LMFDB - Embedded newform 930.2.br.b.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(1.39578 + 1.02558i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.64438 - 0.544062i) q^{6} +(0.359918 + 3.42439i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.896389 + 2.86295i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(1.39578 + 1.02558i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.64438 - 0.544062i) q^{6} +(0.359918 + 3.42439i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.896389 + 2.86295i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-4.28029 - 1.90571i) q^{11} +(1.73203 + 0.00929082i) q^{12} +(0.215242 + 1.01263i) q^{13} +(-1.40050 - 3.14556i) q^{14} +(-1.72157 - 0.190286i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.82371 + 2.14765i) q^{17} +(-1.73722 - 2.44583i) q^{18} +(1.67953 + 0.356996i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-3.00960 + 5.14880i) q^{21} +(4.65969 + 0.489754i) q^{22} +(0.800242 + 0.581410i) q^{23} +(-1.65013 + 0.526389i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.517629 - 0.896559i) q^{26} +(-1.68501 + 4.91536i) q^{27} +(2.30398 + 2.55883i) q^{28} +(-2.44496 - 7.52482i) q^{29} +(1.69611 - 0.351021i) q^{30} +(-5.07797 - 2.28347i) q^{31} +1.00000i q^{32} +(-4.01989 - 7.04971i) q^{33} +(3.92396 - 3.53315i) q^{34} +(-2.02389 - 2.78565i) q^{35} +(2.40799 + 1.78929i) q^{36} +(-2.37140 - 1.36913i) q^{37} +(-1.70765 + 0.179481i) q^{38} +(-0.738103 + 1.63416i) q^{39} +(0.104528 - 0.994522i) q^{40} +(5.93336 + 5.34242i) q^{41} +(1.27123 - 5.82682i) q^{42} +(0.0691375 - 0.325266i) q^{43} +(-4.58298 + 0.974141i) q^{44} +(-2.20777 - 2.03119i) q^{45} +(-0.940741 - 0.305665i) q^{46} +(5.39065 + 1.75153i) q^{47} +(1.40670 - 1.01054i) q^{48} +(-4.74985 + 1.00961i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-8.93540 - 1.94943i) q^{51} +(0.769346 + 0.692722i) q^{52} +(-1.22235 + 11.6299i) q^{53} +(0.0836141 - 5.19548i) q^{54} +(4.65969 - 0.489754i) q^{55} +(-2.98194 - 1.72162i) q^{56} +(1.97813 + 2.22077i) q^{57} +(4.65060 + 6.40099i) q^{58} +(-2.64517 + 2.38172i) q^{59} +(-1.50462 + 0.857967i) q^{60} +1.89691i q^{61} +(5.53507 + 0.602535i) q^{62} +(-9.48122 + 4.10001i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.692722 - 0.769346i) q^{65} +(6.00162 + 5.46246i) q^{66} +(1.43290 + 2.48185i) q^{67} +(-2.64010 + 4.57279i) q^{68} +(0.520680 + 1.63223i) q^{69} +(2.78565 + 2.02389i) q^{70} +(-10.5085 - 1.10449i) q^{71} +(-2.84306 - 0.957606i) q^{72} +(1.87339 - 4.20771i) q^{73} +(2.67842 + 0.569316i) q^{74} +(1.58606 - 0.695991i) q^{75} +(1.56861 - 0.698389i) q^{76} +(4.98533 - 15.3433i) q^{77} +(0.196995 - 1.78226i) q^{78} +(4.71772 + 10.5962i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-7.39297 + 5.13263i) q^{81} +(-7.29386 - 3.24744i) q^{82} +(4.44010 - 4.93123i) q^{83} +(0.591571 + 5.93447i) q^{84} +(3.10363 - 4.27177i) q^{85} +(0.0347592 + 0.330711i) q^{86} +(4.30465 - 13.0105i) q^{87} +(4.05764 - 2.34268i) q^{88} +(7.36112 - 5.34817i) q^{89} +(2.72739 + 1.24954i) q^{90} +(-3.39018 + 1.10154i) q^{91} +0.989153 q^{92} +(-4.74584 - 8.39506i) q^{93} -5.66807 q^{94} +(-1.63302 + 0.530599i) q^{95} +(-1.02558 + 1.39578i) q^{96} +(4.67822 - 3.39893i) q^{97} +(4.20539 - 2.42798i) q^{98} +(1.61914 - 13.9625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	1.39578	+	1.02558i	0.805852	+	0.592116i
$3$	1.39578	+	1.02558i	0.805852	+	0.592116i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.64438	−	0.544062i	−0.671317	−	0.222112i
$7$	0.359918	+	3.42439i	0.136036	+	1.29430i	0.823182	+	0.567777i	$0.192197\pi$
$7$	0.359918	+	3.42439i	0.136036	+	1.29430i	−0.687146	+	0.726519i	$0.741137\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.896389	+	2.86295i	0.298796	+	0.954317i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−4.28029	−	1.90571i	−1.29056	−	0.574593i	−0.357362	−	0.933966i	$-0.616324\pi$
$11$	−4.28029	−	1.90571i	−1.29056	−	0.574593i	−0.933194	+	0.359373i	$0.882991\pi$
$12$	1.73203	+	0.00929082i	0.499993	+	0.00268203i
$13$	0.215242	+	1.01263i	0.0596974	+	0.280854i	0.997864	−	0.0653308i	$-0.0208103\pi$
$13$	0.215242	+	1.01263i	0.0596974	+	0.280854i	−0.938166	+	0.346185i	$0.887477\pi$
$14$	−1.40050	−	3.14556i	−0.374298	−	0.840688i
$15$	−1.72157	−	0.190286i	−0.444507	−	0.0491316i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.82371	+	2.14765i	−1.16992	+	0.520882i	−0.897378	−	0.441262i	$-0.854531\pi$
$17$	−4.82371	+	2.14765i	−1.16992	+	0.520882i	−0.272542	+	0.962144i	$0.587864\pi$
$18$	−1.73722	−	2.44583i	−0.409466	−	0.576487i
$19$	1.67953	+	0.356996i	0.385311	+	0.0819004i	0.396495	−	0.918037i	$-0.370227\pi$
$19$	1.67953	+	0.356996i	0.385311	+	0.0819004i	−0.0111835	+	0.999937i	$0.503560\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	−3.00960	+	5.14880i	−0.656749	+	1.12356i
$22$	4.65969	+	0.489754i	0.993450	+	0.104416i
$23$	0.800242	+	0.581410i	0.166862	+	0.121232i	0.668082	−	0.744087i	$-0.267115\pi$
$23$	0.800242	+	0.581410i	0.166862	+	0.121232i	−0.501220	+	0.865320i	$0.667115\pi$
$24$	−1.65013	+	0.526389i	−0.336830	+	0.107449i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.517629	−	0.896559i	−0.101515	−	0.175830i
$27$	−1.68501	+	4.91536i	−0.324281	+	0.945961i
$28$	2.30398	+	2.55883i	0.435412	+	0.483574i
$29$	−2.44496	−	7.52482i	−0.454018	−	1.39732i	−0.872284	−	0.489000i	$-0.837362\pi$
$29$	−2.44496	−	7.52482i	−0.454018	−	1.39732i	0.418266	−	0.908325i	$-0.362638\pi$
$30$	1.69611	−	0.351021i	0.309666	−	0.0640873i
$31$	−5.07797	−	2.28347i	−0.912030	−	0.410124i
$31$	−5.07797	−	2.28347i	−0.912030	−	0.410124i
$32$			1.00000i			0.176777i
$33$	−4.01989	−	7.04971i	−0.699772	−	1.22720i
$34$	3.92396	−	3.53315i	0.672953	−	0.605929i
$35$	−2.02389	−	2.78565i	−0.342100	−	0.470860i
$36$	2.40799	+	1.78929i	0.401332	+	0.298215i
$37$	−2.37140	−	1.36913i	−0.389856	−	0.225083i	0.292242	−	0.956344i	$-0.405599\pi$
$37$	−2.37140	−	1.36913i	−0.389856	−	0.225083i	−0.682098	+	0.731261i	$0.738932\pi$
$38$	−1.70765	+	0.179481i	−0.277017	+	0.0291157i
$39$	−0.738103	+	1.63416i	−0.118191	+	0.261675i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	5.93336	+	5.34242i	0.926635	+	0.834346i	0.986483	−	0.163861i	$-0.0523950\pi$
$41$	5.93336	+	5.34242i	0.926635	+	0.834346i	−0.0598481	+	0.998207i	$0.519062\pi$
$42$	1.27123	−	5.82682i	0.196156	−	0.899098i
$43$	0.0691375	−	0.325266i	0.0105434	−	0.0496027i	−0.972561	−	0.232646i	$-0.925262\pi$
$43$	0.0691375	−	0.325266i	0.0105434	−	0.0496027i	0.983105	+	0.183044i	$0.0585949\pi$
$44$	−4.58298	+	0.974141i	−0.690910	+	0.146857i
$45$	−2.20777	−	2.03119i	−0.329115	−	0.302792i
$46$	−0.940741	−	0.305665i	−0.138705	−	0.0450679i
$47$	5.39065	+	1.75153i	0.786308	+	0.255487i	0.674531	−	0.738247i	$-0.264346\pi$
$47$	5.39065	+	1.75153i	0.786308	+	0.255487i	0.111777	+	0.993733i	$0.464346\pi$
$48$	1.40670	−	1.01054i	0.203040	−	0.145859i
$49$	−4.74985	+	1.00961i	−0.678550	+	0.144230i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	−8.93540	−	1.94943i	−1.25121	−	0.272975i
$52$	0.769346	+	0.692722i	0.106689	+	0.0960633i
$53$	−1.22235	+	11.6299i	−0.167903	+	1.59749i	0.508567	+	0.861023i	$0.330176\pi$
$53$	−1.22235	+	11.6299i	−0.167903	+	1.59749i	−0.676470	+	0.736470i	$0.736491\pi$
$54$	0.0836141	−	5.19548i	0.0113784	−	0.707015i
$55$	4.65969	−	0.489754i	0.628313	−	0.0660384i
$56$	−2.98194	−	1.72162i	−0.398479	−	0.230062i
$57$	1.97813	+	2.22077i	0.262009	+	0.294149i
$58$	4.65060	+	6.40099i	0.610653	+	0.840492i
$59$	−2.64517	+	2.38172i	−0.344372	+	0.310074i	−0.823108	−	0.567885i	$-0.807762\pi$
$59$	−2.64517	+	2.38172i	−0.344372	+	0.310074i	0.478736	+	0.877959i	$0.341095\pi$
$60$	−1.50462	+	0.857967i	−0.194246	+	0.110763i
$61$			1.89691i			0.242875i	0.992599	+	0.121437i	$0.0387504\pi$
$61$			1.89691i			0.242875i	−0.992599	+	0.121437i	$0.961250\pi$
$62$	5.53507	+	0.602535i	0.702954	+	0.0765220i
$63$	−9.48122	+	4.10001i	−1.19452	+	0.516553i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−0.692722	−	0.769346i	−0.0859216	−	0.0954256i
$66$	6.00162	+	5.46246i	0.738748	+	0.672382i
$67$	1.43290	+	2.48185i	0.175056	+	0.303206i	0.940181	−	0.340676i	$-0.110656\pi$
$67$	1.43290	+	2.48185i	0.175056	+	0.303206i	−0.765125	+	0.643882i	$0.777323\pi$
$68$	−2.64010	+	4.57279i	−0.320159	+	0.554532i
$69$	0.520680	+	1.63223i	0.0626825	+	0.196497i
$70$	2.78565	+	2.02389i	0.332949	+	0.241901i
$71$	−10.5085	−	1.10449i	−1.24713	−	0.131079i	−0.542137	−	0.840290i	$-0.682385\pi$
$71$	−10.5085	−	1.10449i	−1.24713	−	0.131079i	−0.704997	+	0.709211i	$0.749051\pi$
$72$	−2.84306	−	0.957606i	−0.335058	−	0.112855i
$73$	1.87339	−	4.20771i	0.219264	−	0.492476i	−0.770102	−	0.637921i	$-0.779795\pi$
$73$	1.87339	−	4.20771i	0.219264	−	0.492476i	0.989366	+	0.145445i	$0.0464614\pi$
$74$	2.67842	+	0.569316i	0.311360	+	0.0661816i
$75$	1.58606	−	0.695991i	0.183143	−	0.0803661i
$76$	1.56861	−	0.698389i	0.179932	−	0.0801107i
$77$	4.98533	−	15.3433i	0.568131	−	1.74853i
$78$	0.196995	−	1.78226i	0.0223053	−	0.201802i
$79$	4.71772	+	10.5962i	0.530785	+	1.19216i	0.957673	+	0.287859i	$0.0929433\pi$
$79$	4.71772	+	10.5962i	0.530785	+	1.19216i	−0.426888	+	0.904305i	$0.640390\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−7.39297	+	5.13263i	−0.821442	+	0.570293i
$82$	−7.29386	−	3.24744i	−0.805472	−	0.358619i
$83$	4.44010	−	4.93123i	0.487364	−	0.541273i	−0.448431	−	0.893818i	$-0.648017\pi$
$83$	4.44010	−	4.93123i	0.487364	−	0.541273i	0.935795	+	0.352545i	$0.114684\pi$
$84$	0.591571	+	5.93447i	0.0645457	+	0.647504i
$85$	3.10363	−	4.27177i	0.336635	−	0.463339i
$86$	0.0347592	+	0.330711i	0.00374818	+	0.0356615i
$87$	4.30465	−	13.0105i	0.461507	−	1.39487i
$88$	4.05764	−	2.34268i	0.432546	−	0.249731i
$89$	7.36112	−	5.34817i	0.780277	−	0.566905i	−0.124785	−	0.992184i	$-0.539824\pi$
$89$	7.36112	−	5.34817i	0.780277	−	0.566905i	0.905062	+	0.425279i	$0.139824\pi$
$90$	2.72739	+	1.24954i	0.287492	+	0.131713i
$91$	−3.39018	+	1.10154i	−0.355388	+	0.115472i
$92$	0.989153			0.103126
$93$	−4.74584	−	8.39506i	−0.492120	−	0.870527i
$94$	−5.66807			−0.584617
$95$	−1.63302	+	0.530599i	−0.167544	+	0.0544383i
$96$	−1.02558	+	1.39578i	−0.104672	+	0.142456i
$97$	4.67822	−	3.39893i	0.475002	−	0.345109i	−0.324386	−	0.945925i	$-0.605158\pi$
$97$	4.67822	−	3.39893i	0.475002	−	0.345109i	0.799387	+	0.600816i	$0.205158\pi$
$98$	4.20539	−	2.42798i	0.424808	−	0.245263i
$99$	1.61914	−	13.9625i	0.162730	−	1.40329i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−3.43741	+	4.73119i	−0.342035	+	0.470771i	−0.945035	−	0.326970i	$-0.893972\pi$
$101$	−3.43741	+	4.73119i	−0.342035	+	0.470771i	0.602999	+	0.797742i	$0.293972\pi$
$102$	9.10048	−	0.907171i	0.901081	−	0.0898233i
$103$	−7.90146	+	8.77546i	−0.778554	+	0.864672i	−0.993719	−	0.111906i	$-0.964304\pi$
$103$	−7.90146	+	8.77546i	−0.778554	+	0.864672i	0.215165	+	0.976578i	$0.430971\pi$
$104$	−0.945754	−	0.421077i	−0.0927389	−	0.0412900i
$105$	0.0319906	−	5.96380i	0.00312196	−	0.582007i
$106$	−2.43132	−	11.4384i	−0.236150	−	1.11100i
$107$	−2.20513	−	4.95281i	−0.213178	−	0.478806i	0.775030	−	0.631925i	$-0.217735\pi$
$107$	−2.20513	−	4.95281i	−0.213178	−	0.478806i	−0.988208	+	0.153119i	$0.951068\pi$
$108$	1.52597	+	4.96703i	0.146837	+	0.477953i
$109$	−4.35524	+	13.4040i	−0.417156	+	1.28387i	0.493152	+	0.869943i	$0.335845\pi$
$109$	−4.35524	+	13.4040i	−0.417156	+	1.28387i	−0.910308	+	0.413931i	$0.864155\pi$
$110$	−4.28029	+	1.90571i	−0.408110	+	0.181702i
$111$	−1.90580	−	4.34305i	−0.180891	−	0.412224i
$112$	3.36801	+	0.715892i	0.318247	+	0.0676454i
$113$	−7.92369	+	17.7969i	−0.745398	+	1.67419i	−0.00686304	+	0.999976i	$0.502185\pi$
$113$	−7.92369	+	17.7969i	−0.745398	+	1.67419i	−0.738535	+	0.674215i	$0.764482\pi$
$114$	−2.56757	−	1.50081i	−0.240475	−	0.140563i
$115$	−0.983734	−	0.103395i	−0.0917337	−	0.00964160i
$116$	−6.40099	−	4.65060i	−0.594317	−	0.431797i
$117$	−2.70618	+	1.52394i	−0.250187	+	0.140888i
$118$	1.77971	−	3.08255i	0.163836	−	0.283772i
$119$	−9.09053	−	15.7453i	−0.833327	−	1.44337i
$120$	1.16586	−	1.28093i	0.106428	−	0.116932i
$121$	7.32873	+	8.13938i	0.666248	+	0.739944i
$122$	−0.586179	−	1.80407i	−0.0530701	−	0.163333i
$123$	2.80259	+	13.5419i	0.252701	+	1.22104i
$124$	−5.45035	+	1.13738i	−0.489456	+	0.102140i
$125$			1.00000i			0.0894427i
$126$	7.75021	−	6.82920i	0.690443	−	0.608393i
$127$	2.94752	−	2.65396i	0.261550	−	0.235501i	−0.527914	−	0.849298i	$-0.677026\pi$
$127$	2.94752	−	2.65396i	0.261550	−	0.235501i	0.789463	+	0.613798i	$0.210359\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	0.430086	−	0.383094i	0.0378670	−	0.0337295i
$130$	0.896559	+	0.517629i	0.0786334	+	0.0453990i
$131$	−18.0248	+	1.89449i	−1.57484	+	0.165522i	−0.851268	−	0.524731i	$-0.824166\pi$
$131$	−18.0248	+	1.89449i	−1.57484	+	0.165522i	−0.723568	+	0.690253i	$0.757499\pi$
$132$	−7.39587	−	3.34050i	−0.643728	−	0.290754i
$133$	−0.617998	+	5.87986i	−0.0535872	+	0.509848i
$134$	−2.12970	−	1.91759i	−0.183978	−	0.165654i
$135$	−0.998414	−	5.09933i	−0.0859298	−	0.438880i
$136$	1.09782	−	5.16482i	0.0941369	−	0.442880i
$137$	15.4826	−	3.29093i	1.32277	−	0.281163i	0.508204	−	0.861236i	$-0.330309\pi$
$137$	15.4826	−	3.29093i	1.32277	−	0.281163i	0.814564	+	0.580073i	$0.196976\pi$
$138$	−0.999582	−	1.39144i	−0.0850900	−	0.118447i
$139$	−15.2529	−	4.95597i	−1.29373	−	0.420360i	−0.420337	−	0.907368i	$-0.638088\pi$
$139$	−15.2529	−	4.95597i	−1.29373	−	0.420360i	−0.873397	+	0.487008i	$0.838088\pi$
$140$	−3.27472	−	1.06402i	−0.276765	−	0.0899263i
$141$	5.72783	+	7.97327i	0.482370	+	0.671470i
$142$	10.3355	−	2.19688i	0.867338	−	0.184358i
$143$	1.00849	−	4.74456i	0.0843339	−	0.396760i
$144$	2.99983	+	0.0321839i	0.249986	+	0.00268199i
$145$	5.87981	+	5.29420i	0.488292	+	0.439660i
$146$	−0.481449	+	4.58068i	−0.0398450	+	0.379100i
$147$	−7.66517	−	3.46214i	−0.632212	−	0.285552i
$148$	−2.72326	+	0.286226i	−0.223850	+	0.0235276i
$149$	20.4618	+	11.8136i	1.67630	+	0.967811i	0.963988	+	0.265947i	$0.0856846\pi$
$149$	20.4618	+	11.8136i	1.67630	+	0.967811i	0.712311	+	0.701864i	$0.247649\pi$
$150$	−1.29336	+	1.15205i	−0.105603	+	0.0940643i
$151$	10.6937	+	14.7187i	0.870244	+	1.19779i	0.979029	+	0.203723i	$0.0653042\pi$
$151$	10.6937	+	14.7187i	0.870244	+	1.19779i	−0.108784	+	0.994065i	$0.534696\pi$
$152$	−1.27602	+	1.14893i	−0.103499	+	0.0931908i
$153$	−10.4725	−	11.8849i	−0.846655	−	0.960837i
$154$			16.1329i			1.30002i
$155$	5.53939	−	0.561437i	0.444934	−	0.0450957i
$156$	0.363397	+	1.75591i	0.0290950	+	0.140585i
$157$	−7.56247	−	23.2749i	−0.603551	−	1.85754i	−0.506459	−	0.862264i	$-0.669046\pi$
$157$	−7.56247	−	23.2749i	−0.603551	−	1.85754i	−0.0970918	−	0.995275i	$-0.530954\pi$
$158$	−7.76122	−	8.61971i	−0.617450	−	0.685747i
$159$	−13.6335	+	14.9792i	−1.08121	+	1.18793i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−1.70295	+	2.94960i	−0.134211	+	0.232461i
$162$	5.44506	−	7.16598i	0.427805	−	0.563013i
$163$	−1.62740	−	1.18238i	−0.127468	−	0.0926108i	0.522225	−	0.852808i	$-0.325102\pi$
$163$	−1.62740	−	1.18238i	−0.127468	−	0.0926108i	−0.649692	+	0.760197i	$0.725102\pi$
$164$	7.94039	+	0.834568i	0.620040	+	0.0651688i
$165$	7.00618	+	4.09528i	0.545430	+	0.318817i
$166$	−2.69895	+	6.06194i	−0.209479	+	0.470498i
$167$	9.93849	+	2.11249i	0.769064	+	0.163469i	0.575704	−	0.817658i	$-0.304728\pi$
$167$	9.93849	+	2.11249i	0.769064	+	0.163469i	0.193360	+	0.981128i	$0.438062\pi$
$168$	−2.39647	−	5.46121i	−0.184892	−	0.421342i
$169$	10.8970	−	4.85165i	0.838230	−	0.373204i
$170$	−1.63167	+	5.02177i	−0.125144	+	0.385152i
$171$	0.483453	+	5.12842i	0.0369706	+	0.392180i
$172$	−0.135253	−	0.303784i	−0.0103130	−	0.0231633i
$173$	3.78907	+	17.8262i	0.288078	+	1.35530i	0.849421	+	0.527716i	$0.176951\pi$
$173$	3.78907	+	17.8262i	0.288078	+	1.35530i	−0.561343	+	0.827583i	$0.689715\pi$
$174$	−0.0735095	+	13.7039i	−0.00557274	+	1.03889i
$175$	3.14556	+	1.40050i	0.237782	+	0.105868i
$176$	−3.13512	+	3.48190i	−0.236318	+	0.262458i
$177$	−6.13470	+	0.611531i	−0.461112	+	0.0459655i
$178$	−5.34817	+	7.36112i	−0.400862	+	0.551739i
$179$	−1.51299	−	14.3951i	−0.113086	−	1.07594i	−0.893000	−	0.450056i	$-0.851404\pi$
$179$	−1.51299	−	14.3951i	−0.113086	−	1.07594i	0.779914	−	0.625886i	$-0.215263\pi$
$180$	−2.98003	−	0.345575i	−0.222118	−	0.0257576i
$181$	−6.32634	+	3.65251i	−0.470233	+	0.271489i	−0.716337	−	0.697754i	$-0.754183\pi$
$181$	−6.32634	+	3.65251i	−0.470233	+	0.271489i	0.246104	+	0.969243i	$0.420849\pi$
$182$	2.88386	−	2.09525i	0.213766	−	0.155310i
$183$	−1.94543	+	2.64767i	−0.143810	+	0.195721i
$184$	−0.940741	+	0.305665i	−0.0693523	+	0.0225339i
$185$	2.73826			0.201321
$186$	7.10777	+	6.51763i	0.521167	+	0.477896i
$187$	24.7397			1.80914
$188$	5.39065	−	1.75153i	0.393154	−	0.127743i
$189$	−17.4385	−	4.00101i	−1.26847	−	0.291031i
$190$	1.38913	−	1.00926i	0.100778	−	0.0732193i
$191$	18.7851	−	10.8456i	1.35924	−	0.784758i	0.369719	−	0.929144i	$-0.379454\pi$
$191$	18.7851	−	10.8456i	1.35924	−	0.784758i	0.989522	+	0.144385i	$0.0461205\pi$
$192$	0.544062	−	1.64438i	0.0392643	−	0.118673i
$193$	−0.456525	−	4.34355i	−0.0328614	−	0.312655i	−0.998589	−	0.0530986i	$-0.983090\pi$
$193$	−0.456525	−	4.34355i	−0.0328614	−	0.312655i	0.965728	−	0.259557i	$-0.0835764\pi$
$194$	−3.39893	+	4.67822i	−0.244029	+	0.335877i
$195$	−0.177863	−	1.78427i	−0.0127371	−	0.127775i
$196$	−3.24928	+	3.60869i	−0.232091	+	0.257763i
$197$	13.1523	+	5.85576i	0.937059	+	0.417206i	0.817700	−	0.575645i	$-0.195249\pi$
$197$	13.1523	+	5.85576i	0.937059	+	0.417206i	0.119360	+	0.992851i	$0.461916\pi$
$198$	2.77476	+	13.7795i	0.197193	+	0.979265i
$199$	2.84702	+	13.3942i	0.201820	+	0.949489i	0.956124	+	0.292963i	$0.0946413\pi$
$199$	2.84702	+	13.3942i	0.201820	+	0.949489i	−0.754304	+	0.656526i	$0.772025\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−0.545320	+	4.93365i	−0.0384639	+	0.347993i
$202$	1.80716	−	5.56185i	0.127151	−	0.391331i
$203$	24.8879	−	11.0808i	1.74679	−	0.777721i
$204$	−8.37474	+	3.67497i	−0.586349	+	0.257300i
$205$	−7.80965	−	1.65999i	−0.545450	−	0.115939i
$206$	4.80297	−	10.7876i	0.334639	−	0.751611i
$207$	−0.947219	+	2.81222i	−0.0658363	+	0.195463i
$208$	1.02959	+	0.108214i	0.0713889	+	0.00750328i
$209$	−6.50856	−	4.72874i	−0.450206	−	0.327094i
$210$	1.81249	+	5.68179i	0.125074	+	0.392081i
$211$	−10.6572	+	18.4589i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$211$	−10.6572	+	18.4589i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904471\pi$
$212$	5.84699	+	10.1273i	0.401573	+	0.695545i
$213$	−13.5348	−	12.3189i	−0.927392	−	0.844079i
$214$	3.62771	+	4.02898i	0.247985	+	0.275415i
$215$	0.102758	+	0.316258i	0.00700806	+	0.0215686i
$216$	−2.98618	−	4.25238i	−0.203184	−	0.289338i
$217$	5.99185	−	18.2108i	0.406753	−	1.23623i
$218$		−	14.0938i		−	0.954555i
$219$	6.93017	−	3.95172i	0.468298	−	0.267033i
$220$	3.48190	−	3.13512i	0.234750	−	0.211370i
$221$	−3.21305	−	4.42238i	−0.216133	−	0.297482i
$222$	3.15460	+	3.54156i	0.211723	+	0.237694i
$223$	11.9544	+	6.90186i	0.800524	+	0.462183i	0.843654	−	0.536886i	$-0.180400\pi$
$223$	11.9544	+	6.90186i	0.800524	+	0.462183i	−0.0431301	+	0.999069i	$0.513733\pi$
$224$	−3.42439	+	0.359918i	−0.228801	+	0.0240480i
$225$	2.92758	+	0.655180i	0.195172	+	0.0436786i
$226$	2.03633	−	19.3744i	0.135455	−	1.28877i
$227$	8.47556	+	7.63143i	0.562543	+	0.506516i	0.900623	−	0.434602i	$-0.143111\pi$
$227$	8.47556	+	7.63143i	0.562543	+	0.506516i	−0.338080	+	0.941117i	$0.609777\pi$
$228$	2.90568	+	0.633930i	0.192433	+	0.0419830i
$229$	1.43859	−	6.76801i	0.0950644	−	0.447243i	−0.904711	−	0.426027i	$-0.859913\pi$
$229$	1.43859	−	6.76801i	0.0950644	−	0.447243i	0.999775	−	0.0212160i	$-0.00675376\pi$
$230$	0.967538	−	0.205657i	0.0637976	−	0.0135606i
$231$	22.6941	−	16.3030i	1.49316	−	1.07266i
$232$	7.52482	+	2.44496i	0.494029	+	0.160520i
$233$	8.17971	+	2.65775i	0.535870	+	0.174115i	0.564436	−	0.825477i	$-0.309094\pi$
$233$	8.17971	+	2.65775i	0.535870	+	0.174115i	−0.0285652	+	0.999592i	$0.509094\pi$
$234$	2.10281	−	2.28561i	0.137465	−	0.149415i
$235$	−5.54421	+	1.17846i	−0.361664	+	0.0768741i
$236$	−0.740046	+	3.48164i	−0.0481729	+	0.226636i
$237$	−4.28229	+	19.6283i	−0.278165	+	1.27499i
$238$	13.5112	+	12.1655i	0.875798	+	0.788572i
$239$	−0.732522	+	6.96949i	−0.0473829	+	0.450819i	0.944949	+	0.327217i	$0.106111\pi$
$239$	−0.732522	+	6.96949i	−0.0473829	+	0.450819i	−0.992332	+	0.123601i	$0.960556\pi$
$240$	−0.712966	+	1.57851i	−0.0460218	+	0.101892i
$241$	17.1313	−	1.80057i	1.10352	−	0.115985i	0.464795	−	0.885418i	$-0.346128\pi$
$241$	17.1313	−	1.80057i	1.10352	−	0.115985i	0.638727	+	0.769433i	$0.279461\pi$
$242$	−9.48524	−	5.47631i	−0.609734	−	0.352030i
$243$	−15.5829	−	0.418039i	−0.999640	−	0.0268172i
$244$	1.11498	+	1.53464i	0.0713791	+	0.0982450i
$245$	3.60869	−	3.24928i	0.230550	−	0.207589i
$246$	−6.85011	−	12.0131i	−0.436747	−	0.765928i
$247$			1.77759i			0.113105i
$248$	4.83212	−	2.76597i	0.306840	−	0.175639i
$249$	11.2547	−	2.32924i	0.713240	−	0.147610i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	6.98635	+	7.75912i	0.440974	+	0.489752i	0.922128	−	0.386885i	$-0.126449\pi$
$251$	6.98635	+	7.75912i	0.440974	+	0.489752i	−0.481154	+	0.876636i	$0.659782\pi$
$252$	−5.26055	+	8.88990i	−0.331383	+	0.560011i
$253$	−2.31727	−	4.01363i	−0.145686	−	0.252335i
$254$	−1.98314	+	3.43490i	−0.124433	+	0.215524i
$255$	8.71300	−	2.77944i	0.545629	−	0.174055i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	12.8632	+	1.35198i	0.802385	+	0.0843341i	0.496838	−	0.867843i	$-0.334494\pi$
$257$	12.8632	+	1.35198i	0.802385	+	0.0843341i	0.305547	+	0.952177i	$0.401161\pi$
$258$	−0.290654	+	0.497248i	−0.0180953	+	0.0309573i
$259$	3.83492	−	8.61337i	0.238290	−	0.535209i
$260$	−1.01263	−	0.215242i	−0.0628009	−	0.0133487i
$261$	19.3516	−	13.7450i	1.19783	−	0.850793i
$262$	16.5572	−	7.37174i	1.02291	−	0.455428i
$263$	−1.14851	+	3.53476i	−0.0708204	+	0.217963i	−0.980202	−	0.198000i	$-0.936555\pi$
$263$	−1.14851	+	3.53476i	−0.0708204	+	0.217963i	0.909382	+	0.415963i	$0.136555\pi$
$264$	8.06616	+	0.891558i	0.496438	+	0.0548716i
$265$	−4.75637	−	10.6830i	−0.292182	−	0.656251i
$266$	−1.22922	−	5.78305i	−0.0753686	−	0.354581i
$267$	15.7594	+	0.0845357i	0.964462	+	0.00517350i
$268$	2.61803	+	1.16562i	0.159922	+	0.0712017i
$269$	17.5444	−	19.4850i	1.06970	−	1.18802i	0.0882894	−	0.996095i	$-0.471860\pi$
$269$	17.5444	−	19.4850i	1.06970	−	1.18802i	0.981409	−	0.191926i	$-0.0614734\pi$
$270$	2.52533	+	4.54122i	0.153687	+	0.276370i
$271$	6.01925	−	8.28479i	0.365644	−	0.503265i	−0.586067	−	0.810263i	$-0.699324\pi$
$271$	6.01925	−	8.28479i	0.365644	−	0.503265i	0.951710	+	0.306998i	$0.0993244\pi$
$272$	0.551932	+	5.25128i	0.0334658	+	0.318405i
$273$	−5.86165	−	1.93939i	−0.354763	−	0.117377i
$274$	−13.7079	+	7.91425i	−0.828124	+	0.478117i
$275$	−3.79054	+	2.75399i	−0.228578	+	0.166072i
$276$	1.38064	+	1.01445i	0.0831046	+	0.0610628i
$277$	−5.14297	+	1.67105i	−0.309011	+	0.100404i	−0.459418	−	0.888220i	$-0.651942\pi$
$277$	−5.14297	+	1.67105i	−0.309011	+	0.100404i	0.150406	+	0.988624i	$0.451942\pi$
$278$	16.0379			0.961886
$279$	1.98564	−	16.5848i	0.118877	−	0.992909i
$280$	3.44325			0.205774
$281$	−3.88372	+	1.26190i	−0.231683	+	0.0752785i	−0.422558	−	0.906336i	$-0.638868\pi$
$281$	−3.88372	+	1.26190i	−0.231683	+	0.0752785i	0.190874	+	0.981614i	$0.438868\pi$
$282$	−7.91136	−	5.81303i	−0.471115	−	0.346161i
$283$	8.02626	−	5.83142i	0.477111	−	0.346642i	−0.323095	−	0.946367i	$-0.604723\pi$
$283$	8.02626	−	5.83142i	0.477111	−	0.346642i	0.800206	+	0.599725i	$0.204723\pi$
$284$	−9.15079	+	5.28321i	−0.542999	+	0.313501i
$285$	−2.82349	−	0.934183i	−0.167249	−	0.0553362i
$286$	0.507021	+	4.82398i	0.0299808	+	0.285248i
$287$	−16.1590	+	22.2410i	−0.953836	+	1.31284i
$288$	−2.86295	+	0.896389i	−0.168701	+	0.0528202i
$289$	7.28051	−	8.08582i	0.428265	−	0.475637i
$290$	−7.22803	−	3.21813i	−0.424445	−	0.188975i
$291$	10.0156	+	0.0537251i	0.587126	+	0.00314942i
$292$	−0.957624	−	4.50527i	−0.0560407	−	0.263651i
$293$	−11.0412	−	24.7990i	−0.645036	−	1.44877i	−0.879140	−	0.476563i	$-0.841882\pi$
$293$	−11.0412	−	24.7990i	−0.645036	−	1.44877i	0.234104	−	0.972211i	$-0.424784\pi$
$294$	8.35987	+	0.924022i	0.487557	+	0.0538901i
$295$	1.09992	−	3.38521i	0.0640400	−	0.197095i
$296$	2.50152	−	1.11375i	0.145398	−	0.0647354i
$297$	16.5796	−	17.8280i	0.962045	−	1.03449i
$298$	−23.1110	−	4.91239i	−1.33878	−	0.284567i
$299$	−0.416510	+	0.935496i	−0.0240874	+	0.0541011i
$300$	0.874059	−	1.49533i	0.0504638	−	0.0863331i
$301$	1.13872	+	0.119685i	0.0656348	+	0.00689850i
$302$	−14.7187	−	10.6937i	−0.846964	−	0.615356i
$303$	−9.65006	+	3.07837i	−0.554382	+	0.176847i
$304$	0.858527	−	1.48701i	0.0492399	−	0.0852860i
$305$	−0.948457	−	1.64278i	−0.0543085	−	0.0940650i
$306$	13.6326	+	8.06702i	0.779325	+	0.461161i
$307$	7.69603	+	8.54730i	0.439236	+	0.487820i	0.921595	−	0.388153i	$-0.126887\pi$
$307$	7.69603	+	8.54730i	0.439236	+	0.487820i	−0.482359	+	0.875973i	$0.660220\pi$
$308$	−4.98533	−	15.3433i	−0.284066	−	0.874264i
$309$	−20.0286	+	4.14504i	−1.13939	+	0.235803i
$310$	−5.09477	+	2.24572i	−0.289364	+	0.127548i
$311$			22.0667i			1.25129i	0.780109	+	0.625644i	$0.215164\pi$
$311$			22.0667i			1.25129i	−0.780109	+	0.625644i	$0.784836\pi$
$312$	−0.888216	−	1.55767i	−0.0502853	−	0.0881858i
$313$	3.21364	−	2.89358i	0.181646	−	0.163555i	−0.573292	−	0.819351i	$-0.694334\pi$
$313$	3.21364	−	2.89358i	0.181646	−	0.163555i	0.754938	+	0.655797i	$0.227667\pi$
$314$	14.3847	+	19.7988i	0.811774	+	1.11731i
$315$	6.16098	−	8.29132i	0.347132	−	0.467163i
$316$	10.0450	+	5.79948i	0.565075	+	0.326246i
$317$	18.6915	−	1.96455i	1.04982	−	0.110340i	0.436125	−	0.899886i	$-0.356350\pi$
$317$	18.6915	−	1.96455i	1.04982	−	0.110340i	0.613692	+	0.789546i	$0.289684\pi$
$318$	8.33741	−	18.4590i	0.467539	−	1.03513i
$319$	−3.87496	+	36.8678i	−0.216956	+	2.06420i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	2.00161	−	9.17455i	0.111719	−	0.512073i
$322$	0.708127	−	3.33147i	0.0394624	−	0.185656i
$323$	−8.86827	+	1.88501i	−0.493444	+	0.104885i
$324$	−2.96415	+	8.49787i	−0.164675	+	0.472104i
$325$	0.984588	+	0.319912i	0.0546151	+	0.0177455i
$326$	1.91312	+	0.621611i	0.105958	+	0.0344279i
$327$	−19.8258	+	14.2424i	−1.09637	+	0.787608i
$328$	−7.80965	+	1.65999i	−0.431216	+	0.0916578i
$329$	−4.05772	+	19.0901i	−0.223710	+	1.05247i
$330$	−7.92878	−	1.72982i	−0.436465	−	0.0952233i
$331$	−19.5111	−	17.5679i	−1.07243	−	0.965619i	−0.0729318	−	0.997337i	$-0.523236\pi$
$331$	−19.5111	−	17.5679i	−1.07243	−	0.965619i	−0.999497	+	0.0317179i	$0.989902\pi$
$332$	0.693612	−	6.59927i	0.0380669	−	0.362182i
$333$	1.79405	−	8.01648i	0.0983134	−	0.439300i
$334$	−10.1049	+	1.06206i	−0.552913	+	0.0581135i
$335$	−2.48185	−	1.43290i	−0.135598	−	0.0782874i
$336$	3.96679	+	4.45337i	0.216406	+	0.242951i
$337$	2.77751	+	3.82292i	0.151301	+	0.208248i	0.877939	−	0.478773i	$-0.158918\pi$
$337$	2.77751	+	3.82292i	0.151301	+	0.208248i	−0.726638	+	0.687020i	$0.758918\pi$
$338$	−8.86441	+	7.98155i	−0.482160	+	0.434139i
$339$	−29.3118	+	16.7142i	−1.59200	+	0.907789i
$340$		−	5.28020i		−	0.286359i
$341$	17.3835	+	19.4511i	0.941371	+	1.05333i
$342$	−2.04456	−	4.72803i	−0.110557	−	0.255662i
$343$	2.28130	+	7.02112i	0.123179	+	0.379105i
$344$	0.222508	+	0.247120i	0.0119968	+	0.0133238i
$345$	−1.26704	−	1.15321i	−0.0682149	−	0.0620867i
$346$	−9.11221	−	15.7828i	−0.489875	−	0.848489i
$347$	−6.77714	+	11.7384i	−0.363816	+	0.630148i	−0.988585	−	0.150661i	$-0.951860\pi$
$347$	−6.77714	+	11.7384i	−0.363816	+	0.630148i	0.624769	+	0.780809i	$0.285193\pi$
$348$	−4.16483	−	13.0559i	−0.223258	−	0.699870i
$349$	−9.48771	−	6.89322i	−0.507865	−	0.368986i	0.304148	−	0.952625i	$-0.401628\pi$
$349$	−9.48771	−	6.89322i	−0.507865	−	0.368986i	−0.812013	+	0.583639i	$0.801628\pi$
$350$	−3.42439	−	0.359918i	−0.183041	−	0.0192384i
$351$	−5.34014	−	0.648311i	−0.285036	−	0.0346043i
$352$	1.90571	−	4.28029i	0.101575	−	0.228140i
$353$	−11.6135	−	2.46852i	−0.618122	−	0.131386i	−0.111801	−	0.993731i	$-0.535662\pi$
$353$	−11.6135	−	2.46852i	−0.618122	−	0.131386i	−0.506322	+	0.862345i	$0.668995\pi$
$354$	5.64547	−	2.47733i	0.300054	−	0.131668i
$355$	9.65291	−	4.29775i	0.512323	−	0.228101i
$356$	2.81170	−	8.65352i	0.149020	−	0.458635i
$357$	3.45960	−	31.2999i	0.183101	−	1.65657i
$358$	5.88728	+	13.2230i	0.311152	+	0.698860i
$359$	6.77162	+	31.8579i	0.357392	+	1.68140i	0.678694	+	0.734421i	$0.262546\pi$
$359$	6.77162	+	31.8579i	0.357392	+	1.68140i	−0.321302	+	0.946977i	$0.604120\pi$
$360$	2.94097	−	0.592219i	0.155002	−	0.0312127i
$361$	−14.6640	−	6.52883i	−0.771789	−	0.343622i
$362$	4.88801	−	5.42869i	0.256908	−	0.285326i
$363$	1.88173	+	18.8769i	0.0987650	+	0.990782i
$364$	−2.09525	+	2.88386i	−0.109821	+	0.151155i
$365$	0.481449	+	4.58068i	0.0252002	+	0.239764i
$366$	1.03204	−	3.11925i	0.0539455	−	0.163046i
$367$	−8.93281	+	5.15736i	−0.466289	+	0.269212i	−0.714685	−	0.699447i	$-0.753430\pi$
$367$	−8.93281	+	5.15736i	−0.466289	+	0.269212i	0.248396	+	0.968659i	$0.420097\pi$
$368$	0.800242	−	0.581410i	0.0417155	−	0.0303081i
$369$	−9.97649	+	21.7758i	−0.519355	+	1.13360i
$370$	−2.60424	+	0.846169i	−0.135388	+	0.0439902i
$371$	−40.2653			−2.09047
$372$	−8.77395	−	4.00221i	−0.454908	−	0.207505i
$373$	22.2339			1.15123			0.575614	−	0.817721i	$-0.304763\pi$
$373$	22.2339			1.15123			0.575614	+	0.817721i	$0.304763\pi$
$374$	−23.5288	+	7.64498i	−1.21665	+	0.395312i
$375$	−1.02558	+	1.39578i	−0.0529605	+	0.0720776i
$376$	−4.58556	+	3.33161i	−0.236482	+	0.171815i
$377$	7.09363	−	4.09551i	0.365341	−	0.210930i
$378$	17.8214	−	1.58362i	0.916635	−	0.0814525i
$379$	−0.936045	−	8.90587i	−0.0480814	−	0.457464i	−0.991902	−	0.127006i	$-0.959463\pi$
$379$	−0.936045	−	8.90587i	−0.0480814	−	0.457464i	0.943821	−	0.330458i	$-0.107203\pi$
$380$	−1.00926	+	1.38913i	−0.0517739	+	0.0712606i
$381$	6.83591	−	0.681430i	0.350214	−	0.0349107i
$382$	−14.5142	+	16.1197i	−0.742611	+	0.824754i
$383$	−3.01959	−	1.34441i	−0.154294	−	0.0686961i	0.328137	−	0.944630i	$-0.393579\pi$
$383$	−3.01959	−	1.34441i	−0.154294	−	0.0686961i	−0.482431	+	0.875934i	$0.660246\pi$
$384$	−0.00929082	+	1.73203i	−0.000474120	+	0.0883871i
$385$	3.35421	+	15.7803i	0.170946	+	0.804240i
$386$	1.77641	+	3.98988i	0.0904169	+	0.203080i
$387$	0.993196	−	0.0936280i	0.0504870	−	0.00475938i
$388$	1.78692	−	5.49958i	0.0907172	−	0.279199i
$389$	26.2835	−	11.7022i	1.33263	−	0.593324i	0.388058	−	0.921635i	$-0.373146\pi$
$389$	26.2835	−	11.7022i	1.33263	−	0.593324i	0.944570	+	0.328310i	$0.106479\pi$
$390$	0.720529	+	1.64198i	0.0364854	+	0.0831451i
$391$	−5.10880	−	1.08591i	−0.258363	−	0.0549167i
$392$	1.97510	−	4.43615i	0.0997576	−	0.224059i
$393$	−27.1016	−	15.8415i	−1.36709	−	0.799100i
$394$	−14.3181	−	1.50489i	−0.721334	−	0.0758152i
$395$	−9.38376	−	6.81770i	−0.472148	−	0.343036i
$396$	−6.89705	−	12.2476i	−0.346590	−	0.615466i
$397$	3.19343	−	5.53119i	0.160274	−	0.277602i	−0.774693	−	0.632337i	$-0.782096\pi$
$397$	3.19343	−	5.53119i	0.160274	−	0.277602i	0.934967	+	0.354735i	$0.115429\pi$
$398$	−6.84671	−	11.8589i	−0.343195	−	0.594430i
$399$	−6.89282	+	7.57317i	−0.345073	+	0.379133i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−8.40212	−	25.8591i	−0.419582	−	1.29134i	−0.908088	−	0.418779i	$-0.862458\pi$
$401$	−8.40212	−	25.8591i	−0.419582	−	1.29134i	0.488506	−	0.872560i	$-0.337542\pi$
$402$	−1.00595	−	4.86069i	−0.0501723	−	0.242429i
$403$	1.21933	−	5.63362i	0.0607393	−	0.280631i
$404$			5.84808i			0.290953i
$405$	3.83619	−	8.14148i	0.190622	−	0.404553i
$406$	−20.2457	+	18.2293i	−1.00477	+	0.904703i
$407$	7.54113	+	10.3795i	0.373800	+	0.514491i
$408$	6.82922	−	6.08304i	0.338097	−	0.301156i
$409$	20.0478	+	11.5746i	0.991300	+	0.572327i	0.905663	−	0.423999i	$-0.139374\pi$
$409$	20.0478	+	11.5746i	0.991300	+	0.572327i	0.0856374	+	0.996326i	$0.472707\pi$
$410$	7.94039	−	0.834568i	0.392148	−	0.0412164i
$411$	24.9854	+	11.2852i	1.23244	+	0.556657i
$412$	−1.23433	+	11.7439i	−0.0608110	+	0.578578i
$413$	−9.10797	−	8.20086i	−0.448174	−	0.403538i
$414$	0.0318348	−	2.96729i	0.00156459	−	0.145834i
$415$	−1.37962	+	6.49062i	−0.0677231	+	0.318612i
$416$	−1.01263	+	0.215242i	−0.0496485	+	0.0105531i
$417$	−16.2069	−	22.5604i	−0.793657	−	1.10479i
$418$	7.65127	+	2.48605i	0.374236	+	0.121597i
$419$	−19.8273	−	6.44228i	−0.968627	−	0.314726i	−0.218365	−	0.975867i	$-0.570072\pi$
$419$	−19.8273	−	6.44228i	−0.968627	−	0.314726i	−0.750262	+	0.661141i	$0.770072\pi$
$420$	−3.47955	−	4.84362i	−0.169785	−	0.236344i
$421$	−32.9634	+	7.00658i	−1.60654	+	0.341480i	−0.921907	−	0.387411i	$-0.873369\pi$
$421$	−32.9634	+	7.00658i	−1.60654	+	0.341480i	−0.684629	+	0.728891i	$0.740036\pi$
$422$	4.43153	−	20.8487i	0.215723	−	1.01490i
$423$	−0.182420	+	17.0032i	−0.00886958	+	0.826725i
$424$	−8.69032	−	7.82480i	−0.422039	−	0.380006i
$425$	−0.551932	+	5.25128i	−0.0267726	+	0.254724i
$426$	16.6792	+	7.53350i	0.808108	+	0.364999i
$427$	−6.49577	+	0.682732i	−0.314352	+	0.0330397i
$428$	−4.69518	−	2.71076i	−0.226950	−	0.131030i
$429$	6.27353	−	5.58807i	0.302889	−	0.269794i
$430$	−0.195458	−	0.269025i	−0.00942582	−	0.0129735i
$431$	−7.88657	+	7.10110i	−0.379883	+	0.342048i	−0.836847	−	0.547437i	$-0.815604\pi$
$431$	−7.88657	+	7.10110i	−0.379883	+	0.342048i	0.456964	+	0.889485i	$0.348937\pi$
$432$	4.15408	+	3.12147i	0.199863	+	0.150182i
$433$		−	11.5612i		−	0.555598i	−0.960639	−	0.277799i	$-0.910395\pi$
$433$		−	11.5612i		−	0.555598i	0.960639	−	0.277799i	$-0.0896049\pi$
$434$	−0.0711454	+	19.1711i	−0.00341509	+	0.920241i
$435$	2.77730	+	13.4197i	0.133161	+	0.643426i
$436$	4.35524	+	13.4040i	0.208578	+	0.641937i
$437$	1.13647	+	1.26218i	0.0543648	+	0.0603782i
$438$	−5.36983	+	5.89985i	−0.256581	+	0.281906i
$439$	−6.04463	−	10.4696i	−0.288494	−	0.499687i	0.684956	−	0.728584i	$-0.259821\pi$
$439$	−6.04463	−	10.4696i	−0.288494	−	0.499687i	−0.973451	+	0.228897i	$0.926488\pi$
$440$	−2.34268	+	4.05764i	−0.111683	+	0.193441i
$441$	−7.14818	−	12.6936i	−0.340390	−	0.604456i
$442$	4.42238	+	3.21305i	0.210351	+	0.152829i
$443$	17.4249	+	1.83143i	0.827883	+	0.0870140i	0.508985	−	0.860775i	$-0.330021\pi$
$443$	17.4249	+	1.83143i	0.827883	+	0.0870140i	0.318898	+	0.947789i	$0.396687\pi$
$444$	−4.09461	−	2.39340i	−0.194322	−	0.113586i
$445$	−3.70083	+	8.31221i	−0.175436	+	0.394037i
$446$	−13.5021	−	2.86996i	−0.639342	−	0.135896i
$447$	16.4444	+	37.4744i	0.777792	+	1.77248i
$448$	3.14556	−	1.40050i	0.148614	−	0.0661672i
$449$	2.83819	−	8.73506i	0.133943	−	0.412233i	−0.861481	−	0.507789i	$-0.830463\pi$
$449$	2.83819	−	8.73506i	0.133943	−	0.412233i	0.995424	+	0.0955561i	$0.0304629\pi$
$450$	−2.98676	+	0.281560i	−0.140797	+	0.0132729i
$451$	−15.2154	−	34.1744i	−0.716466	−	1.60921i
$452$	4.05036	+	19.0554i	0.190513	+	0.896292i
$453$	−0.169030	+	31.5112i	−0.00794174	+	1.48053i
$454$	−10.4190	−	4.63883i	−0.488987	−	0.217711i
$455$	2.38522	−	2.64905i	0.111821	−	0.124189i
$456$	−2.95936	+	0.295000i	−0.138585	+	0.0138147i
$457$	6.02587	−	8.29389i	0.281878	−	0.387972i	−0.644477	−	0.764624i	$-0.722925\pi$
$457$	6.02587	−	8.29389i	0.281878	−	0.387972i	0.926355	+	0.376652i	$0.122925\pi$
$458$	0.723255	+	6.88131i	0.0337955	+	0.321542i
$459$	−2.42847	−	27.3291i	−0.113351	−	1.27561i
$460$	−0.856632	+	0.494577i	−0.0399407	+	0.0230598i
$461$	−2.30103	+	1.67180i	−0.107170	+	0.0778634i	−0.640079	−	0.768309i	$-0.721099\pi$
$461$	−2.30103	+	1.67180i	−0.107170	+	0.0778634i	0.532910	+	0.846172i	$0.321099\pi$
$462$	−16.5455	+	22.5179i	−0.769765	+	1.04763i
$463$	−20.7720	+	6.74922i	−0.965355	+	0.313663i	−0.748940	−	0.662638i	$-0.769437\pi$
$463$	−20.7720	+	6.74922i	−0.965355	+	0.313663i	−0.216416	+	0.976301i	$0.569437\pi$
$464$	−7.91206			−0.367308
$465$	8.30754	+	4.89742i	0.385253	+	0.227112i
$466$	−8.60065			−0.398418
$467$	−14.8399	+	4.82179i	−0.686711	+	0.223126i	−0.631531	−	0.775351i	$-0.717573\pi$
$467$	−14.8399	+	4.82179i	−0.686711	+	0.223126i	−0.0551797	+	0.998476i	$0.517573\pi$
$468$	−1.29360	+	2.82355i	−0.0597965	+	0.130519i
$469$	−7.98308	+	5.80005i	−0.368624	+	0.267821i
$470$	4.90869	−	2.83403i	0.226421	−	0.130724i
$471$	13.3146	−	40.2425i	0.613506	−	1.85428i
$472$	−0.372061	−	3.53993i	−0.0171255	−	0.162938i
$473$	−0.915792	+	1.26048i	−0.0421081	+	0.0579569i
$474$	−1.99277	−	19.9909i	−0.0915311	−	0.918213i
$475$	1.14893	−	1.27602i	0.0527167	−	0.0585478i
$476$	−16.6092	−	7.39490i	−0.761282	−	0.338945i
$477$	−34.3916	+	6.92540i	−1.57468	+	0.317092i
$478$	−1.45702	−	6.85474i	−0.0666425	−	0.313528i
$479$	1.78766	+	4.01516i	0.0816805	+	0.183457i	0.949769	−	0.312952i	$-0.101318\pi$
$479$	1.78766	+	4.01516i	0.0816805	+	0.183457i	−0.868088	+	0.496410i	$0.834651\pi$
$480$	0.190286	−	1.72157i	0.00868532	−	0.0785784i
$481$	0.876002	−	2.69606i	0.0399423	−	0.122930i
$482$	−15.7364	+	7.00630i	−0.716774	+	0.319128i
$483$	−5.40197	+	2.37048i	−0.245798	+	0.107860i
$484$	10.7133	+	2.27718i	0.486967	+	0.103508i
$485$	−2.35200	+	5.28267i	−0.106799	+	0.239874i
$486$	14.9494	−	4.41779i	0.678116	−	0.200395i
$487$	−26.6767	−	2.80383i	−1.20884	−	0.127054i	−0.521408	−	0.853307i	$-0.674593\pi$
$487$	−26.6767	−	2.80383i	−1.20884	−	0.127054i	−0.687427	+	0.726254i	$0.741260\pi$
$488$	−1.53464	−	1.11498i	−0.0694697	−	0.0504727i
$489$	−1.05887	−	3.31935i	−0.0478839	−	0.150106i
$490$	−2.42798	+	4.20539i	−0.109685	+	0.189980i
$491$	−6.35296	−	11.0037i	−0.286705	−	0.496588i	0.686316	−	0.727303i	$-0.259227\pi$
$491$	−6.35296	−	11.0037i	−0.286705	−	0.496588i	−0.973021	+	0.230716i	$0.925893\pi$
$492$	10.2271	+	9.30834i	0.461073	+	0.419652i
$493$	27.9545	+	31.0466i	1.25901	+	1.39827i
$494$	−0.549306	−	1.69059i	−0.0247145	−	0.0760633i
$495$	5.57904	+	12.9015i	0.250759	+	0.579878i
$496$	−3.74089	+	4.12380i	−0.167971	+	0.185164i
$497$		−	36.3828i		−	1.63199i
$498$	−9.98412	+	5.69315i	−0.447399	+	0.255116i
$499$	−2.54376	+	2.29041i	−0.113874	+	0.102533i	−0.724101	−	0.689694i	$-0.757745\pi$
$499$	−2.54376	+	2.29041i	−0.113874	+	0.102533i	0.610227	+	0.792227i	$0.291078\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	11.7054	+	13.1412i	0.522959	+	0.587107i
$502$	−9.04211	−	5.22047i	−0.403569	−	0.233001i
$503$	−3.86680	+	0.406417i	−0.172412	+	0.0181212i	−0.190341	−	0.981718i	$-0.560959\pi$
$503$	−3.86680	+	0.406417i	−0.172412	+	0.0181212i	0.0179291	+	0.999839i	$0.494293\pi$
$504$	2.25595	−	10.0804i	0.100488	−	0.449017i
$505$	0.611291	−	5.81604i	0.0272021	−	0.258810i
$506$	3.44413	+	3.10111i	0.153110	+	0.137861i
$507$	20.1855	+	4.40386i	0.896470	+	0.195582i
$508$	0.824635	−	3.87960i	0.0365873	−	0.172130i
$509$	18.9269	−	4.02304i	0.838922	−	0.178318i	0.231637	−	0.972802i	$-0.425592\pi$
$509$	18.9269	−	4.02304i	0.838922	−	0.178318i	0.607285	+	0.794484i	$0.292259\pi$
$510$	−7.42766	+	5.33587i	−0.328902	+	0.236276i
$511$	15.0831	+	4.90080i	0.667237	+	0.216799i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−4.58479	+	7.65396i	−0.202424	+	0.337930i
$514$	−12.6514	+	2.68914i	−0.558030	+	0.118613i
$515$	2.45513	−	11.5505i	0.108186	−	0.508976i
$516$	0.122770	−	0.562728i	0.00540465	−	0.0247727i
$517$	−19.7357	−	17.7701i	−0.867973	−	0.781527i
$518$	−0.985547	+	9.37686i	−0.0433025	+	0.411995i
$519$	−12.9934	+	28.7673i	−0.570346	+	1.26275i
$520$	1.02959	−	0.108214i	0.0451503	−	0.00474549i
$521$	−16.3405	−	9.43419i	−0.715890	−	0.413319i	0.0973482	−	0.995250i	$-0.468964\pi$
$521$	−16.3405	−	9.43419i	−0.715890	−	0.413319i	−0.813238	+	0.581931i	$0.802297\pi$
$522$	−14.1570	+	19.0522i	−0.619635	+	0.833892i
$523$	−4.68155	−	6.44359i	−0.204710	−	0.281759i	0.694302	−	0.719684i	$-0.255713\pi$
$523$	−4.68155	−	6.44359i	−0.204710	−	0.281759i	−0.899011	+	0.437925i	$0.855713\pi$
$524$	−13.4688	+	12.1274i	−0.588389	+	0.529788i
$525$	2.95419	+	5.18079i	0.128932	+	0.226108i
$526$		−	3.71667i		−	0.162054i
$527$	29.3987	+	0.109101i	1.28063	+	0.00475251i
$528$	−7.94688	+	1.64466i	−0.345844	+	0.0715746i
$529$	−6.80504	−	20.9438i	−0.295871	−	0.910598i
$530$	7.82480	+	8.69032i	0.339888	+	0.377484i
$531$	−9.18985	−	5.43804i	−0.398805	−	0.235991i
$532$	2.95612	+	5.12015i	0.128164	+	0.221987i
$533$	−4.13281	+	7.15824i	−0.179012	+	0.310058i
$534$	−15.0142	+	4.78954i	−0.649730	+	0.207263i
$535$	4.38610	+	3.18669i	0.189628	+	0.137773i
$536$	−2.85009	−	0.299557i	−0.123105	−	0.0129389i
$537$	12.6515	−	21.6441i	0.545953	−	0.934011i
$538$	−10.6645	+	23.9528i	−0.459779	+	1.03268i
$539$	22.2548	+	4.73040i	0.958581	+	0.203753i
$540$	−3.80505	−	3.53859i	−0.163743	−	0.152277i
$541$	24.0868	−	10.7242i	1.03557	−	0.461067i	0.182692	−	0.983170i	$-0.441519\pi$
$541$	24.0868	−	10.7242i	1.03557	−	0.461067i	0.852883	+	0.522103i	$0.174852\pi$
$542$	−3.16451	+	9.73936i	−0.135927	+	0.418341i
$543$	−12.5761	−	1.39004i	−0.539691	−	0.0596525i
$544$	−2.14765	−	4.82371i	−0.0920798	−	0.206815i
$545$	−2.93027	−	13.7859i	−0.125519	−	0.590521i
$546$	6.17406	+	0.0331185i	0.264226	+	0.00141734i
$547$	−13.9964	−	6.23162i	−0.598444	−	0.266445i	0.0850778	−	0.996374i	$-0.472886\pi$
$547$	−13.9964	−	6.23162i	−0.598444	−	0.266445i	−0.683522	+	0.729930i	$0.739553\pi$
$548$	10.5913	−	11.7629i	0.452439	−	0.502485i
$549$	−5.43077	+	1.70037i	−0.231780	+	0.0725701i
$550$	2.75399	−	3.79054i	0.117430	−	0.161629i
$551$	−1.42007	−	13.5110i	−0.0604968	−	0.575589i
$552$	−1.62655	−	0.538160i	−0.0692304	−	0.0229056i
$553$	−34.5874	+	19.9691i	−1.47081	+	0.849171i
$554$	4.37487	−	3.17853i	0.185871	−	0.135043i
$555$	3.82200	+	2.80829i	0.162235	+	0.119205i
$556$	−15.2529	+	4.95597i	−0.646867	+	0.210180i
$557$	−12.8110			−0.542818			−0.271409	−	0.962464i	$-0.587490\pi$
$557$	−12.8110			−0.542818			−0.271409	+	0.962464i	$0.587490\pi$
$558$	3.23654	+	16.3867i	0.137014	+	0.693705i
$559$	0.344257			0.0145605
$560$	−3.27472	+	1.06402i	−0.138382	+	0.0449632i
$561$	34.5311	+	25.3724i	1.45790	+	1.07122i
$562$	3.30369	−	2.40027i	0.139358	−	0.101249i
$563$	−17.6058	+	10.1647i	−0.741995	+	0.428391i	−0.822794	−	0.568340i	$-0.807586\pi$
$563$	−17.6058	+	10.1647i	−0.741995	+	0.428391i	0.0807995	+	0.996730i	$0.474253\pi$
$564$	9.32048	+	3.08378i	0.392463	+	0.129850i
$565$	−2.03633	−	19.3744i	−0.0856692	−	0.815088i
$566$	−5.83142	+	8.02626i	−0.245113	+	0.337369i
$567$	−20.2370	−	23.4691i	−0.849874	−	0.985609i
$568$	7.07032	−	7.85238i	0.296664	−	0.329479i
$569$	−37.3367	−	16.6234i	−1.56523	−	0.696887i	−0.572803	−	0.819693i	$-0.694144\pi$
$569$	−37.3367	−	16.6234i	−1.56523	−	0.696887i	−0.992431	+	0.122806i	$0.960811\pi$
$570$	2.97398	+	0.0159528i	0.124566	+	0.000668190i
$571$	5.33557	+	25.1019i	0.223287	+	1.05048i	0.936807	+	0.349847i	$0.113766\pi$
$571$	5.33557	+	25.1019i	0.223287	+	1.05048i	−0.713520	+	0.700635i	$0.752900\pi$
$572$	−1.97290	−	4.43120i	−0.0824910	−	0.185278i
$573$	37.3427	+	4.12752i	1.56002	+	0.172430i
$574$	8.49529	−	26.1458i	0.354586	−	1.09131i
$575$	0.903636	−	0.402325i	0.0376842	−	0.0167781i
$576$	2.44583	−	1.73722i	0.101910	−	0.0723840i
$577$	−22.7188	−	4.82902i	−0.945795	−	0.201035i	−0.290899	−	0.956754i	$-0.593954\pi$
$577$	−22.7188	−	4.82902i	−0.945795	−	0.201035i	−0.654896	+	0.755719i	$0.727288\pi$
$578$	−4.42552	+	9.93987i	−0.184077	+	0.413444i
$579$	3.81743	−	6.53082i	0.158647	−	0.271412i
$580$	7.86872	+	0.827036i	0.326731	+	0.0343408i
$581$	18.4845	+	13.4298i	0.766867	+	0.557161i
$582$	−9.54202	+	3.04390i	−0.395529	+	0.126174i
$583$	27.3953	−	47.4500i	1.13460	−	1.96518i
$584$	2.30296	+	3.98884i	0.0952971	+	0.165059i
$585$	1.58165	−	2.67286i	0.0653932	−	0.110509i
$586$	18.1642	+	20.1733i	0.750355	+	0.833353i
$587$	10.9395	+	33.6682i	0.451520	+	1.38963i	0.875173	+	0.483810i	$0.160748\pi$
$587$	10.9395	+	33.6682i	0.451520	+	1.38963i	−0.423653	+	0.905824i	$0.639252\pi$
$588$	−8.23625	+	1.70454i	−0.339657	+	0.0702942i
$589$	−7.71342	−	5.64798i	−0.317826	−	0.232721i
$590$			3.55943i			0.146539i
$591$	12.3521	+	21.6620i	0.508097	+	0.891055i
$592$	−2.03492	+	1.83225i	−0.0836348	+	0.0753051i
$593$	0.441382	+	0.607510i	0.0181254	+	0.0249475i	0.817984	−	0.575242i	$-0.195092\pi$
$593$	0.441382	+	0.607510i	0.0181254	+	0.0249475i	−0.799858	+	0.600189i	$0.795092\pi$
$594$	−10.2590	+	22.0788i	−0.420930	+	0.905905i
$595$	15.7453	+	9.09053i	0.645493	+	0.372675i
$596$	23.4979	−	2.46972i	0.962509	−	0.101164i
$597$	−9.76294	+	21.6151i	−0.399571	+	0.884649i
$598$	0.107040	−	1.01842i	0.00437719	−	0.0416462i
$599$	−5.23864	−	4.71689i	−0.214045	−	0.192727i	0.555133	−	0.831762i	$-0.312667\pi$
$599$	−5.23864	−	4.71689i	−0.214045	−	0.192727i	−0.769178	+	0.639035i	$0.779334\pi$
$600$	−0.369196	+	1.69225i	−0.0150724	+	0.0690856i
$601$	8.32833	−	39.1817i	0.339720	−	1.59826i	−0.394203	−	0.919023i	$-0.628979\pi$
$601$	8.32833	−	39.1817i	0.339720	−	1.59826i	0.733923	−	0.679233i	$-0.237687\pi$
$602$	−1.11997	+	0.238058i	−0.0456467	+	0.00970251i
$603$	−5.82097	+	6.32701i	−0.237048	+	0.257656i
$604$	17.3028	+	5.62203i	0.704042	+	0.228757i
$605$	−10.4166	−	3.38454i	−0.423493	−	0.137601i
$606$	8.22649	−	5.90973i	0.334178	−	0.240066i
$607$	4.71858	−	1.00297i	0.191521	−	0.0407091i	−0.111152	−	0.993803i	$-0.535454\pi$
$607$	4.71858	−	1.00297i	0.191521	−	0.0407091i	0.302674	+	0.953094i	$0.402121\pi$
$608$	−0.356996	+	1.67953i	−0.0144781	+	0.0681140i
$609$	46.1022	+	10.0581i	1.86816	+	0.407574i
$610$	1.40968	+	1.26928i	0.0570763	+	0.0513918i
$611$	−0.613363	+	5.83576i	−0.0248140	+	0.236090i
$612$	−15.4582	−	3.45948i	−0.624862	−	0.139841i
$613$	36.3747	−	3.82314i	1.46916	−	0.154415i	0.664116	−	0.747629i	$-0.268808\pi$
$613$	36.3747	−	3.82314i	1.46916	−	0.154415i	0.805045	+	0.593214i	$0.202141\pi$
$614$	−9.96062	−	5.75077i	−0.401978	−	0.232082i
$615$	−9.19809	−	10.3264i	−0.370903	−	0.416399i
$616$	9.48266	+	13.0518i	0.382067	+	0.525871i
$617$	−33.9746	+	30.5909i	−1.36777	+	1.23154i	−0.422040	+	0.906577i	$0.638686\pi$
$617$	−33.9746	+	30.5909i	−1.36777	+	1.23154i	−0.945726	+	0.324964i	$0.894648\pi$
$618$	17.7674	−	10.1313i	0.714710	−	0.407542i
$619$		−	40.7171i		−	1.63656i	−0.574820	−	0.818280i	$-0.694928\pi$
$619$		−	40.7171i		−	1.63656i	0.574820	−	0.818280i	$-0.305072\pi$
$620$	4.15145	−	3.71018i	0.166726	−	0.149004i
$621$	−4.20625	+	2.95379i	−0.168791	+	0.118532i
$622$	−6.81898	−	20.9867i	−0.273416	−	0.841489i
$623$	20.9636	+	23.2824i	0.839889	+	0.932791i
$624$	1.32609	+	1.20696i	0.0530861	+	0.0483171i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.16219	+	3.74503i	−0.0864186	+	0.149681i
$627$	−4.23481	−	13.2753i	−0.169122	−	0.530164i
$628$	−19.7988	−	14.3847i	−0.790059	−	0.574011i
$629$	14.3794	+	1.51133i	0.573343	+	0.0602607i
$630$	−3.29728	+	9.78936i	−0.131367	+	0.390018i
$631$	−14.6255	+	32.8494i	−0.582232	+	1.30772i	0.346877	+	0.937911i	$0.387242\pi$
$631$	−14.6255	+	32.8494i	−0.582232	+	1.30772i	−0.929109	+	0.369805i	$0.879425\pi$
$632$	−11.3455	−	2.41156i	−0.451300	−	0.0959267i
$633$	−33.8061	+	14.8347i	−1.34367	+	0.589625i
$634$	−17.1696	+	7.64438i	−0.681890	+	0.303597i
$635$	−1.22565	+	3.77215i	−0.0486383	+	0.149693i
$636$	−2.22520	+	20.1320i	−0.0882350	+	0.798285i
$637$	−2.04474	−	4.59255i	−0.0810154	−	0.181963i
$638$	−7.70747	−	36.2608i	−0.305142	−	1.43558i
$639$	−6.25763	−	31.0755i	−0.247548	−	1.22933i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−18.1752	+	20.1856i	−0.717876	+	0.797282i	−0.986114	−	0.166071i	$-0.946892\pi$
$641$	−18.1752	+	20.1856i	−0.717876	+	0.797282i	0.268238	+	0.963353i	$0.413559\pi$
$642$	0.931451	+	9.34404i	0.0367614	+	0.368780i
$643$	−10.8641	+	14.9531i	−0.428437	+	0.589692i	−0.967594	−	0.252513i	$-0.918743\pi$
$643$	−10.8641	+	14.9531i	−0.428437	+	0.589692i	0.539157	+	0.842205i	$0.318743\pi$
$644$	0.356014	+	3.38724i	0.0140289	+	0.133476i
$645$	−0.180918	+	0.546812i	−0.00712366	+	0.0215307i
$646$	7.85173	−	4.53320i	0.308922	−	0.178356i
$647$	−29.9293	+	21.7449i	−1.17664	+	0.854881i	−0.991789	−	0.127885i	$-0.959181\pi$
$647$	−29.9293	+	21.7449i	−1.17664	+	0.854881i	−0.184854	+	0.982766i	$0.559181\pi$
$648$	0.193092	−	8.99793i	0.00758537	−	0.353472i
$649$	15.8610	−	5.15354i	0.622597	−	0.202294i
$650$	−1.03526			−0.0406061
$651$	27.0398	−	19.2731i	1.05977	−	0.755373i
$652$	−2.01158			−0.0787794
$653$	15.3928	−	5.00144i	0.602368	−	0.195721i	0.00807185	−	0.999967i	$-0.497431\pi$
$653$	15.3928	−	5.00144i	0.602368	−	0.195721i	0.594296	+	0.804246i	$0.297431\pi$
$654$	14.4543	−	19.6719i	0.565208	−	0.769231i
$655$	14.6627	−	10.6531i	0.572920	−	0.416250i
$656$	6.91445	−	3.99206i	0.269964	−	0.155864i
$657$	13.7258	+	1.59169i	0.535493	+	0.0620977i
$658$	−2.04004	−	19.4097i	−0.0795289	−	0.756667i
$659$	28.7727	−	39.6023i	1.12083	−	1.54269i	0.316408	−	0.948623i	$-0.397523\pi$
$659$	28.7727	−	39.6023i	1.12083	−	1.54269i	0.804419	−	0.594063i	$-0.202477\pi$
$660$	8.07526	−	0.804974i	0.314329	−	0.0313336i
$661$	18.8464	−	20.9311i	0.733042	−	0.814125i	−0.255222	−	0.966882i	$-0.582149\pi$
$661$	18.8464	−	20.9311i	0.733042	−	0.814125i	0.988264	+	0.152757i	$0.0488152\pi$
$662$	23.9850	+	10.6788i	0.932202	+	0.415043i
$663$	0.0507870	−	9.46789i	0.00197240	−	0.367702i
$664$	1.37962	+	6.49062i	0.0535398	+	0.251885i
$665$	−2.40473	−	5.40110i	−0.0932513	−	0.209446i
$666$	0.770984	+	8.17852i	0.0298750	+	0.316911i
$667$	2.41844	−	7.44320i	0.0936425	−	0.288202i
$668$	9.28210	−	4.13266i	0.359135	−	0.159897i
$669$	9.60727	+	21.8936i	0.371438	+	0.846455i
$670$	2.80317	+	0.595831i	0.108296	+	0.0230190i
$671$	3.61496	−	8.11934i	0.139554	−	0.313444i
$672$	−5.14880	−	3.00960i	−0.198619	−	0.116098i
$673$	13.3377	+	1.40184i	0.514129	+	0.0540371i	0.358041	−	0.933706i	$-0.383445\pi$
$673$	13.3377	+	1.40184i	0.514129	+	0.0540371i	0.156088	+	0.987743i	$0.450112\pi$
$674$	−3.82292	−	2.77751i	−0.147253	−	0.106986i
$675$	3.41432	+	3.91694i	0.131417	+	0.150763i
$676$	5.96412	−	10.3302i	0.229389	−	0.397314i
$677$	0.542697	+	0.939979i	0.0208576	+	0.0361263i	0.876266	−	0.481828i	$-0.160027\pi$
$677$	0.542697	+	0.939979i	0.0208576	+	0.0361263i	−0.855408	+	0.517954i	$0.826694\pi$
$678$	22.7122	−	24.9540i	0.872257	−	0.958351i
$679$	13.3230	+	14.7967i	0.511291	+	0.567846i
$680$	1.63167	+	5.02177i	0.0625718	+	0.192576i
$681$	4.00339	+	19.3441i	0.153410	+	0.741268i
$682$	−22.5434	−	13.1272i	−0.863233	−	0.502668i
$683$		−	10.7091i		−	0.409773i	−0.978786	−	0.204887i	$-0.934317\pi$
$683$		−	10.7091i		−	0.409773i	0.978786	−	0.204887i	$-0.0656825\pi$
$684$	3.40553	+	3.86482i	0.130214	+	0.147775i
$685$	−11.7629	+	10.5913i	−0.449436	+	0.404674i
$686$	−4.33929	−	5.97252i	−0.165675	−	0.228032i
$687$	8.94905	−	7.97126i	0.341428	−	0.304123i
$688$	−0.287982	−	0.166267i	−0.0109792	−	0.00633885i
$689$	−12.0400	+	1.26545i	−0.458686	+	0.0482098i
$690$	1.56138	+	0.705233i	0.0594409	+	0.0268477i
$691$	5.26306	−	50.0746i	0.200216	−	1.90493i	−0.186047	−	0.982541i	$-0.559568\pi$
$691$	5.26306	−	50.0746i	0.200216	−	1.90493i	0.386263	−	0.922389i	$-0.373766\pi$
$692$	13.5434	+	12.1945i	0.514842	+	0.463566i
$693$	48.3958	+	0.519218i	1.83841	+	0.0197235i
$694$	2.81809	−	13.2581i	0.106973	−	0.503270i
$695$	15.6874	−	3.33446i	0.595056	−	0.126483i
$696$	7.99548	+	11.1299i	0.303068	+	0.421878i
$697$	−40.0945	−	13.0275i	−1.51869	−	0.493451i
$698$	11.1535	+	3.62398i	0.422165	+	0.137170i
$699$	8.69133	+	12.0985i	0.328736	+	0.457609i
$700$	3.36801	−	0.715892i	0.127299	−	0.0270582i
$701$	−3.97108	+	18.6825i	−0.149986	+	0.705627i	0.837309	+	0.546729i	$0.184127\pi$
$701$	−3.97108	+	18.6825i	−0.149986	+	0.705627i	−0.987295	+	0.158898i	$0.949206\pi$
$702$	5.27912	−	1.03362i	0.199247	−	0.0390113i
$703$	−3.49407	−	3.14608i	−0.131781	−	0.118657i
$704$	−0.489754	+	4.65969i	−0.0184583	+	0.175619i
$705$	−8.94708	−	4.04114i	−0.336966	−	0.152198i
$706$	11.8079	−	1.24106i	0.444395	−	0.0467078i
$707$	−17.4386	−	10.0682i	−0.655847	−	0.378653i
$708$	−4.60363	+	4.10063i	−0.173015	+	0.154111i
$709$	2.39721	+	3.29947i	0.0900290	+	0.123914i	0.851656	−	0.524102i	$-0.175599\pi$
$709$	2.39721	+	3.29947i	0.0900290	+	0.123914i	−0.761627	+	0.648016i	$0.775599\pi$
$710$	−7.85238	+	7.07032i	−0.294695	+	0.265344i
$711$	−26.1074	+	23.0049i	−0.979105	+	0.862751i
$712$			9.09885i			0.340994i
$713$	−2.73597	−	4.77971i	−0.102463	−	0.179002i
$714$	6.38193	+	30.8370i	0.238838	+	1.15405i
$715$	1.49890	+	4.61315i	0.0560558	+	0.172522i
$716$	−9.68528	−	10.7566i	−0.361956	−	0.401993i
$717$	−8.17017	+	8.97659i	−0.305121	+	0.335237i
$718$	−16.2848	−	28.2062i	−0.607745	−	1.05264i
$719$	9.89179	−	17.1331i	0.368902	−	0.638956i	−0.620493	−	0.784212i	$-0.713067\pi$
$719$	9.89179	−	17.1331i	0.368902	−	0.638956i	0.989394	+	0.145256i	$0.0464006\pi$
$720$	−2.61402	+	1.47204i	−0.0974187	+	0.0548598i
$721$	−32.8944	−	23.8992i	−1.22505	−	0.890053i
$722$	15.9638	+	1.67786i	0.594111	+	0.0624436i
$723$	25.7581	+	15.0562i	0.957953	+	0.559947i
$724$	−2.97122	+	6.67347i	−0.110425	+	0.248018i
$725$	−7.73917	−	1.64501i	−0.287425	−	0.0610942i
$726$	−7.62292	−	17.3715i	−0.282913	−	0.644718i
$727$	−36.5797	+	16.2863i	−1.35667	+	0.604027i	−0.950772	−	0.309893i	$-0.899707\pi$
$727$	−36.5797	+	16.2863i	−1.35667	+	0.604027i	−0.405895	+	0.913920i	$0.633040\pi$
$728$	1.10154	−	3.39018i	0.0408257	−	0.125649i
$729$	−21.3215	−	16.5649i	−0.789684	−	0.613514i
$730$	−1.87339	−	4.20771i	−0.0693374	−	0.155734i
$731$	0.365060	+	1.71747i	0.0135022	+	0.0635230i
$732$	−0.0176239	+	3.28550i	−0.000651397	+	0.121436i
$733$	2.03775	+	0.907266i	0.0752661	+	0.0335106i	0.444024	−	0.896015i	$-0.353550\pi$
$733$	2.03775	+	0.907266i	0.0752661	+	0.0335106i	−0.368758	+	0.929525i	$0.620217\pi$
$734$	6.90190	−	7.66533i	0.254754	−	0.282933i
$735$	8.36930	−	0.834284i	0.308706	−	0.0307730i
$736$	−0.581410	+	0.800242i	−0.0214310	+	0.0294973i
$737$	−1.40353	−	13.3537i	−0.0516997	−	0.491890i
$738$	2.75911	−	23.7929i	0.101564	−	0.875830i
$739$	26.9167	−	15.5404i	0.990146	−	0.571661i	0.0848284	−	0.996396i	$-0.472966\pi$
$739$	26.9167	−	15.5404i	0.990146	−	0.571661i	0.905318	+	0.424734i	$0.139632\pi$
$740$	2.21530	−	1.60951i	0.0814360	−	0.0591667i
$741$	−1.82306	+	2.48112i	−0.0669716	+	0.0911463i
$742$	38.2946	−	12.4427i	1.40584	−	0.456785i
$743$	−48.2816			−1.77128			−0.885639	−	0.464374i	$-0.846279\pi$
$743$	−48.2816			−1.77128			−0.885639	+	0.464374i	$0.846279\pi$
$744$	9.58128	+	1.09503i	0.351267	+	0.0401458i
$745$	−23.6273			−0.865637
$746$	−21.1457	+	6.87066i	−0.774200	+	0.251553i
$747$	18.0979	+	8.29149i	0.662168	+	0.303370i
$748$	20.0148	−	14.5416i	0.731814	−	0.531694i
$749$	16.1667	−	9.33383i	0.590717	−	0.341051i
$750$	0.544062	−	1.64438i	0.0198663	−	0.0600444i
$751$	5.30266	+	50.4515i	0.193497	+	1.84100i	0.473250	+	0.880928i	$0.343081\pi$
$751$	5.30266	+	50.4515i	0.193497	+	1.84100i	−0.279753	+	0.960072i	$0.590253\pi$
$752$	3.33161	−	4.58556i	0.121491	−	0.167218i
$753$	1.79382	+	17.9950i	0.0653703	+	0.655776i
$754$	−5.48086	+	6.08712i	−0.199601	+	0.221680i
$755$	−16.6204	−	7.39987i	−0.604878	−	0.269309i
$756$	−16.4598	+	7.01323i	−0.598638	+	0.255069i
$757$	10.2228	+	48.0943i	0.371553	+	1.74802i	0.624959	+	0.780658i	$0.285116\pi$
$757$	10.2228	+	48.0943i	0.371553	+	1.74802i	−0.253406	+	0.967360i	$0.581551\pi$
$758$	3.64230	+	8.18074i	0.132294	+	0.297138i
$759$	0.881888	−	7.97867i	0.0320105	−	0.289607i
$760$	0.530599	−	1.63302i	0.0192468	−	0.0592357i
$761$	35.5096	−	15.8099i	1.28722	−	0.573108i	0.354956	−	0.934883i	$-0.384496\pi$
$761$	35.5096	−	15.8099i	1.28722	−	0.573108i	0.932265	+	0.361775i	$0.117829\pi$
$762$	−6.29076	+	2.76049i	−0.227890	+	0.100002i
$763$	−47.4681	−	10.0897i	−1.71846	−	0.365270i
$764$	8.82258	−	19.8158i	0.319190	−	0.716912i
$765$	15.0119	+	5.05636i	0.542758	+	0.182813i
$766$	3.28725	+	0.345504i	0.118773	+	0.0124835i
$767$	−2.98116	−	2.16594i	−0.107644	−	0.0782076i
$768$	−0.526389	−	1.65013i	−0.0189944	−	0.0595438i
$769$	4.97345	−	8.61426i	0.179347	−	0.310638i	−0.762310	−	0.647212i	$-0.775935\pi$
$769$	4.97345	−	8.61426i	0.179347	−	0.310638i	0.941657	+	0.336574i	$0.109268\pi$
$770$	−8.06643	−	13.9715i	−0.290694	−	0.503497i
$771$	16.5676	+	15.0793i	0.596668	+	0.543066i
$772$	−2.92241	−	3.24566i	−0.105180	−	0.116814i
$773$	5.60124	+	17.2389i	0.201463	+	0.620039i	0.999840	+	0.0178811i	$0.00569205\pi$
$773$	5.60124	+	17.2389i	0.201463	+	0.620039i	−0.798377	+	0.602157i	$0.794308\pi$
$774$	−0.915653	+	0.395960i	−0.0329125	+	0.0142325i
$775$	−4.51653	+	3.25591i	−0.162239	+	0.116956i
$776$			5.78260i			0.207583i
$777$	14.1864	−	8.08935i	0.508933	−	0.290204i
$778$	−21.3810	+	19.2515i	−0.766544	+	0.690200i
$779$	8.05805	+	11.0910i	0.288710	+	0.397375i
$780$	−1.19266	−	1.33896i	−0.0427043	−	0.0479426i
$781$	42.8748	+	24.7538i	1.53418	+	0.885759i
$782$	5.19432	−	0.545945i	0.185748	−	0.0195229i
$783$	41.1070	+	0.661560i	1.46904	+	0.0236422i
$784$	−0.507587	+	4.82936i	−0.0181281	+	0.172477i
$785$	18.1867	+	16.3754i	0.649113	+	0.584464i
$786$	30.6704	+	6.69135i	1.09398	+	0.238673i
$787$	−9.11705	+	42.8923i	−0.324988	+	1.52895i	0.447714	+	0.894177i	$0.352238\pi$
$787$	−9.11705	+	42.8923i	−0.324988	+	1.52895i	−0.772702	+	0.634770i	$0.781095\pi$
$788$	14.0823	−	2.99329i	0.501662	−	0.106632i
$789$	−5.22823	+	3.75585i	−0.186130	+	0.133712i
$790$	11.0313	+	3.58428i	0.392475	+	0.127523i
$791$	−63.7953	−	20.7284i	−2.26830	−	0.737016i
$792$	10.3442	+	9.51688i	0.367565	+	0.338167i
$793$	−1.92088	+	0.408296i	−0.0682124	+	0.0144990i
$794$	−1.32790	+	6.24730i	−0.0471255	+	0.221708i
$795$	4.31738	−	19.7891i	0.153122	−	0.701847i
$796$	10.1762	+	9.16269i	0.360686	+	0.324763i
$797$	1.43943	−	13.6952i	0.0509871	−	0.485110i	−0.938996	−	0.343927i	$-0.888243\pi$
$797$	1.43943	−	13.6952i	0.0509871	−	0.485110i	0.989984	−	0.141183i	$-0.0450905\pi$
$798$	4.21523	−	9.33251i	0.149217	−	0.330367i
$799$	−29.7646	+	3.12839i	−1.05300	+	0.110674i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	21.9100	+	16.2805i	0.774151	+	0.575243i
$802$	15.9818	+	21.9970i	0.564336	+	0.776742i
$803$	−16.0373	+	14.4401i	−0.565946	+	0.509580i
$804$	2.45875	+	4.31194i	0.0867135	+	0.152070i
$805$		−	3.40590i		−	0.120042i
$806$	0.581231	+	5.73469i	0.0204730	+	0.201996i
$807$	44.4714	−	9.20364i	1.56547	−	0.323983i
$808$	−1.80716	−	5.56185i	−0.0635755	−	0.195665i
$809$	12.5366	+	13.9233i	0.440765	+	0.489519i	0.922064	−	0.387038i	$-0.126502\pi$
$809$	12.5366	+	13.9233i	0.440765	+	0.489519i	−0.481299	+	0.876556i	$0.659835\pi$
$810$	−1.13257	+	8.92845i	−0.0397946	+	0.313714i
$811$	−2.44333	−	4.23197i	−0.0857969	−	0.148605i	0.819934	−	0.572459i	$-0.194010\pi$
$811$	−2.44333	−	4.23197i	−0.0857969	−	0.148605i	−0.905731	+	0.423854i	$0.860677\pi$
$812$	13.6216	−	23.5933i	0.478025	−	0.827963i
$813$	16.8982	−	5.39052i	0.592646	−	0.189054i
$814$	−10.3795	−	7.54113i	−0.363800	−	0.264316i
$815$	2.00056	+	0.210267i	0.0700765	+	0.00736533i
$816$	−4.61521	+	7.89566i	−0.161565	+	0.276403i
$817$	0.232237	−	0.521614i	0.00812496	−	0.0182490i
$818$	−22.6433	−	4.81299i	−0.791706	−	0.168282i
$819$	−6.19257	−	8.71852i	−0.216386	−	0.304650i
$820$	−7.29386	+	3.24744i	−0.254713	+	0.113405i
$821$	3.97314	−	12.2281i	0.138663	−	0.426762i	−0.857478	−	0.514520i	$-0.827970\pi$
$821$	3.97314	−	12.2281i	0.138663	−	0.426762i	0.996142	+	0.0877577i	$0.0279701\pi$
$822$	−27.2498	−	3.01194i	−0.950447	−	0.105054i
$823$	−0.571113	−	1.28274i	−0.0199078	−	0.0447135i	0.903318	−	0.428972i	$-0.141124\pi$
$823$	−0.571113	−	1.28274i	−0.0199078	−	0.0447135i	−0.923226	+	0.384258i	$0.874457\pi$
$824$	−2.45513	−	11.5505i	−0.0855287	−	0.402381i
$825$	−8.11517	−	0.0435308i	−0.282534	−	0.00151555i
$826$	11.1964	+	4.98496i	0.389573	+	0.173449i
$827$	35.2281	−	39.1248i	1.22500	−	1.36050i	0.313297	−	0.949655i	$-0.398566\pi$
$827$	35.2281	−	39.1248i	1.22500	−	1.36050i	0.911704	−	0.410847i	$-0.134767\pi$
$828$	0.886666	+	2.83190i	0.0308138	+	0.0984152i
$829$	24.8467	−	34.1985i	0.862962	−	1.18776i	−0.117894	−	0.993026i	$-0.537614\pi$
$829$	24.8467	−	34.1985i	0.862962	−	1.18776i	0.980855	−	0.194738i	$-0.0623858\pi$
$830$	−0.693612	−	6.59927i	−0.0240756	−	0.229064i
$831$	−8.89224	−	2.94209i	−0.308468	−	0.102060i
$832$	0.896559	−	0.517629i	0.0310826	−	0.0179455i
$833$	20.7436	−	15.0711i	0.718723	−	0.522183i
$834$	22.3853	+	16.4480i	0.775139	+	0.569549i
$835$	−9.66323	+	3.13977i	−0.334410	+	0.108656i
$836$	−8.04502			−0.278243
$837$	19.7805	−	21.1123i	0.683715	−	0.729749i
$838$	20.8477			0.720170
$839$	22.8744	−	7.43234i	0.789712	−	0.256593i	0.113731	−	0.993512i	$-0.463720\pi$
$839$	22.8744	−	7.43234i	0.789712	−	0.256593i	0.675981	+	0.736919i	$0.263720\pi$
$840$	4.80601	+	3.53131i	0.165823	+	0.121842i
$841$	−27.1836	+	19.7500i	−0.937365	+	0.681036i
$842$	29.1849	−	16.8499i	1.00578	−	0.580686i
$843$	−6.71498	−	2.22172i	−0.231276	−	0.0765202i
$844$	2.22797	+	21.1977i	0.0766898	+	0.729655i
$845$	−7.01125	+	9.65015i	−0.241194	+	0.331975i
$846$	−5.08079	−	16.2274i	−0.174681	−	0.557910i
$847$	−25.2346	+	28.0259i	−0.867073	+	0.962982i
$848$	10.6830	+	4.75637i	0.366855	+	0.163334i
$849$	17.1834	+	0.0921742i	0.589734	+	0.00316341i
$850$	−1.09782	−	5.16482i	−0.0376548	−	0.177152i
$851$	−1.10167	−	2.47439i	−0.0377647	−	0.0848210i
$852$	−18.1908	−	2.01064i	−0.623206	−	0.0688834i
$853$	−15.8609	+	48.8149i	−0.543068	+	1.67139i	0.182472	+	0.983211i	$0.441590\pi$
$853$	−15.8609	+	48.8149i	−0.543068	+	1.67139i	−0.725540	+	0.688180i	$0.758410\pi$
$854$	5.96686	−	2.65662i	0.204182	−	0.0909076i
$855$	−2.98289	−	4.19962i	−0.102013	−	0.143624i
$856$	5.30305	+	1.12720i	0.181255	+	0.0385268i
$857$	19.6264	−	44.0816i	0.670425	−	1.50580i	−0.182192	−	0.983263i	$-0.558319\pi$
$857$	19.6264	−	44.0816i	0.670425	−	1.50580i	0.852617	−	0.522536i	$-0.175014\pi$
$858$	−4.23967	+	7.25319i	−0.144740	+	0.247620i
$859$	14.4728	+	1.52115i	0.493806	+	0.0519011i	0.348159	−	0.937436i	$-0.386807\pi$
$859$	14.4728	+	1.52115i	0.493806	+	0.0519011i	0.145647	+	0.989337i	$0.453474\pi$
$860$	0.269025	+	0.195458i	0.00917367	+	0.00666506i
$861$	−45.3641	+	14.4711i	−1.54601	+	0.493175i
$862$	5.30622	−	9.19064i	0.180730	−	0.313034i
$863$	5.95000	+	10.3057i	0.202540	+	0.350810i	0.949346	−	0.314232i	$-0.101747\pi$
$863$	5.95000	+	10.3057i	0.202540	+	0.350810i	−0.746806	+	0.665042i	$0.768414\pi$
$864$	−4.91536	−	1.68501i	−0.167224	−	0.0573253i
$865$	−12.1945	−	13.5434i	−0.414626	−	0.460489i
$866$	3.57262	+	10.9954i	0.121403	+	0.373639i
$867$	18.4546	−	3.81930i	0.626751	−	0.129710i
$868$	−5.85652	−	18.2548i	−0.198783	−	0.619607i
$869$		−	54.3453i		−	1.84354i
$870$	−6.78829	−	11.9047i	−0.230145	−	0.403606i
$871$	−2.20478	+	1.98520i	−0.0747063	+	0.0672658i
$872$	−8.28415	−	11.4022i	−0.280537	−	0.386126i
$873$	13.9245	+	10.3468i	0.471272	+	0.350185i
$874$	−1.47088	−	0.849215i	−0.0497533	−	0.0287251i
$875$	−3.42439	+	0.359918i	−0.115765	+	0.0121674i
$876$	3.28386	−	7.27046i	0.110951	−	0.245646i
$877$	−3.26222	+	31.0379i	−0.110157	+	1.04808i	0.790178	+	0.612878i	$0.209988\pi$
$877$	−3.26222	+	31.0379i	−0.110157	+	1.04808i	−0.900335	+	0.435198i	$0.856678\pi$
$878$	8.98407	+	8.08929i	0.303198	+	0.273000i
$879$	10.0222	−	45.9375i	0.338039	−	1.54943i
$880$	0.974141	−	4.58298i	0.0328383	−	0.154492i
$881$	−41.6222	+	8.84708i	−1.40229	+	0.298066i	−0.846115	−	0.533000i	$-0.821064\pi$
$881$	−41.6222	+	8.84708i	−1.40229	+	0.298066i	−0.556174	+	0.831066i	$0.687731\pi$
$882$	10.7209	+	9.86341i	0.360990	+	0.332118i
$883$	−16.5767	−	5.38610i	−0.557851	−	0.181257i	0.0165032	−	0.999864i	$-0.494747\pi$
$883$	−16.5767	−	5.38610i	−0.557851	−	0.181257i	−0.574354	+	0.818607i	$0.694747\pi$
$884$	−5.19882	−	1.68920i	−0.174855	−	0.0568140i
$885$	5.00704	−	3.59695i	0.168310	−	0.120910i
$886$	−17.1380	+	3.64280i	−0.575763	+	0.122382i
$887$	−6.09281	+	28.6644i	−0.204577	+	0.962457i	0.749294	+	0.662238i	$0.230393\pi$
$887$	−6.09281	+	28.6644i	−0.204577	+	0.962457i	−0.953870	+	0.300219i	$0.902940\pi$
$888$	4.63381	+	1.01095i	0.155500	+	0.0339254i
$889$	10.1490	+	9.13823i	0.340388	+	0.306486i
$890$	0.951088	−	9.04900i	0.0318806	−	0.303323i
$891$	41.4254	−	7.88032i	1.38780	−	0.264001i
$892$	13.7281	−	1.44288i	0.459651	−	0.0483113i
$893$	8.42849	+	4.86619i	0.282049	+	0.162841i
$894$	−27.2197	−	30.5587i	−0.910364	−	1.02203i
$895$	8.50785	+	11.7101i	0.284386	+	0.391424i
$896$	−2.55883	+	2.30398i	−0.0854846	+	0.0769707i
$897$	−1.54078	+	0.878582i	−0.0514450	+	0.0293350i
$898$			9.18458i			0.306494i
$899$	−4.76730	+	43.7938i	−0.158998	+	1.46060i
$900$	2.75357	−	1.19074i	0.0917856	−	0.0396913i
$901$	−19.0808	−	58.7245i	−0.635672	−	1.95640i
$902$	25.0312	+	27.7999i	0.833447	+	0.925637i
$903$	1.46666	+	1.33490i	0.0488073	+	0.0444226i
$904$	−9.74057	−	16.8712i	−0.323966	−	0.561126i
$905$	3.65251	−	6.32634i	0.121414	−	0.210294i
$906$	−9.57675	−	30.0212i	−0.318166	−	0.997387i
$907$	15.5614	+	11.3060i	0.516708	+	0.375410i	0.815362	−	0.578951i	$-0.196538\pi$
$907$	15.5614	+	11.3060i	0.516708	+	0.375410i	−0.298655	+	0.954361i	$0.596538\pi$
$908$	11.3425	+	1.19215i	0.376415	+	0.0395628i
$909$	−16.6264	−	5.60016i	−0.551464	−	0.185745i
$910$	−1.44987	+	3.25647i	−0.0480628	+	0.107951i
$911$	−13.8913	−	2.95269i	−0.460240	−	0.0978271i	−0.0280440	−	0.999607i	$-0.508928\pi$
$911$	−13.8913	−	2.95269i	−0.460240	−	0.0978271i	−0.432196	+	0.901780i	$0.642261\pi$
$912$	2.72336	−	1.19505i	0.0901793	−	0.0395722i
$913$	−28.4024	+	12.6456i	−0.939982	+	0.418507i
$914$	−3.16798	+	9.75005i	−0.104788	+	0.322503i
$915$	0.360956	−	3.26566i	0.0119328	−	0.107959i
$916$	−2.81430	−	6.32102i	−0.0929870	−	0.208852i
$917$	−12.9749	−	61.0421i	−0.428469	−	2.01579i
$918$	10.7548	+	25.2410i	0.354960	+	0.833078i
$919$	28.1907	+	12.5513i	0.929924	+	0.414029i	0.815076	−	0.579354i	$-0.196695\pi$
$919$	28.1907	+	12.5513i	0.929924	+	0.414029i	0.114848	+	0.993383i	$0.463362\pi$
$920$	0.661873	−	0.735084i	0.0218213	−	0.0242350i
$921$	1.97603	+	19.8230i	0.0651125	+	0.653190i
$922$	1.67180	−	2.30103i	0.0550577	−	0.0757804i
$923$	−1.14343	−	10.8790i	−0.0376366	−	0.358088i
$924$	8.77727	−	26.5286i	0.288751	−	0.872728i
$925$	−2.37140	+	1.36913i	−0.0779712	+	0.0450167i
$926$	17.6697	−	12.8378i	0.580662	−	0.421876i
$927$	−32.2065	−	14.7553i	−1.05780	−	0.484626i
$928$	7.52482	−	2.44496i	0.247014	−	0.0802598i
$929$	−42.6782			−1.40023			−0.700114	−	0.714032i	$-0.746867\pi$
$929$	−42.6782			−1.40023			−0.700114	+	0.714032i	$0.746867\pi$
$930$	−9.41433	−	2.09055i	−0.308708	−	0.0685518i
$931$	−8.33795			−0.273265
$932$	8.17971	−	2.65775i	0.267935	−	0.0870574i
$933$	−22.6311	+	30.8002i	−0.740908	+	1.00835i
$934$	12.6236	−	9.17159i	0.413057	−	0.300104i
$935$	−21.4252	+	12.3698i	−0.700678	+	0.404537i
$936$	0.357759	−	3.08510i	0.0116937	−	0.100840i
$937$	6.11277	+	58.1591i	0.199695	+	1.89997i	0.394123	+	0.919058i	$0.371049\pi$
$937$	6.11277	+	58.1591i	0.199695	+	1.89997i	−0.194427	+	0.980917i	$0.562285\pi$
$938$	5.80005	−	7.98308i	0.189378	−	0.260657i
$939$	7.45312	−	0.742956i	0.243223	−	0.0242454i
$940$	−3.79268	+	4.21220i	−0.123704	+	0.137387i
$941$	28.6666	+	12.7632i	0.934505	+	0.416069i	0.816761	−	0.576975i	$-0.195767\pi$
$941$	28.6666	+	12.7632i	0.934505	+	0.416069i	0.117744	+	0.993044i	$0.462434\pi$
$942$	−0.227371	+	42.3873i	−0.00740815	+	1.38105i
$943$	1.64199	+	7.72494i	0.0534705	+	0.251559i
$944$	1.44775	+	3.25170i	0.0471202	+	0.105834i
$945$	17.1027	−	5.25429i	0.556352	−	0.170922i
$946$	0.481460	−	1.48178i	0.0156536	−	0.0481769i
$947$	37.0792	−	16.5087i	1.20491	−	0.536462i	0.296700	−	0.954971i	$-0.404114\pi$
$947$	37.0792	−	16.5087i	1.20491	−	0.536462i	0.908213	+	0.418509i	$0.137447\pi$
$948$	8.07277	+	18.3967i	0.262191	+	0.597497i
$949$	4.66411	+	0.991387i	0.151403	+	0.0321818i
$950$	−0.698389	+	1.56861i	−0.0226587	+	0.0508923i
$951$	28.1039	+	16.4274i	0.911332	+	0.532696i
$952$	18.0815	+	1.90044i	0.586023	+	0.0615935i
$953$	15.4664	+	11.2370i	0.501005	+	0.364001i	0.809401	−	0.587257i	$-0.199792\pi$
$953$	15.4664	+	11.2370i	0.501005	+	0.364001i	−0.308396	+	0.951258i	$0.599792\pi$
$954$	30.5683	−	17.2140i	0.989685	−	0.557325i
$955$	−10.8456	+	18.7851i	−0.350954	+	0.607871i
$956$	3.50394	+	6.06900i	0.113325	+	0.196285i
$957$	−43.2193	+	47.4852i	−1.39708	+	1.53498i
$958$	−2.94092	−	3.26623i	−0.0950169	−	0.105527i
$959$	16.8419	+	51.8340i	0.543853	+	1.67381i
$960$	0.351021	+	1.69611i	0.0113291	+	0.0547417i
$961$	20.5715	+	23.1908i	0.663597	+	0.748091i
$962$			2.83480i			0.0913977i
$963$	12.2030	−	10.7528i	0.393236	−	0.346505i
$964$	12.8011	−	11.5262i	0.412297	−	0.371234i
$965$	2.56714	+	3.53336i	0.0826390	+	0.113743i
$966$	4.40507	−	3.92376i	0.141731	−	0.126245i
$967$	2.46305	+	1.42204i	0.0792064	+	0.0457298i	0.539080	−	0.842254i	$-0.318772\pi$
$967$	2.46305	+	1.42204i	0.0792064	+	0.0457298i	−0.459874	+	0.887984i	$0.652105\pi$
$968$	−10.8926	+	1.14486i	−0.350102	+	0.0367972i
$969$	−14.3113	−	6.46403i	−0.459747	−	0.207655i
$970$	0.604447	−	5.75092i	0.0194076	−	0.184651i
$971$	24.8345	+	22.3611i	0.796978	+	0.717603i	0.963288	−	0.268471i	$-0.0865184\pi$
$971$	24.8345	+	22.3611i	0.796978	+	0.717603i	−0.166309	+	0.986074i	$0.553185\pi$
$972$	−12.8525	+	8.82117i	−0.412244	+	0.282939i
$973$	11.4814	−	54.0156i	0.368076	−	1.73166i
$974$	26.2374	−	5.57694i	0.840702	−	0.178697i
$975$	1.04617	+	1.45630i	0.0335043	+	0.0466388i
$976$	1.80407	+	0.586179i	0.0577469	+	0.0187631i
$977$	41.1447	+	13.3687i	1.31634	+	0.427704i	0.881235	−	0.472678i	$-0.156712\pi$
$977$	41.1447	+	13.3687i	1.31634	+	0.427704i	0.435102	+	0.900381i	$0.356712\pi$
$978$	2.03278	+	2.82968i	0.0650013	+	0.0904833i
$979$	−41.6998	+	8.86356i	−1.33273	+	0.283281i
$980$	1.00961	−	4.74985i	0.0322509	−	0.151728i
$981$	−42.2791	−	0.453594i	−1.34987	−	0.0144821i
$982$	9.44234	+	8.50192i	0.301317	+	0.271307i
$983$	−2.73304	+	26.0031i	−0.0871704	+	0.829371i	0.860356	+	0.509693i	$0.170241\pi$
$983$	−2.73304	+	26.0031i	−0.0871704	+	0.829371i	−0.947527	+	0.319677i	$0.896426\pi$
$984$	−12.6030	−	5.69241i	−0.401768	−	0.181467i
$985$	−14.3181	+	1.50489i	−0.456212	+	0.0479498i
$986$	−36.1802	−	20.8887i	−1.15221	−	0.665230i
$987$	−25.2420	+	22.4840i	−0.803462	+	0.715674i
$988$	1.04484	+	1.43810i	0.0332409	+	0.0457521i
$989$	0.244440	−	0.220095i	0.00777273	−	0.00699860i
$990$	−9.29275	−	10.5460i	−0.295343	−	0.335174i
$991$		−	8.74566i		−	0.277815i	−0.990305	−	0.138908i	$-0.955641\pi$
$991$		−	8.74566i		−	0.277815i	0.990305	−	0.138908i	$-0.0443591\pi$
$992$	2.28347	−	5.07797i	0.0725004	−	0.161226i
$993$	−9.21598	−	44.5310i	−0.292460	−	1.41315i
$994$	11.2429	+	34.6021i	0.356603	+	1.09751i
$995$	−9.16269	−	10.1762i	−0.290477	−	0.322607i
$996$	7.73618	−	8.49977i	0.245130	−	0.269325i
$997$	−20.8077	−	36.0400i	−0.658986	−	1.14140i	−0.980878	−	0.194621i	$-0.937652\pi$
$997$	−20.8077	−	36.0400i	−0.658986	−	1.14140i	0.321892	−	0.946776i	$-0.395681\pi$
$998$	1.71148	−	2.96438i	0.0541761	−	0.0938357i
$999$	10.7256	−	9.34928i	0.339343	−	0.295798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.10	✓	176
3.2	odd	2	inner	930.2.br.b.11.15	yes	176
31.17	odd	30	inner	930.2.br.b.761.15	yes	176
93.17	even	30	inner	930.2.br.b.761.10	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.10	✓	176	1.1	even	1	trivial
930.2.br.b.11.15	yes	176	3.2	odd	2	inner
930.2.br.b.761.10	yes	176	93.17	even	30	inner
930.2.br.b.761.15	yes	176	31.17	odd	30	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.39578 + 1.02558i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.64438 - 0.544062i) q^{6} +(0.359918 + 3.42439i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.896389 + 2.86295i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.39578 + 1.02558i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.64438 - 0.544062i) q^{6} +(0.359918 + 3.42439i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.896389 + 2.86295i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-4.28029 - 1.90571i) q^{11} +(1.73203 + 0.00929082i) q^{12} +(0.215242 + 1.01263i) q^{13} +(-1.40050 - 3.14556i) q^{14} +(-1.72157 - 0.190286i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.82371 + 2.14765i) q^{17} +(-1.73722 - 2.44583i) q^{18} +(1.67953 + 0.356996i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-3.00960 + 5.14880i) q^{21} +(4.65969 + 0.489754i) q^{22} +(0.800242 + 0.581410i) q^{23} +(-1.65013 + 0.526389i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.517629 - 0.896559i) q^{26} +(-1.68501 + 4.91536i) q^{27} +(2.30398 + 2.55883i) q^{28} +(-2.44496 - 7.52482i) q^{29} +(1.69611 - 0.351021i) q^{30} +(-5.07797 - 2.28347i) q^{31} +1.00000i q^{32} +(-4.01989 - 7.04971i) q^{33} +(3.92396 - 3.53315i) q^{34} +(-2.02389 - 2.78565i) q^{35} +(2.40799 + 1.78929i) q^{36} +(-2.37140 - 1.36913i) q^{37} +(-1.70765 + 0.179481i) q^{38} +(-0.738103 + 1.63416i) q^{39} +(0.104528 - 0.994522i) q^{40} +(5.93336 + 5.34242i) q^{41} +(1.27123 - 5.82682i) q^{42} +(0.0691375 - 0.325266i) q^{43} +(-4.58298 + 0.974141i) q^{44} +(-2.20777 - 2.03119i) q^{45} +(-0.940741 - 0.305665i) q^{46} +(5.39065 + 1.75153i) q^{47} +(1.40670 - 1.01054i) q^{48} +(-4.74985 + 1.00961i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-8.93540 - 1.94943i) q^{51} +(0.769346 + 0.692722i) q^{52} +(-1.22235 + 11.6299i) q^{53} +(0.0836141 - 5.19548i) q^{54} +(4.65969 - 0.489754i) q^{55} +(-2.98194 - 1.72162i) q^{56} +(1.97813 + 2.22077i) q^{57} +(4.65060 + 6.40099i) q^{58} +(-2.64517 + 2.38172i) q^{59} +(-1.50462 + 0.857967i) q^{60} +1.89691i q^{61} +(5.53507 + 0.602535i) q^{62} +(-9.48122 + 4.10001i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.692722 - 0.769346i) q^{65} +(6.00162 + 5.46246i) q^{66} +(1.43290 + 2.48185i) q^{67} +(-2.64010 + 4.57279i) q^{68} +(0.520680 + 1.63223i) q^{69} +(2.78565 + 2.02389i) q^{70} +(-10.5085 - 1.10449i) q^{71} +(-2.84306 - 0.957606i) q^{72} +(1.87339 - 4.20771i) q^{73} +(2.67842 + 0.569316i) q^{74} +(1.58606 - 0.695991i) q^{75} +(1.56861 - 0.698389i) q^{76} +(4.98533 - 15.3433i) q^{77} +(0.196995 - 1.78226i) q^{78} +(4.71772 + 10.5962i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-7.39297 + 5.13263i) q^{81} +(-7.29386 - 3.24744i) q^{82} +(4.44010 - 4.93123i) q^{83} +(0.591571 + 5.93447i) q^{84} +(3.10363 - 4.27177i) q^{85} +(0.0347592 + 0.330711i) q^{86} +(4.30465 - 13.0105i) q^{87} +(4.05764 - 2.34268i) q^{88} +(7.36112 - 5.34817i) q^{89} +(2.72739 + 1.24954i) q^{90} +(-3.39018 + 1.10154i) q^{91} +0.989153 q^{92} +(-4.74584 - 8.39506i) q^{93} -5.66807 q^{94} +(-1.63302 + 0.530599i) q^{95} +(-1.02558 + 1.39578i) q^{96} +(4.67822 - 3.39893i) q^{97} +(4.20539 - 2.42798i) q^{98} +(1.61914 - 13.9625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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