LMFDB - Embedded newform 324.3.d.e.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.d (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3636603.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} + 12x^{2} + 3 $ x^6 + 8x^4 + 12x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.4
Root			$-2.47367i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.e.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.195350 + 1.99044i) q^{2} +(-3.92368 - 0.777662i) q^{4} -7.23805 q^{5} +6.88025i q^{7} +(2.31438 - 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} -17.9526i q^{11} +7.67526 q^{13} +(-13.6947 - 1.34405i) q^{14} +(14.7905 + 6.10259i) q^{16} +1.43720 q^{17} +13.8943i q^{19} +(28.3998 + 5.62876i) q^{20} +(35.7336 + 3.50704i) q^{22} -16.5824i q^{23} +27.3894 q^{25} +(-1.49936 + 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +37.5019 q^{29} -53.9918i q^{31} +(-15.0361 + 28.2474i) q^{32} +(-0.280757 + 2.86066i) q^{34} -49.7996i q^{35} +44.4415 q^{37} +(-27.6558 - 2.71425i) q^{38} +(-16.7516 + 55.4284i) q^{40} -56.9911 q^{41} -67.6185i q^{43} +(-13.9611 + 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +9.43453i q^{47} +1.66212 q^{49} +(-5.35051 + 54.5169i) q^{50} +(-30.1152 - 5.96876i) q^{52} +7.82662 q^{53} +129.942i q^{55} +(52.6884 + 15.9235i) q^{56} +(-7.32598 + 74.6451i) q^{58} -22.4125i q^{59} -67.1814 q^{61} +(107.467 + 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} -55.5539 q^{65} -69.2040i q^{67} +(-5.63912 - 1.11766i) q^{68} +(99.1230 + 9.72834i) q^{70} -7.14792i q^{71} -80.4410 q^{73} +(-8.68162 + 88.4579i) q^{74} +(10.8051 - 54.5169i) q^{76} +123.519 q^{77} +46.8439i q^{79} +(-107.054 - 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} -142.199i q^{83} -10.4026 q^{85} +(134.590 + 13.2092i) q^{86} +(-137.480 - 41.5492i) q^{88} -42.1078 q^{89} +52.8077i q^{91} +(-12.8955 + 65.0642i) q^{92} +(-18.7788 - 1.84303i) q^{94} -100.568i q^{95} +62.8955 q^{97} +(-0.324695 + 3.30835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{4} - 2 q^{5} - 7 q^{8} + 9 q^{10} + 6 q^{13} - 15 q^{16} + 10 q^{17} + 67 q^{20} + 48 q^{22} + 73 q^{26} - 48 q^{28} + 22 q^{29} - 31 q^{32} + 81 q^{34} + 54 q^{37} - 168 q^{38} - 81 q^{40}+ \cdots + 407 q^{98}+O(q^{100}) $ 6 * q - q^2 - 3 * q^4 - 2 * q^5 - 7 * q^8 + 9 * q^10 + 6 * q^13 - 15 * q^16 + 10 * q^17 + 67 * q^20 + 48 * q^22 + 73 * q^26 - 48 * q^28 + 22 * q^29 - 31 * q^32 + 81 * q^34 + 54 * q^37 - 168 * q^38 - 81 * q^40 - 92 * q^41 - 168 * q^44 + 120 * q^46 - 66 * q^49 + 48 * q^50 - 117 * q^52 - 116 * q^53 + 312 * q^56 + 201 * q^58 + 54 * q^61 + 312 * q^62 - 255 * q^64 - 82 * q^65 - 53 * q^68 + 264 * q^70 - 78 * q^73 - 383 * q^74 - 192 * q^76 + 168 * q^77 - 377 * q^80 + 150 * q^82 + 66 * q^85 + 144 * q^86 - 336 * q^88 + 250 * q^89 + 504 * q^92 + 216 * q^94 - 204 * q^97 + 407 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

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 $

$2$	−0.195350	+	1.99044i	−0.0976748	+	0.995218i
$2$	−0.195350	+	1.99044i	−0.0976748	+	0.995218i
$3$		0			0
$3$		0			0
$4$	−3.92368	−	0.777662i	−0.980919	−	0.194416i
$5$	−7.23805			−1.44761			−0.723805	−	0.690004i	$-0.757609\pi$
$5$	−7.23805			−1.44761			−0.723805	+	0.690004i	$0.757609\pi$
$6$		0			0
$7$			6.88025i			0.982893i	0.870908	+	0.491447i	$0.163532\pi$
$7$			6.88025i			0.982893i	−0.870908	+	0.491447i	$0.836468\pi$
$8$	2.31438	−	7.65792i	0.289297	−	0.957239i
$9$		0			0
$10$	1.41395	−	14.4069i	0.141395	−	1.44069i
$11$		−	17.9526i		−	1.63206i	−0.578010	−	0.816029i	$-0.696171\pi$
$11$		−	17.9526i		−	1.63206i	0.578010	−	0.816029i	$-0.303829\pi$
$12$		0			0
$13$	7.67526			0.590404			0.295202	−	0.955435i	$-0.404613\pi$
$13$	7.67526			0.590404			0.295202	+	0.955435i	$0.404613\pi$
$14$	−13.6947	−	1.34405i	−0.978193	−	0.0960039i
$15$		0			0
$16$	14.7905	+	6.10259i	0.924405	+	0.381412i
$17$	1.43720			0.0845413			0.0422707	−	0.999106i	$-0.486541\pi$
$17$	1.43720			0.0845413			0.0422707	+	0.999106i	$0.486541\pi$
$18$		0			0
$19$			13.8943i			0.731281i	0.930756	+	0.365641i	$0.119150\pi$
$19$			13.8943i			0.731281i	−0.930756	+	0.365641i	$0.880850\pi$
$20$	28.3998	+	5.62876i	1.41999	+	0.281438i
$21$		0			0
$22$	35.7336	+	3.50704i	1.62426	+	0.159411i
$23$		−	16.5824i		−	0.720976i	−0.932764	−	0.360488i	$-0.882610\pi$
$23$		−	16.5824i		−	0.720976i	0.932764	−	0.360488i	$-0.117390\pi$
$24$		0			0
$25$	27.3894			1.09558
$26$	−1.49936	+	15.2771i	−0.0576676	+	0.587581i
$27$		0			0
$28$	5.35051	−	26.9959i	0.191090	−	0.964139i
$29$	37.5019			1.29317			0.646584	−	0.762843i	$-0.276197\pi$
$29$	37.5019			1.29317			0.646584	+	0.762843i	$0.276197\pi$
$30$		0			0
$31$		−	53.9918i		−	1.74167i	−0.491575	−	0.870835i	$-0.663579\pi$
$31$		−	53.9918i		−	1.74167i	0.491575	−	0.870835i	$-0.336421\pi$
$32$	−15.0361	+	28.2474i	−0.469879	+	0.882731i
$33$		0			0
$34$	−0.280757	+	2.86066i	−0.00825756	+	0.0841371i
$35$		−	49.7996i		−	1.42285i
$36$		0			0
$37$	44.4415			1.20112			0.600560	−	0.799580i	$-0.294944\pi$
$37$	44.4415			1.20112			0.600560	+	0.799580i	$0.294944\pi$
$38$	−27.6558	−	2.71425i	−0.727784	−	0.0714277i
$39$		0			0
$40$	−16.7516	+	55.4284i	−0.418789	+	1.38571i
$41$	−56.9911			−1.39003			−0.695014	−	0.718997i	$-0.744602\pi$
$41$	−56.9911			−1.39003			−0.695014	+	0.718997i	$0.744602\pi$
$42$		0			0
$43$		−	67.6185i		−	1.57252i	−0.617894	−	0.786261i	$-0.712014\pi$
$43$		−	67.6185i		−	1.57252i	0.617894	−	0.786261i	$-0.287986\pi$
$44$	−13.9611	+	70.4404i	−0.317298	+	1.60092i
$45$		0			0
$46$	33.0063	+	3.23938i	0.717529	+	0.0704212i
$47$			9.43453i			0.200735i	0.994950	+	0.100367i	$0.0320018\pi$
$47$			9.43453i			0.200735i	−0.994950	+	0.100367i	$0.967998\pi$
$48$		0			0
$49$	1.66212			0.0339208
$50$	−5.35051	+	54.5169i	−0.107010	+	1.09034i
$51$		0			0
$52$	−30.1152	−	5.96876i	−0.579139	−	0.114784i
$53$	7.82662			0.147672			0.0738360	−	0.997270i	$-0.476476\pi$
$53$	7.82662			0.147672			0.0738360	+	0.997270i	$0.476476\pi$
$54$		0			0
$55$			129.942i			2.36259i
$56$	52.6884	+	15.9235i	0.940864	+	0.284348i
$57$		0			0
$58$	−7.32598	+	74.6451i	−0.126310	+	1.28698i
$59$		−	22.4125i		−	0.379872i	−0.981796	−	0.189936i	$-0.939172\pi$
$59$		−	22.4125i		−	0.379872i	0.981796	−	0.189936i	$-0.0608281\pi$
$60$		0			0
$61$	−67.1814			−1.10133			−0.550667	−	0.834725i	$-0.685627\pi$
$61$	−67.1814			−1.10133			−0.550667	+	0.834725i	$0.685627\pi$
$62$	107.467	+	10.5473i	1.73334	+	0.170117i
$63$		0			0
$64$	−53.2873	−	35.4466i	−0.832614	−	0.553853i
$65$	−55.5539			−0.854676
$66$		0			0
$67$		−	69.2040i		−	1.03290i	−0.856319	−	0.516448i	$-0.827254\pi$
$67$		−	69.2040i		−	1.03290i	0.856319	−	0.516448i	$-0.172746\pi$
$68$	−5.63912	−	1.11766i	−0.0829282	−	0.0164362i
$69$		0			0
$70$	99.1230	+	9.72834i	1.41604	+	0.138976i
$71$		−	7.14792i		−	0.100675i	−0.998732	−	0.0503375i	$-0.983970\pi$
$71$		−	7.14792i		−	0.100675i	0.998732	−	0.0503375i	$-0.0160297\pi$
$72$		0			0
$73$	−80.4410			−1.10193			−0.550965	−	0.834528i	$-0.685740\pi$
$73$	−80.4410			−1.10193			−0.550965	+	0.834528i	$0.685740\pi$
$74$	−8.68162	+	88.4579i	−0.117319	+	1.19538i
$75$		0			0
$76$	10.8051	−	54.5169i	0.142172	−	0.717328i
$77$	123.519			1.60414
$78$		0			0
$79$			46.8439i			0.592960i	0.955039	+	0.296480i	$0.0958129\pi$
$79$			46.8439i			0.592960i	−0.955039	+	0.296480i	$0.904187\pi$
$80$	−107.054	−	44.1709i	−1.33818	−	0.552136i
$81$		0			0
$82$	11.1332	−	113.437i	0.135771	−	1.38338i
$83$		−	142.199i		−	1.71324i	−0.515950	−	0.856619i	$-0.672561\pi$
$83$		−	142.199i		−	1.71324i	0.515950	−	0.856619i	$-0.327439\pi$
$84$		0			0
$85$	−10.4026			−0.122383
$86$	134.590	+	13.2092i	1.56500	+	0.153596i
$87$		0			0
$88$	−137.480	−	41.5492i	−1.56227	−	0.472150i
$89$	−42.1078			−0.473122			−0.236561	−	0.971617i	$-0.576020\pi$
$89$	−42.1078			−0.473122			−0.236561	+	0.971617i	$0.576020\pi$
$90$		0			0
$91$			52.8077i			0.580304i
$92$	−12.8955	+	65.0642i	−0.140169	+	0.707219i
$93$		0			0
$94$	−18.7788	−	1.84303i	−0.199775	−	0.0196067i
$95$		−	100.568i		−	1.05861i
$96$		0			0
$97$	62.8955			0.648408			0.324204	−	0.945987i	$-0.394904\pi$
$97$	62.8955			0.648408			0.324204	+	0.945987i	$0.394904\pi$
$98$	−0.324695	+	3.30835i	−0.00331321	+	0.0337586i
$99$		0			0
$100$	−107.467	−	21.2997i	−1.07467	−	0.212997i
$101$	−47.6143			−0.471429			−0.235715	−	0.971822i	$-0.575743\pi$
$101$	−47.6143			−0.471429			−0.235715	+	0.971822i	$0.575743\pi$
$102$		0			0
$103$			53.7241i			0.521593i	0.965394	+	0.260797i	$0.0839852\pi$
$103$			53.7241i			0.521593i	−0.965394	+	0.260797i	$0.916015\pi$
$104$	17.7634	−	58.7765i	0.170802	−	0.565158i
$105$		0			0
$106$	−1.52893	+	15.5784i	−0.0144238	+	0.146966i
$107$			26.4708i			0.247390i	0.992320	+	0.123695i	$0.0394745\pi$
$107$			26.4708i			0.247390i	−0.992320	+	0.123695i	$0.960525\pi$
$108$		0			0
$109$	83.0647			0.762061			0.381031	−	0.924562i	$-0.375569\pi$
$109$	83.0647			0.762061			0.381031	+	0.924562i	$0.375569\pi$
$110$	−258.642	−	25.3842i	−2.35129	−	0.230765i
$111$		0			0
$112$	−41.9874	+	101.762i	−0.374887	+	0.908592i
$113$	15.5276			0.137413			0.0687064	−	0.997637i	$-0.478113\pi$
$113$	15.5276			0.137413			0.0687064	+	0.997637i	$0.478113\pi$
$114$		0			0
$115$			120.025i			1.04369i
$116$	−147.145	−	29.1638i	−1.26849	−	0.251412i
$117$		0			0
$118$	44.6106	+	4.37827i	0.378056	+	0.0371039i
$119$			9.88832i			0.0830951i
$120$		0			0
$121$	−201.298			−1.66362
$122$	13.1239	−	133.720i	0.107573	−	1.09607i
$123$		0			0
$124$	−41.9874	+	211.846i	−0.338608	+	1.70844i
$125$	−17.2947			−0.138358
$126$		0			0
$127$		−	157.463i		−	1.23987i	−0.784654	−	0.619934i	$-0.787159\pi$
$127$		−	157.463i		−	1.23987i	0.784654	−	0.619934i	$-0.212841\pi$
$128$	80.9639	−	99.1406i	0.632530	−	0.774536i
$129$		0			0
$130$	10.8524	−	110.577i	0.0834803	−	0.850589i
$131$			47.0592i			0.359231i	0.983737	+	0.179615i	$0.0574853\pi$
$131$			47.0592i			0.359231i	−0.983737	+	0.179615i	$0.942515\pi$
$132$		0			0
$133$	−95.5966			−0.718771
$134$	137.746	+	13.5190i	1.02796	+	0.100888i
$135$		0			0
$136$	3.32623	−	11.0060i	0.0244576	−	0.0809263i
$137$	−117.497			−0.857644			−0.428822	−	0.903389i	$-0.641071\pi$
$137$	−117.497			−0.857644			−0.428822	+	0.903389i	$0.641071\pi$
$138$		0			0
$139$		−	39.6959i		−	0.285582i	−0.989753	−	0.142791i	$-0.954392\pi$
$139$		−	39.6959i		−	0.285582i	0.989753	−	0.142791i	$-0.0456077\pi$
$140$	−38.7273	+	195.398i	−0.276624	+	1.39570i
$141$		0			0
$142$	14.2275	+	1.39634i	0.100194	+	0.00983341i
$143$		−	137.791i		−	0.963575i
$144$		0			0
$145$	−271.441			−1.87200
$146$	15.7141	−	160.113i	0.107631	−	1.09666i
$147$		0			0
$148$	−174.374	−	34.5604i	−1.17820	−	0.233516i
$149$	114.827			0.770652			0.385326	−	0.922781i	$-0.374089\pi$
$149$	114.827			0.770652			0.385326	+	0.922781i	$0.374089\pi$
$150$		0			0
$151$		−	160.122i		−	1.06041i	−0.847869	−	0.530206i	$-0.822115\pi$
$151$		−	160.122i		−	1.06041i	0.847869	−	0.530206i	$-0.177885\pi$
$152$	106.402	+	32.1567i	0.700011	+	0.211557i
$153$		0			0
$154$	−24.1293	+	245.856i	−0.156684	+	1.59647i
$155$			390.795i			2.52126i
$156$		0			0
$157$	225.337			1.43527			0.717634	−	0.696421i	$-0.245225\pi$
$157$	225.337			1.43527			0.717634	+	0.696421i	$0.245225\pi$
$158$	−93.2397	−	9.15093i	−0.590125	−	0.0579173i
$159$		0			0
$160$	108.832	−	204.456i	0.680202	−	1.27785i
$161$	114.091			0.708643
$162$		0			0
$163$		−	147.165i		−	0.902850i	−0.892309	−	0.451425i	$-0.850916\pi$
$163$		−	147.165i		−	0.902850i	0.892309	−	0.451425i	$-0.149084\pi$
$164$	223.615	+	44.3198i	1.36350	+	0.270243i
$165$		0			0
$166$	283.038	+	27.7785i	1.70505	+	0.167340i
$167$			105.944i			0.634396i	0.948359	+	0.317198i	$0.102742\pi$
$167$			105.944i			0.634396i	−0.948359	+	0.317198i	$0.897258\pi$
$168$		0			0
$169$	−110.090			−0.651423
$170$	2.03213	−	20.7056i	0.0119537	−	0.121798i
$171$		0			0
$172$	−52.5843	+	265.313i	−0.305723	+	1.54252i
$173$	186.424			1.07759			0.538797	−	0.842436i	$-0.318879\pi$
$173$	186.424			1.07759			0.538797	+	0.842436i	$0.318879\pi$
$174$		0			0
$175$			188.446i			1.07683i
$176$	109.558	−	265.528i	0.622487	−	1.50868i
$177$		0			0
$178$	8.22575	−	83.8130i	0.0462121	−	0.470859i
$179$			191.597i			1.07037i	0.844734	+	0.535187i	$0.179759\pi$
$179$			191.597i			1.07037i	−0.844734	+	0.535187i	$0.820241\pi$
$180$		0			0
$181$	204.960			1.13237			0.566187	−	0.824277i	$-0.308418\pi$
$181$	204.960			1.13237			0.566187	+	0.824277i	$0.308418\pi$
$182$	−105.110	−	10.3160i	−0.577530	−	0.0566811i
$183$		0			0
$184$	−126.987	−	38.3780i	−0.690147	−	0.208576i
$185$	−321.670			−1.73875
$186$		0			0
$187$		−	25.8016i		−	0.137976i
$188$	7.33688	−	37.0180i	0.0390259	−	0.196904i
$189$		0			0
$190$	200.174	+	19.6459i	1.05355	+	0.103400i
$191$		−	89.8155i		−	0.470238i	−0.971967	−	0.235119i	$-0.924452\pi$
$191$		−	89.8155i		−	0.470238i	0.971967	−	0.235119i	$-0.0755480\pi$
$192$		0			0
$193$	167.596			0.868374			0.434187	−	0.900823i	$-0.357036\pi$
$193$	167.596			0.868374			0.434187	+	0.900823i	$0.357036\pi$
$194$	−12.2866	+	125.190i	−0.0633331	+	0.645307i
$195$		0			0
$196$	−6.52163	−	1.29257i	−0.0332736	−	0.00659474i
$197$	−185.277			−0.940492			−0.470246	−	0.882535i	$-0.655835\pi$
$197$	−185.277			−0.940492			−0.470246	+	0.882535i	$0.655835\pi$
$198$		0			0
$199$		−	137.625i		−	0.691585i	−0.938311	−	0.345793i	$-0.887610\pi$
$199$		−	137.625i		−	0.691585i	0.938311	−	0.345793i	$-0.112390\pi$
$200$	63.3894	−	209.746i	0.316947	−	1.04873i
$201$		0			0
$202$	9.30144	−	94.7733i	0.0460467	−	0.469175i
$203$			258.022i			1.27105i
$204$		0			0
$205$	412.505			2.01222
$206$	−106.934	−	10.4950i	−0.519099	−	0.0509465i
$207$		0			0
$208$	113.521	+	46.8389i	0.545773	+	0.225187i
$209$	249.440			1.19349
$210$		0			0
$211$			305.254i			1.44670i	0.690482	+	0.723350i	$0.257398\pi$
$211$			305.254i			1.44670i	−0.690482	+	0.723350i	$0.742602\pi$
$212$	−30.7091	−	6.08647i	−0.144854	−	0.0287097i
$213$		0			0
$214$	−52.6884	−	5.17106i	−0.246207	−	0.0241638i
$215$			489.426i			2.27640i
$216$		0			0
$217$	371.477			1.71188
$218$	−16.2267	+	165.335i	−0.0744342	+	0.758417i
$219$		0			0
$220$	101.051	−	509.851i	0.459323	−	2.31751i
$221$	11.0309			0.0499136
$222$		0			0
$223$			17.2224i			0.0772303i	0.999254	+	0.0386152i	$0.0122946\pi$
$223$			17.2224i			0.0772303i	−0.999254	+	0.0386152i	$0.987705\pi$
$224$	−194.349	−	103.452i	−0.867630	−	0.461841i
$225$		0			0
$226$	−3.03332	+	30.9068i	−0.0134218	+	0.136756i
$227$		−	40.9846i		−	0.180549i	−0.995917	−	0.0902744i	$-0.971226\pi$
$227$		−	40.9846i		−	0.180549i	0.995917	−	0.0902744i	$-0.0287744\pi$
$228$		0			0
$229$	−133.453			−0.582763			−0.291381	−	0.956607i	$-0.594115\pi$
$229$	−133.453			−0.582763			−0.291381	+	0.956607i	$0.594115\pi$
$230$	−238.901	−	23.4468i	−1.03870	−	0.101942i
$231$		0			0
$232$	86.7935	−	287.186i	0.374110	−	1.23787i
$233$	368.345			1.58088			0.790441	−	0.612539i	$-0.209852\pi$
$233$	368.345			1.58088			0.790441	+	0.612539i	$0.209852\pi$
$234$		0			0
$235$		−	68.2876i		−	0.290586i
$236$	−17.4293	+	87.9393i	−0.0738531	+	0.372624i
$237$		0			0
$238$	−19.6821	−	1.93168i	−0.0826978	−	0.00811630i
$239$			288.560i			1.20737i	0.797225	+	0.603683i	$0.206301\pi$
$239$			288.560i			1.20737i	−0.797225	+	0.603683i	$0.793699\pi$
$240$		0			0
$241$	−102.987			−0.427333			−0.213667	−	0.976907i	$-0.568541\pi$
$241$	−102.987			−0.427333			−0.213667	+	0.976907i	$0.568541\pi$
$242$	39.3234	−	400.670i	0.162493	−	1.65566i
$243$		0			0
$244$	263.598	+	52.2444i	1.08032	+	0.214116i
$245$	−12.0305			−0.0491042
$246$		0			0
$247$			106.643i			0.431751i
$248$	−413.464	−	124.957i	−1.66720	−	0.503860i
$249$		0			0
$250$	3.37852	−	34.4241i	0.0135141	−	0.137696i
$251$		−	69.9866i		−	0.278831i	−0.990234	−	0.139416i	$-0.955478\pi$
$251$		−	69.9866i		−	0.278831i	0.990234	−	0.139416i	$-0.0445224\pi$
$252$		0			0
$253$	−297.699			−1.17668
$254$	313.421	+	30.7604i	1.23394	+	0.121104i
$255$		0			0
$256$	181.517	+	180.521i	0.709050	+	0.705158i
$257$	−97.0819			−0.377751			−0.188875	−	0.982001i	$-0.560484\pi$
$257$	−97.0819			−0.377751			−0.188875	+	0.982001i	$0.560484\pi$
$258$		0			0
$259$			305.768i			1.18057i
$260$	217.976	+	43.2022i	0.838368	+	0.166162i
$261$		0			0
$262$	−93.6684	−	9.19301i	−0.357513	−	0.0350878i
$263$			8.40472i			0.0319571i	0.999872	+	0.0159785i	$0.00508635\pi$
$263$			8.40472i			0.0319571i	−0.999872	+	0.0159785i	$0.994914\pi$
$264$		0			0
$265$	−56.6495			−0.213772
$266$	18.6748	−	190.279i	0.0702058	−	0.715334i
$267$		0			0
$268$	−53.8174	+	271.534i	−0.200811	+	1.01319i
$269$	−281.198			−1.04535			−0.522673	−	0.852533i	$-0.675065\pi$
$269$	−281.198			−1.04535			−0.522673	+	0.852533i	$0.675065\pi$
$270$		0			0
$271$		−	369.456i		−	1.36331i	−0.731675	−	0.681654i	$-0.761261\pi$
$271$		−	369.456i		−	1.36331i	0.731675	−	0.681654i	$-0.238739\pi$
$272$	21.2569	+	8.77066i	0.0781505	+	0.0322451i
$273$		0			0
$274$	22.9530	−	233.871i	0.0837702	−	0.853543i
$275$		−	491.713i		−	1.78805i
$276$		0			0
$277$	132.909			0.479817			0.239908	−	0.970796i	$-0.422883\pi$
$277$	132.909			0.479817			0.239908	+	0.970796i	$0.422883\pi$
$278$	79.0123	+	7.75459i	0.284217	+	0.0278942i
$279$		0			0
$280$	−381.361	−	115.255i	−1.36200	−	0.411625i
$281$	−37.3154			−0.132795			−0.0663974	−	0.997793i	$-0.521151\pi$
$281$	−37.3154			−0.132795			−0.0663974	+	0.997793i	$0.521151\pi$
$282$		0			0
$283$			156.168i			0.551832i	0.961182	+	0.275916i	$0.0889811\pi$
$283$			156.168i			0.551832i	−0.961182	+	0.275916i	$0.911019\pi$
$284$	−5.55867	+	28.0461i	−0.0195728	+	0.0987540i
$285$		0			0
$286$	274.265	+	26.9175i	0.958967	+	0.0941170i
$287$		−	392.113i		−	1.36625i
$288$		0			0
$289$	−286.934			−0.992853
$290$	53.0258	−	540.285i	0.182848	−	1.86305i
$291$		0			0
$292$	315.624	+	62.5559i	1.08091	+	0.214232i
$293$	−25.9762			−0.0886561			−0.0443280	−	0.999017i	$-0.514115\pi$
$293$	−25.9762			−0.0886561			−0.0443280	+	0.999017i	$0.514115\pi$
$294$		0			0
$295$			162.223i			0.549907i
$296$	102.854	−	340.329i	0.347481	−	1.14976i
$297$		0			0
$298$	−22.4314	+	228.556i	−0.0752733	+	0.766967i
$299$		−	127.275i		−	0.425667i
$300$		0			0
$301$	465.232			1.54562
$302$	318.713	+	31.2798i	1.05534	+	0.103575i
$303$		0			0
$304$	−84.7915	+	205.504i	−0.278919	+	0.676000i
$305$	486.262			1.59430
$306$		0			0
$307$		−	111.670i		−	0.363745i	−0.983322	−	0.181872i	$-0.941784\pi$
$307$		−	111.670i		−	0.363745i	0.983322	−	0.181872i	$-0.0582158\pi$
$308$	−484.648	−	96.0559i	−1.57353	−	0.311870i
$309$		0			0
$310$	−777.854	−	76.3417i	−2.50920	−	0.246264i
$311$			323.742i			1.04097i	0.853871	+	0.520485i	$0.174249\pi$
$311$			323.742i			1.04097i	−0.853871	+	0.520485i	$0.825751\pi$
$312$		0			0
$313$	−366.181			−1.16991			−0.584953	−	0.811067i	$-0.698887\pi$
$313$	−366.181			−1.16991			−0.584953	+	0.811067i	$0.698887\pi$
$314$	−44.0195	+	448.519i	−0.140189	+	1.42840i
$315$		0			0
$316$	36.4287	−	183.800i	0.115281	−	0.581646i
$317$	−65.0029			−0.205056			−0.102528	−	0.994730i	$-0.532693\pi$
$317$	−65.0029			−0.205056			−0.102528	+	0.994730i	$0.532693\pi$
$318$		0			0
$319$		−	673.258i		−	2.11053i
$320$	385.696	+	256.564i	1.20530	+	0.801764i
$321$		0			0
$322$	−22.2877	+	227.092i	−0.0692165	+	0.705254i
$323$			19.9690i			0.0618235i
$324$		0			0
$325$	210.221			0.646833
$326$	292.922	+	28.7485i	0.898533	+	0.0881857i
$327$		0			0
$328$	−131.899	+	436.433i	−0.402131	+	1.33059i
$329$	−64.9119			−0.197301
$330$		0			0
$331$		−	439.440i		−	1.32761i	−0.747904	−	0.663807i	$-0.768940\pi$
$331$		−	439.440i		−	1.32761i	0.747904	−	0.663807i	$-0.231060\pi$
$332$	−110.583	+	557.942i	−0.333080	+	1.68055i
$333$		0			0
$334$	−210.875	−	20.6962i	−0.631363	−	0.0619645i
$335$			500.902i			1.49523i
$336$		0			0
$337$	−374.818			−1.11222			−0.556109	−	0.831109i	$-0.687706\pi$
$337$	−374.818			−1.11222			−0.556109	+	0.831109i	$0.687706\pi$
$338$	21.5061	−	219.128i	0.0636276	−	0.648308i
$339$		0			0
$340$	40.8163	+	8.08967i	0.120048	+	0.0237931i
$341$	−969.295			−2.84251
$342$		0			0
$343$			348.568i			1.01623i
$344$	−517.816	−	156.495i	−1.50528	−	0.454926i
$345$		0			0
$346$	−36.4178	+	371.065i	−0.105254	+	1.07244i
$347$		−	329.030i		−	0.948213i	−0.880467	−	0.474107i	$-0.842771\pi$
$347$		−	329.030i		−	0.948213i	0.880467	−	0.474107i	$-0.157229\pi$
$348$		0			0
$349$	372.506			1.06735			0.533676	−	0.845689i	$-0.320810\pi$
$349$	372.506			1.06735			0.533676	+	0.845689i	$0.320810\pi$
$350$	−375.090	−	36.8129i	−1.07169	−	0.105180i
$351$		0			0
$352$	507.115	+	269.938i	1.44067	+	0.766871i
$353$	−217.758			−0.616879			−0.308440	−	0.951244i	$-0.599807\pi$
$353$	−217.758			−0.616879			−0.308440	+	0.951244i	$0.599807\pi$
$354$		0			0
$355$			51.7370i			0.145738i
$356$	165.218	+	32.7457i	0.464094	+	0.0919822i
$357$		0			0
$358$	−381.361	−	37.4284i	−1.06526	−	0.104549i
$359$		−	145.576i		−	0.405505i	−0.979230	−	0.202753i	$-0.935011\pi$
$359$		−	145.576i		−	0.405505i	0.979230	−	0.202753i	$-0.0649887\pi$
$360$		0			0
$361$	167.947			0.465228
$362$	−40.0388	+	407.959i	−0.110604	+	1.12696i
$363$		0			0
$364$	41.0666	−	207.200i	0.112820	−	0.569232i
$365$	582.236			1.59517
$366$		0			0
$367$			53.4769i			0.145714i	0.997342	+	0.0728568i	$0.0232116\pi$
$367$			53.4769i			0.145714i	−0.997342	+	0.0728568i	$0.976788\pi$
$368$	101.196	−	245.262i	0.274989	−	0.666474i
$369$		0			0
$370$	62.8380	−	640.263i	0.169833	−	1.73044i
$371$			53.8491i			0.145146i
$372$		0			0
$373$	−341.504			−0.915561			−0.457781	−	0.889065i	$-0.651355\pi$
$373$	−341.504			−0.915561			−0.457781	+	0.889065i	$0.651355\pi$
$374$	51.3565	+	5.04033i	0.137317	+	0.0134768i
$375$		0			0
$376$	72.2488	+	21.8350i	0.192151	+	0.0580719i
$377$	287.837			0.763492
$378$		0			0
$379$			220.189i			0.580972i	0.956879	+	0.290486i	$0.0938170\pi$
$379$			220.189i			0.580972i	−0.956879	+	0.290486i	$0.906183\pi$
$380$	−78.2079	+	394.596i	−0.205810	+	1.03841i
$381$		0			0
$382$	178.772	+	17.5454i	0.467990	+	0.0459304i
$383$		−	671.073i		−	1.75215i	−0.482175	−	0.876075i	$-0.660153\pi$
$383$		−	671.073i		−	1.75215i	0.482175	−	0.876075i	$-0.339847\pi$
$384$		0			0
$385$	−894.035			−2.32217
$386$	−32.7399	+	333.590i	−0.0848183	+	0.864222i
$387$		0			0
$388$	−246.782	−	48.9115i	−0.636036	−	0.126061i
$389$	−484.924			−1.24659			−0.623296	−	0.781986i	$-0.714207\pi$
$389$	−484.924			−1.24659			−0.623296	+	0.781986i	$0.714207\pi$
$390$		0			0
$391$		−	23.8323i		−	0.0609523i
$392$	3.84677	−	12.7284i	0.00981320	−	0.0324704i
$393$		0			0
$394$	36.1938	−	368.782i	0.0918624	−	0.935995i
$395$		−	339.058i		−	0.858376i
$396$		0			0
$397$	−279.373			−0.703711			−0.351855	−	0.936054i	$-0.614449\pi$
$397$	−279.373			−0.703711			−0.351855	+	0.936054i	$0.614449\pi$
$398$	273.935	+	26.8851i	0.688278	+	0.0675505i
$399$		0			0
$400$	405.103	+	167.146i	1.01276	+	0.417866i
$401$	582.199			1.45187			0.725934	−	0.687765i	$-0.241408\pi$
$401$	582.199			1.45187			0.725934	+	0.687765i	$0.241408\pi$
$402$		0			0
$403$		−	414.401i		−	1.02829i
$404$	186.823	+	37.0279i	0.462434	+	0.0916531i
$405$		0			0
$406$	−513.577	−	50.4046i	−1.26497	−	0.124149i
$407$		−	797.842i		−	1.96030i
$408$		0			0
$409$	−436.661			−1.06763			−0.533815	−	0.845601i	$-0.679242\pi$
$409$	−436.661			−1.06763			−0.533815	+	0.845601i	$0.679242\pi$
$410$	−80.5827	+	821.065i	−0.196543	+	2.00260i
$411$		0			0
$412$	41.7792	−	210.796i	0.101406	−	0.511641i
$413$	154.203			0.373374
$414$		0			0
$415$			1029.24i			2.48010i
$416$	−115.406	+	216.806i	−0.277419	+	0.521168i
$417$		0			0
$418$	−48.7281	+	496.495i	−0.116574	+	1.18779i
$419$			758.271i			1.80972i	0.425714	+	0.904858i	$0.360023\pi$
$419$			758.271i			1.80972i	−0.425714	+	0.904858i	$0.639977\pi$
$420$		0			0
$421$	523.348			1.24311			0.621553	−	0.783372i	$-0.286502\pi$
$421$	523.348			1.24311			0.621553	+	0.783372i	$0.286502\pi$
$422$	−607.588	−	59.6312i	−1.43978	−	0.141306i
$423$		0			0
$424$	18.1137	−	59.9356i	0.0427211	−	0.141358i
$425$	39.3641			0.0926215
$426$		0			0
$427$		−	462.225i		−	1.08249i
$428$	20.5853	−	103.863i	0.0480965	−	0.242670i
$429$		0			0
$430$	−974.171	−	95.6092i	−2.26551	−	0.222347i
$431$			729.146i			1.69176i	0.533377	+	0.845878i	$0.320923\pi$
$431$			729.146i			1.69176i	−0.533377	+	0.845878i	$0.679077\pi$
$432$		0			0
$433$	−491.219			−1.13445			−0.567227	−	0.823561i	$-0.691984\pi$
$433$	−491.219			−1.13445			−0.567227	+	0.823561i	$0.691984\pi$
$434$	−72.5679	+	739.402i	−0.167207	+	1.70369i
$435$		0			0
$436$	−325.919	−	64.5963i	−0.747521	−	0.148157i
$437$	230.402			0.527236
$438$		0			0
$439$			188.693i			0.429825i	0.976633	+	0.214913i	$0.0689467\pi$
$439$			188.693i			0.429825i	−0.976633	+	0.214913i	$0.931053\pi$
$440$	995.087	+	300.735i	2.26156	+	0.683489i
$441$		0			0
$442$	−2.15488	+	21.9563i	−0.00487530	+	0.0496749i
$443$		−	413.208i		−	0.932749i	−0.884587	−	0.466375i	$-0.845560\pi$
$443$		−	413.208i		−	0.932749i	0.884587	−	0.466375i	$-0.154440\pi$
$444$		0			0
$445$	304.779			0.684896
$446$	−34.2800	−	3.36438i	−0.0768610	−	0.00754346i
$447$		0			0
$448$	243.882	−	366.630i	0.544378	−	0.818371i
$449$	638.253			1.42150			0.710749	−	0.703446i	$-0.248356\pi$
$449$	638.253			1.42150			0.710749	+	0.703446i	$0.248356\pi$
$450$		0			0
$451$			1023.14i			2.26861i
$452$	−60.9255	−	12.0753i	−0.134791	−	0.0267152i
$453$		0			0
$454$	81.5772	+	8.00633i	0.179686	+	0.0176351i
$455$		−	382.225i		−	0.840055i
$456$		0			0
$457$	−230.687			−0.504786			−0.252393	−	0.967625i	$-0.581218\pi$
$457$	−230.687			−0.504786			−0.252393	+	0.967625i	$0.581218\pi$
$458$	26.0699	−	265.629i	0.0569213	−	0.579976i
$459$		0			0
$460$	93.3386	−	470.938i	0.202910	−	1.02378i
$461$	400.188			0.868088			0.434044	−	0.900892i	$-0.357086\pi$
$461$	400.188			0.868088			0.434044	+	0.900892i	$0.357086\pi$
$462$		0			0
$463$			296.656i			0.640727i	0.947295	+	0.320363i	$0.103805\pi$
$463$			296.656i			0.640727i	−0.947295	+	0.320363i	$0.896195\pi$
$464$	554.671	+	228.859i	1.19541	+	0.493230i
$465$		0			0
$466$	−71.9561	+	733.168i	−0.154412	+	1.57332i
$467$		−	127.057i		−	0.272070i	−0.990704	−	0.136035i	$-0.956564\pi$
$467$		−	127.057i		−	0.272070i	0.990704	−	0.136035i	$-0.0434359\pi$
$468$		0			0
$469$	476.141			1.01523
$470$	135.922	+	13.3400i	0.289196	+	0.0283829i
$471$		0			0
$472$	−171.633	−	51.8709i	−0.363629	−	0.109896i
$473$	−1213.93			−2.56645
$474$		0			0
$475$			380.558i			0.801174i
$476$	7.68977	−	38.7986i	0.0161550	−	0.0815096i
$477$		0			0
$478$	−574.361	−	56.3701i	−1.20159	−	0.117929i
$479$			12.3150i			0.0257098i	0.999917	+	0.0128549i	$0.00409195\pi$
$479$			12.3150i			0.0257098i	−0.999917	+	0.0128549i	$0.995908\pi$
$480$		0			0
$481$	341.100			0.709147
$482$	20.1185	−	204.990i	0.0417397	−	0.425290i
$483$		0			0
$484$	789.827	+	156.542i	1.63187	+	0.323433i
$485$	−455.241			−0.938642
$486$		0			0
$487$		−	181.054i		−	0.371773i	−0.982571	−	0.185887i	$-0.940484\pi$
$487$		−	181.054i		−	0.371773i	0.982571	−	0.185887i	$-0.0595157\pi$
$488$	−155.483	+	514.469i	−0.318613	+	1.05424i
$489$		0			0
$490$	2.35016	−	23.9460i	0.00479624	−	0.0488694i
$491$		−	497.080i		−	1.01238i	−0.862421	−	0.506191i	$-0.831053\pi$
$491$		−	497.080i		−	1.01238i	0.862421	−	0.506191i	$-0.168947\pi$
$492$		0			0
$493$	53.8978			0.109326
$494$	−212.265	−	20.8326i	−0.429687	−	0.0421712i
$495$		0			0
$496$	329.490	−	798.565i	0.664294	−	1.61001i
$497$	49.1795			0.0989527
$498$		0			0
$499$		−	762.567i		−	1.52819i	−0.645103	−	0.764096i	$-0.723186\pi$
$499$		−	762.567i		−	1.52819i	0.645103	−	0.764096i	$-0.276814\pi$
$500$	67.8589	+	13.4495i	0.135718	+	0.0268989i
$501$		0			0
$502$	139.304	+	13.6719i	0.277498	+	0.0272348i
$503$		−	994.596i		−	1.97733i	−0.150146	−	0.988664i	$-0.547974\pi$
$503$		−	994.596i		−	1.97733i	0.150146	−	0.988664i	$-0.452026\pi$
$504$		0			0
$505$	344.635			0.682446
$506$	58.1554	−	592.551i	0.114932	−	1.17105i
$507$		0			0
$508$	−122.453	+	617.835i	−0.241050	+	1.21621i
$509$	−53.7310			−0.105562			−0.0527810	−	0.998606i	$-0.516809\pi$
$509$	−53.7310			−0.105562			−0.0527810	+	0.998606i	$0.516809\pi$
$510$		0			0
$511$		−	553.454i		−	1.08308i
$512$	−394.774	+	326.033i	−0.771043	+	0.636783i
$513$		0			0
$514$	18.9649	−	193.235i	0.0368967	−	0.375944i
$515$		−	388.858i		−	0.755064i
$516$		0			0
$517$	169.375			0.327611
$518$	−608.613	−	59.7318i	−1.17493	−	0.115312i
$519$		0			0
$520$	−128.573	+	425.427i	−0.247255	+	0.818129i
$521$	−616.206			−1.18274			−0.591369	−	0.806401i	$-0.701412\pi$
$521$	−616.206			−1.18274			−0.591369	+	0.806401i	$0.701412\pi$
$522$		0			0
$523$		−	683.938i		−	1.30772i	−0.756615	−	0.653860i	$-0.773148\pi$
$523$		−	683.938i		−	1.30772i	0.756615	−	0.653860i	$-0.226852\pi$
$524$	36.5962	−	184.645i	0.0698401	−	0.352376i
$525$		0			0
$526$	−16.7291	−	1.64186i	−0.0318043	−	0.00312140i
$527$		−	77.5971i		−	0.147243i
$528$		0			0
$529$	254.022			0.480194
$530$	11.0665	−	112.757i	0.0208801	−	0.212749i
$531$		0			0
$532$	375.090	+	74.3418i	0.705057	+	0.139740i
$533$	−437.421			−0.820678
$534$		0			0
$535$		−	191.597i		−	0.358125i
$536$	−529.959	−	160.164i	−0.988729	−	0.298814i
$537$		0			0
$538$	54.9320	−	559.707i	0.102104	−	1.04035i
$539$		−	29.8395i		−	0.0553608i
$540$		0			0
$541$	518.000			0.957486			0.478743	−	0.877955i	$-0.341093\pi$
$541$	518.000			0.957486			0.478743	+	0.877955i	$0.341093\pi$
$542$	735.379	+	72.1731i	1.35679	+	0.133161i
$543$		0			0
$544$	−21.6100	+	40.5972i	−0.0397242	+	0.0746272i
$545$	−601.227			−1.10317
$546$		0			0
$547$			294.263i			0.537957i	0.963146	+	0.268979i	$0.0866861\pi$
$547$			294.263i			0.537957i	−0.963146	+	0.268979i	$0.913314\pi$
$548$	461.021	+	91.3732i	0.841280	+	0.166739i
$549$		0			0
$550$	978.723	+	96.0559i	1.77950	+	0.174647i
$551$			521.064i			0.945669i
$552$		0			0
$553$	−322.298			−0.582817
$554$	−25.9638	+	264.547i	−0.0468660	+	0.477522i
$555$		0			0
$556$	−30.8700	+	155.754i	−0.0555216	+	0.280133i
$557$	−395.706			−0.710424			−0.355212	−	0.934786i	$-0.615591\pi$
$557$	−395.706			−0.710424			−0.355212	+	0.934786i	$0.615591\pi$
$558$		0			0
$559$		−	518.989i		−	0.928424i
$560$	303.907	−	736.561i	0.542691	−	1.31529i
$561$		0			0
$562$	7.28954	−	74.2739i	0.0129707	−	0.132160i
$563$			259.253i			0.460484i	0.973133	+	0.230242i	$0.0739518\pi$
$563$			259.253i			0.460484i	−0.973133	+	0.230242i	$0.926048\pi$
$564$		0			0
$565$	−112.390			−0.198920
$566$	−310.843	−	30.5074i	−0.549193	−	0.0539001i
$567$		0			0
$568$	−54.7382	−	16.5430i	−0.0963700	−	0.0291250i
$569$	247.188			0.434426			0.217213	−	0.976124i	$-0.430303\pi$
$569$	247.188			0.434426			0.217213	+	0.976124i	$0.430303\pi$
$570$		0			0
$571$		−	601.307i		−	1.05308i	−0.850151	−	0.526539i	$-0.823489\pi$
$571$		−	601.307i		−	1.05308i	0.850151	−	0.526539i	$-0.176511\pi$
$572$	−107.155	+	540.648i	−0.187334	+	0.945189i
$573$		0			0
$574$	780.477	+	76.5992i	1.35972	+	0.133448i
$575$		−	454.184i		−	0.789885i
$576$		0			0
$577$	−754.648			−1.30788			−0.653941	−	0.756545i	$-0.726886\pi$
$577$	−754.648			−1.30788			−0.653941	+	0.756545i	$0.726886\pi$
$578$	56.0525	−	571.125i	0.0969767	−	0.988105i
$579$		0			0
$580$	1065.05	+	211.089i	1.83628	+	0.363947i
$581$	978.363			1.68393
$582$		0			0
$583$		−	140.509i		−	0.241010i
$584$	−186.171	+	616.010i	−0.318785	+	1.05481i
$585$		0			0
$586$	5.07445	−	51.7040i	0.00865946	−	0.0882321i
$587$			243.805i			0.415342i	0.978199	+	0.207671i	$0.0665883\pi$
$587$			243.805i			0.415342i	−0.978199	+	0.207671i	$0.933412\pi$
$588$		0			0
$589$	750.180			1.27365
$590$	−322.894	−	31.6901i	−0.547278	−	0.0537121i
$591$		0			0
$592$	657.311	+	271.208i	1.11032	+	0.458122i
$593$	1091.73			1.84103			0.920516	−	0.390704i	$-0.127768\pi$
$593$	1091.73			1.84103			0.920516	+	0.390704i	$0.127768\pi$
$594$		0			0
$595$		−	71.5722i		−	0.120289i
$596$	−450.545	−	89.2967i	−0.755947	−	0.149827i
$597$		0			0
$598$	253.332	+	24.8630i	0.423632	+	0.0415770i
$599$		−	940.721i		−	1.57049i	−0.619188	−	0.785243i	$-0.712538\pi$
$599$		−	940.721i		−	1.57049i	0.619188	−	0.785243i	$-0.287462\pi$
$600$		0			0
$601$	1052.23			1.75079			0.875396	−	0.483406i	$-0.160600\pi$
$601$	1052.23			1.75079			0.875396	+	0.483406i	$0.160600\pi$
$602$	−90.8829	+	926.015i	−0.150968	+	1.53823i
$603$		0			0
$604$	−124.521	+	628.267i	−0.206160	+	1.04018i
$605$	1457.00			2.40827
$606$		0			0
$607$			439.798i			0.724544i	0.932072	+	0.362272i	$0.117999\pi$
$607$			439.798i			0.724544i	−0.932072	+	0.362272i	$0.882001\pi$
$608$	−392.479	−	208.917i	−0.645524	−	0.343614i
$609$		0			0
$610$	−94.9912	+	967.875i	−0.155723	+	1.58668i
$611$			72.4124i			0.118515i
$612$		0			0
$613$	449.866			0.733876			0.366938	−	0.930245i	$-0.380406\pi$
$613$	449.866			0.733876			0.366938	+	0.930245i	$0.380406\pi$
$614$	222.271	+	21.8146i	0.362005	+	0.0355287i
$615$		0			0
$616$	285.869	−	945.896i	0.464073	−	1.53555i
$617$	−848.536			−1.37526			−0.687630	−	0.726061i	$-0.741349\pi$
$617$	−848.536			−1.37526			−0.687630	+	0.726061i	$0.741349\pi$
$618$		0			0
$619$			539.918i			0.872242i	0.899888	+	0.436121i	$0.143648\pi$
$619$			539.918i			0.872242i	−0.899888	+	0.436121i	$0.856352\pi$
$620$	303.907	−	1533.35i	0.490172	−	2.47315i
$621$		0			0
$622$	−644.387	−	63.2428i	−1.03599	−	0.101677i
$623$		−	289.713i		−	0.465028i
$624$		0			0
$625$	−559.555			−0.895288
$626$	71.5332	−	728.859i	0.114270	−	1.16431i
$627$		0			0
$628$	−884.150	−	175.236i	−1.40788	−	0.279038i
$629$	63.8714			0.101544
$630$		0			0
$631$			43.6036i			0.0691024i	0.999403	+	0.0345512i	$0.0110002\pi$
$631$			43.6036i			0.0691024i	−0.999403	+	0.0345512i	$0.989000\pi$
$632$	358.726	+	108.414i	0.567605	+	0.171542i
$633$		0			0
$634$	12.6983	−	129.384i	0.0200288	−	0.204076i
$635$			1139.73i			1.79485i
$636$		0			0
$637$	12.7572			0.0200270
$638$	1340.08	+	131.521i	2.10043	+	0.206145i
$639$		0			0
$640$	−586.021	+	717.585i	−0.915657	+	1.12123i
$641$	−167.263			−0.260940			−0.130470	−	0.991452i	$-0.541649\pi$
$641$	−167.263			−0.260940			−0.130470	+	0.991452i	$0.541649\pi$
$642$		0			0
$643$			745.770i			1.15983i	0.814678	+	0.579914i	$0.196914\pi$
$643$			745.770i			1.15983i	−0.814678	+	0.579914i	$0.803086\pi$
$644$	−447.658	−	88.7246i	−0.695121	−	0.137771i
$645$		0			0
$646$	−39.7470	−	3.90093i	−0.0615279	−	0.00603860i
$647$			596.836i			0.922467i	0.887279	+	0.461233i	$0.152593\pi$
$647$			596.836i			0.922467i	−0.887279	+	0.461233i	$0.847407\pi$
$648$		0			0
$649$	−402.363			−0.619974
$650$	−41.0666	+	418.431i	−0.0631793	+	0.643740i
$651$		0			0
$652$	−114.444	+	577.426i	−0.175528	+	0.885623i
$653$	−790.871			−1.21113			−0.605567	−	0.795794i	$-0.707054\pi$
$653$	−790.871			−1.21113			−0.605567	+	0.795794i	$0.707054\pi$
$654$		0			0
$655$		−	340.617i		−	0.520026i
$656$	−842.926	−	347.793i	−1.28495	−	0.530173i
$657$		0			0
$658$	12.6805	−	129.203i	0.0192713	−	0.196357i
$659$			402.569i			0.610878i	0.952212	+	0.305439i	$0.0988033\pi$
$659$			402.569i			0.610878i	−0.952212	+	0.305439i	$0.901197\pi$
$660$		0			0
$661$	486.544			0.736072			0.368036	−	0.929811i	$-0.380030\pi$
$661$	486.544			0.736072			0.368036	+	0.929811i	$0.380030\pi$
$662$	874.678	+	85.8445i	1.32127	+	0.129674i
$663$		0			0
$664$	−1088.95	−	329.101i	−1.63998	−	0.495634i
$665$	691.933			1.04050
$666$		0			0
$667$		−	621.873i		−	0.932343i
$668$	82.3888	−	415.691i	0.123337	−	0.622292i
$669$		0			0
$670$	−997.015	−	97.8511i	−1.48808	−	0.146046i
$671$			1206.08i			1.79744i
$672$		0			0
$673$	−171.727			−0.255167			−0.127583	−	0.991828i	$-0.540722\pi$
$673$	−171.727			−0.255167			−0.127583	+	0.991828i	$0.540722\pi$
$674$	73.2205	−	746.051i	0.108636	−	1.10690i
$675$		0			0
$676$	431.959	+	85.6132i	0.638993	+	0.126647i
$677$	213.095			0.314763			0.157382	−	0.987538i	$-0.449695\pi$
$677$	213.095			0.314763			0.157382	+	0.987538i	$0.449695\pi$
$678$		0			0
$679$			432.737i			0.637316i
$680$	−24.0754	+	79.6619i	−0.0354050	+	0.117150i
$681$		0			0
$682$	189.352	−	1929.32i	0.277642	−	2.82892i
$683$			602.265i			0.881794i	0.897558	+	0.440897i	$0.145340\pi$
$683$			602.265i			0.881794i	−0.897558	+	0.440897i	$0.854660\pi$
$684$		0			0
$685$	850.451			1.24153
$686$	−693.803	−	68.0927i	−1.01137	−	0.0992605i
$687$		0			0
$688$	412.648	−	1000.11i	0.599779	−	1.45365i
$689$	60.0713			0.0871862
$690$		0			0
$691$		−	1227.31i		−	1.77614i	−0.459705	−	0.888071i	$-0.652045\pi$
$691$		−	1227.31i		−	1.77614i	0.459705	−	0.888071i	$-0.347955\pi$
$692$	−731.466	−	144.975i	−1.05703	−	0.209501i
$693$		0			0
$694$	654.913	+	64.2759i	0.943679	+	0.0926166i
$695$			287.321i			0.413412i
$696$		0			0
$697$	−81.9078			−0.117515
$698$	−72.7689	+	741.449i	−0.104253	+	1.06225i
$699$		0			0
$700$	146.547	−	739.402i	0.209353	−	1.05629i
$701$	−133.314			−0.190176			−0.0950882	−	0.995469i	$-0.530313\pi$
$701$	−133.314			−0.190176			−0.0950882	+	0.995469i	$0.530313\pi$
$702$		0			0
$703$			617.485i			0.878357i
$704$	−636.360	+	956.649i	−0.903921	+	1.35888i
$705$		0			0
$706$	42.5390	−	433.434i	0.0602536	−	0.613929i
$707$		−	327.599i		−	0.463364i
$708$		0			0
$709$	−610.256			−0.860728			−0.430364	−	0.902655i	$-0.641615\pi$
$709$	−610.256			−0.860728			−0.430364	+	0.902655i	$0.641615\pi$
$710$	−102.979	−	10.1068i	−0.145041	−	0.0142349i
$711$		0			0
$712$	−97.4534	+	322.458i	−0.136873	+	0.452891i
$713$	−895.316			−1.25570
$714$		0			0
$715$			997.340i			1.39488i
$716$	148.998	−	751.764i	0.208097	−	1.04995i
$717$		0			0
$718$	289.761	+	28.4383i	0.403566	+	0.0396077i
$719$			967.279i			1.34531i	0.739956	+	0.672656i	$0.234846\pi$
$719$			967.279i			1.34531i	−0.739956	+	0.672656i	$0.765154\pi$
$720$		0			0
$721$	−369.635			−0.512671
$722$	−32.8084	+	334.289i	−0.0454411	+	0.463004i
$723$		0			0
$724$	−804.196	−	159.389i	−1.11077	−	0.220151i
$725$	1027.15			1.41676
$726$		0			0
$727$			1396.59i			1.92103i	0.278220	+	0.960517i	$0.410256\pi$
$727$			1396.59i			1.92103i	−0.278220	+	0.960517i	$0.589744\pi$
$728$	404.397	+	122.217i	0.555490	+	0.167880i
$729$		0			0
$730$	−113.740	+	1158.90i	−0.155808	+	1.58754i
$731$		−	97.1814i		−	0.132943i
$732$		0			0
$733$	−306.229			−0.417775			−0.208888	−	0.977940i	$-0.566984\pi$
$733$	−306.229			−0.417775			−0.208888	+	0.977940i	$0.566984\pi$
$734$	−106.442	−	10.4467i	−0.145017	−	0.0142325i
$735$		0			0
$736$	468.411	+	249.336i	0.636428	+	0.338772i
$737$	−1242.40			−1.68575
$738$		0			0
$739$		−	463.182i		−	0.626769i	−0.949626	−	0.313384i	$-0.898537\pi$
$739$		−	463.182i		−	0.626769i	0.949626	−	0.313384i	$-0.101463\pi$
$740$	1262.13	+	250.150i	1.70558	+	0.338041i
$741$		0			0
$742$	−107.183	−	10.5194i	−0.144452	−	0.0141771i
$743$			810.697i			1.09111i	0.838074	+	0.545557i	$0.183682\pi$
$743$			810.697i			1.09111i	−0.838074	+	0.545557i	$0.816318\pi$
$744$		0			0
$745$	−831.125			−1.11560
$746$	66.7128	−	679.743i	0.0894273	−	0.911183i
$747$		0			0
$748$	−20.0649	+	101.237i	−0.0268248	+	0.135344i
$749$	−182.126			−0.243158
$750$		0			0
$751$			990.928i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$751$			990.928i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$752$	−57.5751	+	139.541i	−0.0765626	+	0.185560i
$753$		0			0
$754$	−56.2288	+	572.920i	−0.0745739	+	0.759841i
$755$			1158.97i			1.53506i
$756$		0			0
$757$	−320.001			−0.422723			−0.211361	−	0.977408i	$-0.567790\pi$
$757$	−320.001			−0.422723			−0.211361	+	0.977408i	$0.567790\pi$
$758$	−438.271	−	43.0137i	−0.578194	−	0.0567464i
$759$		0			0
$760$	−770.141	−	232.752i	−1.01334	−	0.306253i
$761$	635.976			0.835710			0.417855	−	0.908514i	$-0.362782\pi$
$761$	635.976			0.835710			0.417855	+	0.908514i	$0.362782\pi$
$762$		0			0
$763$			571.506i			0.749025i
$764$	−69.8461	+	352.407i	−0.0914217	+	0.461266i
$765$		0			0
$766$	1335.73	+	131.094i	1.74377	+	0.171141i
$767$		−	172.021i		−	0.224278i
$768$		0			0
$769$	305.852			0.397727			0.198864	−	0.980027i	$-0.436275\pi$
$769$	305.852			0.397727			0.198864	+	0.980027i	$0.436275\pi$
$770$	174.649	−	1779.52i	0.226818	−	2.31107i
$771$		0			0
$772$	−657.593	−	130.333i	−0.851805	−	0.168825i
$773$	−187.263			−0.242255			−0.121128	−	0.992637i	$-0.538651\pi$
$773$	−187.263			−0.242255			−0.121128	+	0.992637i	$0.538651\pi$
$774$		0			0
$775$		−	1478.80i		−	1.90813i
$776$	145.564	−	481.649i	0.187582	−	0.620681i
$777$		0			0
$778$	94.7298	−	965.211i	0.121761	−	1.24063i
$779$		−	791.854i		−	1.01650i
$780$		0			0
$781$	−128.324			−0.164307
$782$	47.4368	+	4.65564i	0.0606608	+	0.00595350i
$783$		0			0
$784$	24.5836	+	10.1432i	0.0313566	+	0.0129378i
$785$	−1631.00			−2.07771
$786$		0			0
$787$			185.475i			0.235674i	0.993033	+	0.117837i	$0.0375960\pi$
$787$			185.475i			0.235674i	−0.993033	+	0.117837i	$0.962404\pi$
$788$	726.967	+	144.083i	0.922547	+	0.182846i
$789$		0			0
$790$	674.874	+	66.2349i	0.854271	+	0.0838417i
$791$			106.834i			0.135062i
$792$		0			0
$793$	−515.634			−0.650232
$794$	54.5754	−	556.075i	0.0687348	−	0.700346i
$795$		0			0
$796$	−107.026	+	539.998i	−0.134455	+	0.678389i
$797$	1092.40			1.37064			0.685322	−	0.728240i	$-0.259662\pi$
$797$	1092.40			1.37064			0.685322	+	0.728240i	$0.259662\pi$
$798$		0			0
$799$			13.5593i			0.0169704i
$800$	−411.831	+	773.679i	−0.514789	+	0.967099i
$801$		0			0
$802$	−113.732	+	1158.83i	−0.141811	+	1.44493i
$803$			1444.13i			1.79842i
$804$		0			0
$805$	−825.800			−1.02584
$806$	824.838	+	80.9530i	1.02337	+	0.100438i
$807$		0			0
$808$	−110.197	+	364.627i	−0.136383	+	0.451270i
$809$	51.1143			0.0631821			0.0315911	−	0.999501i	$-0.489943\pi$
$809$	51.1143			0.0631821			0.0315911	+	0.999501i	$0.489943\pi$
$810$		0			0
$811$			680.159i			0.838667i	0.907832	+	0.419333i	$0.137736\pi$
$811$			680.159i			0.838667i	−0.907832	+	0.419333i	$0.862264\pi$
$812$	200.654	−	1012.40i	0.247111	−	1.24679i
$813$		0			0
$814$	1588.05	+	155.858i	1.95093	+	0.191472i
$815$			1065.19i			1.30698i
$816$		0			0
$817$	939.514			1.14996
$818$	85.3016	−	869.146i	0.104281	−	1.06253i
$819$		0			0
$820$	−1618.54	−	320.789i	−1.97382	−	0.391207i
$821$	124.267			0.151361			0.0756805	−	0.997132i	$-0.475887\pi$
$821$	124.267			0.151361			0.0756805	+	0.997132i	$0.475887\pi$
$822$		0			0
$823$		−	1107.83i		−	1.34609i	−0.739602	−	0.673044i	$-0.764986\pi$
$823$		−	1107.83i		−	1.34609i	0.739602	−	0.673044i	$-0.235014\pi$
$824$	411.415	+	124.338i	0.499290	+	0.150895i
$825$		0			0
$826$	−30.1236	+	306.932i	−0.0364692	+	0.371588i
$827$		−	856.831i		−	1.03607i	−0.855359	−	0.518036i	$-0.826663\pi$
$827$		−	856.831i		−	1.03607i	0.855359	−	0.518036i	$-0.173337\pi$
$828$		0			0
$829$	−59.5071			−0.0717818			−0.0358909	−	0.999356i	$-0.511427\pi$
$829$	−59.5071			−0.0717818			−0.0358909	+	0.999356i	$0.511427\pi$
$830$	−2048.64	−	201.062i	−2.46824	−	0.242243i
$831$		0			0
$832$	−408.994	−	272.062i	−0.491579	−	0.326997i
$833$	2.38881			0.00286771
$834$		0			0
$835$		−	766.830i		−	0.918359i
$836$	−978.723	−	193.980i	−1.17072	−	0.232034i
$837$		0			0
$838$	−1509.29	−	148.128i	−1.80106	−	0.176764i
$839$			464.691i			0.553863i	0.960890	+	0.276932i	$0.0893176\pi$
$839$			464.691i			0.553863i	−0.960890	+	0.276932i	$0.910682\pi$
$840$		0			0
$841$	565.391			0.672284
$842$	−102.236	+	1041.69i	−0.121420	+	1.23716i
$843$		0			0
$844$	237.384	−	1197.72i	0.281261	−	1.41910i
$845$	796.840			0.943006
$846$		0			0
$847$		−	1384.98i		−	1.63516i
$848$	115.759	+	47.7627i	0.136509	+	0.0563239i
$849$		0			0
$850$	−7.68977	+	78.3518i	−0.00904679	+	0.0921786i
$851$		−	736.948i		−	0.865979i
$852$		0			0
$853$	−1366.33			−1.60179			−0.800896	−	0.598803i	$-0.795643\pi$
$853$	−1366.33			−1.60179			−0.800896	+	0.598803i	$0.795643\pi$
$854$	920.029	+	90.2955i	1.07732	+	0.105732i
$855$		0			0
$856$	202.711	+	61.2633i	0.236812	+	0.0715693i
$857$	1677.60			1.95752			0.978762	−	0.205000i	$-0.0657193\pi$
$857$	1677.60			1.95752			0.978762	+	0.205000i	$0.0657193\pi$
$858$		0			0
$859$			1645.03i			1.91505i	0.288355	+	0.957524i	$0.406892\pi$
$859$			1645.03i			1.91505i	−0.288355	+	0.957524i	$0.593108\pi$
$860$	380.608	−	1920.35i	0.442568	−	2.23296i
$861$		0			0
$862$	−1451.32	−	142.439i	−1.68367	−	0.165242i
$863$		−	294.311i		−	0.341033i	−0.985355	−	0.170516i	$-0.945456\pi$
$863$		−	294.311i		−	0.341033i	0.985355	−	0.170516i	$-0.0545436\pi$
$864$		0			0
$865$	−1349.34			−1.55994
$866$	95.9594	−	977.740i	0.110808	−	1.12903i
$867$		0			0
$868$	−1457.56	−	288.884i	−1.67921	−	0.332815i
$869$	840.971			0.967746
$870$		0			0
$871$		−	531.159i		−	0.609826i
$872$	192.243	−	636.102i	0.220462	−	0.729475i
$873$		0			0
$874$	−45.0090	+	458.601i	−0.0514977	+	0.524715i
$875$		−	118.992i		−	0.135991i
$876$		0			0
$877$	719.169			0.820033			0.410016	−	0.912078i	$-0.365523\pi$
$877$	719.169			0.820033			0.410016	+	0.912078i	$0.365523\pi$
$878$	−375.582	−	36.8612i	−0.427770	−	0.0419831i
$879$		0			0
$880$	−792.984	+	1921.91i	−0.901118	+	2.18399i
$881$	16.3083			0.0185112			0.00925559	−	0.999957i	$-0.497054\pi$
$881$	16.3083			0.0185112			0.00925559	+	0.999957i	$0.497054\pi$
$882$		0			0
$883$		−	1190.35i		−	1.34807i	−0.738698	−	0.674036i	$-0.764559\pi$
$883$		−	1190.35i		−	1.34807i	0.738698	−	0.674036i	$-0.235441\pi$
$884$	−43.2817	−	8.57831i	−0.0489612	−	0.00970398i
$885$		0			0
$886$	822.464	+	80.7200i	0.928289	+	0.0911061i
$887$		−	400.666i		−	0.451709i	−0.974161	−	0.225855i	$-0.927483\pi$
$887$		−	400.666i		−	0.451709i	0.974161	−	0.225855i	$-0.0725174\pi$
$888$		0			0
$889$	1083.39			1.21866
$890$	−59.5384	+	606.643i	−0.0668971	+	0.681621i
$891$		0			0
$892$	13.3932	−	67.5750i	0.0150148	−	0.0757567i
$893$	−131.087			−0.146793
$894$		0			0
$895$		−	1386.79i		−	1.54948i
$896$	682.112	+	557.052i	0.761286	+	0.621710i
$897$		0			0
$898$	−124.682	+	1270.40i	−0.138845	+	1.41470i
$899$		−	2024.79i		−	2.25227i
$900$		0			0
$901$	11.2484			0.0124844
$902$	−2036.50	−	199.870i	−2.25776	−	0.221586i
$903$		0			0
$904$	35.9368	−	118.909i	0.0397531	−	0.131537i
$905$	−1483.51			−1.63924
$906$		0			0
$907$			1260.24i			1.38946i	0.719270	+	0.694731i	$0.244476\pi$
$907$			1260.24i			1.38946i	−0.719270	+	0.694731i	$0.755524\pi$
$908$	−31.8722	+	160.810i	−0.0351015	+	0.177104i
$909$		0			0
$910$	760.795	+	74.6675i	0.836038	+	0.0820522i
$911$			964.398i			1.05862i	0.848430	+	0.529308i	$0.177548\pi$
$911$			964.398i			1.05862i	−0.848430	+	0.529308i	$0.822452\pi$
$912$		0			0
$913$	−2552.84			−2.79610
$914$	45.0646	−	459.168i	0.0493048	−	0.502372i
$915$		0			0
$916$	523.625	+	103.781i	0.571643	+	0.113298i
$917$	−323.779			−0.353086
$918$		0			0
$919$		−	424.406i		−	0.461813i	−0.972976	−	0.230906i	$-0.925831\pi$
$919$		−	424.406i		−	0.461813i	0.972976	−	0.230906i	$-0.0741691\pi$
$920$	919.139	+	277.782i	0.999064	+	0.301937i
$921$		0			0
$922$	−78.1767	+	796.550i	−0.0847903	+	0.863937i
$923$		−	54.8621i		−	0.0594389i
$924$		0			0
$925$	1217.23			1.31592
$926$	−590.476	−	57.9517i	−0.637663	−	0.0625829i
$927$		0			0
$928$	−563.883	+	1059.33i	−0.607633	+	1.14152i
$929$	−858.458			−0.924067			−0.462033	−	0.886862i	$-0.652880\pi$
$929$	−858.458			−0.924067			−0.462033	+	0.886862i	$0.652880\pi$
$930$		0			0
$931$			23.0941i			0.0248057i
$932$	−1445.27	−	286.448i	−1.55072	−	0.307348i
$933$		0			0
$934$	252.898	+	24.8205i	0.270769	+	0.0265744i
$935$			186.753i			0.199736i
$936$		0			0
$937$	858.258			0.915964			0.457982	−	0.888962i	$-0.348572\pi$
$937$	858.258			0.915964			0.457982	+	0.888962i	$0.348572\pi$
$938$	−93.0140	+	947.729i	−0.0991621	+	1.01037i
$939$		0			0
$940$	−53.1047	+	267.939i	−0.0564944	+	0.285041i
$941$	−937.106			−0.995862			−0.497931	−	0.867217i	$-0.665907\pi$
$941$	−937.106			−0.995862			−0.497931	+	0.867217i	$0.665907\pi$
$942$		0			0
$943$			945.052i			1.00218i
$944$	136.774	−	331.491i	0.144888	−	0.351156i
$945$		0			0
$946$	237.141	−	2416.25i	0.250677	−	2.55418i
$947$		−	887.159i		−	0.936810i	−0.883514	−	0.468405i	$-0.844829\pi$
$947$		−	887.159i		−	0.936810i	0.883514	−	0.468405i	$-0.155171\pi$
$948$		0			0
$949$	−617.405			−0.650585
$950$	−757.476	−	74.3418i	−0.797344	−	0.0782546i
$951$		0			0
$952$	75.7239	+	22.8853i	0.0795419	+	0.0240392i
$953$	1078.46			1.13164			0.565821	−	0.824528i	$-0.308559\pi$
$953$	1078.46			1.13164			0.565821	+	0.824528i	$0.308559\pi$
$954$		0			0
$955$			650.090i			0.680722i
$956$	224.402	−	1132.22i	0.234731	−	1.18433i
$957$		0			0
$958$	−24.5122	−	2.40573i	−0.0255868	−	0.00251120i
$959$		−	808.411i		−	0.842973i
$960$		0			0
$961$	−1954.11			−2.03342
$962$	−66.6337	+	678.937i	−0.0692658	+	0.705756i
$963$		0			0
$964$	404.089	+	80.0894i	0.419180	+	0.0830803i
$965$	−1213.07			−1.25707
$966$		0			0
$967$		−	119.065i		−	0.123128i	−0.998103	−	0.0615640i	$-0.980391\pi$
$967$		−	119.065i		−	0.123128i	0.998103	−	0.0615640i	$-0.0196088\pi$
$968$	−465.878	+	1541.52i	−0.481279	+	1.59248i
$969$		0			0
$970$	88.9312	−	906.129i	0.0916817	−	0.934154i
$971$			1516.56i			1.56185i	0.624624	+	0.780926i	$0.285252\pi$
$971$			1516.56i			1.56185i	−0.624624	+	0.780926i	$0.714748\pi$
$972$		0			0
$973$	273.118			0.280697
$974$	360.376	+	35.3687i	0.369996	+	0.0363129i
$975$		0			0
$976$	−993.645	−	409.980i	−1.01808	−	0.420062i
$977$	1578.30			1.61546			0.807729	−	0.589555i	$-0.200697\pi$
$977$	1578.30			1.61546			0.807729	+	0.589555i	$0.200697\pi$
$978$		0			0
$979$			755.947i			0.772162i
$980$	47.2039	+	9.35568i	0.0481672	+	0.00954661i
$981$		0			0
$982$	989.406	+	97.1044i	1.00754	+	0.0988843i
$983$		−	592.742i		−	0.602993i	−0.953467	−	0.301497i	$-0.902514\pi$
$983$		−	592.742i		−	0.602993i	0.953467	−	0.301497i	$-0.0974862\pi$
$984$		0			0
$985$	1341.04			1.36147
$986$	−10.5289	+	107.280i	−0.0106784	+	0.108803i
$987$		0			0
$988$	82.9319	−	418.431i	0.0839392	−	0.423513i
$989$	−1121.28			−1.13375
$990$		0			0
$991$			1896.17i			1.91339i	0.291098	+	0.956693i	$0.405980\pi$
$991$			1896.17i			1.91339i	−0.291098	+	0.956693i	$0.594020\pi$
$992$	1525.13	+	811.828i	1.53743	+	0.818375i
$993$		0			0
$994$	−9.60720	+	97.8887i	−0.00966519	+	0.0984796i
$995$			996.141i			1.00115i
$996$		0			0
$997$	69.7126			0.0699224			0.0349612	−	0.999389i	$-0.488869\pi$
$997$	69.7126			0.0699224			0.0349612	+	0.999389i	$0.488869\pi$
$998$	1517.84	+	148.967i	1.52088	+	0.149266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.e.163.4	yes	6
3.2	odd	2		324.3.d.f.163.3	yes	6
4.3	odd	2	inner	324.3.d.e.163.3	✓	6
9.2	odd	6		324.3.f.q.271.1		12
9.4	even	3		324.3.f.r.55.2		12
9.5	odd	6		324.3.f.q.55.5		12
9.7	even	3		324.3.f.r.271.6		12
12.11	even	2		324.3.d.f.163.4	yes	6
36.7	odd	6		324.3.f.r.271.2		12
36.11	even	6		324.3.f.q.271.5		12
36.23	even	6		324.3.f.q.55.1		12
36.31	odd	6		324.3.f.r.55.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.e.163.3	✓	6	4.3	odd	2	inner
324.3.d.e.163.4	yes	6	1.1	even	1	trivial
324.3.d.f.163.3	yes	6	3.2	odd	2
324.3.d.f.163.4	yes	6	12.11	even	2
324.3.f.q.55.1		12	36.23	even	6
324.3.f.q.55.5		12	9.5	odd	6
324.3.f.q.271.1		12	9.2	odd	6
324.3.f.q.271.5		12	36.11	even	6
324.3.f.r.55.2		12	9.4	even	3
324.3.f.r.55.6		12	36.31	odd	6
324.3.f.r.271.2		12	36.7	odd	6
324.3.f.r.271.6		12	9.7	even	3

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.195350 + 1.99044i) q^{2} +(-3.92368 - 0.777662i) q^{4} -7.23805 q^{5} +6.88025i q^{7} +(2.31438 - 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} -17.9526i q^{11} +7.67526 q^{13} +(-13.6947 - 1.34405i) q^{14} +(14.7905 + 6.10259i) q^{16} +1.43720 q^{17} +13.8943i q^{19} +(28.3998 + 5.62876i) q^{20} +(35.7336 + 3.50704i) q^{22} -16.5824i q^{23} +27.3894 q^{25} +(-1.49936 + 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +37.5019 q^{29} -53.9918i q^{31} +(-15.0361 + 28.2474i) q^{32} +(-0.280757 + 2.86066i) q^{34} -49.7996i q^{35} +44.4415 q^{37} +(-27.6558 - 2.71425i) q^{38} +(-16.7516 + 55.4284i) q^{40} -56.9911 q^{41} -67.6185i q^{43} +(-13.9611 + 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +9.43453i q^{47} +1.66212 q^{49} +(-5.35051 + 54.5169i) q^{50} +(-30.1152 - 5.96876i) q^{52} +7.82662 q^{53} +129.942i q^{55} +(52.6884 + 15.9235i) q^{56} +(-7.32598 + 74.6451i) q^{58} -22.4125i q^{59} -67.1814 q^{61} +(107.467 + 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} -55.5539 q^{65} -69.2040i q^{67} +(-5.63912 - 1.11766i) q^{68} +(99.1230 + 9.72834i) q^{70} -7.14792i q^{71} -80.4410 q^{73} +(-8.68162 + 88.4579i) q^{74} +(10.8051 - 54.5169i) q^{76} +123.519 q^{77} +46.8439i q^{79} +(-107.054 - 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} -142.199i q^{83} -10.4026 q^{85} +(134.590 + 13.2092i) q^{86} +(-137.480 - 41.5492i) q^{88} -42.1078 q^{89} +52.8077i q^{91} +(-12.8955 + 65.0642i) q^{92} +(-18.7788 - 1.84303i) q^{94} -100.568i q^{95} +62.8955 q^{97} +(-0.324695 + 3.30835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{4} - 2 q^{5} - 7 q^{8} + 9 q^{10} + 6 q^{13} - 15 q^{16} + 10 q^{17} + 67 q^{20} + 48 q^{22} + 73 q^{26} - 48 q^{28} + 22 q^{29} - 31 q^{32} + 81 q^{34} + 54 q^{37} - 168 q^{38} - 81 q^{40}+ \cdots + 407 q^{98}+O(q^{100}) \) 6 * q - q^2 - 3 * q^4 - 2 * q^5 - 7 * q^8 + 9 * q^10 + 6 * q^13 - 15 * q^16 + 10 * q^17 + 67 * q^20 + 48 * q^22 + 73 * q^26 - 48 * q^28 + 22 * q^29 - 31 * q^32 + 81 * q^34 + 54 * q^37 - 168 * q^38 - 81 * q^40 - 92 * q^41 - 168 * q^44 + 120 * q^46 - 66 * q^49 + 48 * q^50 - 117 * q^52 - 116 * q^53 + 312 * q^56 + 201 * q^58 + 54 * q^61 + 312 * q^62 - 255 * q^64 - 82 * q^65 - 53 * q^68 + 264 * q^70 - 78 * q^73 - 383 * q^74 - 192 * q^76 + 168 * q^77 - 377 * q^80 + 150 * q^82 + 66 * q^85 + 144 * q^86 - 336 * q^88 + 250 * q^89 + 504 * q^92 + 216 * q^94 - 204 * q^97 + 407 * q^98

Introduction

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