LMFDB - Embedded newform 504.2.c.e.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(253,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("504.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.72339481600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{4} - 4x^{2} + 16 $ x^8 - x^6 - 2x^4 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			253.2
Root			$-1.38758 + 0.273147i$ of defining polynomial
Character	$\chi$	$=$	504.253
Dual form			504.2.c.e.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38758 + 0.273147i) q^{2} +(1.85078 - 0.758030i) q^{4} -3.66103i q^{5} -1.00000 q^{7} +(-2.36106 + 1.55737i) q^{8} +O(q^{10})$	\(q+(-1.38758 + 0.273147i) q^{2} +(1.85078 - 0.758030i) q^{4} -3.66103i q^{5} -1.00000 q^{7} +(-2.36106 + 1.55737i) q^{8} +(1.00000 + 5.07999i) q^{10} -2.56844i q^{11} -3.03212i q^{13} +(1.38758 - 0.273147i) q^{14} +(2.85078 - 2.80590i) q^{16} -7.49729 q^{17} +7.12785i q^{19} +(-2.77517 - 6.77576i) q^{20} +(0.701562 + 3.56393i) q^{22} +3.60338 q^{23} -8.40312 q^{25} +(0.828216 + 4.20732i) q^{26} +(-1.85078 + 0.758030i) q^{28} +6.22947i q^{29} -5.40312 q^{31} +(-3.18928 + 4.67210i) q^{32} +(10.4031 - 2.04787i) q^{34} +3.66103i q^{35} -7.12785i q^{37} +(-1.94695 - 9.89049i) q^{38} +(5.70156 + 8.64391i) q^{40} -3.60338 q^{41} -10.1600i q^{43} +(-1.94695 - 4.75362i) q^{44} +(-5.00000 + 0.984255i) q^{46} +1.00000 q^{49} +(11.6600 - 2.29529i) q^{50} +(-2.29844 - 5.61179i) q^{52} -8.41464i q^{53} -9.40312 q^{55} +(2.36106 - 1.55737i) q^{56} +(-1.70156 - 8.64391i) q^{58} +2.18518i q^{59} -3.03212i q^{61} +(7.49729 - 1.47585i) q^{62} +(3.14922 - 7.35408i) q^{64} -11.1007 q^{65} -10.1600i q^{67} +(-13.8758 + 5.68317i) q^{68} +(-1.00000 - 5.07999i) q^{70} +7.49729 q^{71} -6.00000 q^{73} +(1.94695 + 9.89049i) q^{74} +(5.40312 + 13.1921i) q^{76} +2.56844i q^{77} +(-10.2725 - 10.4368i) q^{80} +(5.00000 - 0.984255i) q^{82} +7.32206i q^{83} +27.4478i q^{85} +(2.77517 + 14.0978i) q^{86} +(4.00000 + 6.06424i) q^{88} +3.60338 q^{89} +3.03212i q^{91} +(6.66908 - 2.73147i) q^{92} +26.0953 q^{95} -8.80625 q^{97} +(-1.38758 + 0.273147i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 8 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 8 * q^7	$ 8 q + 2 q^{4} - 8 q^{7} + 8 q^{10} + 10 q^{16} - 20 q^{22} - 16 q^{25} - 2 q^{28} + 8 q^{31} + 32 q^{34} + 20 q^{40} - 40 q^{46} + 8 q^{49} - 44 q^{52} - 24 q^{55} + 12 q^{58} + 38 q^{64} - 8 q^{70} - 48 q^{73} - 8 q^{76} + 40 q^{82} + 32 q^{88} + 32 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 8 * q^7 + 8 * q^10 + 10 * q^16 - 20 * q^22 - 16 * q^25 - 2 * q^28 + 8 * q^31 + 32 * q^34 + 20 * q^40 - 40 * q^46 + 8 * q^49 - 44 * q^52 - 24 * q^55 + 12 * q^58 + 38 * q^64 - 8 * q^70 - 48 * q^73 - 8 * q^76 + 40 * q^82 + 32 * q^88 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.38758	+	0.273147i	−0.981170	+	0.193144i
$2$	−1.38758	+	0.273147i	−0.981170	+	0.193144i
$3$		0			0
$3$		0			0
$4$	1.85078	−	0.758030i	0.925391	−	0.379015i
$5$		−	3.66103i		−	1.63726i	−0.574320	−	0.818631i	$-0.694734\pi$
$5$		−	3.66103i		−	1.63726i	0.574320	−	0.818631i	$-0.305266\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.36106	+	1.55737i	−0.834761	+	0.550612i
$9$		0			0
$10$	1.00000	+	5.07999i	0.316228	+	1.60643i
$11$		−	2.56844i		−	0.774413i	−0.921993	−	0.387207i	$-0.873440\pi$
$11$		−	2.56844i		−	0.774413i	0.921993	−	0.387207i	$-0.126560\pi$
$12$		0			0
$13$		−	3.03212i		−	0.840959i	−0.907302	−	0.420479i	$-0.861862\pi$
$13$		−	3.03212i		−	0.840959i	0.907302	−	0.420479i	$-0.138138\pi$
$14$	1.38758	−	0.273147i	0.370848	−	0.0730017i
$15$		0			0
$16$	2.85078	−	2.80590i	0.712695	−	0.701474i
$17$	−7.49729			−1.81836			−0.909180	−	0.416403i	$-0.863290\pi$
$17$	−7.49729			−1.81836			−0.909180	+	0.416403i	$0.863290\pi$
$18$		0			0
$19$			7.12785i			1.63524i	0.575758	+	0.817620i	$0.304707\pi$
$19$			7.12785i			1.63524i	−0.575758	+	0.817620i	$0.695293\pi$
$20$	−2.77517	−	6.77576i	−0.620547	−	1.51511i
$21$		0			0
$22$	0.701562	+	3.56393i	0.149574	+	0.759831i
$23$	3.60338			0.751358			0.375679	−	0.926750i	$-0.377410\pi$
$23$	3.60338			0.751358			0.375679	+	0.926750i	$0.377410\pi$
$24$		0			0
$25$	−8.40312			−1.68062
$26$	0.828216	+	4.20732i	0.162426	+	0.825124i
$27$		0			0
$28$	−1.85078	+	0.758030i	−0.349765	+	0.143254i
$29$			6.22947i			1.15678i	0.815759	+	0.578391i	$0.196319\pi$
$29$			6.22947i			1.15678i	−0.815759	+	0.578391i	$0.803681\pi$
$30$		0			0
$31$	−5.40312			−0.970430			−0.485215	−	0.874395i	$-0.661259\pi$
$31$	−5.40312			−0.970430			−0.485215	+	0.874395i	$0.661259\pi$
$32$	−3.18928	+	4.67210i	−0.563790	+	0.825918i
$33$		0			0
$34$	10.4031	−	2.04787i	1.78412	−	0.351206i
$35$			3.66103i			0.618827i
$36$		0			0
$37$		−	7.12785i		−	1.17181i	−0.810379	−	0.585906i	$-0.800739\pi$
$37$		−	7.12785i		−	1.17181i	0.810379	−	0.585906i	$-0.199261\pi$
$38$	−1.94695	−	9.89049i	−0.315838	−	1.60445i
$39$		0			0
$40$	5.70156	+	8.64391i	0.901496	+	1.36672i
$41$	−3.60338			−0.562754			−0.281377	−	0.959597i	$-0.590791\pi$
$41$	−3.60338			−0.562754			−0.281377	+	0.959597i	$0.590791\pi$
$42$		0			0
$43$		−	10.1600i		−	1.54938i	−0.632341	−	0.774690i	$-0.717906\pi$
$43$		−	10.1600i		−	1.54938i	0.632341	−	0.774690i	$-0.282094\pi$
$44$	−1.94695	−	4.75362i	−0.293514	−	0.716635i
$45$		0			0
$46$	−5.00000	+	0.984255i	−0.737210	+	0.145120i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	11.6600	−	2.29529i	1.64898	−	0.324603i
$51$		0			0
$52$	−2.29844	−	5.61179i	−0.318736	−	0.778215i
$53$		−	8.41464i		−	1.15584i	−0.816093	−	0.577920i	$-0.803864\pi$
$53$		−	8.41464i		−	1.15584i	0.816093	−	0.577920i	$-0.196136\pi$
$54$		0			0
$55$	−9.40312			−1.26792
$56$	2.36106	−	1.55737i	0.315510	−	0.208112i
$57$		0			0
$58$	−1.70156	−	8.64391i	−0.223426	−	1.13500i
$59$			2.18518i			0.284486i	0.989832	+	0.142243i	$0.0454314\pi$
$59$			2.18518i			0.284486i	−0.989832	+	0.142243i	$0.954569\pi$
$60$		0			0
$61$		−	3.03212i		−	0.388223i	−0.980979	−	0.194112i	$-0.937818\pi$
$61$		−	3.03212i		−	0.388223i	0.980979	−	0.194112i	$-0.0621824\pi$
$62$	7.49729	−	1.47585i	0.952157	−	0.187433i
$63$		0			0
$64$	3.14922	−	7.35408i	0.393652	−	0.919259i
$65$	−11.1007			−1.37687
$66$		0			0
$67$		−	10.1600i		−	1.24124i	−0.784112	−	0.620619i	$-0.786881\pi$
$67$		−	10.1600i		−	1.24124i	0.784112	−	0.620619i	$-0.213119\pi$
$68$	−13.8758	+	5.68317i	−1.68269	+	0.689186i
$69$		0			0
$70$	−1.00000	−	5.07999i	−0.119523	−	0.607174i
$71$	7.49729			0.889765			0.444882	−	0.895589i	$-0.353245\pi$
$71$	7.49729			0.889765			0.444882	+	0.895589i	$0.353245\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	1.94695	+	9.89049i	0.226329	+	1.14975i
$75$		0			0
$76$	5.40312	+	13.1921i	0.619781	+	1.51324i
$77$			2.56844i			0.292701i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−10.2725	−	10.4368i	−1.14850	−	1.16687i
$81$		0			0
$82$	5.00000	−	0.984255i	0.552158	−	0.108693i
$83$			7.32206i			0.803700i	0.915706	+	0.401850i	$0.131633\pi$
$83$			7.32206i			0.803700i	−0.915706	+	0.401850i	$0.868367\pi$
$84$		0			0
$85$			27.4478i			2.97713i
$86$	2.77517	+	14.0978i	0.299254	+	1.52021i
$87$		0			0
$88$	4.00000	+	6.06424i	0.426401	+	0.646450i
$89$	3.60338			0.381958			0.190979	−	0.981594i	$-0.438834\pi$
$89$	3.60338			0.381958			0.190979	+	0.981594i	$0.438834\pi$
$90$		0			0
$91$			3.03212i			0.317853i
$92$	6.66908	−	2.73147i	0.695299	−	0.284776i
$93$		0			0
$94$		0			0
$95$	26.0953			2.67732
$96$		0			0
$97$	−8.80625			−0.894139			−0.447070	−	0.894499i	$-0.647532\pi$
$97$	−8.80625			−0.894139			−0.447070	+	0.894499i	$0.647532\pi$
$98$	−1.38758	+	0.273147i	−0.140167	+	0.0275920i
$99$		0			0
$100$	−15.5523	+	6.36982i	−1.55523	+	0.636982i
$101$		−	5.84621i		−	0.581719i	−0.956766	−	0.290860i	$-0.906059\pi$
$101$		−	5.84621i		−	0.581719i	0.956766	−	0.290860i	$-0.0939413\pi$
$102$		0			0
$103$	9.40312			0.926517			0.463259	−	0.886223i	$-0.346680\pi$
$103$	9.40312			0.926517			0.463259	+	0.886223i	$0.346680\pi$
$104$	4.72212	+	7.15902i	0.463042	+	0.702000i
$105$		0			0
$106$	2.29844	+	11.6760i	0.223244	+	1.13408i
$107$		−	7.70532i		−	0.744901i	−0.928052	−	0.372450i	$-0.878518\pi$
$107$		−	7.70532i		−	0.744901i	0.928052	−	0.372450i	$-0.121482\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	13.0476	−	2.56844i	1.24404	−	0.244891i
$111$		0			0
$112$	−2.85078	+	2.80590i	−0.269373	+	0.265132i
$113$	3.89391			0.366308			0.183154	−	0.983084i	$-0.441369\pi$
$113$	3.89391			0.366308			0.183154	+	0.983084i	$0.441369\pi$
$114$		0			0
$115$		−	13.1921i		−	1.23017i
$116$	4.72212	+	11.5294i	0.438438	+	1.07048i
$117$		0			0
$118$	−0.596876	−	3.03212i	−0.0549469	−	0.279129i
$119$	7.49729			0.687276
$120$		0			0
$121$	4.40312			0.400284
$122$	0.828216	+	4.20732i	0.0749831	+	0.380913i
$123$		0			0
$124$	−10.0000	+	4.09573i	−0.898027	+	0.367807i
$125$			12.4589i			1.11436i
$126$		0			0
$127$	18.8062			1.66878			0.834392	−	0.551171i	$-0.185819\pi$
$127$	18.8062			1.66878			0.834392	+	0.551171i	$0.185819\pi$
$128$	−2.36106	+	11.0646i	−0.208690	+	0.977982i
$129$		0			0
$130$	15.4031	−	3.03212i	1.35094	−	0.265935i
$131$		−	7.32206i		−	0.639731i	−0.947463	−	0.319865i	$-0.896362\pi$
$131$		−	7.32206i		−	0.639731i	0.947463	−	0.319865i	$-0.103638\pi$
$132$		0			0
$133$		−	7.12785i		−	0.618063i
$134$	2.77517	+	14.0978i	0.239738	+	1.21787i
$135$		0			0
$136$	17.7016	−	11.6760i	1.51790	−	1.00121i
$137$	−7.20677			−0.615716			−0.307858	−	0.951432i	$-0.599612\pi$
$137$	−7.20677			−0.615716			−0.307858	+	0.951432i	$0.599612\pi$
$138$		0			0
$139$			8.19146i			0.694791i	0.937719	+	0.347395i	$0.112934\pi$
$139$			8.19146i			0.694791i	−0.937719	+	0.347395i	$0.887066\pi$
$140$	2.77517	+	6.77576i	0.234545	+	0.572656i
$141$		0			0
$142$	−10.4031	+	2.04787i	−0.873011	+	0.171853i
$143$	−7.78781			−0.651250
$144$		0			0
$145$	22.8062			1.89396
$146$	8.32551	−	1.63888i	0.689024	−	0.135635i
$147$		0			0
$148$	−5.40312	−	13.1921i	−0.444134	−	1.08438i
$149$		−	10.5998i		−	0.868371i	−0.900823	−	0.434186i	$-0.857036\pi$
$149$		−	10.5998i		−	0.868371i	0.900823	−	0.434186i	$-0.142964\pi$
$150$		0			0
$151$	−18.8062			−1.53043			−0.765215	−	0.643774i	$-0.777368\pi$
$151$	−18.8062			−1.53043			−0.765215	+	0.643774i	$0.777368\pi$
$152$	−11.1007	−	16.8293i	−0.900384	−	1.36504i
$153$		0			0
$154$	−0.701562	−	3.56393i	−0.0565335	−	0.287189i
$155$			19.7810i			1.58885i
$156$		0			0
$157$			3.03212i			0.241990i	0.992653	+	0.120995i	$0.0386084\pi$
$157$			3.03212i			0.241990i	−0.992653	+	0.120995i	$0.961392\pi$
$158$		0			0
$159$		0			0
$160$	17.1047	+	11.6760i	1.35224	+	0.923071i
$161$	−3.60338			−0.283986
$162$		0			0
$163$			22.2885i			1.74577i	0.487929	+	0.872883i	$0.337752\pi$
$163$			22.2885i			1.74577i	−0.487929	+	0.872883i	$0.662248\pi$
$164$	−6.66908	+	2.73147i	−0.520767	+	0.213292i
$165$		0			0
$166$	−2.00000	−	10.1600i	−0.155230	−	0.788567i
$167$	14.9946			1.16032			0.580158	−	0.814504i	$-0.302991\pi$
$167$	14.9946			1.16032			0.580158	+	0.814504i	$0.302991\pi$
$168$		0			0
$169$	3.80625			0.292788
$170$	−7.49729	−	38.0861i	−0.575016	−	2.92107i
$171$		0			0
$172$	−7.70156	−	18.8039i	−0.587239	−	1.43378i
$173$			8.03139i			0.610615i	0.952254	+	0.305307i	$0.0987592\pi$
$173$			8.03139i			0.610615i	−0.952254	+	0.305307i	$0.901241\pi$
$174$		0			0
$175$	8.40312			0.635216
$176$	−7.20677	−	7.32206i	−0.543231	−	0.551921i
$177$		0			0
$178$	−5.00000	+	0.984255i	−0.374766	+	0.0737730i
$179$			12.0757i			0.902578i	0.892378	+	0.451289i	$0.149036\pi$
$179$			12.0757i			0.902578i	−0.892378	+	0.451289i	$0.850964\pi$
$180$		0			0
$181$		−	23.3521i		−	1.73574i	−0.496787	−	0.867872i	$-0.665487\pi$
$181$		−	23.3521i		−	1.73574i	0.496787	−	0.867872i	$-0.334513\pi$
$182$	−0.828216	−	4.20732i	−0.0613914	−	0.311867i
$183$		0			0
$184$	−8.50781	+	5.61179i	−0.627204	+	0.413707i
$185$	−26.0953			−1.91856
$186$		0			0
$187$			19.2563i			1.40816i
$188$		0			0
$189$		0			0
$190$	−36.2094	+	7.12785i	−2.62690	+	0.517109i
$191$	7.49729			0.542485			0.271242	−	0.962511i	$-0.412565\pi$
$191$	7.49729			0.542485			0.271242	+	0.962511i	$0.412565\pi$
$192$		0			0
$193$	11.4031			0.820815			0.410407	−	0.911902i	$-0.365386\pi$
$193$	11.4031			0.820815			0.410407	+	0.911902i	$0.365386\pi$
$194$	12.2194	−	2.40540i	0.877303	−	0.172698i
$195$		0			0
$196$	1.85078	−	0.758030i	0.132199	−	0.0541450i
$197$		−	11.3663i		−	0.809818i	−0.914357	−	0.404909i	$-0.867303\pi$
$197$		−	11.3663i		−	0.809818i	0.914357	−	0.404909i	$-0.132697\pi$
$198$		0			0
$199$	14.8062			1.04959			0.524794	−	0.851230i	$-0.324143\pi$
$199$	14.8062			1.04959			0.524794	+	0.851230i	$0.324143\pi$
$200$	19.8403	−	13.0867i	1.40292	−	0.925373i
$201$		0			0
$202$	1.59688	+	8.11211i	0.112356	+	0.570766i
$203$		−	6.22947i		−	0.437223i
$204$		0			0
$205$			13.1921i			0.921376i
$206$	−13.0476	+	2.56844i	−0.909071	+	0.178952i
$207$		0			0
$208$	−8.50781	−	8.64391i	−0.589911	−	0.599347i
$209$	18.3074			1.26635
$210$		0			0
$211$		−	4.09573i		−	0.281962i	−0.990012	−	0.140981i	$-0.954974\pi$
$211$		−	4.09573i		−	0.281962i	0.990012	−	0.140981i	$-0.0450256\pi$
$212$	−6.37855	−	15.5737i	−0.438081	−	1.06960i
$213$		0			0
$214$	2.10469	+	10.6918i	0.143873	+	0.730875i
$215$	−37.1959			−2.53674
$216$		0			0
$217$	5.40312			0.366788
$218$		0			0
$219$		0			0
$220$	−17.4031	+	7.12785i	−1.17332	+	0.480560i
$221$			22.7327i			1.52917i
$222$		0			0
$223$	−14.8062			−0.991500			−0.495750	−	0.868465i	$-0.665107\pi$
$223$	−14.8062			−0.991500			−0.495750	+	0.868465i	$0.665107\pi$
$224$	3.18928	−	4.67210i	0.213093	−	0.312168i
$225$		0			0
$226$	−5.40312	+	1.06361i	−0.359410	+	0.0707503i
$227$		−	19.7810i		−	1.31291i	−0.754365	−	0.656455i	$-0.772055\pi$
$227$		−	19.7810i		−	1.31291i	0.754365	−	0.656455i	$-0.227945\pi$
$228$		0			0
$229$		−	11.2236i		−	0.741675i	−0.928698	−	0.370838i	$-0.879071\pi$
$229$		−	11.2236i		−	0.741675i	0.928698	−	0.370838i	$-0.120929\pi$
$230$	3.60338	+	18.3051i	0.237600	+	1.20701i
$231$		0			0
$232$	−9.70156	−	14.7082i	−0.636939	−	0.965637i
$233$	−18.8885			−1.23743			−0.618713	−	0.785617i	$-0.712346\pi$
$233$	−18.8885			−1.23743			−0.618713	+	0.785617i	$0.712346\pi$
$234$		0			0
$235$		0			0
$236$	1.65643	+	4.04429i	0.107824	+	0.263261i
$237$		0			0
$238$	−10.4031	+	2.04787i	−0.674334	+	0.132743i
$239$	−14.7041			−0.951127			−0.475563	−	0.879682i	$-0.657756\pi$
$239$	−14.7041			−0.951127			−0.475563	+	0.879682i	$0.657756\pi$
$240$		0			0
$241$	−0.806248			−0.0519350			−0.0259675	−	0.999663i	$-0.508267\pi$
$241$	−0.806248			−0.0519350			−0.0259675	+	0.999663i	$0.508267\pi$
$242$	−6.10971	+	1.20270i	−0.392747	+	0.0773126i
$243$		0			0
$244$	−2.29844	−	5.61179i	−0.147142	−	0.359258i
$245$		−	3.66103i		−	0.233894i
$246$		0			0
$247$	21.6125			1.37517
$248$	12.7571	−	8.41464i	0.810077	−	0.534330i
$249$		0			0
$250$	−3.40312	−	17.2878i	−0.215232	−	1.09338i
$251$		−	9.50723i		−	0.600091i	−0.953925	−	0.300046i	$-0.902998\pi$
$251$		−	9.50723i		−	0.600091i	0.953925	−	0.300046i	$-0.0970019\pi$
$252$		0			0
$253$		−	9.25507i		−	0.581861i
$254$	−26.0953	+	5.13688i	−1.63736	+	0.322316i
$255$		0			0
$256$	0.253905	−	15.9980i	0.0158691	−	0.999874i
$257$	18.5980			1.16011			0.580055	−	0.814578i	$-0.303031\pi$
$257$	18.5980			1.16011			0.580055	+	0.814578i	$0.303031\pi$
$258$		0			0
$259$			7.12785i			0.442903i
$260$	−20.5449	+	8.41464i	−1.27414	+	0.521854i
$261$		0			0
$262$	2.00000	+	10.1600i	0.123560	+	0.627685i
$263$	−11.3912			−0.702411			−0.351206	−	0.936298i	$-0.614228\pi$
$263$	−11.3912			−0.702411			−0.351206	+	0.936298i	$0.614228\pi$
$264$		0			0
$265$	−30.8062			−1.89241
$266$	1.94695	+	9.89049i	0.119375	+	0.606425i
$267$		0			0
$268$	−7.70156	−	18.8039i	−0.470448	−	1.14863i
$269$		−	19.0717i		−	1.16282i	−0.813611	−	0.581410i	$-0.802501\pi$
$269$		−	19.0717i		−	1.16282i	0.813611	−	0.581410i	$-0.197499\pi$
$270$		0			0
$271$	−6.59688			−0.400732			−0.200366	−	0.979721i	$-0.564213\pi$
$271$	−6.59688			−0.400732			−0.200366	+	0.979721i	$0.564213\pi$
$272$	−21.3731	+	21.0366i	−1.29594	+	1.27553i
$273$		0			0
$274$	10.0000	−	1.96851i	0.604122	−	0.118922i
$275$			21.5829i			1.30150i
$276$		0			0
$277$			1.06361i			0.0639061i	0.999489	+	0.0319531i	$0.0101727\pi$
$277$			1.06361i			0.0639061i	−0.999489	+	0.0319531i	$0.989827\pi$
$278$	−2.23748	−	11.3663i	−0.134195	−	0.681708i
$279$		0			0
$280$	−5.70156	−	8.64391i	−0.340734	−	0.516572i
$281$	33.3020			1.98663			0.993316	−	0.115425i	$-0.0368231\pi$
$281$	33.3020			1.98663			0.993316	+	0.115425i	$0.0368231\pi$
$282$		0			0
$283$		−	1.06361i		−	0.0632251i	−0.999500	−	0.0316125i	$-0.989936\pi$
$283$		−	1.06361i		−	0.0632251i	0.999500	−	0.0316125i	$-0.0100643\pi$
$284$	13.8758	−	5.68317i	0.823380	−	0.337234i
$285$		0			0
$286$	10.8062	−	2.12722i	0.638987	−	0.125785i
$287$	3.60338			0.212701
$288$		0			0
$289$	39.2094			2.30643
$290$	−31.6456	+	6.22947i	−1.85829	+	0.365807i
$291$		0			0
$292$	−11.1047	+	4.54818i	−0.649853	+	0.266162i
$293$		−	21.2568i		−	1.24184i	−0.783875	−	0.620919i	$-0.786760\pi$
$293$		−	21.2568i		−	1.24184i	0.783875	−	0.620919i	$-0.213240\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$	11.1007	+	16.8293i	0.645214	+	0.978183i
$297$		0			0
$298$	2.89531	+	14.7082i	0.167721	+	0.852020i
$299$		−	10.9259i		−	0.631861i
$300$		0			0
$301$			10.1600i			0.585611i
$302$	26.0953	−	5.13688i	1.50161	−	0.295594i
$303$		0			0
$304$	20.0000	+	20.3199i	1.14708	+	1.16543i
$305$	−11.1007			−0.635623
$306$		0			0
$307$		−	7.12785i		−	0.406808i	−0.979095	−	0.203404i	$-0.934800\pi$
$307$		−	7.12785i		−	0.406808i	0.979095	−	0.203404i	$-0.0652005\pi$
$308$	1.94695	+	4.75362i	0.110938	+	0.270862i
$309$		0			0
$310$	−5.40312	−	27.4478i	−0.306877	−	1.55893i
$311$	22.2014			1.25892			0.629462	−	0.777032i	$-0.283276\pi$
$311$	22.2014			1.25892			0.629462	+	0.777032i	$0.283276\pi$
$312$		0			0
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	−0.828216	−	4.20732i	−0.0467389	−	0.237433i
$315$		0			0
$316$		0			0
$317$		−	6.22947i		−	0.349882i	−0.984579	−	0.174941i	$-0.944027\pi$
$317$		−	6.22947i		−	0.349882i	0.984579	−	0.174941i	$-0.0559734\pi$
$318$		0			0
$319$	16.0000			0.895828
$320$	−26.9235	−	11.5294i	−1.50507	−	0.644512i
$321$		0			0
$322$	5.00000	−	0.984255i	0.278639	−	0.0548504i
$323$		−	53.4396i		−	2.97346i
$324$		0			0
$325$			25.4793i			1.41334i
$326$	−6.08803	−	30.9271i	−0.337185	−	1.71289i
$327$		0			0
$328$	8.50781	−	5.61179i	0.469765	−	0.309859i
$329$		0			0
$330$		0			0
$331$		−	22.2885i		−	1.22508i	−0.790438	−	0.612542i	$-0.790147\pi$
$331$		−	22.2885i		−	1.22508i	0.790438	−	0.612542i	$-0.209853\pi$
$332$	5.55034	+	13.5515i	0.304614	+	0.743736i
$333$		0			0
$334$	−20.8062	+	4.09573i	−1.13847	+	0.224108i
$335$	−37.1959			−2.03223
$336$		0			0
$337$	28.8062			1.56918			0.784588	−	0.620017i	$-0.212874\pi$
$337$	28.8062			1.56918			0.784588	+	0.620017i	$0.212874\pi$
$338$	−5.28149	+	1.03967i	−0.287275	+	0.0565504i
$339$		0			0
$340$	20.8062	+	50.7999i	1.12838	+	2.75501i
$341$			13.8776i			0.751514i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	15.8228	+	23.9883i	0.853108	+	1.29336i
$345$		0			0
$346$	−2.19375	−	11.1442i	−0.117937	−	0.599117i
$347$			26.7198i			1.43439i	0.696871	+	0.717197i	$0.254575\pi$
$347$			26.7198i			1.43439i	−0.696871	+	0.717197i	$0.745425\pi$
$348$		0			0
$349$			5.15934i			0.276173i	0.990420	+	0.138087i	$0.0440952\pi$
$349$			5.15934i			0.276173i	−0.990420	+	0.138087i	$0.955905\pi$
$350$	−11.6600	+	2.29529i	−0.623256	+	0.122688i
$351$		0			0
$352$	12.0000	+	8.19146i	0.639602	+	0.436606i
$353$	3.60338			0.191789			0.0958944	−	0.995392i	$-0.469429\pi$
$353$	3.60338			0.191789			0.0958944	+	0.995392i	$0.469429\pi$
$354$		0			0
$355$		−	27.4478i		−	1.45678i
$356$	6.66908	−	2.73147i	0.353460	−	0.144768i
$357$		0			0
$358$	−3.29844	−	16.7560i	−0.174328	−	0.885583i
$359$	−7.49729			−0.395692			−0.197846	−	0.980233i	$-0.563395\pi$
$359$	−7.49729			−0.395692			−0.197846	+	0.980233i	$0.563395\pi$
$360$		0			0
$361$	−31.8062			−1.67401
$362$	6.37855	+	32.4030i	0.335249	+	1.70306i
$363$		0			0
$364$	2.29844	+	5.61179i	0.120471	+	0.294138i
$365$			21.9662i			1.14976i
$366$		0			0
$367$	−22.8062			−1.19048			−0.595238	−	0.803549i	$-0.702942\pi$
$367$	−22.8062			−1.19048			−0.595238	+	0.803549i	$0.702942\pi$
$368$	10.2725	−	10.1107i	0.535489	−	0.527058i
$369$		0			0
$370$	36.2094	−	7.12785i	1.88244	−	0.370559i
$371$			8.41464i			0.436867i
$372$		0			0
$373$			6.06424i			0.313994i	0.987599	+	0.156997i	$0.0501814\pi$
$373$			6.06424i			0.313994i	−0.987599	+	0.156997i	$0.949819\pi$
$374$	−5.25982	−	26.7198i	−0.271979	−	1.38165i
$375$		0			0
$376$		0			0
$377$	18.8885			0.972807
$378$		0			0
$379$			16.2242i			0.833382i	0.909048	+	0.416691i	$0.136810\pi$
$379$			16.2242i			0.833382i	−0.909048	+	0.416691i	$0.863190\pi$
$380$	48.2966	−	19.7810i	2.47756	−	1.01474i
$381$		0			0
$382$	−10.4031	+	2.04787i	−0.532270	+	0.104778i
$383$	−29.4081			−1.50268			−0.751342	−	0.659913i	$-0.770593\pi$
$383$	−29.4081			−1.50268			−0.751342	+	0.659913i	$0.770593\pi$
$384$		0			0
$385$	9.40312			0.479228
$386$	−15.8228	+	3.11473i	−0.805359	+	0.158536i
$387$		0			0
$388$	−16.2984	+	6.67540i	−0.827428	+	0.338892i
$389$			10.5998i			0.537432i	0.963219	+	0.268716i	$0.0865994\pi$
$389$			10.5998i			0.537432i	−0.963219	+	0.268716i	$0.913401\pi$
$390$		0			0
$391$	−27.0156			−1.36624
$392$	−2.36106	+	1.55737i	−0.119252	+	0.0786589i
$393$		0			0
$394$	3.10469	+	15.7718i	0.156412	+	0.794570i
$395$		0			0
$396$		0			0
$397$			29.4163i			1.47636i	0.674603	+	0.738181i	$0.264315\pi$
$397$			29.4163i			1.47636i	−0.674603	+	0.738181i	$0.735685\pi$
$398$	−20.5449	+	4.04429i	−1.02982	+	0.202722i
$399$		0			0
$400$	−23.9555	+	23.5783i	−1.19777	+	1.17891i
$401$	−7.20677			−0.359889			−0.179944	−	0.983677i	$-0.557592\pi$
$401$	−7.20677			−0.359889			−0.179944	+	0.983677i	$0.557592\pi$
$402$		0			0
$403$			16.3829i			0.816091i
$404$	−4.43160	−	10.8200i	−0.220480	−	0.538318i
$405$		0			0
$406$	1.70156	+	8.64391i	0.0844471	+	0.428990i
$407$	−18.3074			−0.907466
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$	−3.60338	−	18.3051i	−0.177958	−	0.904026i
$411$		0			0
$412$	17.4031	−	7.12785i	0.857390	−	0.351164i
$413$		−	2.18518i		−	0.107526i
$414$		0			0
$415$	26.8062			1.31587
$416$	14.1664	+	9.67027i	0.694563	+	0.474124i
$417$		0			0
$418$	−25.4031	+	5.00063i	−1.24251	+	0.244589i
$419$		−	2.18518i		−	0.106753i	−0.998574	−	0.0533765i	$-0.983002\pi$
$419$		−	2.18518i		−	0.106753i	0.998574	−	0.0533765i	$-0.0169983\pi$
$420$		0			0
$421$		−	13.1921i		−	0.642943i	−0.946919	−	0.321472i	$-0.895823\pi$
$421$		−	13.1921i		−	0.642943i	0.946919	−	0.321472i	$-0.104177\pi$
$422$	1.11874	+	5.68317i	0.0544593	+	0.276652i
$423$		0			0
$424$	13.1047	+	19.8675i	0.636420	+	0.964851i
$425$	63.0007			3.05598
$426$		0			0
$427$			3.03212i			0.146735i
$428$	−5.84086	−	14.2609i	−0.282329	−	0.689324i
$429$		0			0
$430$	51.6125	−	10.1600i	2.48898	−	0.489957i
$431$	26.3858			1.27096			0.635479	−	0.772118i	$-0.280803\pi$
$431$	26.3858			1.27096			0.635479	+	0.772118i	$0.280803\pi$
$432$		0			0
$433$	3.19375			0.153482			0.0767410	−	0.997051i	$-0.475549\pi$
$433$	3.19375			0.153482			0.0767410	+	0.997051i	$0.475549\pi$
$434$	−7.49729	+	1.47585i	−0.359881	+	0.0708430i
$435$		0			0
$436$		0			0
$437$			25.6844i			1.22865i
$438$		0			0
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$	22.2014	−	14.6441i	1.05841	−	0.698131i
$441$		0			0
$442$	−6.20937	−	31.5435i	−0.295350	−	1.50037i
$443$		−	6.93880i		−	0.329672i	−0.986321	−	0.164836i	$-0.947290\pi$
$443$		−	6.93880i		−	0.329672i	0.986321	−	0.164836i	$-0.0527095\pi$
$444$		0			0
$445$		−	13.1921i		−	0.625365i
$446$	20.5449	−	4.04429i	0.972830	−	0.191503i
$447$		0			0
$448$	−3.14922	+	7.35408i	−0.148787	+	0.347447i
$449$	18.3074			0.863982			0.431991	−	0.901878i	$-0.357811\pi$
$449$	18.3074			0.863982			0.431991	+	0.901878i	$0.357811\pi$
$450$		0			0
$451$			9.25507i			0.435804i
$452$	7.20677	−	2.95170i	0.338978	−	0.138836i
$453$		0			0
$454$	5.40312	+	27.4478i	0.253581	+	1.28819i
$455$	11.1007			0.520408
$456$		0			0
$457$	−22.0000			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$458$	3.06569	+	15.5737i	0.143250	+	0.727710i
$459$		0			0
$460$	−10.0000	−	24.4157i	−0.466252	−	1.13839i
$461$		−	11.7496i		−	0.547234i	−0.961839	−	0.273617i	$-0.911780\pi$
$461$		−	11.7496i		−	0.547234i	0.961839	−	0.273617i	$-0.0882200\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	17.4792	+	17.7588i	0.811453	+	0.824434i
$465$		0			0
$466$	26.2094	−	5.15934i	1.21413	−	0.239002i
$467$			40.3285i			1.86618i	0.359643	+	0.933090i	$0.382899\pi$
$467$			40.3285i			1.86618i	−0.359643	+	0.933090i	$0.617101\pi$
$468$		0			0
$469$			10.1600i			0.469144i
$470$		0			0
$471$		0			0
$472$	−3.40312	−	5.15934i	−0.156641	−	0.237478i
$473$	−26.0953			−1.19986
$474$		0			0
$475$		−	59.8962i		−	2.74823i
$476$	13.8758	−	5.68317i	0.635998	−	0.260488i
$477$		0			0
$478$	20.4031	−	4.01637i	0.933217	−	0.183705i
$479$	−14.4135			−0.658571			−0.329286	−	0.944230i	$-0.606808\pi$
$479$	−14.4135			−0.658571			−0.329286	+	0.944230i	$0.606808\pi$
$480$		0			0
$481$	−21.6125			−0.985445
$482$	1.11874	−	0.220225i	0.0509571	−	0.0100310i
$483$		0			0
$484$	8.14922	−	3.33770i	0.370419	−	0.151714i
$485$			32.2399i			1.46394i
$486$		0			0
$487$	−8.00000			−0.362515			−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000			−0.362515			−0.181257	+	0.983436i	$0.558017\pi$
$488$	4.72212	+	7.15902i	0.213760	+	0.324074i
$489$		0			0
$490$	1.00000	+	5.07999i	0.0451754	+	0.229490i
$491$			42.1304i			1.90132i	0.310236	+	0.950659i	$0.399592\pi$
$491$			42.1304i			1.90132i	−0.310236	+	0.950659i	$0.600408\pi$
$492$		0			0
$493$		−	46.7041i		−	2.10345i
$494$	−29.9892	+	5.90340i	−1.34928	+	0.265606i
$495$		0			0
$496$	−15.4031	+	15.1606i	−0.691621	+	0.680731i
$497$	−7.49729			−0.336299
$498$		0			0
$499$			8.03275i			0.359595i	0.983704	+	0.179798i	$0.0575443\pi$
$499$			8.03275i			0.359595i	−0.983704	+	0.179798i	$0.942456\pi$
$500$	9.44424	+	23.0588i	0.422359	+	1.03122i
$501$		0			0
$502$	2.59688	+	13.1921i	0.115904	+	0.588792i
$503$	−7.20677			−0.321334			−0.160667	−	0.987009i	$-0.551365\pi$
$503$	−7.20677			−0.321334			−0.160667	+	0.987009i	$0.551365\pi$
$504$		0			0
$505$	−21.4031			−0.952427
$506$	2.52800	+	12.8422i	0.112383	+	0.570905i
$507$		0			0
$508$	34.8062	−	14.2557i	1.54428	−	0.632494i
$509$		−	9.56442i		−	0.423936i	−0.977277	−	0.211968i	$-0.932013\pi$
$509$		−	9.56442i		−	0.423936i	0.977277	−	0.211968i	$-0.0679872\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$	4.01749	+	22.2679i	0.177550	+	0.984112i
$513$		0			0
$514$	−25.8062	+	5.07999i	−1.13826	+	0.224069i
$515$		−	34.4251i		−	1.51695i
$516$		0			0
$517$		0			0
$518$	−1.94695	−	9.89049i	−0.0855442	−	0.434563i
$519$		0			0
$520$	26.2094	−	17.2878i	1.14936	−	0.758121i
$521$	37.4865			1.64231			0.821156	−	0.570704i	$-0.193330\pi$
$521$	37.4865			1.64231			0.821156	+	0.570704i	$0.193330\pi$
$522$		0			0
$523$		−	28.5114i		−	1.24672i	−0.781936	−	0.623358i	$-0.785768\pi$
$523$		−	28.5114i		−	1.24672i	0.781936	−	0.623358i	$-0.214232\pi$
$524$	−5.55034	−	13.5515i	−0.242468	−	0.592001i
$525$		0			0
$526$	15.8062	−	3.11148i	0.689185	−	0.135667i
$527$	40.5088			1.76459
$528$		0			0
$529$	−10.0156			−0.435462
$530$	42.7463	−	8.41464i	1.85678	−	0.365509i
$531$		0			0
$532$	−5.40312	−	13.1921i	−0.234255	−	0.571950i
$533$			10.9259i			0.473253i
$534$		0			0
$535$	−28.2094			−1.21960
$536$	15.8228	+	23.9883i	0.683441	+	1.03614i
$537$		0			0
$538$	5.20937	+	26.4635i	0.224592	+	1.14092i
$539$		−	2.56844i		−	0.110630i
$540$		0			0
$541$			1.06361i			0.0457282i	0.999739	+	0.0228641i	$0.00727850\pi$
$541$			1.06361i			0.0457282i	−0.999739	+	0.0228641i	$0.992722\pi$
$542$	9.15372	−	1.80192i	0.393186	−	0.0773991i
$543$		0			0
$544$	23.9109	−	35.0281i	1.02517	−	1.50182i
$545$		0			0
$546$		0			0
$547$			36.5442i			1.56252i	0.624209	+	0.781258i	$0.285421\pi$
$547$			36.5442i			1.56252i	−0.624209	+	0.781258i	$0.714579\pi$
$548$	−13.3382	+	5.46295i	−0.569778	+	0.233366i
$549$		0			0
$550$	−5.89531	−	29.9481i	−0.251377	−	1.27699i
$551$	−44.4027			−1.89162
$552$		0			0
$553$		0			0
$554$	−0.290522	−	1.47585i	−0.0123431	−	0.0627028i
$555$		0			0
$556$	6.20937	+	15.1606i	0.263336	+	0.642953i
$557$		−	42.0732i		−	1.78270i	−0.453316	−	0.891350i	$-0.649759\pi$
$557$		−	42.0732i		−	1.78270i	0.453316	−	0.891350i	$-0.350241\pi$
$558$		0			0
$559$	−30.8062			−1.30297
$560$	10.2725	+	10.4368i	0.434091	+	0.441035i
$561$		0			0
$562$	−46.2094	+	9.09636i	−1.94922	+	0.383707i
$563$			16.8293i			0.709270i	0.935005	+	0.354635i	$0.115395\pi$
$563$			16.8293i			0.709270i	−0.935005	+	0.354635i	$0.884605\pi$
$564$		0			0
$565$		−	14.2557i		−	0.599742i
$566$	0.290522	+	1.47585i	0.0122116	+	0.0620346i
$567$		0			0
$568$	−17.7016	+	11.6760i	−0.742741	+	0.489915i
$569$	26.6763			1.11833			0.559164	−	0.829057i	$-0.311122\pi$
$569$	26.6763			1.11833			0.559164	+	0.829057i	$0.311122\pi$
$570$		0			0
$571$			10.1600i			0.425182i	0.977141	+	0.212591i	$0.0681901\pi$
$571$			10.1600i			0.425182i	−0.977141	+	0.212591i	$0.931810\pi$
$572$	−14.4135	+	5.90340i	−0.602660	+	0.246833i
$573$		0			0
$574$	−5.00000	+	0.984255i	−0.208696	+	0.0410820i
$575$	−30.2797			−1.26275
$576$		0			0
$577$	28.8062			1.19922			0.599610	−	0.800292i	$-0.295322\pi$
$577$	28.8062			1.19922			0.599610	+	0.800292i	$0.295322\pi$
$578$	−54.4063	+	10.7099i	−2.26300	+	0.445475i
$579$		0			0
$580$	42.2094	−	17.2878i	1.75265	−	0.717838i
$581$		−	7.32206i		−	0.303770i
$582$		0			0
$583$	−21.6125			−0.895098
$584$	14.1664	−	9.34420i	0.586208	−	0.386666i
$585$		0			0
$586$	5.80625	+	29.4957i	0.239854	+	1.21845i
$587$		−	38.7955i		−	1.60126i	−0.599159	−	0.800630i	$-0.704498\pi$
$587$		−	38.7955i		−	1.60126i	0.599159	−	0.800630i	$-0.295502\pi$
$588$		0			0
$589$		−	38.5127i		−	1.58689i
$590$	−11.1007	+	2.18518i	−0.457008	+	0.0899624i
$591$		0			0
$592$	−20.0000	−	20.3199i	−0.821995	−	0.835144i
$593$	44.1122			1.81147			0.905735	−	0.423844i	$-0.139320\pi$
$593$	44.1122			1.81147			0.905735	+	0.423844i	$0.139320\pi$
$594$		0			0
$595$		−	27.4478i		−	1.12525i
$596$	−8.03498	−	19.6180i	−0.329126	−	0.803583i
$597$		0			0
$598$	2.98438	+	15.1606i	0.122040	+	0.619963i
$599$	−0.290522			−0.0118704			−0.00593521	−	0.999982i	$-0.501889\pi$
$599$	−0.290522			−0.0118704			−0.00593521	+	0.999982i	$0.501889\pi$
$600$		0			0
$601$	−39.6125			−1.61583			−0.807914	−	0.589301i	$-0.799403\pi$
$601$	−39.6125			−1.61583			−0.807914	+	0.589301i	$0.799403\pi$
$602$	−2.77517	−	14.0978i	−0.113107	−	0.574584i
$603$		0			0
$604$	−34.8062	+	14.2557i	−1.41625	+	0.580056i
$605$		−	16.1200i		−	0.655370i
$606$		0			0
$607$	−22.8062			−0.925677			−0.462839	−	0.886443i	$-0.653169\pi$
$607$	−22.8062			−0.925677			−0.462839	+	0.886443i	$0.653169\pi$
$608$	−33.3020	−	22.7327i	−1.35058	−	0.921932i
$609$		0			0
$610$	15.4031	−	3.03212i	0.623654	−	0.122767i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	1.94695	+	9.89049i	0.0785726	+	0.399148i
$615$		0			0
$616$	−4.00000	−	6.06424i	−0.161165	−	0.244335i
$617$	−14.9946			−0.603659			−0.301830	−	0.953362i	$-0.597597\pi$
$617$	−14.9946			−0.603659			−0.301830	+	0.953362i	$0.597597\pi$
$618$		0			0
$619$			40.6399i			1.63345i	0.577024	+	0.816727i	$0.304214\pi$
$619$			40.6399i			1.63345i	−0.577024	+	0.816727i	$0.695786\pi$
$620$	14.9946	+	36.6103i	0.602197	+	1.47030i
$621$		0			0
$622$	−30.8062	+	6.06424i	−1.23522	+	0.243154i
$623$	−3.60338			−0.144367
$624$		0			0
$625$	3.59688			0.143875
$626$	19.4262	−	3.82406i	0.776426	−	0.152840i
$627$		0			0
$628$	2.29844	+	5.61179i	0.0917177	+	0.223935i
$629$			53.4396i			2.13078i
$630$		0			0
$631$	10.8062			0.430190			0.215095	−	0.976593i	$-0.430994\pi$
$631$	10.8062			0.430190			0.215095	+	0.976593i	$0.430994\pi$
$632$		0			0
$633$		0			0
$634$	1.70156	+	8.64391i	0.0675777	+	0.343294i
$635$		−	68.8502i		−	2.73224i
$636$		0			0
$637$		−	3.03212i		−	0.120137i
$638$	−22.2014	+	4.37036i	−0.878960	+	0.173024i
$639$		0			0
$640$	40.5078	+	8.64391i	1.60121	+	0.341681i
$641$	−14.9946			−0.592250			−0.296125	−	0.955149i	$-0.595695\pi$
$641$	−14.9946			−0.592250			−0.296125	+	0.955149i	$0.595695\pi$
$642$		0			0
$643$			15.3193i			0.604135i	0.953287	+	0.302067i	$0.0976767\pi$
$643$			15.3193i			0.604135i	−0.953287	+	0.302067i	$0.902323\pi$
$644$	−6.66908	+	2.73147i	−0.262798	+	0.107635i
$645$		0			0
$646$	14.5969	+	74.1519i	0.574306	+	2.91747i
$647$	22.7824			0.895668			0.447834	−	0.894117i	$-0.352195\pi$
$647$	22.7824			0.895668			0.447834	+	0.894117i	$0.352195\pi$
$648$		0			0
$649$	5.61250			0.220310
$650$	−6.95960	−	35.3547i	−0.272978	−	1.38672i
$651$		0			0
$652$	16.8953	+	41.2510i	0.661672	+	1.61552i
$653$		−	17.9219i		−	0.701337i	−0.936500	−	0.350669i	$-0.885954\pi$
$653$		−	17.9219i		−	0.701337i	0.936500	−	0.350669i	$-0.114046\pi$
$654$		0			0
$655$	−26.8062			−1.04741
$656$	−10.2725	+	10.1107i	−0.401072	+	0.394757i
$657$		0			0
$658$		0			0
$659$		−	25.9533i		−	1.01100i	−0.862828	−	0.505498i	$-0.831309\pi$
$659$		−	25.9533i		−	1.01100i	0.862828	−	0.505498i	$-0.168691\pi$
$660$		0			0
$661$		−	39.7350i		−	1.54551i	−0.634703	−	0.772756i	$-0.718878\pi$
$661$		−	39.7350i		−	1.54551i	0.634703	−	0.772756i	$-0.281122\pi$
$662$	6.08803	+	30.9271i	0.236618	+	1.20202i
$663$		0			0
$664$	−11.4031	−	17.2878i	−0.442527	−	0.670898i
$665$	−26.0953			−1.01193
$666$		0			0
$667$			22.4472i			0.869158i
$668$	27.7517	−	11.3663i	1.07375	−	0.439777i
$669$		0			0
$670$	51.6125	−	10.1600i	1.99396	−	0.392514i
$671$	−7.78781			−0.300645
$672$		0			0
$673$	20.5969			0.793951			0.396976	−	0.917829i	$-0.370060\pi$
$673$	20.5969			0.793951			0.396976	+	0.917829i	$0.370060\pi$
$674$	−39.9711	+	7.86835i	−1.53963	+	0.303078i
$675$		0			0
$676$	7.04453	−	2.88525i	0.270944	−	0.110971i
$677$			29.9976i			1.15290i	0.817133	+	0.576450i	$0.195562\pi$
$677$			29.9976i			1.15290i	−0.817133	+	0.576450i	$0.804438\pi$
$678$		0			0
$679$	8.80625			0.337953
$680$	−42.7463	−	64.8059i	−1.63924	−	2.48519i
$681$		0			0
$682$	−3.79063	−	19.2563i	−0.145151	−	0.737363i
$683$		−	8.47183i		−	0.324166i	−0.986777	−	0.162083i	$-0.948179\pi$
$683$		−	8.47183i		−	0.324166i	0.986777	−	0.162083i	$-0.0518212\pi$
$684$		0			0
$685$			26.3842i			1.00809i
$686$	1.38758	−	0.273147i	0.0529782	−	0.0104288i
$687$		0			0
$688$	−28.5078	−	28.9639i	−1.08685	−	1.10424i
$689$	−25.5142			−0.972014
$690$		0			0
$691$			8.19146i			0.311618i	0.987787	+	0.155809i	$0.0497984\pi$
$691$			8.19146i			0.311618i	−0.987787	+	0.155809i	$0.950202\pi$
$692$	6.08803	+	14.8643i	0.231432	+	0.565057i
$693$		0			0
$694$	−7.29844	−	37.0760i	−0.277045	−	1.40738i
$695$	29.9892			1.13755
$696$		0			0
$697$	27.0156			1.02329
$698$	−1.40926	−	7.15902i	−0.0533413	−	0.270973i
$699$		0			0
$700$	15.5523	−	6.36982i	0.587823	−	0.240757i
$701$		−	40.6546i		−	1.53550i	−0.640748	−	0.767751i	$-0.721376\pi$
$701$		−	40.6546i		−	1.53550i	0.640748	−	0.767751i	$-0.278624\pi$
$702$		0			0
$703$	50.8062			1.91619
$704$	−18.8885	−	8.08857i	−0.711887	−	0.304850i
$705$		0			0
$706$	−5.00000	+	0.984255i	−0.188177	+	0.0370429i
$707$			5.84621i			0.219869i
$708$		0			0
$709$			40.6399i			1.52626i	0.646243	+	0.763131i	$0.276339\pi$
$709$			40.6399i			1.52626i	−0.646243	+	0.763131i	$0.723661\pi$
$710$	7.49729	+	38.0861i	0.281368	+	1.42935i
$711$		0			0
$712$	−8.50781	+	5.61179i	−0.318844	+	0.210311i
$713$	−19.4695			−0.729140
$714$		0			0
$715$			28.5114i			1.06627i
$716$	9.15372	+	22.3494i	0.342091	+	0.835237i
$717$		0			0
$718$	10.4031	−	2.04787i	0.388241	−	0.0764256i
$719$	−29.4081			−1.09674			−0.548369	−	0.836237i	$-0.684751\pi$
$719$	−29.4081			−1.09674			−0.548369	+	0.836237i	$0.684751\pi$
$720$		0			0
$721$	−9.40312			−0.350191
$722$	44.1339	−	8.68779i	1.64249	−	0.323326i
$723$		0			0
$724$	−17.7016	−	43.2196i	−0.657873	−	1.60624i
$725$		−	52.3470i		−	1.94412i
$726$		0			0
$727$	39.0156			1.44701			0.723505	−	0.690320i	$-0.242530\pi$
$727$	39.0156			1.44701			0.723505	+	0.690320i	$0.242530\pi$
$728$	−4.72212	−	7.15902i	−0.175013	−	0.265331i
$729$		0			0
$730$	−6.00000	−	30.4799i	−0.222070	−	1.12811i
$731$			76.1723i			2.81733i
$732$		0			0
$733$			19.4150i			0.717111i	0.933508	+	0.358555i	$0.116731\pi$
$733$			19.4150i			0.717111i	−0.933508	+	0.358555i	$0.883269\pi$
$734$	31.6456	−	6.22947i	1.16806	−	0.229934i
$735$		0			0
$736$	−11.4922	+	16.8354i	−0.423608	+	0.620560i
$737$	−26.0953			−0.961231
$738$		0			0
$739$		−	46.8628i		−	1.72388i	−0.507013	−	0.861939i	$-0.669250\pi$
$739$		−	46.8628i		−	1.72388i	0.507013	−	0.861939i	$-0.330750\pi$
$740$	−48.2966	+	19.7810i	−1.77542	+	0.727164i
$741$		0			0
$742$	−2.29844	−	11.6760i	−0.0843783	−	0.428641i
$743$	−37.4865			−1.37524			−0.687622	−	0.726069i	$-0.741345\pi$
$743$	−37.4865			−1.37524			−0.687622	+	0.726069i	$0.741345\pi$
$744$		0			0
$745$	−38.8062			−1.42175
$746$	−1.65643	−	8.41464i	−0.0606462	−	0.308082i
$747$		0			0
$748$	14.5969	+	35.6393i	0.533715	+	1.30310i
$749$			7.70532i			0.281546i
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$		0			0
$754$	−26.2094	+	5.15934i	−0.954489	+	0.187892i
$755$			68.8502i			2.50572i
$756$		0			0
$757$		−	28.5114i		−	1.03626i	−0.855301	−	0.518132i	$-0.826628\pi$
$757$		−	28.5114i		−	1.03626i	0.855301	−	0.518132i	$-0.173372\pi$
$758$	−4.43160	−	22.5125i	−0.160963	−	0.817689i
$759$		0			0
$760$	−61.6125	+	40.6399i	−2.23492	+	1.47416i
$761$	−7.49729			−0.271777			−0.135888	−	0.990724i	$-0.543389\pi$
$761$	−7.49729			−0.271777			−0.135888	+	0.990724i	$0.543389\pi$
$762$		0			0
$763$		0			0
$764$	13.8758	−	5.68317i	0.502010	−	0.205610i
$765$		0			0
$766$	40.8062	−	8.03275i	1.47439	−	0.290235i
$767$	6.62572			0.239241
$768$		0			0
$769$	16.8062			0.606049			0.303024	−	0.952983i	$-0.402004\pi$
$769$	16.8062			0.606049			0.303024	+	0.952983i	$0.402004\pi$
$770$	−13.0476	+	2.56844i	−0.470204	+	0.0925601i
$771$		0			0
$772$	21.1047	−	8.64391i	0.759574	−	0.311101i
$773$			33.7158i			1.21267i	0.795209	+	0.606336i	$0.207361\pi$
$773$			33.7158i			1.21267i	−0.795209	+	0.606336i	$0.792639\pi$
$774$		0			0
$775$	45.4031			1.63093
$776$	20.7921	−	13.7146i	0.746393	−	0.492324i
$777$		0			0
$778$	−2.89531	−	14.7082i	−0.103802	−	0.527313i
$779$		−	25.6844i		−	0.920239i
$780$		0			0
$781$		−	19.2563i		−	0.689046i
$782$	37.4865	−	7.37925i	1.34051	−	0.263881i
$783$		0			0
$784$	2.85078	−	2.80590i	0.101814	−	0.100211i
$785$	11.1007			0.396200
$786$		0			0
$787$		−	8.19146i		−	0.291994i	−0.989285	−	0.145997i	$-0.953361\pi$
$787$		−	8.19146i		−	0.291994i	0.989285	−	0.145997i	$-0.0466390\pi$
$788$	−8.61603	−	21.0366i	−0.306933	−	0.749398i
$789$		0			0
$790$		0			0
$791$	−3.89391			−0.138451
$792$		0			0
$793$	−9.19375			−0.326480
$794$	−8.03498	−	40.8176i	−0.285151	−	1.44856i
$795$		0			0
$796$	27.4031	−	11.2236i	0.971278	−	0.397809i
$797$			9.56442i			0.338789i	0.985548	+	0.169395i	$0.0541812\pi$
$797$			9.56442i			0.338789i	−0.985548	+	0.169395i	$0.945819\pi$
$798$		0			0
$799$		0			0
$800$	26.7999	−	39.2602i	0.947519	−	1.38806i
$801$		0			0
$802$	10.0000	−	1.96851i	0.353112	−	0.0695105i
$803$			15.4106i			0.543829i
$804$		0			0
$805$			13.1921i			0.464960i
$806$	−4.47495	−	22.7327i	−0.157623	−	0.800725i
$807$		0			0
$808$	9.10469	+	13.8033i	0.320302	+	0.485597i
$809$	−3.89391			−0.136902			−0.0684512	−	0.997654i	$-0.521806\pi$
$809$	−3.89391			−0.136902			−0.0684512	+	0.997654i	$0.521806\pi$
$810$		0			0
$811$			12.1285i			0.425889i	0.977064	+	0.212944i	$0.0683053\pi$
$811$			12.1285i			0.425889i	−0.977064	+	0.212944i	$0.931695\pi$
$812$	−4.72212	−	11.5294i	−0.165714	−	0.404602i
$813$		0			0
$814$	25.4031	−	5.00063i	0.890379	−	0.175272i
$815$	81.5986			2.85828
$816$		0			0
$817$	72.4187			2.53361
$818$	13.8758	−	2.73147i	0.485158	−	0.0955037i
$819$		0			0
$820$	10.0000	+	24.4157i	0.349215	+	0.852632i
$821$			1.85911i			0.0648833i	0.999474	+	0.0324417i	$0.0103283\pi$
$821$			1.85911i			0.0648833i	−0.999474	+	0.0324417i	$0.989672\pi$
$822$		0			0
$823$	−5.19375			−0.181043			−0.0905214	−	0.995895i	$-0.528853\pi$
$823$	−5.19375			−0.181043			−0.0905214	+	0.995895i	$0.528853\pi$
$824$	−22.2014	+	14.6441i	−0.773421	+	0.510152i
$825$		0			0
$826$	0.596876	+	3.03212i	0.0207680	+	0.105501i
$827$			20.8164i			0.723857i	0.932206	+	0.361928i	$0.117882\pi$
$827$			20.8164i			0.723857i	−0.932206	+	0.361928i	$0.882118\pi$
$828$		0			0
$829$			29.4163i			1.02167i	0.859679	+	0.510835i	$0.170664\pi$
$829$			29.4163i			1.02167i	−0.859679	+	0.510835i	$0.829336\pi$
$830$	−37.1959	+	7.32206i	−1.29109	+	0.254152i
$831$		0			0
$832$	−22.2984	−	9.54881i	−0.773059	−	0.331045i
$833$	−7.49729			−0.259766
$834$		0			0
$835$		−	54.8956i		−	1.89974i
$836$	33.8831	−	13.8776i	1.17187	−	0.479967i
$837$		0			0
$838$	0.596876	+	3.03212i	0.0206187	+	0.104743i
$839$	−44.9837			−1.55301			−0.776506	−	0.630110i	$-0.783010\pi$
$839$	−44.9837			−1.55301			−0.776506	+	0.630110i	$0.783010\pi$
$840$		0			0
$841$	−9.80625			−0.338146
$842$	3.60338	+	18.3051i	0.124181	+	0.630837i
$843$		0			0
$844$	−3.10469	−	7.58030i	−0.106868	−	0.260925i
$845$		−	13.9348i		−	0.479371i
$846$		0			0
$847$	−4.40312			−0.151293
$848$	−23.6106	−	23.9883i	−0.810792	−	0.823762i
$849$		0			0
$850$	−87.4187	+	17.2085i	−2.99844	+	0.590245i
$851$		−	25.6844i		−	0.880449i
$852$		0			0
$853$			51.8635i			1.77577i	0.460064	+	0.887886i	$0.347826\pi$
$853$			51.8635i			1.77577i	−0.460064	+	0.887886i	$0.652174\pi$
$854$	−0.828216	−	4.20732i	−0.0283410	−	0.143972i
$855$		0			0
$856$	12.0000	+	18.1927i	0.410152	+	0.621814i
$857$	−29.6986			−1.01449			−0.507243	−	0.861803i	$-0.669335\pi$
$857$	−29.6986			−1.01449			−0.507243	+	0.861803i	$0.669335\pi$
$858$		0			0
$859$			9.25507i			0.315779i	0.987457	+	0.157889i	$0.0504690\pi$
$859$			9.25507i			0.315779i	−0.987457	+	0.157889i	$0.949531\pi$
$860$	−68.8415	+	28.1956i	−2.34748	+	0.961463i
$861$		0			0
$862$	−36.6125	+	7.20721i	−1.24703	+	0.245478i
$863$	0.290522			0.00988949			0.00494475	−	0.999988i	$-0.498426\pi$
$863$	0.290522			0.00988949			0.00494475	+	0.999988i	$0.498426\pi$
$864$		0			0
$865$	29.4031			0.999736
$866$	−4.43160	+	0.872365i	−0.150592	+	0.0296442i
$867$		0			0
$868$	10.0000	−	4.09573i	0.339422	−	0.139018i
$869$		0			0
$870$		0			0
$871$	−30.8062			−1.04383
$872$		0			0
$873$		0			0
$874$	−7.01562	−	35.6393i	−0.237307	−	1.20552i
$875$		−	12.4589i		−	0.421189i
$876$		0			0
$877$		−	16.3829i		−	0.553212i	−0.960983	−	0.276606i	$-0.910790\pi$
$877$		−	16.3829i		−	0.553212i	0.960983	−	0.276606i	$-0.0892097\pi$
$878$	−22.2014	+	4.37036i	−0.749259	+	0.147492i
$879$		0			0
$880$	−26.8062	+	26.3842i	−0.903638	+	0.889411i
$881$	−6.91625			−0.233014			−0.116507	−	0.993190i	$-0.537170\pi$
$881$	−6.91625			−0.233014			−0.116507	+	0.993190i	$0.537170\pi$
$882$		0			0
$883$		−	4.09573i		−	0.137832i	−0.997622	−	0.0689161i	$-0.978046\pi$
$883$		−	4.09573i		−	0.137832i	0.997622	−	0.0689161i	$-0.0219541\pi$
$884$	17.2321	+	42.0732i	0.579577	+	1.41508i
$885$		0			0
$886$	1.89531	+	9.62817i	0.0636743	+	0.323465i
$887$	37.1959			1.24892			0.624459	−	0.781058i	$-0.285320\pi$
$887$	37.1959			1.24892			0.624459	+	0.781058i	$0.285320\pi$
$888$		0			0
$889$	−18.8062			−0.630741
$890$	3.60338	+	18.3051i	0.120786	+	0.613590i
$891$		0			0
$892$	−27.4031	+	11.2236i	−0.917524	+	0.375793i
$893$		0			0
$894$		0			0
$895$	44.2094			1.47776
$896$	2.36106	−	11.0646i	0.0788775	−	0.369642i
$897$		0			0
$898$	−25.4031	+	5.00063i	−0.847713	+	0.166873i
$899$		−	33.6586i		−	1.12258i
$900$		0			0
$901$			63.0870i			2.10173i
$902$	−2.52800	−	12.8422i	−0.0841731	−	0.427598i
$903$		0			0
$904$	−9.19375	+	6.06424i	−0.305780	+	0.201694i
$905$	−85.4925			−2.84187
$906$		0			0
$907$		−	6.22295i		−	0.206630i	−0.994649	−	0.103315i	$-0.967055\pi$
$907$		−	6.22295i		−	0.206630i	0.994649	−	0.103315i	$-0.0329449\pi$
$908$	−14.9946	−	36.6103i	−0.497613	−	1.21495i
$909$		0			0
$910$	−15.4031	+	3.03212i	−0.510609	+	0.100514i
$911$	−18.0169			−0.596927			−0.298464	−	0.954421i	$-0.596474\pi$
$911$	−18.0169			−0.596927			−0.298464	+	0.954421i	$0.596474\pi$
$912$		0			0
$913$	18.8062			0.622396
$914$	30.5269	−	6.00924i	1.00974	−	0.198768i
$915$		0			0
$916$	−8.50781	−	20.7724i	−0.281106	−	0.686339i
$917$			7.32206i			0.241796i
$918$		0			0
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$	20.5449	+	31.1473i	0.677346	+	1.02690i
$921$		0			0
$922$	3.20937	+	16.3036i	0.105695	+	0.536929i
$923$		−	22.7327i		−	0.748255i
$924$		0			0
$925$			59.8962i			1.96938i
$926$	33.3020	−	6.55554i	1.09437	−	0.215428i
$927$		0			0
$928$	−29.1047	−	19.8675i	−0.955408	−	0.652182i
$929$	41.3804			1.35765			0.678823	−	0.734302i	$-0.262490\pi$
$929$	41.3804			1.35765			0.678823	+	0.734302i	$0.262490\pi$
$930$		0			0
$931$			7.12785i			0.233606i
$932$	−34.9585	+	14.3180i	−1.14510	+	0.469003i
$933$		0			0
$934$	−11.0156	−	55.9592i	−0.360442	−	1.83104i
$935$	70.4980			2.30553
$936$		0			0
$937$	3.61250			0.118015			0.0590076	−	0.998258i	$-0.481206\pi$
$937$	3.61250			0.118015			0.0590076	+	0.998258i	$0.481206\pi$
$938$	−2.77517	−	14.0978i	−0.0906125	−	0.460310i
$939$		0			0
$940$		0			0
$941$			14.7013i			0.479249i	0.970866	+	0.239624i	$0.0770243\pi$
$941$			14.7013i			0.479249i	−0.970866	+	0.239624i	$0.922976\pi$
$942$		0			0
$943$	−12.9844			−0.422830
$944$	6.13138	+	6.22947i	0.199559	+	0.202752i
$945$		0			0
$946$	36.2094	−	7.12785i	1.17727	−	0.231746i
$947$			40.5974i			1.31924i	0.751600	+	0.659619i	$0.229282\pi$
$947$			40.5974i			1.31924i	−0.751600	+	0.659619i	$0.770718\pi$
$948$		0			0
$949$			18.1927i			0.590561i
$950$	16.3605	+	83.1110i	0.530804	+	2.69648i
$951$		0			0
$952$	−17.7016	+	11.6760i	−0.573711	+	0.378422i
$953$	−22.2014			−0.719172			−0.359586	−	0.933112i	$-0.617082\pi$
$953$	−22.2014			−0.719172			−0.359586	+	0.933112i	$0.617082\pi$
$954$		0			0
$955$		−	27.4478i		−	0.888190i
$956$	−27.2140	+	11.1461i	−0.880164	+	0.360491i
$957$		0			0
$958$	20.0000	−	3.93702i	0.646171	−	0.127199i
$959$	7.20677			0.232719
$960$		0			0
$961$	−1.80625			−0.0582661
$962$	29.9892	−	5.90340i	0.966889	−	0.190333i
$963$		0			0
$964$	−1.49219	+	0.611161i	−0.0480602	+	0.0196842i
$965$		−	41.7472i		−	1.34389i
$966$		0			0
$967$	42.8062			1.37656			0.688278	−	0.725447i	$-0.258367\pi$
$967$	42.8062			1.37656			0.688278	+	0.725447i	$0.258367\pi$
$968$	−10.3960	+	6.85728i	−0.334142	+	0.220401i
$969$		0			0
$970$	−8.80625	−	44.7356i	−0.282752	−	1.43637i
$971$		−	38.0289i		−	1.22041i	−0.792245	−	0.610203i	$-0.791088\pi$
$971$		−	38.0289i		−	1.22041i	0.792245	−	0.610203i	$-0.208912\pi$
$972$		0			0
$973$		−	8.19146i		−	0.262606i
$974$	11.1007	−	2.18518i	0.355689	−	0.0700176i
$975$		0			0
$976$	−8.50781	−	8.64391i	−0.272328	−	0.276685i
$977$	−55.5034			−1.77571			−0.887855	−	0.460123i	$-0.847805\pi$
$977$	−55.5034			−1.77571			−0.887855	+	0.460123i	$0.847805\pi$
$978$		0			0
$979$		−	9.25507i		−	0.295793i
$980$	−2.77517	−	6.77576i	−0.0886495	−	0.216444i
$981$		0			0
$982$	−11.5078	−	58.4595i	−0.367229	−	1.86552i
$983$	14.4135			0.459720			0.229860	−	0.973224i	$-0.426173\pi$
$983$	14.4135			0.459720			0.229860	+	0.973224i	$0.426173\pi$
$984$		0			0
$985$	−41.6125			−1.32588
$986$	12.7571	+	64.8059i	0.406269	+	2.06384i
$987$		0			0
$988$	40.0000	−	16.3829i	1.27257	−	0.521210i
$989$		−	36.6103i		−	1.16414i
$990$		0			0
$991$	21.1938			0.673242			0.336621	−	0.941640i	$-0.390716\pi$
$991$	21.1938			0.673242			0.336621	+	0.941640i	$0.390716\pi$
$992$	17.2321	−	25.2439i	0.547118	−	0.801496i
$993$		0			0
$994$	10.4031	−	2.04787i	0.329967	−	0.0649543i
$995$		−	54.2061i		−	1.71845i
$996$		0			0
$997$		−	23.3521i		−	0.739567i	−0.929118	−	0.369784i	$-0.879432\pi$
$997$		−	23.3521i		−	0.739567i	0.929118	−	0.369784i	$-0.120568\pi$
$998$	−2.19412	−	11.1461i	−0.0694538	−	0.352824i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.c.e.253.2	yes	8
3.2	odd	2	inner	504.2.c.e.253.7	yes	8
4.3	odd	2		2016.2.c.f.1009.1		8
8.3	odd	2		2016.2.c.f.1009.8		8
8.5	even	2	inner	504.2.c.e.253.1	✓	8
12.11	even	2		2016.2.c.f.1009.7		8
24.5	odd	2	inner	504.2.c.e.253.8	yes	8
24.11	even	2		2016.2.c.f.1009.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.c.e.253.1	✓	8	8.5	even	2	inner
504.2.c.e.253.2	yes	8	1.1	even	1	trivial
504.2.c.e.253.7	yes	8	3.2	odd	2	inner
504.2.c.e.253.8	yes	8	24.5	odd	2	inner
2016.2.c.f.1009.1		8	4.3	odd	2
2016.2.c.f.1009.2		8	24.11	even	2
2016.2.c.f.1009.7		8	12.11	even	2
2016.2.c.f.1009.8		8	8.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38758 + 0.273147i) q^{2} +(1.85078 - 0.758030i) q^{4} -3.66103i q^{5} -1.00000 q^{7} +(-2.36106 + 1.55737i) q^{8} +O(q^{10})\)	\(q+(-1.38758 + 0.273147i) q^{2} +(1.85078 - 0.758030i) q^{4} -3.66103i q^{5} -1.00000 q^{7} +(-2.36106 + 1.55737i) q^{8} +(1.00000 + 5.07999i) q^{10} -2.56844i q^{11} -3.03212i q^{13} +(1.38758 - 0.273147i) q^{14} +(2.85078 - 2.80590i) q^{16} -7.49729 q^{17} +7.12785i q^{19} +(-2.77517 - 6.77576i) q^{20} +(0.701562 + 3.56393i) q^{22} +3.60338 q^{23} -8.40312 q^{25} +(0.828216 + 4.20732i) q^{26} +(-1.85078 + 0.758030i) q^{28} +6.22947i q^{29} -5.40312 q^{31} +(-3.18928 + 4.67210i) q^{32} +(10.4031 - 2.04787i) q^{34} +3.66103i q^{35} -7.12785i q^{37} +(-1.94695 - 9.89049i) q^{38} +(5.70156 + 8.64391i) q^{40} -3.60338 q^{41} -10.1600i q^{43} +(-1.94695 - 4.75362i) q^{44} +(-5.00000 + 0.984255i) q^{46} +1.00000 q^{49} +(11.6600 - 2.29529i) q^{50} +(-2.29844 - 5.61179i) q^{52} -8.41464i q^{53} -9.40312 q^{55} +(2.36106 - 1.55737i) q^{56} +(-1.70156 - 8.64391i) q^{58} +2.18518i q^{59} -3.03212i q^{61} +(7.49729 - 1.47585i) q^{62} +(3.14922 - 7.35408i) q^{64} -11.1007 q^{65} -10.1600i q^{67} +(-13.8758 + 5.68317i) q^{68} +(-1.00000 - 5.07999i) q^{70} +7.49729 q^{71} -6.00000 q^{73} +(1.94695 + 9.89049i) q^{74} +(5.40312 + 13.1921i) q^{76} +2.56844i q^{77} +(-10.2725 - 10.4368i) q^{80} +(5.00000 - 0.984255i) q^{82} +7.32206i q^{83} +27.4478i q^{85} +(2.77517 + 14.0978i) q^{86} +(4.00000 + 6.06424i) q^{88} +3.60338 q^{89} +3.03212i q^{91} +(6.66908 - 2.73147i) q^{92} +26.0953 q^{95} -8.80625 q^{97} +(-1.38758 + 0.273147i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 8 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 8 * q^7	\( 8 q + 2 q^{4} - 8 q^{7} + 8 q^{10} + 10 q^{16} - 20 q^{22} - 16 q^{25} - 2 q^{28} + 8 q^{31} + 32 q^{34} + 20 q^{40} - 40 q^{46} + 8 q^{49} - 44 q^{52} - 24 q^{55} + 12 q^{58} + 38 q^{64} - 8 q^{70} - 48 q^{73} - 8 q^{76} + 40 q^{82} + 32 q^{88} + 32 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 8 * q^7 + 8 * q^10 + 10 * q^16 - 20 * q^22 - 16 * q^25 - 2 * q^28 + 8 * q^31 + 32 * q^34 + 20 * q^40 - 40 * q^46 + 8 * q^49 - 44 * q^52 - 24 * q^55 + 12 * q^58 + 38 * q^64 - 8 * q^70 - 48 * q^73 - 8 * q^76 + 40 * q^82 + 32 * q^88 + 32 * q^97

Introduction

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