LMFDB - Embedded newform 1008.2.q.i.625.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (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			625.5
Root			$-1.02682 - 1.77851i$ of defining polynomial
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.i.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70867 - 0.283604i) q^{3} +(0.0731228 + 0.126652i) q^{5} +(2.33035 + 1.25278i) q^{7} +(2.83914 - 0.969173i) q^{9} +O(q^{10})$	\(q+(1.70867 - 0.283604i) q^{3} +(0.0731228 + 0.126652i) q^{5} +(2.33035 + 1.25278i) q^{7} +(2.83914 - 0.969173i) q^{9} +(0.832020 - 1.44110i) q^{11} +(0.0999454 - 0.173111i) q^{13} +(0.160862 + 0.195670i) q^{15} +(3.13555 + 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} +(4.33711 + 1.47969i) q^{21} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +(4.57630 - 2.46119i) q^{27} +(-2.46757 - 4.27396i) q^{29} +2.51780 q^{31} +(1.01295 - 2.69834i) q^{33} +(0.0117348 + 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(0.121679 - 0.324134i) q^{39} +(1.15895 - 2.00736i) q^{41} +(0.940993 + 1.62985i) q^{43} +(0.330354 + 0.288715i) q^{45} +1.81177 q^{47} +(3.86110 + 5.83883i) q^{49} +(6.89787 + 8.39045i) q^{51} +(-2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +(-4.21093 + 11.2172i) q^{57} +4.57099 q^{59} -0.678276 q^{61} +(7.83035 + 1.29829i) q^{63} +0.0292332 q^{65} +6.18684 q^{67} +(-6.79968 - 8.27101i) q^{69} -1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(3.03063 - 8.07311i) q^{75} +(3.74428 - 2.31594i) q^{77} -12.7957 q^{79} +(7.12141 - 5.50323i) q^{81} +(-3.75687 - 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} +(-5.42839 - 6.60299i) q^{87} +(4.53394 - 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +(4.30209 - 0.714056i) q^{93} -1.01167 q^{95} +(-3.98514 - 6.90246i) q^{97} +(0.965543 - 4.89786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.70867	−	0.283604i	0.986504	−	0.163739i
$3$	1.70867	−	0.283604i	0.986504	−	0.163739i
$4$		0			0
$5$	0.0731228	+	0.126652i	0.0327015	+	0.0566407i	0.881913	−	0.471412i	$-0.156256\pi$
$5$	0.0731228	+	0.126652i	0.0327015	+	0.0566407i	−0.849211	+	0.528053i	$0.822922\pi$
$6$		0			0
$7$	2.33035	+	1.25278i	0.880791	+	0.473505i
$7$	2.33035	+	1.25278i	0.880791	+	0.473505i
$8$		0			0
$9$	2.83914	−	0.969173i	0.946379	−	0.323058i
$10$		0			0
$11$	0.832020	−	1.44110i	0.250864	−	0.434508i	−0.712900	−	0.701265i	$-0.752619\pi$
$11$	0.832020	−	1.44110i	0.250864	−	0.434508i	0.963764	+	0.266757i	$0.0859521\pi$
$12$		0			0
$13$	0.0999454	−	0.173111i	0.0277199	−	0.0480122i	−0.851833	−	0.523814i	$-0.824509\pi$
$13$	0.0999454	−	0.173111i	0.0277199	−	0.0480122i	0.879553	+	0.475802i	$0.157842\pi$
$14$		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
$21$	4.33711	+	1.47969i	0.946435	+	0.322895i
$22$		0			0
$23$	−3.09092	−	5.35363i	−0.644501	−	1.11631i	−0.984417	−	0.175852i	$-0.943732\pi$
$23$	−3.09092	−	5.35363i	−0.644501	−	1.11631i	0.339916	−	0.940456i	$-0.389601\pi$
$24$		0			0
$25$	2.48931	−	4.31160i	0.497861	−	0.862321i
$26$		0			0
$27$	4.57630	−	2.46119i	0.880710	−	0.473657i
$28$		0			0
$29$	−2.46757	−	4.27396i	−0.458217	−	0.793655i	0.540650	−	0.841248i	$-0.318178\pi$
$29$	−2.46757	−	4.27396i	−0.458217	−	0.793655i	−0.998867	+	0.0475930i	$0.984845\pi$
$30$		0			0
$31$	2.51780			0.452209			0.226105	−	0.974103i	$-0.427401\pi$
$31$	2.51780			0.452209			0.226105	+	0.974103i	$0.427401\pi$
$32$		0			0
$33$	1.01295	−	2.69834i	0.176332	−	0.469720i
$34$		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
$39$	0.121679	−	0.324134i	0.0194843	−	0.0519030i
$40$		0			0
$41$	1.15895	−	2.00736i	0.180998	−	0.313498i	−0.761223	−	0.648491i	$-0.775401\pi$
$41$	1.15895	−	2.00736i	0.180998	−	0.313498i	0.942221	+	0.334993i	$0.108734\pi$
$42$		0			0
$43$	0.940993	+	1.62985i	0.143500	+	0.248550i	0.928812	−	0.370550i	$-0.120831\pi$
$43$	0.940993	+	1.62985i	0.143500	+	0.248550i	−0.785312	+	0.619100i	$0.787498\pi$
$44$		0			0
$45$	0.330354	+	0.288715i	0.0492463	+	0.0430391i
$46$		0			0
$47$	1.81177			0.264275			0.132137	−	0.991231i	$-0.457816\pi$
$47$	1.81177			0.264275			0.132137	+	0.991231i	$0.457816\pi$
$48$		0			0
$49$	3.86110	+	5.83883i	0.551586	+	0.834118i
$50$		0			0
$51$	6.89787	+	8.39045i	0.965895	+	1.17490i
$52$		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
$59$	4.57099			0.595092			0.297546	−	0.954708i	$-0.403832\pi$
$59$	4.57099			0.595092			0.297546	+	0.954708i	$0.403832\pi$
$60$		0			0
$61$	−0.678276			−0.0868443			−0.0434221	−	0.999057i	$-0.513826\pi$
$61$	−0.678276			−0.0868443			−0.0434221	+	0.999057i	$0.513826\pi$
$62$		0			0
$63$	7.83035	+	1.29829i	0.986532	+	0.163569i
$64$		0			0
$65$	0.0292332			0.00362593
$66$		0			0
$67$	6.18684			0.755842			0.377921	−	0.925838i	$-0.376639\pi$
$67$	6.18684			0.755842			0.377921	+	0.925838i	$0.376639\pi$
$68$		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
$75$	3.03063	−	8.07311i	0.349947	−	0.932202i
$76$		0			0
$77$	3.74428	−	2.31594i	0.426700	−	0.263926i
$78$		0			0
$79$	−12.7957			−1.43963			−0.719817	−	0.694164i	$-0.755774\pi$
$79$	−12.7957			−1.43963			−0.719817	+	0.694164i	$0.755774\pi$
$80$		0			0
$81$	7.12141	−	5.50323i	0.791267	−	0.611470i
$82$		0			0
$83$	−3.75687	−	6.50709i	−0.412370	−	0.714246i	0.582778	−	0.812631i	$-0.301966\pi$
$83$	−3.75687	−	6.50709i	−0.412370	−	0.714246i	−0.995148	+	0.0983854i	$0.968632\pi$
$84$		0			0
$85$	−0.458561	+	0.794251i	−0.0497379	+	0.0861486i
$86$		0			0
$87$	−5.42839	−	6.60299i	−0.581984	−	0.707915i
$88$		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
$93$	4.30209	−	0.714056i	0.446106	−	0.0740442i
$94$		0			0
$95$	−1.01167			−0.103795
$96$		0			0
$97$	−3.98514	−	6.90246i	−0.404630	−	0.700839i	0.589649	−	0.807660i	$-0.299266\pi$
$97$	−3.98514	−	6.90246i	−0.404630	−	0.700839i	−0.994278	+	0.106821i	$0.965933\pi$
$98$		0			0
$99$	0.965543	−	4.89786i	0.0970408	−	0.492253i
$100$		0			0
$101$	−7.42150	+	12.8544i	−0.738467	+	1.27906i	0.214719	+	0.976676i	$0.431117\pi$
$101$	−7.42150	+	12.8544i	−0.738467	+	1.27906i	−0.953186	+	0.302386i	$0.902217\pi$
$102$		0			0
$103$	−0.101974	−	0.176624i	−0.0100478	−	0.0174033i	0.860958	−	0.508676i	$-0.169865\pi$
$103$	−0.101974	−	0.176624i	−0.0100478	−	0.0174033i	−0.871006	+	0.491273i	$0.836532\pi$
$104$		0			0
$105$	0.129735	+	0.657505i	0.0126609	+	0.0641659i
$106$		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	−0.866933	−	0.498425i	$-0.833912\pi$
$113$	−0.0193234	+	0.0334691i	−0.00181779	+	0.00314851i	0.865115	+	0.501573i	$0.167245\pi$
$114$		0			0
$115$	0.452033	−	0.782945i	0.0421523	−	0.0730100i
$116$		0			0
$117$	0.115985	−	0.588349i	0.0107228	−	0.0543929i
$118$		0			0
$119$	0.503195	+	16.5841i	0.0461278	+	1.52027i
$120$		0			0
$121$	4.11548	+	7.12823i	0.374135	+	0.648021i
$122$		0			0
$123$	1.41098	−	3.75862i	0.127223	−	0.338903i
$124$		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
$129$	2.07008	+	2.51801i	0.182261	+	0.221698i
$130$		0			0
$131$	−9.91665	−	17.1761i	−0.866422	−	1.50069i	−0.865628	−	0.500687i	$-0.833081\pi$
$131$	−9.91665	−	17.1761i	−0.866422	−	1.50069i	−0.000793988	−	1.00000i	$-0.500253\pi$
$132$		0			0
$133$	−15.5653	+	9.62759i	−1.34969	+	0.834818i
$134$		0			0
$135$	0.646348	+	0.399630i	0.0556288	+	0.0343947i
$136$		0			0
$137$	3.22255	−	5.58162i	0.275321	−	0.476870i	−0.694895	−	0.719111i	$-0.744549\pi$
$137$	3.22255	−	5.58162i	0.275321	−	0.476870i	0.970216	+	0.242241i	$0.0778826\pi$
$138$		0			0
$139$	−6.26527	+	10.8518i	−0.531413	+	0.920435i	0.467914	+	0.883774i	$0.345006\pi$
$139$	−6.26527	+	10.8518i	−0.531413	+	0.920435i	−0.999328	+	0.0366611i	$0.988328\pi$
$140$		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
$147$	8.25328	+	8.88163i	0.680719	+	0.732545i
$148$		0			0
$149$	−8.88364	−	15.3869i	−0.727776	−	1.26054i	−0.957821	−	0.287365i	$-0.907221\pi$
$149$	−8.88364	−	15.3869i	−0.727776	−	1.26054i	0.230045	−	0.973180i	$-0.426113\pi$
$150$		0			0
$151$	4.23300	−	7.33177i	0.344476	−	0.596651i	−0.640782	−	0.767723i	$-0.721390\pi$
$151$	4.23300	−	7.33177i	0.344476	−	0.596651i	0.985259	+	0.171072i	$0.0547231\pi$
$152$		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
$157$	5.69935			0.454858			0.227429	−	0.973795i	$-0.426968\pi$
$157$	5.69935			0.454858			0.227429	+	0.973795i	$0.426968\pi$
$158$		0			0
$159$	−5.88046	−	7.15288i	−0.466351	−	0.567261i
$160$		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
$165$	0.415821	−	0.0690175i	0.0323716	−	0.00537300i
$166$		0			0
$167$	5.78723	−	10.0238i	0.447829	−	0.775663i	−0.550415	−	0.834891i	$-0.685530\pi$
$167$	5.78723	−	10.0238i	0.447829	−	0.775663i	0.998244	+	0.0592278i	$0.0188638\pi$
$168$		0			0
$169$	6.48002	+	11.2237i	0.498463	+	0.863364i
$170$		0			0
$171$	−4.01386	+	20.3609i	−0.306947	+	1.55703i
$172$		0			0
$173$	−15.9109			−1.20968			−0.604842	−	0.796345i	$-0.706764\pi$
$173$	−15.9109			−1.20968			−0.604842	+	0.796345i	$0.706764\pi$
$174$		0			0
$175$	11.2024	−	6.92902i	0.846825	−	0.523785i
$176$		0			0
$177$	7.81033	−	1.29635i	0.587060	−	0.0974395i
$178$		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
$185$	−1.02379			−0.0752703
$186$		0			0
$187$	10.4354			0.763110
$188$		0			0
$189$	13.7477	−	0.00236321i	1.00000	−	0.000171898i
$190$		0			0
$191$	4.96765			0.359447			0.179723	−	0.983717i	$-0.442480\pi$
$191$	4.96765			0.359447			0.179723	+	0.983717i	$0.442480\pi$
$192$		0			0
$193$	−14.9044			−1.07284			−0.536422	−	0.843950i	$-0.680224\pi$
$193$	−14.9044			−1.07284			−0.536422	+	0.843950i	$0.680224\pi$
$194$		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
$201$	10.5713	−	1.75461i	0.745641	−	0.123761i
$202$		0			0
$203$	−0.395997	−	13.0512i	−0.0277935	−	0.916012i
$204$		0			0
$205$	0.338983			0.0236756
$206$		0			0
$207$	−13.9641	−	12.2040i	−0.970574	−	0.848240i
$208$		0			0
$209$	5.75556	+	9.96893i	0.398121	+	0.689565i
$210$		0			0
$211$	−11.7569	+	20.3636i	−0.809381	+	1.40189i	0.103912	+	0.994587i	$0.466864\pi$
$211$	−11.7569	+	20.3636i	−0.809381	+	1.40189i	−0.913293	+	0.407303i	$0.866469\pi$
$212$		0			0
$213$	−2.18282	+	0.362302i	−0.149564	+	0.0248245i
$214$		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
$219$	−1.71284	−	2.08347i	−0.115743	−	0.140788i
$220$		0			0
$221$	1.25354			0.0843220
$222$		0			0
$223$	−2.03052	−	3.51696i	−0.135974	−	0.235513i	0.789995	−	0.613113i	$-0.210083\pi$
$223$	−2.03052	−	3.51696i	−0.135974	−	0.235513i	−0.925969	+	0.377600i	$0.876750\pi$
$224$		0			0
$225$	2.88879	−	14.6538i	0.192586	−	0.976921i
$226$		0			0
$227$	−1.92643	+	3.33667i	−0.127861	+	0.221462i	−0.922848	−	0.385165i	$-0.874145\pi$
$227$	−1.92643	+	3.33667i	−0.127861	+	0.221462i	0.794986	+	0.606627i	$0.207478\pi$
$228$		0			0
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	0.563788	−	0.825919i	$-0.309343\pi$
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	−0.997161	+	0.0752952i	$0.976010\pi$
$230$		0			0
$231$	5.74095	−	5.01908i	0.377727	−	0.330231i
$232$		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	−0.959752	−	0.280849i	$-0.909384\pi$
$239$	−3.65857	+	6.33683i	−0.236653	+	0.409895i	0.723099	+	0.690745i	$0.242717\pi$
$240$		0			0
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	−0.948751	−	0.316026i	$-0.897651\pi$
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	0.748062	+	0.663629i	$0.230985\pi$
$242$		0			0
$243$	10.6074	−	11.4229i	0.680467	−	0.732779i
$244$		0			0
$245$	−0.457167	+	0.915969i	−0.0292074	+	0.0585191i
$246$		0			0
$247$	0.691380	+	1.19751i	0.0439915	+	0.0761954i
$248$		0			0
$249$	−8.26470	−	10.0530i	−0.523754	−	0.637085i
$250$		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
$255$	−0.558279	+	1.48717i	−0.0349608	+	0.0931299i
$256$		0			0
$257$	−5.90082	−	10.2205i	−0.368083	−	0.637539i	0.621183	−	0.783666i	$-0.286653\pi$
$257$	−5.90082	−	10.2205i	−0.368083	−	0.637539i	−0.989266	+	0.146127i	$0.953319\pi$
$258$		0			0
$259$	−15.7518	+	9.74293i	−0.978770	+	0.605396i
$260$		0			0
$261$	−11.1480	−	9.74286i	−0.690043	−	0.603068i
$262$		0			0
$263$	−11.1200	+	19.2605i	−0.685691	+	1.18765i	0.287528	+	0.957772i	$0.407166\pi$
$263$	−11.1200	+	19.2605i	−0.685691	+	1.18765i	−0.973219	+	0.229879i	$0.926167\pi$
$264$		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
$273$	0.689624	−	0.602911i	0.0417380	−	0.0364898i
$274$		0			0
$275$	−4.14231	−	7.17469i	−0.249790	−	0.432650i
$276$		0			0
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	−0.788283	−	0.615312i	$-0.789030\pi$
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	0.927018	+	0.375017i	$0.122363\pi$
$278$		0			0
$279$	7.14837	−	2.44018i	0.427962	−	0.146090i
$280$		0			0
$281$	5.90841	+	10.2337i	0.352466	+	0.610489i	0.986681	−	0.162668i	$-0.0520098\pi$
$281$	5.90841	+	10.2337i	0.352466	+	0.610489i	−0.634215	+	0.773157i	$0.718676\pi$
$282$		0			0
$283$	−15.8497			−0.942165			−0.471082	−	0.882089i	$-0.656137\pi$
$283$	−15.8497			−0.942165			−0.471082	+	0.882089i	$0.656137\pi$
$284$		0			0
$285$	−1.72861	+	0.286912i	−0.102394	+	0.0169952i
$286$		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
$291$	−8.76687	−	10.6639i	−0.513923	−	0.625127i
$292$		0			0
$293$	7.04804	−	12.2076i	0.411751	−	0.713173i	−0.583330	−	0.812235i	$-0.698251\pi$
$293$	7.04804	−	12.2076i	0.411751	−	0.713173i	0.995081	+	0.0990615i	$0.0315841\pi$
$294$		0			0
$295$	0.334243	+	0.578927i	0.0194604	+	0.0337064i
$296$		0			0
$297$	0.260748	−	8.64268i	0.0151302	−	0.501499i
$298$		0			0
$299$	−1.23569			−0.0714619
$300$		0			0
$301$	0.151011	+	4.97698i	0.00870413	+	0.286868i
$302$		0			0
$303$	−9.03537	+	24.0688i	−0.519068	+	1.38272i
$304$		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
$311$	14.0557			0.797026			0.398513	−	0.917163i	$-0.369526\pi$
$311$	14.0557			0.797026			0.398513	+	0.917163i	$0.369526\pi$
$312$		0			0
$313$	21.7446			1.22908			0.614540	−	0.788886i	$-0.289342\pi$
$313$	21.7446			1.22908			0.614540	+	0.788886i	$0.289342\pi$
$314$		0			0
$315$	0.408146	+	1.08667i	0.0229964	+	0.0612268i
$316$		0			0
$317$	8.56297			0.480944			0.240472	−	0.970656i	$-0.422698\pi$
$317$	8.56297			0.480944			0.240472	+	0.970656i	$0.422698\pi$
$318$		0			0
$319$	−8.21228			−0.459799
$320$		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
$327$	7.32692	+	8.91233i	0.405179	+	0.492853i
$328$		0			0
$329$	4.22208	+	2.26975i	0.232771	+	0.125135i
$330$		0			0
$331$	−10.8472			−0.596216			−0.298108	−	0.954532i	$-0.596356\pi$
$331$	−10.8472			−0.596216			−0.298108	+	0.954532i	$0.596356\pi$
$332$		0			0
$333$	−4.06195	+	20.6048i	−0.222593	+	1.12914i
$334$		0			0
$335$	0.452399	+	0.783578i	0.0247172	+	0.0428114i
$336$		0			0
$337$	1.67411	−	2.89964i	0.0911945	−	0.157954i	−0.816819	−	0.576893i	$-0.804265\pi$
$337$	1.67411	−	2.89964i	0.0911945	−	0.157954i	0.908014	+	0.418940i	$0.137598\pi$
$338$		0			0
$339$	−0.0235254	+	0.0626679i	−0.00127772	+	0.00340365i
$340$		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
$345$	0.550332	−	1.46600i	0.0296289	−	0.0789266i
$346$		0			0
$347$	11.5330			0.619126			0.309563	−	0.950879i	$-0.399817\pi$
$347$	11.5330			0.619126			0.309563	+	0.950879i	$0.399817\pi$
$348$		0			0
$349$	−4.44917	−	7.70619i	−0.238159	−	0.412503i	0.722027	−	0.691865i	$-0.243211\pi$
$349$	−4.44917	−	7.70619i	−0.238159	−	0.412503i	−0.960186	+	0.279362i	$0.909877\pi$
$350$		0			0
$351$	0.0313221	−	1.03819i	0.00167185	−	0.0554145i
$352$		0			0
$353$	1.32349	−	2.29236i	0.0704424	−	0.122010i	−0.828653	−	0.559763i	$-0.810892\pi$
$353$	1.32349	−	2.29236i	0.0704424	−	0.122010i	0.899095	+	0.437753i	$0.144226\pi$
$354$		0			0
$355$	−0.0934139	−	0.161798i	−0.00495790	−	0.00858733i
$356$		0			0
$357$	5.56312	+	28.1942i	0.294432	+	1.49220i
$358$		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
$367$	8.79371	−	15.2312i	0.459028	−	0.795060i	−0.539882	−	0.841741i	$-0.681531\pi$
$367$	8.79371	−	15.2312i	0.459028	−	0.795060i	0.998910	+	0.0466808i	$0.0148644\pi$
$368$		0			0
$369$	1.34494	−	6.82241i	0.0700148	−	0.355160i
$370$		0			0
$371$	−0.428975	−	14.1380i	−0.0222713	−	0.734011i
$372$		0			0
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	0.855282	−	0.518163i	$-0.173384\pi$
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	−0.876383	+	0.481614i	$0.840051\pi$
$374$		0			0
$375$	2.49352	−	0.413871i	0.128765	−	0.0213722i
$376$		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
$381$	−23.0310	+	3.82265i	−1.17991	+	0.195840i
$382$		0			0
$383$	8.94638	+	15.4956i	0.457139	+	0.791788i	0.998808	−	0.0488039i	$-0.0155409\pi$
$383$	8.94638	+	15.4956i	0.457139	+	0.791788i	−0.541670	+	0.840591i	$0.682208\pi$
$384$		0			0
$385$	0.567112	+	0.304874i	0.0289027	+	0.0155378i
$386$		0			0
$387$	4.25121	+	3.71538i	0.216101	+	0.188863i
$388$		0			0
$389$	−7.81392	+	13.5341i	−0.396181	+	0.686206i	−0.993251	−	0.115983i	$-0.962998\pi$
$389$	−7.81392	+	13.5341i	−0.396181	+	0.686206i	0.597070	+	0.802189i	$0.296331\pi$
$390$		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
$399$	−23.8657	+	20.8648i	−1.19478	+	1.04455i
$400$		0			0
$401$	−7.15064	−	12.3853i	−0.357086	−	0.618491i	0.630387	−	0.776281i	$-0.282896\pi$
$401$	−7.15064	−	12.3853i	−0.357086	−	0.618491i	−0.987473	+	0.157790i	$0.949563\pi$
$402$		0			0
$403$	0.251642	−	0.435857i	0.0125352	−	0.0217116i
$404$		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
$409$	31.8610			1.57542			0.787712	−	0.616044i	$-0.211266\pi$
$409$	31.8610			1.57542			0.787712	+	0.616044i	$0.211266\pi$
$410$		0			0
$411$	3.92332	−	10.4511i	0.193523	−	0.515514i
$412$		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
$417$	−7.62771	+	20.3190i	−0.373530	+	0.995025i
$418$		0			0
$419$	−11.9480	+	20.6945i	−0.583697	+	1.01099i	0.411339	+	0.911482i	$0.365061\pi$
$419$	−11.9480	+	20.6945i	−0.583697	+	1.01099i	−0.995036	+	0.0995110i	$0.968272\pi$
$420$		0			0
$421$	−1.22251	−	2.11744i	−0.0595813	−	0.103198i	0.834696	−	0.550711i	$-0.185643\pi$
$421$	−1.22251	−	2.11744i	−0.0595813	−	0.103198i	−0.894278	+	0.447513i	$0.852310\pi$
$422$		0			0
$423$	5.14388	−	1.75592i	0.250104	−	0.0853759i
$424$		0			0
$425$	31.2214			1.51446
$426$		0			0
$427$	−1.58062	−	0.849728i	−0.0764917	−	0.0411212i
$428$		0			0
$429$	−0.365871	−	0.445039i	−0.0176644	−	0.0214867i
$430$		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
$437$	42.7633			2.04565
$438$		0			0
$439$	−2.44822			−0.116847			−0.0584235	−	0.998292i	$-0.518607\pi$
$439$	−2.44822			−0.116847			−0.0584235	+	0.998292i	$0.518607\pi$
$440$		0			0
$441$	16.6210	+	12.8352i	0.791478	+	0.611198i
$442$		0			0
$443$	26.2950			1.24931			0.624657	−	0.780899i	$-0.285239\pi$
$443$	26.2950			1.24931			0.624657	+	0.780899i	$0.285239\pi$
$444$		0			0
$445$	1.32614			0.0628650
$446$		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
$453$	5.15350	−	13.7281i	0.242132	−	0.645002i
$454$		0			0
$455$	0.0681236	+	0.0366226i	0.00319368	+	0.00171690i
$456$		0			0
$457$	−9.15511			−0.428258			−0.214129	−	0.976805i	$-0.568691\pi$
$457$	−9.15511			−0.428258			−0.214129	+	0.976805i	$0.568691\pi$
$458$		0			0
$459$	27.7158	+	17.1364i	1.29366	+	0.799859i
$460$		0			0
$461$	14.6152	+	25.3143i	0.680698	+	1.17900i	0.974768	+	0.223220i	$0.0716568\pi$
$461$	14.6152	+	25.3143i	0.680698	+	1.17900i	−0.294070	+	0.955784i	$0.595010\pi$
$462$		0			0
$463$	8.21031	−	14.2207i	0.381565	−	0.660891i	−0.609721	−	0.792616i	$-0.708718\pi$
$463$	8.21031	−	14.2207i	0.381565	−	0.660891i	0.991286	+	0.131726i	$0.0420518\pi$
$464$		0			0
$465$	0.405018	+	0.492657i	0.0187823	+	0.0228464i
$466$		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
$471$	9.73834	−	1.61636i	0.448719	−	0.0744779i
$472$		0			0
$473$	3.13170			0.143996
$474$		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
$479$	−18.9646	+	32.8476i	−0.866513	+	1.50084i	−0.000975329		1.00000i	$0.500310\pi$
$479$	−18.9646	+	32.8476i	−0.866513	+	1.50084i	−0.865537	+	0.500844i	$0.833023\pi$
$480$		0			0
$481$	0.699663	+	1.21185i	0.0319019	+	0.0552557i
$482$		0			0
$483$	−5.48393	−	27.7929i	−0.249528	−	1.26462i
$484$		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	−0.287904	−	0.957659i	$-0.592958\pi$
$491$	15.1876	−	26.3056i	0.685405	−	1.18716i	0.973309	−	0.229497i	$-0.0737082\pi$
$492$		0			0
$493$	15.4744	−	26.8024i	0.696932	−	1.20712i
$494$		0			0
$495$	0.690929	−	0.235857i	0.0310549	−	0.0106010i
$496$		0			0
$497$	−2.97701	−	1.60041i	−0.133537	−	0.0717884i
$498$		0			0
$499$	4.63436	+	8.02694i	0.207462	+	0.359335i	0.950914	−	0.309454i	$-0.100146\pi$
$499$	4.63436	+	8.02694i	0.207462	+	0.359335i	−0.743452	+	0.668789i	$0.766813\pi$
$500$		0			0
$501$	7.04571	−	18.7687i	0.314779	−	0.838522i
$502$		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
$507$	14.2553	+	17.3399i	0.633102	+	0.770094i
$508$		0			0
$509$	18.8207	+	32.5984i	0.834213	+	1.44490i	0.894670	+	0.446728i	$0.147411\pi$
$509$	18.8207	+	32.5984i	0.834213	+	1.44490i	−0.0604572	+	0.998171i	$0.519256\pi$
$510$		0			0
$511$	−0.124951	−	4.11808i	−0.00552748	−	0.182173i
$512$		0			0
$513$	−1.08396	+	35.9284i	−0.0478578	+	1.58628i
$514$		0			0
$515$	0.0149133	−	0.0258306i	0.000657158	−	0.00113823i
$516$		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
$525$	17.1762	−	15.0165i	0.749632	−	0.655374i
$526$		0			0
$527$	7.89468	+	13.6740i	0.343898	+	0.595648i
$528$		0			0
$529$	−7.60755	+	13.1767i	−0.330763	+	0.572898i
$530$		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
$535$	−1.01917			−0.0440626
$536$		0			0
$537$	−8.52822	−	10.3736i	−0.368020	−	0.447652i
$538$		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
$543$	−20.7806	+	3.44914i	−0.891782	+	0.148017i
$544$		0			0
$545$	−0.487083	+	0.843653i	−0.0208643	+	0.0361381i
$546$		0			0
$547$	10.0046	+	17.3284i	0.427765	+	0.740910i	0.996674	−	0.0814901i	$-0.0259679\pi$
$547$	10.0046	+	17.3284i	0.427765	+	0.740910i	−0.568910	+	0.822400i	$0.692635\pi$
$548$		0			0
$549$	−1.92572	+	0.657366i	−0.0821876	+	0.0280557i
$550$		0			0
$551$	34.1392			1.45438
$552$		0			0
$553$	−29.8186	−	16.0302i	−1.26802	−	0.681674i
$554$		0			0
$555$	−1.74932	+	0.290350i	−0.0742544	+	0.0123247i
$556$		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
$563$	44.2509			1.86495			0.932477	−	0.361230i	$-0.117643\pi$
$563$	44.2509			1.86495			0.932477	+	0.361230i	$0.117643\pi$
$564$		0			0
$565$	−0.00565192			−0.000237778
$566$		0			0
$567$	23.4897	−	3.90295i	0.986476	−	0.163908i
$568$		0			0
$569$	−5.53533			−0.232053			−0.116027	−	0.993246i	$-0.537016\pi$
$569$	−5.53533			−0.232053			−0.116027	+	0.993246i	$0.537016\pi$
$570$		0			0
$571$	4.10381			0.171739			0.0858696	−	0.996306i	$-0.472633\pi$
$571$	4.10381			0.171739			0.0858696	+	0.996306i	$0.472633\pi$
$572$		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
$579$	−25.4668	+	4.22695i	−1.05836	+	0.175666i
$580$		0			0
$581$	−0.602904	−	19.8703i	−0.0250127	−	0.824360i
$582$		0			0
$583$	−8.89619			−0.368442
$584$		0			0
$585$	0.0829970	−	0.0283320i	0.00343150	−	0.00117138i
$586$		0			0
$587$	−9.36644	−	16.2232i	−0.386595	−	0.669601i	0.605394	−	0.795926i	$-0.293015\pi$
$587$	−9.36644	−	16.2232i	−0.386595	−	0.669601i	−0.991989	+	0.126324i	$0.959682\pi$
$588$		0			0
$589$	−8.70852	+	15.0836i	−0.358828	+	0.621509i
$590$		0			0
$591$	−36.3278	+	6.02965i	−1.49433	+	0.248027i
$592$		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
$597$	21.9375	+	26.6844i	0.897842	+	1.09212i
$598$		0			0
$599$	−2.67451			−0.109278			−0.0546388	−	0.998506i	$-0.517401\pi$
$599$	−2.67451			−0.109278			−0.0546388	+	0.998506i	$0.517401\pi$
$600$		0			0
$601$	−6.60716	−	11.4439i	−0.269511	−	0.466808i	0.699224	−	0.714902i	$-0.253529\pi$
$601$	−6.60716	−	11.4439i	−0.269511	−	0.466808i	−0.968736	+	0.248095i	$0.920196\pi$
$602$		0			0
$603$	17.5653	−	5.99612i	0.715313	−	0.244181i
$604$		0			0
$605$	−0.601872	+	1.04247i	−0.0244696	+	0.0423825i
$606$		0			0
$607$	12.9026	+	22.3480i	0.523701	+	0.907076i	0.999619	+	0.0275869i	$0.00878231\pi$
$607$	12.9026	+	22.3480i	0.523701	+	0.907076i	−0.475919	+	0.879489i	$0.657884\pi$
$608$		0			0
$609$	−4.37799	−	22.1879i	−0.177405	−	0.899098i
$610$		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	−0.945869	−	0.324549i	$-0.894788\pi$
$617$	−4.76588	+	8.25474i	−0.191867	+	0.332323i	0.754002	+	0.656872i	$0.228121\pi$
$618$		0			0
$619$	17.3536	−	30.0573i	0.697499	−	1.20810i	−0.271832	−	0.962345i	$-0.587630\pi$
$619$	17.3536	−	30.0573i	0.697499	−	1.20810i	0.969331	−	0.245759i	$-0.0790371\pi$
$620$		0			0
$621$	−27.3213	−	16.8925i	−1.09637	−	0.677871i
$622$		0			0
$623$	20.4038	−	12.6203i	0.817459	−	0.505621i
$624$		0			0
$625$	−12.3398	−	21.3732i	−0.493593	−	0.854928i
$626$		0			0
$627$	12.6616	+	15.4014i	0.505656	+	0.615071i
$628$		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
$633$	−14.3136	+	38.1291i	−0.568914	+	1.51550i
$634$		0			0
$635$	−0.985611	−	1.70713i	−0.0391128	−	0.0677453i
$636$		0			0
$637$	1.39666	−	0.0848329i	0.0553378	−	0.00336120i
$638$		0			0
$639$	−3.62698	+	1.23811i	−0.143481	+	0.0489790i
$640$		0			0
$641$	22.0922	−	38.2648i	0.872590	−	1.51137i	0.0132813	−	0.999912i	$-0.495772\pi$
$641$	22.0922	−	38.2648i	0.872590	−	1.51137i	0.859308	−	0.511458i	$-0.170894\pi$
$642$		0			0
$643$	−7.24065	+	12.5412i	−0.285543	+	0.494575i	−0.972741	−	0.231895i	$-0.925507\pi$
$643$	−7.24065	+	12.5412i	−0.285543	+	0.494575i	0.687197	+	0.726471i	$0.258841\pi$
$644$		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
$651$	10.9200	+	3.72556i	0.427987	+	0.146016i
$652$		0			0
$653$	4.53322	+	7.85176i	0.177398	+	0.307263i	0.940989	−	0.338438i	$-0.109899\pi$
$653$	4.53322	+	7.85176i	0.177398	+	0.307263i	−0.763590	+	0.645701i	$0.776565\pi$
$654$		0			0
$655$	1.45027	−	2.51194i	0.0566666	−	0.0981495i
$656$		0			0
$657$	−3.51757	−	3.07420i	−0.137233	−	0.119936i
$658$		0			0
$659$	−16.1806	−	28.0256i	−0.630305	−	1.09172i	−0.987489	−	0.157686i	$-0.949596\pi$
$659$	−16.1806	−	28.0256i	−0.630305	−	1.09172i	0.357184	−	0.934034i	$-0.383737\pi$
$660$		0			0
$661$	−8.65915			−0.336802			−0.168401	−	0.985719i	$-0.553860\pi$
$661$	−8.65915			−0.336802			−0.168401	+	0.985719i	$0.553860\pi$
$662$		0			0
$663$	2.14189	−	0.355508i	0.0831839	−	0.0138068i
$664$		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
$669$	−4.46692	−	5.43348i	−0.172701	−	0.210070i
$670$		0			0
$671$	−0.564339	+	0.977464i	−0.0217861	+	0.0377346i
$672$		0			0
$673$	7.24842	+	12.5546i	0.279406	+	0.483946i	0.971237	−	0.238114i	$-0.0765291\pi$
$673$	7.24842	+	12.5546i	0.279406	+	0.483946i	−0.691831	+	0.722059i	$0.743196\pi$
$674$		0			0
$675$	0.780128	−	25.8579i	0.0300271	−	0.995270i
$676$		0			0
$677$	38.3315			1.47320			0.736600	−	0.676329i	$-0.236430\pi$
$677$	38.3315			1.47320			0.736600	+	0.676329i	$0.236430\pi$
$678$		0			0
$679$	−0.639537	−	21.0777i	−0.0245432	−	0.808887i
$680$		0			0
$681$	−2.34534	+	6.24762i	−0.0898738	+	0.239409i
$682$		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
$689$	−1.06864			−0.0407121
$690$		0			0
$691$	23.3875			0.889704			0.444852	−	0.895604i	$-0.353256\pi$
$691$	23.3875			0.889704			0.444852	+	0.895604i	$0.353256\pi$
$692$		0			0
$693$	8.38598	−	10.2041i	0.318557	−	0.387623i
$694$		0			0
$695$	−1.83254			−0.0695121
$696$		0			0
$697$	14.5358			0.550583
$698$		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
$705$	0.291446	+	0.354510i	0.0109765	+	0.0133516i
$706$		0			0
$707$	−33.3984	+	20.6579i	−1.25608	+	0.776918i
$708$		0			0
$709$	14.2355			0.534626			0.267313	−	0.963610i	$-0.413864\pi$
$709$	14.2355			0.534626			0.267313	+	0.963610i	$0.413864\pi$
$710$		0			0
$711$	−36.3289	+	12.4013i	−1.36244	+	0.465085i
$712$		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
$717$	−4.45416	+	11.8652i	−0.166344	+	0.443113i
$718$		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
$723$	−3.79303	+	10.1040i	−0.141064	+	0.375773i
$724$		0			0
$725$	−24.5702			−0.912513
$726$		0			0
$727$	−15.7000	−	27.1932i	−0.582280	−	1.00854i	−0.995208	−	0.0977755i	$-0.968827\pi$
$727$	−15.7000	−	27.1932i	−0.582280	−	1.00854i	0.412928	−	0.910764i	$-0.364506\pi$
$728$		0			0
$729$	14.8851	−	22.5263i	0.551299	−	0.834308i
$730$		0			0
$731$	−5.90107	+	10.2209i	−0.218259	+	0.378035i
$732$		0			0
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	0.999949	−	0.0100658i	$-0.00320409\pi$
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	−0.508692	+	0.860949i	$0.669871\pi$
$734$		0			0
$735$	−0.521378	+	1.69475i	−0.0192313	+	0.0625117i
$736$		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	0.257493	+	0.966280i	$0.417103\pi$
$743$	−19.3008	+	33.4299i	−0.708076	+	1.22642i	−0.965570	+	0.260144i	$0.916230\pi$
$744$		0			0
$745$	1.29919	−	2.25027i	0.0475988	−	0.0824435i
$746$		0			0
$747$	−16.9728	−	14.8335i	−0.621001	−	0.542728i
$748$		0			0
$749$	−15.6808	+	9.69900i	−0.572964	+	0.354394i
$750$		0			0
$751$	−18.9498	−	32.8220i	−0.691487	−	1.19769i	−0.971351	−	0.237651i	$-0.923622\pi$
$751$	−18.9498	−	32.8220i	−0.691487	−	1.19769i	0.279863	−	0.960040i	$-0.409711\pi$
$752$		0			0
$753$	−9.65885	+	1.60316i	−0.351988	+	0.0584226i
$754$		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
$759$	−17.5768	+	2.91738i	−0.637999	+	0.105894i
$760$		0			0
$761$	−13.8735	−	24.0296i	−0.502913	−	0.871072i	−0.999994	−	0.00336738i	$-0.998928\pi$
$761$	−13.8735	−	24.0296i	−0.502913	−	0.871072i	0.497081	−	0.867704i	$-0.334405\pi$
$762$		0			0
$763$	0.534493	+	17.6157i	0.0193500	+	0.637730i
$764$		0			0
$765$	−0.532151	+	2.69941i	−0.0192400	+	0.0975974i
$766$		0			0
$767$	0.456849	−	0.791286i	0.0164959	−	0.0285717i
$768$		0			0
$769$	−6.07668	+	10.5251i	−0.219131	+	0.379546i	−0.954542	−	0.298075i	$-0.903655\pi$
$769$	−6.07668	+	10.5251i	−0.219131	+	0.379546i	0.735412	+	0.677621i	$0.236989\pi$
$770$		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
$777$	−24.1516	+	21.1148i	−0.866434	+	0.757488i
$778$		0			0
$779$	8.01714	+	13.8861i	0.287244	+	0.497521i
$780$		0			0
$781$	−1.06290	+	1.84100i	−0.0380336	+	0.0658761i
$782$		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
$787$	20.8969			0.744893			0.372446	−	0.928054i	$-0.378519\pi$
$787$	20.8969			0.744893			0.372446	+	0.928054i	$0.378519\pi$
$788$		0			0
$789$	−13.5382	+	36.0636i	−0.481972	+	1.28390i
$790$		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
$795$	0.475934	−	1.26781i	0.0168797	−	0.0449647i
$796$		0			0
$797$	−0.319383	+	0.553188i	−0.0113131	+	0.0195949i	−0.871627	−	0.490171i	$-0.836934\pi$
$797$	−0.319383	+	0.553188i	−0.0113131	+	0.0195949i	0.860313	+	0.509765i	$0.170268\pi$
$798$		0			0
$799$	5.68091	+	9.83963i	0.200976	+	0.348101i
$800$		0			0
$801$	5.26155	−	26.6900i	0.185908	−	0.943043i
$802$		0			0
$803$	−2.59125			−0.0914433
$804$		0			0
$805$	2.03425	−	1.25824i	0.0716980	−	0.0443472i
$806$		0			0
$807$	−2.62759	−	3.19616i	−0.0924957	−	0.112510i
$808$		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
$815$	0.310823			0.0108876
$816$		0			0
$817$	−13.0188			−0.455470
$818$		0			0
$819$	1.00736	−	1.22576i	0.0351999	−	0.0428315i
$820$		0			0
$821$	43.4413			1.51611			0.758056	−	0.652189i	$-0.226149\pi$
$821$	43.4413			1.51611			0.758056	+	0.652189i	$0.226149\pi$
$822$		0			0
$823$	−3.96546			−0.138227			−0.0691136	−	0.997609i	$-0.522017\pi$
$823$	−3.96546			−0.138227			−0.0691136	+	0.997609i	$0.522017\pi$
$824$		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
$831$	2.81111	−	7.48836i	0.0975165	−	0.259768i
$832$		0			0
$833$	−19.6036	+	39.2773i	−0.679225	+	1.36088i
$834$		0			0
$835$	1.69272			0.0585788
$836$		0			0
$837$	11.5222	−	6.19678i	0.398265	−	0.214192i
$838$		0			0
$839$	18.7921	+	32.5489i	0.648777	+	1.12371i	0.983415	+	0.181368i	$0.0580524\pi$
$839$	18.7921	+	32.5489i	0.648777	+	1.12371i	−0.334639	+	0.942347i	$0.608614\pi$
$840$		0			0
$841$	2.32218	−	4.02213i	0.0800750	−	0.138694i
$842$		0			0
$843$	12.9979	+	15.8104i	0.447670	+	0.544538i
$844$		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
$849$	−27.0819	+	4.49503i	−0.929449	+	0.154269i
$850$		0			0
$851$	43.2757			1.48347
$852$		0			0
$853$	16.3849	+	28.3795i	0.561009	+	0.971696i	0.997409	+	0.0719434i	$0.0229201\pi$
$853$	16.3849	+	28.3795i	0.561009	+	0.971696i	−0.436400	+	0.899753i	$0.643747\pi$
$854$		0			0
$855$	−2.87226	+	0.980479i	−0.0982291	+	0.0335317i
$856$		0			0
$857$	−13.7673	+	23.8457i	−0.470283	+	0.814554i	−0.999422	−	0.0339808i	$-0.989181\pi$
$857$	−13.7673	+	23.8457i	−0.470283	+	0.814554i	0.529139	+	0.848535i	$0.322515\pi$
$858$		0			0
$859$	−23.2550	−	40.2789i	−0.793451	−	1.37430i	−0.923818	−	0.382832i	$-0.874949\pi$
$859$	−23.2550	−	40.2789i	−0.793451	−	1.37430i	0.130366	−	0.991466i	$-0.458385\pi$
$860$		0			0
$861$	7.99678	−	6.99127i	0.272530	−	0.238262i
$862$		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
$871$	0.618346	−	1.07101i	0.0209518	−	0.0362897i
$872$		0			0
$873$	−18.0040	−	15.7348i	−0.609345	−	0.532541i
$874$		0			0
$875$	3.40075	+	1.82821i	0.114966	+	0.0618049i
$876$		0			0
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	−0.979729	−	0.200326i	$-0.935800\pi$
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	0.316378	−	0.948633i	$-0.397533\pi$
$878$		0			0
$879$	8.58070	−	22.8576i	0.289420	−	0.770968i
$880$		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
$885$	0.735299	+	0.894404i	0.0247168	+	0.0300651i
$886$		0			0
$887$	−11.4800	−	19.8840i	−0.385461	−	0.667638i	0.606372	−	0.795181i	$-0.292624\pi$
$887$	−11.4800	−	19.8840i	−0.385461	−	0.667638i	−0.991833	+	0.127543i	$0.959291\pi$
$888$		0			0
$889$	−31.4105	−	16.8860i	−1.05347	−	0.566338i
$890$		0			0
$891$	−2.00556	−	14.8415i	−0.0671889	−	0.497208i
$892$		0			0
$893$	−6.26655	+	10.8540i	−0.209702	+	0.363214i
$894$		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
$903$	1.66952	+	8.46121i	0.0555581	+	0.281571i
$904$		0			0
$905$	−0.889308	−	1.54033i	−0.0295616	−	0.0512022i
$906$		0			0
$907$	−13.9491	+	24.1606i	−0.463173	+	0.802238i	−0.999117	−	0.0420148i	$-0.986622\pi$
$907$	−13.9491	+	24.1606i	−0.463173	+	0.802238i	0.535944	+	0.844253i	$0.319956\pi$
$908$		0			0
$909$	−8.61250	+	43.6882i	−0.285659	+	1.44905i
$910$		0			0
$911$	18.7381	+	32.4553i	0.620820	+	1.07529i	0.989333	+	0.145670i	$0.0465337\pi$
$911$	18.7381	+	32.4553i	0.620820	+	1.07529i	−0.368513	+	0.929623i	$0.620133\pi$
$912$		0			0
$913$	−12.5032			−0.413794
$914$		0			0
$915$	−0.109109	−	0.132718i	−0.00360703	−	0.00438753i
$916$		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
$921$	−46.8033	+	7.76836i	−1.54222	+	0.255976i
$922$		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
$927$	−0.460698	−	0.402631i	−0.0151313	−	0.0132241i
$928$		0			0
$929$	−45.9351			−1.50708			−0.753540	−	0.657402i	$-0.771656\pi$
$929$	−45.9351			−1.50708			−0.753540	+	0.657402i	$0.771656\pi$
$930$		0			0
$931$	−48.3340	+	2.93579i	−1.58408	+	0.0962167i
$932$		0			0
$933$	24.0166	−	3.98625i	0.786269	−	0.130504i
$934$		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
$941$	49.4003			1.61040			0.805202	−	0.593000i	$-0.202057\pi$
$941$	49.4003			1.61040			0.805202	+	0.593000i	$0.202057\pi$
$942$		0			0
$943$	−14.3289			−0.466613
$944$		0			0
$945$	1.00557	+	1.74101i	0.0327113	+	0.0566351i
$946$		0			0
$947$	−31.6505			−1.02850			−0.514252	−	0.857639i	$-0.671930\pi$
$947$	−31.6505			−1.02850			−0.514252	+	0.857639i	$0.671930\pi$
$948$		0			0
$949$	−0.311271			−0.0101043
$950$		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
$957$	−14.0321	+	2.32903i	−0.453594	+	0.0752870i
$958$		0			0
$959$	14.5022	−	8.97001i	0.468300	−	0.289657i
$960$		0			0
$961$	−24.6607			−0.795507
$962$		0			0
$963$	−4.04363	+	20.5119i	−0.130304	+	0.660987i
$964$		0			0
$965$	−1.08985	−	1.88768i	−0.0350836	−	0.0607666i
$966$		0			0
$967$	−4.98525	+	8.63470i	−0.160315	+	0.277673i	−0.934982	−	0.354696i	$-0.884584\pi$
$967$	−4.98525	+	8.63470i	−0.160315	+	0.277673i	0.774667	+	0.632370i	$0.217918\pi$
$968$		0			0
$969$	−74.1237	+	12.3030i	−2.38120	+	0.395228i
$970$		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
$975$	−1.09464	−	1.33150i	−0.0350566	−	0.0426422i
$976$		0			0
$977$	−18.8862			−0.604222			−0.302111	−	0.953273i	$-0.597691\pi$
$977$	−18.8862			−0.604222			−0.302111	+	0.953273i	$0.597691\pi$
$978$		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
$983$	1.14446	−	1.98226i	0.0365025	−	0.0632242i	−0.847197	−	0.531279i	$-0.821712\pi$
$983$	1.14446	−	1.98226i	0.0365025	−	0.0632242i	0.883700	+	0.468055i	$0.155045\pi$
$984$		0			0
$985$	−1.55465	−	2.69274i	−0.0495353	−	0.0857977i
$986$		0			0
$987$	7.85786	+	2.68087i	0.250119	+	0.0853329i
$988$		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
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	0.408593	+	0.912717i	$0.366020\pi$
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	−0.994732	+	0.102507i	$0.967314\pi$
$998$		0			0
$999$	−1.09694	+	36.3589i	−0.0347057	+	1.15034i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	28.11	odd	6
63.2.g.b.16.1	yes	10	36.7	odd	6
63.2.h.b.25.5	yes	10	252.151	odd	6
63.2.h.b.58.5	yes	10	4.3	odd	2
189.2.g.b.100.5		10	36.11	even	6
189.2.g.b.172.5		10	84.11	even	6
189.2.h.b.37.1		10	12.11	even	2
189.2.h.b.46.1		10	252.11	even	6
441.2.f.e.148.1		10	28.23	odd	6
441.2.f.e.295.1		10	252.79	odd	6
441.2.f.f.148.1		10	28.19	even	6
441.2.f.f.295.1		10	252.187	even	6
441.2.g.f.67.1		10	28.3	even	6
441.2.g.f.79.1		10	252.223	even	6
441.2.h.f.214.5		10	252.115	even	6
441.2.h.f.373.5		10	28.27	even	2
567.2.e.e.163.5		10	36.23	even	6
567.2.e.e.487.5		10	252.95	even	6
567.2.e.f.163.1		10	36.31	odd	6
567.2.e.f.487.1		10	252.67	odd	6
1008.2.q.i.529.5		10	63.25	even	3	inner
1008.2.q.i.625.5		10	1.1	even	1	trivial
1008.2.t.i.193.2		10	7.4	even	3
1008.2.t.i.961.2		10	9.7	even	3
1323.2.f.e.442.5		10	84.23	even	6
1323.2.f.e.883.5		10	252.191	even	6
1323.2.f.f.442.5		10	84.47	odd	6
1323.2.f.f.883.5		10	252.47	odd	6
1323.2.g.f.361.5		10	84.59	odd	6
1323.2.g.f.667.5		10	252.83	odd	6
1323.2.h.f.226.1		10	84.83	odd	2
1323.2.h.f.802.1		10	252.227	odd	6
3024.2.q.i.2305.3		10	3.2	odd	2
3024.2.q.i.2881.3		10	63.11	odd	6
3024.2.t.i.289.3		10	9.2	odd	6
3024.2.t.i.1873.3		10	21.11	odd	6
3969.2.a.z.1.5		5	252.247	odd	6
3969.2.a.ba.1.5		5	252.103	even	6
3969.2.a.bb.1.1		5	252.131	odd	6
3969.2.a.bc.1.1		5	252.23	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70867 - 0.283604i) q^{3} +(0.0731228 + 0.126652i) q^{5} +(2.33035 + 1.25278i) q^{7} +(2.83914 - 0.969173i) q^{9} +O(q^{10})\)	\(q+(1.70867 - 0.283604i) q^{3} +(0.0731228 + 0.126652i) q^{5} +(2.33035 + 1.25278i) q^{7} +(2.83914 - 0.969173i) q^{9} +(0.832020 - 1.44110i) q^{11} +(0.0999454 - 0.173111i) q^{13} +(0.160862 + 0.195670i) q^{15} +(3.13555 + 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} +(4.33711 + 1.47969i) q^{21} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +(4.57630 - 2.46119i) q^{27} +(-2.46757 - 4.27396i) q^{29} +2.51780 q^{31} +(1.01295 - 2.69834i) q^{33} +(0.0117348 + 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(0.121679 - 0.324134i) q^{39} +(1.15895 - 2.00736i) q^{41} +(0.940993 + 1.62985i) q^{43} +(0.330354 + 0.288715i) q^{45} +1.81177 q^{47} +(3.86110 + 5.83883i) q^{49} +(6.89787 + 8.39045i) q^{51} +(-2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +(-4.21093 + 11.2172i) q^{57} +4.57099 q^{59} -0.678276 q^{61} +(7.83035 + 1.29829i) q^{63} +0.0292332 q^{65} +6.18684 q^{67} +(-6.79968 - 8.27101i) q^{69} -1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(3.03063 - 8.07311i) q^{75} +(3.74428 - 2.31594i) q^{77} -12.7957 q^{79} +(7.12141 - 5.50323i) q^{81} +(-3.75687 - 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} +(-5.42839 - 6.60299i) q^{87} +(4.53394 - 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +(4.30209 - 0.714056i) q^{93} -1.01167 q^{95} +(-3.98514 - 6.90246i) q^{97} +(0.965543 - 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more