LMFDB - Embedded newform 288.3.u.a.235.4

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			235.4
Character	$\chi$	$=$	288.235
Dual form			288.3.u.a.163.4

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$

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	−0.844130	−	0.536139i	$-0.819882\pi$
$5$	0.659338	−	1.59178i	0.131868	−	0.318356i	0.975997	+	0.217782i	$0.0698823\pi$
$6$		0			0
$7$	9.54718	−	9.54718i	1.36388	−	1.36388i	0.494975	−	0.868907i	$-0.335177\pi$
$7$	9.54718	−	9.54718i	1.36388	−	1.36388i	0.868907	−	0.494975i	$-0.164823\pi$
$8$	−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	−0.634799	−	0.772677i	$-0.718917\pi$
$11$	3.96481	−	9.57189i	0.360437	−	0.870172i	0.995236	−	0.0974947i	$-0.0310829\pi$
$12$		0			0
$13$	1.91784	+	4.63007i	0.147526	+	0.356159i	0.980317	−	0.197428i	$-0.0632587\pi$
$13$	1.91784	+	4.63007i	0.147526	+	0.356159i	−0.832792	+	0.553587i	$0.813259\pi$
$14$	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	$-0.851274\pi$
$17$		−	15.3143i		−	0.900842i	0.892816	−	0.450421i	$-0.148726\pi$
$18$		0			0
$19$	0.827335	−	0.342693i	0.0435439	−	0.0180365i	−0.360805	−	0.932641i	$-0.617498\pi$
$19$	0.827335	−	0.342693i	0.0435439	−	0.0180365i	0.404349	+	0.914605i	$0.367498\pi$
$20$	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	0.929839	−	0.367968i	$-0.119946\pi$
$23$	12.9230	+	12.9230i	0.561871	+	0.561871i	−0.367968	+	0.929839i	$0.619946\pi$
$24$		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	−0.753080	−	0.657929i	$-0.771433\pi$
$29$	−23.7905	+	9.85436i	−0.820363	+	0.339805i	−0.0672825	+	0.997734i	$0.521433\pi$
$30$		0			0
$31$			25.1562i			0.811491i	0.913986	+	0.405746i	$0.132988\pi$
$31$			25.1562i			0.811491i	−0.913986	+	0.405746i	$0.867012\pi$
$32$	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	−0.626076	−	0.779762i	$-0.715340\pi$
$37$	13.6161	−	32.8721i	0.368001	−	0.888434i	0.994078	−	0.108672i	$-0.0346599\pi$
$38$	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	−0.180799	−	0.983520i	$-0.557868\pi$
$41$	32.9116	−	32.9116i	0.802721	−	0.802721i	0.983520	+	0.180799i	$0.0578684\pi$
$42$		0			0
$43$	−17.9473	+	43.3286i	−0.417379	+	1.00764i	0.565725	+	0.824594i	$0.308596\pi$
$43$	−17.9473	+	43.3286i	−0.417379	+	1.00764i	−0.983104	+	0.183048i	$0.941404\pi$
$44$	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	0.0266698	−	0.999644i	$-0.491510\pi$
$53$	−35.0503	−	14.5183i	−0.661327	−	0.273931i	−0.687997	+	0.725714i	$0.741510\pi$
$54$		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	0.832104	−	0.554619i	$-0.187136\pi$
$59$	60.6706	+	25.1306i	1.02832	+	0.425942i	0.196212	+	0.980562i	$0.437136\pi$
$60$		0			0
$61$	−27.9825	+	11.5907i	−0.458730	+	0.190012i	−0.600067	−	0.799949i	$-0.704860\pi$
$61$	−27.9825	+	11.5907i	−0.458730	+	0.190012i	0.141338	+	0.989961i	$0.454860\pi$
$62$	−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	0.932117	−	0.362157i	$-0.117960\pi$
$67$	1.13412	+	2.73801i	0.0169272	+	0.0408659i	−0.915190	+	0.403023i	$0.867960\pi$
$68$	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	−0.308702	−	0.951159i	$-0.599895\pi$
$71$	45.6144	−	45.6144i	0.642456	−	0.642456i	0.951159	+	0.308702i	$0.0998947\pi$
$72$		0			0
$73$	−29.1727	+	29.1727i	−0.399626	+	0.399626i	−0.878101	−	0.478475i	$-0.841190\pi$
$73$	−29.1727	+	29.1727i	−0.399626	+	0.399626i	0.478475	+	0.878101i	$0.341190\pi$
$74$	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	−0.697555	−	0.716531i	$-0.745729\pi$
$83$	−56.7834	+	23.5205i	−0.684138	+	0.283379i	0.0134176	+	0.999910i	$0.495729\pi$
$84$		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	0.911458	−	0.411392i	$-0.134957\pi$
$89$	44.5059	+	44.5059i	0.500066	+	0.500066i	−0.411392	+	0.911458i	$0.634957\pi$
$90$		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	−0.940797	−	0.338969i	$-0.889922\pi$
$101$	−3.62243	+	8.74531i	−0.0358656	+	0.0865872i	0.904932	+	0.425557i	$0.139922\pi$
$102$		0			0
$103$	26.0911	−	26.0911i	0.253312	−	0.253312i	−0.569015	−	0.822327i	$-0.692675\pi$
$103$	26.0911	−	26.0911i	0.253312	−	0.253312i	0.822327	+	0.569015i	$0.192675\pi$
$104$	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	0.699235	+	0.714892i	$0.253524\pi$
$107$	−32.1753	+	77.6781i	−0.300704	+	0.725963i	−0.999939	+	0.0110713i	$0.996476\pi$
$108$		0			0
$109$	−36.0541	−	87.0422i	−0.330771	−	0.798553i	−0.998531	−	0.0541760i	$-0.982747\pi$
$109$	−36.0541	−	87.0422i	−0.330771	−	0.798553i	0.667760	−	0.744377i	$-0.267253\pi$
$110$	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	$-0.991091\pi$
$113$		−	6.32445i		−	0.0559686i	0.999608	−	0.0279843i	$-0.00890884\pi$
$114$		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	$-0.956503\pi$
$127$		−	34.6015i		−	0.272453i	0.990678	−	0.136226i	$-0.0434975\pi$
$128$	−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	0.938443	+	0.345434i	$0.112268\pi$
$131$	68.0051	+	164.179i	0.519123	+	1.25327i	−0.419320	+	0.907838i	$0.637732\pi$
$132$		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	−0.918309	−	0.395865i	$-0.870445\pi$
$137$	−71.5748	+	71.5748i	−0.522444	+	0.522444i	0.395865	+	0.918309i	$0.370445\pi$
$138$		0			0
$139$	−75.1916	+	181.529i	−0.540947	+	1.30596i	0.383109	+	0.923703i	$0.374853\pi$
$139$	−75.1916	+	181.529i	−0.540947	+	1.30596i	−0.924056	+	0.382258i	$0.875147\pi$
$140$	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	−0.465665	−	0.884961i	$-0.654185\pi$
$149$	−211.685	−	87.6826i	−1.42070	−	0.588474i	−0.955037	+	0.296487i	$0.904185\pi$
$150$		0			0
$151$	10.5820	+	10.5820i	0.0700794	+	0.0700794i	0.741278	−	0.671198i	$-0.234220\pi$
$151$	10.5820	+	10.5820i	0.0700794	+	0.0700794i	−0.671198	+	0.741278i	$0.734220\pi$
$152$	−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	−0.295154	−	0.955450i	$-0.595371\pi$
$157$	26.9641	−	11.1689i	0.171746	−	0.0711394i	0.466900	+	0.884310i	$0.345371\pi$
$158$	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	0.753579	+	0.657357i	$0.228326\pi$
$163$	111.743	+	269.771i	0.685540	+	1.65504i	−0.0680396	+	0.997683i	$0.521674\pi$
$164$	−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	−0.675388	−	0.737462i	$-0.736024\pi$
$167$	10.3664	−	10.3664i	0.0620741	−	0.0620741i	0.737462	+	0.675388i	$0.236024\pi$
$168$		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	0.942461	+	0.334317i	$0.108506\pi$
$173$	88.6518	+	214.024i	0.512438	+	1.23714i	−0.430022	+	0.902818i	$0.641494\pi$
$174$		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	−0.389887	−	0.920863i	$-0.627486\pi$
$179$	−2.58312	+	1.06996i	−0.0144308	+	0.00597744i	0.375456	+	0.926840i	$0.377486\pi$
$180$		0			0
$181$	−184.394	−	76.3786i	−1.01875	−	0.421981i	−0.190112	−	0.981762i	$-0.560885\pi$
$181$	−184.394	−	76.3786i	−1.01875	−	0.421981i	−0.828640	+	0.559781i	$0.810885\pi$
$182$	−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	$0.161658\pi$
$191$			185.771i			0.972625i	−0.873785	+	0.486313i	$0.838342\pi$
$192$		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	0.212558	+	0.977148i	$0.431820\pi$
$197$	−123.852	+	299.006i	−0.628691	+	1.51780i	−0.841250	+	0.540647i	$0.818180\pi$
$198$		0			0
$199$	−253.762	+	253.762i	−1.27519	+	1.27519i	−0.331858	+	0.943329i	$0.607676\pi$
$199$	−253.762	+	253.762i	−1.27519	+	1.27519i	−0.943329	+	0.331858i	$0.892324\pi$
$200$	−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	−0.126244	−	0.991999i	$-0.540292\pi$
$211$	102.533	−	42.4705i	0.485938	−	0.201282i	0.612182	+	0.790717i	$0.290292\pi$
$212$	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	$-0.862161\pi$
$223$		−	187.153i		−	0.839252i	0.907697	−	0.419626i	$-0.137839\pi$
$224$	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	0.929765	−	0.368154i	$-0.120010\pi$
$227$	2.72348	+	6.57507i	0.0119977	+	0.0289650i	−0.917767	+	0.397119i	$0.870010\pi$
$228$		0			0
$229$	−124.655	+	300.944i	−0.544345	+	1.31416i	0.377286	+	0.926097i	$0.376857\pi$
$229$	−124.655	+	300.944i	−0.544345	+	1.31416i	−0.921631	+	0.388068i	$0.873143\pi$
$230$	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	−0.101891	−	0.994796i	$-0.532489\pi$
$233$	208.047	−	208.047i	0.892904	−	0.892904i	0.994796	+	0.101891i	$0.0324894\pi$
$234$		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	$-0.958096\pi$
$241$		−	63.2696i		−	0.262529i	0.991347	−	0.131265i	$-0.0419038\pi$
$242$	−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	0.0359886	−	0.999352i	$-0.488542\pi$
$251$	−161.948	−	67.0812i	−0.645212	−	0.267256i	−0.681201	+	0.732097i	$0.738542\pi$
$252$		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	−0.366272	−	0.930508i	$-0.619366\pi$
$263$	148.394	−	148.394i	0.564235	−	0.564235i	0.930508	+	0.366272i	$0.119366\pi$
$264$		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	0.707391	−	0.706822i	$-0.249872\pi$
$269$	−78.7117	−	190.027i	−0.292609	−	0.706420i	−1.00000		0.000402393i	$0.999872\pi$
$270$		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	−0.400431	−	0.916327i	$-0.631140\pi$
$277$	−368.831	−	152.775i	−1.33152	−	0.551534i	−0.931089	+	0.364793i	$0.881140\pi$
$278$	−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	0.999997	−	0.00263807i	$-0.000839724\pi$
$281$	280.258	+	280.258i	0.997358	+	0.997358i	−0.00263807	+	0.999997i	$0.500840\pi$
$282$		0			0
$283$	−176.650	−	73.1708i	−0.624204	−	0.258554i	0.0480840	−	0.998843i	$-0.484688\pi$
$283$	−176.650	−	73.1708i	−0.624204	−	0.258554i	−0.672288	+	0.740289i	$0.734688\pi$
$284$	−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	−0.942078	−	0.335395i	$-0.891130\pi$
$293$	−11.3590	+	27.4231i	−0.0387679	+	0.0935940i	0.903310	+	0.428989i	$0.141130\pi$
$294$		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	0.535122	−	0.844775i	$-0.320266\pi$
$307$	463.833	−	192.126i	1.51086	−	0.625817i	0.975734	+	0.218957i	$0.0702655\pi$
$308$	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	0.231601	−	0.972811i	$-0.425604\pi$
$311$	−230.516	−	230.516i	−0.741210	−	0.741210i	−0.972811	+	0.231601i	$0.925604\pi$
$312$		0			0
$313$	2.89884	+	2.89884i	0.00926146	+	0.00926146i	0.711722	−	0.702461i	$-0.247915\pi$
$313$	2.89884	+	2.89884i	0.00926146	+	0.00926146i	−0.702461	+	0.711722i	$0.747915\pi$
$314$	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	−0.992666	−	0.120887i	$-0.961426\pi$
$317$	−510.087	+	211.285i	−1.60911	+	0.666514i	−0.616441	+	0.787401i	$0.711426\pi$
$318$		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	−0.999975	−	0.00701670i	$-0.997766\pi$
$331$	−95.3030	+	230.082i	−0.287924	+	0.695111i	0.712051	+	0.702128i	$0.247766\pi$
$332$	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	$-0.902123\pi$
$337$		−	203.997i		−	0.605334i	0.953096	−	0.302667i	$-0.0978769\pi$
$338$	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	0.549773	−	0.835314i	$-0.314714\pi$
$347$	120.709	+	49.9993i	0.347865	+	0.144090i	−0.201908	+	0.979404i	$0.564714\pi$
$348$		0			0
$349$	279.116	−	115.614i	0.799759	−	0.331271i	0.0548993	−	0.998492i	$-0.482516\pi$
$349$	279.116	−	115.614i	0.799759	−	0.331271i	0.744860	+	0.667221i	$0.232516\pi$
$350$	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	−0.925293	−	0.379252i	$-0.876181\pi$
$359$	−196.029	+	196.029i	−0.546041	+	0.546041i	0.379252	+	0.925293i	$0.376181\pi$
$360$		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	0.532201	−	0.846618i	$-0.321365\pi$
$373$	115.583	+	47.8760i	0.309874	+	0.128354i	−0.222327	+	0.974972i	$0.571365\pi$
$374$	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	0.589438	−	0.807813i	$-0.299349\pi$
$379$	164.874	+	68.2930i	0.435024	+	0.180193i	−0.154415	+	0.988006i	$0.549349\pi$
$380$	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	$-0.868598\pi$
$383$		−	307.309i		−	0.802373i	0.915996	−	0.401186i	$-0.131402\pi$
$384$		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	−0.407024	−	0.913418i	$-0.633433\pi$
$389$	204.874	−	494.611i	0.526669	−	1.27149i	0.933693	−	0.358075i	$-0.116567\pi$
$390$		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	−0.904705	−	0.426040i	$-0.859908\pi$
$397$	−224.796	−	542.706i	−0.566237	−	1.36702i	0.338467	−	0.940978i	$-0.390092\pi$
$398$	−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	$-0.949868\pi$
$401$		−	125.790i		−	0.313691i	0.987623	−	0.156846i	$-0.0501325\pi$
$402$		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	0.972544	+	0.232717i	$0.0747617\pi$
$409$	492.952	+	492.952i	1.20526	+	1.20526i	0.232717	+	0.972544i	$0.425238\pi$
$410$	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	−0.956925	−	0.290336i	$-0.906233\pi$
$419$	−203.456	−	491.187i	−0.485576	−	1.17228i	0.471349	−	0.881947i	$-0.343767\pi$
$420$		0			0
$421$	−0.995616	+	2.40363i	−0.00236488	+	0.00570934i	−0.925058	−	0.379827i	$-0.875984\pi$
$421$	−0.995616	+	2.40363i	−0.00236488	+	0.00570934i	0.922693	+	0.385536i	$0.125984\pi$
$422$	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	$-0.827603\pi$
$433$		−	446.431i		−	1.03102i	0.856884	−	0.515509i	$-0.172397\pi$
$434$	−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	0.436914	−	0.899503i	$-0.356072\pi$
$439$	−203.077	−	203.077i	−0.462590	−	0.462590i	−0.899503	+	0.436914i	$0.856072\pi$
$440$	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	0.819478	−	0.573111i	$-0.194264\pi$
$443$	440.203	+	182.338i	0.993685	+	0.411598i	0.174207	+	0.984709i	$0.444264\pi$
$444$		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	−0.980866	−	0.194685i	$-0.937632\pi$
$457$	−359.285	+	359.285i	−0.786181	+	0.786181i	0.194685	+	0.980866i	$0.437632\pi$
$458$	−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	0.832462	−	0.554083i	$-0.186931\pi$
$461$	−68.2156	−	164.687i	−0.147973	−	0.357239i	−0.980435	+	0.196844i	$0.936931\pi$
$462$		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	0.862718	−	0.505685i	$-0.168760\pi$
$467$	854.762	−	354.054i	1.83033	−	0.758146i	0.967607	−	0.252461i	$-0.0812399\pi$
$468$		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	$0.418542\pi$
$479$			926.802i			1.93487i	−0.253122	+	0.967434i	$0.581458\pi$
$480$		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	0.230127	−	0.973161i	$-0.426086\pi$
$487$	586.001	−	586.001i	1.20329	−	1.20329i	0.973161	−	0.230127i	$-0.0739141\pi$
$488$	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	−0.905448	−	0.424458i	$-0.860465\pi$
$491$	17.1543	−	41.4142i	0.0349375	−	0.0843466i	0.940385	+	0.340111i	$0.110465\pi$
$492$		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	−0.521612	−	0.853183i	$-0.674669\pi$
$499$	−143.291	+	59.3531i	−0.287156	+	0.118944i	0.234456	+	0.972127i	$0.424669\pi$
$500$	−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	0.629610	−	0.776912i	$-0.283215\pi$
$503$	−74.0929	−	74.0929i	−0.147302	−	0.147302i	−0.776912	+	0.629610i	$0.783215\pi$
$504$		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	−0.791322	−	0.611400i	$-0.790607\pi$
$509$	−467.540	+	193.661i	−0.918546	+	0.380474i	−0.127224	+	0.991874i	$0.540607\pi$
$510$		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	−0.429644	+	0.902998i	$0.641361\pi$
$521$	−694.307	+	694.307i	−1.33264	+	1.33264i	−0.902998	+	0.429644i	$0.858639\pi$
$522$		0			0
$523$	67.4311	−	162.793i	0.128931	−	0.311268i	−0.846211	−	0.532848i	$-0.821122\pi$
$523$	67.4311	−	162.793i	0.128931	−	0.311268i	0.975142	+	0.221581i	$0.0711216\pi$
$524$	−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	−0.263620	−	0.964626i	$-0.584917\pi$
$541$	125.547	−	52.0035i	0.232066	−	0.0961247i	0.495686	+	0.868502i	$0.334917\pi$
$542$	−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	−0.943910	−	0.330204i	$-0.892883\pi$
$547$	−278.945	−	673.432i	−0.509954	−	1.23114i	0.433956	−	0.900934i	$-0.357117\pi$
$548$	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	0.985214	+	0.171326i	$0.0548051\pi$
$557$	228.207	+	550.942i	0.409708	+	0.989123i	−0.575506	+	0.817797i	$0.695195\pi$
$558$		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	−0.162239	−	0.986752i	$-0.551871\pi$
$563$	236.899	−	98.1268i	0.420780	−	0.174293i	0.583019	+	0.812459i	$0.301871\pi$
$564$		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	0.914191	−	0.405284i	$-0.132827\pi$
$569$	289.568	+	289.568i	0.508907	+	0.508907i	−0.405284	+	0.914191i	$0.632827\pi$
$570$		0			0
$571$	801.877	+	332.148i	1.40434	+	0.581695i	0.950874	−	0.309579i	$-0.100188\pi$
$571$	801.877	+	332.148i	1.40434	+	0.581695i	0.453464	+	0.891275i	$0.350188\pi$
$572$	−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	−0.452384	−	0.891823i	$-0.649426\pi$
$587$	292.393	−	705.899i	0.498114	−	1.20255i	0.950498	−	0.310730i	$-0.100574\pi$
$588$		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	$0.0668298\pi$
$593$			247.178i			0.416826i	−0.978041	+	0.208413i	$0.933170\pi$
$594$		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	0.998277	+	0.0586768i	$0.0186881\pi$
$599$	633.115	+	633.115i	1.05695	+	1.05695i	0.0586768	+	0.998277i	$0.481312\pi$
$600$		0			0
$601$	−147.019	−	147.019i	−0.244624	−	0.244624i	0.574136	−	0.818760i	$-0.305338\pi$
$601$	−147.019	−	147.019i	−0.244624	−	0.244624i	−0.818760	+	0.574136i	$0.805338\pi$
$602$	−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	$0.0138116\pi$
$607$			52.6594i			0.0867536i	−0.999059	+	0.0433768i	$0.986188\pi$
$608$	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	0.367939	+	0.929850i	$0.380064\pi$
$613$	−336.988	+	813.562i	−0.549737	+	1.32718i	−0.917675	+	0.397331i	$0.869936\pi$
$614$	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	−0.574769	−	0.818316i	$-0.694908\pi$
$617$	150.269	−	150.269i	0.243547	−	0.243547i	0.818316	+	0.574769i	$0.194908\pi$
$618$		0			0
$619$	4.34083	−	10.4797i	0.00701265	−	0.0169300i	−0.920334	−	0.391132i	$-0.872083\pi$
$619$	4.34083	−	10.4797i	0.00701265	−	0.0169300i	0.927347	+	0.374202i	$0.122083\pi$
$620$	−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	0.930710	−	0.365758i	$-0.119190\pi$
$631$	356.485	+	356.485i	0.564952	+	0.564952i	−0.365758	+	0.930710i	$0.619190\pi$
$632$	−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	0.999899	−	0.0142385i	$-0.00453240\pi$
$643$	181.837	+	438.994i	0.282795	+	0.682729i	−0.717103	+	0.696967i	$0.754532\pi$
$644$	−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	−0.983746	−	0.179566i	$-0.942531\pi$
$647$	−520.304	+	520.304i	−0.804180	+	0.804180i	0.179566	+	0.983746i	$0.442531\pi$
$648$		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	0.750301	−	0.661096i	$-0.229909\pi$
$653$	−161.753	−	390.507i	−0.247708	−	0.598019i	−0.998009	+	0.0630771i	$0.979909\pi$
$654$		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	−0.435299	−	0.900286i	$-0.643357\pi$
$659$	−70.1853	+	29.0717i	−0.106503	+	0.0441149i	0.328796	+	0.944401i	$0.393357\pi$
$660$		0			0
$661$	−81.1193	−	33.6007i	−0.122722	−	0.0508331i	0.320477	−	0.947256i	$-0.396157\pi$
$661$	−81.1193	−	33.6007i	−0.122722	−	0.0508331i	−0.443199	+	0.896423i	$0.646157\pi$
$662$	−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	−0.346335	−	0.938111i	$-0.612574\pi$
$677$	380.410	−	918.390i	0.561905	−	1.35656i	0.908241	−	0.418448i	$-0.137426\pi$
$678$		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	0.225297	+	0.974290i	$0.427665\pi$
$683$	−425.467	+	1027.17i	−0.622939	+	1.50391i	−0.848236	+	0.529618i	$0.822335\pi$
$684$		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	−0.185793	−	0.982589i	$-0.559485\pi$
$691$	260.940	−	108.085i	0.377627	−	0.156418i	0.563420	+	0.826171i	$0.309485\pi$
$692$	−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	0.201999	−	0.979386i	$-0.435256\pi$
$701$	727.192	−	301.213i	1.03736	−	0.429690i	0.835365	+	0.549695i	$0.185256\pi$
$702$		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	−0.628261	−	0.778003i	$-0.716233\pi$
$709$	259.577	−	626.675i	0.366118	−	0.883886i	0.994379	−	0.105883i	$-0.0337670\pi$
$710$	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	0.845813	−	0.533480i	$-0.179116\pi$
$727$	227.066	+	227.066i	0.312332	+	0.312332i	−0.533480	+	0.845813i	$0.679116\pi$
$728$	−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	0.397879	−	0.917438i	$-0.369746\pi$
$733$	973.386	−	403.190i	1.32795	−	0.550054i	0.930070	+	0.367384i	$0.119746\pi$
$734$	−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	0.935490	+	0.353354i	$0.114959\pi$
$739$	387.131	+	934.616i	0.523857	+	1.26470i	−0.411632	+	0.911350i	$0.635041\pi$
$740$	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	−0.966898	−	0.255163i	$-0.917871\pi$
$743$	−528.819	+	528.819i	−0.711735	+	0.711735i	0.255163	+	0.966898i	$0.417871\pi$
$744$		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	0.342797	−	0.939410i	$-0.388626\pi$
$757$	−59.8575	−	24.7938i	−0.0790720	−	0.0327527i	−0.421869	+	0.906657i	$0.638626\pi$
$758$	−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	0.0605844	−	0.998163i	$-0.480704\pi$
$761$	−713.497	−	713.497i	−0.937579	−	0.937579i	−0.998163	+	0.0605844i	$0.980704\pi$
$762$		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	−0.976774	−	0.214273i	$-0.931262\pi$
$773$	−104.027	+	251.144i	−0.134576	+	0.324896i	0.842198	+	0.539169i	$0.181262\pi$
$774$		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	0.357248	−	0.934010i	$-0.383715\pi$
$787$	999.730	−	414.102i	1.27031	−	0.526178i	0.913057	+	0.407832i	$0.133715\pi$
$788$	−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	0.471162	−	0.882047i	$-0.343835\pi$
$797$	1138.14	−	471.431i	1.42802	−	0.591507i	0.956863	+	0.290540i	$0.0938348\pi$
$798$		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	−0.594496	−	0.804099i	$-0.702648\pi$
$809$	169.569	−	169.569i	0.209603	−	0.209603i	0.804099	+	0.594496i	$0.202648\pi$
$810$		0			0
$811$	−437.562	+	1056.37i	−0.539534	+	1.30255i	0.385514	+	0.922702i	$0.374024\pi$
$811$	−437.562	+	1056.37i	−0.539534	+	1.30255i	−0.925048	+	0.379849i	$0.875976\pi$
$812$	−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	0.869019	−	0.494779i	$-0.164751\pi$
$821$	930.724	+	385.518i	1.13365	+	0.469572i	0.264627	+	0.964351i	$0.414751\pi$
$822$		0			0
$823$	−320.389	−	320.389i	−0.389294	−	0.389294i	0.485142	−	0.874435i	$-0.338768\pi$
$823$	−320.389	−	320.389i	−0.389294	−	0.389294i	−0.874435	+	0.485142i	$0.838768\pi$
$824$	−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	0.373814	−	0.927504i	$-0.378050\pi$
$827$	−14.6406	−	6.06433i	−0.0177032	−	0.00733293i	−0.391517	+	0.920171i	$0.628050\pi$
$828$		0			0
$829$	−753.878	+	312.267i	−0.909383	+	0.376679i	−0.787820	−	0.615905i	$-0.788790\pi$
$829$	−753.878	+	312.267i	−0.909383	+	0.376679i	−0.121562	+	0.992584i	$0.538790\pi$
$830$	−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	−0.553979	−	0.832531i	$-0.686891\pi$
$839$	233.705	−	233.705i	0.278552	−	0.278552i	0.832531	+	0.553979i	$0.186891\pi$
$840$		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	−0.274395	−	0.961617i	$-0.588477\pi$
$853$	−979.574	−	405.753i	−1.14839	−	0.475677i	−0.873992	+	0.485940i	$0.838477\pi$
$854$	−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	0.152461	−	0.988309i	$-0.451280\pi$
$857$	−716.322	−	716.322i	−0.835848	−	0.835848i	−0.988309	+	0.152461i	$0.951280\pi$
$858$		0			0
$859$	398.325	+	164.992i	0.463708	+	0.192074i	0.602291	−	0.798277i	$-0.294255\pi$
$859$	398.325	+	164.992i	0.463708	+	0.192074i	−0.138583	+	0.990351i	$0.544255\pi$
$860$	−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	$-0.734126\pi$
$863$		−	1279.79i		−	1.48295i	0.670980	−	0.741475i	$-0.265874\pi$
$864$		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	−0.987432	−	0.158046i	$-0.949481\pi$
$877$	−351.648	−	848.954i	−0.400967	−	0.968021i	0.586464	−	0.809975i	$-0.300519\pi$
$878$	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	$0.271471\pi$
$881$			1327.06i			1.50632i	−0.657839	+	0.753158i	$0.728529\pi$
$882$		0			0
$883$	412.717	−	170.953i	0.467403	−	0.193605i	−0.136536	−	0.990635i	$-0.543597\pi$
$883$	412.717	−	170.953i	0.467403	−	0.193605i	0.603939	+	0.797030i	$0.293597\pi$
$884$	−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	0.900021	−	0.435847i	$-0.143551\pi$
$887$	411.723	+	411.723i	0.464174	+	0.464174i	−0.435847	+	0.900021i	$0.643551\pi$
$888$		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	−0.659156	−	0.752006i	$-0.729086\pi$
$907$	307.189	−	741.619i	0.338687	−	0.817662i	0.997842	−	0.0656553i	$-0.0209138\pi$
$908$	−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	0.960817	−	0.277183i	$-0.0894007\pi$
$919$	628.260	+	628.260i	0.683635	+	0.683635i	−0.277183	+	0.960817i	$0.589401\pi$
$920$	−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	−0.462853	−	0.886435i	$-0.653174\pi$
$937$	396.897	−	396.897i	0.423583	−	0.423583i	0.886435	+	0.462853i	$0.153174\pi$
$938$	−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	−0.939809	−	0.341699i	$-0.888998\pi$
$941$	−486.386	−	1174.24i	−0.516882	−	1.24786i	0.422928	−	0.906163i	$-0.361002\pi$
$942$		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	−0.207646	−	0.978204i	$-0.566580\pi$
$947$	319.348	−	132.278i	0.337221	−	0.139681i	0.544867	+	0.838523i	$0.316580\pi$
$948$		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	0.573322	−	0.819330i	$-0.305654\pi$
$953$	−234.445	−	234.445i	−0.246007	−	0.246007i	−0.819330	+	0.573322i	$0.805654\pi$
$954$		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	−0.447584	−	0.894242i	$-0.647715\pi$
$967$	431.918	−	431.918i	0.446658	−	0.446658i	0.894242	+	0.447584i	$0.147715\pi$
$968$	−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	−0.583841	−	0.811868i	$-0.698451\pi$
$971$	391.385	−	944.887i	0.403074	−	0.973107i	0.986915	−	0.161239i	$-0.0515490\pi$
$972$		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	$-0.798093\pi$
$977$		−	1157.98i		−	1.18524i	0.805481	−	0.592621i	$-0.201907\pi$
$978$		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	0.476038	−	0.879425i	$-0.342072\pi$
$983$	−396.529	−	396.529i	−0.403386	−	0.403386i	−0.879425	+	0.476038i	$0.842072\pi$
$984$		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	$0.0215802\pi$
$991$			134.269i			0.135489i	−0.997703	+	0.0677444i	$0.978420\pi$
$992$	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	−0.491190	−	0.871052i	$-0.663438\pi$
$997$	470.645	−	1136.24i	0.472061	−	1.13966i	0.963251	−	0.268603i	$-0.0865620\pi$
$998$	−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.235.4		28
3.2	odd	2		32.3.h.a.11.4	yes	28
12.11	even	2		128.3.h.a.79.6		28
24.5	odd	2		256.3.h.b.159.6		28
24.11	even	2		256.3.h.a.159.2		28
32.3	odd	8	inner	288.3.u.a.163.4		28
96.29	odd	8		128.3.h.a.47.6		28
96.35	even	8		32.3.h.a.3.4	✓	28
96.77	odd	8		256.3.h.a.95.2		28
96.83	even	8		256.3.h.b.95.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.4	✓	28	96.35	even	8
32.3.h.a.11.4	yes	28	3.2	odd	2
128.3.h.a.47.6		28	96.29	odd	8
128.3.h.a.79.6		28	12.11	even	2
256.3.h.a.95.2		28	96.77	odd	8
256.3.h.a.159.2		28	24.11	even	2
256.3.h.b.95.6		28	96.83	even	8
256.3.h.b.159.6		28	24.5	odd	2
288.3.u.a.163.4		28	32.3	odd	8	inner
288.3.u.a.235.4		28	1.1	even	1	trivial

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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