LMFDB - Embedded newform 684.3.g.c.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:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78242 - 0.907175i) q^{2} +(2.35407 + 3.23394i) q^{4} +3.42194 q^{5} +1.09734i q^{7} +(-1.26219 - 7.89980i) q^{8} +O(q^{10})$	\(q+(-1.78242 - 0.907175i) q^{2} +(2.35407 + 3.23394i) q^{4} +3.42194 q^{5} +1.09734i q^{7} +(-1.26219 - 7.89980i) q^{8} +(-6.09935 - 3.10430i) q^{10} -15.1885i q^{11} -3.52450 q^{13} +(0.995475 - 1.95592i) q^{14} +(-4.91674 + 15.2258i) q^{16} -12.8708 q^{17} -4.35890i q^{19} +(8.05549 + 11.0664i) q^{20} +(-13.7786 + 27.0723i) q^{22} +4.00522i q^{23} -13.2903 q^{25} +(6.28215 + 3.19734i) q^{26} +(-3.54872 + 2.58320i) q^{28} -42.9404 q^{29} -36.9996i q^{31} +(22.5762 - 22.6785i) q^{32} +(22.9412 + 11.6760i) q^{34} +3.75502i q^{35} +56.3720 q^{37} +(-3.95428 + 7.76940i) q^{38} +(-4.31915 - 27.0327i) q^{40} +1.67907 q^{41} +5.06487i q^{43} +(49.1187 - 35.7547i) q^{44} +(3.63343 - 7.13899i) q^{46} -32.3170i q^{47} +47.7959 q^{49} +(23.6889 + 12.0566i) q^{50} +(-8.29690 - 11.3980i) q^{52} -69.3744 q^{53} -51.9742i q^{55} +(8.66873 - 1.38505i) q^{56} +(76.5379 + 38.9544i) q^{58} -32.2677i q^{59} -68.1965 q^{61} +(-33.5651 + 65.9490i) q^{62} +(-60.8137 + 19.9421i) q^{64} -12.0606 q^{65} -52.6766i q^{67} +(-30.2987 - 41.6233i) q^{68} +(3.40646 - 6.69304i) q^{70} +3.42161i q^{71} +29.6657 q^{73} +(-100.479 - 51.1393i) q^{74} +(14.0964 - 10.2611i) q^{76} +16.6669 q^{77} -68.4637i q^{79} +(-16.8248 + 52.1019i) q^{80} +(-2.99282 - 1.52321i) q^{82} +51.1729i q^{83} -44.0431 q^{85} +(4.59473 - 9.02775i) q^{86} +(-119.986 + 19.1708i) q^{88} -1.78749 q^{89} -3.86756i q^{91} +(-12.9526 + 9.42855i) q^{92} +(-29.3172 + 57.6025i) q^{94} -14.9159i q^{95} -114.257 q^{97} +(-85.1925 - 43.3592i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8	$ 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8} + 8 q^{10} - 24 q^{13} + 12 q^{14} + 4 q^{16} + 40 q^{17} + 80 q^{20} + 12 q^{22} + 284 q^{25} + 112 q^{26} - 48 q^{28} - 104 q^{29} - 44 q^{32} + 140 q^{34} - 184 q^{37} + 180 q^{40} + 200 q^{41} - 96 q^{44} - 28 q^{46} - 332 q^{49} - 176 q^{50} + 276 q^{52} - 264 q^{53} + 192 q^{56} - 184 q^{58} + 40 q^{61} + 240 q^{62} - 372 q^{64} - 176 q^{65} + 104 q^{68} - 60 q^{70} + 424 q^{73} + 104 q^{74} + 400 q^{77} - 704 q^{80} + 528 q^{82} - 128 q^{85} - 668 q^{86} - 496 q^{88} + 520 q^{89} + 456 q^{92} - 32 q^{94} - 440 q^{97} + 472 q^{98}+O(q^{100}) $ 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8 + 8 * q^10 - 24 * q^13 + 12 * q^14 + 4 * q^16 + 40 * q^17 + 80 * q^20 + 12 * q^22 + 284 * q^25 + 112 * q^26 - 48 * q^28 - 104 * q^29 - 44 * q^32 + 140 * q^34 - 184 * q^37 + 180 * q^40 + 200 * q^41 - 96 * q^44 - 28 * q^46 - 332 * q^49 - 176 * q^50 + 276 * q^52 - 264 * q^53 + 192 * q^56 - 184 * q^58 + 40 * q^61 + 240 * q^62 - 372 * q^64 - 176 * q^65 + 104 * q^68 - 60 * q^70 + 424 * q^73 + 104 * q^74 + 400 * q^77 - 704 * q^80 + 528 * q^82 - 128 * q^85 - 668 * q^86 - 496 * q^88 + 520 * q^89 + 456 * q^92 - 32 * q^94 - 440 * q^97 + 472 * q^98

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 $

$2$	−1.78242	−	0.907175i	−0.891212	−	0.453588i
$2$	−1.78242	−	0.907175i	−0.891212	−	0.453588i
$3$		0			0
$3$		0			0
$4$	2.35407	+	3.23394i	0.588517	+	0.808485i
$5$	3.42194			0.684389			0.342194	−	0.939629i	$-0.388830\pi$
$5$	3.42194			0.684389			0.342194	+	0.939629i	$0.388830\pi$
$6$		0			0
$7$			1.09734i			0.156762i	0.996923	+	0.0783811i	$0.0249751\pi$
$7$			1.09734i			0.156762i	−0.996923	+	0.0783811i	$0.975025\pi$
$8$	−1.26219	−	7.89980i	−0.157774	−	0.987475i
$9$		0			0
$10$	−6.09935	−	3.10430i	−0.609935	−	0.310430i
$11$		−	15.1885i		−	1.38077i	−0.723442	−	0.690386i	$-0.757441\pi$
$11$		−	15.1885i		−	1.38077i	0.723442	−	0.690386i	$-0.242559\pi$
$12$		0			0
$13$	−3.52450			−0.271115			−0.135558	−	0.990769i	$-0.543283\pi$
$13$	−3.52450			−0.271115			−0.135558	+	0.990769i	$0.543283\pi$
$14$	0.995475	−	1.95592i	0.0711054	−	0.139708i
$15$		0			0
$16$	−4.91674	+	15.2258i	−0.307296	+	0.951614i
$17$	−12.8708			−0.757104			−0.378552	−	0.925580i	$-0.623578\pi$
$17$	−12.8708			−0.757104			−0.378552	+	0.925580i	$0.623578\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	8.05549	+	11.0664i	0.402774	+	0.553318i
$21$		0			0
$22$	−13.7786	+	27.0723i	−0.626301	+	1.23056i
$23$			4.00522i			0.174140i	0.996202	+	0.0870699i	$0.0277504\pi$
$23$			4.00522i			0.174140i	−0.996202	+	0.0870699i	$0.972250\pi$
$24$		0			0
$25$	−13.2903			−0.531612
$26$	6.28215	+	3.19734i	0.241621	+	0.122974i
$27$		0			0
$28$	−3.54872	+	2.58320i	−0.126740	+	0.0922572i
$29$	−42.9404			−1.48070			−0.740351	−	0.672220i	$-0.765341\pi$
$29$	−42.9404			−1.48070			−0.740351	+	0.672220i	$0.765341\pi$
$30$		0			0
$31$		−	36.9996i		−	1.19354i	−0.802414	−	0.596768i	$-0.796451\pi$
$31$		−	36.9996i		−	1.19354i	0.802414	−	0.596768i	$-0.203549\pi$
$32$	22.5762	−	22.6785i	0.705506	−	0.708704i
$33$		0			0
$34$	22.9412	+	11.6760i	0.674740	+	0.343413i
$35$			3.75502i			0.107286i
$36$		0			0
$37$	56.3720			1.52357			0.761784	−	0.647831i	$-0.224324\pi$
$37$	56.3720			1.52357			0.761784	+	0.647831i	$0.224324\pi$
$38$	−3.95428	+	7.76940i	−0.104060	+	0.204458i
$39$		0			0
$40$	−4.31915	−	27.0327i	−0.107979	−	0.675817i
$41$	1.67907			0.0409530			0.0204765	−	0.999790i	$-0.493482\pi$
$41$	1.67907			0.0409530			0.0204765	+	0.999790i	$0.493482\pi$
$42$		0			0
$43$			5.06487i			0.117788i	0.998264	+	0.0588939i	$0.0187574\pi$
$43$			5.06487i			0.117788i	−0.998264	+	0.0588939i	$0.981243\pi$
$44$	49.1187	−	35.7547i	1.11633	−	0.812607i
$45$		0			0
$46$	3.63343	−	7.13899i	0.0789877	−	0.155195i
$47$		−	32.3170i		−	0.687595i	−0.939044	−	0.343798i	$-0.888287\pi$
$47$		−	32.3170i		−	0.687595i	0.939044	−	0.343798i	$-0.111713\pi$
$48$		0			0
$49$	47.7959			0.975426
$50$	23.6889	+	12.0566i	0.473779	+	0.241132i
$51$		0			0
$52$	−8.29690	−	11.3980i	−0.159556	−	0.219193i
$53$	−69.3744			−1.30895			−0.654475	−	0.756083i	$-0.727110\pi$
$53$	−69.3744			−1.30895			−0.654475	+	0.756083i	$0.727110\pi$
$54$		0			0
$55$		−	51.9742i		−	0.944985i
$56$	8.66873	−	1.38505i	0.154799	−	0.0247330i
$57$		0			0
$58$	76.5379	+	38.9544i	1.31962	+	0.671628i
$59$		−	32.2677i		−	0.546910i	−0.961885	−	0.273455i	$-0.911834\pi$
$59$		−	32.2677i		−	0.546910i	0.961885	−	0.273455i	$-0.0881665\pi$
$60$		0			0
$61$	−68.1965			−1.11798			−0.558988	−	0.829176i	$-0.688810\pi$
$61$	−68.1965			−1.11798			−0.558988	+	0.829176i	$0.688810\pi$
$62$	−33.5651	+	65.9490i	−0.541373	+	1.06369i
$63$		0			0
$64$	−60.8137	+	19.9421i	−0.950215	+	0.311596i
$65$	−12.0606			−0.185548
$66$		0			0
$67$		−	52.6766i		−	0.786219i	−0.919492	−	0.393109i	$-0.871399\pi$
$67$		−	52.6766i		−	0.786219i	0.919492	−	0.393109i	$-0.128601\pi$
$68$	−30.2987	−	41.6233i	−0.445568	−	0.612107i
$69$		0			0
$70$	3.40646	−	6.69304i	0.0486637	−	0.0956148i
$71$			3.42161i			0.0481917i	0.999710	+	0.0240959i	$0.00767069\pi$
$71$			3.42161i			0.0481917i	−0.999710	+	0.0240959i	$0.992329\pi$
$72$		0			0
$73$	29.6657			0.406380			0.203190	−	0.979139i	$-0.434869\pi$
$73$	29.6657			0.406380			0.203190	+	0.979139i	$0.434869\pi$
$74$	−100.479	−	51.1393i	−1.35782	−	0.691072i
$75$		0			0
$76$	14.0964	−	10.2611i	0.185479	−	0.135015i
$77$	16.6669			0.216453
$78$		0			0
$79$		−	68.4637i		−	0.866629i	−0.901243	−	0.433314i	$-0.857344\pi$
$79$		−	68.4637i		−	0.866629i	0.901243	−	0.433314i	$-0.142656\pi$
$80$	−16.8248	+	52.1019i	−0.210310	+	0.651274i
$81$		0			0
$82$	−2.99282	−	1.52321i	−0.0364978	−	0.0185758i
$83$			51.1729i			0.616541i	0.951299	+	0.308270i	$0.0997502\pi$
$83$			51.1729i			0.616541i	−0.951299	+	0.308270i	$0.900250\pi$
$84$		0			0
$85$	−44.0431			−0.518154
$86$	4.59473	−	9.02775i	0.0534270	−	0.104974i
$87$		0			0
$88$	−119.986	+	19.1708i	−1.36348	+	0.217850i
$89$	−1.78749			−0.0200841			−0.0100421	−	0.999950i	$-0.503197\pi$
$89$	−1.78749			−0.0200841			−0.0100421	+	0.999950i	$0.503197\pi$
$90$		0			0
$91$		−	3.86756i		−	0.0425006i
$92$	−12.9526	+	9.42855i	−0.140789	+	0.102484i
$93$		0			0
$94$	−29.3172	+	57.6025i	−0.311885	+	0.612793i
$95$		−	14.9159i		−	0.157010i
$96$		0			0
$97$	−114.257			−1.17790			−0.588952	−	0.808168i	$-0.700459\pi$
$97$	−114.257			−1.17790			−0.588952	+	0.808168i	$0.700459\pi$
$98$	−85.1925	−	43.3592i	−0.869311	−	0.442441i
$99$		0			0
$100$	−31.2862	−	42.9800i	−0.312862	−	0.429800i
$101$	−142.326			−1.40917			−0.704583	−	0.709622i	$-0.748866\pi$
$101$	−142.326			−1.40917			−0.704583	+	0.709622i	$0.748866\pi$
$102$		0			0
$103$		−	56.5941i		−	0.549457i	−0.961522	−	0.274729i	$-0.911412\pi$
$103$		−	56.5941i		−	0.549457i	0.961522	−	0.274729i	$-0.0885880\pi$
$104$	4.44860	+	27.8428i	0.0427750	+	0.267719i
$105$		0			0
$106$	123.655	+	62.9347i	1.16655	+	0.593724i
$107$		−	190.866i		−	1.78380i	−0.452237	−	0.891898i	$-0.649374\pi$
$107$		−	190.866i		−	1.78380i	0.452237	−	0.891898i	$-0.350626\pi$
$108$		0			0
$109$	−136.983			−1.25672			−0.628361	−	0.777922i	$-0.716274\pi$
$109$	−136.983			−1.25672			−0.628361	+	0.777922i	$0.716274\pi$
$110$	−47.1497	+	92.6400i	−0.428633	+	0.842181i
$111$		0			0
$112$	−16.7078	−	5.39531i	−0.149177	−	0.0481724i
$113$	63.0026			0.557545			0.278773	−	0.960357i	$-0.410072\pi$
$113$	63.0026			0.557545			0.278773	+	0.960357i	$0.410072\pi$
$114$		0			0
$115$			13.7056i			0.119179i
$116$	−101.085	−	138.867i	−0.871418	−	1.19713i
$117$		0			0
$118$	−29.2724	+	57.5147i	−0.248072	+	0.487413i
$119$		−	14.1236i		−	0.118685i
$120$		0			0
$121$	−109.690			−0.906529
$122$	121.555	+	61.8662i	0.996353	+	0.507100i
$123$		0			0
$124$	119.655	−	87.0996i	0.964956	−	0.702416i
$125$	−131.027			−1.04822
$126$		0			0
$127$		−	131.614i		−	1.03633i	−0.855280	−	0.518166i	$-0.826615\pi$
$127$		−	131.614i		−	1.03633i	0.855280	−	0.518166i	$-0.173385\pi$
$128$	126.487	+	19.6234i	0.988179	+	0.153307i
$129$		0			0
$130$	21.4972	+	10.9411i	0.165363	+	0.0841624i
$131$			126.299i			0.964113i	0.876140	+	0.482056i	$0.160110\pi$
$131$			126.299i			0.964113i	−0.876140	+	0.482056i	$0.839890\pi$
$132$		0			0
$133$	4.78317			0.0359637
$134$	−47.7869	+	93.8921i	−0.356619	+	0.700687i
$135$		0			0
$136$	16.2454	+	101.677i	0.119451	+	0.747622i
$137$	206.449			1.50693			0.753465	−	0.657488i	$-0.228381\pi$
$137$	206.449			1.50693			0.753465	+	0.657488i	$0.228381\pi$
$138$		0			0
$139$		−	169.116i		−	1.21666i	−0.793684	−	0.608330i	$-0.791840\pi$
$139$		−	169.116i		−	1.21666i	0.793684	−	0.608330i	$-0.208160\pi$
$140$	−12.1435	+	8.83957i	−0.0867394	+	0.0631398i
$141$		0			0
$142$	3.10400	−	6.09876i	0.0218592	−	0.0429490i
$143$			53.5318i			0.374348i
$144$		0			0
$145$	−146.940			−1.01338
$146$	−52.8769	−	26.9120i	−0.362170	−	0.184329i
$147$		0			0
$148$	132.703	+	182.304i	0.896645	+	1.23178i
$149$	16.2018			0.108737			0.0543685	−	0.998521i	$-0.482685\pi$
$149$	16.2018			0.108737			0.0543685	+	0.998521i	$0.482685\pi$
$150$		0			0
$151$			228.478i			1.51310i	0.653935	+	0.756551i	$0.273117\pi$
$151$			228.478i			1.51310i	−0.653935	+	0.756551i	$0.726883\pi$
$152$	−34.4344	+	5.50177i	−0.226542	+	0.0361959i
$153$		0			0
$154$	−29.7074	−	15.1198i	−0.192905	−	0.0981803i
$155$		−	126.611i		−	0.816843i
$156$		0			0
$157$	21.5361			0.137173			0.0685863	−	0.997645i	$-0.478151\pi$
$157$	21.5361			0.137173			0.0685863	+	0.997645i	$0.478151\pi$
$158$	−62.1085	+	122.031i	−0.393092	+	0.772350i
$159$		0			0
$160$	77.2545	−	77.6046i	0.482841	−	0.485029i
$161$	−4.39507			−0.0272985
$162$		0			0
$163$			167.384i			1.02689i	0.858121	+	0.513447i	$0.171632\pi$
$163$			167.384i			1.02689i	−0.858121	+	0.513447i	$0.828368\pi$
$164$	3.95265	+	5.43003i	0.0241015	+	0.0331099i
$165$		0			0
$166$	46.4228	−	91.2118i	0.279655	−	0.549468i
$167$		−	2.31649i		−	0.0138712i	−0.999976	−	0.00693560i	$-0.997792\pi$
$167$		−	2.31649i		−	0.0138712i	0.999976	−	0.00693560i	$-0.00220769\pi$
$168$		0			0
$169$	−156.578			−0.926497
$170$	78.5034	+	39.9548i	0.461785	+	0.235028i
$171$		0			0
$172$	−16.3795	+	11.9230i	−0.0952296	+	0.0693200i
$173$	103.387			0.597612			0.298806	−	0.954314i	$-0.403412\pi$
$173$	103.387			0.597612			0.298806	+	0.954314i	$0.403412\pi$
$174$		0			0
$175$		−	14.5839i		−	0.0833366i
$176$	231.257	+	74.6778i	1.31396	+	0.424306i
$177$		0			0
$178$	3.18606	+	1.62156i	0.0178992	+	0.00910990i
$179$		−	261.074i		−	1.45851i	−0.684240	−	0.729257i	$-0.739866\pi$
$179$		−	261.074i		−	1.45851i	0.684240	−	0.729257i	$-0.260134\pi$
$180$		0			0
$181$	41.3242			0.228310			0.114155	−	0.993463i	$-0.463584\pi$
$181$	41.3242			0.228310			0.114155	+	0.993463i	$0.463584\pi$
$182$	−3.50855	+	6.89362i	−0.0192777	+	0.0378770i
$183$		0			0
$184$	31.6404	−	5.05536i	0.171959	−	0.0274748i
$185$	192.902			1.04271
$186$		0			0
$187$			195.488i			1.04539i
$188$	104.511	−	76.0763i	0.555910	−	0.404661i
$189$		0			0
$190$	−13.5313	+	26.5865i	−0.0712176	+	0.139929i
$191$		−	204.518i		−	1.07077i	−0.844607	−	0.535387i	$-0.820166\pi$
$191$		−	204.518i		−	1.07077i	0.844607	−	0.535387i	$-0.179834\pi$
$192$		0			0
$193$	74.7204			0.387152			0.193576	−	0.981085i	$-0.437991\pi$
$193$	74.7204			0.387152			0.193576	+	0.981085i	$0.437991\pi$
$194$	203.654	+	103.651i	1.04976	+	0.534282i
$195$		0			0
$196$	112.515	+	154.569i	0.574054	+	0.788617i
$197$	241.437			1.22557			0.612784	−	0.790250i	$-0.290049\pi$
$197$	241.437			1.22557			0.612784	+	0.790250i	$0.290049\pi$
$198$		0			0
$199$		−	41.2820i		−	0.207447i	−0.994606	−	0.103724i	$-0.966924\pi$
$199$		−	41.2820i		−	0.207447i	0.994606	−	0.103724i	$-0.0330758\pi$
$200$	16.7749	+	104.991i	0.0838746	+	0.524953i
$201$		0			0
$202$	253.685	+	129.114i	1.25586	+	0.639180i
$203$		−	47.1200i		−	0.232118i
$204$		0			0
$205$	5.74570			0.0280278
$206$	−51.3408	+	100.875i	−0.249227	+	0.489683i
$207$		0			0
$208$	17.3290	−	53.6634i	0.0833127	−	0.257997i
$209$	−66.2051			−0.316771
$210$		0			0
$211$		−	15.2564i		−	0.0723051i	−0.999346	−	0.0361526i	$-0.988490\pi$
$211$		−	15.2564i		−	0.0723051i	0.999346	−	0.0361526i	$-0.0115102\pi$
$212$	−163.312	−	224.353i	−0.770339	−	1.05827i
$213$		0			0
$214$	−173.149	+	340.204i	−0.809108	+	1.58974i
$215$			17.3317i			0.0806126i
$216$		0			0
$217$	40.6010			0.187101
$218$	244.161	+	124.267i	1.12001	+	0.570034i
$219$		0			0
$220$	168.081	−	122.351i	0.764006	−	0.556139i
$221$	45.3630			0.205262
$222$		0			0
$223$		−	376.770i		−	1.68955i	−0.535119	−	0.844776i	$-0.679733\pi$
$223$		−	376.770i		−	1.68955i	0.535119	−	0.844776i	$-0.320267\pi$
$224$	24.8859	+	24.7737i	0.111098	+	0.110597i
$225$		0			0
$226$	−112.297	−	57.1544i	−0.496891	−	0.252896i
$227$		−	10.7868i		−	0.0475191i	−0.999718	−	0.0237596i	$-0.992436\pi$
$227$		−	10.7868i		−	0.0475191i	0.999718	−	0.0237596i	$-0.00756362\pi$
$228$		0			0
$229$	409.128			1.78659			0.893293	−	0.449475i	$-0.148389\pi$
$229$	409.128			1.78659			0.893293	+	0.449475i	$0.148389\pi$
$230$	12.4334	−	24.4292i	0.0540583	−	0.106214i
$231$		0			0
$232$	54.1990	+	339.220i	0.233617	+	1.46216i
$233$	−136.723			−0.586792			−0.293396	−	0.955991i	$-0.594785\pi$
$233$	−136.723			−0.586792			−0.293396	+	0.955991i	$0.594785\pi$
$234$		0			0
$235$		−	110.587i		−	0.470582i
$236$	104.352	−	75.9603i	0.442169	−	0.321866i
$237$		0			0
$238$	−12.8125	+	25.1742i	−0.0538342	+	0.105774i
$239$			252.663i			1.05717i	0.848882	+	0.528583i	$0.177276\pi$
$239$			252.663i			1.05717i	−0.848882	+	0.528583i	$0.822724\pi$
$240$		0			0
$241$	352.816			1.46397			0.731983	−	0.681323i	$-0.238595\pi$
$241$	352.816			1.46397			0.731983	+	0.681323i	$0.238595\pi$
$242$	195.514	+	99.5081i	0.807910	+	0.411190i
$243$		0			0
$244$	−160.539	−	220.543i	−0.657947	−	0.903866i
$245$	163.555			0.667571
$246$		0			0
$247$			15.3629i			0.0621981i
$248$	−292.290	+	46.7007i	−1.17859	+	0.188309i
$249$		0			0
$250$	233.546	+	118.865i	0.934184	+	0.475459i
$251$			456.020i			1.81681i	0.418089	+	0.908406i	$0.362700\pi$
$251$			456.020i			1.81681i	−0.418089	+	0.908406i	$0.637300\pi$
$252$		0			0
$253$	60.8332			0.240447
$254$	−119.397	+	234.592i	−0.470067	+	0.923591i
$255$		0			0
$256$	−207.651	−	149.723i	−0.811138	−	0.584855i
$257$	466.591			1.81553			0.907764	−	0.419480i	$-0.137788\pi$
$257$	466.591			1.81553			0.907764	+	0.419480i	$0.137788\pi$
$258$		0			0
$259$			61.8590i			0.238838i
$260$	−28.3915	−	39.0034i	−0.109198	−	0.150013i
$261$		0			0
$262$	114.575	−	225.118i	0.437310	−	0.859229i
$263$			254.295i			0.966901i	0.875372	+	0.483450i	$0.160617\pi$
$263$			254.295i			0.966901i	−0.875372	+	0.483450i	$0.839383\pi$
$264$		0			0
$265$	−237.395			−0.895832
$266$	−8.52564	−	4.33918i	−0.0320513	−	0.0163127i
$267$		0			0
$268$	170.353	−	124.004i	0.635646	−	0.462703i
$269$	−361.778			−1.34490			−0.672451	−	0.740142i	$-0.734758\pi$
$269$	−361.778			−1.34490			−0.672451	+	0.740142i	$0.734758\pi$
$270$		0			0
$271$			110.301i			0.407016i	0.979073	+	0.203508i	$0.0652342\pi$
$271$			110.301i			0.407016i	−0.979073	+	0.203508i	$0.934766\pi$
$272$	63.2823	−	195.968i	0.232655	−	0.720471i
$273$		0			0
$274$	−367.980	−	187.286i	−1.34299	−	0.683525i
$275$			201.859i			0.734034i
$276$		0			0
$277$	395.836			1.42901			0.714505	−	0.699631i	$-0.246652\pi$
$277$	395.836			1.42901			0.714505	+	0.699631i	$0.246652\pi$
$278$	−153.418	+	301.436i	−0.551862	+	1.08430i
$279$		0			0
$280$	29.6639	−	4.73956i	0.105943	−	0.0169270i
$281$	−395.060			−1.40591			−0.702954	−	0.711235i	$-0.748136\pi$
$281$	−395.060			−1.40591			−0.702954	+	0.711235i	$0.748136\pi$
$282$		0			0
$283$		−	253.450i		−	0.895582i	−0.894138	−	0.447791i	$-0.852211\pi$
$283$		−	253.450i		−	0.895582i	0.894138	−	0.447791i	$-0.147789\pi$
$284$	−11.0653	+	8.05470i	−0.0389623	+	0.0283616i
$285$		0			0
$286$	48.5627	−	95.4163i	0.169800	−	0.333623i
$287$			1.84251i			0.00641989i
$288$		0			0
$289$	−123.343			−0.426793
$290$	261.909	+	133.300i	0.903133	+	0.459655i
$291$		0			0
$292$	69.8351	+	95.9372i	0.239161	+	0.328552i
$293$	−187.619			−0.640338			−0.320169	−	0.947360i	$-0.603740\pi$
$293$	−187.619			−0.640338			−0.320169	+	0.947360i	$0.603740\pi$
$294$		0			0
$295$		−	110.418i		−	0.374299i
$296$	−71.1524	−	445.328i	−0.240380	−	1.50449i
$297$		0			0
$298$	−28.8785	−	14.6979i	−0.0969076	−	0.0493217i
$299$		−	14.1164i		−	0.0472120i
$300$		0			0
$301$	−5.55786			−0.0184647
$302$	207.270	−	407.245i	0.686324	−	1.34849i
$303$		0			0
$304$	66.3678	+	21.4316i	0.218315	+	0.0704986i
$305$	−233.365			−0.765130
$306$		0			0
$307$		−	55.4720i		−	0.180691i	−0.995911	−	0.0903453i	$-0.971203\pi$
$307$		−	55.4720i		−	0.180691i	0.995911	−	0.0903453i	$-0.0287971\pi$
$308$	39.2349	+	53.8996i	0.127386	+	0.174999i
$309$		0			0
$310$	−114.858	+	225.674i	−0.370510	+	0.727980i
$311$			342.779i			1.10218i	0.834445	+	0.551091i	$0.185788\pi$
$311$			342.779i			1.10218i	−0.834445	+	0.551091i	$0.814212\pi$
$312$		0			0
$313$	227.749			0.727633			0.363817	−	0.931471i	$-0.381473\pi$
$313$	227.749			0.727633			0.363817	+	0.931471i	$0.381473\pi$
$314$	−38.3865	−	19.5370i	−0.122250	−	0.0622198i
$315$		0			0
$316$	221.407	−	161.168i	0.700656	−	0.510025i
$317$	182.998			0.577280			0.288640	−	0.957438i	$-0.406797\pi$
$317$	182.998			0.577280			0.288640	+	0.957438i	$0.406797\pi$
$318$		0			0
$319$			652.199i			2.04451i
$320$	−208.101	+	68.2409i	−0.650316	+	0.213253i
$321$		0			0
$322$	7.83387	+	3.98709i	0.0243288	+	0.0123823i
$323$			56.1024i			0.173692i
$324$		0			0
$325$	46.8416			0.144128
$326$	151.846	−	298.349i	0.465787	−	0.915180i
$327$		0			0
$328$	−2.11932	−	13.2644i	−0.00646133	−	0.0404401i
$329$	35.4626			0.107789
$330$		0			0
$331$		−	228.937i		−	0.691653i	−0.938298	−	0.345826i	$-0.887599\pi$
$331$		−	228.937i		−	0.691653i	0.938298	−	0.345826i	$-0.112401\pi$
$332$	−165.490	+	120.464i	−0.498464	+	0.362845i
$333$		0			0
$334$	−2.10146	+	4.12897i	−0.00629181	+	0.0123622i
$335$		−	180.257i		−	0.538079i
$336$		0			0
$337$	−301.984			−0.896095			−0.448048	−	0.894010i	$-0.647881\pi$
$337$	−301.984			−0.896095			−0.448048	+	0.894010i	$0.647881\pi$
$338$	279.088	+	142.044i	0.825705	+	0.420247i
$339$		0			0
$340$	−103.680	−	142.433i	−0.304942	−	0.418920i
$341$	−561.968			−1.64800
$342$		0			0
$343$			106.218i			0.309672i
$344$	40.0115	−	6.39285i	0.116312	−	0.0185839i
$345$		0			0
$346$	−184.279	−	93.7901i	−0.532599	−	0.271070i
$347$			45.9375i			0.132385i	0.997807	+	0.0661923i	$0.0210851\pi$
$347$			45.9375i			0.132385i	−0.997807	+	0.0661923i	$0.978915\pi$
$348$		0			0
$349$	310.999			0.891116			0.445558	−	0.895253i	$-0.353005\pi$
$349$	310.999			0.891116			0.445558	+	0.895253i	$0.353005\pi$
$350$	−13.2302	+	25.9947i	−0.0378005	+	0.0742706i
$351$		0			0
$352$	−344.452	−	342.898i	−0.978558	−	0.974143i
$353$	238.500			0.675637			0.337818	−	0.941211i	$-0.390311\pi$
$353$	238.500			0.675637			0.337818	+	0.941211i	$0.390311\pi$
$354$		0			0
$355$			11.7086i			0.0329819i
$356$	−4.20786	−	5.78062i	−0.0118198	−	0.0162377i
$357$		0			0
$358$	−236.840	+	465.344i	−0.661563	+	1.29984i
$359$			530.898i			1.47882i	0.673253	+	0.739412i	$0.264896\pi$
$359$			530.898i			1.47882i	−0.673253	+	0.739412i	$0.735104\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−73.6572	−	37.4883i	−0.203473	−	0.103559i
$363$		0			0
$364$	12.5074	−	9.10448i	0.0343611	−	0.0250123i
$365$	101.514			0.278122
$366$		0			0
$367$			338.362i			0.921968i	0.887408	+	0.460984i	$0.152504\pi$
$367$			338.362i			0.921968i	−0.887408	+	0.460984i	$0.847496\pi$
$368$	−60.9827	−	19.6926i	−0.165714	−	0.0535125i
$369$		0			0
$370$	−343.833	−	174.996i	−0.929278	−	0.472962i
$371$		−	76.1270i		−	0.205194i
$372$		0			0
$373$	108.938			0.292060			0.146030	−	0.989280i	$-0.453350\pi$
$373$	108.938			0.292060			0.146030	+	0.989280i	$0.453350\pi$
$374$	177.341	−	348.442i	0.474175	−	0.931662i
$375$		0			0
$376$	−255.298	+	40.7903i	−0.678983	+	0.108485i
$377$	151.343			0.401441
$378$		0			0
$379$			495.638i			1.30775i	0.756602	+	0.653876i	$0.226858\pi$
$379$			495.638i			1.30775i	−0.756602	+	0.653876i	$0.773142\pi$
$380$	48.2372	−	35.1130i	0.126940	−	0.0924028i
$381$		0			0
$382$	−185.533	+	364.537i	−0.485690	+	0.954286i
$383$		−	69.6825i		−	0.181939i	−0.995854	−	0.0909694i	$-0.971003\pi$
$383$		−	69.6825i		−	0.181939i	0.995854	−	0.0909694i	$-0.0289965\pi$
$384$		0			0
$385$	57.0331			0.148138
$386$	−133.183	−	67.7845i	−0.345035	−	0.175608i
$387$		0			0
$388$	−268.968	−	369.499i	−0.693216	−	0.952317i
$389$	−276.727			−0.711381			−0.355690	−	0.934604i	$-0.615754\pi$
$389$	−276.727			−0.711381			−0.355690	+	0.934604i	$0.615754\pi$
$390$		0			0
$391$		−	51.5502i		−	0.131842i
$392$	−60.3276	−	377.578i	−0.153897	−	0.963209i
$393$		0			0
$394$	−430.343	−	219.026i	−1.09224	−	0.555903i
$395$		−	234.279i		−	0.593111i
$396$		0			0
$397$	−455.070			−1.14627			−0.573136	−	0.819460i	$-0.694273\pi$
$397$	−455.070			−1.14627			−0.573136	+	0.819460i	$0.694273\pi$
$398$	−37.4500	+	73.5820i	−0.0940955	+	0.184880i
$399$		0			0
$400$	65.3449	−	202.356i	0.163362	−	0.505889i
$401$	38.5054			0.0960235			0.0480117	−	0.998847i	$-0.484712\pi$
$401$	38.5054			0.0960235			0.0480117	+	0.998847i	$0.484712\pi$
$402$		0			0
$403$			130.405i			0.323586i
$404$	−335.044	−	460.273i	−0.829317	−	1.13929i
$405$		0			0
$406$	−42.7461	+	83.9878i	−0.105286	+	0.206866i
$407$		−	856.205i		−	2.10370i
$408$		0			0
$409$	−423.191			−1.03470			−0.517348	−	0.855775i	$-0.673081\pi$
$409$	−423.191			−1.03470			−0.517348	+	0.855775i	$0.673081\pi$
$410$	−10.2413	−	5.21236i	−0.0249787	−	0.0127131i
$411$		0			0
$412$	183.022	−	133.226i	0.444228	−	0.323365i
$413$	35.4085			0.0857348
$414$		0			0
$415$			175.111i			0.421954i
$416$	−79.5698	+	79.9304i	−0.191273	+	0.192140i
$417$		0			0
$418$	118.005	+	60.0596i	0.282310	+	0.143683i
$419$		−	782.531i		−	1.86762i	−0.357775	−	0.933808i	$-0.616464\pi$
$419$		−	782.531i		−	1.86762i	0.357775	−	0.933808i	$-0.383536\pi$
$420$		0			0
$421$	735.211			1.74634			0.873172	−	0.487412i	$-0.162059\pi$
$421$	735.211			1.74634			0.873172	+	0.487412i	$0.162059\pi$
$422$	−13.8402	+	27.1933i	−0.0327967	+	0.0644392i
$423$		0			0
$424$	87.5639	+	548.044i	0.206519	+	1.29256i
$425$	171.056			0.402485
$426$		0			0
$427$		−	74.8344i		−	0.175256i
$428$	617.250	−	449.312i	1.44217	−	1.04979i
$429$		0			0
$430$	15.7229	−	30.8924i	0.0365649	−	0.0718429i
$431$		−	225.461i		−	0.523111i	−0.965188	−	0.261555i	$-0.915765\pi$
$431$		−	225.461i		−	0.523111i	0.965188	−	0.261555i	$-0.0842354\pi$
$432$		0			0
$433$	−213.659			−0.493438			−0.246719	−	0.969087i	$-0.579352\pi$
$433$	−213.659			−0.493438			−0.246719	+	0.969087i	$0.579352\pi$
$434$	−72.3682	−	36.8322i	−0.166747	−	0.0848669i
$435$		0			0
$436$	−322.467	−	442.994i	−0.739602	−	1.01604i
$437$	17.4583			0.0399504
$438$		0			0
$439$			641.592i			1.46149i	0.682653	+	0.730743i	$0.260826\pi$
$439$			641.592i			1.46149i	−0.682653	+	0.730743i	$0.739174\pi$
$440$	−410.586	+	65.6014i	−0.933149	+	0.149094i
$441$		0			0
$442$	−80.8561	−	41.1522i	−0.182932	−	0.0931045i
$443$			831.547i			1.87708i	0.345168	+	0.938541i	$0.387822\pi$
$443$			831.547i			1.87708i	−0.345168	+	0.938541i	$0.612178\pi$
$444$		0			0
$445$	−6.11668			−0.0137453
$446$	−341.797	+	671.564i	−0.766360	+	1.50575i
$447$		0			0
$448$	−21.8832	−	66.7331i	−0.0488465	−	0.148958i
$449$	222.733			0.496065			0.248032	−	0.968752i	$-0.420216\pi$
$449$	222.733			0.496065			0.248032	+	0.968752i	$0.420216\pi$
$450$		0			0
$451$		−	25.5026i		−	0.0565468i
$452$	148.312	+	203.747i	0.328125	+	0.450767i
$453$		0			0
$454$	−9.78555	+	19.2267i	−0.0215541	+	0.0423496i
$455$		−	13.2346i		−	0.0290869i
$456$		0			0
$457$	−625.280			−1.36823			−0.684114	−	0.729376i	$-0.739811\pi$
$457$	−625.280			−1.36823			−0.684114	+	0.729376i	$0.739811\pi$
$458$	−729.240	−	371.151i	−1.59223	−	0.810373i
$459$		0			0
$460$	−44.3232	+	32.2640i	−0.0963548	+	0.0701391i
$461$	38.6449			0.0838284			0.0419142	−	0.999121i	$-0.486654\pi$
$461$	38.6449			0.0838284			0.0419142	+	0.999121i	$0.486654\pi$
$462$		0			0
$463$		−	129.791i		−	0.280327i	−0.990128	−	0.140163i	$-0.955237\pi$
$463$		−	129.791i		−	0.280327i	0.990128	−	0.140163i	$-0.0447628\pi$
$464$	211.127	−	653.803i	0.455014	−	1.40906i
$465$		0			0
$466$	243.698	+	124.031i	0.522956	+	0.266162i
$467$		−	560.733i		−	1.20071i	−0.799732	−	0.600357i	$-0.795025\pi$
$467$		−	560.733i		−	1.20071i	0.799732	−	0.600357i	$-0.204975\pi$
$468$		0			0
$469$	57.8039			0.123249
$470$	−100.322	+	197.113i	−0.213450	+	0.419389i
$471$		0			0
$472$	−254.908	+	40.7281i	−0.540060	+	0.0862883i
$473$	76.9277			0.162638
$474$		0			0
$475$			57.9310i			0.121960i
$476$	45.6747	−	33.2478i	0.0959553	−	0.0698483i
$477$		0			0
$478$	229.209	−	450.352i	0.479517	−	0.942158i
$479$			216.834i			0.452681i	0.974048	+	0.226341i	$0.0726763\pi$
$479$			216.834i			0.452681i	−0.974048	+	0.226341i	$0.927324\pi$
$480$		0			0
$481$	−198.683			−0.413062
$482$	−628.867	−	320.066i	−1.30470	−	0.664037i
$483$		0			0
$484$	−258.218	−	354.731i	−0.533508	−	0.732915i
$485$	−390.980			−0.806144
$486$		0			0
$487$		−	494.674i		−	1.01576i	−0.861428	−	0.507879i	$-0.830430\pi$
$487$		−	494.674i		−	1.01576i	0.861428	−	0.507879i	$-0.169570\pi$
$488$	86.0771	+	538.739i	0.176388	+	1.10397i
$489$		0			0
$490$	−291.524	−	148.373i	−0.594947	−	0.302802i
$491$			253.258i			0.515801i	0.966171	+	0.257901i	$0.0830307\pi$
$491$			253.258i			0.515801i	−0.966171	+	0.257901i	$0.916969\pi$
$492$		0			0
$493$	552.676			1.12105
$494$	13.9369	−	27.3832i	0.0282123	−	0.0554317i
$495$		0			0
$496$	563.350	+	181.918i	1.13579	+	0.366769i
$497$	−3.75466			−0.00755464
$498$		0			0
$499$		−	137.797i		−	0.276147i	−0.990422	−	0.138073i	$-0.955909\pi$
$499$		−	137.797i		−	0.276147i	0.990422	−	0.138073i	$-0.0440910\pi$
$500$	−308.447	−	423.734i	−0.616894	−	0.847469i
$501$		0			0
$502$	413.690	−	812.820i	0.824083	−	1.61916i
$503$			170.929i			0.339818i	0.985460	+	0.169909i	$0.0543475\pi$
$503$			170.929i			0.339818i	−0.985460	+	0.169909i	$0.945653\pi$
$504$		0			0
$505$	−487.031			−0.964417
$506$	−108.430	−	55.1863i	−0.214289	−	0.109064i
$507$		0			0
$508$	425.632	−	309.828i	0.837858	−	0.609898i
$509$	5.97470			0.0117381			0.00586906	−	0.999983i	$-0.498132\pi$
$509$	5.97470			0.0117381			0.00586906	+	0.999983i	$0.498132\pi$
$510$		0			0
$511$			32.5532i			0.0637050i
$512$	234.298	+	455.246i	0.457613	+	0.889152i
$513$		0			0
$514$	−831.663	−	423.280i	−1.61802	−	0.823501i
$515$		−	193.662i		−	0.376043i
$516$		0			0
$517$	−490.846			−0.949412
$518$	56.1170	−	110.259i	0.108334	−	0.212855i
$519$		0			0
$520$	15.2228	+	95.2766i	0.0292747	+	0.183224i
$521$	695.484			1.33490			0.667451	−	0.744654i	$-0.267385\pi$
$521$	695.484			1.33490			0.667451	+	0.744654i	$0.267385\pi$
$522$		0			0
$523$		−	622.889i		−	1.19099i	−0.803358	−	0.595496i	$-0.796956\pi$
$523$		−	622.889i		−	1.19099i	0.803358	−	0.595496i	$-0.203044\pi$
$524$	−408.443	+	297.316i	−0.779471	+	0.567396i
$525$		0			0
$526$	230.690	−	453.261i	0.438574	−	0.861713i
$527$			476.214i			0.903631i
$528$		0			0
$529$	512.958			0.969675
$530$	423.139	+	215.359i	0.798376	+	0.406338i
$531$		0			0
$532$	11.2599	+	15.4685i	0.0211652	+	0.0290761i
$533$	−5.91789			−0.0111030
$534$		0			0
$535$		−	653.133i		−	1.22081i
$536$	−416.135	+	66.4881i	−0.776371	+	0.124045i
$537$		0			0
$538$	644.842	+	328.196i	1.19859	+	0.610031i
$539$		−	725.947i		−	1.34684i
$540$		0			0
$541$	−960.900			−1.77615			−0.888077	−	0.459694i	$-0.847959\pi$
$541$	−960.900			−1.77615			−0.888077	+	0.459694i	$0.847959\pi$
$542$	100.063	−	196.603i	0.184617	−	0.362737i
$543$		0			0
$544$	−290.573	+	291.890i	−0.534142	+	0.536563i
$545$	−468.747			−0.860087
$546$		0			0
$547$			987.060i			1.80450i	0.431215	+	0.902249i	$0.358085\pi$
$547$			987.060i			1.80450i	−0.431215	+	0.902249i	$0.641915\pi$
$548$	485.996	+	667.645i	0.886853	+	1.21833i
$549$		0			0
$550$	183.122	−	359.799i	0.332949	−	0.654180i
$551$			187.173i			0.339696i
$552$		0			0
$553$	75.1276			0.135855
$554$	−705.547	−	359.092i	−1.27355	−	0.648181i
$555$		0			0
$556$	546.910	−	398.110i	0.983651	−	0.716025i
$557$	−75.4101			−0.135386			−0.0676931	−	0.997706i	$-0.521564\pi$
$557$	−75.4101			−0.135386			−0.0676931	+	0.997706i	$0.521564\pi$
$558$		0			0
$559$		−	17.8511i		−	0.0319340i
$560$	−57.1733	−	18.4625i	−0.102095	−	0.0329687i
$561$		0			0
$562$	704.165	+	358.389i	1.25296	+	0.637703i
$563$			825.440i			1.46615i	0.680150	+	0.733073i	$0.261914\pi$
$563$			825.440i			1.46615i	−0.680150	+	0.733073i	$0.738086\pi$
$564$		0			0
$565$	215.591			0.381578
$566$	−229.923	+	451.755i	−0.406225	+	0.798153i
$567$		0			0
$568$	27.0301	−	4.31873i	0.0475881	−	0.00760341i
$569$	−929.541			−1.63364			−0.816820	−	0.576893i	$-0.804265\pi$
$569$	−929.541			−1.63364			−0.816820	+	0.576893i	$0.804265\pi$
$570$		0			0
$571$			443.030i			0.775885i	0.921684	+	0.387942i	$0.126814\pi$
$571$			443.030i			0.775885i	−0.921684	+	0.387942i	$0.873186\pi$
$572$	−173.119	+	126.017i	−0.302655	+	0.220310i
$573$		0			0
$574$	1.67148	−	3.28413i	0.00291198	−	0.00572148i
$575$		−	53.2305i		−	0.0925748i
$576$		0			0
$577$	744.989			1.29114			0.645571	−	0.763700i	$-0.276620\pi$
$577$	744.989			1.29114			0.645571	+	0.763700i	$0.276620\pi$
$578$	219.850	+	111.894i	0.380363	+	0.193588i
$579$		0			0
$580$	−345.906	−	475.194i	−0.596389	−	0.819300i
$581$	−56.1538			−0.0966503
$582$		0			0
$583$			1053.69i			1.80736i
$584$	−37.4439	−	234.353i	−0.0641162	−	0.401290i
$585$		0			0
$586$	334.417	+	170.203i	0.570677	+	0.290450i
$587$		−	509.617i		−	0.868172i	−0.900871	−	0.434086i	$-0.857071\pi$
$587$		−	509.617i		−	0.868172i	0.900871	−	0.434086i	$-0.142929\pi$
$588$		0			0
$589$	−161.278			−0.273816
$590$	−100.169	+	196.812i	−0.169777	+	0.333580i
$591$		0			0
$592$	−277.167	+	858.310i	−0.468187	+	1.44985i
$593$	1087.55			1.83399			0.916994	−	0.398902i	$-0.130608\pi$
$593$	1087.55			1.83399			0.916994	+	0.398902i	$0.130608\pi$
$594$		0			0
$595$		−	48.3300i		−	0.0812269i
$596$	38.1401	+	52.3957i	0.0639935	+	0.0879122i
$597$		0			0
$598$	−12.8060	+	25.1614i	−0.0214148	+	0.0420758i
$599$			898.934i			1.50073i	0.661027	+	0.750363i	$0.270121\pi$
$599$			898.934i			1.50073i	−0.661027	+	0.750363i	$0.729879\pi$
$600$		0			0
$601$	188.733			0.314032			0.157016	−	0.987596i	$-0.449813\pi$
$601$	188.733			0.314032			0.157016	+	0.987596i	$0.449813\pi$
$602$	9.90646	+	5.04195i	0.0164559	+	0.00837534i
$603$		0			0
$604$	−738.885	+	537.853i	−1.22332	+	0.890486i
$605$	−375.353			−0.620419
$606$		0			0
$607$			1073.94i			1.76925i	0.466300	+	0.884626i	$0.345587\pi$
$607$			1073.94i			1.76925i	−0.466300	+	0.884626i	$0.654413\pi$
$608$	−98.8534	−	98.4074i	−0.162588	−	0.161854i
$609$		0			0
$610$	415.955	+	211.703i	0.681893	+	0.347053i
$611$			113.901i			0.186417i
$612$		0			0
$613$	520.604			0.849272			0.424636	−	0.905364i	$-0.360402\pi$
$613$	520.604			0.849272			0.424636	+	0.905364i	$0.360402\pi$
$614$	−50.3228	+	98.8746i	−0.0819590	+	0.161034i
$615$		0			0
$616$	−21.0368	−	131.665i	−0.0341506	−	0.213742i
$617$	972.303			1.57586			0.787928	−	0.615767i	$-0.211154\pi$
$617$	972.303			1.57586			0.787928	+	0.615767i	$0.211154\pi$
$618$		0			0
$619$		−	1216.61i		−	1.96544i	−0.185106	−	0.982718i	$-0.559263\pi$
$619$		−	1216.61i		−	1.96544i	0.185106	−	0.982718i	$-0.440737\pi$
$620$	409.451	−	298.050i	0.660405	−	0.480726i
$621$		0			0
$622$	310.960	−	610.977i	0.499936	−	0.982278i
$623$		−	1.96147i		−	0.00314843i
$624$		0			0
$625$	−116.111			−0.185777
$626$	−405.945	−	206.608i	−0.648475	−	0.330045i
$627$		0			0
$628$	50.6974	+	69.6465i	0.0807284	+	0.110902i
$629$	−725.551			−1.15350
$630$		0			0
$631$			118.157i			0.187254i	0.995607	+	0.0936268i	$0.0298461\pi$
$631$			118.157i			0.187254i	−0.995607	+	0.0936268i	$0.970154\pi$
$632$	−540.849	+	86.4144i	−0.855774	+	0.136732i
$633$		0			0
$634$	−326.180	−	166.011i	−0.514479	−	0.261847i
$635$		−	450.376i		−	0.709254i
$636$		0			0
$637$	−168.456			−0.264453
$638$	591.659	−	1162.50i	0.927365	−	1.82209i
$639$		0			0
$640$	432.831	+	67.1500i	0.676298	+	0.104922i
$641$	−1009.00			−1.57411			−0.787055	−	0.616883i	$-0.788395\pi$
$641$	−1009.00			−1.57411			−0.787055	+	0.616883i	$0.788395\pi$
$642$		0			0
$643$			596.414i			0.927550i	0.885953	+	0.463775i	$0.153505\pi$
$643$			596.414i			0.927550i	−0.885953	+	0.463775i	$0.846495\pi$
$644$	−10.3463	−	14.2134i	−0.0160656	−	0.0220705i
$645$		0			0
$646$	50.8947	−	99.9982i	0.0787844	−	0.154796i
$647$			428.660i			0.662535i	0.943537	+	0.331267i	$0.107476\pi$
$647$			428.660i			0.662535i	−0.943537	+	0.331267i	$0.892524\pi$
$648$		0			0
$649$	−490.097			−0.755158
$650$	−83.4916	−	42.4935i	−0.128449	−	0.0653747i
$651$		0			0
$652$	−541.309	+	394.033i	−0.830229	+	0.604344i
$653$	710.928			1.08871			0.544355	−	0.838855i	$-0.316774\pi$
$653$	710.928			1.08871			0.544355	+	0.838855i	$0.316774\pi$
$654$		0			0
$655$			432.187i			0.659828i
$656$	−8.25557	+	25.5653i	−0.0125847	+	0.0389715i
$657$		0			0
$658$	−63.2093	−	32.1707i	−0.0960627	−	0.0488917i
$659$		−	882.670i		−	1.33941i	−0.742628	−	0.669704i	$-0.766421\pi$
$659$		−	882.670i		−	1.33941i	0.742628	−	0.669704i	$-0.233579\pi$
$660$		0			0
$661$	982.979			1.48711			0.743555	−	0.668675i	$-0.233138\pi$
$661$	982.979			1.48711			0.743555	+	0.668675i	$0.233138\pi$
$662$	−207.686	+	408.063i	−0.313725	+	0.616409i
$663$		0			0
$664$	404.256	−	64.5901i	0.608819	−	0.0972742i
$665$	16.3678			0.0246132
$666$		0			0
$667$		−	171.986i		−	0.257849i
$668$	7.49139	−	5.45317i	0.0112147	−	0.00816343i
$669$		0			0
$670$	−163.524	+	321.294i	−0.244066	+	0.479543i
$671$			1035.80i			1.54367i
$672$		0			0
$673$	1277.40			1.89807			0.949035	−	0.315170i	$-0.102061\pi$
$673$	1277.40			1.89807			0.949035	+	0.315170i	$0.102061\pi$
$674$	538.264	+	273.953i	0.798611	+	0.406458i
$675$		0			0
$676$	−368.595	−	506.364i	−0.545259	−	0.749059i
$677$	1157.24			1.70937			0.854685	−	0.519147i	$-0.173750\pi$
$677$	1157.24			1.70937			0.854685	+	0.519147i	$0.173750\pi$
$678$		0			0
$679$		−	125.378i		−	0.184651i
$680$	55.5909	+	347.932i	0.0817513	+	0.511664i
$681$		0			0
$682$	1001.67	+	509.804i	1.46872	+	0.747513i
$683$		−	1193.34i		−	1.74720i	−0.486647	−	0.873599i	$-0.661780\pi$
$683$		−	1193.34i		−	1.74720i	0.486647	−	0.873599i	$-0.338220\pi$
$684$		0			0
$685$	706.458			1.03133
$686$	96.3579	−	189.325i	0.140463	−	0.275983i
$687$		0			0
$688$	−77.1168	−	24.9027i	−0.112088	−	0.0361957i
$689$	244.510			0.354876
$690$		0			0
$691$		−	864.424i		−	1.25098i	−0.780234	−	0.625488i	$-0.784900\pi$
$691$		−	864.424i		−	1.25098i	0.780234	−	0.625488i	$-0.215100\pi$
$692$	243.380	+	334.347i	0.351705	+	0.483161i
$693$		0			0
$694$	41.6733	−	81.8800i	0.0600480	−	0.117983i
$695$		−	578.705i		−	0.832669i
$696$		0			0
$697$	−21.6110			−0.0310057
$698$	−554.333	−	282.131i	−0.794173	−	0.404199i
$699$		0			0
$700$	47.1635	−	34.3315i	0.0673764	−	0.0490450i
$701$	459.736			0.655828			0.327914	−	0.944708i	$-0.393654\pi$
$701$	459.736			0.655828			0.327914	+	0.944708i	$0.393654\pi$
$702$		0			0
$703$		−	245.720i		−	0.349530i
$704$	302.891	+	923.668i	0.430243	+	1.31203i
$705$		0			0
$706$	−425.107	−	216.361i	−0.602135	−	0.306460i
$707$		−	156.179i		−	0.220904i
$708$		0			0
$709$	−1008.64			−1.42262			−0.711310	−	0.702878i	$-0.751898\pi$
$709$	−1008.64			−1.42262			−0.711310	+	0.702878i	$0.751898\pi$
$710$	10.6217	−	20.8696i	0.0149602	−	0.0293938i
$711$		0			0
$712$	2.25615	+	14.1208i	0.00316875	+	0.0198326i
$713$	148.192			0.207842
$714$		0			0
$715$			183.183i			0.256200i
$716$	844.297	−	614.585i	1.17919	−	0.858359i
$717$		0			0
$718$	481.617	−	946.285i	0.670776	−	1.31795i
$719$			404.053i			0.561965i	0.959713	+	0.280983i	$0.0906603\pi$
$719$			404.053i			0.561965i	−0.959713	+	0.280983i	$0.909340\pi$
$720$		0			0
$721$	62.1027			0.0861341
$722$	33.8660	+	17.2363i	0.0469059	+	0.0238730i
$723$		0			0
$724$	97.2799	+	133.640i	0.134364	+	0.184586i
$725$	570.690			0.787159
$726$		0			0
$727$			256.630i			0.352999i	0.984301	+	0.176500i	$0.0564774\pi$
$727$			256.630i			0.352999i	−0.984301	+	0.176500i	$0.943523\pi$
$728$	−30.5529	+	4.88160i	−0.0419683	+	0.00670550i
$729$		0			0
$730$	−180.942	−	92.0914i	−0.247865	−	0.126153i
$731$		−	65.1888i		−	0.0891776i
$732$		0			0
$733$	−204.399			−0.278852			−0.139426	−	0.990232i	$-0.544526\pi$
$733$	−204.399			−0.278852			−0.139426	+	0.990232i	$0.544526\pi$
$734$	306.954	−	603.105i	0.418193	−	0.821669i
$735$		0			0
$736$	90.8324	+	90.4226i	0.123414	+	0.122857i
$737$	−800.078			−1.08559
$738$		0			0
$739$		−	1459.41i		−	1.97485i	−0.158100	−	0.987423i	$-0.550537\pi$
$739$		−	1459.41i		−	1.97485i	0.158100	−	0.987423i	$-0.449463\pi$
$740$	454.104	+	623.833i	0.613654	+	0.843018i
$741$		0			0
$742$	−69.0605	+	135.691i	−0.0930735	+	0.182871i
$743$			1022.36i			1.37599i	0.725717	+	0.687993i	$0.241508\pi$
$743$			1022.36i			1.37599i	−0.725717	+	0.687993i	$0.758492\pi$
$744$		0			0
$745$	55.4417			0.0744183
$746$	−194.174	−	98.8261i	−0.260287	−	0.132475i
$747$		0			0
$748$	−632.195	+	460.191i	−0.845180	+	0.615228i
$749$	209.444			0.279632
$750$		0			0
$751$		−	299.399i		−	0.398667i	−0.979932	−	0.199334i	$-0.936122\pi$
$751$		−	299.399i		−	0.398667i	0.979932	−	0.199334i	$-0.0638777\pi$
$752$	492.052	+	158.894i	0.654325	+	0.211295i
$753$		0			0
$754$	−269.758	−	137.295i	−0.357769	−	0.182089i
$755$			781.840i			1.03555i
$756$		0			0
$757$	−931.935			−1.23109			−0.615545	−	0.788102i	$-0.711064\pi$
$757$	−931.935			−1.23109			−0.615545	+	0.788102i	$0.711064\pi$
$758$	449.631	−	883.437i	0.593180	−	1.16548i
$759$		0			0
$760$	−117.833	+	18.8268i	−0.155043	+	0.0247721i
$761$	119.523			0.157060			0.0785300	−	0.996912i	$-0.474977\pi$
$761$	119.523			0.157060			0.0785300	+	0.996912i	$0.474977\pi$
$762$		0			0
$763$		−	150.316i		−	0.197007i
$764$	661.398	−	481.449i	0.865705	−	0.630168i
$765$		0			0
$766$	−63.2143	+	124.204i	−0.0825251	+	0.162146i
$767$			113.727i			0.148276i
$768$		0			0
$769$	−219.147			−0.284977			−0.142489	−	0.989796i	$-0.545510\pi$
$769$	−219.147			−0.284977			−0.142489	+	0.989796i	$0.545510\pi$
$770$	−101.657	−	51.7390i	−0.132022	−	0.0671935i
$771$		0			0
$772$	175.897	+	241.641i	0.227846	+	0.313007i
$773$	908.079			1.17475			0.587373	−	0.809316i	$-0.300162\pi$
$773$	908.079			1.17475			0.587373	+	0.809316i	$0.300162\pi$
$774$		0			0
$775$			491.736i			0.634498i
$776$	144.214	+	902.605i	0.185843	+	1.16315i
$777$		0			0
$778$	493.245	+	251.040i	0.633991	+	0.322673i
$779$		−	7.31892i		−	0.00939527i
$780$		0			0
$781$	51.9691			0.0665417
$782$	−46.7651	+	91.8843i	−0.0598019	+	0.117499i
$783$		0			0
$784$	−235.000	+	727.731i	−0.299745	+	0.928229i
$785$	73.6954			0.0938794
$786$		0			0
$787$			276.800i			0.351715i	0.984416	+	0.175857i	$0.0562698\pi$
$787$			276.800i			0.351715i	−0.984416	+	0.175857i	$0.943730\pi$
$788$	568.359	+	780.793i	0.721267	+	0.990854i
$789$		0			0
$790$	−212.532	+	417.584i	−0.269028	+	0.528588i
$791$			69.1350i			0.0874020i
$792$		0			0
$793$	240.358			0.303100
$794$	811.128	+	412.828i	1.02157	+	0.519935i
$795$		0			0
$796$	133.504	−	97.1806i	0.167718	−	0.122086i
$797$	−669.972			−0.840617			−0.420309	−	0.907381i	$-0.638078\pi$
$797$	−669.972			−0.840617			−0.420309	+	0.907381i	$0.638078\pi$
$798$		0			0
$799$			415.944i			0.520581i
$800$	−300.044	+	301.404i	−0.375055	+	0.376755i
$801$		0			0
$802$	−68.6329	−	34.9312i	−0.0855772	−	0.0435551i
$803$		−	450.577i		−	0.561117i
$804$		0			0
$805$	−15.0397			−0.0186828
$806$	118.300	−	232.437i	0.146774	−	0.288383i
$807$		0			0
$808$	179.643	+	1124.35i	0.222330	+	1.39152i
$809$	192.312			0.237716			0.118858	−	0.992911i	$-0.462077\pi$
$809$	192.312			0.237716			0.118858	+	0.992911i	$0.462077\pi$
$810$		0			0
$811$		−	973.092i		−	1.19987i	−0.800050	−	0.599934i	$-0.795194\pi$
$811$		−	973.092i		−	1.19987i	0.800050	−	0.599934i	$-0.204806\pi$
$812$	152.383	−	110.924i	0.187664	−	0.136605i
$813$		0			0
$814$	−776.728	+	1526.12i	−0.954212	+	1.87484i
$815$			572.778i			0.702795i
$816$		0			0
$817$	22.0773			0.0270224
$818$	754.305	+	383.908i	0.922134	+	0.469326i
$819$		0			0
$820$	13.5258	+	18.5813i	0.0164948	+	0.0226601i
$821$	−1069.44			−1.30261			−0.651306	−	0.758815i	$-0.725779\pi$
$821$	−1069.44			−1.30261			−0.651306	+	0.758815i	$0.725779\pi$
$822$		0			0
$823$			82.3572i			0.100069i	0.998747	+	0.0500347i	$0.0159332\pi$
$823$			82.3572i			0.100069i	−0.998747	+	0.0500347i	$0.984067\pi$
$824$	−447.082	+	71.4327i	−0.542576	+	0.0866902i
$825$		0			0
$826$	−63.1129	−	32.1217i	−0.0764079	−	0.0388882i
$827$		−	1243.38i		−	1.50348i	−0.659458	−	0.751741i	$-0.729214\pi$
$827$		−	1243.38i		−	1.50348i	0.659458	−	0.751741i	$-0.270786\pi$
$828$		0			0
$829$	−991.491			−1.19601			−0.598004	−	0.801493i	$-0.704039\pi$
$829$	−991.491			−1.19601			−0.598004	+	0.801493i	$0.704039\pi$
$830$	158.856	−	312.122i	0.191393	−	0.376050i
$831$		0			0
$832$	214.338	−	70.2860i	0.257618	−	0.0844784i
$833$	−615.170			−0.738499
$834$		0			0
$835$		−	7.92690i		−	0.00949330i
$836$	−155.851	−	214.103i	−0.186425	−	0.256104i
$837$		0			0
$838$	−709.893	+	1394.80i	−0.847127	+	1.66444i
$839$			518.848i			0.618412i	0.950995	+	0.309206i	$0.100063\pi$
$839$			518.848i			0.618412i	−0.950995	+	0.309206i	$0.899937\pi$
$840$		0			0
$841$	1002.88			1.19248
$842$	−1310.46	−	666.965i	−1.55636	−	0.792120i
$843$		0			0
$844$	49.3382	−	35.9145i	0.0584576	−	0.0425528i
$845$	−535.801			−0.634084
$846$		0			0
$847$		−	120.367i		−	0.142110i
$848$	341.096	−	1056.28i	0.402236	−	1.24562i
$849$		0			0
$850$	−304.895	−	155.178i	−0.358700	−	0.182562i
$851$			225.782i			0.265314i
$852$		0			0
$853$	−682.035			−0.799572			−0.399786	−	0.916609i	$-0.630916\pi$
$853$	−682.035			−0.799572			−0.399786	+	0.916609i	$0.630916\pi$
$854$	−67.8879	+	133.387i	−0.0794941	+	0.156190i
$855$		0			0
$856$	−1507.80	+	240.910i	−1.76145	+	0.281437i
$857$	−257.918			−0.300955			−0.150477	−	0.988613i	$-0.548081\pi$
$857$	−257.918			−0.300955			−0.150477	+	0.988613i	$0.548081\pi$
$858$		0			0
$859$		−	800.297i		−	0.931661i	−0.884874	−	0.465831i	$-0.845756\pi$
$859$		−	800.297i		−	0.931661i	0.884874	−	0.465831i	$-0.154244\pi$
$860$	−56.0497	+	40.8000i	−0.0651741	+	0.0474419i
$861$		0			0
$862$	−204.532	+	401.867i	−0.237277	+	0.466202i
$863$			97.9073i			0.113450i	0.998390	+	0.0567250i	$0.0180658\pi$
$863$			97.9073i			0.113450i	−0.998390	+	0.0567250i	$0.981934\pi$
$864$		0			0
$865$	353.784			0.408999
$866$	380.830	+	193.826i	0.439757	+	0.223817i
$867$		0			0
$868$	95.5774	+	131.301i	0.110112	+	0.151269i
$869$	−1039.86			−1.19662
$870$		0			0
$871$			185.659i			0.213156i
$872$	172.899	+	1082.14i	0.198278	+	1.24098i
$873$		0			0
$874$	−31.1181	−	15.8378i	−0.0356043	−	0.0181210i
$875$		−	143.781i		−	0.164321i
$876$		0			0
$877$	−286.418			−0.326588			−0.163294	−	0.986577i	$-0.552212\pi$
$877$	−286.418			−0.326588			−0.163294	+	0.986577i	$0.552212\pi$
$878$	582.037	−	1143.59i	0.662912	−	1.30249i
$879$		0			0
$880$	791.349	+	255.543i	0.899260	+	0.290390i
$881$	−401.330			−0.455539			−0.227770	−	0.973715i	$-0.573143\pi$
$881$	−401.330			−0.455539			−0.227770	+	0.973715i	$0.573143\pi$
$882$		0			0
$883$			675.471i			0.764973i	0.923961	+	0.382486i	$0.124932\pi$
$883$			675.471i			0.764973i	−0.923961	+	0.382486i	$0.875068\pi$
$884$	106.788	+	146.701i	0.120800	+	0.165952i
$885$		0			0
$886$	754.359	−	1482.17i	0.851421	−	1.67288i
$887$		−	906.749i		−	1.02227i	−0.859502	−	0.511133i	$-0.829226\pi$
$887$		−	906.749i		−	1.02227i	0.859502	−	0.511133i	$-0.170774\pi$
$888$		0			0
$889$	144.425			0.162458
$890$	10.9025	+	5.54890i	0.0122500	+	0.00623471i
$891$		0			0
$892$	1218.45	−	886.942i	1.36598	−	0.994330i
$893$	−140.866			−0.157745
$894$		0			0
$895$		−	893.380i		−	0.998190i
$896$	−21.5334	+	138.798i	−0.0240328	+	0.154909i
$897$		0			0
$898$	−397.004	−	202.058i	−0.442098	−	0.225009i
$899$			1588.78i			1.76727i
$900$		0			0
$901$	892.902			0.991012
$902$	−23.1353	+	45.4564i	−0.0256489	+	0.0503951i
$903$		0			0
$904$	−79.5214	−	497.708i	−0.0879662	−	0.550562i
$905$	141.409			0.156253
$906$		0			0
$907$			114.996i			0.126787i	0.997989	+	0.0633935i	$0.0201923\pi$
$907$			114.996i			0.126787i	−0.997989	+	0.0633935i	$0.979808\pi$
$908$	34.8840	−	25.3929i	0.0384185	−	0.0279658i
$909$		0			0
$910$	−12.0061	+	23.5896i	−0.0131935	+	0.0259226i
$911$		−	522.402i		−	0.573439i	−0.958015	−	0.286719i	$-0.907435\pi$
$911$		−	522.402i		−	0.573439i	0.958015	−	0.286719i	$-0.0925647\pi$
$912$		0			0
$913$	777.239			0.851302
$914$	1114.51	+	567.238i	1.21938	+	0.620611i
$915$		0			0
$916$	963.115	+	1323.10i	1.05144	+	1.44443i
$917$	−138.592			−0.151136
$918$		0			0
$919$		−	1145.11i		−	1.24604i	−0.782206	−	0.623020i	$-0.785905\pi$
$919$		−	1145.11i		−	1.24604i	0.782206	−	0.623020i	$-0.214095\pi$
$920$	108.272	−	17.2992i	0.117687	−	0.0188034i
$921$		0			0
$922$	−68.8816	−	35.0577i	−0.0747088	−	0.0380235i
$923$		−	12.0595i		−	0.0130655i
$924$		0			0
$925$	−749.201			−0.809947
$926$	−117.743	+	231.343i	−0.127153	+	0.249830i
$927$		0			0
$928$	−969.431	+	973.824i	−1.04465	+	1.04938i
$929$	−854.884			−0.920220			−0.460110	−	0.887862i	$-0.652190\pi$
$929$	−854.884			−0.920220			−0.460110	+	0.887862i	$0.652190\pi$
$930$		0			0
$931$		−	208.337i		−	0.223778i
$932$	−321.854	−	442.153i	−0.345337	−	0.474413i
$933$		0			0
$934$	−508.683	+	999.464i	−0.544629	+	1.07009i
$935$			668.947i			0.715452i
$936$		0			0
$937$	−1305.11			−1.39286			−0.696432	−	0.717623i	$-0.745230\pi$
$937$	−1305.11			−1.39286			−0.696432	+	0.717623i	$0.745230\pi$
$938$	−103.031	−	52.4383i	−0.109841	−	0.0559044i
$939$		0			0
$940$	357.631	−	260.329i	0.380459	−	0.276946i
$941$	1007.79			1.07098			0.535491	−	0.844541i	$-0.320127\pi$
$941$	1007.79			1.07098			0.535491	+	0.844541i	$0.320127\pi$
$942$		0			0
$943$			6.72506i			0.00713156i
$944$	491.302	+	158.652i	0.520447	+	0.168063i
$945$		0			0
$946$	−137.118	−	69.7869i	−0.144945	−	0.0737705i
$947$		−	1192.09i		−	1.25880i	−0.777080	−	0.629401i	$-0.783300\pi$
$947$		−	1192.09i		−	1.25880i	0.777080	−	0.629401i	$-0.216700\pi$
$948$		0			0
$949$	−104.557			−0.110176
$950$	52.5536	−	103.258i	0.0553196	−	0.108692i
$951$		0			0
$952$	−111.573	+	17.8267i	−0.117199	+	0.0187255i
$953$	728.571			0.764503			0.382251	−	0.924058i	$-0.375149\pi$
$953$	728.571			0.764503			0.382251	+	0.924058i	$0.375149\pi$
$954$		0			0
$955$		−	699.849i		−	0.732826i
$956$	−817.096	+	594.784i	−0.854703	+	0.622159i
$957$		0			0
$958$	196.707	−	386.491i	0.205331	−	0.403435i
$959$			226.544i			0.236230i
$960$		0			0
$961$	−407.972			−0.424529
$962$	354.137	+	180.240i	0.368126	+	0.187360i
$963$		0			0
$964$	830.552	+	1140.99i	0.861568	+	1.18359i
$965$	255.689			0.264963
$966$		0			0
$967$		−	571.802i		−	0.591315i	−0.955294	−	0.295657i	$-0.904461\pi$
$967$		−	571.802i		−	0.591315i	0.955294	−	0.295657i	$-0.0955387\pi$
$968$	138.450	+	866.530i	0.143027	+	0.895175i
$969$		0			0
$970$	696.892	+	354.687i	0.718445	+	0.365657i
$971$		−	456.799i		−	0.470442i	−0.971942	−	0.235221i	$-0.924419\pi$
$971$		−	456.799i		−	0.470442i	0.971942	−	0.235221i	$-0.0755814\pi$
$972$		0			0
$973$	185.577			0.190726
$974$	−448.756	+	881.719i	−0.460735	+	0.905256i
$975$		0			0
$976$	335.304	−	1038.35i	0.343550	−	1.06388i
$977$	−565.223			−0.578529			−0.289264	−	0.957249i	$-0.593411\pi$
$977$	−565.223			−0.578529			−0.289264	+	0.957249i	$0.593411\pi$
$978$		0			0
$979$			27.1492i			0.0277316i
$980$	385.019	+	528.926i	0.392876	+	0.539721i
$981$		0			0
$982$	229.750	−	451.414i	0.233961	−	0.459688i
$983$		−	838.013i		−	0.852506i	−0.904604	−	0.426253i	$-0.859833\pi$
$983$		−	838.013i		−	0.852506i	0.904604	−	0.426253i	$-0.140167\pi$
$984$		0			0
$985$	826.184			0.838766
$986$	−985.102	−	501.374i	−0.999089	−	0.508493i
$987$		0			0
$988$	−49.6828	+	36.1653i	−0.0502862	+	0.0366046i
$989$	−20.2859			−0.0205115
$990$		0			0
$991$		−	993.095i		−	1.00211i	−0.865414	−	0.501057i	$-0.832945\pi$
$991$		−	993.095i		−	1.00211i	0.865414	−	0.501057i	$-0.167055\pi$
$992$	−839.097	−	835.311i	−0.845863	−	0.842047i
$993$		0			0
$994$	6.69239	+	3.40613i	0.00673278	+	0.00342669i
$995$		−	141.265i		−	0.141975i
$996$		0			0
$997$	−203.135			−0.203746			−0.101873	−	0.994797i	$-0.532484\pi$
$997$	−203.135			−0.203746			−0.101873	+	0.994797i	$0.532484\pi$
$998$	−125.006	+	245.613i	−0.125257	+	0.246105i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.c.343.7		36
3.2	odd	2		228.3.g.a.115.30	yes	36
4.3	odd	2	inner	684.3.g.c.343.8		36
12.11	even	2		228.3.g.a.115.29	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.g.a.115.29	✓	36	12.11	even	2
228.3.g.a.115.30	yes	36	3.2	odd	2
684.3.g.c.343.7		36	1.1	even	1	trivial
684.3.g.c.343.8		36	4.3	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)

\(f(q)\)	\(=\)	\(q+(-1.78242 - 0.907175i) q^{2} +(2.35407 + 3.23394i) q^{4} +3.42194 q^{5} +1.09734i q^{7} +(-1.26219 - 7.89980i) q^{8} +O(q^{10})\)	\(q+(-1.78242 - 0.907175i) q^{2} +(2.35407 + 3.23394i) q^{4} +3.42194 q^{5} +1.09734i q^{7} +(-1.26219 - 7.89980i) q^{8} +(-6.09935 - 3.10430i) q^{10} -15.1885i q^{11} -3.52450 q^{13} +(0.995475 - 1.95592i) q^{14} +(-4.91674 + 15.2258i) q^{16} -12.8708 q^{17} -4.35890i q^{19} +(8.05549 + 11.0664i) q^{20} +(-13.7786 + 27.0723i) q^{22} +4.00522i q^{23} -13.2903 q^{25} +(6.28215 + 3.19734i) q^{26} +(-3.54872 + 2.58320i) q^{28} -42.9404 q^{29} -36.9996i q^{31} +(22.5762 - 22.6785i) q^{32} +(22.9412 + 11.6760i) q^{34} +3.75502i q^{35} +56.3720 q^{37} +(-3.95428 + 7.76940i) q^{38} +(-4.31915 - 27.0327i) q^{40} +1.67907 q^{41} +5.06487i q^{43} +(49.1187 - 35.7547i) q^{44} +(3.63343 - 7.13899i) q^{46} -32.3170i q^{47} +47.7959 q^{49} +(23.6889 + 12.0566i) q^{50} +(-8.29690 - 11.3980i) q^{52} -69.3744 q^{53} -51.9742i q^{55} +(8.66873 - 1.38505i) q^{56} +(76.5379 + 38.9544i) q^{58} -32.2677i q^{59} -68.1965 q^{61} +(-33.5651 + 65.9490i) q^{62} +(-60.8137 + 19.9421i) q^{64} -12.0606 q^{65} -52.6766i q^{67} +(-30.2987 - 41.6233i) q^{68} +(3.40646 - 6.69304i) q^{70} +3.42161i q^{71} +29.6657 q^{73} +(-100.479 - 51.1393i) q^{74} +(14.0964 - 10.2611i) q^{76} +16.6669 q^{77} -68.4637i q^{79} +(-16.8248 + 52.1019i) q^{80} +(-2.99282 - 1.52321i) q^{82} +51.1729i q^{83} -44.0431 q^{85} +(4.59473 - 9.02775i) q^{86} +(-119.986 + 19.1708i) q^{88} -1.78749 q^{89} -3.86756i q^{91} +(-12.9526 + 9.42855i) q^{92} +(-29.3172 + 57.6025i) q^{94} -14.9159i q^{95} -114.257 q^{97} +(-85.1925 - 43.3592i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8	\( 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8} + 8 q^{10} - 24 q^{13} + 12 q^{14} + 4 q^{16} + 40 q^{17} + 80 q^{20} + 12 q^{22} + 284 q^{25} + 112 q^{26} - 48 q^{28} - 104 q^{29} - 44 q^{32} + 140 q^{34} - 184 q^{37} + 180 q^{40} + 200 q^{41} - 96 q^{44} - 28 q^{46} - 332 q^{49} - 176 q^{50} + 276 q^{52} - 264 q^{53} + 192 q^{56} - 184 q^{58} + 40 q^{61} + 240 q^{62} - 372 q^{64} - 176 q^{65} + 104 q^{68} - 60 q^{70} + 424 q^{73} + 104 q^{74} + 400 q^{77} - 704 q^{80} + 528 q^{82} - 128 q^{85} - 668 q^{86} - 496 q^{88} + 520 q^{89} + 456 q^{92} - 32 q^{94} - 440 q^{97} + 472 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8 + 8 * q^10 - 24 * q^13 + 12 * q^14 + 4 * q^16 + 40 * q^17 + 80 * q^20 + 12 * q^22 + 284 * q^25 + 112 * q^26 - 48 * q^28 - 104 * q^29 - 44 * q^32 + 140 * q^34 - 184 * q^37 + 180 * q^40 + 200 * q^41 - 96 * q^44 - 28 * q^46 - 332 * q^49 - 176 * q^50 + 276 * q^52 - 264 * q^53 + 192 * q^56 - 184 * q^58 + 40 * q^61 + 240 * q^62 - 372 * q^64 - 176 * q^65 + 104 * q^68 - 60 * q^70 + 424 * q^73 + 104 * q^74 + 400 * q^77 - 704 * q^80 + 528 * q^82 - 128 * q^85 - 668 * q^86 - 496 * q^88 + 520 * q^89 + 456 * q^92 - 32 * q^94 - 440 * q^97 + 472 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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