LMFDB - Embedded newform 825.2.n.i.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.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:	$6.58765816676$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.2
Root			$-0.755243 + 0.548716i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.i.526.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.288477 + 0.887841i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.912991 - 0.663327i) q^{4} +(0.288477 - 0.887841i) q^{6} +(-1.65127 + 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.288477 + 0.887841i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.912991 - 0.663327i) q^{4} +(0.288477 - 0.887841i) q^{6} +(-1.65127 + 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.85274 + 2.75088i) q^{11} -1.12852 q^{12} +(0.447591 + 1.37754i) q^{13} +(-1.54151 - 1.11997i) q^{14} +(-0.145054 + 0.446431i) q^{16} +(-0.267937 + 0.824626i) q^{17} +(-0.755243 + 0.548716i) q^{18} +(-2.53103 - 1.83890i) q^{19} +2.04108 q^{21} +(-1.90788 + 2.43850i) q^{22} +4.70547 q^{23} +(-0.902506 - 2.77763i) q^{24} +(-1.09392 + 0.794779i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.711789 + 2.19066i) q^{28} +(-1.64906 + 1.19811i) q^{29} +(3.27979 + 10.0941i) q^{31} +5.40294 q^{32} +(0.118034 - 3.31452i) q^{33} -0.809430 q^{34} +(0.912991 + 0.663327i) q^{36} +(3.36279 - 2.44321i) q^{37} +(0.902506 - 2.77763i) q^{38} +(0.447591 - 1.37754i) q^{39} +(0.651268 + 0.473174i) q^{41} +(0.588805 + 1.81215i) q^{42} +2.34089 q^{43} +(3.51627 + 1.28256i) q^{44} +(1.35742 + 4.17771i) q^{46} +(8.39782 + 6.10137i) q^{47} +(0.379757 - 0.275910i) q^{48} +(-0.875752 + 2.69529i) q^{49} +(0.701468 - 0.509647i) q^{51} +(1.32241 + 0.960786i) q^{52} +(-2.22985 - 6.86278i) q^{53} +0.933531 q^{54} -5.96112 q^{56} +(0.966766 + 2.97540i) q^{57} +(-1.53945 - 1.11847i) q^{58} +(6.73386 - 4.89243i) q^{59} +(-2.70931 + 8.33841i) q^{61} +(-8.01586 + 5.82386i) q^{62} +(-1.65127 - 1.19972i) q^{63} +(1.84873 + 5.68981i) q^{64} +(2.97682 - 0.851369i) q^{66} +3.15664 q^{67} +(0.302372 + 0.930606i) q^{68} +(-3.80681 - 2.76581i) q^{69} +(3.97725 - 12.2407i) q^{71} +(-0.902506 + 2.77763i) q^{72} +(-11.9075 + 8.65128i) q^{73} +(3.13927 + 2.28081i) q^{74} -3.53059 q^{76} +(-6.35965 - 2.31969i) q^{77} +1.35216 q^{78} +(-5.25303 - 16.1672i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.232227 + 0.714723i) q^{82} +(-1.89782 + 5.84089i) q^{83} +(1.86349 - 1.35390i) q^{84} +(0.675292 + 2.07833i) q^{86} +2.03835 q^{87} +(-0.344727 + 9.68030i) q^{88} +3.77194 q^{89} +(-2.39175 - 1.73771i) q^{91} +(4.29606 - 3.12127i) q^{92} +(3.27979 - 10.0941i) q^{93} +(-2.99447 + 9.21604i) q^{94} +(-4.37107 - 3.17577i) q^{96} +(0.598859 + 1.84310i) q^{97} -2.64562 q^{98} +(-2.04372 + 2.61213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 9 q^{7} + 19 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 9 * q^7 + 19 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 9 q^{7} + 19 q^{8} - 2 q^{9} - 3 q^{11} + 18 q^{12} - 10 q^{13} + 24 q^{14} + 4 q^{16} + 2 q^{17} + 3 q^{18} - 2 q^{19} + 16 q^{21} + 7 q^{22} + 2 q^{23} - 16 q^{24} + 14 q^{26} - 2 q^{27} - 13 q^{28} + 14 q^{29} - 5 q^{31} + 16 q^{32} - 8 q^{33} - 70 q^{34} - 2 q^{36} + 27 q^{37} + 16 q^{38} - 10 q^{39} + q^{41} - 31 q^{42} + 28 q^{43} + 47 q^{44} + 42 q^{46} + 27 q^{47} - 11 q^{48} - 15 q^{49} - 8 q^{51} - 22 q^{52} + q^{53} - 2 q^{54} - 24 q^{56} + 3 q^{57} - 18 q^{58} + 13 q^{59} - 3 q^{61} - 15 q^{62} - 9 q^{63} + 19 q^{64} + 37 q^{66} - 10 q^{67} + 33 q^{68} - 3 q^{69} + 9 q^{71} - 16 q^{72} - 5 q^{73} - 17 q^{74} - 46 q^{76} - q^{77} - 36 q^{78} - 10 q^{79} - 2 q^{81} + 33 q^{82} + 25 q^{83} - 18 q^{84} + 20 q^{86} + 34 q^{87} - 29 q^{88} + 4 q^{89} - 43 q^{91} + 22 q^{92} - 5 q^{93} + 57 q^{94} + 6 q^{96} - 13 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 9 * q^7 + 19 * q^8 - 2 * q^9 - 3 * q^11 + 18 * q^12 - 10 * q^13 + 24 * q^14 + 4 * q^16 + 2 * q^17 + 3 * q^18 - 2 * q^19 + 16 * q^21 + 7 * q^22 + 2 * q^23 - 16 * q^24 + 14 * q^26 - 2 * q^27 - 13 * q^28 + 14 * q^29 - 5 * q^31 + 16 * q^32 - 8 * q^33 - 70 * q^34 - 2 * q^36 + 27 * q^37 + 16 * q^38 - 10 * q^39 + q^41 - 31 * q^42 + 28 * q^43 + 47 * q^44 + 42 * q^46 + 27 * q^47 - 11 * q^48 - 15 * q^49 - 8 * q^51 - 22 * q^52 + q^53 - 2 * q^54 - 24 * q^56 + 3 * q^57 - 18 * q^58 + 13 * q^59 - 3 * q^61 - 15 * q^62 - 9 * q^63 + 19 * q^64 + 37 * q^66 - 10 * q^67 + 33 * q^68 - 3 * q^69 + 9 * q^71 - 16 * q^72 - 5 * q^73 - 17 * q^74 - 46 * q^76 - q^77 - 36 * q^78 - 10 * q^79 - 2 * q^81 + 33 * q^82 + 25 * q^83 - 18 * q^84 + 20 * q^86 + 34 * q^87 - 29 * q^88 + 4 * q^89 - 43 * q^91 + 22 * q^92 - 5 * q^93 + 57 * q^94 + 6 * q^96 - 13 * q^97 + 2 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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	$0.792933\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	0.912991	−	0.663327i	0.456496	−	0.331664i
$5$		0			0
$5$		0			0
$6$	0.288477	−	0.887841i	0.117770	−	0.362460i
$7$	−1.65127	+	1.19972i	−0.624121	+	0.453450i	−0.854358	−	0.519684i	$-0.826050\pi$
$7$	−1.65127	+	1.19972i	−0.624121	+	0.453450i	0.230238	+	0.973134i	$0.426050\pi$
$8$	2.36279	+	1.71667i	0.835373	+	0.606934i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	1.85274	+	2.75088i	0.558621	+	0.829423i
$11$	1.85274	+	2.75088i	0.558621	+	0.829423i
$12$	−1.12852			−0.325775
$13$	0.447591	+	1.37754i	0.124139	+	0.382062i	0.993743	−	0.111688i	$-0.0356258\pi$
$13$	0.447591	+	1.37754i	0.124139	+	0.382062i	−0.869604	+	0.493750i	$0.835626\pi$
$14$	−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	$0.133531\pi$
$18$	−0.755243	+	0.548716i	−0.178012	+	0.129334i
$19$	−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			0
$21$	2.04108			0.445400
$22$	−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	$0.336785\pi$
$24$	−0.902506	−	2.77763i	−0.184223	−	0.566981i
$25$		0			0
$26$	−1.09392	+	0.794779i	−0.214535	+	0.155869i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.711789	+	2.19066i	−0.134516	+	0.413996i
$29$	−1.64906	+	1.19811i	−0.306223	+	0.222484i	−0.730274	−	0.683154i	$-0.760608\pi$
$29$	−1.64906	+	1.19811i	−0.306223	+	0.222484i	0.424051	+	0.905638i	$0.360608\pi$
$30$		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
$33$	0.118034	−	3.31452i	0.0205471	−	0.576985i
$34$	−0.809430			−0.138816
$35$		0			0
$36$	0.912991	+	0.663327i	0.152165	+	0.110555i
$37$	3.36279	−	2.44321i	0.552839	−	0.401661i	−0.275992	−	0.961160i	$-0.589006\pi$
$37$	3.36279	−	2.44321i	0.552839	−	0.401661i	0.828831	+	0.559499i	$0.189006\pi$
$38$	0.902506	−	2.77763i	0.146406	−	0.450591i
$39$	0.447591	−	1.37754i	0.0716719	−	0.220583i
$40$		0			0
$41$	0.651268	+	0.473174i	0.101711	+	0.0738974i	0.637478	−	0.770468i	$-0.279978\pi$
$41$	0.651268	+	0.473174i	0.101711	+	0.0738974i	−0.535767	+	0.844366i	$0.679978\pi$
$42$	0.588805	+	1.81215i	0.0908545	+	0.279622i
$43$	2.34089			0.356982			0.178491	−	0.983942i	$-0.442878\pi$
$43$	2.34089			0.356982			0.178491	+	0.983942i	$0.442878\pi$
$44$	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	$0.426635\pi$
$48$	0.379757	−	0.275910i	0.0548132	−	0.0398241i
$49$	−0.875752	+	2.69529i	−0.125107	+	0.385041i
$50$		0			0
$51$	0.701468	−	0.509647i	0.0982252	−	0.0713648i
$52$	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	$-0.265050\pi$
$54$	0.933531			0.127038
$55$		0			0
$56$	−5.96112			−0.796588
$57$	0.966766	+	2.97540i	0.128051	+	0.394101i
$58$	−1.53945	−	1.11847i	−0.202139	−	0.146863i
$59$	6.73386	−	4.89243i	0.876674	−	0.636941i	−0.0556956	−	0.998448i	$-0.517738\pi$
$59$	6.73386	−	4.89243i	0.876674	−	0.636941i	0.932369	+	0.361507i	$0.117738\pi$
$60$		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
$63$	−1.65127	−	1.19972i	−0.208040	−	0.151150i
$64$	1.84873	+	5.68981i	0.231091	+	0.711226i
$65$		0			0
$66$	2.97682	−	0.851369i	0.366421	−	0.104796i
$67$	3.15664			0.385645			0.192822	−	0.981234i	$-0.438236\pi$
$67$	3.15664			0.385645			0.192822	+	0.981234i	$0.438236\pi$
$68$	0.302372	+	0.930606i	0.0366680	+	0.112853i
$69$	−3.80681	−	2.76581i	−0.458286	−	0.332964i
$70$		0			0
$71$	3.97725	−	12.2407i	0.472013	−	1.45271i	−0.377931	−	0.925834i	$-0.623364\pi$
$71$	3.97725	−	12.2407i	0.472013	−	1.45271i	0.849944	−	0.526873i	$-0.176636\pi$
$72$	−0.902506	+	2.77763i	−0.106361	+	0.327347i
$73$	−11.9075	+	8.65128i	−1.39366	+	1.01256i	−0.398211	+	0.917294i	$0.630369\pi$
$73$	−11.9075	+	8.65128i	−1.39366	+	1.01256i	−0.995452	+	0.0952617i	$0.969631\pi$
$74$	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
$78$	1.35216			0.153102
$79$	−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			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−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	$0.990568\pi$
$84$	1.86349	−	1.35390i	0.203323	−	0.147723i
$85$		0			0
$86$	0.675292	+	2.07833i	0.0728186	+	0.224113i
$87$	2.03835			0.218534
$88$	−0.344727	+	9.68030i	−0.0367480	+	1.03192i
$89$	3.77194			0.399825			0.199913	−	0.979814i	$-0.435934\pi$
$89$	3.77194			0.399825			0.199913	+	0.979814i	$0.435934\pi$
$90$		0			0
$91$	−2.39175	−	1.73771i	−0.250724	−	0.182162i
$92$	4.29606	−	3.12127i	0.447895	−	0.325415i
$93$	3.27979	−	10.0941i	0.340098	−	1.04671i
$94$	−2.99447	+	9.21604i	−0.308856	+	0.950562i
$95$		0			0
$96$	−4.37107	−	3.17577i	−0.446120	−	0.324125i
$97$	0.598859	+	1.84310i	0.0608049	+	0.187138i	0.976845	−	0.213949i	$-0.0686325\pi$
$97$	0.598859	+	1.84310i	0.0608049	+	0.187138i	−0.916040	+	0.401087i	$0.868633\pi$
$98$	−2.64562			−0.267248
$99$	−2.04372	+	2.61213i	−0.205402	+	0.262529i
$100$		0			0
$101$	−1.62288	−	4.99472i	−0.161483	−	0.496993i	0.837277	−	0.546779i	$-0.184146\pi$
$101$	−1.62288	−	4.99472i	−0.161483	−	0.496993i	−0.998760	+	0.0497857i	$0.984146\pi$
$102$	0.654843	+	0.475771i	0.0648391	+	0.0471084i
$103$	−11.0032	+	7.99426i	−1.08417	+	0.787698i	−0.978406	−	0.206693i	$-0.933730\pi$
$103$	−11.0032	+	7.99426i	−1.08417	+	0.787698i	−0.105768	+	0.994391i	$0.533730\pi$
$104$	−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	$0.860422\pi$
$108$	−0.348732	−	1.07329i	−0.0335567	−	0.103277i
$109$	−6.75183			−0.646708			−0.323354	−	0.946278i	$-0.604811\pi$
$109$	−6.75183			−0.646708			−0.323354	+	0.946278i	$0.604811\pi$
$110$		0			0
$111$	−4.15664			−0.394531
$112$	−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	$0.779342\pi$
$114$	−2.36279	+	1.71667i	−0.221296	+	0.160781i
$115$		0			0
$116$	−0.710837	+	2.18773i	−0.0659996	+	0.203126i
$117$	−1.17181	+	0.851369i	−0.108334	+	0.0787091i
$118$	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
$123$	−0.248762	−	0.765612i	−0.0224301	−	0.0690329i
$124$	9.69014	+	7.04030i	0.870200	+	0.632237i
$125$		0			0
$126$	0.588805	−	1.81215i	0.0524549	−	0.161440i
$127$	6.38897	−	19.6632i	0.566929	−	1.74483i	−0.0952195	−	0.995456i	$-0.530355\pi$
$127$	6.38897	−	19.6632i	0.566929	−	1.74483i	0.662149	−	0.749372i	$-0.269645\pi$
$128$	4.22380	−	3.06877i	0.373335	−	0.271244i
$129$	−1.89382	−	1.37594i	−0.166741	−	0.121145i
$130$		0			0
$131$	20.3089			1.77439			0.887197	−	0.461392i	$-0.152650\pi$
$131$	20.3089			1.77439			0.887197	+	0.461392i	$0.152650\pi$
$132$	−2.09085	−	3.10443i	−0.181985	−	0.270206i
$133$	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	$0.0525071\pi$
$138$	1.35742	−	4.17771i	0.115551	−	0.355630i
$139$	−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	$0.336948\pi$
$140$		0			0
$141$	−3.20768	−	9.87223i	−0.270136	−	0.831392i
$142$	12.0152			1.00829
$143$	−2.96019	+	3.78350i	−0.247544	+	0.316392i
$144$	−0.469405			−0.0391171
$145$		0			0
$146$	−11.1160	−	8.07624i	−0.919966	−	0.668394i
$147$	2.29275	−	1.66578i	0.189103	−	0.137391i
$148$	1.44955	−	4.46126i	0.119152	−	0.366713i
$149$	−2.81465	+	8.66261i	−0.230585	+	0.709669i	0.767091	+	0.641538i	$0.221703\pi$
$149$	−2.81465	+	8.66261i	−0.230585	+	0.709669i	−0.997676	+	0.0681306i	$0.978297\pi$
$150$		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
$153$	−0.867063			−0.0700979
$154$	0.224903	−	6.31553i	0.0181232	−	0.508920i
$155$		0			0
$156$	−0.505115	−	1.55458i	−0.0404416	−	0.124466i
$157$	−19.2497	−	13.9857i	−1.53629	−	1.11618i	−0.952607	−	0.304205i	$-0.901609\pi$
$157$	−19.2497	−	13.9857i	−1.53629	−	1.11618i	−0.583688	−	0.811978i	$-0.698391\pi$
$158$	12.8385	−	9.32772i	1.02138	−	0.742073i
$159$	−2.22985	+	6.86278i	−0.176839	+	0.544254i
$160$		0			0
$161$	−7.77000	+	5.64523i	−0.612362	+	0.444907i
$162$	−0.755243	−	0.548716i	−0.0593375	−	0.0431112i
$163$	0.557258	+	1.71506i	0.0436478	+	0.134334i	0.970506	−	0.241078i	$-0.0775011\pi$
$163$	0.557258	+	1.71506i	0.0436478	+	0.134334i	−0.926858	+	0.375412i	$0.877501\pi$
$164$	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	$0.499733\pi$
$168$	4.82265	+	3.50386i	0.372075	+	0.270328i
$169$	8.81993	−	6.40806i	0.678456	−	0.492927i
$170$		0			0
$171$	0.966766	−	2.97540i	0.0739304	−	0.227534i
$172$	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	$0.911357\pi$
$174$	0.588017	+	1.80973i	0.0445775	+	0.137195i
$175$		0			0
$176$	−1.49683	+	0.428092i	−0.112828	+	0.0322686i
$177$	−8.32351			−0.625633
$178$	1.08812	+	3.34888i	0.0815579	+	0.251010i
$179$	−13.7287	−	9.97452i	−1.02613	−	0.745530i	−0.0586031	−	0.998281i	$-0.518665\pi$
$179$	−13.7287	−	9.97452i	−1.02613	−	0.745530i	−0.967531	+	0.252751i	$0.918665\pi$
$180$		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
$183$	7.09308	−	5.15342i	0.524335	−	0.380952i
$184$	11.1181	+	8.07774i	0.819634	+	0.595499i
$185$		0			0
$186$	9.90814			0.726500
$187$	−2.76487	+	0.790750i	−0.202187	+	0.0578254i
$188$	11.7143			0.854356
$189$	0.630728	+	1.94118i	0.0458787	+	0.141200i
$190$		0			0
$191$	12.4577	−	9.05102i	0.901405	−	0.654909i	−0.0374216	−	0.999300i	$-0.511914\pi$
$191$	12.4577	−	9.05102i	0.901405	−	0.654909i	0.938826	+	0.344391i	$0.111914\pi$
$192$	1.84873	−	5.68981i	0.133421	−	0.410627i
$193$	2.28037	−	7.01824i	0.164144	−	0.505184i	−0.834828	−	0.550511i	$-0.814433\pi$
$193$	2.28037	−	7.01824i	0.164144	−	0.505184i	0.998972	+	0.0453268i	$0.0144329\pi$
$194$	−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	$0.535757\pi$
$198$	−2.90872	−	1.06096i	−0.206714	−	0.0753991i
$199$	−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			0
$201$	−2.55377	−	1.85543i	−0.180129	−	0.130872i
$202$	3.96635	−	2.88172i	0.279072	−	0.202757i
$203$	1.28564	−	3.95681i	0.0902346	−	0.277713i
$204$	0.302372	−	0.930606i	0.0211703	−	0.0651554i
$205$		0			0
$206$	−10.2718	−	7.46290i	−0.715670	−	0.519965i
$207$	1.45407	+	4.47517i	0.101065	+	0.311046i
$208$	−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
$213$	−10.4126	+	7.56518i	−0.713458	+	0.518358i
$214$	2.88207	−	8.87009i	0.197014	−	0.606347i
$215$		0			0
$216$	2.36279	−	1.71667i	0.160768	−	0.116804i
$217$	−17.5259	−	12.7333i	−1.18974	−	0.864395i
$218$	−1.94775	−	5.99455i	−0.131918	−	0.406002i
$219$	14.7184			0.994580
$220$		0			0
$221$	−1.25588			−0.0844799
$222$	−1.19909	−	3.69043i	−0.0804780	−	0.247686i
$223$	8.47862	+	6.16008i	0.567770	+	0.412509i	0.834295	−	0.551319i	$-0.185875\pi$
$223$	8.47862	+	6.16008i	0.567770	+	0.412509i	−0.266524	+	0.963828i	$0.585875\pi$
$224$	−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	$0.100504\pi$
$228$	2.85631	+	2.07523i	0.189164	+	0.137436i
$229$	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	$0.856431\pi$
$230$		0			0
$231$	3.78158	+	5.61478i	0.248810	+	0.369425i
$232$	−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	$-0.246956\pi$
$234$	−1.09392	−	0.794779i	−0.0715118	−	0.0519563i
$235$		0			0
$236$	2.90267	−	8.93350i	0.188948	−	0.581521i
$237$	−5.25303	+	16.1672i	−0.341221	+	1.05017i
$238$	1.33659	−	0.971087i	0.0866380	−	0.0629462i
$239$	−6.47725	−	4.70600i	−0.418979	−	0.304406i	0.358248	−	0.933626i	$-0.383374\pi$
$239$	−6.47725	−	4.70600i	−0.418979	−	0.304406i	−0.777227	+	0.629221i	$0.783374\pi$
$240$		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
$243$	1.00000			0.0641500
$244$	3.05751	+	9.41006i	0.195737	+	0.602417i
$245$		0			0
$246$	0.607979	−	0.441723i	0.0387633	−	0.0281632i
$247$	1.40030	−	4.30967i	0.0890988	−	0.274218i
$248$	−9.57885	+	29.4807i	−0.608258	+	1.87202i
$249$	4.96856	−	3.60987i	0.314870	−	0.228766i
$250$		0			0
$251$	−5.72933	−	17.6331i	−0.361632	−	1.11299i	−0.952063	−	0.305901i	$-0.901042\pi$
$251$	−5.72933	−	17.6331i	−0.361632	−	1.11299i	0.590431	−	0.807088i	$-0.298958\pi$
$252$	−2.30340			−0.145100
$253$	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	$0.226069\pi$
$258$	0.675292	−	2.07833i	0.0420418	−	0.129391i
$259$	−2.62171	+	8.06879i	−0.162905	+	0.501370i
$260$		0			0
$261$	−1.64906	−	1.19811i	−0.102074	−	0.0741613i
$262$	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	$0.469930\pi$
$264$	5.96883	−	7.62890i	0.367356	−	0.469527i
$265$		0			0
$266$	1.84209	+	5.66936i	0.112946	+	0.347611i
$267$	−3.05157	−	2.21709i	−0.186753	−	0.135684i
$268$	2.88198	−	2.09388i	0.176045	−	0.127904i
$269$	−5.46345	+	16.8148i	−0.333112	+	1.02521i	0.634532	+	0.772896i	$0.281193\pi$
$269$	−5.46345	+	16.8148i	−0.333112	+	1.02521i	−0.967644	+	0.252318i	$0.918807\pi$
$270$		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
$273$	0.913569	+	2.81168i	0.0552917	+	0.170170i
$274$	3.24852			0.196250
$275$		0			0
$276$	−5.31022			−0.319638
$277$	5.50785	+	16.9514i	0.330934	+	1.01851i	0.968690	+	0.248273i	$0.0798629\pi$
$277$	5.50785	+	16.9514i	0.330934	+	1.01851i	−0.637756	+	0.770239i	$0.720137\pi$
$278$	−2.06246	−	1.49847i	−0.123698	−	0.0898721i
$279$	−8.58660	+	6.23853i	−0.514066	+	0.373491i
$280$		0			0
$281$	−5.34568	+	16.4523i	−0.318896	+	0.981462i	0.655224	+	0.755434i	$0.272574\pi$
$281$	−5.34568	+	16.4523i	−0.318896	+	0.981462i	−0.974121	+	0.226028i	$0.927426\pi$
$282$	7.83963	−	5.69582i	0.466843	−	0.339181i
$283$	−20.8535	−	15.1510i	−1.23961	−	0.900633i	−0.242042	−	0.970266i	$-0.577817\pi$
$283$	−20.8535	−	15.1510i	−1.23961	−	0.900633i	−0.997573	+	0.0696333i	$0.977817\pi$
$284$	−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
$288$	1.66960	+	5.13850i	0.0983821	+	0.302789i
$289$	13.1451	+	9.55045i	0.773240	+	0.561791i
$290$		0			0
$291$	0.598859	−	1.84310i	0.0351058	−	0.108044i
$292$	−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	$0.170664\pi$
$294$	2.14035	+	1.55506i	0.124828	+	0.0906928i
$295$		0			0
$296$	12.1398			0.705609
$297$	3.18877	−	0.911987i	0.185031	−	0.0529189i
$298$	−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
$303$	−1.62288	+	4.99472i	−0.0932322	+	0.286939i
$304$	1.18808	−	0.863188i	0.0681409	−	0.0495073i
$305$		0			0
$306$	−0.250128	−	0.769814i	−0.0142988	−	0.0440073i
$307$	13.0268			0.743478			0.371739	−	0.928337i	$-0.378762\pi$
$307$	13.0268			0.743478			0.371739	+	0.928337i	$0.378762\pi$
$308$	−7.34502	+	2.10067i	−0.418521	+	0.119697i
$309$	13.6007			0.773714
$310$		0			0
$311$	−1.53971	−	1.11867i	−0.0873092	−	0.0634339i	0.543274	−	0.839555i	$-0.317184\pi$
$311$	−1.53971	−	1.11867i	−0.0873092	−	0.0634339i	−0.630584	+	0.776121i	$0.717184\pi$
$312$	3.42235	−	2.48648i	0.193752	−	0.140769i
$313$	−3.37829	+	10.3973i	−0.190952	+	0.587691i	−1.00000		5.23383e-5i	$-0.999983\pi$
$313$	−3.37829	+	10.3973i	−0.190952	+	0.587691i	0.809048	+	0.587743i	$0.199983\pi$
$314$	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	$0.750941\pi$
$318$	−6.73632			−0.377754
$319$	−6.35114	−	2.31659i	−0.355596	−	0.129704i
$320$		0			0
$321$	3.08727	+	9.50166i	0.172315	+	0.530331i
$322$	−7.25354	−	5.27000i	−0.404224	−	0.293686i
$323$	2.19456	−	1.59444i	0.122108	−	0.0887170i
$324$	−0.348732	+	1.07329i	−0.0193740	+	0.0596270i
$325$		0			0
$326$	−1.36195	+	0.989513i	−0.0754313	+	0.0548040i
$327$	5.46235	+	3.96863i	0.302069	+	0.219466i
$328$	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
$333$	3.36279	+	2.44321i	0.184280	+	0.133887i
$334$	−18.5695	+	13.4915i	−1.01608	+	0.738222i
$335$		0			0
$336$	−0.296067	+	0.911202i	−0.0161518	+	0.0497101i
$337$	−2.23564	+	1.62429i	−0.121783	+	0.0884805i	−0.647009	−	0.762482i	$-0.723981\pi$
$337$	−2.23564	+	1.62429i	−0.121783	+	0.0884805i	0.525227	+	0.850962i	$0.323981\pi$
$338$	8.23368	+	5.98212i	0.447853	+	0.325384i
$339$	1.62067	+	4.98792i	0.0880229	+	0.270907i
$340$		0			0
$341$	−21.6913	+	27.7241i	−1.17465	+	1.50135i
$342$	2.92057			0.157926
$343$	−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	$0.0732532\pi$
$348$	1.86100	−	1.35209i	0.0997598	−	0.0724798i
$349$	−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			0
$351$	1.44843			0.0773117
$352$	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	$0.592781\pi$
$354$	−2.40114	−	7.38995i	−0.127619	−	0.392771i
$355$		0			0
$356$	3.44375	−	2.50203i	0.182518	−	0.132607i
$357$	−0.546881	+	1.68313i	−0.0289440	+	0.0890805i
$358$	4.89536	−	15.0664i	0.258728	−	0.796282i
$359$	−19.3934	+	14.0901i	−1.02354	+	0.743649i	−0.967007	−	0.254752i	$-0.918006\pi$
$359$	−19.3934	+	14.0901i	−1.02354	+	0.743649i	−0.0565382	+	0.998400i	$0.518006\pi$
$360$		0			0
$361$	−2.84678	−	8.76148i	−0.149830	−	0.461131i
$362$	17.1310			0.900388
$363$	9.33656	−	5.81624i	0.490042	−	0.305274i
$364$	−3.33632			−0.174871
$365$		0			0
$366$	6.62161	+	4.81088i	0.346117	+	0.251469i
$367$	7.17831	−	5.21534i	0.374705	−	0.272239i	−0.384455	−	0.923144i	$-0.625610\pi$
$367$	7.17831	−	5.21534i	0.374705	−	0.272239i	0.759159	+	0.650905i	$0.225610\pi$
$368$	−0.682549	+	2.10067i	−0.0355803	+	0.109505i
$369$	−0.248762	+	0.765612i	−0.0129501	+	0.0398562i
$370$		0			0
$371$	11.9155	+	8.65711i	0.618621	+	0.449455i
$372$	−3.70130	−	11.3914i	−0.191904	−	0.590619i
$373$	26.3389			1.36378			0.681888	−	0.731456i	$-0.261159\pi$
$373$	26.3389			1.36378			0.681888	+	0.731456i	$0.261159\pi$
$374$	−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
$378$	−1.54151	+	1.11997i	−0.0792868	+	0.0576052i
$379$	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	$0.0615145\pi$
$380$		0			0
$381$	−16.7265	+	12.1525i	−0.856926	+	0.622593i
$382$	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	$0.843597\pi$
$384$	−5.22091			−0.266428
$385$		0			0
$386$	6.88892			0.350637
$387$	0.723374	+	2.22631i	0.0367711	+	0.113170i
$388$	1.76933	+	1.28549i	0.0898242	+	0.0652611i
$389$	−1.94538	+	1.41340i	−0.0986348	+	0.0716624i	−0.636009	−	0.771681i	$-0.719416\pi$
$389$	−1.94538	+	1.41340i	−0.0986348	+	0.0716624i	0.537375	+	0.843344i	$0.319416\pi$
$390$		0			0
$391$	−1.26077	+	3.88025i	−0.0637599	+	0.196233i
$392$	−6.69613	+	4.86503i	−0.338206	+	0.245721i
$393$	−16.4302	−	11.9372i	−0.828795	−	0.602155i
$394$	−0.907768	−	2.79382i	−0.0457327	−	0.140751i
$395$		0			0
$396$	−0.133204	+	3.74050i	−0.00669373	+	0.187967i
$397$	−37.6715			−1.89068			−0.945338	−	0.326091i	$-0.894268\pi$
$397$	−37.6715			−1.89068			−0.945338	+	0.326091i	$0.894268\pi$
$398$	−0.939734	−	2.89221i	−0.0471046	−	0.144973i
$399$	−5.16602	−	3.75334i	−0.258625	−	0.187902i
$400$		0			0
$401$	−3.86791	+	11.9042i	−0.193154	+	0.594467i	0.806839	+	0.590771i	$0.201176\pi$
$401$	−3.86791	+	11.9042i	−0.193154	+	0.594467i	−0.999993	+	0.00369578i	$0.998824\pi$
$402$	0.910618	−	2.80259i	0.0454175	−	0.139781i
$403$	−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
$408$	2.53232			0.125368
$409$	−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			0
$411$	−2.81523	+	2.04539i	−0.138865	+	0.100891i
$412$	−4.74298	+	14.5974i	−0.233670	+	0.719162i
$413$	−5.24987	+	16.1574i	−0.258329	+	0.795056i
$414$	−3.55377	+	2.58197i	−0.174658	+	0.126897i
$415$		0			0
$416$	2.41831	+	7.44278i	0.118567	+	0.364912i
$417$	2.73086			0.133731
$418$	9.31304	−	2.66352i	0.455516	−	0.130277i
$419$	30.9711			1.51304			0.756518	−	0.653973i	$-0.226899\pi$
$419$	30.9711			1.51304			0.756518	+	0.653973i	$0.226899\pi$
$420$		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
$423$	−3.20768	+	9.87223i	−0.155963	+	0.480004i
$424$	6.51245	−	20.0432i	0.316272	−	0.973386i
$425$		0			0
$426$	−9.72047	−	7.06233i	−0.470958	−	0.342171i
$427$	−5.52993	−	17.0194i	−0.267612	−	0.823625i
$428$	−11.2746			−0.544979
$429$	4.61873	−	1.32095i	0.222994	−	0.0637763i
$430$		0			0
$431$	9.37829	+	28.8634i	0.451736	+	1.39030i	0.874924	+	0.484260i	$0.160911\pi$
$431$	9.37829	+	28.8634i	0.451736	+	1.39030i	−0.423188	+	0.906042i	$0.639089\pi$
$432$	0.379757	+	0.275910i	0.0182711	+	0.0132747i
$433$	10.2755	−	7.46560i	0.493810	−	0.358774i	−0.312838	−	0.949807i	$-0.601280\pi$
$433$	10.2755	−	7.46560i	0.493810	−	0.358774i	0.806648	+	0.591033i	$0.201280\pi$
$434$	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
$438$	4.24593	+	13.0676i	0.202878	+	0.624395i
$439$	−25.6564			−1.22451			−0.612257	−	0.790659i	$-0.709738\pi$
$439$	−25.6564			−1.22451			−0.612257	+	0.790659i	$0.709738\pi$
$440$		0			0
$441$	−2.83399			−0.134952
$442$	−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	$0.913985\pi$
$444$	−3.79498	+	2.75721i	−0.180102	+	0.130851i
$445$		0			0
$446$	−3.02328	+	9.30470i	−0.143157	+	0.440590i
$447$	7.36886	−	5.35379i	0.348535	−	0.253226i
$448$	−9.87891	−	7.17745i	−0.466735	−	0.339103i
$449$	−3.71010	−	11.4185i	−0.175091	−	0.538873i	0.824547	−	0.565793i	$-0.191430\pi$
$449$	−3.71010	−	11.4185i	−0.175091	−	0.538873i	−0.999638	+	0.0269202i	$0.991430\pi$
$450$		0			0
$451$	−0.0950188	+	2.66823i	−0.00447426	+	0.125642i
$452$	−5.91864			−0.278390
$453$	6.66687	+	20.5185i	0.313237	+	0.964044i
$454$	13.3475	+	9.69752i	0.626429	+	0.455127i
$455$		0			0
$456$	−2.82351	+	8.68986i	−0.132223	+	0.406940i
$457$	−4.26104	+	13.1141i	−0.199323	+	0.613453i	0.800576	+	0.599231i	$0.204527\pi$
$457$	−4.26104	+	13.1141i	−0.199323	+	0.613453i	−0.999899	+	0.0142215i	$0.995473\pi$
$458$	−3.11891	+	2.26602i	−0.145737	+	0.105884i
$459$	0.701468	+	0.509647i	0.0327417	+	0.0237883i
$460$		0			0
$461$	11.3262			0.527515			0.263758	−	0.964589i	$-0.415038\pi$
$461$	11.3262			0.527515			0.263758	+	0.964589i	$0.415038\pi$
$462$	−3.89413	+	4.97718i	−0.181171	+	0.231559i
$463$	−6.18784			−0.287573			−0.143787	−	0.989609i	$-0.545928\pi$
$463$	−6.18784			−0.287573			−0.143787	+	0.989609i	$0.545928\pi$
$464$	−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	$0.162883\pi$
$468$	−0.505115	+	1.55458i	−0.0233490	+	0.0718607i
$469$	−5.21246	+	3.78707i	−0.240689	+	0.174871i
$470$		0			0
$471$	7.35274	+	22.6294i	0.338796	+	1.04271i
$472$	24.3094			1.11893
$473$	4.33705	+	6.43951i	0.199418	+	0.296089i
$474$	−15.8693			−0.728899
$475$		0			0
$476$	−1.61576	−	1.17392i	−0.0740583	−	0.0538065i
$477$	5.83783	−	4.24143i	0.267296	−	0.194202i
$478$	2.30964	−	7.10834i	0.105640	−	0.325128i
$479$	2.85394	−	8.78352i	0.130400	−	0.401329i	−0.864446	−	0.502725i	$-0.832331\pi$
$479$	2.85394	−	8.78352i	0.130400	−	0.401329i	0.994846	+	0.101396i	$0.0323309\pi$
$480$		0			0
$481$	4.87078	+	3.53883i	0.222089	+	0.161357i
$482$	−0.144799	−	0.445645i	−0.00659541	−	0.0202986i
$483$	9.60425			0.437008
$484$	2.98654	+	12.0491i	0.135752	+	0.547686i
$485$		0			0
$486$	0.288477	+	0.887841i	0.0130856	+	0.0402733i
$487$	16.3185	+	11.8561i	0.739461	+	0.537250i	0.892542	−	0.450964i	$-0.148920\pi$
$487$	16.3185	+	11.8561i	0.739461	+	0.537250i	−0.153081	+	0.988214i	$0.548920\pi$
$488$	−20.7158	+	15.0509i	−0.937762	+	0.681324i
$489$	0.557258	−	1.71506i	0.0252001	−	0.0775578i
$490$		0			0
$491$	4.31686	−	3.13638i	0.194817	−	0.141543i	−0.486100	−	0.873903i	$-0.661581\pi$
$491$	4.31686	−	3.13638i	0.194817	−	0.141543i	0.680918	+	0.732360i	$0.261581\pi$
$492$	−0.734969	−	0.533986i	−0.0331350	−	0.0240740i
$493$	−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
$498$	4.63831	+	3.36993i	0.207848	+	0.151010i
$499$	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			0
$501$	7.59792	−	23.3840i	0.339450	−	1.04472i
$502$	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	$0.442889\pi$
$504$	−1.84209	−	5.66936i	−0.0820531	−	0.252533i
$505$		0			0
$506$	−8.97746	+	11.4743i	−0.399097	+	0.510095i
$507$	−10.9020			−0.484176
$508$	−7.21007	−	22.1903i	−0.319895	−	0.984536i
$509$	13.8064	+	10.0309i	0.611958	+	0.444613i	0.850103	−	0.526616i	$-0.176539\pi$
$509$	13.8064	+	10.0309i	0.611958	+	0.444613i	−0.238145	+	0.971229i	$0.576539\pi$
$510$		0			0
$511$	9.28333	−	28.5712i	0.410671	−	1.26391i
$512$	−1.63100	+	5.01971i	−0.0720808	+	0.221842i
$513$	−2.53103	+	1.83890i	−0.111747	+	0.0811893i
$514$	5.57376	+	4.04958i	0.245848	+	0.178619i
$515$		0			0
$516$	−2.64174			−0.116296
$517$	−1.22523	+	34.4057i	−0.0538854	+	1.51316i
$518$	−7.92011			−0.347990
$519$	5.00964	+	15.4181i	0.219899	+	0.676779i
$520$		0			0
$521$	12.1733	−	8.84445i	0.533324	−	0.387482i	−0.288276	−	0.957547i	$-0.593082\pi$
$521$	12.1733	−	8.84445i	0.533324	−	0.387482i	0.821600	+	0.570065i	$0.193082\pi$
$522$	0.588017	−	1.80973i	0.0257368	−	0.0792097i
$523$	11.4465	−	35.2287i	0.500520	−	1.54044i	−0.307653	−	0.951499i	$-0.599544\pi$
$523$	11.4465	−	35.2287i	0.500520	−	1.54044i	0.808173	−	0.588945i	$-0.200456\pi$
$524$	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
$528$	1.46259	+	0.533480i	0.0636508	+	0.0232167i
$529$	−0.858520			−0.0373270
$530$		0			0
$531$	6.73386	+	4.89243i	0.292225	+	0.212314i
$532$	5.82996	−	4.23571i	0.252761	−	0.183641i
$533$	−0.360316	+	1.10894i	−0.0156070	+	0.0480335i
$534$	1.08812	−	3.34888i	0.0470875	−	0.144920i
$535$		0			0
$536$	7.45848	+	5.41890i	0.322157	+	0.234061i
$537$	5.24391	+	16.1391i	0.226292	+	0.696454i
$538$	−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
$543$	−14.8461	+	10.7863i	−0.637108	+	0.462886i
$544$	−1.44765	+	4.45540i	−0.0620674	+	0.191024i
$545$		0			0
$546$	−2.23278	+	1.62221i	−0.0955541	+	0.0694241i
$547$	0.981092	+	0.712805i	0.0419484	+	0.0304773i	0.608562	−	0.793506i	$-0.291747\pi$
$547$	0.981092	+	0.712805i	0.0419484	+	0.0304773i	−0.566613	+	0.823984i	$0.691747\pi$
$548$	−1.21352	−	3.73484i	−0.0518391	−	0.159544i
$549$	−8.76752			−0.374189
$550$		0			0
$551$	6.37702			0.271670
$552$	−4.24672	−	13.0701i	−0.180752	−	0.556298i
$553$	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	$0.286924\pi$
$558$	−8.01586	−	5.82386i	−0.339338	−	0.246544i
$559$	1.04776	+	3.22467i	0.0443155	+	0.136389i
$560$		0			0
$561$	2.70162	+	0.985418i	0.114062	+	0.0416044i
$562$	−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	$0.754115\pi$
$564$	−9.47710	−	6.88552i	−0.399058	−	0.289933i
$565$		0			0
$566$	7.43590	−	22.8853i	0.312554	−	0.961943i
$567$	0.630728	−	1.94118i	0.0264881	−	0.0815220i
$568$	30.4107	−	22.0946i	1.27600	−	0.927071i
$569$	31.8556	+	23.1444i	1.33546	+	0.970265i	0.999598	+	0.0283521i	$0.00902596\pi$
$569$	31.8556	+	23.1444i	1.33546	+	0.970265i	0.335857	+	0.941913i	$0.390974\pi$
$570$		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
$573$	−15.3985			−0.643282
$574$	−0.473995	−	1.45881i	−0.0197842	−	0.0608894i
$575$		0			0
$576$	−4.84004	+	3.51650i	−0.201668	+	0.146521i
$577$	10.7241	−	33.0053i	0.446448	−	1.37403i	−0.434439	−	0.900701i	$-0.643053\pi$
$577$	10.7241	−	33.0053i	0.446448	−	1.37403i	0.880887	−	0.473326i	$-0.156947\pi$
$578$	−4.68723	+	14.4258i	−0.194963	+	0.600035i
$579$	−5.97007	+	4.33751i	−0.248108	+	0.180261i
$580$		0			0
$581$	−3.87361	−	11.9217i	−0.160704	−	0.494597i
$582$	1.80914			0.0749911
$583$	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	$0.246826\pi$
$588$	0.988303	−	3.04168i	0.0407569	−	0.125437i
$589$	10.2609	−	31.5797i	0.422792	−	1.30122i
$590$		0			0
$591$	2.54578	+	1.84962i	0.104719	+	0.0760832i
$592$	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	$0.303909\pi$
$594$	1.72959	+	2.56804i	0.0709658	+	0.105368i
$595$		0			0
$596$	3.17639	+	9.77593i	0.130110	+	0.400438i
$597$	2.63543	+	1.91475i	0.107861	+	0.0783656i
$598$	−5.14741	+	3.73981i	−0.210493	+	0.152932i
$599$	−8.83751	+	27.1991i	−0.361091	+	1.11132i	0.591302	+	0.806450i	$0.298614\pi$
$599$	−8.83751	+	27.1991i	−0.361091	+	1.11132i	−0.952393	+	0.304873i	$0.901386\pi$
$600$		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
$603$	0.975455	+	3.00214i	0.0397236	+	0.122257i
$604$	−24.3472			−0.990672
$605$		0			0
$606$	−4.90268			−0.199158
$607$	1.65258	+	5.08611i	0.0670761	+	0.206439i	0.978977	−	0.203972i	$-0.0653852\pi$
$607$	1.65258	+	5.08611i	0.0670761	+	0.206439i	−0.911901	+	0.410411i	$0.865385\pi$
$608$	−13.6750	−	9.93545i	−0.554593	−	0.402936i
$609$	−3.36586	+	2.44544i	−0.136392	+	0.0990943i
$610$		0			0
$611$	−4.64612	+	14.2993i	−0.187962	+	0.578487i
$612$	−0.791621	+	0.575146i	−0.0319994	+	0.0232489i
$613$	−3.75464	−	2.72790i	−0.151648	−	0.110179i	0.509374	−	0.860545i	$-0.329877\pi$
$613$	−3.75464	−	2.72790i	−0.151648	−	0.110179i	−0.661022	+	0.750366i	$0.729877\pi$
$614$	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	$0.664782\pi$
$618$	3.92348	+	12.0752i	0.157825	+	0.485737i
$619$	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	$0.660636\pi$
$620$		0			0
$621$	1.45407	−	4.47517i	0.0583499	−	0.179582i
$622$	0.549027	−	1.68973i	0.0220140	−	0.0677521i
$623$	−6.22849	+	4.52526i	−0.249539	+	0.181301i
$624$	0.550053	+	0.399637i	0.0220197	+	0.0159983i
$625$		0			0
$626$	−10.2057			−0.407902
$627$	−6.39382	+	8.17209i	−0.255344	+	0.326362i
$628$	−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
$633$	6.15690	−	18.9490i	0.244715	−	0.753155i
$634$	−12.1385	+	8.81910i	−0.482080	+	0.350251i
$635$		0			0
$636$	2.51643	+	7.74479i	0.0997831	+	0.307101i
$637$	−4.10485			−0.162640
$638$	0.224603	−	6.30708i	0.00889210	−	0.249700i
$639$	12.8707			0.509155
$640$		0			0
$641$	−32.2492	−	23.4304i	−1.27377	−	0.925444i	−0.274419	−	0.961610i	$-0.588486\pi$
$641$	−32.2492	−	23.4304i	−1.27377	−	0.925444i	−0.999346	+	0.0361657i	$0.988486\pi$
$642$	−7.54535	+	5.48202i	−0.297791	+	0.216358i
$643$	5.52097	−	16.9918i	0.217726	−	0.670091i	−0.781223	−	0.624252i	$-0.785404\pi$
$643$	5.52097	−	16.9918i	0.217726	−	0.670091i	0.998949	−	0.0458392i	$-0.0145962\pi$
$644$	−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	$0.931592\pi$
$648$	−2.92057			−0.114731
$649$	25.9346	+	9.45968i	1.01802	+	0.371325i
$650$		0			0
$651$	6.69431	+	20.6030i	0.262371	+	0.807494i
$652$	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	$0.00653963\pi$
$654$	−1.94775	+	5.99455i	−0.0761630	+	0.234406i
$655$		0			0
$656$	−0.305709	+	0.222111i	−0.0119359	+	0.00867196i
$657$	−11.9075	−	8.65128i	−0.464554	−	0.337519i
$658$	−6.11196	−	18.8107i	−0.238269	−	0.733316i
$659$	48.7556			1.89925			0.949624	−	0.313390i	$-0.101465\pi$
$659$	48.7556			1.89925			0.949624	+	0.313390i	$0.101465\pi$
$660$		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
$663$	1.01603	+	0.738190i	0.0394594	+	0.0286689i
$664$	−14.5110	+	10.5429i	−0.563137	+	0.409143i
$665$		0			0
$666$	−1.19909	+	3.69043i	−0.0464640	+	0.143001i
$667$	−7.75960	+	5.63768i	−0.300453	+	0.218292i
$668$	22.4481	+	16.3095i	0.868542	+	0.631033i
$669$	−3.23854	−	9.96721i	−0.125209	−	0.385355i
$670$		0			0
$671$	−27.9577	+	7.99587i	−1.07929	+	0.308677i
$672$	11.0278			0.425408
$673$	9.42305	+	29.0012i	0.363232	+	1.11791i	0.951081	+	0.308942i	$0.0999750\pi$
$673$	9.42305	+	29.0012i	0.363232	+	1.11791i	−0.587849	+	0.808971i	$0.700025\pi$
$674$	−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	$-0.214424\pi$
$678$	−3.96095	+	2.87780i	−0.152120	+	0.110521i
$679$	−3.20007	−	2.32499i	−0.122808	−	0.0892249i
$680$		0			0
$681$	−17.6731			−0.677235
$682$	−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	$0.185990\pi$
$684$	−1.09101	−	3.35779i	−0.0417160	−	0.128388i
$685$		0			0
$686$	15.1592	−	11.0138i	0.578781	−	0.420509i
$687$	1.27614	−	3.92755i	0.0486878	−	0.149846i
$688$	−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
$693$	0.240917	−	6.76521i	0.00915167	−	0.256989i
$694$	2.91900			0.110804
$695$		0			0
$696$	4.81619	+	3.49917i	0.182557	+	0.132636i
$697$	−0.564690	+	0.410272i	−0.0213892	+	0.0155401i
$698$	3.78704	−	11.6553i	0.143342	−	0.441160i
$699$	−4.20231	+	12.9334i	−0.158946	+	0.489186i
$700$		0			0
$701$	−7.35189	−	5.34146i	−0.277677	−	0.201744i	0.440226	−	0.897887i	$-0.354898\pi$
$701$	−7.35189	−	5.34146i	−0.277677	−	0.201744i	−0.717904	+	0.696143i	$0.754898\pi$
$702$	0.417840	+	1.28598i	0.0157704	+	0.0485362i
$703$	−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
$708$	−7.59929	+	5.52121i	−0.285599	+	0.207500i
$709$	−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	$0.129064\pi$
$710$		0			0
$711$	13.7526	−	9.99186i	0.515764	−	0.374724i
$712$	8.91231	+	6.47517i	0.334003	+	0.242667i
$713$	15.4330	+	47.4977i	0.577969	+	1.77880i
$714$	−1.65211			−0.0618287
$715$		0			0
$716$	−19.1506			−0.715691
$717$	2.47409	+	7.61447i	0.0923966	+	0.284367i
$718$	−18.1043	−	13.1536i	−0.675648	−	0.490887i
$719$	−19.3383	+	14.0501i	−0.721196	+	0.523980i	−0.886766	−	0.462218i	$-0.847054\pi$
$719$	−19.3383	+	14.0501i	−0.721196	+	0.523980i	0.165570	+	0.986198i	$0.447054\pi$
$720$		0			0
$721$	8.57832	−	26.4014i	0.319473	−	0.983238i
$722$	6.95757	−	5.05497i	0.258934	−	0.188127i
$723$	0.406080	+	0.295035i	0.0151023	+	0.0109725i
$724$	−6.39951	−	19.6957i	−0.237836	−	0.731983i
$725$		0			0
$726$	7.85728	+	6.61153i	0.291611	+	0.245377i
$727$	11.3674			0.421592			0.210796	−	0.977530i	$-0.432394\pi$
$727$	11.3674			0.421592			0.210796	+	0.977530i	$0.432394\pi$
$728$	−2.66814	−	8.21170i	−0.0988879	−	0.304346i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−0.627210	+	1.93035i	−0.0231982	+	0.0713967i
$732$	3.05751	−	9.41006i	0.113009	−	0.347806i
$733$	−27.6019	+	20.0539i	−1.01950	+	0.740709i	−0.966180	−	0.257869i	$-0.916980\pi$
$733$	−27.6019	+	20.0539i	−1.01950	+	0.740709i	−0.0533185	+	0.998578i	$0.516980\pi$
$734$	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
$738$	−0.751504			−0.0276632
$739$	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	$0.886305\pi$
$740$		0			0
$741$	−3.66602	+	2.66352i	−0.134675	+	0.0978470i
$742$	−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	$0.185625\pi$
$744$	25.0778	−	18.2201i	0.919395	−	0.667980i
$745$		0			0
$746$	7.59817	+	23.3848i	0.278189	+	0.856177i
$747$	−6.14148			−0.224705
$748$	−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
$753$	−5.72933	+	17.6331i	−0.208788	+	0.642585i
$754$	0.851704	−	2.62128i	0.0310172	−	0.0954612i
$755$		0			0
$756$	1.86349	+	1.35390i	0.0677744	+	0.0492410i
$757$	−12.4774	−	38.4015i	−0.453499	−	1.39573i	−0.872888	−	0.487921i	$-0.837756\pi$
$757$	−12.4774	−	38.4015i	−0.453499	−	1.39573i	0.419389	−	0.907807i	$-0.362244\pi$
$758$	4.38396			0.159233
$759$	0.555406	−	15.5964i	0.0201600	−	0.566114i
$760$		0			0
$761$	−15.4190	−	47.4549i	−0.558940	−	1.72024i	−0.685304	−	0.728257i	$-0.740331\pi$
$761$	−15.4190	−	47.4549i	−0.558940	−	1.72024i	0.126364	−	0.991984i	$-0.459669\pi$
$762$	−15.6147	−	11.3448i	−0.565662	−	0.410978i
$763$	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
$768$	−5.20358	−	16.0150i	−0.187768	−	0.577890i
$769$	4.93932			0.178116			0.0890582	−	0.996026i	$-0.471614\pi$
$769$	4.93932			0.178116			0.0890582	+	0.996026i	$0.471614\pi$
$770$		0			0
$771$	−7.38010			−0.265788
$772$	−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	$0.905603\pi$
$774$	−1.76794	+	1.28448i	−0.0635472	+	0.0461697i
$775$		0			0
$776$	−1.74901	+	5.38290i	−0.0627858	+	0.193235i
$777$	6.86373	−	4.98679i	0.246235	−	0.178900i
$778$	−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
$783$	0.629885	+	1.93859i	0.0225102	+	0.0692794i
$784$	−1.07623	−	0.781926i	−0.0384367	−	0.0279259i
$785$		0			0
$786$	5.85864	−	18.0310i	0.208971	−	0.643146i
$787$	−8.01590	+	24.6704i	−0.285736	+	0.879405i	0.700441	+	0.713710i	$0.252987\pi$
$787$	−8.01590	+	24.6704i	−0.285736	+	0.879405i	−0.986177	+	0.165695i	$0.947013\pi$
$788$	−2.87296	+	2.08733i	−0.102345	+	0.0743581i
$789$	−2.47519	−	1.79833i	−0.0881191	−	0.0640222i
$790$		0			0
$791$	10.7047			0.380614
$792$	−9.31304	+	2.66352i	−0.330924	+	0.0946442i
$793$	−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	$0.155888\pi$
$798$	1.84209	−	5.66936i	0.0652092	−	0.200693i
$799$	−7.28144	+	5.29027i	−0.257599	+	0.187156i
$800$		0			0
$801$	1.16559	+	3.58733i	0.0411842	+	0.126752i
$802$	−11.6848			−0.412606
$803$	−45.8601	−	16.7275i	−1.61837	−	0.590301i
$804$	−3.56233			−0.125634
$805$		0			0
$806$	−11.6104	−	8.43548i	−0.408960	−	0.297127i
$807$	14.3035	−	10.3921i	0.503507	−	0.365819i
$808$	4.73974	−	14.5874i	0.166744	−	0.513184i
$809$	−10.2158	+	31.4410i	−0.359168	+	1.10541i	0.594385	+	0.804181i	$0.297396\pi$
$809$	−10.2158	+	31.4410i	−0.359168	+	1.10541i	−0.953553	+	0.301225i	$0.902604\pi$
$810$		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
$813$	−15.2992			−0.536565
$814$	−0.458013	+	12.8615i	−0.0160534	+	0.450796i
$815$		0			0
$816$	0.125771	+	0.387084i	0.00440287	+	0.0135506i
$817$	−5.92484	−	4.30465i	−0.207284	−	0.150601i
$818$	19.9854	−	14.5202i	0.698773	−	0.507689i
$819$	0.913569	−	2.81168i	0.0319227	−	0.0982479i
$820$		0			0
$821$	1.32625	−	0.963576i	0.0462864	−	0.0336290i	−0.564401	−	0.825500i	$-0.690893\pi$
$821$	1.32625	−	0.963576i	0.0462864	−	0.0336290i	0.610688	+	0.791871i	$0.290893\pi$
$822$	−2.62811	−	1.90943i	−0.0916657	−	0.0665991i
$823$	5.52814	+	17.0139i	0.192699	+	0.593066i	0.999996	+	0.00292037i	$0.000929584\pi$
$823$	5.52814	+	17.0139i	0.192699	+	0.593066i	−0.807297	+	0.590145i	$0.799070\pi$
$824$	−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	$-0.312061\pi$
$828$	4.29606	+	3.12127i	0.149298	+	0.108472i
$829$	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	$0.144965\pi$
$830$		0			0
$831$	5.50785	−	16.9514i	0.191065	−	0.588038i
$832$	−7.01049	+	5.09342i	−0.243045	+	0.176582i
$833$	−1.98796	−	1.44433i	−0.0688786	−	0.0500432i
$834$	0.787791	+	2.42457i	0.0272790	+	0.0839560i
$835$		0			0
$836$	−6.54126	−	9.71226i	−0.226234	−	0.335905i
$837$	10.6136			0.366860
$838$	8.93444	+	27.4974i	0.308635	+	0.949881i
$839$	9.57654	+	6.95776i	0.330619	+	0.240209i	0.740693	−	0.671843i	$-0.234497\pi$
$839$	9.57654	+	6.95776i	0.330619	+	0.240209i	−0.410074	+	0.912052i	$0.634497\pi$
$840$		0			0
$841$	−7.67757	+	23.6291i	−0.264744	+	0.814797i
$842$	5.26282	−	16.1973i	0.181369	−	0.558195i
$843$	13.9952	−	10.1681i	0.482019	−	0.350207i
$844$	18.1906	+	13.2162i	0.626146	+	0.454922i
$845$		0			0
$846$	−9.69031			−0.333160
$847$	−5.40155	−	21.7924i	−0.185600	−	0.748797i
$848$	3.38721			0.116317
$849$	7.96534	+	24.5148i	0.273370	+	0.841346i
$850$		0			0
$851$	15.8235	−	11.4965i	0.542423	−	0.394094i
$852$	−4.48840	+	13.8139i	−0.153770	+	0.473256i
$853$	9.36453	−	28.8211i	0.320635	−	0.986814i	−0.652737	−	0.757585i	$-0.726379\pi$
$853$	9.36453	−	28.8211i	0.320635	−	0.986814i	0.973372	−	0.229230i	$-0.0736207\pi$
$854$	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	$0.333602\pi$
$858$	2.50519	+	3.71963i	0.0855259	+	0.126986i
$859$	−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			0
$861$	1.32929	+	0.965786i	0.0453021	+	0.0329139i
$862$	−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	$0.834034\pi$
$864$	1.66960	−	5.13850i	0.0568009	−	0.174815i
$865$		0			0
$866$	9.59252	+	6.96937i	0.325967	+	0.236829i
$867$	−5.02097	−	15.4530i	−0.170521	−	0.524810i
$868$	−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
$873$	−1.56783	+	1.13910i	−0.0530631	+	0.0385526i
$874$	4.24672	−	13.0701i	0.143647	−	0.442101i
$875$		0			0
$876$	13.4378	−	9.76314i	0.454021	−	0.329866i
$877$	−8.99407	−	6.53457i	−0.303708	−	0.220657i	0.425484	−	0.904966i	$-0.360104\pi$
$877$	−8.99407	−	6.53457i	−0.303708	−	0.220657i	−0.729192	+	0.684309i	$0.760104\pi$
$878$	−7.40129	−	22.7788i	−0.249781	−	0.768748i
$879$	−13.5306			−0.456377
$880$		0			0
$881$	−39.1155			−1.31783			−0.658917	−	0.752216i	$-0.728985\pi$
$881$	−39.1155			−1.31783			−0.658917	+	0.752216i	$0.728985\pi$
$882$	−0.817542	−	2.51613i	−0.0275281	−	0.0847227i
$883$	15.7910	+	11.4728i	0.531408	+	0.386091i	0.820884	−	0.571094i	$-0.193481\pi$
$883$	15.7910	+	11.4728i	0.531408	+	0.386091i	−0.289476	+	0.957185i	$0.593481\pi$
$884$	−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	$0.327776\pi$
$888$	−9.82127	−	7.13557i	−0.329580	−	0.239454i
$889$	13.0404	+	40.1342i	0.437361	+	1.34606i
$890$		0			0
$891$	−3.11582	−	1.13650i	−0.104384	−	0.0380742i
$892$	11.8270			0.395999
$893$	−10.0353	−	30.8855i	−0.335818	−	1.03354i
$894$	6.87906	+	4.99793i	0.230070	+	0.167156i
$895$		0			0
$896$	−3.29298	+	10.1347i	−0.110011	+	0.338578i
$897$	2.10613	−	6.48199i	0.0703215	−	0.216427i
$898$	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
$903$	4.77794			0.159000
$904$	−4.73329	−	14.5676i	−0.157427	−	0.484510i
$905$		0			0
$906$	−16.2939	+	11.8382i	−0.541330	+	0.393299i
$907$	13.1140	−	40.3608i	0.435444	−	1.34016i	−0.457187	−	0.889371i	$-0.651143\pi$
$907$	13.1140	−	40.3608i	0.435444	−	1.34016i	0.892631	−	0.450789i	$-0.148857\pi$
$908$	6.16318	−	18.9683i	0.204532	−	0.629485i
$909$	4.24876	−	3.08691i	0.140923	−	0.102386i
$910$		0			0
$911$	−6.10306	−	18.7833i	−0.202203	−	0.622318i	−0.999817	−	0.0191487i	$-0.993904\pi$
$911$	−6.10306	−	18.7833i	−0.202203	−	0.622318i	0.797613	−	0.603169i	$-0.206096\pi$
$912$	−1.46854			−0.0486283
$913$	−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
$918$	−0.250128	+	0.769814i	−0.00825544	+	0.0254076i
$919$	−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	$0.967672\pi$
$920$		0			0
$921$	−10.5389	−	7.65695i	−0.347268	−	0.252305i
$922$	3.26736	+	10.0559i	0.107605	+	0.331173i
$923$	18.6423			0.613619
$924$	7.17699	+	2.61781i	0.236105	+	0.0861198i
$925$		0			0
$926$	−1.78505	−	5.49382i	−0.0586604	−	0.180538i
$927$	−11.0032	−	7.99426i	−0.361391	−	0.262566i
$928$	−8.90976	+	6.47332i	−0.292477	+	0.212497i
$929$	−1.87044	+	5.75664i	−0.0613673	+	0.188869i	−0.977040	−	0.213055i	$-0.931659\pi$
$929$	−1.87044	+	5.75664i	−0.0613673	+	0.188869i	0.915673	+	0.401924i	$0.131659\pi$
$930$		0			0
$931$	7.17291	−	5.21142i	0.235083	−	0.170797i
$932$	−12.4157	−	9.02056i	−0.406691	−	0.295478i
$933$	0.588119	+	1.81004i	0.0192541	+	0.0592582i
$934$	−7.91903			−0.259119
$935$		0			0
$936$	−4.23026			−0.138270
$937$	−2.11326	−	6.50394i	−0.0690372	−	0.212475i	0.910586	−	0.413320i	$-0.135631\pi$
$937$	−2.11326	−	6.50394i	−0.0690372	−	0.212475i	−0.979623	+	0.200846i	$0.935631\pi$
$938$	−4.86599	−	3.53535i	−0.158880	−	0.115433i
$939$	8.84448	−	6.42589i	0.288629	−	0.209701i
$940$		0			0
$941$	−1.22191	+	3.76064i	−0.0398330	+	0.122593i	−0.968996	−	0.247078i	$-0.920530\pi$
$941$	−1.22191	+	3.76064i	−0.0398330	+	0.122593i	0.929163	+	0.369671i	$0.120530\pi$
$942$	−17.9702	+	13.0561i	−0.585501	+	0.425391i
$943$	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	$0.273618\pi$
$948$	5.92815	+	18.2450i	0.192537	+	0.592569i
$949$	−17.2472	−	12.5308i	−0.559867	−	0.406767i
$950$		0			0
$951$	4.96660	−	15.2856i	0.161053	−	0.495670i
$952$	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	$0.532876\pi$
$954$	5.44980	+	3.95951i	0.176444	+	0.128194i
$955$		0			0
$956$	−9.03529			−0.292222
$957$	3.77652	+	5.60726i	0.122078	+	0.181257i
$958$	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
$963$	3.08727	−	9.50166i	0.0994860	−	0.306187i
$964$	−0.458269	+	0.332952i	−0.0147599	+	0.0107237i
$965$		0			0
$966$	2.77060	+	8.52704i	0.0891427	+	0.274353i
$967$	−9.16826			−0.294831			−0.147416	−	0.989075i	$-0.547096\pi$
$967$	−9.16826			−0.294831			−0.147416	+	0.989075i	$0.547096\pi$
$968$	−27.2681	+	16.9867i	−0.876429	+	0.545975i
$969$	−2.71262			−0.0871420
$970$		0			0
$971$	3.00359	+	2.18224i	0.0963899	+	0.0700313i	0.634936	−	0.772565i	$-0.281026\pi$
$971$	3.00359	+	2.18224i	0.0963899	+	0.0700313i	−0.538546	+	0.842596i	$0.681026\pi$
$972$	0.912991	−	0.663327i	0.0292842	−	0.0212762i
$973$	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	$0.963525\pi$
$978$	1.68346			0.0538311
$979$	6.98842	+	10.3762i	0.223351	+	0.331624i
$980$		0			0
$981$	−2.08643	−	6.42137i	−0.0666146	−	0.205019i
$982$	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	$0.178845\pi$
$984$	0.726528	−	2.23602i	0.0231609	−	0.0712818i
$985$		0			0
$986$	1.33480	−	0.969788i	0.0425086	−	0.0308843i
$987$	17.1406	+	12.4534i	0.545592	+	0.396396i
$988$	−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
$993$	−1.12922	−	0.820424i	−0.0358346	−	0.0260354i
$994$	−19.8403	+	14.4148i	−0.629295	+	0.457209i
$995$		0			0
$996$	2.14173	−	6.59156i	0.0678633	−	0.208862i
$997$	6.37174	−	4.62934i	0.201795	−	0.146613i	−0.482299	−	0.876007i	$-0.660198\pi$
$997$	6.37174	−	4.62934i	0.201795	−	0.146613i	0.684094	+	0.729394i	$0.260198\pi$
$998$	29.6671	+	21.5544i	0.939097	+	0.682294i
$999$	−1.28447	−	3.95320i	−0.0406389	−	0.125074i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.16.1	✓	8	5.4	even	2
165.2.m.b.31.1	yes	8	55.9	even	10
495.2.n.b.181.2		8	15.14	odd	2
495.2.n.b.361.2		8	165.119	odd	10
825.2.n.i.526.2		8	11.9	even	5	inner
825.2.n.i.676.2		8	1.1	even	1	trivial
825.2.bx.g.49.2		16	5.2	odd	4
825.2.bx.g.49.3		16	5.3	odd	4
825.2.bx.g.724.2		16	55.53	odd	20
825.2.bx.g.724.3		16	55.42	odd	20
1815.2.a.r.1.3		4	55.19	odd	10
1815.2.a.v.1.2		4	55.14	even	10
5445.2.a.bk.1.3		4	165.14	odd	10
5445.2.a.br.1.2		4	165.74	even	10
9075.2.a.cq.1.3		4	11.3	even	5
9075.2.a.dg.1.2		4	11.8	odd	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.288477 + 0.887841i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.912991 - 0.663327i) q^{4} +(0.288477 - 0.887841i) q^{6} +(-1.65127 + 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.288477 + 0.887841i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.912991 - 0.663327i) q^{4} +(0.288477 - 0.887841i) q^{6} +(-1.65127 + 1.19972i) q^{7} +(2.36279 + 1.71667i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.85274 + 2.75088i) q^{11} -1.12852 q^{12} +(0.447591 + 1.37754i) q^{13} +(-1.54151 - 1.11997i) q^{14} +(-0.145054 + 0.446431i) q^{16} +(-0.267937 + 0.824626i) q^{17} +(-0.755243 + 0.548716i) q^{18} +(-2.53103 - 1.83890i) q^{19} +2.04108 q^{21} +(-1.90788 + 2.43850i) q^{22} +4.70547 q^{23} +(-0.902506 - 2.77763i) q^{24} +(-1.09392 + 0.794779i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.711789 + 2.19066i) q^{28} +(-1.64906 + 1.19811i) q^{29} +(3.27979 + 10.0941i) q^{31} +5.40294 q^{32} +(0.118034 - 3.31452i) q^{33} -0.809430 q^{34} +(0.912991 + 0.663327i) q^{36} +(3.36279 - 2.44321i) q^{37} +(0.902506 - 2.77763i) q^{38} +(0.447591 - 1.37754i) q^{39} +(0.651268 + 0.473174i) q^{41} +(0.588805 + 1.81215i) q^{42} +2.34089 q^{43} +(3.51627 + 1.28256i) q^{44} +(1.35742 + 4.17771i) q^{46} +(8.39782 + 6.10137i) q^{47} +(0.379757 - 0.275910i) q^{48} +(-0.875752 + 2.69529i) q^{49} +(0.701468 - 0.509647i) q^{51} +(1.32241 + 0.960786i) q^{52} +(-2.22985 - 6.86278i) q^{53} +0.933531 q^{54} -5.96112 q^{56} +(0.966766 + 2.97540i) q^{57} +(-1.53945 - 1.11847i) q^{58} +(6.73386 - 4.89243i) q^{59} +(-2.70931 + 8.33841i) q^{61} +(-8.01586 + 5.82386i) q^{62} +(-1.65127 - 1.19972i) q^{63} +(1.84873 + 5.68981i) q^{64} +(2.97682 - 0.851369i) q^{66} +3.15664 q^{67} +(0.302372 + 0.930606i) q^{68} +(-3.80681 - 2.76581i) q^{69} +(3.97725 - 12.2407i) q^{71} +(-0.902506 + 2.77763i) q^{72} +(-11.9075 + 8.65128i) q^{73} +(3.13927 + 2.28081i) q^{74} -3.53059 q^{76} +(-6.35965 - 2.31969i) q^{77} +1.35216 q^{78} +(-5.25303 - 16.1672i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.232227 + 0.714723i) q^{82} +(-1.89782 + 5.84089i) q^{83} +(1.86349 - 1.35390i) q^{84} +(0.675292 + 2.07833i) q^{86} +2.03835 q^{87} +(-0.344727 + 9.68030i) q^{88} +3.77194 q^{89} +(-2.39175 - 1.73771i) q^{91} +(4.29606 - 3.12127i) q^{92} +(3.27979 - 10.0941i) q^{93} +(-2.99447 + 9.21604i) q^{94} +(-4.37107 - 3.17577i) q^{96} +(0.598859 + 1.84310i) q^{97} -2.64562 q^{98} +(-2.04372 + 2.61213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 9 q^{7} + 19 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 9 * q^7 + 19 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} - 9 q^{7} + 19 q^{8} - 2 q^{9} - 3 q^{11} + 18 q^{12} - 10 q^{13} + 24 q^{14} + 4 q^{16} + 2 q^{17} + 3 q^{18} - 2 q^{19} + 16 q^{21} + 7 q^{22} + 2 q^{23} - 16 q^{24} + 14 q^{26} - 2 q^{27} - 13 q^{28} + 14 q^{29} - 5 q^{31} + 16 q^{32} - 8 q^{33} - 70 q^{34} - 2 q^{36} + 27 q^{37} + 16 q^{38} - 10 q^{39} + q^{41} - 31 q^{42} + 28 q^{43} + 47 q^{44} + 42 q^{46} + 27 q^{47} - 11 q^{48} - 15 q^{49} - 8 q^{51} - 22 q^{52} + q^{53} - 2 q^{54} - 24 q^{56} + 3 q^{57} - 18 q^{58} + 13 q^{59} - 3 q^{61} - 15 q^{62} - 9 q^{63} + 19 q^{64} + 37 q^{66} - 10 q^{67} + 33 q^{68} - 3 q^{69} + 9 q^{71} - 16 q^{72} - 5 q^{73} - 17 q^{74} - 46 q^{76} - q^{77} - 36 q^{78} - 10 q^{79} - 2 q^{81} + 33 q^{82} + 25 q^{83} - 18 q^{84} + 20 q^{86} + 34 q^{87} - 29 q^{88} + 4 q^{89} - 43 q^{91} + 22 q^{92} - 5 q^{93} + 57 q^{94} + 6 q^{96} - 13 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 - 9 * q^7 + 19 * q^8 - 2 * q^9 - 3 * q^11 + 18 * q^12 - 10 * q^13 + 24 * q^14 + 4 * q^16 + 2 * q^17 + 3 * q^18 - 2 * q^19 + 16 * q^21 + 7 * q^22 + 2 * q^23 - 16 * q^24 + 14 * q^26 - 2 * q^27 - 13 * q^28 + 14 * q^29 - 5 * q^31 + 16 * q^32 - 8 * q^33 - 70 * q^34 - 2 * q^36 + 27 * q^37 + 16 * q^38 - 10 * q^39 + q^41 - 31 * q^42 + 28 * q^43 + 47 * q^44 + 42 * q^46 + 27 * q^47 - 11 * q^48 - 15 * q^49 - 8 * q^51 - 22 * q^52 + q^53 - 2 * q^54 - 24 * q^56 + 3 * q^57 - 18 * q^58 + 13 * q^59 - 3 * q^61 - 15 * q^62 - 9 * q^63 + 19 * q^64 + 37 * q^66 - 10 * q^67 + 33 * q^68 - 3 * q^69 + 9 * q^71 - 16 * q^72 - 5 * q^73 - 17 * q^74 - 46 * q^76 - q^77 - 36 * q^78 - 10 * q^79 - 2 * q^81 + 33 * q^82 + 25 * q^83 - 18 * q^84 + 20 * q^86 + 34 * q^87 - 29 * q^88 + 4 * q^89 - 43 * q^91 + 22 * q^92 - 5 * q^93 + 57 * q^94 + 6 * q^96 - 13 * q^97 + 2 * q^98 - 3 * q^99

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