LMFDB - Embedded newform 1000.2.m.c.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(201,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1000.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.m (of order $5$, degree $4$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 12 x^{14} - 18 x^{13} + 100 x^{12} + 23 x^{11} + 567 x^{10} + 556 x^{9} + 3841 x^{8} + \cdots + 6400 $ x^16 - x^15 + 12x^14 - 18x^13 + 100x^12 + 23x^11 + 567x^10 + 556x^9 + 3841x^8 + 1155x^7 + 7575x^6 - 875x^5 + 7485x^4 + 900x^3 + 2000x^2 + 1600x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.3
Root			$-0.462625 - 1.42381i$ of defining polynomial
Character	$\chi$	$=$	1000.201
Dual form			1000.2.m.c.801.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.462625 + 1.42381i) q^{3} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +O(q^{10})$	\(q+(0.462625 + 1.42381i) q^{3} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +(-1.04731 - 0.760912i) q^{11} +(0.663861 - 0.482323i) q^{13} +(0.676707 - 2.08269i) q^{17} +(1.98926 - 6.12233i) q^{19} +(2.28551 + 7.03407i) q^{21} +(1.79177 + 1.30180i) q^{23} +(4.55246 + 3.30755i) q^{27} +(-1.64801 - 5.07207i) q^{29} +(0.218880 - 0.673643i) q^{31} +(0.598887 - 1.84318i) q^{33} +(-5.78922 + 4.20612i) q^{37} +(0.993856 + 0.722078i) q^{39} +(-8.19030 + 5.95060i) q^{41} -5.26985 q^{43} +(-2.48612 - 7.65150i) q^{47} +17.4067 q^{49} +3.27842 q^{51} +(4.08608 + 12.5757i) q^{53} +9.63732 q^{57} +(-7.76420 + 5.64102i) q^{59} +(5.29271 + 3.84538i) q^{61} +(3.03252 - 2.20325i) q^{63} +(2.26224 - 6.96246i) q^{67} +(-1.02460 + 3.15339i) q^{69} +(-0.197864 - 0.608964i) q^{71} +(9.68999 + 7.04019i) q^{73} +(-5.17402 - 3.75914i) q^{77} +(-0.692240 - 2.13050i) q^{79} +(-1.89987 + 5.84719i) q^{81} +(-3.53986 + 10.8946i) q^{83} +(6.45926 - 4.69293i) q^{87} +(2.56905 + 1.86652i) q^{89} +(3.27968 - 2.38283i) q^{91} +1.06040 q^{93} +(5.09821 + 15.6907i) q^{97} -0.982218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 6 q^{7} - 11 q^{9}+O(q^{10}) $ 16 * q - q^3 + 6 * q^7 - 11 * q^9	$ 16 q - q^{3} + 6 q^{7} - 11 q^{9} - 10 q^{11} - q^{13} + 4 q^{17} - 3 q^{21} - 11 q^{23} - 13 q^{27} + 5 q^{29} - 9 q^{31} - 16 q^{33} - 30 q^{37} + 14 q^{39} - 2 q^{41} + 42 q^{43} + 16 q^{47} + 18 q^{49} + 100 q^{51} - 11 q^{53} + 64 q^{57} - 53 q^{59} + 4 q^{61} + 38 q^{63} + 14 q^{67} - 7 q^{69} - 6 q^{71} + 24 q^{73} - 23 q^{77} - 22 q^{79} - 6 q^{81} - 33 q^{83} - 37 q^{87} + 20 q^{89} - 27 q^{91} - 40 q^{93} - 11 q^{97} + 122 q^{99}+O(q^{100}) $ 16 * q - q^3 + 6 * q^7 - 11 * q^9 - 10 * q^11 - q^13 + 4 * q^17 - 3 * q^21 - 11 * q^23 - 13 * q^27 + 5 * q^29 - 9 * q^31 - 16 * q^33 - 30 * q^37 + 14 * q^39 - 2 * q^41 + 42 * q^43 + 16 * q^47 + 18 * q^49 + 100 * q^51 - 11 * q^53 + 64 * q^57 - 53 * q^59 + 4 * q^61 + 38 * q^63 + 14 * q^67 - 7 * q^69 - 6 * q^71 + 24 * q^73 - 23 * q^77 - 22 * q^79 - 6 * q^81 - 33 * q^83 - 37 * q^87 + 20 * q^89 - 27 * q^91 - 40 * q^93 - 11 * q^97 + 122 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.462625	+	1.42381i	0.267096	+	0.822038i	0.991203	+	0.132350i	$0.0422523\pi$
$3$	0.462625	+	1.42381i	0.267096	+	0.822038i	−0.724107	+	0.689688i	$0.757748\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.94031			1.86726			0.933631	−	0.358237i	$-0.116622\pi$
$7$	4.94031			1.86726			0.933631	+	0.358237i	$0.116622\pi$
$8$		0			0
$9$	0.613832	−	0.445975i	0.204611	−	0.148658i
$10$		0			0
$11$	−1.04731	−	0.760912i	−0.315775	−	0.229424i	0.418596	−	0.908173i	$-0.362522\pi$
$11$	−1.04731	−	0.760912i	−0.315775	−	0.229424i	−0.734370	+	0.678749i	$0.762522\pi$
$12$		0			0
$13$	0.663861	−	0.482323i	0.184122	−	0.133772i	−0.491906	−	0.870648i	$-0.663700\pi$
$13$	0.663861	−	0.482323i	0.184122	−	0.133772i	0.676028	+	0.736876i	$0.263700\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.676707	−	2.08269i	0.164126	−	0.505126i	−0.834845	−	0.550485i	$-0.814443\pi$
$17$	0.676707	−	2.08269i	0.164126	−	0.505126i	0.998971	+	0.0453583i	$0.0144429\pi$
$18$		0			0
$19$	1.98926	−	6.12233i	0.456369	−	1.40456i	−0.413152	−	0.910662i	$-0.635572\pi$
$19$	1.98926	−	6.12233i	0.456369	−	1.40456i	0.869521	−	0.493896i	$-0.164428\pi$
$20$		0			0
$21$	2.28551	+	7.03407i	0.498739	+	1.53496i
$22$		0			0
$23$	1.79177	+	1.30180i	0.373610	+	0.271444i	0.758706	−	0.651433i	$-0.225832\pi$
$23$	1.79177	+	1.30180i	0.373610	+	0.271444i	−0.385096	+	0.922876i	$0.625832\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.55246	+	3.30755i	0.876121	+	0.636539i
$28$		0			0
$29$	−1.64801	−	5.07207i	−0.306029	−	0.941859i	−0.979291	−	0.202456i	$-0.935108\pi$
$29$	−1.64801	−	5.07207i	−0.306029	−	0.941859i	0.673263	−	0.739403i	$-0.264892\pi$
$30$		0			0
$31$	0.218880	−	0.673643i	0.0393120	−	0.120990i	−0.929475	−	0.368886i	$-0.879739\pi$
$31$	0.218880	−	0.673643i	0.0393120	−	0.120990i	0.968787	+	0.247896i	$0.0797392\pi$
$32$		0			0
$33$	0.598887	−	1.84318i	0.104253	−	0.320857i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.78922	+	4.20612i	−0.951742	+	0.691481i	−0.951218	−	0.308519i	$-0.900167\pi$
$37$	−5.78922	+	4.20612i	−0.951742	+	0.691481i	−0.000523879		1.00000i	$0.500167\pi$
$38$		0			0
$39$	0.993856	+	0.722078i	0.159144	+	0.115625i
$40$		0			0
$41$	−8.19030	+	5.95060i	−1.27911	+	0.929328i	−0.999526	−	0.0307933i	$-0.990197\pi$
$41$	−8.19030	+	5.95060i	−1.27911	+	0.929328i	−0.279584	+	0.960121i	$0.590197\pi$
$42$		0			0
$43$	−5.26985			−0.803645			−0.401823	−	0.915718i	$-0.631623\pi$
$43$	−5.26985			−0.803645			−0.401823	+	0.915718i	$0.631623\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.48612	−	7.65150i	−0.362638	−	1.11609i	−0.951447	−	0.307813i	$-0.900403\pi$
$47$	−2.48612	−	7.65150i	−0.362638	−	1.11609i	0.588809	−	0.808273i	$-0.299597\pi$
$48$		0			0
$49$	17.4067			2.48667
$50$		0			0
$51$	3.27842			0.459071
$52$		0			0
$53$	4.08608	+	12.5757i	0.561266	+	1.72740i	0.678792	+	0.734331i	$0.262504\pi$
$53$	4.08608	+	12.5757i	0.561266	+	1.72740i	−0.117526	+	0.993070i	$0.537496\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.63732			1.27649
$58$		0			0
$59$	−7.76420	+	5.64102i	−1.01081	+	0.734398i	−0.964379	−	0.264523i	$-0.914785\pi$
$59$	−7.76420	+	5.64102i	−1.01081	+	0.734398i	−0.0464331	+	0.998921i	$0.514785\pi$
$60$		0			0
$61$	5.29271	+	3.84538i	0.677662	+	0.492350i	0.872581	−	0.488469i	$-0.162445\pi$
$61$	5.29271	+	3.84538i	0.677662	+	0.492350i	−0.194919	+	0.980819i	$0.562445\pi$
$62$		0			0
$63$	3.03252	−	2.20325i	0.382061	−	0.277584i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.26224	−	6.96246i	0.276377	−	0.850600i	−0.712475	−	0.701697i	$-0.752426\pi$
$67$	2.26224	−	6.96246i	0.276377	−	0.850600i	0.988852	−	0.148903i	$-0.0475741\pi$
$68$		0			0
$69$	−1.02460	+	3.15339i	−0.123347	+	0.379624i
$70$		0			0
$71$	−0.197864	−	0.608964i	−0.0234822	−	0.0722707i	0.938629	−	0.344929i	$-0.112097\pi$
$71$	−0.197864	−	0.608964i	−0.0234822	−	0.0722707i	−0.962111	+	0.272658i	$0.912097\pi$
$72$		0			0
$73$	9.68999	+	7.04019i	1.13413	+	0.823992i	0.986290	−	0.165020i	$-0.0527689\pi$
$73$	9.68999	+	7.04019i	1.13413	+	0.823992i	0.147837	+	0.989012i	$0.452769\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.17402	−	3.75914i	−0.589634	−	0.428394i
$78$		0			0
$79$	−0.692240	−	2.13050i	−0.0778831	−	0.239700i	0.904533	−	0.426403i	$-0.140220\pi$
$79$	−0.692240	−	2.13050i	−0.0778831	−	0.239700i	−0.982416	+	0.186704i	$0.940220\pi$
$80$		0			0
$81$	−1.89987	+	5.84719i	−0.211096	+	0.649688i
$82$		0			0
$83$	−3.53986	+	10.8946i	−0.388550	+	1.19583i	0.545322	+	0.838226i	$0.316407\pi$
$83$	−3.53986	+	10.8946i	−0.388550	+	1.19583i	−0.933872	+	0.357607i	$0.883593\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.45926	−	4.69293i	0.692505	−	0.503135i
$88$		0			0
$89$	2.56905	+	1.86652i	0.272319	+	0.197851i	0.715560	−	0.698551i	$-0.246172\pi$
$89$	2.56905	+	1.86652i	0.272319	+	0.197851i	−0.443241	+	0.896402i	$0.646172\pi$
$90$		0			0
$91$	3.27968	−	2.38283i	0.343804	−	0.249788i
$92$		0			0
$93$	1.06040			0.109958
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.09821	+	15.6907i	0.517645	+	1.59315i	0.778418	+	0.627747i	$0.216023\pi$
$97$	5.09821	+	15.6907i	0.517645	+	1.59315i	−0.260773	+	0.965400i	$0.583977\pi$
$98$		0			0
$99$	−0.982218			−0.0987166
$100$		0			0
$101$	−10.4077			−1.03561			−0.517804	−	0.855499i	$-0.673250\pi$
$101$	−10.4077			−1.03561			−0.517804	+	0.855499i	$0.673250\pi$
$102$		0			0
$103$	0.528090	+	1.62529i	0.0520343	+	0.160145i	0.973697	−	0.227847i	$-0.0731687\pi$
$103$	0.528090	+	1.62529i	0.0520343	+	0.160145i	−0.921663	+	0.387992i	$0.873169\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.83747			−0.274308			−0.137154	−	0.990550i	$-0.543796\pi$
$107$	−2.83747			−0.274308			−0.137154	+	0.990550i	$0.543796\pi$
$108$		0			0
$109$	−6.66885	+	4.84520i	−0.638760	+	0.464086i	−0.859424	−	0.511264i	$-0.829178\pi$
$109$	−6.66885	+	4.84520i	−0.638760	+	0.464086i	0.220664	+	0.975350i	$0.429178\pi$
$110$		0			0
$111$	−8.66695	−	6.29691i	−0.822631	−	0.597676i
$112$		0			0
$113$	3.16114	−	2.29670i	0.297375	−	0.216055i	−0.429085	−	0.903264i	$-0.641164\pi$
$113$	3.16114	−	2.29670i	0.297375	−	0.216055i	0.726460	+	0.687208i	$0.241164\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.192395	−	0.592130i	0.0177869	−	0.0547425i
$118$		0			0
$119$	3.34314	−	10.2891i	0.306465	−	0.943203i
$120$		0			0
$121$	−2.88132	−	8.86781i	−0.261939	−	0.806164i
$122$		0			0
$123$	−12.2616	−	8.90855i	−1.10559	−	0.803257i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−11.5930	−	8.42282i	−1.02871	−	0.747404i	−0.0606629	−	0.998158i	$-0.519321\pi$
$127$	−11.5930	−	8.42282i	−1.02871	−	0.747404i	−0.968051	+	0.250754i	$0.919321\pi$
$128$		0			0
$129$	−2.43796	−	7.50328i	−0.214651	−	0.660627i
$130$		0			0
$131$	−3.15766	+	9.71827i	−0.275886	+	0.849089i	0.713098	+	0.701065i	$0.247292\pi$
$131$	−3.15766	+	9.71827i	−0.275886	+	0.849089i	−0.988984	+	0.148025i	$0.952708\pi$
$132$		0			0
$133$	9.82758	−	30.2462i	0.852159	−	2.62268i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.93150	+	4.30949i	−0.506762	+	0.368184i	−0.811594	−	0.584222i	$-0.801400\pi$
$137$	−5.93150	+	4.30949i	−0.506762	+	0.368184i	0.304832	+	0.952406i	$0.401400\pi$
$138$		0			0
$139$	−5.41640	−	3.93524i	−0.459413	−	0.333783i	0.333888	−	0.942613i	$-0.391639\pi$
$139$	−5.41640	−	3.93524i	−0.459413	−	0.333783i	−0.793301	+	0.608830i	$0.791639\pi$
$140$		0			0
$141$	9.74415	−	7.07954i	0.820606	−	0.596205i
$142$		0			0
$143$	−1.06227			−0.0888316
$144$		0			0
$145$		0			0
$146$		0			0
$147$	8.05275	+	24.7838i	0.664180	+	2.04413i
$148$		0			0
$149$	−1.30424			−0.106847			−0.0534236	−	0.998572i	$-0.517013\pi$
$149$	−1.30424			−0.106847			−0.0534236	+	0.998572i	$0.517013\pi$
$150$		0			0
$151$	0.227988			0.0185534			0.00927670	−	0.999957i	$-0.497047\pi$
$151$	0.227988			0.0185534			0.00927670	+	0.999957i	$0.497047\pi$
$152$		0			0
$153$	−0.513443	−	1.58022i	−0.0415094	−	0.127753i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.75041			−0.618550			−0.309275	−	0.950973i	$-0.600086\pi$
$157$	−7.75041			−0.618550			−0.309275	+	0.950973i	$0.600086\pi$
$158$		0			0
$159$	−16.0151	+	11.6356i	−1.27008	+	0.922765i
$160$		0			0
$161$	8.85191	+	6.43129i	0.697628	+	0.506856i
$162$		0			0
$163$	−6.78410	+	4.92893i	−0.531371	+	0.386064i	−0.820870	−	0.571114i	$-0.806511\pi$
$163$	−6.78410	+	4.92893i	−0.531371	+	0.386064i	0.289499	+	0.957178i	$0.406511\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.21859	−	6.82811i	0.171680	−	0.528375i	−0.827787	−	0.561043i	$-0.810400\pi$
$167$	2.21859	−	6.82811i	0.171680	−	0.528375i	0.999466	+	0.0326676i	$0.0104003\pi$
$168$		0			0
$169$	−3.80915	+	11.7233i	−0.293011	+	0.901796i
$170$		0			0
$171$	−1.50933	−	4.64524i	−0.115421	−	0.355230i
$172$		0			0
$173$	−12.1252	−	8.80946i	−0.921861	−	0.669771i	0.0221258	−	0.999755i	$-0.492957\pi$
$173$	−12.1252	−	8.80946i	−0.921861	−	0.669771i	−0.943986	+	0.329984i	$0.892957\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.6237	−	8.44508i	−0.873688	−	0.634771i
$178$		0			0
$179$	−5.70579	−	17.5606i	−0.426471	−	1.31254i	−0.901579	−	0.432615i	$-0.857591\pi$
$179$	−5.70579	−	17.5606i	−0.426471	−	1.31254i	0.475108	−	0.879927i	$-0.342409\pi$
$180$		0			0
$181$	6.21242	−	19.1199i	0.461766	−	1.42117i	−0.401239	−	0.915973i	$-0.631420\pi$
$181$	6.21242	−	19.1199i	0.461766	−	1.42117i	0.863005	−	0.505195i	$-0.168580\pi$
$182$		0			0
$183$	−3.02656	+	9.31479i	−0.223730	+	0.688569i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.29346	+	1.66630i	−0.167715	+	0.121852i
$188$		0			0
$189$	22.4906	+	16.3403i	1.63595	+	1.18859i
$190$		0			0
$191$	17.8233	−	12.9494i	1.28965	−	0.936982i	0.289848	−	0.957073i	$-0.406395\pi$
$191$	17.8233	−	12.9494i	1.28965	−	0.936982i	0.999798	+	0.0200904i	$0.00639539\pi$
$192$		0			0
$193$	−16.9231			−1.21815			−0.609077	−	0.793111i	$-0.708460\pi$
$193$	−16.9231			−1.21815			−0.609077	+	0.793111i	$0.708460\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.13633	+	3.49728i	0.0809605	+	0.249171i	0.983341	−	0.181769i	$-0.0581822\pi$
$197$	1.13633	+	3.49728i	0.0809605	+	0.249171i	−0.902381	+	0.430939i	$0.858182\pi$
$198$		0			0
$199$	26.4847			1.87745			0.938724	−	0.344669i	$-0.112009\pi$
$199$	26.4847			1.87745			0.938724	+	0.344669i	$0.112009\pi$
$200$		0			0
$201$	10.9598			0.773045
$202$		0			0
$203$	−8.14170	−	25.0576i	−0.571436	−	1.75870i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.68042			0.116797
$208$		0			0
$209$	−6.74192	+	4.89829i	−0.466349	+	0.338822i
$210$		0			0
$211$	2.51041	+	1.82392i	0.172823	+	0.125564i	0.670834	−	0.741607i	$-0.265936\pi$
$211$	2.51041	+	1.82392i	0.172823	+	0.125564i	−0.498011	+	0.867171i	$0.665936\pi$
$212$		0			0
$213$	0.775514	−	0.563444i	0.0531373	−	0.0386065i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.08133	−	3.32801i	0.0734058	−	0.225920i
$218$		0			0
$219$	−5.54108	+	17.0537i	−0.374431	+	1.15238i
$220$		0			0
$221$	−0.555290	−	1.70901i	−0.0373529	−	0.114960i
$222$		0			0
$223$	6.61578	+	4.80665i	0.443026	+	0.321877i	0.786836	−	0.617162i	$-0.211718\pi$
$223$	6.61578	+	4.80665i	0.443026	+	0.321877i	−0.343810	+	0.939039i	$0.611718\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.2020	−	8.86529i	−0.809877	−	0.588410i	0.103918	−	0.994586i	$-0.466862\pi$
$227$	−12.2020	−	8.86529i	−0.809877	−	0.588410i	−0.913795	+	0.406176i	$0.866862\pi$
$228$		0			0
$229$	−2.70693	−	8.33109i	−0.178879	−	0.550534i	0.820910	−	0.571057i	$-0.193467\pi$
$229$	−2.70693	−	8.33109i	−0.178879	−	0.550534i	−0.999789	+	0.0205237i	$0.993467\pi$
$230$		0			0
$231$	2.95869	−	9.10590i	0.194667	−	0.599124i
$232$		0			0
$233$	−2.45112	+	7.54378i	−0.160578	+	0.494209i	−0.998683	−	0.0512996i	$-0.983664\pi$
$233$	−2.45112	+	7.54378i	−0.160578	+	0.494209i	0.838105	+	0.545509i	$0.183664\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.71318	−	1.97124i	0.176240	−	0.128046i
$238$		0			0
$239$	−0.759253	−	0.551629i	−0.0491120	−	0.0356819i	0.562958	−	0.826485i	$-0.309663\pi$
$239$	−0.759253	−	0.551629i	−0.0491120	−	0.0356819i	−0.612070	+	0.790803i	$0.709663\pi$
$240$		0			0
$241$	−8.86395	+	6.44003i	−0.570977	+	0.414839i	−0.835460	−	0.549551i	$-0.814799\pi$
$241$	−8.86395	+	6.44003i	−0.570977	+	0.414839i	0.264483	+	0.964390i	$0.414799\pi$
$242$		0			0
$243$	7.67721			0.492494
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.63234	−	5.02384i	−0.103864	−	0.319659i
$248$		0			0
$249$	−17.1494			−1.08680
$250$		0			0
$251$	−0.246980			−0.0155893			−0.00779463	−	0.999970i	$-0.502481\pi$
$251$	−0.246980			−0.0155893			−0.00779463	+	0.999970i	$0.502481\pi$
$252$		0			0
$253$	−0.885979	−	2.72676i	−0.0557010	−	0.171430i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.97244			−0.497307			−0.248654	−	0.968592i	$-0.579988\pi$
$257$	−7.97244			−0.497307			−0.248654	+	0.968592i	$0.579988\pi$
$258$		0			0
$259$	−28.6005	+	20.7795i	−1.77715	+	1.29118i
$260$		0			0
$261$	−3.27362	−	2.37842i	−0.202632	−	0.147221i
$262$		0			0
$263$	6.31136	−	4.58547i	0.389175	−	0.282752i	−0.375942	−	0.926643i	$-0.622681\pi$
$263$	6.31136	−	4.58547i	0.389175	−	0.282752i	0.765117	+	0.643891i	$0.222681\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.46907	+	4.52135i	−0.0899059	+	0.276702i
$268$		0			0
$269$	0.440424	−	1.35549i	0.0268531	−	0.0826454i	−0.936732	−	0.350048i	$-0.886165\pi$
$269$	0.440424	−	1.35549i	0.0268531	−	0.0826454i	0.963585	+	0.267402i	$0.0861653\pi$
$270$		0			0
$271$	−7.94569	−	24.4543i	−0.482666	−	1.48549i	−0.835333	−	0.549745i	$-0.814725\pi$
$271$	−7.94569	−	24.4543i	−0.482666	−	1.48549i	0.352667	−	0.935749i	$-0.385275\pi$
$272$		0			0
$273$	4.90996	+	3.56729i	0.297164	+	0.215902i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.1633	+	7.38406i	0.610652	+	0.443665i	0.849644	−	0.527357i	$-0.176817\pi$
$277$	10.1633	+	7.38406i	0.610652	+	0.443665i	−0.238992	+	0.971022i	$0.576817\pi$
$278$		0			0
$279$	−0.166072	−	0.511118i	−0.00994250	−	0.0305999i
$280$		0			0
$281$	−1.79351	+	5.51985i	−0.106992	+	0.329287i	−0.990193	−	0.139708i	$-0.955384\pi$
$281$	−1.79351	+	5.51985i	−0.106992	+	0.329287i	0.883201	+	0.468995i	$0.155384\pi$
$282$		0			0
$283$	1.05349	−	3.24232i	0.0626236	−	0.192736i	−0.914850	−	0.403794i	$-0.867691\pi$
$283$	1.05349	−	3.24232i	0.0626236	−	0.192736i	0.977473	+	0.211059i	$0.0676911\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−40.4626	+	29.3978i	−2.38843	+	1.73530i
$288$		0			0
$289$	9.87363	+	7.17361i	0.580801	+	0.421977i
$290$		0			0
$291$	−19.9820	+	14.5178i	−1.17137	+	0.851048i
$292$		0			0
$293$	0.336923			0.0196832			0.00984162	−	0.999952i	$-0.496867\pi$
$293$	0.336923			0.0196832			0.00984162	+	0.999952i	$0.496867\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.25106	−	6.92804i	−0.130620	−	0.402006i
$298$		0			0
$299$	1.81737			0.105101
$300$		0			0
$301$	−26.0347			−1.50062
$302$		0			0
$303$	−4.81487	−	14.8187i	−0.276607	−	0.851309i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	23.5065			1.34159			0.670793	−	0.741645i	$-0.265954\pi$
$307$	23.5065			1.34159			0.670793	+	0.741645i	$0.265954\pi$
$308$		0			0
$309$	−2.06981	+	1.50380i	−0.117747	+	0.0855483i
$310$		0			0
$311$	−5.87972	−	4.27187i	−0.333408	−	0.242235i	0.408467	−	0.912773i	$-0.366063\pi$
$311$	−5.87972	−	4.27187i	−0.333408	−	0.242235i	−0.741875	+	0.670538i	$0.766063\pi$
$312$		0			0
$313$	−9.58493	+	6.96386i	−0.541772	+	0.393621i	−0.824743	−	0.565508i	$-0.808680\pi$
$313$	−9.58493	+	6.96386i	−0.541772	+	0.393621i	0.282971	+	0.959129i	$0.408680\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.56828	−	4.82667i	0.0880833	−	0.271093i	−0.897306	−	0.441409i	$-0.854479\pi$
$317$	1.56828	−	4.82667i	0.0880833	−	0.271093i	0.985389	+	0.170316i	$0.0544789\pi$
$318$		0			0
$319$	−2.13342	+	6.56600i	−0.119449	+	0.367626i
$320$		0			0
$321$	−1.31268	−	4.04002i	−0.0732667	−	0.225492i
$322$		0			0
$323$	−11.4048	−	8.28604i	−0.634578	−	0.461048i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.98383	−	7.25368i	−0.552107	−	0.401129i
$328$		0			0
$329$	−12.2822	−	37.8008i	−0.677140	−	2.08402i
$330$		0			0
$331$	0.361461	−	1.11246i	0.0198677	−	0.0611465i	−0.940631	−	0.339431i	$-0.889766\pi$
$331$	0.361461	−	1.11246i	0.0198677	−	0.0611465i	0.960499	+	0.278284i	$0.0897657\pi$
$332$		0			0
$333$	−1.67779	+	5.16369i	−0.0919421	+	0.282969i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−12.7113	+	9.23533i	−0.692431	+	0.503081i	−0.877458	−	0.479653i	$-0.840763\pi$
$337$	−12.7113	+	9.23533i	−0.692431	+	0.503081i	0.185027	+	0.982733i	$0.440763\pi$
$338$		0			0
$339$	4.73249	+	3.43836i	0.257034	+	0.186746i
$340$		0			0
$341$	−0.741818	+	0.538962i	−0.0401717	+	0.0291864i
$342$		0			0
$343$	51.4121			2.77599
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.95872	+	6.02832i	0.105150	+	0.323617i	0.989766	−	0.142703i	$-0.0455795\pi$
$347$	1.95872	+	6.02832i	0.105150	+	0.323617i	−0.884616	+	0.466320i	$0.845579\pi$
$348$		0			0
$349$	−32.3947			−1.73405			−0.867023	−	0.498268i	$-0.833970\pi$
$349$	−32.3947			−1.73405			−0.867023	+	0.498268i	$0.833970\pi$
$350$		0			0
$351$	4.61751			0.246464
$352$		0			0
$353$	3.16369	+	9.73685i	0.168386	+	0.518240i	0.999270	−	0.0382063i	$-0.0121644\pi$
$353$	3.16369	+	9.73685i	0.168386	+	0.518240i	−0.830883	+	0.556447i	$0.812164\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	16.1964			0.857205
$358$		0			0
$359$	23.2637	−	16.9020i	1.22781	−	0.892056i	0.231085	−	0.972933i	$-0.425772\pi$
$359$	23.2637	−	16.9020i	1.22781	−	0.892056i	0.996724	+	0.0808776i	$0.0257723\pi$
$360$		0			0
$361$	−18.1544	−	13.1899i	−0.955494	−	0.694207i
$362$		0			0
$363$	11.2931	−	8.20493i	0.592735	−	0.430647i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.30732	−	13.2566i	0.224840	−	0.691988i	−0.773467	−	0.633836i	$-0.781479\pi$
$367$	4.30732	−	13.2566i	0.224840	−	0.691988i	0.998308	−	0.0581516i	$-0.0185207\pi$
$368$		0			0
$369$	−2.37365	+	7.30534i	−0.123567	+	0.380301i
$370$		0			0
$371$	20.1865	+	62.1277i	1.04803	+	3.22551i
$372$		0			0
$373$	10.7964	+	7.84401i	0.559014	+	0.406147i	0.831098	−	0.556126i	$-0.187713\pi$
$373$	10.7964	+	7.84401i	0.559014	+	0.406147i	−0.272084	+	0.962274i	$0.587713\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.54043	−	2.57227i	−0.182341	−	0.132479i
$378$		0			0
$379$	7.44745	+	22.9209i	0.382550	+	1.17737i	0.938242	+	0.345979i	$0.112453\pi$
$379$	7.44745	+	22.9209i	0.382550	+	1.17737i	−0.555693	+	0.831388i	$0.687547\pi$
$380$		0			0
$381$	6.62930	−	20.4029i	0.339629	−	1.04527i
$382$		0			0
$383$	−10.6304	+	32.7170i	−0.543188	+	1.67176i	0.182072	+	0.983285i	$0.441720\pi$
$383$	−10.6304	+	32.7170i	−0.543188	+	1.67176i	−0.725260	+	0.688475i	$0.758280\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.23480	+	2.35022i	−0.164434	+	0.119469i
$388$		0			0
$389$	2.77533	+	2.01639i	0.140715	+	0.102235i	0.655916	−	0.754834i	$-0.272283\pi$
$389$	2.77533	+	2.01639i	0.140715	+	0.102235i	−0.515201	+	0.857069i	$0.672283\pi$
$390$		0			0
$391$	3.92375	−	2.85077i	0.198432	−	0.144170i
$392$		0			0
$393$	−15.2978			−0.771672
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.29725	−	28.6140i	−0.466615	−	1.43609i	−0.856940	−	0.515417i	$-0.827637\pi$
$397$	−9.29725	−	28.6140i	−0.466615	−	1.43609i	0.390324	−	0.920678i	$-0.372363\pi$
$398$		0			0
$399$	47.6114			2.38355
$400$		0			0
$401$	36.3896			1.81721			0.908604	−	0.417658i	$-0.137149\pi$
$401$	36.3896			1.81721			0.908604	+	0.417658i	$0.137149\pi$
$402$		0			0
$403$	−0.179608	−	0.552776i	−0.00894690	−	0.0275357i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.26357			0.459178
$408$		0			0
$409$	−2.97690	+	2.16284i	−0.147198	+	0.106946i	−0.658947	−	0.752189i	$-0.728998\pi$
$409$	−2.97690	+	2.16284i	−0.147198	+	0.106946i	0.511749	+	0.859135i	$0.328998\pi$
$410$		0			0
$411$	−8.87996	−	6.45167i	−0.438016	−	0.318237i
$412$		0			0
$413$	−38.3575	+	27.8684i	−1.88745	+	1.37131i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.09729	−	9.53247i	0.151675	−	0.466807i
$418$		0			0
$419$	−2.09891	+	6.45979i	−0.102539	+	0.315582i	−0.989145	−	0.146943i	$-0.953056\pi$
$419$	−2.09891	+	6.45979i	−0.102539	+	0.315582i	0.886606	+	0.462525i	$0.153056\pi$
$420$		0			0
$421$	6.70805	+	20.6452i	0.326930	+	1.00619i	0.970562	+	0.240852i	$0.0774269\pi$
$421$	6.70805	+	20.6452i	0.326930	+	1.00619i	−0.643632	+	0.765335i	$0.722573\pi$
$422$		0			0
$423$	−4.93844	−	3.58798i	−0.240115	−	0.174454i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	26.1476	+	18.9974i	1.26537	+	0.919346i
$428$		0			0
$429$	−0.491433	−	1.51247i	−0.0237266	−	0.0730229i
$430$		0			0
$431$	−5.17386	+	15.9235i	−0.249216	+	0.767009i	0.745698	+	0.666284i	$0.232116\pi$
$431$	−5.17386	+	15.9235i	−0.249216	+	0.767009i	−0.994914	+	0.100725i	$0.967884\pi$
$432$		0			0
$433$	7.55488	−	23.2515i	0.363065	−	1.11740i	−0.588120	−	0.808774i	$-0.700132\pi$
$433$	7.55488	−	23.2515i	0.363065	−	1.11740i	0.951184	−	0.308624i	$-0.0998684\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.5343	−	8.38019i	0.551762	−	0.400879i
$438$		0			0
$439$	18.4800	+	13.4265i	0.882002	+	0.640812i	0.933780	−	0.357847i	$-0.116489\pi$
$439$	18.4800	+	13.4265i	0.882002	+	0.640812i	−0.0517783	+	0.998659i	$0.516489\pi$
$440$		0			0
$441$	10.6848	−	7.76293i	0.508798	−	0.369663i
$442$		0			0
$443$	8.95402			0.425418			0.212709	−	0.977116i	$-0.431771\pi$
$443$	8.95402			0.425418			0.212709	+	0.977116i	$0.431771\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.603372	−	1.85699i	−0.0285385	−	0.0878325i
$448$		0			0
$449$	5.23228			0.246927			0.123463	−	0.992349i	$-0.460600\pi$
$449$	5.23228			0.246927			0.123463	+	0.992349i	$0.460600\pi$
$450$		0			0
$451$	13.1056			0.617120
$452$		0			0
$453$	0.105473	+	0.324612i	0.00495555	+	0.0152516i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	27.3114			1.27758			0.638788	−	0.769383i	$-0.279436\pi$
$457$	27.3114			1.27758			0.638788	+	0.769383i	$0.279436\pi$
$458$		0			0
$459$	9.96929	−	7.24311i	0.465327	−	0.338080i
$460$		0			0
$461$	5.00159	+	3.63387i	0.232947	+	0.169246i	0.698135	−	0.715966i	$-0.254013\pi$
$461$	5.00159	+	3.63387i	0.232947	+	0.169246i	−0.465188	+	0.885212i	$0.654013\pi$
$462$		0			0
$463$	−5.22490	+	3.79611i	−0.242822	+	0.176420i	−0.702539	−	0.711645i	$-0.747951\pi$
$463$	−5.22490	+	3.79611i	−0.242822	+	0.176420i	0.459718	+	0.888065i	$0.347951\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.120762	−	0.371668i	0.00558821	−	0.0171988i	−0.948224	−	0.317604i	$-0.897122\pi$
$467$	0.120762	−	0.371668i	0.00558821	−	0.0171988i	0.953812	+	0.300405i	$0.0971218\pi$
$468$		0			0
$469$	11.1762	−	34.3967i	0.516068	−	1.58829i
$470$		0			0
$471$	−3.58553	−	11.0351i	−0.165212	−	0.508472i
$472$		0			0
$473$	5.51915	+	4.00990i	0.253771	+	0.184375i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.11660	+	5.89705i	0.371633	+	0.270008i
$478$		0			0
$479$	−9.00958	−	27.7286i	−0.411658	−	1.26695i	−0.915206	−	0.402986i	$-0.867972\pi$
$479$	−9.00958	−	27.7286i	−0.411658	−	1.26695i	0.503548	−	0.863967i	$-0.332028\pi$
$480$		0			0
$481$	−1.81453	+	5.58455i	−0.0827355	+	0.254634i
$482$		0			0
$483$	−5.06183	+	15.5787i	−0.230321	+	0.708857i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.6467	−	12.0945i	0.754333	−	0.548055i	−0.142834	−	0.989747i	$-0.545621\pi$
$487$	16.6467	−	12.0945i	0.754333	−	0.548055i	0.897167	+	0.441692i	$0.145621\pi$
$488$		0			0
$489$	−10.1564	−	7.37903i	−0.459287	−	0.333691i
$490$		0			0
$491$	−25.9067	+	18.8223i	−1.16915	+	0.849438i	−0.990907	−	0.134548i	$-0.957042\pi$
$491$	−25.9067	+	18.8223i	−1.16915	+	0.849438i	−0.178245	+	0.983986i	$0.557042\pi$
$492$		0			0
$493$	−11.6788			−0.525985
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.977512	−	3.00847i	−0.0438474	−	0.134948i
$498$		0			0
$499$	9.59439			0.429504			0.214752	−	0.976669i	$-0.431106\pi$
$499$	9.59439			0.429504			0.214752	+	0.976669i	$0.431106\pi$
$500$		0			0
$501$	10.7483			0.480200
$502$		0			0
$503$	3.29380	+	10.1373i	0.146863	+	0.451998i	0.997246	−	0.0741664i	$-0.0236296\pi$
$503$	3.29380	+	10.1373i	0.146863	+	0.451998i	−0.850383	+	0.526165i	$0.823630\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−18.4540			−0.819573
$508$		0			0
$509$	14.0177	−	10.1844i	0.621323	−	0.451417i	−0.232061	−	0.972701i	$-0.574547\pi$
$509$	14.0177	−	10.1844i	0.621323	−	0.451417i	0.853383	+	0.521284i	$0.174547\pi$
$510$		0			0
$511$	47.8715	+	34.7807i	2.11771	+	1.53861i
$512$		0			0
$513$	29.3060	−	21.2920i	1.29389	−	0.940066i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.21839	+	9.90518i	−0.141545	+	0.435629i
$518$		0			0
$519$	6.93361	−	21.3395i	0.304352	−	0.936698i
$520$		0			0
$521$	−10.1237	−	31.1575i	−0.443527	−	1.36504i	−0.884091	−	0.467315i	$-0.845221\pi$
$521$	−10.1237	−	31.1575i	−0.443527	−	1.36504i	0.440564	−	0.897721i	$-0.354779\pi$
$522$		0			0
$523$	−2.03218	−	1.47647i	−0.0888611	−	0.0645614i	0.542468	−	0.840077i	$-0.317490\pi$
$523$	−2.03218	−	1.47647i	−0.0888611	−	0.0645614i	−0.631329	+	0.775515i	$0.717490\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.25487	−	0.911718i	−0.0546631	−	0.0397150i
$528$		0			0
$529$	−5.59162	−	17.2092i	−0.243114	−	0.748228i
$530$		0			0
$531$	−2.25016	+	6.92527i	−0.0976485	+	0.300531i
$532$		0			0
$533$	−2.56711	+	7.90074i	−0.111194	+	0.342219i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	22.3634	−	16.2479i	0.965051	−	0.701150i
$538$		0			0
$539$	−18.2301	−	13.2449i	−0.785226	−	0.570500i
$540$		0			0
$541$	−3.65744	+	2.65729i	−0.157246	+	0.114246i	−0.663626	−	0.748065i	$-0.730983\pi$
$541$	−3.65744	+	2.65729i	−0.157246	+	0.114246i	0.506380	+	0.862310i	$0.330983\pi$
$542$		0			0
$543$	30.0971			1.29159
$544$		0			0
$545$		0			0
$546$		0			0
$547$	10.6011	+	32.6267i	0.453269	+	1.39502i	0.873156	+	0.487441i	$0.162070\pi$
$547$	10.6011	+	32.6267i	0.453269	+	1.39502i	−0.419887	+	0.907576i	$0.637930\pi$
$548$		0			0
$549$	4.96377			0.211849
$550$		0			0
$551$	−34.3312			−1.46256
$552$		0			0
$553$	−3.41988	−	10.5253i	−0.145428	−	0.447582i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.34120			0.0991997			0.0495998	−	0.998769i	$-0.484205\pi$
$557$	2.34120			0.0991997			0.0495998	+	0.998769i	$0.484205\pi$
$558$		0			0
$559$	−3.49845	+	2.54177i	−0.147969	+	0.107505i
$560$		0			0
$561$	−3.43351	−	2.49459i	−0.144963	−	0.105322i
$562$		0			0
$563$	1.40822	−	1.02313i	0.0593493	−	0.0431198i	−0.557715	−	0.830032i	$-0.688322\pi$
$563$	1.40822	−	1.02313i	0.0593493	−	0.0431198i	0.617064	+	0.786913i	$0.288322\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−9.38594	+	28.8869i	−0.394172	+	1.21314i
$568$		0			0
$569$	−12.8853	+	39.6568i	−0.540178	+	1.66250i	0.192008	+	0.981393i	$0.438500\pi$
$569$	−12.8853	+	39.6568i	−0.540178	+	1.66250i	−0.732186	+	0.681105i	$0.761500\pi$
$570$		0			0
$571$	−0.601693	−	1.85182i	−0.0251801	−	0.0774963i	0.937677	−	0.347509i	$-0.112972\pi$
$571$	−0.601693	−	1.85182i	−0.0251801	−	0.0774963i	−0.962857	+	0.270012i	$0.912972\pi$
$572$		0			0
$573$	26.6829	+	19.3863i	1.11470	+	0.809873i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	11.2592	+	8.18026i	0.468725	+	0.340549i	0.796944	−	0.604053i	$-0.206448\pi$
$577$	11.2592	+	8.18026i	0.468725	+	0.340549i	−0.328219	+	0.944602i	$0.606448\pi$
$578$		0			0
$579$	−7.82905	−	24.0954i	−0.325364	−	1.00137i
$580$		0			0
$581$	−17.4880	+	53.8225i	−0.725524	+	2.23293i
$582$		0			0
$583$	5.28960	−	16.2797i	0.219073	−	0.674237i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.9830	−	10.1593i	0.577142	−	0.419318i	−0.260551	−	0.965460i	$-0.583904\pi$
$587$	13.9830	−	10.1593i	0.577142	−	0.419318i	0.837693	+	0.546142i	$0.183904\pi$
$588$		0			0
$589$	−3.68885	−	2.68011i	−0.151996	−	0.110432i
$590$		0			0
$591$	−4.45377	+	3.23585i	−0.183204	+	0.133105i
$592$		0			0
$593$	−26.1715			−1.07474			−0.537368	−	0.843348i	$-0.680581\pi$
$593$	−26.1715			−1.07474			−0.537368	+	0.843348i	$0.680581\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	12.2525	+	37.7092i	0.501460	+	1.54333i
$598$		0			0
$599$	−34.0712			−1.39211			−0.696055	−	0.717988i	$-0.745063\pi$
$599$	−34.0712			−1.39211			−0.696055	+	0.717988i	$0.745063\pi$
$600$		0			0
$601$	−37.2599			−1.51986			−0.759931	−	0.650004i	$-0.774767\pi$
$601$	−37.2599			−1.51986			−0.759931	+	0.650004i	$0.774767\pi$
$602$		0			0
$603$	−1.71645	−	5.28268i	−0.0698991	−	0.215127i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	0.110015			0.00446537			0.00223268	−	0.999998i	$-0.499289\pi$
$607$	0.110015			0.00446537			0.00223268	+	0.999998i	$0.499289\pi$
$608$		0			0
$609$	31.9107	−	23.1845i	1.29309	−	0.939484i
$610$		0			0
$611$	−5.34093	−	3.88042i	−0.216071	−	0.156985i
$612$		0			0
$613$	2.40870	−	1.75003i	0.0972866	−	0.0706829i	−0.538079	−	0.842895i	$-0.680850\pi$
$613$	2.40870	−	1.75003i	0.0972866	−	0.0706829i	0.635365	+	0.772212i	$0.280850\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.2881	−	34.7412i	0.454442	−	1.39863i	−0.417347	−	0.908747i	$-0.637040\pi$
$617$	11.2881	−	34.7412i	0.454442	−	1.39863i	0.871789	−	0.489881i	$-0.162960\pi$
$618$		0			0
$619$	10.3624	−	31.8923i	0.416501	−	1.28186i	−0.494401	−	0.869234i	$-0.664612\pi$
$619$	10.3624	−	31.8923i	0.416501	−	1.28186i	0.910901	−	0.412624i	$-0.135388\pi$
$620$		0			0
$621$	3.85120	+	11.8528i	0.154543	+	0.475635i
$622$		0			0
$623$	12.6919	+	9.22121i	0.508490	+	0.369440i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−10.0932	−	7.33316i	−0.403085	−	0.292858i
$628$		0			0
$629$	4.84243	+	14.9035i	0.193080	+	0.594240i
$630$		0			0
$631$	4.01985	−	12.3718i	0.160028	−	0.492515i	−0.838608	−	0.544736i	$-0.816630\pi$
$631$	4.01985	−	12.3718i	0.160028	−	0.492515i	0.998636	+	0.0522207i	$0.0166299\pi$
$632$		0			0
$633$	−1.43554	+	4.41813i	−0.0570576	+	0.175605i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	11.5556	−	8.39563i	0.457849	−	0.332647i
$638$		0			0
$639$	−0.393038	−	0.285559i	−0.0155484	−	0.0112965i
$640$		0			0
$641$	16.5293	−	12.0092i	0.652867	−	0.474336i	−0.211379	−	0.977404i	$-0.567796\pi$
$641$	16.5293	−	12.0092i	0.652867	−	0.474336i	0.864247	+	0.503068i	$0.167796\pi$
$642$		0			0
$643$	9.64777			0.380471			0.190235	−	0.981738i	$-0.439075\pi$
$643$	9.64777			0.380471			0.190235	+	0.981738i	$0.439075\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.8829	−	39.6496i	−0.506481	−	1.55879i	−0.798266	−	0.602304i	$-0.794249\pi$
$647$	−12.8829	−	39.6496i	−0.506481	−	1.55879i	0.291786	−	0.956484i	$-0.405751\pi$
$648$		0			0
$649$	12.4238			0.487677
$650$		0			0
$651$	5.23871			0.205321
$652$		0			0
$653$	11.0289	+	33.9436i	0.431596	+	1.32831i	0.896535	+	0.442972i	$0.146076\pi$
$653$	11.0289	+	33.9436i	0.431596	+	1.32831i	−0.464940	+	0.885342i	$0.653924\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.08777			0.354548
$658$		0			0
$659$	−20.7470	+	15.0735i	−0.808187	+	0.587182i	−0.913304	−	0.407278i	$-0.866478\pi$
$659$	−20.7470	+	15.0735i	−0.808187	+	0.587182i	0.105118	+	0.994460i	$0.466478\pi$
$660$		0			0
$661$	2.10868	+	1.53205i	0.0820182	+	0.0595897i	0.628039	−	0.778182i	$-0.283858\pi$
$661$	2.10868	+	1.53205i	0.0820182	+	0.0595897i	−0.546021	+	0.837772i	$0.683858\pi$
$662$		0			0
$663$	2.17641	−	1.58126i	0.0845249	−	0.0614110i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.64994	−	11.2334i	0.141326	−	0.434958i
$668$		0			0
$669$	−3.78314	+	11.6433i	−0.146265	+	0.450156i
$670$		0			0
$671$	−2.61709	−	8.05457i	−0.101032	−	0.310943i
$672$		0			0
$673$	−10.8025	−	7.84844i	−0.416404	−	0.302535i	0.359785	−	0.933035i	$-0.382850\pi$
$673$	−10.8025	−	7.84844i	−0.416404	−	0.302535i	−0.776189	+	0.630500i	$0.782850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.3250	−	8.95467i	−0.473690	−	0.344156i	0.325188	−	0.945650i	$-0.394573\pi$
$677$	−12.3250	−	8.95467i	−0.473690	−	0.344156i	−0.798878	+	0.601494i	$0.794573\pi$
$678$		0			0
$679$	25.1867	+	77.5168i	0.966578	+	2.97482i
$680$		0			0
$681$	6.97755	−	21.4747i	0.267380	−	0.822912i
$682$		0			0
$683$	−6.86573	+	21.1306i	−0.262710	+	0.808538i	0.729502	+	0.683979i	$0.239752\pi$
$683$	−6.86573	+	21.1306i	−0.262710	+	0.808538i	−0.992212	+	0.124560i	$0.960248\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	10.6096	−	7.70833i	0.404782	−	0.294091i
$688$		0			0
$689$	8.77812	+	6.37768i	0.334420	+	0.242970i
$690$		0			0
$691$	9.50955	−	6.90909i	0.361760	−	0.262834i	−0.392026	−	0.919954i	$-0.628226\pi$
$691$	9.50955	−	6.90909i	0.361760	−	0.262834i	0.753786	+	0.657120i	$0.228226\pi$
$692$		0			0
$693$	−4.85246			−0.184330
$694$		0			0
$695$		0			0
$696$		0			0
$697$	6.85082	+	21.0847i	0.259493	+	0.798639i
$698$		0			0
$699$	−11.8749			−0.449149
$700$		0			0
$701$	11.7537			0.443932			0.221966	−	0.975054i	$-0.428753\pi$
$701$	11.7537			0.443932			0.221966	+	0.975054i	$0.428753\pi$
$702$		0			0
$703$	14.2349	+	43.8106i	0.536880	+	1.65235i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−51.4174			−1.93375
$708$		0			0
$709$	7.29158	−	5.29764i	0.273841	−	0.198957i	−0.442386	−	0.896825i	$-0.645868\pi$
$709$	7.29158	−	5.29764i	0.273841	−	0.198957i	0.716227	+	0.697868i	$0.245868\pi$
$710$		0			0
$711$	−1.37507	−	0.999045i	−0.0515690	−	0.0374671i
$712$		0			0
$713$	1.26913	−	0.922077i	0.0475293	−	0.0345321i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.434168	−	1.33623i	0.0162143	−	0.0499025i
$718$		0			0
$719$	13.6946	−	42.1476i	0.510721	−	1.57184i	−0.280213	−	0.959938i	$-0.590405\pi$
$719$	13.6946	−	42.1476i	0.510721	−	1.57184i	0.790934	−	0.611901i	$-0.209595\pi$
$720$		0			0
$721$	2.60893	+	8.02946i	0.0971616	+	0.299033i
$722$		0			0
$723$	−13.2701	−	9.64128i	−0.493520	−	0.358563i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	4.07391	+	2.95987i	0.151093	+	0.109775i	0.660763	−	0.750594i	$-0.270233\pi$
$727$	4.07391	+	2.95987i	0.151093	+	0.109775i	−0.509671	+	0.860370i	$0.670233\pi$
$728$		0			0
$729$	9.25127	+	28.4725i	0.342640	+	1.05454i
$730$		0			0
$731$	−3.56615	+	10.9755i	−0.131899	+	0.405942i
$732$		0			0
$733$	2.00643	−	6.17517i	0.0741094	−	0.228085i	−0.907140	−	0.420830i	$-0.861739\pi$
$733$	2.00643	−	6.17517i	0.0741094	−	0.228085i	0.981249	+	0.192745i	$0.0617389\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.66708	+	5.57046i	−0.282421	+	0.205191i
$738$		0			0
$739$	−5.42854	−	3.94406i	−0.199692	−	0.145085i	0.483446	−	0.875374i	$-0.339385\pi$
$739$	−5.42854	−	3.94406i	−0.199692	−	0.145085i	−0.683138	+	0.730290i	$0.739385\pi$
$740$		0			0
$741$	6.39784	−	4.64830i	0.235031	−	0.170760i
$742$		0			0
$743$	−27.9505			−1.02541			−0.512703	−	0.858566i	$-0.671356\pi$
$743$	−27.9505			−1.02541			−0.512703	+	0.858566i	$0.671356\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.68582	+	8.26612i	0.0982692	+	0.302441i
$748$		0			0
$749$	−14.0180			−0.512205
$750$		0			0
$751$	−16.0513			−0.585719			−0.292860	−	0.956155i	$-0.594607\pi$
$751$	−16.0513			−0.585719			−0.292860	+	0.956155i	$0.594607\pi$
$752$		0			0
$753$	−0.114259	−	0.351654i	−0.00416384	−	0.0128150i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−37.5640			−1.36529			−0.682643	−	0.730752i	$-0.739169\pi$
$757$	−37.5640			−1.36529			−0.682643	+	0.730752i	$0.739169\pi$
$758$		0			0
$759$	3.47252	−	2.52294i	0.126045	−	0.0915767i
$760$		0			0
$761$	7.57148	+	5.50100i	0.274466	+	0.199411i	0.716500	−	0.697587i	$-0.245743\pi$
$761$	7.57148	+	5.50100i	0.274466	+	0.199411i	−0.442034	+	0.896998i	$0.645743\pi$
$762$		0			0
$763$	−32.9462	+	23.9368i	−1.19273	+	0.866570i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.43355	+	7.48970i	−0.0878705	+	0.270438i
$768$		0			0
$769$	−8.80986	+	27.1140i	−0.317692	+	0.977754i	0.656941	+	0.753942i	$0.271850\pi$
$769$	−8.80986	+	27.1140i	−0.317692	+	0.977754i	−0.974632	+	0.223812i	$0.928150\pi$
$770$		0			0
$771$	−3.68825	−	11.3513i	−0.132829	−	0.408806i
$772$		0			0
$773$	8.69439	+	6.31684i	0.312715	+	0.227201i	0.733061	−	0.680163i	$-0.238091\pi$
$773$	8.69439	+	6.31684i	0.312715	+	0.227201i	−0.420345	+	0.907364i	$0.638091\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−42.8174	−	31.1087i	−1.53607	−	1.11602i
$778$		0			0
$779$	20.1388	+	61.9810i	0.721549	+	2.22070i
$780$		0			0
$781$	−0.256144	+	0.788329i	−0.00916554	+	0.0282086i
$782$		0			0
$783$	9.27362	−	28.5413i	0.331412	−	1.01998i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	11.9226	−	8.66229i	0.424995	−	0.308777i	−0.354649	−	0.934999i	$-0.615400\pi$
$787$	11.9226	−	8.66229i	0.424995	−	0.308777i	0.779645	+	0.626222i	$0.215400\pi$
$788$		0			0
$789$	9.44863	+	6.86483i	0.336380	+	0.244395i
$790$		0			0
$791$	15.6170	−	11.3464i	0.555277	−	0.403432i
$792$		0			0
$793$	5.36833			0.190635
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.73244	−	5.33189i	−0.0613660	−	0.188865i	0.915674	−	0.401923i	$-0.131658\pi$
$797$	−1.73244	−	5.33189i	−0.0613660	−	0.188865i	−0.977040	+	0.213057i	$0.931658\pi$
$798$		0			0
$799$	−17.6181			−0.623283
$800$		0			0
$801$	2.40939			0.0851315
$802$		0			0
$803$	−4.79142	−	14.7465i	−0.169085	−	0.520391i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.13371			0.0751100
$808$		0			0
$809$	−18.8090	+	13.6655i	−0.661290	+	0.480455i	−0.867098	−	0.498137i	$-0.834018\pi$
$809$	−18.8090	+	13.6655i	−0.661290	+	0.480455i	0.205809	+	0.978592i	$0.434018\pi$
$810$		0			0
$811$	27.9935	+	20.3385i	0.982984	+	0.714180i	0.958373	−	0.285518i	$-0.0921655\pi$
$811$	27.9935	+	20.3385i	0.982984	+	0.714180i	0.0246104	+	0.999697i	$0.492165\pi$
$812$		0			0
$813$	31.1425	−	22.6263i	1.09221	−	0.793540i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−10.4831	+	32.2638i	−0.366758	+	1.12877i
$818$		0			0
$819$	0.950490	−	2.92531i	0.0332128	−	0.102219i
$820$		0			0
$821$	−8.45765	−	26.0300i	−0.295174	−	0.908452i	−0.983163	−	0.182731i	$-0.941506\pi$
$821$	−8.45765	−	26.0300i	−0.295174	−	0.908452i	0.687989	−	0.725721i	$-0.258494\pi$
$822$		0			0
$823$	−34.9184	−	25.3697i	−1.21718	−	0.884331i	−0.221315	−	0.975202i	$-0.571035\pi$
$823$	−34.9184	−	25.3697i	−1.21718	−	0.884331i	−0.995863	+	0.0908711i	$0.971035\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.6576	+	18.6413i	0.892202	+	0.648223i	0.936451	−	0.350798i	$-0.114090\pi$
$827$	25.6576	+	18.6413i	0.892202	+	0.648223i	−0.0442493	+	0.999021i	$0.514090\pi$
$828$		0			0
$829$	−7.62684	−	23.4730i	−0.264891	−	0.815251i	−0.991718	−	0.128431i	$-0.959006\pi$
$829$	−7.62684	−	23.4730i	−0.264891	−	0.815251i	0.726827	−	0.686820i	$-0.240994\pi$
$830$		0			0
$831$	−5.81172	+	17.8866i	−0.201606	+	0.620481i
$832$		0			0
$833$	11.7792	−	36.2527i	0.408125	−	1.25608i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.22455	−	2.34277i	0.111457	−	0.0809781i
$838$		0			0
$839$	−31.3138	−	22.7508i	−1.08107	−	0.785444i	−0.103202	−	0.994660i	$-0.532909\pi$
$839$	−31.3138	−	22.7508i	−1.08107	−	0.785444i	−0.977869	+	0.209216i	$0.932909\pi$
$840$		0			0
$841$	0.451574	−	0.328088i	0.0155715	−	0.0113134i
$842$		0			0
$843$	−8.68895			−0.299263
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.2346	−	43.8097i	−0.489108	−	1.50532i
$848$		0			0
$849$	5.10382			0.175163
$850$		0			0
$851$	−15.8485			−0.543279
$852$		0			0
$853$	−4.75488	−	14.6340i	−0.162804	−	0.501059i	0.836064	−	0.548632i	$-0.184851\pi$
$853$	−4.75488	−	14.6340i	−0.162804	−	0.501059i	−0.998868	+	0.0475731i	$0.984851\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−39.2764			−1.34166			−0.670829	−	0.741612i	$-0.734061\pi$
$857$	−39.2764			−1.34166			−0.670829	+	0.741612i	$0.734061\pi$
$858$		0			0
$859$	35.1666	−	25.5500i	1.19987	−	0.871755i	0.205596	−	0.978637i	$-0.434087\pi$
$859$	35.1666	−	25.5500i	1.19987	−	0.871755i	0.994272	+	0.106882i	$0.0340866\pi$
$860$		0			0
$861$	−60.5760	−	44.0110i	−2.06442	−	1.49989i
$862$		0			0
$863$	14.8393	−	10.7814i	0.505134	−	0.367002i	−0.305840	−	0.952083i	$-0.598937\pi$
$863$	14.8393	−	10.7814i	0.505134	−	0.367002i	0.810975	+	0.585081i	$0.198937\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−5.64609	+	17.3769i	−0.191751	+	0.590150i
$868$		0			0
$869$	−0.896134	+	2.75802i	−0.0303993	+	0.0935593i
$870$		0			0
$871$	−1.85634	−	5.71324i	−0.0628998	−	0.193586i
$872$		0			0
$873$	10.1271	+	7.35776i	0.342750	+	0.249023i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	17.2904	+	12.5622i	0.583855	+	0.424196i	0.840112	−	0.542413i	$-0.182489\pi$
$877$	17.2904	+	12.5622i	0.583855	+	0.424196i	−0.256257	+	0.966609i	$0.582489\pi$
$878$		0			0
$879$	0.155869	+	0.479715i	0.00525732	+	0.0161804i
$880$		0			0
$881$	−3.08008	+	9.47952i	−0.103771	+	0.319373i	−0.989440	−	0.144943i	$-0.953700\pi$
$881$	−3.08008	+	9.47952i	−0.103771	+	0.319373i	0.885669	+	0.464317i	$0.153700\pi$
$882$		0			0
$883$	1.77903	−	5.47528i	0.0598690	−	0.184258i	−0.916649	−	0.399693i	$-0.869117\pi$
$883$	1.77903	−	5.47528i	0.0598690	−	0.184258i	0.976518	+	0.215435i	$0.0691168\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.61165	+	6.25673i	−0.289151	+	0.210080i	−0.722899	−	0.690954i	$-0.757191\pi$
$887$	−8.61165	+	6.25673i	−0.289151	+	0.210080i	0.433748	+	0.901034i	$0.357191\pi$
$888$		0			0
$889$	−57.2731	−	41.6113i	−1.92088	−	1.39560i
$890$		0			0
$891$	6.43895	−	4.67817i	0.215713	−	0.156725i
$892$		0			0
$893$	−51.7905			−1.73310
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.840762	+	2.58760i	0.0280722	+	0.0863974i
$898$		0			0
$899$	−3.77748			−0.125986
$900$		0			0
$901$	28.9563			0.964674
$902$		0			0
$903$	−12.0443	−	37.0685i	−0.400809	−	1.23356i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−23.4462			−0.778518			−0.389259	−	0.921128i	$-0.627269\pi$
$907$	−23.4462			−0.778518			−0.389259	+	0.921128i	$0.627269\pi$
$908$		0			0
$909$	−6.38860	+	4.64159i	−0.211896	+	0.153952i
$910$		0			0
$911$	−27.6056	−	20.0567i	−0.914616	−	0.664507i	0.0275624	−	0.999620i	$-0.491226\pi$
$911$	−27.6056	−	20.0567i	−0.914616	−	0.664507i	−0.942178	+	0.335113i	$0.891226\pi$
$912$		0			0
$913$	11.9971	−	8.71642i	0.397047	−	0.288471i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.5998	+	48.0113i	−0.515151	+	1.58547i
$918$		0			0
$919$	−14.9065	+	45.8775i	−0.491720	+	1.51336i	0.330286	+	0.943881i	$0.392855\pi$
$919$	−14.9065	+	45.8775i	−0.491720	+	1.51336i	−0.822006	+	0.569479i	$0.807145\pi$
$920$		0			0
$921$	10.8747	+	33.4688i	0.358333	+	1.10283i
$922$		0			0
$923$	−0.425072	−	0.308833i	−0.0139914	−	0.0101654i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.04900	+	0.762142i	0.0344536	+	0.0250320i
$928$		0			0
$929$	3.84435	+	11.8317i	0.126129	+	0.388186i	0.994105	−	0.108421i	$-0.0345793\pi$
$929$	3.84435	+	11.8317i	0.126129	+	0.388186i	−0.867976	+	0.496606i	$0.834579\pi$
$930$		0			0
$931$	34.6264	−	106.569i	1.13484	−	3.49267i
$932$		0			0
$933$	3.36223	−	10.3479i	0.110075	−	0.338775i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−48.2420	+	35.0499i	−1.57600	+	1.14503i	−0.654890	+	0.755724i	$0.727285\pi$
$937$	−48.2420	+	35.0499i	−1.57600	+	1.14503i	−0.921109	+	0.389306i	$0.872715\pi$
$938$		0			0
$939$	−14.3494	−	10.4255i	−0.468277	−	0.340223i
$940$		0			0
$941$	−5.16826	+	3.75496i	−0.168480	+	0.122408i	−0.668830	−	0.743415i	$-0.733205\pi$
$941$	−5.16826	+	3.75496i	−0.168480	+	0.122408i	0.500350	+	0.865823i	$0.333205\pi$
$942$		0			0
$943$	−22.4216			−0.730149
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.704405	+	2.16794i	0.0228901	+	0.0704485i	0.961849	−	0.273581i	$-0.0882081\pi$
$947$	0.704405	+	2.16794i	0.0228901	+	0.0704485i	−0.938959	+	0.344029i	$0.888208\pi$
$948$		0			0
$949$	9.82845			0.319045
$950$		0			0
$951$	7.59779			0.246375
$952$		0			0
$953$	1.25775	+	3.87094i	0.0407424	+	0.125392i	0.969359	−	0.245649i	$-0.0790010\pi$
$953$	1.25775	+	3.87094i	0.0407424	+	0.125392i	−0.928617	+	0.371041i	$0.879001\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−10.3357			−0.334107
$958$		0			0
$959$	−29.3034	+	21.2902i	−0.946258	+	0.687496i
$960$		0			0
$961$	24.6736	+	17.9264i	0.795924	+	0.578273i
$962$		0			0
$963$	−1.74173	+	1.26544i	−0.0561264	+	0.0407782i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.9040	+	33.5590i	−0.350649	+	1.07919i	0.607841	+	0.794059i	$0.292036\pi$
$967$	−10.9040	+	33.5590i	−0.350649	+	1.07919i	−0.958490	+	0.285127i	$0.907964\pi$
$968$		0			0
$969$	6.52164	−	20.0716i	0.209505	−	0.644791i
$970$		0			0
$971$	−5.31316	−	16.3522i	−0.170508	−	0.524768i	0.828892	−	0.559408i	$-0.188972\pi$
$971$	−5.31316	−	16.3522i	−0.170508	−	0.524768i	−0.999400	+	0.0346399i	$0.988972\pi$
$972$		0			0
$973$	−26.7587	−	19.4413i	−0.857844	−	0.623260i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	36.6659	+	26.6394i	1.17305	+	0.852269i	0.991371	−	0.131089i	$-0.0418475\pi$
$977$	36.6659	+	26.6394i	1.17305	+	0.852269i	0.181677	+	0.983358i	$0.441848\pi$
$978$		0			0
$979$	−1.27032	−	3.90965i	−0.0405996	−	0.124953i
$980$		0			0
$981$	−1.93271	+	5.94828i	−0.0617068	+	0.189914i
$982$		0			0
$983$	−1.22263	+	3.76288i	−0.0389960	+	0.120017i	−0.968659	−	0.248393i	$-0.920098\pi$
$983$	−1.22263	+	3.76288i	−0.0389960	+	0.120017i	0.929663	+	0.368410i	$0.120098\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	48.1391	−	34.9751i	1.53229	−	1.11327i
$988$		0			0
$989$	−9.44237	−	6.86029i	−0.300250	−	0.218144i
$990$		0			0
$991$	−20.2739	+	14.7298i	−0.644020	+	0.467908i	−0.861229	−	0.508217i	$-0.830305\pi$
$991$	−20.2739	+	14.7298i	−0.644020	+	0.467908i	0.217209	+	0.976125i	$0.430305\pi$
$992$		0			0
$993$	1.75116			0.0555713
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.8857	−	48.8913i	−0.503106	−	1.54840i	−0.803931	−	0.594722i	$-0.797262\pi$
$997$	−15.8857	−	48.8913i	−0.503106	−	1.54840i	0.300825	−	0.953679i	$-0.402738\pi$
$998$		0			0
$999$	−40.2671			−1.27400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.m.c.201.3		16
5.2	odd	4		1000.2.q.d.49.6		32
5.3	odd	4		1000.2.q.d.49.3		32
5.4	even	2		200.2.m.c.41.2	✓	16
20.19	odd	2		400.2.u.g.241.3		16
25.2	odd	20		1000.2.q.d.449.3		32
25.6	even	5		5000.2.a.m.1.6		8
25.11	even	5	inner	1000.2.m.c.801.3		16
25.14	even	10		200.2.m.c.161.2	yes	16
25.19	even	10		5000.2.a.l.1.3		8
25.23	odd	20		1000.2.q.d.449.6		32
100.19	odd	10		10000.2.a.bk.1.6		8
100.31	odd	10		10000.2.a.bh.1.3		8
100.39	odd	10		400.2.u.g.161.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.c.41.2	✓	16	5.4	even	2
200.2.m.c.161.2	yes	16	25.14	even	10
400.2.u.g.161.3		16	100.39	odd	10
400.2.u.g.241.3		16	20.19	odd	2
1000.2.m.c.201.3		16	1.1	even	1	trivial
1000.2.m.c.801.3		16	25.11	even	5	inner
1000.2.q.d.49.3		32	5.3	odd	4
1000.2.q.d.49.6		32	5.2	odd	4
1000.2.q.d.449.3		32	25.2	odd	20
1000.2.q.d.449.6		32	25.23	odd	20
5000.2.a.l.1.3		8	25.19	even	10
5000.2.a.m.1.6		8	25.6	even	5
10000.2.a.bh.1.3		8	100.31	odd	10
10000.2.a.bk.1.6		8	100.19	odd	10

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.462625 + 1.42381i) q^{3} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +O(q^{10})\)	\(q+(0.462625 + 1.42381i) q^{3} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +(-1.04731 - 0.760912i) q^{11} +(0.663861 - 0.482323i) q^{13} +(0.676707 - 2.08269i) q^{17} +(1.98926 - 6.12233i) q^{19} +(2.28551 + 7.03407i) q^{21} +(1.79177 + 1.30180i) q^{23} +(4.55246 + 3.30755i) q^{27} +(-1.64801 - 5.07207i) q^{29} +(0.218880 - 0.673643i) q^{31} +(0.598887 - 1.84318i) q^{33} +(-5.78922 + 4.20612i) q^{37} +(0.993856 + 0.722078i) q^{39} +(-8.19030 + 5.95060i) q^{41} -5.26985 q^{43} +(-2.48612 - 7.65150i) q^{47} +17.4067 q^{49} +3.27842 q^{51} +(4.08608 + 12.5757i) q^{53} +9.63732 q^{57} +(-7.76420 + 5.64102i) q^{59} +(5.29271 + 3.84538i) q^{61} +(3.03252 - 2.20325i) q^{63} +(2.26224 - 6.96246i) q^{67} +(-1.02460 + 3.15339i) q^{69} +(-0.197864 - 0.608964i) q^{71} +(9.68999 + 7.04019i) q^{73} +(-5.17402 - 3.75914i) q^{77} +(-0.692240 - 2.13050i) q^{79} +(-1.89987 + 5.84719i) q^{81} +(-3.53986 + 10.8946i) q^{83} +(6.45926 - 4.69293i) q^{87} +(2.56905 + 1.86652i) q^{89} +(3.27968 - 2.38283i) q^{91} +1.06040 q^{93} +(5.09821 + 15.6907i) q^{97} -0.982218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 6 q^{7} - 11 q^{9}+O(q^{10}) \) 16 * q - q^3 + 6 * q^7 - 11 * q^9	\( 16 q - q^{3} + 6 q^{7} - 11 q^{9} - 10 q^{11} - q^{13} + 4 q^{17} - 3 q^{21} - 11 q^{23} - 13 q^{27} + 5 q^{29} - 9 q^{31} - 16 q^{33} - 30 q^{37} + 14 q^{39} - 2 q^{41} + 42 q^{43} + 16 q^{47} + 18 q^{49} + 100 q^{51} - 11 q^{53} + 64 q^{57} - 53 q^{59} + 4 q^{61} + 38 q^{63} + 14 q^{67} - 7 q^{69} - 6 q^{71} + 24 q^{73} - 23 q^{77} - 22 q^{79} - 6 q^{81} - 33 q^{83} - 37 q^{87} + 20 q^{89} - 27 q^{91} - 40 q^{93} - 11 q^{97} + 122 q^{99}+O(q^{100}) \) 16 * q - q^3 + 6 * q^7 - 11 * q^9 - 10 * q^11 - q^13 + 4 * q^17 - 3 * q^21 - 11 * q^23 - 13 * q^27 + 5 * q^29 - 9 * q^31 - 16 * q^33 - 30 * q^37 + 14 * q^39 - 2 * q^41 + 42 * q^43 + 16 * q^47 + 18 * q^49 + 100 * q^51 - 11 * q^53 + 64 * q^57 - 53 * q^59 + 4 * q^61 + 38 * q^63 + 14 * q^67 - 7 * q^69 - 6 * q^71 + 24 * q^73 - 23 * q^77 - 22 * q^79 - 6 * q^81 - 33 * q^83 - 37 * q^87 + 20 * q^89 - 27 * q^91 - 40 * q^93 - 11 * q^97 + 122 * q^99

Introduction

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