LMFDB - Embedded newform 684.2.cl.a.173.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(173,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("684.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cl (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.11
Character	$\chi$	$=$	684.173
Dual form			684.2.cl.a.257.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0101717 + 1.73202i) q^{3} +(2.40941 - 2.87142i) q^{5} -4.42209 q^{7} +(-2.99979 + 0.0352353i) q^{9} +O(q^{10})$	\(q+(0.0101717 + 1.73202i) q^{3} +(2.40941 - 2.87142i) q^{5} -4.42209 q^{7} +(-2.99979 + 0.0352353i) q^{9} +(2.56537 - 1.48112i) q^{11} +(0.954891 - 2.62354i) q^{13} +(4.99786 + 4.14393i) q^{15} +(6.34117 + 1.11812i) q^{17} +(2.70257 - 3.41996i) q^{19} +(-0.0449803 - 7.65915i) q^{21} +(2.27203 - 0.400620i) q^{23} +(-1.57156 - 8.91278i) q^{25} +(-0.0915414 - 5.19535i) q^{27} +(-4.35582 - 1.58539i) q^{29} +(4.36328 + 2.51914i) q^{31} +(2.59142 + 4.42822i) q^{33} +(-10.6546 + 12.6977i) q^{35} -1.57987i q^{37} +(4.55374 + 1.62721i) q^{39} +(1.42674 - 8.09144i) q^{41} +(-1.65710 + 9.39789i) q^{43} +(-7.12654 + 8.69856i) q^{45} +(-0.689144 + 1.89341i) q^{47} +12.5549 q^{49} +(-1.87211 + 10.9944i) q^{51} +(-9.93212 - 3.61499i) q^{53} +(1.92811 - 10.9349i) q^{55} +(5.95094 + 4.64611i) q^{57} +(5.51179 - 2.00613i) q^{59} +(4.87165 - 4.08780i) q^{61} +(13.2654 - 0.155814i) q^{63} +(-5.23257 - 9.06307i) q^{65} +(-10.2007 - 12.1568i) q^{67} +(0.716993 + 3.93113i) q^{69} +(-4.85709 + 1.76784i) q^{71} +(9.94525 + 8.34506i) q^{73} +(15.4211 - 2.81264i) q^{75} +(-11.3443 + 6.54964i) q^{77} +(3.25163 + 8.93378i) q^{79} +(8.99752 - 0.211397i) q^{81} +14.2321i q^{83} +(18.4890 - 15.5141i) q^{85} +(2.70162 - 7.56050i) q^{87} +(-5.39845 + 4.52984i) q^{89} +(-4.22261 + 11.6015i) q^{91} +(-4.31882 + 7.58292i) q^{93} +(-3.30856 - 16.0003i) q^{95} +(-2.51006 + 2.99138i) q^{97} +(-7.64340 + 4.53344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{3} - 3 q^{9}+O(q^{10}) $ 120 * q + 3 * q^3 - 3 * q^9	$ 120 q + 3 q^{3} - 3 q^{9} - 3 q^{13} + 21 q^{15} - 27 q^{17} - 3 q^{19} - 9 q^{27} + 27 q^{29} + 30 q^{33} + 30 q^{39} + 9 q^{41} + 12 q^{43} - 27 q^{45} + 120 q^{49} + 9 q^{51} + 24 q^{57} - 18 q^{59} + 42 q^{61} - 24 q^{63} + 12 q^{67} + 27 q^{69} + 39 q^{73} - 3 q^{79} - 3 q^{81} - 36 q^{87} + 54 q^{89} - 12 q^{91} - 24 q^{93} - 9 q^{97} - 6 q^{99}+O(q^{100}) $ 120 * q + 3 * q^3 - 3 * q^9 - 3 * q^13 + 21 * q^15 - 27 * q^17 - 3 * q^19 - 9 * q^27 + 27 * q^29 + 30 * q^33 + 30 * q^39 + 9 * q^41 + 12 * q^43 - 27 * q^45 + 120 * q^49 + 9 * q^51 + 24 * q^57 - 18 * q^59 + 42 * q^61 - 24 * q^63 + 12 * q^67 + 27 * q^69 + 39 * q^73 - 3 * q^79 - 3 * q^81 - 36 * q^87 + 54 * q^89 - 12 * q^91 - 24 * q^93 - 9 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.0101717	+	1.73202i	0.00587266	+	0.999983i
$3$	0.0101717	+	1.73202i	0.00587266	+	0.999983i
$4$		0			0
$5$	2.40941	−	2.87142i	1.07752	−	1.28414i	0.120941	−	0.992660i	$-0.461409\pi$
$5$	2.40941	−	2.87142i	1.07752	−	1.28414i	0.956578	−	0.291477i	$-0.0941468\pi$
$6$		0			0
$7$	−4.42209			−1.67139			−0.835696	−	0.549192i	$-0.814936\pi$
$7$	−4.42209			−1.67139			−0.835696	+	0.549192i	$0.814936\pi$
$8$		0			0
$9$	−2.99979	+	0.0352353i	−0.999931	+	0.0117451i
$10$		0			0
$11$	2.56537	−	1.48112i	0.773489	−	0.446574i	−0.0606286	−	0.998160i	$-0.519311\pi$
$11$	2.56537	−	1.48112i	0.773489	−	0.446574i	0.834118	+	0.551586i	$0.185977\pi$
$12$		0			0
$13$	0.954891	−	2.62354i	0.264839	−	0.727640i	−0.733985	−	0.679165i	$-0.762342\pi$
$13$	0.954891	−	2.62354i	0.264839	−	0.727640i	0.998824	−	0.0484743i	$-0.0154359\pi$
$14$		0			0
$15$	4.99786	+	4.14393i	1.29044	+	1.06996i
$16$		0			0
$17$	6.34117	+	1.11812i	1.53796	+	0.271184i	0.877463	−	0.479645i	$-0.159234\pi$
$17$	6.34117	+	1.11812i	1.53796	+	0.271184i	0.660497	+	0.750829i	$0.270346\pi$
$18$		0			0
$19$	2.70257	−	3.41996i	0.620011	−	0.784593i
$19$	2.70257	−	3.41996i	0.620011	−	0.784593i
$20$		0			0
$21$	−0.0449803	−	7.65915i	−0.00981551	−	1.67136i
$22$		0			0
$23$	2.27203	−	0.400620i	0.473751	−	0.0835351i	0.0683253	−	0.997663i	$-0.478234\pi$
$23$	2.27203	−	0.400620i	0.473751	−	0.0835351i	0.405426	+	0.914128i	$0.367123\pi$
$24$		0			0
$25$	−1.57156	−	8.91278i	−0.314313	−	1.78256i
$26$		0			0
$27$	−0.0915414	−	5.19535i	−0.0176172	−	0.999845i
$28$		0			0
$29$	−4.35582	−	1.58539i	−0.808855	−	0.294399i	−0.0957045	−	0.995410i	$-0.530510\pi$
$29$	−4.35582	−	1.58539i	−0.808855	−	0.294399i	−0.713151	+	0.701010i	$0.752733\pi$
$30$		0			0
$31$	4.36328	+	2.51914i	0.783668	+	0.452451i	0.837729	−	0.546087i	$-0.183883\pi$
$31$	4.36328	+	2.51914i	0.783668	+	0.452451i	−0.0540606	+	0.998538i	$0.517216\pi$
$32$		0			0
$33$	2.59142	+	4.42822i	0.451109	+	0.770853i
$34$		0			0
$35$	−10.6546	+	12.6977i	−1.80096	+	2.14630i
$36$		0			0
$37$		−	1.57987i		−	0.259729i	−0.991532	−	0.129865i	$-0.958546\pi$
$37$		−	1.57987i		−	0.259729i	0.991532	−	0.129865i	$-0.0414543\pi$
$38$		0			0
$39$	4.55374	+	1.62721i	0.729183	+	0.260561i
$40$		0			0
$41$	1.42674	−	8.09144i	0.222819	−	1.26367i	−0.643991	−	0.765033i	$-0.722723\pi$
$41$	1.42674	−	8.09144i	0.222819	−	1.26367i	0.866810	−	0.498638i	$-0.166166\pi$
$42$		0			0
$43$	−1.65710	+	9.39789i	−0.252706	+	1.43316i	0.549189	+	0.835698i	$0.314937\pi$
$43$	−1.65710	+	9.39789i	−0.252706	+	1.43316i	−0.801894	+	0.597466i	$0.796174\pi$
$44$		0			0
$45$	−7.12654	+	8.69856i	−1.06236	+	1.29670i
$46$		0			0
$47$	−0.689144	+	1.89341i	−0.100522	+	0.276182i	−0.979752	−	0.200216i	$-0.935836\pi$
$47$	−0.689144	+	1.89341i	−0.100522	+	0.276182i	0.879230	+	0.476398i	$0.158058\pi$
$48$		0			0
$49$	12.5549			1.79355
$50$		0			0
$51$	−1.87211	+	10.9944i	−0.262147	+	1.53953i
$52$		0			0
$53$	−9.93212	−	3.61499i	−1.36428	−	0.496558i	−0.446906	−	0.894581i	$-0.647474\pi$
$53$	−9.93212	−	3.61499i	−1.36428	−	0.496558i	−0.917375	+	0.398023i	$0.869696\pi$
$54$		0			0
$55$	1.92811	−	10.9349i	0.259987	−	1.47446i
$56$		0			0
$57$	5.95094	+	4.64611i	0.788221	+	0.615393i
$58$		0			0
$59$	5.51179	−	2.00613i	0.717574	−	0.261176i	0.0426784	−	0.999089i	$-0.486411\pi$
$59$	5.51179	−	2.00613i	0.717574	−	0.261176i	0.674895	+	0.737913i	$0.264189\pi$
$60$		0			0
$61$	4.87165	−	4.08780i	0.623751	−	0.523389i	−0.275229	−	0.961379i	$-0.588754\pi$
$61$	4.87165	−	4.08780i	0.623751	−	0.523389i	0.898980	+	0.437989i	$0.144309\pi$
$62$		0			0
$63$	13.2654	−	0.155814i	1.67128	−	0.0196307i
$64$		0			0
$65$	−5.23257	−	9.06307i	−0.649020	−	1.12414i
$66$		0			0
$67$	−10.2007	−	12.1568i	−1.24622	−	1.48519i	−0.811204	−	0.584764i	$-0.801187\pi$
$67$	−10.2007	−	12.1568i	−1.24622	−	1.48519i	−0.435016	−	0.900423i	$-0.643257\pi$
$68$		0			0
$69$	0.716993	+	3.93113i	0.0863158	+	0.473252i
$70$		0			0
$71$	−4.85709	+	1.76784i	−0.576431	+	0.209804i	−0.613751	−	0.789500i	$-0.710340\pi$
$71$	−4.85709	+	1.76784i	−0.576431	+	0.209804i	0.0373202	+	0.999303i	$0.488118\pi$
$72$		0			0
$73$	9.94525	+	8.34506i	1.16400	+	0.976715i	0.999953	−	0.00973685i	$-0.00309939\pi$
$73$	9.94525	+	8.34506i	1.16400	+	0.976715i	0.164051	+	0.986452i	$0.447544\pi$
$74$		0			0
$75$	15.4211	−	2.81264i	1.78068	−	0.324776i
$76$		0			0
$77$	−11.3443	+	6.54964i	−1.29280	+	0.746401i
$78$		0			0
$79$	3.25163	+	8.93378i	0.365837	+	1.00513i	0.976928	+	0.213568i	$0.0685086\pi$
$79$	3.25163	+	8.93378i	0.365837	+	1.00513i	−0.611091	+	0.791560i	$0.709269\pi$
$80$		0			0
$81$	8.99752	−	0.211397i	0.999724	−	0.0234886i
$82$		0			0
$83$			14.2321i			1.56217i	0.624424	+	0.781086i	$0.285334\pi$
$83$			14.2321i			1.56217i	−0.624424	+	0.781086i	$0.714666\pi$
$84$		0			0
$85$	18.4890	−	15.5141i	2.00542	−	1.68275i
$86$		0			0
$87$	2.70162	−	7.56050i	0.289644	−	0.810570i
$88$		0			0
$89$	−5.39845	+	4.52984i	−0.572235	+	0.480162i	−0.882387	−	0.470525i	$-0.844064\pi$
$89$	−5.39845	+	4.52984i	−0.572235	+	0.480162i	0.310152	+	0.950687i	$0.399620\pi$
$90$		0			0
$91$	−4.22261	+	11.6015i	−0.442650	+	1.21617i
$92$		0			0
$93$	−4.31882	+	7.58292i	−0.447841	+	0.786312i
$94$		0			0
$95$	−3.30856	−	16.0003i	−0.339451	−	1.64159i
$96$		0			0
$97$	−2.51006	+	2.99138i	−0.254858	+	0.303728i	−0.878270	−	0.478166i	$-0.841302\pi$
$97$	−2.51006	+	2.99138i	−0.254858	+	0.303728i	0.623411	+	0.781894i	$0.285746\pi$
$98$		0			0
$99$	−7.64340	+	4.53344i	−0.768191	+	0.455628i
$100$		0			0
$101$	−3.60017	+	0.634807i	−0.358230	+	0.0631657i	−0.349867	−	0.936799i	$-0.613773\pi$
$101$	−3.60017	+	0.634807i	−0.358230	+	0.0631657i	−0.00836332	+	0.999965i	$0.502662\pi$
$102$		0			0
$103$		−	1.32340i		−	0.130399i	−0.997872	−	0.0651993i	$-0.979232\pi$
$103$		−	1.32340i		−	0.130399i	0.997872	−	0.0651993i	$-0.0207683\pi$
$104$		0			0
$105$	−22.1010	−	18.3248i	−2.15684	−	1.78832i
$106$		0			0
$107$	−2.79142	−	4.83489i	−0.269857	−	0.467406i	0.698968	−	0.715153i	$-0.253643\pi$
$107$	−2.79142	−	4.83489i	−0.269857	−	0.467406i	−0.968825	+	0.247747i	$0.920310\pi$
$108$		0			0
$109$	−2.28547	−	6.27926i	−0.218908	−	0.601444i	0.780820	−	0.624756i	$-0.214801\pi$
$109$	−2.28547	−	6.27926i	−0.218908	−	0.601444i	−0.999728	+	0.0233111i	$0.992579\pi$
$110$		0			0
$111$	2.73637	−	0.0160700i	0.259725	−	0.00152530i
$112$		0			0
$113$	6.42410	+	11.1269i	0.604329	+	1.04673i	0.992157	+	0.124996i	$0.0398919\pi$
$113$	6.42410	+	11.1269i	0.604329	+	1.04673i	−0.387828	+	0.921732i	$0.626775\pi$
$114$		0			0
$115$	4.32389	−	7.48920i	0.403205	−	0.698372i
$116$		0			0
$117$	−2.77204	+	7.90373i	−0.256275	+	0.730700i
$118$		0			0
$119$	−28.0412	−	4.94442i	−2.57053	−	0.453255i
$120$		0			0
$121$	−1.11257	+	1.92703i	−0.101143	+	0.175185i
$122$		0			0
$123$	14.0291	+	2.38884i	1.26496	+	0.215394i
$124$		0			0
$125$	−13.1479	−	7.59096i	−1.17599	−	0.678956i
$126$		0			0
$127$	−8.06457	−	9.61098i	−0.715615	−	0.852837i	0.278582	−	0.960413i	$-0.410136\pi$
$127$	−8.06457	−	9.61098i	−0.715615	−	0.852837i	−0.994197	+	0.107576i	$0.965691\pi$
$128$		0			0
$129$	−16.2942	−	2.77454i	−1.43462	−	0.244285i
$130$		0			0
$131$	2.04643	+	5.62253i	0.178798	+	0.491243i	0.996423	−	0.0845083i	$-0.0269319\pi$
$131$	2.04643	+	5.62253i	0.178798	+	0.491243i	−0.817625	+	0.575751i	$0.804710\pi$
$132$		0			0
$133$	−11.9510	+	15.1234i	−1.03628	+	1.31136i
$134$		0			0
$135$	−15.1386	−	12.2548i	−1.30292	−	1.05473i
$136$		0			0
$137$	7.79432	+	9.28890i	0.665913	+	0.793605i	0.988222	−	0.153030i	$-0.0489032\pi$
$137$	7.79432	+	9.28890i	0.665913	+	0.793605i	−0.322308	+	0.946635i	$0.604459\pi$
$138$		0			0
$139$	−5.44598	−	1.98217i	−0.461922	−	0.168126i	0.100568	−	0.994930i	$-0.467934\pi$
$139$	−5.44598	−	1.98217i	−0.461922	−	0.168126i	−0.562489	+	0.826804i	$0.690156\pi$
$140$		0			0
$141$	−3.28643	−	1.17435i	−0.276767	−	0.0988983i
$142$		0			0
$143$	−1.43613	−	8.14467i	−0.120095	−	0.681092i
$144$		0			0
$145$	−15.0473	+	8.68753i	−1.24961	+	0.721460i
$146$		0			0
$147$	0.127705	+	21.7453i	0.0105329	+	1.79352i
$148$		0			0
$149$	3.62647	+	0.639445i	0.297092	+	0.0523853i	0.320207	−	0.947347i	$-0.396247\pi$
$149$	3.62647	+	0.639445i	0.297092	+	0.0523853i	−0.0231154	+	0.999733i	$0.507359\pi$
$150$		0			0
$151$	−14.1419	−	8.16484i	−1.15085	−	0.664446i	−0.201758	−	0.979435i	$-0.564666\pi$
$151$	−14.1419	−	8.16484i	−1.15085	−	0.664446i	−0.949095	+	0.314990i	$0.897999\pi$
$152$		0			0
$153$	−19.0616	−	3.13069i	−1.54104	−	0.253102i
$154$		0			0
$155$	17.7464	−	6.45917i	1.42543	−	0.518813i
$156$		0			0
$157$	−7.34594	−	6.16397i	−0.586270	−	0.491939i	0.300730	−	0.953709i	$-0.402770\pi$
$157$	−7.34594	−	6.16397i	−0.586270	−	0.491939i	−0.886999	+	0.461771i	$0.847214\pi$
$158$		0			0
$159$	6.16022	−	17.2394i	0.488537	−	1.36717i
$160$		0			0
$161$	−10.0471	+	1.77158i	−0.791824	+	0.139620i
$162$		0			0
$163$	−0.100075	+	0.173334i	−0.00783845	+	0.0135766i	−0.869918	−	0.493196i	$-0.835828\pi$
$163$	−0.100075	+	0.173334i	−0.00783845	+	0.0135766i	0.862080	+	0.506773i	$0.169162\pi$
$164$		0			0
$165$	18.9590	+	3.22831i	1.47596	+	0.251323i
$166$		0			0
$167$	3.69785	+	20.9716i	0.286148	+	1.62283i	0.701154	+	0.713010i	$0.252669\pi$
$167$	3.69785	+	20.9716i	0.286148	+	1.62283i	−0.415006	+	0.909819i	$0.636220\pi$
$168$		0			0
$169$	3.98742	+	3.34584i	0.306725	+	0.257373i
$170$		0			0
$171$	−7.98663	+	10.3544i	−0.610753	+	0.791821i
$172$		0			0
$173$	3.48967	+	2.92818i	0.265315	+	0.222625i	0.765733	−	0.643158i	$-0.222376\pi$
$173$	3.48967	+	2.92818i	0.265315	+	0.222625i	−0.500419	+	0.865783i	$0.666821\pi$
$174$		0			0
$175$	6.94959	+	39.4131i	0.525340	+	2.97935i
$176$		0			0
$177$	3.53072	+	9.52613i	0.265385	+	0.716028i
$178$		0			0
$179$	5.08511	−	8.80767i	0.380079	−	0.658316i	−0.610994	−	0.791635i	$-0.709230\pi$
$179$	5.08511	−	8.80767i	0.380079	−	0.658316i	0.991073	+	0.133319i	$0.0425634\pi$
$180$		0			0
$181$	9.57324	−	1.68802i	0.711573	−	0.125470i	0.193867	−	0.981028i	$-0.437897\pi$
$181$	9.57324	−	1.68802i	0.711573	−	0.125470i	0.517706	+	0.855558i	$0.326786\pi$
$182$		0			0
$183$	7.12971	+	8.39622i	0.527043	+	0.620667i
$184$		0			0
$185$	−4.53647	−	3.80655i	−0.333528	−	0.279863i
$186$		0			0
$187$	17.9235	−	6.52364i	1.31070	−	0.477056i
$188$		0			0
$189$	0.404804	+	22.9743i	0.0294452	+	1.67113i
$190$		0			0
$191$	−7.21441	−	4.16524i	−0.522016	−	0.301386i	0.215743	−	0.976450i	$-0.430783\pi$
$191$	−7.21441	−	4.16524i	−0.522016	−	0.301386i	−0.737759	+	0.675064i	$0.764116\pi$
$192$		0			0
$193$	10.9741	+	1.93504i	0.789936	+	0.139287i	0.554039	−	0.832491i	$-0.313086\pi$
$193$	10.9741	+	1.93504i	0.789936	+	0.139287i	0.235897	+	0.971778i	$0.424197\pi$
$194$		0			0
$195$	15.6442	−	9.15510i	1.12030	−	0.655610i
$196$		0			0
$197$	−14.7981	+	8.54369i	−1.05432	+	0.608713i	−0.923856	−	0.382740i	$-0.874980\pi$
$197$	−14.7981	+	8.54369i	−1.05432	+	0.608713i	−0.130465	+	0.991453i	$0.541647\pi$
$198$		0			0
$199$	−2.29317	−	13.0052i	−0.162558	−	0.921914i	−0.951546	−	0.307505i	$-0.900506\pi$
$199$	−2.29317	−	13.0052i	−0.162558	−	0.921914i	0.788988	−	0.614408i	$-0.210605\pi$
$200$		0			0
$201$	20.9520	−	17.7916i	1.47784	−	1.25492i
$202$		0			0
$203$	19.2618	+	7.01073i	1.35192	+	0.492057i
$204$		0			0
$205$	−19.7963	−	23.5923i	−1.38263	−	1.64776i
$206$		0			0
$207$	−6.80150	+	1.28183i	−0.472737	+	0.0890936i
$208$		0			0
$209$	1.86772	−	12.7763i	0.129193	−	0.883755i
$210$		0			0
$211$	0.728505	+	2.00155i	0.0501524	+	0.137792i	0.962240	−	0.272203i	$-0.0877524\pi$
$211$	0.728505	+	2.00155i	0.0501524	+	0.137792i	−0.912087	+	0.409996i	$0.865530\pi$
$212$		0			0
$213$	−3.11133	−	8.39460i	−0.213185	−	0.575189i
$214$		0			0
$215$	22.9926	+	27.4016i	1.56808	+	1.86877i
$216$		0			0
$217$	−19.2948	−	11.1399i	−1.30982	−	0.756223i
$218$		0			0
$219$	−14.3527	+	17.3103i	−0.969862	+	1.16972i
$220$		0			0
$221$	8.98856	−	15.5686i	0.604636	−	1.04726i
$222$		0			0
$223$	17.4361	+	3.07446i	1.16761	+	0.205881i	0.723650	−	0.690167i	$-0.242463\pi$
$223$	17.4361	+	3.07446i	1.16761	+	0.205881i	0.443958	+	0.896048i	$0.353574\pi$
$224$		0			0
$225$	5.02841	+	26.6811i	0.335227	+	1.77874i
$226$		0			0
$227$	7.14886	−	12.3822i	0.474487	−	0.821835i	−0.525086	−	0.851049i	$-0.675967\pi$
$227$	7.14886	−	12.3822i	0.474487	−	0.821835i	0.999573	+	0.0292138i	$0.00930037\pi$
$228$		0			0
$229$	−1.72842	−	2.99372i	−0.114217	−	0.197830i	0.803249	−	0.595643i	$-0.203103\pi$
$229$	−1.72842	−	2.99372i	−0.114217	−	0.197830i	−0.917467	+	0.397813i	$0.869769\pi$
$230$		0			0
$231$	−11.4595	−	19.5820i	−0.753980	−	1.28840i
$232$		0			0
$233$	3.89728	+	10.7077i	0.255319	+	0.701484i	0.999441	+	0.0334396i	$0.0106461\pi$
$233$	3.89728	+	10.7077i	0.255319	+	0.701484i	−0.744121	+	0.668044i	$0.767132\pi$
$234$		0			0
$235$	3.77634	+	6.54081i	0.246341	+	0.426675i
$236$		0			0
$237$	−15.4404	+	5.72276i	−1.00296	+	0.371733i
$238$		0			0
$239$			24.8331i			1.60632i	0.595765	+	0.803158i	$0.296849\pi$
$239$			24.8331i			1.60632i	−0.595765	+	0.803158i	$0.703151\pi$
$240$		0			0
$241$	8.14192	−	1.43564i	0.524467	−	0.0924777i	0.0948548	−	0.995491i	$-0.469761\pi$
$241$	8.14192	−	1.43564i	0.524467	−	0.0924777i	0.429612	+	0.903013i	$0.358650\pi$
$242$		0			0
$243$	0.457665	+	15.5817i	0.0293592	+	0.999569i
$244$		0			0
$245$	30.2498	−	36.0503i	1.93259	−	2.30317i
$246$		0			0
$247$	−6.39176	−	10.3560i	−0.406698	−	0.658936i
$248$		0			0
$249$	−24.6502	+	0.144765i	−1.56214	+	0.00917409i
$250$		0			0
$251$	−2.11018	+	5.79768i	−0.133194	+	0.365946i	−0.988303	−	0.152501i	$-0.951267\pi$
$251$	−2.11018	+	5.79768i	−0.133194	+	0.365946i	0.855110	+	0.518447i	$0.173490\pi$
$252$		0			0
$253$	5.23524	−	4.39289i	0.329137	−	0.276178i
$254$		0			0
$255$	27.0589	+	31.8656i	1.69449	+	1.99550i
$256$		0			0
$257$	−5.88562	+	4.93862i	−0.367135	+	0.308063i	−0.807627	−	0.589694i	$-0.799248\pi$
$257$	−5.88562	+	4.93862i	−0.367135	+	0.308063i	0.440492	+	0.897757i	$0.354804\pi$
$258$		0			0
$259$			6.98633i			0.434110i
$260$		0			0
$261$	13.1224	+	4.60236i	0.812257	+	0.284879i
$262$		0			0
$263$	−2.27610	−	6.25353i	−0.140350	−	0.385609i	0.849525	−	0.527548i	$-0.176889\pi$
$263$	−2.27610	−	6.25353i	−0.140350	−	0.385609i	−0.989875	+	0.141939i	$0.954666\pi$
$264$		0			0
$265$	−34.3107	+	19.8093i	−2.10769	+	1.21687i
$266$		0			0
$267$	−7.90069	−	9.30415i	−0.483514	−	0.569405i
$268$		0			0
$269$	−16.3337	−	13.7056i	−0.995884	−	0.835646i	−0.00947554	−	0.999955i	$-0.503016\pi$
$269$	−16.3337	−	13.7056i	−0.995884	−	0.835646i	−0.986409	+	0.164309i	$0.947461\pi$
$270$		0			0
$271$	16.5447	−	6.02176i	1.00502	−	0.365796i	0.213500	−	0.976943i	$-0.431514\pi$
$271$	16.5447	−	6.02176i	1.00502	−	0.365796i	0.791517	+	0.611147i	$0.209292\pi$
$272$		0			0
$273$	−20.1371	−	7.19565i	−1.21875	−	0.435501i
$274$		0			0
$275$	−17.2325	−	20.5369i	−1.03916	−	1.23842i
$276$		0			0
$277$	4.87940	+	8.45137i	0.293175	+	0.507794i	0.974559	−	0.224132i	$-0.0719548\pi$
$277$	4.87940	+	8.45137i	0.293175	+	0.507794i	−0.681384	+	0.731926i	$0.738621\pi$
$278$		0			0
$279$	−13.1777	−	7.40316i	−0.788928	−	0.443216i
$280$		0			0
$281$	−14.8832	+	12.4885i	−0.887858	+	0.745001i	−0.967779	−	0.251800i	$-0.918978\pi$
$281$	−14.8832	+	12.4885i	−0.887858	+	0.745001i	0.0799214	+	0.996801i	$0.474533\pi$
$282$		0			0
$283$	−18.4857	+	6.72826i	−1.09886	+	0.399953i	−0.826897	−	0.562353i	$-0.809896\pi$
$283$	−18.4857	+	6.72826i	−1.09886	+	0.399953i	−0.271966	+	0.962307i	$0.587674\pi$
$284$		0			0
$285$	27.6791	−	5.89325i	1.63957	−	0.349086i
$286$		0			0
$287$	−6.30917	+	35.7811i	−0.372419	+	2.11209i
$288$		0			0
$289$	22.9855	+	8.36603i	1.35209	+	0.492120i
$290$		0			0
$291$	−5.20666	−	4.31706i	−0.305220	−	0.253070i
$292$		0			0
$293$	7.92108			0.462754			0.231377	−	0.972864i	$-0.425677\pi$
$293$	7.92108			0.462754			0.231377	+	0.972864i	$0.425677\pi$
$294$		0			0
$295$	7.51971	−	20.6602i	0.437814	−	1.20288i
$296$		0			0
$297$	−7.92976	−	13.1924i	−0.460132	−	0.765502i
$298$		0			0
$299$	1.11850	−	6.34331i	0.0646844	−	0.366843i
$300$		0			0
$301$	7.32785	−	41.5583i	0.422370	−	2.39538i
$302$		0			0
$303$	−1.13612	−	6.22912i	−0.0652684	−	0.357853i
$304$		0			0
$305$		−	23.8377i		−	1.36494i
$306$		0			0
$307$	5.41129	−	6.44893i	0.308839	−	0.368060i	−0.589191	−	0.807993i	$-0.700554\pi$
$307$	5.41129	−	6.44893i	0.308839	−	0.368060i	0.898030	+	0.439934i	$0.144998\pi$
$308$		0			0
$309$	2.29216	−	0.0134613i	0.130396	−	0.000765786i
$310$		0			0
$311$	−2.08649	−	1.20464i	−0.118314	−	0.0683086i	0.439675	−	0.898157i	$-0.355094\pi$
$311$	−2.08649	−	1.20464i	−0.118314	−	0.0683086i	−0.557989	+	0.829848i	$0.688427\pi$
$312$		0			0
$313$	27.4486	+	9.99047i	1.55149	+	0.564695i	0.968766	−	0.247978i	$-0.0797661\pi$
$313$	27.4486	+	9.99047i	1.55149	+	0.564695i	0.582720	+	0.812673i	$0.301988\pi$
$314$		0			0
$315$	31.5142	−	38.4658i	1.77562	−	2.16730i
$316$		0			0
$317$	1.84368	+	10.4560i	0.103551	+	0.587269i	0.991789	+	0.127885i	$0.0408187\pi$
$317$	1.84368	+	10.4560i	0.103551	+	0.587269i	−0.888238	+	0.459384i	$0.848070\pi$
$318$		0			0
$319$	−13.5225	+	2.38437i	−0.757112	+	0.133499i
$320$		0			0
$321$	8.34574	−	4.88398i	0.465814	−	0.272597i
$322$		0			0
$323$	20.9614	−	18.6648i	1.16632	−	1.03854i
$324$		0			0
$325$	−24.8837	−	4.38767i	−1.38030	−	0.243384i
$326$		0			0
$327$	10.8526	−	4.02234i	0.600149	−	0.222436i
$328$		0			0
$329$	3.04746	−	8.37282i	0.168012	−	0.461608i
$330$		0			0
$331$	−13.1030	+	7.56501i	−0.720205	+	0.415810i	−0.814828	−	0.579703i	$-0.803169\pi$
$331$	−13.1030	+	7.56501i	−0.720205	+	0.415810i	0.0946234	+	0.995513i	$0.469835\pi$
$332$		0			0
$333$	0.0556673	+	4.73929i	0.00305055	+	0.259711i
$334$		0			0
$335$	−59.4849			−3.25001
$336$		0			0
$337$	−8.44726	+	10.0671i	−0.460152	+	0.548387i	−0.945367	−	0.326007i	$-0.894297\pi$
$337$	−8.44726	+	10.0671i	−0.460152	+	0.548387i	0.485216	+	0.874395i	$0.338741\pi$
$338$		0			0
$339$	−19.2066	+	11.2399i	−1.04316	+	0.610465i
$340$		0			0
$341$	14.9246			0.808212
$342$		0			0
$343$	−24.5641			−1.32634
$344$		0			0
$345$	13.0154	+	7.41289i	0.700728	+	0.399097i
$346$		0			0
$347$	−2.23825	+	2.66744i	−0.120156	+	0.143196i	−0.822769	−	0.568376i	$-0.807572\pi$
$347$	−2.23825	+	2.66744i	−0.120156	+	0.143196i	0.702613	+	0.711572i	$0.252016\pi$
$348$		0			0
$349$	21.4642			1.14895			0.574476	−	0.818521i	$-0.305206\pi$
$349$	21.4642			1.14895			0.574476	+	0.818521i	$0.305206\pi$
$350$		0			0
$351$	−13.7176	−	4.72083i	−0.732193	−	0.251979i
$352$		0			0
$353$	1.20679	−	0.696741i	0.0642310	−	0.0370838i	−0.467541	−	0.883972i	$-0.654860\pi$
$353$	1.20679	−	0.696741i	0.0642310	−	0.0370838i	0.531772	+	0.846888i	$0.321526\pi$
$354$		0			0
$355$	−6.62650	+	18.2062i	−0.351698	+	0.966283i
$356$		0			0
$357$	8.27862	−	48.6183i	0.438151	−	2.57315i
$358$		0			0
$359$	9.64904	+	1.70139i	0.509257	+	0.0897957i	0.422372	−	0.906423i	$-0.361198\pi$
$359$	9.64904	+	1.70139i	0.509257	+	0.0897957i	0.0868849	+	0.996218i	$0.472309\pi$
$360$		0			0
$361$	−4.39228	−	18.4853i	−0.231172	−	0.972913i
$362$		0			0
$363$	−3.34897	−	1.90740i	−0.175776	−	0.100112i
$364$		0			0
$365$	47.9243	−	8.45034i	2.50847	−	0.442311i
$366$		0			0
$367$	−0.871573	−	4.94294i	−0.0454958	−	0.258019i	0.953573	−	0.301161i	$-0.0973743\pi$
$367$	−0.871573	−	4.94294i	−0.0454958	−	0.258019i	−0.999069	+	0.0431421i	$0.986263\pi$
$368$		0			0
$369$	−3.99482	+	24.3229i	−0.207962	+	1.26620i
$370$		0			0
$371$	43.9207	+	15.9858i	2.28025	+	0.829943i
$372$		0			0
$373$	24.8549	+	14.3500i	1.28694	+	0.743013i	0.978107	−	0.208105i	$-0.0667295\pi$
$373$	24.8549	+	14.3500i	1.28694	+	0.743013i	0.308829	+	0.951118i	$0.400063\pi$
$374$		0			0
$375$	13.0140	−	22.8497i	0.672038	−	1.17995i
$376$		0			0
$377$	−8.31867	+	9.91380i	−0.428433	+	0.510587i
$378$		0			0
$379$		−	18.7719i		−	0.964246i	−0.876104	−	0.482123i	$-0.839866\pi$
$379$		−	18.7719i		−	0.964246i	0.876104	−	0.482123i	$-0.160134\pi$
$380$		0			0
$381$	16.5644	−	14.0658i	0.848620	−	0.720611i
$382$		0			0
$383$	1.62003	−	9.18766i	0.0827798	−	0.469468i	−0.915034	−	0.403377i	$-0.867836\pi$
$383$	1.62003	−	9.18766i	0.0827798	−	0.469468i	0.997814	−	0.0660906i	$-0.0210526\pi$
$384$		0			0
$385$	−8.52629	+	48.3550i	−0.434540	+	2.46440i
$386$		0			0
$387$	4.63982	−	28.2501i	0.235855	−	1.43603i
$388$		0			0
$389$	−1.06709	+	2.93182i	−0.0541038	+	0.148649i	−0.963801	−	0.266624i	$-0.914092\pi$
$389$	−1.06709	+	2.93182i	−0.0541038	+	0.148649i	0.909697	+	0.415273i	$0.136314\pi$
$390$		0			0
$391$	14.8553			0.751263
$392$		0			0
$393$	−9.71753	+	3.60166i	−0.490184	+	0.181680i
$394$		0			0
$395$	33.4871	+	12.1883i	1.68492	+	0.613260i
$396$		0			0
$397$	−5.18515	+	29.4065i	−0.260235	+	1.47587i	0.522032	+	0.852926i	$0.325174\pi$
$397$	−5.18515	+	29.4065i	−0.260235	+	1.47587i	−0.782268	+	0.622943i	$0.785937\pi$
$398$		0			0
$399$	−26.3156	−	20.5455i	−1.31743	−	1.02856i
$400$		0			0
$401$	2.09287	−	0.761743i	0.104513	−	0.0380396i	−0.289234	−	0.957258i	$-0.593401\pi$
$401$	2.09287	−	0.761743i	0.104513	−	0.0380396i	0.393747	+	0.919219i	$0.371178\pi$
$402$		0			0
$403$	10.7755	−	9.04174i	0.536767	−	0.450401i
$404$		0			0
$405$	21.0717	−	26.3450i	1.04706	−	1.30909i
$406$		0			0
$407$	−2.33998	−	4.05296i	−0.115988	−	0.200898i
$408$		0			0
$409$	21.8843	+	26.0807i	1.08211	+	1.28961i	0.954639	+	0.297767i	$0.0962418\pi$
$409$	21.8843	+	26.0807i	1.08211	+	1.28961i	0.127472	+	0.991842i	$0.459314\pi$
$410$		0			0
$411$	−16.0093	+	13.5944i	−0.789680	+	0.670562i
$412$		0			0
$413$	−24.3736	+	8.87127i	−1.19935	+	0.436527i
$414$		0			0
$415$	40.8662	+	34.2908i	2.00604	+	1.68327i
$416$		0			0
$417$	3.37777	−	9.45271i	0.165410	−	0.462901i
$418$		0			0
$419$	17.8144	−	10.2852i	0.870291	−	0.502463i	0.00284595	−	0.999996i	$-0.499094\pi$
$419$	17.8144	−	10.2852i	0.870291	−	0.502463i	0.867445	+	0.497533i	$0.165761\pi$
$420$		0			0
$421$	3.06210	+	8.41305i	0.149238	+	0.410027i	0.991675	−	0.128767i	$-0.0411021\pi$
$421$	3.06210	+	8.41305i	0.149238	+	0.410027i	−0.842437	+	0.538795i	$0.818880\pi$
$422$		0			0
$423$	2.00057	−	5.70411i	0.0972712	−	0.277343i
$424$		0			0
$425$		−	58.2747i		−	2.82674i
$426$		0			0
$427$	−21.5429	+	18.0766i	−1.04253	+	0.874789i
$428$		0			0
$429$	14.0921	−	2.57025i	0.680375	−	0.124093i
$430$		0			0
$431$	−6.26773	+	5.25925i	−0.301906	+	0.253329i	−0.781137	−	0.624359i	$-0.785360\pi$
$431$	−6.26773	+	5.25925i	−0.301906	+	0.253329i	0.479231	+	0.877689i	$0.340916\pi$
$432$		0			0
$433$	−7.08682	+	19.4709i	−0.340571	+	0.935711i	0.644658	+	0.764471i	$0.277000\pi$
$433$	−7.08682	+	19.4709i	−0.340571	+	0.935711i	−0.985229	+	0.171240i	$0.945223\pi$
$434$		0			0
$435$	−15.2000	−	25.9738i	−0.728786	−	1.24535i
$436$		0			0
$437$	4.77020	−	8.85296i	0.228190	−	0.423494i
$438$		0			0
$439$	8.04035	−	9.58211i	0.383745	−	0.457329i	−0.539248	−	0.842147i	$-0.681291\pi$
$439$	8.04035	−	9.58211i	0.383745	−	0.457329i	0.922993	+	0.384818i	$0.125736\pi$
$440$		0			0
$441$	−37.6620	+	0.442375i	−1.79343	+	0.0210655i
$442$		0			0
$443$	−15.7582	+	2.77860i	−0.748697	+	0.132015i	−0.534962	−	0.844876i	$-0.679674\pi$
$443$	−15.7582	+	2.77860i	−0.748697	+	0.132015i	−0.213735	+	0.976892i	$0.568563\pi$
$444$		0			0
$445$			26.4154i			1.25221i
$446$		0			0
$447$	−1.07064	+	6.28763i	−0.0506397	+	0.297395i
$448$		0			0
$449$	5.31362	+	9.20345i	0.250765	+	0.434338i	0.963737	−	0.266855i	$-0.0859845\pi$
$449$	5.31362	+	9.20345i	0.250765	+	0.434338i	−0.712972	+	0.701193i	$0.752651\pi$
$450$		0			0
$451$	−8.32427	−	22.8707i	−0.391975	−	1.07694i
$452$		0			0
$453$	13.9978	−	24.5772i	0.657676	−	1.15474i
$454$		0			0
$455$	23.1389	+	40.0777i	1.08477	+	1.87887i
$456$		0			0
$457$	−7.90239	+	13.6873i	−0.369658	+	0.640266i	−0.989512	−	0.144451i	$-0.953858\pi$
$457$	−7.90239	+	13.6873i	−0.369658	+	0.640266i	0.619854	+	0.784717i	$0.287192\pi$
$458$		0			0
$459$	5.22854	−	33.0469i	0.244047	−	1.54250i
$460$		0			0
$461$	−4.60118	−	0.811312i	−0.214298	−	0.0377866i	0.0654682	−	0.997855i	$-0.479146\pi$
$461$	−4.60118	−	0.811312i	−0.214298	−	0.0377866i	−0.279766	+	0.960068i	$0.590257\pi$
$462$		0			0
$463$	14.8186	−	25.6665i	0.688678	−	1.19282i	−0.283588	−	0.958946i	$-0.591525\pi$
$463$	14.8186	−	25.6665i	0.688678	−	1.19282i	0.972266	−	0.233878i	$-0.0751418\pi$
$464$		0			0
$465$	11.3679	+	30.6715i	0.527175	+	1.42235i
$466$		0			0
$467$	1.79491	+	1.03629i	0.0830584	+	0.0479538i	0.540954	−	0.841052i	$-0.318063\pi$
$467$	1.79491	+	1.03629i	0.0830584	+	0.0479538i	−0.457896	+	0.889006i	$0.651397\pi$
$468$		0			0
$469$	45.1086	+	53.7583i	2.08292	+	2.48233i
$470$		0			0
$471$	10.6014	−	12.7860i	0.488487	−	0.589148i
$472$		0			0
$473$	9.66831	+	26.5635i	0.444549	+	1.22139i
$474$		0			0
$475$	−34.7286	−	18.7127i	−1.59346	−	0.858597i
$476$		0			0
$477$	29.9217	+	10.4943i	1.37002	+	0.480500i
$478$		0			0
$479$	13.4289	+	16.0039i	0.613580	+	0.731237i	0.979952	−	0.199232i	$-0.0638447\pi$
$479$	13.4289	+	16.0039i	0.613580	+	0.731237i	−0.366372	+	0.930468i	$0.619400\pi$
$480$		0			0
$481$	−4.14486	−	1.50861i	−0.188989	−	0.0687865i
$482$		0			0
$483$	−3.17061	−	17.3838i	−0.144268	−	0.790990i
$484$		0			0
$485$	2.54173	+	14.4149i	0.115414	+	0.654546i
$486$		0			0
$487$	−15.5470	+	8.97604i	−0.704500	+	0.406743i	−0.809021	−	0.587779i	$-0.800002\pi$
$487$	−15.5470	+	8.97604i	−0.704500	+	0.406743i	0.104521	+	0.994523i	$0.466669\pi$
$488$		0			0
$489$	−0.301237	−	0.171568i	−0.0136224	−	0.00775858i
$490$		0			0
$491$	−1.52588	−	0.269053i	−0.0688619	−	0.0121422i	0.139111	−	0.990277i	$-0.455575\pi$
$491$	−1.52588	−	0.269053i	−0.0688619	−	0.0121422i	−0.207973	+	0.978135i	$0.566687\pi$
$492$		0			0
$493$	−25.8483	−	14.9236i	−1.16415	−	0.672123i
$494$		0			0
$495$	−5.39865	+	32.8703i	−0.242651	+	1.47741i
$496$		0			0
$497$	21.4785	−	7.81753i	0.963442	−	0.350664i
$498$		0			0
$499$	−21.6058	−	18.1294i	−0.967208	−	0.811584i	0.0149022	−	0.999889i	$-0.495256\pi$
$499$	−21.6058	−	18.1294i	−0.967208	−	0.811584i	−0.982111	+	0.188305i	$0.939701\pi$
$500$		0			0
$501$	−36.2856	+	6.61808i	−1.62112	+	0.295674i
$502$		0			0
$503$	−25.8755	+	4.56255i	−1.15373	+	0.203434i	−0.717605	−	0.696451i	$-0.754761\pi$
$503$	−25.8755	+	4.56255i	−1.15373	+	0.203434i	−0.436128	+	0.899885i	$0.643650\pi$
$504$		0			0
$505$	−6.85148	+	11.8671i	−0.304887	+	0.528079i
$506$		0			0
$507$	−5.75451	+	6.94033i	−0.255567	+	0.308231i
$508$		0			0
$509$	0.215632	+	1.22291i	0.00955770	+	0.0542044i	0.989214	−	0.146480i	$-0.0467945\pi$
$509$	0.215632	+	1.22291i	0.00955770	+	0.0542044i	−0.979656	+	0.200685i	$0.935683\pi$
$510$		0			0
$511$	−43.9788	−	36.9026i	−1.94551	−	1.63247i
$512$		0			0
$513$	−18.0153	−	13.7277i	−0.795394	−	0.606093i
$514$		0			0
$515$	−3.80004	−	3.18861i	−0.167450	−	0.140507i
$516$		0			0
$517$	1.03645	+	5.87800i	0.0455830	+	0.258514i
$518$		0			0
$519$	−5.03617	+	6.07397i	−0.221064	+	0.266618i
$520$		0			0
$521$	12.1376	−	21.0230i	0.531758	−	0.921033i	−0.467554	−	0.883964i	$-0.654865\pi$
$521$	12.1376	−	21.0230i	0.531758	−	0.921033i	0.999313	−	0.0370683i	$-0.0118019\pi$
$522$		0			0
$523$	9.80572	−	1.72901i	0.428774	−	0.0756044i	0.0449035	−	0.998991i	$-0.485702\pi$
$523$	9.80572	−	1.72901i	0.428774	−	0.0756044i	0.383871	+	0.923387i	$0.374591\pi$
$524$		0			0
$525$	−68.1936	+	12.4377i	−2.97621	+	0.542828i
$526$		0			0
$527$	24.8516	+	20.8530i	1.08255	+	0.908370i
$528$		0			0
$529$	−16.6113	+	6.04602i	−0.722231	+	0.262871i
$530$		0			0
$531$	−16.4635	+	6.21218i	−0.714457	+	0.269585i
$532$		0			0
$533$	−19.8659	−	11.4696i	−0.860486	−	0.496802i
$534$		0			0
$535$	−20.6087	−	3.63386i	−0.890990	−	0.157106i
$536$		0			0
$537$	15.3068	+	8.71793i	0.660537	+	0.376207i
$538$		0			0
$539$	32.2079	−	18.5953i	1.38729	−	0.800955i
$540$		0			0
$541$	1.35293	+	7.67282i	0.0581668	+	0.329881i	0.999980	−	0.00625509i	$-0.00199107\pi$
$541$	1.35293	+	7.67282i	0.0581668	+	0.329881i	−0.941814	+	0.336136i	$0.890880\pi$
$542$		0			0
$543$	3.02106	+	16.5639i	0.129646	+	0.710824i
$544$		0			0
$545$	−23.5370	−	8.56677i	−1.00821	−	0.366960i
$546$		0			0
$547$	22.0142	+	26.2355i	0.941260	+	1.12175i	0.992399	+	0.123059i	$0.0392704\pi$
$547$	22.0142	+	26.2355i	0.941260	+	1.12175i	−0.0511389	+	0.998692i	$0.516285\pi$
$548$		0			0
$549$	−14.4699	+	12.4342i	−0.617561	+	0.530679i
$550$		0			0
$551$	−17.1939	+	10.6121i	−0.732483	+	0.452092i
$552$		0			0
$553$	−14.3790	−	39.5060i	−0.611457	−	1.67996i
$554$		0			0
$555$	6.54688	−	7.89598i	0.277900	−	0.335166i
$556$		0			0
$557$	26.0657	+	31.0638i	1.10444	+	1.31622i	0.944286	+	0.329125i	$0.106754\pi$
$557$	26.0657	+	31.0638i	1.10444	+	1.31622i	0.160151	+	0.987093i	$0.448802\pi$
$558$		0			0
$559$	23.0734	+	13.3214i	0.975901	+	0.563437i
$560$		0			0
$561$	11.4814	+	30.9776i	0.484745	+	1.30788i
$562$		0			0
$563$	−16.2161	+	28.0871i	−0.683426	+	1.18373i	0.290502	+	0.956874i	$0.406178\pi$
$563$	−16.2161	+	28.0871i	−0.683426	+	1.18373i	−0.973929	+	0.226855i	$0.927156\pi$
$564$		0			0
$565$	47.4282	+	8.36286i	1.99532	+	0.351828i
$566$		0			0
$567$	−39.7878	+	0.934818i	−1.67093	+	0.0392587i
$568$		0			0
$569$	15.6043	−	27.0274i	0.654164	−	1.13305i	−0.327938	−	0.944699i	$-0.606354\pi$
$569$	15.6043	−	27.0274i	0.654164	−	1.13305i	0.982103	−	0.188347i	$-0.0603128\pi$
$570$		0			0
$571$	−2.64699	−	4.58473i	−0.110773	−	0.191865i	0.805309	−	0.592855i	$-0.201999\pi$
$571$	−2.64699	−	4.58473i	−0.110773	−	0.191865i	−0.916082	+	0.400990i	$0.868666\pi$
$572$		0			0
$573$	7.14090	−	12.5379i	0.298316	−	0.523777i
$574$		0			0
$575$	−7.14128	−	19.6205i	−0.297812	−	0.818231i
$576$		0			0
$577$	−23.2987	−	40.3545i	−0.969936	−	1.67998i	−0.695724	−	0.718310i	$-0.744916\pi$
$577$	−23.2987	−	40.3545i	−0.969936	−	1.67998i	−0.274213	−	0.961669i	$-0.588417\pi$
$578$		0			0
$579$	−3.23990	+	19.0271i	−0.134646	+	0.790740i
$580$		0			0
$581$		−	62.9354i		−	2.61100i
$582$		0			0
$583$	−30.8338	+	5.43684i	−1.27701	+	0.225171i
$584$		0			0
$585$	16.0160	+	27.0030i	0.662178	+	1.11644i
$586$		0			0
$587$	−1.39780	+	1.66583i	−0.0576934	+	0.0687563i	−0.794119	−	0.607762i	$-0.792068\pi$
$587$	−1.39780	+	1.66583i	−0.0576934	+	0.0687563i	0.736426	+	0.676518i	$0.236512\pi$
$588$		0			0
$589$	20.4074	−	8.11411i	0.840873	−	0.334336i
$590$		0			0
$591$	−14.9484	−	25.5437i	−0.614894	−	1.05073i
$592$		0			0
$593$	−7.53011	+	20.6888i	−0.309224	+	0.849587i	0.683584	+	0.729872i	$0.260420\pi$
$593$	−7.53011	+	20.6888i	−0.309224	+	0.849587i	−0.992808	+	0.119715i	$0.961802\pi$
$594$		0			0
$595$	−81.7602	+	68.6049i	−3.35184	+	2.81253i
$596$		0			0
$597$	22.5019	−	4.10410i	0.920943	−	0.167970i
$598$		0			0
$599$	−0.593883	+	0.498327i	−0.0242654	+	0.0203611i	−0.654840	−	0.755768i	$-0.727264\pi$
$599$	−0.593883	+	0.498327i	−0.0242654	+	0.0203611i	0.630574	+	0.776129i	$0.282819\pi$
$600$		0			0
$601$		−	19.5910i		−	0.799133i	−0.916704	−	0.399567i	$-0.869161\pi$
$601$		−	19.5910i		−	0.799133i	0.916704	−	0.399567i	$-0.130839\pi$
$602$		0			0
$603$	31.0285	+	36.1084i	1.26358	+	1.47045i
$604$		0			0
$605$	2.85267	+	7.83766i	0.115978	+	0.318646i
$606$		0			0
$607$	2.30482	−	1.33069i	0.0935499	−	0.0540110i	−0.452495	−	0.891767i	$-0.649466\pi$
$607$	2.30482	−	1.33069i	0.0935499	−	0.0540110i	0.546045	+	0.837756i	$0.316133\pi$
$608$		0			0
$609$	−11.9468	+	33.4332i	−0.484109	+	1.35478i
$610$		0			0
$611$	4.30938	+	3.61600i	0.174339	+	0.146288i
$612$		0			0
$613$	2.17960	−	0.793311i	0.0880334	−	0.0320415i	−0.297628	−	0.954682i	$-0.596196\pi$
$613$	2.17960	−	0.793311i	0.0880334	−	0.0320415i	0.385661	+	0.922640i	$0.373973\pi$
$614$		0			0
$615$	40.6611	−	34.5276i	1.63961	−	1.39229i
$616$		0			0
$617$	0.660750	+	0.787451i	0.0266008	+	0.0317016i	0.779181	−	0.626799i	$-0.215635\pi$
$617$	0.660750	+	0.787451i	0.0266008	+	0.0317016i	−0.752580	+	0.658501i	$0.771191\pi$
$618$		0			0
$619$	−15.6725	−	27.1456i	−0.629932	−	1.09107i	−0.987565	−	0.157212i	$-0.949749\pi$
$619$	−15.6725	−	27.1456i	−0.629932	−	1.09107i	0.357632	−	0.933862i	$-0.383584\pi$
$620$		0			0
$621$	−2.28934	−	11.7673i	−0.0918682	−	0.472206i
$622$		0			0
$623$	23.8724	−	20.0313i	0.956429	−	0.802539i
$624$		0			0
$625$	−10.9531	+	3.98662i	−0.438126	+	0.159465i
$626$		0			0
$627$	22.1478	+	3.10497i	0.884499	+	0.124001i
$628$		0			0
$629$	1.76649	−	10.0182i	0.0704344	−	0.399453i
$630$		0			0
$631$	11.6333	+	4.23419i	0.463116	+	0.168560i	0.563031	−	0.826436i	$-0.309635\pi$
$631$	11.6333	+	4.23419i	0.463116	+	0.168560i	−0.0999156	+	0.994996i	$0.531857\pi$
$632$		0			0
$633$	−3.45932	+	1.28215i	−0.137496	+	0.0509607i
$634$		0			0
$635$	−47.0280			−1.86625
$636$		0			0
$637$	11.9885	−	32.9382i	0.475003	−	1.30506i
$638$		0			0
$639$	14.5080	−	5.47429i	0.573927	−	0.216559i
$640$		0			0
$641$	2.31519	−	13.1301i	0.0914444	−	0.518607i	−0.904335	−	0.426824i	$-0.859632\pi$
$641$	2.31519	−	13.1301i	0.0914444	−	0.518607i	0.995779	−	0.0917827i	$-0.0292565\pi$
$642$		0			0
$643$	1.07086	−	6.07313i	0.0422305	−	0.239501i	−0.956385	−	0.292110i	$-0.905643\pi$
$643$	1.07086	−	6.07313i	0.0422305	−	0.239501i	0.998615	+	0.0526092i	$0.0167538\pi$
$644$		0			0
$645$	−47.2262	+	40.1024i	−1.85953	+	1.57903i
$646$		0			0
$647$		−	34.1214i		−	1.34145i	−0.741706	−	0.670725i	$-0.765983\pi$
$647$		−	34.1214i		−	1.34145i	0.741706	−	0.670725i	$-0.234017\pi$
$648$		0			0
$649$	11.1685	−	13.3101i	0.438401	−	0.522466i
$650$		0			0
$651$	19.0982	−	33.5323i	0.748518	−	1.31424i
$652$		0			0
$653$	22.7603	+	13.1407i	0.890680	+	0.514234i	0.874165	−	0.485630i	$-0.161410\pi$
$653$	22.7603	+	13.1407i	0.890680	+	0.514234i	0.0165149	+	0.999864i	$0.494743\pi$
$654$		0			0
$655$	21.0753	+	7.67079i	0.823481	+	0.299723i
$656$		0			0
$657$	−30.1277	−	24.6830i	−1.17539	−	0.962976i
$658$		0			0
$659$	−1.95451	−	11.0846i	−0.0761371	−	0.431795i	−0.998920	−	0.0464734i	$-0.985202\pi$
$659$	−1.95451	−	11.0846i	−0.0761371	−	0.431795i	0.922782	−	0.385321i	$-0.125909\pi$
$660$		0			0
$661$	−23.9889	+	4.22989i	−0.933060	+	0.164524i	−0.619457	−	0.785031i	$-0.712647\pi$
$661$	−23.9889	+	4.22989i	−0.933060	+	0.164524i	−0.313603	+	0.949554i	$0.601536\pi$
$662$		0			0
$663$	27.0567	+	15.4100i	1.05079	+	0.598476i
$664$		0			0
$665$	14.6308	+	70.7546i	0.567356	+	2.74375i
$666$		0			0
$667$	−10.5317	−	1.85702i	−0.407789	−	0.0719041i
$668$		0			0
$669$	−5.14767	+	30.2310i	−0.199020	+	1.16880i
$670$		0			0
$671$	6.44309	−	17.7022i	0.248733	−	0.683387i
$672$		0			0
$673$	−32.3308	+	18.6662i	−1.24626	+	0.719529i	−0.970362	−	0.241658i	$-0.922309\pi$
$673$	−32.3308	+	18.6662i	−1.24626	+	0.719529i	−0.275899	+	0.961187i	$0.588975\pi$
$674$		0			0
$675$	−46.1611	+	8.98071i	−1.77674	+	0.345668i
$676$		0			0
$677$	−43.4090			−1.66834			−0.834172	−	0.551504i	$-0.814054\pi$
$677$	−43.4090			−1.66834			−0.834172	+	0.551504i	$0.814054\pi$
$678$		0			0
$679$	11.0997	−	13.2281i	0.425969	−	0.507650i
$680$		0			0
$681$	21.5189	+	12.2560i	0.824607	+	0.469652i
$682$		0			0
$683$	37.6697			1.44139			0.720696	−	0.693251i	$-0.243822\pi$
$683$	37.6697			1.44139			0.720696	+	0.693251i	$0.243822\pi$
$684$		0			0
$685$	45.4520			1.73663
$686$		0			0
$687$	5.16760	−	3.02412i	0.197156	−	0.115377i
$688$		0			0
$689$	−18.9682	+	22.6054i	−0.722630	+	0.861197i
$690$		0			0
$691$	−29.4497			−1.12032			−0.560160	−	0.828384i	$-0.689260\pi$
$691$	−29.4497			−1.12032			−0.560160	+	0.828384i	$0.689260\pi$
$692$		0			0
$693$	33.7998	−	20.0473i	1.28395	−	0.761534i
$694$		0			0
$695$	−18.8132	+	10.8618i	−0.713626	+	0.412012i
$696$		0			0
$697$	18.0944	−	49.7140i	0.685374	−	1.88305i
$698$		0			0
$699$	−18.5063	+	6.85909i	−0.699972	+	0.259434i
$700$		0			0
$701$	37.2823	+	6.57387i	1.40813	+	0.248292i	0.825480	−	0.564431i	$-0.190904\pi$
$701$	37.2823	+	6.57387i	1.40813	+	0.248292i	0.582651	+	0.812722i	$0.302015\pi$
$702$		0			0
$703$	−5.40310	−	4.26971i	−0.203782	−	0.161035i
$704$		0			0
$705$	−11.2904	+	6.60722i	−0.425221	+	0.248842i
$706$		0			0
$707$	15.9203	−	2.80717i	0.598744	−	0.105575i
$708$		0			0
$709$	−4.59406	−	26.0542i	−0.172534	−	0.978486i	−0.940952	−	0.338539i	$-0.890067\pi$
$709$	−4.59406	−	26.0542i	−0.172534	−	0.978486i	0.768419	−	0.639947i	$-0.221044\pi$
$710$		0			0
$711$	−10.0690	−	26.6849i	−0.377617	−	1.00076i
$712$		0			0
$713$	10.9227	+	3.97554i	0.409059	+	0.148885i
$714$		0			0
$715$	−26.8470	−	15.5001i	−1.00402	−	0.579671i
$716$		0			0
$717$	−43.0114	+	0.252595i	−1.60629	+	0.00943335i
$718$		0			0
$719$	14.9999	−	17.8762i	0.559402	−	0.666669i	−0.410018	−	0.912078i	$-0.634478\pi$
$719$	14.9999	−	17.8762i	0.559402	−	0.666669i	0.969420	+	0.245408i	$0.0789220\pi$
$720$		0			0
$721$			5.85220i			0.217947i
$722$		0			0
$723$	2.56938	+	14.0874i	0.0955561	+	0.523915i
$724$		0			0
$725$	−7.28477	+	41.3140i	−0.270550	+	1.53436i
$726$		0			0
$727$	−0.328062	+	1.86053i	−0.0121671	+	0.0690032i	−0.990287	−	0.139040i	$-0.955598\pi$
$727$	−0.328062	+	1.86053i	−0.0121671	+	0.0690032i	0.978120	+	0.208043i	$0.0667095\pi$
$728$		0			0
$729$	−26.9832	+	0.951179i	−0.999379	+	0.0352288i
$730$		0			0
$731$	−21.0159	+	57.7408i	−0.777302	+	2.13562i
$732$		0			0
$733$	23.7921			0.878782			0.439391	−	0.898296i	$-0.355194\pi$
$733$	23.7921			0.878782			0.439391	+	0.898296i	$0.355194\pi$
$734$		0			0
$735$	62.7475	+	52.0266i	2.31448	+	1.91903i
$736$		0			0
$737$	−44.1744	−	16.0782i	−1.62718	−	0.592246i
$738$		0			0
$739$	−5.21074	+	29.5516i	−0.191680	+	1.08707i	0.725388	+	0.688340i	$0.241660\pi$
$739$	−5.21074	+	29.5516i	−0.191680	+	1.08707i	−0.917068	+	0.398731i	$0.869451\pi$
$740$		0			0
$741$	17.8718	−	11.1760i	0.656536	−	0.410561i
$742$		0			0
$743$	−37.6814	+	13.7149i	−1.38239	+	0.503151i	−0.922903	−	0.385032i	$-0.874191\pi$
$743$	−37.6814	+	13.7149i	−1.38239	+	0.503151i	−0.459492	+	0.888182i	$0.651968\pi$
$744$		0			0
$745$	10.5737	−	8.87243i	0.387392	−	0.325061i
$746$		0			0
$747$	−0.501471	−	42.6932i	−0.0183479	−	1.56206i
$748$		0			0
$749$	12.3439	+	21.3803i	0.451037	+	0.781220i
$750$		0			0
$751$	29.0906	+	34.6688i	1.06153	+	1.26508i	0.962871	+	0.269962i	$0.0870110\pi$
$751$	29.0906	+	34.6688i	1.06153	+	1.26508i	0.0986594	+	0.995121i	$0.468545\pi$
$752$		0			0
$753$	−10.0632	−	3.59591i	−0.366722	−	0.131042i
$754$		0			0
$755$	−57.5183	+	20.9350i	−2.09331	+	0.761901i
$756$		0			0
$757$	−0.215233	−	0.180602i	−0.00782277	−	0.00656408i	0.638868	−	0.769316i	$-0.279403\pi$
$757$	−0.215233	−	0.180602i	−0.00782277	−	0.00656408i	−0.646691	+	0.762752i	$0.723848\pi$
$758$		0			0
$759$	7.66182	+	9.02286i	0.278107	+	0.327509i
$760$		0			0
$761$	−33.4002	+	19.2836i	−1.21076	+	0.699030i	−0.962924	−	0.269773i	$-0.913051\pi$
$761$	−33.4002	+	19.2836i	−1.21076	+	0.699030i	−0.247831	+	0.968803i	$0.579718\pi$
$762$		0			0
$763$	10.1065	+	27.7675i	0.365881	+	1.00525i
$764$		0			0
$765$	−54.9167	+	47.1907i	−1.98552	+	1.70618i
$766$		0			0
$767$		−	16.3760i		−	0.591305i
$768$		0			0
$769$	3.23569	−	2.71507i	0.116682	−	0.0979078i	−0.582580	−	0.812774i	$-0.697957\pi$
$769$	3.23569	−	2.71507i	0.116682	−	0.0979078i	0.699262	+	0.714866i	$0.253512\pi$
$770$		0			0
$771$	−8.61367	−	10.1438i	−0.310214	−	0.365320i
$772$		0			0
$773$	16.6634	−	13.9823i	0.599341	−	0.502907i	−0.291893	−	0.956451i	$-0.594285\pi$
$773$	16.6634	−	13.9823i	0.599341	−	0.502907i	0.891234	+	0.453544i	$0.149841\pi$
$774$		0			0
$775$	15.5954	−	42.8479i	0.560202	−	1.53914i
$776$		0			0
$777$	−12.1005	+	0.0710632i	−0.434102	+	0.00254938i
$778$		0			0
$779$	−23.8166	−	26.7471i	−0.853317	−	0.958313i
$780$		0			0
$781$	−9.84188	+	11.7291i	−0.352170	+	0.419700i
$782$		0			0
$783$	−7.83791	+	22.7751i	−0.280104	+	0.813916i
$784$		0			0
$785$	−35.3987	+	6.24174i	−1.26343	+	0.222777i
$786$		0			0
$787$			20.7663i			0.740239i	0.928984	+	0.370119i	$0.120683\pi$
$787$			20.7663i			0.740239i	−0.928984	+	0.370119i	$0.879317\pi$
$788$		0			0
$789$	10.8081	−	4.00586i	0.384778	−	0.142612i
$790$		0			0
$791$	−28.4080	−	49.2040i	−1.01007	−	1.74949i
$792$		0			0
$793$	−6.07262	−	16.6844i	−0.215645	−	0.592480i
$794$		0			0
$795$	−34.6591	−	59.2253i	−1.22923	−	2.10050i
$796$		0			0
$797$	−24.9663	−	43.2429i	−0.884353	−	1.53174i	−0.846454	−	0.532462i	$-0.821267\pi$
$797$	−24.9663	−	43.2429i	−0.884353	−	1.53174i	−0.0378986	−	0.999282i	$-0.512066\pi$
$798$		0			0
$799$	−6.48704	+	11.2359i	−0.229495	+	0.397497i
$800$		0			0
$801$	16.0346	−	13.7788i	0.566556	−	0.486850i
$802$		0			0
$803$	37.8733	+	6.67809i	1.33652	+	0.235665i
$804$		0			0
$805$	−19.1206	+	33.1179i	−0.673914	+	1.16725i
$806$		0			0
$807$	23.5723	−	28.4298i	0.829783	−	1.00077i
$808$		0			0
$809$	−41.4228	−	23.9155i	−1.45635	−	0.840824i	−0.457520	−	0.889199i	$-0.651262\pi$
$809$	−41.4228	−	23.9155i	−1.45635	−	0.840824i	−0.998829	+	0.0483758i	$0.984595\pi$
$810$		0			0
$811$	18.4886	+	22.0339i	0.649224	+	0.773715i	0.985797	−	0.167942i	$-0.0537123\pi$
$811$	18.4886	+	22.0339i	0.649224	+	0.773715i	−0.336573	+	0.941657i	$0.609268\pi$
$812$		0			0
$813$	10.5981	+	28.5945i	0.371692	+	1.00285i
$814$		0			0
$815$	0.256595	+	0.704989i	0.00898813	+	0.0246947i
$816$		0			0
$817$	27.6620	+	31.0656i	0.967771	+	1.08685i
$818$		0			0
$819$	12.2582	−	34.9510i	0.428336	−	1.22129i
$820$		0			0
$821$	−11.7544	−	14.0084i	−0.410232	−	0.488896i	0.520879	−	0.853630i	$-0.325604\pi$
$821$	−11.7544	−	14.0084i	−0.410232	−	0.488896i	−0.931112	+	0.364735i	$0.881160\pi$
$822$		0			0
$823$	−16.0503	−	5.84182i	−0.559477	−	0.203633i	0.0467749	−	0.998905i	$-0.485106\pi$
$823$	−16.0503	−	5.84182i	−0.559477	−	0.203633i	−0.606252	+	0.795272i	$0.707328\pi$
$824$		0			0
$825$	35.3951	−	30.0560i	1.23230	−	1.04642i
$826$		0			0
$827$	−9.28820	−	52.6760i	−0.322982	−	1.83172i	−0.523489	−	0.852032i	$-0.675370\pi$
$827$	−9.28820	−	52.6760i	−0.322982	−	1.83172i	0.200507	−	0.979692i	$-0.435741\pi$
$828$		0			0
$829$	6.97376	−	4.02630i	0.242209	−	0.139839i	−0.373983	−	0.927436i	$-0.622008\pi$
$829$	6.97376	−	4.02630i	0.242209	−	0.139839i	0.616191	+	0.787596i	$0.288675\pi$
$830$		0			0
$831$	−14.5883	+	8.53719i	−0.506063	+	0.296152i
$832$		0			0
$833$	79.6126	+	14.0378i	2.75841	+	0.486383i
$834$		0			0
$835$	69.1278	+	39.9109i	2.39226	+	1.38117i
$836$		0			0
$837$	12.6884	−	22.8994i	0.438575	−	0.791517i
$838$		0			0
$839$	18.2844	−	6.65498i	0.631248	−	0.229755i	−0.00652643	−	0.999979i	$-0.502077\pi$
$839$	18.2844	−	6.65498i	0.631248	−	0.229755i	0.637774	+	0.770223i	$0.279855\pi$
$840$		0			0
$841$	−5.75558	−	4.82950i	−0.198468	−	0.166535i
$842$		0			0
$843$	−21.7817	−	25.6510i	−0.750202	−	0.883467i
$844$		0			0
$845$	19.2146	−	3.38806i	0.661003	−	0.116553i
$846$		0			0
$847$	4.91989	−	8.52150i	0.169049	−	0.292802i
$848$		0			0
$849$	−11.8415	−	31.9493i	−0.406400	−	1.09650i
$850$		0			0
$851$	−0.632928	−	3.58952i	−0.0216965	−	0.123047i
$852$		0			0
$853$	3.42451	+	2.87351i	0.117253	+	0.0983870i	0.699529	−	0.714604i	$-0.253393\pi$
$853$	3.42451	+	2.87351i	0.117253	+	0.0983870i	−0.582276	+	0.812991i	$0.697838\pi$
$854$		0			0
$855$	10.4888	+	47.8809i	0.358709	+	1.63749i
$856$		0			0
$857$	25.6973	+	21.5626i	0.877804	+	0.736565i	0.965726	−	0.259563i	$-0.0835784\pi$
$857$	25.6973	+	21.5626i	0.877804	+	0.736565i	−0.0879226	+	0.996127i	$0.528023\pi$
$858$		0			0
$859$	−1.18830	−	6.73917i	−0.0405442	−	0.229938i	0.957802	−	0.287430i	$-0.0928007\pi$
$859$	−1.18830	−	6.73917i	−0.0405442	−	0.229938i	−0.998346	+	0.0574920i	$0.981690\pi$
$860$		0			0
$861$	−62.0378	−	10.5637i	−2.11424	−	0.360009i
$862$		0			0
$863$	−9.09561	+	15.7541i	−0.309618	+	0.536274i	−0.978279	−	0.207293i	$-0.933535\pi$
$863$	−9.09561	+	15.7541i	−0.309618	+	0.536274i	0.668661	+	0.743568i	$0.266868\pi$
$864$		0			0
$865$	16.8161	−	2.96513i	0.571763	−	0.100817i
$866$		0			0
$867$	−14.2563	+	39.8964i	−0.484171	+	1.35495i
$868$		0			0
$869$	21.5736	+	18.1024i	0.731835	+	0.614083i
$870$		0			0
$871$	−41.6344	+	15.1537i	−1.41073	+	0.513463i
$872$		0			0
$873$	7.42427	−	9.06196i	0.251274	−	0.306701i
$874$		0			0
$875$	58.1413	+	33.5679i	1.96554	+	1.13480i
$876$		0			0
$877$	16.7079	+	2.94606i	0.564187	+	0.0994814i	0.448465	−	0.893800i	$-0.351971\pi$
$877$	16.7079	+	2.94606i	0.564187	+	0.0994814i	0.115722	+	0.993282i	$0.463082\pi$
$878$		0			0
$879$	0.0805711	+	13.7195i	0.00271760	+	0.462746i
$880$		0			0
$881$	−33.0686	+	19.0922i	−1.11411	+	0.643231i	−0.939891	−	0.341476i	$-0.889073\pi$
$881$	−33.0686	+	19.0922i	−1.11411	+	0.643231i	−0.174219	+	0.984707i	$0.555740\pi$
$882$		0			0
$883$	−9.33906	−	52.9645i	−0.314284	−	1.78240i	−0.576204	−	0.817306i	$-0.695466\pi$
$883$	−9.33906	−	52.9645i	−0.314284	−	1.78240i	0.261919	−	0.965090i	$-0.415645\pi$
$884$		0			0
$885$	35.8604	+	12.8141i	1.20544	+	0.430743i
$886$		0			0
$887$	−23.0945	−	8.40572i	−0.775438	−	0.282236i	−0.0761689	−	0.997095i	$-0.524269\pi$
$887$	−23.0945	−	8.40572i	−0.775438	−	0.282236i	−0.699269	+	0.714859i	$0.746491\pi$
$888$		0			0
$889$	35.6623	+	42.5006i	1.19607	+	1.42543i
$890$		0			0
$891$	22.7689	−	13.8687i	0.762786	−	0.464619i
$892$		0			0
$893$	4.61292	+	7.47390i	0.154366	+	0.250105i
$894$		0			0
$895$	−13.0384	−	35.8227i	−0.435826	−	1.19742i
$896$		0			0
$897$	10.9981	+	1.87274i	0.367217	+	0.0625289i
$898$		0			0
$899$	−15.0118	−	17.8904i	−0.500673	−	0.596679i
$900$		0			0
$901$	−58.9393	−	34.0286i	−1.96355	−	1.13366i
$902$		0			0
$903$	72.0544	+	12.2693i	2.39782	+	0.408296i
$904$		0			0
$905$	18.2188	−	31.5559i	0.605614	−	1.04895i
$906$		0			0
$907$	−35.3806	−	6.23855i	−1.17479	−	0.207148i	−0.448019	−	0.894024i	$-0.647870\pi$
$907$	−35.3806	−	6.23855i	−1.17479	−	0.207148i	−0.726774	+	0.686876i	$0.758981\pi$
$908$		0			0
$909$	10.7774	−	2.03114i	0.357464	−	0.0673688i
$910$		0			0
$911$	−29.0194	+	50.2631i	−0.961457	+	1.66529i	−0.242609	+	0.970124i	$0.578003\pi$
$911$	−29.0194	+	50.2631i	−0.961457	+	1.66529i	−0.718848	+	0.695168i	$0.755330\pi$
$912$		0			0
$913$	21.0794	+	36.5105i	0.697625	+	1.20832i
$914$		0			0
$915$	41.2874	−	0.242471i	1.36492	−	0.00801584i
$916$		0			0
$917$	−9.04951	−	24.8633i	−0.298841	−	0.821060i
$918$		0			0
$919$	11.7005	+	20.2659i	0.385965	+	0.668510i	0.991903	−	0.127002i	$-0.0405354\pi$
$919$	11.7005	+	20.2659i	0.385965	+	0.668510i	−0.605938	+	0.795512i	$0.707202\pi$
$920$		0			0
$921$	11.2247	+	9.30688i	0.369867	+	0.306672i
$922$		0			0
$923$			14.4309i			0.474998i
$924$		0			0
$925$	−14.0811	+	2.48287i	−0.462982	+	0.0816362i
$926$		0			0
$927$	0.0466305	+	3.96993i	0.00153155	+	0.130390i
$928$		0			0
$929$	−3.90416	+	4.65279i	−0.128091	+	0.152653i	−0.826278	−	0.563262i	$-0.809546\pi$
$929$	−3.90416	+	4.65279i	−0.128091	+	0.152653i	0.698187	+	0.715916i	$0.253990\pi$
$930$		0			0
$931$	33.9304	−	42.9372i	1.11202	−	1.40721i
$932$		0			0
$933$	2.06523	−	3.62610i	0.0676126	−	0.118713i
$934$		0			0
$935$	24.4530	−	67.1841i	0.799699	−	2.19715i
$936$		0			0
$937$	34.6327	−	29.0603i	1.13140	−	0.949358i	0.132278	−	0.991213i	$-0.457771\pi$
$937$	34.6327	−	29.0603i	1.13140	−	0.949358i	0.999124	+	0.0418543i	$0.0133265\pi$
$938$		0			0
$939$	−17.0245	+	47.6432i	−0.555574	+	1.55478i
$940$		0			0
$941$	−1.41429	+	1.18673i	−0.0461044	+	0.0386862i	−0.665549	−	0.746354i	$-0.731802\pi$
$941$	−1.41429	+	1.18673i	−0.0461044	+	0.0386862i	0.619444	+	0.785041i	$0.287358\pi$
$942$		0			0
$943$		−	18.9556i		−	0.617279i
$944$		0			0
$945$	66.9441	+	54.1920i	2.17769	+	1.76287i
$946$		0			0
$947$	−0.262536	−	0.721313i	−0.00853128	−	0.0234395i	0.935354	−	0.353713i	$-0.115081\pi$
$947$	−0.262536	−	0.721313i	−0.00853128	−	0.0234395i	−0.943885	+	0.330274i	$0.892859\pi$
$948$		0			0
$949$	31.3902	−	18.1232i	1.01897	−	0.588303i
$950$		0			0
$951$	−18.0913	+	3.29965i	−0.586651	+	0.106998i
$952$		0			0
$953$	30.1620	+	25.3089i	0.977044	+	0.819837i	0.983641	−	0.180141i	$-0.0576554\pi$
$953$	30.1620	+	25.3089i	0.977044	+	0.819837i	−0.00659692	+	0.999978i	$0.502100\pi$
$954$		0			0
$955$	−29.3426	+	10.6798i	−0.949504	+	0.345591i
$956$		0			0
$957$	−4.26733	−	23.3969i	−0.137943	−	0.756315i
$958$		0			0
$959$	−34.4672	−	41.0764i	−1.11300	−	1.32642i
$960$		0			0
$961$	−2.80786	−	4.86336i	−0.0905762	−	0.156883i
$962$		0			0
$963$	8.54405	+	14.4053i	0.275328	+	0.464205i
$964$		0			0
$965$	31.9974	−	26.8490i	1.03003	−	0.864301i
$966$		0			0
$967$	−25.7812	+	9.38358i	−0.829067	+	0.301756i	−0.721476	−	0.692440i	$-0.756536\pi$
$967$	−25.7812	+	9.38358i	−0.829067	+	0.301756i	−0.107591	+	0.994195i	$0.534314\pi$
$968$		0			0
$969$	32.5410	+	36.1157i	1.04537	+	1.16020i
$970$		0			0
$971$	−3.33960	+	18.9398i	−0.107173	+	0.607808i	0.883157	+	0.469077i	$0.155413\pi$
$971$	−3.33960	+	18.9398i	−0.107173	+	0.607808i	−0.990330	+	0.138731i	$0.955698\pi$
$972$		0			0
$973$	24.0826	+	8.76535i	0.772052	+	0.281004i
$974$		0			0
$975$	7.34643	−	43.1438i	0.235274	−	1.38171i
$976$		0			0
$977$	46.0907			1.47457			0.737285	−	0.675581i	$-0.236107\pi$
$977$	46.0907			1.47457			0.737285	+	0.675581i	$0.236107\pi$
$978$		0			0
$979$	−7.13981	+	19.6165i	−0.228189	+	0.626945i
$980$		0			0
$981$	7.07718	+	18.7560i	0.225957	+	0.598832i
$982$		0			0
$983$	−10.2044	+	57.8720i	−0.325470	+	1.84583i	0.180884	+	0.983504i	$0.442104\pi$
$983$	−10.2044	+	57.8720i	−0.325470	+	1.84583i	−0.506354	+	0.862326i	$0.669007\pi$
$984$		0			0
$985$	−11.1221	+	63.0767i	−0.354381	+	2.00979i
$986$		0			0
$987$	14.5329	+	5.19309i	0.462587	+	0.165298i
$988$		0			0
$989$			22.0161i			0.700073i
$990$		0			0
$991$	29.8935	−	35.6257i	0.949598	−	1.13169i	−0.0415780	−	0.999135i	$-0.513239\pi$
$991$	29.8935	−	35.6257i	0.949598	−	1.13169i	0.991176	−	0.132552i	$-0.0423170\pi$
$992$		0			0
$993$	−13.2360	−	22.6177i	−0.420033	−	0.717750i
$994$		0			0
$995$	−42.8685	−	24.7501i	−1.35902	−	0.784632i
$996$		0			0
$997$	−38.0365	−	13.8441i	−1.20463	−	0.438448i	−0.339790	−	0.940501i	$-0.610356\pi$
$997$	−38.0365	−	13.8441i	−1.20463	−	0.438448i	−0.864837	+	0.502053i	$0.832578\pi$
$998$		0			0
$999$	−8.20798	+	0.144624i	−0.259689	+	0.00457569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cl.a.173.11	yes	120
9.5	odd	6		684.2.bv.a.401.1	yes	120
19.10	odd	18		684.2.bv.a.29.1	✓	120
171.86	even	18	inner	684.2.cl.a.257.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bv.a.29.1	✓	120	19.10	odd	18
684.2.bv.a.401.1	yes	120	9.5	odd	6
684.2.cl.a.173.11	yes	120	1.1	even	1	trivial
684.2.cl.a.257.11	yes	120	171.86	even	18	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cl (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0101717 + 1.73202i) q^{3} +(2.40941 - 2.87142i) q^{5} -4.42209 q^{7} +(-2.99979 + 0.0352353i) q^{9} +O(q^{10})\)	\(q+(0.0101717 + 1.73202i) q^{3} +(2.40941 - 2.87142i) q^{5} -4.42209 q^{7} +(-2.99979 + 0.0352353i) q^{9} +(2.56537 - 1.48112i) q^{11} +(0.954891 - 2.62354i) q^{13} +(4.99786 + 4.14393i) q^{15} +(6.34117 + 1.11812i) q^{17} +(2.70257 - 3.41996i) q^{19} +(-0.0449803 - 7.65915i) q^{21} +(2.27203 - 0.400620i) q^{23} +(-1.57156 - 8.91278i) q^{25} +(-0.0915414 - 5.19535i) q^{27} +(-4.35582 - 1.58539i) q^{29} +(4.36328 + 2.51914i) q^{31} +(2.59142 + 4.42822i) q^{33} +(-10.6546 + 12.6977i) q^{35} -1.57987i q^{37} +(4.55374 + 1.62721i) q^{39} +(1.42674 - 8.09144i) q^{41} +(-1.65710 + 9.39789i) q^{43} +(-7.12654 + 8.69856i) q^{45} +(-0.689144 + 1.89341i) q^{47} +12.5549 q^{49} +(-1.87211 + 10.9944i) q^{51} +(-9.93212 - 3.61499i) q^{53} +(1.92811 - 10.9349i) q^{55} +(5.95094 + 4.64611i) q^{57} +(5.51179 - 2.00613i) q^{59} +(4.87165 - 4.08780i) q^{61} +(13.2654 - 0.155814i) q^{63} +(-5.23257 - 9.06307i) q^{65} +(-10.2007 - 12.1568i) q^{67} +(0.716993 + 3.93113i) q^{69} +(-4.85709 + 1.76784i) q^{71} +(9.94525 + 8.34506i) q^{73} +(15.4211 - 2.81264i) q^{75} +(-11.3443 + 6.54964i) q^{77} +(3.25163 + 8.93378i) q^{79} +(8.99752 - 0.211397i) q^{81} +14.2321i q^{83} +(18.4890 - 15.5141i) q^{85} +(2.70162 - 7.56050i) q^{87} +(-5.39845 + 4.52984i) q^{89} +(-4.22261 + 11.6015i) q^{91} +(-4.31882 + 7.58292i) q^{93} +(-3.30856 - 16.0003i) q^{95} +(-2.51006 + 2.99138i) q^{97} +(-7.64340 + 4.53344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{3} - 3 q^{9}+O(q^{10}) \) 120 * q + 3 * q^3 - 3 * q^9	\( 120 q + 3 q^{3} - 3 q^{9} - 3 q^{13} + 21 q^{15} - 27 q^{17} - 3 q^{19} - 9 q^{27} + 27 q^{29} + 30 q^{33} + 30 q^{39} + 9 q^{41} + 12 q^{43} - 27 q^{45} + 120 q^{49} + 9 q^{51} + 24 q^{57} - 18 q^{59} + 42 q^{61} - 24 q^{63} + 12 q^{67} + 27 q^{69} + 39 q^{73} - 3 q^{79} - 3 q^{81} - 36 q^{87} + 54 q^{89} - 12 q^{91} - 24 q^{93} - 9 q^{97} - 6 q^{99}+O(q^{100}) \) 120 * q + 3 * q^3 - 3 * q^9 - 3 * q^13 + 21 * q^15 - 27 * q^17 - 3 * q^19 - 9 * q^27 + 27 * q^29 + 30 * q^33 + 30 * q^39 + 9 * q^41 + 12 * q^43 - 27 * q^45 + 120 * q^49 + 9 * q^51 + 24 * q^57 - 18 * q^59 + 42 * q^61 - 24 * q^63 + 12 * q^67 + 27 * q^69 + 39 * q^73 - 3 * q^79 - 3 * q^81 - 36 * q^87 + 54 * q^89 - 12 * q^91 - 24 * q^93 - 9 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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