LMFDB - Embedded newform 315.2.bf.b.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.5
Root			$2.07845 - 0.556918i$ of defining polynomial
Character	$\chi$	$=$	315.289
Dual form			315.2.bf.b.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248840 + 0.143668i) q^{2} +(-0.958719 - 1.66055i) q^{4} +(-1.47507 + 1.68052i) q^{5} +(1.11487 - 2.39939i) q^{7} -1.12562i q^{8} +O(q^{10})$	\(q+(0.248840 + 0.143668i) q^{2} +(-0.958719 - 1.66055i) q^{4} +(-1.47507 + 1.68052i) q^{5} +(1.11487 - 2.39939i) q^{7} -1.12562i q^{8} +(-0.608495 + 0.206261i) q^{10} +(-1.66520 - 2.88421i) q^{11} -4.54754i q^{13} +(0.622139 - 0.436894i) q^{14} +(-1.75572 + 3.04100i) q^{16} +(4.80431 - 2.77377i) q^{17} +(-0.828617 + 1.43521i) q^{19} +(4.20477 + 0.838284i) q^{20} -0.956942i q^{22} +(-6.61094 - 3.81683i) q^{23} +(-0.648315 - 4.95779i) q^{25} +(0.653336 - 1.13161i) q^{26} +(-5.05315 + 0.449051i) q^{28} -0.118657 q^{29} +(3.13010 + 5.42150i) q^{31} +(-2.82342 + 1.63010i) q^{32} +1.59401 q^{34} +(2.38772 + 5.41284i) q^{35} +(6.71665 + 3.87786i) q^{37} +(-0.412386 + 0.238091i) q^{38} +(1.89163 + 1.66037i) q^{40} -0.0701896 q^{41} +2.92981i q^{43} +(-3.19291 + 5.53029i) q^{44} +(-1.09671 - 1.89956i) q^{46} +(5.53029 + 3.19291i) q^{47} +(-4.51415 - 5.35000i) q^{49} +(0.550949 - 1.32684i) q^{50} +(-7.55142 + 4.35981i) q^{52} +(-0.640682 + 0.369898i) q^{53} +(7.30326 + 1.45601i) q^{55} +(-2.70080 - 1.25492i) q^{56} +(-0.0295266 - 0.0170472i) q^{58} +(0.815051 + 1.41171i) q^{59} +(3.65901 - 6.33759i) q^{61} +1.79878i q^{62} +6.08612 q^{64} +(7.64225 + 6.70796i) q^{65} +(-2.62934 + 1.51805i) q^{67} +(-9.21197 - 5.31853i) q^{68} +(-0.183490 + 1.68997i) q^{70} +3.77048 q^{71} +(2.03961 - 1.17757i) q^{73} +(1.11425 + 1.92993i) q^{74} +3.17764 q^{76} +(-8.77681 + 0.779956i) q^{77} +(-5.97016 + 10.3406i) q^{79} +(-2.52065 - 7.43623i) q^{80} +(-0.0174660 - 0.0100840i) q^{82} -1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +(-0.420920 + 0.729054i) q^{86} +(-3.24652 + 1.87438i) q^{88} +(6.50007 - 11.2585i) q^{89} +(-10.9113 - 5.06990i) q^{91} +14.6371i q^{92} +(0.917438 + 1.58905i) q^{94} +(-1.18963 - 3.50954i) q^{95} +3.04306i q^{97} +(-0.354679 - 1.97983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 - 2 * q^5	$ 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.248840	+	0.143668i	0.175957	+	0.101589i	0.585392	−	0.810751i	$-0.300941\pi$
$2$	0.248840	+	0.143668i	0.175957	+	0.101589i	−0.409435	+	0.912339i	$0.634274\pi$
$3$		0			0
$3$		0			0
$4$	−0.958719	−	1.66055i	−0.479360	−	0.830275i
$5$	−1.47507	+	1.68052i	−0.659673	+	0.751553i
$5$	−1.47507	+	1.68052i	−0.659673	+	0.751553i
$6$		0			0
$7$	1.11487	−	2.39939i	0.421380	−	0.906884i
$7$	1.11487	−	2.39939i	0.421380	−	0.906884i
$8$		−	1.12562i		−	0.397967i
$9$		0			0
$10$	−0.608495	+	0.206261i	−0.192423	+	0.0652254i
$11$	−1.66520	−	2.88421i	−0.502076	−	0.869621i	−0.999997	−	0.00239862i	$-0.999236\pi$
$11$	−1.66520	−	2.88421i	−0.502076	−	0.869621i	0.497921	−	0.867222i	$-0.334097\pi$
$12$		0			0
$13$		−	4.54754i		−	1.26126i	−0.776083	−	0.630630i	$-0.782796\pi$
$13$		−	4.54754i		−	1.26126i	0.776083	−	0.630630i	$-0.217204\pi$
$14$	0.622139	−	0.436894i	0.166274	−	0.116765i
$15$		0			0
$16$	−1.75572	+	3.04100i	−0.438931	+	0.760250i
$17$	4.80431	−	2.77377i	1.16522	−	0.672738i	0.212668	−	0.977125i	$-0.431785\pi$
$17$	4.80431	−	2.77377i	1.16522	−	0.672738i	0.952549	+	0.304386i	$0.0984514\pi$
$18$		0			0
$19$	−0.828617	+	1.43521i	−0.190098	+	0.329259i	−0.945282	−	0.326253i	$-0.894214\pi$
$19$	−0.828617	+	1.43521i	−0.190098	+	0.329259i	0.755185	+	0.655512i	$0.227547\pi$
$20$	4.20477	+	0.838284i	0.940216	+	0.187446i
$21$		0			0
$22$		−	0.956942i		−	0.204021i
$23$	−6.61094	−	3.81683i	−1.37848	−	0.795864i	−0.386500	−	0.922289i	$-0.626316\pi$
$23$	−6.61094	−	3.81683i	−1.37848	−	0.795864i	−0.991976	+	0.126425i	$0.959650\pi$
$24$		0			0
$25$	−0.648315	−	4.95779i	−0.129663	−	0.991558i
$26$	0.653336	−	1.13161i	0.128130	−	0.221927i
$27$		0			0
$28$	−5.05315	+	0.449051i	−0.954956	+	0.0848627i
$29$	−0.118657			−0.0220341			−0.0110170	−	0.999939i	$-0.503507\pi$
$29$	−0.118657			−0.0220341			−0.0110170	+	0.999939i	$0.503507\pi$
$30$		0			0
$31$	3.13010	+	5.42150i	0.562183	+	0.973729i	0.997306	+	0.0733583i	$0.0233717\pi$
$31$	3.13010	+	5.42150i	0.562183	+	0.973729i	−0.435123	+	0.900371i	$0.643295\pi$
$32$	−2.82342	+	1.63010i	−0.499115	+	0.288164i
$33$		0			0
$34$	1.59401			0.273370
$35$	2.38772	+	5.41284i	0.403599	+	0.914936i
$36$		0			0
$37$	6.71665	+	3.87786i	1.10421	+	0.637516i	0.937324	−	0.348460i	$-0.113295\pi$
$37$	6.71665	+	3.87786i	1.10421	+	0.637516i	0.166887	+	0.985976i	$0.446628\pi$
$38$	−0.412386	+	0.238091i	−0.0668979	+	0.0386235i
$39$		0			0
$40$	1.89163	+	1.66037i	0.299093	+	0.262528i
$41$	−0.0701896			−0.0109618			−0.00548089	−	0.999985i	$-0.501745\pi$
$41$	−0.0701896			−0.0109618			−0.00548089	+	0.999985i	$0.501745\pi$
$42$		0			0
$43$			2.92981i			0.446792i	0.974728	+	0.223396i	$0.0717143\pi$
$43$			2.92981i			0.446792i	−0.974728	+	0.223396i	$0.928286\pi$
$44$	−3.19291	+	5.53029i	−0.481350	+	0.833722i
$45$		0			0
$46$	−1.09671	−	1.89956i	−0.161701	−	0.280075i
$47$	5.53029	+	3.19291i	0.806675	+	0.465734i	0.845800	−	0.533500i	$-0.179124\pi$
$47$	5.53029	+	3.19291i	0.806675	+	0.465734i	−0.0391247	+	0.999234i	$0.512457\pi$
$48$		0			0
$49$	−4.51415	−	5.35000i	−0.644879	−	0.764285i
$50$	0.550949	−	1.32684i	0.0779159	−	0.187643i
$51$		0			0
$52$	−7.55142	+	4.35981i	−1.04719	+	0.604597i
$53$	−0.640682	+	0.369898i	−0.0880044	+	0.0508094i	−0.543356	−	0.839502i	$-0.682847\pi$
$53$	−0.640682	+	0.369898i	−0.0880044	+	0.0508094i	0.455352	+	0.890311i	$0.349513\pi$
$54$		0			0
$55$	7.30326	+	1.45601i	0.984772	+	0.196329i
$56$	−2.70080	−	1.25492i	−0.360910	−	0.167695i
$57$		0			0
$58$	−0.0295266	−	0.0170472i	−0.00387704	−	0.00223841i
$59$	0.815051	+	1.41171i	0.106111	+	0.183789i	0.914191	−	0.405283i	$-0.132827\pi$
$59$	0.815051	+	1.41171i	0.106111	+	0.183789i	−0.808081	+	0.589072i	$0.799494\pi$
$60$		0			0
$61$	3.65901	−	6.33759i	0.468488	−	0.811446i	−0.530863	−	0.847458i	$-0.678132\pi$
$61$	3.65901	−	6.33759i	0.468488	−	0.811446i	0.999351	+	0.0360120i	$0.0114655\pi$
$62$			1.79878i			0.228445i
$63$		0			0
$64$	6.08612			0.760765
$65$	7.64225	+	6.70796i	0.947904	+	0.832020i
$66$		0			0
$67$	−2.62934	+	1.51805i	−0.321224	+	0.185459i	−0.651938	−	0.758272i	$-0.726044\pi$
$67$	−2.62934	+	1.51805i	−0.321224	+	0.185459i	0.330714	+	0.943731i	$0.392711\pi$
$68$	−9.21197	−	5.31853i	−1.11712	−	0.644967i
$69$		0			0
$70$	−0.183490	+	1.68997i	−0.0219312	+	0.201990i
$71$	3.77048			0.447474			0.223737	−	0.974650i	$-0.428174\pi$
$71$	3.77048			0.447474			0.223737	+	0.974650i	$0.428174\pi$
$72$		0			0
$73$	2.03961	−	1.17757i	0.238718	−	0.137824i	−0.375869	−	0.926673i	$-0.622656\pi$
$73$	2.03961	−	1.17757i	0.238718	−	0.137824i	0.614588	+	0.788849i	$0.289322\pi$
$74$	1.11425	+	1.92993i	0.129529	+	0.224350i
$75$		0			0
$76$	3.17764			0.364501
$77$	−8.77681	+	0.779956i	−1.00021	+	0.0888843i
$78$		0			0
$79$	−5.97016	+	10.3406i	−0.671696	+	1.16341i	0.305727	+	0.952119i	$0.401101\pi$
$79$	−5.97016	+	10.3406i	−0.671696	+	1.16341i	−0.977423	+	0.211292i	$0.932233\pi$
$80$	−2.52065	−	7.43623i	−0.281817	−	0.831396i
$81$		0			0
$82$	−0.0174660	−	0.0100840i	−0.00192880	−	0.00111359i
$83$		−	1.22411i		−	0.134363i	−0.997741	−	0.0671817i	$-0.978599\pi$
$83$		−	1.22411i		−	0.134363i	0.997741	−	0.0671817i	$-0.0214007\pi$
$84$		0			0
$85$	−2.42533	+	12.1653i	−0.263064	+	1.31951i
$86$	−0.420920	+	0.729054i	−0.0453889	+	0.0786160i
$87$		0			0
$88$	−3.24652	+	1.87438i	−0.346080	+	0.199810i
$89$	6.50007	−	11.2585i	0.689006	−	1.19339i	−0.283153	−	0.959075i	$-0.591381\pi$
$89$	6.50007	−	11.2585i	0.689006	−	1.19339i	0.972160	−	0.234319i	$-0.0752862\pi$
$90$		0			0
$91$	−10.9113	−	5.06990i	−1.14382	−	0.531470i
$92$			14.6371i			1.52602i
$93$		0			0
$94$	0.917438	+	1.58905i	0.0946265	+	0.163898i
$95$	−1.18963	−	3.50954i	−0.122053	−	0.360072i
$96$		0			0
$97$			3.04306i			0.308976i	0.987995	+	0.154488i	$0.0493728\pi$
$97$			3.04306i			0.308976i	−0.987995	+	0.154488i	$0.950627\pi$
$98$	−0.354679	−	1.97983i	−0.0358280	−	0.199993i
$99$		0			0
$100$	−7.61111	+	5.82969i	−0.761111	+	0.582969i
$101$	8.01983	+	13.8907i	0.798002	+	1.38218i	0.920915	+	0.389763i	$0.127443\pi$
$101$	8.01983	+	13.8907i	0.798002	+	1.38218i	−0.122913	+	0.992417i	$0.539224\pi$
$102$		0			0
$103$	−4.58293	−	2.64596i	−0.451570	−	0.260714i	0.256923	−	0.966432i	$-0.417291\pi$
$103$	−4.58293	−	2.64596i	−0.451570	−	0.260714i	−0.708493	+	0.705718i	$0.750625\pi$
$104$	−5.11880			−0.501940
$105$		0			0
$106$	−0.212570			−0.0206466
$107$	−4.47018	−	2.58086i	−0.432148	−	0.249501i	0.268113	−	0.963387i	$-0.413600\pi$
$107$	−4.47018	−	2.58086i	−0.432148	−	0.249501i	−0.700261	+	0.713886i	$0.746933\pi$
$108$		0			0
$109$	1.62043	+	2.80668i	0.155209	+	0.268831i	0.933135	−	0.359525i	$-0.117061\pi$
$109$	1.62043	+	2.80668i	0.155209	+	0.268831i	−0.777926	+	0.628356i	$0.783728\pi$
$110$	1.60816	+	1.41156i	0.153332	+	0.134587i
$111$		0			0
$112$	5.33915	+	7.60297i	0.504503	+	0.718413i
$113$		−	12.6608i		−	1.19103i	−0.803345	−	0.595513i	$-0.796949\pi$
$113$		−	12.6608i		−	1.19103i	0.803345	−	0.595513i	$-0.203051\pi$
$114$		0			0
$115$	16.1659	−	5.47973i	1.50748	−	0.510988i
$116$	0.113759	+	0.197036i	0.0105622	+	0.0182943i
$117$		0			0
$118$			0.468387i			0.0431185i
$119$	−1.29920	−	14.6198i	−0.119097	−	1.34019i
$120$		0			0
$121$	−0.0457629	+	0.0792637i	−0.00416027	+	0.00720579i
$122$	1.82102	−	1.05136i	0.164867	−	0.0951861i
$123$		0			0
$124$	6.00178	−	10.3954i	0.538976	−	0.933533i
$125$	9.28799	+	6.22360i	0.830743	+	0.556656i
$126$		0			0
$127$		−	16.5475i		−	1.46836i	−0.678957	−	0.734178i	$-0.737568\pi$
$127$		−	16.5475i		−	1.46836i	0.678957	−	0.734178i	$-0.262432\pi$
$128$	7.16131	+	4.13458i	0.632976	+	0.365449i
$129$		0			0
$130$	0.937979	+	2.76715i	0.0822662	+	0.242696i
$131$	−2.64893	+	4.58808i	−0.231438	+	0.400862i	−0.958231	−	0.285994i	$-0.907676\pi$
$131$	−2.64893	+	4.58808i	−0.231438	+	0.400862i	0.726794	+	0.686856i	$0.241010\pi$
$132$		0			0
$133$	2.51982	+	3.58824i	0.218496	+	0.311140i
$134$	−0.872379			−0.0753621
$135$		0			0
$136$	−3.12221	−	5.40783i	−0.267727	−	0.463718i
$137$	12.8779	−	7.43507i	1.10023	−	0.635221i	0.163952	−	0.986468i	$-0.447576\pi$
$137$	12.8779	−	7.43507i	1.10023	−	0.635221i	0.936283	+	0.351247i	$0.114242\pi$
$138$		0			0
$139$	9.51685			0.807209			0.403605	−	0.914934i	$-0.367757\pi$
$139$	9.51685			0.807209			0.403605	+	0.914934i	$0.367757\pi$
$140$	6.69913	−	9.15432i	0.566180	−	0.773681i
$141$		0			0
$142$	0.938247	+	0.541697i	0.0787359	+	0.0454582i
$143$	−13.1160	+	7.57255i	−1.09682	+	0.633249i
$144$		0			0
$145$	0.175028	−	0.199406i	0.0145353	−	0.0165598i
$146$	0.676716			0.0560054
$147$		0			0
$148$		−	14.8711i		−	1.22240i
$149$	−5.68502	+	9.84675i	−0.465735	+	0.806677i	−0.999234	−	0.0391236i	$-0.987543\pi$
$149$	−5.68502	+	9.84675i	−0.465735	+	0.806677i	0.533499	+	0.845801i	$0.320877\pi$
$150$		0			0
$151$	−4.47016	−	7.74255i	−0.363777	−	0.630080i	0.624802	−	0.780783i	$-0.285180\pi$
$151$	−4.47016	−	7.74255i	−0.363777	−	0.630080i	−0.988579	+	0.150703i	$0.951846\pi$
$152$	1.61550	+	0.932708i	0.131034	+	0.0756526i
$153$		0			0
$154$	−2.29608	−	1.06686i	−0.185023	−	0.0859701i
$155$	−13.7281	−	2.73690i	−1.10267	−	0.219833i
$156$		0			0
$157$	2.89800	−	1.67316i	0.231286	−	0.133533i	−0.379879	−	0.925036i	$-0.624035\pi$
$157$	2.89800	−	1.67316i	0.231286	−	0.133533i	0.611165	+	0.791503i	$0.290701\pi$
$158$	−2.97123	+	1.71544i	−0.236379	+	0.136473i
$159$		0			0
$160$	1.42533	−	7.14934i	0.112682	−	0.565205i
$161$	−16.5284	+	11.6070i	−1.30262	+	0.914758i
$162$		0			0
$163$	−13.6450	−	7.87793i	−1.06876	−	0.617047i	−0.140916	−	0.990022i	$-0.545005\pi$
$163$	−13.6450	−	7.87793i	−1.06876	−	0.617047i	−0.927842	+	0.372974i	$0.878338\pi$
$164$	0.0672922	+	0.116553i	0.00525463	+	0.00910129i
$165$		0			0
$166$	0.175865	−	0.304608i	0.0136498	−	0.0236421i
$167$		−	22.5942i		−	1.74839i	−0.485577	−	0.874194i	$-0.661390\pi$
$167$		−	22.5942i		−	1.74839i	0.485577	−	0.874194i	$-0.338610\pi$
$168$		0			0
$169$	−7.68012			−0.590779
$170$	−2.35128	+	2.67877i	−0.180335	+	0.205452i
$171$		0			0
$172$	4.86510	−	2.80887i	0.370960	−	0.214174i
$173$	7.38391	+	4.26310i	0.561388	+	0.324118i	0.753703	−	0.657216i	$-0.228266\pi$
$173$	7.38391	+	4.26310i	0.561388	+	0.324118i	−0.192314	+	0.981333i	$0.561599\pi$
$174$		0			0
$175$	−12.6185	−	3.97171i	−0.953866	−	0.300233i
$176$	11.6945			0.881506
$177$		0			0
$178$	3.23496	−	1.86770i	0.242470	−	0.139990i
$179$	5.89031	+	10.2023i	0.440262	+	0.762557i	0.997709	−	0.0676564i	$-0.0215522\pi$
$179$	5.89031	+	10.2023i	0.440262	+	0.762557i	−0.557446	+	0.830213i	$0.688219\pi$
$180$		0			0
$181$	9.08967			0.675630			0.337815	−	0.941213i	$-0.390312\pi$
$181$	9.08967			0.675630			0.337815	+	0.941213i	$0.390312\pi$
$182$	−1.98679	−	2.82920i	−0.147271	−	0.209714i
$183$		0			0
$184$	−4.29630	+	7.44141i	−0.316727	+	0.548588i
$185$	−16.4244	+	5.56736i	−1.20755	+	0.409320i
$186$		0			0
$187$	−16.0002	−	9.23775i	−1.17005	−	0.675531i
$188$		−	12.2444i		−	0.893016i
$189$		0			0
$190$	0.208182	−	1.04423i	0.0151031	−	0.0757562i
$191$	10.2478	−	17.7498i	0.741507	−	1.28433i	−0.210302	−	0.977637i	$-0.567445\pi$
$191$	10.2478	−	17.7498i	0.741507	−	1.28433i	0.951809	−	0.306692i	$-0.0992220\pi$
$192$		0			0
$193$	7.39842	−	4.27148i	0.532550	−	0.307468i	−0.209504	−	0.977808i	$-0.567185\pi$
$193$	7.39842	−	4.27148i	0.532550	−	0.307468i	0.742054	+	0.670340i	$0.233852\pi$
$194$	−0.437190	+	0.757235i	−0.0313884	+	0.0543663i
$195$		0			0
$196$	−4.55613	+	12.6251i	−0.325438	+	0.901794i
$197$			13.8086i			0.983820i	0.870646	+	0.491910i	$0.163701\pi$
$197$			13.8086i			0.983820i	−0.870646	+	0.491910i	$0.836299\pi$
$198$		0			0
$199$	1.89549	+	3.28309i	0.134368	+	0.232732i	0.925356	−	0.379100i	$-0.123766\pi$
$199$	1.89549	+	3.28309i	0.134368	+	0.232732i	−0.790988	+	0.611832i	$0.790433\pi$
$200$	−5.58059	+	0.729756i	−0.394607	+	0.0516016i
$201$		0			0
$202$			4.60877i			0.324272i
$203$	−0.132287	+	0.284705i	−0.00928471	+	0.0199824i
$204$		0			0
$205$	0.103535	−	0.117955i	0.00723119	−	0.00823836i
$206$	−0.760278	−	1.31684i	−0.0529711	−	0.0917486i
$207$		0			0
$208$	13.8291	+	7.98422i	0.958874	+	0.553606i
$209$	5.51924			0.381774
$210$		0			0
$211$	−0.114416			−0.00787674			−0.00393837	−	0.999992i	$-0.501254\pi$
$211$	−0.114416			−0.00787674			−0.00393837	+	0.999992i	$0.501254\pi$
$212$	1.22847	+	0.709256i	0.0843715	+	0.0487119i
$213$		0			0
$214$	−0.741573	−	1.28444i	−0.0506929	−	0.0878026i
$215$	−4.92361	−	4.32169i	−0.335788	−	0.294737i
$216$		0			0
$217$	16.4979	−	1.46610i	1.11995	−	0.0995253i
$218$			0.931218i			0.0630700i
$219$		0			0
$220$	−4.58399	−	13.5233i	−0.309053	−	0.911744i
$221$	−12.6138	−	21.8478i	−0.848498	−	1.46964i
$222$		0			0
$223$			7.86673i			0.526795i	0.964687	+	0.263398i	$0.0848431\pi$
$223$			7.86673i			0.526795i	−0.964687	+	0.263398i	$0.915157\pi$
$224$	0.763518	+	8.59183i	0.0510147	+	0.574066i
$225$		0			0
$226$	1.81895	−	3.15051i	0.120995	−	0.209569i
$227$	7.77575	−	4.48933i	0.516095	−	0.297967i	−0.219241	−	0.975671i	$-0.570358\pi$
$227$	7.77575	−	4.48933i	0.516095	−	0.297967i	0.735335	+	0.677703i	$0.237025\pi$
$228$		0			0
$229$	−2.54306	+	4.40471i	−0.168050	+	0.291071i	−0.937734	−	0.347354i	$-0.887080\pi$
$229$	−2.54306	+	4.40471i	−0.168050	+	0.291071i	0.769684	+	0.638425i	$0.220414\pi$
$230$	4.80999	+	0.958942i	0.317161	+	0.0632308i
$231$		0			0
$232$			0.133563i			0.00876883i
$233$	18.8952	+	10.9091i	1.23786	+	0.714681i	0.968657	−	0.248401i	$-0.0799052\pi$
$233$	18.8952	+	10.9091i	1.23786	+	0.714681i	0.269207	+	0.963082i	$0.413239\pi$
$234$		0			0
$235$	−13.5233	+	4.58399i	−0.882166	+	0.299027i
$236$	1.56281	−	2.70687i	0.101730	−	0.176202i
$237$		0			0
$238$	1.77710	−	3.82465i	0.115193	−	0.247915i
$239$	7.44905			0.481839			0.240920	−	0.970545i	$-0.422551\pi$
$239$	7.44905			0.481839			0.240920	+	0.970545i	$0.422551\pi$
$240$		0			0
$241$	12.0879	+	20.9368i	0.778650	+	1.34866i	0.932720	+	0.360601i	$0.117428\pi$
$241$	12.0879	+	20.9368i	0.778650	+	1.34866i	−0.154070	+	0.988060i	$0.549238\pi$
$242$	−0.0227753	+	0.0131493i	−0.00146405	+	0.000845271i
$243$		0			0
$244$	−14.0319			−0.898297
$245$	15.6495	+	0.305506i	0.999810	+	0.0195180i
$246$		0			0
$247$	6.52666	+	3.76817i	0.415281	+	0.239763i
$248$	6.10255	−	3.52331i	0.387512	−	0.223730i
$249$		0			0
$250$	1.41709	+	2.88307i	0.0896249	+	0.182341i
$251$	−6.00200			−0.378843			−0.189421	−	0.981896i	$-0.560661\pi$
$251$	−6.00200			−0.378843			−0.189421	+	0.981896i	$0.560661\pi$
$252$		0			0
$253$			25.4231i			1.59834i
$254$	2.37735	−	4.11769i	0.149168	−	0.258367i
$255$		0			0
$256$	−4.89810	−	8.48376i	−0.306131	−	0.530235i
$257$	−6.35139	−	3.66697i	−0.396189	−	0.228740i	0.288650	−	0.957435i	$-0.406794\pi$
$257$	−6.35139	−	3.66697i	−0.396189	−	0.228740i	−0.684838	+	0.728695i	$0.740127\pi$
$258$		0			0
$259$	16.7927	−	11.7926i	1.04345	−	0.732755i
$260$	3.81213	−	19.1214i	0.236418	−	1.18586i
$261$		0			0
$262$	−1.31832	+	0.761132i	−0.0814460	+	0.0470229i
$263$	−8.21661	+	4.74386i	−0.506658	+	0.292519i	−0.731459	−	0.681886i	$-0.761160\pi$
$263$	−8.21661	+	4.74386i	−0.506658	+	0.292519i	0.224801	+	0.974405i	$0.427827\pi$
$264$		0			0
$265$	0.323431	−	1.62231i	0.0198682	−	0.0996575i
$266$	0.111519	+	1.25492i	0.00683766	+	0.0769438i
$267$		0			0
$268$	5.04159	+	2.91076i	0.307964	+	0.177803i
$269$	−8.02423	−	13.8984i	−0.489246	−	0.847399i	0.510677	−	0.859772i	$-0.329395\pi$
$269$	−8.02423	−	13.8984i	−0.489246	−	0.847399i	−0.999923	+	0.0123733i	$0.996061\pi$
$270$		0			0
$271$	−12.0845	+	20.9309i	−0.734080	+	1.27146i	0.221045	+	0.975264i	$0.429053\pi$
$271$	−12.0845	+	20.9309i	−0.734080	+	1.27146i	−0.955126	+	0.296201i	$0.904280\pi$
$272$			19.4799i			1.18114i
$273$		0			0
$274$	4.27272			0.258125
$275$	−13.2197	+	10.1256i	−0.797179	+	0.610595i
$276$		0			0
$277$	−20.1071	+	11.6088i	−1.20812	+	0.697508i	−0.962348	−	0.271820i	$-0.912374\pi$
$277$	−20.1071	+	11.6088i	−1.20812	+	0.697508i	−0.245771	+	0.969328i	$0.579041\pi$
$278$	2.36818	+	1.36727i	0.142034	+	0.0820032i
$279$		0			0
$280$	6.09280	−	2.68767i	0.364114	−	0.160619i
$281$	−12.4472			−0.742538			−0.371269	−	0.928525i	$-0.621077\pi$
$281$	−12.4472			−0.742538			−0.371269	+	0.928525i	$0.621077\pi$
$282$		0			0
$283$	−7.50649	+	4.33388i	−0.446215	+	0.257622i	−0.706230	−	0.707982i	$-0.749606\pi$
$283$	−7.50649	+	4.33388i	−0.446215	+	0.257622i	0.260016	+	0.965604i	$0.416272\pi$
$284$	−3.61483	−	6.26107i	−0.214501	−	0.371526i
$285$		0			0
$286$	−4.35173			−0.257323
$287$	−0.0782520	+	0.168412i	−0.00461907	+	0.00994107i
$288$		0			0
$289$	6.88760	−	11.9297i	0.405153	−	0.701746i
$290$	0.0722022	−	0.0244743i	0.00423986	−	0.00143718i
$291$		0			0
$292$	−3.91083	−	2.25792i	−0.228864	−	0.132135i
$293$			27.0063i			1.57772i	0.614571	+	0.788862i	$0.289329\pi$
$293$			27.0063i			1.57772i	−0.614571	+	0.788862i	$0.710671\pi$
$294$		0			0
$295$	−3.57467	−	0.712664i	−0.208125	−	0.0414929i
$296$	4.36500	−	7.56040i	0.253710	−	0.439439i
$297$		0			0
$298$	−2.82932	+	1.63351i	−0.163898	+	0.0946267i
$299$	−17.3572	+	30.0635i	−1.00379	+	1.73862i
$300$		0			0
$301$	7.02976	+	3.26634i	0.405189	+	0.188269i
$302$		−	2.56888i		−	0.147822i
$303$		0			0
$304$	−2.90964	−	5.03965i	−0.166879	−	0.289044i
$305$	5.25316	+	15.4975i	0.300795	+	0.887382i
$306$		0			0
$307$		−	2.24681i		−	0.128232i	−0.997942	−	0.0641161i	$-0.979577\pi$
$307$		−	2.24681i		−	0.128232i	0.997942	−	0.0641161i	$-0.0204228\pi$
$308$	9.70965	+	13.8266i	0.553259	+	0.787842i
$309$		0			0
$310$	−3.02289	−	2.65333i	−0.171689	−	0.150699i
$311$	14.2994	+	24.7672i	0.810843	+	1.40442i	0.912275	+	0.409578i	$0.134324\pi$
$311$	14.2994	+	24.7672i	0.810843	+	1.40442i	−0.101432	+	0.994842i	$0.532343\pi$
$312$		0			0
$313$	11.5429	+	6.66427i	0.652441	+	0.376687i	0.789391	−	0.613891i	$-0.210397\pi$
$313$	11.5429	+	6.66427i	0.652441	+	0.376687i	−0.136950	+	0.990578i	$0.543730\pi$
$314$	0.961518			0.0542616
$315$		0			0
$316$	22.8948			1.28794
$317$	−25.2815	−	14.5963i	−1.41995	−	0.819808i	−0.423656	−	0.905823i	$-0.639253\pi$
$317$	−25.2815	−	14.5963i	−1.41995	−	0.819808i	−0.996294	+	0.0860147i	$0.972587\pi$
$318$		0			0
$319$	0.197587	+	0.342231i	0.0110628	+	0.0191613i
$320$	−8.97747	+	10.2279i	−0.501856	+	0.571755i
$321$		0			0
$322$	−5.78047	+	0.513685i	−0.322133	+	0.0286266i
$323$			9.19357i			0.511544i
$324$		0			0
$325$	−22.5458	+	2.94824i	−1.25061	+	0.163539i
$326$	−2.26361	−	3.92069i	−0.125370	−	0.217147i
$327$		0			0
$328$			0.0790069i			0.00436243i
$329$	13.8266	−	9.70965i	0.762283	−	0.535310i
$330$		0			0
$331$	12.4457	−	21.5566i	0.684080	−	1.18486i	−0.289646	−	0.957134i	$-0.593537\pi$
$331$	12.4457	−	21.5566i	0.684080	−	1.18486i	0.973725	−	0.227727i	$-0.0731293\pi$
$332$	−2.03270	+	1.17358i	−0.111559	+	0.0644084i
$333$		0			0
$334$	3.24605	−	5.62233i	0.177616	−	0.307640i
$335$	1.32735	−	6.65789i	0.0725209	−	0.363759i
$336$		0			0
$337$		−	4.72659i		−	0.257474i	−0.991679	−	0.128737i	$-0.958908\pi$
$337$		−	4.72659i		−	0.257474i	0.991679	−	0.128737i	$-0.0410923\pi$
$338$	−1.91112	−	1.10339i	−0.103951	−	0.0600164i
$339$		0			0
$340$	22.5263	−	7.63570i	1.22166	−	0.414104i
$341$	10.4245	−	18.0557i	0.564517	−	0.977772i
$342$		0			0
$343$	−17.8694	+	4.86668i	−0.964857	+	0.262776i
$344$	3.29785			0.177808
$345$		0			0
$346$	1.22494	+	2.12166i	0.0658533	+	0.114061i
$347$	−12.2615	+	7.07915i	−0.658229	+	0.380029i	−0.791602	−	0.611037i	$-0.790753\pi$
$347$	−12.2615	+	7.07915i	−0.658229	+	0.380029i	0.133373	+	0.991066i	$0.457419\pi$
$348$		0			0
$349$	−5.04930			−0.270283			−0.135141	−	0.990826i	$-0.543149\pi$
$349$	−5.04930			−0.270283			−0.135141	+	0.990826i	$0.543149\pi$
$350$	−2.56937	−	2.80119i	−0.137339	−	0.149730i
$351$		0			0
$352$	9.40310	+	5.42888i	0.501187	+	0.289360i
$353$	13.9417	−	8.04924i	0.742042	−	0.428418i	−0.0807694	−	0.996733i	$-0.525738\pi$
$353$	13.9417	−	8.04924i	0.742042	−	0.428418i	0.822811	+	0.568315i	$0.192404\pi$
$354$		0			0
$355$	−5.56174	+	6.33638i	−0.295186	+	0.336300i
$356$	−24.9270			−1.32113
$357$		0			0
$358$			3.38499i			0.178902i
$359$	−0.153241	+	0.265421i	−0.00808776	+	0.0140084i	−0.870041	−	0.492979i	$-0.835908\pi$
$359$	−0.153241	+	0.265421i	−0.00808776	+	0.0140084i	0.861953	+	0.506988i	$0.169241\pi$
$360$		0			0
$361$	8.12679	+	14.0760i	0.427726	+	0.740843i
$362$	2.26188	+	1.30589i	0.118882	+	0.0686363i
$363$		0			0
$364$	2.04208	+	22.9794i	0.107034	+	1.20445i
$365$	−1.02964	+	5.16461i	−0.0538940	+	0.270328i
$366$		0			0
$367$	−20.4813	+	11.8249i	−1.06911	+	0.617253i	−0.927939	−	0.372732i	$-0.878421\pi$
$367$	−20.4813	+	11.8249i	−1.06911	+	0.617253i	−0.141174	+	0.989985i	$0.545088\pi$
$368$	23.2140	−	13.4026i	1.21011	−	0.698658i
$369$		0			0
$370$	−4.88690	−	0.974276i	−0.254058	−	0.0506502i
$371$	0.173255	+	1.94963i	0.00899496	+	0.101220i
$372$		0			0
$373$	16.3140	+	9.41887i	0.844705	+	0.487691i	0.858861	−	0.512209i	$-0.171173\pi$
$373$	16.3140	+	9.41887i	0.844705	+	0.487691i	−0.0141557	+	0.999900i	$0.504506\pi$
$374$	−2.65434	−	4.59744i	−0.137252	−	0.237728i
$375$		0			0
$376$	3.59401	−	6.22500i	0.185347	−	0.321030i
$377$			0.539598i			0.0277907i
$378$		0			0
$379$	−14.2534			−0.732147			−0.366074	−	0.930586i	$-0.619298\pi$
$379$	−14.2534			−0.732147			−0.366074	+	0.930586i	$0.619298\pi$
$380$	−4.68726	+	5.34010i	−0.240451	+	0.273941i
$381$		0			0
$382$	5.10014	−	2.94457i	0.260946	−	0.150657i
$383$	21.6995	+	12.5282i	1.10879	+	0.640161i	0.938516	−	0.345235i	$-0.112201\pi$
$383$	21.6995	+	12.5282i	1.10879	+	0.640161i	0.170276	+	0.985396i	$0.445534\pi$
$384$		0			0
$385$	11.6357	−	15.9001i	0.593010	−	0.810345i
$386$	2.45470			0.124941
$387$		0			0
$388$	5.05315	−	2.91744i	0.256535	−	0.148110i
$389$	6.73590	+	11.6669i	0.341524	+	0.591536i	0.984716	−	0.174169i	$-0.0557238\pi$
$389$	6.73590	+	11.6669i	0.341524	+	0.591536i	−0.643192	+	0.765705i	$0.722390\pi$
$390$		0			0
$391$	−42.3480			−2.14163
$392$	−6.02206	+	5.08122i	−0.304160	+	0.256640i
$393$		0			0
$394$	−1.98385	+	3.43613i	−0.0999449	+	0.173110i
$395$	−8.57123	−	25.2862i	−0.431265	−	1.27229i
$396$		0			0
$397$	15.9768	+	9.22418i	0.801850	+	0.462948i	0.844118	−	0.536158i	$-0.180125\pi$
$397$	15.9768	+	9.22418i	0.801850	+	0.462948i	−0.0422675	+	0.999106i	$0.513458\pi$
$398$			1.08929i			0.0546010i
$399$		0			0
$400$	16.2149	+	6.73298i	0.810745	+	0.336649i
$401$	12.7093	−	22.0131i	0.634670	−	1.09928i	−0.351915	−	0.936032i	$-0.614469\pi$
$401$	12.7093	−	22.0131i	0.634670	−	1.09928i	0.986585	−	0.163249i	$-0.0521973\pi$
$402$		0			0
$403$	24.6545	−	14.2343i	1.22813	−	0.709059i
$404$	15.3775	−	26.6346i	0.765060	−	1.32512i
$405$		0			0
$406$	−0.0738212	+	0.0518406i	−0.00366368	+	0.00257281i
$407$		−	25.8296i		−	1.28033i
$408$		0			0
$409$	−9.36556	−	16.2216i	−0.463097	−	0.802108i	0.536016	−	0.844208i	$-0.319929\pi$
$409$	−9.36556	−	16.2216i	−0.463097	−	0.802108i	−0.999113	+	0.0420997i	$0.986595\pi$
$410$	0.0427100	−	0.0144774i	0.00210930	−	0.000714986i
$411$		0			0
$412$			10.1469i			0.499903i
$413$	4.29592	−	0.381759i	0.211388	−	0.0187851i
$414$		0			0
$415$	2.05714	+	1.80565i	0.100981	+	0.0886360i
$416$	7.41296	+	12.8396i	0.363450	+	0.629514i
$417$		0			0
$418$	1.37341	+	0.792938i	0.0671756	+	0.0387839i
$419$	2.04745			0.100024			0.0500121	−	0.998749i	$-0.484074\pi$
$419$	2.04745			0.100024			0.0500121	+	0.998749i	$0.484074\pi$
$420$		0			0
$421$	−16.0512			−0.782287			−0.391144	−	0.920330i	$-0.627920\pi$
$421$	−16.0512			−0.782287			−0.391144	+	0.920330i	$0.627920\pi$
$422$	−0.0284714	−	0.0164380i	−0.00138596	−	0.000800187i
$423$		0			0
$424$	0.416364	+	0.721164i	0.0202204	+	0.0350228i
$425$	−16.8665	−	22.0205i	−0.818144	−	1.06815i
$426$		0			0
$427$	−11.1271	−	15.8450i	−0.538476	−	0.766791i
$428$			9.89727i			0.478403i
$429$		0			0
$430$	−0.604305	−	1.78277i	−0.0291422	−	0.0859730i
$431$	18.3063	+	31.7075i	0.881784	+	1.52729i	0.849356	+	0.527820i	$0.176991\pi$
$431$	18.3063	+	31.7075i	0.881784	+	1.52729i	0.0324277	+	0.999474i	$0.489676\pi$
$432$		0			0
$433$		−	18.0047i		−	0.865252i	−0.901574	−	0.432626i	$-0.857587\pi$
$433$		−	18.0047i		−	0.865252i	0.901574	−	0.432626i	$-0.142413\pi$
$434$	4.31598	+	2.00540i	0.207174	+	0.0962622i
$435$		0			0
$436$	3.10708	−	5.38163i	0.148802	−	0.257733i
$437$	10.9559	−	6.32538i	0.524090	−	0.302584i
$438$		0			0
$439$	−9.68731	+	16.7789i	−0.462350	+	0.800814i	−0.999078	−	0.0429418i	$-0.986327\pi$
$439$	−9.68731	+	16.7789i	−0.462350	+	0.800814i	0.536727	+	0.843756i	$0.319660\pi$
$440$	1.63892	−	8.22070i	0.0781324	−	0.391907i
$441$		0			0
$442$		−	7.24881i		−	0.344791i
$443$	−14.2396	−	8.22121i	−0.676542	−	0.390602i	0.122009	−	0.992529i	$-0.461066\pi$
$443$	−14.2396	−	8.22121i	−0.676542	−	0.390602i	−0.798551	+	0.601927i	$0.794400\pi$
$444$		0			0
$445$	9.33201	+	27.5306i	0.442380	+	1.30507i
$446$	−1.13020	+	1.95756i	−0.0535164	+	0.0926931i
$447$		0			0
$448$	6.78520	−	14.6030i	0.320571	−	0.689926i
$449$	−32.7245			−1.54436			−0.772182	−	0.635401i	$-0.780835\pi$
$449$	−32.7245			−1.54436			−0.772182	+	0.635401i	$0.780835\pi$
$450$		0			0
$451$	0.116880	+	0.202441i	0.00550365	+	0.00953259i
$452$	−21.0239	+	12.1381i	−0.988880	+	0.570930i
$453$		0			0
$454$	2.57989			0.121080
$455$	24.6151	−	10.8583i	1.15397	−	0.509043i
$456$		0			0
$457$	−32.4156	−	18.7152i	−1.51634	−	0.875459i	−0.999816	−	0.0191857i	$-0.993893\pi$
$457$	−32.4156	−	18.7152i	−1.51634	−	0.875459i	−0.516523	−	0.856273i	$-0.672774\pi$
$458$	−1.26563	+	0.730712i	−0.0591390	+	0.0341439i
$459$		0			0
$460$	−24.5979	−	21.5908i	−1.14688	−	1.00667i
$461$	−28.3604			−1.32088			−0.660438	−	0.750881i	$-0.729629\pi$
$461$	−28.3604			−1.32088			−0.660438	+	0.750881i	$0.729629\pi$
$462$		0			0
$463$		−	7.20833i		−	0.334999i	−0.985872	−	0.167500i	$-0.946431\pi$
$463$		−	7.20833i		−	0.334999i	0.985872	−	0.167500i	$-0.0535693\pi$
$464$	0.208329	−	0.360836i	0.00967143	−	0.0167514i
$465$		0			0
$466$	3.13458	+	5.42926i	0.145207	+	0.251506i
$467$	−10.4607	−	6.03950i	−0.484065	−	0.279475i	0.238044	−	0.971254i	$-0.423494\pi$
$467$	−10.4607	−	6.03950i	−0.484065	−	0.279475i	−0.722109	+	0.691779i	$0.756827\pi$
$468$		0			0
$469$	0.711033	+	8.00122i	0.0328325	+	0.369462i
$470$	−4.02372	−	0.802189i	−0.185601	−	0.0370022i
$471$		0			0
$472$	1.58905	−	0.917438i	0.0731419	−	0.0422285i
$473$	8.45018	−	4.87871i	0.388540	−	0.224323i
$474$		0			0
$475$	7.65266	+	3.17764i	0.351128	+	0.145800i
$476$	−23.0313	+	16.1737i	−1.05564	+	0.741319i
$477$		0			0
$478$	1.85362	+	1.07019i	0.0847827	+	0.0489493i
$479$	−10.0708	−	17.4432i	−0.460149	−	0.797001i	0.538819	−	0.842421i	$-0.318871\pi$
$479$	−10.0708	−	17.4432i	−0.460149	−	0.797001i	−0.998968	+	0.0454204i	$0.985537\pi$
$480$		0			0
$481$	17.6347	−	30.5443i	0.804075	−	1.39270i
$482$			6.94657i			0.316408i
$483$		0			0
$484$	0.175495			0.00797705
$485$	−5.11393	−	4.48874i	−0.232212	−	0.203823i
$486$		0			0
$487$	34.5887	−	19.9698i	1.56737	−	0.904919i	0.570891	−	0.821026i	$-0.306598\pi$
$487$	34.5887	−	19.9698i	1.56737	−	0.904919i	0.996475	−	0.0838930i	$-0.0267354\pi$
$488$	−7.13372	−	4.11866i	−0.322928	−	0.186443i
$489$		0			0
$490$	3.85033	+	2.32435i	0.173940	+	0.105004i
$491$	31.5989			1.42604			0.713019	−	0.701145i	$-0.247327\pi$
$491$	31.5989			1.42604			0.713019	+	0.701145i	$0.247327\pi$
$492$		0			0
$493$	−0.570066	+	0.329127i	−0.0256745	+	0.0148232i
$494$	1.08273	+	1.87534i	0.0487143	+	0.0843757i
$495$		0			0
$496$	−21.9824			−0.987037
$497$	4.20358	−	9.04686i	0.188556	−	0.405807i
$498$		0			0
$499$	19.8929	−	34.4556i	0.890530	−	1.54244i	0.0512890	−	0.998684i	$-0.483667\pi$
$499$	19.8929	−	34.4556i	0.890530	−	1.54244i	0.839241	−	0.543759i	$-0.183000\pi$
$500$	1.43002	−	21.3899i	0.0639525	−	0.956584i
$501$		0			0
$502$	−1.49354	−	0.862295i	−0.0666599	−	0.0384861i
$503$			12.8734i			0.573995i	0.957931	+	0.286997i	$0.0926571\pi$
$503$			12.8734i			0.573995i	−0.957931	+	0.286997i	$0.907343\pi$
$504$		0			0
$505$	−35.1735	−	7.01237i	−1.56520	−	0.312046i
$506$	−3.65248	+	6.32628i	−0.162373	+	0.281238i
$507$		0			0
$508$	−27.4780	+	15.8644i	−1.21914	+	0.703871i
$509$	−16.6981	+	28.9219i	−0.740128	+	1.28194i	0.212308	+	0.977203i	$0.431902\pi$
$509$	−16.6981	+	28.9219i	−0.740128	+	1.28194i	−0.952437	+	0.304737i	$0.901431\pi$
$510$		0			0
$511$	−0.551558	−	6.20665i	−0.0243995	−	0.274566i
$512$		−	19.3531i		−	0.855296i
$513$		0			0
$514$	−1.05365	−	1.82498i	−0.0464746	−	0.0804965i
$515$	11.2068	−	3.79874i	0.493828	−	0.167392i
$516$		0			0
$517$		−	21.2673i		−	0.935335i
$518$	5.87290	−	0.521899i	0.258041	−	0.0229309i
$519$		0			0
$520$	7.55061	−	8.60227i	0.331116	−	0.377234i
$521$	6.77589	+	11.7362i	0.296857	+	0.514172i	0.975415	−	0.220375i	$-0.0707281\pi$
$521$	6.77589	+	11.7362i	0.296857	+	0.514172i	−0.678558	+	0.734547i	$0.737395\pi$
$522$		0			0
$523$	−17.5052	−	10.1066i	−0.765450	−	0.441933i	0.0657991	−	0.997833i	$-0.479040\pi$
$523$	−17.5052	−	10.1066i	−0.765450	−	0.441933i	−0.831249	+	0.555900i	$0.812374\pi$
$524$	10.1583			0.443768
$525$		0			0
$526$	−2.72616			−0.118866
$527$	30.0760	+	17.3644i	1.31013	+	0.756404i
$528$		0			0
$529$	17.6364	+	30.5471i	0.766798	+	1.32813i
$530$	0.313556	−	0.357228i	0.0136200	−	0.0155170i
$531$		0			0
$532$	3.54264	−	7.62441i	0.153593	−	0.330560i
$533$			0.319190i			0.0138257i
$534$		0			0
$535$	10.9310	−	3.70528i	0.472590	−	0.160193i
$536$	1.70875	+	2.95963i	0.0738066	+	0.127837i
$537$		0			0
$538$		−	4.61130i		−	0.198807i
$539$	−7.91354	+	21.9285i	−0.340860	+	0.944529i
$540$		0			0
$541$	16.4854	−	28.5535i	0.708762	−	1.22761i	−0.256554	−	0.966530i	$-0.582587\pi$
$541$	16.4854	−	28.5535i	0.708762	−	1.22761i	0.965317	−	0.261082i	$-0.0840794\pi$
$542$	−6.01421	+	3.47231i	−0.258332	+	0.149148i
$543$		0			0
$544$	−9.04306	+	15.6630i	−0.387718	+	0.671547i
$545$	−7.10694	−	1.41688i	−0.304428	−	0.0606923i
$546$		0			0
$547$			24.6221i			1.05277i	0.850248	+	0.526383i	$0.176452\pi$
$547$			24.6221i			1.05277i	−0.850248	+	0.526383i	$0.823548\pi$
$548$	−24.6926	−	14.2563i	−1.05482	−	0.608998i
$549$		0			0
$550$	−4.74432	+	0.620399i	−0.202298	+	0.0264539i
$551$	0.0983213	−	0.170297i	0.00418863	−	0.00725491i
$552$		0			0
$553$	18.1553	+	25.8532i	0.772041	+	1.09939i
$554$	−6.67127			−0.283435
$555$		0			0
$556$	−9.12399	−	15.8032i	−0.386943	−	0.670206i
$557$	20.7796	−	11.9971i	0.880460	−	0.508334i	0.00964963	−	0.999953i	$-0.496928\pi$
$557$	20.7796	−	11.9971i	0.880460	−	0.508334i	0.870810	+	0.491620i	$0.163595\pi$
$558$		0			0
$559$	13.3234			0.563521
$560$	−20.6526	−	2.24237i	−0.872732	−	0.0947575i
$561$		0			0
$562$	−3.09736	−	1.78826i	−0.130654	−	0.0754333i
$563$	−0.196151	+	0.113248i	−0.00826680	+	0.00477284i	−0.504128	−	0.863629i	$-0.668186\pi$
$563$	−0.196151	+	0.113248i	−0.00826680	+	0.00477284i	0.495861	+	0.868402i	$0.334853\pi$
$564$		0			0
$565$	21.2767	+	18.6756i	0.895119	+	0.785688i
$566$	−2.49056			−0.104686
$567$		0			0
$568$		−	4.24413i		−	0.178080i
$569$	6.40275	−	11.0899i	0.268417	−	0.464912i	−0.700036	−	0.714108i	$-0.746833\pi$
$569$	6.40275	−	11.0899i	0.268417	−	0.464912i	0.968453	+	0.249195i	$0.0801660\pi$
$570$		0			0
$571$	0.780149	+	1.35126i	0.0326482	+	0.0565484i	0.881888	−	0.471459i	$-0.156273\pi$
$571$	0.780149	+	1.35126i	0.0326482	+	0.0565484i	−0.849240	+	0.528008i	$0.822939\pi$
$572$	25.1492	+	14.5199i	1.05154	+	0.607107i
$573$		0			0
$574$	−0.0436677	+	0.0306655i	−0.00182265	+	0.00127995i
$575$	−14.6371	+	35.2502i	−0.610408	+	1.47003i
$576$		0			0
$577$	37.8018	−	21.8249i	1.57371	−	0.908581i	0.578000	−	0.816037i	$-0.303833\pi$
$577$	37.8018	−	21.8249i	1.57371	−	0.908581i	0.995709	−	0.0925443i	$-0.0295000\pi$
$578$	3.42782	−	1.97905i	0.142579	−	0.0823178i
$579$		0			0
$580$	−0.498926	−	0.0994684i	−0.0207168	−	0.00413020i
$581$	−2.93712	−	1.36472i	−0.121852	−	0.0566180i
$582$		0			0
$583$	2.13372	+	1.23191i	0.0883697	+	0.0510203i
$584$	−1.32550	−	2.29583i	−0.0548494	−	0.0950020i
$585$		0			0
$586$	−3.87994	+	6.72025i	−0.160279	+	0.277611i
$587$		−	13.6961i		−	0.565297i	−0.959224	−	0.282648i	$-0.908787\pi$
$587$		−	13.6961i		−	0.565297i	0.959224	−	0.282648i	$-0.0912129\pi$
$588$		0			0
$589$	−10.3746			−0.427479
$590$	−0.787135	−	0.690905i	−0.0324058	−	0.0284441i
$591$		0			0
$592$	−23.5852	+	13.6169i	−0.969344	+	0.559651i
$593$	−7.92838	−	4.57745i	−0.325579	−	0.187973i	0.328297	−	0.944574i	$-0.393525\pi$
$593$	−7.92838	−	4.57745i	−0.325579	−	0.187973i	−0.653877	+	0.756601i	$0.726859\pi$
$594$		0			0
$595$	26.4853	+	19.3820i	1.08579	+	0.794583i
$596$	21.8014			0.893018
$597$		0			0
$598$	−8.63833	+	4.98734i	−0.353247	+	0.203948i
$599$	−20.1368	−	34.8780i	−0.822767	−	1.42507i	−0.903614	−	0.428348i	$-0.859096\pi$
$599$	−20.1368	−	34.8780i	−0.822767	−	1.42507i	0.0808467	−	0.996727i	$-0.474238\pi$
$600$		0			0
$601$	−8.82450			−0.359959			−0.179980	−	0.983670i	$-0.557603\pi$
$601$	−8.82450			−0.359959			−0.179980	+	0.983670i	$0.557603\pi$
$602$	1.28002	+	1.82275i	0.0521696	+	0.0742897i
$603$		0			0
$604$	−8.57126	+	14.8459i	−0.348760	+	0.604070i
$605$	−0.0657008	−	0.193826i	−0.00267112	−	0.00788013i
$606$		0			0
$607$	24.3409	+	14.0532i	0.987966	+	0.570402i	0.904666	−	0.426122i	$-0.140121\pi$
$607$	24.3409	+	14.0532i	0.987966	+	0.570402i	0.0833003	+	0.996524i	$0.473454\pi$
$608$		−	5.40292i		−	0.219117i
$609$		0			0
$610$	−0.919292	+	4.61110i	−0.0372211	+	0.186698i
$611$	14.5199	−	25.1492i	0.587412	−	1.01743i
$612$		0			0
$613$	−1.83025	+	1.05670i	−0.0739232	+	0.0426796i	−0.536506	−	0.843896i	$-0.680256\pi$
$613$	−1.83025	+	1.05670i	−0.0739232	+	0.0426796i	0.462583	+	0.886576i	$0.346923\pi$
$614$	0.322795	−	0.559097i	0.0130269	−	0.0225633i
$615$		0			0
$616$	0.877935	+	9.87935i	0.0353730	+	0.398050i
$617$			18.0390i			0.726221i	0.931746	+	0.363111i	$0.118285\pi$
$617$			18.0390i			0.726221i	−0.931746	+	0.363111i	$0.881715\pi$
$618$		0			0
$619$	−7.31895	−	12.6768i	−0.294173	−	0.509523i	0.680619	−	0.732638i	$-0.261711\pi$
$619$	−7.31895	−	12.6768i	−0.294173	−	0.509523i	−0.974792	+	0.223114i	$0.928378\pi$
$620$	8.61662	+	25.4201i	0.346052	+	1.02090i
$621$		0			0
$622$			8.21744i			0.329489i
$623$	−19.7667	−	28.1479i	−0.791937	−	1.12772i
$624$		0			0
$625$	−24.1594	+	6.42842i	−0.966375	+	0.257137i
$626$	1.91488	+	3.31668i	0.0765341	+	0.132561i
$627$		0			0
$628$	−5.55673	−	3.20818i	−0.221738	−	0.128020i
$629$	43.0252			1.71553
$630$		0			0
$631$	12.1251			0.482692			0.241346	−	0.970439i	$-0.422411\pi$
$631$	12.1251			0.482692			0.241346	+	0.970439i	$0.422411\pi$
$632$	11.6396	+	6.72014i	0.462999	+	0.267313i
$633$		0			0
$634$	−4.19403	−	7.26428i	−0.166566	−	0.288501i
$635$	27.8085	+	24.4088i	1.10355	+	0.968635i
$636$		0			0
$637$	−24.3293	+	20.5283i	−0.963963	+	0.813360i
$638$			0.113548i			0.00449540i
$639$		0			0
$640$	−17.5117	+	5.93593i	−0.692212	+	0.234638i
$641$	−6.52024	−	11.2934i	−0.257534	−	0.446062i	0.708047	−	0.706166i	$-0.249577\pi$
$641$	−6.52024	−	11.2934i	−0.257534	−	0.446062i	−0.965581	+	0.260104i	$0.916243\pi$
$642$		0			0
$643$			27.0185i			1.06550i	0.846271	+	0.532752i	$0.178842\pi$
$643$			27.0185i			1.06550i	−0.846271	+	0.532752i	$0.821158\pi$
$644$	35.1200	+	16.3184i	1.38392	+	0.643033i
$645$		0			0
$646$	−1.32082	+	2.28773i	−0.0519670	+	0.0900095i
$647$	−30.2927	+	17.4895i	−1.19093	+	0.687582i	−0.958517	−	0.285035i	$-0.907995\pi$
$647$	−30.2927	+	17.4895i	−1.19093	+	0.687582i	−0.232411	+	0.972618i	$0.574661\pi$
$648$		0			0
$649$	2.71444	−	4.70155i	0.106551	−	0.184552i
$650$	−6.03386	−	2.50546i	−0.236667	−	0.0982723i
$651$		0			0
$652$			30.2109i			1.18315i
$653$	28.0168	+	16.1755i	1.09638	+	0.632997i	0.935269	−	0.353939i	$-0.115158\pi$
$653$	28.0168	+	16.1755i	1.09638	+	0.632997i	0.161114	+	0.986936i	$0.448491\pi$
$654$		0			0
$655$	−3.80300	−	11.2193i	−0.148596	−	0.438376i
$656$	0.123234	−	0.213447i	0.00481146	−	0.00833370i
$657$		0			0
$658$	4.83557	−	0.429716i	0.188510	−	0.0167521i
$659$	8.54282			0.332781			0.166390	−	0.986060i	$-0.446789\pi$
$659$	8.54282			0.332781			0.166390	+	0.986060i	$0.446789\pi$
$660$		0			0
$661$	15.1715	+	26.2779i	0.590104	+	1.02209i	0.994218	+	0.107382i	$0.0342467\pi$
$661$	15.1715	+	26.2779i	0.590104	+	1.02209i	−0.404114	+	0.914709i	$0.632420\pi$
$662$	6.19400	−	3.57611i	0.240737	−	0.138989i
$663$		0			0
$664$	−1.37788			−0.0534722
$665$	−9.74704	−	1.05829i	−0.377974	−	0.0410388i
$666$		0			0
$667$	0.784435	+	0.452894i	0.0303734	+	0.0175361i
$668$	−37.5187	+	21.6614i	−1.45164	+	0.838107i
$669$		0			0
$670$	1.28682	−	1.46605i	0.0497143	−	0.0566386i
$671$	−24.3719			−0.940867
$672$		0			0
$673$		−	40.5075i		−	1.56145i	−0.624875	−	0.780725i	$-0.714850\pi$
$673$		−	40.5075i		−	1.56145i	0.624875	−	0.780725i	$-0.285150\pi$
$674$	0.679059	−	1.17617i	0.0261564	−	0.0453042i
$675$		0			0
$676$	7.36308	+	12.7532i	0.283195	+	0.490509i
$677$	−20.2833	−	11.7105i	−0.779549	−	0.450073i	0.0567215	−	0.998390i	$-0.481935\pi$
$677$	−20.2833	−	11.7105i	−0.779549	−	0.450073i	−0.836270	+	0.548317i	$0.815269\pi$
$678$		0			0
$679$	7.30149	+	3.39260i	0.280205	+	0.130196i
$680$	13.6935	+	2.73000i	0.525121	+	0.104691i
$681$		0			0
$682$	5.18806	−	2.99533i	0.198661	−	0.114697i
$683$	−44.1887	+	25.5124i	−1.69083	+	0.976204i	−0.736989	+	0.675904i	$0.763753\pi$
$683$	−44.1887	+	25.5124i	−1.69083	+	0.976204i	−0.953845	+	0.300299i	$0.902913\pi$
$684$		0			0
$685$	−6.50107	+	32.6089i	−0.248393	+	1.24592i
$686$	−5.14581	−	1.35623i	−0.196468	−	0.0517812i
$687$		0			0
$688$	−8.90956	−	5.14393i	−0.339674	−	0.196111i
$689$	1.68212	+	2.91353i	0.0640838	+	0.110996i
$690$		0			0
$691$	−12.3057	+	21.3142i	−0.468133	+	0.810829i	−0.999337	−	0.0364144i	$-0.988406\pi$
$691$	−12.3057	+	21.3142i	−0.468133	+	0.810829i	0.531204	+	0.847244i	$0.321740\pi$
$692$		−	16.3485i		−	0.621476i
$693$		0			0
$694$	−4.06819			−0.154426
$695$	−14.0381	+	15.9933i	−0.532494	+	0.606660i
$696$		0			0
$697$	−0.337213	+	0.194690i	−0.0127728	+	0.00737441i
$698$	−1.25647	−	0.725422i	−0.0475580	−	0.0274576i
$699$		0			0
$700$	5.50234	+	24.7613i	0.207969	+	0.935891i
$701$	−25.7244			−0.971595			−0.485798	−	0.874071i	$-0.661471\pi$
$701$	−25.7244			−0.971595			−0.485798	+	0.874071i	$0.661471\pi$
$702$		0			0
$703$	−11.1311	+	6.42652i	−0.419816	+	0.242381i
$704$	−10.1346	−	17.5536i	−0.381962	−	0.661577i
$705$		0			0
$706$	4.62567			0.174089
$707$	42.2703	−	3.75638i	1.58974	−	0.141273i
$708$		0			0
$709$	5.85482	−	10.1408i	0.219882	−	0.380848i	−0.734889	−	0.678187i	$-0.762766\pi$
$709$	5.85482	−	10.1408i	0.219882	−	0.380848i	0.954772	+	0.297339i	$0.0960993\pi$
$710$	−2.29432	+	0.777702i	−0.0861042	+	0.0291867i
$711$		0			0
$712$	−12.6727	−	7.31661i	−0.474931	−	0.274202i
$713$		−	47.7883i		−	1.78968i
$714$		0			0
$715$	6.62129	−	33.2119i	0.247622	−	1.24205i
$716$	11.2943	−	19.5623i	0.422088	−	0.731077i
$717$		0			0
$718$	−0.0762651	+	0.0440317i	−0.00284619	+	0.00164325i
$719$	6.16037	−	10.6701i	0.229743	−	0.397927i	−0.727989	−	0.685589i	$-0.759545\pi$
$719$	6.16037	−	10.6701i	0.229743	−	0.397927i	0.957732	+	0.287662i	$0.0928781\pi$
$720$		0			0
$721$	−11.4580	+	8.04635i	−0.426719	+	0.299662i
$722$			4.67023i			0.173808i
$723$		0			0
$724$	−8.71444	−	15.0939i	−0.323870	−	0.560959i
$725$	0.0769272	+	0.588277i	0.00285700	+	0.0218481i
$726$		0			0
$727$			17.6540i			0.654751i	0.944894	+	0.327376i	$0.106164\pi$
$727$			17.6540i			0.654751i	−0.944894	+	0.327376i	$0.893836\pi$
$728$	−5.70678	+	12.2820i	−0.211507	+	0.455202i
$729$		0			0
$730$	−0.998206	+	1.13724i	−0.0369452	+	0.0420910i
$731$	8.12662	+	14.0757i	0.300574	+	0.520609i
$732$		0			0
$733$	−8.69135	−	5.01795i	−0.321022	−	0.185342i	0.330826	−	0.943692i	$-0.392673\pi$
$733$	−8.69135	−	5.01795i	−0.321022	−	0.185342i	−0.651848	+	0.758349i	$0.726006\pi$
$734$	−6.79541			−0.250823
$735$		0			0
$736$	24.8873			0.917357
$737$	8.75672	+	5.05570i	0.322558	+	0.186229i
$738$		0			0
$739$	−15.5360	−	26.9092i	−0.571502	−	0.989870i	−0.996412	−	0.0846345i	$-0.973028\pi$
$739$	−15.5360	−	26.9092i	−0.571502	−	0.989870i	0.424910	−	0.905235i	$-0.360306\pi$
$740$	24.9913	+	21.9360i	0.918697	+	0.806383i
$741$		0			0
$742$	−0.236987	+	0.510038i	−0.00870005	+	0.0187241i
$743$			4.04189i			0.148283i	0.997248	+	0.0741413i	$0.0236216\pi$
$743$			4.04189i			0.148283i	−0.997248	+	0.0741413i	$0.976378\pi$
$744$		0			0
$745$	−8.16186	−	24.0785i	−0.299027	−	0.882168i
$746$	2.70638	+	4.68759i	0.0990876	+	0.171625i
$747$		0			0
$748$			35.4256i			1.29529i
$749$	−11.1761	+	7.84839i	−0.408367	+	0.286774i
$750$		0			0
$751$	−7.34725	+	12.7258i	−0.268105	+	0.464371i	−0.968372	−	0.249509i	$-0.919731\pi$
$751$	−7.34725	+	12.7258i	−0.268105	+	0.464371i	0.700268	+	0.713881i	$0.253064\pi$
$752$	−19.4193	+	11.2117i	−0.708149	+	0.408850i
$753$		0			0
$754$	−0.0775229	+	0.134274i	−0.00282322	+	0.00488996i
$755$	19.6054	+	3.90862i	0.713512	+	0.142249i
$756$		0			0
$757$			29.6087i			1.07615i	0.842898	+	0.538073i	$0.180847\pi$
$757$			29.6087i			1.07615i	−0.842898	+	0.538073i	$0.819153\pi$
$758$	−3.54681	−	2.04775i	−0.128826	−	0.0743778i
$759$		0			0
$760$	−3.95041	+	1.33907i	−0.143297	+	0.0485731i
$761$	−7.12611	+	12.3428i	−0.258321	+	0.447426i	−0.965792	−	0.259317i	$-0.916503\pi$
$761$	−7.12611	+	12.3428i	−0.258321	+	0.447426i	0.707471	+	0.706742i	$0.249836\pi$
$762$		0			0
$763$	8.54088	−	0.758990i	0.309200	−	0.0274773i
$764$	−39.2992			−1.42179
$765$		0			0
$766$	3.59980	+	6.23504i	0.130066	+	0.225281i
$767$	6.41981	−	3.70648i	0.231806	−	0.133833i
$768$		0			0
$769$	20.6367			0.744178			0.372089	−	0.928197i	$-0.378642\pi$
$769$	20.6367			0.744178			0.372089	+	0.928197i	$0.378642\pi$
$770$	5.17977	−	2.28491i	0.186666	−	0.0823425i
$771$		0			0
$772$	−14.1860	−	8.19030i	−0.510566	−	0.294775i
$773$	36.8580	−	21.2800i	1.32569	−	0.765387i	0.341059	−	0.940042i	$-0.389214\pi$
$773$	36.8580	−	21.2800i	1.32569	−	0.765387i	0.984630	+	0.174655i	$0.0558811\pi$
$774$		0			0
$775$	24.8494	−	19.0332i	0.892615	−	0.683694i
$776$	3.42533			0.122962
$777$		0			0
$778$			3.87093i			0.138780i
$779$	0.0581603	−	0.100737i	0.00208381	−	0.00360926i
$780$		0			0
$781$	−6.27860	−	10.8748i	−0.224666	−	0.389133i
$782$	−10.5379	−	6.08405i	−0.376834	−	0.217565i
$783$		0			0
$784$	24.1949	−	4.33442i	0.864105	−	0.154801i
$785$	−1.46298	+	7.33819i	−0.0522159	+	0.261911i
$786$		0			0
$787$	21.8231	−	12.5996i	0.777909	−	0.449126i	−0.0577798	−	0.998329i	$-0.518402\pi$
$787$	21.8231	−	12.5996i	0.777909	−	0.449126i	0.835689	+	0.549203i	$0.185069\pi$
$788$	22.9298	−	13.2385i	0.816842	−	0.471604i
$789$		0			0
$790$	1.49995	−	7.52363i	0.0533657	−	0.267679i
$791$	−30.3782	−	14.1151i	−1.08012	−	0.501874i
$792$		0			0
$793$	−28.8205	−	16.6395i	−1.02344	−	0.590886i
$794$	2.65044	+	4.59069i	0.0940605	+	0.162918i
$795$		0			0
$796$	3.63449	−	6.29512i	0.128821	−	0.223125i
$797$			51.7211i			1.83205i	0.401116	+	0.916027i	$0.368623\pi$
$797$			51.7211i			1.83205i	−0.401116	+	0.916027i	$0.631377\pi$
$798$		0			0
$799$	35.4256			1.25327
$800$	9.91217	+	12.9411i	0.350448	+	0.457537i
$801$		0			0
$802$	6.32515	−	3.65182i	0.223349	−	0.128950i
$803$	−6.79271	−	3.92177i	−0.239709	−	0.138396i
$804$		0			0
$805$	4.87477	−	44.8975i	0.171813	−	1.58243i
$806$	8.18003			0.288129
$807$		0			0
$808$	15.6357	−	9.02728i	0.550062	−	0.317579i
$809$	25.8890	+	44.8410i	0.910207	+	1.57653i	0.813770	+	0.581187i	$0.197411\pi$
$809$	25.8890	+	44.8410i	0.910207	+	1.57653i	0.0964371	+	0.995339i	$0.469255\pi$
$810$		0			0
$811$	12.0263			0.422299			0.211149	−	0.977454i	$-0.432279\pi$
$811$	12.0263			0.422299			0.211149	+	0.977454i	$0.432279\pi$
$812$	0.599592	−	0.0532831i	0.0210416	−	0.00186987i
$813$		0			0
$814$	3.71089	−	6.42744i	0.130067	−	0.225282i
$815$	33.3664	−	11.3102i	1.16877	−	0.396178i
$816$		0			0
$817$	−4.20488	−	2.42769i	−0.147110	−	0.0849341i
$818$		−	5.38212i		−	0.188182i
$819$		0			0
$820$	−0.295132	−	0.0588389i	−0.0103064	−	0.00205474i
$821$	4.03967	−	6.99692i	0.140985	−	0.244194i	−0.786882	−	0.617103i	$-0.788306\pi$
$821$	4.03967	−	6.99692i	0.140985	−	0.244194i	0.927868	+	0.372909i	$0.121640\pi$
$822$		0			0
$823$	−4.42994	+	2.55762i	−0.154418	+	0.0891532i	−0.575218	−	0.818000i	$-0.695083\pi$
$823$	−4.42994	+	2.55762i	−0.154418	+	0.0891532i	0.420800	+	0.907153i	$0.361749\pi$
$824$	−2.97834	+	5.15864i	−0.103755	+	0.179710i
$825$		0			0
$826$	1.12384	+	0.522188i	0.0391035	+	0.0181693i
$827$			0.705254i			0.0245241i	0.999925	+	0.0122620i	$0.00390323\pi$
$827$			0.705254i			0.0245241i	−0.999925	+	0.0122620i	$0.996097\pi$
$828$		0			0
$829$	12.4790	+	21.6143i	0.433415	+	0.750696i	0.997165	−	0.0752491i	$-0.0239752\pi$
$829$	12.4790	+	21.6143i	0.433415	+	0.750696i	−0.563750	+	0.825945i	$0.690642\pi$
$830$	0.252486	+	0.744864i	0.00876391	+	0.0258546i
$831$		0			0
$832$		−	27.6769i		−	0.959523i
$833$	−36.5270	−	13.1818i	−1.26559	−	0.456723i
$834$		0			0
$835$	37.9700	+	33.3280i	1.31401	+	1.15336i
$836$	−5.29140	−	9.16498i	−0.183007	−	0.316977i
$837$		0			0
$838$	0.509487	+	0.294152i	0.0175999	+	0.0101613i
$839$	−11.6389			−0.401819			−0.200909	−	0.979610i	$-0.564390\pi$
$839$	−11.6389			−0.401819			−0.200909	+	0.979610i	$0.564390\pi$
$840$		0			0
$841$	−28.9859			−0.999514
$842$	−3.99418	−	2.30604i	−0.137649	−	0.0794714i
$843$		0			0
$844$	0.109693	+	0.189994i	0.00377579	+	0.00653986i
$845$	11.3287	−	12.9066i	0.389721	−	0.444001i
$846$		0			0
$847$	0.139165	+	0.198172i	0.00478177	+	0.00680926i
$848$		−	2.59775i		−	0.0892071i
$849$		0			0
$850$	−1.03342	−	7.90275i	−0.0354460	−	0.271062i
$851$	−29.6023	−	51.2726i	−1.01475	−	1.75760i
$852$		0			0
$853$		−	32.5996i		−	1.11619i	−0.829778	−	0.558094i	$-0.811533\pi$
$853$		−	32.5996i		−	1.11619i	0.829778	−	0.558094i	$-0.188467\pi$
$854$	−0.492445	−	5.54146i	−0.0168511	−	0.189625i
$855$		0			0
$856$	−2.90507	+	5.03172i	−0.0992931	+	0.171981i
$857$	−27.4455	+	15.8456i	−0.937519	+	0.541277i	−0.889182	−	0.457554i	$-0.848726\pi$
$857$	−27.4455	+	15.8456i	−0.937519	+	0.541277i	−0.0483371	+	0.998831i	$0.515392\pi$
$858$		0			0
$859$	−21.8456	+	37.8377i	−0.745363	+	1.29101i	0.204662	+	0.978833i	$0.434390\pi$
$859$	−21.8456	+	37.8377i	−0.745363	+	1.29101i	−0.950025	+	0.312174i	$0.898943\pi$
$860$	−2.45601	+	12.3192i	−0.0837494	+	0.420081i
$861$		0			0
$862$			10.5201i			0.358317i
$863$	−33.6005	−	19.3992i	−1.14377	−	0.660358i	−0.196411	−	0.980522i	$-0.562929\pi$
$863$	−33.6005	−	19.3992i	−1.14377	−	0.660358i	−0.947362	+	0.320164i	$0.896262\pi$
$864$		0			0
$865$	−18.0561	+	6.12044i	−0.613924	+	0.208101i
$866$	2.58670	−	4.48030i	0.0878997	−	0.152247i
$867$		0			0
$868$	−18.2514	−	25.9901i	−0.619493	−	0.882160i
$869$	39.7660			1.34897
$870$		0			0
$871$	6.90338	+	11.9570i	0.233912	+	0.405148i
$872$	3.15925	−	1.82399i	0.106986	−	0.0617682i
$873$		0			0
$874$	3.63501			0.122956
$875$	25.2877	−	15.3470i	0.854881	−	0.518825i
$876$		0			0
$877$	3.72454	+	2.15036i	0.125769	+	0.0726127i	0.561565	−	0.827433i	$-0.310200\pi$
$877$	3.72454	+	2.15036i	0.125769	+	0.0726127i	−0.435796	+	0.900046i	$0.643533\pi$
$878$	−4.82118	+	2.78351i	−0.162707	+	0.0939390i
$879$		0			0
$880$	−17.2502	+	19.6529i	−0.581506	+	0.662498i
$881$	1.29308			0.0435650			0.0217825	−	0.999763i	$-0.493066\pi$
$881$	1.29308			0.0435650			0.0217825	+	0.999763i	$0.493066\pi$
$882$		0			0
$883$			1.49533i			0.0503218i	0.999683	+	0.0251609i	$0.00800981\pi$
$883$			1.49533i			0.0503218i	−0.999683	+	0.0251609i	$0.991990\pi$
$884$	−24.1862	+	41.8918i	−0.813471	+	1.40897i
$885$		0			0
$886$	−2.36225	−	4.09153i	−0.0793613	−	0.137458i
$887$	−8.73964	−	5.04584i	−0.293449	−	0.169423i	0.346047	−	0.938217i	$-0.387524\pi$
$887$	−8.73964	−	5.04584i	−0.293449	−	0.169423i	−0.639496	+	0.768794i	$0.720857\pi$
$888$		0			0
$889$	−39.7040	−	18.4483i	−1.33163	−	0.618736i
$890$	−1.63308	+	8.19142i	−0.0547410	+	0.274577i
$891$		0			0
$892$	13.0631	−	7.54198i	0.437385	−	0.252524i
$893$	−9.16498	+	5.29140i	−0.306694	+	0.177070i
$894$		0			0
$895$	−25.8339	−	5.15036i	−0.863531	−	0.172158i
$896$	17.9044	−	12.5733i	0.598143	−	0.420044i
$897$		0			0
$898$	−8.14317	−	4.70146i	−0.271741	−	0.156890i
$899$	−0.371409	−	0.643299i	−0.0123872	−	0.0214552i
$900$		0			0
$901$	−2.05202	+	3.55421i	−0.0683628	+	0.118408i
$902$			0.0671674i			0.00223643i
$903$		0			0
$904$	−14.2512			−0.473989
$905$	−13.4079	+	15.2754i	−0.445695	+	0.507772i
$906$		0			0
$907$	−3.69531	+	2.13349i	−0.122701	+	0.0708414i	−0.560094	−	0.828429i	$-0.689235\pi$
$907$	−3.69531	+	2.13349i	−0.122701	+	0.0708414i	0.437393	+	0.899270i	$0.355902\pi$
$908$	−14.9095	−	8.60802i	−0.494790	−	0.285667i
$909$		0			0
$910$	7.68520	+	0.834427i	0.254762	+	0.0276610i
$911$	28.5451			0.945742			0.472871	−	0.881132i	$-0.343218\pi$
$911$	28.5451			0.945742			0.472871	+	0.881132i	$0.343218\pi$
$912$		0			0
$913$	−3.53058	+	2.03838i	−0.116845	+	0.0674606i
$914$	−5.37754	−	9.31417i	−0.177873	−	0.308085i
$915$		0			0
$916$	9.75231			0.322226
$917$	8.05539	+	11.4709i	0.266012	+	0.378802i
$918$		0			0
$919$	−23.2822	+	40.3259i	−0.768008	+	1.33023i	0.170634	+	0.985335i	$0.445419\pi$
$919$	−23.2822	+	40.3259i	−0.768008	+	1.33023i	−0.938642	+	0.344894i	$0.887915\pi$
$920$	−6.16810	−	18.1967i	−0.203356	−	0.599926i
$921$		0			0
$922$	−7.05720	−	4.07448i	−0.232417	−	0.134186i
$923$		−	17.1464i		−	0.564381i
$924$		0			0
$925$	14.8711	−	35.8138i	0.488959	−	1.17755i
$926$	1.03561	−	1.79372i	0.0340321	−	0.0589453i
$927$		0			0
$928$	0.335019	−	0.193423i	0.0109975	−	0.00634943i
$929$	−3.69774	+	6.40467i	−0.121319	+	0.210130i	−0.920288	−	0.391242i	$-0.872046\pi$
$929$	−3.69774	+	6.40467i	−0.121319	+	0.210130i	0.798969	+	0.601372i	$0.205379\pi$
$930$		0			0
$931$	11.4188	−	2.04564i	0.374238	−	0.0670432i
$932$		−	41.8352i		−	1.37036i
$933$		0			0
$934$	−1.73537	−	3.00574i	−0.0567829	−	0.0983509i
$935$	39.1258	−	13.2624i	1.27955	−	0.433728i
$936$		0			0
$937$		−	44.1988i		−	1.44391i	−0.691939	−	0.721956i	$-0.743243\pi$
$937$		−	44.1988i		−	1.44391i	0.691939	−	0.721956i	$-0.256757\pi$
$938$	−0.972585	+	2.09318i	−0.0317560	+	0.0683447i
$939$		0			0
$940$	20.5770	+	18.0614i	0.671149	+	0.589099i
$941$	18.0180	+	31.2080i	0.587369	+	1.01735i	0.994576	+	0.104017i	$0.0331696\pi$
$941$	18.0180	+	31.2080i	0.587369	+	1.01735i	−0.407206	+	0.913336i	$0.633497\pi$
$942$		0			0
$943$	0.464020	+	0.267902i	0.0151106	+	0.00872408i
$944$	−5.72401			−0.186301
$945$		0			0
$946$	2.80366			0.0911548
$947$	29.6476	+	17.1170i	0.963417	+	0.556229i	0.897223	−	0.441577i	$-0.145581\pi$
$947$	29.6476	+	17.1170i	0.963417	+	0.556229i	0.0661943	+	0.997807i	$0.478914\pi$
$948$		0			0
$949$	−5.35504	−	9.27521i	−0.173832	−	0.301086i
$950$	1.44776	+	1.89017i	0.0469716	+	0.0613251i
$951$		0			0
$952$	−16.4563	+	1.46240i	−0.533353	+	0.0473967i
$953$		−	30.9689i		−	1.00318i	−0.865105	−	0.501591i	$-0.832748\pi$
$953$		−	30.9689i		−	1.00318i	0.865105	−	0.501591i	$-0.167252\pi$
$954$		0			0
$955$	14.7126	+	43.4039i	0.476088	+	1.40452i
$956$	−7.14155	−	12.3695i	−0.230974	−	0.400059i
$957$		0			0
$958$		−	5.78743i		−	0.186983i
$959$	−3.48249	−	39.1883i	−0.112455	−	1.26545i
$960$		0			0
$961$	−4.09508	+	7.09289i	−0.132099	+	0.228803i
$962$	8.77646	−	5.06709i	0.282964	−	0.163370i
$963$		0			0
$964$	23.1778	−	40.1451i	0.746506	−	1.29299i
$965$	−3.73490	+	18.7340i	−0.120231	+	0.603068i
$966$		0			0
$967$		−	21.0270i		−	0.676184i	−0.941113	−	0.338092i	$-0.890218\pi$
$967$		−	21.0270i		−	0.676184i	0.941113	−	0.338092i	$-0.109782\pi$
$968$	0.0892209	+	0.0515117i	0.00286767	+	0.00165565i
$969$		0			0
$970$	−0.627664	−	1.85169i	−0.0201531	−	0.0594540i
$971$	22.3468	−	38.7058i	0.717144	−	1.24213i	−0.244983	−	0.969527i	$-0.578782\pi$
$971$	22.3468	−	38.7058i	0.717144	−	1.24213i	0.962127	−	0.272602i	$-0.0878843\pi$
$972$		0			0
$973$	10.6100	−	22.8346i	0.340141	−	0.732045i
$974$	11.4761			0.367718
$975$		0			0
$976$	12.8484	+	22.2541i	0.411268	+	0.712337i
$977$	−12.5029	+	7.21858i	−0.400005	+	0.230943i	−0.686486	−	0.727143i	$-0.740848\pi$
$977$	−12.5029	+	7.21858i	−0.400005	+	0.230943i	0.286481	+	0.958086i	$0.407514\pi$
$978$		0			0
$979$	−43.2956			−1.38373
$980$	−14.4962	−	26.2797i	−0.463063	−	0.839473i
$981$		0			0
$982$	7.86307	+	4.53974i	0.250921	+	0.144869i
$983$	14.5389	−	8.39401i	0.463717	−	0.267727i	−0.249889	−	0.968275i	$-0.580394\pi$
$983$	14.5389	−	8.39401i	0.463717	−	0.267727i	0.713606	+	0.700547i	$0.247061\pi$
$984$		0			0
$985$	−23.2056	−	20.3687i	−0.739393	−	0.649000i
$986$	−0.189140			−0.00602345
$987$		0			0
$988$		−	14.4505i		−	0.459730i
$989$	11.1826	−	19.3688i	0.355585	−	0.615892i
$990$		0			0
$991$	−20.0539	−	34.7344i	−0.637033	−	1.10337i	−0.986081	−	0.166268i	$-0.946828\pi$
$991$	−20.0539	−	34.7344i	−0.637033	−	1.10337i	0.349048	−	0.937105i	$-0.386505\pi$
$992$	−17.6752	−	10.2048i	−0.561188	−	0.324002i
$993$		0			0
$994$	2.34576	−	1.64730i	0.0744031	−	0.0522492i
$995$	−8.31330	−	1.65738i	−0.263549	−	0.0525425i
$996$		0			0
$997$	−44.4447	+	25.6602i	−1.40758	+	0.812666i	−0.995154	−	0.0983259i	$-0.968651\pi$
$997$	−44.4447	+	25.6602i	−1.40758	+	0.812666i	−0.412424	+	0.910992i	$0.635318\pi$
$998$	9.90032	−	5.71595i	0.313389	−	0.180935i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.b.289.5		16
3.2	odd	2		105.2.q.a.79.4	yes	16
5.4	even	2	inner	315.2.bf.b.289.4		16
7.2	even	3		2205.2.d.s.1324.4		8
7.4	even	3	inner	315.2.bf.b.109.4		16
7.5	odd	6		2205.2.d.o.1324.4		8
12.11	even	2		1680.2.di.d.289.7		16
15.2	even	4		525.2.i.h.226.3		8
15.8	even	4		525.2.i.k.226.2		8
15.14	odd	2		105.2.q.a.79.5	yes	16
21.2	odd	6		735.2.d.d.589.5		8
21.5	even	6		735.2.d.e.589.5		8
21.11	odd	6		105.2.q.a.4.5	yes	16
21.17	even	6		735.2.q.g.214.5		16
21.20	even	2		735.2.q.g.79.4		16
35.4	even	6	inner	315.2.bf.b.109.5		16
35.9	even	6		2205.2.d.s.1324.5		8
35.19	odd	6		2205.2.d.o.1324.5		8
60.59	even	2		1680.2.di.d.289.3		16
84.11	even	6		1680.2.di.d.529.3		16
105.2	even	12		3675.2.a.bz.1.2		4
105.23	even	12		3675.2.a.bp.1.3		4
105.32	even	12		525.2.i.h.151.3		8
105.44	odd	6		735.2.d.d.589.4		8
105.47	odd	12		3675.2.a.cb.1.2		4
105.53	even	12		525.2.i.k.151.2		8
105.59	even	6		735.2.q.g.214.4		16
105.68	odd	12		3675.2.a.bn.1.3		4
105.74	odd	6		105.2.q.a.4.4	✓	16
105.89	even	6		735.2.d.e.589.4		8
105.104	even	2		735.2.q.g.79.5		16
420.179	even	6		1680.2.di.d.529.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	105.74	odd	6
105.2.q.a.4.5	yes	16	21.11	odd	6
105.2.q.a.79.4	yes	16	3.2	odd	2
105.2.q.a.79.5	yes	16	15.14	odd	2
315.2.bf.b.109.4		16	7.4	even	3	inner
315.2.bf.b.109.5		16	35.4	even	6	inner
315.2.bf.b.289.4		16	5.4	even	2	inner
315.2.bf.b.289.5		16	1.1	even	1	trivial
525.2.i.h.151.3		8	105.32	even	12
525.2.i.h.226.3		8	15.2	even	4
525.2.i.k.151.2		8	105.53	even	12
525.2.i.k.226.2		8	15.8	even	4
735.2.d.d.589.4		8	105.44	odd	6
735.2.d.d.589.5		8	21.2	odd	6
735.2.d.e.589.4		8	105.89	even	6
735.2.d.e.589.5		8	21.5	even	6
735.2.q.g.79.4		16	21.20	even	2
735.2.q.g.79.5		16	105.104	even	2
735.2.q.g.214.4		16	105.59	even	6
735.2.q.g.214.5		16	21.17	even	6
1680.2.di.d.289.3		16	60.59	even	2
1680.2.di.d.289.7		16	12.11	even	2
1680.2.di.d.529.3		16	84.11	even	6
1680.2.di.d.529.7		16	420.179	even	6
2205.2.d.o.1324.4		8	7.5	odd	6
2205.2.d.o.1324.5		8	35.19	odd	6
2205.2.d.s.1324.4		8	7.2	even	3
2205.2.d.s.1324.5		8	35.9	even	6
3675.2.a.bn.1.3		4	105.68	odd	12
3675.2.a.bp.1.3		4	105.23	even	12
3675.2.a.bz.1.2		4	105.2	even	12
3675.2.a.cb.1.2		4	105.47	odd	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248840 + 0.143668i) q^{2} +(-0.958719 - 1.66055i) q^{4} +(-1.47507 + 1.68052i) q^{5} +(1.11487 - 2.39939i) q^{7} -1.12562i q^{8} +O(q^{10})\)	\(q+(0.248840 + 0.143668i) q^{2} +(-0.958719 - 1.66055i) q^{4} +(-1.47507 + 1.68052i) q^{5} +(1.11487 - 2.39939i) q^{7} -1.12562i q^{8} +(-0.608495 + 0.206261i) q^{10} +(-1.66520 - 2.88421i) q^{11} -4.54754i q^{13} +(0.622139 - 0.436894i) q^{14} +(-1.75572 + 3.04100i) q^{16} +(4.80431 - 2.77377i) q^{17} +(-0.828617 + 1.43521i) q^{19} +(4.20477 + 0.838284i) q^{20} -0.956942i q^{22} +(-6.61094 - 3.81683i) q^{23} +(-0.648315 - 4.95779i) q^{25} +(0.653336 - 1.13161i) q^{26} +(-5.05315 + 0.449051i) q^{28} -0.118657 q^{29} +(3.13010 + 5.42150i) q^{31} +(-2.82342 + 1.63010i) q^{32} +1.59401 q^{34} +(2.38772 + 5.41284i) q^{35} +(6.71665 + 3.87786i) q^{37} +(-0.412386 + 0.238091i) q^{38} +(1.89163 + 1.66037i) q^{40} -0.0701896 q^{41} +2.92981i q^{43} +(-3.19291 + 5.53029i) q^{44} +(-1.09671 - 1.89956i) q^{46} +(5.53029 + 3.19291i) q^{47} +(-4.51415 - 5.35000i) q^{49} +(0.550949 - 1.32684i) q^{50} +(-7.55142 + 4.35981i) q^{52} +(-0.640682 + 0.369898i) q^{53} +(7.30326 + 1.45601i) q^{55} +(-2.70080 - 1.25492i) q^{56} +(-0.0295266 - 0.0170472i) q^{58} +(0.815051 + 1.41171i) q^{59} +(3.65901 - 6.33759i) q^{61} +1.79878i q^{62} +6.08612 q^{64} +(7.64225 + 6.70796i) q^{65} +(-2.62934 + 1.51805i) q^{67} +(-9.21197 - 5.31853i) q^{68} +(-0.183490 + 1.68997i) q^{70} +3.77048 q^{71} +(2.03961 - 1.17757i) q^{73} +(1.11425 + 1.92993i) q^{74} +3.17764 q^{76} +(-8.77681 + 0.779956i) q^{77} +(-5.97016 + 10.3406i) q^{79} +(-2.52065 - 7.43623i) q^{80} +(-0.0174660 - 0.0100840i) q^{82} -1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +(-0.420920 + 0.729054i) q^{86} +(-3.24652 + 1.87438i) q^{88} +(6.50007 - 11.2585i) q^{89} +(-10.9113 - 5.06990i) q^{91} +14.6371i q^{92} +(0.917438 + 1.58905i) q^{94} +(-1.18963 - 3.50954i) q^{95} +3.04306i q^{97} +(-0.354679 - 1.97983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 - 2 * q^5	\( 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

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