LMFDB - Embedded newform 360.2.q.e.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(121,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("360.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.385731i$ of defining polynomial
Character	$\chi$	$=$	360.121
Dual form			360.2.q.e.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73065 + 0.0696054i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.165947 + 0.287429i) q^{7} +(2.99031 - 0.240925i) q^{9} +O(q^{10})$	\(q+(-1.73065 + 0.0696054i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.165947 + 0.287429i) q^{7} +(2.99031 - 0.240925i) q^{9} +(-2.20380 - 3.81710i) q^{11} +(-3.49031 + 6.04539i) q^{13} +(0.805046 - 1.53359i) q^{15} -3.07139 q^{17} -7.55364 q^{19} +(-0.307204 - 0.485889i) q^{21} +(-0.834053 + 1.44462i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.15842 + 0.625100i) q^{27} +(-1.78651 - 3.09432i) q^{29} +(-2.82220 + 4.88820i) q^{31} +(4.07971 + 6.45267i) q^{33} -0.331895 q^{35} +7.64441 q^{37} +(5.61972 - 10.7054i) q^{39} +(-2.74919 + 4.76174i) q^{41} +(3.53570 + 6.12401i) q^{43} +(-1.28651 + 2.71015i) q^{45} +(-3.98815 - 6.90768i) q^{47} +(3.44492 - 5.96678i) q^{49} +(5.31551 - 0.213786i) q^{51} -5.47900 q^{53} +4.40761 q^{55} +(13.0727 - 0.525774i) q^{57} +(3.69411 - 6.39839i) q^{59} +(-0.296197 - 0.513029i) q^{61} +(0.565483 + 0.819522i) q^{63} +(-3.49031 - 6.04539i) q^{65} +(-2.61087 + 4.52216i) q^{67} +(1.34290 - 2.55819i) q^{69} +8.98062 q^{71} -8.05202 q^{73} +(0.925606 + 1.46399i) q^{75} +(0.731430 - 1.26687i) q^{77} +(5.49838 + 9.52347i) q^{79} +(8.88391 - 1.44088i) q^{81} +(3.14657 + 5.45002i) q^{83} +(1.53570 - 2.65991i) q^{85} +(3.30720 + 5.23084i) q^{87} +11.9060 q^{89} -2.31683 q^{91} +(4.54401 - 8.65622i) q^{93} +(3.77682 - 6.54164i) q^{95} +(0.622718 + 1.07858i) q^{97} +(-7.50969 - 10.8834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + q^7	$ 8 q - 4 q^{5} + q^{7} - q^{11} - 4 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{19} - 7 q^{23} - 4 q^{25} - 18 q^{27} - 7 q^{29} + 2 q^{31} - 3 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} - 12 q^{41} + 11 q^{43} - 3 q^{45} - 7 q^{47} - 3 q^{49} + 39 q^{51} + 24 q^{53} + 2 q^{55} + 27 q^{57} - 11 q^{59} - 19 q^{61} - 33 q^{63} - 4 q^{65} + 10 q^{67} - 9 q^{69} + 24 q^{71} + 18 q^{73} - 3 q^{75} - 32 q^{77} + 24 q^{79} - 12 q^{81} - 23 q^{83} - 5 q^{85} + 24 q^{87} + 42 q^{89} + 28 q^{91} + 18 q^{93} - q^{95} - q^{97} - 84 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 + q^7 - q^11 - 4 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^19 - 7 * q^23 - 4 * q^25 - 18 * q^27 - 7 * q^29 + 2 * q^31 - 3 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 - 12 * q^41 + 11 * q^43 - 3 * q^45 - 7 * q^47 - 3 * q^49 + 39 * q^51 + 24 * q^53 + 2 * q^55 + 27 * q^57 - 11 * q^59 - 19 * q^61 - 33 * q^63 - 4 * q^65 + 10 * q^67 - 9 * q^69 + 24 * q^71 + 18 * q^73 - 3 * q^75 - 32 * q^77 + 24 * q^79 - 12 * q^81 - 23 * q^83 - 5 * q^85 + 24 * q^87 + 42 * q^89 + 28 * q^91 + 18 * q^93 - q^95 - q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.73065	+	0.0696054i	−0.999192	+	0.0401867i
$3$	−1.73065	+	0.0696054i	−0.999192	+	0.0401867i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.165947	+	0.287429i	0.0627222	+	0.108638i	0.895681	−	0.444696i	$-0.146688\pi$
$7$	0.165947	+	0.287429i	0.0627222	+	0.108638i	−0.832959	+	0.553335i	$0.813355\pi$
$8$		0			0
$9$	2.99031	−	0.240925i	0.996770	−	0.0803085i
$10$		0			0
$11$	−2.20380	−	3.81710i	−0.664472	−	1.15090i	−0.979428	−	0.201792i	$-0.935323\pi$
$11$	−2.20380	−	3.81710i	−0.664472	−	1.15090i	0.314957	−	0.949106i	$-0.398010\pi$
$12$		0			0
$13$	−3.49031	+	6.04539i	−0.968038	+	1.67669i	−0.266816	+	0.963747i	$0.585972\pi$
$13$	−3.49031	+	6.04539i	−0.968038	+	1.67669i	−0.701222	+	0.712943i	$0.747362\pi$
$14$		0			0
$15$	0.805046	−	1.53359i	0.207862	−	0.395971i
$16$		0			0
$17$	−3.07139			−0.744923			−0.372461	−	0.928048i	$-0.621486\pi$
$17$	−3.07139			−0.744923			−0.372461	+	0.928048i	$0.621486\pi$
$18$		0			0
$19$	−7.55364			−1.73292			−0.866461	−	0.499244i	$-0.833611\pi$
$19$	−7.55364			−1.73292			−0.866461	+	0.499244i	$0.833611\pi$
$20$		0			0
$21$	−0.307204	−	0.485889i	−0.0670373	−	0.106030i
$22$		0			0
$23$	−0.834053	+	1.44462i	−0.173912	+	0.301224i	−0.939784	−	0.341768i	$-0.888974\pi$
$23$	−0.834053	+	1.44462i	−0.173912	+	0.301224i	0.765872	+	0.642993i	$0.222307\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−5.15842	+	0.625100i	−0.992738	+	0.120301i
$28$		0			0
$29$	−1.78651	−	3.09432i	−0.331746	−	0.574601i	0.651108	−	0.758985i	$-0.274304\pi$
$29$	−1.78651	−	3.09432i	−0.331746	−	0.574601i	−0.982854	+	0.184384i	$0.940971\pi$
$30$		0			0
$31$	−2.82220	+	4.88820i	−0.506883	+	0.877947i	0.493085	+	0.869981i	$0.335869\pi$
$31$	−2.82220	+	4.88820i	−0.506883	+	0.877947i	−0.999968	+	0.00796608i	$0.997464\pi$
$32$		0			0
$33$	4.07971	+	6.45267i	0.710186	+	1.12327i
$34$		0			0
$35$	−0.331895			−0.0561004
$36$		0			0
$37$	7.64441			1.25673			0.628367	−	0.777917i	$-0.283724\pi$
$37$	7.64441			1.25673			0.628367	+	0.777917i	$0.283724\pi$
$38$		0			0
$39$	5.61972	−	10.7054i	0.899875	−	1.71424i
$40$		0			0
$41$	−2.74919	+	4.76174i	−0.429351	+	0.743658i	−0.996816	−	0.0797396i	$-0.974591\pi$
$41$	−2.74919	+	4.76174i	−0.429351	+	0.743658i	0.567464	+	0.823398i	$0.307924\pi$
$42$		0			0
$43$	3.53570	+	6.12401i	0.539189	+	0.933902i	0.998948	+	0.0458587i	$0.0146024\pi$
$43$	3.53570	+	6.12401i	0.539189	+	0.933902i	−0.459759	+	0.888044i	$0.652064\pi$
$44$		0			0
$45$	−1.28651	+	2.71015i	−0.191781	+	0.404005i
$46$		0			0
$47$	−3.98815	−	6.90768i	−0.581732	−	1.00759i	−0.995274	−	0.0971042i	$-0.969042\pi$
$47$	−3.98815	−	6.90768i	−0.581732	−	1.00759i	0.413542	−	0.910485i	$-0.364291\pi$
$48$		0			0
$49$	3.44492	−	5.96678i	0.492132	−	0.852397i
$50$		0			0
$51$	5.31551	−	0.213786i	0.744321	−	0.0299360i
$52$		0			0
$53$	−5.47900			−0.752599			−0.376299	−	0.926498i	$-0.622804\pi$
$53$	−5.47900			−0.752599			−0.376299	+	0.926498i	$0.622804\pi$
$54$		0			0
$55$	4.40761			0.594321
$56$		0			0
$57$	13.0727	−	0.525774i	1.73152	−	0.0696405i
$58$		0			0
$59$	3.69411	−	6.39839i	0.480933	−	0.833000i	−0.518828	−	0.854879i	$-0.673632\pi$
$59$	3.69411	−	6.39839i	0.480933	−	0.833000i	0.999761	+	0.0218790i	$0.00696486\pi$
$60$		0			0
$61$	−0.296197	−	0.513029i	−0.0379242	−	0.0656866i	0.846440	−	0.532484i	$-0.178741\pi$
$61$	−0.296197	−	0.513029i	−0.0379242	−	0.0656866i	−0.884364	+	0.466797i	$0.845408\pi$
$62$		0			0
$63$	0.565483	+	0.819522i	0.0712442	+	0.103250i
$64$		0			0
$65$	−3.49031	−	6.04539i	−0.432920	−	0.749839i
$66$		0			0
$67$	−2.61087	+	4.52216i	−0.318969	+	0.552470i	−0.980273	−	0.197648i	$-0.936670\pi$
$67$	−2.61087	+	4.52216i	−0.318969	+	0.552470i	0.661305	+	0.750118i	$0.270003\pi$
$68$		0			0
$69$	1.34290	−	2.55819i	0.161666	−	0.307970i
$70$		0			0
$71$	8.98062			1.06580			0.532902	−	0.846177i	$-0.321102\pi$
$71$	8.98062			1.06580			0.532902	+	0.846177i	$0.321102\pi$
$72$		0			0
$73$	−8.05202			−0.942417			−0.471209	−	0.882022i	$-0.656182\pi$
$73$	−8.05202			−0.942417			−0.471209	+	0.882022i	$0.656182\pi$
$74$		0			0
$75$	0.925606	+	1.46399i	0.106880	+	0.169046i
$76$		0			0
$77$	0.731430	−	1.26687i	0.0833542	−	0.144374i
$78$		0			0
$79$	5.49838	+	9.52347i	0.618616	+	1.07147i	0.989739	+	0.142891i	$0.0456397\pi$
$79$	5.49838	+	9.52347i	0.618616	+	1.07147i	−0.371122	+	0.928584i	$0.621027\pi$
$80$		0			0
$81$	8.88391	−	1.44088i	0.987101	−	0.160098i
$82$		0			0
$83$	3.14657	+	5.45002i	0.345381	+	0.598217i	0.985423	−	0.170123i	$-0.0544165\pi$
$83$	3.14657	+	5.45002i	0.345381	+	0.598217i	−0.640042	+	0.768340i	$0.721083\pi$
$84$		0			0
$85$	1.53570	−	2.65991i	0.166570	−	0.288507i
$86$		0			0
$87$	3.30720	+	5.23084i	0.354569	+	0.560805i
$88$		0			0
$89$	11.9060			1.26203			0.631016	−	0.775770i	$-0.282638\pi$
$89$	11.9060			1.26203			0.631016	+	0.775770i	$0.282638\pi$
$90$		0			0
$91$	−2.31683			−0.242870
$92$		0			0
$93$	4.54401	−	8.65622i	0.471192	−	0.897608i
$94$		0			0
$95$	3.77682	−	6.54164i	0.387493	−	0.671158i
$96$		0			0
$97$	0.622718	+	1.07858i	0.0632274	+	0.109513i	0.895906	−	0.444243i	$-0.146527\pi$
$97$	0.622718	+	1.07858i	0.0632274	+	0.109513i	−0.832679	+	0.553756i	$0.813194\pi$
$98$		0			0
$99$	−7.50969	−	10.8834i	−0.754752	−	1.09382i
$100$		0			0
$101$	−2.33189	−	4.03896i	−0.232032	−	0.401892i	0.726374	−	0.687300i	$-0.241204\pi$
$101$	−2.33189	−	4.03896i	−0.232032	−	0.401892i	−0.958406	+	0.285408i	$0.907871\pi$
$102$		0			0
$103$	2.08270	−	3.60735i	0.205215	−	0.355443i	−0.744986	−	0.667080i	$-0.767544\pi$
$103$	2.08270	−	3.60735i	0.205215	−	0.355443i	0.950201	+	0.311637i	$0.100877\pi$
$104$		0			0
$105$	0.574394	−	0.0231017i	0.0560551	−	0.00225449i
$106$		0			0
$107$	−6.57409			−0.635541			−0.317771	−	0.948168i	$-0.602934\pi$
$107$	−6.57409			−0.635541			−0.317771	+	0.948168i	$0.602934\pi$
$108$		0			0
$109$	0.743816			0.0712446			0.0356223	−	0.999365i	$-0.488659\pi$
$109$	0.743816			0.0712446			0.0356223	+	0.999365i	$0.488659\pi$
$110$		0			0
$111$	−13.2298	+	0.532092i	−1.25572	+	0.0505040i
$112$		0			0
$113$	−8.31252	+	14.3977i	−0.781976	+	1.35442i	0.148814	+	0.988865i	$0.452455\pi$
$113$	−8.31252	+	14.3977i	−0.781976	+	1.35442i	−0.930789	+	0.365556i	$0.880879\pi$
$114$		0			0
$115$	−0.834053	−	1.44462i	−0.0777758	−	0.134712i
$116$		0			0
$117$	−8.98062	+	18.9185i	−0.830259	+	1.74902i
$118$		0			0
$119$	−0.509690	−	0.882809i	−0.0467232	−	0.0809269i
$120$		0			0
$121$	−4.21349	+	7.29798i	−0.383045	+	0.663453i
$122$		0			0
$123$	4.42645	−	8.43227i	0.399119	−	0.760312i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	4.79152			0.425178			0.212589	−	0.977142i	$-0.431810\pi$
$127$	4.79152			0.425178			0.212589	+	0.977142i	$0.431810\pi$
$128$		0			0
$129$	−6.54532	−	10.3524i	−0.576284	−	0.911480i
$130$		0			0
$131$	−9.88985	+	17.1297i	−0.864080	+	1.49663i	0.00387809	+	0.999992i	$0.498766\pi$
$131$	−9.88985	+	17.1297i	−0.864080	+	1.49663i	−0.867958	+	0.496638i	$0.834568\pi$
$132$		0			0
$133$	−1.25351	−	2.17114i	−0.108693	−	0.188261i
$134$		0			0
$135$	2.03786	−	4.77987i	0.175391	−	0.411386i
$136$		0			0
$137$	−9.26713	−	16.0511i	−0.791744	−	1.37134i	−0.924886	−	0.380244i	$-0.875840\pi$
$137$	−9.26713	−	16.0511i	−0.791744	−	1.37134i	0.133142	−	0.991097i	$-0.457493\pi$
$138$		0			0
$139$	−2.68980	+	4.65887i	−0.228146	+	0.395160i	−0.957259	−	0.289234i	$-0.906600\pi$
$139$	−2.68980	+	4.65887i	−0.228146	+	0.395160i	0.729113	+	0.684393i	$0.239933\pi$
$140$		0			0
$141$	7.38291	+	11.6772i	0.621754	+	0.983397i
$142$		0			0
$143$	30.7678			2.57293
$144$		0			0
$145$	3.57301			0.296723
$146$		0			0
$147$	−5.54664	+	10.5662i	−0.457479	+	0.871486i
$148$		0			0
$149$	−5.51794	+	9.55735i	−0.452047	+	0.782969i	−0.998513	−	0.0545128i	$-0.982639\pi$
$149$	−5.51794	+	9.55735i	−0.452047	+	0.782969i	0.546466	+	0.837481i	$0.315973\pi$
$150$		0			0
$151$	0.750810	+	1.30044i	0.0611001	+	0.105828i	0.894957	−	0.446152i	$-0.147206\pi$
$151$	0.750810	+	1.30044i	0.0611001	+	0.105828i	−0.833857	+	0.551980i	$0.813872\pi$
$152$		0			0
$153$	−9.18442	+	0.739977i	−0.742517	+	0.0598236i
$154$		0			0
$155$	−2.82220	−	4.88820i	−0.226685	−	0.392630i
$156$		0			0
$157$	11.8109	−	20.4571i	0.942612	−	1.63265i	0.182149	−	0.983271i	$-0.441695\pi$
$157$	11.8109	−	20.4571i	0.942612	−	1.63265i	0.760463	−	0.649381i	$-0.224972\pi$
$158$		0			0
$159$	9.48224	−	0.381368i	0.751991	−	0.0302445i
$160$		0			0
$161$	−0.553635			−0.0436326
$162$		0			0
$163$	−9.16217			−0.717636			−0.358818	−	0.933407i	$-0.616820\pi$
$163$	−9.16217			−0.717636			−0.358818	+	0.933407i	$0.616820\pi$
$164$		0			0
$165$	−7.62803	+	0.306793i	−0.593841	+	0.0238838i
$166$		0			0
$167$	0.324363	−	0.561813i	0.0250999	−	0.0434744i	−0.853203	−	0.521580i	$-0.825343\pi$
$167$	0.324363	−	0.561813i	0.0250999	−	0.0434744i	0.878303	+	0.478105i	$0.158676\pi$
$168$		0			0
$169$	−17.8645	−	30.9423i	−1.37419	−	2.38017i
$170$		0			0
$171$	−22.5877	+	1.81986i	−1.72733	+	0.139168i
$172$		0			0
$173$	−4.40761	−	7.63420i	−0.335104	−	0.580417i	0.648401	−	0.761299i	$-0.275438\pi$
$173$	−4.40761	−	7.63420i	−0.335104	−	0.580417i	−0.983505	+	0.180882i	$0.942105\pi$
$174$		0			0
$175$	0.165947	−	0.287429i	0.0125444	−	0.0217276i
$176$		0			0
$177$	−5.94786	+	11.3305i	−0.447069	+	0.851654i
$178$		0			0
$179$	9.16217			0.684813			0.342406	−	0.939552i	$-0.388758\pi$
$179$	9.16217			0.684813			0.342406	+	0.939552i	$0.388758\pi$
$180$		0			0
$181$	13.5730			1.00887			0.504437	−	0.863448i	$-0.331700\pi$
$181$	13.5730			1.00887			0.504437	+	0.863448i	$0.331700\pi$
$182$		0			0
$183$	0.548324	+	0.867257i	0.0405333	+	0.0641095i
$184$		0			0
$185$	−3.82220	+	6.62025i	−0.281014	+	0.486731i
$186$		0			0
$187$	6.76875	+	11.7238i	0.494980	+	0.857330i
$188$		0			0
$189$	−1.03570	−	1.37895i	−0.0753359	−	0.100304i
$190$		0			0
$191$	5.13472	+	8.89360i	0.371535	+	0.643518i	0.989802	−	0.142450i	$-0.0454981\pi$
$191$	5.13472	+	8.89360i	0.371535	+	0.643518i	−0.618267	+	0.785968i	$0.712165\pi$
$192$		0			0
$193$	−4.53570	+	7.85606i	−0.326487	+	0.565491i	−0.981812	−	0.189855i	$-0.939198\pi$
$193$	−4.53570	+	7.85606i	−0.326487	+	0.565491i	0.655325	+	0.755347i	$0.272531\pi$
$194$		0			0
$195$	6.46130	+	10.2195i	0.462704	+	0.731836i
$196$		0			0
$197$	−4.80658			−0.342455			−0.171227	−	0.985232i	$-0.554773\pi$
$197$	−4.80658			−0.342455			−0.171227	+	0.985232i	$0.554773\pi$
$198$		0			0
$199$	−18.4596			−1.30857			−0.654284	−	0.756249i	$-0.727030\pi$
$199$	−18.4596			−1.30857			−0.654284	+	0.756249i	$0.727030\pi$
$200$		0			0
$201$	4.20374	−	8.00801i	0.296509	−	0.564842i
$202$		0			0
$203$	0.592932	−	1.02699i	0.0416157	−	0.0720805i
$204$		0			0
$205$	−2.74919	−	4.76174i	−0.192012	−	0.332574i
$206$		0			0
$207$	−2.14603	+	4.52081i	−0.149159	+	0.314218i
$208$		0			0
$209$	16.6467	+	28.8330i	1.15148	+	1.99442i
$210$		0			0
$211$	−0.177795	+	0.307950i	−0.0122399	+	0.0212002i	−0.872080	−	0.489362i	$-0.837230\pi$
$211$	−0.177795	+	0.307950i	−0.0122399	+	0.0212002i	0.859841	+	0.510563i	$0.170563\pi$
$212$		0			0
$213$	−15.5423	+	0.625100i	−1.06494	+	0.0428311i
$214$		0			0
$215$	−7.07139			−0.482265
$216$		0			0
$217$	−1.87335			−0.127171
$218$		0			0
$219$	13.9352	−	0.560464i	0.941656	−	0.0378726i
$220$		0			0
$221$	10.7201	−	18.5678i	0.721113	−	1.24900i
$222$		0			0
$223$	−1.65194	−	2.86125i	−0.110622	−	0.191603i	0.805399	−	0.592733i	$-0.201951\pi$
$223$	−1.65194	−	2.86125i	−0.110622	−	0.191603i	−0.916021	+	0.401130i	$0.868618\pi$
$224$		0			0
$225$	−1.70380	−	2.46922i	−0.113587	−	0.164615i
$226$		0			0
$227$	2.36921	+	4.10360i	0.157250	+	0.272365i	0.933876	−	0.357597i	$-0.116404\pi$
$227$	2.36921	+	4.10360i	0.157250	+	0.272365i	−0.776626	+	0.629962i	$0.783070\pi$
$228$		0			0
$229$	−9.53032	+	16.5070i	−0.629781	+	1.09081i	0.357814	+	0.933793i	$0.383522\pi$
$229$	−9.53032	+	16.5070i	−0.629781	+	1.09081i	−0.987595	+	0.157021i	$0.949811\pi$
$230$		0			0
$231$	−1.17767	+	2.24343i	−0.0774850	+	0.147607i
$232$		0			0
$233$	−13.3721			−0.876035			−0.438017	−	0.898967i	$-0.644319\pi$
$233$	−13.3721			−0.876035			−0.438017	+	0.898967i	$0.644319\pi$
$234$		0			0
$235$	7.97630			0.520317
$236$		0			0
$237$	−10.1787	−	16.0991i	−0.661175	−	1.04575i
$238$		0			0
$239$	−9.64873	+	16.7121i	−0.624124	+	1.08101i	0.364585	+	0.931170i	$0.381211\pi$
$239$	−9.64873	+	16.7121i	−0.624124	+	1.08101i	−0.988710	+	0.149845i	$0.952123\pi$
$240$		0			0
$241$	−9.99031	−	17.3037i	−0.643532	−	1.11463i	−0.984638	−	0.174606i	$-0.944135\pi$
$241$	−9.99031	−	17.3037i	−0.643532	−	1.11463i	0.341106	−	0.940025i	$-0.389199\pi$
$242$		0			0
$243$	−15.2747	+	3.11204i	−0.979870	+	0.199637i
$244$		0			0
$245$	3.44492	+	5.96678i	0.220088	+	0.381204i
$246$		0			0
$247$	26.3645	−	45.6647i	1.67753	−	2.90558i
$248$		0			0
$249$	−5.82496	−	9.21306i	−0.369142	−	0.583854i
$250$		0			0
$251$	−0.889846			−0.0561666			−0.0280833	−	0.999606i	$-0.508940\pi$
$251$	−0.889846			−0.0561666			−0.0280833	+	0.999606i	$0.508940\pi$
$252$		0			0
$253$	7.35235			0.462238
$254$		0			0
$255$	−2.47261	+	4.71026i	−0.154841	+	0.294968i
$256$		0			0
$257$	−8.36222	+	14.4838i	−0.521621	+	0.903474i	0.478063	+	0.878326i	$0.341339\pi$
$257$	−8.36222	+	14.4838i	−0.521621	+	0.903474i	−0.999684	+	0.0251482i	$0.991994\pi$
$258$		0			0
$259$	1.26857	+	2.19723i	0.0788251	+	0.136529i
$260$		0			0
$261$	−6.08771	−	8.82257i	−0.376820	−	0.546103i
$262$		0			0
$263$	3.56170	+	6.16905i	0.219624	+	0.380400i	0.954693	−	0.297592i	$-0.0961836\pi$
$263$	3.56170	+	6.16905i	0.219624	+	0.380400i	−0.735069	+	0.677992i	$0.762850\pi$
$264$		0			0
$265$	2.73950	−	4.74495i	0.168286	−	0.291480i
$266$		0			0
$267$	−20.6051	+	0.828721i	−1.26101	+	0.0507169i
$268$		0			0
$269$	23.5030			1.43300			0.716502	−	0.697585i	$-0.245742\pi$
$269$	23.5030			1.43300			0.716502	+	0.697585i	$0.245742\pi$
$270$		0			0
$271$	−8.49838			−0.516240			−0.258120	−	0.966113i	$-0.583103\pi$
$271$	−8.49838			−0.516240			−0.258120	+	0.966113i	$0.583103\pi$
$272$		0			0
$273$	4.00963	−	0.161264i	0.242674	−	0.00976014i
$274$		0			0
$275$	−2.20380	+	3.81710i	−0.132894	+	0.230180i
$276$		0			0
$277$	11.1153	+	19.2523i	0.667856	+	1.15676i	0.978502	+	0.206235i	$0.0661212\pi$
$277$	11.1153	+	19.2523i	0.667856	+	1.15676i	−0.310646	+	0.950526i	$0.600545\pi$
$278$		0			0
$279$	−7.26158	+	15.2972i	−0.434739	+	0.915818i
$280$		0			0
$281$	5.87029	+	10.1676i	0.350192	+	0.606550i	0.986283	−	0.165064i	$-0.0527830\pi$
$281$	5.87029	+	10.1676i	0.350192	+	0.606550i	−0.636091	+	0.771614i	$0.719450\pi$
$282$		0			0
$283$	11.8667	−	20.5537i	0.705401	−	1.22179i	−0.261145	−	0.965300i	$-0.584100\pi$
$283$	11.8667	−	20.5537i	0.705401	−	1.22179i	0.966546	−	0.256491i	$-0.0825666\pi$
$284$		0			0
$285$	−6.08102	+	11.5842i	−0.360209	+	0.686188i
$286$		0			0
$287$	−1.82488			−0.107719
$288$		0			0
$289$	−7.56653			−0.445090
$290$		0			0
$291$	−1.15278	−	1.82330i	−0.0675773	−	0.106884i
$292$		0			0
$293$	10.1347	−	17.5538i	0.592077	−	1.02551i	−0.401876	−	0.915694i	$-0.631642\pi$
$293$	10.1347	−	17.5538i	0.592077	−	1.02551i	0.993952	−	0.109813i	$-0.0350251\pi$
$294$		0			0
$295$	3.69411	+	6.39839i	0.215080	+	0.372529i
$296$		0			0
$297$	13.7542	+	18.3126i	0.798099	+	1.06260i
$298$		0			0
$299$	−5.82220	−	10.0844i	−0.336707	−	0.583193i
$300$		0			0
$301$	−1.17348	+	2.03253i	−0.0676382	+	0.117153i
$302$		0			0
$303$	4.31683	+	6.82772i	0.247995	+	0.392242i
$304$		0			0
$305$	0.592395			0.0339204
$306$		0			0
$307$	2.05094			0.117053			0.0585267	−	0.998286i	$-0.481360\pi$
$307$	2.05094			0.117053			0.0585267	+	0.998286i	$0.481360\pi$
$308$		0			0
$309$	−3.35335	+	6.38803i	−0.190765	+	0.363403i
$310$		0			0
$311$	9.89792	−	17.1437i	0.561259	−	0.972130i	−0.436128	−	0.899885i	$-0.643650\pi$
$311$	9.89792	−	17.1437i	0.561259	−	0.972130i	0.997387	−	0.0722448i	$-0.0230163\pi$
$312$		0			0
$313$	0.0577727	+	0.100065i	0.00326551	+	0.00565603i	0.867654	−	0.497169i	$-0.165627\pi$
$313$	0.0577727	+	0.100065i	0.00326551	+	0.00565603i	−0.864388	+	0.502825i	$0.832294\pi$
$314$		0			0
$315$	−0.992468	+	0.0799619i	−0.0559192	+	0.00450534i
$316$		0			0
$317$	−11.8936	−	20.6003i	−0.668011	−	1.15703i	−0.978459	−	0.206439i	$-0.933813\pi$
$317$	−11.8936	−	20.6003i	−0.668011	−	1.15703i	0.310448	−	0.950590i	$-0.399521\pi$
$318$		0			0
$319$	−7.87422	+	13.6385i	−0.440872	+	0.763612i
$320$		0			0
$321$	11.3775	−	0.457592i	0.635028	−	0.0255403i
$322$		0			0
$323$	23.2002			1.29089
$324$		0			0
$325$	6.98062			0.387215
$326$		0			0
$327$	−1.28729	+	0.0517736i	−0.0711871	+	0.00286309i
$328$		0			0
$329$	1.32365	−	2.29262i	0.0729750	−	0.126396i
$330$		0			0
$331$	−17.3125	−	29.9862i	−0.951582	−	1.64819i	−0.742003	−	0.670396i	$-0.766124\pi$
$331$	−17.3125	−	29.9862i	−0.951582	−	1.64819i	−0.209579	−	0.977792i	$-0.567209\pi$
$332$		0			0
$333$	22.8592	−	1.84173i	1.25267	−	0.100926i
$334$		0			0
$335$	−2.61087	−	4.52216i	−0.142647	−	0.247072i
$336$		0			0
$337$	5.26713	−	9.12293i	0.286919	−	0.496958i	−0.686154	−	0.727456i	$-0.740702\pi$
$337$	5.26713	−	9.12293i	0.286919	−	0.496958i	0.973073	+	0.230499i	$0.0740357\pi$
$338$		0			0
$339$	13.3839	−	25.4960i	0.726914	−	1.38475i
$340$		0			0
$341$	24.8783			1.34724
$342$		0			0
$343$	4.60997			0.248915
$344$		0			0
$345$	1.54401	+	2.44208i	0.0831266	+	0.131477i
$346$		0			0
$347$	2.94654	−	5.10356i	0.158179	−	0.273974i	−0.776033	−	0.630692i	$-0.782771\pi$
$347$	2.94654	−	5.10356i	0.158179	−	0.273974i	0.934212	+	0.356718i	$0.116104\pi$
$348$		0			0
$349$	11.5066	+	19.9301i	0.615936	+	1.06683i	0.990220	+	0.139518i	$0.0445552\pi$
$349$	11.5066	+	19.9301i	0.615936	+	1.06683i	−0.374284	+	0.927314i	$0.622111\pi$
$350$		0			0
$351$	14.2255	−	33.3664i	0.759301	−	1.78097i
$352$		0			0
$353$	7.36222	+	12.7517i	0.391851	+	0.678706i	0.992694	−	0.120661i	$-0.0385014\pi$
$353$	7.36222	+	12.7517i	0.391851	+	0.678706i	−0.600842	+	0.799367i	$0.705168\pi$
$354$		0			0
$355$	−4.49031	+	7.77745i	−0.238321	+	0.412784i
$356$		0			0
$357$	0.943544	+	1.49236i	0.0499376	+	0.0789839i
$358$		0			0
$359$	4.02262			0.212306			0.106153	−	0.994350i	$-0.466147\pi$
$359$	4.02262			0.212306			0.106153	+	0.994350i	$0.466147\pi$
$360$		0			0
$361$	38.0574			2.00302
$362$		0			0
$363$	6.78411	−	12.9235i	0.356073	−	0.678310i
$364$		0			0
$365$	4.02601	−	6.97325i	0.210731	−	0.364997i
$366$		0			0
$367$	4.43830	+	7.68735i	0.231677	+	0.401277i	0.958302	−	0.285758i	$-0.0922454\pi$
$367$	4.43830	+	7.68735i	0.231677	+	0.401277i	−0.726625	+	0.687035i	$0.758912\pi$
$368$		0			0
$369$	−7.07371	+	14.9014i	−0.368242	+	0.775737i
$370$		0			0
$371$	−0.909226	−	1.57482i	−0.0472046	−	0.0817608i
$372$		0			0
$373$	−15.3645	+	26.6121i	−0.795545	+	1.37792i	0.126947	+	0.991909i	$0.459482\pi$
$373$	−15.3645	+	26.6121i	−0.795545	+	1.37792i	−0.922492	+	0.386015i	$0.873851\pi$
$374$		0			0
$375$	−1.73065	+	0.0696054i	−0.0893705	+	0.00359441i
$376$		0			0
$377$	24.9419			1.28457
$378$		0			0
$379$	−4.24004			−0.217796			−0.108898	−	0.994053i	$-0.534732\pi$
$379$	−4.24004			−0.217796			−0.108898	+	0.994053i	$0.534732\pi$
$380$		0			0
$381$	−8.29244	+	0.333515i	−0.424835	+	0.0170865i
$382$		0			0
$383$	−16.0439	+	27.7889i	−0.819807	+	1.41995i	0.0860167	+	0.996294i	$0.472586\pi$
$383$	−16.0439	+	27.7889i	−0.819807	+	1.41995i	−0.905824	+	0.423654i	$0.860747\pi$
$384$		0			0
$385$	0.731430	+	1.26687i	0.0372771	+	0.0645659i
$386$		0			0
$387$	12.0483	+	17.4608i	0.612448	+	0.887584i
$388$		0			0
$389$	14.1667	+	24.5374i	0.718278	+	1.24409i	0.961681	+	0.274169i	$0.0884029\pi$
$389$	14.1667	+	24.5374i	0.718278	+	1.24409i	−0.243403	+	0.969925i	$0.578264\pi$
$390$		0			0
$391$	2.56170	−	4.43700i	0.129551	−	0.224389i
$392$		0			0
$393$	15.9236	−	30.3340i	0.803237	−	1.53015i
$394$		0			0
$395$	−10.9968			−0.553307
$396$		0			0
$397$	13.1395			0.659455			0.329728	−	0.944076i	$-0.393043\pi$
$397$	13.1395			0.659455			0.329728	+	0.944076i	$0.393043\pi$
$398$		0			0
$399$	2.32050	+	3.67023i	0.116171	+	0.183741i
$400$		0			0
$401$	−7.59471	+	13.1544i	−0.379262	+	0.656900i	−0.990955	−	0.134195i	$-0.957155\pi$
$401$	−7.59471	+	13.1544i	−0.379262	+	0.656900i	0.611693	+	0.791095i	$0.290489\pi$
$402$		0			0
$403$	−19.7007	−	34.1227i	−0.981364	−	1.69977i
$404$		0			0
$405$	−3.19411	+	8.41413i	−0.158717	+	0.418102i
$406$		0			0
$407$	−16.8468	−	29.1795i	−0.835063	−	1.44637i
$408$		0			0
$409$	5.10064	−	8.83457i	0.252211	−	0.436841i	−0.711924	−	0.702257i	$-0.752176\pi$
$409$	5.10064	−	8.83457i	0.252211	−	0.436841i	0.964134	+	0.265415i	$0.0855091\pi$
$410$		0			0
$411$	17.1554	+	27.1339i	0.846214	+	1.33842i
$412$		0			0
$413$	2.45211			0.120661
$414$		0			0
$415$	−6.29314			−0.308918
$416$		0			0
$417$	4.33082	−	8.25010i	0.212081	−	0.404009i
$418$		0			0
$419$	−6.32058	+	10.9476i	−0.308781	+	0.534824i	−0.978096	−	0.208155i	$-0.933254\pi$
$419$	−6.32058	+	10.9476i	−0.308781	+	0.534824i	0.669315	+	0.742979i	$0.266588\pi$
$420$		0			0
$421$	−0.501620	−	0.868832i	−0.0244475	−	0.0423443i	0.853543	−	0.521023i	$-0.174449\pi$
$421$	−0.501620	−	0.868832i	−0.0244475	−	0.0423443i	−0.877990	+	0.478678i	$0.841116\pi$
$422$		0			0
$423$	−13.5900	−	19.6953i	−0.660771	−	0.957617i
$424$		0			0
$425$	1.53570	+	2.65991i	0.0744923	+	0.129024i
$426$		0			0
$427$	0.0983063	−	0.170272i	0.00475738	−	0.00824002i
$428$		0			0
$429$	−53.2484	+	2.14161i	−2.57086	+	0.103398i
$430$		0			0
$431$	−39.0685			−1.88186			−0.940932	−	0.338596i	$-0.890048\pi$
$431$	−39.0685			−1.88186			−0.940932	+	0.338596i	$0.890048\pi$
$432$		0			0
$433$	−29.6663			−1.42567			−0.712836	−	0.701331i	$-0.752589\pi$
$433$	−29.6663			−1.42567			−0.712836	+	0.701331i	$0.752589\pi$
$434$		0			0
$435$	−6.18364	+	0.248701i	−0.296483	+	0.0119243i
$436$		0			0
$437$	6.30013	−	10.9121i	0.301376	−	0.521999i
$438$		0			0
$439$	16.1223	+	27.9247i	0.769477	+	1.33277i	0.937847	+	0.347049i	$0.112816\pi$
$439$	16.1223	+	27.9247i	0.769477	+	1.33277i	−0.168370	+	0.985724i	$0.553850\pi$
$440$		0			0
$441$	8.86384	−	18.6725i	0.422088	−	0.889167i
$442$		0			0
$443$	2.22372	+	3.85160i	0.105652	+	0.182995i	0.914004	−	0.405704i	$-0.132974\pi$
$443$	2.22372	+	3.85160i	0.105652	+	0.182995i	−0.808352	+	0.588699i	$0.799640\pi$
$444$		0			0
$445$	−5.95299	+	10.3109i	−0.282199	+	0.488783i
$446$		0			0
$447$	8.88438	−	16.9245i	0.420217	−	0.800502i
$448$		0			0
$449$	−13.0639			−0.616523			−0.308261	−	0.951302i	$-0.599747\pi$
$449$	−13.0639			−0.616523			−0.308261	+	0.951302i	$0.599747\pi$
$450$		0			0
$451$	24.2347			1.14117
$452$		0			0
$453$	−1.38991	−	2.19835i	−0.0653036	−	0.103288i
$454$		0			0
$455$	1.15842	−	2.00643i	0.0543074	−	0.0940631i
$456$		0			0
$457$	−8.16504	−	14.1423i	−0.381945	−	0.661547i	0.609396	−	0.792866i	$-0.291412\pi$
$457$	−8.16504	−	14.1423i	−0.381945	−	0.661547i	−0.991340	+	0.131319i	$0.958079\pi$
$458$		0			0
$459$	15.8435	−	1.91993i	0.739513	−	0.0896146i
$460$		0			0
$461$	−10.7639	−	18.6436i	−0.501324	−	0.868319i	−0.999999	−	0.00152975i	$-0.999513\pi$
$461$	−10.7639	−	18.6436i	−0.501324	−	0.868319i	0.498675	−	0.866789i	$-0.333820\pi$
$462$		0			0
$463$	11.1584	−	19.3269i	0.518576	−	0.898199i	−0.481192	−	0.876616i	$-0.659796\pi$
$463$	11.1584	−	19.3269i	0.518576	−	0.898199i	0.999767	−	0.0215837i	$-0.00687083\pi$
$464$		0			0
$465$	5.22450	+	8.26333i	0.242280	+	0.383203i
$466$		0			0
$467$	−36.5203			−1.68996			−0.844978	−	0.534801i	$-0.820387\pi$
$467$	−36.5203			−1.68996			−0.844978	+	0.534801i	$0.820387\pi$
$468$		0			0
$469$	−1.73307			−0.0800256
$470$		0			0
$471$	−19.0166	+	36.2262i	−0.876240	+	1.66921i
$472$		0			0
$473$	15.5840	−	26.9922i	0.716551	−	1.24110i
$474$		0			0
$475$	3.77682	+	6.54164i	0.173292	+	0.300151i
$476$		0			0
$477$	−16.3839	+	1.32003i	−0.750168	+	0.0604401i
$478$		0			0
$479$	−4.47900	−	7.75786i	−0.204651	−	0.354465i	0.745371	−	0.666650i	$-0.232273\pi$
$479$	−4.47900	−	7.75786i	−0.204651	−	0.354465i	−0.950021	+	0.312185i	$0.898939\pi$
$480$		0			0
$481$	−26.6814	+	46.2135i	−1.21657	+	2.10715i
$482$		0			0
$483$	0.958150	−	0.0385360i	0.0435973	−	0.00175345i
$484$		0			0
$485$	−1.24544			−0.0565523
$486$		0			0
$487$	−29.5016			−1.33685			−0.668423	−	0.743781i	$-0.733030\pi$
$487$	−29.5016			−1.33685			−0.668423	+	0.743781i	$0.733030\pi$
$488$		0			0
$489$	15.8565	−	0.637737i	0.717057	−	0.0288395i
$490$		0			0
$491$	5.17635	−	8.96571i	0.233606	−	0.404617i	−0.725261	−	0.688474i	$-0.758281\pi$
$491$	5.17635	−	8.96571i	0.233606	−	0.404617i	0.958867	+	0.283857i	$0.0916142\pi$
$492$		0			0
$493$	5.48707	+	9.50388i	0.247125	+	0.428033i
$494$		0			0
$495$	13.1801	−	1.06190i	0.592402	−	0.0477291i
$496$		0			0
$497$	1.49031	+	2.58129i	0.0668495	+	0.115787i
$498$		0			0
$499$	−11.1925	+	19.3860i	−0.501045	+	0.867835i	0.498954	+	0.866628i	$0.333717\pi$
$499$	−11.1925	+	19.3860i	−0.501045	+	0.867835i	−0.999999	+	0.00120683i	$0.999616\pi$
$500$		0			0
$501$	−0.522254	+	0.994880i	−0.0233326	+	0.0444480i
$502$		0			0
$503$	−42.8654			−1.91127			−0.955637	−	0.294546i	$-0.904832\pi$
$503$	−42.8654			−1.91127			−0.955637	+	0.294546i	$0.904832\pi$
$504$		0			0
$505$	4.66379			0.207536
$506$		0			0
$507$	33.0710	+	52.3068i	1.46874	+	2.32303i
$508$		0			0
$509$	3.54539	−	6.14079i	0.157147	−	0.272186i	−0.776692	−	0.629881i	$-0.783104\pi$
$509$	3.54539	−	6.14079i	0.157147	−	0.272186i	0.933839	+	0.357695i	$0.116437\pi$
$510$		0			0
$511$	−1.33621	−	2.31438i	−0.0591105	−	0.102382i
$512$		0			0
$513$	38.9648	−	4.72178i	1.72034	−	0.208472i
$514$		0			0
$515$	2.08270	+	3.60735i	0.0917749	+	0.158959i
$516$		0			0
$517$	−17.5782	+	30.4463i	−0.773088	+	1.33903i
$518$		0			0
$519$	8.15941	+	12.9053i	0.358158	+	0.566482i
$520$		0			0
$521$	−39.5863			−1.73431			−0.867153	−	0.498042i	$-0.834053\pi$
$521$	−39.5863			−1.73431			−0.867153	+	0.498042i	$0.834053\pi$
$522$		0			0
$523$	25.9375			1.13417			0.567085	−	0.823659i	$-0.308071\pi$
$523$	25.9375			1.13417			0.567085	+	0.823659i	$0.308071\pi$
$524$		0			0
$525$	−0.267190	+	0.508991i	−0.0116611	+	0.0222142i
$526$		0			0
$527$	8.66811	−	15.0136i	0.377589	−	0.654003i
$528$		0			0
$529$	10.1087	+	17.5088i	0.439509	+	0.761252i
$530$		0			0
$531$	9.50501	−	20.0232i	0.412482	−	0.868932i
$532$		0			0
$533$	−19.1911	−	33.2399i	−0.831257	−	1.43978i
$534$		0			0
$535$	3.28705	−	5.69333i	0.142111	−	0.246144i
$536$		0			0
$537$	−15.8565	+	0.637737i	−0.684259	+	0.0275204i
$538$		0			0
$539$	−30.3677			−1.30803
$540$		0			0
$541$	−38.7929			−1.66784			−0.833920	−	0.551886i	$-0.813908\pi$
$541$	−38.7929			−1.66784			−0.833920	+	0.551886i	$0.813908\pi$
$542$		0			0
$543$	−23.4902	+	0.944756i	−1.00806	+	0.0405433i
$544$		0			0
$545$	−0.371908	+	0.644164i	−0.0159308	+	0.0275929i
$546$		0			0
$547$	5.02655	+	8.70623i	0.214920	+	0.372252i	0.953248	−	0.302190i	$-0.0977177\pi$
$547$	5.02655	+	8.70623i	0.214920	+	0.372252i	−0.738328	+	0.674442i	$0.764384\pi$
$548$		0			0
$549$	−1.00932	−	1.46275i	−0.0430769	−	0.0624288i
$550$		0			0
$551$	13.4946	+	23.3734i	0.574890	+	0.995739i
$552$		0			0
$553$	−1.82488	+	3.16079i	−0.0776019	+	0.134410i
$554$		0			0
$555$	6.15410	−	11.7234i	0.261227	−	0.497631i
$556$		0			0
$557$	−23.4316			−0.992829			−0.496415	−	0.868086i	$-0.665350\pi$
$557$	−23.4316			−0.992829			−0.496415	+	0.868086i	$0.665350\pi$
$558$		0			0
$559$	−49.3627			−2.08782
$560$		0			0
$561$	−12.5304	−	19.8187i	−0.529033	−	0.836746i
$562$		0			0
$563$	20.7580	−	35.9539i	0.874844	−	1.51527i	0.0179159	−	0.999839i	$-0.494297\pi$
$563$	20.7580	−	35.9539i	0.874844	−	1.51527i	0.856928	−	0.515435i	$-0.172370\pi$
$564$		0			0
$565$	−8.31252	−	14.3977i	−0.349710	−	0.605716i
$566$		0			0
$567$	1.88841	+	2.31438i	0.0793059	+	0.0971950i
$568$		0			0
$569$	17.5990	+	30.4824i	0.737789	+	1.27789i	0.953489	+	0.301429i	$0.0974636\pi$
$569$	17.5990	+	30.4824i	0.737789	+	1.27789i	−0.215699	+	0.976460i	$0.569203\pi$
$570$		0			0
$571$	0.689797	−	1.19476i	0.0288671	−	0.0499993i	−0.851231	−	0.524791i	$-0.824143\pi$
$571$	0.689797	−	1.19476i	0.0288671	−	0.0499993i	0.880098	+	0.474792i	$0.157477\pi$
$572$		0			0
$573$	−9.50545	−	15.0343i	−0.397096	−	0.628067i
$574$		0			0
$575$	1.66811			0.0695648
$576$		0			0
$577$	−17.3322			−0.721549			−0.360775	−	0.932653i	$-0.617488\pi$
$577$	−17.3322			−0.721549			−0.360775	+	0.932653i	$0.617488\pi$
$578$		0			0
$579$	7.30289	−	13.9118i	0.303498	−	0.578155i
$580$		0			0
$581$	−1.04433	+	1.80883i	−0.0433261	+	0.0750430i
$582$		0			0
$583$	12.0746	+	20.9139i	0.500080	+	0.866164i
$584$		0			0
$585$	−11.8936	−	17.2367i	−0.491740	−	0.712650i
$586$		0			0
$587$	22.8450	+	39.5687i	0.942914	+	1.63317i	0.759875	+	0.650069i	$0.225260\pi$
$587$	22.8450	+	39.5687i	0.942914	+	1.63317i	0.183039	+	0.983106i	$0.441407\pi$
$588$		0			0
$589$	21.3179	−	36.9237i	0.878389	−	1.52141i
$590$		0			0
$591$	8.31851	−	0.334564i	0.342178	−	0.0137621i
$592$		0			0
$593$	10.4661			0.429791			0.214896	−	0.976637i	$-0.431059\pi$
$593$	10.4661			0.429791			0.214896	+	0.976637i	$0.431059\pi$
$594$		0			0
$595$	1.01938			0.0417905
$596$		0			0
$597$	31.9472	−	1.28489i	1.30751	−	0.0525870i
$598$		0			0
$599$	−10.5698	+	18.3074i	−0.431869	+	0.748020i	−0.997034	−	0.0769583i	$-0.975479\pi$
$599$	−10.5698	+	18.3074i	−0.431869	+	0.748020i	0.565165	+	0.824978i	$0.308812\pi$
$600$		0			0
$601$	5.33421	+	9.23912i	0.217587	+	0.376871i	0.954070	−	0.299585i	$-0.0968481\pi$
$601$	5.33421	+	9.23912i	0.217587	+	0.376871i	−0.736483	+	0.676456i	$0.763515\pi$
$602$		0			0
$603$	−6.71781	+	14.1517i	−0.273570	+	0.576301i
$604$		0			0
$605$	−4.21349	−	7.29798i	−0.171303	−	0.296705i
$606$		0			0
$607$	−0.651942	+	1.12920i	−0.0264615	+	0.0458327i	−0.878953	−	0.476909i	$-0.841757\pi$
$607$	−0.651942	+	1.12920i	−0.0264615	+	0.0458327i	0.852491	+	0.522741i	$0.175091\pi$
$608$		0			0
$609$	−0.954675	+	1.81863i	−0.0386854	+	0.0736947i
$610$		0			0
$611$	55.6796			2.25255
$612$		0			0
$613$	30.9741			1.25103			0.625517	−	0.780211i	$-0.284888\pi$
$613$	30.9741			1.25103			0.625517	+	0.780211i	$0.284888\pi$
$614$		0			0
$615$	5.08933	+	8.04955i	0.205222	+	0.324589i
$616$		0			0
$617$	1.29190	−	2.23763i	0.0520099	−	0.0900838i	−0.838848	−	0.544365i	$-0.816771\pi$
$617$	1.29190	−	2.23763i	0.0520099	−	0.0900838i	0.890858	+	0.454281i	$0.150104\pi$
$618$		0			0
$619$	0.465378	+	0.806058i	0.0187051	+	0.0323982i	0.875226	−	0.483713i	$-0.160712\pi$
$619$	0.465378	+	0.806058i	0.0187051	+	0.0323982i	−0.856521	+	0.516112i	$0.827379\pi$
$620$		0			0
$621$	3.39936	−	7.97332i	0.136412	−	0.319958i
$622$		0			0
$623$	1.97577	+	3.42213i	0.0791574	+	0.137105i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−30.8166	−	48.7411i	−1.23070	−	1.94653i
$628$		0			0
$629$	−23.4790			−0.936169
$630$		0			0
$631$	20.6250			0.821069			0.410535	−	0.911845i	$-0.365342\pi$
$631$	20.6250			0.821069			0.410535	+	0.911845i	$0.365342\pi$
$632$		0			0
$633$	0.286266	−	0.545330i	0.0113781	−	0.0216749i
$634$		0			0
$635$	−2.39576	+	4.14957i	−0.0950727	+	0.164671i
$636$		0			0
$637$	24.0477	+	41.6518i	0.952805	+	1.65031i
$638$		0			0
$639$	26.8548	−	2.16366i	1.06236	−	0.0855931i
$640$		0			0
$641$	−11.9516	−	20.7007i	−0.472058	−	0.817628i	0.527431	−	0.849598i	$-0.323155\pi$
$641$	−11.9516	−	20.7007i	−0.472058	−	0.817628i	−0.999489	+	0.0319697i	$0.989822\pi$
$642$		0			0
$643$	−1.12863	+	1.95484i	−0.0445088	+	0.0770915i	−0.887422	−	0.460959i	$-0.847506\pi$
$643$	−1.12863	+	1.95484i	−0.0445088	+	0.0770915i	0.842913	+	0.538050i	$0.180839\pi$
$644$		0			0
$645$	12.2381	−	0.492207i	0.481876	−	0.0193806i
$646$		0			0
$647$	−12.7262			−0.500320			−0.250160	−	0.968204i	$-0.580483\pi$
$647$	−12.7262			−0.500320			−0.250160	+	0.968204i	$0.580483\pi$
$648$		0			0
$649$	−32.5644			−1.27826
$650$		0			0
$651$	3.24212	−	0.130395i	0.127069	−	0.00511059i
$652$		0			0
$653$	−0.585400	+	1.01394i	−0.0229085	+	0.0396787i	−0.877252	−	0.480029i	$-0.840626\pi$
$653$	−0.585400	+	1.01394i	−0.0229085	+	0.0396787i	0.854344	+	0.519708i	$0.173959\pi$
$654$		0			0
$655$	−9.88985	−	17.1297i	−0.386428	−	0.669313i
$656$		0			0
$657$	−24.0780	+	1.93994i	−0.939373	+	0.0756841i
$658$		0			0
$659$	−17.3678	−	30.0819i	−0.676552	−	1.17182i	−0.976013	−	0.217714i	$-0.930140\pi$
$659$	−17.3678	−	30.0819i	−0.676552	−	1.17182i	0.299460	−	0.954109i	$-0.403193\pi$
$660$		0			0
$661$	−17.5730	+	30.4374i	−0.683511	+	1.18388i	0.290391	+	0.956908i	$0.406215\pi$
$661$	−17.5730	+	30.4374i	−0.683511	+	1.18388i	−0.973902	+	0.226968i	$0.927119\pi$
$662$		0			0
$663$	−17.2604	+	32.8806i	−0.670337	+	1.27698i
$664$		0			0
$665$	2.50701			0.0972177
$666$		0			0
$667$	5.96017			0.230779
$668$		0			0
$669$	3.05809	+	4.83684i	0.118233	+	0.187003i
$670$		0			0
$671$	−1.30552	+	2.26123i	−0.0503991	+	0.0872938i
$672$		0			0
$673$	13.6374	+	23.6207i	0.525684	+	0.910511i	0.999552	+	0.0299154i	$0.00952380\pi$
$673$	13.6374	+	23.6207i	0.525684	+	0.910511i	−0.473869	+	0.880596i	$0.657143\pi$
$674$		0			0
$675$	3.12056	+	4.15477i	0.120110	+	0.159917i
$676$		0			0
$677$	−4.56602	−	7.90858i	−0.175486	−	0.303951i	0.764843	−	0.644217i	$-0.222816\pi$
$677$	−4.56602	−	7.90858i	−0.175486	−	0.303951i	−0.940330	+	0.340265i	$0.889483\pi$
$678$		0			0
$679$	−0.206677	+	0.357975i	−0.00793153	+	0.0137378i
$680$		0			0
$681$	−4.38591	−	6.93699i	−0.168069	−	0.265826i
$682$		0			0
$683$	−29.0326			−1.11090			−0.555451	−	0.831549i	$-0.687455\pi$
$683$	−29.0326			−1.11090			−0.555451	+	0.831549i	$0.687455\pi$
$684$		0			0
$685$	18.5343			0.708158
$686$		0			0
$687$	15.3447	−	29.2312i	0.585437	−	1.11524i
$688$		0			0
$689$	19.1234	−	33.1227i	0.728544	−	1.26188i
$690$		0			0
$691$	8.38823	+	14.5288i	0.319103	+	0.552703i	0.980301	−	0.197509i	$-0.0632850\pi$
$691$	8.38823	+	14.5288i	0.319103	+	0.552703i	−0.661198	+	0.750211i	$0.729952\pi$
$692$		0			0
$693$	1.88198	−	3.96457i	0.0714906	−	0.150602i
$694$		0			0
$695$	−2.68980	−	4.65887i	−0.102030	−	0.176721i
$696$		0			0
$697$	8.44385	−	14.6252i	0.319834	−	0.553968i
$698$		0			0
$699$	23.1424	−	0.930770i	0.875327	−	0.0352049i
$700$		0			0
$701$	2.93400			0.110816			0.0554078	−	0.998464i	$-0.482354\pi$
$701$	2.93400			0.110816			0.0554078	+	0.998464i	$0.482354\pi$
$702$		0			0
$703$	−57.7431			−2.17782
$704$		0			0
$705$	−13.8042	+	0.555194i	−0.519896	+	0.0209098i
$706$		0			0
$707$	0.773944	−	1.34051i	0.0291071	−	0.0504150i
$708$		0			0
$709$	−13.9293	−	24.1263i	−0.523126	−	0.906080i	−0.999638	−	0.0269124i	$-0.991432\pi$
$709$	−13.9293	−	24.1263i	−0.523126	−	0.906080i	0.476512	−	0.879168i	$-0.341901\pi$
$710$		0			0
$711$	18.7363	+	27.1534i	0.702666	+	1.01833i
$712$		0			0
$713$	−4.70773	−	8.15404i	−0.176306	−	0.305371i
$714$		0			0
$715$	−15.3839	+	26.6457i	−0.575326	+	0.996493i
$716$		0			0
$717$	15.5353	−	29.5944i	0.580178	−	1.10522i
$718$		0			0
$719$	6.95585			0.259409			0.129705	−	0.991553i	$-0.458597\pi$
$719$	6.95585			0.259409			0.129705	+	0.991553i	$0.458597\pi$
$720$		0			0
$721$	1.38248			0.0514861
$722$		0			0
$723$	18.4942	+	29.2513i	0.687806	+	1.08787i
$724$		0			0
$725$	−1.78651	+	3.09432i	−0.0663492	+	0.114920i
$726$		0			0
$727$	2.51023	+	4.34784i	0.0930992	+	0.161253i	0.908814	−	0.417202i	$-0.136989\pi$
$727$	2.51023	+	4.34784i	0.0930992	+	0.161253i	−0.815715	+	0.578455i	$0.803656\pi$
$728$		0			0
$729$	26.2185	−	6.44905i	0.971056	−	0.238854i
$730$		0			0
$731$	−10.8595	−	18.8092i	−0.401654	−	0.695685i
$732$		0			0
$733$	10.2368	−	17.7307i	0.378105	−	0.654897i	−0.612682	−	0.790330i	$-0.709909\pi$
$733$	10.2368	−	17.7307i	0.378105	−	0.654897i	0.990787	+	0.135433i	$0.0432425\pi$
$734$		0			0
$735$	−6.37728	−	10.0866i	−0.235230	−	0.372051i
$736$		0			0
$737$	23.0154			0.847782
$738$		0			0
$739$	51.1614			1.88200			0.941002	−	0.338401i	$-0.109886\pi$
$739$	51.1614			1.88200			0.941002	+	0.338401i	$0.109886\pi$
$740$		0			0
$741$	−42.4493	+	80.8648i	−1.55941	+	2.97064i
$742$		0			0
$743$	3.07086	−	5.31888i	0.112659	−	0.195131i	−0.804183	−	0.594382i	$-0.797397\pi$
$743$	3.07086	−	5.31888i	0.112659	−	0.195131i	0.916841	+	0.399251i	$0.130730\pi$
$744$		0			0
$745$	−5.51794	−	9.55735i	−0.202162	−	0.350154i
$746$		0			0
$747$	10.7223	+	15.5391i	0.392307	+	0.568548i
$748$		0			0
$749$	−1.09095	−	1.88959i	−0.0398626	−	0.0690440i
$750$		0			0
$751$	7.54557	−	13.0693i	0.275342	−	0.476906i	−0.694880	−	0.719126i	$-0.744542\pi$
$751$	7.54557	−	13.0693i	0.275342	−	0.476906i	0.970221	+	0.242220i	$0.0778757\pi$
$752$		0			0
$753$	1.54001	−	0.0619381i	0.0561212	−	0.00225715i
$754$		0			0
$755$	−1.50162			−0.0546496
$756$		0			0
$757$	−2.87659			−0.104551			−0.0522757	−	0.998633i	$-0.516647\pi$
$757$	−2.87659			−0.104551			−0.0522757	+	0.998633i	$0.516647\pi$
$758$		0			0
$759$	−12.7244	+	0.511763i	−0.461865	+	0.0185758i
$760$		0			0
$761$	−0.119478	+	0.206941i	−0.00433106	+	0.00750162i	−0.868183	−	0.496245i	$-0.834712\pi$
$761$	−0.119478	+	0.206941i	−0.00433106	+	0.00750162i	0.863852	+	0.503746i	$0.168045\pi$
$762$		0			0
$763$	0.123434	+	0.213794i	0.00446862	+	0.00773988i
$764$		0			0
$765$	3.95137	−	8.32393i	0.142862	−	0.300952i
$766$		0			0
$767$	25.7872	+	44.6647i	0.931122	+	1.61275i
$768$		0			0
$769$	1.92930	−	3.34164i	0.0695722	−	0.120503i	−0.829141	−	0.559040i	$-0.811170\pi$
$769$	1.92930	−	3.34164i	0.0695722	−	0.120503i	0.898713	+	0.438537i	$0.144503\pi$
$770$		0			0
$771$	13.4639	−	25.6484i	0.484892	−	0.923706i
$772$		0			0
$773$	−5.22355			−0.187878			−0.0939390	−	0.995578i	$-0.529946\pi$
$773$	−5.22355			−0.187878			−0.0939390	+	0.995578i	$0.529946\pi$
$774$		0			0
$775$	5.64441			0.202753
$776$		0			0
$777$	−2.34839	−	3.71434i	−0.0842481	−	0.133251i
$778$		0			0
$779$	20.7664	−	35.9684i	0.744033	−	1.28870i
$780$		0			0
$781$	−19.7915	−	34.2799i	−0.708196	−	1.22663i
$782$		0			0
$783$	11.1498	+	14.8451i	0.398462	+	0.530519i
$784$		0			0
$785$	11.8109	+	20.4571i	0.421549	+	0.730144i
$786$		0			0
$787$	10.8818	−	18.8478i	0.387893	−	0.671851i	−0.604273	−	0.796778i	$-0.706536\pi$
$787$	10.8818	−	18.8478i	0.387893	−	0.671851i	0.992166	+	0.124927i	$0.0398695\pi$
$788$		0			0
$789$	−6.59347	−	10.4286i	−0.234734	−	0.371267i
$790$		0			0
$791$	−5.51776			−0.196189
$792$		0			0
$793$	4.13528			0.146848
$794$		0			0
$795$	−4.41085	+	8.40255i	−0.156437	+	0.298008i
$796$		0			0
$797$	−12.7228	+	22.0365i	−0.450665	+	0.780574i	−0.998427	−	0.0560596i	$-0.982146\pi$
$797$	−12.7228	+	22.0365i	−0.450665	+	0.780574i	0.547763	+	0.836634i	$0.315480\pi$
$798$		0			0
$799$	12.2492	+	21.2162i	0.433345	+	0.750576i
$800$		0			0
$801$	35.6026	−	2.86846i	1.25796	−	0.101352i
$802$		0			0
$803$	17.7451	+	30.7353i	0.626209	+	1.08463i
$804$		0			0
$805$	0.276818	−	0.479462i	0.00975654	−	0.0168988i
$806$		0			0
$807$	−40.6755	+	1.63594i	−1.43185	+	0.0575877i
$808$		0			0
$809$	−11.0854			−0.389741			−0.194871	−	0.980829i	$-0.562429\pi$
$809$	−11.0854			−0.389741			−0.194871	+	0.980829i	$0.562429\pi$
$810$		0			0
$811$	42.4869			1.49192			0.745958	−	0.665993i	$-0.231992\pi$
$811$	42.4869			1.49192			0.745958	+	0.665993i	$0.231992\pi$
$812$		0			0
$813$	14.7077	−	0.591533i	0.515823	−	0.0207460i
$814$		0			0
$815$	4.58108	−	7.93467i	0.160468	−	0.277939i
$816$		0			0
$817$	−26.7074	−	46.2585i	−0.934373	−	1.61838i
$818$		0			0
$819$	−6.92804	+	0.558184i	−0.242085	+	0.0195045i
$820$		0			0
$821$	15.0673	+	26.0973i	0.525851	+	0.910800i	0.999547	+	0.0301119i	$0.00958635\pi$
$821$	15.0673	+	26.0973i	0.525851	+	0.910800i	−0.473696	+	0.880689i	$0.657080\pi$
$822$		0			0
$823$	−10.8109	+	18.7251i	−0.376845	+	0.652715i	−0.990601	−	0.136781i	$-0.956324\pi$
$823$	−10.8109	+	18.7251i	−0.376845	+	0.652715i	0.613756	+	0.789495i	$0.289658\pi$
$824$		0			0
$825$	3.54832	−	6.75946i	0.123537	−	0.235334i
$826$		0			0
$827$	−1.82488			−0.0634574			−0.0317287	−	0.999497i	$-0.510101\pi$
$827$	−1.82488			−0.0634574			−0.0317287	+	0.999497i	$0.510101\pi$
$828$		0			0
$829$	30.4374			1.05713			0.528567	−	0.848892i	$-0.322730\pi$
$829$	30.4374			1.05713			0.528567	+	0.848892i	$0.322730\pi$
$830$		0			0
$831$	−20.5768	−	32.5454i	−0.713803	−	1.12899i
$832$		0			0
$833$	−10.5807	+	18.3263i	−0.366600	+	0.634970i
$834$		0			0
$835$	0.324363	+	0.561813i	0.0112250	+	0.0194423i
$836$		0			0
$837$	11.5025	−	26.9795i	0.397584	−	0.932549i
$838$		0			0
$839$	−16.7834	−	29.0698i	−0.579429	−	1.00360i	−0.995545	−	0.0942887i	$-0.969942\pi$
$839$	−16.7834	−	29.0698i	−0.579429	−	1.00360i	0.416116	−	0.909312i	$-0.363391\pi$
$840$		0			0
$841$	8.11678	−	14.0587i	0.279889	−	0.484782i
$842$		0			0
$843$	−10.8671	−	17.1880i	−0.374284	−	0.591987i
$844$		0			0
$845$	35.7291			1.22912
$846$		0			0
$847$	−2.79687			−0.0961016
$848$		0			0
$849$	−19.1065	+	36.3973i	−0.655732	+	1.24915i
$850$		0			0
$851$	−6.37584	+	11.0433i	−0.218561	+	0.378559i
$852$		0			0
$853$	11.8775	+	20.5724i	0.406676	+	0.704384i	0.994515	−	0.104594i	$-0.0333543\pi$
$853$	11.8775	+	20.5724i	0.406676	+	0.704384i	−0.587839	+	0.808978i	$0.700021\pi$
$854$		0			0
$855$	9.71781	−	20.4715i	0.332342	−	0.700109i
$856$		0			0
$857$	13.0052	+	22.5256i	0.444249	+	0.769461i	0.998000	−	0.0632211i	$-0.0201373\pi$
$857$	13.0052	+	22.5256i	0.444249	+	0.769461i	−0.553751	+	0.832682i	$0.686804\pi$
$858$		0			0
$859$	25.3835	−	43.9656i	0.866075	−	1.50009i	9.98605e−5	−	1.00000i	$-0.499968\pi$
$859$	25.3835	−	43.9656i	0.866075	−	1.50009i	0.865975	−	0.500086i	$-0.166698\pi$
$860$		0			0
$861$	3.15824	−	0.127022i	0.107632	−	0.00432889i
$862$		0			0
$863$	32.9343			1.12110			0.560548	−	0.828122i	$-0.310590\pi$
$863$	32.9343			1.12110			0.560548	+	0.828122i	$0.310590\pi$
$864$		0			0
$865$	8.81521			0.299726
$866$		0			0
$867$	13.0950	−	0.526672i	0.444731	−	0.0178867i
$868$		0			0
$869$	24.2347	−	41.9757i	0.822105	−	1.42393i
$870$		0			0
$871$	−18.2255	−	31.5675i	−0.617547	−	1.06962i
$872$		0			0
$873$	2.12198	+	3.07526i	0.0718181	+	0.104082i
$874$		0			0
$875$	0.165947	+	0.287429i	0.00561004	+	0.00971688i
$876$		0			0
$877$	−8.56170	+	14.8293i	−0.289108	+	0.500750i	−0.973597	−	0.228273i	$-0.926692\pi$
$877$	−8.56170	+	14.8293i	−0.289108	+	0.500750i	0.684489	+	0.729023i	$0.260025\pi$
$878$		0			0
$879$	−16.3178	+	31.0850i	−0.550387	+	1.04847i
$880$		0			0
$881$	−46.7617			−1.57544			−0.787721	−	0.616032i	$-0.788739\pi$
$881$	−46.7617			−1.57544			−0.787721	+	0.616032i	$0.788739\pi$
$882$		0			0
$883$	−21.1356			−0.711269			−0.355635	−	0.934625i	$-0.615735\pi$
$883$	−21.1356			−0.711269			−0.355635	+	0.934625i	$0.615735\pi$
$884$		0			0
$885$	−6.83859	−	10.8163i	−0.229877	−	0.363584i
$886$		0			0
$887$	22.9887	−	39.8176i	0.771885	−	1.33694i	−0.164644	−	0.986353i	$-0.552648\pi$
$887$	22.9887	−	39.8176i	0.771885	−	1.33694i	0.936529	−	0.350590i	$-0.114019\pi$
$888$		0			0
$889$	0.795139	+	1.37722i	0.0266681	+	0.0461905i
$890$		0			0
$891$	−25.0784	−	30.7353i	−0.840157	−	1.02967i
$892$		0			0
$893$	30.1250	+	52.1781i	1.00810	+	1.74607i
$894$		0			0
$895$	−4.58108	+	7.93467i	−0.153129	+	0.265227i
$896$		0			0
$897$	10.7781	+	17.0472i	0.359871	+	0.569191i
$898$		0			0
$899$	20.1676			0.672626
$900$		0			0
$901$	16.8282			0.560628
$902$		0			0
$903$	1.88941	−	3.59927i	0.0628756	−	0.119776i
$904$		0			0
$905$	−6.78651	+	11.7546i	−0.225591	+	0.390735i
$906$		0			0
$907$	3.29404	+	5.70544i	0.109377	+	0.189446i	0.915518	−	0.402277i	$-0.131781\pi$
$907$	3.29404	+	5.70544i	0.109377	+	0.189446i	−0.806141	+	0.591723i	$0.798448\pi$
$908$		0			0
$909$	−7.94618	−	11.5159i	−0.263558	−	0.381959i
$910$		0			0
$911$	11.8855	+	20.5863i	0.393785	+	0.682056i	0.992945	−	0.118573i	$-0.0378321\pi$
$911$	11.8855	+	20.5863i	0.393785	+	0.682056i	−0.599160	+	0.800629i	$0.704499\pi$
$912$		0			0
$913$	13.8688	−	24.0215i	0.458991	−	0.794996i
$914$		0			0
$915$	−1.02523	+	0.0412339i	−0.0338930	+	0.00136315i
$916$		0			0
$917$	−6.56477			−0.216788
$918$		0			0
$919$	46.1305			1.52171			0.760853	−	0.648924i	$-0.224781\pi$
$919$	46.1305			1.52171			0.760853	+	0.648924i	$0.224781\pi$
$920$		0			0
$921$	−3.54946	+	0.142757i	−0.116959	+	0.00470399i
$922$		0			0
$923$	−31.3452	+	54.2914i	−1.03174	+	1.78702i
$924$		0			0
$925$	−3.82220	−	6.62025i	−0.125673	−	0.217673i
$926$		0			0
$927$	5.35883	−	11.2889i	0.176007	−	0.370775i
$928$		0			0
$929$	−11.3082	−	19.5864i	−0.371010	−	0.642608i	0.618711	−	0.785619i	$-0.287655\pi$
$929$	−11.3082	−	19.5864i	−0.371010	−	0.642608i	−0.989721	+	0.143010i	$0.954322\pi$
$930$		0			0
$931$	−26.0217	+	45.0709i	−0.852826	+	1.47714i
$932$		0			0
$933$	−15.9365	+	30.3587i	−0.521739	+	0.993899i
$934$		0			0
$935$	−13.5375			−0.442723
$936$		0			0
$937$	−47.5830			−1.55447			−0.777235	−	0.629211i	$-0.783378\pi$
$937$	−47.5830			−1.55447			−0.777235	+	0.629211i	$0.783378\pi$
$938$		0			0
$939$	−0.106950	−	0.169157i	−0.00349017	−	0.00552023i
$940$		0			0
$941$	21.4991	−	37.2375i	0.700850	−	1.21391i	−0.267319	−	0.963608i	$-0.586138\pi$
$941$	21.4991	−	37.2375i	0.700850	−	1.21391i	0.968169	−	0.250299i	$-0.0805290\pi$
$942$		0			0
$943$	−4.58594	−	7.94308i	−0.149339	−	0.258662i
$944$		0			0
$945$	1.71205	−	0.207467i	0.0556930	−	0.00674891i
$946$		0			0
$947$	24.0274	+	41.6167i	0.780786	+	1.35236i	0.931484	+	0.363781i	$0.118514\pi$
$947$	24.0274	+	41.6167i	0.780786	+	1.35236i	−0.150698	+	0.988580i	$0.548152\pi$
$948$		0			0
$949$	28.1040	−	48.6776i	0.912295	−	1.58014i
$950$		0			0
$951$	22.0176	+	34.8241i	0.713969	+	1.12925i
$952$		0			0
$953$	−39.0413			−1.26467			−0.632335	−	0.774695i	$-0.717904\pi$
$953$	−39.0413			−1.26467			−0.632335	+	0.774695i	$0.717904\pi$
$954$		0			0
$955$	−10.2694			−0.332311
$956$		0			0
$957$	12.6782	−	24.1517i	0.409828	−	0.780712i
$958$		0			0
$959$	3.07571	−	5.32729i	0.0993199	−	0.172027i
$960$		0			0
$961$	−0.429681	−	0.744229i	−0.0138607	−	0.0240074i
$962$		0			0
$963$	−19.6586	+	1.58387i	−0.633489	+	0.0510394i
$964$		0			0
$965$	−4.53570	−	7.85606i	−0.146009	−	0.252895i
$966$		0			0
$967$	1.02423	−	1.77402i	0.0329371	−	0.0570488i	−0.849087	−	0.528253i	$-0.822847\pi$
$967$	1.02423	−	1.77402i	0.0329371	−	0.0570488i	0.882024	+	0.471204i	$0.156181\pi$
$968$		0			0
$969$	−40.1515	+	1.61486i	−1.28985	+	0.0518768i
$970$		0			0
$971$	27.4068			0.879527			0.439764	−	0.898114i	$-0.355062\pi$
$971$	27.4068			0.879527			0.439764	+	0.898114i	$0.355062\pi$
$972$		0			0
$973$	−1.78546			−0.0572392
$974$		0			0
$975$	−12.0810	+	0.485889i	−0.386902	+	0.0155609i
$976$		0			0
$977$	2.04914	−	3.54922i	0.0655578	−	0.113549i	−0.831383	−	0.555699i	$-0.812451\pi$
$977$	2.04914	−	3.54922i	0.0655578	−	0.113549i	0.896941	+	0.442150i	$0.145784\pi$
$978$		0			0
$979$	−26.2384	−	45.4463i	−0.838584	−	1.45247i
$980$		0			0
$981$	2.22424	−	0.179204i	0.0710145	−	0.00572155i
$982$		0			0
$983$	3.05903	+	5.29840i	0.0975680	+	0.168993i	0.910677	−	0.413118i	$-0.135560\pi$
$983$	3.05903	+	5.29840i	0.0975680	+	0.168993i	−0.813109	+	0.582111i	$0.802227\pi$
$984$		0			0
$985$	2.40329	−	4.16262i	0.0765752	−	0.132632i
$986$		0			0
$987$	−2.13119	+	4.05987i	−0.0678366	+	0.129227i
$988$		0			0
$989$	−11.7958			−0.375086
$990$		0			0
$991$	14.9881			0.476114			0.238057	−	0.971251i	$-0.423490\pi$
$991$	14.9881			0.476114			0.238057	+	0.971251i	$0.423490\pi$
$992$		0			0
$993$	32.0491	+	50.6905i	1.01705	+	1.60862i
$994$		0			0
$995$	9.22981	−	15.9865i	0.292605	−	0.506806i
$996$		0			0
$997$	6.74813	+	11.6881i	0.213715	+	0.370166i	0.952874	−	0.303365i	$-0.0981101\pi$
$997$	6.74813	+	11.6881i	0.213715	+	0.370166i	−0.739159	+	0.673531i	$0.764777\pi$
$998$		0			0
$999$	−39.4330	+	4.77852i	−1.24761	+	0.151186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.q.e.121.1	✓	8
3.2	odd	2		1080.2.q.e.361.3		8
4.3	odd	2		720.2.q.l.481.4		8
9.2	odd	6		1080.2.q.e.721.3		8
9.4	even	3		3240.2.a.u.1.2		4
9.5	odd	6		3240.2.a.s.1.2		4
9.7	even	3	inner	360.2.q.e.241.1	yes	8
12.11	even	2		2160.2.q.l.1441.2		8
36.7	odd	6		720.2.q.l.241.4		8
36.11	even	6		2160.2.q.l.721.2		8
36.23	even	6		6480.2.a.bz.1.3		4
36.31	odd	6		6480.2.a.cb.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.e.121.1	✓	8	1.1	even	1	trivial
360.2.q.e.241.1	yes	8	9.7	even	3	inner
720.2.q.l.241.4		8	36.7	odd	6
720.2.q.l.481.4		8	4.3	odd	2
1080.2.q.e.361.3		8	3.2	odd	2
1080.2.q.e.721.3		8	9.2	odd	6
2160.2.q.l.721.2		8	36.11	even	6
2160.2.q.l.1441.2		8	12.11	even	2
3240.2.a.s.1.2		4	9.5	odd	6
3240.2.a.u.1.2		4	9.4	even	3
6480.2.a.bz.1.3		4	36.23	even	6
6480.2.a.cb.1.3		4	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73065 + 0.0696054i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.165947 + 0.287429i) q^{7} +(2.99031 - 0.240925i) q^{9} +O(q^{10})\)	\(q+(-1.73065 + 0.0696054i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.165947 + 0.287429i) q^{7} +(2.99031 - 0.240925i) q^{9} +(-2.20380 - 3.81710i) q^{11} +(-3.49031 + 6.04539i) q^{13} +(0.805046 - 1.53359i) q^{15} -3.07139 q^{17} -7.55364 q^{19} +(-0.307204 - 0.485889i) q^{21} +(-0.834053 + 1.44462i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.15842 + 0.625100i) q^{27} +(-1.78651 - 3.09432i) q^{29} +(-2.82220 + 4.88820i) q^{31} +(4.07971 + 6.45267i) q^{33} -0.331895 q^{35} +7.64441 q^{37} +(5.61972 - 10.7054i) q^{39} +(-2.74919 + 4.76174i) q^{41} +(3.53570 + 6.12401i) q^{43} +(-1.28651 + 2.71015i) q^{45} +(-3.98815 - 6.90768i) q^{47} +(3.44492 - 5.96678i) q^{49} +(5.31551 - 0.213786i) q^{51} -5.47900 q^{53} +4.40761 q^{55} +(13.0727 - 0.525774i) q^{57} +(3.69411 - 6.39839i) q^{59} +(-0.296197 - 0.513029i) q^{61} +(0.565483 + 0.819522i) q^{63} +(-3.49031 - 6.04539i) q^{65} +(-2.61087 + 4.52216i) q^{67} +(1.34290 - 2.55819i) q^{69} +8.98062 q^{71} -8.05202 q^{73} +(0.925606 + 1.46399i) q^{75} +(0.731430 - 1.26687i) q^{77} +(5.49838 + 9.52347i) q^{79} +(8.88391 - 1.44088i) q^{81} +(3.14657 + 5.45002i) q^{83} +(1.53570 - 2.65991i) q^{85} +(3.30720 + 5.23084i) q^{87} +11.9060 q^{89} -2.31683 q^{91} +(4.54401 - 8.65622i) q^{93} +(3.77682 - 6.54164i) q^{95} +(0.622718 + 1.07858i) q^{97} +(-7.50969 - 10.8834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + q^7	\( 8 q - 4 q^{5} + q^{7} - q^{11} - 4 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{19} - 7 q^{23} - 4 q^{25} - 18 q^{27} - 7 q^{29} + 2 q^{31} - 3 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} - 12 q^{41} + 11 q^{43} - 3 q^{45} - 7 q^{47} - 3 q^{49} + 39 q^{51} + 24 q^{53} + 2 q^{55} + 27 q^{57} - 11 q^{59} - 19 q^{61} - 33 q^{63} - 4 q^{65} + 10 q^{67} - 9 q^{69} + 24 q^{71} + 18 q^{73} - 3 q^{75} - 32 q^{77} + 24 q^{79} - 12 q^{81} - 23 q^{83} - 5 q^{85} + 24 q^{87} + 42 q^{89} + 28 q^{91} + 18 q^{93} - q^{95} - q^{97} - 84 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 + q^7 - q^11 - 4 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^19 - 7 * q^23 - 4 * q^25 - 18 * q^27 - 7 * q^29 + 2 * q^31 - 3 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 - 12 * q^41 + 11 * q^43 - 3 * q^45 - 7 * q^47 - 3 * q^49 + 39 * q^51 + 24 * q^53 + 2 * q^55 + 27 * q^57 - 11 * q^59 - 19 * q^61 - 33 * q^63 - 4 * q^65 + 10 * q^67 - 9 * q^69 + 24 * q^71 + 18 * q^73 - 3 * q^75 - 32 * q^77 + 24 * q^79 - 12 * q^81 - 23 * q^83 - 5 * q^85 + 24 * q^87 + 42 * q^89 + 28 * q^91 + 18 * q^93 - q^95 - q^97 - 84 * q^99

Introduction

L-functions

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