LMFDB - Embedded newform 912.2.bb.h.559.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(31,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 30x^{5} - 5x^{4} + 114x^{3} + 300x^{2} + 116x + 19 $ x^8 - 2x^7 - 30x^5 - 5x^4 + 114x^3 + 300x^2 + 116x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.4
Root			$-0.213988 + 0.172868i$ of defining polynomial
Character	$\chi$	$=$	912.559
Dual form			912.2.bb.h.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(2.00488 - 3.47255i) q^{5} +1.92982i q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(2.00488 - 3.47255i) q^{5} +1.92982i q^{7} +(-0.500000 - 0.866025i) q^{9} -1.38632i q^{11} +(0.470689 - 0.271753i) q^{13} +(-2.00488 - 3.47255i) q^{15} +(1.83360 - 3.17590i) q^{17} +(1.80429 + 3.96794i) q^{19} +(1.67127 + 0.964910i) q^{21} +(7.04394 - 4.06682i) q^{23} +(-5.53907 - 9.59394i) q^{25} -1.00000 q^{27} +(-2.40117 + 1.38632i) q^{29} -7.06838 q^{31} +(-1.20058 - 0.693158i) q^{33} +(6.70140 + 3.86905i) q^{35} +2.12759i q^{37} -0.543505i q^{39} +(-8.24453 - 4.75998i) q^{41} +(5.88649 + 3.39857i) q^{43} -4.00975 q^{45} +(-6.18590 + 3.57143i) q^{47} +3.27579 q^{49} +(-1.83360 - 3.17590i) q^{51} +(0.171273 - 0.0988847i) q^{53} +(-4.81405 - 2.77939i) q^{55} +(4.33848 + 0.421405i) q^{57} +(-2.80917 + 4.86563i) q^{59} +(0.871857 + 1.51010i) q^{61} +(1.67127 - 0.964910i) q^{63} -2.17932i q^{65} +(-7.34824 - 12.7275i) q^{67} -8.13364i q^{69} +(2.17615 - 3.76920i) q^{71} +(3.50975 - 6.07907i) q^{73} -11.0781 q^{75} +2.67534 q^{77} +(-4.54394 + 7.87034i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.7625i q^{83} +(-7.35230 - 12.7346i) q^{85} +2.77263i q^{87} +(15.3572 - 8.86647i) q^{89} +(0.524434 + 0.908346i) q^{91} +(-3.53419 + 6.12139i) q^{93} +(17.3962 + 1.68973i) q^{95} +(7.97069 + 4.60188i) q^{97} +(-1.20058 + 0.693158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9	$ 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9} + 2 q^{15} + 4 q^{17} + 6 q^{21} + 6 q^{23} - 12 q^{25} - 8 q^{27} - 12 q^{29} - 28 q^{31} - 6 q^{33} + 18 q^{35} - 12 q^{41} - 18 q^{43} + 4 q^{45} + 12 q^{47} - 24 q^{49} - 4 q^{51} - 6 q^{53} + 12 q^{55} + 6 q^{57} + 10 q^{59} - 4 q^{61} + 6 q^{63} + 6 q^{67} - 8 q^{71} - 8 q^{73} - 24 q^{75} + 28 q^{77} + 14 q^{79} - 4 q^{81} - 8 q^{85} + 54 q^{89} + 26 q^{91} - 14 q^{93} + 38 q^{95} + 60 q^{97} - 6 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9 + 2 * q^15 + 4 * q^17 + 6 * q^21 + 6 * q^23 - 12 * q^25 - 8 * q^27 - 12 * q^29 - 28 * q^31 - 6 * q^33 + 18 * q^35 - 12 * q^41 - 18 * q^43 + 4 * q^45 + 12 * q^47 - 24 * q^49 - 4 * q^51 - 6 * q^53 + 12 * q^55 + 6 * q^57 + 10 * q^59 - 4 * q^61 + 6 * q^63 + 6 * q^67 - 8 * q^71 - 8 * q^73 - 24 * q^75 + 28 * q^77 + 14 * q^79 - 4 * q^81 - 8 * q^85 + 54 * q^89 + 26 * q^91 - 14 * q^93 + 38 * q^95 + 60 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	2.00488	−	3.47255i	0.896608	−	1.55297i	0.0648070	−	0.997898i	$-0.479357\pi$
$5$	2.00488	−	3.47255i	0.896608	−	1.55297i	0.831801	−	0.555073i	$-0.187310\pi$
$6$		0			0
$7$			1.92982i			0.729403i	0.931124	+	0.364702i	$0.118829\pi$
$7$			1.92982i			0.729403i	−0.931124	+	0.364702i	$0.881171\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$		−	1.38632i		−	0.417990i	−0.977917	−	0.208995i	$-0.932981\pi$
$11$		−	1.38632i		−	0.417990i	0.977917	−	0.208995i	$-0.0670192\pi$
$12$		0			0
$13$	0.470689	−	0.271753i	0.130546	−	0.0753706i	−0.433305	−	0.901247i	$-0.642653\pi$
$13$	0.470689	−	0.271753i	0.130546	−	0.0753706i	0.563851	+	0.825877i	$0.309319\pi$
$14$		0			0
$15$	−2.00488	−	3.47255i	−0.517657	−	0.896608i
$16$		0			0
$17$	1.83360	−	3.17590i	0.444714	−	0.770268i	−0.553318	−	0.832970i	$-0.686639\pi$
$17$	1.83360	−	3.17590i	0.444714	−	0.770268i	0.998032	+	0.0627024i	$0.0199719\pi$
$18$		0			0
$19$	1.80429	+	3.96794i	0.413933	+	0.910307i
$19$	1.80429	+	3.96794i	0.413933	+	0.910307i
$20$		0			0
$21$	1.67127	+	0.964910i	0.364702	+	0.210561i
$22$		0			0
$23$	7.04394	−	4.06682i	1.46876	−	0.847991i	0.469376	−	0.882998i	$-0.344479\pi$
$23$	7.04394	−	4.06682i	1.46876	−	0.847991i	0.999387	+	0.0350071i	$0.0111454\pi$
$24$		0			0
$25$	−5.53907	−	9.59394i	−1.10781	−	1.91879i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.40117	+	1.38632i	−0.445886	+	0.257432i	−0.706091	−	0.708121i	$-0.749543\pi$
$29$	−2.40117	+	1.38632i	−0.445886	+	0.257432i	0.260205	+	0.965553i	$0.416210\pi$
$30$		0			0
$31$	−7.06838			−1.26952			−0.634759	−	0.772710i	$-0.718901\pi$
$31$	−7.06838			−1.26952			−0.634759	+	0.772710i	$0.718901\pi$
$32$		0			0
$33$	−1.20058	−	0.693158i	−0.208995	−	0.120663i
$34$		0			0
$35$	6.70140	+	3.86905i	1.13274	+	0.653989i
$36$		0			0
$37$			2.12759i			0.349774i	0.984589	+	0.174887i	$0.0559559\pi$
$37$			2.12759i			0.349774i	−0.984589	+	0.174887i	$0.944044\pi$
$38$		0			0
$39$		−	0.543505i		−	0.0870305i
$40$		0			0
$41$	−8.24453	−	4.75998i	−1.28758	−	0.743384i	−0.309357	−	0.950946i	$-0.600114\pi$
$41$	−8.24453	−	4.75998i	−1.28758	−	0.743384i	−0.978222	+	0.207562i	$0.933447\pi$
$42$		0			0
$43$	5.88649	+	3.39857i	0.897681	+	0.518276i	0.876447	−	0.481498i	$-0.159907\pi$
$43$	5.88649	+	3.39857i	0.897681	+	0.518276i	0.0212340	+	0.999775i	$0.493240\pi$
$44$		0			0
$45$	−4.00975			−0.597739
$46$		0			0
$47$	−6.18590	+	3.57143i	−0.902307	+	0.520947i	−0.877948	−	0.478756i	$-0.841088\pi$
$47$	−6.18590	+	3.57143i	−0.902307	+	0.520947i	−0.0243590	+	0.999703i	$0.507754\pi$
$48$		0			0
$49$	3.27579			0.467971
$50$		0			0
$51$	−1.83360	−	3.17590i	−0.256756	−	0.444714i
$52$		0			0
$53$	0.171273	−	0.0988847i	0.0235262	−	0.0135829i	−0.488191	−	0.872737i	$-0.662343\pi$
$53$	0.171273	−	0.0988847i	0.0235262	−	0.0135829i	0.511717	+	0.859154i	$0.329010\pi$
$54$		0			0
$55$	−4.81405	−	2.77939i	−0.649126	−	0.374773i
$56$		0			0
$57$	4.33848	+	0.421405i	0.574646	+	0.0558165i
$58$		0			0
$59$	−2.80917	+	4.86563i	−0.365723	+	0.633451i	−0.988892	−	0.148637i	$-0.952512\pi$
$59$	−2.80917	+	4.86563i	−0.365723	+	0.633451i	0.623169	+	0.782087i	$0.285845\pi$
$60$		0			0
$61$	0.871857	+	1.51010i	0.111630	+	0.193349i	0.916428	−	0.400201i	$-0.131060\pi$
$61$	0.871857	+	1.51010i	0.111630	+	0.193349i	−0.804798	+	0.593549i	$0.797726\pi$
$62$		0			0
$63$	1.67127	−	0.964910i	0.210561	−	0.121567i
$64$		0			0
$65$		−	2.17932i		−	0.270312i
$66$		0			0
$67$	−7.34824	−	12.7275i	−0.897730	−	1.55491i	−0.830389	−	0.557184i	$-0.811882\pi$
$67$	−7.34824	−	12.7275i	−0.897730	−	1.55491i	−0.0673405	−	0.997730i	$-0.521451\pi$
$68$		0			0
$69$		−	8.13364i		−	0.979176i
$70$		0			0
$71$	2.17615	−	3.76920i	0.258262	−	0.447322i	−0.707515	−	0.706699i	$-0.750184\pi$
$71$	2.17615	−	3.76920i	0.258262	−	0.447322i	0.965776	+	0.259376i	$0.0835170\pi$
$72$		0			0
$73$	3.50975	−	6.07907i	0.410786	−	0.711502i	−0.584190	−	0.811617i	$-0.698588\pi$
$73$	3.50975	−	6.07907i	0.410786	−	0.711502i	0.994976	+	0.100115i	$0.0319211\pi$
$74$		0			0
$75$	−11.0781			−1.27919
$76$		0			0
$77$	2.67534			0.304883
$78$		0			0
$79$	−4.54394	+	7.87034i	−0.511233	+	0.885482i	0.488682	+	0.872462i	$0.337478\pi$
$79$	−4.54394	+	7.87034i	−0.511233	+	0.885482i	−0.999915	+	0.0130202i	$0.995855\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			14.7625i			1.62040i	0.586154	+	0.810200i	$0.300641\pi$
$83$			14.7625i			1.62040i	−0.586154	+	0.810200i	$0.699359\pi$
$84$		0			0
$85$	−7.35230	−	12.7346i	−0.797469	−	1.38126i
$86$		0			0
$87$			2.77263i			0.297257i
$88$		0			0
$89$	15.3572	−	8.86647i	1.62786	−	0.939844i	0.643127	−	0.765760i	$-0.277637\pi$
$89$	15.3572	−	8.86647i	1.62786	−	0.939844i	0.984731	−	0.174084i	$-0.0556966\pi$
$90$		0			0
$91$	0.524434	+	0.908346i	0.0549756	+	0.0952205i
$92$		0			0
$93$	−3.53419	+	6.12139i	−0.366478	+	0.634759i
$94$		0			0
$95$	17.3962	+	1.68973i	1.78482	+	0.173363i
$96$		0			0
$97$	7.97069	+	4.60188i	0.809301	+	0.467250i	0.846713	−	0.532050i	$-0.178578\pi$
$97$	7.97069	+	4.60188i	0.809301	+	0.467250i	−0.0374122	+	0.999300i	$0.511911\pi$
$98$		0			0
$99$	−1.20058	+	0.693158i	−0.120663	+	0.0696650i
$100$		0			0
$101$	4.90198	+	8.49048i	0.487765	+	0.844834i	0.999901	−	0.0140704i	$-0.00447888\pi$
$101$	4.90198	+	8.49048i	0.487765	+	0.844834i	−0.512136	+	0.858904i	$0.671146\pi$
$102$		0			0
$103$	−5.34255			−0.526417			−0.263208	−	0.964739i	$-0.584781\pi$
$103$	−5.34255			−0.526417			−0.263208	+	0.964739i	$0.584781\pi$
$104$		0			0
$105$	6.70140	−	3.86905i	0.653989	−	0.377581i
$106$		0			0
$107$	14.1563			1.36854			0.684269	−	0.729230i	$-0.260122\pi$
$107$	14.1563			1.36854			0.684269	+	0.729230i	$0.260122\pi$
$108$		0			0
$109$	1.37186	+	0.792042i	0.131400	+	0.0758639i	0.564259	−	0.825598i	$-0.309162\pi$
$109$	1.37186	+	0.792042i	0.131400	+	0.0758639i	−0.432859	+	0.901462i	$0.642495\pi$
$110$		0			0
$111$	1.84255	+	1.06379i	0.174887	+	0.100971i
$112$		0			0
$113$			10.5901i			0.996230i	0.867111	+	0.498115i	$0.165974\pi$
$113$			10.5901i			0.996230i	−0.867111	+	0.498115i	$0.834026\pi$
$114$		0			0
$115$		−	32.6139i		−	3.04126i
$116$		0			0
$117$	−0.470689	−	0.271753i	−0.0435152	−	0.0251235i
$118$		0			0
$119$	6.12891	+	3.53853i	0.561836	+	0.324376i
$120$		0			0
$121$	9.07813			0.825285
$122$		0			0
$123$	−8.24453	+	4.75998i	−0.743384	+	0.429193i
$124$		0			0
$125$	−24.3718			−2.17988
$126$		0			0
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$		0			0
$129$	5.88649	−	3.39857i	0.518276	−	0.299227i
$130$		0			0
$131$	5.50081	+	3.17590i	0.480608	+	0.277479i	0.720670	−	0.693278i	$-0.243834\pi$
$131$	5.50081	+	3.17590i	0.480608	+	0.277479i	−0.240062	+	0.970758i	$0.577168\pi$
$132$		0			0
$133$	−7.65741	+	3.48196i	−0.663981	+	0.301924i
$134$		0			0
$135$	−2.00488	+	3.47255i	−0.172552	+	0.298869i
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	15.4853	−	8.94045i	1.31345	−	0.758319i	0.330782	−	0.943707i	$-0.392687\pi$
$139$	15.4853	−	8.94045i	1.31345	−	0.758319i	0.982665	+	0.185388i	$0.0593541\pi$
$140$		0			0
$141$			7.14287i			0.601538i
$142$		0			0
$143$	−0.376735	−	0.652524i	−0.0315041	−	0.0545668i
$144$		0			0
$145$			11.1176i			0.923264i
$146$		0			0
$147$	1.63790	−	2.83692i	0.135091	−	0.233985i
$148$		0			0
$149$	−4.77986	+	8.27896i	−0.391581	+	0.678239i	−0.992658	−	0.120952i	$-0.961405\pi$
$149$	−4.77986	+	8.27896i	−0.391581	+	0.678239i	0.601077	+	0.799191i	$0.294739\pi$
$150$		0			0
$151$	−16.0195			−1.30365			−0.651825	−	0.758370i	$-0.725996\pi$
$151$	−16.0195			−1.30365			−0.651825	+	0.758370i	$0.725996\pi$
$152$		0			0
$153$	−3.66721			−0.296476
$154$		0			0
$155$	−14.1712	+	24.5453i	−1.13826	+	1.97152i
$156$		0			0
$157$	−7.16721	+	12.4140i	−0.572005	+	0.990742i	0.424354	+	0.905496i	$0.360501\pi$
$157$	−7.16721	+	12.4140i	−0.572005	+	0.990742i	−0.996360	+	0.0852463i	$0.972832\pi$
$158$		0			0
$159$		−	0.197769i		−	0.0156841i
$160$		0			0
$161$	7.84824	+	13.5935i	0.618528	+	1.07132i
$162$		0			0
$163$		−	4.30691i		−	0.337343i	−0.985672	−	0.168672i	$-0.946052\pi$
$163$		−	4.30691i		−	0.337343i	0.985672	−	0.168672i	$-0.0539478\pi$
$164$		0			0
$165$	−4.81405	+	2.77939i	−0.374773	+	0.216375i
$166$		0			0
$167$	1.95606	+	3.38799i	0.151364	+	0.262171i	0.931729	−	0.363154i	$-0.118300\pi$
$167$	1.95606	+	3.38799i	0.151364	+	0.262171i	−0.780365	+	0.625324i	$0.784967\pi$
$168$		0			0
$169$	−6.35230	+	11.0025i	−0.488639	+	0.846347i
$170$		0			0
$171$	2.53419	−	3.54653i	0.193794	−	0.271210i
$172$		0			0
$173$	4.80234	+	2.77263i	0.365115	+	0.210799i	0.671322	−	0.741166i	$-0.265727\pi$
$173$	4.80234	+	2.77263i	0.365115	+	0.210799i	−0.306207	+	0.951965i	$0.599060\pi$
$174$		0			0
$175$	18.5146	−	10.6894i	1.39957	−	0.808043i
$176$		0			0
$177$	2.80917	+	4.86563i	0.211150	+	0.365723i
$178$		0			0
$179$	17.1058			1.27855			0.639273	−	0.768980i	$-0.279236\pi$
$179$	17.1058			1.27855			0.639273	+	0.768980i	$0.279236\pi$
$180$		0			0
$181$	−10.6574	+	6.15306i	−0.792159	+	0.457353i	−0.840722	−	0.541467i	$-0.817869\pi$
$181$	−10.6574	+	6.15306i	−0.792159	+	0.457353i	0.0485632	+	0.998820i	$0.484536\pi$
$182$		0			0
$183$	1.74371			0.128899
$184$		0			0
$185$	7.38816	+	4.26556i	0.543188	+	0.313610i
$186$		0			0
$187$	−4.40279	−	2.54195i	−0.321964	−	0.185886i
$188$		0			0
$189$		−	1.92982i		−	0.140374i
$190$		0			0
$191$		−	7.34257i		−	0.531289i	−0.964071	−	0.265645i	$-0.914415\pi$
$191$		−	7.34257i		−	0.531289i	0.964071	−	0.265645i	$-0.0855848\pi$
$192$		0			0
$193$	19.6465	+	11.3429i	1.41418	+	0.816479i	0.995779	−	0.0917821i	$-0.0292563\pi$
$193$	19.6465	+	11.3429i	1.41418	+	0.816479i	0.418404	+	0.908261i	$0.362590\pi$
$194$		0			0
$195$	−1.88735	−	1.08966i	−0.135156	−	0.0780322i
$196$		0			0
$197$	−10.0098			−0.713165			−0.356583	−	0.934264i	$-0.616058\pi$
$197$	−10.0098			−0.713165			−0.356583	+	0.934264i	$0.616058\pi$
$198$		0			0
$199$	−15.7709	+	9.10532i	−1.11797	+	0.645459i	−0.940881	−	0.338737i	$-0.890000\pi$
$199$	−15.7709	+	9.10532i	−1.11797	+	0.645459i	−0.177086	+	0.984195i	$0.556667\pi$
$200$		0			0
$201$	−14.6965			−1.03661
$202$		0			0
$203$	−2.67534	−	4.63382i	−0.187772	−	0.325231i
$204$		0			0
$205$	−33.0585	+	19.0863i	−2.30891	+	1.33305i
$206$		0			0
$207$	−7.04394	−	4.06682i	−0.489588	−	0.282664i
$208$		0			0
$209$	5.50081	−	2.50132i	0.380499	−	0.173020i
$210$		0			0
$211$	−9.28766	+	16.0867i	−0.639389	+	1.10745i	0.346178	+	0.938169i	$0.387479\pi$
$211$	−9.28766	+	16.0867i	−0.639389	+	1.10745i	−0.985567	+	0.169285i	$0.945854\pi$
$212$		0			0
$213$	−2.17615	−	3.76920i	−0.149107	−	0.258262i
$214$		0			0
$215$	23.6034	−	13.6274i	1.60974	−	0.929382i
$216$		0			0
$217$		−	13.6407i		−	0.925991i
$218$		0			0
$219$	−3.50975	−	6.07907i	−0.237167	−	0.410786i
$220$		0			0
$221$		−	1.99315i		−	0.134074i
$222$		0			0
$223$	−3.46581	+	6.00296i	−0.232088	+	0.401988i	−0.958422	−	0.285353i	$-0.907889\pi$
$223$	−3.46581	+	6.00296i	−0.232088	+	0.401988i	0.726334	+	0.687341i	$0.241222\pi$
$224$		0			0
$225$	−5.53907	+	9.59394i	−0.369271	+	0.639596i
$226$		0			0
$227$	−21.9706			−1.45824			−0.729121	−	0.684384i	$-0.760071\pi$
$227$	−21.9706			−1.45824			−0.729121	+	0.684384i	$0.760071\pi$
$228$		0			0
$229$	23.0976			1.52633			0.763167	−	0.646201i	$-0.223643\pi$
$229$	23.0976			1.52633			0.763167	+	0.646201i	$0.223643\pi$
$230$		0			0
$231$	1.33767	−	2.31691i	0.0880122	−	0.152442i
$232$		0			0
$233$	−8.84336	+	15.3171i	−0.579348	+	1.00346i	0.416207	+	0.909270i	$0.363359\pi$
$233$	−8.84336	+	15.3171i	−0.579348	+	1.00346i	−0.995554	+	0.0941895i	$0.969974\pi$
$234$		0			0
$235$			28.6411i			1.86834i
$236$		0			0
$237$	4.54394	+	7.87034i	0.295161	+	0.511233i
$238$		0			0
$239$		−	6.62890i		−	0.428788i	−0.976747	−	0.214394i	$-0.931222\pi$
$239$		−	6.62890i		−	0.428788i	0.976747	−	0.214394i	$-0.0687776\pi$
$240$		0			0
$241$	12.6449	−	7.30053i	0.814529	−	0.470268i	−0.0339975	−	0.999422i	$-0.510824\pi$
$241$	12.6449	−	7.30053i	0.814529	−	0.470268i	0.848526	+	0.529154i	$0.177490\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	6.56756	−	11.3754i	0.419586	−	0.726745i
$246$		0			0
$247$	1.92756	+	1.37734i	0.122648	+	0.0876383i
$248$		0			0
$249$	12.7847	+	7.38127i	0.810200	+	0.467769i
$250$		0			0
$251$	9.68509	−	5.59169i	0.611318	−	0.352944i	−0.162163	−	0.986764i	$-0.551847\pi$
$251$	9.68509	−	5.59169i	0.611318	−	0.352944i	0.773481	+	0.633820i	$0.218514\pi$
$252$		0			0
$253$	−5.63790	−	9.76512i	−0.354452	−	0.613928i
$254$		0			0
$255$	−14.7046			−0.920838
$256$		0			0
$257$	2.57244	−	1.48520i	0.160464	−	0.0926442i	−0.417617	−	0.908623i	$-0.637135\pi$
$257$	2.57244	−	1.48520i	0.160464	−	0.0926442i	0.578082	+	0.815979i	$0.303801\pi$
$258$		0			0
$259$	−4.10587			−0.255126
$260$		0			0
$261$	2.40117	+	1.38632i	0.148629	+	0.0858108i
$262$		0			0
$263$	3.44219	+	1.98735i	0.212255	+	0.122545i	0.602359	−	0.798226i	$-0.294228\pi$
$263$	3.44219	+	1.98735i	0.212255	+	0.122545i	−0.390104	+	0.920771i	$0.627561\pi$
$264$		0			0
$265$		−	0.793007i		−	0.0487140i
$266$		0			0
$267$		−	17.7329i		−	1.08524i
$268$		0			0
$269$	11.5724	+	6.68135i	0.705584	+	0.407369i	0.809424	−	0.587225i	$-0.199780\pi$
$269$	11.5724	+	6.68135i	0.705584	+	0.407369i	−0.103840	+	0.994594i	$0.533113\pi$
$270$		0			0
$271$	7.83160	+	4.52158i	0.475736	+	0.274666i	0.718638	−	0.695385i	$-0.244766\pi$
$271$	7.83160	+	4.52158i	0.475736	+	0.274666i	−0.242902	+	0.970051i	$0.578099\pi$
$272$		0			0
$273$	1.04887			0.0634803
$274$		0			0
$275$	−13.3002	+	7.67889i	−0.802034	+	0.463054i
$276$		0			0
$277$	26.9195			1.61744			0.808718	−	0.588197i	$-0.200162\pi$
$277$	26.9195			1.61744			0.808718	+	0.588197i	$0.200162\pi$
$278$		0			0
$279$	3.53419	+	6.12139i	0.211586	+	0.366478i
$280$		0			0
$281$	18.3864	−	10.6154i	1.09684	−	0.633263i	0.161453	−	0.986880i	$-0.448382\pi$
$281$	18.3864	−	10.6154i	1.09684	−	0.633263i	0.935390	+	0.353618i	$0.115049\pi$
$282$		0			0
$283$	0.685093	+	0.395539i	0.0407246	+	0.0235123i	0.520224	−	0.854030i	$-0.325848\pi$
$283$	0.685093	+	0.395539i	0.0407246	+	0.0235123i	−0.479499	+	0.877542i	$0.659182\pi$
$284$		0			0
$285$	10.1615	−	14.2207i	0.601914	−	0.842363i
$286$		0			0
$287$	9.18590	−	15.9105i	0.542227	−	0.939164i
$288$		0			0
$289$	1.77579	+	3.07577i	0.104458	+	0.180927i
$290$		0			0
$291$	7.97069	−	4.60188i	0.467250	−	0.269767i
$292$		0			0
$293$			8.64761i			0.505199i	0.967571	+	0.252599i	$0.0812855\pi$
$293$			8.64761i			0.505199i	−0.967571	+	0.252599i	$0.918715\pi$
$294$		0			0
$295$	11.2641	+	19.5100i	0.655820	+	1.13591i
$296$		0			0
$297$			1.38632i			0.0804422i
$298$		0			0
$299$	2.21034	−	3.82842i	0.127827	−	0.221403i
$300$		0			0
$301$	−6.55862	+	11.3599i	−0.378033	+	0.654772i
$302$		0			0
$303$	9.80396			0.563223
$304$		0			0
$305$	6.99187			0.400353
$306$		0			0
$307$	0.195707	−	0.338974i	0.0111696	−	0.0193463i	−0.860387	−	0.509642i	$-0.829778\pi$
$307$	0.195707	−	0.338974i	0.0111696	−	0.0193463i	0.871556	+	0.490296i	$0.163111\pi$
$308$		0			0
$309$	−2.67127	+	4.62678i	−0.151963	+	0.263208i
$310$		0			0
$311$			21.6941i			1.23016i	0.788464	+	0.615080i	$0.210876\pi$
$311$			21.6941i			1.23016i	−0.788464	+	0.615080i	$0.789124\pi$
$312$		0			0
$313$	−13.6672	−	23.6722i	−0.772514	−	1.33803i	−0.936181	−	0.351517i	$-0.885666\pi$
$313$	−13.6672	−	23.6722i	−0.772514	−	1.33803i	0.163668	−	0.986516i	$-0.447667\pi$
$314$		0			0
$315$		−	7.73811i		−	0.435993i
$316$		0			0
$317$	−28.6896	+	16.5639i	−1.61137	+	0.930324i	−0.622314	+	0.782768i	$0.713807\pi$
$317$	−28.6896	+	16.5639i	−1.61137	+	0.930324i	−0.989054	+	0.147556i	$0.952859\pi$
$318$		0			0
$319$	1.92187	+	3.32878i	0.107604	+	0.186376i
$320$		0			0
$321$	7.07813	−	12.2597i	0.395063	−	0.684269i
$322$		0			0
$323$	15.9101	+	1.54538i	0.885262	+	0.0859872i
$324$		0			0
$325$	−5.21436	−	3.01051i	−0.289240	−	0.166993i
$326$		0			0
$327$	1.37186	−	0.792042i	0.0758639	−	0.0438000i
$328$		0			0
$329$	−6.89223	−	11.9377i	−0.379981	−	0.658146i
$330$		0			0
$331$	−9.87071			−0.542543			−0.271272	−	0.962503i	$-0.587444\pi$
$331$	−9.87071			−0.542543			−0.271272	+	0.962503i	$0.587444\pi$
$332$		0			0
$333$	1.84255	−	1.06379i	0.100971	−	0.0582956i
$334$		0			0
$335$	−58.9292			−3.21965
$336$		0			0
$337$	−16.3609	−	9.44598i	−0.891236	−	0.514555i	−0.0168891	−	0.999857i	$-0.505376\pi$
$337$	−16.3609	−	9.44598i	−0.891236	−	0.514555i	−0.874346	+	0.485302i	$0.838710\pi$
$338$		0			0
$339$	9.17127	+	5.29504i	0.498115	+	0.287587i
$340$		0			0
$341$			9.79900i			0.530645i
$342$		0			0
$343$			19.8304i			1.07074i
$344$		0			0
$345$	−28.2445	−	16.3070i	−1.52063	−	0.877937i
$346$		0			0
$347$	−6.08334	−	3.51222i	−0.326571	−	0.188546i	0.327747	−	0.944766i	$-0.393711\pi$
$347$	−6.08334	−	3.51222i	−0.326571	−	0.188546i	−0.654318	+	0.756220i	$0.727044\pi$
$348$		0			0
$349$	28.1976			1.50938			0.754691	−	0.656081i	$-0.227787\pi$
$349$	28.1976			1.50938			0.754691	+	0.656081i	$0.227787\pi$
$350$		0			0
$351$	−0.470689	+	0.271753i	−0.0251235	+	0.0145051i
$352$		0			0
$353$	5.14488			0.273835			0.136917	−	0.990582i	$-0.456281\pi$
$353$	5.14488			0.273835			0.136917	+	0.990582i	$0.456281\pi$
$354$		0			0
$355$	−8.72583	−	15.1136i	−0.463119	−	0.802146i
$356$		0			0
$357$	6.12891	−	3.53853i	0.324376	−	0.187279i
$358$		0			0
$359$	−27.8332	−	16.0695i	−1.46898	−	0.848117i	−0.469586	−	0.882887i	$-0.655597\pi$
$359$	−27.8332	−	16.0695i	−1.46898	−	0.848117i	−0.999395	+	0.0347700i	$0.988930\pi$
$360$		0			0
$361$	−12.4891	+	14.3186i	−0.657319	+	0.753613i
$362$		0			0
$363$	4.53907	−	7.86189i	0.238239	−	0.412642i
$364$		0			0
$365$	−14.0733	−	24.3756i	−0.736628	−	1.27588i
$366$		0			0
$367$	10.3974	−	6.00296i	0.542742	−	0.313352i	−0.203448	−	0.979086i	$-0.565215\pi$
$367$	10.3974	−	6.00296i	0.542742	−	0.313352i	0.746189	+	0.665734i	$0.231881\pi$
$368$		0			0
$369$			9.51996i			0.495589i
$370$		0			0
$371$	0.190830	+	0.330527i	0.00990739	+	0.0171601i
$372$		0			0
$373$			32.1371i			1.66400i	0.554778	+	0.831998i	$0.312803\pi$
$373$			32.1371i			1.66400i	−0.554778	+	0.831998i	$0.687197\pi$
$374$		0			0
$375$	−12.1859	+	21.1066i	−0.629277	+	1.08994i
$376$		0			0
$377$	−0.753469	+	1.30505i	−0.0388056	+	0.0672134i
$378$		0			0
$379$	−14.1488			−0.726775			−0.363387	−	0.931638i	$-0.618380\pi$
$379$	−14.1488			−0.726775			−0.363387	+	0.931638i	$0.618380\pi$
$380$		0			0
$381$	−2.00000			−0.102463
$382$		0			0
$383$	17.3784	−	30.1002i	0.887993	−	1.53805i	0.0457478	−	0.998953i	$-0.485433\pi$
$383$	17.3784	−	30.1002i	0.887993	−	1.53805i	0.842245	−	0.539095i	$-0.181234\pi$
$384$		0			0
$385$	5.36373	−	9.29025i	0.273361	−	0.473475i
$386$		0			0
$387$		−	6.79713i		−	0.345518i
$388$		0			0
$389$	−0.122120	−	0.211519i	−0.00619174	−	0.0107244i	0.862913	−	0.505353i	$-0.168638\pi$
$389$	−0.122120	−	0.211519i	−0.00619174	−	0.0107244i	−0.869105	+	0.494628i	$0.835304\pi$
$390$		0			0
$391$		−	29.8278i		−	1.50845i
$392$		0			0
$393$	5.50081	−	3.17590i	0.277479	−	0.160203i
$394$		0			0
$395$	18.2201	+	31.5581i	0.916752	+	1.58786i
$396$		0			0
$397$	6.82299	−	11.8178i	0.342436	−	0.593117i	−0.642448	−	0.766329i	$-0.722081\pi$
$397$	6.82299	−	11.8178i	0.342436	−	0.593117i	0.984885	+	0.173212i	$0.0554147\pi$
$398$		0			0
$399$	−0.813236	+	8.37249i	−0.0407127	+	0.419149i
$400$		0			0
$401$	−8.13025	−	4.69400i	−0.406005	−	0.234407i	0.283067	−	0.959100i	$-0.408648\pi$
$401$	−8.13025	−	4.69400i	−0.406005	−	0.234407i	−0.689072	+	0.724693i	$0.741982\pi$
$402$		0			0
$403$	−3.32701	+	1.92085i	−0.165730	+	0.0956843i
$404$		0			0
$405$	2.00488	+	3.47255i	0.0996231	+	0.172552i
$406$		0			0
$407$	2.94951			0.146202
$408$		0			0
$409$	10.3719	−	5.98819i	0.512855	−	0.296097i	−0.221151	−	0.975240i	$-0.570981\pi$
$409$	10.3719	−	5.98819i	0.512855	−	0.296097i	0.734007	+	0.679142i	$0.237648\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$		0			0
$413$	−9.38978	−	5.42119i	−0.462041	−	0.266760i
$414$		0			0
$415$	51.2637	+	29.5971i	2.51643	+	1.45286i
$416$		0			0
$417$		−	17.8809i		−	0.875632i
$418$		0			0
$419$		−	12.1896i		−	0.595501i	−0.954644	−	0.297751i	$-0.903764\pi$
$419$		−	12.1896i		−	0.595501i	0.954644	−	0.297751i	$-0.0962364\pi$
$420$		0			0
$421$	−19.2344	−	11.1050i	−0.937429	−	0.541225i	−0.0482757	−	0.998834i	$-0.515373\pi$
$421$	−19.2344	−	11.1050i	−0.937429	−	0.541225i	−0.889154	+	0.457609i	$0.848706\pi$
$422$		0			0
$423$	6.18590	+	3.57143i	0.300769	+	0.173649i
$424$		0			0
$425$	−40.6258			−1.97064
$426$		0			0
$427$	−2.91422	+	1.68253i	−0.141029	+	0.0814232i
$428$		0			0
$429$	−0.753469			−0.0363778
$430$		0			0
$431$	−11.5008	−	19.9200i	−0.553975	−	0.959512i	−0.997983	−	0.0634893i	$-0.979777\pi$
$431$	−11.5008	−	19.9200i	−0.553975	−	0.959512i	0.444008	−	0.896023i	$-0.353556\pi$
$432$		0			0
$433$	−32.9304	+	19.0124i	−1.58253	+	0.913676i	−0.588045	+	0.808828i	$0.700102\pi$
$433$	−32.9304	+	19.0124i	−1.58253	+	0.913676i	−0.994488	+	0.104848i	$0.966564\pi$
$434$		0			0
$435$	9.62809	+	5.55878i	0.461632	+	0.266523i
$436$		0			0
$437$	28.8462	+	20.6122i	1.37990	+	0.986014i
$438$		0			0
$439$	10.0920	−	17.4798i	0.481663	−	0.834264i	−0.518116	−	0.855310i	$-0.673366\pi$
$439$	10.0920	−	17.4798i	0.481663	−	0.834264i	0.999778	+	0.0210464i	$0.00669978\pi$
$440$		0			0
$441$	−1.63790	−	2.83692i	−0.0779951	−	0.135091i
$442$		0			0
$443$	3.56957	−	2.06089i	0.169595	−	0.0979159i	−0.412800	−	0.910822i	$-0.635449\pi$
$443$	3.56957	−	2.06089i	0.169595	−	0.0979159i	0.582395	+	0.812906i	$0.302116\pi$
$444$		0			0
$445$		−	71.1047i		−	3.37069i
$446$		0			0
$447$	4.77986	+	8.27896i	0.226080	+	0.391581i
$448$		0			0
$449$		−	32.5346i		−	1.53540i	−0.640808	−	0.767701i	$-0.721401\pi$
$449$		−	32.5346i		−	1.53540i	0.640808	−	0.767701i	$-0.278599\pi$
$450$		0			0
$451$	−6.59883	+	11.4295i	−0.310727	+	0.538195i
$452$		0			0
$453$	−8.00975	+	13.8733i	−0.376331	+	0.651825i
$454$		0			0
$455$	4.20570			0.197166
$456$		0			0
$457$	−39.9000			−1.86644			−0.933221	−	0.359303i	$-0.883015\pi$
$457$	−39.9000			−1.86644			−0.933221	+	0.359303i	$0.883015\pi$
$458$		0			0
$459$	−1.83360	+	3.17590i	−0.0855853	+	0.148238i
$460$		0			0
$461$	2.44707	−	4.23844i	0.113971	−	0.197404i	−0.803397	−	0.595444i	$-0.796976\pi$
$461$	2.44707	−	4.23844i	0.113971	−	0.197404i	0.917368	+	0.398040i	$0.130309\pi$
$462$		0			0
$463$		−	4.34070i		−	0.201730i	−0.994900	−	0.100865i	$-0.967839\pi$
$463$		−	4.34070i		−	0.201730i	0.994900	−	0.100865i	$-0.0321609\pi$
$464$		0			0
$465$	14.1712	+	24.5453i	0.657175	+	1.13826i
$466$		0			0
$467$			14.6039i			0.675786i	0.941184	+	0.337893i	$0.109714\pi$
$467$			14.6039i			0.675786i	−0.941184	+	0.337893i	$0.890286\pi$
$468$		0			0
$469$	24.5618	−	14.1808i	1.13416	−	0.654807i
$470$		0			0
$471$	7.16721	+	12.4140i	0.330247	+	0.572005i
$472$		0			0
$473$	4.71148	−	8.16053i	0.216634	−	0.375222i
$474$		0			0
$475$	28.0741	−	39.2889i	1.28813	−	1.80270i
$476$		0			0
$477$	−0.171273	−	0.0988847i	−0.00784207	−	0.00452762i
$478$		0			0
$479$	−1.01760	+	0.587512i	−0.0464953	+	0.0268441i	−0.523067	−	0.852291i	$-0.675212\pi$
$479$	−1.01760	+	0.587512i	−0.0464953	+	0.0268441i	0.476572	+	0.879135i	$0.341879\pi$
$480$		0			0
$481$	0.578178	+	1.00143i	0.0263626	+	0.0456614i
$482$		0			0
$483$	15.6965			0.714214
$484$		0			0
$485$	31.9605	−	18.4524i	1.45125	−	0.837881i
$486$		0			0
$487$	−21.0999			−0.956129			−0.478065	−	0.878325i	$-0.658661\pi$
$487$	−21.0999			−0.956129			−0.478065	+	0.878325i	$0.658661\pi$
$488$		0			0
$489$	−3.72989	−	2.15346i	−0.168672	−	0.0973826i
$490$		0			0
$491$	−32.9881	−	19.0457i	−1.48873	−	0.859521i	−0.488817	−	0.872386i	$-0.662571\pi$
$491$	−32.9881	−	19.0457i	−1.48873	−	0.859521i	−0.999917	+	0.0128653i	$0.995905\pi$
$492$		0			0
$493$			10.1678i			0.457935i
$494$		0			0
$495$			5.55878i			0.249849i
$496$		0			0
$497$	7.27388	+	4.19958i	0.326278	+	0.188377i
$498$		0			0
$499$	−32.2482	−	18.6185i	−1.44363	−	0.833479i	−0.445539	−	0.895263i	$-0.646988\pi$
$499$	−32.2482	−	18.6185i	−1.44363	−	0.833479i	−0.998090	+	0.0617836i	$0.980321\pi$
$500$		0			0
$501$	3.91212			0.174780
$502$		0			0
$503$	6.54183	−	3.77693i	0.291686	−	0.168405i	−0.347016	−	0.937859i	$-0.612805\pi$
$503$	6.54183	−	3.77693i	0.291686	−	0.168405i	0.638702	+	0.769454i	$0.279472\pi$
$504$		0			0
$505$	39.3115			1.74934
$506$		0			0
$507$	6.35230	+	11.0025i	0.282116	+	0.488639i
$508$		0			0
$509$	28.9446	−	16.7112i	1.28295	−	0.740710i	0.305562	−	0.952172i	$-0.401156\pi$
$509$	28.9446	−	16.7112i	1.28295	−	0.740710i	0.977386	+	0.211462i	$0.0678224\pi$
$510$		0			0
$511$	11.7315	+	6.77320i	0.518972	+	0.299629i
$512$		0			0
$513$	−1.80429	−	3.96794i	−0.0796615	−	0.175189i
$514$		0			0
$515$	−10.7112	+	18.5523i	−0.471990	+	0.817510i
$516$		0			0
$517$	4.95113	+	8.57561i	0.217751	+	0.377155i
$518$		0			0
$519$	4.80234	−	2.77263i	0.210799	−	0.121705i
$520$		0			0
$521$			2.50904i			0.109923i	0.998488	+	0.0549616i	$0.0175036\pi$
$521$			2.50904i			0.109923i	−0.998488	+	0.0549616i	$0.982496\pi$
$522$		0			0
$523$	16.9666	+	29.3870i	0.741897	+	1.28500i	0.951631	+	0.307244i	$0.0994068\pi$
$523$	16.9666	+	29.3870i	0.741897	+	1.28500i	−0.209734	+	0.977758i	$0.567260\pi$
$524$		0			0
$525$		−	21.3788i		−	0.933047i
$526$		0			0
$527$	−12.9606	+	22.4484i	−0.564573	+	0.977869i
$528$		0			0
$529$	21.5781	−	37.3743i	0.938178	−	1.62497i
$530$		0			0
$531$	5.61834			0.243815
$532$		0			0
$533$	−5.17415			−0.224117
$534$		0			0
$535$	28.3816	−	49.1583i	1.22704	−	2.12530i
$536$		0			0
$537$	8.55289	−	14.8140i	0.369084	−	0.639273i
$538$		0			0
$539$		−	4.54128i		−	0.195607i
$540$		0			0
$541$	−4.83442	−	8.37345i	−0.207848	−	0.360003i	0.743189	−	0.669082i	$-0.233313\pi$
$541$	−4.83442	−	8.37345i	−0.207848	−	0.360003i	−0.951036	+	0.309079i	$0.899979\pi$
$542$		0			0
$543$			12.3061i			0.528106i
$544$		0			0
$545$	5.50081	−	3.17590i	0.235629	−	0.136040i
$546$		0			0
$547$	14.1525	+	24.5129i	0.605118	+	1.04810i	0.992033	+	0.125980i	$0.0402076\pi$
$547$	14.1525	+	24.5129i	0.605118	+	1.04810i	−0.386914	+	0.922116i	$0.626459\pi$
$548$		0			0
$549$	0.871857	−	1.51010i	0.0372100	−	0.0644496i
$550$		0			0
$551$	−9.83322	−	7.02637i	−0.418909	−	0.299333i
$552$		0			0
$553$	−15.1883	−	8.76899i	−0.645874	−	0.372895i
$554$		0			0
$555$	7.38816	−	4.26556i	0.313610	−	0.181063i
$556$		0			0
$557$	−11.0879	−	19.2048i	−0.469809	−	0.813733i	0.529595	−	0.848250i	$-0.322344\pi$
$557$	−11.0879	−	19.2048i	−0.469809	−	0.813733i	−0.999404	+	0.0345178i	$0.989010\pi$
$558$		0			0
$559$	3.69428			0.156251
$560$		0			0
$561$	−4.40279	+	2.54195i	−0.185886	+	0.107321i
$562$		0			0
$563$	−11.8275			−0.498469			−0.249234	−	0.968443i	$-0.580179\pi$
$563$	−11.8275			−0.498469			−0.249234	+	0.968443i	$0.580179\pi$
$564$		0			0
$565$	36.7746	+	21.2318i	1.54712	+	0.893228i
$566$		0			0
$567$	−1.67127	−	0.964910i	−0.0701869	−	0.0405224i
$568$		0			0
$569$			0.147084i			0.00616609i	0.999995	+	0.00308304i	$0.000981365\pi$
$569$			0.147084i			0.00616609i	−0.999995	+	0.00308304i	$0.999019\pi$
$570$		0			0
$571$		−	43.8288i		−	1.83418i	−0.398684	−	0.917088i	$-0.630533\pi$
$571$		−	43.8288i		−	1.83418i	0.398684	−	0.917088i	$-0.369467\pi$
$572$		0			0
$573$	−6.35885	−	3.67128i	−0.265645	−	0.153370i
$574$		0			0
$575$	−78.0337	−	45.0528i	−3.25423	−	1.87883i
$576$		0			0
$577$	25.5656			1.06431			0.532154	−	0.846648i	$-0.321383\pi$
$577$	25.5656			1.06431			0.532154	+	0.846648i	$0.321383\pi$
$578$		0			0
$579$	19.6465	−	11.3429i	0.816479	−	0.471394i
$580$		0			0
$581$	−28.4891			−1.18193
$582$		0			0
$583$	−0.137085	−	0.237439i	−0.00567750	−	0.00983371i
$584$		0			0
$585$	−1.88735	+	1.08966i	−0.0780322	+	0.0450519i
$586$		0			0
$587$	26.5623	+	15.3357i	1.09634	+	0.632973i	0.935258	−	0.353967i	$-0.115168\pi$
$587$	26.5623	+	15.3357i	1.09634	+	0.632973i	0.161084	+	0.986941i	$0.448501\pi$
$588$		0			0
$589$	−12.7534	−	28.0469i	−0.525496	−	1.15565i
$590$		0			0
$591$	−5.00488	+	8.66870i	−0.205873	+	0.356583i
$592$		0			0
$593$	−13.2986	−	23.0338i	−0.546106	−	0.945884i	−0.998536	−	0.0540840i	$-0.982776\pi$
$593$	−13.2986	−	23.0338i	−0.546106	−	0.945884i	0.452430	−	0.891800i	$-0.350557\pi$
$594$		0			0
$595$	24.5754	−	14.1886i	1.00749	−	0.581677i
$596$		0			0
$597$			18.2106i			0.745312i
$598$		0			0
$599$	6.65091	+	11.5197i	0.271749	+	0.470682i	0.969310	−	0.245843i	$-0.0790647\pi$
$599$	6.65091	+	11.5197i	0.271749	+	0.470682i	−0.697561	+	0.716525i	$0.745731\pi$
$600$		0			0
$601$		−	4.69908i		−	0.191679i	−0.995397	−	0.0958397i	$-0.969446\pi$
$601$		−	4.69908i		−	0.191679i	0.995397	−	0.0958397i	$-0.0305536\pi$
$602$		0			0
$603$	−7.34824	+	12.7275i	−0.299243	+	0.518305i
$604$		0			0
$605$	18.2005	−	31.5243i	0.739957	−	1.28164i
$606$		0			0
$607$	−6.63403			−0.269267			−0.134634	−	0.990895i	$-0.542986\pi$
$607$	−6.63403			−0.269267			−0.134634	+	0.990895i	$0.542986\pi$
$608$		0			0
$609$	−5.35068			−0.216820
$610$		0			0
$611$	−1.94109	+	3.36207i	−0.0785282	+	0.136015i
$612$		0			0
$613$	−3.02931	+	5.24692i	−0.122353	+	0.211921i	−0.920695	−	0.390283i	$-0.872377\pi$
$613$	−3.02931	+	5.24692i	−0.122353	+	0.211921i	0.798342	+	0.602204i	$0.205711\pi$
$614$		0			0
$615$			38.1727i			1.53927i
$616$		0			0
$617$	12.3259	+	21.3491i	0.496222	+	0.859483i	0.999991	−	0.00435641i	$-0.00138669\pi$
$617$	12.3259	+	21.3491i	0.496222	+	0.859483i	−0.503768	+	0.863839i	$0.668053\pi$
$618$		0			0
$619$			38.4236i			1.54438i	0.635394	+	0.772188i	$0.280838\pi$
$619$			38.4236i			1.54438i	−0.635394	+	0.772188i	$0.719162\pi$
$620$		0			0
$621$	−7.04394	+	4.06682i	−0.282664	+	0.163196i
$622$		0			0
$623$	17.1107	+	29.6366i	0.685526	+	1.18737i
$624$		0			0
$625$	−21.1672	+	36.6626i	−0.846686	+	1.46650i
$626$		0			0
$627$	0.584200	−	6.01450i	0.0233307	−	0.240196i
$628$		0			0
$629$	6.75700	+	3.90116i	0.269419	+	0.155549i
$630$		0			0
$631$	−42.7314	+	24.6710i	−1.70111	+	0.982137i	−0.756472	+	0.654026i	$0.773079\pi$
$631$	−42.7314	+	24.6710i	−1.70111	+	0.982137i	−0.944639	+	0.328111i	$0.893588\pi$
$632$		0			0
$633$	9.28766	+	16.0867i	0.369151	+	0.639389i
$634$		0			0
$635$	−8.01951			−0.318244
$636$		0			0
$637$	1.54188	−	0.890205i	0.0610915	−	0.0352712i
$638$		0			0
$639$	−4.35230			−0.172174
$640$		0			0
$641$	16.9020	+	9.75836i	0.667588	+	0.385432i	0.795162	−	0.606397i	$-0.207386\pi$
$641$	16.9020	+	9.75836i	0.667588	+	0.385432i	−0.127574	+	0.991829i	$0.540719\pi$
$642$		0			0
$643$	−4.44425	−	2.56589i	−0.175264	−	0.101189i	0.409802	−	0.912175i	$-0.365598\pi$
$643$	−4.44425	−	2.56589i	−0.175264	−	0.101189i	−0.585066	+	0.810986i	$0.698931\pi$
$644$		0			0
$645$		−	27.2548i		−	1.07316i
$646$		0			0
$647$			9.76841i			0.384036i	0.981391	+	0.192018i	$0.0615032\pi$
$647$			9.76841i			0.384036i	−0.981391	+	0.192018i	$0.938497\pi$
$648$		0			0
$649$	6.74529	+	3.89440i	0.264776	+	0.152868i
$650$		0			0
$651$	−11.8132	−	6.82035i	−0.462995	−	0.267310i
$652$		0			0
$653$	−33.4522			−1.30909			−0.654543	−	0.756024i	$-0.727139\pi$
$653$	−33.4522			−1.30909			−0.654543	+	0.756024i	$0.727139\pi$
$654$		0			0
$655$	22.0569	−	12.7346i	0.861835	−	0.497580i
$656$		0			0
$657$	−7.01951			−0.273857
$658$		0			0
$659$	−16.7603	−	29.0297i	−0.652889	−	1.13084i	−0.982419	−	0.186691i	$-0.940224\pi$
$659$	−16.7603	−	29.0297i	−0.652889	−	1.13084i	0.329530	−	0.944145i	$-0.393110\pi$
$660$		0			0
$661$	−28.2562	+	16.3137i	−1.09904	+	0.634530i	−0.935968	−	0.352084i	$-0.885473\pi$
$661$	−28.2562	+	16.3137i	−1.09904	+	0.634530i	−0.163070	+	0.986614i	$0.552140\pi$
$662$		0			0
$663$	−1.72612	−	0.996573i	−0.0670368	−	0.0387037i
$664$		0			0
$665$	−3.26088	+	33.5716i	−0.126451	+	1.30185i
$666$		0			0
$667$	−11.2758	+	19.5302i	−0.436600	+	0.756214i
$668$		0			0
$669$	3.46581	+	6.00296i	0.133996	+	0.232088i
$670$		0			0
$671$	2.09348	−	1.20867i	0.0808178	−	0.0466602i
$672$		0			0
$673$			28.7891i			1.10974i	0.831937	+	0.554869i	$0.187232\pi$
$673$			28.7891i			1.10974i	−0.831937	+	0.554869i	$0.812768\pi$
$674$		0			0
$675$	5.53907	+	9.59394i	0.213199	+	0.369271i
$676$		0			0
$677$		−	0.302677i		−	0.0116328i	−0.999983	−	0.00581642i	$-0.998149\pi$
$677$		−	0.302677i		−	0.0116328i	0.999983	−	0.00581642i	$-0.00185143\pi$
$678$		0			0
$679$	−8.88080	+	15.3820i	−0.340814	+	0.590307i
$680$		0			0
$681$	−10.9853	+	19.0271i	−0.420958	+	0.729121i
$682$		0			0
$683$	−30.0684			−1.15053			−0.575267	−	0.817966i	$-0.695102\pi$
$683$	−30.0684			−1.15053			−0.575267	+	0.817966i	$0.695102\pi$
$684$		0			0
$685$	−24.0585			−0.919229
$686$		0			0
$687$	11.5488	−	20.0031i	0.440615	−	0.763167i
$688$		0			0
$689$	0.0537443	−	0.0930879i	0.00204750	−	0.00354637i
$690$		0			0
$691$		−	5.71631i		−	0.217459i	−0.994071	−	0.108729i	$-0.965322\pi$
$691$		−	5.71631i		−	0.217459i	0.994071	−	0.108729i	$-0.0346782\pi$
$692$		0			0
$693$	−1.33767	−	2.31691i	−0.0508139	−	0.0880122i
$694$		0			0
$695$		−	71.6981i		−	2.71966i
$696$		0			0
$697$	−30.2344	+	17.4558i	−1.14521	+	0.661187i
$698$		0			0
$699$	8.84336	+	15.3171i	0.334487	+	0.579348i
$700$		0			0
$701$	17.6721	−	30.6089i	0.667465	−	1.15608i	−0.311145	−	0.950362i	$-0.600713\pi$
$701$	17.6721	−	30.6089i	0.667465	−	1.15608i	0.978611	−	0.205722i	$-0.0659541\pi$
$702$		0			0
$703$	−8.44214	+	3.83880i	−0.318401	+	0.144783i
$704$		0			0
$705$	24.8040	+	14.3206i	0.934171	+	0.539344i
$706$		0			0
$707$	−16.3851	+	9.45994i	−0.616225	+	0.355778i
$708$		0			0
$709$	−3.67419	−	6.36389i	−0.137987	−	0.239001i	0.788747	−	0.614717i	$-0.210730\pi$
$709$	−3.67419	−	6.36389i	−0.137987	−	0.239001i	−0.926735	+	0.375717i	$0.877397\pi$
$710$		0			0
$711$	9.08788			0.340822
$712$		0			0
$713$	−49.7892	+	28.7458i	−1.86462	+	1.07654i
$714$		0			0
$715$	−3.02123			−0.112987
$716$		0			0
$717$	−5.74079	−	3.31445i	−0.214394	−	0.123780i
$718$		0			0
$719$	−1.48613	−	0.858019i	−0.0554234	−	0.0319987i	0.472032	−	0.881581i	$-0.343521\pi$
$719$	−1.48613	−	0.858019i	−0.0554234	−	0.0319987i	−0.527456	+	0.849583i	$0.676854\pi$
$720$		0			0
$721$		−	10.3102i		−	0.383970i
$722$		0			0
$723$		−	14.6011i		−	0.543019i
$724$		0			0
$725$	26.6005	+	15.3578i	0.987916	+	0.570374i
$726$		0			0
$727$	−44.2307	−	25.5366i	−1.64042	−	0.947099i	−0.980682	−	0.195607i	$-0.937332\pi$
$727$	−44.2307	−	25.5366i	−1.64042	−	0.947099i	−0.659742	−	0.751492i	$-0.729334\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	21.5870	−	12.4632i	0.798423	−	0.460970i
$732$		0			0
$733$	−18.2149			−0.672782			−0.336391	−	0.941722i	$-0.609206\pi$
$733$	−18.2149			−0.672782			−0.336391	+	0.941722i	$0.609206\pi$
$734$		0			0
$735$	−6.56756	−	11.3754i	−0.242248	−	0.419586i
$736$		0			0
$737$	−17.6443	+	10.1870i	−0.649938	+	0.375242i
$738$		0			0
$739$	18.1033	+	10.4520i	0.665942	+	0.384482i	0.794537	−	0.607216i	$-0.207714\pi$
$739$	18.1033	+	10.4520i	0.665942	+	0.384482i	−0.128595	+	0.991697i	$0.541047\pi$
$740$		0			0
$741$	2.15659	−	0.980642i	0.0792245	−	0.0360248i
$742$		0			0
$743$	16.9283	−	29.3207i	0.621040	−	1.07567i	−0.368253	−	0.929726i	$-0.620044\pi$
$743$	16.9283	−	29.3207i	0.621040	−	1.07567i	0.989292	−	0.145947i	$-0.0466229\pi$
$744$		0			0
$745$	19.1661	+	33.1966i	0.702190	+	1.21623i
$746$		0			0
$747$	12.7847	−	7.38127i	0.467769	−	0.270067i
$748$		0			0
$749$			27.3190i			0.998216i
$750$		0			0
$751$	24.9845	+	43.2744i	0.911696	+	1.57910i	0.811668	+	0.584119i	$0.198560\pi$
$751$	24.9845	+	43.2744i	0.911696	+	1.57910i	0.100028	+	0.994985i	$0.468107\pi$
$752$		0			0
$753$		−	11.1834i		−	0.407545i
$754$		0			0
$755$	−32.1171	+	55.6285i	−1.16886	+	2.02453i
$756$		0			0
$757$	−2.34369	+	4.05939i	−0.0851829	+	0.147541i	−0.905469	−	0.424412i	$-0.860481\pi$
$757$	−2.34369	+	4.05939i	−0.0851829	+	0.147541i	0.820286	+	0.571953i	$0.193814\pi$
$758$		0			0
$759$	−11.2758			−0.409285
$760$		0			0
$761$	8.06446			0.292337			0.146168	−	0.989260i	$-0.453306\pi$
$761$	8.06446			0.292337			0.146168	+	0.989260i	$0.453306\pi$
$762$		0			0
$763$	−1.52850	+	2.64744i	−0.0553354	+	0.0958437i
$764$		0			0
$765$	−7.35230	+	12.7346i	−0.265823	+	0.460419i
$766$		0			0
$767$			3.05360i			0.110259i
$768$		0			0
$769$	−15.5976	−	27.0159i	−0.562465	−	0.974218i	−0.997281	−	0.0736987i	$-0.976520\pi$
$769$	−15.5976	−	27.0159i	−0.562465	−	0.974218i	0.434815	−	0.900520i	$-0.356814\pi$
$770$		0			0
$771$		−	2.97040i		−	0.106976i
$772$		0			0
$773$	−12.5796	+	7.26284i	−0.452457	+	0.261226i	−0.708867	−	0.705342i	$-0.750794\pi$
$773$	−12.5796	+	7.26284i	−0.452457	+	0.261226i	0.256410	+	0.966568i	$0.417460\pi$
$774$		0			0
$775$	39.1522	+	67.8136i	1.40639	+	2.43594i
$776$		0			0
$777$	−2.05293	+	3.55578i	−0.0736486	+	0.127563i
$778$		0			0
$779$	4.01176	−	41.3022i	0.143736	−	1.47980i
$780$		0			0
$781$	−5.22530	−	3.01683i	−0.186976	−	0.107951i
$782$		0			0
$783$	2.40117	−	1.38632i	0.0858108	−	0.0495429i
$784$		0			0
$785$	28.7387	+	49.7770i	1.02573	+	1.77662i
$786$		0			0
$787$	19.2481			0.686119			0.343060	−	0.939314i	$-0.388537\pi$
$787$	19.2481			0.686119			0.343060	+	0.939314i	$0.388537\pi$
$788$		0			0
$789$	3.44219	−	1.98735i	0.122545	−	0.0707515i
$790$		0			0
$791$	−20.4369			−0.726654
$792$		0			0
$793$	0.820748	+	0.473859i	0.0291456	+	0.0168272i
$794$		0			0
$795$	−0.686764	−	0.396503i	−0.0243570	−	0.0140625i
$796$		0			0
$797$		−	12.6223i		−	0.447105i	−0.974692	−	0.223553i	$-0.928235\pi$
$797$		−	12.6223i		−	0.447105i	0.974692	−	0.223553i	$-0.0717655\pi$
$798$		0			0
$799$			26.1944i			0.926691i
$800$		0			0
$801$	−15.3572	−	8.86647i	−0.542619	−	0.313281i
$802$		0			0
$803$	−8.42751	−	4.86563i	−0.297400	−	0.171704i
$804$		0			0
$805$	62.9390			2.21831
$806$		0			0
$807$	11.5724	−	6.68135i	0.407369	−	0.235195i
$808$		0			0
$809$	−12.1660			−0.427734			−0.213867	−	0.976863i	$-0.568606\pi$
$809$	−12.1660			−0.427734			−0.213867	+	0.976863i	$0.568606\pi$
$810$		0			0
$811$	8.74534	+	15.1474i	0.307090	+	0.531896i	0.977725	−	0.209892i	$-0.0673113\pi$
$811$	8.74534	+	15.1474i	0.307090	+	0.531896i	−0.670634	+	0.741788i	$0.733978\pi$
$812$		0			0
$813$	7.83160	−	4.52158i	0.274666	−	0.158579i
$814$		0			0
$815$	−14.9560	−	8.63483i	−0.523885	−	0.302465i
$816$		0			0
$817$	−2.86435	+	29.4892i	−0.100211	+	1.03170i
$818$		0			0
$819$	0.524434	−	0.908346i	0.0183252	−	0.0317402i
$820$		0			0
$821$	10.8316	+	18.7609i	0.378025	+	0.654759i	0.990775	−	0.135518i	$-0.0432698\pi$
$821$	10.8316	+	18.7609i	0.378025	+	0.654759i	−0.612749	+	0.790277i	$0.709937\pi$
$822$		0			0
$823$	17.2579	−	9.96386i	0.601573	−	0.347318i	−0.168087	−	0.985772i	$-0.553759\pi$
$823$	17.2579	−	9.96386i	0.601573	−	0.347318i	0.769660	+	0.638454i	$0.220426\pi$
$824$		0			0
$825$			15.3578i			0.534689i
$826$		0			0
$827$	18.0976	+	31.3460i	0.629317	+	1.09001i	0.987689	+	0.156430i	$0.0499984\pi$
$827$	18.0976	+	31.3460i	0.629317	+	1.09001i	−0.358373	+	0.933579i	$0.616668\pi$
$828$		0			0
$829$			22.3831i			0.777397i	0.921365	+	0.388699i	$0.127075\pi$
$829$			22.3831i			0.777397i	−0.921365	+	0.388699i	$0.872925\pi$
$830$		0			0
$831$	13.4597	−	23.3130i	0.466913	−	0.808718i
$832$		0			0
$833$	6.00651	−	10.4036i	0.208113	−	0.360463i
$834$		0			0
$835$	15.6866			0.542858
$836$		0			0
$837$	7.06838			0.244319
$838$		0			0
$839$	24.2122	−	41.9368i	0.835900	−	1.44782i	−0.0573963	−	0.998351i	$-0.518280\pi$
$839$	24.2122	−	41.9368i	0.835900	−	1.44782i	0.893296	−	0.449469i	$-0.148387\pi$
$840$		0			0
$841$	−10.6563	+	18.4572i	−0.367457	+	0.636455i
$842$		0			0
$843$		−	21.2308i		−	0.731229i
$844$		0			0
$845$	25.4712	+	44.1174i	0.876235	+	1.51768i
$846$		0			0
$847$			17.5192i			0.601965i
$848$		0			0
$849$	0.685093	−	0.395539i	0.0235123	−	0.0135749i
$850$		0			0
$851$	8.65253	+	14.9866i	0.296605	+	0.513735i
$852$		0			0
$853$	−1.74653	+	3.02508i	−0.0598001	+	0.103577i	−0.894376	−	0.447317i	$-0.852380\pi$
$853$	−1.74653	+	3.02508i	−0.0598001	+	0.103577i	0.834576	+	0.550894i	$0.185713\pi$
$854$		0			0
$855$	−7.23477	−	15.9105i	−0.247424	−	0.544126i
$856$		0			0
$857$	−41.7964	−	24.1312i	−1.42774	−	0.824305i	−0.430796	−	0.902449i	$-0.641767\pi$
$857$	−41.7964	−	24.1312i	−1.42774	−	0.824305i	−0.996942	+	0.0781446i	$0.975100\pi$
$858$		0			0
$859$	0.867314	−	0.500744i	0.0295924	−	0.0170852i	−0.485131	−	0.874442i	$-0.661228\pi$
$859$	0.867314	−	0.500744i	0.0295924	−	0.0170852i	0.514723	+	0.857356i	$0.327895\pi$
$860$		0			0
$861$	−9.18590	−	15.9105i	−0.313055	−	0.542227i
$862$		0			0
$863$	−48.6453			−1.65591			−0.827953	−	0.560798i	$-0.810495\pi$
$863$	−48.6453			−1.65591			−0.827953	+	0.560798i	$0.810495\pi$
$864$		0			0
$865$	19.2562	−	11.1176i	0.654730	−	0.378009i
$866$		0			0
$867$	3.55159			0.120618
$868$		0			0
$869$	10.9108	+	6.29934i	0.370123	+	0.213690i
$870$		0			0
$871$	−6.91747	−	3.99380i	−0.234390	−	0.135325i
$872$		0			0
$873$		−	9.20376i		−	0.311500i
$874$		0			0
$875$		−	47.0332i		−	1.59001i
$876$		0			0
$877$	31.4488	+	18.1570i	1.06195	+	0.613118i	0.925972	−	0.377593i	$-0.123248\pi$
$877$	31.4488	+	18.1570i	1.06195	+	0.613118i	0.135980	+	0.990712i	$0.456582\pi$
$878$		0			0
$879$	7.48905	+	4.32381i	0.252599	+	0.145838i
$880$		0			0
$881$	−2.36606			−0.0797147			−0.0398574	−	0.999205i	$-0.512690\pi$
$881$	−2.36606			−0.0797147			−0.0398574	+	0.999205i	$0.512690\pi$
$882$		0			0
$883$	−11.4284	+	6.59820i	−0.384597	+	0.222047i	−0.679816	−	0.733382i	$-0.737941\pi$
$883$	−11.4284	+	6.59820i	−0.384597	+	0.222047i	0.295220	+	0.955429i	$0.404607\pi$
$884$		0			0
$885$	22.5282			0.757276
$886$		0			0
$887$	4.34938	+	7.53335i	0.146038	+	0.252945i	0.929760	−	0.368167i	$-0.120015\pi$
$887$	4.34938	+	7.53335i	0.146038	+	0.252945i	−0.783722	+	0.621112i	$0.786681\pi$
$888$		0			0
$889$	3.34255	−	1.92982i	0.112105	−	0.0647241i
$890$		0			0
$891$	1.20058	+	0.693158i	0.0402211	+	0.0232217i
$892$		0			0
$893$	−25.3324	−	18.1014i	−0.847717	−	0.605739i
$894$		0			0
$895$	34.2950	−	59.4006i	1.14635	−	1.98554i
$896$		0			0
$897$	−2.21034	−	3.82842i	−0.0738011	−	0.127827i
$898$		0			0
$899$	16.9724	−	9.79900i	0.566060	−	0.326815i
$900$		0			0
$901$		−	0.725262i		−	0.0241620i
$902$		0			0
$903$	6.55862	+	11.3599i	0.218257	+	0.378033i
$904$		0			0
$905$			49.3445i			1.64027i
$906$		0			0
$907$	2.59883	−	4.50131i	0.0862928	−	0.149463i	−0.819649	−	0.572867i	$-0.805831\pi$
$907$	2.59883	−	4.50131i	0.0862928	−	0.149463i	0.905941	+	0.423403i	$0.139165\pi$
$908$		0			0
$909$	4.90198	−	8.49048i	0.162588	−	0.281611i
$910$		0			0
$911$	40.7983			1.35171			0.675854	−	0.737035i	$-0.263775\pi$
$911$	40.7983			1.35171			0.675854	+	0.737035i	$0.263775\pi$
$912$		0			0
$913$	20.4655			0.677310
$914$		0			0
$915$	3.49593	−	6.05514i	0.115572	−	0.200177i
$916$		0			0
$917$	−6.12891	+	10.6156i	−0.202394	+	0.350557i
$918$		0			0
$919$			53.8593i			1.77665i	0.459210	+	0.888327i	$0.348132\pi$
$919$			53.8593i			1.77665i	−0.459210	+	0.888327i	$0.651868\pi$
$920$		0			0
$921$	−0.195707	−	0.338974i	−0.00644876	−	0.0111696i
$922$		0			0
$923$		−	2.36550i		−	0.0778613i
$924$		0			0
$925$	20.4120	−	11.7849i	0.671142	−	0.387484i
$926$		0			0
$927$	2.67127	+	4.62678i	0.0877361	+	0.151963i
$928$		0			0
$929$	10.0635	−	17.4305i	0.330173	−	0.571876i	−0.652373	−	0.757898i	$-0.726226\pi$
$929$	10.0635	−	17.4305i	0.330173	−	0.571876i	0.982546	+	0.186022i	$0.0595597\pi$
$930$		0			0
$931$	5.91049	+	12.9981i	0.193709	+	0.425997i
$932$		0			0
$933$	18.7877	+	10.8471i	0.615080	+	0.355117i
$934$		0			0
$935$	−17.6541	+	10.1926i	−0.577351	+	0.333334i
$936$		0			0
$937$	−16.1753	−	28.0164i	−0.528424	−	0.915257i	−0.999451	−	0.0331380i	$-0.989450\pi$
$937$	−16.1753	−	28.0164i	−0.528424	−	0.915257i	0.471027	−	0.882119i	$-0.343883\pi$
$938$		0			0
$939$	−27.3343			−0.892022
$940$		0			0
$941$	−37.9446	+	21.9073i	−1.23696	+	0.714159i	−0.968472	−	0.249124i	$-0.919857\pi$
$941$	−37.9446	+	21.9073i	−1.23696	+	0.714159i	−0.268488	+	0.963283i	$0.586524\pi$
$942$		0			0
$943$	−77.4320			−2.52153
$944$		0			0
$945$	−6.70140	−	3.86905i	−0.217996	−	0.125860i
$946$		0			0
$947$	36.1917	+	20.8953i	1.17607	+	0.679006i	0.955103	−	0.296274i	$-0.0957441\pi$
$947$	36.1917	+	20.8953i	1.17607	+	0.679006i	0.220971	+	0.975280i	$0.429077\pi$
$948$		0			0
$949$		−	3.81514i		−	0.123845i
$950$		0			0
$951$			33.1279i			1.07425i
$952$		0			0
$953$	−35.1610	−	20.3002i	−1.13898	−	0.657589i	−0.192801	−	0.981238i	$-0.561757\pi$
$953$	−35.1610	−	20.3002i	−1.13898	−	0.657589i	−0.946177	+	0.323649i	$0.895090\pi$
$954$		0			0
$955$	−25.4974	−	14.7209i	−0.825077	−	0.476359i
$956$		0			0
$957$	3.84374			0.124250
$958$		0			0
$959$	10.0276	−	5.78946i	0.323809	−	0.186951i
$960$		0			0
$961$	18.9619			0.611675
$962$		0			0
$963$	−7.07813	−	12.2597i	−0.228090	−	0.395063i
$964$		0			0
$965$	78.7775	−	45.4822i	2.53594	−	1.46412i
$966$		0			0
$967$	−19.2089	−	11.0902i	−0.617715	−	0.356638i	0.158264	−	0.987397i	$-0.449410\pi$
$967$	−19.2089	−	11.0902i	−0.617715	−	0.356638i	−0.775979	+	0.630759i	$0.782744\pi$
$968$		0			0
$969$	9.29339	−	13.0059i	0.298547	−	0.417809i
$970$		0			0
$971$	5.91173	−	10.2394i	0.189717	−	0.328599i	−0.755439	−	0.655219i	$-0.772576\pi$
$971$	5.91173	−	10.2394i	0.189717	−	0.328599i	0.945156	+	0.326620i	$0.105910\pi$
$972$		0			0
$973$	17.2535	+	29.8839i	0.553121	+	0.958033i
$974$		0			0
$975$	−5.21436	+	3.01051i	−0.166993	+	0.0964135i
$976$		0			0
$977$		−	28.0985i		−	0.898951i	−0.893293	−	0.449476i	$-0.851611\pi$
$977$		−	28.0985i		−	0.898951i	0.893293	−	0.449476i	$-0.148389\pi$
$978$		0			0
$979$	−12.2917	−	21.2899i	−0.392845	−	0.680428i
$980$		0			0
$981$		−	1.58408i		−	0.0505759i
$982$		0			0
$983$	21.7678	−	37.7029i	0.694284	−	1.20254i	−0.276138	−	0.961118i	$-0.589055\pi$
$983$	21.7678	−	37.7029i	0.694284	−	1.20254i	0.970421	−	0.241417i	$-0.0776121\pi$
$984$		0			0
$985$	−20.0683	+	34.7594i	−0.639430	+	1.10753i
$986$		0			0
$987$	−13.7845			−0.438764
$988$		0			0
$989$	55.2855			1.75798
$990$		0			0
$991$	14.6791	−	25.4249i	0.466296	−	0.807648i	−0.532963	−	0.846139i	$-0.678921\pi$
$991$	14.6791	−	25.4249i	0.466296	−	0.807648i	0.999259	+	0.0384901i	$0.0122548\pi$
$992$		0			0
$993$	−4.93536	+	8.54829i	−0.156619	+	0.271272i
$994$		0			0
$995$			73.0202i			2.31489i
$996$		0			0
$997$	2.18672	+	3.78750i	0.0692540	+	0.119951i	0.898573	−	0.438824i	$-0.144605\pi$
$997$	2.18672	+	3.78750i	0.0692540	+	0.119951i	−0.829319	+	0.558775i	$0.811271\pi$
$998$		0			0
$999$		−	2.12759i		−	0.0673140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bb.h.559.4	yes	8
3.2	odd	2		2736.2.bm.r.559.1		8
4.3	odd	2		912.2.bb.g.559.4	yes	8
12.11	even	2		2736.2.bm.s.559.1		8
19.12	odd	6		912.2.bb.g.31.4	✓	8
57.50	even	6		2736.2.bm.s.1855.1		8
76.31	even	6	inner	912.2.bb.h.31.4	yes	8
228.107	odd	6		2736.2.bm.r.1855.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.g.31.4	✓	8	19.12	odd	6
912.2.bb.g.559.4	yes	8	4.3	odd	2
912.2.bb.h.31.4	yes	8	76.31	even	6	inner
912.2.bb.h.559.4	yes	8	1.1	even	1	trivial
2736.2.bm.r.559.1		8	3.2	odd	2
2736.2.bm.r.1855.1		8	228.107	odd	6
2736.2.bm.s.559.1		8	12.11	even	2
2736.2.bm.s.1855.1		8	57.50	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(2.00488 - 3.47255i) q^{5} +1.92982i q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(2.00488 - 3.47255i) q^{5} +1.92982i q^{7} +(-0.500000 - 0.866025i) q^{9} -1.38632i q^{11} +(0.470689 - 0.271753i) q^{13} +(-2.00488 - 3.47255i) q^{15} +(1.83360 - 3.17590i) q^{17} +(1.80429 + 3.96794i) q^{19} +(1.67127 + 0.964910i) q^{21} +(7.04394 - 4.06682i) q^{23} +(-5.53907 - 9.59394i) q^{25} -1.00000 q^{27} +(-2.40117 + 1.38632i) q^{29} -7.06838 q^{31} +(-1.20058 - 0.693158i) q^{33} +(6.70140 + 3.86905i) q^{35} +2.12759i q^{37} -0.543505i q^{39} +(-8.24453 - 4.75998i) q^{41} +(5.88649 + 3.39857i) q^{43} -4.00975 q^{45} +(-6.18590 + 3.57143i) q^{47} +3.27579 q^{49} +(-1.83360 - 3.17590i) q^{51} +(0.171273 - 0.0988847i) q^{53} +(-4.81405 - 2.77939i) q^{55} +(4.33848 + 0.421405i) q^{57} +(-2.80917 + 4.86563i) q^{59} +(0.871857 + 1.51010i) q^{61} +(1.67127 - 0.964910i) q^{63} -2.17932i q^{65} +(-7.34824 - 12.7275i) q^{67} -8.13364i q^{69} +(2.17615 - 3.76920i) q^{71} +(3.50975 - 6.07907i) q^{73} -11.0781 q^{75} +2.67534 q^{77} +(-4.54394 + 7.87034i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.7625i q^{83} +(-7.35230 - 12.7346i) q^{85} +2.77263i q^{87} +(15.3572 - 8.86647i) q^{89} +(0.524434 + 0.908346i) q^{91} +(-3.53419 + 6.12139i) q^{93} +(17.3962 + 1.68973i) q^{95} +(7.97069 + 4.60188i) q^{97} +(-1.20058 + 0.693158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9	\( 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9} + 2 q^{15} + 4 q^{17} + 6 q^{21} + 6 q^{23} - 12 q^{25} - 8 q^{27} - 12 q^{29} - 28 q^{31} - 6 q^{33} + 18 q^{35} - 12 q^{41} - 18 q^{43} + 4 q^{45} + 12 q^{47} - 24 q^{49} - 4 q^{51} - 6 q^{53} + 12 q^{55} + 6 q^{57} + 10 q^{59} - 4 q^{61} + 6 q^{63} + 6 q^{67} - 8 q^{71} - 8 q^{73} - 24 q^{75} + 28 q^{77} + 14 q^{79} - 4 q^{81} - 8 q^{85} + 54 q^{89} + 26 q^{91} - 14 q^{93} + 38 q^{95} + 60 q^{97} - 6 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9 + 2 * q^15 + 4 * q^17 + 6 * q^21 + 6 * q^23 - 12 * q^25 - 8 * q^27 - 12 * q^29 - 28 * q^31 - 6 * q^33 + 18 * q^35 - 12 * q^41 - 18 * q^43 + 4 * q^45 + 12 * q^47 - 24 * q^49 - 4 * q^51 - 6 * q^53 + 12 * q^55 + 6 * q^57 + 10 * q^59 - 4 * q^61 + 6 * q^63 + 6 * q^67 - 8 * q^71 - 8 * q^73 - 24 * q^75 + 28 * q^77 + 14 * q^79 - 4 * q^81 - 8 * q^85 + 54 * q^89 + 26 * q^91 - 14 * q^93 + 38 * q^95 + 60 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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