LMFDB - Embedded newform 363.2.e.n.124.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.22502537891856000000000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 45x^{12} + 287x^{10} + 1829x^{8} + 1148x^{6} + 720x^{4} + 448x^{2} + 256 $ x^16 + 7x^14 + 45x^12 + 287x^10 + 1829x^8 + 1148x^6 + 720x^4 + 448*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			124.3
Root			$0.640974 + 0.465695i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.n.202.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.640974 - 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(0.640974 + 0.465695i) q^{6} +(-0.780063 + 2.40079i) q^{7} +(0.825636 + 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.640974 - 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(0.640974 + 0.465695i) q^{6} +(-0.780063 + 2.40079i) q^{7} +(0.825636 + 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.67181 q^{10} -1.37228 q^{12} +(-4.72544 + 3.43323i) q^{13} +(0.618034 + 1.90211i) q^{14} +(1.04209 - 3.20723i) q^{15} +(-0.507835 - 0.368964i) q^{16} +(2.16154 + 1.57045i) q^{17} +(-0.244830 + 0.753510i) q^{18} +(0.290403 + 0.893769i) q^{19} +(3.74390 - 2.72010i) q^{20} -2.52434 q^{21} +2.00000 q^{23} +(-2.16154 + 1.57045i) q^{24} +(1.96914 + 6.06040i) q^{25} +(-1.43004 + 4.40122i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.80252 - 2.03615i) q^{28} +(0.244830 - 0.753510i) q^{29} +(-0.825636 - 2.54105i) q^{30} +(-1.31685 + 0.956749i) q^{31} -5.84096 q^{32} +2.11684 q^{34} +(6.88698 - 5.00368i) q^{35} +(-0.424058 - 1.30512i) q^{36} +(1.54508 - 4.75528i) q^{37} +(0.602364 + 0.437643i) q^{38} +(-4.72544 - 3.43323i) q^{39} +(2.78428 - 8.56912i) q^{40} +(3.36508 + 10.3567i) q^{41} +(-1.61803 + 1.17557i) q^{42} +6.63325 q^{43} +3.37228 q^{45} +(1.28195 - 0.931389i) q^{46} +(-3.93829 - 12.1208i) q^{47} +(0.193976 - 0.596996i) q^{48} +(0.507835 + 0.368964i) q^{49} +(4.08446 + 2.96754i) q^{50} +(-0.825636 + 2.54105i) q^{51} +(-2.47691 - 7.62314i) q^{52} +(3.33060 - 2.41982i) q^{53} -0.792287 q^{54} -6.74456 q^{56} +(-0.760285 + 0.552379i) q^{57} +(-0.193976 - 0.596996i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(3.74390 + 2.72010i) q^{60} +(4.84475 + 3.51992i) q^{61} +(-0.398515 + 1.22650i) q^{62} +(-0.780063 - 2.40079i) q^{63} +(-2.72823 + 1.98218i) q^{64} +19.6974 q^{65} -1.11684 q^{67} +(-2.96625 + 2.15510i) q^{68} +(0.618034 + 1.90211i) q^{69} +(2.08418 - 6.41446i) q^{70} +(8.69253 + 6.31550i) q^{71} +(-2.16154 - 1.57045i) q^{72} +(-2.82985 + 8.70938i) q^{73} +(-1.22415 - 3.76755i) q^{74} +(-5.15528 + 3.74553i) q^{75} -1.28962 q^{76} -4.62772 q^{78} +(3.32418 - 2.41516i) q^{79} +(0.654141 + 2.01324i) q^{80} +(0.309017 - 0.951057i) q^{81} +(6.97997 + 5.07125i) q^{82} +(-1.52057 - 1.10476i) q^{83} +(1.07047 - 3.29456i) q^{84} +(-2.78428 - 8.56912i) q^{85} +(4.25174 - 3.08907i) q^{86} +0.792287 q^{87} -0.627719 q^{89} +(2.16154 - 1.57045i) q^{90} +(-4.55632 - 14.0229i) q^{91} +(-0.848116 + 2.61023i) q^{92} +(-1.31685 - 0.956749i) q^{93} +(-8.16893 - 5.93507i) q^{94} +(0.979321 - 3.01404i) q^{95} +(-1.80496 - 5.55509i) q^{96} +(-8.48588 + 6.16535i) q^{97} +0.497333 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9	$ 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9} + 24 q^{12} - 8 q^{14} - 2 q^{15} - 14 q^{16} + 30 q^{20} + 32 q^{23} - 14 q^{25} + 30 q^{26} - 4 q^{27} - 18 q^{31} - 104 q^{34} - 6 q^{36} - 20 q^{37} - 20 q^{38} - 8 q^{42} + 8 q^{45} + 28 q^{47} - 14 q^{48} + 14 q^{49} - 18 q^{53} - 16 q^{56} + 14 q^{58} + 24 q^{59} + 30 q^{60} - 2 q^{64} + 120 q^{67} - 8 q^{69} - 4 q^{70} + 20 q^{71} - 14 q^{75} - 120 q^{78} + 26 q^{80} - 4 q^{81} + 46 q^{82} + 44 q^{86} - 56 q^{89} + 36 q^{91} - 12 q^{92} - 18 q^{93} + 4 q^{97}+O(q^{100}) $ 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9 + 24 * q^12 - 8 * q^14 - 2 * q^15 - 14 * q^16 + 30 * q^20 + 32 * q^23 - 14 * q^25 + 30 * q^26 - 4 * q^27 - 18 * q^31 - 104 * q^34 - 6 * q^36 - 20 * q^37 - 20 * q^38 - 8 * q^42 + 8 * q^45 + 28 * q^47 - 14 * q^48 + 14 * q^49 - 18 * q^53 - 16 * q^56 + 14 * q^58 + 24 * q^59 + 30 * q^60 - 2 * q^64 + 120 * q^67 - 8 * q^69 - 4 * q^70 + 20 * q^71 - 14 * q^75 - 120 * q^78 + 26 * q^80 - 4 * q^81 + 46 * q^82 + 44 * q^86 - 56 * q^89 + 36 * q^91 - 12 * q^92 - 18 * q^93 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.640974	−	0.465695i	0.453237	−	0.329296i	−0.337636	−	0.941277i	$-0.609627\pi$
$2$	0.640974	−	0.465695i	0.453237	−	0.329296i	0.790872	+	0.611981i	$0.209627\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.424058	+	1.30512i	−0.212029	+	0.652559i
$5$	−2.72823	−	1.98218i	−1.22010	−	0.886457i	−0.223994	−	0.974590i	$-0.571910\pi$
$5$	−2.72823	−	1.98218i	−1.22010	−	0.886457i	−0.996109	+	0.0881339i	$0.971910\pi$
$6$	0.640974	+	0.465695i	0.261676	+	0.190119i
$7$	−0.780063	+	2.40079i	−0.294836	+	0.907413i	0.688440	+	0.725293i	$0.258296\pi$
$7$	−0.780063	+	2.40079i	−0.294836	+	0.907413i	−0.983276	+	0.182119i	$0.941704\pi$
$8$	0.825636	+	2.54105i	0.291906	+	0.898396i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−2.67181			−0.844902
$11$		0			0
$11$		0			0
$12$	−1.37228			−0.396143
$13$	−4.72544	+	3.43323i	−1.31060	+	0.952207i	−0.310602	+	0.950540i	$0.600531\pi$
$13$	−4.72544	+	3.43323i	−1.31060	+	0.952207i	−0.999999	+	0.00166711i	$0.999469\pi$
$14$	0.618034	+	1.90211i	0.165177	+	0.508361i
$15$	1.04209	−	3.20723i	0.269067	−	0.828103i
$16$	−0.507835	−	0.368964i	−0.126959	−	0.0922409i
$17$	2.16154	+	1.57045i	0.524251	+	0.380891i	0.818203	−	0.574929i	$-0.194970\pi$
$17$	2.16154	+	1.57045i	0.524251	+	0.380891i	−0.293952	+	0.955820i	$0.594970\pi$
$18$	−0.244830	+	0.753510i	−0.0577070	+	0.177604i
$19$	0.290403	+	0.893769i	0.0666230	+	0.205045i	0.978826	−	0.204694i	$-0.0656199\pi$
$19$	0.290403	+	0.893769i	0.0666230	+	0.205045i	−0.912203	+	0.409739i	$0.865620\pi$
$20$	3.74390	−	2.72010i	0.837162	−	0.608234i
$21$	−2.52434			−0.550856
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	−2.16154	+	1.57045i	−0.441223	+	0.320567i
$25$	1.96914	+	6.06040i	0.393829	+	1.21208i
$26$	−1.43004	+	4.40122i	−0.280455	+	0.863151i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−2.80252	−	2.03615i	−0.529626	−	0.384796i
$29$	0.244830	−	0.753510i	0.0454638	−	0.139923i	−0.925748	−	0.378141i	$-0.876563\pi$
$29$	0.244830	−	0.753510i	0.0454638	−	0.139923i	0.971212	+	0.238218i	$0.0765633\pi$
$30$	−0.825636	−	2.54105i	−0.150740	−	0.463930i
$31$	−1.31685	+	0.956749i	−0.236514	+	0.171837i	−0.699729	−	0.714409i	$-0.746696\pi$
$31$	−1.31685	+	0.956749i	−0.236514	+	0.171837i	0.463215	+	0.886246i	$0.346696\pi$
$32$	−5.84096			−1.03255
$33$		0			0
$34$	2.11684			0.363036
$35$	6.88698	−	5.00368i	1.16411	−	0.845777i
$36$	−0.424058	−	1.30512i	−0.0706764	−	0.217520i
$37$	1.54508	−	4.75528i	0.254010	−	0.781764i	−0.740013	−	0.672593i	$-0.765181\pi$
$37$	1.54508	−	4.75528i	0.254010	−	0.781764i	0.994023	−	0.109171i	$-0.0348195\pi$
$38$	0.602364	+	0.437643i	0.0977163	+	0.0709951i
$39$	−4.72544	−	3.43323i	−0.756676	−	0.549757i
$40$	2.78428	−	8.56912i	0.440233	−	1.35490i
$41$	3.36508	+	10.3567i	0.525538	+	1.61744i	0.763250	+	0.646103i	$0.223602\pi$
$41$	3.36508	+	10.3567i	0.525538	+	1.61744i	−0.237712	+	0.971336i	$0.576398\pi$
$42$	−1.61803	+	1.17557i	−0.249668	+	0.181394i
$43$	6.63325			1.01156			0.505781	−	0.862662i	$-0.331205\pi$
$43$	6.63325			1.01156			0.505781	+	0.862662i	$0.331205\pi$
$44$		0			0
$45$	3.37228			0.502710
$46$	1.28195	−	0.931389i	0.189013	−	0.137326i
$47$	−3.93829	−	12.1208i	−0.574458	−	1.76800i	−0.638017	−	0.770022i	$-0.720245\pi$
$47$	−3.93829	−	12.1208i	−0.574458	−	1.76800i	0.0635590	−	0.997978i	$-0.479755\pi$
$48$	0.193976	−	0.596996i	0.0279980	−	0.0861689i
$49$	0.507835	+	0.368964i	0.0725479	+	0.0527091i
$50$	4.08446	+	2.96754i	0.577630	+	0.419673i
$51$	−0.825636	+	2.54105i	−0.115612	+	0.355818i
$52$	−2.47691	−	7.62314i	−0.343485	−	1.05714i
$53$	3.33060	−	2.41982i	0.457493	−	0.332388i	−0.335054	−	0.942199i	$-0.608755\pi$
$53$	3.33060	−	2.41982i	0.457493	−	0.332388i	0.792547	+	0.609811i	$0.208755\pi$
$54$	−0.792287			−0.107817
$55$		0			0
$56$	−6.74456			−0.901280
$57$	−0.760285	+	0.552379i	−0.100702	+	0.0731644i
$58$	−0.193976	−	0.596996i	−0.0254703	−	0.0783894i
$59$	−1.85410	+	5.70634i	−0.241384	+	0.742902i	0.754827	+	0.655924i	$0.227721\pi$
$59$	−1.85410	+	5.70634i	−0.241384	+	0.742902i	−0.996210	+	0.0869778i	$0.972279\pi$
$60$	3.74390	+	2.72010i	0.483336	+	0.351164i
$61$	4.84475	+	3.51992i	0.620307	+	0.450679i	0.853029	−	0.521864i	$-0.174763\pi$
$61$	4.84475	+	3.51992i	0.620307	+	0.450679i	−0.232722	+	0.972543i	$0.574763\pi$
$62$	−0.398515	+	1.22650i	−0.0506114	+	0.155766i
$63$	−0.780063	−	2.40079i	−0.0982787	−	0.302471i
$64$	−2.72823	+	1.98218i	−0.341029	+	0.247772i
$65$	19.6974			2.44316
$66$		0			0
$67$	−1.11684			−0.136444			−0.0682221	−	0.997670i	$-0.521733\pi$
$67$	−1.11684			−0.136444			−0.0682221	+	0.997670i	$0.521733\pi$
$68$	−2.96625	+	2.15510i	−0.359710	+	0.261345i
$69$	0.618034	+	1.90211i	0.0744025	+	0.228988i
$70$	2.08418	−	6.41446i	0.249108	−	0.766675i
$71$	8.69253	+	6.31550i	1.03161	+	0.749511i	0.968631	−	0.248503i	$-0.0799386\pi$
$71$	8.69253	+	6.31550i	1.03161	+	0.749511i	0.0629829	+	0.998015i	$0.479939\pi$
$72$	−2.16154	−	1.57045i	−0.254740	−	0.185080i
$73$	−2.82985	+	8.70938i	−0.331209	+	1.01936i	0.637351	+	0.770574i	$0.280030\pi$
$73$	−2.82985	+	8.70938i	−0.331209	+	1.01936i	−0.968559	+	0.248782i	$0.919970\pi$
$74$	−1.22415	−	3.76755i	−0.142305	−	0.437969i
$75$	−5.15528	+	3.74553i	−0.595281	+	0.432497i
$76$	−1.28962			−0.147930
$77$		0			0
$78$	−4.62772			−0.523986
$79$	3.32418	−	2.41516i	0.373999	−	0.271726i	−0.384868	−	0.922972i	$-0.625753\pi$
$79$	3.32418	−	2.41516i	0.373999	−	0.271726i	0.758867	+	0.651245i	$0.225753\pi$
$80$	0.654141	+	2.01324i	0.0731352	+	0.225087i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	6.97997	+	5.07125i	0.770809	+	0.560025i
$83$	−1.52057	−	1.10476i	−0.166904	−	0.121263i	0.501198	−	0.865333i	$-0.332893\pi$
$83$	−1.52057	−	1.10476i	−0.166904	−	0.121263i	−0.668102	+	0.744070i	$0.732893\pi$
$84$	1.07047	−	3.29456i	0.116797	−	0.359466i
$85$	−2.78428	−	8.56912i	−0.301997	−	0.929452i
$86$	4.25174	−	3.08907i	0.458477	−	0.333103i
$87$	0.792287			0.0849421
$88$		0			0
$89$	−0.627719			−0.0665380			−0.0332690	−	0.999446i	$-0.510592\pi$
$89$	−0.627719			−0.0665380			−0.0332690	+	0.999446i	$0.510592\pi$
$90$	2.16154	−	1.57045i	0.227847	−	0.165540i
$91$	−4.55632	−	14.0229i	−0.477632	−	1.47000i
$92$	−0.848116	+	2.61023i	−0.0884223	+	0.272136i
$93$	−1.31685	−	0.956749i	−0.136551	−	0.0992103i
$94$	−8.16893	−	5.93507i	−0.842561	−	0.612156i
$95$	0.979321	−	3.01404i	0.100476	−	0.309234i
$96$	−1.80496	−	5.55509i	−0.184218	−	0.566964i
$97$	−8.48588	+	6.16535i	−0.861611	+	0.625997i	−0.928323	−	0.371776i	$-0.878749\pi$
$97$	−8.48588	+	6.16535i	−0.861611	+	0.625997i	0.0667120	+	0.997772i	$0.478749\pi$
$98$	0.497333			0.0502383
$99$		0			0
$100$	−8.74456			−0.874456
$101$	9.68950	−	7.03983i	0.964141	−	0.700490i	0.0100323	−	0.999950i	$-0.496807\pi$
$101$	9.68950	−	7.03983i	0.964141	−	0.700490i	0.954109	+	0.299460i	$0.0968066\pi$
$102$	0.654141	+	2.01324i	0.0647696	+	0.199340i
$103$	−2.81726	+	8.67063i	−0.277593	+	0.854343i	0.710929	+	0.703264i	$0.248275\pi$
$103$	−2.81726	+	8.67063i	−0.277593	+	0.854343i	−0.988522	+	0.151079i	$0.951725\pi$
$104$	−12.6255	−	9.17296i	−1.23803	−	0.899483i
$105$	6.88698	+	5.00368i	0.672101	+	0.488310i
$106$	1.00793	−	3.10208i	0.0978986	−	0.301301i
$107$	−4.19072	−	12.8977i	−0.405132	−	1.24687i	−0.920785	−	0.390071i	$-0.872451\pi$
$107$	−4.19072	−	12.8977i	−0.405132	−	1.24687i	0.515653	−	0.856798i	$-0.327549\pi$
$108$	1.11020	−	0.806607i	0.106829	−	0.0776158i
$109$	−9.94987			−0.953025			−0.476513	−	0.879168i	$-0.658099\pi$
$109$	−9.94987			−0.953025			−0.476513	+	0.879168i	$0.658099\pi$
$110$		0			0
$111$	5.00000			0.474579
$112$	1.28195	−	0.931389i	0.121133	−	0.0880080i
$113$	0.424058	+	1.30512i	0.0398920	+	0.122775i	0.969019	−	0.246985i	$-0.0794399\pi$
$113$	0.424058	+	1.30512i	0.0398920	+	0.122775i	−0.929127	+	0.369760i	$0.879440\pi$
$114$	−0.230083	+	0.708121i	−0.0215492	+	0.0663216i
$115$	−5.45647	−	3.96435i	−0.508818	−	0.369678i
$116$	0.879596	+	0.639064i	0.0816685	+	0.0593356i
$117$	1.80496	−	5.55509i	0.166868	−	0.513568i
$118$	1.46898	+	4.52106i	0.135231	+	0.416197i
$119$	−5.45647	+	3.96435i	−0.500193	+	0.363412i
$120$	9.01011			0.822507
$121$		0			0
$122$	4.74456			0.429553
$123$	−8.80990	+	6.40077i	−0.794362	+	0.577138i
$124$	−0.690248	−	2.12436i	−0.0619861	−	0.190773i
$125$	1.43004	−	4.40122i	0.127907	−	0.393657i
$126$	−1.61803	−	1.17557i	−0.144146	−	0.104728i
$127$	−7.88589	−	5.72943i	−0.699759	−	0.508405i	0.180094	−	0.983649i	$-0.442360\pi$
$127$	−7.88589	−	5.72943i	−0.699759	−	0.508405i	−0.879854	+	0.475244i	$0.842360\pi$
$128$	2.78428	−	8.56912i	0.246098	−	0.757411i
$129$	2.04979	+	6.30860i	0.180474	+	0.555441i
$130$	12.6255	−	9.17296i	1.10733	−	0.804522i
$131$	−6.63325			−0.579550			−0.289775	−	0.957095i	$-0.593580\pi$
$131$	−6.63325			−0.579550			−0.289775	+	0.957095i	$0.593580\pi$
$132$		0			0
$133$	−2.37228			−0.205703
$134$	−0.715868	+	0.520108i	−0.0618415	+	0.0449305i
$135$	1.04209	+	3.20723i	0.0896890	+	0.276034i
$136$	−2.20595	+	6.78921i	−0.189158	+	0.582170i
$137$	8.69253	+	6.31550i	0.742653	+	0.539569i	0.893541	−	0.448982i	$-0.148213\pi$
$137$	8.69253	+	6.31550i	0.742653	+	0.539569i	−0.150888	+	0.988551i	$0.548213\pi$
$138$	1.28195	+	0.931389i	0.109127	+	0.0792851i
$139$	−3.21140	+	9.88367i	−0.272387	+	0.838322i	0.717512	+	0.696547i	$0.245281\pi$
$139$	−3.21140	+	9.88367i	−0.272387	+	0.838322i	−0.989899	+	0.141775i	$0.954719\pi$
$140$	3.60991	+	11.1102i	0.305093	+	0.938981i
$141$	10.3106	−	7.49107i	0.868306	−	0.630862i
$142$	8.51278			0.714376
$143$		0			0
$144$	0.627719			0.0523099
$145$	−2.16154	+	1.57045i	−0.179506	+	0.130419i
$146$	2.24205	+	6.90033i	0.185554	+	0.571075i
$147$	−0.193976	+	0.596996i	−0.0159988	+	0.0492394i
$148$	5.55099	+	4.03303i	0.456289	+	0.331513i
$149$	2.16154	+	1.57045i	0.177081	+	0.128657i	0.672795	−	0.739829i	$-0.265094\pi$
$149$	2.16154	+	1.57045i	0.177081	+	0.128657i	−0.495714	+	0.868486i	$0.665094\pi$
$150$	−1.56013	+	4.80158i	−0.127384	+	0.392047i
$151$	6.82131	+	20.9938i	0.555111	+	1.70845i	0.695651	+	0.718380i	$0.255116\pi$
$151$	6.82131	+	20.9938i	0.555111	+	1.70845i	−0.140541	+	0.990075i	$0.544884\pi$
$152$	−2.03134	+	1.47586i	−0.164763	+	0.119708i
$153$	−2.67181			−0.216003
$154$		0			0
$155$	5.48913			0.440897
$156$	6.48463	−	4.71136i	0.519186	−	0.377211i
$157$	3.82325	+	11.7667i	0.305128	+	0.939088i	0.979629	+	0.200814i	$0.0643588\pi$
$157$	3.82325	+	11.7667i	0.305128	+	0.939088i	−0.674501	+	0.738274i	$0.735641\pi$
$158$	1.00599	−	3.09610i	0.0800319	−	0.246313i
$159$	3.33060	+	2.41982i	0.264134	+	0.191904i
$160$	15.9355	+	11.5778i	1.25981	+	0.915307i
$161$	−1.56013	+	4.80158i	−0.122955	+	0.378417i
$162$	−0.244830	−	0.753510i	−0.0192357	−	0.0592013i
$163$	2.93489	−	2.13232i	0.229878	−	0.167016i	−0.466884	−	0.884319i	$-0.654623\pi$
$163$	2.93489	−	2.13232i	0.229878	−	0.167016i	0.696762	+	0.717302i	$0.254623\pi$
$164$	−14.9436			−1.16690
$165$		0			0
$166$	−1.48913			−0.115579
$167$	−19.1404	+	13.9063i	−1.48113	+	1.07610i	−0.503935	+	0.863741i	$0.668115\pi$
$167$	−19.1404	+	13.9063i	−1.48113	+	1.07610i	−0.977192	+	0.212360i	$0.931885\pi$
$168$	−2.08418	−	6.41446i	−0.160798	−	0.494886i
$169$	6.52546	−	20.0833i	0.501959	−	1.54487i
$170$	−5.77524	−	4.19596i	−0.442941	−	0.321815i
$171$	−0.760285	−	0.552379i	−0.0581404	−	0.0422415i
$172$	−2.81288	+	8.65717i	−0.214480	+	0.660103i
$173$	−2.14093	−	6.58911i	−0.162772	−	0.500961i	0.836093	−	0.548588i	$-0.184834\pi$
$173$	−2.14093	−	6.58911i	−0.162772	−	0.500961i	−0.998865	+	0.0476266i	$0.984834\pi$
$174$	0.507835	−	0.368964i	0.0384989	−	0.0279711i
$175$	−16.0858			−1.21597
$176$		0			0
$177$	−6.00000			−0.450988
$178$	−0.402351	+	0.292325i	−0.0301575	+	0.0219107i
$179$	3.16238	+	9.73282i	0.236368	+	0.727465i	0.996937	+	0.0782082i	$0.0249199\pi$
$179$	3.16238	+	9.73282i	0.236368	+	0.727465i	−0.760569	+	0.649257i	$0.775080\pi$
$180$	−1.43004	+	4.40122i	−0.106589	+	0.328048i
$181$	−13.7533	−	9.99235i	−1.02227	−	0.742725i	−0.0555261	−	0.998457i	$-0.517684\pi$
$181$	−13.7533	−	9.99235i	−1.02227	−	0.742725i	−0.966748	+	0.255732i	$0.917684\pi$
$182$	−9.45088	−	6.86646i	−0.700546	−	0.508976i
$183$	−1.85053	+	5.69534i	−0.136795	+	0.421012i
$184$	1.65127	+	5.08209i	0.121733	+	0.374657i
$185$	−13.6412	+	9.91089i	−1.00292	+	0.728663i
$186$	−1.28962			−0.0945596
$187$		0			0
$188$	17.4891			1.27553
$189$	2.04223	−	1.48377i	0.148551	−	0.107928i
$190$	−0.775903	−	2.38798i	−0.0562899	−	0.173243i
$191$	1.69623	−	5.22047i	0.122735	−	0.377740i	−0.870747	−	0.491732i	$-0.836364\pi$
$191$	1.69623	−	5.22047i	0.122735	−	0.377740i	0.993482	+	0.113992i	$0.0363639\pi$
$192$	−2.72823	−	1.98218i	−0.196893	−	0.143051i
$193$	8.52686	+	6.19513i	0.613777	+	0.445935i	0.850742	−	0.525583i	$-0.176153\pi$
$193$	8.52686	+	6.19513i	0.613777	+	0.445935i	−0.236965	+	0.971518i	$0.576153\pi$
$194$	−2.56805	+	7.90366i	−0.184376	+	0.567450i
$195$	6.08682	+	18.7333i	0.435886	+	1.34152i
$196$	−0.696893	+	0.506322i	−0.0497780	+	0.0361659i
$197$	−2.08191			−0.148330			−0.0741649	−	0.997246i	$-0.523629\pi$
$197$	−2.08191			−0.148330			−0.0741649	+	0.997246i	$0.523629\pi$
$198$		0			0
$199$	21.8614			1.54971			0.774857	−	0.632137i	$-0.217822\pi$
$199$	21.8614			1.54971			0.774857	+	0.632137i	$0.217822\pi$
$200$	−13.7740	+	10.0074i	−0.973966	+	0.707628i
$201$	−0.345124	−	1.06218i	−0.0243432	−	0.0749205i
$202$	2.93230	−	9.02469i	0.206316	−	0.634975i
$203$	1.61803	+	1.17557i	0.113564	+	0.0825089i
$204$	−2.96625	−	2.15510i	−0.207679	−	0.150887i
$205$	11.3480	−	34.9256i	0.792579	−	2.43931i
$206$	2.23208	+	6.86963i	0.155516	+	0.478630i
$207$	−1.61803	+	1.17557i	−0.112461	+	0.0817078i
$208$	3.66648			0.254225
$209$		0			0
$210$	6.74456			0.465419
$211$	8.69059	−	6.31408i	0.598285	−	0.434679i	−0.246985	−	0.969019i	$-0.579440\pi$
$211$	8.69059	−	6.31408i	0.598285	−	0.434679i	0.845270	+	0.534340i	$0.179440\pi$
$212$	1.74578	+	5.37296i	0.119901	+	0.369017i
$213$	−3.32025	+	10.2187i	−0.227500	+	0.700173i
$214$	−8.69253	−	6.31550i	−0.594209	−	0.431718i
$215$	−18.0970	−	13.1483i	−1.23421	−	0.896705i
$216$	0.825636	−	2.54105i	0.0561774	−	0.172896i
$217$	−1.26972	−	3.90781i	−0.0861945	−	0.265279i
$218$	−6.37761	+	4.63360i	−0.431946	+	0.313827i
$219$	−9.15759			−0.618812
$220$		0			0
$221$	−15.6060			−1.04977
$222$	3.20487	−	2.32847i	0.215097	−	0.156277i
$223$	7.37358	+	22.6935i	0.493771	+	1.51967i	0.818863	+	0.573990i	$0.194605\pi$
$223$	7.37358	+	22.6935i	0.493771	+	1.51967i	−0.325091	+	0.945683i	$0.605395\pi$
$224$	4.55632	−	14.0229i	0.304432	−	0.936945i
$225$	−5.15528	−	3.74553i	−0.343686	−	0.249702i
$226$	0.879596	+	0.639064i	0.0585099	+	0.0425099i
$227$	−2.44830	+	7.53510i	−0.162499	+	0.500122i	−0.998843	−	0.0480833i	$-0.984689\pi$
$227$	−2.44830	+	7.53510i	−0.162499	+	0.500122i	0.836344	+	0.548205i	$0.184689\pi$
$228$	−0.398515	−	1.22650i	−0.0263923	−	0.0812271i
$229$	7.58233	−	5.50889i	0.501055	−	0.364038i	−0.308365	−	0.951268i	$-0.599782\pi$
$229$	7.58233	−	5.50889i	0.501055	−	0.364038i	0.809420	+	0.587231i	$0.199782\pi$
$230$	−5.34363			−0.352348
$231$		0			0
$232$	2.11684			0.138978
$233$	0.640974	−	0.465695i	0.0419916	−	0.0305087i	−0.566591	−	0.823999i	$-0.691738\pi$
$233$	0.640974	−	0.465695i	0.0419916	−	0.0305087i	0.608583	+	0.793490i	$0.291738\pi$
$234$	−1.43004	−	4.40122i	−0.0934849	−	0.287717i
$235$	−13.2810	+	40.8747i	−0.866358	+	2.66637i
$236$	−6.66119	−	4.83964i	−0.433607	−	0.315034i
$237$	3.32418	+	2.41516i	0.215929	+	0.156881i
$238$	−1.65127	+	5.08209i	−0.107036	+	0.329423i
$239$	−7.00360	−	21.5549i	−0.453025	−	1.39427i	−0.873438	−	0.486936i	$-0.838115\pi$
$239$	−7.00360	−	21.5549i	−0.453025	−	1.39427i	0.420412	−	0.907333i	$-0.361885\pi$
$240$	−1.71256	+	1.24425i	−0.110545	+	0.0803160i
$241$	13.2665			0.854570			0.427285	−	0.904117i	$-0.359470\pi$
$241$	13.2665			0.854570			0.427285	+	0.904117i	$0.359470\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−6.64836	+	4.83032i	−0.425618	+	0.309229i
$245$	−0.654141	−	2.01324i	−0.0417915	−	0.128621i
$246$	−2.66611	+	8.20545i	−0.169985	+	0.523160i
$247$	−4.44080	−	3.22643i	−0.282561	−	0.205293i
$248$	−3.51838	−	2.55626i	−0.223418	−	0.162322i
$249$	0.580806	−	1.78754i	0.0368071	−	0.113281i
$250$	−1.13301	−	3.48703i	−0.0716575	−	0.220539i
$251$	19.0031	−	13.8066i	1.19947	−	0.871462i	0.205233	−	0.978713i	$-0.434205\pi$
$251$	19.0031	−	13.8066i	1.19947	−	0.871462i	0.994232	+	0.107251i	$0.0342047\pi$
$252$	3.46410			0.218218
$253$		0			0
$254$	−7.72281			−0.484572
$255$	7.28933	−	5.29601i	0.456476	−	0.331649i
$256$	−4.29013	−	13.2037i	−0.268133	−	0.825229i
$257$	5.75628	−	17.7160i	0.359067	−	1.10509i	−0.594547	−	0.804061i	$-0.702668\pi$
$257$	5.75628	−	17.7160i	0.359067	−	1.10509i	0.953614	−	0.301033i	$-0.0973316\pi$
$258$	4.25174	+	3.08907i	0.264702	+	0.192317i
$259$	10.2112	+	7.41884i	0.634491	+	0.460984i
$260$	−8.35283	+	25.7074i	−0.518021	+	1.59430i
$261$	0.244830	+	0.753510i	0.0151546	+	0.0466411i
$262$	−4.25174	+	3.08907i	−0.262673	+	0.190843i
$263$	−15.7359			−0.970319			−0.485160	−	0.874426i	$-0.661239\pi$
$263$	−15.7359			−0.970319			−0.485160	+	0.874426i	$0.661239\pi$
$264$		0			0
$265$	−13.8832			−0.852835
$266$	−1.52057	+	1.10476i	−0.0932321	+	0.0677371i
$267$	−0.193976	−	0.596996i	−0.0118711	−	0.0365356i
$268$	0.473607	−	1.45761i	0.0289301	−	0.0890378i
$269$	6.56666	+	4.77096i	0.400377	+	0.290891i	0.769694	−	0.638413i	$-0.220409\pi$
$269$	6.56666	+	4.77096i	0.400377	+	0.290891i	−0.369318	+	0.929303i	$0.620409\pi$
$270$	2.16154	+	1.57045i	0.131547	+	0.0955747i
$271$	−3.21140	+	9.88367i	−0.195079	+	0.600390i	0.804897	+	0.593414i	$0.202220\pi$
$271$	−3.21140	+	9.88367i	−0.195079	+	0.600390i	−0.999976	+	0.00697572i	$0.997780\pi$
$272$	−0.518267	−	1.59506i	−0.0314246	−	0.0967149i
$273$	11.9286	−	8.66664i	0.721952	−	0.524529i
$274$	8.51278			0.514276
$275$		0			0
$276$	−2.74456			−0.165203
$277$	7.00629	−	5.09037i	0.420967	−	0.305851i	−0.357060	−	0.934082i	$-0.616221\pi$
$277$	7.00629	−	5.09037i	0.420967	−	0.305851i	0.778027	+	0.628231i	$0.216221\pi$
$278$	2.54435	+	7.83070i	0.152600	+	0.469654i
$279$	0.502993	−	1.54805i	0.0301134	−	0.0926795i
$280$	18.4007	+	13.3689i	1.09965	+	0.798946i
$281$	21.9429	+	15.9424i	1.30900	+	0.951046i	1.00000		1.45384e-5i	$-4.62772e-6\pi$
$281$	21.9429	+	15.9424i	1.30900	+	0.951046i	0.309003	+	0.951061i	$0.400005\pi$
$282$	3.12025	−	9.60315i	0.185808	−	0.571859i
$283$	2.34019	+	7.20236i	0.139110	+	0.428136i	0.996207	−	0.0870193i	$-0.0277342\pi$
$283$	2.34019	+	7.20236i	0.139110	+	0.428136i	−0.857097	+	0.515155i	$0.827734\pi$
$284$	−11.9286	+	8.66664i	−0.707832	+	0.514270i
$285$	3.16915			0.187724
$286$		0			0
$287$	−27.4891			−1.62263
$288$	4.72544	−	3.43323i	0.278449	−	0.202305i
$289$	−3.04734	−	9.37876i	−0.179255	−	0.551691i
$290$	−0.654141	+	2.01324i	−0.0384125	+	0.118221i
$291$	−8.48588	−	6.16535i	−0.497451	−	0.361419i
$292$	−10.1667	−	7.38657i	−0.594964	−	0.432266i
$293$	9.20707	−	28.3365i	0.537883	−	1.65543i	−0.199453	−	0.979907i	$-0.563916\pi$
$293$	9.20707	−	28.3365i	0.537883	−	1.65543i	0.737336	−	0.675526i	$-0.236084\pi$
$294$	0.153684	+	0.472992i	0.00896306	+	0.0275855i
$295$	16.3694	−	11.8931i	0.953063	−	0.692441i
$296$	13.3591			0.776480
$297$		0			0
$298$	2.11684			0.122625
$299$	−9.45088	+	6.86646i	−0.546558	+	0.397098i
$300$	−2.70222	−	8.31657i	−0.156013	−	0.480158i
$301$	−5.17435	+	15.9250i	−0.298245	+	0.917903i
$302$	14.1490	+	10.2798i	0.814183	+	0.591539i
$303$	9.68950	+	7.03983i	0.556647	+	0.404428i
$304$	0.182291	−	0.561035i	0.0104551	−	0.0321776i
$305$	−6.24051	−	19.2063i	−0.357330	−	1.09975i
$306$	−1.71256	+	1.24425i	−0.0979007	+	0.0711290i
$307$	−1.23472			−0.0704690			−0.0352345	−	0.999379i	$-0.511218\pi$
$307$	−1.23472			−0.0704690			−0.0352345	+	0.999379i	$0.511218\pi$
$308$		0			0
$309$	−9.11684			−0.518639
$310$	3.51838	−	2.55626i	0.199831	−	0.145186i
$311$	−9.11264	−	28.0458i	−0.516730	−	1.59033i	−0.780111	−	0.625641i	$-0.784838\pi$
$311$	−9.11264	−	28.0458i	−0.516730	−	1.59033i	0.263381	−	0.964692i	$-0.415162\pi$
$312$	4.82251	−	14.8422i	0.273021	−	0.840272i
$313$	6.56666	+	4.77096i	0.371170	+	0.269671i	0.757696	−	0.652608i	$-0.226325\pi$
$313$	6.56666	+	4.77096i	0.371170	+	0.269671i	−0.386526	+	0.922278i	$0.626325\pi$
$314$	7.93031	+	5.76170i	0.447533	+	0.325152i
$315$	−2.63059	+	8.09613i	−0.148217	+	0.456165i
$316$	1.74242	+	5.36261i	0.0980187	+	0.301670i
$317$	−21.6368	+	15.7201i	−1.21524	+	0.882927i	−0.995696	−	0.0926753i	$-0.970458\pi$
$317$	−21.6368	+	15.7201i	−1.21524	+	0.882927i	−0.219548	+	0.975602i	$0.570458\pi$
$318$	3.26172			0.182908
$319$		0			0
$320$	11.3723			0.635730
$321$	10.9714	−	7.97122i	0.612366	−	0.444910i
$322$	1.23607	+	3.80423i	0.0688834	+	0.212001i
$323$	−0.775903	+	2.38798i	−0.0431724	+	0.132871i
$324$	1.11020	+	0.806607i	0.0616777	+	0.0448115i
$325$	−30.1118	−	21.8775i	−1.67030	−	1.21355i
$326$	0.888175	−	2.73352i	0.0491915	−	0.151396i
$327$	−3.07468	−	9.46289i	−0.170030	−	0.523299i
$328$	−23.5384	+	17.1017i	−1.29969	+	0.944282i
$329$	32.1716			1.77368
$330$		0			0
$331$	−6.37228			−0.350252			−0.175126	−	0.984546i	$-0.556033\pi$
$331$	−6.37228			−0.350252			−0.175126	+	0.984546i	$0.556033\pi$
$332$	2.08665	−	1.51604i	0.114520	−	0.0832035i
$333$	1.54508	+	4.75528i	0.0846701	+	0.260588i
$334$	−5.79239	+	17.8271i	−0.316945	+	0.975458i
$335$	3.04701	+	2.21378i	0.166476	+	0.120952i
$336$	1.28195	+	0.931389i	0.0699360	+	0.0508114i
$337$	0.626379	−	1.92780i	0.0341210	−	0.105014i	−0.932545	−	0.361053i	$-0.882417\pi$
$337$	0.626379	−	1.92780i	0.0341210	−	0.105014i	0.966666	+	0.256039i	$0.0824175\pi$
$338$	−5.17004	−	15.9117i	−0.281213	−	0.865485i
$339$	−1.11020	+	0.806607i	−0.0602977	+	0.0438089i
$340$	12.3644			0.670554
$341$		0			0
$342$	−0.744563			−0.0402613
$343$	−15.5776	+	11.3178i	−0.841110	+	0.611102i
$344$	5.47665	+	16.8554i	0.295281	+	0.908782i
$345$	2.08418	−	6.41446i	0.112209	−	0.345343i
$346$	−4.44080	−	3.22643i	−0.238739	−	0.173454i
$347$	−22.9862	−	16.7005i	−1.23396	−	0.896528i	−0.236784	−	0.971562i	$-0.576093\pi$
$347$	−22.9862	−	16.7005i	−1.23396	−	0.896528i	−0.997181	+	0.0750345i	$0.976093\pi$
$348$	−0.335976	+	1.03403i	−0.0180102	+	0.0554297i
$349$	−8.02850	−	24.7092i	−0.429756	−	1.32265i	−0.898366	−	0.439247i	$-0.855245\pi$
$349$	−8.02850	−	24.7092i	−0.429756	−	1.32265i	0.468611	−	0.883405i	$-0.344755\pi$
$350$	−10.3106	+	7.49107i	−0.551123	+	0.400414i
$351$	5.84096			0.311768
$352$		0			0
$353$	22.3505			1.18960			0.594799	−	0.803874i	$-0.297231\pi$
$353$	22.3505			1.18960			0.594799	+	0.803874i	$0.297231\pi$
$354$	−3.84584	+	2.79417i	−0.204404	+	0.148508i
$355$	−11.1968	−	34.4603i	−0.594266	−	1.82896i
$356$	0.266189	−	0.819246i	0.0141080	−	0.0434200i
$357$	−5.45647	−	3.96435i	−0.288787	−	0.209816i
$358$	6.55952	+	4.76577i	0.346682	+	0.251879i
$359$	5.75085	−	17.6993i	0.303518	−	0.934132i	−0.676708	−	0.736251i	$-0.736594\pi$
$359$	5.75085	−	17.6993i	0.303518	−	0.934132i	0.980226	−	0.197881i	$-0.0634060\pi$
$360$	2.78428	+	8.56912i	0.146744	+	0.451633i
$361$	14.6568	−	10.6488i	0.771412	−	0.560464i
$362$	−13.4689			−0.707909
$363$		0			0
$364$	20.2337			1.06053
$365$	24.9840	−	18.1520i	1.30772	−	0.950117i
$366$	1.46615	+	4.51235i	0.0766369	+	0.235864i
$367$	10.4209	−	32.0723i	0.543968	−	1.67416i	−0.179464	−	0.983765i	$-0.557436\pi$
$367$	10.4209	−	32.0723i	0.543968	−	1.67416i	0.723432	−	0.690396i	$-0.242564\pi$
$368$	−1.01567	−	0.737928i	−0.0529455	−	0.0384671i
$369$	−8.80990	−	6.40077i	−0.458625	−	0.333211i
$370$	−4.12818	+	12.7052i	−0.214614	+	0.660514i
$371$	3.21140	+	9.88367i	0.166728	+	0.513135i
$372$	1.80709	−	1.31293i	0.0936933	−	0.0680722i
$373$	5.39853			0.279525			0.139763	−	0.990185i	$-0.455366\pi$
$373$	5.39853			0.279525			0.139763	+	0.990185i	$0.455366\pi$
$374$		0			0
$375$	4.62772			0.238974
$376$	27.5479	−	20.0147i	1.42068	−	1.03218i
$377$	1.43004	+	4.40122i	0.0736510	+	0.226674i
$378$	0.618034	−	1.90211i	0.0317882	−	0.0978341i
$379$	27.2823	+	19.8218i	1.40140	+	1.01818i	0.994504	+	0.104701i	$0.0333886\pi$
$379$	27.2823	+	19.8218i	1.40140	+	1.01818i	0.406895	+	0.913475i	$0.366611\pi$
$380$	3.51838	+	2.55626i	0.180489	+	0.131133i
$381$	3.01214	−	9.27042i	0.154317	−	0.474938i
$382$	−1.34390	−	4.13611i	−0.0687601	−	0.211622i
$383$	0.413306	−	0.300285i	0.0211190	−	0.0153438i	−0.577176	−	0.816620i	$-0.695845\pi$
$383$	0.413306	−	0.300285i	0.0211190	−	0.0153438i	0.598295	+	0.801276i	$0.295845\pi$
$384$	9.01011			0.459795
$385$		0			0
$386$	8.35053			0.425031
$387$	−5.36641	+	3.89893i	−0.272790	+	0.198194i
$388$	−4.44800	−	13.6895i	−0.225813	−	0.694981i
$389$	2.50824	−	7.71958i	0.127173	−	0.391398i	−0.867118	−	0.498103i	$-0.834030\pi$
$389$	2.50824	−	7.71958i	0.127173	−	0.391398i	0.994291	+	0.106705i	$0.0340301\pi$
$390$	12.6255	+	9.17296i	0.639317	+	0.464491i
$391$	4.32309	+	3.14091i	0.218628	+	0.158842i
$392$	−0.518267	+	1.59506i	−0.0261764	+	0.0805628i
$393$	−2.04979	−	6.30860i	−0.103398	−	0.318227i
$394$	−1.33445	+	0.969533i	−0.0672285	+	0.0488444i
$395$	−13.8564			−0.697191
$396$		0			0
$397$	1.51087			0.0758286			0.0379143	−	0.999281i	$-0.487929\pi$
$397$	1.51087			0.0758286			0.0379143	+	0.999281i	$0.487929\pi$
$398$	14.0126	−	10.1807i	0.702387	−	0.510314i
$399$	−0.733075	−	2.25617i	−0.0366997	−	0.112950i
$400$	1.23607	−	3.80423i	0.0618034	−	0.190211i
$401$	1.52351	+	1.10689i	0.0760802	+	0.0552755i	0.625175	−	0.780484i	$-0.285027\pi$
$401$	1.52351	+	1.10689i	0.0760802	+	0.0552755i	−0.549095	+	0.835760i	$0.685027\pi$
$402$	−0.715868	−	0.520108i	−0.0357042	−	0.0259406i
$403$	2.93796	−	9.04212i	0.146350	−	0.450420i
$404$	5.07889	+	15.6312i	0.252684	+	0.777683i
$405$	−2.72823	+	1.98218i	−0.135567	+	0.0984952i
$406$	1.58457			0.0786411
$407$		0			0
$408$	−7.13859			−0.353413
$409$	−16.4572	+	11.9568i	−0.813755	+	0.591227i	−0.914917	−	0.403643i	$-0.867744\pi$
$409$	−16.4572	+	11.9568i	−0.813755	+	0.591227i	0.101162	+	0.994870i	$0.467744\pi$
$410$	−8.99088	−	27.6711i	−0.444028	−	1.36658i
$411$	−3.32025	+	10.2187i	−0.163776	+	0.504051i
$412$	−10.1215	−	7.35371i	−0.498651	−	0.362291i
$413$	−12.2534	−	8.90261i	−0.602950	−	0.438069i
$414$	−0.489660	+	1.50702i	−0.0240655	+	0.0740660i
$415$	1.95864	+	6.02808i	0.0961459	+	0.295907i
$416$	27.6011	−	20.0534i	1.35326	−	0.983198i
$417$	−10.3923			−0.508913
$418$		0			0
$419$	−31.4891			−1.53834			−0.769172	−	0.639042i	$-0.779331\pi$
$419$	−31.4891			−1.53834			−0.769172	+	0.639042i	$0.779331\pi$
$420$	−9.45088	+	6.86646i	−0.461156	+	0.335049i
$421$	10.7728	+	33.1552i	0.525033	+	1.61588i	0.764251	+	0.644918i	$0.223109\pi$
$421$	10.7728	+	33.1552i	0.525033	+	1.61588i	−0.239219	+	0.970966i	$0.576891\pi$
$422$	2.63000	−	8.09432i	0.128027	−	0.394025i
$423$	10.3106	+	7.49107i	0.501317	+	0.364228i
$424$	8.89874	+	6.46531i	0.432161	+	0.313983i
$425$	−5.26119	+	16.1923i	−0.255205	+	0.785440i
$426$	2.63059	+	8.09613i	0.127453	+	0.392259i
$427$	−12.2298	+	8.88546i	−0.591841	+	0.429997i
$428$	18.6101			0.899555
$429$		0			0
$430$	−17.7228			−0.854670
$431$	2.32527	−	1.68941i	0.112004	−	0.0813760i	−0.530373	−	0.847764i	$-0.677948\pi$
$431$	2.32527	−	1.68941i	0.112004	−	0.0813760i	0.642378	+	0.766388i	$0.277948\pi$
$432$	0.193976	+	0.596996i	0.00933266	+	0.0287230i
$433$	3.47140	−	10.6839i	0.166825	−	0.513434i	−0.832341	−	0.554263i	$-0.813000\pi$
$433$	3.47140	−	10.6839i	0.166825	−	0.513434i	0.999166	+	0.0408294i	$0.0130000\pi$
$434$	−2.63370	−	1.91350i	−0.126422	−	0.0918508i
$435$	−2.16154	−	1.57045i	−0.103638	−	0.0752975i
$436$	4.21933	−	12.9858i	0.202069	−	0.621905i
$437$	0.580806	+	1.78754i	0.0277837	+	0.0855095i
$438$	−5.86977	+	4.26464i	−0.280469	+	0.203772i
$439$	−5.39853			−0.257658			−0.128829	−	0.991667i	$-0.541122\pi$
$439$	−5.39853			−0.257658			−0.128829	+	0.991667i	$0.541122\pi$
$440$		0			0
$441$	−0.627719			−0.0298914
$442$	−10.0030	+	7.26762i	−0.475795	+	0.345685i
$443$	2.86009	+	8.80244i	0.135887	+	0.418217i	0.995727	−	0.0923468i	$-0.0294368\pi$
$443$	2.86009	+	8.80244i	0.135887	+	0.418217i	−0.859840	+	0.510563i	$0.829437\pi$
$444$	−2.12029	+	6.52559i	−0.100625	+	0.309691i
$445$	1.71256	+	1.24425i	0.0811833	+	0.0589831i
$446$	15.2945	+	11.1121i	0.724217	+	0.526175i
$447$	−0.825636	+	2.54105i	−0.0390512	+	0.120187i
$448$	−2.63059	−	8.09613i	−0.124284	−	0.382506i
$449$	12.6255	−	9.17296i	0.595834	−	0.432899i	−0.248564	−	0.968616i	$-0.579959\pi$
$449$	12.6255	−	9.17296i	0.595834	−	0.432899i	0.844398	+	0.535717i	$0.179959\pi$
$450$	−5.04868			−0.237997
$451$		0			0
$452$	−1.88316			−0.0885762
$453$	−17.8584	+	12.9749i	−0.839062	+	0.609614i
$454$	1.93976	+	5.96996i	0.0910373	+	0.280184i
$455$	−15.3652	+	47.2892i	−0.720331	+	2.21695i
$456$	−2.03134	−	1.47586i	−0.0951262	−	0.0691132i
$457$	30.9914	+	22.5166i	1.44972	+	1.05328i	0.985897	+	0.167352i	$0.0535216\pi$
$457$	30.9914	+	22.5166i	1.44972	+	1.05328i	0.463820	+	0.885929i	$0.346478\pi$
$458$	2.29462	−	7.06210i	0.107220	−	0.329990i
$459$	−0.825636	−	2.54105i	−0.0385374	−	0.118606i
$460$	7.48781	−	5.44021i	0.349121	−	0.253651i
$461$	4.55134			0.211977			0.105989	−	0.994367i	$-0.466199\pi$
$461$	4.55134			0.211977			0.105989	+	0.994367i	$0.466199\pi$
$462$		0			0
$463$	−14.7446			−0.685238			−0.342619	−	0.939474i	$-0.611314\pi$
$463$	−14.7446			−0.685238			−0.342619	+	0.939474i	$0.611314\pi$
$464$	−0.402351	+	0.292325i	−0.0186787	+	0.0135709i
$465$	1.69623	+	5.22047i	0.0786609	+	0.242093i
$466$	0.193976	−	0.596996i	0.00898575	−	0.0276553i
$467$	−9.89726	−	7.19078i	−0.457991	−	0.332750i	0.334752	−	0.942306i	$-0.391347\pi$
$467$	−9.89726	−	7.19078i	−0.457991	−	0.332750i	−0.792743	+	0.609557i	$0.791347\pi$
$468$	6.48463	+	4.71136i	0.299752	+	0.217783i
$469$	0.871209	−	2.68131i	0.0402287	−	0.123811i
$470$	10.5224	+	32.3845i	0.485361	+	1.49379i
$471$	−10.0094	+	7.27224i	−0.461208	+	0.335087i
$472$	−16.0309			−0.737881
$473$		0			0
$474$	3.25544			0.149527
$475$	−4.84475	+	3.51992i	−0.222292	+	0.161505i
$476$	−2.86009	−	8.80244i	−0.131092	−	0.403459i
$477$	−1.27217	+	3.91535i	−0.0582489	+	0.179272i
$478$	−14.5271	−	10.5546i	−0.664455	−	0.482755i
$479$	−8.88480	−	6.45518i	−0.405957	−	0.294945i	0.366006	−	0.930612i	$-0.380725\pi$
$479$	−8.88480	−	6.45518i	−0.405957	−	0.294945i	−0.771963	+	0.635668i	$0.780725\pi$
$480$	−6.08682	+	18.7333i	−0.277824	+	0.855055i
$481$	9.02478	+	27.7754i	0.411495	+	1.26645i
$482$	8.50348	−	6.17814i	0.387323	−	0.281406i
$483$	−5.04868			−0.229723
$484$		0			0
$485$	35.3723			1.60617
$486$	0.640974	−	0.465695i	0.0290752	−	0.0211243i
$487$	−0.387951	−	1.19399i	−0.0175798	−	0.0541049i	0.941882	−	0.335944i	$-0.109055\pi$
$487$	−0.387951	−	1.19399i	−0.0175798	−	0.0541049i	−0.959462	+	0.281839i	$0.909055\pi$
$488$	−4.94427	+	15.2169i	−0.223817	+	0.688837i
$489$	2.93489	+	2.13232i	0.132720	+	0.0964268i
$490$	−1.35684	−	0.985803i	−0.0612958	−	0.0445340i
$491$	−0.398515	+	1.22650i	−0.0179847	+	0.0553513i	−0.959646	−	0.281211i	$-0.909264\pi$
$491$	−0.398515	+	1.22650i	−0.0179847	+	0.0553513i	0.941661	+	0.336562i	$0.109264\pi$
$492$	−4.61784	−	14.2123i	−0.208188	−	0.640738i
$493$	1.71256	−	1.24425i	0.0771299	−	0.0560382i
$494$	−4.34896			−0.195669
$495$		0			0
$496$	1.02175			0.0458779
$497$	−21.9429	+	15.9424i	−0.984273	+	0.715116i
$498$	−0.460165	−	1.41624i	−0.0206205	−	0.0634633i
$499$	11.3841	−	35.0366i	0.509621	−	1.56845i	−0.283238	−	0.959050i	$-0.591409\pi$
$499$	11.3841	−	35.0366i	0.509621	−	1.56845i	0.792860	−	0.609404i	$-0.208591\pi$
$500$	5.13769	+	3.73275i	0.229764	+	0.166934i
$501$	−19.1404	−	13.9063i	−0.855129	−	0.621287i
$502$	5.75085	−	17.6993i	0.256673	−	0.789958i
$503$	0.671952	+	2.06805i	0.0299608	+	0.0922100i	0.964919	−	0.262549i	$-0.0845630\pi$
$503$	0.671952	+	2.06805i	0.0299608	+	0.0922100i	−0.934958	+	0.354759i	$0.884563\pi$
$504$	5.45647	−	3.96435i	0.243050	−	0.176586i
$505$	−40.3894			−1.79730
$506$		0			0
$507$	21.1168			0.937832
$508$	10.8217	−	7.86239i	0.480133	−	0.348837i
$509$	1.53836	+	4.73460i	0.0681868	+	0.209857i	0.979344	−	0.202202i	$-0.0648097\pi$
$509$	1.53836	+	4.73460i	0.0681868	+	0.209857i	−0.911157	+	0.412059i	$0.864810\pi$
$510$	2.20595	−	6.78921i	0.0976810	−	0.300631i
$511$	−18.7019	−	13.5877i	−0.827324	−	0.601086i
$512$	5.67993	+	4.12671i	0.251020	+	0.182377i
$513$	0.290403	−	0.893769i	0.0128216	−	0.0394608i
$514$	−4.56063	−	14.0362i	−0.201161	−	0.619109i
$515$	24.8729	−	18.0712i	1.09603	−	0.796312i
$516$	−9.10268			−0.400723
$517$		0			0
$518$	10.0000			0.439375
$519$	5.60503	−	4.07230i	0.246034	−	0.178754i
$520$	16.2629	+	50.0519i	0.713174	+	2.19492i
$521$	−8.95477	+	27.5600i	−0.392316	+	1.20742i	0.538717	+	0.842487i	$0.318909\pi$
$521$	−8.95477	+	27.5600i	−0.392316	+	1.20742i	−0.931032	+	0.364937i	$0.881091\pi$
$522$	0.507835	+	0.368964i	0.0222273	+	0.0161491i
$523$	−29.3515	−	21.3251i	−1.28345	−	0.932483i	−0.283802	−	0.958883i	$-0.591596\pi$
$523$	−29.3515	−	21.3251i	−1.28345	−	0.932483i	−0.999651	+	0.0263998i	$0.991596\pi$
$524$	2.81288	−	8.65717i	0.122881	−	0.378190i
$525$	−4.97078	−	15.2985i	−0.216943	−	0.667681i
$526$	−10.0863	+	7.32814i	−0.439784	+	0.319522i
$527$	−4.34896			−0.189444
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−8.89874	+	6.46531i	−0.386536	+	0.280835i
$531$	−1.85410	−	5.70634i	−0.0804612	−	0.247634i
$532$	1.00599	−	3.09610i	0.0436150	−	0.134233i
$533$	−51.4583	−	37.3867i	−2.22891	−	1.61940i
$534$	−0.402351	−	0.292325i	−0.0174114	−	0.0126501i
$535$	−14.1323	+	43.4947i	−0.610992	+	1.88044i
$536$	−0.922107	−	2.83795i	−0.0398289	−	0.122581i
$537$	−8.27923	+	6.01521i	−0.357275	+	0.259576i
$538$	6.43087			0.277254
$539$		0			0
$540$	−4.62772			−0.199145
$541$	22.4201	−	16.2892i	0.963917	−	0.700327i	0.00985982	−	0.999951i	$-0.496861\pi$
$541$	22.4201	−	16.2892i	0.963917	−	0.700327i	0.954057	+	0.299625i	$0.0968615\pi$
$542$	2.54435	+	7.83070i	0.109289	+	0.336357i
$543$	5.25329	−	16.1680i	0.225440	−	0.693834i
$544$	−12.6255	−	9.17296i	−0.541314	−	0.393287i
$545$	27.1456	+	19.7224i	1.16279	+	0.844815i
$546$	3.60991	−	11.1102i	0.154490	−	0.475471i
$547$	−5.47741	−	16.8577i	−0.234197	−	0.720785i	−0.997227	−	0.0744212i	$-0.976289\pi$
$547$	−5.47741	−	16.8577i	−0.234197	−	0.720785i	0.763030	−	0.646363i	$-0.223711\pi$
$548$	−11.9286	+	8.66664i	−0.509565	+	0.370220i
$549$	−5.98844			−0.255580
$550$		0			0
$551$	0.744563			0.0317194
$552$	−4.32309	+	3.14091i	−0.184003	+	0.133686i
$553$	3.20521	+	9.86463i	0.136299	+	0.419487i
$554$	2.12029	−	6.52559i	0.0900825	−	0.277246i
$555$	−13.6412	−	9.91089i	−0.579035	−	0.420694i
$556$	−11.5375	−	8.38250i	−0.489300	−	0.355497i
$557$	−9.36076	+	28.8095i	−0.396628	+	1.22070i	0.531058	+	0.847335i	$0.321795\pi$
$557$	−9.36076	+	28.8095i	−0.396628	+	1.22070i	−0.927686	+	0.373360i	$0.878205\pi$
$558$	−0.398515	−	1.22650i	−0.0168705	−	0.0519220i
$559$	−31.3450	+	22.7735i	−1.32575	+	0.963216i
$560$	−5.34363			−0.225810
$561$		0			0
$562$	21.4891			0.906464
$563$	25.7887	−	18.7366i	1.08687	−	0.789654i	0.107998	−	0.994151i	$-0.465556\pi$
$563$	25.7887	−	18.7366i	1.08687	−	0.789654i	0.978867	+	0.204497i	$0.0655559\pi$
$564$	5.40444	+	16.6331i	0.227568	+	0.700382i
$565$	1.43004	−	4.40122i	0.0601624	−	0.185161i
$566$	4.85410	+	3.52671i	0.204033	+	0.148239i
$567$	2.04223	+	1.48377i	0.0857657	+	0.0623124i
$568$	−8.87110	+	27.3024i	−0.372223	+	1.14558i
$569$	11.6840	+	35.9596i	0.489818	+	1.50750i	0.824879	+	0.565309i	$0.191243\pi$
$569$	11.6840	+	35.9596i	0.489818	+	1.50750i	−0.335061	+	0.942196i	$0.608757\pi$
$570$	2.03134	−	1.47586i	0.0850835	−	0.0618168i
$571$	14.5012			0.606857			0.303429	−	0.952854i	$-0.401869\pi$
$571$	14.5012			0.606857			0.303429	+	0.952854i	$0.401869\pi$
$572$		0			0
$573$	5.48913			0.229311
$574$	−17.6198	+	12.8015i	−0.735436	+	0.534326i
$575$	3.93829	+	12.1208i	0.164238	+	0.505472i
$576$	1.04209	−	3.20723i	0.0434205	−	0.133635i
$577$	−5.24981	−	3.81421i	−0.218553	−	0.158788i	0.473122	−	0.880997i	$-0.343127\pi$
$577$	−5.24981	−	3.81421i	−0.218553	−	0.158788i	−0.691675	+	0.722209i	$0.743127\pi$
$578$	−6.32090	−	4.59240i	−0.262915	−	0.191019i
$579$	−3.25697	+	10.0239i	−0.135355	+	0.416580i
$580$	−1.13301	−	3.48703i	−0.0470455	−	0.144791i
$581$	3.83843	−	2.78878i	0.159245	−	0.115698i
$582$	−8.31040			−0.344477
$583$		0			0
$584$	−24.4674			−1.01247
$585$	−15.9355	+	11.5778i	−0.658852	+	0.478684i
$586$	−7.29465	−	22.4506i	−0.301339	−	0.927426i
$587$	−2.15640	+	6.63671i	−0.0890041	+	0.273926i	−0.985645	−	0.168833i	$-0.946000\pi$
$587$	−2.15640	+	6.63671i	−0.0890041	+	0.273926i	0.896641	+	0.442759i	$0.146000\pi$
$588$	−0.696893	−	0.506322i	−0.0287394	−	0.0208804i
$589$	−1.23753	−	0.899118i	−0.0509915	−	0.0370475i
$590$	4.95382	−	15.2463i	0.203945	−	0.627679i
$591$	−0.643345	−	1.98001i	−0.0264637	−	0.0814468i
$592$	−2.53918	+	1.84482i	−0.104359	+	0.0758216i
$593$	−8.71516			−0.357889			−0.178944	−	0.983859i	$-0.557268\pi$
$593$	−8.71516			−0.357889			−0.178944	+	0.983859i	$0.557268\pi$
$594$		0			0
$595$	22.7446			0.932436
$596$	−2.96625	+	2.15510i	−0.121502	+	0.0882765i
$597$	6.75555	+	20.7914i	0.276486	+	0.850937i
$598$	−2.86009	+	8.80244i	−0.116958	+	0.359959i
$599$	23.0306	+	16.7327i	0.941004	+	0.683680i	0.948662	−	0.316291i	$-0.102438\pi$
$599$	23.0306	+	16.7327i	0.941004	+	0.683680i	−0.00765781	+	0.999971i	$0.502438\pi$
$600$	−13.7740	−	10.0074i	−0.562320	−	0.408549i
$601$	6.01264	−	18.5050i	0.245261	−	0.754835i	−0.750333	−	0.661060i	$-0.770107\pi$
$601$	6.01264	−	18.5050i	0.245261	−	0.754835i	0.995593	−	0.0937746i	$-0.0298933\pi$
$602$	4.09957	+	12.6172i	0.167086	+	0.514238i
$603$	0.903546	−	0.656464i	0.0367952	−	0.0267333i
$604$	−30.2921			−1.23257
$605$		0			0
$606$	9.48913			0.385469
$607$	−26.5046	+	19.2567i	−1.07579	+	0.781606i	−0.976944	−	0.213497i	$-0.931515\pi$
$607$	−26.5046	+	19.2567i	−1.07579	+	0.781606i	−0.0988448	+	0.995103i	$0.531515\pi$
$608$	−1.69623	−	5.22047i	−0.0687913	−	0.211718i
$609$	−0.618034	+	1.90211i	−0.0250440	+	0.0770775i
$610$	−12.9443	−	9.40456i	−0.524098	−	0.380780i
$611$	60.2236	+	43.7550i	2.43639	+	1.77014i
$612$	1.13301	−	3.48703i	0.0457990	−	0.140955i
$613$	9.13290	+	28.1082i	0.368874	+	1.13528i	0.947519	+	0.319699i	$0.103582\pi$
$613$	9.13290	+	28.1082i	0.368874	+	1.13528i	−0.578645	+	0.815579i	$0.696418\pi$
$614$	−0.791421	+	0.575001i	−0.0319392	+	0.0232052i
$615$	36.7229			1.48081
$616$		0			0
$617$	15.1386			0.609457			0.304728	−	0.952439i	$-0.401434\pi$
$617$	15.1386			0.609457			0.304728	+	0.952439i	$0.401434\pi$
$618$	−5.84366	+	4.24567i	−0.235066	+	0.170786i
$619$	−7.48862	−	23.0476i	−0.300993	−	0.926362i	−0.981142	−	0.193288i	$-0.938085\pi$
$619$	−7.48862	−	23.0476i	−0.300993	−	0.926362i	0.680149	−	0.733074i	$-0.261915\pi$
$620$	−2.32771	+	7.16395i	−0.0934830	+	0.287711i
$621$	−1.61803	−	1.17557i	−0.0649295	−	0.0471740i
$622$	−18.9018	−	13.7329i	−0.757891	−	0.550640i
$623$	0.489660	−	1.50702i	0.0196178	−	0.0603775i
$624$	1.13301	+	3.48703i	0.0453565	+	0.139593i
$625$	13.1509	−	9.55471i	0.526037	−	0.382188i
$626$	6.43087			0.257029
$627$		0			0
$628$	−16.9783			−0.677506
$629$	10.8077	−	7.85227i	0.430932	−	0.313090i
$630$	2.08418	+	6.41446i	0.0830359	+	0.255558i
$631$	−3.78042	+	11.6349i	−0.150496	+	0.463179i	−0.997677	−	0.0681257i	$-0.978298\pi$
$631$	−3.78042	+	11.6349i	−0.150496	+	0.463179i	0.847181	+	0.531305i	$0.178298\pi$
$632$	8.88159	+	6.45285i	0.353291	+	0.256681i
$633$	8.69059	+	6.31408i	0.345420	+	0.250962i
$634$	−6.54788	+	20.1523i	−0.260049	+	0.800350i
$635$	10.1578	+	31.2625i	0.403100	+	1.24061i
$636$	−4.57052	+	3.32067i	−0.181233	+	0.131673i
$637$	−3.66648			−0.145271
$638$		0			0
$639$	−10.7446			−0.425048
$640$	−24.5817	+	17.8596i	−0.971676	+	0.705964i
$641$	−3.12628	−	9.62169i	−0.123481	−	0.380034i	0.870141	−	0.492803i	$-0.164028\pi$
$641$	−3.12628	−	9.62169i	−0.123481	−	0.380034i	−0.993621	+	0.112770i	$0.964028\pi$
$642$	3.32025	−	10.2187i	0.131040	−	0.403299i
$643$	34.0556	+	24.7429i	1.34302	+	0.975764i	0.999327	+	0.0366830i	$0.0116792\pi$
$643$	34.0556	+	24.7429i	1.34302	+	0.975764i	0.343697	+	0.939081i	$0.388321\pi$
$644$	−5.60503	−	4.07230i	−0.220869	−	0.160471i
$645$	6.91246	−	21.2744i	0.272178	−	0.837677i
$646$	0.614738	+	1.89197i	0.0241865	+	0.0744385i
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	−0.380364	−	0.924837i	$-0.624201\pi$
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	0.762033	+	0.647538i	$0.224201\pi$
$648$	2.67181			0.104959
$649$		0			0
$650$	−29.4891			−1.15666
$651$	3.32418	−	2.41516i	0.130285	−	0.0946575i
$652$	1.53836	+	4.73460i	0.0602470	+	0.185421i
$653$	8.49461	−	26.1437i	0.332420	−	1.02308i	−0.635559	−	0.772052i	$-0.719231\pi$
$653$	8.49461	−	26.1437i	0.332420	−	1.02308i	0.967979	−	0.251031i	$-0.0807695\pi$
$654$	−6.37761	−	4.63360i	−0.249384	−	0.181188i
$655$	18.0970	+	13.1483i	0.707110	+	0.513746i
$656$	2.11233	−	6.50107i	0.0824725	−	0.253824i
$657$	−2.82985	−	8.70938i	−0.110403	−	0.339785i
$658$	20.6211	−	14.9821i	0.803896	−	0.584064i
$659$	15.7359			0.612985			0.306492	−	0.951873i	$-0.400845\pi$
$659$	15.7359			0.612985			0.306492	+	0.951873i	$0.400845\pi$
$660$		0			0
$661$	30.7228			1.19498			0.597489	−	0.801877i	$-0.296165\pi$
$661$	30.7228			1.19498			0.597489	+	0.801877i	$0.296165\pi$
$662$	−4.08446	+	2.96754i	−0.158747	+	0.115337i
$663$	−4.82251	−	14.8422i	−0.187291	−	0.576422i
$664$	1.55181	−	4.77597i	0.0602217	−	0.185343i
$665$	6.47214	+	4.70228i	0.250979	+	0.182347i
$666$	3.20487	+	2.32847i	0.124186	+	0.0902265i
$667$	0.489660	−	1.50702i	0.0189597	−	0.0583520i
$668$	−10.0327	−	30.8775i	−0.388177	−	1.19469i
$669$	−19.3043	+	14.0254i	−0.746347	+	0.542253i
$670$	2.98400			0.115282
$671$		0			0
$672$	14.7446			0.568784
$673$	1.32636	−	0.963660i	0.0511276	−	0.0371464i	−0.561928	−	0.827186i	$-0.689940\pi$
$673$	1.32636	−	0.963660i	0.0511276	−	0.0371464i	0.613056	+	0.790040i	$0.289940\pi$
$674$	−0.496272	−	1.52737i	−0.0191157	−	0.0588320i
$675$	1.96914	−	6.06040i	0.0757924	−	0.233265i
$676$	23.4439	+	17.0330i	0.901688	+	0.655115i
$677$	5.53014	+	4.01788i	0.212541	+	0.154420i	0.688962	−	0.724797i	$-0.258066\pi$
$677$	5.53014	+	4.01788i	0.212541	+	0.154420i	−0.476422	+	0.879217i	$0.658066\pi$
$678$	−0.335976	+	1.03403i	−0.0129031	+	0.0397116i
$679$	−8.18218	−	25.1822i	−0.314003	−	0.966403i
$680$	19.4757	−	14.1500i	0.746861	−	0.542626i
$681$	−7.92287			−0.303605
$682$		0			0
$683$	2.00000			0.0765279			0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000			0.0765279			0.0382639	+	0.999268i	$0.487817\pi$
$684$	1.04332	−	0.758020i	0.0398925	−	0.0289836i
$685$	−11.1968	−	34.4603i	−0.427809	−	1.31666i
$686$	−4.71419	+	14.5088i	−0.179989	+	0.553948i
$687$	7.58233	+	5.50889i	0.289284	+	0.210177i
$688$	−3.36860	−	2.44743i	−0.128427	−	0.0933073i
$689$	−7.43073	+	22.8694i	−0.283088	+	0.871256i
$690$	−1.65127	−	5.08209i	−0.0628629	−	0.193472i
$691$	−10.6117	+	7.70989i	−0.403690	+	0.293298i	−0.771042	−	0.636784i	$-0.780264\pi$
$691$	−10.6117	+	7.70989i	−0.403690	+	0.293298i	0.367352	+	0.930082i	$0.380264\pi$
$692$	9.50744			0.361419
$693$		0			0
$694$	−22.5109			−0.854501
$695$	28.3526	−	20.5994i	1.07548	−	0.781379i
$696$	0.654141	+	2.01324i	0.0247951	+	0.0763116i
$697$	−8.99088	+	27.6711i	−0.340554	+	1.04812i
$698$	−16.6530	−	12.0991i	−0.630325	−	0.457958i
$699$	0.640974	+	0.465695i	0.0242438	+	0.0176142i
$700$	6.82131	−	20.9938i	0.257821	−	0.793493i
$701$	10.2775	+	31.6310i	0.388177	+	1.19469i	0.934149	+	0.356883i	$0.116161\pi$
$701$	10.2775	+	31.6310i	0.388177	+	1.19469i	−0.545972	+	0.837804i	$0.683839\pi$
$702$	3.74390	−	2.72010i	0.141305	−	0.102664i
$703$	4.69882			0.177219
$704$		0			0
$705$	−42.9783			−1.61865
$706$	14.3261	−	10.4085i	0.539170	−	0.391730i
$707$	9.34272	+	28.7539i	0.351369	+	1.08140i
$708$	2.54435	−	7.83070i	0.0956225	−	0.294296i
$709$	−4.85410	−	3.52671i	−0.182300	−	0.132448i	0.492893	−	0.870090i	$-0.335939\pi$
$709$	−4.85410	−	3.52671i	−0.182300	−	0.132448i	−0.675192	+	0.737642i	$0.735939\pi$
$710$	−23.2248	−	16.8738i	−0.871613	−	0.633264i
$711$	−1.26972	+	3.90781i	−0.0476184	+	0.146554i
$712$	−0.518267	−	1.59506i	−0.0194229	−	0.0597775i
$713$	−2.63370	+	1.91350i	−0.0986330	+	0.0716611i
$714$	−5.34363			−0.199980
$715$		0			0
$716$	−14.0435			−0.524830
$717$	18.3357	−	13.3216i	0.684758	−	0.497506i
$718$	−4.55632	−	14.0229i	−0.170040	−	0.523330i
$719$	−1.85410	+	5.70634i	−0.0691463	+	0.212811i	−0.979659	−	0.200672i	$-0.935688\pi$
$719$	−1.85410	+	5.70634i	−0.0691463	+	0.212811i	0.910512	+	0.413482i	$0.135688\pi$
$720$	−1.71256	−	1.24425i	−0.0638234	−	0.0463704i
$721$	−18.6187	−	13.5273i	−0.693397	−	0.503782i
$722$	4.43555	−	13.6512i	0.165074	−	0.508046i
$723$	4.09957	+	12.6172i	0.152465	+	0.469238i
$724$	18.8734	−	13.7123i	0.701424	−	0.509614i
$725$	5.04868			0.187503
$726$		0			0
$727$	18.7446			0.695197			0.347599	−	0.937643i	$-0.386997\pi$
$727$	18.7446			0.695197			0.347599	+	0.937643i	$0.386997\pi$
$728$	31.8710	−	23.1556i	1.18122	−	0.858205i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	7.56083	−	23.2699i	0.279839	−	0.861256i
$731$	14.3381	+	10.4172i	0.530312	+	0.385294i
$732$	−6.64836	−	4.83032i	−0.245730	−	0.178534i
$733$	2.29462	−	7.06210i	0.0847536	−	0.260845i	−0.899695	−	0.436520i	$-0.856211\pi$
$733$	2.29462	−	7.06210i	0.0847536	−	0.260845i	0.984448	+	0.175675i	$0.0562108\pi$
$734$	−8.25636	−	25.4105i	−0.304748	−	0.937917i
$735$	1.71256	−	1.24425i	0.0631688	−	0.0458948i
$736$	−11.6819			−0.430601
$737$		0			0
$738$	−8.62772			−0.317591
$739$	28.7855	−	20.9139i	1.05889	−	0.769329i	0.0850074	−	0.996380i	$-0.472909\pi$
$739$	28.7855	−	20.9139i	1.05889	−	0.769329i	0.973883	+	0.227052i	$0.0729086\pi$
$740$	−7.15022	−	22.0061i	−0.262847	−	0.808961i
$741$	1.69623	−	5.22047i	0.0623127	−	0.191779i
$742$	6.66119	+	4.83964i	0.244540	+	0.177669i
$743$	−28.3526	−	20.5994i	−1.04016	−	0.755718i	−0.0698409	−	0.997558i	$-0.522249\pi$
$743$	−28.3526	−	20.5994i	−1.04016	−	0.755718i	−0.970316	+	0.241840i	$0.922249\pi$
$744$	1.34390	−	4.13611i	0.0492699	−	0.151637i
$745$	−2.78428	−	8.56912i	−0.102008	−	0.313948i
$746$	3.46032	−	2.51407i	0.126691	−	0.0920465i
$747$	1.87953			0.0687683
$748$		0			0
$749$	34.2337			1.25087
$750$	2.96625	−	2.15510i	0.108312	−	0.0786933i
$751$	10.9239	+	33.6204i	0.398619	+	1.22682i	0.926107	+	0.377261i	$0.123134\pi$
$751$	10.9239	+	33.6204i	0.398619	+	1.22682i	−0.527488	+	0.849563i	$0.676866\pi$
$752$	−2.47214	+	7.60845i	−0.0901495	+	0.277452i
$753$	19.0031	+	13.8066i	0.692512	+	0.503139i
$754$	2.96625	+	2.15510i	0.108024	+	0.0784842i
$755$	23.0034	−	70.7971i	0.837179	−	2.57657i
$756$	1.07047	+	3.29456i	0.0389325	+	0.119822i
$757$	−26.2843	+	19.0966i	−0.955317	+	0.694079i	−0.952059	−	0.305916i	$-0.901037\pi$
$757$	−26.2843	+	19.0966i	−0.955317	+	0.694079i	−0.00325894	+	0.999995i	$0.501037\pi$
$758$	26.7181			0.970447
$759$		0			0
$760$	8.46738			0.307144
$761$	−30.1867	+	21.9319i	−1.09427	+	0.795032i	−0.980115	−	0.198431i	$-0.936415\pi$
$761$	−30.1867	+	21.9319i	−1.09427	+	0.795032i	−0.114153	+	0.993463i	$0.536415\pi$
$762$	−2.38648	−	7.34483i	−0.0864531	−	0.266075i
$763$	7.76153	−	23.8875i	0.280986	−	0.864787i
$764$	6.09402	+	4.42757i	0.220474	+	0.160184i
$765$	7.28933	+	5.29601i	0.263546	+	0.191478i
$766$	0.125078	−	0.384949i	0.00451923	−	0.0139088i
$767$	−10.8297	−	33.3305i	−0.391039	−	1.20350i
$768$	11.2317	−	8.16031i	0.405289	−	0.294460i
$769$	41.4217			1.49371			0.746853	−	0.664989i	$-0.231564\pi$
$769$	41.4217			1.49371			0.746853	+	0.664989i	$0.231564\pi$
$770$		0			0
$771$	18.6277			0.670861
$772$	−11.7013	+	8.50146i	−0.421137	+	0.305974i
$773$	−14.5893	−	44.9012i	−0.524740	−	1.61498i	−0.764829	−	0.644234i	$-0.777176\pi$
$773$	−14.5893	−	44.9012i	−0.524740	−	1.61498i	0.240088	−	0.970751i	$-0.422824\pi$
$774$	−1.62402	+	4.99822i	−0.0583742	+	0.179657i
$775$	−8.39135	−	6.09667i	−0.301426	−	0.218999i
$776$	−22.6727	−	16.4727i	−0.813902	−	0.591335i
$777$	−3.90032	+	12.0039i	−0.139923	+	0.430639i
$778$	−1.98725	−	6.11612i	−0.0712463	−	0.219274i
$779$	−8.27923	+	6.01521i	−0.296634	+	0.215517i
$780$	−27.0303			−0.967841
$781$		0			0
$782$	4.23369			0.151396
$783$	−0.640974	+	0.465695i	−0.0229065	+	0.0166426i
$784$	−0.121762	−	0.374746i	−0.00434865	−	0.0133838i
$785$	12.8931	−	39.6808i	0.460173	−	1.41627i
$786$	−4.25174	−	3.08907i	−0.151654	−	0.110183i
$787$	−12.2534	−	8.90261i	−0.436786	−	0.317344i	0.347570	−	0.937654i	$-0.387007\pi$
$787$	−12.2534	−	8.90261i	−0.436786	−	0.317344i	−0.784357	+	0.620310i	$0.787007\pi$
$788$	0.882850	−	2.71713i	0.0314502	−	0.0967938i
$789$	−4.86267	−	14.9658i	−0.173116	−	0.532795i
$790$	−8.88159	+	6.45285i	−0.315993	+	0.229582i
$791$	−3.46410			−0.123169
$792$		0			0
$793$	−34.9783			−1.24211
$794$	0.968431	−	0.703606i	0.0343683	−	0.0249700i
$795$	−4.29013	−	13.2037i	−0.152155	−	0.468286i
$796$	−9.27051	+	28.5317i	−0.328585	+	1.01128i
$797$	−4.85410	−	3.52671i	−0.171941	−	0.124923i	0.498487	−	0.866897i	$-0.333889\pi$
$797$	−4.85410	−	3.52671i	−0.171941	−	0.124923i	−0.670428	+	0.741975i	$0.733889\pi$
$798$	−1.52057	−	1.10476i	−0.0538276	−	0.0391080i
$799$	10.5224	−	32.3845i	0.372255	−	1.14568i
$800$	−11.5017	−	35.3986i	−0.406646	−	1.25153i
$801$	0.507835	−	0.368964i	0.0179435	−	0.0130367i
$802$	1.49200			0.0526844
$803$		0			0
$804$	1.53262			0.0540515
$805$	13.7740	−	10.0074i	0.485468	−	0.352713i
$806$	−2.32771	−	7.16395i	−0.0819900	−	0.252339i
$807$	−2.50824	+	7.71958i	−0.0882943	+	0.271742i
$808$	25.8885	+	18.8091i	0.910756	+	0.661703i
$809$	−20.9884	−	15.2490i	−0.737913	−	0.536125i	0.154144	−	0.988048i	$-0.450738\pi$
$809$	−20.9884	−	15.2490i	−0.737913	−	0.536125i	−0.892057	+	0.451923i	$0.850738\pi$
$810$	−0.825636	+	2.54105i	−0.0290099	+	0.0892833i
$811$	−12.0083	−	36.9578i	−0.421669	−	1.29776i	−0.906148	−	0.422961i	$-0.860991\pi$
$811$	−12.0083	−	36.9578i	−0.421669	−	1.29776i	0.484479	−	0.874803i	$-0.339009\pi$
$812$	−2.22040	+	1.61321i	−0.0779207	+	0.0566127i
$813$	−10.3923			−0.364474
$814$		0			0
$815$	−12.2337			−0.428527
$816$	1.35684	−	0.985803i	0.0474989	−	0.0345100i
$817$	1.92632	+	5.92859i	0.0673932	+	0.207415i
$818$	−4.98038	+	15.3280i	−0.174135	+	0.535932i
$819$	11.9286	+	8.66664i	0.416819	+	0.302837i
$820$	40.7697	+	29.6210i	1.42374	+	1.03441i
$821$	−14.2234	+	43.7752i	−0.496401	+	1.52777i	0.318361	+	0.947970i	$0.396868\pi$
$821$	−14.2234	+	43.7752i	−0.496401	+	1.52777i	−0.814762	+	0.579796i	$0.803132\pi$
$822$	2.63059	+	8.09613i	0.0917525	+	0.282385i
$823$	−15.6549	+	11.3740i	−0.545696	+	0.396471i	−0.826196	−	0.563383i	$-0.809500\pi$
$823$	−15.6549	+	11.3740i	−0.545696	+	0.396471i	0.280500	+	0.959854i	$0.409500\pi$
$824$	−24.3585			−0.848569
$825$		0			0
$826$	−12.0000			−0.417533
$827$	−29.8732	+	21.7041i	−1.03879	+	0.754727i	−0.970050	−	0.242907i	$-0.921899\pi$
$827$	−29.8732	+	21.7041i	−1.03879	+	0.754727i	−0.0687433	+	0.997634i	$0.521899\pi$
$828$	−0.848116	−	2.61023i	−0.0294741	−	0.0907119i
$829$	−10.4276	+	32.0930i	−0.362167	+	1.11464i	0.589569	+	0.807718i	$0.299298\pi$
$829$	−10.4276	+	32.0930i	−0.362167	+	1.11464i	−0.951736	+	0.306918i	$0.900702\pi$
$830$	4.06268	+	2.95171i	0.141018	+	0.102455i
$831$	7.00629	+	5.09037i	0.243046	+	0.176583i
$832$	6.08682	−	18.7333i	0.211023	−	0.649461i
$833$	0.518267	+	1.59506i	0.0179569	+	0.0552656i
$834$	−6.66119	+	4.83964i	−0.230658	+	0.167583i
$835$	79.7841			2.76104
$836$		0			0
$837$	1.62772			0.0562622
$838$	−20.1837	+	14.6643i	−0.697234	+	0.506570i
$839$	−5.86460	−	18.0494i	−0.202469	−	0.623134i	−0.999808	−	0.0196028i	$-0.993760\pi$
$839$	−5.86460	−	18.0494i	−0.202469	−	0.623134i	0.797339	−	0.603531i	$-0.206240\pi$
$840$	−7.02846	+	21.6314i	−0.242505	+	0.746353i
$841$	22.9537	+	16.6768i	0.791505	+	0.575062i
$842$	22.3452	+	16.2348i	0.770068	+	0.559487i
$843$	−8.38144	+	25.7954i	−0.288672	+	0.888441i
$844$	4.55530	+	14.0198i	0.156800	+	0.482581i
$845$	−57.6117	+	41.8573i	−1.98190	+	1.43994i
$846$	10.0974			0.347154
$847$		0			0
$848$	−2.58422			−0.0887425
$849$	−6.12670	+	4.45131i	−0.210268	+	0.152768i
$850$	4.16837	+	12.8289i	0.142974	+	0.440028i
$851$	3.09017	−	9.51057i	0.105930	−	0.326018i
$852$	−11.9286	−	8.66664i	−0.408667	−	0.296914i
$853$	17.2619	+	12.5415i	0.591035	+	0.429412i	0.842686	−	0.538406i	$-0.180973\pi$
$853$	17.2619	+	12.5415i	0.591035	+	0.429412i	−0.251650	+	0.967818i	$0.580973\pi$
$854$	−3.70106	+	11.3907i	−0.126648	+	0.389781i
$855$	0.979321	+	3.01404i	0.0334921	+	0.103078i
$856$	29.3137	−	21.2976i	1.00192	−	0.727938i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	5.11684			0.174584			0.0872922	−	0.996183i	$-0.472179\pi$
$859$	5.11684			0.174584			0.0872922	+	0.996183i	$0.472179\pi$
$860$	24.8342	−	18.0431i	0.846841	−	0.615266i
$861$	−8.49461	−	26.1437i	−0.289495	−	0.890975i
$862$	0.703689	−	2.16573i	0.0239678	−	0.0737652i
$863$	−31.9474	−	23.2111i	−1.08750	−	0.790116i	−0.108526	−	0.994094i	$-0.534613\pi$
$863$	−31.9474	−	23.2111i	−1.08750	−	0.790116i	−0.978976	+	0.203978i	$0.934613\pi$
$864$	4.72544	+	3.43323i	0.160763	+	0.116801i
$865$	−7.21983	+	22.2203i	−0.245481	+	0.755514i
$866$	−2.75035	−	8.46469i	−0.0934605	−	0.287642i
$867$	7.97805	−	5.79639i	0.270949	−	0.196856i
$868$	5.63858			0.191386
$869$		0			0
$870$	−2.11684			−0.0717677
$871$	5.27758	−	3.83438i	0.178824	−	0.129923i
$872$	−8.21498	−	25.2831i	−0.278194	−	0.856194i
$873$	3.24132	−	9.97575i	0.109702	−	0.337628i
$874$	1.20473	+	0.875286i	0.0407505	+	0.0296070i
$875$	9.45088	+	6.86646i	0.319498	+	0.232129i
$876$	3.88335	−	11.9517i	0.131206	−	0.403811i
$877$	−0.352942	−	1.08624i	−0.0119180	−	0.0366798i	0.944921	−	0.327299i	$-0.106139\pi$
$877$	−0.352942	−	1.08624i	−0.0119180	−	0.0366798i	−0.956839	+	0.290620i	$0.906139\pi$
$878$	−3.46032	+	2.51407i	−0.116780	+	0.0848457i
$879$	29.7947			1.00495
$880$		0			0
$881$	−45.6060			−1.53650			−0.768252	−	0.640147i	$-0.778873\pi$
$881$	−45.6060			−1.53650			−0.768252	+	0.640147i	$0.778873\pi$
$882$	−0.402351	+	0.292325i	−0.0135479	+	0.00984310i
$883$	7.37358	+	22.6935i	0.248141	+	0.763699i	0.995104	+	0.0988333i	$0.0315111\pi$
$883$	7.37358	+	22.6935i	0.248141	+	0.763699i	−0.746963	+	0.664865i	$0.768489\pi$
$884$	6.61784	−	20.3676i	0.222582	−	0.685037i
$885$	16.3694	+	11.8931i	0.550251	+	0.399781i
$886$	5.93249	+	4.31021i	0.199306	+	0.144804i
$887$	−15.5101	+	47.7352i	−0.520779	+	1.60279i	0.251736	+	0.967796i	$0.418999\pi$
$887$	−15.5101	+	47.7352i	−0.520779	+	1.60279i	−0.772515	+	0.634997i	$0.781001\pi$
$888$	4.12818	+	12.7052i	0.138533	+	0.426360i
$889$	19.9066	−	14.4630i	0.667648	−	0.485074i
$890$	1.67715			0.0562181
$891$		0			0
$892$	−32.7446			−1.09637
$893$	9.68950	−	7.03983i	0.324247	−	0.235579i
$894$	0.654141	+	2.01324i	0.0218777	+	0.0673328i
$895$	10.6644	−	32.8218i	0.356473	−	1.09711i
$896$	18.4007	+	13.3689i	0.614726	+	0.446624i
$897$	−9.45088	−	6.86646i	−0.315556	−	0.229265i
$898$	3.82081	−	11.7592i	0.127502	−	0.392411i
$899$	0.398515	+	1.22650i	0.0132912	+	0.0409061i
$900$	7.07450	−	5.13992i	0.235817	−	0.171331i
$901$	10.9994			0.366445
$902$		0			0
$903$	−16.7446			−0.557224
$904$	−2.96625	+	2.15510i	−0.0986559	+	0.0716777i
$905$	17.7156	+	54.5229i	0.588885	+	1.81240i
$906$	−5.40444	+	16.6331i	−0.179550	+	0.552599i
$907$	−12.4188	−	9.02282i	−0.412361	−	0.299598i	0.362196	−	0.932102i	$-0.382027\pi$
$907$	−12.4188	−	9.02282i	−0.412361	−	0.299598i	−0.774557	+	0.632504i	$0.782027\pi$
$908$	−8.79596	−	6.39064i	−0.291904	−	0.212081i
$909$	−3.70106	+	11.3907i	−0.122756	+	0.377805i
$910$	12.1736	+	37.4666i	0.403552	+	1.24201i
$911$	−3.04701	+	2.21378i	−0.100952	+	0.0733459i	−0.637116	−	0.770768i	$-0.719873\pi$
$911$	−3.04701	+	2.21378i	−0.100952	+	0.0733459i	0.536164	+	0.844114i	$0.319873\pi$
$912$	0.589907			0.0195338
$913$		0			0
$914$	30.3505			1.00391
$915$	16.3379	−	11.8701i	0.540113	−	0.392415i
$916$	3.97439	+	12.2319i	0.131318	+	0.404154i
$917$	5.17435	−	15.9250i	0.170872	−	0.525891i
$918$	−1.71256	−	1.24425i	−0.0565230	−	0.0410664i
$919$	12.2090	+	8.87034i	0.402737	+	0.292606i	0.770655	−	0.637253i	$-0.219929\pi$
$919$	12.2090	+	8.87034i	0.402737	+	0.292606i	−0.367918	+	0.929858i	$0.619929\pi$
$920$	5.56855	−	17.1382i	0.183590	−	0.565031i
$921$	−0.381549	−	1.17429i	−0.0125725	−	0.0386940i
$922$	2.91729	−	2.11954i	0.0960758	−	0.0698032i
$923$	−62.7586			−2.06572
$924$		0			0
$925$	31.8614			1.04760
$926$	−9.45088	+	6.86646i	−0.310575	+	0.225646i
$927$	−2.81726	−	8.67063i	−0.0925309	−	0.284781i
$928$	−1.43004	+	4.40122i	−0.0469435	+	0.144477i
$929$	42.1634	+	30.6335i	1.38334	+	1.00505i	0.996560	+	0.0828797i	$0.0264117\pi$
$929$	42.1634	+	30.6335i	1.38334	+	1.00505i	0.386777	+	0.922173i	$0.373588\pi$
$930$	3.51838	+	2.55626i	0.115372	+	0.0838229i
$931$	−0.182291	+	0.561035i	−0.00597436	+	0.0183872i
$932$	0.335976	+	1.03403i	0.0110053	+	0.0338707i
$933$	23.8572	−	17.3333i	0.781050	−	0.567466i
$934$	−9.69259			−0.317151
$935$		0			0
$936$	15.6060			0.510097
$937$	15.7413	−	11.4367i	0.514246	−	0.373622i	−0.300186	−	0.953881i	$-0.597049\pi$
$937$	15.7413	−	11.4367i	0.514246	−	0.373622i	0.814432	+	0.580259i	$0.197049\pi$
$938$	−0.690248	−	2.12436i	−0.0225374	−	0.0693629i
$939$	−2.50824	+	7.71958i	−0.0818534	+	0.251919i
$940$	−47.7144	−	34.6665i	−1.55627	−	1.13070i
$941$	−10.5691	−	7.67890i	−0.344543	−	0.250325i	0.402033	−	0.915625i	$-0.368304\pi$
$941$	−10.5691	−	7.67890i	−0.344543	−	0.250325i	−0.746576	+	0.665300i	$0.768304\pi$
$942$	−3.02911	+	9.32263i	−0.0986937	+	0.303748i
$943$	6.73017	+	20.7133i	0.219164	+	0.674519i
$944$	3.04701	−	2.21378i	0.0991717	−	0.0720525i
$945$	−8.51278			−0.276921
$946$		0			0
$947$	−8.51087			−0.276566			−0.138283	−	0.990393i	$-0.544158\pi$
$947$	−8.51087			−0.276566			−0.138283	+	0.990393i	$0.544158\pi$
$948$	−4.56171	+	3.31428i	−0.148157	+	0.107643i
$949$	−16.5290	−	50.8712i	−0.536556	−	1.65135i
$950$	−1.46615	+	4.51235i	−0.0475682	+	0.146400i
$951$	−21.6368	−	15.7201i	−0.701621	−	0.509758i
$952$	−14.5787	−	10.5920i	−0.472497	−	0.343289i
$953$	−9.48051	+	29.1780i	−0.307104	+	0.945169i	0.671780	+	0.740751i	$0.265530\pi$
$953$	−9.48051	+	29.1780i	−0.307104	+	0.945169i	−0.978884	+	0.204418i	$0.934470\pi$
$954$	1.00793	+	3.10208i	0.0326329	+	0.100434i
$955$	−14.9756	+	10.8804i	−0.484599	+	0.352082i
$956$	31.1016			1.00590
$957$		0			0
$958$	−8.70106			−0.281119
$959$	−21.9429	+	15.9424i	−0.708573	+	0.514808i
$960$	3.51423	+	10.8157i	0.113421	+	0.349075i
$961$	−8.76080	+	26.9630i	−0.282606	+	0.869773i
$962$	18.7195	+	13.6005i	0.603541	+	0.438498i
$963$	10.9714	+	7.97122i	0.353550	+	0.256869i
$964$	−5.62577	+	17.3143i	−0.181194	+	0.557657i
$965$	−10.9834	−	33.8035i	−0.353569	−	1.08817i
$966$	−3.23607	+	2.35114i	−0.104119	+	0.0756467i
$967$	−25.2983			−0.813538			−0.406769	−	0.913531i	$-0.633345\pi$
$967$	−25.2983			−0.813538			−0.406769	+	0.913531i	$0.633345\pi$
$968$		0			0
$969$	−2.51087			−0.0806609
$970$	22.6727	−	16.4727i	0.727977	−	0.528906i
$971$	11.2825	+	34.7239i	0.362072	+	1.11434i	0.951794	+	0.306737i	$0.0992372\pi$
$971$	11.2825	+	34.7239i	0.362072	+	1.11434i	−0.589722	+	0.807606i	$0.700763\pi$
$972$	−0.424058	+	1.30512i	−0.0136017	+	0.0418617i
$973$	−21.2235	−	15.4198i	−0.680394	−	0.494335i
$974$	−0.804702	−	0.584650i	−0.0257843	−	0.0187334i
$975$	11.5017	−	35.3986i	0.368349	−	1.13366i
$976$	−1.16161	−	3.57507i	−0.0371823	−	0.114435i
$977$	3.33060	−	2.41982i	0.106555	−	0.0774169i	−0.533232	−	0.845969i	$-0.679023\pi$
$977$	3.33060	−	2.41982i	0.106555	−	0.0774169i	0.639787	+	0.768552i	$0.279023\pi$
$978$	2.87419			0.0919066
$979$		0			0
$980$	2.90491			0.0927938
$981$	8.04962	−	5.84839i	0.257005	−	0.186725i
$982$	0.315738	+	0.971741i	0.0100756	+	0.0310095i
$983$	−6.72616	+	20.7010i	−0.214531	+	0.660259i	0.784655	+	0.619932i	$0.212840\pi$
$983$	−6.72616	+	20.7010i	−0.214531	+	0.660259i	−0.999187	+	0.0403269i	$0.987160\pi$
$984$	−23.5384	−	17.1017i	−0.750378	−	0.545181i
$985$	5.67993	+	4.12671i	0.180978	+	0.131488i
$986$	0.518267	−	1.59506i	0.0165050	−	0.0507971i
$987$	9.94157	+	30.5970i	0.316444	+	0.973913i
$988$	6.09402	−	4.42757i	0.193877	−	0.140860i
$989$	13.2665			0.421850
$990$		0			0
$991$	57.4891			1.82620			0.913101	−	0.407733i	$-0.133681\pi$
$991$	57.4891			1.82620			0.913101	+	0.407733i	$0.133681\pi$
$992$	7.69168	−	5.58834i	0.244211	−	0.177430i
$993$	−1.96914	−	6.06040i	−0.0624889	−	0.192321i
$994$	−6.64050	+	20.4374i	−0.210624	+	0.648234i
$995$	−59.6430	−	43.3332i	−1.89081	−	1.37375i
$996$	2.08665	+	1.51604i	0.0661180	+	0.0480376i
$997$	−9.62256	+	29.6152i	−0.304749	+	0.937922i	0.675021	+	0.737798i	$0.264134\pi$
$997$	−9.62256	+	29.6152i	−0.304749	+	0.937922i	−0.979771	+	0.200124i	$0.935866\pi$
$998$	−9.01946	−	27.7590i	−0.285506	−	0.878697i
$999$	−4.04508	+	2.93893i	−0.127981	+	0.0929835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.n.124.3		16
11.2	odd	10		363.2.a.j.1.3	yes	4
11.3	even	5	inner	363.2.e.n.148.2		16
11.4	even	5	inner	363.2.e.n.202.3		16
11.5	even	5	inner	363.2.e.n.130.2		16
11.6	odd	10	inner	363.2.e.n.130.3		16
11.7	odd	10	inner	363.2.e.n.202.2		16
11.8	odd	10	inner	363.2.e.n.148.3		16
11.9	even	5		363.2.a.j.1.2	✓	4
11.10	odd	2	inner	363.2.e.n.124.2		16
33.2	even	10		1089.2.a.u.1.2		4
33.20	odd	10		1089.2.a.u.1.3		4
44.31	odd	10		5808.2.a.ck.1.4		4
44.35	even	10		5808.2.a.ck.1.3		4
55.9	even	10		9075.2.a.cv.1.3		4
55.24	odd	10		9075.2.a.cv.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.a.j.1.2	✓	4	11.9	even	5
363.2.a.j.1.3	yes	4	11.2	odd	10
363.2.e.n.124.2		16	11.10	odd	2	inner
363.2.e.n.124.3		16	1.1	even	1	trivial
363.2.e.n.130.2		16	11.5	even	5	inner
363.2.e.n.130.3		16	11.6	odd	10	inner
363.2.e.n.148.2		16	11.3	even	5	inner
363.2.e.n.148.3		16	11.8	odd	10	inner
363.2.e.n.202.2		16	11.7	odd	10	inner
363.2.e.n.202.3		16	11.4	even	5	inner
1089.2.a.u.1.2		4	33.2	even	10
1089.2.a.u.1.3		4	33.20	odd	10
5808.2.a.ck.1.3		4	44.35	even	10
5808.2.a.ck.1.4		4	44.31	odd	10
9075.2.a.cv.1.2		4	55.24	odd	10
9075.2.a.cv.1.3		4	55.9	even	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.640974 - 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(0.640974 + 0.465695i) q^{6} +(-0.780063 + 2.40079i) q^{7} +(0.825636 + 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.640974 - 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(0.640974 + 0.465695i) q^{6} +(-0.780063 + 2.40079i) q^{7} +(0.825636 + 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.67181 q^{10} -1.37228 q^{12} +(-4.72544 + 3.43323i) q^{13} +(0.618034 + 1.90211i) q^{14} +(1.04209 - 3.20723i) q^{15} +(-0.507835 - 0.368964i) q^{16} +(2.16154 + 1.57045i) q^{17} +(-0.244830 + 0.753510i) q^{18} +(0.290403 + 0.893769i) q^{19} +(3.74390 - 2.72010i) q^{20} -2.52434 q^{21} +2.00000 q^{23} +(-2.16154 + 1.57045i) q^{24} +(1.96914 + 6.06040i) q^{25} +(-1.43004 + 4.40122i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.80252 - 2.03615i) q^{28} +(0.244830 - 0.753510i) q^{29} +(-0.825636 - 2.54105i) q^{30} +(-1.31685 + 0.956749i) q^{31} -5.84096 q^{32} +2.11684 q^{34} +(6.88698 - 5.00368i) q^{35} +(-0.424058 - 1.30512i) q^{36} +(1.54508 - 4.75528i) q^{37} +(0.602364 + 0.437643i) q^{38} +(-4.72544 - 3.43323i) q^{39} +(2.78428 - 8.56912i) q^{40} +(3.36508 + 10.3567i) q^{41} +(-1.61803 + 1.17557i) q^{42} +6.63325 q^{43} +3.37228 q^{45} +(1.28195 - 0.931389i) q^{46} +(-3.93829 - 12.1208i) q^{47} +(0.193976 - 0.596996i) q^{48} +(0.507835 + 0.368964i) q^{49} +(4.08446 + 2.96754i) q^{50} +(-0.825636 + 2.54105i) q^{51} +(-2.47691 - 7.62314i) q^{52} +(3.33060 - 2.41982i) q^{53} -0.792287 q^{54} -6.74456 q^{56} +(-0.760285 + 0.552379i) q^{57} +(-0.193976 - 0.596996i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(3.74390 + 2.72010i) q^{60} +(4.84475 + 3.51992i) q^{61} +(-0.398515 + 1.22650i) q^{62} +(-0.780063 - 2.40079i) q^{63} +(-2.72823 + 1.98218i) q^{64} +19.6974 q^{65} -1.11684 q^{67} +(-2.96625 + 2.15510i) q^{68} +(0.618034 + 1.90211i) q^{69} +(2.08418 - 6.41446i) q^{70} +(8.69253 + 6.31550i) q^{71} +(-2.16154 - 1.57045i) q^{72} +(-2.82985 + 8.70938i) q^{73} +(-1.22415 - 3.76755i) q^{74} +(-5.15528 + 3.74553i) q^{75} -1.28962 q^{76} -4.62772 q^{78} +(3.32418 - 2.41516i) q^{79} +(0.654141 + 2.01324i) q^{80} +(0.309017 - 0.951057i) q^{81} +(6.97997 + 5.07125i) q^{82} +(-1.52057 - 1.10476i) q^{83} +(1.07047 - 3.29456i) q^{84} +(-2.78428 - 8.56912i) q^{85} +(4.25174 - 3.08907i) q^{86} +0.792287 q^{87} -0.627719 q^{89} +(2.16154 - 1.57045i) q^{90} +(-4.55632 - 14.0229i) q^{91} +(-0.848116 + 2.61023i) q^{92} +(-1.31685 - 0.956749i) q^{93} +(-8.16893 - 5.93507i) q^{94} +(0.979321 - 3.01404i) q^{95} +(-1.80496 - 5.55509i) q^{96} +(-8.48588 + 6.16535i) q^{97} +0.497333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9	\( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9} + 24 q^{12} - 8 q^{14} - 2 q^{15} - 14 q^{16} + 30 q^{20} + 32 q^{23} - 14 q^{25} + 30 q^{26} - 4 q^{27} - 18 q^{31} - 104 q^{34} - 6 q^{36} - 20 q^{37} - 20 q^{38} - 8 q^{42} + 8 q^{45} + 28 q^{47} - 14 q^{48} + 14 q^{49} - 18 q^{53} - 16 q^{56} + 14 q^{58} + 24 q^{59} + 30 q^{60} - 2 q^{64} + 120 q^{67} - 8 q^{69} - 4 q^{70} + 20 q^{71} - 14 q^{75} - 120 q^{78} + 26 q^{80} - 4 q^{81} + 46 q^{82} + 44 q^{86} - 56 q^{89} + 36 q^{91} - 12 q^{92} - 18 q^{93} + 4 q^{97}+O(q^{100}) \) 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9 + 24 * q^12 - 8 * q^14 - 2 * q^15 - 14 * q^16 + 30 * q^20 + 32 * q^23 - 14 * q^25 + 30 * q^26 - 4 * q^27 - 18 * q^31 - 104 * q^34 - 6 * q^36 - 20 * q^37 - 20 * q^38 - 8 * q^42 + 8 * q^45 + 28 * q^47 - 14 * q^48 + 14 * q^49 - 18 * q^53 - 16 * q^56 + 14 * q^58 + 24 * q^59 + 30 * q^60 - 2 * q^64 + 120 * q^67 - 8 * q^69 - 4 * q^70 + 20 * q^71 - 14 * q^75 - 120 * q^78 + 26 * q^80 - 4 * q^81 + 46 * q^82 + 44 * q^86 - 56 * q^89 + 36 * q^91 - 12 * q^92 - 18 * q^93 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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