LMFDB - Embedded newform 300.3.f.c.199.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(199,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("300.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 14x^13 + 23x^12 - 26x^11 + 18x^10 - 10x^9 + 9x^8 - 20x^7 + 72x^6 - 208x^5 + 368x^4 - 448x^3 + 512x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.7
Root			$-0.152947 - 1.40592i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.c.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.305673 - 1.97650i) q^{2} +1.73205 q^{3} +(-3.81313 + 1.20833i) q^{4} +(-0.529441 - 3.42340i) q^{6} +0.329898 q^{7} +(3.55383 + 7.16731i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-0.305673 - 1.97650i) q^{2} +1.73205 q^{3} +(-3.81313 + 1.20833i) q^{4} +(-0.529441 - 3.42340i) q^{6} +0.329898 q^{7} +(3.55383 + 7.16731i) q^{8} +3.00000 q^{9} -20.4920i q^{11} +(-6.60453 + 2.09288i) q^{12} +0.416712i q^{13} +(-0.100841 - 0.652044i) q^{14} +(13.0799 - 9.21501i) q^{16} -18.5884i q^{17} +(-0.917019 - 5.92951i) q^{18} -12.4503i q^{19} +0.571400 q^{21} +(-40.5024 + 6.26384i) q^{22} -23.2304 q^{23} +(6.15542 + 12.4141i) q^{24} +(0.823633 - 0.127378i) q^{26} +5.19615 q^{27} +(-1.25794 + 0.398624i) q^{28} +23.9166 q^{29} -42.0148i q^{31} +(-22.2117 - 23.0357i) q^{32} -35.4931i q^{33} +(-36.7400 + 5.68197i) q^{34} +(-11.4394 + 3.62498i) q^{36} +50.9523i q^{37} +(-24.6081 + 3.80573i) q^{38} +0.721767i q^{39} +46.7073 q^{41} +(-0.174661 - 1.12937i) q^{42} -55.5866 q^{43} +(24.7610 + 78.1385i) q^{44} +(7.10090 + 45.9149i) q^{46} +81.7616 q^{47} +(22.6550 - 15.9609i) q^{48} -48.8912 q^{49} -32.1960i q^{51} +(-0.503524 - 1.58898i) q^{52} +29.9744i q^{53} +(-1.58832 - 10.2702i) q^{54} +(1.17240 + 2.36448i) q^{56} -21.5646i q^{57} +(-7.31067 - 47.2713i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(-83.0424 + 12.8428i) q^{62} +0.989693 q^{63} +(-38.7406 + 50.9428i) q^{64} +(-70.1523 + 10.8493i) q^{66} +72.8008 q^{67} +(22.4608 + 70.8799i) q^{68} -40.2362 q^{69} +39.2803i q^{71} +(10.6615 + 21.5019i) q^{72} +46.5814i q^{73} +(100.707 - 15.5747i) q^{74} +(15.0441 + 47.4747i) q^{76} -6.76026i q^{77} +(1.42657 - 0.220625i) q^{78} -101.920i q^{79} +9.00000 q^{81} +(-14.2771 - 92.3170i) q^{82} -5.88913 q^{83} +(-2.17882 + 0.690438i) q^{84} +(16.9913 + 109.867i) q^{86} +41.4248 q^{87} +(146.872 - 72.8250i) q^{88} +61.0100 q^{89} +0.137472i q^{91} +(88.5804 - 28.0699i) q^{92} -72.7718i q^{93} +(-24.9923 - 161.602i) q^{94} +(-38.4717 - 39.8989i) q^{96} +95.5437i q^{97} +(14.9447 + 96.6335i) q^{98} -61.4759i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9	$ 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9} - 44 q^{14} + 80 q^{16} + 48 q^{21} + 72 q^{24} - 132 q^{26} + 64 q^{29} - 248 q^{34} + 48 q^{36} - 32 q^{41} - 80 q^{44} - 152 q^{46} - 32 q^{49} - 36 q^{54} - 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{66} + 192 q^{69} + 216 q^{74} + 240 q^{76} + 144 q^{81} + 288 q^{84} + 428 q^{86} - 256 q^{89} - 24 q^{94} + 192 q^{96}+O(q^{100}) $ 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9 - 44 * q^14 + 80 * q^16 + 48 * q^21 + 72 * q^24 - 132 * q^26 + 64 * q^29 - 248 * q^34 + 48 * q^36 - 32 * q^41 - 80 * q^44 - 152 * q^46 - 32 * q^49 - 36 * q^54 - 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^66 + 192 * q^69 + 216 * q^74 + 240 * q^76 + 144 * q^81 + 288 * q^84 + 428 * q^86 - 256 * q^89 - 24 * q^94 + 192 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.305673	−	1.97650i	−0.152836	−	0.988251i
$2$	−0.305673	−	1.97650i	−0.152836	−	0.988251i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−3.81313	+	1.20833i	−0.953282	+	0.302082i
$5$		0			0
$5$		0			0
$6$	−0.529441	−	3.42340i	−0.0882402	−	0.570567i
$7$	0.329898			0.0471283			0.0235641	−	0.999722i	$-0.492499\pi$
$7$	0.329898			0.0471283			0.0235641	+	0.999722i	$0.492499\pi$
$8$	3.55383	+	7.16731i	0.444229	+	0.895913i
$9$	3.00000			0.333333
$10$		0			0
$11$		−	20.4920i		−	1.86291i	−0.363861	−	0.931453i	$-0.618542\pi$
$11$		−	20.4920i		−	1.86291i	0.363861	−	0.931453i	$-0.381458\pi$
$12$	−6.60453	+	2.09288i	−0.550378	+	0.174407i
$13$			0.416712i			0.0320548i	0.999872	+	0.0160274i	$0.00510189\pi$
$13$			0.416712i			0.0320548i	−0.999872	+	0.0160274i	$0.994898\pi$
$14$	−0.100841	−	0.652044i	−0.00720292	−	0.0465746i
$15$		0			0
$16$	13.0799	−	9.21501i	0.817493	−	0.575938i
$17$		−	18.5884i		−	1.09343i	−0.837317	−	0.546717i	$-0.815877\pi$
$17$		−	18.5884i		−	1.09343i	0.837317	−	0.546717i	$-0.184123\pi$
$18$	−0.917019	−	5.92951i	−0.0509455	−	0.329417i
$19$		−	12.4503i		−	0.655281i	−0.944803	−	0.327640i	$-0.893747\pi$
$19$		−	12.4503i		−	0.655281i	0.944803	−	0.327640i	$-0.106253\pi$
$20$		0			0
$21$	0.571400			0.0272095
$22$	−40.5024	+	6.26384i	−1.84102	+	0.284720i
$23$	−23.2304			−1.01002			−0.505008	−	0.863114i	$-0.668511\pi$
$23$	−23.2304			−1.01002			−0.505008	+	0.863114i	$0.668511\pi$
$24$	6.15542	+	12.4141i	0.256476	+	0.517256i
$25$		0			0
$26$	0.823633	−	0.127378i	0.0316782	−	0.00489914i
$27$	5.19615			0.192450
$28$	−1.25794	+	0.398624i	−0.0449265	+	0.0142366i
$29$	23.9166			0.824712			0.412356	−	0.911023i	$-0.364706\pi$
$29$	23.9166			0.824712			0.412356	+	0.911023i	$0.364706\pi$
$30$		0			0
$31$		−	42.0148i		−	1.35532i	−0.735377	−	0.677658i	$-0.762995\pi$
$31$		−	42.0148i		−	1.35532i	0.735377	−	0.677658i	$-0.237005\pi$
$32$	−22.2117	−	23.0357i	−0.694115	−	0.719865i
$33$		−	35.4931i		−	1.07555i
$34$	−36.7400	+	5.68197i	−1.08059	+	0.167117i
$35$		0			0
$36$	−11.4394	+	3.62498i	−0.317761	+	0.100694i
$37$			50.9523i			1.37709i	0.725194	+	0.688545i	$0.241750\pi$
$37$			50.9523i			1.37709i	−0.725194	+	0.688545i	$0.758250\pi$
$38$	−24.6081	+	3.80573i	−0.647582	+	0.100151i
$39$			0.721767i			0.0185068i
$40$		0			0
$41$	46.7073			1.13920			0.569601	−	0.821921i	$-0.307098\pi$
$41$	46.7073			1.13920			0.569601	+	0.821921i	$0.307098\pi$
$42$	−0.174661	−	1.12937i	−0.00415861	−	0.0268898i
$43$	−55.5866			−1.29271			−0.646356	−	0.763036i	$-0.723708\pi$
$43$	−55.5866			−1.29271			−0.646356	+	0.763036i	$0.723708\pi$
$44$	24.7610	+	78.1385i	0.562750	+	1.77588i
$45$		0			0
$46$	7.10090	+	45.9149i	0.154367	+	0.998151i
$47$	81.7616			1.73961			0.869804	−	0.493397i	$-0.164245\pi$
$47$	81.7616			1.73961			0.869804	+	0.493397i	$0.164245\pi$
$48$	22.6550	−	15.9609i	0.471980	−	0.332518i
$49$	−48.8912			−0.997779
$50$		0			0
$51$		−	32.1960i		−	0.631295i
$52$	−0.503524	−	1.58898i	−0.00968316	−	0.0305572i
$53$			29.9744i			0.565554i	0.959186	+	0.282777i	$0.0912557\pi$
$53$			29.9744i			0.565554i	−0.959186	+	0.282777i	$0.908744\pi$
$54$	−1.58832	−	10.2702i	−0.0294134	−	0.190189i
$55$		0			0
$56$	1.17240	+	2.36448i	0.0209357	+	0.0422228i
$57$		−	21.5646i		−	0.378326i
$58$	−7.31067	−	47.2713i	−0.126046	−	0.815023i
$59$		−	24.3311i		−	0.412391i	−0.978511	−	0.206196i	$-0.933892\pi$
$59$		−	24.3311i		−	0.412391i	0.978511	−	0.206196i	$-0.0661083\pi$
$60$		0			0
$61$	−74.8416			−1.22691			−0.613456	−	0.789729i	$-0.710221\pi$
$61$	−74.8416			−1.22691			−0.613456	+	0.789729i	$0.710221\pi$
$62$	−83.0424	+	12.8428i	−1.33939	+	0.207142i
$63$	0.989693			0.0157094
$64$	−38.7406	+	50.9428i	−0.605321	+	0.795981i
$65$		0			0
$66$	−70.1523	+	10.8493i	−1.06291	+	0.164383i
$67$	72.8008			1.08658			0.543290	−	0.839545i	$-0.317178\pi$
$67$	72.8008			1.08658			0.543290	+	0.839545i	$0.317178\pi$
$68$	22.4608	+	70.8799i	0.330307	+	1.04235i
$69$	−40.2362			−0.583133
$70$		0			0
$71$			39.2803i			0.553244i	0.960979	+	0.276622i	$0.0892150\pi$
$71$			39.2803i			0.553244i	−0.960979	+	0.276622i	$0.910785\pi$
$72$	10.6615	+	21.5019i	0.148076	+	0.298638i
$73$			46.5814i			0.638101i	0.947738	+	0.319051i	$0.103364\pi$
$73$			46.5814i			0.638101i	−0.947738	+	0.319051i	$0.896636\pi$
$74$	100.707	−	15.5747i	1.36091	−	0.210469i
$75$		0			0
$76$	15.0441	+	47.4747i	0.197948	+	0.624667i
$77$		−	6.76026i		−	0.0877955i
$78$	1.42657	−	0.220625i	0.0182894	−	0.00282852i
$79$		−	101.920i		−	1.29012i	−0.764131	−	0.645062i	$-0.776832\pi$
$79$		−	101.920i		−	1.29012i	0.764131	−	0.645062i	$-0.223168\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−14.2771	−	92.3170i	−0.174112	−	1.12582i
$83$	−5.88913			−0.0709534			−0.0354767	−	0.999371i	$-0.511295\pi$
$83$	−5.88913			−0.0709534			−0.0354767	+	0.999371i	$0.511295\pi$
$84$	−2.17882	+	0.690438i	−0.0259383	+	0.00821950i
$85$		0			0
$86$	16.9913	+	109.867i	0.197574	+	1.27752i
$87$	41.4248			0.476148
$88$	146.872	−	72.8250i	1.66900	−	0.827557i
$89$	61.0100			0.685506			0.342753	−	0.939426i	$-0.388641\pi$
$89$	61.0100			0.685506			0.342753	+	0.939426i	$0.388641\pi$
$90$		0			0
$91$			0.137472i			0.00151069i
$92$	88.5804	−	28.0699i	0.962831	−	0.305108i
$93$		−	72.7718i		−	0.782492i
$94$	−24.9923	−	161.602i	−0.265876	−	1.71917i
$95$		0			0
$96$	−38.4717	−	39.8989i	−0.400747	−	0.415614i
$97$			95.5437i			0.984987i	0.870316	+	0.492494i	$0.163914\pi$
$97$			95.5437i			0.984987i	−0.870316	+	0.492494i	$0.836086\pi$
$98$	14.9447	+	96.6335i	0.152497	+	0.986057i
$99$		−	61.4759i		−	0.620969i
$100$		0			0
$101$	162.675			1.61064			0.805322	−	0.592838i	$-0.201992\pi$
$101$	162.675			1.61064			0.805322	+	0.592838i	$0.201992\pi$
$102$	−63.6355	+	9.84145i	−0.623878	+	0.0964848i
$103$	158.196			1.53588			0.767941	−	0.640521i	$-0.221282\pi$
$103$	158.196			1.53588			0.767941	+	0.640521i	$0.221282\pi$
$104$	−2.98670	+	1.48092i	−0.0287183	+	0.0142397i
$105$		0			0
$106$	59.2445	−	9.16236i	0.558910	−	0.0864373i
$107$	−18.1827			−0.169932			−0.0849660	−	0.996384i	$-0.527078\pi$
$107$	−18.1827			−0.169932			−0.0849660	+	0.996384i	$0.527078\pi$
$108$	−19.8136	+	6.27865i	−0.183459	+	0.0581357i
$109$	156.842			1.43891			0.719457	−	0.694537i	$-0.244391\pi$
$109$	156.842			1.43891			0.719457	+	0.694537i	$0.244391\pi$
$110$		0			0
$111$			88.2520i			0.795063i
$112$	4.31503	−	3.04001i	0.0385270	−	0.0271430i
$113$			98.7245i			0.873668i	0.899542	+	0.436834i	$0.143900\pi$
$113$			98.7245i			0.873668i	−0.899542	+	0.436834i	$0.856100\pi$
$114$	−42.6225	+	6.59172i	−0.373882	+	0.0578221i
$115$		0			0
$116$	−91.1972	+	28.8991i	−0.786183	+	0.249130i
$117$			1.25014i			0.0106849i
$118$	−48.0904	+	7.43735i	−0.407546	+	0.0630284i
$119$		−	6.13227i		−	0.0515317i
$120$		0			0
$121$	−298.921			−2.47042
$122$	22.8770	+	147.925i	0.187517	+	1.21250i
$123$	80.8994			0.657718
$124$	50.7676	+	160.208i	0.409416	+	1.29200i
$125$		0			0
$126$	−0.302523	−	1.95613i	−0.00240097	−	0.0155249i
$127$	−27.0938			−0.213337			−0.106669	−	0.994295i	$-0.534018\pi$
$127$	−27.0938			−0.213337			−0.106669	+	0.994295i	$0.534018\pi$
$128$	112.531	+	60.9990i	0.879145	+	0.476555i
$129$	−96.2789			−0.746348
$130$		0			0
$131$		−	4.45811i		−	0.0340314i	−0.999855	−	0.0170157i	$-0.994583\pi$
$131$		−	4.45811i		−	0.0340314i	0.999855	−	0.0170157i	$-0.00541653\pi$
$132$	42.8873	+	135.340i	0.324904	+	1.02530i
$133$		−	4.10734i		−	0.0308822i
$134$	−22.2533	−	143.891i	−0.166069	−	1.07381i
$135$		0			0
$136$	133.229	−	66.0600i	0.979622	−	0.485735i
$137$		−	181.700i		−	1.32628i	−0.748496	−	0.663139i	$-0.769224\pi$
$137$		−	181.700i		−	1.32628i	0.748496	−	0.663139i	$-0.230776\pi$
$138$	12.2991	+	79.5270i	0.0891241	+	0.576282i
$139$			223.419i			1.60733i	0.595083	+	0.803664i	$0.297119\pi$
$139$			223.419i			1.60733i	−0.595083	+	0.803664i	$0.702881\pi$
$140$		0			0
$141$	141.615			1.00436
$142$	77.6377	−	12.0069i	0.546744	−	0.0845559i
$143$	8.53925			0.0597151
$144$	39.2397	−	27.6450i	0.272498	−	0.191979i
$145$		0			0
$146$	92.0683	−	14.2387i	0.630604	−	0.0975251i
$147$	−84.6820			−0.576068
$148$	−61.5670	−	194.288i	−0.415994	−	1.31275i
$149$	−123.867			−0.831324			−0.415662	−	0.909519i	$-0.636450\pi$
$149$	−123.867			−0.831324			−0.415662	+	0.909519i	$0.636450\pi$
$150$		0			0
$151$			76.0961i			0.503948i	0.967734	+	0.251974i	$0.0810797\pi$
$151$			76.0961i			0.503948i	−0.967734	+	0.251974i	$0.918920\pi$
$152$	89.2353	−	44.2464i	0.587075	−	0.291095i
$153$		−	55.7651i		−	0.364478i
$154$	−13.3617	+	2.06643i	−0.0867641	+	0.0134184i
$155$		0			0
$156$	−0.872130	−	2.75219i	−0.00559058	−	0.0176422i
$157$			34.2940i			0.218433i	0.994018	+	0.109217i	$0.0348342\pi$
$157$			34.2940i			0.218433i	−0.994018	+	0.109217i	$0.965166\pi$
$158$	−201.445	+	31.1541i	−1.27497	+	0.197178i
$159$			51.9172i			0.326523i
$160$		0			0
$161$	−7.66365			−0.0476003
$162$	−2.75106	−	17.7885i	−0.0169818	−	0.109806i
$163$	−165.538			−1.01557			−0.507786	−	0.861483i	$-0.669536\pi$
$163$	−165.538			−1.01557			−0.507786	+	0.861483i	$0.669536\pi$
$164$	−178.101	+	56.4377i	−1.08598	+	0.344132i
$165$		0			0
$166$	1.80015	+	11.6399i	0.0108443	+	0.0701198i
$167$	−83.6064			−0.500637			−0.250319	−	0.968164i	$-0.580535\pi$
$167$	−83.6064			−0.500637			−0.250319	+	0.968164i	$0.580535\pi$
$168$	2.03066	+	4.09540i	0.0120873	+	0.0243774i
$169$	168.826			0.998972
$170$		0			0
$171$		−	37.3510i		−	0.218427i
$172$	211.959	−	67.1668i	1.23232	−	0.390505i
$173$		−	192.900i		−	1.11503i	−0.830168	−	0.557513i	$-0.811756\pi$
$173$		−	192.900i		−	1.11503i	0.830168	−	0.557513i	$-0.188244\pi$
$174$	−12.6625	−	81.8763i	−0.0727727	−	0.470554i
$175$		0			0
$176$	−188.834	−	268.033i	−1.07292	−	1.52291i
$177$		−	42.1427i		−	0.238094i
$178$	−18.6491	−	120.587i	−0.104770	−	0.677452i
$179$			120.939i			0.675637i	0.941211	+	0.337819i	$0.109689\pi$
$179$			120.939i			0.675637i	−0.941211	+	0.337819i	$0.890311\pi$
$180$		0			0
$181$	−107.583			−0.594381			−0.297191	−	0.954818i	$-0.596050\pi$
$181$	−107.583			−0.594381			−0.297191	+	0.954818i	$0.596050\pi$
$182$	0.271715	−	0.0420216i	0.00149294	−	0.000230888i
$183$	−129.629			−0.708357
$184$	−82.5569	−	166.499i	−0.448679	−	0.904887i
$185$		0			0
$186$	−143.834	+	22.2444i	−0.773299	+	0.119593i
$187$	−380.913			−2.03697
$188$	−311.767	+	98.7947i	−1.65834	+	0.525504i
$189$	1.71420			0.00906984
$190$		0			0
$191$			279.706i			1.46443i	0.681075	+	0.732214i	$0.261513\pi$
$191$			279.706i			1.46443i	−0.681075	+	0.732214i	$0.738487\pi$
$192$	−67.1006	+	88.2355i	−0.349482	+	0.459560i
$193$			102.534i			0.531263i	0.964075	+	0.265632i	$0.0855805\pi$
$193$			102.534i			0.531263i	−0.964075	+	0.265632i	$0.914420\pi$
$194$	188.842	−	29.2051i	0.973415	−	0.150542i
$195$		0			0
$196$	186.428	−	59.0765i	0.951165	−	0.301411i
$197$			38.9632i			0.197783i	0.995098	+	0.0988913i	$0.0315296\pi$
$197$			38.9632i			0.197783i	−0.995098	+	0.0988913i	$0.968470\pi$
$198$	−121.507	+	18.7915i	−0.613673	+	0.0949067i
$199$			147.646i			0.741940i	0.928645	+	0.370970i	$0.120975\pi$
$199$			147.646i			0.741940i	−0.928645	+	0.370970i	$0.879025\pi$
$200$		0			0
$201$	126.095			0.627337
$202$	−49.7254	−	321.528i	−0.246165	−	1.59172i
$203$	7.89005			0.0388672
$204$	38.9033	+	122.768i	0.190703	+	0.601802i
$205$		0			0
$206$	−48.3562	−	312.674i	−0.234739	−	1.51784i
$207$	−69.6912			−0.336672
$208$	3.84001	+	5.45055i	0.0184616	+	0.0262046i
$209$	−255.132			−1.22073
$210$		0			0
$211$		−	233.336i		−	1.10586i	−0.833229	−	0.552928i	$-0.813510\pi$
$211$		−	233.336i		−	1.10586i	0.833229	−	0.552928i	$-0.186490\pi$
$212$	−36.2189	−	114.296i	−0.170844	−	0.539133i
$213$			68.0355i			0.319416i
$214$	5.55797	+	35.9382i	0.0259718	+	0.167936i
$215$		0			0
$216$	18.4663	+	37.2424i	0.0854919	+	0.172419i
$217$		−	13.8606i		−	0.0638737i
$218$	−47.9422	−	309.998i	−0.219918	−	1.42201i
$219$			80.6813i			0.368408i
$220$		0			0
$221$	7.74600			0.0350498
$222$	174.430	−	26.9762i	0.785722	−	0.121515i
$223$	82.7105			0.370899			0.185450	−	0.982654i	$-0.440626\pi$
$223$	82.7105			0.370899			0.185450	+	0.982654i	$0.440626\pi$
$224$	−7.32758	−	7.59941i	−0.0327124	−	0.0339260i
$225$		0			0
$226$	195.129	−	30.1774i	0.863403	−	0.133528i
$227$	−361.534			−1.59266			−0.796330	−	0.604862i	$-0.793228\pi$
$227$	−361.534			−1.59266			−0.796330	+	0.604862i	$0.793228\pi$
$228$	26.0571	+	82.2286i	0.114286	+	0.360652i
$229$	−121.818			−0.531955			−0.265977	−	0.963979i	$-0.585695\pi$
$229$	−121.818			−0.531955			−0.265977	+	0.963979i	$0.585695\pi$
$230$		0			0
$231$		−	11.7091i		−	0.0506888i
$232$	84.9957	+	171.418i	0.366361	+	0.738870i
$233$		−	136.615i		−	0.586329i	−0.956062	−	0.293164i	$-0.905292\pi$
$233$		−	136.615i		−	0.586329i	0.956062	−	0.293164i	$-0.0947083\pi$
$234$	2.47090	−	0.382133i	0.0105594	−	0.00163305i
$235$		0			0
$236$	29.3999	+	92.7775i	0.124576	+	0.393125i
$237$		−	176.530i		−	0.744853i
$238$	−12.1204	+	1.87447i	−0.0509262	+	0.00787592i
$239$			56.4632i			0.236248i	0.992999	+	0.118124i	$0.0376880\pi$
$239$			56.4632i			0.236248i	−0.992999	+	0.118124i	$0.962312\pi$
$240$		0			0
$241$	−2.24158			−0.00930117			−0.00465059	−	0.999989i	$-0.501480\pi$
$241$	−2.24158			−0.00930117			−0.00465059	+	0.999989i	$0.501480\pi$
$242$	91.3720	+	590.818i	0.377570	+	2.44140i
$243$	15.5885			0.0641500
$244$	285.381	−	90.4331i	1.16959	−	0.370627i
$245$		0			0
$246$	−24.7287	−	159.898i	−0.100523	−	0.649991i
$247$	5.18820			0.0210049
$248$	301.133	−	149.314i	1.21425	−	0.602071i
$249$	−10.2003			−0.0409650
$250$		0			0
$251$		−	395.809i		−	1.57693i	−0.615081	−	0.788464i	$-0.710877\pi$
$251$		−	395.809i		−	1.57693i	0.615081	−	0.788464i	$-0.289123\pi$
$252$	−3.77383	+	1.19587i	−0.0149755	+	0.00474553i
$253$			476.036i			1.88157i
$254$	8.28184	+	53.5510i	0.0326057	+	0.210831i
$255$		0			0
$256$	86.1671	−	241.063i	0.336590	−	0.941651i
$257$			109.778i			0.427151i	0.976927	+	0.213576i	$0.0685110\pi$
$257$			109.778i			0.427151i	−0.976927	+	0.213576i	$0.931489\pi$
$258$	29.4298	+	190.295i	0.114069	+	0.737579i
$259$			16.8091i			0.0648998i
$260$		0			0
$261$	71.7499			0.274904
$262$	−8.81147	+	1.36272i	−0.0336316	+	0.00520124i
$263$	327.702			1.24601			0.623007	−	0.782216i	$-0.285911\pi$
$263$	327.702			1.24601			0.623007	+	0.782216i	$0.285911\pi$
$264$	254.390	−	126.137i	0.963599	−	0.477790i
$265$		0			0
$266$	−8.11816	+	1.25550i	−0.0305194	+	0.00471993i
$267$	105.673			0.395777
$268$	−277.599	+	87.9672i	−1.03582	+	0.328236i
$269$	130.032			0.483392			0.241696	−	0.970352i	$-0.422296\pi$
$269$	130.032			0.483392			0.241696	+	0.970352i	$0.422296\pi$
$270$		0			0
$271$			329.669i			1.21649i	0.793750	+	0.608245i	$0.208126\pi$
$271$			329.669i			1.21649i	−0.793750	+	0.608245i	$0.791874\pi$
$272$	−171.292	−	243.134i	−0.629751	−	0.893875i
$273$			0.238109i			0.000872195i
$274$	−359.131	+	55.5408i	−1.31070	+	0.202704i
$275$		0			0
$276$	153.426	−	48.6185i	0.555891	−	0.176154i
$277$			304.124i			1.09792i	0.835849	+	0.548960i	$0.184976\pi$
$277$			304.124i			1.09792i	−0.835849	+	0.548960i	$0.815024\pi$
$278$	441.588	−	68.2930i	1.58844	−	0.245658i
$279$		−	126.044i		−	0.451772i
$280$		0			0
$281$	240.099			0.854446			0.427223	−	0.904146i	$-0.359492\pi$
$281$	240.099			0.854446			0.427223	+	0.904146i	$0.359492\pi$
$282$	−43.2879	−	279.903i	−0.153503	−	0.992563i
$283$	−86.6730			−0.306265			−0.153133	−	0.988206i	$-0.548936\pi$
$283$	−86.6730			−0.306265			−0.153133	+	0.988206i	$0.548936\pi$
$284$	−47.4635	−	149.781i	−0.167125	−	0.527398i
$285$		0			0
$286$	−2.61022	−	16.8779i	−0.00912664	−	0.0590135i
$287$	15.4086			0.0536886
$288$	−66.6350	−	69.1070i	−0.231372	−	0.239955i
$289$	−56.5280			−0.195599
$290$		0			0
$291$			165.487i			0.568683i
$292$	−56.2856	−	177.621i	−0.192759	−	0.608290i
$293$		−	390.339i		−	1.33222i	−0.745855	−	0.666108i	$-0.767959\pi$
$293$		−	390.339i		−	1.33222i	0.745855	−	0.666108i	$-0.232041\pi$
$294$	25.8850	+	167.374i	0.0880442	+	0.569300i
$295$		0			0
$296$	−365.191	+	181.076i	−1.23375	+	0.611743i
$297$		−	106.479i		−	0.358517i
$298$	37.8629	+	244.824i	0.127057	+	0.821557i
$299$		−	9.68038i		−	0.0323759i
$300$		0			0
$301$	−18.3379			−0.0609233
$302$	150.404	−	23.2605i	0.498027	−	0.0770216i
$303$	281.761			0.929906
$304$	−114.730	−	162.849i	−0.377401	−	0.535687i
$305$		0			0
$306$	−110.220	+	17.0459i	−0.360196	+	0.0557056i
$307$	60.2318			0.196195			0.0980973	−	0.995177i	$-0.468724\pi$
$307$	60.2318			0.196195			0.0980973	+	0.995177i	$0.468724\pi$
$308$	8.16860	+	25.7777i	0.0265214	+	0.0836939i
$309$	274.003			0.886741
$310$		0			0
$311$			106.594i			0.342747i	0.985206	+	0.171373i	$0.0548205\pi$
$311$			106.594i			0.342747i	−0.985206	+	0.171373i	$0.945180\pi$
$312$	−5.17312	+	2.56504i	−0.0165805	+	0.00822127i
$313$			46.2243i			0.147682i	0.997270	+	0.0738408i	$0.0235257\pi$
$313$			46.2243i			0.147682i	−0.997270	+	0.0738408i	$0.976474\pi$
$314$	67.7823	−	10.4828i	0.215867	−	0.0333846i
$315$		0			0
$316$	123.152	+	388.633i	0.389723	+	1.22985i
$317$		−	8.36780i		−	0.0263969i	−0.999913	−	0.0131984i	$-0.995799\pi$
$317$		−	8.36780i		−	0.0263969i	0.999913	−	0.0131984i	$-0.00420131\pi$
$318$	102.614	−	15.8697i	0.322687	−	0.0499046i
$319$		−	490.099i		−	1.53636i
$320$		0			0
$321$	−31.4934			−0.0981103
$322$	2.34257	+	15.1472i	0.00727507	+	0.0470411i
$323$	−231.432			−0.716506
$324$	−34.3182	+	10.8749i	−0.105920	+	0.0335646i
$325$		0			0
$326$	50.6006	+	327.187i	0.155217	+	1.00364i
$327$	271.658			0.830757
$328$	165.990	+	334.765i	0.506066	+	1.02063i
$329$	26.9730			0.0819847
$330$		0			0
$331$		−	111.072i		−	0.335564i	−0.985824	−	0.167782i	$-0.946339\pi$
$331$		−	111.072i		−	0.335564i	0.985824	−	0.167782i	$-0.0536605\pi$
$332$	22.4560	−	7.11600i	0.0676386	−	0.0214337i
$333$			152.857i			0.459030i
$334$	25.5562	+	165.248i	0.0765156	+	0.494755i
$335$		0			0
$336$	7.47385	−	5.26546i	0.0222436	−	0.0156710i
$337$		−	231.853i		−	0.687990i	−0.938972	−	0.343995i	$-0.888220\pi$
$337$		−	231.853i		−	0.687990i	0.938972	−	0.343995i	$-0.111780\pi$
$338$	−51.6057	−	333.686i	−0.152679	−	0.987236i
$339$			170.996i			0.504412i
$340$		0			0
$341$	−860.966			−2.52483
$342$	−73.8244	+	11.4172i	−0.215861	+	0.0333836i
$343$	−32.2941			−0.0941518
$344$	−197.546	−	398.406i	−0.574260	−	1.15816i
$345$		0			0
$346$	−381.266	+	58.9642i	−1.10193	+	0.170417i
$347$	402.088			1.15875			0.579377	−	0.815059i	$-0.303296\pi$
$347$	402.088			1.15875			0.579377	+	0.815059i	$0.303296\pi$
$348$	−157.958	+	50.0548i	−0.453903	+	0.143835i
$349$	163.284			0.467864			0.233932	−	0.972253i	$-0.424841\pi$
$349$	163.284			0.467864			0.233932	+	0.972253i	$0.424841\pi$
$350$		0			0
$351$			2.16530i			0.00616894i
$352$	−472.046	+	455.161i	−1.34104	+	1.29307i
$353$		−	175.851i		−	0.498161i	−0.968483	−	0.249081i	$-0.919872\pi$
$353$		−	175.851i		−	0.498161i	0.968483	−	0.249081i	$-0.0801285\pi$
$354$	−83.2951	+	12.8819i	−0.235297	+	0.0363895i
$355$		0			0
$356$	−232.639	+	73.7201i	−0.653481	+	0.207079i
$357$		−	10.6214i		−	0.0297518i
$358$	239.037	−	36.9678i	0.667700	−	0.103262i
$359$		−	345.628i		−	0.962753i	−0.876514	−	0.481377i	$-0.840137\pi$
$359$		−	345.628i		−	0.962753i	0.876514	−	0.481377i	$-0.159863\pi$
$360$		0			0
$361$	205.989			0.570607
$362$	32.8852	+	212.638i	0.0908431	+	0.587398i
$363$	−517.746			−1.42630
$364$	−0.166112	−	0.524200i	−0.000456351	−	0.00144011i
$365$		0			0
$366$	39.6242	+	256.213i	0.108263	+	0.700035i
$367$	728.998			1.98637			0.993185	−	0.116546i	$-0.0371823\pi$
$367$	728.998			1.98637			0.993185	+	0.116546i	$0.0371823\pi$
$368$	−303.851	+	214.068i	−0.825682	+	0.581707i
$369$	140.122			0.379734
$370$		0			0
$371$			9.88848i			0.0266536i
$372$	87.9321	+	277.488i	0.236377	+	0.745936i
$373$			46.6749i			0.125134i	0.998041	+	0.0625668i	$0.0199287\pi$
$373$			46.6749i			0.125134i	−0.998041	+	0.0625668i	$0.980071\pi$
$374$	116.435	+	752.875i	0.311323	+	2.01303i
$375$		0			0
$376$	290.567	+	586.010i	0.772784	+	1.55854i
$377$			9.96635i			0.0264360i
$378$	−0.523984	−	3.38812i	−0.00138620	−	0.00896328i
$379$		−	117.629i		−	0.310368i	−0.987886	−	0.155184i	$-0.950403\pi$
$379$		−	117.629i		−	0.310368i	0.987886	−	0.155184i	$-0.0495970\pi$
$380$		0			0
$381$	−46.9278			−0.123170
$382$	552.839	−	85.4985i	1.44722	−	0.223818i
$383$	251.669			0.657100			0.328550	−	0.944487i	$-0.393440\pi$
$383$	251.669			0.657100			0.328550	+	0.944487i	$0.393440\pi$
$384$	194.909	+	105.653i	0.507575	+	0.275139i
$385$		0			0
$386$	202.658	−	31.3418i	0.525022	−	0.0811964i
$387$	−166.760			−0.430904
$388$	−115.448	−	364.321i	−0.297547	−	0.938970i
$389$	−356.890			−0.917454			−0.458727	−	0.888577i	$-0.651694\pi$
$389$	−356.890			−0.917454			−0.458727	+	0.888577i	$0.651694\pi$
$390$		0			0
$391$			431.815i			1.10439i
$392$	−173.751	−	350.418i	−0.443242	−	0.893923i
$393$		−	7.72168i		−	0.0196480i
$394$	77.0108	−	11.9100i	0.195459	−	0.0302284i
$395$		0			0
$396$	74.2830	+	234.416i	0.187583	+	0.591958i
$397$		−	103.819i		−	0.261508i	−0.991415	−	0.130754i	$-0.958260\pi$
$397$		−	103.819i		−	0.261508i	0.991415	−	0.130754i	$-0.0417398\pi$
$398$	291.823	−	45.1314i	0.733224	−	0.113396i
$399$		−	7.11412i		−	0.0178299i
$400$		0			0
$401$	−121.598			−0.303237			−0.151618	−	0.988439i	$-0.548449\pi$
$401$	−121.598			−0.303237			−0.151618	+	0.988439i	$0.548449\pi$
$402$	−38.5438	−	249.227i	−0.0958800	−	0.619967i
$403$	17.5081			0.0434444
$404$	−620.301	+	196.565i	−1.53540	+	0.486546i
$405$		0			0
$406$	−2.41177	−	15.5947i	−0.00594033	−	0.0384106i
$407$	1044.11			2.56539
$408$	230.759	−	114.419i	0.565585	−	0.280439i
$409$	−182.788			−0.446915			−0.223457	−	0.974714i	$-0.571734\pi$
$409$	−182.788			−0.446915			−0.223457	+	0.974714i	$0.571734\pi$
$410$		0			0
$411$		−	314.714i		−	0.765727i
$412$	−603.221	+	191.152i	−1.46413	+	0.463962i
$413$		−	8.02677i		−	0.0194353i
$414$	21.3027	+	137.745i	0.0514558	+	0.332717i
$415$		0			0
$416$	9.59924	−	9.25587i	0.0230751	−	0.0222497i
$417$			386.972i			0.927991i
$418$	77.9869	+	504.269i	0.186572	+	1.20638i
$419$		−	168.020i		−	0.401003i	−0.979693	−	0.200502i	$-0.935743\pi$
$419$		−	168.020i		−	0.401003i	0.979693	−	0.200502i	$-0.0642572\pi$
$420$		0			0
$421$	625.291			1.48525			0.742626	−	0.669706i	$-0.233580\pi$
$421$	625.291			1.48525			0.742626	+	0.669706i	$0.233580\pi$
$422$	−461.189	+	71.3244i	−1.09286	+	0.169015i
$423$	245.285			0.579869
$424$	−214.836	+	106.524i	−0.506688	+	0.251236i
$425$		0			0
$426$	134.472	−	20.7966i	0.315663	−	0.0488184i
$427$	−24.6901			−0.0578222
$428$	69.3331	−	21.9707i	0.161993	−	0.0513334i
$429$	14.7904			0.0344765
$430$		0			0
$431$			133.413i			0.309544i	0.987950	+	0.154772i	$0.0494643\pi$
$431$			133.413i			0.309544i	−0.987950	+	0.154772i	$0.950536\pi$
$432$	67.9651	−	47.8826i	0.157327	−	0.110839i
$433$		−	706.716i		−	1.63214i	−0.577954	−	0.816069i	$-0.696149\pi$
$433$		−	706.716i		−	1.63214i	0.577954	−	0.816069i	$-0.303851\pi$
$434$	−27.3955	+	4.23681i	−0.0631233	+	0.00976223i
$435$		0			0
$436$	−598.057	+	189.516i	−1.37169	+	0.434670i
$437$			289.226i			0.661844i
$438$	159.467	−	24.6621i	0.364080	−	0.0563062i
$439$			507.488i			1.15601i	0.816033	+	0.578005i	$0.196169\pi$
$439$			507.488i			1.15601i	−0.816033	+	0.578005i	$0.803831\pi$
$440$		0			0
$441$	−146.674			−0.332593
$442$	−2.36774	−	15.3100i	−0.00535689	−	0.0346380i
$443$	−412.172			−0.930410			−0.465205	−	0.885203i	$-0.654019\pi$
$443$	−412.172			−0.930410			−0.465205	+	0.885203i	$0.654019\pi$
$444$	−106.637	−	336.516i	−0.240174	−	0.757919i
$445$		0			0
$446$	−25.2824	−	163.478i	−0.0566869	−	0.366542i
$447$	−214.544			−0.479965
$448$	−12.7804	+	16.8059i	−0.0285277	+	0.0375132i
$449$	808.617			1.80093			0.900465	−	0.434929i	$-0.143227\pi$
$449$	808.617			1.80093			0.900465	+	0.434929i	$0.143227\pi$
$450$		0			0
$451$		−	957.124i		−	2.12223i
$452$	−119.291	−	376.449i	−0.263919	−	0.832852i
$453$			131.802i			0.290955i
$454$	110.511	+	714.573i	0.243417	+	1.57395i
$455$		0			0
$456$	154.560	−	76.6370i	0.338948	−	0.168064i
$457$			472.873i			1.03473i	0.855764	+	0.517367i	$0.173088\pi$
$457$			472.873i			1.03473i	−0.855764	+	0.517367i	$0.826912\pi$
$458$	37.2364	+	240.773i	0.0813021	+	0.525705i
$459$		−	96.5881i		−	0.210432i
$460$		0			0
$461$	433.776			0.940946			0.470473	−	0.882414i	$-0.344083\pi$
$461$	433.776			0.940946			0.470473	+	0.882414i	$0.344083\pi$
$462$	−23.1431	+	3.57916i	−0.0500933	+	0.00774709i
$463$	−530.624			−1.14606			−0.573028	−	0.819536i	$-0.694231\pi$
$463$	−530.624			−1.14606			−0.573028	+	0.819536i	$0.694231\pi$
$464$	312.827	−	220.392i	0.674196	−	0.474983i
$465$		0			0
$466$	−270.019	+	41.7594i	−0.579440	+	0.0896124i
$467$	−355.266			−0.760741			−0.380370	−	0.924834i	$-0.624203\pi$
$467$	−355.266			−0.760741			−0.380370	+	0.924834i	$0.624203\pi$
$468$	−1.51057	−	4.76693i	−0.00322772	−	0.0101857i
$469$	24.0168			0.0512086
$470$		0			0
$471$			59.3990i			0.126113i
$472$	174.388	−	86.4686i	0.369467	−	0.183196i
$473$			1139.08i			2.40820i
$474$	−348.912	+	53.9605i	−0.736102	+	0.113841i
$475$		0			0
$476$	7.40978	+	23.3831i	0.0155668	+	0.0491242i
$477$			89.9232i			0.188518i
$478$	111.600	−	17.2593i	0.233472	−	0.0361072i
$479$		−	548.640i		−	1.14539i	−0.819770	−	0.572693i	$-0.805899\pi$
$479$		−	548.640i		−	1.14539i	0.819770	−	0.572693i	$-0.194101\pi$
$480$		0			0
$481$	−21.2324			−0.0441423
$482$	0.685191	+	4.43050i	0.00142156	+	0.00919190i
$483$	−13.2738			−0.0274821
$484$	1139.82	−	361.194i	2.35501	−	0.746269i
$485$		0			0
$486$	−4.76497	−	30.8106i	−0.00980446	−	0.0633964i
$487$	134.618			0.276422			0.138211	−	0.990403i	$-0.455865\pi$
$487$	134.618			0.276422			0.138211	+	0.990403i	$0.455865\pi$
$488$	−265.974	−	536.412i	−0.545029	−	1.09921i
$489$	−286.721			−0.586341
$490$		0			0
$491$		−	756.810i		−	1.54136i	−0.637220	−	0.770682i	$-0.719916\pi$
$491$		−	756.810i		−	1.54136i	0.637220	−	0.770682i	$-0.280084\pi$
$492$	−308.480	+	97.7529i	−0.626991	+	0.198685i
$493$		−	444.572i		−	0.901768i
$494$	−1.58589	−	10.2545i	−0.00321031	−	0.0207581i
$495$		0			0
$496$	−387.167	−	549.549i	−0.780579	−	1.10796i
$497$			12.9585i			0.0260734i
$498$	3.11795	+	20.1609i	0.00626094	+	0.0404837i
$499$		−	706.956i		−	1.41675i	−0.705838	−	0.708373i	$-0.749430\pi$
$499$		−	706.956i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$500$		0			0
$501$	−144.811			−0.289043
$502$	−782.318	+	120.988i	−1.55840	+	0.241012i
$503$	100.567			0.199935			0.0999673	−	0.994991i	$-0.468126\pi$
$503$	100.567			0.199935			0.0999673	+	0.994991i	$0.468126\pi$
$504$	3.51720	+	7.09344i	0.00697858	+	0.0140743i
$505$		0			0
$506$	940.887	−	145.511i	1.85946	−	0.287572i
$507$	292.416			0.576757
$508$	103.312	−	32.7382i	0.203370	−	0.0644452i
$509$	−753.185			−1.47973			−0.739867	−	0.672753i	$-0.765112\pi$
$509$	−753.185			−1.47973			−0.739867	+	0.672753i	$0.765112\pi$
$510$		0			0
$511$			15.3671i			0.0300726i
$512$	−502.800	−	96.6232i	−0.982031	−	0.188717i
$513$		−	64.6938i		−	0.126109i
$514$	216.976	−	33.5561i	0.422133	−	0.0652843i
$515$		0			0
$516$	367.124	−	116.336i	0.711480	−	0.225458i
$517$		−	1675.46i		−	3.24073i
$518$	33.2231	−	5.13807i	0.0641373	−	0.00991906i
$519$		−	334.112i		−	0.643761i
$520$		0			0
$521$	117.708			0.225926			0.112963	−	0.993599i	$-0.463966\pi$
$521$	117.708			0.225926			0.112963	+	0.993599i	$0.463966\pi$
$522$	−21.9320	−	141.814i	−0.0420153	−	0.271674i
$523$	617.411			1.18052			0.590259	−	0.807214i	$-0.299026\pi$
$523$	617.411			1.18052			0.590259	+	0.807214i	$0.299026\pi$
$524$	5.38686	+	16.9994i	0.0102803	+	0.0324415i
$525$		0			0
$526$	−100.170	−	647.704i	−0.190437	−	1.23138i
$527$	−780.988			−1.48195
$528$	−327.070	−	464.246i	−0.619450	−	0.879254i
$529$	10.6508			0.0201338
$530$		0			0
$531$		−	72.9932i		−	0.137464i
$532$	4.96301	+	15.6618i	0.00932896	+	0.0294395i
$533$			19.4635i			0.0365169i
$534$	−32.3012	−	208.862i	−0.0604892	−	0.391127i
$535$		0			0
$536$	258.722	+	521.786i	0.482690	+	0.973481i
$537$			209.473i			0.390079i
$538$	−39.7474	−	257.009i	−0.0738799	−	0.477713i
$539$			1001.88i			1.85877i
$540$		0			0
$541$	352.762			0.652056			0.326028	−	0.945360i	$-0.394290\pi$
$541$	352.762			0.652056			0.326028	+	0.945360i	$0.394290\pi$
$542$	651.591	−	100.771i	1.20220	−	0.185924i
$543$	−186.339			−0.343166
$544$	−428.196	+	412.879i	−0.787125	+	0.758969i
$545$		0			0
$546$	0.470623	−	0.0727835i	0.000861948	−	0.000133303i
$547$	−295.110			−0.539507			−0.269753	−	0.962929i	$-0.586942\pi$
$547$	−295.110			−0.539507			−0.269753	+	0.962929i	$0.586942\pi$
$548$	219.553	+	692.846i	0.400644	+	1.26432i
$549$	−224.525			−0.408970
$550$		0			0
$551$		−	297.770i		−	0.540418i
$552$	−142.993	−	288.385i	−0.259045	−	0.522437i
$553$		−	33.6231i		−	0.0608013i
$554$	601.102	−	92.9624i	1.08502	−	0.167802i
$555$		0			0
$556$	−269.963	−	851.924i	−0.485545	−	1.53224i
$557$			31.8538i			0.0571882i	0.999591	+	0.0285941i	$0.00910302\pi$
$557$			31.8538i			0.0571882i	−0.999591	+	0.0285941i	$0.990897\pi$
$558$	−249.127	+	38.5284i	−0.446465	+	0.0690473i
$559$		−	23.1636i		−	0.0414376i
$560$		0			0
$561$	−659.760			−1.17604
$562$	−73.3919	−	474.557i	−0.130591	−	0.844408i
$563$	−906.668			−1.61042			−0.805211	−	0.592988i	$-0.797948\pi$
$563$	−906.668			−1.61042			−0.805211	+	0.592988i	$0.797948\pi$
$564$	−539.997	+	171.117i	−0.957441	+	0.303400i
$565$		0			0
$566$	26.4936	+	171.310i	0.0468085	+	0.302667i
$567$	2.96908			0.00523647
$568$	−281.534	+	139.596i	−0.495659	+	0.245767i
$569$	465.009			0.817239			0.408620	−	0.912705i	$-0.366010\pi$
$569$	465.009			0.817239			0.408620	+	0.912705i	$0.366010\pi$
$570$		0			0
$571$		−	265.895i		−	0.465666i	−0.972517	−	0.232833i	$-0.925200\pi$
$571$		−	265.895i		−	0.465666i	0.972517	−	0.232833i	$-0.0747995\pi$
$572$	−32.5613	+	10.3182i	−0.0569253	+	0.0180388i
$573$			484.464i			0.845488i
$574$	−4.71000	−	30.4552i	−0.00820557	−	0.0530578i
$575$		0			0
$576$	−116.222	+	152.828i	−0.201774	+	0.265327i
$577$			138.097i			0.239336i	0.992814	+	0.119668i	$0.0381830\pi$
$577$			138.097i			0.239336i	−0.992814	+	0.119668i	$0.961817\pi$
$578$	17.2791	+	111.728i	0.0298946	+	0.193301i
$579$			177.594i			0.306725i
$580$		0			0
$581$	−1.94281			−0.00334391
$582$	327.085	−	50.5848i	0.562001	−	0.0869154i
$583$	614.234			1.05358
$584$	−333.863	+	165.542i	−0.571683	+	0.283463i
$585$		0			0
$586$	−771.507	+	119.316i	−1.31656	+	0.203611i
$587$	−648.473			−1.10472			−0.552362	−	0.833604i	$-0.686273\pi$
$587$	−648.473			−1.10472			−0.552362	+	0.833604i	$0.686273\pi$
$588$	322.903	−	102.324i	0.549155	−	0.174020i
$589$	−523.098			−0.888113
$590$		0			0
$591$			67.4862i			0.114190i
$592$	469.526	+	666.451i	0.793118	+	1.12576i
$593$			350.392i			0.590880i	0.955361	+	0.295440i	$0.0954662\pi$
$593$			350.392i			0.590880i	−0.955361	+	0.295440i	$0.904534\pi$
$594$	−210.457	+	32.5479i	−0.354304	+	0.0547944i
$595$		0			0
$596$	472.322	−	149.672i	0.792486	−	0.251128i
$597$			255.731i			0.428359i
$598$	−19.1333	+	2.95903i	−0.0319955	+	0.00494821i
$599$			276.745i			0.462012i	0.972952	+	0.231006i	$0.0742017\pi$
$599$			276.745i			0.462012i	−0.972952	+	0.231006i	$0.925798\pi$
$600$		0			0
$601$	815.487			1.35688			0.678442	−	0.734654i	$-0.262656\pi$
$601$	815.487			1.35688			0.678442	+	0.734654i	$0.262656\pi$
$602$	5.60540	+	36.2449i	0.00931130	+	0.0602075i
$603$	218.403			0.362193
$604$	−91.9490	−	290.164i	−0.152233	−	0.480405i
$605$		0			0
$606$	−86.1269	−	556.902i	−0.142124	−	0.918981i
$607$	247.049			0.407001			0.203500	−	0.979075i	$-0.434768\pi$
$607$	247.049			0.407001			0.203500	+	0.979075i	$0.434768\pi$
$608$	−286.802	+	276.543i	−0.471713	+	0.454840i
$609$	13.6660			0.0224400
$610$		0			0
$611$			34.0710i			0.0557627i
$612$	67.3825	+	212.640i	0.110102	+	0.347450i
$613$		−	1005.15i		−	1.63972i	−0.572561	−	0.819862i	$-0.694050\pi$
$613$		−	1005.15i		−	1.63972i	0.572561	−	0.819862i	$-0.305950\pi$
$614$	−18.4112	−	119.048i	−0.0299857	−	0.193890i
$615$		0			0
$616$	48.4528	−	24.0248i	0.0786572	−	0.0390013i
$617$			533.282i			0.864314i	0.901798	+	0.432157i	$0.142247\pi$
$617$			533.282i			0.864314i	−0.901798	+	0.432157i	$0.857753\pi$
$618$	−83.7553	−	541.568i	−0.135526	−	0.876324i
$619$			1136.85i			1.83659i	0.395900	+	0.918294i	$0.370433\pi$
$619$			1136.85i			1.83659i	−0.395900	+	0.918294i	$0.629567\pi$
$620$		0			0
$621$	−120.709			−0.194378
$622$	210.684	−	32.5830i	0.338720	−	0.0523842i
$623$	20.1271			0.0323067
$624$	6.65109	+	9.44063i	0.0106588	+	0.0151292i
$625$		0			0
$626$	91.3625	−	14.1295i	0.145946	−	0.0225711i
$627$	−441.901			−0.704787
$628$	−41.4384	−	130.768i	−0.0659847	−	0.208229i
$629$	947.121			1.50576
$630$		0			0
$631$			936.738i			1.48453i	0.670107	+	0.742265i	$0.266248\pi$
$631$			936.738i			1.48453i	−0.670107	+	0.742265i	$0.733752\pi$
$632$	730.490	−	362.206i	1.15584	−	0.573110i
$633$		−	404.149i		−	0.638466i
$634$	−16.5390	+	2.55781i	−0.0260867	+	0.00403440i
$635$		0			0
$636$	−62.7329	−	197.967i	−0.0986366	−	0.311269i
$637$		−	20.3735i		−	0.0319836i
$638$	−968.682	+	149.810i	−1.51831	+	0.234812i
$639$			117.841i			0.184415i
$640$		0			0
$641$	214.558			0.334723			0.167362	−	0.985896i	$-0.446475\pi$
$641$	214.558			0.334723			0.167362	+	0.985896i	$0.446475\pi$
$642$	9.62669	+	62.2468i	0.0149948	+	0.0969577i
$643$	−786.394			−1.22301			−0.611504	−	0.791241i	$-0.709435\pi$
$643$	−786.394			−1.22301			−0.611504	+	0.791241i	$0.709435\pi$
$644$	29.2225	−	9.26020i	0.0453765	−	0.0143792i
$645$		0			0
$646$	70.7424	+	457.425i	0.109508	+	0.708088i
$647$	316.550			0.489258			0.244629	−	0.969617i	$-0.421334\pi$
$647$	316.550			0.489258			0.244629	+	0.969617i	$0.421334\pi$
$648$	31.9845	+	64.5058i	0.0493588	+	0.0995459i
$649$	−498.592			−0.768246
$650$		0			0
$651$		−	24.0073i		−	0.0368775i
$652$	631.219	−	200.024i	0.968127	−	0.306786i
$653$			516.391i			0.790797i	0.918510	+	0.395399i	$0.129394\pi$
$653$			516.391i			0.790797i	−0.918510	+	0.395399i	$0.870606\pi$
$654$	−83.0384	−	536.932i	−0.126970	−	0.820997i
$655$		0			0
$656$	610.926	−	430.408i	0.931290	−	0.656110i
$657$			139.744i			0.212700i
$658$	−8.24491	−	53.3121i	−0.0125303	−	0.0810215i
$659$			285.118i			0.432653i	0.976321	+	0.216326i	$0.0694076\pi$
$659$			285.118i			0.432653i	−0.976321	+	0.216326i	$0.930592\pi$
$660$		0			0
$661$	−391.847			−0.592809			−0.296405	−	0.955062i	$-0.595788\pi$
$661$	−391.847			−0.592809			−0.296405	+	0.955062i	$0.595788\pi$
$662$	−219.534	+	33.9516i	−0.331622	+	0.0512865i
$663$	13.4165			0.0202360
$664$	−20.9290	−	42.2092i	−0.0315196	−	0.0635681i
$665$		0			0
$666$	302.122	−	46.7242i	0.453637	−	0.0701565i
$667$	−555.593			−0.832973
$668$	318.802	−	101.024i	0.477248	−	0.151233i
$669$	143.259			0.214139
$670$		0			0
$671$			1533.65i			2.28562i
$672$	−12.6917	−	13.1626i	−0.0188865	−	0.0195872i
$673$		−	1213.59i		−	1.80325i	−0.432517	−	0.901626i	$-0.642375\pi$
$673$		−	1213.59i		−	1.80325i	0.432517	−	0.901626i	$-0.357625\pi$
$674$	−458.257	+	70.8711i	−0.679907	+	0.105150i
$675$		0			0
$676$	−643.756	+	203.997i	−0.952303	+	0.301771i
$677$		−	251.863i		−	0.372028i	−0.982547	−	0.186014i	$-0.940443\pi$
$677$		−	251.863i		−	0.372028i	0.982547	−	0.186014i	$-0.0595570\pi$
$678$	337.974	−	52.2688i	0.498486	−	0.0770926i
$679$			31.5197i			0.0464207i
$680$		0			0
$681$	−626.195			−0.919523
$682$	263.174	+	1701.70i	0.385886	+	2.49517i
$683$	664.793			0.973342			0.486671	−	0.873585i	$-0.338211\pi$
$683$	664.793			0.973342			0.486671	+	0.873585i	$0.338211\pi$
$684$	45.1322	+	142.424i	0.0659828	+	0.208222i
$685$		0			0
$686$	9.87143	+	63.8293i	0.0143898	+	0.0930457i
$687$	−210.994			−0.307124
$688$	−727.067	+	512.231i	−1.05678	+	0.744522i
$689$	−12.4907			−0.0181287
$690$		0			0
$691$			654.347i			0.946957i	0.880805	+	0.473479i	$0.157002\pi$
$691$			654.347i			0.946957i	−0.880805	+	0.473479i	$0.842998\pi$
$692$	233.086	+	735.551i	0.336829	+	1.06293i
$693$		−	20.2808i		−	0.0292652i
$694$	−122.907	−	794.728i	−0.177100	−	1.14514i
$695$		0			0
$696$	147.217	+	296.904i	0.211519	+	0.426587i
$697$		−	868.213i		−	1.24564i
$698$	−49.9117	−	322.732i	−0.0715067	−	0.462367i
$699$		−	236.623i		−	0.338517i
$700$		0			0
$701$	−1266.25			−1.80635			−0.903174	−	0.429275i	$-0.858769\pi$
$701$	−1266.25			−1.80635			−0.903174	+	0.429275i	$0.858769\pi$
$702$	4.27972	−	0.661874i	0.00609647	−	0.000942840i
$703$	634.373			0.902380
$704$	1043.92	+	793.870i	1.48284	+	1.12766i
$705$		0			0
$706$	−347.570	+	53.7529i	−0.492309	+	0.0761372i
$707$	53.6661			0.0759068
$708$	50.9221	+	160.695i	0.0719239	+	0.226971i
$709$	493.220			0.695656			0.347828	−	0.937558i	$-0.386919\pi$
$709$	493.220			0.695656			0.347828	+	0.937558i	$0.386919\pi$
$710$		0			0
$711$		−	305.759i		−	0.430041i
$712$	216.819	+	437.278i	0.304522	+	0.614154i
$713$			976.020i			1.36889i
$714$	−20.9932	+	3.24667i	−0.0294023	+	0.00454716i
$715$		0			0
$716$	−146.134	−	461.156i	−0.204098	−	0.644073i
$717$			97.7971i			0.136398i
$718$	−683.135	+	105.649i	−0.951442	+	0.147144i
$719$			60.3910i			0.0839930i	0.999118	+	0.0419965i	$0.0133718\pi$
$719$			60.3910i			0.0839930i	−0.999118	+	0.0419965i	$0.986628\pi$
$720$		0			0
$721$	52.1884			0.0723834
$722$	−62.9653	−	407.138i	−0.0872096	−	0.563904i
$723$	−3.88254			−0.00537003
$724$	410.228	−	129.995i	0.566613	−	0.179552i
$725$		0			0
$726$	158.261	+	1023.33i	0.217990	+	1.40954i
$727$	−994.690			−1.36821			−0.684106	−	0.729383i	$-0.739807\pi$
$727$	−994.690			−1.36821			−0.684106	+	0.729383i	$0.739807\pi$
$728$	−0.985307	+	0.488554i	−0.00135344	+	0.000671090i
$729$	27.0000			0.0370370
$730$		0			0
$731$			1033.27i			1.41350i
$732$	494.294	−	156.635i	0.675264	−	0.213982i
$733$			1167.65i			1.59298i	0.604654	+	0.796488i	$0.293311\pi$
$733$			1167.65i			1.59298i	−0.604654	+	0.796488i	$0.706689\pi$
$734$	−222.835	−	1440.87i	−0.303590	−	1.96303i
$735$		0			0
$736$	515.986	+	535.127i	0.701067	+	0.727075i
$737$		−	1491.83i		−	2.02420i
$738$	−42.8314	−	276.951i	−0.0580372	−	0.375273i
$739$		−	79.9863i		−	0.108236i	−0.998535	−	0.0541179i	$-0.982765\pi$
$739$		−	79.9863i		−	0.108236i	0.998535	−	0.0541179i	$-0.0172347\pi$
$740$		0			0
$741$	8.98623			0.0121272
$742$	19.5446	−	3.02264i	0.0263405	−	0.00407364i
$743$	402.122			0.541214			0.270607	−	0.962690i	$-0.412776\pi$
$743$	402.122			0.541214			0.270607	+	0.962690i	$0.412776\pi$
$744$	521.578	−	258.619i	0.701045	−	0.347606i
$745$		0			0
$746$	92.2530	−	14.2672i	0.123664	−	0.0191250i
$747$	−17.6674			−0.0236511
$748$	1452.47	−	460.267i	1.94180	−	0.615330i
$749$	−5.99844			−0.00800860
$750$		0			0
$751$			58.7486i			0.0782271i	0.999235	+	0.0391136i	$0.0124534\pi$
$751$			58.7486i			0.0782271i	−0.999235	+	0.0391136i	$0.987547\pi$
$752$	1069.43	−	753.434i	1.42212	−	1.00191i
$753$		−	685.561i		−	0.910440i
$754$	19.6985	−	3.04644i	0.0261254	−	0.00404038i
$755$		0			0
$756$	−6.53646	+	2.07131i	−0.00864611	+	0.00273983i
$757$			1040.91i			1.37504i	0.726164	+	0.687522i	$0.241301\pi$
$757$			1040.91i			1.37504i	−0.726164	+	0.687522i	$0.758699\pi$
$758$	−232.495	+	35.9561i	−0.306721	+	0.0474355i
$759$			824.519i			1.08632i
$760$		0			0
$761$	750.095			0.985670			0.492835	−	0.870123i	$-0.335961\pi$
$761$	750.095			0.985670			0.492835	+	0.870123i	$0.335961\pi$
$762$	14.3446	+	92.7530i	0.0188249	+	0.121723i
$763$	51.7417			0.0678135
$764$	−337.976	−	1066.55i	−0.442377	−	1.39601i
$765$		0			0
$766$	−76.9285	−	497.425i	−0.100429	−	0.649380i
$767$	10.1391			0.0132191
$768$	149.246	−	417.533i	0.194331	−	0.543663i
$769$	−1065.98			−1.38619			−0.693094	−	0.720847i	$-0.743753\pi$
$769$	−1065.98			−1.38619			−0.693094	+	0.720847i	$0.743753\pi$
$770$		0			0
$771$			190.141i			0.246616i
$772$	−123.894	−	390.975i	−0.160485	−	0.506444i
$773$		−	947.271i		−	1.22545i	−0.790297	−	0.612724i	$-0.790074\pi$
$773$		−	947.271i		−	1.22545i	0.790297	−	0.612724i	$-0.209926\pi$
$774$	50.9740	+	329.601i	0.0658579	+	0.425842i
$775$		0			0
$776$	−684.791	+	339.546i	−0.882463	+	0.437560i
$777$			29.1141i			0.0374699i
$778$	109.092	+	705.393i	0.140220	+	0.906675i
$779$		−	581.521i		−	0.746497i
$780$		0			0
$781$	804.931			1.03064
$782$	853.484	−	131.994i	1.09141	−	0.168791i
$783$	124.275			0.158716
$784$	−639.491	+	450.533i	−0.815678	+	0.574659i
$785$		0			0
$786$	−15.2619	+	2.36031i	−0.0194172	+	0.00300294i
$787$	11.5874			0.0147236			0.00736178	−	0.999973i	$-0.497657\pi$
$787$	11.5874			0.0147236			0.00736178	+	0.999973i	$0.497657\pi$
$788$	−47.0803	−	148.572i	−0.0597465	−	0.188543i
$789$	567.596			0.719387
$790$		0			0
$791$			32.5690i			0.0411744i
$792$	440.617	−	218.475i	0.556334	−	0.275852i
$793$		−	31.1874i		−	0.0393284i
$794$	−205.198	+	31.7345i	−0.258436	+	0.0399679i
$795$		0			0
$796$	−178.405	−	562.994i	−0.224127	−	0.707278i
$797$			780.220i			0.978946i	0.872018	+	0.489473i	$0.162811\pi$
$797$			780.220i			0.978946i	−0.872018	+	0.489473i	$0.837189\pi$
$798$	−14.0611	+	2.17459i	−0.0176204	+	0.00272505i
$799$		−	1519.82i		−	1.90215i
$800$		0			0
$801$	183.030			0.228502
$802$	37.1692	+	240.339i	0.0463457	+	0.299674i
$803$	954.545			1.18872
$804$	−480.815	+	152.364i	−0.598029	+	0.189507i
$805$		0			0
$806$	−5.35175	−	34.6048i	−0.00663989	−	0.0429340i
$807$	225.223			0.279086
$808$	578.120	+	1165.94i	0.715495	+	1.44300i
$809$	1061.80			1.31249			0.656243	−	0.754549i	$-0.272145\pi$
$809$	1061.80			1.31249			0.656243	+	0.754549i	$0.272145\pi$
$810$		0			0
$811$			309.236i			0.381302i	0.981658	+	0.190651i	$0.0610599\pi$
$811$			309.236i			0.381302i	−0.981658	+	0.190651i	$0.938940\pi$
$812$	−30.0858	+	9.53376i	−0.0370514	+	0.0117411i
$813$			571.003i			0.702341i
$814$	−319.157	−	2063.69i	−0.392085	−	2.53525i
$815$		0			0
$816$	−296.687	−	421.121i	−0.363587	−	0.516079i
$817$			692.072i			0.847089i
$818$	55.8734	+	361.281i	0.0683049	+	0.441664i
$819$			0.412417i			0.000503562i
$820$		0			0
$821$	−1156.76			−1.40897			−0.704483	−	0.709721i	$-0.748821\pi$
$821$	−1156.76			−1.40897			−0.704483	+	0.709721i	$0.748821\pi$
$822$	−622.033	+	96.1995i	−0.756731	+	0.117031i
$823$	1441.89			1.75200			0.875998	−	0.482314i	$-0.160204\pi$
$823$	1441.89			1.75200			0.875998	+	0.482314i	$0.160204\pi$
$824$	562.201	+	1133.84i	0.682283	+	1.37602i
$825$		0			0
$826$	−15.8649	+	2.45357i	−0.0192069	+	0.00297042i
$827$	367.599			0.444497			0.222249	−	0.974990i	$-0.428660\pi$
$827$	367.599			0.444497			0.222249	+	0.974990i	$0.428660\pi$
$828$	265.741	−	84.2097i	0.320944	−	0.101703i
$829$	−172.743			−0.208375			−0.104188	−	0.994558i	$-0.533224\pi$
$829$	−172.743			−0.208375			−0.104188	+	0.994558i	$0.533224\pi$
$830$		0			0
$831$			526.758i			0.633884i
$832$	−21.2285	−	16.1437i	−0.0255150	−	0.0194034i
$833$			908.808i			1.09101i
$834$	764.852	−	118.287i	0.917089	−	0.141831i
$835$		0			0
$836$	972.850	−	308.283i	1.16370	−	0.368759i
$837$		−	218.315i		−	0.260831i
$838$	−332.093	+	51.3593i	−0.396292	+	0.0612879i
$839$			1083.17i			1.29103i	0.763748	+	0.645514i	$0.223357\pi$
$839$			1083.17i			1.29103i	−0.763748	+	0.645514i	$0.776643\pi$
$840$		0			0
$841$	−268.994			−0.319850
$842$	−191.135	−	1235.89i	−0.227001	−	1.46780i
$843$	415.864			0.493315
$844$	281.946	+	889.739i	0.334059	+	1.05419i
$845$		0			0
$846$	−74.9769	−	484.806i	−0.0886252	−	0.573057i
$847$	−98.6133			−0.116427
$848$	276.214	+	392.062i	0.325724	+	0.462337i
$849$	−150.122			−0.176822
$850$		0			0
$851$		−	1183.64i		−	1.39088i
$852$	−82.2092	−	259.428i	−0.0964896	−	0.304493i
$853$			1218.00i			1.42790i	0.700196	+	0.713951i	$0.253096\pi$
$853$			1218.00i			1.42790i	−0.700196	+	0.713951i	$0.746904\pi$
$854$	7.54709	+	48.8000i	0.00883734	+	0.0571429i
$855$		0			0
$856$	−64.6184	−	130.321i	−0.0754888	−	0.152244i
$857$			207.055i			0.241604i	0.992677	+	0.120802i	$0.0385466\pi$
$857$			207.055i			0.241604i	−0.992677	+	0.120802i	$0.961453\pi$
$858$	−4.52103	−	29.2333i	−0.00526927	−	0.0340715i
$859$			1186.36i			1.38109i	0.723290	+	0.690544i	$0.242629\pi$
$859$			1186.36i			1.38109i	−0.723290	+	0.690544i	$0.757371\pi$
$860$		0			0
$861$	26.6885			0.0309971
$862$	263.692	−	40.7809i	0.305907	−	0.0473096i
$863$	−885.953			−1.02660			−0.513298	−	0.858210i	$-0.671577\pi$
$863$	−885.953			−1.02660			−0.513298	+	0.858210i	$0.671577\pi$
$864$	−115.415	−	119.697i	−0.133582	−	0.138538i
$865$		0			0
$866$	−1396.83	+	216.024i	−1.61296	+	0.249450i
$867$	−97.9093			−0.112929
$868$	16.7481	+	52.8522i	0.0192951	+	0.0608897i
$869$	−2088.54			−2.40338
$870$		0			0
$871$			30.3370i			0.0348301i
$872$	557.389	+	1124.13i	0.639207	+	1.28914i
$873$			286.631i			0.328329i
$874$	571.656	−	88.4086i	0.654069	−	0.101154i
$875$		0			0
$876$	−97.4894	−	307.648i	−0.111289	−	0.351197i
$877$		−	643.339i		−	0.733567i	−0.930306	−	0.366784i	$-0.880459\pi$
$877$		−	643.339i		−	0.733567i	0.930306	−	0.366784i	$-0.119541\pi$
$878$	1003.05	−	155.125i	1.14243	−	0.176680i
$879$		−	676.088i		−	0.769155i
$880$		0			0
$881$	353.918			0.401723			0.200861	−	0.979620i	$-0.435626\pi$
$881$	353.918			0.401723			0.200861	+	0.979620i	$0.435626\pi$
$882$	44.8341	+	289.901i	0.0508323	+	0.328686i
$883$	−1093.51			−1.23840			−0.619200	−	0.785233i	$-0.712543\pi$
$883$	−1093.51			−1.23840			−0.619200	+	0.785233i	$0.712543\pi$
$884$	−29.5365	+	9.35971i	−0.0334123	+	0.0105879i
$885$		0			0
$886$	125.990	+	814.659i	0.142201	+	0.919479i
$887$	−520.234			−0.586510			−0.293255	−	0.956034i	$-0.594738\pi$
$887$	−520.234			−0.586510			−0.293255	+	0.956034i	$0.594738\pi$
$888$	−632.529	+	313.633i	−0.712307	+	0.353190i
$889$	−8.93819			−0.0100542
$890$		0			0
$891$		−	184.428i		−	0.206990i
$892$	−315.386	+	99.9413i	−0.353571	+	0.112042i
$893$		−	1017.96i		−	1.13993i
$894$	65.5804	+	424.048i	0.0733562	+	0.474326i
$895$		0			0
$896$	37.1236	+	20.1234i	0.0414326	+	0.0224592i
$897$		−	16.7669i		−	0.0186922i
$898$	−247.172	−	1598.23i	−0.275248	−	1.77977i
$899$		−	1004.85i		−	1.11775i
$900$		0			0
$901$	557.175			0.618397
$902$	−1891.76	+	292.567i	−2.09729	+	0.324354i
$903$	−31.7622			−0.0351741
$904$	−707.588	+	350.850i	−0.782730	+	0.388109i
$905$		0			0
$906$	260.508	−	40.2884i	0.287536	−	0.0444685i
$907$	567.834			0.626057			0.313029	−	0.949744i	$-0.398656\pi$
$907$	567.834			0.626057			0.313029	+	0.949744i	$0.398656\pi$
$908$	1378.58	−	436.851i	1.51825	−	0.481114i
$909$	488.025			0.536881
$910$		0			0
$911$		−	1180.19i		−	1.29549i	−0.761858	−	0.647744i	$-0.775713\pi$
$911$		−	1180.19i		−	1.29549i	0.761858	−	0.647744i	$-0.224287\pi$
$912$	−198.718	−	282.063i	−0.217893	−	0.309279i
$913$			120.680i			0.132180i
$914$	934.635	−	144.545i	1.02258	−	0.158145i
$915$		0			0
$916$	464.506	−	147.196i	0.507103	−	0.160694i
$917$		−	1.47072i		−	0.00160384i
$918$	−190.907	+	29.5244i	−0.207959	+	0.0321616i
$919$			54.5449i			0.0593524i	0.999560	+	0.0296762i	$0.00944761\pi$
$919$			54.5449i			0.0593524i	−0.999560	+	0.0296762i	$0.990552\pi$
$920$		0			0
$921$	104.324			0.113273
$922$	−132.594	−	857.360i	−0.143811	−	0.929892i
$923$	−16.3686			−0.0177341
$924$	14.1484	+	44.6483i	0.0153122	+	0.0483207i
$925$		0			0
$926$	162.197	+	1048.78i	0.175159	+	1.13259i
$927$	474.587			0.511960
$928$	−531.228	−	550.936i	−0.572444	−	0.593681i
$929$	−175.428			−0.188835			−0.0944175	−	0.995533i	$-0.530099\pi$
$929$	−175.428			−0.188835			−0.0944175	+	0.995533i	$0.530099\pi$
$930$		0			0
$931$			608.711i			0.653825i
$932$	165.075	+	520.929i	0.177119	+	0.558937i
$933$			184.627i			0.197885i
$934$	108.595	+	702.184i	0.116269	+	0.751803i
$935$		0			0
$936$	−8.96011	+	4.44277i	−0.00957277	+	0.00474655i
$937$		−	335.374i		−	0.357923i	−0.983856	−	0.178962i	$-0.942726\pi$
$937$		−	335.374i		−	0.357923i	0.983856	−	0.178962i	$-0.0572738\pi$
$938$	−7.34130	−	47.4694i	−0.00782654	−	0.0506070i
$939$			80.0629i			0.0852640i
$940$		0			0
$941$	709.182			0.753647			0.376823	−	0.926285i	$-0.377016\pi$
$941$	709.182			0.753647			0.376823	+	0.926285i	$0.377016\pi$
$942$	117.402	−	18.1567i	0.124631	−	0.0192746i
$943$	−1085.03			−1.15061
$944$	−224.211	−	318.248i	−0.237512	−	0.337127i
$945$		0			0
$946$	2251.39	−	348.186i	2.37991	−	0.368061i
$947$	−992.486			−1.04803			−0.524016	−	0.851708i	$-0.675567\pi$
$947$	−992.486			−1.04803			−0.524016	+	0.851708i	$0.675567\pi$
$948$	213.306	+	673.132i	0.225007	+	0.710055i
$949$	−19.4110			−0.0204542
$950$		0			0
$951$		−	14.4935i		−	0.0152402i
$952$	43.9518	−	21.7930i	0.0461679	−	0.0228919i
$953$		−	1438.16i		−	1.50908i	−0.656251	−	0.754542i	$-0.727859\pi$
$953$		−	1438.16i		−	1.50908i	0.656251	−	0.754542i	$-0.272141\pi$
$954$	177.733	−	27.4871i	0.186303	−	0.0288124i
$955$		0			0
$956$	−68.2260	−	215.301i	−0.0713661	−	0.225211i
$957$		−	848.877i		−	0.887018i
$958$	−1084.39	+	167.704i	−1.13193	+	0.175057i
$959$		−	59.9425i		−	0.0625052i
$960$		0			0
$961$	−804.245			−0.836883
$962$	6.49018	+	41.9660i	0.00674655	+	0.0436237i
$963$	−54.5482			−0.0566440
$964$	8.54744	−	2.70857i	0.00886664	−	0.00280971i
$965$		0			0
$966$	4.05745	+	26.2358i	0.00420026	+	0.0271592i
$967$	1376.32			1.42329			0.711646	−	0.702539i	$-0.247950\pi$
$967$	1376.32			1.42329			0.711646	+	0.702539i	$0.247950\pi$
$968$	−1062.31	−	2142.46i	−1.09743	−	2.21328i
$969$	−400.851			−0.413675
$970$		0			0
$971$		−	652.667i		−	0.672159i	−0.941834	−	0.336080i	$-0.890899\pi$
$971$		−	652.667i		−	0.672159i	0.941834	−	0.336080i	$-0.109101\pi$
$972$	−59.4408	+	18.8360i	−0.0611531	+	0.0193786i
$973$			73.7053i			0.0757506i
$974$	−41.1490	−	266.072i	−0.0422474	−	0.273175i
$975$		0			0
$976$	−978.920	+	689.666i	−1.00299	+	0.706625i
$977$			467.260i			0.478260i	0.970988	+	0.239130i	$0.0768622\pi$
$977$			467.260i			0.478260i	−0.970988	+	0.239130i	$0.923138\pi$
$978$	87.6428	+	566.705i	0.0896143	+	0.579453i
$979$		−	1250.22i		−	1.27703i
$980$		0			0
$981$	470.525			0.479638
$982$	−1495.84	+	231.336i	−1.52326	+	0.235577i
$983$	−1044.27			−1.06233			−0.531165	−	0.847268i	$-0.678246\pi$
$983$	−1044.27			−1.06233			−0.531165	+	0.847268i	$0.678246\pi$
$984$	287.503	+	579.830i	0.292178	+	0.589259i
$985$		0			0
$986$	−878.697	+	135.894i	−0.891174	+	0.137823i
$987$	46.7185			0.0473339
$988$	−19.7833	+	6.26905i	−0.0200236	+	0.00634519i
$989$	1291.30			1.30566
$990$		0			0
$991$		−	1705.99i		−	1.72148i	−0.509044	−	0.860740i	$-0.670001\pi$
$991$		−	1705.99i		−	1.72148i	0.509044	−	0.860740i	$-0.329999\pi$
$992$	−967.839	+	933.219i	−0.975644	+	0.940745i
$993$		−	192.382i		−	0.193738i
$994$	25.6125	−	3.96106i	0.0257671	−	0.00398497i
$995$		0			0
$996$	38.8950	−	12.3253i	0.0390512	−	0.0123748i
$997$			1262.24i			1.26604i	0.774136	+	0.633020i	$0.218185\pi$
$997$			1262.24i			1.26604i	−0.774136	+	0.633020i	$0.781815\pi$
$998$	−1397.30	+	216.097i	−1.40010	+	0.216530i
$999$			264.756i			0.265021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.f.c.199.7		16
3.2	odd	2		900.3.f.h.199.10		16
4.3	odd	2	inner	300.3.f.c.199.9		16
5.2	odd	4		300.3.c.g.151.7	yes	8
5.3	odd	4		300.3.c.e.151.2	yes	8
5.4	even	2	inner	300.3.f.c.199.10		16
12.11	even	2		900.3.f.h.199.8		16
15.2	even	4		900.3.c.n.451.2		8
15.8	even	4		900.3.c.t.451.7		8
15.14	odd	2		900.3.f.h.199.7		16
20.3	even	4		300.3.c.e.151.1	✓	8
20.7	even	4		300.3.c.g.151.8	yes	8
20.19	odd	2	inner	300.3.f.c.199.8		16
60.23	odd	4		900.3.c.t.451.8		8
60.47	odd	4		900.3.c.n.451.1		8
60.59	even	2		900.3.f.h.199.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.1	✓	8	20.3	even	4
300.3.c.e.151.2	yes	8	5.3	odd	4
300.3.c.g.151.7	yes	8	5.2	odd	4
300.3.c.g.151.8	yes	8	20.7	even	4
300.3.f.c.199.7		16	1.1	even	1	trivial
300.3.f.c.199.8		16	20.19	odd	2	inner
300.3.f.c.199.9		16	4.3	odd	2	inner
300.3.f.c.199.10		16	5.4	even	2	inner
900.3.c.n.451.1		8	60.47	odd	4
900.3.c.n.451.2		8	15.2	even	4
900.3.c.t.451.7		8	15.8	even	4
900.3.c.t.451.8		8	60.23	odd	4
900.3.f.h.199.7		16	15.14	odd	2
900.3.f.h.199.8		16	12.11	even	2
900.3.f.h.199.9		16	60.59	even	2
900.3.f.h.199.10		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.305673 - 1.97650i) q^{2} +1.73205 q^{3} +(-3.81313 + 1.20833i) q^{4} +(-0.529441 - 3.42340i) q^{6} +0.329898 q^{7} +(3.55383 + 7.16731i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-0.305673 - 1.97650i) q^{2} +1.73205 q^{3} +(-3.81313 + 1.20833i) q^{4} +(-0.529441 - 3.42340i) q^{6} +0.329898 q^{7} +(3.55383 + 7.16731i) q^{8} +3.00000 q^{9} -20.4920i q^{11} +(-6.60453 + 2.09288i) q^{12} +0.416712i q^{13} +(-0.100841 - 0.652044i) q^{14} +(13.0799 - 9.21501i) q^{16} -18.5884i q^{17} +(-0.917019 - 5.92951i) q^{18} -12.4503i q^{19} +0.571400 q^{21} +(-40.5024 + 6.26384i) q^{22} -23.2304 q^{23} +(6.15542 + 12.4141i) q^{24} +(0.823633 - 0.127378i) q^{26} +5.19615 q^{27} +(-1.25794 + 0.398624i) q^{28} +23.9166 q^{29} -42.0148i q^{31} +(-22.2117 - 23.0357i) q^{32} -35.4931i q^{33} +(-36.7400 + 5.68197i) q^{34} +(-11.4394 + 3.62498i) q^{36} +50.9523i q^{37} +(-24.6081 + 3.80573i) q^{38} +0.721767i q^{39} +46.7073 q^{41} +(-0.174661 - 1.12937i) q^{42} -55.5866 q^{43} +(24.7610 + 78.1385i) q^{44} +(7.10090 + 45.9149i) q^{46} +81.7616 q^{47} +(22.6550 - 15.9609i) q^{48} -48.8912 q^{49} -32.1960i q^{51} +(-0.503524 - 1.58898i) q^{52} +29.9744i q^{53} +(-1.58832 - 10.2702i) q^{54} +(1.17240 + 2.36448i) q^{56} -21.5646i q^{57} +(-7.31067 - 47.2713i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(-83.0424 + 12.8428i) q^{62} +0.989693 q^{63} +(-38.7406 + 50.9428i) q^{64} +(-70.1523 + 10.8493i) q^{66} +72.8008 q^{67} +(22.4608 + 70.8799i) q^{68} -40.2362 q^{69} +39.2803i q^{71} +(10.6615 + 21.5019i) q^{72} +46.5814i q^{73} +(100.707 - 15.5747i) q^{74} +(15.0441 + 47.4747i) q^{76} -6.76026i q^{77} +(1.42657 - 0.220625i) q^{78} -101.920i q^{79} +9.00000 q^{81} +(-14.2771 - 92.3170i) q^{82} -5.88913 q^{83} +(-2.17882 + 0.690438i) q^{84} +(16.9913 + 109.867i) q^{86} +41.4248 q^{87} +(146.872 - 72.8250i) q^{88} +61.0100 q^{89} +0.137472i q^{91} +(88.5804 - 28.0699i) q^{92} -72.7718i q^{93} +(-24.9923 - 161.602i) q^{94} +(-38.4717 - 39.8989i) q^{96} +95.5437i q^{97} +(14.9447 + 96.6335i) q^{98} -61.4759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9} - 44 q^{14} + 80 q^{16} + 48 q^{21} + 72 q^{24} - 132 q^{26} + 64 q^{29} - 248 q^{34} + 48 q^{36} - 32 q^{41} - 80 q^{44} - 152 q^{46} - 32 q^{49} - 36 q^{54} - 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{66} + 192 q^{69} + 216 q^{74} + 240 q^{76} + 144 q^{81} + 288 q^{84} + 428 q^{86} - 256 q^{89} - 24 q^{94} + 192 q^{96}+O(q^{100}) \) 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9 - 44 * q^14 + 80 * q^16 + 48 * q^21 + 72 * q^24 - 132 * q^26 + 64 * q^29 - 248 * q^34 + 48 * q^36 - 32 * q^41 - 80 * q^44 - 152 * q^46 - 32 * q^49 - 36 * q^54 - 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^66 + 192 * q^69 + 216 * q^74 + 240 * q^76 + 144 * q^81 + 288 * q^84 + 428 * q^86 - 256 * q^89 - 24 * q^94 + 192 * q^96

Introduction

L-functions

Modular forms

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Database

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