LMFDB - Embedded newform 264.3.e.a.109.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [264,3,Mod(109,264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(264, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("264.109");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	264.e (of order $2$, degree $1$, 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:	$7.19347897911$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.48
Character	$\chi$	$=$	264.109
Dual form			264.3.e.a.109.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98900 + 0.209509i) q^{2} -1.73205i q^{3} +(3.91221 + 0.833424i) q^{4} +4.86020i q^{5} +(0.362880 - 3.44504i) q^{6} -11.9744i q^{7} +(7.60677 + 2.47732i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.98900 + 0.209509i) q^{2} -1.73205i q^{3} +(3.91221 + 0.833424i) q^{4} +4.86020i q^{5} +(0.362880 - 3.44504i) q^{6} -11.9744i q^{7} +(7.60677 + 2.47732i) q^{8} -3.00000 q^{9} +(-1.01825 + 9.66691i) q^{10} +(1.44010 - 10.9053i) q^{11} +(1.44353 - 6.77615i) q^{12} +20.4277 q^{13} +(2.50874 - 23.8170i) q^{14} +8.41811 q^{15} +(14.6108 + 6.52106i) q^{16} +26.3096i q^{17} +(-5.96699 - 0.628526i) q^{18} +12.5628 q^{19} +(-4.05060 + 19.0141i) q^{20} -20.7402 q^{21} +(5.14912 - 21.3889i) q^{22} -35.3899 q^{23} +(4.29084 - 13.1753i) q^{24} +1.37849 q^{25} +(40.6306 + 4.27978i) q^{26} +5.19615i q^{27} +(9.97974 - 46.8463i) q^{28} -13.2504 q^{29} +(16.7436 + 1.76367i) q^{30} -19.6674 q^{31} +(27.6946 + 16.0315i) q^{32} +(-18.8886 - 2.49433i) q^{33} +(-5.51210 + 52.3298i) q^{34} +58.1978 q^{35} +(-11.7366 - 2.50027i) q^{36} -9.27077i q^{37} +(24.9874 + 2.63202i) q^{38} -35.3818i q^{39} +(-12.0403 + 36.9704i) q^{40} -13.7607i q^{41} +(-41.2522 - 4.34526i) q^{42} -23.0956 q^{43} +(14.7227 - 41.4637i) q^{44} -14.5806i q^{45} +(-70.3903 - 7.41448i) q^{46} -63.7164 q^{47} +(11.2948 - 25.3067i) q^{48} -94.3858 q^{49} +(2.74182 + 0.288806i) q^{50} +45.5696 q^{51} +(79.9175 + 17.0249i) q^{52} +21.7323i q^{53} +(-1.08864 + 10.3351i) q^{54} +(53.0020 + 6.99917i) q^{55} +(29.6644 - 91.0863i) q^{56} -21.7595i q^{57} +(-26.3551 - 2.77608i) q^{58} +66.8708i q^{59} +(32.9334 + 7.01585i) q^{60} -50.9978 q^{61} +(-39.1185 - 4.12050i) q^{62} +35.9231i q^{63} +(51.7258 + 37.6888i) q^{64} +99.2826i q^{65} +(-37.0467 - 8.91853i) q^{66} +87.6588i q^{67} +(-21.9271 + 102.929i) q^{68} +61.2970i q^{69} +(115.755 + 12.1930i) q^{70} +13.1449 q^{71} +(-22.8203 - 7.43196i) q^{72} -47.7609i q^{73} +(1.94231 - 18.4395i) q^{74} -2.38762i q^{75} +(49.1485 + 10.4702i) q^{76} +(-130.584 - 17.2443i) q^{77} +(7.41279 - 70.3743i) q^{78} +39.2459i q^{79} +(-31.6936 + 71.0114i) q^{80} +9.00000 q^{81} +(2.88299 - 27.3700i) q^{82} +60.8874 q^{83} +(-81.1402 - 17.2854i) q^{84} -127.870 q^{85} +(-45.9371 - 4.83873i) q^{86} +22.9504i q^{87} +(37.9705 - 79.3867i) q^{88} +25.2453 q^{89} +(3.05476 - 29.0007i) q^{90} -244.609i q^{91} +(-138.453 - 29.4948i) q^{92} +34.0650i q^{93} +(-126.732 - 13.3491i) q^{94} +61.0579i q^{95} +(27.7673 - 47.9685i) q^{96} +107.717 q^{97} +(-187.733 - 19.7746i) q^{98} +(-4.32030 + 32.7160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 12 * q^4 - 144 * q^9	$ 48 q - 12 q^{4} - 144 q^{9} + 24 q^{12} - 36 q^{14} + 68 q^{16} - 20 q^{20} - 44 q^{22} - 128 q^{23} - 240 q^{25} + 44 q^{26} + 48 q^{34} + 36 q^{36} + 128 q^{38} - 108 q^{42} + 100 q^{44} + 48 q^{48} - 336 q^{49} - 128 q^{55} + 92 q^{56} + 368 q^{58} - 36 q^{60} + 444 q^{64} - 96 q^{66} - 24 q^{70} + 512 q^{71} - 348 q^{78} - 692 q^{80} + 432 q^{81} - 320 q^{82} + 568 q^{86} + 244 q^{88} + 436 q^{92} - 32 q^{97}+O(q^{100}) $ 48 * q - 12 * q^4 - 144 * q^9 + 24 * q^12 - 36 * q^14 + 68 * q^16 - 20 * q^20 - 44 * q^22 - 128 * q^23 - 240 * q^25 + 44 * q^26 + 48 * q^34 + 36 * q^36 + 128 * q^38 - 108 * q^42 + 100 * q^44 + 48 * q^48 - 336 * q^49 - 128 * q^55 + 92 * q^56 + 368 * q^58 - 36 * q^60 + 444 * q^64 - 96 * q^66 - 24 * q^70 + 512 * q^71 - 348 * q^78 - 692 * q^80 + 432 * q^81 - 320 * q^82 + 568 * q^86 + 244 * q^88 + 436 * q^92 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	1.98900	+	0.209509i	0.994498	+	0.104754i
$2$	1.98900	+	0.209509i	0.994498	+	0.104754i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.91221	+	0.833424i	0.978053	+	0.208356i
$5$			4.86020i			0.972039i	0.873948	+	0.486020i	$0.161552\pi$
$5$			4.86020i			0.972039i	−0.873948	+	0.486020i	$0.838448\pi$
$6$	0.362880	−	3.44504i	0.0604800	−	0.574174i
$7$		−	11.9744i		−	1.71063i	−0.518112	−	0.855313i	$-0.673365\pi$
$7$		−	11.9744i		−	1.71063i	0.518112	−	0.855313i	$-0.326635\pi$
$8$	7.60677	+	2.47732i	0.950846	+	0.309665i
$9$	−3.00000			−0.333333
$10$	−1.01825	+	9.66691i	−0.101825	+	0.966691i
$11$	1.44010	−	10.9053i	0.130918	−	0.991393i
$11$	1.44010	−	10.9053i	0.130918	−	0.991393i
$12$	1.44353	−	6.77615i	0.120294	−	0.564679i
$13$	20.4277			1.57136			0.785680	−	0.618633i	$-0.212313\pi$
$13$	20.4277			1.57136			0.785680	+	0.618633i	$0.212313\pi$
$14$	2.50874	−	23.8170i	0.179195	−	1.70121i
$15$	8.41811			0.561207
$16$	14.6108	+	6.52106i	0.913176	+	0.407566i
$17$			26.3096i			1.54763i	0.633414	+	0.773813i	$0.281653\pi$
$17$			26.3096i			1.54763i	−0.633414	+	0.773813i	$0.718347\pi$
$18$	−5.96699	−	0.628526i	−0.331499	−	0.0349181i
$19$	12.5628			0.661202			0.330601	−	0.943771i	$-0.392749\pi$
$19$	12.5628			0.661202			0.330601	+	0.943771i	$0.392749\pi$
$20$	−4.05060	+	19.0141i	−0.202530	+	0.950706i
$21$	−20.7402			−0.987630
$22$	5.14912	−	21.3889i	0.234051	−	0.972224i
$23$	−35.3899			−1.53869			−0.769345	−	0.638834i	$-0.779417\pi$
$23$	−35.3899			−1.53869			−0.769345	+	0.638834i	$0.779417\pi$
$24$	4.29084	−	13.1753i	0.178785	−	0.548971i
$25$	1.37849			0.0551397
$26$	40.6306	+	4.27978i	1.56272	+	0.164607i
$27$			5.19615i			0.192450i
$28$	9.97974	−	46.8463i	0.356419	−	1.67308i
$29$	−13.2504			−0.456912			−0.228456	−	0.973554i	$-0.573368\pi$
$29$	−13.2504			−0.456912			−0.228456	+	0.973554i	$0.573368\pi$
$30$	16.7436	+	1.76367i	0.558119	+	0.0587889i
$31$	−19.6674			−0.634434			−0.317217	−	0.948353i	$-0.602748\pi$
$31$	−19.6674			−0.634434			−0.317217	+	0.948353i	$0.602748\pi$
$32$	27.6946	+	16.0315i	0.865457	+	0.500983i
$33$	−18.8886	−	2.49433i	−0.572381	−	0.0755857i
$34$	−5.51210	+	52.3298i	−0.162121	+	1.53911i
$35$	58.1978			1.66280
$36$	−11.7366	−	2.50027i	−0.326018	−	0.0694520i
$37$		−	9.27077i		−	0.250561i	−0.992121	−	0.125281i	$-0.960017\pi$
$37$		−	9.27077i		−	0.250561i	0.992121	−	0.125281i	$-0.0399832\pi$
$38$	24.9874	+	2.63202i	0.657564	+	0.0692638i
$39$		−	35.3818i		−	0.907226i
$40$	−12.0403	+	36.9704i	−0.301007	+	0.924259i
$41$		−	13.7607i		−	0.335627i	−0.985819	−	0.167814i	$-0.946329\pi$
$41$		−	13.7607i		−	0.335627i	0.985819	−	0.167814i	$-0.0536707\pi$
$42$	−41.2522	−	4.34526i	−0.982196	−	0.103459i
$43$	−23.0956			−0.537107			−0.268554	−	0.963265i	$-0.586546\pi$
$43$	−23.0956			−0.537107			−0.268554	+	0.963265i	$0.586546\pi$
$44$	14.7227	−	41.4637i	0.334608	−	0.942357i
$45$		−	14.5806i		−	0.324013i
$46$	−70.3903	−	7.41448i	−1.53022	−	0.161184i
$47$	−63.7164			−1.35567			−0.677834	−	0.735215i	$-0.737081\pi$
$47$	−63.7164			−1.35567			−0.677834	+	0.735215i	$0.737081\pi$
$48$	11.2948	−	25.3067i	0.235309	−	0.527222i
$49$	−94.3858			−1.92624
$50$	2.74182	+	0.288806i	0.0548363	+	0.00577612i
$51$	45.5696			0.893522
$52$	79.9175	+	17.0249i	1.53687	+	0.327402i
$53$			21.7323i			0.410043i	0.978757	+	0.205022i	$0.0657265\pi$
$53$			21.7323i			0.410043i	−0.978757	+	0.205022i	$0.934274\pi$
$54$	−1.08864	+	10.3351i	−0.0201600	+	0.191391i
$55$	53.0020	+	6.99917i	0.963673	+	0.127258i
$56$	29.6644	−	91.0863i	0.529721	−	1.62654i
$57$		−	21.7595i		−	0.381745i
$58$	−26.3551	−	2.77608i	−0.454398	−	0.0478635i
$59$			66.8708i			1.13340i	0.823923	+	0.566702i	$0.191781\pi$
$59$			66.8708i			1.13340i	−0.823923	+	0.566702i	$0.808219\pi$
$60$	32.9334	+	7.01585i	0.548890	+	0.116931i
$61$	−50.9978			−0.836029			−0.418015	−	0.908440i	$-0.637274\pi$
$61$	−50.9978			−0.836029			−0.418015	+	0.908440i	$0.637274\pi$
$62$	−39.1185	−	4.12050i	−0.630943	−	0.0664597i
$63$			35.9231i			0.570209i
$64$	51.7258	+	37.6888i	0.808215	+	0.588887i
$65$			99.2826i			1.52742i
$66$	−37.0467	−	8.91853i	−0.561314	−	0.135129i
$67$			87.6588i			1.30834i	0.756347	+	0.654171i	$0.226982\pi$
$67$			87.6588i			1.30834i	−0.756347	+	0.654171i	$0.773018\pi$
$68$	−21.9271	+	102.929i	−0.322457	+	1.51366i
$69$			61.2970i			0.888363i
$70$	115.755	+	12.1930i	1.65365	+	0.174185i
$71$	13.1449			0.185140			0.0925700	−	0.995706i	$-0.470492\pi$
$71$	13.1449			0.185140			0.0925700	+	0.995706i	$0.470492\pi$
$72$	−22.8203	−	7.43196i	−0.316949	−	0.103222i
$73$		−	47.7609i		−	0.654259i	−0.944980	−	0.327130i	$-0.893919\pi$
$73$		−	47.7609i		−	0.654259i	0.944980	−	0.327130i	$-0.106081\pi$
$74$	1.94231	−	18.4395i	0.0262474	−	0.249183i
$75$		−	2.38762i		−	0.0318349i
$76$	49.1485	+	10.4702i	0.646691	+	0.137765i
$77$	−130.584	−	17.2443i	−1.69590	−	0.223952i
$78$	7.41279	−	70.3743i	0.0950358	−	0.902234i
$79$			39.2459i			0.496784i	0.968660	+	0.248392i	$0.0799021\pi$
$79$			39.2459i			0.496784i	−0.968660	+	0.248392i	$0.920098\pi$
$80$	−31.6936	+	71.0114i	−0.396171	+	0.887642i
$81$	9.00000			0.111111
$82$	2.88299	−	27.3700i	0.0351584	−	0.333781i
$83$	60.8874			0.733583			0.366791	−	0.930303i	$-0.380456\pi$
$83$	60.8874			0.733583			0.366791	+	0.930303i	$0.380456\pi$
$84$	−81.1402	−	17.2854i	−0.965955	−	0.205779i
$85$	−127.870			−1.50435
$86$	−45.9371	−	4.83873i	−0.534152	−	0.0562643i
$87$			22.9504i			0.263798i
$88$	37.9705	−	79.3867i	0.431483	−	0.902121i
$89$	25.2453			0.283655			0.141827	−	0.989891i	$-0.454702\pi$
$89$	25.2453			0.283655			0.141827	+	0.989891i	$0.454702\pi$
$90$	3.05476	−	29.0007i	0.0339418	−	0.322230i
$91$		−	244.609i		−	2.68801i
$92$	−138.453	−	29.4948i	−1.50492	−	0.320595i
$93$			34.0650i			0.366291i
$94$	−126.732	−	13.3491i	−1.34821	−	0.142012i
$95$			61.0579i			0.642714i
$96$	27.7673	−	47.9685i	0.289243	−	0.499672i
$97$	107.717			1.11048			0.555240	−	0.831690i	$-0.312626\pi$
$97$	107.717			1.11048			0.555240	+	0.831690i	$0.312626\pi$
$98$	−187.733	−	19.7746i	−1.91564	−	0.201782i
$99$	−4.32030	+	32.7160i	−0.0436394	+	0.330464i
$100$	5.39295	+	1.14887i	0.0539295	+	0.0114887i
$101$	81.8762			0.810655			0.405328	−	0.914171i	$-0.367157\pi$
$101$	81.8762			0.810655			0.405328	+	0.914171i	$0.367157\pi$
$102$	90.6378	+	9.54723i	0.888606	+	0.0936003i
$103$	−176.532			−1.71390			−0.856951	−	0.515398i	$-0.827644\pi$
$103$	−176.532			−1.71390			−0.856951	+	0.515398i	$0.827644\pi$
$104$	155.389	+	50.6059i	1.49412	+	0.486595i
$105$		−	100.802i		−	0.960015i
$106$	−4.55311	+	43.2255i	−0.0429538	+	0.407787i
$107$	29.2228			0.273111			0.136555	−	0.990632i	$-0.456397\pi$
$107$	29.2228			0.273111			0.136555	+	0.990632i	$0.456397\pi$
$108$	−4.33060	+	20.3285i	−0.0400981	+	0.188226i
$109$	−29.8090			−0.273477			−0.136738	−	0.990607i	$-0.543662\pi$
$109$	−29.8090			−0.273477			−0.136738	+	0.990607i	$0.543662\pi$
$110$	103.954	+	25.0257i	0.945040	+	0.227507i
$111$	−16.0575			−0.144662
$112$	78.0857	−	174.955i	0.697194	−	1.56210i
$113$	128.899			1.14070			0.570349	−	0.821403i	$-0.306808\pi$
$113$	128.899			1.14070			0.570349	+	0.821403i	$0.306808\pi$
$114$	4.55880	−	43.2795i	0.0399895	−	0.379645i
$115$		−	172.002i		−	1.49567i
$116$	−51.8386	−	11.0432i	−0.446884	−	0.0952003i
$117$	−61.2831			−0.523787
$118$	−14.0100	+	133.006i	−0.118729	+	1.12717i
$119$	315.042			2.64741
$120$	64.0346	+	20.8543i	0.533621	+	0.173786i
$121$	−116.852	−	31.4095i	−0.965721	−	0.259583i
$122$	−101.434	−	10.6845i	−0.831430	−	0.0875777i
$123$	−23.8343			−0.193775
$124$	−76.9432	−	16.3913i	−0.620510	−	0.132188i
$125$			128.205i			1.02564i
$126$	−7.52621	+	71.4510i	−0.0597318	+	0.567071i
$127$		−	88.8698i		−	0.699763i	−0.936794	−	0.349881i	$-0.886222\pi$
$127$		−	88.8698i		−	0.699763i	0.936794	−	0.349881i	$-0.113778\pi$
$128$	94.9862	+	85.7998i	0.742080	+	0.670311i
$129$			40.0028i			0.310099i
$130$	−20.8006	+	197.473i	−0.160004	+	1.51902i
$131$	4.84006			0.0369470			0.0184735	−	0.999829i	$-0.494119\pi$
$131$	4.84006			0.0369470			0.0184735	+	0.999829i	$0.494119\pi$
$132$	−71.8173	−	25.5005i	−0.544070	−	0.193186i
$133$		−	150.432i		−	1.13107i
$134$	−18.3653	+	174.353i	−0.137054	+	1.30114i
$135$	−25.2543			−0.187069
$136$	−65.1774	+	200.131i	−0.479245	+	1.47155i
$137$	−185.886			−1.35683			−0.678416	−	0.734678i	$-0.737333\pi$
$137$	−185.886			−1.35683			−0.678416	+	0.734678i	$0.737333\pi$
$138$	−12.8423	+	121.920i	−0.0930599	+	0.883475i
$139$	225.347			1.62120			0.810601	−	0.585599i	$-0.199141\pi$
$139$	225.347			1.62120			0.810601	+	0.585599i	$0.199141\pi$
$140$	227.682	+	48.5035i	1.62630	+	0.346453i
$141$			110.360i			0.782695i
$142$	26.1452	+	2.75398i	0.184121	+	0.0193942i
$143$	29.4179	−	222.771i	0.205720	−	1.55784i
$144$	−43.8324	−	19.5632i	−0.304392	−	0.135855i
$145$		−	64.3998i		−	0.444136i
$146$	10.0063	−	94.9963i	0.0685365	−	0.650659i
$147$			163.481i			1.11212i
$148$	7.72649	−	36.2692i	0.0522060	−	0.245062i
$149$	−167.306			−1.12286			−0.561428	−	0.827525i	$-0.689748\pi$
$149$	−167.306			−1.12286			−0.561428	+	0.827525i	$0.689748\pi$
$150$	0.500227	−	4.74896i	0.00333485	−	0.0316598i
$151$			201.617i			1.33521i	0.744515	+	0.667606i	$0.232681\pi$
$151$			201.617i			1.33521i	−0.744515	+	0.667606i	$0.767319\pi$
$152$	95.5626	+	31.1222i	0.628701	+	0.204751i
$153$		−	78.9289i		−	0.515875i
$154$	−256.119	−	61.6575i	−1.66311	−	0.400373i
$155$		−	95.5876i		−	0.616695i
$156$	29.4880	−	138.421i	0.189026	−	0.887315i
$157$		−	303.154i		−	1.93091i	−0.260562	−	0.965457i	$-0.583908\pi$
$157$		−	303.154i		−	1.93091i	0.260562	−	0.965457i	$-0.416092\pi$
$158$	−8.22236	+	78.0600i	−0.0520402	+	0.494050i
$159$	37.6414			0.236739
$160$	−77.9161	+	134.601i	−0.486975	+	0.841258i
$161$			423.772i			2.63212i
$162$	17.9010	+	1.88558i	0.110500	+	0.0116394i
$163$			131.153i			0.804617i	0.915504	+	0.402308i	$0.131792\pi$
$163$			131.153i			0.804617i	−0.915504	+	0.402308i	$0.868208\pi$
$164$	11.4685	−	53.8349i	0.0699300	−	0.328261i
$165$	12.1229	−	91.8022i	0.0734723	−	0.556377i
$166$	121.105	+	12.7564i	0.729547	+	0.0768460i
$167$		−	208.910i		−	1.25096i	−0.780242	−	0.625478i	$-0.784904\pi$
$167$		−	208.910i		−	1.25096i	0.780242	−	0.625478i	$-0.215096\pi$
$168$	−157.766	−	51.3802i	−0.939084	−	0.305834i
$169$	248.290			1.46917
$170$	−254.333	−	26.7899i	−1.49608	−	0.157588i
$171$	−37.6885			−0.220401
$172$	−90.3549	−	19.2484i	−0.525319	−	0.111910i
$173$	68.6927			0.397068			0.198534	−	0.980094i	$-0.436382\pi$
$173$	68.6927			0.397068			0.198534	+	0.980094i	$0.436382\pi$
$174$	−4.80832	+	45.6483i	−0.0276340	+	0.262347i
$175$		−	16.5066i		−	0.0943234i
$176$	92.1554	−	149.945i	0.523610	−	0.851958i
$177$	115.824			0.654371
$178$	50.2128	+	5.28911i	0.282094	+	0.0297141i
$179$			98.8446i			0.552204i	0.961128	+	0.276102i	$0.0890428\pi$
$179$			98.8446i			0.552204i	−0.961128	+	0.276102i	$0.910957\pi$
$180$	12.1518	−	57.0424i	0.0675101	−	0.316902i
$181$			79.2186i			0.437672i	0.975762	+	0.218836i	$0.0702260\pi$
$181$			79.2186i			0.437672i	−0.975762	+	0.218836i	$0.929774\pi$
$182$	51.2477	−	486.526i	0.281581	−	2.67322i
$183$			88.3308i			0.482682i
$184$	−269.202	−	87.6720i	−1.46306	−	0.476478i
$185$	45.0578			0.243556
$186$	−7.13692	+	67.7552i	−0.0383705	+	0.364275i
$187$	286.915	+	37.8885i	1.53431	+	0.202613i
$188$	−249.272	−	53.1027i	−1.32591	−	0.282461i
$189$	62.2207			0.329210
$190$	−12.7922	+	121.444i	−0.0673271	+	0.639178i
$191$	−188.156			−0.985111			−0.492555	−	0.870281i	$-0.663937\pi$
$191$	−188.156			−0.985111			−0.492555	+	0.870281i	$0.663937\pi$
$192$	65.2789	−	89.5917i	0.339994	−	0.466623i
$193$		−	152.773i		−	0.791572i	−0.918343	−	0.395786i	$-0.870472\pi$
$193$		−	152.773i		−	0.791572i	0.918343	−	0.395786i	$-0.129528\pi$
$194$	214.248	+	22.5676i	1.10437	+	0.116328i
$195$	171.962			0.881859
$196$	−369.257	−	78.6634i	−1.88396	−	0.401344i
$197$	268.063			1.36073			0.680364	−	0.732874i	$-0.261822\pi$
$197$	268.063			1.36073			0.680364	+	0.732874i	$0.261822\pi$
$198$	−15.4473	+	64.1668i	−0.0780169	+	0.324075i
$199$	314.609			1.58095			0.790475	−	0.612494i	$-0.209834\pi$
$199$	314.609			1.58095			0.790475	+	0.612494i	$0.209834\pi$
$200$	10.4859	+	3.41497i	0.0524293	+	0.0170748i
$201$	151.830			0.755371
$202$	162.851	+	17.1538i	0.806195	+	0.0849197i
$203$			158.666i			0.781605i
$204$	178.278	+	37.9788i	0.873912	+	0.186171i
$205$	66.8798			0.326243
$206$	−351.121	−	36.9850i	−1.70447	−	0.179539i
$207$	106.170			0.512896
$208$	298.465	+	133.210i	1.43493	+	0.640434i
$209$	18.0918	−	137.002i	0.0865634	−	0.655511i
$210$	21.1188	−	200.494i	0.100566	−	0.954733i
$211$	−365.685			−1.73310			−0.866552	−	0.499086i	$-0.833669\pi$
$211$	−365.685			−1.73310			−0.866552	+	0.499086i	$0.833669\pi$
$212$	−18.1122	+	85.0214i	−0.0854350	+	0.401044i
$213$		−	22.7677i		−	0.106891i
$214$	58.1241	+	6.12244i	0.271608	+	0.0286095i
$215$		−	112.249i		−	0.522089i
$216$	−12.8725	+	39.5259i	−0.0595951	+	0.182990i
$217$			235.505i			1.08528i
$218$	−59.2899	−	6.24524i	−0.271972	−	0.0286479i
$219$	−82.7243			−0.377737
$220$	201.522	+	71.5554i	0.916008	+	0.325252i
$221$			537.445i			2.43188i
$222$	−31.9382	−	3.36418i	−0.143866	−	0.0151539i
$223$	−74.2015			−0.332742			−0.166371	−	0.986063i	$-0.553205\pi$
$223$	−74.2015			−0.332742			−0.166371	+	0.986063i	$0.553205\pi$
$224$	191.967	−	331.626i	0.856995	−	1.48047i
$225$	−4.13548			−0.0183799
$226$	256.379	+	27.0054i	1.13442	+	0.119493i
$227$	−133.968			−0.590166			−0.295083	−	0.955472i	$-0.595347\pi$
$227$	−133.968			−0.590166			−0.295083	+	0.955472i	$0.595347\pi$
$228$	18.1349	−	85.1277i	0.0795389	−	0.373367i
$229$		−	165.628i		−	0.723266i	−0.932321	−	0.361633i	$-0.882219\pi$
$229$		−	165.628i		−	0.723266i	0.932321	−	0.361633i	$-0.117781\pi$
$230$	36.0358	−	342.111i	0.156678	−	1.48744i
$231$	−29.8680	+	226.179i	−0.129299	+	0.979130i
$232$	−100.793	−	32.8256i	−0.434453	−	0.141490i
$233$		−	287.599i		−	1.23433i	−0.786834	−	0.617165i	$-0.788281\pi$
$233$		−	287.599i		−	1.23433i	0.786834	−	0.617165i	$-0.211719\pi$
$234$	−121.892	−	12.8393i	−0.520905	−	0.0548690i
$235$		−	309.674i		−	1.31776i
$236$	−55.7318	+	261.613i	−0.236152	+	1.10853i
$237$	67.9759			0.286818
$238$	626.616	+	66.0039i	2.63284	+	0.277327i
$239$		−	122.493i		−	0.512524i	−0.966607	−	0.256262i	$-0.917509\pi$
$239$		−	122.493i		−	0.512524i	0.966607	−	0.256262i	$-0.0824910\pi$
$240$	122.995	+	54.8950i	0.512481	+	0.228729i
$241$		−	159.428i		−	0.661527i	−0.943714	−	0.330764i	$-0.892694\pi$
$241$		−	159.428i		−	0.661527i	0.943714	−	0.330764i	$-0.107306\pi$
$242$	−225.838	−	86.9550i	−0.933215	−	0.359318i
$243$		−	15.5885i		−	0.0641500i
$244$	−199.514	−	42.5028i	−0.817681	−	0.174192i
$245$		−	458.733i		−	1.87238i
$246$	−47.4063	−	4.99349i	−0.192708	−	0.0202987i
$247$	256.630			1.03899
$248$	−149.606	−	48.7226i	−0.603249	−	0.196462i
$249$		−	105.460i		−	0.423534i
$250$	−26.8600	+	254.999i	−0.107440	+	1.01999i
$251$		−	180.790i		−	0.720278i	−0.932899	−	0.360139i	$-0.882729\pi$
$251$		−	180.790i		−	0.720278i	0.932899	−	0.360139i	$-0.117271\pi$
$252$	−29.9392	+	140.539i	−0.118806	+	0.557694i
$253$	−50.9650	+	385.938i	−0.201443	+	1.52545i
$254$	18.6190	−	176.762i	0.0733032	−	0.695913i
$255$			221.477i			0.868539i
$256$	170.951	+	190.556i	0.667779	+	0.744359i
$257$	227.534			0.885348			0.442674	−	0.896683i	$-0.354030\pi$
$257$	227.534			0.885348			0.442674	+	0.896683i	$0.354030\pi$
$258$	−8.38093	+	79.5654i	−0.0324842	+	0.308393i
$259$	−111.012			−0.428617
$260$	−82.7445	+	388.415i	−0.318248	+	1.49390i
$261$	39.7513			0.152304
$262$	9.62685	+	1.01403i	0.0367437	+	0.00387036i
$263$		−	379.305i		−	1.44222i	−0.692818	−	0.721112i	$-0.743631\pi$
$263$		−	379.305i		−	1.44222i	0.692818	−	0.721112i	$-0.256369\pi$
$264$	−137.502	−	65.7668i	−0.520840	−	0.249117i
$265$	−105.623			−0.398578
$266$	31.5168	−	299.209i	0.118484	−	1.12485i
$267$		−	43.7261i		−	0.163768i
$268$	−73.0570	+	342.940i	−0.272601	+	1.27963i
$269$		−	412.994i		−	1.53529i	−0.640874	−	0.767646i	$-0.721428\pi$
$269$		−	412.994i		−	1.53529i	0.640874	−	0.767646i	$-0.278572\pi$
$270$	−50.2307	−	5.29100i	−0.186040	−	0.0195963i
$271$			297.160i			1.09653i	0.836305	+	0.548265i	$0.184711\pi$
$271$			297.160i			1.09653i	−0.836305	+	0.548265i	$0.815289\pi$
$272$	−171.567	+	384.405i	−0.630760	+	1.41325i
$273$	−423.675			−1.55192
$274$	−369.727	−	38.9447i	−1.34937	−	0.142134i
$275$	1.98517	−	15.0329i	0.00721879	−	0.0546651i
$276$	−51.0864	+	239.807i	−0.185096	+	0.868866i
$277$	−84.8580			−0.306347			−0.153173	−	0.988199i	$-0.548949\pi$
$277$	−84.8580			−0.306347			−0.153173	+	0.988199i	$0.548949\pi$
$278$	448.214	+	47.2122i	1.61228	+	0.169828i
$279$	59.0023			0.211478
$280$	442.697	+	144.175i	1.58106	+	0.514909i
$281$			376.397i			1.33949i	0.742591	+	0.669745i	$0.233596\pi$
$281$			376.397i			1.33949i	−0.742591	+	0.669745i	$0.766404\pi$
$282$	−23.1214	+	219.506i	−0.0819907	+	0.778389i
$283$	−22.1706			−0.0783415			−0.0391708	−	0.999233i	$-0.512472\pi$
$283$	−22.1706			−0.0783415			−0.0391708	+	0.999233i	$0.512472\pi$
$284$	51.4258	+	10.9553i	0.181077	+	0.0385750i
$285$	105.755			0.371071
$286$	105.185	−	436.927i	0.367778	−	1.52772i
$287$	−164.776			−0.574133
$288$	−83.0839	−	48.0944i	−0.288486	−	0.166994i
$289$	−403.197			−1.39515
$290$	13.4923	−	128.091i	0.0465252	−	0.441693i
$291$		−	186.571i		−	0.641136i
$292$	39.8051	−	186.851i	0.136319	−	0.639900i
$293$	63.7547			0.217593			0.108796	−	0.994064i	$-0.465300\pi$
$293$	63.7547			0.217593			0.108796	+	0.994064i	$0.465300\pi$
$294$	−34.2507	+	325.163i	−0.116499	+	1.10600i
$295$	−325.005			−1.10171
$296$	22.9667	−	70.5206i	0.0775901	−	0.238245i
$297$	56.6657	+	7.48299i	0.190794	+	0.0251952i
$298$	−332.770	−	35.0520i	−1.11668	−	0.117624i
$299$	−722.933			−2.41784
$300$	1.98990	−	9.34087i	0.00663300	−	0.0311362i
$301$			276.556i			0.918789i
$302$	−42.2405	+	401.016i	−0.139869	+	1.32787i
$303$		−	141.814i		−	0.468032i
$304$	183.553	+	81.9231i	0.603793	+	0.269484i
$305$		−	247.859i		−	0.812653i
$306$	16.5363	−	156.989i	0.0540402	−	0.513037i
$307$	−162.646			−0.529793			−0.264896	−	0.964277i	$-0.585338\pi$
$307$	−162.646			−0.529793			−0.264896	+	0.964277i	$0.585338\pi$
$308$	−496.502	−	176.296i	−1.61202	−	0.572389i
$309$			305.762i			0.989522i
$310$	20.0264	−	190.123i	0.0646014	−	0.613302i
$311$	−116.979			−0.376139			−0.188069	−	0.982156i	$-0.560223\pi$
$311$	−116.979			−0.376139			−0.188069	+	0.982156i	$0.560223\pi$
$312$	87.6520	−	269.141i	0.280936	−	0.862632i
$313$	270.622			0.864606			0.432303	−	0.901729i	$-0.357701\pi$
$313$	270.622			0.864606			0.432303	+	0.901729i	$0.357701\pi$
$314$	63.5133	−	602.971i	0.202272	−	1.92029i
$315$	−174.593			−0.554265
$316$	−32.7085	+	153.538i	−0.103508	+	0.485881i
$317$		−	32.6056i		−	0.102857i	−0.998677	−	0.0514284i	$-0.983623\pi$
$317$		−	32.6056i		−	0.102857i	0.998677	−	0.0514284i	$-0.0163774\pi$
$318$	74.8687	+	7.88621i	0.235436	+	0.0247994i
$319$	−19.0820	+	144.500i	−0.0598181	+	0.452979i
$320$	−183.175	+	251.397i	−0.572421	+	0.785617i
$321$		−	50.6154i		−	0.157680i
$322$	−88.7838	+	842.880i	−0.275726	+	2.61764i
$323$			330.524i			1.02329i
$324$	35.2099	+	7.50082i	0.108673	+	0.0231507i
$325$	28.1594			0.0866443
$326$	−27.4776	+	260.862i	−0.0842871	+	0.800190i
$327$			51.6306i			0.157892i
$328$	34.0897	−	104.675i	0.103932	−	0.319130i
$329$			762.964i			2.31904i
$330$	43.3458	−	180.054i	0.131351	−	0.545619i
$331$			450.105i			1.35983i	0.733290	+	0.679917i	$0.237984\pi$
$331$			450.105i			1.35983i	−0.733290	+	0.679917i	$0.762016\pi$
$332$	238.204	+	50.7450i	0.717483	+	0.152846i
$333$			27.8123i			0.0835205i
$334$	43.7684	−	415.521i	0.131043	−	1.24407i
$335$	−426.039			−1.27176
$336$	−303.032	−	135.248i	−0.901880	−	0.402525i
$337$			300.954i			0.893039i	0.894774	+	0.446519i	$0.147337\pi$
$337$			300.954i			0.893039i	−0.894774	+	0.446519i	$0.852663\pi$
$338$	493.849	+	52.0190i	1.46109	+	0.153902i
$339$		−	223.259i		−	0.658582i
$340$	−500.255	−	106.570i	−1.47134	−	0.313441i
$341$	−28.3231	+	214.480i	−0.0830590	+	0.628973i
$342$	−74.9623	−	7.89607i	−0.219188	−	0.0230879i
$343$			543.466i			1.58445i
$344$	−175.683	−	57.2152i	−0.510706	−	0.166323i
$345$	−297.916			−0.863523
$346$	136.630	+	14.3917i	0.394883	+	0.0415946i
$347$	−110.465			−0.318342			−0.159171	−	0.987251i	$-0.550882\pi$
$347$	−110.465			−0.318342			−0.159171	+	0.987251i	$0.550882\pi$
$348$	−19.1275	+	89.7870i	−0.0549639	+	0.258009i
$349$	396.482			1.13605			0.568026	−	0.823010i	$-0.307707\pi$
$349$	396.482			1.13605			0.568026	+	0.823010i	$0.307707\pi$
$350$	3.45827	−	32.8315i	0.00988078	−	0.0938044i
$351$			106.145i			0.302409i
$352$	214.711	−	278.932i	0.609975	−	0.792420i
$353$	68.7998			0.194900			0.0974502	−	0.995240i	$-0.468931\pi$
$353$	68.7998			0.194900			0.0974502	+	0.995240i	$0.468931\pi$
$354$	230.373	+	24.2661i	0.650771	+	0.0685482i
$355$			63.8870i			0.179963i
$356$	98.7649	+	21.0400i	0.277429	+	0.0591012i
$357$		−	545.668i		−	1.52848i
$358$	−20.7088	+	196.601i	−0.0578458	+	0.549166i
$359$		−	289.584i		−	0.806642i	−0.915059	−	0.403321i	$-0.867856\pi$
$359$		−	289.584i		−	0.806642i	0.915059	−	0.403321i	$-0.132144\pi$
$360$	36.1208	−	110.911i	0.100336	−	0.308086i
$361$	−203.175			−0.562812
$362$	−16.5970	+	157.566i	−0.0458480	+	0.435264i
$363$	−54.4029	+	202.394i	−0.149870	+	0.557559i
$364$	203.863	−	956.962i	0.560063	−	2.62902i
$365$	232.127			0.635965
$366$	−18.5061	+	175.690i	−0.0505630	+	0.480026i
$367$	−177.690			−0.484169			−0.242084	−	0.970255i	$-0.577831\pi$
$367$	−177.690			−0.484169			−0.242084	+	0.970255i	$0.577831\pi$
$368$	−517.074	−	230.779i	−1.40509	−	0.627118i
$369$			41.2822i			0.111876i
$370$	89.6198	+	9.44000i	0.242216	+	0.0255135i
$371$	260.231			0.701431
$372$	−28.3906	+	133.270i	−0.0763188	+	0.358252i
$373$	250.697			0.672109			0.336055	−	0.941843i	$-0.390907\pi$
$373$	250.697			0.672109			0.336055	+	0.941843i	$0.390907\pi$
$374$	562.735	+	135.471i	1.50464	+	0.362223i
$375$	222.057			0.592152
$376$	−484.675	−	157.846i	−1.28903	−	0.419803i
$377$	−270.676			−0.717973
$378$	123.757	+	13.0358i	0.327399	+	0.0344862i
$379$			76.5238i			0.201910i	0.994891	+	0.100955i	$0.0321898\pi$
$379$			76.5238i			0.201910i	−0.994891	+	0.100955i	$0.967810\pi$
$380$	−50.8871	+	238.871i	−0.133913	+	0.628609i
$381$	−153.927			−0.404008
$382$	−374.242	−	39.4203i	−0.979691	−	0.103195i
$383$	−276.986			−0.723201			−0.361600	−	0.932333i	$-0.617770\pi$
$383$	−276.986			−0.723201			−0.361600	+	0.932333i	$0.617770\pi$
$384$	148.610	−	164.521i	0.387004	−	0.428440i
$385$	83.8108	−	634.666i	0.217690	−	1.64848i
$386$	32.0073	−	303.866i	0.0829206	−	0.787217i
$387$	69.2868			0.179036
$388$	421.410	+	89.7735i	1.08611	+	0.231375i
$389$		−	199.141i		−	0.511929i	−0.966686	−	0.255965i	$-0.917607\pi$
$389$		−	199.141i		−	0.511929i	0.966686	−	0.255965i	$-0.0823931\pi$
$390$	342.033	+	36.0276i	0.877007	+	0.0923785i
$391$		−	931.094i		−	2.38131i
$392$	−717.970	−	233.824i	−1.83156	−	0.596489i
$393$		−	8.38322i		−	0.0213314i
$394$	533.177	+	56.1616i	1.35324	+	0.142542i
$395$	−190.743			−0.482893
$396$	−44.1682	+	124.391i	−0.111536	+	0.314119i
$397$		−	325.529i		−	0.819972i	−0.912092	−	0.409986i	$-0.865534\pi$
$397$		−	325.529i		−	0.819972i	0.912092	−	0.409986i	$-0.134466\pi$
$398$	625.757	+	65.9134i	1.57225	+	0.165611i
$399$	−260.556			−0.653023
$400$	20.1409	+	8.98924i	0.0503522	+	0.0224731i
$401$	−187.031			−0.466411			−0.233205	−	0.972428i	$-0.574921\pi$
$401$	−187.031			−0.466411			−0.233205	+	0.972428i	$0.574921\pi$
$402$	301.988	+	31.8096i	0.751215	+	0.0791284i
$403$	−401.760			−0.996924
$404$	320.317	+	68.2376i	0.792864	+	0.168905i
$405$			43.7418i			0.108004i
$406$	−33.2419	+	315.586i	−0.0818765	+	0.777305i
$407$	−101.101	−	13.3509i	−0.248405	−	0.0328031i
$408$	346.637	+	112.891i	0.849602	+	0.276692i
$409$		−	495.269i		−	1.21093i	−0.795874	−	0.605463i	$-0.792988\pi$
$409$		−	495.269i		−	1.21093i	0.795874	−	0.605463i	$-0.207012\pi$
$410$	133.024	+	14.0119i	0.324448	+	0.0341754i
$411$			321.964i			0.783368i
$412$	−690.630	−	147.126i	−1.67629	−	0.357102i
$413$	800.737			1.93883
$414$	211.171	+	22.2434i	0.510075	+	0.0537281i
$415$			295.925i			0.713071i
$416$	565.737	+	327.486i	1.35995	+	0.787225i
$417$		−	390.312i		−	0.936001i
$418$	64.6875	−	268.706i	0.154755	−	0.642837i
$419$			390.401i			0.931745i	0.884852	+	0.465872i	$0.154259\pi$
$419$			390.401i			0.931745i	−0.884852	+	0.465872i	$0.845741\pi$
$420$	84.0105	−	394.357i	0.200025	−	0.938946i
$421$			87.5019i			0.207843i	0.994585	+	0.103922i	$0.0331391\pi$
$421$			87.5019i			0.207843i	−0.994585	+	0.103922i	$0.966861\pi$
$422$	−727.346	−	76.6142i	−1.72357	−	0.181550i
$423$	191.149			0.451889
$424$	−53.8379	+	165.313i	−0.126976	+	0.389888i
$425$			36.2676i			0.0853356i
$426$	4.77003	−	45.2849i	0.0111973	−	0.106303i
$427$			610.667i			1.43013i
$428$	114.326	+	24.3550i	0.267117	+	0.0569042i
$429$	−385.850	−	50.9534i	−0.899417	−	0.118772i
$430$	23.5172	−	223.263i	0.0546911	−	0.519217i
$431$			165.880i			0.384873i	0.981309	+	0.192436i	$0.0616389\pi$
$431$			165.880i			0.384873i	−0.981309	+	0.192436i	$0.938361\pi$
$432$	−33.8844	+	75.9200i	−0.0784362	+	0.175741i
$433$	−639.331			−1.47651			−0.738257	−	0.674519i	$-0.764351\pi$
$433$	−639.331			−1.47651			−0.738257	+	0.674519i	$0.764351\pi$
$434$	−49.3404	+	468.419i	−0.113688	+	1.07931i
$435$	−111.544			−0.256422
$436$	−116.619	−	24.8435i	−0.267475	−	0.0569805i
$437$	−444.597			−1.01738
$438$	−164.538	−	17.3315i	−0.375658	−	0.0395696i
$439$			242.448i			0.552274i	0.961118	+	0.276137i	$0.0890544\pi$
$439$			242.448i			0.552274i	−0.961118	+	0.276137i	$0.910946\pi$
$440$	385.835	+	184.544i	0.876897	+	0.419418i
$441$	283.157			0.642080
$442$	−112.599	+	1068.98i	−0.254750	+	2.41850i
$443$		−	704.372i		−	1.59000i	−0.606606	−	0.795002i	$-0.707470\pi$
$443$		−	704.372i		−	1.59000i	0.606606	−	0.795002i	$-0.292530\pi$
$444$	−62.8202	−	13.3827i	−0.141487	−	0.0301411i
$445$			122.697i			0.275724i
$446$	−147.586	−	15.5459i	−0.330911	−	0.0348562i
$447$			289.782i			0.648282i
$448$	451.300	−	619.384i	1.00737	−	1.38255i
$449$	608.936			1.35621			0.678103	−	0.734967i	$-0.262802\pi$
$449$	608.936			1.35621			0.678103	+	0.734967i	$0.262802\pi$
$450$	−8.22545	−	0.866418i	−0.0182788	−	0.00192537i
$451$	−150.065	−	19.8168i	−0.332739	−	0.0439398i
$452$	504.279	+	107.427i	1.11566	+	0.237671i
$453$	349.211			0.770885
$454$	−266.461	−	28.0674i	−0.586919	−	0.0618225i
$455$	1188.85			2.61285
$456$	53.9052	−	165.519i	0.118213	−	0.362981i
$457$			234.175i			0.512417i	0.966621	+	0.256209i	$0.0824734\pi$
$457$			234.175i			0.512417i	−0.966621	+	0.256209i	$0.917527\pi$
$458$	34.7005	−	329.433i	0.0757653	−	0.719287i
$459$	−136.709			−0.297841
$460$	143.350	−	672.907i	0.311631	−	1.46284i
$461$	−238.716			−0.517822			−0.258911	−	0.965901i	$-0.583364\pi$
$461$	−238.716			−0.517822			−0.258911	+	0.965901i	$0.583364\pi$
$462$	−106.794	+	443.612i	−0.231156	+	0.960198i
$463$	−42.6873			−0.0921972			−0.0460986	−	0.998937i	$-0.514679\pi$
$463$	−42.6873			−0.0921972			−0.0460986	+	0.998937i	$0.514679\pi$
$464$	−193.600	−	86.4070i	−0.417241	−	0.186222i
$465$	−165.563			−0.356049
$466$	60.2545	−	572.033i	0.129301	−	1.22754i
$467$		−	604.273i		−	1.29395i	−0.762513	−	0.646973i	$-0.776035\pi$
$467$		−	604.273i		−	1.29395i	0.762513	−	0.646973i	$-0.223965\pi$
$468$	−239.752	−	51.0748i	−0.512291	−	0.109134i
$469$	1049.66			2.23808
$470$	64.8794	−	615.940i	0.138041	−	1.31051i
$471$	−525.077			−1.11481
$472$	−165.660	+	508.671i	−0.350976	+	1.07769i
$473$	−33.2600	+	251.865i	−0.0703172	+	0.532484i
$474$	135.204	+	14.2415i	0.285240	+	0.0300455i
$475$	17.3178			0.0364585
$476$	1232.51	+	262.563i	2.58931	+	0.551603i
$477$		−	65.1969i		−	0.136681i
$478$	25.6634	−	243.639i	0.0536891	−	0.509704i
$479$		−	295.948i		−	0.617845i	−0.951087	−	0.308923i	$-0.900032\pi$
$479$		−	295.948i		−	0.617845i	0.951087	−	0.308923i	$-0.0999684\pi$
$480$	233.136	+	134.955i	0.485701	+	0.281155i
$481$		−	189.381i		−	0.393722i
$482$	33.4016	−	317.102i	0.0692978	−	0.657887i
$483$	733.994			1.51966
$484$	−430.973	−	220.268i	−0.890440	−	0.455100i
$485$			523.524i			1.07943i
$486$	3.26592	−	31.0054i	0.00671999	−	0.0637971i
$487$	797.217			1.63700			0.818498	−	0.574510i	$-0.194807\pi$
$487$	797.217			1.63700			0.818498	+	0.574510i	$0.194807\pi$
$488$	−387.928	−	126.338i	−0.794935	−	0.258889i
$489$	227.163			0.464546
$490$	96.1086	−	912.419i	0.196140	−	1.86208i
$491$	446.042			0.908436			0.454218	−	0.890891i	$-0.349919\pi$
$491$	446.042			0.908436			0.454218	+	0.890891i	$0.349919\pi$
$492$	−93.2447	−	19.8641i	−0.189522	−	0.0403741i
$493$		−	348.614i		−	0.707129i
$494$	510.436	+	53.7662i	1.03327	+	0.108838i
$495$	−159.006	−	20.9975i	−0.321224	−	0.0424192i
$496$	−287.357	−	128.253i	−0.579349	−	0.258574i
$497$		−	157.403i		−	0.316705i
$498$	22.0948	−	209.760i	0.0443671	−	0.421204i
$499$		−	536.083i		−	1.07432i	−0.843482	−	0.537158i	$-0.819498\pi$
$499$		−	536.083i		−	1.07432i	0.843482	−	0.537158i	$-0.180502\pi$
$500$	−106.849	+	501.564i	−0.213698	+	1.00313i
$501$	−361.842			−0.722240
$502$	37.8770	−	359.590i	0.0754523	−	0.716315i
$503$			955.799i			1.90020i	0.311950	+	0.950099i	$0.399018\pi$
$503$			955.799i			1.90020i	−0.311950	+	0.950099i	$0.600982\pi$
$504$	−88.9931	+	273.259i	−0.176574	+	0.542180i
$505$			397.934i			0.787989i
$506$	−182.226	+	756.951i	−0.360131	+	1.49595i
$507$		−	430.052i		−	0.848228i
$508$	74.0663	−	347.678i	0.145800	−	0.684405i
$509$			310.852i			0.610710i	0.952239	+	0.305355i	$0.0987752\pi$
$509$			310.852i			0.610710i	−0.952239	+	0.305355i	$0.901225\pi$
$510$	−46.4014	+	440.518i	−0.0909832	+	0.863760i
$511$	−571.907			−1.11919
$512$	300.099	+	414.831i	0.586130	+	0.810217i
$513$			65.2784i			0.127248i
$514$	452.565	+	47.6704i	0.880477	+	0.0927440i
$515$		−	857.980i		−	1.66598i
$516$	−33.3393	+	156.499i	−0.0646110	+	0.303293i
$517$	−91.7580	+	694.848i	−0.177482	+	1.34400i
$518$	−220.802	−	23.2579i	−0.426259	−	0.0448995i
$519$		−	118.979i		−	0.229247i
$520$	−245.955	+	755.219i	−0.472990	+	1.45234i
$521$	−677.923			−1.30120			−0.650598	−	0.759422i	$-0.725482\pi$
$521$	−677.923			−1.30120			−0.650598	+	0.759422i	$0.725482\pi$
$522$	79.0653	+	8.32825i	0.151466	+	0.0159545i
$523$	673.578			1.28791			0.643956	−	0.765062i	$-0.277292\pi$
$523$	673.578			1.28791			0.643956	+	0.765062i	$0.277292\pi$
$524$	18.9353	+	4.03382i	0.0361361	+	0.00769813i
$525$	−28.5903			−0.0544576
$526$	79.4677	−	754.436i	0.151079	−	1.43429i
$527$		−	517.443i		−	0.981866i
$528$	−259.712	−	159.618i	−0.491878	−	0.302306i
$529$	723.442			1.36756
$530$	−210.084	−	22.1290i	−0.396385	−	0.0417528i
$531$		−	200.613i		−	0.377801i
$532$	125.374	−	588.523i	0.235665	−	1.10625i
$533$		−	281.100i		−	0.527392i
$534$	9.16100	−	86.9711i	0.0171554	−	0.162867i
$535$			142.029i			0.265474i
$536$	−217.159	+	666.800i	−0.405147	+	1.24403i
$537$	171.204			0.318815
$538$	86.5258	−	821.443i	0.160829	−	1.52685i
$539$	−135.925	+	1029.31i	−0.252180	+	1.90966i
$540$	−98.8003	−	21.0476i	−0.182963	−	0.0389770i
$541$	140.980			0.260592			0.130296	−	0.991475i	$-0.458407\pi$
$541$	140.980			0.260592			0.130296	+	0.991475i	$0.458407\pi$
$542$	−62.2575	+	591.049i	−0.114866	+	1.09050i
$543$	137.211			0.252690
$544$	−421.782	+	728.635i	−0.775334	+	1.33940i
$545$		−	144.877i		−	0.265830i
$546$	−842.688	−	88.7636i	−1.54338	−	0.162571i
$547$	−116.001			−0.212067			−0.106033	−	0.994363i	$-0.533815\pi$
$547$	−116.001			−0.212067			−0.106033	+	0.994363i	$0.533815\pi$
$548$	−727.226	−	154.922i	−1.32705	−	0.282704i
$549$	152.993			0.278676
$550$	7.09802	−	29.4845i	0.0129055	−	0.0536082i
$551$	−166.463			−0.302111
$552$	−151.852	+	466.272i	−0.275095	+	0.844696i
$553$	469.945			0.849811
$554$	−168.782	−	17.7785i	−0.304661	−	0.0320911i
$555$		−	78.0424i		−	0.140617i
$556$	881.605	+	187.810i	1.58562	+	0.337787i
$557$	−300.194			−0.538947			−0.269474	−	0.963008i	$-0.586850\pi$
$557$	−300.194			−0.538947			−0.269474	+	0.963008i	$0.586850\pi$
$558$	117.355	+	12.3615i	0.210314	+	0.0221532i
$559$	−471.790			−0.843989
$560$	850.317	+	379.512i	1.51842	+	0.677700i
$561$	65.6249	−	496.952i	0.116978	−	0.885832i
$562$	−78.8584	+	748.651i	−0.140317	+	1.33212i
$563$	1050.47			1.86584			0.932920	−	0.360085i	$-0.117252\pi$
$563$	1050.47			1.86584			0.932920	+	0.360085i	$0.117252\pi$
$564$	−91.9767	+	431.752i	−0.163079	+	0.765517i
$565$			626.473i			1.10880i
$566$	−44.0973	−	4.64494i	−0.0779105	−	0.00820661i
$567$		−	107.769i		−	0.190070i
$568$	99.9905	+	32.5642i	0.176040	+	0.0573314i
$569$			354.672i			0.623326i	0.950193	+	0.311663i	$0.100886\pi$
$569$			354.672i			0.623326i	−0.950193	+	0.311663i	$0.899114\pi$
$570$	210.347	+	22.1567i	0.369030	+	0.0388713i
$571$	−752.067			−1.31711			−0.658553	−	0.752535i	$-0.728831\pi$
$571$	−752.067			−1.31711			−0.658553	+	0.752535i	$0.728831\pi$
$572$	300.752	−	847.008i	0.525789	−	1.48078i
$573$			325.896i			0.568754i
$574$	−327.739	−	34.5220i	−0.570974	−	0.0601429i
$575$	−48.7846			−0.0848429
$576$	−155.177	−	113.066i	−0.269405	−	0.196296i
$577$	652.998			1.13171			0.565856	−	0.824504i	$-0.308546\pi$
$577$	652.998			1.13171			0.565856	+	0.824504i	$0.308546\pi$
$578$	−801.957	−	84.4733i	−1.38747	−	0.146148i
$579$	−264.611			−0.457014
$580$	53.6723	−	251.946i	0.0925385	−	0.434389i
$581$		−	729.089i		−	1.25489i
$582$	39.0881	−	371.088i	0.0671618	−	0.637608i
$583$	236.998	+	31.2967i	0.406514	+	0.0536822i
$584$	118.319	−	363.306i	0.202601	−	0.622099i
$585$		−	297.848i		−	0.509141i
$586$	126.808	+	13.3572i	0.216396	+	0.0227938i
$587$			235.350i			0.400936i	0.979700	+	0.200468i	$0.0642463\pi$
$587$			235.350i			0.400936i	−0.979700	+	0.200468i	$0.935754\pi$
$588$	−136.249	+	639.572i	−0.231716	+	1.08771i
$589$	−247.079			−0.419489
$590$	−646.435	−	68.0915i	−1.09565	−	0.115409i
$591$		−	464.299i		−	0.785617i
$592$	60.4553	−	135.454i	0.102120	−	0.228807i
$593$			544.105i			0.917546i	0.888554	+	0.458773i	$0.151711\pi$
$593$			544.105i			0.917546i	−0.888554	+	0.458773i	$0.848289\pi$
$594$	111.140	+	26.7556i	0.187105	+	0.0450431i
$595$			1531.16i			2.57338i
$596$	−654.535	−	139.437i	−1.09821	−	0.233954i
$597$		−	544.919i		−	0.912762i
$598$	−1437.91	−	151.461i	−2.40453	−	0.253279i
$599$	15.9242			0.0265846			0.0132923	−	0.999912i	$-0.495769\pi$
$599$	15.9242			0.0265846			0.0132923	+	0.999912i	$0.495769\pi$
$600$	5.91489	−	18.1621i	0.00985816	−	0.0302701i
$601$		−	1122.93i		−	1.86843i	−0.356705	−	0.934217i	$-0.616100\pi$
$601$		−	1122.93i		−	1.86843i	0.356705	−	0.934217i	$-0.383900\pi$
$602$	−57.9408	+	550.068i	−0.0962472	+	0.913734i
$603$		−	262.977i		−	0.436114i
$604$	−168.033	+	788.769i	−0.278200	+	1.30591i
$605$	152.657	−	567.925i	0.252325	−	0.938719i
$606$	29.7112	−	282.067i	0.0490284	−	0.465457i
$607$		−	191.642i		−	0.315720i	−0.987462	−	0.157860i	$-0.949541\pi$
$607$		−	191.642i		−	0.315720i	0.987462	−	0.157860i	$-0.0504595\pi$
$608$	347.923	+	201.401i	0.572242	+	0.331251i
$609$	274.817			0.451260
$610$	51.9287	−	492.991i	0.0851290	−	0.808182i
$611$	−1301.58			−2.13024
$612$	65.7812	−	308.787i	0.107486	−	0.504553i
$613$	−830.770			−1.35525			−0.677626	−	0.735406i	$-0.736991\pi$
$613$	−830.770			−1.35525			−0.677626	+	0.735406i	$0.736991\pi$
$614$	−323.503	−	34.0758i	−0.526878	−	0.0554981i
$615$		−	115.839i		−	0.188356i
$616$	−950.606	−	454.673i	−1.54319	−	0.738106i
$617$	−708.354			−1.14806			−0.574031	−	0.818834i	$-0.694621\pi$
$617$	−708.354			−1.14806			−0.574031	+	0.818834i	$0.694621\pi$
$618$	−64.0598	+	608.160i	−0.103657	+	0.984078i
$619$		−	235.751i		−	0.380858i	−0.981701	−	0.190429i	$-0.939012\pi$
$619$		−	235.751i		−	0.380858i	0.981701	−	0.190429i	$-0.0609878\pi$
$620$	79.6650	−	373.959i	0.128492	−	0.603160i
$621$		−	183.891i		−	0.296121i
$622$	−232.671	−	24.5081i	−0.374069	−	0.0394021i
$623$		−	302.297i		−	0.485227i
$624$	230.727	−	516.957i	0.369755	−	0.828456i
$625$	−588.637			−0.941820
$626$	538.265	+	56.6976i	0.859849	+	0.0905712i
$627$	−237.294	−	31.3358i	−0.378459	−	0.0499774i
$628$	252.655	−	1186.00i	0.402318	−	1.88854i
$629$	243.911			0.387775
$630$	−347.266	−	36.5789i	−0.551216	−	0.0580617i
$631$	922.285			1.46162			0.730812	−	0.682579i	$-0.239142\pi$
$631$	922.285			1.46162			0.730812	+	0.682579i	$0.239142\pi$
$632$	−97.2247	+	298.534i	−0.153836	+	0.472365i
$633$			633.385i			1.00061i
$634$	6.83116	−	64.8525i	0.0107747	−	0.102291i
$635$	431.925			0.680197
$636$	147.261	+	31.3713i	0.231543	+	0.0493259i
$637$	−1928.08			−3.02682
$638$	−68.2281	+	283.413i	−0.106941	+	0.444221i
$639$	−39.4348			−0.0617133
$640$	−417.004	+	461.652i	−0.651569	+	0.721331i
$641$	−640.847			−0.999761			−0.499881	−	0.866094i	$-0.666623\pi$
$641$	−640.847			−0.999761			−0.499881	+	0.866094i	$0.666623\pi$
$642$	10.6044	−	100.674i	0.0165177	−	0.156813i
$643$		−	784.730i		−	1.22042i	−0.792240	−	0.610210i	$-0.791085\pi$
$643$		−	784.730i		−	1.22042i	0.792240	−	0.610210i	$-0.208915\pi$
$644$	−353.181	+	1657.88i	−0.548418	+	2.57435i
$645$	−194.421			−0.301428
$646$	−69.2476	+	657.410i	−0.107194	+	1.01766i
$647$	926.595			1.43214			0.716070	−	0.698028i	$-0.245939\pi$
$647$	926.595			1.43214			0.716070	+	0.698028i	$0.245939\pi$
$648$	68.4609	+	22.2959i	0.105650	+	0.0344072i
$649$	729.248	+	96.3008i	1.12365	+	0.148383i
$650$	56.0090	+	5.89964i	0.0861676	+	0.00907637i
$651$	407.907			0.626586
$652$	−109.306	+	513.096i	−0.167647	+	0.786958i
$653$		−	325.852i		−	0.499007i	−0.968374	−	0.249504i	$-0.919733\pi$
$653$		−	325.852i		−	0.499007i	0.968374	−	0.249504i	$-0.0802675\pi$
$654$	−10.8171	+	102.693i	−0.0165399	+	0.157023i
$655$			23.5236i			0.0359139i
$656$	89.7345	−	201.055i	0.136790	−	0.306487i
$657$			143.283i			0.218086i
$658$	−159.848	+	1517.53i	−0.242929	+	2.30628i
$659$	1131.91			1.71761			0.858805	−	0.512302i	$-0.171207\pi$
$659$	1131.91			1.71761			0.858805	+	0.512302i	$0.171207\pi$
$660$	123.938	−	349.046i	0.187784	−	0.528858i
$661$			681.797i			1.03146i	0.856750	+	0.515732i	$0.172480\pi$
$661$			681.797i			1.03146i	−0.856750	+	0.515732i	$0.827520\pi$
$662$	−94.3009	+	895.257i	−0.142448	+	1.35235i
$663$	930.882			1.40405
$664$	463.156	+	150.837i	0.697524	+	0.227165i
$665$	731.130			1.09944
$666$	−5.82692	+	55.3186i	−0.00874913	+	0.0830610i
$667$	468.931			0.703045
$668$	174.110	−	817.299i	0.260644	−	1.22350i
$669$			128.521i			0.192109i
$670$	−847.390	−	89.2589i	−1.26476	−	0.133222i
$671$	−73.4420	+	556.148i	−0.109452	+	0.828834i
$672$	−574.393	−	332.496i	−0.854751	−	0.494786i
$673$			357.156i			0.530692i	0.964153	+	0.265346i	$0.0854862\pi$
$673$			357.156i			0.530692i	−0.964153	+	0.265346i	$0.914514\pi$
$674$	−63.0525	+	598.596i	−0.0935497	+	0.888125i
$675$			7.16286i			0.0106116i
$676$	971.365	+	206.931i	1.43693	+	0.306111i
$677$	−824.839			−1.21837			−0.609187	−	0.793027i	$-0.708504\pi$
$677$	−824.839			−1.21837			−0.609187	+	0.793027i	$0.708504\pi$
$678$	46.7748	−	444.062i	0.0689893	−	0.654958i
$679$		−	1289.84i		−	1.89962i
$680$	−972.677	−	316.775i	−1.43041	−	0.465845i
$681$			232.039i			0.340733i
$682$	−101.270	+	420.666i	−0.148490	+	0.616812i
$683$			710.849i			1.04078i	0.853930	+	0.520388i	$0.174213\pi$
$683$			710.849i			1.04078i	−0.853930	+	0.520388i	$0.825787\pi$
$684$	−147.445	−	31.4105i	−0.215564	−	0.0459218i
$685$		−	903.443i		−	1.31889i
$686$	−113.861	+	1080.95i	−0.165978	+	1.57573i
$687$	−286.876			−0.417578
$688$	−337.446	−	150.608i	−0.490473	−	0.218907i
$689$			443.941i			0.644326i
$690$	−592.553	−	62.4159i	−0.858772	−	0.0904578i
$691$			237.467i			0.343657i	0.985127	+	0.171828i	$0.0549674\pi$
$691$			237.467i			0.343657i	−0.985127	+	0.171828i	$0.945033\pi$
$692$	268.740	+	57.2502i	0.388353	+	0.0827314i
$693$	391.753	+	51.7330i	0.565301	+	0.0746507i
$694$	−219.714	−	23.1433i	−0.316590	−	0.0333477i
$695$			1095.23i			1.57587i
$696$	−56.8556	+	174.579i	−0.0816891	+	0.250831i
$697$	362.040			0.519425
$698$	788.602	+	83.0665i	1.12980	+	0.119006i
$699$	−498.136			−0.712641
$700$	13.7570	−	64.5773i	0.0196528	−	0.0922533i
$701$	−516.111			−0.736250			−0.368125	−	0.929776i	$-0.620000\pi$
$701$	−516.111			−0.736250			−0.368125	+	0.929776i	$0.620000\pi$
$702$	−22.2384	+	211.123i	−0.0316786	+	0.300745i
$703$		−	116.467i		−	0.165672i
$704$	485.499	−	509.811i	0.689629	−	0.724163i
$705$	−536.371			−0.760810
$706$	136.843	+	14.4142i	0.193828	+	0.0204167i
$707$		−	980.416i		−	1.38673i
$708$	453.127	+	96.5303i	0.640010	+	0.136342i
$709$			160.225i			0.225988i	0.993596	+	0.112994i	$0.0360440\pi$
$709$			160.225i			0.225988i	−0.993596	+	0.112994i	$0.963956\pi$
$710$	−13.3849	+	127.071i	−0.0188519	+	0.178973i
$711$		−	117.738i		−	0.165595i
$712$	192.035	+	62.5406i	0.269712	+	0.0878380i
$713$	696.028			0.976196
$714$	114.322	−	1085.33i	0.160115	−	1.52007i
$715$	1082.71	+	142.977i	1.51428	+	0.199968i
$716$	−82.3794	+	386.701i	−0.115055	+	0.540085i
$717$	−212.164			−0.295906
$718$	60.6704	−	575.982i	0.0844992	−	0.802204i
$719$	−140.837			−0.195878			−0.0979392	−	0.995192i	$-0.531225\pi$
$719$	−140.837			−0.195878			−0.0979392	+	0.995192i	$0.531225\pi$
$720$	95.0809	−	213.034i	0.132057	−	0.295881i
$721$			2113.86i			2.93184i
$722$	−404.115	−	42.5670i	−0.559715	−	0.0589570i
$723$	−276.137			−0.381933
$724$	−66.0227	+	309.920i	−0.0911916	+	0.428066i
$725$	−18.2656			−0.0251940
$726$	−150.611	+	391.163i	−0.207453	+	0.538792i
$727$	525.474			0.722798			0.361399	−	0.932411i	$-0.382299\pi$
$727$	525.474			0.722798			0.361399	+	0.932411i	$0.382299\pi$
$728$	605.974	−	1860.68i	0.832382	−	2.55588i
$729$	−27.0000			−0.0370370
$730$	461.700	+	48.6327i	0.632466	+	0.0666201i
$731$		−	607.637i		−	0.831241i
$732$	−73.6170	+	345.569i	−0.100570	+	0.472088i
$733$	537.444			0.733211			0.366606	−	0.930376i	$-0.380520\pi$
$733$	537.444			0.733211			0.366606	+	0.930376i	$0.380520\pi$
$734$	−353.425	−	37.2276i	−0.481505	−	0.0507188i
$735$	−794.549			−1.08102
$736$	−980.109	−	567.351i	−1.33167	−	0.770857i
$737$	955.948	+	126.238i	1.29708	+	0.171286i
$738$	−8.64897	+	82.1101i	−0.0117195	+	0.111260i
$739$	1006.41			1.36186			0.680928	−	0.732350i	$-0.261577\pi$
$739$	1006.41			1.36186			0.680928	+	0.732350i	$0.261577\pi$
$740$	176.276	+	37.5522i	0.238210	+	0.0507463i
$741$		−	444.496i		−	0.599859i
$742$	517.598	+	54.5206i	0.697572	+	0.0734779i
$743$		−	556.837i		−	0.749445i	−0.927137	−	0.374722i	$-0.877738\pi$
$743$		−	556.837i		−	0.749445i	0.927137	−	0.374722i	$-0.122262\pi$
$744$	−84.3899	+	259.125i	−0.113427	+	0.348286i
$745$		−	813.138i		−	1.09146i
$746$	498.635	+	52.5231i	0.668411	+	0.0704063i
$747$	−182.662			−0.244528
$748$	1090.90	+	387.350i	1.45842	+	0.517848i
$749$		−	349.925i		−	0.467190i
$750$	441.670	+	46.5229i	0.588894	+	0.0620305i
$751$	−768.649			−1.02350			−0.511750	−	0.859134i	$-0.671003\pi$
$751$	−768.649			−1.02350			−0.511750	+	0.859134i	$0.671003\pi$
$752$	−930.948	−	415.498i	−1.23796	−	0.552524i
$753$	−313.137			−0.415853
$754$	−538.373	−	56.7090i	−0.714023	−	0.0752108i
$755$	−979.899			−1.29788
$756$	243.421	+	51.8562i	0.321985	+	0.0685929i
$757$			532.098i			0.702903i	0.936206	+	0.351452i	$0.114312\pi$
$757$			532.098i			0.702903i	−0.936206	+	0.351452i	$0.885688\pi$
$758$	−16.0324	+	152.206i	−0.0211509	+	0.200799i
$759$	668.464	+	88.2739i	0.880717	+	0.116303i
$760$	−151.260	+	464.453i	−0.199026	+	0.611122i
$761$		−	1136.37i		−	1.49326i	−0.665242	−	0.746628i	$-0.731672\pi$
$761$		−	1136.37i		−	1.49326i	0.665242	−	0.746628i	$-0.268328\pi$
$762$	−306.160	−	32.2491i	−0.401785	−	0.0423216i
$763$			356.944i			0.467816i
$764$	−736.107	−	156.814i	−0.963490	−	0.205254i
$765$	383.610			0.501451
$766$	−550.924	−	58.0310i	−0.719222	−	0.0757584i
$767$			1366.02i			1.78099i
$768$	330.053	−	296.097i	0.429756	−	0.385542i
$769$			874.120i			1.13670i	0.822788	+	0.568349i	$0.192418\pi$
$769$			874.120i			1.13670i	−0.822788	+	0.568349i	$0.807582\pi$
$770$	299.667	−	1244.79i	0.389178	−	1.61661i
$771$		−	394.101i		−	0.511156i
$772$	127.325	−	597.682i	0.164929	−	0.774199i
$773$			417.756i			0.540434i	0.962799	+	0.270217i	$0.0870955\pi$
$773$			417.756i			0.540434i	−0.962799	+	0.270217i	$0.912905\pi$
$774$	137.811	+	14.5162i	0.178051	+	0.0187548i
$775$	−27.1114			−0.0349825
$776$	819.374	+	266.848i	1.05589	+	0.343877i
$777$			192.278i			0.247462i
$778$	41.7217	−	396.090i	0.0536268	−	0.509113i
$779$		−	172.874i		−	0.221917i
$780$	672.754	+	143.318i	0.862505	+	0.183741i
$781$	18.9300	−	143.350i	0.0242382	−	0.183547i
$782$	195.072	−	1851.94i	0.249453	−	2.36821i
$783$		−	68.8513i		−	0.0879327i
$784$	−1379.05	−	615.495i	−1.75900	−	0.785071i
$785$	1473.39			1.87692
$786$	1.75636	−	16.6742i	0.00223455	−	0.0212140i
$787$	847.047			1.07630			0.538150	−	0.842849i	$-0.319124\pi$
$787$	847.047			1.07630			0.538150	+	0.842849i	$0.319124\pi$
$788$	1048.72	+	223.410i	1.33086	+	0.283516i
$789$	−656.976			−0.832669
$790$	−379.387	−	39.9623i	−0.480236	−	0.0505852i
$791$		−	1543.48i		−	1.95131i
$792$	−113.911	+	238.160i	−0.143828	+	0.300707i
$793$	−1041.77			−1.31370
$794$	68.2011	−	647.476i	0.0858957	−	0.815461i
$795$			182.945i			0.230119i
$796$	1230.82	+	262.203i	1.54625	+	0.329401i
$797$			847.736i			1.06366i	0.846852	+	0.531829i	$0.178495\pi$
$797$			847.736i			1.06366i	−0.846852	+	0.531829i	$0.821505\pi$
$798$	−518.245	−	54.5888i	−0.649430	−	0.0684070i
$799$		−	1676.35i		−	2.09807i
$800$	38.1768	+	22.0992i	0.0477210	+	0.0276241i
$801$	−75.7358			−0.0945516
$802$	−372.003	−	39.1845i	−0.463844	−	0.0488585i
$803$	−520.848	−	68.7805i	−0.648628	−	0.0856545i
$804$	593.990	+	126.538i	0.738793	+	0.157386i
$805$	−2059.61			−2.55853
$806$	−799.100	−	84.1723i	−0.991439	−	0.104432i
$807$	−715.326			−0.886402
$808$	622.813	+	202.833i	0.770808	+	0.251032i
$809$			0.607771i			0.000751262i	1.00000		0.000375631i	$0.000119567\pi$
$809$			0.607771i			0.000751262i	−1.00000		0.000375631i	$0.999880\pi$
$810$	−9.16428	+	87.0022i	−0.0113139	+	0.107410i
$811$	−146.430			−0.180554			−0.0902772	−	0.995917i	$-0.528775\pi$
$811$	−146.430			−0.180554			−0.0902772	+	0.995917i	$0.528775\pi$
$812$	−132.236	+	620.734i	−0.162852	+	0.764451i
$813$	514.695			0.633082
$814$	−198.292	−	47.7363i	−0.243602	−	0.0586441i
$815$	−637.427			−0.782119
$816$	665.809	+	297.162i	0.815942	+	0.364170i
$817$	−290.146			−0.355136
$818$	103.763	−	985.087i	0.126850	−	1.20426i
$819$			733.827i			0.896003i
$820$	261.648	+	55.7392i	0.319083	+	0.0679747i
$821$	−440.937			−0.537073			−0.268537	−	0.963269i	$-0.586540\pi$
$821$	−440.937			−0.537073			−0.268537	+	0.963269i	$0.586540\pi$
$822$	−67.4543	+	640.385i	−0.0820612	+	0.779058i
$823$	960.312			1.16684			0.583421	−	0.812170i	$-0.301714\pi$
$823$	960.312			1.16684			0.583421	+	0.812170i	$0.301714\pi$
$824$	−1342.84	−	437.326i	−1.62966	−	0.530735i
$825$	−26.0378	−	3.43841i	−0.0315609	−	0.00416777i
$826$	1592.66	+	167.761i	1.92816	+	0.203101i
$827$	215.542			0.260631			0.130316	−	0.991473i	$-0.458401\pi$
$827$	215.542			0.260631			0.130316	+	0.991473i	$0.458401\pi$
$828$	415.358	+	88.4843i	0.501640	+	0.106865i
$829$			745.907i			0.899767i	0.893087	+	0.449883i	$0.148534\pi$
$829$			745.907i			0.899767i	−0.893087	+	0.449883i	$0.851466\pi$
$830$	−61.9988	+	588.593i	−0.0746973	+	0.709148i
$831$			146.978i			0.176869i
$832$	1056.64	+	769.895i	1.27000	+	0.925354i
$833$		−	2483.25i		−	2.98110i
$834$	81.7738	−	776.330i	0.0980502	−	0.930851i
$835$	1015.34			1.21598
$836$	184.959	−	520.902i	0.221243	−	0.623089i
$837$		−	102.195i		−	0.122097i
$838$	−81.7924	+	776.506i	−0.0976043	+	0.926618i
$839$	−874.084			−1.04182			−0.520908	−	0.853613i	$-0.674407\pi$
$839$	−874.084			−1.04182			−0.520908	+	0.853613i	$0.674407\pi$
$840$	249.718	−	766.774i	0.297283	−	0.912826i
$841$	−665.426			−0.791232
$842$	−18.3324	+	174.041i	−0.0217725	+	0.206700i
$843$	651.938			0.773355
$844$	−1430.64	−	304.771i	−1.69507	−	0.361103i
$845$			1206.74i			1.42810i
$846$	380.195	+	40.0474i	0.449403	+	0.0473373i
$847$	−376.110	+	1399.23i	−0.444049	+	1.65199i
$848$	−141.718	+	317.526i	−0.167120	+	0.374442i
$849$			38.4007i			0.0452305i
$850$	−7.59838	+	72.1362i	−0.00893927	+	0.0848661i
$851$			328.091i			0.385536i
$852$	18.9752	−	89.0721i	0.0222713	−	0.104545i
$853$	1467.81			1.72076			0.860382	−	0.509650i	$-0.170225\pi$
$853$	1467.81			1.72076			0.860382	+	0.509650i	$0.170225\pi$
$854$	−127.940	+	1214.61i	−0.149813	+	1.42226i
$855$		−	183.174i		−	0.214238i
$856$	222.291	+	72.3943i	0.259686	+	0.0845728i
$857$		−	967.730i		−	1.12921i	−0.825362	−	0.564603i	$-0.809029\pi$
$857$		−	967.730i		−	1.12921i	0.825362	−	0.564603i	$-0.190971\pi$
$858$	−756.779	−	182.185i	−0.882027	−	0.212337i
$859$		−	481.940i		−	0.561047i	−0.959847	−	0.280524i	$-0.909492\pi$
$859$		−	481.940i		−	0.561047i	0.959847	−	0.280524i	$-0.0905081\pi$
$860$	93.5512	−	439.143i	0.108780	−	0.510631i
$861$			285.401i			0.331476i
$862$	−34.7533	+	329.935i	−0.0403171	+	0.382755i
$863$	−762.815			−0.883910			−0.441955	−	0.897037i	$-0.645715\pi$
$863$	−762.815			−0.883910			−0.441955	+	0.897037i	$0.645715\pi$
$864$	−83.3019	+	143.905i	−0.0964143	+	0.166557i
$865$			333.860i			0.385965i
$866$	−1271.63	−	133.945i	−1.46839	−	0.154671i
$867$			698.358i			0.805487i
$868$	−196.276	+	921.347i	−0.226124	+	1.06146i
$869$	427.989	+	56.5181i	0.492508	+	0.0650381i
$870$	−221.860	−	23.3694i	−0.255011	−	0.0268613i
$871$			1790.67i			2.05588i
$872$	−226.750	−	73.8463i	−0.260034	−	0.0846861i
$873$	−323.150			−0.370160
$874$	−884.302	−	93.1469i	−1.01179	−	0.106575i
$875$	1535.17			1.75448
$876$	−323.635	−	68.9444i	−0.369446	−	0.0787037i
$877$	1184.53			1.35066			0.675330	−	0.737515i	$-0.264001\pi$
$877$	1184.53			1.35066			0.675330	+	0.737515i	$0.264001\pi$
$878$	−50.7950	+	482.229i	−0.0578531	+	0.549236i
$879$		−	110.426i		−	0.125627i
$880$	728.760	+	447.893i	0.828137	+	0.508969i
$881$	−1031.60			−1.17094			−0.585471	−	0.810693i	$-0.699090\pi$
$881$	−1031.60			−1.17094			−0.585471	+	0.810693i	$0.699090\pi$
$882$	563.199	+	59.3239i	0.638547	+	0.0672607i
$883$		−	773.139i		−	0.875582i	−0.899077	−	0.437791i	$-0.855761\pi$
$883$		−	773.139i		−	0.875582i	0.899077	−	0.437791i	$-0.144239\pi$
$884$	−447.920	+	2102.60i	−0.506696	+	2.37851i
$885$			562.926i			0.636075i
$886$	147.572	−	1400.99i	0.166560	−	1.58126i
$887$		−	379.167i		−	0.427471i	−0.976892	−	0.213736i	$-0.931437\pi$
$887$		−	379.167i		−	0.427471i	0.976892	−	0.213736i	$-0.0685631\pi$
$888$	−122.145	−	39.7794i	−0.137551	−	0.0447967i
$889$	−1064.16			−1.19703
$890$	−25.7061	+	244.044i	−0.0288832	+	0.274207i
$891$	12.9609	−	98.1479i	0.0145465	−	0.110155i
$892$	−290.292	−	61.8413i	−0.325439	−	0.0693288i
$893$	−800.458			−0.896370
$894$	−60.7118	+	576.375i	−0.0679103	+	0.644715i
$895$	−480.404			−0.536764
$896$	1027.40	−	1137.40i	1.14665	−	1.26942i
$897$			1252.16i			1.39594i
$898$	1211.17	+	127.577i	1.34874	+	0.142068i
$899$	260.602			0.289880
$900$	−16.1789	−	3.44661i	−0.0179765	−	0.00382956i
$901$	−571.769			−0.634594
$902$	−294.327	−	70.8556i	−0.326305	−	0.0785538i
$903$	479.008			0.530463
$904$	980.503	+	319.324i	1.08463	+	0.353234i
$905$	−385.018			−0.425434
$906$	694.579	+	73.1628i	0.766644	+	0.0807536i
$907$		−	404.375i		−	0.445837i	−0.974837	−	0.222919i	$-0.928442\pi$
$907$		−	404.375i		−	0.445837i	0.974837	−	0.222919i	$-0.0715585\pi$
$908$	−524.110	−	111.652i	−0.577214	−	0.122965i
$909$	−245.629			−0.270218
$910$	2364.61	+	249.074i	2.59848	+	0.273708i
$911$	693.987			0.761786			0.380893	−	0.924619i	$-0.375617\pi$
$911$	693.987			0.761786			0.380893	+	0.924619i	$0.375617\pi$
$912$	141.895	−	317.923i	0.155587	−	0.348600i
$913$	87.6840	−	663.997i	0.0960394	−	0.727269i
$914$	−49.0617	+	465.773i	−0.0536780	+	0.509598i
$915$	−429.305			−0.469186
$916$	138.038	−	647.972i	0.150697	−	0.707393i
$917$		−	57.9567i		−	0.0632025i
$918$	−271.913	−	28.6417i	−0.296202	−	0.0312001i
$919$		−	166.808i		−	0.181511i	−0.995873	−	0.0907554i	$-0.971072\pi$
$919$		−	166.808i		−	0.181511i	0.995873	−	0.0907554i	$-0.0289281\pi$
$920$	426.103	−	1308.38i	0.463155	−	1.42215i
$921$			281.712i			0.305876i
$922$	−474.805	−	50.0131i	−0.514973	−	0.0542441i
$923$	268.521			0.290922
$924$	−305.353	+	859.967i	−0.330469	+	0.930701i
$925$		−	12.7797i		−	0.0138159i
$926$	−84.9049	−	8.94336i	−0.0916900	−	0.00965806i
$927$	529.596			0.571301
$928$	−366.966	−	212.424i	−0.395438	−	0.228905i
$929$	−1163.16			−1.25205			−0.626027	−	0.779802i	$-0.715320\pi$
$929$	−1163.16			−1.25205			−0.626027	+	0.779802i	$0.715320\pi$
$930$	−329.304	−	34.6868i	−0.354090	−	0.0372977i
$931$	−1185.75			−1.27363
$932$	239.692	−	1125.15i	0.257180	−	1.20724i
$933$			202.614i			0.217164i
$934$	126.600	−	1201.90i	0.135547	−	1.28683i
$935$	−184.146	+	1394.46i	−0.196947	+	1.49141i
$936$	−466.166	−	151.818i	−0.498041	−	0.162198i
$937$		−	1454.88i		−	1.55270i	−0.630301	−	0.776351i	$-0.717069\pi$
$937$		−	1454.88i		−	1.55270i	0.630301	−	0.776351i	$-0.282931\pi$
$938$	2087.77	+	219.913i	2.22577	+	0.234449i
$939$		−	468.730i		−	0.499180i
$940$	258.090	−	1211.51i	0.274564	−	1.28884i
$941$	−270.375			−0.287328			−0.143664	−	0.989627i	$-0.545888\pi$
$941$	−270.375			−0.287328			−0.143664	+	0.989627i	$0.545888\pi$
$942$	−1044.38	−	110.008i	−1.10868	−	0.116782i
$943$			486.990i			0.516426i
$944$	−436.069	+	977.037i	−0.461938	+	1.03500i
$945$			302.405i			0.320005i
$946$	−118.922	+	493.991i	−0.125710	+	0.522189i
$947$		−	362.572i		−	0.382864i	−0.981506	−	0.191432i	$-0.938687\pi$
$947$		−	362.572i		−	0.382864i	0.981506	−	0.191432i	$-0.0613131\pi$
$948$	265.936	+	56.6528i	0.280523	+	0.0597603i
$949$		−	975.645i		−	1.02808i
$950$	34.4450	+	3.62822i	0.0362579	+	0.00381918i
$951$	−56.4746			−0.0593844
$952$	2396.45	+	780.459i	2.51728	+	0.819809i
$953$		−	1341.52i		−	1.40768i	−0.710360	−	0.703839i	$-0.751468\pi$
$953$		−	1341.52i		−	1.40768i	0.710360	−	0.703839i	$-0.248532\pi$
$954$	13.6593	−	129.676i	0.0143179	−	0.135929i
$955$		−	914.476i		−	0.957566i
$956$	102.089	−	479.219i	0.106787	−	0.501276i
$957$	250.282	+	33.0510i	0.261528	+	0.0345360i
$958$	62.0036	−	588.639i	0.0647220	−	0.614446i
$959$			2225.87i			2.32103i
$960$	435.433	+	317.268i	0.453576	+	0.330488i
$961$	−574.192			−0.597494
$962$	39.6769	−	376.677i	0.0412441	−	0.391556i
$963$	−87.6685			−0.0910369
$964$	132.871	−	623.716i	0.137833	−	0.647009i
$965$	742.508			0.769439
$966$	1459.91	+	153.778i	1.51129	+	0.159191i
$967$		−	1394.99i		−	1.44259i	−0.692627	−	0.721296i	$-0.743547\pi$
$967$		−	1394.99i		−	1.44259i	0.692627	−	0.721296i	$-0.256453\pi$
$968$	−811.056	−	528.405i	−0.837868	−	0.545873i
$969$	572.484			0.590799
$970$	−109.683	+	1041.29i	−0.113075	+	1.07349i
$971$			827.553i			0.852269i	0.904660	+	0.426134i	$0.140125\pi$
$971$			827.553i			0.852269i	−0.904660	+	0.426134i	$0.859875\pi$
$972$	12.9918	−	60.9854i	0.0133660	−	0.0627421i
$973$		−	2698.39i		−	2.77327i
$974$	1585.66	+	167.024i	1.62799	+	0.171482i
$975$		−	48.7735i		−	0.0500241i
$976$	−745.119	−	332.560i	−0.763442	−	0.340738i
$977$	564.845			0.578142			0.289071	−	0.957308i	$-0.406654\pi$
$977$	564.845			0.578142			0.289071	+	0.957308i	$0.406654\pi$
$978$	451.826	+	47.5926i	0.461990	+	0.0486632i
$979$	36.3558	−	275.308i	0.0371356	−	0.281213i
$980$	382.319	−	1794.66i	0.390122	−	1.83129i
$981$	89.4269			0.0911589
$982$	887.176	+	93.4497i	0.903438	+	0.0951626i
$983$	−540.105			−0.549445			−0.274723	−	0.961524i	$-0.588586\pi$
$983$	−540.105			−0.549445			−0.274723	+	0.961524i	$0.588586\pi$
$984$	−181.302	−	59.0451i	−0.184250	−	0.0600052i
$985$			1302.84i			1.32268i
$986$	73.0377	−	693.393i	0.0740748	−	0.703238i
$987$	1321.49			1.33890
$988$	1003.99	+	213.881i	1.01618	+	0.216479i
$989$	817.350			0.826441
$990$	−311.863	−	75.0771i	−0.315013	−	0.0758355i
$991$	−1701.26			−1.71671			−0.858357	−	0.513053i	$-0.828514\pi$
$991$	−1701.26			−1.71671			−0.858357	+	0.513053i	$0.828514\pi$
$992$	−544.683	−	315.298i	−0.549075	−	0.317841i
$993$	779.604			0.785100
$994$	32.9772	−	313.073i	0.0331763	−	0.314963i
$995$			1529.06i			1.53675i
$996$	87.8929	−	412.582i	0.0882459	−	0.414239i
$997$	251.928			0.252686			0.126343	−	0.991987i	$-0.459676\pi$
$997$	251.928			0.252686			0.126343	+	0.991987i	$0.459676\pi$
$998$	112.314	−	1066.27i	0.112539	−	1.06840i
$999$	48.1724			0.0482206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.3.e.a.109.48	yes	48
4.3	odd	2		1056.3.e.a.241.42		48
8.3	odd	2		1056.3.e.a.241.8		48
8.5	even	2	inner	264.3.e.a.109.2	yes	48
11.10	odd	2	inner	264.3.e.a.109.1	✓	48
44.43	even	2		1056.3.e.a.241.41		48
88.21	odd	2	inner	264.3.e.a.109.47	yes	48
88.43	even	2		1056.3.e.a.241.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.3.e.a.109.1	✓	48	11.10	odd	2	inner
264.3.e.a.109.2	yes	48	8.5	even	2	inner
264.3.e.a.109.47	yes	48	88.21	odd	2	inner
264.3.e.a.109.48	yes	48	1.1	even	1	trivial
1056.3.e.a.241.7		48	88.43	even	2
1056.3.e.a.241.8		48	8.3	odd	2
1056.3.e.a.241.41		48	44.43	even	2
1056.3.e.a.241.42		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	264.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.98900 + 0.209509i) q^{2} -1.73205i q^{3} +(3.91221 + 0.833424i) q^{4} +4.86020i q^{5} +(0.362880 - 3.44504i) q^{6} -11.9744i q^{7} +(7.60677 + 2.47732i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.98900 + 0.209509i) q^{2} -1.73205i q^{3} +(3.91221 + 0.833424i) q^{4} +4.86020i q^{5} +(0.362880 - 3.44504i) q^{6} -11.9744i q^{7} +(7.60677 + 2.47732i) q^{8} -3.00000 q^{9} +(-1.01825 + 9.66691i) q^{10} +(1.44010 - 10.9053i) q^{11} +(1.44353 - 6.77615i) q^{12} +20.4277 q^{13} +(2.50874 - 23.8170i) q^{14} +8.41811 q^{15} +(14.6108 + 6.52106i) q^{16} +26.3096i q^{17} +(-5.96699 - 0.628526i) q^{18} +12.5628 q^{19} +(-4.05060 + 19.0141i) q^{20} -20.7402 q^{21} +(5.14912 - 21.3889i) q^{22} -35.3899 q^{23} +(4.29084 - 13.1753i) q^{24} +1.37849 q^{25} +(40.6306 + 4.27978i) q^{26} +5.19615i q^{27} +(9.97974 - 46.8463i) q^{28} -13.2504 q^{29} +(16.7436 + 1.76367i) q^{30} -19.6674 q^{31} +(27.6946 + 16.0315i) q^{32} +(-18.8886 - 2.49433i) q^{33} +(-5.51210 + 52.3298i) q^{34} +58.1978 q^{35} +(-11.7366 - 2.50027i) q^{36} -9.27077i q^{37} +(24.9874 + 2.63202i) q^{38} -35.3818i q^{39} +(-12.0403 + 36.9704i) q^{40} -13.7607i q^{41} +(-41.2522 - 4.34526i) q^{42} -23.0956 q^{43} +(14.7227 - 41.4637i) q^{44} -14.5806i q^{45} +(-70.3903 - 7.41448i) q^{46} -63.7164 q^{47} +(11.2948 - 25.3067i) q^{48} -94.3858 q^{49} +(2.74182 + 0.288806i) q^{50} +45.5696 q^{51} +(79.9175 + 17.0249i) q^{52} +21.7323i q^{53} +(-1.08864 + 10.3351i) q^{54} +(53.0020 + 6.99917i) q^{55} +(29.6644 - 91.0863i) q^{56} -21.7595i q^{57} +(-26.3551 - 2.77608i) q^{58} +66.8708i q^{59} +(32.9334 + 7.01585i) q^{60} -50.9978 q^{61} +(-39.1185 - 4.12050i) q^{62} +35.9231i q^{63} +(51.7258 + 37.6888i) q^{64} +99.2826i q^{65} +(-37.0467 - 8.91853i) q^{66} +87.6588i q^{67} +(-21.9271 + 102.929i) q^{68} +61.2970i q^{69} +(115.755 + 12.1930i) q^{70} +13.1449 q^{71} +(-22.8203 - 7.43196i) q^{72} -47.7609i q^{73} +(1.94231 - 18.4395i) q^{74} -2.38762i q^{75} +(49.1485 + 10.4702i) q^{76} +(-130.584 - 17.2443i) q^{77} +(7.41279 - 70.3743i) q^{78} +39.2459i q^{79} +(-31.6936 + 71.0114i) q^{80} +9.00000 q^{81} +(2.88299 - 27.3700i) q^{82} +60.8874 q^{83} +(-81.1402 - 17.2854i) q^{84} -127.870 q^{85} +(-45.9371 - 4.83873i) q^{86} +22.9504i q^{87} +(37.9705 - 79.3867i) q^{88} +25.2453 q^{89} +(3.05476 - 29.0007i) q^{90} -244.609i q^{91} +(-138.453 - 29.4948i) q^{92} +34.0650i q^{93} +(-126.732 - 13.3491i) q^{94} +61.0579i q^{95} +(27.7673 - 47.9685i) q^{96} +107.717 q^{97} +(-187.733 - 19.7746i) q^{98} +(-4.32030 + 32.7160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 12 * q^4 - 144 * q^9	\( 48 q - 12 q^{4} - 144 q^{9} + 24 q^{12} - 36 q^{14} + 68 q^{16} - 20 q^{20} - 44 q^{22} - 128 q^{23} - 240 q^{25} + 44 q^{26} + 48 q^{34} + 36 q^{36} + 128 q^{38} - 108 q^{42} + 100 q^{44} + 48 q^{48} - 336 q^{49} - 128 q^{55} + 92 q^{56} + 368 q^{58} - 36 q^{60} + 444 q^{64} - 96 q^{66} - 24 q^{70} + 512 q^{71} - 348 q^{78} - 692 q^{80} + 432 q^{81} - 320 q^{82} + 568 q^{86} + 244 q^{88} + 436 q^{92} - 32 q^{97}+O(q^{100}) \) 48 * q - 12 * q^4 - 144 * q^9 + 24 * q^12 - 36 * q^14 + 68 * q^16 - 20 * q^20 - 44 * q^22 - 128 * q^23 - 240 * q^25 + 44 * q^26 + 48 * q^34 + 36 * q^36 + 128 * q^38 - 108 * q^42 + 100 * q^44 + 48 * q^48 - 336 * q^49 - 128 * q^55 + 92 * q^56 + 368 * q^58 - 36 * q^60 + 444 * q^64 - 96 * q^66 - 24 * q^70 + 512 * q^71 - 348 * q^78 - 692 * q^80 + 432 * q^81 - 320 * q^82 + 568 * q^86 + 244 * q^88 + 436 * q^92 - 32 * q^97

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