LMFDB - Embedded newform 756.2.bb.a.611.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (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			611.18
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.301845 + 1.38163i) q^{2} +(-1.81778 - 0.834072i) q^{4} +(-0.434289 + 0.250737i) q^{5} +(0.412779 - 2.61335i) q^{7} +(1.70106 - 2.25973i) q^{8} +O(q^{10})$	\(q+(-0.301845 + 1.38163i) q^{2} +(-1.81778 - 0.834072i) q^{4} +(-0.434289 + 0.250737i) q^{5} +(0.412779 - 2.61335i) q^{7} +(1.70106 - 2.25973i) q^{8} +(-0.215337 - 0.675709i) q^{10} +(-0.848493 + 1.46963i) q^{11} +(-1.89819 + 3.28776i) q^{13} +(3.48608 + 1.35913i) q^{14} +(2.60865 + 3.03232i) q^{16} +(-4.12962 + 2.38424i) q^{17} +(-0.0919457 - 0.0530849i) q^{19} +(0.998575 - 0.0935560i) q^{20} +(-1.77437 - 1.61590i) q^{22} +(3.77997 + 6.54710i) q^{23} +(-2.37426 + 4.11234i) q^{25} +(-3.96950 - 3.61498i) q^{26} +(-2.93007 + 4.40621i) q^{28} +(-6.33235 + 3.65598i) q^{29} +4.05307i q^{31} +(-4.97694 + 2.68888i) q^{32} +(-2.04762 - 6.42526i) q^{34} +(0.475999 + 1.23845i) q^{35} +(3.83900 - 6.64935i) q^{37} +(0.101097 - 0.111011i) q^{38} +(-0.172155 + 1.40790i) q^{40} +(2.60966 + 1.50669i) q^{41} +(3.98023 - 2.29799i) q^{43} +(2.76815 - 1.96377i) q^{44} +(-10.1866 + 3.24630i) q^{46} -4.07341 q^{47} +(-6.65923 - 2.15747i) q^{49} +(-4.96506 - 4.52163i) q^{50} +(6.19272 - 4.39320i) q^{52} +(-8.79953 + 5.08041i) q^{53} -0.850995i q^{55} +(-5.20331 - 5.37825i) q^{56} +(-3.13982 - 9.85248i) q^{58} -3.35792 q^{59} -1.83880 q^{61} +(-5.59982 - 1.22340i) q^{62} +(-2.21277 - 7.68789i) q^{64} -1.90379i q^{65} -3.90768i q^{67} +(9.49537 - 0.889617i) q^{68} +(-1.85475 + 0.283833i) q^{70} +9.65339 q^{71} +(5.55175 + 9.61592i) q^{73} +(8.02813 + 7.31113i) q^{74} +(0.122860 + 0.173186i) q^{76} +(3.49043 + 2.82405i) q^{77} +4.70354i q^{79} +(-1.89322 - 0.662820i) q^{80} +(-2.86939 + 3.15079i) q^{82} +(-6.75864 - 11.7063i) q^{83} +(1.19563 - 2.07090i) q^{85} +(1.97355 + 6.19283i) q^{86} +(1.87764 + 4.41731i) q^{88} +(4.73824 + 2.73562i) q^{89} +(7.80855 + 6.31776i) q^{91} +(-1.41040 - 15.0540i) q^{92} +(1.22954 - 5.62793i) q^{94} +0.0532414 q^{95} +(6.45605 + 11.1822i) q^{97} +(4.99087 - 8.54934i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.301845	+	1.38163i	−0.213436	+	0.976957i
$2$	−0.301845	+	1.38163i	−0.213436	+	0.976957i
$3$		0			0
$3$		0			0
$4$	−1.81778	−	0.834072i	−0.908890	−	0.417036i
$5$	−0.434289	+	0.250737i	−0.194220	+	0.112133i	−0.593957	−	0.804497i	$-0.702435\pi$
$5$	−0.434289	+	0.250737i	−0.194220	+	0.112133i	0.399737	+	0.916630i	$0.369102\pi$
$6$		0			0
$7$	0.412779	−	2.61335i	0.156016	−	0.987755i
$7$	0.412779	−	2.61335i	0.156016	−	0.987755i
$8$	1.70106	−	2.25973i	0.601417	−	0.798936i
$9$		0			0
$10$	−0.215337	−	0.675709i	−0.0680955	−	0.213678i
$11$	−0.848493	+	1.46963i	−0.255830	+	0.443111i	−0.965121	−	0.261805i	$-0.915682\pi$
$11$	−0.848493	+	1.46963i	−0.255830	+	0.443111i	0.709290	+	0.704916i	$0.249016\pi$
$12$		0			0
$13$	−1.89819	+	3.28776i	−0.526463	+	0.911861i	0.473061	+	0.881030i	$0.343149\pi$
$13$	−1.89819	+	3.28776i	−0.526463	+	0.911861i	−0.999525	+	0.0308317i	$0.990184\pi$
$14$	3.48608	+	1.35913i	0.931694	+	0.363243i
$15$		0			0
$16$	2.60865	+	3.03232i	0.652162	+	0.758080i
$17$	−4.12962	+	2.38424i	−1.00158	+	0.578263i	−0.908716	−	0.417416i	$-0.862936\pi$
$17$	−4.12962	+	2.38424i	−1.00158	+	0.578263i	−0.0928651	+	0.995679i	$0.529603\pi$
$18$		0			0
$19$	−0.0919457	−	0.0530849i	−0.0210938	−	0.0121785i	0.489416	−	0.872050i	$-0.337210\pi$
$19$	−0.0919457	−	0.0530849i	−0.0210938	−	0.0121785i	−0.510510	+	0.859872i	$0.670543\pi$
$20$	0.998575	−	0.0935560i	0.223288	−	0.0209198i
$21$		0			0
$22$	−1.77437	−	1.61590i	−0.378297	−	0.344511i
$23$	3.77997	+	6.54710i	0.788178	+	1.36516i	0.927082	+	0.374859i	$0.122309\pi$
$23$	3.77997	+	6.54710i	0.788178	+	1.36516i	−0.138904	+	0.990306i	$0.544358\pi$
$24$		0			0
$25$	−2.37426	+	4.11234i	−0.474852	+	0.822468i
$26$	−3.96950	−	3.61498i	−0.778483	−	0.708956i
$27$		0			0
$28$	−2.93007	+	4.40621i	−0.553731	+	0.832696i
$29$	−6.33235	+	3.65598i	−1.17589	+	0.678899i	−0.955060	−	0.296413i	$-0.904209\pi$
$29$	−6.33235	+	3.65598i	−1.17589	+	0.678899i	−0.220828	+	0.975313i	$0.570876\pi$
$30$		0			0
$31$			4.05307i			0.727952i	0.931408	+	0.363976i	$0.118581\pi$
$31$			4.05307i			0.727952i	−0.931408	+	0.363976i	$0.881419\pi$
$32$	−4.97694	+	2.68888i	−0.879807	+	0.475332i
$33$		0			0
$34$	−2.04762	−	6.42526i	−0.351164	−	1.10192i
$35$	0.475999	+	1.23845i	0.0804585	+	0.209336i
$36$		0			0
$37$	3.83900	−	6.64935i	0.631128	−	1.09315i	−0.356193	−	0.934412i	$-0.615926\pi$
$37$	3.83900	−	6.64935i	0.631128	−	1.09315i	0.987321	−	0.158734i	$-0.0507411\pi$
$38$	0.101097	−	0.111011i	0.0164001	−	0.0180084i
$39$		0			0
$40$	−0.172155	+	1.40790i	−0.0272201	+	0.222608i
$41$	2.60966	+	1.50669i	0.407560	+	0.235305i	0.689741	−	0.724056i	$-0.257724\pi$
$41$	2.60966	+	1.50669i	0.407560	+	0.235305i	−0.282181	+	0.959361i	$0.591058\pi$
$42$		0			0
$43$	3.98023	−	2.29799i	0.606980	−	0.350440i	−0.164803	−	0.986327i	$-0.552699\pi$
$43$	3.98023	−	2.29799i	0.606980	−	0.350440i	0.771783	+	0.635887i	$0.219365\pi$
$44$	2.76815	−	1.96377i	0.417315	−	0.296049i
$45$		0			0
$46$	−10.1866	+	3.24630i	−1.50193	+	0.478641i
$47$	−4.07341			−0.594168			−0.297084	−	0.954851i	$-0.596014\pi$
$47$	−4.07341			−0.594168			−0.297084	+	0.954851i	$0.596014\pi$
$48$		0			0
$49$	−6.65923	−	2.15747i	−0.951318	−	0.308211i
$50$	−4.96506	−	4.52163i	−0.702166	−	0.639455i
$51$		0			0
$52$	6.19272	−	4.39320i	0.858776	−	0.609227i
$53$	−8.79953	+	5.08041i	−1.20871	+	0.697848i	−0.962477	−	0.271363i	$-0.912526\pi$
$53$	−8.79953	+	5.08041i	−1.20871	+	0.697848i	−0.246231	+	0.969211i	$0.579192\pi$
$54$		0			0
$55$		−	0.850995i		−	0.114748i
$56$	−5.20331	−	5.37825i	−0.695322	−	0.718699i
$57$		0			0
$58$	−3.13982	−	9.85248i	−0.412278	−	1.29369i
$59$	−3.35792			−0.437164			−0.218582	−	0.975819i	$-0.570143\pi$
$59$	−3.35792			−0.437164			−0.218582	+	0.975819i	$0.570143\pi$
$60$		0			0
$61$	−1.83880			−0.235435			−0.117717	−	0.993047i	$-0.537558\pi$
$61$	−1.83880			−0.235435			−0.117717	+	0.993047i	$0.537558\pi$
$62$	−5.59982	−	1.22340i	−0.711178	−	0.155371i
$63$		0			0
$64$	−2.21277	−	7.68789i	−0.276596	−	0.960986i
$65$		−	1.90379i		−	0.236136i
$66$		0			0
$67$		−	3.90768i		−	0.477399i	−0.971093	−	0.238699i	$-0.923279\pi$
$67$		−	3.90768i		−	0.477399i	0.971093	−	0.238699i	$-0.0767211\pi$
$68$	9.49537	−	0.889617i	1.15148	−	0.107882i
$69$		0			0
$70$	−1.85475	+	0.283833i	−0.221685	+	0.0339245i
$71$	9.65339			1.14565			0.572823	−	0.819679i	$-0.305848\pi$
$71$	9.65339			1.14565			0.572823	+	0.819679i	$0.305848\pi$
$72$		0			0
$73$	5.55175	+	9.61592i	0.649784	+	1.12546i	0.983174	+	0.182670i	$0.0584738\pi$
$73$	5.55175	+	9.61592i	0.649784	+	1.12546i	−0.333391	+	0.942789i	$0.608193\pi$
$74$	8.02813	+	7.31113i	0.933251	+	0.849902i
$75$		0			0
$76$	0.122860	+	0.173186i	0.0140931	+	0.0198658i
$77$	3.49043	+	2.82405i	0.397771	+	0.321830i
$78$		0			0
$79$			4.70354i			0.529189i	0.964360	+	0.264595i	$0.0852382\pi$
$79$			4.70354i			0.529189i	−0.964360	+	0.264595i	$0.914762\pi$
$80$	−1.89322	−	0.662820i	−0.211669	−	0.0741055i
$81$		0			0
$82$	−2.86939	+	3.15079i	−0.316871	+	0.347946i
$83$	−6.75864	−	11.7063i	−0.741858	−	1.28494i	−0.951649	−	0.307189i	$-0.900612\pi$
$83$	−6.75864	−	11.7063i	−0.741858	−	1.28494i	0.209791	−	0.977746i	$-0.432722\pi$
$84$		0			0
$85$	1.19563	−	2.07090i	0.129685	−	0.224621i
$86$	1.97355	+	6.19283i	0.212813	+	0.667790i
$87$		0			0
$88$	1.87764	+	4.41731i	0.200157	+	0.470886i
$89$	4.73824	+	2.73562i	0.502252	+	0.289975i	0.729643	−	0.683828i	$-0.239686\pi$
$89$	4.73824	+	2.73562i	0.502252	+	0.289975i	−0.227391	+	0.973804i	$0.573020\pi$
$90$		0			0
$91$	7.80855	+	6.31776i	0.818558	+	0.662281i
$92$	−1.41040	−	15.0540i	−0.147044	−	1.56948i
$93$		0			0
$94$	1.22954	−	5.62793i	0.126817	−	0.580476i
$95$	0.0532414			0.00546245
$96$		0			0
$97$	6.45605	+	11.1822i	0.655512	+	1.13538i	0.981765	+	0.190098i	$0.0608806\pi$
$97$	6.45605	+	11.1822i	0.655512	+	1.13538i	−0.326253	+	0.945283i	$0.605786\pi$
$98$	4.99087	−	8.54934i	0.504154	−	0.863614i
$99$		0			0
$100$	7.74588	−	5.49503i	0.774588	−	0.549503i
$101$	−9.07402	−	5.23889i	−0.902899	−	0.521289i	−0.0247592	−	0.999693i	$-0.507882\pi$
$101$	−9.07402	−	5.23889i	−0.902899	−	0.521289i	−0.878140	+	0.478405i	$0.841215\pi$
$102$		0			0
$103$	−16.4667	+	9.50707i	−1.62251	+	0.936759i	−0.636270	+	0.771467i	$0.719524\pi$
$103$	−16.4667	+	9.50707i	−1.62251	+	0.936759i	−0.986245	+	0.165293i	$0.947143\pi$
$104$	4.20052	+	9.88209i	0.411895	+	0.969019i
$105$		0			0
$106$	−4.36314	−	13.6911i	−0.423785	−	1.32980i
$107$	5.50504	−	9.53502i	0.532193	−	0.921785i	−0.467101	−	0.884204i	$-0.654702\pi$
$107$	5.50504	−	9.53502i	0.532193	−	0.921785i	0.999294	−	0.0375808i	$-0.0119652\pi$
$108$		0			0
$109$	2.16757	+	3.75434i	0.207615	+	0.359600i	0.950963	−	0.309305i	$-0.100096\pi$
$109$	2.16757	+	3.75434i	0.207615	+	0.359600i	−0.743348	+	0.668905i	$0.766763\pi$
$110$	1.17576	+	0.256868i	0.112104	+	0.0244914i
$111$		0			0
$112$	9.00132	−	5.56564i	0.850544	−	0.525903i
$113$	−2.92804	−	1.69051i	−0.275447	−	0.159029i	0.355913	−	0.934519i	$-0.384170\pi$
$113$	−2.92804	−	1.69051i	−0.275447	−	0.159029i	−0.631360	+	0.775490i	$0.717503\pi$
$114$		0			0
$115$	−3.28320	−	1.89556i	−0.306160	−	0.176762i
$116$	14.5602	−	1.36414i	1.35188	−	0.126657i
$117$		0			0
$118$	1.01357	−	4.63939i	0.0933067	−	0.427091i
$119$	4.52624	+	11.7763i	0.414919	+	1.07953i
$120$		0			0
$121$	4.06012	+	7.03233i	0.369102	+	0.639303i
$122$	0.555033	−	2.54054i	0.0502503	−	0.230010i
$123$		0			0
$124$	3.38055	−	7.36758i	0.303582	−	0.661628i
$125$		−	4.88863i		−	0.437253i
$126$		0			0
$127$		−	8.51215i		−	0.755332i	−0.925942	−	0.377666i	$-0.876727\pi$
$127$		−	8.51215i		−	0.755332i	0.925942	−	0.377666i	$-0.123273\pi$
$128$	11.2897	−	0.736673i	0.997878	−	0.0651133i
$129$		0			0
$130$	2.63032	+	0.574648i	0.230694	+	0.0503999i
$131$	−4.21018	−	7.29224i	−0.367845	−	0.637126i	0.621383	−	0.783507i	$-0.286571\pi$
$131$	−4.21018	−	7.29224i	−0.367845	−	0.637126i	−0.989228	+	0.146380i	$0.953238\pi$
$132$		0			0
$133$	−0.176683	+	0.218374i	−0.0153203	+	0.0189354i
$134$	5.39895	+	1.17951i	0.466398	+	0.101894i
$135$		0			0
$136$	−1.63701	+	13.3876i	−0.140372	+	1.14798i
$137$	3.68374	+	2.12681i	0.314723	+	0.181706i	0.649038	−	0.760756i	$-0.275172\pi$
$137$	3.68374	+	2.12681i	0.314723	+	0.181706i	−0.334315	+	0.942461i	$0.608505\pi$
$138$		0			0
$139$	−0.535435	−	0.309134i	−0.0454150	−	0.0262204i	0.477121	−	0.878838i	$-0.341680\pi$
$139$	−0.535435	−	0.309134i	−0.0454150	−	0.0262204i	−0.522536	+	0.852617i	$0.675014\pi$
$140$	0.167696	−	2.64825i	0.0141729	−	0.223818i
$141$		0			0
$142$	−2.91382	+	13.3374i	−0.244523	+	1.11925i
$143$	−3.22120	−	5.57929i	−0.269371	−	0.466564i
$144$		0			0
$145$	1.83338	−	3.17551i	0.152254	−	0.263712i
$146$	−14.9614	+	4.76793i	−1.23821	+	0.394597i
$147$		0			0
$148$	−12.5245	+	8.88504i	−1.02951	+	0.730346i
$149$	5.20674	−	3.00611i	0.426553	−	0.246270i	−0.271324	−	0.962488i	$-0.587462\pi$
$149$	5.20674	−	3.00611i	0.426553	−	0.246270i	0.697877	+	0.716218i	$0.254128\pi$
$150$		0			0
$151$	−19.1862	−	11.0771i	−1.56135	−	0.901444i	−0.997121	−	0.0758241i	$-0.975841\pi$
$151$	−19.1862	−	11.0771i	−1.56135	−	0.901444i	−0.564226	−	0.825620i	$-0.690825\pi$
$152$	−0.276363	+	0.117472i	−0.0224160	+	0.00952822i
$153$		0			0
$154$	−4.95534	+	3.97005i	−0.399313	+	0.319915i
$155$	−1.01625	−	1.76020i	−0.0816275	−	0.141383i
$156$		0			0
$157$	3.89816			0.311107			0.155553	−	0.987827i	$-0.450284\pi$
$157$	3.89816			0.311107			0.155553	+	0.987827i	$0.450284\pi$
$158$	−6.49853	−	1.41974i	−0.516995	−	0.112948i
$159$		0			0
$160$	1.48723	−	2.41566i	0.117576	−	0.190974i
$161$	18.6702	−	7.17589i	1.47142	−	0.565539i
$162$		0			0
$163$	16.9101	+	9.76307i	1.32450	+	0.764703i	0.984444	−	0.175701i	$-0.0562192\pi$
$163$	16.9101	+	9.76307i	1.32450	+	0.764703i	0.340060	+	0.940404i	$0.389553\pi$
$164$	−3.48710	−	4.91547i	−0.272297	−	0.383834i
$165$		0			0
$166$	18.2138	−	5.80443i	1.41367	−	0.450511i
$167$	2.20243	−	3.81473i	0.170430	−	0.295193i	−0.768141	−	0.640281i	$-0.778818\pi$
$167$	2.20243	−	3.81473i	0.170430	−	0.295193i	0.938570	+	0.345089i	$0.112151\pi$
$168$		0			0
$169$	−0.706255	−	1.22327i	−0.0543273	−	0.0940976i
$170$	2.50031	+	2.27701i	0.191765	+	0.174639i
$171$		0			0
$172$	−9.15188	+	0.857435i	−0.697824	+	0.0653788i
$173$			17.9628i			1.36569i	0.730564	+	0.682844i	$0.239257\pi$
$173$			17.9628i			1.36569i	−0.730564	+	0.682844i	$0.760743\pi$
$174$		0			0
$175$	9.76696	+	7.90227i	0.738312	+	0.597356i
$176$	−6.66982	+	1.26085i	−0.502756	+	0.0950402i
$177$		0			0
$178$	−5.20982	+	5.72074i	−0.390492	+	0.428787i
$179$	4.24475	+	7.35212i	0.317267	+	0.549523i	0.979917	−	0.199406i	$-0.0639014\pi$
$179$	4.24475	+	7.35212i	0.317267	+	0.549523i	−0.662649	+	0.748930i	$0.730568\pi$
$180$		0			0
$181$	−24.6598			−1.83295			−0.916476	−	0.400090i	$-0.868979\pi$
$181$	−24.6598			−1.83295			−0.916476	+	0.400090i	$0.868979\pi$
$182$	−11.0858	+	8.88151i	−0.821730	+	0.658342i
$183$		0			0
$184$	21.2247	+	2.59531i	1.56470	+	0.191329i
$185$			3.85032i			0.283081i
$186$		0			0
$187$		−	8.09204i		−	0.591749i
$188$	7.40456	+	3.39752i	0.540033	+	0.247789i
$189$		0			0
$190$	−0.0160706	+	0.0735596i	−0.00116589	+	0.00533658i
$191$	5.92072			0.428408			0.214204	−	0.976789i	$-0.431284\pi$
$191$	5.92072			0.428408			0.214204	+	0.976789i	$0.431284\pi$
$192$		0			0
$193$	16.4871			1.18676			0.593382	−	0.804921i	$-0.297792\pi$
$193$	16.4871			1.18676			0.593382	+	0.804921i	$0.297792\pi$
$194$	−17.3983	+	5.54456i	−1.24913	+	0.398076i
$195$		0			0
$196$	10.3055	+	9.47609i	0.736108	+	0.676864i
$197$			4.24471i			0.302423i	0.988501	+	0.151212i	$0.0483175\pi$
$197$			4.24471i			0.302423i	−0.988501	+	0.151212i	$0.951683\pi$
$198$		0			0
$199$	18.9984	−	10.9688i	1.34676	−	0.777555i	0.358974	−	0.933347i	$-0.383127\pi$
$199$	18.9984	−	10.9688i	1.34676	−	0.777555i	0.987790	+	0.155793i	$0.0497932\pi$
$200$	5.25402	+	12.3605i	0.371515	+	0.874023i
$201$		0			0
$202$	9.97713	−	10.9556i	0.701988	−	0.770831i
$203$	6.94052	+	18.0578i	0.487129	+	1.26741i
$204$		0			0
$205$	−1.51113			−0.105542
$206$	−8.16482	−	25.6205i	−0.568870	−	1.78507i
$207$		0			0
$208$	−14.9213	+	2.82069i	−1.03460	+	0.195580i
$209$	0.156031	−	0.0900843i	0.0107929	−	0.00623126i
$210$		0			0
$211$	8.25342	+	4.76511i	0.568189	+	0.328044i	0.756426	−	0.654080i	$-0.226944\pi$
$211$	8.25342	+	4.76511i	0.568189	+	0.328044i	−0.188237	+	0.982124i	$0.560277\pi$
$212$	20.2330	−	1.89562i	1.38961	−	0.130192i
$213$		0			0
$214$	11.5122	+	10.4840i	0.786955	+	0.716672i
$215$	−1.15238	+	1.99598i	−0.0785918	+	0.136125i
$216$		0			0
$217$	10.5921	+	1.67302i	0.719038	+	0.113572i
$218$	−5.84136	+	1.86154i	−0.395627	+	0.126079i
$219$		0			0
$220$	−0.709791	+	1.54692i	−0.0478541	+	0.104293i
$221$		−	18.1030i		−	1.21774i
$222$		0			0
$223$	9.02007	−	5.20774i	0.604029	−	0.348736i	−0.166596	−	0.986025i	$-0.553278\pi$
$223$	9.02007	−	5.20774i	0.604029	−	0.348736i	0.770625	+	0.637289i	$0.219944\pi$
$224$	4.97263	+	14.1164i	0.332248	+	0.943192i
$225$		0			0
$226$	3.21946	−	3.53519i	0.214155	−	0.235157i
$227$	−2.89895	+	5.02113i	−0.192410	+	0.333264i	−0.946048	−	0.324025i	$-0.894964\pi$
$227$	−2.89895	+	5.02113i	−0.192410	+	0.333264i	0.753638	+	0.657289i	$0.228297\pi$
$228$		0			0
$229$	2.46681	+	4.27263i	0.163011	+	0.282344i	0.935947	−	0.352140i	$-0.114546\pi$
$229$	2.46681	+	4.27263i	0.163011	+	0.282344i	−0.772936	+	0.634484i	$0.781213\pi$
$230$	3.60997	−	3.96399i	0.238034	−	0.261378i
$231$		0			0
$232$	−2.51019	+	20.5285i	−0.164802	+	1.34776i
$233$	−9.83606	−	5.67885i	−0.644382	−	0.372034i	0.141919	−	0.989878i	$-0.454673\pi$
$233$	−9.83606	−	5.67885i	−0.644382	−	0.372034i	−0.786300	+	0.617844i	$0.788006\pi$
$234$		0			0
$235$	1.76904	−	1.02135i	0.115399	−	0.0666258i
$236$	6.10396	+	2.80075i	0.397334	+	0.182313i
$237$		0			0
$238$	−17.6367	+	2.69894i	−1.14322	+	0.174947i
$239$	−7.21752	+	12.5011i	−0.466862	+	0.808629i	−0.999283	−	0.0378504i	$-0.987949\pi$
$239$	−7.21752	+	12.5011i	−0.466862	+	0.808629i	0.532421	+	0.846480i	$0.321282\pi$
$240$		0			0
$241$	7.04044	−	12.1944i	0.453515	−	0.785511i	−0.545087	−	0.838380i	$-0.683503\pi$
$241$	7.04044	−	12.1944i	0.453515	−	0.785511i	0.998601	+	0.0528690i	$0.0168366\pi$
$242$	−10.9416	+	3.48689i	−0.703351	+	0.224146i
$243$		0			0
$244$	3.34254	+	1.53370i	0.213984	+	0.0981848i
$245$	3.43299	−	0.732747i	0.219326	−	0.0468135i
$246$		0			0
$247$	0.349061	−	0.201530i	0.0222102	−	0.0128231i
$248$	9.15884	+	6.89452i	0.581587	+	0.437803i
$249$		0			0
$250$	6.75426	+	1.47561i	0.427177	+	0.0933256i
$251$	−25.2044			−1.59089			−0.795445	−	0.606026i	$-0.792763\pi$
$251$	−25.2044			−1.59089			−0.795445	+	0.606026i	$0.792763\pi$
$252$		0			0
$253$	−12.8291			−0.806560
$254$	11.7606	+	2.56935i	0.737926	+	0.161215i
$255$		0			0
$256$	−2.38993	+	15.8205i	−0.149371	+	0.988781i
$257$	−6.16791	+	3.56105i	−0.384744	+	0.222132i	−0.679880	−	0.733323i	$-0.737968\pi$
$257$	−6.16791	+	3.56105i	−0.384744	+	0.222132i	0.295136	+	0.955455i	$0.404635\pi$
$258$		0			0
$259$	−15.7924	−	12.7774i	−0.981294	−	0.793948i
$260$	−1.58790	+	3.46066i	−0.0984771	+	0.214621i
$261$		0			0
$262$	11.3460	−	3.61577i	0.700957	−	0.223383i
$263$	13.6958	−	23.7218i	0.844520	−	1.46275i	−0.0415174	−	0.999138i	$-0.513219\pi$
$263$	13.6958	−	23.7218i	0.844520	−	1.46275i	0.886037	−	0.463614i	$-0.153447\pi$
$264$		0			0
$265$	2.54769	−	4.41273i	0.156504	−	0.271072i
$266$	−0.248381	−	0.310025i	−0.0152292	−	0.0190088i
$267$		0			0
$268$	−3.25929	+	7.10330i	−0.199093	+	0.433903i
$269$	4.90694	−	2.83302i	0.299181	−	0.172732i	−0.342894	−	0.939374i	$-0.611407\pi$
$269$	4.90694	−	2.83302i	0.299181	−	0.172732i	0.642075	+	0.766642i	$0.278074\pi$
$270$		0			0
$271$	−14.0632	−	8.11940i	−0.854279	−	0.493218i	0.00781341	−	0.999969i	$-0.497513\pi$
$271$	−14.0632	−	8.11940i	−0.854279	−	0.493218i	−0.862092	+	0.506751i	$0.830846\pi$
$272$	−18.0025	−	6.30270i	−1.09156	−	0.382157i
$273$		0			0
$274$	−4.05037	+	4.44759i	−0.244692	+	0.268689i
$275$	−4.02909	−	6.97859i	−0.242963	−	0.420825i
$276$		0			0
$277$	1.38817	−	2.40438i	0.0834071	−	0.144465i	−0.821304	−	0.570490i	$-0.806753\pi$
$277$	1.38817	−	2.40438i	0.0834071	−	0.144465i	0.904711	+	0.426025i	$0.140086\pi$
$278$	0.588725	−	0.646461i	0.0353094	−	0.0387721i
$279$		0			0
$280$	3.60827	+	1.03105i	0.215635	+	0.0616172i
$281$	25.4336	−	14.6841i	1.51724	−	0.875981i	0.517448	−	0.855714i	$-0.326882\pi$
$281$	25.4336	−	14.6841i	1.51724	−	0.875981i	0.999795	−	0.0202663i	$-0.00645142\pi$
$282$		0			0
$283$			30.6584i			1.82245i	0.411904	+	0.911227i	$0.364864\pi$
$283$			30.6584i			1.82245i	−0.411904	+	0.911227i	$0.635136\pi$
$284$	−17.5477	−	8.05162i	−1.04127	−	0.477776i
$285$		0			0
$286$	8.68079	−	2.76642i	0.513306	−	0.163582i
$287$	5.01472	−	6.19803i	0.296010	−	0.365858i
$288$		0			0
$289$	2.86919	−	4.96958i	0.168776	−	0.292328i
$290$	3.83397	+	3.49156i	0.225138	+	0.205031i
$291$		0			0
$292$	−2.07149	−	22.1102i	−0.121225	−	1.29390i
$293$	1.86213	+	1.07510i	0.108787	+	0.0628079i	0.553406	−	0.832912i	$-0.313328\pi$
$293$	1.86213	+	1.07510i	0.108787	+	0.0628079i	−0.444620	+	0.895720i	$0.646661\pi$
$294$		0			0
$295$	1.45831	−	0.841955i	0.0849060	−	0.0490205i
$296$	−8.49535	−	19.9861i	−0.493782	−	1.16167i
$297$		0			0
$298$	2.58170	+	8.10114i	0.149554	+	0.469287i
$299$	−28.7004			−1.65979
$300$		0			0
$301$	−4.36250	−	11.3503i	−0.251450	−	0.654221i
$302$	21.0957	−	23.1645i	1.21392	−	1.33297i
$303$		0			0
$304$	−0.0788835	−	0.417288i	−0.00452428	−	0.0239331i
$305$	0.798573	−	0.461056i	0.0457262	−	0.0264000i
$306$		0			0
$307$		−	19.1505i		−	1.09298i	−0.837467	−	0.546488i	$-0.815964\pi$
$307$		−	19.1505i		−	1.09298i	0.837467	−	0.546488i	$-0.184036\pi$
$308$	−3.98937	−	8.04477i	−0.227316	−	0.458393i
$309$		0			0
$310$	2.73869	−	0.872775i	0.155547	−	0.0495703i
$311$	−5.69121			−0.322719			−0.161360	−	0.986896i	$-0.551588\pi$
$311$	−5.69121			−0.322719			−0.161360	+	0.986896i	$0.551588\pi$
$312$		0			0
$313$	−24.6144			−1.39129			−0.695645	−	0.718386i	$-0.744881\pi$
$313$	−24.6144			−1.39129			−0.695645	+	0.718386i	$0.744881\pi$
$314$	−1.17664	+	5.38580i	−0.0664015	+	0.303938i
$315$		0			0
$316$	3.92309	−	8.55000i	0.220691	−	0.480975i
$317$		−	11.8774i		−	0.667102i	−0.942732	−	0.333551i	$-0.891753\pi$
$317$		−	11.8774i		−	0.667102i	0.942732	−	0.333551i	$-0.108247\pi$
$318$		0			0
$319$		−	12.4083i		−	0.694732i
$320$	2.88862	+	2.78394i	0.161479	+	0.155627i
$321$		0			0
$322$	4.27890	+	27.9612i	0.238454	+	1.55822i
$323$	0.506268			0.0281695
$324$		0			0
$325$	−9.01360	−	15.6120i	−0.499985	−	0.865999i
$326$	−18.5931	+	20.4165i	−1.02978	+	1.13077i
$327$		0			0
$328$	7.84390	−	3.33416i	0.433107	−	0.184098i
$329$	−1.68142	+	10.6453i	−0.0926996	+	0.586892i
$330$		0			0
$331$			15.9548i			0.876956i	0.898742	+	0.438478i	$0.144482\pi$
$331$			15.9548i			0.876956i	−0.898742	+	0.438478i	$0.855518\pi$
$332$	2.52181	+	26.9167i	0.138402	+	1.47725i
$333$		0			0
$334$	4.60573	+	4.19440i	0.252015	+	0.229507i
$335$	0.979800	+	1.69706i	0.0535322	+	0.0927204i
$336$		0			0
$337$	6.26967	−	10.8594i	0.341531	−	0.591549i	−0.643186	−	0.765710i	$-0.722388\pi$
$337$	6.26967	−	10.8594i	0.341531	−	0.591549i	0.984717	+	0.174161i	$0.0557213\pi$
$338$	1.90328	−	0.606543i	0.103525	−	0.0329916i
$339$		0			0
$340$	−3.90068	+	2.76719i	−0.211544	+	0.150072i
$341$	−5.95652	−	3.43900i	−0.322564	−	0.186232i
$342$		0			0
$343$	−8.38703	+	16.5123i	−0.452857	+	0.891583i
$344$	1.57779	−	12.9033i	0.0850688	−	0.695698i
$345$		0			0
$346$	−24.8179	−	5.42198i	−1.33422	−	0.291487i
$347$	23.2769			1.24957			0.624784	−	0.780798i	$-0.285187\pi$
$347$	23.2769			1.24957			0.624784	+	0.780798i	$0.285187\pi$
$348$		0			0
$349$	−11.9434	−	20.6866i	−0.639317	−	1.10733i	−0.985583	−	0.169193i	$-0.945884\pi$
$349$	−11.9434	−	20.6866i	−0.639317	−	1.10733i	0.346266	−	0.938136i	$-0.387449\pi$
$350$	−13.8661	+	11.1090i	−0.741174	+	0.593802i
$351$		0			0
$352$	0.271224	−	9.59577i	0.0144563	−	0.511456i
$353$	26.4000	+	15.2421i	1.40513	+	0.811253i	0.994913	−	0.100734i	$-0.0321191\pi$
$353$	26.4000	+	15.2421i	1.40513	+	0.811253i	0.410219	+	0.911987i	$0.365452\pi$
$354$		0			0
$355$	−4.19236	+	2.42046i	−0.222507	+	0.128465i
$356$	−6.33136	−	8.92479i	−0.335561	−	0.473013i
$357$		0			0
$358$	−11.4391	+	3.64546i	−0.604577	+	0.192668i
$359$	−8.47002	+	14.6705i	−0.447031	+	0.774280i	−0.998191	−	0.0601193i	$-0.980852\pi$
$359$	−8.47002	+	14.6705i	−0.447031	+	0.774280i	0.551160	+	0.834399i	$0.314185\pi$
$360$		0			0
$361$	−9.49436	−	16.4447i	−0.499703	−	0.865512i
$362$	7.44344	−	34.0707i	0.391219	−	1.79072i
$363$		0			0
$364$	−8.92475	−	17.9972i	−0.467784	−	0.943309i
$365$	−4.82213	−	2.78406i	−0.252402	−	0.145724i
$366$		0			0
$367$	−12.2763	−	7.08772i	−0.640818	−	0.369976i	0.144112	−	0.989561i	$-0.453967\pi$
$367$	−12.2763	−	7.08772i	−0.640818	−	0.369976i	−0.784929	+	0.619585i	$0.787301\pi$
$368$	−9.99230	+	28.5411i	−0.520885	+	1.48781i
$369$		0			0
$370$	−5.31970	−	1.16220i	−0.276558	−	0.0604198i
$371$	9.64464	+	25.0934i	0.500725	+	1.30278i
$372$		0			0
$373$	1.35731	+	2.35093i	0.0702790	+	0.121727i	0.899024	−	0.437900i	$-0.144278\pi$
$373$	1.35731	+	2.35093i	0.0702790	+	0.121727i	−0.828745	+	0.559627i	$0.810944\pi$
$374$	11.1802	+	2.44254i	0.578113	+	0.126301i
$375$		0			0
$376$	−6.92912	+	9.20481i	−0.357342	+	0.474702i
$377$		−	27.7590i		−	1.42966i
$378$		0			0
$379$			14.5807i			0.748961i	0.927235	+	0.374480i	$0.122179\pi$
$379$			14.5807i			0.748961i	−0.927235	+	0.374480i	$0.877821\pi$
$380$	−0.0967811	−	0.0444072i	−0.00496476	−	0.00227804i
$381$		0			0
$382$	−1.78714	+	8.18021i	−0.0914378	+	0.418536i
$383$	−11.1110	−	19.2449i	−0.567747	−	0.983367i	−0.996788	−	0.0800822i	$-0.974482\pi$
$383$	−11.1110	−	19.2449i	−0.567747	−	0.983367i	0.429041	−	0.903285i	$-0.358852\pi$
$384$		0			0
$385$	−2.22395	−	0.351273i	−0.113343	−	0.0179025i
$386$	−4.97653	+	22.7789i	−0.253299	+	1.15942i
$387$		0			0
$388$	−2.40891	−	25.7116i	−0.122294	−	1.30531i
$389$	−7.02972	−	4.05861i	−0.356421	−	0.205780i	0.311089	−	0.950381i	$-0.399306\pi$
$389$	−7.02972	−	4.05861i	−0.356421	−	0.205780i	−0.667510	+	0.744601i	$0.732640\pi$
$390$		0			0
$391$	−31.2197	−	18.0247i	−1.57885	−	0.911549i
$392$	−16.2031	+	11.3781i	−0.818379	+	0.574679i
$393$		0			0
$394$	−5.86460	−	1.28124i	−0.295454	−	0.0645481i
$395$	−1.17935	−	2.04270i	−0.0593396	−	0.102779i
$396$		0			0
$397$	8.63142	−	14.9501i	0.433199	−	0.750322i	−0.563948	−	0.825810i	$-0.690718\pi$
$397$	8.63142	−	14.9501i	0.433199	−	0.750322i	0.997147	+	0.0754882i	$0.0240515\pi$
$398$	9.42014	+	29.5596i	0.472189	+	1.48169i
$399$		0			0
$400$	−18.6635	+	3.52812i	−0.933177	+	0.176406i
$401$	−0.786900	+	0.454317i	−0.0392959	+	0.0226875i	−0.519519	−	0.854459i	$-0.673889\pi$
$401$	−0.786900	+	0.454317i	−0.0392959	+	0.0226875i	0.480223	+	0.877146i	$0.340556\pi$
$402$		0			0
$403$	−13.3255	−	7.69349i	−0.663791	−	0.383240i
$404$	12.1250	+	17.0915i	0.603239	+	0.850336i
$405$		0			0
$406$	−27.0441	+	4.13855i	−1.34217	+	0.205393i
$407$	6.51473	+	11.2839i	0.322923	+	0.559320i
$408$		0			0
$409$	−34.6194			−1.71182			−0.855909	−	0.517127i	$-0.827002\pi$
$409$	−34.6194			−1.71182			−0.855909	+	0.517127i	$0.827002\pi$
$410$	0.456126	−	2.08782i	0.0225265	−	0.103110i
$411$		0			0
$412$	37.8625	−	3.54731i	1.86535	−	0.174764i
$413$	−1.38608	+	8.77543i	−0.0682045	+	0.431811i
$414$		0			0
$415$	5.87041	+	3.38929i	0.288167	+	0.166373i
$416$	0.606764	−	21.4670i	0.0297490	−	1.05251i
$417$		0			0
$418$	0.0773658	+	0.242767i	0.00378409	+	0.0118741i
$419$	18.7089	−	32.4047i	0.913989	−	1.58308i	0.105614	−	0.994407i	$-0.466319\pi$
$419$	18.7089	−	32.4047i	0.913989	−	1.58308i	0.808375	−	0.588668i	$-0.200347\pi$
$420$		0			0
$421$	−2.84045	−	4.91981i	−0.138435	−	0.239777i	0.788469	−	0.615074i	$-0.210874\pi$
$421$	−2.84045	−	4.91981i	−0.138435	−	0.239777i	−0.926904	+	0.375297i	$0.877541\pi$
$422$	−9.07485	+	9.96481i	−0.441757	+	0.485080i
$423$		0			0
$424$	−3.48819	+	28.5267i	−0.169401	+	1.38538i
$425$		−	22.6432i		−	1.09836i
$426$		0			0
$427$	−0.759020	+	4.80545i	−0.0367316	+	0.232552i
$428$	−17.9599	+	12.7410i	−0.868122	+	0.615857i
$429$		0			0
$430$	−2.40986	−	2.19464i	−0.116214	−	0.105835i
$431$	5.53553	+	9.58782i	0.266637	+	0.461829i	0.967991	−	0.250984i	$-0.0807541\pi$
$431$	5.53553	+	9.58782i	0.266637	+	0.461829i	−0.701354	+	0.712813i	$0.747421\pi$
$432$		0			0
$433$	13.1104			0.630044			0.315022	−	0.949084i	$-0.397988\pi$
$433$	13.1104			0.630044			0.315022	+	0.949084i	$0.397988\pi$
$434$	−5.50865	+	14.1293i	−0.264424	+	0.678229i
$435$		0			0
$436$	−0.808771	−	8.63247i	−0.0387331	−	0.413420i
$437$		−	0.802637i		−	0.0383953i
$438$		0			0
$439$			35.6477i			1.70137i	0.525673	+	0.850687i	$0.323814\pi$
$439$			35.6477i			1.70137i	−0.525673	+	0.850687i	$0.676186\pi$
$440$	−1.92302	−	1.44760i	−0.0916763	−	0.0690114i
$441$		0			0
$442$	25.0115	+	5.46428i	1.18968	+	0.259909i
$443$	11.9641			0.568430			0.284215	−	0.958761i	$-0.408267\pi$
$443$	11.9641			0.568430			0.284215	+	0.958761i	$0.408267\pi$
$444$		0			0
$445$	−2.74369			−0.130063
$446$	4.47249	+	14.0343i	0.211779	+	0.664543i
$447$		0			0
$448$	−21.0046	+	2.60935i	−0.992372	+	0.123280i
$449$			2.61389i			0.123357i	0.998096	+	0.0616786i	$0.0196454\pi$
$449$			2.61389i			0.123357i	−0.998096	+	0.0616786i	$0.980355\pi$
$450$		0			0
$451$	−4.42856	+	2.55683i	−0.208533	+	0.120396i
$452$	3.91253	+	5.51516i	0.184030	+	0.259412i
$453$		0			0
$454$	−6.06229	−	5.52087i	−0.284517	−	0.259107i
$455$	−4.97527	−	0.785843i	−0.233244	−	0.0368409i
$456$		0			0
$457$	17.7861			0.831997			0.415998	−	0.909365i	$-0.363432\pi$
$457$	17.7861			0.831997			0.415998	+	0.909365i	$0.363432\pi$
$458$	−6.64777	+	2.11853i	−0.310630	+	0.0989925i
$459$		0			0
$460$	4.38710	+	6.18413i	0.204550	+	0.288337i
$461$	−28.0337	+	16.1853i	−1.30566	+	0.753824i	−0.981369	−	0.192133i	$-0.938460\pi$
$461$	−28.0337	+	16.1853i	−1.30566	+	0.753824i	−0.324293	+	0.945957i	$0.605126\pi$
$462$		0			0
$463$	20.5925	+	11.8891i	0.957015	+	0.552533i	0.895253	−	0.445558i	$-0.146995\pi$
$463$	20.5925	+	11.8891i	0.957015	+	0.552533i	0.0617618	+	0.998091i	$0.480328\pi$
$464$	−27.6050	−	9.66454i	−1.28153	−	0.448665i
$465$		0			0
$466$	10.8150	−	11.8756i	0.500996	−	0.550128i
$467$	−3.53691	+	6.12611i	−0.163669	+	0.283483i	−0.936182	−	0.351516i	$-0.885666\pi$
$467$	−3.53691	+	6.12611i	−0.163669	+	0.283483i	0.772513	+	0.634999i	$0.219000\pi$
$468$		0			0
$469$	−10.2121	−	1.61301i	−0.471553	−	0.0744818i
$470$	0.877155	+	2.75244i	0.0404602	+	0.126961i
$471$		0			0
$472$	−5.71204	+	7.58800i	−0.262918	+	0.349266i
$473$			7.79931i			0.358613i
$474$		0			0
$475$	0.436606	−	0.252075i	0.0200329	−	0.0115660i
$476$	1.59461	−	25.1820i	0.0730888	−	1.15421i
$477$		0			0
$478$	−15.0933	−	13.7453i	−0.690351	−	0.628695i
$479$	7.62713	−	13.2106i	0.348492	−	0.603607i	−0.637489	−	0.770459i	$-0.720027\pi$
$479$	7.62713	−	13.2106i	0.348492	−	0.603607i	0.985982	+	0.166852i	$0.0533604\pi$
$480$		0			0
$481$	14.5743	+	25.2435i	0.664532	+	1.15100i
$482$	14.7230	+	13.4081i	0.670614	+	0.610721i
$483$		0			0
$484$	−1.51493	−	16.1697i	−0.0688603	−	0.734985i
$485$	−5.60759	−	3.23754i	−0.254627	−	0.147009i
$486$		0			0
$487$	11.0078	−	6.35536i	0.498811	−	0.287989i	−0.229411	−	0.973330i	$-0.573680\pi$
$487$	11.0078	−	6.35536i	0.498811	−	0.287989i	0.728222	+	0.685341i	$0.240347\pi$
$488$	−3.12792	+	4.15520i	−0.141594	+	0.188097i
$489$		0			0
$490$	−0.0238475	+	4.96428i	−0.00107732	+	0.224263i
$491$	−12.0966	+	20.9519i	−0.545911	+	0.945546i	0.452638	+	0.891695i	$0.350483\pi$
$491$	−12.0966	+	20.9519i	−0.545911	+	0.945546i	−0.998549	+	0.0538515i	$0.982850\pi$
$492$		0			0
$493$	17.4335	−	30.1957i	0.785165	−	1.35994i
$494$	0.173077	+	0.543102i	0.00778712	+	0.0244353i
$495$		0			0
$496$	−12.2902	+	10.5730i	−0.551846	+	0.474743i
$497$	3.98472	−	25.2277i	0.178739	−	1.13162i
$498$		0			0
$499$	−14.0057	+	8.08621i	−0.626983	+	0.361989i	−0.779583	−	0.626299i	$-0.784569\pi$
$499$	−14.0057	+	8.08621i	−0.626983	+	0.361989i	0.152600	+	0.988288i	$0.451235\pi$
$500$	−4.07747	+	8.88646i	−0.182350	+	0.397414i
$501$		0			0
$502$	7.60782	−	34.8231i	0.339554	−	1.55423i
$503$	5.44592			0.242822			0.121411	−	0.992602i	$-0.461258\pi$
$503$	5.44592			0.242822			0.121411	+	0.992602i	$0.461258\pi$
$504$		0			0
$505$	5.25433			0.233815
$506$	3.87240	−	17.7250i	0.172149	−	0.787974i
$507$		0			0
$508$	−7.09975	+	15.4732i	−0.315001	+	0.686513i
$509$	−6.38373	+	3.68565i	−0.282954	+	0.163364i	−0.634760	−	0.772709i	$-0.718901\pi$
$509$	−6.38373	+	3.68565i	−0.282954	+	0.163364i	0.351806	+	0.936073i	$0.385568\pi$
$510$		0			0
$511$	27.4214	−	10.5394i	1.21305	−	0.466237i
$512$	−21.1366	−	8.07732i	−0.934116	−	0.356970i
$513$		0			0
$514$	−3.05828	−	9.59663i	−0.134895	−	0.423289i
$515$	4.76755	−	8.25763i	0.210083	−	0.363875i
$516$		0			0
$517$	3.45626	−	5.98642i	0.152006	−	0.263282i
$518$	22.4204	−	17.9624i	0.985096	−	0.789225i
$519$		0			0
$520$	−4.30205	−	3.23846i	−0.188657	−	0.142016i
$521$	−0.235443	+	0.135933i	−0.0103150	+	0.00595534i	−0.505149	−	0.863032i	$-0.668562\pi$
$521$	−0.235443	+	0.135933i	−0.0103150	+	0.00595534i	0.494834	+	0.868988i	$0.335229\pi$
$522$		0			0
$523$	7.10967	+	4.10477i	0.310884	+	0.179489i	0.647322	−	0.762217i	$-0.275889\pi$
$523$	7.10967	+	4.10477i	0.310884	+	0.179489i	−0.336438	+	0.941706i	$0.609222\pi$
$524$	1.57092	+	16.7673i	0.0686259	+	0.732482i
$525$		0			0
$526$	28.6407	+	26.0828i	1.24879	+	1.13726i
$527$	−9.66348	−	16.7376i	−0.420948	−	0.729103i
$528$		0			0
$529$	−17.0764	+	29.5771i	−0.742450	+	1.28596i
$530$	5.32774	+	4.85192i	0.231422	+	0.210754i
$531$		0			0
$532$	0.503310	−	0.249590i	0.0218213	−	0.0108211i
$533$	−9.90726	+	5.71996i	−0.429131	+	0.247759i
$534$		0			0
$535$			5.52127i			0.238705i
$536$	−8.83030	−	6.64721i	−0.381411	−	0.287116i
$537$		0			0
$538$	2.43304	+	7.63468i	0.104896	+	0.329154i
$539$	8.82101	−	7.95602i	0.379948	−	0.342690i
$540$		0			0
$541$	−14.2672	+	24.7116i	−0.613396	+	1.06243i	0.377267	+	0.926104i	$0.376864\pi$
$541$	−14.2672	+	24.7116i	−0.613396	+	1.06243i	−0.990664	+	0.136329i	$0.956469\pi$
$542$	15.4629	−	16.9793i	0.664187	−	0.729323i
$543$		0			0
$544$	14.1419	−	22.9703i	0.606330	−	0.984843i
$545$	−1.88270	−	1.08698i	−0.0806461	−	0.0465611i
$546$		0			0
$547$	9.56519	−	5.52246i	0.408978	−	0.236123i	−0.281373	−	0.959599i	$-0.590790\pi$
$547$	9.56519	−	5.52246i	0.408978	−	0.236123i	0.690350	+	0.723475i	$0.257456\pi$
$548$	−4.92232	−	6.93858i	−0.210271	−	0.296402i
$549$		0			0
$550$	10.8580	−	3.46025i	0.462985	−	0.147545i
$551$	0.776310			0.0330719
$552$		0			0
$553$	12.2920	+	1.94152i	0.522709	+	0.0825619i
$554$	2.90295	+	2.64368i	0.123334	+	0.112319i
$555$		0			0
$556$	0.715463	+	1.00853i	0.0303424	+	0.0427711i
$557$	4.13074	−	2.38488i	0.175025	−	0.101051i	−0.409928	−	0.912118i	$-0.634446\pi$
$557$	4.13074	−	2.38488i	0.175025	−	0.101051i	0.584953	+	0.811067i	$0.301113\pi$
$558$		0			0
$559$			17.4481i			0.737975i
$560$	−2.51366	+	4.67406i	−0.106222	+	0.197515i
$561$		0			0
$562$	12.6109	+	39.5721i	0.531961	+	1.66925i
$563$	12.0197			0.506568			0.253284	−	0.967392i	$-0.418489\pi$
$563$	12.0197			0.506568			0.253284	+	0.967392i	$0.418489\pi$
$564$		0			0
$565$	1.69549			0.0713298
$566$	−42.3585	−	9.25408i	−1.78046	−	0.388978i
$567$		0			0
$568$	16.4210	−	21.8141i	0.689011	−	0.915298i
$569$			13.7512i			0.576481i	0.957558	+	0.288240i	$0.0930702\pi$
$569$			13.7512i			0.576481i	−0.957558	+	0.288240i	$0.906930\pi$
$570$		0			0
$571$		−	42.5287i		−	1.77977i	−0.456185	−	0.889885i	$-0.650784\pi$
$571$		−	42.5287i		−	1.77977i	0.456185	−	0.889885i	$-0.349216\pi$
$572$	1.20191	+	12.8286i	0.0502543	+	0.536392i
$573$		0			0
$574$	7.04970	+	8.79931i	0.294249	+	0.367276i
$575$	−35.8986			−1.49707
$576$		0			0
$577$	22.8935	+	39.6527i	0.953069	+	1.65076i	0.738727	+	0.674004i	$0.235427\pi$
$577$	22.8935	+	39.6527i	0.953069	+	1.65076i	0.214341	+	0.976759i	$0.431240\pi$
$578$	6.00006	+	5.46419i	0.249569	+	0.227280i
$579$		0			0
$580$	−5.98129	+	4.24320i	−0.248360	+	0.176189i
$581$	−33.3826	+	12.8306i	−1.38494	+	0.532303i
$582$		0			0
$583$		−	17.2428i		−	0.714123i
$584$	31.1733	+	3.81181i	1.28996	+	0.157734i
$585$		0			0
$586$	−2.04746	+	2.24825i	−0.0845796	+	0.0928743i
$587$	−5.33958	−	9.24842i	−0.220388	−	0.381723i	0.734538	−	0.678568i	$-0.237399\pi$
$587$	−5.33958	−	9.24842i	−0.220388	−	0.381723i	−0.954926	+	0.296845i	$0.904066\pi$
$588$		0			0
$589$	0.215157	−	0.372662i	0.00886537	−	0.0153553i
$590$	0.723084	+	2.26898i	0.0297689	+	0.0934123i
$591$		0			0
$592$	30.1775	−	5.70471i	1.24029	−	0.234462i
$593$	29.7776	+	17.1921i	1.22282	+	0.705995i	0.965518	−	0.260336i	$-0.0838335\pi$
$593$	29.7776	+	17.1921i	1.22282	+	0.705995i	0.257301	+	0.966331i	$0.417167\pi$
$594$		0			0
$595$	−4.91846	−	3.97944i	−0.201637	−	0.163141i
$596$	−11.9720	+	1.12165i	−0.490393	+	0.0459447i
$597$		0			0
$598$	8.66306	−	39.6532i	0.354259	−	1.62154i
$599$	−21.7556			−0.888909			−0.444454	−	0.895801i	$-0.646602\pi$
$599$	−21.7556			−0.888909			−0.444454	+	0.895801i	$0.646602\pi$
$600$		0			0
$601$	17.5245	+	30.3533i	0.714839	+	1.23814i	0.963022	+	0.269424i	$0.0868334\pi$
$601$	17.5245	+	30.3533i	0.714839	+	1.23814i	−0.248183	+	0.968713i	$0.579833\pi$
$602$	16.9987	−	2.60131i	0.692815	−	0.106021i
$603$		0			0
$604$	25.6371	+	36.1384i	1.04316	+	1.47045i
$605$	−3.52653	−	2.03604i	−0.143374	−	0.0827770i
$606$		0			0
$607$	3.12347	−	1.80333i	0.126778	−	0.0731951i	−0.435270	−	0.900300i	$-0.643347\pi$
$607$	3.12347	−	1.80333i	0.126778	−	0.0731951i	0.562048	+	0.827105i	$0.310014\pi$
$608$	0.600347	+	0.0169688i	0.0243473	+	0.000688175i
$609$		0			0
$610$	0.395962	+	1.24250i	0.0160321	+	0.0503072i
$611$	7.73211	−	13.3924i	0.312808	−	0.541799i
$612$		0			0
$613$	−4.90678	−	8.49879i	−0.198183	−	0.343263i	0.749756	−	0.661714i	$-0.230171\pi$
$613$	−4.90678	−	8.49879i	−0.198183	−	0.343263i	−0.947939	+	0.318451i	$0.896837\pi$
$614$	26.4588	+	5.78047i	1.06779	+	0.233281i
$615$		0			0
$616$	12.3190	−	3.08355i	0.496348	−	0.124240i
$617$	18.4047	+	10.6260i	0.740945	+	0.427785i	0.822413	−	0.568891i	$-0.192627\pi$
$617$	18.4047	+	10.6260i	0.740945	+	0.427785i	−0.0814679	+	0.996676i	$0.525961\pi$
$618$		0			0
$619$	24.6653	+	14.2405i	0.991382	+	0.572374i	0.905687	−	0.423947i	$-0.139356\pi$
$619$	24.6653	+	14.2405i	0.991382	+	0.572374i	0.0856946	+	0.996321i	$0.472689\pi$
$620$	0.379189	+	4.04729i	0.0152286	+	0.162543i
$621$		0			0
$622$	1.71786	−	7.86313i	0.0688800	−	0.315283i
$623$	9.10499	−	11.2535i	0.364784	−	0.450861i
$624$		0			0
$625$	−10.6455	−	18.4386i	−0.425822	−	0.737545i
$626$	7.42973	−	34.0079i	0.296952	−	1.35923i
$627$		0			0
$628$	−7.08599	−	3.25135i	−0.282762	−	0.129743i
$629$			36.6124i			1.45983i
$630$		0			0
$631$			21.2573i			0.846239i	0.906074	+	0.423119i	$0.139065\pi$
$631$			21.2573i			0.846239i	−0.906074	+	0.423119i	$0.860935\pi$
$632$	10.6287	+	8.00101i	0.422788	+	0.318263i
$633$		0			0
$634$	16.4102	+	3.58513i	0.651730	+	0.142384i
$635$	2.13431	+	3.69674i	0.0846976	+	0.146701i
$636$		0			0
$637$	19.7337	−	17.7987i	0.781879	−	0.705209i
$638$	17.1436	+	3.74538i	0.678723	+	0.148281i
$639$		0			0
$640$	−4.71828	+	3.15067i	−0.186507	+	0.124541i
$641$	31.8426	+	18.3844i	1.25771	+	0.726138i	0.972629	−	0.232365i	$-0.0746465\pi$
$641$	31.8426	+	18.3844i	1.25771	+	0.726138i	0.285080	+	0.958504i	$0.407980\pi$
$642$		0			0
$643$	0.592243	+	0.341931i	0.0233558	+	0.0134845i	0.511632	−	0.859204i	$-0.329041\pi$
$643$	0.592243	+	0.341931i	0.0233558	+	0.0134845i	−0.488277	+	0.872689i	$0.662374\pi$
$644$	−39.9235	−	2.52809i	−1.57321	−	0.0996208i
$645$		0			0
$646$	−0.152814	+	0.699473i	−0.00601240	+	0.0275204i
$647$	20.1867	+	34.9643i	0.793619	+	1.37459i	0.923712	+	0.383087i	$0.125139\pi$
$647$	20.1867	+	34.9643i	0.793619	+	1.37459i	−0.130093	+	0.991502i	$0.541528\pi$
$648$		0			0
$649$	2.84917	−	4.93491i	0.111840	−	0.193712i
$650$	24.2907	−	7.74102i	0.952759	−	0.303628i
$651$		0			0
$652$	−22.5958	−	31.8514i	−0.884919	−	1.24740i
$653$	−0.662624	+	0.382566i	−0.0259305	+	0.0149710i	−0.512909	−	0.858443i	$-0.671432\pi$
$653$	−0.662624	+	0.382566i	−0.0259305	+	0.0149710i	0.486979	+	0.873414i	$0.338099\pi$
$654$		0			0
$655$	3.65687	+	2.11130i	0.142886	+	0.0824952i
$656$	2.23892	+	11.8437i	0.0874151	+	0.462420i
$657$		0			0
$658$	−14.2002	−	5.53630i	−0.553583	−	0.215828i
$659$	20.6707	+	35.8027i	0.805215	+	1.39467i	0.916146	+	0.400845i	$0.131284\pi$
$659$	20.6707	+	35.8027i	0.805215	+	1.39467i	−0.110930	+	0.993828i	$0.535383\pi$
$660$		0			0
$661$	−27.0002			−1.05019			−0.525093	−	0.851045i	$-0.675969\pi$
$661$	−27.0002			−1.05019			−0.525093	+	0.851045i	$0.675969\pi$
$662$	−22.0436	−	4.81587i	−0.856748	−	0.187174i
$663$		0			0
$664$	−37.9500	−	4.64046i	−1.47275	−	0.180085i
$665$	0.0219769	−	0.139138i	0.000852228	−	0.00539556i
$666$		0			0
$667$	−47.8722	−	27.6390i	−1.85362	−	1.07019i
$668$	−7.18530	+	5.09735i	−0.278008	+	0.197222i
$669$		0			0
$670$	−2.64045	+	0.841467i	−0.102010	+	0.0325087i
$671$	1.56021	−	2.70237i	0.0602314	−	0.104324i
$672$		0			0
$673$	14.7318	+	25.5163i	0.567871	+	0.983581i	0.996776	+	0.0802316i	$0.0255660\pi$
$673$	14.7318	+	25.5163i	0.567871	+	0.983581i	−0.428906	+	0.903349i	$0.641101\pi$
$674$	13.1111	+	11.9402i	0.505023	+	0.459919i
$675$		0			0
$676$	0.263521	+	2.81270i	0.0101354	+	0.108181i
$677$		−	17.2308i		−	0.662233i	−0.943590	−	0.331117i	$-0.892575\pi$
$677$		−	17.2308i		−	0.662233i	0.943590	−	0.331117i	$-0.107425\pi$
$678$		0			0
$679$	31.8880	−	12.2562i	1.22375	−	0.470348i
$680$	−2.64583	−	6.22454i	−0.101463	−	0.238700i
$681$		0			0
$682$	6.54935	−	7.19164i	0.250788	−	0.275382i
$683$	−16.6012	−	28.7542i	−0.635228	−	1.10025i	−0.986467	−	0.163962i	$-0.947573\pi$
$683$	−16.6012	−	28.7542i	−0.635228	−	1.10025i	0.351238	−	0.936286i	$-0.385761\pi$
$684$		0			0
$685$	−2.13308			−0.0815008
$686$	−20.2823	−	16.5719i	−0.774382	−	0.632718i
$687$		0			0
$688$	17.3513	+	6.07470i	0.661511	+	0.231596i
$689$		−	38.5743i		−	1.46957i
$690$		0			0
$691$			10.6328i			0.404490i	0.979335	+	0.202245i	$0.0648237\pi$
$691$			10.6328i			0.404490i	−0.979335	+	0.202245i	$0.935176\pi$
$692$	14.9823	−	32.6524i	0.569541	−	1.24126i
$693$		0			0
$694$	−7.02599	+	32.1599i	−0.266703	+	1.22077i
$695$	0.310045			0.0117607
$696$		0			0
$697$	−14.3692			−0.544273
$698$	32.1862	−	10.2572i	1.21827	−	0.388241i
$699$		0			0
$700$	−11.1631	−	22.5109i	−0.421926	−	0.850834i
$701$			14.3639i			0.542518i	0.962506	+	0.271259i	$0.0874399\pi$
$701$			14.3639i			0.542518i	−0.962506	+	0.271259i	$0.912560\pi$
$702$		0			0
$703$	−0.705959	+	0.407586i	−0.0266258	+	0.0153724i
$704$	13.1759	+	3.27116i	0.496585	+	0.123287i
$705$		0			0
$706$	−29.0275	+	31.8742i	−1.09247	+	1.19960i
$707$	−17.4366	+	21.5511i	−0.655772	+	0.810513i
$708$		0			0
$709$	−22.3525			−0.839467			−0.419734	−	0.907647i	$-0.637876\pi$
$709$	−22.3525			−0.839467			−0.419734	+	0.907647i	$0.637876\pi$
$710$	−2.07873	−	6.52288i	−0.0780134	−	0.244799i
$711$		0			0
$712$	14.2418	−	6.05367i	0.533734	−	0.226871i
$713$	−26.5358	+	15.3205i	−0.993775	+	0.573756i
$714$		0			0
$715$	2.79787	+	1.61535i	0.104634	+	0.0604107i
$716$	−1.58382	−	16.9050i	−0.0591900	−	0.631768i
$717$		0			0
$718$	−17.7125	−	16.1306i	−0.661026	−	0.601989i
$719$	−6.77863	+	11.7409i	−0.252800	+	0.437863i	−0.964296	−	0.264828i	$-0.914685\pi$
$719$	−6.77863	+	11.7409i	−0.252800	+	0.437863i	0.711496	+	0.702691i	$0.248018\pi$
$720$		0			0
$721$	18.0482	+	46.9577i	0.672150	+	1.74880i
$722$	25.5863	−	8.15391i	0.952222	−	0.303457i
$723$		0			0
$724$	44.8262	+	20.5681i	1.66595	+	0.764407i
$725$		−	34.7211i		−	1.28951i
$726$		0			0
$727$	−18.9137	+	10.9198i	−0.701469	+	0.404993i	−0.807894	−	0.589327i	$-0.799393\pi$
$727$	−18.9137	+	10.9198i	−0.701469	+	0.404993i	0.106425	+	0.994321i	$0.466059\pi$
$728$	27.5593	−	6.89832i	1.02141	−	0.255669i
$729$		0			0
$730$	5.30206	−	5.82203i	0.196238	−	0.215483i
$731$	−10.9579	+	18.9797i	−0.405293	+	0.701988i
$732$		0			0
$733$	23.8503	+	41.3098i	0.880929	+	1.52581i	0.850309	+	0.526283i	$0.176415\pi$
$733$	23.8503	+	41.3098i	0.880929	+	1.52581i	0.0306197	+	0.999531i	$0.490252\pi$
$734$	13.4981	−	14.8219i	0.498225	−	0.547085i
$735$		0			0
$736$	−36.4171	−	22.4206i	−1.34235	−	0.826435i
$737$	5.74285	+	3.31564i	0.211541	+	0.122133i
$738$		0			0
$739$	1.03773	−	0.599135i	0.0381736	−	0.0220395i	−0.480792	−	0.876835i	$-0.659651\pi$
$739$	1.03773	−	0.599135i	0.0381736	−	0.0220395i	0.518965	+	0.854795i	$0.326317\pi$
$740$	3.21145	−	6.99903i	0.118055	−	0.257290i
$741$		0			0
$742$	−37.5808	+	5.75099i	−1.37963	+	0.211126i
$743$	14.0688	−	24.3679i	0.516134	−	0.893970i	−0.483690	−	0.875239i	$-0.660704\pi$
$743$	14.0688	−	24.3679i	0.516134	−	0.893970i	0.999825	−	0.0187314i	$-0.00596273\pi$
$744$		0			0
$745$	−1.50749	+	2.61104i	−0.0552301	+	0.0956613i
$746$	−3.65781	+	1.16568i	−0.133922	+	0.0426786i
$747$		0			0
$748$	−6.74935	+	14.7096i	−0.246781	+	0.537834i
$749$	−22.6460	−	18.3225i	−0.827467	−	0.669489i
$750$		0			0
$751$	2.85689	−	1.64943i	0.104249	−	0.0601884i	−0.446969	−	0.894550i	$-0.647497\pi$
$751$	2.85689	−	1.64943i	0.104249	−	0.0601884i	0.551218	+	0.834361i	$0.314163\pi$
$752$	−10.6261	−	12.3519i	−0.387493	−	0.450427i
$753$		0			0
$754$	38.3526	+	8.37891i	1.39672	+	0.305142i
$755$	11.1098			0.404327
$756$		0			0
$757$	5.01338			0.182215			0.0911073	−	0.995841i	$-0.470959\pi$
$757$	5.01338			0.182215			0.0911073	+	0.995841i	$0.470959\pi$
$758$	−20.1451	−	4.40111i	−0.731702	−	0.159855i
$759$		0			0
$760$	0.0905669	−	0.120311i	0.00328521	−	0.00436415i
$761$	−10.4943	+	6.05888i	−0.380418	+	0.219634i	−0.678000	−	0.735062i	$-0.737153\pi$
$761$	−10.4943	+	6.05888i	−0.380418	+	0.219634i	0.297582	+	0.954696i	$0.403820\pi$
$762$		0			0
$763$	10.7061	−	4.11491i	0.387588	−	0.148970i
$764$	−10.7626	−	4.93831i	−0.389376	−	0.178662i
$765$		0			0
$766$	29.9430	−	9.54233i	1.08189	−	0.344778i
$767$	6.37397	−	11.0400i	0.230151	−	0.398633i
$768$		0			0
$769$	6.90320	−	11.9567i	0.248936	−	0.431170i	−0.714295	−	0.699845i	$-0.753252\pi$
$769$	6.90320	−	11.9567i	0.248936	−	0.431170i	0.963231	+	0.268675i	$0.0865858\pi$
$770$	1.15661	−	2.96664i	0.0416815	−	0.106910i
$771$		0			0
$772$	−29.9698	−	13.7514i	−1.07864	−	0.494924i
$773$	−13.5671	+	7.83300i	−0.487976	+	0.281733i	−0.723735	−	0.690078i	$-0.757576\pi$
$773$	−13.5671	+	7.83300i	−0.487976	+	0.281733i	0.235758	+	0.971812i	$0.424243\pi$
$774$		0			0
$775$	−16.6676	−	9.62304i	−0.598718	−	0.345670i
$776$	36.2509	+	4.43270i	1.30133	+	0.159125i
$777$		0			0
$778$	7.72937	−	8.48737i	0.277111	−	0.304287i
$779$	−0.159965	−	0.277067i	−0.00573133	−	0.00992695i
$780$		0			0
$781$	−8.19083	+	14.1869i	−0.293091	+	0.507649i
$782$	34.3269	−	37.6933i	1.22753	−	1.34791i
$783$		0			0
$784$	−10.8294	−	25.8210i	−0.386765	−	0.922178i
$785$	−1.69293	+	0.977413i	−0.0604232	+	0.0348854i
$786$		0			0
$787$		−	43.6810i		−	1.55706i	−0.627607	−	0.778530i	$-0.715966\pi$
$787$		−	43.6810i		−	1.55706i	0.627607	−	0.778530i	$-0.284034\pi$
$788$	3.54040	−	7.71595i	0.126121	−	0.274869i
$789$		0			0
$790$	3.17822	−	1.01285i	0.113076	−	0.0360354i
$791$	−5.62652	+	6.95420i	−0.200056	+	0.247263i
$792$		0			0
$793$	3.49040	−	6.04555i	0.123948	−	0.214684i
$794$	18.0500	+	16.4380i	0.640572	+	0.583362i
$795$		0			0
$796$	−43.6837	+	4.09271i	−1.54833	+	0.145062i
$797$	44.7621	+	25.8434i	1.58556	+	0.915422i	0.994027	+	0.109139i	$0.0348092\pi$
$797$	44.7621	+	25.8434i	1.58556	+	0.915422i	0.591530	+	0.806283i	$0.298524\pi$
$798$		0			0
$799$	16.8216	−	9.71198i	0.595107	−	0.343585i
$800$	0.758942	−	26.8510i	0.0268326	−	0.949326i
$801$		0			0
$802$	−0.390175	−	1.22433i	−0.0137775	−	0.0432328i
$803$	−18.8425			−0.664937
$804$		0			0
$805$	−6.30900	+	7.79772i	−0.222363	+	0.274833i
$806$	14.6518	−	16.0886i	0.516086	−	0.566698i
$807$		0			0
$808$	−27.2740	+	11.5932i	−0.959494	+	0.407846i
$809$	−18.7111	+	10.8029i	−0.657848	+	0.379809i	−0.791457	−	0.611225i	$-0.790677\pi$
$809$	−18.7111	+	10.8029i	−0.657848	+	0.379809i	0.133608	+	0.991034i	$0.457344\pi$
$810$		0			0
$811$			1.10006i			0.0386283i	0.999813	+	0.0193141i	$0.00614826\pi$
$811$			1.10006i			0.0386283i	−0.999813	+	0.0193141i	$0.993852\pi$
$812$	2.44517	−	38.6140i	0.0858086	−	1.35508i
$813$		0			0
$814$	−17.5565	+	5.59496i	−0.615355	+	0.196103i
$815$	−9.79185			−0.342994
$816$		0			0
$817$	−0.487954			−0.0170713
$818$	10.4497	−	47.8310i	0.365364	−	1.67237i
$819$		0			0
$820$	2.74690	+	1.26039i	0.0959259	+	0.0440148i
$821$			31.5197i			1.10004i	0.835150	+	0.550022i	$0.185381\pi$
$821$			31.5197i			1.10004i	−0.835150	+	0.550022i	$0.814619\pi$
$822$		0			0
$823$		−	20.0998i		−	0.700634i	−0.936631	−	0.350317i	$-0.886074\pi$
$823$		−	20.0998i		−	0.700634i	0.936631	−	0.350317i	$-0.113926\pi$
$824$	−6.52752	+	53.3825i	−0.227397	+	1.85967i
$825$		0			0
$826$	−11.7060	−	4.56386i	−0.407303	−	0.158797i
$827$	14.3246			0.498114			0.249057	−	0.968489i	$-0.419879\pi$
$827$	14.3246			0.498114			0.249057	+	0.968489i	$0.419879\pi$
$828$		0			0
$829$	15.2497	+	26.4133i	0.529646	+	0.917373i	0.999402	+	0.0345771i	$0.0110084\pi$
$829$	15.2497	+	26.4133i	0.529646	+	0.917373i	−0.469756	+	0.882796i	$0.655658\pi$
$830$	−6.45468	+	7.08768i	−0.224045	+	0.246017i
$831$		0			0
$832$	29.4762	+	7.31802i	1.02190	+	0.253707i
$833$	32.6440	−	6.96763i	1.13105	−	0.241414i
$834$		0			0
$835$			2.20893i			0.0764431i
$836$	−0.358766	+	0.0336126i	−0.0124082	+	0.00116252i
$837$		0			0
$838$	39.1241	+	35.6299i	1.35152	+	1.23081i
$839$	5.36379	+	9.29036i	0.185179	+	0.320739i	0.943637	−	0.330983i	$-0.107380\pi$
$839$	5.36379	+	9.29036i	0.185179	+	0.320739i	−0.758458	+	0.651722i	$0.774047\pi$
$840$		0			0
$841$	12.2325	−	21.1872i	0.421809	−	0.730594i
$842$	7.65471	−	2.43943i	0.263799	−	0.0840682i
$843$		0			0
$844$	−11.0284	−	15.5459i	−0.379615	−	0.535111i
$845$	0.613438	+	0.354168i	0.0211029	+	0.0121838i
$846$		0			0
$847$	20.0539	−	7.70772i	0.689060	−	0.264841i
$848$	−38.3603	−	13.4300i	−1.31730	−	0.461188i
$849$		0			0
$850$	31.2845	+	6.83474i	1.07305	+	0.234429i
$851$	58.0453			1.98977
$852$		0			0
$853$	−4.00604	−	6.93866i	−0.137164	−	0.237575i	0.789258	−	0.614062i	$-0.210465\pi$
$853$	−4.00604	−	6.93866i	−0.137164	−	0.237575i	−0.926422	+	0.376487i	$0.877132\pi$
$854$	−6.41022	−	2.49918i	−0.219353	−	0.0855201i
$855$		0			0
$856$	−12.1821	−	28.6596i	−0.416377	−	0.979564i
$857$	−8.14808	−	4.70430i	−0.278333	−	0.160696i	0.354335	−	0.935118i	$-0.384707\pi$
$857$	−8.14808	−	4.70430i	−0.278333	−	0.160696i	−0.632669	+	0.774423i	$0.718040\pi$
$858$		0			0
$859$	−7.10018	+	4.09929i	−0.242255	+	0.139866i	−0.616213	−	0.787580i	$-0.711334\pi$
$859$	−7.10018	+	4.09929i	−0.242255	+	0.139866i	0.373958	+	0.927446i	$0.378001\pi$
$860$	3.75957	−	2.66709i	0.128200	−	0.0909470i
$861$		0			0
$862$	−14.9177	+	4.75400i	−0.508097	+	0.161922i
$863$	−14.3575	+	24.8680i	−0.488736	+	0.846516i	−0.999916	−	0.0129580i	$-0.995875\pi$
$863$	−14.3575	+	24.8680i	−0.488736	+	0.846516i	0.511180	+	0.859474i	$0.329209\pi$
$864$		0			0
$865$	−4.50394	−	7.80106i	−0.153139	−	0.265244i
$866$	−3.95729	+	18.1136i	−0.134474	+	0.615526i
$867$		0			0
$868$	−17.8587	−	11.8758i	−0.606163	−	0.403089i
$869$	−6.91248	−	3.99092i	−0.234490	−	0.135383i
$870$		0			0
$871$	12.8475	+	7.41752i	0.435322	+	0.251333i
$872$	12.1710	+	1.48824i	0.412161	+	0.0503983i
$873$		0			0
$874$	1.10894	+	0.242272i	0.0375106	+	0.00819496i
$875$	−12.7757	−	2.01792i	−0.431898	−	0.0682183i
$876$		0			0
$877$	2.97476	+	5.15243i	0.100450	+	0.173985i	0.911870	−	0.410478i	$-0.134638\pi$
$877$	2.97476	+	5.15243i	0.100450	+	0.173985i	−0.811420	+	0.584464i	$0.801305\pi$
$878$	−49.2518	−	10.7601i	−1.66217	−	0.363135i
$879$		0			0
$880$	2.58049	−	2.21994i	0.0869882	−	0.0748343i
$881$		−	20.0536i		−	0.675622i	−0.941214	−	0.337811i	$-0.890314\pi$
$881$		−	20.0536i		−	0.675622i	0.941214	−	0.337811i	$-0.109686\pi$
$882$		0			0
$883$		−	1.14562i		−	0.0385533i	−0.999814	−	0.0192766i	$-0.993864\pi$
$883$		−	1.14562i		−	0.0385533i	0.999814	−	0.0192766i	$-0.00613632\pi$
$884$	−15.0992	+	32.9072i	−0.507840	+	1.10679i
$885$		0			0
$886$	−3.61129	+	16.5299i	−0.121324	+	0.555332i
$887$	7.42383	+	12.8585i	0.249268	+	0.431745i	0.963323	−	0.268345i	$-0.0864767\pi$
$887$	7.42383	+	12.8585i	0.249268	+	0.431745i	−0.714055	+	0.700090i	$0.753143\pi$
$888$		0			0
$889$	−22.2453	−	3.51364i	−0.746082	−	0.117844i
$890$	0.828167	−	3.79075i	0.0277602	−	0.127066i
$891$		0			0
$892$	−20.7401	+	1.94313i	−0.694431	+	0.0650609i
$893$	0.374532	+	0.216236i	0.0125332	+	0.00723607i
$894$		0			0
$895$	−3.68690	−	2.12863i	−0.123239	−	0.0711523i
$896$	2.73497	−	29.8081i	0.0913688	−	0.995817i
$897$		0			0
$898$	−3.61142	−	0.788989i	−0.120515	−	0.0263289i
$899$	−14.8180	−	25.6654i	−0.494206	−	0.855990i
$900$		0			0
$901$	24.2258	−	41.9603i	0.807079	−	1.39790i
$902$	−2.19584	−	6.89037i	−0.0731136	−	0.229424i
$903$		0			0
$904$	−8.80087	+	3.74093i	−0.292713	+	0.124421i
$905$	10.7095	−	6.18314i	0.355996	−	0.205534i
$906$		0			0
$907$	33.7029	+	19.4584i	1.11909	+	0.646104i	0.941167	−	0.337941i	$-0.109731\pi$
$907$	33.7029	+	19.4584i	1.11909	+	0.646104i	0.177918	+	0.984045i	$0.443064\pi$
$908$	9.45764	−	6.70937i	0.313863	−	0.222658i
$909$		0			0
$910$	2.58750	−	6.63675i	0.0857747	−	0.220006i
$911$	−10.5139	−	18.2107i	−0.348342	−	0.603346i	0.637613	−	0.770357i	$-0.279922\pi$
$911$	−10.5139	−	18.2107i	−0.348342	−	0.603346i	−0.985955	+	0.167010i	$0.946589\pi$
$912$		0			0
$913$	22.9387			0.759159
$914$	−5.36862	+	24.5737i	−0.177578	+	0.812825i
$915$		0			0
$916$	−0.920424	−	9.82420i	−0.0304117	−	0.324601i
$917$	−20.7951	+	7.99260i	−0.686714	+	0.263939i
$918$		0			0
$919$	−16.2723	−	9.39484i	−0.536775	−	0.309907i	0.206996	−	0.978342i	$-0.433631\pi$
$919$	−16.2723	−	9.39484i	−0.536775	−	0.309907i	−0.743771	+	0.668435i	$0.766965\pi$
$920$	−9.86838	+	4.19469i	−0.325351	+	0.138295i
$921$		0			0
$922$	−13.9002	−	43.6176i	−0.457778	−	1.43647i
$923$	−18.3240	+	31.7380i	−0.603141	+	1.04467i
$924$		0			0
$925$	18.2296	+	31.5746i	0.599385	+	1.03817i
$926$	−22.6420	+	24.8625i	−0.744062	+	0.817032i
$927$		0			0
$928$	21.6852	−	35.2226i	0.711851	−	1.15624i
$929$		−	30.7325i		−	1.00830i	−0.863616	−	0.504151i	$-0.831806\pi$
$929$		−	30.7325i		−	1.00830i	0.863616	−	0.504151i	$-0.168194\pi$
$930$		0			0
$931$	0.497758	+	0.551875i	0.0163134	+	0.0180870i
$932$	13.1432	+	18.5269i	0.430520	+	0.606868i
$933$		0			0
$934$	−7.39640	−	6.73583i	−0.242018	−	0.220403i
$935$	2.02897	+	3.51429i	0.0663546	+	0.114929i
$936$		0			0
$937$	23.7669			0.776431			0.388215	−	0.921569i	$-0.373092\pi$
$937$	23.7669			0.776431			0.388215	+	0.921569i	$0.373092\pi$
$938$	5.31105	−	13.6225i	0.173412	−	0.444790i
$939$		0			0
$940$	−4.06760	+	0.381092i	−0.132671	+	0.0124298i
$941$			5.48583i			0.178833i	0.995994	+	0.0894164i	$0.0285002\pi$
$941$			5.48583i			0.178833i	−0.995994	+	0.0894164i	$0.971500\pi$
$942$		0			0
$943$			22.7809i			0.741849i
$944$	−8.75963	−	10.1823i	−0.285102	−	0.331405i
$945$		0			0
$946$	−10.7757	−	2.35418i	−0.350349	−	0.0765410i
$947$	−33.5087			−1.08889			−0.544443	−	0.838798i	$-0.683259\pi$
$947$	−33.5087			−1.08889			−0.544443	+	0.838798i	$0.683259\pi$
$948$		0			0
$949$	−42.1531			−1.36835
$950$	0.216486	+	0.679314i	0.00702373	+	0.0220399i
$951$		0			0
$952$	34.3107	+	9.80419i	1.11202	+	0.317756i
$953$		−	21.1120i		−	0.683884i	−0.939721	−	0.341942i	$-0.888915\pi$
$953$		−	21.1120i		−	0.683884i	0.939721	−	0.341942i	$-0.111085\pi$
$954$		0			0
$955$	−2.57130	+	1.48454i	−0.0832054	+	0.0480387i
$956$	23.5467	−	16.7043i	0.761554	−	0.540256i
$957$		0			0
$958$	15.9499	+	14.5254i	0.515317	+	0.469294i
$959$	7.07868	−	8.74902i	0.228582	−	0.282521i
$960$		0			0
$961$	14.5726			0.470085
$962$	−39.2762	+	12.5167i	−1.26632	+	0.403553i
$963$		0			0
$964$	−22.9690	+	16.2945i	−0.739781	+	0.524811i
$965$	−7.16015	+	4.13392i	−0.230493	+	0.133075i
$966$		0			0
$967$	19.5455	+	11.2846i	0.628540	+	0.362888i	0.780186	−	0.625547i	$-0.215124\pi$
$967$	19.5455	+	11.2846i	0.628540	+	0.362888i	−0.151646	+	0.988435i	$0.548457\pi$
$968$	22.7977	+	2.78766i	0.732746	+	0.0895988i
$969$		0			0
$970$	6.16569	−	6.77035i	0.197968	−	0.217383i
$971$	26.7170	−	46.2752i	0.857388	−	1.48504i	−0.0170228	−	0.999855i	$-0.505419\pi$
$971$	26.7170	−	46.2752i	0.857388	−	1.48504i	0.874411	−	0.485185i	$-0.161248\pi$
$972$		0			0
$973$	−1.02889	+	1.27168i	−0.0329847	+	0.0407681i
$974$	5.45808	+	17.1270i	0.174888	+	0.548784i
$975$		0			0
$976$	−4.79679	−	5.57584i	−0.153542	−	0.178478i
$977$			26.2486i			0.839767i	0.907578	+	0.419884i	$0.137929\pi$
$977$			26.2486i			0.839767i	−0.907578	+	0.419884i	$0.862071\pi$
$978$		0			0
$979$	−8.04072	+	4.64231i	−0.256983	+	0.148369i
$980$	−6.85158	−	1.53139i	−0.218866	−	0.0489185i
$981$		0			0
$982$	−25.2964	−	23.0372i	−0.807241	−	0.735146i
$983$	−14.3790	+	24.9052i	−0.458620	+	0.794352i	−0.998888	−	0.0471402i	$-0.984989\pi$
$983$	−14.3790	+	24.9052i	−0.458620	+	0.794352i	0.540269	+	0.841493i	$0.318323\pi$
$984$		0			0
$985$	−1.06431	−	1.84343i	−0.0339116	−	0.0587366i
$986$	36.4569	+	33.2010i	1.16103	+	1.05733i
$987$		0			0
$988$	−0.802607	+	0.0751958i	−0.0255343	+	0.00239230i
$989$	30.0903	+	17.3727i	0.956817	+	0.552418i
$990$		0			0
$991$	−26.2389	+	15.1490i	−0.833506	+	0.481225i	−0.855051	−	0.518543i	$-0.826475\pi$
$991$	−26.2389	+	15.1490i	−0.833506	+	0.481225i	0.0215459	+	0.999768i	$0.493141\pi$
$992$	−10.8982	−	20.1719i	−0.346019	−	0.640457i
$993$		0			0
$994$	33.6525	+	13.1202i	1.06739	+	0.416148i
$995$	−5.50055	+	9.52723i	−0.174379	+	0.302033i
$996$		0			0
$997$	−10.1245	+	17.5361i	−0.320645	+	0.555374i	−0.980621	−	0.195913i	$-0.937233\pi$
$997$	−10.1245	+	17.5361i	−0.320645	+	0.555374i	0.659976	+	0.751287i	$0.270566\pi$
$998$	−6.94457	−	21.7915i	−0.219826	−	0.689797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.18		88
3.2	odd	2		252.2.bb.a.23.27	yes	88
4.3	odd	2	inner	756.2.bb.a.611.27		88
7.4	even	3		756.2.o.a.179.11		88
9.2	odd	6		756.2.o.a.359.5		88
9.7	even	3		252.2.o.a.191.40	yes	88
12.11	even	2		252.2.bb.a.23.18	yes	88
21.11	odd	6		252.2.o.a.95.34	✓	88
28.11	odd	6		756.2.o.a.179.5		88
36.7	odd	6		252.2.o.a.191.34	yes	88
36.11	even	6		756.2.o.a.359.11		88
63.11	odd	6	inner	756.2.bb.a.683.27		88
63.25	even	3		252.2.bb.a.11.18	yes	88
84.11	even	6		252.2.o.a.95.40	yes	88
252.11	even	6	inner	756.2.bb.a.683.18		88
252.151	odd	6		252.2.bb.a.11.27	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.34	✓	88	21.11	odd	6
252.2.o.a.95.40	yes	88	84.11	even	6
252.2.o.a.191.34	yes	88	36.7	odd	6
252.2.o.a.191.40	yes	88	9.7	even	3
252.2.bb.a.11.18	yes	88	63.25	even	3
252.2.bb.a.11.27	yes	88	252.151	odd	6
252.2.bb.a.23.18	yes	88	12.11	even	2
252.2.bb.a.23.27	yes	88	3.2	odd	2
756.2.o.a.179.5		88	28.11	odd	6
756.2.o.a.179.11		88	7.4	even	3
756.2.o.a.359.5		88	9.2	odd	6
756.2.o.a.359.11		88	36.11	even	6
756.2.bb.a.611.18		88	1.1	even	1	trivial
756.2.bb.a.611.27		88	4.3	odd	2	inner
756.2.bb.a.683.18		88	252.11	even	6	inner
756.2.bb.a.683.27		88	63.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.301845 + 1.38163i) q^{2} +(-1.81778 - 0.834072i) q^{4} +(-0.434289 + 0.250737i) q^{5} +(0.412779 - 2.61335i) q^{7} +(1.70106 - 2.25973i) q^{8} +O(q^{10})\)	\(q+(-0.301845 + 1.38163i) q^{2} +(-1.81778 - 0.834072i) q^{4} +(-0.434289 + 0.250737i) q^{5} +(0.412779 - 2.61335i) q^{7} +(1.70106 - 2.25973i) q^{8} +(-0.215337 - 0.675709i) q^{10} +(-0.848493 + 1.46963i) q^{11} +(-1.89819 + 3.28776i) q^{13} +(3.48608 + 1.35913i) q^{14} +(2.60865 + 3.03232i) q^{16} +(-4.12962 + 2.38424i) q^{17} +(-0.0919457 - 0.0530849i) q^{19} +(0.998575 - 0.0935560i) q^{20} +(-1.77437 - 1.61590i) q^{22} +(3.77997 + 6.54710i) q^{23} +(-2.37426 + 4.11234i) q^{25} +(-3.96950 - 3.61498i) q^{26} +(-2.93007 + 4.40621i) q^{28} +(-6.33235 + 3.65598i) q^{29} +4.05307i q^{31} +(-4.97694 + 2.68888i) q^{32} +(-2.04762 - 6.42526i) q^{34} +(0.475999 + 1.23845i) q^{35} +(3.83900 - 6.64935i) q^{37} +(0.101097 - 0.111011i) q^{38} +(-0.172155 + 1.40790i) q^{40} +(2.60966 + 1.50669i) q^{41} +(3.98023 - 2.29799i) q^{43} +(2.76815 - 1.96377i) q^{44} +(-10.1866 + 3.24630i) q^{46} -4.07341 q^{47} +(-6.65923 - 2.15747i) q^{49} +(-4.96506 - 4.52163i) q^{50} +(6.19272 - 4.39320i) q^{52} +(-8.79953 + 5.08041i) q^{53} -0.850995i q^{55} +(-5.20331 - 5.37825i) q^{56} +(-3.13982 - 9.85248i) q^{58} -3.35792 q^{59} -1.83880 q^{61} +(-5.59982 - 1.22340i) q^{62} +(-2.21277 - 7.68789i) q^{64} -1.90379i q^{65} -3.90768i q^{67} +(9.49537 - 0.889617i) q^{68} +(-1.85475 + 0.283833i) q^{70} +9.65339 q^{71} +(5.55175 + 9.61592i) q^{73} +(8.02813 + 7.31113i) q^{74} +(0.122860 + 0.173186i) q^{76} +(3.49043 + 2.82405i) q^{77} +4.70354i q^{79} +(-1.89322 - 0.662820i) q^{80} +(-2.86939 + 3.15079i) q^{82} +(-6.75864 - 11.7063i) q^{83} +(1.19563 - 2.07090i) q^{85} +(1.97355 + 6.19283i) q^{86} +(1.87764 + 4.41731i) q^{88} +(4.73824 + 2.73562i) q^{89} +(7.80855 + 6.31776i) q^{91} +(-1.41040 - 15.0540i) q^{92} +(1.22954 - 5.62793i) q^{94} +0.0532414 q^{95} +(6.45605 + 11.1822i) q^{97} +(4.99087 - 8.54934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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