LMFDB - Embedded newform 672.3.bf.b.241.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,3,Mod(145,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	672.bf (of order $6$, degree $2$, not 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:	$18.3106737650$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.16
Character	$\chi$	$=$	672.241
Dual form			672.3.bf.b.145.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{3} +(-4.33205 - 7.50333i) q^{5} +(-2.39482 + 6.57760i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 1.50000i) q^{3} +(-4.33205 - 7.50333i) q^{5} +(-2.39482 + 6.57760i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-9.70954 - 5.60581i) q^{11} -15.6975 q^{13} -15.0067 q^{15} +(29.3084 + 16.9212i) q^{17} +(6.81708 + 11.8075i) q^{19} +(7.79243 + 9.28860i) q^{21} +(-0.498987 - 0.864271i) q^{23} +(-25.0333 + 43.3590i) q^{25} -5.19615 q^{27} +13.0538i q^{29} +(-6.91318 - 3.99133i) q^{31} +(-16.8174 + 9.70954i) q^{33} +(59.7284 - 10.5254i) q^{35} +(-11.3499 + 6.55286i) q^{37} +(-13.5945 + 23.5463i) q^{39} -0.655069i q^{41} -5.93612i q^{43} +(-12.9962 + 22.5100i) q^{45} +(21.8643 - 12.6233i) q^{47} +(-37.5297 - 31.5043i) q^{49} +(50.7636 - 29.3084i) q^{51} +(57.5500 + 33.2265i) q^{53} +97.1385i q^{55} +23.6150 q^{57} +(-12.4419 + 21.5500i) q^{59} +(47.8480 + 82.8752i) q^{61} +(20.6813 - 3.64448i) q^{63} +(68.0026 + 117.784i) q^{65} +(-29.6779 - 17.1345i) q^{67} -1.72854 q^{69} -61.8795 q^{71} +(-28.0314 - 16.1839i) q^{73} +(43.3590 + 75.1000i) q^{75} +(60.1254 - 50.4406i) q^{77} +(23.6567 + 40.9746i) q^{79} +(-4.50000 + 7.79423i) q^{81} -117.340 q^{83} -293.214i q^{85} +(19.5807 + 11.3049i) q^{87} +(-101.251 + 58.4574i) q^{89} +(37.5928 - 103.252i) q^{91} +(-11.9740 + 6.91318i) q^{93} +(59.0638 - 102.302i) q^{95} +48.9751i q^{97} +33.6348i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 26 q^{7} - 90 q^{9}+O(q^{10}) $ 60 * q - 26 * q^7 - 90 * q^9	$ 60 q - 26 q^{7} - 90 q^{9} - 12 q^{15} - 36 q^{17} + 28 q^{23} - 204 q^{25} - 18 q^{31} - 30 q^{33} + 36 q^{39} - 828 q^{47} - 126 q^{49} - 312 q^{57} + 12 q^{63} + 36 q^{65} - 760 q^{71} - 648 q^{73} - 114 q^{79} - 270 q^{81} + 174 q^{87} - 72 q^{89} + 492 q^{95}+O(q^{100}) $ 60 * q - 26 * q^7 - 90 * q^9 - 12 * q^15 - 36 * q^17 + 28 * q^23 - 204 * q^25 - 18 * q^31 - 30 * q^33 + 36 * q^39 - 828 * q^47 - 126 * q^49 - 312 * q^57 + 12 * q^63 + 36 * q^65 - 760 * q^71 - 648 * q^73 - 114 * q^79 - 270 * q^81 + 174 * q^87 - 72 * q^89 + 492 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$		0			0
$5$	−4.33205	−	7.50333i	−0.866410	−	1.50067i	−0.865640	−	0.500667i	$-0.833088\pi$
$5$	−4.33205	−	7.50333i	−0.866410	−	1.50067i	−0.000769783	−	1.00000i	$-0.500245\pi$
$6$		0			0
$7$	−2.39482	+	6.57760i	−0.342117	+	0.939657i
$7$	−2.39482	+	6.57760i	−0.342117	+	0.939657i
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−9.70954	−	5.60581i	−0.882686	−	0.509619i	−0.0111427	−	0.999938i	$-0.503547\pi$
$11$	−9.70954	−	5.60581i	−0.882686	−	0.509619i	−0.871543	+	0.490319i	$0.836880\pi$
$12$		0			0
$13$	−15.6975			−1.20750			−0.603752	−	0.797172i	$-0.706328\pi$
$13$	−15.6975			−1.20750			−0.603752	+	0.797172i	$0.706328\pi$
$14$		0			0
$15$	−15.0067			−1.00044
$16$		0			0
$17$	29.3084	+	16.9212i	1.72402	+	0.995364i	0.910099	+	0.414392i	$0.136006\pi$
$17$	29.3084	+	16.9212i	1.72402	+	0.995364i	0.813923	+	0.580972i	$0.197328\pi$
$18$		0			0
$19$	6.81708	+	11.8075i	0.358793	+	0.621449i	0.987760	−	0.155984i	$-0.0498549\pi$
$19$	6.81708	+	11.8075i	0.358793	+	0.621449i	−0.628966	+	0.777433i	$0.716522\pi$
$20$		0			0
$21$	7.79243	+	9.28860i	0.371068	+	0.442314i
$22$		0			0
$23$	−0.498987	−	0.864271i	−0.0216951	−	0.0375770i	0.854974	−	0.518671i	$-0.173573\pi$
$23$	−0.498987	−	0.864271i	−0.0216951	−	0.0375770i	−0.876669	+	0.481094i	$0.840240\pi$
$24$		0			0
$25$	−25.0333	+	43.3590i	−1.00133	+	1.73436i
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$			13.0538i			0.450130i	0.974344	+	0.225065i	$0.0722595\pi$
$29$			13.0538i			0.450130i	−0.974344	+	0.225065i	$0.927741\pi$
$30$		0			0
$31$	−6.91318	−	3.99133i	−0.223006	−	0.128753i	0.384335	−	0.923194i	$-0.374431\pi$
$31$	−6.91318	−	3.99133i	−0.223006	−	0.128753i	−0.607341	+	0.794441i	$0.707764\pi$
$32$		0			0
$33$	−16.8174	+	9.70954i	−0.509619	+	0.294229i
$34$		0			0
$35$	59.7284	−	10.5254i	1.70653	−	0.300725i
$36$		0			0
$37$	−11.3499	+	6.55286i	−0.306754	+	0.177104i	−0.645473	−	0.763783i	$-0.723340\pi$
$37$	−11.3499	+	6.55286i	−0.306754	+	0.177104i	0.338719	+	0.940887i	$0.390006\pi$
$38$		0			0
$39$	−13.5945	+	23.5463i	−0.348576	+	0.603752i
$40$		0			0
$41$		−	0.655069i		−	0.0159773i	−0.999968	−	0.00798864i	$-0.997457\pi$
$41$		−	0.655069i		−	0.0159773i	0.999968	−	0.00798864i	$-0.00254289\pi$
$42$		0			0
$43$		−	5.93612i		−	0.138049i	−0.997615	−	0.0690247i	$-0.978011\pi$
$43$		−	5.93612i		−	0.138049i	0.997615	−	0.0690247i	$-0.0219887\pi$
$44$		0			0
$45$	−12.9962	+	22.5100i	−0.288803	+	0.500222i
$46$		0			0
$47$	21.8643	−	12.6233i	0.465197	−	0.268582i	−0.249030	−	0.968496i	$-0.580112\pi$
$47$	21.8643	−	12.6233i	0.465197	−	0.268582i	0.714227	+	0.699914i	$0.246778\pi$
$48$		0			0
$49$	−37.5297	−	31.5043i	−0.765912	−	0.642946i
$50$		0			0
$51$	50.7636	−	29.3084i	0.995364	−	0.574674i
$52$		0			0
$53$	57.5500	+	33.2265i	1.08585	+	0.626915i	0.932468	−	0.361252i	$-0.117651\pi$
$53$	57.5500	+	33.2265i	1.08585	+	0.626915i	0.153380	+	0.988167i	$0.450984\pi$
$54$		0			0
$55$			97.1385i			1.76616i
$56$		0			0
$57$	23.6150			0.414299
$58$		0			0
$59$	−12.4419	+	21.5500i	−0.210879	+	0.365254i	−0.951990	−	0.306129i	$-0.900966\pi$
$59$	−12.4419	+	21.5500i	−0.210879	+	0.365254i	0.741111	+	0.671383i	$0.234299\pi$
$60$		0			0
$61$	47.8480	+	82.8752i	0.784394	+	1.35861i	0.929360	+	0.369174i	$0.120359\pi$
$61$	47.8480	+	82.8752i	0.784394	+	1.35861i	−0.144966	+	0.989437i	$0.546307\pi$
$62$		0			0
$63$	20.6813	−	3.64448i	0.328275	−	0.0578489i
$64$		0			0
$65$	68.0026	+	117.784i	1.04619	+	1.81206i
$66$		0			0
$67$	−29.6779	−	17.1345i	−0.442953	−	0.255739i	0.261896	−	0.965096i	$-0.415652\pi$
$67$	−29.6779	−	17.1345i	−0.442953	−	0.255739i	−0.704850	+	0.709357i	$0.748985\pi$
$68$		0			0
$69$	−1.72854			−0.0250513
$70$		0			0
$71$	−61.8795			−0.871542			−0.435771	−	0.900058i	$-0.643524\pi$
$71$	−61.8795			−0.871542			−0.435771	+	0.900058i	$0.643524\pi$
$72$		0			0
$73$	−28.0314	−	16.1839i	−0.383992	−	0.221698i	0.295562	−	0.955324i	$-0.404493\pi$
$73$	−28.0314	−	16.1839i	−0.383992	−	0.221698i	−0.679554	+	0.733626i	$0.737827\pi$
$74$		0			0
$75$	43.3590	+	75.1000i	0.578120	+	1.00133i
$76$		0			0
$77$	60.1254	−	50.4406i	0.780849	−	0.655073i
$78$		0			0
$79$	23.6567	+	40.9746i	0.299452	+	0.518666i	0.976011	−	0.217723i	$-0.0698628\pi$
$79$	23.6567	+	40.9746i	0.299452	+	0.518666i	−0.676559	+	0.736389i	$0.736529\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−117.340			−1.41374			−0.706870	−	0.707343i	$-0.749894\pi$
$83$	−117.340			−1.41374			−0.706870	+	0.707343i	$0.749894\pi$
$84$		0			0
$85$		−	293.214i		−	3.44957i
$86$		0			0
$87$	19.5807	+	11.3049i	0.225065	+	0.129941i
$88$		0			0
$89$	−101.251	+	58.4574i	−1.13765	+	0.656824i	−0.945848	−	0.324609i	$-0.894767\pi$
$89$	−101.251	+	58.4574i	−1.13765	+	0.656824i	−0.191805	+	0.981433i	$0.561434\pi$
$90$		0			0
$91$	37.5928	−	103.252i	0.413108	−	1.13464i
$92$		0			0
$93$	−11.9740	+	6.91318i	−0.128753	+	0.0743353i
$94$		0			0
$95$	59.0638	−	102.302i	0.621725	−	1.07686i
$96$		0			0
$97$			48.9751i			0.504898i	0.967610	+	0.252449i	$0.0812360\pi$
$97$			48.9751i			0.504898i	−0.967610	+	0.252449i	$0.918764\pi$
$98$		0			0
$99$			33.6348i			0.339746i
$100$		0			0
$101$	−49.8929	+	86.4170i	−0.493989	+	0.855614i	−0.999976	−	0.00692737i	$-0.997795\pi$
$101$	−49.8929	+	86.4170i	−0.493989	+	0.855614i	0.505987	+	0.862541i	$0.331128\pi$
$102$		0			0
$103$	−125.370	+	72.3824i	−1.21718	+	0.702742i	−0.964315	−	0.264759i	$-0.914708\pi$
$103$	−125.370	+	72.3824i	−1.21718	+	0.702742i	−0.252870	+	0.967500i	$0.581374\pi$
$104$		0			0
$105$	35.9382	−	98.7078i	0.342269	−	0.940075i
$106$		0			0
$107$	−35.5663	+	20.5342i	−0.332396	+	0.191909i	−0.656904	−	0.753974i	$-0.728134\pi$
$107$	−35.5663	+	20.5342i	−0.332396	+	0.191909i	0.324509	+	0.945883i	$0.394801\pi$
$108$		0			0
$109$	−114.967	−	66.3763i	−1.05474	−	0.608957i	−0.130771	−	0.991413i	$-0.541745\pi$
$109$	−114.967	−	66.3763i	−1.05474	−	0.608957i	−0.923974	+	0.382455i	$0.875079\pi$
$110$		0			0
$111$			22.6998i			0.204502i
$112$		0			0
$113$	−150.727			−1.33386			−0.666932	−	0.745119i	$-0.732393\pi$
$113$	−150.727			−1.33386			−0.666932	+	0.745119i	$0.732393\pi$
$114$		0			0
$115$	−4.32327	+	7.48813i	−0.0375937	+	0.0651142i
$116$		0			0
$117$	23.5463	+	40.7834i	0.201251	+	0.348576i
$118$		0			0
$119$	−181.489	+	152.256i	−1.52512	+	1.27946i
$120$		0			0
$121$	2.35014	+	4.07057i	0.0194227	+	0.0336410i
$122$		0			0
$123$	−0.982603	−	0.567306i	−0.00798864	−	0.00461225i
$124$		0			0
$125$	217.180			1.73744
$126$		0			0
$127$	144.141			1.13497			0.567484	−	0.823385i	$-0.307917\pi$
$127$	144.141			1.13497			0.567484	+	0.823385i	$0.307917\pi$
$128$		0			0
$129$	−8.90419	−	5.14083i	−0.0690247	−	0.0398514i
$130$		0			0
$131$	125.999	+	218.236i	0.961822	+	1.66592i	0.717921	+	0.696124i	$0.245094\pi$
$131$	125.999	+	218.236i	0.961822	+	1.66592i	0.243901	+	0.969800i	$0.421573\pi$
$132$		0			0
$133$	−93.9908	+	16.5631i	−0.706698	+	0.124535i
$134$		0			0
$135$	22.5100	+	38.9885i	0.166741	+	0.288803i
$136$		0			0
$137$	92.7717	−	160.685i	0.677165	−	1.17288i	−0.298666	−	0.954358i	$-0.596541\pi$
$137$	92.7717	−	160.685i	0.677165	−	1.17288i	0.975831	−	0.218527i	$-0.0701252\pi$
$138$		0			0
$139$	−177.155			−1.27449			−0.637247	−	0.770660i	$-0.719927\pi$
$139$	−177.155			−1.27449			−0.637247	+	0.770660i	$0.719927\pi$
$140$		0			0
$141$		−	43.7286i		−	0.310132i
$142$		0			0
$143$	152.416	+	87.9974i	1.06585	+	0.615367i
$144$		0			0
$145$	97.9468	−	56.5496i	0.675495	−	0.389997i
$146$		0			0
$147$	−79.7582	+	29.0110i	−0.542572	+	0.197354i
$148$		0			0
$149$	20.5747	−	11.8788i	0.138085	−	0.0797237i	−0.429366	−	0.903131i	$-0.641263\pi$
$149$	20.5747	−	11.8788i	0.138085	−	0.0797237i	0.567451	+	0.823407i	$0.307930\pi$
$150$		0			0
$151$	44.8515	−	77.6850i	0.297030	−	0.514470i	−0.678425	−	0.734669i	$-0.737337\pi$
$151$	44.8515	−	77.6850i	0.297030	−	0.514470i	0.975455	+	0.220199i	$0.0706706\pi$
$152$		0			0
$153$		−	101.527i		−	0.663576i
$154$		0			0
$155$			69.1626i			0.446210i
$156$		0			0
$157$	−96.7479	+	167.572i	−0.616229	+	1.06734i	0.373939	+	0.927453i	$0.378007\pi$
$157$	−96.7479	+	167.572i	−0.616229	+	1.06734i	−0.990168	+	0.139886i	$0.955326\pi$
$158$		0			0
$159$	99.6795	−	57.5500i	0.626915	−	0.361950i
$160$		0			0
$161$	6.87981	−	1.21237i	0.0427318	−	0.00753022i
$162$		0			0
$163$	64.8970	−	37.4683i	0.398141	−	0.229867i	−0.287540	−	0.957769i	$-0.592838\pi$
$163$	64.8970	−	37.4683i	0.398141	−	0.229867i	0.685682	+	0.727902i	$0.259504\pi$
$164$		0			0
$165$	145.708	+	84.1244i	0.883078	+	0.509845i
$166$		0			0
$167$		−	311.218i		−	1.86358i	−0.362997	−	0.931790i	$-0.618246\pi$
$167$		−	311.218i		−	1.86358i	0.362997	−	0.931790i	$-0.381754\pi$
$168$		0			0
$169$	77.4130			0.458065
$170$		0			0
$171$	20.4512	−	35.4226i	0.119598	−	0.207150i
$172$		0			0
$173$	3.52322	+	6.10239i	0.0203654	+	0.0352739i	0.876028	−	0.482259i	$-0.160184\pi$
$173$	3.52322	+	6.10239i	0.0203654	+	0.0352739i	−0.855663	+	0.517533i	$0.826850\pi$
$174$		0			0
$175$	−225.248	−	268.496i	−1.28713	−	1.53426i
$176$		0			0
$177$	21.5500	+	37.3256i	0.121751	+	0.210879i
$178$		0			0
$179$	42.0060	+	24.2522i	0.234670	+	0.135487i	0.612725	−	0.790296i	$-0.290073\pi$
$179$	42.0060	+	24.2522i	0.234670	+	0.135487i	−0.378054	+	0.925783i	$0.623407\pi$
$180$		0			0
$181$	−100.024			−0.552617			−0.276308	−	0.961069i	$-0.589111\pi$
$181$	−100.024			−0.552617			−0.276308	+	0.961069i	$0.589111\pi$
$182$		0			0
$183$	165.750			0.905740
$184$		0			0
$185$	98.3365	+	56.7746i	0.531549	+	0.306890i
$186$		0			0
$187$	−189.714	−	328.594i	−1.01451	−	1.75719i
$188$		0			0
$189$	12.4438	−	34.1782i	0.0658405	−	0.180837i
$190$		0			0
$191$	−32.6745	−	56.5938i	−0.171071	−	0.296303i	0.767724	−	0.640781i	$-0.221389\pi$
$191$	−32.6745	−	56.5938i	−0.171071	−	0.296303i	−0.938794	+	0.344478i	$0.888056\pi$
$192$		0			0
$193$	−49.2249	+	85.2601i	−0.255051	+	0.441762i	−0.964909	−	0.262583i	$-0.915426\pi$
$193$	−49.2249	+	85.2601i	−0.255051	+	0.441762i	0.709858	+	0.704345i	$0.248759\pi$
$194$		0			0
$195$	235.568			1.20804
$196$		0			0
$197$			78.4827i			0.398390i	0.979960	+	0.199195i	$0.0638326\pi$
$197$			78.4827i			0.398390i	−0.979960	+	0.199195i	$0.936167\pi$
$198$		0			0
$199$	89.5798	+	51.7189i	0.450150	+	0.259894i	0.707894	−	0.706319i	$-0.249646\pi$
$199$	89.5798	+	51.7189i	0.450150	+	0.259894i	−0.257744	+	0.966213i	$0.582979\pi$
$200$		0			0
$201$	−51.4036	+	29.6779i	−0.255739	+	0.147651i
$202$		0			0
$203$	−85.8625	−	31.2614i	−0.422968	−	0.153997i
$204$		0			0
$205$	−4.91520	+	2.83779i	−0.0239766	+	0.0138429i
$206$		0			0
$207$	−1.49696	+	2.59281i	−0.00723170	+	0.0125257i
$208$		0			0
$209$		−	152.861i		−	0.731392i
$210$		0			0
$211$			4.82651i			0.0228745i	0.999935	+	0.0114372i	$0.00364066\pi$
$211$			4.82651i			0.0228745i	−0.999935	+	0.0114372i	$0.996359\pi$
$212$		0			0
$213$	−53.5892	+	92.8192i	−0.251592	+	0.435771i
$214$		0			0
$215$	−44.5407	+	25.7156i	−0.207166	+	0.119607i
$216$		0			0
$217$	42.8092	−	35.9137i	0.197277	−	0.165501i
$218$		0			0
$219$	−48.5518	+	28.0314i	−0.221698	+	0.127997i
$220$		0			0
$221$	−460.070	−	265.621i	−2.08176	−	1.20191i
$222$		0			0
$223$			81.4317i			0.365164i	0.983191	+	0.182582i	$0.0584456\pi$
$223$			81.4317i			0.365164i	−0.983191	+	0.182582i	$0.941554\pi$
$224$		0			0
$225$	150.200			0.667555
$226$		0			0
$227$	158.218	−	274.041i	0.696995	−	1.20723i	−0.272509	−	0.962153i	$-0.587854\pi$
$227$	158.218	−	274.041i	0.696995	−	1.20723i	0.969504	−	0.245077i	$-0.0788132\pi$
$228$		0			0
$229$	−84.9134	−	147.074i	−0.370801	−	0.642246i	0.618888	−	0.785479i	$-0.287583\pi$
$229$	−84.9134	−	147.074i	−0.370801	−	0.642246i	−0.989689	+	0.143233i	$0.954250\pi$
$230$		0			0
$231$	−23.5908	−	133.871i	−0.102125	−	0.579528i
$232$		0			0
$233$	−73.4322	−	127.188i	−0.315160	−	0.545873i	0.664312	−	0.747456i	$-0.268725\pi$
$233$	−73.4322	−	127.188i	−0.315160	−	0.545873i	−0.979471	+	0.201583i	$0.935391\pi$
$234$		0			0
$235$	−189.434	−	109.370i	−0.806104	−	0.465404i
$236$		0			0
$237$	81.9492			0.345777
$238$		0			0
$239$	163.827			0.685471			0.342735	−	0.939432i	$-0.388647\pi$
$239$	163.827			0.685471			0.342735	+	0.939432i	$0.388647\pi$
$240$		0			0
$241$	−139.660	−	80.6329i	−0.579503	−	0.334576i	0.181433	−	0.983403i	$-0.441927\pi$
$241$	−139.660	−	80.6329i	−0.579503	−	0.334576i	−0.760936	+	0.648827i	$0.775260\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−73.8070	+	418.076i	−0.301253	+	1.70643i
$246$		0			0
$247$	−107.011	−	185.349i	−0.433244	−	0.750401i
$248$		0			0
$249$	−101.620	+	176.011i	−0.408112	+	0.706870i
$250$		0			0
$251$	−107.745			−0.429263			−0.214631	−	0.976695i	$-0.568855\pi$
$251$	−107.745			−0.429263			−0.214631	+	0.976695i	$0.568855\pi$
$252$		0			0
$253$			11.1889i			0.0442249i
$254$		0			0
$255$	−439.821	−	253.931i	−1.72479	−	0.995806i
$256$		0			0
$257$	10.8076	−	6.23980i	0.0420531	−	0.0242794i	−0.478826	−	0.877910i	$-0.658938\pi$
$257$	10.8076	−	6.23980i	0.0420531	−	0.0242794i	0.520879	+	0.853630i	$0.325604\pi$
$258$		0			0
$259$	−15.9212	−	90.3479i	−0.0614717	−	0.348834i
$260$		0			0
$261$	33.9147	−	19.5807i	0.129941	−	0.0750217i
$262$		0			0
$263$	213.667	−	370.083i	0.812423	−	1.40716i	−0.0987400	−	0.995113i	$-0.531481\pi$
$263$	213.667	−	370.083i	0.812423	−	1.40716i	0.911163	−	0.412045i	$-0.135185\pi$
$264$		0			0
$265$		−	575.755i		−	2.17266i
$266$		0			0
$267$			202.502i			0.758436i
$268$		0			0
$269$	44.8327	−	77.6525i	0.166664	−	0.288671i	−0.770581	−	0.637342i	$-0.780034\pi$
$269$	44.8327	−	77.6525i	0.166664	−	0.288671i	0.937245	+	0.348671i	$0.113367\pi$
$270$		0			0
$271$	−358.921	+	207.223i	−1.32443	+	0.764661i	−0.984432	−	0.175764i	$-0.943760\pi$
$271$	−358.921	+	207.223i	−1.32443	+	0.764661i	−0.340000	+	0.940425i	$0.610427\pi$
$272$		0			0
$273$	−122.322	−	145.808i	−0.448066	−	0.534096i
$274$		0			0
$275$	486.124	−	280.664i	1.76772	−	1.02060i
$276$		0			0
$277$	−155.672	−	89.8772i	−0.561992	−	0.324466i	0.191953	−	0.981404i	$-0.438518\pi$
$277$	−155.672	−	89.8772i	−0.561992	−	0.324466i	−0.753945	+	0.656938i	$0.771851\pi$
$278$		0			0
$279$			23.9480i			0.0858350i
$280$		0			0
$281$	139.706			0.497175			0.248588	−	0.968609i	$-0.420034\pi$
$281$	139.706			0.497175			0.248588	+	0.968609i	$0.420034\pi$
$282$		0			0
$283$	−131.928	+	228.505i	−0.466176	+	0.807440i	−0.999254	−	0.0386263i	$-0.987702\pi$
$283$	−131.928	+	228.505i	−0.466176	+	0.807440i	0.533078	+	0.846066i	$0.321035\pi$
$284$		0			0
$285$	−102.302	−	177.191i	−0.358953	−	0.621725i
$286$		0			0
$287$	4.30878	+	1.56877i	0.0150132	+	0.00546610i
$288$		0			0
$289$	428.154	+	741.584i	1.48150	+	2.56603i
$290$		0			0
$291$	73.4627	+	42.4137i	0.252449	+	0.145752i
$292$		0			0
$293$	330.985			1.12964			0.564821	−	0.825213i	$-0.308945\pi$
$293$	330.985			1.12964			0.564821	+	0.825213i	$0.308945\pi$
$294$		0			0
$295$	215.595			0.730831
$296$		0			0
$297$	50.4523	+	29.1286i	0.169873	+	0.0980762i
$298$		0			0
$299$	7.83287	+	13.5669i	0.0261969	+	0.0453744i
$300$		0			0
$301$	39.0455	+	14.2159i	0.129719	+	0.0472291i
$302$		0			0
$303$	86.4170	+	149.679i	0.285205	+	0.493989i
$304$		0			0
$305$	414.560	−	718.039i	1.35921	−	2.35423i
$306$		0			0
$307$	−4.65829			−0.0151736			−0.00758680	−	0.999971i	$-0.502415\pi$
$307$	−4.65829			−0.0151736			−0.00758680	+	0.999971i	$0.502415\pi$
$308$		0			0
$309$			250.740i			0.811456i
$310$		0			0
$311$	276.765	+	159.790i	0.889919	+	0.513795i	0.873916	−	0.486077i	$-0.161572\pi$
$311$	276.765	+	159.790i	0.889919	+	0.513795i	0.0160032	+	0.999872i	$0.494906\pi$
$312$		0			0
$313$	−372.667	+	215.159i	−1.19063	+	0.687410i	−0.958449	−	0.285262i	$-0.907919\pi$
$313$	−372.667	+	215.159i	−1.19063	+	0.687410i	−0.232180	+	0.972673i	$0.574586\pi$
$314$		0			0
$315$	−116.938	−	139.391i	−0.371233	−	0.442511i
$316$		0			0
$317$	34.9652	−	20.1872i	0.110300	−	0.0636819i	−0.443835	−	0.896109i	$-0.646382\pi$
$317$	34.9652	−	20.1872i	0.110300	−	0.0636819i	0.554135	+	0.832427i	$0.313049\pi$
$318$		0			0
$319$	73.1769	−	126.746i	0.229395	−	0.397323i
$320$		0			0
$321$			71.1327i			0.221597i
$322$		0			0
$323$			461.412i			1.42852i
$324$		0			0
$325$	392.962	−	680.630i	1.20911	−	2.09424i
$326$		0			0
$327$	−199.129	+	114.967i	−0.608957	+	0.351582i
$328$		0			0
$329$	30.6704	+	174.045i	0.0932230	+	0.529013i
$330$		0			0
$331$	189.572	−	109.449i	0.572725	−	0.330663i	−0.185512	−	0.982642i	$-0.559394\pi$
$331$	189.572	−	109.449i	0.572725	−	0.330663i	0.758237	+	0.651979i	$0.226061\pi$
$332$		0			0
$333$	34.0496	+	19.6586i	0.102251	+	0.0590348i
$334$		0			0
$335$			296.910i			0.886300i
$336$		0			0
$337$	−415.576			−1.23316			−0.616582	−	0.787291i	$-0.711483\pi$
$337$	−415.576			−1.23316			−0.616582	+	0.787291i	$0.711483\pi$
$338$		0			0
$339$	−130.533	+	226.090i	−0.385053	+	0.666932i
$340$		0			0
$341$	44.7492	+	77.5080i	0.131229	+	0.227296i
$342$		0			0
$343$	297.100	−	171.408i	0.866180	−	0.499732i
$344$		0			0
$345$	7.48813	+	12.9698i	0.0217047	+	0.0375937i
$346$		0			0
$347$	−156.085	−	90.1160i	−0.449814	−	0.259700i	0.257938	−	0.966162i	$-0.416957\pi$
$347$	−156.085	−	90.1160i	−0.449814	−	0.259700i	−0.707752	+	0.706461i	$0.750290\pi$
$348$		0			0
$349$	131.310			0.376247			0.188123	−	0.982145i	$-0.439760\pi$
$349$	131.310			0.376247			0.188123	+	0.982145i	$0.439760\pi$
$350$		0			0
$351$	81.5668			0.232384
$352$		0			0
$353$	359.128	+	207.342i	1.01736	+	0.587372i	0.913338	−	0.407203i	$-0.133496\pi$
$353$	359.128	+	207.342i	1.01736	+	0.587372i	0.104021	+	0.994575i	$0.466829\pi$
$354$		0			0
$355$	268.065	+	464.302i	0.755112	+	1.30789i
$356$		0			0
$357$	71.2092	+	404.091i	0.199465	+	1.13191i
$358$		0			0
$359$	193.471	+	335.101i	0.538915	+	0.933429i	0.998963	+	0.0455343i	$0.0144990\pi$
$359$	193.471	+	335.101i	0.538915	+	0.933429i	−0.460048	+	0.887894i	$0.652168\pi$
$360$		0			0
$361$	87.5549	−	151.650i	0.242534	−	0.420082i
$362$		0			0
$363$	8.14113			0.0224274
$364$		0			0
$365$			280.439i			0.768325i
$366$		0			0
$367$	−393.315	−	227.081i	−1.07170	−	0.618748i	−0.143057	−	0.989714i	$-0.545693\pi$
$367$	−393.315	−	227.081i	−1.07170	−	0.618748i	−0.928646	+	0.370966i	$0.879027\pi$
$368$		0			0
$369$	−1.70192	+	0.982603i	−0.00461225	+	0.00266288i
$370$		0			0
$371$	−356.372	+	298.969i	−0.960573	+	0.805847i
$372$		0			0
$373$	−394.924	+	228.009i	−1.05878	+	0.611285i	−0.925094	−	0.379739i	$-0.876014\pi$
$373$	−394.924	+	228.009i	−1.05878	+	0.611285i	−0.133683	+	0.991024i	$0.542681\pi$
$374$		0			0
$375$	188.083	−	325.770i	0.501555	−	0.868719i
$376$		0			0
$377$		−	204.912i		−	0.543534i
$378$		0			0
$379$		−	31.8832i		−	0.0841245i	−0.999115	−	0.0420623i	$-0.986607\pi$
$379$		−	31.8832i		−	0.0841245i	0.999115	−	0.0420623i	$-0.0133928\pi$
$380$		0			0
$381$	124.830	−	216.211i	0.327637	−	0.567484i
$382$		0			0
$383$	−500.563	+	289.000i	−1.30695	+	0.754569i	−0.981586	−	0.191019i	$-0.938821\pi$
$383$	−500.563	+	289.000i	−1.30695	+	0.754569i	−0.325366	+	0.945588i	$0.605487\pi$
$384$		0			0
$385$	−638.939	−	232.629i	−1.65958	−	0.604232i
$386$		0			0
$387$	−15.4225	+	8.90419i	−0.0398514	+	0.0230082i
$388$		0			0
$389$	−343.343	−	198.229i	−0.882631	−	0.509587i	−0.0111058	−	0.999938i	$-0.503535\pi$
$389$	−343.343	−	198.229i	−0.882631	−	0.509587i	−0.871525	+	0.490351i	$0.836869\pi$
$390$		0			0
$391$		−	33.7738i		−	0.0863781i
$392$		0			0
$393$	436.472			1.11062
$394$		0			0
$395$	204.964	−	355.008i	0.518896	−	0.898755i
$396$		0			0
$397$	98.9328	+	171.357i	0.249201	+	0.431629i	0.963304	−	0.268412i	$-0.0864987\pi$
$397$	98.9328	+	171.357i	0.249201	+	0.431629i	−0.714103	+	0.700040i	$0.753165\pi$
$398$		0			0
$399$	−56.5538	+	155.330i	−0.141739	+	0.389299i
$400$		0			0
$401$	−23.4522	−	40.6205i	−0.0584844	−	0.101298i	0.835301	−	0.549793i	$-0.185293\pi$
$401$	−23.4522	−	40.6205i	−0.0584844	−	0.101298i	−0.893785	+	0.448495i	$0.851960\pi$
$402$		0			0
$403$	108.520	+	62.6541i	0.269281	+	0.155469i
$404$		0			0
$405$	77.9769			0.192536
$406$		0			0
$407$	146.936			0.361023
$408$		0			0
$409$	104.273	+	60.2022i	0.254947	+	0.147194i	0.622027	−	0.782996i	$-0.286309\pi$
$409$	104.273	+	60.2022i	0.254947	+	0.147194i	−0.367080	+	0.930189i	$0.619643\pi$
$410$		0			0
$411$	−160.685	−	278.315i	−0.390962	−	0.677165i
$412$		0			0
$413$	−111.951	−	133.446i	−0.271068	−	0.323114i
$414$		0			0
$415$	508.325	+	880.445i	1.22488	+	2.12155i
$416$		0			0
$417$	−153.420	+	265.732i	−0.367915	+	0.637247i
$418$		0			0
$419$	546.963			1.30540			0.652701	−	0.757616i	$-0.273636\pi$
$419$	546.963			1.30540			0.652701	+	0.757616i	$0.273636\pi$
$420$		0			0
$421$		−	302.426i		−	0.718351i	−0.933270	−	0.359176i	$-0.883058\pi$
$421$		−	302.426i		−	0.718351i	0.933270	−	0.359176i	$-0.116942\pi$
$422$		0			0
$423$	−65.5928	−	37.8700i	−0.155066	−	0.0895273i
$424$		0			0
$425$	−1467.37	+	847.187i	−3.45264	+	1.99338i
$426$		0			0
$427$	−659.708	+	116.254i	−1.54498	+	0.272258i
$428$		0			0
$429$	263.992	−	152.416i	0.615367	−	0.355282i
$430$		0			0
$431$	−281.450	+	487.485i	−0.653015	+	1.13106i	0.329372	+	0.944200i	$0.393163\pi$
$431$	−281.450	+	487.485i	−0.653015	+	1.13106i	−0.982387	+	0.186856i	$0.940170\pi$
$432$		0			0
$433$			204.891i			0.473189i	0.971609	+	0.236594i	$0.0760312\pi$
$433$			204.891i			0.473189i	−0.971609	+	0.236594i	$0.923969\pi$
$434$		0			0
$435$		−	195.894i		−	0.450330i
$436$		0			0
$437$	6.80327	−	11.7836i	0.0155681	−	0.0269648i
$438$		0			0
$439$	246.898	−	142.546i	0.562409	−	0.324707i	−0.191703	−	0.981453i	$-0.561401\pi$
$439$	246.898	−	142.546i	0.562409	−	0.324707i	0.754112	+	0.656746i	$0.228068\pi$
$440$		0			0
$441$	−25.5561	+	144.761i	−0.0579504	+	0.328257i
$442$		0			0
$443$	−705.036	+	407.052i	−1.59150	+	0.918854i	−0.598453	+	0.801158i	$0.704218\pi$
$443$	−705.036	+	407.052i	−1.59150	+	0.918854i	−0.993050	+	0.117696i	$0.962449\pi$
$444$		0			0
$445$	877.250	+	506.481i	1.97135	+	1.13816i
$446$		0			0
$447$		−	41.1495i		−	0.0920570i
$448$		0			0
$449$	−451.470			−1.00550			−0.502750	−	0.864432i	$-0.667678\pi$
$449$	−451.470			−1.00550			−0.502750	+	0.864432i	$0.667678\pi$
$450$		0			0
$451$	−3.67219	+	6.36042i	−0.00814233	+	0.0141029i
$452$		0			0
$453$	−77.6850	−	134.554i	−0.171490	−	0.297030i
$454$		0			0
$455$	−937.589	+	165.223i	−2.06064	+	0.363127i
$456$		0			0
$457$	334.931	+	580.117i	0.732890	+	1.26940i	0.955643	+	0.294528i	$0.0951625\pi$
$457$	334.931	+	580.117i	0.732890	+	1.26940i	−0.222753	+	0.974875i	$0.571504\pi$
$458$		0			0
$459$	−152.291	−	87.9251i	−0.331788	−	0.191558i
$460$		0			0
$461$	−426.215			−0.924544			−0.462272	−	0.886738i	$-0.652966\pi$
$461$	−426.215			−0.924544			−0.462272	+	0.886738i	$0.652966\pi$
$462$		0			0
$463$	5.80051			0.0125281			0.00626405	−	0.999980i	$-0.498006\pi$
$463$	5.80051			0.0125281			0.00626405	+	0.999980i	$0.498006\pi$
$464$		0			0
$465$	103.744	+	59.8965i	0.223105	+	0.128810i
$466$		0			0
$467$	−215.428	−	373.132i	−0.461302	−	0.798998i	0.537724	−	0.843121i	$-0.319284\pi$
$467$	−215.428	−	373.132i	−0.461302	−	0.798998i	−0.999026	+	0.0441227i	$0.985951\pi$
$468$		0			0
$469$	183.777	−	154.175i	0.391849	−	0.328732i
$470$		0			0
$471$	167.572	+	290.244i	0.355780	+	0.616229i
$472$		0			0
$473$	−33.2768	+	57.6371i	−0.0703526	+	0.121854i
$474$		0			0
$475$	−682.616			−1.43709
$476$		0			0
$477$		−	199.359i		−	0.417943i
$478$		0			0
$479$	290.926	+	167.966i	0.607362	+	0.350661i	0.771932	−	0.635705i	$-0.219290\pi$
$479$	290.926	+	167.966i	0.607362	+	0.350661i	−0.164570	+	0.986365i	$0.552624\pi$
$480$		0			0
$481$	178.165	−	102.864i	0.370406	−	0.213854i
$482$		0			0
$483$	4.13955	−	11.3697i	0.00857049	−	0.0235397i
$484$		0			0
$485$	367.477	−	212.163i	0.757684	−	0.437449i
$486$		0			0
$487$	−334.353	+	579.116i	−0.686556	+	1.18915i	0.286389	+	0.958113i	$0.407545\pi$
$487$	−334.353	+	579.116i	−0.686556	+	1.18915i	−0.972945	+	0.231036i	$0.925788\pi$
$488$		0			0
$489$		−	129.794i		−	0.265427i
$490$		0			0
$491$		−	729.226i		−	1.48518i	−0.669744	−	0.742592i	$-0.733596\pi$
$491$		−	729.226i		−	1.48518i	0.669744	−	0.742592i	$-0.266404\pi$
$492$		0			0
$493$	−220.885	+	382.585i	−0.448044	+	0.776034i
$494$		0			0
$495$	252.373	−	145.708i	0.509845	−	0.294359i
$496$		0			0
$497$	148.190	−	407.018i	0.298169	−	0.818951i
$498$		0			0
$499$	696.518	−	402.135i	1.39583	−	0.805882i	0.401876	−	0.915694i	$-0.368358\pi$
$499$	696.518	−	402.135i	1.39583	−	0.805882i	0.993952	+	0.109812i	$0.0350250\pi$
$500$		0			0
$501$	−466.827	−	269.523i	−0.931790	−	0.537969i
$502$		0			0
$503$		−	383.284i		−	0.761997i	−0.924576	−	0.380998i	$-0.875580\pi$
$503$		−	383.284i		−	0.761997i	0.924576	−	0.380998i	$-0.124420\pi$
$504$		0			0
$505$	864.554			1.71199
$506$		0			0
$507$	67.0416	−	116.119i	0.132232	−	0.229033i
$508$		0			0
$509$	46.4944	+	80.5307i	0.0913446	+	0.158214i	0.908077	−	0.418803i	$-0.137550\pi$
$509$	46.4944	+	80.5307i	0.0913446	+	0.158214i	−0.816733	+	0.577016i	$0.804217\pi$
$510$		0			0
$511$	173.582	−	145.622i	0.339690	−	0.284974i
$512$		0			0
$513$	−35.4226	−	61.3537i	−0.0690498	−	0.119598i
$514$		0			0
$515$	1086.22	+	627.128i	2.10916	+	1.21773i
$516$		0			0
$517$	−283.056			−0.547498
$518$		0			0
$519$	12.2048			0.0235160
$520$		0			0
$521$	−407.887	−	235.494i	−0.782893	−	0.452003i	0.0545619	−	0.998510i	$-0.482624\pi$
$521$	−407.887	−	235.494i	−0.782893	−	0.452003i	−0.837454	+	0.546507i	$0.815957\pi$
$522$		0			0
$523$	347.347	+	601.622i	0.664143	+	1.15033i	0.979517	+	0.201362i	$0.0645367\pi$
$523$	347.347	+	601.622i	0.664143	+	1.15033i	−0.315374	+	0.948967i	$0.602130\pi$
$524$		0			0
$525$	−597.814	+	105.347i	−1.13869	+	0.200661i
$526$		0			0
$527$	−135.076	−	233.959i	−0.256311	−	0.443944i
$528$		0			0
$529$	264.002	−	457.265i	0.499059	−	0.864395i
$530$		0			0
$531$	74.6512			0.140586
$532$		0			0
$533$			10.2830i			0.0192926i
$534$		0			0
$535$	308.150	+	177.911i	0.575982	+	0.332543i
$536$		0			0
$537$	72.7565	−	42.0060i	0.135487	−	0.0782234i
$538$		0			0
$539$	187.789	+	516.277i	0.348402	+	0.957842i
$540$		0			0
$541$	−112.726	+	65.0826i	−0.208367	+	0.120301i	−0.600552	−	0.799586i	$-0.705052\pi$
$541$	−112.726	+	65.0826i	−0.208367	+	0.120301i	0.392185	+	0.919886i	$0.371719\pi$
$542$		0			0
$543$	−86.6230	+	150.035i	−0.159527	+	0.276308i
$544$		0			0
$545$			1150.18i			2.11043i
$546$		0			0
$547$		−	795.308i		−	1.45395i	−0.686666	−	0.726973i	$-0.740927\pi$
$547$		−	795.308i		−	1.45395i	0.686666	−	0.726973i	$-0.259073\pi$
$548$		0			0
$549$	143.544	−	248.626i	0.261465	−	0.452870i
$550$		0			0
$551$	−154.133	+	88.9886i	−0.279733	+	0.161504i
$552$		0			0
$553$	−326.168	+	57.4776i	−0.589816	+	0.103938i
$554$		0			0
$555$	170.324	−	98.3365i	0.306890	−	0.177183i
$556$		0			0
$557$	456.727	+	263.691i	0.819976	+	0.473413i	0.850408	−	0.526124i	$-0.176355\pi$
$557$	456.727	+	263.691i	0.819976	+	0.473413i	−0.0304323	+	0.999537i	$0.509688\pi$
$558$		0			0
$559$			93.1826i			0.166695i
$560$		0			0
$561$	−657.188			−1.17146
$562$		0			0
$563$	36.9792	−	64.0499i	0.0656825	−	0.113765i	−0.831314	−	0.555803i	$-0.812411\pi$
$563$	36.9792	−	64.0499i	0.0656825	−	0.113765i	0.896997	+	0.442038i	$0.145744\pi$
$564$		0			0
$565$	652.955	+	1130.95i	1.15567	+	2.00168i
$566$		0			0
$567$	−40.4906	−	48.2650i	−0.0714121	−	0.0851234i
$568$		0			0
$569$	341.691	+	591.826i	0.600512	+	1.04012i	0.992744	+	0.120250i	$0.0383697\pi$
$569$	341.691	+	591.826i	0.600512	+	1.04012i	−0.392232	+	0.919866i	$0.628297\pi$
$570$		0			0
$571$	473.012	+	273.094i	0.828392	+	0.478273i	0.853302	−	0.521417i	$-0.174596\pi$
$571$	473.012	+	273.094i	0.828392	+	0.478273i	−0.0249095	+	0.999690i	$0.507930\pi$
$572$		0			0
$573$	−113.188			−0.197535
$574$		0			0
$575$	49.9652			0.0868960
$576$		0			0
$577$	556.261	+	321.157i	0.964057	+	0.556599i	0.897419	−	0.441179i	$-0.145439\pi$
$577$	556.261	+	321.157i	0.964057	+	0.556599i	0.0666378	+	0.997777i	$0.478773\pi$
$578$		0			0
$579$	85.2601	+	147.675i	0.147254	+	0.255051i
$580$		0			0
$581$	281.009	−	771.819i	0.483665	−	1.32843i
$582$		0			0
$583$	−372.523	−	645.228i	−0.638975	−	1.10674i
$584$		0			0
$585$	204.008	−	353.352i	0.348731	−	0.604020i
$586$		0			0
$587$	−271.221			−0.462046			−0.231023	−	0.972948i	$-0.574207\pi$
$587$	−271.221			−0.462046			−0.231023	+	0.972948i	$0.574207\pi$
$588$		0			0
$589$		−	108.837i		−	0.184782i
$590$		0			0
$591$	117.724	+	67.9680i	0.199195	+	0.115005i
$592$		0			0
$593$	280.252	−	161.804i	0.472600	−	0.272856i	−0.244727	−	0.969592i	$-0.578698\pi$
$593$	280.252	−	161.804i	0.472600	−	0.272856i	0.717328	+	0.696736i	$0.245365\pi$
$594$		0			0
$595$	1928.64	+	702.194i	3.24142	+	1.18016i
$596$		0			0
$597$	155.157	−	89.5798i	0.259894	−	0.150050i
$598$		0			0
$599$	47.3860	−	82.0750i	0.0791086	−	0.137020i	−0.823757	−	0.566943i	$-0.808126\pi$
$599$	47.3860	−	82.0750i	0.0791086	−	0.137020i	0.902866	+	0.429923i	$0.141459\pi$
$600$		0			0
$601$			297.172i			0.494463i	0.968956	+	0.247232i	$0.0795209\pi$
$601$			297.172i			0.494463i	−0.968956	+	0.247232i	$0.920479\pi$
$602$		0			0
$603$			102.807i			0.170493i
$604$		0			0
$605$	20.3619	−	35.2678i	0.0336560	−	0.0582939i
$606$		0			0
$607$	−625.913	+	361.371i	−1.03116	+	0.595339i	−0.917316	−	0.398160i	$-0.869649\pi$
$607$	−625.913	+	361.371i	−1.03116	+	0.595339i	−0.113841	+	0.993499i	$0.536316\pi$
$608$		0			0
$609$	−121.251	+	101.721i	−0.199099	+	0.167029i
$610$		0			0
$611$	−343.216	+	198.156i	−0.561728	+	0.324314i
$612$		0			0
$613$	54.1732	+	31.2769i	0.0883740	+	0.0510227i	0.543536	−	0.839386i	$-0.317085\pi$
$613$	54.1732	+	31.2769i	0.0883740	+	0.0510227i	−0.455162	+	0.890409i	$0.650419\pi$
$614$		0			0
$615$			9.83040i			0.0159844i
$616$		0			0
$617$	648.161			1.05050			0.525252	−	0.850947i	$-0.323971\pi$
$617$	648.161			1.05050			0.525252	+	0.850947i	$0.323971\pi$
$618$		0			0
$619$	−440.821	+	763.525i	−0.712151	+	1.23348i	0.251898	+	0.967754i	$0.418945\pi$
$619$	−440.821	+	763.525i	−0.712151	+	1.23348i	−0.964048	+	0.265727i	$0.914388\pi$
$620$		0			0
$621$	2.59281	+	4.49088i	0.00417522	+	0.00723170i
$622$		0			0
$623$	−142.031	−	805.985i	−0.227979	−	1.29372i
$624$		0			0
$625$	−315.001	−	545.598i	−0.504002	−	0.872957i
$626$		0			0
$627$	−229.291	−	132.381i	−0.365696	−	0.211135i
$628$		0			0
$629$	−443.529			−0.705133
$630$		0			0
$631$	−983.113			−1.55802			−0.779012	−	0.627009i	$-0.784279\pi$
$631$	−983.113			−1.55802			−0.779012	+	0.627009i	$0.784279\pi$
$632$		0			0
$633$	7.23977	+	4.17988i	0.0114372	+	0.00660329i
$634$		0			0
$635$	−624.426	−	1081.54i	−0.983347	−	1.70321i
$636$		0			0
$637$	589.124	+	494.541i	0.924841	+	0.776359i
$638$		0			0
$639$	92.8192	+	160.768i	0.145257	+	0.251592i
$640$		0			0
$641$	340.966	−	590.571i	0.531929	−	0.921328i	−0.467376	−	0.884058i	$-0.654801\pi$
$641$	340.966	−	590.571i	0.531929	−	0.921328i	0.999305	−	0.0372695i	$-0.0118660\pi$
$642$		0			0
$643$	−1.19182			−0.00185353			−0.000926763	−	1.00000i	$-0.500295\pi$
$643$	−1.19182			−0.00185353			−0.000926763		1.00000i	$0.500295\pi$
$644$		0			0
$645$			89.0814i			0.138111i
$646$		0			0
$647$	250.570	+	144.667i	0.387280	+	0.223596i	0.680981	−	0.732301i	$-0.261554\pi$
$647$	250.570	+	144.667i	0.387280	+	0.223596i	−0.293701	+	0.955897i	$0.594887\pi$
$648$		0			0
$649$	241.610	−	139.493i	0.372280	−	0.214936i
$650$		0			0
$651$	−16.7966	−	95.3159i	−0.0258013	−	0.146415i
$652$		0			0
$653$	−222.449	+	128.431i	−0.340656	+	0.196678i	−0.660562	−	0.750771i	$-0.729682\pi$
$653$	−222.449	+	128.431i	−0.340656	+	0.196678i	0.319906	+	0.947449i	$0.396349\pi$
$654$		0			0
$655$	1091.67	−	1890.82i	1.66666	−	2.88675i
$656$		0			0
$657$			97.1037i			0.147799i
$658$		0			0
$659$			114.610i			0.173915i	0.996212	+	0.0869576i	$0.0277145\pi$
$659$			114.610i			0.173915i	−0.996212	+	0.0869576i	$0.972286\pi$
$660$		0			0
$661$	−364.595	+	631.497i	−0.551581	+	0.955366i	0.446580	+	0.894744i	$0.352642\pi$
$661$	−364.595	+	631.497i	−0.551581	+	0.955366i	−0.998161	+	0.0606225i	$0.980691\pi$
$662$		0			0
$663$	−796.864	+	460.070i	−1.20191	+	0.693921i
$664$		0			0
$665$	531.452	+	633.492i	0.799175	+	0.952620i
$666$		0			0
$667$	11.2820	−	6.51367i	0.0169145	−	0.00976562i
$668$		0			0
$669$	122.148	+	70.5219i	0.182582	+	0.105414i
$670$		0			0
$671$		−	1072.91i		−	1.59897i
$672$		0			0
$673$	−423.130			−0.628723			−0.314361	−	0.949303i	$-0.601790\pi$
$673$	−423.130			−0.628723			−0.314361	+	0.949303i	$0.601790\pi$
$674$		0			0
$675$	130.077	−	225.300i	0.192707	−	0.333778i
$676$		0			0
$677$	200.455	+	347.198i	0.296093	+	0.512849i	0.975239	−	0.221155i	$-0.0709828\pi$
$677$	200.455	+	347.198i	0.296093	+	0.512849i	−0.679145	+	0.734004i	$0.737649\pi$
$678$		0			0
$679$	−322.139	−	117.287i	−0.474431	−	0.172734i
$680$		0			0
$681$	−274.041	−	474.653i	−0.402410	−	0.696995i
$682$		0			0
$683$	−1155.01	−	666.848i	−1.69109	−	0.976351i	−0.953640	−	0.300950i	$-0.902696\pi$
$683$	−1155.01	−	666.848i	−1.69109	−	0.976351i	−0.737450	−	0.675402i	$-0.763970\pi$
$684$		0			0
$685$	−1607.57			−2.34681
$686$		0			0
$687$	−294.149			−0.428164
$688$		0			0
$689$	−903.393	−	521.574i	−1.31117	−	0.757002i
$690$		0			0
$691$	542.994	+	940.493i	0.785809	+	1.36106i	0.928515	+	0.371295i	$0.121086\pi$
$691$	542.994	+	940.493i	0.785809	+	1.36106i	−0.142706	+	0.989765i	$0.545580\pi$
$692$		0			0
$693$	−221.237	−	80.5494i	−0.319245	−	0.116233i
$694$		0			0
$695$	767.443	+	1329.25i	1.10423	+	1.91259i
$696$		0			0
$697$	11.0845	−	19.1990i	0.0159032	−	0.0275452i
$698$		0			0
$699$	−254.377			−0.363915
$700$		0			0
$701$		−	656.518i		−	0.936544i	−0.883584	−	0.468272i	$-0.844877\pi$
$701$		−	656.518i		−	0.936544i	0.883584	−	0.468272i	$-0.155123\pi$
$702$		0			0
$703$	−154.746	−	89.3427i	−0.220122	−	0.127088i
$704$		0			0
$705$	−328.110	+	189.434i	−0.465404	+	0.268701i
$706$		0			0
$707$	−448.932	−	535.128i	−0.634982	−	0.756900i
$708$		0			0
$709$	746.403	−	430.936i	1.05275	−	0.607808i	0.129335	−	0.991601i	$-0.458716\pi$
$709$	746.403	−	430.936i	1.05275	−	0.607808i	0.923419	+	0.383793i	$0.125382\pi$
$710$		0			0
$711$	70.9701	−	122.924i	0.0998173	−	0.172889i
$712$		0			0
$713$			7.96649i			0.0111732i
$714$		0			0
$715$		−	1524.84i		−	2.13264i
$716$		0			0
$717$	141.879	−	245.741i	0.197878	−	0.342735i
$718$		0			0
$719$	598.298	−	345.428i	0.832126	−	0.480428i	−0.0224543	−	0.999748i	$-0.507148\pi$
$719$	598.298	−	345.428i	0.832126	−	0.480428i	0.854580	+	0.519320i	$0.173815\pi$
$720$		0			0
$721$	−175.864	−	997.977i	−0.243917	−	1.38416i
$722$		0			0
$723$	−241.899	+	139.660i	−0.334576	+	0.193168i
$724$		0			0
$725$	−565.998	−	326.779i	−0.780687	−	0.450730i
$726$		0			0
$727$			930.093i			1.27936i	0.768642	+	0.639679i	$0.220933\pi$
$727$			930.093i			1.27936i	−0.768642	+	0.639679i	$0.779067\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$	100.446	−	173.978i	0.137409	−	0.238000i
$732$		0			0
$733$	−340.313	−	589.440i	−0.464275	−	0.804147i	0.534894	−	0.844919i	$-0.320352\pi$
$733$	−340.313	−	589.440i	−0.464275	−	0.804147i	−0.999168	+	0.0407720i	$0.987018\pi$
$734$		0			0
$735$	563.195	+	472.775i	0.766252	+	0.643231i
$736$		0			0
$737$	192.106	+	332.737i	0.260659	+	0.451475i
$738$		0			0
$739$	−571.849	−	330.157i	−0.773815	−	0.446762i	0.0604187	−	0.998173i	$-0.480756\pi$
$739$	−571.849	−	330.157i	−0.773815	−	0.446762i	−0.834234	+	0.551411i	$0.814090\pi$
$740$		0			0
$741$	−370.698			−0.500268
$742$		0			0
$743$	178.644			0.240435			0.120218	−	0.992748i	$-0.461641\pi$
$743$	178.644			0.240435			0.120218	+	0.992748i	$0.461641\pi$
$744$		0			0
$745$	−178.262	−	102.919i	−0.239277	−	0.138147i
$746$		0			0
$747$	176.011	+	304.860i	0.235623	+	0.408112i
$748$		0			0
$749$	−49.8911	−	283.117i	−0.0666102	−	0.377993i
$750$		0			0
$751$	379.327	+	657.013i	0.505095	+	0.874851i	0.999983	+	0.00589360i	$0.00187600\pi$
$751$	379.327	+	657.013i	0.505095	+	0.874851i	−0.494887	+	0.868957i	$0.664791\pi$
$752$		0			0
$753$	−93.3099	+	161.617i	−0.123918	+	0.214631i
$754$		0			0
$755$	−777.195			−1.02940
$756$		0			0
$757$			121.445i			0.160430i	0.996778	+	0.0802148i	$0.0255606\pi$
$757$			121.445i			0.160430i	−0.996778	+	0.0802148i	$0.974439\pi$
$758$		0			0
$759$	16.7834	+	9.68987i	0.0221125	+	0.0127666i
$760$		0			0
$761$	266.676	−	153.966i	0.350429	−	0.202320i	−0.314445	−	0.949276i	$-0.601818\pi$
$761$	266.676	−	153.966i	0.350429	−	0.202320i	0.664874	+	0.746955i	$0.268485\pi$
$762$		0			0
$763$	711.923	−	597.249i	0.933057	−	0.782764i
$764$		0			0
$765$	−761.792	+	439.821i	−0.995806	+	0.574929i
$766$		0			0
$767$	195.307	−	338.281i	0.254637	−	0.441045i
$768$		0			0
$769$			92.7247i			0.120578i	0.998181	+	0.0602891i	$0.0192023\pi$
$769$			92.7247i			0.120578i	−0.998181	+	0.0602891i	$0.980798\pi$
$770$		0			0
$771$		−	21.6153i		−	0.0280354i
$772$		0			0
$773$	−527.812	+	914.197i	−0.682809	+	1.18266i	0.291311	+	0.956629i	$0.405909\pi$
$773$	−527.812	+	914.197i	−0.682809	+	1.18266i	−0.974120	+	0.226032i	$0.927425\pi$
$774$		0			0
$775$	346.120	−	199.832i	0.446606	−	0.257848i
$776$		0			0
$777$	−149.310	−	54.3618i	−0.192162	−	0.0699637i
$778$		0			0
$779$	7.73474	−	4.46565i	0.00992906	−	0.00573255i
$780$		0			0
$781$	600.821	+	346.884i	0.769297	+	0.444154i
$782$		0			0
$783$		−	67.8294i		−	0.0866276i
$784$		0			0
$785$	1676.47			2.13563
$786$		0			0
$787$	113.609	−	196.776i	0.144357	−	0.250033i	−0.784776	−	0.619779i	$-0.787222\pi$
$787$	113.609	−	196.776i	0.144357	−	0.250033i	0.929133	+	0.369746i	$0.120555\pi$
$788$		0			0
$789$	−370.083	−	641.002i	−0.469053	−	0.812423i
$790$		0			0
$791$	360.963	−	991.419i	0.456337	−	1.25337i
$792$		0			0
$793$	−751.097	−	1300.94i	−0.947159	−	1.64053i
$794$		0			0
$795$	−863.633	−	498.619i	−1.08633	−	0.627193i
$796$		0			0
$797$	623.447			0.782243			0.391121	−	0.920339i	$-0.372087\pi$
$797$	623.447			0.782243			0.391121	+	0.920339i	$0.372087\pi$
$798$		0			0
$799$	854.409			1.06935
$800$		0			0
$801$	303.753	+	175.372i	0.379218	+	0.218941i
$802$		0			0
$803$	181.448	+	314.277i	0.225963	+	0.391379i
$804$		0			0
$805$	−38.9005	−	46.3695i	−0.0483236	−	0.0576019i
$806$		0			0
$807$	−77.6525	−	134.498i	−0.0962237	−	0.166664i
$808$		0			0
$809$	−466.973	+	808.821i	−0.577222	+	0.999778i	0.418574	+	0.908183i	$0.362530\pi$
$809$	−466.973	+	808.821i	−0.577222	+	0.999778i	−0.995796	+	0.0915957i	$0.970803\pi$
$810$		0			0
$811$	−110.425			−0.136159			−0.0680795	−	0.997680i	$-0.521687\pi$
$811$	−110.425			−0.136159			−0.0680795	+	0.997680i	$0.521687\pi$
$812$		0			0
$813$			717.842i			0.882955i
$814$		0			0
$815$	−562.274	−	324.629i	−0.689907	−	0.398318i
$816$		0			0
$817$	70.0909	−	40.4670i	0.0857906	−	0.0495312i
$818$		0			0
$819$	−324.646	+	57.2094i	−0.396394	+	0.0698527i
$820$		0			0
$821$	771.380	−	445.357i	0.939562	−	0.542456i	0.0497389	−	0.998762i	$-0.484161\pi$
$821$	771.380	−	445.357i	0.939562	−	0.542456i	0.889823	+	0.456306i	$0.150828\pi$
$822$		0			0
$823$	352.585	−	610.696i	0.428415	−	0.742036i	−0.568318	−	0.822809i	$-0.692406\pi$
$823$	352.585	−	610.696i	0.428415	−	0.742036i	0.996733	+	0.0807732i	$0.0257389\pi$
$824$		0			0
$825$		−	972.248i		−	1.17848i
$826$		0			0
$827$			721.630i			0.872588i	0.899804	+	0.436294i	$0.143709\pi$
$827$			721.630i			0.872588i	−0.899804	+	0.436294i	$0.856291\pi$
$828$		0			0
$829$	401.589	−	695.572i	0.484426	−	0.839050i	−0.515414	−	0.856941i	$-0.672362\pi$
$829$	401.589	−	695.572i	0.484426	−	0.839050i	0.999840	+	0.0178913i	$0.00569528\pi$
$830$		0			0
$831$	−269.632	+	155.672i	−0.324466	+	0.187331i
$832$		0			0
$833$	−566.843	−	1558.39i	−0.680484	−	1.87081i
$834$		0			0
$835$	−2335.17	+	1348.21i	−2.79661	+	1.61463i
$836$		0			0
$837$	35.9220	+	20.7396i	0.0429175	+	0.0247784i
$838$		0			0
$839$		−	1150.33i		−	1.37107i	−0.728037	−	0.685537i	$-0.759567\pi$
$839$		−	1150.33i		−	1.37107i	0.728037	−	0.685537i	$-0.240433\pi$
$840$		0			0
$841$	670.599			0.797383
$842$		0			0
$843$	120.989	−	209.559i	0.143522	−	0.248588i
$844$		0			0
$845$	−335.357	−	580.855i	−0.396872	−	0.687403i
$846$		0			0
$847$	−32.4027	+	5.71003i	−0.0382559	+	0.00674148i
$848$		0			0
$849$	228.505	+	395.783i	0.269147	+	0.466176i
$850$		0			0
$851$	11.3269	+	6.53958i	0.0133101	+	0.00768459i
$852$		0			0
$853$	−247.862			−0.290576			−0.145288	−	0.989389i	$-0.546411\pi$
$853$	−247.862			−0.290576			−0.145288	+	0.989389i	$0.546411\pi$
$854$		0			0
$855$	−354.383			−0.414483
$856$		0			0
$857$	−1410.46	−	814.329i	−1.64581	−	0.950209i	−0.978712	−	0.205241i	$-0.934202\pi$
$857$	−1410.46	−	814.329i	−1.64581	−	0.950209i	−0.667099	−	0.744969i	$-0.732464\pi$
$858$		0			0
$859$	490.166	+	848.992i	0.570624	+	0.988349i	0.996502	+	0.0835688i	$0.0266318\pi$
$859$	490.166	+	848.992i	0.570624	+	0.988349i	−0.425878	+	0.904780i	$0.640035\pi$
$860$		0			0
$861$	6.08467	−	5.10458i	0.00706698	−	0.00592866i
$862$		0			0
$863$	−333.473	−	577.592i	−0.386411	−	0.669284i	0.605552	−	0.795805i	$-0.292952\pi$
$863$	−333.473	−	577.592i	−0.386411	−	0.669284i	−0.991964	+	0.126521i	$0.959619\pi$
$864$		0			0
$865$	30.5255	−	52.8717i	0.0352896	−	0.0611234i
$866$		0			0
$867$	1483.17			1.71069
$868$		0			0
$869$		−	530.460i		−	0.610426i
$870$		0			0
$871$	465.870	+	268.970i	0.534868	+	0.308806i
$872$		0			0
$873$	127.241	−	73.4627i	0.145752	−	0.0841497i
$874$		0			0
$875$	−520.106	+	1428.52i	−0.594407	+	1.63260i
$876$		0			0
$877$	729.217	−	421.013i	0.831490	−	0.480061i	−0.0228726	−	0.999738i	$-0.507281\pi$
$877$	729.217	−	421.013i	0.831490	−	0.480061i	0.854363	+	0.519677i	$0.173948\pi$
$878$		0			0
$879$	286.642	−	496.478i	0.326100	−	0.564821i
$880$		0			0
$881$			24.6644i			0.0279959i	0.999902	+	0.0139980i	$0.00445584\pi$
$881$			24.6644i			0.0279959i	−0.999902	+	0.0139980i	$0.995544\pi$
$882$		0			0
$883$			1434.33i			1.62439i	0.583389	+	0.812193i	$0.301727\pi$
$883$			1434.33i			1.62439i	−0.583389	+	0.812193i	$0.698273\pi$
$884$		0			0
$885$	186.711	−	323.393i	0.210973	−	0.365416i
$886$		0			0
$887$	192.616	−	111.207i	0.217155	−	0.125374i	−0.387477	−	0.921879i	$-0.626653\pi$
$887$	192.616	−	111.207i	0.217155	−	0.125374i	0.604632	+	0.796505i	$0.293320\pi$
$888$		0			0
$889$	−345.191	+	948.101i	−0.388292	+	1.06648i
$890$		0			0
$891$	87.3859	−	50.4523i	0.0980762	−	0.0566243i
$892$		0			0
$893$	298.101	+	172.109i	0.333820	+	0.192731i
$894$		0			0
$895$		−	420.246i		−	0.469549i
$896$		0			0
$897$	27.1339			0.0302496
$898$		0			0
$899$	52.1019	−	90.2432i	0.0579554	−	0.100382i
$900$		0			0
$901$	1124.46	+	1947.63i	1.24802	+	2.16163i
$902$		0			0
$903$	55.1383	−	46.2568i	0.0610612	−	0.0512257i
$904$		0			0
$905$	433.307	+	750.510i	0.478793	+	0.829293i
$906$		0			0
$907$	130.244	+	75.1964i	0.143599	+	0.0829067i	0.570078	−	0.821591i	$-0.306913\pi$
$907$	130.244	+	75.1964i	0.143599	+	0.0829067i	−0.426479	+	0.904497i	$0.640246\pi$
$908$		0			0
$909$	299.357			0.329326
$910$		0			0
$911$	−661.735			−0.726383			−0.363192	−	0.931714i	$-0.618313\pi$
$911$	−661.735			−0.726383			−0.363192	+	0.931714i	$0.618313\pi$
$912$		0			0
$913$	1139.32	+	657.788i	1.24789	+	0.720469i
$914$		0			0
$915$	−718.039	−	1243.68i	−0.784743	−	1.35921i
$916$		0			0
$917$	−1737.21	+	306.133i	−1.89445	+	0.333842i
$918$		0			0
$919$	185.915	+	322.014i	0.202301	+	0.350396i	0.949269	−	0.314464i	$-0.101825\pi$
$919$	185.915	+	322.014i	0.202301	+	0.350396i	−0.746968	+	0.664860i	$0.768491\pi$
$920$		0			0
$921$	−4.03420	+	6.98744i	−0.00438024	+	0.00758680i
$922$		0			0
$923$	971.356			1.05239
$924$		0			0
$925$		−	656.159i		−	0.709361i
$926$		0			0
$927$	376.110	+	217.147i	0.405728	+	0.234247i
$928$		0			0
$929$	1452.82	−	838.787i	1.56386	−	0.902892i	0.566994	−	0.823722i	$-0.308106\pi$
$929$	1452.82	−	838.787i	1.56386	−	0.902892i	0.996861	−	0.0791705i	$-0.0252271\pi$
$930$		0			0
$931$	116.145	−	657.900i	0.124753	−	0.706659i
$932$		0			0
$933$	479.371	−	276.765i	0.513795	−	0.296640i
$934$		0			0
$935$	−1643.70	+	2846.97i	−1.75797	+	3.04489i
$936$		0			0
$937$		−	1609.04i		−	1.71723i	−0.512623	−	0.858614i	$-0.671326\pi$
$937$		−	1609.04i		−	1.71723i	0.512623	−	0.858614i	$-0.328674\pi$
$938$		0			0
$939$			745.334i			0.793753i
$940$		0			0
$941$	443.422	−	768.030i	0.471224	−	0.816185i	−0.528234	−	0.849099i	$-0.677146\pi$
$941$	443.422	−	768.030i	0.471224	−	0.816185i	0.999458	+	0.0329144i	$0.0104789\pi$
$942$		0			0
$943$	−0.566157	+	0.326871i	−0.000600379	+	0.000346629i
$944$		0			0
$945$	−310.358	+	54.6915i	−0.328421	+	0.0578746i
$946$		0			0
$947$	1169.78	−	675.375i	1.23525	−	0.713173i	0.267132	−	0.963660i	$-0.413924\pi$
$947$	1169.78	−	675.375i	1.23525	−	0.713173i	0.968120	+	0.250487i	$0.0805907\pi$
$948$		0			0
$949$	440.024	+	254.048i	0.463672	+	0.267701i
$950$		0			0
$951$		−	69.9304i		−	0.0735335i
$952$		0			0
$953$	−630.482			−0.661576			−0.330788	−	0.943705i	$-0.607315\pi$
$953$	−630.482			−0.661576			−0.330788	+	0.943705i	$0.607315\pi$
$954$		0			0
$955$	−283.095	+	490.335i	−0.296434	+	0.513439i
$956$		0			0
$957$	−126.746	−	219.531i	−0.132441	−	0.229395i
$958$		0			0
$959$	834.752	+	995.027i	0.870440	+	1.03757i
$960$		0			0
$961$	−448.639	−	777.065i	−0.466846	−	0.808600i
$962$		0			0
$963$	106.699	+	61.6027i	0.110799	+	0.0639696i
$964$		0			0
$965$	852.979			0.883916
$966$		0			0
$967$	−810.364			−0.838018			−0.419009	−	0.907982i	$-0.637623\pi$
$967$	−810.364			−0.838018			−0.419009	+	0.907982i	$0.637623\pi$
$968$		0			0
$969$	692.118	+	399.595i	0.714261	+	0.412379i
$970$		0			0
$971$	281.062	+	486.813i	0.289456	+	0.501352i	0.973680	−	0.227919i	$-0.0731923\pi$
$971$	281.062	+	486.813i	0.289456	+	0.501352i	−0.684224	+	0.729272i	$0.739859\pi$
$972$		0			0
$973$	424.253	−	1165.25i	0.436026	−	1.19759i
$974$		0			0
$975$	−680.630	−	1178.89i	−0.698082	−	1.20911i
$976$		0			0
$977$	−68.7246	+	119.035i	−0.0703425	+	0.121837i	−0.899051	−	0.437843i	$-0.855743\pi$
$977$	−68.7246	+	119.035i	−0.0703425	+	0.121837i	0.828709	+	0.559680i	$0.189076\pi$
$978$		0			0
$979$	1310.80			1.33892
$980$		0			0
$981$			398.258i			0.405971i
$982$		0			0
$983$	−533.162	−	307.821i	−0.542382	−	0.313145i	0.203662	−	0.979041i	$-0.434716\pi$
$983$	−533.162	−	307.821i	−0.542382	−	0.313145i	−0.746044	+	0.665897i	$0.768049\pi$
$984$		0			0
$985$	588.882	−	339.991i	0.597850	−	0.345169i
$986$		0			0
$987$	287.629	+	104.722i	0.291417	+	0.106101i
$988$		0			0
$989$	−5.13042	+	2.96205i	−0.00518748	+	0.00299499i
$990$		0			0
$991$	45.9802	−	79.6401i	0.0463978	−	0.0803634i	−0.841894	−	0.539643i	$-0.818559\pi$
$991$	45.9802	−	79.6401i	0.0463978	−	0.0803634i	0.888292	+	0.459280i	$0.151892\pi$
$992$		0			0
$993$		−	379.144i		−	0.381817i
$994$		0			0
$995$		−	896.196i		−	0.900700i
$996$		0			0
$997$	−199.505	+	345.553i	−0.200105	+	0.346593i	−0.948562	−	0.316591i	$-0.897462\pi$
$997$	−199.505	+	345.553i	−0.200105	+	0.346593i	0.748457	+	0.663184i	$0.230795\pi$
$998$		0			0
$999$	58.9757	−	34.0496i	0.0590348	−	0.0340837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bf.b.241.16		60
4.3	odd	2		168.3.x.b.157.28	yes	60
7.5	odd	6	inner	672.3.bf.b.145.15		60
8.3	odd	2		168.3.x.b.157.7	yes	60
8.5	even	2	inner	672.3.bf.b.241.15		60
28.19	even	6		168.3.x.b.61.7	✓	60
56.5	odd	6	inner	672.3.bf.b.145.16		60
56.19	even	6		168.3.x.b.61.28	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.x.b.61.7	✓	60	28.19	even	6
168.3.x.b.61.28	yes	60	56.19	even	6
168.3.x.b.157.7	yes	60	8.3	odd	2
168.3.x.b.157.28	yes	60	4.3	odd	2
672.3.bf.b.145.15		60	7.5	odd	6	inner
672.3.bf.b.145.16		60	56.5	odd	6	inner
672.3.bf.b.241.15		60	8.5	even	2	inner
672.3.bf.b.241.16		60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(-4.33205 - 7.50333i) q^{5} +(-2.39482 + 6.57760i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 1.50000i) q^{3} +(-4.33205 - 7.50333i) q^{5} +(-2.39482 + 6.57760i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-9.70954 - 5.60581i) q^{11} -15.6975 q^{13} -15.0067 q^{15} +(29.3084 + 16.9212i) q^{17} +(6.81708 + 11.8075i) q^{19} +(7.79243 + 9.28860i) q^{21} +(-0.498987 - 0.864271i) q^{23} +(-25.0333 + 43.3590i) q^{25} -5.19615 q^{27} +13.0538i q^{29} +(-6.91318 - 3.99133i) q^{31} +(-16.8174 + 9.70954i) q^{33} +(59.7284 - 10.5254i) q^{35} +(-11.3499 + 6.55286i) q^{37} +(-13.5945 + 23.5463i) q^{39} -0.655069i q^{41} -5.93612i q^{43} +(-12.9962 + 22.5100i) q^{45} +(21.8643 - 12.6233i) q^{47} +(-37.5297 - 31.5043i) q^{49} +(50.7636 - 29.3084i) q^{51} +(57.5500 + 33.2265i) q^{53} +97.1385i q^{55} +23.6150 q^{57} +(-12.4419 + 21.5500i) q^{59} +(47.8480 + 82.8752i) q^{61} +(20.6813 - 3.64448i) q^{63} +(68.0026 + 117.784i) q^{65} +(-29.6779 - 17.1345i) q^{67} -1.72854 q^{69} -61.8795 q^{71} +(-28.0314 - 16.1839i) q^{73} +(43.3590 + 75.1000i) q^{75} +(60.1254 - 50.4406i) q^{77} +(23.6567 + 40.9746i) q^{79} +(-4.50000 + 7.79423i) q^{81} -117.340 q^{83} -293.214i q^{85} +(19.5807 + 11.3049i) q^{87} +(-101.251 + 58.4574i) q^{89} +(37.5928 - 103.252i) q^{91} +(-11.9740 + 6.91318i) q^{93} +(59.0638 - 102.302i) q^{95} +48.9751i q^{97} +33.6348i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 26 q^{7} - 90 q^{9}+O(q^{10}) \) 60 * q - 26 * q^7 - 90 * q^9	\( 60 q - 26 q^{7} - 90 q^{9} - 12 q^{15} - 36 q^{17} + 28 q^{23} - 204 q^{25} - 18 q^{31} - 30 q^{33} + 36 q^{39} - 828 q^{47} - 126 q^{49} - 312 q^{57} + 12 q^{63} + 36 q^{65} - 760 q^{71} - 648 q^{73} - 114 q^{79} - 270 q^{81} + 174 q^{87} - 72 q^{89} + 492 q^{95}+O(q^{100}) \) 60 * q - 26 * q^7 - 90 * q^9 - 12 * q^15 - 36 * q^17 + 28 * q^23 - 204 * q^25 - 18 * q^31 - 30 * q^33 + 36 * q^39 - 828 * q^47 - 126 * q^49 - 312 * q^57 + 12 * q^63 + 36 * q^65 - 760 * q^71 - 648 * q^73 - 114 * q^79 - 270 * q^81 + 174 * q^87 - 72 * q^89 + 492 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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