LMFDB - Embedded newform 1456.2.cc.f.673.2

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			673.2
Root			$2.42977i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.f.225.2

$q$-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 $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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	−0.967970	−	0.251067i	$-0.919219\pi$
$3$	−1.21489	−	2.10425i	−0.701415	−	1.21489i	0.266554	−	0.963820i	$-0.414115\pi$
$4$		0			0
$5$			3.63781i			1.62688i	0.581651	+	0.813439i	$0.302407\pi$
$5$			3.63781i			1.62688i	−0.581651	+	0.813439i	$0.697593\pi$
$6$		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	−0.911096	−	0.412193i	$-0.864763\pi$
$11$	−3.34871	+	1.93338i	−1.00967	+	0.582936i	−0.0985783	+	0.995129i	$0.531430\pi$
$12$		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	−0.749663	−	0.661819i	$-0.769785\pi$
$17$	0.817697	−	1.41629i	0.198321	−	0.343501i	0.947984	+	0.318318i	$0.103118\pi$
$18$		0			0
$19$	−1.74226	−	1.00589i	−0.399702	−	0.230768i	0.286654	−	0.958034i	$-0.407457\pi$
$19$	−1.74226	−	1.00589i	−0.399702	−	0.230768i	−0.686355	+	0.727266i	$0.740790\pi$
$20$		0			0
$21$		−	2.42977i		−	0.530220i
$22$		0			0
$23$	1.20706	+	2.09068i	0.251689	+	0.435937i	0.963991	−	0.265935i	$-0.0856808\pi$
$23$	1.20706	+	2.09068i	0.251689	+	0.435937i	−0.712302	+	0.701873i	$0.752347\pi$
$24$		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	0.616041	−	0.787714i	$-0.288736\pi$
$29$	−2.01491	−	3.48993i	−0.374160	−	0.648064i	−0.990201	+	0.139650i	$0.955402\pi$
$30$		0			0
$31$		−	9.12236i		−	1.63842i	−0.573490	−	0.819212i	$-0.694411\pi$
$31$		−	9.12236i		−	1.63842i	0.573490	−	0.819212i	$-0.305589\pi$
$32$		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	0.780485	−	0.625175i	$-0.214972\pi$
$37$	10.4146	−	6.01285i	1.71214	−	0.988507i	0.931660	−	0.363332i	$-0.118361\pi$
$38$		0			0
$39$	3.63879	+	7.96923i	0.582672	+	1.27610i
$40$		0			0
$41$	8.28088	−	4.78097i	1.29326	−	0.746661i	0.314026	−	0.949414i	$-0.398322\pi$
$41$	8.28088	−	4.78097i	1.29326	−	0.746661i	0.979230	+	0.202753i	$0.0649889\pi$
$42$		0			0
$43$	4.93046	−	8.53981i	0.751888	−	1.30231i	−0.195018	−	0.980800i	$-0.562477\pi$
$43$	4.93046	−	8.53981i	0.751888	−	1.30231i	0.946906	−	0.321509i	$-0.104190\pi$
$44$		0			0
$45$	−9.14823	−	5.28173i	−1.36374	−	0.787354i
$46$		0			0
$47$		−	8.94009i		−	1.30405i	−0.758199	−	0.652023i	$-0.773921\pi$
$47$		−	8.94009i		−	1.30405i	0.758199	−	0.652023i	$-0.226079\pi$
$48$		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	0.493489	−	0.869752i	$-0.335721\pi$
$59$	−0.0998109	−	0.0576258i	−0.0129943	−	0.00750224i	−0.506483	+	0.862250i	$0.669055\pi$
$60$		0			0
$61$	2.47037	−	4.27881i	0.316299	−	0.547846i	−0.663414	−	0.748253i	$-0.730893\pi$
$61$	2.47037	−	4.27881i	0.316299	−	0.547846i	0.979713	+	0.200407i	$0.0642264\pi$
$62$		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	−0.897633	−	0.440744i	$-0.854715\pi$
$67$	−7.89684	+	4.55925i	−0.964753	+	0.557000i	−0.0671204	+	0.997745i	$0.521381\pi$
$68$		0			0
$69$	2.93287	−	5.07988i	0.353076	−	0.611546i
$70$		0			0
$71$	0.253741	+	0.146497i	0.0301135	+	0.0173860i	0.514981	−	0.857201i	$-0.327799\pi$
$71$	0.253741	+	0.146497i	0.0301135	+	0.0173860i	−0.484868	+	0.874588i	$0.661132\pi$
$72$		0			0
$73$			1.89250i			0.221500i	0.993848	+	0.110750i	$0.0353254\pi$
$73$			1.89250i			0.221500i	−0.993848	+	0.110750i	$0.964675\pi$
$74$		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	$0.224254\pi$
$83$			11.8010i			1.29533i	−0.761926	+	0.647664i	$0.775746\pi$
$84$		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	−0.382625	−	0.923904i	$-0.624980\pi$
$89$	2.13383	−	1.23197i	0.226186	−	0.130588i	0.608811	+	0.793315i	$0.291647\pi$
$90$		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	−0.999031	−	0.0440072i	$-0.985988\pi$
$97$	−15.1343	−	8.73781i	−1.53666	−	0.887190i	−0.537627	−	0.843183i	$-0.680679\pi$
$98$		0			0
$99$		−	11.2283i		−	1.12849i
$100$		0			0
$101$	−5.14126	−	8.90493i	−0.511575	−	0.886074i	−0.999910	−	0.0134176i	$-0.995729\pi$
$101$	−5.14126	−	8.90493i	−0.511575	−	0.886074i	0.488335	−	0.872656i	$-0.337604\pi$
$102$		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	0.959296	+	0.282404i	$0.0911317\pi$
$107$	7.49135	+	12.9754i	0.724216	+	1.25438i	−0.235079	+	0.971976i	$0.575535\pi$
$108$		0			0
$109$		−	8.82413i		−	0.845198i	−0.906317	−	0.422599i	$-0.861118\pi$
$109$		−	8.82413i		−	0.845198i	0.906317	−	0.422599i	$-0.138882\pi$
$110$		0			0
$111$	−25.3050	−	14.6099i	−2.40185	−	1.38671i
$112$		0			0
$113$	−2.74315	+	4.75128i	−0.258054	+	0.446963i	−0.965721	−	0.259584i	$-0.916415\pi$
$113$	−2.74315	+	4.75128i	−0.258054	+	0.446963i	0.707666	+	0.706547i	$0.249748\pi$
$114$		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	0.999114	+	0.0420953i	$0.0134033\pi$
$127$	6.04055	+	10.4625i	0.536012	+	0.928401i	−0.463101	+	0.886305i	$0.653263\pi$
$128$		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	0.247645	−	0.968851i	$-0.420343\pi$
$137$	−5.47291	−	3.15979i	−0.467582	−	0.269959i	−0.715227	+	0.698892i	$0.753677\pi$
$138$		0			0
$139$	−1.34093	+	2.32256i	−0.113736	+	0.196997i	−0.917274	−	0.398257i	$-0.869615\pi$
$139$	−1.34093	+	2.32256i	−0.113736	+	0.196997i	0.803538	+	0.595254i	$0.202948\pi$
$140$		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	0.937460	−	0.348093i	$-0.113171\pi$
$149$	13.4850	+	7.78555i	1.10473	+	0.637817i	0.167272	+	0.985911i	$0.446504\pi$
$150$		0			0
$151$		−	15.7761i		−	1.28384i	−0.766771	−	0.641920i	$-0.778138\pi$
$151$		−	15.7761i		−	1.28384i	0.766771	−	0.641920i	$-0.221862\pi$
$152$		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	−0.00282942	−	0.999996i	$-0.500901\pi$
$163$	−11.1108	−	6.41483i	−0.870266	−	0.502448i	−0.867437	+	0.497548i	$0.834234\pi$
$164$		0			0
$165$	−17.0892	+	29.5994i	−1.33040	+	2.30431i
$166$		0			0
$167$	9.01741	−	5.20620i	0.697788	−	0.402868i	−0.108735	−	0.994071i	$-0.534680\pi$
$167$	9.01741	−	5.20620i	0.697788	−	0.402868i	0.806523	+	0.591203i	$0.201347\pi$
$168$		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	−0.536174	−	0.844107i	$-0.680131\pi$
$173$	6.08891	−	10.5463i	0.462931	−	0.801820i	0.999106	+	0.0422871i	$0.0134644\pi$
$174$		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	0.857148	−	0.515071i	$-0.172234\pi$
$179$	−0.234009	−	0.405316i	−0.0174907	−	0.0302947i	−0.874638	+	0.484776i	$0.838901\pi$
$180$		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	−0.922213	−	0.386683i	$-0.873621\pi$
$191$	−1.74453	+	3.02161i	−0.126230	+	0.218636i	0.795983	+	0.605319i	$0.206954\pi$
$192$		0			0
$193$	2.98367	−	1.72262i	0.214769	−	0.123997i	−0.388757	−	0.921340i	$-0.627095\pi$
$193$	2.98367	−	1.72262i	0.214769	−	0.123997i	0.603526	+	0.797343i	$0.293762\pi$
$194$		0			0
$195$	−28.9905	+	13.2372i	−2.07606	+	0.947936i
$196$		0			0
$197$	−10.9318	+	6.31147i	−0.778857	+	0.449674i	−0.836025	−	0.548691i	$-0.815126\pi$
$197$	−10.9318	+	6.31147i	−0.778857	+	0.449674i	0.0571678	+	0.998365i	$0.481793\pi$
$198$		0			0
$199$	5.52335	−	9.56672i	0.391540	−	0.678167i	−0.601113	−	0.799164i	$-0.705276\pi$
$199$	5.52335	−	9.56672i	0.391540	−	0.678167i	0.992653	+	0.120997i	$0.0386091\pi$
$200$		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	0.848198	−	0.529680i	$-0.177688\pi$
$211$	−0.502843	−	0.870949i	−0.0346171	−	0.0599586i	−0.882815	+	0.469721i	$0.844355\pi$
$212$		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	0.314185	−	0.949362i	$-0.398269\pi$
$223$	19.3153	−	11.1517i	1.29345	−	0.746773i	0.979264	+	0.202589i	$0.0649355\pi$
$224$		0			0
$225$	11.9544	−	20.7057i	0.796962	−	1.38038i
$226$		0			0
$227$	−13.8976	−	8.02375i	−0.922413	−	0.532555i	−0.0380088	−	0.999277i	$-0.512101\pi$
$227$	−13.8976	−	8.02375i	−0.922413	−	0.532555i	−0.884404	+	0.466722i	$0.845435\pi$
$228$		0			0
$229$			12.2285i			0.808082i	0.914741	+	0.404041i	$0.132395\pi$
$229$			12.2285i			0.808082i	−0.914741	+	0.404041i	$0.867605\pi$
$230$		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	$0.100826\pi$
$239$			9.63081i			0.622965i	−0.950252	+	0.311483i	$0.899174\pi$
$240$		0			0
$241$	−0.123908	−	0.0715383i	−0.00798162	−	0.00460819i	0.496004	−	0.868320i	$-0.334800\pi$
$241$	−0.123908	−	0.0715383i	−0.00798162	−	0.00460819i	−0.503986	+	0.863712i	$0.668134\pi$
$242$		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	−0.980913	−	0.194449i	$-0.937708\pi$
$251$	−5.10237	+	8.83756i	−0.322059	+	0.557822i	0.658854	+	0.752271i	$0.271041\pi$
$252$		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	−0.987802	−	0.155718i	$-0.950231\pi$
$257$	−10.0797	−	17.4586i	−0.628756	−	1.08904i	0.359045	−	0.933320i	$-0.383102\pi$
$258$		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	0.849655	+	0.527338i	$0.176810\pi$
$263$	14.2958	+	24.7610i	0.881516	+	1.52683i	0.0318605	+	0.999492i	$0.489857\pi$
$264$		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	0.332639	−	0.943054i	$-0.392061\pi$
$269$	16.1229	−	27.9256i	0.983028	−	1.70266i	0.650389	−	0.759601i	$-0.274606\pi$
$270$		0			0
$271$	−20.9296	+	12.0837i	−1.27139	+	0.734035i	−0.975249	−	0.221111i	$-0.929032\pi$
$271$	−20.9296	+	12.0837i	−1.27139	+	0.734035i	−0.296137	+	0.955146i	$0.595698\pi$
$272$		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	0.385861	+	0.922557i	$0.373905\pi$
$277$	−10.0863	+	17.4700i	−0.606027	+	1.04967i	−0.991888	+	0.127113i	$0.959429\pi$
$278$		0			0
$279$	22.9406	+	13.2448i	1.37342	+	0.792943i
$280$		0			0
$281$		−	24.0074i		−	1.43216i	−0.698018	−	0.716080i	$-0.745934\pi$
$281$		−	24.0074i		−	1.43216i	0.698018	−	0.716080i	$-0.254066\pi$
$282$		0			0
$283$	−6.77682	−	11.7378i	−0.402840	−	0.697739i	0.591227	−	0.806505i	$-0.298644\pi$
$283$	−6.77682	−	11.7378i	−0.402840	−	0.697739i	−0.994067	+	0.108765i	$0.965310\pi$
$284$		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	0.0933803	−	0.995631i	$-0.470233\pi$
$293$	−12.3616	−	7.13696i	−0.722171	−	0.416945i	−0.815551	+	0.578685i	$0.803566\pi$
$294$		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	$-0.701108\pi$
$307$		−	28.2784i		−	1.61393i	0.590598	−	0.806966i	$-0.298892\pi$
$308$		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	$-0.618428\pi$
$317$		−	33.1727i		−	1.86317i	0.363527	−	0.931584i	$-0.381572\pi$
$318$		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	0.841102	−	0.540877i	$-0.181908\pi$
$331$	14.4317	+	8.33216i	0.793239	+	0.457977i	−0.0478625	+	0.998854i	$0.515241\pi$
$332$		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	−0.988933	−	0.148364i	$-0.952599\pi$
$347$	−6.81743	+	11.8081i	−0.365979	+	0.633894i	0.622954	+	0.782259i	$0.285932\pi$
$348$		0			0
$349$	2.05749	−	1.18789i	0.110135	−	0.0635864i	−0.443921	−	0.896066i	$-0.646413\pi$
$349$	2.05749	−	1.18789i	0.110135	−	0.0635864i	0.554056	+	0.832480i	$0.313080\pi$
$350$		0			0
$351$	0.838953	+	0.0801665i	0.0447800	+	0.00427897i
$352$		0			0
$353$	−0.236165	+	0.136350i	−0.0125698	+	0.00725717i	−0.506272	−	0.862374i	$-0.668977\pi$
$353$	−0.236165	+	0.136350i	−0.0125698	+	0.00725717i	0.493702	+	0.869631i	$0.335643\pi$
$354$		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	$-0.979721\pi$
$359$		−	2.41260i		−	0.127332i	0.997971	−	0.0636661i	$-0.0202793\pi$
$360$		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	0.965486	+	0.260455i	$0.0838726\pi$
$367$	13.5691	+	23.5025i	0.708304	+	1.22682i	−0.257182	+	0.966363i	$0.582794\pi$
$368$		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	0.222613	+	0.974907i	$0.428541\pi$
$373$	−14.1563	+	24.5195i	−0.732988	+	1.26957i	−0.955601	+	0.294665i	$0.904792\pi$
$374$		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	−0.0180520	−	0.999837i	$-0.505746\pi$
$379$	16.3298	−	9.42802i	0.838806	−	0.484285i	0.856858	+	0.515552i	$0.172413\pi$
$380$		0			0
$381$	14.6772	−	25.4216i	0.751935	−	1.30239i
$382$		0			0
$383$	−33.3217	−	19.2383i	−1.70266	−	0.983031i	−0.943049	−	0.332654i	$-0.892056\pi$
$383$	−33.3217	−	19.2383i	−1.70266	−	0.983031i	−0.759611	−	0.650377i	$-0.774611\pi$
$384$		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	0.638447	−	0.769666i	$-0.279577\pi$
$397$	5.80052	+	3.34893i	0.291120	+	0.168078i	−0.347327	+	0.937744i	$0.612911\pi$
$398$		0			0
$399$	−2.44409	+	4.23330i	−0.122358	+	0.211930i
$400$		0			0
$401$	−17.7884	+	10.2701i	−0.888308	+	0.512865i	−0.873389	−	0.487024i	$-0.838082\pi$
$401$	−17.7884	+	10.2701i	−0.888308	+	0.512865i	−0.0149193	+	0.999889i	$0.504749\pi$
$402$		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	0.151901	−	0.988396i	$-0.451461\pi$
$409$	−12.7030	−	7.33410i	−0.628125	−	0.362648i	−0.780025	+	0.625748i	$0.784794\pi$
$410$		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	0.981482	+	0.191553i	$0.0613525\pi$
$419$	13.4409	+	23.2803i	0.656631	+	1.13732i	−0.324851	+	0.945765i	$0.605314\pi$
$420$		0			0
$421$		−	4.54437i		−	0.221479i	−0.993849	−	0.110739i	$-0.964678\pi$
$421$		−	4.54437i		−	0.221479i	0.993849	−	0.110739i	$-0.0353219\pi$
$422$		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	−0.220506	−	0.975386i	$-0.570771\pi$
$431$	10.6699	−	6.16025i	0.513949	−	0.296729i	0.734456	+	0.678657i	$0.237438\pi$
$432$		0			0
$433$	−12.2232	+	21.1711i	−0.587408	+	1.01742i	0.407163	+	0.913356i	$0.366518\pi$
$433$	−12.2232	+	21.1711i	−0.587408	+	1.01742i	−0.994571	+	0.104064i	$0.966815\pi$
$434$		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	0.795749	−	0.605626i	$-0.207077\pi$
$439$	−2.65283	−	4.59484i	−0.126613	−	0.219300i	−0.922362	+	0.386326i	$0.873744\pi$
$440$		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	0.896813	−	0.442409i	$-0.145876\pi$
$449$	20.3862	+	11.7700i	0.962082	+	0.555458i	0.0652689	+	0.997868i	$0.479209\pi$
$450$		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	−0.889660	−	0.456623i	$-0.849059\pi$
$457$	−20.0744	+	11.5900i	−0.939043	+	0.542157i	−0.0493828	+	0.998780i	$0.515725\pi$
$458$		0			0
$459$	−0.191132	+	0.331050i	−0.00892126	+	0.0154521i
$460$		0			0
$461$	−31.1249	−	17.9700i	−1.44963	−	0.836945i	−0.451173	−	0.892437i	$-0.648994\pi$
$461$	−31.1249	−	17.9700i	−1.44963	−	0.836945i	−0.998459	+	0.0554911i	$0.982328\pi$
$462$		0			0
$463$		−	12.9147i		−	0.600197i	−0.953908	−	0.300098i	$-0.902981\pi$
$463$		−	12.9147i		−	0.600197i	0.953908	−	0.300098i	$-0.0970195\pi$
$464$		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	−0.0503632	−	0.998731i	$-0.516038\pi$
$479$	17.2765	−	9.97457i	0.789382	−	0.455750i	0.839745	+	0.542981i	$0.182705\pi$
$480$		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	0.0659562	−	0.997823i	$-0.478990\pi$
$487$	−16.8866	−	9.74949i	−0.765205	−	0.441791i	−0.831162	+	0.556031i	$0.812324\pi$
$488$		0			0
$489$			31.1732i			1.40970i
$490$		0			0
$491$	−9.52733	−	16.5018i	−0.429962	−	0.744717i	0.566907	−	0.823782i	$-0.308140\pi$
$491$	−9.52733	−	16.5018i	−0.429962	−	0.744717i	−0.996869	+	0.0790649i	$0.974807\pi$
$492$		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	$0.0989548\pi$
$499$			13.6662i			0.611785i	−0.952066	+	0.305892i	$0.901045\pi$
$500$		0			0
$501$	−21.9103	−	12.6499i	−0.978878	−	0.565156i
$502$		0			0
$503$	−1.15076	+	1.99318i	−0.0513100	+	0.0888715i	−0.890540	−	0.454906i	$-0.849673\pi$
$503$	−1.15076	+	1.99318i	−0.0513100	+	0.0888715i	0.839230	+	0.543777i	$0.183006\pi$
$504$		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	−0.862097	−	0.506744i	$-0.830849\pi$
$509$	−19.2737	+	11.1277i	−0.854292	+	0.493226i	0.00780455	+	0.999970i	$0.497516\pi$
$510$		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	−0.861696	−	0.507425i	$-0.830598\pi$
$523$	−19.9028	−	34.4727i	−0.870291	−	1.50739i	−0.00859463	−	0.999963i	$-0.502736\pi$
$524$		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	$-0.867784\pi$
$541$		−	18.7716i		−	0.807055i	0.914968	−	0.403527i	$-0.132216\pi$
$542$		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	−0.000714272	−	1.00000i	$-0.500227\pi$
$557$	20.4136	−	11.7858i	0.864954	−	0.499381i	0.865668	+	0.500618i	$0.166894\pi$
$558$		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	−0.488427	−	0.872605i	$-0.662429\pi$
$563$	12.1363	−	21.0207i	0.511484	−	0.885917i	0.999911	−	0.0133121i	$-0.00423750\pi$
$564$		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	0.824934	+	0.565228i	$0.191212\pi$
$569$	21.5153	+	37.2656i	0.901969	+	1.56226i	0.0770349	+	0.997028i	$0.475455\pi$
$570$		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	$0.0794456\pi$
$577$			11.8664i			0.494005i	−0.969015	+	0.247003i	$0.920554\pi$
$578$		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	−0.0359686	−	0.999353i	$-0.511452\pi$
$587$	19.6614	−	11.3515i	0.811512	−	0.468527i	0.847481	+	0.530826i	$0.178118\pi$
$588$		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	$0.319331\pi$
$593$			41.0665i			1.68640i	−0.537600	+	0.843200i	$0.680669\pi$
$594$		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	0.912788	−	0.408433i	$-0.133925\pi$
$601$	2.51726	+	4.36002i	0.102681	+	0.177849i	−0.810107	+	0.586282i	$0.800591\pi$
$602$		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	−0.947763	−	0.318974i	$-0.896662\pi$
$607$	−4.86938	+	8.43401i	−0.197642	+	0.342326i	0.750121	+	0.661300i	$0.229995\pi$
$608$		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	−0.168148	−	0.985762i	$-0.553779\pi$
$613$	14.8918	−	8.59776i	0.601473	−	0.347260i	0.769621	+	0.638501i	$0.220445\pi$
$614$		0			0
$615$	42.2592	−	73.1951i	1.70406	−	2.95151i
$616$		0			0
$617$	−15.4804	−	8.93760i	−0.623216	−	0.359814i	0.154904	−	0.987930i	$-0.450493\pi$
$617$	−15.4804	−	8.93760i	−0.623216	−	0.359814i	−0.778120	+	0.628115i	$0.783827\pi$
$618$		0			0
$619$			21.3112i			0.856568i	0.903644	+	0.428284i	$0.140882\pi$
$619$			21.3112i			0.856568i	−0.903644	+	0.428284i	$0.859118\pi$
$620$		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	0.701315	−	0.712852i	$-0.252597\pi$
$631$	10.9176	+	6.30330i	0.434624	+	0.250930i	−0.266691	+	0.963782i	$0.585930\pi$
$632$		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	−0.846580	−	0.532261i	$-0.821342\pi$
$641$	0.953524	−	1.65155i	0.0376619	−	0.0652324i	0.884242	+	0.467029i	$0.154676\pi$
$642$		0			0
$643$	9.56862	+	5.52444i	0.377349	+	0.217863i	0.676664	−	0.736292i	$-0.263425\pi$
$643$	9.56862	+	5.52444i	0.377349	+	0.217863i	−0.299315	+	0.954154i	$0.596758\pi$
$644$		0			0
$645$		−	87.1612i		−	3.43197i
$646$		0			0
$647$	−22.3945	−	38.7885i	−0.880420	−	1.52493i	−0.850875	−	0.525368i	$-0.823928\pi$
$647$	−22.3945	−	38.7885i	−0.880420	−	1.52493i	−0.0295447	−	0.999563i	$-0.509406\pi$
$648$		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	0.586223	−	0.810150i	$-0.300614\pi$
$653$	−10.4387	−	18.0804i	−0.408499	−	0.707541i	−0.994722	+	0.102609i	$0.967281\pi$
$654$		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	−0.847953	−	0.530071i	$-0.822165\pi$
$659$	0.900509	−	1.55973i	0.0350788	−	0.0607583i	0.883032	+	0.469313i	$0.155498\pi$
$660$		0			0
$661$	8.46403	−	4.88671i	0.329213	−	0.190071i	−0.326279	−	0.945274i	$-0.605795\pi$
$661$	8.46403	−	4.88671i	0.329213	−	0.190071i	0.655491	+	0.755203i	$0.272462\pi$
$662$		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	0.660024	−	0.751244i	$-0.270546\pi$
$673$	−8.31668	−	14.4049i	−0.320584	−	0.555268i	−0.980609	+	0.195976i	$0.937213\pi$
$674$		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	0.839086	−	0.543999i	$-0.183091\pi$
$683$	20.5810	+	11.8825i	0.787511	+	0.454670i	−0.0515745	+	0.998669i	$0.516424\pi$
$684$		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	−0.410918	−	0.911672i	$-0.634792\pi$
$691$	4.55167	−	2.62791i	0.173154	−	0.0999702i	0.584072	+	0.811702i	$0.301459\pi$
$692$		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	0.780444	−	0.625225i	$-0.214993\pi$
$709$	16.7539	+	9.67286i	0.629205	+	0.363272i	−0.151239	+	0.988497i	$0.548326\pi$
$710$		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	0.0644212	−	0.997923i	$-0.479480\pi$
$719$	24.0372	−	41.6337i	0.896437	−	1.55267i	0.832016	−	0.554752i	$-0.187187\pi$
$720$		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	$-0.810780\pi$
$733$		−	30.3258i		−	1.12011i	0.828456	−	0.560055i	$-0.189220\pi$
$734$		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	−0.337306	−	0.941395i	$-0.609516\pi$
$739$	8.40853	−	4.85467i	0.309313	−	0.178582i	0.646619	+	0.762813i	$0.276182\pi$
$740$		0			0
$741$	1.67649	−	17.5447i	0.0615874	−	0.644521i
$742$		0			0
$743$	−36.4578	+	21.0489i	−1.33751	+	0.772211i	−0.986437	−	0.164138i	$-0.947516\pi$
$743$	−36.4578	+	21.0489i	−1.33751	+	0.772211i	−0.351071	+	0.936349i	$0.614182\pi$
$744$		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	0.549971	−	0.835184i	$-0.314639\pi$
$751$	−12.2855	−	21.2791i	−0.448305	−	0.776486i	−0.998276	+	0.0586972i	$0.981305\pi$
$752$		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	−0.981577	−	0.191066i	$-0.938805\pi$
$757$	−18.0560	−	31.2739i	−0.656257	−	1.13667i	0.325320	−	0.945604i	$-0.394528\pi$
$758$		0			0
$759$			22.6814i			0.823284i
$760$		0			0
$761$	−13.3419	−	7.70294i	−0.483643	−	0.279231i	0.238291	−	0.971194i	$-0.423413\pi$
$761$	−13.3419	−	7.70294i	−0.483643	−	0.279231i	−0.721933	+	0.691963i	$0.756746\pi$
$762$		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	−0.146133	−	0.989265i	$-0.546683\pi$
$769$	17.6792	−	10.2071i	0.637529	−	0.368078i	0.783662	+	0.621187i	$0.213349\pi$
$770$		0			0
$771$	−24.4915	+	42.4205i	−0.882038	+	1.52774i
$772$		0			0
$773$	42.5514	+	24.5671i	1.53047	+	0.883616i	0.999340	+	0.0363252i	$0.0115652\pi$
$773$	42.5514	+	24.5671i	1.53047	+	0.883616i	0.531129	+	0.847291i	$0.321768\pi$
$774$		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	0.678263	−	0.734819i	$-0.262733\pi$
$787$	10.6890	+	6.17132i	0.381023	+	0.219984i	−0.297240	+	0.954803i	$0.596066\pi$
$788$		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	−0.988475	−	0.151387i	$-0.951626\pi$
$797$	−10.2517	+	17.7564i	−0.363133	+	0.628964i	0.625342	+	0.780351i	$0.284959\pi$
$798$		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	0.924301	−	0.381664i	$-0.124649\pi$
$809$	3.74367	+	6.48422i	0.131620	+	0.227973i	−0.792681	+	0.609637i	$0.791315\pi$
$810$		0			0
$811$			22.8692i			0.803048i	0.915849	+	0.401524i	$0.131519\pi$
$811$			22.8692i			0.803048i	−0.915849	+	0.401524i	$0.868481\pi$
$812$		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	−0.965660	−	0.259808i	$-0.916341\pi$
$821$	−35.0568	+	20.2400i	−1.22349	+	0.706382i	−0.257830	+	0.966190i	$0.583007\pi$
$822$		0			0
$823$	11.3481	−	19.6555i	0.395570	−	0.685146i	−0.597604	−	0.801791i	$-0.703881\pi$
$823$	11.3481	−	19.6555i	0.395570	−	0.685146i	0.993174	+	0.116645i	$0.0372139\pi$
$824$		0			0
$825$	−66.9940	−	38.6790i	−2.33243	−	1.34663i
$826$		0			0
$827$		−	15.7414i		−	0.547383i	−0.961818	−	0.273691i	$-0.911755\pi$
$827$		−	15.7414i		−	0.547383i	0.961818	−	0.273691i	$-0.0882447\pi$
$828$		0			0
$829$	9.84390	+	17.0501i	0.341893	+	0.592176i	0.984784	−	0.173782i	$-0.0555987\pi$
$829$	9.84390	+	17.0501i	0.341893	+	0.592176i	−0.642891	+	0.765957i	$0.722265\pi$
$830$		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	0.532589	−	0.846374i	$-0.321219\pi$
$839$	1.90889	+	1.10210i	0.0659023	+	0.0380487i	−0.466687	+	0.884423i	$0.654552\pi$
$840$		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	$0.0142017\pi$
$853$			2.60526i			0.0892026i	−0.999005	+	0.0446013i	$0.985798\pi$
$854$		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	$-0.989969\pi$
$863$		−	1.85114i		−	0.0630134i	0.999504	−	0.0315067i	$-0.0100306\pi$
$864$		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	0.654633	−	0.755947i	$-0.272823\pi$
$877$	9.69212	+	5.59575i	0.327280	+	0.188955i	−0.327353	+	0.944902i	$0.606157\pi$
$878$		0			0
$879$			34.6824i			1.16981i
$880$		0			0
$881$	9.39753	+	16.2770i	0.316611	+	0.548386i	0.979779	−	0.200085i	$-0.0641217\pi$
$881$	9.39753	+	16.2770i	0.316611	+	0.548386i	−0.663168	+	0.748471i	$0.730788\pi$
$882$		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	0.999238	−	0.0390377i	$-0.0124292\pi$
$887$	13.8730	+	24.0288i	0.465811	+	0.806809i	−0.533426	+	0.845846i	$0.679096\pi$
$888$		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	0.741448	−	0.671010i	$-0.234139\pi$
$907$	−6.33612	−	10.9745i	−0.210388	−	0.364402i	−0.951836	+	0.306608i	$0.900806\pi$
$908$		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	−0.511545	−	0.859256i	$-0.670927\pi$
$919$	14.8048	−	25.6427i	0.488365	−	0.845873i	0.999910	+	0.0133831i	$0.00426010\pi$
$920$		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	0.983944	−	0.178478i	$-0.0571173\pi$
$929$	40.2741	+	23.2522i	1.32135	+	0.762881i	0.337406	+	0.941359i	$0.390451\pi$
$930$		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	$-0.687420\pi$
$941$		−	51.0205i		−	1.66322i	0.555360	−	0.831610i	$-0.312580\pi$
$942$		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	−0.627774	−	0.778395i	$-0.716034\pi$
$947$	−8.23345	+	4.75358i	−0.267551	+	0.154471i	0.360223	+	0.932866i	$0.382701\pi$
$948$		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	−0.956311	−	0.292350i	$-0.905563\pi$
$953$	−6.94507	+	12.0292i	−0.224973	+	0.389665i	0.731338	+	0.682015i	$0.238896\pi$
$954$		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	$-0.837157\pi$
$967$		−	30.4473i		−	0.979120i	0.871970	−	0.489560i	$-0.162843\pi$
$968$		0			0
$969$	6.92311	+	3.99706i	0.222402	+	0.128404i
$970$		0			0
$971$	6.88995	−	11.9337i	0.221109	−	0.382972i	−0.734036	−	0.679110i	$-0.762366\pi$
$971$	6.88995	−	11.9337i	0.221109	−	0.382972i	0.955145	+	0.296139i	$0.0956990\pi$
$972$		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	−0.519723	−	0.854335i	$-0.673965\pi$
$977$	−1.24120	+	0.716604i	−0.0397094	+	0.0229262i	0.480014	+	0.877261i	$0.340632\pi$
$978$		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	$-0.831616\pi$
$983$		−	31.6454i		−	1.00933i	0.863315	−	0.504665i	$-0.168384\pi$
$984$		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	0.819123	−	0.573618i	$-0.194461\pi$
$991$	−2.74528	−	4.75496i	−0.0872066	−	0.151046i	−0.906329	+	0.422572i	$0.861127\pi$
$992$		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	−0.992047	−	0.125871i	$-0.959828\pi$
$997$	−12.2202	+	21.1659i	−0.387016	+	0.670332i	0.605030	+	0.796202i	$0.293161\pi$
$998$		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.673.2		16
4.3	odd	2		364.2.u.a.309.7	yes	16
12.11	even	2		3276.2.cf.c.1765.1		16
13.4	even	6	inner	1456.2.cc.f.225.2		16
28.3	even	6		2548.2.bb.c.569.2		16
28.11	odd	6		2548.2.bb.d.569.7		16
28.19	even	6		2548.2.bq.c.361.7		16
28.23	odd	6		2548.2.bq.e.361.2		16
28.27	even	2		2548.2.u.c.1765.2		16
52.3	odd	6		4732.2.g.k.337.4		16
52.11	even	12		4732.2.a.t.1.2		8
52.15	even	12		4732.2.a.s.1.2		8
52.23	odd	6		4732.2.g.k.337.3		16
52.43	odd	6		364.2.u.a.225.7	✓	16
156.95	even	6		3276.2.cf.c.2773.8		16
364.95	odd	6		2548.2.bq.e.1941.2		16
364.199	even	6		2548.2.bq.c.1941.7		16
364.251	even	6		2548.2.u.c.589.2		16
364.303	odd	6		2548.2.bb.d.1733.7		16
364.355	even	6		2548.2.bb.c.1733.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.7	✓	16	52.43	odd	6
364.2.u.a.309.7	yes	16	4.3	odd	2
1456.2.cc.f.225.2		16	13.4	even	6	inner
1456.2.cc.f.673.2		16	1.1	even	1	trivial
2548.2.u.c.589.2		16	364.251	even	6
2548.2.u.c.1765.2		16	28.27	even	2
2548.2.bb.c.569.2		16	28.3	even	6
2548.2.bb.c.1733.2		16	364.355	even	6
2548.2.bb.d.569.7		16	28.11	odd	6
2548.2.bb.d.1733.7		16	364.303	odd	6
2548.2.bq.c.361.7		16	28.19	even	6
2548.2.bq.c.1941.7		16	364.199	even	6
2548.2.bq.e.361.2		16	28.23	odd	6
2548.2.bq.e.1941.2		16	364.95	odd	6
3276.2.cf.c.1765.1		16	12.11	even	2
3276.2.cf.c.2773.8		16	156.95	even	6
4732.2.a.s.1.2		8	52.15	even	12
4732.2.a.t.1.2		8	52.11	even	12
4732.2.g.k.337.3		16	52.23	odd	6
4732.2.g.k.337.4		16	52.3	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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