LMFDB - Embedded newform 224.4.i.e.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,4,Mod(65,224)]

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([0, 0, 2]))

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

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

chi := DirichletCharacter("224.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	224.i (of order $3$, 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:	$13.2164278413$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 2 x^{11} - 4 x^{10} - 116 x^{9} - 217 x^{8} - 2018 x^{7} + 4474 x^{6} - 105024 x^{5} + \cdots + 292052964 $ x^12 - 2x^11 - 4x^10 - 116x^9 - 217x^8 - 2018x^7 + 4474x^6 - 105024x^5 + 602862x^4 - 563232x^3 + 27785196x^2 + 36865344*x + 292052964
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.2
Root			$-1.98748 - 4.22573i$ of defining polynomial
Character	$\chi$	$=$	224.65
Dual form			224.4.i.e.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.78574 - 4.82504i) q^{3} +(2.27739 - 3.94456i) q^{5} +(3.15583 + 18.2494i) q^{7} +(-2.02069 + 3.49995i) q^{9} +O(q^{10})$	\(q+(-2.78574 - 4.82504i) q^{3} +(2.27739 - 3.94456i) q^{5} +(3.15583 + 18.2494i) q^{7} +(-2.02069 + 3.49995i) q^{9} +(32.8812 + 56.9520i) q^{11} +73.6042 q^{13} -25.3769 q^{15} +(-65.5016 - 113.452i) q^{17} +(13.2261 - 22.9083i) q^{19} +(79.2628 - 66.0651i) q^{21} +(41.0709 - 71.1369i) q^{23} +(52.1270 + 90.2866i) q^{25} -127.913 q^{27} +4.65118 q^{29} +(-40.0340 - 69.3410i) q^{31} +(183.197 - 317.307i) q^{33} +(79.1729 + 29.1127i) q^{35} +(133.861 - 231.854i) q^{37} +(-205.042 - 355.144i) q^{39} +328.215 q^{41} +289.643 q^{43} +(9.20383 + 15.9415i) q^{45} +(59.6350 - 103.291i) q^{47} +(-323.082 + 115.184i) q^{49} +(-364.941 + 632.096i) q^{51} +(75.1052 + 130.086i) q^{53} +299.534 q^{55} -147.378 q^{57} +(211.594 + 366.491i) q^{59} +(251.152 - 435.008i) q^{61} +(-70.2489 - 25.8312i) q^{63} +(167.626 - 290.336i) q^{65} +(195.116 + 337.950i) q^{67} -457.651 q^{69} -803.592 q^{71} +(184.228 + 319.092i) q^{73} +(290.424 - 503.030i) q^{75} +(-935.572 + 779.794i) q^{77} +(276.400 - 478.738i) q^{79} +(410.892 + 711.686i) q^{81} -62.3318 q^{83} -596.691 q^{85} +(-12.9570 - 22.4421i) q^{87} +(-237.684 + 411.681i) q^{89} +(232.282 + 1343.23i) q^{91} +(-223.049 + 386.332i) q^{93} +(-60.2420 - 104.342i) q^{95} +11.8811 q^{97} -265.772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 10 q^{5} - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 10 * q^5 - 4 * q^7 - 40 * q^9	$ 12 q + 6 q^{3} + 10 q^{5} - 4 q^{7} - 40 q^{9} + 42 q^{11} - 16 q^{13} + 52 q^{15} - 70 q^{17} + 158 q^{19} + 178 q^{21} - 158 q^{23} - 72 q^{25} - 492 q^{27} - 112 q^{29} + 2 q^{31} - 262 q^{33} + 418 q^{35} + 102 q^{37} - 280 q^{39} + 96 q^{41} - 368 q^{43} + 392 q^{45} + 766 q^{47} + 132 q^{49} - 394 q^{51} - 562 q^{53} - 372 q^{55} + 1316 q^{57} + 854 q^{59} - 106 q^{61} + 1864 q^{63} - 488 q^{65} - 906 q^{67} - 2788 q^{69} - 2976 q^{71} - 202 q^{73} + 2248 q^{75} + 590 q^{77} - 942 q^{79} - 674 q^{81} + 1232 q^{83} + 1996 q^{85} + 1656 q^{87} - 858 q^{89} + 4192 q^{91} + 1362 q^{93} - 2386 q^{95} + 3392 q^{97} - 11504 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 10 * q^5 - 4 * q^7 - 40 * q^9 + 42 * q^11 - 16 * q^13 + 52 * q^15 - 70 * q^17 + 158 * q^19 + 178 * q^21 - 158 * q^23 - 72 * q^25 - 492 * q^27 - 112 * q^29 + 2 * q^31 - 262 * q^33 + 418 * q^35 + 102 * q^37 - 280 * q^39 + 96 * q^41 - 368 * q^43 + 392 * q^45 + 766 * q^47 + 132 * q^49 - 394 * q^51 - 562 * q^53 - 372 * q^55 + 1316 * q^57 + 854 * q^59 - 106 * q^61 + 1864 * q^63 - 488 * q^65 - 906 * q^67 - 2788 * q^69 - 2976 * q^71 - 202 * q^73 + 2248 * q^75 + 590 * q^77 - 942 * q^79 - 674 * q^81 + 1232 * q^83 + 1996 * q^85 + 1656 * q^87 - 858 * q^89 + 4192 * q^91 + 1362 * q^93 - 2386 * q^95 + 3392 * q^97 - 11504 * q^99

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
$3$	−2.78574	−	4.82504i	−0.536116	−	0.928580i	−0.999108	−	0.0422178i	$-0.986558\pi$
$3$	−2.78574	−	4.82504i	−0.536116	−	0.928580i	0.462993	−	0.886362i	$-0.346776\pi$
$4$		0			0
$5$	2.27739	−	3.94456i	0.203696	−	0.352812i	−0.746020	−	0.665923i	$-0.768038\pi$
$5$	2.27739	−	3.94456i	0.203696	−	0.352812i	0.949717	+	0.313111i	$0.101371\pi$
$6$		0			0
$7$	3.15583	+	18.2494i	0.170399	+	0.985375i
$7$	3.15583	+	18.2494i	0.170399	+	0.985375i
$8$		0			0
$9$	−2.02069	+	3.49995i	−0.0748405	+	0.129628i
$10$		0			0
$11$	32.8812	+	56.9520i	0.901279	+	1.56106i	0.825836	+	0.563911i	$0.190704\pi$
$11$	32.8812	+	56.9520i	0.901279	+	1.56106i	0.0754429	+	0.997150i	$0.475963\pi$
$12$		0			0
$13$	73.6042			1.57032			0.785159	−	0.619294i	$-0.212581\pi$
$13$	73.6042			1.57032			0.785159	+	0.619294i	$0.212581\pi$
$14$		0			0
$15$	−25.3769			−0.436819
$16$		0			0
$17$	−65.5016	−	113.452i	−0.934498	−	1.61860i	−0.775526	−	0.631316i	$-0.782515\pi$
$17$	−65.5016	−	113.452i	−0.934498	−	1.61860i	−0.158973	−	0.987283i	$-0.550818\pi$
$18$		0			0
$19$	13.2261	−	22.9083i	0.159699	−	0.276606i	−0.775061	−	0.631886i	$-0.782281\pi$
$19$	13.2261	−	22.9083i	0.159699	−	0.276606i	0.934760	+	0.355280i	$0.115614\pi$
$20$		0			0
$21$	79.2628	−	66.0651i	0.823646	−	0.686504i
$22$		0			0
$23$	41.0709	−	71.1369i	0.372342	−	0.644916i	−0.617583	−	0.786506i	$-0.711888\pi$
$23$	41.0709	−	71.1369i	0.372342	−	0.644916i	0.989925	+	0.141590i	$0.0452214\pi$
$24$		0			0
$25$	52.1270	+	90.2866i	0.417016	+	0.722292i
$26$		0			0
$27$	−127.913			−0.911739
$28$		0			0
$29$	4.65118			0.0297828			0.0148914	−	0.999889i	$-0.495260\pi$
$29$	4.65118			0.0297828			0.0148914	+	0.999889i	$0.495260\pi$
$30$		0			0
$31$	−40.0340	−	69.3410i	−0.231946	−	0.401742i	0.726435	−	0.687235i	$-0.241176\pi$
$31$	−40.0340	−	69.3410i	−0.231946	−	0.401742i	−0.958381	+	0.285493i	$0.907843\pi$
$32$		0			0
$33$	183.197	−	317.307i	0.966380	−	1.67382i
$34$		0			0
$35$	79.1729	+	29.1127i	0.382362	+	0.140598i
$36$		0			0
$37$	133.861	−	231.854i	0.594774	−	1.03018i	−0.398805	−	0.917036i	$-0.630575\pi$
$37$	133.861	−	231.854i	0.594774	−	1.03018i	0.993579	−	0.113143i	$-0.0360918\pi$
$38$		0			0
$39$	−205.042	−	355.144i	−0.841873	−	1.45817i
$40$		0			0
$41$	328.215			1.25021			0.625104	−	0.780541i	$-0.285057\pi$
$41$	328.215			1.25021			0.625104	+	0.780541i	$0.285057\pi$
$42$		0			0
$43$	289.643			1.02721			0.513606	−	0.858026i	$-0.328309\pi$
$43$	289.643			1.02721			0.513606	+	0.858026i	$0.328309\pi$
$44$		0			0
$45$	9.20383	+	15.9415i	0.0304895	+	0.0528093i
$46$		0			0
$47$	59.6350	−	103.291i	0.185078	−	0.320564i	−0.758525	−	0.651644i	$-0.774080\pi$
$47$	59.6350	−	103.291i	0.185078	−	0.320564i	0.943603	+	0.331080i	$0.107413\pi$
$48$		0			0
$49$	−323.082	+	115.184i	−0.941929	+	0.335813i
$50$		0			0
$51$	−364.941	+	632.096i	−1.00200	+	1.73551i
$52$		0			0
$53$	75.1052	+	130.086i	0.194651	+	0.337145i	0.946786	−	0.321864i	$-0.104309\pi$
$53$	75.1052	+	130.086i	0.194651	+	0.337145i	−0.752135	+	0.659009i	$0.770976\pi$
$54$		0			0
$55$	299.534			0.734348
$56$		0			0
$57$	−147.378			−0.342468
$58$		0			0
$59$	211.594	+	366.491i	0.466901	+	0.808696i	0.999285	−	0.0378067i	$-0.0120371\pi$
$59$	211.594	+	366.491i	0.466901	+	0.808696i	−0.532384	+	0.846503i	$0.678704\pi$
$60$		0			0
$61$	251.152	−	435.008i	0.527160	−	0.913068i	−0.472339	−	0.881417i	$-0.656590\pi$
$61$	251.152	−	435.008i	0.527160	−	0.913068i	0.999499	−	0.0316507i	$-0.0100764\pi$
$62$		0			0
$63$	−70.2489	−	25.8312i	−0.140485	−	0.0516576i
$64$		0			0
$65$	167.626	−	290.336i	0.319868	−	0.554027i
$66$		0			0
$67$	195.116	+	337.950i	0.355778	+	0.616226i	0.987251	−	0.159172i	$-0.0508824\pi$
$67$	195.116	+	337.950i	0.355778	+	0.616226i	−0.631472	+	0.775398i	$0.717549\pi$
$68$		0			0
$69$	−457.651			−0.798475
$70$		0			0
$71$	−803.592			−1.34322			−0.671611	−	0.740904i	$-0.734397\pi$
$71$	−803.592			−1.34322			−0.671611	+	0.740904i	$0.734397\pi$
$72$		0			0
$73$	184.228	+	319.092i	0.295373	+	0.511601i	0.975072	−	0.221890i	$-0.0712227\pi$
$73$	184.228	+	319.092i	0.295373	+	0.511601i	−0.679698	+	0.733492i	$0.737889\pi$
$74$		0			0
$75$	290.424	−	503.030i	0.447138	−	0.774465i
$76$		0			0
$77$	−935.572	+	779.794i	−1.38465	+	1.15410i
$78$		0			0
$79$	276.400	−	478.738i	0.393638	−	0.681801i	−0.599289	−	0.800533i	$-0.704550\pi$
$79$	276.400	−	478.738i	0.393638	−	0.681801i	0.992926	+	0.118733i	$0.0378831\pi$
$80$		0			0
$81$	410.892	+	711.686i	0.563638	+	0.976250i
$82$		0			0
$83$	−62.3318			−0.0824313			−0.0412157	−	0.999150i	$-0.513123\pi$
$83$	−62.3318			−0.0824313			−0.0412157	+	0.999150i	$0.513123\pi$
$84$		0			0
$85$	−596.691			−0.761415
$86$		0			0
$87$	−12.9570	−	22.4421i	−0.0159671	−	0.0276557i
$88$		0			0
$89$	−237.684	+	411.681i	−0.283084	+	0.490315i	−0.972143	−	0.234390i	$-0.924691\pi$
$89$	−237.684	+	411.681i	−0.283084	+	0.490315i	0.689059	+	0.724705i	$0.258024\pi$
$90$		0			0
$91$	232.282	+	1343.23i	0.267580	+	1.54735i
$92$		0			0
$93$	−223.049	+	386.332i	−0.248700	+	0.430761i
$94$		0			0
$95$	−60.2420	−	104.342i	−0.0650600	−	0.112687i
$96$		0			0
$97$	11.8811			0.0124365			0.00621824	−	0.999981i	$-0.498021\pi$
$97$	11.8811			0.0124365			0.00621824	+	0.999981i	$0.498021\pi$
$98$		0			0
$99$	−265.772			−0.269809
$100$		0			0
$101$	−367.220	−	636.043i	−0.361779	−	0.626620i	0.626474	−	0.779442i	$-0.284497\pi$
$101$	−367.220	−	636.043i	−0.361779	−	0.626620i	−0.988254	+	0.152822i	$0.951164\pi$
$102$		0			0
$103$	561.493	−	972.535i	0.537141	−	0.930356i	−0.461915	−	0.886924i	$-0.652837\pi$
$103$	561.493	−	972.535i	0.537141	−	0.930356i	0.999056	−	0.0434320i	$-0.0138292\pi$
$104$		0			0
$105$	−80.0851	−	463.113i	−0.0744334	−	0.430431i
$106$		0			0
$107$	202.334	−	350.452i	0.182807	−	0.316631i	−0.760028	−	0.649890i	$-0.774815\pi$
$107$	202.334	−	350.452i	0.182807	−	0.316631i	0.942835	+	0.333259i	$0.108148\pi$
$108$		0			0
$109$	972.773	+	1684.89i	0.854814	+	1.48058i	0.876817	+	0.480823i	$0.159662\pi$
$109$	972.773	+	1684.89i	0.854814	+	1.48058i	−0.0220035	+	0.999758i	$0.507005\pi$
$110$		0			0
$111$	−1491.61			−1.27547
$112$		0			0
$113$	−1661.80			−1.38344			−0.691722	−	0.722164i	$-0.743148\pi$
$113$	−1661.80			−1.38344			−0.691722	+	0.722164i	$0.743148\pi$
$114$		0			0
$115$	−187.069	−	324.013i	−0.151689	−	0.262734i
$116$		0			0
$117$	−148.732	+	257.611i	−0.117523	+	0.203557i
$118$		0			0
$119$	1863.72	−	1553.40i	1.43569	−	1.19664i
$120$		0			0
$121$	−1496.85	+	2592.62i	−1.12461	+	1.94788i
$122$		0			0
$123$	−914.321	−	1583.65i	−0.670257	−	1.16092i
$124$		0			0
$125$	1044.20			0.747170
$126$		0			0
$127$	−2187.49			−1.52841			−0.764205	−	0.644973i	$-0.776869\pi$
$127$	−2187.49			−1.52841			−0.764205	+	0.644973i	$0.776869\pi$
$128$		0			0
$129$	−806.870	−	1397.54i	−0.550705	−	0.953849i
$130$		0			0
$131$	−45.1460	+	78.1952i	−0.0301101	+	0.0521523i	−0.880688	−	0.473697i	$-0.842919\pi$
$131$	−45.1460	+	78.1952i	−0.0301101	+	0.0521523i	0.850578	+	0.525849i	$0.176252\pi$
$132$		0			0
$133$	459.801	+	169.074i	0.299773	+	0.110230i
$134$		0			0
$135$	−291.309	+	504.562i	−0.185718	+	0.321673i
$136$		0			0
$137$	−683.139	−	1183.23i	−0.426018	−	0.737885i	0.570497	−	0.821300i	$-0.306751\pi$
$137$	−683.139	−	1183.23i	−0.426018	−	0.737885i	−0.996515	+	0.0834149i	$0.973417\pi$
$138$		0			0
$139$	213.957			0.130558			0.0652791	−	0.997867i	$-0.479206\pi$
$139$	213.957			0.130558			0.0652791	+	0.997867i	$0.479206\pi$
$140$		0			0
$141$	−664.511			−0.396893
$142$		0			0
$143$	2420.20	+	4191.91i	1.41529	+	2.45136i
$144$		0			0
$145$	10.5926	−	18.3469i	0.00606665	−	0.0105077i
$146$		0			0
$147$	1455.79	+	1238.01i	0.816812	+	0.694621i
$148$		0			0
$149$	1115.35	−	1931.84i	0.613240	−	1.06216i	−0.377450	−	0.926030i	$-0.623199\pi$
$149$	1115.35	−	1931.84i	0.613240	−	1.06216i	0.990690	−	0.136134i	$-0.0434677\pi$
$150$		0			0
$151$	440.520	+	763.004i	0.237411	+	0.411208i	0.959971	−	0.280101i	$-0.0903679\pi$
$151$	440.520	+	763.004i	0.237411	+	0.411208i	−0.722560	+	0.691309i	$0.757035\pi$
$152$		0			0
$153$	529.435			0.279753
$154$		0			0
$155$	−364.693			−0.188986
$156$		0			0
$157$	1080.82	+	1872.03i	0.549417	+	0.951618i	0.998315	+	0.0580350i	$0.0184835\pi$
$157$	1080.82	+	1872.03i	0.549417	+	0.951618i	−0.448897	+	0.893583i	$0.648183\pi$
$158$		0			0
$159$	418.447	−	724.771i	0.208711	−	0.361498i
$160$		0			0
$161$	1427.82	+	525.024i	0.698931	+	0.257004i
$162$		0			0
$163$	−1484.49	+	2571.22i	−0.713340	+	1.23554i	0.250257	+	0.968179i	$0.419485\pi$
$163$	−1484.49	+	2571.22i	−0.713340	+	1.23554i	−0.963596	+	0.267361i	$0.913848\pi$
$164$		0			0
$165$	−834.424	−	1445.26i	−0.393696	−	0.681901i
$166$		0			0
$167$	2216.74			1.02716			0.513582	−	0.858041i	$-0.328318\pi$
$167$	2216.74			1.02716			0.513582	+	0.858041i	$0.328318\pi$
$168$		0			0
$169$	3220.58			1.46590
$170$		0			0
$171$	53.4518	+	92.5812i	0.0239038	+	0.0414027i
$172$		0			0
$173$	372.066	−	644.437i	0.163512	−	0.283212i	−0.772614	−	0.634877i	$-0.781051\pi$
$173$	372.066	−	644.437i	0.163512	−	0.283212i	0.936126	+	0.351665i	$0.114384\pi$
$174$		0			0
$175$	−1483.17	+	1236.21i	−0.640670	+	0.533995i
$176$		0			0
$177$	1178.89	−	2041.90i	0.500626	−	0.867110i
$178$		0			0
$179$	−1456.26	−	2522.32i	−0.608080	−	1.05323i	−0.991557	−	0.129675i	$-0.958607\pi$
$179$	−1456.26	−	2522.32i	−0.608080	−	1.05323i	0.383476	−	0.923551i	$-0.374727\pi$
$180$		0			0
$181$	−2630.43			−1.08021			−0.540106	−	0.841597i	$-0.681616\pi$
$181$	−2630.43			−1.08021			−0.540106	+	0.841597i	$0.681616\pi$
$182$		0			0
$183$	−2798.58			−1.13048
$184$		0			0
$185$	−609.709	−	1056.05i	−0.242306	−	0.419687i
$186$		0			0
$187$	4307.55	−	7460.89i	1.68449	−	2.91762i
$188$		0			0
$189$	−403.673	−	2334.34i	−0.155359	−	0.898405i
$190$		0			0
$191$	−720.272	+	1247.55i	−0.272864	+	0.472615i	−0.969594	−	0.244719i	$-0.921304\pi$
$191$	−720.272	+	1247.55i	−0.272864	+	0.472615i	0.696730	+	0.717334i	$0.254638\pi$
$192$		0			0
$193$	468.126	+	810.817i	0.174593	+	0.302404i	0.940020	−	0.341119i	$-0.110806\pi$
$193$	468.126	+	810.817i	0.174593	+	0.302404i	−0.765427	+	0.643522i	$0.777472\pi$
$194$		0			0
$195$	−1867.85			−0.685945
$196$		0			0
$197$	4679.21			1.69228			0.846141	−	0.532959i	$-0.178920\pi$
$197$	4679.21			1.69228			0.846141	+	0.532959i	$0.178920\pi$
$198$		0			0
$199$	1172.71	+	2031.19i	0.417745	+	0.723556i	0.995712	−	0.0925044i	$-0.0294872\pi$
$199$	1172.71	+	2031.19i	0.417745	+	0.723556i	−0.577967	+	0.816060i	$0.696154\pi$
$200$		0			0
$201$	1087.08	−	1882.88i	0.381477	−	0.660738i
$202$		0			0
$203$	14.6783	+	84.8813i	0.00507496	+	0.0293473i
$204$		0			0
$205$	747.474	−	1294.66i	0.254663	−	0.441089i
$206$		0			0
$207$	165.984	+	287.492i	0.0557326	+	0.0965317i
$208$		0			0
$209$	1739.56			0.575732
$210$		0			0
$211$	−3403.64			−1.11050			−0.555251	−	0.831683i	$-0.687378\pi$
$211$	−3403.64			−1.11050			−0.555251	+	0.831683i	$0.687378\pi$
$212$		0			0
$213$	2238.60	+	3877.36i	0.720123	+	1.24729i
$214$		0			0
$215$	659.631	−	1142.51i	0.209239	−	0.362413i
$216$		0			0
$217$	1139.09	−	949.426i	0.356344	−	0.297010i
$218$		0			0
$219$	1026.42	−	1777.82i	0.316709	−	0.548555i
$220$		0			0
$221$	−4821.20	−	8350.56i	−1.46746	−	2.54172i
$222$		0			0
$223$	−367.463			−0.110346			−0.0551729	−	0.998477i	$-0.517571\pi$
$223$	−367.463			−0.110346			−0.0551729	+	0.998477i	$0.517571\pi$
$224$		0			0
$225$	−421.331			−0.124839
$226$		0			0
$227$	−1152.73	−	1996.58i	−0.337045	−	0.583778i	0.646831	−	0.762634i	$-0.276094\pi$
$227$	−1152.73	−	1996.58i	−0.337045	−	0.583778i	−0.983875	+	0.178855i	$0.942761\pi$
$228$		0			0
$229$	−1433.78	+	2483.38i	−0.413742	+	0.716622i	−0.995295	−	0.0968860i	$-0.969112\pi$
$229$	−1433.78	+	2483.38i	−0.413742	+	0.716622i	0.581553	+	0.813508i	$0.302445\pi$
$230$		0			0
$231$	6368.80	+	2341.87i	1.81401	+	0.667030i
$232$		0			0
$233$	814.260	−	1410.34i	0.228944	−	0.396543i	−0.728551	−	0.684991i	$-0.759806\pi$
$233$	814.260	−	1410.34i	0.228944	−	0.396543i	0.957495	+	0.288448i	$0.0931394\pi$
$234$		0			0
$235$	−271.625	−	470.468i	−0.0753994	−	0.130596i
$236$		0			0
$237$	−3079.91			−0.844142
$238$		0			0
$239$	−4494.70			−1.21648			−0.608238	−	0.793755i	$-0.708123\pi$
$239$	−4494.70			−1.21648			−0.608238	+	0.793755i	$0.708123\pi$
$240$		0			0
$241$	844.949	+	1463.49i	0.225842	+	0.391170i	0.956572	−	0.291497i	$-0.0941533\pi$
$241$	844.949	+	1463.49i	0.225842	+	0.391170i	−0.730730	+	0.682667i	$0.760820\pi$
$242$		0			0
$243$	562.447	−	974.187i	0.148481	−	0.257177i
$244$		0			0
$245$	−281.433	+	1536.73i	−0.0733883	+	0.400728i
$246$		0			0
$247$	973.496	−	1686.14i	0.250778	−	0.434359i
$248$		0			0
$249$	173.640	+	300.753i	0.0441928	+	0.0765441i
$250$		0			0
$251$	−4402.52			−1.10711			−0.553555	−	0.832813i	$-0.686729\pi$
$251$	−4402.52			−1.10711			−0.553555	+	0.832813i	$0.686729\pi$
$252$		0			0
$253$	5401.85			1.34234
$254$		0			0
$255$	1662.23	+	2879.06i	0.408207	+	0.707035i
$256$		0			0
$257$	−2736.87	+	4740.40i	−0.664286	+	1.15058i	0.315192	+	0.949028i	$0.397931\pi$
$257$	−2736.87	+	4740.40i	−0.664286	+	1.15058i	−0.979478	+	0.201549i	$0.935402\pi$
$258$		0			0
$259$	4653.65	+	1711.19i	1.11646	+	0.410534i
$260$		0			0
$261$	−9.39861	+	16.2789i	−0.00222896	+	0.00386068i
$262$		0			0
$263$	−2872.36	−	4975.07i	−0.673449	−	1.16645i	−0.976920	−	0.213607i	$-0.931479\pi$
$263$	−2872.36	−	4975.07i	−0.673449	−	1.16645i	0.303471	−	0.952841i	$-0.401855\pi$
$264$		0			0
$265$	684.176			0.158598
$266$		0			0
$267$	2648.50			0.607063
$268$		0			0
$269$	−1016.84	−	1761.22i	−0.230475	−	0.399194i	0.727473	−	0.686136i	$-0.240695\pi$
$269$	−1016.84	−	1761.22i	−0.230475	−	0.399194i	−0.957948	+	0.286942i	$0.907361\pi$
$270$		0			0
$271$	−772.577	+	1338.14i	−0.173176	+	0.299950i	−0.939529	−	0.342471i	$-0.888736\pi$
$271$	−772.577	+	1338.14i	−0.173176	+	0.299950i	0.766353	+	0.642420i	$0.222070\pi$
$272$		0			0
$273$	5834.08	−	4862.67i	1.29339	−	1.07803i
$274$		0			0
$275$	−3428.00	+	5937.47i	−0.751695	+	1.30197i
$276$		0			0
$277$	2000.97	+	3465.78i	0.434031	+	0.751763i	0.997216	−	0.0745674i	$-0.0237576\pi$
$277$	2000.97	+	3465.78i	0.434031	+	0.751763i	−0.563185	+	0.826331i	$0.690424\pi$
$278$		0			0
$279$	323.586			0.0694359
$280$		0			0
$281$	−6546.87			−1.38987			−0.694935	−	0.719072i	$-0.744567\pi$
$281$	−6546.87			−1.38987			−0.694935	+	0.719072i	$0.744567\pi$
$282$		0			0
$283$	2155.47	+	3733.38i	0.452753	+	0.784192i	0.998556	−	0.0537219i	$-0.0171084\pi$
$283$	2155.47	+	3733.38i	0.452753	+	0.784192i	−0.545802	+	0.837914i	$0.683775\pi$
$284$		0			0
$285$	−335.637	+	581.340i	−0.0697594	+	0.120827i
$286$		0			0
$287$	1035.79	+	5989.72i	0.213034	+	1.23192i
$288$		0			0
$289$	−6124.42	+	10607.8i	−1.24657	+	2.15913i
$290$		0			0
$291$	−33.0975	−	57.3266i	−0.00666739	−	0.0115483i
$292$		0			0
$293$	357.486			0.0712783			0.0356392	−	0.999365i	$-0.488653\pi$
$293$	357.486			0.0712783			0.0356392	+	0.999365i	$0.488653\pi$
$294$		0			0
$295$	1927.53			0.380424
$296$		0			0
$297$	−4205.95	−	7284.92i	−0.821731	−	1.42328i
$298$		0			0
$299$	3022.99	−	5235.98i	0.584696	−	1.01272i
$300$		0			0
$301$	914.063	+	5285.81i	0.175036	+	1.01219i
$302$		0			0
$303$	−2045.96	+	3543.70i	−0.387911	+	0.671882i
$304$		0			0
$305$	−1143.94	−	1981.37i	−0.214761	−	0.371977i
$306$		0			0
$307$	−4336.47			−0.806173			−0.403087	−	0.915162i	$-0.632063\pi$
$307$	−4336.47			−0.806173			−0.403087	+	0.915162i	$0.632063\pi$
$308$		0			0
$309$	−6256.70			−1.15188
$310$		0			0
$311$	−465.530	−	806.321i	−0.0848803	−	0.147017i	0.820460	−	0.571704i	$-0.193717\pi$
$311$	−465.530	−	806.321i	−0.0848803	−	0.147017i	−0.905340	+	0.424687i	$0.860384\pi$
$312$		0			0
$313$	−3841.03	+	6652.85i	−0.693635	+	1.20141i	0.277004	+	0.960869i	$0.410658\pi$
$313$	−3841.03	+	6652.85i	−0.693635	+	1.20141i	−0.970639	+	0.240542i	$0.922675\pi$
$314$		0			0
$315$	−261.877	+	218.273i	−0.0468416	+	0.0390422i
$316$		0			0
$317$	−2307.54	+	3996.77i	−0.408846	+	0.708142i	−0.994761	−	0.102230i	$-0.967402\pi$
$317$	−2307.54	+	3996.77i	−0.408846	+	0.708142i	0.585914	+	0.810373i	$0.300735\pi$
$318$		0			0
$319$	152.937	+	264.894i	0.0268426	+	0.0464928i
$320$		0			0
$321$	−2254.60			−0.392023
$322$		0			0
$323$	−3465.32			−0.596952
$324$		0			0
$325$	3836.77	+	6645.47i	0.654848	+	1.13423i
$326$		0			0
$327$	5419.78	−	9387.34i	0.916559	−	1.58753i
$328$		0			0
$329$	2073.20	+	762.336i	0.347413	+	0.127748i
$330$		0			0
$331$	1636.16	−	2833.91i	0.271696	−	0.470591i	−0.697600	−	0.716487i	$-0.745749\pi$
$331$	1636.16	−	2833.91i	0.271696	−	0.470591i	0.969296	+	0.245896i	$0.0790822\pi$
$332$		0			0
$333$	540.985	+	937.013i	0.0890264	+	0.154198i
$334$		0			0
$335$	1777.42			0.289883
$336$		0			0
$337$	164.690			0.0266209			0.0133104	−	0.999911i	$-0.495763\pi$
$337$	164.690			0.0266209			0.0133104	+	0.999911i	$0.495763\pi$
$338$		0			0
$339$	4629.35	+	8018.26i	0.741686	+	1.28464i
$340$		0			0
$341$	2632.74	−	4560.04i	0.418096	−	0.724164i
$342$		0			0
$343$	−3121.63	−	5532.54i	−0.491405	−	0.870931i
$344$		0			0
$345$	−1042.25	+	1805.23i	−0.162646	+	0.281712i
$346$		0			0
$347$	877.357	+	1519.63i	0.135732	+	0.235095i	0.925877	−	0.377825i	$-0.123328\pi$
$347$	877.357	+	1519.63i	0.135732	+	0.235095i	−0.790145	+	0.612920i	$0.789995\pi$
$348$		0			0
$349$	−4237.15			−0.649884			−0.324942	−	0.945734i	$-0.605345\pi$
$349$	−4237.15			−0.649884			−0.324942	+	0.945734i	$0.605345\pi$
$350$		0			0
$351$	−9414.97			−1.43172
$352$		0			0
$353$	−2312.34	−	4005.09i	−0.348650	−	0.603879i	0.637360	−	0.770566i	$-0.280026\pi$
$353$	−2312.34	−	4005.09i	−0.348650	−	0.603879i	−0.986010	+	0.166687i	$0.946693\pi$
$354$		0			0
$355$	−1830.09	+	3169.81i	−0.273609	+	0.473905i
$356$		0			0
$357$	−12687.1	−	4665.17i	−1.88087	−	0.691616i
$358$		0			0
$359$	−1733.64	+	3002.76i	−0.254870	+	0.441447i	−0.964860	−	0.262764i	$-0.915366\pi$
$359$	−1733.64	+	3002.76i	−0.254870	+	0.441447i	0.709990	+	0.704211i	$0.248699\pi$
$360$		0			0
$361$	3079.64	+	5334.10i	0.448993	+	0.777678i
$362$		0			0
$363$	16679.4			2.41168
$364$		0			0
$365$	1678.24			0.240666
$366$		0			0
$367$	−4098.15	−	7098.20i	−0.582892	−	1.00960i	−0.995135	−	0.0985250i	$-0.968588\pi$
$367$	−4098.15	−	7098.20i	−0.582892	−	1.00960i	0.412242	−	0.911074i	$-0.364746\pi$
$368$		0			0
$369$	−663.222	+	1148.73i	−0.0935662	+	0.162061i
$370$		0			0
$371$	−2136.97	+	1781.15i	−0.299046	+	0.249253i
$372$		0			0
$373$	3277.84	−	5677.39i	0.455014	−	0.788107i	−0.543675	−	0.839296i	$-0.682968\pi$
$373$	3277.84	−	5677.39i	0.455014	−	0.788107i	0.998689	+	0.0511884i	$0.0163009\pi$
$374$		0			0
$375$	−2908.88	−	5038.32i	−0.400570	−	0.693807i
$376$		0			0
$377$	342.346			0.0467685
$378$		0			0
$379$	−10883.3			−1.47503			−0.737517	−	0.675328i	$-0.764002\pi$
$379$	−10883.3			−1.47503			−0.737517	+	0.675328i	$0.764002\pi$
$380$		0			0
$381$	6093.77	+	10554.7i	0.819405	+	1.41925i
$382$		0			0
$383$	7232.35	−	12526.8i	0.964898	−	1.67125i	0.255008	−	0.966939i	$-0.417922\pi$
$383$	7232.35	−	12526.8i	0.964898	−	1.67125i	0.709890	−	0.704313i	$-0.248745\pi$
$384$		0			0
$385$	945.277	+	5466.32i	0.125132	+	0.723608i
$386$		0			0
$387$	−585.280	+	1013.73i	−0.0768771	+	0.133155i
$388$		0			0
$389$	543.603	+	941.549i	0.0708529	+	0.122721i	0.899275	−	0.437383i	$-0.144095\pi$
$389$	543.603	+	941.549i	0.0708529	+	0.122721i	−0.828422	+	0.560104i	$0.810761\pi$
$390$		0			0
$391$	−10760.8			−1.39181
$392$		0			0
$393$	503.060			0.0645701
$394$		0			0
$395$	−1258.94	−	2180.55i	−0.160365	−	0.277760i
$396$		0			0
$397$	680.622	−	1178.87i	0.0860439	−	0.149032i	−0.819792	−	0.572662i	$-0.805911\pi$
$397$	680.622	−	1178.87i	0.0860439	−	0.149032i	0.905836	+	0.423629i	$0.139244\pi$
$398$		0			0
$399$	−465.099	−	2689.56i	−0.0583560	−	0.337459i
$400$		0			0
$401$	551.902	−	955.923i	0.0687299	−	0.119044i	−0.829613	−	0.558339i	$-0.811439\pi$
$401$	551.902	−	955.923i	0.0687299	−	0.119044i	0.898342	+	0.439296i	$0.144772\pi$
$402$		0			0
$403$	−2946.67	−	5103.79i	−0.364229	−	0.630863i
$404$		0			0
$405$	3743.05			0.459244
$406$		0			0
$407$	17606.1			2.14423
$408$		0			0
$409$	−3738.13	−	6474.63i	−0.451928	−	0.782763i	0.546577	−	0.837409i	$-0.315930\pi$
$409$	−3738.13	−	6474.63i	−0.451928	−	0.782763i	−0.998506	+	0.0546457i	$0.982597\pi$
$410$		0			0
$411$	−3806.09	+	6592.35i	−0.456790	+	0.791184i
$412$		0			0
$413$	−6020.49	+	5018.04i	−0.717310	+	0.597873i
$414$		0			0
$415$	−141.954	+	245.871i	−0.0167909	+	0.0290828i
$416$		0			0
$417$	−596.028	−	1032.35i	−0.0699943	−	0.121234i
$418$		0			0
$419$	−1048.13			−0.122206			−0.0611030	−	0.998131i	$-0.519462\pi$
$419$	−1048.13			−0.122206			−0.0611030	+	0.998131i	$0.519462\pi$
$420$		0			0
$421$	−1023.21			−0.118452			−0.0592259	−	0.998245i	$-0.518863\pi$
$421$	−1023.21			−0.118452			−0.0592259	+	0.998245i	$0.518863\pi$
$422$		0			0
$423$	241.008	+	417.439i	0.0277027	+	0.0479824i
$424$		0			0
$425$	6828.80	−	11827.8i	0.779401	−	1.34996i
$426$		0			0
$427$	8731.24	+	3210.57i	0.989542	+	0.363865i
$428$		0			0
$429$	13484.1	−	23355.1i	1.51752	−	2.62843i
$430$		0			0
$431$	4049.26	+	7013.52i	0.452543	+	0.783827i	0.998543	−	0.0539578i	$-0.0171836\pi$
$431$	4049.26	+	7013.52i	0.452543	+	0.783827i	−0.546000	+	0.837785i	$0.683850\pi$
$432$		0			0
$433$	14919.0			1.65580			0.827901	−	0.560875i	$-0.189535\pi$
$433$	14919.0			1.65580			0.827901	+	0.560875i	$0.189535\pi$
$434$		0			0
$435$	−118.032			−0.0130097
$436$		0			0
$437$	−1086.41	−	1881.73i	−0.118925	−	0.205984i
$438$		0			0
$439$	−6719.81	+	11639.1i	−0.730568	+	1.26538i	0.226073	+	0.974110i	$0.427411\pi$
$439$	−6719.81	+	11639.1i	−0.730568	+	1.26538i	−0.956641	+	0.291270i	$0.905922\pi$
$440$		0			0
$441$	249.711	−	1363.52i	0.0269638	−	0.147232i
$442$		0			0
$443$	791.275	−	1370.53i	0.0848637	−	0.146988i	−0.820469	−	0.571690i	$-0.806288\pi$
$443$	791.275	−	1370.53i	0.0848637	−	0.146988i	0.905333	+	0.424702i	$0.139621\pi$
$444$		0			0
$445$	1082.60	+	1875.12i	0.115326	+	0.199751i
$446$		0			0
$447$	−12428.3			−1.31507
$448$		0			0
$449$	−497.311			−0.0522707			−0.0261353	−	0.999658i	$-0.508320\pi$
$449$	−497.311			−0.0522707			−0.0261353	+	0.999658i	$0.508320\pi$
$450$		0			0
$451$	10792.1	+	18692.5i	1.12679	+	1.95165i
$452$		0			0
$453$	2454.35	−	4251.06i	0.254560	−	0.440910i
$454$		0			0
$455$	5827.46	+	2142.82i	0.600430	+	0.220784i
$456$		0			0
$457$	−1170.79	+	2027.87i	−0.119841	+	0.207571i	−0.919705	−	0.392611i	$-0.871572\pi$
$457$	−1170.79	+	2027.87i	−0.119841	+	0.207571i	0.799863	+	0.600182i	$0.204905\pi$
$458$		0			0
$459$	8378.54	+	14512.1i	0.852019	+	1.47574i
$460$		0			0
$461$	−16842.4			−1.70158			−0.850792	−	0.525503i	$-0.823877\pi$
$461$	−16842.4			−1.70158			−0.850792	+	0.525503i	$0.823877\pi$
$462$		0			0
$463$	4464.62			0.448139			0.224069	−	0.974573i	$-0.428066\pi$
$463$	4464.62			0.448139			0.224069	+	0.974573i	$0.428066\pi$
$464$		0			0
$465$	1015.94	+	1759.66i	0.101318	+	0.175489i
$466$		0			0
$467$	−8175.33	+	14160.1i	−0.810084	+	1.40311i	0.102721	+	0.994710i	$0.467245\pi$
$467$	−8175.33	+	14160.1i	−0.810084	+	1.40311i	−0.912805	+	0.408396i	$0.866088\pi$
$468$		0			0
$469$	−5551.64	+	4627.25i	−0.546590	+	0.455579i
$470$		0			0
$471$	6021.74	−	10430.0i	0.589102	−	1.02036i
$472$		0			0
$473$	9523.82	+	16495.7i	0.925805	+	1.60354i
$474$		0			0
$475$	2757.74			0.266387
$476$		0			0
$477$	−607.058			−0.0582711
$478$		0			0
$479$	−3563.37	−	6171.93i	−0.339905	−	0.588732i	0.644510	−	0.764596i	$-0.277062\pi$
$479$	−3563.37	−	6171.93i	−0.339905	−	0.588732i	−0.984415	+	0.175864i	$0.943728\pi$
$480$		0			0
$481$	9852.75	−	17065.5i	0.933984	−	1.61771i
$482$		0			0
$483$	−1444.27	−	8351.87i	−0.136059	−	0.786797i
$484$		0			0
$485$	27.0578	−	46.8655i	0.00253326	−	0.00438774i
$486$		0			0
$487$	−6869.62	−	11898.5i	−0.639204	−	1.10713i	−0.985608	−	0.169048i	$-0.945931\pi$
$487$	−6869.62	−	11898.5i	−0.639204	−	1.10713i	0.346404	−	0.938085i	$-0.387403\pi$
$488$		0			0
$489$	16541.6			1.52973
$490$		0			0
$491$	−10840.2			−0.996362			−0.498181	−	0.867073i	$-0.665998\pi$
$491$	−10840.2			−0.996362			−0.498181	+	0.867073i	$0.665998\pi$
$492$		0			0
$493$	−304.660	−	527.686i	−0.0278320	−	0.0482065i
$494$		0			0
$495$	−605.267	+	1048.35i	−0.0549590	+	0.0951918i
$496$		0			0
$497$	−2536.00	−	14665.1i	−0.228883	−	1.32358i
$498$		0			0
$499$	8638.65	−	14962.6i	0.774989	−	1.34232i	−0.159812	−	0.987147i	$-0.551089\pi$
$499$	8638.65	−	14962.6i	0.774989	−	1.34232i	0.934801	−	0.355172i	$-0.115578\pi$
$500$		0			0
$501$	−6175.26	−	10695.9i	−0.550679	−	0.953804i
$502$		0			0
$503$	8368.03			0.741774			0.370887	−	0.928678i	$-0.379054\pi$
$503$	8368.03			0.741774			0.370887	+	0.928678i	$0.379054\pi$
$504$		0			0
$505$	−3345.21			−0.294772
$506$		0			0
$507$	−8971.70	−	15539.4i	−0.785892	−	1.36121i
$508$		0			0
$509$	6998.07	−	12121.0i	0.609398	−	1.05551i	−0.381941	−	0.924187i	$-0.624744\pi$
$509$	6998.07	−	12121.0i	0.609398	−	1.05551i	0.991340	−	0.131323i	$-0.0419223\pi$
$510$		0			0
$511$	−5241.85	+	4369.05i	−0.453788	+	0.378230i
$512$		0			0
$513$	−1691.79	+	2930.27i	−0.145603	+	0.252192i
$514$		0			0
$515$	−2557.48	−	4429.69i	−0.218827	−	0.379020i
$516$		0			0
$517$	7843.50			0.667228
$518$		0			0
$519$	−4145.92			−0.350647
$520$		0			0
$521$	−10463.1	−	18122.6i	−0.879838	−	1.52392i	−0.851518	−	0.524325i	$-0.824318\pi$
$521$	−10463.1	−	18122.6i	−0.879838	−	1.52392i	−0.0283192	−	0.999599i	$-0.509015\pi$
$522$		0			0
$523$	2297.44	−	3979.28i	0.192084	−	0.332699i	−0.753857	−	0.657039i	$-0.771809\pi$
$523$	2297.44	−	3979.28i	0.192084	−	0.332699i	0.945941	+	0.324340i	$0.105142\pi$
$524$		0			0
$525$	10096.5	+	3712.60i	0.839330	+	0.308630i
$526$		0			0
$527$	−5244.59	+	9083.89i	−0.433506	+	0.750855i
$528$		0			0
$529$	2709.86	+	4693.62i	0.222722	+	0.385766i
$530$		0			0
$531$	−1710.27			−0.139772
$532$		0			0
$533$	24158.0			1.96322
$534$		0			0
$535$	−921.587	−	1596.23i	−0.0744741	−	0.128993i
$536$		0			0
$537$	−8113.55	+	14053.1i	−0.652003	+	1.12930i
$538$		0			0
$539$	−17183.3	−	14612.7i	−1.37317	−	1.16775i
$540$		0			0
$541$	−5490.24	+	9509.37i	−0.436310	+	0.755711i	−0.997402	−	0.0720427i	$-0.977048\pi$
$541$	−5490.24	+	9509.37i	−0.436310	+	0.755711i	0.561092	+	0.827754i	$0.310382\pi$
$542$		0			0
$543$	7327.70	+	12692.0i	0.579119	+	1.00306i
$544$		0			0
$545$	8861.54			0.696489
$546$		0			0
$547$	20353.1			1.59092			0.795462	−	0.606003i	$-0.207228\pi$
$547$	20353.1			1.59092			0.795462	+	0.606003i	$0.207228\pi$
$548$		0			0
$549$	1015.00	+	1758.04i	0.0789058	+	0.136669i
$550$		0			0
$551$	61.5169	−	106.550i	0.00475628	−	0.00823811i
$552$		0			0
$553$	9608.95	+	3533.31i	0.738905	+	0.271703i
$554$		0			0
$555$	−3396.98	+	5883.74i	−0.259809	+	0.450002i
$556$		0			0
$557$	5784.40	+	10018.9i	0.440024	+	0.762143i	0.997691	−	0.0679216i	$-0.0216368\pi$
$557$	5784.40	+	10018.9i	0.440024	+	0.762143i	−0.557667	+	0.830065i	$0.688303\pi$
$558$		0			0
$559$	21318.9			1.61305
$560$		0			0
$561$	−47998.8			−3.61232
$562$		0			0
$563$	−4159.87	−	7205.11i	−0.311399	−	0.539359i	0.667266	−	0.744819i	$-0.267464\pi$
$563$	−4159.87	−	7205.11i	−0.311399	−	0.539359i	−0.978666	+	0.205460i	$0.934131\pi$
$564$		0			0
$565$	−3784.57	+	6555.07i	−0.281802	+	0.488096i
$566$		0			0
$567$	−11691.1	+	9744.50i	−0.865930	+	0.721747i
$568$		0			0
$569$	−6839.67	+	11846.7i	−0.503926	+	0.872826i	0.496064	+	0.868286i	$0.334778\pi$
$569$	−6839.67	+	11846.7i	−0.503926	+	0.872826i	−0.999990	+	0.00453945i	$0.998555\pi$
$570$		0			0
$571$	2980.95	+	5163.16i	0.218475	+	0.378409i	0.954342	−	0.298717i	$-0.0965586\pi$
$571$	2980.95	+	5163.16i	0.218475	+	0.378409i	−0.735867	+	0.677126i	$0.763225\pi$
$572$		0			0
$573$	8025.96			0.585147
$574$		0			0
$575$	8563.61			0.621091
$576$		0			0
$577$	−9122.89	−	15801.3i	−0.658217	−	1.14006i	−0.981077	−	0.193618i	$-0.937978\pi$
$577$	−9122.89	−	15801.3i	−0.658217	−	1.14006i	0.322860	−	0.946447i	$-0.395356\pi$
$578$		0			0
$579$	2608.15	−	4517.45i	0.187204	−	0.324247i
$580$		0			0
$581$	−196.708	−	1137.52i	−0.0140462	−	0.0812258i
$582$		0			0
$583$	−4939.10	+	8554.78i	−0.350869	+	0.607723i
$584$		0			0
$585$	677.441	+	1173.36i	0.0478782	+	0.0829274i
$586$		0			0
$587$	2476.93			0.174163			0.0870816	−	0.996201i	$-0.472246\pi$
$587$	2476.93			0.174163			0.0870816	+	0.996201i	$0.472246\pi$
$588$		0			0
$589$	−2117.97			−0.148166
$590$		0			0
$591$	−13035.1	−	22577.4i	−0.907260	−	1.57142i
$592$		0			0
$593$	−563.058	+	975.245i	−0.0389916	+	0.0675354i	−0.884863	−	0.465852i	$-0.845748\pi$
$593$	−563.058	+	975.245i	−0.0389916	+	0.0675354i	0.845871	+	0.533387i	$0.179081\pi$
$594$		0			0
$595$	−1883.06	−	10889.3i	−0.129744	−	0.750279i
$596$		0			0
$597$	6533.73	−	11316.8i	0.447919	−	0.775819i
$598$		0			0
$599$	3269.00	+	5662.08i	0.222985	+	0.386221i	0.955713	−	0.294301i	$-0.0950867\pi$
$599$	3269.00	+	5662.08i	0.222985	+	0.386221i	−0.732728	+	0.680521i	$0.761753\pi$
$600$		0			0
$601$	−11848.0			−0.804143			−0.402072	−	0.915608i	$-0.631710\pi$
$601$	−11848.0			−0.804143			−0.402072	+	0.915608i	$0.631710\pi$
$602$		0			0
$603$	−1577.08			−0.106507
$604$		0			0
$605$	6817.84	+	11808.8i	0.458156	+	0.793550i
$606$		0			0
$607$	−4972.08	+	8611.90i	−0.332472	+	0.575859i	−0.982996	−	0.183627i	$-0.941216\pi$
$607$	−4972.08	+	8611.90i	−0.332472	+	0.575859i	0.650524	+	0.759486i	$0.274549\pi$
$608$		0			0
$609$	368.666	−	307.281i	0.0245305	−	0.0204460i
$610$		0			0
$611$	4389.39	−	7602.65i	0.290631	−	0.503388i
$612$		0			0
$613$	−2778.87	−	4813.15i	−0.183096	−	0.317131i	0.759838	−	0.650113i	$-0.225278\pi$
$613$	−2778.87	−	4813.15i	−0.183096	−	0.317131i	−0.942933	+	0.332982i	$0.891945\pi$
$614$		0			0
$615$	−8329.07			−0.546115
$616$		0			0
$617$	18075.0			1.17937			0.589686	−	0.807633i	$-0.299252\pi$
$617$	18075.0			1.17937			0.589686	+	0.807633i	$0.299252\pi$
$618$		0			0
$619$	2121.53	+	3674.59i	0.137757	+	0.238602i	0.926647	−	0.375932i	$-0.122677\pi$
$619$	2121.53	+	3674.59i	0.137757	+	0.238602i	−0.788890	+	0.614534i	$0.789344\pi$
$620$		0			0
$621$	−5253.52	+	9099.37i	−0.339479	+	0.587995i
$622$		0			0
$623$	−8263.02	−	3038.40i	−0.531382	−	0.195395i
$624$		0			0
$625$	−4137.81	+	7166.90i	−0.264820	+	0.458682i
$626$		0			0
$627$	−4845.96	−	8393.45i	−0.308659	−	0.534613i
$628$		0			0
$629$	−35072.5			−2.22326
$630$		0			0
$631$	29769.9			1.87816			0.939082	−	0.343692i	$-0.111678\pi$
$631$	29769.9			1.87816			0.939082	+	0.343692i	$0.111678\pi$
$632$		0			0
$633$	9481.65	+	16422.7i	0.595358	+	1.03119i
$634$		0			0
$635$	−4981.77	+	8628.68i	−0.311331	+	0.539242i
$636$		0			0
$637$	−23780.2	+	8478.02i	−1.47913	+	0.527334i
$638$		0			0
$639$	1623.81	−	2812.53i	0.100527	−	0.174119i
$640$		0			0
$641$	−4069.32	−	7048.27i	−0.250746	−	0.434306i	0.712985	−	0.701179i	$-0.247343\pi$
$641$	−4069.32	−	7048.27i	−0.250746	−	0.434306i	−0.963732	+	0.266874i	$0.914009\pi$
$642$		0			0
$643$	−14788.0			−0.906971			−0.453486	−	0.891264i	$-0.649820\pi$
$643$	−14788.0			−0.906971			−0.453486	+	0.891264i	$0.649820\pi$
$644$		0			0
$645$	−7350.24			−0.448706
$646$		0			0
$647$	14177.5	+	24556.2i	0.861477	+	1.49212i	0.870504	+	0.492162i	$0.163793\pi$
$647$	14177.5	+	24556.2i	0.861477	+	1.49212i	−0.00902698	+	0.999959i	$0.502873\pi$
$648$		0			0
$649$	−13914.9	+	24101.4i	−0.841616	+	1.45772i
$650$		0			0
$651$	−7754.23	−	2851.31i	−0.466839	−	0.171662i
$652$		0			0
$653$	−592.944	+	1027.01i	−0.0355340	+	0.0615466i	−0.883245	−	0.468911i	$-0.844647\pi$
$653$	−592.944	+	1027.01i	−0.0355340	+	0.0615466i	0.847711	+	0.530458i	$0.177980\pi$
$654$		0			0
$655$	205.630	+	356.162i	0.0122666	+	0.0212464i
$656$		0			0
$657$	−1489.07			−0.0884236
$658$		0			0
$659$	7804.32			0.461325			0.230662	−	0.973034i	$-0.425911\pi$
$659$	7804.32			0.461325			0.230662	+	0.973034i	$0.425911\pi$
$660$		0			0
$661$	4344.92	+	7525.62i	0.255670	+	0.442833i	0.965077	−	0.261966i	$-0.0843707\pi$
$661$	4344.92	+	7525.62i	0.255670	+	0.442833i	−0.709408	+	0.704799i	$0.751037\pi$
$662$		0			0
$663$	−26861.2	+	46525.0i	−1.57346	+	2.72531i
$664$		0			0
$665$	1714.07	−	1428.67i	0.0999530	−	0.0833102i
$666$		0			0
$667$	191.028	−	330.870i	0.0110894	−	0.0192074i
$668$		0			0
$669$	1023.66	+	1773.02i	0.0591582	+	0.102465i
$670$		0			0
$671$	33032.8			1.90047
$672$		0			0
$673$	31681.3			1.81460			0.907300	−	0.420483i	$-0.138139\pi$
$673$	31681.3			1.81460			0.907300	+	0.420483i	$0.138139\pi$
$674$		0			0
$675$	−6667.74	−	11548.9i	−0.380210	−	0.658542i
$676$		0			0
$677$	−9283.75	+	16079.9i	−0.527036	+	0.912853i	0.472467	+	0.881348i	$0.343363\pi$
$677$	−9283.75	+	16079.9i	−0.527036	+	0.912853i	−0.999504	+	0.0315052i	$0.989970\pi$
$678$		0			0
$679$	37.4946	+	216.822i	0.00211916	+	0.0122546i
$680$		0			0
$681$	−6422.39	+	11123.9i	−0.361390	+	0.625946i
$682$		0			0
$683$	6943.95	+	12027.3i	0.389023	+	0.673808i	0.992318	−	0.123710i	$-0.0394793\pi$
$683$	6943.95	+	12027.3i	0.389023	+	0.673808i	−0.603295	+	0.797518i	$0.706146\pi$
$684$		0			0
$685$	−6223.10			−0.347113
$686$		0			0
$687$	15976.6			0.887255
$688$		0			0
$689$	5528.06	+	9574.88i	0.305664	+	0.529425i
$690$		0			0
$691$	−5112.48	+	8855.08i	−0.281459	+	0.487501i	−0.971744	−	0.236036i	$-0.924152\pi$
$691$	−5112.48	+	8855.08i	−0.281459	+	0.487501i	0.690286	+	0.723537i	$0.257485\pi$
$692$		0			0
$693$	−838.730	−	4850.18i	−0.0459751	−	0.265863i
$694$		0			0
$695$	487.264	−	843.965i	0.0265942	−	0.0460625i
$696$		0			0
$697$	−21498.6	−	37236.7i	−1.16832	−	2.02359i
$698$		0			0
$699$	−9073.27			−0.490962
$700$		0			0
$701$	−17766.2			−0.957232			−0.478616	−	0.878024i	$-0.658861\pi$
$701$	−17766.2			−0.957232			−0.478616	+	0.878024i	$0.658861\pi$
$702$		0			0
$703$	−3540.92	−	6133.05i	−0.189969	−	0.329036i
$704$		0			0
$705$	−1513.35	+	2621.20i	−0.0808456	+	0.140029i
$706$		0			0
$707$	10448.5	−	8708.78i	0.555809	−	0.463264i
$708$		0			0
$709$	7584.77	−	13137.2i	0.401766	−	0.695879i	−0.592173	−	0.805811i	$-0.701730\pi$
$709$	7584.77	−	13137.2i	0.401766	−	0.695879i	0.993939	+	0.109932i	$0.0350632\pi$
$710$		0			0
$711$	1117.04	+	1934.77i	0.0589201	+	0.102053i
$712$		0			0
$713$	−6576.94			−0.345453
$714$		0			0
$715$	22047.0			1.15316
$716$		0			0
$717$	12521.1	+	21687.1i	0.652172	+	1.12960i
$718$		0			0
$719$	−2855.78	+	4946.35i	−0.148126	+	0.256562i	−0.930535	−	0.366203i	$-0.880657\pi$
$719$	−2855.78	+	4946.35i	−0.148126	+	0.256562i	0.782409	+	0.622765i	$0.213991\pi$
$720$		0			0
$721$	19520.2	+	7177.76i	1.00828	+	0.370754i
$722$		0			0
$723$	4707.61	−	8153.83i	0.242155	−	0.419425i
$724$		0			0
$725$	242.452	+	419.939i	0.0124199	+	0.0215119i
$726$		0			0
$727$	−38137.1			−1.94557			−0.972783	−	0.231719i	$-0.925565\pi$
$727$	−38137.1			−1.94557			−0.972783	+	0.231719i	$0.925565\pi$
$728$		0			0
$729$	15920.9			0.808864
$730$		0			0
$731$	−18972.1	−	32860.6i	−0.959929	−	1.66265i
$732$		0			0
$733$	14783.8	−	25606.3i	0.744956	−	1.29030i	−0.205260	−	0.978708i	$-0.565804\pi$
$733$	14783.8	−	25606.3i	0.744956	−	1.29030i	0.950215	−	0.311594i	$-0.100863\pi$
$734$		0			0
$735$	8198.80	−	2923.01i	0.411452	−	0.146690i
$736$		0			0
$737$	−12831.3	+	22224.4i	−0.641311	+	1.11078i
$738$		0			0
$739$	1505.28	+	2607.23i	0.0749293	+	0.129781i	0.901056	−	0.433704i	$-0.142794\pi$
$739$	1505.28	+	2607.23i	0.0749293	+	0.129781i	−0.826126	+	0.563485i	$0.809460\pi$
$740$		0			0
$741$	−10847.6			−0.537783
$742$		0			0
$743$	−10229.6			−0.505100			−0.252550	−	0.967584i	$-0.581269\pi$
$743$	−10229.6			−0.505100			−0.252550	+	0.967584i	$0.581269\pi$
$744$		0			0
$745$	−5080.17	−	8799.11i	−0.249829	−	0.432717i
$746$		0			0
$747$	125.953	−	218.158i	0.00616921	−	0.0106854i
$748$		0			0
$749$	7034.08	+	2586.50i	0.343150	+	0.126180i
$750$		0			0
$751$	14630.9	−	25341.5i	0.710906	−	1.23132i	−0.253612	−	0.967306i	$-0.581619\pi$
$751$	14630.9	−	25341.5i	0.710906	−	1.23132i	0.964518	−	0.264019i	$-0.0850481\pi$
$752$		0			0
$753$	12264.3	+	21242.3i	0.593539	+	1.02804i
$754$		0			0
$755$	4012.95			0.193439
$756$		0			0
$757$	10735.1			0.515420			0.257710	−	0.966222i	$-0.417032\pi$
$757$	10735.1			0.515420			0.257710	+	0.966222i	$0.417032\pi$
$758$		0			0
$759$	−15048.1	−	26064.2i	−0.719648	−	1.24647i
$760$		0			0
$761$	−1827.51	+	3165.34i	−0.0870527	+	0.150780i	−0.906264	−	0.422712i	$-0.861078\pi$
$761$	−1827.51	+	3165.34i	−0.0870527	+	0.150780i	0.819211	+	0.573492i	$0.194412\pi$
$762$		0			0
$763$	−27678.4	+	23069.7i	−1.31327	+	1.09460i
$764$		0			0
$765$	1205.73	−	2088.39i	0.0569847	−	0.0987004i
$766$		0			0
$767$	15574.2	+	26975.3i	0.733183	+	1.26991i
$768$		0			0
$769$	−24785.4			−1.16227			−0.581133	−	0.813808i	$-0.697390\pi$
$769$	−24785.4			−1.16227			−0.581133	+	0.813808i	$0.697390\pi$
$770$		0			0
$771$	30496.9			1.42454
$772$		0			0
$773$	4961.99	+	8594.42i	0.230880	+	0.399896i	0.958067	−	0.286543i	$-0.0925061\pi$
$773$	4961.99	+	8594.42i	0.230880	+	0.399896i	−0.727187	+	0.686439i	$0.759173\pi$
$774$		0			0
$775$	4173.71	−	7229.07i	0.193450	−	0.335066i
$776$		0			0
$777$	−4707.26	−	27221.0i	−0.217339	−	1.25682i
$778$		0			0
$779$	4341.00	−	7518.83i	0.199656	−	0.345815i
$780$		0			0
$781$	−26423.1	−	45766.1i	−1.21062	−	2.09685i
$782$		0			0
$783$	−594.948			−0.0271542
$784$		0			0
$785$	9845.76			0.447657
$786$		0			0
$787$	−16491.9	−	28564.7i	−0.746978	−	1.29380i	−0.949265	−	0.314477i	$-0.898171\pi$
$787$	−16491.9	−	28564.7i	−0.746978	−	1.29380i	0.202288	−	0.979326i	$-0.435162\pi$
$788$		0			0
$789$	−16003.3	+	27718.5i	−0.722094	+	1.25070i
$790$		0			0
$791$	−5244.36	−	30326.9i	−0.235737	−	1.36321i
$792$		0			0
$793$	18485.9	−	32018.5i	0.827809	−	1.43381i
$794$		0			0
$795$	−1905.94	−	3301.18i	−0.0850271	−	0.147271i
$796$		0			0
$797$	14832.3			0.659207			0.329603	−	0.944119i	$-0.393085\pi$
$797$	14832.3			0.659207			0.329603	+	0.944119i	$0.393085\pi$
$798$		0			0
$799$	−15624.8			−0.691820
$800$		0			0
$801$	−960.573	−	1663.76i	−0.0423723	−	0.0733909i
$802$		0			0
$803$	−12115.3	+	20984.3i	−0.532427	+	0.922191i
$804$		0			0
$805$	5322.69	−	4436.43i	0.233044	−	0.194241i
$806$		0			0
$807$	−5665.30	+	9812.58i	−0.247123	+	0.428029i
$808$		0			0
$809$	−2249.77	−	3896.72i	−0.0977722	−	0.169346i	0.812990	−	0.582278i	$-0.197838\pi$
$809$	−2249.77	−	3896.72i	−0.0977722	−	0.169346i	−0.910762	+	0.412931i	$0.864505\pi$
$810$		0			0
$811$	24307.3			1.05246			0.526229	−	0.850343i	$-0.323605\pi$
$811$	24307.3			1.05246			0.526229	+	0.850343i	$0.323605\pi$
$812$		0			0
$813$	8608.79			0.371370
$814$		0			0
$815$	6761.54	+	11711.3i	0.290609	+	0.503350i
$816$		0			0
$817$	3830.84	−	6635.21i	0.164044	−	0.284133i
$818$		0			0
$819$	−5170.61	−	1901.29i	−0.220605	−	0.0811189i
$820$		0			0
$821$	−533.897	+	924.737i	−0.0226957	+	0.0393100i	−0.877150	−	0.480216i	$-0.840558\pi$
$821$	−533.897	+	924.737i	−0.0226957	+	0.0393100i	0.854454	+	0.519526i	$0.173892\pi$
$822$		0			0
$823$	8752.96	+	15160.6i	0.370728	+	0.642120i	0.989678	−	0.143311i	$-0.0457749\pi$
$823$	8752.96	+	15160.6i	0.370728	+	0.642120i	−0.618950	+	0.785431i	$0.712442\pi$
$824$		0			0
$825$	38198.1			1.61198
$826$		0			0
$827$	−32525.9			−1.36764			−0.683818	−	0.729653i	$-0.739682\pi$
$827$	−32525.9			−1.36764			−0.683818	+	0.729653i	$0.739682\pi$
$828$		0			0
$829$	−17962.1	−	31111.2i	−0.752532	−	1.30342i	−0.946592	−	0.322433i	$-0.895499\pi$
$829$	−17962.1	−	31111.2i	−0.752532	−	1.30342i	0.194061	−	0.980990i	$-0.437834\pi$
$830$		0			0
$831$	11148.4	−	19309.5i	0.465382	−	0.806064i
$832$		0			0
$833$	34230.2	+	29109.5i	1.42378	+	1.21079i
$834$		0			0
$835$	5048.38	−	8744.06i	0.209229	−	0.362396i
$836$		0			0
$837$	5120.89	+	8869.65i	0.211474	+	0.366284i
$838$		0			0
$839$	11760.4			0.483927			0.241964	−	0.970285i	$-0.422209\pi$
$839$	11760.4			0.483927			0.241964	+	0.970285i	$0.422209\pi$
$840$		0			0
$841$	−24367.4			−0.999113
$842$		0			0
$843$	18237.9	+	31588.9i	0.745132	+	1.29061i
$844$		0			0
$845$	7334.53	−	12703.8i	0.298598	−	0.517187i
$846$		0			0
$847$	−52037.6	−	19134.8i	−2.11102	−	0.776244i
$848$		0			0
$849$	12009.1	−	20800.4i	0.485457	−	0.840836i
$850$		0			0
$851$	−10995.6	−	19044.9i	−0.442919	−	0.767158i
$852$		0			0
$853$	31670.4			1.27125			0.635624	−	0.771999i	$-0.280743\pi$
$853$	31670.4			1.27125			0.635624	+	0.771999i	$0.280743\pi$
$854$		0			0
$855$	486.922			0.0194765
$856$		0			0
$857$	−10349.1	−	17925.2i	−0.412508	−	0.714485i	0.582655	−	0.812720i	$-0.302014\pi$
$857$	−10349.1	−	17925.2i	−0.412508	−	0.714485i	−0.995163	+	0.0982343i	$0.968681\pi$
$858$		0			0
$859$	−11826.5	+	20484.1i	−0.469749	+	0.813629i	−0.999402	−	0.0345855i	$-0.988989\pi$
$859$	−11826.5	+	20484.1i	−0.469749	+	0.813629i	0.529653	+	0.848215i	$0.322322\pi$
$860$		0			0
$861$	26015.2	−	21683.5i	1.02973	−	0.858273i
$862$		0			0
$863$	16195.0	−	28050.5i	0.638799	−	1.10643i	−0.346897	−	0.937903i	$-0.612765\pi$
$863$	16195.0	−	28050.5i	0.638799	−	1.10643i	0.985697	−	0.168530i	$-0.0539020\pi$
$864$		0			0
$865$	−1694.68	−	2935.27i	−0.0666137	−	0.115378i
$866$		0			0
$867$	68244.2			2.67323
$868$		0			0
$869$	36353.4			1.41911
$870$		0			0
$871$	14361.3	+	24874.6i	0.558686	+	0.967672i
$872$		0			0
$873$	−24.0080	+	41.5831i	−0.000930753	+	0.00161211i
$874$		0			0
$875$	3295.32	+	19056.1i	0.127317	+	0.736243i
$876$		0			0
$877$	−19202.3	+	33259.3i	−0.739356	+	1.28060i	0.213430	+	0.976958i	$0.431537\pi$
$877$	−19202.3	+	33259.3i	−0.739356	+	1.28060i	−0.952786	+	0.303644i	$0.901797\pi$
$878$		0			0
$879$	−995.863	−	1724.88i	−0.0382134	−	0.0661876i
$880$		0			0
$881$	4438.83			0.169748			0.0848740	−	0.996392i	$-0.472951\pi$
$881$	4438.83			0.169748			0.0848740	+	0.996392i	$0.472951\pi$
$882$		0			0
$883$	29750.2			1.13383			0.566917	−	0.823775i	$-0.308136\pi$
$883$	29750.2			1.13383			0.566917	+	0.823775i	$0.308136\pi$
$884$		0			0
$885$	−5369.59	−	9300.40i	−0.203951	−	0.353254i
$886$		0			0
$887$	−18748.4	+	32473.2i	−0.709707	+	1.22925i	0.255259	+	0.966873i	$0.417839\pi$
$887$	−18748.4	+	32473.2i	−0.709707	+	1.22925i	−0.964966	+	0.262376i	$0.915494\pi$
$888$		0			0
$889$	−6903.33	−	39920.4i	−0.260439	−	1.50606i
$890$		0			0
$891$	−27021.3	+	46802.3i	−1.01599	+	1.75975i
$892$		0			0
$893$	−1577.48	−	2732.27i	−0.0591134	−	0.102387i
$894$		0			0
$895$	−13265.9			−0.495454
$896$		0			0
$897$	−33685.1			−1.25386
$898$		0			0
$899$	−186.206	−	322.517i	−0.00690801	−	0.0119650i
$900$		0			0
$901$	9839.02	−	17041.7i	0.363802	−	0.630123i
$902$		0			0
$903$	22957.9	−	19135.3i	0.846060	−	0.705186i
$904$		0			0
$905$	−5990.53	+	10375.9i	−0.220035	+	0.381112i
$906$		0			0
$907$	17782.3	+	30799.8i	0.650993	+	1.12755i	0.982882	+	0.184235i	$0.0589806\pi$
$907$	17782.3	+	30799.8i	0.650993	+	1.12755i	−0.331889	+	0.943318i	$0.607686\pi$
$908$		0			0
$909$	2968.15			0.108303
$910$		0			0
$911$	19554.7			0.711170			0.355585	−	0.934644i	$-0.384282\pi$
$911$	19554.7			0.711170			0.355585	+	0.934644i	$0.384282\pi$
$912$		0			0
$913$	−2049.55	−	3549.92i	−0.0742936	−	0.128680i
$914$		0			0
$915$	−6373.46	+	11039.2i	−0.230273	+	0.398845i
$916$		0			0
$917$	−1569.49	−	577.117i	−0.0565203	−	0.0207831i
$918$		0			0
$919$	−9949.36	+	17232.8i	−0.357126	+	0.618561i	−0.987479	−	0.157748i	$-0.949577\pi$
$919$	−9949.36	+	17232.8i	−0.357126	+	0.618561i	0.630353	+	0.776309i	$0.282910\pi$
$920$		0			0
$921$	12080.3	+	20923.6i	0.432202	+	0.748596i
$922$		0			0
$923$	−59147.7			−2.10929
$924$		0			0
$925$	27911.1			0.992120
$926$		0			0
$927$	2269.21	+	3930.39i	0.0803999	+	0.139257i
$928$		0			0
$929$	3504.98	−	6070.80i	0.123783	−	0.214399i	−0.797473	−	0.603354i	$-0.793831\pi$
$929$	3504.98	−	6070.80i	0.123783	−	0.214399i	0.921257	+	0.388955i	$0.127164\pi$
$930$		0			0
$931$	−1634.44	+	8924.67i	−0.0575367	+	0.314172i
$932$		0			0
$933$	−2593.69	+	4492.40i	−0.0910113	+	0.157636i
$934$		0			0
$935$	−19620.0	−	33982.8i	−0.686247	−	1.18861i
$936$		0			0
$937$	−813.410			−0.0283596			−0.0141798	−	0.999899i	$-0.504514\pi$
$937$	−813.410			−0.0283596			−0.0141798	+	0.999899i	$0.504514\pi$
$938$		0			0
$939$	42800.4			1.48747
$940$		0			0
$941$	7123.15	+	12337.7i	0.246767	+	0.427414i	0.962627	−	0.270831i	$-0.0872983\pi$
$941$	7123.15	+	12337.7i	0.246767	+	0.427414i	−0.715860	+	0.698244i	$0.753965\pi$
$942$		0			0
$943$	13480.1	−	23348.2i	0.465506	−	0.806279i
$944$		0			0
$945$	−10127.3	−	3723.91i	−0.348614	−	0.128189i
$946$		0			0
$947$	−17053.1	+	29536.9i	−0.585167	+	1.01354i	0.409688	+	0.912226i	$0.365638\pi$
$947$	−17053.1	+	29536.9i	−0.585167	+	1.01354i	−0.994855	+	0.101312i	$0.967696\pi$
$948$		0			0
$949$	13560.0	+	23486.5i	0.463830	+	0.803377i
$950$		0			0
$951$	25712.8			0.876756
$952$		0			0
$953$	10497.7			0.356826			0.178413	−	0.983956i	$-0.442904\pi$
$953$	10497.7			0.356826			0.178413	+	0.983956i	$0.442904\pi$
$954$		0			0
$955$	3280.68	+	5682.31i	0.111163	+	0.192540i
$956$		0			0
$957$	852.083	−	1475.85i	0.0287815	−	0.0498511i
$958$		0			0
$959$	19437.4	−	16200.9i	0.654501	−	0.545522i
$960$		0			0
$961$	11690.1	−	20247.8i	0.392402	−	0.679660i
$962$		0			0
$963$	817.709	+	1416.31i	0.0273627	+	0.0473937i
$964$		0			0
$965$	4264.42			0.142256
$966$		0			0
$967$	−47342.5			−1.57439			−0.787193	−	0.616707i	$-0.788466\pi$
$967$	−47342.5			−1.57439			−0.787193	+	0.616707i	$0.788466\pi$
$968$		0			0
$969$	9653.48	+	16720.3i	0.320036	+	0.554318i
$970$		0			0
$971$	−817.140	+	1415.33i	−0.0270065	+	0.0467766i	−0.879213	−	0.476429i	$-0.841931\pi$
$971$	−817.140	+	1415.33i	−0.0270065	+	0.0467766i	0.852206	+	0.523206i	$0.175264\pi$
$972$		0			0
$973$	675.211	+	3904.58i	0.0222469	+	0.128649i
$974$		0			0
$975$	21376.5	−	37025.1i	0.702148	−	1.21616i
$976$		0			0
$977$	−12531.7	−	21705.6i	−0.410364	−	0.710772i	0.584565	−	0.811347i	$-0.301265\pi$
$977$	−12531.7	−	21705.6i	−0.410364	−	0.710772i	−0.994930	+	0.100575i	$0.967932\pi$
$978$		0			0
$979$	−31261.4			−1.02055
$980$		0			0
$981$	−7862.71			−0.255899
$982$		0			0
$983$	−29562.1	−	51203.1i	−0.959191	−	1.66137i	−0.724472	−	0.689305i	$-0.757916\pi$
$983$	−29562.1	−	51203.1i	−0.959191	−	1.66137i	−0.234720	−	0.972063i	$-0.575417\pi$
$984$		0			0
$985$	10656.4	−	18457.4i	0.344711	−	0.597058i
$986$		0			0
$987$	−2097.08	−	12126.9i	−0.0676300	−	0.391089i
$988$		0			0
$989$	11895.9	−	20604.3i	0.382475	−	0.662466i
$990$		0			0
$991$	−19487.5	−	33753.4i	−0.624664	−	1.08195i	−0.988606	−	0.150528i	$-0.951903\pi$
$991$	−19487.5	−	33753.4i	−0.624664	−	1.08195i	0.363942	−	0.931422i	$-0.381431\pi$
$992$		0			0
$993$	−18231.6			−0.582642
$994$		0			0
$995$	10682.9			0.340372
$996$		0			0
$997$	−22151.9	−	38368.2i	−0.703668	−	1.21879i	−0.967170	−	0.254129i	$-0.918211\pi$
$997$	−22151.9	−	38368.2i	−0.703668	−	1.21879i	0.263503	−	0.964659i	$-0.415122\pi$
$998$		0			0
$999$	−17122.6	+	29657.3i	−0.542279	+	0.939254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.4.i.e.65.2	yes	12
4.3	odd	2		224.4.i.c.65.5	✓	12
7.2	even	3		1568.4.a.be.1.5		6
7.4	even	3	inner	224.4.i.e.193.2	yes	12
7.5	odd	6		1568.4.a.bj.1.2		6
8.3	odd	2		448.4.i.q.65.2		12
8.5	even	2		448.4.i.o.65.5		12
28.11	odd	6		224.4.i.c.193.5	yes	12
28.19	even	6		1568.4.a.bf.1.5		6
28.23	odd	6		1568.4.a.bi.1.2		6
56.11	odd	6		448.4.i.q.193.2		12
56.53	even	6		448.4.i.o.193.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.4.i.c.65.5	✓	12	4.3	odd	2
224.4.i.c.193.5	yes	12	28.11	odd	6
224.4.i.e.65.2	yes	12	1.1	even	1	trivial
224.4.i.e.193.2	yes	12	7.4	even	3	inner
448.4.i.o.65.5		12	8.5	even	2
448.4.i.o.193.5		12	56.53	even	6
448.4.i.q.65.2		12	8.3	odd	2
448.4.i.q.193.2		12	56.11	odd	6
1568.4.a.be.1.5		6	7.2	even	3
1568.4.a.bf.1.5		6	28.19	even	6
1568.4.a.bi.1.2		6	28.23	odd	6
1568.4.a.bj.1.2		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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	224.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.78574 - 4.82504i) q^{3} +(2.27739 - 3.94456i) q^{5} +(3.15583 + 18.2494i) q^{7} +(-2.02069 + 3.49995i) q^{9} +O(q^{10})\)	\(q+(-2.78574 - 4.82504i) q^{3} +(2.27739 - 3.94456i) q^{5} +(3.15583 + 18.2494i) q^{7} +(-2.02069 + 3.49995i) q^{9} +(32.8812 + 56.9520i) q^{11} +73.6042 q^{13} -25.3769 q^{15} +(-65.5016 - 113.452i) q^{17} +(13.2261 - 22.9083i) q^{19} +(79.2628 - 66.0651i) q^{21} +(41.0709 - 71.1369i) q^{23} +(52.1270 + 90.2866i) q^{25} -127.913 q^{27} +4.65118 q^{29} +(-40.0340 - 69.3410i) q^{31} +(183.197 - 317.307i) q^{33} +(79.1729 + 29.1127i) q^{35} +(133.861 - 231.854i) q^{37} +(-205.042 - 355.144i) q^{39} +328.215 q^{41} +289.643 q^{43} +(9.20383 + 15.9415i) q^{45} +(59.6350 - 103.291i) q^{47} +(-323.082 + 115.184i) q^{49} +(-364.941 + 632.096i) q^{51} +(75.1052 + 130.086i) q^{53} +299.534 q^{55} -147.378 q^{57} +(211.594 + 366.491i) q^{59} +(251.152 - 435.008i) q^{61} +(-70.2489 - 25.8312i) q^{63} +(167.626 - 290.336i) q^{65} +(195.116 + 337.950i) q^{67} -457.651 q^{69} -803.592 q^{71} +(184.228 + 319.092i) q^{73} +(290.424 - 503.030i) q^{75} +(-935.572 + 779.794i) q^{77} +(276.400 - 478.738i) q^{79} +(410.892 + 711.686i) q^{81} -62.3318 q^{83} -596.691 q^{85} +(-12.9570 - 22.4421i) q^{87} +(-237.684 + 411.681i) q^{89} +(232.282 + 1343.23i) q^{91} +(-223.049 + 386.332i) q^{93} +(-60.2420 - 104.342i) q^{95} +11.8811 q^{97} -265.772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 10 q^{5} - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 10 * q^5 - 4 * q^7 - 40 * q^9	\( 12 q + 6 q^{3} + 10 q^{5} - 4 q^{7} - 40 q^{9} + 42 q^{11} - 16 q^{13} + 52 q^{15} - 70 q^{17} + 158 q^{19} + 178 q^{21} - 158 q^{23} - 72 q^{25} - 492 q^{27} - 112 q^{29} + 2 q^{31} - 262 q^{33} + 418 q^{35} + 102 q^{37} - 280 q^{39} + 96 q^{41} - 368 q^{43} + 392 q^{45} + 766 q^{47} + 132 q^{49} - 394 q^{51} - 562 q^{53} - 372 q^{55} + 1316 q^{57} + 854 q^{59} - 106 q^{61} + 1864 q^{63} - 488 q^{65} - 906 q^{67} - 2788 q^{69} - 2976 q^{71} - 202 q^{73} + 2248 q^{75} + 590 q^{77} - 942 q^{79} - 674 q^{81} + 1232 q^{83} + 1996 q^{85} + 1656 q^{87} - 858 q^{89} + 4192 q^{91} + 1362 q^{93} - 2386 q^{95} + 3392 q^{97} - 11504 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 10 * q^5 - 4 * q^7 - 40 * q^9 + 42 * q^11 - 16 * q^13 + 52 * q^15 - 70 * q^17 + 158 * q^19 + 178 * q^21 - 158 * q^23 - 72 * q^25 - 492 * q^27 - 112 * q^29 + 2 * q^31 - 262 * q^33 + 418 * q^35 + 102 * q^37 - 280 * q^39 + 96 * q^41 - 368 * q^43 + 392 * q^45 + 766 * q^47 + 132 * q^49 - 394 * q^51 - 562 * q^53 - 372 * q^55 + 1316 * q^57 + 854 * q^59 - 106 * q^61 + 1864 * q^63 - 488 * q^65 - 906 * q^67 - 2788 * q^69 - 2976 * q^71 - 202 * q^73 + 2248 * q^75 + 590 * q^77 - 942 * q^79 - 674 * q^81 + 1232 * q^83 + 1996 * q^85 + 1656 * q^87 - 858 * q^89 + 4192 * q^91 + 1362 * q^93 - 2386 * q^95 + 3392 * q^97 - 11504 * q^99

Introduction

L-functions

Modular forms

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Database

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