LMFDB - Embedded newform 1620.2.e.b.971.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.13
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04383 - 0.954154i) q^{2} +(0.179181 + 1.99196i) q^{4} +1.00000i q^{5} +0.851747i q^{7} +(1.71360 - 2.25024i) q^{8} +O(q^{10})$	\(q+(-1.04383 - 0.954154i) q^{2} +(0.179181 + 1.99196i) q^{4} +1.00000i q^{5} +0.851747i q^{7} +(1.71360 - 2.25024i) q^{8} +(0.954154 - 1.04383i) q^{10} -1.56992 q^{11} +4.53169 q^{13} +(0.812698 - 0.889083i) q^{14} +(-3.93579 + 0.713842i) q^{16} +4.69106i q^{17} +7.37999i q^{19} +(-1.99196 + 0.179181i) q^{20} +(1.63873 + 1.49794i) q^{22} -5.72216 q^{23} -1.00000 q^{25} +(-4.73033 - 4.32393i) q^{26} +(-1.69664 + 0.152617i) q^{28} -7.57168i q^{29} -2.98739i q^{31} +(4.78943 + 3.01021i) q^{32} +(4.47599 - 4.89669i) q^{34} -0.851747 q^{35} -3.39705 q^{37} +(7.04165 - 7.70349i) q^{38} +(2.25024 + 1.71360i) q^{40} -3.99519i q^{41} +6.88087i q^{43} +(-0.281299 - 3.12721i) q^{44} +(5.97298 + 5.45982i) q^{46} +0.279010 q^{47} +6.27453 q^{49} +(1.04383 + 0.954154i) q^{50} +(0.811993 + 9.02693i) q^{52} +0.417914i q^{53} -1.56992i q^{55} +(1.91664 + 1.45955i) q^{56} +(-7.22455 + 7.90359i) q^{58} -4.87952 q^{59} -8.33373 q^{61} +(-2.85043 + 3.11834i) q^{62} +(-2.12716 - 7.71202i) q^{64} +4.53169i q^{65} +6.24776i q^{67} +(-9.34439 + 0.840549i) q^{68} +(0.889083 + 0.812698i) q^{70} +3.43839 q^{71} -12.2419 q^{73} +(3.54596 + 3.24131i) q^{74} +(-14.7006 + 1.32236i) q^{76} -1.33717i q^{77} +5.63456i q^{79} +(-0.713842 - 3.93579i) q^{80} +(-3.81203 + 4.17032i) q^{82} -15.1126 q^{83} -4.69106 q^{85} +(6.56540 - 7.18249i) q^{86} +(-2.69021 + 3.53269i) q^{88} +8.75330i q^{89} +3.85985i q^{91} +(-1.02530 - 11.3983i) q^{92} +(-0.291240 - 0.266218i) q^{94} -7.37999 q^{95} +12.9201 q^{97} +(-6.54957 - 5.98686i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.04383	−	0.954154i	−0.738102	−	0.674689i
$2$	−1.04383	−	0.954154i	−0.738102	−	0.674689i
$3$		0			0
$3$		0			0
$4$	0.179181	+	1.99196i	0.0895906	+	0.995979i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			0.851747i			0.321930i	0.986960	+	0.160965i	$0.0514607\pi$
$7$			0.851747i			0.321930i	−0.986960	+	0.160965i	$0.948539\pi$
$8$	1.71360	−	2.25024i	0.605848	−	0.795580i
$9$		0			0
$10$	0.954154	−	1.04383i	0.301730	−	0.330089i
$11$	−1.56992			−0.473348			−0.236674	−	0.971589i	$-0.576057\pi$
$11$	−1.56992			−0.473348			−0.236674	+	0.971589i	$0.576057\pi$
$12$		0			0
$13$	4.53169			1.25686			0.628432	−	0.777865i	$-0.283697\pi$
$13$	4.53169			1.25686			0.628432	+	0.777865i	$0.283697\pi$
$14$	0.812698	−	0.889083i	0.217203	−	0.237617i
$15$		0			0
$16$	−3.93579	+	0.713842i	−0.983947	+	0.178461i
$17$			4.69106i			1.13775i	0.822424	+	0.568875i	$0.192621\pi$
$17$			4.69106i			1.13775i	−0.822424	+	0.568875i	$0.807379\pi$
$18$		0			0
$19$			7.37999i			1.69309i	0.532320	+	0.846543i	$0.321320\pi$
$19$			7.37999i			1.69309i	−0.532320	+	0.846543i	$0.678680\pi$
$20$	−1.99196	+	0.179181i	−0.445415	+	0.0400661i
$21$		0			0
$22$	1.63873	+	1.49794i	0.349379	+	0.319362i
$23$	−5.72216			−1.19315			−0.596576	−	0.802557i	$-0.703473\pi$
$23$	−5.72216			−1.19315			−0.596576	+	0.802557i	$0.703473\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−4.73033	−	4.32393i	−0.927694	−	0.847992i
$27$		0			0
$28$	−1.69664	+	0.152617i	−0.320636	+	0.0288419i
$29$		−	7.57168i		−	1.40603i	−0.711177	−	0.703013i	$-0.751837\pi$
$29$		−	7.57168i		−	1.40603i	0.711177	−	0.703013i	$-0.248163\pi$
$30$		0			0
$31$		−	2.98739i		−	0.536550i	−0.963342	−	0.268275i	$-0.913546\pi$
$31$		−	2.98739i		−	0.536550i	0.963342	−	0.268275i	$-0.0864536\pi$
$32$	4.78943	+	3.01021i	0.846659	+	0.532136i
$33$		0			0
$34$	4.47599	−	4.89669i	0.767627	−	0.839776i
$35$	−0.851747			−0.143972
$36$		0			0
$37$	−3.39705			−0.558471			−0.279236	−	0.960223i	$-0.590081\pi$
$37$	−3.39705			−0.558471			−0.279236	+	0.960223i	$0.590081\pi$
$38$	7.04165	−	7.70349i	1.14231	−	1.24967i
$39$		0			0
$40$	2.25024	+	1.71360i	0.355794	+	0.270944i
$41$		−	3.99519i		−	0.623945i	−0.950091	−	0.311972i	$-0.899010\pi$
$41$		−	3.99519i		−	0.623945i	0.950091	−	0.311972i	$-0.100990\pi$
$42$		0			0
$43$			6.88087i			1.04932i	0.851311	+	0.524661i	$0.175808\pi$
$43$			6.88087i			1.04932i	−0.851311	+	0.524661i	$0.824192\pi$
$44$	−0.281299	−	3.12721i	−0.0424075	−	0.471444i
$45$		0			0
$46$	5.97298	+	5.45982i	0.880668	+	0.805006i
$47$	0.279010			0.0406978			0.0203489	−	0.999793i	$-0.493522\pi$
$47$	0.279010			0.0406978			0.0203489	+	0.999793i	$0.493522\pi$
$48$		0			0
$49$	6.27453			0.896361
$50$	1.04383	+	0.954154i	0.147620	+	0.134938i
$51$		0			0
$52$	0.811993	+	9.02693i	0.112603	+	1.25181i
$53$			0.417914i			0.0574049i	0.999588	+	0.0287025i	$0.00913754\pi$
$53$			0.417914i			0.0574049i	−0.999588	+	0.0287025i	$0.990862\pi$
$54$		0			0
$55$		−	1.56992i		−	0.211688i
$56$	1.91664	+	1.45955i	0.256121	+	0.195041i
$57$		0			0
$58$	−7.22455	+	7.90359i	−0.948630	+	1.03779i
$59$	−4.87952			−0.635259			−0.317630	−	0.948215i	$-0.602887\pi$
$59$	−4.87952			−0.635259			−0.317630	+	0.948215i	$0.602887\pi$
$60$		0			0
$61$	−8.33373			−1.06702			−0.533512	−	0.845792i	$-0.679128\pi$
$61$	−8.33373			−1.06702			−0.533512	+	0.845792i	$0.679128\pi$
$62$	−2.85043	+	3.11834i	−0.362004	+	0.396029i
$63$		0			0
$64$	−2.12716	−	7.71202i	−0.265895	−	0.964002i
$65$			4.53169i			0.562087i
$66$		0			0
$67$			6.24776i			0.763285i	0.924310	+	0.381642i	$0.124641\pi$
$67$			6.24776i			0.763285i	−0.924310	+	0.381642i	$0.875359\pi$
$68$	−9.34439	+	0.840549i	−1.13317	+	0.101932i
$69$		0			0
$70$	0.889083	+	0.812698i	0.106266	+	0.0971360i
$71$	3.43839			0.408062			0.204031	−	0.978964i	$-0.434596\pi$
$71$	3.43839			0.408062			0.204031	+	0.978964i	$0.434596\pi$
$72$		0			0
$73$	−12.2419			−1.43281			−0.716404	−	0.697686i	$-0.754213\pi$
$73$	−12.2419			−1.43281			−0.716404	+	0.697686i	$0.754213\pi$
$74$	3.54596	+	3.24131i	0.412209	+	0.376794i
$75$		0			0
$76$	−14.7006	+	1.32236i	−1.68628	+	0.151685i
$77$		−	1.33717i		−	0.152385i
$78$		0			0
$79$			5.63456i			0.633937i	0.948436	+	0.316969i	$0.102665\pi$
$79$			5.63456i			0.633937i	−0.948436	+	0.316969i	$0.897335\pi$
$80$	−0.713842	−	3.93579i	−0.0798100	−	0.440035i
$81$		0			0
$82$	−3.81203	+	4.17032i	−0.420968	+	0.460535i
$83$	−15.1126			−1.65882			−0.829412	−	0.558637i	$-0.811324\pi$
$83$	−15.1126			−1.65882			−0.829412	+	0.558637i	$0.811324\pi$
$84$		0			0
$85$	−4.69106			−0.508817
$86$	6.56540	−	7.18249i	0.707966	−	0.774507i
$87$		0			0
$88$	−2.69021	+	3.53269i	−0.286777	+	0.376586i
$89$			8.75330i			0.927848i	0.885875	+	0.463924i	$0.153559\pi$
$89$			8.75330i			0.927848i	−0.885875	+	0.463924i	$0.846441\pi$
$90$		0			0
$91$			3.85985i			0.404622i
$92$	−1.02530	−	11.3983i	−0.106895	−	1.18835i
$93$		0			0
$94$	−0.291240	−	0.266218i	−0.0300391	−	0.0274583i
$95$	−7.37999			−0.757171
$96$		0			0
$97$	12.9201			1.31184			0.655919	−	0.754831i	$-0.272281\pi$
$97$	12.9201			1.31184			0.655919	+	0.754831i	$0.272281\pi$
$98$	−6.54957	−	5.98686i	−0.661606	−	0.604765i
$99$		0			0
$100$	−0.179181	−	1.99196i	−0.0179181	−	0.199196i
$101$			18.2209i			1.81305i	0.422150	+	0.906526i	$0.361275\pi$
$101$			18.2209i			1.81305i	−0.422150	+	0.906526i	$0.638725\pi$
$102$		0			0
$103$			12.1980i			1.20191i	0.799284	+	0.600953i	$0.205212\pi$
$103$			12.1980i			1.20191i	−0.799284	+	0.600953i	$0.794788\pi$
$104$	7.76549	−	10.1974i	0.761469	−	0.999936i
$105$		0			0
$106$	0.398755	−	0.436233i	0.0387305	−	0.0423707i
$107$	−7.16752			−0.692910			−0.346455	−	0.938067i	$-0.612615\pi$
$107$	−7.16752			−0.692910			−0.346455	+	0.938067i	$0.612615\pi$
$108$		0			0
$109$	7.50605			0.718949			0.359475	−	0.933155i	$-0.382956\pi$
$109$	7.50605			0.718949			0.359475	+	0.933155i	$0.382956\pi$
$110$	−1.49794	+	1.63873i	−0.142823	+	0.156247i
$111$		0			0
$112$	−0.608013	−	3.35230i	−0.0574518	−	0.316762i
$113$			2.23453i			0.210207i	0.994461	+	0.105103i	$0.0335174\pi$
$113$			2.23453i			0.210207i	−0.994461	+	0.105103i	$0.966483\pi$
$114$		0			0
$115$		−	5.72216i		−	0.533594i
$116$	15.0825	−	1.35670i	1.40037	−	0.125967i
$117$		0			0
$118$	5.09341	+	4.65581i	0.468886	+	0.428602i
$119$	−3.99560			−0.366276
$120$		0			0
$121$	−8.53536			−0.775942
$122$	8.69904	+	7.95166i	0.787574	+	0.719909i
$123$		0			0
$124$	5.95074	−	0.535283i	0.534393	−	0.0480698i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			4.18101i			0.371005i	0.982644	+	0.185502i	$0.0593913\pi$
$127$			4.18101i			0.371005i	−0.982644	+	0.185502i	$0.940609\pi$
$128$	−5.13804	+	10.0797i	−0.454143	+	0.890929i
$129$		0			0
$130$	4.32393	−	4.73033i	0.379233	−	0.414878i
$131$	13.0156			1.13718			0.568591	−	0.822621i	$-0.307489\pi$
$131$	13.0156			1.13718			0.568591	+	0.822621i	$0.307489\pi$
$132$		0			0
$133$	−6.28589			−0.545056
$134$	5.96132	−	6.52162i	0.514980	−	0.563382i
$135$		0			0
$136$	10.5560	+	8.03859i	0.905171	+	0.689304i
$137$			14.3255i			1.22391i	0.790893	+	0.611955i	$0.209616\pi$
$137$			14.3255i			1.22391i	−0.790893	+	0.611955i	$0.790384\pi$
$138$		0			0
$139$		−	19.3112i		−	1.63796i	−0.573823	−	0.818979i	$-0.694540\pi$
$139$		−	19.3112i		−	1.63796i	0.573823	−	0.818979i	$-0.305460\pi$
$140$	−0.152617	−	1.69664i	−0.0128985	−	0.143393i
$141$		0			0
$142$	−3.58911	−	3.28075i	−0.301192	−	0.275315i
$143$	−7.11437			−0.594934
$144$		0			0
$145$	7.57168			0.628794
$146$	12.7785	+	11.6807i	1.05756	+	0.966699i
$147$		0			0
$148$	−0.608687	−	6.76678i	−0.0500338	−	0.556226i
$149$			16.8735i			1.38233i	0.722697	+	0.691165i	$0.242902\pi$
$149$			16.8735i			1.38233i	−0.722697	+	0.691165i	$0.757098\pi$
$150$		0			0
$151$		−	1.36231i		−	0.110863i	−0.998462	−	0.0554317i	$-0.982346\pi$
$151$		−	1.36231i		−	0.110863i	0.998462	−	0.0554317i	$-0.0176535\pi$
$152$	16.6068	+	12.6463i	1.34699	+	1.02575i
$153$		0			0
$154$	−1.27587	+	1.39579i	−0.102812	+	0.112476i
$155$	2.98739			0.239953
$156$		0			0
$157$	−9.94254			−0.793501			−0.396750	−	0.917927i	$-0.629862\pi$
$157$	−9.94254			−0.793501			−0.396750	+	0.917927i	$0.629862\pi$
$158$	5.37623	−	5.88155i	0.427710	−	0.467911i
$159$		0			0
$160$	−3.01021	+	4.78943i	−0.237978	+	0.378637i
$161$		−	4.87383i		−	0.384112i
$162$		0			0
$163$			4.30812i			0.337438i	0.985664	+	0.168719i	$0.0539631\pi$
$163$			4.30812i			0.337438i	−0.985664	+	0.168719i	$0.946037\pi$
$164$	7.95826	−	0.715863i	0.621435	−	0.0558995i
$165$		0			0
$166$	15.7751	+	14.4198i	1.22438	+	1.11919i
$167$	−18.3963			−1.42355			−0.711776	−	0.702407i	$-0.752109\pi$
$167$	−18.3963			−1.42355			−0.711776	+	0.702407i	$0.752109\pi$
$168$		0			0
$169$	7.53619			0.579707
$170$	4.89669	+	4.47599i	0.375559	+	0.343293i
$171$		0			0
$172$	−13.7064	+	1.23292i	−1.04510	+	0.0940094i
$173$		−	2.97748i		−	0.226374i	−0.993574	−	0.113187i	$-0.963894\pi$
$173$		−	2.97748i		−	0.226374i	0.993574	−	0.113187i	$-0.0361059\pi$
$174$		0			0
$175$		−	0.851747i		−	0.0643860i
$176$	6.17886	−	1.12067i	0.465749	−	0.0844739i
$177$		0			0
$178$	8.35199	−	9.13699i	0.626008	−	0.684847i
$179$	−4.23878			−0.316821			−0.158411	−	0.987373i	$-0.550637\pi$
$179$	−4.23878			−0.316821			−0.158411	+	0.987373i	$0.550637\pi$
$180$		0			0
$181$	7.13624			0.530433			0.265216	−	0.964189i	$-0.414557\pi$
$181$	7.13624			0.530433			0.265216	+	0.964189i	$0.414557\pi$
$182$	3.68289	−	4.02905i	0.272994	−	0.298653i
$183$		0			0
$184$	−9.80548	+	12.8762i	−0.722869	+	0.949248i
$185$		−	3.39705i		−	0.249756i
$186$		0			0
$187$		−	7.36458i		−	0.538551i
$188$	0.0499933	+	0.555776i	0.00364614	+	0.0405341i
$189$		0			0
$190$	7.70349	+	7.04165i	0.558870	+	0.510855i
$191$	5.33967			0.386365			0.193182	−	0.981163i	$-0.438119\pi$
$191$	5.33967			0.386365			0.193182	+	0.981163i	$0.438119\pi$
$192$		0			0
$193$	−15.0247			−1.08150			−0.540751	−	0.841183i	$-0.681860\pi$
$193$	−15.0247			−1.08150			−0.540751	+	0.841183i	$0.681860\pi$
$194$	−13.4865	−	12.3278i	−0.968271	−	0.885083i
$195$		0			0
$196$	1.12428	+	12.4986i	0.0803055	+	0.892756i
$197$			8.98496i			0.640152i	0.947392	+	0.320076i	$0.103708\pi$
$197$			8.98496i			0.640152i	−0.947392	+	0.320076i	$0.896292\pi$
$198$		0			0
$199$		−	17.8451i		−	1.26500i	−0.774558	−	0.632502i	$-0.782028\pi$
$199$		−	17.8451i		−	1.26500i	0.774558	−	0.632502i	$-0.217972\pi$
$200$	−1.71360	+	2.25024i	−0.121170	+	0.159116i
$201$		0			0
$202$	17.3856	−	19.0196i	1.22325	−	1.33822i
$203$	6.44916			0.452642
$204$		0			0
$205$	3.99519			0.279036
$206$	11.6388	−	12.7327i	0.810913	−	0.887130i
$207$		0			0
$208$	−17.8358	+	3.23491i	−1.23669	+	0.224301i
$209$		−	11.5860i		−	0.801419i
$210$		0			0
$211$			3.56126i			0.245167i	0.992458	+	0.122584i	$0.0391179\pi$
$211$			3.56126i			0.245167i	−0.992458	+	0.122584i	$0.960882\pi$
$212$	−0.832468	+	0.0748824i	−0.0571741	+	0.00514294i
$213$		0			0
$214$	7.48170	+	6.83891i	0.511439	+	0.467498i
$215$	−6.88087			−0.469271
$216$		0			0
$217$	2.54450			0.172732
$218$	−7.83508	−	7.16193i	−0.530658	−	0.485067i
$219$		0			0
$220$	3.12721	−	0.281299i	0.210836	−	0.0189652i
$221$			21.2584i			1.43000i
$222$		0			0
$223$			6.34980i			0.425214i	0.977138	+	0.212607i	$0.0681954\pi$
$223$			6.34980i			0.425214i	−0.977138	+	0.212607i	$0.931805\pi$
$224$	−2.56394	+	4.07938i	−0.171311	+	0.272565i
$225$		0			0
$226$	2.13208	−	2.33248i	0.141824	−	0.155154i
$227$	26.9736			1.79030			0.895150	−	0.445765i	$-0.147068\pi$
$227$	26.9736			1.79030			0.895150	+	0.445765i	$0.147068\pi$
$228$		0			0
$229$	25.9794			1.71677			0.858384	−	0.513007i	$-0.171469\pi$
$229$	25.9794			1.71677			0.858384	+	0.513007i	$0.171469\pi$
$230$	−5.45982	+	5.97298i	−0.360010	+	0.393847i
$231$		0			0
$232$	−17.0381	−	12.9748i	−1.11861	−	0.851839i
$233$			6.79353i			0.445059i	0.974926	+	0.222530i	$0.0714314\pi$
$233$			6.79353i			0.445059i	−0.974926	+	0.222530i	$0.928569\pi$
$234$		0			0
$235$			0.279010i			0.0182006i
$236$	−0.874318	−	9.71979i	−0.0569132	−	0.632705i
$237$		0			0
$238$	4.17074	+	3.81242i	0.270349	+	0.247122i
$239$	24.9044			1.61093			0.805465	−	0.592644i	$-0.201916\pi$
$239$	24.9044			1.61093			0.805465	+	0.592644i	$0.201916\pi$
$240$		0			0
$241$	−17.2531			−1.11137			−0.555684	−	0.831394i	$-0.687543\pi$
$241$	−17.2531			−1.11137			−0.555684	+	0.831394i	$0.687543\pi$
$242$	8.90950	+	8.14405i	0.572725	+	0.523519i
$243$		0			0
$244$	−1.49325	−	16.6004i	−0.0955953	−	1.06273i
$245$			6.27453i			0.400865i
$246$		0			0
$247$			33.4438i			2.12798i
$248$	−6.72233	−	5.11918i	−0.426869	−	0.325068i
$249$		0			0
$250$	−0.954154	+	1.04383i	−0.0603460	+	0.0660179i
$251$	−2.16537			−0.136677			−0.0683383	−	0.997662i	$-0.521770\pi$
$251$	−2.16537			−0.136677			−0.0683383	+	0.997662i	$0.521770\pi$
$252$		0			0
$253$	8.98331			0.564776
$254$	3.98933	−	4.36429i	0.250313	−	0.273840i
$255$		0			0
$256$	14.9809	−	5.61906i	0.936304	−	0.351191i
$257$			8.51409i			0.531094i	0.964098	+	0.265547i	$0.0855526\pi$
$257$			8.51409i			0.531094i	−0.964098	+	0.265547i	$0.914447\pi$
$258$		0			0
$259$		−	2.89343i		−	0.179789i
$260$	−9.02693	+	0.811993i	−0.559826	+	0.0503577i
$261$		0			0
$262$	−13.5862	−	12.4189i	−0.839356	−	0.767243i
$263$	−11.1468			−0.687340			−0.343670	−	0.939090i	$-0.611670\pi$
$263$	−11.1468			−0.687340			−0.343670	+	0.939090i	$0.611670\pi$
$264$		0			0
$265$	−0.417914			−0.0256723
$266$	6.56143	+	5.99770i	0.402307	+	0.367743i
$267$		0			0
$268$	−12.4453	+	1.11948i	−0.760215	+	0.0683831i
$269$		−	5.68724i		−	0.346757i	−0.984855	−	0.173378i	$-0.944532\pi$
$269$		−	5.68724i		−	0.346757i	0.984855	−	0.173378i	$-0.0554684\pi$
$270$		0			0
$271$		−	28.4853i		−	1.73036i	−0.501464	−	0.865179i	$-0.667205\pi$
$271$		−	28.4853i		−	1.73036i	0.501464	−	0.865179i	$-0.332795\pi$
$272$	−3.34868	−	18.4630i	−0.203043	−	1.11949i
$273$		0			0
$274$	13.6687	−	14.9534i	0.825758	−	0.903370i
$275$	1.56992			0.0946696
$276$		0			0
$277$	30.0845			1.80760			0.903802	−	0.427952i	$-0.140765\pi$
$277$	30.0845			1.80760			0.903802	+	0.427952i	$0.140765\pi$
$278$	−18.4259	+	20.1577i	−1.10511	+	1.20898i
$279$		0			0
$280$	−1.45955	+	1.91664i	−0.0872250	+	0.114541i
$281$		−	12.2792i		−	0.732516i	−0.930513	−	0.366258i	$-0.880639\pi$
$281$		−	12.2792i		−	0.732516i	0.930513	−	0.366258i	$-0.119361\pi$
$282$		0			0
$283$		−	24.7385i		−	1.47055i	−0.677769	−	0.735275i	$-0.737053\pi$
$283$		−	24.7385i		−	1.47055i	0.677769	−	0.735275i	$-0.262947\pi$
$284$	0.616095	+	6.84913i	0.0365585	+	0.406421i
$285$		0			0
$286$	7.42623	+	6.78821i	0.439122	+	0.401395i
$287$	3.40290			0.200867
$288$		0			0
$289$	−5.00605			−0.294474
$290$	−7.90359	−	7.22455i	−0.464115	−	0.424240i
$291$		0			0
$292$	−2.19352	−	24.3854i	−0.128366	−	1.42705i
$293$			12.2519i			0.715764i	0.933767	+	0.357882i	$0.116501\pi$
$293$			12.2519i			0.715764i	−0.933767	+	0.357882i	$0.883499\pi$
$294$		0			0
$295$		−	4.87952i		−	0.284097i
$296$	−5.82118	+	7.64418i	−0.338349	+	0.444309i
$297$		0			0
$298$	16.0999	−	17.6131i	0.932643	−	1.02030i
$299$	−25.9310			−1.49963
$300$		0			0
$301$	−5.86076			−0.337809
$302$	−1.29986	+	1.42203i	−0.0747983	+	0.0818286i
$303$		0			0
$304$	−5.26815	−	29.0461i	−0.302149	−	1.66591i
$305$		−	8.33373i		−	0.477188i
$306$		0			0
$307$		−	1.01623i		−	0.0579995i	−0.999579	−	0.0289997i	$-0.990768\pi$
$307$		−	1.01623i		−	0.0579995i	0.999579	−	0.0289997i	$-0.00923220\pi$
$308$	2.66359	−	0.239596i	0.151772	−	0.0136523i
$309$		0			0
$310$	−3.11834	−	2.85043i	−0.177110	−	0.161893i
$311$	−22.2559			−1.26202			−0.631009	−	0.775776i	$-0.717359\pi$
$311$	−22.2559			−1.26202			−0.631009	+	0.775776i	$0.717359\pi$
$312$		0			0
$313$	−19.1065			−1.07996			−0.539982	−	0.841676i	$-0.681569\pi$
$313$	−19.1065			−1.07996			−0.539982	+	0.841676i	$0.681569\pi$
$314$	10.3784	+	9.48671i	0.585685	+	0.535366i
$315$		0			0
$316$	−11.2238	+	1.00961i	−0.631388	+	0.0567948i
$317$			6.58393i			0.369790i	0.982758	+	0.184895i	$0.0591946\pi$
$317$			6.58393i			0.369790i	−0.982758	+	0.184895i	$0.940805\pi$
$318$		0			0
$319$			11.8869i			0.665540i
$320$	7.71202	−	2.12716i	0.431115	−	0.118912i
$321$		0			0
$322$	−4.65038	+	5.08747i	−0.259156	+	0.283514i
$323$	−34.6200			−1.92631
$324$		0			0
$325$	−4.53169			−0.251373
$326$	4.11061	−	4.49697i	0.227666	−	0.249064i
$327$		0			0
$328$	−8.99015	−	6.84616i	−0.496398	−	0.378016i
$329$			0.237646i			0.0131018i
$330$		0			0
$331$		−	16.0384i		−	0.881553i	−0.897617	−	0.440776i	$-0.854703\pi$
$331$		−	16.0384i		−	0.881553i	0.897617	−	0.440776i	$-0.145297\pi$
$332$	−2.70789	−	30.1037i	−0.148615	−	1.65215i
$333$		0			0
$334$	19.2027	+	17.5529i	1.05073	+	0.960454i
$335$	−6.24776			−0.341351
$336$		0			0
$337$	3.42155			0.186384			0.0931920	−	0.995648i	$-0.470293\pi$
$337$	3.42155			0.186384			0.0931920	+	0.995648i	$0.470293\pi$
$338$	−7.86653	−	7.19068i	−0.427883	−	0.391122i
$339$		0			0
$340$	−0.840549	−	9.34439i	−0.0455852	−	0.506771i
$341$			4.68995i			0.253975i
$342$		0			0
$343$			11.3065i			0.610496i
$344$	15.4836	+	11.7910i	0.834820	+	0.635730i
$345$		0			0
$346$	−2.84098	+	3.10800i	−0.152732	+	0.167087i
$347$	14.6614			0.787066			0.393533	−	0.919310i	$-0.371253\pi$
$347$	14.6614			0.787066			0.393533	+	0.919310i	$0.371253\pi$
$348$		0			0
$349$	−14.5726			−0.780056			−0.390028	−	0.920803i	$-0.627535\pi$
$349$	−14.5726			−0.780056			−0.390028	+	0.920803i	$0.627535\pi$
$350$	−0.812698	+	0.889083i	−0.0434405	+	0.0475235i
$351$		0			0
$352$	−7.51900	−	4.72579i	−0.400764	−	0.251885i
$353$		−	4.27765i		−	0.227676i	−0.993499	−	0.113838i	$-0.963685\pi$
$353$		−	4.27765i		−	0.227676i	0.993499	−	0.113838i	$-0.0363145\pi$
$354$		0			0
$355$			3.43839i			0.182491i
$356$	−17.4362	+	1.56843i	−0.924116	+	0.0831264i
$357$		0			0
$358$	4.42458	+	4.04445i	0.233846	+	0.213756i
$359$	16.2554			0.857929			0.428964	−	0.903321i	$-0.358879\pi$
$359$	16.2554			0.857929			0.428964	+	0.903321i	$0.358879\pi$
$360$		0			0
$361$	−35.4643			−1.86654
$362$	−7.44905	−	6.80907i	−0.391514	−	0.357877i
$363$		0			0
$364$	−7.68866	+	0.691613i	−0.402995	+	0.0362503i
$365$		−	12.2419i		−	0.640771i
$366$		0			0
$367$		−	1.32326i		−	0.0690736i	−0.999403	−	0.0345368i	$-0.989004\pi$
$367$		−	1.32326i		−	0.0690736i	0.999403	−	0.0345368i	$-0.0109956\pi$
$368$	22.5212	−	4.08472i	1.17400	−	0.212931i
$369$		0			0
$370$	−3.24131	+	3.54596i	−0.168508	+	0.184346i
$371$	−0.355957			−0.0184804
$372$		0			0
$373$	18.5475			0.960355			0.480178	−	0.877171i	$-0.340572\pi$
$373$	18.5475			0.960355			0.480178	+	0.877171i	$0.340572\pi$
$374$	−7.02694	+	7.68740i	−0.363354	+	0.397506i
$375$		0			0
$376$	0.478111	−	0.627840i	0.0246567	−	0.0323784i
$377$		−	34.3125i		−	1.76718i
$378$		0			0
$379$			0.0332516i			0.00170802i	1.00000		0.000854010i	$0.000271840\pi$
$379$			0.0332516i			0.00170802i	−1.00000		0.000854010i	$0.999728\pi$
$380$	−1.32236	−	14.7006i	−0.0678354	−	0.754126i
$381$		0			0
$382$	−5.57373	−	5.09487i	−0.285177	−	0.260676i
$383$	−29.7465			−1.51997			−0.759987	−	0.649938i	$-0.774795\pi$
$383$	−29.7465			−1.51997			−0.759987	+	0.649938i	$0.774795\pi$
$384$		0			0
$385$	1.33717			0.0681486
$386$	15.6833	+	14.3359i	0.798260	+	0.729677i
$387$		0			0
$388$	2.31504	+	25.7363i	0.117528	+	1.30656i
$389$			13.1313i			0.665785i	0.942965	+	0.332892i	$0.108025\pi$
$389$			13.1313i			0.665785i	−0.942965	+	0.332892i	$0.891975\pi$
$390$		0			0
$391$		−	26.8430i		−	1.35751i
$392$	10.7520	−	14.1192i	0.543059	−	0.713127i
$393$		0			0
$394$	8.57304	−	9.37881i	0.431903	−	0.472498i
$395$	−5.63456			−0.283505
$396$		0			0
$397$	34.0967			1.71126			0.855632	−	0.517585i	$-0.173169\pi$
$397$	34.0967			1.71126			0.855632	+	0.517585i	$0.173169\pi$
$398$	−17.0270	+	18.6273i	−0.853484	+	0.933703i
$399$		0			0
$400$	3.93579	−	0.713842i	0.196789	−	0.0356921i
$401$		−	11.5908i		−	0.578815i	−0.957206	−	0.289408i	$-0.906542\pi$
$401$		−	11.5908i		−	0.578815i	0.957206	−	0.289408i	$-0.0934583\pi$
$402$		0			0
$403$		−	13.5379i		−	0.674371i
$404$	−36.2953	+	3.26485i	−1.80576	+	0.162432i
$405$		0			0
$406$	−6.73186	−	6.15349i	−0.334096	−	0.305393i
$407$	5.33308			0.264351
$408$		0			0
$409$	−4.89402			−0.241994			−0.120997	−	0.992653i	$-0.538609\pi$
$409$	−4.89402			−0.241994			−0.120997	+	0.992653i	$0.538609\pi$
$410$	−4.17032	−	3.81203i	−0.205958	−	0.188263i
$411$		0			0
$412$	−24.2979	+	2.18565i	−1.19707	+	0.107679i
$413$		−	4.15612i		−	0.204509i
$414$		0			0
$415$		−	15.1126i		−	0.741849i
$416$	21.7042	+	13.6413i	1.06414	+	0.668822i
$417$		0			0
$418$	−11.0548	+	12.0938i	−0.540708	+	0.591529i
$419$	−3.03017			−0.148033			−0.0740166	−	0.997257i	$-0.523582\pi$
$419$	−3.03017			−0.148033			−0.0740166	+	0.997257i	$0.523582\pi$
$420$		0			0
$421$	13.8719			0.676073			0.338036	−	0.941133i	$-0.390237\pi$
$421$	13.8719			0.676073			0.338036	+	0.941133i	$0.390237\pi$
$422$	3.39799	−	3.71736i	0.165411	−	0.180958i
$423$		0			0
$424$	0.940408	+	0.716137i	0.0456702	+	0.0347787i
$425$		−	4.69106i		−	0.227550i
$426$		0			0
$427$		−	7.09823i		−	0.343508i
$428$	−1.28428	−	14.2774i	−0.0620782	−	0.690124i
$429$		0			0
$430$	7.18249	+	6.56540i	0.346370	+	0.316612i
$431$	30.9625			1.49141			0.745706	−	0.666275i	$-0.232112\pi$
$431$	30.9625			1.49141			0.745706	+	0.666275i	$0.232112\pi$
$432$		0			0
$433$	15.8716			0.762740			0.381370	−	0.924423i	$-0.375452\pi$
$433$	15.8716			0.762740			0.381370	+	0.924423i	$0.375452\pi$
$434$	−2.65603	−	2.42784i	−0.127494	−	0.116540i
$435$		0			0
$436$	1.34494	+	14.9517i	0.0644111	+	0.716058i
$437$		−	42.2295i		−	2.02011i
$438$		0			0
$439$			5.91673i			0.282390i	0.989982	+	0.141195i	$0.0450945\pi$
$439$			5.91673i			0.282390i	−0.989982	+	0.141195i	$0.954906\pi$
$440$	−3.53269	−	2.69021i	−0.168414	−	0.128251i
$441$		0			0
$442$	20.2838	−	22.1903i	0.964802	−	1.05548i
$443$	−3.50433			−0.166496			−0.0832479	−	0.996529i	$-0.526529\pi$
$443$	−3.50433			−0.166496			−0.0832479	+	0.996529i	$0.526529\pi$
$444$		0			0
$445$	−8.75330			−0.414946
$446$	6.05868	−	6.62814i	0.286887	−	0.313851i
$447$		0			0
$448$	6.56869	−	1.81180i	0.310341	−	0.0855997i
$449$			11.8538i			0.559416i	0.960085	+	0.279708i	$0.0902377\pi$
$449$			11.8538i			0.559416i	−0.960085	+	0.279708i	$0.909762\pi$
$450$		0			0
$451$			6.27212i			0.295343i
$452$	−4.45109	+	0.400385i	−0.209362	+	0.0188325i
$453$		0			0
$454$	−28.1560	−	25.7370i	−1.32142	−	1.20790i
$455$	−3.85985			−0.180953
$456$		0			0
$457$	−27.8805			−1.30419			−0.652097	−	0.758136i	$-0.726110\pi$
$457$	−27.8805			−1.30419			−0.652097	+	0.758136i	$0.726110\pi$
$458$	−27.1182	−	24.7884i	−1.26715	−	1.15828i
$459$		0			0
$460$	11.3983	−	1.02530i	0.531448	−	0.0478050i
$461$		−	23.3753i		−	1.08869i	−0.838860	−	0.544347i	$-0.816777\pi$
$461$		−	23.3753i		−	1.08869i	0.838860	−	0.544347i	$-0.183223\pi$
$462$		0			0
$463$		−	19.2646i		−	0.895302i	−0.894208	−	0.447651i	$-0.852261\pi$
$463$		−	19.2646i		−	0.895302i	0.894208	−	0.447651i	$-0.147739\pi$
$464$	5.40499	+	29.8005i	0.250920	+	1.38346i
$465$		0			0
$466$	6.48207	−	7.09132i	0.300276	−	0.328499i
$467$	19.9734			0.924260			0.462130	−	0.886812i	$-0.347085\pi$
$467$	19.9734			0.924260			0.462130	+	0.886812i	$0.347085\pi$
$468$		0			0
$469$	−5.32151			−0.245724
$470$	0.266218	−	0.291240i	0.0122797	−	0.0134339i
$471$		0			0
$472$	−8.36154	+	10.9801i	−0.384871	+	0.505400i
$473$		−	10.8024i		−	0.496694i
$474$		0			0
$475$		−	7.37999i		−	0.338617i
$476$	−0.715936	−	7.95906i	−0.0328149	−	0.364803i
$477$		0			0
$478$	−25.9960	−	23.7626i	−1.18903	−	1.08688i
$479$	4.31193			0.197017			0.0985086	−	0.995136i	$-0.468593\pi$
$479$	4.31193			0.197017			0.0985086	+	0.995136i	$0.468593\pi$
$480$		0			0
$481$	−15.3944			−0.701922
$482$	18.0093	+	16.4621i	0.820303	+	0.749827i
$483$		0			0
$484$	−1.52938	−	17.0021i	−0.0695171	−	0.772822i
$485$			12.9201i			0.586672i
$486$		0			0
$487$			2.98520i			0.135272i	0.997710	+	0.0676361i	$0.0215457\pi$
$487$			2.98520i			0.135272i	−0.997710	+	0.0676361i	$0.978454\pi$
$488$	−14.2807	+	18.7529i	−0.646455	+	0.848904i
$489$		0			0
$490$	5.98686	−	6.54957i	0.270459	−	0.295879i
$491$	39.1365			1.76621			0.883103	−	0.469179i	$-0.155450\pi$
$491$	39.1365			1.76621			0.883103	+	0.469179i	$0.155450\pi$
$492$		0			0
$493$	35.5192			1.59971
$494$	31.9105	−	34.9098i	1.43572	−	1.57067i
$495$		0			0
$496$	2.13252	+	11.7577i	0.0957531	+	0.527937i
$497$			2.92864i			0.131367i
$498$		0			0
$499$		−	4.90799i		−	0.219712i	−0.993948	−	0.109856i	$-0.964961\pi$
$499$		−	4.90799i		−	0.219712i	0.993948	−	0.109856i	$-0.0350390\pi$
$500$	1.99196	−	0.179181i	0.0890830	−	0.00801322i
$501$		0			0
$502$	2.26028	+	2.06609i	0.100881	+	0.0922142i
$503$	14.0218			0.625201			0.312601	−	0.949885i	$-0.398800\pi$
$503$	14.0218			0.625201			0.312601	+	0.949885i	$0.398800\pi$
$504$		0			0
$505$	−18.2209			−0.810821
$506$	−9.37709	−	8.57146i	−0.416862	−	0.381048i
$507$		0			0
$508$	−8.32840	+	0.749159i	−0.369513	+	0.0332385i
$509$		−	15.5325i		−	0.688467i	−0.938884	−	0.344234i	$-0.888139\pi$
$509$		−	15.5325i		−	0.688467i	0.938884	−	0.344234i	$-0.111861\pi$
$510$		0			0
$511$		−	10.4270i		−	0.461264i
$512$	−20.9990	−	8.42867i	−0.928033	−	0.372498i
$513$		0			0
$514$	8.12375	−	8.88730i	0.358323	−	0.392002i
$515$	−12.1980			−0.537509
$516$		0			0
$517$	−0.438023			−0.0192642
$518$	−2.76077	+	3.02026i	−0.121301	+	0.132703i
$519$		0			0
$520$	10.1974	+	7.76549i	0.447185	+	0.340539i
$521$			3.85505i			0.168893i	0.996428	+	0.0844464i	$0.0269122\pi$
$521$			3.85505i			0.168893i	−0.996428	+	0.0844464i	$0.973088\pi$
$522$		0			0
$523$			2.48755i			0.108773i	0.998520	+	0.0543866i	$0.0173203\pi$
$523$			2.48755i			0.108773i	−0.998520	+	0.0543866i	$0.982680\pi$
$524$	2.33216	+	25.9266i	0.101881	+	1.13261i
$525$		0			0
$526$	11.6354	+	10.6357i	0.507327	+	0.463740i
$527$	14.0140			0.610460
$528$		0			0
$529$	9.74306			0.423611
$530$	0.436233	+	0.398755i	0.0189488	+	0.0173208i
$531$		0			0
$532$	−1.12631	−	12.5212i	−0.0488318	−	0.542864i
$533$		−	18.1050i		−	0.784213i
$534$		0			0
$535$		−	7.16752i		−	0.309879i
$536$	14.0590	+	10.7061i	0.607254	+	0.462435i
$537$		0			0
$538$	−5.42650	+	5.93653i	−0.233953	+	0.255942i
$539$	−9.85049			−0.424290
$540$		0			0
$541$	−24.7633			−1.06466			−0.532328	−	0.846538i	$-0.678683\pi$
$541$	−24.7633			−1.06466			−0.532328	+	0.846538i	$0.678683\pi$
$542$	−27.1793	+	29.7339i	−1.16745	+	1.27718i
$543$		0			0
$544$	−14.1211	+	22.4675i	−0.605437	+	0.963286i
$545$			7.50605i			0.321524i
$546$		0			0
$547$			39.7991i			1.70169i	0.525420	+	0.850843i	$0.323908\pi$
$547$			39.7991i			1.70169i	−0.525420	+	0.850843i	$0.676092\pi$
$548$	−28.5358	+	2.56686i	−1.21899	+	0.109651i
$549$		0			0
$550$	−1.63873	−	1.49794i	−0.0698758	−	0.0638725i
$551$	55.8790			2.38052
$552$		0			0
$553$	−4.79922			−0.204084
$554$	−31.4033	−	28.7053i	−1.33420	−	1.21957i
$555$		0			0
$556$	38.4672	−	3.46021i	1.63137	−	0.146746i
$557$		−	1.19351i		−	0.0505707i	−0.999680	−	0.0252853i	$-0.991951\pi$
$557$		−	1.19351i		−	0.0505707i	0.999680	−	0.0252853i	$-0.00804943\pi$
$558$		0			0
$559$			31.1819i			1.31886i
$560$	3.35230	−	0.608013i	0.141660	−	0.0256932i
$561$		0			0
$562$	−11.7162	+	12.8175i	−0.494220	+	0.540672i
$563$	−18.2795			−0.770389			−0.385194	−	0.922835i	$-0.625866\pi$
$563$	−18.2795			−0.770389			−0.385194	+	0.922835i	$0.625866\pi$
$564$		0			0
$565$	−2.23453			−0.0940074
$566$	−23.6043	+	25.8229i	−0.992164	+	1.08542i
$567$		0			0
$568$	5.89202	−	7.73721i	0.247224	−	0.324646i
$569$			17.1443i			0.718725i	0.933198	+	0.359363i	$0.117006\pi$
$569$			17.1443i			0.718725i	−0.933198	+	0.359363i	$0.882994\pi$
$570$		0			0
$571$		−	30.5760i		−	1.27957i	−0.768555	−	0.639784i	$-0.779024\pi$
$571$		−	30.5760i		−	1.27957i	0.768555	−	0.639784i	$-0.220976\pi$
$572$	−1.27476	−	14.1715i	−0.0533004	−	0.592541i
$573$		0			0
$574$	−3.55206	−	3.24689i	−0.148260	−	0.135522i
$575$	5.72216			0.238630
$576$		0			0
$577$	13.2010			0.549564			0.274782	−	0.961507i	$-0.411394\pi$
$577$	13.2010			0.549564			0.274782	+	0.961507i	$0.411394\pi$
$578$	5.22549	+	4.77654i	0.217352	+	0.198678i
$579$		0			0
$580$	1.35670	+	15.0825i	0.0563340	+	0.626266i
$581$		−	12.8721i		−	0.534026i
$582$		0			0
$583$		−	0.656091i		−	0.0271725i
$584$	−20.9777	+	27.5473i	−0.868064	+	1.13991i
$585$		0			0
$586$	11.6902	−	12.7890i	0.482918	−	0.528307i
$587$	−0.305488			−0.0126088			−0.00630442	−	0.999980i	$-0.502007\pi$
$587$	−0.305488			−0.0126088			−0.00630442	+	0.999980i	$0.502007\pi$
$588$		0			0
$589$	22.0469			0.908426
$590$	−4.65581	+	5.09341i	−0.191677	+	0.209692i
$591$		0			0
$592$	13.3701	−	2.42496i	0.549506	−	0.0996651i
$593$			12.8287i			0.526811i	0.964685	+	0.263405i	$0.0848457\pi$
$593$			12.8287i			0.526811i	−0.964685	+	0.263405i	$0.915154\pi$
$594$		0			0
$595$		−	3.99560i		−	0.163804i
$596$	−33.6113	+	3.02341i	−1.37677	+	0.123844i
$597$		0			0
$598$	27.0677	+	24.7422i	1.10688	+	1.01178i
$599$	−16.8614			−0.688938			−0.344469	−	0.938798i	$-0.611941\pi$
$599$	−16.8614			−0.688938			−0.344469	+	0.938798i	$0.611941\pi$
$600$		0			0
$601$	−19.3017			−0.787333			−0.393667	−	0.919253i	$-0.628794\pi$
$601$	−19.3017			−0.787333			−0.393667	+	0.919253i	$0.628794\pi$
$602$	6.11766	+	5.59206i	0.249337	+	0.227916i
$603$		0			0
$604$	2.71367	−	0.244101i	0.110418	−	0.00993232i
$605$		−	8.53536i		−	0.347012i
$606$		0			0
$607$			12.9115i			0.524060i	0.965060	+	0.262030i	$0.0843920\pi$
$607$			12.9115i			0.524060i	−0.965060	+	0.262030i	$0.915608\pi$
$608$	−22.2154	+	35.3459i	−0.900952	+	1.43347i
$609$		0			0
$610$	−7.95166	+	8.69904i	−0.321953	+	0.352214i
$611$	1.26439			0.0511516
$612$		0			0
$613$	7.10289			0.286883			0.143441	−	0.989659i	$-0.454183\pi$
$613$	7.10289			0.286883			0.143441	+	0.989659i	$0.454183\pi$
$614$	−0.969643	+	1.06078i	−0.0391316	+	0.0428096i
$615$		0			0
$616$	−3.00896	−	2.29138i	−0.121234	−	0.0923222i
$617$		−	2.07663i		−	0.0836021i	−0.999126	−	0.0418010i	$-0.986690\pi$
$617$		−	2.07663i		−	0.0836021i	0.999126	−	0.0418010i	$-0.0133096\pi$
$618$		0			0
$619$			34.4346i			1.38404i	0.721876	+	0.692022i	$0.243280\pi$
$619$			34.4346i			1.38404i	−0.721876	+	0.692022i	$0.756720\pi$
$620$	0.535283	+	5.95074i	0.0214975	+	0.238988i
$621$		0			0
$622$	23.2315	+	21.2356i	0.931498	+	0.851469i
$623$	−7.45560			−0.298702
$624$		0			0
$625$	1.00000			0.0400000
$626$	19.9440	+	18.2306i	0.797124	+	0.728640i
$627$		0			0
$628$	−1.78151	−	19.8051i	−0.0710902	−	0.790310i
$629$		−	15.9358i		−	0.635400i
$630$		0			0
$631$		−	22.1958i		−	0.883600i	−0.897114	−	0.441800i	$-0.854340\pi$
$631$		−	22.1958i		−	0.883600i	0.897114	−	0.441800i	$-0.145660\pi$
$632$	12.6791	+	9.65537i	0.504348	+	0.384070i
$633$		0			0
$634$	6.28208	−	6.87254i	0.249493	−	0.272943i
$635$	−4.18101			−0.165918
$636$		0			0
$637$	28.4342			1.12660
$638$	11.3419	−	12.4080i	0.449032	−	0.491236i
$639$		0			0
$640$	−10.0797	−	5.13804i	−0.398435	−	0.203099i
$641$		−	25.6352i		−	1.01253i	−0.862378	−	0.506265i	$-0.831026\pi$
$641$		−	25.6352i		−	1.01253i	0.862378	−	0.506265i	$-0.168974\pi$
$642$		0			0
$643$			32.1435i			1.26761i	0.773491	+	0.633807i	$0.218509\pi$
$643$			32.1435i			1.26761i	−0.773491	+	0.633807i	$0.781491\pi$
$644$	9.70846	−	0.873298i	0.382567	−	0.0344128i
$645$		0			0
$646$	36.1375	+	33.0328i	1.42181	+	1.29966i
$647$	−13.2669			−0.521574			−0.260787	−	0.965396i	$-0.583982\pi$
$647$	−13.2669			−0.521574			−0.260787	+	0.965396i	$0.583982\pi$
$648$		0			0
$649$	7.66044			0.300699
$650$	4.73033	+	4.32393i	0.185539	+	0.169598i
$651$		0			0
$652$	−8.58160	+	0.771934i	−0.336081	+	0.0302313i
$653$		−	13.1291i		−	0.513781i	−0.966441	−	0.256890i	$-0.917302\pi$
$653$		−	13.1291i		−	0.513781i	0.966441	−	0.256890i	$-0.0826979\pi$
$654$		0			0
$655$			13.0156i			0.508563i
$656$	2.85194	+	15.7242i	0.111349	+	0.613928i
$657$		0			0
$658$	0.226751	−	0.248063i	0.00883967	−	0.00967051i
$659$	25.5278			0.994421			0.497211	−	0.867630i	$-0.334358\pi$
$659$	25.5278			0.994421			0.497211	+	0.867630i	$0.334358\pi$
$660$		0			0
$661$	17.0132			0.661735			0.330868	−	0.943677i	$-0.392659\pi$
$661$	17.0132			0.661735			0.330868	+	0.943677i	$0.392659\pi$
$662$	−15.3031	+	16.7415i	−0.594774	+	0.650676i
$663$		0			0
$664$	−25.8969	+	34.0070i	−1.00500	+	1.31973i
$665$		−	6.28589i		−	0.243756i
$666$		0			0
$667$			43.3264i			1.67760i
$668$	−3.29628	−	36.6447i	−0.127537	−	1.41783i
$669$		0			0
$670$	6.52162	+	5.96132i	0.251952	+	0.230306i
$671$	13.0833			0.505074
$672$		0			0
$673$	−5.19939			−0.200422			−0.100211	−	0.994966i	$-0.531952\pi$
$673$	−5.19939			−0.200422			−0.100211	+	0.994966i	$0.531952\pi$
$674$	−3.57154	−	3.26469i	−0.137570	−	0.125751i
$675$		0			0
$676$	1.35034	+	15.0118i	0.0519363	+	0.577376i
$677$		−	3.84385i		−	0.147731i	−0.997268	−	0.0738656i	$-0.976466\pi$
$677$		−	3.84385i		−	0.147731i	0.997268	−	0.0738656i	$-0.0235336\pi$
$678$		0			0
$679$			11.0047i			0.422320i
$680$	−8.03859	+	10.5560i	−0.308266	+	0.404805i
$681$		0			0
$682$	4.47493	−	4.89553i	0.171354	−	0.187459i
$683$	31.2053			1.19404			0.597019	−	0.802227i	$-0.296352\pi$
$683$	31.2053			1.19404			0.597019	+	0.802227i	$0.296352\pi$
$684$		0			0
$685$	−14.3255			−0.547349
$686$	10.7882	−	11.8022i	0.411895	−	0.450609i
$687$		0			0
$688$	−4.91185	−	27.0816i	−0.187263	−	1.03248i
$689$			1.89386i			0.0721502i
$690$		0			0
$691$		−	25.0475i		−	0.952853i	−0.879214	−	0.476427i	$-0.841932\pi$
$691$		−	25.0475i		−	0.952853i	0.879214	−	0.476427i	$-0.158068\pi$
$692$	5.93102	−	0.533508i	0.225463	−	0.0202809i
$693$		0			0
$694$	−15.3041	−	13.9892i	−0.580935	−	0.531024i
$695$	19.3112			0.732517
$696$		0			0
$697$	18.7417			0.709893
$698$	15.2114	+	13.9045i	0.575761	+	0.526295i
$699$		0			0
$700$	1.69664	−	0.152617i	0.0641271	−	0.00576838i
$701$			40.2124i			1.51880i	0.650624	+	0.759400i	$0.274507\pi$
$701$			40.2124i			1.51880i	−0.650624	+	0.759400i	$0.725493\pi$
$702$		0			0
$703$		−	25.0702i		−	0.945540i
$704$	3.33947	+	12.1072i	0.125861	+	0.456308i
$705$		0			0
$706$	−4.08153	+	4.46516i	−0.153611	+	0.168048i
$707$	−15.5196			−0.583676
$708$		0			0
$709$	−5.46789			−0.205351			−0.102675	−	0.994715i	$-0.532740\pi$
$709$	−5.46789			−0.205351			−0.102675	+	0.994715i	$0.532740\pi$
$710$	3.28075	−	3.58911i	0.123125	−	0.134697i
$711$		0			0
$712$	19.6970	+	14.9996i	0.738177	+	0.562135i
$713$			17.0943i			0.640186i
$714$		0			0
$715$		−	7.11437i		−	0.266062i
$716$	−0.759509	−	8.44347i	−0.0283842	−	0.315547i
$717$		0			0
$718$	−16.9680	−	15.5102i	−0.633239	−	0.578835i
$719$	39.5459			1.47481			0.737406	−	0.675450i	$-0.236051\pi$
$719$	39.5459			1.47481			0.737406	+	0.675450i	$0.236051\pi$
$720$		0			0
$721$	−10.3896			−0.386930
$722$	37.0189	+	33.8384i	1.37770	+	1.25933i
$723$		0			0
$724$	1.27868	+	14.2151i	0.0475217	+	0.528300i
$725$			7.57168i			0.281205i
$726$		0			0
$727$		−	31.2073i		−	1.15741i	−0.815536	−	0.578707i	$-0.803558\pi$
$727$		−	31.2073i		−	1.15741i	0.815536	−	0.578707i	$-0.196442\pi$
$728$	8.68559	+	6.61424i	0.321910	+	0.245140i
$729$		0			0
$730$	−11.6807	+	12.7785i	−0.432321	+	0.472955i
$731$	−32.2786			−1.19387
$732$		0			0
$733$	22.2693			0.822535			0.411267	−	0.911515i	$-0.365086\pi$
$733$	22.2693			0.822535			0.411267	+	0.911515i	$0.365086\pi$
$734$	−1.26259	+	1.38126i	−0.0466032	+	0.0509834i
$735$		0			0
$736$	−27.4058	−	17.2249i	−1.01019	−	0.634919i
$737$		−	9.80846i		−	0.361299i
$738$		0			0
$739$			24.8012i			0.912328i	0.889896	+	0.456164i	$0.150777\pi$
$739$			24.8012i			0.912328i	−0.889896	+	0.456164i	$0.849223\pi$
$740$	6.76678	−	0.608687i	0.248752	−	0.0223758i
$741$		0			0
$742$	0.371561	+	0.339638i	0.0136404	+	0.0124685i
$743$	27.4683			1.00772			0.503858	−	0.863787i	$-0.331914\pi$
$743$	27.4683			1.00772			0.503858	+	0.863787i	$0.331914\pi$
$744$		0			0
$745$	−16.8735			−0.618197
$746$	−19.3606	−	17.6972i	−0.708841	−	0.647941i
$747$		0			0
$748$	14.6699	−	1.31959i	0.536385	−	0.0482491i
$749$		−	6.10491i		−	0.223069i
$750$		0			0
$751$		−	4.00069i		−	0.145987i	−0.997332	−	0.0729936i	$-0.976745\pi$
$751$		−	4.00069i		−	0.145987i	0.997332	−	0.0729936i	$-0.0232553\pi$
$752$	−1.09812	+	0.199169i	−0.0400445	+	0.00726295i
$753$		0			0
$754$	−32.7394	+	35.8166i	−1.19230	+	1.30436i
$755$	1.36231			0.0495796
$756$		0			0
$757$	−6.91531			−0.251341			−0.125671	−	0.992072i	$-0.540108\pi$
$757$	−6.91531			−0.251341			−0.125671	+	0.992072i	$0.540108\pi$
$758$	0.0317272	−	0.0347092i	0.00115238	−	0.00126069i
$759$		0			0
$760$	−12.6463	+	16.6068i	−0.458731	+	0.602390i
$761$			3.37639i			0.122394i	0.998126	+	0.0611971i	$0.0194918\pi$
$761$			3.37639i			0.122394i	−0.998126	+	0.0611971i	$0.980508\pi$
$762$		0			0
$763$			6.39326i			0.231452i
$764$	0.956768	+	10.6364i	0.0346146	+	0.384811i
$765$		0			0
$766$	31.0504	+	28.3827i	1.12190	+	1.02551i
$767$	−22.1125			−0.798434
$768$		0			0
$769$	−27.2171			−0.981472			−0.490736	−	0.871308i	$-0.663272\pi$
$769$	−27.2171			−0.981472			−0.490736	+	0.871308i	$0.663272\pi$
$770$	−1.39579	−	1.27587i	−0.0503007	−	0.0459791i
$771$		0			0
$772$	−2.69214	−	29.9286i	−0.0968924	−	1.07715i
$773$		−	36.3065i		−	1.30585i	−0.757420	−	0.652927i	$-0.773541\pi$
$773$		−	36.3065i		−	1.30585i	0.757420	−	0.652927i	$-0.226459\pi$
$774$		0			0
$775$			2.98739i			0.107310i
$776$	22.1399	−	29.0734i	0.794775	−	1.04367i
$777$		0			0
$778$	12.5293	−	13.7069i	0.449197	−	0.491417i
$779$	29.4845			1.05639
$780$		0			0
$781$	−5.39799			−0.193155
$782$	−25.6123	+	28.0196i	−0.915895	+	1.00198i
$783$		0			0
$784$	−24.6952	+	4.47902i	−0.881972	+	0.159965i
$785$		−	9.94254i		−	0.354864i
$786$		0			0
$787$		−	24.9334i		−	0.888781i	−0.895833	−	0.444390i	$-0.853420\pi$
$787$		−	24.9334i		−	0.888781i	0.895833	−	0.444390i	$-0.146580\pi$
$788$	−17.8977	+	1.60994i	−0.637578	+	0.0573516i
$789$		0			0
$790$	5.88155	+	5.37623i	0.209256	+	0.191278i
$791$	−1.90325			−0.0676719
$792$		0			0
$793$	−37.7659			−1.34110
$794$	−35.5913	−	32.5335i	−1.26309	−	1.15457i
$795$		0			0
$796$	35.5466	−	3.19750i	1.25992	−	0.113332i
$797$			8.46163i			0.299726i	0.988707	+	0.149863i	$0.0478833\pi$
$797$			8.46163i			0.299726i	−0.988707	+	0.149863i	$0.952117\pi$
$798$		0			0
$799$			1.30885i			0.0463039i
$800$	−4.78943	−	3.01021i	−0.169332	−	0.106427i
$801$		0			0
$802$	−11.0594	+	12.0988i	−0.390520	+	0.427225i
$803$	19.2188			0.678216
$804$		0			0
$805$	4.87383			0.171780
$806$	−12.9172	+	14.1313i	−0.454990	+	0.497755i
$807$		0			0
$808$	41.0015	+	31.2234i	1.44243	+	1.09843i
$809$			2.61185i			0.0918276i	0.998945	+	0.0459138i	$0.0146200\pi$
$809$			2.61185i			0.0918276i	−0.998945	+	0.0459138i	$0.985380\pi$
$810$		0			0
$811$			11.2199i			0.393985i	0.980405	+	0.196993i	$0.0631175\pi$
$811$			11.2199i			0.393985i	−0.980405	+	0.196993i	$0.936882\pi$
$812$	1.15557	+	12.8465i	0.0405525	+	0.450822i
$813$		0			0
$814$	−5.56686	−	5.08858i	−0.195118	−	0.178355i
$815$	−4.30812			−0.150907
$816$		0			0
$817$	−50.7807			−1.77659
$818$	5.10855	+	4.66965i	0.178616	+	0.163270i
$819$		0			0
$820$	0.715863	+	7.95826i	0.0249990	+	0.277914i
$821$			29.6218i			1.03381i	0.856044	+	0.516903i	$0.172915\pi$
$821$			29.6218i			1.03381i	−0.856044	+	0.516903i	$0.827085\pi$
$822$		0			0
$823$			38.8526i			1.35432i	0.735838	+	0.677158i	$0.236789\pi$
$823$			38.8526i			1.35432i	−0.735838	+	0.677158i	$0.763211\pi$
$824$	27.4485	+	20.9025i	0.956213	+	0.728173i
$825$		0			0
$826$	−3.96557	+	4.33830i	−0.137980	+	0.150949i
$827$	32.7738			1.13966			0.569829	−	0.821764i	$-0.307010\pi$
$827$	32.7738			1.13966			0.569829	+	0.821764i	$0.307010\pi$
$828$		0			0
$829$	42.2021			1.46574			0.732869	−	0.680369i	$-0.238181\pi$
$829$	42.2021			1.46574			0.732869	+	0.680369i	$0.238181\pi$
$830$	−14.4198	+	15.7751i	−0.500517	+	0.547560i
$831$		0			0
$832$	−9.63963	−	34.9484i	−0.334194	−	1.21162i
$833$			29.4342i			1.01983i
$834$		0			0
$835$		−	18.3963i		−	0.636631i
$836$	23.0788	−	2.07599i	0.798196	−	0.0717996i
$837$		0			0
$838$	3.16299	+	2.89124i	0.109264	+	0.0998763i
$839$	17.9091			0.618292			0.309146	−	0.951015i	$-0.399957\pi$
$839$	17.9091			0.618292			0.309146	+	0.951015i	$0.399957\pi$
$840$		0			0
$841$	−28.3304			−0.976910
$842$	−14.4799	−	13.2359i	−0.499011	−	0.456139i
$843$		0			0
$844$	−7.09387	+	0.638110i	−0.244181	+	0.0219647i
$845$			7.53619i			0.259253i
$846$		0			0
$847$		−	7.26997i		−	0.249799i
$848$	−0.298325	−	1.64482i	−0.0102445	−	0.0564834i
$849$		0			0
$850$	−4.47599	+	4.89669i	−0.153525	+	0.167955i
$851$	19.4384			0.666341
$852$		0			0
$853$	−13.0360			−0.446344			−0.223172	−	0.974779i	$-0.571641\pi$
$853$	−13.0360			−0.446344			−0.223172	+	0.974779i	$0.571641\pi$
$854$	−6.77280	+	7.40938i	−0.231761	+	0.253544i
$855$		0			0
$856$	−12.2822	+	16.1286i	−0.419798	+	0.551265i
$857$		−	5.91825i		−	0.202164i	−0.994878	−	0.101082i	$-0.967770\pi$
$857$		−	5.91825i		−	0.202164i	0.994878	−	0.101082i	$-0.0322304\pi$
$858$		0			0
$859$			57.3145i			1.95554i	0.209670	+	0.977772i	$0.432761\pi$
$859$			57.3145i			1.95554i	−0.209670	+	0.977772i	$0.567239\pi$
$860$	−1.23292	−	13.7064i	−0.0420423	−	0.467384i
$861$		0			0
$862$	−32.3198	−	29.5430i	−1.10082	−	1.00624i
$863$	−10.8816			−0.370413			−0.185207	−	0.982700i	$-0.559295\pi$
$863$	−10.8816			−0.370413			−0.185207	+	0.982700i	$0.559295\pi$
$864$		0			0
$865$	2.97748			0.101237
$866$	−16.5673	−	15.1439i	−0.562980	−	0.514612i
$867$		0			0
$868$	0.455926	+	5.06853i	0.0154751	+	0.172037i
$869$		−	8.84579i		−	0.300073i
$870$		0			0
$871$			28.3129i			0.959345i
$872$	12.8624	−	16.8904i	0.435574	−	0.571982i
$873$		0			0
$874$	−40.2934	+	44.0806i	−1.36294	+	1.49105i
$875$	0.851747			0.0287943
$876$		0			0
$877$	30.2139			1.02025			0.510125	−	0.860100i	$-0.329599\pi$
$877$	30.2139			1.02025			0.510125	+	0.860100i	$0.329599\pi$
$878$	5.64547	−	6.17609i	0.190525	−	0.208433i
$879$		0			0
$880$	1.12067	+	6.17886i	0.0377779	+	0.208289i
$881$		−	23.1986i		−	0.781582i	−0.920479	−	0.390791i	$-0.872202\pi$
$881$		−	23.1986i		−	0.781582i	0.920479	−	0.390791i	$-0.127798\pi$
$882$		0			0
$883$		−	6.25279i		−	0.210423i	−0.994450	−	0.105212i	$-0.966448\pi$
$883$		−	6.25279i		−	0.210423i	0.994450	−	0.105212i	$-0.0335520\pi$
$884$	−42.3459	+	3.80911i	−1.42425	+	0.128114i
$885$		0			0
$886$	3.65794	+	3.34367i	0.122891	+	0.112333i
$887$	45.4638			1.52652			0.763262	−	0.646089i	$-0.223597\pi$
$887$	45.4638			1.52652			0.763262	+	0.646089i	$0.223597\pi$
$888$		0			0
$889$	−3.56117			−0.119438
$890$	9.13699	+	8.35199i	0.306273	+	0.279959i
$891$		0			0
$892$	−12.6485	+	1.13776i	−0.423504	+	0.0380951i
$893$			2.05909i			0.0689049i
$894$		0			0
$895$		−	4.23878i		−	0.141687i
$896$	−8.58536	−	4.37631i	−0.286817	−	0.146202i
$897$		0			0
$898$	11.3104	−	12.3734i	0.377432	−	0.412907i
$899$	−22.6195			−0.754404
$900$		0			0
$901$	−1.96046			−0.0653124
$902$	5.98457	−	6.54706i	0.199264	−	0.217993i
$903$		0			0
$904$	5.02823	+	3.82909i	0.167236	+	0.127353i
$905$			7.13624i			0.237217i
$906$		0			0
$907$			50.6828i			1.68290i	0.540338	+	0.841448i	$0.318296\pi$
$907$			50.6828i			1.68290i	−0.540338	+	0.841448i	$0.681704\pi$
$908$	4.83316	+	53.7302i	0.160394	+	1.78310i
$909$		0			0
$910$	4.02905	+	3.68289i	0.133562	+	0.122087i
$911$	−18.1930			−0.602762			−0.301381	−	0.953504i	$-0.597448\pi$
$911$	−18.1930			−0.602762			−0.301381	+	0.953504i	$0.597448\pi$
$912$		0			0
$913$	23.7255			0.785201
$914$	29.1026	+	26.6022i	0.962628	+	0.879924i
$915$		0			0
$916$	4.65502	+	51.7499i	0.153806	+	1.70986i
$917$			11.0860i			0.366093i
$918$		0			0
$919$		−	12.3419i		−	0.407121i	−0.979062	−	0.203560i	$-0.934749\pi$
$919$		−	12.3419i		−	0.407121i	0.979062	−	0.203560i	$-0.0652513\pi$
$920$	−12.8762	−	9.80548i	−0.424517	−	0.323277i
$921$		0			0
$922$	−22.3036	+	24.3999i	−0.734530	+	0.803568i
$923$	15.5817			0.512878
$924$		0			0
$925$	3.39705			0.111694
$926$	−18.3814	+	20.1091i	−0.604050	+	0.660825i
$927$		0			0
$928$	22.7924	−	36.2640i	0.748197	−	1.19043i
$929$		−	30.0608i		−	0.986262i	−0.869955	−	0.493131i	$-0.835852\pi$
$929$		−	30.0608i		−	0.986262i	0.869955	−	0.493131i	$-0.164148\pi$
$930$		0			0
$931$			46.3060i			1.51762i
$932$	−13.5324	+	1.21727i	−0.443269	+	0.0398731i
$933$		0			0
$934$	−20.8489	−	19.0577i	−0.682198	−	0.623588i
$935$	7.36458			0.240847
$936$		0			0
$937$	18.8946			0.617259			0.308629	−	0.951182i	$-0.400130\pi$
$937$	18.8946			0.617259			0.308629	+	0.951182i	$0.400130\pi$
$938$	5.55477	+	5.07754i	0.181370	+	0.165787i
$939$		0			0
$940$	−0.555776	+	0.0499933i	−0.0181274	+	0.00163060i
$941$			16.2027i			0.528192i	0.964496	+	0.264096i	$0.0850736\pi$
$941$			16.2027i			0.528192i	−0.964496	+	0.264096i	$0.914926\pi$
$942$		0			0
$943$			22.8611i			0.744461i
$944$	19.2048	−	3.48321i	0.625062	−	0.113369i
$945$		0			0
$946$	−10.3071	+	11.2759i	−0.335114	+	0.366611i
$947$	16.5307			0.537176			0.268588	−	0.963255i	$-0.413443\pi$
$947$	16.5307			0.537176			0.268588	+	0.963255i	$0.413443\pi$
$948$		0			0
$949$	−55.4765			−1.80084
$950$	−7.04165	+	7.70349i	−0.228461	+	0.249934i
$951$		0			0
$952$	−6.84685	+	8.99106i	−0.221908	+	0.291402i
$953$		−	21.1623i		−	0.685515i	−0.939424	−	0.342758i	$-0.888639\pi$
$953$		−	21.1623i		−	0.685515i	0.939424	−	0.342758i	$-0.111361\pi$
$954$		0			0
$955$			5.33967i			0.172788i
$956$	4.46239	+	49.6084i	0.144324	+	1.60445i
$957$		0			0
$958$	−4.50094	−	4.11424i	−0.145419	−	0.132925i
$959$	−12.2017			−0.394013
$960$		0			0
$961$	22.0755			0.712114
$962$	16.0692	+	14.6886i	0.518091	+	0.473579i
$963$		0			0
$964$	−3.09142	−	34.3674i	−0.0995680	−	1.10690i
$965$		−	15.0247i		−	0.483663i
$966$		0			0
$967$			18.4607i			0.593657i	0.954931	+	0.296829i	$0.0959290\pi$
$967$			18.4607i			0.593657i	−0.954931	+	0.296829i	$0.904071\pi$
$968$	−14.6262	+	19.2066i	−0.470103	+	0.617324i
$969$		0			0
$970$	12.3278	−	13.4865i	0.395821	−	0.433024i
$971$	−12.2603			−0.393451			−0.196726	−	0.980459i	$-0.563031\pi$
$971$	−12.2603			−0.393451			−0.196726	+	0.980459i	$0.563031\pi$
$972$		0			0
$973$	16.4483			0.527308
$974$	2.84834	−	3.11605i	0.0912667	−	0.0998448i
$975$		0			0
$976$	32.7998	−	5.94897i	1.04990	−	0.190422i
$977$			43.5533i			1.39339i	0.717366	+	0.696697i	$0.245348\pi$
$977$			43.5533i			1.39339i	−0.717366	+	0.696697i	$0.754652\pi$
$978$		0			0
$979$		−	13.7420i		−	0.439195i
$980$	−12.4986	+	1.12428i	−0.399253	+	0.0359137i
$981$		0			0
$982$	−40.8521	−	37.3423i	−1.30364	−	1.19164i
$983$	16.0245			0.511101			0.255550	−	0.966796i	$-0.417743\pi$
$983$	16.0245			0.511101			0.255550	+	0.966796i	$0.417743\pi$
$984$		0			0
$985$	−8.98496			−0.286285
$986$	−37.0762	−	33.8908i	−1.18075	−	1.07930i
$987$		0			0
$988$	−66.6187	+	5.99250i	−2.11942	+	0.190647i
$989$		−	39.3734i		−	1.25200i
$990$		0			0
$991$		−	10.0391i		−	0.318902i	−0.987206	−	0.159451i	$-0.949028\pi$
$991$		−	10.0391i		−	0.318902i	0.987206	−	0.159451i	$-0.0509725\pi$
$992$	8.99267	−	14.3079i	0.285518	−	0.454275i
$993$		0			0
$994$	2.79437	−	3.05702i	0.0886321	−	0.0969627i
$995$	17.8451			0.565727
$996$		0			0
$997$	27.9052			0.883767			0.441883	−	0.897072i	$-0.354310\pi$
$997$	27.9052			0.883767			0.441883	+	0.897072i	$0.354310\pi$
$998$	−4.68298	+	5.12313i	−0.148237	+	0.162170i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.13		48
3.2	odd	2	inner	1620.2.e.b.971.36		48
4.3	odd	2	inner	1620.2.e.b.971.35		48
9.2	odd	6		180.2.q.a.131.14	yes	48
9.4	even	3		180.2.q.a.11.22	yes	48
9.5	odd	6		540.2.q.a.251.3		48
9.7	even	3		540.2.q.a.71.11		48
12.11	even	2	inner	1620.2.e.b.971.14		48
36.7	odd	6		540.2.q.a.71.3		48
36.11	even	6		180.2.q.a.131.22	yes	48
36.23	even	6		540.2.q.a.251.11		48
36.31	odd	6		180.2.q.a.11.14	✓	48
45.2	even	12		900.2.o.c.599.22		48
45.4	even	6		900.2.r.f.551.3		48
45.13	odd	12		900.2.o.c.299.11		48
45.22	odd	12		900.2.o.b.299.14		48
45.29	odd	6		900.2.r.f.851.11		48
45.38	even	12		900.2.o.b.599.3		48
180.47	odd	12		900.2.o.c.599.11		48
180.67	even	12		900.2.o.b.299.3		48
180.83	odd	12		900.2.o.b.599.14		48
180.103	even	12		900.2.o.c.299.22		48
180.119	even	6		900.2.r.f.851.3		48
180.139	odd	6		900.2.r.f.551.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.14	✓	48	36.31	odd	6
180.2.q.a.11.22	yes	48	9.4	even	3
180.2.q.a.131.14	yes	48	9.2	odd	6
180.2.q.a.131.22	yes	48	36.11	even	6
540.2.q.a.71.3		48	36.7	odd	6
540.2.q.a.71.11		48	9.7	even	3
540.2.q.a.251.3		48	9.5	odd	6
540.2.q.a.251.11		48	36.23	even	6
900.2.o.b.299.3		48	180.67	even	12
900.2.o.b.299.14		48	45.22	odd	12
900.2.o.b.599.3		48	45.38	even	12
900.2.o.b.599.14		48	180.83	odd	12
900.2.o.c.299.11		48	45.13	odd	12
900.2.o.c.299.22		48	180.103	even	12
900.2.o.c.599.11		48	180.47	odd	12
900.2.o.c.599.22		48	45.2	even	12
900.2.r.f.551.3		48	45.4	even	6
900.2.r.f.551.11		48	180.139	odd	6
900.2.r.f.851.3		48	180.119	even	6
900.2.r.f.851.11		48	45.29	odd	6
1620.2.e.b.971.13		48	1.1	even	1	trivial
1620.2.e.b.971.14		48	12.11	even	2	inner
1620.2.e.b.971.35		48	4.3	odd	2	inner
1620.2.e.b.971.36		48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04383 - 0.954154i) q^{2} +(0.179181 + 1.99196i) q^{4} +1.00000i q^{5} +0.851747i q^{7} +(1.71360 - 2.25024i) q^{8} +O(q^{10})\)	\(q+(-1.04383 - 0.954154i) q^{2} +(0.179181 + 1.99196i) q^{4} +1.00000i q^{5} +0.851747i q^{7} +(1.71360 - 2.25024i) q^{8} +(0.954154 - 1.04383i) q^{10} -1.56992 q^{11} +4.53169 q^{13} +(0.812698 - 0.889083i) q^{14} +(-3.93579 + 0.713842i) q^{16} +4.69106i q^{17} +7.37999i q^{19} +(-1.99196 + 0.179181i) q^{20} +(1.63873 + 1.49794i) q^{22} -5.72216 q^{23} -1.00000 q^{25} +(-4.73033 - 4.32393i) q^{26} +(-1.69664 + 0.152617i) q^{28} -7.57168i q^{29} -2.98739i q^{31} +(4.78943 + 3.01021i) q^{32} +(4.47599 - 4.89669i) q^{34} -0.851747 q^{35} -3.39705 q^{37} +(7.04165 - 7.70349i) q^{38} +(2.25024 + 1.71360i) q^{40} -3.99519i q^{41} +6.88087i q^{43} +(-0.281299 - 3.12721i) q^{44} +(5.97298 + 5.45982i) q^{46} +0.279010 q^{47} +6.27453 q^{49} +(1.04383 + 0.954154i) q^{50} +(0.811993 + 9.02693i) q^{52} +0.417914i q^{53} -1.56992i q^{55} +(1.91664 + 1.45955i) q^{56} +(-7.22455 + 7.90359i) q^{58} -4.87952 q^{59} -8.33373 q^{61} +(-2.85043 + 3.11834i) q^{62} +(-2.12716 - 7.71202i) q^{64} +4.53169i q^{65} +6.24776i q^{67} +(-9.34439 + 0.840549i) q^{68} +(0.889083 + 0.812698i) q^{70} +3.43839 q^{71} -12.2419 q^{73} +(3.54596 + 3.24131i) q^{74} +(-14.7006 + 1.32236i) q^{76} -1.33717i q^{77} +5.63456i q^{79} +(-0.713842 - 3.93579i) q^{80} +(-3.81203 + 4.17032i) q^{82} -15.1126 q^{83} -4.69106 q^{85} +(6.56540 - 7.18249i) q^{86} +(-2.69021 + 3.53269i) q^{88} +8.75330i q^{89} +3.85985i q^{91} +(-1.02530 - 11.3983i) q^{92} +(-0.291240 - 0.266218i) q^{94} -7.37999 q^{95} +12.9201 q^{97} +(-6.54957 - 5.98686i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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