LMFDB - Embedded newform 684.3.g.d.343.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.7
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55174 - 1.26178i) q^{2} +(0.815807 + 3.91592i) q^{4} +2.61138 q^{5} -10.9942i q^{7} +(3.67512 - 7.10587i) q^{8} +O(q^{10})$	\(q+(-1.55174 - 1.26178i) q^{2} +(0.815807 + 3.91592i) q^{4} +2.61138 q^{5} -10.9942i q^{7} +(3.67512 - 7.10587i) q^{8} +(-4.05218 - 3.29499i) q^{10} -21.8516i q^{11} -4.95476 q^{13} +(-13.8723 + 17.0601i) q^{14} +(-14.6689 + 6.38927i) q^{16} +20.1023 q^{17} +4.35890i q^{19} +(2.13038 + 10.2260i) q^{20} +(-27.5720 + 33.9081i) q^{22} +9.15603i q^{23} -18.1807 q^{25} +(7.68851 + 6.25183i) q^{26} +(43.0523 - 8.96912i) q^{28} +1.24974 q^{29} +39.9294i q^{31} +(30.8243 + 8.59449i) q^{32} +(-31.1935 - 25.3647i) q^{34} -28.7099i q^{35} -56.6170 q^{37} +(5.49999 - 6.76389i) q^{38} +(9.59714 - 18.5561i) q^{40} +31.6717 q^{41} -23.3377i q^{43} +(85.5693 - 17.8267i) q^{44} +(11.5529 - 14.2078i) q^{46} -64.7865i q^{47} -71.8718 q^{49} +(28.2118 + 22.9401i) q^{50} +(-4.04213 - 19.4025i) q^{52} -80.8467 q^{53} -57.0628i q^{55} +(-78.1232 - 40.4050i) q^{56} +(-1.93928 - 1.57690i) q^{58} +12.2009i q^{59} +64.3769 q^{61} +(50.3822 - 61.9601i) q^{62} +(-36.9869 - 52.2300i) q^{64} -12.9387 q^{65} -82.9847i q^{67} +(16.3996 + 78.7189i) q^{68} +(-36.2257 + 44.5504i) q^{70} +16.4217i q^{71} -63.6386 q^{73} +(87.8549 + 71.4383i) q^{74} +(-17.0691 + 3.55602i) q^{76} -240.241 q^{77} -19.2738i q^{79} +(-38.3061 + 16.6848i) q^{80} +(-49.1463 - 39.9628i) q^{82} +29.3102i q^{83} +52.4946 q^{85} +(-29.4471 + 36.2140i) q^{86} +(-155.275 - 80.3075i) q^{88} +21.4346 q^{89} +54.4735i q^{91} +(-35.8543 + 7.46955i) q^{92} +(-81.7465 + 100.532i) q^{94} +11.3827i q^{95} +74.7316 q^{97} +(111.527 + 90.6867i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.55174	−	1.26178i	−0.775871	−	0.630892i
$2$	−1.55174	−	1.26178i	−0.775871	−	0.630892i
$3$		0			0
$3$		0			0
$4$	0.815807	+	3.91592i	0.203952	+	0.978981i
$5$	2.61138			0.522275			0.261138	−	0.965302i	$-0.415902\pi$
$5$	2.61138			0.522275			0.261138	+	0.965302i	$0.415902\pi$
$6$		0			0
$7$		−	10.9942i		−	1.57060i	−0.619118	−	0.785298i	$-0.712510\pi$
$7$		−	10.9942i		−	1.57060i	0.619118	−	0.785298i	$-0.287490\pi$
$8$	3.67512	−	7.10587i	0.459391	−	0.888234i
$9$		0			0
$10$	−4.05218	−	3.29499i	−0.405218	−	0.329499i
$11$		−	21.8516i		−	1.98651i	−0.115944	−	0.993256i	$-0.536989\pi$
$11$		−	21.8516i		−	1.98651i	0.115944	−	0.993256i	$-0.463011\pi$
$12$		0			0
$13$	−4.95476			−0.381135			−0.190568	−	0.981674i	$-0.561033\pi$
$13$	−4.95476			−0.381135			−0.190568	+	0.981674i	$0.561033\pi$
$14$	−13.8723	+	17.0601i	−0.990876	+	1.21858i
$15$		0			0
$16$	−14.6689	+	6.38927i	−0.916807	+	0.399330i
$17$	20.1023			1.18249			0.591243	−	0.806493i	$-0.298637\pi$
$17$	20.1023			1.18249			0.591243	+	0.806493i	$0.298637\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	2.13038	+	10.2260i	0.106519	+	0.511298i
$21$		0			0
$22$	−27.5720	+	33.9081i	−1.25327	+	1.54128i
$23$			9.15603i			0.398088i	0.979991	+	0.199044i	$0.0637837\pi$
$23$			9.15603i			0.398088i	−0.979991	+	0.199044i	$0.936216\pi$
$24$		0			0
$25$	−18.1807			−0.727228
$26$	7.68851	+	6.25183i	0.295712	+	0.240455i
$27$		0			0
$28$	43.0523	−	8.96912i	1.53758	−	0.320326i
$29$	1.24974			0.0430945			0.0215473	−	0.999768i	$-0.493141\pi$
$29$	1.24974			0.0430945			0.0215473	+	0.999768i	$0.493141\pi$
$30$		0			0
$31$			39.9294i			1.28804i	0.765007	+	0.644022i	$0.222735\pi$
$31$			39.9294i			1.28804i	−0.765007	+	0.644022i	$0.777265\pi$
$32$	30.8243	+	8.59449i	0.963258	+	0.268578i
$33$		0			0
$34$	−31.1935	−	25.3647i	−0.917457	−	0.746021i
$35$		−	28.7099i		−	0.820284i
$36$		0			0
$37$	−56.6170			−1.53019			−0.765094	−	0.643918i	$-0.777308\pi$
$37$	−56.6170			−1.53019			−0.765094	+	0.643918i	$0.777308\pi$
$38$	5.49999	−	6.76389i	0.144736	−	0.177997i
$39$		0			0
$40$	9.59714	−	18.5561i	0.239928	−	0.463903i
$41$	31.6717			0.772480			0.386240	−	0.922398i	$-0.373774\pi$
$41$	31.6717			0.772480			0.386240	+	0.922398i	$0.373774\pi$
$42$		0			0
$43$		−	23.3377i		−	0.542736i	−0.962476	−	0.271368i	$-0.912524\pi$
$43$		−	23.3377i		−	0.542736i	0.962476	−	0.271368i	$-0.0874761\pi$
$44$	85.5693	−	17.8267i	1.94476	−	0.405152i
$45$		0			0
$46$	11.5529	−	14.2078i	0.251151	−	0.308865i
$47$		−	64.7865i		−	1.37844i	−0.724554	−	0.689218i	$-0.757954\pi$
$47$		−	64.7865i		−	1.37844i	0.724554	−	0.689218i	$-0.242046\pi$
$48$		0			0
$49$	−71.8718			−1.46677
$50$	28.2118	+	22.9401i	0.564236	+	0.458802i
$51$		0			0
$52$	−4.04213	−	19.4025i	−0.0777332	−	0.373124i
$53$	−80.8467			−1.52541			−0.762705	−	0.646747i	$-0.776129\pi$
$53$	−80.8467			−1.52541			−0.762705	+	0.646747i	$0.776129\pi$
$54$		0			0
$55$		−	57.0628i		−	1.03751i
$56$	−78.1232	−	40.4050i	−1.39506	−	0.721517i
$57$		0			0
$58$	−1.93928	−	1.57690i	−0.0334358	−	0.0271880i
$59$			12.2009i			0.206795i	0.994640	+	0.103398i	$0.0329714\pi$
$59$			12.2009i			0.206795i	−0.994640	+	0.103398i	$0.967029\pi$
$60$		0			0
$61$	64.3769			1.05536			0.527679	−	0.849444i	$-0.323062\pi$
$61$	64.3769			1.05536			0.527679	+	0.849444i	$0.323062\pi$
$62$	50.3822	−	61.9601i	0.812616	−	0.999356i
$63$		0			0
$64$	−36.9869	−	52.2300i	−0.577921	−	0.816093i
$65$	−12.9387			−0.199058
$66$		0			0
$67$		−	82.9847i		−	1.23858i	−0.785163	−	0.619289i	$-0.787421\pi$
$67$		−	82.9847i		−	1.23858i	0.785163	−	0.619289i	$-0.212579\pi$
$68$	16.3996	+	78.7189i	0.241170	+	1.15763i
$69$		0			0
$70$	−36.2257	+	44.5504i	−0.517510	+	0.636434i
$71$			16.4217i			0.231291i	0.993291	+	0.115646i	$0.0368937\pi$
$71$			16.4217i			0.231291i	−0.993291	+	0.115646i	$0.963106\pi$
$72$		0			0
$73$	−63.6386			−0.871761			−0.435881	−	0.900004i	$-0.643563\pi$
$73$	−63.6386			−0.871761			−0.435881	+	0.900004i	$0.643563\pi$
$74$	87.8549	+	71.4383i	1.18723	+	0.965383i
$75$		0			0
$76$	−17.0691	+	3.55602i	−0.224594	+	0.0467897i
$77$	−240.241			−3.12001
$78$		0			0
$79$		−	19.2738i		−	0.243972i	−0.992532	−	0.121986i	$-0.961074\pi$
$79$		−	19.2738i		−	0.243972i	0.992532	−	0.121986i	$-0.0389264\pi$
$80$	−38.3061	+	16.6848i	−0.478826	+	0.208560i
$81$		0			0
$82$	−49.1463	−	39.9628i	−0.599345	−	0.487351i
$83$			29.3102i			0.353135i	0.984289	+	0.176567i	$0.0564993\pi$
$83$			29.3102i			0.353135i	−0.984289	+	0.176567i	$0.943501\pi$
$84$		0			0
$85$	52.4946			0.617583
$86$	−29.4471	+	36.2140i	−0.342408	+	0.421093i
$87$		0			0
$88$	−155.275	−	80.3075i	−1.76449	−	0.912585i
$89$	21.4346			0.240838			0.120419	−	0.992723i	$-0.461576\pi$
$89$	21.4346			0.240838			0.120419	+	0.992723i	$0.461576\pi$
$90$		0			0
$91$			54.4735i			0.598610i
$92$	−35.8543	+	7.46955i	−0.389721	+	0.0811908i
$93$		0			0
$94$	−81.7465	+	100.532i	−0.869644	+	1.06949i
$95$			11.3827i			0.119818i
$96$		0			0
$97$	74.7316			0.770429			0.385214	−	0.922827i	$-0.374128\pi$
$97$	74.7316			0.770429			0.385214	+	0.922827i	$0.374128\pi$
$98$	111.527	+	90.6867i	1.13803	+	0.925374i
$99$		0			0
$100$	−14.8319	−	71.1943i	−0.148319	−	0.711943i
$101$	81.5165			0.807094			0.403547	−	0.914959i	$-0.367777\pi$
$101$	81.5165			0.807094			0.403547	+	0.914959i	$0.367777\pi$
$102$		0			0
$103$			168.311i			1.63409i	0.576574	+	0.817045i	$0.304389\pi$
$103$			168.311i			1.63409i	−0.576574	+	0.817045i	$0.695611\pi$
$104$	−18.2094	+	35.2079i	−0.175090	+	0.338538i
$105$		0			0
$106$	125.453	+	102.011i	1.18352	+	0.962368i
$107$		−	133.057i		−	1.24352i	−0.783207	−	0.621761i	$-0.786418\pi$
$107$		−	133.057i		−	1.24352i	0.783207	−	0.621761i	$-0.213582\pi$
$108$		0			0
$109$	47.9550			0.439954			0.219977	−	0.975505i	$-0.429402\pi$
$109$	47.9550			0.439954			0.219977	+	0.975505i	$0.429402\pi$
$110$	−72.0009	+	88.5468i	−0.654554	+	0.804971i
$111$		0			0
$112$	70.2448	+	161.273i	0.627186	+	1.43993i
$113$	−140.249			−1.24114			−0.620572	−	0.784150i	$-0.713099\pi$
$113$	−140.249			−1.24114			−0.620572	+	0.784150i	$0.713099\pi$
$114$		0			0
$115$			23.9098i			0.207912i
$116$	1.01955	+	4.89389i	0.00878920	+	0.0421887i
$117$		0			0
$118$	15.3949	−	18.9327i	0.130465	−	0.160447i
$119$		−	221.008i		−	1.85721i
$120$		0			0
$121$	−356.494			−2.94623
$122$	−99.8963	−	81.2297i	−0.818822	−	0.665817i
$123$		0			0
$124$	−156.360	+	32.5746i	−1.26097	+	0.262699i
$125$	−112.761			−0.902089
$126$		0			0
$127$		−	12.3426i		−	0.0971857i	−0.998819	−	0.0485929i	$-0.984526\pi$
$127$		−	12.3426i		−	0.0971857i	0.998819	−	0.0485929i	$-0.0154737\pi$
$128$	−8.50872	+	127.717i	−0.0664744	+	0.997788i
$129$		0			0
$130$	20.0776	+	16.3259i	0.154443	+	0.125584i
$131$		−	188.792i		−	1.44116i	−0.693372	−	0.720580i	$-0.743876\pi$
$131$		−	188.792i		−	1.44116i	0.693372	−	0.720580i	$-0.256124\pi$
$132$		0			0
$133$	47.9225			0.360319
$134$	−104.709	+	128.771i	−0.781408	+	0.960977i
$135$		0			0
$136$	73.8783	−	142.844i	0.543223	−	1.05032i
$137$	3.88636			0.0283676			0.0141838	−	0.999899i	$-0.495485\pi$
$137$	3.88636			0.0283676			0.0141838	+	0.999899i	$0.495485\pi$
$138$		0			0
$139$			202.870i			1.45949i	0.683717	+	0.729747i	$0.260362\pi$
$139$			202.870i			1.45949i	−0.683717	+	0.729747i	$0.739638\pi$
$140$	112.426	−	23.4218i	0.803042	−	0.167298i
$141$		0			0
$142$	20.7206	−	25.4822i	0.145920	−	0.179452i
$143$			108.270i			0.757130i
$144$		0			0
$145$	3.26355			0.0225072
$146$	98.7506	+	80.2981i	0.676374	+	0.549987i
$147$		0			0
$148$	−46.1885	−	221.708i	−0.312085	−	1.49803i
$149$	−91.4567			−0.613803			−0.306902	−	0.951741i	$-0.599292\pi$
$149$	−91.4567			−0.613803			−0.306902	+	0.951741i	$0.599292\pi$
$150$		0			0
$151$		−	170.959i		−	1.13218i	−0.824344	−	0.566089i	$-0.808456\pi$
$151$		−	170.959i		−	1.13218i	0.824344	−	0.566089i	$-0.191544\pi$
$152$	30.9738	+	16.0195i	0.203775	+	0.105391i
$153$		0			0
$154$	372.791	+	303.131i	2.42072	+	1.96839i
$155$			104.271i			0.672714i
$156$		0			0
$157$	259.323			1.65174			0.825868	−	0.563863i	$-0.190685\pi$
$157$	259.323			1.65174			0.825868	+	0.563863i	$0.190685\pi$
$158$	−24.3194	+	29.9080i	−0.153920	+	0.189291i
$159$		0			0
$160$	80.4937	+	22.4434i	0.503086	+	0.140272i
$161$	100.663			0.625236
$162$		0			0
$163$		−	148.560i		−	0.911413i	−0.890130	−	0.455707i	$-0.849387\pi$
$163$		−	148.560i		−	0.911413i	0.890130	−	0.455707i	$-0.150613\pi$
$164$	25.8380	+	124.024i	0.157549	+	0.756244i
$165$		0			0
$166$	36.9831	−	45.4818i	0.222790	−	0.273987i
$167$		−	304.827i		−	1.82531i	−0.408732	−	0.912654i	$-0.634029\pi$
$167$		−	304.827i		−	1.82531i	0.408732	−	0.912654i	$-0.365971\pi$
$168$		0			0
$169$	−144.450			−0.854736
$170$	−81.4581	−	66.2368i	−0.479165	−	0.389628i
$171$		0			0
$172$	91.3885	−	19.0390i	0.531328	−	0.110692i
$173$	100.537			0.581140			0.290570	−	0.956854i	$-0.406155\pi$
$173$	100.537			0.581140			0.290570	+	0.956854i	$0.406155\pi$
$174$		0			0
$175$			199.882i			1.14218i
$176$	139.616	+	320.540i	0.793273	+	1.82125i
$177$		0			0
$178$	−33.2610	−	27.0458i	−0.186859	−	0.151943i
$179$			247.870i			1.38475i	0.721538	+	0.692375i	$0.243435\pi$
$179$			247.870i			1.38475i	−0.721538	+	0.692375i	$0.756565\pi$
$180$		0			0
$181$	−151.580			−0.837457			−0.418729	−	0.908111i	$-0.637524\pi$
$181$	−151.580			−0.837457			−0.418729	+	0.908111i	$0.637524\pi$
$182$	68.7337	−	84.5288i	0.377658	−	0.464444i
$183$		0			0
$184$	65.0616	+	33.6496i	0.353596	+	0.182878i
$185$	−147.848			−0.799180
$186$		0			0
$187$		−	439.267i		−	2.34902i
$188$	253.699	−	52.8533i	1.34946	−	0.281134i
$189$		0			0
$190$	14.3625	−	17.6631i	0.0755923	−	0.0929635i
$191$		−	197.412i		−	1.03357i	−0.856115	−	0.516786i	$-0.827128\pi$
$191$		−	197.412i		−	1.03357i	0.856115	−	0.516786i	$-0.172872\pi$
$192$		0			0
$193$	367.555			1.90443			0.952214	−	0.305432i	$-0.0988008\pi$
$193$	367.555			1.90443			0.952214	+	0.305432i	$0.0988008\pi$
$194$	−115.964	−	94.2950i	−0.597753	−	0.486057i
$195$		0			0
$196$	−58.6335	−	281.445i	−0.299151	−	1.43594i
$197$	175.819			0.892481			0.446240	−	0.894913i	$-0.352763\pi$
$197$	175.819			0.892481			0.446240	+	0.894913i	$0.352763\pi$
$198$		0			0
$199$			114.703i			0.576398i	0.957571	+	0.288199i	$0.0930564\pi$
$199$			114.703i			0.576398i	−0.957571	+	0.288199i	$0.906944\pi$
$200$	−66.8164	+	129.190i	−0.334082	+	0.645949i
$201$		0			0
$202$	−126.493	−	102.856i	−0.626201	−	0.509189i
$203$		−	13.7399i		−	0.0676841i
$204$		0			0
$205$	82.7067			0.403447
$206$	212.372	−	261.176i	1.03093	−	1.26784i
$207$		0			0
$208$	72.6810	−	31.6573i	0.349428	−	0.152199i
$209$	95.2490			0.455737
$210$		0			0
$211$		−	95.5737i		−	0.452956i	−0.974016	−	0.226478i	$-0.927279\pi$
$211$		−	95.5737i		−	0.452956i	0.974016	−	0.226478i	$-0.0727211\pi$
$212$	−65.9553	−	316.589i	−0.311110	−	1.49335i
$213$		0			0
$214$	−167.889	+	206.470i	−0.784527	+	0.964812i
$215$		−	60.9434i		−	0.283458i
$216$		0			0
$217$	438.990			2.02300
$218$	−74.4138	−	60.5088i	−0.341348	−	0.277563i
$219$		0			0
$220$	223.454	−	46.5522i	1.01570	−	0.211601i
$221$	−99.6019			−0.450687
$222$		0			0
$223$			35.6704i			0.159957i	0.996797	+	0.0799786i	$0.0254852\pi$
$223$			35.6704i			0.159957i	−0.996797	+	0.0799786i	$0.974515\pi$
$224$	94.4893	−	338.887i	0.421827	−	1.51289i
$225$		0			0
$226$	217.631	+	176.964i	0.962967	+	0.783027i
$227$			1.37974i			0.00607816i	0.999995	+	0.00303908i	$0.000967371\pi$
$227$			1.37974i			0.00607816i	−0.999995	+	0.00303908i	$0.999033\pi$
$228$		0			0
$229$	364.515			1.59177			0.795884	−	0.605449i	$-0.207006\pi$
$229$	364.515			1.59177			0.795884	+	0.605449i	$0.207006\pi$
$230$	30.1690	−	37.1019i	0.131170	−	0.161313i
$231$		0			0
$232$	4.59296	−	8.88051i	0.0197972	−	0.0382780i
$233$	−431.919			−1.85373			−0.926865	−	0.375395i	$-0.877507\pi$
$233$	−431.919			−1.85373			−0.926865	+	0.375395i	$0.877507\pi$
$234$		0			0
$235$		−	169.182i		−	0.719923i
$236$	−47.7779	+	9.95360i	−0.202449	+	0.0421763i
$237$		0			0
$238$	−278.864	+	342.947i	−1.17170	+	1.44095i
$239$			126.600i			0.529706i	0.964289	+	0.264853i	$0.0853235\pi$
$239$			126.600i			0.529706i	−0.964289	+	0.264853i	$0.914677\pi$
$240$		0			0
$241$	−161.602			−0.670546			−0.335273	−	0.942121i	$-0.608829\pi$
$241$	−161.602			−0.670546			−0.335273	+	0.942121i	$0.608829\pi$
$242$	553.186	+	449.818i	2.28589	+	1.85875i
$243$		0			0
$244$	52.5191	+	252.095i	0.215242	+	1.03318i
$245$	−187.684			−0.766059
$246$		0			0
$247$		−	21.5973i		−	0.0874385i
$248$	283.733	+	146.745i	1.14408	+	0.591715i
$249$		0			0
$250$	174.976	+	142.280i	0.699905	+	0.569120i
$251$		−	137.957i		−	0.549630i	−0.961497	−	0.274815i	$-0.911383\pi$
$251$		−	137.957i		−	0.549630i	0.961497	−	0.274815i	$-0.0886166\pi$
$252$		0			0
$253$	200.074			0.790807
$254$	−15.5737	+	19.1525i	−0.0613137	+	0.0754036i
$255$		0			0
$256$	174.354	−	187.447i	0.681072	−	0.732217i
$257$	250.971			0.976541			0.488271	−	0.872692i	$-0.337628\pi$
$257$	250.971			0.976541			0.488271	+	0.872692i	$0.337628\pi$
$258$		0			0
$259$			622.457i			2.40331i
$260$	−10.5555	−	50.6671i	−0.0405981	−	0.194874i
$261$		0			0
$262$	−238.215	+	292.956i	−0.909216	+	1.11815i
$263$			243.090i			0.924295i	0.886803	+	0.462147i	$0.152921\pi$
$263$			243.090i			0.924295i	−0.886803	+	0.462147i	$0.847079\pi$
$264$		0			0
$265$	−211.121			−0.796684
$266$	−74.3633	−	60.4678i	−0.279561	−	0.227322i
$267$		0			0
$268$	324.962	−	67.6995i	1.21254	−	0.252610i
$269$	21.9177			0.0814784			0.0407392	−	0.999170i	$-0.487029\pi$
$269$	21.9177			0.0814784			0.0407392	+	0.999170i	$0.487029\pi$
$270$		0			0
$271$			204.167i			0.753382i	0.926339	+	0.376691i	$0.122938\pi$
$271$			204.167i			0.753382i	−0.926339	+	0.376691i	$0.877062\pi$
$272$	−294.878	+	128.439i	−1.08411	+	0.472202i
$273$		0			0
$274$	−6.03062	−	4.90374i	−0.0220096	−	0.0178969i
$275$			397.278i			1.44465i
$276$		0			0
$277$	−344.707			−1.24443			−0.622214	−	0.782847i	$-0.713767\pi$
$277$	−344.707			−1.24443			−0.622214	+	0.782847i	$0.713767\pi$
$278$	255.978	−	314.802i	0.920783	−	1.13238i
$279$		0			0
$280$	−204.009	−	105.513i	−0.728604	−	0.376831i
$281$	164.108			0.584013			0.292007	−	0.956416i	$-0.405677\pi$
$281$	164.108			0.584013			0.292007	+	0.956416i	$0.405677\pi$
$282$		0			0
$283$		−	395.081i		−	1.39605i	−0.716076	−	0.698023i	$-0.754063\pi$
$283$		−	395.081i		−	1.39605i	0.716076	−	0.698023i	$-0.245937\pi$
$284$	−64.3060	+	13.3969i	−0.226430	+	0.0471722i
$285$		0			0
$286$	136.613	−	168.006i	0.477667	−	0.587435i
$287$		−	348.204i		−	1.21325i
$288$		0			0
$289$	115.101			0.398273
$290$	−5.06418	−	4.11789i	−0.0174627	−	0.0141996i
$291$		0			0
$292$	−51.9168	−	249.204i	−0.177797	−	0.853438i
$293$	485.090			1.65560			0.827798	−	0.561026i	$-0.189593\pi$
$293$	485.090			1.65560			0.827798	+	0.561026i	$0.189593\pi$
$294$		0			0
$295$			31.8612i			0.108004i
$296$	−208.074	+	402.313i	−0.702954	+	1.35917i
$297$		0			0
$298$	141.917	+	115.399i	0.476232	+	0.387243i
$299$		−	45.3659i		−	0.151726i
$300$		0			0
$301$	−256.578			−0.852419
$302$	−215.713	+	265.284i	−0.714282	+	0.878424i
$303$		0			0
$304$	−27.8502	−	63.9403i	−0.0916125	−	0.210330i
$305$	168.112			0.551188
$306$		0			0
$307$			271.066i			0.882953i	0.897273	+	0.441476i	$0.145545\pi$
$307$			271.066i			0.882953i	−0.897273	+	0.441476i	$0.854455\pi$
$308$	−195.990	−	940.764i	−0.636331	−	3.05443i
$309$		0			0
$310$	131.567	−	161.801i	0.424409	−	0.521939i
$311$			102.844i			0.330687i	0.986236	+	0.165344i	$0.0528733\pi$
$311$			102.844i			0.330687i	−0.986236	+	0.165344i	$0.947127\pi$
$312$		0			0
$313$	24.5571			0.0784571			0.0392285	−	0.999230i	$-0.487510\pi$
$313$	24.5571			0.0784571			0.0392285	+	0.999230i	$0.487510\pi$
$314$	−402.402	−	327.209i	−1.28153	−	1.04207i
$315$		0			0
$316$	75.4748	−	15.7237i	0.238844	−	0.0497586i
$317$	71.3125			0.224961			0.112480	−	0.993654i	$-0.464120\pi$
$317$	71.3125			0.224961			0.112480	+	0.993654i	$0.464120\pi$
$318$		0			0
$319$		−	27.3089i		−	0.0856078i
$320$	−96.5868	−	136.392i	−0.301834	−	0.426225i
$321$		0			0
$322$	−156.203	−	127.015i	−0.485102	−	0.394456i
$323$			87.6237i			0.271281i
$324$		0			0
$325$	90.0811			0.277172
$326$	−187.451	+	230.527i	−0.575003	+	0.707139i
$327$		0			0
$328$	116.397	−	225.055i	0.354870	−	0.686144i
$329$	−712.274			−2.16497
$330$		0			0
$331$			448.461i			1.35487i	0.735583	+	0.677434i	$0.236908\pi$
$331$			448.461i			1.35487i	−0.735583	+	0.677434i	$0.763092\pi$
$332$	−114.776	+	23.9114i	−0.345712	+	0.0720224i
$333$		0			0
$334$	−384.625	+	473.012i	−1.15157	+	1.41620i
$335$		−	216.704i		−	0.646879i
$336$		0			0
$337$	300.502			0.891699			0.445849	−	0.895108i	$-0.352902\pi$
$337$	300.502			0.891699			0.445849	+	0.895108i	$0.352902\pi$
$338$	224.150	+	182.265i	0.663165	+	0.539246i
$339$		0			0
$340$	42.8254	+	205.565i	0.125957	+	0.604602i
$341$	872.521			2.55871
$342$		0			0
$343$			251.457i			0.733110i
$344$	−165.834	−	85.7688i	−0.482077	−	0.249328i
$345$		0			0
$346$	−156.008	−	126.856i	−0.450890	−	0.366636i
$347$		−	305.369i		−	0.880025i	−0.897992	−	0.440013i	$-0.854974\pi$
$347$		−	305.369i		−	0.880025i	0.897992	−	0.440013i	$-0.145026\pi$
$348$		0			0
$349$	−305.406			−0.875089			−0.437544	−	0.899197i	$-0.644152\pi$
$349$	−305.406			−0.875089			−0.437544	+	0.899197i	$0.644152\pi$
$350$	252.208	−	310.165i	0.720593	−	0.886186i
$351$		0			0
$352$	187.804	−	673.560i	0.533533	−	1.91352i
$353$	273.264			0.774119			0.387059	−	0.922055i	$-0.373491\pi$
$353$	273.264			0.774119			0.387059	+	0.922055i	$0.373491\pi$
$354$		0			0
$355$			42.8832i			0.120798i
$356$	17.4865	+	83.9362i	0.0491193	+	0.235776i
$357$		0			0
$358$	312.758	−	384.631i	0.873627	−	1.07439i
$359$		−	322.334i		−	0.897866i	−0.893565	−	0.448933i	$-0.851804\pi$
$359$		−	322.334i		−	0.897866i	0.893565	−	0.448933i	$-0.148196\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	235.213	+	191.261i	0.649759	+	0.528345i
$363$		0			0
$364$	−213.314	+	44.4398i	−0.586028	+	0.122087i
$365$	−166.184			−0.455299
$366$		0			0
$367$		−	489.127i		−	1.33277i	−0.745608	−	0.666385i	$-0.767841\pi$
$367$		−	489.127i		−	1.33277i	0.745608	−	0.666385i	$-0.232159\pi$
$368$	−58.5004	−	134.309i	−0.158968	−	0.364970i
$369$		0			0
$370$	229.422	+	186.552i	0.620060	+	0.504196i
$371$			888.842i			2.39580i
$372$		0			0
$373$	56.5754			0.151677			0.0758383	−	0.997120i	$-0.475837\pi$
$373$	56.5754			0.151677			0.0758383	+	0.997120i	$0.475837\pi$
$374$	−554.260	+	681.629i	−1.48198	+	1.82254i
$375$		0			0
$376$	−460.365	−	238.098i	−1.22437	−	0.633241i
$377$	−6.19217			−0.0164248
$378$		0			0
$379$		−	427.669i		−	1.12842i	−0.825633	−	0.564208i	$-0.809182\pi$
$379$		−	427.669i		−	1.12842i	0.825633	−	0.564208i	$-0.190818\pi$
$380$	−44.5739	+	9.28611i	−0.117300	+	0.0244371i
$381$		0			0
$382$	−249.091	+	306.333i	−0.652072	+	0.801918i
$383$			592.062i			1.54585i	0.634494	+	0.772927i	$0.281208\pi$
$383$			592.062i			1.54585i	−0.634494	+	0.772927i	$0.718792\pi$
$384$		0			0
$385$	−627.359			−1.62950
$386$	−570.350	−	463.774i	−1.47759	−	1.20149i
$387$		0			0
$388$	60.9665	+	292.643i	0.157130	+	0.754235i
$389$	318.932			0.819877			0.409938	−	0.912113i	$-0.365550\pi$
$389$	318.932			0.819877			0.409938	+	0.912113i	$0.365550\pi$
$390$		0			0
$391$			184.057i			0.470734i
$392$	−264.138	+	510.712i	−0.673821	+	1.30284i
$393$		0			0
$394$	−272.825	−	221.845i	−0.692450	−	0.563059i
$395$		−	50.3312i		−	0.127421i
$396$		0			0
$397$	543.126			1.36808			0.684038	−	0.729446i	$-0.260222\pi$
$397$	543.126			1.36808			0.684038	+	0.729446i	$0.260222\pi$
$398$	144.730	−	177.990i	0.363644	−	0.447210i
$399$		0			0
$400$	266.691	−	116.162i	0.666728	−	0.290404i
$401$	149.069			0.371743			0.185872	−	0.982574i	$-0.440489\pi$
$401$	149.069			0.371743			0.185872	+	0.982574i	$0.440489\pi$
$402$		0			0
$403$		−	197.840i		−	0.490919i
$404$	66.5017	+	319.213i	0.164608	+	0.790130i
$405$		0			0
$406$	−17.3367	+	21.3207i	−0.0427013	+	0.0525141i
$407$			1237.17i			3.03974i
$408$		0			0
$409$	239.293			0.585069			0.292535	−	0.956255i	$-0.405501\pi$
$409$	239.293			0.585069			0.292535	+	0.956255i	$0.405501\pi$
$410$	−128.340	−	104.358i	−0.313023	−	0.254532i
$411$		0			0
$412$	−659.094	+	137.310i	−1.59974	+	0.333275i
$413$	134.139			0.324792
$414$		0			0
$415$			76.5399i			0.184434i
$416$	−152.727	−	42.5836i	−0.367132	−	0.102364i
$417$		0			0
$418$	−147.802	−	120.184i	−0.353593	−	0.287521i
$419$		−	60.5956i		−	0.144620i	−0.997382	−	0.0723098i	$-0.976963\pi$
$419$		−	60.5956i		−	0.144620i	0.997382	−	0.0723098i	$-0.0230370\pi$
$420$		0			0
$421$	−356.491			−0.846771			−0.423385	−	0.905950i	$-0.639158\pi$
$421$	−356.491			−0.846771			−0.423385	+	0.905950i	$0.639158\pi$
$422$	−120.593	+	148.306i	−0.285766	+	0.351435i
$423$		0			0
$424$	−297.122	+	574.486i	−0.700759	+	1.35492i
$425$	−365.473			−0.859938
$426$		0			0
$427$		−	707.771i		−	1.65754i
$428$	521.040	−	108.549i	1.21738	−	0.253618i
$429$		0			0
$430$	−76.8974	+	94.5685i	−0.178831	+	0.219927i
$431$			413.002i			0.958241i	0.877749	+	0.479120i	$0.159044\pi$
$431$			413.002i			0.958241i	−0.877749	+	0.479120i	$0.840956\pi$
$432$		0			0
$433$	267.426			0.617612			0.308806	−	0.951125i	$-0.400071\pi$
$433$	267.426			0.617612			0.308806	+	0.951125i	$0.400071\pi$
$434$	−681.200	−	553.910i	−1.56958	−	1.27629i
$435$		0			0
$436$	39.1220	+	187.788i	0.0897294	+	0.430707i
$437$	−39.9102			−0.0913277
$438$		0			0
$439$			137.021i			0.312121i	0.987747	+	0.156061i	$0.0498796\pi$
$439$			137.021i			0.312121i	−0.987747	+	0.156061i	$0.950120\pi$
$440$	−405.481	−	209.713i	−0.921548	−	0.476620i
$441$		0			0
$442$	154.556	+	125.676i	0.349675	+	0.284335i
$443$		−	192.762i		−	0.435129i	−0.976046	−	0.217565i	$-0.930189\pi$
$443$		−	192.762i		−	0.435129i	0.976046	−	0.217565i	$-0.0698113\pi$
$444$		0			0
$445$	55.9738			0.125784
$446$	45.0084	−	55.3513i	0.100916	−	0.124106i
$447$		0			0
$448$	−574.225	+	406.641i	−1.28175	+	0.907680i
$449$	−157.944			−0.351768			−0.175884	−	0.984411i	$-0.556278\pi$
$449$	−157.944			−0.351768			−0.175884	+	0.984411i	$0.556278\pi$
$450$		0			0
$451$		−	692.078i		−	1.53454i
$452$	−114.416	−	549.205i	−0.253133	−	1.21506i
$453$		0			0
$454$	1.74094	−	2.14100i	0.00383466	−	0.00471587i
$455$			142.251i			0.312639i
$456$		0			0
$457$	−810.971			−1.77455			−0.887277	−	0.461237i	$-0.847406\pi$
$457$	−810.971			−1.77455			−0.887277	+	0.461237i	$0.847406\pi$
$458$	−565.633	−	459.939i	−1.23501	−	1.00423i
$459$		0			0
$460$	−93.6291	+	19.5058i	−0.203542	+	0.0424039i
$461$	−437.664			−0.949379			−0.474689	−	0.880153i	$-0.657440\pi$
$461$	−437.664			−0.949379			−0.474689	+	0.880153i	$0.657440\pi$
$462$		0			0
$463$			220.543i			0.476335i	0.971224	+	0.238168i	$0.0765468\pi$
$463$			220.543i			0.476335i	−0.971224	+	0.238168i	$0.923453\pi$
$464$	−18.3324	+	7.98494i	−0.0395094	+	0.0172089i
$465$		0			0
$466$	670.227	+	544.988i	1.43826	+	1.16950i
$467$		−	339.834i		−	0.727695i	−0.931458	−	0.363848i	$-0.881463\pi$
$467$		−	339.834i		−	0.727695i	0.931458	−	0.363848i	$-0.118537\pi$
$468$		0			0
$469$	−912.348			−1.94531
$470$	−213.471	+	262.527i	−0.454194	+	0.558568i
$471$		0			0
$472$	86.6983	+	44.8399i	0.183683	+	0.0949999i
$473$	−509.966			−1.07815
$474$		0			0
$475$		−	79.2479i		−	0.166838i
$476$	865.450	−	180.300i	1.81817	−	0.378781i
$477$		0			0
$478$	159.741	−	196.450i	0.334187	−	0.410984i
$479$		−	22.5784i		−	0.0471366i	−0.999722	−	0.0235683i	$-0.992497\pi$
$479$		−	22.5784i		−	0.0471366i	0.999722	−	0.0235683i	$-0.00750271\pi$
$480$		0			0
$481$	280.523			0.583209
$482$	250.764	+	203.906i	0.520257	+	0.423042i
$483$		0			0
$484$	−290.830	−	1396.00i	−0.600888	−	2.88430i
$485$	195.152			0.402376
$486$		0			0
$487$			75.8170i			0.155682i	0.996966	+	0.0778409i	$0.0248026\pi$
$487$			75.8170i			0.155682i	−0.996966	+	0.0778409i	$0.975197\pi$
$488$	236.593	−	457.454i	0.484822	−	0.937406i
$489$		0			0
$490$	291.238	+	236.817i	0.594363	+	0.483300i
$491$		−	576.470i		−	1.17407i	−0.809560	−	0.587037i	$-0.800294\pi$
$491$		−	576.470i		−	1.17407i	0.809560	−	0.587037i	$-0.199706\pi$
$492$		0			0
$493$	25.1226			0.0509587
$494$	−27.2511	+	33.5134i	−0.0551642	+	0.0678410i
$495$		0			0
$496$	−255.120	−	585.721i	−0.514354	−	1.18089i
$497$	180.543			0.363265
$498$		0			0
$499$		−	74.3934i		−	0.149085i	−0.997218	−	0.0745425i	$-0.976250\pi$
$499$		−	74.3934i		−	0.149085i	0.997218	−	0.0745425i	$-0.0237496\pi$
$500$	−91.9913	−	441.564i	−0.183983	−	0.883128i
$501$		0			0
$502$	−174.072	+	214.074i	−0.346757	+	0.426442i
$503$		−	52.1597i		−	0.103697i	−0.998655	−	0.0518486i	$-0.983489\pi$
$503$		−	52.1597i		−	0.103697i	0.998655	−	0.0518486i	$-0.0165113\pi$
$504$		0			0
$505$	212.870			0.421526
$506$	−310.464	−	252.450i	−0.613564	−	0.498913i
$507$		0			0
$508$	48.3326	−	10.0692i	0.0951430	−	0.0198212i
$509$	−356.915			−0.701208			−0.350604	−	0.936524i	$-0.614024\pi$
$509$	−356.915			−0.701208			−0.350604	+	0.936524i	$0.614024\pi$
$510$		0			0
$511$			699.653i			1.36918i
$512$	−507.071	+	70.8728i	−0.990373	+	0.138423i
$513$		0			0
$514$	−389.442	−	316.671i	−0.757670	−	0.616092i
$515$			439.524i			0.853445i
$516$		0			0
$517$	−1415.69			−2.73828
$518$	785.405	−	965.892i	1.51623	−	1.86466i
$519$		0			0
$520$	−47.5515	+	91.9411i	−0.0914452	+	0.176810i
$521$	690.445			1.32523			0.662615	−	0.748960i	$-0.269446\pi$
$521$	690.445			1.32523			0.662615	+	0.748960i	$0.269446\pi$
$522$		0			0
$523$			223.239i			0.426843i	0.976960	+	0.213421i	$0.0684607\pi$
$523$			223.239i			0.426843i	−0.976960	+	0.213421i	$0.931539\pi$
$524$	739.295	−	154.018i	1.41087	−	0.293927i
$525$		0			0
$526$	306.726	−	377.212i	0.583130	−	0.717134i
$527$			802.671i			1.52309i
$528$		0			0
$529$	445.167			0.841526
$530$	327.606	+	266.389i	0.618124	+	0.502621i
$531$		0			0
$532$	39.0955	+	187.661i	0.0734878	+	0.352746i
$533$	−156.926			−0.294420
$534$		0			0
$535$		−	347.461i		−	0.649460i
$536$	−589.679	−	304.979i	−1.10015	−	0.568991i
$537$		0			0
$538$	−34.0106	−	27.6554i	−0.0632168	−	0.0514041i
$539$			1570.52i			2.91376i
$540$		0			0
$541$	−457.379			−0.845433			−0.422717	−	0.906262i	$-0.638923\pi$
$541$	−457.379			−0.845433			−0.422717	+	0.906262i	$0.638923\pi$
$542$	257.614	−	316.814i	0.475302	−	0.584527i
$543$		0			0
$544$	619.637	+	172.769i	1.13904	+	0.317589i
$545$	125.229			0.229777
$546$		0			0
$547$		−	861.942i		−	1.57576i	−0.615827	−	0.787881i	$-0.711178\pi$
$547$		−	861.942i		−	1.57576i	0.615827	−	0.787881i	$-0.288822\pi$
$548$	3.17052	+	15.2187i	0.00578561	+	0.0277713i
$549$		0			0
$550$	501.279	−	616.473i	0.911416	−	1.12086i
$551$			5.44750i			0.00988656i
$552$		0			0
$553$	−211.900			−0.383182
$554$	534.896	+	434.945i	0.965516	+	0.785099i
$555$		0			0
$556$	−794.423	+	165.503i	−1.42882	+	0.297666i
$557$	843.824			1.51494			0.757472	−	0.652868i	$-0.226434\pi$
$557$	843.824			1.51494			0.757472	+	0.652868i	$0.226434\pi$
$558$		0			0
$559$			115.632i			0.206856i
$560$	183.436	+	421.144i	0.327564	+	0.752042i
$561$		0			0
$562$	−254.653	−	207.068i	−0.453119	−	0.368449i
$563$		−	1004.70i		−	1.78454i	−0.451503	−	0.892270i	$-0.649112\pi$
$563$		−	1004.70i		−	1.78454i	0.451503	−	0.892270i	$-0.350888\pi$
$564$		0			0
$565$	−366.244			−0.648219
$566$	−498.506	+	613.064i	−0.880753	+	1.08315i
$567$		0			0
$568$	116.690	+	60.3517i	0.205441	+	0.106253i
$569$	878.437			1.54383			0.771913	−	0.635728i	$-0.219300\pi$
$569$	878.437			1.54383			0.771913	+	0.635728i	$0.219300\pi$
$570$		0			0
$571$		−	269.358i		−	0.471731i	−0.971786	−	0.235865i	$-0.924208\pi$
$571$		−	269.358i		−	0.471731i	0.971786	−	0.235865i	$-0.0757924\pi$
$572$	−423.975	+	88.3270i	−0.741216	+	0.154418i
$573$		0			0
$574$	−439.358	+	540.323i	−0.765432	+	0.941329i
$575$		−	166.463i		−	0.289501i
$576$		0			0
$577$	882.889			1.53014			0.765068	−	0.643949i	$-0.222705\pi$
$577$	882.889			1.53014			0.765068	+	0.643949i	$0.222705\pi$
$578$	−178.607	−	145.233i	−0.309009	−	0.251267i
$579$		0			0
$580$	2.66242	+	12.7798i	0.00459038	+	0.0220341i
$581$	322.241			0.554632
$582$		0			0
$583$			1766.63i			3.03024i
$584$	−233.880	+	452.208i	−0.400479	+	0.774328i
$585$		0			0
$586$	−752.734	−	612.078i	−1.28453	−	1.04450i
$587$			461.666i			0.786484i	0.919435	+	0.393242i	$0.128646\pi$
$587$			461.666i			0.786484i	−0.919435	+	0.393242i	$0.871354\pi$
$588$		0			0
$589$	−174.048			−0.295498
$590$	40.2019	−	49.4404i	0.0681389	−	0.0837973i
$591$		0			0
$592$	830.510	−	361.741i	1.40289	−	0.611050i
$593$	788.632			1.32990			0.664951	−	0.746887i	$-0.268453\pi$
$593$	788.632			1.32990			0.664951	+	0.746887i	$0.268453\pi$
$594$		0			0
$595$		−	577.135i		−	0.969974i
$596$	−74.6110	−	358.138i	−0.125186	−	0.600902i
$597$		0			0
$598$	−57.2420	+	70.3962i	−0.0957224	+	0.117719i
$599$		−	284.551i		−	0.475043i	−0.971382	−	0.237521i	$-0.923665\pi$
$599$		−	284.551i		−	0.475043i	0.971382	−	0.237521i	$-0.0763350\pi$
$600$		0			0
$601$	−290.399			−0.483192			−0.241596	−	0.970377i	$-0.577671\pi$
$601$	−290.399			−0.483192			−0.241596	+	0.970377i	$0.577671\pi$
$602$	398.143	+	323.746i	0.661367	+	0.537784i
$603$		0			0
$604$	669.462	−	139.469i	1.10838	−	0.230910i
$605$	−930.939			−1.53874
$606$		0			0
$607$			886.175i			1.45993i	0.683487	+	0.729963i	$0.260463\pi$
$607$			886.175i			1.45993i	−0.683487	+	0.729963i	$0.739537\pi$
$608$	−37.4625	+	134.360i	−0.0616160	+	0.220987i
$609$		0			0
$610$	−260.867	−	212.121i	−0.427651	−	0.347740i
$611$			321.002i			0.525371i
$612$		0			0
$613$	196.758			0.320975			0.160488	−	0.987038i	$-0.448693\pi$
$613$	196.758			0.320975			0.160488	+	0.987038i	$0.448693\pi$
$614$	342.027	−	420.625i	0.557047	−	0.685057i
$615$		0			0
$616$	−882.914	+	1707.12i	−1.43330	+	2.77130i
$617$	601.962			0.975628			0.487814	−	0.872948i	$-0.337795\pi$
$617$	601.962			0.975628			0.487814	+	0.872948i	$0.337795\pi$
$618$		0			0
$619$		−	186.061i		−	0.300583i	−0.988642	−	0.150292i	$-0.951979\pi$
$619$		−	186.061i		−	0.300583i	0.988642	−	0.150292i	$-0.0480212\pi$
$620$	−408.316	+	85.0647i	−0.658574	+	0.137201i
$621$		0			0
$622$	129.766	−	159.587i	0.208628	−	0.256571i
$623$		−	235.656i		−	0.378259i
$624$		0			0
$625$	160.056			0.256090
$626$	−38.1062	−	30.9857i	−0.0608726	−	0.0494979i
$627$		0			0
$628$	211.557	+	1015.49i	0.336874	+	1.61702i
$629$	−1138.13			−1.80943
$630$		0			0
$631$			719.486i			1.14023i	0.821564	+	0.570116i	$0.193102\pi$
$631$			719.486i			1.14023i	−0.821564	+	0.570116i	$0.806898\pi$
$632$	−136.957	−	70.8337i	−0.216705	−	0.112079i
$633$		0			0
$634$	−110.659	−	89.9810i	−0.174540	−	0.141926i
$635$		−	32.2311i		−	0.0507577i
$636$		0			0
$637$	356.108			0.559039
$638$	−34.4579	+	42.3763i	−0.0540092	+	0.0664206i
$639$		0			0
$640$	−22.2195	+	333.517i	−0.0347179	+	0.521120i
$641$	948.094			1.47909			0.739543	−	0.673110i	$-0.235042\pi$
$641$	948.094			1.47909			0.739543	+	0.673110i	$0.235042\pi$
$642$		0			0
$643$		−	72.1092i		−	0.112145i	−0.998427	−	0.0560725i	$-0.982142\pi$
$643$		−	72.1092i		−	0.112145i	0.998427	−	0.0560725i	$-0.0178578\pi$
$644$	82.1216	+	394.189i	0.127518	+	0.612094i
$645$		0			0
$646$	110.562	−	135.969i	0.171149	−	0.210479i
$647$		−	323.878i		−	0.500584i	−0.968170	−	0.250292i	$-0.919473\pi$
$647$		−	323.878i		−	0.500584i	0.968170	−	0.250292i	$-0.0805266\pi$
$648$		0			0
$649$	266.610			0.410801
$650$	−139.783	−	113.663i	−0.215050	−	0.174866i
$651$		0			0
$652$	581.751	−	121.197i	0.892256	−	0.185884i
$653$	200.031			0.306326			0.153163	−	0.988201i	$-0.451054\pi$
$653$	200.031			0.306326			0.153163	+	0.988201i	$0.451054\pi$
$654$		0			0
$655$		−	493.007i		−	0.752682i
$656$	−464.590	+	202.359i	−0.708216	+	0.308474i
$657$		0			0
$658$	1105.27	+	898.735i	1.67973	+	1.36586i
$659$		−	599.936i		−	0.910374i	−0.890396	−	0.455187i	$-0.849572\pi$
$659$		−	599.936i		−	0.910374i	0.890396	−	0.455187i	$-0.150428\pi$
$660$		0			0
$661$	220.336			0.333337			0.166668	−	0.986013i	$-0.446699\pi$
$661$	220.336			0.333337			0.166668	+	0.986013i	$0.446699\pi$
$662$	565.861	−	695.896i	0.854775	−	1.05120i
$663$		0			0
$664$	208.274	+	107.719i	0.313666	+	0.162227i
$665$	125.144			0.188186
$666$		0			0
$667$			11.4427i			0.0171554i
$668$	1193.68	−	248.680i	1.78694	−	0.372275i
$669$		0			0
$670$	−273.434	+	336.269i	−0.408110	+	0.501894i
$671$		−	1406.74i		−	2.09648i
$672$		0			0
$673$	−786.871			−1.16920			−0.584599	−	0.811322i	$-0.698748\pi$
$673$	−786.871			−1.16920			−0.584599	+	0.811322i	$0.698748\pi$
$674$	−466.302	−	379.169i	−0.691843	−	0.562565i
$675$		0			0
$676$	−117.844	−	565.657i	−0.174325	−	0.836770i
$677$	385.498			0.569421			0.284711	−	0.958613i	$-0.408102\pi$
$677$	385.498			0.569421			0.284711	+	0.958613i	$0.408102\pi$
$678$		0			0
$679$		−	821.612i		−	1.21003i
$680$	192.924	−	373.020i	0.283712	−	0.548559i
$681$		0			0
$682$	−1353.93	−	1100.93i	−1.98523	−	1.61427i
$683$		−	474.430i		−	0.694626i	−0.937749	−	0.347313i	$-0.887094\pi$
$683$		−	474.430i		−	0.694626i	0.937749	−	0.347313i	$-0.112906\pi$
$684$		0			0
$685$	10.1487			0.0148157
$686$	317.284	−	390.196i	0.462513	−	0.568799i
$687$		0			0
$688$	149.111	+	342.338i	0.216731	+	0.497585i
$689$	400.576			0.581387
$690$		0			0
$691$		−	317.710i		−	0.459784i	−0.973216	−	0.229892i	$-0.926163\pi$
$691$		−	317.710i		−	0.459784i	0.973216	−	0.229892i	$-0.0738372\pi$
$692$	82.0189	+	393.696i	0.118524	+	0.568925i
$693$		0			0
$694$	−385.309	+	473.854i	−0.555201	+	0.682786i
$695$			529.769i			0.762258i
$696$		0			0
$697$	636.673			0.913447
$698$	473.911	+	385.356i	0.678956	+	0.552086i
$699$		0			0
$700$	−782.722	+	163.065i	−1.11817	+	0.232950i
$701$	1220.64			1.74128			0.870640	−	0.491921i	$-0.163705\pi$
$701$	1220.64			1.74128			0.870640	+	0.491921i	$0.163705\pi$
$702$		0			0
$703$		−	246.788i		−	0.351049i
$704$	−1141.31	+	808.224i	−1.62118	+	1.14805i
$705$		0			0
$706$	−424.035	−	344.800i	−0.600616	−	0.488385i
$707$		−	896.207i		−	1.26762i
$708$		0			0
$709$	448.866			0.633097			0.316548	−	0.948576i	$-0.397476\pi$
$709$	448.866			0.633097			0.316548	+	0.948576i	$0.397476\pi$
$710$	54.1092	−	66.5436i	0.0762102	−	0.0937234i
$711$		0			0
$712$	78.7748	−	152.312i	0.110639	−	0.213921i
$713$	−365.594			−0.512755
$714$		0			0
$715$			282.733i			0.395430i
$716$	−970.641	+	202.214i	−1.35564	+	0.282422i
$717$		0			0
$718$	−406.716	+	500.179i	−0.566456	+	0.696629i
$719$			256.712i			0.357040i	0.983936	+	0.178520i	$0.0571309\pi$
$719$			256.712i			0.357040i	−0.983936	+	0.178520i	$0.942869\pi$
$720$		0			0
$721$	1850.44			2.56650
$722$	29.4831	+	23.9739i	0.0408353	+	0.0332048i
$723$		0			0
$724$	−123.660	−	593.575i	−0.170801	−	0.819854i
$725$	−22.7212			−0.0313396
$726$		0			0
$727$			25.0120i			0.0344043i	0.999852	+	0.0172022i	$0.00547589\pi$
$727$			25.0120i			0.0344043i	−0.999852	+	0.0172022i	$0.994524\pi$
$728$	387.082	+	200.197i	0.531706	+	0.274996i
$729$		0			0
$730$	257.875	+	209.689i	0.353254	+	0.287245i
$731$		−	469.140i		−	0.641778i
$732$		0			0
$733$	1006.20			1.37271			0.686356	−	0.727266i	$-0.259209\pi$
$733$	1006.20			1.37271			0.686356	+	0.727266i	$0.259209\pi$
$734$	−617.172	+	758.998i	−0.840833	+	1.03406i
$735$		0			0
$736$	−78.6914	+	282.228i	−0.106918	+	0.383462i
$737$	−1813.35			−2.46045
$738$		0			0
$739$			710.886i			0.961956i	0.876733	+	0.480978i	$0.159718\pi$
$739$			710.886i			0.961956i	−0.876733	+	0.480978i	$0.840282\pi$
$740$	−120.616	−	578.962i	−0.162994	−	0.782382i
$741$		0			0
$742$	1121.53	−	1379.25i	1.51149	−	1.85883i
$743$		−	521.430i		−	0.701790i	−0.936415	−	0.350895i	$-0.885877\pi$
$743$		−	521.430i		−	0.701790i	0.936415	−	0.350895i	$-0.114123\pi$
$744$		0			0
$745$	−238.828			−0.320574
$746$	−87.7904	−	71.3858i	−0.117681	−	0.0956915i
$747$		0			0
$748$	1720.14	−	358.357i	2.29965	−	0.479087i
$749$	−1462.85			−1.95307
$750$		0			0
$751$			650.897i			0.866707i	0.901224	+	0.433354i	$0.142670\pi$
$751$			650.897i			0.866707i	−0.901224	+	0.433354i	$0.857330\pi$
$752$	413.939	+	950.348i	0.550451	+	1.26376i
$753$		0			0
$754$	9.60865	+	7.81317i	0.0127436	+	0.0103623i
$755$		−	446.438i		−	0.591309i
$756$		0			0
$757$	744.251			0.983159			0.491579	−	0.870833i	$-0.336420\pi$
$757$	744.251			0.983159			0.491579	+	0.870833i	$0.336420\pi$
$758$	−539.626	+	663.633i	−0.711908	+	0.875505i
$759$		0			0
$760$	80.8842	+	41.8329i	0.106427	+	0.0550433i
$761$	−378.670			−0.497595			−0.248797	−	0.968556i	$-0.580035\pi$
$761$	−378.670			−0.497595			−0.248797	+	0.968556i	$0.580035\pi$
$762$		0			0
$763$		−	527.226i		−	0.690990i
$764$	773.051	−	161.050i	1.01185	−	0.210799i
$765$		0			0
$766$	747.054	−	918.728i	0.975267	−	1.19938i
$767$		−	60.4527i		−	0.0788170i
$768$		0			0
$769$	−0.255290			−0.000331977			−0.000165989	−	1.00000i	$-0.500053\pi$
$769$	−0.255290			−0.000331977			−0.000165989		1.00000i	$0.500053\pi$
$770$	973.499	+	791.590i	1.26428	+	1.02804i
$771$		0			0
$772$	299.854	+	1439.32i	0.388411	+	1.86440i
$773$	398.489			0.515510			0.257755	−	0.966210i	$-0.417017\pi$
$773$	398.489			0.515510			0.257755	+	0.966210i	$0.417017\pi$
$774$		0			0
$775$		−	725.944i		−	0.936702i
$776$	274.648	−	531.033i	0.353928	−	0.684321i
$777$		0			0
$778$	−494.900	−	402.423i	−0.636118	−	0.517253i
$779$			138.054i			0.177219i
$780$		0			0
$781$	358.840			0.459462
$782$	232.240	−	285.609i	0.296982	−	0.365229i
$783$		0			0
$784$	1054.28	−	459.209i	1.34475	−	0.585726i
$785$	677.189			0.862661
$786$		0			0
$787$			530.707i			0.674342i	0.941443	+	0.337171i	$0.109470\pi$
$787$			530.707i			0.674342i	−0.941443	+	0.337171i	$0.890530\pi$
$788$	143.434	+	688.493i	0.182023	+	0.873722i
$789$		0			0
$790$	−63.5071	+	78.1011i	−0.0803887	+	0.0988621i
$791$			1541.92i			1.94934i
$792$		0			0
$793$	−318.972			−0.402235
$794$	−842.792	−	685.308i	−1.06145	−	0.863108i
$795$		0			0
$796$	−449.169	+	93.5756i	−0.564282	+	0.117557i
$797$	−1343.23			−1.68536			−0.842678	−	0.538418i	$-0.819022\pi$
$797$	−1343.23			−1.68536			−0.842678	+	0.538418i	$0.819022\pi$
$798$		0			0
$799$		−	1302.36i		−	1.62998i
$800$	−560.407	−	156.254i	−0.700509	−	0.195317i
$801$		0			0
$802$	−231.317	−	188.093i	−0.288425	−	0.234530i
$803$			1390.61i			1.73176i
$804$		0			0
$805$	262.869			0.326545
$806$	−249.632	+	306.997i	−0.309717	+	0.380890i
$807$		0			0
$808$	299.583	−	579.246i	0.370772	−	0.716889i
$809$	−596.997			−0.737945			−0.368972	−	0.929440i	$-0.620290\pi$
$809$	−596.997			−0.737945			−0.368972	+	0.929440i	$0.620290\pi$
$810$		0			0
$811$		−	254.062i		−	0.313270i	−0.987657	−	0.156635i	$-0.949935\pi$
$811$		−	254.062i		−	0.313270i	0.987657	−	0.156635i	$-0.0500647\pi$
$812$	53.8043	−	11.2091i	0.0662614	−	0.0138043i
$813$		0			0
$814$	1561.04	−	1919.77i	1.91774	−	2.35844i
$815$		−	387.947i		−	0.476009i
$816$		0			0
$817$	101.726			0.124512
$818$	−371.321	−	301.936i	−0.453938	−	0.369115i
$819$		0			0
$820$	67.4727	+	323.873i	0.0822838	+	0.394967i
$821$	−1111.21			−1.35348			−0.676739	−	0.736223i	$-0.736607\pi$
$821$	−1111.21			−1.35348			−0.676739	+	0.736223i	$0.736607\pi$
$822$		0			0
$823$		−	745.561i		−	0.905906i	−0.891534	−	0.452953i	$-0.850371\pi$
$823$		−	745.561i		−	0.905906i	0.891534	−	0.452953i	$-0.149629\pi$
$824$	1196.00	+	618.565i	1.45146	+	0.750686i
$825$		0			0
$826$	−208.149	−	169.254i	−0.251997	−	0.204909i
$827$		−	108.732i		−	0.131477i	−0.997837	−	0.0657387i	$-0.979060\pi$
$827$		−	108.732i		−	0.131477i	0.997837	−	0.0657387i	$-0.0209404\pi$
$828$		0			0
$829$	−342.192			−0.412777			−0.206388	−	0.978470i	$-0.566171\pi$
$829$	−342.192			−0.412777			−0.206388	+	0.978470i	$0.566171\pi$
$830$	96.5768	−	118.770i	0.116358	−	0.143097i
$831$		0			0
$832$	183.261	+	258.787i	0.220266	+	0.311042i
$833$	−1444.79			−1.73444
$834$		0			0
$835$		−	796.017i		−	0.953314i
$836$	77.7048	+	372.988i	0.0929483	+	0.446158i
$837$		0			0
$838$	−76.4586	+	94.0288i	−0.0912393	+	0.112206i
$839$			1448.05i			1.72592i	0.505270	+	0.862961i	$0.331393\pi$
$839$			1448.05i			1.72592i	−0.505270	+	0.862961i	$0.668607\pi$
$840$		0			0
$841$	−839.438			−0.998143
$842$	553.181	+	449.814i	0.656985	+	0.534221i
$843$		0			0
$844$	374.259	−	77.9697i	0.443435	−	0.0923811i
$845$	−377.214			−0.446407
$846$		0			0
$847$			3919.35i			4.62733i
$848$	1185.93	−	516.552i	1.39851	−	0.609141i
$849$		0			0
$850$	567.121	+	461.148i	0.667201	+	0.542527i
$851$		−	518.387i		−	0.609150i
$852$		0			0
$853$	474.240			0.555968			0.277984	−	0.960586i	$-0.410334\pi$
$853$	474.240			0.555968			0.277984	+	0.960586i	$0.410334\pi$
$854$	−893.053	+	1098.28i	−1.04573	+	1.28604i
$855$		0			0
$856$	−945.485	−	489.000i	−1.10454	−	0.571262i
$857$	1081.61			1.26209			0.631046	−	0.775746i	$-0.282626\pi$
$857$	1081.61			1.26209			0.631046	+	0.775746i	$0.282626\pi$
$858$		0			0
$859$			412.312i			0.479991i	0.970774	+	0.239995i	$0.0771459\pi$
$859$			412.312i			0.479991i	−0.970774	+	0.239995i	$0.922854\pi$
$860$	238.650	−	49.7181i	0.277500	−	0.0578117i
$861$		0			0
$862$	521.119	−	640.872i	0.604546	−	0.743471i
$863$		−	714.308i		−	0.827703i	−0.910344	−	0.413852i	$-0.864183\pi$
$863$		−	714.308i		−	0.827703i	0.910344	−	0.413852i	$-0.135817\pi$
$864$		0			0
$865$	262.540			0.303515
$866$	−414.976	−	337.434i	−0.479188	−	0.389646i
$867$		0			0
$868$	358.131	+	1719.05i	0.412594	+	1.98048i
$869$	−421.164			−0.484654
$870$		0			0
$871$			411.169i			0.472066i
$872$	176.241	−	340.762i	0.202111	−	0.390782i
$873$		0			0
$874$	61.9304	+	50.3580i	0.0708585	+	0.0576179i
$875$			1239.72i			1.41682i
$876$		0			0
$877$	−953.647			−1.08740			−0.543698	−	0.839281i	$-0.682976\pi$
$877$	−953.647			−1.08740			−0.543698	+	0.839281i	$0.682976\pi$
$878$	172.891	−	212.622i	0.196915	−	0.242166i
$879$		0			0
$880$	364.590	+	837.050i	0.414307	+	0.951193i
$881$	−685.401			−0.777981			−0.388990	−	0.921242i	$-0.627176\pi$
$881$	−685.401			−0.777981			−0.388990	+	0.921242i	$0.627176\pi$
$882$		0			0
$883$		−	761.761i		−	0.862696i	−0.902186	−	0.431348i	$-0.858038\pi$
$883$		−	761.761i		−	0.862696i	0.902186	−	0.431348i	$-0.141962\pi$
$884$	−81.2559	−	390.033i	−0.0919184	−	0.441214i
$885$		0			0
$886$	−243.224	+	299.117i	−0.274519	+	0.337604i
$887$		−	1281.41i		−	1.44465i	−0.691553	−	0.722325i	$-0.743073\pi$
$887$		−	1281.41i		−	1.44465i	0.691553	−	0.722325i	$-0.256927\pi$
$888$		0			0
$889$	−135.697			−0.152640
$890$	−86.8569	−	70.6268i	−0.0975920	−	0.0793559i
$891$		0			0
$892$	−139.683	+	29.1002i	−0.156595	+	0.0326235i
$893$	282.398			0.316235
$894$		0			0
$895$			647.282i			0.723221i
$896$	1404.14	+	93.5463i	1.56712	+	0.104404i
$897$		0			0
$898$	245.088	+	199.291i	0.272926	+	0.221927i
$899$			49.9014i			0.0555076i
$900$		0			0
$901$	−1625.20			−1.80378
$902$	−873.252	+	1073.93i	−0.968129	+	1.19061i
$903$		0			0
$904$	−515.433	+	996.594i	−0.570170	+	1.10243i
$905$	−395.832			−0.437383
$906$		0			0
$907$		−	895.017i		−	0.986788i	−0.869806	−	0.493394i	$-0.835756\pi$
$907$		−	895.017i		−	0.986788i	0.869806	−	0.493394i	$-0.164244\pi$
$908$	−5.40297	+	1.12560i	−0.00595040	+	0.00123965i
$909$		0			0
$910$	179.490	−	220.737i	0.197241	−	0.242568i
$911$		−	1336.00i		−	1.46652i	−0.679948	−	0.733260i	$-0.737998\pi$
$911$		−	1336.00i		−	1.46652i	0.679948	−	0.733260i	$-0.262002\pi$
$912$		0			0
$913$	640.475			0.701506
$914$	1258.42	+	1023.27i	1.37683	+	1.11955i
$915$		0			0
$916$	297.374	+	1427.41i	0.324644	+	1.55831i
$917$	−2075.61			−2.26348
$918$		0			0
$919$			1242.95i			1.35250i	0.736673	+	0.676249i	$0.236396\pi$
$919$			1242.95i			1.35250i	−0.736673	+	0.676249i	$0.763604\pi$
$920$	169.900	+	87.8717i	0.184674	+	0.0955127i
$921$		0			0
$922$	679.141	+	552.237i	0.736595	+	0.598955i
$923$		−	81.3654i		−	0.0881532i
$924$		0			0
$925$	1029.34			1.11280
$926$	278.278	−	342.226i	0.300516	−	0.369575i
$927$		0			0
$928$	38.5223	+	10.7409i	0.0415112	+	0.0115742i
$929$	1198.80			1.29042			0.645212	−	0.764004i	$-0.276769\pi$
$929$	1198.80			1.29042			0.645212	+	0.764004i	$0.276769\pi$
$930$		0			0
$931$		−	313.282i		−	0.336501i
$932$	−352.363	−	1691.36i	−0.378071	−	1.81477i
$933$		0			0
$934$	−428.796	+	527.334i	−0.459097	+	0.564598i
$935$		−	1147.09i		−	1.22684i
$936$		0			0
$937$	−1480.41			−1.57994			−0.789971	−	0.613144i	$-0.789904\pi$
$937$	−1480.41			−1.57994			−0.789971	+	0.613144i	$0.789904\pi$
$938$	1415.73	+	1151.19i	1.50931	+	1.22728i
$939$		0			0
$940$	662.504	−	138.020i	0.704791	−	0.146830i
$941$	638.982			0.679046			0.339523	−	0.940598i	$-0.389734\pi$
$941$	638.982			0.679046			0.339523	+	0.940598i	$0.389734\pi$
$942$		0			0
$943$			289.987i			0.307515i
$944$	−77.9551	−	178.974i	−0.0825795	−	0.189592i
$945$		0			0
$946$	791.335	+	643.466i	0.836507	+	0.680197i
$947$		−	715.258i		−	0.755288i	−0.925951	−	0.377644i	$-0.876734\pi$
$947$		−	715.258i		−	0.755288i	0.925951	−	0.377644i	$-0.123266\pi$
$948$		0			0
$949$	315.314			0.332259
$950$	−99.9936	+	122.972i	−0.105256	+	0.129445i
$951$		0			0
$952$	−1570.45	−	812.231i	−1.64964	−	0.853184i
$953$	−1419.89			−1.48992			−0.744959	−	0.667110i	$-0.767531\pi$
$953$	−1419.89			−1.48992			−0.744959	+	0.667110i	$0.767531\pi$
$954$		0			0
$955$		−	515.518i		−	0.539809i
$956$	−495.755	+	103.281i	−0.518572	+	0.108034i
$957$		0			0
$958$	−28.4891	+	35.0359i	−0.0297381	+	0.0365719i
$959$		−	42.7273i		−	0.0445540i
$960$		0			0
$961$	−633.354			−0.659057
$962$	−435.300	−	353.960i	−0.452495	−	0.367942i
$963$		0			0
$964$	−131.836	−	632.819i	−0.136759	−	0.656452i
$965$	959.824			0.994636
$966$		0			0
$967$		−	289.245i		−	0.299116i	−0.988753	−	0.149558i	$-0.952215\pi$
$967$		−	289.245i		−	0.299116i	0.988753	−	0.149558i	$-0.0477851\pi$
$968$	−1310.16	+	2533.20i	−1.35347	+	2.61694i
$969$		0			0
$970$	−302.826	−	246.240i	−0.312192	−	0.253856i
$971$		−	1893.95i		−	1.95051i	−0.221073	−	0.975257i	$-0.570956\pi$
$971$		−	1893.95i		−	1.95051i	0.221073	−	0.975257i	$-0.429044\pi$
$972$		0			0
$973$	2230.39			2.29228
$974$	95.6646	−	117.648i	0.0982183	−	0.120789i
$975$		0			0
$976$	−944.339	+	411.322i	−0.967561	+	0.421436i
$977$	−1575.22			−1.61230			−0.806150	−	0.591711i	$-0.798453\pi$
$977$	−1575.22			−1.61230			−0.806150	+	0.591711i	$0.798453\pi$
$978$		0			0
$979$		−	468.381i		−	0.478428i
$980$	−153.114	−	734.958i	−0.156239	−	0.749957i
$981$		0			0
$982$	−727.380	+	894.533i	−0.740713	+	0.910929i
$983$			906.607i			0.922286i	0.887326	+	0.461143i	$0.152560\pi$
$983$			906.607i			0.922286i	−0.887326	+	0.461143i	$0.847440\pi$
$984$		0			0
$985$	459.129			0.466121
$986$	−38.9838	−	31.6993i	−0.0395374	−	0.0321494i
$987$		0			0
$988$	84.5734	−	17.6192i	0.0856006	−	0.0178332i
$989$	213.680			0.216057
$990$		0			0
$991$		−	1283.89i		−	1.29555i	−0.761831	−	0.647776i	$-0.775699\pi$
$991$		−	1283.89i		−	1.29555i	0.761831	−	0.647776i	$-0.224301\pi$
$992$	−343.172	+	1230.79i	−0.345940	+	1.24072i
$993$		0			0
$994$	−280.156	−	227.806i	−0.281847	−	0.229181i
$995$			299.533i			0.301038i
$996$		0			0
$997$	153.327			0.153789			0.0768944	−	0.997039i	$-0.475500\pi$
$997$	153.327			0.153789			0.0768944	+	0.997039i	$0.475500\pi$
$998$	−93.8683	+	115.439i	−0.0940565	+	0.115671i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.7	✓	36
3.2	odd	2	inner	684.3.g.d.343.30	yes	36
4.3	odd	2	inner	684.3.g.d.343.8	yes	36
12.11	even	2	inner	684.3.g.d.343.29	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.7	✓	36	1.1	even	1	trivial
684.3.g.d.343.8	yes	36	4.3	odd	2	inner
684.3.g.d.343.29	yes	36	12.11	even	2	inner
684.3.g.d.343.30	yes	36	3.2	odd	2	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55174 - 1.26178i) q^{2} +(0.815807 + 3.91592i) q^{4} +2.61138 q^{5} -10.9942i q^{7} +(3.67512 - 7.10587i) q^{8} +O(q^{10})\)	\(q+(-1.55174 - 1.26178i) q^{2} +(0.815807 + 3.91592i) q^{4} +2.61138 q^{5} -10.9942i q^{7} +(3.67512 - 7.10587i) q^{8} +(-4.05218 - 3.29499i) q^{10} -21.8516i q^{11} -4.95476 q^{13} +(-13.8723 + 17.0601i) q^{14} +(-14.6689 + 6.38927i) q^{16} +20.1023 q^{17} +4.35890i q^{19} +(2.13038 + 10.2260i) q^{20} +(-27.5720 + 33.9081i) q^{22} +9.15603i q^{23} -18.1807 q^{25} +(7.68851 + 6.25183i) q^{26} +(43.0523 - 8.96912i) q^{28} +1.24974 q^{29} +39.9294i q^{31} +(30.8243 + 8.59449i) q^{32} +(-31.1935 - 25.3647i) q^{34} -28.7099i q^{35} -56.6170 q^{37} +(5.49999 - 6.76389i) q^{38} +(9.59714 - 18.5561i) q^{40} +31.6717 q^{41} -23.3377i q^{43} +(85.5693 - 17.8267i) q^{44} +(11.5529 - 14.2078i) q^{46} -64.7865i q^{47} -71.8718 q^{49} +(28.2118 + 22.9401i) q^{50} +(-4.04213 - 19.4025i) q^{52} -80.8467 q^{53} -57.0628i q^{55} +(-78.1232 - 40.4050i) q^{56} +(-1.93928 - 1.57690i) q^{58} +12.2009i q^{59} +64.3769 q^{61} +(50.3822 - 61.9601i) q^{62} +(-36.9869 - 52.2300i) q^{64} -12.9387 q^{65} -82.9847i q^{67} +(16.3996 + 78.7189i) q^{68} +(-36.2257 + 44.5504i) q^{70} +16.4217i q^{71} -63.6386 q^{73} +(87.8549 + 71.4383i) q^{74} +(-17.0691 + 3.55602i) q^{76} -240.241 q^{77} -19.2738i q^{79} +(-38.3061 + 16.6848i) q^{80} +(-49.1463 - 39.9628i) q^{82} +29.3102i q^{83} +52.4946 q^{85} +(-29.4471 + 36.2140i) q^{86} +(-155.275 - 80.3075i) q^{88} +21.4346 q^{89} +54.4735i q^{91} +(-35.8543 + 7.46955i) q^{92} +(-81.7465 + 100.532i) q^{94} +11.3827i q^{95} +74.7316 q^{97} +(111.527 + 90.6867i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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