LMFDB - Embedded newform 273.2.c.c.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(64,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("273.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.265727878144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 15x^{6} + 67x^{4} + 77x^{2} + 4 $ x^8 + 15x^6 + 67x^4 + 77*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.8
Root			$2.60520i$ of defining polynomial
Character	$\chi$	$=$	273.64
Dual form			273.2.c.c.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.60520i q^{2} -1.00000 q^{3} -4.78706 q^{4} -3.78706i q^{5} -2.60520i q^{6} -1.00000i q^{7} -7.26084i q^{8} +1.00000 q^{9} +9.86604 q^{10} +2.55475i q^{11} +4.78706 q^{12} +(0.0504439 - 3.60520i) q^{13} +2.60520 q^{14} +3.78706i q^{15} +9.34181 q^{16} -3.21040 q^{17} +2.60520i q^{18} -8.44270i q^{19} +18.1289i q^{20} +1.00000i q^{21} -6.65564 q^{22} +3.97809 q^{23} +7.26084i q^{24} -9.34181 q^{25} +(9.39226 + 0.131416i) q^{26} -1.00000 q^{27} +4.78706i q^{28} -2.86858 q^{29} -9.86604 q^{30} +0.868584i q^{31} +9.81560i q^{32} -2.55475i q^{33} -8.36372i q^{34} -3.78706 q^{35} -4.78706 q^{36} -5.10951i q^{37} +21.9949 q^{38} +(-0.0504439 + 3.60520i) q^{39} -27.4972 q^{40} -3.34436i q^{41} -2.60520 q^{42} +4.86858 q^{43} -12.2298i q^{44} -3.78706i q^{45} +10.3637i q^{46} +11.0983i q^{47} -9.34181 q^{48} -1.00000 q^{49} -24.3373i q^{50} +3.21040 q^{51} +(-0.241478 + 17.2583i) q^{52} +1.33319 q^{53} -2.60520i q^{54} +9.67501 q^{55} -7.26084 q^{56} +8.44270i q^{57} -7.47323i q^{58} +10.6556i q^{59} -18.1289i q^{60} -4.10089 q^{61} -2.26283 q^{62} -1.00000i q^{63} -6.88795 q^{64} +(-13.6531 - 0.191034i) q^{65} +6.65564 q^{66} -10.8467i q^{67} +15.3684 q^{68} -3.97809 q^{69} -9.86604i q^{70} -2.55475i q^{71} -7.26084i q^{72} -6.76770i q^{73} +13.3113 q^{74} +9.34181 q^{75} +40.4157i q^{76} +2.55475 q^{77} +(-9.39226 - 0.131416i) q^{78} -1.23230 q^{79} -35.3780i q^{80} +1.00000 q^{81} +8.71272 q^{82} -11.0983i q^{83} -4.78706i q^{84} +12.1580i q^{85} +12.6836i q^{86} +2.86858 q^{87} +18.5497 q^{88} +5.52423i q^{89} +9.86604 q^{90} +(-3.60520 - 0.0504439i) q^{91} -19.0434 q^{92} -0.868584i q^{93} -28.9134 q^{94} -31.9730 q^{95} -9.81560i q^{96} +5.65819i q^{97} -2.60520i q^{98} +2.55475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - 14 q^{4} + 8 q^{9} + 4 q^{10} + 14 q^{12} - 6 q^{13} - 2 q^{14} + 34 q^{16} + 20 q^{17} - 24 q^{22} - 6 q^{23} - 34 q^{25} + 28 q^{26} - 8 q^{27} - 18 q^{29} - 4 q^{30} - 6 q^{35} - 14 q^{36}+ \cdots - 78 q^{95}+O(q^{100}) $ 8 * q - 8 * q^3 - 14 * q^4 + 8 * q^9 + 4 * q^10 + 14 * q^12 - 6 * q^13 - 2 * q^14 + 34 * q^16 + 20 * q^17 - 24 * q^22 - 6 * q^23 - 34 * q^25 + 28 * q^26 - 8 * q^27 - 18 * q^29 - 4 * q^30 - 6 * q^35 - 14 * q^36 + 36 * q^38 + 6 * q^39 - 8 * q^40 + 2 * q^42 + 34 * q^43 - 34 * q^48 - 8 * q^49 - 20 * q^51 + 18 * q^52 - 10 * q^53 + 16 * q^55 - 6 * q^56 - 20 * q^61 - 28 * q^62 - 18 * q^64 - 10 * q^65 + 24 * q^66 - 24 * q^68 + 6 * q^69 + 48 * q^74 + 34 * q^75 + 4 * q^77 - 28 * q^78 - 2 * q^79 + 8 * q^81 - 48 * q^82 + 18 * q^87 - 8 * q^88 + 4 * q^90 - 6 * q^91 + 56 * q^92 - 72 * q^94 - 78 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.60520i			1.84215i	0.389381	+	0.921077i	$0.372689\pi$
$2$			2.60520i			1.84215i	−0.389381	+	0.921077i	$0.627311\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−4.78706			−2.39353
$5$		−	3.78706i		−	1.69362i	−0.531892	−	0.846812i	$-0.678519\pi$
$5$		−	3.78706i		−	1.69362i	0.531892	−	0.846812i	$-0.321481\pi$
$6$		−	2.60520i		−	1.06357i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	7.26084i		−	2.56709i
$9$	1.00000			0.333333
$10$	9.86604			3.11992
$11$			2.55475i			0.770287i	0.922857	+	0.385144i	$0.125848\pi$
$11$			2.55475i			0.770287i	−0.922857	+	0.385144i	$0.874152\pi$
$12$	4.78706			1.38190
$13$	0.0504439	−	3.60520i	0.0139906	−	0.999902i
$13$	0.0504439	−	3.60520i	0.0139906	−	0.999902i
$14$	2.60520			0.696269
$15$			3.78706i			0.977814i
$16$	9.34181			2.33545
$17$	−3.21040			−0.778636			−0.389318	−	0.921103i	$-0.627289\pi$
$17$	−3.21040			−0.778636			−0.389318	+	0.921103i	$0.627289\pi$
$18$			2.60520i			0.614051i
$19$		−	8.44270i		−	1.93689i	−0.249230	−	0.968444i	$-0.580178\pi$
$19$		−	8.44270i		−	1.93689i	0.249230	−	0.968444i	$-0.419822\pi$
$20$			18.1289i			4.05374i
$21$			1.00000i			0.218218i
$22$	−6.65564			−1.41899
$23$	3.97809			0.829490			0.414745	−	0.909938i	$-0.363871\pi$
$23$	3.97809			0.829490			0.414745	+	0.909938i	$0.363871\pi$
$24$			7.26084i			1.48211i
$25$	−9.34181			−1.86836
$26$	9.39226	+	0.131416i	1.84197	+	0.0257729i
$27$	−1.00000			−0.192450
$28$			4.78706i			0.904669i
$29$	−2.86858			−0.532683			−0.266341	−	0.963879i	$-0.585815\pi$
$29$	−2.86858			−0.532683			−0.266341	+	0.963879i	$0.585815\pi$
$30$	−9.86604			−1.80128
$31$			0.868584i			0.156002i	0.996953	+	0.0780011i	$0.0248538\pi$
$31$			0.868584i			0.156002i	−0.996953	+	0.0780011i	$0.975146\pi$
$32$			9.81560i			1.73517i
$33$		−	2.55475i		−	0.444726i
$34$		−	8.36372i		−	1.43437i
$35$	−3.78706			−0.640130
$36$	−4.78706			−0.797843
$37$		−	5.10951i		−	0.839998i	−0.907525	−	0.419999i	$-0.862030\pi$
$37$		−	5.10951i		−	0.839998i	0.907525	−	0.419999i	$-0.137970\pi$
$38$	21.9949			3.56805
$39$	−0.0504439	+	3.60520i	−0.00807749	+	0.577294i
$40$	−27.4972			−4.34769
$41$		−	3.34436i		−	0.522301i	−0.965298	−	0.261150i	$-0.915898\pi$
$41$		−	3.34436i		−	0.522301i	0.965298	−	0.261150i	$-0.0841019\pi$
$42$	−2.60520			−0.401991
$43$	4.86858			0.742452			0.371226	−	0.928543i	$-0.378938\pi$
$43$	4.86858			0.742452			0.371226	+	0.928543i	$0.378938\pi$
$44$		−	12.2298i		−	1.84371i
$45$		−	3.78706i		−	0.564541i
$46$			10.3637i			1.52805i
$47$			11.0983i			1.61886i	0.587217	+	0.809430i	$0.300224\pi$
$47$			11.0983i			1.61886i	−0.587217	+	0.809430i	$0.699776\pi$
$48$	−9.34181			−1.34837
$49$	−1.00000			−0.142857
$50$		−	24.3373i		−	3.44181i
$51$	3.21040			0.449545
$52$	−0.241478	+	17.2583i	−0.0334870	+	2.39330i
$53$	1.33319			0.183128			0.0915640	−	0.995799i	$-0.470813\pi$
$53$	1.33319			0.183128			0.0915640	+	0.995799i	$0.470813\pi$
$54$		−	2.60520i		−	0.354523i
$55$	9.67501			1.30458
$56$	−7.26084			−0.970271
$57$			8.44270i			1.11826i
$58$		−	7.47323i		−	0.981283i
$59$			10.6556i			1.38725i	0.720338	+	0.693623i	$0.243987\pi$
$59$			10.6556i			1.38725i	−0.720338	+	0.693623i	$0.756013\pi$
$60$		−	18.1289i		−	2.34043i
$61$	−4.10089			−0.525065			−0.262532	−	0.964923i	$-0.584558\pi$
$61$	−4.10089			−0.525065			−0.262532	+	0.964923i	$0.584558\pi$
$62$	−2.26283			−0.287380
$63$		−	1.00000i		−	0.125988i
$64$	−6.88795			−0.860993
$65$	−13.6531	−	0.191034i	−1.69346	−	0.0236949i
$66$	6.65564			0.819253
$67$		−	10.8467i		−	1.32513i	−0.749003	−	0.662566i	$-0.769467\pi$
$67$		−	10.8467i		−	1.32513i	0.749003	−	0.662566i	$-0.230533\pi$
$68$	15.3684			1.86369
$69$	−3.97809			−0.478906
$70$		−	9.86604i		−	1.17922i
$71$		−	2.55475i		−	0.303194i	−0.988442	−	0.151597i	$-0.951558\pi$
$71$		−	2.55475i		−	0.303194i	0.988442	−	0.151597i	$-0.0484415\pi$
$72$		−	7.26084i		−	0.855698i
$73$		−	6.76770i		−	0.792099i	−0.918229	−	0.396049i	$-0.870381\pi$
$73$		−	6.76770i		−	0.792099i	0.918229	−	0.396049i	$-0.129619\pi$
$74$	13.3113			1.54741
$75$	9.34181			1.07870
$76$			40.4157i			4.63600i
$77$	2.55475			0.291141
$78$	−9.39226	−	0.131416i	−1.06346	−	0.0148800i
$79$	−1.23230			−0.138645			−0.0693225	−	0.997594i	$-0.522084\pi$
$79$	−1.23230			−0.138645			−0.0693225	+	0.997594i	$0.522084\pi$
$80$		−	35.3780i		−	3.95538i
$81$	1.00000			0.111111
$82$	8.71272			0.962158
$83$		−	11.0983i		−	1.21820i	−0.793093	−	0.609101i	$-0.791531\pi$
$83$		−	11.0983i		−	1.21820i	0.793093	−	0.609101i	$-0.208469\pi$
$84$		−	4.78706i		−	0.522311i
$85$			12.1580i			1.31872i
$86$			12.6836i			1.36771i
$87$	2.86858			0.307544
$88$	18.5497			1.97740
$89$			5.52423i			0.585567i	0.956179	+	0.292783i	$0.0945815\pi$
$89$			5.52423i			0.585567i	−0.956179	+	0.292783i	$0.905419\pi$
$90$	9.86604			1.03997
$91$	−3.60520	−	0.0504439i	−0.377927	−	0.00528796i
$92$	−19.0434			−1.98541
$93$		−	0.868584i		−	0.0900679i
$94$	−28.9134			−2.98219
$95$	−31.9730			−3.28036
$96$		−	9.81560i		−	1.00180i
$97$			5.65819i			0.574502i	0.957855	+	0.287251i	$0.0927414\pi$
$97$			5.65819i			0.574502i	−0.957855	+	0.287251i	$0.907259\pi$
$98$		−	2.60520i		−	0.263165i
$99$			2.55475i			0.256762i
$100$	44.7198			4.47198
$101$	−8.94756			−0.890316			−0.445158	−	0.895452i	$-0.646852\pi$
$101$	−8.94756			−0.890316			−0.445158	+	0.895452i	$0.646852\pi$
$102$			8.36372i			0.828132i
$103$	−1.67501			−0.165043			−0.0825216	−	0.996589i	$-0.526297\pi$
$103$	−1.67501			−0.165043			−0.0825216	+	0.996589i	$0.526297\pi$
$104$	−26.1768	−	0.366265i	−2.56684	−	0.0359152i
$105$	3.78706			0.369579
$106$			3.47323i			0.337350i
$107$	−0.846676			−0.0818513			−0.0409256	−	0.999162i	$-0.513031\pi$
$107$	−0.846676			−0.0818513			−0.0409256	+	0.999162i	$0.513031\pi$
$108$	4.78706			0.460635
$109$			17.9949i			1.72360i	0.507248	+	0.861800i	$0.330663\pi$
$109$			17.9949i			1.72360i	−0.507248	+	0.861800i	$0.669337\pi$
$110$			25.2053i			2.40323i
$111$			5.10951i			0.484973i
$112$		−	9.34181i		−	0.882718i
$113$	2.86858			0.269854			0.134927	−	0.990856i	$-0.456920\pi$
$113$	2.86858			0.269854			0.134927	+	0.990856i	$0.456920\pi$
$114$	−21.9949			−2.06001
$115$		−	15.0653i		−	1.40484i
$116$	13.7321			1.27499
$117$	0.0504439	−	3.60520i	0.00466354	−	0.333301i
$118$	−27.7601			−2.55552
$119$			3.21040i			0.294297i
$120$	27.4972			2.51014
$121$	4.47323			0.406657
$122$		−	10.6836i		−	0.967250i
$123$			3.34436i			0.301551i
$124$		−	4.15796i		−	0.373396i
$125$			16.4427i			1.47068i
$126$	2.60520			0.232090
$127$	17.2053			1.52672			0.763362	−	0.645971i	$-0.223547\pi$
$127$	17.2053			1.52672			0.763362	+	0.645971i	$0.223547\pi$
$128$			1.68672i			0.149087i
$129$	−4.86858			−0.428655
$130$	0.497681	−	35.5690i	0.0436496	−	3.11961i
$131$	16.6836			1.45766			0.728828	−	0.684697i	$-0.240066\pi$
$131$	16.6836			1.45766			0.728828	+	0.684697i	$0.240066\pi$
$132$			12.2298i			1.06446i
$133$	−8.44270			−0.732075
$134$	28.2577			2.44110
$135$			3.78706i			0.325938i
$136$			23.3102i			1.99883i
$137$		−	18.9134i		−	1.61588i	−0.589265	−	0.807940i	$-0.700583\pi$
$137$		−	18.9134i		−	1.61588i	0.589265	−	0.807940i	$-0.299417\pi$
$138$		−	10.3637i		−	0.882218i
$139$	5.67501			0.481348			0.240674	−	0.970606i	$-0.422632\pi$
$139$	5.67501			0.481348			0.240674	+	0.970606i	$0.422632\pi$
$140$	18.1289			1.53217
$141$		−	11.0983i		−	0.934649i
$142$	6.65564			0.558529
$143$	9.21040	+	0.128872i	0.770212	+	0.0107768i
$144$	9.34181			0.778484
$145$			10.8635i			0.902164i
$146$	17.6312			1.45917
$147$	1.00000			0.0824786
$148$			24.4595i			2.01056i
$149$			8.49259i			0.695740i	0.937543	+	0.347870i	$0.113095\pi$
$149$			8.49259i			0.695740i	−0.937543	+	0.347870i	$0.886905\pi$
$150$			24.3373i			1.98713i
$151$			14.2190i			1.15713i	0.815637	+	0.578564i	$0.196387\pi$
$151$			14.2190i			1.15713i	−0.815637	+	0.578564i	$0.803613\pi$
$152$	−61.3011			−4.97218
$153$	−3.21040			−0.259545
$154$			6.65564i			0.536327i
$155$	3.28938			0.264209
$156$	0.241478	−	17.2583i	0.0193337	−	1.38177i
$157$	8.42079			0.672052			0.336026	−	0.941853i	$-0.390917\pi$
$157$	8.42079			0.672052			0.336026	+	0.941853i	$0.390917\pi$
$158$		−	3.21040i		−	0.255405i
$159$	−1.33319			−0.105729
$160$	37.1722			2.93872
$161$		−	3.97809i		−	0.313518i
$162$			2.60520i			0.204684i
$163$		−	3.77589i		−	0.295751i	−0.989006	−	0.147875i	$-0.952757\pi$
$163$		−	3.77589i		−	0.295751i	0.989006	−	0.147875i	$-0.0472435\pi$
$164$			16.0096i			1.25014i
$165$	−9.67501			−0.753198
$166$	28.9134			2.24411
$167$			8.83551i			0.683712i	0.939752	+	0.341856i	$0.111056\pi$
$167$			8.83551i			0.683712i	−0.939752	+	0.341856i	$0.888944\pi$
$168$	7.26084			0.560186
$169$	−12.9949	−	0.363721i	−0.999609	−	0.0279785i
$170$	−31.6739			−2.42928
$171$		−	8.44270i		−	0.645629i
$172$	−23.3062			−1.77708
$173$	17.6750			1.34381			0.671903	−	0.740639i	$-0.265477\pi$
$173$	17.6750			1.34381			0.671903	+	0.740639i	$0.265477\pi$
$174$			7.47323i			0.566544i
$175$			9.34181i			0.706175i
$176$			23.8660i			1.79897i
$177$		−	10.6556i		−	0.800927i
$178$	−14.3917			−1.07870
$179$	16.9073			1.26371			0.631856	−	0.775086i	$-0.282293\pi$
$179$	16.9073			1.26371			0.631856	+	0.775086i	$0.282293\pi$
$180$			18.1289i			1.35125i
$181$	7.73717			0.575099			0.287550	−	0.957766i	$-0.407159\pi$
$181$	7.73717			0.575099			0.287550	+	0.957766i	$0.407159\pi$
$182$	0.131416	−	9.39226i	0.00974123	−	0.696200i
$183$	4.10089			0.303146
$184$		−	28.8843i		−	2.12938i
$185$	−19.3500			−1.42264
$186$	2.26283			0.165919
$187$		−	8.20178i		−	0.599773i
$188$		−	53.1284i		−	3.87479i
$189$			1.00000i			0.0727393i
$190$		−	83.2960i		−	6.04293i
$191$	5.57412			0.403329			0.201664	−	0.979455i	$-0.435365\pi$
$191$	5.57412			0.403329			0.201664	+	0.979455i	$0.435365\pi$
$192$	6.88795			0.497095
$193$		−	7.57412i		−	0.545197i	−0.962128	−	0.272598i	$-0.912117\pi$
$193$		−	7.57412i		−	0.545197i	0.962128	−	0.272598i	$-0.0878830\pi$
$194$	−14.7407			−1.05832
$195$	13.6531	+	0.191034i	0.977719	+	0.0136802i
$196$	4.78706			0.341933
$197$		−	13.3444i		−	0.950746i	−0.879784	−	0.475373i	$-0.842313\pi$
$197$		−	13.3444i		−	0.950746i	0.879784	−	0.475373i	$-0.157687\pi$
$198$	−6.65564			−0.472996
$199$	−16.8854			−1.19697			−0.598487	−	0.801132i	$-0.704231\pi$
$199$	−16.8854			−1.19697			−0.598487	+	0.801132i	$0.704231\pi$
$200$			67.8294i			4.79626i
$201$			10.8467i			0.765066i
$202$		−	23.3102i		−	1.64010i
$203$			2.86858i			0.201335i
$204$	−15.3684			−1.07600
$205$	−12.6653			−0.884581
$206$		−	4.36372i		−	0.304035i
$207$	3.97809			0.276497
$208$	0.471237	−	33.6791i	0.0326744	−	2.33522i
$209$	21.5690			1.49196
$210$			9.86604i			0.680821i
$211$	11.6969			0.805249			0.402624	−	0.915365i	$-0.368098\pi$
$211$	11.6969			0.805249			0.402624	+	0.915365i	$0.368098\pi$
$212$	−6.38207			−0.438322
$213$			2.55475i			0.175049i
$214$		−	2.20576i		−	0.150783i
$215$		−	18.4376i		−	1.25743i
$216$			7.26084i			0.494038i
$217$	0.868584			0.0589633
$218$	−46.8803			−3.17514
$219$			6.76770i			0.457319i
$220$	−46.3148			−3.12254
$221$	−0.161945	+	11.5741i	−0.0108936	+	0.778559i
$222$	−13.3113			−0.893395
$223$			4.24093i			0.283993i	0.989867	+	0.141997i	$0.0453522\pi$
$223$			4.24093i			0.283993i	−0.989867	+	0.141997i	$0.954648\pi$
$224$	9.81560			0.655832
$225$	−9.34181			−0.622788
$226$			7.47323i			0.497112i
$227$		−	1.72643i		−	0.114587i	−0.998357	−	0.0572934i	$-0.981753\pi$
$227$		−	1.72643i		−	0.114587i	0.998357	−	0.0572934i	$-0.0182471\pi$
$228$		−	40.4157i		−	2.67660i
$229$			6.82833i			0.451229i	0.974217	+	0.225614i	$0.0724389\pi$
$229$			6.82833i			0.451229i	−0.974217	+	0.225614i	$0.927561\pi$
$230$	39.2480			2.58794
$231$	−2.55475			−0.168091
$232$			20.8283i			1.36745i
$233$	−1.33319			−0.0873403			−0.0436702	−	0.999046i	$-0.513905\pi$
$233$	−1.33319			−0.0873403			−0.0436702	+	0.999046i	$0.513905\pi$
$234$	9.39226	+	0.131416i	0.613991	+	0.00859096i
$235$	42.0301			2.74174
$236$		−	51.0092i		−	3.32042i
$237$	1.23230			0.0800468
$238$	−8.36372			−0.542139
$239$			3.90985i			0.252907i	0.991973	+	0.126454i	$0.0403595\pi$
$239$			3.90985i			0.252907i	−0.991973	+	0.126454i	$0.959640\pi$
$240$			35.3780i			2.28364i
$241$		−	25.3903i		−	1.63553i	−0.575552	−	0.817765i	$-0.695213\pi$
$241$		−	25.3903i		−	1.63553i	0.575552	−	0.817765i	$-0.304787\pi$
$242$			11.6537i			0.749125i
$243$	−1.00000			−0.0641500
$244$	19.6312			1.25676
$245$			3.78706i			0.241946i
$246$	−8.71272			−0.555502
$247$	−30.4376	−	0.425883i	−1.93670	−	0.0270983i
$248$	6.30665			0.400473
$249$			11.0983i			0.703329i
$250$	−42.8365			−2.70922
$251$	−25.7708			−1.62664			−0.813319	−	0.581818i	$-0.802342\pi$
$251$	−25.7708			−1.62664			−0.813319	+	0.581818i	$0.802342\pi$
$252$			4.78706i			0.301556i
$253$			10.1631i			0.638945i
$254$			44.8232i			2.81246i
$255$		−	12.1580i		−	0.761361i
$256$	−18.1701			−1.13563
$257$	5.87678			0.366584			0.183292	−	0.983059i	$-0.441325\pi$
$257$	5.87678			0.366584			0.183292	+	0.983059i	$0.441325\pi$
$258$		−	12.6836i		−	0.789648i
$259$	−5.10951			−0.317489
$260$	65.3582	+	0.914491i	4.05334	+	0.0567143i
$261$	−2.86858			−0.177561
$262$			43.4642i			2.68522i
$263$	−10.2409			−0.631483			−0.315741	−	0.948845i	$-0.602253\pi$
$263$	−10.2409			−0.631483			−0.315741	+	0.948845i	$0.602253\pi$
$264$	−18.5497			−1.14165
$265$		−	5.04888i		−	0.310150i
$266$		−	21.9949i		−	1.34859i
$267$		−	5.52423i		−	0.338077i
$268$			51.9237i			3.17174i
$269$	−16.1396			−0.984050			−0.492025	−	0.870581i	$-0.663743\pi$
$269$	−16.1396			−0.984050			−0.492025	+	0.870581i	$0.663743\pi$
$270$	−9.86604			−0.600428
$271$		−	12.2577i		−	0.744605i	−0.928111	−	0.372302i	$-0.878568\pi$
$271$		−	12.2577i		−	0.744605i	0.928111	−	0.372302i	$-0.121432\pi$
$272$	−29.9909			−1.81847
$273$	3.60520	+	0.0504439i	0.218197	+	0.00305300i
$274$	49.2731			2.97670
$275$		−	23.8660i		−	1.43918i
$276$	19.0434			1.14628
$277$	9.81504			0.589729			0.294864	−	0.955539i	$-0.404726\pi$
$277$	9.81504			0.589729			0.294864	+	0.955539i	$0.404726\pi$
$278$			14.7845i			0.886716i
$279$			0.868584i			0.0520007i
$280$			27.4972i			1.64327i
$281$			16.1910i			0.965876i	0.875655	+	0.482938i	$0.160430\pi$
$281$			16.1910i			0.965876i	−0.875655	+	0.482938i	$0.839570\pi$
$282$	28.9134			1.72177
$283$	19.1482			1.13824			0.569122	−	0.822253i	$-0.307283\pi$
$283$	19.1482			1.13824			0.569122	+	0.822253i	$0.307283\pi$
$284$			12.2298i			0.725703i
$285$	31.9730			1.89392
$286$	−0.335737	+	23.9949i	−0.0198525	+	1.41885i
$287$	−3.34436			−0.197411
$288$			9.81560i			0.578389i
$289$	−6.69335			−0.393727
$290$	−28.3016			−1.66192
$291$		−	5.65819i		−	0.331689i
$292$			32.3974i			1.89591i
$293$		−	24.6725i		−	1.44138i	−0.693257	−	0.720690i	$-0.743825\pi$
$293$		−	24.6725i		−	1.44138i	0.693257	−	0.720690i	$-0.256175\pi$
$294$			2.60520i			0.151938i
$295$	40.3535			2.34947
$296$	−37.0993			−2.15635
$297$		−	2.55475i		−	0.148242i
$298$	−22.1249			−1.28166
$299$	0.200670	−	14.3418i	0.0116051	−	0.829408i
$300$	−44.7198			−2.58190
$301$		−	4.86858i		−	0.280620i
$302$	−37.0434			−2.13161
$303$	8.94756			0.514024
$304$		−	78.8701i		−	4.52351i
$305$			15.5303i			0.889263i
$306$		−	8.36372i		−	0.478122i
$307$		−	13.7540i		−	0.784981i	−0.919756	−	0.392491i	$-0.871614\pi$
$307$		−	13.7540i		−	0.784981i	0.919756	−	0.392491i	$-0.128386\pi$
$308$	−12.2298			−0.696855
$309$	1.67501			0.0952877
$310$			8.56948i			0.486714i
$311$	12.1580			0.689415			0.344707	−	0.938710i	$-0.387978\pi$
$311$	12.1580			0.689415			0.344707	+	0.938710i	$0.387978\pi$
$312$	26.1768	+	0.366265i	1.48197	+	0.0207357i
$313$	21.6699			1.22486			0.612428	−	0.790526i	$-0.290193\pi$
$313$	21.6699			1.22486			0.612428	+	0.790526i	$0.290193\pi$
$314$			21.9378i			1.23802i
$315$	−3.78706			−0.213377
$316$	5.89911			0.331851
$317$		−	29.3780i		−	1.65003i	−0.565109	−	0.825016i	$-0.691166\pi$
$317$		−	29.3780i		−	1.65003i	0.565109	−	0.825016i	$-0.308834\pi$
$318$		−	3.47323i		−	0.194769i
$319$		−	7.32853i		−	0.410319i
$320$			26.0851i			1.45820i
$321$	0.846676			0.0472569
$322$	10.3637			0.577548
$323$			27.1044i			1.50813i
$324$	−4.78706			−0.265948
$325$	−0.471237	+	33.6791i	−0.0261396	+	1.86818i
$326$	9.83695			0.544818
$327$		−	17.9949i		−	0.995121i
$328$	−24.2828			−1.34080
$329$	11.0983			0.611871
$330$		−	25.2053i		−	1.38751i
$331$			23.9124i			1.31434i	0.753741	+	0.657171i	$0.228247\pi$
$331$			23.9124i			1.31434i	−0.753741	+	0.657171i	$0.771753\pi$
$332$			53.1284i			2.91580i
$333$		−	5.10951i		−	0.279999i
$334$	−23.0183			−1.25950
$335$	−41.0770			−2.24428
$336$			9.34181i			0.509638i
$337$	−15.5706			−0.848182			−0.424091	−	0.905620i	$-0.639406\pi$
$337$	−15.5706			−0.848182			−0.424091	+	0.905620i	$0.639406\pi$
$338$	0.947564	−	33.8543i	0.0515407	−	1.84143i
$339$	−2.86858			−0.155800
$340$		−	58.2009i		−	3.15639i
$341$	−2.21902			−0.120167
$342$	21.9949			1.18935
$343$			1.00000i			0.0539949i
$344$		−	35.3500i		−	1.90594i
$345$			15.0653i			0.811087i
$346$			46.0469i			2.47550i
$347$	1.04845			0.0562838			0.0281419	−	0.999604i	$-0.491041\pi$
$347$	1.04845			0.0562838			0.0281419	+	0.999604i	$0.491041\pi$
$348$	−13.7321			−0.736117
$349$			13.8721i			0.742557i	0.928521	+	0.371279i	$0.121081\pi$
$349$			13.8721i			0.742557i	−0.928521	+	0.371279i	$0.878919\pi$
$350$	−24.3373			−1.30088
$351$	−0.0504439	+	3.60520i	−0.00269250	+	0.192431i
$352$	−25.0764			−1.33658
$353$		−	9.96693i		−	0.530486i	−0.964182	−	0.265243i	$-0.914548\pi$
$353$		−	9.96693i		−	0.530486i	0.964182	−	0.265243i	$-0.0854522\pi$
$354$	27.7601			1.47543
$355$	−9.67501			−0.513496
$356$		−	26.4448i		−	1.40157i
$357$		−	3.21040i		−	0.169912i
$358$			44.0469i			2.32795i
$359$		−	18.9705i		−	1.00122i	−0.865672	−	0.500611i	$-0.833109\pi$
$359$		−	18.9705i		−	1.00122i	0.865672	−	0.500611i	$-0.166891\pi$
$360$	−27.4972			−1.44923
$361$	−52.2792			−2.75154
$362$			20.1569i			1.05942i
$363$	−4.47323			−0.234784
$364$	17.2583	+	0.241478i	0.904581	+	0.0126569i
$365$	−25.6297			−1.34152
$366$			10.6836i			0.558442i
$367$	22.3586			1.16711			0.583556	−	0.812073i	$-0.301661\pi$
$367$	22.3586			1.16711			0.583556	+	0.812073i	$0.301661\pi$
$368$	37.1626			1.93723
$369$		−	3.34436i		−	0.174100i
$370$		−	50.4106i		−	2.62072i
$371$		−	1.33319i		−	0.0692159i
$372$			4.15796i			0.215580i
$373$	26.0958			1.35119			0.675595	−	0.737273i	$-0.263887\pi$
$373$	26.0958			1.35119			0.675595	+	0.737273i	$0.263887\pi$
$374$	21.3673			1.10487
$375$		−	16.4427i		−	0.849097i
$376$	80.5833			4.15577
$377$	−0.144703	+	10.3418i	−0.00745256	+	0.532630i
$378$	−2.60520			−0.133997
$379$		−	12.0000i		−	0.616399i	−0.951322	−	0.308199i	$-0.900274\pi$
$379$		−	12.0000i		−	0.616399i	0.951322	−	0.308199i	$-0.0997264\pi$
$380$	153.057			7.85164
$381$	−17.2053			−0.881455
$382$			14.5217i			0.742994i
$383$		−	4.96229i		−	0.253561i	−0.991931	−	0.126781i	$-0.959536\pi$
$383$		−	4.96229i		−	0.253561i	0.991931	−	0.126781i	$-0.0404644\pi$
$384$		−	1.68672i		−	0.0860752i
$385$		−	9.67501i		−	0.493084i
$386$	19.7321			1.00434
$387$	4.86858			0.247484
$388$		−	27.0861i		−	1.37509i
$389$	17.8757			0.906333			0.453166	−	0.891426i	$-0.350294\pi$
$389$	17.8757			0.906333			0.453166	+	0.891426i	$0.350294\pi$
$390$	−0.497681	+	35.5690i	−0.0252011	+	1.80111i
$391$	−12.7713			−0.645870
$392$			7.26084i			0.366728i
$393$	−16.6836			−0.841578
$394$	34.7647			1.75142
$395$			4.66681i			0.234813i
$396$		−	12.2298i		−	0.614569i
$397$			7.06925i			0.354796i	0.984139	+	0.177398i	$0.0567679\pi$
$397$			7.06925i			0.354796i	−0.984139	+	0.177398i	$0.943232\pi$
$398$		−	43.9898i		−	2.20501i
$399$	8.44270			0.422664
$400$	−87.2695			−4.36347
$401$		−	9.12025i		−	0.455444i	−0.973726	−	0.227722i	$-0.926872\pi$
$401$		−	9.12025i		−	0.455444i	0.973726	−	0.227722i	$-0.0731277\pi$
$402$	−28.2577			−1.40937
$403$	3.13142	+	0.0438147i	0.155987	+	0.00218257i
$404$	42.8325			2.13100
$405$		−	3.78706i		−	0.188180i
$406$	−7.47323			−0.370890
$407$	13.0535			0.647040
$408$		−	23.3102i		−	1.15403i
$409$		−	18.2542i		−	0.902611i	−0.892369	−	0.451306i	$-0.850958\pi$
$409$		−	18.2542i		−	0.902611i	0.892369	−	0.451306i	$-0.149042\pi$
$410$		−	32.9956i		−	1.62953i
$411$			18.9134i			0.932929i
$412$	8.01835			0.395036
$413$	10.6556			0.524330
$414$			10.3637i			0.509349i
$415$	−42.0301			−2.06318
$416$	35.3872	+	0.495137i	1.73500	+	0.0242761i
$417$	−5.67501			−0.277906
$418$			56.1916i			2.74842i
$419$	13.6934			0.668964			0.334482	−	0.942402i	$-0.391439\pi$
$419$	13.6934			0.668964			0.334482	+	0.942402i	$0.391439\pi$
$420$	−18.1289			−0.884598
$421$		−	33.8146i		−	1.64802i	−0.566573	−	0.824012i	$-0.691731\pi$
$421$		−	33.8146i		−	1.64802i	0.566573	−	0.824012i	$-0.308269\pi$
$422$			30.4728i			1.48339i
$423$			11.0983i			0.539620i
$424$		−	9.68009i		−	0.470107i
$425$	29.9909			1.45477
$426$	−6.65564			−0.322467
$427$			4.10089i			0.198456i
$428$	4.05309			0.195913
$429$	−9.21040	−	0.128872i	−0.444682	−	0.00622199i
$430$	48.0336			2.31639
$431$			20.3256i			0.979048i	0.871990	+	0.489524i	$0.162829\pi$
$431$			20.3256i			0.979048i	−0.871990	+	0.489524i	$0.837171\pi$
$432$	−9.34181			−0.449458
$433$	−17.1106			−0.822284			−0.411142	−	0.911571i	$-0.634870\pi$
$433$	−17.1106			−0.822284			−0.411142	+	0.911571i	$0.634870\pi$
$434$			2.26283i			0.108619i
$435$		−	10.8635i		−	0.520865i
$436$		−	86.1427i		−	4.12549i
$437$		−	33.5858i		−	1.60663i
$438$	−17.6312			−0.842451
$439$	−1.67501			−0.0799436			−0.0399718	−	0.999201i	$-0.512727\pi$
$439$	−1.67501			−0.0799436			−0.0399718	+	0.999201i	$0.512727\pi$
$440$		−	70.2487i		−	3.34897i
$441$	−1.00000			−0.0476190
$442$	−30.1529	−	0.421899i	−1.43423	−	0.0200677i
$443$	−12.9073			−0.613245			−0.306622	−	0.951831i	$-0.599199\pi$
$443$	−12.9073			−0.613245			−0.306622	+	0.951831i	$0.599199\pi$
$444$		−	24.4595i		−	1.16080i
$445$	20.9206			0.991730
$446$	−11.0485			−0.523159
$447$		−	8.49259i		−	0.401686i
$448$			6.88795i			0.325425i
$449$			21.1762i			0.999368i	0.866208	+	0.499684i	$0.166550\pi$
$449$			21.1762i			0.999368i	−0.866208	+	0.499684i	$0.833450\pi$
$450$		−	24.3373i		−	1.14727i
$451$	8.54401			0.402322
$452$	−13.7321			−0.645903
$453$		−	14.2190i		−	0.668068i
$454$	4.49768			0.211087
$455$	−0.191034	+	13.6531i	−0.00895581	+	0.640067i
$456$	61.3011			2.87069
$457$		−	8.41570i		−	0.393670i	−0.980437	−	0.196835i	$-0.936934\pi$
$457$		−	8.41570i		−	0.393670i	0.980437	−	0.196835i	$-0.0630663\pi$
$458$	−17.7892			−0.831232
$459$	3.21040			0.149848
$460$			72.1183i			3.36253i
$461$			1.76515i			0.0822113i	0.999155	+	0.0411056i	$0.0130880\pi$
$461$			1.76515i			0.0822113i	−0.999155	+	0.0411056i	$0.986912\pi$
$462$		−	6.65564i		−	0.309649i
$463$			38.9241i			1.80896i	0.426519	+	0.904479i	$0.359740\pi$
$463$			38.9241i			1.80896i	−0.426519	+	0.904479i	$0.640260\pi$
$464$	−26.7978			−1.24406
$465$	−3.28938			−0.152541
$466$		−	3.47323i		−	0.160894i
$467$	−30.4544			−1.40926			−0.704631	−	0.709573i	$-0.748888\pi$
$467$	−30.4544			−1.40926			−0.704631	+	0.709573i	$0.748888\pi$
$468$	−0.241478	+	17.2583i	−0.0111623	+	0.797765i
$469$	−10.8467			−0.500853
$470$			109.497i			5.05071i
$471$	−8.42079			−0.388010
$472$	77.3689			3.56119
$473$			12.4380i			0.571902i
$474$			3.21040i			0.147458i
$475$			78.8701i			3.61881i
$476$		−	15.3684i		−	0.704408i
$477$	1.33319			0.0610427
$478$	−10.1859			−0.465894
$479$		−	3.54656i		−	0.162046i	−0.996712	−	0.0810232i	$-0.974181\pi$
$479$		−	3.54656i		−	0.162046i	0.996712	−	0.0810232i	$-0.0258188\pi$
$480$	−37.1722			−1.69667
$481$	−18.4208	−	0.257744i	−0.839916	−	0.0117521i
$482$	66.1467			3.01290
$483$			3.97809i			0.181009i
$484$	−21.4136			−0.973346
$485$	21.4279			0.972990
$486$		−	2.60520i		−	0.118174i
$487$			39.9898i			1.81211i	0.423158	+	0.906056i	$0.360922\pi$
$487$			39.9898i			1.81211i	−0.423158	+	0.906056i	$0.639078\pi$
$488$			29.7759i			1.34789i
$489$			3.77589i			0.170752i
$490$	−9.86604			−0.445702
$491$	−9.69844			−0.437685			−0.218842	−	0.975760i	$-0.570228\pi$
$491$	−9.69844			−0.437685			−0.218842	+	0.975760i	$0.570228\pi$
$492$		−	16.0096i		−	0.721770i
$493$	9.20929			0.414766
$494$	1.10951	−	79.2960i	0.0499192	−	3.56770i
$495$	9.67501			0.434859
$496$			8.11415i			0.364336i
$497$	−2.55475			−0.114596
$498$	−28.9134			−1.29564
$499$			24.0336i			1.07589i	0.842979	+	0.537947i	$0.180800\pi$
$499$			24.0336i			1.07589i	−0.842979	+	0.537947i	$0.819200\pi$
$500$		−	78.7122i		−	3.52012i
$501$		−	8.83551i		−	0.394741i
$502$		−	67.1381i		−	2.99652i
$503$	3.67390			0.163811			0.0819056	−	0.996640i	$-0.473899\pi$
$503$	3.67390			0.163811			0.0819056	+	0.996640i	$0.473899\pi$
$504$	−7.26084			−0.323424
$505$			33.8849i			1.50786i
$506$	−26.4768			−1.17704
$507$	12.9949	+	0.363721i	0.577124	+	0.0161534i
$508$	−82.3628			−3.65426
$509$			19.3612i			0.858169i	0.903264	+	0.429085i	$0.141164\pi$
$509$			19.3612i			0.858169i	−0.903264	+	0.429085i	$0.858836\pi$
$510$	31.6739			1.40254
$511$	−6.76770			−0.299385
$512$		−	43.9634i		−	1.94293i
$513$			8.44270i			0.372754i
$514$			15.3102i			0.675303i
$515$			6.34334i			0.279521i
$516$	23.3062			1.02600
$517$	−28.3535			−1.24699
$518$		−	13.3113i		−	0.584864i
$519$	−17.6750			−0.775847
$520$	−1.38707	+	99.1330i	−0.0608269	+	4.34727i
$521$	34.1130			1.49452			0.747260	−	0.664532i	$-0.231369\pi$
$521$	34.1130			1.49452			0.747260	+	0.664532i	$0.231369\pi$
$522$		−	7.47323i		−	0.327094i
$523$	−33.0250			−1.44408			−0.722042	−	0.691850i	$-0.756796\pi$
$523$	−33.0250			−1.44408			−0.722042	+	0.691850i	$0.756796\pi$
$524$	−79.8655			−3.48894
$525$		−	9.34181i		−	0.407710i
$526$		−	26.6796i		−	1.16329i
$527$		−	2.78850i		−	0.121469i
$528$		−	23.8660i		−	1.03864i
$529$	−7.17478			−0.311947
$530$	13.1533			0.571344
$531$			10.6556i			0.462415i
$532$	40.4157			1.75224
$533$	−12.0571	−	0.168702i	−0.522250	−	0.00730731i
$534$	14.3917			0.622790
$535$			3.20641i			0.138625i
$536$	−78.7560			−3.40174
$537$	−16.9073			−0.729604
$538$		−	42.0469i		−	1.81277i
$539$		−	2.55475i		−	0.110041i
$540$		−	18.1289i		−	0.780142i
$541$		−	24.8416i		−	1.06802i	−0.845477	−	0.534012i	$-0.820684\pi$
$541$		−	24.8416i		−	1.06802i	0.845477	−	0.534012i	$-0.179316\pi$
$542$	31.9339			1.37168
$543$	−7.73717			−0.332034
$544$		−	31.5120i		−	1.35106i
$545$	68.1478			2.91913
$546$	−0.131416	+	9.39226i	−0.00562410	+	0.401951i
$547$	8.14114			0.348090			0.174045	−	0.984738i	$-0.444316\pi$
$547$	8.14114			0.348090			0.174045	+	0.984738i	$0.444316\pi$
$548$			90.5395i			3.86766i
$549$	−4.10089			−0.175022
$550$	62.1758			2.65118
$551$			24.2186i			1.03175i
$552$			28.8843i			1.22940i
$553$			1.23230i			0.0524029i
$554$			25.5701i			1.08637i
$555$	19.3500			0.821362
$556$	−27.1666			−1.15212
$557$			8.11052i			0.343654i	0.985127	+	0.171827i	$0.0549670\pi$
$557$			8.11052i			0.343654i	−0.985127	+	0.171827i	$0.945033\pi$
$558$	−2.26283			−0.0957933
$559$	0.245590	−	17.5522i	0.0103874	−	0.742379i
$560$	−35.3780			−1.49499
$561$			8.20178i			0.346279i
$562$	−42.1809			−1.77929
$563$	11.1044			0.467995			0.233998	−	0.972237i	$-0.424819\pi$
$563$	11.1044			0.467995			0.233998	+	0.972237i	$0.424819\pi$
$564$			53.1284i			2.23711i
$565$		−	10.8635i		−	0.457031i
$566$			49.8849i			2.09682i
$567$		−	1.00000i		−	0.0419961i
$568$	−18.5497			−0.778327
$569$	2.86858			0.120257			0.0601286	−	0.998191i	$-0.480849\pi$
$569$	2.86858			0.120257			0.0601286	+	0.998191i	$0.480849\pi$
$570$			83.2960i			3.48889i
$571$	32.4947			1.35986			0.679930	−	0.733277i	$-0.262010\pi$
$571$	32.4947			1.35986			0.679930	+	0.733277i	$0.262010\pi$
$572$	−44.0907	−	0.616917i	−1.84353	−	0.0257946i
$573$	−5.57412			−0.232862
$574$		−	8.71272i		−	0.363662i
$575$	−37.1626			−1.54979
$576$	−6.88795			−0.286998
$577$		−	24.3759i		−	1.01478i	−0.861716	−	0.507390i	$-0.830610\pi$
$577$		−	24.3759i		−	1.01478i	0.861716	−	0.507390i	$-0.169390\pi$
$578$		−	17.4375i		−	0.725305i
$579$			7.57412i			0.314770i
$580$		−	52.0042i		−	2.15936i
$581$	−11.0983			−0.460437
$582$	14.7407			0.611022
$583$			3.40598i			0.141061i
$584$	−49.1392			−2.03339
$585$	−13.6531	−	0.191034i	−0.564486	−	0.00789828i
$586$	64.2767			2.65524
$587$		−	11.7483i		−	0.484906i	−0.970163	−	0.242453i	$-0.922048\pi$
$587$		−	11.7483i		−	0.484906i	0.970163	−	0.242453i	$-0.0779520\pi$
$588$	−4.78706			−0.197415
$589$	7.33319			0.302159
$590$			105.129i			4.32809i
$591$			13.3444i			0.548914i
$592$		−	47.7321i		−	1.96178i
$593$			46.6459i			1.91552i	0.287574	+	0.957759i	$0.407151\pi$
$593$			46.6459i			1.91552i	−0.287574	+	0.957759i	$0.592849\pi$
$594$	6.65564			0.273084
$595$	12.1580			0.498428
$596$		−	40.6545i		−	1.66527i
$597$	16.8854			0.691073
$598$	37.3633	+	0.522786i	1.52790	+	0.0213783i
$599$	−20.8197			−0.850669			−0.425335	−	0.905036i	$-0.639844\pi$
$599$	−20.8197			−0.850669			−0.425335	+	0.905036i	$0.639844\pi$
$600$		−	67.8294i		−	2.76912i
$601$	24.2588			0.989539			0.494770	−	0.869024i	$-0.335252\pi$
$601$	24.2588			0.989539			0.494770	+	0.869024i	$0.335252\pi$
$602$	12.6836			0.516946
$603$		−	10.8467i		−	0.441711i
$604$		−	68.0673i		−	2.76962i
$605$		−	16.9404i		−	0.688724i
$606$			23.3102i			0.946911i
$607$	6.20067			0.251677			0.125839	−	0.992051i	$-0.459838\pi$
$607$	6.20067			0.251677			0.125839	+	0.992051i	$0.459838\pi$
$608$	82.8701			3.36083
$609$		−	2.86858i		−	0.116241i
$610$	−40.4595			−1.63816
$611$	40.0117	+	0.559844i	1.61870	+	0.0226489i
$612$	15.3684			0.621229
$613$		−	14.9026i		−	0.601912i	−0.953638	−	0.300956i	$-0.902694\pi$
$613$		−	14.9026i		−	0.601912i	0.953638	−	0.300956i	$-0.0973058\pi$
$614$	35.8319			1.44606
$615$	12.6653			0.510713
$616$		−	18.5497i		−	0.747387i
$617$		−	24.1472i		−	0.972130i	−0.873923	−	0.486065i	$-0.838432\pi$
$617$		−	24.1472i		−	0.972130i	0.873923	−	0.486065i	$-0.161568\pi$
$618$			4.36372i			0.175535i
$619$			43.9339i			1.76585i	0.469513	+	0.882925i	$0.344429\pi$
$619$			43.9339i			1.76585i	−0.469513	+	0.882925i	$0.655571\pi$
$620$	−15.7464			−0.632392
$621$	−3.97809			−0.159635
$622$			31.6739i			1.27001i
$623$	5.52423			0.221323
$624$	−0.471237	+	33.6791i	−0.0188646	+	1.34824i
$625$	15.5604			0.622416
$626$			56.4544i			2.25637i
$627$	−21.5690			−0.861384
$628$	−40.3108			−1.60858
$629$			16.4036i			0.654052i
$630$		−	9.86604i		−	0.393072i
$631$		−	25.9511i		−	1.03310i	−0.856258	−	0.516548i	$-0.827217\pi$
$631$		−	25.9511i		−	1.03310i	0.856258	−	0.516548i	$-0.172783\pi$
$632$			8.94756i			0.355915i
$633$	−11.6969			−0.464911
$634$	76.5355			3.03961
$635$		−	65.1575i		−	2.58570i
$636$	6.38207			0.253065
$637$	−0.0504439	+	3.60520i	−0.00199866	+	0.142843i
$638$	19.0923			0.755870
$639$		−	2.55475i		−	0.101065i
$640$	6.38772			0.252497
$641$	−39.5858			−1.56355			−0.781773	−	0.623563i	$-0.785685\pi$
$641$	−39.5858			−1.56355			−0.781773	+	0.623563i	$0.785685\pi$
$642$			2.20576i			0.0870544i
$643$		−	17.0434i		−	0.672125i	−0.941840	−	0.336062i	$-0.890905\pi$
$643$		−	17.0434i		−	0.672125i	0.941840	−	0.336062i	$-0.109095\pi$
$644$			19.0434i			0.750414i
$645$			18.4376i			0.725980i
$646$	−70.6124			−2.77821
$647$	−27.7544			−1.09114			−0.545569	−	0.838066i	$-0.683687\pi$
$647$	−27.7544			−1.09114			−0.545569	+	0.838066i	$0.683687\pi$
$648$		−	7.26084i		−	0.285233i
$649$	−27.2225			−1.06858
$650$	−87.7407	−	1.22767i	−3.44147	−	0.0481531i
$651$	−0.868584			−0.0340425
$652$			18.0754i			0.707888i
$653$	−7.77080			−0.304095			−0.152048	−	0.988373i	$-0.548587\pi$
$653$	−7.77080			−0.304095			−0.152048	+	0.988373i	$0.548587\pi$
$654$	46.8803			1.83317
$655$		−	63.1819i		−	2.46872i
$656$		−	31.2424i		−	1.21981i
$657$		−	6.76770i		−	0.264033i
$658$			28.9134i			1.12716i
$659$	−4.74935			−0.185008			−0.0925042	−	0.995712i	$-0.529487\pi$
$659$	−4.74935			−0.185008			−0.0925042	+	0.995712i	$0.529487\pi$
$660$	46.3148			1.80280
$661$		−	38.0301i		−	1.47920i	−0.673047	−	0.739599i	$-0.735015\pi$
$661$		−	38.0301i		−	1.47920i	0.673047	−	0.739599i	$-0.264985\pi$
$662$	−62.2965			−2.42122
$663$	0.161945	−	11.5741i	0.00628942	−	0.449501i
$664$	−80.5833			−3.12724
$665$			31.9730i			1.23986i
$666$	13.3113			0.515802
$667$	−11.4115			−0.441855
$668$		−	42.2961i		−	1.63649i
$669$		−	4.24093i		−	0.163964i
$670$		−	107.014i		−	4.13430i
$671$		−	10.4768i		−	0.404451i
$672$	−9.81560			−0.378645
$673$	23.0602			0.888905			0.444452	−	0.895803i	$-0.353398\pi$
$673$	23.0602			0.888905			0.444452	+	0.895803i	$0.353398\pi$
$674$		−	40.5644i		−	1.56248i
$675$	9.34181			0.359567
$676$	62.2074	+	1.74115i	2.39259	+	0.0669674i
$677$	−44.3759			−1.70550			−0.852752	−	0.522317i	$-0.825068\pi$
$677$	−44.3759			−1.70550			−0.852752	+	0.522317i	$0.825068\pi$
$678$		−	7.47323i		−	0.287008i
$679$	5.65819			0.217141
$680$	88.2770			3.38527
$681$			1.72643i			0.0661568i
$682$		−	5.78098i		−	0.221365i
$683$			5.91494i			0.226329i	0.993576	+	0.113165i	$0.0360987\pi$
$683$			5.91494i			0.226329i	−0.993576	+	0.113165i	$0.963901\pi$
$684$			40.4157i			1.54533i
$685$	−71.6261			−2.73669
$686$	−2.60520			−0.0994669
$687$		−	6.82833i		−	0.260517i
$688$	45.4814			1.73396
$689$	0.0672514	−	4.80642i	0.00256207	−	0.183110i
$690$	−39.2480			−1.49415
$691$		−	12.6883i		−	0.482685i	−0.970440	−	0.241343i	$-0.922412\pi$
$691$		−	12.6883i		−	0.482685i	0.970440	−	0.241343i	$-0.0775878\pi$
$692$	−84.6113			−3.21644
$693$	2.55475			0.0970471
$694$			2.73143i			0.103683i
$695$		−	21.4916i		−	0.815222i
$696$		−	20.8283i		−	0.789496i
$697$			10.7367i			0.406682i
$698$	−36.1396			−1.36790
$699$	1.33319			0.0504260
$700$		−	44.7198i		−	1.69025i
$701$	25.8487			0.976291			0.488146	−	0.872762i	$-0.337674\pi$
$701$	25.8487			0.976291			0.488146	+	0.872762i	$0.337674\pi$
$702$	−9.39226	−	0.131416i	−0.354488	−	0.00495999i
$703$	−43.1381			−1.62698
$704$		−	17.5970i		−	0.663212i
$705$	−42.0301			−1.58294
$706$	25.9658			0.977237
$707$			8.94756i			0.336508i
$708$			51.0092i			1.91704i
$709$			18.8803i			0.709065i	0.935044	+	0.354533i	$0.115360\pi$
$709$			18.8803i			0.709065i	−0.935044	+	0.354533i	$0.884640\pi$
$710$		−	25.2053i		−	0.945938i
$711$	−1.23230			−0.0462150
$712$	40.1105			1.50321
$713$			3.45531i			0.129402i
$714$	8.36372			0.313004
$715$	0.488045	−	34.8803i	0.0182518	−	1.30445i
$716$	−80.9363			−3.02473
$717$		−	3.90985i		−	0.146016i
$718$	49.4218			1.84441
$719$	−40.1580			−1.49764			−0.748820	−	0.662774i	$-0.769379\pi$
$719$	−40.1580			−1.49764			−0.748820	+	0.662774i	$0.769379\pi$
$720$		−	35.3780i		−	1.31846i
$721$			1.67501i			0.0623804i
$722$		−	136.198i		−	5.06875i
$723$			25.3903i			0.944274i
$724$	−37.0383			−1.37652
$725$	26.7978			0.995244
$726$		−	11.6537i		−	0.432508i
$727$	−32.0336			−1.18806			−0.594031	−	0.804442i	$-0.702464\pi$
$727$	−32.0336			−1.18806			−0.594031	+	0.804442i	$0.702464\pi$
$728$	−0.366265	+	26.1768i	−0.0135747	+	0.970176i
$729$	1.00000			0.0370370
$730$		−	66.7704i		−	2.47128i
$731$	−15.6301			−0.578100
$732$	−19.6312			−0.725590
$733$			48.3265i			1.78498i	0.451066	+	0.892491i	$0.351044\pi$
$733$			48.3265i			1.78498i	−0.451066	+	0.892491i	$0.648956\pi$
$734$			58.2487i			2.15000i
$735$		−	3.78706i		−	0.139688i
$736$			39.0473i			1.43930i
$737$	27.7106			1.02073
$738$	8.71272			0.320719
$739$			35.7321i			1.31443i	0.753705	+	0.657213i	$0.228265\pi$
$739$			35.7321i			1.31443i	−0.753705	+	0.657213i	$0.771735\pi$
$740$	92.6296			3.40513
$741$	30.4376	+	0.425883i	1.11815	+	0.0156452i
$742$	3.47323			0.127506
$743$		−	45.0092i		−	1.65123i	−0.564236	−	0.825613i	$-0.690829\pi$
$743$		−	45.0092i		−	1.65123i	0.564236	−	0.825613i	$-0.309171\pi$
$744$	−6.30665			−0.231213
$745$	32.1619			1.17832
$746$			67.9847i			2.48910i
$747$		−	11.0983i		−	0.406067i
$748$			39.2624i			1.43557i
$749$			0.846676i			0.0309369i
$750$	42.8365			1.56417
$751$	5.39425			0.196839			0.0984195	−	0.995145i	$-0.468621\pi$
$751$	5.39425			0.196839			0.0984195	+	0.995145i	$0.468621\pi$
$752$			103.679i			3.78077i
$753$	25.7708			0.939140
$754$	−26.9425	−	0.376979i	−0.981187	−	0.0137288i
$755$	53.8483			1.95974
$756$		−	4.78706i		−	0.174104i
$757$	13.7896			0.501191			0.250595	−	0.968092i	$-0.419374\pi$
$757$	13.7896			0.501191			0.250595	+	0.968092i	$0.419374\pi$
$758$	31.2624			1.13550
$759$		−	10.1631i		−	0.368895i
$760$			232.151i			8.42100i
$761$			30.6674i			1.11169i	0.831286	+	0.555846i	$0.187605\pi$
$761$			30.6674i			1.11169i	−0.831286	+	0.555846i	$0.812395\pi$
$762$		−	44.8232i		−	1.62377i
$763$	17.9949			0.651460
$764$	−26.6836			−0.965380
$765$			12.1580i			0.439572i
$766$	12.9277			0.467099
$767$	38.4157	+	0.537512i	1.38711	+	0.0194084i
$768$	18.1701			0.655659
$769$		−	48.6160i		−	1.75314i	−0.481278	−	0.876568i	$-0.659827\pi$
$769$		−	48.6160i		−	1.75314i	0.481278	−	0.876568i	$-0.340173\pi$
$770$	25.2053			0.908336
$771$	−5.87678			−0.211647
$772$			36.2577i			1.30494i
$773$			18.6729i			0.671617i	0.941930	+	0.335808i	$0.109009\pi$
$773$			18.6729i			0.671617i	−0.941930	+	0.335808i	$0.890991\pi$
$774$			12.6836i			0.455904i
$775$		−	8.11415i		−	0.291469i
$776$	41.0832			1.47480
$777$	5.10951			0.183303
$778$			46.5697i			1.66960i
$779$	−28.2354			−1.01164
$780$	−65.3582	−	0.914491i	−2.34020	−	0.0327440i
$781$	6.52677			0.233546
$782$		−	33.2717i		−	1.18979i
$783$	2.86858			0.102515
$784$	−9.34181			−0.333636
$785$		−	31.8900i		−	1.13820i
$786$		−	43.4642i		−	1.55032i
$787$		−	9.61751i		−	0.342827i	−0.985199	−	0.171414i	$-0.945167\pi$
$787$		−	9.61751i		−	0.342827i	0.985199	−	0.171414i	$-0.0548334\pi$
$788$			63.8802i			2.27564i
$789$	10.2409			0.364587
$790$	−12.1580			−0.432561
$791$		−	2.86858i		−	0.101995i
$792$	18.5497			0.659134
$793$	−0.206865	+	14.7845i	−0.00734598	+	0.525013i
$794$	−18.4168			−0.653588
$795$			5.04888i			0.179065i
$796$	80.8314			2.86499
$797$	−3.73606			−0.132338			−0.0661691	−	0.997808i	$-0.521078\pi$
$797$	−3.73606			−0.132338			−0.0661691	+	0.997808i	$0.521078\pi$
$798$			21.9949i			0.778611i
$799$		−	35.6301i		−	1.26050i
$800$		−	91.6955i		−	3.24192i
$801$			5.52423i			0.195189i
$802$	23.7601			0.838997
$803$	17.2898			0.610144
$804$		−	51.9237i		−	1.83121i
$805$	−15.0653			−0.530981
$806$	−0.114146	+	8.15796i	−0.00402062	+	0.287352i
$807$	16.1396			0.568141
$808$			64.9668i			2.28553i
$809$	−10.1850			−0.358084			−0.179042	−	0.983841i	$-0.557300\pi$
$809$	−10.1850			−0.358084			−0.179042	+	0.983841i	$0.557300\pi$
$810$	9.86604			0.346657
$811$			6.21902i			0.218379i	0.994021	+	0.109190i	$0.0348256\pi$
$811$			6.21902i			0.218379i	−0.994021	+	0.109190i	$0.965174\pi$
$812$		−	13.7321i		−	0.481901i
$813$			12.2577i			0.429898i
$814$			34.0071i			1.19195i
$815$	−14.2995			−0.500891
$816$	29.9909			1.04989
$817$		−	41.1040i		−	1.43805i
$818$	47.5558			1.66275
$819$	−3.60520	−	0.0504439i	−0.125976	−	0.00176265i
$820$	60.6294			2.11727
$821$		−	55.4534i		−	1.93534i	−0.252224	−	0.967669i	$-0.581162\pi$
$821$		−	55.4534i		−	1.93534i	0.252224	−	0.967669i	$-0.418838\pi$
$822$	−49.2731			−1.71860
$823$	−20.4380			−0.712425			−0.356213	−	0.934405i	$-0.615932\pi$
$823$	−20.4380			−0.712425			−0.356213	+	0.934405i	$0.615932\pi$
$824$			12.1619i			0.423681i
$825$			23.8660i			0.830909i
$826$			27.7601i			0.965896i
$827$		−	14.1289i		−	0.491309i	−0.969357	−	0.245655i	$-0.920997\pi$
$827$		−	14.1289i		−	0.491309i	0.969357	−	0.245655i	$-0.0790029\pi$
$828$	−19.0434			−0.661803
$829$	34.9159			1.21268			0.606340	−	0.795206i	$-0.292637\pi$
$829$	34.9159			1.21268			0.606340	+	0.795206i	$0.292637\pi$
$830$		−	109.497i		−	3.80069i
$831$	−9.81504			−0.340480
$832$	−0.347455	+	24.8324i	−0.0120458	+	0.860909i
$833$	3.21040			0.111234
$834$		−	14.7845i		−	0.511946i
$835$	33.4606			1.15795
$836$	−103.252			−3.57105
$837$		−	0.868584i		−	0.0300226i
$838$			35.6739i			1.23233i
$839$			46.4437i			1.60341i	0.597717	+	0.801707i	$0.296075\pi$
$839$			46.4437i			1.60341i	−0.597717	+	0.801707i	$0.703925\pi$
$840$		−	27.4972i		−	0.948745i
$841$	−20.7712			−0.716249
$842$	88.0938			3.03591
$843$		−	16.1910i		−	0.557649i
$844$	−55.9938			−1.92739
$845$	−1.37743	+	49.2125i	−0.0473851	+	1.69296i
$846$	−28.9134			−0.994063
$847$		−	4.47323i		−	0.153702i
$848$	12.4544			0.427687
$849$	−19.1482			−0.657166
$850$			78.1323i			2.67992i
$851$		−	20.3261i		−	0.696770i
$852$		−	12.2298i		−	0.418985i
$853$			41.4462i			1.41909i	0.704659	+	0.709546i	$0.251100\pi$
$853$			41.4462i			1.41909i	−0.704659	+	0.709546i	$0.748900\pi$
$854$	−10.6836			−0.365586
$855$	−31.9730			−1.09345
$856$			6.14758i			0.210120i
$857$	33.8666			1.15686			0.578431	−	0.815732i	$-0.303665\pi$
$857$	33.8666			1.15686			0.578431	+	0.815732i	$0.303665\pi$
$858$	0.335737	−	23.9949i	0.0114619	−	0.819173i
$859$	−37.2890			−1.27228			−0.636141	−	0.771573i	$-0.719470\pi$
$859$	−37.2890			−1.27228			−0.636141	+	0.771573i	$0.719470\pi$
$860$			88.2619i			3.00971i
$861$	3.34436			0.113975
$862$	−52.9521			−1.80356
$863$			38.7464i			1.31894i	0.751730	+	0.659471i	$0.229219\pi$
$863$			38.7464i			1.31894i	−0.751730	+	0.659471i	$0.770781\pi$
$864$		−	9.81560i		−	0.333933i
$865$		−	66.9363i		−	2.27590i
$866$		−	44.5765i		−	1.51477i
$867$	6.69335			0.227318
$868$	−4.15796			−0.141130
$869$		−	3.14823i		−	0.106797i
$870$	28.3016			0.959513
$871$	−39.1044	−	0.547149i	−1.32500	−	0.0185394i
$872$	130.658			4.42464
$873$			5.65819i			0.191501i
$874$	87.4978			2.95966
$875$	16.4427			0.555865
$876$		−	32.3974i		−	1.09461i
$877$			51.8319i			1.75024i	0.483908	+	0.875119i	$0.339217\pi$
$877$			51.8319i			1.75024i	−0.483908	+	0.875119i	$0.660783\pi$
$878$		−	4.36372i		−	0.147268i
$879$			24.6725i			0.832181i
$880$	90.3821			3.04678
$881$	20.7896			0.700420			0.350210	−	0.936671i	$-0.386110\pi$
$881$	20.7896			0.700420			0.350210	+	0.936671i	$0.386110\pi$
$882$		−	2.60520i		−	0.0877216i
$883$	17.5292			0.589904			0.294952	−	0.955512i	$-0.404696\pi$
$883$	17.5292			0.589904			0.294952	+	0.955512i	$0.404696\pi$
$884$	0.775240	−	55.4060i	0.0260741	−	1.86350i
$885$	−40.3535			−1.35647
$886$		−	33.6261i		−	1.12969i
$887$	9.53539			0.320167			0.160084	−	0.987103i	$-0.448824\pi$
$887$	9.53539			0.320167			0.160084	+	0.987103i	$0.448824\pi$
$888$	37.0993			1.24497
$889$		−	17.2053i		−	0.577047i
$890$			54.5022i			1.82692i
$891$			2.55475i			0.0855875i
$892$		−	20.3016i		−	0.679746i
$893$	93.7000			3.13555
$894$	22.1249			0.739967
$895$		−	64.0290i		−	2.14025i
$896$	1.68672			0.0563495
$897$	−0.200670	+	14.3418i	−0.00670019	+	0.478859i
$898$	−55.1683			−1.84099
$899$		−	2.49160i		−	0.0830997i
$900$	44.7198			1.49066
$901$	−4.28008			−0.142590
$902$			22.2588i			0.741139i
$903$			4.86858i			0.162016i
$904$		−	20.8283i		−	0.692740i
$905$		−	29.3011i		−	0.974002i
$906$	37.0434			1.23068
$907$	27.3270			0.907378			0.453689	−	0.891160i	$-0.350108\pi$
$907$	27.3270			0.907378			0.453689	+	0.891160i	$0.350108\pi$
$908$			8.26450i			0.274267i
$909$	−8.94756			−0.296772
$910$	−35.5690	−	0.497681i	−1.17910	−	0.0164980i
$911$	−38.9582			−1.29074			−0.645371	−	0.763869i	$-0.723297\pi$
$911$	−38.9582			−1.29074			−0.645371	+	0.763869i	$0.723297\pi$
$912$			78.8701i			2.61165i
$913$	28.3535			0.938365
$914$	21.9246			0.725201
$915$		−	15.5303i		−	0.513416i
$916$		−	32.6876i		−	1.08003i
$917$		−	16.6836i		−	0.550942i
$918$			8.36372i			0.276044i
$919$	9.94293			0.327987			0.163993	−	0.986461i	$-0.447562\pi$
$919$	9.94293			0.327987			0.163993	+	0.986461i	$0.447562\pi$
$920$	−109.387			−3.60637
$921$			13.7540i			0.453209i
$922$	−4.59857			−0.151446
$923$	−9.21040	−	0.128872i	−0.303164	−	0.00424187i
$924$	12.2298			0.402330
$925$			47.7321i			1.56942i
$926$	−101.405			−3.33238
$927$	−1.67501			−0.0550144
$928$		−	28.1569i		−	0.924294i
$929$		−	7.80854i		−	0.256190i	−0.991762	−	0.128095i	$-0.959114\pi$
$929$		−	7.80854i		−	0.256190i	0.991762	−	0.128095i	$-0.0408862\pi$
$930$		−	8.56948i		−	0.281004i
$931$			8.44270i			0.276698i
$932$	6.38207			0.209052
$933$	−12.1580			−0.398034
$934$		−	79.3398i		−	2.59608i
$935$	−31.0606			−1.01579
$936$	−26.1768	−	0.366265i	−0.855615	−	0.0119717i
$937$	−9.59246			−0.313372			−0.156686	−	0.987648i	$-0.550081\pi$
$937$	−9.59246			−0.313372			−0.156686	+	0.987648i	$0.550081\pi$
$938$		−	28.2577i		−	0.922648i
$939$	−21.6699			−0.707171
$940$	−201.200			−6.56243
$941$			28.5043i			0.929214i	0.885517	+	0.464607i	$0.153804\pi$
$941$			28.5043i			0.929214i	−0.885517	+	0.464607i	$0.846196\pi$
$942$		−	21.9378i		−	0.714773i
$943$		−	13.3042i		−	0.433243i
$944$			99.5430i			3.23985i
$945$	3.78706			0.123193
$946$	−32.4036			−1.05353
$947$			47.8997i			1.55653i	0.627936	+	0.778265i	$0.283900\pi$
$947$			47.8997i			1.55653i	−0.627936	+	0.778265i	$0.716100\pi$
$948$	−5.89911			−0.191594
$949$	−24.3989	−	0.341389i	−0.792021	−	0.0110820i
$950$	−205.472			−6.66640
$951$			29.3780i			0.952647i
$952$	23.3102			0.755487
$953$	32.5181			1.05337			0.526683	−	0.850062i	$-0.323436\pi$
$953$	32.5181			1.05337			0.526683	+	0.850062i	$0.323436\pi$
$954$			3.47323i			0.112450i
$955$		−	21.1095i		−	0.683088i
$956$		−	18.7167i		−	0.605341i
$957$			7.32853i			0.236898i
$958$	9.23949			0.298514
$959$	−18.9134			−0.610745
$960$		−	26.0851i		−	0.841892i
$961$	30.2456			0.975663
$962$	0.671473	−	47.9898i	0.0216492	−	1.54725i
$963$	−0.846676			−0.0272838
$964$			121.545i			3.91469i
$965$	−28.6836			−0.923359
$966$	−10.3637			−0.333447
$967$			18.0387i			0.580086i	0.957014	+	0.290043i	$0.0936697\pi$
$967$			18.0387i			0.580086i	−0.957014	+	0.290043i	$0.906330\pi$
$968$		−	32.4794i		−	1.04393i
$969$		−	27.1044i		−	0.870719i
$970$			55.8239i			1.79240i
$971$	30.2190			0.969774			0.484887	−	0.874577i	$-0.338861\pi$
$971$	30.2190			0.969774			0.484887	+	0.874577i	$0.338861\pi$
$972$	4.78706			0.153545
$973$		−	5.67501i		−	0.181932i
$974$	−104.181			−3.33819
$975$	0.471237	−	33.6791i	0.0150917	−	1.07859i
$976$	−38.3097			−1.22626
$977$		−	38.4652i		−	1.23061i	−0.788289	−	0.615305i	$-0.789033\pi$
$977$		−	38.4652i		−	1.23061i	0.788289	−	0.615305i	$-0.210967\pi$
$978$	−9.83695			−0.314551
$979$	−14.1130			−0.451055
$980$		−	18.1289i		−	0.579106i
$981$			17.9949i			0.574533i
$982$		−	25.2664i		−	0.806282i
$983$			12.1742i			0.388297i	0.980972	+	0.194149i	$0.0621944\pi$
$983$			12.1742i			0.388297i	−0.980972	+	0.194149i	$0.937806\pi$
$984$	24.2828			0.774109
$985$	−50.5359			−1.61021
$986$			23.9920i			0.764062i
$987$	−11.0983			−0.353264
$988$	145.707	+	2.03873i	4.63555	+	0.0648605i
$989$	19.3677			0.615856
$990$			25.2053i			0.801077i
$991$	14.4982			0.460552			0.230276	−	0.973125i	$-0.426037\pi$
$991$	14.4982			0.460552			0.230276	+	0.973125i	$0.426037\pi$
$992$	−8.52567			−0.270690
$993$		−	23.9124i		−	0.758836i
$994$		−	6.65564i		−	0.211104i
$995$			63.9460i			2.02722i
$996$		−	53.1284i		−	1.68344i
$997$	−9.35086			−0.296145			−0.148072	−	0.988977i	$-0.547307\pi$
$997$	−9.35086			−0.296145			−0.148072	+	0.988977i	$0.547307\pi$
$998$	−62.6124			−1.98196
$999$			5.10951i			0.161658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.c.c.64.8	yes	8
3.2	odd	2		819.2.c.d.64.1		8
4.3	odd	2		4368.2.h.q.337.1		8
7.6	odd	2		1911.2.c.l.883.8		8
13.5	odd	4		3549.2.a.v.1.4		4
13.8	odd	4		3549.2.a.x.1.1		4
13.12	even	2	inner	273.2.c.c.64.1	✓	8
39.38	odd	2		819.2.c.d.64.8		8
52.51	odd	2		4368.2.h.q.337.8		8
91.90	odd	2		1911.2.c.l.883.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.c.c.64.1	✓	8	13.12	even	2	inner
273.2.c.c.64.8	yes	8	1.1	even	1	trivial
819.2.c.d.64.1		8	3.2	odd	2
819.2.c.d.64.8		8	39.38	odd	2
1911.2.c.l.883.1		8	91.90	odd	2
1911.2.c.l.883.8		8	7.6	odd	2
3549.2.a.v.1.4		4	13.5	odd	4
3549.2.a.x.1.1		4	13.8	odd	4
4368.2.h.q.337.1		8	4.3	odd	2
4368.2.h.q.337.8		8	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.60520i q^{2} -1.00000 q^{3} -4.78706 q^{4} -3.78706i q^{5} -2.60520i q^{6} -1.00000i q^{7} -7.26084i q^{8} +1.00000 q^{9} +9.86604 q^{10} +2.55475i q^{11} +4.78706 q^{12} +(0.0504439 - 3.60520i) q^{13} +2.60520 q^{14} +3.78706i q^{15} +9.34181 q^{16} -3.21040 q^{17} +2.60520i q^{18} -8.44270i q^{19} +18.1289i q^{20} +1.00000i q^{21} -6.65564 q^{22} +3.97809 q^{23} +7.26084i q^{24} -9.34181 q^{25} +(9.39226 + 0.131416i) q^{26} -1.00000 q^{27} +4.78706i q^{28} -2.86858 q^{29} -9.86604 q^{30} +0.868584i q^{31} +9.81560i q^{32} -2.55475i q^{33} -8.36372i q^{34} -3.78706 q^{35} -4.78706 q^{36} -5.10951i q^{37} +21.9949 q^{38} +(-0.0504439 + 3.60520i) q^{39} -27.4972 q^{40} -3.34436i q^{41} -2.60520 q^{42} +4.86858 q^{43} -12.2298i q^{44} -3.78706i q^{45} +10.3637i q^{46} +11.0983i q^{47} -9.34181 q^{48} -1.00000 q^{49} -24.3373i q^{50} +3.21040 q^{51} +(-0.241478 + 17.2583i) q^{52} +1.33319 q^{53} -2.60520i q^{54} +9.67501 q^{55} -7.26084 q^{56} +8.44270i q^{57} -7.47323i q^{58} +10.6556i q^{59} -18.1289i q^{60} -4.10089 q^{61} -2.26283 q^{62} -1.00000i q^{63} -6.88795 q^{64} +(-13.6531 - 0.191034i) q^{65} +6.65564 q^{66} -10.8467i q^{67} +15.3684 q^{68} -3.97809 q^{69} -9.86604i q^{70} -2.55475i q^{71} -7.26084i q^{72} -6.76770i q^{73} +13.3113 q^{74} +9.34181 q^{75} +40.4157i q^{76} +2.55475 q^{77} +(-9.39226 - 0.131416i) q^{78} -1.23230 q^{79} -35.3780i q^{80} +1.00000 q^{81} +8.71272 q^{82} -11.0983i q^{83} -4.78706i q^{84} +12.1580i q^{85} +12.6836i q^{86} +2.86858 q^{87} +18.5497 q^{88} +5.52423i q^{89} +9.86604 q^{90} +(-3.60520 - 0.0504439i) q^{91} -19.0434 q^{92} -0.868584i q^{93} -28.9134 q^{94} -31.9730 q^{95} -9.81560i q^{96} +5.65819i q^{97} -2.60520i q^{98} +2.55475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 14 q^{4} + 8 q^{9} + 4 q^{10} + 14 q^{12} - 6 q^{13} - 2 q^{14} + 34 q^{16} + 20 q^{17} - 24 q^{22} - 6 q^{23} - 34 q^{25} + 28 q^{26} - 8 q^{27} - 18 q^{29} - 4 q^{30} - 6 q^{35} - 14 q^{36}+ \cdots - 78 q^{95}+O(q^{100}) \) 8 * q - 8 * q^3 - 14 * q^4 + 8 * q^9 + 4 * q^10 + 14 * q^12 - 6 * q^13 - 2 * q^14 + 34 * q^16 + 20 * q^17 - 24 * q^22 - 6 * q^23 - 34 * q^25 + 28 * q^26 - 8 * q^27 - 18 * q^29 - 4 * q^30 - 6 * q^35 - 14 * q^36 + 36 * q^38 + 6 * q^39 - 8 * q^40 + 2 * q^42 + 34 * q^43 - 34 * q^48 - 8 * q^49 - 20 * q^51 + 18 * q^52 - 10 * q^53 + 16 * q^55 - 6 * q^56 - 20 * q^61 - 28 * q^62 - 18 * q^64 - 10 * q^65 + 24 * q^66 - 24 * q^68 + 6 * q^69 + 48 * q^74 + 34 * q^75 + 4 * q^77 - 28 * q^78 - 2 * q^79 + 8 * q^81 - 48 * q^82 + 18 * q^87 - 8 * q^88 + 4 * q^90 - 6 * q^91 + 56 * q^92 - 72 * q^94 - 78 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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