LMFDB - Embedded newform 252.4.x.a.209.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.14
Character	$\chi$	$=$	252.209
Dual form			252.4.x.a.41.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.316211 - 5.18652i) q^{3} +(5.49690 + 9.52092i) q^{5} +(6.85688 + 17.2042i) q^{7} +(-26.8000 - 3.28007i) q^{9} +O(q^{10})$	\(q+(0.316211 - 5.18652i) q^{3} +(5.49690 + 9.52092i) q^{5} +(6.85688 + 17.2042i) q^{7} +(-26.8000 - 3.28007i) q^{9} +(13.8268 + 7.98293i) q^{11} +(-77.4289 + 44.7036i) q^{13} +(51.1186 - 25.4992i) q^{15} -106.953 q^{17} +8.31634i q^{19} +(91.3980 - 30.1232i) q^{21} +(-123.893 + 71.5294i) q^{23} +(2.06812 - 3.58208i) q^{25} +(-25.4866 + 137.962i) q^{27} +(129.721 + 74.8943i) q^{29} +(-37.1952 + 21.4747i) q^{31} +(45.7759 - 69.1890i) q^{33} +(-126.108 + 159.853i) q^{35} +390.706 q^{37} +(207.372 + 415.722i) q^{39} +(172.486 + 298.755i) q^{41} +(28.5593 - 49.4661i) q^{43} +(-116.088 - 273.191i) q^{45} +(8.13282 - 14.0864i) q^{47} +(-248.966 + 235.934i) q^{49} +(-33.8198 + 554.714i) q^{51} -445.230i q^{53} +175.526i q^{55} +(43.1329 + 2.62972i) q^{57} +(193.350 + 334.892i) q^{59} +(-420.857 - 242.982i) q^{61} +(-127.334 - 483.563i) q^{63} +(-851.238 - 491.463i) q^{65} +(-251.821 - 436.167i) q^{67} +(331.813 + 665.190i) q^{69} +751.418i q^{71} -507.533i q^{73} +(-17.9246 - 11.8590i) q^{75} +(-42.5306 + 292.617i) q^{77} +(381.570 - 660.899i) q^{79} +(707.482 + 175.812i) q^{81} +(-607.241 + 1051.77i) q^{83} +(-587.911 - 1018.29i) q^{85} +(429.460 - 649.117i) q^{87} +425.727 q^{89} +(-1300.01 - 1025.57i) q^{91} +(99.6173 + 199.704i) q^{93} +(-79.1792 + 45.7141i) q^{95} +(494.582 + 285.547i) q^{97} +(-344.375 - 259.296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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
$3$	0.316211	−	5.18652i	0.0608549	−	0.998147i
$3$	0.316211	−	5.18652i	0.0608549	−	0.998147i
$4$		0			0
$5$	5.49690	+	9.52092i	0.491658	+	0.851577i	0.999954	−	0.00960594i	$-0.00305771\pi$
$5$	5.49690	+	9.52092i	0.491658	+	0.851577i	−0.508296	+	0.861182i	$0.669724\pi$
$6$		0			0
$7$	6.85688	+	17.2042i	0.370237	+	0.928937i
$7$	6.85688	+	17.2042i	0.370237	+	0.928937i
$8$		0			0
$9$	−26.8000	−	3.28007i	−0.992593	−	0.121484i
$10$		0			0
$11$	13.8268	+	7.98293i	0.378996	+	0.218813i	0.677381	−	0.735632i	$-0.263115\pi$
$11$	13.8268	+	7.98293i	0.378996	+	0.218813i	−0.298386	+	0.954445i	$0.596448\pi$
$12$		0			0
$13$	−77.4289	+	44.7036i	−1.65192	+	0.953734i	−0.675633	+	0.737238i	$0.736130\pi$
$13$	−77.4289	+	44.7036i	−1.65192	+	0.953734i	−0.976283	+	0.216496i	$0.930537\pi$
$14$		0			0
$15$	51.1186	−	25.4992i	0.879918	−	0.438924i
$16$		0			0
$17$	−106.953			−1.52588			−0.762939	−	0.646471i	$-0.776244\pi$
$17$	−106.953			−1.52588			−0.762939	+	0.646471i	$0.776244\pi$
$18$		0			0
$19$			8.31634i			0.100416i	0.998739	+	0.0502079i	$0.0159884\pi$
$19$			8.31634i			0.100416i	−0.998739	+	0.0502079i	$0.984012\pi$
$20$		0			0
$21$	91.3980	−	30.1232i	0.949746	−	0.313020i
$22$		0			0
$23$	−123.893	+	71.5294i	−1.12319	+	0.648474i	−0.942214	−	0.335013i	$-0.891259\pi$
$23$	−123.893	+	71.5294i	−1.12319	+	0.648474i	−0.180977	+	0.983487i	$0.557926\pi$
$24$		0			0
$25$	2.06812	−	3.58208i	0.0165449	−	0.0286567i
$26$		0			0
$27$	−25.4866	+	137.962i	−0.181663	+	0.983361i
$28$		0			0
$29$	129.721	+	74.8943i	0.830639	+	0.479570i	0.854072	−	0.520156i	$-0.174126\pi$
$29$	129.721	+	74.8943i	0.830639	+	0.479570i	−0.0234322	+	0.999725i	$0.507459\pi$
$30$		0			0
$31$	−37.1952	+	21.4747i	−0.215499	+	0.124418i	−0.603864	−	0.797087i	$-0.706373\pi$
$31$	−37.1952	+	21.4747i	−0.215499	+	0.124418i	0.388366	+	0.921505i	$0.373040\pi$
$32$		0			0
$33$	45.7759	−	69.1890i	0.241471	−	0.364977i
$34$		0			0
$35$	−126.108	+	159.853i	−0.609031	+	0.772004i
$36$		0			0
$37$	390.706			1.73599			0.867997	−	0.496570i	$-0.165407\pi$
$37$	390.706			1.73599			0.867997	+	0.496570i	$0.165407\pi$
$38$		0			0
$39$	207.372	+	415.722i	0.851440	+	1.70689i
$40$		0			0
$41$	172.486	+	298.755i	0.657021	+	1.13799i	0.981383	+	0.192060i	$0.0615169\pi$
$41$	172.486	+	298.755i	0.657021	+	1.13799i	−0.324363	+	0.945933i	$0.605150\pi$
$42$		0			0
$43$	28.5593	−	49.4661i	0.101285	−	0.175430i	−0.810929	−	0.585144i	$-0.801038\pi$
$43$	28.5593	−	49.4661i	0.101285	−	0.175430i	0.912214	+	0.409714i	$0.134371\pi$
$44$		0			0
$45$	−116.088	−	273.191i	−0.384563	−	0.904998i
$46$		0			0
$47$	8.13282	−	14.0864i	0.0252403	−	0.0437174i	−0.853129	−	0.521699i	$-0.825298\pi$
$47$	8.13282	−	14.0864i	0.0252403	−	0.0437174i	0.878370	+	0.477982i	$0.158632\pi$
$48$		0			0
$49$	−248.966	+	235.934i	−0.725849	+	0.687854i
$50$		0			0
$51$	−33.8198	+	554.714i	−0.0928571	+	1.52305i
$52$		0			0
$53$		−	445.230i		−	1.15391i	−0.816777	−	0.576954i	$-0.804241\pi$
$53$		−	445.230i		−	1.15391i	0.816777	−	0.576954i	$-0.195759\pi$
$54$		0			0
$55$			175.526i			0.430325i
$56$		0			0
$57$	43.1329	+	2.62972i	0.100230	+	0.00611079i
$58$		0			0
$59$	193.350	+	334.892i	0.426644	+	0.738969i	0.996572	−	0.0827250i	$-0.0263623\pi$
$59$	193.350	+	334.892i	0.426644	+	0.738969i	−0.569928	+	0.821695i	$0.693029\pi$
$60$		0			0
$61$	−420.857	−	242.982i	−0.883365	−	0.510011i	−0.0115982	−	0.999933i	$-0.503692\pi$
$61$	−420.857	−	242.982i	−0.883365	−	0.510011i	−0.871766	+	0.489922i	$0.837025\pi$
$62$		0			0
$63$	−127.334	−	483.563i	−0.254643	−	0.967035i
$64$		0			0
$65$	−851.238	−	491.463i	−1.62436	−	0.937822i
$66$		0			0
$67$	−251.821	−	436.167i	−0.459177	−	0.795318i	0.539741	−	0.841831i	$-0.318522\pi$
$67$	−251.821	−	436.167i	−0.459177	−	0.795318i	−0.998918	+	0.0465137i	$0.985189\pi$
$68$		0			0
$69$	331.813	+	665.190i	0.578921	+	1.16057i
$70$		0			0
$71$			751.418i			1.25601i	0.778208	+	0.628007i	$0.216129\pi$
$71$			751.418i			1.25601i	−0.778208	+	0.628007i	$0.783871\pi$
$72$		0			0
$73$		−	507.533i		−	0.813729i	−0.913489	−	0.406865i	$-0.866622\pi$
$73$		−	507.533i		−	0.813729i	0.913489	−	0.406865i	$-0.133378\pi$
$74$		0			0
$75$	−17.9246	−	11.8590i	−0.0275967	−	0.0182582i
$76$		0			0
$77$	−42.5306	+	292.617i	−0.0629456	+	0.433076i
$78$		0			0
$79$	381.570	−	660.899i	0.543418	−	0.941228i	−0.455287	−	0.890345i	$-0.650463\pi$
$79$	381.570	−	660.899i	0.543418	−	0.941228i	0.998705	−	0.0508826i	$-0.0162034\pi$
$80$		0			0
$81$	707.482	+	175.812i	0.970483	+	0.241169i
$82$		0			0
$83$	−607.241	+	1051.77i	−0.803052	+	1.39093i	0.114546	+	0.993418i	$0.463459\pi$
$83$	−607.241	+	1051.77i	−0.803052	+	1.39093i	−0.917598	+	0.397509i	$0.869875\pi$
$84$		0			0
$85$	−587.911	−	1018.29i	−0.750210	−	1.29940i
$86$		0			0
$87$	429.460	−	649.117i	0.529229	−	0.799916i
$88$		0			0
$89$	425.727			0.507045			0.253523	−	0.967329i	$-0.418411\pi$
$89$	425.727			0.507045			0.253523	+	0.967329i	$0.418411\pi$
$90$		0			0
$91$	−1300.01	−	1025.57i	−1.49756	−	1.18142i
$92$		0			0
$93$	99.6173	+	199.704i	0.111073	+	0.222671i
$94$		0			0
$95$	−79.1792	+	45.7141i	−0.0855117	+	0.0493702i
$96$		0			0
$97$	494.582	+	285.547i	0.517703	+	0.298896i	0.735994	−	0.676988i	$-0.236715\pi$
$97$	494.582	+	285.547i	0.517703	+	0.298896i	−0.218291	+	0.975884i	$0.570048\pi$
$98$		0			0
$99$	−344.375	−	259.296i	−0.349606	−	0.263234i
$100$		0			0
$101$	353.385	−	612.081i	0.348150	−	0.603013i	−0.637771	−	0.770226i	$-0.720143\pi$
$101$	353.385	−	612.081i	0.348150	−	0.603013i	0.985921	+	0.167213i	$0.0534768\pi$
$102$		0			0
$103$	−217.607	+	125.635i	−0.208169	+	0.120187i	−0.600460	−	0.799655i	$-0.705016\pi$
$103$	−217.607	+	125.635i	−0.208169	+	0.120187i	0.392291	+	0.919841i	$0.371683\pi$
$104$		0			0
$105$	789.207	+	704.608i	0.733511	+	0.654883i
$106$		0			0
$107$			739.962i			0.668549i	0.942476	+	0.334275i	$0.108491\pi$
$107$			739.962i			0.668549i	−0.942476	+	0.334275i	$0.891509\pi$
$108$		0			0
$109$	1497.38			1.31580			0.657902	−	0.753104i	$-0.271444\pi$
$109$	1497.38			1.31580			0.657902	+	0.753104i	$0.271444\pi$
$110$		0			0
$111$	123.546	−	2026.41i	0.105644	−	1.73278i
$112$		0			0
$113$	−861.916	+	497.627i	−0.717542	+	0.414273i	−0.813847	−	0.581079i	$-0.802631\pi$
$113$	−861.916	+	497.627i	−0.717542	+	0.414273i	0.0963056	+	0.995352i	$0.469297\pi$
$114$		0			0
$115$	−1362.05	−	786.380i	−1.10445	−	0.637655i
$116$		0			0
$117$	2221.73	−	944.085i	1.75554	−	0.745989i
$118$		0			0
$119$	−733.365	−	1840.04i	−0.564936	−	1.41744i
$120$		0			0
$121$	−538.046	−	931.922i	−0.404242	−	0.700167i
$122$		0			0
$123$	1604.04	−	800.135i	1.17587	−	0.586550i
$124$		0			0
$125$	1419.70			1.01585
$126$		0			0
$127$	2469.41			1.72539			0.862696	−	0.505724i	$-0.168774\pi$
$127$	2469.41			1.72539			0.862696	+	0.505724i	$0.168774\pi$
$128$		0			0
$129$	−247.526	−	163.765i	−0.168942	−	0.111773i
$130$		0			0
$131$	769.787	+	1333.31i	0.513409	+	0.889251i	0.999879	+	0.0155535i	$0.00495103\pi$
$131$	769.787	+	1333.31i	0.513409	+	0.889251i	−0.486470	+	0.873697i	$0.661716\pi$
$132$		0			0
$133$	−143.076	+	57.0242i	−0.0932800	+	0.0371776i
$134$		0			0
$135$	−1453.62	+	515.706i	−0.926723	+	0.328777i
$136$		0			0
$137$	−1419.80	−	819.722i	−0.885414	−	0.511194i	−0.0129744	−	0.999916i	$-0.504130\pi$
$137$	−1419.80	−	819.722i	−0.885414	−	0.511194i	−0.872440	+	0.488722i	$0.837463\pi$
$138$		0			0
$139$	−899.533	+	519.345i	−0.548902	+	0.316909i	−0.748679	−	0.662933i	$-0.769312\pi$
$139$	−899.533	+	519.345i	−0.548902	+	0.316909i	0.199777	+	0.979841i	$0.435978\pi$
$140$		0			0
$141$	−70.4880	−	46.6353i	−0.0421004	−	0.0278539i
$142$		0			0
$143$	−1427.46			−0.834759
$144$		0			0
$145$			1646.75i			0.943137i
$146$		0			0
$147$	1144.95	+	1365.87i	0.642407	+	0.766363i
$148$		0			0
$149$	−1523.17	+	879.401i	−0.837468	+	0.483512i	−0.856403	−	0.516308i	$-0.827306\pi$
$149$	−1523.17	+	879.401i	−0.837468	+	0.483512i	0.0189346	+	0.999821i	$0.493973\pi$
$150$		0			0
$151$	352.401	−	610.376i	0.189920	−	0.328952i	−0.755303	−	0.655376i	$-0.772510\pi$
$151$	352.401	−	610.376i	0.189920	−	0.328952i	0.945223	+	0.326424i	$0.105844\pi$
$152$		0			0
$153$	2866.34	+	350.814i	1.51458	+	0.185370i
$154$		0			0
$155$	−408.917	−	236.088i	−0.211903	−	0.122342i
$156$		0			0
$157$	579.051	−	334.315i	0.294352	−	0.169944i	−0.345551	−	0.938400i	$-0.612308\pi$
$157$	579.051	−	334.315i	0.294352	−	0.169944i	0.639903	+	0.768456i	$0.278975\pi$
$158$		0			0
$159$	−2309.20	−	140.787i	−1.15177	−	0.0702209i
$160$		0			0
$161$	−2080.12	−	1641.00i	−1.01824	−	0.803285i
$162$		0			0
$163$	−3926.19			−1.88665			−0.943323	−	0.331877i	$-0.892318\pi$
$163$	−3926.19			−1.88665			−0.943323	+	0.331877i	$0.892318\pi$
$164$		0			0
$165$	910.368	+	55.5032i	0.429527	+	0.0261874i
$166$		0			0
$167$	−966.800	−	1674.55i	−0.447984	−	0.775930i	0.550271	−	0.834986i	$-0.314524\pi$
$167$	−966.800	−	1674.55i	−0.447984	−	0.775930i	−0.998255	+	0.0590557i	$0.981191\pi$
$168$		0			0
$169$	2898.32	−	5020.04i	1.31922	−	2.28495i
$170$		0			0
$171$	27.2782	−	222.878i	0.0121989	−	0.0996720i
$172$		0			0
$173$	−850.018	+	1472.27i	−0.373559	+	0.647023i	−0.990110	−	0.140292i	$-0.955196\pi$
$173$	−850.018	+	1472.27i	−0.373559	+	0.647023i	0.616551	+	0.787315i	$0.288529\pi$
$174$		0			0
$175$	75.8075	+	11.0183i	0.0327458	+	0.00475945i
$176$		0			0
$177$	1798.06	−	896.917i	0.763563	−	0.380884i
$178$		0			0
$179$			1175.15i			0.490697i	0.969435	+	0.245349i	$0.0789024\pi$
$179$			1175.15i			0.490697i	−0.969435	+	0.245349i	$0.921098\pi$
$180$		0			0
$181$		−	3506.89i		−	1.44014i	−0.693902	−	0.720070i	$-0.744110\pi$
$181$		−	3506.89i		−	1.44014i	0.693902	−	0.720070i	$-0.255890\pi$
$182$		0			0
$183$	−1393.31	+	2105.95i	−0.562823	+	0.850691i
$184$		0			0
$185$	2147.68	+	3719.88i	0.853515	+	1.47833i
$186$		0			0
$187$	−1478.82	−	853.799i	−0.578301	−	0.333882i
$188$		0			0
$189$	−2548.27	+	507.511i	−0.980739	+	0.195323i
$190$		0			0
$191$	1228.14	+	709.068i	0.465263	+	0.268620i	0.714255	−	0.699886i	$-0.246766\pi$
$191$	1228.14	+	709.068i	0.465263	+	0.268620i	−0.248992	+	0.968506i	$0.580099\pi$
$192$		0			0
$193$	746.819	+	1293.53i	0.278535	+	0.482436i	0.971021	−	0.238995i	$-0.0768179\pi$
$193$	746.819	+	1293.53i	0.278535	+	0.482436i	−0.692486	+	0.721431i	$0.743485\pi$
$194$		0			0
$195$	−2818.15	+	4259.56i	−1.03493	+	1.56427i
$196$		0			0
$197$			2384.42i			0.862351i	0.902268	+	0.431175i	$0.141901\pi$
$197$			2384.42i			0.862351i	−0.902268	+	0.431175i	$0.858099\pi$
$198$		0			0
$199$			4960.24i			1.76695i	0.468482	+	0.883473i	$0.344801\pi$
$199$			4960.24i			1.76695i	−0.468482	+	0.883473i	$0.655199\pi$
$200$		0			0
$201$	−2341.82	+	1168.15i	−0.821787	+	0.409927i
$202$		0			0
$203$	−399.014	+	2745.28i	−0.137957	+	0.949166i
$204$		0			0
$205$	−1896.28	+	3284.46i	−0.646059	+	1.11901i
$206$		0			0
$207$	3554.94	−	1510.61i	1.19365	−	0.507221i
$208$		0			0
$209$	−66.3888	+	114.989i	−0.0219723	+	0.0380571i
$210$		0			0
$211$	1973.64	+	3418.45i	0.643939	+	1.11534i	0.984545	+	0.175129i	$0.0560343\pi$
$211$	1973.64	+	3418.45i	0.643939	+	1.11534i	−0.340606	+	0.940206i	$0.610632\pi$
$212$		0			0
$213$	3897.25	+	237.607i	1.25369	+	0.0764345i
$214$		0			0
$215$	627.950			0.199190
$216$		0			0
$217$	−624.497	−	492.663i	−0.195362	−	0.154121i
$218$		0			0
$219$	−2632.33	−	160.488i	−0.812221	−	0.0495194i
$220$		0			0
$221$	8281.26	−	4781.19i	2.52062	−	1.45528i
$222$		0			0
$223$	−1397.46	−	806.825i	−0.419646	−	0.242283i	0.275280	−	0.961364i	$-0.411229\pi$
$223$	−1397.46	−	806.825i	−0.419646	−	0.242283i	−0.694926	+	0.719082i	$0.744563\pi$
$224$		0			0
$225$	−67.1750	+	89.2163i	−0.0199037	+	0.0264345i
$226$		0			0
$227$	1749.96	−	3031.01i	0.511668	−	0.886235i	−0.488240	−	0.872709i	$-0.662361\pi$
$227$	1749.96	−	3031.01i	0.511668	−	0.886235i	0.999909	−	0.0135262i	$-0.00430565\pi$
$228$		0			0
$229$	−1654.24	+	955.078i	−0.477360	+	0.275604i	−0.719316	−	0.694683i	$-0.755544\pi$
$229$	−1654.24	+	955.078i	−0.477360	+	0.275604i	0.241956	+	0.970287i	$0.422211\pi$
$230$		0			0
$231$	1504.22	+	313.115i	0.428443	+	0.0891837i
$232$		0			0
$233$			4408.26i			1.23946i	0.784814	+	0.619731i	$0.212758\pi$
$233$			4408.26i			1.23946i	−0.784814	+	0.619731i	$0.787242\pi$
$234$		0			0
$235$	178.821			0.0496383
$236$		0			0
$237$	−3307.11	−	2188.01i	−0.906413	−	0.599689i
$238$		0			0
$239$	3715.64	−	2145.23i	1.00563	−	0.580599i	0.0957187	−	0.995408i	$-0.469485\pi$
$239$	3715.64	−	2145.23i	1.00563	−	0.580599i	0.909908	+	0.414809i	$0.136152\pi$
$240$		0			0
$241$	−1413.43	−	816.047i	−0.377790	−	0.218117i	0.299066	−	0.954232i	$-0.403325\pi$
$241$	−1413.43	−	816.047i	−0.377790	−	0.218117i	−0.676856	+	0.736115i	$0.736658\pi$
$242$		0			0
$243$	1135.57	−	3613.78i	0.299780	−	0.954008i
$244$		0			0
$245$	−3614.85	−	1073.48i	−0.942630	−	0.279927i
$246$		0			0
$247$	−371.770	−	643.925i	−0.0957700	−	0.165878i
$248$		0			0
$249$	5263.02	+	3482.05i	1.33948	+	0.886209i
$250$		0			0
$251$	−3912.60			−0.983908			−0.491954	−	0.870621i	$-0.663717\pi$
$251$	−3912.60			−0.983908			−0.491954	+	0.870621i	$0.663717\pi$
$252$		0			0
$253$	−2284.06			−0.567579
$254$		0			0
$255$	−5467.29	+	2727.22i	−1.34265	+	0.669745i
$256$		0			0
$257$	1054.61	+	1826.64i	0.255971	+	0.443356i	0.965159	−	0.261664i	$-0.0842714\pi$
$257$	1054.61	+	1826.64i	0.255971	+	0.443356i	−0.709187	+	0.705020i	$0.750938\pi$
$258$		0			0
$259$	2679.03	+	6721.78i	0.642729	+	1.61263i
$260$		0			0
$261$	−3230.86	−	2432.66i	−0.766227	−	0.576927i
$262$		0			0
$263$	3827.74	+	2209.95i	0.897448	+	0.518142i	0.876371	−	0.481636i	$-0.159957\pi$
$263$	3827.74	+	2209.95i	0.897448	+	0.518142i	0.0210765	+	0.999778i	$0.493291\pi$
$264$		0			0
$265$	4239.00	−	2447.39i	0.982641	−	0.567328i
$266$		0			0
$267$	134.620	−	2208.04i	0.0308562	−	0.506105i
$268$		0			0
$269$	−4557.94			−1.03309			−0.516547	−	0.856259i	$-0.672783\pi$
$269$	−4557.94			−1.03309			−0.516547	+	0.856259i	$0.672783\pi$
$270$		0			0
$271$		−	128.189i		−	0.0287341i	−0.999897	−	0.0143671i	$-0.995427\pi$
$271$		−	128.189i		−	0.0287341i	0.999897	−	0.0143671i	$-0.00457334\pi$
$272$		0			0
$273$	−5730.23	+	6418.23i	−1.27036	+	1.42289i
$274$		0			0
$275$	57.1910	−	33.0193i	0.0125409	−	0.00724050i
$276$		0			0
$277$	1020.01	−	1766.71i	0.221251	−	0.383218i	−0.733937	−	0.679217i	$-0.762319\pi$
$277$	1020.01	−	1766.71i	0.221251	−	0.383218i	0.955188	+	0.296000i	$0.0956527\pi$
$278$		0			0
$279$	1067.27	−	453.518i	0.229017	−	0.0973170i
$280$		0			0
$281$	1506.57	+	869.820i	0.319838	+	0.184659i	0.651321	−	0.758803i	$-0.274215\pi$
$281$	1506.57	+	869.820i	0.319838	+	0.184659i	−0.331482	+	0.943462i	$0.607549\pi$
$282$		0			0
$283$	1080.52	−	623.836i	0.226961	−	0.131036i	−0.382208	−	0.924076i	$-0.624836\pi$
$283$	1080.52	−	623.836i	0.226961	−	0.131036i	0.609169	+	0.793040i	$0.291503\pi$
$284$		0			0
$285$	212.060	+	425.120i	0.0440749	+	0.0883576i
$286$		0			0
$287$	−3957.11	+	5016.01i	−0.813871	+	1.03166i
$288$		0			0
$289$	6525.95			1.32830
$290$		0			0
$291$	1637.39	−	2474.87i	0.329847	−	0.498554i
$292$		0			0
$293$	−2395.59	−	4149.28i	−0.477651	−	0.827316i	0.522021	−	0.852933i	$-0.325178\pi$
$293$	−2395.59	−	4149.28i	−0.477651	−	0.827316i	−0.999672	+	0.0256168i	$0.991845\pi$
$294$		0			0
$295$	−2125.65	+	3681.74i	−0.419526	+	0.726640i
$296$		0			0
$297$	−1453.74	+	1704.12i	−0.284022	+	0.332939i
$298$		0			0
$299$	6395.24	−	11076.9i	1.23694	−	2.14245i
$300$		0			0
$301$	1046.85	+	152.155i	0.200463	+	0.0291364i
$302$		0			0
$303$	−3062.83	−	2026.39i	−0.580709	−	0.384201i
$304$		0			0
$305$		−	5342.59i		−	1.00300i
$306$		0			0
$307$			4679.41i			0.869929i	0.900448	+	0.434965i	$0.143239\pi$
$307$			4679.41i			0.869929i	−0.900448	+	0.434965i	$0.856761\pi$
$308$		0			0
$309$	582.801	+	1168.35i	0.107296	+	0.215097i
$310$		0			0
$311$	919.164	+	1592.04i	0.167592	+	0.290277i	0.937573	−	0.347790i	$-0.113068\pi$
$311$	919.164	+	1592.04i	0.167592	+	0.290277i	−0.769981	+	0.638067i	$0.779734\pi$
$312$		0			0
$313$	5160.13	+	2979.20i	0.931846	+	0.538001i	0.887395	−	0.461010i	$-0.152513\pi$
$313$	5160.13	+	2979.20i	0.931846	+	0.538001i	0.0444510	+	0.999012i	$0.485846\pi$
$314$		0			0
$315$	3904.02	−	3870.43i	0.698307	−	0.692299i
$316$		0			0
$317$	−8986.17	−	5188.17i	−1.59216	−	0.919232i	−0.992936	−	0.118648i	$-0.962144\pi$
$317$	−8986.17	−	5188.17i	−1.59216	−	0.919232i	−0.599220	−	0.800584i	$-0.704523\pi$
$318$		0			0
$319$	1195.75	+	2071.10i	0.209872	+	0.363510i
$320$		0			0
$321$	3837.83	+	233.984i	0.667310	+	0.0406845i
$322$		0			0
$323$		−	889.458i		−	0.153222i
$324$		0			0
$325$			369.809i			0.0631179i
$326$		0			0
$327$	473.487	−	7766.17i	0.0800731	−	1.31337i
$328$		0			0
$329$	298.111	+	43.3291i	0.0499557	+	0.00726083i
$330$		0			0
$331$	−2421.65	+	4194.42i	−0.402132	+	0.696514i	−0.993983	−	0.109534i	$-0.965064\pi$
$331$	−2421.65	+	4194.42i	−0.402132	+	0.696514i	0.591851	+	0.806048i	$0.298398\pi$
$332$		0			0
$333$	−10470.9	−	1281.55i	−1.72314	−	0.210896i
$334$		0			0
$335$	2768.47	−	4795.13i	0.451516	−	0.782048i
$336$		0			0
$337$	−559.013	−	968.240i	−0.0903602	−	0.156509i	0.817302	−	0.576209i	$-0.195469\pi$
$337$	−559.013	−	968.240i	−0.0903602	−	0.156509i	−0.907663	+	0.419700i	$0.862135\pi$
$338$		0			0
$339$	2308.41	+	4627.70i	0.369839	+	0.741422i
$340$		0			0
$341$	−685.723			−0.108897
$342$		0			0
$343$	−5766.18	−	2665.49i	−0.907709	−	0.419600i
$344$		0			0
$345$	−4509.27	+	6815.64i	−0.703685	+	1.06360i
$346$		0			0
$347$	3834.85	−	2214.05i	0.593273	−	0.342526i	−0.173118	−	0.984901i	$-0.555384\pi$
$347$	3834.85	−	2214.05i	0.593273	−	0.342526i	0.766391	+	0.642375i	$0.222051\pi$
$348$		0			0
$349$	1980.13	+	1143.23i	0.303707	+	0.175345i	0.644107	−	0.764935i	$-0.277229\pi$
$349$	1980.13	+	1143.23i	0.303707	+	0.175345i	−0.340400	+	0.940281i	$0.610562\pi$
$350$		0			0
$351$	−4193.98	−	11821.6i	−0.637773	−	1.79769i
$352$		0			0
$353$	4027.88	−	6976.50i	0.607316	−	1.05190i	−0.384364	−	0.923181i	$-0.625579\pi$
$353$	4027.88	−	6976.50i	0.607316	−	1.05190i	0.991681	−	0.128721i	$-0.0410873\pi$
$354$		0			0
$355$	−7154.19	+	4130.47i	−1.06959	+	0.617529i
$356$		0			0
$357$	−9775.29	+	3221.77i	−1.44920	+	0.477631i
$358$		0			0
$359$		−	5537.25i		−	0.814053i	−0.913416	−	0.407027i	$-0.866566\pi$
$359$		−	5537.25i		−	0.814053i	0.913416	−	0.407027i	$-0.133434\pi$
$360$		0			0
$361$	6789.84			0.989917
$362$		0			0
$363$	−5003.57	+	2495.90i	−0.723469	+	0.360884i
$364$		0			0
$365$	4832.18	−	2789.86i	0.692953	−	0.400076i
$366$		0			0
$367$	4668.87	+	2695.58i	0.664069	+	0.383400i	0.793825	−	0.608146i	$-0.208086\pi$
$367$	4668.87	+	2695.58i	0.664069	+	0.383400i	−0.129757	+	0.991546i	$0.541420\pi$
$368$		0			0
$369$	−3642.70	−	8572.41i	−0.513906	−	1.20938i
$370$		0			0
$371$	7659.81	−	3052.89i	1.07191	−	0.427219i
$372$		0			0
$373$	1062.08	+	1839.58i	0.147433	+	0.255362i	0.930278	−	0.366855i	$-0.119566\pi$
$373$	1062.08	+	1839.58i	0.147433	+	0.255362i	−0.782845	+	0.622217i	$0.786232\pi$
$374$		0			0
$375$	448.925	−	7363.30i	0.0618196	−	1.01397i
$376$		0			0
$377$	−13392.2			−1.82953
$378$		0			0
$379$	−5358.80			−0.726288			−0.363144	−	0.931733i	$-0.618297\pi$
$379$	−5358.80			−0.726288			−0.363144	+	0.931733i	$0.618297\pi$
$380$		0			0
$381$	780.855	−	12807.6i	0.104998	−	1.72219i
$382$		0			0
$383$	2729.23	+	4727.16i	0.364118	+	0.630670i	0.988634	−	0.150341i	$-0.0480373\pi$
$383$	2729.23	+	4727.16i	0.364118	+	0.630670i	−0.624517	+	0.781012i	$0.714704\pi$
$384$		0			0
$385$	−3019.77	+	1203.56i	−0.399745	+	0.159322i
$386$		0			0
$387$	−927.641	+	1232.02i	−0.121847	+	0.161827i
$388$		0			0
$389$	1416.25	+	817.670i	0.184593	+	0.106575i	0.589449	−	0.807806i	$-0.299345\pi$
$389$	1416.25	+	817.670i	0.184593	+	0.106575i	−0.404856	+	0.914380i	$0.632678\pi$
$390$		0			0
$391$	13250.7	−	7650.29i	1.71385	−	0.989493i
$392$		0			0
$393$	7158.66	−	3570.91i	0.918846	−	0.458342i
$394$		0			0
$395$	8389.82			1.06870
$396$		0			0
$397$		−	7694.41i		−	0.972724i	−0.873757	−	0.486362i	$-0.838324\pi$
$397$		−	7694.41i		−	0.972724i	0.873757	−	0.486362i	$-0.161676\pi$
$398$		0			0
$399$	250.515	+	760.097i	0.0314322	+	0.0953695i
$400$		0			0
$401$	4800.46	−	2771.55i	0.597815	−	0.345148i	−0.170367	−	0.985381i	$-0.554495\pi$
$401$	4800.46	−	2771.55i	0.597815	−	0.345148i	0.768181	+	0.640232i	$0.221162\pi$
$402$		0			0
$403$	1919.99	−	3325.52i	0.237324	−	0.411057i
$404$		0			0
$405$	2215.07	+	7702.30i	0.271772	+	0.945013i
$406$		0			0
$407$	5402.24	+	3118.98i	0.657934	+	0.379858i
$408$		0			0
$409$	6361.70	−	3672.93i	0.769109	−	0.444045i	−0.0634474	−	0.997985i	$-0.520210\pi$
$409$	6361.70	−	3672.93i	0.769109	−	0.444045i	0.832557	+	0.553940i	$0.186876\pi$
$410$		0			0
$411$	−4700.46	+	7104.62i	−0.564128	+	0.852664i
$412$		0			0
$413$	−4435.75	+	5622.74i	−0.528497	+	0.669920i
$414$		0			0
$415$	−13351.8			−1.57931
$416$		0			0
$417$	2409.15	+	4829.67i	0.282918	+	0.567170i
$418$		0			0
$419$	1717.45	+	2974.72i	0.200246	+	0.346836i	0.948608	−	0.316455i	$-0.102492\pi$
$419$	1717.45	+	2974.72i	0.200246	+	0.346836i	−0.748362	+	0.663291i	$0.769159\pi$
$420$		0			0
$421$	−7241.13	+	12542.0i	−0.838269	+	1.45192i	0.0530719	+	0.998591i	$0.483099\pi$
$421$	−7241.13	+	12542.0i	−0.838269	+	1.45192i	−0.891341	+	0.453334i	$0.850235\pi$
$422$		0			0
$423$	−264.164	+	350.841i	−0.0303643	+	0.0403274i
$424$		0			0
$425$	−221.191	+	383.115i	−0.0252455	+	0.0437266i
$426$		0			0
$427$	1294.53	−	8906.59i	0.146714	−	1.00942i
$428$		0			0
$429$	−451.380	+	7403.57i	−0.0507991	+	0.833212i
$430$		0			0
$431$			13632.5i			1.52356i	0.647839	+	0.761778i	$0.275673\pi$
$431$			13632.5i			1.52356i	−0.647839	+	0.761778i	$0.724327\pi$
$432$		0			0
$433$		−	6735.48i		−	0.747544i	−0.927521	−	0.373772i	$-0.878064\pi$
$433$		−	6735.48i		−	0.747544i	0.927521	−	0.373772i	$-0.121936\pi$
$434$		0			0
$435$	8540.89	+	520.720i	0.941389	+	0.0573945i
$436$		0			0
$437$	−594.863	−	1030.33i	−0.0651170	−	0.112786i
$438$		0			0
$439$	9181.17	+	5300.75i	0.998162	+	0.576289i	0.907704	−	0.419611i	$-0.137834\pi$
$439$	9181.17	+	5300.75i	0.998162	+	0.576289i	0.0904581	+	0.995900i	$0.471167\pi$
$440$		0			0
$441$	7446.18	−	5506.40i	0.804037	−	0.594580i
$442$		0			0
$443$	−3111.86	−	1796.64i	−0.333745	−	0.192688i	0.323757	−	0.946140i	$-0.395054\pi$
$443$	−3111.86	−	1796.64i	−0.333745	−	0.192688i	−0.657503	+	0.753452i	$0.728387\pi$
$444$		0			0
$445$	2340.18	+	4053.31i	0.249293	+	0.431788i
$446$		0			0
$447$	4079.39	+	8178.02i	0.431652	+	0.865340i
$448$		0			0
$449$		−	8675.98i		−	0.911904i	−0.890004	−	0.455952i	$-0.849299\pi$
$449$		−	8675.98i		−	0.911904i	0.890004	−	0.455952i	$-0.150701\pi$
$450$		0			0
$451$			5507.79i			0.575059i
$452$		0			0
$453$	−3054.29	−	2020.74i	−0.316784	−	0.209587i
$454$		0			0
$455$	2618.36	−	18014.7i	0.269782	−	1.85614i
$456$		0			0
$457$	−1466.35	+	2539.79i	−0.150094	+	0.259970i	−0.931262	−	0.364351i	$-0.881291\pi$
$457$	−1466.35	+	2539.79i	−0.150094	+	0.259970i	0.781168	+	0.624321i	$0.214624\pi$
$458$		0			0
$459$	2725.87	−	14755.4i	0.277196	−	1.50049i
$460$		0			0
$461$	3015.81	−	5223.53i	0.304686	−	0.527731i	−0.672506	−	0.740092i	$-0.734782\pi$
$461$	3015.81	−	5223.53i	0.304686	−	0.527731i	0.977191	+	0.212361i	$0.0681152\pi$
$462$		0			0
$463$	295.638	+	512.060i	0.0296748	+	0.0513983i	0.880481	−	0.474081i	$-0.157219\pi$
$463$	295.638	+	512.060i	0.0296748	+	0.0513983i	−0.850807	+	0.525479i	$0.823886\pi$
$464$		0			0
$465$	−1353.78	+	2046.20i	−0.135011	+	0.204065i
$466$		0			0
$467$	16674.6			1.65227			0.826134	−	0.563473i	$-0.190535\pi$
$467$	16674.6			1.65227			0.826134	+	0.563473i	$0.190535\pi$
$468$		0			0
$469$	5777.18	−	7323.12i	0.568796	−	0.721002i
$470$		0			0
$471$	−1550.83	−	3108.98i	−0.151717	−	0.304149i
$472$		0			0
$473$	789.769	−	455.973i	0.0767730	−	0.0443249i
$474$		0			0
$475$	29.7898	+	17.1992i	0.00287758	+	0.00166137i
$476$		0			0
$477$	−1460.39	+	11932.2i	−0.140181	+	1.14536i
$478$		0			0
$479$	−8608.73	+	14910.8i	−0.821175	+	1.42232i	0.0836331	+	0.996497i	$0.473348\pi$
$479$	−8608.73	+	14910.8i	−0.821175	+	1.42232i	−0.904808	+	0.425820i	$0.859986\pi$
$480$		0			0
$481$	−30252.0	+	17466.0i	−2.86772	+	1.65568i
$482$		0			0
$483$	−9168.83	+	10269.7i	−0.863761	+	0.967468i
$484$		0			0
$485$			6278.50i			0.587818i
$486$		0			0
$487$	8745.94			0.813792			0.406896	−	0.913475i	$-0.366611\pi$
$487$	8745.94			0.813792			0.406896	+	0.913475i	$0.366611\pi$
$488$		0			0
$489$	−1241.51	+	20363.3i	−0.114812	+	1.88315i
$490$		0			0
$491$	653.319	−	377.194i	0.0600486	−	0.0346691i	−0.469675	−	0.882839i	$-0.655629\pi$
$491$	653.319	−	377.194i	0.0600486	−	0.0346691i	0.529724	+	0.848170i	$0.322296\pi$
$492$		0			0
$493$	−13874.0	−	8010.17i	−1.26745	−	0.731765i
$494$		0			0
$495$	575.737	−	4704.09i	0.0522777	−	0.427138i
$496$		0			0
$497$	−12927.5	+	5152.39i	−1.16676	+	0.465022i
$498$		0			0
$499$	−2480.24	−	4295.90i	−0.222506	−	0.385392i	0.733062	−	0.680162i	$-0.238090\pi$
$499$	−2480.24	−	4295.90i	−0.222506	−	0.385392i	−0.955568	+	0.294769i	$0.904757\pi$
$500$		0			0
$501$	−8990.79	+	4484.82i	−0.801754	+	0.399934i
$502$		0			0
$503$	−5299.83			−0.469797			−0.234898	−	0.972020i	$-0.575476\pi$
$503$	−5299.83			−0.469797			−0.234898	+	0.972020i	$0.575476\pi$
$504$		0			0
$505$	7770.09			0.684682
$506$		0			0
$507$	−25120.1	−	16619.6i	−2.20044	−	1.45582i
$508$		0			0
$509$	9344.81	+	16185.7i	0.813755	+	1.40947i	0.910218	+	0.414129i	$0.135914\pi$
$509$	9344.81	+	16185.7i	0.813755	+	1.40947i	−0.0964627	+	0.995337i	$0.530753\pi$
$510$		0			0
$511$	8731.68	−	3480.09i	0.755903	−	0.301273i
$512$		0			0
$513$	−1147.34	−	211.956i	−0.0987449	−	0.0182418i
$514$		0			0
$515$	−2392.33	−	1381.21i	−0.204696	−	0.118181i
$516$		0			0
$517$	224.902	−	129.847i	0.0191319	−	0.0110458i
$518$		0			0
$519$	7367.20	+	4874.19i	0.623091	+	0.412241i
$520$		0			0
$521$	−8964.93			−0.753859			−0.376930	−	0.926242i	$-0.623020\pi$
$521$	−8964.93			−0.753859			−0.376930	+	0.926242i	$0.623020\pi$
$522$		0			0
$523$			20614.1i			1.72350i	0.507330	+	0.861752i	$0.330633\pi$
$523$			20614.1i			1.72350i	−0.507330	+	0.861752i	$0.669367\pi$
$524$		0			0
$525$	81.1178	−	389.693i	0.00674337	−	0.0323955i
$526$		0			0
$527$	3978.14	−	2296.78i	0.328825	−	0.189847i
$528$		0			0
$529$	4149.41	−	7186.99i	0.341038	−	0.590695i
$530$		0			0
$531$	−4083.31	−	9609.31i	−0.333711	−	0.785327i
$532$		0			0
$533$	−26710.9	−	15421.5i	−2.17069	−	1.25325i
$534$		0			0
$535$	−7045.11	+	4067.50i	−0.569321	+	0.328698i
$536$		0			0
$537$	6094.94	+	371.595i	0.489788	+	0.0298613i
$538$		0			0
$539$	−5325.86	+	1274.74i	−0.425605	+	0.101868i
$540$		0			0
$541$	9376.65			0.745164			0.372582	−	0.927999i	$-0.378473\pi$
$541$	9376.65			0.745164			0.372582	+	0.927999i	$0.378473\pi$
$542$		0			0
$543$	−18188.6	−	1108.92i	−1.43747	−	0.0876395i
$544$		0			0
$545$	8230.93	+	14256.4i	0.646925	+	1.12051i
$546$		0			0
$547$	1172.25	−	2030.40i	0.0916305	−	0.158709i	−0.816567	−	0.577251i	$-0.804125\pi$
$547$	1172.25	−	2030.40i	0.0916305	−	0.158709i	0.908197	+	0.418542i	$0.137459\pi$
$548$		0			0
$549$	10482.0	+	7892.36i	0.814864	+	0.613548i
$550$		0			0
$551$	−622.847	+	1078.80i	−0.0481564	+	0.0834093i
$552$		0			0
$553$	13986.6	+	2032.89i	1.07553	+	0.156324i
$554$		0			0
$555$	19972.4	−	9962.70i	1.52753	−	0.761969i
$556$		0			0
$557$			15368.4i			1.16908i	0.811364	+	0.584541i	$0.198725\pi$
$557$			15368.4i			1.16908i	−0.811364	+	0.584541i	$0.801275\pi$
$558$		0			0
$559$			5106.81i			0.386395i
$560$		0			0
$561$	−4895.87	+	7399.97i	−0.368456	+	0.556911i
$562$		0			0
$563$	−6447.73	−	11167.8i	−0.482664	−	0.835998i	0.517138	−	0.855902i	$-0.326997\pi$
$563$	−6447.73	−	11167.8i	−0.482664	−	0.835998i	−0.999802	+	0.0199041i	$0.993664\pi$
$564$		0			0
$565$	−9475.73	−	5470.82i	−0.705570	−	0.407361i
$566$		0			0
$567$	1826.42	+	13377.2i	0.135278	+	0.990808i
$568$		0			0
$569$	20989.2	+	12118.1i	1.54642	+	0.892824i	0.998411	+	0.0563492i	$0.0179460\pi$
$569$	20989.2	+	12118.1i	1.54642	+	0.892824i	0.548005	+	0.836475i	$0.315387\pi$
$570$		0			0
$571$	−3678.38	−	6371.14i	−0.269589	−	0.466942i	0.699167	−	0.714959i	$-0.253555\pi$
$571$	−3678.38	−	6371.14i	−0.269589	−	0.466942i	−0.968756	+	0.248017i	$0.920221\pi$
$572$		0			0
$573$	4065.95	−	6145.57i	0.296435	−	0.448054i
$574$		0			0
$575$			591.724i			0.0429158i
$576$		0			0
$577$			11928.2i			0.860617i	0.902682	+	0.430308i	$0.141595\pi$
$577$			11928.2i			0.860617i	−0.902682	+	0.430308i	$0.858405\pi$
$578$		0			0
$579$	6945.07	−	3464.37i	0.498493	−	0.248660i
$580$		0			0
$581$	−22258.6	−	3235.19i	−1.58940	−	0.231013i
$582$		0			0
$583$	3554.24	−	6156.13i	0.252490	−	0.437326i
$584$		0			0
$585$	21201.2	+	15963.3i	1.49839	+	1.12821i
$586$		0			0
$587$	−2638.36	+	4569.77i	−0.185514	+	0.321320i	−0.943750	−	0.330661i	$-0.892728\pi$
$587$	−2638.36	+	4569.77i	−0.185514	+	0.321320i	0.758236	+	0.651981i	$0.226062\pi$
$588$		0			0
$589$	−178.591	−	309.328i	−0.0124935	−	0.0216395i
$590$		0			0
$591$	12366.9	+	753.981i	0.860752	+	0.0524782i
$592$		0			0
$593$	5290.53			0.366367			0.183184	−	0.983079i	$-0.441360\pi$
$593$	5290.53			0.366367			0.183184	+	0.983079i	$0.441360\pi$
$594$		0			0
$595$	13487.6	−	17096.8i	0.929308	−	1.17798i
$596$		0			0
$597$	25726.4	+	1568.48i	1.76367	+	0.107527i
$598$		0			0
$599$	−8568.78	+	4947.19i	−0.584492	+	0.337457i	−0.762917	−	0.646497i	$-0.776233\pi$
$599$	−8568.78	+	4947.19i	−0.584492	+	0.337457i	0.178424	+	0.983954i	$0.442900\pi$
$600$		0			0
$601$	2305.57	+	1331.12i	0.156483	+	0.0903454i	0.576197	−	0.817311i	$-0.304536\pi$
$601$	2305.57	+	1331.12i	0.156483	+	0.0903454i	−0.419714	+	0.907656i	$0.637870\pi$
$602$		0			0
$603$	5318.15	+	12515.3i	0.359157	+	0.845210i
$604$		0			0
$605$	5915.17	−	10245.4i	0.397497	−	0.688485i
$606$		0			0
$607$	−9797.65	+	5656.68i	−0.655147	+	0.378249i	−0.790425	−	0.612558i	$-0.790141\pi$
$607$	−9797.65	+	5656.68i	−0.655147	+	0.378249i	0.135278	+	0.990808i	$0.456807\pi$
$608$		0			0
$609$	14112.3	+	2937.58i	0.939012	+	0.195463i
$610$		0			0
$611$			1454.26i			0.0962901i
$612$		0			0
$613$	−23984.5			−1.58030			−0.790151	−	0.612912i	$-0.789998\pi$
$613$	−23984.5			−1.58030			−0.790151	+	0.612912i	$0.789998\pi$
$614$		0			0
$615$	16435.3	+	10873.7i	1.07762	+	0.712958i
$616$		0			0
$617$	−14063.1	+	8119.31i	−0.917597	+	0.529775i	−0.882868	−	0.469622i	$-0.844390\pi$
$617$	−14063.1	+	8119.31i	−0.917597	+	0.529775i	−0.0347291	+	0.999397i	$0.511057\pi$
$618$		0			0
$619$	−14971.6	−	8643.88i	−0.972150	−	0.561271i	−0.0722590	−	0.997386i	$-0.523021\pi$
$619$	−14971.6	−	8643.88i	−0.972150	−	0.561271i	−0.899891	+	0.436115i	$0.856354\pi$
$620$		0			0
$621$	−6710.71	−	18915.5i	−0.433642	−	1.22231i
$622$		0			0
$623$	2919.16	+	7324.28i	0.187727	+	0.471013i
$624$		0			0
$625$	7545.43	+	13069.1i	0.482908	+	0.836421i
$626$		0			0
$627$	575.399	+	380.688i	0.0366495	+	0.0242475i
$628$		0			0
$629$	−41787.2			−2.64891
$630$		0			0
$631$	348.827			0.0220073			0.0110036	−	0.999939i	$-0.496497\pi$
$631$	348.827			0.0220073			0.0110036	+	0.999939i	$0.496497\pi$
$632$		0			0
$633$	18354.0	−	9155.39i	1.15246	−	0.574872i
$634$		0			0
$635$	13574.1	+	23511.0i	0.848302	+	1.46930i
$636$		0			0
$637$	8730.10	−	29397.8i	0.543013	−	1.82854i
$638$		0			0
$639$	2464.71	−	20138.0i	0.152586	−	1.24671i
$640$		0			0
$641$	−14508.8	−	8376.64i	−0.894013	−	0.516158i	−0.0187597	−	0.999824i	$-0.505972\pi$
$641$	−14508.8	−	8376.64i	−0.894013	−	0.516158i	−0.875253	+	0.483666i	$0.839305\pi$
$642$		0			0
$643$	10660.5	−	6154.87i	0.653827	−	0.377487i	−0.136094	−	0.990696i	$-0.543455\pi$
$643$	10660.5	−	6154.87i	0.653827	−	0.377487i	0.789921	+	0.613209i	$0.210122\pi$
$644$		0			0
$645$	198.565	−	3256.88i	0.0121217	−	0.198821i
$646$		0			0
$647$	32197.6			1.95644			0.978220	−	0.207570i	$-0.0665555\pi$
$647$	32197.6			1.95644			0.978220	+	0.207570i	$0.0665555\pi$
$648$		0			0
$649$			6174.00i			0.373422i
$650$		0			0
$651$	−2752.68	+	3083.18i	−0.165724	+	0.185621i
$652$		0			0
$653$	−15436.6	+	8912.32i	−0.925085	+	0.534098i	−0.885254	−	0.465108i	$-0.846015\pi$
$653$	−15436.6	+	8912.32i	−0.925085	+	0.534098i	−0.0398315	+	0.999206i	$0.512682\pi$
$654$		0			0
$655$	−8462.89	+	14658.2i	−0.504843	+	0.874415i
$656$		0			0
$657$	−1664.74	+	13601.9i	−0.0988552	+	0.807702i
$658$		0			0
$659$	17782.9	+	10267.0i	1.05117	+	0.606895i	0.922978	−	0.384853i	$-0.125748\pi$
$659$	17782.9	+	10267.0i	1.05117	+	0.606895i	0.128196	+	0.991749i	$0.459081\pi$
$660$		0			0
$661$	8819.60	−	5092.00i	0.518975	−	0.299630i	−0.217540	−	0.976051i	$-0.569803\pi$
$661$	8819.60	−	5092.00i	0.518975	−	0.299630i	0.736515	+	0.676421i	$0.236470\pi$
$662$		0			0
$663$	−22179.1	−	44462.8i	−1.29919	−	2.60451i
$664$		0			0
$665$	−1329.40	−	1048.75i	−0.0775214	−	0.0611563i
$666$		0			0
$667$	−21428.6			−1.24395
$668$		0			0
$669$	−4626.51	+	6992.84i	−0.267371	+	0.404124i
$670$		0			0
$671$	−3879.42	−	6719.35i	−0.223194	−	0.386584i
$672$		0			0
$673$	8773.58	−	15196.3i	0.502521	−	0.870392i	−0.497475	−	0.867478i	$-0.665739\pi$
$673$	8773.58	−	15196.3i	0.502521	−	0.870392i	0.999996	−	0.00291344i	$-0.000927377\pi$
$674$		0			0
$675$	441.481	+	376.616i	0.0251742	+	0.0214755i
$676$		0			0
$677$	4832.83	−	8370.70i	0.274358	−	0.475203i	−0.695615	−	0.718415i	$-0.744868\pi$
$677$	4832.83	−	8370.70i	0.274358	−	0.475203i	0.969973	+	0.243212i	$0.0782012\pi$
$678$		0			0
$679$	−1521.31	+	10466.8i	−0.0859829	+	0.591576i
$680$		0			0
$681$	−15167.1	−	10034.6i	−0.853455	−	0.564652i
$682$		0			0
$683$		−	4376.97i		−	0.245213i	−0.992455	−	0.122606i	$-0.960875\pi$
$683$		−	4376.97i		−	0.245213i	0.992455	−	0.122606i	$-0.0391253\pi$
$684$		0			0
$685$		−	18023.7i		−	1.00533i
$686$		0			0
$687$	4430.44	+	8881.77i	0.246043	+	0.493247i
$688$		0			0
$689$	19903.4	+	34473.7i	1.10052	+	1.90616i
$690$		0			0
$691$	−17526.8	−	10119.1i	−0.964905	−	0.557088i	−0.0672260	−	0.997738i	$-0.521415\pi$
$691$	−17526.8	−	10119.1i	−0.964905	−	0.557088i	−0.897679	+	0.440649i	$0.854748\pi$
$692$		0			0
$693$	2099.63	−	7702.65i	0.115091	−	0.422221i
$694$		0			0
$695$	−9889.29	−	5709.58i	−0.539744	−	0.311621i
$696$		0			0
$697$	−18447.9	−	31952.8i	−1.00253	−	1.73644i
$698$		0			0
$699$	22863.5	+	1393.94i	1.23717	+	0.0754273i
$700$		0			0
$701$		−	33130.3i		−	1.78504i	−0.451004	−	0.892522i	$-0.648934\pi$
$701$		−	33130.3i		−	1.78504i	0.451004	−	0.892522i	$-0.351066\pi$
$702$		0			0
$703$			3249.25i			0.174321i
$704$		0			0
$705$	56.5453	−	927.460i	0.00302073	−	0.0495463i
$706$		0			0
$707$	12953.5	+	1882.73i	0.689059	+	0.100152i
$708$		0			0
$709$	17606.6	−	30495.5i	0.932623	−	1.61535i	0.153804	−	0.988101i	$-0.450847\pi$
$709$	17606.6	−	30495.5i	0.932623	−	1.61535i	0.778819	−	0.627249i	$-0.215819\pi$
$710$		0			0
$711$	−12393.9	+	16460.5i	−0.653737	+	0.868240i
$712$		0			0
$713$	3072.14	−	5321.10i	0.161364	−	0.279491i
$714$		0			0
$715$	−7846.63	−	13590.8i	−0.410416	−	0.710861i
$716$		0			0
$717$	−9951.34	−	19949.6i	−0.518326	−	1.03910i
$718$		0			0
$719$	21789.0			1.13017			0.565086	−	0.825032i	$-0.308843\pi$
$719$	21789.0			1.13017			0.565086	+	0.825032i	$0.308843\pi$
$720$		0			0
$721$	−3653.55	−	2882.28i	−0.188718	−	0.148879i
$722$		0			0
$723$	−4679.39	+	7072.77i	−0.240703	+	0.363816i
$724$		0			0
$725$	536.555	−	309.780i	0.0274857	−	0.0158689i
$726$		0			0
$727$	685.180	+	395.589i	0.0349545	+	0.0201810i	0.517375	−	0.855759i	$-0.326909\pi$
$727$	685.180	+	395.589i	0.0349545	+	0.0201810i	−0.482421	+	0.875940i	$0.660242\pi$
$728$		0			0
$729$	−18383.9	−	7032.36i	−0.933997	−	0.357281i
$730$		0			0
$731$	−3054.50	+	5290.55i	−0.154548	+	0.267685i
$732$		0			0
$733$	195.132	−	112.659i	0.00983269	−	0.00567691i	−0.495076	−	0.868850i	$-0.664860\pi$
$733$	195.132	−	112.659i	0.00983269	−	0.00567691i	0.504908	+	0.863173i	$0.331526\pi$
$734$		0			0
$735$	−6710.69	+	18409.1i	−0.336772	+	0.923848i
$736$		0			0
$737$		−	8041.08i		−	0.401896i
$738$		0			0
$739$	−2564.36			−0.127648			−0.0638238	−	0.997961i	$-0.520330\pi$
$739$	−2564.36			−0.127648			−0.0638238	+	0.997961i	$0.520330\pi$
$740$		0			0
$741$	−3457.29	+	1724.58i	−0.171399	+	0.0854980i
$742$		0			0
$743$	−30419.9	+	17563.0i	−1.50202	+	0.867190i	−0.502020	+	0.864856i	$0.667410\pi$
$743$	−30419.9	+	17563.0i	−1.50202	+	0.867190i	−0.999997	+	0.00233421i	$0.999257\pi$
$744$		0			0
$745$	−16745.4	−	9667.97i	−0.823496	−	0.475446i
$746$		0			0
$747$	19724.0	−	26195.7i	0.966080	−	1.28307i
$748$		0			0
$749$	−12730.4	+	5073.83i	−0.621041	+	0.247522i
$750$		0			0
$751$	−5213.77	−	9030.52i	−0.253333	−	0.438786i	0.711108	−	0.703083i	$-0.248194\pi$
$751$	−5213.77	−	9030.52i	−0.253333	−	0.438786i	−0.964441	+	0.264297i	$0.914860\pi$
$752$		0			0
$753$	−1237.21	+	20292.8i	−0.0598756	+	0.982084i
$754$		0			0
$755$	7748.45			0.373503
$756$		0			0
$757$	−14031.2			−0.673677			−0.336838	−	0.941562i	$-0.609358\pi$
$757$	−14031.2			−0.673677			−0.336838	+	0.941562i	$0.609358\pi$
$758$		0			0
$759$	−722.245	+	11846.3i	−0.0345399	+	0.566527i
$760$		0			0
$761$	5435.63	+	9414.79i	0.258924	+	0.448470i	0.965954	−	0.258714i	$-0.0832986\pi$
$761$	5435.63	+	9414.79i	0.258924	+	0.448470i	−0.707030	+	0.707184i	$0.749965\pi$
$762$		0			0
$763$	10267.3	+	25761.1i	0.487159	+	1.22230i
$764$		0			0
$765$	12415.9	+	29218.6i	0.586797	+	1.38092i
$766$		0			0
$767$	−29941.7	−	17286.9i	−1.40956	−	0.813811i
$768$		0			0
$769$	17962.0	−	10370.3i	0.842295	−	0.486299i	−0.0157486	−	0.999876i	$-0.505013\pi$
$769$	17962.0	−	10370.3i	0.842295	−	0.486299i	0.858044	+	0.513577i	$0.171680\pi$
$770$		0			0
$771$	9807.36	−	4892.15i	0.458111	−	0.228517i
$772$		0			0
$773$	7445.62			0.346443			0.173221	−	0.984883i	$-0.444582\pi$
$773$	7445.62			0.346443			0.173221	+	0.984883i	$0.444582\pi$
$774$		0			0
$775$			177.648i			0.00823396i
$776$		0			0
$777$	35709.8	−	11769.3i	1.64875	−	0.543401i
$778$		0			0
$779$	−2484.55	+	1434.46i	−0.114272	+	0.0659752i
$780$		0			0
$781$	−5998.52	+	10389.7i	−0.274832	+	0.476023i
$782$		0			0
$783$	−13638.7	+	15987.7i	−0.622487	+	0.729698i
$784$		0			0
$785$	6365.97	+	3675.40i	0.289441	+	0.167109i
$786$		0			0
$787$	−14417.6	+	8323.99i	−0.653025	+	0.377024i	−0.789614	−	0.613603i	$-0.789719\pi$
$787$	−14417.6	+	8323.99i	−0.653025	+	0.377024i	0.136589	+	0.990628i	$0.456386\pi$
$788$		0			0
$789$	12672.3	−	19153.9i	0.571796	−	0.864253i
$790$		0			0
$791$	−14471.3	−	11416.4i	−0.650494	−	0.513172i
$792$		0			0
$793$	43448.7			1.94566
$794$		0			0
$795$	−11353.0	−	22759.6i	−0.506478	−	1.01534i
$796$		0			0
$797$	−14318.8	−	24800.9i	−0.636383	−	1.10225i	−0.986220	−	0.165437i	$-0.947097\pi$
$797$	−14318.8	−	24800.9i	−0.636383	−	1.10225i	0.349837	−	0.936810i	$-0.386237\pi$
$798$		0			0
$799$	−869.829	+	1506.59i	−0.0385136	+	0.0667075i
$800$		0			0
$801$	−11409.5	−	1396.42i	−0.503290	−	0.0615980i
$802$		0			0
$803$	4051.60	−	7017.58i	0.178055	−	0.308400i
$804$		0			0
$805$	4189.59	−	28825.1i	0.183433	−	1.26205i
$806$		0			0
$807$	−1441.27	+	23639.8i	−0.0628688	+	1.03118i
$808$		0			0
$809$			49.4260i			0.00214799i	0.999999	+	0.00107400i	$0.000341863\pi$
$809$			49.4260i			0.00214799i	−0.999999	+	0.00107400i	$0.999658\pi$
$810$		0			0
$811$		−	37292.7i		−	1.61470i	−0.590072	−	0.807350i	$-0.700901\pi$
$811$		−	37292.7i		−	1.61470i	0.590072	−	0.807350i	$-0.299099\pi$
$812$		0			0
$813$	−664.857	−	40.5349i	−0.0286809	−	0.00174861i
$814$		0			0
$815$	−21581.9	−	37380.9i	−0.927584	−	1.60662i
$816$		0			0
$817$	411.377	+	237.509i	0.0176160	+	0.0101706i
$818$		0			0
$819$	31476.3	+	31749.5i	1.34294	+	1.35460i
$820$		0			0
$821$	−699.390	−	403.793i	−0.0297307	−	0.0171650i	0.485061	−	0.874480i	$-0.338797\pi$
$821$	−699.390	−	403.793i	−0.0297307	−	0.0171650i	−0.514792	+	0.857315i	$0.672131\pi$
$822$		0			0
$823$	10340.2	+	17909.8i	0.437957	+	0.758563i	0.997532	−	0.0702164i	$-0.0223690\pi$
$823$	10340.2	+	17909.8i	0.437957	+	0.758563i	−0.559575	+	0.828780i	$0.689036\pi$
$824$		0			0
$825$	−153.171	−	307.064i	−0.00646390	−	0.0129583i
$826$		0			0
$827$			44485.5i			1.87051i	0.353976	+	0.935255i	$0.384830\pi$
$827$			44485.5i			1.87051i	−0.353976	+	0.935255i	$0.615170\pi$
$828$		0			0
$829$			7797.19i			0.326668i	0.986571	+	0.163334i	$0.0522248\pi$
$829$			7797.19i			0.326668i	−0.986571	+	0.163334i	$0.947775\pi$
$830$		0			0
$831$	−8840.54	−	5848.96i	−0.369043	−	0.244161i
$832$		0			0
$833$	26627.7	−	25233.8i	1.10756	−	1.04958i
$834$		0			0
$835$	10628.8	−	18409.7i	0.440509	−	0.762985i
$836$		0			0
$837$	−2014.70	−	5678.83i	−0.0831998	−	0.234515i
$838$		0			0
$839$	−14737.7	+	25526.4i	−0.606439	+	1.05038i	0.385384	+	0.922756i	$0.374069\pi$
$839$	−14737.7	+	25526.4i	−0.606439	+	1.05038i	−0.991822	+	0.127626i	$0.959264\pi$
$840$		0			0
$841$	−976.184	−	1690.80i	−0.0400256	−	0.0693263i
$842$		0			0
$843$	4987.74	−	7538.83i	0.203780	−	0.308008i
$844$		0			0
$845$	63727.2			2.59442
$846$		0			0
$847$	12343.6	−	15646.7i	0.500746	−	0.634743i
$848$		0			0
$849$	−2893.87	−	5801.38i	−0.116981	−	0.234515i
$850$		0			0
$851$	−48405.6	+	27947.0i	−1.94985	+	1.12575i
$852$		0			0
$853$	−8459.43	−	4884.05i	−0.339561	−	0.196045i	0.320517	−	0.947243i	$-0.396143\pi$
$853$	−8459.43	−	4884.05i	−0.339561	−	0.196045i	−0.660078	+	0.751197i	$0.729477\pi$
$854$		0			0
$855$	2271.95	−	965.426i	0.0908761	−	0.0386162i
$856$		0			0
$857$	−11406.2	+	19756.0i	−0.454641	+	0.787461i	−0.998667	−	0.0516072i	$-0.983566\pi$
$857$	−11406.2	+	19756.0i	−0.454641	+	0.787461i	0.544027	+	0.839068i	$0.316899\pi$
$858$		0			0
$859$	−30803.4	+	17784.3i	−1.22351	+	0.706396i	−0.965665	−	0.259790i	$-0.916347\pi$
$859$	−30803.4	+	17784.3i	−1.22351	+	0.706396i	−0.257848	+	0.966186i	$0.583013\pi$
$860$		0			0
$861$	24764.4	+	22109.8i	0.980218	+	0.875144i
$862$		0			0
$863$		−	34594.9i		−	1.36457i	−0.731087	−	0.682285i	$-0.760986\pi$
$863$		−	34594.9i		−	1.36457i	0.731087	−	0.682285i	$-0.239014\pi$
$864$		0			0
$865$	−18689.9			−0.734653
$866$		0			0
$867$	2063.58	−	33847.0i	0.0808337	−	1.32584i
$868$		0			0
$869$	10551.8	−	6092.10i	0.411906	−	0.237814i
$870$		0			0
$871$	38996.5	+	22514.6i	1.51704	+	0.875865i
$872$		0			0
$873$	−12318.2	−	9274.93i	−0.477558	−	0.359575i
$874$		0			0
$875$	9734.71	+	24424.7i	0.376106	+	0.943664i
$876$		0			0
$877$	11651.8	+	20181.6i	0.448637	+	0.777063i	0.998298	−	0.0583256i	$-0.0185762\pi$
$877$	11651.8	+	20181.6i	0.448637	+	0.777063i	−0.549660	+	0.835388i	$0.685243\pi$
$878$		0			0
$879$	−22277.9	+	11112.7i	−0.854850	+	0.426420i
$880$		0			0
$881$	8387.34			0.320745			0.160373	−	0.987057i	$-0.448730\pi$
$881$	8387.34			0.320745			0.160373	+	0.987057i	$0.448730\pi$
$882$		0			0
$883$	4287.17			0.163391			0.0816957	−	0.996657i	$-0.473966\pi$
$883$	4287.17			0.163391			0.0816957	+	0.996657i	$0.473966\pi$
$884$		0			0
$885$	18423.2	+	12188.9i	0.699763	+	0.462968i
$886$		0			0
$887$	−6730.67	−	11657.9i	−0.254784	−	0.441299i	0.710053	−	0.704149i	$-0.248671\pi$
$887$	−6730.67	−	11657.9i	−0.254784	−	0.441299i	−0.964837	+	0.262849i	$0.915338\pi$
$888$		0			0
$889$	16932.5	+	42484.1i	0.638803	+	1.60278i
$890$		0			0
$891$	8378.75	+	8078.71i	0.315038	+	0.303756i
$892$		0			0
$893$	117.148	+	67.6353i	0.00438992	+	0.00253452i
$894$		0			0
$895$	−11188.5	+	6459.68i	−0.417866	+	0.241255i
$896$		0			0
$897$	−55428.3	−	36671.7i	−2.06321	−	1.36503i
$898$		0			0
$899$	−6433.32			−0.238669
$900$		0			0
$901$			47618.7i			1.76072i
$902$		0			0
$903$	1120.18	−	5381.40i	0.0412816	−	0.198319i
$904$		0			0
$905$	33388.8	−	19277.0i	1.22639	−	0.708056i
$906$		0			0
$907$	−6942.32	+	12024.4i	−0.254152	+	0.440204i	−0.964665	−	0.263480i	$-0.915130\pi$
$907$	−6942.32	+	12024.4i	−0.254152	+	0.440204i	0.710513	+	0.703684i	$0.248463\pi$
$908$		0			0
$909$	−11478.4	+	15244.6i	−0.418828	+	0.556252i
$910$		0			0
$911$	45460.5	+	26246.6i	1.65332	+	0.954543i	0.975695	+	0.219133i	$0.0703228\pi$
$911$	45460.5	+	26246.6i	1.65332	+	0.954543i	0.677622	+	0.735410i	$0.263011\pi$
$912$		0			0
$913$	−16792.5	+	9695.13i	−0.608707	+	0.351437i
$914$		0			0
$915$	−27709.5	−	1689.39i	−1.00114	−	0.0610376i
$916$		0			0
$917$	−17660.1	+	22385.9i	−0.635975	+	0.806158i
$918$		0			0
$919$	29789.5			1.06928			0.534639	−	0.845081i	$-0.320448\pi$
$919$	29789.5			1.06928			0.534639	+	0.845081i	$0.320448\pi$
$920$		0			0
$921$	24269.9	+	1479.68i	0.868317	+	0.0529394i
$922$		0			0
$923$	−33591.1	−	58181.5i	−1.19790	−	2.07483i
$924$		0			0
$925$	808.026	−	1399.54i	0.0287219	−	0.0497478i
$926$		0			0
$927$	6243.96	−	2653.26i	0.221228	−	0.0940071i
$928$		0			0
$929$	−9157.11	+	15860.6i	−0.323396	+	0.560139i	−0.981186	−	0.193062i	$-0.938158\pi$
$929$	−9157.11	+	15860.6i	−0.323396	+	0.560139i	0.657790	+	0.753201i	$0.271491\pi$
$930$		0			0
$931$	−1962.11	−	2070.49i	−0.0690714	−	0.0728867i
$932$		0			0
$933$	8547.79	−	4263.84i	0.299938	−	0.149616i
$934$		0			0
$935$		−	18773.0i		−	0.656623i
$936$		0			0
$937$			4717.18i			0.164465i	0.996613	+	0.0822325i	$0.0262050\pi$
$937$			4717.18i			0.164465i	−0.996613	+	0.0822325i	$0.973795\pi$
$938$		0			0
$939$	17083.4	−	25821.1i	0.593712	−	0.897379i
$940$		0			0
$941$	20464.4	+	35445.4i	0.708950	+	1.22794i	0.965247	+	0.261339i	$0.0841640\pi$
$941$	20464.4	+	35445.4i	0.708950	+	1.22794i	−0.256298	+	0.966598i	$0.582503\pi$
$942$		0			0
$943$	−42739.5	−	24675.7i	−1.47592	−	0.852122i
$944$		0			0
$945$	−18839.6	−	21472.2i	−0.648520	−	0.739142i
$946$		0			0
$947$	21626.2	+	12485.9i	0.742088	+	0.428445i	0.822828	−	0.568290i	$-0.192395\pi$
$947$	21626.2	+	12485.9i	0.742088	+	0.428445i	−0.0807398	+	0.996735i	$0.525728\pi$
$948$		0			0
$949$	22688.5	+	39297.7i	0.776081	+	1.34421i
$950$		0			0
$951$	−29750.1	+	44966.4i	−1.01442	+	1.53327i
$952$		0			0
$953$			14607.3i			0.496512i	0.968694	+	0.248256i	$0.0798574\pi$
$953$			14607.3i			0.496512i	−0.968694	+	0.248256i	$0.920143\pi$
$954$		0			0
$955$			15590.7i			0.528276i
$956$		0			0
$957$	11119.9	−	5546.89i	0.375608	−	0.187362i
$958$		0			0
$959$	4367.23	−	30047.2i	0.147054	−	1.01176i
$960$		0			0
$961$	−13973.2	+	24202.3i	−0.469040	+	0.812402i
$962$		0			0
$963$	2427.13	−	19831.0i	0.0812182	−	0.663598i
$964$		0			0
$965$	−8210.38	+	14220.8i	−0.273888	+	0.474387i
$966$		0			0
$967$	13828.2	+	23951.1i	0.459859	+	0.796499i	0.998953	−	0.0457467i	$-0.0145667\pi$
$967$	13828.2	+	23951.1i	0.459859	+	0.796499i	−0.539094	+	0.842245i	$0.681233\pi$
$968$		0			0
$969$	−4613.19	−	281.257i	−0.152938	−	0.00932432i
$970$		0			0
$971$	5235.20			0.173023			0.0865117	−	0.996251i	$-0.472428\pi$
$971$	5235.20			0.173023			0.0865117	+	0.996251i	$0.472428\pi$
$972$		0			0
$973$	−15102.9	−	11914.6i	−0.497612	−	0.392564i
$974$		0			0
$975$	1918.02	+	116.938i	0.0630009	+	0.00384103i
$976$		0			0
$977$	3972.26	−	2293.38i	0.130076	−	0.0750991i	−0.433550	−	0.901129i	$-0.642739\pi$
$977$	3972.26	−	2293.38i	0.130076	−	0.0750991i	0.563626	+	0.826030i	$0.309406\pi$
$978$		0			0
$979$	5886.47	+	3398.55i	0.192168	+	0.110948i
$980$		0			0
$981$	−40129.7	−	4911.50i	−1.30606	−	0.159849i
$982$		0			0
$983$	1967.14	−	3407.18i	0.0638270	−	0.110552i	−0.832346	−	0.554256i	$-0.813003\pi$
$983$	1967.14	−	3407.18i	0.0638270	−	0.110552i	0.896173	+	0.443705i	$0.146336\pi$
$984$		0			0
$985$	−22701.9	+	13106.9i	−0.734358	+	0.423982i
$986$		0			0
$987$	318.994	−	1532.46i	0.0102874	−	0.0494212i
$988$		0			0
$989$			8171.31i			0.262722i
$990$		0			0
$991$	−17434.1			−0.558841			−0.279421	−	0.960169i	$-0.590142\pi$
$991$	−17434.1			−0.558841			−0.279421	+	0.960169i	$0.590142\pi$
$992$		0			0
$993$	20988.7	+	13886.3i	0.670751	+	0.443773i
$994$		0			0
$995$	−47226.0	+	27266.0i	−1.50469	+	0.868733i
$996$		0			0
$997$	12254.1	+	7074.88i	0.389258	+	0.224738i	0.681838	−	0.731503i	$-0.261181\pi$
$997$	12254.1	+	7074.88i	0.389258	+	0.224738i	−0.292581	+	0.956241i	$0.594514\pi$
$998$		0			0
$999$	−9957.79	+	53902.5i	−0.315366	+	1.70711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.209.14	yes	48
3.2	odd	2		756.4.x.a.629.6		48
7.6	odd	2	inner	252.4.x.a.209.11	yes	48
9.2	odd	6		2268.4.f.a.1133.38		48
9.4	even	3		756.4.x.a.125.19		48
9.5	odd	6	inner	252.4.x.a.41.11	✓	48
9.7	even	3		2268.4.f.a.1133.11		48
21.20	even	2		756.4.x.a.629.19		48
63.13	odd	6		756.4.x.a.125.6		48
63.20	even	6		2268.4.f.a.1133.12		48
63.34	odd	6		2268.4.f.a.1133.37		48
63.41	even	6	inner	252.4.x.a.41.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.11	✓	48	9.5	odd	6	inner
252.4.x.a.41.14	yes	48	63.41	even	6	inner
252.4.x.a.209.11	yes	48	7.6	odd	2	inner
252.4.x.a.209.14	yes	48	1.1	even	1	trivial
756.4.x.a.125.6		48	63.13	odd	6
756.4.x.a.125.19		48	9.4	even	3
756.4.x.a.629.6		48	3.2	odd	2
756.4.x.a.629.19		48	21.20	even	2
2268.4.f.a.1133.11		48	9.7	even	3
2268.4.f.a.1133.12		48	63.20	even	6
2268.4.f.a.1133.37		48	63.34	odd	6
2268.4.f.a.1133.38		48	9.2	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.316211 - 5.18652i) q^{3} +(5.49690 + 9.52092i) q^{5} +(6.85688 + 17.2042i) q^{7} +(-26.8000 - 3.28007i) q^{9} +O(q^{10})\)	\(q+(0.316211 - 5.18652i) q^{3} +(5.49690 + 9.52092i) q^{5} +(6.85688 + 17.2042i) q^{7} +(-26.8000 - 3.28007i) q^{9} +(13.8268 + 7.98293i) q^{11} +(-77.4289 + 44.7036i) q^{13} +(51.1186 - 25.4992i) q^{15} -106.953 q^{17} +8.31634i q^{19} +(91.3980 - 30.1232i) q^{21} +(-123.893 + 71.5294i) q^{23} +(2.06812 - 3.58208i) q^{25} +(-25.4866 + 137.962i) q^{27} +(129.721 + 74.8943i) q^{29} +(-37.1952 + 21.4747i) q^{31} +(45.7759 - 69.1890i) q^{33} +(-126.108 + 159.853i) q^{35} +390.706 q^{37} +(207.372 + 415.722i) q^{39} +(172.486 + 298.755i) q^{41} +(28.5593 - 49.4661i) q^{43} +(-116.088 - 273.191i) q^{45} +(8.13282 - 14.0864i) q^{47} +(-248.966 + 235.934i) q^{49} +(-33.8198 + 554.714i) q^{51} -445.230i q^{53} +175.526i q^{55} +(43.1329 + 2.62972i) q^{57} +(193.350 + 334.892i) q^{59} +(-420.857 - 242.982i) q^{61} +(-127.334 - 483.563i) q^{63} +(-851.238 - 491.463i) q^{65} +(-251.821 - 436.167i) q^{67} +(331.813 + 665.190i) q^{69} +751.418i q^{71} -507.533i q^{73} +(-17.9246 - 11.8590i) q^{75} +(-42.5306 + 292.617i) q^{77} +(381.570 - 660.899i) q^{79} +(707.482 + 175.812i) q^{81} +(-607.241 + 1051.77i) q^{83} +(-587.911 - 1018.29i) q^{85} +(429.460 - 649.117i) q^{87} +425.727 q^{89} +(-1300.01 - 1025.57i) q^{91} +(99.6173 + 199.704i) q^{93} +(-79.1792 + 45.7141i) q^{95} +(494.582 + 285.547i) q^{97} +(-344.375 - 259.296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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