LMFDB - Embedded newform 1456.2.cc.f.225.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.2
Root			$-2.42977i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.f.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21489 + 2.10425i) q^{3} -3.63781i q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.45190 - 2.51476i) q^{9} +(-3.34871 - 1.93338i) q^{11} +(-3.58920 + 0.342967i) q^{13} +(7.65484 + 4.41953i) q^{15} +(0.817697 + 1.41629i) q^{17} +(-1.74226 + 1.00589i) q^{19} +2.42977i q^{21} +(1.20706 - 2.09068i) q^{23} -8.23365 q^{25} -0.233744 q^{27} +(-2.01491 + 3.48993i) q^{29} +9.12236i q^{31} +(8.13661 - 4.69768i) q^{33} +(-1.81890 - 3.15043i) q^{35} +(10.4146 + 6.01285i) q^{37} +(3.63879 - 7.96923i) q^{39} +(8.28088 + 4.78097i) q^{41} +(4.93046 + 8.53981i) q^{43} +(-9.14823 + 5.28173i) q^{45} +8.94009i q^{47} +(0.500000 - 0.866025i) q^{49} -3.97364 q^{51} -6.91625 q^{53} +(-7.03327 + 12.1820i) q^{55} -4.88819i q^{57} +(-0.0998109 + 0.0576258i) q^{59} +(2.47037 + 4.27881i) q^{61} +(-2.51476 - 1.45190i) q^{63} +(1.24765 + 13.0568i) q^{65} +(-7.89684 - 4.55925i) q^{67} +(2.93287 + 5.07988i) q^{69} +(0.253741 - 0.146497i) q^{71} -1.89250i q^{73} +(10.0030 - 17.3256i) q^{75} -3.86676 q^{77} -5.12890 q^{79} +(4.63967 - 8.03615i) q^{81} -11.8010i q^{83} +(5.15220 - 2.97463i) q^{85} +(-4.89578 - 8.47975i) q^{87} +(2.13383 + 1.23197i) q^{89} +(-2.93686 + 2.09162i) q^{91} +(-19.1957 - 11.0826i) q^{93} +(3.65925 + 6.33801i) q^{95} +(-15.1343 + 8.73781i) q^{97} +11.2283i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.21489	+	2.10425i	−0.701415	+	1.21489i	0.266554	+	0.963820i	$0.414115\pi$
$3$	−1.21489	+	2.10425i	−0.701415	+	1.21489i	−0.967970	+	0.251067i	$0.919219\pi$
$4$		0			0
$5$		−	3.63781i		−	1.62688i	−0.581651	−	0.813439i	$-0.697593\pi$
$5$		−	3.63781i		−	1.62688i	0.581651	−	0.813439i	$-0.302407\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		0			0
$9$	−1.45190	−	2.51476i	−0.483967	−	0.838255i
$10$		0			0
$11$	−3.34871	−	1.93338i	−1.00967	−	0.582936i	−0.0985783	−	0.995129i	$-0.531430\pi$
$11$	−3.34871	−	1.93338i	−1.00967	−	0.582936i	−0.911096	+	0.412193i	$0.864763\pi$
$12$		0			0
$13$	−3.58920	+	0.342967i	−0.995466	+	0.0951220i
$13$	−3.58920	+	0.342967i	−0.995466	+	0.0951220i
$14$		0			0
$15$	7.65484	+	4.41953i	1.97647	+	1.14112i
$16$		0			0
$17$	0.817697	+	1.41629i	0.198321	+	0.343501i	0.947984	−	0.318318i	$-0.103118\pi$
$17$	0.817697	+	1.41629i	0.198321	+	0.343501i	−0.749663	+	0.661819i	$0.769785\pi$
$18$		0			0
$19$	−1.74226	+	1.00589i	−0.399702	+	0.230768i	−0.686355	−	0.727266i	$-0.740790\pi$
$19$	−1.74226	+	1.00589i	−0.399702	+	0.230768i	0.286654	+	0.958034i	$0.407457\pi$
$20$		0			0
$21$			2.42977i			0.530220i
$22$		0			0
$23$	1.20706	−	2.09068i	0.251689	−	0.435937i	−0.712302	−	0.701873i	$-0.752347\pi$
$23$	1.20706	−	2.09068i	0.251689	−	0.435937i	0.963991	+	0.265935i	$0.0856808\pi$
$24$		0			0
$25$	−8.23365			−1.64673
$26$		0			0
$27$	−0.233744			−0.0449840
$28$		0			0
$29$	−2.01491	+	3.48993i	−0.374160	+	0.648064i	−0.990201	−	0.139650i	$-0.955402\pi$
$29$	−2.01491	+	3.48993i	−0.374160	+	0.648064i	0.616041	+	0.787714i	$0.288736\pi$
$30$		0			0
$31$			9.12236i			1.63842i	0.573490	+	0.819212i	$0.305589\pi$
$31$			9.12236i			1.63842i	−0.573490	+	0.819212i	$0.694411\pi$
$32$		0			0
$33$	8.13661	−	4.69768i	1.41640	−	0.817760i
$34$		0			0
$35$	−1.81890	−	3.15043i	−0.307451	−	0.532521i
$36$		0			0
$37$	10.4146	+	6.01285i	1.71214	+	0.988507i	0.931660	+	0.363332i	$0.118361\pi$
$37$	10.4146	+	6.01285i	1.71214	+	0.988507i	0.780485	+	0.625175i	$0.214972\pi$
$38$		0			0
$39$	3.63879	−	7.96923i	0.582672	−	1.27610i
$40$		0			0
$41$	8.28088	+	4.78097i	1.29326	+	0.746661i	0.979230	−	0.202753i	$-0.0649889\pi$
$41$	8.28088	+	4.78097i	1.29326	+	0.746661i	0.314026	+	0.949414i	$0.398322\pi$
$42$		0			0
$43$	4.93046	+	8.53981i	0.751888	+	1.30231i	0.946906	+	0.321509i	$0.104190\pi$
$43$	4.93046	+	8.53981i	0.751888	+	1.30231i	−0.195018	+	0.980800i	$0.562477\pi$
$44$		0			0
$45$	−9.14823	+	5.28173i	−1.36374	+	0.787354i
$46$		0			0
$47$			8.94009i			1.30405i	0.758199	+	0.652023i	$0.226079\pi$
$47$			8.94009i			1.30405i	−0.758199	+	0.652023i	$0.773921\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−3.97364			−0.556421
$52$		0			0
$53$	−6.91625			−0.950020			−0.475010	−	0.879980i	$-0.657556\pi$
$53$	−6.91625			−0.950020			−0.475010	+	0.879980i	$0.657556\pi$
$54$		0			0
$55$	−7.03327	+	12.1820i	−0.948365	+	1.64262i
$56$		0			0
$57$		−	4.88819i		−	0.647457i
$58$		0			0
$59$	−0.0998109	+	0.0576258i	−0.0129943	+	0.00750224i	−0.506483	−	0.862250i	$-0.669055\pi$
$59$	−0.0998109	+	0.0576258i	−0.0129943	+	0.00750224i	0.493489	+	0.869752i	$0.335721\pi$
$60$		0			0
$61$	2.47037	+	4.27881i	0.316299	+	0.547846i	0.979713	−	0.200407i	$-0.0642264\pi$
$61$	2.47037	+	4.27881i	0.316299	+	0.547846i	−0.663414	+	0.748253i	$0.730893\pi$
$62$		0			0
$63$	−2.51476	−	1.45190i	−0.316831	−	0.182922i
$64$		0			0
$65$	1.24765	+	13.0568i	0.154752	+	1.61950i
$66$		0			0
$67$	−7.89684	−	4.55925i	−0.964753	−	0.557000i	−0.0671204	−	0.997745i	$-0.521381\pi$
$67$	−7.89684	−	4.55925i	−0.964753	−	0.557000i	−0.897633	+	0.440744i	$0.854715\pi$
$68$		0			0
$69$	2.93287	+	5.07988i	0.353076	+	0.611546i
$70$		0			0
$71$	0.253741	−	0.146497i	0.0301135	−	0.0173860i	−0.484868	−	0.874588i	$-0.661132\pi$
$71$	0.253741	−	0.146497i	0.0301135	−	0.0173860i	0.514981	+	0.857201i	$0.327799\pi$
$72$		0			0
$73$		−	1.89250i		−	0.221500i	−0.993848	−	0.110750i	$-0.964675\pi$
$73$		−	1.89250i		−	0.221500i	0.993848	−	0.110750i	$-0.0353254\pi$
$74$		0			0
$75$	10.0030	−	17.3256i	1.15504	−	2.00059i
$76$		0			0
$77$	−3.86676			−0.440658
$78$		0			0
$79$	−5.12890			−0.577046			−0.288523	−	0.957473i	$-0.593164\pi$
$79$	−5.12890			−0.577046			−0.288523	+	0.957473i	$0.593164\pi$
$80$		0			0
$81$	4.63967	−	8.03615i	0.515519	−	0.892905i
$82$		0			0
$83$		−	11.8010i		−	1.29533i	−0.761926	−	0.647664i	$-0.775746\pi$
$83$		−	11.8010i		−	1.29533i	0.761926	−	0.647664i	$-0.224254\pi$
$84$		0			0
$85$	5.15220	−	2.97463i	0.558835	−	0.322643i
$86$		0			0
$87$	−4.89578	−	8.47975i	−0.524883	−	0.909124i
$88$		0			0
$89$	2.13383	+	1.23197i	0.226186	+	0.130588i	0.608811	−	0.793315i	$-0.291647\pi$
$89$	2.13383	+	1.23197i	0.226186	+	0.130588i	−0.382625	+	0.923904i	$0.624980\pi$
$90$		0			0
$91$	−2.93686	+	2.09162i	−0.307866	+	0.219261i
$92$		0			0
$93$	−19.1957	−	11.0826i	−1.99050	−	1.14922i
$94$		0			0
$95$	3.65925	+	6.33801i	0.375431	+	0.650266i
$96$		0			0
$97$	−15.1343	+	8.73781i	−1.53666	+	0.887190i	−0.537627	+	0.843183i	$0.680679\pi$
$97$	−15.1343	+	8.73781i	−1.53666	+	0.887190i	−0.999031	+	0.0440072i	$0.985988\pi$
$98$		0			0
$99$			11.2283i			1.12849i
$100$		0			0
$101$	−5.14126	+	8.90493i	−0.511575	+	0.886074i	0.488335	+	0.872656i	$0.337604\pi$
$101$	−5.14126	+	8.90493i	−0.511575	+	0.886074i	−0.999910	+	0.0134176i	$0.995729\pi$
$102$		0			0
$103$	−7.17129			−0.706608			−0.353304	−	0.935509i	$-0.614942\pi$
$103$	−7.17129			−0.706608			−0.353304	+	0.935509i	$0.614942\pi$
$104$		0			0
$105$	8.83905			0.862603
$106$		0			0
$107$	7.49135	−	12.9754i	0.724216	−	1.25438i	−0.235079	−	0.971976i	$-0.575535\pi$
$107$	7.49135	−	12.9754i	0.724216	−	1.25438i	0.959296	−	0.282404i	$-0.0911317\pi$
$108$		0			0
$109$			8.82413i			0.845198i	0.906317	+	0.422599i	$0.138882\pi$
$109$			8.82413i			0.845198i	−0.906317	+	0.422599i	$0.861118\pi$
$110$		0			0
$111$	−25.3050	+	14.6099i	−2.40185	+	1.38671i
$112$		0			0
$113$	−2.74315	−	4.75128i	−0.258054	−	0.446963i	0.707666	−	0.706547i	$-0.249748\pi$
$113$	−2.74315	−	4.75128i	−0.258054	−	0.446963i	−0.965721	+	0.259584i	$0.916415\pi$
$114$		0			0
$115$	−7.60550	−	4.39104i	−0.709217	−	0.409466i
$116$		0			0
$117$	6.07365	+	8.52805i	0.561509	+	0.788418i
$118$		0			0
$119$	1.41629	+	0.817697i	0.129831	+	0.0749582i
$120$		0			0
$121$	1.97592	+	3.42239i	0.179629	+	0.311126i
$122$		0			0
$123$	−20.1207	+	11.6167i	−1.81422	+	1.04744i
$124$		0			0
$125$			11.7634i			1.05215i
$126$		0			0
$127$	6.04055	−	10.4625i	0.536012	−	0.928401i	−0.463101	−	0.886305i	$-0.653263\pi$
$127$	6.04055	−	10.4625i	0.536012	−	0.928401i	0.999114	−	0.0420953i	$-0.0134033\pi$
$128$		0			0
$129$	−23.9598			−2.10954
$130$		0			0
$131$	−3.82950			−0.334585			−0.167293	−	0.985907i	$-0.553502\pi$
$131$	−3.82950			−0.334585			−0.167293	+	0.985907i	$0.553502\pi$
$132$		0			0
$133$	−1.00589	+	1.74226i	−0.0872221	+	0.151073i
$134$		0			0
$135$			0.850315i			0.0731834i
$136$		0			0
$137$	−5.47291	+	3.15979i	−0.467582	+	0.269959i	−0.715227	−	0.698892i	$-0.753677\pi$
$137$	−5.47291	+	3.15979i	−0.467582	+	0.269959i	0.247645	+	0.968851i	$0.420343\pi$
$138$		0			0
$139$	−1.34093	−	2.32256i	−0.113736	−	0.196997i	0.803538	−	0.595254i	$-0.202948\pi$
$139$	−1.34093	−	2.32256i	−0.113736	−	0.196997i	−0.917274	+	0.398257i	$0.869615\pi$
$140$		0			0
$141$	−18.8121	−	10.8612i	−1.58427	−	0.914677i
$142$		0			0
$143$	12.6823	+	5.79079i	1.06055	+	0.484250i
$144$		0			0
$145$	12.6957	+	7.32987i	1.05432	+	0.608713i
$146$		0			0
$147$	1.21489	+	2.10425i	0.100202	+	0.173555i
$148$		0			0
$149$	13.4850	−	7.78555i	1.10473	−	0.637817i	0.167272	−	0.985911i	$-0.446504\pi$
$149$	13.4850	−	7.78555i	1.10473	−	0.637817i	0.937460	+	0.348093i	$0.113171\pi$
$150$		0			0
$151$			15.7761i			1.28384i	0.766771	+	0.641920i	$0.221862\pi$
$151$			15.7761i			1.28384i	−0.766771	+	0.641920i	$0.778138\pi$
$152$		0			0
$153$	2.37443	−	4.11263i	0.191961	−	0.332487i
$154$		0			0
$155$	33.1854			2.66552
$156$		0			0
$157$	−9.67555			−0.772193			−0.386096	−	0.922458i	$-0.626177\pi$
$157$	−9.67555			−0.772193			−0.386096	+	0.922458i	$0.626177\pi$
$158$		0			0
$159$	8.40246	−	14.5535i	0.666359	−	1.15417i
$160$		0			0
$161$		−	2.41411i		−	0.190259i
$162$		0			0
$163$	−11.1108	+	6.41483i	−0.870266	+	0.502448i	−0.867437	−	0.497548i	$-0.834234\pi$
$163$	−11.1108	+	6.41483i	−0.870266	+	0.502448i	−0.00282942	+	0.999996i	$0.500901\pi$
$164$		0			0
$165$	−17.0892	−	29.5994i	−1.33040	−	2.30431i
$166$		0			0
$167$	9.01741	+	5.20620i	0.697788	+	0.402868i	0.806523	−	0.591203i	$-0.201347\pi$
$167$	9.01741	+	5.20620i	0.697788	+	0.402868i	−0.108735	+	0.994071i	$0.534680\pi$
$168$		0			0
$169$	12.7647	−	2.46196i	0.981904	−	0.189381i
$170$		0			0
$171$	5.05917	+	2.92092i	0.386885	+	0.223368i
$172$		0			0
$173$	6.08891	+	10.5463i	0.462931	+	0.801820i	0.999106	−	0.0422871i	$-0.0134644\pi$
$173$	6.08891	+	10.5463i	0.462931	+	0.801820i	−0.536174	+	0.844107i	$0.680131\pi$
$174$		0			0
$175$	−7.13055	+	4.11682i	−0.539019	+	0.311203i
$176$		0			0
$177$		−	0.280035i		−	0.0210488i
$178$		0			0
$179$	−0.234009	+	0.405316i	−0.0174907	+	0.0302947i	−0.874638	−	0.484776i	$-0.838901\pi$
$179$	−0.234009	+	0.405316i	−0.0174907	+	0.0302947i	0.857148	+	0.515071i	$0.172234\pi$
$180$		0			0
$181$	−20.4110			−1.51714			−0.758570	−	0.651592i	$-0.774102\pi$
$181$	−20.4110			−1.51714			−0.758570	+	0.651592i	$0.774102\pi$
$182$		0			0
$183$	−12.0049			−0.887427
$184$		0			0
$185$	21.8736	−	37.8862i	1.60818	−	2.78545i
$186$		0			0
$187$		−	6.32368i		−	0.462433i
$188$		0			0
$189$	−0.202428	+	0.116872i	−0.0147245	+	0.00850118i
$190$		0			0
$191$	−1.74453	−	3.02161i	−0.126230	−	0.218636i	0.795983	−	0.605319i	$-0.206954\pi$
$191$	−1.74453	−	3.02161i	−0.126230	−	0.218636i	−0.922213	+	0.386683i	$0.873621\pi$
$192$		0			0
$193$	2.98367	+	1.72262i	0.214769	+	0.123997i	0.603526	−	0.797343i	$-0.293762\pi$
$193$	2.98367	+	1.72262i	0.214769	+	0.123997i	−0.388757	+	0.921340i	$0.627095\pi$
$194$		0			0
$195$	−28.9905	−	13.2372i	−2.07606	−	0.947936i
$196$		0			0
$197$	−10.9318	−	6.31147i	−0.778857	−	0.449674i	0.0571678	−	0.998365i	$-0.481793\pi$
$197$	−10.9318	−	6.31147i	−0.778857	−	0.449674i	−0.836025	+	0.548691i	$0.815126\pi$
$198$		0			0
$199$	5.52335	+	9.56672i	0.391540	+	0.678167i	0.992653	−	0.120997i	$-0.0386091\pi$
$199$	5.52335	+	9.56672i	0.391540	+	0.678167i	−0.601113	+	0.799164i	$0.705276\pi$
$200$		0			0
$201$	19.1875	−	11.0779i	1.35339	−	0.781377i
$202$		0			0
$203$			4.02983i			0.282838i
$204$		0			0
$205$	17.3922	−	30.1242i	1.21473	−	2.10397i
$206$		0			0
$207$	−7.01010			−0.487236
$208$		0			0
$209$	7.77910			0.538092
$210$		0			0
$211$	−0.502843	+	0.870949i	−0.0346171	+	0.0599586i	−0.882815	−	0.469721i	$-0.844355\pi$
$211$	−0.502843	+	0.870949i	−0.0346171	+	0.0599586i	0.848198	+	0.529680i	$0.177688\pi$
$212$		0			0
$213$			0.711910i			0.0487793i
$214$		0			0
$215$	31.0662	−	17.9361i	2.11870	−	1.22323i
$216$		0			0
$217$	4.56118	+	7.90020i	0.309633	+	0.536300i
$218$		0			0
$219$	3.98229	+	2.29917i	0.269098	+	0.155364i
$220$		0			0
$221$	−3.42062	−	4.80292i	−0.230096	−	0.323079i
$222$		0			0
$223$	19.3153	+	11.1517i	1.29345	+	0.746773i	0.979264	−	0.202589i	$-0.0649355\pi$
$223$	19.3153	+	11.1517i	1.29345	+	0.746773i	0.314185	+	0.949362i	$0.398269\pi$
$224$		0			0
$225$	11.9544	+	20.7057i	0.796962	+	1.38038i
$226$		0			0
$227$	−13.8976	+	8.02375i	−0.922413	+	0.532555i	−0.884404	−	0.466722i	$-0.845435\pi$
$227$	−13.8976	+	8.02375i	−0.922413	+	0.532555i	−0.0380088	+	0.999277i	$0.512101\pi$
$228$		0			0
$229$		−	12.2285i		−	0.808082i	−0.914741	−	0.404041i	$-0.867605\pi$
$229$		−	12.2285i		−	0.808082i	0.914741	−	0.404041i	$-0.132395\pi$
$230$		0			0
$231$	4.69768	−	8.13661i	0.309084	−	0.535350i
$232$		0			0
$233$	−7.66467			−0.502129			−0.251065	−	0.967970i	$-0.580781\pi$
$233$	−7.66467			−0.502129			−0.251065	+	0.967970i	$0.580781\pi$
$234$		0			0
$235$	32.5223			2.12152
$236$		0			0
$237$	6.23103	−	10.7925i	0.404749	−	0.701046i
$238$		0			0
$239$		−	9.63081i		−	0.622965i	−0.950252	−	0.311483i	$-0.899174\pi$
$239$		−	9.63081i		−	0.622965i	0.950252	−	0.311483i	$-0.100826\pi$
$240$		0			0
$241$	−0.123908	+	0.0715383i	−0.00798162	+	0.00460819i	−0.503986	−	0.863712i	$-0.668134\pi$
$241$	−0.123908	+	0.0715383i	−0.00798162	+	0.00460819i	0.496004	+	0.868320i	$0.334800\pi$
$242$		0			0
$243$	10.9227	+	18.9187i	0.700694	+	1.21364i
$244$		0			0
$245$	−3.15043	−	1.81890i	−0.201274	−	0.116206i
$246$		0			0
$247$	5.90833	−	4.20790i	0.375938	−	0.267742i
$248$		0			0
$249$	24.8322	+	14.3369i	1.57368	+	0.908563i
$250$		0			0
$251$	−5.10237	−	8.83756i	−0.322059	−	0.557822i	0.658854	−	0.752271i	$-0.271041\pi$
$251$	−5.10237	−	8.83756i	−0.322059	−	0.557822i	−0.980913	+	0.194449i	$0.937708\pi$
$252$		0			0
$253$	−8.08417	+	4.66740i	−0.508247	+	0.293437i
$254$		0			0
$255$			14.4553i			0.905228i
$256$		0			0
$257$	−10.0797	+	17.4586i	−0.628756	+	1.08904i	0.359045	+	0.933320i	$0.383102\pi$
$257$	−10.0797	+	17.4586i	−0.628756	+	1.08904i	−0.987802	+	0.155718i	$0.950231\pi$
$258$		0			0
$259$	12.0257			0.747241
$260$		0			0
$261$	11.7018			0.724324
$262$		0			0
$263$	14.2958	−	24.7610i	0.881516	−	1.52683i	0.0318605	−	0.999492i	$-0.489857\pi$
$263$	14.2958	−	24.7610i	0.881516	−	1.52683i	0.849655	−	0.527338i	$-0.176810\pi$
$264$		0			0
$265$			25.1600i			1.54557i
$266$		0			0
$267$	−5.18473	+	2.99340i	−0.317300	+	0.183193i
$268$		0			0
$269$	16.1229	+	27.9256i	0.983028	+	1.70266i	0.650389	+	0.759601i	$0.274606\pi$
$269$	16.1229	+	27.9256i	0.983028	+	1.70266i	0.332639	+	0.943054i	$0.392061\pi$
$270$		0			0
$271$	−20.9296	−	12.0837i	−1.27139	−	0.734035i	−0.296137	−	0.955146i	$-0.595698\pi$
$271$	−20.9296	−	12.0837i	−1.27139	−	0.734035i	−0.975249	+	0.221111i	$0.929032\pi$
$272$		0			0
$273$	−0.833333	−	8.72095i	−0.0504356	−	0.527816i
$274$		0			0
$275$	27.5721	+	15.9188i	1.66266	+	0.959938i
$276$		0			0
$277$	−10.0863	−	17.4700i	−0.606027	−	1.04967i	−0.991888	−	0.127113i	$-0.959429\pi$
$277$	−10.0863	−	17.4700i	−0.606027	−	1.04967i	0.385861	−	0.922557i	$-0.373905\pi$
$278$		0			0
$279$	22.9406	−	13.2448i	1.37342	−	0.792943i
$280$		0			0
$281$			24.0074i			1.43216i	0.698018	+	0.716080i	$0.254066\pi$
$281$			24.0074i			1.43216i	−0.698018	+	0.716080i	$0.745934\pi$
$282$		0			0
$283$	−6.77682	+	11.7378i	−0.402840	+	0.697739i	−0.994067	−	0.108765i	$-0.965310\pi$
$283$	−6.77682	+	11.7378i	−0.402840	+	0.697739i	0.591227	+	0.806505i	$0.298644\pi$
$284$		0			0
$285$	−17.7823			−1.05333
$286$		0			0
$287$	9.56193			0.564423
$288$		0			0
$289$	7.16274	−	12.4062i	0.421338	−	0.729779i
$290$		0			0
$291$		−	42.4618i		−	2.48915i
$292$		0			0
$293$	−12.3616	+	7.13696i	−0.722171	+	0.416945i	−0.815551	−	0.578685i	$-0.803566\pi$
$293$	−12.3616	+	7.13696i	−0.722171	+	0.416945i	0.0933803	+	0.995631i	$0.470233\pi$
$294$		0			0
$295$	0.209632	+	0.363093i	0.0122052	+	0.0211401i
$296$		0			0
$297$	0.782740	+	0.451915i	0.0454192	+	0.0262228i
$298$		0			0
$299$	−3.61533	+	7.91786i	−0.209080	+	0.457902i
$300$		0			0
$301$	8.53981	+	4.93046i	0.492226	+	0.284187i
$302$		0			0
$303$	−12.4921	−	21.6370i	−0.717653	−	1.24301i
$304$		0			0
$305$	15.5655	−	8.98674i	0.891278	−	0.514579i
$306$		0			0
$307$			28.2784i			1.61393i	0.590598	+	0.806966i	$0.298892\pi$
$307$			28.2784i			1.61393i	−0.590598	+	0.806966i	$0.701108\pi$
$308$		0			0
$309$	8.71230	−	15.0901i	0.495626	−	0.858449i
$310$		0			0
$311$	−6.86783			−0.389439			−0.194719	−	0.980859i	$-0.562380\pi$
$311$	−6.86783			−0.389439			−0.194719	+	0.980859i	$0.562380\pi$
$312$		0			0
$313$	−19.8476			−1.12185			−0.560927	−	0.827865i	$-0.689555\pi$
$313$	−19.8476			−1.12185			−0.560927	+	0.827865i	$0.689555\pi$
$314$		0			0
$315$	−5.28173	+	9.14823i	−0.297592	+	0.515444i
$316$		0			0
$317$			33.1727i			1.86317i	0.363527	+	0.931584i	$0.381572\pi$
$317$			33.1727i			1.86317i	−0.363527	+	0.931584i	$0.618428\pi$
$318$		0			0
$319$	13.4947	−	7.79119i	0.755560	−	0.436223i
$320$		0			0
$321$	18.2023	+	31.5273i	1.01595	+	1.75968i
$322$		0			0
$323$	−2.84928	−	1.64503i	−0.158538	−	0.0915321i
$324$		0			0
$325$	29.5522	−	2.82387i	1.63926	−	0.156640i
$326$		0			0
$327$	−18.5681	−	10.7203i	−1.02682	−	0.592835i
$328$		0			0
$329$	4.47004	+	7.74234i	0.246441	+	0.426849i
$330$		0			0
$331$	14.4317	−	8.33216i	0.793239	−	0.457977i	−0.0478625	−	0.998854i	$-0.515241\pi$
$331$	14.4317	−	8.33216i	0.793239	−	0.457977i	0.841102	+	0.540877i	$0.181908\pi$
$332$		0			0
$333$		−	34.9203i		−	1.91362i
$334$		0			0
$335$	−16.5857	+	28.7272i	−0.906171	+	1.56953i
$336$		0			0
$337$	2.84905			0.155198			0.0775989	−	0.996985i	$-0.475275\pi$
$337$	2.84905			0.155198			0.0775989	+	0.996985i	$0.475275\pi$
$338$		0			0
$339$	13.3305			0.724013
$340$		0			0
$341$	17.6370	−	30.5482i	0.955097	−	1.65428i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	18.4796	−	10.6692i	0.994911	−	0.574412i
$346$		0			0
$347$	−6.81743	−	11.8081i	−0.365979	−	0.633894i	0.622954	−	0.782259i	$-0.285932\pi$
$347$	−6.81743	−	11.8081i	−0.365979	−	0.633894i	−0.988933	+	0.148364i	$0.952599\pi$
$348$		0			0
$349$	2.05749	+	1.18789i	0.110135	+	0.0635864i	0.554056	−	0.832480i	$-0.313080\pi$
$349$	2.05749	+	1.18789i	0.110135	+	0.0635864i	−0.443921	+	0.896066i	$0.646413\pi$
$350$		0			0
$351$	0.838953	−	0.0801665i	0.0447800	−	0.00427897i
$352$		0			0
$353$	−0.236165	−	0.136350i	−0.0125698	−	0.00725717i	0.493702	−	0.869631i	$-0.335643\pi$
$353$	−0.236165	−	0.136350i	−0.0125698	−	0.00725717i	−0.506272	+	0.862374i	$0.668977\pi$
$354$		0			0
$355$	−0.532929	−	0.923060i	−0.0282849	−	0.0489909i
$356$		0			0
$357$	−3.44127	+	1.98682i	−0.182131	+	0.105154i
$358$		0			0
$359$			2.41260i			0.127332i	0.997971	+	0.0636661i	$0.0202793\pi$
$359$			2.41260i			0.127332i	−0.997971	+	0.0636661i	$0.979721\pi$
$360$		0			0
$361$	−7.47635	+	12.9494i	−0.393492	+	0.681549i
$362$		0			0
$363$	−9.60206			−0.503977
$364$		0			0
$365$	−6.88455			−0.360354
$366$		0			0
$367$	13.5691	−	23.5025i	0.708304	−	1.22682i	−0.257182	−	0.966363i	$-0.582794\pi$
$367$	13.5691	−	23.5025i	0.708304	−	1.22682i	0.965486	−	0.260455i	$-0.0838726\pi$
$368$		0			0
$369$		−	27.7659i		−	1.44544i
$370$		0			0
$371$	−5.98965	+	3.45813i	−0.310967	+	0.179537i
$372$		0			0
$373$	−14.1563	−	24.5195i	−0.732988	−	1.26957i	−0.955601	−	0.294665i	$-0.904792\pi$
$373$	−14.1563	−	24.5195i	−0.732988	−	1.26957i	0.222613	−	0.974907i	$-0.428541\pi$
$374$		0			0
$375$	−24.7531	−	14.2912i	−1.27824	−	0.737994i
$376$		0			0
$377$	6.03500	−	13.2171i	0.310818	−	0.680717i
$378$		0			0
$379$	16.3298	+	9.42802i	0.838806	+	0.484285i	0.856858	−	0.515552i	$-0.172413\pi$
$379$	16.3298	+	9.42802i	0.838806	+	0.484285i	−0.0180520	+	0.999837i	$0.505746\pi$
$380$		0			0
$381$	14.6772	+	25.4216i	0.751935	+	1.30239i
$382$		0			0
$383$	−33.3217	+	19.2383i	−1.70266	+	0.983031i	−0.759611	+	0.650377i	$0.774611\pi$
$383$	−33.3217	+	19.2383i	−1.70266	+	0.983031i	−0.943049	+	0.332654i	$0.892056\pi$
$384$		0			0
$385$			14.0665i			0.716897i
$386$		0			0
$387$	14.3171	−	24.7979i	0.727778	−	1.26055i
$388$		0			0
$389$	25.6279			1.29938			0.649692	−	0.760198i	$-0.274898\pi$
$389$	25.6279			1.29938			0.649692	+	0.760198i	$0.274898\pi$
$390$		0			0
$391$	3.94802			0.199660
$392$		0			0
$393$	4.65241	−	8.05822i	0.234683	−	0.406483i
$394$		0			0
$395$			18.6579i			0.938783i
$396$		0			0
$397$	5.80052	−	3.34893i	0.291120	−	0.168078i	−0.347327	−	0.937744i	$-0.612911\pi$
$397$	5.80052	−	3.34893i	0.291120	−	0.168078i	0.638447	+	0.769666i	$0.279577\pi$
$398$		0			0
$399$	−2.44409	−	4.23330i	−0.122358	−	0.211930i
$400$		0			0
$401$	−17.7884	−	10.2701i	−0.888308	−	0.512865i	−0.0149193	−	0.999889i	$-0.504749\pi$
$401$	−17.7884	−	10.2701i	−0.888308	−	0.512865i	−0.873389	+	0.487024i	$0.838082\pi$
$402$		0			0
$403$	−3.12867	−	32.7420i	−0.155850	−	1.63100i
$404$		0			0
$405$	−29.2340	−	16.8782i	−1.45265	−	0.838686i
$406$		0			0
$407$	−23.2503	−	40.2706i	−1.15247	−	1.99614i
$408$		0			0
$409$	−12.7030	+	7.33410i	−0.628125	+	0.362648i	−0.780025	−	0.625748i	$-0.784794\pi$
$409$	−12.7030	+	7.33410i	−0.628125	+	0.362648i	0.151901	+	0.988396i	$0.451461\pi$
$410$		0			0
$411$		−	15.3551i		−	0.757413i
$412$		0			0
$413$	−0.0576258	+	0.0998109i	−0.00283558	+	0.00491137i
$414$		0			0
$415$	−42.9298			−2.10734
$416$		0			0
$417$	6.51631			0.319105
$418$		0			0
$419$	13.4409	−	23.2803i	0.656631	−	1.13732i	−0.324851	−	0.945765i	$-0.605314\pi$
$419$	13.4409	−	23.2803i	0.656631	−	1.13732i	0.981482	−	0.191553i	$-0.0613525\pi$
$420$		0			0
$421$			4.54437i			0.221479i	0.993849	+	0.110739i	$0.0353219\pi$
$421$			4.54437i			0.221479i	−0.993849	+	0.110739i	$0.964678\pi$
$422$		0			0
$423$	22.4822	−	12.9801i	1.09312	−	0.631115i
$424$		0			0
$425$	−6.73263	−	11.6613i	−0.326581	−	0.565654i
$426$		0			0
$427$	4.27881	+	2.47037i	0.207066	+	0.119550i
$428$		0			0
$429$	−27.5928	+	19.6515i	−1.33219	+	0.948783i
$430$		0			0
$431$	10.6699	+	6.16025i	0.513949	+	0.296729i	0.734456	−	0.678657i	$-0.237438\pi$
$431$	10.6699	+	6.16025i	0.513949	+	0.296729i	−0.220506	+	0.975386i	$0.570771\pi$
$432$		0			0
$433$	−12.2232	−	21.1711i	−0.587408	−	1.01742i	−0.994571	−	0.104064i	$-0.966815\pi$
$433$	−12.2232	−	21.1711i	−0.587408	−	1.01742i	0.407163	−	0.913356i	$-0.366518\pi$
$434$		0			0
$435$	−30.8477	+	17.8099i	−1.47903	+	0.853921i
$436$		0			0
$437$			4.85668i			0.232327i
$438$		0			0
$439$	−2.65283	+	4.59484i	−0.126613	+	0.219300i	−0.922362	−	0.386326i	$-0.873744\pi$
$439$	−2.65283	+	4.59484i	−0.126613	+	0.219300i	0.795749	+	0.605626i	$0.207077\pi$
$440$		0			0
$441$	−2.90380			−0.138276
$442$		0			0
$443$	1.26200			0.0599596			0.0299798	−	0.999551i	$-0.490456\pi$
$443$	1.26200			0.0599596			0.0299798	+	0.999551i	$0.490456\pi$
$444$		0			0
$445$	4.48166	−	7.76247i	0.212451	−	0.367976i
$446$		0			0
$447$			37.8343i			1.78950i
$448$		0			0
$449$	20.3862	−	11.7700i	0.962082	−	0.555458i	0.0652689	−	0.997868i	$-0.479209\pi$
$449$	20.3862	−	11.7700i	0.962082	−	0.555458i	0.896813	+	0.442409i	$0.145876\pi$
$450$		0			0
$451$	−18.4868	−	32.0202i	−0.870512	−	1.50777i
$452$		0			0
$453$	−33.1968	−	19.1662i	−1.55972	−	0.900505i
$454$		0			0
$455$	7.60891	+	10.6837i	0.356711	+	0.500861i
$456$		0			0
$457$	−20.0744	−	11.5900i	−0.939043	−	0.542157i	−0.0493828	−	0.998780i	$-0.515725\pi$
$457$	−20.0744	−	11.5900i	−0.939043	−	0.542157i	−0.889660	+	0.456623i	$0.849059\pi$
$458$		0			0
$459$	−0.191132	−	0.331050i	−0.00892126	−	0.0154521i
$460$		0			0
$461$	−31.1249	+	17.9700i	−1.44963	+	0.836945i	−0.998459	−	0.0554911i	$-0.982328\pi$
$461$	−31.1249	+	17.9700i	−1.44963	+	0.836945i	−0.451173	+	0.892437i	$0.648994\pi$
$462$		0			0
$463$			12.9147i			0.600197i	0.953908	+	0.300098i	$0.0970195\pi$
$463$			12.9147i			0.600197i	−0.953908	+	0.300098i	$0.902981\pi$
$464$		0			0
$465$	−40.3165	+	69.8303i	−1.86963	+	3.23830i
$466$		0			0
$467$	13.6014			0.629398			0.314699	−	0.949192i	$-0.398096\pi$
$467$	13.6014			0.629398			0.314699	+	0.949192i	$0.398096\pi$
$468$		0			0
$469$	−9.11849			−0.421053
$470$		0			0
$471$	11.7547	−	20.3597i	0.541628	−	0.938127i
$472$		0			0
$473$		−	38.1298i		−	1.75321i
$474$		0			0
$475$	14.3452	−	8.28218i	0.658201	−	0.380012i
$476$		0			0
$477$	10.0417	+	17.3927i	0.459778	+	0.796359i
$478$		0			0
$479$	17.2765	+	9.97457i	0.789382	+	0.455750i	0.839745	−	0.542981i	$-0.182705\pi$
$479$	17.2765	+	9.97457i	0.789382	+	0.455750i	−0.0503632	+	0.998731i	$0.516038\pi$
$480$		0			0
$481$	−39.4422	−	18.0095i	−1.79841	−	0.821162i
$482$		0			0
$483$	5.07988	+	2.93287i	0.231143	+	0.133450i
$484$		0			0
$485$	31.7865	+	55.0558i	1.44335	+	2.49995i
$486$		0			0
$487$	−16.8866	+	9.74949i	−0.765205	+	0.441791i	−0.831162	−	0.556031i	$-0.812324\pi$
$487$	−16.8866	+	9.74949i	−0.765205	+	0.441791i	0.0659562	+	0.997823i	$0.478990\pi$
$488$		0			0
$489$		−	31.1732i		−	1.40970i
$490$		0			0
$491$	−9.52733	+	16.5018i	−0.429962	+	0.744717i	−0.996869	−	0.0790649i	$-0.974807\pi$
$491$	−9.52733	+	16.5018i	−0.429962	+	0.744717i	0.566907	+	0.823782i	$0.308140\pi$
$492$		0			0
$493$	−6.59036			−0.296815
$494$		0			0
$495$	40.8464			1.83591
$496$		0			0
$497$	0.146497	−	0.253741i	0.00657130	−	0.0113818i
$498$		0			0
$499$		−	13.6662i		−	0.611785i	−0.952066	−	0.305892i	$-0.901045\pi$
$499$		−	13.6662i		−	0.611785i	0.952066	−	0.305892i	$-0.0989548\pi$
$500$		0			0
$501$	−21.9103	+	12.6499i	−0.978878	+	0.565156i
$502$		0			0
$503$	−1.15076	−	1.99318i	−0.0513100	−	0.0888715i	0.839230	−	0.543777i	$-0.183006\pi$
$503$	−1.15076	−	1.99318i	−0.0513100	−	0.0888715i	−0.890540	+	0.454906i	$0.849673\pi$
$504$		0			0
$505$	32.3944	+	18.7029i	1.44153	+	0.832270i
$506$		0			0
$507$	−10.3272	+	29.8512i	−0.458645	+	1.32574i
$508$		0			0
$509$	−19.2737	−	11.1277i	−0.854292	−	0.493226i	0.00780455	−	0.999970i	$-0.497516\pi$
$509$	−19.2737	−	11.1277i	−0.854292	−	0.493226i	−0.862097	+	0.506744i	$0.830849\pi$
$510$		0			0
$511$	−0.946250	−	1.63895i	−0.0418596	−	0.0725030i
$512$		0			0
$513$	0.407242	−	0.235121i	0.0179802	−	0.0103809i
$514$		0			0
$515$			26.0878i			1.14956i
$516$		0			0
$517$	17.2846	−	29.9378i	0.760175	−	1.31666i
$518$		0			0
$519$	−29.5893			−1.29883
$520$		0			0
$521$	13.1581			0.576465			0.288233	−	0.957560i	$-0.406932\pi$
$521$	13.1581			0.576465			0.288233	+	0.957560i	$0.406932\pi$
$522$		0			0
$523$	−19.9028	+	34.4727i	−0.870291	+	1.50739i	−0.00859463	+	0.999963i	$0.502736\pi$
$523$	−19.9028	+	34.4727i	−0.870291	+	1.50739i	−0.861696	+	0.507425i	$0.830598\pi$
$524$		0			0
$525$		−	20.0059i		−	0.873129i
$526$		0			0
$527$	−12.9199	+	7.45933i	−0.562801	+	0.324934i
$528$		0			0
$529$	8.58603	+	14.8714i	0.373306	+	0.646584i
$530$		0			0
$531$	0.289831	+	0.167334i	0.0125776	+	0.00726167i
$532$		0			0
$533$	−31.3615	−	14.3198i	−1.35842	−	0.620259i
$534$		0			0
$535$	−47.2020	−	27.2521i	−2.04072	−	1.17821i
$536$		0			0
$537$	−0.568589	−	0.984825i	−0.0245364	−	0.0424983i
$538$		0			0
$539$	−3.34871	+	1.93338i	−0.144239	+	0.0832766i
$540$		0			0
$541$			18.7716i			0.807055i	0.914968	+	0.403527i	$0.132216\pi$
$541$			18.7716i			0.807055i	−0.914968	+	0.403527i	$0.867784\pi$
$542$		0			0
$543$	24.7971	−	42.9498i	1.06415	−	1.84315i
$544$		0			0
$545$	32.1005			1.37503
$546$		0			0
$547$	−43.1197			−1.84366			−0.921832	−	0.387589i	$-0.873308\pi$
$547$	−43.1197			−1.84366			−0.921832	+	0.387589i	$0.873308\pi$
$548$		0			0
$549$	7.17347	−	12.4248i	0.306156	−	0.530278i
$550$		0			0
$551$		−	8.10716i		−	0.345377i
$552$		0			0
$553$	−4.44176	+	2.56445i	−0.188883	+	0.109051i
$554$		0			0
$555$	53.1479	+	92.0549i	2.25600	+	3.90751i
$556$		0			0
$557$	20.4136	+	11.7858i	0.864954	+	0.499381i	0.865668	−	0.500618i	$-0.166894\pi$
$557$	20.4136	+	11.7858i	0.864954	+	0.499381i	−0.000714272		1.00000i	$0.500227\pi$
$558$		0			0
$559$	−20.6253	−	28.9601i	−0.872357	−	1.22488i
$560$		0			0
$561$	13.3066	+	7.68255i	0.561804	+	0.324358i
$562$		0			0
$563$	12.1363	+	21.0207i	0.511484	+	0.885917i	0.999911	+	0.0133121i	$0.00423750\pi$
$563$	12.1363	+	21.0207i	0.511484	+	0.885917i	−0.488427	+	0.872605i	$0.662429\pi$
$564$		0			0
$565$	−17.2843	+	9.97907i	−0.727154	+	0.419823i
$566$		0			0
$567$		−	9.27934i		−	0.389696i
$568$		0			0
$569$	21.5153	−	37.2656i	0.901969	−	1.56226i	0.0770349	−	0.997028i	$-0.475455\pi$
$569$	21.5153	−	37.2656i	0.901969	−	1.56226i	0.824934	−	0.565228i	$-0.191212\pi$
$570$		0			0
$571$	10.1365			0.424201			0.212101	−	0.977248i	$-0.431970\pi$
$571$	10.1365			0.424201			0.212101	+	0.977248i	$0.431970\pi$
$572$		0			0
$573$	8.47761			0.354157
$574$		0			0
$575$	−9.93848	+	17.2139i	−0.414463	+	0.717871i
$576$		0			0
$577$		−	11.8664i		−	0.494005i	−0.969015	−	0.247003i	$-0.920554\pi$
$577$		−	11.8664i		−	0.494005i	0.969015	−	0.247003i	$-0.0794456\pi$
$578$		0			0
$579$	−7.24965	+	4.18559i	−0.301285	+	0.173947i
$580$		0			0
$581$	−5.90050	−	10.2200i	−0.244794	−	0.423996i
$582$		0			0
$583$	23.1605	+	13.3717i	0.959211	+	0.553801i
$584$		0			0
$585$	31.0234	−	22.0948i	1.28266	−	0.913506i
$586$		0			0
$587$	19.6614	+	11.3515i	0.811512	+	0.468527i	0.847481	−	0.530826i	$-0.178118\pi$
$587$	19.6614	+	11.3515i	0.811512	+	0.468527i	−0.0359686	+	0.999353i	$0.511452\pi$
$588$		0			0
$589$	−9.17613	−	15.8935i	−0.378096	−	0.654881i
$590$		0			0
$591$	26.5618	−	15.3354i	1.09260	−	0.630816i
$592$		0			0
$593$		−	41.0665i		−	1.68640i	−0.537600	−	0.843200i	$-0.680669\pi$
$593$		−	41.0665i		−	1.68640i	0.537600	−	0.843200i	$-0.319331\pi$
$594$		0			0
$595$	2.97463	−	5.15220i	0.121948	−	0.211220i
$596$		0			0
$597$	−26.8410			−1.09853
$598$		0			0
$599$	20.8122			0.850362			0.425181	−	0.905108i	$-0.360211\pi$
$599$	20.8122			0.850362			0.425181	+	0.905108i	$0.360211\pi$
$600$		0			0
$601$	2.51726	−	4.36002i	0.102681	−	0.177849i	−0.810107	−	0.586282i	$-0.800591\pi$
$601$	2.51726	−	4.36002i	0.102681	−	0.177849i	0.912788	+	0.408433i	$0.133925\pi$
$602$		0			0
$603$			26.4783i			1.07828i
$604$		0			0
$605$	12.4500	−	7.18800i	0.506164	−	0.292234i
$606$		0			0
$607$	−4.86938	−	8.43401i	−0.197642	−	0.342326i	0.750121	−	0.661300i	$-0.229995\pi$
$607$	−4.86938	−	8.43401i	−0.197642	−	0.342326i	−0.947763	+	0.318974i	$0.896662\pi$
$608$		0			0
$609$	−8.47975	−	4.89578i	−0.343617	−	0.198387i
$610$		0			0
$611$	−3.06616	−	32.0878i	−0.124043	−	1.29813i
$612$		0			0
$613$	14.8918	+	8.59776i	0.601473	+	0.347260i	0.769621	−	0.638501i	$-0.220445\pi$
$613$	14.8918	+	8.59776i	0.601473	+	0.347260i	−0.168148	+	0.985762i	$0.553779\pi$
$614$		0			0
$615$	42.2592	+	73.1951i	1.70406	+	2.95151i
$616$		0			0
$617$	−15.4804	+	8.93760i	−0.623216	+	0.359814i	−0.778120	−	0.628115i	$-0.783827\pi$
$617$	−15.4804	+	8.93760i	−0.623216	+	0.359814i	0.154904	+	0.987930i	$0.450493\pi$
$618$		0			0
$619$		−	21.3112i		−	0.856568i	−0.903644	−	0.428284i	$-0.859118\pi$
$619$		−	21.3112i		−	0.856568i	0.903644	−	0.428284i	$-0.140882\pi$
$620$		0			0
$621$	−0.282142	+	0.488684i	−0.0113220	+	0.0196102i
$622$		0			0
$623$	2.46394			0.0987155
$624$		0			0
$625$	1.62474			0.0649895
$626$		0			0
$627$	−9.45073	+	16.3691i	−0.377426	+	0.653721i
$628$		0			0
$629$			19.6668i			0.784166i
$630$		0			0
$631$	10.9176	−	6.30330i	0.434624	−	0.250930i	−0.266691	−	0.963782i	$-0.585930\pi$
$631$	10.9176	−	6.30330i	0.434624	−	0.250930i	0.701315	+	0.712852i	$0.252597\pi$
$632$		0			0
$633$	−1.22179	−	2.11621i	−0.0485620	−	0.0841118i
$634$		0			0
$635$	−38.0607	−	21.9744i	−1.51039	−	0.872026i
$636$		0			0
$637$	−1.49758	+	3.27982i	−0.0593364	+	0.129951i
$638$		0			0
$639$	−0.736812	−	0.425399i	−0.0291478	−	0.0168285i
$640$		0			0
$641$	0.953524	+	1.65155i	0.0376619	+	0.0652324i	0.884242	−	0.467029i	$-0.154676\pi$
$641$	0.953524	+	1.65155i	0.0376619	+	0.0652324i	−0.846580	+	0.532261i	$0.821342\pi$
$642$		0			0
$643$	9.56862	−	5.52444i	0.377349	−	0.217863i	−0.299315	−	0.954154i	$-0.596758\pi$
$643$	9.56862	−	5.52444i	0.377349	−	0.217863i	0.676664	+	0.736292i	$0.263425\pi$
$644$		0			0
$645$			87.1612i			3.43197i
$646$		0			0
$647$	−22.3945	+	38.7885i	−0.880420	+	1.52493i	−0.0295447	+	0.999563i	$0.509406\pi$
$647$	−22.3945	+	38.7885i	−0.880420	+	1.52493i	−0.850875	+	0.525368i	$0.823928\pi$
$648$		0			0
$649$	0.445651			0.0174933
$650$		0			0
$651$	−22.1653			−0.868726
$652$		0			0
$653$	−10.4387	+	18.0804i	−0.408499	+	0.707541i	−0.994722	−	0.102609i	$-0.967281\pi$
$653$	−10.4387	+	18.0804i	−0.408499	+	0.707541i	0.586223	+	0.810150i	$0.300614\pi$
$654$		0			0
$655$			13.9310i			0.544329i
$656$		0			0
$657$	−4.75919	+	2.74772i	−0.185674	+	0.107199i
$658$		0			0
$659$	0.900509	+	1.55973i	0.0350788	+	0.0607583i	0.883032	−	0.469313i	$-0.155498\pi$
$659$	0.900509	+	1.55973i	0.0350788	+	0.0607583i	−0.847953	+	0.530071i	$0.822165\pi$
$660$		0			0
$661$	8.46403	+	4.88671i	0.329213	+	0.190071i	0.655491	−	0.755203i	$-0.272462\pi$
$661$	8.46403	+	4.88671i	0.329213	+	0.190071i	−0.326279	+	0.945274i	$0.605795\pi$
$662$		0			0
$663$	14.2622	−	1.36283i	0.553898	−	0.0529279i
$664$		0			0
$665$	6.33801	+	3.65925i	0.245777	+	0.141900i
$666$		0			0
$667$	4.86423	+	8.42509i	0.188344	+	0.326221i
$668$		0			0
$669$	−46.9318	+	27.0961i	−1.81449	+	1.04760i
$670$		0			0
$671$		−	19.1047i		−	0.737528i
$672$		0			0
$673$	−8.31668	+	14.4049i	−0.320584	+	0.555268i	−0.980609	−	0.195976i	$-0.937213\pi$
$673$	−8.31668	+	14.4049i	−0.320584	+	0.555268i	0.660024	+	0.751244i	$0.270546\pi$
$674$		0			0
$675$	1.92456			0.0740765
$676$		0			0
$677$	33.5232			1.28840			0.644201	−	0.764856i	$-0.277190\pi$
$677$	33.5232			1.28840			0.644201	+	0.764856i	$0.277190\pi$
$678$		0			0
$679$	−8.73781	+	15.1343i	−0.335326	+	0.580802i
$680$		0			0
$681$		−	38.9918i		−	1.49417i
$682$		0			0
$683$	20.5810	−	11.8825i	0.787511	−	0.454670i	−0.0515745	−	0.998669i	$-0.516424\pi$
$683$	20.5810	−	11.8825i	0.787511	−	0.454670i	0.839086	+	0.543999i	$0.183091\pi$
$684$		0			0
$685$	11.4947	+	19.9094i	0.439190	+	0.760699i
$686$		0			0
$687$	25.7318	+	14.8562i	0.981728	+	0.566801i
$688$		0			0
$689$	24.8238	−	2.37205i	0.945712	−	0.0903678i
$690$		0			0
$691$	4.55167	+	2.62791i	0.173154	+	0.0999702i	0.584072	−	0.811702i	$-0.301459\pi$
$691$	4.55167	+	2.62791i	0.173154	+	0.0999702i	−0.410918	+	0.911672i	$0.634792\pi$
$692$		0			0
$693$	5.61415	+	9.72399i	0.213264	+	0.369384i
$694$		0			0
$695$	−8.44902	+	4.87804i	−0.320489	+	0.185035i
$696$		0			0
$697$			15.6375i			0.592314i
$698$		0			0
$699$	9.31171	−	16.1284i	0.352201	−	0.610030i
$700$		0			0
$701$	10.3164			0.389646			0.194823	−	0.980838i	$-0.437587\pi$
$701$	10.3164			0.389646			0.194823	+	0.980838i	$0.437587\pi$
$702$		0			0
$703$	−24.1932			−0.912463
$704$		0			0
$705$	−39.5109	+	68.4349i	−1.48807	+	2.57741i
$706$		0			0
$707$			10.2825i			0.386714i
$708$		0			0
$709$	16.7539	−	9.67286i	0.629205	−	0.363272i	−0.151239	−	0.988497i	$-0.548326\pi$
$709$	16.7539	−	9.67286i	0.629205	−	0.363272i	0.780444	+	0.625225i	$0.214993\pi$
$710$		0			0
$711$	7.44665	+	12.8980i	0.279271	+	0.483712i
$712$		0			0
$713$	19.0720	+	11.0112i	0.714251	+	0.412373i
$714$		0			0
$715$	21.0658	−	46.1357i	0.787816	−	1.72538i
$716$		0			0
$717$	20.2656	+	11.7003i	0.756833	+	0.436957i
$718$		0			0
$719$	24.0372	+	41.6337i	0.896437	+	1.55267i	0.832016	+	0.554752i	$0.187187\pi$
$719$	24.0372	+	41.6337i	0.896437	+	1.55267i	0.0644212	+	0.997923i	$0.479480\pi$
$720$		0			0
$721$	−6.21052	+	3.58564i	−0.231292	+	0.133536i
$722$		0			0
$723$		−	0.347644i		−	0.0129290i
$724$		0			0
$725$	16.5901	−	28.7349i	0.616141	−	1.06719i
$726$		0			0
$727$	−11.6338			−0.431475			−0.215738	−	0.976451i	$-0.569216\pi$
$727$	−11.6338			−0.431475			−0.215738	+	0.976451i	$0.569216\pi$
$728$		0			0
$729$	−25.2415			−0.934872
$730$		0			0
$731$	−8.06325	+	13.9660i	−0.298230	+	0.516549i
$732$		0			0
$733$			30.3258i			1.12011i	0.828456	+	0.560055i	$0.189220\pi$
$733$			30.3258i			1.12011i	−0.828456	+	0.560055i	$0.810780\pi$
$734$		0			0
$735$	7.65484	−	4.41953i	0.282353	−	0.163017i
$736$		0			0
$737$	17.6295	+	30.5352i	0.649391	+	1.12478i
$738$		0			0
$739$	8.40853	+	4.85467i	0.309313	+	0.178582i	0.646619	−	0.762813i	$-0.276182\pi$
$739$	8.40853	+	4.85467i	0.309313	+	0.178582i	−0.337306	+	0.941395i	$0.609516\pi$
$740$		0			0
$741$	1.67649	+	17.5447i	0.0615874	+	0.644521i
$742$		0			0
$743$	−36.4578	−	21.0489i	−1.33751	−	0.772211i	−0.351071	−	0.936349i	$-0.614182\pi$
$743$	−36.4578	−	21.0489i	−1.33751	−	0.772211i	−0.986437	+	0.164138i	$0.947516\pi$
$744$		0			0
$745$	−28.3224	−	49.0557i	−1.03765	−	1.79726i
$746$		0			0
$747$	−29.6767	+	17.1339i	−1.08581	+	0.626896i
$748$		0			0
$749$		−	14.9827i		−	0.547456i
$750$		0			0
$751$	−12.2855	+	21.2791i	−0.448305	+	0.776486i	−0.998276	−	0.0586972i	$-0.981305\pi$
$751$	−12.2855	+	21.2791i	−0.448305	+	0.776486i	0.549971	+	0.835184i	$0.314639\pi$
$752$		0			0
$753$	24.7952			0.903587
$754$		0			0
$755$	57.3904			2.08865
$756$		0			0
$757$	−18.0560	+	31.2739i	−0.656257	+	1.13667i	0.325320	+	0.945604i	$0.394528\pi$
$757$	−18.0560	+	31.2739i	−0.656257	+	1.13667i	−0.981577	+	0.191066i	$0.938805\pi$
$758$		0			0
$759$		−	22.6814i		−	0.823284i
$760$		0			0
$761$	−13.3419	+	7.70294i	−0.483643	+	0.279231i	−0.721933	−	0.691963i	$-0.756746\pi$
$761$	−13.3419	+	7.70294i	−0.483643	+	0.279231i	0.238291	+	0.971194i	$0.423413\pi$
$762$		0			0
$763$	4.41207	+	7.64192i	0.159727	+	0.276656i
$764$		0			0
$765$	−14.9610	−	8.63772i	−0.540915	−	0.312297i
$766$		0			0
$767$	0.338478	−	0.241063i	0.0122217	−	0.00870427i
$768$		0			0
$769$	17.6792	+	10.2071i	0.637529	+	0.368078i	0.783662	−	0.621187i	$-0.213349\pi$
$769$	17.6792	+	10.2071i	0.637529	+	0.368078i	−0.146133	+	0.989265i	$0.546683\pi$
$770$		0			0
$771$	−24.4915	−	42.4205i	−0.882038	−	1.52774i
$772$		0			0
$773$	42.5514	−	24.5671i	1.53047	−	0.883616i	0.531129	−	0.847291i	$-0.321768\pi$
$773$	42.5514	−	24.5671i	1.53047	−	0.883616i	0.999340	−	0.0363252i	$-0.0115652\pi$
$774$		0			0
$775$		−	75.1103i		−	2.69804i
$776$		0			0
$777$	−14.6099	+	25.3050i	−0.524126	+	0.907813i
$778$		0			0
$779$	−19.2366			−0.689222
$780$		0			0
$781$	−1.13294			−0.0405398
$782$		0			0
$783$	0.470973	−	0.815750i	0.0168312	−	0.0291525i
$784$		0			0
$785$			35.1978i			1.25626i
$786$		0			0
$787$	10.6890	−	6.17132i	0.381023	−	0.219984i	−0.297240	−	0.954803i	$-0.596066\pi$
$787$	10.6890	−	6.17132i	0.381023	−	0.219984i	0.678263	+	0.734819i	$0.262733\pi$
$788$		0			0
$789$	34.7355	+	60.1637i	1.23662	+	2.14188i
$790$		0			0
$791$	−4.75128	−	2.74315i	−0.168936	−	0.0975353i
$792$		0			0
$793$	−10.3342	−	14.5103i	−0.366977	−	0.515275i
$794$		0			0
$795$	−52.9428	−	30.5665i	−1.87769	−	1.08408i
$796$		0			0
$797$	−10.2517	−	17.7564i	−0.363133	−	0.628964i	0.625342	−	0.780351i	$-0.284959\pi$
$797$	−10.2517	−	17.7564i	−0.363133	−	0.628964i	−0.988475	+	0.151387i	$0.951626\pi$
$798$		0			0
$799$	−12.6618	+	7.31028i	−0.447942	+	0.258619i
$800$		0			0
$801$		−	7.15478i		−	0.252802i
$802$		0			0
$803$	−3.65892	+	6.33744i	−0.129121	+	0.223643i
$804$		0			0
$805$	−8.78208			−0.309528
$806$		0			0
$807$	−78.3498			−2.75804
$808$		0			0
$809$	3.74367	−	6.48422i	0.131620	−	0.227973i	−0.792681	−	0.609637i	$-0.791315\pi$
$809$	3.74367	−	6.48422i	0.131620	−	0.227973i	0.924301	+	0.381664i	$0.124649\pi$
$810$		0			0
$811$		−	22.8692i		−	0.803048i	−0.915849	−	0.401524i	$-0.868481\pi$
$811$		−	22.8692i		−	0.803048i	0.915849	−	0.401524i	$-0.131519\pi$
$812$		0			0
$813$	50.8543	−	29.3608i	1.78354	−	1.02973i
$814$		0			0
$815$	23.3359	+	40.4190i	0.817422	+	1.41582i
$816$		0			0
$817$	−17.1803	−	9.91904i	−0.601062	−	0.347023i
$818$		0			0
$819$	9.52395	+	4.34868i	0.332794	+	0.151955i
$820$		0			0
$821$	−35.0568	−	20.2400i	−1.22349	−	0.706382i	−0.257830	−	0.966190i	$-0.583007\pi$
$821$	−35.0568	−	20.2400i	−1.22349	−	0.706382i	−0.965660	+	0.259808i	$0.916341\pi$
$822$		0			0
$823$	11.3481	+	19.6555i	0.395570	+	0.685146i	0.993174	−	0.116645i	$-0.0372139\pi$
$823$	11.3481	+	19.6555i	0.395570	+	0.685146i	−0.597604	+	0.801791i	$0.703881\pi$
$824$		0			0
$825$	−66.9940	+	38.6790i	−2.33243	+	1.34663i
$826$		0			0
$827$			15.7414i			0.547383i	0.961818	+	0.273691i	$0.0882447\pi$
$827$			15.7414i			0.547383i	−0.961818	+	0.273691i	$0.911755\pi$
$828$		0			0
$829$	9.84390	−	17.0501i	0.341893	−	0.592176i	−0.642891	−	0.765957i	$-0.722265\pi$
$829$	9.84390	−	17.0501i	0.341893	−	0.592176i	0.984784	+	0.173782i	$0.0555987\pi$
$830$		0			0
$831$	49.0149			1.70031
$832$		0			0
$833$	1.63539			0.0566630
$834$		0			0
$835$	18.9392	−	32.8036i	0.655417	−	1.13522i
$836$		0			0
$837$		−	2.13229i		−	0.0737029i
$838$		0			0
$839$	1.90889	−	1.10210i	0.0659023	−	0.0380487i	−0.466687	−	0.884423i	$-0.654552\pi$
$839$	1.90889	−	1.10210i	0.0659023	−	0.0380487i	0.532589	+	0.846374i	$0.321219\pi$
$840$		0			0
$841$	6.38024	+	11.0509i	0.220008	+	0.381066i
$842$		0			0
$843$	−50.5174	−	29.1663i	−1.73991	−	1.00454i
$844$		0			0
$845$	−8.95613	−	46.4357i	−0.308100	−	1.59744i
$846$		0			0
$847$	3.42239	+	1.97592i	0.117595	+	0.0678933i
$848$		0			0
$849$	−16.4661	−	28.5202i	−0.565116	−	0.978810i
$850$		0			0
$851$	25.1419	−	14.5157i	0.861854	−	0.497592i
$852$		0			0
$853$		−	2.60526i		−	0.0892026i	−0.999005	−	0.0446013i	$-0.985798\pi$
$853$		−	2.60526i		−	0.0892026i	0.999005	−	0.0446013i	$-0.0142017\pi$
$854$		0			0
$855$	10.6257	−	18.4043i	0.363392	−	0.629414i
$856$		0			0
$857$	−33.0023			−1.12734			−0.563668	−	0.826001i	$-0.690610\pi$
$857$	−33.0023			−1.12734			−0.563668	+	0.826001i	$0.690610\pi$
$858$		0			0
$859$	−17.0404			−0.581411			−0.290706	−	0.956813i	$-0.593890\pi$
$859$	−17.0404			−0.581411			−0.290706	+	0.956813i	$0.593890\pi$
$860$		0			0
$861$	−11.6167	+	20.1207i	−0.395895	+	0.685710i
$862$		0			0
$863$			1.85114i			0.0630134i	0.999504	+	0.0315067i	$0.0100306\pi$
$863$			1.85114i			0.0630134i	−0.999504	+	0.0315067i	$0.989969\pi$
$864$		0			0
$865$	38.3654	−	22.1503i	1.30446	−	0.753132i
$866$		0			0
$867$	17.4038	+	30.1443i	0.591066	+	1.02376i
$868$		0			0
$869$	17.1752	+	9.91611i	0.582629	+	0.336381i
$870$		0			0
$871$	29.9070	+	13.6557i	1.01336	+	0.462705i
$872$		0			0
$873$	43.9471	+	25.3728i	1.48738	+	0.858741i
$874$		0			0
$875$	5.88170	+	10.1874i	0.198838	+	0.344397i
$876$		0			0
$877$	9.69212	−	5.59575i	0.327280	−	0.188955i	−0.327353	−	0.944902i	$-0.606157\pi$
$877$	9.69212	−	5.59575i	0.327280	−	0.188955i	0.654633	+	0.755947i	$0.272823\pi$
$878$		0			0
$879$		−	34.6824i		−	1.16981i
$880$		0			0
$881$	9.39753	−	16.2770i	0.316611	−	0.548386i	−0.663168	−	0.748471i	$-0.730788\pi$
$881$	9.39753	−	16.2770i	0.316611	−	0.548386i	0.979779	+	0.200085i	$0.0641217\pi$
$882$		0			0
$883$	7.53316			0.253511			0.126756	−	0.991934i	$-0.459544\pi$
$883$	7.53316			0.253511			0.126756	+	0.991934i	$0.459544\pi$
$884$		0			0
$885$	−1.01872			−0.0342437
$886$		0			0
$887$	13.8730	−	24.0288i	0.465811	−	0.806809i	−0.533426	−	0.845846i	$-0.679096\pi$
$887$	13.8730	−	24.0288i	0.465811	−	0.806809i	0.999238	+	0.0390377i	$0.0124292\pi$
$888$		0			0
$889$		−	12.0811i		−	0.405187i
$890$		0			0
$891$	−31.0739	+	17.9405i	−1.04101	+	0.601029i
$892$		0			0
$893$	−8.99278	−	15.5759i	−0.300932	−	0.521229i
$894$		0			0
$895$	1.47446	+	0.851280i	0.0492858	+	0.0284552i
$896$		0			0
$897$	−12.2689	−	17.2269i	−0.409647	−	0.575188i
$898$		0			0
$899$	−31.8364	−	18.3808i	−1.06180	−	0.613033i
$900$		0			0
$901$	−5.65540	−	9.79544i	−0.188409	−	0.326333i
$902$		0			0
$903$	−20.7498	+	11.9799i	−0.690510	+	0.398666i
$904$		0			0
$905$			74.2514i			2.46820i
$906$		0			0
$907$	−6.33612	+	10.9745i	−0.210388	+	0.364402i	−0.951836	−	0.306608i	$-0.900806\pi$
$907$	−6.33612	+	10.9745i	−0.210388	+	0.364402i	0.741448	+	0.671010i	$0.234139\pi$
$908$		0			0
$909$	29.8584			0.990341
$910$		0			0
$911$	−53.8605			−1.78448			−0.892239	−	0.451564i	$-0.850866\pi$
$911$	−53.8605			−1.78448			−0.892239	+	0.451564i	$0.850866\pi$
$912$		0			0
$913$	−22.8158	+	39.5181i	−0.755093	+	1.30786i
$914$		0			0
$915$			43.6715i			1.44374i
$916$		0			0
$917$	−3.31645	+	1.91475i	−0.109519	+	0.0632307i
$918$		0			0
$919$	14.8048	+	25.6427i	0.488365	+	0.845873i	0.999910	−	0.0133831i	$-0.00426010\pi$
$919$	14.8048	+	25.6427i	0.488365	+	0.845873i	−0.511545	+	0.859256i	$0.670927\pi$
$920$		0			0
$921$	−59.5046	−	34.3550i	−1.96074	−	1.13204i
$922$		0			0
$923$	−0.860483	+	0.612833i	−0.0283231	+	0.0201716i
$924$		0			0
$925$	−85.7499	−	49.5077i	−2.81944	−	1.62780i
$926$		0			0
$927$	10.4120	+	18.0341i	0.341975	+	0.592317i
$928$		0			0
$929$	40.2741	−	23.2522i	1.32135	−	0.762881i	0.337406	−	0.941359i	$-0.390451\pi$
$929$	40.2741	−	23.2522i	1.32135	−	0.762881i	0.983944	+	0.178478i	$0.0571173\pi$
$930$		0			0
$931$			2.01179i			0.0659337i
$932$		0			0
$933$	8.34364	−	14.4516i	0.273158	−	0.473124i
$934$		0			0
$935$	−23.0043			−0.752322
$936$		0			0
$937$	25.7685			0.841821			0.420911	−	0.907102i	$-0.361711\pi$
$937$	25.7685			0.841821			0.420911	+	0.907102i	$0.361711\pi$
$938$		0			0
$939$	24.1126	−	41.7643i	0.786885	−	1.36293i
$940$		0			0
$941$			51.0205i			1.66322i	0.555360	+	0.831610i	$0.312580\pi$
$941$			51.0205i			1.66322i	−0.555360	+	0.831610i	$0.687420\pi$
$942$		0			0
$943$	19.9910	−	11.5418i	0.650995	−	0.375852i
$944$		0			0
$945$	0.425157	+	0.736394i	0.0138304	+	0.0239549i
$946$		0			0
$947$	−8.23345	−	4.75358i	−0.267551	−	0.154471i	0.360223	−	0.932866i	$-0.382701\pi$
$947$	−8.23345	−	4.75358i	−0.267551	−	0.154471i	−0.627774	+	0.778395i	$0.716034\pi$
$948$		0			0
$949$	0.649066	+	6.79257i	0.0210696	+	0.220496i
$950$		0			0
$951$	−69.8036	−	40.3011i	−2.26354	−	1.30685i
$952$		0			0
$953$	−6.94507	−	12.0292i	−0.224973	−	0.389665i	0.731338	−	0.682015i	$-0.238896\pi$
$953$	−6.94507	−	12.0292i	−0.224973	−	0.389665i	−0.956311	+	0.292350i	$0.905563\pi$
$954$		0			0
$955$	−10.9920	+	6.34626i	−0.355694	+	0.205360i
$956$		0			0
$957$			37.8616i			1.22389i
$958$		0			0
$959$	−3.15979	+	5.47291i	−0.102035	+	0.176729i
$960$		0			0
$961$	−52.2175			−1.68444
$962$		0			0
$963$	−43.5068			−1.40199
$964$		0			0
$965$	6.26657	−	10.8540i	0.201728	−	0.349403i
$966$		0			0
$967$			30.4473i			0.979120i	0.871970	+	0.489560i	$0.162843\pi$
$967$			30.4473i			0.979120i	−0.871970	+	0.489560i	$0.837157\pi$
$968$		0			0
$969$	6.92311	−	3.99706i	0.222402	−	0.128404i
$970$		0			0
$971$	6.88995	+	11.9337i	0.221109	+	0.382972i	0.955145	−	0.296139i	$-0.0956990\pi$
$971$	6.88995	+	11.9337i	0.221109	+	0.382972i	−0.734036	+	0.679110i	$0.762366\pi$
$972$		0			0
$973$	−2.32256	−	1.34093i	−0.0744577	−	0.0429882i
$974$		0			0
$975$	−29.9605	+	65.6158i	−0.959504	+	2.10139i
$976$		0			0
$977$	−1.24120	−	0.716604i	−0.0397094	−	0.0229262i	0.480014	−	0.877261i	$-0.340632\pi$
$977$	−1.24120	−	0.716604i	−0.0397094	−	0.0229262i	−0.519723	+	0.854335i	$0.673965\pi$
$978$		0			0
$979$	−4.76373	−	8.25102i	−0.152249	−	0.263704i
$980$		0			0
$981$	22.1906	−	12.8118i	0.708492	−	0.409048i
$982$		0			0
$983$			31.6454i			1.00933i	0.863315	+	0.504665i	$0.168384\pi$
$983$			31.6454i			1.00933i	−0.863315	+	0.504665i	$0.831616\pi$
$984$		0			0
$985$	−22.9599	+	39.7677i	−0.731564	+	1.26711i
$986$		0			0
$987$	−21.7224			−0.691431
$988$		0			0
$989$	23.8054			0.756967
$990$		0			0
$991$	−2.74528	+	4.75496i	−0.0872066	+	0.151046i	−0.906329	−	0.422572i	$-0.861127\pi$
$991$	−2.74528	+	4.75496i	−0.0872066	+	0.151046i	0.819123	+	0.573618i	$0.194461\pi$
$992$		0			0
$993$			40.4905i			1.28493i
$994$		0			0
$995$	34.8019	−	20.0929i	1.10329	−	0.636987i
$996$		0			0
$997$	−12.2202	−	21.1659i	−0.387016	−	0.670332i	0.605030	−	0.796202i	$-0.293161\pi$
$997$	−12.2202	−	21.1659i	−0.387016	−	0.670332i	−0.992047	+	0.125871i	$0.959828\pi$
$998$		0			0
$999$	−2.43434	−	1.40547i	−0.0770191	−	0.0444670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.f.225.2		16
4.3	odd	2		364.2.u.a.225.7	✓	16
12.11	even	2		3276.2.cf.c.2773.8		16
13.10	even	6	inner	1456.2.cc.f.673.2		16
28.3	even	6		2548.2.bq.c.1941.7		16
28.11	odd	6		2548.2.bq.e.1941.2		16
28.19	even	6		2548.2.bb.c.1733.2		16
28.23	odd	6		2548.2.bb.d.1733.7		16
28.27	even	2		2548.2.u.c.589.2		16
52.7	even	12		4732.2.a.s.1.2		8
52.19	even	12		4732.2.a.t.1.2		8
52.23	odd	6		364.2.u.a.309.7	yes	16
52.35	odd	6		4732.2.g.k.337.3		16
52.43	odd	6		4732.2.g.k.337.4		16
156.23	even	6		3276.2.cf.c.1765.1		16
364.23	odd	6		2548.2.bq.e.361.2		16
364.75	even	6		2548.2.bq.c.361.7		16
364.179	odd	6		2548.2.bb.d.569.7		16
364.283	even	6		2548.2.bb.c.569.2		16
364.335	even	6		2548.2.u.c.1765.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.7	✓	16	4.3	odd	2
364.2.u.a.309.7	yes	16	52.23	odd	6
1456.2.cc.f.225.2		16	1.1	even	1	trivial
1456.2.cc.f.673.2		16	13.10	even	6	inner
2548.2.u.c.589.2		16	28.27	even	2
2548.2.u.c.1765.2		16	364.335	even	6
2548.2.bb.c.569.2		16	364.283	even	6
2548.2.bb.c.1733.2		16	28.19	even	6
2548.2.bb.d.569.7		16	364.179	odd	6
2548.2.bb.d.1733.7		16	28.23	odd	6
2548.2.bq.c.361.7		16	364.75	even	6
2548.2.bq.c.1941.7		16	28.3	even	6
2548.2.bq.e.361.2		16	364.23	odd	6
2548.2.bq.e.1941.2		16	28.11	odd	6
3276.2.cf.c.1765.1		16	156.23	even	6
3276.2.cf.c.2773.8		16	12.11	even	2
4732.2.a.s.1.2		8	52.7	even	12
4732.2.a.t.1.2		8	52.19	even	12
4732.2.g.k.337.3		16	52.35	odd	6
4732.2.g.k.337.4		16	52.43	odd	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21489 + 2.10425i) q^{3} -3.63781i q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.45190 - 2.51476i) q^{9} +(-3.34871 - 1.93338i) q^{11} +(-3.58920 + 0.342967i) q^{13} +(7.65484 + 4.41953i) q^{15} +(0.817697 + 1.41629i) q^{17} +(-1.74226 + 1.00589i) q^{19} +2.42977i q^{21} +(1.20706 - 2.09068i) q^{23} -8.23365 q^{25} -0.233744 q^{27} +(-2.01491 + 3.48993i) q^{29} +9.12236i q^{31} +(8.13661 - 4.69768i) q^{33} +(-1.81890 - 3.15043i) q^{35} +(10.4146 + 6.01285i) q^{37} +(3.63879 - 7.96923i) q^{39} +(8.28088 + 4.78097i) q^{41} +(4.93046 + 8.53981i) q^{43} +(-9.14823 + 5.28173i) q^{45} +8.94009i q^{47} +(0.500000 - 0.866025i) q^{49} -3.97364 q^{51} -6.91625 q^{53} +(-7.03327 + 12.1820i) q^{55} -4.88819i q^{57} +(-0.0998109 + 0.0576258i) q^{59} +(2.47037 + 4.27881i) q^{61} +(-2.51476 - 1.45190i) q^{63} +(1.24765 + 13.0568i) q^{65} +(-7.89684 - 4.55925i) q^{67} +(2.93287 + 5.07988i) q^{69} +(0.253741 - 0.146497i) q^{71} -1.89250i q^{73} +(10.0030 - 17.3256i) q^{75} -3.86676 q^{77} -5.12890 q^{79} +(4.63967 - 8.03615i) q^{81} -11.8010i q^{83} +(5.15220 - 2.97463i) q^{85} +(-4.89578 - 8.47975i) q^{87} +(2.13383 + 1.23197i) q^{89} +(-2.93686 + 2.09162i) q^{91} +(-19.1957 - 11.0826i) q^{93} +(3.65925 + 6.33801i) q^{95} +(-15.1343 + 8.73781i) q^{97} +11.2283i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Introduction

L-functions

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