LMFDB - Embedded newform 324.3.f.s.271.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,3,Mod(55,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.55"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + x^{12} + 40x^{10} - 80x^{8} + 640x^{6} + 256x^{4} - 20480x^{2} + 65536 $ x^16 - 5x^14 + x^12 + 40x^10 - 80x^8 + 640x^6 + 256x^4 - 20480x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.4
Root			$-1.88429 + 0.670410i$ of defining polynomial
Character	$\chi$	$=$	324.271
Dual form			324.3.f.s.55.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.361553 + 1.96705i) q^{2} +(-3.73856 - 1.42238i) q^{4} +(-3.91150 + 6.77492i) q^{5} +(-10.7296 + 6.19472i) q^{7} +(4.14959 - 6.83966i) q^{8} +(-11.9124 - 10.1436i) q^{10} +(9.60079 - 5.54302i) q^{11} +(-1.77492 + 3.07425i) q^{13} +(-8.30601 - 23.3453i) q^{14} +(11.9536 + 10.6353i) q^{16} +8.77534 q^{17} -19.2016i q^{19} +(24.2599 - 19.7648i) q^{20} +(7.43220 + 20.8893i) q^{22} +(-0.617421 - 0.356468i) q^{23} +(-18.0997 - 31.3495i) q^{25} +(-5.40547 - 4.60285i) q^{26} +(48.9244 - 7.89776i) q^{28} +(-9.10765 - 15.7749i) q^{29} +(-9.66017 - 5.57730i) q^{31} +(-25.2421 + 19.6682i) q^{32} +(-3.17275 + 17.2615i) q^{34} -96.9226i q^{35} -35.5498 q^{37} +(37.7705 + 6.94239i) q^{38} +(30.1070 + 54.8664i) q^{40} +(6.09095 - 10.5498i) q^{41} +(-57.4086 + 33.1448i) q^{43} +(-43.7774 + 7.06689i) q^{44} +(0.924421 - 1.08561i) q^{46} +(-35.9335 + 20.7462i) q^{47} +(52.2492 - 90.4982i) q^{49} +(68.2101 - 24.2684i) q^{50} +(11.0084 - 8.96864i) q^{52} +74.7659 q^{53} +86.7261i q^{55} +(-2.15349 + 99.0922i) q^{56} +(34.3229 - 12.2117i) q^{58} +(17.9667 + 10.3731i) q^{59} +(-24.4244 - 42.3043i) q^{61} +(14.4635 - 16.9855i) q^{62} +(-29.5619 - 56.7635i) q^{64} +(-13.8852 - 24.0498i) q^{65} +(6.96889 + 4.02349i) q^{67} +(-32.8071 - 12.4819i) q^{68} +(190.652 + 35.0427i) q^{70} +87.9754i q^{71} +62.0997 q^{73} +(12.8531 - 69.9282i) q^{74} +(-27.3120 + 71.7863i) q^{76} +(-68.6750 + 118.949i) q^{77} +(-8.59076 + 4.95988i) q^{79} +(-118.810 + 39.3848i) q^{80} +(18.5498 + 15.7955i) q^{82} +(-19.2016 + 11.0860i) q^{83} +(-34.3248 + 59.4522i) q^{85} +(-44.4413 - 124.909i) q^{86} +(1.92694 - 88.6674i) q^{88} -106.231 q^{89} -43.9805i q^{91} +(1.80123 + 2.21089i) q^{92} +(-27.8169 - 78.1838i) q^{94} +(130.089 + 75.1070i) q^{95} +(-65.5498 - 113.536i) q^{97} +(159.124 + 135.497i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{4} - 100 q^{10} + 32 q^{13} + 46 q^{16} + 36 q^{22} - 48 q^{25} + 360 q^{28} + 122 q^{34} - 448 q^{37} - 154 q^{40} - 408 q^{46} + 232 q^{49} - 154 q^{52} + 86 q^{58} + 32 q^{61} - 20 q^{64}+ \cdots - 928 q^{97}+O(q^{100}) $ 16 * q + 10 * q^4 - 100 * q^10 + 32 * q^13 + 46 * q^16 + 36 * q^22 - 48 * q^25 + 360 * q^28 + 122 * q^34 - 448 * q^37 - 154 * q^40 - 408 * q^46 + 232 * q^49 - 154 * q^52 + 86 * q^58 + 32 * q^61 - 20 * q^64 + 492 * q^70 + 752 * q^73 - 516 * q^76 + 176 * q^82 - 368 * q^85 - 516 * q^88 + 672 * q^94 - 928 * q^97

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.361553	+	1.96705i	−0.180776	+	0.983524i
$2$	−0.361553	+	1.96705i	−0.180776	+	0.983524i
$3$		0			0
$3$		0			0
$4$	−3.73856	−	1.42238i	−0.934640	−	0.355596i
$5$	−3.91150	+	6.77492i	−0.782300	+	1.35498i	0.148299	+	0.988943i	$0.452620\pi$
$5$	−3.91150	+	6.77492i	−0.782300	+	1.35498i	−0.930599	+	0.366041i	$0.880713\pi$
$6$		0			0
$7$	−10.7296	+	6.19472i	−1.53280	+	0.884960i	−0.533565	+	0.845759i	$0.679148\pi$
$7$	−10.7296	+	6.19472i	−1.53280	+	0.884960i	−0.999231	+	0.0392013i	$0.987519\pi$
$8$	4.14959	−	6.83966i	0.518698	−	0.854957i
$9$		0			0
$10$	−11.9124	−	10.1436i	−1.19124	−	1.01436i
$11$	9.60079	−	5.54302i	0.872799	−	0.503911i	0.00452195	−	0.999990i	$-0.498561\pi$
$11$	9.60079	−	5.54302i	0.872799	−	0.503911i	0.868278	+	0.496079i	$0.165227\pi$
$12$		0			0
$13$	−1.77492	+	3.07425i	−0.136532	+	0.236481i	−0.926182	−	0.377078i	$-0.876929\pi$
$13$	−1.77492	+	3.07425i	−0.136532	+	0.236481i	0.789650	+	0.613558i	$0.210262\pi$
$14$	−8.30601	−	23.3453i	−0.593286	−	1.66752i
$15$		0			0
$16$	11.9536	+	10.6353i	0.747103	+	0.664708i
$17$	8.77534			0.516197			0.258098	−	0.966119i	$-0.416904\pi$
$17$	8.77534			0.516197			0.258098	+	0.966119i	$0.416904\pi$
$18$		0			0
$19$		−	19.2016i		−	1.01061i	−0.862941	−	0.505305i	$-0.831380\pi$
$19$		−	19.2016i		−	1.01061i	0.862941	−	0.505305i	$-0.168620\pi$
$20$	24.2599	−	19.7648i	1.21300	−	0.988239i
$21$		0			0
$22$	7.43220	+	20.8893i	0.337827	+	0.949515i
$23$	−0.617421	−	0.356468i	−0.0268444	−	0.0154986i	0.486518	−	0.873671i	$-0.338267\pi$
$23$	−0.617421	−	0.356468i	−0.0268444	−	0.0154986i	−0.513362	+	0.858172i	$0.671600\pi$
$24$		0			0
$25$	−18.0997	−	31.3495i	−0.723987	−	1.25398i
$26$	−5.40547	−	4.60285i	−0.207903	−	0.177033i
$27$		0			0
$28$	48.9244	−	7.89776i	1.74730	−	0.282063i
$29$	−9.10765	−	15.7749i	−0.314057	−	0.543963i	0.665180	−	0.746683i	$-0.268355\pi$
$29$	−9.10765	−	15.7749i	−0.314057	−	0.543963i	−0.979237	+	0.202721i	$0.935022\pi$
$30$		0			0
$31$	−9.66017	−	5.57730i	−0.311618	−	0.179913i	0.336032	−	0.941851i	$-0.390915\pi$
$31$	−9.66017	−	5.57730i	−0.311618	−	0.179913i	−0.647650	+	0.761938i	$0.724248\pi$
$32$	−25.2421	+	19.6682i	−0.788815	+	0.614630i
$33$		0			0
$34$	−3.17275	+	17.2615i	−0.0933162	+	0.507692i
$35$		−	96.9226i		−	2.76922i
$36$		0			0
$37$	−35.5498			−0.960806			−0.480403	−	0.877048i	$-0.659510\pi$
$37$	−35.5498			−0.960806			−0.480403	+	0.877048i	$0.659510\pi$
$38$	37.7705	+	6.94239i	0.993959	+	0.182694i
$39$		0			0
$40$	30.1070	+	54.8664i	0.752676	+	1.37166i
$41$	6.09095	−	10.5498i	0.148560	−	0.257313i	−0.782136	−	0.623108i	$-0.785870\pi$
$41$	6.09095	−	10.5498i	0.148560	−	0.257313i	0.930695	+	0.365795i	$0.119203\pi$
$42$		0			0
$43$	−57.4086	+	33.1448i	−1.33508	+	0.770810i	−0.986074	−	0.166309i	$-0.946815\pi$
$43$	−57.4086	+	33.1448i	−1.33508	+	0.770810i	−0.349009	+	0.937119i	$0.613482\pi$
$44$	−43.7774	+	7.06689i	−0.994942	+	0.160611i
$45$		0			0
$46$	0.924421	−	1.08561i	0.0200961	−	0.0236003i
$47$	−35.9335	+	20.7462i	−0.764542	+	0.441409i	−0.830924	−	0.556386i	$-0.812188\pi$
$47$	−35.9335	+	20.7462i	−0.764542	+	0.441409i	0.0663819	+	0.997794i	$0.478854\pi$
$48$		0			0
$49$	52.2492	−	90.4982i	1.06631	−	1.84690i
$50$	68.2101	−	24.2684i	1.36420	−	0.485368i
$51$		0			0
$52$	11.0084	−	8.96864i	0.211700	−	0.172474i
$53$	74.7659			1.41068			0.705339	−	0.708870i	$-0.250795\pi$
$53$	74.7659			1.41068			0.705339	+	0.708870i	$0.250795\pi$
$54$		0			0
$55$			86.7261i			1.57684i
$56$	−2.15349	+	99.0922i	−0.0384553	+	1.76950i
$57$		0			0
$58$	34.3229	−	12.2117i	0.591775	−	0.210547i
$59$	17.9667	+	10.3731i	0.304521	+	0.175815i	0.644472	−	0.764628i	$-0.277077\pi$
$59$	17.9667	+	10.3731i	0.304521	+	0.175815i	−0.339951	+	0.940443i	$0.610410\pi$
$60$		0			0
$61$	−24.4244	−	42.3043i	−0.400400	−	0.693514i	0.593374	−	0.804927i	$-0.297796\pi$
$61$	−24.4244	−	42.3043i	−0.400400	−	0.693514i	−0.993774	+	0.111413i	$0.964462\pi$
$62$	14.4635	−	16.9855i	0.233282	−	0.273960i
$63$		0			0
$64$	−29.5619	−	56.7635i	−0.461904	−	0.886930i
$65$	−13.8852	−	24.0498i	−0.213618	−	0.369997i
$66$		0			0
$67$	6.96889	+	4.02349i	0.104013	+	0.0600521i	0.551104	−	0.834436i	$-0.314207\pi$
$67$	6.96889	+	4.02349i	0.104013	+	0.0600521i	−0.447091	+	0.894489i	$0.647540\pi$
$68$	−32.8071	−	12.4819i	−0.482458	−	0.183557i
$69$		0			0
$70$	190.652	+	35.0427i	2.72359	+	0.500609i
$71$			87.9754i			1.23909i	0.784961	+	0.619545i	$0.212683\pi$
$71$			87.9754i			1.23909i	−0.784961	+	0.619545i	$0.787317\pi$
$72$		0			0
$73$	62.0997			0.850680			0.425340	−	0.905034i	$-0.360154\pi$
$73$	62.0997			0.850680			0.425340	+	0.905034i	$0.360154\pi$
$74$	12.8531	−	69.9282i	0.173691	−	0.944976i
$75$		0			0
$76$	−27.3120	+	71.7863i	−0.359369	+	0.944556i
$77$	−68.6750	+	118.949i	−0.891883	+	1.54479i
$78$		0			0
$79$	−8.59076	+	4.95988i	−0.108744	+	0.0627833i	−0.553386	−	0.832925i	$-0.686664\pi$
$79$	−8.59076	+	4.95988i	−0.108744	+	0.0627833i	0.444642	+	0.895709i	$0.353331\pi$
$80$	−118.810	+	39.3848i	−1.48513	+	0.492311i
$81$		0			0
$82$	18.5498	+	15.7955i	0.226217	+	0.192628i
$83$	−19.2016	+	11.0860i	−0.231344	+	0.133567i	−0.611192	−	0.791482i	$-0.709310\pi$
$83$	−19.2016	+	11.0860i	−0.231344	+	0.133567i	0.379848	+	0.925049i	$0.375976\pi$
$84$		0			0
$85$	−34.3248	+	59.4522i	−0.403821	+	0.699438i
$86$	−44.4413	−	124.909i	−0.516759	−	1.45243i
$87$		0			0
$88$	1.92694	−	88.6674i	0.0218971	−	1.00758i
$89$	−106.231			−1.19360			−0.596801	−	0.802389i	$-0.703562\pi$
$89$	−106.231			−1.19360			−0.596801	+	0.802389i	$0.703562\pi$
$90$		0			0
$91$		−	43.9805i		−	0.483302i
$92$	1.80123	+	2.21089i	0.0195786	+	0.0240314i
$93$		0			0
$94$	−27.8169	−	78.1838i	−0.295925	−	0.831742i
$95$	130.089	+	75.1070i	1.36936	+	0.790600i
$96$		0			0
$97$	−65.5498	−	113.536i	−0.675771	−	1.17047i	−0.976243	−	0.216680i	$-0.930477\pi$
$97$	−65.5498	−	113.536i	−0.675771	−	1.17047i	0.300471	−	0.953791i	$-0.402856\pi$
$98$	159.124	+	135.497i	1.62371	+	1.38262i
$99$		0			0
$100$	23.0756	+	142.947i	0.230756	+	1.42947i
$101$	−22.9195	−	39.6977i	−0.226925	−	0.393046i	0.729970	−	0.683479i	$-0.239534\pi$
$101$	−22.9195	−	39.6977i	−0.226925	−	0.393046i	−0.956895	+	0.290433i	$0.906201\pi$
$102$		0			0
$103$	−173.812	−	100.350i	−1.68750	−	0.974276i	−0.956427	−	0.291971i	$-0.905689\pi$
$103$	−173.812	−	100.350i	−1.68750	−	0.974276i	−0.731068	−	0.682305i	$-0.760978\pi$
$104$	13.6616	+	24.8967i	0.131362	+	0.239391i
$105$		0			0
$106$	−27.0318	+	147.068i	−0.255017	+	1.38744i
$107$			90.1142i			0.842189i	0.907017	+	0.421094i	$0.138354\pi$
$107$			90.1142i			0.842189i	−0.907017	+	0.421094i	$0.861646\pi$
$108$		0			0
$109$	−183.447			−1.68300			−0.841499	−	0.540258i	$-0.818327\pi$
$109$	−183.447			−1.68300			−0.841499	+	0.540258i	$0.818327\pi$
$110$	−170.594	−	31.3561i	−1.55086	−	0.285055i
$111$		0			0
$112$	−194.140	−	40.0631i	−1.73340	−	0.357706i
$113$	44.1098	−	76.4003i	0.390352	−	0.676109i	−0.602144	−	0.798387i	$-0.705687\pi$
$113$	44.1098	−	76.4003i	0.390352	−	0.676109i	0.992496	+	0.122278i	$0.0390201\pi$
$114$		0			0
$115$	4.83008	−	2.78865i	0.0420007	−	0.0242491i
$116$	11.6115	+	71.9300i	0.100099	+	0.620087i
$117$		0			0
$118$	−26.9003	+	31.5910i	−0.227969	+	0.267721i
$119$	−94.1557	+	54.3608i	−0.791224	+	0.456813i
$120$		0			0
$121$	0.950166	−	1.64574i	0.00785261	−	0.0136011i
$122$	92.0454	−	32.7488i	0.754470	−	0.268432i
$123$		0			0
$124$	28.1820	+	34.5915i	0.227275	+	0.278964i
$125$	87.6124			0.700899
$126$		0			0
$127$		−	37.1683i		−	0.292664i	−0.989236	−	0.146332i	$-0.953253\pi$
$127$		−	37.1683i		−	0.292664i	0.989236	−	0.146332i	$-0.0467468\pi$
$128$	122.345	−	37.6266i	0.955818	−	0.293958i
$129$		0			0
$130$	52.3274	−	18.6175i	0.402519	−	0.143212i
$131$	−101.904	−	58.8344i	−0.777895	−	0.449118i	0.0577889	−	0.998329i	$-0.481595\pi$
$131$	−101.904	−	58.8344i	−0.777895	−	0.449118i	−0.835684	+	0.549211i	$0.814928\pi$
$132$		0			0
$133$	118.949	+	206.025i	0.894350	+	1.54906i
$134$	−10.4340	+	12.2534i	−0.0778659	+	0.0914436i
$135$		0			0
$136$	36.4140	−	60.0203i	0.267750	−	0.441326i
$137$	18.4743	+	31.9983i	0.134849	+	0.233565i	0.925540	−	0.378651i	$-0.123612\pi$
$137$	18.4743	+	31.9983i	0.134849	+	0.233565i	−0.790691	+	0.612215i	$0.790279\pi$
$138$		0			0
$139$	−13.9378	−	8.04699i	−0.100272	−	0.0578920i	0.449025	−	0.893519i	$-0.351771\pi$
$139$	−13.9378	−	8.04699i	−0.100272	−	0.0578920i	−0.549297	+	0.835627i	$0.685105\pi$
$140$	−137.861	+	362.351i	−0.984723	+	2.58822i
$141$		0			0
$142$	−173.052	−	31.8078i	−1.21868	−	0.223998i
$143$			39.3536i			0.275200i
$144$		0			0
$145$	142.498			0.982747
$146$	−22.4523	+	122.153i	−0.153783	+	0.836665i
$147$		0			0
$148$	132.905	+	50.5655i	0.898008	+	0.341659i
$149$	4.14168	−	7.17359i	0.0277965	−	0.0481449i	−0.851793	−	0.523879i	$-0.824484\pi$
$149$	4.14168	−	7.17359i	0.0277965	−	0.0481449i	0.879589	+	0.475734i	$0.157818\pi$
$150$		0			0
$151$	181.333	−	104.693i	1.20088	−	0.693330i	0.240132	−	0.970740i	$-0.422809\pi$
$151$	181.333	−	104.693i	1.20088	−	0.693330i	0.960752	+	0.277410i	$0.0894761\pi$
$152$	−131.332	−	79.6786i	−0.864028	−	0.524202i
$153$		0			0
$154$	−209.148	−	178.093i	−1.35810	−	1.15645i
$155$	75.5715	−	43.6312i	0.487558	−	0.281492i
$156$		0			0
$157$	19.2251	−	33.2988i	0.122453	−	0.212094i	−0.798282	−	0.602284i	$-0.794257\pi$
$157$	19.2251	−	33.2988i	0.122453	−	0.212094i	0.920734	+	0.390190i	$0.127591\pi$
$158$	−6.65031	−	18.6917i	−0.0420906	−	0.118302i
$159$		0			0
$160$	−34.5157	−	247.945i	−0.215723	−	1.54966i
$161$	8.83289			0.0548626
$162$		0			0
$163$			266.353i			1.63406i	0.576592	+	0.817032i	$0.304382\pi$
$163$			266.353i			1.63406i	−0.576592	+	0.817032i	$0.695618\pi$
$164$	−37.7773	+	30.7775i	−0.230349	+	0.187668i
$165$		0			0
$166$	−14.8644	−	41.7786i	−0.0895445	−	0.251679i
$167$	−257.091	−	148.432i	−1.53947	−	0.888813i	−0.998870	−	0.0475320i	$-0.984864\pi$
$167$	−257.091	−	148.432i	−1.53947	−	0.888813i	−0.540599	−	0.841281i	$-0.681802\pi$
$168$		0			0
$169$	78.1993	+	135.445i	0.462718	+	0.801451i
$170$	−104.535	−	89.0136i	−0.614913	−	0.523609i
$171$		0			0
$172$	261.770	−	42.2569i	1.52192	−	0.245680i
$173$	84.7684	+	146.823i	0.489990	+	0.848688i	0.999934	−	0.0115197i	$-0.00366691\pi$
$173$	84.7684	+	146.823i	0.489990	+	0.848688i	−0.509943	+	0.860208i	$0.670334\pi$
$174$		0			0
$175$	388.403	+	224.245i	2.21945	+	1.28140i
$176$	173.716	+	35.8483i	0.987025	+	0.203684i
$177$		0			0
$178$	38.4080	−	208.961i	0.215775	−	1.17394i
$179$			15.0427i			0.0840375i	0.999117	+	0.0420188i	$0.0133789\pi$
$179$			15.0427i			0.0840375i	−0.999117	+	0.0420188i	$0.986621\pi$
$180$		0			0
$181$	99.1960			0.548044			0.274022	−	0.961723i	$-0.411646\pi$
$181$	99.1960			0.548044			0.274022	+	0.961723i	$0.411646\pi$
$182$	86.5117	+	15.9013i	0.475339	+	0.0873696i
$183$		0			0
$184$	−5.00016	+	2.74375i	−0.0271748	+	0.0149117i
$185$	139.053	−	240.847i	0.751639	−	1.30188i
$186$		0			0
$187$	84.2502	−	48.6419i	0.450536	−	0.260117i
$188$	163.849	−	26.4497i	0.871535	−	0.140690i
$189$		0			0
$190$	−194.773	+	228.737i	−1.02512	+	1.20388i
$191$	235.420	−	135.920i	1.23257	−	0.711622i	0.265001	−	0.964248i	$-0.414628\pi$
$191$	235.420	−	135.920i	1.23257	−	0.711622i	0.967564	+	0.252626i	$0.0812943\pi$
$192$		0			0
$193$	−72.9502	+	126.353i	−0.377980	+	0.654681i	−0.990768	−	0.135566i	$-0.956715\pi$
$193$	−72.9502	+	126.353i	−0.377980	+	0.654681i	0.612788	+	0.790247i	$0.290048\pi$
$194$	247.030	−	87.8906i	1.27335	−	0.453044i
$195$		0			0
$196$	−324.060	+	264.015i	−1.65337	+	1.34701i
$197$	−187.202			−0.950266			−0.475133	−	0.879914i	$-0.657600\pi$
$197$	−187.202			−0.950266			−0.475133	+	0.879914i	$0.657600\pi$
$198$		0			0
$199$		−	338.220i		−	1.69960i	−0.527109	−	0.849798i	$-0.676724\pi$
$199$		−	338.220i		−	1.69960i	0.527109	−	0.849798i	$-0.323276\pi$
$200$	−289.526	−	6.29206i	−1.44763	−	0.0314603i
$201$		0			0
$202$	86.3739	−	30.7309i	0.427593	−	0.152133i
$203$	195.442	+	112.839i	0.962771	+	0.555856i
$204$		0			0
$205$	47.6495	+	82.5314i	0.232437	+	0.402592i
$206$	260.236	−	305.615i	1.26328	−	1.48357i
$207$		0			0
$208$	−53.9124	+	17.8716i	−0.259194	+	0.0859213i
$209$	−106.435	−	184.350i	−0.509257	−	0.882060i
$210$		0			0
$211$	102.466	+	59.1586i	0.485619	+	0.280372i	0.722755	−	0.691104i	$-0.242875\pi$
$211$	102.466	+	59.1586i	0.485619	+	0.280372i	−0.237136	+	0.971476i	$0.576209\pi$
$212$	−279.517	−	106.346i	−1.31848	−	0.501631i
$213$		0			0
$214$	−177.259	−	32.5811i	−0.828313	−	0.152248i
$215$		−	518.584i		−	2.41202i
$216$		0			0
$217$	138.199			0.636863
$218$	66.3257	−	360.849i	0.304247	−	1.65527i
$219$		0			0
$220$	123.358	−	324.231i	0.560718	−	1.47378i
$221$	−15.5755	+	26.9776i	−0.0704774	+	0.122070i
$222$		0			0
$223$	−212.417	+	122.639i	−0.952543	+	0.549951i	−0.893870	−	0.448326i	$-0.852020\pi$
$223$	−212.417	+	122.639i	−0.952543	+	0.549951i	−0.0586732	+	0.998277i	$0.518687\pi$
$224$	148.998	−	367.399i	0.665170	−	1.64017i
$225$		0			0
$226$	134.335	+	114.389i	0.594403	+	0.506145i
$227$	−27.5675	+	15.9161i	−0.121443	+	0.0701151i	−0.559491	−	0.828836i	$-0.689003\pi$
$227$	−27.5675	+	15.9161i	−0.121443	+	0.0701151i	0.438048	+	0.898952i	$0.355670\pi$
$228$		0			0
$229$	−71.6719	+	124.139i	−0.312978	+	0.542094i	−0.979006	−	0.203833i	$-0.934660\pi$
$229$	−71.6719	+	124.139i	−0.312978	+	0.542094i	0.666028	+	0.745927i	$0.267993\pi$
$230$	3.73908	+	10.5093i	0.0162569	+	0.0456924i
$231$		0			0
$232$	−145.688	−	3.16613i	−0.627966	−	0.0136471i
$233$	−329.147			−1.41265			−0.706324	−	0.707888i	$-0.749648\pi$
$233$	−329.147			−1.41265			−0.706324	+	0.707888i	$0.749648\pi$
$234$		0			0
$235$		−	324.595i		−	1.38126i
$236$	−52.4152	−	64.3361i	−0.222098	−	0.272611i
$237$		0			0
$238$	−72.8881	−	204.863i	−0.306252	−	0.860769i
$239$	75.5715	+	43.6312i	0.316199	+	0.182557i	0.649697	−	0.760193i	$-0.274896\pi$
$239$	75.5715	+	43.6312i	0.316199	+	0.182557i	−0.333498	+	0.942751i	$0.608229\pi$
$240$		0			0
$241$	−89.5997	−	155.191i	−0.371783	−	0.643947i	0.618057	−	0.786133i	$-0.287920\pi$
$241$	−89.5997	−	155.191i	−0.371783	−	0.643947i	−0.989840	+	0.142186i	$0.954587\pi$
$242$	2.89371	+	2.46404i	0.0119575	+	0.0101820i
$243$		0			0
$244$	31.1391	+	192.898i	0.127619	+	0.790566i
$245$	408.745	+	707.968i	1.66835	+	2.88966i
$246$		0			0
$247$	59.0304	+	34.0812i	0.238990	+	0.137981i
$248$	−78.2325	+	42.9288i	−0.315454	+	0.173100i
$249$		0			0
$250$	−31.6765	+	172.338i	−0.126706	+	0.689352i
$251$			410.968i			1.63732i	0.574278	+	0.818660i	$0.305283\pi$
$251$			410.968i			1.63732i	−0.574278	+	0.818660i	$0.694717\pi$
$252$		0			0
$253$	−7.90364			−0.0312397
$254$	73.1119	+	13.4383i	0.287842	+	0.0529068i
$255$		0			0
$256$	29.7793	+	254.262i	0.116325	+	0.993211i
$257$	−99.3887	+	172.146i	−0.386726	+	0.669830i	−0.992007	−	0.126183i	$-0.959728\pi$
$257$	−99.3887	+	172.146i	−0.386726	+	0.669830i	0.605281	+	0.796012i	$0.293061\pi$
$258$		0			0
$259$	381.435	−	220.221i	1.47272	−	0.850276i
$260$	17.7025	+	109.662i	0.0680864	+	0.421776i
$261$		0			0
$262$	152.574	−	179.179i	0.582343	−	0.683888i
$263$	268.822	−	155.205i	1.02214	−	0.590132i	0.107415	−	0.994214i	$-0.465743\pi$
$263$	268.822	−	155.205i	1.02214	−	0.590132i	0.914722	+	0.404083i	$0.132409\pi$
$264$		0			0
$265$	−292.447	+	506.533i	−1.10357	+	1.91144i
$266$	−448.267	+	159.489i	−1.68521	+	0.599581i
$267$		0			0
$268$	−20.3307	−	24.9545i	−0.0758607	−	0.0931138i
$269$	199.384			0.741206			0.370603	−	0.928791i	$-0.379151\pi$
$269$	199.384			0.741206			0.370603	+	0.928791i	$0.379151\pi$
$270$		0			0
$271$		−	68.1625i		−	0.251522i	−0.992061	−	0.125761i	$-0.959863\pi$
$271$		−	68.1625i		−	0.251522i	0.992061	−	0.125761i	$-0.0401372\pi$
$272$	104.897	+	93.3287i	0.385652	+	0.343120i
$273$		0			0
$274$	−69.6217	+	24.7707i	−0.254094	+	0.0904038i
$275$	−347.542	−	200.654i	−1.26379	−	0.729650i
$276$		0			0
$277$	146.100	+	253.052i	0.527436	+	0.913545i	0.999489	+	0.0319752i	$0.0101797\pi$
$277$	146.100	+	253.052i	0.527436	+	0.913545i	−0.472053	+	0.881570i	$0.656487\pi$
$278$	20.8681	−	24.5069i	0.0750650	−	0.0881543i
$279$		0			0
$280$	−662.918	−	402.189i	−2.36756	−	1.43639i
$281$	−234.316	−	405.847i	−0.833865	−	1.44430i	−0.894951	−	0.446164i	$-0.852790\pi$
$281$	−234.316	−	405.847i	−0.833865	−	1.44430i	0.0610867	−	0.998132i	$-0.480543\pi$
$282$		0			0
$283$	−11.7990	−	6.81214i	−0.0416925	−	0.0240712i	0.479009	−	0.877810i	$-0.340996\pi$
$283$	−11.7990	−	6.81214i	−0.0416925	−	0.0240712i	−0.520701	+	0.853739i	$0.674330\pi$
$284$	125.135	−	328.901i	0.440616	−	1.15810i
$285$		0			0
$286$	−77.4105	−	14.2284i	−0.270666	−	0.0497497i
$287$			150.927i			0.525878i
$288$		0			0
$289$	−211.993			−0.733541
$290$	−51.5207	+	280.301i	−0.177658	+	0.966556i
$291$		0			0
$292$	−232.163	−	88.3296i	−0.795080	−	0.302499i
$293$	16.8731	−	29.2251i	0.0575874	−	0.0997443i	−0.835795	−	0.549042i	$-0.814993\pi$
$293$	16.8731	−	29.2251i	0.0575874	−	0.0997443i	0.893382	+	0.449298i	$0.148326\pi$
$294$		0			0
$295$	−140.554	+	81.1488i	−0.476454	+	0.275081i
$296$	−147.517	+	243.149i	−0.498369	+	0.821449i
$297$		0			0
$298$	12.6134	+	10.7405i	0.0423267	+	0.0360420i
$299$	2.19174	−	1.26540i	0.00733024	−	0.00423212i
$300$		0			0
$301$	410.646	−	711.260i	1.36427	−	2.36299i
$302$	140.374	+	394.543i	0.464816	+	1.30644i
$303$		0			0
$304$	204.215	−	229.529i	0.671761	−	0.755030i
$305$	382.145			1.25293
$306$		0			0
$307$			141.264i			0.460144i	0.973174	+	0.230072i	$0.0738962\pi$
$307$			141.264i			0.460144i	−0.973174	+	0.230072i	$0.926104\pi$
$308$	425.936	−	347.014i	1.38291	−	1.12667i
$309$		0			0
$310$	58.5016	+	164.428i	0.188715	+	0.530412i
$311$	−344.394	−	198.836i	−1.10738	−	0.639343i	−0.169227	−	0.985577i	$-0.554127\pi$
$311$	−344.394	−	198.836i	−1.10738	−	0.639343i	−0.938148	+	0.346234i	$0.887460\pi$
$312$		0			0
$313$	239.194	+	414.297i	0.764199	+	1.32363i	0.940669	+	0.339326i	$0.110199\pi$
$313$	239.194	+	414.297i	0.764199	+	1.32363i	−0.176470	+	0.984306i	$0.556468\pi$
$314$	58.5495	+	49.8560i	0.186463	+	0.158777i
$315$		0			0
$316$	39.1719	−	6.32344i	0.123962	−	0.0200109i
$317$	−111.727	−	193.517i	−0.352452	−	0.610465i	0.634226	−	0.773147i	$-0.281319\pi$
$317$	−111.727	−	193.517i	−0.352452	−	0.610465i	−0.986679	+	0.162682i	$0.947985\pi$
$318$		0			0
$319$	−174.881	−	100.968i	−0.548218	−	0.316514i
$320$	500.199	+	21.7512i	1.56312	+	0.0679724i
$321$		0			0
$322$	−3.19356	+	17.3747i	−0.00991787	+	0.0539587i
$323$		−	168.500i		−	0.521673i
$324$		0			0
$325$	128.502			0.395390
$326$	−523.928	−	96.3005i	−1.60714	−	0.295400i
$327$		0			0
$328$	−46.8824	−	85.4375i	−0.142934	−	0.260480i
$329$	257.034	−	445.196i	0.781258	−	1.35318i
$330$		0			0
$331$	−281.660	+	162.617i	−0.850937	+	0.491289i	−0.860967	−	0.508661i	$-0.830141\pi$
$331$	−281.660	+	162.617i	−0.850937	+	0.491289i	0.0100298	+	0.999950i	$0.496807\pi$
$332$	87.5549	−	14.1338i	0.263720	−	0.0425716i
$333$		0			0
$334$	384.924	−	452.045i	1.15247	−	1.35343i
$335$	−54.5177	+	31.4758i	−0.162739	+	0.0939576i
$336$		0			0
$337$	−128.849	+	223.173i	−0.382341	+	0.662234i	−0.991396	−	0.130894i	$-0.958215\pi$
$337$	−128.849	+	223.173i	−0.382341	+	0.662234i	0.609056	+	0.793128i	$0.291549\pi$
$338$	−294.701	+	104.851i	−0.871895	+	0.310211i
$339$		0			0
$340$	212.889	−	173.443i	0.626144	−	0.510125i
$341$	−123.660			−0.362640
$342$		0			0
$343$			687.594i			2.00465i
$344$	−11.5223	+	530.192i	−0.0334950	+	1.54126i
$345$		0			0
$346$	−319.456	+	113.659i	−0.923284	+	0.328495i
$347$	377.580	+	217.996i	1.08813	+	0.628230i	0.933077	−	0.359677i	$-0.117113\pi$
$347$	377.580	+	217.996i	1.08813	+	0.628230i	0.155049	+	0.987907i	$0.450446\pi$
$348$		0			0
$349$	−180.746	−	313.061i	−0.517896	−	0.897023i	−0.999784	−	0.0207898i	$-0.993382\pi$
$349$	−180.746	−	313.061i	−0.517896	−	0.897023i	0.481887	−	0.876233i	$-0.339951\pi$
$350$	−581.529	+	682.932i	−1.66151	+	1.95123i
$351$		0			0
$352$	−133.323	+	328.747i	−0.378759	+	0.933942i
$353$	−251.550	−	435.698i	−0.712607	−	1.23427i	−0.963875	−	0.266354i	$-0.914181\pi$
$353$	−251.550	−	435.698i	−0.712607	−	1.23427i	0.251269	−	0.967917i	$-0.419152\pi$
$354$		0			0
$355$	−596.026	−	344.116i	−1.67895	−	0.969340i
$356$	397.149	+	151.101i	1.11559	+	0.424440i
$357$		0			0
$358$	−29.5898	−	5.43874i	−0.0826530	−	0.0151920i
$359$			221.008i			0.615621i	0.951448	+	0.307810i	$0.0995963\pi$
$359$			221.008i			0.615621i	−0.951448	+	0.307810i	$0.900404\pi$
$360$		0			0
$361$	−7.70099			−0.0213324
$362$	−35.8646	+	195.123i	−0.0990735	+	0.539015i
$363$		0			0
$364$	−62.5571	+	164.424i	−0.171860	+	0.451713i
$365$	−242.903	+	420.720i	−0.665487	+	1.15266i
$366$		0			0
$367$	291.802	−	168.472i	0.795100	−	0.459051i	−0.0466548	−	0.998911i	$-0.514856\pi$
$367$	291.802	−	168.472i	0.795100	−	0.459051i	0.841755	+	0.539860i	$0.181523\pi$
$368$	−3.58927	−	10.8276i	−0.00975346	−	0.0294228i
$369$		0			0
$370$	423.483	+	360.603i	1.14455	+	0.974604i
$371$	−802.206	+	463.154i	−2.16228	+	1.24839i
$372$		0			0
$373$	228.595	−	395.938i	0.612854	−	1.06150i	−0.377902	−	0.925845i	$-0.623355\pi$
$373$	228.595	−	395.938i	0.612854	−	1.06150i	0.990757	−	0.135650i	$-0.0433121\pi$
$374$	65.2201	+	183.311i	0.174385	+	0.490136i
$375$		0			0
$376$	−7.21208	+	331.861i	−0.0191811	+	0.882609i
$377$	64.6613			0.171515
$378$		0			0
$379$			74.3367i			0.196139i	0.995180	+	0.0980695i	$0.0312667\pi$
$379$			74.3367i			0.196139i	−0.995180	+	0.0980695i	$0.968733\pi$
$380$	−379.515	−	465.829i	−0.998724	−	1.22587i
$381$		0			0
$382$	182.244	+	512.225i	0.477079	+	1.34090i
$383$	493.685	+	285.029i	1.28899	+	0.744201i	0.978475	−	0.206367i	$-0.0661639\pi$
$383$	493.685	+	285.029i	1.28899	+	0.744201i	0.310519	+	0.950567i	$0.399497\pi$
$384$		0			0
$385$	−537.244	−	930.534i	−1.39544	−	2.41697i
$386$	−222.168	−	189.180i	−0.575564	−	0.490103i
$387$		0			0
$388$	83.5706	+	517.697i	0.215388	+	1.33427i
$389$	317.860	+	550.550i	0.817121	+	1.41530i	0.907795	+	0.419415i	$0.137765\pi$
$389$	317.860	+	550.550i	0.817121	+	1.41530i	−0.0906738	+	0.995881i	$0.528902\pi$
$390$		0			0
$391$	−5.41808	−	3.12813i	−0.0138570	−	0.00800033i
$392$	−402.165	−	732.897i	−1.02593	−	1.86963i
$393$		0			0
$394$	67.6836	−	368.236i	0.171786	−	0.934610i
$395$		−	77.6023i		−	0.196462i
$396$		0			0
$397$	−482.849			−1.21624			−0.608122	−	0.793844i	$-0.708077\pi$
$397$	−482.849			−1.21624			−0.608122	+	0.793844i	$0.708077\pi$
$398$	665.294	+	122.284i	1.67159	+	0.307247i
$399$		0			0
$400$	117.056	−	567.237i	0.292640	−	1.41809i
$401$	−78.6040	+	136.146i	−0.196020	+	0.339517i	−0.947234	−	0.320542i	$-0.896135\pi$
$401$	−78.6040	+	136.146i	−0.196020	+	0.339517i	0.751214	+	0.660058i	$0.229468\pi$
$402$		0			0
$403$	34.2920	−	19.7985i	0.0850918	−	0.0491278i
$404$	29.2204	+	181.012i	0.0723278	+	0.448051i
$405$		0			0
$406$	−292.622	+	343.648i	−0.720744	+	0.846423i
$407$	−341.307	+	197.053i	−0.838591	+	0.484161i
$408$		0			0
$409$	−150.651	+	260.935i	−0.368340	+	0.637984i	−0.989306	−	0.145854i	$-0.953407\pi$
$409$	−150.651	+	260.935i	−0.368340	+	0.637984i	0.620966	+	0.783838i	$0.286741\pi$
$410$	−179.571	+	63.8894i	−0.437978	+	0.155828i
$411$		0			0
$412$	507.070	+	622.393i	1.23075	+	1.51066i
$413$	−257.034			−0.622358
$414$		0			0
$415$		−	173.452i		−	0.417957i
$416$	−15.6622	−	112.510i	−0.0376494	−	0.270456i
$417$		0			0
$418$	401.108	−	142.710i	0.959589	−	0.341411i
$419$	419.409	+	242.146i	1.00098	+	0.577914i	0.908537	−	0.417804i	$-0.137200\pi$
$419$	419.409	+	242.146i	1.00098	+	0.577914i	0.0924398	+	0.995718i	$0.470533\pi$
$420$		0			0
$421$	2.57558	+	4.46103i	0.00611777	+	0.0105963i	0.869068	−	0.494693i	$-0.164719\pi$
$421$	2.57558	+	4.46103i	0.00611777	+	0.0105963i	−0.862950	+	0.505289i	$0.831386\pi$
$422$	−153.415	+	180.166i	−0.363542	+	0.426934i
$423$		0			0
$424$	310.248	−	511.373i	0.731716	−	1.20607i
$425$	−158.831	−	275.103i	−0.373719	−	0.647301i
$426$		0			0
$427$	524.127	+	302.605i	1.22746	+	0.708677i
$428$	128.177	−	336.897i	0.299479	−	0.787143i
$429$		0			0
$430$	1020.08	+	187.496i	2.37228	+	0.436036i
$431$			317.539i			0.736748i	0.929678	+	0.368374i	$0.120085\pi$
$431$			317.539i			0.736748i	−0.929678	+	0.368374i	$0.879915\pi$
$432$		0			0
$433$	190.203			0.439267			0.219634	−	0.975582i	$-0.429514\pi$
$433$	190.203			0.439267			0.219634	+	0.975582i	$0.429514\pi$
$434$	−49.9664	+	271.845i	−0.115130	+	0.626370i
$435$		0			0
$436$	685.827	+	260.932i	1.57300	+	0.598468i
$437$	−6.84476	+	11.8555i	−0.0156631	+	0.0271292i
$438$		0			0
$439$	−100.879	+	58.2427i	−0.229793	+	0.132671i	−0.610477	−	0.792034i	$-0.709022\pi$
$439$	−100.879	+	58.2427i	−0.229793	+	0.132671i	0.380683	+	0.924705i	$0.375689\pi$
$440$	593.177	+	359.877i	1.34813	+	0.817903i
$441$		0			0
$442$	−47.4348	−	40.3916i	−0.107319	−	0.0913837i
$443$	424.905	−	245.319i	0.959153	−	0.553767i	0.0632405	−	0.997998i	$-0.479856\pi$
$443$	424.905	−	245.319i	0.959153	−	0.553767i	0.895912	+	0.444231i	$0.146523\pi$
$444$		0			0
$445$	415.521	−	719.703i	0.933755	−	1.61731i
$446$	−164.437	−	462.175i	−0.368693	−	1.03627i
$447$		0			0
$448$	668.821	+	425.921i	1.49290	+	0.950716i
$449$	−155.936			−0.347297			−0.173649	−	0.984808i	$-0.555556\pi$
$449$	−155.936			−0.347297			−0.173649	+	0.984808i	$0.555556\pi$
$450$		0			0
$451$		−	135.049i		−	0.299444i
$452$	−273.578	+	222.886i	−0.605260	+	0.493111i
$453$		0			0
$454$	−21.3407	−	59.9812i	−0.0470059	−	0.132117i
$455$	297.964	+	172.030i	0.654866	+	0.378087i
$456$		0			0
$457$	−61.2492	−	106.087i	−0.134024	−	0.232137i	0.791200	−	0.611558i	$-0.209457\pi$
$457$	−61.2492	−	106.087i	−0.134024	−	0.232137i	−0.925224	+	0.379420i	$0.876123\pi$
$458$	−218.275	−	185.865i	−0.476583	−	0.405819i
$459$		0			0
$460$	−22.0241	+	3.55530i	−0.0478785	+	0.00772891i
$461$	234.722	+	406.550i	0.509158	+	0.881887i	0.999944	+	0.0106068i	$0.00337630\pi$
$461$	234.722	+	406.550i	0.509158	+	0.881887i	−0.490786	+	0.871280i	$0.663290\pi$
$462$		0			0
$463$	−331.547	−	191.419i	−0.716085	−	0.413432i	0.0972250	−	0.995262i	$-0.469003\pi$
$463$	−331.547	−	191.419i	−0.716085	−	0.413432i	−0.813310	+	0.581831i	$0.802337\pi$
$464$	58.9019	−	285.431i	0.126944	−	0.615152i
$465$		0			0
$466$	119.004	−	647.448i	0.255374	−	1.38937i
$467$		−	253.232i		−	0.542253i	−0.962544	−	0.271127i	$-0.912604\pi$
$467$		−	253.232i		−	0.542253i	0.962544	−	0.271127i	$-0.0873962\pi$
$468$		0			0
$469$	−99.6977			−0.212575
$470$	638.495	+	117.358i	1.35850	+	0.249699i
$471$		0			0
$472$	145.503	−	79.8423i	0.308269	−	0.169157i
$473$	−367.445	+	636.434i	−0.776840	+	1.34553i
$474$		0			0
$475$	−601.961	+	347.542i	−1.26729	+	0.731668i
$476$	429.329	−	69.3055i	0.901951	−	0.145600i
$477$		0			0
$478$	−113.148	+	132.878i	−0.236711	+	0.277987i
$479$	−716.139	+	413.463i	−1.49507	+	0.863179i	−0.999984	−	0.00566464i	$-0.998197\pi$
$479$	−716.139	+	413.463i	−1.49507	+	0.863179i	−0.495086	+	0.868844i	$0.664864\pi$
$480$		0			0
$481$	63.0980	−	109.289i	0.131181	−	0.227212i
$482$	337.664	−	120.137i	0.700547	−	0.249247i
$483$		0			0
$484$	−5.89312	+	4.80118i	−0.0121759	+	0.00991979i
$485$	1025.59			2.11462
$486$		0			0
$487$			320.932i			0.658997i	0.944156	+	0.329499i	$0.106880\pi$
$487$			320.932i			0.658997i	−0.944156	+	0.329499i	$0.893120\pi$
$488$	−390.698	−	8.49075i	−0.800612	−	0.0173991i
$489$		0			0
$490$	−1540.39	+	548.054i	−3.14365	+	1.11848i
$491$	−486.615	−	280.947i	−0.991069	−	0.572194i	−0.0854754	−	0.996340i	$-0.527241\pi$
$491$	−486.615	−	280.947i	−0.991069	−	0.572194i	−0.905594	+	0.424146i	$0.860574\pi$
$492$		0			0
$493$	−79.9228	−	138.430i	−0.162115	−	0.280792i
$494$	−88.3821	+	103.794i	−0.178911	+	0.210108i
$495$		0			0
$496$	−56.1578	−	169.408i	−0.113221	−	0.341549i
$497$	−544.983	−	943.939i	−1.09655	−	1.89927i
$498$		0			0
$499$	−26.2892	−	15.1781i	−0.0526838	−	0.0304170i	0.473427	−	0.880833i	$-0.343017\pi$
$499$	−26.2892	−	15.1781i	−0.0526838	−	0.0304170i	−0.526111	+	0.850416i	$0.676350\pi$
$500$	−327.544	−	124.619i	−0.655088	−	0.249237i
$501$		0			0
$502$	−808.393	−	148.587i	−1.61034	−	0.295989i
$503$		−	12.8329i		−	0.0255126i	−0.999919	−	0.0127563i	$-0.995939\pi$
$503$		−	12.8329i		−	0.0255126i	0.999919	−	0.0127563i	$-0.00406057\pi$
$504$		0			0
$505$	358.598			0.710095
$506$	2.85759	−	15.5468i	0.00564740	−	0.0307250i
$507$		0			0
$508$	−52.8677	+	138.956i	−0.104070	+	0.273535i
$509$	−378.770	+	656.048i	−0.744145	+	1.28890i	0.206449	+	0.978457i	$0.433809\pi$
$509$	−378.770	+	656.048i	−0.744145	+	1.28890i	−0.950593	+	0.310439i	$0.899524\pi$
$510$		0			0
$511$	−666.303	+	384.690i	−1.30392	+	0.752818i
$512$	−510.913	−	33.3518i	−0.997876	−	0.0651403i
$513$		0			0
$514$	−302.686	−	257.742i	−0.588883	−	0.501444i
$515$	1359.73	−	785.041i	2.64025	−	1.52435i
$516$		0			0
$517$	−229.993	+	398.360i	−0.444861	+	0.770523i
$518$	295.277	+	829.922i	0.570033	+	1.60217i
$519$		0			0
$520$	−222.110	−	4.82696i	−0.427135	−	0.00928261i
$521$	−495.775			−0.951584			−0.475792	−	0.879558i	$-0.657838\pi$
$521$	−495.775			−0.951584			−0.475792	+	0.879558i	$0.657838\pi$
$522$		0			0
$523$			359.891i			0.688128i	0.938946	+	0.344064i	$0.111804\pi$
$523$			359.891i			0.688128i	−0.938946	+	0.344064i	$0.888196\pi$
$524$	297.290	+	364.903i	0.567347	+	0.696380i
$525$		0			0
$526$	208.101	+	584.901i	0.395630	+	1.11198i
$527$	−84.7713	−	48.9427i	−0.160856	−	0.0928704i
$528$		0			0
$529$	−264.246	−	457.687i	−0.499520	−	0.865193i
$530$	−890.640	−	758.396i	−1.68045	−	1.43093i
$531$		0			0
$532$	−151.650	−	939.427i	−0.285055	−	1.76584i
$533$	21.6219	+	37.4502i	0.0405663	+	0.0702630i
$534$		0			0
$535$	−610.516	−	352.482i	−1.14115	−	0.658844i
$536$	56.4373	−	30.9690i	0.105294	−	0.0577780i
$537$		0			0
$538$	−72.0880	+	392.199i	−0.133993	+	0.728994i
$539$		−	1158.47i		−	2.14930i
$540$		0			0
$541$	−292.354			−0.540395			−0.270198	−	0.962805i	$-0.587089\pi$
$541$	−292.354			−0.540395			−0.270198	+	0.962805i	$0.587089\pi$
$542$	134.079	+	24.6443i	0.247378	+	0.0454693i
$543$		0			0
$544$	−221.508	+	172.595i	−0.407184	+	0.317270i
$545$	717.552	−	1242.84i	1.31661	−	2.28044i
$546$		0			0
$547$	−508.532	+	293.601i	−0.929675	+	0.536748i	−0.886709	−	0.462329i	$-0.847014\pi$
$547$	−508.532	+	293.601i	−0.929675	+	0.536748i	−0.0429660	+	0.999077i	$0.513681\pi$
$548$	−23.5531	−	145.905i	−0.0429802	−	0.266250i
$549$		0			0
$550$	520.350	−	611.086i	0.946092	−	1.11107i
$551$	−302.903	+	174.881i	−0.549734	+	0.317389i
$552$		0			0
$553$	61.4502	−	106.435i	0.111121	−	0.192468i
$554$	−550.588	+	195.893i	−0.993842	+	0.353598i
$555$		0			0
$556$	40.6613	+	49.9090i	0.0731319	+	0.0897644i
$557$	523.617			0.940067			0.470034	−	0.882649i	$-0.344242\pi$
$557$	523.617			0.940067			0.470034	+	0.882649i	$0.344242\pi$
$558$		0			0
$559$		−	235.317i		−	0.420961i
$560$	1030.80	−	1158.58i	1.84072	−	2.06889i
$561$		0			0
$562$	883.039	−	314.176i	1.57124	−	0.559031i
$563$	−753.245	−	434.886i	−1.33791	−	0.772445i	−0.351416	−	0.936219i	$-0.614300\pi$
$563$	−753.245	−	434.886i	−1.33791	−	0.772445i	−0.986498	+	0.163775i	$0.947633\pi$
$564$		0			0
$565$	345.071	+	597.680i	0.610744	+	1.05784i
$566$	17.6658	−	20.7462i	0.0312116	−	0.0366541i
$567$		0			0
$568$	601.722	+	365.061i	1.05937	+	0.642714i
$569$	−129.012	−	223.455i	−0.226734	−	0.392716i	0.730104	−	0.683336i	$-0.239472\pi$
$569$	−129.012	−	223.455i	−0.226734	−	0.392716i	−0.956838	+	0.290621i	$0.906138\pi$
$570$		0			0
$571$	71.8277	+	41.4698i	0.125793	+	0.0726266i	0.561576	−	0.827425i	$-0.310195\pi$
$571$	71.8277	+	41.4698i	0.125793	+	0.0726266i	−0.435783	+	0.900052i	$0.643529\pi$
$572$	55.9760	−	147.126i	0.0978601	−	0.257213i
$573$		0			0
$574$	−296.881	−	54.5681i	−0.517214	−	0.0950664i
$575$			25.8078i			0.0448832i
$576$		0			0
$577$	−167.694			−0.290631			−0.145316	−	0.989385i	$-0.546420\pi$
$577$	−167.694			−0.290631			−0.145316	+	0.989385i	$0.546420\pi$
$578$	76.6468	−	417.001i	0.132607	−	0.721455i
$579$		0			0
$580$	−532.738	−	202.687i	−0.918515	−	0.349461i
$581$	137.350	−	237.897i	0.236403	−	0.409461i
$582$		0			0
$583$	717.812	−	414.429i	1.23124	−	0.710856i
$584$	257.688	−	424.741i	0.441246	−	0.727296i
$585$		0			0
$586$	51.3866	+	43.7566i	0.0876905	+	0.0746700i
$587$	−449.447	+	259.488i	−0.765667	+	0.442058i	−0.831327	−	0.555784i	$-0.812418\pi$
$587$	−449.447	+	259.488i	−0.765667	+	0.442058i	0.0656596	+	0.997842i	$0.479085\pi$
$588$		0			0
$589$	−107.093	+	185.491i	−0.181822	+	0.314925i
$590$	−108.806	−	305.816i	−0.184417	−	0.518332i
$591$		0			0
$592$	−424.950	−	378.084i	−0.717821	−	0.638656i
$593$	865.433			1.45941			0.729707	−	0.683760i	$-0.239656\pi$
$593$	865.433			1.45941			0.729707	+	0.683760i	$0.239656\pi$
$594$		0			0
$595$		−	850.529i		−	1.42946i
$596$	−25.6875	+	20.9278i	−0.0430998	+	0.0351138i
$597$		0			0
$598$	1.69668	+	4.76877i	0.00283725	+	0.00797454i
$599$	−37.8473	−	21.8511i	−0.0631841	−	0.0364794i	0.468075	−	0.883689i	$-0.344948\pi$
$599$	−37.8473	−	21.8511i	−0.0631841	−	0.0364794i	−0.531259	+	0.847209i	$0.678281\pi$
$600$		0			0
$601$	71.0498	+	123.062i	0.118219	+	0.204762i	0.919062	−	0.394113i	$-0.128948\pi$
$601$	71.0498	+	123.062i	0.118219	+	0.204762i	−0.800843	+	0.598875i	$0.795615\pi$
$602$	1250.61	+	1064.92i	2.07743	+	1.76897i
$603$		0			0
$604$	−826.839	+	133.475i	−1.36894	+	0.220985i
$605$	7.43315	+	12.8746i	0.0122862	+	0.0212803i
$606$		0			0
$607$	98.7760	+	57.0284i	0.162728	+	0.0939512i	0.579153	−	0.815219i	$-0.303384\pi$
$607$	98.7760	+	57.0284i	0.162728	+	0.0939512i	−0.416424	+	0.909170i	$0.636717\pi$
$608$	377.660	+	484.688i	0.621151	+	0.797185i
$609$		0			0
$610$	−138.165	+	751.697i	−0.226501	+	1.23229i
$611$		−	147.291i		−	0.241066i
$612$		0			0
$613$	−515.196			−0.840450			−0.420225	−	0.907420i	$-0.638049\pi$
$613$	−515.196			−0.840450			−0.420225	+	0.907420i	$0.638049\pi$
$614$	−277.874	−	51.0745i	−0.452563	−	0.0831833i
$615$		0			0
$616$	528.595	+	963.300i	0.858108	+	1.56380i
$617$	286.853	−	496.844i	0.464916	−	0.805257i	−0.534282	−	0.845306i	$-0.679418\pi$
$617$	286.853	−	496.844i	0.464916	−	0.805257i	0.999198	+	0.0400487i	$0.0127513\pi$
$618$		0			0
$619$	563.320	−	325.233i	0.910049	−	0.525417i	0.0296022	−	0.999562i	$-0.490576\pi$
$619$	563.320	−	325.233i	0.910049	−	0.525417i	0.880447	+	0.474145i	$0.157243\pi$
$620$	−344.589	+	55.6262i	−0.555789	+	0.0897197i
$621$		0			0
$622$	515.636	−	605.550i	0.828997	−	0.973552i
$623$	1139.81	−	658.069i	1.82955	−	1.05629i
$624$		0			0
$625$	109.796	−	190.172i	0.175673	−	0.304275i
$626$	−901.423	+	320.717i	−1.43997	+	0.512327i
$627$		0			0
$628$	−119.238	+	97.1441i	−0.189869	+	0.154688i
$629$	−311.962			−0.495965
$630$		0			0
$631$		−	915.625i		−	1.45107i	−0.688185	−	0.725535i	$-0.741592\pi$
$631$		−	915.625i		−	1.45107i	0.688185	−	0.725535i	$-0.258408\pi$
$632$	−1.72422	+	79.3394i	−0.00272820	+	0.125537i
$633$		0			0
$634$	421.054	−	149.806i	0.664122	−	0.236288i
$635$	251.812	+	145.384i	0.396555	+	0.228951i
$636$		0			0
$637$	185.476	+	321.254i	0.291171	+	0.504323i
$638$	261.837	−	307.495i	0.410404	−	0.481967i
$639$		0			0
$640$	−223.634	+	976.052i	−0.349428	+	1.52508i
$641$	502.925	+	871.091i	0.784594	+	1.35896i	0.929241	+	0.369474i	$0.120462\pi$
$641$	502.925	+	871.091i	0.784594	+	1.35896i	−0.144647	+	0.989483i	$0.546205\pi$
$642$		0			0
$643$	559.043	+	322.764i	0.869429	+	0.501965i	0.867158	−	0.498032i	$-0.165944\pi$
$643$	559.043	+	322.764i	0.869429	+	0.501965i	0.00227048	+	0.999997i	$0.499277\pi$
$644$	−33.0223	−	12.5638i	−0.0512768	−	0.0195089i
$645$		0			0
$646$	331.449	+	60.9218i	0.513078	+	0.0943063i
$647$		−	469.962i		−	0.726372i	−0.931717	−	0.363186i	$-0.881689\pi$
$647$		−	469.962i		−	0.726372i	0.931717	−	0.363186i	$-0.118311\pi$
$648$		0			0
$649$	229.993			0.354381
$650$	−46.4601	+	252.769i	−0.0714772	+	0.388875i
$651$		0			0
$652$	378.856	−	995.775i	0.581067	−	1.52726i
$653$	−363.699	+	629.945i	−0.556966	+	0.964694i	0.440781	+	0.897615i	$0.354701\pi$
$653$	−363.699	+	629.945i	−0.556966	+	0.964694i	−0.997748	+	0.0670795i	$0.978632\pi$
$654$		0			0
$655$	797.197	−	460.262i	1.21709	−	0.702690i
$656$	185.010	−	61.3297i	0.282028	−	0.0934904i
$657$		0			0
$658$	782.791	+	666.560i	1.18965	+	1.01301i
$659$	−230.141	+	132.872i	−0.349228	+	0.201627i	−0.664345	−	0.747426i	$-0.731289\pi$
$659$	−230.141	+	132.872i	−0.349228	+	0.201627i	0.315117	+	0.949053i	$0.397956\pi$
$660$		0			0
$661$	−321.125	+	556.206i	−0.485818	+	0.841461i	−0.999867	−	0.0162998i	$-0.994811\pi$
$661$	−321.125	+	556.206i	−0.485818	+	0.841461i	0.514050	+	0.857760i	$0.328145\pi$
$662$	−218.040	−	612.834i	−0.329365	−	0.925731i
$663$		0			0
$664$	−3.85388	+	177.335i	−0.00580404	+	0.267070i
$665$	−1861.07			−2.79860
$666$		0			0
$667$			12.9864i			0.0194698i
$668$	750.024	+	920.603i	1.12279	+	1.37815i
$669$		0			0
$670$	−42.2034	−	118.619i	−0.0629901	−	0.177043i
$671$	−468.988	−	270.770i	−0.698938	−	0.403532i
$672$		0			0
$673$	−243.053	−	420.980i	−0.361149	−	0.625528i	0.627001	−	0.779018i	$-0.284282\pi$
$673$	−243.053	−	420.980i	−0.361149	−	0.625528i	−0.988150	+	0.153490i	$0.950949\pi$
$674$	−392.406	−	334.141i	−0.582205	−	0.495758i
$675$		0			0
$676$	−99.6977	−	617.599i	−0.147482	−	0.913609i
$677$	537.134	+	930.344i	0.793404	+	1.37422i	0.923848	+	0.382760i	$0.125026\pi$
$677$	537.134	+	930.344i	0.793404	+	1.37422i	−0.130444	+	0.991456i	$0.541640\pi$
$678$		0			0
$679$	1406.64	+	812.126i	2.07164	+	1.19606i
$680$	264.199	+	481.472i	0.388529	+	0.708047i
$681$		0			0
$682$	44.7098	−	243.246i	0.0655569	−	0.356666i
$683$			545.105i			0.798104i	0.916928	+	0.399052i	$0.130661\pi$
$683$			545.105i			0.798104i	−0.916928	+	0.399052i	$0.869339\pi$
$684$		0			0
$685$	−289.048			−0.421968
$686$	−1352.53	−	248.602i	−1.97162	−	0.362393i
$687$		0			0
$688$	−1038.75	−	214.357i	−1.50981	−	0.311566i
$689$	−132.703	+	229.849i	−0.192603	+	0.333598i
$690$		0			0
$691$	−1079.86	+	623.455i	−1.56274	+	0.902250i	−0.565765	+	0.824567i	$0.691419\pi$
$691$	−1079.86	+	623.455i	−1.56274	+	0.902250i	−0.996978	+	0.0776832i	$0.975248\pi$
$692$	−108.073	−	669.480i	−0.156174	−	0.967457i
$693$		0			0
$694$	−565.323	+	663.900i	−0.814587	+	0.956629i
$695$	109.035	−	62.9516i	0.156885	−	0.0905778i
$696$		0			0
$697$	53.4502	−	92.5784i	0.0766860	−	0.132824i
$698$	681.155	−	242.348i	0.975867	−	0.347203i
$699$		0			0
$700$	−1133.11	−	1390.81i	−1.61872	−	1.98687i
$701$	−474.890			−0.677446			−0.338723	−	0.940886i	$-0.609995\pi$
$701$	−474.890			−0.677446			−0.338723	+	0.940886i	$0.609995\pi$
$702$		0			0
$703$			682.613i			0.971000i
$704$	−598.459	−	381.113i	−0.850084	−	0.541353i
$705$		0			0
$706$	947.987	−	337.284i	1.34276	−	0.477739i
$707$	491.832	+	283.959i	0.695661	+	0.401640i
$708$		0			0
$709$	441.318	+	764.385i	0.622452	+	1.07812i	0.989028	+	0.147730i	$0.0471966\pi$
$709$	441.318	+	764.385i	0.622452	+	1.07812i	−0.366576	+	0.930388i	$0.619470\pi$
$710$	892.387	−	1048.00i	1.25688	−	1.47605i
$711$		0			0
$712$	−440.813	+	726.581i	−0.619119	+	1.02048i
$713$	3.97626	+	6.88709i	0.00557680	+	0.00965931i
$714$		0			0
$715$	−266.617	−	153.932i	−0.372892	−	0.215289i
$716$	21.3965	−	56.2381i	0.0298834	−	0.0785448i
$717$		0			0
$718$	−434.733	−	79.9061i	−0.605478	−	0.111290i
$719$			193.132i			0.268612i	0.990940	+	0.134306i	$0.0428806\pi$
$719$			193.132i			0.268612i	−0.990940	+	0.134306i	$0.957119\pi$
$720$		0			0
$721$	2486.57			3.44878
$722$	2.78432	−	15.1482i	0.00385639	−	0.0209809i
$723$		0			0
$724$	−370.850	−	141.095i	−0.512224	−	0.194882i
$725$	−329.691	+	571.042i	−0.454746	+	0.787644i
$726$		0			0
$727$	−314.330	+	181.479i	−0.432366	+	0.249627i	−0.700354	−	0.713795i	$-0.746975\pi$
$727$	−314.330	+	181.479i	−0.432366	+	0.249627i	0.267988	+	0.963422i	$0.413641\pi$
$728$	−300.811	−	182.501i	−0.413203	−	0.250688i
$729$		0			0
$730$	−739.755	−	629.914i	−1.01336	−	0.862896i
$731$	−503.780	+	290.857i	−0.689165	+	0.397890i
$732$		0			0
$733$	−227.096	+	393.342i	−0.309818	+	0.536620i	−0.978322	−	0.207088i	$-0.933601\pi$
$733$	−227.096	+	393.342i	−0.309818	+	0.536620i	0.668505	+	0.743708i	$0.266935\pi$
$734$	225.890	+	634.900i	0.307753	+	0.864986i
$735$		0			0
$736$	22.5961	−	3.14553i	0.0307012	−	0.00427382i
$737$	89.2092			0.121044
$738$		0			0
$739$			999.841i			1.35296i	0.736459	+	0.676482i	$0.236496\pi$
$739$			999.841i			1.35296i	−0.736459	+	0.676482i	$0.763504\pi$
$740$	−862.436	+	702.634i	−1.16545	+	0.949506i
$741$		0			0
$742$	−621.006	−	1745.43i	−0.836936	−	2.35234i
$743$	1147.83	+	662.703i	1.54487	+	0.891928i	0.998521	+	0.0543677i	$0.0173143\pi$
$743$	1147.83	+	662.703i	1.54487	+	0.891928i	0.546344	+	0.837561i	$0.316019\pi$
$744$		0			0
$745$	32.4003	+	56.1190i	0.0434904	+	0.0753275i
$746$	696.179	+	592.809i	0.933216	+	0.794650i
$747$		0			0
$748$	−384.162	+	62.0144i	−0.513586	+	0.0829070i
$749$	−558.233	−	966.887i	−0.745304	−	1.29090i
$750$		0			0
$751$	−313.368	−	180.923i	−0.417267	−	0.240909i	0.276640	−	0.960974i	$-0.410779\pi$
$751$	−313.368	−	180.923i	−0.417267	−	0.240909i	−0.693907	+	0.720064i	$0.744112\pi$
$752$	−650.179	−	134.172i	−0.864600	−	0.178420i
$753$		0			0
$754$	−23.3785	+	127.192i	−0.0310060	+	0.168690i
$755$			1638.02i			2.16957i
$756$		0			0
$757$	99.1960			0.131038			0.0655192	−	0.997851i	$-0.479130\pi$
$757$	99.1960			0.131038			0.0655192	+	0.997851i	$0.479130\pi$
$758$	−146.224	−	26.8766i	−0.192907	−	0.0354573i
$759$		0			0
$760$	1053.52	−	578.103i	1.38621	−	0.760661i
$761$	697.772	−	1208.58i	0.916915	−	1.58814i	0.112841	−	0.993613i	$-0.464005\pi$
$761$	697.772	−	1208.58i	0.916915	−	1.58814i	0.804074	−	0.594529i	$-0.202662\pi$
$762$		0			0
$763$	1968.31	−	1136.40i	2.57969	−	1.48939i
$764$	−1073.46	+	173.286i	−1.40505	+	0.226815i
$765$		0			0
$766$	−739.159	+	868.048i	−0.964959	+	1.13322i
$767$	−63.7790	+	36.8228i	−0.0831538	+	0.0480089i
$768$		0			0
$769$	−240.950	+	417.338i	−0.313329	+	0.542702i	−0.979081	−	0.203471i	$-0.934778\pi$
$769$	−240.950	+	417.338i	−0.313329	+	0.542702i	0.665752	+	0.746173i	$0.268111\pi$
$770$	2024.65	−	720.348i	2.62941	−	0.935517i
$771$		0			0
$772$	452.452	−	368.616i	0.586077	−	0.477482i
$773$	1026.09			1.32741			0.663707	−	0.747993i	$-0.268982\pi$
$773$	1026.09			1.32741			0.663707	+	0.747993i	$0.268982\pi$
$774$		0			0
$775$			403.789i			0.521018i
$776$	−1048.55	−	22.7873i	−1.35122	−	0.0293651i
$777$		0			0
$778$	−1197.88	+	426.193i	−1.53969	+	0.547806i
$779$	−202.574	−	116.956i	−0.260043	−	0.150136i
$780$		0			0
$781$	487.650	+	844.634i	0.624391	+	1.08148i
$782$	8.11211	−	9.52664i	0.0103735	−	0.0121824i
$783$		0			0
$784$	1587.05	−	526.096i	2.02429	−	0.671041i
$785$	150.398	+	260.497i	0.191590	+	0.331843i
$786$		0			0
$787$	589.681	+	340.452i	0.749277	+	0.432595i	0.825432	−	0.564501i	$-0.190931\pi$
$787$	589.681	+	340.452i	0.749277	+	0.432595i	−0.0761559	+	0.997096i	$0.524265\pi$
$788$	699.868	+	266.274i	0.888157	+	0.337911i
$789$		0			0
$790$	152.647	+	28.0573i	0.193225	+	0.0355156i
$791$			1092.99i			1.38178i
$792$		0			0
$793$	173.405			0.218670
$794$	174.575	−	949.787i	0.219868	−	1.19621i
$795$		0			0
$796$	−481.078	+	1264.45i	−0.604370	+	1.58851i
$797$	98.0177	−	169.772i	0.122983	−	0.213013i	−0.797960	−	0.602711i	$-0.794087\pi$
$797$	98.0177	−	169.772i	0.122983	−	0.213013i	0.920943	+	0.389698i	$0.127421\pi$
$798$		0			0
$799$	−315.329	+	182.055i	−0.394654	+	0.227854i
$800$	1073.46	+	435.341i	1.34183	+	0.544176i
$801$		0			0
$802$	−239.387	−	203.842i	−0.298487	−	0.254167i
$803$	596.206	−	344.220i	0.742473	−	0.428667i
$804$		0			0
$805$	−34.5498	+	59.8421i	−0.0429190	+	0.0743380i
$806$	26.5462	+	74.6122i	0.0329358	+	0.0925710i
$807$		0			0
$808$	−366.625	−	7.96758i	−0.453744	−	0.00986087i
$809$	−579.944			−0.716865			−0.358432	−	0.933556i	$-0.616689\pi$
$809$	−579.944			−0.716865			−0.358432	+	0.933556i	$0.616689\pi$
$810$		0			0
$811$		−	527.766i		−	0.650759i	−0.945583	−	0.325380i	$-0.894508\pi$
$811$		−	527.766i		−	0.650759i	0.945583	−	0.325380i	$-0.105492\pi$
$812$	−570.173	−	699.849i	−0.702184	−	0.861883i
$813$		0			0
$814$	−264.213	−	742.612i	−0.324586	−	0.912300i
$815$	−1804.52	−	1041.84i	−2.21413	−	1.27833i
$816$		0			0
$817$	636.434	+	1102.34i	0.778989	+	1.34925i
$818$	−458.804	−	390.680i	−0.560885	−	0.477604i
$819$		0			0
$820$	−60.7492	−	376.324i	−0.0740844	−	0.458932i
$821$	324.749	+	562.483i	0.395554	+	0.685119i	0.993172	−	0.116662i	$-0.0372194\pi$
$821$	324.749	+	562.483i	0.395554	+	0.685119i	−0.597618	+	0.801781i	$0.703886\pi$
$822$		0			0
$823$	−232.736	−	134.370i	−0.282790	−	0.163269i	0.351896	−	0.936039i	$-0.385537\pi$
$823$	−232.736	−	134.370i	−0.282790	−	0.163269i	−0.634686	+	0.772770i	$0.718870\pi$
$824$	−1407.61	+	772.402i	−1.70826	+	0.937381i
$825$		0			0
$826$	92.9314	−	505.598i	0.112508	−	0.612105i
$827$			799.300i			0.966505i	0.875481	+	0.483253i	$0.160545\pi$
$827$			799.300i			0.966505i	−0.875481	+	0.483253i	$0.839455\pi$
$828$		0			0
$829$	−1149.38			−1.38647			−0.693234	−	0.720712i	$-0.743815\pi$
$829$	−1149.38			−1.38647			−0.693234	+	0.720712i	$0.743815\pi$
$830$	341.189	+	62.7122i	0.411071	+	0.0755568i
$831$		0			0
$832$	226.975	+	9.87001i	0.272806	+	0.0118630i
$833$	458.504	−	794.153i	0.550425	−	0.953365i
$834$		0			0
$835$	2011.22	−	1161.18i	2.40865	−	1.39064i
$836$	135.696	+	840.596i	0.162315	+	1.00550i
$837$		0			0
$838$	−627.952	+	737.450i	−0.749346	+	0.880012i
$839$	153.674	−	88.7239i	0.183164	−	0.105750i	−0.405615	−	0.914044i	$-0.632942\pi$
$839$	153.674	−	88.7239i	0.183164	−	0.105750i	0.588778	+	0.808295i	$0.299609\pi$
$840$		0			0
$841$	254.601	−	440.982i	0.302736	−	0.524355i
$842$	−9.70628	+	3.45339i	−0.0115276	+	0.00410141i
$843$		0			0
$844$	−298.928	−	366.913i	−0.354180	−	0.434731i
$845$	−1223.51			−1.44794
$846$		0			0
$847$			23.5440i			0.0277970i
$848$	893.725	+	795.160i	1.05392	+	0.937689i
$849$		0			0
$850$	598.567	−	212.964i	0.704196	−	0.250545i
$851$	21.9492	+	12.6724i	0.0257923	+	0.0148912i
$852$		0			0
$853$	−550.498	−	953.491i	−0.645367	−	1.11781i	−0.984217	−	0.176968i	$-0.943371\pi$
$853$	−550.498	−	953.491i	−0.645367	−	1.11781i	0.338849	−	0.940841i	$-0.389962\pi$
$854$	−784.738	+	921.576i	−0.918897	+	1.07913i
$855$		0			0
$856$	616.350	+	373.937i	0.720036	+	0.436842i
$857$	−413.229	−	715.734i	−0.482181	−	0.835163i	0.517609	−	0.855617i	$-0.326822\pi$
$857$	−413.229	−	715.734i	−0.482181	−	0.835163i	−0.999791	+	0.0204545i	$0.993489\pi$
$858$		0			0
$859$	−1032.11	−	595.887i	−1.20152	−	0.693699i	−0.240628	−	0.970617i	$-0.577353\pi$
$859$	−1032.11	−	595.887i	−1.20152	−	0.693699i	−0.960893	+	0.276919i	$0.910687\pi$
$860$	−737.626	+	1938.76i	−0.857705	+	2.25437i
$861$		0			0
$862$	−624.614	−	114.807i	−0.724610	−	0.133187i
$863$		−	1491.45i		−	1.72821i	−0.503311	−	0.864106i	$-0.667885\pi$
$863$		−	1491.45i		−	1.72821i	0.503311	−	0.864106i	$-0.332115\pi$
$864$		0			0
$865$	−1326.29			−1.53328
$866$	−68.7683	+	374.138i	−0.0794092	+	0.432030i
$867$		0			0
$868$	−516.666	−	196.573i	−0.595238	−	0.226466i
$869$	−54.9854	+	95.2376i	−0.0632744	+	0.109594i
$870$		0			0
$871$	−24.7384	+	14.2827i	−0.0284023	+	0.0163981i
$872$	−761.228	+	1254.71i	−0.872968	+	1.43889i
$873$		0			0
$874$	−20.8455	−	17.7503i	−0.0238507	−	0.0203093i
$875$	−940.044	+	542.735i	−1.07434	+	0.620268i
$876$		0			0
$877$	−405.270	+	701.948i	−0.462109	+	0.800397i	−0.999066	−	0.0432130i	$-0.986241\pi$
$877$	−405.270	+	701.948i	−0.462109	+	0.800397i	0.536956	+	0.843610i	$0.319574\pi$
$878$	−78.0930	−	219.492i	−0.0889442	−	0.249991i
$879$		0			0
$880$	−922.361	+	1036.69i	−1.04814	+	1.17806i
$881$	−251.884			−0.285907			−0.142953	−	0.989729i	$-0.545660\pi$
$881$	−251.884			−0.285907			−0.142953	+	0.989729i	$0.545660\pi$
$882$		0			0
$883$		−	1150.98i		−	1.30349i	−0.758437	−	0.651746i	$-0.774037\pi$
$883$		−	1150.98i		−	1.30349i	0.758437	−	0.651746i	$-0.225963\pi$
$884$	96.6024	−	78.7029i	0.109279	−	0.0890304i
$885$		0			0
$886$	328.928	+	924.504i	0.371251	+	1.04346i
$887$	146.265	+	84.4462i	0.164899	+	0.0952043i	0.580178	−	0.814490i	$-0.302983\pi$
$887$	146.265	+	84.4462i	0.164899	+	0.0952043i	−0.415279	+	0.909694i	$0.636316\pi$
$888$		0			0
$889$	230.248	+	398.800i	0.258996	+	0.448594i
$890$	1265.46	+	1077.56i	1.42186	+	1.21074i
$891$		0			0
$892$	968.574	−	156.355i	1.08585	−	0.175286i
$893$	398.360	+	689.980i	0.446092	+	0.772654i
$894$		0			0
$895$	−101.913	−	58.8396i	−0.113869	−	0.0657426i
$896$	−1079.62	+	1161.61i	−1.20493	+	1.29644i
$897$		0			0
$898$	56.3793	−	306.734i	0.0627831	−	0.341575i
$899$			203.184i			0.226012i
$900$		0			0
$901$	656.096			0.728187
$902$	265.648	+	48.8274i	0.294510	+	0.0541324i
$903$		0			0
$904$	−339.515	−	618.725i	−0.375570	−	0.684431i
$905$	−388.005	+	672.045i	−0.428735	+	0.742591i
$906$		0			0
$907$	−408.758	+	235.996i	−0.450670	+	0.260194i	−0.708113	−	0.706099i	$-0.750453\pi$
$907$	−408.758	+	235.996i	−0.450670	+	0.260194i	0.257443	+	0.966293i	$0.417120\pi$
$908$	125.702	−	20.2917i	0.138438	−	0.0223477i
$909$		0			0
$910$	−446.120	+	523.912i	−0.490242	+	0.575727i
$911$	164.788	−	95.1403i	0.180887	−	0.104435i	−0.406822	−	0.913507i	$-0.633363\pi$
$911$	164.788	−	95.1403i	0.180887	−	0.104435i	0.587709	+	0.809072i	$0.300030\pi$
$912$		0			0
$913$	−122.900	+	212.870i	−0.134612	+	0.233154i
$914$	230.822	−	82.1241i	0.252541	−	0.0898514i
$915$		0			0
$916$	444.524	−	362.158i	0.485288	−	0.395369i
$917$	1457.85			1.58981
$918$		0			0
$919$		−	1046.89i		−	1.13916i	−0.821936	−	0.569580i	$-0.807106\pi$
$919$		−	1046.89i		−	1.13916i	0.821936	−	0.569580i	$-0.192894\pi$
$920$	0.969429	−	44.6079i	0.00105373	−	0.0484868i
$921$		0			0
$922$	−884.568	+	314.720i	−0.959401	+	0.341344i
$923$	−270.458	−	156.149i	−0.293021	−	0.169176i
$924$		0			0
$925$	643.440	+	1114.47i	0.695611	+	1.20483i
$926$	496.402	−	582.962i	0.536072	−	0.629548i
$927$		0			0
$928$	540.160	+	219.061i	0.582069	+	0.236057i
$929$	345.832	+	598.998i	0.372262	+	0.644778i	0.989913	−	0.141675i	$-0.0452488\pi$
$929$	345.832	+	598.998i	0.372262	+	0.644778i	−0.617651	+	0.786453i	$0.711915\pi$
$930$		0			0
$931$	−1737.71	−	1003.27i	−1.86650	−	1.07762i
$932$	1230.54	+	468.174i	1.32032	+	0.502332i
$933$		0			0
$934$	498.120	+	91.5568i	0.533319	+	0.0980266i
$935$			761.051i			0.813959i
$936$		0			0
$937$	−1413.88			−1.50894			−0.754472	−	0.656332i	$-0.772107\pi$
$937$	−1413.88			−1.50894			−0.754472	+	0.656332i	$0.772107\pi$
$938$	36.0460	−	196.110i	0.0384286	−	0.209073i
$939$		0			0
$940$	−461.699	+	1213.52i	−0.491169	+	1.29098i
$941$	561.243	−	972.102i	0.596433	−	1.03305i	−0.396910	−	0.917858i	$-0.629917\pi$
$941$	561.243	−	972.102i	0.596433	−	1.03305i	0.993343	−	0.115195i	$-0.0367492\pi$
$942$		0			0
$943$	−7.52136	+	4.34246i	−0.00797599	+	0.00460494i
$944$	104.447	+	315.079i	0.110643	+	0.333770i
$945$		0			0
$946$	−1119.04	−	952.887i	−1.18292	−	1.00728i
$947$	−1428.85	+	824.947i	−1.50882	+	0.871116i	−0.508871	+	0.860843i	$0.669937\pi$
$947$	−1428.85	+	824.947i	−1.50882	+	0.871116i	−0.999947	+	0.0102736i	$0.996730\pi$
$948$		0			0
$949$	−110.222	+	190.910i	−0.116145	+	0.201169i
$950$	−465.992	−	1309.74i	−0.490518	−	1.37868i
$951$		0			0
$952$	−18.8976	+	869.568i	−0.0198505	+	0.913411i
$953$	828.887			0.869766			0.434883	−	0.900487i	$-0.356790\pi$
$953$	828.887			0.869766			0.434883	+	0.900487i	$0.356790\pi$
$954$		0			0
$955$			2126.60i			2.22681i
$956$	−220.468	−	270.610i	−0.230615	−	0.283064i
$957$		0			0
$958$	−554.379	−	1558.17i	−0.578684	−	1.62648i
$959$	−396.442	−	228.886i	−0.413391	−	0.238671i
$960$		0			0
$961$	−418.287	−	724.495i	−0.435263	−	0.753897i
$962$	192.163	+	163.631i	0.199754	+	0.170094i
$963$		0			0
$964$	114.232	+	707.637i	0.118498	+	0.734063i
$965$	−570.689	−	988.463i	−0.591388	−	1.02431i
$966$		0			0
$967$	1216.72	+	702.473i	1.25824	+	0.726446i	0.972732	−	0.231930i	$-0.0745040\pi$
$967$	1216.72	+	702.473i	1.25824	+	0.726446i	0.285509	+	0.958376i	$0.407837\pi$
$968$	−7.31347	−	13.3279i	−0.00755524	−	0.0137685i
$969$		0			0
$970$	−370.806	+	2017.39i	−0.382274	+	2.07978i
$971$		−	331.476i		−	0.341376i	−0.985325	−	0.170688i	$-0.945401\pi$
$971$		−	331.476i		−	0.341376i	0.985325	−	0.170688i	$-0.0545991\pi$
$972$		0			0
$973$	199.395			0.204928
$974$	−631.288	−	116.034i	−0.648140	−	0.119131i
$975$		0			0
$976$	157.960	−	765.453i	0.161844	−	0.784276i
$977$	−558.546	+	967.430i	−0.571695	+	0.990205i	0.424697	+	0.905336i	$0.360381\pi$
$977$	−558.546	+	967.430i	−0.571695	+	0.990205i	−0.996392	+	0.0848694i	$0.972953\pi$
$978$		0			0
$979$	−1019.90	+	588.838i	−1.04177	+	0.601469i
$980$	−521.116	−	3228.17i	−0.531751	−	3.29405i
$981$		0			0
$982$	728.574	−	855.618i	0.741929	−	0.871301i
$983$	1205.44	−	695.961i	1.22629	−	0.707997i	0.260035	−	0.965599i	$-0.416266\pi$
$983$	1205.44	−	695.961i	1.22629	−	0.707997i	0.966251	+	0.257602i	$0.0829324\pi$
$984$		0			0
$985$	732.243	−	1268.28i	0.743393	−	1.28760i
$986$	301.195	−	107.162i	0.305472	−	0.108684i
$987$		0			0
$988$	−172.212	−	211.379i	−0.174304	−	0.213946i
$989$	47.2603			0.0477860
$990$		0			0
$991$		−	226.715i		−	0.228773i	−0.993436	−	0.114387i	$-0.963510\pi$
$991$		−	226.715i		−	0.228773i	0.993436	−	0.114387i	$-0.0364903\pi$
$992$	353.538	−	49.2150i	0.356389	−	0.0496119i
$993$		0			0
$994$	2053.81	−	730.725i	2.06621	−	0.735135i
$995$	2291.41	+	1322.95i	2.30292	+	1.32959i
$996$		0			0
$997$	−639.868	−	1108.28i	−0.641793	−	1.11162i	−0.985032	−	0.172371i	$-0.944857\pi$
$997$	−639.868	−	1108.28i	−0.641793	−	1.11162i	0.343239	−	0.939248i	$-0.388476\pi$
$998$	39.3610	−	46.2245i	0.0394399	−	0.0463171i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.s.271.4		16
3.2	odd	2	inner	324.3.f.s.271.5		16
4.3	odd	2	inner	324.3.f.s.271.7		16
9.2	odd	6	inner	324.3.f.s.55.2		16
9.4	even	3		324.3.d.h.163.1	✓	8
9.5	odd	6		324.3.d.h.163.8	yes	8
9.7	even	3	inner	324.3.f.s.55.7		16
12.11	even	2	inner	324.3.f.s.271.2		16
36.7	odd	6	inner	324.3.f.s.55.4		16
36.11	even	6	inner	324.3.f.s.55.5		16
36.23	even	6		324.3.d.h.163.7	yes	8
36.31	odd	6		324.3.d.h.163.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.h.163.1	✓	8	9.4	even	3
324.3.d.h.163.2	yes	8	36.31	odd	6
324.3.d.h.163.7	yes	8	36.23	even	6
324.3.d.h.163.8	yes	8	9.5	odd	6
324.3.f.s.55.2		16	9.2	odd	6	inner
324.3.f.s.55.4		16	36.7	odd	6	inner
324.3.f.s.55.5		16	36.11	even	6	inner
324.3.f.s.55.7		16	9.7	even	3	inner
324.3.f.s.271.2		16	12.11	even	2	inner
324.3.f.s.271.4		16	1.1	even	1	trivial
324.3.f.s.271.5		16	3.2	odd	2	inner
324.3.f.s.271.7		16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.361553 + 1.96705i) q^{2} +(-3.73856 - 1.42238i) q^{4} +(-3.91150 + 6.77492i) q^{5} +(-10.7296 + 6.19472i) q^{7} +(4.14959 - 6.83966i) q^{8} +(-11.9124 - 10.1436i) q^{10} +(9.60079 - 5.54302i) q^{11} +(-1.77492 + 3.07425i) q^{13} +(-8.30601 - 23.3453i) q^{14} +(11.9536 + 10.6353i) q^{16} +8.77534 q^{17} -19.2016i q^{19} +(24.2599 - 19.7648i) q^{20} +(7.43220 + 20.8893i) q^{22} +(-0.617421 - 0.356468i) q^{23} +(-18.0997 - 31.3495i) q^{25} +(-5.40547 - 4.60285i) q^{26} +(48.9244 - 7.89776i) q^{28} +(-9.10765 - 15.7749i) q^{29} +(-9.66017 - 5.57730i) q^{31} +(-25.2421 + 19.6682i) q^{32} +(-3.17275 + 17.2615i) q^{34} -96.9226i q^{35} -35.5498 q^{37} +(37.7705 + 6.94239i) q^{38} +(30.1070 + 54.8664i) q^{40} +(6.09095 - 10.5498i) q^{41} +(-57.4086 + 33.1448i) q^{43} +(-43.7774 + 7.06689i) q^{44} +(0.924421 - 1.08561i) q^{46} +(-35.9335 + 20.7462i) q^{47} +(52.2492 - 90.4982i) q^{49} +(68.2101 - 24.2684i) q^{50} +(11.0084 - 8.96864i) q^{52} +74.7659 q^{53} +86.7261i q^{55} +(-2.15349 + 99.0922i) q^{56} +(34.3229 - 12.2117i) q^{58} +(17.9667 + 10.3731i) q^{59} +(-24.4244 - 42.3043i) q^{61} +(14.4635 - 16.9855i) q^{62} +(-29.5619 - 56.7635i) q^{64} +(-13.8852 - 24.0498i) q^{65} +(6.96889 + 4.02349i) q^{67} +(-32.8071 - 12.4819i) q^{68} +(190.652 + 35.0427i) q^{70} +87.9754i q^{71} +62.0997 q^{73} +(12.8531 - 69.9282i) q^{74} +(-27.3120 + 71.7863i) q^{76} +(-68.6750 + 118.949i) q^{77} +(-8.59076 + 4.95988i) q^{79} +(-118.810 + 39.3848i) q^{80} +(18.5498 + 15.7955i) q^{82} +(-19.2016 + 11.0860i) q^{83} +(-34.3248 + 59.4522i) q^{85} +(-44.4413 - 124.909i) q^{86} +(1.92694 - 88.6674i) q^{88} -106.231 q^{89} -43.9805i q^{91} +(1.80123 + 2.21089i) q^{92} +(-27.8169 - 78.1838i) q^{94} +(130.089 + 75.1070i) q^{95} +(-65.5498 - 113.536i) q^{97} +(159.124 + 135.497i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{4} - 100 q^{10} + 32 q^{13} + 46 q^{16} + 36 q^{22} - 48 q^{25} + 360 q^{28} + 122 q^{34} - 448 q^{37} - 154 q^{40} - 408 q^{46} + 232 q^{49} - 154 q^{52} + 86 q^{58} + 32 q^{61} - 20 q^{64}+ \cdots - 928 q^{97}+O(q^{100}) \) 16 * q + 10 * q^4 - 100 * q^10 + 32 * q^13 + 46 * q^16 + 36 * q^22 - 48 * q^25 + 360 * q^28 + 122 * q^34 - 448 * q^37 - 154 * q^40 - 408 * q^46 + 232 * q^49 - 154 * q^52 + 86 * q^58 + 32 * q^61 - 20 * q^64 + 492 * q^70 + 752 * q^73 - 516 * q^76 + 176 * q^82 - 368 * q^85 - 516 * q^88 + 672 * q^94 - 928 * q^97

Introduction

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