LMFDB - Embedded newform 756.2.o.a.179.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(179,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.o (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.7
Character	$\chi$	$=$	756.179
Dual form			756.2.o.a.359.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20615 + 0.738385i) q^{2} +(0.909574 - 1.78120i) q^{4} +1.66943i q^{5} +(2.08401 + 1.63000i) q^{7} +(0.218133 + 2.82000i) q^{8} +O(q^{10})$	\(q+(-1.20615 + 0.738385i) q^{2} +(0.909574 - 1.78120i) q^{4} +1.66943i q^{5} +(2.08401 + 1.63000i) q^{7} +(0.218133 + 2.82000i) q^{8} +(-1.23268 - 2.01358i) q^{10} -5.54604 q^{11} +(-0.458226 + 0.793672i) q^{13} +(-3.71719 - 0.427218i) q^{14} +(-2.34535 - 3.24027i) q^{16} +(-0.105306 - 0.0607985i) q^{17} +(-6.59665 + 3.80857i) q^{19} +(2.97359 + 1.51847i) q^{20} +(6.68933 - 4.09511i) q^{22} +4.30652 q^{23} +2.21299 q^{25} +(-0.0333475 - 1.29563i) q^{26} +(4.79892 - 2.22943i) q^{28} +(0.684776 - 0.395356i) q^{29} +(-2.34362 + 1.35309i) q^{31} +(5.22140 + 2.17646i) q^{32} +(0.171907 - 0.00442463i) q^{34} +(-2.72118 + 3.47911i) q^{35} +(-4.12969 - 7.15284i) q^{37} +(5.14432 - 9.46456i) q^{38} +(-4.70781 + 0.364158i) q^{40} +(1.71368 + 0.989393i) q^{41} +(-10.5968 + 6.11808i) q^{43} +(-5.04453 + 9.87860i) q^{44} +(-5.19429 + 3.17987i) q^{46} +(-2.19575 + 3.80316i) q^{47} +(1.68619 + 6.79388i) q^{49} +(-2.66919 + 1.63404i) q^{50} +(0.996897 + 1.53810i) q^{52} +(2.75730 + 1.59193i) q^{53} -9.25874i q^{55} +(-4.14202 + 6.23247i) q^{56} +(-0.534015 + 0.982486i) q^{58} +(-4.32111 - 7.48439i) q^{59} +(-1.91723 + 3.32074i) q^{61} +(1.82764 - 3.36252i) q^{62} +(-7.90484 + 1.23027i) q^{64} +(-1.32498 - 0.764978i) q^{65} +(-1.40237 + 0.809658i) q^{67} +(-0.204078 + 0.132270i) q^{68} +(0.713212 - 6.20560i) q^{70} -10.7356 q^{71} +(-1.05389 + 1.82540i) q^{73} +(10.2626 + 5.57806i) q^{74} +(0.783696 + 15.2141i) q^{76} +(-11.5580 - 9.04005i) q^{77} +(9.47711 + 5.47161i) q^{79} +(5.40941 - 3.91540i) q^{80} +(-2.79750 + 0.0720033i) q^{82} +(0.658615 + 1.14075i) q^{83} +(0.101499 - 0.175801i) q^{85} +(8.26381 - 15.2038i) q^{86} +(-1.20977 - 15.6398i) q^{88} +(-8.14004 + 4.69966i) q^{89} +(-2.24863 + 0.907109i) q^{91} +(3.91710 - 7.67077i) q^{92} +(-0.159796 - 6.20847i) q^{94} +(-6.35816 - 11.0127i) q^{95} +(3.33897 + 5.78326i) q^{97} +(-7.05029 - 6.94935i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.20615	+	0.738385i	−0.852874	+	0.522117i
$2$	−1.20615	+	0.738385i	−0.852874	+	0.522117i
$3$		0			0
$3$		0			0
$4$	0.909574	−	1.78120i	0.454787	−	0.890600i
$5$			1.66943i			0.746593i	0.927712	+	0.373297i	$0.121773\pi$
$5$			1.66943i			0.746593i	−0.927712	+	0.373297i	$0.878227\pi$
$6$		0			0
$7$	2.08401	+	1.63000i	0.787681	+	0.616083i
$7$	2.08401	+	1.63000i	0.787681	+	0.616083i
$8$	0.218133	+	2.82000i	0.0771217	+	0.997022i
$9$		0			0
$10$	−1.23268	−	2.01358i	−0.389809	−	0.636750i
$11$	−5.54604			−1.67219			−0.836096	−	0.548583i	$-0.815168\pi$
$11$	−5.54604			−1.67219			−0.836096	+	0.548583i	$0.815168\pi$
$12$		0			0
$13$	−0.458226	+	0.793672i	−0.127089	+	0.220125i	−0.922548	−	0.385883i	$-0.873897\pi$
$13$	−0.458226	+	0.793672i	−0.127089	+	0.220125i	0.795458	+	0.606008i	$0.207230\pi$
$14$	−3.71719	−	0.427218i	−0.993460	−	0.114179i
$15$		0			0
$16$	−2.34535	−	3.24027i	−0.586337	−	0.810067i
$17$	−0.105306	−	0.0607985i	−0.0255405	−	0.0147458i	0.487175	−	0.873304i	$-0.338027\pi$
$17$	−0.105306	−	0.0607985i	−0.0255405	−	0.0147458i	−0.512716	+	0.858558i	$0.671361\pi$
$18$		0			0
$19$	−6.59665	+	3.80857i	−1.51337	+	0.873747i	−0.513497	+	0.858092i	$0.671650\pi$
$19$	−6.59665	+	3.80857i	−1.51337	+	0.873747i	−0.999877	+	0.0156555i	$0.995016\pi$
$20$	2.97359	+	1.51847i	0.664916	+	0.339541i
$21$		0			0
$22$	6.68933	−	4.09511i	1.42617	−	0.873081i
$23$	4.30652			0.897971			0.448985	−	0.893539i	$-0.351785\pi$
$23$	4.30652			0.897971			0.448985	+	0.893539i	$0.351785\pi$
$24$		0			0
$25$	2.21299			0.442599
$26$	−0.0333475	−	1.29563i	−0.00653999	−	0.254094i
$27$		0			0
$28$	4.79892	−	2.22943i	0.906911	−	0.421323i
$29$	0.684776	−	0.395356i	0.127160	−	0.0734157i	−0.435071	−	0.900396i	$-0.643277\pi$
$29$	0.684776	−	0.395356i	0.127160	−	0.0734157i	0.562231	+	0.826980i	$0.309943\pi$
$30$		0			0
$31$	−2.34362	+	1.35309i	−0.420926	+	0.243022i	−0.695474	−	0.718552i	$-0.744805\pi$
$31$	−2.34362	+	1.35309i	−0.420926	+	0.243022i	0.274547	+	0.961574i	$0.411472\pi$
$32$	5.22140	+	2.17646i	0.923022	+	0.384748i
$33$		0			0
$34$	0.171907	−	0.00442463i	0.0294818	−	0.000758817i
$35$	−2.72118	+	3.47911i	−0.459963	+	0.588077i
$36$		0			0
$37$	−4.12969	−	7.15284i	−0.678917	−	1.17592i	−0.975307	−	0.220852i	$-0.929116\pi$
$37$	−4.12969	−	7.15284i	−0.678917	−	1.17592i	0.296390	−	0.955067i	$-0.404217\pi$
$38$	5.14432	−	9.46456i	0.834519	−	1.53535i
$39$		0			0
$40$	−4.70781	+	0.364158i	−0.744370	+	0.0575785i
$41$	1.71368	+	0.989393i	0.267632	+	0.154517i	0.627811	−	0.778366i	$-0.283951\pi$
$41$	1.71368	+	0.989393i	0.267632	+	0.154517i	−0.360179	+	0.932883i	$0.617284\pi$
$42$		0			0
$43$	−10.5968	+	6.11808i	−1.61600	+	0.932998i	−0.628060	+	0.778165i	$0.716151\pi$
$43$	−10.5968	+	6.11808i	−1.61600	+	0.932998i	−0.987941	+	0.154834i	$0.950516\pi$
$44$	−5.04453	+	9.87860i	−0.760492	+	1.48926i
$45$		0			0
$46$	−5.19429	+	3.17987i	−0.765856	+	0.468846i
$47$	−2.19575	+	3.80316i	−0.320284	+	0.554747i	−0.980546	−	0.196287i	$-0.937112\pi$
$47$	−2.19575	+	3.80316i	−0.320284	+	0.554747i	0.660263	+	0.751035i	$0.270445\pi$
$48$		0			0
$49$	1.68619	+	6.79388i	0.240884	+	0.970554i
$50$	−2.66919	+	1.63404i	−0.377481	+	0.231088i
$51$		0			0
$52$	0.996897	+	1.53810i	0.138245	+	0.213296i
$53$	2.75730	+	1.59193i	0.378744	+	0.218668i	0.677272	−	0.735733i	$-0.263162\pi$
$53$	2.75730	+	1.59193i	0.378744	+	0.218668i	−0.298528	+	0.954401i	$0.596495\pi$
$54$		0			0
$55$		−	9.25874i		−	1.24845i
$56$	−4.14202	+	6.23247i	−0.553501	+	0.832849i
$57$		0			0
$58$	−0.534015	+	0.982486i	−0.0701196	+	0.129007i
$59$	−4.32111	−	7.48439i	−0.562561	−	0.974384i	−0.997272	−	0.0738142i	$-0.976483\pi$
$59$	−4.32111	−	7.48439i	−0.562561	−	0.974384i	0.434711	−	0.900570i	$-0.356851\pi$
$60$		0			0
$61$	−1.91723	+	3.32074i	−0.245477	+	0.425178i	−0.962265	−	0.272112i	$-0.912278\pi$
$61$	−1.91723	+	3.32074i	−0.245477	+	0.425178i	0.716789	+	0.697290i	$0.245611\pi$
$62$	1.82764	−	3.36252i	0.232111	−	0.427040i
$63$		0			0
$64$	−7.90484	+	1.23027i	−0.988104	+	0.153784i
$65$	−1.32498	−	0.764978i	−0.164344	−	0.0948839i
$66$		0			0
$67$	−1.40237	+	0.809658i	−0.171327	+	0.0989155i	−0.583211	−	0.812321i	$-0.698204\pi$
$67$	−1.40237	+	0.809658i	−0.171327	+	0.0989155i	0.411885	+	0.911236i	$0.364871\pi$
$68$	−0.204078	+	0.132270i	−0.0247481	+	0.0160402i
$69$		0			0
$70$	0.713212	−	6.20560i	0.0852452	−	0.741711i
$71$	−10.7356			−1.27408			−0.637041	−	0.770830i	$-0.719842\pi$
$71$	−10.7356			−1.27408			−0.637041	+	0.770830i	$0.719842\pi$
$72$		0			0
$73$	−1.05389	+	1.82540i	−0.123349	+	0.213647i	−0.921086	−	0.389358i	$-0.872697\pi$
$73$	−1.05389	+	1.82540i	−0.123349	+	0.213647i	0.797737	+	0.603005i	$0.206030\pi$
$74$	10.2626	+	5.57806i	1.19300	+	0.648436i
$75$		0			0
$76$	0.783696	+	15.2141i	0.0898960	+	1.74518i
$77$	−11.5580	−	9.04005i	−1.31716	−	1.03021i
$78$		0			0
$79$	9.47711	+	5.47161i	1.06626	+	0.615604i	0.927157	−	0.374674i	$-0.122245\pi$
$79$	9.47711	+	5.47161i	1.06626	+	0.615604i	0.139101	+	0.990278i	$0.455579\pi$
$80$	5.40941	−	3.91540i	0.604790	−	0.437755i
$81$		0			0
$82$	−2.79750	+	0.0720033i	−0.308932	+	0.00795143i
$83$	0.658615	+	1.14075i	0.0722924	+	0.125214i	0.899906	−	0.436085i	$-0.143635\pi$
$83$	0.658615	+	1.14075i	0.0722924	+	0.125214i	−0.827613	+	0.561299i	$0.810302\pi$
$84$		0			0
$85$	0.101499	−	0.175801i	0.0110091	−	0.0190683i
$86$	8.26381	−	15.2038i	0.891110	−	1.63947i
$87$		0			0
$88$	−1.20977	−	15.6398i	−0.128962	−	1.66721i
$89$	−8.14004	+	4.69966i	−0.862843	+	0.498163i	−0.864963	−	0.501835i	$-0.832658\pi$
$89$	−8.14004	+	4.69966i	−0.862843	+	0.498163i	0.00212043	+	0.999998i	$0.499325\pi$
$90$		0			0
$91$	−2.24863	+	0.907109i	−0.235721	+	0.0950908i
$92$	3.91710	−	7.67077i	0.408386	−	0.799733i
$93$		0			0
$94$	−0.159796	−	6.20847i	−0.0164817	−	0.640355i
$95$	−6.35816	−	11.0127i	−0.652334	−	1.12987i
$96$		0			0
$97$	3.33897	+	5.78326i	0.339021	+	0.587201i	0.984249	−	0.176789i	$-0.0565710\pi$
$97$	3.33897	+	5.78326i	0.339021	+	0.587201i	−0.645228	+	0.763990i	$0.723238\pi$
$98$	−7.05029	−	6.94935i	−0.712186	−	0.701990i
$99$		0			0
$100$	2.01288	−	3.94178i	0.201288	−	0.394178i
$101$			10.2793i			1.02283i	0.859333	+	0.511417i	$0.170879\pi$
$101$			10.2793i			1.02283i	−0.859333	+	0.511417i	$0.829121\pi$
$102$		0			0
$103$		−	10.5329i		−	1.03784i	−0.854824	−	0.518919i	$-0.826335\pi$
$103$		−	10.5329i		−	1.03784i	0.854824	−	0.518919i	$-0.173665\pi$
$104$	−2.33811	−	1.11907i	−0.229271	−	0.109734i
$105$		0			0
$106$	−4.50116	+	0.115853i	−0.437191	+	0.0112526i
$107$	2.93403	+	5.08188i	0.283643	+	0.491284i	0.972279	−	0.233823i	$-0.0751236\pi$
$107$	2.93403	+	5.08188i	0.283643	+	0.491284i	−0.688636	+	0.725107i	$0.741790\pi$
$108$		0			0
$109$	4.50624	−	7.80503i	0.431619	−	0.747586i	−0.565394	−	0.824821i	$-0.691276\pi$
$109$	4.50624	−	7.80503i	0.431619	−	0.747586i	0.997013	+	0.0772348i	$0.0246091\pi$
$110$	6.83651	+	11.1674i	0.651836	+	1.06477i
$111$		0			0
$112$	0.393915	−	10.5757i	0.0372215	−	0.999307i
$113$	−6.14559	−	3.54816i	−0.578129	−	0.333783i	0.182261	−	0.983250i	$-0.441659\pi$
$113$	−6.14559	−	3.54816i	−0.578129	−	0.333783i	−0.760389	+	0.649468i	$0.774992\pi$
$114$		0			0
$115$			7.18944i			0.670419i
$116$	−0.0813529	−	1.57933i	−0.00755343	−	0.146637i
$117$		0			0
$118$	10.7383	+	5.83661i	0.988536	+	0.537304i
$119$	−0.120357	−	0.298354i	−0.0110331	−	0.0273500i
$120$		0			0
$121$	19.7585			1.79623
$122$	−0.139527	−	5.42096i	−0.0126322	−	0.490790i
$123$		0			0
$124$	0.278427	+	5.40519i	0.0250035	+	0.485400i
$125$			12.0416i			1.07703i
$126$		0			0
$127$			6.84278i			0.607198i	0.952800	+	0.303599i	$0.0981884\pi$
$127$			6.84278i			0.607198i	−0.952800	+	0.303599i	$0.901812\pi$
$128$	8.62597	−	7.32070i	0.762435	−	0.647065i
$129$		0			0
$130$	2.16297	−	0.0556715i	0.189705	−	0.00488271i
$131$	19.9793			1.74560			0.872801	−	0.488076i	$-0.162301\pi$
$131$	19.9793			1.74560			0.872801	+	0.488076i	$0.162301\pi$
$132$		0			0
$133$	−19.9555	−	2.81544i	−1.73036	−	0.244130i
$134$	1.09362	−	2.01205i	0.0944745	−	0.173815i
$135$		0			0
$136$	0.148481	−	0.310226i	0.0127322	−	0.0266016i
$137$			1.59568i			0.136328i	0.997674	+	0.0681642i	$0.0217142\pi$
$137$			1.59568i			0.136328i	−0.997674	+	0.0681642i	$0.978286\pi$
$138$		0			0
$139$	−7.13703	−	4.12056i	−0.605355	−	0.349502i	0.165791	−	0.986161i	$-0.446982\pi$
$139$	−7.13703	−	4.12056i	−0.605355	−	0.349502i	−0.771145	+	0.636659i	$0.780316\pi$
$140$	3.72188	+	8.01148i	0.314557	+	0.677093i
$141$		0			0
$142$	12.9487	−	7.92702i	1.08663	−	0.665220i
$143$	2.54134	−	4.40173i	0.212518	−	0.368091i
$144$		0			0
$145$	0.660020	+	1.14319i	0.0548117	+	0.0949366i
$146$	−0.0766974	−	2.97988i	−0.00634752	−	0.246616i
$147$		0			0
$148$	−16.4969	+	0.849772i	−1.35604	+	0.0698508i
$149$			0.901183i			0.0738278i	0.999318	+	0.0369139i	$0.0117527\pi$
$149$			0.901183i			0.0738278i	−0.999318	+	0.0369139i	$0.988247\pi$
$150$		0			0
$151$			0.908327i			0.0739186i	0.999317	+	0.0369593i	$0.0117672\pi$
$151$			0.908327i			0.0739186i	−0.999317	+	0.0369593i	$0.988233\pi$
$152$	−12.1791	−	17.7718i	−0.987859	−	1.44148i
$153$		0			0
$154$	20.6157	+	2.36937i	1.66126	+	0.190929i
$155$	−2.25889	−	3.91252i	−0.181439	−	0.314261i
$156$		0			0
$157$	4.14443	+	7.17837i	0.330762	+	0.572896i	0.982661	−	0.185409i	$-0.0593611\pi$
$157$	4.14443	+	7.17837i	0.330762	+	0.572896i	−0.651900	+	0.758305i	$0.726028\pi$
$158$	−15.4709	+	0.398198i	−1.23080	+	0.0316789i
$159$		0			0
$160$	−3.63346	+	8.71678i	−0.287250	+	0.689122i
$161$	8.97482	+	7.01963i	0.707315	+	0.553225i
$162$		0			0
$163$	10.3387	−	5.96905i	0.809789	−	0.467532i	−0.0370935	−	0.999312i	$-0.511810\pi$
$163$	10.3387	−	5.96905i	0.809789	−	0.467532i	0.846883	+	0.531780i	$0.178477\pi$
$164$	3.32102	−	2.15248i	0.259328	−	0.168080i
$165$		0			0
$166$	−1.63670	−	0.889605i	−0.127033	−	0.0690467i
$167$	−12.2867	+	21.2811i	−0.950771	+	1.64678i	−0.207010	+	0.978339i	$0.566373\pi$
$167$	−12.2867	+	21.2811i	−0.950771	+	1.64678i	−0.743761	+	0.668445i	$0.766960\pi$
$168$		0			0
$169$	6.08006	+	10.5310i	0.467697	+	0.810074i
$170$	0.00738662	+	0.286988i	0.000566528	+	0.0220109i
$171$		0			0
$172$	1.25893	+	24.4399i	0.0959922	+	1.86353i
$173$	7.86421	+	4.54041i	0.597905	+	0.345201i	0.768217	−	0.640190i	$-0.221144\pi$
$173$	7.86421	+	4.54041i	0.597905	+	0.345201i	−0.170312	+	0.985390i	$0.554478\pi$
$174$		0			0
$175$	4.61190	+	3.60718i	0.348627	+	0.272677i
$176$	13.0074	+	17.9706i	0.980469	+	1.35459i
$177$		0			0
$178$	6.34792	−	11.6790i	0.475797	−	0.875375i
$179$	3.23833	−	5.60895i	0.242044	−	0.419233i	−0.719252	−	0.694749i	$-0.755515\pi$
$179$	3.23833	−	5.60895i	0.242044	−	0.419233i	0.961296	+	0.275516i	$0.0888488\pi$
$180$		0			0
$181$	10.1548			0.754801			0.377400	−	0.926050i	$-0.376818\pi$
$181$	10.1548			0.754801			0.377400	+	0.926050i	$0.376818\pi$
$182$	2.04238	−	2.75446i	0.151392	−	0.204174i
$183$		0			0
$184$	0.939394	+	12.1444i	0.0692530	+	0.895297i
$185$	11.9412	−	6.89424i	0.877933	−	0.506875i
$186$		0			0
$187$	0.584031	+	0.337191i	0.0427086	+	0.0246578i
$188$	4.77698	+	7.37033i	0.348397	+	0.537537i
$189$		0			0
$190$	15.8005	+	8.58810i	1.14629	+	0.623046i
$191$	3.00931	−	5.21228i	0.217746	−	0.377147i	−0.736372	−	0.676576i	$-0.763463\pi$
$191$	3.00931	−	5.21228i	0.217746	−	0.377147i	0.954119	+	0.299429i	$0.0967962\pi$
$192$		0			0
$193$	−7.59973	−	13.1631i	−0.547040	−	0.947502i	−0.998475	−	0.0551978i	$-0.982421\pi$
$193$	−7.59973	−	13.1631i	−0.547040	−	0.947502i	0.451435	−	0.892304i	$-0.350912\pi$
$194$	−8.29755	−	4.51001i	−0.595729	−	0.323800i
$195$		0			0
$196$	13.6350	+	3.17610i	0.973926	+	0.226864i
$197$		−	12.5929i		−	0.897208i	−0.893731	−	0.448604i	$-0.851921\pi$
$197$		−	12.5929i		−	0.897208i	0.893731	−	0.448604i	$-0.148079\pi$
$198$		0			0
$199$	4.98014	+	2.87528i	0.353033	+	0.203824i	0.666020	−	0.745934i	$-0.267996\pi$
$199$	4.98014	+	2.87528i	0.353033	+	0.203824i	−0.312987	+	0.949757i	$0.601330\pi$
$200$	0.482727	+	6.24065i	0.0341340	+	0.441281i
$201$		0			0
$202$	−7.59012	−	12.3984i	−0.534039	−	0.872348i
$203$	2.07151	+	0.292262i	0.145392	+	0.0205128i
$204$		0			0
$205$	−1.65172	+	2.86087i	−0.115361	+	0.199812i
$206$	7.77734	+	12.7042i	0.541873	+	0.885144i
$207$		0			0
$208$	3.64641	−	0.376660i	0.252833	−	0.0261167i
$209$	36.5852	−	21.1225i	2.53065	−	1.46107i
$210$		0			0
$211$	10.7631	+	6.21407i	0.740961	+	0.427794i	0.822419	−	0.568883i	$-0.192624\pi$
$211$	10.7631	+	6.21407i	0.740961	+	0.427794i	−0.0814576	+	0.996677i	$0.525958\pi$
$212$	5.34351	−	3.46333i	0.366994	−	0.237862i
$213$		0			0
$214$	−7.29125	−	3.96305i	−0.498420	−	0.270909i
$215$	−10.2137	−	17.6907i	−0.696570	−	1.20650i
$216$		0			0
$217$	−7.08966	−	1.00025i	−0.481278	−	0.0679017i
$218$	0.327942	+	12.7413i	0.0222111	+	0.862952i
$219$		0			0
$220$	−16.4917	−	8.42151i	−1.11187	−	0.567778i
$221$	0.0965081	−	0.0557190i	0.00649184	−	0.00374806i
$222$		0			0
$223$	6.62650	−	3.82581i	0.443743	−	0.256195i	−0.261441	−	0.965219i	$-0.584198\pi$
$223$	6.62650	−	3.82581i	0.443743	−	0.256195i	0.705184	+	0.709024i	$0.250864\pi$
$224$	7.33380	+	13.0467i	0.490010	+	0.871717i
$225$		0			0
$226$	10.0324	−	0.258218i	0.667344	−	0.0171764i
$227$	21.7901			1.44626			0.723130	−	0.690712i	$-0.242703\pi$
$227$	21.7901			1.44626			0.723130	+	0.690712i	$0.242703\pi$
$228$		0			0
$229$	25.6867			1.69742			0.848711	−	0.528856i	$-0.177379\pi$
$229$	25.6867			1.69742			0.848711	+	0.528856i	$0.177379\pi$
$230$	−5.30858	−	8.67151i	−0.350037	−	0.571783i
$231$		0			0
$232$	1.26428	+	1.84483i	0.0830039	+	0.121119i
$233$	1.90679	−	1.10089i	0.124918	−	0.0721214i	−0.436239	−	0.899831i	$-0.643690\pi$
$233$	1.90679	−	1.10089i	0.124918	−	0.0721214i	0.561157	+	0.827709i	$0.310356\pi$
$234$		0			0
$235$	−6.34911	−	3.66566i	−0.414171	−	0.239121i
$236$	−17.2616	+	0.889161i	−1.12363	+	0.0578795i
$237$		0			0
$238$	0.365468	+	0.270988i	0.0236898	+	0.0175655i
$239$	2.99588	−	5.18902i	0.193787	−	0.335650i	−0.752715	−	0.658347i	$-0.771256\pi$
$239$	2.99588	−	5.18902i	0.193787	−	0.335650i	0.946502	+	0.322697i	$0.104589\pi$
$240$		0			0
$241$	11.0436			0.711383			0.355692	−	0.934603i	$-0.384245\pi$
$241$	11.0436			0.711383			0.355692	+	0.934603i	$0.384245\pi$
$242$	−23.8316	+	14.5894i	−1.53196	+	0.937842i
$243$		0			0
$244$	4.17105	+	6.43544i	0.267024	+	0.411987i
$245$	−11.3419	+	2.81498i	−0.724609	+	0.179842i
$246$		0			0
$247$		−	6.98076i		−	0.444175i
$248$	−4.32694	−	6.31386i	−0.274761	−	0.400931i
$249$		0			0
$250$	−8.89135	−	14.5239i	−0.562338	−	0.918574i
$251$	17.4191			1.09948			0.549742	−	0.835335i	$-0.314726\pi$
$251$	17.4191			1.09948			0.549742	+	0.835335i	$0.314726\pi$
$252$		0			0
$253$	−23.8841			−1.50158
$254$	−5.05261	−	8.25339i	−0.317029	−	0.517864i
$255$		0			0
$256$	−4.99868	+	15.1991i	−0.312417	+	0.949945i
$257$			11.0155i			0.687130i	0.939129	+	0.343565i	$0.111635\pi$
$257$			11.0155i			0.687130i	−0.939129	+	0.343565i	$0.888365\pi$
$258$		0			0
$259$	3.05282	−	21.6380i	0.189693	−	1.34452i
$260$	−2.56775	+	1.66425i	−0.159245	+	0.103213i
$261$		0			0
$262$	−24.0980	+	14.7524i	−1.48878	+	0.911409i
$263$	−5.42263			−0.334374			−0.167187	−	0.985925i	$-0.553468\pi$
$263$	−5.42263			−0.334374			−0.167187	+	0.985925i	$0.553468\pi$
$264$		0			0
$265$	−2.65762	+	4.60313i	−0.163256	+	0.282768i
$266$	26.1481	−	11.3390i	1.60324	−	0.695238i
$267$		0			0
$268$	0.166604	+	3.23434i	0.0101770	+	0.197569i
$269$	−13.3178	−	7.68901i	−0.811998	−	0.468807i	0.0356515	−	0.999364i	$-0.488649\pi$
$269$	−13.3178	−	7.68901i	−0.811998	−	0.468807i	−0.847649	+	0.530557i	$0.821983\pi$
$270$		0			0
$271$	−9.75508	+	5.63210i	−0.592579	+	0.342126i	−0.766117	−	0.642702i	$-0.777814\pi$
$271$	−9.75508	+	5.63210i	−0.592579	+	0.342126i	0.173538	+	0.984827i	$0.444480\pi$
$272$	0.0499761	+	0.483814i	0.00303025	+	0.0293355i
$273$		0			0
$274$	−1.17823	−	1.92463i	−0.0711794	−	0.116271i
$275$	−12.2733			−0.740110
$276$		0			0
$277$	−29.4820			−1.77140			−0.885701	−	0.464256i	$-0.846322\pi$
$277$	−29.4820			−1.77140			−0.885701	+	0.464256i	$0.846322\pi$
$278$	11.6509	−	0.299875i	0.698772	−	0.0179853i
$279$		0			0
$280$	−10.4047	−	6.91482i	−0.621799	−	0.413240i
$281$	−9.71995	+	5.61182i	−0.579844	+	0.334773i	−0.761071	−	0.648668i	$-0.775326\pi$
$281$	−9.71995	+	5.61182i	−0.579844	+	0.334773i	0.181228	+	0.983441i	$0.441993\pi$
$282$		0			0
$283$	12.8559	−	7.42238i	0.764206	−	0.441215i	−0.0665979	−	0.997780i	$-0.521214\pi$
$283$	12.8559	−	7.42238i	0.764206	−	0.441215i	0.830804	+	0.556565i	$0.187881\pi$
$284$	−9.76483	+	19.1223i	−0.579436	+	1.13470i
$285$		0			0
$286$	0.184947	+	7.18562i	0.0109361	+	0.424894i
$287$	1.95861	+	4.85520i	0.115613	+	0.286594i
$288$		0			0
$289$	−8.49261	−	14.7096i	−0.499565	−	0.865272i
$290$	−1.64019	−	0.891503i	−0.0963155	−	0.0523508i
$291$		0			0
$292$	2.29281	+	3.53753i	0.134176	+	0.207018i
$293$	15.3131	+	8.84101i	0.894600	+	0.516497i	0.875444	−	0.483319i	$-0.160569\pi$
$293$	15.3131	+	8.84101i	0.894600	+	0.516497i	0.0191554	+	0.999817i	$0.493902\pi$
$294$		0			0
$295$	12.4947	−	7.21381i	0.727469	−	0.420004i
$296$	19.2702	−	13.2060i	1.12006	−	0.767584i
$297$		0			0
$298$	−0.665420	−	1.08696i	−0.0385467	−	0.0629658i
$299$	−1.97336	+	3.41796i	−0.114122	+	0.197666i
$300$		0			0
$301$	−32.0564	−	4.52271i	−1.84770	−	0.260685i
$302$	−0.670695	−	1.09557i	−0.0385942	−	0.0630432i
$303$		0			0
$304$	27.8122	+	12.4425i	1.59514	+	0.713624i
$305$	−5.54376	−	3.20069i	−0.317435	−	0.183271i
$306$		0			0
$307$			11.5845i			0.661160i	0.943778	+	0.330580i	$0.107244\pi$
$307$			11.5845i			0.661160i	−0.943778	+	0.330580i	$0.892756\pi$
$308$	−26.6150	+	12.3645i	−1.51653	+	0.704533i
$309$		0			0
$310$	5.61350	+	3.05113i	0.318825	+	0.173293i
$311$	14.4129	+	24.9639i	0.817283	+	1.41558i	0.907677	+	0.419669i	$0.137854\pi$
$311$	14.4129	+	24.9639i	0.817283	+	1.41558i	−0.0903946	+	0.995906i	$0.528813\pi$
$312$		0			0
$313$	−10.2999	+	17.8399i	−0.582182	+	1.00837i	0.413038	+	0.910714i	$0.364468\pi$
$313$	−10.2999	+	17.8399i	−0.582182	+	1.00837i	−0.995220	+	0.0976556i	$0.968866\pi$
$314$	−10.2992	−	5.59797i	−0.581217	−	0.315912i
$315$		0			0
$316$	18.3662	−	11.9038i	1.03318	−	0.669640i
$317$	−23.0260	−	13.2941i	−1.29327	−	0.746669i	−0.314036	−	0.949411i	$-0.601681\pi$
$317$	−23.0260	−	13.2941i	−1.29327	−	0.746669i	−0.979232	+	0.202742i	$0.935015\pi$
$318$		0			0
$319$	−3.79780	+	2.19266i	−0.212636	+	0.122765i
$320$	−2.05386	−	13.1966i	−0.114814	−	0.737712i
$321$		0			0
$322$	−16.0081	−	1.83982i	−0.892098	−	0.102529i
$323$	0.926223			0.0515364
$324$		0			0
$325$	−1.01405	+	1.75639i	−0.0562495	+	0.0974270i
$326$	−8.06251	+	14.8335i	−0.446541	+	0.821551i
$327$		0			0
$328$	−2.41628	+	5.04840i	−0.133417	+	0.278751i
$329$	−10.7751	+	4.34673i	−0.594052	+	0.239643i
$330$		0			0
$331$	3.46649	+	2.00138i	0.190536	+	0.110006i	0.592233	−	0.805767i	$-0.298246\pi$
$331$	3.46649	+	2.00138i	0.190536	+	0.110006i	−0.401698	+	0.915772i	$0.631580\pi$
$332$	2.63097	−	0.135524i	0.144393	−	0.00743785i
$333$		0			0
$334$	−0.894166	−	34.7405i	−0.0489266	−	1.90091i
$335$	−1.35167	−	2.34116i	−0.0738496	−	0.127911i
$336$		0			0
$337$	−5.34969	+	9.26594i	−0.291416	+	0.504748i	−0.974145	−	0.225924i	$-0.927460\pi$
$337$	−5.34969	+	9.26594i	−0.291416	+	0.504748i	0.682729	+	0.730672i	$0.260793\pi$
$338$	−15.1093	−	8.21246i	−0.821840	−	0.446699i
$339$		0			0
$340$	−0.220817	−	0.340695i	−0.0119755	−	0.0184768i
$341$	12.9978	−	7.50428i	0.703870	−	0.406380i
$342$		0			0
$343$	−7.56001	+	16.9070i	−0.408202	+	0.912892i
$344$	−19.5645	−	28.5485i	−1.05485	−	1.53923i
$345$		0			0
$346$	−12.8380	+	0.330429i	−0.690173	+	0.0177640i
$347$	−10.9056	−	18.8890i	−0.585442	−	1.01401i	−0.994820	−	0.101650i	$-0.967588\pi$
$347$	−10.9056	−	18.8890i	−0.585442	−	1.01401i	0.409379	−	0.912365i	$-0.365745\pi$
$348$		0			0
$349$	−8.16332	−	14.1393i	−0.436972	−	0.756859i	0.560482	−	0.828167i	$-0.310616\pi$
$349$	−8.16332	−	14.1393i	−0.436972	−	0.756859i	−0.997454	+	0.0713082i	$0.977283\pi$
$350$	−8.22611	−	0.945431i	−0.439704	−	0.0505354i
$351$		0			0
$352$	−28.9581	−	12.0707i	−1.54347	−	0.643373i
$353$		−	25.7140i		−	1.36862i	−0.729192	−	0.684309i	$-0.760104\pi$
$353$		−	25.7140i		−	1.36862i	0.729192	−	0.684309i	$-0.239896\pi$
$354$		0			0
$355$		−	17.9224i		−	0.951221i
$356$	0.967054	+	18.7737i	0.0512538	+	0.995006i
$357$		0			0
$358$	0.235670	+	9.15634i	0.0124556	+	0.483928i
$359$	4.17336	+	7.22847i	0.220261	+	0.381504i	0.954887	−	0.296969i	$-0.0959757\pi$
$359$	4.17336	+	7.22847i	0.220261	+	0.381504i	−0.734626	+	0.678472i	$0.762642\pi$
$360$		0			0
$361$	19.5105	−	33.7932i	1.02687	−	1.77859i
$362$	−12.2482	+	7.49816i	−0.643750	+	0.394095i
$363$		0			0
$364$	−0.429558	+	4.83035i	−0.0225150	+	0.253179i
$365$	−3.04738	−	1.75941i	−0.159507	−	0.0920915i
$366$		0			0
$367$		−	22.3287i		−	1.16555i	−0.812635	−	0.582773i	$-0.801967\pi$
$367$		−	22.3287i		−	1.16555i	0.812635	−	0.582773i	$-0.198033\pi$
$368$	−10.1003	−	13.9543i	−0.526514	−	0.727417i
$369$		0			0
$370$	−9.31219	+	17.1327i	−0.484118	+	0.890684i
$371$	3.15139	+	7.81200i	0.163612	+	0.405579i
$372$		0			0
$373$	16.1626			0.836869			0.418434	−	0.908247i	$-0.362579\pi$
$373$	16.1626			0.836869			0.418434	+	0.908247i	$0.362579\pi$
$374$	−0.953403	+	0.0245391i	−0.0492993	+	0.00126889i
$375$		0			0
$376$	−11.2039	−	5.36244i	−0.577796	−	0.276547i
$377$			0.724650i			0.0373214i
$378$		0			0
$379$			0.319037i			0.0163878i	0.999966	+	0.00819391i	$0.00260823\pi$
$379$			0.319037i			0.0163878i	−0.999966	+	0.00819391i	$0.997392\pi$
$380$	−25.3990	+	1.30833i	−1.30294	+	0.0671158i
$381$		0			0
$382$	0.219003	+	8.50880i	0.0112052	+	0.435348i
$383$	10.9844			0.561276			0.280638	−	0.959814i	$-0.409454\pi$
$383$	10.9844			0.561276			0.280638	+	0.959814i	$0.409454\pi$
$384$		0			0
$385$	15.0918	−	19.2953i	0.769147	−	0.983379i
$386$	18.8858	+	10.2651i	0.961263	+	0.522480i
$387$		0			0
$388$	13.3382	−	0.687063i	0.677143	−	0.0348804i
$389$			12.9501i			0.656596i	0.944574	+	0.328298i	$0.106475\pi$
$389$			12.9501i			0.656596i	−0.944574	+	0.328298i	$0.893525\pi$
$390$		0			0
$391$	−0.453502	−	0.261830i	−0.0229346	−	0.0132413i
$392$	−18.7909	+	6.23702i	−0.949086	+	0.315017i
$393$		0			0
$394$	9.29842	+	15.1889i	0.468448	+	0.765205i
$395$	−9.13449	+	15.8214i	−0.459606	+	0.796061i
$396$		0			0
$397$	10.3112	+	17.8595i	0.517504	+	0.896343i	0.999793	+	0.0203308i	$0.00647195\pi$
$397$	10.3112	+	17.8595i	0.517504	+	0.896343i	−0.482290	+	0.876012i	$0.660195\pi$
$398$	−8.12984	+	0.209250i	−0.407512	+	0.0104887i
$399$		0			0
$400$	−5.19024	−	7.17069i	−0.259512	−	0.358535i
$401$		−	13.6049i		−	0.679396i	−0.940535	−	0.339698i	$-0.889675\pi$
$401$		−	13.6049i		−	0.679396i	0.940535	−	0.339698i	$-0.110325\pi$
$402$		0			0
$403$		−	2.48009i		−	0.123542i
$404$	18.3096	+	9.34983i	0.910936	+	0.465171i
$405$		0			0
$406$	−2.71435	+	1.17706i	−0.134711	+	0.0584167i
$407$	22.9034	+	39.6699i	1.13528	+	1.96636i
$408$		0			0
$409$	0.130776	+	0.226511i	0.00646648	+	0.0112003i	0.869241	−	0.494389i	$-0.164608\pi$
$409$	0.130776	+	0.226511i	0.00646648	+	0.0112003i	−0.862774	+	0.505590i	$0.831275\pi$
$410$	−0.120205	−	4.67024i	−0.00593649	−	0.230647i
$411$		0			0
$412$	−18.7612	−	9.58045i	−0.924298	−	0.471995i
$413$	3.19433	−	22.6410i	0.157183	−	1.11409i
$414$		0			0
$415$	−1.90441	+	1.09951i	−0.0934840	+	0.0539730i
$416$	−4.11998	+	3.14676i	−0.201999	+	0.154283i
$417$		0			0
$418$	−28.5306	+	52.4908i	−1.39548	+	2.56741i
$419$	0.252372	−	0.437122i	0.0123292	−	0.0213548i	−0.859795	−	0.510639i	$-0.829409\pi$
$419$	0.252372	−	0.437122i	0.0123292	−	0.0213548i	0.872124	+	0.489285i	$0.162742\pi$
$420$		0			0
$421$	0.908510	+	1.57359i	0.0442781	+	0.0766919i	0.887315	−	0.461164i	$-0.152568\pi$
$421$	0.908510	+	1.57359i	0.0442781	+	0.0766919i	−0.843037	+	0.537856i	$0.819235\pi$
$422$	−17.5702	+	0.452230i	−0.855305	+	0.0220142i
$423$		0			0
$424$	−3.88778	+	8.12285i	−0.188807	+	0.394480i
$425$	−0.233042	−	0.134547i	−0.0113042	−	0.00652647i
$426$		0			0
$427$	−9.40835	+	3.79537i	−0.455302	+	0.183671i
$428$	11.7206	−	0.603739i	0.566535	−	0.0291828i
$429$		0			0
$430$	25.3818	+	13.7959i	1.22402	+	0.665297i
$431$	1.15815	−	2.00597i	0.0557860	−	0.0966241i	−0.836784	−	0.547533i	$-0.815567\pi$
$431$	1.15815	−	2.00597i	0.0557860	−	0.0966241i	0.892570	+	0.450909i	$0.148900\pi$
$432$		0			0
$433$	15.5029			0.745021			0.372510	−	0.928028i	$-0.378497\pi$
$433$	15.5029			0.745021			0.372510	+	0.928028i	$0.378497\pi$
$434$	9.28974	−	4.02845i	0.445922	−	0.193372i
$435$		0			0
$436$	−9.80356	−	15.1258i	−0.469506	−	0.724393i
$437$	−28.4086	+	16.4017i	−1.35897	+	0.784599i
$438$		0			0
$439$	11.5921	+	6.69270i	0.553260	+	0.319425i	0.750436	−	0.660943i	$-0.229844\pi$
$439$	11.5921	+	6.69270i	0.553260	+	0.319425i	−0.197176	+	0.980368i	$0.563177\pi$
$440$	26.1097	−	2.01964i	1.24473	−	0.0962824i
$441$		0			0
$442$	−0.0752607	+	0.138465i	−0.00357979	+	0.00658612i
$443$	14.5734	−	25.2418i	0.692401	−	1.19927i	−0.278648	−	0.960393i	$-0.589886\pi$
$443$	14.5734	−	25.2418i	0.692401	−	1.19927i	0.971049	−	0.238880i	$-0.0767803\pi$
$444$		0			0
$445$	−7.84576	−	13.5893i	−0.371925	−	0.644193i
$446$	−5.16760	+	9.50739i	−0.244693	+	0.450188i
$447$		0			0
$448$	−18.4791	−	10.3210i	−0.873055	−	0.487621i
$449$			7.62756i			0.359967i	0.983670	+	0.179984i	$0.0576044\pi$
$449$			7.62756i			0.359967i	−0.983670	+	0.179984i	$0.942396\pi$
$450$		0			0
$451$	−9.50412	−	5.48721i	−0.447532	−	0.258383i
$452$	−11.9099	+	7.71921i	−0.560192	+	0.363081i
$453$		0			0
$454$	−26.2820	+	16.0895i	−1.23348	+	0.755117i
$455$	−1.51436	−	3.75394i	−0.0709941	−	0.175988i
$456$		0			0
$457$	1.26464	−	2.19042i	0.0591574	−	0.102464i	−0.834930	−	0.550356i	$-0.814492\pi$
$457$	1.26464	−	2.19042i	0.0591574	−	0.102464i	0.894087	+	0.447892i	$0.147825\pi$
$458$	−30.9819	+	18.9667i	−1.44769	+	0.886254i
$459$		0			0
$460$	12.8058	+	6.53933i	0.597075	+	0.304898i
$461$	−28.7899	+	16.6219i	−1.34088	+	0.774158i	−0.986937	−	0.161108i	$-0.948493\pi$
$461$	−28.7899	+	16.6219i	−1.34088	+	0.774158i	−0.353945	+	0.935266i	$0.615160\pi$
$462$		0			0
$463$	14.0141	+	8.09107i	0.651292	+	0.376024i	0.788951	−	0.614456i	$-0.210624\pi$
$463$	14.0141	+	8.09107i	0.651292	+	0.376024i	−0.137659	+	0.990480i	$0.543958\pi$
$464$	−2.88710	−	1.29161i	−0.134030	−	0.0599616i
$465$		0			0
$466$	−1.48699	+	2.73577i	−0.0688834	+	0.126732i
$467$	14.6712	+	25.4112i	0.678900	+	1.17589i	0.975312	+	0.220830i	$0.0708764\pi$
$467$	14.6712	+	25.4112i	0.678900	+	1.17589i	−0.296412	+	0.955060i	$0.595790\pi$
$468$		0			0
$469$	−4.24229	−	0.598530i	−0.195891	−	0.0276375i
$470$	10.3646	−	0.266769i	0.478085	−	0.0123052i
$471$		0			0
$472$	20.1634	−	13.8181i	0.928097	−	0.636032i
$473$	58.7704	−	33.9311i	2.70226	−	1.56015i
$474$		0			0
$475$	−14.5983	+	8.42835i	−0.669818	+	0.386719i
$476$	−0.640902	−	0.0569947i	−0.0293757	−	0.00261235i
$477$		0			0
$478$	0.218026	+	8.47082i	0.00997227	+	0.387446i
$479$	−34.3393			−1.56900			−0.784501	−	0.620127i	$-0.787081\pi$
$479$	−34.3393			−1.56900			−0.784501	+	0.620127i	$0.787081\pi$
$480$		0			0
$481$	7.56934			0.345132
$482$	−13.3202	+	8.15446i	−0.606720	+	0.371425i
$483$		0			0
$484$	17.9718	−	35.1939i	0.816902	−	1.59972i
$485$	−9.65476	+	5.57418i	−0.438400	+	0.253110i
$486$		0			0
$487$	−25.7769	−	14.8823i	−1.16806	−	0.674382i	−0.214841	−	0.976649i	$-0.568923\pi$
$487$	−25.7769	−	14.8823i	−1.16806	−	0.674382i	−0.953223	+	0.302267i	$0.902257\pi$
$488$	−9.78272	−	4.68224i	−0.442843	−	0.211955i
$489$		0			0
$490$	11.6015	−	11.7700i	0.524101	−	0.531713i
$491$	−16.8442	+	29.1751i	−0.760170	+	1.31665i	0.182593	+	0.983189i	$0.441551\pi$
$491$	−16.8442	+	29.1751i	−0.760170	+	1.31665i	−0.942763	+	0.333464i	$0.891782\pi$
$492$		0			0
$493$	−0.0961482			−0.00433030
$494$	5.15449	+	8.41981i	0.231911	+	0.378825i
$495$		0			0
$496$	9.88098	+	4.42049i	0.443669	+	0.198486i
$497$	−22.3731	−	17.4991i	−1.00357	−	0.784940i
$498$		0			0
$499$			31.6743i			1.41794i	0.705240	+	0.708969i	$0.250839\pi$
$499$			31.6743i			1.41794i	−0.705240	+	0.708969i	$0.749161\pi$
$500$	21.4485	+	10.9527i	0.959207	+	0.489821i
$501$		0			0
$502$	−21.0100	+	12.8620i	−0.937721	+	0.574059i
$503$	20.0868			0.895625			0.447813	−	0.894127i	$-0.352203\pi$
$503$	20.0868			0.895625			0.447813	+	0.894127i	$0.352203\pi$
$504$		0			0
$505$	−17.1607			−0.763640
$506$	28.8077	−	17.6357i	1.28066	−	0.784001i
$507$		0			0
$508$	12.1884	+	6.22402i	0.540771	+	0.276146i
$509$			41.4689i			1.83808i	0.394169	+	0.919038i	$0.371033\pi$
$509$			41.4689i			1.83808i	−0.394169	+	0.919038i	$0.628967\pi$
$510$		0			0
$511$	−5.17173	+	2.08630i	−0.228784	+	0.0922924i
$512$	−5.19368	−	22.0233i	−0.229530	−	0.973302i
$513$		0			0
$514$	−8.13371	−	13.2863i	−0.358762	−	0.586035i
$515$	17.5840			0.774842
$516$		0			0
$517$	12.1777	−	21.0924i	0.535576	−	0.927645i
$518$	12.2950	+	28.3527i	0.540212	+	1.24575i
$519$		0			0
$520$	1.86822	−	3.90332i	0.0819268	−	0.171172i
$521$	−3.10992	−	1.79551i	−0.136248	−	0.0786628i	0.430327	−	0.902673i	$-0.358398\pi$
$521$	−3.10992	−	1.79551i	−0.136248	−	0.0786628i	−0.566575	+	0.824010i	$0.691732\pi$
$522$		0			0
$523$	24.9616	−	14.4116i	1.09149	−	0.630174i	0.157519	−	0.987516i	$-0.449650\pi$
$523$	24.9616	−	14.4116i	1.09149	−	0.630174i	0.933974	+	0.357342i	$0.116317\pi$
$524$	18.1727	−	35.5872i	0.793878	−	1.55463i
$525$		0			0
$526$	6.54048	−	4.00399i	0.285178	−	0.174582i
$527$	0.329063			0.0143342
$528$		0			0
$529$	−4.45391			−0.193648
$530$	−0.193409	−	7.51439i	−0.00840114	−	0.326404i
$531$		0			0
$532$	−23.1658	+	32.9838i	−1.00437	+	1.43003i
$533$	−1.57051	+	0.906732i	−0.0680262	+	0.0392749i
$534$		0			0
$535$	−8.48387	+	4.89816i	−0.366789	+	0.211766i
$536$	−2.58914	−	3.77807i	−0.111834	−	0.163188i
$537$		0			0
$538$	21.7406	−	0.559569i	0.937304	−	0.0241247i
$539$	−9.35165	−	37.6791i	−0.402804	−	1.62295i
$540$		0			0
$541$	1.44238	+	2.49828i	0.0620128	+	0.107409i	0.895365	−	0.445333i	$-0.146915\pi$
$541$	1.44238	+	2.49828i	0.0620128	+	0.107409i	−0.833352	+	0.552742i	$0.813581\pi$
$542$	7.60739	−	13.9961i	0.326765	−	0.601186i
$543$		0			0
$544$	−0.417519	−	0.546648i	−0.0179010	−	0.0234373i
$545$	13.0300	+	7.52286i	0.558143	+	0.322244i
$546$		0			0
$547$	−19.3894	+	11.1945i	−0.829030	+	0.478641i	−0.853520	−	0.521059i	$-0.825537\pi$
$547$	−19.3894	+	11.1945i	−0.829030	+	0.478641i	0.0244906	+	0.999700i	$0.492204\pi$
$548$	2.84223	+	1.45139i	0.121414	+	0.0620004i
$549$		0			0
$550$	14.8034	−	9.06246i	0.631221	−	0.386424i
$551$	−3.01149	+	5.21605i	−0.128294	+	0.222211i
$552$		0			0
$553$	10.8316	+	26.8506i	0.460608	+	1.14180i
$554$	35.5596	−	21.7691i	1.51078	−	0.924879i
$555$		0			0
$556$	−13.8312	+	8.96451i	−0.586574	+	0.380180i
$557$	5.45852	+	3.15148i	0.231285	+	0.133532i	0.611165	−	0.791503i	$-0.290701\pi$
$557$	5.45852	+	3.15148i	0.231285	+	0.133532i	−0.379880	+	0.925036i	$0.624035\pi$
$558$		0			0
$559$		−	11.2139i		−	0.474296i
$560$	17.6554	+	0.657615i	0.746076	+	0.0277893i
$561$		0			0
$562$	7.58000	−	13.9457i	0.319743	−	0.588266i
$563$	−1.33127	−	2.30583i	−0.0561064	−	0.0971791i	0.836608	−	0.547802i	$-0.184535\pi$
$563$	−1.33127	−	2.30583i	−0.0561064	−	0.0971791i	−0.892714	+	0.450623i	$0.851202\pi$
$564$		0			0
$565$	5.92341	−	10.2597i	0.249200	−	0.431627i
$566$	−10.0256	+	18.4451i	−0.421405	+	0.775305i
$567$		0			0
$568$	−2.34179	−	30.2745i	−0.0982594	−	1.27029i
$569$	24.4674	+	14.1263i	1.02573	+	0.592204i	0.915758	−	0.401731i	$-0.131591\pi$
$569$	24.4674	+	14.1263i	1.02573	+	0.592204i	0.109970	+	0.993935i	$0.464925\pi$
$570$		0			0
$571$	27.4469	−	15.8465i	1.14862	−	0.663155i	0.200069	−	0.979782i	$-0.435884\pi$
$571$	27.4469	−	15.8465i	1.14862	−	0.663155i	0.948550	+	0.316627i	$0.102550\pi$
$572$	−5.52883	−	8.53034i	−0.231172	−	0.356671i
$573$		0			0
$574$	−5.94738	−	4.40987i	−0.248239	−	0.184065i
$575$	9.53030			0.397441
$576$		0			0
$577$	2.73814	−	4.74260i	0.113990	−	0.197437i	−0.803385	−	0.595459i	$-0.796970\pi$
$577$	2.73814	−	4.74260i	0.113990	−	0.197437i	0.917376	+	0.398022i	$0.130303\pi$
$578$	21.1047	+	11.4711i	0.877839	+	0.477136i
$579$		0			0
$580$	2.63658	−	0.135813i	0.109478	−	0.00563934i
$581$	−0.486873	+	3.45089i	−0.0201989	+	0.143167i
$582$		0			0
$583$	−15.2921	−	8.82889i	−0.633333	−	0.365655i
$584$	−5.37752	−	2.57381i	−0.222523	−	0.106505i
$585$		0			0
$586$	−24.9979	+	0.643407i	−1.03265	+	0.0265789i
$587$	−20.5491	−	35.5920i	−0.848151	−	1.46904i	−0.882857	−	0.469643i	$-0.844383\pi$
$587$	−20.5491	−	35.5920i	−0.848151	−	1.46904i	0.0347057	−	0.999398i	$-0.488951\pi$
$588$		0			0
$589$	10.3067	−	17.8517i	0.424679	−	0.735566i
$590$	−9.74384	+	17.9268i	−0.401147	+	0.738034i
$591$		0			0
$592$	−13.4915	+	30.1572i	−0.554499	+	1.23945i
$593$	−6.86958	+	3.96615i	−0.282100	+	0.162870i	−0.634374	−	0.773027i	$-0.718742\pi$
$593$	−6.86958	+	3.96615i	−0.282100	+	0.162870i	0.352274	+	0.935897i	$0.385409\pi$
$594$		0			0
$595$	0.498082	−	0.200928i	0.0204194	−	0.00823725i
$596$	1.60519	+	0.819693i	0.0657510	+	0.0335759i
$597$		0			0
$598$	−0.143612	−	5.57966i	−0.00587272	−	0.228169i
$599$	0.276326	+	0.478610i	0.0112904	+	0.0195555i	0.871615	−	0.490190i	$-0.163073\pi$
$599$	0.276326	+	0.478610i	0.0112904	+	0.0195555i	−0.860325	+	0.509746i	$0.829739\pi$
$600$		0			0
$601$	11.6785	+	20.2278i	0.476376	+	0.825108i	0.999634	−	0.0270668i	$-0.00861669\pi$
$601$	11.6785	+	20.2278i	0.476376	+	0.825108i	−0.523257	+	0.852175i	$0.675283\pi$
$602$	42.0041	−	18.2149i	1.71196	−	0.742384i
$603$		0			0
$604$	1.61791	+	0.826191i	0.0658319	+	0.0336172i
$605$			32.9855i			1.34105i
$606$		0			0
$607$		−	33.2193i		−	1.34833i	−0.738581	−	0.674165i	$-0.764504\pi$
$607$		−	33.2193i		−	1.34833i	0.738581	−	0.674165i	$-0.235496\pi$
$608$	−42.7329	+	5.52873i	−1.73305	+	0.224220i
$609$		0			0
$610$	9.04993	−	0.232931i	0.366421	−	0.00943111i
$611$	−2.01230	−	3.48541i	−0.0814091	−	0.141005i
$612$		0			0
$613$	−14.8721	+	25.7592i	−0.600677	+	1.04040i	0.392041	+	0.919948i	$0.371769\pi$
$613$	−14.8721	+	25.7592i	−0.600677	+	1.04040i	−0.992719	+	0.120456i	$0.961564\pi$
$614$	−8.55379	−	13.9725i	−0.345203	−	0.563886i
$615$		0			0
$616$	22.9718	−	34.5655i	0.925560	−	1.39268i
$617$	−1.33304	−	0.769632i	−0.0536663	−	0.0309842i	0.472927	−	0.881102i	$-0.343197\pi$
$617$	−1.33304	−	0.769632i	−0.0536663	−	0.0309842i	−0.526593	+	0.850117i	$0.676531\pi$
$618$		0			0
$619$			13.9541i			0.560861i	0.959874	+	0.280431i	$0.0904773\pi$
$619$			13.9541i			0.560861i	−0.959874	+	0.280431i	$0.909523\pi$
$620$	−9.02360	+	0.464815i	−0.362397	+	0.0186674i
$621$		0			0
$622$	−35.8171	−	19.4678i	−1.43614	−	0.780589i
$623$	−24.6244	−	3.47416i	−0.986555	−	0.139189i
$624$		0			0
$625$	−9.03769			−0.361508
$626$	−0.749575	−	29.1228i	−0.0299590	−	1.16398i
$627$		0			0
$628$	16.5558	−	0.852805i	0.660647	−	0.0340306i
$629$			1.00432i			0.0400447i
$630$		0			0
$631$		−	32.8617i		−	1.30820i	−0.756407	−	0.654102i	$-0.773047\pi$
$631$		−	32.8617i		−	1.30820i	0.756407	−	0.654102i	$-0.226953\pi$
$632$	−13.3627	+	27.9190i	−0.531539	+	1.11056i
$633$		0			0
$634$	37.5888	−	0.967479i	1.49284	−	0.0384235i
$635$	−11.4236			−0.453330
$636$		0			0
$637$	−6.16476	−	1.77486i	−0.244257	−	0.0703224i
$638$	2.96167	−	5.44890i	0.117254	−	0.215724i
$639$		0			0
$640$	12.2214	+	14.4005i	0.483094	+	0.569229i
$641$		−	18.2422i		−	0.720525i	−0.932851	−	0.360262i	$-0.882687\pi$
$641$		−	18.2422i		−	0.720525i	0.932851	−	0.360262i	$-0.117313\pi$
$642$		0			0
$643$	−0.902277	−	0.520930i	−0.0355823	−	0.0205435i	0.482103	−	0.876114i	$-0.339873\pi$
$643$	−0.902277	−	0.520930i	−0.0355823	−	0.0205435i	−0.517686	+	0.855571i	$0.673206\pi$
$644$	20.6666	−	9.60108i	0.814380	−	0.378335i
$645$		0			0
$646$	−1.11716	+	0.683909i	−0.0439540	+	0.0269080i
$647$	2.46961	−	4.27748i	0.0970902	−	0.168165i	−0.813389	−	0.581720i	$-0.802380\pi$
$647$	2.46961	−	4.27748i	0.0970902	−	0.168165i	0.910479	+	0.413555i	$0.135713\pi$
$648$		0			0
$649$	23.9651	+	41.5087i	0.940711	+	1.62936i
$650$	−0.0737979	−	2.86722i	−0.00289459	−	0.112462i
$651$		0			0
$652$	−1.22826	−	23.8446i	−0.0481023	−	0.933826i
$653$		−	0.0193072i		−	0.000755548i	−1.00000		0.000377774i	$-0.999880\pi$
$653$		−	0.0193072i		−	0.000755548i	1.00000		0.000377774i	$-0.000120249\pi$
$654$		0			0
$655$			33.3542i			1.30325i
$656$	−0.813276	−	7.87325i	−0.0317531	−	0.307399i
$657$		0			0
$658$	9.78680	−	13.1990i	0.381529	−	0.514550i
$659$	−5.49141	−	9.51140i	−0.213915	−	0.370512i	0.739021	−	0.673682i	$-0.235288\pi$
$659$	−5.49141	−	9.51140i	−0.213915	−	0.370512i	−0.952936	+	0.303170i	$0.901955\pi$
$660$		0			0
$661$	0.305604	+	0.529321i	0.0118866	+	0.0205882i	0.871908	−	0.489671i	$-0.162883\pi$
$661$	0.305604	+	0.529321i	0.0118866	+	0.0205882i	−0.860021	+	0.510259i	$0.829550\pi$
$662$	−5.65889	+	0.145651i	−0.219939	+	0.00566089i
$663$		0			0
$664$	−3.07327	+	2.10613i	−0.119266	+	0.0817338i
$665$	4.70019	−	33.3143i	0.182266	−	1.29187i
$666$		0			0
$667$	2.94900	−	1.70261i	0.114186	−	0.0659252i
$668$	26.7303	+	41.2418i	1.03423	+	1.59569i
$669$		0			0
$670$	3.35899	+	1.82573i	0.129769	+	0.0705340i
$671$	10.6330	−	18.4170i	0.410484	−	0.710979i
$672$		0			0
$673$	11.2929	+	19.5598i	0.435308	+	0.753976i	0.997321	−	0.0731525i	$-0.0233060\pi$
$673$	11.2929	+	19.5598i	0.435308	+	0.753976i	−0.562012	+	0.827129i	$0.689973\pi$
$674$	−0.389325	−	15.1262i	−0.0149962	−	0.582640i
$675$		0			0
$676$	24.2880	−	1.25110i	0.934155	−	0.0481193i
$677$	19.5969	+	11.3143i	0.753170	+	0.434843i	0.826838	−	0.562440i	$-0.190137\pi$
$677$	19.5969	+	11.3143i	0.753170	+	0.434843i	−0.0736681	+	0.997283i	$0.523471\pi$
$678$		0			0
$679$	−2.46829	+	17.4949i	−0.0947242	+	0.671392i
$680$	0.517901	+	0.247879i	0.0198606	+	0.00950574i
$681$		0			0
$682$	−10.1362	+	18.6486i	−0.388135	+	0.714093i
$683$	−20.8314	+	36.0811i	−0.797093	+	1.38060i	0.124409	+	0.992231i	$0.460296\pi$
$683$	−20.8314	+	36.0811i	−0.797093	+	1.38060i	−0.921502	+	0.388374i	$0.873037\pi$
$684$		0			0
$685$	−2.66388			−0.101782
$686$	−3.36540	−	25.9745i	−0.128492	−	0.991711i
$687$		0			0
$688$	44.6775	+	19.9875i	1.70331	+	0.762017i
$689$	−2.52694	+	1.45893i	−0.0962686	+	0.0555807i
$690$		0			0
$691$	31.3196	+	18.0824i	1.19145	+	0.687885i	0.958636	−	0.284636i	$-0.0918726\pi$
$691$	31.3196	+	18.0824i	1.19145	+	0.687885i	0.232816	+	0.972521i	$0.425206\pi$
$692$	15.2405	−	9.87790i	0.579355	−	0.375501i
$693$		0			0
$694$	27.1011	+	14.7304i	1.02874	+	0.559157i
$695$	6.87901	−	11.9148i	0.260936	−	0.451954i
$696$		0			0
$697$	−0.120307	−	0.208378i	−0.00455696	−	0.00789288i
$698$	20.2864	+	11.0264i	0.767851	+	0.417354i
$699$		0			0
$700$	10.6200	−	4.93371i	0.401398	−	0.186477i
$701$		−	8.15056i		−	0.307842i	−0.988083	−	0.153921i	$-0.950810\pi$
$701$		−	8.15056i		−	0.307842i	0.988083	−	0.153921i	$-0.0491902\pi$
$702$		0			0
$703$	54.4842	+	31.4565i	2.05491	+	1.18640i
$704$	43.8405	−	6.82313i	1.65230	−	0.257156i
$705$		0			0
$706$	18.9868	+	31.0148i	0.714579	+	1.16726i
$707$	−16.7554	+	21.4223i	−0.630150	+	0.805667i
$708$		0			0
$709$	−10.8288	+	18.7560i	−0.406683	+	0.704396i	−0.994516	−	0.104586i	$-0.966648\pi$
$709$	−10.8288	+	18.7560i	−0.406683	+	0.704396i	0.587832	+	0.808983i	$0.299981\pi$
$710$	13.2336	+	21.6170i	0.496649	+	0.811272i
$711$		0			0
$712$	−15.0287	−	21.9298i	−0.563223	−	0.821854i
$713$	−10.0928	+	5.82710i	−0.377980	+	0.218227i
$714$		0			0
$715$	7.34840	+	4.24260i	0.274814	+	0.158664i
$716$	−7.04516	−	10.8699i	−0.263290	−	0.406226i
$717$		0			0
$718$	−10.3711	−	5.63704i	−0.387045	−	0.210372i
$719$	−16.3507	−	28.3202i	−0.609778	−	1.05617i	−0.991277	−	0.131798i	$-0.957925\pi$
$719$	−16.3507	−	28.3202i	−0.609778	−	1.05617i	0.381498	−	0.924370i	$-0.375408\pi$
$720$		0			0
$721$	17.1686	−	21.9506i	0.639394	−	0.817485i
$722$	1.41988	+	55.1657i	0.0528425	+	2.05306i
$723$		0			0
$724$	9.23655	−	18.0877i	0.343274	−	0.672226i
$725$	1.51541	−	0.874920i	0.0562808	−	0.0324937i
$726$		0			0
$727$	−39.0531	+	22.5473i	−1.44840	+	0.836233i	−0.998386	−	0.0567887i	$-0.981914\pi$
$727$	−39.0531	+	22.5473i	−1.44840	+	0.836233i	−0.450013	+	0.893022i	$0.648581\pi$
$728$	−3.04855	−	6.14329i	−0.112987	−	0.227685i
$729$		0			0
$730$	4.97470	−	0.128041i	0.184122	−	0.00473902i
$731$	1.48788			0.0550312
$732$		0			0
$733$	−50.7824			−1.87569			−0.937846	−	0.347052i	$-0.887183\pi$
$733$	−50.7824			−1.87569			−0.937846	+	0.347052i	$0.887183\pi$
$734$	16.4872	+	26.9316i	0.608552	+	0.994064i
$735$		0			0
$736$	22.4860	+	9.37298i	0.828847	+	0.345493i
$737$	7.77759	−	4.49039i	0.286491	−	0.165406i
$738$		0			0
$739$	−14.8941	−	8.59913i	−0.547890	−	0.316324i	0.200381	−	0.979718i	$-0.435782\pi$
$739$	−14.8941	−	8.59913i	−0.547890	−	0.316324i	−0.748270	+	0.663394i	$0.769115\pi$
$740$	−1.41864	−	27.5405i	−0.0521502	−	1.01241i
$741$		0			0
$742$	−9.56930	−	7.09546i	−0.351300	−	0.260483i
$743$	25.7102	−	44.5314i	0.943217	−	1.63370i	0.183933	−	0.982939i	$-0.441117\pi$
$743$	25.7102	−	44.5314i	0.943217	−	1.63370i	0.759283	−	0.650760i	$-0.225550\pi$
$744$		0			0
$745$	−1.50446			−0.0551193
$746$	−19.4945	+	11.9342i	−0.713743	+	0.436944i
$747$		0			0
$748$	1.13182	−	0.733577i	0.0413836	−	0.0268222i
$749$	−2.16894	+	15.3732i	−0.0792514	+	0.561723i
$750$		0			0
$751$		−	16.9691i		−	0.619210i	−0.950865	−	0.309605i	$-0.899803\pi$
$751$		−	16.9691i		−	0.619210i	0.950865	−	0.309605i	$-0.100197\pi$
$752$	17.4731	−	1.80490i	0.637177	−	0.0658179i
$753$		0			0
$754$	−0.535071	−	0.874034i	−0.0194861	−	0.0318304i
$755$	−1.51639			−0.0551871
$756$		0			0
$757$	−26.0926			−0.948353			−0.474177	−	0.880430i	$-0.657254\pi$
$757$	−26.0926			−0.948353			−0.474177	+	0.880430i	$0.657254\pi$
$758$	−0.235572	−	0.384805i	−0.00855637	−	0.0139767i
$759$		0			0
$760$	29.6688	−	20.3323i	1.07620	−	0.737528i
$761$			13.8630i			0.502535i	0.967918	+	0.251268i	$0.0808474\pi$
$761$			13.8630i			0.502535i	−0.967918	+	0.251268i	$0.919153\pi$
$762$		0			0
$763$	22.1133	−	8.92058i	0.800553	−	0.322947i
$764$	−6.54692	−	10.1011i	−0.236859	−	0.365446i
$765$		0			0
$766$	−13.2488	+	8.11071i	−0.478697	+	0.293052i
$767$	7.92019			0.285982
$768$		0			0
$769$	−15.6264	+	27.0657i	−0.563501	+	0.976013i	0.433686	+	0.901064i	$0.357213\pi$
$769$	−15.6264	+	27.0657i	−0.563501	+	0.976013i	−0.997187	+	0.0749490i	$0.976121\pi$
$770$	−3.95550	+	34.4165i	−0.142546	+	1.24028i
$771$		0			0
$772$	−30.3587	+	1.56381i	−1.09263	+	0.0562826i
$773$	23.3161	+	13.4616i	0.838622	+	0.484179i	0.856796	−	0.515656i	$-0.172452\pi$
$773$	23.3161	+	13.4616i	0.838622	+	0.484179i	−0.0181735	+	0.999835i	$0.505785\pi$
$774$		0			0
$775$	−5.18641	+	2.99438i	−0.186302	+	0.107561i
$776$	−15.5805	+	10.6774i	−0.559306	+	0.383297i
$777$		0			0
$778$	−9.56215	−	15.6197i	−0.342820	−	0.559993i
$779$	−15.0727			−0.540036
$780$		0			0
$781$	59.5401			2.13051
$782$	0.740321	−	0.0190547i	0.0264738	−	0.000681396i
$783$		0			0
$784$	18.0593	−	21.3977i	0.644975	−	0.764204i
$785$	−11.9838	+	6.91885i	−0.427720	+	0.246944i
$786$		0			0
$787$	−36.3051	+	20.9608i	−1.29414	+	0.747170i	−0.979385	−	0.202003i	$-0.935255\pi$
$787$	−36.3051	+	20.9608i	−1.29414	+	0.747170i	−0.314752	+	0.949174i	$0.601921\pi$
$788$	−22.4305	−	11.4542i	−0.799053	−	0.408039i
$789$		0			0
$790$	−0.664764	−	25.8277i	−0.0236513	−	0.918907i
$791$	−7.02396	−	17.4117i	−0.249743	−	0.619090i
$792$		0			0
$793$	−1.75705	−	3.04331i	−0.0623948	−	0.108071i
$794$	−25.6240	−	13.9275i	−0.909361	−	0.494269i
$795$		0			0
$796$	9.65126	−	6.25534i	0.342080	−	0.221715i
$797$	−38.7013	−	22.3442i	−1.37087	−	0.791473i	−0.379833	−	0.925055i	$-0.624019\pi$
$797$	−38.7013	−	22.3442i	−1.37087	−	0.791473i	−0.991038	+	0.133583i	$0.957352\pi$
$798$		0			0
$799$	0.462452	−	0.266997i	0.0163604	−	0.00944567i
$800$	11.5549	+	4.81650i	0.408528	+	0.170289i
$801$		0			0
$802$	10.0456	+	16.4095i	0.354724	+	0.579439i
$803$	5.84494	−	10.1237i	0.206263	−	0.357259i
$804$		0			0
$805$	−11.7188	+	14.9829i	−0.413034	+	0.528076i
$806$	1.83126	+	2.99134i	0.0645033	+	0.105366i
$807$		0			0
$808$	−28.9878	+	2.24227i	−1.01979	+	0.0788826i
$809$	30.1213	+	17.3905i	1.05901	+	0.611418i	0.925158	−	0.379583i	$-0.123933\pi$
$809$	30.1213	+	17.3905i	1.05901	+	0.611418i	0.133850	+	0.991002i	$0.457266\pi$
$810$		0			0
$811$			16.9568i			0.595433i	0.954654	+	0.297717i	$0.0962251\pi$
$811$			16.9568i			0.595433i	−0.954654	+	0.297717i	$0.903775\pi$
$812$	2.40477	−	3.42394i	0.0843909	−	0.120157i
$813$		0			0
$814$	−56.9165	−	30.9361i	−1.99492	−	1.08431i
$815$	9.96493	+	17.2598i	0.349056	+	0.604583i
$816$		0			0
$817$	46.6023	−	80.7176i	1.63041	−	2.82395i
$818$	−0.324988	−	0.176642i	−0.0113629	−	0.00617616i
$819$		0			0
$820$	3.59342	+	5.54423i	0.125488	+	0.193613i
$821$	41.6762	+	24.0617i	1.45451	+	0.839761i	0.998732	−	0.0503337i	$-0.0160285\pi$
$821$	41.6762	+	24.0617i	1.45451	+	0.839761i	0.455776	+	0.890095i	$0.349362\pi$
$822$		0			0
$823$	−37.6353	+	21.7288i	−1.31188	+	0.757417i	−0.982408	−	0.186747i	$-0.940206\pi$
$823$	−37.6353	+	21.7288i	−1.31188	+	0.757417i	−0.329477	+	0.944164i	$0.606872\pi$
$824$	29.7028	−	2.29757i	1.03475	−	0.0800397i
$825$		0			0
$826$	12.8649	+	29.6669i	0.447628	+	1.03224i
$827$	−22.3765			−0.778107			−0.389054	−	0.921215i	$-0.627198\pi$
$827$	−22.3765			−0.778107			−0.389054	+	0.921215i	$0.627198\pi$
$828$		0			0
$829$	−19.6304	+	34.0009i	−0.681793	+	1.18090i	0.292640	+	0.956223i	$0.405466\pi$
$829$	−19.6304	+	34.0009i	−0.681793	+	1.18090i	−0.974433	+	0.224678i	$0.927867\pi$
$830$	1.48514	−	2.73237i	0.0515498	−	0.0948418i
$831$		0			0
$832$	2.64577	−	6.83759i	0.0917257	−	0.237051i
$833$	0.235492	−	0.817954i	0.00815931	−	0.0283404i
$834$		0			0
$835$	−35.5274	−	20.5118i	−1.22948	−	0.709839i
$836$	−4.34640	−	84.3781i	−0.150324	−	2.91828i
$837$		0			0
$838$	0.0183665	+	0.713581i	0.000634459	+	0.0246502i
$839$	−13.5646	−	23.4946i	−0.468302	−	0.811123i	0.531042	−	0.847346i	$-0.321801\pi$
$839$	−13.5646	−	23.4946i	−0.468302	−	0.811123i	−0.999344	+	0.0362228i	$0.988467\pi$
$840$		0			0
$841$	−14.1874	+	24.5733i	−0.489220	+	0.847354i
$842$	−2.25771	−	1.22714i	−0.0778058	−	0.0422901i
$843$		0			0
$844$	20.8583	−	13.5190i	0.717973	−	0.465345i
$845$	−17.5807	+	10.1502i	−0.604796	+	0.349179i
$846$		0			0
$847$	41.1769	+	32.2064i	1.41486	+	1.10663i
$848$	−1.30856	−	12.6680i	−0.0449360	−	0.435021i
$849$		0			0
$850$	0.380430	−	0.00979167i	0.0130486	−	0.000335851i
$851$	−17.7846	−	30.8038i	−0.609648	−	1.05594i
$852$		0			0
$853$	−7.93576	−	13.7451i	−0.271715	−	0.470625i	0.697586	−	0.716501i	$-0.254258\pi$
$853$	−7.93576	−	13.7451i	−0.271715	−	0.470625i	−0.969301	+	0.245877i	$0.920924\pi$
$854$	8.54540	−	11.5248i	0.292417	−	0.394369i
$855$		0			0
$856$	−13.6909	+	9.38249i	−0.467946	+	0.320687i
$857$		−	11.3573i		−	0.387959i	−0.981006	−	0.193980i	$-0.937860\pi$
$857$		−	11.3573i		−	0.387959i	0.981006	−	0.193980i	$-0.0621395\pi$
$858$		0			0
$859$			37.8203i			1.29041i	0.764008	+	0.645206i	$0.223229\pi$
$859$			37.8203i			1.29041i	−0.764008	+	0.645206i	$0.776771\pi$
$860$	−40.8008	+	2.10169i	−1.39130	+	0.0716671i
$861$		0			0
$862$	0.0842844	+	3.27465i	0.00287074	+	0.111535i
$863$	6.51097	+	11.2773i	0.221636	+	0.383885i	0.955305	−	0.295622i	$-0.0955269\pi$
$863$	6.51097	+	11.2773i	0.221636	+	0.383885i	−0.733669	+	0.679507i	$0.762194\pi$
$864$		0			0
$865$	−7.57990	+	13.1288i	−0.257724	+	0.446392i
$866$	−18.6987	+	11.4471i	−0.635409	+	0.388988i
$867$		0			0
$868$	−8.23023	+	11.7183i	−0.279352	+	0.397745i
$869$	−52.5604	−	30.3457i	−1.78299	−	1.02941i
$870$		0			0
$871$		−	1.48403i		−	0.0502843i
$872$	22.9932	+	11.0051i	0.778647	+	0.372679i
$873$		0			0
$874$	22.1541	−	40.7593i	0.749374	−	1.37870i
$875$	−19.6278	+	25.0948i	−0.663542	+	0.848360i
$876$		0			0
$877$	−6.58284			−0.222287			−0.111143	−	0.993804i	$-0.535451\pi$
$877$	−6.58284			−0.222287			−0.111143	+	0.993804i	$0.535451\pi$
$878$	−18.9235	+	0.487063i	−0.638639	+	0.0164376i
$879$		0			0
$880$	−30.0008	+	21.7150i	−1.01133	+	0.732011i
$881$		−	5.82071i		−	0.196105i	−0.995181	−	0.0980524i	$-0.968739\pi$
$881$		−	5.82071i		−	0.196105i	0.995181	−	0.0980524i	$-0.0312613\pi$
$882$		0			0
$883$		−	36.2156i		−	1.21875i	−0.792881	−	0.609376i	$-0.791420\pi$
$883$		−	36.2156i		−	1.21875i	0.792881	−	0.609376i	$-0.208580\pi$
$884$	−0.0114654	−	0.222581i	−0.000385622	−	0.00748620i
$885$		0			0
$886$	1.06058	+	41.2060i	0.0356309	+	1.38434i
$887$	12.3894			0.415994			0.207997	−	0.978129i	$-0.433306\pi$
$887$	12.3894			0.415994			0.207997	+	0.978129i	$0.433306\pi$
$888$		0			0
$889$	−11.1537	+	14.2604i	−0.374085	+	0.478279i
$890$	19.4972	+	10.5974i	0.653549	+	0.355227i
$891$		0			0
$892$	−0.787242	−	15.2830i	−0.0263588	−	0.511712i
$893$		−	33.4508i		−	1.11939i
$894$		0			0
$895$	9.36376	+	5.40617i	0.312996	+	0.180708i
$896$	29.9094	−	1.19606i	0.999201	−	0.0399576i
$897$		0			0
$898$	−5.63208	−	9.19995i	−0.187945	−	0.307006i
$899$	−1.06990	+	1.85313i	−0.0356833	+	0.0618053i
$900$		0			0
$901$	−0.193574	−	0.335279i	−0.00644887	−	0.0111698i
$902$	15.5150	−	0.399333i	0.516594	−	0.0132963i
$903$		0			0
$904$	8.66526	−	18.1046i	0.288202	−	0.602149i
$905$			16.9528i			0.563529i
$906$		0			0
$907$		−	6.02720i		−	0.200130i	−0.994981	−	0.100065i	$-0.968095\pi$
$907$		−	6.02720i		−	0.200130i	0.994981	−	0.100065i	$-0.0319050\pi$
$908$	19.8197	−	38.8125i	0.657740	−	1.28804i
$909$		0			0
$910$	4.59839	+	3.40962i	0.152435	+	0.113028i
$911$	−12.7116	−	22.0171i	−0.421153	−	0.729458i	0.574900	−	0.818224i	$-0.305041\pi$
$911$	−12.7116	−	22.0171i	−0.421153	−	0.729458i	−0.996053	+	0.0887660i	$0.971708\pi$
$912$		0			0
$913$	−3.65270	−	6.32667i	−0.120887	−	0.209382i
$914$	0.0920346	+	3.57576i	0.00304423	+	0.118276i
$915$		0			0
$916$	23.3639	−	45.7531i	0.771966	−	1.51172i
$917$	41.6371	+	32.5663i	1.37498	+	1.07544i
$918$		0			0
$919$	−19.2980	+	11.1417i	−0.636583	+	0.367532i	−0.783297	−	0.621647i	$-0.786464\pi$
$919$	−19.2980	+	11.1417i	−0.636583	+	0.367532i	0.146714	+	0.989179i	$0.453130\pi$
$920$	−20.2742	+	1.56825i	−0.668422	+	0.0517038i
$921$		0			0
$922$	22.4515	−	41.3065i	0.739401	−	1.36036i
$923$	4.91934	−	8.52055i	0.161922	−	0.280457i
$924$		0			0
$925$	−9.13898	−	15.8292i	−0.300488	−	0.520460i
$926$	−22.8774	+	0.588829i	−0.751799	+	0.0193501i
$927$		0			0
$928$	4.43597	−	0.573919i	0.145618	−	0.0188398i
$929$	−29.1530	−	16.8315i	−0.956478	−	0.552223i	−0.0613907	−	0.998114i	$-0.519554\pi$
$929$	−29.1530	−	16.8315i	−0.956478	−	0.552223i	−0.895087	+	0.445891i	$0.852887\pi$
$930$		0			0
$931$	−36.9982	−	38.3948i	−1.21257	−	1.25834i
$932$	−0.226531	−	4.39771i	−0.00742026	−	0.144052i
$933$		0			0
$934$	−36.4588	−	19.8166i	−1.19297	−	0.648420i
$935$	−0.562917	+	0.975001i	−0.0184094	+	0.0318859i
$936$		0			0
$937$	24.2247			0.791387			0.395693	−	0.918383i	$-0.370504\pi$
$937$	24.2247			0.791387			0.395693	+	0.918383i	$0.370504\pi$
$938$	5.55877	−	2.41053i	0.181500	−	0.0787067i
$939$		0			0
$940$	−12.3043	+	7.97485i	−0.401321	+	0.260111i
$941$	18.4585	−	10.6570i	0.601729	−	0.347408i	−0.167993	−	0.985788i	$-0.553728\pi$
$941$	18.4585	−	10.6570i	0.601729	−	0.347408i	0.769721	+	0.638380i	$0.220395\pi$
$942$		0			0
$943$	7.37999	+	4.26084i	0.240325	+	0.138752i
$944$	−14.1169	+	31.5551i	−0.459466	+	1.02703i
$945$		0			0
$946$	−45.8314	+	84.3210i	−1.49011	+	2.74151i
$947$	−17.6150	+	30.5101i	−0.572412	+	0.991446i	0.423906	+	0.905706i	$0.360659\pi$
$947$	−17.6150	+	30.5101i	−0.572412	+	0.991446i	−0.996318	+	0.0857398i	$0.972675\pi$
$948$		0			0
$949$	−0.965845	−	1.67289i	−0.0313526	−	0.0543044i
$950$	11.3843	−	20.9450i	0.369357	−	0.679546i
$951$		0			0
$952$	0.815105	−	0.404488i	0.0264177	−	0.0131095i
$953$		−	11.4706i		−	0.371569i	−0.982590	−	0.185785i	$-0.940517\pi$
$953$		−	11.4706i		−	0.371569i	0.982590	−	0.185785i	$-0.0594827\pi$
$954$		0			0
$955$	8.70155	+	5.02384i	0.281576	+	0.162568i
$956$	−6.51770	−	10.0561i	−0.210798	−	0.325236i
$957$		0			0
$958$	41.4182	−	25.3556i	1.33816	−	0.819203i
$959$	−2.60097	+	3.32542i	−0.0839896	+	0.107383i
$960$		0			0
$961$	−11.8383	+	20.5045i	−0.381881	+	0.661437i
$962$	−9.12972	+	5.58909i	−0.294354	+	0.180199i
$963$		0			0
$964$	10.0450	−	19.6709i	0.323528	−	0.633558i
$965$	21.9749	−	12.6872i	0.707398	−	0.408417i
$966$		0			0
$967$	8.24220	+	4.75864i	0.265051	+	0.153027i	0.626637	−	0.779312i	$-0.284431\pi$
$967$	8.24220	+	4.75864i	0.265051	+	0.153027i	−0.361585	+	0.932339i	$0.617764\pi$
$968$	4.30999	+	55.7191i	0.138528	+	1.79088i
$969$		0			0
$970$	7.52915	−	13.8522i	0.241747	−	0.444767i
$971$	29.2431	+	50.6506i	0.938457	+	1.62545i	0.768351	+	0.640029i	$0.221078\pi$
$971$	29.2431	+	50.6506i	0.938457	+	1.62545i	0.170106	+	0.985426i	$0.445589\pi$
$972$		0			0
$973$	−8.15710	−	20.2207i	−0.261505	−	0.648245i
$974$	42.0796	−	1.08306i	1.34832	−	0.0347036i
$975$		0			0
$976$	15.2567	−	1.57596i	0.488355	−	0.0504451i
$977$	−4.60653	+	2.65958i	−0.147376	+	0.0850875i	−0.571875	−	0.820341i	$-0.693784\pi$
$977$	−4.60653	+	2.65958i	−0.147376	+	0.0850875i	0.424499	+	0.905428i	$0.360450\pi$
$978$		0			0
$979$	45.1450	−	26.0645i	1.44284	−	0.833024i
$980$	−5.30229	+	22.7627i	−0.169375	+	0.727127i
$981$		0			0
$982$	−1.22584	−	47.6269i	−0.0391182	−	1.51984i
$983$	−0.796845			−0.0254154			−0.0127077	−	0.999919i	$-0.504045\pi$
$983$	−0.796845			−0.0254154			−0.0127077	+	0.999919i	$0.504045\pi$
$984$		0			0
$985$	21.0230			0.669849
$986$	0.115969	−	0.0709944i	0.00369320	−	0.00226092i
$987$		0			0
$988$	−12.4341	−	6.34952i	−0.395582	−	0.202005i
$989$	−45.6354	+	26.3476i	−1.45112	+	0.837806i
$990$		0			0
$991$	−12.7041	−	7.33474i	−0.403560	−	0.232996i	0.284459	−	0.958688i	$-0.408186\pi$
$991$	−12.7041	−	7.33474i	−0.403560	−	0.232996i	−0.688019	+	0.725693i	$0.741519\pi$
$992$	−15.1819	+	1.96422i	−0.482026	+	0.0623639i
$993$		0			0
$994$	39.9063	+	4.58645i	1.26575	+	0.145473i
$995$	−4.80009	+	8.31401i	−0.152173	+	0.263572i
$996$		0			0
$997$	−20.3527			−0.644578			−0.322289	−	0.946641i	$-0.604452\pi$
$997$	−20.3527			−0.644578			−0.322289	+	0.946641i	$0.604452\pi$
$998$	−23.3879	−	38.2038i	−0.740330	−	1.20932i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.179.7		88
3.2	odd	2		252.2.o.a.95.38	yes	88
4.3	odd	2	inner	756.2.o.a.179.21		88
7.2	even	3		756.2.bb.a.611.37		88
9.2	odd	6		756.2.bb.a.683.8		88
9.7	even	3		252.2.bb.a.11.37	yes	88
12.11	even	2		252.2.o.a.95.24	✓	88
21.2	odd	6		252.2.bb.a.23.8	yes	88
28.23	odd	6		756.2.bb.a.611.8		88
36.7	odd	6		252.2.bb.a.11.8	yes	88
36.11	even	6		756.2.bb.a.683.37		88
63.2	odd	6	inner	756.2.o.a.359.21		88
63.16	even	3		252.2.o.a.191.24	yes	88
84.23	even	6		252.2.bb.a.23.37	yes	88
252.79	odd	6		252.2.o.a.191.38	yes	88
252.191	even	6	inner	756.2.o.a.359.7		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.24	✓	88	12.11	even	2
252.2.o.a.95.38	yes	88	3.2	odd	2
252.2.o.a.191.24	yes	88	63.16	even	3
252.2.o.a.191.38	yes	88	252.79	odd	6
252.2.bb.a.11.8	yes	88	36.7	odd	6
252.2.bb.a.11.37	yes	88	9.7	even	3
252.2.bb.a.23.8	yes	88	21.2	odd	6
252.2.bb.a.23.37	yes	88	84.23	even	6
756.2.o.a.179.7		88	1.1	even	1	trivial
756.2.o.a.179.21		88	4.3	odd	2	inner
756.2.o.a.359.7		88	252.191	even	6	inner
756.2.o.a.359.21		88	63.2	odd	6	inner
756.2.bb.a.611.8		88	28.23	odd	6
756.2.bb.a.611.37		88	7.2	even	3
756.2.bb.a.683.8		88	9.2	odd	6
756.2.bb.a.683.37		88	36.11	even	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20615 + 0.738385i) q^{2} +(0.909574 - 1.78120i) q^{4} +1.66943i q^{5} +(2.08401 + 1.63000i) q^{7} +(0.218133 + 2.82000i) q^{8} +O(q^{10})\)	\(q+(-1.20615 + 0.738385i) q^{2} +(0.909574 - 1.78120i) q^{4} +1.66943i q^{5} +(2.08401 + 1.63000i) q^{7} +(0.218133 + 2.82000i) q^{8} +(-1.23268 - 2.01358i) q^{10} -5.54604 q^{11} +(-0.458226 + 0.793672i) q^{13} +(-3.71719 - 0.427218i) q^{14} +(-2.34535 - 3.24027i) q^{16} +(-0.105306 - 0.0607985i) q^{17} +(-6.59665 + 3.80857i) q^{19} +(2.97359 + 1.51847i) q^{20} +(6.68933 - 4.09511i) q^{22} +4.30652 q^{23} +2.21299 q^{25} +(-0.0333475 - 1.29563i) q^{26} +(4.79892 - 2.22943i) q^{28} +(0.684776 - 0.395356i) q^{29} +(-2.34362 + 1.35309i) q^{31} +(5.22140 + 2.17646i) q^{32} +(0.171907 - 0.00442463i) q^{34} +(-2.72118 + 3.47911i) q^{35} +(-4.12969 - 7.15284i) q^{37} +(5.14432 - 9.46456i) q^{38} +(-4.70781 + 0.364158i) q^{40} +(1.71368 + 0.989393i) q^{41} +(-10.5968 + 6.11808i) q^{43} +(-5.04453 + 9.87860i) q^{44} +(-5.19429 + 3.17987i) q^{46} +(-2.19575 + 3.80316i) q^{47} +(1.68619 + 6.79388i) q^{49} +(-2.66919 + 1.63404i) q^{50} +(0.996897 + 1.53810i) q^{52} +(2.75730 + 1.59193i) q^{53} -9.25874i q^{55} +(-4.14202 + 6.23247i) q^{56} +(-0.534015 + 0.982486i) q^{58} +(-4.32111 - 7.48439i) q^{59} +(-1.91723 + 3.32074i) q^{61} +(1.82764 - 3.36252i) q^{62} +(-7.90484 + 1.23027i) q^{64} +(-1.32498 - 0.764978i) q^{65} +(-1.40237 + 0.809658i) q^{67} +(-0.204078 + 0.132270i) q^{68} +(0.713212 - 6.20560i) q^{70} -10.7356 q^{71} +(-1.05389 + 1.82540i) q^{73} +(10.2626 + 5.57806i) q^{74} +(0.783696 + 15.2141i) q^{76} +(-11.5580 - 9.04005i) q^{77} +(9.47711 + 5.47161i) q^{79} +(5.40941 - 3.91540i) q^{80} +(-2.79750 + 0.0720033i) q^{82} +(0.658615 + 1.14075i) q^{83} +(0.101499 - 0.175801i) q^{85} +(8.26381 - 15.2038i) q^{86} +(-1.20977 - 15.6398i) q^{88} +(-8.14004 + 4.69966i) q^{89} +(-2.24863 + 0.907109i) q^{91} +(3.91710 - 7.67077i) q^{92} +(-0.159796 - 6.20847i) q^{94} +(-6.35816 - 11.0127i) q^{95} +(3.33897 + 5.78326i) q^{97} +(-7.05029 - 6.94935i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

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