LMFDB - Embedded newform 243.3.f.b.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,3,Mod(26,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("243.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	243.53
Dual form			243.3.f.b.188.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0402544 - 0.110598i) q^{2} +(3.05357 + 2.56225i) q^{4} +(6.10375 + 1.07626i) q^{5} +(6.10801 - 5.12523i) q^{7} +(0.814011 - 0.469969i) q^{8} +O(q^{10})$	\(q+(0.0402544 - 0.110598i) q^{2} +(3.05357 + 2.56225i) q^{4} +(6.10375 + 1.07626i) q^{5} +(6.10801 - 5.12523i) q^{7} +(0.814011 - 0.469969i) q^{8} +(0.364735 - 0.631740i) q^{10} +(-11.2696 + 1.98713i) q^{11} +(7.75779 - 2.82360i) q^{13} +(-0.320966 - 0.881848i) q^{14} +(2.74954 + 15.5934i) q^{16} +(-20.7128 - 11.9585i) q^{17} +(6.12102 + 10.6019i) q^{19} +(15.8806 + 18.9257i) q^{20} +(-0.233878 + 1.32639i) q^{22} +(9.48274 - 11.3011i) q^{23} +(12.6052 + 4.58790i) q^{25} -0.971660i q^{26} +31.7833 q^{28} +(-6.08561 + 16.7201i) q^{29} +(9.97455 + 8.36964i) q^{31} +(5.53792 + 0.976485i) q^{32} +(-2.15637 + 1.80941i) q^{34} +(42.7978 - 24.7093i) q^{35} +(8.53500 - 14.7831i) q^{37} +(1.41895 - 0.250199i) q^{38} +(5.47433 - 1.99249i) q^{40} +(10.5123 + 28.8822i) q^{41} +(-6.91641 - 39.2249i) q^{43} +(-39.5040 - 22.8076i) q^{44} +(-0.868158 - 1.50369i) q^{46} +(-37.5253 - 44.7209i) q^{47} +(2.53105 - 14.3543i) q^{49} +(1.01483 - 1.20942i) q^{50} +(30.9237 + 11.2553i) q^{52} +91.2612i q^{53} -70.9255 q^{55} +(2.56328 - 7.04257i) q^{56} +(1.60424 + 1.34612i) q^{58} +(-20.3483 - 3.58796i) q^{59} +(-26.7802 + 22.4713i) q^{61} +(1.32719 - 0.766252i) q^{62} +(-31.3370 + 54.2773i) q^{64} +(50.3906 - 8.88521i) q^{65} +(-48.4527 + 17.6354i) q^{67} +(-32.6072 - 89.5875i) q^{68} +(-1.01001 - 5.72802i) q^{70} +(-2.28181 - 1.31740i) q^{71} +(-34.5072 - 59.7683i) q^{73} +(-1.29141 - 1.53904i) q^{74} +(-8.47378 + 48.0572i) q^{76} +(-58.6503 + 69.8967i) q^{77} +(-142.302 - 51.7939i) q^{79} +98.1375i q^{80} +3.61748 q^{82} +(18.4924 - 50.8076i) q^{83} +(-113.555 - 95.2842i) q^{85} +(-4.61662 - 0.814035i) q^{86} +(-8.23968 + 6.91392i) q^{88} +(141.225 - 81.5361i) q^{89} +(32.9130 - 57.0070i) q^{91} +(57.9124 - 10.2115i) q^{92} +(-6.45661 + 2.35001i) q^{94} +(25.9508 + 71.2992i) q^{95} +(9.90005 + 56.1460i) q^{97} +(-1.48567 - 0.857754i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8}+O(q^{10}) $ 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8	$ 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29} + 48 q^{31} - 117 q^{32} + 99 q^{34} + 252 q^{35} - 3 q^{37} + 237 q^{38} + 201 q^{40} - 129 q^{41} + 183 q^{43} - 639 q^{44} - 3 q^{46} + 348 q^{47} + 147 q^{49} + 471 q^{50} + 45 q^{52} - 12 q^{55} - 570 q^{56} - 267 q^{58} - 426 q^{59} - 285 q^{61} + 900 q^{62} - 51 q^{64} + 213 q^{65} - 366 q^{67} - 378 q^{68} - 483 q^{70} - 315 q^{71} - 66 q^{73} - 159 q^{74} - 201 q^{76} + 654 q^{77} - 15 q^{79} - 12 q^{82} - 624 q^{83} + 18 q^{85} + 411 q^{86} + 51 q^{88} - 72 q^{89} + 96 q^{91} + 561 q^{92} - 96 q^{94} + 75 q^{95} - 114 q^{97} - 882 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0402544	−	0.110598i	0.0201272	−	0.0552991i	−0.929222	−	0.369522i	$-0.879522\pi$
$2$	0.0402544	−	0.110598i	0.0201272	−	0.0552991i	0.949349	+	0.314223i	$0.101744\pi$
$3$		0			0
$3$		0			0
$4$	3.05357	+	2.56225i	0.763392	+	0.640562i
$5$	6.10375	+	1.07626i	1.22075	+	0.215251i	0.746649	−	0.665219i	$-0.231662\pi$
$5$	6.10375	+	1.07626i	1.22075	+	0.215251i	0.474102	+	0.880470i	$0.342773\pi$
$6$		0			0
$7$	6.10801	−	5.12523i	0.872573	−	0.732175i	−0.0920655	−	0.995753i	$-0.529347\pi$
$7$	6.10801	−	5.12523i	0.872573	−	0.732175i	0.964638	+	0.263578i	$0.0849025\pi$
$8$	0.814011	−	0.469969i	0.101751	−	0.0587462i
$9$		0			0
$10$	0.364735	−	0.631740i	0.0364735	−	0.0631740i
$11$	−11.2696	+	1.98713i	−1.02451	+	0.180649i	−0.660562	−	0.750771i	$-0.729682\pi$
$11$	−11.2696	+	1.98713i	−1.02451	+	0.180649i	−0.363947	+	0.931420i	$0.618571\pi$
$12$		0			0
$13$	7.75779	−	2.82360i	0.596753	−	0.217200i	−0.0259440	−	0.999663i	$-0.508259\pi$
$13$	7.75779	−	2.82360i	0.596753	−	0.217200i	0.622697	+	0.782463i	$0.286037\pi$
$14$	−0.320966	−	0.881848i	−0.0229262	−	0.0629891i
$15$		0			0
$16$	2.74954	+	15.5934i	0.171846	+	0.974588i
$17$	−20.7128	−	11.9585i	−1.21840	−	0.703443i	−0.253824	−	0.967250i	$-0.581689\pi$
$17$	−20.7128	−	11.9585i	−1.21840	−	0.703443i	−0.964576	+	0.263807i	$0.915022\pi$
$18$		0			0
$19$	6.12102	+	10.6019i	0.322159	+	0.557995i	0.980933	−	0.194345i	$-0.0622582\pi$
$19$	6.12102	+	10.6019i	0.322159	+	0.557995i	−0.658774	+	0.752341i	$0.728925\pi$
$20$	15.8806	+	18.9257i	0.794029	+	0.946287i
$21$		0			0
$22$	−0.233878	+	1.32639i	−0.0106308	+	0.0602904i
$23$	9.48274	−	11.3011i	0.412293	−	0.491352i	−0.519434	−	0.854510i	$-0.673857\pi$
$23$	9.48274	−	11.3011i	0.412293	−	0.491352i	0.931727	+	0.363159i	$0.118302\pi$
$24$		0			0
$25$	12.6052	+	4.58790i	0.504206	+	0.183516i
$26$		−	0.971660i		−	0.0373715i
$27$		0			0
$28$	31.7833			1.13512
$29$	−6.08561	+	16.7201i	−0.209849	+	0.576555i	−0.999306	−	0.0372510i	$-0.988140\pi$
$29$	−6.08561	+	16.7201i	−0.209849	+	0.576555i	0.789457	+	0.613806i	$0.210362\pi$
$30$		0			0
$31$	9.97455	+	8.36964i	0.321760	+	0.269989i	0.789332	−	0.613966i	$-0.210427\pi$
$31$	9.97455	+	8.36964i	0.321760	+	0.269989i	−0.467573	+	0.883955i	$0.654871\pi$
$32$	5.53792	+	0.976485i	0.173060	+	0.0305151i
$33$		0			0
$34$	−2.15637	+	1.80941i	−0.0634228	+	0.0532180i
$35$	42.7978	−	24.7093i	1.22280	−	0.705981i
$36$		0			0
$37$	8.53500	−	14.7831i	0.230676	−	0.399542i	−0.727331	−	0.686286i	$-0.759240\pi$
$37$	8.53500	−	14.7831i	0.230676	−	0.399542i	0.958007	+	0.286744i	$0.0925730\pi$
$38$	1.41895	−	0.250199i	0.0373408	−	0.00658419i
$39$		0			0
$40$	5.47433	−	1.99249i	0.136858	−	0.0498123i
$41$	10.5123	+	28.8822i	0.256397	+	0.704444i	0.999383	+	0.0351368i	$0.0111867\pi$
$41$	10.5123	+	28.8822i	0.256397	+	0.704444i	−0.742986	+	0.669307i	$0.766591\pi$
$42$		0			0
$43$	−6.91641	−	39.2249i	−0.160847	−	0.912207i	−0.953244	−	0.302202i	$-0.902278\pi$
$43$	−6.91641	−	39.2249i	−0.160847	−	0.912207i	0.792397	−	0.610005i	$-0.208833\pi$
$44$	−39.5040	−	22.8076i	−0.897818	−	0.518356i
$45$		0			0
$46$	−0.868158	−	1.50369i	−0.0188730	−	0.0326890i
$47$	−37.5253	−	44.7209i	−0.798410	−	0.951508i	0.201197	−	0.979551i	$-0.435517\pi$
$47$	−37.5253	−	44.7209i	−0.798410	−	0.951508i	−0.999607	+	0.0280428i	$0.991073\pi$
$48$		0			0
$49$	2.53105	−	14.3543i	0.0516541	−	0.292945i
$50$	1.01483	−	1.20942i	0.0202965	−	0.0241885i
$51$		0			0
$52$	30.9237	+	11.2553i	0.594686	+	0.216448i
$53$			91.2612i			1.72191i	0.508681	+	0.860955i	$0.330133\pi$
$53$			91.2612i			1.72191i	−0.508681	+	0.860955i	$0.669867\pi$
$54$		0			0
$55$	−70.9255			−1.28956
$56$	2.56328	−	7.04257i	0.0457729	−	0.125760i
$57$		0			0
$58$	1.60424	+	1.34612i	0.0276593	+	0.0232089i
$59$	−20.3483	−	3.58796i	−0.344887	−	0.0608129i	−0.00147818	−	0.999999i	$-0.500471\pi$
$59$	−20.3483	−	3.58796i	−0.344887	−	0.0608129i	−0.343409	+	0.939186i	$0.611582\pi$
$60$		0			0
$61$	−26.7802	+	22.4713i	−0.439020	+	0.368382i	−0.835343	−	0.549730i	$-0.814731\pi$
$61$	−26.7802	+	22.4713i	−0.439020	+	0.368382i	0.396322	+	0.918111i	$0.370286\pi$
$62$	1.32719	−	0.766252i	0.0214063	−	0.0123589i
$63$		0			0
$64$	−31.3370	+	54.2773i	−0.489641	+	0.848083i
$65$	50.3906	−	8.88521i	0.775239	−	0.136696i
$66$		0			0
$67$	−48.4527	+	17.6354i	−0.723175	+	0.263214i	−0.677273	−	0.735732i	$-0.736838\pi$
$67$	−48.4527	+	17.6354i	−0.723175	+	0.263214i	−0.0459021	+	0.998946i	$0.514616\pi$
$68$	−32.6072	−	89.5875i	−0.479517	−	1.31746i
$69$		0			0
$70$	−1.01001	−	5.72802i	−0.0144286	−	0.0818289i
$71$	−2.28181	−	1.31740i	−0.0321381	−	0.0185549i	0.483845	−	0.875154i	$-0.339240\pi$
$71$	−2.28181	−	1.31740i	−0.0321381	−	0.0185549i	−0.515983	+	0.856599i	$0.672573\pi$
$72$		0			0
$73$	−34.5072	−	59.7683i	−0.472702	−	0.818743i	0.526810	−	0.849983i	$-0.323388\pi$
$73$	−34.5072	−	59.7683i	−0.472702	−	0.818743i	−0.999512	+	0.0312395i	$0.990055\pi$
$74$	−1.29141	−	1.53904i	−0.0174515	−	0.0207978i
$75$		0			0
$76$	−8.47378	+	48.0572i	−0.111497	+	0.632332i
$77$	−58.6503	+	69.8967i	−0.761692	+	0.907750i
$78$		0			0
$79$	−142.302	−	51.7939i	−1.80130	−	0.655618i	−0.998213	−	0.0597517i	$-0.980969\pi$
$79$	−142.302	−	51.7939i	−1.80130	−	0.655618i	−0.803083	−	0.595867i	$-0.796809\pi$
$80$			98.1375i			1.22672i
$81$		0			0
$82$	3.61748			0.0441157
$83$	18.4924	−	50.8076i	0.222801	−	0.612139i	−0.777050	−	0.629439i	$-0.783285\pi$
$83$	18.4924	−	50.8076i	0.222801	−	0.612139i	0.999850	+	0.0172997i	$0.00550693\pi$
$84$		0			0
$85$	−113.555	−	95.2842i	−1.33595	−	1.12099i
$86$	−4.61662	−	0.814035i	−0.0536816	−	0.00946552i
$87$		0			0
$88$	−8.23968	+	6.91392i	−0.0936328	+	0.0785672i
$89$	141.225	−	81.5361i	1.58679	−	0.916136i	0.592962	−	0.805230i	$-0.297958\pi$
$89$	141.225	−	81.5361i	1.58679	−	0.916136i	0.993831	−	0.110906i	$-0.0353751\pi$
$90$		0			0
$91$	32.9130	−	57.0070i	0.361682	−	0.626451i
$92$	57.9124	−	10.2115i	0.629482	−	0.110995i
$93$		0			0
$94$	−6.45661	+	2.35001i	−0.0686873	+	0.0250001i
$95$	25.9508	+	71.2992i	0.273166	+	0.750518i
$96$		0			0
$97$	9.90005	+	56.1460i	0.102062	+	0.578825i	0.992353	+	0.123432i	$0.0393900\pi$
$97$	9.90005	+	56.1460i	0.102062	+	0.578825i	−0.890291	+	0.455393i	$0.849499\pi$
$98$	−1.48567	−	0.857754i	−0.0151599	−	0.00875259i
$99$		0			0
$100$	26.7353	+	46.3070i	0.267353	+	0.463070i
$101$	17.8525	+	21.2758i	0.176757	+	0.210651i	0.847148	−	0.531357i	$-0.178318\pi$
$101$	17.8525	+	21.2758i	0.176757	+	0.210651i	−0.670390	+	0.742009i	$0.733873\pi$
$102$		0			0
$103$	14.2561	−	80.8506i	0.138409	−	0.784957i	−0.834016	−	0.551741i	$-0.813964\pi$
$103$	14.2561	−	80.8506i	0.138409	−	0.784957i	0.972425	−	0.233217i	$-0.0749251\pi$
$104$	4.98792	−	5.94437i	0.0479607	−	0.0571574i
$105$		0			0
$106$	10.0933	+	3.67367i	0.0952200	+	0.0346573i
$107$		−	35.8639i		−	0.335177i	−0.985857	−	0.167588i	$-0.946402\pi$
$107$		−	35.8639i		−	0.335177i	0.985857	−	0.167588i	$-0.0535980\pi$
$108$		0			0
$109$	1.41546			0.0129859			0.00649295	−	0.999979i	$-0.497933\pi$
$109$	1.41546			0.0129859			0.00649295	+	0.999979i	$0.497933\pi$
$110$	−2.85507	+	7.84423i	−0.0259552	+	0.0713112i
$111$		0			0
$112$	96.7140	+	81.1527i	0.863518	+	0.724577i
$113$	−146.768	−	25.8792i	−1.29883	−	0.229019i	−0.518874	−	0.854850i	$-0.673649\pi$
$113$	−146.768	−	25.8792i	−1.29883	−	0.229019i	−0.779959	+	0.625831i	$0.784760\pi$
$114$		0			0
$115$	70.0432	−	58.7732i	0.609071	−	0.511071i
$116$	−61.4238	+	35.4630i	−0.529515	+	0.305716i
$117$		0			0
$118$	−1.21593	+	2.10606i	−0.0103045	+	0.0178479i
$119$	−187.804	+	33.1149i	−1.57819	+	0.278277i
$120$		0			0
$121$	9.35241	−	3.40400i	0.0772926	−	0.0281322i
$122$	1.40726	+	3.86642i	0.0115349	+	0.0316919i
$123$		0			0
$124$	9.01287	+	51.1145i	0.0726844	+	0.412214i
$125$	−62.1878	−	35.9041i	−0.497502	−	0.287233i
$126$		0			0
$127$	−8.57044	−	14.8444i	−0.0674838	−	0.116885i	0.830309	−	0.557303i	$-0.188164\pi$
$127$	−8.57044	−	14.8444i	−0.0674838	−	0.116885i	−0.897793	+	0.440417i	$0.854830\pi$
$128$	19.2000	+	22.8817i	0.150000	+	0.178763i
$129$		0			0
$130$	1.04576	−	5.93077i	0.00804427	−	0.0456213i
$131$	93.8009	−	111.788i	0.716037	−	0.853340i	−0.278202	−	0.960523i	$-0.589739\pi$
$131$	93.8009	−	111.788i	0.716037	−	0.853340i	0.994239	+	0.107183i	$0.0341830\pi$
$132$		0			0
$133$	91.7245	+	33.3850i	0.689658	+	0.251015i
$134$			6.06869i			0.0452887i
$135$		0			0
$136$	−22.4806			−0.165298
$137$	29.7610	−	81.7677i	0.217234	−	0.596845i	−0.782431	−	0.622737i	$-0.786021\pi$
$137$	29.7610	−	81.7677i	0.217234	−	0.596845i	0.999665	+	0.0258926i	$0.00824279\pi$
$138$		0			0
$139$	28.2371	+	23.6938i	0.203145	+	0.170459i	0.738685	−	0.674051i	$-0.235447\pi$
$139$	28.2371	+	23.6938i	0.203145	+	0.170459i	−0.535540	+	0.844510i	$0.679892\pi$
$140$	193.997	+	34.2070i	1.38570	+	0.244336i
$141$		0			0
$142$	−0.237555	+	0.199332i	−0.00167292	+	0.00140375i
$143$	−81.8163	+	47.2367i	−0.572142	+	0.330326i
$144$		0			0
$145$	−55.1402	+	95.5056i	−0.380277	+	0.658659i
$146$	−7.99933	+	1.41050i	−0.0547899	+	0.00966094i
$147$		0			0
$148$	63.9400	−	23.2723i	0.432027	−	0.157245i
$149$	22.0936	+	60.7015i	0.148279	+	0.407393i	0.991489	−	0.130191i	$-0.0415592\pi$
$149$	22.0936	+	60.7015i	0.148279	+	0.407393i	−0.843210	+	0.537584i	$0.819337\pi$
$150$		0			0
$151$	−26.8211	−	152.110i	−0.177623	−	1.00735i	−0.935073	−	0.354456i	$-0.884666\pi$
$151$	−26.8211	−	152.110i	−0.177623	−	1.00735i	0.757450	−	0.652893i	$-0.226445\pi$
$152$	9.96515	+	5.75338i	0.0655602	+	0.0378512i
$153$		0			0
$154$	5.36951	+	9.30027i	0.0348670	+	0.0603914i
$155$	51.8743	+	61.8214i	0.334673	+	0.398848i
$156$		0			0
$157$	−33.4367	+	189.629i	−0.212972	+	1.20783i	0.671418	+	0.741079i	$0.265685\pi$
$157$	−33.4367	+	189.629i	−0.212972	+	1.20783i	−0.884391	+	0.466747i	$0.845426\pi$
$158$	−11.4566	+	13.6535i	−0.0725102	+	0.0864143i
$159$		0			0
$160$	32.7511	+	11.9204i	0.204695	+	0.0745027i
$161$		−	117.628i		−	0.730611i
$162$		0			0
$163$	171.309			1.05098			0.525488	−	0.850801i	$-0.323883\pi$
$163$	171.309			1.05098			0.525488	+	0.850801i	$0.323883\pi$
$164$	−41.9034	+	115.129i	−0.255509	+	0.702004i
$165$		0			0
$166$	−4.87482	−	4.09046i	−0.0293664	−	0.0246413i
$167$	154.992	+	27.3293i	0.928098	+	0.163649i	0.617211	−	0.786798i	$-0.288263\pi$
$167$	154.992	+	27.3293i	0.928098	+	0.163649i	0.310888	+	0.950447i	$0.399374\pi$
$168$		0			0
$169$	−77.2510	+	64.8212i	−0.457106	+	0.383558i
$170$	−15.1094	+	8.72340i	−0.0888786	+	0.0513141i
$171$		0			0
$172$	79.3842	−	137.497i	0.461536	−	0.799404i
$173$	51.7074	−	9.11741i	0.298887	−	0.0527018i	−0.0221939	−	0.999754i	$-0.507065\pi$
$173$	51.7074	−	9.11741i	0.298887	−	0.0527018i	0.321080	+	0.947052i	$0.395954\pi$
$174$		0			0
$175$	100.506	−	36.5813i	0.574322	−	0.209036i
$176$	−61.9724	−	170.268i	−0.352116	−	0.967431i
$177$		0			0
$178$	−3.33282	−	18.9014i	−0.0187237	−	0.106187i
$179$	57.9711	+	33.4697i	0.323861	+	0.186981i	0.653112	−	0.757261i	$-0.273463\pi$
$179$	57.9711	+	33.4697i	0.323861	+	0.186981i	−0.329251	+	0.944242i	$0.606796\pi$
$180$		0			0
$181$	64.7294	+	112.115i	0.357621	+	0.619418i	0.987563	−	0.157225i	$-0.0502547\pi$
$181$	64.7294	+	112.115i	0.357621	+	0.619418i	−0.629942	+	0.776642i	$0.716921\pi$
$182$	−4.97998	−	5.93491i	−0.0273625	−	0.0326094i
$183$		0			0
$184$	2.40789	−	13.6558i	0.0130863	−	0.0742163i
$185$	68.0059	−	81.0463i	0.367599	−	0.438088i
$186$		0			0
$187$	257.188	+	93.6088i	1.37534	+	0.500582i
$188$		−	232.707i		−	1.23780i
$189$		0			0
$190$	8.93020			0.0470011
$191$	−92.8061	+	254.983i	−0.485896	+	1.33499i	0.418470	+	0.908230i	$0.362566\pi$
$191$	−92.8061	+	254.983i	−0.485896	+	1.33499i	−0.904366	+	0.426757i	$0.859656\pi$
$192$		0			0
$193$	158.942	+	133.368i	0.823534	+	0.691027i	0.953797	−	0.300453i	$-0.0971377\pi$
$193$	158.942	+	133.368i	0.823534	+	0.691027i	−0.130263	+	0.991479i	$0.541582\pi$
$194$	6.60816	+	1.16520i	0.0340627	+	0.00600617i
$195$		0			0
$196$	44.5080	−	37.3466i	0.227082	−	0.190544i
$197$	−154.871	+	89.4146i	−0.786145	+	0.453881i	−0.838604	−	0.544742i	$-0.816628\pi$
$197$	−154.871	+	89.4146i	−0.786145	+	0.453881i	0.0524583	+	0.998623i	$0.483294\pi$
$198$		0			0
$199$	12.8040	−	22.1772i	0.0643418	−	0.111443i	−0.832060	−	0.554686i	$-0.812839\pi$
$199$	12.8040	−	22.1772i	0.0643418	−	0.111443i	0.896402	+	0.443242i	$0.146172\pi$
$200$	12.4169	−	2.18943i	0.0620845	−	0.0109472i
$201$		0			0
$202$	3.07170	−	1.11801i	0.0152065	−	0.00553470i
$203$	48.5233	+	133.317i	0.239031	+	0.656732i
$204$		0			0
$205$	33.0796	+	187.604i	0.161364	+	0.915140i
$206$	−8.36806	−	4.83130i	−0.0406216	−	0.0234529i
$207$		0			0
$208$	65.3600	+	113.207i	0.314231	+	0.544263i
$209$	−90.0489	−	107.316i	−0.430856	−	0.513474i
$210$		0			0
$211$	62.5630	−	354.812i	0.296507	−	1.68157i	−0.364507	−	0.931201i	$-0.618763\pi$
$211$	62.5630	−	354.812i	0.296507	−	1.68157i	0.661014	−	0.750374i	$-0.270126\pi$
$212$	−233.834	+	278.672i	−1.10299	+	1.31449i
$213$		0			0
$214$	−3.96648	−	1.44368i	−0.0185350	−	0.00674618i
$215$		−	246.863i		−	1.14820i
$216$		0			0
$217$	103.821			0.478438
$218$	0.0569787	−	0.156548i	0.000261370	−	0.000718108i
$219$		0			0
$220$	−216.576	−	181.729i	−0.984435	−	0.826039i
$221$	−194.452	−	34.2871i	−0.879872	−	0.155145i
$222$		0			0
$223$	6.88399	−	5.77635i	0.0308699	−	0.0259029i	−0.627222	−	0.778840i	$-0.715808\pi$
$223$	6.88399	−	5.77635i	0.0308699	−	0.0259029i	0.658092	+	0.752937i	$0.271364\pi$
$224$	38.8304	−	22.4187i	0.173350	−	0.100084i
$225$		0			0
$226$	−8.77026	+	15.1905i	−0.0388065	+	0.0672148i
$227$	70.6895	−	12.4645i	0.311408	−	0.0549096i	−0.0157602	−	0.999876i	$-0.505017\pi$
$227$	70.6895	−	12.4645i	0.311408	−	0.0549096i	0.327168	+	0.944966i	$0.393906\pi$
$228$		0			0
$229$	−50.6838	+	18.4474i	−0.221327	+	0.0805563i	−0.450303	−	0.892876i	$-0.648684\pi$
$229$	−50.6838	+	18.4474i	−0.221327	+	0.0805563i	0.228977	+	0.973432i	$0.426462\pi$
$230$	−3.68066	−	10.1125i	−0.0160029	−	0.0439675i
$231$		0			0
$232$	2.90417	+	16.4704i	0.0125180	+	0.0709930i
$233$	314.078	+	181.333i	1.34798	+	0.778254i	0.987962	−	0.154694i	$-0.0494391\pi$
$233$	314.078	+	181.333i	1.34798	+	0.778254i	0.360013	+	0.932947i	$0.382772\pi$
$234$		0			0
$235$	−180.914	−	313.352i	−0.769846	−	1.33341i
$236$	−52.9417	−	63.0935i	−0.224329	−	0.267345i
$237$		0			0
$238$	−3.89750	+	22.1038i	−0.0163761	+	0.0928732i
$239$	161.707	−	192.715i	0.676597	−	0.806337i	−0.313069	−	0.949731i	$-0.601357\pi$
$239$	161.707	−	192.715i	0.676597	−	0.806337i	0.989666	+	0.143393i	$0.0458014\pi$
$240$		0			0
$241$	−378.604	−	137.801i	−1.57097	−	0.571787i	−0.597756	−	0.801678i	$-0.703941\pi$
$241$	−378.604	−	137.801i	−1.57097	−	0.571787i	−0.973217	+	0.229890i	$0.926163\pi$
$242$		−	1.17139i		−	0.00484043i
$243$		0			0
$244$	−139.352			−0.571116
$245$	30.8978	−	84.8910i	0.126114	−	0.346494i
$246$		0			0
$247$	77.4212	+	64.9641i	0.313446	+	0.263012i
$248$	12.0529	+	2.12525i	0.0486003	+	0.00856954i
$249$		0			0
$250$	−6.47427	+	5.43255i	−0.0258971	+	0.0217302i
$251$	−329.280	+	190.110i	−1.31187	+	0.757409i	−0.982406	−	0.186759i	$-0.940202\pi$
$251$	−329.280	+	190.110i	−1.31187	+	0.757409i	−0.329465	+	0.944168i	$0.606868\pi$
$252$		0			0
$253$	−84.4099	+	146.202i	−0.333636	+	0.577875i
$254$	−1.98677	+	0.350321i	−0.00782192	+	0.00137922i
$255$		0			0
$256$	−232.274	+	84.5407i	−0.907319	+	0.330237i
$257$	−7.41792	−	20.3806i	−0.0288635	−	0.0793018i	0.924424	−	0.381366i	$-0.124546\pi$
$257$	−7.41792	−	20.3806i	−0.0288635	−	0.0793018i	−0.953287	+	0.302065i	$0.902324\pi$
$258$		0			0
$259$	−23.6347	−	134.039i	−0.0912536	−	0.517525i
$260$	176.637	+	101.981i	0.679373	+	0.392236i
$261$		0			0
$262$	−8.58759	−	14.8742i	−0.0327771	−	0.0567716i
$263$	43.6309	+	51.9973i	0.165897	+	0.197708i	0.842588	−	0.538559i	$-0.181031\pi$
$263$	43.6309	+	51.9973i	0.165897	+	0.197708i	−0.676691	+	0.736267i	$0.736587\pi$
$264$		0			0
$265$	−98.2205	+	557.036i	−0.370643	+	2.10202i
$266$	7.38463	−	8.80066i	0.0277618	−	0.0330852i
$267$		0			0
$268$	−193.140	−	70.2971i	−0.720671	−	0.262303i
$269$			290.581i			1.08023i	0.841592	+	0.540113i	$0.181619\pi$
$269$			290.581i			1.08023i	−0.841592	+	0.540113i	$0.818381\pi$
$270$		0			0
$271$	−414.644			−1.53005			−0.765026	−	0.644000i	$-0.777274\pi$
$271$	−414.644			−1.53005			−0.765026	+	0.644000i	$0.777274\pi$
$272$	129.524	−	355.864i	0.476190	−	1.30832i
$273$		0			0
$274$	−7.84535	−	6.58303i	−0.0286327	−	0.0240256i
$275$	−151.172	−	26.6557i	−0.549716	−	0.0969297i
$276$		0			0
$277$	134.157	−	112.571i	0.484321	−	0.406394i	−0.367665	−	0.929958i	$-0.619843\pi$
$277$	134.157	−	112.571i	0.484321	−	0.406394i	0.851986	+	0.523565i	$0.175398\pi$
$278$	3.75716	−	2.16919i	0.0135149	−	0.00780286i
$279$		0			0
$280$	23.2253	−	40.2273i	0.0829474	−	0.143669i
$281$	369.562	−	65.1637i	1.31517	−	0.231899i	0.528318	−	0.849046i	$-0.322823\pi$
$281$	369.562	−	65.1637i	1.31517	−	0.231899i	0.786848	+	0.617147i	$0.211712\pi$
$282$		0			0
$283$	−13.8854	+	5.05389i	−0.0490652	+	0.0178583i	−0.366436	−	0.930443i	$-0.619422\pi$
$283$	−13.8854	+	5.05389i	−0.0490652	+	0.0178583i	0.317371	+	0.948301i	$0.397200\pi$
$284$	−3.59214	−	9.86932i	−0.0126484	−	0.0347511i
$285$		0			0
$286$	1.93082	+	10.9502i	0.00675112	+	0.0382875i
$287$	212.237	+	122.535i	0.739501	+	0.426951i
$288$		0			0
$289$	141.513	+	245.108i	0.489665	+	0.848125i
$290$	8.34310	+	9.94292i	0.0287693	+	0.0342859i
$291$		0			0
$292$	47.7709	−	270.922i	0.163599	−	0.927816i
$293$	85.4559	−	101.842i	0.291659	−	0.347585i	−0.600241	−	0.799819i	$-0.704929\pi$
$293$	85.4559	−	101.842i	0.291659	−	0.347585i	0.891899	+	0.452234i	$0.149373\pi$
$294$		0			0
$295$	−120.340	−	43.8000i	−0.407931	−	0.148475i
$296$		−	16.0448i		−	0.0542053i
$297$		0			0
$298$	7.60284			0.0255129
$299$	41.6553	−	114.447i	0.139315	−	0.382766i
$300$		0			0
$301$	−243.282	−	204.138i	−0.808246	−	0.678199i
$302$	−17.9027	−	3.15673i	−0.0592806	−	0.0104528i
$303$		0			0
$304$	−148.490	+	124.598i	−0.488454	+	0.409862i
$305$	−187.645	+	108.337i	−0.615229	+	0.355203i
$306$		0			0
$307$	−35.2589	+	61.0701i	−0.114850	+	0.198926i	−0.917720	−	0.397229i	$-0.869972\pi$
$307$	−35.2589	+	61.0701i	−0.114850	+	0.198926i	0.802870	+	0.596154i	$0.203305\pi$
$308$	−358.185	+	63.1577i	−1.16294	+	0.205058i
$309$		0			0
$310$	8.92551	−	3.24862i	0.0287920	−	0.0104794i
$311$	20.8558	+	57.3009i	0.0670605	+	0.184247i	0.968696	−	0.248249i	$-0.0798551\pi$
$311$	20.8558	+	57.3009i	0.0670605	+	0.184247i	−0.901636	+	0.432496i	$0.857633\pi$
$312$		0			0
$313$	36.6975	+	208.122i	0.117245	+	0.664927i	0.985614	+	0.169010i	$0.0540569\pi$
$313$	36.6975	+	208.122i	0.117245	+	0.664927i	−0.868370	+	0.495917i	$0.834832\pi$
$314$	19.6266	+	11.3314i	0.0625051	+	0.0360874i
$315$		0			0
$316$	−301.821	−	522.770i	−0.955131	−	1.65433i
$317$	−85.9984	−	102.489i	−0.271288	−	0.323309i	0.613150	−	0.789967i	$-0.289902\pi$
$317$	−85.9984	−	102.489i	−0.271288	−	0.323309i	−0.884438	+	0.466658i	$0.845458\pi$
$318$		0			0
$319$	35.3574	−	200.522i	0.110838	−	0.628594i
$320$	−249.690	+	297.568i	−0.780280	+	0.929901i
$321$		0			0
$322$	−13.0095	−	4.73507i	−0.0404021	−	0.0147052i
$323$		−	292.794i		−	0.906482i
$324$		0			0
$325$	110.743			0.340746
$326$	6.89595	−	18.9465i	0.0211532	−	0.0581180i
$327$		0			0
$328$	22.1308	+	18.5700i	0.0674721	+	0.0566158i
$329$	−458.409	−	80.8300i	−1.39334	−	0.245684i
$330$		0			0
$331$	−67.5661	+	56.6947i	−0.204127	+	0.171283i	−0.739120	−	0.673573i	$-0.764759\pi$
$331$	−67.5661	+	56.6947i	−0.204127	+	0.171283i	0.534993	+	0.844856i	$0.320314\pi$
$332$	186.649	−	107.762i	0.562197	−	0.324585i
$333$		0			0
$334$	9.26171	−	16.0418i	0.0277297	−	0.0480292i
$335$	−314.724	+	55.4943i	−0.939474	+	0.165655i
$336$		0			0
$337$	−38.7005	+	14.0858i	−0.114838	+	0.0417978i	−0.398800	−	0.917038i	$-0.630573\pi$
$337$	−38.7005	+	14.0858i	−0.114838	+	0.0417978i	0.283962	+	0.958836i	$0.408351\pi$
$338$	4.05942	+	11.1532i	0.0120101	+	0.0329975i
$339$		0			0
$340$	−102.607	−	581.913i	−0.301785	−	1.71151i
$341$	−129.041	−	74.5018i	−0.378419	−	0.218480i
$342$		0			0
$343$	137.240	+	237.706i	0.400116	+	0.693022i
$344$	−24.0645	−	28.6790i	−0.0699550	−	0.0833692i
$345$		0			0
$346$	1.07308	−	6.08576i	0.00310140	−	0.0175889i
$347$	−220.437	+	262.707i	−0.635265	+	0.757079i	−0.983614	−	0.180285i	$-0.942298\pi$
$347$	−220.437	+	262.707i	−0.635265	+	0.757079i	0.348349	+	0.937365i	$0.386742\pi$
$348$		0			0
$349$	553.713	+	201.535i	1.58657	+	0.577464i	0.976619	−	0.214976i	$-0.0689672\pi$
$349$	553.713	+	201.535i	1.58657	+	0.577464i	0.609950	+	0.792440i	$0.291189\pi$
$350$		−	12.5884i		−	0.0359668i
$351$		0			0
$352$	−64.3505			−0.182814
$353$	43.0949	−	118.402i	0.122082	−	0.335417i	−0.863565	−	0.504238i	$-0.831774\pi$
$353$	43.0949	−	118.402i	0.122082	−	0.335417i	0.985647	+	0.168821i	$0.0539958\pi$
$354$		0			0
$355$	−12.5097	−	10.4969i	−0.0352386	−	0.0295687i
$356$	640.154	+	112.876i	1.79819	+	0.317069i
$357$		0			0
$358$	6.03528	−	5.06420i	0.0168583	−	0.0141458i
$359$	298.332	−	172.242i	0.831007	−	0.479782i	−0.0231901	−	0.999731i	$-0.507382\pi$
$359$	298.332	−	172.242i	0.831007	−	0.479782i	0.854197	+	0.519949i	$0.174049\pi$
$360$		0			0
$361$	105.566	−	182.846i	0.292427	−	0.506499i
$362$	15.0053	−	2.64584i	0.0414511	−	0.00730895i
$363$		0			0
$364$	246.568	−	89.7435i	0.677385	−	0.246548i
$365$	−146.298	−	401.949i	−0.400815	−	1.10123i
$366$		0			0
$367$	58.6453	+	332.594i	0.159796	+	0.906250i	0.954269	+	0.298950i	$0.0966363\pi$
$367$	58.6453	+	332.594i	0.159796	+	0.906250i	−0.794472	+	0.607300i	$0.792253\pi$
$368$	202.296	+	116.795i	0.549717	+	0.317379i
$369$		0			0
$370$	−6.22603	−	10.7838i	−0.0168271	−	0.0291454i
$371$	467.735	+	557.424i	1.26074	+	1.50249i
$372$		0			0
$373$	17.2087	−	97.5951i	0.0461358	−	0.261649i	−0.953012	−	0.302934i	$-0.902034\pi$
$373$	17.2087	−	97.5951i	0.0461358	−	0.261649i	0.999147	+	0.0412846i	$0.0131450\pi$
$374$	20.7059	−	24.6764i	0.0553635	−	0.0659796i
$375$		0			0
$376$	−51.5634	−	18.7675i	−0.137137	−	0.0499137i
$377$			146.894i			0.389640i
$378$		0			0
$379$	599.859			1.58274			0.791370	−	0.611337i	$-0.209368\pi$
$379$	599.859			1.58274			0.791370	+	0.611337i	$0.209368\pi$
$380$	−103.444	+	284.209i	−0.272220	+	0.747919i
$381$		0			0
$382$	24.4648	+	20.5284i	0.0640439	+	0.0537392i
$383$	111.938	+	19.7377i	0.292267	+	0.0515346i	0.317859	−	0.948138i	$-0.397036\pi$
$383$	111.938	+	19.7377i	0.292267	+	0.0515346i	−0.0255922	+	0.999672i	$0.508147\pi$
$384$		0			0
$385$	−433.214	+	363.509i	−1.12523	+	0.944181i
$386$	21.1484	−	12.2100i	0.0547886	−	0.0316322i
$387$		0			0
$388$	−113.629	+	196.812i	−0.292859	+	0.507247i
$389$	357.366	−	63.0132i	0.918678	−	0.161988i	0.305736	−	0.952116i	$-0.401097\pi$
$389$	357.366	−	63.0132i	0.918678	−	0.161988i	0.612941	+	0.790129i	$0.289986\pi$
$390$		0			0
$391$	−331.559	+	120.677i	−0.847976	+	0.308638i
$392$	−4.68578	−	12.8741i	−0.0119535	−	0.0328420i
$393$		0			0
$394$	3.65486	+	20.7277i	0.00927630	+	0.0526085i
$395$	−812.835	−	469.291i	−2.05781	−	1.18808i
$396$		0			0
$397$	239.208	+	414.320i	0.602539	+	1.04363i	0.992435	+	0.122769i	$0.0391775\pi$
$397$	239.208	+	414.320i	0.602539	+	1.04363i	−0.389896	+	0.920859i	$0.627489\pi$
$398$	−1.93734	−	2.30883i	−0.00486769	−	0.00580109i
$399$		0			0
$400$	−36.8827	+	209.172i	−0.0922066	+	0.522930i
$401$	410.108	−	488.748i	1.02271	−	1.21882i	0.0471994	−	0.998885i	$-0.484970\pi$
$401$	410.108	−	488.748i	1.02271	−	1.21882i	0.975514	−	0.219937i	$-0.0705852\pi$
$402$		0			0
$403$	101.013	+	36.7657i	0.250653	+	0.0912301i
$404$			110.709i			0.274033i
$405$		0			0
$406$	16.6978			0.0411277
$407$	−66.8101	+	183.559i	−0.164153	+	0.451006i
$408$		0			0
$409$	469.185	+	393.693i	1.14715	+	0.962575i	0.999649	−	0.0264868i	$-0.00843198\pi$
$409$	469.185	+	393.693i	1.14715	+	0.962575i	0.147503	+	0.989062i	$0.452876\pi$
$410$	22.0802	+	3.89334i	0.0538542	+	0.00949595i
$411$		0			0
$412$	250.691	−	210.355i	0.608474	−	0.510570i
$413$	−142.677	+	82.3746i	−0.345465	+	0.199454i
$414$		0			0
$415$	167.555	−	290.214i	0.403748	−	0.699311i
$416$	45.7192	−	8.06153i	0.109902	−	0.0193787i
$417$		0			0
$418$	−15.4938	+	5.63929i	−0.0370666	+	0.0134911i
$419$	179.434	+	492.992i	0.428244	+	1.17659i	0.946877	+	0.321595i	$0.104219\pi$
$419$	179.434	+	492.992i	0.428244	+	1.17659i	−0.518633	+	0.854997i	$0.673559\pi$
$420$		0			0
$421$	−63.9481	−	362.668i	−0.151896	−	0.861444i	−0.961569	−	0.274563i	$-0.911467\pi$
$421$	−63.9481	−	362.668i	−0.151896	−	0.861444i	0.809673	−	0.586881i	$-0.199644\pi$
$422$	−36.7231	−	21.2021i	−0.0870217	−	0.0502420i
$423$		0			0
$424$	42.8900	+	74.2876i	0.101156	+	0.175207i
$425$	−206.223	−	245.767i	−0.485231	−	0.578276i
$426$		0			0
$427$	−48.4035	+	274.510i	−0.113357	+	0.642880i
$428$	91.8922	−	109.513i	0.214701	−	0.255871i
$429$		0			0
$430$	−27.3026	−	9.93733i	−0.0634944	−	0.0231101i
$431$			178.021i			0.413043i	0.978442	+	0.206521i	$0.0662143\pi$
$431$			178.021i			0.413043i	−0.978442	+	0.206521i	$0.933786\pi$
$432$		0			0
$433$	−710.746			−1.64144			−0.820722	−	0.571327i	$-0.806429\pi$
$433$	−710.746			−1.64144			−0.820722	+	0.571327i	$0.806429\pi$
$434$	4.17926	−	11.4824i	0.00962962	−	0.0264572i
$435$		0			0
$436$	4.32221	+	3.62677i	0.00991333	+	0.00831827i
$437$	177.857	+	31.3610i	0.406996	+	0.0717644i
$438$		0			0
$439$	487.813	−	409.324i	1.11119	−	0.932400i	0.113065	−	0.993588i	$-0.463933\pi$
$439$	487.813	−	409.324i	1.11119	−	0.932400i	0.998126	+	0.0611873i	$0.0194887\pi$
$440$	−57.7341	+	33.3328i	−0.131214	+	0.0757564i
$441$		0			0
$442$	−11.6196	+	20.1258i	−0.0262888	+	0.0455335i
$443$	−317.960	+	56.0649i	−0.717743	+	0.126557i	−0.520579	−	0.853813i	$-0.674284\pi$
$443$	−317.960	+	56.0649i	−0.717743	+	0.126557i	−0.197163	+	0.980371i	$0.563173\pi$
$444$		0			0
$445$	949.754	−	345.682i	2.13428	−	0.776814i
$446$	−0.361743	−	0.993880i	−0.000811083	−	0.00222843i
$447$		0			0
$448$	86.7768	+	492.135i	0.193698	+	1.09852i
$449$	−22.4287	−	12.9492i	−0.0499526	−	0.0288401i	0.474816	−	0.880085i	$-0.342515\pi$
$449$	−22.4287	−	12.9492i	−0.0499526	−	0.0288401i	−0.524768	+	0.851245i	$0.675848\pi$
$450$		0			0
$451$	−175.862	−	304.602i	−0.389938	−	0.675392i
$452$	−381.857	−	455.080i	−0.844817	−	1.00681i
$453$		0			0
$454$	1.46702	−	8.31988i	0.00323132	−	0.0183257i
$455$	262.247	−	312.534i	0.576367	−	0.686888i
$456$		0			0
$457$	371.612	+	135.256i	0.813155	+	0.295964i	0.714926	−	0.699200i	$-0.246460\pi$
$457$	371.612	+	135.256i	0.813155	+	0.295964i	0.0982284	+	0.995164i	$0.468682\pi$
$458$			6.34813i			0.0138605i
$459$		0			0
$460$	364.473			0.792332
$461$	−306.756	+	842.804i	−0.665413	+	1.82821i	−0.114908	+	0.993376i	$0.536657\pi$
$461$	−306.756	+	842.804i	−0.665413	+	1.82821i	−0.550505	+	0.834832i	$0.685565\pi$
$462$		0			0
$463$	−227.973	−	191.292i	−0.492382	−	0.413158i	0.362497	−	0.931985i	$-0.381924\pi$
$463$	−227.973	−	191.292i	−0.492382	−	0.413158i	−0.854879	+	0.518827i	$0.826369\pi$
$464$	−277.456	−	48.9229i	−0.597965	−	0.105437i
$465$		0			0
$466$	32.6982	−	27.4370i	0.0701677	−	0.0588777i
$467$	684.460	−	395.173i	1.46565	−	0.846196i	0.466391	−	0.884579i	$-0.345554\pi$
$467$	684.460	−	395.173i	1.46565	−	0.846196i	0.999263	+	0.0383833i	$0.0122208\pi$
$468$		0			0
$469$	−205.565	+	356.048i	−0.438304	+	0.759165i
$470$	−41.9387	+	7.39493i	−0.0892314	+	0.0157339i
$471$		0			0
$472$	−18.2500	+	6.64245i	−0.0386652	+	0.0140730i
$473$	155.890	+	428.305i	0.329578	+	0.905508i
$474$		0			0
$475$	28.5158	+	161.721i	0.0600333	+	0.340466i
$476$	−658.321	−	380.082i	−1.38303	−	0.798491i
$477$		0			0
$478$	−14.8045	−	25.6421i	−0.0309717	−	0.0536445i
$479$	0.695366	+	0.828705i	0.00145170	+	0.00173007i	0.766770	−	0.641922i	$-0.221863\pi$
$479$	0.695366	+	0.828705i	0.00145170	+	0.00173007i	−0.765318	+	0.643652i	$0.777418\pi$
$480$		0			0
$481$	24.4712	−	138.783i	0.0508758	−	0.288531i
$482$	−30.4810	+	36.3259i	−0.0632386	+	0.0753649i
$483$		0			0
$484$	37.2801	+	13.5688i	0.0770249	+	0.0280348i
$485$			353.356i			0.728569i
$486$		0			0
$487$	647.606			1.32979			0.664893	−	0.746939i	$-0.268477\pi$
$487$	647.606			1.32979			0.664893	+	0.746939i	$0.268477\pi$
$488$	−11.2386	+	30.8778i	−0.0230299	+	0.0632741i
$489$		0			0
$490$	−8.14502	−	6.83448i	−0.0166225	−	0.0139479i
$491$	307.570	+	54.2328i	0.626415	+	0.110454i	0.477839	−	0.878447i	$-0.341420\pi$
$491$	307.570	+	54.2328i	0.626415	+	0.110454i	0.148575	+	0.988901i	$0.452531\pi$
$492$		0			0
$493$	325.998	−	273.545i	0.661253	−	0.554857i
$494$	10.3015	−	5.94755i	0.0208531	−	0.0120396i
$495$		0			0
$496$	−103.086	+	178.550i	−0.207834	+	0.359980i
$497$	−20.6893	+	3.64808i	−0.0416283	+	0.00734019i
$498$		0			0
$499$	−43.1250	+	15.6962i	−0.0864229	+	0.0314554i	−0.384870	−	0.922971i	$-0.625754\pi$
$499$	−43.1250	+	15.6962i	−0.0864229	+	0.0314554i	0.298447	+	0.954426i	$0.403531\pi$
$500$	−97.8993	−	268.976i	−0.195799	−	0.537952i
$501$		0			0
$502$	7.77081	+	44.0705i	0.0154797	+	0.0877898i
$503$	−493.829	−	285.113i	−0.981768	−	0.566824i	−0.0789646	−	0.996877i	$-0.525161\pi$
$503$	−493.829	−	285.113i	−0.981768	−	0.566824i	−0.902803	+	0.430053i	$0.858495\pi$
$504$		0			0
$505$	86.0690	+	149.076i	0.170434	+	0.295200i
$506$	12.7718	+	15.2209i	0.0252408	+	0.0300808i
$507$		0			0
$508$	11.8647	−	67.2881i	0.0233557	−	0.132457i
$509$	−334.300	+	398.403i	−0.656777	+	0.782717i	−0.986919	−	0.161215i	$-0.948459\pi$
$509$	−334.300	+	398.403i	−0.656777	+	0.782717i	0.330142	+	0.943931i	$0.392903\pi$
$510$		0			0
$511$	−517.096	−	188.208i	−1.01193	−	0.368313i
$512$			148.572i			0.290179i
$513$		0			0
$514$	−2.55266			−0.00496626
$515$	174.032	−	478.149i	0.337926	−	0.928445i
$516$		0			0
$517$	511.761	+	429.419i	0.989867	+	0.830597i
$518$	−15.7759	−	2.78171i	−0.0304553	−	0.00537009i
$519$		0			0
$520$	36.8427	−	30.9147i	0.0708513	−	0.0594513i
$521$	365.719	−	211.148i	0.701956	−	0.405275i	−0.106119	−	0.994353i	$-0.533843\pi$
$521$	365.719	−	211.148i	0.701956	−	0.405275i	0.808076	+	0.589079i	$0.200509\pi$
$522$		0			0
$523$	500.529	−	866.942i	0.957035	−	1.65763i	0.227394	−	0.973803i	$-0.426979\pi$
$523$	500.529	−	866.942i	0.957035	−	1.65763i	0.729641	−	0.683831i	$-0.239687\pi$
$524$	572.854	−	101.010i	1.09323	−	0.192767i
$525$		0			0
$526$	7.50714	−	2.73238i	0.0142721	−	0.00519463i
$527$	−106.512	−	292.640i	−0.202110	−	0.555294i
$528$		0			0
$529$	54.0676	+	306.633i	0.102207	+	0.579646i
$530$	57.6533	+	33.2862i	0.108780	+	0.0628041i
$531$		0			0
$532$	194.546	+	336.964i	0.365688	+	0.633391i
$533$	163.104	+	194.380i	0.306011	+	0.364690i
$534$		0			0
$535$	38.5988	−	218.905i	0.0721472	−	0.409167i
$536$	−31.1530	+	37.1267i	−0.0581212	+	0.0692662i
$537$		0			0
$538$	32.1377	+	11.6972i	0.0597356	+	0.0217420i
$539$			166.797i			0.309456i
$540$		0			0
$541$	−192.818			−0.356410			−0.178205	−	0.983993i	$-0.557029\pi$
$541$	−192.818			−0.356410			−0.178205	+	0.983993i	$0.557029\pi$
$542$	−16.6913	+	45.8589i	−0.0307957	+	0.0846105i
$543$		0			0
$544$	−103.028	−	86.4511i	−0.189391	−	0.158918i
$545$	8.63964	+	1.52340i	0.0158525	+	0.00279523i
$546$		0			0
$547$	−578.816	+	485.684i	−1.05816	+	0.887905i	−0.993928	−	0.110030i	$-0.964905\pi$
$547$	−578.816	+	485.684i	−1.05816	+	0.887905i	−0.0642358	+	0.997935i	$0.520461\pi$
$548$	300.386	−	173.428i	0.548150	−	0.316475i
$549$		0			0
$550$	−9.03341	+	15.6463i	−0.0164244	+	0.0284479i
$551$	−214.515	+	37.8248i	−0.389319	+	0.0686475i
$552$		0			0
$553$	−1134.64	+	412.975i	−2.05179	+	0.746790i
$554$	−7.04974	−	19.3690i	−0.0127252	−	0.0349621i
$555$		0			0
$556$	25.5147	+	144.701i	0.0458897	+	0.260253i
$557$	741.183	+	427.922i	1.33067	+	0.768262i	0.985402	−	0.170242i	$-0.0544551\pi$
$557$	741.183	+	427.922i	1.33067	+	0.768262i	0.345267	+	0.938505i	$0.387788\pi$
$558$		0			0
$559$	−164.412	−	284.769i	−0.294118	−	0.509427i
$560$	502.977	+	599.425i	0.898174	+	1.07040i
$561$		0			0
$562$	7.66951	−	43.4960i	0.0136468	−	0.0773950i
$563$	−100.118	+	119.316i	−0.177829	+	0.211929i	−0.847595	−	0.530644i	$-0.821950\pi$
$563$	−100.118	+	119.316i	−0.177829	+	0.211929i	0.669766	+	0.742573i	$0.266395\pi$
$564$		0			0
$565$	−867.984	−	315.920i	−1.53625	−	0.559151i
$566$			1.73915i			0.00307270i
$567$		0			0
$568$	−2.47655			−0.00436013
$569$	217.530	−	597.660i	0.382303	−	1.05037i	−0.588081	−	0.808802i	$-0.700116\pi$
$569$	217.530	−	597.660i	0.382303	−	1.05037i	0.970384	−	0.241567i	$-0.0776613\pi$
$570$		0			0
$571$	−769.247	−	645.475i	−1.34719	−	1.13043i	−0.979715	−	0.200396i	$-0.935777\pi$
$571$	−769.247	−	645.475i	−1.34719	−	1.13043i	−0.367477	−	0.930032i	$-0.619778\pi$
$572$	−370.864	−	65.3932i	−0.648363	−	0.114324i
$573$		0			0
$574$	22.0956	−	18.5404i	0.0384941	−	0.0323004i
$575$	171.380	−	98.9461i	0.298052	−	0.172080i
$576$		0			0
$577$	−414.908	+	718.642i	−0.719079	+	1.24548i	0.242287	+	0.970205i	$0.422103\pi$
$577$	−414.908	+	718.642i	−0.719079	+	1.24548i	−0.961365	+	0.275276i	$0.911231\pi$
$578$	32.8051	−	5.78442i	0.0567562	−	0.0100076i
$579$		0			0
$580$	−413.083	+	150.350i	−0.712212	+	0.259224i
$581$	−147.448	−	405.111i	−0.253784	−	0.697265i
$582$		0			0
$583$	−181.348	−	1028.48i	−0.311061	−	1.76411i
$584$	−56.1785	−	32.4347i	−0.0961961	−	0.0555388i
$585$		0			0
$586$	−7.82361	−	13.5509i	−0.0133509	−	0.0231244i
$587$	−188.692	−	224.874i	−0.321451	−	0.383090i	0.580985	−	0.813914i	$-0.302667\pi$
$587$	−188.692	−	224.874i	−0.321451	−	0.383090i	−0.902436	+	0.430824i	$0.858223\pi$
$588$		0			0
$589$	−27.6798	+	156.980i	−0.0469946	+	0.266520i
$590$	−9.68841	+	11.5462i	−0.0164210	+	0.0195698i
$591$		0			0
$592$	253.986	+	92.4432i	0.429030	+	0.156154i
$593$			720.027i			1.21421i	0.794621	+	0.607106i	$0.207670\pi$
$593$			720.027i			1.21421i	−0.794621	+	0.607106i	$0.792330\pi$
$594$		0			0
$595$	−1181.95			−1.98647
$596$	−88.0682	+	241.965i	−0.147765	+	0.405982i
$597$		0			0
$598$	−10.9808	−	9.21400i	−0.0183626	−	0.0154080i
$599$	−456.429	−	80.4808i	−0.761985	−	0.134359i	−0.220866	−	0.975304i	$-0.570888\pi$
$599$	−456.429	−	80.4808i	−0.761985	−	0.134359i	−0.541120	+	0.840946i	$0.681999\pi$
$600$		0			0
$601$	−417.548	+	350.364i	−0.694755	+	0.582969i	−0.920276	−	0.391269i	$-0.872036\pi$
$601$	−417.548	+	350.364i	−0.694755	+	0.582969i	0.225521	+	0.974238i	$0.427592\pi$
$602$	−32.3705	+	18.6891i	−0.0537715	+	0.0310450i
$603$		0			0
$604$	307.843	−	533.199i	0.509674	−	0.882781i
$605$	60.7484	−	10.7116i	0.100410	−	0.0177051i
$606$		0			0
$607$	957.815	−	348.616i	1.57795	−	0.574326i	0.603192	−	0.797596i	$-0.293895\pi$
$607$	957.815	−	348.616i	1.57795	−	0.574326i	0.974757	+	0.223270i	$0.0716730\pi$
$608$	23.5451	+	64.6896i	0.0387255	+	0.106397i
$609$		0			0
$610$	4.42831	+	25.1142i	0.00725953	+	0.0411709i
$611$	−417.387	−	240.979i	−0.683122	−	0.394400i
$612$		0			0
$613$	−496.963	−	860.765i	−0.810706	−	1.40418i	−0.912370	−	0.409366i	$-0.865750\pi$
$613$	−496.963	−	860.765i	−0.810706	−	1.40418i	0.101664	−	0.994819i	$-0.467583\pi$
$614$	5.33492	+	6.35791i	0.00868880	+	0.0103549i
$615$		0			0
$616$	−14.8927	+	84.4605i	−0.0241764	+	0.137111i
$617$	−607.136	+	723.556i	−0.984012	+	1.17270i	0.000962187		1.00000i	$0.499694\pi$
$617$	−607.136	+	723.556i	−0.984012	+	1.17270i	−0.984974	+	0.172701i	$0.944751\pi$
$618$		0			0
$619$	440.916	+	160.480i	0.712303	+	0.259257i	0.672655	−	0.739956i	$-0.265154\pi$
$619$	440.916	+	160.480i	0.712303	+	0.259257i	0.0396487	+	0.999214i	$0.487376\pi$
$620$			321.691i			0.518856i
$621$		0			0
$622$	7.17691			0.0115384
$623$	444.710	−	1221.83i	0.713821	−	1.96121i
$624$		0			0
$625$	−597.832	−	501.641i	−0.956531	−	0.802625i
$626$	24.4952	+	4.31916i	0.0391296	+	0.00689961i
$627$		0			0
$628$	−587.976	+	493.371i	−0.936268	+	0.785622i
$629$	−353.568	+	204.132i	−0.562111	+	0.324535i
$630$		0			0
$631$	−510.282	+	883.835i	−0.808689	+	1.40069i	0.105084	+	0.994463i	$0.466489\pi$
$631$	−510.282	+	883.835i	−0.808689	+	1.40069i	−0.913773	+	0.406226i	$0.866844\pi$
$632$	−140.177	+	24.7170i	−0.221799	+	0.0391092i
$633$		0			0
$634$	−14.7969	+	5.38563i	−0.0233390	+	0.00849468i
$635$	−36.3354	−	99.8308i	−0.0572212	−	0.157214i
$636$		0			0
$637$	−20.8955	−	118.504i	−0.0328030	−	0.186035i
$638$	−20.7540	−	11.9823i	−0.0325298	−	0.0187811i
$639$		0			0
$640$	92.5655	+	160.328i	0.144634	+	0.250513i
$641$	−723.530	−	862.269i	−1.12875	−	1.34519i	−0.931033	−	0.364935i	$-0.881091\pi$
$641$	−723.530	−	862.269i	−1.12875	−	1.34519i	−0.197719	−	0.980259i	$-0.563353\pi$
$642$		0			0
$643$	−37.0770	+	210.274i	−0.0576626	+	0.327021i	−0.999970	−	0.00772768i	$-0.997540\pi$
$643$	−37.0770	+	210.274i	−0.0576626	+	0.327021i	0.942308	+	0.334748i	$0.108651\pi$
$644$	301.393	−	359.186i	0.468001	−	0.557742i
$645$		0			0
$646$	−32.3825	−	11.7862i	−0.0501276	−	0.0182450i
$647$			267.943i			0.414132i	0.978327	+	0.207066i	$0.0663914\pi$
$647$			267.943i			0.414132i	−0.978327	+	0.207066i	$0.933609\pi$
$648$		0			0
$649$	236.447			0.364326
$650$	4.45788	−	12.2479i	0.00685828	−	0.0188430i
$651$		0			0
$652$	523.104	+	438.936i	0.802307	+	0.673215i
$653$	52.3571	+	9.23197i	0.0801793	+	0.0141378i	0.213594	−	0.976923i	$-0.431483\pi$
$653$	52.3571	+	9.23197i	0.0801793	+	0.0141378i	−0.133415	+	0.991060i	$0.542594\pi$
$654$		0			0
$655$	692.849	−	581.370i	1.05779	−	0.887587i
$656$	−421.468	+	243.335i	−0.642482	+	0.370937i
$657$		0			0
$658$	−27.3927	+	47.4455i	−0.0416302	+	0.0721056i
$659$	−493.780	+	87.0667i	−0.749286	+	0.132119i	−0.535235	−	0.844703i	$-0.679777\pi$
$659$	−493.780	+	87.0667i	−0.749286	+	0.132119i	−0.214051	+	0.976822i	$0.568666\pi$
$660$		0			0
$661$	−545.513	+	198.550i	−0.825284	+	0.300379i	−0.719922	−	0.694055i	$-0.755822\pi$
$661$	−545.513	+	198.550i	−0.825284	+	0.300379i	−0.105362	+	0.994434i	$0.533600\pi$
$662$	3.55049	+	9.75490i	0.00536328	+	0.0147355i
$663$		0			0
$664$	−8.82495	−	50.0488i	−0.0132906	−	0.0753747i
$665$	523.933	+	302.493i	0.787869	+	0.454876i
$666$		0			0
$667$	131.247	+	227.326i	0.196772	+	0.340819i
$668$	403.255	+	480.581i	0.603675	+	0.719432i
$669$		0			0
$670$	−6.53146	+	37.0418i	−0.00974845	+	0.0552862i
$671$	257.149	−	306.459i	0.383233	−	0.456719i
$672$		0			0
$673$	111.926	+	40.7377i	0.166309	+	0.0605316i	0.423833	−	0.905740i	$-0.360684\pi$
$673$	111.926	+	40.7377i	0.166309	+	0.0605316i	−0.257524	+	0.966272i	$0.582907\pi$
$674$			4.84723i			0.00719173i
$675$		0			0
$676$	−401.979			−0.594643
$677$	−159.960	+	439.485i	−0.236277	+	0.649166i	0.763716	+	0.645552i	$0.223373\pi$
$677$	−159.960	+	439.485i	−0.236277	+	0.649166i	−0.999993	+	0.00361412i	$0.998850\pi$
$678$		0			0
$679$	348.231	+	292.200i	0.512858	+	0.430339i
$680$	−137.216	−	24.1949i	−0.201788	−	0.0355807i
$681$		0			0
$682$	−13.4342	+	11.2727i	−0.0196983	+	0.0165288i
$683$	271.489	−	156.744i	0.397495	−	0.229494i	−0.287908	−	0.957658i	$-0.592960\pi$
$683$	271.489	−	156.744i	0.397495	−	0.229494i	0.685402	+	0.728164i	$0.259626\pi$
$684$		0			0
$685$	269.657	−	467.059i	0.393660	−	0.681839i
$686$	31.8144	−	5.60974i	0.0463767	−	0.00817746i
$687$		0			0
$688$	592.633	−	215.701i	0.861385	−	0.313519i
$689$	257.686	+	707.985i	0.373999	+	1.02755i
$690$		0			0
$691$	−116.796	−	662.386i	−0.169025	−	0.958590i	−0.944816	−	0.327600i	$-0.893760\pi$
$691$	−116.796	−	662.386i	−0.169025	−	0.958590i	0.775791	−	0.630990i	$-0.217351\pi$
$692$	181.253	+	104.646i	0.261926	+	0.151223i
$693$		0			0
$694$	20.1813	+	34.9550i	0.0290797	+	0.0503675i
$695$	146.852	+	175.011i	0.211298	+	0.251815i
$696$		0			0
$697$	127.651	−	723.942i	0.183143	−	1.03865i
$698$	44.5788	−	53.1269i	0.0638665	−	0.0761131i
$699$		0			0
$700$	400.633	+	145.819i	0.572333	+	0.208312i
$701$		−	906.580i		−	1.29327i	−0.762801	−	0.646633i	$-0.776176\pi$
$701$		−	906.580i		−	1.29327i	0.762801	−	0.646633i	$-0.223824\pi$
$702$		0			0
$703$	208.972			0.297257
$704$	245.299	−	673.954i	0.348436	−	0.957321i
$705$		0			0
$706$	−11.3603	−	9.53243i	−0.0160911	−	0.0135020i
$707$	218.086	+	38.4545i	0.308467	+	0.0543911i
$708$		0			0
$709$	−22.2471	+	18.6675i	−0.0313781	+	0.0263294i	−0.658342	−	0.752719i	$-0.728742\pi$
$709$	−22.2471	+	18.6675i	−0.0313781	+	0.0263294i	0.626964	+	0.779048i	$0.284297\pi$
$710$	−1.66451	+	0.961005i	−0.00234438	+	0.00135353i
$711$		0			0
$712$	76.6389	−	132.742i	0.107639	−	0.186436i
$713$	189.172	−	33.3562i	0.265319	−	0.0467829i
$714$		0			0
$715$	−550.225	+	200.266i	−0.769546	+	0.280092i
$716$	91.2612	+	250.738i	0.127460	+	0.350193i
$717$		0			0
$718$	−7.04046	−	39.9284i	−0.00980566	−	0.0556106i
$719$	837.314	+	483.423i	1.16455	+	0.672355i	0.952391	−	0.304879i	$-0.0986161\pi$
$719$	837.314	+	483.423i	1.16455	+	0.672355i	0.212162	+	0.977234i	$0.431949\pi$
$720$		0			0
$721$	−327.301	−	566.902i	−0.453955	−	0.786272i
$722$	−15.9729	−	19.0358i	−0.0221232	−	0.0263654i
$723$		0			0
$724$	−89.6097	+	508.202i	−0.123770	+	0.701936i
$725$	−153.420	+	182.839i	−0.211614	+	0.252192i
$726$		0			0
$727$	−824.450	−	300.075i	−1.13404	−	0.412758i	−0.294285	−	0.955718i	$-0.595082\pi$
$727$	−824.450	−	300.075i	−1.13404	−	0.412758i	−0.839759	+	0.542959i	$0.817304\pi$
$728$		−	61.8725i		−	0.0849896i
$729$		0			0
$730$	−50.3440			−0.0689644
$731$	−325.814	+	895.168i	−0.445711	+	1.22458i
$732$		0			0
$733$	27.7272	+	23.2659i	0.0378270	+	0.0317406i	0.661505	−	0.749941i	$-0.269918\pi$
$733$	27.7272	+	23.2659i	0.0378270	+	0.0317406i	−0.623678	+	0.781681i	$0.714362\pi$
$734$	39.1450	+	6.90232i	0.0533311	+	0.00940370i
$735$		0			0
$736$	63.5500	−	53.3248i	0.0863451	−	0.0724521i
$737$	510.999	−	295.026i	0.693350	−	0.400306i
$738$		0			0
$739$	237.815	−	411.907i	0.321806	−	0.557384i	−0.659055	−	0.752095i	$-0.729043\pi$
$739$	237.815	−	411.907i	0.321806	−	0.557384i	0.980861	+	0.194711i	$0.0623768\pi$
$740$	415.321	−	73.2323i	0.561245	−	0.0989626i
$741$		0			0
$742$	80.4785	−	29.2918i	0.108462	−	0.0394768i
$743$	17.4029	+	47.8140i	0.0234224	+	0.0643526i	0.950853	−	0.309643i	$-0.100210\pi$
$743$	17.4029	+	47.8140i	0.0234224	+	0.0643526i	−0.927430	+	0.373996i	$0.877987\pi$
$744$		0			0
$745$	69.5232	+	394.285i	0.0933197	+	0.529242i
$746$	−10.1011	−	5.83188i	−0.0135404	−	0.00781754i
$747$		0			0
$748$	545.492	+	944.820i	0.729268	+	1.26313i
$749$	−183.811	−	219.057i	−0.245408	−	0.292466i
$750$		0			0
$751$	8.19552	−	46.4791i	0.0109128	−	0.0618896i	−0.978865	−	0.204507i	$-0.934441\pi$
$751$	8.19552	−	46.4791i	0.0109128	−	0.0618896i	0.989778	+	0.142618i	$0.0455519\pi$
$752$	594.174	−	708.109i	0.790125	−	0.941634i
$753$		0			0
$754$	16.2462	+	5.91315i	0.0215467	+	0.00784237i
$755$		−	957.307i		−	1.26796i
$756$		0			0
$757$	973.584			1.28611			0.643054	−	0.765821i	$-0.277667\pi$
$757$	973.584			1.28611			0.643054	+	0.765821i	$0.277667\pi$
$758$	24.1470	−	66.3433i	0.0318562	−	0.0875241i
$759$		0			0
$760$	54.6327	+	45.8423i	0.0718851	+	0.0603188i
$761$	−16.0585	−	2.83155i	−0.0211019	−	0.00372083i	0.163087	−	0.986612i	$-0.447855\pi$
$761$	−16.0585	−	2.83155i	−0.0211019	−	0.00372083i	−0.184189	+	0.982891i	$0.558966\pi$
$762$		0			0
$763$	8.64566	−	7.25457i	0.0113311	−	0.00950796i
$764$	−936.718	+	540.814i	−1.22607	+	0.707872i
$765$		0			0
$766$	6.68897	−	11.5856i	0.00873234	−	0.0151249i
$767$	−167.989	+	29.6210i	−0.219021	+	0.0386193i
$768$		0			0
$769$	−133.465	+	48.5774i	−0.173557	+	0.0631696i	−0.427337	−	0.904092i	$-0.640548\pi$
$769$	−133.465	+	48.5774i	−0.173557	+	0.0631696i	0.253780	+	0.967262i	$0.418326\pi$
$770$	22.7647	+	62.5455i	0.0295646	+	0.0812280i
$771$		0			0
$772$	143.618	+	814.497i	0.186033	+	1.05505i
$773$	−991.099	−	572.211i	−1.28215	−	0.740248i	−0.304906	−	0.952382i	$-0.598625\pi$
$773$	−991.099	−	572.211i	−1.28215	−	0.740248i	−0.977240	+	0.212135i	$0.931958\pi$
$774$		0			0
$775$	87.3317	+	151.263i	0.112686	+	0.195178i
$776$	34.4456	+	41.0507i	0.0443887	+	0.0529004i
$777$		0			0
$778$	7.41641	−	42.0605i	0.00953266	−	0.0540624i
$779$	−241.861	+	288.239i	−0.310476	+	0.370011i
$780$		0			0
$781$	28.3329	+	10.3123i	0.0362777	+	0.0132040i
$782$			41.5276i			0.0531043i
$783$		0			0
$784$	230.792			0.294377
$785$	−408.178	+	1121.46i	−0.519972	+	1.42861i
$786$		0			0
$787$	−198.543	−	166.597i	−0.252278	−	0.211686i	0.507875	−	0.861431i	$-0.330431\pi$
$787$	−198.543	−	166.597i	−0.252278	−	0.211686i	−0.760152	+	0.649745i	$0.774876\pi$
$788$	−702.010	−	123.783i	−0.890876	−	0.157085i
$789$		0			0
$790$	−84.6229	+	71.0071i	−0.107118	+	0.0898824i
$791$	−1029.10	+	594.150i	−1.30101	+	0.751138i
$792$		0			0
$793$	−144.305	+	249.944i	−0.181974	+	0.315188i
$794$	55.4523	−	9.77773i	0.0698391	−	0.0123145i
$795$		0			0
$796$	95.9214	−	34.9125i	0.120504	−	0.0438600i
$797$	−363.027	−	997.408i	−0.455492	−	1.25145i	−0.928808	−	0.370561i	$-0.879165\pi$
$797$	−363.027	−	997.408i	−0.455492	−	1.25145i	0.473316	−	0.880893i	$-0.343057\pi$
$798$		0			0
$799$	242.457	+	1375.04i	0.303451	+	1.72095i
$800$	65.3263	+	37.7162i	0.0816579	+	0.0471452i
$801$		0			0
$802$	−37.5459	−	65.0315i	−0.0468154	−	0.0810866i
$803$	507.650	+	604.994i	0.632192	+	0.753417i
$804$		0			0
$805$	126.598	−	717.975i	0.157265	−	0.891894i
$806$	8.13245	−	9.69188i	0.0100899	−	0.0120247i
$807$		0			0
$808$	24.5311	+	8.92858i	0.0303602	+	0.0110502i
$809$		−	1471.80i		−	1.81928i	−0.415398	−	0.909640i	$-0.636358\pi$
$809$		−	1471.80i		−	1.81928i	0.415398	−	0.909640i	$-0.363642\pi$
$810$		0			0
$811$	128.574			0.158537			0.0792685	−	0.996853i	$-0.474742\pi$
$811$	128.574			0.158537			0.0792685	+	0.996853i	$0.474742\pi$
$812$	−193.421	+	531.419i	−0.238203	+	0.654458i
$813$		0			0
$814$	17.6119	+	14.7782i	0.0216363	+	0.0181550i
$815$	1045.63	+	184.373i	1.28298	+	0.226224i
$816$		0			0
$817$	373.524	−	313.424i	0.457189	−	0.383627i
$818$	62.4285	−	36.0431i	0.0763185	−	0.0440625i
$819$		0			0
$820$	−379.676	+	657.618i	−0.463020	+	0.801974i
$821$	1464.74	−	258.273i	1.78409	−	0.314584i	0.818474	−	0.574544i	$-0.194820\pi$
$821$	1464.74	−	258.273i	1.78409	−	0.314584i	0.965619	+	0.259960i	$0.0837093\pi$
$822$		0			0
$823$	1127.37	−	410.328i	1.36983	−	0.498576i	0.450748	−	0.892651i	$-0.351157\pi$
$823$	1127.37	−	410.328i	1.36983	−	0.498576i	0.919078	+	0.394076i	$0.128935\pi$
$824$	−26.3927	−	72.5132i	−0.0320299	−	0.0880015i
$825$		0			0
$826$	3.36710	+	19.0957i	0.00407639	+	0.0231183i
$827$	609.332	+	351.798i	0.736798	+	0.425391i	0.820904	−	0.571066i	$-0.193470\pi$
$827$	609.332	+	351.798i	0.736798	+	0.425391i	−0.0841057	+	0.996457i	$0.526803\pi$
$828$		0			0
$829$	112.799	+	195.374i	0.136066	+	0.235674i	0.926004	−	0.377513i	$-0.123221\pi$
$829$	112.799	+	195.374i	0.136066	+	0.235674i	−0.789938	+	0.613187i	$0.789887\pi$
$830$	−25.3523	−	30.2137i	−0.0305450	−	0.0364021i
$831$		0			0
$832$	−89.8483	+	509.555i	−0.107991	+	0.612446i
$833$	−224.082	+	267.050i	−0.269005	+	0.320588i
$834$		0			0
$835$	916.622	+	333.623i	1.09775	+	0.399549i
$836$		−	558.424i		−	0.667971i
$837$		0			0
$838$	61.7470			0.0736838
$839$	−244.311	+	671.238i	−0.291193	+	0.800045i	0.704700	+	0.709505i	$0.251082\pi$
$839$	−244.311	+	671.238i	−0.291193	+	0.800045i	−0.995893	+	0.0905401i	$0.971141\pi$
$840$		0			0
$841$	401.717	+	337.081i	0.477666	+	0.400809i
$842$	−42.6846	−	7.52645i	−0.0506943	−	0.00893877i
$843$		0			0
$844$	1100.16	−	923.141i	1.30350	−	1.09377i
$845$	−541.285	+	312.511i	−0.640574	+	0.369836i
$846$		0			0
$847$	39.6783	−	68.7249i	0.0468457	−	0.0811392i
$848$	−1423.07	+	250.926i	−1.67815	+	0.295904i
$849$		0			0
$850$	−35.4828	+	12.9147i	−0.0417445	+	0.0151938i
$851$	−86.1295	−	236.639i	−0.101210	−	0.278071i
$852$		0			0
$853$	45.2523	+	256.639i	0.0530508	+	0.300866i	0.999776	−	0.0211774i	$-0.00674148\pi$
$853$	45.2523	+	256.639i	0.0530508	+	0.300866i	−0.946725	+	0.322043i	$0.895630\pi$
$854$	28.4118	+	16.4036i	0.0332691	+	0.0192079i
$855$		0			0
$856$	−16.8549	−	29.1936i	−0.0196904	−	0.0341047i
$857$	−665.388	−	792.979i	−0.776416	−	0.925296i	0.222350	−	0.974967i	$-0.428627\pi$
$857$	−665.388	−	792.979i	−0.776416	−	0.925296i	−0.998766	+	0.0496705i	$0.984183\pi$
$858$		0			0
$859$	−97.0077	+	550.158i	−0.112931	+	0.640463i	0.874823	+	0.484443i	$0.160978\pi$
$859$	−97.0077	+	550.158i	−0.112931	+	0.640463i	−0.987754	+	0.156020i	$0.950133\pi$
$860$	632.524	−	753.812i	0.735493	−	0.876526i
$861$		0			0
$862$	19.6888	+	7.16615i	0.0228409	+	0.00831340i
$863$			251.585i			0.291523i	0.989320	+	0.145762i	$0.0465633\pi$
$863$			251.585i			0.291523i	−0.989320	+	0.145762i	$0.953437\pi$
$864$		0			0
$865$	325.422			0.376210
$866$	−28.6107	+	78.6072i	−0.0330377	+	0.0907704i
$867$		0			0
$868$	317.024	+	266.015i	0.365235	+	0.306469i
$869$	1706.61	+	300.922i	1.96388	+	0.346285i
$870$		0			0
$871$	−326.091	+	273.623i	−0.374387	+	0.314148i
$872$	1.15220	−	0.665224i	0.00132133	−	0.000762872i
$873$		0			0
$874$	10.6280	−	18.4083i	0.0121602	−	0.0210621i
$875$	−563.860	+	99.4238i	−0.644412	+	0.113627i
$876$		0			0
$877$	457.847	−	166.643i	0.522060	−	0.190014i	−0.0675294	−	0.997717i	$-0.521512\pi$
$877$	457.847	−	166.643i	0.522060	−	0.190014i	0.589590	+	0.807703i	$0.299289\pi$
$878$	−25.6338	−	70.4283i	−0.0291957	−	0.0802145i
$879$		0			0
$880$	−195.012	−	1105.97i	−0.221605	−	1.25678i
$881$	53.6224	+	30.9589i	0.0608654	+	0.0351407i	0.530124	−	0.847920i	$-0.322145\pi$
$881$	53.6224	+	30.9589i	0.0608654	+	0.0351407i	−0.469258	+	0.883061i	$0.655479\pi$
$882$		0			0
$883$	50.9265	+	88.2073i	0.0576744	+	0.0998950i	0.893421	−	0.449220i	$-0.148298\pi$
$883$	50.9265	+	88.2073i	0.0576744	+	0.0998950i	−0.835747	+	0.549115i	$0.814965\pi$
$884$	−505.919	−	602.931i	−0.572307	−	0.682049i
$885$		0			0
$886$	−6.59862	+	37.4227i	−0.00744766	+	0.0422378i
$887$	−808.390	+	963.402i	−0.911376	+	1.08614i	0.0845914	+	0.996416i	$0.473041\pi$
$887$	−808.390	+	963.402i	−0.911376	+	1.08614i	−0.995967	+	0.0897195i	$0.971403\pi$
$888$		0			0
$889$	−128.430	−	46.7445i	−0.144465	−	0.0525810i
$890$		−	118.956i		−	0.133659i
$891$		0			0
$892$	35.8212			0.0401582
$893$	244.434	−	671.577i	0.273722	−	0.752046i
$894$		0			0
$895$	317.820	+	266.682i	0.355106	+	0.297969i
$896$	234.547	+	41.3570i	0.261772	+	0.0461574i
$897$		0			0
$898$	−2.33502	+	1.95931i	−0.00260024	+	0.00218186i
$899$	−200.642	+	115.841i	−0.223184	+	0.128855i
$900$		0			0
$901$	1091.35	−	1890.27i	1.21127	−	2.09797i
$902$	−40.7676	+	7.18843i	−0.0451969	+	0.00796943i
$903$		0			0
$904$	−131.633	+	47.9106i	−0.145612	+	0.0529984i
$905$	274.428	+	753.985i	0.303235	+	0.833133i
$906$		0			0
$907$	−144.873	−	821.614i	−0.159727	−	0.905859i	−0.954336	−	0.298737i	$-0.903435\pi$
$907$	−144.873	−	821.614i	−0.159727	−	0.905859i	0.794608	−	0.607123i	$-0.207676\pi$
$908$	247.792	+	143.063i	0.272899	+	0.157558i
$909$		0			0
$910$	−24.0091	−	41.5849i	−0.0263836	−	0.0456977i
$911$	460.076	+	548.297i	0.505023	+	0.601863i	0.956972	−	0.290181i	$-0.0937155\pi$
$911$	460.076	+	548.297i	0.505023	+	0.601863i	−0.451949	+	0.892044i	$0.649271\pi$
$912$		0			0
$913$	−107.441	+	609.328i	−0.117679	+	0.667391i
$914$	29.9180	−	35.6549i	0.0327331	−	0.0390098i
$915$		0			0
$916$	−202.033	−	73.5340i	−0.220560	−	0.0802773i
$917$		−	1163.55i		−	1.26887i
$918$		0			0
$919$	−714.401			−0.777367			−0.388684	−	0.921371i	$-0.627070\pi$
$919$	−714.401			−0.777367			−0.388684	+	0.921371i	$0.627070\pi$
$920$	29.3943	−	80.7602i	0.0319503	−	0.0877828i
$921$		0			0
$922$	80.8643	+	67.8532i	0.0877053	+	0.0735935i
$923$	−21.4216	−	3.77720i	−0.0232087	−	0.00409231i
$924$		0			0
$925$	175.408	−	147.185i	0.189630	−	0.159119i
$926$	−30.3335	+	17.5130i	−0.0327576	+	0.0189126i
$927$		0			0
$928$	−50.0285	+	86.6520i	−0.0539101	+	0.0933749i
$929$	−318.470	+	56.1549i	−0.342810	+	0.0604466i	−0.342403	−	0.939553i	$-0.611241\pi$
$929$	−318.470	+	56.1549i	−0.342810	+	0.0604466i	−0.000407190		1.00000i	$0.500130\pi$
$930$		0			0
$931$	167.676	−	61.0289i	0.180103	−	0.0655520i
$932$	494.438	+	1358.46i	0.530513	+	1.45757i
$933$		0			0
$934$	−16.1529	−	91.6075i	−0.0172943	−	0.0980809i
$935$	1469.07	+	848.166i	1.57119	+	0.907129i
$936$		0			0
$937$	530.062	+	918.094i	0.565701	+	0.979823i	0.996984	+	0.0776063i	$0.0247277\pi$
$937$	530.062	+	918.094i	0.565701	+	0.979823i	−0.431283	+	0.902217i	$0.641939\pi$
$938$	31.1034	+	37.0676i	0.0331593	+	0.0395177i
$939$		0			0
$940$	250.453	−	1420.39i	0.266439	−	1.51105i
$941$	835.871	−	996.152i	0.888279	−	1.05861i	−0.109630	−	0.993972i	$-0.534967\pi$
$941$	835.871	−	996.152i	0.888279	−	1.05861i	0.997909	−	0.0646372i	$-0.0205890\pi$
$942$		0			0
$943$	426.085	+	155.082i	0.451840	+	0.164456i
$944$		−	327.165i		−	0.346573i
$945$		0			0
$946$	53.6451			0.0567073
$947$	562.112	−	1544.39i	0.593571	−	1.63082i	−0.170255	−	0.985400i	$-0.554459\pi$
$947$	562.112	−	1544.39i	0.593571	−	1.63082i	0.763826	−	0.645423i	$-0.223319\pi$
$948$		0			0
$949$	−436.462	−	366.235i	−0.459918	−	0.385917i
$950$	19.0340	+	3.35620i	0.0200358	+	0.00353285i
$951$		0			0
$952$	−137.312	+	115.218i	−0.144235	+	0.121027i
$953$	−404.262	+	233.401i	−0.424199	+	0.244912i	−0.696872	−	0.717195i	$-0.745426\pi$
$953$	−404.262	+	233.401i	−0.424199	+	0.244912i	0.272673	+	0.962107i	$0.412092\pi$
$954$		0			0
$955$	−840.892	+	1456.47i	−0.880515	+	1.52510i
$956$	987.564	−	174.134i	1.03302	−	0.182149i
$957$		0			0
$958$	0.119645	−	0.0435471i	0.000124890	−	4.54563e-5i
$959$	−237.298	−	651.970i	−0.247443	−	0.679844i
$960$		0			0
$961$	−137.435	−	779.433i	−0.143013	−	0.811065i
$962$	−14.3641	−	8.29312i	−0.0149315	−	0.00862071i
$963$		0			0
$964$	−803.014	−	1390.86i	−0.833002	−	1.44280i
$965$	826.605	+	985.109i	0.856585	+	1.02084i
$966$		0			0
$967$	−199.040	+	1128.81i	−0.205832	+	1.16733i	0.690292	+	0.723531i	$0.257482\pi$
$967$	−199.040	+	1128.81i	−0.205832	+	1.16733i	−0.896124	+	0.443803i	$0.853629\pi$
$968$	6.01318	−	7.16623i	0.00621197	−	0.00740313i
$969$		0			0
$970$	39.0806	+	14.2242i	0.0402892	+	0.0146641i
$971$			1439.65i			1.48264i	0.671150	+	0.741322i	$0.265801\pi$
$971$			1439.65i			1.48264i	−0.671150	+	0.741322i	$0.734199\pi$
$972$		0			0
$973$	293.908			0.302064
$974$	26.0690	−	71.6240i	0.0267649	−	0.0735360i
$975$		0			0
$976$	−424.037	−	355.810i	−0.434465	−	0.364559i
$977$	−1356.17	−	239.129i	−1.38809	−	0.244758i	−0.570851	−	0.821054i	$-0.693387\pi$
$977$	−1356.17	−	239.129i	−1.38809	−	0.244758i	−0.817241	+	0.576296i	$0.804498\pi$
$978$		0			0
$979$	−1429.52	+	1199.51i	−1.46019	+	1.22524i
$980$	311.860	−	180.053i	0.318225	−	0.183727i
$981$		0			0
$982$	18.3791	−	31.8335i	0.0187160	−	0.0324170i
$983$	−1214.26	+	214.107i	−1.23526	+	0.217809i	−0.752882	−	0.658155i	$-0.771337\pi$
$983$	−1214.26	+	214.107i	−1.23526	+	0.217809i	−0.482376	+	0.875965i	$0.660226\pi$
$984$		0			0
$985$	−1041.53	+	379.084i	−1.05739	+	0.384857i
$986$	−17.1307	−	47.0661i	−0.0173739	−	0.0477344i
$987$		0			0
$988$	69.9567	+	396.744i	0.0708064	+	0.401563i
$989$	−508.871	−	293.797i	−0.514531	−	0.297064i
$990$		0			0
$991$	25.7878	+	44.6657i	0.0260220	+	0.0450714i	0.878743	−	0.477295i	$-0.158383\pi$
$991$	25.7878	+	44.6657i	0.0260220	+	0.0450714i	−0.852721	+	0.522366i	$0.825049\pi$
$992$	47.0654	+	56.0904i	0.0474450	+	0.0565428i
$993$		0			0
$994$	−0.429364	+	2.43505i	−0.000431956	+	0.00244974i
$995$	102.021	−	121.584i	0.102534	−	0.122195i
$996$		0			0
$997$	775.774	+	282.359i	0.778108	+	0.283208i	0.700384	−	0.713767i	$-0.253012\pi$
$997$	775.774	+	282.359i	0.778108	+	0.283208i	0.0777245	+	0.996975i	$0.475235\pi$
$998$			5.40139i			0.00541222i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.b.53.3		30
3.2	odd	2		243.3.f.c.53.3		30
9.2	odd	6		27.3.f.a.14.3	yes	30
9.4	even	3		243.3.f.a.134.3		30
9.5	odd	6		243.3.f.d.134.3		30
9.7	even	3		81.3.f.a.71.3		30
27.2	odd	18		243.3.f.a.107.3		30
27.7	even	9		243.3.f.c.188.3		30
27.11	odd	18		81.3.f.a.8.3		30
27.13	even	9		729.3.b.a.728.16		30
27.14	odd	18		729.3.b.a.728.15		30
27.16	even	9		27.3.f.a.2.3	✓	30
27.20	odd	18	inner	243.3.f.b.188.3		30
27.25	even	9		243.3.f.d.107.3		30
36.11	even	6		432.3.bc.a.257.1		30
108.43	odd	18		432.3.bc.a.353.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.3	✓	30	27.16	even	9
27.3.f.a.14.3	yes	30	9.2	odd	6
81.3.f.a.8.3		30	27.11	odd	18
81.3.f.a.71.3		30	9.7	even	3
243.3.f.a.107.3		30	27.2	odd	18
243.3.f.a.134.3		30	9.4	even	3
243.3.f.b.53.3		30	1.1	even	1	trivial
243.3.f.b.188.3		30	27.20	odd	18	inner
243.3.f.c.53.3		30	3.2	odd	2
243.3.f.c.188.3		30	27.7	even	9
243.3.f.d.107.3		30	27.25	even	9
243.3.f.d.134.3		30	9.5	odd	6
432.3.bc.a.257.1		30	36.11	even	6
432.3.bc.a.353.1		30	108.43	odd	18
729.3.b.a.728.15		30	27.14	odd	18
729.3.b.a.728.16		30	27.13	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0402544 - 0.110598i) q^{2} +(3.05357 + 2.56225i) q^{4} +(6.10375 + 1.07626i) q^{5} +(6.10801 - 5.12523i) q^{7} +(0.814011 - 0.469969i) q^{8} +O(q^{10})\)	\(q+(0.0402544 - 0.110598i) q^{2} +(3.05357 + 2.56225i) q^{4} +(6.10375 + 1.07626i) q^{5} +(6.10801 - 5.12523i) q^{7} +(0.814011 - 0.469969i) q^{8} +(0.364735 - 0.631740i) q^{10} +(-11.2696 + 1.98713i) q^{11} +(7.75779 - 2.82360i) q^{13} +(-0.320966 - 0.881848i) q^{14} +(2.74954 + 15.5934i) q^{16} +(-20.7128 - 11.9585i) q^{17} +(6.12102 + 10.6019i) q^{19} +(15.8806 + 18.9257i) q^{20} +(-0.233878 + 1.32639i) q^{22} +(9.48274 - 11.3011i) q^{23} +(12.6052 + 4.58790i) q^{25} -0.971660i q^{26} +31.7833 q^{28} +(-6.08561 + 16.7201i) q^{29} +(9.97455 + 8.36964i) q^{31} +(5.53792 + 0.976485i) q^{32} +(-2.15637 + 1.80941i) q^{34} +(42.7978 - 24.7093i) q^{35} +(8.53500 - 14.7831i) q^{37} +(1.41895 - 0.250199i) q^{38} +(5.47433 - 1.99249i) q^{40} +(10.5123 + 28.8822i) q^{41} +(-6.91641 - 39.2249i) q^{43} +(-39.5040 - 22.8076i) q^{44} +(-0.868158 - 1.50369i) q^{46} +(-37.5253 - 44.7209i) q^{47} +(2.53105 - 14.3543i) q^{49} +(1.01483 - 1.20942i) q^{50} +(30.9237 + 11.2553i) q^{52} +91.2612i q^{53} -70.9255 q^{55} +(2.56328 - 7.04257i) q^{56} +(1.60424 + 1.34612i) q^{58} +(-20.3483 - 3.58796i) q^{59} +(-26.7802 + 22.4713i) q^{61} +(1.32719 - 0.766252i) q^{62} +(-31.3370 + 54.2773i) q^{64} +(50.3906 - 8.88521i) q^{65} +(-48.4527 + 17.6354i) q^{67} +(-32.6072 - 89.5875i) q^{68} +(-1.01001 - 5.72802i) q^{70} +(-2.28181 - 1.31740i) q^{71} +(-34.5072 - 59.7683i) q^{73} +(-1.29141 - 1.53904i) q^{74} +(-8.47378 + 48.0572i) q^{76} +(-58.6503 + 69.8967i) q^{77} +(-142.302 - 51.7939i) q^{79} +98.1375i q^{80} +3.61748 q^{82} +(18.4924 - 50.8076i) q^{83} +(-113.555 - 95.2842i) q^{85} +(-4.61662 - 0.814035i) q^{86} +(-8.23968 + 6.91392i) q^{88} +(141.225 - 81.5361i) q^{89} +(32.9130 - 57.0070i) q^{91} +(57.9124 - 10.2115i) q^{92} +(-6.45661 + 2.35001i) q^{94} +(25.9508 + 71.2992i) q^{95} +(9.90005 + 56.1460i) q^{97} +(-1.48567 - 0.857754i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8}+O(q^{10}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29} + 48 q^{31} - 117 q^{32} + 99 q^{34} + 252 q^{35} - 3 q^{37} + 237 q^{38} + 201 q^{40} - 129 q^{41} + 183 q^{43} - 639 q^{44} - 3 q^{46} + 348 q^{47} + 147 q^{49} + 471 q^{50} + 45 q^{52} - 12 q^{55} - 570 q^{56} - 267 q^{58} - 426 q^{59} - 285 q^{61} + 900 q^{62} - 51 q^{64} + 213 q^{65} - 366 q^{67} - 378 q^{68} - 483 q^{70} - 315 q^{71} - 66 q^{73} - 159 q^{74} - 201 q^{76} + 654 q^{77} - 15 q^{79} - 12 q^{82} - 624 q^{83} + 18 q^{85} + 411 q^{86} + 51 q^{88} - 72 q^{89} + 96 q^{91} + 561 q^{92} - 96 q^{94} + 75 q^{95} - 114 q^{97} - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

Introduction

L-functions

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