LMFDB - Embedded newform 1008.2.bf.i.943.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(31,1008)]

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([3, 0, 2, 1]))

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

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

chi := DirichletCharacter("1008.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			943.11
Character	$\chi$	$=$	1008.943
Dual form			1008.2.bf.i.31.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.840104 + 1.51467i) q^{3} +2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} +(-1.58845 + 2.54496i) q^{9} +O(q^{10})$	\(q+(0.840104 + 1.51467i) q^{3} +2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} +(-1.58845 + 2.54496i) q^{9} +0.442942i q^{11} +(-1.96099 + 1.13218i) q^{13} +(-3.55698 + 1.97286i) q^{15} +(4.01950 - 2.32066i) q^{17} +(-3.30879 + 5.73100i) q^{19} +(1.63434 + 4.28123i) q^{21} -1.13645i q^{23} -0.514760 q^{25} +(-5.18924 - 0.267947i) q^{27} +(4.37712 - 7.58140i) q^{29} +(-2.32034 + 4.01894i) q^{31} +(-0.670912 + 0.372118i) q^{33} +(-0.877649 + 6.15086i) q^{35} +(-1.41316 + 2.44767i) q^{37} +(-3.36231 - 2.01911i) q^{39} +(4.55283 - 2.62858i) q^{41} +(-3.81500 - 2.20259i) q^{43} +(-5.97646 - 3.73024i) q^{45} +(-2.67363 - 4.63087i) q^{47} +(6.72065 + 1.95776i) q^{49} +(6.89183 + 4.13862i) q^{51} +(-1.54428 - 2.67478i) q^{53} -1.04018 q^{55} +(-11.4603 - 0.197096i) q^{57} +(-0.689570 + 1.19437i) q^{59} +(-8.88607 + 5.13038i) q^{61} +(-5.11163 + 6.07217i) q^{63} +(-2.65875 - 4.60510i) q^{65} +(2.10780 + 1.21694i) q^{67} +(1.72134 - 0.954732i) q^{69} +7.20644i q^{71} +(3.17824 - 1.83496i) q^{73} +(-0.432452 - 0.779691i) q^{75} +(-0.165541 + 1.16016i) q^{77} +(7.26542 - 4.19469i) q^{79} +(-3.95365 - 8.08509i) q^{81} +(-7.87941 + 13.6475i) q^{83} +(5.44973 + 9.43920i) q^{85} +(15.1606 + 0.260733i) q^{87} +(5.32537 + 3.07461i) q^{89} +(-5.55940 + 2.23255i) q^{91} +(-8.03670 - 0.138216i) q^{93} +(-13.4584 - 7.77021i) q^{95} +(14.9489 + 8.63074i) q^{97} +(-1.12727 - 0.703592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9}+O(q^{10}) $ 32 * q - 4 * q^9	$ 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77} - 16 q^{81} - 12 q^{85} - 18 q^{89} + 58 q^{93} - 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.840104	+	1.51467i	0.485034	+	0.874495i
$3$	0.840104	+	1.51467i	0.485034	+	0.874495i
$4$		0			0
$5$			2.34835i			1.05022i	0.851036	+	0.525108i	$0.175975\pi$
$5$			2.34835i			1.05022i	−0.851036	+	0.525108i	$0.824025\pi$
$6$		0			0
$7$	2.61922	+	0.373730i	0.989973	+	0.141257i
$7$	2.61922	+	0.373730i	0.989973	+	0.141257i
$8$		0			0
$9$	−1.58845	+	2.54496i	−0.529484	+	0.848320i
$10$		0			0
$11$			0.442942i			0.133552i	0.997768	+	0.0667761i	$0.0212713\pi$
$11$			0.442942i			0.133552i	−0.997768	+	0.0667761i	$0.978729\pi$
$12$		0			0
$13$	−1.96099	+	1.13218i	−0.543881	+	0.314010i	−0.746650	−	0.665217i	$-0.768339\pi$
$13$	−1.96099	+	1.13218i	−0.543881	+	0.314010i	0.202769	+	0.979226i	$0.435006\pi$
$14$		0			0
$15$	−3.55698	+	1.97286i	−0.918408	+	0.509390i
$16$		0			0
$17$	4.01950	−	2.32066i	0.974872	−	0.562843i	0.0741541	−	0.997247i	$-0.476374\pi$
$17$	4.01950	−	2.32066i	0.974872	−	0.562843i	0.900718	+	0.434404i	$0.143041\pi$
$18$		0			0
$19$	−3.30879	+	5.73100i	−0.759089	+	1.31478i	0.184227	+	0.982884i	$0.441022\pi$
$19$	−3.30879	+	5.73100i	−0.759089	+	1.31478i	−0.943316	+	0.331897i	$0.892311\pi$
$20$		0			0
$21$	1.63434	+	4.28123i	0.356643	+	0.934241i
$22$		0			0
$23$		−	1.13645i		−	0.236965i	−0.992956	−	0.118483i	$-0.962197\pi$
$23$		−	1.13645i		−	0.236965i	0.992956	−	0.118483i	$-0.0378030\pi$
$24$		0			0
$25$	−0.514760			−0.102952
$26$		0			0
$27$	−5.18924	−	0.267947i	−0.998670	−	0.0515664i
$28$		0			0
$29$	4.37712	−	7.58140i	0.812811	−	1.40783i	−0.0980775	−	0.995179i	$-0.531269\pi$
$29$	4.37712	−	7.58140i	0.812811	−	1.40783i	0.910889	−	0.412652i	$-0.135397\pi$
$30$		0			0
$31$	−2.32034	+	4.01894i	−0.416745	+	0.721824i	−0.995610	−	0.0935998i	$-0.970163\pi$
$31$	−2.32034	+	4.01894i	−0.416745	+	0.721824i	0.578865	+	0.815424i	$0.303496\pi$
$32$		0			0
$33$	−0.670912	+	0.372118i	−0.116791	+	0.0647774i
$34$		0			0
$35$	−0.877649	+	6.15086i	−0.148350	+	1.03968i
$36$		0			0
$37$	−1.41316	+	2.44767i	−0.232323	+	0.402395i	−0.958491	−	0.285122i	$-0.907966\pi$
$37$	−1.41316	+	2.44767i	−0.232323	+	0.402395i	0.726169	+	0.687517i	$0.241299\pi$
$38$		0			0
$39$	−3.36231	−	2.01911i	−0.538401	−	0.323316i
$40$		0			0
$41$	4.55283	−	2.62858i	0.711032	−	0.410515i	−0.100411	−	0.994946i	$-0.532016\pi$
$41$	4.55283	−	2.62858i	0.711032	−	0.410515i	0.811443	+	0.584431i	$0.198682\pi$
$42$		0			0
$43$	−3.81500	−	2.20259i	−0.581782	−	0.335892i	0.180059	−	0.983656i	$-0.442371\pi$
$43$	−3.81500	−	2.20259i	−0.581782	−	0.335892i	−0.761841	+	0.647764i	$0.775704\pi$
$44$		0			0
$45$	−5.97646	−	3.73024i	−0.890919	−	0.556072i
$46$		0			0
$47$	−2.67363	−	4.63087i	−0.389989	−	0.675481i	0.602458	−	0.798150i	$-0.294188\pi$
$47$	−2.67363	−	4.63087i	−0.389989	−	0.675481i	−0.992448	+	0.122669i	$0.960855\pi$
$48$		0			0
$49$	6.72065	+	1.95776i	0.960093	+	0.279680i
$50$		0			0
$51$	6.89183	+	4.13862i	0.965050	+	0.579523i
$52$		0			0
$53$	−1.54428	−	2.67478i	−0.212124	−	0.367409i	0.740255	−	0.672326i	$-0.234705\pi$
$53$	−1.54428	−	2.67478i	−0.212124	−	0.367409i	−0.952379	+	0.304917i	$0.901371\pi$
$54$		0			0
$55$	−1.04018			−0.140259
$56$		0			0
$57$	−11.4603	−	0.197096i	−1.51795	−	0.0261060i
$58$		0			0
$59$	−0.689570	+	1.19437i	−0.0897743	+	0.155494i	−0.907416	−	0.420234i	$-0.861948\pi$
$59$	−0.689570	+	1.19437i	−0.0897743	+	0.155494i	0.817641	+	0.575728i	$0.195281\pi$
$60$		0			0
$61$	−8.88607	+	5.13038i	−1.13775	+	0.656877i	−0.945871	−	0.324542i	$-0.894790\pi$
$61$	−8.88607	+	5.13038i	−1.13775	+	0.656877i	−0.191874	+	0.981420i	$0.561456\pi$
$62$		0			0
$63$	−5.11163	+	6.07217i	−0.644005	+	0.765021i
$64$		0			0
$65$	−2.65875	−	4.60510i	−0.329778	−	0.571192i
$66$		0			0
$67$	2.10780	+	1.21694i	0.257509	+	0.148673i	0.623198	−	0.782064i	$-0.285833\pi$
$67$	2.10780	+	1.21694i	0.257509	+	0.148673i	−0.365689	+	0.930737i	$0.619167\pi$
$68$		0			0
$69$	1.72134	−	0.954732i	0.207225	−	0.114936i
$70$		0			0
$71$			7.20644i			0.855247i	0.903957	+	0.427623i	$0.140649\pi$
$71$			7.20644i			0.855247i	−0.903957	+	0.427623i	$0.859351\pi$
$72$		0			0
$73$	3.17824	−	1.83496i	0.371984	−	0.214765i	−0.302341	−	0.953200i	$-0.597768\pi$
$73$	3.17824	−	1.83496i	0.371984	−	0.214765i	0.674325	+	0.738435i	$0.264435\pi$
$74$		0			0
$75$	−0.432452	−	0.779691i	−0.0499352	−	0.0900309i
$76$		0			0
$77$	−0.165541	+	1.16016i	−0.0188651	+	0.132213i
$78$		0			0
$79$	7.26542	−	4.19469i	0.817423	−	0.471939i	−0.0321039	−	0.999485i	$-0.510221\pi$
$79$	7.26542	−	4.19469i	0.817423	−	0.471939i	0.849527	+	0.527545i	$0.176887\pi$
$80$		0			0
$81$	−3.95365	−	8.08509i	−0.439294	−	0.898343i
$82$		0			0
$83$	−7.87941	+	13.6475i	−0.864878	+	1.49801i	0.00229000	+	0.999997i	$0.499271\pi$
$83$	−7.87941	+	13.6475i	−0.864878	+	1.49801i	−0.867168	+	0.498015i	$0.834062\pi$
$84$		0			0
$85$	5.44973	+	9.43920i	0.591106	+	1.02383i
$86$		0			0
$87$	15.1606	+	0.260733i	1.62538	+	0.0279535i
$88$		0			0
$89$	5.32537	+	3.07461i	0.564488	+	0.325908i	0.754945	−	0.655788i	$-0.227664\pi$
$89$	5.32537	+	3.07461i	0.564488	+	0.325908i	−0.190457	+	0.981696i	$0.560997\pi$
$90$		0			0
$91$	−5.55940	+	2.23255i	−0.582783	+	0.234034i
$92$		0			0
$93$	−8.03670	−	0.138216i	−0.833367	−	0.0143324i
$94$		0			0
$95$	−13.4584	−	7.77021i	−1.38080	−	0.797207i
$96$		0			0
$97$	14.9489	+	8.63074i	1.51783	+	0.876319i	0.999780	+	0.0209677i	$0.00667473\pi$
$97$	14.9489	+	8.63074i	1.51783	+	0.876319i	0.518049	+	0.855351i	$0.326659\pi$
$98$		0			0
$99$	−1.12727	−	0.703592i	−0.113295	−	0.0707137i
$100$		0			0
$101$		−	17.3667i		−	1.72806i	−0.503444	−	0.864028i	$-0.667934\pi$
$101$		−	17.3667i		−	1.72806i	0.503444	−	0.864028i	$-0.332066\pi$
$102$		0			0
$103$	−9.23888			−0.910334			−0.455167	−	0.890406i	$-0.650420\pi$
$103$	−9.23888			−0.910334			−0.455167	+	0.890406i	$0.650420\pi$
$104$		0			0
$105$	−10.0538	+	3.83801i	−0.981154	+	0.374551i
$106$		0			0
$107$	7.76296	+	4.48195i	0.750474	+	0.433286i	0.825865	−	0.563868i	$-0.190687\pi$
$107$	7.76296	+	4.48195i	0.750474	+	0.433286i	−0.0753911	+	0.997154i	$0.524021\pi$
$108$		0			0
$109$	−6.46206	−	11.1926i	−0.618953	−	1.07206i	−0.989677	−	0.143315i	$-0.954224\pi$
$109$	−6.46206	−	11.1926i	−0.618953	−	1.07206i	0.370724	−	0.928743i	$-0.379110\pi$
$110$		0			0
$111$	−4.89462	−	0.0841783i	−0.464577	−	0.00798985i
$112$		0			0
$113$	−2.12502	−	3.68064i	−0.199905	−	0.346246i	0.748592	−	0.663031i	$-0.230730\pi$
$113$	−2.12502	−	3.68064i	−0.199905	−	0.346246i	−0.948497	+	0.316785i	$0.897397\pi$
$114$		0			0
$115$	2.66877			0.248864
$116$		0			0
$117$	0.233587	−	6.78905i	0.0215951	−	0.627648i
$118$		0			0
$119$	11.3953	−	4.57612i	1.04460	−	0.419492i
$120$		0			0
$121$	10.8038			0.982164
$122$		0			0
$123$	7.80628	+	4.68776i	0.703868	+	0.422681i
$124$		0			0
$125$			10.5329i			0.942094i
$126$		0			0
$127$		−	19.6660i		−	1.74507i	−0.488549	−	0.872536i	$-0.662474\pi$
$127$		−	19.6660i		−	1.74507i	0.488549	−	0.872536i	$-0.337526\pi$
$128$		0			0
$129$	0.131202	−	7.62887i	0.0115517	−	0.671685i
$130$		0			0
$131$	17.0737			1.49173			0.745867	−	0.666095i	$-0.232035\pi$
$131$	17.0737			1.49173			0.745867	+	0.666095i	$0.232035\pi$
$132$		0			0
$133$	−10.8083	+	13.7742i	−0.937199	+	1.19437i
$134$		0			0
$135$	0.629234	−	12.1862i	0.0541559	−	1.04882i
$136$		0			0
$137$	−3.51361			−0.300188			−0.150094	−	0.988672i	$-0.547958\pi$
$137$	−3.51361			−0.300188			−0.150094	+	0.988672i	$0.547958\pi$
$138$		0			0
$139$	8.66086	+	15.0011i	0.734605	+	1.27237i	0.954896	+	0.296939i	$0.0959658\pi$
$139$	8.66086	+	15.0011i	0.734605	+	1.27237i	−0.220292	+	0.975434i	$0.570701\pi$
$140$		0			0
$141$	4.76811	−	7.94008i	0.401547	−	0.668675i
$142$		0			0
$143$	−0.501490	−	0.868606i	−0.0419367	−	0.0726365i
$144$		0			0
$145$	17.8038	+	10.2790i	1.47853	+	0.853627i
$146$		0			0
$147$	2.68068	+	11.8243i	0.221099	+	0.975251i
$148$		0			0
$149$	−6.08533			−0.498529			−0.249265	−	0.968435i	$-0.580189\pi$
$149$	−6.08533			−0.498529			−0.249265	+	0.968435i	$0.580189\pi$
$150$		0			0
$151$		−	2.61258i		−	0.212609i	−0.994334	−	0.106304i	$-0.966098\pi$
$151$		−	2.61258i		−	0.212609i	0.994334	−	0.106304i	$-0.0339018\pi$
$152$		0			0
$153$	−0.478791	+	13.9157i	−0.0387079	+	1.12502i
$154$		0			0
$155$	−9.43790	−	5.44897i	−0.758070	−	0.437672i
$156$		0			0
$157$	16.2746	+	9.39612i	1.29885	+	0.749892i	0.980206	−	0.197982i	$-0.0634386\pi$
$157$	16.2746	+	9.39612i	1.29885	+	0.749892i	0.318646	+	0.947874i	$0.396772\pi$
$158$		0			0
$159$	2.75405	−	4.58617i	0.218410	−	0.363707i
$160$		0			0
$161$	0.424723	−	2.97660i	0.0334729	−	0.234589i
$162$		0			0
$163$	−2.90466	−	1.67700i	−0.227510	−	0.131353i	0.381913	−	0.924198i	$-0.375266\pi$
$163$	−2.90466	−	1.67700i	−0.227510	−	0.131353i	−0.609423	+	0.792845i	$0.708599\pi$
$164$		0			0
$165$	−0.873863	−	1.57554i	−0.0680302	−	0.122655i
$166$		0			0
$167$	−4.58344	−	7.93876i	−0.354678	−	0.614320i	0.632385	−	0.774654i	$-0.282076\pi$
$167$	−4.58344	−	7.93876i	−0.354678	−	0.614320i	−0.987063	+	0.160335i	$0.948743\pi$
$168$		0			0
$169$	−3.93635	+	6.81795i	−0.302796	+	0.524458i
$170$		0			0
$171$	−9.32931	−	17.5241i	−0.713430	−	1.34011i
$172$		0			0
$173$	19.6171	−	11.3260i	1.49146	−	0.861097i	0.491511	−	0.870871i	$-0.336445\pi$
$173$	19.6171	−	11.3260i	1.49146	−	0.861097i	0.999952	+	0.00977454i	$0.00311138\pi$
$174$		0			0
$175$	−1.34827	−	0.192381i	−0.101920	−	0.0145426i
$176$		0			0
$177$	−2.38839	−	0.0410758i	−0.179522	−	0.00308744i
$178$		0			0
$179$	19.2752	−	11.1285i	1.44069	−	0.831785i	0.442799	−	0.896621i	$-0.353986\pi$
$179$	19.2752	−	11.1285i	1.44069	−	0.831785i	0.997896	+	0.0648357i	$0.0206523\pi$
$180$		0			0
$181$		−	4.33319i		−	0.322084i	−0.986948	−	0.161042i	$-0.948515\pi$
$181$		−	4.33319i		−	0.322084i	0.986948	−	0.161042i	$-0.0514854\pi$
$182$		0			0
$183$	−15.2361	−	9.14942i	−1.12628	−	0.676344i
$184$		0			0
$185$	−5.74799	−	3.31861i	−0.422601	−	0.243989i
$186$		0			0
$187$	1.02792	+	1.78041i	0.0751689	+	0.130196i
$188$		0			0
$189$	−13.4916	−	2.64119i	−0.981372	−	0.192118i
$190$		0			0
$191$	−21.5649	+	12.4505i	−1.56038	+	0.900885i	−0.563160	+	0.826348i	$0.690415\pi$
$191$	−21.5649	+	12.4505i	−1.56038	+	0.900885i	−0.997218	+	0.0745371i	$0.976252\pi$
$192$		0			0
$193$	−10.6627	+	18.4683i	−0.767517	+	1.32938i	0.171389	+	0.985204i	$0.445175\pi$
$193$	−10.6627	+	18.4683i	−0.767517	+	1.32938i	−0.938906	+	0.344175i	$0.888159\pi$
$194$		0			0
$195$	4.74157	−	7.89589i	0.339551	−	0.565437i
$196$		0			0
$197$	18.5315			1.32032			0.660158	−	0.751127i	$-0.270489\pi$
$197$	18.5315			1.32032			0.660158	+	0.751127i	$0.270489\pi$
$198$		0			0
$199$	0.918721	+	1.59127i	0.0651264	+	0.112802i	0.896750	−	0.442537i	$-0.145922\pi$
$199$	0.918721	+	1.59127i	0.0651264	+	0.112802i	−0.831624	+	0.555340i	$0.812588\pi$
$200$		0			0
$201$	−0.0724898	+	4.21498i	−0.00511303	+	0.297302i
$202$		0			0
$203$	14.2981	−	18.2215i	1.00353	−	1.27890i
$204$		0			0
$205$	6.17283	+	10.6916i	0.431129	+	0.746737i
$206$		0			0
$207$	2.89221	+	1.80519i	0.201022	+	0.125469i
$208$		0			0
$209$	−2.53850	−	1.46560i	−0.175592	−	0.101378i
$210$		0			0
$211$	17.5295	−	10.1207i	1.20678	−	0.696735i	0.244725	−	0.969592i	$-0.421302\pi$
$211$	17.5295	−	10.1207i	1.20678	−	0.696735i	0.962054	+	0.272858i	$0.0879689\pi$
$212$		0			0
$213$	−10.9154	+	6.05416i	−0.747909	+	0.414824i
$214$		0			0
$215$	5.17246	−	8.95897i	0.352759	−	0.610997i
$216$		0			0
$217$	−7.57948	+	9.65933i	−0.514529	+	0.655718i
$218$		0			0
$219$	5.44940	+	3.27243i	0.368236	+	0.221130i
$220$		0			0
$221$	−5.25480	+	9.10158i	−0.353476	+	0.612239i
$222$		0			0
$223$	0.492098	−	0.852339i	0.0329533	−	0.0570768i	−0.849078	−	0.528267i	$-0.822842\pi$
$223$	0.492098	−	0.852339i	0.0329533	−	0.0570768i	0.882032	+	0.471190i	$0.156175\pi$
$224$		0			0
$225$	0.817670	−	1.31004i	0.0545113	−	0.0873362i
$226$		0			0
$227$	−13.1928			−0.875639			−0.437820	−	0.899063i	$-0.644249\pi$
$227$	−13.1928			−0.875639			−0.437820	+	0.899063i	$0.644249\pi$
$228$		0			0
$229$		−	5.67964i		−	0.375321i	−0.982234	−	0.187660i	$-0.939910\pi$
$229$		−	5.67964i		−	0.375321i	0.982234	−	0.187660i	$-0.0600905\pi$
$230$		0			0
$231$	−1.89634	+	0.723919i	−0.124770	+	0.0476304i
$232$		0			0
$233$	7.42995	−	12.8691i	0.486752	−	0.843080i	−0.513132	−	0.858310i	$-0.671515\pi$
$233$	7.42995	−	12.8691i	0.486752	−	0.843080i	0.999884	+	0.0152301i	$0.00484808\pi$
$234$		0			0
$235$	10.8749	−	6.27863i	0.709401	−	0.409573i
$236$		0			0
$237$	12.4573	+	7.48073i	0.809187	+	0.485926i
$238$		0			0
$239$	15.6484	−	9.03459i	1.01221	−	0.584399i	0.100371	−	0.994950i	$-0.467997\pi$
$239$	15.6484	−	9.03459i	1.01221	−	0.584399i	0.911837	+	0.410551i	$0.134664\pi$
$240$		0			0
$241$		−	20.7503i		−	1.33664i	−0.743872	−	0.668322i	$-0.767013\pi$
$241$		−	20.7503i		−	1.33664i	0.743872	−	0.668322i	$-0.232987\pi$
$242$		0			0
$243$	8.92477	−	12.7808i	0.572524	−	0.819888i
$244$		0			0
$245$	−4.59752	+	15.7825i	−0.293725	+	1.00830i
$246$		0			0
$247$		−	14.9846i		−	0.953445i
$248$		0			0
$249$	−27.2911	−	0.469355i	−1.72950	−	0.0297442i
$250$		0			0
$251$	−9.53037			−0.601552			−0.300776	−	0.953695i	$-0.597246\pi$
$251$	−9.53037			−0.601552			−0.300776	+	0.953695i	$0.597246\pi$
$252$		0			0
$253$	0.503380			0.0316472
$254$		0			0
$255$	−9.71894	+	16.1845i	−0.608624	+	1.01351i
$256$		0			0
$257$		−	11.3949i		−	0.710796i	−0.934715	−	0.355398i	$-0.884345\pi$
$257$		−	11.3949i		−	0.710796i	0.934715	−	0.355398i	$-0.115655\pi$
$258$		0			0
$259$	−4.61616	+	5.88285i	−0.286834	+	0.365543i
$260$		0			0
$261$	12.3415	+	23.1823i	0.763921	+	1.43495i
$262$		0			0
$263$		−	6.23768i		−	0.384632i	−0.981333	−	0.192316i	$-0.938400\pi$
$263$		−	6.23768i		−	0.384632i	0.981333	−	0.192316i	$-0.0615998\pi$
$264$		0			0
$265$	6.28132	−	3.62652i	0.385859	−	0.222776i
$266$		0			0
$267$	−0.183146	+	10.6492i	−0.0112083	+	0.651719i
$268$		0			0
$269$	22.5563	−	13.0229i	1.37528	−	0.794018i	0.383693	−	0.923461i	$-0.374652\pi$
$269$	22.5563	−	13.0229i	1.37528	−	0.794018i	0.991587	+	0.129443i	$0.0413188\pi$
$270$		0			0
$271$	−10.3180	+	17.8713i	−0.626775	+	1.08561i	0.361420	+	0.932403i	$0.382292\pi$
$271$	−10.3180	+	17.8713i	−0.626775	+	1.08561i	−0.988195	+	0.153203i	$0.951041\pi$
$272$		0			0
$273$	−8.05204	−	6.54508i	−0.487332	−	0.396126i
$274$		0			0
$275$		−	0.228009i		−	0.0137494i
$276$		0			0
$277$	−12.0722			−0.725350			−0.362675	−	0.931916i	$-0.618136\pi$
$277$	−12.0722			−0.725350			−0.362675	+	0.931916i	$0.618136\pi$
$278$		0			0
$279$	−6.54231	−	12.2891i	−0.391678	−	0.735727i
$280$		0			0
$281$	−3.67299	+	6.36180i	−0.219112	+	0.379513i	−0.954537	−	0.298093i	$-0.903649\pi$
$281$	−3.67299	+	6.36180i	−0.219112	+	0.379513i	0.735425	+	0.677606i	$0.236983\pi$
$282$		0			0
$283$	8.65315	−	14.9877i	0.514376	−	0.890926i	−0.485484	−	0.874245i	$-0.661357\pi$
$283$	8.65315	−	14.9877i	0.514376	−	0.890926i	0.999861	−	0.0166808i	$-0.00530990\pi$
$284$		0			0
$285$	0.462850	−	26.9128i	0.0274169	−	1.59418i
$286$		0			0
$287$	12.9072	−	5.18330i	0.761891	−	0.305961i
$288$		0			0
$289$	2.27092	−	3.93336i	0.133584	−	0.231374i
$290$		0			0
$291$	−0.514110	+	29.8933i	−0.0301376	+	1.75238i
$292$		0			0
$293$	0.965862	−	0.557641i	0.0564263	−	0.0325777i	−0.471521	−	0.881855i	$-0.656295\pi$
$293$	0.965862	−	0.557641i	0.0564263	−	0.0325777i	0.527948	+	0.849277i	$0.322962\pi$
$294$		0			0
$295$	−2.80480	−	1.61935i	−0.163302	−	0.0942823i
$296$		0			0
$297$	0.118685	−	2.29853i	0.00688681	−	0.133374i
$298$		0			0
$299$	1.28666	+	2.22856i	0.0744094	+	0.128881i
$300$		0			0
$301$	−9.16916	−	7.19486i	−0.528502	−	0.414705i
$302$		0			0
$303$	26.3049	−	14.5899i	1.51118	−	0.838166i
$304$		0			0
$305$	−12.0479	−	20.8676i	−0.689863	−	1.19488i
$306$		0			0
$307$	30.5465			1.74338			0.871690	−	0.490058i	$-0.163025\pi$
$307$	30.5465			1.74338			0.871690	+	0.490058i	$0.163025\pi$
$308$		0			0
$309$	−7.76162	−	13.9939i	−0.441543	−	0.796083i
$310$		0			0
$311$	3.44800	−	5.97210i	0.195518	−	0.338647i	−0.751552	−	0.659674i	$-0.770695\pi$
$311$	3.44800	−	5.97210i	0.195518	−	0.338647i	0.947070	+	0.321027i	$0.104028\pi$
$312$		0			0
$313$	12.1393	−	7.00865i	0.686156	−	0.396153i	−0.116014	−	0.993248i	$-0.537012\pi$
$313$	12.1393	−	7.00865i	0.686156	−	0.396153i	0.802171	+	0.597095i	$0.203678\pi$
$314$		0			0
$315$	−14.2596	−	12.0039i	−0.803437	−	0.676344i
$316$		0			0
$317$	10.0887	+	17.4742i	0.566638	+	0.981446i	0.996895	+	0.0787397i	$0.0250896\pi$
$317$	10.0887	+	17.4742i	0.566638	+	0.981446i	−0.430257	+	0.902706i	$0.641577\pi$
$318$		0			0
$319$	3.35812	+	1.93881i	0.188019	+	0.108553i
$320$		0			0
$321$	−0.266978	+	15.5236i	−0.0149012	+	0.866445i
$322$		0			0
$323$			30.7143i			1.70899i
$324$		0			0
$325$	1.00944	−	0.582800i	0.0559936	−	0.0323279i
$326$		0			0
$327$	11.5243	−	19.1909i	0.637296	−	1.06126i
$328$		0			0
$329$	−5.27214	−	13.1285i	−0.290663	−	0.723797i
$330$		0			0
$331$	−27.9703	+	16.1486i	−1.53738	+	0.887609i	−0.538394	+	0.842693i	$0.680969\pi$
$331$	−27.9703	+	16.1486i	−1.53738	+	0.887609i	−0.998991	+	0.0449159i	$0.985698\pi$
$332$		0			0
$333$	−3.98449	−	7.48445i	−0.218348	−	0.410145i
$334$		0			0
$335$	−2.85780	+	4.94986i	−0.156138	+	0.270440i
$336$		0			0
$337$	−10.1378	−	17.5591i	−0.552239	−	0.956506i	−0.998113	−	0.0614102i	$-0.980440\pi$
$337$	−10.1378	−	17.5591i	−0.552239	−	0.956506i	0.445873	−	0.895096i	$-0.352893\pi$
$338$		0			0
$339$	3.78972	−	6.31083i	0.205829	−	0.342757i
$340$		0			0
$341$	−1.78016	−	1.02778i	−0.0964011	−	0.0556572i
$342$		0			0
$343$	16.8712	+	7.63953i	0.910960	+	0.412496i
$344$		0			0
$345$	2.24205	+	4.04231i	0.120708	+	0.217631i
$346$		0			0
$347$	−3.63139	−	2.09658i	−0.194943	−	0.112550i	0.399352	−	0.916798i	$-0.369235\pi$
$347$	−3.63139	−	2.09658i	−0.194943	−	0.112550i	−0.594295	+	0.804247i	$0.702569\pi$
$348$		0			0
$349$	−6.54079	−	3.77632i	−0.350120	−	0.202142i	0.314618	−	0.949218i	$-0.398124\pi$
$349$	−6.54079	−	3.77632i	−0.350120	−	0.202142i	−0.664738	+	0.747076i	$0.731457\pi$
$350$		0			0
$351$	10.4794	−	5.34970i	0.559350	−	0.285546i
$352$		0			0
$353$		−	17.5410i		−	0.933613i	−0.884359	−	0.466807i	$-0.845404\pi$
$353$		−	17.5410i		−	0.933613i	0.884359	−	0.466807i	$-0.154596\pi$
$354$		0			0
$355$	−16.9233			−0.898193
$356$		0			0
$357$	16.5045	+	13.4157i	0.873512	+	0.710032i
$358$		0			0
$359$	18.3430	+	10.5904i	0.968108	+	0.558937i	0.898659	−	0.438648i	$-0.144543\pi$
$359$	18.3430	+	10.5904i	0.968108	+	0.558937i	0.0694490	+	0.997586i	$0.477876\pi$
$360$		0			0
$361$	−12.3962	−	21.4709i	−0.652432	−	1.13005i
$362$		0			0
$363$	9.07632	+	16.3642i	0.476383	+	0.858898i
$364$		0			0
$365$	4.30912	+	7.46362i	0.225550	+	0.390664i
$366$		0			0
$367$	−2.22135			−0.115954			−0.0579768	−	0.998318i	$-0.518465\pi$
$367$	−2.22135			−0.115954			−0.0579768	+	0.998318i	$0.518465\pi$
$368$		0			0
$369$	−0.542319	+	15.7621i	−0.0282320	+	0.820544i
$370$		0			0
$371$	−3.04518	−	7.58298i	−0.158098	−	0.393689i
$372$		0			0
$373$	−7.61418			−0.394248			−0.197124	−	0.980379i	$-0.563160\pi$
$373$	−7.61418			−0.394248			−0.197124	+	0.980379i	$0.563160\pi$
$374$		0			0
$375$	−15.9539	+	8.84875i	−0.823856	+	0.456948i
$376$		0			0
$377$			19.8227i			1.02092i
$378$		0			0
$379$		−	4.06894i		−	0.209007i	−0.994525	−	0.104504i	$-0.966675\pi$
$379$		−	4.06894i		−	0.209007i	0.994525	−	0.104504i	$-0.0333254\pi$
$380$		0			0
$381$	29.7875	−	16.5215i	1.52606	−	0.846420i
$382$		0			0
$383$	2.04253			0.104368			0.0521842	−	0.998637i	$-0.483382\pi$
$383$	2.04253			0.104368			0.0521842	+	0.998637i	$0.483382\pi$
$384$		0			0
$385$	−2.72448	−	0.388748i	−0.138852	−	0.0198124i
$386$		0			0
$387$	11.6655	−	6.21032i	0.592988	−	0.315688i
$388$		0			0
$389$	−24.3587			−1.23503			−0.617517	−	0.786558i	$-0.711861\pi$
$389$	−24.3587			−1.23503			−0.617517	+	0.786558i	$0.711861\pi$
$390$		0			0
$391$	−2.63730	−	4.56794i	−0.133374	−	0.231011i
$392$		0			0
$393$	14.3437	+	25.8610i	0.723542	+	1.30451i
$394$		0			0
$395$	9.85061	+	17.0618i	0.495638	+	0.858470i
$396$		0			0
$397$	−12.6996	−	7.33213i	−0.637375	−	0.367989i	0.146227	−	0.989251i	$-0.453287\pi$
$397$	−12.6996	−	7.33213i	−0.637375	−	0.367989i	−0.783603	+	0.621262i	$0.786620\pi$
$398$		0			0
$399$	−29.9434	−	4.79929i	−1.49905	−	0.240265i
$400$		0			0
$401$	13.5778			0.678045			0.339022	−	0.940778i	$-0.389904\pi$
$401$	13.5778			0.678045			0.339022	+	0.940778i	$0.389904\pi$
$402$		0			0
$403$		−	10.5081i		−	0.523448i
$404$		0			0
$405$	18.9866	−	9.28456i	0.943454	−	0.461354i
$406$		0			0
$407$	−1.08418	−	0.625950i	−0.0537407	−	0.0310272i
$408$		0			0
$409$	−5.70365	−	3.29300i	−0.282027	−	0.162828i	0.352314	−	0.935882i	$-0.385395\pi$
$409$	−5.70365	−	3.29300i	−0.282027	−	0.162828i	−0.634341	+	0.773054i	$0.718728\pi$
$410$		0			0
$411$	−2.95180	−	5.32197i	−0.145602	−	0.262513i
$412$		0			0
$413$	−2.25251	+	2.87061i	−0.110839	+	0.141253i
$414$		0			0
$415$	−32.0493	−	18.5036i	−1.57324	−	0.908308i
$416$		0			0
$417$	−15.4456	+	25.7208i	−0.756375	+	1.25955i
$418$		0			0
$419$	−11.4919	−	19.9046i	−0.561416	−	0.972401i	−0.997373	−	0.0724336i	$-0.976923\pi$
$419$	−11.4919	−	19.9046i	−0.561416	−	0.972401i	0.435957	−	0.899967i	$-0.356410\pi$
$420$		0			0
$421$	−1.00338	+	1.73790i	−0.0489017	+	0.0847003i	−0.889440	−	0.457052i	$-0.848905\pi$
$421$	−1.00338	+	1.73790i	−0.0489017	+	0.0847003i	0.840538	+	0.541752i	$0.182239\pi$
$422$		0			0
$423$	16.0323	+	0.551615i	0.779517	+	0.0268204i
$424$		0			0
$425$	−2.06908	+	1.19458i	−0.100365	+	0.0579457i
$426$		0			0
$427$	−25.1920	+	10.1166i	−1.21913	+	0.489577i
$428$		0			0
$429$	0.894347	−	1.48931i	0.0431795	−	0.0719046i
$430$		0			0
$431$	−28.7684	+	16.6095i	−1.38573	+	0.800049i	−0.992830	−	0.119534i	$-0.961860\pi$
$431$	−28.7684	+	16.6095i	−1.38573	+	0.800049i	−0.392896	+	0.919583i	$0.628527\pi$
$432$		0			0
$433$			35.6573i			1.71358i	0.515663	+	0.856791i	$0.327546\pi$
$433$			35.6573i			1.71358i	−0.515663	+	0.856791i	$0.672454\pi$
$434$		0			0
$435$	−0.612294	+	35.6023i	−0.0293572	+	1.70700i
$436$		0			0
$437$	6.51296	+	3.76026i	0.311557	+	0.179878i
$438$		0			0
$439$	4.29613	+	7.44111i	0.205043	+	0.355145i	0.950146	−	0.311804i	$-0.100933\pi$
$439$	4.29613	+	7.44111i	0.205043	+	0.355145i	−0.745103	+	0.666949i	$0.767600\pi$
$440$		0			0
$441$	−15.6579	+	13.9940i	−0.745612	+	0.666380i
$442$		0			0
$443$	−31.5462	+	18.2132i	−1.49880	+	0.865335i	−0.999999	−	0.00137907i	$-0.999561\pi$
$443$	−31.5462	+	18.2132i	−1.49880	+	0.865335i	−0.498805	+	0.866714i	$0.666228\pi$
$444$		0			0
$445$	−7.22026	+	12.5059i	−0.342273	+	0.592834i
$446$		0			0
$447$	−5.11231	−	9.21726i	−0.241804	−	0.435962i
$448$		0			0
$449$	−12.2858			−0.579801			−0.289900	−	0.957057i	$-0.593622\pi$
$449$	−12.2858			−0.579801			−0.289900	+	0.957057i	$0.593622\pi$
$450$		0			0
$451$	1.16431	+	2.01664i	0.0548251	+	0.0949599i
$452$		0			0
$453$	3.95720	−	2.19484i	0.185925	−	0.103123i
$454$		0			0
$455$	−5.24280	−	13.0554i	−0.245786	−	0.612048i
$456$		0			0
$457$	3.64674	+	6.31634i	0.170587	+	0.295466i	0.938625	−	0.344938i	$-0.112100\pi$
$457$	3.64674	+	6.31634i	0.170587	+	0.295466i	−0.768038	+	0.640404i	$0.778767\pi$
$458$		0			0
$459$	−21.4800	+	10.9654i	−1.00260	+	0.511823i
$460$		0			0
$461$	7.33329	+	4.23388i	0.341545	+	0.197191i	0.660955	−	0.750425i	$-0.270151\pi$
$461$	7.33329	+	4.23388i	0.341545	+	0.197191i	−0.319410	+	0.947617i	$0.603485\pi$
$462$		0			0
$463$	−4.53400	+	2.61771i	−0.210713	+	0.121655i	−0.601643	−	0.798765i	$-0.705487\pi$
$463$	−4.53400	+	2.61771i	−0.210713	+	0.121655i	0.390930	+	0.920421i	$0.372154\pi$
$464$		0			0
$465$	0.324580	−	18.8730i	0.0150521	−	0.875215i
$466$		0			0
$467$	−9.96542	+	17.2606i	−0.461145	+	0.798726i	−0.999018	−	0.0442995i	$-0.985894\pi$
$467$	−9.96542	+	17.2606i	−0.461145	+	0.798726i	0.537874	+	0.843025i	$0.319228\pi$
$468$		0			0
$469$	5.06599	+	3.97518i	0.233926	+	0.183557i
$470$		0			0
$471$	−0.559701	+	32.5443i	−0.0257897	+	1.49956i
$472$		0			0
$473$	0.975621	−	1.68983i	0.0448591	−	0.0776983i
$474$		0			0
$475$	1.70323	−	2.95008i	0.0781497	−	0.135359i
$476$		0			0
$477$	9.26023	+	0.318611i	0.423997	+	0.0145882i
$478$		0			0
$479$	−29.0246			−1.32617			−0.663083	−	0.748545i	$-0.730753\pi$
$479$	−29.0246			−1.32617			−0.663083	+	0.748545i	$0.730753\pi$
$480$		0			0
$481$		−	6.39981i		−	0.291806i
$482$		0			0
$483$	4.86538	−	1.85734i	0.221383	−	0.0845119i
$484$		0			0
$485$	−20.2680	+	35.1052i	−0.920323	+	1.59405i
$486$		0			0
$487$	11.9472	−	6.89770i	0.541378	−	0.312565i	−0.204259	−	0.978917i	$-0.565479\pi$
$487$	11.9472	−	6.89770i	0.541378	−	0.312565i	0.745637	+	0.666352i	$0.232145\pi$
$488$		0			0
$489$	0.0998946	−	5.80845i	0.00451739	−	0.262667i
$490$		0			0
$491$	−14.6069	+	8.43329i	−0.659200	+	0.380589i	−0.791972	−	0.610557i	$-0.790945\pi$
$491$	−14.6069	+	8.43329i	−0.659200	+	0.380589i	0.132772	+	0.991147i	$0.457612\pi$
$492$		0			0
$493$		−	40.6313i		−	1.82994i
$494$		0			0
$495$	1.65228	−	2.64723i	0.0742646	−	0.118984i
$496$		0			0
$497$	−2.69326	+	18.8753i	−0.120809	+	0.846671i
$498$		0			0
$499$		−	16.7654i		−	0.750523i	−0.926919	−	0.375262i	$-0.877553\pi$
$499$		−	16.7654i		−	0.750523i	0.926919	−	0.375262i	$-0.122447\pi$
$500$		0			0
$501$	8.17403	−	13.6118i	0.365189	−	0.608130i
$502$		0			0
$503$	36.2366			1.61571			0.807856	−	0.589380i	$-0.200628\pi$
$503$	36.2366			1.61571			0.807856	+	0.589380i	$0.200628\pi$
$504$		0			0
$505$	40.7832			1.81483
$506$		0			0
$507$	−13.6339	−	0.234477i	−0.605502	−	0.0104135i
$508$		0			0
$509$			29.0797i			1.28894i	0.764631	+	0.644468i	$0.222921\pi$
$509$			29.0797i			1.28894i	−0.764631	+	0.644468i	$0.777079\pi$
$510$		0			0
$511$	9.01028	−	3.61835i	0.398591	−	0.160067i
$512$		0			0
$513$	18.7057	−	28.8529i	0.825878	−	1.27389i
$514$		0			0
$515$		−	21.6962i		−	0.956047i
$516$		0			0
$517$	2.05121	−	1.18427i	0.0902120	−	0.0520839i
$518$		0			0
$519$	33.6355	+	20.1985i	1.47644	+	0.886616i
$520$		0			0
$521$	−31.1742	+	17.9984i	−1.36576	+	0.788524i	−0.990384	−	0.138346i	$-0.955821\pi$
$521$	−31.1742	+	17.9984i	−1.36576	+	0.788524i	−0.375381	+	0.926871i	$0.622488\pi$
$522$		0			0
$523$	−17.0333	+	29.5026i	−0.744816	+	1.29006i	0.205465	+	0.978664i	$0.434129\pi$
$523$	−17.0333	+	29.5026i	−0.744816	+	1.29006i	−0.950281	+	0.311394i	$0.899204\pi$
$524$		0			0
$525$	−0.841293	−	2.20380i	−0.0367170	−	0.0961819i
$526$		0			0
$527$			21.5389i			0.938248i
$528$		0			0
$529$	21.7085			0.943848
$530$		0			0
$531$	−1.94428	−	3.65212i	−0.0843744	−	0.158489i
$532$		0			0
$533$	−5.95203	+	10.3092i	−0.257811	+	0.446542i
$534$		0			0
$535$	−10.5252	+	18.2302i	−0.455044	+	0.788159i
$536$		0			0
$537$	33.0492	+	19.8464i	1.42618	+	0.856436i
$538$		0			0
$539$	−0.867176	+	2.97686i	−0.0373519	+	0.128223i
$540$		0			0
$541$	−4.04194	+	7.00084i	−0.173777	+	0.300990i	−0.939737	−	0.341898i	$-0.888930\pi$
$541$	−4.04194	+	7.00084i	−0.173777	+	0.300990i	0.765961	+	0.642887i	$0.222264\pi$
$542$		0			0
$543$	6.56335	−	3.64033i	0.281660	−	0.156222i
$544$		0			0
$545$	26.2842	−	15.1752i	1.12589	−	0.650034i
$546$		0			0
$547$	22.5917	+	13.0433i	0.965950	+	0.557691i	0.897999	−	0.439997i	$-0.145021\pi$
$547$	22.5917	+	13.0433i	0.965950	+	0.557691i	0.0679508	+	0.997689i	$0.478354\pi$
$548$		0			0
$549$	1.05848	−	30.7641i	0.0451749	−	1.31298i
$550$		0			0
$551$	28.9660	+	50.1705i	1.23399	+	2.13734i
$552$		0			0
$553$	20.5974	−	8.27152i	0.875891	−	0.351741i
$554$		0			0
$555$	0.197680	−	11.4943i	0.00839106	−	0.487905i
$556$		0			0
$557$	6.12408	+	10.6072i	0.259486	+	0.449442i	0.966104	−	0.258152i	$-0.0831137\pi$
$557$	6.12408	+	10.6072i	0.259486	+	0.449442i	−0.706619	+	0.707595i	$0.749780\pi$
$558$		0			0
$559$	9.97491			0.421894
$560$		0			0
$561$	−1.83317	+	3.05268i	−0.0773965	+	0.128884i
$562$		0			0
$563$	11.4252	−	19.7890i	0.481515	−	0.834008i	−0.518260	−	0.855223i	$-0.673420\pi$
$563$	11.4252	−	19.7890i	0.481515	−	0.834008i	0.999775	+	0.0212152i	$0.00675352\pi$
$564$		0			0
$565$	8.64345	−	4.99030i	0.363633	−	0.209943i
$566$		0			0
$567$	−7.33385	−	22.6542i	−0.307993	−	0.951389i
$568$		0			0
$569$	2.86898	+	4.96922i	0.120274	+	0.208321i	0.919876	−	0.392210i	$-0.128289\pi$
$569$	2.86898	+	4.96922i	0.120274	+	0.208321i	−0.799602	+	0.600531i	$0.794956\pi$
$570$		0			0
$571$	21.6157	+	12.4798i	0.904588	+	0.522264i	0.878686	−	0.477401i	$-0.158421\pi$
$571$	21.6157	+	12.4798i	0.904588	+	0.522264i	0.0259018	+	0.999664i	$0.491754\pi$
$572$		0			0
$573$	−36.9751	−	22.2039i	−1.54466	−	0.927583i
$574$		0			0
$575$			0.584996i			0.0243960i
$576$		0			0
$577$	−18.7652	+	10.8341i	−0.781206	+	0.451030i	−0.836858	−	0.547421i	$-0.815610\pi$
$577$	−18.7652	+	10.8341i	−0.781206	+	0.451030i	0.0556514	+	0.998450i	$0.482276\pi$
$578$		0			0
$579$	−36.9312	−	0.635147i	−1.53481	−	0.0263958i
$580$		0			0
$581$	−25.7384	+	32.8012i	−1.06781	+	1.36082i
$582$		0			0
$583$	1.18477	−	0.684029i	0.0490683	−	0.0283296i
$584$		0			0
$585$	15.9431	+	0.548545i	0.659165	+	0.0226795i
$586$		0			0
$587$	14.7121	−	25.4821i	0.607233	−	1.05176i	−0.384461	−	0.923141i	$-0.625613\pi$
$587$	14.7121	−	25.4821i	0.607233	−	1.05176i	0.991694	−	0.128617i	$-0.0410539\pi$
$588$		0			0
$589$	−15.3550	−	26.5957i	−0.632693	−	1.09586i
$590$		0			0
$591$	15.5684	+	28.0691i	0.640398	+	1.15461i
$592$		0			0
$593$	−25.5917	−	14.7754i	−1.05092	−	0.606752i	−0.128017	−	0.991772i	$-0.540861\pi$
$593$	−25.5917	−	14.7754i	−1.05092	−	0.606752i	−0.922908	+	0.385020i	$0.874194\pi$
$594$		0			0
$595$	10.7463	+	26.7601i	0.440557	+	1.09706i
$596$		0			0
$597$	−1.63843	+	2.72839i	−0.0670565	+	0.111666i
$598$		0			0
$599$	−34.4099	−	19.8666i	−1.40595	−	0.811727i	−0.410957	−	0.911655i	$-0.634805\pi$
$599$	−34.4099	−	19.8666i	−1.40595	−	0.811727i	−0.994995	+	0.0999281i	$0.968139\pi$
$600$		0			0
$601$	9.64604	+	5.56915i	0.393470	+	0.227170i	0.683663	−	0.729798i	$-0.260386\pi$
$601$	9.64604	+	5.56915i	0.393470	+	0.227170i	−0.290192	+	0.956968i	$0.593719\pi$
$602$		0			0
$603$	−6.44520	+	3.43122i	−0.262469	+	0.139730i
$604$		0			0
$605$			25.3711i			1.03148i
$606$		0			0
$607$	−34.6629			−1.40692			−0.703461	−	0.710734i	$-0.748363\pi$
$607$	−34.6629			−1.40692			−0.703461	+	0.710734i	$0.748363\pi$
$608$		0			0
$609$	39.6114	+	6.34887i	1.60514	+	0.257269i
$610$		0			0
$611$	10.4859	+	6.05406i	0.424215	+	0.244921i
$612$		0			0
$613$	−16.1482	−	27.9695i	−0.652219	−	1.12968i	−0.982583	−	0.185823i	$-0.940505\pi$
$613$	−16.1482	−	27.9695i	−0.652219	−	1.12968i	0.330365	−	0.943853i	$-0.392828\pi$
$614$		0			0
$615$	−11.0085	+	18.3319i	−0.443906	+	0.739213i
$616$		0			0
$617$	−22.0343	−	38.1645i	−0.887067	−	1.53644i	−0.843327	−	0.537401i	$-0.819406\pi$
$617$	−22.0343	−	38.1645i	−0.887067	−	1.53644i	−0.0437400	−	0.999043i	$-0.513927\pi$
$618$		0			0
$619$	−9.30313			−0.373924			−0.186962	−	0.982367i	$-0.559864\pi$
$619$	−9.30313			−0.373924			−0.186962	+	0.982367i	$0.559864\pi$
$620$		0			0
$621$	−0.304507	+	5.89729i	−0.0122194	+	0.236650i
$622$		0			0
$623$	12.7993	+	10.0433i	0.512792	+	0.402377i
$624$		0			0
$625$	−27.3088			−1.09235
$626$		0			0
$627$	0.0873020	−	5.07625i	0.00348651	−	0.202726i
$628$		0			0
$629$			13.1179i			0.523044i
$630$		0			0
$631$			28.6463i			1.14039i	0.821509	+	0.570196i	$0.193133\pi$
$631$			28.6463i			1.14039i	−0.821509	+	0.570196i	$0.806867\pi$
$632$		0			0
$633$	30.0560	+	18.0490i	1.19462	+	0.717383i
$634$		0			0
$635$	46.1826			1.83270
$636$		0			0
$637$	−15.3957	+	3.76982i	−0.609999	+	0.149366i
$638$		0			0
$639$	−18.3401	−	11.4471i	−0.725523	−	0.452839i
$640$		0			0
$641$	2.03251			0.0802795			0.0401397	−	0.999194i	$-0.487220\pi$
$641$	2.03251			0.0802795			0.0401397	+	0.999194i	$0.487220\pi$
$642$		0			0
$643$	−14.7575	−	25.5608i	−0.581980	−	1.00802i	−0.995245	−	0.0974077i	$-0.968945\pi$
$643$	−14.7575	−	25.5608i	−0.581980	−	1.00802i	0.413265	−	0.910611i	$-0.364388\pi$
$644$		0			0
$645$	17.9153	+	0.308110i	0.705414	+	0.0121318i
$646$		0			0
$647$	8.18434	+	14.1757i	0.321759	+	0.557304i	0.980851	−	0.194759i	$-0.0623924\pi$
$647$	8.18434	+	14.1757i	0.321759	+	0.557304i	−0.659092	+	0.752063i	$0.729059\pi$
$648$		0			0
$649$	−0.529037	−	0.305440i	−0.0207665	−	0.0119896i
$650$		0			0
$651$	−20.9982	−	3.36557i	−0.822986	−	0.131907i
$652$		0			0
$653$	0.178525			0.00698623			0.00349312	−	0.999994i	$-0.498888\pi$
$653$	0.178525			0.00698623			0.00349312	+	0.999994i	$0.498888\pi$
$654$		0			0
$655$			40.0950i			1.56664i
$656$		0			0
$657$	−0.378582	+	11.0032i	−0.0147699	+	0.429276i
$658$		0			0
$659$	−17.4428	−	10.0706i	−0.679474	−	0.392294i	0.120183	−	0.992752i	$-0.461652\pi$
$659$	−17.4428	−	10.0706i	−0.679474	−	0.392294i	−0.799657	+	0.600457i	$0.794985\pi$
$660$		0			0
$661$	−7.59315	−	4.38391i	−0.295339	−	0.170514i	0.345008	−	0.938600i	$-0.387876\pi$
$661$	−7.59315	−	4.38391i	−0.295339	−	0.170514i	−0.640347	+	0.768086i	$0.721210\pi$
$662$		0			0
$663$	−18.2005	−	0.313014i	−0.706848	−	0.0121565i
$664$		0			0
$665$	−32.3466	−	25.3817i	−1.25435	−	0.984261i
$666$		0			0
$667$	−8.61584	−	4.97436i	−0.333607	−	0.192608i
$668$		0			0
$669$	1.70443	+	0.0293129i	0.0658969	+	0.00113330i
$670$		0			0
$671$	−2.27246	−	3.93602i	−0.0877274	−	0.151948i
$672$		0			0
$673$	−1.04120	+	1.80341i	−0.0401353	+	0.0695164i	−0.885395	−	0.464839i	$-0.846112\pi$
$673$	−1.04120	+	1.80341i	−0.0401353	+	0.0695164i	0.845260	+	0.534355i	$0.179446\pi$
$674$		0			0
$675$	2.67121	+	0.137928i	0.102815	+	0.00530886i
$676$		0			0
$677$	−12.0742	+	6.97106i	−0.464050	+	0.267919i	−0.713746	−	0.700405i	$-0.753003\pi$
$677$	−12.0742	+	6.97106i	−0.464050	+	0.267919i	0.249696	+	0.968324i	$0.419669\pi$
$678$		0			0
$679$	35.9289	+	28.1927i	1.37882	+	1.08194i
$680$		0			0
$681$	−11.0834	−	19.9828i	−0.424715	−	0.765742i
$682$		0			0
$683$	−13.5049	+	7.79708i	−0.516752	+	0.298347i	−0.735605	−	0.677411i	$-0.763102\pi$
$683$	−13.5049	+	7.79708i	−0.516752	+	0.298347i	0.218853	+	0.975758i	$0.429769\pi$
$684$		0			0
$685$		−	8.25120i		−	0.315262i
$686$		0			0
$687$	8.60278	−	4.77149i	0.328216	−	0.182044i
$688$		0			0
$689$	6.05665	+	3.49681i	0.230740	+	0.133218i
$690$		0			0
$691$	0.986734	+	1.70907i	0.0375371	+	0.0650162i	0.884184	−	0.467139i	$-0.154715\pi$
$691$	0.986734	+	1.70907i	0.0375371	+	0.0650162i	−0.846646	+	0.532156i	$0.821382\pi$
$692$		0			0
$693$	−2.68962	−	2.26416i	−0.102170	−	0.0860083i
$694$		0			0
$695$	−35.2278	+	20.3388i	−1.33627	+	0.771493i
$696$		0			0
$697$	12.2001	−	21.1311i	0.462110	−	0.800399i
$698$		0			0
$699$	25.7343	+	0.442582i	0.973361	+	0.0167400i
$700$		0			0
$701$	−3.57171			−0.134902			−0.0674508	−	0.997723i	$-0.521487\pi$
$701$	−3.57171			−0.134902			−0.0674508	+	0.997723i	$0.521487\pi$
$702$		0			0
$703$	−9.35173	−	16.1977i	−0.352707	−	0.610907i
$704$		0			0
$705$	18.6461	+	11.1972i	0.702253	+	0.421711i
$706$		0			0
$707$	6.49047	−	45.4874i	0.244099	−	1.71073i
$708$		0			0
$709$	−12.6279	−	21.8721i	−0.474250	−	0.821425i	0.525316	−	0.850907i	$-0.323947\pi$
$709$	−12.6279	−	21.8721i	−0.474250	−	0.821425i	−0.999565	+	0.0294829i	$0.990614\pi$
$710$		0			0
$711$	−0.865434	+	25.1533i	−0.0324563	+	0.943321i
$712$		0			0
$713$	4.56731	+	2.63694i	0.171047	+	0.0987541i
$714$		0			0
$715$	2.03979	−	1.17767i	0.0762839	−	0.0440425i
$716$		0			0
$717$	26.8307	+	16.1121i	1.00201	+	0.601718i
$718$		0			0
$719$	19.0045	−	32.9168i	0.708749	−	1.22759i	−0.256572	−	0.966525i	$-0.582593\pi$
$719$	19.0045	−	32.9168i	0.708749	−	1.22759i	0.965321	−	0.261065i	$-0.0840737\pi$
$720$		0			0
$721$	−24.1987	−	3.45285i	−0.901206	−	0.128591i
$722$		0			0
$723$	31.4299	−	17.4324i	1.16889	−	0.648318i
$724$		0			0
$725$	−2.25317	+	3.90260i	−0.0836805	+	0.144939i
$726$		0			0
$727$	8.14853	−	14.1137i	0.302212	−	0.523447i	−0.674424	−	0.738344i	$-0.735608\pi$
$727$	8.14853	−	14.1137i	0.302212	−	0.523447i	0.976637	+	0.214897i	$0.0689415\pi$
$728$		0			0
$729$	26.8564	+	2.78088i	0.994682	+	0.102996i
$730$		0			0
$731$	−20.4459			−0.756218
$732$		0			0
$733$		−	12.7119i		−	0.469525i	−0.972053	−	0.234763i	$-0.924569\pi$
$733$		−	12.7119i		−	0.469525i	0.972053	−	0.234763i	$-0.0754313\pi$
$734$		0			0
$735$	−27.7676	+	6.29518i	−1.02422	+	0.232201i
$736$		0			0
$737$	−0.539034	+	0.933634i	−0.0198556	+	0.0343909i
$738$		0			0
$739$	21.2467	−	12.2668i	0.781574	−	0.451242i	−0.0554141	−	0.998463i	$-0.517648\pi$
$739$	21.2467	−	12.2668i	0.781574	−	0.451242i	0.836988	+	0.547222i	$0.184315\pi$
$740$		0			0
$741$	22.6967	−	12.5886i	0.833783	−	0.462454i
$742$		0			0
$743$	−25.5305	+	14.7400i	−0.936624	+	0.540760i	−0.888900	−	0.458101i	$-0.848530\pi$
$743$	−25.5305	+	14.7400i	−0.936624	+	0.540760i	−0.0477233	+	0.998861i	$0.515197\pi$
$744$		0			0
$745$		−	14.2905i		−	0.523563i
$746$		0			0
$747$	−22.2164	−	41.7313i	−0.812856	−	1.52687i
$748$		0			0
$749$	18.6579	+	14.6405i	0.681745	+	0.534951i
$750$		0			0
$751$		−	39.7434i		−	1.45026i	−0.688613	−	0.725129i	$-0.741780\pi$
$751$		−	39.7434i		−	1.45026i	0.688613	−	0.725129i	$-0.258220\pi$
$752$		0			0
$753$	−8.00651	−	14.4354i	−0.291773	−	0.526054i
$754$		0			0
$755$	6.13526			0.223285
$756$		0			0
$757$	−3.23130			−0.117444			−0.0587218	−	0.998274i	$-0.518702\pi$
$757$	−3.23130			−0.117444			−0.0587218	+	0.998274i	$0.518702\pi$
$758$		0			0
$759$	0.422891	+	0.762454i	0.0153500	+	0.0276753i
$760$		0			0
$761$			36.8650i			1.33636i	0.744001	+	0.668178i	$0.232926\pi$
$761$			36.8650i			1.33636i	−0.744001	+	0.668178i	$0.767074\pi$
$762$		0			0
$763$	−12.7426	−	31.7310i	−0.461312	−	1.14874i
$764$		0			0
$765$	−32.6790	−	1.12437i	−1.18151	−	0.0406517i
$766$		0			0
$767$		−	3.12286i		−	0.112760i
$768$		0			0
$769$	−21.3838	+	12.3460i	−0.771120	+	0.445206i	−0.833274	−	0.552860i	$-0.813536\pi$
$769$	−21.3838	+	12.3460i	−0.771120	+	0.445206i	0.0621539	+	0.998067i	$0.480203\pi$
$770$		0			0
$771$	17.2595	−	9.57292i	0.621587	−	0.344760i
$772$		0			0
$773$	−18.1598	+	10.4846i	−0.653164	+	0.377104i	−0.789667	−	0.613535i	$-0.789747\pi$
$773$	−18.1598	+	10.4846i	−0.653164	+	0.377104i	0.136503	+	0.990640i	$0.456414\pi$
$774$		0			0
$775$	1.19442	−	2.06879i	0.0429047	−	0.0743131i
$776$		0			0
$777$	−12.7886	−	2.04975i	−0.458790	−	0.0735343i
$778$		0			0
$779$			34.7897i			1.24647i
$780$		0			0
$781$	−3.19204			−0.114220
$782$		0			0
$783$	−24.7454	+	38.1689i	−0.884327	+	1.36404i
$784$		0			0
$785$	−22.0654	+	38.2184i	−0.787548	+	1.36407i
$786$		0			0
$787$	7.44418	−	12.8937i	0.265356	−	0.459611i	−0.702300	−	0.711881i	$-0.747844\pi$
$787$	7.44418	−	12.8937i	0.265356	−	0.459611i	0.967657	+	0.252270i	$0.0811770\pi$
$788$		0			0
$789$	9.44802	−	5.24030i	0.336359	−	0.186560i
$790$		0			0
$791$	−4.19033	−	10.4346i	−0.148991	−	0.371012i
$792$		0			0
$793$	11.6170	−	20.1212i	0.412532	−	0.714526i
$794$		0			0
$795$	10.7700	+	6.46747i	0.381971	+	0.229378i
$796$		0			0
$797$	17.5335	−	10.1230i	0.621068	−	0.358574i	−0.156216	−	0.987723i	$-0.549930\pi$
$797$	17.5335	−	10.1230i	0.621068	−	0.358574i	0.777285	+	0.629149i	$0.216596\pi$
$798$		0			0
$799$	−21.4933	−	12.4092i	−0.760380	−	0.439005i
$800$		0			0
$801$	−16.2838	+	8.66901i	−0.575361	+	0.306304i
$802$		0			0
$803$	0.812779	+	1.40778i	0.0286824	+	0.0496793i
$804$		0			0
$805$	6.99011	+	0.997400i	0.246369	+	0.0351537i
$806$		0			0
$807$	38.6750	+	23.2247i	1.36142	+	0.817550i
$808$		0			0
$809$	−17.2300	−	29.8433i	−0.605775	−	1.04923i	−0.991928	−	0.126799i	$-0.959530\pi$
$809$	−17.2300	−	29.8433i	−0.605775	−	1.04923i	0.386153	−	0.922435i	$-0.373804\pi$
$810$		0			0
$811$	−49.5905			−1.74136			−0.870679	−	0.491852i	$-0.836320\pi$
$811$	−49.5905			−1.74136			−0.870679	+	0.491852i	$0.836320\pi$
$812$		0			0
$813$	−35.7374	−	0.614616i	−1.25336	−	0.0215555i
$814$		0			0
$815$	3.93820	−	6.82116i	0.137949	−	0.238935i
$816$		0			0
$817$	25.2461	−	14.5758i	0.883249	−	0.509944i
$818$		0			0
$819$	3.14909	−	17.6947i	0.110038	−	0.618304i
$820$		0			0
$821$	−19.5801	−	33.9137i	−0.683349	−	1.18360i	−0.973953	−	0.226752i	$-0.927189\pi$
$821$	−19.5801	−	33.9137i	−0.683349	−	1.18360i	0.290604	−	0.956844i	$-0.406144\pi$
$822$		0			0
$823$	33.6699	+	19.4393i	1.17366	+	0.677612i	0.954539	−	0.298087i	$-0.0963484\pi$
$823$	33.6699	+	19.4393i	1.17366	+	0.677612i	0.219119	+	0.975698i	$0.429682\pi$
$824$		0			0
$825$	0.345358	−	0.191551i	0.0120238	−	0.00666895i
$826$		0			0
$827$		−	41.0227i		−	1.42650i	−0.700909	−	0.713250i	$-0.747222\pi$
$827$		−	41.0227i		−	1.42650i	0.700909	−	0.713250i	$-0.252778\pi$
$828$		0			0
$829$	−11.4951	+	6.63672i	−0.399242	+	0.230503i	−0.686157	−	0.727453i	$-0.740704\pi$
$829$	−11.4951	+	6.63672i	−0.399242	+	0.230503i	0.286915	+	0.957956i	$0.407370\pi$
$830$		0			0
$831$	−10.1419	−	18.2854i	−0.351820	−	0.634315i
$832$		0			0
$833$	31.5570	−	7.72712i	1.09338	−	0.267729i
$834$		0			0
$835$	18.6430	−	10.7635i	0.645168	−	0.372488i
$836$		0			0
$837$	13.1177	−	20.2335i	0.453413	−	0.699373i
$838$		0			0
$839$	15.9028	−	27.5445i	0.549025	−	0.950940i	−0.449316	−	0.893373i	$-0.648332\pi$
$839$	15.9028	−	27.5445i	0.549025	−	0.950940i	0.998342	−	0.0575672i	$-0.0183344\pi$
$840$		0			0
$841$	−23.8184	−	41.2547i	−0.821325	−	1.42258i
$842$		0			0
$843$	−12.7217	−	0.218790i	−0.438159	−	0.00753552i
$844$		0			0
$845$	−16.0110	−	9.24393i	−0.550793	−	0.318001i
$846$		0			0
$847$	28.2976	+	4.03770i	0.972316	+	0.138737i
$848$		0			0
$849$	29.9710	+	0.515445i	1.02860	+	0.0176900i
$850$		0			0
$851$	2.78164	+	1.60598i	0.0953535	+	0.0550524i
$852$		0			0
$853$	−0.551551	−	0.318438i	−0.0188847	−	0.0109031i	0.490528	−	0.871425i	$-0.336804\pi$
$853$	−0.551551	−	0.318438i	−0.0188847	−	0.0109031i	−0.509413	+	0.860522i	$0.670137\pi$
$854$		0			0
$855$	41.1529	−	21.9085i	1.40740	−	0.749255i
$856$		0			0
$857$			4.54984i			0.155420i	0.996976	+	0.0777098i	$0.0247608\pi$
$857$			4.54984i			0.155420i	−0.996976	+	0.0777098i	$0.975239\pi$
$858$		0			0
$859$	13.5634			0.462776			0.231388	−	0.972862i	$-0.425673\pi$
$859$	13.5634			0.462776			0.231388	+	0.972862i	$0.425673\pi$
$860$		0			0
$861$	18.6944	+	15.1957i	0.637104	+	0.517869i
$862$		0			0
$863$	−14.1996	−	8.19817i	−0.483361	−	0.279069i	0.238455	−	0.971154i	$-0.423359\pi$
$863$	−14.1996	−	8.19817i	−0.483361	−	0.279069i	−0.721816	+	0.692085i	$0.756692\pi$
$864$		0			0
$865$	26.5973	+	46.0680i	0.904337	+	1.56636i
$866$		0			0
$867$	7.86555	+	0.135273i	0.267128	+	0.00459410i
$868$		0			0
$869$	1.85801	+	3.21816i	0.0630285	+	0.109169i
$870$		0			0
$871$	−5.51117			−0.186739
$872$		0			0
$873$	−45.7105	+	24.3348i	−1.54706	+	0.823608i
$874$		0			0
$875$	−3.93647	+	27.5881i	−0.133077	+	0.932647i
$876$		0			0
$877$	−49.5189			−1.67214			−0.836068	−	0.548626i	$-0.815151\pi$
$877$	−49.5189			−1.67214			−0.836068	+	0.548626i	$0.815151\pi$
$878$		0			0
$879$	1.65607	+	0.994486i	0.0558577	+	0.0335432i
$880$		0			0
$881$			16.2659i			0.548012i	0.961728	+	0.274006i	$0.0883488\pi$
$881$			16.2659i			0.548012i	−0.961728	+	0.274006i	$0.911651\pi$
$882$		0			0
$883$		−	26.6667i		−	0.897404i	−0.893681	−	0.448702i	$-0.851886\pi$
$883$		−	26.6667i		−	0.897404i	0.893681	−	0.448702i	$-0.148114\pi$
$884$		0			0
$885$	0.0964604	−	5.60877i	0.00324248	−	0.188537i
$886$		0			0
$887$	53.9957			1.81300			0.906499	−	0.422208i	$-0.138745\pi$
$887$	53.9957			1.81300			0.906499	+	0.422208i	$0.138745\pi$
$888$		0			0
$889$	7.34976	−	51.5096i	0.246503	−	1.72758i
$890$		0			0
$891$	3.58123	−	1.75124i	0.119976	−	0.0586687i
$892$		0			0
$893$	35.3860			1.18415
$894$		0			0
$895$	26.1337	+	45.2649i	0.873554	+	1.51304i
$896$		0			0
$897$	−2.29460	+	3.82108i	−0.0766146	+	0.127582i
$898$		0			0
$899$	20.3128	+	35.1828i	0.677470	+	1.17341i
$900$		0			0
$901$	−12.4145	−	7.16752i	−0.413587	−	0.238785i
$902$		0			0
$903$	3.19479	−	19.9327i	0.106316	−	0.663318i
$904$		0			0
$905$	10.1759			0.338257
$906$		0			0
$907$		−	45.5452i		−	1.51230i	−0.654397	−	0.756151i	$-0.727077\pi$
$907$		−	45.5452i		−	1.51230i	0.654397	−	0.756151i	$-0.272923\pi$
$908$		0			0
$909$	44.1977	+	27.5862i	1.46594	+	0.914977i
$910$		0			0
$911$	−10.7265	−	6.19296i	−0.355385	−	0.205182i	0.311669	−	0.950191i	$-0.399112\pi$
$911$	−10.7265	−	6.19296i	−0.355385	−	0.205182i	−0.667055	+	0.745009i	$0.732445\pi$
$912$		0			0
$913$	−6.04508	−	3.49013i	−0.200063	−	0.115506i
$914$		0			0
$915$	21.4861	−	35.7796i	0.710307	−	1.18284i
$916$		0			0
$917$	44.7198	+	6.38094i	1.47678	+	0.210717i
$918$		0			0
$919$	−38.9097	−	22.4645i	−1.28351	−	0.741037i	−0.306024	−	0.952024i	$-0.598999\pi$
$919$	−38.9097	−	22.4645i	−1.28351	−	0.741037i	−0.977489	+	0.210987i	$0.932332\pi$
$920$		0			0
$921$	25.6622	+	46.2678i	0.845599	+	1.52458i
$922$		0			0
$923$	−8.15897	−	14.1318i	−0.268556	−	0.465152i
$924$		0			0
$925$	0.727439	−	1.25996i	0.0239181	−	0.0414273i
$926$		0			0
$927$	14.6755	−	23.5126i	0.482007	−	0.772255i
$928$		0			0
$929$	22.1152	−	12.7682i	0.725578	−	0.418912i	−0.0912245	−	0.995830i	$-0.529078\pi$
$929$	22.1152	−	12.7682i	0.725578	−	0.418912i	0.816802	+	0.576918i	$0.195745\pi$
$930$		0			0
$931$	−33.4572	+	32.0382i	−1.09651	+	1.05001i
$932$		0			0
$933$	11.9424	+	0.205388i	0.390978	+	0.00672409i
$934$		0			0
$935$	−4.18102	+	2.41392i	−0.136734	+	0.0789435i
$936$		0			0
$937$		−	29.7933i		−	0.973304i	−0.873596	−	0.486652i	$-0.838218\pi$
$937$		−	29.7933i		−	0.973304i	0.873596	−	0.486652i	$-0.161782\pi$
$938$		0			0
$939$	20.8141	+	12.4991i	0.679243	+	0.407893i
$940$		0			0
$941$	32.9292	+	19.0117i	1.07346	+	0.619763i	0.929125	−	0.369766i	$-0.120562\pi$
$941$	32.9292	+	19.0117i	1.07346	+	0.619763i	0.144336	+	0.989529i	$0.453895\pi$
$942$		0			0
$943$	−2.98723	−	5.17404i	−0.0972777	−	0.168490i
$944$		0			0
$945$	6.20244	−	31.6831i	0.201765	−	1.03065i
$946$		0			0
$947$	23.9431	−	13.8235i	0.778045	−	0.449205i	−0.0576920	−	0.998334i	$-0.518374\pi$
$947$	23.9431	−	13.8235i	0.778045	−	0.449205i	0.835737	+	0.549130i	$0.185041\pi$
$948$		0			0
$949$	−4.15499	+	7.19666i	−0.134877	+	0.233613i
$950$		0			0
$951$	−17.9920	+	29.9612i	−0.583431	+	0.971557i
$952$		0			0
$953$	38.4588			1.24580			0.622901	−	0.782301i	$-0.285954\pi$
$953$	38.4588			1.24580			0.622901	+	0.782301i	$0.285954\pi$
$954$		0			0
$955$	−29.2381	−	50.6419i	−0.946123	−	1.63873i
$956$		0			0
$957$	−0.115490	+	6.71525i	−0.00373326	+	0.217073i
$958$		0			0
$959$	−9.20294	−	1.31314i	−0.297178	−	0.0424036i
$960$		0			0
$961$	4.73206	+	8.19616i	0.152647	+	0.264392i
$962$		0			0
$963$	−23.7375	+	12.6371i	−0.764929	+	0.407224i
$964$		0			0
$965$	−43.3701	−	25.0397i	−1.39613	−	0.806058i
$966$		0			0
$967$	1.40644	−	0.812009i	0.0452281	−	0.0261125i	−0.477215	−	0.878786i	$-0.658354\pi$
$967$	1.40644	−	0.812009i	0.0452281	−	0.0261125i	0.522444	+	0.852674i	$0.325021\pi$
$968$		0			0
$969$	−46.5221	+	25.8032i	−1.49450	+	0.828919i
$970$		0			0
$971$	−19.2966	+	33.4227i	−0.619257	+	1.07258i	0.370365	+	0.928886i	$0.379233\pi$
$971$	−19.2966	+	33.4227i	−0.619257	+	1.07258i	−0.989622	+	0.143698i	$0.954101\pi$
$972$		0			0
$973$	17.0784	+	42.5279i	0.547508	+	1.36338i
$974$		0			0
$975$	1.73078	+	1.03935i	0.0554294	+	0.0332860i
$976$		0			0
$977$	−6.20038	+	10.7394i	−0.198368	+	0.343583i	−0.947999	−	0.318272i	$-0.896897\pi$
$977$	−6.20038	+	10.7394i	−0.198368	+	0.343583i	0.749632	+	0.661855i	$0.230231\pi$
$978$		0			0
$979$	−1.36187	+	2.35883i	−0.0435257	+	0.0753886i
$980$		0			0
$981$	38.7494	+	1.33323i	1.23717	+	0.0425668i
$982$		0			0
$983$	16.9967			0.542112			0.271056	−	0.962564i	$-0.412627\pi$
$983$	16.9967			0.542112			0.271056	+	0.962564i	$0.412627\pi$
$984$		0			0
$985$			43.5185i			1.38662i
$986$		0			0
$987$	15.4562	−	19.0149i	0.491976	−	0.605249i
$988$		0			0
$989$	−2.50313	+	4.33554i	−0.0795947	+	0.137862i
$990$		0			0
$991$	39.0008	−	22.5171i	1.23890	−	0.715280i	0.270032	−	0.962851i	$-0.412966\pi$
$991$	39.0008	−	22.5171i	1.23890	−	0.715280i	0.968870	+	0.247571i	$0.0796324\pi$
$992$		0			0
$993$	−47.9578	−	28.7992i	−1.52189	−	0.913914i
$994$		0			0
$995$	−3.73687	+	2.15748i	−0.118467	+	0.0683967i
$996$		0			0
$997$			8.00101i			0.253395i	0.991941	+	0.126697i	$0.0404377\pi$
$997$			8.00101i			0.253395i	−0.991941	+	0.126697i	$0.959562\pi$
$998$		0			0
$999$	7.98909	−	12.3229i	0.252764	−	0.389879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.i.943.11	yes	32
3.2	odd	2		3024.2.bf.i.2287.3		32
4.3	odd	2	inner	1008.2.bf.i.943.6	yes	32
7.3	odd	6		1008.2.cz.i.367.6	yes	32
9.4	even	3		1008.2.cz.i.607.11	yes	32
9.5	odd	6		3024.2.cz.i.1279.3		32
12.11	even	2		3024.2.bf.i.2287.4		32
21.17	even	6		3024.2.cz.i.2719.4		32
28.3	even	6		1008.2.cz.i.367.11	yes	32
36.23	even	6		3024.2.cz.i.1279.4		32
36.31	odd	6		1008.2.cz.i.607.6	yes	32
63.31	odd	6	inner	1008.2.bf.i.31.6	✓	32
63.59	even	6		3024.2.bf.i.1711.13		32
84.59	odd	6		3024.2.cz.i.2719.3		32
252.31	even	6	inner	1008.2.bf.i.31.11	yes	32
252.59	odd	6		3024.2.bf.i.1711.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.6	✓	32	63.31	odd	6	inner
1008.2.bf.i.31.11	yes	32	252.31	even	6	inner
1008.2.bf.i.943.6	yes	32	4.3	odd	2	inner
1008.2.bf.i.943.11	yes	32	1.1	even	1	trivial
1008.2.cz.i.367.6	yes	32	7.3	odd	6
1008.2.cz.i.367.11	yes	32	28.3	even	6
1008.2.cz.i.607.6	yes	32	36.31	odd	6
1008.2.cz.i.607.11	yes	32	9.4	even	3
3024.2.bf.i.1711.13		32	63.59	even	6
3024.2.bf.i.1711.14		32	252.59	odd	6
3024.2.bf.i.2287.3		32	3.2	odd	2
3024.2.bf.i.2287.4		32	12.11	even	2
3024.2.cz.i.1279.3		32	9.5	odd	6
3024.2.cz.i.1279.4		32	36.23	even	6
3024.2.cz.i.2719.3		32	84.59	odd	6
3024.2.cz.i.2719.4		32	21.17	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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.840104 + 1.51467i) q^{3} +2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} +(-1.58845 + 2.54496i) q^{9} +O(q^{10})\)	\(q+(0.840104 + 1.51467i) q^{3} +2.34835i q^{5} +(2.61922 + 0.373730i) q^{7} +(-1.58845 + 2.54496i) q^{9} +0.442942i q^{11} +(-1.96099 + 1.13218i) q^{13} +(-3.55698 + 1.97286i) q^{15} +(4.01950 - 2.32066i) q^{17} +(-3.30879 + 5.73100i) q^{19} +(1.63434 + 4.28123i) q^{21} -1.13645i q^{23} -0.514760 q^{25} +(-5.18924 - 0.267947i) q^{27} +(4.37712 - 7.58140i) q^{29} +(-2.32034 + 4.01894i) q^{31} +(-0.670912 + 0.372118i) q^{33} +(-0.877649 + 6.15086i) q^{35} +(-1.41316 + 2.44767i) q^{37} +(-3.36231 - 2.01911i) q^{39} +(4.55283 - 2.62858i) q^{41} +(-3.81500 - 2.20259i) q^{43} +(-5.97646 - 3.73024i) q^{45} +(-2.67363 - 4.63087i) q^{47} +(6.72065 + 1.95776i) q^{49} +(6.89183 + 4.13862i) q^{51} +(-1.54428 - 2.67478i) q^{53} -1.04018 q^{55} +(-11.4603 - 0.197096i) q^{57} +(-0.689570 + 1.19437i) q^{59} +(-8.88607 + 5.13038i) q^{61} +(-5.11163 + 6.07217i) q^{63} +(-2.65875 - 4.60510i) q^{65} +(2.10780 + 1.21694i) q^{67} +(1.72134 - 0.954732i) q^{69} +7.20644i q^{71} +(3.17824 - 1.83496i) q^{73} +(-0.432452 - 0.779691i) q^{75} +(-0.165541 + 1.16016i) q^{77} +(7.26542 - 4.19469i) q^{79} +(-3.95365 - 8.08509i) q^{81} +(-7.87941 + 13.6475i) q^{83} +(5.44973 + 9.43920i) q^{85} +(15.1606 + 0.260733i) q^{87} +(5.32537 + 3.07461i) q^{89} +(-5.55940 + 2.23255i) q^{91} +(-8.03670 - 0.138216i) q^{93} +(-13.4584 - 7.77021i) q^{95} +(14.9489 + 8.63074i) q^{97} +(-1.12727 - 0.703592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9}+O(q^{10}) \) 32 * q - 4 * q^9	\( 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77} - 16 q^{81} - 12 q^{85} - 18 q^{89} + 58 q^{93} - 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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