LMFDB - Embedded newform 363.2.e.n.124.2

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			124.2
Root			$-0.640974 - 0.465695i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.n.202.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.640974 + 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(-0.640974 - 0.465695i) q^{6} +(0.780063 - 2.40079i) q^{7} +(-0.825636 - 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(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	−0.790872	−	0.611981i	$-0.790373\pi$
$2$	−0.640974	+	0.465695i	−0.453237	+	0.329296i	0.337636	+	0.941277i	$0.390373\pi$
$3$	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	$-0.741704\pi$
$7$	0.780063	−	2.40079i	0.294836	−	0.907413i	0.983276	−	0.182119i	$-0.0582958\pi$
$8$	−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	$-0.399469\pi$
$13$	4.72544	−	3.43323i	1.31060	−	0.952207i	0.999999	−	0.00166711i	$-0.000530658\pi$
$14$	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	0.293952	−	0.955820i	$-0.405030\pi$
$17$	−2.16154	−	1.57045i	−0.524251	−	0.380891i	−0.818203	+	0.574929i	$0.805030\pi$
$18$	0.244830	−	0.753510i	0.0577070	−	0.177604i
$19$	−0.290403	−	0.893769i	−0.0666230	−	0.205045i	0.912203	−	0.409739i	$-0.134380\pi$
$19$	−0.290403	−	0.893769i	−0.0666230	−	0.205045i	−0.978826	+	0.204694i	$0.934380\pi$
$20$	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	−0.971212	−	0.238218i	$-0.923437\pi$
$29$	−0.244830	+	0.753510i	−0.0454638	+	0.139923i	0.925748	+	0.378141i	$0.123437\pi$
$30$	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	$-0.776398\pi$
$41$	−3.36508	−	10.3567i	−0.525538	−	1.61744i	0.237712	−	0.971336i	$-0.423602\pi$
$42$	−1.61803	+	1.17557i	−0.249668	+	0.181394i
$43$	−6.63325			−1.01156			−0.505781	−	0.862662i	$-0.668795\pi$
$43$	−6.63325			−1.01156			−0.505781	+	0.862662i	$0.668795\pi$
$44$		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	0.232722	−	0.972543i	$-0.425237\pi$
$61$	−4.84475	−	3.51992i	−0.620307	−	0.450679i	−0.853029	+	0.521864i	$0.825237\pi$
$62$	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	$-0.719970\pi$
$73$	2.82985	−	8.70938i	0.331209	−	1.01936i	0.968559	−	0.248782i	$-0.0800303\pi$
$74$	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	−0.758867	−	0.651245i	$-0.774247\pi$
$79$	−3.32418	+	2.41516i	−0.373999	+	0.271726i	0.384868	+	0.922972i	$0.374247\pi$
$80$	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	0.668102	−	0.744070i	$-0.267107\pi$
$83$	1.52057	+	1.10476i	0.166904	+	0.121263i	−0.501198	+	0.865333i	$0.667107\pi$
$84$	−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	−0.954109	−	0.299460i	$-0.903193\pi$
$101$	−9.68950	+	7.03983i	−0.964141	+	0.700490i	−0.0100323	+	0.999950i	$0.503193\pi$
$102$	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	$0.127549\pi$
$107$	4.19072	+	12.8977i	0.405132	+	1.24687i	−0.515653	+	0.856798i	$0.672451\pi$
$108$	1.11020	−	0.806607i	0.106829	−	0.0776158i
$109$	9.94987			0.953025			0.476513	−	0.879168i	$-0.341901\pi$
$109$	9.94987			0.953025			0.476513	+	0.879168i	$0.341901\pi$
$110$		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	0.879854	−	0.475244i	$-0.157640\pi$
$127$	7.88589	+	5.72943i	0.699759	+	0.508405i	−0.180094	+	0.983649i	$0.557640\pi$
$128$	−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	$-0.406420\pi$
$131$	6.63325			0.579550			0.289775	+	0.957095i	$0.406420\pi$
$132$		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	$-0.754719\pi$
$139$	3.21140	−	9.88367i	0.272387	−	0.838322i	0.989899	−	0.141775i	$-0.0452810\pi$
$140$	−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	0.495714	−	0.868486i	$-0.334906\pi$
$149$	−2.16154	−	1.57045i	−0.177081	−	0.128657i	−0.672795	+	0.739829i	$0.734906\pi$
$150$	1.56013	−	4.80158i	0.127384	−	0.392047i
$151$	−6.82131	−	20.9938i	−0.555111	−	1.70845i	−0.695651	−	0.718380i	$-0.744884\pi$
$151$	−6.82131	−	20.9938i	−0.555111	−	1.70845i	0.140541	−	0.990075i	$-0.455116\pi$
$152$	−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	$-0.331885\pi$
$167$	19.1404	−	13.9063i	1.48113	−	1.07610i	0.977192	−	0.212360i	$-0.0681149\pi$
$168$	−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	0.998865	−	0.0476266i	$-0.0151657\pi$
$173$	2.14093	+	6.58911i	0.162772	+	0.500961i	−0.836093	+	0.548588i	$0.815166\pi$
$174$	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	0.236965	−	0.971518i	$-0.423847\pi$
$193$	−8.52686	−	6.19513i	−0.613777	−	0.445935i	−0.850742	+	0.525583i	$0.823847\pi$
$194$	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	$-0.476371\pi$
$197$	2.08191			0.148330			0.0741649	+	0.997246i	$0.476371\pi$
$198$		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	−0.845270	−	0.534340i	$-0.820560\pi$
$211$	−8.69059	+	6.31408i	−0.598285	+	0.434679i	0.246985	+	0.969019i	$0.420560\pi$
$212$	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	−0.836344	−	0.548205i	$-0.815311\pi$
$227$	2.44830	−	7.53510i	0.162499	−	0.500122i	0.998843	+	0.0480833i	$0.0153113\pi$
$228$	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	−0.608583	−	0.793490i	$-0.708262\pi$
$233$	−0.640974	+	0.465695i	−0.0419916	+	0.0305087i	0.566591	+	0.823999i	$0.308262\pi$
$234$	−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	$0.161885\pi$
$239$	7.00360	+	21.5549i	0.453025	+	1.39427i	−0.420412	+	0.907333i	$0.638115\pi$
$240$	−1.71256	+	1.24425i	−0.110545	+	0.0803160i
$241$	−13.2665			−0.854570			−0.427285	−	0.904117i	$-0.640530\pi$
$241$	−13.2665			−0.854570			−0.427285	+	0.904117i	$0.640530\pi$
$242$		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	$-0.338761\pi$
$263$	15.7359			0.970319			0.485160	+	0.874426i	$0.338761\pi$
$264$		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	$-0.797780\pi$
$271$	3.21140	−	9.88367i	0.195079	−	0.600390i	0.999976	−	0.00697572i	$-0.00222046\pi$
$272$	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	−0.778027	−	0.628231i	$-0.783779\pi$
$277$	−7.00629	+	5.09037i	−0.420967	+	0.305851i	0.357060	+	0.934082i	$0.383779\pi$
$278$	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	−0.309003	−	0.951061i	$-0.599995\pi$
$281$	−21.9429	−	15.9424i	−1.30900	−	0.951046i	−1.00000		1.45384e-5i	$0.999995\pi$
$282$	−3.12025	+	9.60315i	−0.185808	+	0.571859i
$283$	−2.34019	−	7.20236i	−0.139110	−	0.428136i	0.857097	−	0.515155i	$-0.172266\pi$
$283$	−2.34019	−	7.20236i	−0.139110	−	0.428136i	−0.996207	+	0.0870193i	$0.972266\pi$
$284$	−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	$0.436084\pi$
$293$	−9.20707	+	28.3365i	−0.537883	+	1.65543i	−0.737336	+	0.675526i	$0.763916\pi$
$294$	−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	$-0.488782\pi$
$307$	1.23472			0.0704690			0.0352345	+	0.999379i	$0.488782\pi$
$308$		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	−0.966666	−	0.256039i	$-0.917583\pi$
$337$	−0.626379	+	1.92780i	−0.0341210	+	0.105014i	0.932545	+	0.361053i	$0.117583\pi$
$338$	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	0.997181	−	0.0750345i	$-0.0239067\pi$
$347$	22.9862	+	16.7005i	1.23396	+	0.896528i	0.236784	+	0.971562i	$0.423907\pi$
$348$	0.335976	−	1.03403i	0.0180102	−	0.0554297i
$349$	8.02850	+	24.7092i	0.429756	+	1.32265i	0.898366	+	0.439247i	$0.144755\pi$
$349$	8.02850	+	24.7092i	0.429756	+	1.32265i	−0.468611	+	0.883405i	$0.655245\pi$
$350$	−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	$0.263406\pi$
$359$	−5.75085	+	17.6993i	−0.303518	+	0.934132i	−0.980226	+	0.197881i	$0.936594\pi$
$360$	−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	$-0.544634\pi$
$373$	−5.39853			−0.279525			−0.139763	+	0.990185i	$0.544634\pi$
$374$		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	−0.101162	−	0.994870i	$-0.532256\pi$
$409$	16.4572	−	11.9568i	0.813755	−	0.591227i	0.914917	+	0.403643i	$0.132256\pi$
$410$	−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	−0.642378	−	0.766388i	$-0.722052\pi$
$431$	−2.32527	+	1.68941i	−0.112004	+	0.0813760i	0.530373	+	0.847764i	$0.322052\pi$
$432$	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	$-0.458878\pi$
$439$	5.39853			0.257658			0.128829	+	0.991667i	$0.458878\pi$
$440$		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	$-0.946478\pi$
$457$	−30.9914	−	22.5166i	−1.44972	−	1.05328i	−0.463820	−	0.885929i	$-0.653522\pi$
$458$	−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	$-0.533801\pi$
$461$	−4.55134			−0.211977			−0.105989	+	0.994367i	$0.533801\pi$
$462$		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	0.771963	−	0.635668i	$-0.219275\pi$
$479$	8.88480	+	6.45518i	0.405957	+	0.294945i	−0.366006	+	0.930612i	$0.619275\pi$
$480$	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	−0.941661	−	0.336562i	$-0.890736\pi$
$491$	0.398515	−	1.22650i	0.0179847	−	0.0553513i	0.959646	+	0.281211i	$0.0907359\pi$
$492$	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	0.934958	−	0.354759i	$-0.115437\pi$
$503$	−0.671952	−	2.06805i	−0.0299608	−	0.0922100i	−0.964919	+	0.262549i	$0.915437\pi$
$504$	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	0.999651	−	0.0263998i	$-0.00840430\pi$
$523$	29.3515	+	21.3251i	1.28345	+	0.932483i	0.283802	+	0.958883i	$0.408404\pi$
$524$	−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	−0.954057	−	0.299625i	$-0.903139\pi$
$541$	−22.4201	+	16.2892i	−0.963917	+	0.700327i	−0.00985982	+	0.999951i	$0.503139\pi$
$542$	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	$0.0237109\pi$
$547$	5.47741	+	16.8577i	0.234197	+	0.720785i	−0.763030	+	0.646363i	$0.776289\pi$
$548$	−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	$-0.678205\pi$
$557$	9.36076	−	28.8095i	0.396628	−	1.22070i	0.927686	−	0.373360i	$-0.121795\pi$
$558$	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	−0.978867	−	0.204497i	$-0.934444\pi$
$563$	−25.7887	+	18.7366i	−1.08687	+	0.789654i	−0.107998	+	0.994151i	$0.534444\pi$
$564$	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	$-0.808757\pi$
$569$	−11.6840	−	35.9596i	−0.489818	−	1.50750i	0.335061	−	0.942196i	$-0.391243\pi$
$570$	2.03134	−	1.47586i	0.0850835	−	0.0618168i
$571$	−14.5012			−0.606857			−0.303429	−	0.952854i	$-0.598131\pi$
$571$	−14.5012			−0.606857			−0.303429	+	0.952854i	$0.598131\pi$
$572$		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	$-0.442732\pi$
$593$	8.71516			0.357889			0.178944	+	0.983859i	$0.442732\pi$
$594$		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	$0.229893\pi$
$601$	−6.01264	+	18.5050i	−0.245261	+	0.754835i	−0.995593	+	0.0937746i	$0.970107\pi$
$602$	−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	0.0988448	−	0.995103i	$-0.468485\pi$
$607$	26.5046	−	19.2567i	1.07579	−	0.781606i	0.976944	+	0.213497i	$0.0684853\pi$
$608$	−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	$-0.896418\pi$
$613$	−9.13290	−	28.1082i	−0.368874	−	1.13528i	0.578645	−	0.815579i	$-0.303582\pi$
$614$	−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	$-0.599155\pi$
$659$	−15.7359			−0.612985			−0.306492	+	0.951873i	$0.599155\pi$
$660$		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	−0.613056	−	0.790040i	$-0.710060\pi$
$673$	−1.32636	+	0.963660i	−0.0511276	+	0.0371464i	0.561928	+	0.827186i	$0.310060\pi$
$674$	−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	0.476422	−	0.879217i	$-0.341934\pi$
$677$	−5.53014	−	4.01788i	−0.212541	−	0.154420i	−0.688962	+	0.724797i	$0.741934\pi$
$678$	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	$-0.883839\pi$
$701$	−10.2775	−	31.6310i	−0.388177	−	1.19469i	0.545972	−	0.837804i	$-0.316161\pi$
$702$	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	−0.984448	−	0.175675i	$-0.943789\pi$
$733$	−2.29462	+	7.06210i	−0.0847536	+	0.260845i	0.899695	+	0.436520i	$0.143789\pi$
$734$	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	−0.973883	−	0.227052i	$-0.927091\pi$
$739$	−28.7855	+	20.9139i	−1.05889	+	0.769329i	−0.0850074	+	0.996380i	$0.527091\pi$
$740$	−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	0.970316	−	0.241840i	$-0.0777509\pi$
$743$	28.3526	+	20.5994i	1.04016	+	0.755718i	0.0698409	+	0.997558i	$0.477751\pi$
$744$	−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	0.114153	−	0.993463i	$-0.463585\pi$
$761$	30.1867	−	21.9319i	1.09427	−	0.795032i	0.980115	+	0.198431i	$0.0635847\pi$
$762$	−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	$-0.768436\pi$
$769$	−41.4217			−1.49371			−0.746853	+	0.664989i	$0.768436\pi$
$770$		0			0
$771$	18.6277			0.670861
$772$	11.7013	−	8.50146i	0.421137	−	0.305974i

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

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