LMFDB - Embedded newform 448.4.i.o.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(65,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, 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("448.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4328556826$
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:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.5
Root			$-1.98748 - 4.22573i$ of defining polynomial
Character	$\chi$	$=$	448.65
Dual form			448.4.i.o.193.5

$q$-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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

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

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	$0.0134423\pi$
$3$	2.78574	+	4.82504i	0.536116	+	0.928580i	−0.462993	+	0.886362i	$0.653224\pi$
$4$		0			0
$5$	−2.27739	+	3.94456i	−0.203696	+	0.352812i	−0.949717	−	0.313111i	$-0.898629\pi$
$5$	−2.27739	+	3.94456i	−0.203696	+	0.352812i	0.746020	+	0.665923i	$0.231962\pi$
$6$		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	$-0.809296\pi$
$11$	−32.8812	−	56.9520i	−0.901279	−	1.56106i	−0.0754429	−	0.997150i	$-0.524037\pi$
$12$		0			0
$13$	−73.6042			−1.57032			−0.785159	−	0.619294i	$-0.787419\pi$
$13$	−73.6042			−1.57032			−0.785159	+	0.619294i	$0.787419\pi$
$14$		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	−0.934760	−	0.355280i	$-0.884386\pi$
$19$	−13.2261	+	22.9083i	−0.159699	+	0.276606i	0.775061	+	0.631886i	$0.217719\pi$
$20$		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	$-0.504740\pi$
$29$	−4.65118			−0.0297828			−0.0148914	+	0.999889i	$0.504740\pi$
$30$		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	$0.369425\pi$
$37$	−133.861	+	231.854i	−0.594774	+	1.03018i	−0.993579	+	0.113143i	$0.963908\pi$
$38$		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	$-0.671691\pi$
$43$	−289.643			−1.02721			−0.513606	+	0.858026i	$0.671691\pi$
$44$		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	0.752135	−	0.659009i	$-0.229024\pi$
$53$	−75.1052	−	130.086i	−0.194651	−	0.337145i	−0.946786	+	0.321864i	$0.895691\pi$
$54$		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	0.532384	−	0.846503i	$-0.321296\pi$
$59$	−211.594	−	366.491i	−0.466901	−	0.808696i	−0.999285	+	0.0378067i	$0.987963\pi$
$60$		0			0
$61$	−251.152	+	435.008i	−0.527160	+	0.913068i	0.472339	+	0.881417i	$0.343410\pi$
$61$	−251.152	+	435.008i	−0.527160	+	0.913068i	−0.999499	+	0.0316507i	$0.989924\pi$
$62$		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	0.631472	−	0.775398i	$-0.282451\pi$
$67$	−195.116	−	337.950i	−0.355778	−	0.616226i	−0.987251	+	0.159172i	$0.949118\pi$
$68$		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	$-0.486877\pi$
$83$	62.3318			0.0824313			0.0412157	+	0.999150i	$0.486877\pi$
$84$		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	0.988254	−	0.152822i	$-0.0488360\pi$
$101$	367.220	+	636.043i	0.361779	+	0.626620i	−0.626474	+	0.779442i	$0.715503\pi$
$102$		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	−0.942835	−	0.333259i	$-0.891852\pi$
$107$	−202.334	+	350.452i	−0.182807	+	0.316631i	0.760028	+	0.649890i	$0.225185\pi$
$108$		0			0
$109$	−972.773	−	1684.89i	−0.854814	−	1.48058i	−0.876817	−	0.480823i	$-0.840338\pi$
$109$	−972.773	−	1684.89i	−0.854814	−	1.48058i	0.0220035	−	0.999758i	$-0.492995\pi$
$110$		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	−0.850578	−	0.525849i	$-0.823748\pi$
$131$	45.1460	−	78.1952i	0.0301101	−	0.0521523i	0.880688	+	0.473697i	$0.157081\pi$
$132$		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	$-0.520794\pi$
$139$	−213.957			−0.130558			−0.0652791	+	0.997867i	$0.520794\pi$
$140$		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	$0.376801\pi$
$149$	−1115.35	+	1931.84i	−0.613240	+	1.06216i	−0.990690	+	0.136134i	$0.956532\pi$
$150$		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	$-0.981516\pi$
$157$	−1080.82	−	1872.03i	−0.549417	−	0.951618i	0.448897	−	0.893583i	$-0.351817\pi$
$158$		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	$-0.580515\pi$
$163$	1484.49	−	2571.22i	0.713340	−	1.23554i	0.963596	−	0.267361i	$-0.0861516\pi$
$164$		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	−0.936126	−	0.351665i	$-0.885616\pi$
$173$	−372.066	+	644.437i	−0.163512	+	0.283212i	0.772614	+	0.634877i	$0.218949\pi$
$174$		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	$0.0413934\pi$
$179$	1456.26	+	2522.32i	0.608080	+	1.05323i	−0.383476	+	0.923551i	$0.625273\pi$
$180$		0			0
$181$	2630.43			1.08021			0.540106	−	0.841597i	$-0.318384\pi$
$181$	2630.43			1.08021			0.540106	+	0.841597i	$0.318384\pi$
$182$		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	$-0.821080\pi$
$197$	−4679.21			−1.69228			−0.846141	+	0.532959i	$0.821080\pi$
$198$		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	$-0.312622\pi$
$211$	3403.64			1.11050			0.555251	+	0.831683i	$0.312622\pi$
$212$		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	0.983875	−	0.178855i	$-0.0572393\pi$
$227$	1152.73	+	1996.58i	0.337045	+	0.583778i	−0.646831	+	0.762634i	$0.723906\pi$
$228$		0			0
$229$	1433.78	−	2483.38i	0.413742	−	0.716622i	−0.581553	−	0.813508i	$-0.697555\pi$
$229$	1433.78	−	2483.38i	0.413742	−	0.716622i	0.995295	+	0.0968860i	$0.0308882\pi$
$230$		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	$-0.313271\pi$
$251$	4402.52			1.10711			0.553555	+	0.832813i	$0.313271\pi$
$252$		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	0.957948	−	0.286942i	$-0.0926387\pi$
$269$	1016.84	+	1761.22i	0.230475	+	0.399194i	−0.727473	+	0.686136i	$0.759305\pi$
$270$		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	0.563185	−	0.826331i	$-0.309576\pi$
$277$	−2000.97	−	3465.78i	−0.434031	−	0.751763i	−0.997216	+	0.0745674i	$0.976242\pi$
$278$		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	0.545802	−	0.837914i	$-0.316225\pi$
$283$	−2155.47	−	3733.38i	−0.452753	−	0.784192i	−0.998556	+	0.0537219i	$0.982892\pi$
$284$		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	$-0.511347\pi$
$293$	−357.486			−0.0712783			−0.0356392	+	0.999365i	$0.511347\pi$
$294$		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	$-0.367937\pi$
$307$	4336.47			0.806173			0.403087	+	0.915162i	$0.367937\pi$
$308$		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	−0.585914	−	0.810373i	$-0.699265\pi$
$317$	2307.54	−	3996.77i	0.408846	−	0.708142i	0.994761	+	0.102230i	$0.0325979\pi$
$318$		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	−0.969296	−	0.245896i	$-0.920918\pi$
$331$	−1636.16	+	2833.91i	−0.271696	+	0.470591i	0.697600	+	0.716487i	$0.254251\pi$
$332$		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	0.790145	−	0.612920i	$-0.210005\pi$
$347$	−877.357	−	1519.63i	−0.135732	−	0.235095i	−0.925877	+	0.377825i	$0.876672\pi$
$348$		0			0
$349$	4237.15			0.649884			0.324942	−	0.945734i	$-0.394655\pi$
$349$	4237.15			0.649884			0.324942	+	0.945734i	$0.394655\pi$
$350$		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	−0.998689	−	0.0511884i	$-0.983699\pi$
$373$	−3277.84	+	5677.39i	−0.455014	+	0.788107i	0.543675	+	0.839296i	$0.317032\pi$
$374$		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	$-0.235998\pi$
$379$	10883.3			1.47503			0.737517	+	0.675328i	$0.235998\pi$
$380$		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	0.828422	−	0.560104i	$-0.189239\pi$
$389$	−543.603	−	941.549i	−0.0708529	−	0.122721i	−0.899275	+	0.437383i	$0.855905\pi$
$390$		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	−0.905836	−	0.423629i	$-0.860756\pi$
$397$	−680.622	+	1178.87i	−0.0860439	+	0.149032i	0.819792	+	0.572662i	$0.194089\pi$
$398$		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	$-0.480538\pi$
$419$	1048.13			0.122206			0.0611030	+	0.998131i	$0.480538\pi$
$420$		0			0
$421$	1023.21			0.118452			0.0592259	−	0.998245i	$-0.481137\pi$
$421$	1023.21			0.118452			0.0592259	+	0.998245i	$0.481137\pi$
$422$		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	−0.905333	−	0.424702i	$-0.860379\pi$
$443$	−791.275	+	1370.53i	−0.0848637	+	0.146988i	0.820469	+	0.571690i	$0.193712\pi$
$444$		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	$-0.176123\pi$
$461$	16842.4			1.70158			0.850792	+	0.525503i	$0.176123\pi$
$462$		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	$-0.532755\pi$
$467$	8175.33	−	14160.1i	0.810084	−	1.40311i	0.912805	−	0.408396i	$-0.133912\pi$
$468$		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	$-0.334002\pi$
$491$	10840.2			0.996362			0.498181	+	0.867073i	$0.334002\pi$
$492$		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	$0.448911\pi$
$499$	−8638.65	+	14962.6i	−0.774989	+	1.34232i	−0.934801	+	0.355172i	$0.884422\pi$
$500$		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	$0.375256\pi$
$509$	−6998.07	+	12121.0i	−0.609398	+	1.05551i	−0.991340	+	0.131323i	$0.958078\pi$
$510$		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	−0.945941	−	0.324340i	$-0.894858\pi$
$523$	−2297.44	+	3979.28i	−0.192084	+	0.332699i	0.753857	+	0.657039i	$0.228191\pi$
$524$		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	−0.561092	−	0.827754i	$-0.689618\pi$
$541$	5490.24	−	9509.37i	0.436310	−	0.755711i	0.997402	+	0.0720427i	$0.0229518\pi$
$542$		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	$-0.792772\pi$
$547$	−20353.1			−1.59092			−0.795462	+	0.606003i	$0.792772\pi$
$548$		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	0.557667	−	0.830065i	$-0.311697\pi$
$557$	−5784.40	−	10018.9i	−0.440024	−	0.762143i	−0.997691	+	0.0679216i	$0.978363\pi$
$558$		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	0.978666	−	0.205460i	$-0.0658690\pi$
$563$	4159.87	+	7205.11i	0.311399	+	0.539359i	−0.667266	+	0.744819i	$0.732536\pi$
$564$		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	0.735867	−	0.677126i	$-0.236775\pi$
$571$	−2980.95	−	5163.16i	−0.218475	−	0.378409i	−0.954342	+	0.298717i	$0.903441\pi$
$572$		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	$-0.527754\pi$
$587$	−2476.93			−0.174163			−0.0870816	+	0.996201i	$0.527754\pi$
$588$		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	0.942933	−	0.332982i	$-0.108055\pi$
$613$	2778.87	+	4813.15i	0.183096	+	0.317131i	−0.759838	+	0.650113i	$0.774722\pi$
$614$		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	0.788890	−	0.614534i	$-0.210656\pi$
$619$	−2121.53	−	3674.59i	−0.137757	−	0.238602i	−0.926647	+	0.375932i	$0.877323\pi$
$620$		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	$-0.350180\pi$
$643$	14788.0			0.906971			0.453486	+	0.891264i	$0.350180\pi$
$644$		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	−0.847711	−	0.530458i	$-0.822020\pi$
$653$	592.944	−	1027.01i	0.0355340	−	0.0615466i	0.883245	+	0.468911i	$0.155353\pi$
$654$		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	$-0.574089\pi$
$659$	−7804.32			−0.461325			−0.230662	+	0.973034i	$0.574089\pi$
$660$		0			0
$661$	−4344.92	−	7525.62i	−0.255670	−	0.442833i	0.709408	−	0.704799i	$-0.248963\pi$
$661$	−4344.92	−	7525.62i	−0.255670	−	0.442833i	−0.965077	+	0.261966i	$0.915629\pi$
$662$		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	$-0.656637\pi$
$677$	9283.75	−	16079.9i	0.527036	−	0.912853i	0.999504	−	0.0315052i	$-0.0100301\pi$
$678$		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	0.603295	−	0.797518i	$-0.293854\pi$
$683$	−6943.95	−	12027.3i	−0.389023	−	0.673808i	−0.992318	+	0.123710i	$0.960521\pi$
$684$		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	−0.690286	−	0.723537i	$-0.742515\pi$
$691$	5112.48	−	8855.08i	0.281459	−	0.487501i	0.971744	+	0.236036i	$0.0758484\pi$
$692$		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	$-0.341139\pi$
$701$	17766.2			0.957232			0.478616	+	0.878024i	$0.341139\pi$
$702$		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	−0.993939	−	0.109932i	$-0.964937\pi$
$709$	−7584.77	+	13137.2i	−0.401766	+	0.695879i	0.592173	+	0.805811i	$0.298270\pi$
$710$		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	$0.434196\pi$
$733$	−14783.8	+	25606.3i	−0.744956	+	1.29030i	−0.950215	+	0.311594i	$0.899137\pi$
$734$		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	0.826126	−	0.563485i	$-0.190540\pi$
$739$	−1505.28	−	2607.23i	−0.0749293	−	0.129781i	−0.901056	+	0.433704i	$0.857206\pi$
$740$		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	$-0.582968\pi$
$757$	−10735.1			−0.515420			−0.257710	+	0.966222i	$0.582968\pi$
$758$		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	0.727187	−	0.686439i	$-0.240827\pi$
$773$	−4961.99	−	8594.42i	−0.230880	−	0.399896i	−0.958067	+	0.286543i	$0.907494\pi$
$774$		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	$0.101829\pi$
$787$	16491.9	+	28564.7i	0.746978	+	1.29380i	−0.202288	+	0.979326i	$0.564838\pi$
$788$		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	$-0.606915\pi$
$797$	−14832.3			−0.659207			−0.329603	+	0.944119i	$0.606915\pi$
$798$		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	$-0.676395\pi$
$811$	−24307.3			−1.05246			−0.526229	+	0.850343i	$0.676395\pi$
$812$		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	−0.854454	−	0.519526i	$-0.826108\pi$
$821$	533.897	−	924.737i	0.0226957	−	0.0393100i	0.877150	+	0.480216i	$0.159442\pi$
$822$		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	$-0.260318\pi$
$827$	32525.9			1.36764			0.683818	+	0.729653i	$0.260318\pi$
$828$		0			0
$829$	17962.1	+	31111.2i	0.752532	+	1.30342i	0.946592	+	0.322433i	$0.104501\pi$
$829$	17962.1	+	31111.2i	0.752532	+	1.30342i	−0.194061	+	0.980990i	$0.562166\pi$
$830$		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	$-0.719257\pi$
$853$	−31670.4			−1.27125			−0.635624	+	0.771999i	$0.719257\pi$
$854$		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	−0.529653	−	0.848215i	$-0.677678\pi$
$859$	11826.5	−	20484.1i	0.469749	−	0.813629i	0.999402	+	0.0345855i	$0.0110111\pi$
$860$		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	$-0.568463\pi$
$877$	19202.3	−	33259.3i	0.739356	−	1.28060i	0.952786	−	0.303644i	$-0.0982032\pi$
$878$		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	$-0.691864\pi$
$883$	−29750.2			−1.13383			−0.566917	+	0.823775i	$0.691864\pi$
$884$		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	$-0.941019\pi$
$907$	−17782.3	−	30799.8i	−0.650993	−	1.12755i	0.331889	−	0.943318i	$-0.392314\pi$
$908$		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	0.715860	−	0.698244i	$-0.246035\pi$
$941$	−7123.15	−	12337.7i	−0.246767	−	0.427414i	−0.962627	+	0.270831i	$0.912702\pi$
$942$		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	$-0.634362\pi$
$947$	17053.1	−	29536.9i	0.585167	−	1.01354i	0.994855	−	0.101312i	$-0.0323042\pi$
$948$		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	−0.852206	−	0.523206i	$-0.824736\pi$
$971$	817.140	−	1415.33i	0.0270065	−	0.0467766i	0.879213	+	0.476429i	$0.158069\pi$
$972$		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	$0.0817889\pi$
$997$	22151.9	+	38368.2i	0.703668	+	1.21879i	−0.263503	+	0.964659i	$0.584878\pi$
$998$		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	448.4.i.o.65.5		12
4.3	odd	2		448.4.i.q.65.2		12
7.4	even	3	inner	448.4.i.o.193.5		12
8.3	odd	2		224.4.i.c.65.5	✓	12
8.5	even	2		224.4.i.e.65.2	yes	12
28.11	odd	6		448.4.i.q.193.2		12
56.5	odd	6		1568.4.a.bj.1.2		6
56.11	odd	6		224.4.i.c.193.5	yes	12
56.19	even	6		1568.4.a.bf.1.5		6
56.37	even	6		1568.4.a.be.1.5		6
56.51	odd	6		1568.4.a.bi.1.2		6
56.53	even	6		224.4.i.e.193.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.4.i.c.65.5	✓	12	8.3	odd	2
224.4.i.c.193.5	yes	12	56.11	odd	6
224.4.i.e.65.2	yes	12	8.5	even	2
224.4.i.e.193.2	yes	12	56.53	even	6
448.4.i.o.65.5		12	1.1	even	1	trivial
448.4.i.o.193.5		12	7.4	even	3	inner
448.4.i.q.65.2		12	4.3	odd	2
448.4.i.q.193.2		12	28.11	odd	6
1568.4.a.be.1.5		6	56.37	even	6
1568.4.a.bf.1.5		6	56.19	even	6
1568.4.a.bi.1.2		6	56.51	odd	6
1568.4.a.bj.1.2		6	56.5	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.i (of order \(3\), degree \(2\), not 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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