LMFDB - Embedded newform 495.2.n.b.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.819390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 $ x^8 - 3x^7 + 10x^6 - 13x^5 + 29x^4 - 7x^3 + 80x^2 + 143*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.2
Root			$-0.755243 + 0.548716i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.288477 + 0.887841i) q^{2} +(0.912991 - 0.663327i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.65127 - 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +O(q^{10})$	\(q+(0.288477 + 0.887841i) q^{2} +(0.912991 - 0.663327i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.65127 - 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +0.933531 q^{10} +(-1.85274 - 2.75088i) q^{11} +(-0.447591 - 1.37754i) q^{13} +(1.54151 + 1.11997i) q^{14} +(-0.145054 + 0.446431i) q^{16} +(-0.267937 + 0.824626i) q^{17} +(-2.53103 - 1.83890i) q^{19} +(-0.348732 - 1.07329i) q^{20} +(1.90788 - 2.43850i) q^{22} +4.70547 q^{23} +(-0.809017 - 0.587785i) q^{25} +(1.09392 - 0.794779i) q^{26} +(0.711789 - 2.19066i) q^{28} +(1.64906 - 1.19811i) q^{29} +(3.27979 + 10.0941i) q^{31} +5.40294 q^{32} -0.809430 q^{34} +(-0.630728 - 1.94118i) q^{35} +(-3.36279 + 2.44321i) q^{37} +(0.902506 - 2.77763i) q^{38} +(2.36279 - 1.71667i) q^{40} +(-0.651268 - 0.473174i) q^{41} -2.34089 q^{43} +(-3.51627 - 1.28256i) q^{44} +(1.35742 + 4.17771i) q^{46} +(8.39782 + 6.10137i) q^{47} +(-0.875752 + 2.69529i) q^{49} +(0.288477 - 0.887841i) q^{50} +(-1.32241 - 0.960786i) q^{52} +(-2.22985 - 6.86278i) q^{53} +(-3.18877 + 0.911987i) q^{55} +5.96112 q^{56} +(1.53945 + 1.11847i) q^{58} +(-6.73386 + 4.89243i) q^{59} +(-2.70931 + 8.33841i) q^{61} +(-8.01586 + 5.82386i) q^{62} +(1.84873 + 5.68981i) q^{64} -1.44843 q^{65} -3.15664 q^{67} +(0.302372 + 0.930606i) q^{68} +(1.54151 - 1.11997i) q^{70} +(-3.97725 + 12.2407i) q^{71} +(11.9075 - 8.65128i) q^{73} +(-3.13927 - 2.28081i) q^{74} -3.53059 q^{76} +(-6.35965 - 2.31969i) q^{77} +(-5.25303 - 16.1672i) q^{79} +(0.379757 + 0.275910i) q^{80} +(0.232227 - 0.714723i) q^{82} +(-1.89782 + 5.84089i) q^{83} +(0.701468 + 0.509647i) q^{85} +(-0.675292 - 2.07833i) q^{86} +(0.344727 - 9.68030i) q^{88} -3.77194 q^{89} +(-2.39175 - 1.73771i) q^{91} +(4.29606 - 3.12127i) q^{92} +(-2.99447 + 9.21604i) q^{94} +(-2.53103 + 1.83890i) q^{95} +(-0.598859 - 1.84310i) q^{97} -2.64562 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8 - 2 * q^10 + 3 * q^11 + 10 * q^13 - 24 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^19 - 7 * q^20 - 7 * q^22 + 2 * q^23 - 2 * q^25 - 14 * q^26 + 13 * q^28 - 14 * q^29 - 5 * q^31 + 16 * q^32 - 70 * q^34 - q^35 - 27 * q^37 + 16 * q^38 + 19 * q^40 - q^41 - 28 * q^43 - 47 * q^44 + 42 * q^46 + 27 * q^47 - 15 * q^49 - 2 * q^50 + 22 * q^52 + q^53 - 7 * q^55 + 24 * q^56 + 18 * q^58 - 13 * q^59 - 3 * q^61 - 15 * q^62 + 19 * q^64 - 30 * q^65 + 10 * q^67 + 33 * q^68 - 24 * q^70 - 9 * q^71 + 5 * q^73 + 17 * q^74 - 46 * q^76 - q^77 - 10 * q^79 - 11 * q^80 - 33 * q^82 + 25 * q^83 - 8 * q^85 - 20 * q^86 + 29 * q^88 - 4 * q^89 - 43 * q^91 + 22 * q^92 + 57 * q^94 - 2 * q^95 + 13 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.288477	+	0.887841i	0.203984	+	0.627798i	0.999754	+	0.0221988i	$0.00706668\pi$
$2$	0.288477	+	0.887841i	0.203984	+	0.627798i	−0.795770	+	0.605600i	$0.792933\pi$
$3$		0			0
$3$		0			0
$4$	0.912991	−	0.663327i	0.456496	−	0.331664i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	1.65127	−	1.19972i	0.624121	−	0.453450i	−0.230238	−	0.973134i	$-0.573950\pi$
$7$	1.65127	−	1.19972i	0.624121	−	0.453450i	0.854358	+	0.519684i	$0.173950\pi$
$8$	2.36279	+	1.71667i	0.835373	+	0.606934i
$9$		0			0
$10$	0.933531			0.295209
$11$	−1.85274	−	2.75088i	−0.558621	−	0.829423i
$11$	−1.85274	−	2.75088i	−0.558621	−	0.829423i
$12$		0			0
$13$	−0.447591	−	1.37754i	−0.124139	−	0.382062i	0.869604	−	0.493750i	$-0.164374\pi$
$13$	−0.447591	−	1.37754i	−0.124139	−	0.382062i	−0.993743	+	0.111688i	$0.964374\pi$
$14$	1.54151	+	1.11997i	0.411986	+	0.299325i
$15$		0			0
$16$	−0.145054	+	0.446431i	−0.0362636	+	0.111608i
$17$	−0.267937	+	0.824626i	−0.0649843	+	0.200001i	−0.978277	−	0.207303i	$-0.933531\pi$
$17$	−0.267937	+	0.824626i	−0.0649843	+	0.200001i	0.913292	+	0.407305i	$0.133531\pi$
$18$		0			0
$19$	−2.53103	−	1.83890i	−0.580657	−	0.421872i	0.258304	−	0.966064i	$-0.416836\pi$
$19$	−2.53103	−	1.83890i	−0.580657	−	0.421872i	−0.838961	+	0.544192i	$0.816836\pi$
$20$	−0.348732	−	1.07329i	−0.0779788	−	0.239994i
$21$		0			0
$22$	1.90788	−	2.43850i	0.406761	−	0.519891i
$23$	4.70547			0.981159			0.490580	−	0.871396i	$-0.336785\pi$
$23$	4.70547			0.981159			0.490580	+	0.871396i	$0.336785\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	1.09392	−	0.794779i	0.214535	−	0.155869i
$27$		0			0
$28$	0.711789	−	2.19066i	0.134516	−	0.413996i
$29$	1.64906	−	1.19811i	0.306223	−	0.222484i	−0.424051	−	0.905638i	$-0.639392\pi$
$29$	1.64906	−	1.19811i	0.306223	−	0.222484i	0.730274	+	0.683154i	$0.239392\pi$
$30$		0			0
$31$	3.27979	+	10.0941i	0.589067	+	1.81296i	0.582284	+	0.812986i	$0.302159\pi$
$31$	3.27979	+	10.0941i	0.589067	+	1.81296i	0.00678348	+	0.999977i	$0.497841\pi$
$32$	5.40294			0.955113
$33$		0			0
$34$	−0.809430			−0.138816
$35$	−0.630728	−	1.94118i	−0.106613	−	0.328120i
$36$		0			0
$37$	−3.36279	+	2.44321i	−0.552839	+	0.401661i	−0.828831	−	0.559499i	$-0.810994\pi$
$37$	−3.36279	+	2.44321i	−0.552839	+	0.401661i	0.275992	+	0.961160i	$0.410994\pi$
$38$	0.902506	−	2.77763i	0.146406	−	0.450591i
$39$		0			0
$40$	2.36279	−	1.71667i	0.373590	−	0.271429i
$41$	−0.651268	−	0.473174i	−0.101711	−	0.0738974i	0.535767	−	0.844366i	$-0.320022\pi$
$41$	−0.651268	−	0.473174i	−0.101711	−	0.0738974i	−0.637478	+	0.770468i	$0.720022\pi$
$42$		0			0
$43$	−2.34089			−0.356982			−0.178491	−	0.983942i	$-0.557122\pi$
$43$	−2.34089			−0.356982			−0.178491	+	0.983942i	$0.557122\pi$
$44$	−3.51627	−	1.28256i	−0.530097	−	0.193354i
$45$		0			0
$46$	1.35742	+	4.17771i	0.200141	+	0.615970i
$47$	8.39782	+	6.10137i	1.22495	+	0.889977i	0.996501	−	0.0835794i	$-0.0266352\pi$
$47$	8.39782	+	6.10137i	1.22495	+	0.889977i	0.228447	+	0.973556i	$0.426635\pi$
$48$		0			0
$49$	−0.875752	+	2.69529i	−0.125107	+	0.385041i
$50$	0.288477	−	0.887841i	0.0407968	−	0.125560i
$51$		0			0
$52$	−1.32241	−	0.960786i	−0.183385	−	0.133237i
$53$	−2.22985	−	6.86278i	−0.306294	−	0.942676i	−0.979191	−	0.202940i	$-0.934950\pi$
$53$	−2.22985	−	6.86278i	−0.306294	−	0.942676i	0.672897	−	0.739736i	$-0.265050\pi$
$54$		0			0
$55$	−3.18877	+	0.911987i	−0.429974	+	0.122972i
$56$	5.96112			0.796588
$57$		0			0
$58$	1.53945	+	1.11847i	0.202139	+	0.146863i
$59$	−6.73386	+	4.89243i	−0.876674	+	0.636941i	−0.932369	−	0.361507i	$-0.882262\pi$
$59$	−6.73386	+	4.89243i	−0.876674	+	0.636941i	0.0556956	+	0.998448i	$0.482262\pi$
$60$		0			0
$61$	−2.70931	+	8.33841i	−0.346892	+	1.06762i	0.613671	+	0.789562i	$0.289692\pi$
$61$	−2.70931	+	8.33841i	−0.346892	+	1.06762i	−0.960563	+	0.278062i	$0.910308\pi$
$62$	−8.01586	+	5.82386i	−1.01801	+	0.739631i
$63$		0			0
$64$	1.84873	+	5.68981i	0.231091	+	0.711226i
$65$	−1.44843			−0.179656
$66$		0			0
$67$	−3.15664			−0.385645			−0.192822	−	0.981234i	$-0.561764\pi$
$67$	−3.15664			−0.385645			−0.192822	+	0.981234i	$0.561764\pi$
$68$	0.302372	+	0.930606i	0.0366680	+	0.112853i
$69$		0			0
$70$	1.54151	−	1.11997i	0.184246	−	0.133862i
$71$	−3.97725	+	12.2407i	−0.472013	+	1.45271i	0.377931	+	0.925834i	$0.376636\pi$
$71$	−3.97725	+	12.2407i	−0.472013	+	1.45271i	−0.849944	+	0.526873i	$0.823364\pi$
$72$		0			0
$73$	11.9075	−	8.65128i	1.39366	−	1.01256i	0.398211	−	0.917294i	$-0.369631\pi$
$73$	11.9075	−	8.65128i	1.39366	−	1.01256i	0.995452	−	0.0952617i	$-0.0303688\pi$
$74$	−3.13927	−	2.28081i	−0.364933	−	0.265139i
$75$		0			0
$76$	−3.53059			−0.404987
$77$	−6.35965	−	2.31969i	−0.724749	−	0.264353i
$78$		0			0
$79$	−5.25303	−	16.1672i	−0.591012	−	1.81895i	−0.573651	−	0.819100i	$-0.694473\pi$
$79$	−5.25303	−	16.1672i	−0.591012	−	1.81895i	−0.0173618	−	0.999849i	$-0.505527\pi$
$80$	0.379757	+	0.275910i	0.0424581	+	0.0308476i
$81$		0			0
$82$	0.232227	−	0.714723i	0.0256452	−	0.0789279i
$83$	−1.89782	+	5.84089i	−0.208313	+	0.641121i	0.791248	+	0.611495i	$0.209432\pi$
$83$	−1.89782	+	5.84089i	−0.208313	+	0.641121i	−0.999561	+	0.0296262i	$0.990568\pi$
$84$		0			0
$85$	0.701468	+	0.509647i	0.0760849	+	0.0552789i
$86$	−0.675292	−	2.07833i	−0.0728186	−	0.224113i
$87$		0			0
$88$	0.344727	−	9.68030i	0.0367480	−	1.03192i
$89$	−3.77194			−0.399825			−0.199913	−	0.979814i	$-0.564066\pi$
$89$	−3.77194			−0.399825			−0.199913	+	0.979814i	$0.564066\pi$
$90$		0			0
$91$	−2.39175	−	1.73771i	−0.250724	−	0.182162i
$92$	4.29606	−	3.12127i	0.447895	−	0.325415i
$93$		0			0
$94$	−2.99447	+	9.21604i	−0.308856	+	0.950562i
$95$	−2.53103	+	1.83890i	−0.259678	+	0.188667i
$96$		0			0
$97$	−0.598859	−	1.84310i	−0.0608049	−	0.187138i	0.916040	−	0.401087i	$-0.131367\pi$
$97$	−0.598859	−	1.84310i	−0.0608049	−	0.187138i	−0.976845	+	0.213949i	$0.931367\pi$
$98$	−2.64562			−0.267248
$99$		0			0
$100$	−1.12852			−0.112852
$101$	1.62288	+	4.99472i	0.161483	+	0.496993i	0.998760	−	0.0497857i	$-0.0158538\pi$
$101$	1.62288	+	4.99472i	0.161483	+	0.496993i	−0.837277	+	0.546779i	$0.815854\pi$
$102$		0			0
$103$	11.0032	−	7.99426i	1.08417	−	0.787698i	0.105768	−	0.994391i	$-0.466270\pi$
$103$	11.0032	−	7.99426i	1.08417	−	0.787698i	0.978406	+	0.206693i	$0.0662700\pi$
$104$	1.30722	−	4.02321i	0.128184	−	0.394508i
$105$		0			0
$106$	5.44980	−	3.95951i	0.529331	−	0.384582i
$107$	−8.08259	−	5.87235i	−0.781374	−	0.567701i	0.124017	−	0.992280i	$-0.460422\pi$
$107$	−8.08259	−	5.87235i	−0.781374	−	0.567701i	−0.905391	+	0.424579i	$0.860422\pi$
$108$		0			0
$109$	−6.75183			−0.646708			−0.323354	−	0.946278i	$-0.604811\pi$
$109$	−6.75183			−0.646708			−0.323354	+	0.946278i	$0.604811\pi$
$110$	−1.72959	−	2.56804i	−0.164910	−	0.244853i
$111$		0			0
$112$	0.296067	+	0.911202i	0.0279757	+	0.0861005i
$113$	−4.24298	−	3.08270i	−0.399146	−	0.289996i	0.370047	−	0.929013i	$-0.379342\pi$
$113$	−4.24298	−	3.08270i	−0.399146	−	0.289996i	−0.769193	+	0.639017i	$0.779342\pi$
$114$		0			0
$115$	1.45407	−	4.47517i	0.135593	−	0.417312i
$116$	0.710837	−	2.18773i	0.0659996	−	0.203126i
$117$		0			0
$118$	−6.28627	−	4.56724i	−0.578698	−	0.420449i
$119$	0.546881	+	1.68313i	0.0501325	+	0.154292i
$120$		0			0
$121$	−4.13473	+	10.1933i	−0.375885	+	0.926666i
$122$	−8.18476			−0.741013
$123$		0			0
$124$	9.69014	+	7.04030i	0.870200	+	0.632237i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−6.38897	+	19.6632i	−0.566929	+	1.74483i	0.0952195	+	0.995456i	$0.469645\pi$
$127$	−6.38897	+	19.6632i	−0.566929	+	1.74483i	−0.662149	+	0.749372i	$0.730355\pi$
$128$	4.22380	−	3.06877i	0.373335	−	0.271244i
$129$		0			0
$130$	−0.417840	−	1.28598i	−0.0366470	−	0.112788i
$131$	−20.3089			−1.77439			−0.887197	−	0.461392i	$-0.847350\pi$
$131$	−20.3089			−1.77439			−0.887197	+	0.461392i	$0.847350\pi$
$132$		0			0
$133$	−6.38556			−0.553698
$134$	−0.910618	−	2.80259i	−0.0786654	−	0.242107i
$135$		0			0
$136$	−2.04869	+	1.48846i	−0.175674	+	0.127634i
$137$	1.07532	−	3.30950i	0.0918710	−	0.282750i	−0.894555	−	0.446959i	$-0.852507\pi$
$137$	1.07532	−	3.30950i	0.0918710	−	0.282750i	0.986426	+	0.164209i	$0.0525071\pi$
$138$		0			0
$139$	−2.20931	+	1.60516i	−0.187392	+	0.136148i	−0.677526	−	0.735499i	$-0.736948\pi$
$139$	−2.20931	+	1.60516i	−0.187392	+	0.136148i	0.490134	+	0.871647i	$0.336948\pi$
$140$	−1.86349	−	1.35390i	−0.157494	−	0.114426i
$141$		0			0
$142$	−12.0152			−1.00829
$143$	−2.96019	+	3.78350i	−0.247544	+	0.316392i
$144$		0			0
$145$	−0.629885	−	1.93859i	−0.0523091	−	0.160991i
$146$	11.1160	+	8.07624i	0.919966	+	0.668394i
$147$		0			0
$148$	−1.44955	+	4.46126i	−0.119152	+	0.366713i
$149$	2.81465	−	8.66261i	0.230585	−	0.709669i	−0.767091	−	0.641538i	$-0.778297\pi$
$149$	2.81465	−	8.66261i	0.230585	−	0.709669i	0.997676	−	0.0681306i	$-0.0217035\pi$
$150$		0			0
$151$	−17.4541	−	12.6811i	−1.42039	−	1.03198i	−0.991706	−	0.128523i	$-0.958976\pi$
$151$	−17.4541	−	12.6811i	−1.42039	−	1.03198i	−0.428687	−	0.903453i	$-0.641024\pi$
$152$	−2.82351	−	8.68986i	−0.229017	−	0.704841i
$153$		0			0
$154$	0.224903	−	6.31553i	0.0181232	−	0.508920i
$155$	10.6136			0.852506
$156$		0			0
$157$	19.2497	+	13.9857i	1.53629	+	1.11618i	0.952607	+	0.304205i	$0.0983909\pi$
$157$	19.2497	+	13.9857i	1.53629	+	1.11618i	0.583688	+	0.811978i	$0.301609\pi$
$158$	12.8385	−	9.32772i	1.02138	−	0.742073i
$159$		0			0
$160$	1.66960	−	5.13850i	0.131993	−	0.406234i
$161$	7.77000	−	5.64523i	0.612362	−	0.444907i
$162$		0			0
$163$	−0.557258	−	1.71506i	−0.0436478	−	0.134334i	0.926858	−	0.375412i	$-0.122499\pi$
$163$	−0.557258	−	1.71506i	−0.0436478	−	0.134334i	−0.970506	+	0.241078i	$0.922499\pi$
$164$	−0.908472			−0.0709397
$165$		0			0
$166$	−5.73326			−0.444988
$167$	7.59792	+	23.3840i	0.587945	+	1.80951i	0.587107	+	0.809509i	$0.300267\pi$
$167$	7.59792	+	23.3840i	0.587945	+	1.80951i	0.000837897		1.00000i	$0.499733\pi$
$168$		0			0
$169$	8.81993	−	6.40806i	0.678456	−	0.492927i
$170$	−0.250128	+	0.769814i	−0.0191839	+	0.0590420i
$171$		0			0
$172$	−2.13721	+	1.55277i	−0.162961	+	0.118398i
$173$	−13.1154	−	9.52890i	−0.997146	−	0.724469i	−0.0356719	−	0.999364i	$-0.511357\pi$
$173$	−13.1154	−	9.52890i	−0.997146	−	0.724469i	−0.961474	+	0.274894i	$0.911357\pi$
$174$		0			0
$175$	−2.04108			−0.154291
$176$	1.49683	−	0.428092i	0.112828	−	0.0322686i
$177$		0			0
$178$	−1.08812	−	3.34888i	−0.0815579	−	0.251010i
$179$	13.7287	+	9.97452i	1.02613	+	0.745530i	0.967531	−	0.252751i	$-0.0813353\pi$
$179$	13.7287	+	9.97452i	1.02613	+	0.745530i	0.0586031	+	0.998281i	$0.481335\pi$
$180$		0			0
$181$	5.67071	−	17.4526i	0.421500	−	1.29725i	−0.484805	−	0.874622i	$-0.661109\pi$
$181$	5.67071	−	17.4526i	0.421500	−	1.29725i	0.906306	−	0.422623i	$-0.138891\pi$
$182$	0.852845	−	2.62479i	0.0632171	−	0.194562i
$183$		0			0
$184$	11.1181	+	8.07774i	0.819634	+	0.595499i
$185$	1.28447	+	3.95320i	0.0944363	+	0.290645i
$186$		0			0
$187$	2.76487	−	0.790750i	0.202187	−	0.0578254i
$188$	11.7143			0.854356
$189$		0			0
$190$	−2.36279	−	1.71667i	−0.171415	−	0.124540i
$191$	−12.4577	+	9.05102i	−0.901405	+	0.654909i	−0.938826	−	0.344391i	$-0.888086\pi$
$191$	−12.4577	+	9.05102i	−0.901405	+	0.654909i	0.0374216	+	0.999300i	$0.488086\pi$
$192$		0			0
$193$	−2.28037	+	7.01824i	−0.164144	+	0.505184i	−0.998972	−	0.0453268i	$-0.985567\pi$
$193$	−2.28037	+	7.01824i	−0.164144	+	0.505184i	0.834828	+	0.550511i	$0.185567\pi$
$194$	1.46362	−	1.06338i	0.105082	−	0.0763465i
$195$		0			0
$196$	0.988303	+	3.04168i	0.0705931	+	0.217263i
$197$	−3.14676			−0.224197			−0.112099	−	0.993697i	$-0.535757\pi$
$197$	−3.14676			−0.224197			−0.112099	+	0.993697i	$0.535757\pi$
$198$		0			0
$199$	−3.25757			−0.230923			−0.115462	−	0.993312i	$-0.536835\pi$
$199$	−3.25757			−0.230923			−0.115462	+	0.993312i	$0.536835\pi$
$200$	−0.902506	−	2.77763i	−0.0638168	−	0.196408i
$201$		0			0
$202$	−3.96635	+	2.88172i	−0.279072	+	0.202757i
$203$	1.28564	−	3.95681i	0.0902346	−	0.277713i
$204$		0			0
$205$	−0.651268	+	0.473174i	−0.0454866	+	0.0330479i
$206$	10.2718	+	7.46290i	0.715670	+	0.519965i
$207$		0			0
$208$	0.679903			0.0471428
$209$	−0.369272	+	10.3696i	−0.0255431	+	0.717277i
$210$		0			0
$211$	6.15690	+	18.9490i	0.423859	+	1.30450i	0.904083	+	0.427357i	$0.140555\pi$
$211$	6.15690	+	18.9490i	0.423859	+	1.30450i	−0.480224	+	0.877146i	$0.659445\pi$
$212$	−6.58811	−	4.78654i	−0.452473	−	0.328741i
$213$		0			0
$214$	2.88207	−	8.87009i	0.197014	−	0.606347i
$215$	−0.723374	+	2.22631i	−0.0493337	+	0.151833i
$216$		0			0
$217$	17.5259	+	12.7333i	1.18974	+	0.864395i
$218$	−1.94775	−	5.99455i	−0.131918	−	0.406002i
$219$		0			0
$220$	−2.30638	+	2.94784i	−0.155496	+	0.198743i
$221$	1.25588			0.0844799
$222$		0			0
$223$	−8.47862	−	6.16008i	−0.567770	−	0.412509i	0.266524	−	0.963828i	$-0.414125\pi$
$223$	−8.47862	−	6.16008i	−0.567770	−	0.412509i	−0.834295	+	0.551319i	$0.814125\pi$
$224$	8.92170	−	6.48199i	0.596106	−	0.433096i
$225$		0			0
$226$	1.51295	−	4.65638i	0.100640	−	0.309738i
$227$	14.2979	−	10.3880i	0.948982	−	0.689476i	−0.00158404	−	0.999999i	$-0.500504\pi$
$227$	14.2979	−	10.3880i	0.948982	−	0.689476i	0.950566	+	0.310523i	$0.100504\pi$
$228$		0			0
$229$	1.27614	+	3.92755i	0.0843297	+	0.259540i	0.984326	−	0.176357i	$-0.0564312\pi$
$229$	1.27614	+	3.92755i	0.0843297	+	0.259540i	−0.899997	+	0.435897i	$0.856431\pi$
$230$	4.39271			0.289646
$231$		0			0
$232$	5.95314			0.390843
$233$	−4.20231	−	12.9334i	−0.275303	−	0.847294i	−0.989139	−	0.146982i	$-0.953044\pi$
$233$	−4.20231	−	12.9334i	−0.275303	−	0.847294i	0.713837	−	0.700312i	$-0.246956\pi$
$234$		0			0
$235$	8.39782	−	6.10137i	0.547813	−	0.398010i
$236$	−2.90267	+	8.93350i	−0.188948	+	0.581521i
$237$		0			0
$238$	−1.33659	+	0.971087i	−0.0866380	+	0.0629462i
$239$	6.47725	+	4.70600i	0.418979	+	0.304406i	0.777227	−	0.629221i	$-0.216626\pi$
$239$	6.47725	+	4.70600i	0.418979	+	0.304406i	−0.358248	+	0.933626i	$0.616626\pi$
$240$		0			0
$241$	−0.501943			−0.0323330			−0.0161665	−	0.999869i	$-0.505146\pi$
$241$	−0.501943			−0.0323330			−0.0161665	+	0.999869i	$0.505146\pi$
$242$	−10.2428	−	0.730444i	−0.658434	−	0.0469547i
$243$		0			0
$244$	3.05751	+	9.41006i	0.195737	+	0.602417i
$245$	2.29275	+	1.66578i	0.146478	+	0.106423i
$246$		0			0
$247$	−1.40030	+	4.30967i	−0.0890988	+	0.274218i
$248$	−9.57885	+	29.4807i	−0.608258	+	1.87202i
$249$		0			0
$250$	−0.755243	−	0.548716i	−0.0477657	−	0.0347038i
$251$	5.72933	+	17.6331i	0.361632	+	1.11299i	0.952063	+	0.305901i	$0.0989578\pi$
$251$	5.72933	+	17.6331i	0.361632	+	1.11299i	−0.590431	+	0.807088i	$0.701042\pi$
$252$		0			0
$253$	−8.71800	−	12.9442i	−0.548096	−	0.813796i
$254$	−19.3009			−1.21105
$255$		0			0
$256$	13.6231	+	9.89779i	0.851446	+	0.618612i
$257$	5.97062	−	4.33791i	0.372437	−	0.270592i	−0.385784	−	0.922589i	$-0.626069\pi$
$257$	5.97062	−	4.33791i	0.372437	−	0.270592i	0.758221	+	0.651998i	$0.226069\pi$
$258$		0			0
$259$	−2.62171	+	8.06879i	−0.162905	+	0.501370i
$260$	−1.32241	+	0.960786i	−0.0820123	+	0.0595854i
$261$		0			0
$262$	−5.85864	−	18.0310i	−0.361948	−	1.11396i
$263$	3.05950			0.188657			0.0943285	−	0.995541i	$-0.469930\pi$
$263$	3.05950			0.188657			0.0943285	+	0.995541i	$0.469930\pi$
$264$		0			0
$265$	−7.21596			−0.443273
$266$	−1.84209	−	5.66936i	−0.112946	−	0.347611i
$267$		0			0
$268$	−2.88198	+	2.09388i	−0.176045	+	0.127904i
$269$	5.46345	−	16.8148i	0.333112	−	1.02521i	−0.634532	−	0.772896i	$-0.718807\pi$
$269$	5.46345	−	16.8148i	0.333112	−	1.02521i	0.967644	−	0.252318i	$-0.0811928\pi$
$270$		0			0
$271$	12.3773	−	8.99262i	0.751866	−	0.546263i	−0.144538	−	0.989499i	$-0.546170\pi$
$271$	12.3773	−	8.99262i	0.751866	−	0.546263i	0.896405	+	0.443236i	$0.146170\pi$
$272$	−0.329273	−	0.239231i	−0.0199651	−	0.0145055i
$273$		0			0
$274$	3.24852			0.196250
$275$	−0.118034	+	3.31452i	−0.00711772	+	0.199873i
$276$		0			0
$277$	−5.50785	−	16.9514i	−0.330934	−	1.01851i	−0.968690	−	0.248273i	$-0.920137\pi$
$277$	−5.50785	−	16.9514i	−0.330934	−	1.01851i	0.637756	−	0.770239i	$-0.279863\pi$
$278$	−2.06246	−	1.49847i	−0.123698	−	0.0898721i
$279$		0			0
$280$	1.84209	−	5.66936i	0.110086	−	0.338809i
$281$	5.34568	−	16.4523i	0.318896	−	0.981462i	−0.655224	−	0.755434i	$-0.727426\pi$
$281$	5.34568	−	16.4523i	0.318896	−	0.981462i	0.974121	−	0.226028i	$-0.0725741\pi$
$282$		0			0
$283$	20.8535	+	15.1510i	1.23961	+	0.900633i	0.997573	−	0.0696333i	$-0.0221829\pi$
$283$	20.8535	+	15.1510i	1.23961	+	0.900633i	0.242042	+	0.970266i	$0.422183\pi$
$284$	4.48840	+	13.8139i	0.266338	+	0.819704i
$285$		0			0
$286$	−4.21309	−	1.53673i	−0.249125	−	0.0908688i
$287$	−1.64309			−0.0969888
$288$		0			0
$289$	13.1451	+	9.55045i	0.773240	+	0.561791i
$290$	1.53945	−	1.11847i	0.0903995	−	0.0656791i
$291$		0			0
$292$	5.13278	−	15.7971i	0.300373	−	0.924454i
$293$	10.9465	−	7.95310i	0.639502	−	0.464625i	−0.220177	−	0.975460i	$-0.570664\pi$
$293$	10.9465	−	7.95310i	0.639502	−	0.464625i	0.859679	+	0.510835i	$0.170664\pi$
$294$		0			0
$295$	2.57211	+	7.91613i	0.149754	+	0.460895i
$296$	−12.1398			−0.705609
$297$		0			0
$298$	8.50299			0.492565
$299$	−2.10613	−	6.48199i	−0.121800	−	0.374863i
$300$		0			0
$301$	−3.86543	+	2.80840i	−0.222800	+	0.161873i
$302$	6.22373	−	19.1547i	0.358135	−	1.10223i
$303$		0			0
$304$	1.18808	−	0.863188i	0.0681409	−	0.0495073i
$305$	7.09308	+	5.15342i	0.406148	+	0.295084i
$306$		0			0
$307$	−13.0268			−0.743478			−0.371739	−	0.928337i	$-0.621238\pi$
$307$	−13.0268			−0.743478			−0.371739	+	0.928337i	$0.621238\pi$
$308$	−7.34502	+	2.10067i	−0.418521	+	0.119697i
$309$		0			0
$310$	3.06178	+	9.42320i	0.173898	+	0.535202i
$311$	1.53971	+	1.11867i	0.0873092	+	0.0634339i	0.630584	−	0.776121i	$-0.282816\pi$
$311$	1.53971	+	1.11867i	0.0873092	+	0.0634339i	−0.543274	+	0.839555i	$0.682816\pi$
$312$		0			0
$313$	3.37829	−	10.3973i	0.190952	−	0.587691i	−0.809048	−	0.587743i	$-0.800017\pi$
$313$	3.37829	−	10.3973i	0.190952	−	0.587691i	1.00000		5.23383e-5i	$1.66598e-5\pi$
$314$	−6.86401	+	21.1252i	−0.387358	+	1.19217i
$315$		0			0
$316$	−15.5201	−	11.2760i	−0.873074	−	0.634325i
$317$	4.96660	+	15.2856i	0.278952	+	0.858526i	0.988147	+	0.153513i	$0.0490588\pi$
$317$	4.96660	+	15.2856i	0.278952	+	0.858526i	−0.709194	+	0.705013i	$0.750941\pi$
$318$		0			0
$319$	−6.35114	−	2.31659i	−0.355596	−	0.129704i
$320$	5.98262			0.334439
$321$		0			0
$322$	7.25354	+	5.27000i	0.404224	+	0.293686i
$323$	2.19456	−	1.59444i	0.122108	−	0.0887170i
$324$		0			0
$325$	−0.447591	+	1.37754i	−0.0248279	+	0.0764124i
$326$	1.36195	−	0.989513i	0.0754313	−	0.0548040i
$327$		0			0
$328$	−0.726528	−	2.23602i	−0.0401158	−	0.123464i
$329$	21.1870			1.16808
$330$		0			0
$331$	1.39579			0.0767195			0.0383597	−	0.999264i	$-0.487787\pi$
$331$	1.39579			0.0767195			0.0383597	+	0.999264i	$0.487787\pi$
$332$	2.14173	+	6.59156i	0.117543	+	0.361759i
$333$		0			0
$334$	−18.5695	+	13.4915i	−1.01608	+	0.738222i
$335$	−0.975455	+	3.00214i	−0.0532948	+	0.164025i
$336$		0			0
$337$	2.23564	−	1.62429i	0.121783	−	0.0884805i	−0.525227	−	0.850962i	$-0.676019\pi$
$337$	2.23564	−	1.62429i	0.121783	−	0.0884805i	0.647009	+	0.762482i	$0.276019\pi$
$338$	8.23368	+	5.98212i	0.447853	+	0.325384i
$339$		0			0
$340$	0.978497			0.0530664
$341$	21.6913	−	27.7241i	1.17465	−	1.50135i
$342$		0			0
$343$	6.20258	+	19.0896i	0.334908	+	1.03074i
$344$	−5.53103	−	4.01853i	−0.298213	−	0.216664i
$345$		0			0
$346$	4.67666	−	14.3933i	0.251419	−	0.773787i
$347$	0.966244	−	2.97379i	0.0518707	−	0.159642i	−0.921766	−	0.387748i	$-0.873253\pi$
$347$	0.966244	−	2.97379i	0.0518707	−	0.159642i	0.973636	+	0.228106i	$0.0732532\pi$
$348$		0			0
$349$	−10.6205	−	7.71626i	−0.568504	−	0.413042i	0.266058	−	0.963957i	$-0.414279\pi$
$349$	−10.6205	−	7.71626i	−0.568504	−	0.413042i	−0.834561	+	0.550915i	$0.814279\pi$
$350$	−0.588805	−	1.81215i	−0.0314729	−	0.0968637i
$351$		0			0
$352$	−10.0102	−	14.8629i	−0.533546	−	0.792193i
$353$	−10.7984			−0.574739			−0.287370	−	0.957820i	$-0.592781\pi$
$353$	−10.7984			−0.574739			−0.287370	+	0.957820i	$0.592781\pi$
$354$		0			0
$355$	10.4126	+	7.56518i	0.552642	+	0.401518i
$356$	−3.44375	+	2.50203i	−0.182518	+	0.132607i
$357$		0			0
$358$	−4.89536	+	15.0664i	−0.258728	+	0.796282i
$359$	19.3934	−	14.0901i	1.02354	−	0.743649i	0.0565382	−	0.998400i	$-0.481994\pi$
$359$	19.3934	−	14.0901i	1.02354	−	0.743649i	0.967007	+	0.254752i	$0.0819937\pi$
$360$		0			0
$361$	−2.84678	−	8.76148i	−0.149830	−	0.461131i
$362$	17.1310			0.900388
$363$		0			0
$364$	−3.33632			−0.174871
$365$	−4.54825	−	13.9981i	−0.238066	−	0.732692i
$366$		0			0
$367$	−7.17831	+	5.21534i	−0.374705	+	0.272239i	−0.759159	−	0.650905i	$-0.774390\pi$
$367$	−7.17831	+	5.21534i	−0.374705	+	0.272239i	0.384455	+	0.923144i	$0.374390\pi$
$368$	−0.682549	+	2.10067i	−0.0355803	+	0.109505i
$369$		0			0
$370$	−3.13927	+	2.28081i	−0.163203	+	0.118574i
$371$	−11.9155	−	8.65711i	−0.618621	−	0.449455i
$372$		0			0
$373$	−26.3389			−1.36378			−0.681888	−	0.731456i	$-0.738841\pi$
$373$	−26.3389			−1.36378			−0.681888	+	0.731456i	$0.738841\pi$
$374$	1.49966	+	2.22665i	0.0775456	+	0.115137i
$375$		0			0
$376$	9.36826	+	28.8325i	0.483131	+	1.48693i
$377$	−2.38855	−	1.73539i	−0.123017	−	0.0893770i
$378$		0			0
$379$	1.45118	−	4.46626i	0.0745419	−	0.229416i	−0.906843	−	0.421469i	$-0.861515\pi$
$379$	1.45118	−	4.46626i	0.0745419	−	0.229416i	0.981385	+	0.192053i	$0.0615145\pi$
$380$	−1.09101	+	3.35779i	−0.0559678	+	0.172251i
$381$		0			0
$382$	−11.6296	−	8.44941i	−0.595023	−	0.432310i
$383$	2.13200	+	6.56163i	0.108940	+	0.335284i	0.990635	−	0.136537i	$-0.0435971\pi$
$383$	2.13200	+	6.56163i	0.108940	+	0.335284i	−0.881695	+	0.471820i	$0.843597\pi$
$384$		0			0
$385$	−4.17140	+	5.33156i	−0.212594	+	0.271722i
$386$	−6.88892			−0.350637
$387$		0			0
$388$	−1.76933	−	1.28549i	−0.0898242	−	0.0652611i
$389$	1.94538	−	1.41340i	0.0986348	−	0.0716624i	−0.537375	−	0.843344i	$-0.680584\pi$
$389$	1.94538	−	1.41340i	0.0986348	−	0.0716624i	0.636009	+	0.771681i	$0.280584\pi$
$390$		0			0
$391$	−1.26077	+	3.88025i	−0.0637599	+	0.196233i
$392$	−6.69613	+	4.86503i	−0.338206	+	0.245721i
$393$		0			0
$394$	−0.907768	−	2.79382i	−0.0457327	−	0.140751i
$395$	−16.9992			−0.855321
$396$		0			0
$397$	37.6715			1.89068			0.945338	−	0.326091i	$-0.105732\pi$
$397$	37.6715			1.89068			0.945338	+	0.326091i	$0.105732\pi$
$398$	−0.939734	−	2.89221i	−0.0471046	−	0.144973i
$399$		0			0
$400$	0.379757	−	0.275910i	0.0189878	−	0.0137955i
$401$	3.86791	−	11.9042i	0.193154	−	0.594467i	−0.806839	−	0.590771i	$-0.798824\pi$
$401$	3.86791	−	11.9042i	0.193154	−	0.594467i	0.999993	−	0.00369578i	$-0.00117641\pi$
$402$		0			0
$403$	12.4371	−	9.03610i	0.619537	−	0.450120i
$404$	4.79481	+	3.48363i	0.238551	+	0.173317i
$405$		0			0
$406$	3.88390			0.192754
$407$	12.9514	+	4.72402i	0.641975	+	0.234161i
$408$		0			0
$409$	−8.17728	−	25.1671i	−0.404340	−	1.24443i	−0.921445	−	0.388510i	$-0.872990\pi$
$409$	−8.17728	−	25.1671i	−0.404340	−	1.24443i	0.517104	−	0.855922i	$-0.327010\pi$
$410$	−0.607979	−	0.441723i	−0.0300260	−	0.0218151i
$411$		0			0
$412$	4.74298	−	14.5974i	0.233670	−	0.719162i
$413$	−5.24987	+	16.1574i	−0.258329	+	0.795056i
$414$		0			0
$415$	4.96856	+	3.60987i	0.243897	+	0.177202i
$416$	−2.41831	−	7.44278i	−0.118567	−	0.364912i
$417$		0			0
$418$	−9.31304	+	2.66352i	−0.455516	+	0.130277i
$419$	−30.9711			−1.51304			−0.756518	−	0.653973i	$-0.773101\pi$
$419$	−30.9711			−1.51304			−0.756518	+	0.653973i	$0.773101\pi$
$420$		0			0
$421$	−14.7593	−	10.7232i	−0.719323	−	0.522618i	0.166845	−	0.985983i	$-0.446642\pi$
$421$	−14.7593	−	10.7232i	−0.719323	−	0.522618i	−0.886168	+	0.463365i	$0.846642\pi$
$422$	−15.0476	+	10.9327i	−0.732505	+	0.532196i
$423$		0			0
$424$	6.51245	−	20.0432i	0.316272	−	0.973386i
$425$	0.701468	−	0.509647i	0.0340262	−	0.0247215i
$426$		0			0
$427$	5.52993	+	17.0194i	0.267612	+	0.823625i
$428$	−11.2746			−0.544979
$429$		0			0
$430$	−2.18529			−0.105384
$431$	−9.37829	−	28.8634i	−0.451736	−	1.39030i	−0.874924	−	0.484260i	$-0.839089\pi$
$431$	−9.37829	−	28.8634i	−0.451736	−	1.39030i	0.423188	−	0.906042i	$-0.360911\pi$
$432$		0			0
$433$	−10.2755	+	7.46560i	−0.493810	+	0.358774i	−0.806648	−	0.591033i	$-0.798720\pi$
$433$	−10.2755	+	7.46560i	−0.493810	+	0.358774i	0.312838	+	0.949807i	$0.398720\pi$
$434$	−6.24935	+	19.2335i	−0.299978	+	0.923238i
$435$		0			0
$436$	−6.16436	+	4.47867i	−0.295220	+	0.214490i
$437$	−11.9097	−	8.65288i	−0.569717	−	0.413924i
$438$		0			0
$439$	−25.6564			−1.22451			−0.612257	−	0.790659i	$-0.709738\pi$
$439$	−25.6564			−1.22451			−0.612257	+	0.790659i	$0.709738\pi$
$440$	−9.09999	−	3.31923i	−0.433825	−	0.158238i
$441$		0			0
$442$	0.362294	+	1.11502i	0.0172325	+	0.0530363i
$443$	−21.2082	−	15.4087i	−1.00763	−	0.732088i	−0.0439211	−	0.999035i	$-0.513985\pi$
$443$	−21.2082	−	15.4087i	−1.00763	−	0.732088i	−0.963711	+	0.266947i	$0.913985\pi$
$444$		0			0
$445$	−1.16559	+	3.58733i	−0.0552545	+	0.170056i
$446$	3.02328	−	9.30470i	0.143157	−	0.440590i
$447$		0			0
$448$	9.87891	+	7.17745i	0.466735	+	0.339103i
$449$	3.71010	+	11.4185i	0.175091	+	0.538873i	0.999638	−	0.0269202i	$-0.00856999\pi$
$449$	3.71010	+	11.4185i	0.175091	+	0.538873i	−0.824547	+	0.565793i	$0.808570\pi$
$450$		0			0
$451$	−0.0950188	+	2.66823i	−0.00447426	+	0.125642i
$452$	−5.91864			−0.278390
$453$		0			0
$454$	13.3475	+	9.69752i	0.626429	+	0.455127i
$455$	−2.39175	+	1.73771i	−0.112127	+	0.0814652i
$456$		0			0
$457$	4.26104	−	13.1141i	0.199323	−	0.613453i	−0.800576	−	0.599231i	$-0.795473\pi$
$457$	4.26104	−	13.1141i	0.199323	−	0.613453i	0.999899	−	0.0142215i	$-0.00452701\pi$
$458$	−3.11891	+	2.26602i	−0.145737	+	0.105884i
$459$		0			0
$460$	−1.64095	−	5.05032i	−0.0765096	−	0.235472i
$461$	−11.3262			−0.527515			−0.263758	−	0.964589i	$-0.584962\pi$
$461$	−11.3262			−0.527515			−0.263758	+	0.964589i	$0.584962\pi$
$462$		0			0
$463$	6.18784			0.287573			0.143787	−	0.989609i	$-0.454072\pi$
$463$	6.18784			0.287573			0.143787	+	0.989609i	$0.454072\pi$
$464$	0.295671	+	0.909983i	0.0137262	+	0.0422449i
$465$		0			0
$466$	10.2705	−	7.46197i	0.475773	−	0.345669i
$467$	−2.62135	+	8.06770i	−0.121302	+	0.373328i	−0.993209	−	0.116342i	$-0.962883\pi$
$467$	−2.62135	+	8.06770i	−0.121302	+	0.373328i	0.871907	+	0.489671i	$0.162883\pi$
$468$		0			0
$469$	−5.21246	+	3.78707i	−0.240689	+	0.174871i
$470$	7.83963	+	5.69582i	0.361615	+	0.262729i
$471$		0			0
$472$	−24.3094			−1.11893
$473$	4.33705	+	6.43951i	0.199418	+	0.296089i
$474$		0			0
$475$	0.966766	+	2.97540i	0.0443582	+	0.136521i
$476$	1.61576	+	1.17392i	0.0740583	+	0.0538065i
$477$		0			0
$478$	−2.30964	+	7.10834i	−0.105640	+	0.325128i
$479$	−2.85394	+	8.78352i	−0.130400	+	0.401329i	−0.994846	−	0.101396i	$-0.967669\pi$
$479$	−2.85394	+	8.78352i	−0.130400	+	0.401329i	0.864446	+	0.502725i	$0.167669\pi$
$480$		0			0
$481$	4.87078	+	3.53883i	0.222089	+	0.161357i
$482$	−0.144799	−	0.445645i	−0.00659541	−	0.0202986i
$483$		0			0
$484$	2.98654	+	12.0491i	0.135752	+	0.547686i
$485$	−1.93795			−0.0879977
$486$		0			0
$487$	−16.3185	−	11.8561i	−0.739461	−	0.537250i	0.153081	−	0.988214i	$-0.451080\pi$
$487$	−16.3185	−	11.8561i	−0.739461	−	0.537250i	−0.892542	+	0.450964i	$0.851080\pi$
$488$	−20.7158	+	15.0509i	−0.937762	+	0.681324i
$489$		0			0
$490$	−0.817542	+	2.51613i	−0.0369328	+	0.113667i
$491$	−4.31686	+	3.13638i	−0.194817	+	0.141543i	−0.680918	−	0.732360i	$-0.738419\pi$
$491$	−4.31686	+	3.13638i	−0.194817	+	0.141543i	0.486100	+	0.873903i	$0.338419\pi$
$492$		0			0
$493$	0.546149	+	1.68087i	0.0245973	+	0.0757028i
$494$	−4.23026			−0.190328
$495$		0			0
$496$	−4.98209			−0.223702
$497$	8.11789	+	24.9843i	0.364137	+	1.12070i
$498$		0			0
$499$	31.7795	−	23.0891i	1.42265	−	1.03361i	0.431317	−	0.902200i	$-0.358049\pi$
$499$	31.7795	−	23.0891i	1.42265	−	1.03361i	0.991328	−	0.131412i	$-0.0419510\pi$
$500$	−0.348732	+	1.07329i	−0.0155958	+	0.0479988i
$501$		0			0
$502$	−14.0026	+	10.1735i	−0.624966	+	0.454064i
$503$	26.2268	+	19.0549i	1.16940	+	0.849616i	0.990936	−	0.134331i	$-0.0428886\pi$
$503$	26.2268	+	19.0549i	1.16940	+	0.849616i	0.178460	+	0.983947i	$0.442889\pi$
$504$		0			0
$505$	5.25176			0.233700
$506$	8.97746	−	11.4743i	0.399097	−	0.510095i
$507$		0			0
$508$	7.21007	+	22.1903i	0.319895	+	0.984536i
$509$	−13.8064	−	10.0309i	−0.611958	−	0.444613i	0.238145	−	0.971229i	$-0.423461\pi$
$509$	−13.8064	−	10.0309i	−0.611958	−	0.444613i	−0.850103	+	0.526616i	$0.823461\pi$
$510$		0			0
$511$	9.28333	−	28.5712i	0.410671	−	1.26391i
$512$	−1.63100	+	5.01971i	−0.0720808	+	0.221842i
$513$		0			0
$514$	5.57376	+	4.04958i	0.245848	+	0.178619i
$515$	−4.20283	−	12.9350i	−0.185199	−	0.569984i
$516$		0			0
$517$	1.22523	−	34.4057i	0.0538854	−	1.51316i
$518$	−7.92011			−0.347990
$519$		0			0
$520$	−3.42235	−	2.48648i	−0.150080	−	0.109039i
$521$	−12.1733	+	8.84445i	−0.533324	+	0.387482i	−0.821600	−	0.570065i	$-0.806918\pi$
$521$	−12.1733	+	8.84445i	−0.533324	+	0.387482i	0.288276	+	0.957547i	$0.406918\pi$
$522$		0			0
$523$	−11.4465	+	35.2287i	−0.500520	+	1.54044i	0.307653	+	0.951499i	$0.400456\pi$
$523$	−11.4465	+	35.2287i	−0.500520	+	1.54044i	−0.808173	+	0.588945i	$0.799544\pi$
$524$	−18.5418	+	13.4714i	−0.810003	+	0.588502i
$525$		0			0
$526$	0.882596	+	2.71635i	0.0384830	+	0.118439i
$527$	−9.20267			−0.400875
$528$		0			0
$529$	−0.858520			−0.0373270
$530$	−2.08164	−	6.40662i	−0.0904206	−	0.278286i
$531$		0			0
$532$	−5.82996	+	4.23571i	−0.252761	+	0.183641i
$533$	−0.360316	+	1.10894i	−0.0156070	+	0.0480335i
$534$		0			0
$535$	−8.08259	+	5.87235i	−0.349441	+	0.253884i
$536$	−7.45848	−	5.41890i	−0.322157	−	0.234061i
$537$		0			0
$538$	16.5049			0.711577
$539$	9.03696	−	2.58457i	0.389250	−	0.111325i
$540$		0			0
$541$	0.0547265	+	0.168431i	0.00235288	+	0.00724141i	0.952226	−	0.305394i	$-0.0987882\pi$
$541$	0.0547265	+	0.168431i	0.00235288	+	0.00724141i	−0.949873	+	0.312635i	$0.898788\pi$
$542$	11.5546	+	8.39489i	0.496312	+	0.360592i
$543$		0			0
$544$	−1.44765	+	4.45540i	−0.0620674	+	0.191024i
$545$	−2.08643	+	6.42137i	−0.0893729	+	0.275061i
$546$		0			0
$547$	−0.981092	−	0.712805i	−0.0419484	−	0.0304773i	0.566613	−	0.823984i	$-0.308253\pi$
$547$	−0.981092	−	0.712805i	−0.0419484	−	0.0304773i	−0.608562	+	0.793506i	$0.708253\pi$
$548$	−1.21352	−	3.73484i	−0.0518391	−	0.159544i
$549$		0			0
$550$	−2.97682	+	0.851369i	−0.126932	+	0.0363025i
$551$	−6.37702			−0.271670
$552$		0			0
$553$	−28.0702	−	20.3942i	−1.19367	−	0.867249i
$554$	13.4613	−	9.78018i	0.571914	−	0.415520i
$555$		0			0
$556$	−0.952338	+	2.93100i	−0.0403881	+	0.124302i
$557$	1.56825	−	1.13940i	0.0664488	−	0.0482778i	−0.554065	−	0.832473i	$-0.686924\pi$
$557$	1.56825	−	1.13940i	0.0664488	−	0.0482778i	0.620514	+	0.784196i	$0.286924\pi$
$558$		0			0
$559$	1.04776	+	3.22467i	0.0443155	+	0.136389i
$560$	0.958094			0.0404869
$561$		0			0
$562$	16.1491			0.681210
$563$	6.48805	+	19.9682i	0.273439	+	0.841558i	0.989628	+	0.143652i	$0.0458845\pi$
$563$	6.48805	+	19.9682i	0.273439	+	0.841558i	−0.716190	+	0.697906i	$0.754115\pi$
$564$		0			0
$565$	−4.24298	+	3.08270i	−0.178503	+	0.129690i
$566$	−7.43590	+	22.8853i	−0.312554	+	0.961943i
$567$		0			0
$568$	−30.4107	+	22.0946i	−1.27600	+	0.927071i
$569$	−31.8556	−	23.1444i	−1.33546	−	0.970265i	−0.999598	−	0.0283521i	$-0.990974\pi$
$569$	−31.8556	−	23.1444i	−1.33546	−	0.970265i	−0.335857	−	0.941913i	$-0.609026\pi$
$570$		0			0
$571$	30.6796			1.28390			0.641950	−	0.766746i	$-0.278126\pi$
$571$	30.6796			1.28390			0.641950	+	0.766746i	$0.278126\pi$
$572$	−0.192937	+	5.41788i	−0.00806709	+	0.226533i
$573$		0			0
$574$	−0.473995	−	1.45881i	−0.0197842	−	0.0608894i
$575$	−3.80681	−	2.76581i	−0.158755	−	0.115342i
$576$		0			0
$577$	−10.7241	+	33.0053i	−0.446448	+	1.37403i	0.434439	+	0.900701i	$0.356947\pi$
$577$	−10.7241	+	33.0053i	−0.446448	+	1.37403i	−0.880887	+	0.473326i	$0.843053\pi$
$578$	−4.68723	+	14.4258i	−0.194963	+	0.600035i
$579$		0			0
$580$	−1.86100	−	1.35209i	−0.0772736	−	0.0561426i
$581$	3.87361	+	11.9217i	0.160704	+	0.494597i
$582$		0			0
$583$	−14.7474	+	18.8490i	−0.610775	+	0.780646i
$584$	42.9862			1.77878
$585$		0			0
$586$	10.2189	+	7.42447i	0.422139	+	0.306702i
$587$	6.51833	−	4.73584i	0.269040	−	0.195469i	−0.445083	−	0.895489i	$-0.646826\pi$
$587$	6.51833	−	4.73584i	0.269040	−	0.195469i	0.714123	+	0.700020i	$0.246826\pi$
$588$		0			0
$589$	10.2609	−	31.5797i	0.422792	−	1.30122i
$590$	−6.28627	+	4.56724i	−0.258802	+	0.188030i
$591$		0			0
$592$	−0.602938	−	1.85565i	−0.0247806	−	0.0762669i
$593$	28.1409			1.15561			0.577805	−	0.816175i	$-0.303909\pi$
$593$	28.1409			1.15561			0.577805	+	0.816175i	$0.303909\pi$
$594$		0			0
$595$	1.76974			0.0725524
$596$	−3.17639	−	9.77593i	−0.130110	−	0.400438i
$597$		0			0
$598$	5.14741	−	3.73981i	0.210493	−	0.152932i
$599$	8.83751	−	27.1991i	0.361091	−	1.11132i	−0.591302	−	0.806450i	$-0.701386\pi$
$599$	8.83751	−	27.1991i	0.361091	−	1.11132i	0.952393	−	0.304873i	$-0.0986141\pi$
$600$		0			0
$601$	5.88649	−	4.27679i	0.240115	−	0.174454i	−0.461219	−	0.887286i	$-0.652588\pi$
$601$	5.88649	−	4.27679i	0.240115	−	0.174454i	0.701335	+	0.712832i	$0.252588\pi$
$602$	−3.60850	−	2.62173i	−0.147072	−	0.106854i
$603$		0			0
$604$	−24.3472			−0.990672
$605$	8.41673	+	7.08228i	0.342189	+	0.287936i
$606$		0			0
$607$	−1.65258	−	5.08611i	−0.0670761	−	0.206439i	0.911901	−	0.410411i	$-0.134615\pi$
$607$	−1.65258	−	5.08611i	−0.0670761	−	0.206439i	−0.978977	+	0.203972i	$0.934615\pi$
$608$	−13.6750	−	9.93545i	−0.554593	−	0.402936i
$609$		0			0
$610$	−2.52923	+	7.78417i	−0.102406	+	0.315172i
$611$	4.64612	−	14.2993i	0.187962	−	0.578487i
$612$		0			0
$613$	3.75464	+	2.72790i	0.151648	+	0.110179i	0.661022	−	0.750366i	$-0.270123\pi$
$613$	3.75464	+	2.72790i	0.151648	+	0.110179i	−0.509374	+	0.860545i	$0.670123\pi$
$614$	−3.75793	−	11.5657i	−0.151658	−	0.466754i
$615$		0			0
$616$	−11.0444	−	16.3983i	−0.444991	−	0.660708i
$617$	−24.5843			−0.989727			−0.494864	−	0.868971i	$-0.664782\pi$
$617$	−24.5843			−0.989727			−0.494864	+	0.868971i	$0.664782\pi$
$618$		0			0
$619$	4.96566	+	3.60776i	0.199587	+	0.145008i	0.683090	−	0.730335i	$-0.260636\pi$
$619$	4.96566	+	3.60776i	0.199587	+	0.145008i	−0.483503	+	0.875343i	$0.660636\pi$
$620$	9.69014	−	7.04030i	0.389165	−	0.282745i
$621$		0			0
$622$	−0.549027	+	1.68973i	−0.0220140	+	0.0677521i
$623$	−6.22849	+	4.52526i	−0.249539	+	0.181301i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	10.2057			0.407902
$627$		0			0
$628$	26.8519			1.07151
$629$	−1.11372	−	3.42767i	−0.0444068	−	0.136670i
$630$		0			0
$631$	14.3265	−	10.4088i	0.570329	−	0.414368i	−0.264896	−	0.964277i	$-0.585338\pi$
$631$	14.3265	−	10.4088i	0.570329	−	0.414368i	0.835225	+	0.549909i	$0.185338\pi$
$632$	15.3419	−	47.2174i	0.610266	−	1.87821i
$633$		0			0
$634$	−12.1385	+	8.81910i	−0.482080	+	0.350251i
$635$	16.7265	+	12.1525i	0.663772	+	0.482259i
$636$		0			0
$637$	4.10485			0.162640
$638$	0.224603	−	6.30708i	0.00889210	−	0.249700i
$639$		0			0
$640$	−1.61335	−	4.96538i	−0.0637732	−	0.196274i
$641$	32.2492	+	23.4304i	1.27377	+	0.925444i	0.999346	−	0.0361657i	$-0.0115144\pi$
$641$	32.2492	+	23.4304i	1.27377	+	0.925444i	0.274419	+	0.961610i	$0.411514\pi$
$642$		0			0
$643$	−5.52097	+	16.9918i	−0.217726	+	0.670091i	0.781223	+	0.624252i	$0.214596\pi$
$643$	−5.52097	+	16.9918i	−0.217726	+	0.670091i	−0.998949	+	0.0458392i	$0.985404\pi$
$644$	3.34931	−	10.3081i	0.131981	−	0.406196i
$645$		0			0
$646$	2.04869	+	1.48846i	0.0806045	+	0.0585626i
$647$	−1.55768	−	4.79404i	−0.0612386	−	0.188473i	0.915757	−	0.401733i	$-0.131592\pi$
$647$	−1.55768	−	4.79404i	−0.0612386	−	0.188473i	−0.976996	+	0.213260i	$0.931592\pi$
$648$		0			0
$649$	25.9346	+	9.45968i	1.01802	+	0.371325i
$650$	−1.35216			−0.0530360
$651$		0			0
$652$	−1.64642	−	1.19619i	−0.0644788	−	0.0468466i
$653$	32.9441	−	23.9353i	1.28920	−	0.936661i	0.289414	−	0.957204i	$-0.406540\pi$
$653$	32.9441	−	23.9353i	1.28920	−	0.936661i	0.999789	+	0.0205434i	$0.00653963\pi$
$654$		0			0
$655$	−6.27578	+	19.3149i	−0.245215	+	0.754695i
$656$	0.305709	−	0.222111i	0.0119359	−	0.00867196i
$657$		0			0
$658$	6.11196	+	18.8107i	0.238269	+	0.733316i
$659$	−48.7556			−1.89925			−0.949624	−	0.313390i	$-0.898535\pi$
$659$	−48.7556			−1.89925			−0.949624	+	0.313390i	$0.898535\pi$
$660$		0			0
$661$	−41.0061			−1.59495			−0.797477	−	0.603350i	$-0.793832\pi$
$661$	−41.0061			−1.59495			−0.797477	+	0.603350i	$0.793832\pi$
$662$	0.402653	+	1.23924i	0.0156495	+	0.0481643i
$663$		0			0
$664$	−14.5110	+	10.5429i	−0.563137	+	0.409143i
$665$	−1.97325	+	6.07303i	−0.0765192	+	0.235502i
$666$		0			0
$667$	7.75960	−	5.63768i	0.300453	−	0.218292i
$668$	22.4481	+	16.3095i	0.868542	+	0.631033i
$669$		0			0
$670$	−2.94682			−0.113846
$671$	27.9577	−	7.99587i	1.07929	−	0.308677i
$672$		0			0
$673$	−9.42305	−	29.0012i	−0.363232	−	1.11791i	−0.951081	−	0.308942i	$-0.900025\pi$
$673$	−9.42305	−	29.0012i	−0.363232	−	1.11791i	0.587849	−	0.808971i	$-0.299975\pi$
$674$	2.08704	+	1.51632i	0.0803897	+	0.0584065i
$675$		0			0
$676$	3.80189	−	11.7010i	0.146226	−	0.450038i
$677$	13.4244	−	41.3161i	0.515943	−	1.58791i	−0.265617	−	0.964079i	$-0.585576\pi$
$677$	13.4244	−	41.3161i	0.515943	−	1.58791i	0.781560	−	0.623830i	$-0.214424\pi$
$678$		0			0
$679$	−3.20007	−	2.32499i	−0.122808	−	0.0892249i
$680$	0.782529	+	2.40838i	0.0300086	+	0.0923570i
$681$		0			0
$682$	30.8720	+	11.2606i	1.18215	+	0.431191i
$683$	43.5970			1.66819			0.834096	−	0.551619i	$-0.185990\pi$
$683$	43.5970			1.66819			0.834096	+	0.551619i	$0.185990\pi$
$684$		0			0
$685$	−2.81523	−	2.04539i	−0.107564	−	0.0781501i
$686$	−15.1592	+	11.0138i	−0.578781	+	0.420509i
$687$		0			0
$688$	0.339555	−	1.04504i	0.0129454	−	0.0398419i
$689$	−8.45572	+	6.14344i	−0.322137	+	0.234046i
$690$		0			0
$691$	−2.56761	−	7.90230i	−0.0976766	−	0.300618i	0.890265	−	0.455442i	$-0.150519\pi$
$691$	−2.56761	−	7.90230i	−0.0976766	−	0.300618i	−0.987942	+	0.154824i	$0.950519\pi$
$692$	−18.2950			−0.695473
$693$		0			0
$694$	2.91900			0.110804
$695$	0.843883	+	2.59720i	0.0320103	+	0.0985176i
$696$		0			0
$697$	0.564690	−	0.410272i	0.0213892	−	0.0155401i
$698$	3.78704	−	11.6553i	0.143342	−	0.441160i
$699$		0			0
$700$	−1.86349	+	1.35390i	−0.0704332	+	0.0511727i
$701$	7.35189	+	5.34146i	0.277677	+	0.201744i	0.717904	−	0.696143i	$-0.245102\pi$
$701$	7.35189	+	5.34146i	0.277677	+	0.201744i	−0.440226	+	0.897887i	$0.645102\pi$
$702$		0			0
$703$	13.0041			0.490460
$704$	12.2268	−	15.6274i	0.460815	−	0.588979i
$705$		0			0
$706$	−3.11508	−	9.58724i	−0.117238	−	0.360821i
$707$	8.67206	+	6.30062i	0.326147	+	0.236959i
$708$		0			0
$709$	−1.50049	+	4.61802i	−0.0563520	+	0.173434i	−0.975271	−	0.221013i	$-0.929064\pi$
$709$	−1.50049	+	4.61802i	−0.0563520	+	0.173434i	0.918919	+	0.394447i	$0.129064\pi$
$710$	−3.71289	+	11.4271i	−0.139342	+	0.428851i
$711$		0			0
$712$	−8.91231	−	6.47517i	−0.334003	−	0.242667i
$713$	15.4330	+	47.4977i	0.577969	+	1.77880i
$714$		0			0
$715$	2.68357	+	3.98448i	0.100360	+	0.149011i
$716$	19.1506			0.715691
$717$		0			0
$718$	18.1043	+	13.1536i	0.675648	+	0.490887i
$719$	19.3383	−	14.0501i	0.721196	−	0.523980i	−0.165570	−	0.986198i	$-0.552946\pi$
$719$	19.3383	−	14.0501i	0.721196	−	0.523980i	0.886766	+	0.462218i	$0.152946\pi$
$720$		0			0
$721$	8.57832	−	26.4014i	0.319473	−	0.983238i
$722$	6.95757	−	5.05497i	0.258934	−	0.188127i
$723$		0			0
$724$	−6.39951	−	19.6957i	−0.237836	−	0.731983i
$725$	−2.03835			−0.0757024
$726$		0			0
$727$	−11.3674			−0.421592			−0.210796	−	0.977530i	$-0.567606\pi$
$727$	−11.3674			−0.421592			−0.210796	+	0.977530i	$0.567606\pi$
$728$	−2.66814	−	8.21170i	−0.0988879	−	0.304346i
$729$		0			0
$730$	11.1160	−	8.07624i	0.411421	−	0.298915i
$731$	0.627210	−	1.93035i	0.0231982	−	0.0713967i
$732$		0			0
$733$	27.6019	−	20.0539i	1.01950	−	0.740709i	0.0533185	−	0.998578i	$-0.483020\pi$
$733$	27.6019	−	20.0539i	1.01950	−	0.740709i	0.966180	+	0.257869i	$0.0830202\pi$
$734$	−6.70117	−	4.86869i	−0.247345	−	0.179707i
$735$		0			0
$736$	25.4234			0.937118
$737$	5.84842	+	8.68355i	0.215429	+	0.319863i
$738$		0			0
$739$	0.722631	+	2.22403i	0.0265824	+	0.0818123i	0.963468	−	0.267825i	$-0.0863049\pi$
$739$	0.722631	+	2.22403i	0.0265824	+	0.0818123i	−0.936885	+	0.349637i	$0.886305\pi$
$740$	3.79498	+	2.75721i	0.139506	+	0.101357i
$741$		0			0
$742$	4.24879	−	13.0764i	0.155978	−	0.480051i
$743$	−4.47721	+	13.7794i	−0.164253	+	0.505518i	−0.998980	−	0.0451450i	$-0.985625\pi$
$743$	−4.47721	+	13.7794i	−0.164253	+	0.505518i	0.834728	+	0.550663i	$0.185625\pi$
$744$		0			0
$745$	−7.36886	−	5.35379i	−0.269974	−	0.196148i
$746$	−7.59817	−	23.3848i	−0.278189	−	0.856177i
$747$		0			0
$748$	1.99977	−	2.55596i	0.0731190	−	0.0934551i
$749$	−20.3917			−0.745096
$750$		0			0
$751$	−26.9567	−	19.5852i	−0.983663	−	0.714673i	−0.0251387	−	0.999684i	$-0.508003\pi$
$751$	−26.9567	−	19.5852i	−0.983663	−	0.714673i	−0.958524	+	0.285011i	$0.908003\pi$
$752$	−3.94198	+	2.86402i	−0.143749	+	0.104440i
$753$		0			0
$754$	0.851704	−	2.62128i	0.0310172	−	0.0954612i
$755$	−17.4541	+	12.6811i	−0.635219	+	0.461514i
$756$		0			0
$757$	12.4774	+	38.4015i	0.453499	+	1.39573i	0.872888	+	0.487921i	$0.162244\pi$
$757$	12.4774	+	38.4015i	0.453499	+	1.39573i	−0.419389	+	0.907807i	$0.637756\pi$
$758$	4.38396			0.159233
$759$		0			0
$760$	−9.13706			−0.331436
$761$	15.4190	+	47.4549i	0.558940	+	1.72024i	0.685304	+	0.728257i	$0.259669\pi$
$761$	15.4190	+	47.4549i	0.558940	+	1.72024i	−0.126364	+	0.991984i	$0.540331\pi$
$762$		0			0
$763$	−11.1491	+	8.10029i	−0.403624	+	0.293250i
$764$	−5.36995	+	16.5270i	−0.194278	+	0.597926i
$765$		0			0
$766$	−5.21065	+	3.78576i	−0.188268	+	0.136785i
$767$	9.75356	+	7.08637i	0.352180	+	0.255874i
$768$		0			0
$769$	4.93932			0.178116			0.0890582	−	0.996026i	$-0.471614\pi$
$769$	4.93932			0.178116			0.0890582	+	0.996026i	$0.471614\pi$
$770$	−5.93693	−	2.16550i	−0.213952	−	0.0780393i
$771$		0			0
$772$	2.57344	+	7.92022i	0.0926200	+	0.285055i
$773$	−27.0786	−	19.6738i	−0.973950	−	0.707616i	−0.0176019	−	0.999845i	$-0.505603\pi$
$773$	−27.0786	−	19.6738i	−0.973950	−	0.707616i	−0.956348	+	0.292229i	$0.905603\pi$
$774$		0			0
$775$	3.27979	−	10.0941i	0.117813	−	0.362593i
$776$	1.74901	−	5.38290i	0.0627858	−	0.193235i
$777$		0			0
$778$	1.81607	+	1.31946i	0.0651094	+	0.0473048i
$779$	0.778258	+	2.39523i	0.0278840	+	0.0858181i
$780$		0			0
$781$	41.0416	−	11.7379i	1.46858	−	0.420014i
$782$	−3.80875			−0.136201
$783$		0			0
$784$	−1.07623	−	0.781926i	−0.0384367	−	0.0279259i
$785$	19.2497	−	13.9857i	0.687052	−	0.499172i
$786$		0			0
$787$	8.01590	−	24.6704i	0.285736	−	0.879405i	−0.700441	−	0.713710i	$-0.747013\pi$
$787$	8.01590	−	24.6704i	0.285736	−	0.879405i	0.986177	−	0.165695i	$-0.0529867\pi$
$788$	−2.87296	+	2.08733i	−0.102345	+	0.0743581i
$789$		0			0
$790$	−4.90387	−	15.0926i	−0.174472	−	0.536969i
$791$	−10.7047			−0.380614
$792$		0			0
$793$	12.6992			0.450961
$794$	10.8674	+	33.4463i	0.385668	+	1.18696i
$795$		0			0
$796$	−2.97413	+	2.16083i	−0.105415	+	0.0765888i
$797$	−3.04772	+	9.37993i	−0.107956	+	0.332254i	−0.990413	−	0.138139i	$-0.955888\pi$
$797$	−3.04772	+	9.37993i	−0.107956	+	0.332254i	0.882457	+	0.470393i	$0.155888\pi$
$798$		0			0
$799$	−7.28144	+	5.29027i	−0.257599	+	0.187156i
$800$	−4.37107	−	3.17577i	−0.154541	−	0.112280i
$801$		0			0
$802$	11.6848			0.412606
$803$	−45.8601	−	16.7275i	−1.61837	−	0.590301i
$804$		0			0
$805$	−2.96788	−	9.13418i	−0.104604	−	0.321938i
$806$	11.6104	+	8.43548i	0.408960	+	0.297127i
$807$		0			0
$808$	−4.73974	+	14.5874i	−0.166744	+	0.513184i
$809$	10.2158	−	31.4410i	0.359168	−	1.10541i	−0.594385	−	0.804181i	$-0.702604\pi$
$809$	10.2158	−	31.4410i	0.359168	−	1.10541i	0.953553	−	0.301225i	$-0.0973956\pi$
$810$		0			0
$811$	−4.21750	−	3.06419i	−0.148096	−	0.107598i	0.511270	−	0.859420i	$-0.329175\pi$
$811$	−4.21750	−	3.06419i	−0.148096	−	0.107598i	−0.659366	+	0.751822i	$0.729175\pi$
$812$	−1.45088	−	4.46533i	−0.0509157	−	0.156703i
$813$		0			0
$814$	−0.458013	+	12.8615i	−0.0160534	+	0.450796i
$815$	−1.80332			−0.0631677
$816$		0			0
$817$	5.92484	+	4.30465i	0.207284	+	0.150601i
$818$	19.9854	−	14.5202i	0.698773	−	0.507689i
$819$		0			0
$820$	−0.280733	+	0.864008i	−0.00980363	+	0.0301725i
$821$	−1.32625	+	0.963576i	−0.0462864	+	0.0336290i	−0.610688	−	0.791871i	$-0.709107\pi$
$821$	−1.32625	+	0.963576i	−0.0462864	+	0.0336290i	0.564401	+	0.825500i	$0.309107\pi$
$822$		0			0
$823$	−5.52814	−	17.0139i	−0.192699	−	0.593066i	−0.999996	−	0.00292037i	$-0.999070\pi$
$823$	−5.52814	−	17.0139i	−0.192699	−	0.593066i	0.807297	−	0.590145i	$-0.200930\pi$
$824$	39.7217			1.38377
$825$		0			0
$826$	−15.8597			−0.551830
$827$	−10.9840	−	33.8052i	−0.381951	−	1.17552i	−0.938668	−	0.344821i	$-0.887939\pi$
$827$	−10.9840	−	33.8052i	−0.381951	−	1.17552i	0.556718	−	0.830702i	$-0.312061\pi$
$828$		0			0
$829$	21.8039	−	15.8415i	0.757282	−	0.550198i	−0.140793	−	0.990039i	$-0.544965\pi$
$829$	21.8039	−	15.8415i	0.757282	−	0.550198i	0.898076	+	0.439841i	$0.144965\pi$
$830$	−1.77168	+	5.45266i	−0.0614958	+	0.189265i
$831$		0			0
$832$	7.01049	−	5.09342i	0.243045	−	0.176582i
$833$	−1.98796	−	1.44433i	−0.0688786	−	0.0500432i
$834$		0			0
$835$	24.5874			0.850882
$836$	6.54126	+	9.71226i	0.226234	+	0.335905i
$837$		0			0
$838$	−8.93444	−	27.4974i	−0.308635	−	0.949881i
$839$	−9.57654	−	6.95776i	−0.330619	−	0.240209i	0.410074	−	0.912052i	$-0.365503\pi$
$839$	−9.57654	−	6.95776i	−0.330619	−	0.240209i	−0.740693	+	0.671843i	$0.765503\pi$
$840$		0			0
$841$	−7.67757	+	23.6291i	−0.264744	+	0.814797i
$842$	5.26282	−	16.1973i	0.181369	−	0.558195i
$843$		0			0
$844$	18.1906	+	13.2162i	0.626146	+	0.454922i
$845$	−3.36891	−	10.3685i	−0.115894	−	0.356686i
$846$		0			0
$847$	5.40155	+	21.7924i	0.185600	+	0.748797i
$848$	3.38721			0.116317
$849$		0			0
$850$	0.654843	+	0.475771i	0.0224609	+	0.0163188i
$851$	−15.8235	+	11.4965i	−0.542423	+	0.394094i
$852$		0			0
$853$	−9.36453	+	28.8211i	−0.320635	+	0.986814i	0.652737	+	0.757585i	$0.273621\pi$
$853$	−9.36453	+	28.8211i	−0.320635	+	0.986814i	−0.973372	+	0.229230i	$0.926379\pi$
$854$	−13.5152	+	9.81939i	−0.462482	+	0.336013i
$855$		0			0
$856$	−9.01660	−	27.7503i	−0.308181	−	0.948484i
$857$	29.2318			0.998540			0.499270	−	0.866446i	$-0.333602\pi$
$857$	29.2318			0.998540			0.499270	+	0.866446i	$0.333602\pi$
$858$		0			0
$859$	−36.7151			−1.25270			−0.626351	−	0.779541i	$-0.715452\pi$
$859$	−36.7151			−1.25270			−0.626351	+	0.779541i	$0.715452\pi$
$860$	0.816341	+	2.51244i	0.0278370	+	0.0856735i
$861$		0			0
$862$	22.9207	−	16.6529i	0.780682	−	0.567199i
$863$	−13.4657	+	41.4431i	−0.458377	+	1.41074i	0.408748	+	0.912647i	$0.365966\pi$
$863$	−13.4657	+	41.4431i	−0.458377	+	1.41074i	−0.867125	+	0.498091i	$0.834034\pi$
$864$		0			0
$865$	−13.1154	+	9.52890i	−0.445937	+	0.323992i
$866$	−9.59252	−	6.96937i	−0.325967	−	0.236829i
$867$		0			0
$868$	24.4474			0.829798
$869$	−34.7415	+	44.4040i	−1.17853	+	1.50630i
$870$		0			0
$871$	1.41288	+	4.34841i	0.0478737	+	0.147340i
$872$	−15.9532	−	11.5907i	−0.540243	−	0.392509i
$873$		0			0
$874$	4.24672	−	13.0701i	0.143647	−	0.442101i
$875$	−0.630728	+	1.94118i	−0.0213225	+	0.0656239i
$876$		0			0
$877$	8.99407	+	6.53457i	0.303708	+	0.220657i	0.729192	−	0.684309i	$-0.239896\pi$
$877$	8.99407	+	6.53457i	0.303708	+	0.220657i	−0.425484	+	0.904966i	$0.639896\pi$
$878$	−7.40129	−	22.7788i	−0.249781	−	0.768748i
$879$		0			0
$880$	0.0554058	−	1.55586i	0.00186773	−	0.0524479i
$881$	39.1155			1.31783			0.658917	−	0.752216i	$-0.271015\pi$
$881$	39.1155			1.31783			0.658917	+	0.752216i	$0.271015\pi$
$882$		0			0
$883$	−15.7910	−	11.4728i	−0.531408	−	0.386091i	0.289476	−	0.957185i	$-0.406519\pi$
$883$	−15.7910	−	11.4728i	−0.531408	−	0.386091i	−0.820884	+	0.571094i	$0.806519\pi$
$884$	1.14661	−	0.833061i	0.0385647	−	0.0280189i
$885$		0			0
$886$	7.56236	−	23.2746i	0.254063	−	0.781924i
$887$	−4.19967	+	3.05124i	−0.141011	+	0.102451i	−0.656054	−	0.754714i	$-0.727776\pi$
$887$	−4.19967	+	3.05124i	−0.141011	+	0.102451i	0.515043	+	0.857164i	$0.327776\pi$
$888$		0			0
$889$	13.0404	+	40.1342i	0.437361	+	1.34606i
$890$	−3.52123			−0.118032
$891$		0			0
$892$	−11.8270			−0.395999
$893$	−10.0353	−	30.8855i	−0.335818	−	1.03354i
$894$		0			0
$895$	13.7287	−	9.97452i	0.458901	−	0.333411i
$896$	3.29298	−	10.1347i	0.110011	−	0.338578i
$897$		0			0
$898$	−9.06755	+	6.58796i	−0.302588	+	0.219843i
$899$	17.5025	+	12.7163i	0.583740	+	0.424112i
$900$		0			0
$901$	6.25669			0.208440
$902$	−2.39638	+	0.685362i	−0.0797906	+	0.0228201i
$903$		0			0
$904$	−4.73329	−	14.5676i	−0.157427	−	0.484510i
$905$	−14.8461	−	10.7863i	−0.493501	−	0.358550i
$906$		0			0
$907$	−13.1140	+	40.3608i	−0.435444	+	1.34016i	0.457187	+	0.889371i	$0.348857\pi$
$907$	−13.1140	+	40.3608i	−0.435444	+	1.34016i	−0.892631	+	0.450789i	$0.851143\pi$
$908$	6.16318	−	18.9683i	0.204532	−	0.629485i
$909$		0			0
$910$	−2.23278	−	1.62221i	−0.0740159	−	0.0537757i
$911$	6.10306	+	18.7833i	0.202203	+	0.622318i	0.999817	+	0.0191487i	$0.00609558\pi$
$911$	6.10306	+	18.7833i	0.202203	+	0.622318i	−0.797613	+	0.603169i	$0.793904\pi$
$912$		0			0
$913$	19.5838	−	5.60095i	0.648129	−	0.185364i
$914$	12.8725			0.425783
$915$		0			0
$916$	3.77036	+	2.73932i	0.124576	+	0.0905098i
$917$	−33.5354	+	24.3649i	−1.10744	+	0.804599i
$918$		0			0
$919$	−7.56638	+	23.2869i	−0.249592	+	0.768165i	0.745255	+	0.666779i	$0.232328\pi$
$919$	−7.56638	+	23.2869i	−0.249592	+	0.768165i	−0.994847	+	0.101385i	$0.967672\pi$
$920$	11.1181	−	8.07774i	0.366551	−	0.266315i
$921$		0			0
$922$	−3.26736	−	10.0559i	−0.107605	−	0.331173i
$923$	18.6423			0.613619
$924$		0			0
$925$	4.15664			0.136669
$926$	1.78505	+	5.49382i	0.0586604	+	0.180538i
$927$		0			0
$928$	8.90976	−	6.47332i	0.292477	−	0.212497i
$929$	1.87044	−	5.75664i	0.0613673	−	0.188869i	−0.915673	−	0.401924i	$-0.868341\pi$
$929$	1.87044	−	5.75664i	0.0613673	−	0.188869i	0.977040	+	0.213055i	$0.0683415\pi$
$930$		0			0
$931$	7.17291	−	5.21142i	0.235083	−	0.170797i
$932$	−12.4157	−	9.02056i	−0.406691	−	0.295478i
$933$		0			0
$934$	−7.91903			−0.259119
$935$	0.102343	−	2.87390i	0.00334697	−	0.0939866i
$936$		0			0
$937$	2.11326	+	6.50394i	0.0690372	+	0.212475i	0.979623	−	0.200846i	$-0.0643690\pi$
$937$	2.11326	+	6.50394i	0.0690372	+	0.212475i	−0.910586	+	0.413320i	$0.864369\pi$
$938$	−4.86599	−	3.53535i	−0.158880	−	0.115433i
$939$		0			0
$940$	3.61993	−	11.1410i	0.118069	−	0.363379i
$941$	1.22191	−	3.76064i	0.0398330	−	0.122593i	−0.929163	−	0.369671i	$-0.879470\pi$
$941$	1.22191	−	3.76064i	0.0398330	−	0.122593i	0.968996	+	0.247078i	$0.0794703\pi$
$942$		0			0
$943$	−3.06453	−	2.22651i	−0.0997947	−	0.0725051i
$944$	−1.20736	−	3.71587i	−0.0392962	−	0.120941i
$945$		0			0
$946$	−4.46612	+	5.70826i	−0.145206	+	0.185591i
$947$	40.1742			1.30549			0.652743	−	0.757579i	$-0.273618\pi$
$947$	40.1742			1.30549			0.652743	+	0.757579i	$0.273618\pi$
$948$		0			0
$949$	−17.2472	−	12.5308i	−0.559867	−	0.406767i
$950$	−2.36279	+	1.71667i	−0.0766591	+	0.0556961i
$951$		0			0
$952$	−1.59720	+	4.91569i	−0.0517657	+	0.159318i
$953$	−33.3696	+	24.2444i	−1.08095	+	0.785353i	−0.977848	−	0.209318i	$-0.932876\pi$
$953$	−33.3696	+	24.2444i	−1.08095	+	0.785353i	−0.103098	+	0.994671i	$0.532876\pi$
$954$		0			0
$955$	4.75840	+	14.6449i	0.153978	+	0.473897i
$956$	9.03529			0.292222
$957$		0			0
$958$	−8.62166			−0.278553
$959$	−2.19482	−	6.75496i	−0.0708744	−	0.218129i
$960$		0			0
$961$	−66.0553	+	47.9920i	−2.13082	+	1.54813i
$962$	−1.73681	+	5.34535i	−0.0559970	+	0.172341i
$963$		0			0
$964$	−0.458269	+	0.332952i	−0.0147599	+	0.0107237i
$965$	5.97007	+	4.33751i	0.192183	+	0.139629i
$966$		0			0
$967$	9.16826			0.294831			0.147416	−	0.989075i	$-0.452904\pi$
$967$	9.16826			0.294831			0.147416	+	0.989075i	$0.452904\pi$
$968$	−27.2681	+	16.9867i	−0.876429	+	0.545975i
$969$		0			0
$970$	−0.559054	−	1.72059i	−0.0179501	−	0.0552448i
$971$	−3.00359	−	2.18224i	−0.0963899	−	0.0700313i	0.538546	−	0.842596i	$-0.318974\pi$
$971$	−3.00359	−	2.18224i	−0.0963899	−	0.0700313i	−0.634936	+	0.772565i	$0.718974\pi$
$972$		0			0
$973$	−1.72243	+	5.30110i	−0.0552186	+	0.169946i
$974$	5.81880	−	17.9084i	0.186446	−	0.573823i
$975$		0			0
$976$	−3.32953	−	2.41904i	−0.106576	−	0.0774317i
$977$	−3.82972	−	11.7867i	−0.122524	−	0.377089i	0.870918	−	0.491428i	$-0.163525\pi$
$977$	−3.82972	−	11.7867i	−0.122524	−	0.377089i	−0.993442	+	0.114339i	$0.963525\pi$
$978$		0			0
$979$	6.98842	+	10.3762i	0.223351	+	0.331624i
$980$	3.19822			0.102163
$981$		0			0
$982$	−4.02993	−	2.92791i	−0.128600	−	0.0934335i
$983$	18.8460	−	13.6924i	0.601093	−	0.436720i	−0.245174	−	0.969479i	$-0.578845\pi$
$983$	18.8460	−	13.6924i	0.601093	−	0.436720i	0.846267	+	0.532760i	$0.178845\pi$
$984$		0			0
$985$	−0.972402	+	2.99275i	−0.0309833	+	0.0953568i
$986$	−1.33480	+	0.969788i	−0.0425086	+	0.0308843i
$987$		0			0
$988$	1.58026	+	4.86355i	0.0502748	+	0.154730i
$989$	−11.0150			−0.350256
$990$		0			0
$991$	−37.7826			−1.20020			−0.600101	−	0.799924i	$-0.704873\pi$
$991$	−37.7826			−1.20020			−0.600101	+	0.799924i	$0.704873\pi$
$992$	17.7205	+	54.5380i	0.562626	+	1.73158i
$993$		0			0
$994$	−19.8403	+	14.4148i	−0.629295	+	0.457209i
$995$	−1.00664	+	3.09813i	−0.0319128	+	0.0982175i
$996$		0			0
$997$	−6.37174	+	4.62934i	−0.201795	+	0.146613i	−0.684094	−	0.729394i	$-0.739802\pi$
$997$	−6.37174	+	4.62934i	−0.201795	+	0.146613i	0.482299	+	0.876007i	$0.339802\pi$
$998$	29.6671	+	21.5544i	0.939097	+	0.682294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.b.181.2		8
3.2	odd	2		165.2.m.b.16.1	✓	8
11.3	even	5		5445.2.a.bk.1.3		4
11.8	odd	10		5445.2.a.br.1.2		4
11.9	even	5	inner	495.2.n.b.361.2		8
15.2	even	4		825.2.bx.g.49.3		16
15.8	even	4		825.2.bx.g.49.2		16
15.14	odd	2		825.2.n.i.676.2		8
33.8	even	10		1815.2.a.r.1.3		4
33.14	odd	10		1815.2.a.v.1.2		4
33.20	odd	10		165.2.m.b.31.1	yes	8
165.14	odd	10		9075.2.a.cq.1.3		4
165.53	even	20		825.2.bx.g.724.3		16
165.74	even	10		9075.2.a.dg.1.2		4
165.119	odd	10		825.2.n.i.526.2		8
165.152	even	20		825.2.bx.g.724.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.16.1	✓	8	3.2	odd	2
165.2.m.b.31.1	yes	8	33.20	odd	10
495.2.n.b.181.2		8	1.1	even	1	trivial
495.2.n.b.361.2		8	11.9	even	5	inner
825.2.n.i.526.2		8	165.119	odd	10
825.2.n.i.676.2		8	15.14	odd	2
825.2.bx.g.49.2		16	15.8	even	4
825.2.bx.g.49.3		16	15.2	even	4
825.2.bx.g.724.2		16	165.152	even	20
825.2.bx.g.724.3		16	165.53	even	20
1815.2.a.r.1.3		4	33.8	even	10
1815.2.a.v.1.2		4	33.14	odd	10
5445.2.a.bk.1.3		4	11.3	even	5
5445.2.a.br.1.2		4	11.8	odd	10
9075.2.a.cq.1.3		4	165.14	odd	10
9075.2.a.dg.1.2		4	165.74	even	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.288477 + 0.887841i) q^{2} +(0.912991 - 0.663327i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.65127 - 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +O(q^{10})\)	\(q+(0.288477 + 0.887841i) q^{2} +(0.912991 - 0.663327i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.65127 - 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +0.933531 q^{10} +(-1.85274 - 2.75088i) q^{11} +(-0.447591 - 1.37754i) q^{13} +(1.54151 + 1.11997i) q^{14} +(-0.145054 + 0.446431i) q^{16} +(-0.267937 + 0.824626i) q^{17} +(-2.53103 - 1.83890i) q^{19} +(-0.348732 - 1.07329i) q^{20} +(1.90788 - 2.43850i) q^{22} +4.70547 q^{23} +(-0.809017 - 0.587785i) q^{25} +(1.09392 - 0.794779i) q^{26} +(0.711789 - 2.19066i) q^{28} +(1.64906 - 1.19811i) q^{29} +(3.27979 + 10.0941i) q^{31} +5.40294 q^{32} -0.809430 q^{34} +(-0.630728 - 1.94118i) q^{35} +(-3.36279 + 2.44321i) q^{37} +(0.902506 - 2.77763i) q^{38} +(2.36279 - 1.71667i) q^{40} +(-0.651268 - 0.473174i) q^{41} -2.34089 q^{43} +(-3.51627 - 1.28256i) q^{44} +(1.35742 + 4.17771i) q^{46} +(8.39782 + 6.10137i) q^{47} +(-0.875752 + 2.69529i) q^{49} +(0.288477 - 0.887841i) q^{50} +(-1.32241 - 0.960786i) q^{52} +(-2.22985 - 6.86278i) q^{53} +(-3.18877 + 0.911987i) q^{55} +5.96112 q^{56} +(1.53945 + 1.11847i) q^{58} +(-6.73386 + 4.89243i) q^{59} +(-2.70931 + 8.33841i) q^{61} +(-8.01586 + 5.82386i) q^{62} +(1.84873 + 5.68981i) q^{64} -1.44843 q^{65} -3.15664 q^{67} +(0.302372 + 0.930606i) q^{68} +(1.54151 - 1.11997i) q^{70} +(-3.97725 + 12.2407i) q^{71} +(11.9075 - 8.65128i) q^{73} +(-3.13927 - 2.28081i) q^{74} -3.53059 q^{76} +(-6.35965 - 2.31969i) q^{77} +(-5.25303 - 16.1672i) q^{79} +(0.379757 + 0.275910i) q^{80} +(0.232227 - 0.714723i) q^{82} +(-1.89782 + 5.84089i) q^{83} +(0.701468 + 0.509647i) q^{85} +(-0.675292 - 2.07833i) q^{86} +(0.344727 - 9.68030i) q^{88} -3.77194 q^{89} +(-2.39175 - 1.73771i) q^{91} +(4.29606 - 3.12127i) q^{92} +(-2.99447 + 9.21604i) q^{94} +(-2.53103 + 1.83890i) q^{95} +(-0.598859 - 1.84310i) q^{97} -2.64562 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8 - 2 * q^10 + 3 * q^11 + 10 * q^13 - 24 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^19 - 7 * q^20 - 7 * q^22 + 2 * q^23 - 2 * q^25 - 14 * q^26 + 13 * q^28 - 14 * q^29 - 5 * q^31 + 16 * q^32 - 70 * q^34 - q^35 - 27 * q^37 + 16 * q^38 + 19 * q^40 - q^41 - 28 * q^43 - 47 * q^44 + 42 * q^46 + 27 * q^47 - 15 * q^49 - 2 * q^50 + 22 * q^52 + q^53 - 7 * q^55 + 24 * q^56 + 18 * q^58 - 13 * q^59 - 3 * q^61 - 15 * q^62 + 19 * q^64 - 30 * q^65 + 10 * q^67 + 33 * q^68 - 24 * q^70 - 9 * q^71 + 5 * q^73 + 17 * q^74 - 46 * q^76 - q^77 - 10 * q^79 - 11 * q^80 - 33 * q^82 + 25 * q^83 - 8 * q^85 - 20 * q^86 + 29 * q^88 - 4 * q^89 - 43 * q^91 + 22 * q^92 + 57 * q^94 - 2 * q^95 + 13 * q^97 + 2 * q^98

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