LMFDB - Embedded newform 288.3.u.a.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			163.4
Character	$\chi$	$=$	288.163
Dual form			288.3.u.a.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658450 - 1.88850i) q^{2} +(-3.13289 - 2.48697i) q^{4} +(0.659338 + 1.59178i) q^{5} +(9.54718 + 9.54718i) q^{7} +(-6.75950 + 4.27892i) q^{8} +O(q^{10})$	\(q+(0.658450 - 1.88850i) q^{2} +(-3.13289 - 2.48697i) q^{4} +(0.659338 + 1.59178i) q^{5} +(9.54718 + 9.54718i) q^{7} +(-6.75950 + 4.27892i) q^{8} +(3.44023 - 0.197052i) q^{10} +(3.96481 + 9.57189i) q^{11} +(1.91784 - 4.63007i) q^{13} +(24.3162 - 11.7435i) q^{14} +(3.62996 + 15.5828i) q^{16} +15.3143i q^{17} +(0.827335 + 0.342693i) q^{19} +(1.89308 - 6.62663i) q^{20} +(20.6872 - 1.18494i) q^{22} +(12.9230 - 12.9230i) q^{23} +(15.5786 - 15.5786i) q^{25} +(-7.48110 - 6.67051i) q^{26} +(-6.16668 - 53.6538i) q^{28} +(-23.7905 - 9.85436i) q^{29} -25.1562i q^{31} +(31.8183 + 3.40530i) q^{32} +(28.9211 + 10.0837i) q^{34} +(-8.90221 + 21.4918i) q^{35} +(13.6161 + 32.8721i) q^{37} +(1.19194 - 1.33678i) q^{38} +(-11.2679 - 7.93840i) q^{40} +(32.9116 + 32.9116i) q^{41} +(-17.9473 - 43.3286i) q^{43} +(11.3837 - 39.8480i) q^{44} +(-15.8960 - 32.9143i) q^{46} -20.1127 q^{47} +133.297i q^{49} +(-19.1625 - 39.6780i) q^{50} +(-17.5232 + 9.73588i) q^{52} +(-35.0503 + 14.5183i) q^{53} +(-12.6222 + 12.6222i) q^{55} +(-105.386 - 23.6825i) q^{56} +(-34.2749 + 38.4399i) q^{58} +(60.6706 - 25.1306i) q^{59} +(-27.9825 - 11.5907i) q^{61} +(-47.5076 - 16.5641i) q^{62} +(27.3817 - 57.8467i) q^{64} +8.63457 q^{65} +(1.13412 - 2.73801i) q^{67} +(38.0862 - 47.9780i) q^{68} +(34.7257 + 30.9632i) q^{70} +(45.6144 + 45.6144i) q^{71} +(-29.1727 - 29.1727i) q^{73} +(71.0445 - 4.06934i) q^{74} +(-1.73968 - 3.13118i) q^{76} +(-53.5318 + 129.237i) q^{77} +3.27983 q^{79} +(-22.4110 + 16.0524i) q^{80} +(83.8242 - 40.4830i) q^{82} +(-56.7834 - 23.5205i) q^{83} +(-24.3770 + 10.0973i) q^{85} +(-93.6436 + 5.36380i) q^{86} +(-67.7575 - 47.7361i) q^{88} +(44.5059 - 44.5059i) q^{89} +(62.5140 - 25.8942i) q^{91} +(-72.6256 + 8.34720i) q^{92} +(-13.2432 + 37.9829i) q^{94} +1.54289i q^{95} -106.417 q^{97} +(251.732 + 87.7695i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$

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 $

$2$	0.658450	−	1.88850i	0.329225	−	0.944251i
$2$	0.658450	−	1.88850i	0.329225	−	0.944251i
$3$		0			0
$3$		0			0
$4$	−3.13289	−	2.48697i	−0.783222	−	0.621742i
$5$	0.659338	+	1.59178i	0.131868	+	0.318356i	0.975997	−	0.217782i	$-0.0698823\pi$
$5$	0.659338	+	1.59178i	0.131868	+	0.318356i	−0.844130	+	0.536139i	$0.819882\pi$
$6$		0			0
$7$	9.54718	+	9.54718i	1.36388	+	1.36388i	0.868907	+	0.494975i	$0.164823\pi$
$7$	9.54718	+	9.54718i	1.36388	+	1.36388i	0.494975	+	0.868907i	$0.335177\pi$
$8$	−6.75950	+	4.27892i	−0.844937	+	0.534865i
$9$		0			0
$10$	3.44023	−	0.197052i	0.344023	−	0.0197052i
$11$	3.96481	+	9.57189i	0.360437	+	0.870172i	0.995236	+	0.0974947i	$0.0310829\pi$
$11$	3.96481	+	9.57189i	0.360437	+	0.870172i	−0.634799	+	0.772677i	$0.718917\pi$
$12$		0			0
$13$	1.91784	−	4.63007i	0.147526	−	0.356159i	−0.832792	−	0.553587i	$-0.813259\pi$
$13$	1.91784	−	4.63007i	0.147526	−	0.356159i	0.980317	+	0.197428i	$0.0632587\pi$
$14$	24.3162	−	11.7435i	1.73687	−	0.838824i
$15$		0			0
$16$	3.62996	+	15.5828i	0.226873	+	0.973924i
$17$			15.3143i			0.900842i	0.892816	+	0.450421i	$0.148726\pi$
$17$			15.3143i			0.900842i	−0.892816	+	0.450421i	$0.851274\pi$
$18$		0			0
$19$	0.827335	+	0.342693i	0.0435439	+	0.0180365i	0.404349	−	0.914605i	$-0.367498\pi$
$19$	0.827335	+	0.342693i	0.0435439	+	0.0180365i	−0.360805	+	0.932641i	$0.617498\pi$
$20$	1.89308	−	6.62663i	0.0946542	−	0.331331i
$21$		0			0
$22$	20.6872	−	1.18494i	0.940326	−	0.0538608i
$23$	12.9230	−	12.9230i	0.561871	−	0.561871i	−0.367968	−	0.929839i	$-0.619946\pi$
$23$	12.9230	−	12.9230i	0.561871	−	0.561871i	0.929839	+	0.367968i	$0.119946\pi$
$24$		0			0
$25$	15.5786	−	15.5786i	0.623145	−	0.623145i
$26$	−7.48110	−	6.67051i	−0.287735	−	0.256558i
$27$		0			0
$28$	−6.16668	−	53.6538i	−0.220239	−	1.91621i
$29$	−23.7905	−	9.85436i	−0.820363	−	0.339805i	−0.0672825	−	0.997734i	$-0.521433\pi$
$29$	−23.7905	−	9.85436i	−0.820363	−	0.339805i	−0.753080	+	0.657929i	$0.771433\pi$
$30$		0			0
$31$		−	25.1562i		−	0.811491i	−0.913986	−	0.405746i	$-0.867012\pi$
$31$		−	25.1562i		−	0.811491i	0.913986	−	0.405746i	$-0.132988\pi$
$32$	31.8183	+	3.40530i	0.994322	+	0.106416i
$33$		0			0
$34$	28.9211	+	10.0837i	0.850621	+	0.296580i
$35$	−8.90221	+	21.4918i	−0.254349	+	0.614053i
$36$		0			0
$37$	13.6161	+	32.8721i	0.368001	+	0.888434i	0.994078	+	0.108672i	$0.0346599\pi$
$37$	13.6161	+	32.8721i	0.368001	+	0.888434i	−0.626076	+	0.779762i	$0.715340\pi$
$38$	1.19194	−	1.33678i	0.0313667	−	0.0351784i
$39$		0			0
$40$	−11.2679	−	7.93840i	−0.281698	−	0.198460i
$41$	32.9116	+	32.9116i	0.802721	+	0.802721i	0.983520	−	0.180799i	$-0.0578684\pi$
$41$	32.9116	+	32.9116i	0.802721	+	0.802721i	−0.180799	+	0.983520i	$0.557868\pi$
$42$		0			0
$43$	−17.9473	−	43.3286i	−0.417379	−	1.00764i	−0.983104	−	0.183048i	$-0.941404\pi$
$43$	−17.9473	−	43.3286i	−0.417379	−	1.00764i	0.565725	−	0.824594i	$-0.308596\pi$
$44$	11.3837	−	39.8480i	0.258721	−	0.905637i
$45$		0			0
$46$	−15.8960	−	32.9143i	−0.345565	−	0.715529i
$47$	−20.1127			−0.427930			−0.213965	−	0.976841i	$-0.568638\pi$
$47$	−20.1127			−0.427930			−0.213965	+	0.976841i	$0.568638\pi$
$48$		0			0
$49$			133.297i			2.72035i
$50$	−19.1625	−	39.6780i	−0.383251	−	0.793561i
$51$		0			0
$52$	−17.5232	+	9.73588i	−0.336985	+	0.187228i
$53$	−35.0503	+	14.5183i	−0.661327	+	0.273931i	−0.687997	−	0.725714i	$-0.741510\pi$
$53$	−35.0503	+	14.5183i	−0.661327	+	0.273931i	0.0266698	+	0.999644i	$0.491510\pi$
$54$		0			0
$55$	−12.6222	+	12.6222i	−0.229495	+	0.229495i
$56$	−105.386	−	23.6825i	−1.88189	−	0.422902i
$57$		0			0
$58$	−34.2749	+	38.4399i	−0.590946	+	0.662756i
$59$	60.6706	−	25.1306i	1.02832	−	0.425942i	0.196212	−	0.980562i	$-0.437136\pi$
$59$	60.6706	−	25.1306i	1.02832	−	0.425942i	0.832104	+	0.554619i	$0.187136\pi$
$60$		0			0
$61$	−27.9825	−	11.5907i	−0.458730	−	0.190012i	0.141338	−	0.989961i	$-0.454860\pi$
$61$	−27.9825	−	11.5907i	−0.458730	−	0.190012i	−0.600067	+	0.799949i	$0.704860\pi$
$62$	−47.5076	−	16.5641i	−0.766252	−	0.267163i
$63$		0			0
$64$	27.3817	−	57.8467i	0.427839	−	0.903855i
$65$	8.63457			0.132839
$66$		0			0
$67$	1.13412	−	2.73801i	0.0169272	−	0.0408659i	−0.915190	−	0.403023i	$-0.867960\pi$
$67$	1.13412	−	2.73801i	0.0169272	−	0.0408659i	0.932117	+	0.362157i	$0.117960\pi$
$68$	38.0862	−	47.9780i	0.560092	−	0.705559i
$69$		0			0
$70$	34.7257	+	30.9632i	0.496082	+	0.442331i
$71$	45.6144	+	45.6144i	0.642456	+	0.642456i	0.951159	−	0.308702i	$-0.0998947\pi$
$71$	45.6144	+	45.6144i	0.642456	+	0.642456i	−0.308702	+	0.951159i	$0.599895\pi$
$72$		0			0
$73$	−29.1727	−	29.1727i	−0.399626	−	0.399626i	0.478475	−	0.878101i	$-0.341190\pi$
$73$	−29.1727	−	29.1727i	−0.399626	−	0.399626i	−0.878101	+	0.478475i	$0.841190\pi$
$74$	71.0445	−	4.06934i	0.960060	−	0.0549911i
$75$		0			0
$76$	−1.73968	−	3.13118i	−0.0228905	−	0.0411997i
$77$	−53.5318	+	129.237i	−0.695219	+	1.67841i
$78$		0			0
$79$	3.27983			0.0415169			0.0207584	−	0.999785i	$-0.493392\pi$
$79$	3.27983			0.0415169			0.0207584	+	0.999785i	$0.493392\pi$
$80$	−22.4110	+	16.0524i	−0.280138	+	0.200655i
$81$		0			0
$82$	83.8242	−	40.4830i	1.02225	−	0.493695i
$83$	−56.7834	−	23.5205i	−0.684138	−	0.283379i	0.0134176	−	0.999910i	$-0.495729\pi$
$83$	−56.7834	−	23.5205i	−0.684138	−	0.283379i	−0.697555	+	0.716531i	$0.745729\pi$
$84$		0			0
$85$	−24.3770	+	10.0973i	−0.286789	+	0.118792i
$86$	−93.6436	+	5.36380i	−1.08888	+	0.0623697i
$87$		0			0
$88$	−67.7575	−	47.7361i	−0.769971	−	0.542456i
$89$	44.5059	−	44.5059i	0.500066	−	0.500066i	−0.411392	−	0.911458i	$-0.634957\pi$
$89$	44.5059	−	44.5059i	0.500066	−	0.500066i	0.911458	+	0.411392i	$0.134957\pi$
$90$		0			0
$91$	62.5140	−	25.8942i	0.686967	−	0.284551i
$92$	−72.6256	+	8.34720i	−0.789408	+	0.0907305i
$93$		0			0
$94$	−13.2432	+	37.9829i	−0.140885	+	0.404074i
$95$			1.54289i			0.0162409i
$96$		0			0
$97$	−106.417			−1.09708			−0.548542	−	0.836123i	$-0.684817\pi$
$97$	−106.417			−1.09708			−0.548542	+	0.836123i	$0.684817\pi$
$98$	251.732	+	87.7695i	2.56869	+	0.895607i
$99$		0			0
$100$	−87.5496	+	10.0625i	−0.875496	+	0.100625i
$101$	−3.62243	−	8.74531i	−0.0358656	−	0.0865872i	0.904932	−	0.425557i	$-0.139922\pi$
$101$	−3.62243	−	8.74531i	−0.0358656	−	0.0865872i	−0.940797	+	0.338969i	$0.889922\pi$
$102$		0			0
$103$	26.0911	+	26.0911i	0.253312	+	0.253312i	0.822327	−	0.569015i	$-0.192675\pi$
$103$	26.0911	+	26.0911i	0.253312	+	0.253312i	−0.569015	+	0.822327i	$0.692675\pi$
$104$	6.84808	+	39.5032i	0.0658469	+	0.379839i
$105$		0			0
$106$	4.33900	+	75.7523i	0.0409340	+	0.714644i
$107$	−32.1753	−	77.6781i	−0.300704	−	0.725963i	−0.999939	−	0.0110713i	$-0.996476\pi$
$107$	−32.1753	−	77.6781i	−0.300704	−	0.725963i	0.699235	−	0.714892i	$-0.253524\pi$
$108$		0			0
$109$	−36.0541	+	87.0422i	−0.330771	+	0.798553i	0.667760	+	0.744377i	$0.267253\pi$
$109$	−36.0541	+	87.0422i	−0.330771	+	0.798553i	−0.998531	+	0.0541760i	$0.982747\pi$
$110$	15.5260	+	32.1482i	0.141145	+	0.292256i
$111$		0			0
$112$	−114.116	+	183.428i	−1.01889	+	1.63775i
$113$			6.32445i			0.0559686i	0.999608	+	0.0279843i	$0.00890884\pi$
$113$			6.32445i			0.0559686i	−0.999608	+	0.0279843i	$0.991091\pi$
$114$		0			0
$115$	29.0913	+	12.0500i	0.252968	+	0.104783i
$116$	50.0255	+	90.0389i	0.431255	+	0.776197i
$117$		0			0
$118$	−7.51063	−	131.124i	−0.0636494	−	1.11122i
$119$	−146.208	+	146.208i	−1.22864	+	1.22864i
$120$		0			0
$121$	9.65850	−	9.65850i	0.0798223	−	0.0798223i
$122$	−40.3142	+	45.2131i	−0.330444	+	0.370599i
$123$		0			0
$124$	−62.5628	+	78.8116i	−0.504539	+	0.635577i
$125$	74.8639	+	31.0096i	0.598911	+	0.248077i
$126$		0			0
$127$			34.6015i			0.272453i	0.990678	+	0.136226i	$0.0434975\pi$
$127$			34.6015i			0.272453i	−0.990678	+	0.136226i	$0.956503\pi$
$128$	−91.2142	−	89.7996i	−0.712611	−	0.701559i
$129$		0			0
$130$	5.68543	−	16.3064i	0.0437341	−	0.125434i
$131$	68.0051	−	164.179i	0.519123	−	1.25327i	−0.419320	−	0.907838i	$-0.637732\pi$
$131$	68.0051	−	164.179i	0.519123	−	1.25327i	0.938443	−	0.345434i	$-0.112268\pi$
$132$		0			0
$133$	4.62696	+	11.1705i	0.0347892	+	0.0839885i
$134$	−4.42398	−	3.94464i	−0.0330148	−	0.0294376i
$135$		0			0
$136$	−65.5287	−	103.517i	−0.481829	−	0.761155i
$137$	−71.5748	−	71.5748i	−0.522444	−	0.522444i	0.395865	−	0.918309i	$-0.370445\pi$
$137$	−71.5748	−	71.5748i	−0.522444	−	0.522444i	−0.918309	+	0.395865i	$0.870445\pi$
$138$		0			0
$139$	−75.1916	−	181.529i	−0.540947	−	1.30596i	−0.924056	−	0.382258i	$-0.875147\pi$
$139$	−75.1916	−	181.529i	−0.540947	−	1.30596i	0.383109	−	0.923703i	$-0.374853\pi$
$140$	81.3392	−	45.1920i	0.580994	−	0.322800i
$141$		0			0
$142$	116.178	−	56.1081i	0.818153	−	0.395128i
$143$	51.9224			0.363094
$144$		0			0
$145$		−	44.3667i		−	0.305977i
$146$	−74.3015	+	35.8840i	−0.508915	+	0.245781i
$147$		0			0
$148$	39.0943	−	136.847i	0.264150	−	0.924643i
$149$	−211.685	+	87.6826i	−1.42070	+	0.588474i	−0.955037	−	0.296487i	$-0.904185\pi$
$149$	−211.685	+	87.6826i	−1.42070	+	0.588474i	−0.465665	+	0.884961i	$0.654185\pi$
$150$		0			0
$151$	10.5820	−	10.5820i	0.0700794	−	0.0700794i	−0.671198	−	0.741278i	$-0.734220\pi$
$151$	10.5820	−	10.5820i	0.0700794	−	0.0700794i	0.741278	+	0.671198i	$0.234220\pi$
$152$	−7.05873	+	1.22366i	−0.0464390	+	0.00805043i
$153$		0			0
$154$	208.817	+	186.191i	1.35595	+	1.20903i
$155$	40.0432	−	16.5864i	0.258343	−	0.107009i
$156$		0			0
$157$	26.9641	+	11.1689i	0.171746	+	0.0711394i	0.466900	−	0.884310i	$-0.345371\pi$
$157$	26.9641	+	11.1689i	0.171746	+	0.0711394i	−0.295154	+	0.955450i	$0.595371\pi$
$158$	2.15961	−	6.19398i	0.0136684	−	0.0392024i
$159$		0			0
$160$	15.5585	+	52.8930i	0.0972407	+	0.330581i
$161$	246.757			1.53265
$162$		0			0
$163$	111.743	−	269.771i	0.685540	−	1.65504i	−0.0680396	−	0.997683i	$-0.521674\pi$
$163$	111.743	−	269.771i	0.685540	−	1.65504i	0.753579	−	0.657357i	$-0.228326\pi$
$164$	−21.2581	−	184.958i	−0.129623	−	1.12779i
$165$		0			0
$166$	−81.8075	+	91.7486i	−0.492816	+	0.552703i
$167$	10.3664	+	10.3664i	0.0620741	+	0.0620741i	0.737462	−	0.675388i	$-0.236024\pi$
$167$	10.3664	+	10.3664i	0.0620741	+	0.0620741i	−0.675388	+	0.737462i	$0.736024\pi$
$168$		0			0
$169$	101.742	+	101.742i	0.602021	+	0.602021i
$170$	3.01772	+	52.6847i	0.0177513	+	0.309910i
$171$		0			0
$172$	−51.5301	+	180.378i	−0.299594	+	1.04871i
$173$	88.6518	−	214.024i	0.512438	−	1.23714i	−0.430022	−	0.902818i	$-0.641494\pi$
$173$	88.6518	−	214.024i	0.512438	−	1.23714i	0.942461	−	0.334317i	$-0.108506\pi$
$174$		0			0
$175$	297.464			1.69979
$176$	−134.765	+	96.5284i	−0.765709	+	0.548457i
$177$		0			0
$178$	−54.7446	−	113.354i	−0.307554	−	0.636822i
$179$	−2.58312	−	1.06996i	−0.0144308	−	0.00597744i	0.375456	−	0.926840i	$-0.377486\pi$
$179$	−2.58312	−	1.06996i	−0.0144308	−	0.00597744i	−0.389887	+	0.920863i	$0.627486\pi$
$180$		0			0
$181$	−184.394	+	76.3786i	−1.01875	+	0.421981i	−0.828640	−	0.559781i	$-0.810885\pi$
$181$	−184.394	+	76.3786i	−1.01875	+	0.421981i	−0.190112	+	0.981762i	$0.560885\pi$
$182$	−7.73883	−	135.108i	−0.0425210	−	0.742351i
$183$		0			0
$184$	−32.0566	+	142.650i	−0.174221	+	0.775271i
$185$	−43.3476	+	43.3476i	−0.234311	+	0.234311i
$186$		0			0
$187$	−146.587	+	60.7183i	−0.783887	+	0.324697i
$188$	63.0109	+	50.0197i	0.335164	+	0.266062i
$189$		0			0
$190$	2.91375	+	1.01591i	0.0153355	+	0.00534692i
$191$		−	185.771i		−	0.972625i	−0.873785	−	0.486313i	$-0.838342\pi$
$191$		−	185.771i		−	0.972625i	0.873785	−	0.486313i	$-0.161658\pi$
$192$		0			0
$193$	208.055			1.07800			0.539002	−	0.842305i	$-0.318802\pi$
$193$	208.055			1.07800			0.539002	+	0.842305i	$0.318802\pi$
$194$	−70.0704	+	200.969i	−0.361188	+	1.03592i
$195$		0			0
$196$	331.506	−	417.605i	1.69136	−	2.13064i
$197$	−123.852	−	299.006i	−0.628691	−	1.51780i	−0.841250	−	0.540647i	$-0.818180\pi$
$197$	−123.852	−	299.006i	−0.628691	−	1.51780i	0.212558	−	0.977148i	$-0.431820\pi$
$198$		0			0
$199$	−253.762	−	253.762i	−1.27519	−	1.27519i	−0.943329	−	0.331858i	$-0.892324\pi$
$199$	−253.762	−	253.762i	−1.27519	−	1.27519i	−0.331858	−	0.943329i	$-0.607676\pi$
$200$	−38.6440	+	171.963i	−0.193220	+	0.859817i
$201$		0			0
$202$	−18.9007	+	1.08261i	−0.0935680	+	0.00535946i
$203$	−133.051	−	321.214i	−0.655424	−	1.58233i
$204$		0			0
$205$	−30.6882	+	74.0879i	−0.149699	+	0.361404i
$206$	66.4529	−	32.0935i	0.322587	−	0.155794i
$207$		0			0
$208$	79.1111	+	13.0783i	0.380342	+	0.0628764i
$209$			9.27787i			0.0443917i
$210$		0			0
$211$	102.533	+	42.4705i	0.485938	+	0.201282i	0.612182	−	0.790717i	$-0.290292\pi$
$211$	102.533	+	42.4705i	0.485938	+	0.201282i	−0.126244	+	0.991999i	$0.540292\pi$
$212$	145.915	+	41.6849i	0.688280	+	0.196627i
$213$		0			0
$214$	−167.881	+	9.61603i	−0.784491	+	0.0449347i
$215$	57.1364	−	57.1364i	0.265751	−	0.265751i
$216$		0			0
$217$	240.171	−	240.171i	1.10678	−	1.10678i
$218$	140.640	+	125.401i	0.645136	+	0.575235i
$219$		0			0
$220$	70.9351	−	8.15291i	0.322432	−	0.0370587i
$221$	70.9063	+	29.3704i	0.320843	+	0.132898i
$222$		0			0
$223$			187.153i			0.839252i	0.907697	+	0.419626i	$0.137839\pi$
$223$			187.153i			0.839252i	−0.907697	+	0.419626i	$0.862161\pi$
$224$	271.264	+	336.286i	1.21100	+	1.50128i
$225$		0			0
$226$	11.9437	+	4.16433i	0.0528484	+	0.0184263i
$227$	2.72348	−	6.57507i	0.0119977	−	0.0289650i	−0.917767	−	0.397119i	$-0.870010\pi$
$227$	2.72348	−	6.57507i	0.0119977	−	0.0289650i	0.929765	+	0.368154i	$0.120010\pi$
$228$		0			0
$229$	−124.655	−	300.944i	−0.544345	−	1.31416i	−0.921631	−	0.388068i	$-0.873143\pi$
$229$	−124.655	−	300.944i	−0.544345	−	1.31416i	0.377286	−	0.926097i	$-0.376857\pi$
$230$	41.9116	−	47.0047i	0.182225	−	0.204368i
$231$		0			0
$232$	202.978	−	35.1872i	0.874905	−	0.151669i
$233$	208.047	+	208.047i	0.892904	+	0.892904i	0.994796	−	0.101891i	$-0.0324894\pi$
$233$	208.047	+	208.047i	0.892904	+	0.892904i	−0.101891	+	0.994796i	$0.532489\pi$
$234$		0			0
$235$	−13.2611	−	32.0151i	−0.0564301	−	0.136234i
$236$	−252.573	−	72.1547i	−1.07023	−	0.305740i
$237$		0			0
$238$	179.844	+	372.386i	0.755647	+	1.56465i
$239$	277.832			1.16248			0.581239	−	0.813733i	$-0.302568\pi$
$239$	277.832			1.16248			0.581239	+	0.813733i	$0.302568\pi$
$240$		0			0
$241$			63.2696i			0.262529i	0.991347	+	0.131265i	$0.0419038\pi$
$241$			63.2696i			0.262529i	−0.991347	+	0.131265i	$0.958096\pi$
$242$	−11.8805	−	24.5997i	−0.0490928	−	0.101652i
$243$		0			0
$244$	58.8402	+	105.904i	0.241148	+	0.434033i
$245$	−212.180	+	87.8879i	−0.866041	+	0.358726i
$246$		0			0
$247$	3.17339	−	3.17339i	0.0128477	−	0.0128477i
$248$	107.641	+	170.043i	0.434038	+	0.685659i
$249$		0			0
$250$	107.856	−	120.962i	0.431424	−	0.483850i
$251$	−161.948	+	67.0812i	−0.645212	+	0.267256i	−0.681201	−	0.732097i	$-0.738542\pi$
$251$	−161.948	+	67.0812i	−0.645212	+	0.267256i	0.0359886	+	0.999352i	$0.488542\pi$
$252$		0			0
$253$	174.935	+	72.4605i	0.691443	+	0.286405i
$254$	65.3451	+	22.7834i	0.257264	+	0.0896983i
$255$		0			0
$256$	−229.647	+	113.130i	−0.897058	+	0.441913i
$257$	82.9690			0.322836			0.161418	−	0.986886i	$-0.448393\pi$
$257$	82.9690			0.322836			0.161418	+	0.986886i	$0.448393\pi$
$258$		0			0
$259$	−183.840	+	443.830i	−0.709809	+	1.71363i
$260$	−27.0511	−	21.4739i	−0.104043	−	0.0825919i
$261$		0			0
$262$	−265.274	−	236.531i	−1.01250	−	0.902791i
$263$	148.394	+	148.394i	0.564235	+	0.564235i	0.930508	−	0.366272i	$-0.119366\pi$
$263$	148.394	+	148.394i	0.564235	+	0.564235i	−0.366272	+	0.930508i	$0.619366\pi$
$264$		0			0
$265$	−46.2200	−	46.2200i	−0.174415	−	0.174415i
$266$	24.1421	−	1.38283i	0.0907597	−	0.00519861i
$267$		0			0
$268$	−10.3624	+	5.75736i	−0.0386658	+	0.0214827i
$269$	−78.7117	+	190.027i	−0.292609	+	0.706420i	−1.00000		0.000402393i	$-0.999872\pi$
$269$	−78.7117	+	190.027i	−0.292609	+	0.706420i	0.707391	+	0.706822i	$0.249872\pi$
$270$		0			0
$271$	−29.7996			−0.109962			−0.0549809	−	0.998487i	$-0.517510\pi$
$271$	−29.7996			−0.109962			−0.0549809	+	0.998487i	$0.517510\pi$
$272$	−238.640	+	55.5903i	−0.877352	+	0.204376i
$273$		0			0
$274$	−182.298	+	88.0408i	−0.665320	+	0.321317i
$275$	210.883	+	87.3507i	0.766848	+	0.317639i
$276$		0			0
$277$	−368.831	+	152.775i	−1.33152	+	0.551534i	−0.931089	−	0.364793i	$-0.881140\pi$
$277$	−368.831	+	152.775i	−1.33152	+	0.551534i	−0.400431	+	0.916327i	$0.631140\pi$
$278$	−392.327	+	22.4721i	−1.41125	+	0.0808347i
$279$		0			0
$280$	−31.7874	−	183.366i	−0.113526	−	0.654878i
$281$	280.258	−	280.258i	0.997358	−	0.997358i	−0.00263807	−	0.999997i	$-0.500840\pi$
$281$	280.258	−	280.258i	0.997358	−	0.997358i	0.999997	+	0.00263807i	$0.000839724\pi$
$282$		0			0
$283$	−176.650	+	73.1708i	−0.624204	+	0.258554i	−0.672288	−	0.740289i	$-0.734688\pi$
$283$	−176.650	+	73.1708i	−0.624204	+	0.258554i	0.0480840	+	0.998843i	$0.484688\pi$
$284$	−29.4631	−	256.346i	−0.103743	−	0.902628i
$285$		0			0
$286$	34.1883	−	98.0556i	0.119540	−	0.342852i
$287$			628.425i			2.18963i
$288$		0			0
$289$	54.4719			0.188484
$290$	−83.7866	−	29.2132i	−0.288919	−	0.100735i
$291$		0			0
$292$	18.8432	+	163.946i	0.0645313	+	0.561461i
$293$	−11.3590	−	27.4231i	−0.0387679	−	0.0935940i	0.903310	−	0.428989i	$-0.141130\pi$
$293$	−11.3590	−	27.4231i	−0.0387679	−	0.0935940i	−0.942078	+	0.335395i	$0.891130\pi$
$294$		0			0
$295$	80.0049	+	80.0049i	0.271203	+	0.271203i
$296$	−232.695	−	163.937i	−0.786130	−	0.553840i
$297$		0			0
$298$	26.2052	+	457.502i	0.0879368	+	1.53524i
$299$	−35.0503	−	84.6188i	−0.117225	−	0.283006i
$300$		0			0
$301$	242.320	−	585.012i	0.805049	−	1.94356i
$302$	−13.0164	−	26.9518i	−0.0431007	−	0.0892444i
$303$		0			0
$304$	−2.33693	+	14.1362i	−0.00768726	+	0.0465005i
$305$		−	52.1843i		−	0.171096i
$306$		0			0
$307$	463.833	+	192.126i	1.51086	+	0.625817i	0.975734	−	0.218957i	$-0.0702655\pi$
$307$	463.833	+	192.126i	1.51086	+	0.625817i	0.535122	+	0.844775i	$0.320266\pi$
$308$	489.118	−	271.754i	1.58805	−	0.882317i
$309$		0			0
$310$	−4.95709	−	86.5431i	−0.0159906	−	0.279171i
$311$	−230.516	+	230.516i	−0.741210	+	0.741210i	−0.972811	−	0.231601i	$-0.925604\pi$
$311$	−230.516	+	230.516i	−0.741210	+	0.741210i	0.231601	+	0.972811i	$0.425604\pi$
$312$		0			0
$313$	2.89884	−	2.89884i	0.00926146	−	0.00926146i	−0.702461	−	0.711722i	$-0.747915\pi$
$313$	2.89884	−	2.89884i	0.00926146	−	0.00926146i	0.711722	+	0.702461i	$0.247915\pi$
$314$	38.8469	−	43.5676i	0.123716	−	0.138750i
$315$		0			0
$316$	−10.2753	−	8.15685i	−0.0325169	−	0.0258128i
$317$	−510.087	−	211.285i	−1.60911	−	0.666514i	−0.616441	−	0.787401i	$-0.711426\pi$
$317$	−510.087	−	211.285i	−1.60911	−	0.666514i	−0.992666	+	0.120887i	$0.961426\pi$
$318$		0			0
$319$		−	266.791i		−	0.836335i
$320$	110.133	+	5.44514i	0.344166	+	0.0170161i
$321$		0			0
$322$	162.477	−	466.001i	0.504587	−	1.44721i
$323$	−5.24811	+	12.6701i	−0.0162480	+	0.0392262i
$324$		0			0
$325$	−42.2528	−	102.007i	−0.130009	−	0.313869i
$326$	−435.887	−	388.658i	−1.33708	−	1.19220i
$327$		0			0
$328$	−363.292	−	81.6397i	−1.10760	−	0.248902i
$329$	−192.020	−	192.020i	−0.583647	−	0.583647i
$330$		0			0
$331$	−95.3030	−	230.082i	−0.287924	−	0.695111i	0.712051	−	0.702128i	$-0.247766\pi$
$331$	−95.3030	−	230.082i	−0.287924	−	0.695111i	−0.999975	+	0.00701670i	$0.997766\pi$
$332$	119.401	+	214.906i	0.359643	+	0.647306i
$333$		0			0
$334$	26.4027	−	12.7512i	0.0790499	−	0.0381772i
$335$	5.10609			0.0152421
$336$		0			0
$337$			203.997i			0.605334i	0.953096	+	0.302667i	$0.0978769\pi$
$337$			203.997i			0.605334i	−0.953096	+	0.302667i	$0.902123\pi$
$338$	259.131	−	125.148i	0.766660	−	0.370259i
$339$		0			0
$340$	101.482	+	28.9913i	0.298477	+	0.0852684i
$341$	240.793	−	99.7396i	0.706137	−	0.292491i
$342$		0			0
$343$	−804.800	+	804.800i	−2.34636	+	2.34636i
$344$	306.714	+	216.085i	0.891612	+	0.628153i
$345$		0			0
$346$	−345.813	−	308.344i	−0.999459	−	0.891167i
$347$	120.709	−	49.9993i	0.347865	−	0.144090i	−0.201908	−	0.979404i	$-0.564714\pi$
$347$	120.709	−	49.9993i	0.347865	−	0.144090i	0.549773	+	0.835314i	$0.314714\pi$
$348$		0			0
$349$	279.116	+	115.614i	0.799759	+	0.331271i	0.744860	−	0.667221i	$-0.232516\pi$
$349$	279.116	+	115.614i	0.799759	+	0.331271i	0.0548993	+	0.998492i	$0.482516\pi$
$350$	195.865	−	561.761i	0.559614	−	1.60503i
$351$		0			0
$352$	93.5583	+	318.063i	0.265791	+	0.903587i
$353$	−608.156			−1.72282			−0.861410	−	0.507910i	$-0.830418\pi$
$353$	−608.156			−1.72282			−0.861410	+	0.507910i	$0.830418\pi$
$354$		0			0
$355$	−42.5329	+	102.683i	−0.119811	+	0.289249i
$356$	−250.117	+	28.7471i	−0.702575	+	0.0807503i
$357$		0			0
$358$	−3.72148	+	4.17371i	−0.0103952	+	0.0116584i
$359$	−196.029	−	196.029i	−0.546041	−	0.546041i	0.379252	−	0.925293i	$-0.376181\pi$
$359$	−196.029	−	196.029i	−0.546041	−	0.546041i	−0.925293	+	0.379252i	$0.876181\pi$
$360$		0			0
$361$	−254.699	−	254.699i	−0.705536	−	0.705536i
$362$	22.8268	+	398.521i	0.0630574	+	1.10089i
$363$		0			0
$364$	−260.247	−	74.3470i	−0.714965	−	0.204250i
$365$	27.2019	−	65.6713i	0.0745259	−	0.179921i
$366$		0			0
$367$	−33.0375			−0.0900203			−0.0450102	−	0.998987i	$-0.514332\pi$
$367$	−33.0375			−0.0900203			−0.0450102	+	0.998987i	$0.514332\pi$
$368$	248.287	+	154.467i	0.674693	+	0.419747i
$369$		0			0
$370$	53.3198	+	110.404i	0.144108	+	0.298390i
$371$	−473.241	−	196.023i	−1.27558	−	0.528363i
$372$		0			0
$373$	115.583	−	47.8760i	0.309874	−	0.128354i	−0.222327	−	0.974972i	$-0.571365\pi$
$373$	115.583	−	47.8760i	0.309874	−	0.128354i	0.532201	+	0.846618i	$0.321365\pi$
$374$	18.1465	+	316.810i	0.0485200	+	0.847085i
$375$		0			0
$376$	135.952	−	86.0608i	0.361574	−	0.228885i
$377$	−91.2527	+	91.2527i	−0.242050	+	0.242050i
$378$		0			0
$379$	164.874	−	68.2930i	0.435024	−	0.180193i	−0.154415	−	0.988006i	$-0.549349\pi$
$379$	164.874	−	68.2930i	0.435024	−	0.180193i	0.589438	+	0.807813i	$0.299349\pi$
$380$	3.83712	−	4.83369i	0.0100977	−	0.0127202i
$381$		0			0
$382$	−350.830	−	122.321i	−0.918403	−	0.320213i
$383$			307.309i			0.802373i	0.915996	+	0.401186i	$0.131402\pi$
$383$			307.309i			0.802373i	−0.915996	+	0.401186i	$0.868598\pi$
$384$		0			0
$385$	−241.013			−0.626008
$386$	136.994	−	392.912i	0.354906	−	1.01791i
$387$		0			0
$388$	333.393	+	264.656i	0.859261	+	0.682104i
$389$	204.874	+	494.611i	0.526669	+	1.27149i	0.933693	+	0.358075i	$0.116567\pi$
$389$	204.874	+	494.611i	0.526669	+	1.27149i	−0.407024	+	0.913418i	$0.633433\pi$
$390$		0			0
$391$	197.907	+	197.907i	0.506157	+	0.506157i
$392$	−570.368	−	901.022i	−1.45502	−	2.29853i
$393$		0			0
$394$	−646.224	+	37.0149i	−1.64016	+	0.0939465i
$395$	2.16252	+	5.22078i	0.00547473	+	0.0132172i
$396$		0			0
$397$	−224.796	+	542.706i	−0.566237	+	1.36702i	0.338467	+	0.940978i	$0.390092\pi$
$397$	−224.796	+	542.706i	−0.566237	+	1.36702i	−0.904705	+	0.426040i	$0.859908\pi$
$398$	−646.321	+	312.141i	−1.62392	+	0.784274i
$399$		0			0
$400$	299.308	+	186.209i	0.748271	+	0.465522i
$401$			125.790i			0.313691i	0.987623	+	0.156846i	$0.0501325\pi$
$401$			125.790i			0.313691i	−0.987623	+	0.156846i	$0.949868\pi$
$402$		0			0
$403$	−116.475	−	48.2456i	−0.289020	−	0.119716i
$404$	−10.4007	+	36.4069i	−0.0257442	+	0.0901162i
$405$		0			0
$406$	−694.220	+	39.7641i	−1.70990	+	0.0979412i
$407$	−260.663	+	260.663i	−0.640449	+	0.640449i
$408$		0			0
$409$	492.952	−	492.952i	1.20526	−	1.20526i	0.232717	−	0.972544i	$-0.425238\pi$
$409$	492.952	−	492.952i	1.20526	−	1.20526i	0.972544	−	0.232717i	$-0.0747617\pi$
$410$	119.708	+	106.738i	0.291972	+	0.260336i
$411$		0			0
$412$	−16.8527	−	146.628i	−0.0409046	−	0.355894i
$413$	819.159	+	339.307i	1.98344	+	0.821567i
$414$		0			0
$415$		−	105.895i		−	0.255168i
$416$	76.7891	−	140.790i	0.184589	−	0.338438i
$417$		0			0
$418$	17.5213	+	6.10902i	0.0419170	+	0.0146149i
$419$	−203.456	+	491.187i	−0.485576	+	1.17228i	0.471349	+	0.881947i	$0.343767\pi$
$419$	−203.456	+	491.187i	−0.485576	+	1.17228i	−0.956925	+	0.290336i	$0.906233\pi$
$420$		0			0
$421$	−0.995616	−	2.40363i	−0.00236488	−	0.00570934i	0.922693	−	0.385536i	$-0.125984\pi$
$421$	−0.995616	−	2.40363i	−0.00236488	−	0.00570934i	−0.925058	+	0.379827i	$0.875984\pi$
$422$	147.718	−	165.669i	0.350044	−	0.392580i
$423$		0			0
$424$	174.800	−	248.114i	0.412264	−	0.585175i
$425$	238.576	+	238.576i	0.561355	+	0.561355i
$426$		0			0
$427$	−156.495	−	377.813i	−0.366499	−	0.884807i
$428$	−92.3814	+	323.376i	−0.215844	+	0.755551i
$429$		0			0
$430$	−70.2808	−	145.524i	−0.163444	−	0.338427i
$431$	−404.244			−0.937920			−0.468960	−	0.883219i	$-0.655371\pi$
$431$	−404.244			−0.937920			−0.468960	+	0.883219i	$0.655371\pi$
$432$		0			0
$433$			446.431i			1.03102i	0.856884	+	0.515509i	$0.172397\pi$
$433$			446.431i			1.03102i	−0.856884	+	0.515509i	$0.827603\pi$
$434$	−295.423	−	611.704i	−0.680698	−	1.40946i
$435$		0			0
$436$	329.425	−	183.028i	0.755561	−	0.419789i
$437$	15.1203	−	6.26304i	0.0346003	−	0.0143319i
$438$		0			0
$439$	−203.077	+	203.077i	−0.462590	+	0.462590i	−0.899503	−	0.436914i	$-0.856072\pi$
$439$	−203.077	+	203.077i	−0.462590	+	0.462590i	0.436914	+	0.899503i	$0.356072\pi$
$440$	31.3104	−	139.329i	0.0711600	−	0.316658i
$441$		0			0
$442$	102.154	−	114.568i	0.231118	−	0.259203i
$443$	440.203	−	182.338i	0.993685	−	0.411598i	0.174207	−	0.984709i	$-0.444264\pi$
$443$	440.203	−	182.338i	0.993685	−	0.411598i	0.819478	+	0.573111i	$0.194264\pi$
$444$		0			0
$445$	100.188	+	41.4993i	0.225142	+	0.0932568i
$446$	353.439	+	123.231i	0.792465	+	0.276303i
$447$		0			0
$448$	813.691	−	290.855i	1.81627	−	0.649230i
$449$	636.256			1.41705			0.708526	−	0.705685i	$-0.249361\pi$
$449$	636.256			1.41705			0.708526	+	0.705685i	$0.249361\pi$
$450$		0			0
$451$	−184.538	+	445.514i	−0.409175	+	0.987836i
$452$	15.7287	−	19.8138i	0.0347980	−	0.0438358i
$453$		0			0
$454$	−10.6238	−	9.47266i	−0.0234003	−	0.0208649i
$455$	82.4357	+	82.4357i	0.181177	+	0.181177i
$456$		0			0
$457$	−359.285	−	359.285i	−0.786181	−	0.786181i	0.194685	−	0.980866i	$-0.437632\pi$
$457$	−359.285	−	359.285i	−0.786181	−	0.786181i	−0.980866	+	0.194685i	$0.937632\pi$
$458$	−650.412	+	37.2549i	−1.42011	+	0.0813425i
$459$		0			0
$460$	−61.1717	−	110.100i	−0.132982	−	0.239349i
$461$	−68.2156	+	164.687i	−0.147973	+	0.357239i	−0.980435	−	0.196844i	$-0.936931\pi$
$461$	−68.2156	+	164.687i	−0.147973	+	0.357239i	0.832462	+	0.554083i	$0.186931\pi$
$462$		0			0
$463$	662.155			1.43014			0.715070	−	0.699053i	$-0.246395\pi$
$463$	662.155			1.43014			0.715070	+	0.699053i	$0.246395\pi$
$464$	67.1997	−	406.494i	0.144827	−	0.876064i
$465$		0			0
$466$	529.885	−	255.908i	1.13709	−	0.549160i
$467$	854.762	+	354.054i	1.83033	+	0.758146i	0.967607	+	0.252461i	$0.0812399\pi$
$467$	854.762	+	354.054i	1.83033	+	0.758146i	0.862718	+	0.505685i	$0.168760\pi$
$468$		0			0
$469$	36.9680	−	15.3126i	0.0788229	−	0.0326495i
$470$	−69.1923	+	3.96326i	−0.147218	+	0.00843246i
$471$		0			0
$472$	−302.571	+	429.475i	−0.641041	+	0.909905i
$473$	343.579	−	343.579i	0.726383	−	0.726383i
$474$		0			0
$475$	18.2274	−	7.55005i	0.0383735	−	0.0158948i
$476$	821.670	−	94.4385i	1.72620	−	0.198400i
$477$		0			0
$478$	182.939	−	524.687i	0.382717	−	1.09767i
$479$		−	926.802i		−	1.93487i	−0.253122	−	0.967434i	$-0.581458\pi$
$479$		−	926.802i		−	1.93487i	0.253122	−	0.967434i	$-0.418542\pi$
$480$		0			0
$481$	178.313			0.370714
$482$	119.485	+	41.6599i	0.247894	+	0.0864312i
$483$		0			0
$484$	−54.2794	+	6.23859i	−0.112147	+	0.0128896i
$485$	−70.1649	−	169.393i	−0.144670	−	0.349264i
$486$		0			0
$487$	586.001	+	586.001i	1.20329	+	1.20329i	0.973161	+	0.230127i	$0.0739141\pi$
$487$	586.001	+	586.001i	1.20329	+	1.20329i	0.230127	+	0.973161i	$0.426086\pi$
$488$	238.744	−	41.3874i	0.489229	−	0.0848102i
$489$		0			0
$490$	26.2665	+	458.572i	0.0536051	+	0.935862i
$491$	17.1543	+	41.4142i	0.0349375	+	0.0843466i	0.940385	−	0.340111i	$-0.110465\pi$
$491$	17.1543	+	41.4142i	0.0349375	+	0.0843466i	−0.905448	+	0.424458i	$0.860465\pi$
$492$		0			0
$493$	150.913	−	364.335i	0.306111	−	0.739017i
$494$	−3.90344	−	8.08247i	−0.00790169	−	0.0163613i
$495$		0			0
$496$	392.004	−	91.3161i	0.790331	−	0.184105i
$497$			870.977i			1.75247i
$498$		0			0
$499$	−143.291	−	59.3531i	−0.287156	−	0.118944i	0.234456	−	0.972127i	$-0.424669\pi$
$499$	−143.291	−	59.3531i	−0.287156	−	0.118944i	−0.521612	+	0.853183i	$0.674669\pi$
$500$	−157.420	−	283.334i	−0.314840	−	0.566668i
$501$		0			0
$502$	20.0481	+	350.009i	0.0399365	+	0.697230i
$503$	−74.0929	+	74.0929i	−0.147302	+	0.147302i	−0.776912	−	0.629610i	$-0.783215\pi$
$503$	−74.0929	+	74.0929i	−0.147302	+	0.147302i	0.629610	+	0.776912i	$0.283215\pi$
$504$		0			0
$505$	11.5322	−	11.5322i	0.0228361	−	0.0228361i
$506$	252.028	−	282.654i	0.498079	−	0.558605i
$507$		0			0
$508$	86.0529	−	108.403i	0.169396	−	0.213391i
$509$	−467.540	−	193.661i	−0.918546	−	0.380474i	−0.127224	−	0.991874i	$-0.540607\pi$
$509$	−467.540	−	193.661i	−0.918546	−	0.380474i	−0.791322	+	0.611400i	$0.790607\pi$
$510$		0			0
$511$		−	557.034i		−	1.09009i
$512$	62.4351	+	508.179i	0.121944	+	0.992537i
$513$		0			0
$514$	54.6309	−	156.687i	0.106286	−	0.304839i
$515$	−24.3285	+	58.7343i	−0.0472399	+	0.114047i
$516$		0			0
$517$	−79.7431	−	192.517i	−0.154242	−	0.372373i
$518$	717.125	+	639.423i	1.38441	+	1.23441i
$519$		0			0
$520$	−58.3653	+	36.9466i	−0.112241	+	0.0710512i
$521$	−694.307	−	694.307i	−1.33264	−	1.33264i	−0.902998	−	0.429644i	$-0.858639\pi$
$521$	−694.307	−	694.307i	−1.33264	−	1.33264i	−0.429644	−	0.902998i	$-0.641361\pi$
$522$		0			0
$523$	67.4311	+	162.793i	0.128931	+	0.311268i	0.975142	−	0.221581i	$-0.0711216\pi$
$523$	67.4311	+	162.793i	0.128931	+	0.311268i	−0.846211	+	0.532848i	$0.821122\pi$
$524$	−621.360	+	345.227i	−1.18580	+	0.658830i
$525$		0			0
$526$	377.952	−	182.532i	0.718540	−	0.347020i
$527$	385.250			0.731025
$528$		0			0
$529$			194.991i			0.368602i
$530$	−117.720	+	56.8531i	−0.222114	+	0.107270i
$531$		0			0
$532$	13.2849	−	46.5029i	0.0249716	−	0.0874115i
$533$	215.502	−	89.2638i	0.404319	−	0.167474i
$534$		0			0
$535$	102.432	−	102.432i	0.191462	−	0.191462i
$536$	4.04964	+	23.3604i	0.00755530	+	0.0435829i
$537$		0			0
$538$	307.039	+	273.771i	0.570704	+	0.508867i
$539$	−1275.91	+	528.498i	−2.36717	+	0.980515i
$540$		0			0
$541$	125.547	+	52.0035i	0.232066	+	0.0961247i	0.495686	−	0.868502i	$-0.334917\pi$
$541$	125.547	+	52.0035i	0.232066	+	0.0961247i	−0.263620	+	0.964626i	$0.584917\pi$
$542$	−19.6216	+	56.2767i	−0.0362022	+	0.103832i
$543$		0			0
$544$	−52.1498	+	487.275i	−0.0958636	+	0.895727i
$545$	−162.324			−0.297842
$546$		0			0
$547$	−278.945	+	673.432i	−0.509954	+	1.23114i	0.433956	+	0.900934i	$0.357117\pi$
$547$	−278.945	+	673.432i	−0.509954	+	1.23114i	−0.943910	+	0.330204i	$0.892883\pi$
$548$	46.2314	+	402.240i	0.0843638	+	0.734015i
$549$		0			0
$550$	303.818	−	340.737i	0.552396	−	0.619523i
$551$	−16.3057	−	16.3057i	−0.0295929	−	0.0295929i
$552$		0			0
$553$	31.3132	+	31.3132i	0.0566241	+	0.0566241i
$554$	45.6589	+	797.133i	0.0824167	+	1.43887i
$555$		0			0
$556$	−215.889	+	755.708i	−0.388290	+	1.35919i
$557$	228.207	−	550.942i	0.409708	−	0.989123i	−0.575506	−	0.817797i	$-0.695195\pi$
$557$	228.207	−	550.942i	0.409708	−	0.989123i	0.985214	−	0.171326i	$-0.0548051\pi$
$558$		0			0
$559$	−235.035			−0.420455
$560$	−367.218	−	60.7068i	−0.655746	−	0.108405i
$561$		0			0
$562$	−344.732	−	713.803i	−0.613402	−	1.27011i
$563$	236.899	+	98.1268i	0.420780	+	0.174293i	0.583019	−	0.812459i	$-0.301871\pi$
$563$	236.899	+	98.1268i	0.420780	+	0.174293i	−0.162239	+	0.986752i	$0.551871\pi$
$564$		0			0
$565$	−10.0671	+	4.16995i	−0.0178180	+	0.00738044i
$566$	21.8681	+	381.783i	0.0386362	+	0.674528i
$567$		0			0
$568$	−503.511	−	113.150i	−0.886463	−	0.199208i
$569$	289.568	−	289.568i	0.508907	−	0.508907i	−0.405284	−	0.914191i	$-0.632827\pi$
$569$	289.568	−	289.568i	0.508907	−	0.508907i	0.914191	+	0.405284i	$0.132827\pi$
$570$		0			0
$571$	801.877	−	332.148i	1.40434	−	0.581695i	0.453464	−	0.891275i	$-0.350188\pi$
$571$	801.877	−	332.148i	1.40434	−	0.581695i	0.950874	+	0.309579i	$0.100188\pi$
$572$	−162.667	−	129.129i	−0.284383	−	0.225751i
$573$		0			0
$574$	1186.78	+	413.786i	2.06756	+	0.720882i
$575$		−	402.646i		−	0.700254i
$576$		0			0
$577$	−107.872			−0.186953			−0.0934767	−	0.995621i	$-0.529798\pi$
$577$	−107.872			−0.186953			−0.0934767	+	0.995621i	$0.529798\pi$
$578$	35.8670	−	102.870i	0.0620537	−	0.177976i
$579$		0			0
$580$	−110.339	+	138.996i	−0.190239	+	0.239648i
$581$	−317.567	−	766.676i	−0.546588	−	1.31958i
$582$		0			0
$583$	−277.936	−	277.936i	−0.476734	−	0.476734i
$584$	322.021	+	72.3652i	0.551405	+	0.123913i
$585$		0			0
$586$	−59.2679	+	3.39479i	−0.101140	+	0.00579316i
$587$	292.393	+	705.899i	0.498114	+	1.20255i	0.950498	+	0.310730i	$0.100574\pi$
$587$	292.393	+	705.899i	0.498114	+	1.20255i	−0.452384	+	0.891823i	$0.649426\pi$
$588$		0			0
$589$	8.62087	−	20.8126i	0.0146365	−	0.0353355i
$590$	203.769	−	98.4102i	0.345371	−	0.166797i
$591$		0			0
$592$	−462.813	+	331.500i	−0.781778	+	0.559967i
$593$		−	247.178i		−	0.416826i	−0.978041	−	0.208413i	$-0.933170\pi$
$593$		−	247.178i		−	0.416826i	0.978041	−	0.208413i	$-0.0668298\pi$
$594$		0			0
$595$	−329.133	−	136.331i	−0.553164	−	0.229128i
$596$	881.248	+	251.753i	1.47860	+	0.422405i
$597$		0			0
$598$	−182.882	+	10.4753i	−0.305822	+	0.0175171i
$599$	633.115	−	633.115i	1.05695	−	1.05695i	0.0586768	−	0.998277i	$-0.481312\pi$
$599$	633.115	−	633.115i	1.05695	−	1.05695i	0.998277	−	0.0586768i	$-0.0186881\pi$
$600$		0			0
$601$	−147.019	+	147.019i	−0.244624	+	0.244624i	−0.818760	−	0.574136i	$-0.805338\pi$
$601$	−147.019	+	147.019i	−0.244624	+	0.244624i	0.574136	+	0.818760i	$0.305338\pi$
$602$	−945.241	−	842.823i	−1.57017	−	1.40004i
$603$		0			0
$604$	−59.4692	+	6.83508i	−0.0984590	+	0.0113164i
$605$	21.7424	+	9.00601i	0.0359379	+	0.0148860i
$606$		0			0
$607$		−	52.6594i		−	0.0867536i	−0.999059	−	0.0433768i	$-0.986188\pi$
$607$		−	52.6594i		−	0.0867536i	0.999059	−	0.0433768i	$-0.0138116\pi$
$608$	25.1574	+	13.7212i	0.0413773	+	0.0225678i
$609$		0			0
$610$	−98.5501	−	34.3607i	−0.161558	−	0.0563291i
$611$	−38.5729	+	93.1233i	−0.0631308	+	0.152411i
$612$		0			0
$613$	−336.988	−	813.562i	−0.549737	−	1.32718i	−0.917675	−	0.397331i	$-0.869936\pi$
$613$	−336.988	−	813.562i	−0.549737	−	1.32718i	0.367939	−	0.929850i	$-0.380064\pi$
$614$	668.241	−	749.445i	1.08834	−	1.22059i
$615$		0			0
$616$	−191.148	−	1102.64i	−0.310305	−	1.79000i
$617$	150.269	+	150.269i	0.243547	+	0.243547i	0.818316	−	0.574769i	$-0.194908\pi$
$617$	150.269	+	150.269i	0.243547	+	0.243547i	−0.574769	+	0.818316i	$0.694908\pi$
$618$		0			0
$619$	4.34083	+	10.4797i	0.00701265	+	0.0169300i	0.927347	−	0.374202i	$-0.122083\pi$
$619$	4.34083	+	10.4797i	0.00701265	+	0.0169300i	−0.920334	+	0.391132i	$0.872083\pi$
$620$	−166.701	−	47.6228i	−0.268872	−	0.0768110i
$621$		0			0
$622$	283.547	+	587.114i	0.455864	+	0.943914i
$623$	849.811			1.36406
$624$		0			0
$625$		−	411.175i		−	0.657880i
$626$	−3.56572	−	7.38320i	−0.00569604	−	0.0117942i
$627$		0			0
$628$	−56.6987	−	102.050i	−0.0902845	−	0.162499i
$629$	−503.413	+	208.520i	−0.800338	+	0.331511i
$630$		0			0
$631$	356.485	−	356.485i	0.564952	−	0.564952i	−0.365758	−	0.930710i	$-0.619190\pi$
$631$	356.485	−	356.485i	0.564952	−	0.564952i	0.930710	+	0.365758i	$0.119190\pi$
$632$	−22.1700	+	14.0341i	−0.0350792	+	0.0222059i
$633$		0			0
$634$	−734.879	+	824.180i	−1.15912	+	1.29997i
$635$	−55.0781	+	22.8141i	−0.0867371	+	0.0359277i
$636$		0			0
$637$	617.175	+	255.642i	0.968878	+	0.401322i
$638$	−503.835	−	175.669i	−0.789711	−	0.275343i
$639$		0			0
$640$	82.8004	−	204.401i	0.129376	−	0.319377i
$641$	−741.748			−1.15717			−0.578587	−	0.815621i	$-0.696396\pi$
$641$	−741.748			−1.15717			−0.578587	+	0.815621i	$0.696396\pi$
$642$		0			0
$643$	181.837	−	438.994i	0.282795	−	0.682729i	−0.717103	−	0.696967i	$-0.754532\pi$
$643$	181.837	−	438.994i	0.282795	−	0.682729i	0.999899	+	0.0142385i	$0.00453240\pi$
$644$	−773.061	−	613.677i	−1.20041	−	0.952915i
$645$		0			0
$646$	20.4718	+	18.2537i	0.0316901	+	0.0282565i
$647$	−520.304	−	520.304i	−0.804180	−	0.804180i	0.179566	−	0.983746i	$-0.442531\pi$
$647$	−520.304	−	520.304i	−0.804180	−	0.804180i	−0.983746	+	0.179566i	$0.942531\pi$
$648$		0			0
$649$	481.095	+	481.095i	0.741286	+	0.741286i
$650$	−220.463	+	12.6278i	−0.339173	+	0.0194275i
$651$		0			0
$652$	−1020.99	+	567.262i	−1.56594	+	0.870034i
$653$	−161.753	+	390.507i	−0.247708	+	0.598019i	−0.998009	−	0.0630771i	$-0.979909\pi$
$653$	−161.753	+	390.507i	−0.247708	+	0.598019i	0.750301	+	0.661096i	$0.229909\pi$
$654$		0			0
$655$	306.175			0.467443
$656$	−393.386	+	632.322i	−0.599674	+	0.963905i
$657$		0			0
$658$	−489.065	+	236.194i	−0.743260	+	0.358958i
$659$	−70.1853	−	29.0717i	−0.106503	−	0.0441149i	0.328796	−	0.944401i	$-0.393357\pi$
$659$	−70.1853	−	29.0717i	−0.106503	−	0.0441149i	−0.435299	+	0.900286i	$0.643357\pi$
$660$		0			0
$661$	−81.1193	+	33.6007i	−0.122722	+	0.0508331i	−0.443199	−	0.896423i	$-0.646157\pi$
$661$	−81.1193	+	33.6007i	−0.122722	+	0.0508331i	0.320477	+	0.947256i	$0.396157\pi$
$662$	−497.262	+	28.4826i	−0.751152	+	0.0430251i
$663$		0			0
$664$	484.470	−	83.9852i	0.729623	−	0.126484i
$665$	−14.7302	+	14.7302i	−0.0221507	+	0.0221507i
$666$		0			0
$667$	−434.794	+	180.097i	−0.651865	+	0.270011i
$668$	−6.69582	−	58.2575i	−0.0100237	−	0.0872119i
$669$		0			0
$670$	3.36210	−	9.64286i	0.00501807	−	0.0143923i
$671$		−	313.801i		−	0.467661i
$672$		0			0
$673$	−851.239			−1.26484			−0.632421	−	0.774625i	$-0.717939\pi$
$673$	−851.239			−1.26484			−0.632421	+	0.774625i	$0.717939\pi$
$674$	385.250	+	134.322i	0.571587	+	0.199291i
$675$		0			0
$676$	−65.7166	−	571.773i	−0.0972139	−	0.845818i
$677$	380.410	+	918.390i	0.561905	+	1.35656i	0.908241	+	0.418448i	$0.137426\pi$
$677$	380.410	+	918.390i	0.561905	+	1.35656i	−0.346335	+	0.938111i	$0.612574\pi$
$678$		0			0
$679$	−1015.98	−	1015.98i	−1.49629	−	1.49629i
$680$	121.571	−	172.560i	0.178781	−	0.253765i
$681$		0			0
$682$	−29.8086	−	520.411i	−0.0437076	−	0.763066i
$683$	−425.467	−	1027.17i	−0.622939	−	1.50391i	−0.848236	−	0.529618i	$-0.822335\pi$
$683$	−425.467	−	1027.17i	−0.622939	−	1.50391i	0.225297	−	0.974290i	$-0.427665\pi$
$684$		0			0
$685$	66.7395	−	161.123i	0.0974299	−	0.235217i
$686$	989.946	+	2049.79i	1.44307	+	2.98803i
$687$		0			0
$688$	610.033	−	436.950i	0.886675	−	0.635102i
$689$			190.129i			0.275950i
$690$		0			0
$691$	260.940	+	108.085i	0.377627	+	0.156418i	0.563420	−	0.826171i	$-0.309485\pi$
$691$	260.940	+	108.085i	0.377627	+	0.156418i	−0.185793	+	0.982589i	$0.559485\pi$
$692$	−810.008	+	450.040i	−1.17053	+	0.650347i
$693$		0			0
$694$	−14.9430	−	260.881i	−0.0215317	−	0.375910i
$695$	239.377	−	239.377i	0.344428	−	0.344428i
$696$		0			0
$697$	−504.018	+	504.018i	−0.723124	+	0.723124i
$698$	402.121	−	450.986i	0.576104	−	0.646111i
$699$		0			0
$700$	−931.920	−	739.783i	−1.33131	−	1.05683i
$701$	727.192	+	301.213i	1.03736	+	0.429690i	0.835365	−	0.549695i	$-0.185256\pi$
$701$	727.192	+	301.213i	1.03736	+	0.429690i	0.201999	+	0.979386i	$0.435256\pi$
$702$		0			0
$703$			31.8623i			0.0453234i
$704$	662.266	+	32.7433i	0.940718	+	0.0465104i
$705$		0			0
$706$	−400.440	+	1148.50i	−0.567196	+	1.62678i
$707$	48.9091	−	118.077i	0.0691783	−	0.167011i
$708$		0			0
$709$	259.577	+	626.675i	0.366118	+	0.883886i	0.994379	+	0.105883i	$0.0337670\pi$
$709$	259.577	+	626.675i	0.366118	+	0.883886i	−0.628261	+	0.778003i	$0.716233\pi$
$710$	165.912	+	147.935i	0.233679	+	0.208360i
$711$		0			0
$712$	−110.400	+	491.275i	−0.155057	+	0.689992i
$713$	−325.095	−	325.095i	−0.455953	−	0.455953i
$714$		0			0
$715$	34.2344	+	82.6491i	0.0478803	+	0.115593i
$716$	5.43165	+	9.77621i	0.00758611	+	0.0136539i
$717$		0			0
$718$	−499.276	+	241.126i	−0.695370	+	0.335830i
$719$	−1034.71			−1.43910			−0.719549	−	0.694442i	$-0.755651\pi$
$719$	−1034.71			−1.43910			−0.719549	+	0.694442i	$0.755651\pi$
$720$		0			0
$721$			498.193i			0.690975i
$722$	−648.705	+	313.293i	−0.898484	+	0.433923i
$723$		0			0
$724$	767.638	+	219.297i	1.06027	+	0.302897i
$725$	−524.141	+	217.106i	−0.722953	+	0.299457i
$726$		0			0
$727$	227.066	−	227.066i	0.312332	−	0.312332i	−0.533480	−	0.845813i	$-0.679116\pi$
$727$	227.066	−	227.066i	0.312332	−	0.312332i	0.845813	+	0.533480i	$0.179116\pi$
$728$	−311.765	+	442.524i	−0.428248	+	0.607863i
$729$		0			0
$730$	−106.109	−	94.6122i	−0.145355	−	0.129606i
$731$	663.548	−	274.850i	0.907726	−	0.375992i
$732$		0			0
$733$	973.386	+	403.190i	1.32795	+	0.550054i	0.930070	−	0.367384i	$-0.119746\pi$
$733$	973.386	+	403.190i	1.32795	+	0.550054i	0.397879	+	0.917438i	$0.369746\pi$
$734$	−21.7535	+	62.3913i	−0.0296369	+	0.0850018i
$735$		0			0
$736$	455.196	−	367.182i	0.618472	−	0.498889i
$737$	30.7045			0.0416615
$738$		0			0
$739$	387.131	−	934.616i	0.523857	−	1.26470i	−0.411632	−	0.911350i	$-0.635041\pi$
$739$	387.131	−	934.616i	0.523857	−	1.26470i	0.935490	−	0.353354i	$-0.114959\pi$
$740$	243.607	−	27.9989i	0.329199	−	0.0378364i
$741$		0			0
$742$	−681.795	+	764.645i	−0.918861	+	1.03052i
$743$	−528.819	−	528.819i	−0.711735	−	0.711735i	0.255163	−	0.966898i	$-0.417871\pi$
$743$	−528.819	−	528.819i	−0.711735	−	0.711735i	−0.966898	+	0.255163i	$0.917871\pi$
$744$		0			0
$745$	−279.143	−	279.143i	−0.374689	−	0.374689i
$746$	−14.3084	−	249.803i	−0.0191802	−	0.334856i
$747$		0			0
$748$	610.245	+	174.334i	0.815835	+	0.233066i
$749$	434.423	−	1048.79i	0.580004	−	1.40025i
$750$		0			0
$751$	−176.760			−0.235366			−0.117683	−	0.993051i	$-0.537547\pi$
$751$	−176.760			−0.235366			−0.117683	+	0.993051i	$0.537547\pi$
$752$	−73.0084	−	313.412i	−0.0970856	−	0.416772i
$753$		0			0
$754$	112.246	+	232.416i	0.148867	+	0.308245i
$755$	23.8213	+	9.86711i	0.0315514	+	0.0130690i
$756$		0			0
$757$	−59.8575	+	24.7938i	−0.0790720	+	0.0327527i	−0.421869	−	0.906657i	$-0.638626\pi$
$757$	−59.8575	+	24.7938i	−0.0790720	+	0.0327527i	0.342797	+	0.939410i	$0.388626\pi$
$758$	−20.4103	−	356.333i	−0.0269265	−	0.470096i
$759$		0			0
$760$	−6.60189	−	10.4292i	−0.00868670	−	0.0137226i
$761$	−713.497	+	713.497i	−0.937579	+	0.937579i	−0.998163	−	0.0605844i	$-0.980704\pi$
$761$	−713.497	+	713.497i	−0.937579	+	0.937579i	0.0605844	+	0.998163i	$0.480704\pi$
$762$		0			0
$763$	−1175.22	+	486.793i	−1.54026	+	0.637999i
$764$	−462.008	+	582.001i	−0.604722	+	0.761781i
$765$		0			0
$766$	580.354	+	202.348i	0.757642	+	0.264161i
$767$		−	329.106i		−	0.429082i
$768$		0			0
$769$	−147.511			−0.191821			−0.0959107	−	0.995390i	$-0.530576\pi$
$769$	−147.511			−0.191821			−0.0959107	+	0.995390i	$0.530576\pi$
$770$	−158.695	+	455.154i	−0.206098	+	0.591109i
$771$		0			0
$772$	−651.811	−	517.426i	−0.844315	−	0.670240i
$773$	−104.027	−	251.144i	−0.134576	−	0.324896i	0.842198	−	0.539169i	$-0.181262\pi$
$773$	−104.027	−	251.144i	−0.134576	−	0.324896i	−0.976774	+	0.214273i	$0.931262\pi$
$774$		0			0
$775$	−391.899	−	391.899i	−0.505677	−	0.505677i
$776$	719.327	−	455.351i	0.926968	−	0.586792i
$777$		0			0
$778$	1068.97	−	61.2295i	1.37400	−	0.0787012i
$779$	15.9503	+	38.5075i	0.0204754	+	0.0494319i
$780$		0			0
$781$	−255.764	+	617.468i	−0.327482	+	0.790612i
$782$	504.061	−	243.436i	0.644579	−	0.311300i
$783$		0			0
$784$	−2077.14	+	483.863i	−2.64942	+	0.617173i
$785$			50.2850i			0.0640573i
$786$		0			0
$787$	999.730	+	414.102i	1.27031	+	0.526178i	0.913057	−	0.407832i	$-0.133715\pi$
$787$	999.730	+	414.102i	1.27031	+	0.526178i	0.357248	+	0.934010i	$0.383715\pi$
$788$	−355.603	+	1244.77i	−0.451273	+	1.57965i
$789$		0			0
$790$	11.2834	−	0.646298i	0.0142827	−	0.000818099i
$791$	−60.3806	+	60.3806i	−0.0763345	+	0.0763345i
$792$		0			0
$793$	−107.332	+	107.332i	−0.135349	+	0.135349i
$794$	876.885	+	781.873i	1.10439	+	0.984727i
$795$		0			0
$796$	163.909	+	1426.11i	0.205916	+	1.79159i
$797$	1138.14	+	471.431i	1.42802	+	0.591507i	0.956863	−	0.290540i	$-0.0938348\pi$
$797$	1138.14	+	471.431i	1.42802	+	0.591507i	0.471162	+	0.882047i	$0.343835\pi$
$798$		0			0
$799$		−	308.012i		−	0.385497i
$800$	548.735	−	442.635i	0.685919	−	0.553294i
$801$		0			0
$802$	237.555	+	82.8265i	0.296203	+	0.103275i
$803$	163.574	−	394.902i	0.203703	−	0.491784i
$804$		0			0
$805$	162.696	+	392.783i	0.202107	+	0.487929i
$806$	−167.805	+	188.196i	−0.208195	+	0.233494i
$807$		0			0
$808$	61.9063	+	43.6138i	0.0766167	+	0.0539775i
$809$	169.569	+	169.569i	0.209603	+	0.209603i	0.804099	−	0.594496i	$-0.202648\pi$
$809$	169.569	+	169.569i	0.209603	+	0.209603i	−0.594496	+	0.804099i	$0.702648\pi$
$810$		0			0
$811$	−437.562	−	1056.37i	−0.539534	−	1.30255i	−0.925048	−	0.379849i	$-0.875976\pi$
$811$	−437.562	−	1056.37i	−0.539534	−	1.30255i	0.385514	−	0.922702i	$-0.374024\pi$
$812$	−382.015	+	1337.22i	−0.470461	+	1.64682i
$813$		0			0
$814$	320.629	+	663.896i	0.393893	+	0.815597i
$815$	503.094			0.617293
$816$		0			0
$817$		−	41.9977i		−	0.0514048i
$818$	−606.357	−	1255.53i	−0.741268	−	1.53487i
$819$		0			0
$820$	280.397	−	155.788i	0.341947	−	0.189986i
$821$	930.724	−	385.518i	1.13365	−	0.469572i	0.264627	−	0.964351i	$-0.414751\pi$
$821$	930.724	−	385.518i	1.13365	−	0.469572i	0.869019	+	0.494779i	$0.164751\pi$
$822$		0			0
$823$	−320.389	+	320.389i	−0.389294	+	0.389294i	−0.874435	−	0.485142i	$-0.838768\pi$
$823$	−320.389	+	320.389i	−0.389294	+	0.389294i	0.485142	+	0.874435i	$0.338768\pi$
$824$	−288.005	−	64.7211i	−0.349520	−	0.0785451i
$825$		0			0
$826$	1180.16	−	1323.57i	1.42876	−	1.60238i
$827$	−14.6406	+	6.06433i	−0.0177032	+	0.00733293i	−0.391517	−	0.920171i	$-0.628050\pi$
$827$	−14.6406	+	6.06433i	−0.0177032	+	0.00733293i	0.373814	+	0.927504i	$0.378050\pi$
$828$		0			0
$829$	−753.878	−	312.267i	−0.909383	−	0.376679i	−0.121562	−	0.992584i	$-0.538790\pi$
$829$	−753.878	−	312.267i	−0.909383	−	0.376679i	−0.787820	+	0.615905i	$0.788790\pi$
$830$	−199.983	−	69.7264i	−0.240943	−	0.0840078i
$831$		0			0
$832$	−215.321	−	237.720i	−0.258799	−	0.285721i
$833$	−2041.35			−2.45061
$834$		0			0
$835$	−9.66607	+	23.3360i	−0.0115761	+	0.0279473i
$836$	23.0738	−	29.0665i	0.0276002	−	0.0347686i
$837$		0			0
$838$	793.642	+	707.649i	0.947066	+	0.844450i
$839$	233.705	+	233.705i	0.278552	+	0.278552i	0.832531	−	0.553979i	$-0.186891\pi$
$839$	233.705	+	233.705i	0.278552	+	0.278552i	−0.553979	+	0.832531i	$0.686891\pi$
$840$		0			0
$841$	−125.796	−	125.796i	−0.149579	−	0.149579i
$842$	−5.19483	+	0.297554i	−0.00616963	+	0.000353389i
$843$		0			0
$844$	−215.601	−	388.052i	−0.255451	−	0.459777i
$845$	−94.8684	+	229.033i	−0.112270	+	0.271044i
$846$		0			0
$847$	184.423			0.217736
$848$	−353.467	−	493.481i	−0.416825	−	0.581935i
$849$		0			0
$850$	607.642	−	293.461i	0.714872	−	0.345248i
$851$	600.767	+	248.846i	0.705954	+	0.292416i
$852$		0			0
$853$	−979.574	+	405.753i	−1.14839	+	0.475677i	−0.873992	−	0.485940i	$-0.838477\pi$
$853$	−979.574	+	405.753i	−1.14839	+	0.475677i	−0.274395	+	0.961617i	$0.588477\pi$
$854$	−816.545	+	46.7707i	−0.956141	+	0.0547667i
$855$		0			0
$856$	549.867	+	387.389i	0.642368	+	0.452558i
$857$	−716.322	+	716.322i	−0.835848	+	0.835848i	−0.988309	−	0.152461i	$-0.951280\pi$
$857$	−716.322	+	716.322i	−0.835848	+	0.835848i	0.152461	+	0.988309i	$0.451280\pi$
$858$		0			0
$859$	398.325	−	164.992i	0.463708	−	0.192074i	−0.138583	−	0.990351i	$-0.544255\pi$
$859$	398.325	−	164.992i	0.463708	−	0.192074i	0.602291	+	0.798277i	$0.294255\pi$
$860$	−321.098	+	36.9054i	−0.373370	+	0.0429132i
$861$		0			0
$862$	−266.174	+	763.415i	−0.308787	+	0.885633i
$863$			1279.79i			1.48295i	0.670980	+	0.741475i	$0.265874\pi$
$863$			1279.79i			1.48295i	−0.670980	+	0.741475i	$0.734126\pi$
$864$		0			0
$865$	399.132			0.461424
$866$	843.086	+	293.952i	0.973541	+	0.339437i
$867$		0			0
$868$	−1349.73	+	155.130i	−1.55498	+	0.178722i
$869$	13.0039	+	31.3942i	0.0149642	+	0.0361268i
$870$		0			0
$871$	−10.5021	−	10.5021i	−0.0120576	−	0.0120576i
$872$	−128.739	−	742.634i	−0.147637	−	0.851645i
$873$		0			0
$874$	−1.87180	−	32.6786i	−0.00214164	−	0.0373898i
$875$	418.684	+	1010.79i	0.478496	+	1.15519i
$876$		0			0
$877$	−351.648	+	848.954i	−0.400967	+	0.968021i	0.586464	+	0.809975i	$0.300519\pi$
$877$	−351.648	+	848.954i	−0.400967	+	0.968021i	−0.987432	+	0.158046i	$0.949481\pi$
$878$	249.795	+	517.227i	0.284505	+	0.589097i
$879$		0			0
$880$	−242.508	−	150.871i	−0.275577	−	0.171445i
$881$		−	1327.06i		−	1.50632i	−0.657839	−	0.753158i	$-0.728529\pi$
$881$		−	1327.06i		−	1.50632i	0.657839	−	0.753158i	$-0.271471\pi$
$882$		0			0
$883$	412.717	+	170.953i	0.467403	+	0.193605i	0.603939	−	0.797030i	$-0.293597\pi$
$883$	412.717	+	170.953i	0.467403	+	0.193605i	−0.136536	+	0.990635i	$0.543597\pi$
$884$	−149.098	−	268.356i	−0.168663	−	0.303570i
$885$		0			0
$886$	−54.4942	−	951.384i	−0.0615058	−	1.07380i
$887$	411.723	−	411.723i	0.464174	−	0.464174i	−0.435847	−	0.900021i	$-0.643551\pi$
$887$	411.723	−	411.723i	0.464174	−	0.464174i	0.900021	+	0.435847i	$0.143551\pi$
$888$		0			0
$889$	−330.347	+	330.347i	−0.371594	+	0.371594i
$890$	144.340	−	161.880i	0.162180	−	0.181888i
$891$		0			0
$892$	465.444	−	586.329i	0.521798	−	0.657320i
$893$	−16.6400	−	6.89250i	−0.0186338	−	0.00771836i
$894$		0			0
$895$		−	4.81723i		−	0.00538238i
$896$	−13.5062	−	1728.17i	−0.0150739	−	1.92876i
$897$		0			0
$898$	418.943	−	1201.57i	0.466529	−	1.33805i
$899$	−247.898	+	598.480i	−0.275749	+	0.665717i
$900$		0			0
$901$	−222.338	−	536.772i	−0.246768	−	0.595751i
$902$	719.845	+	641.849i	0.798055	+	0.711584i
$903$		0			0
$904$	−27.0618	−	42.7501i	−0.0299356	−	0.0472899i
$905$	−243.156	−	243.156i	−0.268681	−	0.268681i
$906$		0			0
$907$	307.189	+	741.619i	0.338687	+	0.817662i	0.997842	+	0.0656553i	$0.0209138\pi$
$907$	307.189	+	741.619i	0.338687	+	0.817662i	−0.659156	+	0.752006i	$0.729086\pi$
$908$	−24.8843	+	13.8257i	−0.0274057	+	0.0152266i
$909$		0			0
$910$	209.960	−	101.400i	0.230725	−	0.111429i
$911$	−708.126			−0.777307			−0.388653	−	0.921384i	$-0.627060\pi$
$911$	−708.126			−0.777307			−0.388653	+	0.921384i	$0.627060\pi$
$912$		0			0
$913$		−	636.779i		−	0.697458i
$914$	−915.082	+	441.939i	−1.00118	+	0.483522i
$915$		0			0
$916$	−357.908	+	1252.84i	−0.390729	+	1.36772i
$917$	2216.70	−	918.187i	2.41734	−	1.00129i
$918$		0			0
$919$	628.260	−	628.260i	0.683635	−	0.683635i	−0.277183	−	0.960817i	$-0.589401\pi$
$919$	628.260	−	628.260i	0.683635	−	0.683635i	0.960817	+	0.277183i	$0.0894007\pi$
$920$	−248.204	+	43.0273i	−0.269787	+	0.0467688i
$921$		0			0
$922$	266.095	+	237.264i	0.288607	+	0.257336i
$923$	298.679	−	123.717i	0.323596	−	0.134038i
$924$		0			0
$925$	724.221	+	299.982i	0.782941	+	0.324305i
$926$	435.996	−	1250.48i	0.470838	−	1.35041i
$927$		0			0
$928$	−723.417	−	394.563i	−0.779544	−	0.425175i
$929$	972.033			1.04632			0.523161	−	0.852234i	$-0.324753\pi$
$929$	972.033			1.04632			0.523161	+	0.852234i	$0.324753\pi$
$930$		0			0
$931$	−45.6801	+	110.281i	−0.0490656	+	0.118455i
$932$	−134.381	−	1169.19i	−0.144186	−	1.25450i
$933$		0			0
$934$	1231.45	−	1381.09i	1.31847	−	1.47869i
$935$	−193.301	−	193.301i	−0.206739	−	0.206739i
$936$		0			0
$937$	396.897	+	396.897i	0.423583	+	0.423583i	0.886435	−	0.462853i	$-0.153174\pi$
$937$	396.897	+	396.897i	0.423583	+	0.423583i	−0.462853	+	0.886435i	$0.653174\pi$
$938$	−4.57639	−	79.8967i	−0.00487888	−	0.0851777i
$939$		0			0
$940$	−38.0751	+	133.280i	−0.0405054	+	0.141787i
$941$	−486.386	+	1174.24i	−0.516882	+	1.24786i	0.422928	+	0.906163i	$0.361002\pi$
$941$	−486.386	+	1174.24i	−0.516882	+	1.24786i	−0.939809	+	0.341699i	$0.888998\pi$
$942$		0			0
$943$	850.634			0.902051
$944$	611.837	+	854.195i	0.648132	+	0.904867i
$945$		0			0
$946$	−422.621	−	875.080i	−0.446745	−	0.925032i
$947$	319.348	+	132.278i	0.337221	+	0.139681i	0.544867	−	0.838523i	$-0.316580\pi$
$947$	319.348	+	132.278i	0.337221	+	0.139681i	−0.207646	+	0.978204i	$0.566580\pi$
$948$		0			0
$949$	−191.020	+	79.1232i	−0.201286	+	0.0833753i
$950$	−2.25644	−	39.3939i	−0.00237520	−	0.0414673i
$951$		0			0
$952$	362.682	−	1613.91i	0.380968	−	1.69528i
$953$	−234.445	+	234.445i	−0.246007	+	0.246007i	−0.819330	−	0.573322i	$-0.805654\pi$
$953$	−234.445	+	234.445i	−0.246007	+	0.246007i	0.573322	+	0.819330i	$0.305654\pi$
$954$		0			0
$955$	295.708	−	122.486i	0.309642	−	0.128258i
$956$	−870.417	−	690.961i	−0.910478	−	0.722762i
$957$		0			0
$958$	−1750.27	−	610.253i	−1.82700	−	0.637007i
$959$		−	1366.67i		−	1.42510i
$960$		0			0
$961$	328.164			0.341482
$962$	117.410	−	336.745i	0.122048	−	0.350047i
$963$		0			0
$964$	157.350	−	198.216i	0.163226	−	0.205619i
$965$	137.178	+	331.178i	0.142154	+	0.343189i
$966$		0			0
$967$	431.918	+	431.918i	0.446658	+	0.446658i	0.894242	−	0.447584i	$-0.147715\pi$
$967$	431.918	+	431.918i	0.446658	+	0.446658i	−0.447584	+	0.894242i	$0.647715\pi$
$968$	−23.9587	+	106.615i	−0.0247507	+	0.110139i
$969$		0			0
$970$	−366.099	+	20.9697i	−0.377422	+	0.0216183i
$971$	391.385	+	944.887i	0.403074	+	0.973107i	0.986915	+	0.161239i	$0.0515490\pi$
$971$	391.385	+	944.887i	0.403074	+	0.973107i	−0.583841	+	0.811868i	$0.698451\pi$
$972$		0			0
$973$	1015.22	−	2450.95i	1.04339	−	2.51897i
$974$	1492.52	−	720.812i	1.53236	−	0.740054i
$975$		0			0
$976$	79.0406	−	478.119i	0.0809842	−	0.489877i
$977$			1157.98i			1.18524i	0.805481	+	0.592621i	$0.201907\pi$
$977$			1157.98i			1.18524i	−0.805481	+	0.592621i	$0.798093\pi$
$978$		0			0
$979$	602.463	+	249.548i	0.615386	+	0.254901i
$980$	883.311	+	252.343i	0.901337	+	0.257493i
$981$		0			0
$982$	89.5061	−	5.12681i	0.0911467	−	0.00522078i
$983$	−396.529	+	396.529i	−0.403386	+	0.403386i	−0.879425	−	0.476038i	$-0.842072\pi$
$983$	−396.529	+	396.529i	−0.403386	+	0.403386i	0.476038	+	0.879425i	$0.342072\pi$
$984$		0			0
$985$	394.291	−	394.291i	0.400296	−	0.400296i
$986$	−588.680	−	524.896i	−0.597039	−	0.532349i
$987$		0			0
$988$	−17.8340	+	2.04975i	−0.0180506	+	0.00207464i
$989$	−791.870	−	328.003i	−0.800678	−	0.331652i
$990$		0			0
$991$		−	134.269i		−	0.135489i	−0.997703	−	0.0677444i	$-0.978420\pi$
$991$		−	134.269i		−	0.135489i	0.997703	−	0.0677444i	$-0.0215802\pi$
$992$	85.6645	−	800.428i	0.0863553	−	0.806883i
$993$		0			0
$994$	1644.84	+	573.495i	1.65477	+	0.576957i
$995$	236.619	−	571.249i	0.237808	−	0.574120i
$996$		0			0
$997$	470.645	+	1136.24i	0.472061	+	1.13966i	0.963251	+	0.268603i	$0.0865620\pi$
$997$	470.645	+	1136.24i	0.472061	+	1.13966i	−0.491190	+	0.871052i	$0.663438\pi$
$998$	−206.439	+	231.525i	−0.206852	+	0.231989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.163.4		28
3.2	odd	2		32.3.h.a.3.4	✓	28
12.11	even	2		128.3.h.a.47.6		28
24.5	odd	2		256.3.h.b.95.6		28
24.11	even	2		256.3.h.a.95.2		28
32.11	odd	8	inner	288.3.u.a.235.4		28
96.5	odd	8		256.3.h.a.159.2		28
96.11	even	8		32.3.h.a.11.4	yes	28
96.53	odd	8		128.3.h.a.79.6		28
96.59	even	8		256.3.h.b.159.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.4	✓	28	3.2	odd	2
32.3.h.a.11.4	yes	28	96.11	even	8
128.3.h.a.47.6		28	12.11	even	2
128.3.h.a.79.6		28	96.53	odd	8
256.3.h.a.95.2		28	24.11	even	2
256.3.h.a.159.2		28	96.5	odd	8
256.3.h.b.95.6		28	24.5	odd	2
256.3.h.b.159.6		28	96.59	even	8
288.3.u.a.163.4		28	1.1	even	1	trivial
288.3.u.a.235.4		28	32.11	odd	8	inner

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658450 - 1.88850i) q^{2} +(-3.13289 - 2.48697i) q^{4} +(0.659338 + 1.59178i) q^{5} +(9.54718 + 9.54718i) q^{7} +(-6.75950 + 4.27892i) q^{8} +O(q^{10})\)	\(q+(0.658450 - 1.88850i) q^{2} +(-3.13289 - 2.48697i) q^{4} +(0.659338 + 1.59178i) q^{5} +(9.54718 + 9.54718i) q^{7} +(-6.75950 + 4.27892i) q^{8} +(3.44023 - 0.197052i) q^{10} +(3.96481 + 9.57189i) q^{11} +(1.91784 - 4.63007i) q^{13} +(24.3162 - 11.7435i) q^{14} +(3.62996 + 15.5828i) q^{16} +15.3143i q^{17} +(0.827335 + 0.342693i) q^{19} +(1.89308 - 6.62663i) q^{20} +(20.6872 - 1.18494i) q^{22} +(12.9230 - 12.9230i) q^{23} +(15.5786 - 15.5786i) q^{25} +(-7.48110 - 6.67051i) q^{26} +(-6.16668 - 53.6538i) q^{28} +(-23.7905 - 9.85436i) q^{29} -25.1562i q^{31} +(31.8183 + 3.40530i) q^{32} +(28.9211 + 10.0837i) q^{34} +(-8.90221 + 21.4918i) q^{35} +(13.6161 + 32.8721i) q^{37} +(1.19194 - 1.33678i) q^{38} +(-11.2679 - 7.93840i) q^{40} +(32.9116 + 32.9116i) q^{41} +(-17.9473 - 43.3286i) q^{43} +(11.3837 - 39.8480i) q^{44} +(-15.8960 - 32.9143i) q^{46} -20.1127 q^{47} +133.297i q^{49} +(-19.1625 - 39.6780i) q^{50} +(-17.5232 + 9.73588i) q^{52} +(-35.0503 + 14.5183i) q^{53} +(-12.6222 + 12.6222i) q^{55} +(-105.386 - 23.6825i) q^{56} +(-34.2749 + 38.4399i) q^{58} +(60.6706 - 25.1306i) q^{59} +(-27.9825 - 11.5907i) q^{61} +(-47.5076 - 16.5641i) q^{62} +(27.3817 - 57.8467i) q^{64} +8.63457 q^{65} +(1.13412 - 2.73801i) q^{67} +(38.0862 - 47.9780i) q^{68} +(34.7257 + 30.9632i) q^{70} +(45.6144 + 45.6144i) q^{71} +(-29.1727 - 29.1727i) q^{73} +(71.0445 - 4.06934i) q^{74} +(-1.73968 - 3.13118i) q^{76} +(-53.5318 + 129.237i) q^{77} +3.27983 q^{79} +(-22.4110 + 16.0524i) q^{80} +(83.8242 - 40.4830i) q^{82} +(-56.7834 - 23.5205i) q^{83} +(-24.3770 + 10.0973i) q^{85} +(-93.6436 + 5.36380i) q^{86} +(-67.7575 - 47.7361i) q^{88} +(44.5059 - 44.5059i) q^{89} +(62.5140 - 25.8942i) q^{91} +(-72.6256 + 8.34720i) q^{92} +(-13.2432 + 37.9829i) q^{94} +1.54289i q^{95} -106.417 q^{97} +(251.732 + 87.7695i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

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