	−	247.387i	−1.29700	−	0.942326i	−0.297079	−	0.954853i	$-0.596013\pi$
$41$	−340.499	−	247.387i	−1.29700	−	0.942326i	−0.999922	+	0.0125265i	$0.996013\pi$
$42$		0			0
$43$	−410.216			−1.45482			−0.727410	−	0.686203i	$-0.759276\pi$
$43$	−410.216			−1.45482			−0.727410	+	0.686203i	$0.759276\pi$
$44$	75.7352	−	281.219i	0.259489	−	0.963530i
$45$		0			0
$46$	1.75660	+	5.40626i	0.00563036	+	0.0173285i
$47$	177.304	+	128.819i	0.550265	+	0.399791i	0.827883	−	0.560901i	$-0.189545\pi$
$47$	177.304	+	128.819i	0.550265	+	0.399791i	−0.277618	+	0.960691i	$0.589545\pi$
$48$		0			0
$49$	−42.4301	+	130.586i	−0.123703	+	0.380718i
$50$	−3.24511	+	9.98743i	−0.00917856	+	0.0282487i
$51$		0			0
$52$	226.086	+	164.261i	0.602933	+	0.438056i
$53$	109.401	+	336.701i	0.283535	+	0.872630i	0.986834	+	0.161736i	$0.0517093\pi$
$53$	109.401	+	336.701i	0.283535	+	0.872630i	−0.703299	+	0.710894i	$0.748291\pi$
$54$		0			0
$55$	87.1660	+	227.940i	0.213699	+	0.558826i
$56$	29.9941			0.0715738
$57$		0			0
$58$	−22.0031	−	15.9862i	−0.0498129	−	0.0361912i
$59$	2.98246	−	2.16688i	0.00658106	−	0.00478142i	−0.584490	−	0.811401i	$-0.698705\pi$
$59$	2.98246	−	2.16688i	0.00658106	−	0.00478142i	0.591071	+	0.806620i	$0.298705\pi$
$60$		0			0
$61$	37.7322	−	116.128i	0.0791985	−	0.243748i	−0.903616	−	0.428343i	$-0.859097\pi$
$61$	37.7322	−	116.128i	0.0791985	−	0.243748i	0.982815	+	0.184595i	$0.0590974\pi$
$62$	13.1290	−	9.53880i	0.0268934	−	0.0195392i
$63$		0			0
$64$	−156.189	−	480.699i	−0.305056	−	0.938866i
$65$	−234.167			−0.446843
$66$		0			0
$67$	−219.635			−0.400487			−0.200244	−	0.979746i	$-0.564173\pi$
$67$	−219.635			−0.400487			−0.200244	+	0.979746i	$0.564173\pi$
$68$	−172.625	−	531.285i	−0.307851	−	0.947467i
$69$		0			0
$70$	−10.1556	+	7.37851i	−0.0173405	+	0.0125986i
$71$	−332.200	+	1022.41i	−0.555280	+	1.70898i	0.139921	+	0.990163i	$0.455315\pi$
$71$	−332.200	+	1022.41i	−0.555280	+	1.70898i	−0.695202	+	0.718815i	$0.744685\pi$
$72$		0			0
$73$	592.358	−	430.373i	0.949729	−	0.690019i	−0.00101345	−	0.999999i	$-0.500323\pi$
$73$	592.358	−	430.373i	0.949729	−	0.690019i	0.950743	+	0.309981i	$0.100323\pi$
$74$	−41.4320	−	30.1021i	−0.0650862	−	0.0472879i
$75$		0			0
$76$	444.216			0.670462
$77$	136.066	−	505.237i	0.201378	−	0.747754i
$78$		0			0
$79$	−85.3301	−	262.619i	−0.121524	−	0.374012i	0.871728	−	0.489990i	$-0.163000\pi$
$79$	−85.3301	−	262.619i	−0.121524	−	0.374012i	−0.993252	+	0.115978i	$0.963000\pi$
$80$	344.121	+	250.018i	0.480923	+	0.349411i
$81$		0			0
$82$	17.0181	−	52.3764i	0.0229188	−	0.0705367i
$83$	117.512	−	361.666i	0.155406	−	0.478289i	−0.842796	−	0.538233i	$-0.819092\pi$
$83$	117.512	−	361.666i	0.155406	−	0.478289i	0.998202	+	0.0599436i	$0.0190921\pi$
$84$		0			0
$85$	378.693	+	275.137i	0.483236	+	0.351092i
$86$	−16.5869	−	51.0493i	−0.0207978	−	0.0640091i
$87$		0			0
$88$	76.1988	−	3.89639i	0.0923048	−	0.00471996i
$89$	1309.41			1.55952			0.779761	−	0.626077i	$-0.215340\pi$
$89$	1309.41			1.55952			0.779761	+	0.626077i	$0.215340\pi$
$90$		0			0
$91$	406.185	+	295.111i	0.467910	+	0.339956i
$92$	280.567	−	203.844i	0.317947	−	0.231002i
$93$		0			0
$94$	−8.86164	+	27.2733i	−0.00972350	+	0.0299258i
$95$	−301.135	+	218.787i	−0.325219	+	0.236285i
$96$		0			0
$97$	242.603	+	746.654i	0.253944	+	0.781559i	0.994036	+	0.109053i	$0.0347819\pi$
$97$	242.603	+	746.654i	0.253944	+	0.781559i	−0.740092	+	0.672506i	$0.765218\pi$
$98$	−17.9665			−0.0185193
$99$		0			0
$100$	640.672			0.640672
$101$	−484.251	−	1490.37i	−0.477077	−	1.46829i	−0.843136	−	0.537701i	$-0.819293\pi$
$101$	−484.251	−	1490.37i	−0.477077	−	1.46829i	0.366059	−	0.930592i	$-0.380707\pi$
$102$		0			0
$103$	128.981	−	93.7100i	0.123387	−	0.0896458i	−0.524380	−	0.851484i	$-0.675703\pi$
$103$	128.981	−	93.7100i	0.123387	−	0.0896458i	0.647767	+	0.761838i	$0.275703\pi$
$104$	−22.6238	+	69.6288i	−0.0213312	+	0.0656507i
$105$		0			0
$106$	−37.4771	+	27.2287i	−0.0343406	+	0.0249499i
$107$	1594.63	+	1158.57i	1.44074	+	1.04676i	0.987888	+	0.155171i	$0.0495929\pi$
$107$	1594.63	+	1158.57i	1.44074	+	1.04676i	0.452850	+	0.891586i	$0.350407\pi$
$108$		0			0
$109$	−1306.85			−1.14838			−0.574192	−	0.818721i	$-0.694684\pi$
$109$	−1306.85			−1.14838			−0.574192	+	0.818721i	$0.694684\pi$
$110$	−24.8415	+	20.0641i	−0.0215322	+	0.0173912i
$111$		0			0
$112$	−281.823	−	867.363i	−0.237766	−	0.731769i
$113$	−1060.53	−	770.518i	−0.882884	−	0.641453i	0.0511286	−	0.998692i	$-0.483718\pi$
$113$	−1060.53	−	770.518i	−0.882884	−	0.641453i	−0.934013	+	0.357239i	$0.883718\pi$
$114$		0			0
$115$	−89.7988	+	276.372i	−0.0728155	+	0.224103i
$116$	−512.739	+	1578.05i	−0.410402	+	1.26309i
$117$		0			0
$118$	0.390252	+	0.283535i	0.000304454	+	0.000221199i
$119$	−310.137	−	954.504i	−0.238910	−	0.735288i
$120$		0			0
$121$	280.036	−	1301.21i	0.210395	−	0.977616i
$122$	15.9772			0.0118566
$123$		0			0
$124$	−800.979	−	581.945i	−0.580081	−	0.421453i
$125$	−1110.76	+	807.017i	−0.794798	+	0.577454i
$126$		0			0
$127$	−389.285	+	1198.10i	−0.271996	+	0.837117i	0.718003	+	0.696040i	$0.245056\pi$
$127$	−389.285	+	1198.10i	−0.271996	+	0.837117i	−0.989999	+	0.141077i	$0.954944\pi$
$128$	215.641	−	156.673i	0.148908	−	0.108188i
$129$		0			0
$130$	−9.46845	−	29.1409i	−0.00638798	−	0.0196602i
$131$	−1789.88			−1.19376			−0.596881	−	0.802330i	$-0.703594\pi$
$131$	−1789.88			−1.19376			−0.596881	+	0.802330i	$0.703594\pi$
$132$		0			0
$133$	798.078			0.520317
$134$	−8.88085	−	27.3324i	−0.00572529	−	0.0176206i
$135$		0			0
$136$	118.398	−	86.0214i	0.0746512	−	0.0542373i
$137$	−226.156	+	696.035i	−0.141035	+	0.434061i	−0.996480	−	0.0838331i	$-0.973284\pi$
$137$	−226.156	+	696.035i	−0.141035	+	0.434061i	0.855445	+	0.517894i	$0.173284\pi$
$138$		0			0
$139$	−1359.71	+	987.889i	−0.829708	+	0.602818i	−0.919477	−	0.393145i	$-0.871387\pi$
$139$	−1359.71	+	987.889i	−0.829708	+	0.602818i	0.0897691	+	0.995963i	$0.471387\pi$
$140$	619.578	+	450.150i	0.374028	+	0.271747i
$141$		0			0
$142$	−140.666			−0.0831297
$143$	1070.23	+	696.951i	0.625856	+	0.407566i
$144$		0			0
$145$	−429.641	−	1322.30i	−0.246067	−	0.757317i
$146$	77.5096	+	56.3140i	0.0439366	+	0.0319218i
$147$		0			0
$148$	−965.493	+	2971.48i	−0.536237	+	1.65037i
$149$	390.773	−	1202.67i	0.214855	−	0.661255i	−0.784309	−	0.620370i	$-0.786982\pi$
$149$	390.773	−	1202.67i	0.214855	−	0.661255i	0.999164	−	0.0408845i	$-0.0130176\pi$
$150$		0			0
$151$	−543.143	−	394.616i	−0.292718	−	0.212672i	0.431728	−	0.902004i	$-0.357904\pi$
$151$	−543.143	−	394.616i	−0.292718	−	0.212672i	−0.724445	+	0.689332i	$0.757904\pi$
$152$	35.9620	+	110.680i	0.0191901	+	0.0590612i
$153$		0			0
$154$	68.3759	−	3.49637i	0.0357785	−	0.00182952i
$155$	829.607			0.429907
$156$		0			0
$157$	−45.0659	−	32.7423i	−0.0229086	−	0.0166441i	0.576272	−	0.817258i	$-0.304507\pi$
$157$	−45.0659	−	32.7423i	−0.0229086	−	0.0166441i	−0.599181	+	0.800614i	$0.704507\pi$
$158$	29.2313	−	21.2378i	0.0147185	−	0.0106936i
$159$		0			0
$160$	−51.7825	+	159.370i	−0.0255860	+	0.0787457i
$161$	504.066	−	366.225i	0.246745	−	0.179271i
$162$		0			0
$163$	235.921	+	726.091i	0.113367	+	0.348907i	0.991603	−	0.129320i	$-0.0412795\pi$
$163$	235.921	+	726.091i	0.113367	+	0.348907i	−0.878236	+	0.478227i	$0.841280\pi$
$164$	−3359.83			−1.59975
$165$		0			0
$166$	49.7591			0.0232654
$167$	−943.529	−	2903.88i	−0.437200	−	1.34556i	−0.890815	−	0.454366i	$-0.849866\pi$
$167$	−943.529	−	2903.88i	−0.437200	−	1.34556i	0.453615	−	0.891198i	$-0.350134\pi$
$168$		0			0
$169$	785.960	−	571.034i	0.357743	−	0.259915i
$170$	−18.9271	+	58.2516i	−0.00853906	+	0.0262805i
$171$		0			0
$172$	−2649.29	+	1924.82i	−1.17446	+	0.853292i
$173$	3475.80	+	2525.32i	1.52752	+	1.10981i	0.957599	+	0.288105i	$0.0930251\pi$
$173$	3475.80	+	2525.32i	1.52752	+	1.10981i	0.569918	+	0.821701i	$0.306975\pi$
$174$		0			0
$175$	1151.03			0.497198
$176$	−828.635	−	2166.89i	−0.354890	−	0.928042i
$177$		0			0
$178$	52.9456	+	162.950i	0.0222946	+	0.0686158i
$179$	2050.48	+	1489.76i	0.856203	+	0.622068i	0.926849	−	0.375434i	$-0.122506\pi$
$179$	2050.48	+	1489.76i	0.856203	+	0.622068i	−0.0706466	+	0.997501i	$0.522506\pi$
$180$		0			0
$181$	464.374	−	1429.20i	0.190700	−	0.586914i	−0.809300	−	0.587395i	$-0.800153\pi$
$181$	464.374	−	1429.20i	0.190700	−	0.586914i	1.00000		0.000481688i	$0.000153326\pi$
$182$	−20.3011	+	62.4805i	−0.00826824	+	0.0254470i
$183$		0			0
$184$	73.5027	+	53.4028i	0.0294494	+	0.0213962i
$185$	−809.018	−	2489.90i	−0.321515	−	0.989520i
$186$		0			0
$187$	−911.885	−	2384.59i	−0.356597	−	0.932505i
$188$	1749.53			0.678709
$189$		0			0
$190$	−39.4033	−	28.6282i	−0.0150453	−	0.0109311i
$191$	−3414.82	+	2481.01i	−1.29365	+	0.939894i	−0.999872	−	0.0159793i	$-0.994913\pi$
$191$	−3414.82	+	2481.01i	−1.29365	+	0.939894i	−0.293780	+	0.955873i	$0.594913\pi$
$192$		0			0
$193$	1100.29	−	3386.36i	0.410368	−	1.26298i	−0.505962	−	0.862556i	$-0.668862\pi$
$193$	1100.29	−	3386.36i	0.410368	−	1.26298i	0.916329	−	0.400426i	$-0.131138\pi$
$194$	−83.1078	+	60.3814i	−0.0307567	+	0.0223460i
$195$		0			0
$196$	338.714	+	1042.46i	0.123438	+	0.379903i
$197$	−1118.82			−0.404632			−0.202316	−	0.979320i	$-0.564847\pi$
$197$	−1118.82			−0.404632			−0.202316	+	0.979320i	$0.564847\pi$
$198$		0			0
$199$	3755.04			1.33763			0.668813	−	0.743431i	$-0.266803\pi$
$199$	3755.04			1.33763			0.668813	+	0.743431i	$0.266803\pi$
$200$	51.8662	+	159.628i	0.0183375	+	0.0564370i
$201$		0			0
$202$	165.889	−	120.525i	0.0577817	−	0.0419808i
$203$	−921.186	+	2835.12i	−0.318495	+	0.980228i
$204$		0			0
$205$	2277.64	−	1654.80i	0.775986	−	0.563787i
$206$	16.8770	+	12.2619i	0.00570815	+	0.00414721i
$207$		0			0
$208$	2226.08			0.742072
$209$	2027.48	−	103.674i	0.671023	−	0.0343124i
$210$		0			0
$211$	338.887	+	1042.99i	0.110569	+	0.340295i	0.990997	−	0.133884i	$-0.0427449\pi$
$211$	338.887	+	1042.99i	0.110569	+	0.340295i	−0.880428	+	0.474179i	$0.842745\pi$
$212$	2286.41	+	1661.18i	0.740715	+	0.538161i
$213$		0			0
$214$	−79.6997	+	245.290i	−0.0254587	+	0.0783538i
$215$	847.936	−	2609.68i	0.268971	−	0.827807i
$216$		0			0
$217$	−1439.04	−	1045.52i	−0.450176	−	0.327072i
$218$	−52.8421	−	162.631i	−0.0164171	−	0.0505265i
$219$		0			0
$220$	1632.49	+	1063.10i	0.500283	+	0.325792i
$221$	2449.73			0.745641
$222$		0			0
$223$	4922.64	+	3576.51i	1.47823	+	1.07399i	0.978123	+	0.208029i	$0.0667050\pi$
$223$	4922.64	+	3576.51i	1.47823	+	1.07399i	0.500104	+	0.865965i	$0.333295\pi$
$224$	290.670	−	211.184i	0.0867017	−	0.0629925i
$225$		0			0
$226$	53.0051	−	163.133i	0.0156011	−	0.0480152i
$227$	1689.15	−	1227.24i	0.493889	−	0.358832i	−0.312789	−	0.949823i	$-0.601263\pi$
$227$	1689.15	−	1227.24i	0.493889	−	0.358832i	0.806678	+	0.590991i	$0.201263\pi$
$228$		0			0
$229$	−695.591	−	2140.81i	−0.200725	−	0.617767i	−0.999862	−	0.0166184i	$-0.994710\pi$
$229$	−695.591	−	2140.81i	−0.200725	−	0.617767i	0.799137	−	0.601149i	$-0.205290\pi$
$230$	−38.0241			−0.0109010
$231$		0			0
$232$	−434.691			−0.123012
$233$	−338.818	−	1042.78i	−0.0952649	−	0.293195i	0.892058	−	0.451921i	$-0.149261\pi$
$233$	−338.818	−	1042.78i	−0.0952649	−	0.293195i	−0.987323	+	0.158726i	$0.949261\pi$
$234$		0			0
$235$	−1186.01	+	861.684i	−0.329219	+	0.239192i
$236$	9.09407	−	27.9887i	0.00250836	−	0.00771994i
$237$		0			0
$238$	106.243	−	77.1901i	0.0289358	−	0.0210231i
$239$	−3309.49	−	2404.48i	−0.895703	−	0.650766i	0.0416560	−	0.999132i	$-0.486737\pi$
$239$	−3309.49	−	2404.48i	−0.895703	−	0.650766i	−0.937359	+	0.348366i	$0.886737\pi$
$240$		0			0
$241$	−6372.09			−1.70316			−0.851581	−	0.524223i	$-0.824356\pi$
$241$	−6372.09			−1.70316			−0.851581	+	0.524223i	$0.824356\pi$
$242$	173.252	−	17.7648i	0.0460209	−	0.00471885i
$243$		0			0
$244$	−301.211	−	927.033i	−0.0790290	−	0.243226i
$245$	−743.049	−	539.857i	−0.193762	−	0.140776i
$246$		0			0
$247$	−601.969	+	1852.67i	−0.155070	+	0.477257i
$248$	80.1516	−	246.681i	0.0205227	−	0.0631624i
$249$		0			0
$250$	−145.343	−	105.598i	−0.0367691	−	0.0267143i
$251$	23.3779	+	71.9497i	0.00587888	+	0.0180933i	0.953953	−	0.299956i	$-0.0969721\pi$
$251$	23.3779	+	71.9497i	0.00587888	+	0.0180933i	−0.948074	+	0.318050i	$0.896972\pi$
$252$		0			0
$253$	1232.98	−	995.860i	0.306391	−	0.247467i
$254$	−164.838			−0.0407198
$255$		0			0
$256$	−3243.04	−	2356.21i	−0.791758	−	0.575246i
$257$	−725.765	+	527.299i	−0.176156	+	0.127985i	−0.672369	−	0.740216i	$-0.734723\pi$
$257$	−725.765	+	527.299i	−0.176156	+	0.127985i	0.496214	+	0.868200i	$0.334723\pi$
$258$		0			0
$259$	−1734.60	+	5338.56i	−0.416150	+	1.28078i
$260$	−1512.32	+	1098.76i	−0.360730	+	0.262086i
$261$		0			0
$262$	−72.3733	−	222.742i	−0.0170658	−	0.0525231i
$263$	2411.17			0.565321			0.282660	−	0.959220i	$-0.408783\pi$
$263$	2411.17			0.565321			0.282660	+	0.959220i	$0.408783\pi$
$264$		0			0
$265$	−2368.13			−0.548956
$266$	32.2700	+	99.3168i	0.00743834	+	0.0228929i
$267$		0			0
$268$	−1418.46	+	1030.57i	−0.323307	+	0.234897i
$269$	−605.489	+	1863.50i	−0.137239	+	0.422378i	−0.995932	−	0.0901127i	$-0.971277\pi$
$269$	−605.489	+	1863.50i	−0.137239	+	0.422378i	0.858693	+	0.512491i	$0.171277\pi$
$270$		0			0
$271$	32.4426	−	23.5709i	0.00727213	−	0.00528351i	−0.584143	−	0.811651i	$-0.698569\pi$
$271$	32.4426	−	23.5709i	0.00727213	−	0.00528351i	0.591415	+	0.806367i	$0.298569\pi$
$272$	−3600.01	−	2615.56i	−0.802510	−	0.583057i
$273$		0			0
$274$	−95.7627			−0.0211140
$275$	2924.14	−	149.524i	0.641208	−	0.0327879i
$276$		0			0
$277$	−1031.67	−	3175.16i	−0.223780	−	0.688725i	−0.998413	−	0.0563135i	$-0.982065\pi$
$277$	−1031.67	−	3175.16i	−0.223780	−	0.688725i	0.774633	−	0.632411i	$-0.217935\pi$
$278$	−177.917	−	129.265i	−0.0383841	−	0.0278877i
$279$		0			0
$280$	−61.9994	+	190.814i	−0.0132328	+	0.0407262i
$281$	121.136	−	372.818i	0.0257166	−	0.0791475i	−0.937375	−	0.348323i	$-0.886751\pi$
$281$	121.136	−	372.818i	0.0257166	−	0.0791475i	0.963091	+	0.269176i	$0.0867512\pi$
$282$		0			0
$283$	5304.54	+	3853.98i	1.11421	+	0.809524i	0.983322	−	0.181873i	$-0.0582160\pi$
$283$	5304.54	+	3853.98i	1.11421	+	0.809524i	0.130892	+	0.991397i	$0.458216\pi$
$284$	2651.91	+	8161.75i	0.554092	+	1.70532i
$285$		0			0
$286$	−43.4576	+	161.366i	−0.00898498	+	0.0333629i
$287$	−6036.27			−1.24150
$288$		0			0
$289$	13.0094	+	9.45189i	0.00264796	+	0.00192385i
$290$	147.181	−	106.933i	0.0298027	−	0.0216529i
$291$		0			0
$292$	1806.21	−	5558.94i	0.361988	−	1.11408i
$293$	−4667.01	+	3390.78i	−0.930545	+	0.676081i	−0.946126	−	0.323798i	$-0.895040\pi$
$293$	−4667.01	+	3390.78i	−0.930545	+	0.676081i	0.0155811	+	0.999879i	$0.495040\pi$
$294$		0			0
$295$	7.62022	+	23.4526i	0.00150395	+	0.00462869i
$296$	−818.528			−0.160730
$297$		0			0
$298$	165.468			0.0321654
$299$	469.957	+	1446.38i	0.0908974	+	0.279754i
$300$		0			0
$301$	−4759.70	+	3458.13i	−0.911444	+	0.662203i
$302$	27.1463	−	83.5476i	0.00517249	−	0.0159193i
$303$		0			0
$304$	2862.71	−	2079.88i	0.540091	−	0.392399i
$305$	660.778	+	480.083i	0.124053	+	0.0901294i
$306$		0			0
$307$	−4161.46			−0.773638			−0.386819	−	0.922156i	$-0.626426\pi$
$307$	−4161.46			−0.773638			−0.386819	+	0.922156i	$0.626426\pi$
$308$	−1491.93	−	3901.41i	−0.276008	−	0.721765i
$309$		0			0
$310$	33.5448	+	103.240i	0.00614587	+	0.0189150i
$311$	−1409.63	−	1024.15i	−0.257018	−	0.186734i	0.451813	−	0.892112i	$-0.350777\pi$
$311$	−1409.63	−	1024.15i	−0.257018	−	0.186734i	−0.708831	+	0.705378i	$0.750777\pi$
$312$		0			0
$313$	1445.67	−	4449.33i	0.261068	−	0.803485i	−0.731505	−	0.681836i	$-0.761182\pi$
$313$	1445.67	−	4449.33i	0.261068	−	0.803485i	0.992573	−	0.121649i	$-0.0388182\pi$
$314$	2.25239	−	6.93215i	0.000404808	−	0.00124587i
$315$		0			0
$316$	−1783.35	−	1295.68i	−0.317473	−	0.230657i
$317$	−588.811	−	1812.18i	−0.104325	−	0.321079i	0.885247	−	0.465122i	$-0.153990\pi$
$317$	−588.811	−	1812.18i	−0.104325	−	0.321079i	−0.989571	+	0.144043i	$0.953990\pi$
$318$		0			0
$319$	−1971.94	+	7322.16i	−0.346104	+	1.28515i
$320$	3380.93			0.590623
$321$		0			0
$322$	65.9566	+	47.9203i	0.0114150	+	0.00829346i
$323$	3150.32	−	2288.84i	0.542688	−	0.394286i
$324$		0			0
$325$	−868.191	+	2672.02i	−0.148180	+	0.456052i
$326$	−80.8190	+	58.7184i	−0.0137305	+	0.00997581i
$327$		0			0
$328$	−271.999	−	837.126i	−0.0457885	−	0.140922i
$329$	3143.19			0.526717
$330$		0			0
$331$	−8459.25			−1.40472			−0.702360	−	0.711822i	$-0.747870\pi$
$331$	−8459.25			−1.40472			−0.702360	+	0.711822i	$0.747870\pi$
$332$	−938.088	−	2887.14i	−0.155073	−	0.477266i
$333$		0			0
$334$	323.222	−	234.835i	0.0529519	−	0.0384718i
$335$	453.996	−	1397.25i	0.0740431	−	0.227881i
$336$		0			0
$337$	2698.53	−	1960.60i	0.436197	−	0.316916i	−0.347925	−	0.937522i	$-0.613114\pi$
$337$	2698.53	−	1960.60i	0.436197	−	0.316916i	0.784122	+	0.620607i	$0.213114\pi$
$338$	102.842	+	74.7193i	0.0165500	+	0.0120242i
$339$		0			0
$340$	3736.71			0.596034
$341$	−3791.63	−	2469.16i	−0.602135	−	0.392119i
$342$		0			0
$343$	2128.68	+	6551.41i	0.335097	+	1.03132i
$344$	−694.058	−	504.263i	−0.108782	−	0.0790350i
$345$		0			0
$346$	−173.721	+	534.657i	−0.0269921	+	0.0830732i
$347$	−2224.10	+	6845.07i	−0.344080	+	1.05897i	0.617994	+	0.786183i	$0.287946\pi$
$347$	−2224.10	+	6845.07i	−0.344080	+	1.05897i	−0.962074	+	0.272787i	$0.912054\pi$
$348$		0			0
$349$	4369.75	+	3174.81i	0.670221	+	0.486944i	0.870099	−	0.492877i	$-0.164055\pi$
$349$	4369.75	+	3174.81i	0.670221	+	0.486944i	−0.199878	+	0.979821i	$0.564055\pi$
$350$	46.5415	+	143.240i	0.00710784	+	0.0218757i
$351$		0			0
$352$	711.000	−	574.263i	0.107660	−	0.0869555i
$353$	3383.09			0.510095			0.255048	−	0.966928i	$-0.417909\pi$
$353$	3383.09			0.510095			0.255048	+	0.966928i	$0.417909\pi$
$354$		0			0
$355$	−5817.60	−	4226.73i	−0.869764	−	0.631920i
$356$	8456.56	−	6144.05i	1.25898	−	0.914702i
$357$		0			0
$358$	−102.483	+	315.410i	−0.0151296	+	0.0465641i
$359$	14.1725	−	10.2969i	0.00208356	−	0.00151379i	−0.586743	−	0.809773i	$-0.699590\pi$
$359$	14.1725	−	10.2969i	0.00208356	−	0.00151379i	0.588827	+	0.808259i	$0.299590\pi$
$360$		0			0
$361$	−1162.68	−	3578.36i	−0.169511	−	0.521703i
$362$	196.633			0.0285492
$363$		0			0
$364$	4007.99			0.577131
$365$	1513.48	+	4658.02i	0.217039	+	0.667978i
$366$		0			0
$367$	3971.35	−	2885.36i	0.564858	−	0.410393i	−0.268376	−	0.963314i	$-0.586487\pi$
$367$	3971.35	−	2885.36i	0.564858	−	0.410393i	0.833234	+	0.552921i	$0.186487\pi$
$368$	853.663	−	2627.30i	0.120925	−	0.372168i
$369$		0			0
$370$	277.144	−	201.357i	0.0389406	−	0.0282920i
$371$	4107.76	+	2984.46i	0.574837	+	0.417643i
$372$		0			0
$373$	8416.78			1.16838			0.584188	−	0.811618i	$-0.301413\pi$
$373$	8416.78			1.16838			0.584188	+	0.811618i	$0.301413\pi$
$374$	259.878	−	209.900i	0.0359305	−	0.0290205i
$375$		0			0
$376$	141.635	+	435.906i	0.0194262	+	0.0597876i
$377$	−5886.66	−	4276.91i	−0.804187	−	0.584276i
$378$		0			0
$379$	1992.17	−	6131.26i	0.270002	−	0.830981i	−0.720497	−	0.693459i	$-0.756086\pi$
$379$	1992.17	−	6131.26i	0.270002	−	0.830981i	0.990499	−	0.137522i	$-0.0439139\pi$
$380$	−918.217	+	2825.98i	−0.123957	+	0.381499i
$381$		0			0
$382$	−446.826	−	324.638i	−0.0598472	−	0.0434815i
$383$	1465.70	+	4510.98i	0.195546	+	0.601828i	0.999970	+	0.00777244i	$0.00247407\pi$
$383$	1465.70	+	4510.98i	0.195546	+	0.601828i	−0.804424	+	0.594056i	$0.797526\pi$
$384$		0			0
$385$	2932.92	+	1909.96i	0.388248	+	0.252833i
$386$	465.906			0.0614352
$387$		0			0
$388$	5070.26	+	3683.76i	0.663411	+	0.481996i
$389$	2402.14	−	1745.26i	0.313093	−	0.227476i	−0.420129	−	0.907464i	$-0.638015\pi$
$389$	2402.14	−	1745.26i	0.313093	−	0.227476i	0.733223	+	0.679989i	$0.238015\pi$
$390$		0			0
$391$	939.427	−	2891.26i	0.121506	−	0.373957i
$392$	−232.314	+	168.786i	−0.0299327	+	0.0217474i
$393$		0			0
$394$	−45.2390	−	139.231i	−0.00578454	−	0.0178030i
$395$	1847.09			0.235284
$396$		0			0
$397$	1573.89			0.198971			0.0994854	−	0.995039i	$-0.468280\pi$
$397$	1573.89			0.198971			0.0994854	+	0.995039i	$0.468280\pi$
$398$	151.834	+	467.296i	0.0191224	+	0.0588528i
$399$		0			0
$400$	4128.75	−	2999.71i	0.516094	−	0.374964i
$401$	1143.43	−	3519.10i	0.142394	−	0.438243i	−0.854273	−	0.519825i	$-0.825997\pi$
$401$	1143.43	−	3519.10i	0.142394	−	0.438243i	0.996667	+	0.0815818i	$0.0259972\pi$
$402$		0			0
$403$	3512.51	−	2551.99i	0.434171	−	0.315443i
$404$	−10120.6	−	7353.03i	−1.24633	−	0.905513i
$405$		0			0
$406$	−390.064			−0.0476812
$407$	−3713.18	+	13787.7i	−0.452224	+	1.67919i
$408$		0			0
$409$	−984.737	−	3030.71i	−0.119052	−	0.366403i	0.873719	−	0.486431i	$-0.161702\pi$
$409$	−984.737	−	3030.71i	−0.119052	−	0.366403i	−0.992771	+	0.120028i	$0.961702\pi$
$410$	298.027	+	216.529i	0.0358988	+	0.0260820i
$411$		0			0
$412$	393.286	−	1210.41i	0.0470287	−	0.144739i
$413$	16.3384	−	50.2843i	0.00194663	−	0.00599112i
$414$		0			0
$415$	2057.92	+	1495.16i	0.243420	+	0.176855i
$416$	271.001	+	834.055i	0.0319397	+	0.0983003i
$417$		0			0
$418$	94.8822	+	248.118i	0.0111025	+	0.0290331i
$419$	−7400.64			−0.862875			−0.431438	−	0.902143i	$-0.641994\pi$
$419$	−7400.64			−0.862875			−0.431438	+	0.902143i	$0.641994\pi$
$420$		0			0
$421$	−1999.14	−	1452.46i	−0.231430	−	0.168144i	0.466027	−	0.884771i	$-0.345685\pi$
$421$	−1999.14	−	1452.46i	−0.231430	−	0.168144i	−0.697457	+	0.716627i	$0.745685\pi$
$422$	−116.092	+	84.3457i	−0.0133916	+	0.00972958i
$423$		0			0
$424$	−228.795	+	704.158i	−0.0262058	+	0.0806531i
$425$	4543.55	−	3301.08i	0.518575	−	0.376767i
$426$		0			0
$427$	−541.155	−	1665.50i	−0.0613310	−	0.188757i
$428$	15734.8			1.77704
$429$		0			0
$430$	359.047			0.0402670
$431$	338.498	+	1041.79i	0.0378303	+	0.116430i	0.968188	−	0.250223i	$-0.0805038\pi$
$431$	338.498	+	1041.79i	0.0378303	+	0.116430i	−0.930358	+	0.366652i	$0.880504\pi$
$432$		0			0
$433$	73.0855	−	53.0997i	0.00811147	−	0.00589333i	−0.583722	−	0.811953i	$-0.698404\pi$
$433$	73.0855	−	53.0997i	0.00811147	−	0.00589333i	0.591834	+	0.806060i	$0.298404\pi$
$434$	71.9229	−	221.356i	0.00795487	−	0.0244826i
$435$		0			0
$436$	−8440.03	+	6132.04i	−0.927074	+	0.673558i
$437$	1955.74	+	1420.93i	0.214087	+	0.155543i
$438$		0			0
$439$	−3930.60			−0.427329			−0.213664	−	0.976907i	$-0.568540\pi$
$439$	−3930.60			−0.427329			−0.213664	+	0.976907i	$0.568540\pi$
$440$	−132.719	+	492.810i	−0.0143798	+	0.0533950i
$441$		0			0
$442$	99.0539	+	304.857i	0.0106595	+	0.0328067i
$443$	3212.40	+	2333.94i	0.344527	+	0.250314i	0.746570	−	0.665307i	$-0.231700\pi$
$443$	3212.40	+	2333.94i	0.344527	+	0.250314i	−0.402042	+	0.915621i	$0.631700\pi$
$444$		0			0
$445$	−2706.62	+	8330.13i	−0.288328	+	0.887384i
$446$	−246.034	+	757.213i	−0.0261211	+	0.0803926i
$447$		0			0
$448$	−5864.55	−	4260.85i	−0.618469	−	0.449344i
$449$	−5497.77	−	16920.4i	−0.577852	−	1.77845i	−0.626254	−	0.779619i	$-0.715413\pi$
$449$	−5497.77	−	16920.4i	−0.577852	−	1.77845i	0.0484019	−	0.998828i	$-0.484587\pi$
$450$		0			0
$451$	−15334.9	+	784.142i	−1.60109	+	0.0818709i
$452$	−10464.6			−1.08897
$453$		0			0
$454$	221.024	+	160.583i	0.0228484	+	0.0166003i
$455$	−2717.02	+	1974.03i	−0.279947	+	0.203393i
$456$		0			0
$457$	−3571.23	+	10991.1i	−0.365547	+	1.12504i	0.584091	+	0.811688i	$0.301451\pi$
$457$	−3571.23	+	10991.1i	−0.365547	+	1.12504i	−0.949638	+	0.313349i	$0.898549\pi$
$458$	238.287	−	173.126i	0.0243110	−	0.0176630i
$459$		0			0
$460$	716.853	+	2206.25i	0.0726596	+	0.223623i
$461$	996.474			0.100673			0.0503367	−	0.998732i	$-0.483971\pi$
$461$	996.474			0.100673			0.0503367	+	0.998732i	$0.483971\pi$
$462$		0			0
$463$	3950.65			0.396549			0.198275	−	0.980146i	$-0.436466\pi$
$463$	3950.65			0.396549			0.198275	+	0.980146i	$0.436466\pi$
$464$	4084.34	+	12570.3i	0.408644	+	1.25768i
$465$		0			0
$466$	116.068	−	84.3285i	0.0115381	−	0.00838292i
$467$	5110.85	−	15729.6i	0.506428	−	1.55862i	−0.291929	−	0.956440i	$-0.594297\pi$
$467$	5110.85	−	15729.6i	0.506428	−	1.55862i	0.798357	−	0.602185i	$-0.205703\pi$
$468$		0			0
$469$	−2548.41	+	1851.53i	−0.250905	+	0.182293i
$470$	−155.188	−	112.751i	−0.0152304	−	0.0110655i
$471$		0			0
$472$	7.70979			0.000751847
$473$	−11642.6	+	9403.53i	−1.13177	+	0.914112i
$474$		0			0
$475$	1380.05	+	4247.34i	0.133307	+	0.410277i
$476$	−6481.70	−	4709.23i	−0.624135	−	0.453460i
$477$		0			0
$478$	165.408	−	509.074i	0.0158276	−	0.0487123i
$479$	1492.05	−	4592.05i	0.142324	−	0.438030i	−0.854333	−	0.519726i	$-0.826034\pi$
$479$	1492.05	−	4592.05i	0.142324	−	0.438030i	0.996657	+	0.0816967i	$0.0260339\pi$
$480$		0			0
$481$	−11084.6	−	8053.46i	−1.05076	−	0.763423i
$482$	−257.653	−	792.974i	−0.0243481	−	0.0749357i
$483$		0			0
$484$	−4297.00	−	9717.56i	−0.403550	−	0.912618i
$485$	−5251.48			−0.491665
$486$		0			0
$487$	756.687	+	549.765i	0.0704081	+	0.0511545i	0.622433	−	0.782673i	$-0.286144\pi$
$487$	756.687	+	549.765i	0.0704081	+	0.0511545i	−0.552024	+	0.833828i	$0.686144\pi$
$488$	206.592	−	150.098i	0.0191639	−	0.0139234i
$489$		0			0
$490$	37.1376	−	114.298i	0.00342389	−	0.0105376i
$491$	9774.71	−	7101.75i	0.898425	−	0.652744i	−0.0396360	−	0.999214i	$-0.512620\pi$
$491$	9774.71	−	7101.75i	0.898425	−	0.652744i	0.938061	+	0.346470i	$0.112620\pi$
$492$		0			0
$493$	4494.68	+	13833.2i	0.410609	+	1.26372i
$494$	−254.896			−0.0232152
$495$		0			0
$496$	−7886.57			−0.713947
$497$	4764.42	+	14663.4i	0.430007	+	1.32343i
$498$		0			0
$499$	1372.15	−	996.922i	0.123098	−	0.0894356i	−0.524533	−	0.851390i	$-0.675760\pi$
$499$	1372.15	−	996.922i	0.123098	−	0.0894356i	0.647631	+	0.761955i	$0.275760\pi$
$500$	−3386.93	+	10423.9i	−0.302936	+	0.932341i
$501$		0			0
$502$	−8.00851	+	5.81852i	−0.000712026	+	0.000517317i
$503$	1799.33	+	1307.29i	0.159499	+	0.115883i	0.664672	−	0.747135i	$-0.268571\pi$
$503$	1799.33	+	1307.29i	0.159499	+	0.115883i	−0.505173	+	0.863018i	$0.668571\pi$
$504$		0			0
$505$	10482.3			0.923676
$506$	173.785	+	113.171i	0.0152682	+	0.00994284i
$507$		0			0
$508$	3107.62	+	9564.26i	0.271414	+	0.835326i
$509$	3040.47	+	2209.03i	0.264767	+	0.192364i	0.712246	−	0.701930i	$-0.247678\pi$
$509$	3040.47	+	2209.03i	0.264767	+	0.192364i	−0.447479	+	0.894294i	$0.647678\pi$
$510$		0			0
$511$	3245.03	−	9987.18i	0.280923	−	0.864593i
$512$	821.028	−	2526.86i	0.0708685	−	0.218111i
$513$		0			0
$514$	−94.9658	−	68.9967i	−0.00814934	−	0.00592085i
$515$	329.547	+	1014.24i	0.0281973	+	0.0867823i
$516$		0			0
$517$	7985.14	−	408.316i	0.679277	−	0.0347345i
$518$	−734.495			−0.0623009
$519$		0			0
$520$	−396.195	−	287.852i	−0.0334121	−	0.0242753i
$521$	−11756.3	+	8541.48i	−0.988588	+	0.718251i	−0.959611	−	0.281329i	$-0.909225\pi$
$521$	−11756.3	+	8541.48i	−0.988588	+	0.718251i	−0.0289765	+	0.999580i	$0.509225\pi$
$522$		0			0
$523$	5823.56	−	17923.1i	0.486896	−	1.49851i	−0.342320	−	0.939584i	$-0.611213\pi$
$523$	5823.56	−	17923.1i	0.486896	−	1.49851i	0.829216	−	0.558929i	$-0.188787\pi$
$524$	−11559.6	+	8398.53i	−0.963707	+	0.700174i
$525$		0			0
$526$	97.4949	+	300.059i	0.00808171	+	0.0248730i
$527$	−8678.91			−0.717380
$528$		0			0
$529$	−10279.7			−0.844884
$530$	−95.7546	−	294.702i	−0.00784776	−	0.0241529i
$531$		0			0
$532$	5154.21	−	3744.75i	0.420044	−	0.305180i
$533$	4553.00	−	14012.7i	0.370004	−	1.13876i
$534$		0			0
$535$	−10666.7	+	7749.80i	−0.861983	+	0.626267i
$536$	−371.608	−	269.989i	−0.0299459	−	0.0217570i
$537$		0			0
$538$	−256.386			−0.0205457
$539$	1789.25	+	4678.90i	0.142984	+	0.373904i
$540$		0			0
$541$	3327.59	+	10241.3i	0.264444	+	0.813874i	0.991821	+	0.127636i	$0.0407391\pi$
$541$	3327.59	+	10241.3i	0.264444	+	0.813874i	−0.727377	+	0.686238i	$0.759261\pi$
$542$	4.24509	+	3.08424i	0.000336425	+	0.000244427i
$543$		0			0
$544$	541.721	−	1667.25i	0.0426950	−	0.131402i
$545$	2701.33	−	8313.84i	0.212316	−	0.653442i
$546$		0			0
$547$	−11180.1	−	8122.79i	−0.873903	−	0.634928i	0.0577281	−	0.998332i	$-0.481614\pi$
$547$	−11180.1	−	8122.79i	−0.873903	−	0.634928i	−0.931632	+	0.363404i	$0.881614\pi$
$548$	1805.37	+	5556.37i	0.140733	+	0.433132i
$549$		0			0
$550$	136.844	+	357.849i	0.0106092	+	0.0277431i
$551$	−11566.2			−0.894257
$552$		0			0
$553$	−3203.96	−	2327.82i	−0.246377	−	0.179003i
$554$	353.417	−	256.773i	0.0271034	−	0.0196917i
$555$		0			0
$556$	−4146.02	+	12760.1i	−0.316242	+	0.973292i
$557$	16061.9	−	11669.7i	1.22184	−	0.887719i	0.225589	−	0.974222i	$-0.427569\pi$
$557$	16061.9	−	11669.7i	1.22184	−	0.887719i	0.996252	+	0.0865030i	$0.0275692\pi$
$558$		0			0
$559$	−4437.63	−	13657.6i	−0.335763	−	1.03337i
$560$	6100.47			0.460343
$561$		0			0
$562$	51.2934			0.00384997
$563$	1236.21	+	3804.66i	0.0925399	+	0.284809i	0.986605	−	0.163129i	$-0.0521587\pi$
$563$	1236.21	+	3804.66i	0.0925399	+	0.284809i	−0.894065	+	0.447938i	$0.852159\pi$
$564$		0			0
$565$	7093.98	−	5154.08i	0.528223	−	0.383777i
$566$	−265.121	+	815.958i	−0.0196888	+	0.0605959i
$567$		0			0
$568$	−1818.87	+	1321.49i	−0.134363	+	0.0976202i
$569$	1788.40	+	1299.35i	0.131764	+	0.0957322i	0.651715	−	0.758464i	$-0.274050\pi$
$569$	1788.40	+	1299.35i	0.131764	+	0.0957322i	−0.519951	+	0.854196i	$0.674050\pi$
$570$		0			0
$571$	23778.7			1.74274			0.871372	−	0.490623i	$-0.163231\pi$
$571$	23778.7			1.74274			0.871372	+	0.490623i	$0.163231\pi$
$572$	10182.1	−	520.658i	0.744293	−	0.0380591i
$573$		0			0
$574$	−244.074	−	751.184i	−0.0177482	−	0.0546233i
$575$	2820.68	+	2049.34i	0.204575	+	0.148632i
$576$		0			0
$577$	−3253.36	+	10012.8i	−0.234730	+	0.722425i	0.762427	+	0.647074i	$0.224008\pi$
$577$	−3253.36	+	10012.8i	−0.234730	+	0.722425i	−0.997157	+	0.0753510i	$0.975992\pi$
$578$	−0.650210	+	2.00114i	−4.67910e−5	+	0.000144008i
$579$		0			0
$580$	−8979.26	−	6523.81i	−0.642833	−	0.467046i
$581$	−1685.37	−	5187.02i	−0.120346	−	0.370385i
$582$		0			0
$583$	10823.3	+	7048.28i	0.768876	+	0.500703i
$584$	1531.27			0.108501
$585$		0			0
$586$	−610.675	−	443.681i	−0.0430491	−	0.0312770i
$587$	3998.49	−	2905.08i	0.281151	−	0.204268i	−0.438268	−	0.898844i	$-0.644408\pi$
$587$	3998.49	−	2905.08i	0.281151	−	0.204268i	0.719419	+	0.694576i	$0.244408\pi$
$588$		0			0
$589$	2132.66	−	6563.64i	0.149193	−	0.459168i
$590$	−2.61044	+	1.89660i	−0.000182153	+	0.000132342i
$591$		0			0
$592$	7690.85	+	23670.0i	0.533939	+	1.64330i
$593$	−3015.99			−0.208856			−0.104428	−	0.994532i	$-0.533301\pi$
$593$	−3015.99			−0.208856			−0.104428	+	0.994532i	$0.533301\pi$
$594$		0			0
$595$	6713.36			0.462556
$596$	−3119.49	−	9600.80i	−0.214395	−	0.659839i
$597$		0			0
$598$	−160.992	+	116.968i	−0.0110091	+	0.00799860i
$599$	7948.47	−	24462.9i	0.542180	−	1.66866i	−0.185422	−	0.982659i	$-0.559365\pi$
$599$	7948.47	−	24462.9i	0.542180	−	1.66866i	0.727602	−	0.686000i	$-0.240635\pi$
$600$		0			0
$601$	19507.5	−	14173.0i	1.32401	−	0.961947i	0.324133	−	0.946012i	$-0.394928\pi$
$601$	19507.5	−	14173.0i	1.32401	−	0.961947i	0.999873	−	0.0159349i	$-0.00507245\pi$
$602$	−622.804	−	452.493i	−0.0421654	−	0.0306350i
$603$		0			0
$604$	−5359.40			−0.361044
$605$	7699.08	+	4471.17i	0.517375	+	0.300461i
$606$		0			0
$607$	−2140.96	−	6589.19i	−0.143161	−	0.440604i	0.853609	−	0.520914i	$-0.174409\pi$
$607$	−2140.96	−	6589.19i	−0.143161	−	0.440604i	−0.996770	+	0.0803101i	$0.974409\pi$
$608$	1127.78	+	819.381i	0.0752262	+	0.0546550i
$609$		0			0
$610$	−33.0256	+	101.642i	−0.00219208	+	0.00674653i
$611$	−2370.83	+	7296.65i	−0.156978	+	0.483128i
$612$		0			0
$613$	13240.1	+	9619.49i	0.872370	+	0.633814i	0.931222	−	0.364453i	$-0.118744\pi$
$613$	13240.1	+	9619.49i	0.872370	+	0.633814i	−0.0588522	+	0.998267i	$0.518744\pi$
$614$	−168.267	−	517.873i	−0.0110598	−	0.0340385i
$615$		0			0
$616$	851.283	−	687.567i	0.0556805	−	0.0449722i
$617$	−11265.9			−0.735087			−0.367543	−	0.930006i	$-0.619801\pi$
$617$	−11265.9			−0.735087			−0.367543	+	0.930006i	$0.619801\pi$
$618$		0			0
$619$	−2263.53	−	1644.55i	−0.146977	−	0.106785i	0.511867	−	0.859065i	$-0.328954\pi$
$619$	−2263.53	−	1644.55i	−0.146977	−	0.106785i	−0.658844	+	0.752280i	$0.728954\pi$
$620$	5357.84	−	3892.70i	0.347058	−	0.252152i
$621$		0			0
$622$	70.4531	−	216.832i	0.00454166	−	0.0139778i
$623$	15193.0	−	11038.4i	0.977040	−	0.709861i
$624$		0			0
$625$	262.033	+	806.456i	0.0167701	+	0.0516132i
$626$	612.152			0.0390839
$627$		0			0
$628$	−444.682			−0.0282560
$629$	8463.52	+	26048.0i	0.536507	+	1.65120i
$630$		0			0
$631$	394.979	−	286.969i	0.0249190	−	0.0181047i	−0.575256	−	0.817973i	$-0.695098\pi$
$631$	394.979	−	286.969i	0.0249190	−	0.0181047i	0.600175	+	0.799869i	$0.295098\pi$
$632$	178.455	−	549.228i	0.0112319	−	0.0345682i
$633$		0			0
$634$	201.708	−	146.549i	0.0126354	−	0.00918015i
$635$	−6817.29	−	4953.05i	−0.426041	−	0.309537i
$636$		0			0
$637$	−4806.71			−0.298978
$638$	−990.941	+	50.6713i	−0.0614918	+	0.00314435i
$639$		0			0
$640$	550.966	+	1695.70i	0.0340295	+	0.104732i
$641$	5133.48	+	3729.69i	0.316318	+	0.229819i	0.734603	−	0.678497i	$-0.237368\pi$
$641$	5133.48	+	3729.69i	0.316318	+	0.229819i	−0.418284	+	0.908316i	$0.637368\pi$
$642$		0			0
$643$	5753.88	−	17708.6i	0.352894	−	1.08610i	−0.604327	−	0.796737i	$-0.706558\pi$
$643$	5753.88	−	17708.6i	0.352894	−	1.08610i	0.957221	−	0.289359i	$-0.0934421\pi$
$644$	1536.99	−	4730.37i	0.0940465	−	0.289445i
$645$		0			0
$646$	412.216	+	299.493i	0.0251059	+	0.0182405i
$647$	6786.89	+	20887.9i	0.412396	+	1.26923i	0.914559	+	0.404452i	$0.132538\pi$
$647$	6786.89	+	20887.9i	0.412396	+	1.26923i	−0.502163	+	0.864773i	$0.667462\pi$
$648$		0			0
$649$	34.9747	−	129.868i	0.00211538	−	0.00785478i
$650$	−367.624			−0.0221837
$651$		0			0
$652$	4930.62	+	3582.31i	0.296163	+	0.215175i
$653$	−10213.3	+	7420.42i	−0.612065	+	0.444691i	−0.850141	−	0.526555i	$-0.823483\pi$
$653$	−10213.3	+	7420.42i	−0.612065	+	0.444691i	0.238076	+	0.971247i	$0.423483\pi$
$654$		0			0
$655$	3699.78	−	11386.8i	0.220706	−	0.679263i
$656$	−21652.1	+	15731.2i	−1.28868	+	0.936280i
$657$		0			0
$658$	127.094	+	391.155i	0.00752984	+	0.0231745i
$659$	151.172			0.00893598			0.00446799	−	0.999990i	$-0.498578\pi$
$659$	151.172			0.00893598			0.00446799	+	0.999990i	$0.498578\pi$
$660$		0			0
$661$	−3426.10			−0.201603			−0.100802	−	0.994907i	$-0.532141\pi$
$661$	−3426.10			−0.201603			−0.100802	+	0.994907i	$0.532141\pi$
$662$	−342.047	−	1052.71i	−0.0200816	−	0.0618048i
$663$		0			0
$664$	643.406	−	467.462i	0.0376039	−	0.0273209i
$665$	−1649.67	+	5077.15i	−0.0961974	+	0.296065i
$666$		0			0
$667$	−7305.19	+	5307.53i	−0.424075	+	0.308109i
$668$	−19719.2	−	14326.9i	−1.14216	−	0.829824i
$669$		0			0
$670$	192.239			0.0110848
$671$	−1591.14	−	4160.84i	−0.0915428	−	0.239385i
$672$		0			0
$673$	−7619.14	−	23449.3i	−0.436398	−	1.34310i	−0.891647	−	0.452732i	$-0.850450\pi$
$673$	−7619.14	−	23449.3i	−0.436398	−	1.34310i	0.455248	−	0.890364i	$-0.349550\pi$
$674$	353.101	+	256.543i	0.0201794	+	0.0146612i
$675$		0			0
$676$	2396.54	−	7375.79i	0.136353	−	0.419652i
$677$	−340.547	+	1048.10i	−0.0193328	+	0.0595001i	−0.960257	−	0.279116i	$-0.909959\pi$
$677$	−340.547	+	1048.10i	−0.0193328	+	0.0595001i	0.940925	+	0.338616i	$0.109959\pi$
$678$		0			0
$679$	9109.21	+	6618.23i	0.514845	+	0.374056i
$680$	302.509	+	931.028i	0.0170598	+	0.0525048i
$681$		0			0
$682$	153.962	−	571.689i	0.00864443	−	0.0320984i
$683$	−9464.22			−0.530217			−0.265109	−	0.964219i	$-0.585408\pi$
$683$	−9464.22			−0.530217			−0.265109	+	0.964219i	$0.585408\pi$
$684$		0			0
$685$	−3960.51	−	2877.48i	−0.220910	−	0.160500i
$686$	−729.218	+	529.808i	−0.0405855	+	0.0294871i
$687$		0			0
$688$	−8060.82	+	24808.6i	−0.446680	+	1.37474i
$689$	−10026.6	+	7284.72i	−0.554400	+	0.402795i
$690$		0			0
$691$	−3887.43	−	11964.3i	−0.214016	−	0.658672i	−0.999222	−	0.0394383i	$-0.987443\pi$
$691$	−3887.43	−	11964.3i	−0.214016	−	0.658672i	0.785206	−	0.619234i	$-0.212557\pi$
$692$	34297.1			1.88407
$693$		0			0
$694$	−941.765			−0.0515114
$695$	−3474.09	−	10692.1i	−0.189611	−	0.583562i
$696$		0			0
$697$	−23827.4	+	17311.7i	−1.29488	+	0.940783i
$698$	−218.400	+	672.165i	−0.0118432	+	0.0364496i
$699$		0			0
$700$	7433.67	−	5400.88i	0.401381	−	0.291620i
$701$	9895.69	+	7189.64i	0.533174	+	0.387374i	0.821544	−	0.570146i	$-0.193113\pi$
$701$	9895.69	+	7189.64i	0.533174	+	0.387374i	−0.288370	+	0.957519i	$0.593113\pi$
$702$		0			0
$703$	−21779.2			−1.16845
$704$	−15452.1	−	10062.7i	−0.827237	−	0.538709i
$705$		0			0
$706$	136.794	+	421.009i	0.00729222	+	0.0224432i
$707$	−18182.6	−	13210.4i	−0.967224	−	0.702729i
$708$		0			0
$709$	−8803.85	+	27095.5i	−0.466341	+	1.43525i	0.390947	+	0.920413i	$0.372147\pi$
$709$	−8803.85	+	27095.5i	−0.466341	+	1.43525i	−0.857288	+	0.514837i	$0.827853\pi$
$710$	290.763	−	894.877i	0.0153692	−	0.0473016i
$711$		0			0
$712$	2215.44	+	1609.61i	0.116611	+	0.0847230i
$713$	−1664.97	−	5124.24i	−0.0874523	−	0.269150i
$714$		0			0
$715$	−6646.04	+	5367.90i	−0.347619	+	0.280766i
$716$	20232.9			1.05606
$717$		0			0
$718$	1.85446	+	1.34735i	9.63899e−5	+	7.00314e-5i
$719$	21391.9	−	15542.1i	1.10957	−	0.806151i	0.126976	−	0.991906i	$-0.459473\pi$
$719$	21391.9	−	15542.1i	1.10957	−	0.806151i	0.982596	+	0.185755i	$0.0594729\pi$
$720$		0			0
$721$	706.577	−	2174.62i	0.0364970	−	0.112326i
$722$	398.296	−	289.379i	0.0205305	−	0.0149163i
$723$		0			0
$724$	−3707.04	−	11409.1i	−0.190292	−	0.585658i
$725$	−16681.3			−0.854523
$726$		0			0
$727$	−10380.5			−0.529559			−0.264780	−	0.964309i	$-0.585299\pi$
$727$	−10380.5			−0.529559			−0.264780	+	0.964309i	$0.585299\pi$
$728$	324.471	+	998.618i	0.0165188	+	0.0508396i
$729$		0			0
$730$	−518.470	+	376.691i	−0.0262869	+	0.0190986i
$731$	−8870.66	+	27301.1i	−0.448828	+	1.38135i
$732$		0			0
$733$	1899.30	−	1379.92i	0.0957058	−	0.0695344i	−0.538903	−	0.842368i	$-0.681161\pi$
$733$	1899.30	−	1379.92i	0.0957058	−	0.0695344i	0.634609	+	0.772833i	$0.281161\pi$
$734$	519.649	+	377.547i	0.0261316	+	0.0189857i
$735$		0			0
$736$	1088.31			0.0545048
$737$	−6233.59	+	5034.77i	−0.311557	+	0.251639i
$738$		0			0
$739$	11989.6	+	36900.1i	0.596811	+	1.83680i	0.545495	+	0.838114i	$0.316342\pi$
$739$	11989.6	+	36900.1i	0.596811	+	1.83680i	0.0513159	+	0.998682i	$0.483658\pi$
$740$	−16908.0	−	12284.4i	−0.839935	−	0.610248i
$741$		0			0
$742$	−205.306	+	631.866i	−0.0101577	+	0.0312622i
$743$	−3775.96	+	11621.2i	−0.186442	+	0.573809i	−0.999970	−	0.00771602i	$-0.997544\pi$
$743$	−3775.96	+	11621.2i	−0.186442	+	0.573809i	0.813528	+	0.581525i	$0.197544\pi$
$744$		0			0
$745$	6843.34	+	4971.98i	0.336538	+	0.244509i
$746$	340.330	+	1047.43i	0.0167029	+	0.0514062i
$747$		0			0
$748$	−17078.2	−	11121.6i	−0.834815	−	0.543644i
$749$	28269.2			1.37908
$750$		0			0
$751$	8583.48	+	6236.26i	0.417065	+	0.303015i	0.776456	−	0.630172i	$-0.217016\pi$
$751$	8583.48	+	6236.26i	0.417065	+	0.303015i	−0.359391	+	0.933187i	$0.617016\pi$
$752$	11274.6	−	8191.51i	0.546734	−	0.397226i
$753$		0			0
$754$	294.215	−	905.501i	0.0142105	−	0.0437353i
$755$	3633.14	−	2639.63i	0.175131	−	0.127240i
$756$		0			0
$757$	−3944.61	−	12140.3i	−0.189391	−	0.582887i	0.810605	−	0.585593i	$-0.199138\pi$
$757$	−3944.61	−	12140.3i	−0.189391	−	0.582887i	−0.999996	+	0.00270668i	$0.999138\pi$
$758$	843.558			0.0404214
$759$		0			0
$760$	−778.448			−0.0371543
$761$	−11176.9	−	34399.1i	−0.532410	−	1.63859i	−0.749181	−	0.662366i	$-0.769553\pi$
$761$	−11176.9	−	34399.1i	−0.532410	−	1.63859i	0.216771	−	0.976222i	$-0.430447\pi$
$762$		0			0
$763$	−15163.3	+	11016.8i	−0.719462	+	0.522720i
$764$	−10412.4	+	32046.2i	−0.493074	+	1.51753i
$765$		0			0
$766$	−502.103	+	364.799i	−0.0236837	+	0.0172072i
$767$	104.407	+	75.8563i	0.00491516	+	0.00357107i
$768$		0			0
$769$	−25178.7			−1.18071			−0.590356	−	0.807143i	$-0.701013\pi$
$769$	−25178.7			−1.18071			−0.590356	+	0.807143i	$0.701013\pi$
$770$	−119.094	+	442.216i	−0.00557381	+	0.0206966i
$771$		0			0
$772$	−8783.52	−	27032.9i	−0.409489	−	1.26028i
$773$	26891.5	+	19537.8i	1.25126	+	0.909091i	0.998294	−	0.0583858i	$-0.0185954\pi$
$773$	26891.5	+	19537.8i	1.25126	+	0.909091i	0.252962	+	0.967476i	$0.418595\pi$
$774$		0			0
$775$	3075.83	−	9466.43i	0.142564	−	0.438767i
$776$	−507.366	+	1561.51i	−0.0234709	+	0.0722359i
$777$		0			0
$778$	314.318	+	228.365i	0.0144844	+	0.0105235i
$779$	−7237.29	−	22274.1i	−0.332866	−	1.02446i
$780$		0			0
$781$	14008.7	+	36632.8i	0.641830	+	1.67839i
$782$	397.788			0.0181904
$783$		0			0
$784$	7063.72	+	5132.10i	0.321780	+	0.233787i
$785$	301.451	−	219.017i	0.0137060	−	0.00995802i
$786$		0			0
$787$	−1198.90	+	3689.82i	−0.0543024	+	0.167126i	−0.974530	−	0.224259i	$-0.928004\pi$
$787$	−1198.90	+	3689.82i	−0.0543024	+	0.167126i	0.920227	+	0.391385i	$0.128004\pi$
$788$	−7225.65	+	5249.74i	−0.326654	+	0.237328i
$789$		0			0
$790$	74.6865	+	229.861i	0.00336358	+	0.0103520i
$791$	−18800.7			−0.845102
$792$		0			0
$793$	4274.50			0.191415
$794$	63.6398	+	195.863i	0.00284445	+	0.00875431i
$795$		0			0
$796$	24251.1	−	17619.5i	1.07985	−	0.784554i
$797$	−3037.48	+	9348.40i	−0.134998	+	0.415480i	−0.995590	−	0.0938152i	$-0.970094\pi$
$797$	−3037.48	+	9348.40i	−0.134998	+	0.415480i	0.860592	+	0.509295i	$0.170094\pi$
$798$		0			0
$799$	12407.4	−	9014.48i	0.549363	−	0.399136i
$800$	1626.54	+	1181.75i	0.0718838	+	0.0522266i
$801$		0			0
$802$	484.169			0.0213174
$803$	6946.48	−	25793.6i	0.305275	−	1.13354i
$804$		0			0
$805$	1287.90	+	3963.73i	0.0563880	+	0.173544i
$806$	459.610	+	333.926i	0.0200857	+	0.0145931i
$807$		0			0
$808$	1012.74	−	3116.89i	0.0440940	−	0.135707i
$809$	−4343.22	+	13367.0i	−0.188751	+	0.580915i	−0.999993	−	0.00379534i	$-0.998792\pi$
$809$	−4343.22	+	13367.0i	−0.188751	+	0.580915i	0.811242	+	0.584711i	$0.198792\pi$
$810$		0			0
$811$	7740.27	+	5623.64i	0.335139	+	0.243493i	0.742608	−	0.669726i	$-0.233589\pi$
$811$	7740.27	+	5623.64i	0.335139	+	0.243493i	−0.407469	+	0.913219i	$0.633589\pi$
$812$	7353.71	+	22632.4i	0.317814	+	0.978130i
$813$		0			0
$814$	−1865.95	+	95.4145i	−0.0803459	+	0.00410845i
$815$	−5106.85			−0.219491
$816$		0			0
$817$	−18467.4	−	13417.3i	−0.790809	−	0.574556i
$818$	337.339	−	245.091i	0.0144191	−	0.0104761i
$819$		0			0
$820$	6944.95	−	21374.3i	0.295766	−	0.910274i
$821$	−29189.7	+	21207.5i	−1.24084	+	0.901520i	−0.997654	−	0.0684608i	$-0.978191\pi$
$821$	−29189.7	+	21207.5i	−1.24084	+	0.901520i	−0.243182	+	0.969981i	$0.578191\pi$
$822$		0			0
$823$	−7651.20	−	23548.0i	−0.324063	−	0.997364i	−0.971862	−	0.235552i	$-0.924310\pi$
$823$	−7651.20	−	23548.0i	−0.324063	−	0.997364i	0.647798	−	0.761812i	$-0.275690\pi$
$824$	333.421			0.0140962
$825$		0			0
$826$	6.91827			0.000291426
$827$	−8085.85	−	24885.7i	−0.339991	−	1.04638i	−0.964211	−	0.265136i	$-0.914583\pi$
$827$	−8085.85	−	24885.7i	−0.339991	−	1.04638i	0.624220	−	0.781249i	$-0.285417\pi$
$828$		0			0
$829$	−5360.16	+	3894.39i	−0.224567	+	0.163158i	−0.694380	−	0.719608i	$-0.744321\pi$
$829$	−5360.16	+	3894.39i	−0.224567	+	0.163158i	0.469813	+	0.882766i	$0.344321\pi$
$830$	−102.855	+	316.554i	−0.00430137	+	0.0132382i
$831$		0			0
$832$	14314.7	−	10400.2i	0.596481	−	0.433369i
$833$	7773.39	+	5647.70i	0.323328	+	0.234911i
$834$		0			0
$835$	20424.0			0.846470
$836$	12607.6	−	10182.9i	0.521582	−	0.421273i
$837$		0			0
$838$	−299.242	−	920.972i	−0.0123355	−	0.0379648i
$839$	−709.265	−	515.311i	−0.0291854	−	0.0212044i	0.573097	−	0.819488i	$-0.305742\pi$
$839$	−709.265	−	515.311i	−0.0291854	−	0.0212044i	−0.602282	+	0.798283i	$0.705742\pi$
$840$		0			0
$841$	5813.71	−	17892.8i	0.238374	−	0.733640i
$842$	99.9170	−	307.513i	0.00408951	−	0.0125862i
$843$		0			0
$844$	7082.56	+	5145.78i	0.288853	+	0.209864i
$845$	2008.14	+	6180.42i	0.0817540	+	0.251613i
$846$		0			0
$847$	−7719.97	−	17458.5i	−0.313177	−	0.708244i
$848$	22512.4			0.911650
$849$		0			0
$850$	594.520	+	431.944i	0.0239904	+	0.0174301i
$851$	−13755.8	+	9994.14i	−0.554102	+	0.402579i
$852$		0			0
$853$	−5723.03	+	17613.7i	−0.229722	+	0.707012i	0.768056	+	0.640383i	$0.221224\pi$
$853$	−5723.03	+	17613.7i	−0.229722	+	0.707012i	−0.997778	+	0.0666287i	$0.978776\pi$
$854$	185.382	−	134.688i	0.00742816	−	0.00539688i
$855$		0			0
$856$	1273.83	+	3920.45i	0.0508629	+	0.156540i
$857$	8236.44			0.328298			0.164149	−	0.986436i	$-0.447512\pi$
$857$	8236.44			0.328298			0.164149	+	0.986436i	$0.447512\pi$
$858$		0			0
$859$	30938.9			1.22890			0.614449	−	0.788957i	$-0.289379\pi$
$859$	30938.9			1.22890			0.614449	+	0.788957i	$0.289379\pi$
$860$	−6768.97	−	20832.7i	−0.268395	−	0.826036i
$861$		0			0
$862$	−115.958	+	84.2487i	−0.00458185	+	0.00332891i
$863$	4465.48	−	13743.3i	0.176138	−	0.542096i	−0.823546	−	0.567249i	$-0.808008\pi$
$863$	4465.48	−	13743.3i	0.176138	−	0.542096i	0.999684	+	0.0251537i	$0.00800753\pi$
$864$		0			0
$865$	−23250.0	+	16892.1i	−0.913902	+	0.663989i
$866$	9.56318	+	6.94806i	0.000375254	+	0.000272638i
$867$		0			0
$868$	−14199.5			−0.555257
$869$	−8441.93	−	5497.51i	−0.329543	−	0.214603i
$870$		0			0
$871$	−2375.96	−	7312.46i	−0.0924299	−	0.284470i
$872$	−2211.11	−	1606.47i	−0.0858689	−	0.0623874i
$873$		0			0
$874$	−97.7480	+	300.837i	−0.00378304	+	0.0116430i
$875$	−6084.94	+	18727.5i	−0.235096	+	0.723550i
$876$		0			0
$877$	29441.4	+	21390.4i	1.13360	+	0.823608i	0.986215	−	0.165472i	$-0.0529146\pi$
$877$	29441.4	+	21390.4i	1.13360	+	0.823608i	0.147384	+	0.989079i	$0.452915\pi$
$878$	−158.932	−	489.144i	−0.00610901	−	0.0188016i
$879$		0			0
$880$	15498.0	−	792.482i	0.593678	−	0.0303574i
$881$	48846.6			1.86797			0.933987	−	0.357306i	$-0.116305\pi$
$881$	48846.6			1.86797			0.933987	+	0.357306i	$0.116305\pi$
$882$		0			0
$883$	16773.1	+	12186.4i	0.639252	+	0.464443i	0.859593	−	0.510979i	$-0.170717\pi$
$883$	16773.1	+	12186.4i	0.639252	+	0.464443i	−0.220341	+	0.975423i	$0.570717\pi$
$884$	15821.0	−	11494.7i	0.601945	−	0.437339i
$885$		0			0
$886$	−160.555	+	494.139i	−0.00608800	+	0.0187369i
$887$	35100.5	−	25502.0i	1.32870	−	0.965359i	0.328923	−	0.944357i	$-0.393314\pi$
$887$	35100.5	−	25502.0i	1.32870	−	0.965359i	0.999779	−	0.0210025i	$-0.00668581\pi$
$888$		0			0
$889$	5583.13	+	17183.1i	0.210632	+	0.648260i
$890$	−1146.08			−0.0431650
$891$		0			0
$892$	48573.6			1.82328
$893$	3768.58	+	11598.5i	0.141222	+	0.434635i
$894$		0			0
$895$	−13715.9	+	9965.19i	−0.512260	+	0.372178i
$896$	1181.32	−	3635.72i	0.0440458	−	0.135559i
$897$		0			0
$898$	1883.36	−	1368.34i	0.0699872	−	0.0508486i
$899$	20855.3	+	15152.3i	0.773707	+	0.562131i
$900$		0			0
$901$	24774.2			0.916034
$902$	−717.643	−	1876.64i	−0.0264910	−	0.0692743i
$903$		0			0
$904$	−847.174	−	2607.33i	−0.0311688	−	0.0959276i
$905$	8132.27	+	5908.44i	0.298703	+	0.217020i
$906$		0			0
$907$	−10209.6	+	31421.8i	−0.373763	+	1.15032i	0.570547	+	0.821265i	$0.306731\pi$
$907$	−10209.6	+	31421.8i	−0.373763	+	1.15032i	−0.944310	+	0.329058i	$0.893269\pi$
$908$	5150.54	−	15851.7i	0.188245	−	0.579359i
$909$		0			0
$910$	−355.520	−	258.300i	−0.0129510	−	0.00940942i
$911$	−516.811	−	1590.58i	−0.0187955	−	0.0578466i	0.941219	−	0.337797i	$-0.109682\pi$
$911$	−516.811	−	1590.58i	−0.0187955	−	0.0578466i	−0.960014	+	0.279951i	$0.909682\pi$
$912$		0			0
$913$	−4955.42	−	12958.5i	−0.179628	−	0.469729i
$914$	−1512.19			−0.0547251
$915$		0			0
$916$	−14537.5	−	10562.1i	−0.524379	−	0.380984i
$917$	−20767.9	+	15088.8i	−0.747892	+	0.543375i
$918$		0			0
$919$	6171.40	−	18993.6i	0.221519	−	0.681765i	−0.777108	−	0.629368i	$-0.783314\pi$
$919$	6171.40	−	18993.6i	0.221519	−	0.681765i	0.998626	−	0.0523969i	$-0.0166861\pi$
$920$	−491.668	+	357.218i	−0.0176194	+	0.0128012i
$921$		0			0
$922$	40.2921	+	124.006i	0.00143921	+	0.00442942i
$923$	−37633.5			−1.34206
$924$		0			0
$925$	−31411.1			−1.11653
$926$	159.743	+	491.639i	0.00566899	+	0.0174474i
$927$		0			0
$928$	−4212.54	+	3060.59i	−0.149012	+	0.108264i
$929$	239.193	−	736.159i	0.00844742	−	0.0259985i	−0.946744	−	0.321987i	$-0.895649\pi$
$929$	239.193	−	736.159i	0.00844742	−	0.0259985i	0.955191	+	0.295989i	$0.0956491\pi$
$930$		0			0
$931$	−6181.36	+	4491.02i	−0.217600	+	0.158096i
$932$	−7081.11	−	5144.73i	−0.248873	−	0.180817i
$933$		0			0
$934$	2164.12			0.0758161
$935$	17055.0	−	872.100i	0.596533	−	0.0305034i
$936$		0			0
$937$	−11510.1	−	35424.5i	−0.401301	−	1.23508i	−0.923944	−	0.382527i	$-0.875054\pi$
$937$	−11510.1	−	35424.5i	−0.401301	−	1.23508i	0.522643	−	0.852552i	$-0.324946\pi$
$938$	−333.457	−	242.271i	−0.0116074	−	0.00843328i
$939$		0			0
$940$	−3616.36	+	11130.0i	−0.125481	+	0.386192i
$941$	14111.0	−	43429.3i	0.488849	−	1.50452i	−0.337479	−	0.941333i	$-0.609574\pi$
$941$	14111.0	−	43429.3i	0.488849	−	1.50452i	0.826328	−	0.563189i	$-0.190426\pi$
$942$		0			0
$943$	−14792.3	−	10747.2i	−0.510820	−	0.371132i
$944$	−72.4408	−	222.950i	−0.00249761	−	0.00768686i
$945$		0			0
$946$	−1640.99	−	1068.63i	−0.0563986	−	0.0367276i
$947$	−19714.7			−0.676497			−0.338249	−	0.941057i	$-0.609834\pi$
$947$	−19714.7			−0.676497			−0.338249	+	0.941057i	$0.609834\pi$
$948$		0			0
$949$	20736.8	+	15066.1i	0.709319	+	0.515350i
$950$	−472.759	+	343.480i	−0.0161456	+	0.0117305i
$951$		0			0
$952$	648.605	−	1996.20i	0.0220813	−	0.0679593i
$953$	−30227.8	+	21961.8i	−1.02747	+	0.746498i	−0.967800	−	0.251720i	$-0.919004\pi$
$953$	−30227.8	+	21961.8i	−1.02747	+	0.746498i	−0.0596665	+	0.998218i	$0.519004\pi$
$954$		0			0
$955$	−8724.91	−	26852.5i	−0.295635	−	0.909871i
$956$	−32656.0			−1.10478
$957$		0			0
$958$	631.788			0.0213071
$959$	3243.53	+	9982.55i	0.109217	+	0.336135i
$960$		0			0
$961$	11657.3	−	8469.51i	0.391302	−	0.284298i
$962$	554.010	−	1705.07i	0.0185676	−	0.0571451i
$963$		0			0
$964$	−41152.7	+	29899.2i	−1.37494	+	0.998951i
$965$	19268.7	+	13999.5i	0.642779	+	0.467007i
$966$		0			0
$967$	−55189.6			−1.83535			−0.917673	−	0.397337i	$-0.869934\pi$
$967$	−55189.6			−1.83535			−0.917673	+	0.397337i	$0.869934\pi$
$968$	2073.33	−	1857.32i	0.0688423	−	0.0616700i
$969$		0			0
$970$	−212.342	−	653.520i	−0.00702874	−	0.0216322i
$971$	15338.2	+	11143.8i	0.506926	+	0.368303i	0.811656	−	0.584135i	$-0.198566\pi$
$971$	15338.2	+	11143.8i	0.506926	+	0.368303i	−0.304730	+	0.952439i	$0.598566\pi$
$972$		0			0
$973$	−7448.73	+	22924.8i	−0.245422	+	0.755330i
$974$	−37.8192	+	116.395i	−0.00124415	+	0.00382911i
$975$		0			0
$976$	−6281.62	−	4563.86i	−0.206014	−	0.149678i
$977$	−7393.34	−	22754.4i	−0.242102	−	0.745114i	−0.996100	−	0.0882365i	$-0.971877\pi$
$977$	−7393.34	−	22754.4i	−0.242102	−	0.745114i	0.753997	−	0.656877i	$-0.228123\pi$
$978$		0			0
$979$	37163.3	−	30016.2i	1.21322	−	0.979899i
$980$	−7331.95			−0.238990
$981$		0			0
$982$	1279.01	+	929.258i	0.0415631	+	0.0301974i
$983$	−37475.9	+	27227.8i	−1.21597	+	0.883451i	−0.995759	−	0.0920022i	$-0.970673\pi$
$983$	−37475.9	+	27227.8i	−1.21597	+	0.883451i	−0.220207	+	0.975453i	$0.570673\pi$
$984$		0			0
$985$	2312.65	−	7117.62i	0.0748094	−	0.230240i
$986$	−1539.73	+	1118.68i	−0.0497313	+	0.0361319i
$987$		0			0
$988$	4805.44	+	14789.6i	0.154738	+	0.476236i
$989$	−17821.0			−0.572977
$990$		0			0
$991$	17231.6			0.552351			0.276175	−	0.961107i	$-0.410933\pi$
$991$	17231.6			0.552351			0.276175	+	0.961107i	$0.410933\pi$
$992$	−960.104	−	2954.89i	−0.0307292	−	0.0945746i
$993$		0			0
$994$	−1632.14	+	1185.82i	−0.0520807	+	0.0378389i
$995$	−7761.85	+	23888.5i	−0.247304	+	0.761123i
$996$		0			0
$997$	26124.4	−	18980.5i	0.829857	−	0.602926i	−0.0896621	−	0.995972i	$-0.528579\pi$
$997$	26124.4	−	18980.5i	0.829857	−	0.602926i	0.919519	+	0.393046i	$0.128579\pi$
$998$	179.544	+	130.447i	0.00569476	+	0.00413749i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.b.82.1		8
3.2	odd	2		33.4.e.b.16.2	✓	8
11.3	even	5		1089.4.a.bg.1.2		4
11.8	odd	10		1089.4.a.z.1.3		4
11.9	even	5	inner	99.4.f.b.64.1		8
33.8	even	10		363.4.a.t.1.2		4
33.14	odd	10		363.4.a.p.1.3		4
33.20	odd	10		33.4.e.b.31.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.16.2	✓	8	3.2	odd	2
33.4.e.b.31.2	yes	8	33.20	odd	10
99.4.f.b.64.1		8	11.9	even	5	inner
99.4.f.b.82.1		8	1.1	even	1	trivial
363.4.a.p.1.3		4	33.14	odd	10
363.4.a.t.1.2		4	33.8	even	10
1089.4.a.z.1.3		4	11.8	odd	10
1089.4.a.bg.1.2		4	11.3	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)

\(f(q)\)	\(=\)	\(q+(0.0404346 + 0.124445i) q^{2} +(6.45828 - 4.69222i) q^{4} +(-2.06705 + 6.36172i) q^{5} +(11.6029 - 8.43002i) q^{7} +(1.69194 + 1.22926i) q^{8} +O(q^{10})\)	\(q+(0.0404346 + 0.124445i) q^{2} +(6.45828 - 4.69222i) q^{4} +(-2.06705 + 6.36172i) q^{5} +(11.6029 - 8.43002i) q^{7} +(1.69194 + 1.22926i) q^{8} -0.875265 q^{10} +(28.3816 - 22.9234i) q^{11} +(10.8178 + 33.2938i) q^{13} +(1.51823 + 1.10306i) q^{14} +(19.6502 - 60.4771i) q^{16} +(21.6244 - 66.5530i) q^{17} +(45.0187 + 32.7080i) q^{19} +(16.5010 + 50.7849i) q^{20} +(4.00030 + 2.60506i) q^{22} +43.4430 q^{23} +(64.9283 + 47.1732i) q^{25} +(-3.70583 + 2.69244i) q^{26} +(35.3795 - 108.887i) q^{28} +(-168.156 + 122.172i) q^{29} +(-38.3253 - 117.953i) q^{31} +25.0514 q^{32} +9.15657 q^{34} +(29.6457 + 91.2399i) q^{35} +(-316.639 + 230.052i) q^{37} +(-2.25003 + 6.92488i) q^{38} +(-11.3175 + 8.22268i) q^{40} +(-340.499 - 247.387i) q^{41} -410.216 q^{43} +(75.7352 - 281.219i) q^{44} +(1.75660 + 5.40626i) q^{46} +(177.304 + 128.819i) q^{47} +(-42.4301 + 130.586i) q^{49} +(-3.24511 + 9.98743i) q^{50} +(226.086 + 164.261i) q^{52} +(109.401 + 336.701i) q^{53} +(87.1660 + 227.940i) q^{55} +29.9941 q^{56} +(-22.0031 - 15.9862i) q^{58} +(2.98246 - 2.16688i) q^{59} +(37.7322 - 116.128i) q^{61} +(13.1290 - 9.53880i) q^{62} +(-156.189 - 480.699i) q^{64} -234.167 q^{65} -219.635 q^{67} +(-172.625 - 531.285i) q^{68} +(-10.1556 + 7.37851i) q^{70} +(-332.200 + 1022.41i) q^{71} +(592.358 - 430.373i) q^{73} +(-41.4320 - 30.1021i) q^{74} +444.216 q^{76} +(136.066 - 505.237i) q^{77} +(-85.3301 - 262.619i) q^{79} +(344.121 + 250.018i) q^{80} +(17.0181 - 52.3764i) q^{82} +(117.512 - 361.666i) q^{83} +(378.693 + 275.137i) q^{85} +(-16.5869 - 51.0493i) q^{86} +(76.1988 - 3.89639i) q^{88} +1309.41 q^{89} +(406.185 + 295.111i) q^{91} +(280.567 - 203.844i) q^{92} +(-8.86164 + 27.2733i) q^{94} +(-301.135 + 218.787i) q^{95} +(242.603 + 746.654i) q^{97} -17.9665 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8}+O(q^{10}) \) 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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