LMFDB - Embedded newform 224.3.r.c.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 28 x^{9} - 100 x^{8} + 140 x^{7} + 392 x^{6} + 1400 x^{5} + 8040 x^{4} + 11256 x^{3} + \cdots + 9604 $ x^12 - 28x^9 - 100x^8 + 140x^7 + 392x^6 + 1400x^5 + 8040x^4 + 11256x^3 + 9800x^2 + 13720*x + 9604
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.3
Root			$0.294251 + 1.09816i$ of defining polynomial
Character	$\chi$	$=$	224.191
Dual form			224.3.r.c.95.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25843 + 1.30391i) q^{3} +(-3.59965 + 6.23477i) q^{5} +(5.36875 - 4.49183i) q^{7} +(-1.09965 + 1.90465i) q^{9} +O(q^{10})$	\(q+(-2.25843 + 1.30391i) q^{3} +(-3.59965 + 6.23477i) q^{5} +(5.36875 - 4.49183i) q^{7} +(-1.09965 + 1.90465i) q^{9} +(3.81789 - 2.20426i) q^{11} -18.1993 q^{13} -18.7744i q^{15} +(-8.58331 - 14.8667i) q^{17} +(-19.4174 - 11.2107i) q^{19} +(-6.26803 + 17.1449i) q^{21} +(-9.53183 - 5.50320i) q^{23} +(-13.4149 - 23.2353i) q^{25} -29.2057i q^{27} +37.4931 q^{29} +(-40.5472 + 23.4100i) q^{31} +(-5.74831 + 9.95636i) q^{33} +(8.67995 + 49.6419i) q^{35} +(-31.3135 + 54.2366i) q^{37} +(41.1019 - 23.7302i) q^{39} +2.97085 q^{41} -43.9347i q^{43} +(-7.91669 - 13.7121i) q^{45} +(18.9763 + 10.9560i) q^{47} +(8.64690 - 48.2310i) q^{49} +(38.7697 + 22.3837i) q^{51} +(2.03606 + 3.52656i) q^{53} +31.7382i q^{55} +58.4707 q^{57} +(12.2884 - 7.09468i) q^{59} +(-40.4837 + 70.1198i) q^{61} +(2.65162 + 15.1650i) q^{63} +(65.5111 - 113.468i) q^{65} +(-20.4791 + 11.8236i) q^{67} +28.7027 q^{69} +96.3589i q^{71} +(16.3462 + 28.3124i) q^{73} +(60.5935 + 34.9837i) q^{75} +(10.5961 - 28.9834i) q^{77} +(-73.2664 - 42.3004i) q^{79} +(28.1847 + 48.8174i) q^{81} +41.1048i q^{83} +123.588 q^{85} +(-84.6757 + 48.8875i) q^{87} +(-49.9313 + 86.4835i) q^{89} +(-97.7074 + 81.7482i) q^{91} +(61.0489 - 105.740i) q^{93} +(139.792 - 80.7089i) q^{95} +61.8520 q^{97} +9.69564i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{5} + 32 q^{9}+O(q^{10}) $ 12 * q + 2 * q^5 + 32 * q^9	$ 12 q + 2 q^{5} + 32 q^{9} - 128 q^{13} - 6 q^{17} - 62 q^{21} - 32 q^{25} + 128 q^{29} - 134 q^{33} - 66 q^{37} + 384 q^{41} - 192 q^{45} - 12 q^{49} - 2 q^{53} + 468 q^{57} - 434 q^{61} + 160 q^{65} + 124 q^{69} - 10 q^{73} - 370 q^{77} + 422 q^{81} + 1020 q^{85} - 522 q^{89} + 306 q^{93} - 768 q^{97}+O(q^{100}) $ 12 * q + 2 * q^5 + 32 * q^9 - 128 * q^13 - 6 * q^17 - 62 * q^21 - 32 * q^25 + 128 * q^29 - 134 * q^33 - 66 * q^37 + 384 * q^41 - 192 * q^45 - 12 * q^49 - 2 * q^53 + 468 * q^57 - 434 * q^61 + 160 * q^65 + 124 * q^69 - 10 * q^73 - 370 * q^77 + 422 * q^81 + 1020 * q^85 - 522 * q^89 + 306 * q^93 - 768 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−2.25843	+	1.30391i	−0.752812	+	0.434636i	−0.826709	−	0.562630i	$-0.809790\pi$
$3$	−2.25843	+	1.30391i	−0.752812	+	0.434636i	0.0738973	+	0.997266i	$0.476456\pi$
$4$		0			0
$5$	−3.59965	+	6.23477i	−0.719930	+	1.24695i	0.241098	+	0.970501i	$0.422493\pi$
$5$	−3.59965	+	6.23477i	−0.719930	+	1.24695i	−0.961027	+	0.276454i	$0.910841\pi$
$6$		0			0
$7$	5.36875	−	4.49183i	0.766964	−	0.641690i
$7$	5.36875	−	4.49183i	0.766964	−	0.641690i
$8$		0			0
$9$	−1.09965	+	1.90465i	−0.122183	+	0.211627i
$10$		0			0
$11$	3.81789	−	2.20426i	0.347081	−	0.200387i	−0.316318	−	0.948653i	$-0.602447\pi$
$11$	3.81789	−	2.20426i	0.347081	−	0.200387i	0.663399	+	0.748266i	$0.269113\pi$
$12$		0			0
$13$	−18.1993			−1.39995			−0.699973	−	0.714169i	$-0.746805\pi$
$13$	−18.1993			−1.39995			−0.699973	+	0.714169i	$0.746805\pi$
$14$		0			0
$15$		−	18.7744i		−	1.25163i
$16$		0			0
$17$	−8.58331	−	14.8667i	−0.504901	−	0.874514i	−0.999984	−	0.00566806i	$-0.998196\pi$
$17$	−8.58331	−	14.8667i	−0.504901	−	0.874514i	0.495083	−	0.868846i	$-0.335138\pi$
$18$		0			0
$19$	−19.4174	−	11.2107i	−1.02197	−	0.590035i	−0.107297	−	0.994227i	$-0.534219\pi$
$19$	−19.4174	−	11.2107i	−1.02197	−	0.590035i	−0.914674	+	0.404192i	$0.867553\pi$
$20$		0			0
$21$	−6.26803	+	17.1449i	−0.298478	+	0.816422i
$22$		0			0
$23$	−9.53183	−	5.50320i	−0.414427	−	0.239270i	0.278263	−	0.960505i	$-0.410241\pi$
$23$	−9.53183	−	5.50320i	−0.414427	−	0.239270i	−0.692690	+	0.721235i	$0.743575\pi$
$24$		0			0
$25$	−13.4149	−	23.2353i	−0.536597	−	0.929413i
$26$		0			0
$27$		−	29.2057i		−	1.08169i
$28$		0			0
$29$	37.4931			1.29287			0.646433	−	0.762971i	$-0.276260\pi$
$29$	37.4931			1.29287			0.646433	+	0.762971i	$0.276260\pi$
$30$		0			0
$31$	−40.5472	+	23.4100i	−1.30798	+	0.755160i	−0.981758	−	0.190135i	$-0.939108\pi$
$31$	−40.5472	+	23.4100i	−1.30798	+	0.755160i	−0.326218	+	0.945295i	$0.605774\pi$
$32$		0			0
$33$	−5.74831	+	9.95636i	−0.174191	+	0.301708i
$34$		0			0
$35$	8.67995	+	49.6419i	0.247999	+	1.41834i
$36$		0			0
$37$	−31.3135	+	54.2366i	−0.846311	+	1.46585i	0.0381662	+	0.999271i	$0.487848\pi$
$37$	−31.3135	+	54.2366i	−0.846311	+	1.46585i	−0.884478	+	0.466583i	$0.845485\pi$
$38$		0			0
$39$	41.1019	−	23.7302i	1.05390	−	0.608467i
$40$		0			0
$41$	2.97085			0.0724597			0.0362299	−	0.999343i	$-0.488465\pi$
$41$	2.97085			0.0724597			0.0362299	+	0.999343i	$0.488465\pi$
$42$		0			0
$43$		−	43.9347i		−	1.02174i	−0.859659	−	0.510868i	$-0.829324\pi$
$43$		−	43.9347i		−	1.02174i	0.859659	−	0.510868i	$-0.170676\pi$
$44$		0			0
$45$	−7.91669	−	13.7121i	−0.175926	−	0.304713i
$46$		0			0
$47$	18.9763	+	10.9560i	0.403750	+	0.233105i	0.688101	−	0.725615i	$-0.258445\pi$
$47$	18.9763	+	10.9560i	0.403750	+	0.233105i	−0.284351	+	0.958720i	$0.591778\pi$
$48$		0			0
$49$	8.64690	−	48.2310i	0.176467	−	0.984307i
$50$		0			0
$51$	38.7697	+	22.3837i	0.760190	+	0.438896i
$52$		0			0
$53$	2.03606	+	3.52656i	0.0384163	+	0.0665389i	0.884594	−	0.466361i	$-0.154435\pi$
$53$	2.03606	+	3.52656i	0.0384163	+	0.0665389i	−0.846178	+	0.532900i	$0.821102\pi$
$54$		0			0
$55$			31.7382i			0.577059i
$56$		0			0
$57$	58.4707			1.02580
$58$		0			0
$59$	12.2884	−	7.09468i	0.208277	−	0.120249i	−0.392233	−	0.919866i	$-0.628297\pi$
$59$	12.2884	−	7.09468i	0.208277	−	0.120249i	0.600510	+	0.799617i	$0.294964\pi$
$60$		0			0
$61$	−40.4837	+	70.1198i	−0.663667	+	1.14950i	0.315978	+	0.948766i	$0.397667\pi$
$61$	−40.4837	+	70.1198i	−0.663667	+	1.14950i	−0.979645	+	0.200738i	$0.935666\pi$
$62$		0			0
$63$	2.65162	+	15.1650i	0.0420892	+	0.240714i
$64$		0			0
$65$	65.5111	−	113.468i	1.00786	−	1.74567i
$66$		0			0
$67$	−20.4791	+	11.8236i	−0.305659	+	0.176472i	−0.644982	−	0.764198i	$-0.723135\pi$
$67$	−20.4791	+	11.8236i	−0.305659	+	0.176472i	0.339323	+	0.940670i	$0.389802\pi$
$68$		0			0
$69$	28.7027			0.415981
$70$		0			0
$71$			96.3589i			1.35717i	0.734523	+	0.678584i	$0.237406\pi$
$71$			96.3589i			1.35717i	−0.734523	+	0.678584i	$0.762594\pi$
$72$		0			0
$73$	16.3462	+	28.3124i	0.223920	+	0.387842i	0.955995	−	0.293383i	$-0.0947811\pi$
$73$	16.3462	+	28.3124i	0.223920	+	0.387842i	−0.732075	+	0.681224i	$0.761448\pi$
$74$		0			0
$75$	60.5935	+	34.9837i	0.807913	+	0.466449i
$76$		0			0
$77$	10.5961	−	28.9834i	0.137612	−	0.376408i
$78$		0			0
$79$	−73.2664	−	42.3004i	−0.927423	−	0.535448i	−0.0414274	−	0.999142i	$-0.513191\pi$
$79$	−73.2664	−	42.3004i	−0.927423	−	0.535448i	−0.885996	+	0.463694i	$0.846524\pi$
$80$		0			0
$81$	28.1847	+	48.8174i	0.347960	+	0.602684i
$82$		0			0
$83$			41.1048i			0.495239i	0.968857	+	0.247619i	$0.0796482\pi$
$83$			41.1048i			0.495239i	−0.968857	+	0.247619i	$0.920352\pi$
$84$		0			0
$85$	123.588			1.45397
$86$		0			0
$87$	−84.6757	+	48.8875i	−0.973284	+	0.561926i
$88$		0			0
$89$	−49.9313	+	86.4835i	−0.561025	+	0.971725i	0.436382	+	0.899762i	$0.356260\pi$
$89$	−49.9313	+	86.4835i	−0.561025	+	0.971725i	−0.997407	+	0.0719630i	$0.977074\pi$
$90$		0			0
$91$	−97.7074	+	81.7482i	−1.07371	+	0.898332i
$92$		0			0
$93$	61.0489	−	105.740i	0.656440	−	1.13699i
$94$		0			0
$95$	139.792	−	80.7089i	1.47149	−	0.849567i
$96$		0			0
$97$	61.8520			0.637649			0.318825	−	0.947814i	$-0.396712\pi$
$97$	61.8520			0.637649			0.318825	+	0.947814i	$0.396712\pi$
$98$		0			0
$99$			9.69564i			0.0979358i
$100$		0			0
$101$	−59.2920	−	102.697i	−0.587050	−	1.01680i	−0.994616	−	0.103625i	$-0.966956\pi$
$101$	−59.2920	−	102.697i	−0.587050	−	1.01680i	0.407567	−	0.913175i	$-0.366377\pi$
$102$		0			0
$103$	147.524	+	85.1728i	1.43227	+	0.826921i	0.997294	−	0.0735216i	$-0.0234238\pi$
$103$	147.524	+	85.1728i	1.43227	+	0.826921i	0.434975	+	0.900442i	$0.356757\pi$
$104$		0			0
$105$	−84.3316	−	100.795i	−0.803158	−	0.959954i
$106$		0			0
$107$	−142.676	−	82.3738i	−1.33342	−	0.769848i	−0.347595	−	0.937645i	$-0.613001\pi$
$107$	−142.676	−	82.3738i	−1.33342	−	0.769848i	−0.985822	+	0.167797i	$0.946335\pi$
$108$		0			0
$109$	21.8153	+	37.7852i	0.200140	+	0.346653i	0.948573	−	0.316557i	$-0.102527\pi$
$109$	21.8153	+	37.7852i	0.200140	+	0.346653i	−0.748433	+	0.663210i	$0.769194\pi$
$110$		0			0
$111$		−	163.320i		−	1.47135i
$112$		0			0
$113$	−176.707			−1.56378			−0.781891	−	0.623415i	$-0.785745\pi$
$113$	−176.707			−1.56378			−0.781891	+	0.623415i	$0.785745\pi$
$114$		0			0
$115$	68.6224	−	39.6192i	0.596717	−	0.344515i
$116$		0			0
$117$	20.0128	−	34.6632i	0.171050	−	0.296267i
$118$		0			0
$119$	−112.860	−	41.2609i	−0.948407	−	0.346731i
$120$		0			0
$121$	−50.7825	+	87.9578i	−0.419690	+	0.726924i
$122$		0			0
$123$	−6.70947	+	3.87371i	−0.0545485	+	0.0314936i
$124$		0			0
$125$	13.1737			0.105389
$126$		0			0
$127$		−	157.837i		−	1.24281i	−0.783490	−	0.621404i	$-0.786563\pi$
$127$		−	157.837i		−	1.24281i	0.783490	−	0.621404i	$-0.213437\pi$
$128$		0			0
$129$	57.2867	+	99.2236i	0.444083	+	0.769175i
$130$		0			0
$131$	141.518	+	81.7054i	1.08029	+	0.623705i	0.930974	−	0.365085i	$-0.118960\pi$
$131$	141.518	+	81.7054i	1.08029	+	0.623705i	0.149315	+	0.988790i	$0.452293\pi$
$132$		0			0
$133$	−154.604	+	27.0327i	−1.16243	+	0.203253i
$134$		0			0
$135$	182.091	+	105.130i	1.34882	+	0.778743i
$136$		0			0
$137$	74.3375	+	128.756i	0.542610	+	0.939827i	0.998753	+	0.0499212i	$0.0158970\pi$
$137$	74.3375	+	128.756i	0.542610	+	0.939827i	−0.456144	+	0.889906i	$0.650770\pi$
$138$		0			0
$139$		−	53.7059i		−	0.386374i	−0.981162	−	0.193187i	$-0.938118\pi$
$139$		−	53.7059i		−	0.386374i	0.981162	−	0.193187i	$-0.0618824\pi$
$140$		0			0
$141$	−57.1422			−0.405264
$142$		0			0
$143$	−69.4829	+	40.1160i	−0.485895	+	0.280531i
$144$		0			0
$145$	−134.962	+	233.761i	−0.930772	+	1.61214i
$146$		0			0
$147$	43.3604	+	120.201i	0.294968	+	0.817696i
$148$		0			0
$149$	14.3023	−	24.7724i	0.0959888	−	0.166257i	−0.814032	−	0.580820i	$-0.802732\pi$
$149$	14.3023	−	24.7724i	0.0959888	−	0.166257i	0.910021	+	0.414562i	$0.136065\pi$
$150$		0			0
$151$	−210.547	+	121.559i	−1.39435	+	0.805028i	−0.993793	−	0.111244i	$-0.964516\pi$
$151$	−210.547	+	121.559i	−1.39435	+	0.805028i	−0.400556	+	0.916272i	$0.631183\pi$
$152$		0			0
$153$	37.7545			0.246761
$154$		0			0
$155$		−	337.070i		−	2.17465i
$156$		0			0
$157$	−46.5817	−	80.6818i	−0.296699	−	0.513897i	0.678680	−	0.734434i	$-0.262552\pi$
$157$	−46.5817	−	80.6818i	−0.296699	−	0.513897i	−0.975379	+	0.220537i	$0.929219\pi$
$158$		0			0
$159$	−9.19663	−	5.30968i	−0.0578404	−	0.0333942i
$160$		0			0
$161$	−75.8934	+	13.2701i	−0.471388	+	0.0824227i
$162$		0			0
$163$	−239.198	−	138.101i	−1.46747	−	0.847246i	−0.468136	−	0.883656i	$-0.655074\pi$
$163$	−239.198	−	138.101i	−1.46747	−	0.847246i	−0.999337	+	0.0364104i	$0.988408\pi$
$164$		0			0
$165$	−41.3837	−	71.6788i	−0.250811	−	0.434417i
$166$		0			0
$167$		−	29.2913i		−	0.175397i	−0.996147	−	0.0876984i	$-0.972049\pi$
$167$		−	29.2913i		−	0.175397i	0.996147	−	0.0876984i	$-0.0279512\pi$
$168$		0			0
$169$	162.214			0.959848
$170$		0			0
$171$	42.7047	−	24.6556i	0.249735	−	0.144185i
$172$		0			0
$173$	−22.2062	+	38.4623i	−0.128360	+	0.222325i	−0.923041	−	0.384701i	$-0.874304\pi$
$173$	−22.2062	+	38.4623i	−0.128360	+	0.222325i	0.794682	+	0.607027i	$0.207638\pi$
$174$		0			0
$175$	−176.391	−	64.4871i	−1.00795	−	0.368497i
$176$		0			0
$177$	−18.5016	+	32.0458i	−0.104529	+	0.181049i
$178$		0			0
$179$	136.879	−	79.0271i	0.764687	−	0.441492i	−0.0662893	−	0.997800i	$-0.521116\pi$
$179$	136.879	−	79.0271i	0.764687	−	0.441492i	0.830976	+	0.556308i	$0.187783\pi$
$180$		0			0
$181$	−75.4380			−0.416785			−0.208392	−	0.978045i	$-0.566823\pi$
$181$	−75.4380			−0.416785			−0.208392	+	0.978045i	$0.566823\pi$
$182$		0			0
$183$		−	211.148i		−	1.15381i
$184$		0			0
$185$	−225.435	−	390.465i	−1.21857	−	2.11062i
$186$		0			0
$187$	−65.5403	−	37.8397i	−0.350483	−	0.202351i
$188$		0			0
$189$	−131.187	−	156.798i	−0.694112	−	0.829619i
$190$		0			0
$191$	98.5940	+	56.9233i	0.516199	+	0.298028i	0.735378	−	0.677657i	$-0.237005\pi$
$191$	98.5940	+	56.9233i	0.516199	+	0.298028i	−0.219179	+	0.975685i	$0.570338\pi$
$192$		0			0
$193$	71.6871	+	124.166i	0.371436	+	0.643346i	0.989787	−	0.142557i	$-0.0455323\pi$
$193$	71.6871	+	124.166i	0.371436	+	0.643346i	−0.618351	+	0.785902i	$0.712199\pi$
$194$		0			0
$195$			341.682i			1.75221i
$196$		0			0
$197$	290.812			1.47620			0.738101	−	0.674690i	$-0.235723\pi$
$197$	290.812			1.47620			0.738101	+	0.674690i	$0.235723\pi$
$198$		0			0
$199$	−168.125	+	97.0672i	−0.844851	+	0.487775i	−0.858910	−	0.512126i	$-0.828858\pi$
$199$	−168.125	+	97.0672i	−0.844851	+	0.487775i	0.0140595	+	0.999901i	$0.495525\pi$
$200$		0			0
$201$	30.8339	−	53.4058i	0.153402	−	0.265701i
$202$		0			0
$203$	201.291	−	168.413i	0.991581	−	0.829619i
$204$		0			0
$205$	−10.6940	+	18.5226i	−0.0521659	+	0.0903540i
$206$		0			0
$207$	20.9633	−	12.1032i	0.101272	−	0.0584694i
$208$		0			0
$209$	−98.8449			−0.472942
$210$		0			0
$211$		−	29.7854i		−	0.141163i	−0.997506	−	0.0705815i	$-0.977515\pi$
$211$		−	29.7854i		−	0.141163i	0.997506	−	0.0705815i	$-0.0224855\pi$
$212$		0			0
$213$	−125.643	−	217.620i	−0.589874	−	1.02169i
$214$		0			0
$215$	273.923	+	158.149i	1.27406	+	0.735578i
$216$		0			0
$217$	−112.534	+	307.814i	−0.518591	+	1.41850i
$218$		0			0
$219$	−73.8336	−	42.6279i	−0.337140	−	0.194648i
$220$		0			0
$221$	156.210	+	270.564i	0.706834	+	1.22427i
$222$		0			0
$223$		−	294.019i		−	1.31847i	−0.751937	−	0.659234i	$-0.770880\pi$
$223$		−	294.019i		−	1.31847i	0.751937	−	0.659234i	$-0.229120\pi$
$224$		0			0
$225$	59.0068			0.262252
$226$		0			0
$227$	−147.997	+	85.4459i	−0.651968	+	0.376414i	−0.789210	−	0.614124i	$-0.789510\pi$
$227$	−147.997	+	85.4459i	−0.651968	+	0.376414i	0.137242	+	0.990538i	$0.456176\pi$
$228$		0			0
$229$	61.4423	−	106.421i	0.268307	−	0.464721i	−0.700118	−	0.714027i	$-0.746869\pi$
$229$	61.4423	−	106.421i	0.268307	−	0.464721i	0.968425	+	0.249306i	$0.0802025\pi$
$230$		0			0
$231$	13.8611	+	79.2736i	0.0600047	+	0.343176i
$232$		0			0
$233$	97.8057	−	169.404i	0.419767	−	0.727058i	−0.576149	−	0.817345i	$-0.695445\pi$
$233$	97.8057	−	169.404i	0.419767	−	0.727058i	0.995916	+	0.0902870i	$0.0287784\pi$
$234$		0			0
$235$	−136.616	+	78.8752i	−0.581344	+	0.335639i
$236$		0			0
$237$	220.623			0.930900
$238$		0			0
$239$			229.735i			0.961233i	0.876931	+	0.480616i	$0.159587\pi$
$239$			229.735i			0.961233i	−0.876931	+	0.480616i	$0.840413\pi$
$240$		0			0
$241$	125.409	+	217.214i	0.520368	+	0.901304i	0.999720	+	0.0236812i	$0.00753866\pi$
$241$	125.409	+	217.214i	0.520368	+	0.901304i	−0.479351	+	0.877623i	$0.659128\pi$
$242$		0			0
$243$	100.329	+	57.9251i	0.412877	+	0.238375i
$244$		0			0
$245$	269.584	+	227.526i	1.10034	+	0.928678i
$246$		0			0
$247$	353.384	+	204.026i	1.43070	+	0.826017i
$248$		0			0
$249$	−53.5969	−	92.8325i	−0.215248	−	0.372821i
$250$		0			0
$251$			481.380i			1.91785i	0.283664	+	0.958924i	$0.408450\pi$
$251$			481.380i			1.91785i	−0.283664	+	0.958924i	$0.591550\pi$
$252$		0			0
$253$	−48.5220			−0.191786
$254$		0			0
$255$	−279.115	+	161.147i	−1.09457	+	0.631948i
$256$		0			0
$257$	154.913	−	268.317i	0.602774	−	1.04404i	−0.389625	−	0.920974i	$-0.627395\pi$
$257$	154.913	−	268.317i	0.602774	−	1.04404i	0.992399	−	0.123062i	$-0.0392715\pi$
$258$		0			0
$259$	75.5073	+	431.838i	0.291534	+	1.66733i
$260$		0			0
$261$	−41.2292	+	71.4111i	−0.157966	+	0.273606i
$262$		0			0
$263$	244.337	−	141.068i	0.929036	−	0.536379i	0.0425297	−	0.999095i	$-0.486458\pi$
$263$	244.337	−	141.068i	0.929036	−	0.536379i	0.886507	+	0.462716i	$0.153125\pi$
$264$		0			0
$265$	−29.3164			−0.110628
$266$		0			0
$267$		−	260.423i		−	0.975367i
$268$		0			0
$269$	147.169	+	254.904i	0.547097	+	0.947599i	0.998472	+	0.0552649i	$0.0176003\pi$
$269$	147.169	+	254.904i	0.547097	+	0.947599i	−0.451375	+	0.892334i	$0.649066\pi$
$270$		0			0
$271$	−193.033	−	111.447i	−0.712297	−	0.411245i	0.0996137	−	0.995026i	$-0.468239\pi$
$271$	−193.033	−	111.447i	−0.712297	−	0.411245i	−0.811911	+	0.583781i	$0.801573\pi$
$272$		0			0
$273$	114.074	−	312.024i	0.417853	−	1.14295i
$274$		0			0
$275$	−102.433	−	59.1400i	−0.372485	−	0.215054i
$276$		0			0
$277$	−23.1994	−	40.1826i	−0.0837525	−	0.145064i	0.821106	−	0.570775i	$-0.193357\pi$
$277$	−23.1994	−	40.1826i	−0.0837525	−	0.145064i	−0.904859	+	0.425712i	$0.860024\pi$
$278$		0			0
$279$		−	102.971i		−	0.369071i
$280$		0			0
$281$	523.027			1.86131			0.930653	−	0.365902i	$-0.119240\pi$
$281$	523.027			1.86131			0.930653	+	0.365902i	$0.119240\pi$
$282$		0			0
$283$	344.794	−	199.067i	1.21835	−	0.703416i	0.253787	−	0.967260i	$-0.418324\pi$
$283$	344.794	−	199.067i	1.21835	−	0.703416i	0.964565	+	0.263844i	$0.0849904\pi$
$284$		0			0
$285$	−210.474	+	364.552i	−0.738505	+	1.27913i
$286$		0			0
$287$	15.9497	−	13.3446i	0.0555740	−	0.0464967i
$288$		0			0
$289$	−2.84646	+	4.93021i	−0.00984934	+	0.0170596i
$290$		0			0
$291$	−139.689	+	80.6493i	−0.480030	+	0.277145i
$292$		0			0
$293$	−81.0068			−0.276474			−0.138237	−	0.990399i	$-0.544144\pi$
$293$	−81.0068			−0.276474			−0.138237	+	0.990399i	$0.544144\pi$
$294$		0			0
$295$			102.153i			0.346283i
$296$		0			0
$297$	−64.3770	−	111.504i	−0.216757	−	0.375435i
$298$		0			0
$299$	173.473	+	100.154i	0.580176	+	0.334965i
$300$		0			0
$301$	−197.347	−	235.874i	−0.655638	−	0.783635i
$302$		0			0
$303$	267.814	+	154.623i	0.883876	+	0.510306i
$304$		0			0
$305$	−291.454	−	504.813i	−0.955586	−	1.65512i
$306$		0			0
$307$		−	214.075i		−	0.697312i	−0.937251	−	0.348656i	$-0.886638\pi$
$307$		−	214.075i		−	0.697312i	0.937251	−	0.348656i	$-0.113362\pi$
$308$		0			0
$309$	−444.230			−1.43764
$310$		0			0
$311$	−167.737	+	96.8432i	−0.539349	+	0.311393i	−0.744815	−	0.667271i	$-0.767462\pi$
$311$	−167.737	+	96.8432i	−0.539349	+	0.311393i	0.205466	+	0.978664i	$0.434129\pi$
$312$		0			0
$313$	73.9149	−	128.024i	0.236150	−	0.409024i	−0.723456	−	0.690370i	$-0.757448\pi$
$313$	73.9149	−	128.024i	0.236150	−	0.409024i	0.959606	+	0.281346i	$0.0907810\pi$
$314$		0			0
$315$	−104.095	−	38.0564i	−0.330461	−	0.120814i
$316$		0			0
$317$	71.0408	−	123.046i	0.224104	−	0.388159i	−0.731947	−	0.681362i	$-0.761388\pi$
$317$	71.0408	−	123.046i	0.224104	−	0.388159i	0.956050	+	0.293203i	$0.0947213\pi$
$318$		0			0
$319$	143.145	−	82.6445i	0.448729	−	0.259074i
$320$		0			0
$321$	429.631			1.33842
$322$		0			0
$323$			384.899i			1.19164i
$324$		0			0
$325$	244.142	+	422.867i	0.751207	+	1.30113i
$326$		0			0
$327$	−98.5368	−	56.8902i	−0.301336	−	0.173976i
$328$		0			0
$329$	151.091	−	26.4185i	0.459243	−	0.0802993i
$330$		0			0
$331$	−265.954	−	153.549i	−0.803487	−	0.463893i	0.0412021	−	0.999151i	$-0.486881\pi$
$331$	−265.954	−	153.549i	−0.803487	−	0.463893i	−0.844689	+	0.535258i	$0.820215\pi$
$332$		0			0
$333$	−68.8677	−	119.282i	−0.206810	−	0.358205i
$334$		0			0
$335$		−	170.244i		−	0.508190i
$336$		0			0
$337$	−100.940			−0.299524			−0.149762	−	0.988722i	$-0.547851\pi$
$337$	−100.940			−0.299524			−0.149762	+	0.988722i	$0.547851\pi$
$338$		0			0
$339$	399.082	−	230.410i	1.17723	−	0.679676i
$340$		0			0
$341$	−103.203	+	178.753i	−0.302649	+	0.524203i
$342$		0			0
$343$	−170.223	−	297.781i	−0.496276	−	0.868165i
$344$		0			0
$345$	−103.320	+	178.955i	−0.299477	+	0.518709i
$346$		0			0
$347$	−271.926	+	156.996i	−0.783647	+	0.452439i	−0.837721	−	0.546098i	$-0.816113\pi$
$347$	−271.926	+	156.996i	−0.783647	+	0.452439i	0.0540741	+	0.998537i	$0.482779\pi$
$348$		0			0
$349$	69.1392			0.198107			0.0990534	−	0.995082i	$-0.468419\pi$
$349$	69.1392			0.198107			0.0990534	+	0.995082i	$0.468419\pi$
$350$		0			0
$351$			531.523i			1.51431i
$352$		0			0
$353$	−172.017	−	297.942i	−0.487300	−	0.844028i	0.512594	−	0.858631i	$-0.328685\pi$
$353$	−172.017	−	297.942i	−0.487300	−	0.844028i	−0.999893	+	0.0146034i	$0.995351\pi$
$354$		0			0
$355$	−600.776	−	346.858i	−1.69233	−	0.977065i
$356$		0			0
$357$	308.689	−	53.9746i	0.864674	−	0.151189i
$358$		0			0
$359$	−466.067	−	269.084i	−1.29824	−	0.749537i	−0.318137	−	0.948045i	$-0.603057\pi$
$359$	−466.067	−	269.084i	−1.29824	−	0.749537i	−0.980099	+	0.198508i	$0.936390\pi$
$360$		0			0
$361$	70.8581	+	122.730i	0.196283	+	0.339972i
$362$		0			0
$363$		−	264.863i		−	0.729649i
$364$		0			0
$365$	−235.362			−0.644828
$366$		0			0
$367$	111.276	−	64.2450i	0.303203	−	0.175054i	−0.340678	−	0.940180i	$-0.610657\pi$
$367$	111.276	−	64.2450i	0.303203	−	0.175054i	0.643881	+	0.765126i	$0.277323\pi$
$368$		0			0
$369$	−3.26689	+	5.65842i	−0.00885335	+	0.0153345i
$370$		0			0
$371$	26.7718	+	9.78758i	0.0721613	+	0.0263816i
$372$		0			0
$373$	−39.7402	+	68.8321i	−0.106542	+	0.184537i	−0.914367	−	0.404886i	$-0.867311\pi$
$373$	−39.7402	+	68.8321i	−0.106542	+	0.184537i	0.807825	+	0.589422i	$0.200645\pi$
$374$		0			0
$375$	−29.7519	+	17.1773i	−0.0793383	+	0.0458060i
$376$		0			0
$377$	−682.348			−1.80994
$378$		0			0
$379$			421.203i			1.11135i	0.831399	+	0.555676i	$0.187541\pi$
$379$			421.203i			1.11135i	−0.831399	+	0.555676i	$0.812459\pi$
$380$		0			0
$381$	205.804	+	356.464i	0.540169	+	0.935600i
$382$		0			0
$383$	−200.635	−	115.837i	−0.523851	−	0.302446i	0.214658	−	0.976689i	$-0.431136\pi$
$383$	−200.635	−	115.837i	−0.523851	−	0.302446i	−0.738509	+	0.674244i	$0.764470\pi$
$384$		0			0
$385$	142.563	+	170.395i	0.370293	+	0.442583i
$386$		0			0
$387$	83.6800	+	48.3126i	0.216227	+	0.124839i
$388$		0			0
$389$	40.0992	+	69.4539i	0.103083	+	0.178545i	0.912953	−	0.408064i	$-0.133796\pi$
$389$	40.0992	+	69.4539i	0.103083	+	0.178545i	−0.809870	+	0.586609i	$0.800463\pi$
$390$		0			0
$391$			188.943i			0.483230i
$392$		0			0
$393$	−426.145			−1.08434
$394$		0			0
$395$	527.467	−	304.533i	1.33536	−	0.770970i
$396$		0			0
$397$	−56.0008	+	96.9961i	−0.141060	+	0.244323i	−0.927896	−	0.372839i	$-0.878384\pi$
$397$	−56.0008	+	96.9961i	−0.141060	+	0.244323i	0.786836	+	0.617162i	$0.211718\pi$
$398$		0			0
$399$	313.915	−	262.641i	0.786753	−	0.658247i
$400$		0			0
$401$	−77.1126	+	133.563i	−0.192301	+	0.333075i	−0.946012	−	0.324131i	$-0.894928\pi$
$401$	−77.1126	+	133.563i	−0.192301	+	0.333075i	0.753712	+	0.657205i	$0.228262\pi$
$402$		0			0
$403$	737.931	−	426.045i	1.83110	−	1.05718i
$404$		0			0
$405$	−405.820			−1.00203
$406$		0			0
$407$			276.093i			0.678360i
$408$		0			0
$409$	51.6192	+	89.4071i	0.126208	+	0.218599i	0.922205	−	0.386702i	$-0.126386\pi$
$409$	51.6192	+	89.4071i	0.126208	+	0.218599i	−0.795996	+	0.605302i	$0.793053\pi$
$410$		0			0
$411$	−335.773	−	193.859i	−0.816966	−	0.471675i
$412$		0			0
$413$	34.1049	−	93.2868i	0.0825785	−	0.225876i
$414$		0			0
$415$	−256.279	−	147.963i	−0.617540	−	0.356537i
$416$		0			0
$417$	70.0276	+	121.291i	0.167932	+	0.290867i
$418$		0			0
$419$		−	384.000i		−	0.916468i	−0.888832	−	0.458234i	$-0.848482\pi$
$419$		−	384.000i		−	0.916468i	0.888832	−	0.458234i	$-0.151518\pi$
$420$		0			0
$421$	−385.061			−0.914635			−0.457317	−	0.889304i	$-0.651190\pi$
$421$	−385.061			−0.914635			−0.457317	+	0.889304i	$0.651190\pi$
$422$		0			0
$423$	−41.7344	+	24.0954i	−0.0986629	+	0.0569631i
$424$		0			0
$425$	−230.289	+	398.872i	−0.541856	+	0.938523i
$426$		0			0
$427$	97.6196	+	558.301i	0.228617	+	1.30750i
$428$		0			0
$429$	104.615	−	181.199i	0.243858	−	0.422375i
$430$		0			0
$431$	445.945	−	257.467i	1.03468	−	0.597370i	0.116355	−	0.993208i	$-0.462879\pi$
$431$	445.945	−	257.467i	1.03468	−	0.597370i	0.918321	+	0.395837i	$0.129546\pi$
$432$		0			0
$433$	−439.034			−1.01393			−0.506967	−	0.861965i	$-0.669234\pi$
$433$	−439.034			−1.01393			−0.506967	+	0.861965i	$0.669234\pi$
$434$		0			0
$435$		−	703.912i		−	1.61819i
$436$		0			0
$437$	123.389	+	213.716i	0.282355	+	0.489053i
$438$		0			0
$439$	200.608	+	115.821i	0.456965	+	0.263829i	0.710767	−	0.703427i	$-0.248348\pi$
$439$	200.608	+	115.821i	0.456965	+	0.263829i	−0.253802	+	0.967256i	$0.581681\pi$
$440$		0			0
$441$	82.3545	+	69.5064i	0.186745	+	0.157611i
$442$		0			0
$443$	110.163	+	63.6026i	0.248675	+	0.143572i	0.619157	−	0.785267i	$-0.287474\pi$
$443$	110.163	+	63.6026i	0.248675	+	0.143572i	−0.370483	+	0.928839i	$0.620808\pi$
$444$		0			0
$445$	−359.470	−	622.620i	−0.807798	−	1.39915i
$446$		0			0
$447$			74.5957i			0.166881i
$448$		0			0
$449$	−736.977			−1.64137			−0.820687	−	0.571378i	$-0.806409\pi$
$449$	−736.977			−1.64137			−0.820687	+	0.571378i	$0.806409\pi$
$450$		0			0
$451$	11.3424	−	6.54853i	0.0251494	−	0.0145200i
$452$		0			0
$453$	317.004	−	549.067i	0.699788	−	1.21207i
$454$		0			0
$455$	−157.969	−	903.448i	−0.347185	−	1.98560i
$456$		0			0
$457$	59.8757	−	103.708i	0.131019	−	0.226932i	−0.793051	−	0.609156i	$-0.791508\pi$
$457$	59.8757	−	103.708i	0.131019	−	0.226932i	0.924070	+	0.382224i	$0.124842\pi$
$458$		0			0
$459$	−434.193	+	250.682i	−0.945955	+	0.546147i
$460$		0			0
$461$	213.385			0.462875			0.231438	−	0.972850i	$-0.425657\pi$
$461$	213.385			0.462875			0.231438	+	0.972850i	$0.425657\pi$
$462$		0			0
$463$			140.406i			0.303253i	0.988438	+	0.151627i	$0.0484511\pi$
$463$			140.406i			0.303253i	−0.988438	+	0.151627i	$0.951549\pi$
$464$		0			0
$465$	439.509	+	761.252i	0.945180	+	1.63710i
$466$		0			0
$467$	−443.927	−	256.302i	−0.950594	−	0.548826i	−0.0573286	−	0.998355i	$-0.518258\pi$
$467$	−443.927	−	256.302i	−0.950594	−	0.548826i	−0.893265	+	0.449530i	$0.851592\pi$
$468$		0			0
$469$	−56.8375	+	155.467i	−0.121189	+	0.331486i
$470$		0			0
$471$	210.403	+	121.476i	0.446716	+	0.257912i
$472$		0			0
$473$	−96.8434	−	167.738i	−0.204743	−	0.354625i
$474$		0			0
$475$			601.561i			1.26644i
$476$		0			0
$477$	−8.95581			−0.0187753
$478$		0			0
$479$	−432.197	+	249.529i	−0.902289	+	0.520937i	−0.877942	−	0.478767i	$-0.841084\pi$
$479$	−432.197	+	249.529i	−0.902289	+	0.520937i	−0.0243471	+	0.999704i	$0.507751\pi$
$480$		0			0
$481$	569.884	−	987.068i	1.18479	−	2.05212i
$482$		0			0
$483$	154.097	−	128.928i	0.319042	−	0.266931i
$484$		0			0
$485$	−222.645	+	385.633i	−0.459062	+	0.795119i
$486$		0			0
$487$	−606.787	+	350.329i	−1.24597	+	0.719360i	−0.970303	−	0.241893i	$-0.922232\pi$
$487$	−606.787	+	350.329i	−1.24597	+	0.719360i	−0.275666	+	0.961254i	$0.588898\pi$
$488$		0			0
$489$	720.284			1.47297
$490$		0			0
$491$			276.736i			0.563618i	0.959471	+	0.281809i	$0.0909344\pi$
$491$			276.736i			0.563618i	−0.959471	+	0.281809i	$0.909066\pi$
$492$		0			0
$493$	−321.815	−	557.400i	−0.652768	−	1.13063i
$494$		0			0
$495$	−60.4501	−	34.9009i	−0.122121	−	0.0705068i
$496$		0			0
$497$	432.828	+	517.326i	0.870881	+	1.04090i
$498$		0			0
$499$	143.156	+	82.6513i	0.286886	+	0.165634i	0.636537	−	0.771246i	$-0.280366\pi$
$499$	143.156	+	82.6513i	0.286886	+	0.165634i	−0.349650	+	0.936880i	$0.613700\pi$
$500$		0			0
$501$	38.1931	+	66.1525i	0.0762338	+	0.132041i
$502$		0			0
$503$		−	140.294i		−	0.278914i	−0.990228	−	0.139457i	$-0.955464\pi$
$503$		−	140.294i		−	0.278914i	0.990228	−	0.139457i	$-0.0445356\pi$
$504$		0			0
$505$	853.722			1.69054
$506$		0			0
$507$	−366.351	+	211.513i	−0.722585	+	0.417185i
$508$		0			0
$509$	315.443	−	546.363i	0.619730	−	1.07340i	−0.369804	−	0.929110i	$-0.620575\pi$
$509$	315.443	−	546.363i	0.619730	−	1.07340i	0.989535	−	0.144295i	$-0.0460914\pi$
$510$		0			0
$511$	214.933	+	78.5780i	0.420613	+	0.153773i
$512$		0			0
$513$	−327.415	+	567.100i	−0.638237	+	1.10546i
$514$		0			0
$515$	−1062.07	+	613.184i	−2.06227	+	1.19065i
$516$		0			0
$517$	96.5991			0.186845
$518$		0			0
$519$		−	115.819i		−	0.223159i
$520$		0			0
$521$	22.9121	+	39.6850i	0.0439773	+	0.0761708i	0.887176	−	0.461431i	$-0.152664\pi$
$521$	22.9121	+	39.6850i	0.0439773	+	0.0761708i	−0.843199	+	0.537602i	$0.819330\pi$
$522$		0			0
$523$	131.869	+	76.1344i	0.252139	+	0.145572i	0.620743	−	0.784014i	$-0.286831\pi$
$523$	131.869	+	76.1344i	0.252139	+	0.145572i	−0.368604	+	0.929586i	$0.620164\pi$
$524$		0			0
$525$	482.452	−	84.3573i	0.918956	−	0.160681i
$526$		0			0
$527$	696.059	+	401.870i	1.32080	+	0.762562i
$528$		0			0
$529$	−203.930	−	353.216i	−0.385500	−	0.667706i
$530$		0			0
$531$			31.2066i			0.0587695i
$532$		0			0
$533$	−54.0674			−0.101440
$534$		0			0
$535$	1027.16	−	593.033i	1.91993	−	1.10847i
$536$		0			0
$537$	−206.088	+	356.955i	−0.383777	+	0.664721i
$538$		0			0
$539$	−73.3008	−	203.201i	−0.135994	−	0.376996i
$540$		0			0
$541$	94.2832	−	163.303i	0.174276	−	0.301855i	−0.765635	−	0.643276i	$-0.777575\pi$
$541$	94.2832	−	163.303i	0.174276	−	0.301855i	0.939910	+	0.341421i	$0.110908\pi$
$542$		0			0
$543$	170.372	−	98.3643i	0.313760	−	0.181150i
$544$		0			0
$545$	−314.109			−0.576347
$546$		0			0
$547$			469.901i			0.859052i	0.903055	+	0.429526i	$0.141319\pi$
$547$			469.901i			0.859052i	−0.903055	+	0.429526i	$0.858681\pi$
$548$		0			0
$549$	−89.0355	−	154.214i	−0.162178	−	0.280900i
$550$		0			0
$551$	−728.020	−	420.323i	−1.32127	−	0.762836i
$552$		0			0
$553$	−583.355	+	102.000i	−1.05489	+	0.184449i
$554$		0			0
$555$	1018.26	+	587.894i	1.83471	+	1.05927i
$556$		0			0
$557$	263.848	+	456.998i	0.473695	+	0.820463i	0.999547	−	0.0301129i	$-0.00958669\pi$
$557$	263.848	+	456.998i	0.473695	+	0.820463i	−0.525852	+	0.850576i	$0.676253\pi$
$558$		0			0
$559$			799.580i			1.43038i
$560$		0			0
$561$	197.358			0.351797
$562$		0			0
$563$	453.298	−	261.712i	0.805148	−	0.464852i	−0.0401201	−	0.999195i	$-0.512774\pi$
$563$	453.298	−	261.712i	0.805148	−	0.464852i	0.845268	+	0.534342i	$0.179441\pi$
$564$		0			0
$565$	636.085	−	1101.73i	1.12581	−	1.94997i
$566$		0			0
$567$	370.596	+	135.487i	0.653609	+	0.238954i
$568$		0			0
$569$	−199.215	+	345.051i	−0.350115	+	0.606417i	−0.986269	−	0.165145i	$-0.947191\pi$
$569$	−199.215	+	345.051i	−0.350115	+	0.606417i	0.636154	+	0.771562i	$0.280524\pi$
$570$		0			0
$571$	−154.445	+	89.1690i	−0.270482	+	0.156163i	−0.629107	−	0.777319i	$-0.716579\pi$
$571$	−154.445	+	89.1690i	−0.270482	+	0.156163i	0.358625	+	0.933482i	$0.383246\pi$
$572$		0			0
$573$	−296.891			−0.518134
$574$		0			0
$575$			295.300i			0.513566i
$576$		0			0
$577$	45.4369	+	78.6991i	0.0787469	+	0.136394i	0.902710	−	0.430251i	$-0.141575\pi$
$577$	45.4369	+	78.6991i	0.0787469	+	0.136394i	−0.823963	+	0.566644i	$0.808241\pi$
$578$		0			0
$579$	−323.801	−	186.947i	−0.559242	−	0.322879i
$580$		0			0
$581$	184.636	+	220.681i	0.317790	+	0.379830i
$582$		0			0
$583$	15.5469	+	8.97602i	0.0266671	+	0.0153963i
$584$		0			0
$585$	144.078	+	249.551i	0.246287	+	0.426582i
$586$		0			0
$587$			18.9786i			0.0323315i	0.999869	+	0.0161658i	$0.00514594\pi$
$587$			18.9786i			0.0323315i	−0.999869	+	0.0161658i	$0.994854\pi$
$588$		0			0
$589$	1049.77			1.78228
$590$		0			0
$591$	−656.780	+	379.192i	−1.11130	+	0.641611i
$592$		0			0
$593$	228.806	−	396.304i	0.385845	−	0.668303i	−0.606041	−	0.795433i	$-0.707243\pi$
$593$	228.806	−	396.304i	0.385845	−	0.668303i	0.991886	+	0.127130i	$0.0405767\pi$
$594$		0			0
$595$	663.511	−	555.135i	1.11514	−	0.932999i
$596$		0			0
$597$	253.133	−	438.440i	0.424009	−	0.734405i
$598$		0			0
$599$	−109.568	+	63.2589i	−0.182918	+	0.105608i	−0.588663	−	0.808379i	$-0.700345\pi$
$599$	−109.568	+	63.2589i	−0.182918	+	0.105608i	0.405745	+	0.913986i	$0.367012\pi$
$600$		0			0
$601$	333.744			0.555315			0.277658	−	0.960680i	$-0.410442\pi$
$601$	333.744			0.555315			0.277658	+	0.960680i	$0.410442\pi$
$602$		0			0
$603$		−	52.0073i		−	0.0862476i
$604$		0			0
$605$	−365.598	−	633.234i	−0.604294	−	1.04667i
$606$		0			0
$607$	503.950	+	290.956i	0.830231	+	0.479334i	0.853932	−	0.520385i	$-0.174211\pi$
$607$	503.950	+	290.956i	0.830231	+	0.479334i	−0.0237005	+	0.999719i	$0.507545\pi$
$608$		0			0
$609$	−235.008	+	642.814i	−0.385891	+	1.05552i
$610$		0			0
$611$	−345.355	−	199.391i	−0.565229	−	0.326335i
$612$		0			0
$613$	−379.921	−	658.043i	−0.619774	−	1.07348i	−0.989527	−	0.144350i	$-0.953891\pi$
$613$	−379.921	−	658.043i	−0.619774	−	1.07348i	0.369753	−	0.929130i	$-0.379442\pi$
$614$		0			0
$615$		−	55.7760i		−	0.0906927i
$616$		0			0
$617$	−906.461			−1.46914			−0.734571	−	0.678532i	$-0.762617\pi$
$617$	−906.461			−1.46914			−0.734571	+	0.678532i	$0.762617\pi$
$618$		0			0
$619$	410.119	−	236.783i	0.662552	−	0.382524i	−0.130697	−	0.991422i	$-0.541721\pi$
$619$	410.119	−	236.783i	0.662552	−	0.382524i	0.793248	+	0.608898i	$0.208388\pi$
$620$		0			0
$621$	−160.725	+	278.384i	−0.258816	+	0.448283i
$622$		0			0
$623$	120.401	+	688.591i	0.193260	+	1.10528i
$624$		0			0
$625$	287.953	−	498.749i	0.460724	−	0.797998i
$626$		0			0
$627$	223.235	−	128.885i	0.356036	−	0.205558i
$628$		0			0
$629$	1075.09			1.70921
$630$		0			0
$631$		−	523.166i		−	0.829106i	−0.910025	−	0.414553i	$-0.863938\pi$
$631$		−	523.166i		−	0.829106i	0.910025	−	0.414553i	$-0.136062\pi$
$632$		0			0
$633$	38.8374	+	67.2683i	0.0613545	+	0.106269i
$634$		0			0
$635$	984.076	+	568.156i	1.54973	+	0.894734i
$636$		0			0
$637$	−157.367	+	877.771i	−0.247045	+	1.37798i
$638$		0			0
$639$	−183.530	−	105.961i	−0.287214	−	0.165823i
$640$		0			0
$641$	595.150	+	1030.83i	0.928472	+	1.60816i	0.785880	+	0.618379i	$0.212210\pi$
$641$	595.150	+	1030.83i	0.928472	+	1.60816i	0.142591	+	0.989782i	$0.454457\pi$
$642$		0			0
$643$			739.763i			1.15049i	0.817982	+	0.575243i	$0.195093\pi$
$643$			739.763i			1.15049i	−0.817982	+	0.575243i	$0.804907\pi$
$644$		0			0
$645$	−824.848			−1.27883
$646$		0			0
$647$	−190.375	+	109.913i	−0.294243	+	0.169882i	−0.639854	−	0.768497i	$-0.721005\pi$
$647$	−190.375	+	109.913i	−0.294243	+	0.169882i	0.345611	+	0.938378i	$0.387672\pi$
$648$		0			0
$649$	31.2771	−	54.1734i	0.0481927	−	0.0834722i
$650$		0			0
$651$	−147.209	−	841.911i	−0.226128	−	1.29326i
$652$		0			0
$653$	−424.090	+	734.546i	−0.649449	+	1.12488i	0.333806	+	0.942642i	$0.391667\pi$
$653$	−424.090	+	734.546i	−0.649449	+	1.12488i	−0.983255	+	0.182236i	$0.941666\pi$
$654$		0			0
$655$	−1018.83	+	588.221i	−1.55546	+	0.898048i
$656$		0			0
$657$	−71.9002			−0.109437
$658$		0			0
$659$			18.3735i			0.0278809i	0.999903	+	0.0139404i	$0.00443752\pi$
$659$			18.3735i			0.0278809i	−0.999903	+	0.0139404i	$0.995562\pi$
$660$		0			0
$661$	456.940	+	791.444i	0.691286	+	1.19734i	0.971417	+	0.237381i	$0.0762890\pi$
$661$	456.940	+	791.444i	0.691286	+	1.19734i	−0.280130	+	0.959962i	$0.590378\pi$
$662$		0			0
$663$	−705.581	−	407.368i	−1.06423	−	0.614431i
$664$		0			0
$665$	387.977	−	1061.23i	0.583424	−	1.59583i
$666$		0			0
$667$	−357.378	−	206.332i	−0.535799	−	0.309343i
$668$		0			0
$669$	383.373	+	664.022i	0.573054	+	0.992559i
$670$		0			0
$671$			356.946i			0.531961i
$672$		0			0
$673$	−1018.88			−1.51393			−0.756966	−	0.653455i	$-0.773319\pi$
$673$	−1018.88			−1.51393			−0.756966	+	0.653455i	$0.773319\pi$
$674$		0			0
$675$	−678.604	+	391.792i	−1.00534	+	0.580433i
$676$		0			0
$677$	231.944	−	401.739i	0.342606	−	0.593410i	−0.642310	−	0.766445i	$-0.722024\pi$
$677$	231.944	−	401.739i	0.342606	−	0.593410i	0.984916	+	0.173035i	$0.0553572\pi$
$678$		0			0
$679$	332.068	−	277.829i	0.489054	−	0.409173i
$680$		0			0
$681$	222.827	−	385.948i	0.327206	−	0.566737i
$682$		0			0
$683$	368.311	−	212.645i	0.539255	−	0.311339i	−0.205522	−	0.978653i	$-0.565889\pi$
$683$	368.311	−	212.645i	0.539255	−	0.311339i	0.744777	+	0.667313i	$0.232556\pi$
$684$		0			0
$685$	−1070.36			−1.56256
$686$		0			0
$687$			320.461i			0.466464i
$688$		0			0
$689$	−37.0549	−	64.1810i	−0.0537807	−	0.0931509i
$690$		0			0
$691$	−221.337	−	127.789i	−0.320314	−	0.184933i	0.331219	−	0.943554i	$-0.392540\pi$
$691$	−221.337	−	127.789i	−0.320314	−	0.184933i	−0.651533	+	0.758621i	$0.725874\pi$
$692$		0			0
$693$	43.5512	+	52.0534i	0.0628444	+	0.0751132i
$694$		0			0
$695$	334.844	+	193.322i	0.481790	+	0.278162i
$696$		0			0
$697$	−25.4997	−	44.1668i	−0.0365850	−	0.0633670i
$698$		0			0
$699$			510.119i			0.729783i
$700$		0			0
$701$	354.151			0.505208			0.252604	−	0.967570i	$-0.418713\pi$
$701$	354.151			0.505208			0.252604	+	0.967570i	$0.418713\pi$
$702$		0			0
$703$	1216.06	−	702.091i	1.72981	−	0.998707i
$704$		0			0
$705$	205.692	−	356.269i	0.291762	−	0.505346i
$706$		0			0
$707$	−779.621	−	285.023i	−1.10272	−	0.403145i
$708$		0			0
$709$	−20.2143	+	35.0122i	−0.0285110	+	0.0493825i	−0.879929	−	0.475106i	$-0.842410\pi$
$709$	−20.2143	+	35.0122i	−0.0285110	+	0.0493825i	0.851418	+	0.524488i	$0.175743\pi$
$710$		0			0
$711$	161.134	−	93.0310i	0.226631	−	0.130845i
$712$		0			0
$713$	515.319			0.722748
$714$		0			0
$715$		−	577.614i		−	0.807851i
$716$		0			0
$717$	−299.553	−	518.841i	−0.417786	−	0.723627i
$718$		0			0
$719$	−364.833	−	210.636i	−0.507417	−	0.292957i	0.224355	−	0.974508i	$-0.427973\pi$
$719$	−364.833	−	210.636i	−0.507417	−	0.292957i	−0.731771	+	0.681551i	$0.761306\pi$
$720$		0			0
$721$	1174.60	−	205.380i	1.62913	−	0.284855i
$722$		0			0
$723$	−566.455	−	327.043i	−0.783479	−	0.452342i
$724$		0			0
$725$	−502.967	−	871.165i	−0.693748	−	1.20161i
$726$		0			0
$727$		−	1056.48i		−	1.45321i	−0.687057	−	0.726603i	$-0.741098\pi$
$727$		−	1056.48i		−	1.45321i	0.687057	−	0.726603i	$-0.258902\pi$
$728$		0			0
$729$	−809.441			−1.11034
$730$		0			0
$731$	−653.165	+	377.105i	−0.893522	+	0.515875i
$732$		0			0
$733$	−333.330	+	577.344i	−0.454747	+	0.787645i	−0.998674	−	0.0514878i	$-0.983604\pi$
$733$	−333.330	+	577.344i	−0.454747	+	0.787645i	0.543927	+	0.839133i	$0.316937\pi$
$734$		0			0
$735$	−905.510	−	162.341i	−1.23199	−	0.220872i
$736$		0			0
$737$	−52.1247	+	90.2827i	−0.0707256	+	0.122500i
$738$		0			0
$739$	654.379	−	377.806i	0.885492	−	0.511239i	0.0130267	−	0.999915i	$-0.495853\pi$
$739$	654.379	−	377.806i	0.885492	−	0.511239i	0.872465	+	0.488676i	$0.162520\pi$
$740$		0			0
$741$	−1064.13			−1.43607
$742$		0			0
$743$		−	616.726i		−	0.830048i	−0.909810	−	0.415024i	$-0.863773\pi$
$743$		−	616.726i		−	0.830048i	0.909810	−	0.415024i	$-0.136227\pi$
$744$		0			0
$745$	102.967	+	178.344i	0.138210	+	0.239387i
$746$		0			0
$747$	−78.2901	−	45.2008i	−0.104806	−	0.0605098i
$748$		0			0
$749$	−1136.00	+	198.631i	−1.51669	+	0.265194i
$750$		0			0
$751$	−315.176	−	181.967i	−0.419675	−	0.242299i	0.275263	−	0.961369i	$-0.411235\pi$
$751$	−315.176	−	181.967i	−0.419675	−	0.242299i	−0.694938	+	0.719069i	$0.744568\pi$
$752$		0			0
$753$	−627.675	−	1087.16i	−0.833566	−	1.44378i
$754$		0			0
$755$		−	1750.28i		−	2.31825i
$756$		0			0
$757$	−730.440			−0.964915			−0.482457	−	0.875919i	$-0.660256\pi$
$757$	−730.440			−0.964915			−0.482457	+	0.875919i	$0.660256\pi$
$758$		0			0
$759$	109.584	−	63.2682i	0.144379	−	0.0833573i
$760$		0			0
$761$	−183.675	+	318.134i	−0.241359	+	0.418047i	−0.961102	−	0.276194i	$-0.910927\pi$
$761$	−183.675	+	318.134i	−0.241359	+	0.418047i	0.719742	+	0.694241i	$0.244260\pi$
$762$		0			0
$763$	286.845	+	104.868i	0.375944	+	0.137442i
$764$		0			0
$765$	−135.903	+	235.391i	−0.177651	+	0.307700i
$766$		0			0
$767$	−223.639	+	129.118i	−0.291577	+	0.168342i
$768$		0			0
$769$	−903.272			−1.17461			−0.587303	−	0.809367i	$-0.699810\pi$
$769$	−903.272			−1.17461			−0.587303	+	0.809367i	$0.699810\pi$
$770$		0			0
$771$			807.969i			1.04795i
$772$		0			0
$773$	555.526	+	962.200i	0.718663	+	1.24476i	0.961530	+	0.274701i	$0.0885787\pi$
$773$	555.526	+	962.200i	0.718663	+	1.24476i	−0.242867	+	0.970060i	$0.578088\pi$
$774$		0			0
$775$	1087.88	+	628.086i	1.40371	+	0.810433i
$776$		0			0
$777$	−733.605	−	876.823i	−0.944151	−	1.12847i
$778$		0			0
$779$	−57.6863	−	33.3052i	−0.0740517	−	0.0427538i
$780$		0			0
$781$	212.400	+	367.888i	0.271959	+	0.471047i
$782$		0			0
$783$		−	1095.01i		−	1.39848i
$784$		0			0
$785$	670.711			0.854408
$786$		0			0
$787$	568.705	−	328.342i	0.722623	−	0.417207i	−0.0930942	−	0.995657i	$-0.529676\pi$
$787$	568.705	−	328.342i	0.722623	−	0.417207i	0.815717	+	0.578451i	$0.196342\pi$
$788$		0			0
$789$	−367.879	+	637.185i	−0.466260	+	0.807585i
$790$		0			0
$791$	−948.698	+	793.740i	−1.19936	+	1.00346i
$792$		0			0
$793$	736.774	−	1276.13i	0.929097	−	1.60924i
$794$		0			0
$795$	66.2093	−	38.2259i	0.0832821	−	0.0480829i
$796$		0			0
$797$	820.253			1.02918			0.514588	−	0.857438i	$-0.327945\pi$
$797$	820.253			1.02918			0.514588	+	0.857438i	$0.327945\pi$
$798$		0			0
$799$		−	376.153i		−	0.470780i
$800$		0			0
$801$	−109.814	−	190.203i	−0.137096	−	0.237457i
$802$		0			0
$803$	124.816	+	72.0625i	0.155437	+	0.0897416i
$804$		0			0
$805$	190.454	−	520.946i	0.236589	−	0.647138i
$806$		0			0
$807$	−664.743	−	383.790i	−0.823721	−	0.475576i
$808$		0			0
$809$	76.3989	+	132.327i	0.0944363	+	0.163568i	0.909373	−	0.415981i	$-0.136562\pi$
$809$	76.3989	+	132.327i	0.0944363	+	0.163568i	−0.814937	+	0.579550i	$0.803228\pi$
$810$		0			0
$811$			203.504i			0.250930i	0.992098	+	0.125465i	$0.0400423\pi$
$811$			203.504i			0.250930i	−0.992098	+	0.125465i	$0.959958\pi$
$812$		0			0
$813$	581.269			0.714968
$814$		0			0
$815$	1722.06	−	994.231i	2.11295	−	1.21991i
$816$		0			0
$817$	−492.537	+	853.099i	−0.602860	+	1.04418i
$818$		0			0
$819$	−48.2576	−	275.992i	−0.0589225	−	0.336987i
$820$		0			0
$821$	−716.357	+	1240.77i	−0.872542	+	1.51129i	−0.0131839	+	0.999913i	$0.504197\pi$
$821$	−716.357	+	1240.77i	−0.872542	+	1.51129i	−0.859358	+	0.511374i	$0.829137\pi$
$822$		0			0
$823$	−141.907	+	81.9300i	−0.172426	+	0.0995504i	−0.583729	−	0.811948i	$-0.698407\pi$
$823$	−141.907	+	81.9300i	−0.172426	+	0.0995504i	0.411303	+	0.911499i	$0.365074\pi$
$824$		0			0
$825$	308.452			0.373882
$826$		0			0
$827$			1380.58i			1.66939i	0.550715	+	0.834693i	$0.314355\pi$
$827$			1380.58i			1.66939i	−0.550715	+	0.834693i	$0.685645\pi$
$828$		0			0
$829$	7.77609	+	13.4686i	0.00938009	+	0.0162468i	0.870677	−	0.491855i	$-0.163681\pi$
$829$	7.77609	+	13.4686i	0.00938009	+	0.0162468i	−0.861297	+	0.508101i	$0.830348\pi$
$830$		0			0
$831$	104.789	+	60.4998i	0.126100	+	0.0728037i
$832$		0			0
$833$	−791.257	+	285.431i	−0.949888	+	0.342654i
$834$		0			0
$835$	182.624	+	105.438i	0.218712	+	0.126273i
$836$		0			0
$837$	683.704	+	1184.21i	0.816851	+	1.41483i
$838$		0			0
$839$			843.862i			1.00580i	0.864346	+	0.502898i	$0.167733\pi$
$839$			843.862i			1.00580i	−0.864346	+	0.502898i	$0.832267\pi$
$840$		0			0
$841$	564.732			0.671500
$842$		0			0
$843$	−1181.22	+	681.979i	−1.40121	+	0.808991i
$844$		0			0
$845$	−583.915	+	1011.37i	−0.691023	+	1.19689i
$846$		0			0
$847$	122.453	+	700.330i	0.144573	+	0.826835i
$848$		0			0
$849$	−519.130	+	899.159i	−0.611460	+	1.05908i
$850$		0			0
$851$	596.950	−	344.649i	0.701469	−	0.404993i
$852$		0			0
$853$	507.417			0.594862			0.297431	−	0.954743i	$-0.403870\pi$
$853$	507.417			0.594862			0.297431	+	0.954743i	$0.403870\pi$
$854$		0			0
$855$			355.005i			0.415211i
$856$		0			0
$857$	204.793	+	354.713i	0.238966	+	0.413900i	0.960418	−	0.278564i	$-0.0898584\pi$
$857$	204.793	+	354.713i	0.238966	+	0.413900i	−0.721452	+	0.692464i	$0.756525\pi$
$858$		0			0
$859$	−543.757	−	313.938i	−0.633011	−	0.365469i	0.148906	−	0.988851i	$-0.452425\pi$
$859$	−543.757	−	313.938i	−0.633011	−	0.365469i	−0.781917	+	0.623382i	$0.785758\pi$
$860$		0			0
$861$	−18.6214	+	50.9348i	−0.0216276	+	0.0591577i
$862$		0			0
$863$	334.919	+	193.365i	0.388086	+	0.224062i	0.681331	−	0.731976i	$-0.261402\pi$
$863$	334.919	+	193.365i	0.388086	+	0.224062i	−0.293244	+	0.956038i	$0.594735\pi$
$864$		0			0
$865$	−159.869	−	276.901i	−0.184820	−	0.320117i
$866$		0			0
$867$		−	14.8461i		−	0.0171235i
$868$		0			0
$869$	−372.964			−0.429188
$870$		0			0
$871$	372.706	−	215.182i	0.427906	−	0.247051i
$872$		0			0
$873$	−68.0154	+	117.806i	−0.0779099	+	0.134944i
$874$		0			0
$875$	70.7261	−	59.1739i	0.0808298	−	0.0676273i
$876$		0			0
$877$	648.580	−	1123.37i	0.739544	−	1.28093i	−0.213157	−	0.977018i	$-0.568375\pi$
$877$	648.580	−	1123.37i	0.739544	−	1.28093i	0.952701	−	0.303909i	$-0.0982920\pi$
$878$		0			0
$879$	182.949	−	105.625i	0.208133	−	0.120165i
$880$		0			0
$881$	869.810			0.987299			0.493649	−	0.869661i	$-0.335663\pi$
$881$	869.810			0.987299			0.493649	+	0.869661i	$0.335663\pi$
$882$		0			0
$883$		−	350.462i		−	0.396899i	−0.980111	−	0.198450i	$-0.936409\pi$
$883$		−	350.462i		−	0.396899i	0.980111	−	0.198450i	$-0.0635906\pi$
$884$		0			0
$885$	−133.199	−	230.707i	−0.150507	−	0.260686i
$886$		0			0
$887$	−1043.07	−	602.215i	−1.17595	−	0.678935i	−0.220876	−	0.975302i	$-0.570891\pi$
$887$	−1043.07	−	602.215i	−1.17595	−	0.678935i	−0.955074	+	0.296367i	$0.904225\pi$
$888$		0			0
$889$	−708.976	−	847.385i	−0.797498	−	0.953189i
$890$		0			0
$891$	215.212	+	124.253i	0.241540	+	0.139453i
$892$		0			0
$893$	−245.647	−	425.473i	−0.275081	−	0.476454i
$894$		0			0
$895$			1137.88i			1.27137i
$896$		0			0
$897$	−522.369			−0.582351
$898$		0			0
$899$	−1520.24	+	877.712i	−1.69104	+	0.976320i
$900$		0			0
$901$	34.9523	−	60.5392i	0.0387928	−	0.0671911i
$902$		0			0
$903$	753.254	+	275.384i	0.834168	+	0.304965i
$904$		0			0
$905$	271.550	−	470.339i	0.300056	−	0.519712i
$906$		0			0
$907$	938.261	−	541.705i	1.03447	−	0.597250i	0.116206	−	0.993225i	$-0.462927\pi$
$907$	938.261	−	541.705i	1.03447	−	0.597250i	0.918261	+	0.395976i	$0.129594\pi$
$908$		0			0
$909$	260.801			0.286910
$910$		0			0
$911$		−	677.413i		−	0.743593i	−0.928314	−	0.371797i	$-0.878742\pi$
$911$		−	677.413i		−	0.743593i	0.928314	−	0.371797i	$-0.121258\pi$
$912$		0			0
$913$	90.6057	+	156.934i	0.0992395	+	0.171888i
$914$		0			0
$915$	1316.46	+	760.058i	1.43875	+	0.830665i
$916$		0			0
$917$	1126.78	−	197.019i	1.22877	−	0.214852i
$918$		0			0
$919$	−834.480	−	481.787i	−0.908031	−	0.524252i	−0.0282338	−	0.999601i	$-0.508988\pi$
$919$	−834.480	−	481.787i	−0.908031	−	0.524252i	−0.879797	+	0.475349i	$0.842322\pi$
$920$		0			0
$921$	279.134	+	483.474i	0.303077	+	0.524945i
$922$		0			0
$923$		−	1753.66i		−	1.89996i
$924$		0			0
$925$	1680.27			1.81651
$926$		0			0
$927$	−324.448	+	187.320i	−0.349998	+	0.202071i
$928$		0			0
$929$	489.329	−	847.543i	0.526727	−	0.912318i	−0.472788	−	0.881176i	$-0.656752\pi$
$929$	489.329	−	847.543i	0.526727	−	0.912318i	0.999515	−	0.0311416i	$-0.00991428\pi$
$930$		0			0
$931$	−708.603	+	839.586i	−0.761120	+	0.901811i
$932$		0			0
$933$	252.549	−	437.428i	0.270685	−	0.468841i
$934$		0			0
$935$	471.844	−	272.419i	0.504646	−	0.291357i
$936$		0			0
$937$	−653.549			−0.697490			−0.348745	−	0.937218i	$-0.613392\pi$
$937$	−653.549			−0.697490			−0.348745	+	0.937218i	$0.613392\pi$
$938$		0			0
$939$			385.513i			0.410557i
$940$		0			0
$941$	−771.643	−	1336.53i	−0.820025	−	1.42032i	−0.905663	−	0.423998i	$-0.860626\pi$
$941$	−771.643	−	1336.53i	−0.820025	−	1.42032i	0.0856385	−	0.996326i	$-0.472707\pi$
$942$		0			0
$943$	−28.3176	−	16.3492i	−0.0300293	−	0.0173374i
$944$		0			0
$945$	1449.83	−	253.504i	1.53421	−	0.268258i
$946$		0			0
$947$	1031.64	+	595.615i	1.08937	+	0.628949i	0.933409	−	0.358814i	$-0.116819\pi$
$947$	1031.64	+	595.615i	1.08937	+	0.628949i	0.155963	+	0.987763i	$0.450152\pi$
$948$		0			0
$949$	−297.489	−	515.266i	−0.313476	−	0.542957i
$950$		0			0
$951$			370.523i			0.389614i
$952$		0			0
$953$	895.795			0.939974			0.469987	−	0.882673i	$-0.344259\pi$
$953$	895.795			0.939974			0.469987	+	0.882673i	$0.344259\pi$
$954$		0			0
$955$	−709.807	+	409.808i	−0.743254	+	0.429118i
$956$		0			0
$957$	−215.522	+	373.295i	−0.225206	+	0.390067i
$958$		0			0
$959$	977.451	+	357.349i	1.01924	+	0.372626i
$960$		0			0
$961$	615.553	−	1066.17i	0.640534	−	1.10944i
$962$		0			0
$963$	313.786	−	181.164i	0.325842	−	0.188125i
$964$		0			0
$965$	−1032.19			−1.06963
$966$		0			0
$967$			160.933i			0.166425i	0.996532	+	0.0832125i	$0.0265180\pi$
$967$			160.933i			0.166425i	−0.996532	+	0.0832125i	$0.973482\pi$
$968$		0			0
$969$	−501.872	−	869.268i	−0.517928	−	0.897078i
$970$		0			0
$971$	93.6821	+	54.0874i	0.0964801	+	0.0557028i	0.547464	−	0.836829i	$-0.315593\pi$
$971$	93.6821	+	54.0874i	0.0964801	+	0.0557028i	−0.450984	+	0.892532i	$0.648927\pi$
$972$		0			0
$973$	−241.238	−	288.334i	−0.247932	−	0.296335i
$974$		0			0
$975$	−1102.76	−	636.678i	−1.13103	−	0.653003i
$976$		0			0
$977$	−587.879	−	1018.24i	−0.601718	−	1.04221i	−0.992561	−	0.121749i	$-0.961150\pi$
$977$	−587.879	−	1018.24i	−0.601718	−	1.04221i	0.390843	−	0.920457i	$-0.372184\pi$
$978$		0			0
$979$			440.246i			0.449689i
$980$		0			0
$981$	−95.9565			−0.0978150
$982$		0			0
$983$	−1445.70	+	834.675i	−1.47070	+	0.849109i	−0.999459	−	0.0328947i	$-0.989527\pi$
$983$	−1445.70	+	834.675i	−1.47070	+	0.849109i	−0.471242	+	0.882004i	$0.656194\pi$
$984$		0			0
$985$	−1046.82	+	1813.15i	−1.06276	+	1.84076i
$986$		0			0
$987$	−306.782	+	256.673i	−0.310823	+	0.260054i
$988$		0			0
$989$	−241.781	+	418.778i	−0.244471	+	0.423435i
$990$		0			0
$991$	186.089	−	107.439i	0.187779	−	0.108414i	−0.403163	−	0.915128i	$-0.632089\pi$
$991$	186.089	−	107.439i	0.187779	−	0.108414i	0.590943	+	0.806714i	$0.298756\pi$
$992$		0			0
$993$	800.853			0.806499
$994$		0			0
$995$		−	1397.63i		−	1.40465i
$996$		0			0
$997$	245.695	+	425.557i	0.246435	+	0.426837i	0.962534	−	0.271161i	$-0.0874076\pi$
$997$	245.695	+	425.557i	0.246435	+	0.426837i	−0.716099	+	0.697998i	$0.754074\pi$
$998$		0			0
$999$	1584.02	+	914.533i	1.58560	+	0.915449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.c.191.3	yes	12
4.3	odd	2	inner	224.3.r.c.191.4	yes	12
7.2	even	3		1568.3.d.j.1471.3		6
7.4	even	3	inner	224.3.r.c.95.4	yes	12
7.5	odd	6		1568.3.d.k.1471.4		6
8.3	odd	2		448.3.r.g.191.3		12
8.5	even	2		448.3.r.g.191.4		12
28.11	odd	6	inner	224.3.r.c.95.3	✓	12
28.19	even	6		1568.3.d.k.1471.3		6
28.23	odd	6		1568.3.d.j.1471.4		6
56.11	odd	6		448.3.r.g.319.4		12
56.53	even	6		448.3.r.g.319.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.c.95.3	✓	12	28.11	odd	6	inner
224.3.r.c.95.4	yes	12	7.4	even	3	inner
224.3.r.c.191.3	yes	12	1.1	even	1	trivial
224.3.r.c.191.4	yes	12	4.3	odd	2	inner
448.3.r.g.191.3		12	8.3	odd	2
448.3.r.g.191.4		12	8.5	even	2
448.3.r.g.319.3		12	56.53	even	6
448.3.r.g.319.4		12	56.11	odd	6
1568.3.d.j.1471.3		6	7.2	even	3
1568.3.d.j.1471.4		6	28.23	odd	6
1568.3.d.k.1471.3		6	28.19	even	6
1568.3.d.k.1471.4		6	7.5	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25843 + 1.30391i) q^{3} +(-3.59965 + 6.23477i) q^{5} +(5.36875 - 4.49183i) q^{7} +(-1.09965 + 1.90465i) q^{9} +O(q^{10})\)	\(q+(-2.25843 + 1.30391i) q^{3} +(-3.59965 + 6.23477i) q^{5} +(5.36875 - 4.49183i) q^{7} +(-1.09965 + 1.90465i) q^{9} +(3.81789 - 2.20426i) q^{11} -18.1993 q^{13} -18.7744i q^{15} +(-8.58331 - 14.8667i) q^{17} +(-19.4174 - 11.2107i) q^{19} +(-6.26803 + 17.1449i) q^{21} +(-9.53183 - 5.50320i) q^{23} +(-13.4149 - 23.2353i) q^{25} -29.2057i q^{27} +37.4931 q^{29} +(-40.5472 + 23.4100i) q^{31} +(-5.74831 + 9.95636i) q^{33} +(8.67995 + 49.6419i) q^{35} +(-31.3135 + 54.2366i) q^{37} +(41.1019 - 23.7302i) q^{39} +2.97085 q^{41} -43.9347i q^{43} +(-7.91669 - 13.7121i) q^{45} +(18.9763 + 10.9560i) q^{47} +(8.64690 - 48.2310i) q^{49} +(38.7697 + 22.3837i) q^{51} +(2.03606 + 3.52656i) q^{53} +31.7382i q^{55} +58.4707 q^{57} +(12.2884 - 7.09468i) q^{59} +(-40.4837 + 70.1198i) q^{61} +(2.65162 + 15.1650i) q^{63} +(65.5111 - 113.468i) q^{65} +(-20.4791 + 11.8236i) q^{67} +28.7027 q^{69} +96.3589i q^{71} +(16.3462 + 28.3124i) q^{73} +(60.5935 + 34.9837i) q^{75} +(10.5961 - 28.9834i) q^{77} +(-73.2664 - 42.3004i) q^{79} +(28.1847 + 48.8174i) q^{81} +41.1048i q^{83} +123.588 q^{85} +(-84.6757 + 48.8875i) q^{87} +(-49.9313 + 86.4835i) q^{89} +(-97.7074 + 81.7482i) q^{91} +(61.0489 - 105.740i) q^{93} +(139.792 - 80.7089i) q^{95} +61.8520 q^{97} +9.69564i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{5} + 32 q^{9}+O(q^{10}) \) 12 * q + 2 * q^5 + 32 * q^9	\( 12 q + 2 q^{5} + 32 q^{9} - 128 q^{13} - 6 q^{17} - 62 q^{21} - 32 q^{25} + 128 q^{29} - 134 q^{33} - 66 q^{37} + 384 q^{41} - 192 q^{45} - 12 q^{49} - 2 q^{53} + 468 q^{57} - 434 q^{61} + 160 q^{65} + 124 q^{69} - 10 q^{73} - 370 q^{77} + 422 q^{81} + 1020 q^{85} - 522 q^{89} + 306 q^{93} - 768 q^{97}+O(q^{100}) \) 12 * q + 2 * q^5 + 32 * q^9 - 128 * q^13 - 6 * q^17 - 62 * q^21 - 32 * q^25 + 128 * q^29 - 134 * q^33 - 66 * q^37 + 384 * q^41 - 192 * q^45 - 12 * q^49 - 2 * q^53 + 468 * q^57 - 434 * q^61 + 160 * q^65 + 124 * q^69 - 10 * q^73 - 370 * q^77 + 422 * q^81 + 1020 * q^85 - 522 * q^89 + 306 * q^93 - 768 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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