LMFDB - Embedded newform 1008.2.r.n.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (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:	10.0.6095158642368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 $ x^10 - 4x^9 + 6x^8 - 7x^7 + 25x^6 - 66x^5 + 75x^4 - 63x^3 + 162x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.1
Root			$1.11541 + 1.32509i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.n.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62713 + 0.593666i) q^{3} +(1.50470 - 2.60622i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.29512 - 1.93195i) q^{9} +O(q^{10})$	\(q+(-1.62713 + 0.593666i) q^{3} +(1.50470 - 2.60622i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.29512 - 1.93195i) q^{9} +(-2.74254 - 4.75022i) q^{11} +(-0.421867 + 0.730695i) q^{13} +(-0.901126 + 5.13396i) q^{15} -4.59024 q^{17} +3.80203 q^{19} +(1.32770 + 1.11231i) q^{21} +(-4.48385 + 7.76626i) q^{23} +(-2.02826 - 3.51305i) q^{25} +(-2.58754 + 4.50607i) q^{27} +(-0.974447 - 1.68779i) q^{29} +(1.68873 - 2.92497i) q^{31} +(7.28252 + 6.10109i) q^{33} -3.00941 q^{35} -7.49050 q^{37} +(0.252645 - 1.43939i) q^{39} +(-3.69144 + 6.39375i) q^{41} +(3.11330 + 5.39240i) q^{43} +(-1.58160 - 8.88860i) q^{45} +(-6.57013 - 11.3798i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(7.46894 - 2.72507i) q^{51} +8.05652 q^{53} -16.5068 q^{55} +(-6.18641 + 2.25714i) q^{57} +(5.04037 - 8.73018i) q^{59} +(-2.84423 - 4.92635i) q^{61} +(-2.82068 - 1.02166i) q^{63} +(1.26957 + 2.19896i) q^{65} +(-2.71969 + 4.71065i) q^{67} +(2.68526 - 15.2986i) q^{69} -5.81144 q^{71} -10.7167 q^{73} +(5.38582 + 4.51209i) q^{75} +(-2.74254 + 4.75022i) q^{77} +(1.37055 + 2.37386i) q^{79} +(1.53517 - 8.86810i) q^{81} +(-6.35164 - 11.0014i) q^{83} +(-6.90695 + 11.9632i) q^{85} +(2.58754 + 2.16776i) q^{87} -8.74898 q^{89} +0.843734 q^{91} +(-1.01134 + 5.76185i) q^{93} +(5.72093 - 9.90894i) q^{95} +(3.83699 + 6.64586i) q^{97} +(-15.4716 - 5.60390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 3 * q^5 - 5 * q^7	$ 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) $ 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.62713	+	0.593666i	−0.939426	+	0.342753i
$3$	−1.62713	+	0.593666i	−0.939426	+	0.342753i
$4$		0			0
$5$	1.50470	−	2.60622i	0.672923	−	1.16554i	−0.304148	−	0.952625i	$-0.598372\pi$
$5$	1.50470	−	2.60622i	0.672923	−	1.16554i	0.977071	−	0.212913i	$-0.0682950\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	2.29512	−	1.93195i	0.765041	−	0.643982i
$10$		0			0
$11$	−2.74254	−	4.75022i	−0.826908	−	1.43225i	−0.900453	−	0.434954i	$-0.856765\pi$
$11$	−2.74254	−	4.75022i	−0.826908	−	1.43225i	0.0735450	−	0.997292i	$-0.476569\pi$
$12$		0			0
$13$	−0.421867	+	0.730695i	−0.117005	+	0.202658i	−0.918579	−	0.395236i	$-0.870663\pi$
$13$	−0.421867	+	0.730695i	−0.117005	+	0.202658i	0.801575	+	0.597895i	$0.203996\pi$
$14$		0			0
$15$	−0.901126	+	5.13396i	−0.232670	+	1.32558i
$16$		0			0
$17$	−4.59024			−1.11330			−0.556649	−	0.830748i	$-0.687913\pi$
$17$	−4.59024			−1.11330			−0.556649	+	0.830748i	$0.687913\pi$
$18$		0			0
$19$	3.80203			0.872246			0.436123	−	0.899887i	$-0.356351\pi$
$19$	3.80203			0.872246			0.436123	+	0.899887i	$0.356351\pi$
$20$		0			0
$21$	1.32770	+	1.11231i	0.289727	+	0.242725i
$22$		0			0
$23$	−4.48385	+	7.76626i	−0.934948	+	1.61938i	−0.160221	+	0.987081i	$0.551221\pi$
$23$	−4.48385	+	7.76626i	−0.934948	+	1.61938i	−0.774727	+	0.632296i	$0.782113\pi$
$24$		0			0
$25$	−2.02826	−	3.51305i	−0.405652	−	0.702610i
$26$		0			0
$27$	−2.58754	+	4.50607i	−0.497972	+	0.867193i
$28$		0			0
$29$	−0.974447	−	1.68779i	−0.180950	−	0.313415i	0.761254	−	0.648454i	$-0.224584\pi$
$29$	−0.974447	−	1.68779i	−0.180950	−	0.313415i	−0.942204	+	0.335039i	$0.891251\pi$
$30$		0			0
$31$	1.68873	−	2.92497i	0.303305	−	0.525339i	−0.673578	−	0.739116i	$-0.735243\pi$
$31$	1.68873	−	2.92497i	0.303305	−	0.525339i	0.976882	+	0.213777i	$0.0685766\pi$
$32$		0			0
$33$	7.28252	+	6.10109i	1.26772	+	1.06206i
$34$		0			0
$35$	−3.00941			−0.508682
$36$		0			0
$37$	−7.49050			−1.23143			−0.615715	−	0.787969i	$-0.711133\pi$
$37$	−7.49050			−1.23143			−0.615715	+	0.787969i	$0.711133\pi$
$38$		0			0
$39$	0.252645	−	1.43939i	0.0404556	−	0.230486i
$40$		0			0
$41$	−3.69144	+	6.39375i	−0.576505	+	0.998537i	0.419371	+	0.907815i	$0.362251\pi$
$41$	−3.69144	+	6.39375i	−0.576505	+	0.998537i	−0.995876	+	0.0907217i	$0.971083\pi$
$42$		0			0
$43$	3.11330	+	5.39240i	0.474774	+	0.822333i	0.999583	−	0.0288873i	$-0.00919639\pi$
$43$	3.11330	+	5.39240i	0.474774	+	0.822333i	−0.524808	+	0.851220i	$0.675863\pi$
$44$		0			0
$45$	−1.58160	−	8.88860i	−0.235771	−	1.32503i
$46$		0			0
$47$	−6.57013	−	11.3798i	−0.958352	−	1.65991i	−0.726505	−	0.687162i	$-0.758856\pi$
$47$	−6.57013	−	11.3798i	−0.958352	−	1.65991i	−0.231847	−	0.972752i	$-0.574477\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	7.46894	−	2.72507i	1.04586	−	0.381586i
$52$		0			0
$53$	8.05652			1.10665			0.553324	−	0.832966i	$-0.313359\pi$
$53$	8.05652			1.10665			0.553324	+	0.832966i	$0.313359\pi$
$54$		0			0
$55$	−16.5068			−2.22578
$56$		0			0
$57$	−6.18641	+	2.25714i	−0.819410	+	0.298965i
$58$		0			0
$59$	5.04037	−	8.73018i	0.656200	−	1.13657i	−0.325391	−	0.945580i	$-0.605496\pi$
$59$	5.04037	−	8.73018i	0.656200	−	1.13657i	0.981591	−	0.190993i	$-0.0611707\pi$
$60$		0			0
$61$	−2.84423	−	4.92635i	−0.364167	−	0.630755i	0.624475	−	0.781044i	$-0.285313\pi$
$61$	−2.84423	−	4.92635i	−0.364167	−	0.630755i	−0.988642	+	0.150289i	$0.951979\pi$
$62$		0			0
$63$	−2.82068	−	1.02166i	−0.355372	−	0.128717i
$64$		0			0
$65$	1.26957	+	2.19896i	0.157471	+	0.272747i
$66$		0			0
$67$	−2.71969	+	4.71065i	−0.332264	+	0.575497i	−0.982955	−	0.183845i	$-0.941146\pi$
$67$	−2.71969	+	4.71065i	−0.332264	+	0.575497i	0.650692	+	0.759342i	$0.274479\pi$
$68$		0			0
$69$	2.68526	−	15.2986i	0.323267	−	1.84174i
$70$		0			0
$71$	−5.81144			−0.689691			−0.344845	−	0.938660i	$-0.612069\pi$
$71$	−5.81144			−0.689691			−0.344845	+	0.938660i	$0.612069\pi$
$72$		0			0
$73$	−10.7167			−1.25429			−0.627146	−	0.778902i	$-0.715777\pi$
$73$	−10.7167			−1.25429			−0.627146	+	0.778902i	$0.715777\pi$
$74$		0			0
$75$	5.38582	+	4.51209i	0.621901	+	0.521011i
$76$		0			0
$77$	−2.74254	+	4.75022i	−0.312542	+	0.541338i
$78$		0			0
$79$	1.37055	+	2.37386i	0.154199	+	0.267080i	0.932767	−	0.360480i	$-0.117387\pi$
$79$	1.37055	+	2.37386i	0.154199	+	0.267080i	−0.778568	+	0.627560i	$0.784054\pi$
$80$		0			0
$81$	1.53517	−	8.86810i	0.170574	−	0.985345i
$82$		0			0
$83$	−6.35164	−	11.0014i	−0.697183	−	1.20756i	−0.969439	−	0.245332i	$-0.921103\pi$
$83$	−6.35164	−	11.0014i	−0.697183	−	1.20756i	0.272256	−	0.962225i	$-0.412230\pi$
$84$		0			0
$85$	−6.90695	+	11.9632i	−0.749164	+	1.29759i
$86$		0			0
$87$	2.58754	+	2.16776i	0.277413	+	0.232409i
$88$		0			0
$89$	−8.74898			−0.927390			−0.463695	−	0.885995i	$-0.653477\pi$
$89$	−8.74898			−0.927390			−0.463695	+	0.885995i	$0.653477\pi$
$90$		0			0
$91$	0.843734			0.0884474
$92$		0			0
$93$	−1.01134	+	5.76185i	−0.104871	+	0.597476i
$94$		0			0
$95$	5.72093	−	9.90894i	0.586955	−	1.01664i
$96$		0			0
$97$	3.83699	+	6.64586i	0.389587	+	0.674785i	0.992394	−	0.123102i	$-0.0392843\pi$
$97$	3.83699	+	6.64586i	0.389587	+	0.674785i	−0.602807	+	0.797887i	$0.705951\pi$
$98$		0			0
$99$	−15.4716	−	5.60390i	−1.55496	−	0.563213i
$100$		0			0
$101$	−3.74033	−	6.47845i	−0.372177	−	0.644630i	0.617723	−	0.786396i	$-0.288055\pi$
$101$	−3.74033	−	6.47845i	−0.372177	−	0.644630i	−0.989900	+	0.141766i	$0.954722\pi$
$102$		0			0
$103$	2.55258	−	4.42120i	0.251513	−	0.435634i	−0.712429	−	0.701744i	$-0.752405\pi$
$103$	2.55258	−	4.42120i	0.251513	−	0.435634i	0.963943	+	0.266110i	$0.0857385\pi$
$104$		0			0
$105$	4.89670	−	1.78658i	0.477869	−	0.174352i
$106$		0			0
$107$	−1.48256			−0.143325			−0.0716623	−	0.997429i	$-0.522830\pi$
$107$	−1.48256			−0.143325			−0.0716623	+	0.997429i	$0.522830\pi$
$108$		0			0
$109$	0.878554			0.0841502			0.0420751	−	0.999114i	$-0.486603\pi$
$109$	0.878554			0.0841502			0.0420751	+	0.999114i	$0.486603\pi$
$110$		0			0
$111$	12.1880	−	4.44685i	1.15684	−	0.422076i
$112$		0			0
$113$	5.30474	−	9.18808i	0.499028	−	0.864342i	−0.500972	−	0.865464i	$-0.667024\pi$
$113$	5.30474	−	9.18808i	0.499028	−	0.864342i	0.999999	+	0.00112222i	$0.000357215\pi$
$114$		0			0
$115$	13.4937	+	23.3718i	1.25830	+	2.17943i
$116$		0			0
$117$	0.443427	+	2.49206i	0.0409949	+	0.230391i
$118$		0			0
$119$	2.29512	+	3.97527i	0.210393	+	0.364412i
$120$		0			0
$121$	−9.54308	+	16.5291i	−0.867552	+	1.50264i
$122$		0			0
$123$	2.21070	−	12.5950i	0.199332	−	1.13565i
$124$		0			0
$125$	2.83932			0.253956
$126$		0			0
$127$	9.55795			0.848131			0.424065	−	0.905632i	$-0.360603\pi$
$127$	9.55795			0.848131			0.424065	+	0.905632i	$0.360603\pi$
$128$		0			0
$129$	−8.26704	−	6.92589i	−0.727872	−	0.609790i
$130$		0			0
$131$	−0.785008	+	1.35967i	−0.0685864	+	0.118795i	−0.898279	−	0.439425i	$-0.855182\pi$
$131$	−0.785008	+	1.35967i	−0.0685864	+	0.118795i	0.829693	+	0.558220i	$0.188516\pi$
$132$		0			0
$133$	−1.90102	−	3.29266i	−0.164839	−	0.285510i
$134$		0			0
$135$	7.85033	+	13.5240i	0.675649	+	1.16396i
$136$		0			0
$137$	−1.15500	−	2.00053i	−0.0986787	−	0.170916i	0.812459	−	0.583018i	$-0.198128\pi$
$137$	−1.15500	−	2.00053i	−0.0986787	−	0.170916i	−0.911138	+	0.412101i	$0.864795\pi$
$138$		0			0
$139$	9.11779	−	15.7925i	0.773361	−	1.33950i	−0.162350	−	0.986733i	$-0.551907\pi$
$139$	9.11779	−	15.7925i	0.773361	−	1.33950i	0.935711	−	0.352768i	$-0.114759\pi$
$140$		0			0
$141$	17.4463	+	14.6160i	1.46924	+	1.23089i
$142$		0			0
$143$	4.62795			0.387009
$144$		0			0
$145$	−5.86501			−0.487063
$146$		0			0
$147$	0.299437	−	1.70597i	0.0246971	−	0.140706i
$148$		0			0
$149$	1.64279	−	2.84540i	0.134583	−	0.233105i	−0.790855	−	0.612003i	$-0.790364\pi$
$149$	1.64279	−	2.84540i	0.134583	−	0.233105i	0.925438	+	0.378899i	$0.123697\pi$
$150$		0			0
$151$	−6.12791	−	10.6138i	−0.498682	−	0.863743i	0.501317	−	0.865264i	$-0.332849\pi$
$151$	−6.12791	−	10.6138i	−0.498682	−	0.863743i	−0.999999	+	0.00152112i	$0.999516\pi$
$152$		0			0
$153$	−10.5352	+	8.86810i	−0.851718	+	0.716944i
$154$		0			0
$155$	−5.08207	−	8.80241i	−0.408202	−	0.707026i
$156$		0			0
$157$	1.58407	−	2.74369i	0.126422	−	0.218970i	−0.795866	−	0.605473i	$-0.792984\pi$
$157$	1.58407	−	2.74369i	0.126422	−	0.218970i	0.922288	+	0.386503i	$0.126317\pi$
$158$		0			0
$159$	−13.1090	+	4.78288i	−1.03961	+	0.379307i
$160$		0			0
$161$	8.96770			0.706754
$162$		0			0
$163$	−8.06739			−0.631887			−0.315943	−	0.948778i	$-0.602321\pi$
$163$	−8.06739			−0.631887			−0.315943	+	0.948778i	$0.602321\pi$
$164$		0			0
$165$	26.8588	−	9.79955i	2.09096	−	0.762894i
$166$		0			0
$167$	0.162965	−	0.282264i	0.0126106	−	0.0218422i	−0.859651	−	0.510881i	$-0.829319\pi$
$167$	0.162965	−	0.282264i	0.0126106	−	0.0218422i	0.872262	+	0.489039i	$0.162652\pi$
$168$		0			0
$169$	6.14406	+	10.6418i	0.472620	+	0.818601i
$170$		0			0
$171$	8.72613	−	7.34532i	0.667304	−	0.561711i
$172$		0			0
$173$	−4.06220	−	7.03593i	−0.308843	−	0.534932i	0.669267	−	0.743022i	$-0.266608\pi$
$173$	−4.06220	−	7.03593i	−0.308843	−	0.534932i	−0.978110	+	0.208091i	$0.933275\pi$
$174$		0			0
$175$	−2.02826	+	3.51305i	−0.153322	+	0.265561i
$176$		0			0
$177$	−3.01854	+	17.1975i	−0.226888	+	1.29264i
$178$		0			0
$179$	17.5470			1.31153			0.655763	−	0.754967i	$-0.272347\pi$
$179$	17.5470			1.31153			0.655763	+	0.754967i	$0.272347\pi$
$180$		0			0
$181$	14.7991			1.10001			0.550004	−	0.835162i	$-0.314626\pi$
$181$	14.7991			1.10001			0.550004	+	0.835162i	$0.314626\pi$
$182$		0			0
$183$	7.55255	+	6.32731i	0.558301	+	0.467728i
$184$		0			0
$185$	−11.2710	+	19.5219i	−0.828658	+	1.43528i
$186$		0			0
$187$	12.5889	+	21.8047i	0.920594	+	1.59452i
$188$		0			0
$189$	5.19614	−	0.0121603i	0.377963	−	0.000884530i
$190$		0			0
$191$	11.6859	+	20.2406i	0.845564	+	1.46456i	0.885131	+	0.465343i	$0.154069\pi$
$191$	11.6859	+	20.2406i	0.845564	+	1.46456i	−0.0395667	+	0.999217i	$0.512598\pi$
$192$		0			0
$193$	−8.80056	+	15.2430i	−0.633478	+	1.09722i	0.353357	+	0.935488i	$0.385040\pi$
$193$	−8.80056	+	15.2430i	−0.633478	+	1.09722i	−0.986835	+	0.161728i	$0.948293\pi$
$194$		0			0
$195$	−3.37120	−	2.82430i	−0.241417	−	0.202252i
$196$		0			0
$197$	9.54413			0.679991			0.339995	−	0.940427i	$-0.389574\pi$
$197$	9.54413			0.679991			0.339995	+	0.940427i	$0.389574\pi$
$198$		0			0
$199$	−8.05652			−0.571111			−0.285556	−	0.958362i	$-0.592178\pi$
$199$	−8.05652			−0.571111			−0.285556	+	0.958362i	$0.592178\pi$
$200$		0			0
$201$	1.62875	−	9.27944i	0.114883	−	0.654521i
$202$		0			0
$203$	−0.974447	+	1.68779i	−0.0683928	+	0.118460i
$204$		0			0
$205$	11.1090	+	19.2414i	0.775888	+	1.34388i
$206$		0			0
$207$	4.71301	+	26.4871i	0.327577	+	1.84098i
$208$		0			0
$209$	−10.4272	−	18.0605i	−0.721267	−	1.24927i
$210$		0			0
$211$	−9.08203	+	15.7305i	−0.625233	+	1.08293i	0.363263	+	0.931687i	$0.381663\pi$
$211$	−9.08203	+	15.7305i	−0.625233	+	1.08293i	−0.988496	+	0.151248i	$0.951671\pi$
$212$		0			0
$213$	9.45598	−	3.45005i	0.647913	−	0.236394i
$214$		0			0
$215$	18.7384			1.27795
$216$		0			0
$217$	−3.37746			−0.229277
$218$		0			0
$219$	17.4375	−	6.36213i	1.17831	−	0.429913i
$220$		0			0
$221$	1.93647	−	3.35407i	0.130261	−	0.225619i
$222$		0			0
$223$	3.47051	+	6.01110i	0.232402	+	0.402533i	0.958515	−	0.285043i	$-0.0920080\pi$
$223$	3.47051	+	6.01110i	0.232402	+	0.402533i	−0.726112	+	0.687576i	$0.758675\pi$
$224$		0			0
$225$	−11.4421	−	4.14439i	−0.762808	−	0.276292i
$226$		0			0
$227$	5.01660	+	8.68901i	0.332964	+	0.576710i	0.983092	−	0.183115i	$-0.0586180\pi$
$227$	5.01660	+	8.68901i	0.332964	+	0.576710i	−0.650128	+	0.759825i	$0.725285\pi$
$228$		0			0
$229$	3.24325	−	5.61748i	0.214320	−	0.371213i	−0.738742	−	0.673988i	$-0.764580\pi$
$229$	3.24325	−	5.61748i	0.214320	−	0.371213i	0.953062	+	0.302775i	$0.0979131\pi$
$230$		0			0
$231$	1.64244	−	9.35740i	0.108064	−	0.615671i
$232$		0			0
$233$	14.9215			0.977538			0.488769	−	0.872413i	$-0.337446\pi$
$233$	14.9215			0.977538			0.488769	+	0.872413i	$0.337446\pi$
$234$		0			0
$235$	−39.5444			−2.57959
$236$		0			0
$237$	−3.63934	−	3.04894i	−0.236401	−	0.198050i
$238$		0			0
$239$	−4.76389	+	8.25130i	−0.308150	+	0.533732i	−0.977958	−	0.208803i	$-0.933043\pi$
$239$	−4.76389	+	8.25130i	−0.308150	+	0.533732i	0.669807	+	0.742535i	$0.266377\pi$
$240$		0			0
$241$	−13.0471	−	22.5982i	−0.840436	−	1.45568i	−0.889527	−	0.456883i	$-0.848966\pi$
$241$	−13.0471	−	22.5982i	−0.840436	−	1.45568i	0.0490912	−	0.998794i	$-0.484367\pi$
$242$		0			0
$243$	2.76676	+	15.3410i	0.177488	+	0.984123i
$244$		0			0
$245$	1.50470	+	2.60622i	0.0961319	+	0.166505i
$246$		0			0
$247$	−1.60395	+	2.77813i	−0.102057	+	0.176768i
$248$		0			0
$249$	16.8661	+	14.1299i	1.06885	+	0.895448i
$250$		0			0
$251$	−26.0711			−1.64560			−0.822798	−	0.568334i	$-0.807588\pi$
$251$	−26.0711			−1.64560			−0.822798	+	0.568334i	$0.807588\pi$
$252$		0			0
$253$	49.1886			3.09246
$254$		0			0
$255$	4.13639	−	23.5661i	0.259031	−	1.47577i
$256$		0			0
$257$	2.43398	−	4.21577i	0.151827	−	0.262973i	−0.780072	−	0.625690i	$-0.784818\pi$
$257$	2.43398	−	4.21577i	0.151827	−	0.262973i	0.931899	+	0.362717i	$0.118151\pi$
$258$		0			0
$259$	3.74525	+	6.48696i	0.232718	+	0.403080i
$260$		0			0
$261$	−5.49720	−	1.99111i	−0.340268	−	0.123247i
$262$		0			0
$263$	−15.6106	−	27.0383i	−0.962588	−	1.66725i	−0.715961	−	0.698141i	$-0.754011\pi$
$263$	−15.6106	−	27.0383i	−0.962588	−	1.66725i	−0.246627	−	0.969110i	$-0.579322\pi$
$264$		0			0
$265$	12.1227	−	20.9971i	0.744689	−	1.28984i
$266$		0			0
$267$	14.2357	−	5.19397i	0.871213	−	0.317866i
$268$		0			0
$269$	11.3736			0.693459			0.346730	−	0.937965i	$-0.387292\pi$
$269$	11.3736			0.693459			0.346730	+	0.937965i	$0.387292\pi$
$270$		0			0
$271$	2.74404			0.166689			0.0833444	−	0.996521i	$-0.473440\pi$
$271$	2.74404			0.166689			0.0833444	+	0.996521i	$0.473440\pi$
$272$		0			0
$273$	−1.37287	+	0.500896i	−0.0830897	+	0.0303156i
$274$		0			0
$275$	−11.1252	+	19.2694i	−0.670873	+	1.16199i
$276$		0			0
$277$	−16.1725	−	28.0116i	−0.971710	−	1.68305i	−0.690389	−	0.723438i	$-0.742561\pi$
$277$	−16.1725	−	28.0116i	−0.971710	−	1.68305i	−0.281321	−	0.959614i	$-0.590773\pi$
$278$		0			0
$279$	−1.77503	−	9.97569i	−0.106269	−	0.597229i
$280$		0			0
$281$	3.74131	+	6.48014i	0.223188	+	0.386573i	0.955774	−	0.294101i	$-0.0950203\pi$
$281$	3.74131	+	6.48014i	0.223188	+	0.386573i	−0.732586	+	0.680674i	$0.761687\pi$
$282$		0			0
$283$	5.02902	−	8.71052i	0.298944	−	0.517787i	−0.676950	−	0.736029i	$-0.736699\pi$
$283$	5.02902	−	8.71052i	0.298944	−	0.517787i	0.975895	+	0.218242i	$0.0700322\pi$
$284$		0			0
$285$	−3.42611	+	19.5195i	−0.202945	+	1.15623i
$286$		0			0
$287$	7.38287			0.435797
$288$		0			0
$289$	4.07034			0.239432
$290$		0			0
$291$	−10.1887	−	8.53581i	−0.597273	−	0.500378i
$292$		0			0
$293$	12.7055	−	22.0066i	0.742263	−	1.28564i	−0.209200	−	0.977873i	$-0.567086\pi$
$293$	12.7055	−	22.0066i	0.742263	−	1.28564i	0.951463	−	0.307764i	$-0.0995806\pi$
$294$		0			0
$295$	−15.1685	−	26.2726i	−0.883145	−	1.52965i
$296$		0			0
$297$	28.5013	−	0.0667001i	1.65381	−	0.00387033i
$298$		0			0
$299$	−3.78318	−	6.55266i	−0.218787	−	0.378950i
$300$		0			0
$301$	3.11330	−	5.39240i	0.179448	−	0.310813i
$302$		0			0
$303$	9.93205	+	8.32079i	0.570582	+	0.478017i
$304$		0			0
$305$	−17.1189			−0.980225
$306$		0			0
$307$	9.82625			0.560814			0.280407	−	0.959881i	$-0.409531\pi$
$307$	9.82625			0.560814			0.280407	+	0.959881i	$0.409531\pi$
$308$		0			0
$309$	−1.52867	+	8.70925i	−0.0869631	+	0.495452i
$310$		0			0
$311$	1.69543	−	2.93657i	0.0961389	−	0.166518i	−0.813944	−	0.580943i	$-0.802684\pi$
$311$	1.69543	−	2.93657i	0.0961389	−	0.166518i	0.910083	+	0.414425i	$0.136017\pi$
$312$		0			0
$313$	11.6346	+	20.1517i	0.657627	+	1.13904i	0.981228	+	0.192850i	$0.0617730\pi$
$313$	11.6346	+	20.1517i	0.657627	+	1.13904i	−0.323601	+	0.946193i	$0.604894\pi$
$314$		0			0
$315$	−6.90695	+	5.81401i	−0.389163	+	0.327582i
$316$		0			0
$317$	−17.2509	−	29.8794i	−0.968904	−	1.67819i	−0.698737	−	0.715378i	$-0.746254\pi$
$317$	−17.2509	−	29.8794i	−0.968904	−	1.67819i	−0.270167	−	0.962813i	$-0.587079\pi$
$318$		0			0
$319$	−5.34492	+	9.25768i	−0.299258	+	0.518330i
$320$		0			0
$321$	2.41232	−	0.880146i	0.134643	−	0.0491249i
$322$		0			0
$323$	−17.4523			−0.971070
$324$		0			0
$325$	3.42262			0.189853
$326$		0			0
$327$	−1.42952	+	0.521567i	−0.0790529	+	0.0288427i
$328$		0			0
$329$	−6.57013	+	11.3798i	−0.362223	+	0.627388i
$330$		0			0
$331$	−7.99741	−	13.8519i	−0.439577	−	0.761370i	0.558080	−	0.829787i	$-0.311538\pi$
$331$	−7.99741	−	13.8519i	−0.439577	−	0.761370i	−0.997657	+	0.0684173i	$0.978205\pi$
$332$		0			0
$333$	−17.1916	+	14.4712i	−0.942094	+	0.793019i
$334$		0			0
$335$	8.18466	+	14.1763i	0.447176	+	0.774531i
$336$		0			0
$337$	−2.83257	+	4.90616i	−0.154300	+	0.267256i	−0.932804	−	0.360384i	$-0.882646\pi$
$337$	−2.83257	+	4.90616i	−0.154300	+	0.267256i	0.778504	+	0.627640i	$0.215979\pi$
$338$		0			0
$339$	−3.17687	+	18.0995i	−0.172544	+	0.983028i
$340$		0			0
$341$	−18.5257			−1.00322
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−35.8311	−	30.0183i	−1.92908	−	1.61613i
$346$		0			0
$347$	−14.2090	+	24.6107i	−0.762780	+	1.32117i	0.178633	+	0.983916i	$0.442833\pi$
$347$	−14.2090	+	24.6107i	−0.762780	+	1.32117i	−0.941412	+	0.337257i	$0.890501\pi$
$348$		0			0
$349$	−8.48661	−	14.6992i	−0.454278	−	0.786832i	0.544368	−	0.838846i	$-0.316769\pi$
$349$	−8.48661	−	14.6992i	−0.454278	−	0.786832i	−0.998646	+	0.0520138i	$0.983436\pi$
$350$		0			0
$351$	−2.20096	−	3.79166i	−0.117479	−	0.202384i
$352$		0			0
$353$	−8.83029	−	15.2945i	−0.469989	−	0.814045i	0.529422	−	0.848359i	$-0.322409\pi$
$353$	−8.83029	−	15.2945i	−0.469989	−	0.814045i	−0.999411	+	0.0343137i	$0.989075\pi$
$354$		0			0
$355$	−8.74448	+	15.1459i	−0.464109	+	0.803860i
$356$		0			0
$357$	−6.09445	−	5.10575i	−0.322552	−	0.270225i
$358$		0			0
$359$	13.7147			0.723834			0.361917	−	0.932210i	$-0.382122\pi$
$359$	13.7147			0.723834			0.361917	+	0.932210i	$0.382122\pi$
$360$		0			0
$361$	−4.54455			−0.239187
$362$		0			0
$363$	5.71510	−	32.5604i	0.299965	−	1.70898i
$364$		0			0
$365$	−16.1254	+	27.9300i	−0.844043	+	1.46192i
$366$		0			0
$367$	−7.33008	−	12.6961i	−0.382627	−	0.662730i	0.608810	−	0.793316i	$-0.291647\pi$
$367$	−7.33008	−	12.6961i	−0.382627	−	0.662730i	−0.991437	+	0.130587i	$0.958314\pi$
$368$		0			0
$369$	3.88009	+	21.8061i	0.201990	+	1.13518i
$370$		0			0
$371$	−4.02826	−	6.97715i	−0.209137	−	0.362236i
$372$		0			0
$373$	2.10543	−	3.64670i	0.109015	−	0.188819i	−0.806357	−	0.591430i	$-0.798564\pi$
$373$	2.10543	−	3.64670i	0.109015	−	0.188819i	0.915371	+	0.402610i	$0.131897\pi$
$374$		0			0
$375$	−4.61995	+	1.68561i	−0.238573	+	0.0870443i
$376$		0			0
$377$	1.64435			0.0846882
$378$		0			0
$379$	17.4637			0.897048			0.448524	−	0.893771i	$-0.351950\pi$
$379$	17.4637			0.897048			0.448524	+	0.893771i	$0.351950\pi$
$380$		0			0
$381$	−15.5520	+	5.67423i	−0.796756	+	0.290699i
$382$		0			0
$383$	12.8196	−	22.2042i	0.655050	−	1.13458i	−0.326831	−	0.945083i	$-0.605981\pi$
$383$	12.8196	−	22.2042i	0.655050	−	1.13458i	0.981881	−	0.189497i	$-0.0606858\pi$
$384$		0			0
$385$	8.25342	+	14.2953i	0.420633	+	0.728558i
$386$		0			0
$387$	17.5632	+	6.36148i	0.892789	+	0.323372i
$388$		0			0
$389$	3.73580	+	6.47059i	0.189413	+	0.328072i	0.945055	−	0.326913i	$-0.106008\pi$
$389$	3.73580	+	6.47059i	0.189413	+	0.328072i	−0.755642	+	0.654985i	$0.772675\pi$
$390$		0			0
$391$	20.5820	−	35.6490i	1.04088	−	1.80285i
$392$		0			0
$393$	0.470120	−	2.67840i	0.0237144	−	0.135107i
$394$		0			0
$395$	8.24907			0.415056
$396$		0			0
$397$	2.65217			0.133109			0.0665544	−	0.997783i	$-0.478799\pi$
$397$	2.65217			0.133109			0.0665544	+	0.997783i	$0.478799\pi$
$398$		0			0
$399$	5.04794	+	4.22902i	0.252713	+	0.211716i
$400$		0			0
$401$	8.78586	−	15.2175i	0.438745	−	0.759928i	−0.558848	−	0.829270i	$-0.688757\pi$
$401$	8.78586	−	15.2175i	0.438745	−	0.759928i	0.997593	+	0.0693419i	$0.0220899\pi$
$402$		0			0
$403$	1.42484	+	2.46789i	0.0709763	+	0.122935i
$404$		0			0
$405$	−20.8023	−	17.3448i	−1.03367	−	0.861872i
$406$		0			0
$407$	20.5430	+	35.5815i	1.01828	+	1.76371i
$408$		0			0
$409$	5.22907	−	9.05702i	0.258561	−	0.447841i	−0.707296	−	0.706918i	$-0.750085\pi$
$409$	5.22907	−	9.05702i	0.258561	−	0.447841i	0.965857	+	0.259077i	$0.0834184\pi$
$410$		0			0
$411$	3.06699	+	2.56944i	0.151283	+	0.126741i
$412$		0			0
$413$	−10.0807			−0.496041
$414$		0			0
$415$	−38.2293			−1.87660
$416$		0			0
$417$	−5.46041	+	31.1094i	−0.267397	+	1.52343i
$418$		0			0
$419$	−4.44830	+	7.70468i	−0.217314	+	0.376398i	−0.953986	−	0.299852i	$-0.903063\pi$
$419$	−4.44830	+	7.70468i	−0.217314	+	0.376398i	0.736672	+	0.676250i	$0.236396\pi$
$420$		0			0
$421$	−10.5280	−	18.2350i	−0.513103	−	0.888721i	−0.999885	−	0.0151973i	$-0.995162\pi$
$421$	−10.5280	−	18.2350i	−0.513103	−	0.888721i	0.486781	−	0.873524i	$-0.338171\pi$
$422$		0			0
$423$	−37.0644	−	13.4249i	−1.80213	−	0.652740i
$424$		0			0
$425$	9.31020	+	16.1257i	0.451611	+	0.782214i
$426$		0			0
$427$	−2.84423	+	4.92635i	−0.137642	+	0.238403i
$428$		0			0
$429$	−7.53029	+	2.74746i	−0.363566	+	0.132648i
$430$		0			0
$431$	26.1233			1.25831			0.629157	−	0.777278i	$-0.283400\pi$
$431$	26.1233			1.25831			0.629157	+	0.777278i	$0.283400\pi$
$432$		0			0
$433$	30.3505			1.45855			0.729276	−	0.684219i	$-0.239857\pi$
$433$	30.3505			1.45855			0.729276	+	0.684219i	$0.239857\pi$
$434$		0			0
$435$	9.54315	−	3.48186i	0.457559	−	0.166942i
$436$		0			0
$437$	−17.0477	+	29.5276i	−0.815504	+	1.41250i
$438$		0			0
$439$	4.82759	+	8.36162i	0.230408	+	0.399079i	0.957928	−	0.287008i	$-0.0926606\pi$
$439$	4.82759	+	8.36162i	0.230408	+	0.399079i	−0.727520	+	0.686086i	$0.759327\pi$
$440$		0			0
$441$	0.525553	+	2.95361i	0.0250263	+	0.140648i
$442$		0			0
$443$	−5.35965	−	9.28318i	−0.254644	−	0.441057i	0.710154	−	0.704046i	$-0.248625\pi$
$443$	−5.35965	−	9.28318i	−0.254644	−	0.441057i	−0.964799	+	0.262989i	$0.915292\pi$
$444$		0			0
$445$	−13.1646	+	22.8018i	−0.624062	+	1.08091i
$446$		0			0
$447$	−0.983826	+	5.60512i	−0.0465334	+	0.265113i
$448$		0			0
$449$	−14.1126			−0.666015			−0.333008	−	0.942924i	$-0.608064\pi$
$449$	−14.1126			−0.666015			−0.333008	+	0.942924i	$0.608064\pi$
$450$		0			0
$451$	40.4957			1.90687
$452$		0			0
$453$	16.2720	+	13.6322i	0.764525	+	0.640497i
$454$		0			0
$455$	1.26957	−	2.19896i	0.0595183	−	0.103089i
$456$		0			0
$457$	14.7102	+	25.4788i	0.688114	+	1.19185i	0.972447	+	0.233123i	$0.0748943\pi$
$457$	14.7102	+	25.4788i	0.688114	+	1.19185i	−0.284334	+	0.958725i	$0.591772\pi$
$458$		0			0
$459$	11.8774	−	20.6840i	0.554391	−	0.965444i
$460$		0			0
$461$	−15.5313	−	26.9009i	−0.723363	−	1.25290i	−0.959644	−	0.281216i	$-0.909262\pi$
$461$	−15.5313	−	26.9009i	−0.723363	−	1.25290i	0.236282	−	0.971685i	$-0.424071\pi$
$462$		0			0
$463$	−6.00276	+	10.3971i	−0.278972	+	0.483194i	−0.971130	−	0.238553i	$-0.923327\pi$
$463$	−6.00276	+	10.3971i	−0.278972	+	0.483194i	0.692158	+	0.721746i	$0.256660\pi$
$464$		0			0
$465$	13.4949	+	11.3056i	0.625811	+	0.524286i
$466$		0			0
$467$	0.115560			0.00534750			0.00267375	−	0.999996i	$-0.499149\pi$
$467$	0.115560			0.00534750			0.00267375	+	0.999996i	$0.499149\pi$
$468$		0			0
$469$	5.43939			0.251168
$470$		0			0
$471$	−0.948657	+	5.40475i	−0.0437118	+	0.249038i
$472$		0			0
$473$	17.0767	−	29.5778i	0.785189	−	1.35999i
$474$		0			0
$475$	−7.71151	−	13.3567i	−0.353828	−	0.612848i
$476$		0			0
$477$	18.4907	−	15.5648i	0.846631	−	0.712661i
$478$		0			0
$479$	−7.92835	−	13.7323i	−0.362256	−	0.627445i	0.626076	−	0.779762i	$-0.284660\pi$
$479$	−7.92835	−	13.7323i	−0.362256	−	0.627445i	−0.988332	+	0.152317i	$0.951327\pi$
$480$		0			0
$481$	3.15999	−	5.47327i	0.144083	−	0.249560i
$482$		0			0
$483$	−14.5916	+	5.32382i	−0.663943	+	0.242242i
$484$		0			0
$485$	23.0941			1.04865
$486$		0			0
$487$	34.9185			1.58231			0.791154	−	0.611617i	$-0.209481\pi$
$487$	34.9185			1.58231			0.791154	+	0.611617i	$0.209481\pi$
$488$		0			0
$489$	13.1267	−	4.78933i	0.593611	−	0.216581i
$490$		0			0
$491$	−11.7104	+	20.2831i	−0.528484	+	0.915362i	0.470964	+	0.882152i	$0.343906\pi$
$491$	−11.7104	+	20.2831i	−0.528484	+	0.915362i	−0.999448	+	0.0332092i	$0.989427\pi$
$492$		0			0
$493$	4.47295	+	7.74737i	0.201451	+	0.348924i
$494$		0			0
$495$	−37.8852	+	31.8903i	−1.70281	+	1.43336i
$496$		0			0
$497$	2.90572	+	5.03285i	0.130339	+	0.225754i
$498$		0			0
$499$	2.22661	−	3.85659i	0.0996765	−	0.172645i	−0.811874	−	0.583832i	$-0.801553\pi$
$499$	2.22661	−	3.85659i	0.0996765	−	0.172645i	0.911551	+	0.411188i	$0.134886\pi$
$500$		0			0
$501$	−0.0975954	+	0.556027i	−0.00436024	+	0.0248415i
$502$		0			0
$503$	13.1429			0.586014			0.293007	−	0.956110i	$-0.405344\pi$
$503$	13.1429			0.586014			0.293007	+	0.956110i	$0.405344\pi$
$504$		0			0
$505$	−22.5124			−1.00179
$506$		0			0
$507$	−16.3149	−	13.6681i	−0.724569	−	0.607023i
$508$		0			0
$509$	−5.41360	+	9.37662i	−0.239953	+	0.415612i	−0.960701	−	0.277586i	$-0.910466\pi$
$509$	−5.41360	+	9.37662i	−0.239953	+	0.415612i	0.720747	+	0.693198i	$0.243799\pi$
$510$		0			0
$511$	5.35834	+	9.28092i	0.237039	+	0.410564i
$512$		0			0
$513$	−9.83790	+	17.1322i	−0.434354	+	0.756406i
$514$		0			0
$515$	−7.68175	−	13.3052i	−0.338498	−	0.586296i
$516$		0			0
$517$	−36.0377	+	62.4191i	−1.58494	+	2.74519i
$518$		0			0
$519$	10.7867	+	9.03681i	0.473485	+	0.396672i
$520$		0			0
$521$	−19.9378			−0.873489			−0.436745	−	0.899586i	$-0.643869\pi$
$521$	−19.9378			−0.873489			−0.436745	+	0.899586i	$0.643869\pi$
$522$		0			0
$523$	−23.6481			−1.03406			−0.517029	−	0.855968i	$-0.672962\pi$
$523$	−23.6481			−1.03406			−0.517029	+	0.855968i	$0.672962\pi$
$524$		0			0
$525$	1.21467	−	6.92030i	0.0530126	−	0.302027i
$526$		0			0
$527$	−7.75168	+	13.4263i	−0.337669	+	0.584859i
$528$		0			0
$529$	−28.7099	−	49.7269i	−1.24825	−	2.16204i
$530$		0			0
$531$	−5.29797	−	29.7745i	−0.229912	−	1.29211i
$532$		0			0
$533$	−3.11459	−	5.39463i	−0.134908	−	0.233667i
$534$		0			0
$535$	−2.23081	+	3.86388i	−0.0964465	+	0.167050i
$536$		0			0
$537$	−28.5513	+	10.4171i	−1.23208	+	0.449529i
$538$		0			0
$539$	5.48508			0.236259
$540$		0			0
$541$	1.93883			0.0833567			0.0416783	−	0.999131i	$-0.486730\pi$
$541$	1.93883			0.0833567			0.0416783	+	0.999131i	$0.486730\pi$
$542$		0			0
$543$	−24.0801	+	8.78571i	−1.03338	+	0.377031i
$544$		0			0
$545$	1.32196	−	2.28971i	0.0566266	−	0.0980802i
$546$		0			0
$547$	−19.8625	−	34.4029i	−0.849259	−	1.47096i	−0.881870	−	0.471492i	$-0.843716\pi$
$547$	−19.8625	−	34.4029i	−0.849259	−	1.47096i	0.0326112	−	0.999468i	$-0.489618\pi$
$548$		0			0
$549$	−16.0453	−	5.81168i	−0.684797	−	0.248037i
$550$		0			0
$551$	−3.70488	−	6.41704i	−0.157833	−	0.273375i
$552$		0			0
$553$	1.37055	−	2.37386i	0.0582817	−	0.100947i
$554$		0			0
$555$	6.74988	−	38.4559i	0.286517	−	1.63236i
$556$		0			0
$557$	24.8445			1.05269			0.526347	−	0.850270i	$-0.323561\pi$
$557$	24.8445			1.05269			0.526347	+	0.850270i	$0.323561\pi$
$558$		0			0
$559$	−5.25360			−0.222204
$560$		0			0
$561$	−33.4286	−	28.0055i	−1.41136	−	1.18239i
$562$		0			0
$563$	−19.7945	+	34.2851i	−0.834240	+	1.44495i	0.0604081	+	0.998174i	$0.480760\pi$
$563$	−19.7945	+	34.2851i	−0.834240	+	1.44495i	−0.894648	+	0.446772i	$0.852574\pi$
$564$		0			0
$565$	−15.9641	−	27.6506i	−0.671615	−	1.16327i
$566$		0			0
$567$	−8.44759	+	3.10456i	−0.354765	+	0.130379i
$568$		0			0
$569$	18.6846	+	32.3626i	0.783298	+	1.35671i	0.930011	+	0.367532i	$0.119797\pi$
$569$	18.6846	+	32.3626i	0.783298	+	1.35671i	−0.146713	+	0.989179i	$0.546869\pi$
$570$		0			0
$571$	−2.24275	+	3.88456i	−0.0938563	+	0.162564i	−0.909131	−	0.416511i	$-0.863253\pi$
$571$	−2.24275	+	3.88456i	−0.0938563	+	0.162564i	0.815274	+	0.579075i	$0.196586\pi$
$572$		0			0
$573$	−31.0307	−	25.9966i	−1.29633	−	1.08603i
$574$		0			0
$575$	36.3777			1.51705
$576$		0			0
$577$	29.6060			1.23251			0.616256	−	0.787546i	$-0.288649\pi$
$577$	29.6060			1.23251			0.616256	+	0.787546i	$0.288649\pi$
$578$		0			0
$579$	5.27042	−	30.0270i	0.219031	−	1.24788i
$580$		0			0
$581$	−6.35164	+	11.0014i	−0.263510	+	0.456413i
$582$		0			0
$583$	−22.0953	−	38.2703i	−0.915096	−	1.58499i
$584$		0			0
$585$	7.16208	+	2.59414i	0.296116	+	0.107254i
$586$		0			0
$587$	6.99150	+	12.1096i	0.288570	+	0.499818i	0.973469	−	0.228820i	$-0.0734869\pi$
$587$	6.99150	+	12.1096i	0.288570	+	0.499818i	−0.684899	+	0.728638i	$0.740154\pi$
$588$		0			0
$589$	6.42061	−	11.1208i	0.264556	−	0.458225i
$590$		0			0
$591$	−15.5296	+	5.66602i	−0.638801	+	0.233069i
$592$		0			0
$593$	27.1799			1.11614			0.558072	−	0.829793i	$-0.311541\pi$
$593$	27.1799			1.11614			0.558072	+	0.829793i	$0.311541\pi$
$594$		0			0
$595$	13.8139			0.566315
$596$		0			0
$597$	13.1090	−	4.78288i	0.536517	−	0.195750i
$598$		0			0
$599$	15.4745	−	26.8026i	0.632270	−	1.09512i	−0.354816	−	0.934936i	$-0.615457\pi$
$599$	15.4745	−	26.8026i	0.632270	−	1.09512i	0.987086	−	0.160188i	$-0.0512101\pi$
$600$		0			0
$601$	−7.69296	−	13.3246i	−0.313803	−	0.543522i	0.665380	−	0.746505i	$-0.268270\pi$
$601$	−7.69296	−	13.3246i	−0.313803	−	0.543522i	−0.979182	+	0.202983i	$0.934936\pi$
$602$		0			0
$603$	2.85869	+	16.0658i	0.116415	+	0.654251i
$604$		0			0
$605$	28.7190	+	49.7427i	1.16759	+	2.02233i
$606$		0			0
$607$	−7.06075	+	12.2296i	−0.286587	+	0.496383i	−0.972993	−	0.230835i	$-0.925854\pi$
$607$	−7.06075	+	12.2296i	−0.286587	+	0.496383i	0.686406	+	0.727219i	$0.259187\pi$
$608$		0			0
$609$	0.583570	−	3.32476i	0.0236475	−	0.134726i
$610$		0			0
$611$	11.0869			0.448527
$612$		0			0
$613$	−28.9248			−1.16826			−0.584130	−	0.811660i	$-0.698564\pi$
$613$	−28.9248			−1.16826			−0.584130	+	0.811660i	$0.698564\pi$
$614$		0			0
$615$	−29.4988	−	24.7133i	−1.18951	−	0.996535i
$616$		0			0
$617$	−12.2196	+	21.1649i	−0.491941	+	0.852066i	−0.999957	−	0.00928127i	$-0.997046\pi$
$617$	−12.2196	+	21.1649i	−0.491941	+	0.852066i	0.508016	+	0.861347i	$0.330379\pi$
$618$		0			0
$619$	14.6690	+	25.4074i	0.589595	+	1.02121i	0.994285	+	0.106755i	$0.0340461\pi$
$619$	14.6690	+	25.4074i	0.589595	+	1.02121i	−0.404690	+	0.914454i	$0.632621\pi$
$620$		0			0
$621$	−23.3932	−	40.3000i	−0.938735	−	1.61718i
$622$		0			0
$623$	4.37449	+	7.57684i	0.175260	+	0.303559i
$624$		0			0
$625$	14.4136	−	24.9651i	0.576545	−	0.998605i
$626$		0			0
$627$	27.6884	+	23.1965i	1.10577	+	0.926381i
$628$		0			0
$629$	34.3832			1.37095
$630$		0			0
$631$	12.9995			0.517501			0.258750	−	0.965944i	$-0.416689\pi$
$631$	12.9995			0.517501			0.258750	+	0.965944i	$0.416689\pi$
$632$		0			0
$633$	5.43899	−	30.9874i	0.216180	−	1.23164i
$634$		0			0
$635$	14.3819	−	24.9101i	0.570727	−	0.988528i
$636$		0			0
$637$	−0.421867	−	0.730695i	−0.0167150	−	0.0289512i
$638$		0			0
$639$	−13.3380	+	11.2274i	−0.527641	+	0.444148i
$640$		0			0
$641$	−9.02698	−	15.6352i	−0.356544	−	0.617553i	0.630837	−	0.775916i	$-0.282712\pi$
$641$	−9.02698	−	15.6352i	−0.356544	−	0.617553i	−0.987381	+	0.158363i	$0.949378\pi$
$642$		0			0
$643$	−1.88663	+	3.26773i	−0.0744013	+	0.128867i	−0.900826	−	0.434181i	$-0.857038\pi$
$643$	−1.88663	+	3.26773i	−0.0744013	+	0.128867i	0.826424	+	0.563048i	$0.190371\pi$
$644$		0			0
$645$	−30.4898	+	11.1243i	−1.20054	+	0.438020i
$646$		0			0
$647$	0.383345			0.0150709			0.00753543	−	0.999972i	$-0.497601\pi$
$647$	0.383345			0.0150709			0.00753543	+	0.999972i	$0.497601\pi$
$648$		0			0
$649$	−55.2937			−2.17047
$650$		0			0
$651$	5.49557	−	2.00508i	0.215389	−	0.0785854i
$652$		0			0
$653$	−0.0983475	+	0.170343i	−0.00384864	+	0.00666603i	−0.867943	−	0.496663i	$-0.834558\pi$
$653$	−0.0983475	+	0.170343i	−0.00384864	+	0.00666603i	0.864095	+	0.503329i	$0.167892\pi$
$654$		0			0
$655$	2.36241	+	4.09181i	0.0923068	+	0.159880i
$656$		0			0
$657$	−24.5961	+	20.7040i	−0.959585	+	0.807742i
$658$		0			0
$659$	−0.919372	−	1.59240i	−0.0358137	−	0.0620311i	0.847563	−	0.530695i	$-0.178069\pi$
$659$	−0.919372	−	1.59240i	−0.0358137	−	0.0620311i	−0.883377	+	0.468664i	$0.844736\pi$
$660$		0			0
$661$	13.5492	−	23.4679i	0.527004	−	0.912797i	−0.472501	−	0.881330i	$-0.656649\pi$
$661$	13.5492	−	23.4679i	0.527004	−	0.912797i	0.999505	−	0.0314671i	$-0.0100179\pi$
$662$		0			0
$663$	−1.15970	+	6.60713i	−0.0450391	+	0.256600i
$664$		0			0
$665$	−11.4419			−0.443696
$666$		0			0
$667$	17.4771			0.676716
$668$		0			0
$669$	−9.21556	−	7.72053i	−0.356294	−	0.298493i
$670$		0			0
$671$	−15.6009	+	27.0215i	−0.602264	+	1.04315i
$672$		0			0
$673$	4.70611	+	8.15122i	0.181407	+	0.314207i	0.942360	−	0.334601i	$-0.108601\pi$
$673$	4.70611	+	8.15122i	0.181407	+	0.314207i	−0.760953	+	0.648807i	$0.775268\pi$
$674$		0			0
$675$	21.0782	−	0.0493284i	0.811301	−	0.00189865i
$676$		0			0
$677$	8.05519	+	13.9520i	0.309586	+	0.536219i	0.978272	−	0.207326i	$-0.0664762\pi$
$677$	8.05519	+	13.9520i	0.309586	+	0.536219i	−0.668686	+	0.743545i	$0.733143\pi$
$678$		0			0
$679$	3.83699	−	6.64586i	0.147250	−	0.255045i
$680$		0			0
$681$	−13.3210	−	11.1600i	−0.510464	−	0.427652i
$682$		0			0
$683$	7.35812			0.281551			0.140775	−	0.990042i	$-0.455040\pi$
$683$	7.35812			0.281551			0.140775	+	0.990042i	$0.455040\pi$
$684$		0			0
$685$	−6.95175			−0.265613
$686$		0			0
$687$	−1.94230	+	11.0658i	−0.0741033	+	0.422186i
$688$		0			0
$689$	−3.39878	+	5.88686i	−0.129483	+	0.224271i
$690$		0			0
$691$	−2.60616	−	4.51400i	−0.0991430	−	0.171721i	0.812187	−	0.583397i	$-0.198277\pi$
$691$	−2.60616	−	4.51400i	−0.0991430	−	0.171721i	−0.911330	+	0.411676i	$0.864943\pi$
$692$		0			0
$693$	2.88270	+	16.2008i	0.109505	+	0.615417i
$694$		0			0
$695$	−27.4391	−	47.5260i	−1.04083	−	1.80276i
$696$		0			0
$697$	16.9446	−	29.3489i	0.641822	−	1.11167i
$698$		0			0
$699$	−24.2792	+	8.85837i	−0.918325	+	0.335054i
$700$		0			0
$701$	−1.50384			−0.0567994			−0.0283997	−	0.999597i	$-0.509041\pi$
$701$	−1.50384			−0.0567994			−0.0283997	+	0.999597i	$0.509041\pi$
$702$		0			0
$703$	−28.4791			−1.07411
$704$		0			0
$705$	64.3439	−	23.4761i	2.42333	−	0.884162i
$706$		0			0
$707$	−3.74033	+	6.47845i	−0.140670	+	0.243647i
$708$		0			0
$709$	22.8248	+	39.5338i	0.857205	+	1.48472i	0.874585	+	0.484873i	$0.161134\pi$
$709$	22.8248	+	39.5338i	0.857205	+	1.48472i	−0.0173798	+	0.999849i	$0.505532\pi$
$710$		0			0
$711$	7.73175	+	2.80047i	0.289963	+	0.105026i
$712$		0			0
$713$	15.1440	+	26.2302i	0.567148	+	0.982330i
$714$		0			0
$715$	6.96369	−	12.0615i	0.260427	−	0.451073i
$716$		0			0
$717$	2.85297	−	16.2541i	0.106546	−	0.607021i
$718$		0			0
$719$	−18.1940			−0.678522			−0.339261	−	0.940692i	$-0.610177\pi$
$719$	−18.1940			−0.678522			−0.339261	+	0.940692i	$0.610177\pi$
$720$		0			0
$721$	−5.10516			−0.190126
$722$		0			0
$723$	34.6451	+	29.0247i	1.28846	+	1.07944i
$724$		0			0
$725$	−3.95286	+	6.84656i	−0.146806	+	0.254275i
$726$		0			0
$727$	8.38218	+	14.5184i	0.310878	+	0.538456i	0.978553	−	0.205997i	$-0.0660436\pi$
$727$	8.38218	+	14.5184i	0.310878	+	0.538456i	−0.667675	+	0.744453i	$0.732710\pi$
$728$		0			0
$729$	−13.6093	−	23.3192i	−0.504048	−	0.863676i
$730$		0			0
$731$	−14.2908	−	24.7524i	−0.528565	−	0.915501i
$732$		0			0
$733$	7.73528	−	13.3979i	0.285709	−	0.494862i	−0.687072	−	0.726589i	$-0.741104\pi$
$733$	7.73528	−	13.3979i	0.285709	−	0.494862i	0.972781	+	0.231727i	$0.0744376\pi$
$734$		0			0
$735$	−3.99557	−	3.34738i	−0.147379	−	0.123470i
$736$		0			0
$737$	29.8355			1.09901
$738$		0			0
$739$	−7.01244			−0.257957			−0.128978	−	0.991647i	$-0.541170\pi$
$739$	−7.01244			−0.257957			−0.128978	+	0.991647i	$0.541170\pi$
$740$		0			0
$741$	0.960564	−	5.47259i	0.0352872	−	0.201041i
$742$		0			0
$743$	9.29512	−	16.0996i	0.341005	−	0.590638i	−0.643615	−	0.765350i	$-0.722566\pi$
$743$	9.29512	−	16.0996i	0.341005	−	0.590638i	0.984620	+	0.174712i	$0.0558994\pi$
$744$		0			0
$745$	−4.94383	−	8.56297i	−0.181128	−	0.313723i
$746$		0			0
$747$	−35.8318	−	12.9784i	−1.31102	−	0.474857i
$748$		0			0
$749$	0.741281	+	1.28394i	0.0270858	+	0.0469140i
$750$		0			0
$751$	27.1237	−	46.9797i	0.989759	−	1.71431i	0.371259	−	0.928529i	$-0.378926\pi$
$751$	27.1237	−	46.9797i	0.989759	−	1.71431i	0.618501	−	0.785784i	$-0.287740\pi$
$752$		0			0
$753$	42.4212	−	15.4775i	1.54591	−	0.564033i
$754$		0			0
$755$	−36.8827			−1.34230
$756$		0			0
$757$	−16.7679			−0.609439			−0.304719	−	0.952442i	$-0.598563\pi$
$757$	−16.7679			−0.609439			−0.304719	+	0.952442i	$0.598563\pi$
$758$		0			0
$759$	−80.0364	+	29.2016i	−2.90514	+	1.05995i
$760$		0			0
$761$	−0.762796	+	1.32120i	−0.0276514	+	0.0478935i	−0.879520	−	0.475862i	$-0.842136\pi$
$761$	−0.762796	+	1.32120i	−0.0276514	+	0.0478935i	0.851869	+	0.523756i	$0.175469\pi$
$762$		0			0
$763$	−0.439277	−	0.760850i	−0.0159029	−	0.0275446i
$764$		0			0
$765$	7.25994	+	40.8008i	0.262484	+	1.47516i
$766$		0			0
$767$	4.25273	+	7.36595i	0.153557	+	0.265969i
$768$		0			0
$769$	22.9904	−	39.8205i	0.829053	−	1.43596i	−0.0697283	−	0.997566i	$-0.522213\pi$
$769$	22.9904	−	39.8205i	0.829053	−	1.43596i	0.898782	−	0.438397i	$-0.144453\pi$
$770$		0			0
$771$	−1.45764	+	8.30459i	−0.0524958	+	0.299083i
$772$		0			0
$773$	16.2008			0.582701			0.291351	−	0.956616i	$-0.405895\pi$
$773$	16.2008			0.582701			0.291351	+	0.956616i	$0.405895\pi$
$774$		0			0
$775$	−13.7007			−0.492145
$776$		0			0
$777$	−9.94510	−	8.33172i	−0.356779	−	0.298899i
$778$		0			0
$779$	−14.0350	+	24.3093i	−0.502855	+	0.870970i
$780$		0			0
$781$	15.9381	+	27.6056i	0.570311	+	0.987807i
$782$		0			0
$783$	10.1267	−	0.0236991i	0.361899	−	0.000846936i
$784$		0			0
$785$	−4.76710	−	8.25686i	−0.170145	−	0.294700i
$786$		0			0
$787$	−10.3187	+	17.8726i	−0.367823	+	0.637088i	−0.989225	−	0.146404i	$-0.953230\pi$
$787$	−10.3187	+	17.8726i	−0.367823	+	0.637088i	0.621402	+	0.783492i	$0.286563\pi$
$788$		0			0
$789$	41.4521	+	34.7274i	1.47574	+	1.23633i
$790$		0			0
$791$	−10.6095			−0.377230
$792$		0			0
$793$	4.79955			0.170437
$794$		0			0
$795$	−7.25994	+	41.3618i	−0.257484	+	1.46695i
$796$		0			0
$797$	−24.3590	+	42.1910i	−0.862839	+	1.49448i	0.00633764	+	0.999980i	$0.497983\pi$
$797$	−24.3590	+	42.1910i	−0.862839	+	1.49448i	−0.869177	+	0.494501i	$0.835351\pi$
$798$		0			0
$799$	30.1585	+	52.2360i	1.06693	+	1.84798i
$800$		0			0
$801$	−20.0800	+	16.9025i	−0.709491	+	0.597222i
$802$		0			0
$803$	29.3909	+	50.9066i	1.03718	+	1.79646i
$804$		0			0
$805$	13.4937	−	23.3718i	0.475591	−	0.823748i
$806$		0			0
$807$	−18.5063	+	6.75210i	−0.651453	+	0.237685i
$808$		0			0
$809$	−0.903622			−0.0317696			−0.0158848	−	0.999874i	$-0.505057\pi$
$809$	−0.903622			−0.0317696			−0.0158848	+	0.999874i	$0.505057\pi$
$810$		0			0
$811$	22.7487			0.798816			0.399408	−	0.916773i	$-0.369216\pi$
$811$	22.7487			0.798816			0.399408	+	0.916773i	$0.369216\pi$
$812$		0			0
$813$	−4.46492	+	1.62905i	−0.156592	+	0.0571331i
$814$		0			0
$815$	−12.1390	+	21.0254i	−0.425212	+	0.736488i
$816$		0			0
$817$	11.8369	+	20.5021i	0.414120	+	0.717277i
$818$		0			0
$819$	1.93647	−	1.63005i	0.0676658	−	0.0569585i
$820$		0			0
$821$	−27.0367	−	46.8290i	−0.943589	−	1.63434i	−0.758553	−	0.651612i	$-0.774093\pi$
$821$	−27.0367	−	46.8290i	−0.943589	−	1.63434i	−0.185036	−	0.982732i	$-0.559240\pi$
$822$		0			0
$823$	9.27471	−	16.0643i	0.323296	−	0.559966i	−0.657870	−	0.753132i	$-0.728542\pi$
$823$	9.27471	−	16.0643i	0.323296	−	0.559966i	0.981166	+	0.193166i	$0.0618756\pi$
$824$		0			0
$825$	6.66257	−	37.9584i	0.231961	−	1.32154i
$826$		0			0
$827$	−40.1856			−1.39739			−0.698695	−	0.715419i	$-0.746236\pi$
$827$	−40.1856			−1.39739			−0.698695	+	0.715419i	$0.746236\pi$
$828$		0			0
$829$	−2.26946			−0.0788217			−0.0394108	−	0.999223i	$-0.512548\pi$
$829$	−2.26946			−0.0788217			−0.0394108	+	0.999223i	$0.512548\pi$
$830$		0			0
$831$	42.9443	+	35.9775i	1.48972	+	1.24804i
$832$		0			0
$833$	2.29512	−	3.97527i	0.0795213	−	0.137735i
$834$		0			0
$835$	−0.490428	−	0.849446i	−0.0169720	−	0.0293963i
$836$		0			0
$837$	8.81044	+	15.1780i	0.304533	+	0.524628i
$838$		0			0
$839$	7.96058	+	13.7881i	0.274830	+	0.476019i	0.970092	−	0.242737i	$-0.0780452\pi$
$839$	7.96058	+	13.7881i	0.274830	+	0.476019i	−0.695262	+	0.718756i	$0.744712\pi$
$840$		0			0
$841$	12.6009	−	21.8254i	0.434514	−	0.752600i
$842$		0			0
$843$	−9.93464	−	8.32296i	−0.342167	−	0.286658i
$844$		0			0
$845$	36.9799			1.27215
$846$		0			0
$847$	19.0862			0.655808
$848$		0			0
$849$	−3.01175	+	17.1587i	−0.103363	+	0.588886i
$850$		0			0
$851$	33.5863	−	58.1731i	1.15132	−	1.99415i
$852$		0			0
$853$	3.87812	+	6.71711i	0.132784	+	0.229989i	0.924749	−	0.380578i	$-0.124275\pi$
$853$	3.87812	+	6.71711i	0.132784	+	0.229989i	−0.791964	+	0.610567i	$0.790942\pi$
$854$		0			0
$855$	−6.01330	−	33.7947i	−0.205651	−	1.15576i
$856$		0			0
$857$	3.17118	+	5.49264i	0.108325	+	0.187625i	0.915092	−	0.403245i	$-0.132118\pi$
$857$	3.17118	+	5.49264i	0.108325	+	0.187625i	−0.806767	+	0.590870i	$0.798785\pi$
$858$		0			0
$859$	14.6252	−	25.3315i	0.499004	−	0.864300i	−0.500995	−	0.865450i	$-0.667033\pi$
$859$	14.6252	−	25.3315i	0.499004	−	0.864300i	0.999999	+	0.00114976i	$0.000365979\pi$
$860$		0			0
$861$	−12.0129	+	4.38296i	−0.409399	+	0.149371i
$862$		0			0
$863$	−41.2373			−1.40374			−0.701868	−	0.712307i	$-0.747650\pi$
$863$	−41.2373			−1.40374			−0.701868	+	0.712307i	$0.747650\pi$
$864$		0			0
$865$	−24.4496			−0.831311
$866$		0			0
$867$	−6.62298	+	2.41642i	−0.224928	+	0.0820660i
$868$		0			0
$869$	7.51758	−	13.0208i	0.255016	−	0.441701i
$870$		0			0
$871$	−2.29470	−	3.97454i	−0.0777529	−	0.134672i
$872$		0			0
$873$	21.6458	+	7.84021i	0.732600	+	0.265351i
$874$		0			0
$875$	−1.41966	−	2.45892i	−0.0479932	−	0.0831267i
$876$		0			0
$877$	18.7306	−	32.4424i	0.632488	−	1.09550i	−0.354553	−	0.935036i	$-0.615367\pi$
$877$	18.7306	−	32.4424i	0.632488	−	1.09550i	0.987041	−	0.160466i	$-0.0512997\pi$
$878$		0			0
$879$	−7.60898	+	43.3504i	−0.256645	+	1.46217i
$880$		0			0
$881$	−42.2889			−1.42475			−0.712375	−	0.701799i	$-0.752380\pi$
$881$	−42.2889			−1.42475			−0.712375	+	0.701799i	$0.752380\pi$
$882$		0			0
$883$	51.1718			1.72207			0.861034	−	0.508547i	$-0.169817\pi$
$883$	51.1718			1.72207			0.861034	+	0.508547i	$0.169817\pi$
$884$		0			0
$885$	40.2784	+	33.7440i	1.35394	+	1.13429i
$886$		0			0
$887$	4.40377	−	7.62755i	0.147864	−	0.256108i	−0.782574	−	0.622558i	$-0.786094\pi$
$887$	4.40377	−	7.62755i	0.147864	−	0.256108i	0.930438	+	0.366450i	$0.119427\pi$
$888$		0			0
$889$	−4.77897	−	8.27743i	−0.160282	−	0.277616i
$890$		0			0
$891$	−46.3357	+	17.0287i	−1.55231	+	0.570485i
$892$		0			0
$893$	−24.9798	−	43.2664i	−0.835918	−	1.44785i
$894$		0			0
$895$	26.4030	−	45.7314i	0.882556	−	1.52863i
$896$		0			0
$897$	10.0458	+	8.41610i	0.335420	+	0.281005i
$898$		0			0
$899$	−6.58231			−0.219532
$900$		0			0
$901$	−36.9814			−1.23203
$902$		0			0
$903$	−1.86447	+	10.6224i	−0.0620458	+	0.353492i
$904$		0			0
$905$	22.2682	−	38.5697i	0.740221	−	1.28210i
$906$		0			0
$907$	8.25169	+	14.2923i	0.273993	+	0.474570i	0.969881	−	0.243581i	$-0.0783222\pi$
$907$	8.25169	+	14.2923i	0.273993	+	0.474570i	−0.695888	+	0.718151i	$0.744989\pi$
$908$		0			0
$909$	−21.1005	−	7.64271i	−0.699861	−	0.253493i
$910$		0			0
$911$	11.4836	+	19.8902i	0.380469	+	0.658992i	0.991129	−	0.132901i	$-0.0424292\pi$
$911$	11.4836	+	19.8902i	0.380469	+	0.658992i	−0.610660	+	0.791893i	$0.709096\pi$
$912$		0			0
$913$	−34.8393	+	60.3434i	−1.15301	+	1.99708i
$914$		0			0
$915$	27.8547	−	10.1629i	0.920848	−	0.335975i
$916$		0			0
$917$	1.57002			0.0518465
$918$		0			0
$919$	23.4537			0.773668			0.386834	−	0.922149i	$-0.373569\pi$
$919$	23.4537			0.773668			0.386834	+	0.922149i	$0.373569\pi$
$920$		0			0
$921$	−15.9886	+	5.83351i	−0.526843	+	0.192221i
$922$		0			0
$923$	2.45165	−	4.24639i	0.0806972	−	0.139772i
$924$		0			0
$925$	15.1927	+	26.3145i	0.499532	+	0.865215i
$926$		0			0
$927$	−2.68303	−	15.0786i	−0.0881224	−	0.495247i
$928$		0			0
$929$	18.8182	+	32.5940i	0.617404	+	1.06938i	0.989958	+	0.141365i	$0.0451491\pi$
$929$	18.8182	+	32.5940i	0.617404	+	1.06938i	−0.372553	+	0.928011i	$0.621518\pi$
$930$		0			0
$931$	−1.90102	+	3.29266i	−0.0623033	+	0.107912i
$932$		0			0
$933$	−1.01535	+	5.78471i	−0.0332410	+	0.189383i
$934$		0			0
$935$	75.7704			2.47796
$936$		0			0
$937$	41.5719			1.35809			0.679047	−	0.734094i	$-0.262393\pi$
$937$	41.5719			1.35809			0.679047	+	0.734094i	$0.262393\pi$
$938$		0			0
$939$	−30.8944	−	25.8825i	−1.00820	−	0.844643i
$940$		0			0
$941$	−13.5785	+	23.5187i	−0.442647	+	0.766686i	−0.997885	−	0.0650049i	$-0.979294\pi$
$941$	−13.5785	+	23.5187i	−0.442647	+	0.766686i	0.555238	+	0.831691i	$0.312627\pi$
$942$		0			0
$943$	−33.1037	−	57.3373i	−1.07800	−	1.86716i
$944$		0			0
$945$	7.78695	−	13.5606i	0.253309	−	0.441126i
$946$		0			0
$947$	15.9444	+	27.6166i	0.518124	+	0.897418i	0.999778	+	0.0210563i	$0.00670293\pi$
$947$	15.9444	+	27.6166i	0.518124	+	0.897418i	−0.481654	+	0.876362i	$0.659964\pi$
$948$		0			0
$949$	4.52101	−	7.83062i	0.146758	−	0.254193i
$950$		0			0
$951$	45.8078	+	38.3764i	1.48542	+	1.24444i
$952$		0			0
$953$	53.5094			1.73334			0.866670	−	0.498881i	$-0.166256\pi$
$953$	53.5094			1.73334			0.866670	+	0.498881i	$0.166256\pi$
$954$		0			0
$955$	70.3354			2.27600
$956$		0			0
$957$	3.20093	−	18.2366i	0.103471	−	0.589505i
$958$		0			0
$959$	−1.15500	+	2.00053i	−0.0372970	+	0.0646004i
$960$		0			0
$961$	9.79638	+	16.9678i	0.316012	+	0.547349i
$962$		0			0
$963$	−3.40266	+	2.86423i	−0.109649	+	0.0922985i
$964$		0			0
$965$	26.4844	+	45.8724i	0.852565	+	1.47669i
$966$		0			0
$967$	−2.46065	+	4.26197i	−0.0791292	+	0.137056i	−0.902874	−	0.429904i	$-0.858547\pi$
$967$	−2.46065	+	4.26197i	−0.0791292	+	0.137056i	0.823745	+	0.566960i	$0.191881\pi$
$968$		0			0
$969$	28.3971	−	10.3608i	0.912248	−	0.332837i
$970$		0			0
$971$	2.43251			0.0780629			0.0390315	−	0.999238i	$-0.487573\pi$
$971$	2.43251			0.0780629			0.0390315	+	0.999238i	$0.487573\pi$
$972$		0			0
$973$	−18.2356			−0.584606
$974$		0			0
$975$	−5.56906	+	2.03189i	−0.178353	+	0.0650727i
$976$		0			0
$977$	−3.15608	+	5.46650i	−0.100972	+	0.174889i	−0.912085	−	0.410000i	$-0.865529\pi$
$977$	−3.15608	+	5.46650i	−0.100972	+	0.174889i	0.811113	+	0.584889i	$0.198862\pi$
$978$		0			0
$979$	23.9944	+	41.5596i	0.766865	+	1.32825i
$980$		0			0
$981$	2.01639	−	1.69732i	0.0643783	−	0.0541912i
$982$		0			0
$983$	−12.9727	−	22.4694i	−0.413766	−	0.716664i	0.581532	−	0.813524i	$-0.302454\pi$
$983$	−12.9727	−	22.4694i	−0.413766	−	0.716664i	−0.995298	+	0.0968597i	$0.969120\pi$
$984$		0			0
$985$	14.3611	−	24.8741i	0.457582	−	0.792555i
$986$		0			0
$987$	3.93468	−	22.4169i	0.125242	−	0.713538i
$988$		0			0
$989$	−55.8384			−1.77556
$990$		0			0
$991$	−40.7413			−1.29419			−0.647094	−	0.762410i	$-0.724016\pi$
$991$	−40.7413			−1.29419			−0.647094	+	0.762410i	$0.724016\pi$
$992$		0			0
$993$	21.2363	+	17.7911i	0.673912	+	0.564584i
$994$		0			0
$995$	−12.1227	+	20.9971i	−0.384314	+	0.665652i
$996$		0			0
$997$	−1.92260	−	3.33004i	−0.0608894	−	0.105464i	0.833974	−	0.551804i	$-0.186060\pi$
$997$	−1.92260	−	3.33004i	−0.0608894	−	0.105464i	−0.894863	+	0.446340i	$0.852727\pi$
$998$		0			0
$999$	19.3819	−	33.7527i	0.613218	−	1.06789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.n.337.1		10
3.2	odd	2		3024.2.r.n.1009.1		10
4.3	odd	2		504.2.r.f.337.5	yes	10
9.2	odd	6		3024.2.r.n.2017.1		10
9.4	even	3		9072.2.a.cn.1.1		5
9.5	odd	6		9072.2.a.cm.1.5		5
9.7	even	3	inner	1008.2.r.n.673.1		10
12.11	even	2		1512.2.r.f.1009.1		10
36.7	odd	6		504.2.r.f.169.5	✓	10
36.11	even	6		1512.2.r.f.505.1		10
36.23	even	6		4536.2.a.bc.1.5		5
36.31	odd	6		4536.2.a.bd.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.f.169.5	✓	10	36.7	odd	6
504.2.r.f.337.5	yes	10	4.3	odd	2
1008.2.r.n.337.1		10	1.1	even	1	trivial
1008.2.r.n.673.1		10	9.7	even	3	inner
1512.2.r.f.505.1		10	36.11	even	6
1512.2.r.f.1009.1		10	12.11	even	2
3024.2.r.n.1009.1		10	3.2	odd	2
3024.2.r.n.2017.1		10	9.2	odd	6
4536.2.a.bc.1.5		5	36.23	even	6
4536.2.a.bd.1.1		5	36.31	odd	6
9072.2.a.cm.1.5		5	9.5	odd	6
9072.2.a.cn.1.1		5	9.4	even	3

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.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62713 + 0.593666i) q^{3} +(1.50470 - 2.60622i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.29512 - 1.93195i) q^{9} +O(q^{10})\)	\(q+(-1.62713 + 0.593666i) q^{3} +(1.50470 - 2.60622i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.29512 - 1.93195i) q^{9} +(-2.74254 - 4.75022i) q^{11} +(-0.421867 + 0.730695i) q^{13} +(-0.901126 + 5.13396i) q^{15} -4.59024 q^{17} +3.80203 q^{19} +(1.32770 + 1.11231i) q^{21} +(-4.48385 + 7.76626i) q^{23} +(-2.02826 - 3.51305i) q^{25} +(-2.58754 + 4.50607i) q^{27} +(-0.974447 - 1.68779i) q^{29} +(1.68873 - 2.92497i) q^{31} +(7.28252 + 6.10109i) q^{33} -3.00941 q^{35} -7.49050 q^{37} +(0.252645 - 1.43939i) q^{39} +(-3.69144 + 6.39375i) q^{41} +(3.11330 + 5.39240i) q^{43} +(-1.58160 - 8.88860i) q^{45} +(-6.57013 - 11.3798i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(7.46894 - 2.72507i) q^{51} +8.05652 q^{53} -16.5068 q^{55} +(-6.18641 + 2.25714i) q^{57} +(5.04037 - 8.73018i) q^{59} +(-2.84423 - 4.92635i) q^{61} +(-2.82068 - 1.02166i) q^{63} +(1.26957 + 2.19896i) q^{65} +(-2.71969 + 4.71065i) q^{67} +(2.68526 - 15.2986i) q^{69} -5.81144 q^{71} -10.7167 q^{73} +(5.38582 + 4.51209i) q^{75} +(-2.74254 + 4.75022i) q^{77} +(1.37055 + 2.37386i) q^{79} +(1.53517 - 8.86810i) q^{81} +(-6.35164 - 11.0014i) q^{83} +(-6.90695 + 11.9632i) q^{85} +(2.58754 + 2.16776i) q^{87} -8.74898 q^{89} +0.843734 q^{91} +(-1.01134 + 5.76185i) q^{93} +(5.72093 - 9.90894i) q^{95} +(3.83699 + 6.64586i) q^{97} +(-15.4716 - 5.60390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 3 * q^5 - 5 * q^7	\( 10 q - 3 q^{5} - 5 q^{7} - 4 q^{11} - 3 q^{13} - 15 q^{15} - 2 q^{19} - 8 q^{23} - 10 q^{25} + 9 q^{27} - 9 q^{29} + 3 q^{31} + 30 q^{33} + 6 q^{35} - 6 q^{37} + 18 q^{39} - 12 q^{41} + 5 q^{43} - 9 q^{45} - 3 q^{47} - 5 q^{49} - 9 q^{51} + 60 q^{53} - 44 q^{55} - 21 q^{57} - 7 q^{59} - 14 q^{61} - 6 q^{63} - 11 q^{65} + 8 q^{67} + 21 q^{69} + 18 q^{71} + 30 q^{73} + 51 q^{75} - 4 q^{77} + 3 q^{79} - 12 q^{81} - 20 q^{83} - 21 q^{85} - 9 q^{87} - 24 q^{89} + 6 q^{91} - 39 q^{93} + 12 q^{95} - 37 q^{97} - 60 q^{99}+O(q^{100}) \) 10 * q - 3 * q^5 - 5 * q^7 - 4 * q^11 - 3 * q^13 - 15 * q^15 - 2 * q^19 - 8 * q^23 - 10 * q^25 + 9 * q^27 - 9 * q^29 + 3 * q^31 + 30 * q^33 + 6 * q^35 - 6 * q^37 + 18 * q^39 - 12 * q^41 + 5 * q^43 - 9 * q^45 - 3 * q^47 - 5 * q^49 - 9 * q^51 + 60 * q^53 - 44 * q^55 - 21 * q^57 - 7 * q^59 - 14 * q^61 - 6 * q^63 - 11 * q^65 + 8 * q^67 + 21 * q^69 + 18 * q^71 + 30 * q^73 + 51 * q^75 - 4 * q^77 + 3 * q^79 - 12 * q^81 - 20 * q^83 - 21 * q^85 - 9 * q^87 - 24 * q^89 + 6 * q^91 - 39 * q^93 + 12 * q^95 - 37 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

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