LMFDB - Embedded newform 1452.2.i.p.1237.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1452,2,Mod(493,1452)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1452.493"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1452, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1452.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1,0,8,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5942783735$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1237.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	1452.1237
Dual form			1452.2.i.p.493.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{3} +(0.881966 - 2.71441i) q^{5} +(3.42705 - 2.48990i) q^{7} +(0.309017 + 0.951057i) q^{9} +(0.545085 + 1.67760i) q^{13} +(2.30902 - 1.67760i) q^{15} +(-1.42705 + 4.39201i) q^{17} +(4.92705 + 3.57971i) q^{19} +4.23607 q^{21} +4.23607 q^{23} +(-2.54508 - 1.84911i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-3.61803 + 2.62866i) q^{29} +(-2.66312 - 8.19624i) q^{31} +(-3.73607 - 11.4984i) q^{35} +(6.66312 - 4.84104i) q^{37} +(-0.545085 + 1.67760i) q^{39} +(0.427051 + 0.310271i) q^{41} -0.527864 q^{43} +2.85410 q^{45} +(-1.11803 - 0.812299i) q^{47} +(3.38197 - 10.4086i) q^{49} +(-3.73607 + 2.71441i) q^{51} +(-4.19098 - 12.8985i) q^{53} +(1.88197 + 5.79210i) q^{57} +(-7.16312 + 5.20431i) q^{59} +(0.118034 - 0.363271i) q^{61} +(3.42705 + 2.48990i) q^{63} +5.03444 q^{65} -6.85410 q^{67} +(3.42705 + 2.48990i) q^{69} +(-1.11803 + 3.44095i) q^{71} +(-1.00000 + 0.726543i) q^{73} +(-0.972136 - 2.99193i) q^{75} +(-3.01722 - 9.28605i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.01722 + 6.20837i) q^{83} +(10.6631 + 7.74721i) q^{85} -4.47214 q^{87} +1.00000 q^{89} +(6.04508 + 4.39201i) q^{91} +(2.66312 - 8.19624i) q^{93} +(14.0623 - 10.2169i) q^{95} +(1.88197 + 5.79210i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 8 q^{5} + 7 q^{7} - q^{9} - 9 q^{13} + 7 q^{15} + q^{17} + 13 q^{19} + 8 q^{21} + 8 q^{23} + q^{25} + q^{27} - 10 q^{29} + 5 q^{31} - 6 q^{35} + 11 q^{37} + 9 q^{39} - 5 q^{41} - 20 q^{43}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q + q^3 + 8 * q^5 + 7 * q^7 - q^9 - 9 * q^13 + 7 * q^15 + q^17 + 13 * q^19 + 8 * q^21 + 8 * q^23 + q^25 + q^27 - 10 * q^29 + 5 * q^31 - 6 * q^35 + 11 * q^37 + 9 * q^39 - 5 * q^41 - 20 * q^43 - 2 * q^45 + 18 * q^49 - 6 * q^51 - 19 * q^53 + 12 * q^57 - 13 * q^59 - 4 * q^61 + 7 * q^63 - 38 * q^65 - 14 * q^67 + 7 * q^69 - 4 * q^73 + 14 * q^75 + 17 * q^79 - q^81 + 21 * q^83 + 27 * q^85 + 4 * q^89 + 13 * q^91 - 5 * q^93 + 16 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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			0
$2$		0			0
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	0.881966	−	2.71441i	0.394427	−	1.21392i	−0.534980	−	0.844865i	$-0.679681\pi$
$5$	0.881966	−	2.71441i	0.394427	−	1.21392i	0.929407	−	0.369057i	$-0.120319\pi$
$6$		0			0
$7$	3.42705	−	2.48990i	1.29530	−	0.941093i	0.295405	−	0.955372i	$-0.404545\pi$
$7$	3.42705	−	2.48990i	1.29530	−	0.941093i	0.999898	+	0.0142789i	$0.00454526\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.545085	+	1.67760i	0.151179	+	0.465282i	0.997754	−	0.0669881i	$-0.0213390\pi$
$13$	0.545085	+	1.67760i	0.151179	+	0.465282i	−0.846574	+	0.532270i	$0.821339\pi$
$14$		0			0
$15$	2.30902	−	1.67760i	0.596186	−	0.433154i
$16$		0			0
$17$	−1.42705	+	4.39201i	−0.346111	+	1.06522i	0.614876	+	0.788624i	$0.289206\pi$
$17$	−1.42705	+	4.39201i	−0.346111	+	1.06522i	−0.960987	+	0.276595i	$0.910794\pi$
$18$		0			0
$19$	4.92705	+	3.57971i	1.13034	+	0.821242i	0.985745	−	0.168248i	$-0.0538110\pi$
$19$	4.92705	+	3.57971i	1.13034	+	0.821242i	0.144598	+	0.989490i	$0.453811\pi$
$20$		0			0
$21$	4.23607			0.924386
$22$		0			0
$23$	4.23607			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$23$	4.23607			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$24$		0			0
$25$	−2.54508	−	1.84911i	−0.509017	−	0.369822i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	−0.870645	−	0.491912i	$-0.836298\pi$
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	0.198793	+	0.980042i	$0.436298\pi$
$30$		0			0
$31$	−2.66312	−	8.19624i	−0.478310	−	1.47209i	−0.841441	−	0.540349i	$-0.818292\pi$
$31$	−2.66312	−	8.19624i	−0.478310	−	1.47209i	0.363130	−	0.931738i	$-0.381708\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.73607	−	11.4984i	−0.631511	−	1.94359i
$36$		0			0
$37$	6.66312	−	4.84104i	1.09541	−	0.795862i	0.115105	−	0.993353i	$-0.463279\pi$
$37$	6.66312	−	4.84104i	1.09541	−	0.795862i	0.980305	+	0.197491i	$0.0632794\pi$
$38$		0			0
$39$	−0.545085	+	1.67760i	−0.0872835	+	0.268631i
$40$		0			0
$41$	0.427051	+	0.310271i	0.0666942	+	0.0484561i	0.620633	−	0.784101i	$-0.286876\pi$
$41$	0.427051	+	0.310271i	0.0666942	+	0.0484561i	−0.553939	+	0.832558i	$0.686876\pi$
$42$		0			0
$43$	−0.527864			−0.0804985			−0.0402493	−	0.999190i	$-0.512815\pi$
$43$	−0.527864			−0.0804985			−0.0402493	+	0.999190i	$0.512815\pi$
$44$		0			0
$45$	2.85410			0.425464
$46$		0			0
$47$	−1.11803	−	0.812299i	−0.163082	−	0.118486i	0.503251	−	0.864140i	$-0.332137\pi$
$47$	−1.11803	−	0.812299i	−0.163082	−	0.118486i	−0.666333	+	0.745654i	$0.732137\pi$
$48$		0			0
$49$	3.38197	−	10.4086i	0.483138	−	1.48695i
$50$		0			0
$51$	−3.73607	+	2.71441i	−0.523154	+	0.380094i
$52$		0			0
$53$	−4.19098	−	12.8985i	−0.575676	−	1.77175i	−0.633867	−	0.773442i	$-0.718533\pi$
$53$	−4.19098	−	12.8985i	−0.575676	−	1.77175i	0.0581908	−	0.998305i	$-0.481467\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.88197	+	5.79210i	0.249272	+	0.767182i
$58$		0			0
$59$	−7.16312	+	5.20431i	−0.932559	+	0.677544i	−0.946618	−	0.322358i	$-0.895525\pi$
$59$	−7.16312	+	5.20431i	−0.932559	+	0.677544i	0.0140593	+	0.999901i	$0.495525\pi$
$60$		0			0
$61$	0.118034	−	0.363271i	0.0151127	−	0.0465121i	−0.943216	−	0.332181i	$-0.892216\pi$
$61$	0.118034	−	0.363271i	0.0151127	−	0.0465121i	0.958328	+	0.285669i	$0.0922156\pi$
$62$		0			0
$63$	3.42705	+	2.48990i	0.431768	+	0.313698i
$64$		0			0
$65$	5.03444			0.624446
$66$		0			0
$67$	−6.85410			−0.837362			−0.418681	−	0.908133i	$-0.637507\pi$
$67$	−6.85410			−0.837362			−0.418681	+	0.908133i	$0.637507\pi$
$68$		0			0
$69$	3.42705	+	2.48990i	0.412568	+	0.299749i
$70$		0			0
$71$	−1.11803	+	3.44095i	−0.132686	+	0.408366i	−0.995223	−	0.0976283i	$-0.968874\pi$
$71$	−1.11803	+	3.44095i	−0.132686	+	0.408366i	0.862537	+	0.505994i	$0.168874\pi$
$72$		0			0
$73$	−1.00000	+	0.726543i	−0.117041	+	0.0850354i	−0.644766	−	0.764380i	$-0.723045\pi$
$73$	−1.00000	+	0.726543i	−0.117041	+	0.0850354i	0.527725	+	0.849415i	$0.323045\pi$
$74$		0			0
$75$	−0.972136	−	2.99193i	−0.112253	−	0.345478i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.01722	−	9.28605i	−0.339464	−	1.04476i	−0.964481	−	0.264152i	$-0.914908\pi$
$79$	−3.01722	−	9.28605i	−0.339464	−	1.04476i	0.625017	−	0.780611i	$-0.285092\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−2.01722	+	6.20837i	−0.221419	+	0.681457i	0.777217	+	0.629233i	$0.216631\pi$
$83$	−2.01722	+	6.20837i	−0.221419	+	0.681457i	−0.998635	+	0.0522238i	$0.983369\pi$
$84$		0			0
$85$	10.6631	+	7.74721i	1.15658	+	0.840303i
$86$		0			0
$87$	−4.47214			−0.479463
$88$		0			0
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	6.04508	+	4.39201i	0.633697	+	0.460408i
$92$		0			0
$93$	2.66312	−	8.19624i	0.276153	−	0.849910i
$94$		0			0
$95$	14.0623	−	10.2169i	1.44276	−	1.04823i
$96$		0			0
$97$	1.88197	+	5.79210i	0.191085	+	0.588098i	1.00000		0.000173013i	$5.50717e-5\pi$
$97$	1.88197	+	5.79210i	0.191085	+	0.588098i	−0.808915	+	0.587925i	$0.799945\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.69098	−	11.3597i	−0.367267	−	1.13033i	−0.948550	−	0.316629i	$-0.897449\pi$
$101$	−3.69098	−	11.3597i	−0.367267	−	1.13033i	0.581283	−	0.813701i	$-0.302551\pi$
$102$		0			0
$103$	−2.85410	+	2.07363i	−0.281223	+	0.204320i	−0.719451	−	0.694544i	$-0.755606\pi$
$103$	−2.85410	+	2.07363i	−0.281223	+	0.204320i	0.438228	+	0.898864i	$0.355606\pi$
$104$		0			0
$105$	3.73607	−	11.4984i	0.364603	−	1.12213i
$106$		0			0
$107$	12.5172	+	9.09429i	1.21009	+	0.879179i	0.995239	−	0.0974692i	$-0.0310748\pi$
$107$	12.5172	+	9.09429i	1.21009	+	0.879179i	0.214847	+	0.976648i	$0.431075\pi$
$108$		0			0
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$		0			0
$111$	8.23607			0.781733
$112$		0			0
$113$	−6.28115	−	4.56352i	−0.590881	−	0.429300i	0.251749	−	0.967792i	$-0.418994\pi$
$113$	−6.28115	−	4.56352i	−0.590881	−	0.429300i	−0.842631	+	0.538492i	$0.818994\pi$
$114$		0			0
$115$	3.73607	−	11.4984i	0.348390	−	1.07223i
$116$		0			0
$117$	−1.42705	+	1.03681i	−0.131931	+	0.0958534i
$118$		0			0
$119$	6.04508	+	18.6049i	0.554152	+	1.70550i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	0.163119	+	0.502029i	0.0147079	+	0.0452664i
$124$		0			0
$125$	4.28115	−	3.11044i	0.382918	−	0.278206i
$126$		0			0
$127$	−0.708204	+	2.17963i	−0.0628429	+	0.193411i	−0.977549	−	0.210710i	$-0.932422\pi$
$127$	−0.708204	+	2.17963i	−0.0628429	+	0.193411i	0.914706	+	0.404121i	$0.132422\pi$
$128$		0			0
$129$	−0.427051	−	0.310271i	−0.0375997	−	0.0273178i
$130$		0			0
$131$	−11.5623			−1.01020			−0.505102	−	0.863060i	$-0.668545\pi$
$131$	−11.5623			−1.01020			−0.505102	+	0.863060i	$0.668545\pi$
$132$		0			0
$133$	25.7984			2.23700
$134$		0			0
$135$	2.30902	+	1.67760i	0.198729	+	0.144385i
$136$		0			0
$137$	−6.48936	+	19.9722i	−0.554423	+	1.70634i	0.143039	+	0.989717i	$0.454313\pi$
$137$	−6.48936	+	19.9722i	−0.554423	+	1.70634i	−0.697462	+	0.716622i	$0.745687\pi$
$138$		0			0
$139$	−16.8262	+	12.2250i	−1.42718	+	1.03691i	−0.436650	+	0.899631i	$0.643835\pi$
$139$	−16.8262	+	12.2250i	−1.42718	+	1.03691i	−0.990533	+	0.137278i	$0.956165\pi$
$140$		0			0
$141$	−0.427051	−	1.31433i	−0.0359642	−	0.110686i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.94427	+	12.1392i	0.327554	+	1.00811i
$146$		0			0
$147$	8.85410	−	6.43288i	0.730274	−	0.530575i
$148$		0			0
$149$	−5.83688	+	17.9641i	−0.478176	+	1.47167i	0.363450	+	0.931614i	$0.381599\pi$
$149$	−5.83688	+	17.9641i	−0.478176	+	1.47167i	−0.841626	+	0.540061i	$0.818401\pi$
$150$		0			0
$151$	−3.61803	−	2.62866i	−0.294431	−	0.213917i	0.430756	−	0.902468i	$-0.358247\pi$
$151$	−3.61803	−	2.62866i	−0.294431	−	0.213917i	−0.725188	+	0.688551i	$0.758247\pi$
$152$		0			0
$153$	−4.61803			−0.373346
$154$		0			0
$155$	−24.5967			−1.97566
$156$		0			0
$157$	10.3262	+	7.50245i	0.824124	+	0.598761i	0.917891	−	0.396833i	$-0.129891\pi$
$157$	10.3262	+	7.50245i	0.824124	+	0.598761i	−0.0937672	+	0.995594i	$0.529891\pi$
$158$		0			0
$159$	4.19098	−	12.8985i	0.332367	−	1.02292i
$160$		0			0
$161$	14.5172	−	10.5474i	1.14412	−	0.831250i
$162$		0			0
$163$	0.572949	+	1.76336i	0.0448768	+	0.138117i	0.970984	−	0.239143i	$-0.0768664\pi$
$163$	0.572949	+	1.76336i	0.0448768	+	0.138117i	−0.926108	+	0.377260i	$0.876866\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.500000	−	1.53884i	−0.0386912	−	0.119079i	0.929845	−	0.367950i	$-0.119940\pi$
$167$	−0.500000	−	1.53884i	−0.0386912	−	0.119079i	−0.968537	+	0.248871i	$0.919940\pi$
$168$		0			0
$169$	8.00000	−	5.81234i	0.615385	−	0.447103i
$170$		0			0
$171$	−1.88197	+	5.79210i	−0.143918	+	0.442933i
$172$		0			0
$173$	−11.7812	−	8.55951i	−0.895704	−	0.650767i	0.0416546	−	0.999132i	$-0.486737\pi$
$173$	−11.7812	−	8.55951i	−0.895704	−	0.650767i	−0.937359	+	0.348365i	$0.886737\pi$
$174$		0			0
$175$	−13.3262			−1.00737
$176$		0			0
$177$	−8.85410			−0.665515
$178$		0			0
$179$	0.0450850	+	0.0327561i	0.00336981	+	0.00244831i	0.589469	−	0.807791i	$-0.299337\pi$
$179$	0.0450850	+	0.0327561i	0.00336981	+	0.00244831i	−0.586099	+	0.810239i	$0.699337\pi$
$180$		0			0
$181$	−3.69098	+	11.3597i	−0.274349	+	0.844358i	0.715042	+	0.699081i	$0.246407\pi$
$181$	−3.69098	+	11.3597i	−0.274349	+	0.844358i	−0.989391	+	0.145277i	$0.953593\pi$
$182$		0			0
$183$	0.309017	−	0.224514i	0.0228432	−	0.0165966i
$184$		0			0
$185$	−7.26393	−	22.3561i	−0.534055	−	1.64365i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.30902	+	4.02874i	0.0952170	+	0.293048i
$190$		0			0
$191$	−7.80902	+	5.67358i	−0.565041	+	0.410526i	−0.833300	−	0.552821i	$-0.813551\pi$
$191$	−7.80902	+	5.67358i	−0.565041	+	0.410526i	0.268260	+	0.963347i	$0.413551\pi$
$192$		0			0
$193$	0.100813	−	0.310271i	0.00725668	−	0.0223338i	−0.947363	−	0.320163i	$-0.896262\pi$
$193$	0.100813	−	0.310271i	0.00725668	−	0.0223338i	0.954619	+	0.297829i	$0.0962625\pi$
$194$		0			0
$195$	4.07295	+	2.95917i	0.291670	+	0.211911i
$196$		0			0
$197$	17.0902			1.21762			0.608812	−	0.793314i	$-0.291646\pi$
$197$	17.0902			1.21762			0.608812	+	0.793314i	$0.291646\pi$
$198$		0			0
$199$	16.4164			1.16373			0.581864	−	0.813286i	$-0.302324\pi$
$199$	16.4164			1.16373			0.581864	+	0.813286i	$0.302324\pi$
$200$		0			0
$201$	−5.54508	−	4.02874i	−0.391120	−	0.284165i
$202$		0			0
$203$	−5.85410	+	18.0171i	−0.410877	+	1.26455i
$204$		0			0
$205$	1.21885	−	0.885544i	0.0851280	−	0.0618491i
$206$		0			0
$207$	1.30902	+	4.02874i	0.0909830	+	0.280017i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	7.33688	+	22.5806i	0.505092	+	1.55451i	0.800616	+	0.599177i	$0.204506\pi$
$211$	7.33688	+	22.5806i	0.505092	+	1.55451i	−0.295525	+	0.955335i	$0.595494\pi$
$212$		0			0
$213$	−2.92705	+	2.12663i	−0.200558	+	0.145714i
$214$		0			0
$215$	−0.465558	+	1.43284i	−0.0317508	+	0.0977189i
$216$		0			0
$217$	−29.5344	−	21.4580i	−2.00493	−	1.45667i
$218$		0			0
$219$	−1.23607			−0.0835257
$220$		0			0
$221$	−8.14590			−0.547952
$222$		0			0
$223$	−1.19098	−	0.865300i	−0.0797541	−	0.0579448i	0.547194	−	0.837006i	$-0.315696\pi$
$223$	−1.19098	−	0.865300i	−0.0797541	−	0.0579448i	−0.626948	+	0.779061i	$0.715696\pi$
$224$		0			0
$225$	0.972136	−	2.99193i	0.0648091	−	0.199462i
$226$		0			0
$227$	−0.572949	+	0.416272i	−0.0380280	+	0.0276289i	−0.606637	−	0.794979i	$-0.707482\pi$
$227$	−0.572949	+	0.416272i	−0.0380280	+	0.0276289i	0.568609	+	0.822608i	$0.307482\pi$
$228$		0			0
$229$	−2.14590	−	6.60440i	−0.141805	−	0.436431i	0.854781	−	0.518988i	$-0.173691\pi$
$229$	−2.14590	−	6.60440i	−0.141805	−	0.436431i	−0.996586	+	0.0825576i	$0.973691\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.97214	−	24.5357i	−0.522272	−	1.60739i	−0.769648	−	0.638468i	$-0.779568\pi$
$233$	−7.97214	−	24.5357i	−0.522272	−	1.60739i	0.247376	−	0.968920i	$-0.420432\pi$
$234$		0			0
$235$	−3.19098	+	2.31838i	−0.208157	+	0.151235i
$236$		0			0
$237$	3.01722	−	9.28605i	0.195990	−	0.603194i
$238$		0			0
$239$	−16.5902	−	12.0535i	−1.07313	−	0.779674i	−0.0966568	−	0.995318i	$-0.530815\pi$
$239$	−16.5902	−	12.0535i	−1.07313	−	0.779674i	−0.976472	+	0.215644i	$0.930815\pi$
$240$		0			0
$241$	10.2918			0.662953			0.331476	−	0.943463i	$-0.392453\pi$
$241$	10.2918			0.662953			0.331476	+	0.943463i	$0.392453\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−25.2705	−	18.3601i	−1.61447	−	1.17298i
$246$		0			0
$247$	−3.31966	+	10.2169i	−0.211225	+	0.650083i
$248$		0			0
$249$	−5.28115	+	3.83698i	−0.334679	+	0.243159i
$250$		0			0
$251$	3.98936	+	12.2780i	0.251806	+	0.774979i	0.994442	+	0.105284i	$0.0335752\pi$
$251$	3.98936	+	12.2780i	0.251806	+	0.774979i	−0.742636	+	0.669695i	$0.766425\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	4.07295	+	12.5352i	0.255058	+	0.784988i
$256$		0			0
$257$	−17.6353	+	12.8128i	−1.10006	+	0.799238i	−0.981069	−	0.193658i	$-0.937965\pi$
$257$	−17.6353	+	12.8128i	−1.10006	+	0.799238i	−0.118988	+	0.992896i	$0.537965\pi$
$258$		0			0
$259$	10.7812	−	33.1810i	0.669908	−	2.06177i
$260$		0			0
$261$	−3.61803	−	2.62866i	−0.223951	−	0.162710i
$262$		0			0
$263$	−17.1459			−1.05726			−0.528631	−	0.848852i	$-0.677294\pi$
$263$	−17.1459			−1.05726			−0.528631	+	0.848852i	$0.677294\pi$
$264$		0			0
$265$	−38.7082			−2.37783
$266$		0			0
$267$	0.809017	+	0.587785i	0.0495110	+	0.0359719i
$268$		0			0
$269$	6.03444	−	18.5721i	0.367926	−	1.13236i	−0.580202	−	0.814473i	$-0.697026\pi$
$269$	6.03444	−	18.5721i	0.367926	−	1.13236i	0.948128	−	0.317888i	$-0.102974\pi$
$270$		0			0
$271$	−18.2533	+	13.2618i	−1.10881	+	0.805596i	−0.982476	−	0.186392i	$-0.940321\pi$
$271$	−18.2533	+	13.2618i	−1.10881	+	0.805596i	−0.126333	+	0.991988i	$0.540321\pi$
$272$		0			0
$273$	2.30902	+	7.10642i	0.139748	+	0.430100i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.42705	+	16.7027i	0.326080	+	1.00357i	0.970951	+	0.239279i	$0.0769111\pi$
$277$	5.42705	+	16.7027i	0.326080	+	1.00357i	−0.644871	+	0.764292i	$0.723089\pi$
$278$		0			0
$279$	6.97214	−	5.06555i	0.417411	−	0.303267i
$280$		0			0
$281$	7.14590	−	21.9928i	0.426289	−	1.31198i	−0.475467	−	0.879734i	$-0.657721\pi$
$281$	7.14590	−	21.9928i	0.426289	−	1.31198i	0.901755	−	0.432247i	$-0.142279\pi$
$282$		0			0
$283$	15.1803	+	11.0292i	0.902378	+	0.655616i	0.939076	−	0.343711i	$-0.111684\pi$
$283$	15.1803	+	11.0292i	0.902378	+	0.655616i	−0.0366980	+	0.999326i	$0.511684\pi$
$284$		0			0
$285$	17.3820			1.02962
$286$		0			0
$287$	2.23607			0.131991
$288$		0			0
$289$	−3.50000	−	2.54290i	−0.205882	−	0.149582i
$290$		0			0
$291$	−1.88197	+	5.79210i	−0.110323	+	0.339539i
$292$		0			0
$293$	−4.04508	+	2.93893i	−0.236316	+	0.171694i	−0.699641	−	0.714495i	$-0.746657\pi$
$293$	−4.04508	+	2.93893i	−0.236316	+	0.171694i	0.463324	+	0.886189i	$0.346657\pi$
$294$		0			0
$295$	7.80902	+	24.0337i	0.454659	+	1.39930i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.30902	+	7.10642i	0.133534	+	0.410975i
$300$		0			0
$301$	−1.80902	+	1.31433i	−0.104270	+	0.0757566i
$302$		0			0
$303$	3.69098	−	11.3597i	0.212041	−	0.652596i
$304$		0			0
$305$	−0.881966	−	0.640786i	−0.0505012	−	0.0366913i
$306$		0			0
$307$	16.3262			0.931788			0.465894	−	0.884841i	$-0.345733\pi$
$307$	16.3262			0.931788			0.465894	+	0.884841i	$0.345733\pi$
$308$		0			0
$309$	−3.52786			−0.200693
$310$		0			0
$311$	5.51722	+	4.00850i	0.312853	+	0.227301i	0.733120	−	0.680100i	$-0.238064\pi$
$311$	5.51722	+	4.00850i	0.312853	+	0.227301i	−0.420267	+	0.907401i	$0.638064\pi$
$312$		0			0
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	−0.959410	−	0.282015i	$-0.908997\pi$
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	0.941943	+	0.335772i	$0.108997\pi$
$314$		0			0
$315$	9.78115	−	7.10642i	0.551106	−	0.400402i
$316$		0			0
$317$	5.39919	+	16.6170i	0.303249	+	0.933303i	0.980325	+	0.197390i	$0.0632466\pi$
$317$	5.39919	+	16.6170i	0.303249	+	0.933303i	−0.677076	+	0.735913i	$0.736753\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	4.78115	+	14.7149i	0.266858	+	0.821304i
$322$		0			0
$323$	−22.7533	+	16.5312i	−1.26603	+	0.919822i
$324$		0			0
$325$	1.71478	−	5.27756i	0.0951190	−	0.292746i
$326$		0			0
$327$	6.47214	+	4.70228i	0.357910	+	0.260037i
$328$		0			0
$329$	−5.85410			−0.322747
$330$		0			0
$331$	−5.94427			−0.326727			−0.163363	−	0.986566i	$-0.552234\pi$
$331$	−5.94427			−0.326727			−0.163363	+	0.986566i	$0.552234\pi$
$332$		0			0
$333$	6.66312	+	4.84104i	0.365137	+	0.265287i
$334$		0			0
$335$	−6.04508	+	18.6049i	−0.330278	+	1.01649i
$336$		0			0
$337$	25.5623	−	18.5721i	1.39247	−	1.01169i	0.396878	−	0.917871i	$-0.370094\pi$
$337$	25.5623	−	18.5721i	1.39247	−	1.01169i	0.995590	−	0.0938155i	$-0.0299064\pi$
$338$		0			0
$339$	−2.39919	−	7.38394i	−0.130306	−	0.401040i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−5.16312	−	15.8904i	−0.278782	−	0.858003i
$344$		0			0
$345$	9.78115	−	7.10642i	0.526600	−	0.382597i
$346$		0			0
$347$	2.47214	−	7.60845i	0.132711	−	0.408443i	−0.862516	−	0.506030i	$-0.831112\pi$
$347$	2.47214	−	7.60845i	0.132711	−	0.408443i	0.995227	+	0.0975871i	$0.0311124\pi$
$348$		0			0
$349$	−19.2254	−	13.9681i	−1.02911	−	0.747695i	−0.0609824	−	0.998139i	$-0.519423\pi$
$349$	−19.2254	−	13.9681i	−1.02911	−	0.747695i	−0.968131	+	0.250444i	$0.919423\pi$
$350$		0			0
$351$	−1.76393			−0.0941517
$352$		0			0
$353$	−1.52786			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$353$	−1.52786			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$354$		0			0
$355$	8.35410	+	6.06961i	0.443390	+	0.322141i
$356$		0			0
$357$	−6.04508	+	18.6049i	−0.319940	+	0.984674i
$358$		0			0
$359$	−15.1803	+	11.0292i	−0.801188	+	0.582097i	−0.911262	−	0.411826i	$-0.864891\pi$
$359$	−15.1803	+	11.0292i	−0.801188	+	0.582097i	0.110075	+	0.993923i	$0.464891\pi$
$360$		0			0
$361$	5.59017	+	17.2048i	0.294219	+	0.905514i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.09017	+	3.35520i	0.0570621	+	0.175619i
$366$		0			0
$367$	6.16312	−	4.47777i	0.321712	−	0.233738i	−0.415194	−	0.909733i	$-0.636286\pi$
$367$	6.16312	−	4.47777i	0.321712	−	0.233738i	0.736906	+	0.675996i	$0.236286\pi$
$368$		0			0
$369$	−0.163119	+	0.502029i	−0.00849163	+	0.0261346i
$370$		0			0
$371$	−46.4787	−	33.7688i	−2.41305	−	1.75319i
$372$		0			0
$373$	−3.94427			−0.204227			−0.102113	−	0.994773i	$-0.532560\pi$
$373$	−3.94427			−0.204227			−0.102113	+	0.994773i	$0.532560\pi$
$374$		0			0
$375$	5.29180			0.273267
$376$		0			0
$377$	−6.38197	−	4.63677i	−0.328688	−	0.238806i
$378$		0			0
$379$	0.218847	−	0.673542i	0.0112414	−	0.0345975i	−0.945278	−	0.326265i	$-0.894210\pi$
$379$	0.218847	−	0.673542i	0.0112414	−	0.0345975i	0.956520	+	0.291667i	$0.0942099\pi$
$380$		0			0
$381$	−1.85410	+	1.34708i	−0.0949885	+	0.0690132i
$382$		0			0
$383$	1.78115	+	5.48183i	0.0910127	+	0.280108i	0.986194	−	0.165594i	$-0.0529541\pi$
$383$	1.78115	+	5.48183i	0.0910127	+	0.280108i	−0.895181	+	0.445702i	$0.852954\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.163119	−	0.502029i	−0.00829180	−	0.0255195i
$388$		0			0
$389$	−3.97214	+	2.88593i	−0.201395	+	0.146322i	−0.683912	−	0.729565i	$-0.739723\pi$
$389$	−3.97214	+	2.88593i	−0.201395	+	0.146322i	0.482517	+	0.875887i	$0.339723\pi$
$390$		0			0
$391$	−6.04508	+	18.6049i	−0.305713	+	0.940888i
$392$		0			0
$393$	−9.35410	−	6.79615i	−0.471852	−	0.342821i
$394$		0			0
$395$	−27.8673			−1.40215
$396$		0			0
$397$	4.81966			0.241892			0.120946	−	0.992659i	$-0.461407\pi$
$397$	4.81966			0.241892			0.120946	+	0.992659i	$0.461407\pi$
$398$		0			0
$399$	20.8713	+	15.1639i	1.04487	+	0.759145i
$400$		0			0
$401$	1.19098	−	3.66547i	0.0594749	−	0.183045i	−0.916905	−	0.399105i	$-0.869321\pi$
$401$	1.19098	−	3.66547i	0.0594749	−	0.183045i	0.976380	+	0.216060i	$0.0693208\pi$
$402$		0			0
$403$	12.2984	−	8.93529i	0.612626	−	0.445099i
$404$		0			0
$405$	0.881966	+	2.71441i	0.0438252	+	0.134880i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	8.00000	+	24.6215i	0.395575	+	1.21745i	0.928513	+	0.371299i	$0.121088\pi$
$409$	8.00000	+	24.6215i	0.395575	+	1.21745i	−0.532939	+	0.846154i	$0.678912\pi$
$410$		0			0
$411$	−16.9894	+	12.3435i	−0.838023	+	0.608859i
$412$		0			0
$413$	−11.5902	+	35.6709i	−0.570315	+	1.75525i
$414$		0			0
$415$	15.0729	+	10.9511i	0.739902	+	0.537570i
$416$		0			0
$417$	−20.7984			−1.01850
$418$		0			0
$419$	11.1459			0.544513			0.272256	−	0.962225i	$-0.412230\pi$
$419$	11.1459			0.544513			0.272256	+	0.962225i	$0.412230\pi$
$420$		0			0
$421$	−19.6353	−	14.2658i	−0.956964	−	0.695275i	−0.00452016	−	0.999990i	$-0.501439\pi$
$421$	−19.6353	−	14.2658i	−0.956964	−	0.695275i	−0.952444	+	0.304715i	$0.901439\pi$
$422$		0			0
$423$	0.427051	−	1.31433i	0.0207639	−	0.0639048i
$424$		0			0
$425$	11.7533	−	8.53926i	0.570118	−	0.414215i
$426$		0			0
$427$	−0.500000	−	1.53884i	−0.0241967	−	0.0744698i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.718847	+	2.21238i	0.0346256	+	0.106567i	0.966876	−	0.255248i	$-0.0821572\pi$
$431$	0.718847	+	2.21238i	0.0346256	+	0.106567i	−0.932250	+	0.361815i	$0.882157\pi$
$432$		0			0
$433$	−2.38197	+	1.73060i	−0.114470	+	0.0831673i	−0.643547	−	0.765406i	$-0.722538\pi$
$433$	−2.38197	+	1.73060i	−0.114470	+	0.0831673i	0.529077	+	0.848574i	$0.322538\pi$
$434$		0			0
$435$	−3.94427	+	12.1392i	−0.189113	+	0.582031i
$436$		0			0
$437$	20.8713	+	15.1639i	0.998411	+	0.725388i
$438$		0			0
$439$	−25.3607			−1.21040			−0.605200	−	0.796074i	$-0.706907\pi$
$439$	−25.3607			−1.21040			−0.605200	+	0.796074i	$0.706907\pi$
$440$		0			0
$441$	10.9443			0.521156
$442$		0			0
$443$	17.9443	+	13.0373i	0.852558	+	0.619420i	0.925850	−	0.377891i	$-0.123351\pi$
$443$	17.9443	+	13.0373i	0.852558	+	0.619420i	−0.0732921	+	0.997311i	$0.523351\pi$
$444$		0			0
$445$	0.881966	−	2.71441i	0.0418092	−	0.128675i
$446$		0			0
$447$	−15.2812	+	11.1024i	−0.722774	+	0.525126i
$448$		0			0
$449$	−5.09017	−	15.6659i	−0.240220	−	0.739321i	−0.996386	−	0.0849412i	$-0.972930\pi$
$449$	−5.09017	−	15.6659i	−0.240220	−	0.739321i	0.756166	−	0.654380i	$-0.227070\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−1.38197	−	4.25325i	−0.0649304	−	0.199835i
$454$		0			0
$455$	17.2533	−	12.5352i	0.808847	−	0.587661i
$456$		0			0
$457$	−2.42705	+	7.46969i	−0.113533	+	0.349418i	−0.991638	−	0.129049i	$-0.958807\pi$
$457$	−2.42705	+	7.46969i	−0.113533	+	0.349418i	0.878105	+	0.478467i	$0.158807\pi$
$458$		0			0
$459$	−3.73607	−	2.71441i	−0.174385	−	0.126698i
$460$		0			0
$461$	0.562306			0.0261892			0.0130946	−	0.999914i	$-0.495832\pi$
$461$	0.562306			0.0261892			0.0130946	+	0.999914i	$0.495832\pi$
$462$		0			0
$463$	−30.2148			−1.40420			−0.702100	−	0.712078i	$-0.747754\pi$
$463$	−30.2148			−1.40420			−0.702100	+	0.712078i	$0.747754\pi$
$464$		0			0
$465$	−19.8992	−	14.4576i	−0.922803	−	0.670455i
$466$		0			0
$467$	−10.4549	+	32.1769i	−0.483796	+	1.48897i	0.349922	+	0.936779i	$0.386208\pi$
$467$	−10.4549	+	32.1769i	−0.483796	+	1.48897i	−0.833717	+	0.552191i	$0.813792\pi$
$468$		0			0
$469$	−23.4894	+	17.0660i	−1.08464	+	0.788035i
$470$		0			0
$471$	3.94427	+	12.1392i	0.181742	+	0.559346i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−5.92047	−	18.2213i	−0.271650	−	0.836053i
$476$		0			0
$477$	10.9721	−	7.97172i	0.502380	−	0.365000i
$478$		0			0
$479$	0.718847	−	2.21238i	0.0328450	−	0.101086i	−0.933290	−	0.359124i	$-0.883076\pi$
$479$	0.718847	−	2.21238i	0.0328450	−	0.101086i	0.966135	+	0.258037i	$0.0830757\pi$
$480$		0			0
$481$	11.7533	+	8.53926i	0.535904	+	0.389357i
$482$		0			0
$483$	17.9443			0.816493
$484$		0			0
$485$	17.3820			0.789274
$486$		0			0
$487$	14.4271	+	10.4819i	0.653752	+	0.474979i	0.864547	−	0.502552i	$-0.167605\pi$
$487$	14.4271	+	10.4819i	0.653752	+	0.474979i	−0.210795	+	0.977530i	$0.567605\pi$
$488$		0			0
$489$	−0.572949	+	1.76336i	−0.0259097	+	0.0797417i
$490$		0			0
$491$	−9.59017	+	6.96767i	−0.432798	+	0.314446i	−0.782767	−	0.622315i	$-0.786192\pi$
$491$	−9.59017	+	6.96767i	−0.432798	+	0.314446i	0.349969	+	0.936761i	$0.386192\pi$
$492$		0			0
$493$	−6.38197	−	19.6417i	−0.287429	−	0.884616i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.73607	+	14.5761i	0.212442	+	0.653828i
$498$		0			0
$499$	14.7812	−	10.7391i	0.661695	−	0.480750i	−0.205540	−	0.978649i	$-0.565895\pi$
$499$	14.7812	−	10.7391i	0.661695	−	0.480750i	0.867235	+	0.497899i	$0.165895\pi$
$500$		0			0
$501$	0.500000	−	1.53884i	0.0223384	−	0.0687504i
$502$		0			0
$503$	10.3262	+	7.50245i	0.460424	+	0.334518i	0.793698	−	0.608312i	$-0.208153\pi$
$503$	10.3262	+	7.50245i	0.460424	+	0.334518i	−0.333273	+	0.942830i	$0.608153\pi$
$504$		0			0
$505$	−34.0902			−1.51699
$506$		0			0
$507$	9.88854			0.439166
$508$		0			0
$509$	24.0623	+	17.4823i	1.06654	+	0.774889i	0.975288	−	0.220939i	$-0.0709121\pi$
$509$	24.0623	+	17.4823i	1.06654	+	0.774889i	0.0912553	+	0.995828i	$0.470912\pi$
$510$		0			0
$511$	−1.61803	+	4.97980i	−0.0715776	+	0.220293i
$512$		0			0
$513$	−4.92705	+	3.57971i	−0.217535	+	0.158048i
$514$		0			0
$515$	3.11146	+	9.57608i	0.137107	+	0.421972i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−4.50000	−	13.8496i	−0.197528	−	0.607929i
$520$		0			0
$521$	31.4164	−	22.8254i	1.37638	−	0.999997i	0.379170	−	0.925327i	$-0.376210\pi$
$521$	31.4164	−	22.8254i	1.37638	−	0.999997i	0.997208	−	0.0746698i	$-0.0237903\pi$
$522$		0			0
$523$	−0.864745	+	2.66141i	−0.0378127	+	0.116375i	−0.968181	−	0.250250i	$-0.919487\pi$
$523$	−0.864745	+	2.66141i	−0.0378127	+	0.116375i	0.930368	+	0.366626i	$0.119487\pi$
$524$		0			0
$525$	−10.7812	−	7.83297i	−0.470528	−	0.341859i
$526$		0			0
$527$	39.7984			1.73364
$528$		0			0
$529$	−5.05573			−0.219814
$530$		0			0
$531$	−7.16312	−	5.20431i	−0.310853	−	0.225848i
$532$		0			0
$533$	−0.287731	+	0.885544i	−0.0124630	+	0.0383572i
$534$		0			0
$535$	35.7254	−	25.9560i	1.54454	−	1.12218i
$536$		0			0
$537$	0.0172209	+	0.0530006i	0.000743138	+	0.00228714i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.88197	−	8.86978i	−0.123905	−	0.381342i	0.869795	−	0.493414i	$-0.164251\pi$
$541$	−2.88197	−	8.86978i	−0.123905	−	0.381342i	−0.993700	+	0.112072i	$0.964251\pi$
$542$		0			0
$543$	−9.66312	+	7.02067i	−0.414684	+	0.301286i
$544$		0			0
$545$	7.05573	−	21.7153i	0.302234	−	0.930181i
$546$		0			0
$547$	−1.88197	−	1.36733i	−0.0804671	−	0.0584627i	0.546824	−	0.837247i	$-0.315837\pi$
$547$	−1.88197	−	1.36733i	−0.0804671	−	0.0584627i	−0.627291	+	0.778785i	$0.715837\pi$
$548$		0			0
$549$	0.381966			0.0163019
$550$		0			0
$551$	−27.2361			−1.16030
$552$		0			0
$553$	−33.4615	−	24.3112i	−1.42293	−	1.03382i
$554$		0			0
$555$	7.26393	−	22.3561i	0.308337	−	0.948963i
$556$		0			0
$557$	−4.92705	+	3.57971i	−0.208766	+	0.151677i	−0.687255	−	0.726416i	$-0.741185\pi$
$557$	−4.92705	+	3.57971i	−0.208766	+	0.151677i	0.478489	+	0.878093i	$0.341185\pi$
$558$		0			0
$559$	−0.287731	−	0.885544i	−0.0121697	−	0.0374545i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.43363	−	25.9560i	−0.355435	−	1.09392i	−0.955757	−	0.294158i	$-0.904961\pi$
$563$	−8.43363	−	25.9560i	−0.355435	−	1.09392i	0.600322	−	0.799759i	$-0.295039\pi$
$564$		0			0
$565$	−17.9271	+	13.0248i	−0.754197	+	0.547956i
$566$		0			0
$567$	−1.30902	+	4.02874i	−0.0549735	+	0.169191i
$568$		0			0
$569$	36.5066	+	26.5236i	1.53044	+	1.11193i	0.955996	+	0.293379i	$0.0947798\pi$
$569$	36.5066	+	26.5236i	1.53044	+	1.11193i	0.574439	+	0.818547i	$0.305220\pi$
$570$		0			0
$571$	−8.67376			−0.362986			−0.181493	−	0.983392i	$-0.558093\pi$
$571$	−8.67376			−0.362986			−0.181493	+	0.983392i	$0.558093\pi$
$572$		0			0
$573$	−9.65248			−0.403238
$574$		0			0
$575$	−10.7812	−	7.83297i	−0.449605	−	0.326657i
$576$		0			0
$577$	7.65248	−	23.5519i	0.318577	−	0.980478i	−0.655680	−	0.755039i	$-0.727618\pi$
$577$	7.65248	−	23.5519i	0.318577	−	0.980478i	0.974257	−	0.225440i	$-0.0723819\pi$
$578$		0			0
$579$	0.263932	−	0.191758i	0.0109686	−	0.00796918i
$580$		0			0
$581$	8.54508	+	26.2991i	0.354510	+	1.09107i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.55573	+	4.78804i	0.0643214	+	0.197961i
$586$		0			0
$587$	−24.4615	+	17.7723i	−1.00963	+	0.733542i	−0.964132	−	0.265422i	$-0.914489\pi$
$587$	−24.4615	+	17.7723i	−1.00963	+	0.733542i	−0.0455016	+	0.998964i	$0.514489\pi$
$588$		0			0
$589$	16.2188	−	49.9165i	0.668286	−	2.05677i
$590$		0			0
$591$	13.8262	+	10.0453i	0.568735	+	0.413210i
$592$		0			0
$593$	36.4508			1.49686			0.748428	−	0.663215i	$-0.230809\pi$
$593$	36.4508			1.49686			0.748428	+	0.663215i	$0.230809\pi$
$594$		0			0
$595$	55.8328			2.28892
$596$		0			0
$597$	13.2812	+	9.64932i	0.543561	+	0.394920i
$598$		0			0
$599$	2.88854	−	8.89002i	0.118023	−	0.363237i	−0.874543	−	0.484948i	$-0.838838\pi$
$599$	2.88854	−	8.89002i	0.118023	−	0.363237i	0.992565	+	0.121712i	$0.0388384\pi$
$600$		0			0
$601$	1.66312	−	1.20833i	0.0678400	−	0.0492887i	−0.553348	−	0.832950i	$-0.686650\pi$
$601$	1.66312	−	1.20833i	0.0678400	−	0.0492887i	0.621188	+	0.783661i	$0.286650\pi$
$602$		0			0
$603$	−2.11803	−	6.51864i	−0.0862530	−	0.265459i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−7.51722	−	23.1356i	−0.305115	−	0.939046i	−0.979634	−	0.200789i	$-0.935649\pi$
$607$	−7.51722	−	23.1356i	−0.305115	−	0.939046i	0.674520	−	0.738257i	$-0.264351\pi$
$608$		0			0
$609$	−15.3262	+	11.1352i	−0.621051	+	0.451220i
$610$		0			0
$611$	0.753289	−	2.31838i	0.0304748	−	0.0937918i
$612$		0			0
$613$	−18.7082	−	13.5923i	−0.755617	−	0.548988i	0.141946	−	0.989874i	$-0.454664\pi$
$613$	−18.7082	−	13.5923i	−0.755617	−	0.548988i	−0.897563	+	0.440886i	$0.854664\pi$
$614$		0			0
$615$	1.50658			0.0607511
$616$		0			0
$617$	−7.00000			−0.281809			−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000			−0.281809			−0.140905	+	0.990023i	$0.545001\pi$
$618$		0			0
$619$	−1.19098	−	0.865300i	−0.0478696	−	0.0347793i	0.563593	−	0.826053i	$-0.309419\pi$
$619$	−1.19098	−	0.865300i	−0.0478696	−	0.0347793i	−0.611463	+	0.791273i	$0.709419\pi$
$620$		0			0
$621$	−1.30902	+	4.02874i	−0.0525290	+	0.161668i
$622$		0			0
$623$	3.42705	−	2.48990i	0.137302	−	0.0997557i
$624$		0			0
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	11.7533	+	36.1729i	0.468634	+	1.44231i
$630$		0			0
$631$	−33.3885	+	24.2582i	−1.32918	+	0.965704i	−0.329408	+	0.944188i	$0.606849\pi$
$631$	−33.3885	+	24.2582i	−1.32918	+	0.965704i	−0.999769	+	0.0215161i	$0.993151\pi$
$632$		0			0
$633$	−7.33688	+	22.5806i	−0.291615	+	0.897498i
$634$		0			0
$635$	5.29180	+	3.84471i	0.209999	+	0.152573i
$636$		0			0
$637$	19.3050			0.764890
$638$		0			0
$639$	−3.61803			−0.143127
$640$		0			0
$641$	17.7812	+	12.9188i	0.702313	+	0.510260i	0.880685	−	0.473703i	$-0.157083\pi$
$641$	17.7812	+	12.9188i	0.702313	+	0.510260i	−0.178371	+	0.983963i	$0.557083\pi$
$642$		0			0
$643$	9.01064	−	27.7319i	0.355345	−	1.09364i	−0.600464	−	0.799652i	$-0.705017\pi$
$643$	9.01064	−	27.7319i	0.355345	−	1.09364i	0.955809	−	0.293988i	$-0.0949826\pi$
$644$		0			0
$645$	−1.21885	+	0.885544i	−0.0479921	+	0.0348683i
$646$		0			0
$647$	−7.62868	−	23.4787i	−0.299914	−	0.923041i	−0.981526	−	0.191327i	$-0.938721\pi$
$647$	−7.62868	−	23.4787i	−0.299914	−	0.923041i	0.681612	−	0.731714i	$-0.261279\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−11.2812	−	34.7198i	−0.442143	−	1.36078i
$652$		0			0
$653$	22.5344	−	16.3722i	0.881841	−	0.640695i	−0.0518970	−	0.998652i	$-0.516527\pi$
$653$	22.5344	−	16.3722i	0.881841	−	0.640695i	0.933738	+	0.357958i	$0.116527\pi$
$654$		0			0
$655$	−10.1976	+	31.3849i	−0.398452	+	1.22631i
$656$		0			0
$657$	−1.00000	−	0.726543i	−0.0390137	−	0.0283451i
$658$		0			0
$659$	3.70820			0.144451			0.0722256	−	0.997388i	$-0.476990\pi$
$659$	3.70820			0.144451			0.0722256	+	0.997388i	$0.476990\pi$
$660$		0			0
$661$	2.32624			0.0904802			0.0452401	−	0.998976i	$-0.485595\pi$
$661$	2.32624			0.0904802			0.0452401	+	0.998976i	$0.485595\pi$
$662$		0			0
$663$	−6.59017	−	4.78804i	−0.255941	−	0.185952i
$664$		0			0
$665$	22.7533	−	70.0274i	0.882335	−	2.71555i
$666$		0			0
$667$	−15.3262	+	11.1352i	−0.593434	+	0.431155i
$668$		0			0
$669$	−0.454915	−	1.40008i	−0.0175880	−	0.0541304i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.19756	−	25.2295i	−0.315993	−	0.972526i	−0.975344	−	0.220691i	$-0.929169\pi$
$673$	−8.19756	−	25.2295i	−0.315993	−	0.972526i	0.659351	−	0.751835i	$-0.270831\pi$
$674$		0			0
$675$	2.54508	−	1.84911i	0.0979604	−	0.0711724i
$676$		0			0
$677$	2.00000	−	6.15537i	0.0768662	−	0.236570i	−0.905239	−	0.424903i	$-0.860308\pi$
$677$	2.00000	−	6.15537i	0.0768662	−	0.236570i	0.982105	+	0.188333i	$0.0603083\pi$
$678$		0			0
$679$	20.8713	+	15.1639i	0.800968	+	0.581937i
$680$		0			0
$681$	−0.708204			−0.0271384
$682$		0			0
$683$	−6.34752			−0.242881			−0.121441	−	0.992599i	$-0.538751\pi$
$683$	−6.34752			−0.242881			−0.121441	+	0.992599i	$0.538751\pi$
$684$		0			0
$685$	48.4894	+	35.2296i	1.85268	+	1.34605i
$686$		0			0
$687$	2.14590	−	6.60440i	0.0818711	−	0.251973i
$688$		0			0
$689$	19.3541	−	14.0616i	0.737333	−	0.535703i
$690$		0			0
$691$	−10.6738	−	32.8505i	−0.406049	−	1.24969i	−0.920016	−	0.391881i	$-0.871825\pi$
$691$	−10.6738	−	32.8505i	−0.406049	−	1.24969i	0.513967	−	0.857810i	$-0.328175\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	18.3435	+	56.4554i	0.695807	+	2.14147i
$696$		0			0
$697$	−1.97214	+	1.43284i	−0.0747000	+	0.0542727i
$698$		0			0
$699$	7.97214	−	24.5357i	0.301534	−	0.928026i
$700$		0			0
$701$	7.69098	+	5.58783i	0.290484	+	0.211049i	0.723478	−	0.690348i	$-0.242543\pi$
$701$	7.69098	+	5.58783i	0.290484	+	0.211049i	−0.432993	+	0.901397i	$0.642543\pi$
$702$		0			0
$703$	50.1591			1.89178
$704$		0			0
$705$	−3.94427			−0.148550
$706$		0			0
$707$	−40.9336	−	29.7400i	−1.53947	−	1.11849i
$708$		0			0
$709$	−7.95492	+	24.4827i	−0.298753	+	0.919468i	0.683182	+	0.730248i	$0.260596\pi$
$709$	−7.95492	+	24.4827i	−0.298753	+	0.919468i	−0.981935	+	0.189219i	$0.939404\pi$
$710$		0			0
$711$	7.89919	−	5.73910i	0.296243	−	0.215233i
$712$		0			0
$713$	−11.2812	−	34.7198i	−0.422482	−	1.30027i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.33688	−	19.5029i	−0.236655	−	0.728350i
$718$		0			0
$719$	31.6074	−	22.9641i	1.17876	−	0.856417i	0.186726	−	0.982412i	$-0.440212\pi$
$719$	31.6074	−	22.9641i	1.17876	−	0.856417i	0.992031	+	0.125995i	$0.0402124\pi$
$720$		0			0
$721$	−4.61803	+	14.2128i	−0.171985	+	0.529314i
$722$		0			0
$723$	8.32624	+	6.04937i	0.309656	+	0.224978i
$724$		0			0
$725$	14.0689			0.522505
$726$		0			0
$727$	−2.14590			−0.0795870			−0.0397935	−	0.999208i	$-0.512670\pi$
$727$	−2.14590			−0.0795870			−0.0397935	+	0.999208i	$0.512670\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	0.753289	−	2.31838i	0.0278614	−	0.0857486i
$732$		0			0
$733$	−18.2361	+	13.2493i	−0.673565	+	0.489373i	−0.871217	−	0.490899i	$-0.836668\pi$
$733$	−18.2361	+	13.2493i	−0.673565	+	0.489373i	0.197652	+	0.980272i	$0.436668\pi$
$734$		0			0
$735$	−9.65248	−	29.7073i	−0.356037	−	1.09577i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	10.8713	+	33.4585i	0.399908	+	1.23079i	0.925073	+	0.379790i	$0.124004\pi$
$739$	10.8713	+	33.4585i	0.399908	+	1.23079i	−0.525165	+	0.851001i	$0.675996\pi$
$740$		0			0
$741$	−8.69098	+	6.31437i	−0.319271	+	0.231964i
$742$		0			0
$743$	−0.781153	+	2.40414i	−0.0286577	+	0.0881994i	−0.964362	−	0.264585i	$-0.914765\pi$
$743$	−0.781153	+	2.40414i	−0.0286577	+	0.0881994i	0.935705	+	0.352784i	$0.114765\pi$
$744$		0			0
$745$	43.6140	+	31.6874i	1.59789	+	1.16094i
$746$		0			0
$747$	−6.52786			−0.238842
$748$		0			0
$749$	65.5410			2.39482
$750$		0			0
$751$	−29.6353	−	21.5313i	−1.08141	−	0.785687i	−0.103478	−	0.994632i	$-0.532997\pi$
$751$	−29.6353	−	21.5313i	−1.08141	−	0.785687i	−0.977928	+	0.208944i	$0.932997\pi$
$752$		0			0
$753$	−3.98936	+	12.2780i	−0.145380	+	0.447434i
$754$		0			0
$755$	−10.3262	+	7.50245i	−0.375810	+	0.273042i
$756$		0			0
$757$	5.07295	+	15.6129i	0.184379	+	0.567462i	0.999937	−	0.0112142i	$-0.00356966\pi$
$757$	5.07295	+	15.6129i	0.184379	+	0.567462i	−0.815558	+	0.578676i	$0.803570\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.8369	−	48.7409i	−0.574086	−	1.76686i	−0.639269	−	0.768983i	$-0.720763\pi$
$761$	−15.8369	−	48.7409i	−0.574086	−	1.76686i	0.0651825	−	0.997873i	$-0.479237\pi$
$762$		0			0
$763$	27.4164	−	19.9192i	0.992541	−	0.721123i
$764$		0			0
$765$	−4.07295	+	12.5352i	−0.147258	+	0.453213i
$766$		0			0
$767$	−12.6353	−	9.18005i	−0.456233	−	0.331472i
$768$		0			0
$769$	13.4377			0.484576			0.242288	−	0.970204i	$-0.422102\pi$
$769$	13.4377			0.484576			0.242288	+	0.970204i	$0.422102\pi$
$770$		0			0
$771$	−21.7984			−0.785049
$772$		0			0
$773$	12.4271	+	9.02878i	0.446970	+	0.324743i	0.788398	−	0.615165i	$-0.210911\pi$
$773$	12.4271	+	9.02878i	0.446970	+	0.324743i	−0.341428	+	0.939908i	$0.610911\pi$
$774$		0			0
$775$	−8.37790	+	25.7845i	−0.300943	+	0.926208i
$776$		0			0
$777$	28.2254	−	20.5070i	1.01258	−	0.735684i
$778$		0			0
$779$	0.993422	+	3.05744i	0.0355930	+	0.109544i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.38197	−	4.25325i	−0.0493874	−	0.151999i
$784$		0			0
$785$	29.4721	−	21.4128i	1.05191	−	0.764254i
$786$		0			0
$787$	−15.2148	+	46.8263i	−0.542348	+	1.66918i	0.184864	+	0.982764i	$0.440816\pi$
$787$	−15.2148	+	46.8263i	−0.542348	+	1.66918i	−0.727212	+	0.686413i	$0.759184\pi$
$788$		0			0
$789$	−13.8713	−	10.0781i	−0.493832	−	0.358790i
$790$		0			0
$791$	−32.8885			−1.16938
$792$		0			0
$793$	0.673762			0.0239260
$794$		0			0
$795$	−31.3156	−	22.7521i	−1.11065	−	0.806934i
$796$		0			0
$797$	8.34752	−	25.6910i	0.295684	−	0.910023i	−0.687306	−	0.726368i	$-0.741207\pi$
$797$	8.34752	−	25.6910i	0.295684	−	0.910023i	0.982991	−	0.183655i	$-0.0587931\pi$
$798$		0			0
$799$	5.16312	−	3.75123i	0.182658	−	0.132709i
$800$		0			0
$801$	0.309017	+	0.951057i	0.0109186	+	0.0336039i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−15.8262	−	48.7082i	−0.557802	−	1.71674i
$806$		0			0
$807$	15.7984	−	11.4782i	0.556129	−	0.404051i
$808$		0			0
$809$	−0.534442	+	1.64484i	−0.0187900	+	0.0578296i	−0.960012	−	0.279959i	$-0.909679\pi$
$809$	−0.534442	+	1.64484i	−0.0187900	+	0.0578296i	0.941222	+	0.337789i	$0.109679\pi$
$810$		0			0
$811$	−21.6803	−	15.7517i	−0.761300	−	0.553117i	0.138009	−	0.990431i	$-0.455930\pi$
$811$	−21.6803	−	15.7517i	−0.761300	−	0.553117i	−0.899309	+	0.437314i	$0.855930\pi$
$812$		0			0
$813$	−22.5623			−0.791295
$814$		0			0
$815$	5.29180			0.185364
$816$		0			0
$817$	−2.60081	−	1.88960i	−0.0909909	−	0.0661088i
$818$		0			0
$819$	−2.30902	+	7.10642i	−0.0806836	+	0.248319i
$820$		0			0
$821$	−14.0451	+	10.2044i	−0.490177	+	0.356134i	−0.805252	−	0.592932i	$-0.797970\pi$
$821$	−14.0451	+	10.2044i	−0.490177	+	0.356134i	0.315075	+	0.949067i	$0.397970\pi$
$822$		0			0
$823$	0.253289	+	0.779543i	0.00882910	+	0.0271732i	0.955374	−	0.295399i	$-0.0954525\pi$
$823$	0.253289	+	0.779543i	0.00882910	+	0.0271732i	−0.946545	+	0.322572i	$0.895453\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.270510	+	0.832544i	0.00940655	+	0.0289504i	0.955650	−	0.294506i	$-0.0951551\pi$
$827$	0.270510	+	0.832544i	0.00940655	+	0.0289504i	−0.946243	+	0.323456i	$0.895155\pi$
$828$		0			0
$829$	30.5344	−	22.1846i	1.06051	−	0.770502i	0.0863233	−	0.996267i	$-0.472488\pi$
$829$	30.5344	−	22.1846i	1.06051	−	0.770502i	0.974182	+	0.225765i	$0.0724882\pi$
$830$		0			0
$831$	−5.42705	+	16.7027i	−0.188262	+	0.579412i
$832$		0			0
$833$	40.8885	+	29.7073i	1.41670	+	1.02930i
$834$		0			0
$835$	−4.61803			−0.159814
$836$		0			0
$837$	8.61803			0.297883
$838$		0			0
$839$	12.8090	+	9.30630i	0.442216	+	0.321289i	0.786515	−	0.617571i	$-0.211883\pi$
$839$	12.8090	+	9.30630i	0.442216	+	0.321289i	−0.344299	+	0.938860i	$0.611883\pi$
$840$		0			0
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$		0			0
$843$	18.7082	−	13.5923i	0.644345	−	0.468144i
$844$		0			0
$845$	−8.72136	−	26.8416i	−0.300024	−	0.923379i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	5.79837	+	17.8456i	0.199000	+	0.612458i
$850$		0			0
$851$	28.2254	−	20.5070i	0.967555	−	0.702970i
$852$		0			0
$853$	−17.1074	+	52.6511i	−0.585746	+	1.80274i	0.0105082	+	0.999945i	$0.496655\pi$
$853$	−17.1074	+	52.6511i	−0.585746	+	1.80274i	−0.596254	+	0.802796i	$0.703345\pi$
$854$		0			0
$855$	14.0623	+	10.2169i	0.480921	+	0.349409i
$856$		0			0
$857$	−48.1935			−1.64626			−0.823129	−	0.567854i	$-0.807774\pi$
$857$	−48.1935			−1.64626			−0.823129	+	0.567854i	$0.807774\pi$
$858$		0			0
$859$	31.1803			1.06386			0.531930	−	0.846788i	$-0.321467\pi$
$859$	31.1803			1.06386			0.531930	+	0.846788i	$0.321467\pi$
$860$		0			0
$861$	1.80902	+	1.31433i	0.0616511	+	0.0447922i
$862$		0			0
$863$	9.38197	−	28.8747i	0.319366	−	0.982907i	−0.654554	−	0.756015i	$-0.727144\pi$
$863$	9.38197	−	28.8747i	0.319366	−	0.982907i	0.973920	−	0.226892i	$-0.0728564\pi$
$864$		0			0
$865$	−33.6246	+	24.4297i	−1.14327	+	0.830635i
$866$		0			0
$867$	−1.33688	−	4.11450i	−0.0454029	−	0.139736i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−3.73607	−	11.4984i	−0.126592	−	0.389610i
$872$		0			0
$873$	−4.92705	+	3.57971i	−0.166755	+	0.121155i
$874$		0			0
$875$	6.92705	−	21.3193i	0.234177	−	0.720723i
$876$		0			0
$877$	−28.2254	−	20.5070i	−0.953105	−	0.692471i	−0.00156570	−	0.999999i	$-0.500498\pi$
$877$	−28.2254	−	20.5070i	−0.953105	−	0.692471i	−0.951539	+	0.307528i	$0.900498\pi$
$878$		0			0
$879$	−5.00000			−0.168646
$880$		0			0
$881$	20.4377			0.688563			0.344282	−	0.938866i	$-0.388122\pi$
$881$	20.4377			0.688563			0.344282	+	0.938866i	$0.388122\pi$
$882$		0			0
$883$	2.38197	+	1.73060i	0.0801595	+	0.0582393i	0.627143	−	0.778904i	$-0.284224\pi$
$883$	2.38197	+	1.73060i	0.0801595	+	0.0582393i	−0.546984	+	0.837143i	$0.684224\pi$
$884$		0			0
$885$	−7.80902	+	24.0337i	−0.262497	+	0.807883i
$886$		0			0
$887$	−37.7877	+	27.4544i	−1.26879	+	0.921828i	−0.999154	−	0.0411345i	$-0.986903\pi$
$887$	−37.7877	+	27.4544i	−1.26879	+	0.921828i	−0.269634	+	0.962963i	$0.586903\pi$
$888$		0			0
$889$	3.00000	+	9.23305i	0.100617	+	0.309667i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.60081	−	8.00448i	−0.0870329	−	0.267860i
$894$		0			0
$895$	0.128677	−	0.0934894i	0.00430120	−	0.00312501i
$896$		0			0
$897$	−2.30902	+	7.10642i	−0.0770958	+	0.237277i
$898$		0			0
$899$	31.1803	+	22.6538i	1.03992	+	0.755548i
$900$		0			0
$901$	62.6312			2.08655
$902$		0			0
$903$	−2.23607			−0.0744117
$904$		0			0
$905$	27.5795	+	20.0377i	0.916774	+	0.666076i
$906$		0			0
$907$	12.3197	−	37.9160i	0.409068	−	1.25898i	−0.508383	−	0.861131i	$-0.669757\pi$
$907$	12.3197	−	37.9160i	0.409068	−	1.25898i	0.917451	−	0.397850i	$-0.130243\pi$
$908$		0			0
$909$	9.66312	−	7.02067i	0.320505	−	0.232861i
$910$		0			0
$911$	−12.8369	−	39.5079i	−0.425305	−	1.30895i	−0.902702	−	0.430266i	$-0.858420\pi$
$911$	−12.8369	−	39.5079i	−0.425305	−	1.30895i	0.477397	−	0.878688i	$-0.341580\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.336881	−	1.03681i	−0.0111369	−	0.0342760i
$916$		0			0
$917$	−39.6246	+	28.7890i	−1.30852	+	0.950695i
$918$		0			0
$919$	−11.6910	+	35.9811i	−0.385650	+	1.18691i	0.550358	+	0.834929i	$0.314491\pi$
$919$	−11.6910	+	35.9811i	−0.385650	+	1.18691i	−0.936008	+	0.351980i	$0.885509\pi$
$920$		0			0
$921$	13.2082	+	9.59632i	0.435225	+	0.316210i
$922$		0			0
$923$	−6.38197			−0.210065
$924$		0			0
$925$	−25.9098			−0.851910
$926$		0			0
$927$	−2.85410	−	2.07363i	−0.0937410	−	0.0681068i
$928$		0			0
$929$	14.3435	−	44.1446i	0.470594	−	1.44834i	−0.381216	−	0.924486i	$-0.624494\pi$
$929$	14.3435	−	44.1446i	0.470594	−	1.44834i	0.851809	−	0.523852i	$-0.175506\pi$
$930$		0			0
$931$	53.9230	−	39.1773i	1.76725	−	1.28399i
$932$		0			0
$933$	2.10739	+	6.48588i	0.0689929	+	0.212338i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−7.48936	−	23.0499i	−0.244667	−	0.753006i	−0.995691	−	0.0927321i	$-0.970440\pi$
$937$	−7.48936	−	23.0499i	−0.244667	−	0.753006i	0.751024	−	0.660274i	$-0.229560\pi$
$938$		0			0
$939$	−0.809017	+	0.587785i	−0.0264013	+	0.0191816i
$940$		0			0
$941$	−5.42705	+	16.7027i	−0.176917	+	0.544494i	−0.999716	−	0.0238385i	$-0.992411\pi$
$941$	−5.42705	+	16.7027i	−0.176917	+	0.544494i	0.822799	+	0.568332i	$0.192411\pi$
$942$		0			0
$943$	1.80902	+	1.31433i	0.0589097	+	0.0428004i
$944$		0			0
$945$	12.0902			0.393293
$946$		0			0
$947$	21.7984			0.708352			0.354176	−	0.935179i	$-0.384761\pi$
$947$	21.7984			0.708352			0.354176	+	0.935179i	$0.384761\pi$
$948$		0			0
$949$	−1.76393	−	1.28157i	−0.0572597	−	0.0416016i
$950$		0			0
$951$	−5.39919	+	16.6170i	−0.175081	+	0.538843i
$952$		0			0
$953$	31.7426	−	23.0624i	1.02825	−	0.747064i	0.0602885	−	0.998181i	$-0.480798\pi$
$953$	31.7426	−	23.0624i	1.02825	−	0.747064i	0.967957	+	0.251117i	$0.0807979\pi$
$954$		0			0
$955$	8.51316	+	26.2008i	0.275479	+	0.847838i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.4894	+	84.6035i	0.887678	+	2.73199i
$960$		0			0
$961$	−35.0066	+	25.4338i	−1.12924	+	0.820444i
$962$		0			0
$963$	−4.78115	+	14.7149i	−0.154071	+	0.474180i
$964$		0			0
$965$	−0.753289	−	0.547296i	−0.0242492	−	0.0176181i
$966$		0			0
$967$	−48.2705			−1.55227			−0.776137	−	0.630564i	$-0.782824\pi$
$967$	−48.2705			−1.55227			−0.776137	+	0.630564i	$0.782824\pi$
$968$		0			0
$969$	−28.1246			−0.903493
$970$		0			0
$971$	34.2705	+	24.8990i	1.09979	+	0.799046i	0.981026	−	0.193876i	$-0.0621059\pi$
$971$	34.2705	+	24.8990i	1.09979	+	0.799046i	0.118767	+	0.992922i	$0.462106\pi$
$972$		0			0
$973$	−27.2254	+	83.7912i	−0.872807	+	2.68622i
$974$		0			0
$975$	4.48936	−	3.26171i	0.143774	−	0.104458i
$976$		0			0
$977$	0.892609	+	2.74717i	0.0285571	+	0.0878897i	0.964319	−	0.264742i	$-0.0852868\pi$
$977$	0.892609	+	2.74717i	0.0285571	+	0.0878897i	−0.935762	+	0.352632i	$0.885287\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	2.47214	+	7.60845i	0.0789292	+	0.242919i
$982$		0			0
$983$	−13.6180	+	9.89408i	−0.434348	+	0.315572i	−0.783385	−	0.621537i	$-0.786509\pi$
$983$	−13.6180	+	9.89408i	−0.434348	+	0.315572i	0.349037	+	0.937109i	$0.386509\pi$
$984$		0			0
$985$	15.0729	−	46.3898i	0.480264	−	1.47810i
$986$		0			0
$987$	−4.73607	−	3.44095i	−0.150751	−	0.109527i
$988$		0			0
$989$	−2.23607			−0.0711028
$990$		0			0
$991$	9.72949			0.309067			0.154534	−	0.987988i	$-0.450612\pi$
$991$	9.72949			0.309067			0.154534	+	0.987988i	$0.450612\pi$
$992$		0			0
$993$	−4.80902	−	3.49396i	−0.152610	−	0.110877i
$994$		0			0
$995$	14.4787	−	44.5609i	0.459006	−	1.41268i
$996$		0			0
$997$	−3.45492	+	2.51014i	−0.109418	+	0.0794970i	−0.641149	−	0.767417i	$-0.721542\pi$
$997$	−3.45492	+	2.51014i	−0.109418	+	0.0794970i	0.531731	+	0.846914i	$0.321542\pi$
$998$		0			0
$999$	2.54508	+	7.83297i	0.0805229	+	0.247824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.p.1237.1		4
11.2	odd	10		1452.2.i.o.493.1		4
11.3	even	5		1452.2.a.i.1.2		2
11.4	even	5		1452.2.i.j.1213.1		4
11.5	even	5		1452.2.i.j.565.1		4
11.6	odd	10		132.2.i.b.37.1	yes	4
11.7	odd	10		132.2.i.b.25.1	✓	4
11.8	odd	10		1452.2.a.j.1.2		2
11.9	even	5	inner	1452.2.i.p.493.1		4
11.10	odd	2		1452.2.i.o.1237.1		4
33.8	even	10		4356.2.a.v.1.1		2
33.14	odd	10		4356.2.a.s.1.1		2
33.17	even	10		396.2.j.c.37.1		4
33.29	even	10		396.2.j.c.289.1		4
44.3	odd	10		5808.2.a.cf.1.2		2
44.7	even	10		528.2.y.a.289.1		4
44.19	even	10		5808.2.a.cc.1.2		2
44.39	even	10		528.2.y.a.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.b.25.1	✓	4	11.7	odd	10
132.2.i.b.37.1	yes	4	11.6	odd	10
396.2.j.c.37.1		4	33.17	even	10
396.2.j.c.289.1		4	33.29	even	10
528.2.y.a.289.1		4	44.7	even	10
528.2.y.a.433.1		4	44.39	even	10
1452.2.a.i.1.2		2	11.3	even	5
1452.2.a.j.1.2		2	11.8	odd	10
1452.2.i.j.565.1		4	11.5	even	5
1452.2.i.j.1213.1		4	11.4	even	5
1452.2.i.o.493.1		4	11.2	odd	10
1452.2.i.o.1237.1		4	11.10	odd	2
1452.2.i.p.493.1		4	11.9	even	5	inner
1452.2.i.p.1237.1		4	1.1	even	1	trivial
4356.2.a.s.1.1		2	33.14	odd	10
4356.2.a.v.1.1		2	33.8	even	10
5808.2.a.cc.1.2		2	44.19	even	10
5808.2.a.cf.1.2		2	44.3	odd	10

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:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(0.881966 - 2.71441i) q^{5} +(3.42705 - 2.48990i) q^{7} +(0.309017 + 0.951057i) q^{9} +(0.545085 + 1.67760i) q^{13} +(2.30902 - 1.67760i) q^{15} +(-1.42705 + 4.39201i) q^{17} +(4.92705 + 3.57971i) q^{19} +4.23607 q^{21} +4.23607 q^{23} +(-2.54508 - 1.84911i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-3.61803 + 2.62866i) q^{29} +(-2.66312 - 8.19624i) q^{31} +(-3.73607 - 11.4984i) q^{35} +(6.66312 - 4.84104i) q^{37} +(-0.545085 + 1.67760i) q^{39} +(0.427051 + 0.310271i) q^{41} -0.527864 q^{43} +2.85410 q^{45} +(-1.11803 - 0.812299i) q^{47} +(3.38197 - 10.4086i) q^{49} +(-3.73607 + 2.71441i) q^{51} +(-4.19098 - 12.8985i) q^{53} +(1.88197 + 5.79210i) q^{57} +(-7.16312 + 5.20431i) q^{59} +(0.118034 - 0.363271i) q^{61} +(3.42705 + 2.48990i) q^{63} +5.03444 q^{65} -6.85410 q^{67} +(3.42705 + 2.48990i) q^{69} +(-1.11803 + 3.44095i) q^{71} +(-1.00000 + 0.726543i) q^{73} +(-0.972136 - 2.99193i) q^{75} +(-3.01722 - 9.28605i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.01722 + 6.20837i) q^{83} +(10.6631 + 7.74721i) q^{85} -4.47214 q^{87} +1.00000 q^{89} +(6.04508 + 4.39201i) q^{91} +(2.66312 - 8.19624i) q^{93} +(14.0623 - 10.2169i) q^{95} +(1.88197 + 5.79210i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 8 q^{5} + 7 q^{7} - q^{9} - 9 q^{13} + 7 q^{15} + q^{17} + 13 q^{19} + 8 q^{21} + 8 q^{23} + q^{25} + q^{27} - 10 q^{29} + 5 q^{31} - 6 q^{35} + 11 q^{37} + 9 q^{39} - 5 q^{41} - 20 q^{43}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q + q^3 + 8 * q^5 + 7 * q^7 - q^9 - 9 * q^13 + 7 * q^15 + q^17 + 13 * q^19 + 8 * q^21 + 8 * q^23 + q^25 + q^27 - 10 * q^29 + 5 * q^31 - 6 * q^35 + 11 * q^37 + 9 * q^39 - 5 * q^41 - 20 * q^43 - 2 * q^45 + 18 * q^49 - 6 * q^51 - 19 * q^53 + 12 * q^57 - 13 * q^59 - 4 * q^61 + 7 * q^63 - 38 * q^65 - 14 * q^67 + 7 * q^69 - 4 * q^73 + 14 * q^75 + 17 * q^79 - q^81 + 21 * q^83 + 27 * q^85 + 4 * q^89 + 13 * q^91 - 5 * q^93 + 16 * q^95 + 12 * q^97

Introduction

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