LMFDB - Embedded newform 1815.2.c.i.364.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, 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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 $ x^12 + 21x^10 + 164x^8 + 589x^6 + 965x^4 + 576*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.9
Root			$1.53672i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.i.364.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.53672i q^{2} -1.00000i q^{3} -0.361523 q^{4} +(1.20807 - 1.88164i) q^{5} +1.53672 q^{6} +2.86503i q^{7} +2.51789i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.53672i q^{2} -1.00000i q^{3} -0.361523 q^{4} +(1.20807 - 1.88164i) q^{5} +1.53672 q^{6} +2.86503i q^{7} +2.51789i q^{8} -1.00000 q^{9} +(2.89156 + 1.85647i) q^{10} +0.361523i q^{12} +2.43598i q^{13} -4.40277 q^{14} +(-1.88164 - 1.20807i) q^{15} -4.59235 q^{16} +3.88488i q^{17} -1.53672i q^{18} -5.93848 q^{19} +(-0.436745 + 0.680257i) q^{20} +2.86503 q^{21} +6.02732i q^{23} +2.51789 q^{24} +(-2.08114 - 4.54630i) q^{25} -3.74343 q^{26} +1.00000i q^{27} -1.03578i q^{28} -4.03698 q^{29} +(1.85647 - 2.89156i) q^{30} -0.783128 q^{31} -2.02140i q^{32} -5.96999 q^{34} +(5.39096 + 3.46116i) q^{35} +0.361523 q^{36} +8.02406i q^{37} -9.12581i q^{38} +2.43598 q^{39} +(4.73776 + 3.04178i) q^{40} -7.54195 q^{41} +4.40277i q^{42} -9.90572i q^{43} +(-1.20807 + 1.88164i) q^{45} -9.26233 q^{46} +0.551103i q^{47} +4.59235i q^{48} -1.20842 q^{49} +(6.98641 - 3.19814i) q^{50} +3.88488 q^{51} -0.880664i q^{52} -2.75907i q^{53} -1.53672 q^{54} -7.21383 q^{56} +5.93848i q^{57} -6.20372i q^{58} +14.5497 q^{59} +(0.680257 + 0.436745i) q^{60} +13.7901 q^{61} -1.20345i q^{62} -2.86503i q^{63} -6.07836 q^{64} +(4.58364 + 2.94283i) q^{65} +3.96724i q^{67} -1.40447i q^{68} +6.02732 q^{69} +(-5.31884 + 8.28443i) q^{70} +9.27271 q^{71} -2.51789i q^{72} -0.615424i q^{73} -12.3308 q^{74} +(-4.54630 + 2.08114i) q^{75} +2.14690 q^{76} +3.74343i q^{78} -4.53993 q^{79} +(-5.54787 + 8.64115i) q^{80} +1.00000 q^{81} -11.5899i q^{82} +11.6797i q^{83} -1.03578 q^{84} +(7.30995 + 4.69320i) q^{85} +15.2224 q^{86} +4.03698i q^{87} -16.9894 q^{89} +(-2.89156 - 1.85647i) q^{90} -6.97917 q^{91} -2.17902i q^{92} +0.783128i q^{93} -0.846893 q^{94} +(-7.17409 + 11.1741i) q^{95} -2.02140 q^{96} +8.95511i q^{97} -1.85700i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9	$ 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9} + 12 q^{10} + 20 q^{14} + 22 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{25} - 24 q^{29} - 8 q^{30} + 36 q^{31} + 2 q^{34} + 24 q^{35} + 18 q^{36} - 4 q^{39} - 22 q^{40} - 12 q^{41} + 2 q^{45} - 22 q^{46} - 24 q^{49} - 58 q^{50} + 4 q^{51} - 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} + 8 q^{61} - 44 q^{64} - 14 q^{65} - 24 q^{69} - 16 q^{70} + 8 q^{74} - 12 q^{75} - 40 q^{76} - 4 q^{79} - 58 q^{80} + 12 q^{81} + 48 q^{84} - 2 q^{85} + 56 q^{86} + 32 q^{89} - 12 q^{90} + 48 q^{91} - 6 q^{94} + 62 q^{96}+O(q^{100}) $ 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9 + 12 * q^10 + 20 * q^14 + 22 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^25 - 24 * q^29 - 8 * q^30 + 36 * q^31 + 2 * q^34 + 24 * q^35 + 18 * q^36 - 4 * q^39 - 22 * q^40 - 12 * q^41 + 2 * q^45 - 22 * q^46 - 24 * q^49 - 58 * q^50 + 4 * q^51 - 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 + 8 * q^61 - 44 * q^64 - 14 * q^65 - 24 * q^69 - 16 * q^70 + 8 * q^74 - 12 * q^75 - 40 * q^76 - 4 * q^79 - 58 * q^80 + 12 * q^81 + 48 * q^84 - 2 * q^85 + 56 * q^86 + 32 * q^89 - 12 * q^90 + 48 * q^91 - 6 * q^94 + 62 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.53672i			1.08663i	0.839529	+	0.543314i	$0.182831\pi$
$2$			1.53672i			1.08663i	−0.839529	+	0.543314i	$0.817169\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.361523			−0.180762
$5$	1.20807	−	1.88164i	0.540264	−	0.841495i
$5$	1.20807	−	1.88164i	0.540264	−	0.841495i
$6$	1.53672			0.627365
$7$			2.86503i			1.08288i	0.840739	+	0.541440i	$0.182121\pi$
$7$			2.86503i			1.08288i	−0.840739	+	0.541440i	$0.817879\pi$
$8$			2.51789i			0.890208i
$9$	−1.00000			−0.333333
$10$	2.89156	+	1.85647i	0.914393	+	0.587067i
$11$		0			0
$11$		0			0
$12$			0.361523i			0.104363i
$13$			2.43598i			0.675620i	0.941214	+	0.337810i	$0.109686\pi$
$13$			2.43598i			0.675620i	−0.941214	+	0.337810i	$0.890314\pi$
$14$	−4.40277			−1.17669
$15$	−1.88164	−	1.20807i	−0.485838	−	0.311922i
$16$	−4.59235			−1.14809
$17$			3.88488i			0.942222i	0.882074	+	0.471111i	$0.156147\pi$
$17$			3.88488i			0.942222i	−0.882074	+	0.471111i	$0.843853\pi$
$18$		−	1.53672i		−	0.362210i
$19$	−5.93848			−1.36238			−0.681191	−	0.732106i	$-0.738538\pi$
$19$	−5.93848			−1.36238			−0.681191	+	0.732106i	$0.738538\pi$
$20$	−0.436745	+	0.680257i	−0.0976591	+	0.152110i
$21$	2.86503			0.625202
$22$		0			0
$23$			6.02732i			1.25678i	0.777897	+	0.628392i	$0.216286\pi$
$23$			6.02732i			1.25678i	−0.777897	+	0.628392i	$0.783714\pi$
$24$	2.51789			0.513962
$25$	−2.08114	−	4.54630i	−0.416229	−	0.909260i
$26$	−3.74343			−0.734148
$27$			1.00000i			0.192450i
$28$		−	1.03578i		−	0.195743i
$29$	−4.03698			−0.749648			−0.374824	−	0.927096i	$-0.622297\pi$
$29$	−4.03698			−0.749648			−0.374824	+	0.927096i	$0.622297\pi$
$30$	1.85647	−	2.89156i	0.338943	−	0.527925i
$31$	−0.783128			−0.140654			−0.0703270	−	0.997524i	$-0.522404\pi$
$31$	−0.783128			−0.140654			−0.0703270	+	0.997524i	$0.522404\pi$
$32$		−	2.02140i		−	0.357336i
$33$		0			0
$34$	−5.96999			−1.02385
$35$	5.39096	+	3.46116i	0.911239	+	0.585042i
$36$	0.361523			0.0602539
$37$			8.02406i			1.31915i	0.751640	+	0.659574i	$0.229263\pi$
$37$			8.02406i			1.31915i	−0.751640	+	0.659574i	$0.770737\pi$
$38$		−	9.12581i		−	1.48040i
$39$	2.43598			0.390069
$40$	4.73776	+	3.04178i	0.749106	+	0.480948i
$41$	−7.54195			−1.17785			−0.588927	−	0.808186i	$-0.700450\pi$
$41$	−7.54195			−1.17785			−0.588927	+	0.808186i	$0.700450\pi$
$42$			4.40277i			0.679362i
$43$		−	9.90572i		−	1.51061i	−0.655374	−	0.755304i	$-0.727489\pi$
$43$		−	9.90572i		−	1.51061i	0.655374	−	0.755304i	$-0.272511\pi$
$44$		0			0
$45$	−1.20807	+	1.88164i	−0.180088	+	0.280498i
$46$	−9.26233			−1.36566
$47$			0.551103i			0.0803866i	0.999192	+	0.0401933i	$0.0127974\pi$
$47$			0.551103i			0.0803866i	−0.999192	+	0.0401933i	$0.987203\pi$
$48$			4.59235i			0.662848i
$49$	−1.20842			−0.172631
$50$	6.98641	−	3.19814i	0.988028	−	0.452286i
$51$	3.88488			0.543992
$52$		−	0.880664i		−	0.122126i
$53$		−	2.75907i		−	0.378987i	−0.981882	−	0.189493i	$-0.939315\pi$
$53$		−	2.75907i		−	0.378987i	0.981882	−	0.189493i	$-0.0606846\pi$
$54$	−1.53672			−0.209122
$55$		0			0
$56$	−7.21383			−0.963989
$57$			5.93848i			0.786571i
$58$		−	6.20372i		−	0.814589i
$59$	14.5497			1.89421			0.947103	−	0.320931i	$-0.103996\pi$
$59$	14.5497			1.89421			0.947103	+	0.320931i	$0.103996\pi$
$60$	0.680257	+	0.436745i	0.0878208	+	0.0563835i
$61$	13.7901			1.76565			0.882824	−	0.469704i	$-0.155639\pi$
$61$	13.7901			1.76565			0.882824	+	0.469704i	$0.155639\pi$
$62$		−	1.20345i		−	0.152839i
$63$		−	2.86503i		−	0.360960i
$64$	−6.07836			−0.759795
$65$	4.58364	+	2.94283i	0.568531	+	0.365013i
$66$		0			0
$67$			3.96724i			0.484675i	0.970192	+	0.242338i	$0.0779142\pi$
$67$			3.96724i			0.484675i	−0.970192	+	0.242338i	$0.922086\pi$
$68$		−	1.40447i		−	0.170318i
$69$	6.02732			0.725604
$70$	−5.31884	+	8.28443i	−0.635723	+	0.990178i
$71$	9.27271			1.10047			0.550234	−	0.835010i	$-0.314538\pi$
$71$	9.27271			1.10047			0.550234	+	0.835010i	$0.314538\pi$
$72$		−	2.51789i		−	0.296736i
$73$		−	0.615424i		−	0.0720300i	−0.999351	−	0.0360150i	$-0.988534\pi$
$73$		−	0.615424i		−	0.0720300i	0.999351	−	0.0360150i	$-0.0114664\pi$
$74$	−12.3308			−1.43342
$75$	−4.54630	+	2.08114i	−0.524961	+	0.240310i
$76$	2.14690			0.246266
$77$		0			0
$78$			3.74343i			0.423861i
$79$	−4.53993			−0.510782			−0.255391	−	0.966838i	$-0.582204\pi$
$79$	−4.53993			−0.510782			−0.255391	+	0.966838i	$0.582204\pi$
$80$	−5.54787	+	8.64115i	−0.620270	+	0.966110i
$81$	1.00000			0.111111
$82$		−	11.5899i		−	1.27989i
$83$			11.6797i			1.28202i	0.767534	+	0.641008i	$0.221483\pi$
$83$			11.6797i			1.28202i	−0.767534	+	0.641008i	$0.778517\pi$
$84$	−1.03578			−0.113012
$85$	7.30995	+	4.69320i	0.792875	+	0.509049i
$86$	15.2224			1.64147
$87$			4.03698i			0.432809i
$88$		0			0
$89$	−16.9894			−1.80087			−0.900437	−	0.434986i	$-0.856753\pi$
$89$	−16.9894			−1.80087			−0.900437	+	0.434986i	$0.856753\pi$
$90$	−2.89156	−	1.85647i	−0.304798	−	0.195689i
$91$	−6.97917			−0.731616
$92$		−	2.17902i		−	0.227178i
$93$			0.783128i			0.0812066i
$94$	−0.846893			−0.0873504
$95$	−7.17409	+	11.1741i	−0.736046	+	1.14644i
$96$	−2.02140			−0.206308
$97$			8.95511i			0.909254i	0.890682	+	0.454627i	$0.150227\pi$
$97$			8.95511i			0.909254i	−0.890682	+	0.454627i	$0.849773\pi$
$98$		−	1.85700i		−	0.187586i
$99$		0			0
$100$	0.752382	+	1.64359i	0.0752382	+	0.164359i
$101$	−4.05035			−0.403024			−0.201512	−	0.979486i	$-0.564586\pi$
$101$	−4.05035			−0.403024			−0.201512	+	0.979486i	$0.564586\pi$
$102$			5.96999i			0.591117i
$103$		−	3.09729i		−	0.305185i	−0.988289	−	0.152593i	$-0.951238\pi$
$103$		−	3.09729i		−	0.305185i	0.988289	−	0.152593i	$-0.0487623\pi$
$104$	−6.13353			−0.601442
$105$	3.46116	−	5.39096i	0.337774	−	0.526104i
$106$	4.23992			0.411818
$107$			5.42307i			0.524268i	0.965032	+	0.262134i	$0.0844262\pi$
$107$			5.42307i			0.524268i	−0.965032	+	0.262134i	$0.915574\pi$
$108$		−	0.361523i		−	0.0347876i
$109$	2.29776			0.220085			0.110043	−	0.993927i	$-0.464901\pi$
$109$	2.29776			0.220085			0.110043	+	0.993927i	$0.464901\pi$
$110$		0			0
$111$	8.02406			0.761610
$112$		−	13.1572i		−	1.24324i
$113$			9.61495i			0.904498i	0.891892	+	0.452249i	$0.149378\pi$
$113$			9.61495i			0.904498i	−0.891892	+	0.452249i	$0.850622\pi$
$114$	−9.12581			−0.854711
$115$	11.3413	+	7.28141i	1.05758	+	0.678995i
$116$	1.45946			0.135508
$117$		−	2.43598i		−	0.225207i
$118$			22.3588i			2.05830i
$119$	−11.1303			−1.02031
$120$	3.04178	−	4.73776i	0.277675	−	0.432496i
$121$		0			0
$122$			21.1917i			1.91860i
$123$			7.54195i			0.680035i
$124$	0.283119			0.0254248
$125$	−11.0687	−	1.57628i	−0.990012	−	0.140986i
$126$	4.40277			0.392230
$127$		−	19.6140i		−	1.74046i	−0.492648	−	0.870229i	$-0.663971\pi$
$127$		−	19.6140i		−	1.74046i	0.492648	−	0.870229i	$-0.336029\pi$
$128$		−	13.3836i		−	1.18295i
$129$	−9.90572			−0.872150
$130$	−4.52232	+	7.04380i	−0.396634	+	0.617782i
$131$	4.00843			0.350218			0.175109	−	0.984549i	$-0.443972\pi$
$131$	4.00843			0.350218			0.175109	+	0.984549i	$0.443972\pi$
$132$		0			0
$133$		−	17.0140i		−	1.47530i
$134$	−6.09655			−0.526662
$135$	1.88164	+	1.20807i	0.161946	+	0.103974i
$136$	−9.78169			−0.838773
$137$			23.1747i			1.97995i	0.141242	+	0.989975i	$0.454891\pi$
$137$			23.1747i			1.97995i	−0.141242	+	0.989975i	$0.545109\pi$
$138$			9.26233i			0.788462i
$139$	13.8238			1.17252			0.586260	−	0.810123i	$-0.300600\pi$
$139$	13.8238			1.17252			0.586260	+	0.810123i	$0.300600\pi$
$140$	−1.94896	−	1.25129i	−0.164717	−	0.105753i
$141$	0.551103			0.0464112
$142$			14.2496i			1.19580i
$143$		0			0
$144$	4.59235			0.382696
$145$	−4.87694	+	7.59614i	−0.405008	+	0.630825i
$146$	0.945738			0.0782698
$147$			1.20842i			0.0996685i
$148$		−	2.90088i		−	0.238451i
$149$	−13.5293			−1.10836			−0.554181	−	0.832396i	$-0.686968\pi$
$149$	−13.5293			−1.10836			−0.554181	+	0.832396i	$0.686968\pi$
$150$	−3.19814	−	6.98641i	−0.261127	−	0.570438i
$151$	21.7316			1.76849			0.884245	−	0.467024i	$-0.154674\pi$
$151$	21.7316			1.76849			0.884245	+	0.467024i	$0.154674\pi$
$152$		−	14.9524i		−	1.21280i
$153$		−	3.88488i		−	0.314074i
$154$		0			0
$155$	−0.946072	+	1.47357i	−0.0759903	+	0.118360i
$156$	−0.880664			−0.0705096
$157$		−	10.0477i		−	0.801894i	−0.916101	−	0.400947i	$-0.868681\pi$
$157$		−	10.0477i		−	0.801894i	0.916101	−	0.400947i	$-0.131319\pi$
$158$		−	6.97662i		−	0.555030i
$159$	−2.75907			−0.218808
$160$	−3.80355	−	2.44199i	−0.300697	−	0.193056i
$161$	−17.2685			−1.36095
$162$			1.53672i			0.120737i
$163$		−	17.0119i		−	1.33248i	−0.745739	−	0.666239i	$-0.767903\pi$
$163$		−	17.0119i		−	1.33248i	0.745739	−	0.666239i	$-0.232097\pi$
$164$	2.72659			0.212911
$165$		0			0
$166$	−17.9485			−1.39308
$167$			8.17422i			0.632540i	0.948669	+	0.316270i	$0.102431\pi$
$167$			8.17422i			0.632540i	−0.948669	+	0.316270i	$0.897569\pi$
$168$			7.21383i			0.556559i
$169$	7.06599			0.543538
$170$	−7.21216	+	11.2334i	−0.553147	+	0.861561i
$171$	5.93848			0.454127
$172$			3.58115i			0.273060i
$173$			0.0419137i			0.00318664i	0.999999	+	0.00159332i	$0.000507170\pi$
$173$			0.0419137i			0.00318664i	−0.999999	+	0.00159332i	$0.999493\pi$
$174$	−6.20372			−0.470303
$175$	13.0253	−	5.96255i	0.984620	−	0.450726i
$176$		0			0
$177$		−	14.5497i		−	1.09362i
$178$		−	26.1081i		−	1.95688i
$179$	21.5288			1.60914			0.804570	−	0.593857i	$-0.202396\pi$
$179$	21.5288			1.60914			0.804570	+	0.593857i	$0.202396\pi$
$180$	0.436745	−	0.680257i	0.0325530	−	0.0507033i
$181$	10.9246			0.812020			0.406010	−	0.913869i	$-0.366920\pi$
$181$	10.9246			0.812020			0.406010	+	0.913869i	$0.366920\pi$
$182$		−	10.7251i		−	0.794995i
$183$		−	13.7901i		−	1.01940i
$184$	−15.1761			−1.11880
$185$	15.0984	+	9.69361i	1.11006	+	0.712689i
$186$	−1.20345			−0.0882414
$187$		0			0
$188$		−	0.199236i		−	0.0145308i
$189$	−2.86503			−0.208401
$190$	−17.1715	−	11.0246i	−1.24575	−	0.799809i
$191$	−0.485281			−0.0351137			−0.0175569	−	0.999846i	$-0.505589\pi$
$191$	−0.485281			−0.0351137			−0.0175569	+	0.999846i	$0.505589\pi$
$192$			6.07836i			0.438668i
$193$		−	12.5864i		−	0.905989i	−0.891513	−	0.452994i	$-0.850356\pi$
$193$		−	12.5864i		−	0.905989i	0.891513	−	0.452994i	$-0.149644\pi$
$194$	−13.7615			−0.988021
$195$	2.94283	−	4.58364i	0.210741	−	0.328242i
$196$	0.436870			0.0312050
$197$		−	15.8941i		−	1.13241i	−0.824265	−	0.566204i	$-0.808412\pi$
$197$		−	15.8941i		−	1.13241i	0.824265	−	0.566204i	$-0.191588\pi$
$198$		0			0
$199$	5.02089			0.355922			0.177961	−	0.984038i	$-0.443050\pi$
$199$	5.02089			0.355922			0.177961	+	0.984038i	$0.443050\pi$
$200$	11.4471	−	5.24009i	0.809430	−	0.370530i
$201$	3.96724			0.279827
$202$		−	6.22427i		−	0.437938i
$203$		−	11.5661i		−	0.811779i
$204$	−1.40447			−0.0983329
$205$	−9.11119	+	14.1912i	−0.636353	+	0.991159i
$206$	4.75969			0.331623
$207$		−	6.02732i		−	0.418928i
$208$		−	11.1869i		−	0.775670i
$209$		0			0
$210$	8.28443	+	5.31884i	0.571680	+	0.367035i
$211$	0.800040			0.0550770			0.0275385	−	0.999621i	$-0.491233\pi$
$211$	0.800040			0.0550770			0.0275385	+	0.999621i	$0.491233\pi$
$212$			0.997466i			0.0685063i
$213$		−	9.27271i		−	0.635356i
$214$	−8.33376			−0.569684
$215$	−18.6390	−	11.9668i	−1.27117	−	0.816128i
$216$	−2.51789			−0.171321
$217$		−	2.24369i		−	0.152311i
$218$			3.53102i			0.239151i
$219$	−0.615424			−0.0415865
$220$		0			0
$221$	−9.46350			−0.636584
$222$			12.3308i			0.827587i
$223$			8.10773i			0.542933i	0.962448	+	0.271467i	$0.0875087\pi$
$223$			8.10773i			0.542933i	−0.962448	+	0.271467i	$0.912491\pi$
$224$	5.79137			0.386952
$225$	2.08114	+	4.54630i	0.138743	+	0.303087i
$226$	−14.7755			−0.982853
$227$			8.70426i			0.577722i	0.957371	+	0.288861i	$0.0932766\pi$
$227$			8.70426i			0.577722i	−0.957371	+	0.288861i	$0.906723\pi$
$228$		−	2.14690i		−	0.142182i
$229$	−29.6210			−1.95741			−0.978705	−	0.205272i	$-0.934192\pi$
$229$	−29.6210			−1.95741			−0.978705	+	0.205272i	$0.934192\pi$
$230$	−11.1895	+	17.4284i	−0.737816	+	1.14919i
$231$		0			0
$232$		−	10.1647i		−	0.667342i
$233$			6.71715i			0.440055i	0.975494	+	0.220028i	$0.0706148\pi$
$233$			6.71715i			0.440055i	−0.975494	+	0.220028i	$0.929385\pi$
$234$	3.74343			0.244716
$235$	1.03698	+	0.665769i	0.0676449	+	0.0434300i
$236$	−5.26004			−0.342400
$237$			4.53993i			0.294900i
$238$		−	17.1042i		−	1.10870i
$239$	−2.23252			−0.144409			−0.0722047	−	0.997390i	$-0.523003\pi$
$239$	−2.23252			−0.144409			−0.0722047	+	0.997390i	$0.523003\pi$
$240$	8.64115	+	5.54787i	0.557784	+	0.358113i
$241$	−8.20298			−0.528400			−0.264200	−	0.964468i	$-0.585108\pi$
$241$	−8.20298			−0.528400			−0.264200	+	0.964468i	$0.585108\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−4.98546			−0.319161
$245$	−1.45985	+	2.27381i	−0.0932663	+	0.145268i
$246$	−11.5899			−0.738945
$247$		−	14.4660i		−	0.920452i
$248$		−	1.97183i		−	0.125211i
$249$	11.6797			0.740172
$250$	2.42230	−	17.0095i	0.153200	−	1.07577i
$251$	−0.900721			−0.0568530			−0.0284265	−	0.999596i	$-0.509050\pi$
$251$	−0.900721			−0.0568530			−0.0284265	+	0.999596i	$0.509050\pi$
$252$			1.03578i			0.0652478i
$253$		0			0
$254$	30.1413			1.89123
$255$	4.69320	−	7.30995i	0.293900	−	0.457767i
$256$	8.41013			0.525633
$257$			4.27720i			0.266804i	0.991062	+	0.133402i	$0.0425902\pi$
$257$			4.27720i			0.266804i	−0.991062	+	0.133402i	$0.957410\pi$
$258$		−	15.2224i		−	0.947703i
$259$	−22.9892			−1.42848
$260$	−1.65709	−	1.06390i	−0.102769	−	0.0659804i
$261$	4.03698			0.249883
$262$			6.15986i			0.380557i
$263$			3.64614i			0.224831i	0.993661	+	0.112415i	$0.0358587\pi$
$263$			3.64614i			0.224831i	−0.993661	+	0.112415i	$0.964141\pi$
$264$		0			0
$265$	−5.19157	−	3.33314i	−0.318916	−	0.204753i
$266$	26.1458			1.60310
$267$			16.9894i			1.03974i
$268$		−	1.43425i		−	0.0876107i
$269$	11.2872			0.688192			0.344096	−	0.938934i	$-0.388185\pi$
$269$	11.2872			0.688192			0.344096	+	0.938934i	$0.388185\pi$
$270$	−1.85647	+	2.89156i	−0.112981	+	0.175975i
$271$	9.58466			0.582227			0.291113	−	0.956689i	$-0.405974\pi$
$271$	9.58466			0.582227			0.291113	+	0.956689i	$0.405974\pi$
$272$		−	17.8407i		−	1.08175i
$273$			6.97917i			0.422399i
$274$	−35.6132			−2.15147
$275$		0			0
$276$	−2.17902			−0.131161
$277$		−	26.9810i		−	1.62113i	−0.585648	−	0.810565i	$-0.699160\pi$
$277$		−	26.9810i		−	1.62113i	0.585648	−	0.810565i	$-0.300840\pi$
$278$			21.2434i			1.27409i
$279$	0.783128			0.0468846
$280$	−8.71480	+	13.5738i	−0.520809	+	0.811192i
$281$	18.9918			1.13296			0.566479	−	0.824076i	$-0.308305\pi$
$281$	18.9918			1.13296			0.566479	+	0.824076i	$0.308305\pi$
$282$			0.846893i			0.0504317i
$283$			27.0944i			1.61060i	0.592870	+	0.805298i	$0.297995\pi$
$283$			27.0944i			1.61060i	−0.592870	+	0.805298i	$0.702005\pi$
$284$	−3.35230			−0.198922
$285$	11.1741	+	7.17409i	0.661896	+	0.424956i
$286$		0			0
$287$		−	21.6079i		−	1.27548i
$288$			2.02140i			0.119112i
$289$	1.90771			0.112218
$290$	−11.6732	−	7.49452i	−0.685473	−	0.440093i
$291$	8.95511			0.524958
$292$			0.222490i			0.0130202i
$293$			9.07599i			0.530225i	0.964218	+	0.265112i	$0.0854091\pi$
$293$			9.07599i			0.530225i	−0.964218	+	0.265112i	$0.914591\pi$
$294$	−1.85700			−0.108303
$295$	17.5770	−	27.3772i	1.02337	−	1.59396i
$296$	−20.2037			−1.17432
$297$		0			0
$298$		−	20.7908i		−	1.20438i
$299$	−14.6824			−0.849108
$300$	1.64359	−	0.752382i	0.0948929	−	0.0434388i
$301$	28.3802			1.63581
$302$			33.3954i			1.92169i
$303$			4.05035i			0.232686i
$304$	27.2716			1.56413
$305$	16.6594	−	25.9481i	0.953917	−	1.48578i
$306$	5.96999			0.341282
$307$		−	6.10964i		−	0.348696i	−0.984684	−	0.174348i	$-0.944218\pi$
$307$		−	6.10964i		−	0.348696i	0.984684	−	0.174348i	$-0.0557817\pi$
$308$		0			0
$309$	−3.09729			−0.176199
$310$	−2.26446	−	1.45385i	−0.128613	−	0.0825732i
$311$	−14.8604			−0.842655			−0.421327	−	0.906909i	$-0.638436\pi$
$311$	−14.8604			−0.842655			−0.421327	+	0.906909i	$0.638436\pi$
$312$			6.13353i			0.347243i
$313$		−	27.4142i		−	1.54954i	−0.632240	−	0.774772i	$-0.717864\pi$
$313$		−	27.4142i		−	1.54954i	0.632240	−	0.774772i	$-0.282136\pi$
$314$	15.4406			0.871361
$315$	−5.39096	−	3.46116i	−0.303746	−	0.195014i
$316$	1.64129			0.0923298
$317$			13.9328i			0.782543i	0.920275	+	0.391272i	$0.127965\pi$
$317$			13.9328i			0.782543i	−0.920275	+	0.391272i	$0.872035\pi$
$318$		−	4.23992i		−	0.237763i
$319$		0			0
$320$	−7.34307	+	11.4373i	−0.410490	+	0.639364i
$321$	5.42307			0.302686
$322$		−	26.5369i		−	1.47884i
$323$		−	23.0703i		−	1.28367i
$324$	−0.361523			−0.0200846
$325$	11.0747	−	5.06963i	0.614314	−	0.281212i
$326$	26.1427			1.44791
$327$		−	2.29776i		−	0.127066i
$328$		−	18.9898i		−	1.04854i
$329$	−1.57893			−0.0870491
$330$		0			0
$331$	24.9385			1.37074			0.685371	−	0.728194i	$-0.259640\pi$
$331$	24.9385			1.37074			0.685371	+	0.728194i	$0.259640\pi$
$332$		−	4.22249i		−	0.231739i
$333$		−	8.02406i		−	0.439716i
$334$	−12.5615			−0.687336
$335$	7.46492	+	4.79269i	0.407852	+	0.261853i
$336$	−13.1572			−0.717786
$337$			16.2380i			0.884541i	0.896882	+	0.442271i	$0.145827\pi$
$337$			16.2380i			0.884541i	−0.896882	+	0.442271i	$0.854173\pi$
$338$			10.8585i			0.590623i
$339$	9.61495			0.522212
$340$	−2.64272	−	1.69670i	−0.143321	−	0.0920165i
$341$		0			0
$342$			9.12581i			0.493468i
$343$			16.5931i			0.895942i
$344$	24.9415			1.34476
$345$	7.28141	−	11.3413i	0.392018	−	0.610592i
$346$	−0.0644098			−0.00346269
$347$			27.4616i			1.47422i	0.675774	+	0.737109i	$0.263809\pi$
$347$			27.4616i			1.47422i	−0.675774	+	0.737109i	$0.736191\pi$
$348$		−	1.45946i		−	0.0782353i
$349$	25.1370			1.34555			0.672777	−	0.739845i	$-0.265101\pi$
$349$	25.1370			1.34555			0.672777	+	0.739845i	$0.265101\pi$
$350$	9.16279	+	20.0163i	0.489772	+	1.06992i
$351$	−2.43598			−0.130023
$352$		0			0
$353$		−	12.2362i		−	0.651267i	−0.945496	−	0.325633i	$-0.894423\pi$
$353$		−	12.2362i		−	0.651267i	0.945496	−	0.325633i	$-0.105577\pi$
$354$	22.3588			1.18836
$355$	11.2021	−	17.4479i	0.594544	−	0.926039i
$356$	6.14207			0.325529
$357$			11.1303i			0.589079i
$358$			33.0839i			1.74854i
$359$	−3.88413			−0.204997			−0.102498	−	0.994733i	$-0.532684\pi$
$359$	−3.88413			−0.204997			−0.102498	+	0.994733i	$0.532684\pi$
$360$	−4.73776	−	3.04178i	−0.249702	−	0.160316i
$361$	16.2656			0.856083
$362$			16.7881i			0.882364i
$363$		0			0
$364$	2.52313			0.132248
$365$	−1.15801	−	0.743474i	−0.0606129	−	0.0389152i
$366$	21.1917			1.10771
$367$		−	19.5703i		−	1.02156i	−0.859712	−	0.510780i	$-0.829357\pi$
$367$		−	19.5703i		−	1.02156i	0.859712	−	0.510780i	$-0.170643\pi$
$368$		−	27.6795i		−	1.44290i
$369$	7.54195			0.392618
$370$	−14.8964	+	23.2021i	−0.774428	+	1.20622i
$371$	7.90482			0.410398
$372$		−	0.283119i		−	0.0146790i
$373$			0.729978i			0.0377968i	0.999821	+	0.0188984i	$0.00601591\pi$
$373$			0.729978i			0.0377968i	−0.999821	+	0.0188984i	$0.993984\pi$
$374$		0			0
$375$	−1.57628	+	11.0687i	−0.0813985	+	0.571583i
$376$	−1.38761			−0.0715608
$377$		−	9.83401i		−	0.506477i
$378$		−	4.40277i		−	0.226454i
$379$	−36.0155			−1.84999			−0.924997	−	0.379975i	$-0.875933\pi$
$379$	−36.0155			−1.84999			−0.924997	+	0.379975i	$0.875933\pi$
$380$	2.59360	−	4.03969i	0.133049	−	0.207232i
$381$	−19.6140			−1.00485
$382$		−	0.745744i		−	0.0381556i
$383$		−	12.4551i		−	0.636428i	−0.948019	−	0.318214i	$-0.896917\pi$
$383$		−	12.4551i		−	0.636428i	0.948019	−	0.318214i	$-0.103083\pi$
$384$	−13.3836			−0.682977
$385$		0			0
$386$	19.3418			0.984473
$387$			9.90572i			0.503536i
$388$		−	3.23748i		−	0.164358i
$389$	20.4612			1.03742			0.518711	−	0.854950i	$-0.326412\pi$
$389$	20.4612			1.03742			0.518711	+	0.854950i	$0.326412\pi$
$390$	7.04380	+	4.52232i	0.356677	+	0.228997i
$391$	−23.4154			−1.18417
$392$		−	3.04266i		−	0.153677i
$393$		−	4.00843i		−	0.202199i
$394$	24.4249			1.23051
$395$	−5.48455	+	8.54252i	−0.275957	+	0.429821i
$396$		0			0
$397$			23.9046i			1.19974i	0.800098	+	0.599869i	$0.204781\pi$
$397$			23.9046i			1.19974i	−0.800098	+	0.599869i	$0.795219\pi$
$398$			7.71573i			0.386755i
$399$	−17.0140			−0.851763
$400$	9.55733	+	20.8782i	0.477867	+	1.04391i
$401$	−9.45101			−0.471961			−0.235980	−	0.971758i	$-0.575830\pi$
$401$	−9.45101			−0.471961			−0.235980	+	0.971758i	$0.575830\pi$
$402$			6.09655i			0.304068i
$403$		−	1.90769i		−	0.0950286i
$404$	1.46429			0.0728513
$405$	1.20807	−	1.88164i	0.0600294	−	0.0934995i
$406$	17.7739			0.882103
$407$		0			0
$408$			9.78169i			0.484266i
$409$	−7.69520			−0.380503			−0.190252	−	0.981735i	$-0.560930\pi$
$409$	−7.69520			−0.380503			−0.190252	+	0.981735i	$0.560930\pi$
$410$	−21.8080	−	14.0014i	−1.07702	−	0.691479i
$411$	23.1747			1.14312
$412$			1.11974i			0.0551658i
$413$			41.6853i			2.05120i
$414$	9.26233			0.455219
$415$	21.9770	+	14.1099i	1.07881	+	0.692628i
$416$	4.92409			0.241423
$417$		−	13.8238i		−	0.676955i
$418$		0			0
$419$	30.0599			1.46852			0.734262	−	0.678866i	$-0.237528\pi$
$419$	30.0599			1.46852			0.734262	+	0.678866i	$0.237528\pi$
$420$	−1.25129	+	1.94896i	−0.0610566	+	0.0950994i
$421$	−23.8194			−1.16088			−0.580442	−	0.814301i	$-0.697120\pi$
$421$	−23.8194			−1.16088			−0.580442	+	0.814301i	$0.697120\pi$
$422$			1.22944i			0.0598482i
$423$		−	0.551103i		−	0.0267955i
$424$	6.94702			0.337377
$425$	17.6618	−	8.08499i	0.856725	−	0.392180i
$426$	14.2496			0.690396
$427$			39.5092i			1.91199i
$428$		−	1.96056i		−	0.0947675i
$429$		0			0
$430$	18.3897	−	28.6430i	0.886828	−	1.38129i
$431$	0.608493			0.0293101			0.0146550	−	0.999893i	$-0.495335\pi$
$431$	0.608493			0.0293101			0.0146550	+	0.999893i	$0.495335\pi$
$432$		−	4.59235i		−	0.220949i
$433$			17.1030i			0.821919i	0.911654	+	0.410959i	$0.134806\pi$
$433$			17.1030i			0.821919i	−0.911654	+	0.410959i	$0.865194\pi$
$434$	3.44793			0.165506
$435$	7.59614	+	4.87694i	0.364207	+	0.233832i
$436$	−0.830693			−0.0397830
$437$		−	35.7931i		−	1.71222i
$438$		−	0.945738i		−	0.0451891i
$439$	11.5579			0.551628			0.275814	−	0.961211i	$-0.411053\pi$
$439$	11.5579			0.551628			0.275814	+	0.961211i	$0.411053\pi$
$440$		0			0
$441$	1.20842			0.0575436
$442$		−	14.5428i		−	0.691730i
$443$		−	17.7741i		−	0.844471i	−0.906486	−	0.422235i	$-0.861246\pi$
$443$		−	17.7741i		−	0.844471i	0.906486	−	0.422235i	$-0.138754\pi$
$444$	−2.90088			−0.137670
$445$	−20.5244	+	31.9680i	−0.972948	+	1.51543i
$446$	−12.4593			−0.589967
$447$			13.5293i			0.639913i
$448$		−	17.4147i		−	0.822768i
$449$	−21.7125			−1.02467			−0.512337	−	0.858784i	$-0.671220\pi$
$449$	−21.7125			−1.02467			−0.512337	+	0.858784i	$0.671220\pi$
$450$	−6.98641	+	3.19814i	−0.329343	+	0.150762i
$451$		0			0
$452$		−	3.47603i		−	0.163499i
$453$		−	21.7316i		−	1.02104i
$454$	−13.3761			−0.627769
$455$	−8.43131	+	13.1323i	−0.395266	+	0.615651i
$456$	−14.9524			−0.700212
$457$			0.874148i			0.0408909i	0.999791	+	0.0204455i	$0.00650845\pi$
$457$			0.874148i			0.0408909i	−0.999791	+	0.0204455i	$0.993492\pi$
$458$		−	45.5193i		−	2.12698i
$459$	−3.88488			−0.181331
$460$	−4.10013	−	2.63240i	−0.191169	−	0.122736i
$461$	−6.51959			−0.303648			−0.151824	−	0.988408i	$-0.548515\pi$
$461$	−6.51959			−0.303648			−0.151824	+	0.988408i	$0.548515\pi$
$462$		0			0
$463$		−	12.5689i		−	0.584124i	−0.956399	−	0.292062i	$-0.905659\pi$
$463$		−	12.5689i		−	0.584124i	0.956399	−	0.292062i	$-0.0943414\pi$
$464$	18.5392			0.860661
$465$	1.47357	+	0.946072i	0.0683350	+	0.0438730i
$466$	−10.3224			−0.478177
$467$		−	26.3110i		−	1.21753i	−0.793352	−	0.608764i	$-0.791666\pi$
$467$		−	26.3110i		−	1.21753i	0.793352	−	0.608764i	$-0.208334\pi$
$468$			0.880664i			0.0407087i
$469$	−11.3663			−0.524846
$470$	−1.02310	+	1.59355i	−0.0471923	+	0.0735049i
$471$	−10.0477			−0.462974
$472$			36.6344i			1.68624i
$473$		0			0
$474$	−6.97662			−0.320447
$475$	12.3588	+	26.9981i	0.567062	+	1.23876i
$476$	4.02387			0.184434
$477$			2.75907i			0.126329i
$478$		−	3.43076i		−	0.156919i
$479$	−6.99425			−0.319575			−0.159788	−	0.987151i	$-0.551081\pi$
$479$	−6.99425			−0.319575			−0.159788	+	0.987151i	$0.551081\pi$
$480$	−2.44199	+	3.80355i	−0.111461	+	0.173607i
$481$	−19.5465			−0.891243
$482$		−	12.6057i		−	0.574175i
$483$			17.2685i			0.785743i
$484$		0			0
$485$	16.8503	+	10.8184i	0.765133	+	0.491237i
$486$	1.53672			0.0697073
$487$		−	6.08580i		−	0.275774i	−0.990448	−	0.137887i	$-0.955969\pi$
$487$		−	6.08580i		−	0.275774i	0.990448	−	0.137887i	$-0.0440311\pi$
$488$			34.7220i			1.57179i
$489$	−17.0119			−0.769306
$490$	−3.49421	−	2.24339i	−0.157852	−	0.101346i
$491$	−4.58064			−0.206722			−0.103361	−	0.994644i	$-0.532960\pi$
$491$	−4.58064			−0.206722			−0.103361	+	0.994644i	$0.532960\pi$
$492$		−	2.72659i		−	0.122924i
$493$		−	15.6832i		−	0.706335i
$494$	22.2303			1.00019
$495$		0			0
$496$	3.59640			0.161483
$497$			26.5666i			1.19168i
$498$			17.9485i			0.804292i
$499$	21.2025			0.949152			0.474576	−	0.880214i	$-0.342601\pi$
$499$	21.2025			0.949152			0.474576	+	0.880214i	$0.342601\pi$
$500$	4.00158	+	0.569860i	0.178956	+	0.0254849i
$501$	8.17422			0.365197
$502$		−	1.38416i		−	0.0617781i
$503$			14.8190i			0.660746i	0.943850	+	0.330373i	$0.107175\pi$
$503$			14.8190i			0.660746i	−0.943850	+	0.330373i	$0.892825\pi$
$504$	7.21383			0.321330
$505$	−4.89309	+	7.62129i	−0.217740	+	0.339143i
$506$		0			0
$507$		−	7.06599i		−	0.313812i
$508$			7.09090i			0.314608i
$509$	23.6991			1.05044			0.525222	−	0.850965i	$-0.323982\pi$
$509$	23.6991			1.05044			0.525222	+	0.850965i	$0.323982\pi$
$510$	11.2334	+	7.21216i	0.497422	+	0.319360i
$511$	1.76321			0.0779999
$512$		−	13.8431i		−	0.611783i
$513$		−	5.93848i		−	0.262190i
$514$	−6.57287			−0.289917
$515$	−5.82799	−	3.74174i	−0.256812	−	0.164881i
$516$	3.58115			0.157651
$517$		0			0
$518$		−	35.3281i		−	1.55223i
$519$	0.0419137			0.00183981
$520$	−7.40972	+	11.5411i	−0.324938	+	0.506111i
$521$	−34.8182			−1.52541			−0.762707	−	0.646745i	$-0.776130\pi$
$521$	−34.8182			−1.52541			−0.762707	+	0.646745i	$0.776130\pi$
$522$			6.20372i			0.271530i
$523$			16.6591i			0.728453i	0.931310	+	0.364226i	$0.118667\pi$
$523$			16.6591i			0.728453i	−0.931310	+	0.364226i	$0.881333\pi$
$524$	−1.44914			−0.0633060
$525$	−5.96255	−	13.0253i	−0.260227	−	0.568471i
$526$	−5.60312			−0.244307
$527$		−	3.04236i		−	0.132527i
$528$		0			0
$529$	−13.3286			−0.579504
$530$	5.12212	−	7.97801i	0.222491	−	0.346543i
$531$	−14.5497			−0.631402
$532$			6.15094i			0.266677i
$533$		−	18.3721i		−	0.795782i
$534$	−26.1081			−1.12981
$535$	10.2043	+	6.55143i	0.441169	+	0.283243i
$536$	−9.98906			−0.431462
$537$		−	21.5288i		−	0.929038i
$538$			17.3453i			0.747810i
$539$		0			0
$540$	−0.680257	−	0.436745i	−0.0292736	−	0.0187945i
$541$	−4.99608			−0.214798			−0.107399	−	0.994216i	$-0.534252\pi$
$541$	−4.99608			−0.214798			−0.107399	+	0.994216i	$0.534252\pi$
$542$			14.7290i			0.632664i
$543$		−	10.9246i		−	0.468820i
$544$	7.85289			0.336690
$545$	2.77585	−	4.32356i	0.118904	−	0.185201i
$546$	−10.7251			−0.458990
$547$		−	27.0209i		−	1.15533i	−0.816274	−	0.577665i	$-0.803964\pi$
$547$		−	27.0209i		−	1.15533i	0.816274	−	0.577665i	$-0.196036\pi$
$548$		−	8.37820i		−	0.357899i
$549$	−13.7901			−0.588549
$550$		0			0
$551$	23.9735			1.02131
$552$			15.1761i			0.645938i
$553$		−	13.0071i		−	0.553116i
$554$	41.4624			1.76157
$555$	9.69361	−	15.0984i	0.411471	−	0.640891i
$556$	−4.99763			−0.211947
$557$		−	8.26537i		−	0.350215i	−0.984549	−	0.175107i	$-0.943973\pi$
$557$		−	8.26537i		−	0.350215i	0.984549	−	0.175107i	$-0.0560273\pi$
$558$			1.20345i			0.0509462i
$559$	24.1302			1.02060
$560$	−24.7572	−	15.8948i	−1.04618	−	0.671679i
$561$		0			0
$562$			29.1852i			1.23110i
$563$		−	18.9867i		−	0.800194i	−0.916473	−	0.400097i	$-0.868976\pi$
$563$		−	18.9867i		−	0.800194i	0.916473	−	0.400097i	$-0.131024\pi$
$564$	−0.199236			−0.00838936
$565$	18.0919	+	11.6155i	0.761131	+	0.488668i
$566$	−41.6367			−1.75012
$567$			2.86503i			0.120320i
$568$			23.3477i			0.979646i
$569$	43.0309			1.80395			0.901974	−	0.431790i	$-0.142118\pi$
$569$	43.0309			1.80395			0.901974	+	0.431790i	$0.142118\pi$
$570$	−11.0246	+	17.1715i	−0.461770	+	0.719235i
$571$	−8.68683			−0.363533			−0.181766	−	0.983342i	$-0.558181\pi$
$571$	−8.68683			−0.363533			−0.181766	+	0.983342i	$0.558181\pi$
$572$		0			0
$573$			0.485281i			0.0202729i
$574$	33.2055			1.38597
$575$	27.4020	−	12.5437i	1.14274	−	0.523109i
$576$	6.07836			0.253265
$577$		−	11.0409i		−	0.459639i	−0.973233	−	0.229819i	$-0.926186\pi$
$577$		−	11.0409i		−	0.459639i	0.973233	−	0.229819i	$-0.0738136\pi$
$578$			2.93162i			0.121939i
$579$	−12.5864			−0.523073
$580$	1.76313	−	2.74618i	0.0732099	−	0.114029i
$581$	−33.4628			−1.38827
$582$			13.7615i			0.570434i
$583$		0			0
$584$	1.54957			0.0641216
$585$	−4.58364	−	2.94283i	−0.189510	−	0.121671i
$586$	−13.9473			−0.576157
$587$			26.1401i			1.07892i	0.842012	+	0.539459i	$0.181371\pi$
$587$			26.1401i			1.07892i	−0.842012	+	0.539459i	$0.818629\pi$
$588$		−	0.436870i		−	0.0180162i
$589$	4.65059			0.191624
$590$	42.0713	+	27.0110i	1.73205	+	1.11202i
$591$	−15.8941			−0.653796
$592$		−	36.8493i		−	1.51450i
$593$		−	12.0171i		−	0.493484i	−0.969081	−	0.246742i	$-0.920640\pi$
$593$		−	12.0171i		−	0.493484i	0.969081	−	0.246742i	$-0.0793601\pi$
$594$		0			0
$595$	−13.4462	+	20.9432i	−0.551239	+	0.858589i
$596$	4.89115			0.200349
$597$		−	5.02089i		−	0.205491i
$598$		−	22.5629i		−	0.922665i
$599$	41.8072			1.70820			0.854098	−	0.520112i	$-0.174110\pi$
$599$	41.8072			1.70820			0.854098	+	0.520112i	$0.174110\pi$
$600$	−5.24009	−	11.4471i	−0.213926	−	0.467325i
$601$	−40.5539			−1.65423			−0.827115	−	0.562033i	$-0.810019\pi$
$601$	−40.5539			−1.65423			−0.827115	+	0.562033i	$0.810019\pi$
$602$			43.6126i			1.77752i
$603$		−	3.96724i		−	0.161558i
$604$	−7.85646			−0.319675
$605$		0			0
$606$	−6.22427			−0.252844
$607$		−	29.2269i		−	1.18628i	−0.805099	−	0.593141i	$-0.797888\pi$
$607$		−	29.2269i		−	1.18628i	0.805099	−	0.593141i	$-0.202112\pi$
$608$			12.0040i			0.486828i
$609$	−11.5661			−0.468681
$610$	39.8751	+	25.6010i	1.61450	+	1.03655i
$611$	−1.34248			−0.0543108
$612$			1.40447i			0.0567725i
$613$			20.1259i			0.812876i	0.913678	+	0.406438i	$0.133229\pi$
$613$			20.1259i			0.812876i	−0.913678	+	0.406438i	$0.866771\pi$
$614$	9.38884			0.378903
$615$	14.1912	+	9.11119i	0.572246	+	0.367399i
$616$		0			0
$617$		−	8.98070i		−	0.361550i	−0.983525	−	0.180775i	$-0.942139\pi$
$617$		−	8.98070i		−	0.361550i	0.983525	−	0.180775i	$-0.0578605\pi$
$618$		−	4.75969i		−	0.191463i
$619$	−24.0303			−0.965860			−0.482930	−	0.875659i	$-0.660427\pi$
$619$	−24.0303			−0.965860			−0.482930	+	0.875659i	$0.660427\pi$
$620$	0.342027	−	0.532728i	0.0137361	−	0.0213949i
$621$	−6.02732			−0.241868
$622$		−	22.8363i		−	0.915653i
$623$		−	48.6752i		−	1.95013i
$624$	−11.1869			−0.447834
$625$	−16.3377	+	18.9230i	−0.653507	+	0.756920i
$626$	42.1282			1.68378
$627$		0			0
$628$			3.63248i			0.144952i
$629$	−31.1725			−1.24293
$630$	5.31884	−	8.28443i	0.211908	−	0.330059i
$631$	23.0323			0.916902			0.458451	−	0.888720i	$-0.348404\pi$
$631$	23.0323			0.916902			0.458451	+	0.888720i	$0.348404\pi$
$632$		−	11.4310i		−	0.454702i
$633$		−	0.800040i		−	0.0317987i
$634$	−21.4109			−0.850334
$635$	−36.9064	−	23.6950i	−1.46459	−	0.940308i
$636$	0.997466			0.0395521
$637$		−	2.94368i		−	0.116633i
$638$		0			0
$639$	−9.27271			−0.366823
$640$	−25.1831	−	16.1683i	−0.995448	−	0.639107i
$641$	17.8410			0.704677			0.352339	−	0.935873i	$-0.385387\pi$
$641$	17.8410			0.704677			0.352339	+	0.935873i	$0.385387\pi$
$642$			8.33376i			0.328907i
$643$		−	21.4561i		−	0.846147i	−0.906095	−	0.423074i	$-0.860951\pi$
$643$		−	21.4561i		−	0.846147i	0.906095	−	0.423074i	$-0.139049\pi$
$644$	6.24295			0.246007
$645$	−11.9668	+	18.6390i	−0.471192	+	0.733910i
$646$	35.4527			1.39487
$647$			7.91168i			0.311040i	0.987833	+	0.155520i	$0.0497054\pi$
$647$			7.91168i			0.311040i	−0.987833	+	0.155520i	$0.950295\pi$
$648$			2.51789i			0.0989120i
$649$		0			0
$650$	7.79062	+	17.0188i	0.305573	+	0.667531i
$651$	−2.24369			−0.0879371
$652$			6.15021i			0.240861i
$653$		−	20.7286i		−	0.811171i	−0.914057	−	0.405585i	$-0.867068\pi$
$653$		−	20.7286i		−	0.811171i	0.914057	−	0.405585i	$-0.132932\pi$
$654$	3.53102			0.138074
$655$	4.84246	−	7.54243i	0.189210	−	0.294707i
$656$	34.6353			1.35228
$657$			0.615424i			0.0240100i
$658$		−	2.42638i		−	0.0945900i
$659$	44.9515			1.75106			0.875531	−	0.483162i	$-0.160512\pi$
$659$	44.9515			1.75106			0.875531	+	0.483162i	$0.160512\pi$
$660$		0			0
$661$	32.0760			1.24761			0.623806	−	0.781579i	$-0.285585\pi$
$661$	32.0760			1.24761			0.623806	+	0.781579i	$0.285585\pi$
$662$			38.3235i			1.48949i
$663$			9.46350i			0.367532i
$664$	−29.4082			−1.14126
$665$	−32.0141	−	20.5540i	−1.24146	−	0.797050i
$666$	12.3308			0.477808
$667$		−	24.3322i		−	0.942145i
$668$		−	2.95517i		−	0.114339i
$669$	8.10773			0.313463
$670$	−7.36505	+	11.4715i	−0.284537	+	0.443184i
$671$		0			0
$672$		−	5.79137i		−	0.223407i
$673$		−	11.0442i		−	0.425723i	−0.977082	−	0.212861i	$-0.931722\pi$
$673$		−	11.0442i		−	0.425723i	0.977082	−	0.212861i	$-0.0682783\pi$
$674$	−24.9534			−0.961168
$675$	4.54630	−	2.08114i	0.174987	−	0.0801032i
$676$	−2.55452			−0.0982507
$677$		−	7.99883i		−	0.307420i	−0.988116	−	0.153710i	$-0.950878\pi$
$677$		−	7.99883i		−	0.307420i	0.988116	−	0.153710i	$-0.0491221\pi$
$678$			14.7755i			0.567451i
$679$	−25.6567			−0.984613
$680$	−11.8169	+	18.4056i	−0.453159	+	0.705824i
$681$	8.70426			0.333548
$682$		0			0
$683$			16.6442i			0.636873i	0.947944	+	0.318436i	$0.103158\pi$
$683$			16.6442i			0.636873i	−0.947944	+	0.318436i	$0.896842\pi$
$684$	−2.14690			−0.0820887
$685$	43.6065	+	27.9966i	1.66612	+	1.06970i
$686$	−25.4990			−0.973556
$687$			29.6210i			1.13011i
$688$			45.4905i			1.73431i
$689$	6.72104			0.256051
$690$	17.4284	+	11.1895i	0.663487	+	0.425978i
$691$	−12.4814			−0.474815			−0.237408	−	0.971410i	$-0.576298\pi$
$691$	−12.4814			−0.474815			−0.237408	+	0.971410i	$0.576298\pi$
$692$		−	0.0151528i		−	0.000576022i
$693$		0			0
$694$	−42.2010			−1.60193
$695$	16.7001	−	26.0115i	0.633471	−	0.986671i
$696$	−10.1647			−0.385290
$697$		−	29.2996i		−	1.10980i
$698$			38.6287i			1.46212i
$699$	6.71715			0.254066
$700$	−4.70895	+	2.15560i	−0.177982	+	0.0814740i
$701$	3.13045			0.118235			0.0591177	−	0.998251i	$-0.481171\pi$
$701$	3.13045			0.118235			0.0591177	+	0.998251i	$0.481171\pi$
$702$		−	3.74343i		−	0.141287i
$703$		−	47.6508i		−	1.79718i
$704$		0			0
$705$	0.665769	−	1.03698i	0.0250743	−	0.0390548i
$706$	18.8037			0.707685
$707$		−	11.6044i		−	0.436427i
$708$			5.26004i			0.197684i
$709$	8.71471			0.327288			0.163644	−	0.986519i	$-0.447675\pi$
$709$	8.71471			0.327288			0.163644	+	0.986519i	$0.447675\pi$
$710$	26.8126	+	17.2145i	1.00626	+	0.646049i
$711$	4.53993			0.170261
$712$		−	42.7774i		−	1.60315i
$713$		−	4.72016i		−	0.176771i
$714$	−17.1042			−0.640110
$715$		0			0
$716$	−7.78317			−0.290871
$717$			2.23252i			0.0833748i
$718$		−	5.96884i		−	0.222755i
$719$	−10.3566			−0.386237			−0.193118	−	0.981175i	$-0.561860\pi$
$719$	−10.3566			−0.386237			−0.193118	+	0.981175i	$0.561860\pi$
$720$	5.54787	−	8.64115i	0.206757	−	0.322037i
$721$	8.87385			0.330479
$722$			24.9957i			0.930244i
$723$			8.20298i			0.305072i
$724$	−3.94950			−0.146782
$725$	8.40153	+	18.3533i	0.312025	+	0.681625i
$726$		0			0
$727$			18.2456i			0.676693i	0.941022	+	0.338346i	$0.109868\pi$
$727$			18.2456i			0.676693i	−0.941022	+	0.338346i	$0.890132\pi$
$728$		−	17.5728i		−	0.651290i
$729$	−1.00000			−0.0370370
$730$	1.14252	−	1.77954i	0.0422864	−	0.0658637i
$731$	38.4825			1.42333
$732$			4.98546i			0.184268i
$733$		−	3.14121i		−	0.116023i	−0.998316	−	0.0580116i	$-0.981524\pi$
$733$		−	3.14121i		−	0.116023i	0.998316	−	0.0580116i	$-0.0184760\pi$
$734$	30.0741			1.11006
$735$	2.27381	+	1.45985i	0.0838706	+	0.0538473i
$736$	12.1836			0.449094
$737$		0			0
$738$			11.5899i			0.426630i
$739$	33.9751			1.24980			0.624898	−	0.780706i	$-0.285141\pi$
$739$	33.9751			1.24980			0.624898	+	0.780706i	$0.285141\pi$
$740$	−5.45842	−	3.50447i	−0.200656	−	0.128827i
$741$	−14.4660			−0.531423
$742$			12.1475i			0.445950i
$743$		−	40.2606i		−	1.47702i	−0.674243	−	0.738510i	$-0.735530\pi$
$743$		−	40.2606i		−	1.47702i	0.674243	−	0.738510i	$-0.264470\pi$
$744$	−1.97183			−0.0722907
$745$	−16.3443	+	25.4572i	−0.598808	+	0.932681i
$746$	−1.12178			−0.0410711
$747$		−	11.6797i		−	0.427339i
$748$		0			0
$749$	−15.5373			−0.567719
$750$	−17.0095	−	2.42230i	−0.621099	−	0.0884499i
$751$	39.7342			1.44992			0.724960	−	0.688791i	$-0.241858\pi$
$751$	39.7342			1.44992			0.724960	+	0.688791i	$0.241858\pi$
$752$		−	2.53085i		−	0.0922908i
$753$			0.900721i			0.0328241i
$754$	15.1122			0.550352
$755$	26.2532	−	40.8910i	0.955452	−	1.48818i
$756$	1.03578			0.0376708
$757$			51.6449i			1.87707i	0.345188	+	0.938533i	$0.387815\pi$
$757$			51.6449i			1.87707i	−0.345188	+	0.938533i	$0.612185\pi$
$758$		−	55.3460i		−	2.01026i
$759$		0			0
$760$	−28.1351	−	18.0636i	−1.02057	−	0.655234i
$761$	−39.8286			−1.44379			−0.721893	−	0.692004i	$-0.756728\pi$
$761$	−39.8286			−1.44379			−0.721893	+	0.692004i	$0.756728\pi$
$762$		−	30.1413i		−	1.09190i
$763$			6.58315i			0.238326i
$764$	0.175440			0.00634721
$765$	−7.30995	−	4.69320i	−0.264292	−	0.169683i
$766$	19.1401			0.691560
$767$			35.4427i			1.27976i
$768$		−	8.41013i		−	0.303475i
$769$	−46.2949			−1.66944			−0.834719	−	0.550676i	$-0.814370\pi$
$769$	−46.2949			−1.66944			−0.834719	+	0.550676i	$0.814370\pi$
$770$		0			0
$771$	4.27720			0.154039
$772$			4.55028i			0.163768i
$773$		−	7.01535i		−	0.252325i	−0.992010	−	0.126162i	$-0.959734\pi$
$773$		−	7.01535i		−	0.252325i	0.992010	−	0.126162i	$-0.0402660\pi$
$774$	−15.2224			−0.547157
$775$	1.62980	+	3.56033i	0.0585442	+	0.127891i
$776$	−22.5480			−0.809425
$777$			22.9892i			0.824733i
$778$			31.4432i			1.12729i
$779$	44.7877			1.60469
$780$	−1.06390	+	1.65709i	−0.0380938	+	0.0593335i
$781$		0			0
$782$		−	35.9830i		−	1.28675i
$783$		−	4.03698i		−	0.144270i
$784$	5.54947			0.198195
$785$	−18.9062	−	12.1383i	−0.674790	−	0.433235i
$786$	6.15986			0.219715
$787$		−	2.77476i		−	0.0989095i	−0.998776	−	0.0494548i	$-0.984252\pi$
$787$		−	2.77476i		−	0.0989095i	0.998776	−	0.0494548i	$-0.0157484\pi$
$788$			5.74608i			0.204696i
$789$	3.64614			0.129806
$790$	−13.1275	−	8.42824i	−0.467056	−	0.299863i
$791$	−27.5471			−0.979464
$792$		0			0
$793$			33.5926i			1.19291i
$794$	−36.7348			−1.30367
$795$	−3.33314	+	5.19157i	−0.118214	+	0.184126i
$796$	−1.81517			−0.0643370
$797$			42.9669i			1.52197i	0.648772	+	0.760983i	$0.275283\pi$
$797$			42.9669i			1.52197i	−0.648772	+	0.760983i	$0.724717\pi$
$798$		−	26.1458i		−	0.925550i
$799$	−2.14097			−0.0757420
$800$	−9.18988	+	4.20682i	−0.324911	+	0.148734i
$801$	16.9894			0.600291
$802$		−	14.5236i		−	0.512846i
$803$		0			0
$804$	−1.43425			−0.0505821
$805$	−20.8615	+	32.4931i	−0.735271	+	1.14523i
$806$	2.93159			0.103261
$807$		−	11.2872i		−	0.397328i
$808$		−	10.1983i		−	0.358775i
$809$	33.2867			1.17030			0.585149	−	0.810926i	$-0.301036\pi$
$809$	33.2867			1.17030			0.585149	+	0.810926i	$0.301036\pi$
$810$	2.89156	+	1.85647i	0.101599	+	0.0652296i
$811$	−37.8675			−1.32971			−0.664855	−	0.746973i	$-0.731507\pi$
$811$	−37.8675			−1.32971			−0.664855	+	0.746973i	$0.731507\pi$
$812$			4.18140i			0.146739i
$813$		−	9.58466i		−	0.336149i
$814$		0			0
$815$	−32.0103	−	20.5516i	−1.12127	−	0.719890i
$816$	−17.8407			−0.624550
$817$			58.8250i			2.05802i
$818$		−	11.8254i		−	0.413465i
$819$	6.97917			0.243872
$820$	3.29391	−	5.13046i	0.115028	−	0.179164i
$821$	−15.5524			−0.542782			−0.271391	−	0.962469i	$-0.587484\pi$
$821$	−15.5524			−0.542782			−0.271391	+	0.962469i	$0.587484\pi$
$822$			35.6132i			1.24215i
$823$			19.7207i			0.687421i	0.939076	+	0.343710i	$0.111684\pi$
$823$			19.7207i			0.687421i	−0.939076	+	0.343710i	$0.888316\pi$
$824$	7.79864			0.271678
$825$		0			0
$826$	−64.0588			−2.22889
$827$		−	5.77933i		−	0.200967i	−0.994939	−	0.100483i	$-0.967961\pi$
$827$		−	5.77933i		−	0.200967i	0.994939	−	0.100483i	$-0.0320390\pi$
$828$			2.17902i			0.0757260i
$829$	−34.0085			−1.18116			−0.590581	−	0.806978i	$-0.701102\pi$
$829$	−34.0085			−1.18116			−0.590581	+	0.806978i	$0.701102\pi$
$830$	−21.6830	+	33.7727i	−0.752629	+	1.17227i
$831$	−26.9810			−0.935960
$832$		−	14.8068i		−	0.513333i
$833$		−	4.69455i		−	0.162657i
$834$	21.2434			0.735599
$835$	15.3809	+	9.87501i	0.532280	+	0.341739i
$836$		0			0
$837$		−	0.783128i		−	0.0270689i
$838$			46.1939i			1.59574i
$839$	−38.0383			−1.31323			−0.656614	−	0.754226i	$-0.728012\pi$
$839$	−38.0383			−1.31323			−0.656614	+	0.754226i	$0.728012\pi$
$840$	13.5738	+	8.71480i	0.468342	+	0.300689i
$841$	−12.7028			−0.438028
$842$		−	36.6038i		−	1.26145i
$843$		−	18.9918i		−	0.654114i
$844$	−0.289233			−0.00995580
$845$	8.53620	−	13.2957i	0.293654	−	0.457384i
$846$	0.846893			0.0291168
$847$		0			0
$848$			12.6706i			0.435110i
$849$	27.0944			0.929878
$850$	12.4244	+	27.1414i	0.426154	+	0.930941i
$851$	−48.3636			−1.65788
$852$			3.35230i			0.114848i
$853$		−	48.9458i		−	1.67587i	−0.545769	−	0.837936i	$-0.683762\pi$
$853$		−	48.9458i		−	1.67587i	0.545769	−	0.837936i	$-0.316238\pi$
$854$	−60.7148			−2.07762
$855$	7.17409	−	11.1741i	0.245349	−	0.382146i
$856$	−13.6547			−0.466707
$857$			27.4604i			0.938030i	0.883190	+	0.469015i	$0.155391\pi$
$857$			27.4604i			0.938030i	−0.883190	+	0.469015i	$0.844609\pi$
$858$		0			0
$859$	1.25914			0.0429613			0.0214806	−	0.999769i	$-0.493162\pi$
$859$	1.25914			0.0429613			0.0214806	+	0.999769i	$0.493162\pi$
$860$	6.73843	+	4.32627i	0.229779	+	0.147525i
$861$	−21.6079			−0.736397
$862$			0.935086i			0.0318491i
$863$		−	26.7154i		−	0.909404i	−0.890644	−	0.454702i	$-0.849746\pi$
$863$		−	26.7154i		−	0.909404i	0.890644	−	0.454702i	$-0.150254\pi$
$864$	2.02140			0.0687694
$865$	0.0788665	+	0.0506346i	0.00268154	+	0.00172163i
$866$	−26.2826			−0.893120
$867$		−	1.90771i		−	0.0647892i
$868$			0.811145i			0.0275321i
$869$		0			0
$870$	−7.49452	+	11.6732i	−0.254088	+	0.395758i
$871$	−9.66412			−0.327456
$872$			5.78550i			0.195922i
$873$		−	8.95511i		−	0.303085i
$874$	55.0042			1.86054
$875$	4.51608	−	31.7121i	0.152671	−	1.07206i
$876$	0.222490			0.00751724
$877$			26.7109i			0.901962i	0.892533	+	0.450981i	$0.148926\pi$
$877$			26.7109i			0.901962i	−0.892533	+	0.450981i	$0.851074\pi$
$878$			17.7613i			0.599415i
$879$	9.07599			0.306125
$880$		0			0
$881$	−31.7144			−1.06849			−0.534243	−	0.845331i	$-0.679403\pi$
$881$	−31.7144			−1.06849			−0.534243	+	0.845331i	$0.679403\pi$
$882$			1.85700i			0.0625286i
$883$			47.8895i			1.61161i	0.592182	+	0.805804i	$0.298267\pi$
$883$			47.8895i			1.61161i	−0.592182	+	0.805804i	$0.701733\pi$
$884$	3.42127			0.115070
$885$	−27.3772	−	17.5770i	−0.920276	−	0.590844i
$886$	27.3138			0.917626
$887$			34.0800i			1.14429i	0.820151	+	0.572147i	$0.193889\pi$
$887$			34.0800i			1.14429i	−0.820151	+	0.572147i	$0.806111\pi$
$888$			20.2037i			0.677991i
$889$	56.1947			1.88471
$890$	−49.1260	−	31.5403i	−1.64671	−	1.05723i
$891$		0			0
$892$		−	2.93113i		−	0.0981415i
$893$		−	3.27271i		−	0.109517i
$894$	−20.7908			−0.695348
$895$	26.0083	−	40.5095i	0.869362	−	1.35408i
$896$	38.3444			1.28100
$897$			14.6824i			0.490233i
$898$		−	33.3661i		−	1.11344i
$899$	3.16147			0.105441
$900$	−0.752382	−	1.64359i	−0.0250794	−	0.0547864i
$901$	10.7186			0.357090
$902$		0			0
$903$		−	28.3802i		−	0.944435i
$904$	−24.2094			−0.805191
$905$	13.1977	−	20.5562i	0.438705	−	0.683311i
$906$	33.3954			1.10949
$907$		−	22.5941i		−	0.750226i	−0.926979	−	0.375113i	$-0.877604\pi$
$907$		−	22.5941i		−	0.750226i	0.926979	−	0.375113i	$-0.122396\pi$
$908$		−	3.14679i		−	0.104430i
$909$	4.05035			0.134341
$910$	−20.1807	−	12.9566i	−0.668984	−	0.429507i
$911$	−15.8393			−0.524779			−0.262390	−	0.964962i	$-0.584511\pi$
$911$	−15.8393			−0.524779			−0.262390	+	0.964962i	$0.584511\pi$
$912$		−	27.2716i		−	0.903052i
$913$		0			0
$914$	−1.34333			−0.0444333
$915$	−25.9481	−	16.6594i	−0.857818	−	0.550744i
$916$	10.7087			0.353825
$917$			11.4843i			0.379245i
$918$		−	5.96999i		−	0.197039i
$919$	0.360925			0.0119058			0.00595291	−	0.999982i	$-0.498105\pi$
$919$	0.360925			0.0119058			0.00595291	+	0.999982i	$0.498105\pi$
$920$	−18.3338	+	28.5560i	−0.604447	+	0.941463i
$921$	−6.10964			−0.201320
$922$		−	10.0188i		−	0.329952i
$923$			22.5882i			0.743499i
$924$		0			0
$925$	36.4798	−	16.6992i	1.19945	−	0.549067i
$926$	19.3149			0.634726
$927$			3.09729i			0.101728i
$928$			8.16034i			0.267876i
$929$	−0.480345			−0.0157596			−0.00787980	−	0.999969i	$-0.502508\pi$
$929$	−0.480345			−0.0157596			−0.00787980	+	0.999969i	$0.502508\pi$
$930$	−1.45385	+	2.26446i	−0.0476737	+	0.0742547i
$931$	7.17616			0.235189
$932$		−	2.42841i		−	0.0795451i
$933$			14.8604i			0.486507i
$934$	40.4328			1.32300
$935$		0			0
$936$	6.13353			0.200481
$937$		−	52.1442i		−	1.70348i	−0.523967	−	0.851739i	$-0.675548\pi$
$937$		−	52.1442i		−	1.70348i	0.523967	−	0.851739i	$-0.324452\pi$
$938$		−	17.4668i		−	0.570312i
$939$	−27.4142			−0.894630
$940$	−0.374891	−	0.240691i	−0.0122276	−	0.00785048i
$941$	−14.9475			−0.487275			−0.243637	−	0.969866i	$-0.578341\pi$
$941$	−14.9475			−0.487275			−0.243637	+	0.969866i	$0.578341\pi$
$942$		−	15.4406i		−	0.503081i
$943$		−	45.4577i		−	1.48031i
$944$	−66.8171			−2.17471
$945$	−3.46116	+	5.39096i	−0.112591	+	0.175368i
$946$		0			0
$947$		−	27.2440i		−	0.885311i	−0.896692	−	0.442656i	$-0.854036\pi$
$947$		−	27.2440i		−	0.885311i	0.896692	−	0.442656i	$-0.145964\pi$
$948$		−	1.64129i		−	0.0533066i
$949$	1.49916			0.0486649
$950$	−41.4887	+	18.9921i	−1.34607	+	0.616186i
$951$	13.9328			0.451802
$952$		−	28.0249i		−	0.908291i
$953$			37.8748i			1.22688i	0.789740	+	0.613442i	$0.210216\pi$
$953$			37.8748i			1.22688i	−0.789740	+	0.613442i	$0.789784\pi$
$954$	−4.23992			−0.137273
$955$	−0.586253	+	0.913125i	−0.0189707	+	0.0295480i
$956$	0.807106			0.0261037
$957$		0			0
$958$		−	10.7482i		−	0.347260i
$959$	−66.3964			−2.14405
$960$	11.4373	+	7.34307i	0.369137	+	0.236997i
$961$	−30.3867			−0.980216
$962$		−	30.0376i		−	0.968450i
$963$		−	5.42307i		−	0.174756i
$964$	2.96557			0.0955144
$965$	−23.6831	−	15.2052i	−0.762385	−	0.489474i
$966$	−26.5369			−0.853811
$967$		−	43.6845i		−	1.40480i	−0.711783	−	0.702400i	$-0.752112\pi$
$967$		−	43.6845i		−	1.40480i	0.711783	−	0.702400i	$-0.247888\pi$
$968$		0			0
$969$	−23.0703			−0.741125
$970$	−16.6249	+	25.8943i	−0.533793	+	0.831415i
$971$	−2.73545			−0.0877848			−0.0438924	−	0.999036i	$-0.513976\pi$
$971$	−2.73545			−0.0877848			−0.0438924	+	0.999036i	$0.513976\pi$
$972$			0.361523i			0.0115959i
$973$			39.6057i			1.26970i
$974$	9.35220			0.299664
$975$	−5.06963	−	11.0747i	−0.162358	−	0.354674i
$976$	−63.3292			−2.02712
$977$			36.5804i			1.17031i	0.810921	+	0.585156i	$0.198967\pi$
$977$			36.5804i			1.17031i	−0.810921	+	0.585156i	$0.801033\pi$
$978$		−	26.1427i		−	0.835950i
$979$		0			0
$980$	0.527769	−	0.822033i	0.0168590	−	0.0262589i
$981$	−2.29776			−0.0733618
$982$		−	7.03919i		−	0.224630i
$983$		−	6.44168i		−	0.205458i	−0.994709	−	0.102729i	$-0.967243\pi$
$983$		−	6.44168i		−	0.205458i	0.994709	−	0.102729i	$-0.0327574\pi$
$984$	−18.9898			−0.605372
$985$	−29.9070	−	19.2011i	−0.952916	−	0.611799i
$986$	24.1007			0.767523
$987$			1.57893i			0.0502578i
$988$			5.22981i			0.166382i
$989$	59.7050			1.89851
$990$		0			0
$991$	−13.5718			−0.431123			−0.215561	−	0.976490i	$-0.569158\pi$
$991$	−13.5718			−0.431123			−0.215561	+	0.976490i	$0.569158\pi$
$992$			1.58301i			0.0502607i
$993$		−	24.9385i		−	0.791398i
$994$	−40.8256			−1.29491
$995$	6.06558	−	9.44752i	0.192292	−	0.299506i
$996$	−4.22249			−0.133795
$997$			1.84851i			0.0585429i	0.999571	+	0.0292715i	$0.00931873\pi$
$997$			1.84851i			0.0585429i	−0.999571	+	0.0292715i	$0.990681\pi$
$998$			32.5823i			1.03138i
$999$	−8.02406			−0.253870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.i.364.9	yes	12
5.2	odd	4		9075.2.a.do.1.2		6
5.3	odd	4		9075.2.a.ds.1.5		6
5.4	even	2	inner	1815.2.c.i.364.4	yes	12
11.10	odd	2		1815.2.c.h.364.4	✓	12
55.32	even	4		9075.2.a.dr.1.5		6
55.43	even	4		9075.2.a.dp.1.2		6
55.54	odd	2		1815.2.c.h.364.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.h.364.4	✓	12	11.10	odd	2
1815.2.c.h.364.9	yes	12	55.54	odd	2
1815.2.c.i.364.4	yes	12	5.4	even	2	inner
1815.2.c.i.364.9	yes	12	1.1	even	1	trivial
9075.2.a.do.1.2		6	5.2	odd	4
9075.2.a.dp.1.2		6	55.43	even	4
9075.2.a.dr.1.5		6	55.32	even	4
9075.2.a.ds.1.5		6	5.3	odd	4

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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.53672i q^{2} -1.00000i q^{3} -0.361523 q^{4} +(1.20807 - 1.88164i) q^{5} +1.53672 q^{6} +2.86503i q^{7} +2.51789i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.53672i q^{2} -1.00000i q^{3} -0.361523 q^{4} +(1.20807 - 1.88164i) q^{5} +1.53672 q^{6} +2.86503i q^{7} +2.51789i q^{8} -1.00000 q^{9} +(2.89156 + 1.85647i) q^{10} +0.361523i q^{12} +2.43598i q^{13} -4.40277 q^{14} +(-1.88164 - 1.20807i) q^{15} -4.59235 q^{16} +3.88488i q^{17} -1.53672i q^{18} -5.93848 q^{19} +(-0.436745 + 0.680257i) q^{20} +2.86503 q^{21} +6.02732i q^{23} +2.51789 q^{24} +(-2.08114 - 4.54630i) q^{25} -3.74343 q^{26} +1.00000i q^{27} -1.03578i q^{28} -4.03698 q^{29} +(1.85647 - 2.89156i) q^{30} -0.783128 q^{31} -2.02140i q^{32} -5.96999 q^{34} +(5.39096 + 3.46116i) q^{35} +0.361523 q^{36} +8.02406i q^{37} -9.12581i q^{38} +2.43598 q^{39} +(4.73776 + 3.04178i) q^{40} -7.54195 q^{41} +4.40277i q^{42} -9.90572i q^{43} +(-1.20807 + 1.88164i) q^{45} -9.26233 q^{46} +0.551103i q^{47} +4.59235i q^{48} -1.20842 q^{49} +(6.98641 - 3.19814i) q^{50} +3.88488 q^{51} -0.880664i q^{52} -2.75907i q^{53} -1.53672 q^{54} -7.21383 q^{56} +5.93848i q^{57} -6.20372i q^{58} +14.5497 q^{59} +(0.680257 + 0.436745i) q^{60} +13.7901 q^{61} -1.20345i q^{62} -2.86503i q^{63} -6.07836 q^{64} +(4.58364 + 2.94283i) q^{65} +3.96724i q^{67} -1.40447i q^{68} +6.02732 q^{69} +(-5.31884 + 8.28443i) q^{70} +9.27271 q^{71} -2.51789i q^{72} -0.615424i q^{73} -12.3308 q^{74} +(-4.54630 + 2.08114i) q^{75} +2.14690 q^{76} +3.74343i q^{78} -4.53993 q^{79} +(-5.54787 + 8.64115i) q^{80} +1.00000 q^{81} -11.5899i q^{82} +11.6797i q^{83} -1.03578 q^{84} +(7.30995 + 4.69320i) q^{85} +15.2224 q^{86} +4.03698i q^{87} -16.9894 q^{89} +(-2.89156 - 1.85647i) q^{90} -6.97917 q^{91} -2.17902i q^{92} +0.783128i q^{93} -0.846893 q^{94} +(-7.17409 + 11.1741i) q^{95} -2.02140 q^{96} +8.95511i q^{97} -1.85700i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9	\( 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9} + 12 q^{10} + 20 q^{14} + 22 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{25} - 24 q^{29} - 8 q^{30} + 36 q^{31} + 2 q^{34} + 24 q^{35} + 18 q^{36} - 4 q^{39} - 22 q^{40} - 12 q^{41} + 2 q^{45} - 22 q^{46} - 24 q^{49} - 58 q^{50} + 4 q^{51} - 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} + 8 q^{61} - 44 q^{64} - 14 q^{65} - 24 q^{69} - 16 q^{70} + 8 q^{74} - 12 q^{75} - 40 q^{76} - 4 q^{79} - 58 q^{80} + 12 q^{81} + 48 q^{84} - 2 q^{85} + 56 q^{86} + 32 q^{89} - 12 q^{90} + 48 q^{91} - 6 q^{94} + 62 q^{96}+O(q^{100}) \) 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9 + 12 * q^10 + 20 * q^14 + 22 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^25 - 24 * q^29 - 8 * q^30 + 36 * q^31 + 2 * q^34 + 24 * q^35 + 18 * q^36 - 4 * q^39 - 22 * q^40 - 12 * q^41 + 2 * q^45 - 22 * q^46 - 24 * q^49 - 58 * q^50 + 4 * q^51 - 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 + 8 * q^61 - 44 * q^64 - 14 * q^65 - 24 * q^69 - 16 * q^70 + 8 * q^74 - 12 * q^75 - 40 * q^76 - 4 * q^79 - 58 * q^80 + 12 * q^81 + 48 * q^84 - 2 * q^85 + 56 * q^86 + 32 * q^89 - 12 * q^90 + 48 * q^91 - 6 * q^94 + 62 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more