LMFDB - Embedded newform 1008.2.t.i.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$-1.02682 - 1.77851i$ of defining polynomial
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.i.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09995 + 1.33795i) q^{3} -0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +(-0.580240 - 2.94335i) q^{9} +O(q^{10})$	\(q+(-1.09995 + 1.33795i) q^{3} -0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +(-0.580240 - 2.94335i) q^{9} -1.66404 q^{11} +(0.0999454 + 0.173111i) q^{13} +(0.160862 - 0.195670i) q^{15} +(3.13555 + 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} +(3.62652 + 2.80149i) q^{21} +6.18184 q^{23} -4.97861 q^{25} +(4.57630 + 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-1.25890 + 2.18047i) q^{31} +(1.83035 - 2.22641i) q^{33} +(0.0117348 + 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(-0.341548 - 0.0566898i) q^{39} +(1.15895 + 2.00736i) q^{41} +(0.940993 - 1.62985i) q^{43} +(0.0848576 + 0.430452i) q^{45} +(-0.905887 - 1.56904i) q^{47} +(-6.98712 + 0.424396i) q^{49} +(-10.7153 - 1.77851i) q^{51} +(-2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-2.28549 + 3.95859i) q^{59} +(0.339138 + 0.587404i) q^{61} +(-7.73724 + 1.77064i) q^{63} +(-0.0146166 - 0.0253167i) q^{65} +(-3.09342 + 5.35796i) q^{67} +(-6.79968 + 8.27101i) q^{69} -1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(5.47620 - 6.66115i) q^{75} +(0.133523 + 4.40061i) q^{77} +(6.39787 + 11.0814i) q^{79} +(-8.32664 + 3.41570i) q^{81} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-3.00417 - 8.00262i) q^{87} +(4.53394 - 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +(-1.53266 - 4.08275i) q^{93} +(0.505833 - 0.876128i) q^{95} +(-3.98514 + 6.90246i) q^{97} +(0.965543 + 4.89786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	−1.09995	+	1.33795i	−0.635054	+	0.772468i
$3$	−1.09995	+	1.33795i	−0.635054	+	0.772468i
$4$		0			0
$5$	−0.146246			−0.0654030			−0.0327015	−	0.999465i	$-0.510411\pi$
$5$	−0.146246			−0.0654030			−0.0327015	+	0.999465i	$0.510411\pi$
$6$		0			0
$7$	−0.0802402	−	2.64453i	−0.0303280	−	0.999540i
$7$	−0.0802402	−	2.64453i	−0.0303280	−	0.999540i
$8$		0			0
$9$	−0.580240	−	2.94335i	−0.193413	−	0.981117i
$10$		0			0
$11$	−1.66404			−0.501727			−0.250864	−	0.968022i	$-0.580715\pi$
$11$	−1.66404			−0.501727			−0.250864	+	0.968022i	$0.580715\pi$
$12$		0			0
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$		0			0
$15$	0.160862	−	0.195670i	0.0415345	−	0.0505218i
$16$		0			0
$17$	3.13555	+	5.43093i	0.760483	+	1.31720i	0.942602	+	0.333919i	$0.108371\pi$
$17$	3.13555	+	5.43093i	0.760483	+	1.31720i	−0.182119	+	0.983277i	$0.558296\pi$
$18$		0			0
$19$	−3.45879	+	5.99080i	−0.793500	+	1.37438i	0.130287	+	0.991476i	$0.458410\pi$
$19$	−3.45879	+	5.99080i	−0.793500	+	1.37438i	−0.923787	+	0.382907i	$0.874923\pi$
$20$		0			0
$21$	3.62652	+	2.80149i	0.791372	+	0.611334i
$22$		0			0
$23$	6.18184			1.28900			0.644501	−	0.764604i	$-0.277065\pi$
$23$	6.18184			1.28900			0.644501	+	0.764604i	$0.277065\pi$
$24$		0			0
$25$	−4.97861			−0.995722
$26$		0			0
$27$	4.57630	+	2.46119i	0.880710	+	0.473657i
$28$		0			0
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	−0.998867	−	0.0475930i	$-0.984845\pi$
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	0.540650	+	0.841248i	$0.318178\pi$
$30$		0			0
$31$	−1.25890	+	2.18047i	−0.226105	+	0.391625i	−0.956650	−	0.291239i	$-0.905932\pi$
$31$	−1.25890	+	2.18047i	−0.226105	+	0.391625i	0.730546	+	0.682864i	$0.239266\pi$
$32$		0			0
$33$	1.83035	−	2.22641i	0.318624	−	0.387568i
$34$		0			0
$35$	0.0117348	+	0.386752i	0.00198354	+	0.0653730i
$36$		0			0
$37$	−3.50023	+	6.06257i	−0.575434	+	0.996681i	0.420560	+	0.907264i	$0.361833\pi$
$37$	−3.50023	+	6.06257i	−0.575434	+	0.996681i	−0.995994	+	0.0894162i	$0.971500\pi$
$38$		0			0
$39$	−0.341548	−	0.0566898i	−0.0546915	−	0.00907763i
$40$		0			0
$41$	1.15895	+	2.00736i	0.180998	+	0.313498i	0.942221	−	0.334993i	$-0.108734\pi$
$41$	1.15895	+	2.00736i	0.180998	+	0.313498i	−0.761223	+	0.648491i	$0.775401\pi$
$42$		0			0
$43$	0.940993	−	1.62985i	0.143500	−	0.248550i	−0.785312	−	0.619100i	$-0.787498\pi$
$43$	0.940993	−	1.62985i	0.143500	−	0.248550i	0.928812	+	0.370550i	$0.120831\pi$
$44$		0			0
$45$	0.0848576	+	0.430452i	0.0126498	+	0.0641681i
$46$		0			0
$47$	−0.905887	−	1.56904i	−0.132137	−	0.228868i	0.792363	−	0.610050i	$-0.208851\pi$
$47$	−0.905887	−	1.56904i	−0.132137	−	0.228868i	−0.924500	+	0.381181i	$0.875517\pi$
$48$		0			0
$49$	−6.98712	+	0.424396i	−0.998160	+	0.0606280i
$50$		0			0
$51$	−10.7153	−	1.77851i	−1.50044	−	0.249041i
$52$		0			0
$53$	−2.67307	−	4.62989i	−0.367174	−	0.635964i	0.621948	−	0.783058i	$-0.286341\pi$
$53$	−2.67307	−	4.62989i	−0.367174	−	0.635964i	−0.989123	+	0.147094i	$0.953008\pi$
$54$		0			0
$55$	0.243359			0.0328145
$56$		0			0
$57$	−4.21093	−	11.2172i	−0.557751	−	1.48576i
$58$		0			0
$59$	−2.28549	+	3.95859i	−0.297546	+	0.515364i	−0.975574	−	0.219672i	$-0.929501\pi$
$59$	−2.28549	+	3.95859i	−0.297546	+	0.515364i	0.678028	+	0.735036i	$0.262835\pi$
$60$		0			0
$61$	0.339138	+	0.587404i	0.0434221	+	0.0752094i	0.886920	−	0.461924i	$-0.152841\pi$
$61$	0.339138	+	0.587404i	0.0434221	+	0.0752094i	−0.843498	+	0.537133i	$0.819507\pi$
$62$		0			0
$63$	−7.73724	+	1.77064i	−0.974800	+	0.223080i
$64$		0			0
$65$	−0.0146166	−	0.0253167i	−0.00181296	−	0.00314015i
$66$		0			0
$67$	−3.09342	+	5.35796i	−0.377921	+	0.654579i	−0.990760	−	0.135630i	$-0.956694\pi$
$67$	−3.09342	+	5.35796i	−0.377921	+	0.654579i	0.612838	+	0.790208i	$0.290028\pi$
$68$		0			0
$69$	−6.79968	+	8.27101i	−0.818586	+	0.995713i
$70$		0			0
$71$	−1.27749			−0.151611			−0.0758053	−	0.997123i	$-0.524153\pi$
$71$	−1.27749			−0.151611			−0.0758053	+	0.997123i	$0.524153\pi$
$72$		0			0
$73$	−0.778603	−	1.34858i	−0.0911286	−	0.157839i	0.816858	−	0.576839i	$-0.195714\pi$
$73$	−0.778603	−	1.34858i	−0.0911286	−	0.157839i	−0.907986	+	0.419000i	$0.862381\pi$
$74$		0			0
$75$	5.47620	−	6.66115i	0.632337	−	0.769164i
$76$		0			0
$77$	0.133523	+	4.40061i	0.0152164	+	0.501496i
$78$		0			0
$79$	6.39787	+	11.0814i	0.719817	+	1.24676i	0.961072	+	0.276298i	$0.0891075\pi$
$79$	6.39787	+	11.0814i	0.719817	+	1.24676i	−0.241255	+	0.970462i	$0.577559\pi$
$80$		0			0
$81$	−8.32664	+	3.41570i	−0.925183	+	0.379522i
$82$		0			0
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	−0.995148	−	0.0983854i	$-0.968632\pi$
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	0.582778	+	0.812631i	$0.301966\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$		0			0
$87$	−3.00417	−	8.00262i	−0.322080	−	0.857971i
$88$		0			0
$89$	4.53394	−	7.85301i	0.480597	−	0.832418i	−0.519155	−	0.854680i	$-0.673753\pi$
$89$	4.53394	−	7.85301i	0.480597	−	0.832418i	0.999752	+	0.0222619i	$0.00708678\pi$
$90$		0			0
$91$	0.449777	−	0.278199i	0.0471494	−	0.0291632i
$92$		0			0
$93$	−1.53266	−	4.08275i	−0.158929	−	0.423361i
$94$		0			0
$95$	0.505833	−	0.876128i	0.0518973	−	0.0898888i
$96$		0			0
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	−0.994278	−	0.106821i	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$		0			0
$99$	0.965543	+	4.89786i	0.0970408	+	0.492253i
$100$		0			0
$101$	14.8430			1.47693			0.738467	−	0.674290i	$-0.235550\pi$
$101$	14.8430			1.47693			0.738467	+	0.674290i	$0.235550\pi$
$102$		0			0
$103$	0.203948			0.0200956			0.0100478	−	0.999950i	$-0.496802\pi$
$103$	0.203948			0.0200956			0.0100478	+	0.999950i	$0.496802\pi$
$104$		0			0
$105$	−0.530363	−	0.409705i	−0.0517582	−	0.0399831i
$106$		0			0
$107$	−3.48444	+	6.03524i	−0.336854	+	0.583448i	−0.983839	−	0.179054i	$-0.942696\pi$
$107$	−3.48444	+	6.03524i	−0.336854	+	0.583448i	0.646985	+	0.762503i	$0.276030\pi$
$108$		0			0
$109$	3.33058	+	5.76874i	0.319012	+	0.552545i	0.980282	−	0.197603i	$-0.0633157\pi$
$109$	3.33058	+	5.76874i	0.319012	+	0.552545i	−0.661270	+	0.750148i	$0.729982\pi$
$110$		0			0
$111$	−4.26138	−	11.3516i	−0.404472	−	1.07745i
$112$		0			0
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	0.865115	−	0.501573i	$-0.167245\pi$
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	−0.866933	+	0.498425i	$0.833912\pi$
$114$		0			0
$115$	−0.904067			−0.0843047
$116$		0			0
$117$	0.451533	−	0.394620i	0.0417442	−	0.0364826i
$118$		0			0
$119$	14.1107	−	8.72785i	1.29353	−	0.800081i
$120$		0			0
$121$	−8.23097			−0.748270
$122$		0			0
$123$	−3.96054	−	0.657366i	−0.357110	−	0.0592727i
$124$		0			0
$125$	1.45933			0.130526
$126$		0			0
$127$	−13.4788			−1.19605			−0.598027	−	0.801476i	$-0.704048\pi$
$127$	−13.4788			−1.19605			−0.598027	+	0.801476i	$0.704048\pi$
$128$		0			0
$129$	1.14562	+	3.05175i	0.100866	+	0.268692i
$130$		0			0
$131$	19.8333			1.73284			0.866422	−	0.499312i	$-0.166414\pi$
$131$	19.8333			1.73284			0.866422	+	0.499312i	$0.166414\pi$
$132$		0			0
$133$	16.1204	+	8.66618i	1.39782	+	0.751453i
$134$		0			0
$135$	−0.669264	−	0.359939i	−0.0576011	−	0.0309786i
$136$		0			0
$137$	−6.44509			−0.550642			−0.275321	−	0.961352i	$-0.588784\pi$
$137$	−6.44509			−0.550642			−0.275321	+	0.961352i	$0.588784\pi$
$138$		0			0
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	−0.999328	−	0.0366611i	$-0.988328\pi$
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	0.467914	−	0.883774i	$-0.345006\pi$
$140$		0			0
$141$	3.09573	+	0.513826i	0.260708	+	0.0432720i
$142$		0			0
$143$	−0.166313	−	0.288063i	−0.0139078	−	0.0240890i
$144$		0			0
$145$	0.360872	−	0.625048i	0.0299688	−	0.0519074i
$146$		0			0
$147$	7.11763	−	9.81526i	0.587052	−	0.809549i
$148$		0			0
$149$	17.7673			1.45555			0.727776	−	0.685815i	$-0.240554\pi$
$149$	17.7673			1.45555			0.727776	+	0.685815i	$0.240554\pi$
$150$		0			0
$151$	−8.46599			−0.688953			−0.344476	−	0.938795i	$-0.611944\pi$
$151$	−8.46599			−0.688953			−0.344476	+	0.938795i	$0.611944\pi$
$152$		0			0
$153$	14.1658	−	12.3803i	1.14524	−	1.00089i
$154$		0			0
$155$	0.184108	−	0.318885i	0.0147879	−	0.0256135i
$156$		0			0
$157$	−2.84968	+	4.93579i	−0.227429	+	0.393919i	−0.957045	−	0.289938i	$-0.906365\pi$
$157$	−2.84968	+	4.93579i	−0.227429	+	0.393919i	0.729616	+	0.683857i	$0.239699\pi$
$158$		0			0
$159$	9.13481	+	1.51618i	0.724437	+	0.120241i
$160$		0			0
$161$	−0.496032	−	16.3481i	−0.0390928	−	1.28841i
$162$		0			0
$163$	1.06267	−	1.84060i	0.0832349	−	0.144167i	−0.821403	−	0.570349i	$-0.806808\pi$
$163$	1.06267	−	1.84060i	0.0832349	−	0.144167i	0.904638	+	0.426181i	$0.140141\pi$
$164$		0			0
$165$	−0.267681	+	0.325603i	−0.0208390	+	0.0253481i
$166$		0			0
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	0.998244	−	0.0592278i	$-0.0188638\pi$
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	−0.550415	+	0.834891i	$0.685530\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$		0			0
$171$	19.6400	+	6.70433i	1.50190	+	0.512693i
$172$		0			0
$173$	7.95546	+	13.7793i	0.604842	+	1.04762i	0.992076	+	0.125636i	$0.0400971\pi$
$173$	7.95546	+	13.7793i	0.604842	+	1.04762i	−0.387234	+	0.921981i	$0.626570\pi$
$174$		0			0
$175$	0.399485	+	13.1661i	0.0301982	+	0.995264i
$176$		0			0
$177$	−2.78249	−	7.41212i	−0.209145	−	0.557129i
$178$		0			0
$179$	−3.87665	−	6.71456i	−0.289755	−	0.501870i	0.683996	−	0.729485i	$-0.260240\pi$
$179$	−3.87665	−	6.71456i	−0.289755	−	0.501870i	−0.973751	+	0.227615i	$0.926907\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$		0			0
$183$	−1.15895	−	0.192362i	−0.0856722	−	0.0142198i
$184$		0			0
$185$	0.511893	−	0.886625i	0.0376351	−	0.0651860i
$186$		0			0
$187$	−5.21769	−	9.03730i	−0.381555	−	0.660873i
$188$		0			0
$189$	6.14150	−	12.2997i	0.446729	−	0.894670i
$190$		0			0
$191$	−2.48383	−	4.30211i	−0.179723	−	0.311290i	0.762062	−	0.647504i	$-0.224187\pi$
$191$	−2.48383	−	4.30211i	−0.179723	−	0.311290i	−0.941786	+	0.336214i	$0.890854\pi$
$192$		0			0
$193$	7.45221	−	12.9076i	0.536422	−	0.929110i	−0.462671	−	0.886530i	$-0.653109\pi$
$193$	7.45221	−	12.9076i	0.536422	−	0.929110i	0.999093	−	0.0425800i	$-0.0135577\pi$
$194$		0			0
$195$	0.0499500	+	0.00829064i	0.00357699	+	0.000593705i
$196$		0			0
$197$	−21.2608			−1.51477			−0.757386	−	0.652968i	$-0.773524\pi$
$197$	−21.2608			−1.51477			−0.757386	+	0.652968i	$0.773524\pi$
$198$		0			0
$199$	9.97208	+	17.2722i	0.706902	+	1.22439i	0.966001	+	0.258540i	$0.0832413\pi$
$199$	9.97208	+	17.2722i	0.706902	+	1.22439i	−0.259098	+	0.965851i	$0.583425\pi$
$200$		0			0
$201$	−3.76611	−	10.0323i	−0.265641	−	0.707625i
$202$		0			0
$203$	11.5006	+	6.18264i	0.807186	+	0.433936i
$204$		0			0
$205$	−0.169492	−	0.293568i	−0.0118378	−	0.0205037i
$206$		0			0
$207$	−3.58695	−	18.1953i	−0.249310	−	1.26466i
$208$		0			0
$209$	5.75556	−	9.96893i	0.398121	−	0.689565i
$210$		0			0
$211$	−11.7569	−	20.3636i	−0.809381	−	1.40189i	−0.913293	−	0.407303i	$-0.866469\pi$
$211$	−11.7569	−	20.3636i	−0.809381	−	1.40189i	0.103912	−	0.994587i	$-0.466864\pi$
$212$		0			0
$213$	1.40517	−	1.70923i	0.0962808	−	0.117114i
$214$		0			0
$215$	−0.137616	+	0.238358i	−0.00938535	+	0.0162559i
$216$		0			0
$217$	5.86735	+	3.15424i	0.398302	+	0.214123i
$218$		0			0
$219$	2.66076	+	0.441629i	0.179797	+	0.0298425i
$220$		0			0
$221$	−0.626768	+	1.08559i	−0.0421610	+	0.0730250i
$222$		0			0
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	−0.925969	−	0.377600i	$-0.876750\pi$
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	0.789995	+	0.613113i	$0.210083\pi$
$224$		0			0
$225$	2.88879	+	14.6538i	0.192586	+	0.976921i
$226$		0			0
$227$	3.85285			0.255723			0.127861	−	0.991792i	$-0.459189\pi$
$227$	3.85285			0.255723			0.127861	+	0.991792i	$0.459189\pi$
$228$		0			0
$229$	13.1162			0.866746			0.433373	−	0.901215i	$-0.357323\pi$
$229$	13.1162			0.866746			0.433373	+	0.901215i	$0.357323\pi$
$230$		0			0
$231$	−6.03468	−	4.66179i	−0.397053	−	0.306723i
$232$		0			0
$233$	−8.75115	+	15.1574i	−0.573307	+	0.992997i	0.422916	+	0.906169i	$0.361007\pi$
$233$	−8.75115	+	15.1574i	−0.573307	+	0.992997i	−0.996223	+	0.0868284i	$0.972327\pi$
$234$		0			0
$235$	0.132482	+	0.229466i	0.00864218	+	0.0149687i
$236$		0			0
$237$	−21.8638	−	3.62892i	−1.42020	−	0.235724i
$238$		0			0
$239$	−3.65857	−	6.33683i	−0.236653	−	0.409895i	0.723099	−	0.690745i	$-0.242717\pi$
$239$	−3.65857	−	6.33683i	−0.236653	−	0.409895i	−0.959752	+	0.280849i	$0.909384\pi$
$240$		0			0
$241$	6.23107			0.401378			0.200689	−	0.979655i	$-0.435682\pi$
$241$	6.23107			0.401378			0.200689	+	0.979655i	$0.435682\pi$
$242$		0			0
$243$	4.58880	−	14.8977i	0.294372	−	0.955691i
$244$		0			0
$245$	1.02184	−	0.0620661i	0.0652827	−	0.00396526i
$246$		0			0
$247$	−1.38276			−0.0879829
$248$		0			0
$249$	−4.57383	−	12.1840i	−0.289855	−	0.772127i
$250$		0			0
$251$	−5.65283			−0.356803			−0.178402	−	0.983958i	$-0.557093\pi$
$251$	−5.65283			−0.356803			−0.178402	+	0.983958i	$0.557093\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$		0			0
$255$	1.56706	+	0.260099i	0.0981333	+	0.0162880i
$256$		0			0
$257$	11.8016			0.736166			0.368083	−	0.929793i	$-0.380014\pi$
$257$	11.8016			0.736166			0.368083	+	0.929793i	$0.380014\pi$
$258$		0			0
$259$	16.3135	+	8.77001i	1.01367	+	0.544942i
$260$		0			0
$261$	14.0116	+	4.78301i	0.867293	+	0.296061i
$262$		0			0
$263$	22.2401			1.37138			0.685691	−	0.727893i	$-0.259500\pi$
$263$	22.2401			1.37138			0.685691	+	0.727893i	$0.259500\pi$
$264$		0			0
$265$	0.390925	+	0.677101i	0.0240143	+	0.0415940i
$266$		0			0
$267$	5.51988	+	14.7041i	0.337811	+	0.899876i
$268$		0			0
$269$	−1.19442	−	2.06880i	−0.0728251	−	0.126137i	0.827313	−	0.561741i	$-0.189868\pi$
$269$	−1.19442	−	2.06880i	−0.0728251	−	0.126137i	−0.900138	+	0.435604i	$0.856535\pi$
$270$		0			0
$271$	11.6129	−	20.1142i	0.705435	−	1.22185i	−0.261100	−	0.965312i	$-0.584085\pi$
$271$	11.6129	−	20.1142i	0.705435	−	1.22185i	0.966534	−	0.256537i	$-0.0825815\pi$
$272$		0			0
$273$	−0.122512	+	0.907785i	−0.00741478	+	0.0549417i
$274$		0			0
$275$	8.28461			0.499581
$276$		0			0
$277$	−4.61800			−0.277469			−0.138734	−	0.990330i	$-0.544303\pi$
$277$	−4.61800			−0.277469			−0.138734	+	0.990330i	$0.544303\pi$
$278$		0			0
$279$	7.14837	+	2.44018i	0.427962	+	0.146090i
$280$		0			0
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	−0.634215	−	0.773157i	$-0.718676\pi$
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	0.986681	+	0.162668i	$0.0520098\pi$
$282$		0			0
$283$	7.92483	−	13.7262i	0.471082	−	0.815939i	−0.528370	−	0.849014i	$-0.677197\pi$
$283$	7.92483	−	13.7262i	0.471082	−	0.815939i	0.999453	+	0.0330753i	$0.0105301\pi$
$284$		0			0
$285$	0.615830	+	1.64047i	0.0364786	+	0.0971733i
$286$		0			0
$287$	5.21555	−	3.22596i	0.307864	−	0.190422i
$288$		0			0
$289$	−11.1634	+	19.3355i	−0.656669	+	1.13738i
$290$		0			0
$291$	−4.85174	−	12.9243i	−0.284414	−	0.757634i
$292$		0			0
$293$	7.04804	+	12.2076i	0.411751	+	0.713173i	0.995081	−	0.0990615i	$-0.0315841\pi$
$293$	7.04804	+	12.2076i	0.411751	+	0.713173i	−0.583330	+	0.812235i	$0.698251\pi$
$294$		0			0
$295$	0.334243	−	0.578927i	0.0194604	−	0.0337064i
$296$		0			0
$297$	−7.61515	−	4.09552i	−0.441876	−	0.237646i
$298$		0			0
$299$	0.617846	+	1.07014i	0.0357310	+	0.0618878i
$300$		0			0
$301$	−4.38569	−	2.35771i	−0.252787	−	0.135896i
$302$		0			0
$303$	−16.3265	+	19.8592i	−0.937932	+	1.14088i
$304$		0			0
$305$	−0.0495974	−	0.0859053i	−0.00283994	−	0.00491892i
$306$		0			0
$307$	−27.3916			−1.56332			−0.781660	−	0.623704i	$-0.785627\pi$
$307$	−27.3916			−1.56332			−0.781660	+	0.623704i	$0.785627\pi$
$308$		0			0
$309$	−0.224332	+	0.272873i	−0.0127618	+	0.0155232i
$310$		0			0
$311$	−7.02785	+	12.1726i	−0.398513	+	0.690244i	−0.993543	−	0.113459i	$-0.963807\pi$
$311$	−7.02785	+	12.1726i	−0.398513	+	0.690244i	0.595030	+	0.803704i	$0.297140\pi$
$312$		0			0
$313$	−10.8723	−	18.8314i	−0.614540	−	1.06441i	−0.990465	−	0.137764i	$-0.956008\pi$
$313$	−10.8723	−	18.8314i	−0.614540	−	1.06441i	0.375925	−	0.926650i	$-0.377325\pi$
$314$		0			0
$315$	1.13154	−	0.258948i	0.0637549	−	0.0145901i
$316$		0			0
$317$	−4.28148	−	7.41575i	−0.240472	−	0.416510i	0.720377	−	0.693583i	$-0.243969\pi$
$317$	−4.28148	−	7.41575i	−0.240472	−	0.416510i	−0.960849	+	0.277073i	$0.910636\pi$
$318$		0			0
$319$	4.10614	−	7.11204i	0.229900	−	0.398198i
$320$		0			0
$321$	−4.24217	−	11.3005i	−0.236775	−	0.630730i
$322$		0			0
$323$	−43.3808			−2.41377
$324$		0			0
$325$	−0.497589	−	0.861850i	−0.0276013	−	0.0478068i
$326$		0			0
$327$	−11.3818	−	1.88913i	−0.629413	−	0.104469i
$328$		0			0
$329$	−4.07670	+	2.52155i	−0.224756	+	0.139018i
$330$		0			0
$331$	5.42360	+	9.39396i	0.298108	+	0.516339i	0.975703	−	0.219097i	$-0.0703110\pi$
$331$	5.42360	+	9.39396i	0.298108	+	0.516339i	−0.677595	+	0.735435i	$0.736978\pi$
$332$		0			0
$333$	19.8753	+	6.78465i	1.08916	+	0.371797i
$334$		0			0
$335$	0.452399	−	0.783578i	0.0247172	−	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$		0			0
$339$	0.0660347	+	0.0109604i	0.00358651	+	0.000595285i
$340$		0			0
$341$	2.09486	−	3.62840i	0.113443	−	0.196489i
$342$		0			0
$343$	1.68298	+	18.4436i	0.0908723	+	0.995863i
$344$		0			0
$345$	0.994424	−	1.20960i	0.0535380	−	0.0651226i
$346$		0			0
$347$	−5.76652	+	9.98790i	−0.309563	+	0.536178i	−0.978267	−	0.207350i	$-0.933516\pi$
$347$	−5.76652	+	9.98790i	−0.309563	+	0.536178i	0.668704	+	0.743529i	$0.266849\pi$
$348$		0			0
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	−0.960186	−	0.279362i	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$		0			0
$351$	0.0313221	+	1.03819i	0.00167185	+	0.0554145i
$352$		0			0
$353$	−2.64699			−0.140885			−0.0704424	−	0.997516i	$-0.522441\pi$
$353$	−2.64699			−0.140885			−0.0704424	+	0.997516i	$0.522441\pi$
$354$		0			0
$355$	0.186828			0.00991579
$356$		0			0
$357$	−3.84353	+	28.4796i	−0.203421	+	1.50730i
$358$		0			0
$359$	12.9835	−	22.4882i	0.685245	−	1.18688i	−0.288114	−	0.957596i	$-0.593028\pi$
$359$	12.9835	−	22.4882i	0.685245	−	1.18688i	0.973360	−	0.229284i	$-0.0736384\pi$
$360$		0			0
$361$	−14.4264	−	24.9873i	−0.759286	−	1.31512i
$362$		0			0
$363$	9.05362	−	11.0127i	0.475192	−	0.578014i
$364$		0			0
$365$	0.113867	+	0.197224i	0.00596009	+	0.0103232i
$366$		0			0
$367$	−17.5874			−0.918056			−0.459028	−	0.888422i	$-0.651802\pi$
$367$	−17.5874			−0.918056			−0.459028	+	0.888422i	$0.651802\pi$
$368$		0			0
$369$	5.23591	−	4.57596i	0.272570	−	0.238215i
$370$		0			0
$371$	−12.0294	+	7.44052i	−0.624536	+	0.386293i
$372$		0			0
$373$	0.815075			0.0422030			0.0211015	−	0.999777i	$-0.493283\pi$
$373$	0.815075			0.0422030			0.0211015	+	0.999777i	$0.493283\pi$
$374$		0			0
$375$	−1.60518	+	1.95251i	−0.0828912	+	0.100827i
$376$		0			0
$377$	−0.986490			−0.0508068
$378$		0			0
$379$	20.4312			1.04948			0.524741	−	0.851262i	$-0.324162\pi$
$379$	20.4312			1.04948			0.524741	+	0.851262i	$0.324162\pi$
$380$		0			0
$381$	14.8260	−	18.0341i	0.759558	−	0.923913i
$382$		0			0
$383$	−17.8928			−0.914278			−0.457139	−	0.889395i	$-0.651126\pi$
$383$	−17.8928			−0.914278			−0.457139	+	0.889395i	$0.651126\pi$
$384$		0			0
$385$	−0.0195272	−	0.643571i	−0.000995196	−	0.0327994i
$386$		0			0
$387$	−5.34322	−	1.82397i	−0.271611	−	0.0927177i
$388$		0			0
$389$	15.6278			0.792363			0.396181	−	0.918172i	$-0.370335\pi$
$389$	15.6278			0.792363			0.396181	+	0.918172i	$0.370335\pi$
$390$		0			0
$391$	19.3835	+	33.5731i	0.980264	+	1.69787i
$392$		0			0
$393$	−21.8156	+	26.5360i	−1.10045	+	1.33857i
$394$		0			0
$395$	−0.935661	−	1.62061i	−0.0470782	−	0.0815419i
$396$		0			0
$397$	9.63064	−	16.6808i	0.483348	−	0.837183i	−0.516469	−	0.856306i	$-0.672754\pi$
$397$	9.63064	−	16.6808i	0.483348	−	0.837183i	0.999817	+	0.0191225i	$0.00608724\pi$
$398$		0			0
$399$	−29.3265	+	12.0360i	−1.46816	+	0.602555i
$400$		0			0
$401$	14.3013			0.714172			0.357086	−	0.934072i	$-0.383770\pi$
$401$	14.3013			0.714172			0.357086	+	0.934072i	$0.383770\pi$
$402$		0			0
$403$	−0.503284			−0.0250704
$404$		0			0
$405$	1.21774	−	0.499532i	0.0605098	−	0.0248219i
$406$		0			0
$407$	5.82452	−	10.0884i	0.288711	−	0.500062i
$408$		0			0
$409$	−15.9305	+	27.5924i	−0.787712	+	1.36436i	0.139654	+	0.990200i	$0.455401\pi$
$409$	−15.9305	+	27.5924i	−0.787712	+	1.36436i	−0.927366	+	0.374156i	$0.877932\pi$
$410$		0			0
$411$	7.08925	−	8.62324i	0.349687	−	0.425353i
$412$		0			0
$413$	10.6520	+	5.72643i	0.524151	+	0.281779i
$414$		0			0
$415$	0.549426	−	0.951633i	0.0269702	−	0.0467138i
$416$		0			0
$417$	21.4106	+	3.55371i	1.04848	+	0.174026i
$418$		0			0
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	−0.995036	−	0.0995110i	$-0.968272\pi$
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	0.411339	−	0.911482i	$-0.365061\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$		0			0
$423$	−4.09261	+	3.57677i	−0.198990	+	0.173908i
$424$		0			0
$425$	−15.6107	−	27.0385i	−0.757230	−	1.31156i
$426$		0			0
$427$	1.52620	−	0.943995i	0.0738579	−	0.0456831i
$428$		0			0
$429$	0.568350	+	0.0943341i	0.0274402	+	0.00455449i
$430$		0			0
$431$	−2.46382	−	4.26746i	−0.118678	−	0.205556i	0.800566	−	0.599244i	$-0.204532\pi$
$431$	−2.46382	−	4.26746i	−0.118678	−	0.205556i	−0.919244	+	0.393688i	$0.871199\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$		0			0
$435$	0.439346	+	1.17035i	0.0210650	+	0.0561139i
$436$		0			0
$437$	−21.3817	+	37.0341i	−1.02282	+	1.77158i
$438$		0			0
$439$	1.22411	+	2.12022i	0.0584235	+	0.101192i	0.893758	−	0.448550i	$-0.148059\pi$
$439$	1.22411	+	2.12022i	0.0584235	+	0.101192i	−0.835334	+	0.549742i	$0.814726\pi$
$440$		0			0
$441$	5.30336	+	20.3193i	0.252541	+	0.967586i
$442$		0			0
$443$	−13.1475	−	22.7722i	−0.624657	−	1.08194i	−0.988607	−	0.150520i	$-0.951905\pi$
$443$	−13.1475	−	22.7722i	−0.624657	−	1.08194i	0.363950	−	0.931419i	$-0.381428\pi$
$444$		0			0
$445$	−0.663069	+	1.14847i	−0.0314325	+	0.0544427i
$446$		0			0
$447$	−19.5430	+	23.7718i	−0.924354	+	1.12437i
$448$		0			0
$449$	−38.7077			−1.82673			−0.913365	−	0.407141i	$-0.866526\pi$
$449$	−38.7077			−1.82673			−0.913365	+	0.407141i	$0.866526\pi$
$450$		0			0
$451$	−1.92854	−	3.34034i	−0.0908116	−	0.157290i
$452$		0			0
$453$	9.31213	−	11.3271i	0.437522	−	0.532194i
$454$		0			0
$455$	−0.0657779	+	0.0406855i	−0.00308372	+	0.00190736i
$456$		0			0
$457$	4.57756	+	7.92856i	0.214129	+	0.370882i	0.953003	−	0.302961i	$-0.0979754\pi$
$457$	4.57756	+	7.92856i	0.214129	+	0.370882i	−0.738874	+	0.673844i	$0.764642\pi$
$458$		0			0
$459$	0.982656	+	32.5708i	0.0458665	+	1.52027i
$460$		0			0
$461$	14.6152	−	25.3143i	0.680698	−	1.17900i	−0.294070	−	0.955784i	$-0.595010\pi$
$461$	14.6152	−	25.3143i	0.680698	−	1.17900i	0.974768	−	0.223220i	$-0.0716568\pi$
$462$		0			0
$463$	8.21031	+	14.2207i	0.381565	+	0.660891i	0.991286	−	0.131726i	$-0.0420518\pi$
$463$	8.21031	+	14.2207i	0.381565	+	0.660891i	−0.609721	+	0.792616i	$0.708718\pi$
$464$		0			0
$465$	0.224144	+	0.597084i	0.0103944	+	0.0276891i
$466$		0			0
$467$	−7.68632	+	13.3131i	−0.355680	+	0.616057i	−0.987234	−	0.159276i	$-0.949084\pi$
$467$	−7.68632	+	13.3131i	−0.355680	+	0.616057i	0.631554	+	0.775332i	$0.282418\pi$
$468$		0			0
$469$	14.4175	+	7.75073i	0.665739	+	0.357895i
$470$		0			0
$471$	−3.46936	−	9.24183i	−0.159860	−	0.425841i
$472$		0			0
$473$	−1.56585	+	2.71213i	−0.0719979	+	0.124704i
$474$		0			0
$475$	17.2200	−	29.8259i	0.790106	−	1.36850i
$476$		0			0
$477$	−12.0764	+	10.5542i	−0.552939	+	0.483245i
$478$		0			0
$479$	37.9291			1.73303			0.866513	−	0.499155i	$-0.166356\pi$
$479$	37.9291			1.73303			0.866513	+	0.499155i	$0.166356\pi$
$480$		0			0
$481$	−1.39933			−0.0638038
$482$		0			0
$483$	22.4186	+	17.3183i	1.02008	+	0.788011i
$484$		0			0
$485$	0.582809	−	1.00946i	0.0264640	−	0.0458370i
$486$		0			0
$487$	−2.30247	−	3.98800i	−0.104335	−	0.180714i	0.809131	−	0.587628i	$-0.199938\pi$
$487$	−2.30247	−	3.98800i	−0.104335	−	0.180714i	−0.913466	+	0.406914i	$0.866605\pi$
$488$		0			0
$489$	1.29376	+	3.44637i	0.0585058	+	0.155850i
$490$		0			0
$491$	15.1876	+	26.3056i	0.685405	+	1.18716i	0.973309	+	0.229497i	$0.0737082\pi$
$491$	15.1876	+	26.3056i	0.685405	+	1.18716i	−0.287904	+	0.957659i	$0.592958\pi$
$492$		0			0
$493$	−30.9488			−1.39386
$494$		0			0
$495$	−0.141207	−	0.716290i	−0.00634676	−	0.0321949i
$496$		0			0
$497$	0.102506	+	3.37837i	0.00459804	+	0.151541i
$498$		0			0
$499$	−9.26871			−0.414925			−0.207462	−	0.978243i	$-0.566520\pi$
$499$	−9.26871			−0.414925			−0.207462	+	0.978243i	$0.566520\pi$
$500$		0			0
$501$	−19.7770	−	3.28256i	−0.883571	−	0.146654i
$502$		0			0
$503$	22.4230			0.999791			0.499896	−	0.866086i	$-0.333372\pi$
$503$	22.4230			0.999791			0.499896	+	0.866086i	$0.333372\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$		0			0
$507$	7.88916	+	21.0155i	0.350370	+	0.933329i
$508$		0			0
$509$	−37.6414			−1.66843			−0.834213	−	0.551443i	$-0.814077\pi$
$509$	−37.6414			−1.66843			−0.834213	+	0.551443i	$0.814077\pi$
$510$		0			0
$511$	−3.50389	+	2.16725i	−0.155003	+	0.0958736i
$512$		0			0
$513$	−30.5730	+	18.9030i	−1.34983	+	0.834586i
$514$		0			0
$515$	−0.0298266			−0.00131432
$516$		0			0
$517$	1.50743	+	2.61095i	0.0662969	+	0.114830i
$518$		0			0
$519$	−27.1866	−	4.51240i	−1.19336	−	0.198072i
$520$		0			0
$521$	17.4641	+	30.2488i	0.765117	+	1.32522i	0.940185	+	0.340666i	$0.110652\pi$
$521$	17.4641	+	30.2488i	0.765117	+	1.32522i	−0.175067	+	0.984556i	$0.556014\pi$
$522$		0			0
$523$	11.8735	−	20.5656i	0.519194	−	0.899270i	−0.480557	−	0.876963i	$-0.659566\pi$
$523$	11.8735	−	20.5656i	0.519194	−	0.899270i	0.999751	−	0.0223069i	$-0.00710109\pi$
$524$		0			0
$525$	−18.0551	−	13.9475i	−0.787987	−	0.608719i
$526$		0			0
$527$	−15.7894			−0.687795
$528$		0			0
$529$	15.2151			0.661526
$530$		0			0
$531$	12.9777	+	4.43008i	0.563182	+	0.192249i
$532$		0			0
$533$	−0.231664	+	0.401254i	−0.0100345	+	0.0173802i
$534$		0			0
$535$	0.509585	−	0.882627i	0.0220313	−	0.0381593i
$536$		0			0
$537$	13.2479	+	2.19887i	0.571688	+	0.0948882i
$538$		0			0
$539$	11.6269	−	0.706212i	0.500804	−	0.0304187i
$540$		0			0
$541$	8.58542	−	14.8704i	0.369116	−	0.639328i	−0.620311	−	0.784356i	$-0.712994\pi$
$541$	8.58542	−	14.8704i	0.369116	−	0.639328i	0.989428	+	0.145028i	$0.0463271\pi$
$542$		0			0
$543$	13.3774	−	16.2720i	0.574077	−	0.698297i
$544$		0			0
$545$	−0.487083	−	0.843653i	−0.0208643	−	0.0361381i
$546$		0			0
$547$	10.0046	−	17.3284i	0.427765	−	0.740910i	−0.568910	−	0.822400i	$-0.692635\pi$
$547$	10.0046	−	17.3284i	0.427765	−	0.740910i	0.996674	+	0.0814901i	$0.0259679\pi$
$548$		0			0
$549$	1.53215	−	1.33904i	0.0653908	−	0.0571487i
$550$		0			0
$551$	−17.0696	−	29.5654i	−0.727190	−	1.25953i
$552$		0			0
$553$	28.7919	−	17.8086i	1.22436	−	0.757297i
$554$		0			0
$555$	0.623209	+	1.66013i	0.0264537	+	0.0704685i
$556$		0			0
$557$	−0.122740	−	0.212593i	−0.00520068	−	0.00900784i	0.863413	−	0.504497i	$-0.168322\pi$
$557$	−0.122740	−	0.212593i	−0.00520068	−	0.00900784i	−0.868614	+	0.495489i	$0.834989\pi$
$558$		0			0
$559$	0.376192			0.0159112
$560$		0			0
$561$	17.8307	+	2.95951i	0.752811	+	0.124951i
$562$		0			0
$563$	−22.1255	+	38.3224i	−0.932477	+	1.61510i	−0.153404	+	0.988164i	$0.549024\pi$
$563$	−22.1255	+	38.3224i	−0.932477	+	1.61510i	−0.779073	+	0.626934i	$0.784310\pi$
$564$		0			0
$565$	0.00282596	+	0.00489471i	0.000118889	+	0.000205922i
$566$		0			0
$567$	9.70107	+	21.7460i	0.407407	+	0.913247i
$568$		0			0
$569$	2.76767	+	4.79374i	0.116027	+	0.200964i	0.918190	−	0.396141i	$-0.129651\pi$
$569$	2.76767	+	4.79374i	0.116027	+	0.200964i	−0.802163	+	0.597105i	$0.796318\pi$
$570$		0			0
$571$	−2.05191	+	3.55400i	−0.0858696	+	0.148730i	−0.905761	−	0.423788i	$-0.860700\pi$
$571$	−2.05191	+	3.55400i	−0.0858696	+	0.148730i	0.819892	+	0.572518i	$0.194034\pi$
$572$		0			0
$573$	8.48810	+	1.40884i	0.354595	+	0.0588553i
$574$		0			0
$575$	−30.7770			−1.28349
$576$		0			0
$577$	−2.82275	−	4.88915i	−0.117513	−	0.203538i	0.801269	−	0.598305i	$-0.204159\pi$
$577$	−2.82275	−	4.88915i	−0.117513	−	0.203538i	−0.918781	+	0.394767i	$0.870825\pi$
$578$		0			0
$579$	9.07276	+	24.1684i	0.377051	+	1.00440i
$580$		0			0
$581$	17.5097	+	9.41304i	0.726423	+	0.390519i
$582$		0			0
$583$	4.44809	+	7.70433i	0.184221	+	0.319081i
$584$		0			0
$585$	−0.0660347	+	0.0577115i	−0.00273020	+	0.00238608i
$586$		0			0
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	−0.991989	−	0.126324i	$-0.959682\pi$
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	0.605394	+	0.795926i	$0.293015\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$		0			0
$591$	23.3858	−	28.4460i	0.961962	−	1.17011i
$592$		0			0
$593$	−9.43516	+	16.3422i	−0.387456	+	0.671093i	−0.992107	−	0.125398i	$-0.959979\pi$
$593$	−9.43516	+	16.3422i	−0.387456	+	0.671093i	0.604651	+	0.796491i	$0.293313\pi$
$594$		0			0
$595$	−2.06363	+	1.27641i	−0.0846005	+	0.0523277i
$596$		0			0
$597$	−34.0781	−	5.65624i	−1.39472	−	0.231495i
$598$		0			0
$599$	1.33726	−	2.31620i	0.0546388	−	0.0946372i	−0.837412	−	0.546572i	$-0.815933\pi$
$599$	1.33726	−	2.31620i	0.0546388	−	0.0946372i	0.892051	+	0.451934i	$0.149266\pi$
$600$		0			0
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	−0.968736	−	0.248095i	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$		0			0
$603$	17.5653	+	5.99612i	0.715313	+	0.244181i
$604$		0			0
$605$	1.20374			0.0489391
$606$		0			0
$607$	−25.8052			−1.04740			−0.523701	−	0.851902i	$-0.675449\pi$
$607$	−25.8052			−1.04740			−0.523701	+	0.851902i	$0.675449\pi$
$608$		0			0
$609$	−20.9221	+	8.58675i	−0.847808	+	0.347953i
$610$		0			0
$611$	0.181079	−	0.313637i	0.00732565	−	0.0126884i
$612$		0			0
$613$	13.4766	+	23.3422i	0.544316	+	0.942784i	0.998650	+	0.0519519i	$0.0165443\pi$
$613$	13.4766	+	23.3422i	0.544316	+	0.942784i	−0.454333	+	0.890832i	$0.650122\pi$
$614$		0			0
$615$	0.579212	+	0.0961370i	0.0233561	+	0.00387662i
$616$		0			0
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	0.754002	−	0.656872i	$-0.228121\pi$
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	−0.945869	+	0.324549i	$0.894788\pi$
$618$		0			0
$619$	−34.7071			−1.39500			−0.697499	−	0.716586i	$-0.745704\pi$
$619$	−34.7071			−1.39500			−0.697499	+	0.716586i	$0.745704\pi$
$620$		0			0
$621$	28.2899	+	15.2147i	1.13524	+	0.610544i
$622$		0			0
$623$	−21.1314	−	11.3600i	−0.846610	−	0.455130i
$624$		0			0
$625$	24.6796			0.987186
$626$		0			0
$627$	7.00716	+	18.6660i	0.279839	+	0.745447i
$628$		0			0
$629$	−43.9006			−1.75043
$630$		0			0
$631$	36.7963			1.46484			0.732419	−	0.680854i	$-0.238391\pi$
$631$	36.7963			1.46484			0.732419	+	0.680854i	$0.238391\pi$
$632$		0			0
$633$	40.1776	+	6.66863i	1.59692	+	0.265054i
$634$		0			0
$635$	1.97122			0.0782256
$636$		0			0
$637$	−0.771798	−	1.16713i	−0.0305798	−	0.0462433i
$638$		0			0
$639$	0.741253	+	3.76011i	0.0293235	+	0.148748i
$640$		0			0
$641$	−44.1844			−1.74518			−0.872590	−	0.488454i	$-0.837561\pi$
$641$	−44.1844			−1.74518			−0.872590	+	0.488454i	$0.837561\pi$
$642$		0			0
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	0.687197	−	0.726471i	$-0.258841\pi$
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	−0.972741	+	0.231895i	$0.925507\pi$
$644$		0			0
$645$	−0.167542	−	0.446305i	−0.00659696	−	0.0175732i
$646$		0			0
$647$	16.6536	+	28.8448i	0.654719	+	1.13401i	0.981964	+	0.189068i	$0.0605465\pi$
$647$	16.6536	+	28.8448i	0.654719	+	1.13401i	−0.327245	+	0.944940i	$0.606120\pi$
$648$		0			0
$649$	3.80315	−	6.58725i	0.149287	−	0.258572i
$650$		0			0
$651$	−10.6740	+	4.38076i	−0.418347	+	0.171696i
$652$		0			0
$653$	−9.06643			−0.354797			−0.177398	−	0.984139i	$-0.556768\pi$
$653$	−9.06643			−0.354797			−0.177398	+	0.984139i	$0.556768\pi$
$654$		0			0
$655$	−2.90054			−0.113333
$656$		0			0
$657$	−3.51757	+	3.07420i	−0.137233	+	0.119936i
$658$		0			0
$659$	−16.1806	+	28.0256i	−0.630305	+	1.09172i	0.357184	+	0.934034i	$0.383737\pi$
$659$	−16.1806	+	28.0256i	−0.630305	+	1.09172i	−0.987489	+	0.157686i	$0.949596\pi$
$660$		0			0
$661$	4.32958	−	7.49905i	0.168401	−	0.291679i	−0.769457	−	0.638699i	$-0.779473\pi$
$661$	4.32958	−	7.49905i	0.168401	−	0.291679i	0.937858	+	0.347020i	$0.112806\pi$
$662$		0			0
$663$	−0.763064	−	2.03268i	−0.0296349	−	0.0789428i
$664$		0			0
$665$	−2.35754	−	1.26739i	−0.0914214	−	0.0491473i
$666$		0			0
$667$	−15.2541	+	26.4209i	−0.590642	+	1.02302i
$668$		0			0
$669$	−2.47207	−	6.58520i	−0.0955758	−	0.254599i
$670$		0			0
$671$	−0.564339	−	0.977464i	−0.0217861	−	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$		0			0
$675$	−22.7836	−	12.2533i	−0.876942	−	0.471631i
$676$		0			0
$677$	−19.1657	−	33.1960i	−0.736600	−	1.27583i	−0.954018	−	0.299749i	$-0.903097\pi$
$677$	−19.1657	−	33.1960i	−0.736600	−	1.27583i	0.217418	−	0.976078i	$-0.430236\pi$
$678$		0			0
$679$	18.5736	+	9.98498i	0.712788	+	0.383188i
$680$		0			0
$681$	−4.23793	+	5.15494i	−0.162398	+	0.197538i
$682$		0			0
$683$	3.31659	+	5.74450i	0.126906	+	0.219807i	0.922476	−	0.386054i	$-0.126162\pi$
$683$	3.31659	+	5.74450i	0.126906	+	0.219807i	−0.795570	+	0.605861i	$0.792829\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$		0			0
$687$	−14.4272	+	17.5489i	−0.550430	+	0.669534i
$688$		0			0
$689$	0.534322	−	0.925472i	0.0203560	−	0.0352577i
$690$		0			0
$691$	−11.6938	−	20.2542i	−0.444852	−	0.770506i	0.553190	−	0.833055i	$-0.313410\pi$
$691$	−11.6938	−	20.2542i	−0.444852	−	0.770506i	−0.998042	+	0.0625490i	$0.980077\pi$
$692$		0			0
$693$	12.8751	−	2.94642i	0.489084	−	0.111925i
$694$		0			0
$695$	0.916269	+	1.58702i	0.0347561	+	0.0601992i
$696$		0			0
$697$	−7.26791	+	12.5884i	−0.275292	+	0.476819i
$698$		0			0
$699$	−10.6542	−	28.3810i	−0.402978	−	1.07347i
$700$		0			0
$701$	9.26736			0.350023			0.175012	−	0.984566i	$-0.444004\pi$
$701$	9.26736			0.350023			0.175012	+	0.984566i	$0.444004\pi$
$702$		0			0
$703$	−24.2131	−	41.9383i	−0.913214	−	1.58173i
$704$		0			0
$705$	−0.452738	−	0.0751449i	−0.0170511	−	0.00283012i
$706$		0			0
$707$	−1.19101	−	39.2528i	−0.0447924	−	1.47625i
$708$		0			0
$709$	−7.11775	−	12.3283i	−0.267313	−	0.462999i	0.700854	−	0.713305i	$-0.252802\pi$
$709$	−7.11775	−	12.3283i	−0.267313	−	0.462999i	−0.968167	+	0.250305i	$0.919469\pi$
$710$		0			0
$711$	28.9043	−	25.2611i	1.08399	−	0.947365i
$712$		0			0
$713$	−7.78230	+	13.4793i	−0.291449	+	0.504805i
$714$		0			0
$715$	0.0243226	+	0.0421280i	0.000909613	+	0.00157550i
$716$		0			0
$717$	12.5026	+	2.07517i	0.466919	+	0.0774986i
$718$		0			0
$719$	−6.92848	+	12.0005i	−0.258389	+	0.447542i	−0.965810	−	0.259249i	$-0.916525\pi$
$719$	−6.92848	+	12.0005i	−0.258389	+	0.447542i	0.707422	+	0.706792i	$0.249858\pi$
$720$		0			0
$721$	−0.0163649	−	0.539348i	−0.000609459	−	0.0200864i
$722$		0			0
$723$	−6.85383	+	8.33688i	−0.254897	+	0.310052i
$724$		0			0
$725$	12.2851	−	21.2784i	0.456257	−	0.790260i
$726$		0			0
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	0.412928	+	0.910764i	$0.364506\pi$
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	−0.995208	+	0.0977755i	$0.968827\pi$
$728$		0			0
$729$	14.8851	+	22.5263i	0.551299	+	0.834308i
$730$		0			0
$731$	11.8021			0.436518
$732$		0			0
$733$	−26.6006			−0.982515			−0.491257	−	0.871014i	$-0.663463\pi$
$733$	−26.6006			−0.982515			−0.491257	+	0.871014i	$0.663463\pi$
$734$		0			0
$735$	−1.04092	+	1.43544i	−0.0383950	+	0.0529470i
$736$		0			0
$737$	5.14757	−	8.91586i	0.189613	−	0.328420i
$738$		0			0
$739$	−16.5019	−	28.5822i	−0.607034	−	1.05141i	−0.991727	−	0.128368i	$-0.959026\pi$
$739$	−16.5019	−	28.5822i	−0.607034	−	1.05141i	0.384693	−	0.923045i	$-0.374307\pi$
$740$		0			0
$741$	1.52096	−	1.85007i	0.0558739	−	0.0679640i
$742$		0			0
$743$	−19.3008	−	33.4299i	−0.708076	−	1.22642i	−0.965570	−	0.260144i	$-0.916230\pi$
$743$	−19.3008	−	33.4299i	−0.708076	−	1.22642i	0.257493	−	0.966280i	$-0.417103\pi$
$744$		0			0
$745$	−2.59839			−0.0951975
$746$		0			0
$747$	21.3325	+	7.28211i	0.780517	+	0.266439i
$748$		0			0
$749$	16.2400	+	8.73047i	0.593396	+	0.319004i
$750$		0			0
$751$	37.8996			1.38297			0.691487	−	0.722389i	$-0.256956\pi$
$751$	37.8996			1.38297			0.691487	+	0.722389i	$0.256956\pi$
$752$		0			0
$753$	6.21780	−	7.56323i	0.226589	−	0.275619i
$754$		0			0
$755$	1.23811			0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$		0			0
$759$	11.3149	−	13.7633i	0.410707	−	0.499576i
$760$		0			0
$761$	27.7470			1.00583			0.502913	−	0.864337i	$-0.332261\pi$
$761$	27.7470			1.00583			0.502913	+	0.864337i	$0.332261\pi$
$762$		0			0
$763$	14.9884	−	9.27072i	0.542616	−	0.335623i
$764$		0			0
$765$	−2.07168	+	1.81056i	−0.0749019	+	0.0654610i
$766$		0			0
$767$	−0.913698			−0.0329917
$768$		0			0
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$		0			0
$771$	−12.9812	+	15.7901i	−0.467505	+	0.568665i
$772$		0			0
$773$	−20.7795	−	35.9912i	−0.747388	−	1.29451i	−0.949071	−	0.315063i	$-0.897974\pi$
$773$	−20.7795	−	35.9912i	−0.747388	−	1.29451i	0.201682	−	0.979451i	$-0.435359\pi$
$774$		0			0
$775$	6.26756	−	10.8557i	0.225137	−	0.389950i
$776$		0			0
$777$	−29.6779	+	12.1802i	−1.06469	+	0.436963i
$778$		0			0
$779$	−16.0343			−0.574488
$780$		0			0
$781$	2.12580			0.0760671
$782$		0			0
$783$	−21.8114	+	13.4858i	−0.779476	+	0.481942i
$784$		0			0
$785$	0.416753	−	0.721837i	0.0148746	−	0.0257635i
$786$		0			0
$787$	−10.4484	+	18.0972i	−0.372446	+	0.645096i	−0.989941	−	0.141479i	$-0.954814\pi$
$787$	−10.4484	+	18.0972i	−0.372446	+	0.645096i	0.617495	+	0.786575i	$0.288148\pi$
$788$		0			0
$789$	−24.4629	+	29.7562i	−0.870901	+	1.05935i
$790$		0			0
$791$	−0.0869596	+	0.0537869i	−0.00309193	+	0.00191244i
$792$		0			0
$793$	−0.0677905	+	0.117417i	−0.00240731	+	0.00416959i
$794$		0			0
$795$	−1.33593	−	0.221735i	−0.0473804	−	0.00786415i
$796$		0			0
$797$	−0.319383	−	0.553188i	−0.0113131	−	0.0195949i	0.860313	−	0.509765i	$-0.170268\pi$
$797$	−0.319383	−	0.553188i	−0.0113131	−	0.0195949i	−0.871627	+	0.490171i	$0.836934\pi$
$798$		0			0
$799$	5.68091	−	9.83963i	0.200976	−	0.348101i
$800$		0			0
$801$	−25.7450	−	8.78835i	−0.909653	−	0.310521i
$802$		0			0
$803$	1.29563	+	2.24409i	0.0457217	+	0.0791923i
$804$		0			0
$805$	0.0725425	+	2.39084i	0.00255679	+	0.0842659i
$806$		0			0
$807$	4.08175	+	0.677484i	0.143684	+	0.0238486i
$808$		0			0
$809$	25.2796	+	43.7856i	0.888783	+	1.53942i	0.841315	+	0.540545i	$0.181782\pi$
$809$	25.2796	+	43.7856i	0.888783	+	1.53942i	0.0474686	+	0.998873i	$0.484885\pi$
$810$		0			0
$811$	0.784071			0.0275325			0.0137662	−	0.999905i	$-0.495618\pi$
$811$	0.784071			0.0275325			0.0137662	+	0.999905i	$0.495618\pi$
$812$		0			0
$813$	14.1382	+	37.6620i	0.495850	+	1.32087i
$814$		0			0
$815$	−0.155411	+	0.269180i	−0.00544382	+	0.00942897i
$816$		0			0
$817$	6.50939	+	11.2746i	0.227735	+	0.394448i
$818$		0			0
$819$	−1.07982	−	1.16243i	−0.0377319	−	0.0406186i
$820$		0			0
$821$	−21.7207	−	37.6213i	−0.758056	−	1.31299i	−0.943841	−	0.330401i	$-0.892816\pi$
$821$	−21.7207	−	37.6213i	−0.758056	−	1.31299i	0.185784	−	0.982591i	$-0.440517\pi$
$822$		0			0
$823$	1.98273	−	3.43419i	0.0691136	−	0.119708i	−0.829398	−	0.558659i	$-0.811316\pi$
$823$	1.98273	−	3.43419i	0.0691136	−	0.119708i	0.898511	+	0.438950i	$0.144650\pi$
$824$		0			0
$825$	−9.11262	+	11.0844i	−0.317261	+	0.385910i
$826$		0			0
$827$	−29.3159			−1.01941			−0.509707	−	0.860348i	$-0.670246\pi$
$827$	−29.3159			−1.01941			−0.509707	+	0.860348i	$0.670246\pi$
$828$		0			0
$829$	−17.5213	−	30.3478i	−0.608541	−	1.05402i	−0.991481	−	0.130251i	$-0.958422\pi$
$829$	−17.5213	−	30.3478i	−0.608541	−	1.05402i	0.382940	−	0.923773i	$-0.374912\pi$
$830$		0			0
$831$	5.07955	−	6.17868i	0.176208	−	0.214336i
$832$		0			0
$833$	−24.2134	−	36.6159i	−0.838943	−	1.26867i
$834$		0			0
$835$	−0.846358	−	1.46593i	−0.0292894	−	0.0507308i
$836$		0			0
$837$	−11.1277	+	6.88012i	−0.384628	+	0.237812i
$838$		0			0
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	−0.334639	−	0.942347i	$-0.608614\pi$
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	0.983415	−	0.181368i	$-0.0580524\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$		0			0
$843$	7.19324	+	19.1617i	0.247749	+	0.659963i
$844$		0			0
$845$	−0.947675	+	1.64142i	−0.0326010	+	0.0564666i
$846$		0			0
$847$	0.660455	+	21.7671i	0.0226935	+	0.747926i
$848$		0			0
$849$	9.64815	+	25.7011i	0.331124	+	0.882061i
$850$		0			0
$851$	−21.6378	+	37.4778i	−0.741735	+	1.28472i
$852$		0			0
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$		0			0
$855$	−2.87226	−	0.980479i	−0.0982291	−	0.0335317i
$856$		0			0
$857$	27.5347			0.940566			0.470283	−	0.882516i	$-0.344152\pi$
$857$	27.5347			0.940566			0.470283	+	0.882516i	$0.344152\pi$
$858$		0			0
$859$	46.5101			1.58690			0.793451	−	0.608634i	$-0.208282\pi$
$859$	46.5101			1.58690			0.793451	+	0.608634i	$0.208282\pi$
$860$		0			0
$861$	−1.42063	+	10.5265i	−0.0484151	+	0.358744i
$862$		0			0
$863$	−2.44007	+	4.22633i	−0.0830610	+	0.143866i	−0.904563	−	0.426339i	$-0.859803\pi$
$863$	−2.44007	+	4.22633i	−0.0830610	+	0.143866i	0.821502	+	0.570205i	$0.193136\pi$
$864$		0			0
$865$	−1.16345	−	2.01516i	−0.0395585	−	0.0685174i
$866$		0			0
$867$	−13.5909	−	36.2041i	−0.461572	−	1.22956i
$868$		0			0
$869$	−10.6463	−	18.4400i	−0.361152	−	0.625533i
$870$		0			0
$871$	−1.23669			−0.0419037
$872$		0			0
$873$	22.6287	+	7.72458i	0.765866	+	0.261437i
$874$		0			0
$875$	−0.117097	−	3.85924i	−0.00395860	−	0.130466i
$876$		0			0
$877$	39.2892			1.32670			0.663352	−	0.748308i	$-0.269133\pi$
$877$	39.2892			1.32670			0.663352	+	0.748308i	$0.269133\pi$
$878$		0			0
$879$	−24.0856	−	3.99770i	−0.812388	−	0.134839i
$880$		0			0
$881$	47.3713			1.59598			0.797990	−	0.602670i	$-0.205897\pi$
$881$	47.3713			1.59598			0.797990	+	0.602670i	$0.205897\pi$
$882$		0			0
$883$	2.67206			0.0899221			0.0449610	−	0.998989i	$-0.485684\pi$
$883$	2.67206			0.0899221			0.0449610	+	0.998989i	$0.485684\pi$
$884$		0			0
$885$	0.406927	+	1.08399i	0.0136787	+	0.0364379i
$886$		0			0
$887$	22.9600			0.770922			0.385461	−	0.922724i	$-0.374042\pi$
$887$	22.9600			0.770922			0.385461	+	0.922724i	$0.374042\pi$
$888$		0			0
$889$	1.08155	+	35.6453i	0.0362739	+	1.19550i
$890$		0			0
$891$	13.8559	−	5.68387i	0.464189	−	0.190417i
$892$		0			0
$893$	12.5331			0.419404
$894$		0			0
$895$	0.566944	+	0.981976i	0.0189508	+	0.0328238i
$896$		0			0
$897$	−2.11140	−	0.350447i	−0.0704975	−	0.0117011i
$898$		0			0
$899$	−6.21284	−	10.7610i	−0.207210	−	0.358898i
$900$		0			0
$901$	16.7631	−	29.0345i	0.558459	−	0.967280i
$902$		0			0
$903$	7.97853	−	3.27450i	0.265509	−	0.108969i
$904$		0			0
$905$	1.77862			0.0591232
$906$		0			0
$907$	27.8982			0.926345			0.463173	−	0.886268i	$-0.346711\pi$
$907$	27.8982			0.926345			0.463173	+	0.886268i	$0.346711\pi$
$908$		0			0
$909$	−8.61250	−	43.6882i	−0.285659	−	1.44905i
$910$		0			0
$911$	18.7381	−	32.4553i	0.620820	−	1.07529i	−0.368513	−	0.929623i	$-0.620133\pi$
$911$	18.7381	−	32.4553i	0.620820	−	1.07529i	0.989333	−	0.145670i	$-0.0465337\pi$
$912$		0			0
$913$	6.25158	−	10.8281i	0.206897	−	0.358356i
$914$		0			0
$915$	0.169492	+	0.0281320i	0.00560322	+	0.000930016i
$916$		0			0
$917$	−1.59143	−	52.4499i	−0.0525536	−	1.73205i
$918$		0			0
$919$	15.1073	−	26.1667i	0.498345	−	0.863160i	−0.501653	−	0.865069i	$-0.667274\pi$
$919$	15.1073	−	26.1667i	0.498345	−	0.863160i	0.999998	+	0.00190951i	$0.000607816\pi$
$920$		0			0
$921$	30.1293	−	36.6487i	0.992793	−	1.20762i
$922$		0			0
$923$	−0.127680	−	0.221147i	−0.00420262	−	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$		0			0
$927$	−0.118339	−	0.600292i	−0.00388676	−	0.0197162i
$928$		0			0
$929$	22.9675	+	39.7809i	0.753540	+	1.30517i	0.946097	+	0.323884i	$0.104989\pi$
$929$	22.9675	+	39.7809i	0.753540	+	1.30517i	−0.192556	+	0.981286i	$0.561678\pi$
$930$		0			0
$931$	21.6245	−	43.3263i	0.708715	−	1.41996i
$932$		0			0
$933$	−8.55612	−	22.7921i	−0.280115	−	0.746181i
$934$		0			0
$935$	0.763064	+	1.32167i	0.0249549	+	0.0432231i
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$		0			0
$939$	37.1545	+	6.16686i	1.21249	+	0.201248i
$940$		0			0
$941$	−24.7002	+	42.7819i	−0.805202	+	1.39465i	0.110952	+	0.993826i	$0.464610\pi$
$941$	−24.7002	+	42.7819i	−0.805202	+	1.39465i	−0.916154	+	0.400825i	$0.868723\pi$
$942$		0			0
$943$	7.16445	+	12.4092i	0.233307	+	0.404099i
$944$		0			0
$945$	−0.898168	+	1.79877i	−0.0292174	+	0.0585141i
$946$		0			0
$947$	15.8253	+	27.4102i	0.514252	+	0.890711i	0.999863	+	0.0165357i	$0.00526371\pi$
$947$	15.8253	+	27.4102i	0.514252	+	0.890711i	−0.485611	+	0.874175i	$0.661403\pi$
$948$		0			0
$949$	0.155636	−	0.269569i	0.00505214	−	0.00875057i
$950$		0			0
$951$	14.6313	+	2.42849i	0.474453	+	0.0787492i
$952$		0			0
$953$	−19.1237			−0.619477			−0.309739	−	0.950822i	$-0.600242\pi$
$953$	−19.1237			−0.619477			−0.309739	+	0.950822i	$0.600242\pi$
$954$		0			0
$955$	0.363249	+	0.629165i	0.0117545	+	0.0203593i
$956$		0			0
$957$	4.99906	+	13.3167i	0.161597	+	0.430467i
$958$		0			0
$959$	0.517156	+	17.0443i	0.0166998	+	0.550388i
$960$		0			0
$961$	12.3304	+	21.3568i	0.397753	+	0.688929i
$962$		0			0
$963$	19.7856	+	6.75406i	0.637583	+	0.217647i
$964$		0			0
$965$	−1.08985	+	1.88768i	−0.0350836	+	0.0607666i
$966$		0			0
$967$	−4.98525	−	8.63470i	−0.160315	−	0.277673i	0.774667	−	0.632370i	$-0.217918\pi$
$967$	−4.98525	−	8.63470i	−0.160315	−	0.277673i	−0.934982	+	0.354696i	$0.884584\pi$
$968$		0			0
$969$	47.7166	−	58.0416i	1.53288	−	1.86456i
$970$		0			0
$971$	−0.522554	+	0.905090i	−0.0167695	+	0.0290457i	−0.874288	−	0.485407i	$-0.838671\pi$
$971$	−0.522554	+	0.905090i	−0.0167695	+	0.0290457i	0.857519	+	0.514453i	$0.172005\pi$
$972$		0			0
$973$	−28.1951	+	17.4395i	−0.903895	+	0.559084i
$974$		0			0
$975$	1.70044	+	0.282237i	0.0544576	+	0.00903880i
$976$		0			0
$977$	9.44308	−	16.3559i	0.302111	−	0.523272i	−0.674503	−	0.738272i	$-0.735642\pi$
$977$	9.44308	−	16.3559i	0.302111	−	0.523272i	0.976614	+	0.215001i	$0.0689753\pi$
$978$		0			0
$979$	−7.54466	+	13.0677i	−0.241128	+	0.417647i
$980$		0			0
$981$	15.0469	−	13.1503i	0.480410	−	0.419858i
$982$		0			0
$983$	−2.28891			−0.0730050			−0.0365025	−	0.999334i	$-0.511622\pi$
$983$	−2.28891			−0.0730050			−0.0365025	+	0.999334i	$0.511622\pi$
$984$		0			0
$985$	3.10930			0.0990707
$986$		0			0
$987$	1.11043	−	8.22800i	0.0353453	−	0.261900i
$988$		0			0
$989$	5.81707	−	10.0755i	0.184972	−	0.320381i
$990$		0			0
$991$	9.53491	+	16.5150i	0.302886	+	0.524615i	0.976789	−	0.214206i	$-0.0687164\pi$
$991$	9.53491	+	16.5150i	0.302886	+	0.524615i	−0.673902	+	0.738821i	$0.735383\pi$
$992$		0			0
$993$	−18.5343	−	3.07631i	−0.588170	−	0.0976237i
$994$		0			0
$995$	−1.45837	−	2.52598i	−0.0462336	−	0.0800789i
$996$		0			0
$997$	37.0151			1.17228			0.586139	−	0.810210i	$-0.300647\pi$
$997$	37.0151			1.17228			0.586139	+	0.810210i	$0.300647\pi$
$998$		0			0
$999$	−30.9392	+	19.1294i	−0.978875	+	0.605228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.i.961.2		10
3.2	odd	2		3024.2.t.i.289.3		10
4.3	odd	2		63.2.g.b.16.1	yes	10
7.4	even	3		1008.2.q.i.529.5		10
9.4	even	3		1008.2.q.i.625.5		10
9.5	odd	6		3024.2.q.i.2305.3		10
12.11	even	2		189.2.g.b.100.5		10
21.11	odd	6		3024.2.q.i.2881.3		10
28.3	even	6		441.2.h.f.214.5		10
28.11	odd	6		63.2.h.b.25.5	yes	10
28.19	even	6		441.2.f.f.295.1		10
28.23	odd	6		441.2.f.e.295.1		10
28.27	even	2		441.2.g.f.79.1		10
36.7	odd	6		567.2.e.f.163.1		10
36.11	even	6		567.2.e.e.163.5		10
36.23	even	6		189.2.h.b.37.1		10
36.31	odd	6		63.2.h.b.58.5	yes	10
63.4	even	3	inner	1008.2.t.i.193.2		10
63.32	odd	6		3024.2.t.i.1873.3		10
84.11	even	6		189.2.h.b.46.1		10
84.23	even	6		1323.2.f.e.883.5		10
84.47	odd	6		1323.2.f.f.883.5		10
84.59	odd	6		1323.2.h.f.802.1		10
84.83	odd	2		1323.2.g.f.667.5		10
252.11	even	6		567.2.e.e.487.5		10
252.23	even	6		1323.2.f.e.442.5		10
252.31	even	6		441.2.g.f.67.1		10
252.47	odd	6		3969.2.a.bb.1.1		5
252.59	odd	6		1323.2.g.f.361.5		10
252.67	odd	6		63.2.g.b.4.1	✓	10
252.79	odd	6		3969.2.a.z.1.5		5
252.95	even	6		189.2.g.b.172.5		10
252.103	even	6		441.2.f.f.148.1		10
252.131	odd	6		1323.2.f.f.442.5		10
252.139	even	6		441.2.h.f.373.5		10
252.151	odd	6		567.2.e.f.487.1		10
252.167	odd	6		1323.2.h.f.226.1		10
252.187	even	6		3969.2.a.ba.1.5		5
252.191	even	6		3969.2.a.bc.1.1		5
252.247	odd	6		441.2.f.e.148.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	252.67	odd	6
63.2.g.b.16.1	yes	10	4.3	odd	2
63.2.h.b.25.5	yes	10	28.11	odd	6
63.2.h.b.58.5	yes	10	36.31	odd	6
189.2.g.b.100.5		10	12.11	even	2
189.2.g.b.172.5		10	252.95	even	6
189.2.h.b.37.1		10	36.23	even	6
189.2.h.b.46.1		10	84.11	even	6
441.2.f.e.148.1		10	252.247	odd	6
441.2.f.e.295.1		10	28.23	odd	6
441.2.f.f.148.1		10	252.103	even	6
441.2.f.f.295.1		10	28.19	even	6
441.2.g.f.67.1		10	252.31	even	6
441.2.g.f.79.1		10	28.27	even	2
441.2.h.f.214.5		10	28.3	even	6
441.2.h.f.373.5		10	252.139	even	6
567.2.e.e.163.5		10	36.11	even	6
567.2.e.e.487.5		10	252.11	even	6
567.2.e.f.163.1		10	36.7	odd	6
567.2.e.f.487.1		10	252.151	odd	6
1008.2.q.i.529.5		10	7.4	even	3
1008.2.q.i.625.5		10	9.4	even	3
1008.2.t.i.193.2		10	63.4	even	3	inner
1008.2.t.i.961.2		10	1.1	even	1	trivial
1323.2.f.e.442.5		10	252.23	even	6
1323.2.f.e.883.5		10	84.23	even	6
1323.2.f.f.442.5		10	252.131	odd	6
1323.2.f.f.883.5		10	84.47	odd	6
1323.2.g.f.361.5		10	252.59	odd	6
1323.2.g.f.667.5		10	84.83	odd	2
1323.2.h.f.226.1		10	252.167	odd	6
1323.2.h.f.802.1		10	84.59	odd	6
3024.2.q.i.2305.3		10	9.5	odd	6
3024.2.q.i.2881.3		10	21.11	odd	6
3024.2.t.i.289.3		10	3.2	odd	2
3024.2.t.i.1873.3		10	63.32	odd	6
3969.2.a.z.1.5		5	252.79	odd	6
3969.2.a.ba.1.5		5	252.187	even	6
3969.2.a.bb.1.1		5	252.47	odd	6
3969.2.a.bc.1.1		5	252.191	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09995 + 1.33795i) q^{3} -0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +(-0.580240 - 2.94335i) q^{9} +O(q^{10})\)	\(q+(-1.09995 + 1.33795i) q^{3} -0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +(-0.580240 - 2.94335i) q^{9} -1.66404 q^{11} +(0.0999454 + 0.173111i) q^{13} +(0.160862 - 0.195670i) q^{15} +(3.13555 + 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} +(3.62652 + 2.80149i) q^{21} +6.18184 q^{23} -4.97861 q^{25} +(4.57630 + 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-1.25890 + 2.18047i) q^{31} +(1.83035 - 2.22641i) q^{33} +(0.0117348 + 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(-0.341548 - 0.0566898i) q^{39} +(1.15895 + 2.00736i) q^{41} +(0.940993 - 1.62985i) q^{43} +(0.0848576 + 0.430452i) q^{45} +(-0.905887 - 1.56904i) q^{47} +(-6.98712 + 0.424396i) q^{49} +(-10.7153 - 1.77851i) q^{51} +(-2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-2.28549 + 3.95859i) q^{59} +(0.339138 + 0.587404i) q^{61} +(-7.73724 + 1.77064i) q^{63} +(-0.0146166 - 0.0253167i) q^{65} +(-3.09342 + 5.35796i) q^{67} +(-6.79968 + 8.27101i) q^{69} -1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(5.47620 - 6.66115i) q^{75} +(0.133523 + 4.40061i) q^{77} +(6.39787 + 11.0814i) q^{79} +(-8.32664 + 3.41570i) q^{81} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-3.00417 - 8.00262i) q^{87} +(4.53394 - 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +(-1.53266 - 4.08275i) q^{93} +(0.505833 - 0.876128i) q^{95} +(-3.98514 + 6.90246i) q^{97} +(0.965543 + 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Introduction

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