LMFDB - Embedded newform 1008.2.q.g.529.3

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.g.625.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64400 + 0.545231i) q^{3} +(-0.794182 + 1.37556i) q^{5} +(-1.23855 - 2.33795i) q^{7} +(2.40545 + 1.79272i) q^{9} +(-0.794182 - 1.37556i) q^{11} +(2.40545 + 4.16635i) q^{13} +(-2.05563 + 1.82841i) q^{15} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-0.761450 - 4.51887i) q^{21} +(0.150186 - 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +2.71201 q^{31} +(-0.555632 - 2.69443i) q^{33} +(4.19963 + 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.68292 + 8.16100i) q^{39} +(2.93818 + 5.08907i) q^{41} +(0.833104 - 1.44298i) q^{43} +(-4.37636 + 1.88510i) q^{45} -2.66621 q^{47} +(-3.93199 + 5.79133i) q^{49} +(-6.98762 + 6.21523i) q^{51} +(2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} -6.47710 q^{59} -4.47710 q^{61} +(1.21201 - 7.84417i) q^{63} -7.64145 q^{65} +10.0531 q^{67} +(0.388736 - 0.345766i) q^{69} -12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(0.866524 + 4.20205i) q^{75} +(-2.23236 + 3.56046i) q^{77} -8.38688 q^{79} +(2.57234 + 8.62456i) q^{81} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(10.7101 - 9.52628i) q^{87} +(1.60507 + 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +(4.45853 + 1.47867i) q^{93} -11.2756 q^{95} +(0.712008 - 1.23323i) q^{97} +(0.555632 - 4.73259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9 + q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 + 2 * q^25 + 7 * q^27 - 5 * q^29 + 40 * q^31 - 3 * q^33 + 13 * q^35 + 3 * q^37 + 5 * q^39 + 6 * q^43 + 9 * q^45 - 18 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 - 28 * q^59 - 16 * q^61 + 31 * q^63 + 24 * q^65 + 2 * q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 - 8 * q^75 + 10 * q^77 + 10 * q^79 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 27 * q^87 - 9 * q^89 + 46 * q^91 - 38 * q^93 - 8 * q^95 + 28 * q^97 + 3 * q^99

Character values

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

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

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
$3$	1.64400	+	0.545231i	0.949162	+	0.314789i
$3$	1.64400	+	0.545231i	0.949162	+	0.314789i
$4$		0			0
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	−0.987147	−	0.159816i	$-0.948910\pi$
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	0.631978	+	0.774986i	$0.282243\pi$
$6$		0			0
$7$	−1.23855	−	2.33795i	−0.468128	−	0.883661i
$7$	−1.23855	−	2.33795i	−0.468128	−	0.883661i
$8$		0			0
$9$	2.40545	+	1.79272i	0.801815	+	0.597572i
$10$		0			0
$11$	−0.794182	−	1.37556i	−0.239455	−	0.414748i	0.721103	−	0.692828i	$-0.243635\pi$
$11$	−0.794182	−	1.37556i	−0.239455	−	0.414748i	−0.960558	+	0.278080i	$0.910302\pi$
$12$		0			0
$13$	2.40545	+	4.16635i	0.667151	+	1.15554i	0.978697	+	0.205308i	$0.0658196\pi$
$13$	2.40545	+	4.16635i	0.667151	+	1.15554i	−0.311547	+	0.950231i	$0.600847\pi$
$14$		0			0
$15$	−2.05563	+	1.82841i	−0.530762	+	0.472093i
$16$		0			0
$17$	−2.69963	+	4.67589i	−0.654756	+	1.13407i	0.327199	+	0.944955i	$0.393895\pi$
$17$	−2.69963	+	4.67589i	−0.654756	+	1.13407i	−0.981955	+	0.189115i	$0.939438\pi$
$18$		0			0
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	0.909831	+	0.414979i	$0.136211\pi$
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	−0.0955331	+	0.995426i	$0.530456\pi$
$20$		0			0
$21$	−0.761450	−	4.51887i	−0.166162	−	0.986098i
$22$		0			0
$23$	0.150186	−	0.260130i	0.0313159	−	0.0542408i	−0.849943	−	0.526875i	$-0.823364\pi$
$23$	0.150186	−	0.260130i	0.0313159	−	0.0542408i	0.881259	+	0.472634i	$0.156697\pi$
$24$		0			0
$25$	1.23855	+	2.14523i	0.247710	+	0.429046i
$26$		0			0
$27$	2.97710	+	4.25874i	0.572943	+	0.819595i
$28$		0			0
$29$	4.13781	−	7.16689i	0.768371	−	1.33086i	−0.170074	−	0.985431i	$-0.554401\pi$
$29$	4.13781	−	7.16689i	0.768371	−	1.33086i	0.938446	−	0.345427i	$-0.112266\pi$
$30$		0			0
$31$	2.71201			0.487091			0.243545	−	0.969889i	$-0.421689\pi$
$31$	2.71201			0.487091			0.243545	+	0.969889i	$0.421689\pi$
$32$		0			0
$33$	−0.555632	−	2.69443i	−0.0967231	−	0.469041i
$34$		0			0
$35$	4.19963	+	0.153051i	0.709867	+	0.0258703i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	1.68292	+	8.16100i	0.269483	+	1.30681i
$40$		0			0
$41$	2.93818	+	5.08907i	0.458866	+	0.794780i	0.998901	−	0.0468628i	$-0.0149223\pi$
$41$	2.93818	+	5.08907i	0.458866	+	0.794780i	−0.540035	+	0.841643i	$0.681589\pi$
$42$		0			0
$43$	0.833104	−	1.44298i	0.127047	−	0.220052i	−0.795484	−	0.605974i	$-0.792783\pi$
$43$	0.833104	−	1.44298i	0.127047	−	0.220052i	0.922531	+	0.385922i	$0.126117\pi$
$44$		0			0
$45$	−4.37636	+	1.88510i	−0.652389	+	0.281014i
$46$		0			0
$47$	−2.66621			−0.388906			−0.194453	−	0.980912i	$-0.562293\pi$
$47$	−2.66621			−0.388906			−0.194453	+	0.980912i	$0.562293\pi$
$48$		0			0
$49$	−3.93199	+	5.79133i	−0.561713	+	0.827332i
$50$		0			0
$51$	−6.98762	+	6.21523i	−0.978463	+	0.870306i
$52$		0			0
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	−0.647871	−	0.761750i	$-0.724340\pi$
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	0.983630	+	0.180197i	$0.0576736\pi$
$54$		0			0
$55$	2.52290			0.340188
$56$		0			0
$57$	2.48329	+	12.0422i	0.328920	+	1.59503i
$58$		0			0
$59$	−6.47710			−0.843247			−0.421623	−	0.906771i	$-0.638540\pi$
$59$	−6.47710			−0.843247			−0.421623	+	0.906771i	$0.638540\pi$
$60$		0			0
$61$	−4.47710			−0.573234			−0.286617	−	0.958045i	$-0.592531\pi$
$61$	−4.47710			−0.573234			−0.286617	+	0.958045i	$0.592531\pi$
$62$		0			0
$63$	1.21201	−	7.84417i	0.152699	−	0.988273i
$64$		0			0
$65$	−7.64145			−0.947805
$66$		0			0
$67$	10.0531			1.22818			0.614090	−	0.789236i	$-0.289523\pi$
$67$	10.0531			1.22818			0.614090	+	0.789236i	$0.289523\pi$
$68$		0			0
$69$	0.388736	−	0.345766i	0.0467983	−	0.0416253i
$70$		0			0
$71$	−12.7207			−1.50967			−0.754833	−	0.655917i	$-0.772282\pi$
$71$	−12.7207			−1.50967			−0.754833	+	0.655917i	$0.772282\pi$
$72$		0			0
$73$	8.02654	−	13.9024i	0.939436	−	1.62715i	0.172909	−	0.984938i	$-0.444683\pi$
$73$	8.02654	−	13.9024i	0.939436	−	1.62715i	0.766527	−	0.642213i	$-0.221983\pi$
$74$		0			0
$75$	0.866524	+	4.20205i	0.100058	+	0.485211i
$76$		0			0
$77$	−2.23236	+	3.56046i	−0.254401	+	0.405752i
$78$		0			0
$79$	−8.38688			−0.943597			−0.471799	−	0.881706i	$-0.656395\pi$
$79$	−8.38688			−0.943597			−0.471799	+	0.881706i	$0.656395\pi$
$80$		0			0
$81$	2.57234	+	8.62456i	0.285816	+	0.958285i
$82$		0			0
$83$	−1.18292	+	2.04887i	−0.129842	+	0.224893i	−0.923615	−	0.383321i	$-0.874780\pi$
$83$	−1.18292	+	2.04887i	−0.129842	+	0.224893i	0.793773	+	0.608214i	$0.208114\pi$
$84$		0			0
$85$	−4.28799	−	7.42702i	−0.465098	−	0.805573i
$86$		0			0
$87$	10.7101	−	9.52628i	1.14825	−	1.02132i
$88$		0			0
$89$	1.60507	+	2.78007i	0.170138	+	0.294687i	0.938468	−	0.345367i	$-0.112245\pi$
$89$	1.60507	+	2.78007i	0.170138	+	0.294687i	−0.768330	+	0.640054i	$0.778912\pi$
$90$		0			0
$91$	6.76145	−	10.7840i	0.708793	−	1.13047i
$92$		0			0
$93$	4.45853	+	1.47867i	0.462328	+	0.153331i
$94$		0			0
$95$	−11.2756			−1.15685
$96$		0			0
$97$	0.712008	−	1.23323i	0.0722934	−	0.125216i	−0.827613	−	0.561300i	$-0.810302\pi$
$97$	0.712008	−	1.23323i	0.0722934	−	0.125216i	0.899906	+	0.436084i	$0.143635\pi$
$98$		0			0
$99$	0.555632	−	4.73259i	0.0558431	−	0.475643i
$100$		0			0
$101$	−6.01671	−	10.4212i	−0.598685	−	1.03695i	−0.993015	−	0.117984i	$-0.962357\pi$
$101$	−6.01671	−	10.4212i	−0.598685	−	1.03695i	0.394330	−	0.918969i	$-0.370977\pi$
$102$		0			0
$103$	−3.04944	+	5.28179i	−0.300470	+	0.520430i	−0.976243	−	0.216680i	$-0.930477\pi$
$103$	−3.04944	+	5.28179i	−0.300470	+	0.520430i	0.675772	+	0.737111i	$0.263810\pi$
$104$		0			0
$105$	6.82072	+	2.54138i	0.665635	+	0.248014i
$106$		0			0
$107$	1.54325	+	2.67299i	0.149192	+	0.258408i	0.930929	−	0.365200i	$-0.118999\pi$
$107$	1.54325	+	2.67299i	0.149192	+	0.258408i	−0.781737	+	0.623608i	$0.785666\pi$
$108$		0			0
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	−0.806023	−	0.591884i	$-0.798384\pi$
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	0.915598	+	0.402095i	$0.131718\pi$
$110$		0			0
$111$	0.349814	+	1.69636i	0.0332029	+	0.161011i
$112$		0			0
$113$	−9.73236	−	16.8569i	−0.915543	−	1.58577i	−0.806104	−	0.591774i	$-0.798428\pi$
$113$	−9.73236	−	16.8569i	−0.915543	−	1.58577i	−0.109440	−	0.993993i	$-0.534906\pi$
$114$		0			0
$115$	0.238550	+	0.413181i	0.0222449	+	0.0385293i
$116$		0			0
$117$	−1.68292	+	14.3342i	−0.155586	+	1.32520i
$118$		0			0
$119$	14.2756	+	0.520259i	1.30864	+	0.0476921i
$120$		0			0
$121$	4.23855	−	7.34138i	0.385323	−	0.667399i
$122$		0			0
$123$	2.05563	+	9.96840i	0.185350	+	0.898821i
$124$		0			0
$125$	−11.8764			−1.06225
$126$		0			0
$127$	13.4400			1.19260			0.596302	−	0.802760i	$-0.296636\pi$
$127$	13.4400			1.19260			0.596302	+	0.802760i	$0.296636\pi$
$128$		0			0
$129$	2.15638	−	1.91802i	0.189858	−	0.168872i
$130$		0			0
$131$	−1.58836	+	2.75113i	−0.138776	+	0.240367i	−0.927034	−	0.374978i	$-0.877650\pi$
$131$	−1.58836	+	2.75113i	−0.138776	+	0.240367i	0.788258	+	0.615345i	$0.210983\pi$
$132$		0			0
$133$	9.97710	−	15.9128i	0.865124	−	1.37981i
$134$		0			0
$135$	−8.22253	+	0.712974i	−0.707683	+	0.0613631i
$136$		0			0
$137$	10.6316	+	18.4145i	0.908320	+	1.57326i	0.816397	+	0.577491i	$0.195968\pi$
$137$	10.6316	+	18.4145i	0.908320	+	1.57326i	0.0919231	+	0.995766i	$0.470699\pi$
$138$		0			0
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	−0.998013	−	0.0630092i	$-0.979930\pi$
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	0.444439	−	0.895809i	$-0.353403\pi$
$140$		0			0
$141$	−4.38323	−	1.45370i	−0.369135	−	0.122424i
$142$		0			0
$143$	3.82072	−	6.61769i	0.319505	−	0.553399i
$144$		0			0
$145$	6.57234	+	11.3836i	0.545803	+	0.945359i
$146$		0			0
$147$	−9.62178	+	7.37708i	−0.793591	+	0.608451i
$148$		0			0
$149$	−2.60439	+	4.51093i	−0.213360	+	0.369550i	−0.952764	−	0.303712i	$-0.901774\pi$
$149$	−2.60439	+	4.51093i	−0.213360	+	0.369550i	0.739404	+	0.673262i	$0.235107\pi$
$150$		0			0
$151$	−0.261450	−	0.452845i	−0.0212765	−	0.0368520i	0.855191	−	0.518313i	$-0.173440\pi$
$151$	−0.261450	−	0.452845i	−0.0212765	−	0.0368520i	−0.876468	+	0.481461i	$0.840106\pi$
$152$		0			0
$153$	−14.8764	+	6.40794i	−1.20268	+	0.518052i
$154$		0			0
$155$	−2.15383	+	3.73054i	−0.173000	+	0.299644i
$156$		0			0
$157$	8.86398			0.707422			0.353711	−	0.935355i	$-0.384920\pi$
$157$	8.86398			0.707422			0.353711	+	0.935355i	$0.384920\pi$
$158$		0			0
$159$	6.32691	−	5.62755i	0.501757	−	0.446294i
$160$		0			0
$161$	−0.794182	−	0.0289431i	−0.0625903	−	0.00228104i
$162$		0			0
$163$	−10.9814	−	19.0204i	−0.860132	−	1.48979i	−0.871801	−	0.489860i	$-0.837048\pi$
$163$	−10.9814	−	19.0204i	−0.860132	−	1.48979i	0.0116689	−	0.999932i	$-0.496286\pi$
$164$		0			0
$165$	4.14764	+	1.37556i	0.322893	+	0.107087i
$166$		0			0
$167$	−1.65019	−	2.85821i	−0.127695	−	0.221175i	0.795088	−	0.606494i	$-0.207425\pi$
$167$	−1.65019	−	2.85821i	−0.127695	−	0.221175i	−0.922783	+	0.385319i	$0.874091\pi$
$168$		0			0
$169$	−5.07234	+	8.78555i	−0.390180	+	0.675812i
$170$		0			0
$171$	−2.48329	+	21.1514i	−0.189902	+	1.61749i
$172$		0			0
$173$	19.1075			1.45272			0.726360	−	0.687315i	$-0.241211\pi$
$173$	19.1075			1.45272			0.726360	+	0.687315i	$0.241211\pi$
$174$		0			0
$175$	3.48143	−	5.55264i	0.263171	−	0.419740i
$176$		0			0
$177$	−10.6483	−	3.53152i	−0.800377	−	0.265445i
$178$		0			0
$179$	8.03706	−	13.9206i	0.600718	−	1.04047i	−0.391994	−	0.919968i	$-0.628215\pi$
$179$	8.03706	−	13.9206i	0.600718	−	1.04047i	0.992712	−	0.120507i	$-0.0384520\pi$
$180$		0			0
$181$	8.05308			0.598581			0.299291	−	0.954162i	$-0.403250\pi$
$181$	8.05308			0.598581			0.299291	+	0.954162i	$0.403250\pi$
$182$		0			0
$183$	−7.36033	−	2.44105i	−0.544092	−	0.180448i
$184$		0			0
$185$	−1.58836			−0.116779
$186$		0			0
$187$	8.57598			0.627138
$188$		0			0
$189$	6.26942	−	12.2350i	0.456033	−	0.889963i
$190$		0			0
$191$	23.9629			1.73389			0.866946	−	0.498402i	$-0.166080\pi$
$191$	23.9629			1.73389			0.866946	+	0.498402i	$0.166080\pi$
$192$		0			0
$193$	9.76509			0.702907			0.351453	−	0.936205i	$-0.385688\pi$
$193$	9.76509			0.702907			0.351453	+	0.936205i	$0.385688\pi$
$194$		0			0
$195$	−12.5625	−	4.16635i	−0.899620	−	0.298359i
$196$		0			0
$197$	−18.2436			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$197$	−18.2436			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$198$		0			0
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	0.343601	+	0.939116i	$0.388353\pi$
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	−0.985098	+	0.171991i	$0.944980\pi$
$200$		0			0
$201$	16.5272	+	5.48125i	1.16574	+	0.386618i
$202$		0			0
$203$	−21.8807	−	0.797418i	−1.53572	−	0.0559678i
$204$		0			0
$205$	−9.33379			−0.651900
$206$		0			0
$207$	0.827603	−	0.356487i	0.0575224	−	0.0247776i
$208$		0			0
$209$	5.63781	−	9.76497i	0.389975	−	0.675457i
$210$		0			0
$211$	−0.166208	−	0.287880i	−0.0114422	−	0.0198185i	0.860248	−	0.509877i	$-0.170309\pi$
$211$	−0.166208	−	0.287880i	−0.0114422	−	0.0198185i	−0.871690	+	0.490058i	$0.836976\pi$
$212$		0			0
$213$	−20.9127	−	6.93570i	−1.43292	−	0.475227i
$214$		0			0
$215$	1.32327	+	2.29197i	0.0902464	+	0.156311i
$216$		0			0
$217$	−3.35896	−	6.34053i	−0.228021	−	0.430423i
$218$		0			0
$219$	20.7756	−	18.4791i	1.40389	−	1.24870i
$220$		0			0
$221$	−25.9752			−1.74728
$222$		0			0
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	−0.952348	−	0.305013i	$-0.901339\pi$
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	0.740323	+	0.672251i	$0.234672\pi$
$224$		0			0
$225$	−0.866524	+	7.38061i	−0.0577683	+	0.492040i
$226$		0			0
$227$	−11.6545	−	20.1862i	−0.773537	−	1.33981i	−0.935613	−	0.353028i	$-0.885152\pi$
$227$	−11.6545	−	20.1862i	−0.773537	−	1.33981i	0.162075	−	0.986778i	$-0.448181\pi$
$228$		0			0
$229$	2.47710	−	4.29046i	0.163691	−	0.283522i	−0.772498	−	0.635017i	$-0.780993\pi$
$229$	2.47710	−	4.29046i	0.163691	−	0.283522i	0.936190	+	0.351495i	$0.114327\pi$
$230$		0			0
$231$	−5.61126	+	4.63623i	−0.369194	+	0.305041i
$232$		0			0
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	0.531702	−	0.846932i	$-0.321553\pi$
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	−0.999315	+	0.0370017i	$0.988219\pi$
$234$		0			0
$235$	2.11745	−	3.66754i	0.138127	−	0.239244i
$236$		0			0
$237$	−13.7880	−	4.57279i	−0.895626	−	0.297034i
$238$		0			0
$239$	−2.48762	−	4.30868i	−0.160911	−	0.278706i	0.774285	−	0.632837i	$-0.218110\pi$
$239$	−2.48762	−	4.30868i	−0.160911	−	0.278706i	−0.935196	+	0.354132i	$0.884776\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$		0			0
$243$	−0.473458	+	15.5813i	−0.0303723	+	0.999539i
$244$		0			0
$245$	−4.84362	−	10.0081i	−0.309448	−	0.639392i
$246$		0			0
$247$	−17.0760	+	29.5765i	−1.08652	+	1.88191i
$248$		0			0
$249$	−3.06182	+	2.72338i	−0.194035	+	0.172587i
$250$		0			0
$251$	−2.43268			−0.153549			−0.0767746	−	0.997048i	$-0.524462\pi$
$251$	−2.43268			−0.153549			−0.0767746	+	0.997048i	$0.524462\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$		0			0
$255$	−3.00000	−	14.5479i	−0.187867	−	0.911027i
$256$		0			0
$257$	0.493810	−	0.855304i	0.0308030	−	0.0533524i	−0.850213	−	0.526439i	$-0.823527\pi$
$257$	0.493810	−	0.855304i	0.0308030	−	0.0533524i	0.881016	+	0.473087i	$0.156860\pi$
$258$		0			0
$259$	1.40545	−	2.24159i	0.0873302	−	0.139286i
$260$		0			0
$261$	22.8015	−	9.82166i	1.41138	−	0.607946i
$262$		0			0
$263$	8.59269	+	14.8830i	0.529848	+	0.917724i	0.999394	+	0.0348158i	$0.0110845\pi$
$263$	8.59269	+	14.8830i	0.529848	+	0.917724i	−0.469545	+	0.882908i	$0.655582\pi$
$264$		0			0
$265$	3.88255	+	6.72477i	0.238503	+	0.413099i
$266$		0			0
$267$	1.12296	+	5.44556i	0.0687237	+	0.333263i
$268$		0			0
$269$	11.4523	−	19.8360i	0.698262	−	1.20942i	−0.270807	−	0.962634i	$-0.587291\pi$
$269$	11.4523	−	19.8360i	0.698262	−	1.20942i	0.969069	−	0.246791i	$-0.0793761\pi$
$270$		0			0
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	0.571021	−	0.820936i	$-0.306548\pi$
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	−0.996462	+	0.0840504i	$0.973214\pi$
$272$		0			0
$273$	16.9956	−	14.0424i	1.02862	−	0.849883i
$274$		0			0
$275$	1.96727	−	3.40741i	0.118631	−	0.205474i
$276$		0			0
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	−0.881163	−	0.472813i	$-0.843239\pi$
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	0.0311139	−	0.999516i	$-0.490095\pi$
$278$		0			0
$279$	6.52359	+	4.86186i	0.390557	+	0.291072i
$280$		0			0
$281$	−8.79782	+	15.2383i	−0.524834	+	0.909039i	0.474748	+	0.880122i	$0.342539\pi$
$281$	−8.79782	+	15.2383i	−0.524834	+	0.909039i	−0.999582	+	0.0289175i	$0.990794\pi$
$282$		0			0
$283$	18.5229			1.10107			0.550536	−	0.834811i	$-0.314423\pi$
$283$	18.5229			1.10107			0.550536	+	0.834811i	$0.314423\pi$
$284$		0			0
$285$	−18.5371	−	6.14781i	−1.09804	−	0.364165i
$286$		0			0
$287$	8.25890	−	13.1724i	0.487508	−	0.777541i
$288$		0			0
$289$	−6.07598	−	10.5239i	−0.357411	−	0.619054i
$290$		0			0
$291$	1.84294	−	1.63922i	0.108035	−	0.0960929i
$292$		0			0
$293$	−7.04256	−	12.1981i	−0.411431	−	0.712619i	0.583616	−	0.812030i	$-0.301638\pi$
$293$	−7.04256	−	12.1981i	−0.411431	−	0.712619i	−0.995046	+	0.0994108i	$0.968304\pi$
$294$		0			0
$295$	5.14400	−	8.90966i	0.299495	−	0.518741i
$296$		0			0
$297$	3.49381	−	7.47741i	0.202731	−	0.433883i
$298$		0			0
$299$	1.44506			0.0835698
$300$		0			0
$301$	−4.40545	−	0.160552i	−0.253926	−	0.00925405i
$302$		0			0
$303$	−4.20946	−	20.4130i	−0.241827	−	1.17270i
$304$		0			0
$305$	3.55563	−	6.15854i	0.203595	−	0.352637i
$306$		0			0
$307$	5.85532			0.334180			0.167090	−	0.985942i	$-0.446563\pi$
$307$	5.85532			0.334180			0.167090	+	0.985942i	$0.446563\pi$
$308$		0			0
$309$	−7.89307	+	7.02059i	−0.449021	+	0.399387i
$310$		0			0
$311$	−0.810892			−0.0459815			−0.0229907	−	0.999736i	$-0.507319\pi$
$311$	−0.810892			−0.0459815			−0.0229907	+	0.999736i	$0.507319\pi$
$312$		0			0
$313$	10.5760			0.597790			0.298895	−	0.954286i	$-0.403382\pi$
$313$	10.5760			0.597790			0.298895	+	0.954286i	$0.403382\pi$
$314$		0			0
$315$	9.82760	+	7.89689i	0.553723	+	0.444940i
$316$		0			0
$317$	12.1964			0.685018			0.342509	−	0.939515i	$-0.388723\pi$
$317$	12.1964			0.685018			0.342509	+	0.939515i	$0.388723\pi$
$318$		0			0
$319$	−13.1447			−0.735961
$320$		0			0
$321$	1.07970	+	5.23582i	0.0602631	+	0.292235i
$322$		0			0
$323$	−38.3287			−2.13267
$324$		0			0
$325$	−5.95853	+	10.3205i	−0.330520	+	0.572477i
$326$		0			0
$327$	2.96108	−	2.63377i	0.163748	−	0.145648i
$328$		0			0
$329$	3.30223	+	6.23345i	0.182058	+	0.343661i
$330$		0			0
$331$	15.6662			0.861093			0.430546	−	0.902568i	$-0.358321\pi$
$331$	15.6662			0.861093			0.430546	+	0.902568i	$0.358321\pi$
$332$		0			0
$333$	−0.349814	+	2.97954i	−0.0191697	+	0.163278i
$334$		0			0
$335$	−7.98398	+	13.8287i	−0.436211	+	0.755540i
$336$		0			0
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	0.728200	−	0.685364i	$-0.240357\pi$
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	−0.957643	+	0.287958i	$0.907024\pi$
$338$		0			0
$339$	−6.80903	−	33.0191i	−0.369816	−	1.79335i
$340$		0			0
$341$	−2.15383	−	3.73054i	−0.116636	−	0.202020i
$342$		0			0
$343$	18.4098	+	2.01993i	0.994035	+	0.109066i
$344$		0			0
$345$	0.166896	+	0.809332i	0.00898539	+	0.0435730i
$346$		0			0
$347$	−0.567323			−0.0304555			−0.0152277	−	0.999884i	$-0.504847\pi$
$347$	−0.567323			−0.0304555			−0.0152277	+	0.999884i	$0.504847\pi$
$348$		0			0
$349$	−0.00364189	+	0.00630794i	−0.000194946	+	0.000337656i	−0.866123	−	0.499831i	$-0.833395\pi$
$349$	−0.00364189	+	0.00630794i	−0.000194946	+	0.000337656i	0.865928	+	0.500169i	$0.166729\pi$
$350$		0			0
$351$	−10.5822	+	22.6478i	−0.564835	+	1.20885i
$352$		0			0
$353$	−3.32691	−	5.76238i	−0.177074	−	0.306701i	0.763803	−	0.645449i	$-0.223330\pi$
$353$	−3.32691	−	5.76238i	−0.177074	−	0.306701i	−0.940877	+	0.338748i	$0.889996\pi$
$354$		0			0
$355$	10.1025	−	17.4981i	0.536186	−	0.928702i
$356$		0			0
$357$	23.1854	+	8.63881i	1.22710	+	0.457214i
$358$		0			0
$359$	0.398568	+	0.690339i	0.0210356	+	0.0364347i	0.876352	−	0.481672i	$-0.159970\pi$
$359$	0.398568	+	0.690339i	0.0210356	+	0.0364347i	−0.855316	+	0.518107i	$0.826637\pi$
$360$		0			0
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$		0			0
$363$	10.9709	−	9.75822i	0.575823	−	0.512174i
$364$		0			0
$365$	12.7491	+	22.0820i	0.667317	+	1.15583i
$366$		0			0
$367$	−7.71634	−	13.3651i	−0.402790	−	0.697652i	0.591272	−	0.806472i	$-0.298626\pi$
$367$	−7.71634	−	13.3651i	−0.402790	−	0.697652i	−0.994061	+	0.108820i	$0.965293\pi$
$368$		0			0
$369$	−2.05563	+	17.5088i	−0.107012	+	0.911472i
$370$		0			0
$371$	−12.9258	−	0.471067i	−0.671074	−	0.0244566i
$372$		0			0
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	−0.967606	−	0.252467i	$-0.918758\pi$
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	0.702445	+	0.711738i	$0.252092\pi$
$374$		0			0
$375$	−19.5247	−	6.47536i	−1.00825	−	0.334386i
$376$		0			0
$377$	39.8131			2.05048
$378$		0			0
$379$	−25.0087			−1.28461			−0.642304	−	0.766450i	$-0.722021\pi$
$379$	−25.0087			−1.28461			−0.642304	+	0.766450i	$0.722021\pi$
$380$		0			0
$381$	22.0952	+	7.32788i	1.13197	+	0.375419i
$382$		0			0
$383$	−3.13348	+	5.42734i	−0.160113	+	0.277324i	−0.934909	−	0.354887i	$-0.884519\pi$
$383$	−3.13348	+	5.42734i	−0.160113	+	0.277324i	0.774796	+	0.632211i	$0.217853\pi$
$384$		0			0
$385$	−3.12474	−	5.89841i	−0.159251	−	0.300611i
$386$		0			0
$387$	4.59084	−	1.97749i	0.233365	−	0.100521i
$388$		0			0
$389$	10.8171	+	18.7357i	0.548448	+	0.949940i	0.998381	+	0.0568774i	$0.0181144\pi$
$389$	10.8171	+	18.7357i	0.548448	+	0.949940i	−0.449933	+	0.893062i	$0.648552\pi$
$390$		0			0
$391$	0.810892	+	1.40451i	0.0410086	+	0.0710290i
$392$		0			0
$393$	−4.11126	+	3.65682i	−0.207386	+	0.184462i
$394$		0			0
$395$	6.66071	−	11.5367i	0.335137	−	0.580473i
$396$		0			0
$397$	2.05308	+	3.55605i	0.103041	+	0.178473i	0.912936	−	0.408102i	$-0.133809\pi$
$397$	2.05308	+	3.55605i	0.103041	+	0.178473i	−0.809895	+	0.586575i	$0.800476\pi$
$398$		0			0
$399$	25.0785	−	20.7207i	1.25549	−	1.03733i
$400$		0			0
$401$	−8.37085	+	14.4987i	−0.418021	+	0.724033i	−0.995740	−	0.0922024i	$-0.970609\pi$
$401$	−8.37085	+	14.4987i	−0.418021	+	0.724033i	0.577720	+	0.816235i	$0.303943\pi$
$402$		0			0
$403$	6.52359	+	11.2992i	0.324963	+	0.562853i
$404$		0			0
$405$	−13.9065	−	3.31105i	−0.691022	−	0.164527i
$406$		0			0
$407$	0.794182	−	1.37556i	0.0393661	−	0.0681842i
$408$		0			0
$409$	−8.76509			−0.433406			−0.216703	−	0.976238i	$-0.569530\pi$
$409$	−8.76509			−0.433406			−0.216703	+	0.976238i	$0.569530\pi$
$410$		0			0
$411$	7.43818	+	36.0701i	0.366898	+	1.77920i
$412$		0			0
$413$	8.02221	+	15.1431i	0.394747	+	0.745144i
$414$		0			0
$415$	−1.87890	−	3.25436i	−0.0922318	−	0.159750i
$416$		0			0
$417$	−4.56615	−	22.1427i	−0.223605	−	1.08433i
$418$		0			0
$419$	0.210149	+	0.363988i	0.0102664	+	0.0177820i	0.871113	−	0.491083i	$-0.163399\pi$
$419$	0.210149	+	0.363988i	0.0102664	+	0.0177820i	−0.860847	+	0.508865i	$0.830065\pi$
$420$		0			0
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	−0.774710	−	0.632316i	$-0.782104\pi$
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	0.934957	+	0.354761i	$0.115438\pi$
$422$		0			0
$423$	−6.41342	−	4.77975i	−0.311831	−	0.232399i
$424$		0			0
$425$	−13.3745			−0.648758
$426$		0			0
$427$	5.54511	+	10.4672i	0.268347	+	0.506544i
$428$		0			0
$429$	9.88942	−	8.79628i	0.477466	−	0.424688i
$430$		0			0
$431$	−11.0439	+	19.1287i	−0.531968	+	0.921395i	0.467336	+	0.884080i	$0.345214\pi$
$431$	−11.0439	+	19.1287i	−0.531968	+	0.921395i	−0.999304	+	0.0373155i	$0.988119\pi$
$432$		0			0
$433$	−9.43268			−0.453306			−0.226653	−	0.973976i	$-0.572778\pi$
$433$	−9.43268			−0.453306			−0.226653	+	0.973976i	$0.572778\pi$
$434$		0			0
$435$	4.59820	+	22.2981i	0.220467	+	1.06911i
$436$		0			0
$437$	2.13231			0.102002
$438$		0			0
$439$	31.2064			1.48940			0.744701	−	0.667398i	$-0.232592\pi$
$439$	31.2064			1.48940			0.744701	+	0.667398i	$0.232592\pi$
$440$		0			0
$441$	−19.8404	+	6.88179i	−0.944780	+	0.327704i
$442$		0			0
$443$	−13.0545			−0.620236			−0.310118	−	0.950698i	$-0.600369\pi$
$443$	−13.0545			−0.620236			−0.310118	+	0.950698i	$0.600369\pi$
$444$		0			0
$445$	−5.09888			−0.241710
$446$		0			0
$447$	−6.74110	+	5.99596i	−0.318843	+	0.283599i
$448$		0			0
$449$	−9.91706			−0.468015			−0.234008	−	0.972235i	$-0.575184\pi$
$449$	−9.91706			−0.468015			−0.234008	+	0.972235i	$0.575184\pi$
$450$		0			0
$451$	4.66690	−	8.08330i	0.219756	−	0.380628i
$452$		0			0
$453$	−0.182918	−	0.887026i	−0.00859423	−	0.0416761i
$454$		0			0
$455$	9.46431	+	17.8653i	0.443694	+	0.837538i
$456$		0			0
$457$	−24.5229			−1.14713			−0.573566	−	0.819159i	$-0.694441\pi$
$457$	−24.5229			−1.14713			−0.573566	+	0.819159i	$0.694441\pi$
$458$		0			0
$459$	−27.9505	+	2.42358i	−1.30462	+	0.113123i
$460$		0			0
$461$	1.75526	−	3.04020i	0.0817506	−	0.141596i	−0.822251	−	0.569125i	$-0.807282\pi$
$461$	1.75526	−	3.04020i	0.0817506	−	0.141596i	0.904002	+	0.427528i	$0.140616\pi$
$462$		0			0
$463$	−8.69413	−	15.0587i	−0.404050	−	0.699836i	0.590160	−	0.807286i	$-0.299065\pi$
$463$	−8.69413	−	15.0587i	−0.404050	−	0.699836i	−0.994210	+	0.107451i	$0.965731\pi$
$464$		0			0
$465$	−5.57489	+	4.95866i	−0.258529	+	0.229952i
$466$		0			0
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	0.668370	−	0.743829i	$-0.266992\pi$
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	−0.978360	+	0.206911i	$0.933659\pi$
$468$		0			0
$469$	−12.4512	−	23.5036i	−0.574945	−	1.08529i
$470$		0			0
$471$	14.5723	+	4.83292i	0.671458	+	0.222689i
$472$		0			0
$473$	−2.64654			−0.121688
$474$		0			0
$475$	−8.79232	+	15.2287i	−0.403419	+	0.698743i
$476$		0			0
$477$	13.4697	−	5.80205i	0.616737	−	0.265658i
$478$		0			0
$479$	10.4029	+	18.0183i	0.475321	+	0.823279i	0.999600	−	0.0282667i	$-0.00899876\pi$
$479$	10.4029	+	18.0183i	0.475321	+	0.823279i	−0.524280	+	0.851546i	$0.675665\pi$
$480$		0			0
$481$	−2.40545	+	4.16635i	−0.109679	+	0.189969i
$482$		0			0
$483$	−1.28985	−	0.480595i	−0.0586903	−	0.0218678i
$484$		0			0
$485$	1.13093	+	1.95882i	0.0513528	+	0.0889456i
$486$		0			0
$487$	−16.2472	+	28.1410i	−0.736231	+	1.27519i	0.217950	+	0.975960i	$0.430063\pi$
$487$	−16.2472	+	28.1410i	−0.736231	+	1.27519i	−0.954181	+	0.299230i	$0.903270\pi$
$488$		0			0
$489$	−7.68292	−	37.2569i	−0.347434	−	1.68481i
$490$		0			0
$491$	9.66071	+	16.7328i	0.435982	+	0.755142i	0.997375	−	0.0724067i	$-0.0230679\pi$
$491$	9.66071	+	16.7328i	0.435982	+	0.755142i	−0.561394	+	0.827549i	$0.689735\pi$
$492$		0			0
$493$	22.3411	+	38.6959i	1.00619	+	1.74277i
$494$		0			0
$495$	6.06870	+	4.52284i	0.272768	+	0.203287i
$496$		0			0
$497$	15.7552	+	29.7402i	0.706717	+	1.33403i
$498$		0			0
$499$	−5.57530	+	9.65670i	−0.249585	+	0.432293i	−0.963411	−	0.268030i	$-0.913627\pi$
$499$	−5.57530	+	9.65670i	−0.249585	+	0.432293i	0.713826	+	0.700323i	$0.246961\pi$
$500$		0			0
$501$	−1.15452	−	5.59861i	−0.0515800	−	0.250128i
$502$		0			0
$503$	40.7651			1.81763			0.908813	−	0.417204i	$-0.136990\pi$
$503$	40.7651			1.81763			0.908813	+	0.417204i	$0.136990\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$		0			0
$507$	−13.1291	+	11.6778i	−0.583082	+	0.518630i
$508$		0			0
$509$	−0.722528	+	1.25146i	−0.0320255	+	0.0554698i	−0.881594	−	0.472009i	$-0.843529\pi$
$509$	−0.722528	+	1.25146i	−0.0320255	+	0.0554698i	0.849568	+	0.527478i	$0.176862\pi$
$510$		0			0
$511$	−42.4443	−	1.54684i	−1.87762	−	0.0684280i
$512$		0			0
$513$	−15.6149	+	33.4188i	−0.689415	+	1.47548i
$514$		0			0
$515$	−4.84362	−	8.38940i	−0.213436	−	0.369681i
$516$		0			0
$517$	2.11745	+	3.66754i	0.0931255	+	0.161298i
$518$		0			0
$519$	31.4127	+	10.4180i	1.37887	+	0.457301i
$520$		0			0
$521$	9.64214	−	16.7007i	0.422430	−	0.731670i	−0.573747	−	0.819033i	$-0.694511\pi$
$521$	9.64214	−	16.7007i	0.422430	−	0.731670i	0.996177	+	0.0873630i	$0.0278440\pi$
$522$		0			0
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	0.918173	+	0.396180i	$0.129665\pi$
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	−0.115984	+	0.993251i	$0.537002\pi$
$524$		0			0
$525$	8.75093	−	7.23033i	0.381922	−	0.315558i
$526$		0			0
$527$	−7.32141	+	12.6811i	−0.318926	+	0.552396i
$528$		0			0
$529$	11.4549	+	19.8404i	0.498039	+	0.862628i
$530$		0			0
$531$	−15.5803	−	11.6116i	−0.676128	−	0.503900i
$532$		0			0
$533$	−14.1353	+	24.4830i	−0.612266	+	1.06048i
$534$		0			0
$535$	−4.90249			−0.211953
$536$		0			0
$537$	20.8028	−	18.5034i	0.897709	−	0.798479i
$538$		0			0
$539$	11.0891	+	0.809332i	0.477639	+	0.0348604i
$540$		0			0
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	0.828967	−	0.559298i	$-0.188929\pi$
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	−0.898849	+	0.438258i	$0.855596\pi$
$542$		0			0
$543$	13.2392	+	4.39079i	0.568150	+	0.188427i
$544$		0			0
$545$	1.81708	+	3.14728i	0.0778352	+	0.134815i
$546$		0			0
$547$	2.95853	−	5.12432i	0.126498	−	0.219100i	−0.795820	−	0.605534i	$-0.792960\pi$
$547$	2.95853	−	5.12432i	0.126498	−	0.219100i	0.922317	+	0.386433i	$0.126293\pi$
$548$		0			0
$549$	−10.7694	−	8.02617i	−0.459628	−	0.342548i
$550$		0			0
$551$	58.7476			2.50273
$552$		0			0
$553$	10.3876	+	19.6081i	0.441724	+	0.833820i
$554$		0			0
$555$	−2.61126	−	0.866025i	−0.110842	−	0.0367607i
$556$		0			0
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	−0.456235	−	0.889859i	$-0.650802\pi$
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	0.998758	−	0.0498188i	$-0.0158644\pi$
$558$		0			0
$559$	8.01594			0.339038
$560$		0			0
$561$	14.0989	+	4.67589i	0.595255	+	0.197416i
$562$		0			0
$563$	46.6377			1.96555			0.982773	−	0.184817i	$-0.0591692\pi$
$563$	46.6377			1.96555			0.982773	+	0.184817i	$0.0591692\pi$
$564$		0			0
$565$	30.9171			1.30069
$566$		0			0
$567$	16.9778	−	16.6959i	0.713000	−	0.701164i
$568$		0			0
$569$	31.1978			1.30788			0.653939	−	0.756547i	$-0.273115\pi$
$569$	31.1978			1.30788			0.653939	+	0.756547i	$0.273115\pi$
$570$		0			0
$571$	15.6762			0.656030			0.328015	−	0.944672i	$-0.393620\pi$
$571$	15.6762			0.656030			0.328015	+	0.944672i	$0.393620\pi$
$572$		0			0
$573$	39.3948	+	13.0653i	1.64574	+	0.545811i
$574$		0			0
$575$	0.744051			0.0310291
$576$		0			0
$577$	6.99567	−	12.1169i	0.291234	−	0.504431i	−0.682868	−	0.730542i	$-0.739268\pi$
$577$	6.99567	−	12.1169i	0.291234	−	0.504431i	0.974102	+	0.226110i	$0.0726010\pi$
$578$		0			0
$579$	16.0538	+	5.32423i	0.667172	+	0.221268i
$580$		0			0
$581$	6.25526	+	0.227966i	0.259512	+	0.00945763i
$582$		0			0
$583$	−7.76509			−0.321597
$584$		0			0
$585$	−18.3811	−	13.6989i	−0.759965	−	0.566382i
$586$		0			0
$587$	−1.44801	+	2.50803i	−0.0597658	+	0.103517i	−0.894360	−	0.447348i	$-0.852369\pi$
$587$	−1.44801	+	2.50803i	−0.0597658	+	0.103517i	0.834594	+	0.550865i	$0.185702\pi$
$588$		0			0
$589$	9.62612	+	16.6729i	0.396637	+	0.686996i
$590$		0			0
$591$	−29.9924	−	9.94696i	−1.23372	−	0.409163i
$592$		0			0
$593$	−2.04394	−	3.54021i	−0.0839346	−	0.145379i	0.821002	−	0.570925i	$-0.193415\pi$
$593$	−2.04394	−	3.54021i	−0.0839346	−	0.145379i	−0.904937	+	0.425546i	$0.860082\pi$
$594$		0			0
$595$	−12.0531	+	19.2238i	−0.494128	+	0.788100i
$596$		0			0
$597$	−23.4233	+	20.8341i	−0.958650	+	0.852683i
$598$		0			0
$599$	19.7651			0.807580			0.403790	−	0.914852i	$-0.367693\pi$
$599$	19.7651			0.807580			0.403790	+	0.914852i	$0.367693\pi$
$600$		0			0
$601$	−13.4320	+	23.2649i	−0.547902	+	0.948994i	0.450516	+	0.892768i	$0.351240\pi$
$601$	−13.4320	+	23.2649i	−0.547902	+	0.948994i	−0.998418	+	0.0562261i	$0.982093\pi$
$602$		0			0
$603$	24.1822	+	18.0223i	0.984773	+	0.733926i
$604$		0			0
$605$	6.73236	+	11.6608i	0.273709	+	0.474079i
$606$		0			0
$607$	−7.62110	+	13.2001i	−0.309331	+	0.535777i	−0.978216	−	0.207589i	$-0.933438\pi$
$607$	−7.62110	+	13.2001i	−0.309331	+	0.535777i	0.668885	+	0.743366i	$0.266772\pi$
$608$		0			0
$609$	−35.5370	−	13.2410i	−1.44003	−	0.536552i
$610$		0			0
$611$	−6.41342	−	11.1084i	−0.259459	−	0.449396i
$612$		0			0
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	−0.892189	−	0.451662i	$-0.850831\pi$
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	0.837246	+	0.546827i	$0.184165\pi$
$614$		0			0
$615$	−15.3447	−	5.08907i	−0.618759	−	0.205211i
$616$		0			0
$617$	−9.21812	−	15.9663i	−0.371108	−	0.642777i	0.618629	−	0.785684i	$-0.287689\pi$
$617$	−9.21812	−	15.9663i	−0.371108	−	0.642777i	−0.989736	+	0.142906i	$0.954355\pi$
$618$		0			0
$619$	0.0537728	+	0.0931373i	0.00216131	+	0.00374350i	0.867104	−	0.498127i	$-0.165979\pi$
$619$	0.0537728	+	0.0931373i	0.00216131	+	0.00374350i	−0.864943	+	0.501871i	$0.832645\pi$
$620$		0			0
$621$	1.55494	−	0.134829i	0.0623977	−	0.00541050i
$622$		0			0
$623$	4.51169	−	7.19583i	0.180757	−	0.288295i
$624$		0			0
$625$	3.23924	−	5.61053i	0.129570	−	0.224421i
$626$		0			0
$627$	14.5927	−	12.9797i	0.582776	−	0.518358i
$628$		0			0
$629$	−5.39926			−0.215282
$630$		0			0
$631$	−35.7266			−1.42225			−0.711126	−	0.703064i	$-0.751815\pi$
$631$	−35.7266			−1.42225			−0.711126	+	0.703064i	$0.751815\pi$
$632$		0			0
$633$	−0.116283	−	0.563895i	−0.00462185	−	0.0224128i
$634$		0			0
$635$	−10.6738	+	18.4875i	−0.423576	+	0.733655i
$636$		0			0
$637$	−33.5869	−	2.45133i	−1.33076	−	0.0971254i
$638$		0			0
$639$	−30.5989	−	22.8045i	−1.21047	−	0.902134i
$640$		0			0
$641$	−8.65638	−	14.9933i	−0.341906	−	0.592199i	0.642880	−	0.765967i	$-0.277739\pi$
$641$	−8.65638	−	14.9933i	−0.341906	−	0.592199i	−0.984787	+	0.173767i	$0.944406\pi$
$642$		0			0
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	−0.996451	−	0.0841700i	$-0.973176\pi$
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	0.425332	−	0.905037i	$-0.360157\pi$
$644$		0			0
$645$	0.925798	+	4.48949i	0.0364533	+	0.176773i
$646$		0			0
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	−0.890056	−	0.455851i	$-0.849335\pi$
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	0.839807	+	0.542886i	$0.182668\pi$
$648$		0			0
$649$	5.14400	+	8.90966i	0.201920	+	0.349735i
$650$		0			0
$651$	−2.06506	−	12.2552i	−0.0809360	−	0.480320i
$652$		0			0
$653$	−14.9883	+	25.9605i	−0.586538	+	1.01591i	0.408144	+	0.912918i	$0.366176\pi$
$653$	−14.9883	+	25.9605i	−0.586538	+	1.01591i	−0.994682	+	0.102996i	$0.967157\pi$
$654$		0			0
$655$	−2.52290	−	4.36979i	−0.0985779	−	0.170742i
$656$		0			0
$657$	44.2304	−	19.0521i	1.72559	−	0.743294i
$658$		0			0
$659$	7.63162	−	13.2183i	0.297286	−	0.514914i	−0.678228	−	0.734851i	$-0.737252\pi$
$659$	7.63162	−	13.2183i	0.297286	−	0.514914i	0.975514	+	0.219937i	$0.0705853\pi$
$660$		0			0
$661$	−27.2522			−1.05999			−0.529994	−	0.848001i	$-0.677806\pi$
$661$	−27.2522			−1.05999			−0.529994	+	0.848001i	$0.677806\pi$
$662$		0			0
$663$	−42.7032	−	14.1625i	−1.65845	−	0.550026i
$664$		0			0
$665$	13.9654	+	26.3618i	0.541555	+	1.02227i
$666$		0			0
$667$	−1.24288	−	2.15273i	−0.0481245	−	0.0833541i
$668$		0			0
$669$	−8.19530	+	7.28941i	−0.316849	+	0.281825i
$670$		0			0
$671$	3.55563	+	6.15854i	0.137264	+	0.237748i
$672$		0			0
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.0620280	−	0.998074i	$-0.480243\pi$
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.833344	−	0.552755i	$-0.186423\pi$
$674$		0			0
$675$	−5.44870	+	11.6612i	−0.209721	+	0.448841i
$676$		0			0
$677$	5.09888			0.195966			0.0979830	−	0.995188i	$-0.468761\pi$
$677$	5.09888			0.195966			0.0979830	+	0.995188i	$0.468761\pi$
$678$		0			0
$679$	−3.76509	−	0.137215i	−0.144491	−	0.00526582i
$680$		0			0
$681$	−8.15383	−	39.5405i	−0.312455	−	1.51519i
$682$		0			0
$683$	7.77197	−	13.4614i	0.297386	−	0.515088i	−0.678151	−	0.734923i	$-0.737218\pi$
$683$	7.77197	−	13.4614i	0.297386	−	0.515088i	0.975537	+	0.219835i	$0.0705518\pi$
$684$		0			0
$685$	−33.7738			−1.29043
$686$		0			0
$687$	6.41164	−	5.70291i	0.244619	−	0.217580i
$688$		0			0
$689$	23.5192			0.896009
$690$		0			0
$691$	−23.2967			−0.886246			−0.443123	−	0.896461i	$-0.646130\pi$
$691$	−23.2967			−0.886246			−0.443123	+	0.896461i	$0.646130\pi$
$692$		0			0
$693$	−11.7527	+	4.56251i	−0.446449	+	0.173315i
$694$		0			0
$695$	20.7330			0.786449
$696$		0			0
$697$	−31.7280			−1.20178
$698$		0			0
$699$	−4.99381	−	24.2165i	−0.188883	−	0.915954i
$700$		0			0
$701$	−45.6464			−1.72404			−0.862020	−	0.506874i	$-0.830801\pi$
$701$	−45.6464			−1.72404			−0.862020	+	0.506874i	$0.830801\pi$
$702$		0			0
$703$	−3.54944	+	6.14781i	−0.133870	+	0.231869i
$704$		0			0
$705$	5.48074	−	4.87492i	0.206417	−	0.183600i
$706$		0			0
$707$	−16.9123	+	26.9740i	−0.636053	+	1.01446i
$708$		0			0
$709$	18.0014			0.676056			0.338028	−	0.941136i	$-0.390240\pi$
$709$	18.0014			0.676056			0.338028	+	0.941136i	$0.390240\pi$
$710$		0			0
$711$	−20.1742	−	15.0353i	−0.756591	−	0.563867i
$712$		0			0
$713$	0.407305	−	0.705474i	0.0152537	−	0.0264202i
$714$		0			0
$715$	6.06870	+	10.5113i	0.226957	+	0.393100i
$716$		0			0
$717$	−1.74041	−	8.43979i	−0.0649968	−	0.315190i
$718$		0			0
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	−0.972595	−	0.232506i	$-0.925307\pi$
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	0.284941	−	0.958545i	$-0.408026\pi$
$720$		0			0
$721$	16.1254	+	0.587674i	0.600542	+	0.0218861i
$722$		0			0
$723$	4.54758	+	22.0527i	0.169126	+	0.820147i
$724$		0			0
$725$	20.4995			0.761333
$726$		0			0
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	0.431692	+	0.902021i	$0.357917\pi$
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	−0.997019	+	0.0771543i	$0.975417\pi$
$728$		0			0
$729$	−9.27375	+	25.3574i	−0.343472	+	0.939163i
$730$		0			0
$731$	4.49814	+	7.79101i	0.166370	+	0.288161i
$732$		0			0
$733$	−3.07530	+	5.32657i	−0.113589	+	0.196741i	−0.917215	−	0.398393i	$-0.869568\pi$
$733$	−3.07530	+	5.32657i	−0.113589	+	0.196741i	0.803626	+	0.595135i	$0.202901\pi$
$734$		0			0
$735$	−2.50619	−	19.0941i	−0.0924422	−	0.704297i
$736$		0			0
$737$	−7.98398	−	13.8287i	−0.294094	−	0.509385i
$738$		0			0
$739$	20.3912	−	35.3186i	0.750103	−	1.29922i	−0.197670	−	0.980269i	$-0.563337\pi$
$739$	20.3912	−	35.3186i	0.750103	−	1.29922i	0.947772	−	0.318947i	$-0.103329\pi$
$740$		0			0
$741$	−44.1989	+	39.3132i	−1.62369	+	1.44421i
$742$		0			0
$743$	−7.25271	−	12.5621i	−0.266076	−	0.460858i	0.701769	−	0.712405i	$-0.252394\pi$
$743$	−7.25271	−	12.5621i	−0.266076	−	0.460858i	−0.967845	+	0.251547i	$0.919061\pi$
$744$		0			0
$745$	−4.13671	−	7.16500i	−0.151557	−	0.262505i
$746$		0			0
$747$	−6.51849	+	2.80782i	−0.238499	+	0.102733i
$748$		0			0
$749$	4.33792	−	6.91867i	0.158504	−	0.252803i
$750$		0			0
$751$	2.09455	−	3.62787i	0.0764314	−	0.132383i	−0.825276	−	0.564729i	$-0.808981\pi$
$751$	2.09455	−	3.62787i	0.0764314	−	0.132383i	0.901708	+	0.432346i	$0.142314\pi$
$752$		0			0
$753$	−3.99931	−	1.32637i	−0.145743	−	0.0483356i
$754$		0			0
$755$	0.830556			0.0302270
$756$		0			0
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$		0			0
$759$	−0.784350	−	0.260130i	−0.0284701	−	0.00944211i
$760$		0			0
$761$	−1.81708	+	3.14728i	−0.0658692	+	0.114089i	−0.897079	−	0.441870i	$-0.854315\pi$
$761$	−1.81708	+	3.14728i	−0.0658692	+	0.114089i	0.831210	+	0.555959i	$0.187649\pi$
$762$		0			0
$763$	−6.04944	−	0.220465i	−0.219005	−	0.00798138i
$764$		0			0
$765$	3.00000	−	25.5524i	0.108465	−	0.923851i
$766$		0			0
$767$	−15.5803	−	26.9859i	−0.562573	−	0.974404i
$768$		0			0
$769$	−19.9672	−	34.5842i	−0.720035	−	1.24714i	−0.960985	−	0.276600i	$-0.910792\pi$
$769$	−19.9672	−	34.5842i	−0.720035	−	1.24714i	0.240950	−	0.970538i	$-0.422541\pi$
$770$		0			0
$771$	1.27816	−	1.13688i	0.0460318	−	0.0409436i
$772$		0			0
$773$	18.0698	−	31.2978i	0.649925	−	1.12570i	−0.333215	−	0.942851i	$-0.608133\pi$
$773$	18.0698	−	31.2978i	0.649925	−	1.12570i	0.983140	−	0.182853i	$-0.0585332\pi$
$774$		0			0
$775$	3.35896	+	5.81788i	0.120657	+	0.208985i
$776$		0			0
$777$	3.53273	−	2.91887i	0.126736	−	0.104714i
$778$		0			0
$779$	−20.8578	+	36.1267i	−0.747308	+	1.29438i
$780$		0			0
$781$	10.1025	+	17.4981i	0.361497	+	0.626131i
$782$		0			0
$783$	42.8406	−	3.71470i	1.53100	−	0.132753i
$784$		0			0
$785$	−7.03961	+	12.1930i	−0.251254	+	0.435186i
$786$		0			0
$787$	44.6377			1.59116			0.795582	−	0.605846i	$-0.207165\pi$
$787$	44.6377			1.59116			0.795582	+	0.605846i	$0.207165\pi$
$788$		0			0
$789$	6.01169	+	29.1526i	0.214022	+	1.03786i
$790$		0			0
$791$	−27.3566	+	43.6319i	−0.972689	+	1.55137i
$792$		0			0
$793$	−10.7694	−	18.6532i	−0.382433	−	0.662394i
$794$		0			0
$795$	2.71634	+	13.1724i	0.0963386	+	0.467176i
$796$		0			0
$797$	26.2836	+	45.5245i	0.931012	+	1.61256i	0.781595	+	0.623786i	$0.214407\pi$
$797$	26.2836	+	45.5245i	0.931012	+	1.61256i	0.149418	+	0.988774i	$0.452260\pi$
$798$		0			0
$799$	7.19777	−	12.4669i	0.254639	−	0.441047i
$800$		0			0
$801$	−1.12296	+	9.56475i	−0.0396777	+	0.337954i
$802$		0			0
$803$	−25.4981			−0.899810
$804$		0			0
$805$	0.670538	−	1.06946i	0.0236334	−	0.0376936i
$806$		0			0
$807$	29.6428	−	26.3662i	1.04348	−	0.928134i
$808$		0			0
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	−0.706042	−	0.708170i	$-0.749521\pi$
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	0.966314	+	0.257365i	$0.0828544\pi$
$810$		0			0
$811$	−27.0704			−0.950571			−0.475285	−	0.879832i	$-0.657655\pi$
$811$	−27.0704			−0.950571			−0.475285	+	0.879832i	$0.657655\pi$
$812$		0			0
$813$	−4.89995	−	23.7614i	−0.171849	−	0.833348i
$814$		0			0
$815$	34.8850			1.22197
$816$		0			0
$817$	11.8282			0.413817
$818$		0			0
$819$	35.5970	−	13.8191i	1.24386	−	0.482878i
$820$		0			0
$821$	43.8182			1.52926			0.764632	−	0.644467i	$-0.222921\pi$
$821$	43.8182			1.52926			0.764632	+	0.644467i	$0.222921\pi$
$822$		0			0
$823$	−31.3425			−1.09253			−0.546265	−	0.837613i	$-0.683951\pi$
$823$	−31.3425			−1.09253			−0.546265	+	0.837613i	$0.683951\pi$
$824$		0			0
$825$	5.09201	−	4.52915i	0.177281	−	0.157685i
$826$		0			0
$827$	14.7665			0.513480			0.256740	−	0.966480i	$-0.417352\pi$
$827$	14.7665			0.513480			0.256740	+	0.966480i	$0.417352\pi$
$828$		0			0
$829$	−15.0036	+	25.9871i	−0.521098	+	0.902568i	0.478601	+	0.878033i	$0.341144\pi$
$829$	−15.0036	+	25.9871i	−0.521098	+	0.902568i	−0.999699	+	0.0245357i	$0.992189\pi$
$830$		0			0
$831$	−9.89809	−	47.9989i	−0.343361	−	1.66506i
$832$		0			0
$833$	−16.4647	−	34.0200i	−0.570469	−	1.17872i
$834$		0			0
$835$	5.24219			0.181414
$836$		0			0
$837$	8.07392	+	11.5497i	0.279075	+	0.399217i
$838$		0			0
$839$	−18.0167	+	31.2059i	−0.622006	+	1.07735i	0.367106	+	0.930179i	$0.380349\pi$
$839$	−18.0167	+	31.2059i	−0.622006	+	1.07735i	−0.989112	+	0.147167i	$0.952985\pi$
$840$		0			0
$841$	−19.7429	−	34.1957i	−0.680789	−	1.17916i
$842$		0			0
$843$	−22.7720	+	20.2548i	−0.784308	+	0.697613i
$844$		0			0
$845$	−8.05673	−	13.9547i	−0.277160	−	0.480055i
$846$		0			0
$847$	−22.4134	−	0.816833i	−0.770134	−	0.0280667i
$848$		0			0
$849$	30.4516	+	10.0993i	1.04510	+	0.346606i
$850$		0			0
$851$	0.300372			0.0102966
$852$		0			0
$853$	−12.2658	+	21.2450i	−0.419972	+	0.727413i	−0.995936	−	0.0900617i	$-0.971294\pi$
$853$	−12.2658	+	21.2450i	−0.419972	+	0.727413i	0.575964	+	0.817475i	$0.304627\pi$
$854$		0			0
$855$	−27.1229	−	20.2140i	−0.927583	−	0.691303i
$856$		0			0
$857$	−14.5240	−	25.1563i	−0.496130	−	0.859323i	0.503860	−	0.863785i	$-0.331913\pi$
$857$	−14.5240	−	25.1563i	−0.496130	−	0.859323i	−0.999990	+	0.00446273i	$0.998579\pi$
$858$		0			0
$859$	12.6476	−	21.9064i	0.431532	−	0.747435i	−0.565474	−	0.824766i	$-0.691307\pi$
$859$	12.6476	−	21.9064i	0.431532	−	0.747435i	0.997005	+	0.0773313i	$0.0246399\pi$
$860$		0			0
$861$	20.7596	−	17.1523i	0.707485	−	0.584550i
$862$		0			0
$863$	1.34981	+	2.33795i	0.0459482	+	0.0795846i	0.888085	−	0.459680i	$-0.152036\pi$
$863$	1.34981	+	2.33795i	0.0459482	+	0.0795846i	−0.842137	+	0.539264i	$0.818702\pi$
$864$		0			0
$865$	−15.1749	+	26.2836i	−0.515961	+	0.893671i
$866$		0			0
$867$	−4.25093	−	20.6141i	−0.144369	−	0.700091i
$868$		0			0
$869$	6.66071	+	11.5367i	0.225949	+	0.391355i
$870$		0			0
$871$	24.1822	+	41.8847i	0.819381	+	1.41921i
$872$		0			0
$873$	3.92353	−	1.69005i	0.132792	−	0.0571995i
$874$		0			0
$875$	14.7095	+	27.7663i	0.497271	+	0.938672i
$876$		0			0
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	−0.757070	−	0.653334i	$-0.773370\pi$
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	0.944339	+	0.328975i	$0.106703\pi$
$878$		0			0
$879$	−4.92718	−	23.8934i	−0.166190	−	0.805905i
$880$		0			0
$881$	−40.3942			−1.36091			−0.680457	−	0.732788i	$-0.738219\pi$
$881$	−40.3942			−1.36091			−0.680457	+	0.732788i	$0.738219\pi$
$882$		0			0
$883$	33.2581			1.11923			0.559613	−	0.828754i	$-0.310950\pi$
$883$	33.2581			1.11923			0.559613	+	0.828754i	$0.310950\pi$
$884$		0			0
$885$	13.3145	−	11.8428i	0.447563	−	0.398091i
$886$		0			0
$887$	20.2836	−	35.1322i	0.681056	−	1.17962i	−0.293603	−	0.955928i	$-0.594854\pi$
$887$	20.2836	−	35.1322i	0.681056	−	1.17962i	0.974659	−	0.223696i	$-0.0718124\pi$
$888$		0			0
$889$	−16.6461	−	31.4219i	−0.558291	−	1.05386i
$890$		0			0
$891$	9.82072	−	10.3879i	0.329007	−	0.348007i
$892$		0			0
$893$	−9.46355	−	16.3913i	−0.316686	−	0.548516i
$894$		0			0
$895$	12.7658	+	22.1110i	0.426713	+	0.739089i
$896$		0			0
$897$	2.37567	+	0.787890i	0.0793212	+	0.0263069i
$898$		0			0
$899$	11.2218	−	19.4367i	0.374267	−	0.648249i
$900$		0			0
$901$	13.1978	+	22.8592i	0.439681	+	0.761551i
$902$		0			0
$903$	−7.15500	−	2.66593i	−0.238103	−	0.0887167i
$904$		0			0
$905$	−6.39561	+	11.0775i	−0.212597	+	0.368230i
$906$		0			0
$907$	15.0567	+	26.0790i	0.499950	+	0.865939i	1.00000		5.72941e-5i	$-1.82373e-5\pi$
$907$	15.0567	+	26.0790i	0.499950	+	0.865939i	−0.500050	+	0.865997i	$0.666685\pi$
$908$		0			0
$909$	4.20946	−	35.8540i	0.139619	−	1.18920i
$910$		0			0
$911$	−14.6113	+	25.3075i	−0.484093	+	0.838473i	−0.999833	−	0.0182717i	$-0.994184\pi$
$911$	−14.6113	+	25.3075i	−0.484093	+	0.838473i	0.515740	+	0.856745i	$0.327517\pi$
$912$		0			0
$913$	3.75781			0.124365
$914$		0			0
$915$	9.20327	−	8.18597i	0.304251	−	0.270620i
$916$		0			0
$917$	8.39926	+	0.306102i	0.277368	+	0.0101084i
$918$		0			0
$919$	5.52359	+	9.56714i	0.182206	+	0.315591i	0.942632	−	0.333835i	$-0.108343\pi$
$919$	5.52359	+	9.56714i	0.182206	+	0.315591i	−0.760425	+	0.649426i	$0.775009\pi$
$920$		0			0
$921$	9.62612	+	3.19250i	0.317191	+	0.105196i
$922$		0			0
$923$	−30.5989	−	52.9988i	−1.00717	−	1.74448i
$924$		0			0
$925$	−1.23855	+	2.14523i	−0.0407233	+	0.0705348i
$926$		0			0
$927$	−16.8040	+	7.23828i	−0.551916	+	0.237736i
$928$		0			0
$929$	−42.3338			−1.38893			−0.694463	−	0.719528i	$-0.744358\pi$
$929$	−42.3338			−1.38893			−0.694463	+	0.719528i	$0.744358\pi$
$930$		0			0
$931$	−49.5604	−	3.61715i	−1.62428	−	0.118547i
$932$		0			0
$933$	−1.33310	−	0.442124i	−0.0436439	−	0.0144745i
$934$		0			0
$935$	−6.81089	+	11.7968i	−0.222740	+	0.385797i
$936$		0			0
$937$	−11.7651			−0.384349			−0.192174	−	0.981361i	$-0.561554\pi$
$937$	−11.7651			−0.384349			−0.192174	+	0.981361i	$0.561554\pi$
$938$		0			0
$939$	17.3869	+	5.76636i	0.567399	+	0.188178i
$940$		0			0
$941$	14.5760			0.475164			0.237582	−	0.971368i	$-0.423645\pi$
$941$	14.5760			0.475164			0.237582	+	0.971368i	$0.423645\pi$
$942$		0			0
$943$	1.76509			0.0574793
$944$		0			0
$945$	11.8509	+	18.3408i	0.385510	+	0.596626i
$946$		0			0
$947$	−6.24357			−0.202889			−0.101444	−	0.994841i	$-0.532346\pi$
$947$	−6.24357			−0.202889			−0.101444	+	0.994841i	$0.532346\pi$
$948$		0			0
$949$	77.2297			2.50698
$950$		0			0
$951$	20.0508	+	6.64985i	0.650192	+	0.215636i
$952$		0			0
$953$	28.0173			0.907570			0.453785	−	0.891111i	$-0.350073\pi$
$953$	28.0173			0.907570			0.453785	+	0.891111i	$0.350073\pi$
$954$		0			0
$955$	−19.0309	+	32.9624i	−0.615825	+	1.06664i
$956$		0			0
$957$	−21.6098	−	7.16689i	−0.698546	−	0.231673i
$958$		0			0
$959$	29.8843	−	47.6634i	0.965015	−	1.53913i
$960$		0			0
$961$	−23.6450			−0.762742
$962$		0			0
$963$	−1.07970	+	9.19635i	−0.0347929	+	0.296348i
$964$		0			0
$965$	−7.75526	+	13.4325i	−0.249651	+	0.432408i
$966$		0			0
$967$	−15.7837	−	27.3381i	−0.507568	−	0.879134i	−0.999962	−	0.00876132i	$-0.997211\pi$
$967$	−15.7837	−	27.3381i	−0.507568	−	0.879134i	0.492393	−	0.870373i	$-0.336122\pi$
$968$		0			0
$969$	−63.0122	−	20.8980i	−2.02424	−	0.671340i
$970$		0			0
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	0.817196	−	0.576359i	$-0.195527\pi$
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	−0.907740	+	0.419533i	$0.862194\pi$
$972$		0			0
$973$	−18.3454	+	29.2596i	−0.588127	+	0.938021i
$974$		0			0
$975$	−15.4228	+	13.7180i	−0.493926	+	0.439329i
$976$		0			0
$977$	6.49304			0.207731			0.103865	−	0.994591i	$-0.466879\pi$
$977$	6.49304			0.207731			0.103865	+	0.994591i	$0.466879\pi$
$978$		0			0
$979$	2.54944	−	4.41576i	0.0814805	−	0.141128i
$980$		0			0
$981$	6.30401	−	2.71543i	0.201272	−	0.0866971i
$982$		0			0
$983$	−15.1531	−	26.2460i	−0.483310	−	0.837118i	0.516506	−	0.856283i	$-0.327232\pi$
$983$	−15.1531	−	26.2460i	−0.483310	−	0.837118i	−0.999816	+	0.0191658i	$0.993899\pi$
$984$		0			0
$985$	14.4887	−	25.0952i	0.461649	−	0.799599i
$986$		0			0
$987$	2.03018	+	12.0482i	0.0646215	+	0.383500i
$988$		0			0
$989$	−0.250241	−	0.433430i	−0.00795720	−	0.0137823i
$990$		0			0
$991$	−11.1669	+	19.3416i	−0.354728	+	0.614407i	−0.987071	−	0.160281i	$-0.948760\pi$
$991$	−11.1669	+	19.3416i	−0.354728	+	0.614407i	0.632343	+	0.774688i	$0.282093\pi$
$992$		0			0
$993$	25.7552	+	8.54170i	0.817316	+	0.271063i
$994$		0			0
$995$	−14.3738	−	24.8962i	−0.455680	−	0.789262i
$996$		0			0
$997$	4.38255	+	7.59079i	0.138797	+	0.240403i	0.927041	−	0.374959i	$-0.122343\pi$
$997$	4.38255	+	7.59079i	0.138797	+	0.240403i	−0.788245	+	0.615362i	$0.789010\pi$
$998$		0			0
$999$	−2.19963	+	4.70761i	−0.0695932	+	0.148942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.g.529.3		6
3.2	odd	2		3024.2.q.g.2881.3		6
4.3	odd	2		126.2.e.c.25.1	✓	6
7.2	even	3		1008.2.t.h.961.1		6
9.4	even	3		1008.2.t.h.193.1		6
9.5	odd	6		3024.2.t.h.1873.1		6
12.11	even	2		378.2.e.d.235.3		6
21.2	odd	6		3024.2.t.h.289.1		6
28.3	even	6		882.2.f.o.295.1		6
28.11	odd	6		882.2.f.n.295.3		6
28.19	even	6		882.2.h.p.79.1		6
28.23	odd	6		126.2.h.d.79.3	yes	6
28.27	even	2		882.2.e.o.655.3		6
36.7	odd	6		1134.2.g.m.487.1		6
36.11	even	6		1134.2.g.l.487.3		6
36.23	even	6		378.2.h.c.361.1		6
36.31	odd	6		126.2.h.d.67.3	yes	6
63.23	odd	6		3024.2.q.g.2305.3		6
63.58	even	3	inner	1008.2.q.g.625.3		6
84.11	even	6		2646.2.f.l.883.3		6
84.23	even	6		378.2.h.c.289.1		6
84.47	odd	6		2646.2.h.o.667.3		6
84.59	odd	6		2646.2.f.m.883.1		6
84.83	odd	2		2646.2.e.p.2125.1		6
252.11	even	6		7938.2.a.ca.1.1		3
252.23	even	6		378.2.e.d.37.3		6
252.31	even	6		882.2.f.o.589.1		6
252.59	odd	6		2646.2.f.m.1765.1		6
252.67	odd	6		882.2.f.n.589.3		6
252.79	odd	6		1134.2.g.m.163.1		6
252.95	even	6		2646.2.f.l.1765.3		6
252.103	even	6		882.2.e.o.373.3		6
252.115	even	6		7938.2.a.bw.1.1		3
252.131	odd	6		2646.2.e.p.1549.1		6
252.139	even	6		882.2.h.p.67.1		6
252.151	odd	6		7938.2.a.bv.1.3		3
252.167	odd	6		2646.2.h.o.361.3		6
252.191	even	6		1134.2.g.l.163.3		6
252.227	odd	6		7938.2.a.bz.1.3		3
252.247	odd	6		126.2.e.c.121.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	4.3	odd	2
126.2.e.c.121.1	yes	6	252.247	odd	6
126.2.h.d.67.3	yes	6	36.31	odd	6
126.2.h.d.79.3	yes	6	28.23	odd	6
378.2.e.d.37.3		6	252.23	even	6
378.2.e.d.235.3		6	12.11	even	2
378.2.h.c.289.1		6	84.23	even	6
378.2.h.c.361.1		6	36.23	even	6
882.2.e.o.373.3		6	252.103	even	6
882.2.e.o.655.3		6	28.27	even	2
882.2.f.n.295.3		6	28.11	odd	6
882.2.f.n.589.3		6	252.67	odd	6
882.2.f.o.295.1		6	28.3	even	6
882.2.f.o.589.1		6	252.31	even	6
882.2.h.p.67.1		6	252.139	even	6
882.2.h.p.79.1		6	28.19	even	6
1008.2.q.g.529.3		6	1.1	even	1	trivial
1008.2.q.g.625.3		6	63.58	even	3	inner
1008.2.t.h.193.1		6	9.4	even	3
1008.2.t.h.961.1		6	7.2	even	3
1134.2.g.l.163.3		6	252.191	even	6
1134.2.g.l.487.3		6	36.11	even	6
1134.2.g.m.163.1		6	252.79	odd	6
1134.2.g.m.487.1		6	36.7	odd	6
2646.2.e.p.1549.1		6	252.131	odd	6
2646.2.e.p.2125.1		6	84.83	odd	2
2646.2.f.l.883.3		6	84.11	even	6
2646.2.f.l.1765.3		6	252.95	even	6
2646.2.f.m.883.1		6	84.59	odd	6
2646.2.f.m.1765.1		6	252.59	odd	6
2646.2.h.o.361.3		6	252.167	odd	6
2646.2.h.o.667.3		6	84.47	odd	6
3024.2.q.g.2305.3		6	63.23	odd	6
3024.2.q.g.2881.3		6	3.2	odd	2
3024.2.t.h.289.1		6	21.2	odd	6
3024.2.t.h.1873.1		6	9.5	odd	6
7938.2.a.bv.1.3		3	252.151	odd	6
7938.2.a.bw.1.1		3	252.115	even	6
7938.2.a.bz.1.3		3	252.227	odd	6
7938.2.a.ca.1.1		3	252.11	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)

\(f(q)\)	\(=\)	\(q+(1.64400 + 0.545231i) q^{3} +(-0.794182 + 1.37556i) q^{5} +(-1.23855 - 2.33795i) q^{7} +(2.40545 + 1.79272i) q^{9} +(-0.794182 - 1.37556i) q^{11} +(2.40545 + 4.16635i) q^{13} +(-2.05563 + 1.82841i) q^{15} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-0.761450 - 4.51887i) q^{21} +(0.150186 - 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +2.71201 q^{31} +(-0.555632 - 2.69443i) q^{33} +(4.19963 + 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.68292 + 8.16100i) q^{39} +(2.93818 + 5.08907i) q^{41} +(0.833104 - 1.44298i) q^{43} +(-4.37636 + 1.88510i) q^{45} -2.66621 q^{47} +(-3.93199 + 5.79133i) q^{49} +(-6.98762 + 6.21523i) q^{51} +(2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} -6.47710 q^{59} -4.47710 q^{61} +(1.21201 - 7.84417i) q^{63} -7.64145 q^{65} +10.0531 q^{67} +(0.388736 - 0.345766i) q^{69} -12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(0.866524 + 4.20205i) q^{75} +(-2.23236 + 3.56046i) q^{77} -8.38688 q^{79} +(2.57234 + 8.62456i) q^{81} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(10.7101 - 9.52628i) q^{87} +(1.60507 + 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +(4.45853 + 1.47867i) q^{93} -11.2756 q^{95} +(0.712008 - 1.23323i) q^{97} +(0.555632 - 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + q^5 - 2 * q^7 + 8 * q^9 + q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 + 2 * q^25 + 7 * q^27 - 5 * q^29 + 40 * q^31 - 3 * q^33 + 13 * q^35 + 3 * q^37 + 5 * q^39 + 6 * q^43 + 9 * q^45 - 18 * q^47 + 12 * q^49 - 6 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 - 28 * q^59 - 16 * q^61 + 31 * q^63 + 24 * q^65 + 2 * q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 - 8 * q^75 + 10 * q^77 + 10 * q^79 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 27 * q^87 - 9 * q^89 + 46 * q^91 - 38 * q^93 - 8 * q^95 + 28 * q^97 + 3 * q^99

Introduction

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