LMFDB - Embedded newform 644.2.i.a.277.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 8 x^{11} + 130 x^{10} - 78 x^{9} + 505 x^{8} - 519 x^{7} + 1508 x^{6} - 955 x^{5} + \cdots + 1 $ x^14 + 13x^12 - 8x^11 + 130x^10 - 78x^9 + 505x^8 - 519x^7 + 1508x^6 - 955x^5 + 1023x^4 + 156x^3 + 107x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.5
Root			$-0.160672 + 0.278292i$ of defining polynomial
Character	$\chi$	$=$	644.277
Dual form			644.2.i.a.93.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.637005 - 1.10333i) q^{3} +(0.712116 + 1.23342i) q^{5} +(2.63107 + 0.278292i) q^{7} +(0.688449 + 1.19243i) q^{9} +O(q^{10})$	\(q+(0.637005 - 1.10333i) q^{3} +(0.712116 + 1.23342i) q^{5} +(2.63107 + 0.278292i) q^{7} +(0.688449 + 1.19243i) q^{9} +(-2.32558 + 4.02802i) q^{11} +3.24942 q^{13} +1.81449 q^{15} +(-3.79656 + 6.57584i) q^{17} +(-2.05760 - 3.56386i) q^{19} +(1.98305 - 2.72566i) q^{21} +(0.500000 + 0.866025i) q^{23} +(1.48578 - 2.57345i) q^{25} +5.57621 q^{27} -3.22668 q^{29} +(2.62962 - 4.55464i) q^{31} +(2.96281 + 5.13174i) q^{33} +(1.53038 + 3.44340i) q^{35} +(0.135954 + 0.235478i) q^{37} +(2.06989 - 3.58516i) q^{39} +5.71808 q^{41} -7.29000 q^{43} +(-0.980512 + 1.69830i) q^{45} +(-2.21659 - 3.83925i) q^{47} +(6.84511 + 1.46442i) q^{49} +(4.83686 + 8.37769i) q^{51} +(3.55701 - 6.16093i) q^{53} -6.62433 q^{55} -5.24280 q^{57} +(5.35868 - 9.28150i) q^{59} +(-1.12963 - 1.95657i) q^{61} +(1.47952 + 3.32896i) q^{63} +(2.31396 + 4.00790i) q^{65} +(3.79348 - 6.57050i) q^{67} +1.27401 q^{69} +5.71833 q^{71} +(-3.46443 + 6.00057i) q^{73} +(-1.89290 - 3.27860i) q^{75} +(-7.23974 + 9.95083i) q^{77} +(-2.32042 - 4.01908i) q^{79} +(1.48673 - 2.57509i) q^{81} +1.57156 q^{83} -10.8144 q^{85} +(-2.05541 + 3.56007i) q^{87} +(-2.26617 - 3.92513i) q^{89} +(8.54945 + 0.904287i) q^{91} +(-3.35017 - 5.80266i) q^{93} +(2.93050 - 5.07577i) q^{95} -10.9242 q^{97} -6.40417 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.637005	−	1.10333i	0.367775	−	0.637005i	−0.621442	−	0.783460i	$-0.713453\pi$
$3$	0.637005	−	1.10333i	0.367775	−	0.637005i	0.989217	+	0.146455i	$0.0467863\pi$
$4$		0			0
$5$	0.712116	+	1.23342i	0.318468	+	0.551603i	0.980169	−	0.198165i	$-0.0634983\pi$
$5$	0.712116	+	1.23342i	0.318468	+	0.551603i	−0.661701	+	0.749768i	$0.730165\pi$
$6$		0			0
$7$	2.63107	+	0.278292i	0.994453	+	0.105185i
$7$	2.63107	+	0.278292i	0.994453	+	0.105185i
$8$		0			0
$9$	0.688449	+	1.19243i	0.229483	+	0.397476i
$10$		0			0
$11$	−2.32558	+	4.02802i	−0.701188	+	1.21449i	0.266861	+	0.963735i	$0.414013\pi$
$11$	−2.32558	+	4.02802i	−0.701188	+	1.21449i	−0.968050	+	0.250759i	$0.919320\pi$
$12$		0			0
$13$	3.24942			0.901226			0.450613	−	0.892719i	$-0.351205\pi$
$13$	3.24942			0.901226			0.450613	+	0.892719i	$0.351205\pi$
$14$		0			0
$15$	1.81449			0.468498
$16$		0			0
$17$	−3.79656	+	6.57584i	−0.920802	+	1.59488i	−0.122624	+	0.992453i	$0.539131\pi$
$17$	−3.79656	+	6.57584i	−0.920802	+	1.59488i	−0.798178	+	0.602422i	$0.794202\pi$
$18$		0			0
$19$	−2.05760	−	3.56386i	−0.472045	−	0.817606i	0.527443	−	0.849590i	$-0.323151\pi$
$19$	−2.05760	−	3.56386i	−0.472045	−	0.817606i	−0.999488	+	0.0319841i	$0.989817\pi$
$20$		0			0
$21$	1.98305	−	2.72566i	0.432738	−	0.594787i
$22$		0			0
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$		0			0
$25$	1.48578	−	2.57345i	0.297156	−	0.514690i
$26$		0			0
$27$	5.57621			1.07314
$28$		0			0
$29$	−3.22668			−0.599179			−0.299589	−	0.954068i	$-0.596850\pi$
$29$	−3.22668			−0.599179			−0.299589	+	0.954068i	$0.596850\pi$
$30$		0			0
$31$	2.62962	−	4.55464i	0.472294	−	0.818037i	−0.527203	−	0.849739i	$-0.676759\pi$
$31$	2.62962	−	4.55464i	0.472294	−	0.818037i	0.999497	+	0.0317018i	$0.0100927\pi$
$32$		0			0
$33$	2.96281	+	5.13174i	0.515759	+	0.893321i
$34$		0			0
$35$	1.53038	+	3.44340i	0.258681	+	0.582041i
$36$		0			0
$37$	0.135954	+	0.235478i	0.0223506	+	0.0387124i	0.876984	−	0.480519i	$-0.159552\pi$
$37$	0.135954	+	0.235478i	0.0223506	+	0.0387124i	−0.854634	+	0.519231i	$0.826218\pi$
$38$		0			0
$39$	2.06989	−	3.58516i	0.331448	−	0.574085i
$40$		0			0
$41$	5.71808			0.893014			0.446507	−	0.894780i	$-0.352668\pi$
$41$	5.71808			0.893014			0.446507	+	0.894780i	$0.352668\pi$
$42$		0			0
$43$	−7.29000			−1.11171			−0.555857	−	0.831278i	$-0.687610\pi$
$43$	−7.29000			−1.11171			−0.555857	+	0.831278i	$0.687610\pi$
$44$		0			0
$45$	−0.980512	+	1.69830i	−0.146166	+	0.253167i
$46$		0			0
$47$	−2.21659	−	3.83925i	−0.323324	−	0.560013i	0.657848	−	0.753151i	$-0.271467\pi$
$47$	−2.21659	−	3.83925i	−0.323324	−	0.560013i	−0.981172	+	0.193138i	$0.938134\pi$
$48$		0			0
$49$	6.84511	+	1.46442i	0.977872	+	0.209202i
$50$		0			0
$51$	4.83686	+	8.37769i	0.677296	+	1.17311i
$52$		0			0
$53$	3.55701	−	6.16093i	0.488594	−	0.846269i	−0.511320	−	0.859390i	$-0.670843\pi$
$53$	3.55701	−	6.16093i	0.488594	−	0.846269i	0.999914	+	0.0131213i	$0.00417676\pi$
$54$		0			0
$55$	−6.62433			−0.893224
$56$		0			0
$57$	−5.24280			−0.694426
$58$		0			0
$59$	5.35868	−	9.28150i	0.697641	−	1.20835i	−0.271642	−	0.962398i	$-0.587567\pi$
$59$	5.35868	−	9.28150i	0.697641	−	1.20835i	0.969282	−	0.245951i	$-0.0791001\pi$
$60$		0			0
$61$	−1.12963	−	1.95657i	−0.144634	−	0.250513i	0.784602	−	0.619999i	$-0.212867\pi$
$61$	−1.12963	−	1.95657i	−0.144634	−	0.250513i	−0.929236	+	0.369486i	$0.879534\pi$
$62$		0			0
$63$	1.47952	+	3.32896i	0.186402	+	0.419409i
$64$		0			0
$65$	2.31396	+	4.00790i	0.287012	+	0.497119i
$66$		0			0
$67$	3.79348	−	6.57050i	0.463448	−	0.802715i	−0.535682	−	0.844420i	$-0.679946\pi$
$67$	3.79348	−	6.57050i	0.463448	−	0.802715i	0.999130	+	0.0417049i	$0.0132789\pi$
$68$		0			0
$69$	1.27401			0.153373
$70$		0			0
$71$	5.71833			0.678640			0.339320	−	0.940671i	$-0.389803\pi$
$71$	5.71833			0.678640			0.339320	+	0.940671i	$0.389803\pi$
$72$		0			0
$73$	−3.46443	+	6.00057i	−0.405481	+	0.702314i	−0.994377	−	0.105895i	$-0.966229\pi$
$73$	−3.46443	+	6.00057i	−0.405481	+	0.702314i	0.588896	+	0.808209i	$0.299563\pi$
$74$		0			0
$75$	−1.89290	−	3.27860i	−0.218573	−	0.378580i
$76$		0			0
$77$	−7.23974	+	9.95083i	−0.825045	+	1.13400i
$78$		0			0
$79$	−2.32042	−	4.01908i	−0.261067	−	0.452182i	0.705459	−	0.708751i	$-0.250741\pi$
$79$	−2.32042	−	4.01908i	−0.261067	−	0.452182i	−0.966526	+	0.256569i	$0.917408\pi$
$80$		0			0
$81$	1.48673	−	2.57509i	0.165192	−	0.286121i
$82$		0			0
$83$	1.57156			0.172501			0.0862506	−	0.996273i	$-0.472511\pi$
$83$	1.57156			0.172501			0.0862506	+	0.996273i	$0.472511\pi$
$84$		0			0
$85$	−10.8144			−1.17298
$86$		0			0
$87$	−2.05541	+	3.56007i	−0.220363	+	0.381680i
$88$		0			0
$89$	−2.26617	−	3.92513i	−0.240214	−	0.416063i	0.720561	−	0.693391i	$-0.243884\pi$
$89$	−2.26617	−	3.92513i	−0.240214	−	0.416063i	−0.960775	+	0.277329i	$0.910551\pi$
$90$		0			0
$91$	8.54945	+	0.904287i	0.896226	+	0.0947951i
$92$		0			0
$93$	−3.35017	−	5.80266i	−0.347396	−	0.601707i
$94$		0			0
$95$	2.93050	−	5.07577i	0.300663	−	0.520763i
$96$		0			0
$97$	−10.9242			−1.10918			−0.554591	−	0.832123i	$-0.687125\pi$
$97$	−10.9242			−1.10918			−0.554591	+	0.832123i	$0.687125\pi$
$98$		0			0
$99$	−6.40417			−0.643643
$100$		0			0
$101$	−4.88548	+	8.46189i	−0.486123	+	0.841990i	−0.999873	−	0.0159503i	$-0.994923\pi$
$101$	−4.88548	+	8.46189i	−0.486123	+	0.841990i	0.513750	+	0.857940i	$0.328256\pi$
$102$		0			0
$103$	−0.245531	−	0.425273i	−0.0241929	−	0.0419034i	0.853675	−	0.520805i	$-0.174368\pi$
$103$	−0.245531	−	0.425273i	−0.0241929	−	0.0419034i	−0.877868	+	0.478902i	$0.841035\pi$
$104$		0			0
$105$	4.77405	+	0.504958i	0.465899	+	0.0492788i
$106$		0			0
$107$	−9.76429	−	16.9122i	−0.943949	−	1.63497i	−0.757841	−	0.652439i	$-0.773746\pi$
$107$	−9.76429	−	16.9122i	−0.943949	−	1.63497i	−0.186108	−	0.982529i	$-0.559587\pi$
$108$		0			0
$109$	−5.36239	+	9.28793i	−0.513624	+	0.889623i	0.486251	+	0.873819i	$0.338364\pi$
$109$	−5.36239	+	9.28793i	−0.513624	+	0.889623i	−0.999875	+	0.0158036i	$0.994969\pi$
$110$		0			0
$111$	0.346412			0.0328800
$112$		0			0
$113$	−11.0011			−1.03490			−0.517450	−	0.855714i	$-0.673119\pi$
$113$	−11.0011			−1.03490			−0.517450	+	0.855714i	$0.673119\pi$
$114$		0			0
$115$	−0.712116	+	1.23342i	−0.0664052	+	0.115017i
$116$		0			0
$117$	2.23706	+	3.87470i	0.206816	+	0.358216i
$118$		0			0
$119$	−11.8190	+	16.2450i	−1.08345	+	1.48917i
$120$		0			0
$121$	−5.31663	−	9.20867i	−0.483330	−	0.837152i
$122$		0			0
$123$	3.64244	−	6.30890i	0.328428	−	0.568854i
$124$		0			0
$125$	11.3534			1.01548
$126$		0			0
$127$	14.8952			1.32174			0.660868	−	0.750502i	$-0.270188\pi$
$127$	14.8952			1.32174			0.660868	+	0.750502i	$0.270188\pi$
$128$		0			0
$129$	−4.64377	+	8.04324i	−0.408861	+	0.708168i
$130$		0			0
$131$	7.41281	+	12.8394i	0.647660	+	1.12178i	0.983680	+	0.179925i	$0.0575856\pi$
$131$	7.41281	+	12.8394i	0.647660	+	1.12178i	−0.336020	+	0.941855i	$0.609081\pi$
$132$		0			0
$133$	−4.42190	−	9.94940i	−0.383427	−	0.862723i
$134$		0			0
$135$	3.97091	+	6.87782i	0.341762	+	0.591949i
$136$		0			0
$137$	0.287014	−	0.497122i	0.0245212	−	0.0424720i	−0.853504	−	0.521086i	$-0.825527\pi$
$137$	0.287014	−	0.497122i	0.0245212	−	0.0424720i	0.878026	+	0.478614i	$0.158861\pi$
$138$		0			0
$139$	14.7923			1.25467			0.627334	−	0.778751i	$-0.284146\pi$
$139$	14.7923			1.25467			0.627334	+	0.778751i	$0.284146\pi$
$140$		0			0
$141$	−5.64793			−0.475641
$142$		0			0
$143$	−7.55677	+	13.0887i	−0.631929	+	1.09453i
$144$		0			0
$145$	−2.29777	−	3.97985i	−0.190819	−	0.330509i
$146$		0			0
$147$	5.97609	−	6.61954i	0.492900	−	0.545970i
$148$		0			0
$149$	−9.95454	−	17.2418i	−0.815508	−	1.41250i	−0.908963	−	0.416878i	$-0.863124\pi$
$149$	−9.95454	−	17.2418i	−0.815508	−	1.41250i	0.0934545	−	0.995624i	$-0.470209\pi$
$150$		0			0
$151$	−11.0689	+	19.1720i	−0.900778	+	1.56019i	−0.0742911	+	0.997237i	$0.523669\pi$
$151$	−11.0689	+	19.1720i	−0.900778	+	1.56019i	−0.826487	+	0.562956i	$0.809664\pi$
$152$		0			0
$153$	−10.4550			−0.845234
$154$		0			0
$155$	7.49039			0.601642
$156$		0			0
$157$	−6.37471	+	11.0413i	−0.508757	+	0.881193i	0.491192	+	0.871052i	$0.336561\pi$
$157$	−6.37471	+	11.0413i	−0.508757	+	0.881193i	−0.999949	+	0.0101413i	$0.996772\pi$
$158$		0			0
$159$	−4.53167	−	7.84909i	−0.359385	−	0.622473i
$160$		0			0
$161$	1.07453	+	2.41772i	0.0846848	+	0.190543i
$162$		0			0
$163$	−9.94055	−	17.2175i	−0.778604	−	1.34858i	−0.932747	−	0.360533i	$-0.882595\pi$
$163$	−9.94055	−	17.2175i	−0.778604	−	1.34858i	0.154143	−	0.988049i	$-0.450738\pi$
$164$		0			0
$165$	−4.21973	+	7.30879i	−0.328506	+	0.568988i
$166$		0			0
$167$	5.23512			0.405106			0.202553	−	0.979271i	$-0.435076\pi$
$167$	5.23512			0.405106			0.202553	+	0.979271i	$0.435076\pi$
$168$		0			0
$169$	−2.44130			−0.187792
$170$		0			0
$171$	2.83310	−	4.90708i	0.216653	−	0.375253i
$172$		0			0
$173$	−2.80216	−	4.85348i	−0.213044	−	0.369003i	0.739622	−	0.673023i	$-0.235005\pi$
$173$	−2.80216	−	4.85348i	−0.213044	−	0.369003i	−0.952666	+	0.304020i	$0.901671\pi$
$174$		0			0
$175$	4.62537	−	6.35745i	0.349645	−	0.480578i
$176$		0			0
$177$	−6.82701	−	11.8247i	−0.513150	−	0.888801i
$178$		0			0
$179$	5.49200	−	9.51242i	0.410491	−	0.710992i	−0.584452	−	0.811428i	$-0.698691\pi$
$179$	5.49200	−	9.51242i	0.410491	−	0.710992i	0.994943	+	0.100436i	$0.0320239\pi$
$180$		0			0
$181$	−8.36002			−0.621395			−0.310698	−	0.950509i	$-0.600563\pi$
$181$	−8.36002			−0.621395			−0.310698	+	0.950509i	$0.600563\pi$
$182$		0			0
$183$	−2.87831			−0.212771
$184$		0			0
$185$	−0.193629	+	0.335376i	−0.0142359	+	0.0246573i
$186$		0			0
$187$	−17.6584	−	30.5853i	−1.29131	−	2.23662i
$188$		0			0
$189$	14.6714	+	1.55182i	1.06719	+	0.112878i
$190$		0			0
$191$	−2.89175	−	5.00866i	−0.209240	−	0.362414i	0.742236	−	0.670139i	$-0.233766\pi$
$191$	−2.89175	−	5.00866i	−0.209240	−	0.362414i	−0.951475	+	0.307725i	$0.900432\pi$
$192$		0			0
$193$	10.1878	−	17.6457i	0.733331	−	1.27017i	−0.222121	−	0.975019i	$-0.571298\pi$
$193$	10.1878	−	17.6457i	0.733331	−	1.27017i	0.955452	−	0.295147i	$-0.0953686\pi$
$194$		0			0
$195$	5.89602			0.422223
$196$		0			0
$197$	−15.2117			−1.08379			−0.541894	−	0.840447i	$-0.682293\pi$
$197$	−15.2117			−1.08379			−0.541894	+	0.840447i	$0.682293\pi$
$198$		0			0
$199$	−5.74995	+	9.95921i	−0.407603	+	0.705990i	−0.994621	−	0.103585i	$-0.966969\pi$
$199$	−5.74995	+	9.95921i	−0.407603	+	0.705990i	0.587017	+	0.809574i	$0.300302\pi$
$200$		0			0
$201$	−4.83293	−	8.37089i	−0.340889	−	0.590437i
$202$		0			0
$203$	−8.48963	−	0.897959i	−0.595855	−	0.0630244i
$204$		0			0
$205$	4.07194	+	7.05280i	0.284396	+	0.492589i
$206$		0			0
$207$	−0.688449	+	1.19243i	−0.0478505	+	0.0828795i
$208$		0			0
$209$	19.1404			1.32397
$210$		0			0
$211$	−12.6486			−0.870765			−0.435382	−	0.900246i	$-0.643387\pi$
$211$	−12.6486			−0.870765			−0.435382	+	0.900246i	$0.643387\pi$
$212$		0			0
$213$	3.64260	−	6.30917i	0.249587	−	0.432297i
$214$		0			0
$215$	−5.19133	−	8.99164i	−0.354046	−	0.613225i
$216$		0			0
$217$	8.18625	−	11.2518i	0.555719	−	0.763821i
$218$		0			0
$219$	4.41372	+	7.64479i	0.298252	+	0.516587i
$220$		0			0
$221$	−12.3366	+	21.3676i	−0.829850	+	1.43734i
$222$		0			0
$223$	20.3730			1.36428			0.682138	−	0.731223i	$-0.261050\pi$
$223$	20.3730			1.36428			0.682138	+	0.731223i	$0.261050\pi$
$224$		0			0
$225$	4.09154			0.272769
$226$		0			0
$227$	−5.57037	+	9.64817i	−0.369719	+	0.640372i	−0.989521	−	0.144386i	$-0.953879\pi$
$227$	−5.57037	+	9.64817i	−0.369719	+	0.640372i	0.619803	+	0.784758i	$0.287213\pi$
$228$		0			0
$229$	11.0611	+	19.1584i	0.730939	+	1.26602i	0.956482	+	0.291790i	$0.0942507\pi$
$229$	11.0611	+	19.1584i	0.730939	+	1.26602i	−0.225544	+	0.974233i	$0.572416\pi$
$230$		0			0
$231$	6.36725	+	14.3265i	0.418934	+	0.942615i
$232$		0			0
$233$	10.6849	+	18.5069i	0.699994	+	1.21242i	0.968468	+	0.249138i	$0.0801473\pi$
$233$	10.6849	+	18.5069i	0.699994	+	1.21242i	−0.268474	+	0.963287i	$0.586519\pi$
$234$		0			0
$235$	3.15695	−	5.46799i	0.205936	−	0.356692i
$236$		0			0
$237$	−5.91247			−0.384056
$238$		0			0
$239$	−7.67232			−0.496281			−0.248141	−	0.968724i	$-0.579820\pi$
$239$	−7.67232			−0.496281			−0.248141	+	0.968724i	$0.579820\pi$
$240$		0			0
$241$	9.94969	−	17.2334i	0.640916	−	1.11010i	−0.344313	−	0.938855i	$-0.611888\pi$
$241$	9.94969	−	17.2334i	0.640916	−	1.11010i	0.985229	−	0.171244i	$-0.0547785\pi$
$242$		0			0
$243$	6.47021	+	11.2067i	0.415064	+	0.718912i
$244$		0			0
$245$	3.06827	+	9.48574i	0.196025	+	0.606021i
$246$		0			0
$247$	−6.68599	−	11.5805i	−0.425419	−	0.736848i
$248$		0			0
$249$	1.00109	−	1.73394i	0.0634417	−	0.109884i
$250$		0			0
$251$	−10.6761			−0.673868			−0.336934	−	0.941528i	$-0.609390\pi$
$251$	−10.6761			−0.673868			−0.336934	+	0.941528i	$0.609390\pi$
$252$		0			0
$253$	−4.65116			−0.292416
$254$		0			0
$255$	−6.88881	+	11.9318i	−0.431394	+	0.747197i
$256$		0			0
$257$	10.6141	+	18.3842i	0.662092	+	1.14678i	0.980065	+	0.198677i	$0.0636644\pi$
$257$	10.6141	+	18.3842i	0.662092	+	1.14678i	−0.317973	+	0.948100i	$0.603002\pi$
$258$		0			0
$259$	0.292172	+	0.657396i	0.0181547	+	0.0408486i
$260$		0			0
$261$	−2.22140	−	3.84758i	−0.137501	−	0.238159i
$262$		0			0
$263$	10.1754	−	17.6243i	0.627440	−	1.08676i	−0.360623	−	0.932711i	$-0.617436\pi$
$263$	10.1754	−	17.6243i	0.627440	−	1.08676i	0.988064	−	0.154047i	$-0.0492306\pi$
$264$		0			0
$265$	10.1320			0.622406
$266$		0			0
$267$	−5.77426			−0.353379
$268$		0			0
$269$	3.08104	−	5.33652i	0.187854	−	0.325373i	−0.756680	−	0.653785i	$-0.773180\pi$
$269$	3.08104	−	5.33652i	0.187854	−	0.325373i	0.944535	+	0.328412i	$0.106513\pi$
$270$		0			0
$271$	−4.77830	−	8.27625i	−0.290261	−	0.502746i	0.683611	−	0.729847i	$-0.260409\pi$
$271$	−4.77830	−	8.27625i	−0.290261	−	0.502746i	−0.973871	+	0.227101i	$0.927075\pi$
$272$		0			0
$273$	6.44377	−	8.85679i	0.389995	−	0.536037i
$274$		0			0
$275$	6.91060	+	11.9695i	0.416725	+	0.721789i
$276$		0			0
$277$	−11.0104	+	19.0706i	−0.661553	+	1.14584i	0.318654	+	0.947871i	$0.396769\pi$
$277$	−11.0104	+	19.0706i	−0.661553	+	1.14584i	−0.980208	+	0.197973i	$0.936564\pi$
$278$		0			0
$279$	7.24144			0.433534
$280$		0			0
$281$	18.8771			1.12611			0.563057	−	0.826418i	$-0.309625\pi$
$281$	18.8771			1.12611			0.563057	+	0.826418i	$0.309625\pi$
$282$		0			0
$283$	6.83994	−	11.8471i	0.406592	−	0.704239i	−0.587913	−	0.808924i	$-0.700050\pi$
$283$	6.83994	−	11.8471i	0.406592	−	0.704239i	0.994505	+	0.104685i	$0.0333836\pi$
$284$		0			0
$285$	−3.73348	−	6.46658i	−0.221152	−	0.383047i
$286$		0			0
$287$	15.0447	+	1.59130i	0.888060	+	0.0939313i
$288$		0			0
$289$	−20.3278	−	35.2087i	−1.19575	−	2.07110i
$290$		0			0
$291$	−6.95876	+	12.0529i	−0.407930	+	0.706555i
$292$		0			0
$293$	17.5344			1.02437			0.512187	−	0.858874i	$-0.328836\pi$
$293$	17.5344			1.02437			0.512187	+	0.858874i	$0.328836\pi$
$294$		0			0
$295$	15.2640			0.888705
$296$		0			0
$297$	−12.9679	+	22.4611i	−0.752475	+	1.30332i
$298$		0			0
$299$	1.62471	+	2.81408i	0.0939593	+	0.162742i
$300$		0			0
$301$	−19.1805	−	2.02875i	−1.10555	−	0.116935i
$302$		0			0
$303$	6.22415	+	10.7805i	0.357568	+	0.619326i
$304$		0			0
$305$	1.60885	−	2.78661i	0.0921225	−	0.159561i
$306$		0			0
$307$	8.48554			0.484295			0.242148	−	0.970239i	$-0.422148\pi$
$307$	8.48554			0.484295			0.242148	+	0.970239i	$0.422148\pi$
$308$		0			0
$309$	−0.625619			−0.0355902
$310$		0			0
$311$	−13.9539	+	24.1689i	−0.791254	+	1.37049i	0.133937	+	0.990990i	$0.457238\pi$
$311$	−13.9539	+	24.1689i	−0.791254	+	1.37049i	−0.925191	+	0.379502i	$0.876095\pi$
$312$		0			0
$313$	15.8892	+	27.5209i	0.898112	+	1.55557i	0.829906	+	0.557904i	$0.188394\pi$
$313$	15.8892	+	27.5209i	0.898112	+	1.55557i	0.0682057	+	0.997671i	$0.478273\pi$
$314$		0			0
$315$	−3.05242	+	4.19547i	−0.171984	+	0.236388i
$316$		0			0
$317$	−0.817767	−	1.41641i	−0.0459304	−	0.0795537i	0.842146	−	0.539249i	$-0.181292\pi$
$317$	−0.817767	−	1.41641i	−0.0459304	−	0.0795537i	−0.888077	+	0.459695i	$0.847959\pi$
$318$		0			0
$319$	7.50389	−	12.9971i	0.420137	−	0.727699i
$320$		0			0
$321$	−24.8796			−1.38864
$322$		0			0
$323$	31.2472			1.73864
$324$		0			0
$325$	4.82792	−	8.36220i	0.267805	−	0.463852i
$326$		0			0
$327$	6.83174	+	11.8329i	0.377796	+	0.654362i
$328$		0			0
$329$	−4.76359	−	10.7182i	−0.262625	−	0.590915i
$330$		0			0
$331$	−8.58602	−	14.8714i	−0.471930	−	0.817407i	0.527554	−	0.849521i	$-0.323109\pi$
$331$	−8.58602	−	14.8714i	−0.471930	−	0.817407i	−0.999484	+	0.0321144i	$0.989776\pi$
$332$		0			0
$333$	−0.187194	+	0.324230i	−0.0102582	+	0.0177677i
$334$		0			0
$335$	10.8056			0.590373
$336$		0			0
$337$	1.63107			0.0888502			0.0444251	−	0.999013i	$-0.485854\pi$
$337$	1.63107			0.0888502			0.0444251	+	0.999013i	$0.485854\pi$
$338$		0			0
$339$	−7.00778	+	12.1378i	−0.380610	+	0.659236i
$340$		0			0
$341$	12.2308	+	21.1843i	0.662334	+	1.14720i
$342$		0			0
$343$	17.6025	+	5.75793i	0.950443	+	0.310899i
$344$		0			0
$345$	0.907243	+	1.57139i	0.0488443	+	0.0846009i
$346$		0			0
$347$	2.65451	−	4.59775i	0.142502	−	0.246820i	−0.785936	−	0.618307i	$-0.787819\pi$
$347$	2.65451	−	4.59775i	0.142502	−	0.246820i	0.928438	+	0.371487i	$0.121152\pi$
$348$		0			0
$349$	21.1576			1.13254			0.566270	−	0.824220i	$-0.308386\pi$
$349$	21.1576			1.13254			0.566270	+	0.824220i	$0.308386\pi$
$350$		0			0
$351$	18.1194			0.967144
$352$		0			0
$353$	−9.32034	+	16.1433i	−0.496072	+	0.859221i	−0.999990	−	0.00453008i	$-0.998558\pi$
$353$	−9.32034	+	16.1433i	−0.496072	+	0.859221i	0.503918	+	0.863751i	$0.331891\pi$
$354$		0			0
$355$	4.07211	+	7.05311i	0.216125	+	0.374340i
$356$		0			0
$357$	10.3947	+	23.3884i	0.550145	+	1.23784i
$358$		0			0
$359$	11.5714	+	20.0423i	0.610717	+	1.05779i	0.991120	+	0.132972i	$0.0424521\pi$
$359$	11.5714	+	20.0423i	0.610717	+	1.05779i	−0.380403	+	0.924821i	$0.624215\pi$
$360$		0			0
$361$	1.03259	−	1.78850i	0.0543468	−	0.0941314i
$362$		0			0
$363$	−13.5469			−0.711027
$364$		0			0
$365$	−9.86831			−0.516531
$366$		0			0
$367$	−8.19393	+	14.1923i	−0.427720	+	0.740832i	−0.996670	−	0.0815396i	$-0.974016\pi$
$367$	−8.19393	+	14.1923i	−0.427720	+	0.740832i	0.568950	+	0.822372i	$0.307350\pi$
$368$		0			0
$369$	3.93661	+	6.81840i	0.204931	+	0.354952i
$370$		0			0
$371$	11.0733	−	15.2200i	0.574898	−	0.790182i
$372$		0			0
$373$	−4.41059	−	7.63936i	−0.228372	−	0.395551i	0.728954	−	0.684563i	$-0.240007\pi$
$373$	−4.41059	−	7.63936i	−0.228372	−	0.395551i	−0.957326	+	0.289011i	$0.906673\pi$
$374$		0			0
$375$	7.23215	−	12.5264i	0.373466	−	0.646863i
$376$		0			0
$377$	−10.4848			−0.539995
$378$		0			0
$379$	−17.1951			−0.883254			−0.441627	−	0.897199i	$-0.645598\pi$
$379$	−17.1951			−0.883254			−0.441627	+	0.897199i	$0.645598\pi$
$380$		0			0
$381$	9.48833	−	16.4343i	0.486102	−	0.841953i
$382$		0			0
$383$	−1.70283	−	2.94939i	−0.0870107	−	0.150707i	0.819236	−	0.573457i	$-0.194398\pi$
$383$	−1.70283	−	2.94939i	−0.0870107	−	0.150707i	−0.906246	+	0.422750i	$0.861065\pi$
$384$		0			0
$385$	−17.4291	−	1.84350i	−0.888269	−	0.0939534i
$386$		0			0
$387$	−5.01880	−	8.69281i	−0.255120	−	0.441880i
$388$		0			0
$389$	11.7762	−	20.3969i	0.597075	−	1.03416i	−0.396175	−	0.918175i	$-0.629663\pi$
$389$	11.7762	−	20.3969i	0.597075	−	1.03416i	0.993250	−	0.115990i	$-0.0370040\pi$
$390$		0			0
$391$	−7.59313			−0.384001
$392$		0			0
$393$	18.8880			0.952773
$394$		0			0
$395$	3.30481	−	5.72410i	0.166283	−	0.288011i
$396$		0			0
$397$	−12.6686	−	21.9426i	−0.635817	−	1.10127i	−0.986341	−	0.164713i	$-0.947330\pi$
$397$	−12.6686	−	21.9426i	−0.635817	−	1.10127i	0.350525	−	0.936553i	$-0.386003\pi$
$398$		0			0
$399$	−13.7942	−	1.45903i	−0.690574	−	0.0730429i
$400$		0			0
$401$	−0.872042	−	1.51042i	−0.0435477	−	0.0754268i	0.843430	−	0.537239i	$-0.180533\pi$
$401$	−0.872042	−	1.51042i	−0.0435477	−	0.0754268i	−0.886978	+	0.461812i	$0.847199\pi$
$402$		0			0
$403$	8.54474	−	14.7999i	0.425644	−	0.737236i
$404$		0			0
$405$	4.23489			0.210434
$406$		0			0
$407$	−1.26468			−0.0626880
$408$		0			0
$409$	−9.24271	+	16.0088i	−0.457022	+	0.791586i	−0.998802	−	0.0489346i	$-0.984417\pi$
$409$	−9.24271	+	16.0088i	−0.457022	+	0.791586i	0.541780	+	0.840521i	$0.317751\pi$
$410$		0			0
$411$	−0.365658	−	0.633339i	−0.0180366	−	0.0312403i
$412$		0			0
$413$	16.6821	−	22.9291i	0.820870	−	1.12826i
$414$		0			0
$415$	1.11913	+	1.93840i	0.0549361	+	0.0951522i
$416$		0			0
$417$	9.42278	−	16.3207i	0.461435	−	0.799230i
$418$		0			0
$419$	−7.09780			−0.346750			−0.173375	−	0.984856i	$-0.555467\pi$
$419$	−7.09780			−0.346750			−0.173375	+	0.984856i	$0.555467\pi$
$420$		0			0
$421$	35.7638			1.74302			0.871509	−	0.490379i	$-0.163142\pi$
$421$	35.7638			1.74302			0.871509	+	0.490379i	$0.163142\pi$
$422$		0			0
$423$	3.05202	−	5.28626i	0.148395	−	0.257027i
$424$		0			0
$425$	11.2817	+	19.5405i	0.547244	+	0.947854i
$426$		0			0
$427$	−2.42763	−	5.46225i	−0.117481	−	0.264337i
$428$		0			0
$429$	9.62740	+	16.6752i	0.464815	+	0.805084i
$430$		0			0
$431$	−7.60575	+	13.1736i	−0.366356	+	0.634548i	−0.988993	−	0.147963i	$-0.952728\pi$
$431$	−7.60575	+	13.1736i	−0.366356	+	0.634548i	0.622637	+	0.782511i	$0.286062\pi$
$432$		0			0
$433$	37.5734			1.80566			0.902832	−	0.429994i	$-0.141484\pi$
$433$	37.5734			1.80566			0.902832	+	0.429994i	$0.141484\pi$
$434$		0			0
$435$	−5.85476			−0.280714
$436$		0			0
$437$	2.05760	−	3.56386i	0.0984282	−	0.170483i
$438$		0			0
$439$	−17.3884	−	30.1175i	−0.829901	−	1.43743i	−0.898115	−	0.439760i	$-0.855063\pi$
$439$	−17.3884	−	30.1175i	−0.829901	−	1.43743i	0.0682140	−	0.997671i	$-0.478270\pi$
$440$		0			0
$441$	2.96630	+	9.17048i	0.141252	+	0.436689i
$442$		0			0
$443$	−19.1758	−	33.2135i	−0.911070	−	1.57802i	−0.812555	−	0.582884i	$-0.801924\pi$
$443$	−19.1758	−	33.2135i	−0.911070	−	1.57802i	−0.0985145	−	0.995136i	$-0.531409\pi$
$444$		0			0
$445$	3.22756	−	5.59029i	0.153001	−	0.265005i
$446$		0			0
$447$	−25.3644			−1.19969
$448$		0			0
$449$	−20.3334			−0.959590			−0.479795	−	0.877381i	$-0.659289\pi$
$449$	−20.3334			−0.959590			−0.479795	+	0.877381i	$0.659289\pi$
$450$		0			0
$451$	−13.2978	+	23.0325i	−0.626171	+	1.08456i
$452$		0			0
$453$	14.1019	+	24.4253i	0.662567	+	1.14760i
$454$		0			0
$455$	4.97284	+	11.1890i	0.233130	+	0.524550i
$456$		0			0
$457$	9.53438	+	16.5140i	0.445999	+	0.772493i	0.998121	−	0.0612699i	$-0.0195150\pi$
$457$	9.53438	+	16.5140i	0.445999	+	0.772493i	−0.552122	+	0.833763i	$0.686182\pi$
$458$		0			0
$459$	−21.1704	+	36.6683i	−0.988152	+	1.71153i
$460$		0			0
$461$	−24.2284			−1.12843			−0.564215	−	0.825628i	$-0.690821\pi$
$461$	−24.2284			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$462$		0			0
$463$	4.58742			0.213195			0.106598	−	0.994302i	$-0.466004\pi$
$463$	4.58742			0.213195			0.106598	+	0.994302i	$0.466004\pi$
$464$		0			0
$465$	4.77141	−	8.26433i	0.221269	−	0.383249i
$466$		0			0
$467$	−11.7709	−	20.3878i	−0.544693	−	0.943437i	−0.998626	−	0.0524008i	$-0.983313\pi$
$467$	−11.7709	−	20.3878i	−0.544693	−	0.943437i	0.453933	−	0.891036i	$-0.350021\pi$
$468$		0			0
$469$	11.8095	−	16.2318i	0.545310	−	0.749514i
$470$		0			0
$471$	8.12144	+	14.0667i	0.374216	+	0.648161i
$472$		0			0
$473$	16.9535	−	29.3643i	0.779521	−	1.35017i
$474$		0			0
$475$	−12.2286			−0.561085
$476$		0			0
$477$	9.79529			0.448496
$478$		0			0
$479$	−15.1175	+	26.1844i	−0.690738	+	1.19639i	0.280858	+	0.959749i	$0.409381\pi$
$479$	−15.1175	+	26.1844i	−0.690738	+	1.19639i	−0.971596	+	0.236645i	$0.923952\pi$
$480$		0			0
$481$	0.441770	+	0.765167i	0.0201430	+	0.0348886i
$482$		0			0
$483$	3.35202	+	0.354547i	0.152522	+	0.0161325i
$484$		0			0
$485$	−7.77929	−	13.4741i	−0.353239	−	0.611828i
$486$		0			0
$487$	−15.3581	+	26.6009i	−0.695940	+	1.20540i	0.273923	+	0.961752i	$0.411679\pi$
$487$	−15.3581	+	26.6009i	−0.695940	+	1.20540i	−0.969863	+	0.243652i	$0.921655\pi$
$488$		0			0
$489$	−25.3287			−1.14540
$490$		0			0
$491$	9.34097			0.421552			0.210776	−	0.977534i	$-0.432401\pi$
$491$	9.34097			0.421552			0.210776	+	0.977534i	$0.432401\pi$
$492$		0			0
$493$	12.2503	−	21.2181i	0.551725	−	0.955615i
$494$		0			0
$495$	−4.56051	−	7.89904i	−0.204980	−	0.355035i
$496$		0			0
$497$	15.0453	+	1.59137i	0.674876	+	0.0713825i
$498$		0			0
$499$	−6.93622	−	12.0139i	−0.310508	−	0.537815i	0.667965	−	0.744193i	$-0.267166\pi$
$499$	−6.93622	−	12.0139i	−0.310508	−	0.537815i	−0.978472	+	0.206378i	$0.933832\pi$
$500$		0			0
$501$	3.33480	−	5.77604i	0.148988	−	0.258055i
$502$		0			0
$503$	−14.0254			−0.625364			−0.312682	−	0.949858i	$-0.601227\pi$
$503$	−14.0254			−0.625364			−0.312682	+	0.949858i	$0.601227\pi$
$504$		0			0
$505$	−13.9161			−0.619259
$506$		0			0
$507$	−1.55512	+	2.69355i	−0.0690653	+	0.119625i
$508$		0			0
$509$	−10.3604	−	17.9447i	−0.459215	−	0.795384i	0.539704	−	0.841855i	$-0.318536\pi$
$509$	−10.3604	−	17.9447i	−0.459215	−	0.795384i	−0.998920	+	0.0464705i	$0.985203\pi$
$510$		0			0
$511$	−10.7851	+	14.8238i	−0.477104	+	0.655767i
$512$		0			0
$513$	−11.4736	−	19.8729i	−0.506572	−	0.877408i
$514$		0			0
$515$	0.349694	−	0.605687i	0.0154093	−	0.0266898i
$516$		0			0
$517$	20.6195			0.906843
$518$		0			0
$519$	−7.13996			−0.313409
$520$		0			0
$521$	11.0974	−	19.2213i	0.486187	−	0.842101i	−0.513687	−	0.857978i	$-0.671721\pi$
$521$	11.0974	−	19.2213i	0.486187	−	0.842101i	0.999874	+	0.0158767i	$0.00505392\pi$
$522$		0			0
$523$	−17.0468	−	29.5259i	−0.745403	−	1.29108i	−0.950006	−	0.312231i	$-0.898924\pi$
$523$	−17.0468	−	29.5259i	−0.745403	−	1.29108i	0.204603	−	0.978845i	$-0.434410\pi$
$524$		0			0
$525$	−4.06795	−	9.15302i	−0.177540	−	0.399470i
$526$		0			0
$527$	19.9671	+	34.5839i	0.869778	+	1.50650i
$528$		0			0
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$		0			0
$531$	14.7567			0.640387
$532$		0			0
$533$	18.5804			0.804807
$534$		0			0
$535$	13.9066	−	24.0870i	0.601235	−	1.04137i
$536$		0			0
$537$	−6.99686	−	12.1189i	−0.301937	−	0.522970i
$538$		0			0
$539$	−21.8175	+	24.1666i	−0.939747	+	1.04093i
$540$		0			0
$541$	17.1596	+	29.7214i	0.737751	+	1.27782i	0.953506	+	0.301374i	$0.0974453\pi$
$541$	17.1596	+	29.7214i	0.737751	+	1.27782i	−0.215755	+	0.976447i	$0.569221\pi$
$542$		0			0
$543$	−5.32537	+	9.22382i	−0.228534	+	0.395832i
$544$		0			0
$545$	−15.2746			−0.654291
$546$		0			0
$547$	−9.69572			−0.414559			−0.207279	−	0.978282i	$-0.566461\pi$
$547$	−9.69572			−0.414559			−0.207279	+	0.978282i	$0.566461\pi$
$548$		0			0
$549$	1.55538	−	2.69400i	0.0663820	−	0.114977i
$550$		0			0
$551$	6.63920	+	11.4994i	0.282839	+	0.489892i
$552$		0			0
$553$	−4.98671	−	11.2203i	−0.212057	−	0.477134i
$554$		0			0
$555$	0.246686	+	0.427272i	0.0104712	+	0.0181367i
$556$		0			0
$557$	−18.5544	+	32.1372i	−0.786177	+	1.36170i	0.142117	+	0.989850i	$0.454609\pi$
$557$	−18.5544	+	32.1372i	−0.786177	+	1.36170i	−0.928294	+	0.371848i	$0.878724\pi$
$558$		0			0
$559$	−23.6882			−1.00191
$560$		0			0
$561$	−44.9940			−1.89965
$562$		0			0
$563$	2.09927	−	3.63605i	0.0884738	−	0.153241i	−0.818392	−	0.574660i	$-0.805134\pi$
$563$	2.09927	−	3.63605i	0.0884738	−	0.153241i	0.906866	+	0.421419i	$0.138468\pi$
$564$		0			0
$565$	−7.83409	−	13.5690i	−0.329583	−	0.570854i
$566$		0			0
$567$	4.62832	−	6.36151i	0.194371	−	0.267158i
$568$		0			0
$569$	−5.81173	−	10.0662i	−0.243640	−	0.421998i	0.718108	−	0.695932i	$-0.245008\pi$
$569$	−5.81173	−	10.0662i	−0.243640	−	0.421998i	−0.961748	+	0.273934i	$0.911675\pi$
$570$		0			0
$571$	−0.764163	+	1.32357i	−0.0319792	+	0.0553896i	−0.881572	−	0.472049i	$-0.843514\pi$
$571$	−0.764163	+	1.32357i	−0.0319792	+	0.0553896i	0.849593	+	0.527439i	$0.176848\pi$
$572$		0			0
$573$	−7.36824			−0.307813
$574$		0			0
$575$	2.97156			0.123923
$576$		0			0
$577$	10.9529	−	18.9709i	0.455974	−	0.789771i	−0.542769	−	0.839882i	$-0.682624\pi$
$577$	10.9529	−	18.9709i	0.455974	−	0.789771i	0.998744	+	0.0501111i	$0.0159575\pi$
$578$		0			0
$579$	−12.9793	−	22.4808i	−0.539402	−	0.934271i
$580$		0			0
$581$	4.13490	+	0.437354i	0.171544	+	0.0181445i
$582$		0			0
$583$	16.5442	+	28.6555i	0.685192	+	1.18679i
$584$		0			0
$585$	−3.18609	+	5.51847i	−0.131729	+	0.228161i
$586$		0			0
$587$	−9.49156			−0.391759			−0.195879	−	0.980628i	$-0.562756\pi$
$587$	−9.49156			−0.391759			−0.195879	+	0.980628i	$0.562756\pi$
$588$		0			0
$589$	−21.6428			−0.891777
$590$		0			0
$591$	−9.68992	+	16.7834i	−0.398590	+	0.690378i
$592$		0			0
$593$	0.477618	+	0.827259i	0.0196134	+	0.0339715i	0.875666	−	0.482918i	$-0.160423\pi$
$593$	0.477618	+	0.827259i	0.0196134	+	0.0339715i	−0.856052	+	0.516890i	$0.827090\pi$
$594$		0			0
$595$	−28.4534	−	3.00956i	−1.16648	−	0.123380i
$596$		0			0
$597$	7.32550	+	12.6881i	0.299813	+	0.519291i
$598$		0			0
$599$	−7.40168	+	12.8201i	−0.302424	+	0.523814i	−0.976685	−	0.214680i	$-0.931129\pi$
$599$	−7.40168	+	12.8201i	−0.302424	+	0.523814i	0.674260	+	0.738494i	$0.264463\pi$
$600$		0			0
$601$	−4.78554			−0.195206			−0.0976032	−	0.995225i	$-0.531118\pi$
$601$	−4.78554			−0.195206			−0.0976032	+	0.995225i	$0.531118\pi$
$602$		0			0
$603$	10.4465			0.425413
$604$		0			0
$605$	7.57212	−	13.1153i	0.307850	−	0.533212i
$606$		0			0
$607$	−17.1632	−	29.7275i	−0.696632	−	1.20660i	−0.969627	−	0.244587i	$-0.921348\pi$
$607$	−17.1632	−	29.7275i	−0.696632	−	1.20660i	0.272995	−	0.962015i	$-0.411986\pi$
$608$		0			0
$609$	−6.39868	+	8.79481i	−0.259287	+	0.356384i
$610$		0			0
$611$	−7.20264	−	12.4753i	−0.291387	−	0.504698i
$612$		0			0
$613$	13.7383	−	23.7954i	0.554885	−	0.961088i	−0.443028	−	0.896508i	$-0.646096\pi$
$613$	13.7383	−	23.7954i	0.554885	−	0.961088i	0.997913	−	0.0645805i	$-0.0205709\pi$
$614$		0			0
$615$	10.3754			0.418375
$616$		0			0
$617$	−38.2112			−1.53833			−0.769163	−	0.639053i	$-0.779327\pi$
$617$	−38.2112			−1.53833			−0.769163	+	0.639053i	$0.779327\pi$
$618$		0			0
$619$	3.93863	−	6.82191i	0.158307	−	0.274196i	−0.775951	−	0.630793i	$-0.782730\pi$
$619$	3.93863	−	6.82191i	0.158307	−	0.274196i	0.934258	+	0.356597i	$0.116063\pi$
$620$		0			0
$621$	2.78811	+	4.82914i	0.111883	+	0.193787i
$622$		0			0
$623$	−4.87014	−	10.9580i	−0.195118	−	0.439022i
$624$		0			0
$625$	0.656004	+	1.13623i	0.0262402	+	0.0454493i
$626$		0			0
$627$	12.1925	−	21.1181i	0.486923	−	0.843376i
$628$		0			0
$629$	−2.06462			−0.0823220
$630$		0			0
$631$	−39.0102			−1.55297			−0.776485	−	0.630136i	$-0.782999\pi$
$631$	−39.0102			−1.55297			−0.776485	+	0.630136i	$0.782999\pi$
$632$		0			0
$633$	−8.05722	+	13.9555i	−0.320246	+	0.554682i
$634$		0			0
$635$	10.6071	+	18.3721i	0.420931	+	0.729074i
$636$		0			0
$637$	22.2426	+	4.75850i	0.881284	+	0.188538i
$638$		0			0
$639$	3.93678	+	6.81870i	0.155736	+	0.269743i
$640$		0			0
$641$	5.43281	−	9.40990i	0.214583	−	0.371669i	−0.738561	−	0.674187i	$-0.764494\pi$
$641$	5.43281	−	9.40990i	0.214583	−	0.371669i	0.953143	+	0.302519i	$0.0978274\pi$
$642$		0			0
$643$	41.0117			1.61734			0.808672	−	0.588260i	$-0.200187\pi$
$643$	41.0117			1.61734			0.808672	+	0.588260i	$0.200187\pi$
$644$		0			0
$645$	−13.2276			−0.520837
$646$		0			0
$647$	−7.10375	+	12.3041i	−0.279277	+	0.483723i	−0.971205	−	0.238244i	$-0.923428\pi$
$647$	−7.10375	+	12.3041i	−0.279277	+	0.483723i	0.691928	+	0.721967i	$0.256762\pi$
$648$		0			0
$649$	24.9241	+	43.1697i	0.978355	+	1.69456i
$650$		0			0
$651$	−7.19970	−	16.1995i	−0.282178	−	0.634910i
$652$		0			0
$653$	−16.3592	−	28.3349i	−0.640184	−	1.10883i	−0.985391	−	0.170304i	$-0.945525\pi$
$653$	−16.3592	−	28.3349i	−0.640184	−	1.10883i	0.345208	−	0.938526i	$-0.387808\pi$
$654$		0			0
$655$	−10.5576	+	18.2862i	−0.412518	+	0.714502i
$656$		0			0
$657$	−9.54034			−0.372204
$658$		0			0
$659$	21.0854			0.821372			0.410686	−	0.911777i	$-0.365289\pi$
$659$	21.0854			0.821372			0.410686	+	0.911777i	$0.365289\pi$
$660$		0			0
$661$	5.51658	−	9.55499i	0.214570	−	0.371646i	−0.738570	−	0.674177i	$-0.764498\pi$
$661$	5.51658	−	9.55499i	0.214570	−	0.371646i	0.953139	+	0.302531i	$0.0978317\pi$
$662$		0			0
$663$	15.7170	+	27.2226i	0.610396	+	1.05724i
$664$		0			0
$665$	9.12290	−	12.5392i	0.353771	−	0.486249i
$666$		0			0
$667$	−1.61334	−	2.79438i	−0.0624687	−	0.108199i
$668$		0			0
$669$	12.9777	−	22.4780i	0.501747	−	0.869051i
$670$		0			0
$671$	10.5081			0.405662
$672$		0			0
$673$	7.37261			0.284193			0.142097	−	0.989853i	$-0.454616\pi$
$673$	7.37261			0.284193			0.142097	+	0.989853i	$0.454616\pi$
$674$		0			0
$675$	8.28503	−	14.3501i	0.318891	−	0.552335i
$676$		0			0
$677$	−12.2604	−	21.2357i	−0.471206	−	0.816153i	0.528251	−	0.849088i	$-0.322848\pi$
$677$	−12.2604	−	21.2357i	−0.471206	−	0.816153i	−0.999458	+	0.0329348i	$0.989515\pi$
$678$		0			0
$679$	−28.7423	−	3.04012i	−1.10303	−	0.116669i
$680$		0			0
$681$	7.09671	+	12.2919i	0.271947	+	0.471025i
$682$		0			0
$683$	−5.88293	+	10.1895i	−0.225104	+	0.389892i	−0.956351	−	0.292221i	$-0.905606\pi$
$683$	−5.88293	+	10.1895i	−0.225104	+	0.389892i	0.731246	+	0.682113i	$0.238939\pi$
$684$		0			0
$685$	0.817548			0.0312369
$686$		0			0
$687$	28.1839			1.07528
$688$		0			0
$689$	11.5582	−	20.0194i	0.440333	−	0.762679i
$690$		0			0
$691$	−5.45661	−	9.45113i	−0.207579	−	0.359538i	0.743372	−	0.668878i	$-0.233225\pi$
$691$	−5.45661	−	9.45113i	−0.207579	−	0.359538i	−0.950951	+	0.309340i	$0.899892\pi$
$692$		0			0
$693$	−16.8498	−	1.78223i	−0.640073	−	0.0677014i
$694$		0			0
$695$	10.5338	+	18.2452i	0.399571	+	0.692078i
$696$		0			0
$697$	−21.7090	+	37.6012i	−0.822289	+	1.42425i
$698$		0			0
$699$	27.2254			1.02976
$700$		0			0
$701$	−33.4930			−1.26501			−0.632506	−	0.774555i	$-0.717974\pi$
$701$	−33.4930			−1.26501			−0.632506	+	0.774555i	$0.717974\pi$
$702$		0			0
$703$	0.559475	−	0.969039i	0.0211010	−	0.0365480i
$704$		0			0
$705$	−4.02198	−	6.96627i	−0.151477	−	0.262365i
$706$		0			0
$707$	−15.2089	+	20.9043i	−0.571991	+	0.786186i
$708$		0			0
$709$	25.4513	+	44.0830i	0.955844	+	1.65557i	0.732425	+	0.680848i	$0.238388\pi$
$709$	25.4513	+	44.0830i	0.955844	+	1.65557i	0.223419	+	0.974723i	$0.428278\pi$
$710$		0			0
$711$	3.19498	−	5.53386i	0.119821	−	0.207536i
$712$		0			0
$713$	5.25924			0.196960
$714$		0			0
$715$	−21.5252			−0.804997
$716$		0			0
$717$	−4.88731	+	8.46507i	−0.182520	+	0.316134i
$718$		0			0
$719$	18.9132	+	32.7586i	0.705343	+	1.22169i	0.966567	+	0.256412i	$0.0825405\pi$
$719$	18.9132	+	32.7586i	0.705343	+	1.22169i	−0.261224	+	0.965278i	$0.584126\pi$
$720$		0			0
$721$	−0.527661	−	1.18725i	−0.0196511	−	0.0442156i
$722$		0			0
$723$	−12.6760	−	21.9555i	−0.471426	−	0.816533i
$724$		0			0
$725$	−4.79413	+	8.30368i	−0.178050	+	0.308391i
$726$		0			0
$727$	−15.7134			−0.582777			−0.291389	−	0.956605i	$-0.594117\pi$
$727$	−15.7134			−0.582777			−0.291389	+	0.956605i	$0.594117\pi$
$728$		0			0
$729$	25.4066			0.940985
$730$		0			0
$731$	27.6770	−	47.9379i	1.02367	−	1.77305i
$732$		0			0
$733$	−4.17990	−	7.23980i	−0.154388	−	0.267408i	0.778448	−	0.627709i	$-0.216007\pi$
$733$	−4.17990	−	7.23980i	−0.154388	−	0.267408i	−0.932836	+	0.360301i	$0.882674\pi$
$734$		0			0
$735$	12.4204	+	2.65716i	0.458132	+	0.0980109i
$736$		0			0
$737$	17.6441	+	30.5604i	0.649928	+	1.12571i
$738$		0			0
$739$	−23.1511	+	40.0989i	−0.851628	+	1.47506i	0.0281097	+	0.999605i	$0.491051\pi$
$739$	−23.1511	+	40.0989i	−0.851628	+	1.47506i	−0.879738	+	0.475459i	$0.842282\pi$
$740$		0			0
$741$	−17.0360			−0.625834
$742$		0			0
$743$	−15.4420			−0.566510			−0.283255	−	0.959045i	$-0.591414\pi$
$743$	−15.4420			−0.566510			−0.283255	+	0.959045i	$0.591414\pi$
$744$		0			0
$745$	14.1776	−	24.5563i	0.519426	−	0.899673i
$746$		0			0
$747$	1.08194	+	1.87398i	0.0395861	+	0.0685652i
$748$		0			0
$749$	−20.9840	−	47.2147i	−0.766739	−	1.72519i
$750$		0			0
$751$	1.87525	+	3.24803i	0.0684289	+	0.118522i	0.898210	−	0.439567i	$-0.144868\pi$
$751$	1.87525	+	3.24803i	0.0684289	+	0.118522i	−0.829781	+	0.558089i	$0.811535\pi$
$752$		0			0
$753$	−6.80071	+	11.7792i	−0.247832	+	0.429257i
$754$		0			0
$755$	−31.5295			−1.14748
$756$		0			0
$757$	25.0530			0.910567			0.455284	−	0.890346i	$-0.349538\pi$
$757$	25.0530			0.910567			0.455284	+	0.890346i	$0.349538\pi$
$758$		0			0
$759$	−2.96281	+	5.13174i	−0.107543	+	0.186270i
$760$		0			0
$761$	10.9079	+	18.8930i	0.395410	+	0.684871i	0.993153	−	0.116817i	$-0.0372691\pi$
$761$	10.9079	+	18.8930i	0.395410	+	0.684871i	−0.597743	+	0.801688i	$0.703936\pi$
$762$		0			0
$763$	−16.6936	+	22.9449i	−0.604349	+	0.830662i
$764$		0			0
$765$	−7.44515	−	12.8954i	−0.269180	−	0.466233i
$766$		0			0
$767$	17.4126	−	30.1595i	0.628732	−	1.08900i
$768$		0			0
$769$	30.8224			1.11148			0.555742	−	0.831355i	$-0.312434\pi$
$769$	30.8224			1.11148			0.555742	+	0.831355i	$0.312434\pi$
$770$		0			0
$771$	27.0450			0.974003
$772$		0			0
$773$	13.7624	−	23.8371i	0.494997	−	0.857361i	−0.504986	−	0.863128i	$-0.668502\pi$
$773$	13.7624	−	23.8371i	0.494997	−	0.857361i	0.999983	+	0.00576682i	$0.00183565\pi$
$774$		0			0
$775$	−7.81409	−	13.5344i	−0.280690	−	0.486170i
$776$		0			0
$777$	0.911437	+	0.0964039i	0.0326976	+	0.00345847i
$778$		0			0
$779$	−11.7655	−	20.3784i	−0.421543	−	0.730134i
$780$		0			0
$781$	−13.2984	+	23.0335i	−0.475855	+	0.824205i
$782$		0			0
$783$	−17.9926			−0.643004
$784$		0			0
$785$	−18.1581			−0.648091
$786$		0			0
$787$	−14.6977	+	25.4571i	−0.523915	+	0.907448i	0.475697	+	0.879609i	$0.342196\pi$
$787$	−14.6977	+	25.4571i	−0.523915	+	0.907448i	−0.999612	+	0.0278389i	$0.991137\pi$
$788$		0			0
$789$	−12.9635	−	22.4535i	−0.461514	−	0.799365i
$790$		0			0
$791$	−28.9448	−	3.06153i	−1.02916	−	0.108856i
$792$		0			0
$793$	−3.67063	−	6.35771i	−0.130348	−	0.225769i
$794$		0			0
$795$	6.45416	−	11.1789i	0.228905	−	0.396476i
$796$		0			0
$797$	−18.5461			−0.656938			−0.328469	−	0.944515i	$-0.606533\pi$
$797$	−18.5461			−0.656938			−0.328469	+	0.944515i	$0.606533\pi$
$798$		0			0
$799$	33.6618			1.19087
$800$		0			0
$801$	3.12029	−	5.40450i	0.110250	−	0.190959i
$802$		0			0
$803$	−16.1136	−	27.9096i	−0.568637	−	0.984908i
$804$		0			0
$805$	−2.21688	+	3.04705i	−0.0781348	+	0.107394i
$806$		0			0
$807$	−3.92527	−	6.79877i	−0.138176	−	0.239328i
$808$		0			0
$809$	−13.0169	+	22.5459i	−0.457648	+	0.792670i	−0.998836	−	0.0482317i	$-0.984641\pi$
$809$	−13.0169	+	22.5459i	−0.457648	+	0.792670i	0.541188	+	0.840902i	$0.317975\pi$
$810$		0			0
$811$	−9.99886			−0.351108			−0.175554	−	0.984470i	$-0.556172\pi$
$811$	−9.99886			−0.351108			−0.175554	+	0.984470i	$0.556172\pi$
$812$		0			0
$813$	−12.1752			−0.427003
$814$		0			0
$815$	14.1576	−	24.5218i	0.495921	−	0.858960i
$816$		0			0
$817$	14.9999	+	25.9806i	0.524780	+	0.908945i
$818$		0			0
$819$	4.80757	+	10.8172i	0.167990	+	0.377983i
$820$		0			0
$821$	5.00887	+	8.67562i	0.174811	+	0.302781i	0.940096	−	0.340910i	$-0.110735\pi$
$821$	5.00887	+	8.67562i	0.174811	+	0.302781i	−0.765285	+	0.643692i	$0.777402\pi$
$822$		0			0
$823$	21.3625	−	37.0009i	0.744649	−	1.28977i	−0.205710	−	0.978613i	$-0.565950\pi$
$823$	21.3625	−	37.0009i	0.744649	−	1.28977i	0.950359	−	0.311156i	$-0.100716\pi$
$824$		0			0
$825$	17.6084			0.613044
$826$		0			0
$827$	19.0103			0.661052			0.330526	−	0.943797i	$-0.392774\pi$
$827$	19.0103			0.661052			0.330526	+	0.943797i	$0.392774\pi$
$828$		0			0
$829$	−12.0765	+	20.9171i	−0.419435	+	0.726482i	−0.995883	−	0.0906515i	$-0.971105\pi$
$829$	−12.0765	+	20.9171i	−0.419435	+	0.726482i	0.576448	+	0.817134i	$0.304438\pi$
$830$		0			0
$831$	14.0274	+	24.2962i	0.486605	+	0.842825i
$832$		0			0
$833$	−35.6176	+	39.4526i	−1.23408	+	1.36695i
$834$		0			0
$835$	3.72802	+	6.45711i	0.129013	+	0.223458i
$836$		0			0
$837$	14.6633	−	25.3976i	0.506839	−	0.877871i
$838$		0			0
$839$	1.65097			0.0569977			0.0284989	−	0.999594i	$-0.490927\pi$
$839$	1.65097			0.0569977			0.0284989	+	0.999594i	$0.490927\pi$
$840$		0			0
$841$	−18.5886			−0.640985
$842$		0			0
$843$	12.0248	−	20.8276i	0.414156	−	0.717340i
$844$		0			0
$845$	−1.73849	−	3.01115i	−0.0598058	−	0.103587i
$846$		0			0
$847$	−11.4257	−	25.7083i	−0.392593	−	0.883347i
$848$		0			0
$849$	−8.71416	−	15.0934i	−0.299069	−	0.518003i
$850$		0			0
$851$	−0.135954	+	0.235478i	−0.00466043	+	0.00807210i
$852$		0			0
$853$	−13.0542			−0.446967			−0.223483	−	0.974708i	$-0.571743\pi$
$853$	−13.0542			−0.446967			−0.223483	+	0.974708i	$0.571743\pi$
$854$		0			0
$855$	8.06999			0.275988
$856$		0			0
$857$	22.2675	−	38.5684i	0.760643	−	1.31747i	−0.181877	−	0.983321i	$-0.558217\pi$
$857$	22.2675	−	38.5684i	0.760643	−	1.31747i	0.942520	−	0.334151i	$-0.108450\pi$
$858$		0			0
$859$	5.54870	+	9.61063i	0.189319	+	0.327910i	0.945023	−	0.327003i	$-0.106039\pi$
$859$	5.54870	+	9.61063i	0.189319	+	0.327910i	−0.755704	+	0.654913i	$0.772705\pi$
$860$		0			0
$861$	11.3393	−	15.5855i	0.386441	−	0.531153i
$862$		0			0
$863$	−4.62968	−	8.01884i	−0.157596	−	0.272965i	0.776405	−	0.630234i	$-0.217041\pi$
$863$	−4.62968	−	8.01884i	−0.157596	−	0.272965i	−0.934001	+	0.357270i	$0.883708\pi$
$864$		0			0
$865$	3.99093	−	6.91249i	0.135696	−	0.235032i
$866$		0			0
$867$	−51.7956			−1.75907
$868$		0			0
$869$	21.5852			0.732229
$870$		0			0
$871$	12.3266	−	21.3503i	0.417671	−	0.723427i
$872$		0			0
$873$	−7.52075	−	13.0263i	−0.254539	−	0.440874i
$874$		0			0
$875$	29.8715	+	3.15955i	1.00984	+	0.106812i
$876$		0			0
$877$	−12.1188	−	20.9903i	−0.409221	−	0.708792i	0.585582	−	0.810614i	$-0.300866\pi$
$877$	−12.1188	−	20.9903i	−0.409221	−	0.708792i	−0.994803	+	0.101822i	$0.967533\pi$
$878$		0			0
$879$	11.1695	−	19.3462i	0.376739	−	0.652531i
$880$		0			0
$881$	−40.4648			−1.36329			−0.681647	−	0.731682i	$-0.738736\pi$
$881$	−40.4648			−1.36329			−0.681647	+	0.731682i	$0.738736\pi$
$882$		0			0
$883$	31.5512			1.06178			0.530891	−	0.847440i	$-0.321857\pi$
$883$	31.5512			1.06178			0.530891	+	0.847440i	$0.321857\pi$
$884$		0			0
$885$	9.72325	−	16.8412i	0.326844	−	0.566110i
$886$		0			0
$887$	18.4664	+	31.9847i	0.620041	+	1.07394i	0.989478	+	0.144686i	$0.0462173\pi$
$887$	18.4664	+	31.9847i	0.620041	+	1.07394i	−0.369437	+	0.929256i	$0.620449\pi$
$888$		0			0
$889$	39.1904	+	4.14522i	1.31440	+	0.139026i
$890$		0			0
$891$	6.91501	+	11.9771i	0.231661	+	0.401249i
$892$		0			0
$893$	−9.12172	+	15.7993i	−0.305247	+	0.528703i
$894$		0			0
$895$	15.6438			0.522913
$896$		0			0
$897$	4.13979			0.138224
$898$		0			0
$899$	−8.48494	+	14.6963i	−0.282989	+	0.490151i
$900$		0			0
$901$	27.0089	+	46.7807i	0.899796	+	1.55849i
$902$		0			0
$903$	−14.4565	+	19.8700i	−0.481081	+	0.661234i
$904$		0			0
$905$	−5.95330	−	10.3114i	−0.197895	−	0.342763i
$906$		0			0
$907$	−24.7523	+	42.8722i	−0.821887	+	1.42355i	0.0823889	+	0.996600i	$0.473745\pi$
$907$	−24.7523	+	42.8722i	−0.821887	+	1.42355i	−0.904276	+	0.426949i	$0.859588\pi$
$908$		0			0
$909$	−13.4536			−0.446228
$910$		0			0
$911$	20.1085			0.666226			0.333113	−	0.942887i	$-0.391901\pi$
$911$	20.1085			0.666226			0.333113	+	0.942887i	$0.391901\pi$
$912$		0			0
$913$	−3.65479	+	6.33028i	−0.120956	+	0.209502i
$914$		0			0
$915$	−2.04969	−	3.55017i	−0.0677607	−	0.117365i
$916$		0			0
$917$	15.9306	+	35.8442i	0.526073	+	1.18368i
$918$		0			0
$919$	26.2223	+	45.4183i	0.864993	+	1.49821i	0.867054	+	0.498214i	$0.166010\pi$
$919$	26.2223	+	45.4183i	0.864993	+	1.49821i	−0.00206150	+	0.999998i	$0.500656\pi$
$920$		0			0
$921$	5.40533	−	9.36231i	0.178112	−	0.308498i
$922$		0			0
$923$	18.5812			0.611608
$924$		0			0
$925$	0.807989			0.0265665
$926$		0			0
$927$	0.338072	−	0.585557i	0.0111037	−	0.0192322i
$928$		0			0
$929$	16.2080	+	28.0732i	0.531769	+	0.921051i	0.999312	+	0.0370805i	$0.0118058\pi$
$929$	16.2080	+	28.0732i	0.531769	+	0.921051i	−0.467543	+	0.883970i	$0.654861\pi$
$930$		0			0
$931$	−8.86549	−	27.4082i	−0.290555	−	0.898267i
$932$		0			0
$933$	17.7774	+	30.7914i	0.582007	+	1.00807i
$934$		0			0
$935$	25.1497	−	43.5605i	0.822482	−	1.42458i
$936$		0			0
$937$	61.1064			1.99626			0.998129	−	0.0611376i	$-0.0194729\pi$
$937$	61.1064			1.99626			0.998129	+	0.0611376i	$0.0194729\pi$
$938$		0			0
$939$	40.4860			1.32121
$940$		0			0
$941$	−20.1683	+	34.9325i	−0.657467	+	1.13877i	0.323802	+	0.946125i	$0.395039\pi$
$941$	−20.1683	+	34.9325i	−0.657467	+	1.13877i	−0.981269	+	0.192642i	$0.938294\pi$
$942$		0			0
$943$	2.85904	+	4.95200i	0.0931031	+	0.161259i
$944$		0			0
$945$	8.53372	+	19.2011i	0.277602	+	0.624613i
$946$		0			0
$947$	11.5181	+	19.9500i	0.374290	+	0.648288i	0.990220	−	0.139512i	$-0.0445533\pi$
$947$	11.5181	+	19.9500i	0.374290	+	0.648288i	−0.615931	+	0.787800i	$0.711220\pi$
$948$		0			0
$949$	−11.2574	+	19.4983i	−0.365430	+	0.632943i
$950$		0			0
$951$	−2.08369			−0.0675682
$952$		0			0
$953$	−3.55998			−0.115319			−0.0576595	−	0.998336i	$-0.518364\pi$
$953$	−3.55998			−0.115319			−0.0576595	+	0.998336i	$0.518364\pi$
$954$		0			0
$955$	4.11852	−	7.13349i	0.133272	−	0.230834i
$956$		0			0
$957$	−9.56003	−	16.5585i	−0.309032	−	0.535259i
$958$		0			0
$959$	0.893499	−	1.22809i	0.0288526	−	0.0396572i
$960$		0			0
$961$	1.67017	+	2.89283i	0.0538766	+	0.0933169i
$962$		0			0
$963$	13.4444	−	23.2864i	0.433241	−	0.750395i
$964$		0			0
$965$	29.0195			0.934170
$966$		0			0
$967$	−20.6098			−0.662766			−0.331383	−	0.943496i	$-0.607515\pi$
$967$	−20.6098			−0.662766			−0.331383	+	0.943496i	$0.607515\pi$
$968$		0			0
$969$	19.9046	−	34.4758i	0.639428	−	1.10752i
$970$		0			0
$971$	20.3280	+	35.2091i	0.652356	+	1.12991i	0.982550	+	0.186001i	$0.0595527\pi$
$971$	20.3280	+	35.2091i	0.652356	+	1.12991i	−0.330193	+	0.943913i	$0.607114\pi$
$972$		0			0
$973$	38.9197	+	4.11659i	1.24771	+	0.131972i
$974$		0			0
$975$	−6.15082	−	10.6535i	−0.196984	−	0.341186i
$976$		0			0
$977$	7.72858	−	13.3863i	0.247259	−	0.428265i	−0.715505	−	0.698607i	$-0.753803\pi$
$977$	7.72858	−	13.3863i	0.247259	−	0.428265i	0.962764	+	0.270342i	$0.0871368\pi$
$978$		0			0
$979$	21.0807			0.673741
$980$		0			0
$981$	−14.7669			−0.471472
$982$		0			0
$983$	10.6292	−	18.4103i	0.339018	−	0.587197i	−0.645230	−	0.763988i	$-0.723239\pi$
$983$	10.6292	−	18.4103i	0.339018	−	0.587197i	0.984248	+	0.176792i	$0.0565719\pi$
$984$		0			0
$985$	−10.8325	−	18.7624i	−0.345152	−	0.597820i
$986$		0			0
$987$	−14.8601	−	1.57177i	−0.473003	−	0.0500301i
$988$		0			0
$989$	−3.64500	−	6.31333i	−0.115904	−	0.200752i
$990$		0			0
$991$	−26.1665	+	45.3216i	−0.831205	+	1.43969i	0.0658787	+	0.997828i	$0.479015\pi$
$991$	−26.1665	+	45.3216i	−0.831205	+	1.43969i	−0.897083	+	0.441861i	$0.854318\pi$
$992$		0			0
$993$	−21.8773			−0.694257
$994$		0			0
$995$	−16.3785			−0.519235
$996$		0			0
$997$	17.0260	−	29.4898i	0.539218	−	0.933953i	−0.459729	−	0.888060i	$-0.652053\pi$
$997$	17.0260	−	29.4898i	0.539218	−	0.933953i	0.998946	−	0.0458932i	$-0.0146134\pi$
$998$		0			0
$999$	0.758106	+	1.31308i	0.0239854	+	0.0415439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.i.a.277.5	yes	14
7.2	even	3	inner	644.2.i.a.93.5	✓	14
7.3	odd	6		4508.2.a.l.1.5		7
7.4	even	3		4508.2.a.m.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.i.a.93.5	✓	14	7.2	even	3	inner
644.2.i.a.277.5	yes	14	1.1	even	1	trivial
4508.2.a.l.1.5		7	7.3	odd	6
4508.2.a.m.1.3		7	7.4	even	3

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.637005 - 1.10333i) q^{3} +(0.712116 + 1.23342i) q^{5} +(2.63107 + 0.278292i) q^{7} +(0.688449 + 1.19243i) q^{9} +O(q^{10})\)	\(q+(0.637005 - 1.10333i) q^{3} +(0.712116 + 1.23342i) q^{5} +(2.63107 + 0.278292i) q^{7} +(0.688449 + 1.19243i) q^{9} +(-2.32558 + 4.02802i) q^{11} +3.24942 q^{13} +1.81449 q^{15} +(-3.79656 + 6.57584i) q^{17} +(-2.05760 - 3.56386i) q^{19} +(1.98305 - 2.72566i) q^{21} +(0.500000 + 0.866025i) q^{23} +(1.48578 - 2.57345i) q^{25} +5.57621 q^{27} -3.22668 q^{29} +(2.62962 - 4.55464i) q^{31} +(2.96281 + 5.13174i) q^{33} +(1.53038 + 3.44340i) q^{35} +(0.135954 + 0.235478i) q^{37} +(2.06989 - 3.58516i) q^{39} +5.71808 q^{41} -7.29000 q^{43} +(-0.980512 + 1.69830i) q^{45} +(-2.21659 - 3.83925i) q^{47} +(6.84511 + 1.46442i) q^{49} +(4.83686 + 8.37769i) q^{51} +(3.55701 - 6.16093i) q^{53} -6.62433 q^{55} -5.24280 q^{57} +(5.35868 - 9.28150i) q^{59} +(-1.12963 - 1.95657i) q^{61} +(1.47952 + 3.32896i) q^{63} +(2.31396 + 4.00790i) q^{65} +(3.79348 - 6.57050i) q^{67} +1.27401 q^{69} +5.71833 q^{71} +(-3.46443 + 6.00057i) q^{73} +(-1.89290 - 3.27860i) q^{75} +(-7.23974 + 9.95083i) q^{77} +(-2.32042 - 4.01908i) q^{79} +(1.48673 - 2.57509i) q^{81} +1.57156 q^{83} -10.8144 q^{85} +(-2.05541 + 3.56007i) q^{87} +(-2.26617 - 3.92513i) q^{89} +(8.54945 + 0.904287i) q^{91} +(-3.35017 - 5.80266i) q^{93} +(2.93050 - 5.07577i) q^{95} -10.9242 q^{97} -6.40417 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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