LMFDB - Embedded newform 1008.2.cz.g.367.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.6
Character	$\chi$	$=$	1008.367
Dual form			1008.2.cz.g.607.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.706216 - 1.58154i) q^{3} +(-1.27943 - 0.738680i) q^{5} +(1.34028 + 2.28115i) q^{7} +(-2.00252 + 2.23381i) q^{9} +O(q^{10})$	\(q+(-0.706216 - 1.58154i) q^{3} +(-1.27943 - 0.738680i) q^{5} +(1.34028 + 2.28115i) q^{7} +(-2.00252 + 2.23381i) q^{9} +(2.40250 - 1.38709i) q^{11} +(0.955418 - 0.551611i) q^{13} +(-0.264694 + 2.54514i) q^{15} +(1.69424 + 0.978168i) q^{17} +(3.46466 + 6.00097i) q^{19} +(2.66120 - 3.73068i) q^{21} +(0.0279687 + 0.0161477i) q^{23} +(-1.40870 - 2.43994i) q^{25} +(4.94707 + 1.58950i) q^{27} +(4.53801 - 7.86007i) q^{29} +0.704107 q^{31} +(-3.89041 - 2.82006i) q^{33} +(-0.0297482 - 3.90862i) q^{35} +(-1.92560 - 3.33523i) q^{37} +(-1.54713 - 1.12147i) q^{39} +(-2.23630 + 1.29113i) q^{41} +(8.95705 + 5.17136i) q^{43} +(4.21216 - 1.37879i) q^{45} +4.28149 q^{47} +(-3.40732 + 6.11475i) q^{49} +(0.350511 - 3.37030i) q^{51} +(3.49123 - 6.04699i) q^{53} -4.09845 q^{55} +(7.04395 - 9.71747i) q^{57} +1.13799 q^{59} -2.58999i q^{61} +(-7.77960 - 1.57412i) q^{63} -1.62986 q^{65} -11.6636i q^{67} +(0.00578629 - 0.0556373i) q^{69} -15.6777i q^{71} +(-4.41573 - 2.54942i) q^{73} +(-2.86401 + 3.95104i) q^{75} +(6.38417 + 3.62140i) q^{77} +8.38410i q^{79} +(-0.979853 - 8.94650i) q^{81} +(-5.34759 + 9.26231i) q^{83} +(-1.44511 - 2.50300i) q^{85} +(-15.6358 - 1.62613i) q^{87} +(8.83761 - 5.10240i) q^{89} +(2.53883 + 1.44015i) q^{91} +(-0.497252 - 1.11357i) q^{93} -10.2371i q^{95} +(6.95620 + 4.01617i) q^{97} +(-1.71256 + 8.14441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.706216	−	1.58154i	−0.407734	−	0.913101i
$3$	−0.706216	−	1.58154i	−0.407734	−	0.913101i
$4$		0			0
$5$	−1.27943	−	0.738680i	−0.572179	−	0.330348i	0.185840	−	0.982580i	$-0.440499\pi$
$5$	−1.27943	−	0.738680i	−0.572179	−	0.330348i	−0.758019	+	0.652232i	$0.773833\pi$
$6$		0			0
$7$	1.34028	+	2.28115i	0.506577	+	0.862195i
$7$	1.34028	+	2.28115i	0.506577	+	0.862195i
$8$		0			0
$9$	−2.00252	+	2.23381i	−0.667506	+	0.744605i
$10$		0			0
$11$	2.40250	−	1.38709i	0.724382	−	0.418222i	−0.0919816	−	0.995761i	$-0.529320\pi$
$11$	2.40250	−	1.38709i	0.724382	−	0.418222i	0.816363	+	0.577539i	$0.195987\pi$
$12$		0			0
$13$	0.955418	−	0.551611i	0.264985	−	0.152989i	−0.361621	−	0.932325i	$-0.617777\pi$
$13$	0.955418	−	0.551611i	0.264985	−	0.152989i	0.626607	+	0.779336i	$0.284443\pi$
$14$		0			0
$15$	−0.264694	+	2.54514i	−0.0683438	+	0.657151i
$16$		0			0
$17$	1.69424	+	0.978168i	0.410913	+	0.237241i	0.691182	−	0.722681i	$-0.257090\pi$
$17$	1.69424	+	0.978168i	0.410913	+	0.237241i	−0.280269	+	0.959921i	$0.590424\pi$
$18$		0			0
$19$	3.46466	+	6.00097i	0.794847	+	1.37672i	0.922936	+	0.384953i	$0.125782\pi$
$19$	3.46466	+	6.00097i	0.794847	+	1.37672i	−0.128089	+	0.991763i	$0.540884\pi$
$20$		0			0
$21$	2.66120	−	3.73068i	0.580722	−	0.814102i
$22$		0			0
$23$	0.0279687	+	0.0161477i	0.00583188	+	0.00336704i	0.502913	−	0.864337i	$-0.332262\pi$
$23$	0.0279687	+	0.0161477i	0.00583188	+	0.00336704i	−0.497081	+	0.867704i	$0.665595\pi$
$24$		0			0
$25$	−1.40870	−	2.43994i	−0.281741	−	0.487989i
$26$		0			0
$27$	4.94707	+	1.58950i	0.952064	+	0.305899i
$28$		0			0
$29$	4.53801	−	7.86007i	0.842688	−	1.45958i	−0.0449259	−	0.998990i	$-0.514305\pi$
$29$	4.53801	−	7.86007i	0.842688	−	1.45958i	0.887614	−	0.460588i	$-0.152361\pi$
$30$		0			0
$31$	0.704107			0.126461			0.0632306	−	0.997999i	$-0.479860\pi$
$31$	0.704107			0.126461			0.0632306	+	0.997999i	$0.479860\pi$
$32$		0			0
$33$	−3.89041	−	2.82006i	−0.677234	−	0.490910i
$34$		0			0
$35$	−0.0297482	−	3.90862i	−0.00502837	−	0.660677i
$36$		0			0
$37$	−1.92560	−	3.33523i	−0.316566	−	0.548309i	0.663203	−	0.748440i	$-0.269197\pi$
$37$	−1.92560	−	3.33523i	−0.316566	−	0.548309i	−0.979769	+	0.200131i	$0.935863\pi$
$38$		0			0
$39$	−1.54713	−	1.12147i	−0.247738	−	0.179579i
$40$		0			0
$41$	−2.23630	+	1.29113i	−0.349252	+	0.201640i	−0.664356	−	0.747417i	$-0.731294\pi$
$41$	−2.23630	+	1.29113i	−0.349252	+	0.201640i	0.315104	+	0.949057i	$0.397961\pi$
$42$		0			0
$43$	8.95705	+	5.17136i	1.36594	+	0.788624i	0.990406	−	0.138185i	$-0.0441270\pi$
$43$	8.95705	+	5.17136i	1.36594	+	0.788624i	0.375531	+	0.926810i	$0.377460\pi$
$44$		0			0
$45$	4.21216	−	1.37879i	0.627912	−	0.205538i
$46$		0			0
$47$	4.28149			0.624520			0.312260	−	0.949997i	$-0.398914\pi$
$47$	4.28149			0.624520			0.312260	+	0.949997i	$0.398914\pi$
$48$		0			0
$49$	−3.40732	+	6.11475i	−0.486760	+	0.873536i
$50$		0			0
$51$	0.350511	−	3.37030i	0.0490814	−	0.471936i
$52$		0			0
$53$	3.49123	−	6.04699i	0.479558	−	0.830618i	−0.520168	−	0.854064i	$-0.674131\pi$
$53$	3.49123	−	6.04699i	0.479558	−	0.830618i	0.999725	+	0.0234462i	$0.00746385\pi$
$54$		0			0
$55$	−4.09845			−0.552635
$56$		0			0
$57$	7.04395	−	9.71747i	0.932994	−	1.28711i
$58$		0			0
$59$	1.13799			0.148154			0.0740768	−	0.997253i	$-0.476399\pi$
$59$	1.13799			0.148154			0.0740768	+	0.997253i	$0.476399\pi$
$60$		0			0
$61$		−	2.58999i		−	0.331614i	−0.986158	−	0.165807i	$-0.946977\pi$
$61$		−	2.58999i		−	0.331614i	0.986158	−	0.165807i	$-0.0530228\pi$
$62$		0			0
$63$	−7.77960	−	1.57412i	−0.980137	−	0.198321i
$64$		0			0
$65$	−1.62986			−0.202159
$66$		0			0
$67$		−	11.6636i		−	1.42493i	−0.701707	−	0.712466i	$-0.747578\pi$
$67$		−	11.6636i		−	1.42493i	0.701707	−	0.712466i	$-0.252422\pi$
$68$		0			0
$69$	0.00578629	−	0.0556373i	0.000696587	−	0.00669795i
$70$		0			0
$71$		−	15.6777i		−	1.86060i	−0.366799	−	0.930300i	$-0.619546\pi$
$71$		−	15.6777i		−	1.86060i	0.366799	−	0.930300i	$-0.380454\pi$
$72$		0			0
$73$	−4.41573	−	2.54942i	−0.516822	−	0.298388i	0.218811	−	0.975767i	$-0.429782\pi$
$73$	−4.41573	−	2.54942i	−0.516822	−	0.298388i	−0.735634	+	0.677380i	$0.763115\pi$
$74$		0			0
$75$	−2.86401	+	3.95104i	−0.330708	+	0.456227i
$76$		0			0
$77$	6.38417	+	3.62140i	0.727544	+	0.412697i
$78$		0			0
$79$			8.38410i			0.943285i	0.881790	+	0.471643i	$0.156339\pi$
$79$			8.38410i			0.943285i	−0.881790	+	0.471643i	$0.843661\pi$
$80$		0			0
$81$	−0.979853	−	8.94650i	−0.108873	−	0.994056i
$82$		0			0
$83$	−5.34759	+	9.26231i	−0.586975	+	1.01667i	0.407651	+	0.913138i	$0.366348\pi$
$83$	−5.34759	+	9.26231i	−0.586975	+	1.01667i	−0.994626	+	0.103532i	$0.966985\pi$
$84$		0			0
$85$	−1.44511	−	2.50300i	−0.156744	−	0.271488i
$86$		0			0
$87$	−15.6358	−	1.62613i	−1.67633	−	0.174339i
$88$		0			0
$89$	8.83761	−	5.10240i	0.936785	−	0.540853i	0.0478337	−	0.998855i	$-0.484768\pi$
$89$	8.83761	−	5.10240i	0.936785	−	0.540853i	0.888951	+	0.458002i	$0.151435\pi$
$90$		0			0
$91$	2.53883	+	1.44015i	0.266142	+	0.150968i
$92$		0			0
$93$	−0.497252	−	1.11357i	−0.0515626	−	0.115472i
$94$		0			0
$95$		−	10.2371i		−	1.05030i
$96$		0			0
$97$	6.95620	+	4.01617i	0.706296	+	0.407780i	0.809688	−	0.586861i	$-0.199636\pi$
$97$	6.95620	+	4.01617i	0.706296	+	0.407780i	−0.103392	+	0.994641i	$0.532970\pi$
$98$		0			0
$99$	−1.71256	+	8.14441i	−0.172119	+	0.818544i
$100$		0			0
$101$	−0.762717	+	0.440355i	−0.0758932	+	0.0438169i	−0.537466	−	0.843285i	$-0.680618\pi$
$101$	−0.762717	+	0.440355i	−0.0758932	+	0.0438169i	0.461573	+	0.887102i	$0.347285\pi$
$102$		0			0
$103$	−0.535717	+	0.927889i	−0.0527858	+	0.0914276i	−0.891211	−	0.453589i	$-0.850143\pi$
$103$	−0.535717	+	0.927889i	−0.0527858	+	0.0914276i	0.838425	+	0.545017i	$0.183477\pi$
$104$		0			0
$105$	−6.16061	+	2.80738i	−0.601214	+	0.273972i
$106$		0			0
$107$	16.4651	−	9.50613i	1.59174	−	0.918993i	0.598734	−	0.800948i	$-0.295671\pi$
$107$	16.4651	−	9.50613i	1.59174	−	0.918993i	0.993008	−	0.118045i	$-0.0376626\pi$
$108$		0			0
$109$	1.39943	−	2.42389i	0.134041	−	0.232166i	−0.791190	−	0.611571i	$-0.790538\pi$
$109$	1.39943	−	2.42389i	0.134041	−	0.232166i	0.925231	+	0.379405i	$0.123871\pi$
$110$		0			0
$111$	−3.91491	+	5.40080i	−0.371586	+	0.512621i
$112$		0			0
$113$	4.66742	+	8.08421i	0.439074	+	0.760499i	0.997618	−	0.0689759i	$-0.0219732\pi$
$113$	4.66742	+	8.08421i	0.439074	+	0.760499i	−0.558544	+	0.829475i	$0.688640\pi$
$114$		0			0
$115$	−0.0238560	−	0.0413199i	−0.00222459	−	0.00385310i
$116$		0			0
$117$	−0.681045	+	3.23884i	−0.0629626	+	0.299431i
$118$		0			0
$119$	0.0393929	+	5.17583i	0.00361114	+	0.474468i
$120$		0			0
$121$	−1.65199	+	2.86133i	−0.150181	+	0.260121i
$122$		0			0
$123$	3.62128	+	2.62498i	0.326520	+	0.236686i
$124$		0			0
$125$			11.5491i			1.03299i
$126$		0			0
$127$			6.43956i			0.571419i	0.958316	+	0.285709i	$0.0922292\pi$
$127$			6.43956i			0.571419i	−0.958316	+	0.285709i	$0.907771\pi$
$128$		0			0
$129$	1.85307	−	17.8180i	0.163154	−	1.56879i
$130$		0			0
$131$	−1.76490	+	3.05690i	−0.154200	+	0.267083i	−0.932768	−	0.360478i	$-0.882613\pi$
$131$	−1.76490	+	3.05690i	−0.154200	+	0.267083i	0.778567	+	0.627561i	$0.215947\pi$
$132$		0			0
$133$	−9.04553	+	15.9464i	−0.784347	+	1.38273i
$134$		0			0
$135$	−5.15531	−	5.68796i	−0.443698	−	0.489541i
$136$		0			0
$137$	9.60299	+	16.6329i	0.820439	+	1.42104i	0.905356	+	0.424654i	$0.139604\pi$
$137$	9.60299	+	16.6329i	0.820439	+	1.42104i	−0.0849170	+	0.996388i	$0.527063\pi$
$138$		0			0
$139$	8.42275	+	14.5886i	0.714408	+	1.23739i	0.963187	+	0.268831i	$0.0866374\pi$
$139$	8.42275	+	14.5886i	0.714408	+	1.23739i	−0.248779	+	0.968560i	$0.580029\pi$
$140$		0			0
$141$	−3.02366	−	6.77134i	−0.254638	−	0.570250i
$142$		0			0
$143$	1.53026	−	2.65049i	0.127967	−	0.221645i
$144$		0			0
$145$	−11.6122	+	6.70428i	−0.964337	+	0.556760i
$146$		0			0
$147$	12.0770	+	1.07047i	0.996095	+	0.0882908i
$148$		0			0
$149$	−10.6203	+	18.3949i	−0.870050	+	1.50697i	−0.00810521	+	0.999967i	$0.502580\pi$
$149$	−10.6203	+	18.3949i	−0.870050	+	1.50697i	−0.861944	+	0.507003i	$0.830753\pi$
$150$		0			0
$151$	12.4787	−	7.20460i	1.01551	−	0.586302i	0.102706	−	0.994712i	$-0.467250\pi$
$151$	12.4787	−	7.20460i	1.01551	−	0.586302i	0.912799	+	0.408410i	$0.133916\pi$
$152$		0			0
$153$	−5.57778	+	1.82581i	−0.450937	+	0.147608i
$154$		0			0
$155$	−0.900856	−	0.520110i	−0.0723585	−	0.0417762i
$156$		0			0
$157$		−	5.69801i		−	0.454751i	−0.973807	−	0.227375i	$-0.926986\pi$
$157$		−	5.69801i		−	0.454751i	0.973807	−	0.227375i	$-0.0730144\pi$
$158$		0			0
$159$	−12.0291	−	1.25103i	−0.953970	−	0.0992129i
$160$		0			0
$161$	0.000650304		0.0854433i	5.12511e−5		0.00673388i
$162$		0			0
$163$	4.25007	−	2.45378i	0.332891	−	0.192195i	−0.324233	−	0.945977i	$-0.605106\pi$
$163$	4.25007	−	2.45378i	0.332891	−	0.192195i	0.657124	+	0.753783i	$0.271773\pi$
$164$		0			0
$165$	2.89439	+	6.48185i	0.225328	+	0.504611i
$166$		0			0
$167$	0.958089	+	1.65946i	0.0741392	+	0.128413i	0.900712	−	0.434418i	$-0.143046\pi$
$167$	0.958089	+	1.65946i	0.0741392	+	0.128413i	−0.826572	+	0.562830i	$0.809712\pi$
$168$		0			0
$169$	−5.89145	+	10.2043i	−0.453188	+	0.784945i
$170$		0			0
$171$	−20.3431	−	4.27763i	−1.55567	−	0.327119i
$172$		0			0
$173$		−	23.8613i		−	1.81414i	−0.420978	−	0.907071i	$-0.638313\pi$
$173$		−	23.8613i		−	1.81414i	0.420978	−	0.907071i	$-0.361687\pi$
$174$		0			0
$175$	3.67784	−	6.48367i	0.278018	−	0.490119i
$176$		0			0
$177$	−0.803667	−	1.79977i	−0.0604073	−	0.135279i
$178$		0			0
$179$	−8.43765	−	4.87148i	−0.630659	−	0.364111i	0.150348	−	0.988633i	$-0.451961\pi$
$179$	−8.43765	−	4.87148i	−0.630659	−	0.364111i	−0.781007	+	0.624522i	$0.785294\pi$
$180$		0			0
$181$		−	1.54520i		−	0.114854i	−0.998350	−	0.0574269i	$-0.981710\pi$
$181$		−	1.54520i		−	0.114854i	0.998350	−	0.0574269i	$-0.0182896\pi$
$182$		0			0
$183$	−4.09616	+	1.82909i	−0.302797	+	0.135210i
$184$		0			0
$185$			5.68961i			0.418308i
$186$		0			0
$187$	5.42721			0.396877
$188$		0			0
$189$	3.00455	+	13.4154i	0.218549	+	0.975826i
$190$		0			0
$191$		−	1.83767i		−	0.132969i	−0.997787	−	0.0664845i	$-0.978822\pi$
$191$		−	1.83767i		−	0.132969i	0.997787	−	0.0664845i	$-0.0211783\pi$
$192$		0			0
$193$	1.87378			0.134878			0.0674389	−	0.997723i	$-0.478517\pi$
$193$	1.87378			0.134878			0.0674389	+	0.997723i	$0.478517\pi$
$194$		0			0
$195$	1.15103	+	2.57768i	0.0824271	+	0.184591i
$196$		0			0
$197$	−21.3079			−1.51812			−0.759061	−	0.651019i	$-0.774342\pi$
$197$	−21.3079			−1.51812			−0.759061	+	0.651019i	$0.774342\pi$
$198$		0			0
$199$	−10.4408	+	18.0840i	−0.740129	+	1.28194i	0.212307	+	0.977203i	$0.431902\pi$
$199$	−10.4408	+	18.0840i	−0.740129	+	1.28194i	−0.952436	+	0.304738i	$0.901431\pi$
$200$		0			0
$201$	−18.4464	+	8.23700i	−1.30111	+	0.580993i
$202$		0			0
$203$	24.0122	−	0.182756i	1.68533	−	0.0128269i
$204$		0			0
$205$	3.81493			0.266446
$206$		0			0
$207$	−0.0920789	+	0.0301408i	−0.00639992	+	0.00209493i
$208$		0			0
$209$	16.6477	+	9.61156i	1.15155	+	0.664845i
$210$		0			0
$211$	−12.5460	+	7.24345i	−0.863704	+	0.498660i	−0.865251	−	0.501339i	$-0.832841\pi$
$211$	−12.5460	+	7.24345i	−0.863704	+	0.498660i	0.00154663	+	0.999999i	$0.499508\pi$
$212$		0			0
$213$	−24.7949	+	11.0718i	−1.69892	+	0.758631i
$214$		0			0
$215$	−7.63996	−	13.2328i	−0.521041	−	0.902469i
$216$		0			0
$217$	0.943697	+	1.60617i	0.0640623	+	0.109034i
$218$		0			0
$219$	−0.913545	+	8.78409i	−0.0617317	+	0.593574i
$220$		0			0
$221$	2.15827			0.145181
$222$		0			0
$223$	−7.93256	+	13.7396i	−0.531204	+	0.920072i	0.468133	+	0.883658i	$0.344927\pi$
$223$	−7.93256	+	13.7396i	−0.531204	+	0.920072i	−0.999337	+	0.0364138i	$0.988407\pi$
$224$		0			0
$225$	8.27133	+	1.73925i	0.551422	+	0.115950i
$226$		0			0
$227$	−9.68469	−	16.7744i	−0.642795	−	1.11335i	−0.984806	−	0.173658i	$-0.944441\pi$
$227$	−9.68469	−	16.7744i	−0.642795	−	1.11335i	0.342011	−	0.939696i	$-0.388892\pi$
$228$		0			0
$229$	17.6120	+	10.1683i	1.16384	+	0.671941i	0.952220	−	0.305411i	$-0.0987940\pi$
$229$	17.6120	+	10.1683i	1.16384	+	0.671941i	0.211616	+	0.977353i	$0.432127\pi$
$230$		0			0
$231$	1.21877	−	12.6543i	0.0801892	−	0.832591i
$232$		0			0
$233$	−13.2043	−	22.8706i	−0.865046	−	1.49830i	−0.867002	−	0.498305i	$-0.833956\pi$
$233$	−13.2043	−	22.8706i	−0.865046	−	1.49830i	0.00195620	−	0.999998i	$-0.499377\pi$
$234$		0			0
$235$	−5.47788	−	3.16266i	−0.357338	−	0.206309i
$236$		0			0
$237$	13.2598	−	5.92099i	0.861314	−	0.384610i
$238$		0			0
$239$	5.27359	−	3.04471i	0.341120	−	0.196946i	−0.319647	−	0.947537i	$-0.603564\pi$
$239$	5.27359	−	3.04471i	0.341120	−	0.196946i	0.660767	+	0.750591i	$0.270231\pi$
$240$		0			0
$241$	0.519055	−	0.299676i	0.0334353	−	0.0193039i	−0.483189	−	0.875516i	$-0.660522\pi$
$241$	0.519055	−	0.299676i	0.0334353	−	0.0193039i	0.516624	+	0.856212i	$0.327188\pi$
$242$		0			0
$243$	−13.4572	+	7.86784i	−0.863282	+	0.504722i
$244$		0			0
$245$	8.87628	−	5.30648i	0.567085	−	0.339019i
$246$		0			0
$247$	6.62040	+	3.82229i	0.421246	+	0.243206i
$248$		0			0
$249$	18.4252	+	1.91623i	1.16765	+	0.121436i
$250$		0			0
$251$	14.7398			0.930366			0.465183	−	0.885215i	$-0.345989\pi$
$251$	14.7398			0.930366			0.465183	+	0.885215i	$0.345989\pi$
$252$		0			0
$253$	0.0895932			0.00563268
$254$		0			0
$255$	−2.93803	+	4.05315i	−0.183986	+	0.253818i
$256$		0			0
$257$	14.1894	+	8.19227i	0.885112	+	0.511020i	0.872341	−	0.488898i	$-0.162601\pi$
$257$	14.1894	+	8.19227i	0.885112	+	0.511020i	0.0127718	+	0.999918i	$0.495934\pi$
$258$		0			0
$259$	5.02735	−	8.86272i	0.312384	−	0.550703i
$260$		0			0
$261$	8.47049	+	25.8770i	0.524310	+	1.60175i
$262$		0			0
$263$	−5.12161	+	2.95696i	−0.315812	+	0.182334i	−0.649524	−	0.760341i	$-0.725032\pi$
$263$	−5.12161	+	2.95696i	−0.315812	+	0.182334i	0.333712	+	0.942675i	$0.391699\pi$
$264$		0			0
$265$	−8.93359	+	5.15781i	−0.548786	+	0.316842i
$266$		0			0
$267$	−14.3109	−	10.3736i	−0.875812	−	0.634854i
$268$		0			0
$269$	−9.08351	−	5.24436i	−0.553831	−	0.319755i	0.196835	−	0.980437i	$-0.436934\pi$
$269$	−9.08351	−	5.24436i	−0.553831	−	0.319755i	−0.750666	+	0.660682i	$0.770267\pi$
$270$		0			0
$271$	−3.68306	−	6.37925i	−0.223730	−	0.387512i	0.732208	−	0.681081i	$-0.238490\pi$
$271$	−3.68306	−	6.37925i	−0.223730	−	0.387512i	−0.955938	+	0.293570i	$0.905157\pi$
$272$		0			0
$273$	0.484677	−	5.03231i	0.0293340	−	0.304569i
$274$		0			0
$275$	−6.76882	−	3.90798i	−0.408175	−	0.235660i
$276$		0			0
$277$	0.887744	+	1.53762i	0.0533394	+	0.0923865i	0.891462	−	0.453095i	$-0.149680\pi$
$277$	0.887744	+	1.53762i	0.0533394	+	0.0923865i	−0.838123	+	0.545481i	$0.816347\pi$
$278$		0			0
$279$	−1.40999	+	1.57284i	−0.0844136	+	0.0941637i
$280$		0			0
$281$	−2.08260	+	3.60717i	−0.124237	+	0.215185i	−0.921435	−	0.388534i	$-0.872982\pi$
$281$	−2.08260	+	3.60717i	−0.124237	+	0.215185i	0.797197	+	0.603719i	$0.206315\pi$
$282$		0			0
$283$	3.40760			0.202561			0.101280	−	0.994858i	$-0.467706\pi$
$283$	3.40760			0.202561			0.101280	+	0.994858i	$0.467706\pi$
$284$		0			0
$285$	−16.1904	+	7.22961i	−0.959034	+	0.428245i
$286$		0			0
$287$	−5.94252	−	3.37088i	−0.350776	−	0.198977i
$288$		0			0
$289$	−6.58637	−	11.4079i	−0.387434	−	0.671055i
$290$		0			0
$291$	1.43913	−	13.8378i	0.0843632	−	0.811185i
$292$		0			0
$293$	−16.1931	+	9.34911i	−0.946013	+	0.546181i	−0.891840	−	0.452351i	$-0.850586\pi$
$293$	−16.1931	+	9.34911i	−0.946013	+	0.546181i	−0.0541729	+	0.998532i	$0.517252\pi$
$294$		0			0
$295$	−1.45598	−	0.840610i	−0.0847704	−	0.0489422i
$296$		0			0
$297$	14.0901	−	3.04324i	0.817591	−	0.176586i
$298$		0			0
$299$	0.0356291			0.00206048
$300$		0			0
$301$	0.208262	+	27.3635i	0.0120040	+	1.57720i
$302$		0			0
$303$	1.23508	+	0.895279i	0.0709535	+	0.0514324i
$304$		0			0
$305$	−1.91317	+	3.31371i	−0.109548	+	0.189742i
$306$		0			0
$307$	13.0627			0.745528			0.372764	−	0.927926i	$-0.378410\pi$
$307$	13.0627			0.745528			0.372764	+	0.927926i	$0.378410\pi$
$308$		0			0
$309$	1.84582	+	0.191966i	0.105005	+	0.0109205i
$310$		0			0
$311$	−30.8740			−1.75070			−0.875352	−	0.483487i	$-0.839370\pi$
$311$	−30.8740			−1.75070			−0.875352	+	0.483487i	$0.839370\pi$
$312$		0			0
$313$			15.9800i			0.903244i	0.892209	+	0.451622i	$0.149154\pi$
$313$			15.9800i			0.903244i	−0.892209	+	0.451622i	$0.850846\pi$
$314$		0			0
$315$	8.79069	+	7.76062i	0.495299	+	0.437261i
$316$		0			0
$317$	3.70957			0.208350			0.104175	−	0.994559i	$-0.466780\pi$
$317$	3.70957			0.208350			0.104175	+	0.994559i	$0.466780\pi$
$318$		0			0
$319$		−	25.1784i		−	1.40972i
$320$		0			0
$321$	−26.6622	−	19.3268i	−1.48814	−	1.07872i
$322$		0			0
$323$			13.5561i			0.754280i
$324$		0			0
$325$	−2.69180	−	1.55411i	−0.149314	−	0.0862066i
$326$		0			0
$327$	−4.82177	−	0.501464i	−0.266644	−	0.0277310i
$328$		0			0
$329$	5.73838	+	9.76675i	0.316367	+	0.538458i
$330$		0			0
$331$			27.8487i			1.53070i	0.643612	+	0.765352i	$0.277435\pi$
$331$			27.8487i			1.53070i	−0.643612	+	0.765352i	$0.722565\pi$
$332$		0			0
$333$	11.3063	+	2.37743i	0.619583	+	0.130283i
$334$		0			0
$335$	−8.61565	+	14.9227i	−0.470723	+	0.815316i
$336$		0			0
$337$	−5.14339	−	8.90861i	−0.280178	−	0.485283i	0.691250	−	0.722615i	$-0.257060\pi$
$337$	−5.14339	−	8.90861i	−0.280178	−	0.485283i	−0.971428	+	0.237333i	$0.923727\pi$
$338$		0			0
$339$	9.48927	−	13.0909i	0.515386	−	0.711000i
$340$		0			0
$341$	1.69162	−	0.976656i	0.0916062	−	0.0528889i
$342$		0			0
$343$	−18.5154	+	0.422825i	−0.999739	+	0.0228304i
$344$		0			0
$345$	−0.0485014	+	0.0669100i	−0.00261123	+	0.00360231i
$346$		0			0
$347$		−	13.5568i		−	0.727767i	−0.931445	−	0.363883i	$-0.881451\pi$
$347$		−	13.5568i		−	0.727767i	0.931445	−	0.363883i	$-0.118549\pi$
$348$		0			0
$349$	−28.9208	−	16.6974i	−1.54809	−	0.893792i	−0.998287	−	0.0584989i	$-0.981369\pi$
$349$	−28.9208	−	16.6974i	−1.54809	−	0.893792i	−0.549805	−	0.835293i	$-0.685298\pi$
$350$		0			0
$351$	5.60331	−	1.21022i	0.299082	−	0.0645969i
$352$		0			0
$353$	24.4575	−	14.1205i	1.30174	−	0.751560i	0.321038	−	0.947066i	$-0.395968\pi$
$353$	24.4575	−	14.1205i	1.30174	−	0.751560i	0.980703	+	0.195506i	$0.0626348\pi$
$354$		0			0
$355$	−11.5808	+	20.0585i	−0.614646	+	1.06460i
$356$		0			0
$357$	8.15795	−	3.71756i	0.431764	−	0.196754i
$358$		0			0
$359$	−4.95868	+	2.86289i	−0.261709	+	0.151098i	−0.625114	−	0.780534i	$-0.714947\pi$
$359$	−4.95868	+	2.86289i	−0.261709	+	0.151098i	0.363405	+	0.931631i	$0.381614\pi$
$360$		0			0
$361$	−14.5077	+	25.1281i	−0.763565	+	1.32253i
$362$		0			0
$363$	5.69196	+	0.591964i	0.298750	+	0.0310700i
$364$		0			0
$365$	3.76642	+	6.52363i	0.197143	+	0.341462i
$366$		0			0
$367$	−10.8969	−	18.8740i	−0.568813	−	0.985213i	−0.996684	−	0.0813728i	$-0.974070\pi$
$367$	−10.8969	−	18.8740i	−0.568813	−	0.985213i	0.427871	−	0.903840i	$-0.359264\pi$
$368$		0			0
$369$	1.59409	−	7.58099i	0.0829849	−	0.394650i
$370$		0			0
$371$	18.4733	−	0.140599i	0.959087	−	0.00729955i
$372$		0			0
$373$	19.0200	−	32.9436i	0.984817	−	1.70575i	0.342073	−	0.939674i	$-0.388871\pi$
$373$	19.0200	−	32.9436i	0.984817	−	1.70575i	0.642745	−	0.766080i	$-0.277796\pi$
$374$		0			0
$375$	18.2654	−	8.15618i	0.943220	−	0.421183i
$376$		0			0
$377$		−	10.0129i		−	0.515689i
$378$		0			0
$379$		−	11.6200i		−	0.596878i	−0.954429	−	0.298439i	$-0.903534\pi$
$379$		−	11.6200i		−	0.596878i	0.954429	−	0.298439i	$-0.0964660\pi$
$380$		0			0
$381$	10.1844	−	4.54773i	0.521763	−	0.232987i
$382$		0			0
$383$	−11.6806	+	20.2313i	−0.596849	+	1.03377i	0.396434	+	0.918063i	$0.370248\pi$
$383$	−11.6806	+	20.2313i	−0.596849	+	1.03377i	−0.993283	+	0.115710i	$0.963086\pi$
$384$		0			0
$385$	−5.49305	−	9.34919i	−0.279952	−	0.476479i
$386$		0			0
$387$	−29.4885	+	9.65266i	−1.49898	+	0.490672i
$388$		0			0
$389$	3.31559	+	5.74277i	0.168107	+	0.291170i	0.937754	−	0.347299i	$-0.112901\pi$
$389$	3.31559	+	5.74277i	0.168107	+	0.291170i	−0.769647	+	0.638469i	$0.779568\pi$
$390$		0			0
$391$	0.0315904	+	0.0547162i	0.00159760	+	0.00276712i
$392$		0			0
$393$	6.08101	+	0.632425i	0.306746	+	0.0319016i
$394$		0			0
$395$	6.19317	−	10.7269i	0.311612	−	0.539728i
$396$		0			0
$397$	21.0152	−	12.1331i	1.05472	−	0.608943i	0.130753	−	0.991415i	$-0.458260\pi$
$397$	21.0152	−	12.1331i	1.05472	−	0.608943i	0.923967	+	0.382472i	$0.124927\pi$
$398$		0			0
$399$	31.6079	+	3.04424i	1.58237	+	0.152403i
$400$		0			0
$401$	−5.84669	+	10.1268i	−0.291970	+	0.505706i	−0.974275	−	0.225361i	$-0.927644\pi$
$401$	−5.84669	+	10.1268i	−0.291970	+	0.505706i	0.682306	+	0.731067i	$0.260977\pi$
$402$		0			0
$403$	0.672716	−	0.388393i	0.0335104	−	0.0193472i
$404$		0			0
$405$	−5.35495	+	12.1702i	−0.266090	+	0.604744i
$406$		0			0
$407$	−9.25251	−	5.34194i	−0.458630	−	0.264790i
$408$		0			0
$409$		−	30.2767i		−	1.49708i	−0.663087	−	0.748542i	$-0.730754\pi$
$409$		−	30.2767i		−	1.49708i	0.663087	−	0.748542i	$-0.269246\pi$
$410$		0			0
$411$	19.5237	−	26.9339i	0.963033	−	1.32855i
$412$		0			0
$413$	1.52522	+	2.59593i	0.0750512	+	0.127737i
$414$		0			0
$415$	13.6838	−	7.90033i	0.671710	−	0.387812i
$416$		0			0
$417$	17.1242	−	23.6236i	0.838574	−	1.15685i
$418$		0			0
$419$	−4.44019	−	7.69063i	−0.216917	−	0.375712i	0.736947	−	0.675951i	$-0.236267\pi$
$419$	−4.44019	−	7.69063i	−0.216917	−	0.375712i	−0.953864	+	0.300239i	$0.902934\pi$
$420$		0			0
$421$	7.59052	−	13.1472i	0.369939	−	0.640753i	−0.619617	−	0.784905i	$-0.712712\pi$
$421$	7.59052	−	13.1472i	0.369939	−	0.640753i	0.989556	+	0.144151i	$0.0460452\pi$
$422$		0			0
$423$	−8.57376	+	9.56406i	−0.416871	+	0.465021i
$424$		0			0
$425$		−	5.51179i		−	0.267361i
$426$		0			0
$427$	5.90815	−	3.47129i	0.285916	−	0.167988i
$428$		0			0
$429$	−5.27255	−	0.548345i	−0.254561	−	0.0264744i
$430$		0			0
$431$	−3.60242	−	2.07986i	−0.173523	−	0.100183i	0.410723	−	0.911760i	$-0.365276\pi$
$431$	−3.60242	−	2.07986i	−0.173523	−	0.100183i	−0.584246	+	0.811577i	$0.698610\pi$
$432$		0			0
$433$			31.2165i			1.50017i	0.661343	+	0.750084i	$0.269987\pi$
$433$			31.2165i			1.50017i	−0.661343	+	0.750084i	$0.730013\pi$
$434$		0			0
$435$	18.8038	+	13.6304i	0.901572	+	0.653527i
$436$		0			0
$437$			0.223786i			0.0107051i
$438$		0			0
$439$	−15.5826			−0.743717			−0.371858	−	0.928289i	$-0.621279\pi$
$439$	−15.5826			−0.743717			−0.371858	+	0.928289i	$0.621279\pi$
$440$		0			0
$441$	−6.83599	−	19.8562i	−0.325524	−	0.945534i
$442$		0			0
$443$			12.4016i			0.589218i	0.955618	+	0.294609i	$0.0951893\pi$
$443$			12.4016i			0.589218i	−0.955618	+	0.294609i	$0.904811\pi$
$444$		0			0
$445$	−15.0762			−0.714678
$446$		0			0
$447$	36.5925	+	3.80562i	1.73076	+	0.180000i
$448$		0			0
$449$	−22.8280			−1.07732			−0.538660	−	0.842524i	$-0.681069\pi$
$449$	−22.8280			−1.07732			−0.538660	+	0.842524i	$0.681069\pi$
$450$		0			0
$451$	−3.58181	+	6.20388i	−0.168661	+	0.292129i
$452$		0			0
$453$	−20.2070	−	14.6476i	−0.949409	−	0.688203i
$454$		0			0
$455$	−2.18446	−	3.71795i	−0.102409	−	0.174300i
$456$		0			0
$457$	22.0978			1.03369			0.516846	−	0.856078i	$-0.327106\pi$
$457$	22.0978			1.03369			0.516846	+	0.856078i	$0.327106\pi$
$458$		0			0
$459$	6.82671	+	7.53205i	0.318644	+	0.351566i
$460$		0			0
$461$	−20.2378	−	11.6843i	−0.942568	−	0.544192i	−0.0518038	−	0.998657i	$-0.516497\pi$
$461$	−20.2378	−	11.6843i	−0.942568	−	0.544192i	−0.890764	+	0.454465i	$0.849830\pi$
$462$		0			0
$463$	21.5837	−	12.4613i	1.00308	−	0.579127i	0.0939203	−	0.995580i	$-0.470060\pi$
$463$	21.5837	−	12.4613i	1.00308	−	0.579127i	0.909157	+	0.416452i	$0.136727\pi$
$464$		0			0
$465$	−0.186373	+	1.79205i	−0.00864284	+	0.0831042i
$466$		0			0
$467$	20.1004	+	34.8149i	0.930137	+	1.61104i	0.783085	+	0.621915i	$0.213645\pi$
$467$	20.1004	+	34.8149i	0.930137	+	1.61104i	0.147052	+	0.989129i	$0.453022\pi$
$468$		0			0
$469$	26.6064	−	15.6324i	1.22857	−	0.721837i
$470$		0			0
$471$	−9.01161	+	4.02403i	−0.415233	+	0.185417i
$472$		0			0
$473$	28.6924			1.31928
$474$		0			0
$475$	9.76135	−	16.9072i	0.447881	−	0.775753i
$476$		0			0
$477$	6.51660	+	19.9080i	0.298375	+	0.911523i
$478$		0			0
$479$	16.4450	+	28.4835i	0.751390	+	1.30145i	0.947149	+	0.320794i	$0.103950\pi$
$479$	16.4450	+	28.4835i	0.751390	+	1.30145i	−0.195759	+	0.980652i	$0.562717\pi$
$480$		0			0
$481$	−3.67950	−	2.12436i	−0.167771	−	0.0968626i
$482$		0			0
$483$	0.134673	−	0.0613700i	0.00612781	−	0.00279243i
$484$		0			0
$485$	−5.93333	−	10.2768i	−0.269418	−	0.466646i
$486$		0			0
$487$	15.3672	+	8.87224i	0.696353	+	0.402040i	0.805988	−	0.591932i	$-0.201635\pi$
$487$	15.3672	+	8.87224i	0.696353	+	0.402040i	−0.109634	+	0.993972i	$0.534968\pi$
$488$		0			0
$489$	−6.88221	−	4.98874i	−0.311224	−	0.225599i
$490$		0			0
$491$	−13.0636	+	7.54226i	−0.589551	+	0.340377i	−0.764920	−	0.644126i	$-0.777221\pi$
$491$	−13.0636	+	7.54226i	−0.589551	+	0.340377i	0.175369	+	0.984503i	$0.443888\pi$
$492$		0			0
$493$	15.3769	−	8.87788i	0.692543	−	0.399840i
$494$		0			0
$495$	8.20722	−	9.15518i	0.368887	−	0.411495i
$496$		0			0
$497$	35.7632	−	21.0124i	1.60420	−	0.942537i
$498$		0			0
$499$	11.7257	+	6.76985i	0.524915	+	0.303060i	0.738943	−	0.673768i	$-0.235325\pi$
$499$	11.7257	+	6.76985i	0.524915	+	0.303060i	−0.214028	+	0.976827i	$0.568658\pi$
$500$		0			0
$501$	1.94788	−	2.68719i	0.0870247	−	0.120055i
$502$		0			0
$503$	19.0537			0.849563			0.424782	−	0.905296i	$-0.360351\pi$
$503$	19.0537			0.849563			0.424782	+	0.905296i	$0.360351\pi$
$504$		0			0
$505$	1.30113			0.0578993
$506$		0			0
$507$	20.2991	+	2.11111i	0.901515	+	0.0937576i
$508$		0			0
$509$	−36.3115	−	20.9644i	−1.60948	−	0.929233i	−0.989487	−	0.144624i	$-0.953803\pi$
$509$	−36.3115	−	20.9644i	−1.60948	−	0.929233i	−0.619992	−	0.784608i	$-0.712864\pi$
$510$		0			0
$511$	−0.102671	−	13.4899i	−0.00454189	−	0.596758i
$512$		0			0
$513$	7.60139	+	35.1943i	0.335610	+	1.55386i
$514$		0			0
$515$	1.37083	−	0.791447i	0.0604058	−	0.0348753i
$516$		0			0
$517$	10.2863	−	5.93880i	0.452391	−	0.261188i
$518$		0			0
$519$	−37.7375	+	16.8513i	−1.65649	+	0.739688i
$520$		0			0
$521$	−16.8365	−	9.72055i	−0.737620	−	0.425865i	0.0835832	−	0.996501i	$-0.473364\pi$
$521$	−16.8365	−	9.72055i	−0.737620	−	0.425865i	−0.821203	+	0.570636i	$0.806697\pi$
$522$		0			0
$523$	−3.84616	−	6.66175i	−0.168181	−	0.291298i	0.769599	−	0.638527i	$-0.220456\pi$
$523$	−3.84616	−	6.66175i	−0.168181	−	0.291298i	−0.937780	+	0.347229i	$0.887123\pi$
$524$		0			0
$525$	−12.8515	−	1.23777i	−0.560886	−	0.0540205i
$526$		0			0
$527$	1.19292	+	0.688735i	0.0519646	+	0.0300018i
$528$		0			0
$529$	−11.4995	−	19.9177i	−0.499977	−	0.865986i
$530$		0			0
$531$	−2.27884	+	2.54206i	−0.0988934	+	0.110316i
$532$		0			0
$533$	−1.42440	+	2.46714i	−0.0616977	+	0.106864i
$534$		0			0
$535$	−28.0880			−1.21435
$536$		0			0
$537$	−1.74562	+	16.7848i	−0.0753289	+	0.724316i
$538$		0			0
$539$	0.295579	+	19.4169i	0.0127315	+	0.836347i
$540$		0			0
$541$	11.0310	+	19.1062i	0.474258	+	0.821439i	0.999566	−	0.0294732i	$-0.00938296\pi$
$541$	11.0310	+	19.1062i	0.474258	+	0.821439i	−0.525307	+	0.850913i	$0.676050\pi$
$542$		0			0
$543$	−2.44379	+	1.09125i	−0.104873	+	0.0468298i
$544$		0			0
$545$	−3.58095	+	2.06746i	−0.153391	+	0.0885605i
$546$		0			0
$547$	−19.5580	−	11.2918i	−0.836240	−	0.482803i	0.0197443	−	0.999805i	$-0.493715\pi$
$547$	−19.5580	−	11.2918i	−0.836240	−	0.482803i	−0.855984	+	0.517002i	$0.827048\pi$
$548$		0			0
$549$	5.78555	+	5.18649i	0.246921	+	0.221354i
$550$		0			0
$551$	62.8907			2.67923
$552$		0			0
$553$	−19.1254	+	11.2370i	−0.813296	+	0.477846i
$554$		0			0
$555$	8.99832	−	4.01809i	0.381957	−	0.170559i
$556$		0			0
$557$	−9.21343	+	15.9581i	−0.390386	+	0.676168i	−0.992500	−	0.122242i	$-0.960992\pi$
$557$	−9.21343	+	15.9581i	−0.390386	+	0.676168i	0.602115	+	0.798410i	$0.294325\pi$
$558$		0			0
$559$	11.4103			0.482605
$560$		0			0
$561$	−3.83279	−	8.58333i	−0.161820	−	0.362389i
$562$		0			0
$563$	−37.5803			−1.58382			−0.791910	−	0.610637i	$-0.790913\pi$
$563$	−37.5803			−1.58382			−0.791910	+	0.610637i	$0.790913\pi$
$564$		0			0
$565$		−	13.7909i		−	0.580189i
$566$		0			0
$567$	19.0951	−	14.2260i	0.801918	−	0.597435i
$568$		0			0
$569$	−31.4967			−1.32041			−0.660204	−	0.751086i	$-0.729530\pi$
$569$	−31.4967			−1.32041			−0.660204	+	0.751086i	$0.729530\pi$
$570$		0			0
$571$		−	9.97991i		−	0.417646i	−0.977953	−	0.208823i	$-0.933037\pi$
$571$		−	9.97991i		−	0.417646i	0.977953	−	0.208823i	$-0.0669633\pi$
$572$		0			0
$573$	−2.90634	+	1.29779i	−0.121414	+	0.0542160i
$574$		0			0
$575$		−	0.0909895i		−	0.00379452i
$576$		0			0
$577$	16.2027	+	9.35463i	0.674527	+	0.389438i	0.797790	−	0.602936i	$-0.206003\pi$
$577$	16.2027	+	9.35463i	0.674527	+	0.389438i	−0.123263	+	0.992374i	$0.539336\pi$
$578$		0			0
$579$	−1.32330	−	2.96346i	−0.0549943	−	0.123157i
$580$		0			0
$581$	−28.2960	+	0.215359i	−1.17392	+	0.00893460i
$582$		0			0
$583$		−	19.3705i		−	0.802246i
$584$		0			0
$585$	3.26382	−	3.64080i	0.134942	−	0.150528i
$586$		0			0
$587$	−16.4635	+	28.5156i	−0.679521	+	1.17697i	0.295604	+	0.955311i	$0.404479\pi$
$587$	−16.4635	+	28.5156i	−0.679521	+	1.17697i	−0.975125	+	0.221655i	$0.928854\pi$
$588$		0			0
$589$	2.43949	+	4.22532i	0.100517	+	0.174101i
$590$		0			0
$591$	15.0480	+	33.6992i	0.618991	+	1.38620i
$592$		0			0
$593$	15.3537	−	8.86447i	0.630502	−	0.364020i	−0.150445	−	0.988618i	$-0.548071\pi$
$593$	15.3537	−	8.86447i	0.630502	−	0.364020i	0.780946	+	0.624598i	$0.214737\pi$
$594$		0			0
$595$	3.77288	−	6.65122i	0.154673	−	0.272673i
$596$		0			0
$597$	35.9740	+	3.74130i	1.47232	+	0.153121i
$598$		0			0
$599$			29.8516i			1.21970i	0.792516	+	0.609852i	$0.208771\pi$
$599$			29.8516i			1.21970i	−0.792516	+	0.609852i	$0.791229\pi$
$600$		0			0
$601$	−15.3153	−	8.84232i	−0.624726	−	0.360686i	0.153981	−	0.988074i	$-0.450791\pi$
$601$	−15.3153	−	8.84232i	−0.624726	−	0.360686i	−0.778707	+	0.627388i	$0.784124\pi$
$602$		0			0
$603$	26.0542	+	23.3565i	1.06101	+	0.951150i
$604$		0			0
$605$	4.22721	−	2.44058i	0.171861	−	0.0992238i
$606$		0			0
$607$	−21.9556	+	38.0282i	−0.891149	+	1.54352i	−0.0526491	+	0.998613i	$0.516766\pi$
$607$	−21.9556	+	38.0282i	−0.891149	+	1.54352i	−0.838500	+	0.544902i	$0.816567\pi$
$608$		0			0
$609$	−17.2469	−	37.8471i	−0.698878	−	1.53364i
$610$		0			0
$611$	4.09062	−	2.36172i	0.165489	−	0.0955450i
$612$		0			0
$613$	15.8984	−	27.5368i	0.642129	−	1.11220i	−0.342828	−	0.939398i	$-0.611385\pi$
$613$	15.8984	−	27.5368i	0.642129	−	1.11220i	0.984957	−	0.172801i	$-0.0552818\pi$
$614$		0			0
$615$	−2.69416	−	6.03345i	−0.108639	−	0.243292i
$616$		0			0
$617$	4.52841	+	7.84343i	0.182307	+	0.315765i	0.942666	−	0.333738i	$-0.108310\pi$
$617$	4.52841	+	7.84343i	0.182307	+	0.315765i	−0.760359	+	0.649503i	$0.774977\pi$
$618$		0			0
$619$	−7.17201	−	12.4223i	−0.288267	−	0.499294i	0.685129	−	0.728422i	$-0.259746\pi$
$619$	−7.17201	−	12.4223i	−0.288267	−	0.499294i	−0.973396	+	0.229128i	$0.926413\pi$
$620$		0			0
$621$	0.112696	+	0.124340i	0.00452235	+	0.00498960i
$622$		0			0
$623$	23.4842	+	13.3213i	0.940874	+	0.533708i
$624$		0			0
$625$	1.48760	−	2.57660i	0.0595040	−	0.103064i
$626$		0			0
$627$	3.44415	−	33.1168i	0.137546	−	1.32256i
$628$		0			0
$629$		−	7.53424i		−	0.300410i
$630$		0			0
$631$		−	22.0848i		−	0.879182i	−0.898198	−	0.439591i	$-0.855123\pi$
$631$		−	22.0848i		−	0.879182i	0.898198	−	0.439591i	$-0.144877\pi$
$632$		0			0
$633$	20.3160	+	14.7266i	0.807489	+	0.585328i
$634$		0			0
$635$	4.75678	−	8.23898i	0.188767	−	0.326954i
$636$		0			0
$637$	0.117545	+	7.72166i	0.00465730	+	0.305943i
$638$		0			0
$639$	35.0211	+	31.3949i	1.38541	+	1.24196i
$640$		0			0
$641$	16.0436	+	27.7883i	0.633683	+	1.09757i	0.986793	+	0.161989i	$0.0517909\pi$
$641$	16.0436	+	27.7883i	0.633683	+	1.09757i	−0.353110	+	0.935582i	$0.614876\pi$
$642$		0			0
$643$	−20.7215	−	35.8906i	−0.817175	−	1.41539i	−0.907756	−	0.419500i	$-0.862206\pi$
$643$	−20.7215	−	35.8906i	−0.817175	−	1.41539i	0.0905805	−	0.995889i	$-0.471128\pi$
$644$		0			0
$645$	−15.5327	+	21.4281i	−0.611599	+	0.843730i
$646$		0			0
$647$	−2.08629	+	3.61356i	−0.0820205	+	0.142064i	−0.904118	−	0.427284i	$-0.859471\pi$
$647$	−2.08629	+	3.61356i	−0.0820205	+	0.142064i	0.822097	+	0.569347i	$0.192804\pi$
$648$		0			0
$649$	2.73402	−	1.57849i	0.107320	−	0.0619611i
$650$		0			0
$651$	1.87377	−	2.62680i	0.0734389	−	0.102952i
$652$		0			0
$653$	3.11613	−	5.39730i	0.121944	−	0.211213i	−0.798590	−	0.601875i	$-0.794421\pi$
$653$	3.11613	−	5.39730i	0.121944	−	0.211213i	0.920534	+	0.390662i	$0.127754\pi$
$654$		0			0
$655$	4.51615	−	2.60740i	0.176460	−	0.101879i
$656$		0			0
$657$	14.5375	−	4.75866i	0.567163	−	0.185653i
$658$		0			0
$659$	−12.0701	−	6.96869i	−0.470186	−	0.271462i	0.246132	−	0.969236i	$-0.420840\pi$
$659$	−12.0701	−	6.96869i	−0.470186	−	0.271462i	−0.716317	+	0.697775i	$0.754174\pi$
$660$		0			0
$661$			8.94427i			0.347892i	0.984755	+	0.173946i	$0.0556518\pi$
$661$			8.94427i			0.347892i	−0.984755	+	0.173946i	$0.944348\pi$
$662$		0			0
$663$	−1.52421	−	3.41339i	−0.0591954	−	0.132565i
$664$		0			0
$665$	23.3524	−	13.7205i	0.905567	−	0.532060i
$666$		0			0
$667$	0.253845	−	0.146557i	0.00982891	−	0.00567472i
$668$		0			0
$669$	27.3318	+	2.84251i	1.05671	+	0.109898i
$670$		0			0
$671$	−3.59253	−	6.22245i	−0.138688	−	0.240215i
$672$		0			0
$673$	10.5409	−	18.2573i	0.406321	−	0.703769i	−0.588153	−	0.808749i	$-0.700145\pi$
$673$	10.5409	−	18.2573i	0.406321	−	0.703769i	0.994474	+	0.104981i	$0.0334782\pi$
$674$		0			0
$675$	−3.09066	−	14.3097i	−0.118960	−	0.550781i
$676$		0			0
$677$		−	42.2089i		−	1.62222i	−0.584894	−	0.811110i	$-0.698864\pi$
$677$		−	42.2089i		−	1.62222i	0.584894	−	0.811110i	$-0.301136\pi$
$678$		0			0
$679$	0.161740	+	21.2509i	0.00620700	+	0.815536i
$680$		0			0
$681$	−19.6898	+	27.1630i	−0.754515	+	1.04089i
$682$		0			0
$683$	−25.4778	−	14.7096i	−0.974880	−	0.562847i	−0.0741597	−	0.997246i	$-0.523627\pi$
$683$	−25.4778	−	14.7096i	−0.974880	−	0.562847i	−0.900721	+	0.434399i	$0.856961\pi$
$684$		0			0
$685$		−	28.3742i		−	1.08412i
$686$		0			0
$687$	3.64365	−	35.0351i	0.139014	−	1.33667i
$688$		0			0
$689$		−	7.70321i		−	0.293469i
$690$		0			0
$691$	−35.2505			−1.34099			−0.670496	−	0.741913i	$-0.733919\pi$
$691$	−35.2505			−1.34099			−0.670496	+	0.741913i	$0.733919\pi$
$692$		0			0
$693$	−20.8739	+	7.00914i	−0.792935	+	0.266255i
$694$		0			0
$695$		−	24.8869i		−	0.944013i
$696$		0			0
$697$	−5.05177			−0.191349
$698$		0			0
$699$	−26.8456	+	37.0348i	−1.01539	+	1.40078i
$700$		0			0
$701$	−21.2983			−0.804426			−0.402213	−	0.915546i	$-0.631759\pi$
$701$	−21.2983			−0.804426			−0.402213	+	0.915546i	$0.631759\pi$
$702$		0			0
$703$	13.3431	−	23.1109i	0.503244	−	0.871644i
$704$		0			0
$705$	−1.13329	+	10.8970i	−0.0426821	+	0.410404i
$706$		0			0
$707$	−2.02677	−	1.14968i	−0.0762244	−	0.0432381i
$708$		0			0
$709$	52.3922			1.96763			0.983815	−	0.179185i	$-0.0573462\pi$
$709$	52.3922			1.96763			0.983815	+	0.179185i	$0.0573462\pi$
$710$		0			0
$711$	−18.7285	−	16.7893i	−0.702375	−	0.629648i
$712$		0			0
$713$	0.0196930	+	0.0113697i	0.000737507	+	0.000425800i
$714$		0			0
$715$	−3.91574	+	2.26075i	−0.146440	+	0.0845473i
$716$		0			0
$717$	−8.53962	−	6.19016i	−0.318918	−	0.231176i
$718$		0			0
$719$	−2.03467	−	3.52415i	−0.0758802	−	0.131428i	0.825588	−	0.564273i	$-0.190843\pi$
$719$	−2.03467	−	3.52415i	−0.0758802	−	0.131428i	−0.901469	+	0.432844i	$0.857510\pi$
$720$		0			0
$721$	−2.83467	+	0.0215745i	−0.105568	+	0.000803475i
$722$		0			0
$723$	−0.840514	−	0.609268i	−0.0312591	−	0.0226589i
$724$		0			0
$725$	−25.5709			−0.949678
$726$		0			0
$727$	−6.63112	+	11.4854i	−0.245935	+	0.425971i	−0.962394	−	0.271658i	$-0.912428\pi$
$727$	−6.63112	+	11.4854i	−0.245935	+	0.425971i	0.716459	+	0.697629i	$0.245762\pi$
$728$		0			0
$729$	21.9470	+	15.7267i	0.812852	+	0.582471i
$730$		0			0
$731$	10.1169	+	17.5230i	0.374188	+	0.648112i
$732$		0			0
$733$	39.4414	+	22.7715i	1.45680	+	0.841084i	0.998852	−	0.0478949i	$-0.0152513\pi$
$733$	39.4414	+	22.7715i	1.45680	+	0.841084i	0.457948	+	0.888979i	$0.348585\pi$
$734$		0			0
$735$	−14.6610	−	10.2906i	−0.540778	−	0.379576i
$736$		0			0
$737$	−16.1784	−	28.0217i	−0.595938	−	1.03219i
$738$		0			0
$739$	−32.1653	−	18.5707i	−1.18322	−	0.683133i	−0.226464	−	0.974020i	$-0.572716\pi$
$739$	−32.1653	−	18.5707i	−1.18322	−	0.683133i	−0.956758	+	0.290886i	$0.906050\pi$
$740$		0			0
$741$	1.36966	−	13.1698i	0.0503156	−	0.483804i
$742$		0			0
$743$	−15.9963	+	9.23546i	−0.586847	+	0.338816i	−0.763850	−	0.645394i	$-0.776693\pi$
$743$	−15.9963	+	9.23546i	−0.586847	+	0.338816i	0.177003	+	0.984210i	$0.443360\pi$
$744$		0			0
$745$	27.1759	−	15.6900i	0.995649	−	0.574838i
$746$		0			0
$747$	−9.98162	−	30.4935i	−0.365208	−	1.11570i
$748$		0			0
$749$	43.7527	+	24.8186i	1.59869	+	0.906852i
$750$		0			0
$751$	16.6822	+	9.63147i	0.608742	+	0.351457i	0.772473	−	0.635048i	$-0.219020\pi$
$751$	16.6822	+	9.63147i	0.608742	+	0.351457i	−0.163731	+	0.986505i	$0.552353\pi$
$752$		0			0
$753$	−10.4095	−	23.3115i	−0.379342	−	0.849517i
$754$		0			0
$755$	−21.2876			−0.774735
$756$		0			0
$757$	8.29756			0.301580			0.150790	−	0.988566i	$-0.451818\pi$
$757$	8.29756			0.301580			0.150790	+	0.988566i	$0.451818\pi$
$758$		0			0
$759$	−0.0632722	−	0.141695i	−0.00229663	−	0.00514320i
$760$		0			0
$761$	−13.2960	−	7.67646i	−0.481980	−	0.278272i	0.239261	−	0.970955i	$-0.423095\pi$
$761$	−13.2960	−	7.67646i	−0.481980	−	0.278272i	−0.721241	+	0.692684i	$0.756428\pi$
$762$		0			0
$763$	7.40488	−	0.0563581i	0.268075	−	0.00204030i
$764$		0			0
$765$	8.48509	+	1.78420i	0.306779	+	0.0645078i
$766$		0			0
$767$	1.08726	−	0.627728i	0.0392585	−	0.0226659i
$768$		0			0
$769$	−32.4625	+	18.7422i	−1.17063	+	0.675862i	−0.953828	−	0.300354i	$-0.902895\pi$
$769$	−32.4625	+	18.7422i	−1.17063	+	0.675862i	−0.216800	+	0.976216i	$0.569562\pi$
$770$		0			0
$771$	2.93557	−	28.2266i	0.105722	−	1.01656i
$772$		0			0
$773$	−36.9329	−	21.3232i	−1.32838	−	0.766942i	−0.343334	−	0.939214i	$-0.611556\pi$
$773$	−36.9329	−	21.3232i	−1.32838	−	0.766942i	−0.985050	+	0.172271i	$0.944889\pi$
$774$		0			0
$775$	−0.991877	−	1.71798i	−0.0356293	−	0.0617117i
$776$		0			0
$777$	−17.5671	−	1.69194i	−0.630217	−	0.0606980i
$778$		0			0
$779$	−15.4960	−	8.94664i	−0.555203	−	0.320547i
$780$		0			0
$781$	−21.7463	−	37.6657i	−0.778144	−	1.34779i
$782$		0			0
$783$	34.9434	−	31.6712i	1.24878	−	1.13183i
$784$		0			0
$785$	−4.20901	+	7.29021i	−0.150226	+	0.260199i
$786$		0			0
$787$	18.1499			0.646972			0.323486	−	0.946233i	$-0.395145\pi$
$787$	18.1499			0.646972			0.323486	+	0.946233i	$0.395145\pi$
$788$		0			0
$789$	8.29350	+	6.01175i	0.295257	+	0.214024i
$790$		0			0
$791$	−12.1857	+	21.4822i	−0.433274	+	0.763819i
$792$		0			0
$793$	−1.42866	−	2.47452i	−0.0507334	−	0.0878728i
$794$		0			0
$795$	14.4663	+	10.4863i	0.513067	+	0.371909i
$796$		0			0
$797$	30.3572	−	17.5268i	1.07531	−	0.620830i	0.145681	−	0.989332i	$-0.453463\pi$
$797$	30.3572	−	17.5268i	1.07531	−	0.620830i	0.929627	+	0.368502i	$0.120129\pi$
$798$		0			0
$799$	7.25387	+	4.18802i	0.256623	+	0.148162i
$800$		0			0
$801$	−6.29966	+	29.9592i	−0.222587	+	1.05856i
$802$		0			0
$803$	−14.1451			−0.499169
$804$		0			0
$805$	0.0622833	−	0.109799i	0.00219520	−	0.00386992i
$806$		0			0
$807$	−1.87923	+	18.0696i	−0.0661522	+	0.636078i
$808$		0			0
$809$	−18.5834	+	32.1874i	−0.653358	+	1.13165i	0.328945	+	0.944349i	$0.393307\pi$
$809$	−18.5834	+	32.1874i	−0.653358	+	1.13165i	−0.982303	+	0.187300i	$0.940026\pi$
$810$		0			0
$811$	−13.3687			−0.469439			−0.234720	−	0.972063i	$-0.575417\pi$
$811$	−13.3687			−0.469439			−0.234720	+	0.972063i	$0.575417\pi$
$812$		0			0
$813$	−7.48798	+	10.3300i	−0.262615	+	0.362290i
$814$		0			0
$815$	−7.25023			−0.253964
$816$		0			0
$817$			71.6679i			2.50734i
$818$		0			0
$819$	−8.30107	+	2.78737i	−0.290063	+	0.0973985i
$820$		0			0
$821$	−21.7944			−0.760629			−0.380315	−	0.924857i	$-0.624184\pi$
$821$	−21.7944			−0.760629			−0.380315	+	0.924857i	$0.624184\pi$
$822$		0			0
$823$		−	13.5246i		−	0.471439i	−0.971821	−	0.235719i	$-0.924255\pi$
$823$		−	13.5246i		−	0.471439i	0.971821	−	0.235719i	$-0.0757446\pi$
$824$		0			0
$825$	−1.40036	+	13.4650i	−0.0487544	+	0.468792i
$826$		0			0
$827$			45.6866i			1.58868i	0.607474	+	0.794339i	$0.292183\pi$
$827$			45.6866i			1.58868i	−0.607474	+	0.794339i	$0.707817\pi$
$828$		0			0
$829$	−30.2094	−	17.4414i	−1.04922	−	0.605766i	−0.126787	−	0.991930i	$-0.540466\pi$
$829$	−30.2094	−	17.4414i	−1.04922	−	0.605766i	−0.922430	+	0.386164i	$0.873800\pi$
$830$		0			0
$831$	1.80486	−	2.48989i	0.0626099	−	0.0863733i
$832$		0			0
$833$	−11.7541	+	7.02690i	−0.407254	+	0.243468i
$834$		0			0
$835$		−	2.83089i		−	0.0979669i
$836$		0			0
$837$	3.48326	+	1.11918i	0.120399	+	0.0386844i
$838$		0			0
$839$	6.74592	−	11.6843i	0.232895	−	0.403386i	−0.725764	−	0.687944i	$-0.758513\pi$
$839$	6.74592	−	11.6843i	0.232895	−	0.403386i	0.958659	+	0.284558i	$0.0918468\pi$
$840$		0			0
$841$	−26.6871	−	46.2235i	−0.920246	−	1.59391i
$842$		0			0
$843$	7.17563	+	0.746266i	0.247142	+	0.0257028i
$844$		0			0
$845$	15.0754	−	8.70380i	0.518610	−	0.299420i
$846$		0			0
$847$	−8.74125	+	0.0665291i	−0.300353	+	0.00228597i
$848$		0			0
$849$	−2.40650	−	5.38925i	−0.0825910	−	0.184958i
$850$		0			0
$851$		−	0.124376i		−	0.00426356i
$852$		0			0
$853$	25.7099	+	14.8436i	0.880291	+	0.508236i	0.870754	−	0.491718i	$-0.163631\pi$
$853$	25.7099	+	14.8436i	0.880291	+	0.508236i	0.00953667	+	0.999955i	$0.496964\pi$
$854$		0			0
$855$	22.8678	+	20.5000i	0.782062	+	0.701084i
$856$		0			0
$857$	−22.0886	+	12.7529i	−0.754534	+	0.435630i	−0.827330	−	0.561717i	$-0.810141\pi$
$857$	−22.0886	+	12.7529i	−0.754534	+	0.435630i	0.0727959	+	0.997347i	$0.476808\pi$
$858$		0			0
$859$	−1.31398	+	2.27588i	−0.0448324	+	0.0776521i	−0.887571	−	0.460671i	$-0.847609\pi$
$859$	−1.31398	+	2.27588i	−0.0448324	+	0.0776521i	0.842738	+	0.538323i	$0.180942\pi$
$860$		0			0
$861$	−1.13446	+	11.7789i	−0.0386622	+	0.401423i
$862$		0			0
$863$	29.6590	−	17.1237i	1.00961	−	0.582896i	0.0985294	−	0.995134i	$-0.468586\pi$
$863$	29.6590	−	17.1237i	1.00961	−	0.582896i	0.911076	+	0.412238i	$0.135253\pi$
$864$		0			0
$865$	−17.6259	+	30.5289i	−0.599298	+	1.03801i
$866$		0			0
$867$	−13.3907	+	18.4731i	−0.454771	+	0.627378i
$868$		0			0
$869$	11.6295	+	20.1428i	0.394503	+	0.683299i
$870$		0			0
$871$	−6.43375	−	11.1436i	−0.217999	−	0.377586i
$872$		0			0
$873$	−22.9013	+	7.49643i	−0.775091	+	0.253716i
$874$		0			0
$875$	−26.3453	+	15.4790i	−0.890635	+	0.523286i
$876$		0			0
$877$	17.7909	−	30.8147i	0.600754	−	1.04054i	−0.391953	−	0.919985i	$-0.628200\pi$
$877$	17.7909	−	30.8147i	0.600754	−	1.04054i	0.992707	−	0.120552i	$-0.0384664\pi$
$878$		0			0
$879$	26.2218	+	19.0075i	0.884440	+	0.641109i
$880$		0			0
$881$			40.8828i			1.37738i	0.725058	+	0.688688i	$0.241813\pi$
$881$			40.8828i			1.37738i	−0.725058	+	0.688688i	$0.758187\pi$
$882$		0			0
$883$		−	13.9504i		−	0.469468i	−0.972060	−	0.234734i	$-0.924578\pi$
$883$		−	13.9504i		−	0.469468i	0.972060	−	0.234734i	$-0.0754219\pi$
$884$		0			0
$885$	−0.301219	+	2.89634i	−0.0101254	+	0.0973594i
$886$		0			0
$887$	−14.9999	+	25.9805i	−0.503646	+	0.872340i	0.496345	+	0.868125i	$0.334675\pi$
$887$	−14.9999	+	25.9805i	−0.503646	+	0.872340i	−0.999991	+	0.00421500i	$0.998658\pi$
$888$		0			0
$889$	−14.6896	+	8.63079i	−0.492675	+	0.289467i
$890$		0			0
$891$	−14.7637	−	20.1349i	−0.494601	−	0.674543i
$892$		0			0
$893$	14.8339	+	25.6931i	0.496398	+	0.859787i
$894$		0			0
$895$	7.19693	+	12.4655i	0.240567	+	0.416674i
$896$		0			0
$897$	−0.0251619	−	0.0563487i	−0.000840130	−	0.00188143i
$898$		0			0
$899$	3.19525	−	5.53433i	0.106567	−	0.184580i
$900$		0			0
$901$	11.8299	−	6.83002i	0.394113	−	0.227541i
$902$		0			0
$903$	43.1292	−	19.6539i	1.43525	−	0.654041i
$904$		0			0
$905$	−1.14141	+	1.97698i	−0.0379417	+	0.0657170i
$906$		0			0
$907$	−34.8441	+	20.1173i	−1.15698	+	0.667983i	−0.950578	−	0.310485i	$-0.899509\pi$
$907$	−34.8441	+	20.1173i	−1.15698	+	0.667983i	−0.206401	+	0.978467i	$0.566175\pi$
$908$		0			0
$909$	0.543683	−	2.58559i	0.0180328	−	0.0857585i
$910$		0			0
$911$	−16.1689	−	9.33513i	−0.535700	−	0.309287i	0.207634	−	0.978206i	$-0.433424\pi$
$911$	−16.1689	−	9.33513i	−0.535700	−	0.309287i	−0.743334	+	0.668920i	$0.766757\pi$
$912$		0			0
$913$			29.6703i			0.981943i
$914$		0			0
$915$	6.59187	+	0.685555i	0.217920	+	0.0226637i
$916$		0			0
$917$	−9.33872	+	0.0710764i	−0.308392	+	0.00234715i
$918$		0			0
$919$	16.6056	−	9.58726i	0.547769	−	0.316254i	−0.200453	−	0.979703i	$-0.564241\pi$
$919$	16.6056	−	9.58726i	0.547769	−	0.316254i	0.748222	+	0.663449i	$0.230908\pi$
$920$		0			0
$921$	−9.22509	−	20.6591i	−0.303977	−	0.680742i
$922$		0			0
$923$	−8.64799	−	14.9788i	−0.284652	−	0.493032i
$924$		0			0
$925$	−5.42519	+	9.39671i	−0.178379	+	0.308962i
$926$		0			0
$927$	−0.999949	−	3.05480i	−0.0328426	−	0.100333i
$928$		0			0
$929$			32.8222i			1.07686i	0.842669	+	0.538431i	$0.180983\pi$
$929$			32.8222i			1.07686i	−0.842669	+	0.538431i	$0.819017\pi$
$930$		0			0
$931$	−48.4996	+	0.738298i	−1.58951	+	0.0241967i
$932$		0			0
$933$	21.8037	+	48.8283i	0.713822	+	1.59857i
$934$		0			0
$935$	−6.94375	−	4.00897i	−0.227085	−	0.131107i
$936$		0			0
$937$		−	5.98141i		−	0.195404i	−0.995216	−	0.0977020i	$-0.968851\pi$
$937$		−	5.98141i		−	0.195404i	0.995216	−	0.0977020i	$-0.0311492\pi$
$938$		0			0
$939$	25.2730	−	11.2854i	0.824753	−	0.368283i
$940$		0			0
$941$			25.2347i			0.822629i	0.911494	+	0.411314i	$0.134930\pi$
$941$			25.2347i			0.822629i	−0.911494	+	0.411314i	$0.865070\pi$
$942$		0			0
$943$	−0.0833953			−0.00271572
$944$		0			0
$945$	6.06557	−	19.3835i	0.197313	−	0.630545i
$946$		0			0
$947$		−	8.61244i		−	0.279867i	−0.990161	−	0.139933i	$-0.955311\pi$
$947$		−	8.61244i		−	0.279867i	0.990161	−	0.139933i	$-0.0446888\pi$
$948$		0			0
$949$	−5.62516			−0.182601
$950$		0			0
$951$	−2.61976	−	5.86681i	−0.0849514	−	0.190244i
$952$		0			0
$953$	12.1465			0.393463			0.196731	−	0.980457i	$-0.436967\pi$
$953$	12.1465			0.393463			0.196731	+	0.980457i	$0.436967\pi$
$954$		0			0
$955$	−1.35745	+	2.35117i	−0.0439260	+	0.0760821i
$956$		0			0
$957$	−39.8206	+	17.7814i	−1.28722	+	0.574792i
$958$		0			0
$959$	−25.0715	+	44.1985i	−0.809600	+	1.42724i
$960$		0			0
$961$	−30.5042			−0.984008
$962$		0			0
$963$	−11.7367	+	55.8162i	−0.378210	+	1.79865i
$964$		0			0
$965$	−2.39738	−	1.38413i	−0.0771743	−	0.0445566i
$966$		0			0
$967$	−10.8574	+	6.26853i	−0.349151	+	0.201582i	−0.664311	−	0.747456i	$-0.731275\pi$
$967$	−10.8574	+	6.26853i	−0.349151	+	0.201582i	0.315160	+	0.949038i	$0.397942\pi$
$968$		0			0
$969$	21.4394	−	9.57353i	0.688734	−	0.307546i
$970$		0			0
$971$	1.23493	+	2.13896i	0.0396308	+	0.0686426i	0.885160	−	0.465286i	$-0.154048\pi$
$971$	1.23493	+	2.13896i	0.0396308	+	0.0686426i	−0.845530	+	0.533929i	$0.820715\pi$
$972$		0			0
$973$	−21.9901	+	38.7664i	−0.704970	+	1.24279i
$974$		0			0
$975$	−0.556891	+	5.35472i	−0.0178348	+	0.171488i
$976$		0			0
$977$	41.3188			1.32191			0.660953	−	0.750428i	$-0.270152\pi$
$977$	41.3188			1.32191			0.660953	+	0.750428i	$0.270152\pi$
$978$		0			0
$979$	14.1549	−	24.5170i	0.452393	−	0.783568i
$980$		0			0
$981$	2.61213	+	7.97994i	0.0833988	+	0.254780i
$982$		0			0
$983$	−4.40445	−	7.62872i	−0.140480	−	0.243319i	0.787197	−	0.616701i	$-0.211531\pi$
$983$	−4.40445	−	7.62872i	−0.140480	−	0.243319i	−0.927677	+	0.373382i	$0.878198\pi$
$984$		0			0
$985$	27.2620	+	15.7397i	0.868639	+	0.501509i
$986$		0			0
$987$	11.3939	−	15.9729i	0.362673	−	0.508423i
$988$		0			0
$989$	0.167011	+	0.289272i	0.00531065	+	0.00919832i
$990$		0			0
$991$	23.1527	+	13.3672i	0.735470	+	0.424624i	0.820420	−	0.571761i	$-0.193740\pi$
$991$	23.1527	+	13.3672i	0.735470	+	0.424624i	−0.0849498	+	0.996385i	$0.527073\pi$
$992$		0			0
$993$	44.0438	−	19.6672i	1.39769	−	0.624120i
$994$		0			0
$995$	26.7166	−	15.4248i	0.846973	−	0.489000i
$996$		0			0
$997$	−26.4192	+	15.2531i	−0.836705	+	0.483072i	−0.856143	−	0.516739i	$-0.827146\pi$
$997$	−26.4192	+	15.2531i	−0.836705	+	0.483072i	0.0194379	+	0.999811i	$0.493812\pi$
$998$		0			0
$999$	−4.22472	−	19.5604i	−0.133664	−	0.618863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.367.6	yes	24
3.2	odd	2		3024.2.cz.h.2719.8		24
4.3	odd	2		1008.2.cz.h.367.7	yes	24
7.5	odd	6		1008.2.bf.g.943.1	yes	24
9.4	even	3		1008.2.bf.h.31.12	yes	24
9.5	odd	6		3024.2.bf.g.1711.5		24
12.11	even	2		3024.2.cz.g.2719.8		24
21.5	even	6		3024.2.bf.h.2287.8		24
28.19	even	6		1008.2.bf.h.943.12	yes	24
36.23	even	6		3024.2.bf.h.1711.5		24
36.31	odd	6		1008.2.bf.g.31.1	✓	24
63.5	even	6		3024.2.cz.g.1279.8		24
63.40	odd	6		1008.2.cz.h.607.7	yes	24
84.47	odd	6		3024.2.bf.g.2287.8		24
252.103	even	6	inner	1008.2.cz.g.607.6	yes	24
252.131	odd	6		3024.2.cz.h.1279.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.1	✓	24	36.31	odd	6
1008.2.bf.g.943.1	yes	24	7.5	odd	6
1008.2.bf.h.31.12	yes	24	9.4	even	3
1008.2.bf.h.943.12	yes	24	28.19	even	6
1008.2.cz.g.367.6	yes	24	1.1	even	1	trivial
1008.2.cz.g.607.6	yes	24	252.103	even	6	inner
1008.2.cz.h.367.7	yes	24	4.3	odd	2
1008.2.cz.h.607.7	yes	24	63.40	odd	6
3024.2.bf.g.1711.5		24	9.5	odd	6
3024.2.bf.g.2287.8		24	84.47	odd	6
3024.2.bf.h.1711.5		24	36.23	even	6
3024.2.bf.h.2287.8		24	21.5	even	6
3024.2.cz.g.1279.8		24	63.5	even	6
3024.2.cz.g.2719.8		24	12.11	even	2
3024.2.cz.h.1279.8		24	252.131	odd	6
3024.2.cz.h.2719.8		24	3.2	odd	2

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.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.706216 - 1.58154i) q^{3} +(-1.27943 - 0.738680i) q^{5} +(1.34028 + 2.28115i) q^{7} +(-2.00252 + 2.23381i) q^{9} +O(q^{10})\)	\(q+(-0.706216 - 1.58154i) q^{3} +(-1.27943 - 0.738680i) q^{5} +(1.34028 + 2.28115i) q^{7} +(-2.00252 + 2.23381i) q^{9} +(2.40250 - 1.38709i) q^{11} +(0.955418 - 0.551611i) q^{13} +(-0.264694 + 2.54514i) q^{15} +(1.69424 + 0.978168i) q^{17} +(3.46466 + 6.00097i) q^{19} +(2.66120 - 3.73068i) q^{21} +(0.0279687 + 0.0161477i) q^{23} +(-1.40870 - 2.43994i) q^{25} +(4.94707 + 1.58950i) q^{27} +(4.53801 - 7.86007i) q^{29} +0.704107 q^{31} +(-3.89041 - 2.82006i) q^{33} +(-0.0297482 - 3.90862i) q^{35} +(-1.92560 - 3.33523i) q^{37} +(-1.54713 - 1.12147i) q^{39} +(-2.23630 + 1.29113i) q^{41} +(8.95705 + 5.17136i) q^{43} +(4.21216 - 1.37879i) q^{45} +4.28149 q^{47} +(-3.40732 + 6.11475i) q^{49} +(0.350511 - 3.37030i) q^{51} +(3.49123 - 6.04699i) q^{53} -4.09845 q^{55} +(7.04395 - 9.71747i) q^{57} +1.13799 q^{59} -2.58999i q^{61} +(-7.77960 - 1.57412i) q^{63} -1.62986 q^{65} -11.6636i q^{67} +(0.00578629 - 0.0556373i) q^{69} -15.6777i q^{71} +(-4.41573 - 2.54942i) q^{73} +(-2.86401 + 3.95104i) q^{75} +(6.38417 + 3.62140i) q^{77} +8.38410i q^{79} +(-0.979853 - 8.94650i) q^{81} +(-5.34759 + 9.26231i) q^{83} +(-1.44511 - 2.50300i) q^{85} +(-15.6358 - 1.62613i) q^{87} +(8.83761 - 5.10240i) q^{89} +(2.53883 + 1.44015i) q^{91} +(-0.497252 - 1.11357i) q^{93} -10.2371i q^{95} +(6.95620 + 4.01617i) q^{97} +(-1.71256 + 8.14441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

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