LMFDB - Embedded newform 405.3.h.i.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(134,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("405.134");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.3
Root			$-2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	405.269
Dual form			405.3.h.i.134.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58114 - 2.73861i) q^{2} +(-3.00000 - 5.19615i) q^{4} +(-3.31735 + 3.74101i) q^{5} +(-2.59808 - 1.50000i) q^{7} -6.32456 q^{8} +(5.00000 + 15.0000i) q^{10} +(-8.21584 - 4.74342i) q^{11} +(-18.1865 + 10.5000i) q^{13} +(-8.21584 + 4.74342i) q^{14} +(2.00000 - 3.46410i) q^{16} -12.6491 q^{17} -31.0000 q^{19} +(29.3909 + 6.01441i) q^{20} +(-25.9808 + 15.0000i) q^{22} +(11.0680 + 19.1703i) q^{23} +(-2.99038 - 24.8205i) q^{25} +66.4078i q^{26} +18.0000i q^{28} +(41.0792 + 23.7171i) q^{29} +(8.00000 + 13.8564i) q^{31} +(-18.9737 - 32.8634i) q^{32} +(-20.0000 + 34.6410i) q^{34} +(14.2302 - 4.74342i) q^{35} -27.0000i q^{37} +(-49.0153 + 84.8970i) q^{38} +(20.9808 - 23.6603i) q^{40} +(41.0792 - 23.7171i) q^{41} +(-41.5692 - 24.0000i) q^{43} +56.9210i q^{44} +70.0000 q^{46} +(6.32456 - 10.9545i) q^{47} +(-20.0000 - 34.6410i) q^{49} +(-72.7020 - 31.0552i) q^{50} +(109.119 + 63.0000i) q^{52} -41.1096 q^{53} +(45.0000 - 15.0000i) q^{55} +(16.4317 + 9.48683i) q^{56} +(129.904 - 75.0000i) q^{58} +(-32.8634 + 18.9737i) q^{59} +(0.500000 - 0.866025i) q^{61} +50.5964 q^{62} -104.000 q^{64} +(21.0504 - 102.868i) q^{65} +(-18.1865 + 10.5000i) q^{67} +(37.9473 + 65.7267i) q^{68} +(9.50962 - 46.4711i) q^{70} -28.4605i q^{71} -27.0000i q^{73} +(-73.9425 - 42.6907i) q^{74} +(93.0000 + 161.081i) q^{76} +(14.2302 + 24.6475i) q^{77} +(0.500000 - 0.866025i) q^{79} +(6.32456 + 18.9737i) q^{80} -150.000i q^{82} +(-55.3399 + 95.8514i) q^{83} +(41.9615 - 47.3205i) q^{85} +(-131.453 + 75.8947i) q^{86} +(51.9615 + 30.0000i) q^{88} -113.842i q^{89} +63.0000 q^{91} +(66.4078 - 115.022i) q^{92} +(-20.0000 - 34.6410i) q^{94} +(102.838 - 115.971i) q^{95} +(-80.5404 - 46.5000i) q^{97} -126.491 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 24 q^{4} + 40 q^{10} + 16 q^{16} - 248 q^{19} + 80 q^{25} + 64 q^{31} - 160 q^{34} - 40 q^{40} + 560 q^{46} - 160 q^{49} + 360 q^{55} + 4 q^{61} - 832 q^{64} + 180 q^{70} + 744 q^{76} + 4 q^{79} - 80 q^{85}+ \cdots - 160 q^{94}+O(q^{100}) $ 8 * q - 24 * q^4 + 40 * q^10 + 16 * q^16 - 248 * q^19 + 80 * q^25 + 64 * q^31 - 160 * q^34 - 40 * q^40 + 560 * q^46 - 160 * q^49 + 360 * q^55 + 4 * q^61 - 832 * q^64 + 180 * q^70 + 744 * q^76 + 4 * q^79 - 80 * q^85 + 504 * q^91 - 160 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.58114	−	2.73861i	0.790569	−	1.36931i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	1.58114	−	2.73861i	0.790569	−	1.36931i	0.925615	−	0.378467i	$-0.123549\pi$
$3$		0			0
$3$		0			0
$4$	−3.00000	−	5.19615i	−0.750000	−	1.29904i
$5$	−3.31735	+	3.74101i	−0.663470	+	0.748203i
$5$	−3.31735	+	3.74101i	−0.663470	+	0.748203i
$6$		0			0
$7$	−2.59808	−	1.50000i	−0.371154	−	0.214286i	0.302809	−	0.953051i	$-0.402076\pi$
$7$	−2.59808	−	1.50000i	−0.371154	−	0.214286i	−0.673962	+	0.738766i	$0.735409\pi$
$8$	−6.32456			−0.790569
$9$		0			0
$10$	5.00000	+	15.0000i	0.500000	+	1.50000i
$11$	−8.21584	−	4.74342i	−0.746894	−	0.431220i	0.0776763	−	0.996979i	$-0.475250\pi$
$11$	−8.21584	−	4.74342i	−0.746894	−	0.431220i	−0.824571	+	0.565759i	$0.808583\pi$
$12$		0			0
$13$	−18.1865	+	10.5000i	−1.39896	+	0.807692i	−0.994284	−	0.106766i	$-0.965950\pi$
$13$	−18.1865	+	10.5000i	−1.39896	+	0.807692i	−0.404680	+	0.914458i	$0.632617\pi$
$14$	−8.21584	+	4.74342i	−0.586846	+	0.338815i
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−12.6491			−0.744065			−0.372033	−	0.928220i	$-0.621339\pi$
$17$	−12.6491			−0.744065			−0.372033	+	0.928220i	$0.621339\pi$
$18$		0			0
$19$	−31.0000			−1.63158			−0.815789	−	0.578349i	$-0.803697\pi$
$19$	−31.0000			−1.63158			−0.815789	+	0.578349i	$0.803697\pi$
$20$	29.3909	+	6.01441i	1.46955	+	0.300721i
$21$		0			0
$22$	−25.9808	+	15.0000i	−1.18094	+	0.681818i
$23$	11.0680	+	19.1703i	0.481216	+	0.833491i	0.999768	−	0.0215556i	$-0.00686188\pi$
$23$	11.0680	+	19.1703i	0.481216	+	0.833491i	−0.518551	+	0.855046i	$0.673529\pi$
$24$		0			0
$25$	−2.99038	−	24.8205i	−0.119615	−	0.992820i
$26$			66.4078i			2.55415i
$27$		0			0
$28$			18.0000i			0.642857i
$29$	41.0792	+	23.7171i	1.41652	+	0.817830i	0.995992	−	0.0894471i	$-0.0285100\pi$
$29$	41.0792	+	23.7171i	1.41652	+	0.817830i	0.420532	+	0.907278i	$0.361843\pi$
$30$		0			0
$31$	8.00000	+	13.8564i	0.258065	+	0.446981i	0.965723	−	0.259573i	$-0.0835820\pi$
$31$	8.00000	+	13.8564i	0.258065	+	0.446981i	−0.707659	+	0.706554i	$0.750249\pi$
$32$	−18.9737	−	32.8634i	−0.592927	−	1.02698i
$33$		0			0
$34$	−20.0000	+	34.6410i	−0.588235	+	1.01885i
$35$	14.2302	−	4.74342i	0.406579	−	0.135526i
$36$		0			0
$37$		−	27.0000i		−	0.729730i	−0.931060	−	0.364865i	$-0.881115\pi$
$37$		−	27.0000i		−	0.729730i	0.931060	−	0.364865i	$-0.118885\pi$
$38$	−49.0153	+	84.8970i	−1.28988	+	2.23413i
$39$		0			0
$40$	20.9808	−	23.6603i	0.524519	−	0.591506i
$41$	41.0792	−	23.7171i	1.00193	−	0.578465i	0.0931123	−	0.995656i	$-0.470318\pi$
$41$	41.0792	−	23.7171i	1.00193	−	0.578465i	0.908819	+	0.417190i	$0.136985\pi$
$42$		0			0
$43$	−41.5692	−	24.0000i	−0.966726	−	0.558140i	−0.0684895	−	0.997652i	$-0.521818\pi$
$43$	−41.5692	−	24.0000i	−0.966726	−	0.558140i	−0.898237	+	0.439512i	$0.855151\pi$
$44$			56.9210i			1.29366i
$45$		0			0
$46$	70.0000			1.52174
$47$	6.32456	−	10.9545i	0.134565	−	0.233073i	−0.790866	−	0.611989i	$-0.790370\pi$
$47$	6.32456	−	10.9545i	0.134565	−	0.233073i	0.925431	+	0.378916i	$0.123703\pi$
$48$		0			0
$49$	−20.0000	−	34.6410i	−0.408163	−	0.706960i
$50$	−72.7020	−	31.0552i	−1.45404	−	0.621103i
$51$		0			0
$52$	109.119	+	63.0000i	2.09845	+	1.21154i
$53$	−41.1096			−0.775653			−0.387827	−	0.921732i	$-0.626774\pi$
$53$	−41.1096			−0.775653			−0.387827	+	0.921732i	$0.626774\pi$
$54$		0			0
$55$	45.0000	−	15.0000i	0.818182	−	0.272727i
$56$	16.4317	+	9.48683i	0.293423	+	0.169408i
$57$		0			0
$58$	129.904	−	75.0000i	2.23972	−	1.29310i
$59$	−32.8634	+	18.9737i	−0.557006	+	0.321588i	−0.751943	−	0.659228i	$-0.770883\pi$
$59$	−32.8634	+	18.9737i	−0.557006	+	0.321588i	0.194937	+	0.980816i	$0.437550\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.00819672	−	0.0141971i	−0.861898	−	0.507082i	$-0.830724\pi$
$61$	0.500000	−	0.866025i	0.00819672	−	0.0141971i	0.870095	+	0.492885i	$0.164058\pi$
$62$	50.5964			0.816072
$63$		0			0
$64$	−104.000			−1.62500
$65$	21.0504	−	102.868i	0.323853	−	1.58259i
$66$		0			0
$67$	−18.1865	+	10.5000i	−0.271441	+	0.156716i	−0.629542	−	0.776966i	$-0.716758\pi$
$67$	−18.1865	+	10.5000i	−0.271441	+	0.156716i	0.358101	+	0.933683i	$0.383424\pi$
$68$	37.9473	+	65.7267i	0.558049	+	0.966569i
$69$		0			0
$70$	9.50962	−	46.4711i	0.135852	−	0.663873i
$71$		−	28.4605i		−	0.400852i	−0.979709	−	0.200426i	$-0.935767\pi$
$71$		−	28.4605i		−	0.400852i	0.979709	−	0.200426i	$-0.0642326\pi$
$72$		0			0
$73$		−	27.0000i		−	0.369863i	−0.982751	−	0.184932i	$-0.940794\pi$
$73$		−	27.0000i		−	0.369863i	0.982751	−	0.184932i	$-0.0592063\pi$
$74$	−73.9425	−	42.6907i	−0.999224	−	0.576902i
$75$		0			0
$76$	93.0000	+	161.081i	1.22368	+	2.11948i
$77$	14.2302	+	24.6475i	0.184808	+	0.320098i
$78$		0			0
$79$	0.500000	−	0.866025i	0.00632911	−	0.0109623i	−0.862844	−	0.505471i	$-0.831319\pi$
$79$	0.500000	−	0.866025i	0.00632911	−	0.0109623i	0.869173	+	0.494509i	$0.164652\pi$
$80$	6.32456	+	18.9737i	0.0790569	+	0.237171i
$81$		0			0
$82$		−	150.000i		−	1.82927i
$83$	−55.3399	+	95.8514i	−0.666745	+	1.15484i	0.312064	+	0.950061i	$0.398980\pi$
$83$	−55.3399	+	95.8514i	−0.666745	+	1.15484i	−0.978809	+	0.204776i	$0.934354\pi$
$84$		0			0
$85$	41.9615	−	47.3205i	0.493665	−	0.556712i
$86$	−131.453	+	75.8947i	−1.52853	+	0.882496i
$87$		0			0
$88$	51.9615	+	30.0000i	0.590472	+	0.340909i
$89$		−	113.842i		−	1.27912i	−0.768740	−	0.639562i	$-0.779116\pi$
$89$		−	113.842i		−	1.27912i	0.768740	−	0.639562i	$-0.220884\pi$
$90$		0			0
$91$	63.0000			0.692308
$92$	66.4078	−	115.022i	0.721824	−	1.25024i
$93$		0			0
$94$	−20.0000	−	34.6410i	−0.212766	−	0.368521i
$95$	102.838	−	115.971i	1.08250	−	1.22075i
$96$		0			0
$97$	−80.5404	−	46.5000i	−0.830313	−	0.479381i	0.0236468	−	0.999720i	$-0.492472\pi$
$97$	−80.5404	−	46.5000i	−0.830313	−	0.479381i	−0.853960	+	0.520339i	$0.825806\pi$
$98$	−126.491			−1.29073
$99$		0			0
$100$	−120.000	+	90.0000i	−1.20000	+	0.900000i
$101$	65.7267	+	37.9473i	0.650759	+	0.375716i	0.788747	−	0.614718i	$-0.210730\pi$
$101$	65.7267	+	37.9473i	0.650759	+	0.375716i	−0.137988	+	0.990434i	$0.544063\pi$
$102$		0			0
$103$	−127.306	+	73.5000i	−1.23598	+	0.713592i	−0.968270	−	0.249908i	$-0.919600\pi$
$103$	−127.306	+	73.5000i	−1.23598	+	0.713592i	−0.267708	+	0.963500i	$0.586266\pi$
$104$	115.022	−	66.4078i	1.10598	−	0.638537i
$105$		0			0
$106$	−65.0000	+	112.583i	−0.613208	+	1.06211i
$107$	−22.1359			−0.206878			−0.103439	−	0.994636i	$-0.532985\pi$
$107$	−22.1359			−0.206878			−0.103439	+	0.994636i	$0.532985\pi$
$108$		0			0
$109$	104.000			0.954128			0.477064	−	0.878868i	$-0.341701\pi$
$109$	104.000			0.954128			0.477064	+	0.878868i	$0.341701\pi$
$110$	30.0721	−	146.955i	0.273382	−	1.33595i
$111$		0			0
$112$	−10.3923	+	6.00000i	−0.0927884	+	0.0535714i
$113$	86.9626	+	150.624i	0.769581	+	1.33295i	0.937790	+	0.347202i	$0.112868\pi$
$113$	86.9626	+	150.624i	0.769581	+	1.33295i	−0.168210	+	0.985751i	$0.553799\pi$
$114$		0			0
$115$	−108.433	−	22.1891i	−0.942893	−	0.192949i
$116$		−	284.605i		−	2.45349i
$117$		0			0
$118$			120.000i			1.01695i
$119$	32.8634	+	18.9737i	0.276163	+	0.159443i
$120$		0			0
$121$	−15.5000	−	26.8468i	−0.128099	−	0.221874i
$122$	−1.58114	−	2.73861i	−0.0129602	−	0.0224476i
$123$		0			0
$124$	48.0000	−	83.1384i	0.387097	−	0.670471i
$125$	102.774	+	71.1512i	0.822192	+	0.569210i
$126$		0			0
$127$			144.000i			1.13386i	0.823767	+	0.566929i	$0.191869\pi$
$127$			144.000i			1.13386i	−0.823767	+	0.566929i	$0.808131\pi$
$128$	−88.5438	+	153.362i	−0.691748	+	1.19814i
$129$		0			0
$130$	−248.433	−	220.298i	−1.91102	−	1.69460i
$131$	65.7267	−	37.9473i	0.501731	−	0.289674i	−0.227697	−	0.973732i	$-0.573120\pi$
$131$	65.7267	−	37.9473i	0.501731	−	0.289674i	0.729428	+	0.684058i	$0.239786\pi$
$132$		0			0
$133$	80.5404	+	46.5000i	0.605567	+	0.349624i
$134$			66.4078i			0.495581i
$135$		0			0
$136$	80.0000			0.588235
$137$	−26.8794	+	46.5564i	−0.196200	+	0.339828i	−0.947293	−	0.320368i	$-0.896193\pi$
$137$	−26.8794	+	46.5564i	−0.196200	+	0.339828i	0.751093	+	0.660196i	$0.229527\pi$
$138$		0			0
$139$	0.500000	+	0.866025i	0.00359712	+	0.00623040i	0.867818	−	0.496882i	$-0.165522\pi$
$139$	0.500000	+	0.866025i	0.00359712	+	0.00623040i	−0.864221	+	0.503112i	$0.832188\pi$
$140$	−67.3383	−	59.7123i	−0.480988	−	0.426516i
$141$		0			0
$142$	−77.9423	−	45.0000i	−0.548889	−	0.316901i
$143$	199.223			1.39317
$144$		0			0
$145$	−225.000	+	75.0000i	−1.55172	+	0.517241i
$146$	−73.9425	−	42.6907i	−0.506456	−	0.292402i
$147$		0			0
$148$	−140.296	+	81.0000i	−0.947947	+	0.547297i
$149$	65.7267	−	37.9473i	0.441119	−	0.254680i	−0.262953	−	0.964809i	$-0.584697\pi$
$149$	65.7267	−	37.9473i	0.441119	−	0.254680i	0.704072	+	0.710128i	$0.251363\pi$
$150$		0			0
$151$	15.5000	−	26.8468i	0.102649	−	0.177793i	−0.810126	−	0.586255i	$-0.800601\pi$
$151$	15.5000	−	26.8468i	0.102649	−	0.177793i	0.912775	+	0.408462i	$0.133935\pi$
$152$	196.061			1.28988
$153$		0			0
$154$	90.0000			0.584416
$155$	−78.3758	−	16.0384i	−0.505650	−	0.103474i
$156$		0			0
$157$	−88.3346	+	51.0000i	−0.562641	+	0.324841i	−0.754205	−	0.656639i	$-0.771977\pi$
$157$	−88.3346	+	51.0000i	−0.562641	+	0.324841i	0.191564	+	0.981480i	$0.438644\pi$
$158$	−1.58114	−	2.73861i	−0.0100072	−	0.0173330i
$159$		0			0
$160$	185.885	+	38.0385i	1.16178	+	0.237740i
$161$		−	66.4078i		−	0.412471i
$162$		0			0
$163$		−	171.000i		−	1.04908i	−0.851386	−	0.524540i	$-0.824237\pi$
$163$		−	171.000i		−	1.04908i	0.851386	−	0.524540i	$-0.175763\pi$
$164$	−246.475	−	142.302i	−1.50290	−	0.867698i
$165$		0			0
$166$	175.000	+	303.109i	1.05422	+	1.82596i
$167$	−145.465	−	251.952i	−0.871047	−	1.50870i	−0.860915	−	0.508748i	$-0.830108\pi$
$167$	−145.465	−	251.952i	−0.871047	−	1.50870i	−0.0101312	−	0.999949i	$-0.503225\pi$
$168$		0			0
$169$	136.000	−	235.559i	0.804734	−	1.39384i
$170$	−63.2456	−	189.737i	−0.372033	−	1.11610i
$171$		0			0
$172$			288.000i			1.67442i
$173$	−12.6491	+	21.9089i	−0.0731162	+	0.126641i	−0.900266	−	0.435341i	$-0.856628\pi$
$173$	−12.6491	+	21.9089i	−0.0731162	+	0.126641i	0.827149	+	0.561982i	$0.189961\pi$
$174$		0			0
$175$	−29.4615	+	68.9711i	−0.168352	+	0.394121i
$176$	−32.8634	+	18.9737i	−0.186724	+	0.107805i
$177$		0			0
$178$	−311.769	−	180.000i	−1.75151	−	1.01124i
$179$		−	199.223i		−	1.11298i	−0.830854	−	0.556490i	$-0.812148\pi$
$179$		−	199.223i		−	1.11298i	0.830854	−	0.556490i	$-0.187852\pi$
$180$		0			0
$181$	−103.000			−0.569061			−0.284530	−	0.958667i	$-0.591838\pi$
$181$	−103.000			−0.569061			−0.284530	+	0.958667i	$0.591838\pi$
$182$	99.6117	−	172.533i	0.547317	−	0.947981i
$183$		0			0
$184$	−70.0000	−	121.244i	−0.380435	−	0.658932i
$185$	101.007	+	89.5684i	0.545986	+	0.484154i
$186$		0			0
$187$	103.923	+	60.0000i	0.555738	+	0.320856i
$188$	−75.8947			−0.403695
$189$		0			0
$190$	−155.000	−	465.000i	−0.815789	−	2.44737i
$191$	−230.043	−	132.816i	−1.20442	−	0.695370i	−0.242882	−	0.970056i	$-0.578093\pi$
$191$	−230.043	−	132.816i	−1.20442	−	0.695370i	−0.961534	+	0.274686i	$0.911426\pi$
$192$		0			0
$193$	184.463	−	106.500i	0.955769	−	0.551813i	0.0609007	−	0.998144i	$-0.480603\pi$
$193$	184.463	−	106.500i	0.955769	−	0.551813i	0.894868	+	0.446330i	$0.147269\pi$
$194$	−254.691	+	147.046i	−1.31284	+	0.757969i
$195$		0			0
$196$	−120.000	+	207.846i	−0.612245	+	1.06044i
$197$	−240.333			−1.21996			−0.609982	−	0.792415i	$-0.708824\pi$
$197$	−240.333			−1.21996			−0.609982	+	0.792415i	$0.708824\pi$
$198$		0			0
$199$	47.0000			0.236181			0.118090	−	0.993003i	$-0.462323\pi$
$199$	47.0000			0.236181			0.118090	+	0.993003i	$0.462323\pi$
$200$	18.9128	+	156.979i	0.0945642	+	0.784893i
$201$		0			0
$202$	207.846	−	120.000i	1.02894	−	0.594059i
$203$	−71.1512	−	123.238i	−0.350499	−	0.607082i
$204$		0			0
$205$	−47.5481	+	232.356i	−0.231942	+	1.13344i
$206$			464.855i			2.25658i
$207$		0			0
$208$			84.0000i			0.403846i
$209$	254.691	+	147.046i	1.21862	+	0.703569i
$210$		0			0
$211$	111.500	+	193.124i	0.528436	+	0.915278i	0.999450	+	0.0331525i	$0.0105547\pi$
$211$	111.500	+	193.124i	0.528436	+	0.915278i	−0.471014	+	0.882126i	$0.656112\pi$
$212$	123.329	+	213.612i	0.581740	+	1.00760i
$213$		0			0
$214$	−35.0000	+	60.6218i	−0.163551	+	0.283279i
$215$	227.684	−	75.8947i	1.05900	−	0.352998i
$216$		0			0
$217$		−	48.0000i		−	0.221198i
$218$	164.438	−	284.816i	0.754305	−	1.30649i
$219$		0			0
$220$	−212.942	−	188.827i	−0.967919	−	0.858304i
$221$	230.043	−	132.816i	1.04092	−	0.600976i
$222$		0			0
$223$	270.200	+	156.000i	1.21166	+	0.699552i	0.963120	−	0.269070i	$-0.0867165\pi$
$223$	270.200	+	156.000i	1.21166	+	0.699552i	0.248538	+	0.968622i	$0.420050\pi$
$224$			113.842i			0.508223i
$225$		0			0
$226$	550.000			2.43363
$227$	−169.182	+	293.032i	−0.745295	+	1.29089i	0.204763	+	0.978812i	$0.434358\pi$
$227$	−169.182	+	293.032i	−0.745295	+	1.29089i	−0.950057	+	0.312076i	$0.898976\pi$
$228$		0			0
$229$	8.00000	+	13.8564i	0.0349345	+	0.0605083i	0.882964	−	0.469441i	$-0.155544\pi$
$229$	8.00000	+	13.8564i	0.0349345	+	0.0605083i	−0.848030	+	0.529949i	$0.822211\pi$
$230$	−232.214	+	261.871i	−1.00963	+	1.13857i
$231$		0			0
$232$	−259.808	−	150.000i	−1.11986	−	0.646552i
$233$	−50.5964			−0.217152			−0.108576	−	0.994088i	$-0.534629\pi$
$233$	−50.5964			−0.217152			−0.108576	+	0.994088i	$0.534629\pi$
$234$		0			0
$235$	20.0000	+	60.0000i	0.0851064	+	0.255319i
$236$	197.180	+	113.842i	0.835509	+	0.482381i
$237$		0			0
$238$	103.923	−	60.0000i	0.436651	−	0.252101i
$239$	90.3742	−	52.1776i	0.378135	−	0.218316i	−0.298872	−	0.954293i	$-0.596610\pi$
$239$	90.3742	−	52.1776i	0.378135	−	0.218316i	0.677006	+	0.735977i	$0.263277\pi$
$240$		0			0
$241$	−143.500	+	248.549i	−0.595436	+	1.03132i	0.398050	+	0.917364i	$0.369687\pi$
$241$	−143.500	+	248.549i	−0.595436	+	1.03132i	−0.993485	+	0.113961i	$0.963646\pi$
$242$	−98.0306			−0.405085
$243$		0			0
$244$	−6.00000			−0.0245902
$245$	195.940	+	40.0961i	0.799753	+	0.163657i
$246$		0			0
$247$	563.783	−	325.500i	2.28252	−	1.31781i
$248$	−50.5964	−	87.6356i	−0.204018	−	0.353369i
$249$		0			0
$250$	357.356	−	168.958i	1.42942	−	0.675833i
$251$			256.144i			1.02050i	0.860027	+	0.510248i	$0.170446\pi$
$251$			256.144i			1.02050i	−0.860027	+	0.510248i	$0.829554\pi$
$252$		0			0
$253$		−	210.000i		−	0.830040i
$254$	394.360	+	227.684i	1.55260	+	0.896394i
$255$		0			0
$256$	72.0000	+	124.708i	0.281250	+	0.487139i
$257$	139.140	+	240.998i	0.541402	+	0.937735i	0.998824	+	0.0484855i	$0.0154395\pi$
$257$	139.140	+	240.998i	0.541402	+	0.937735i	−0.457422	+	0.889250i	$0.651227\pi$
$258$		0			0
$259$	−40.5000	+	70.1481i	−0.156371	+	0.270842i
$260$	−597.670	+	199.223i	−2.29873	+	0.766244i
$261$		0			0
$262$		−	240.000i		−	0.916031i
$263$	177.088	−	306.725i	0.673337	−	1.16625i	−0.303615	−	0.952795i	$-0.598194\pi$
$263$	177.088	−	306.725i	0.673337	−	1.16625i	0.976952	−	0.213459i	$-0.0684729\pi$
$264$		0			0
$265$	136.375	−	153.792i	0.514622	−	0.580346i
$266$	254.691	−	147.046i	0.957485	−	0.552804i
$267$		0			0
$268$	109.119	+	63.0000i	0.407161	+	0.235075i
$269$			113.842i			0.423204i	0.977356	+	0.211602i	$0.0678681\pi$
$269$			113.842i			0.423204i	−0.977356	+	0.211602i	$0.932132\pi$
$270$		0			0
$271$	−121.000			−0.446494			−0.223247	−	0.974762i	$-0.571666\pi$
$271$	−121.000			−0.446494			−0.223247	+	0.974762i	$0.571666\pi$
$272$	−25.2982	+	43.8178i	−0.0930082	+	0.161095i
$273$		0			0
$274$	85.0000	+	147.224i	0.310219	+	0.537315i
$275$	−93.1655	+	218.106i	−0.338784	+	0.793112i
$276$		0			0
$277$	−41.5692	−	24.0000i	−0.150069	−	0.0866426i	0.423085	−	0.906090i	$-0.360947\pi$
$277$	−41.5692	−	24.0000i	−0.150069	−	0.0866426i	−0.573154	+	0.819447i	$0.694280\pi$
$278$	3.16228			0.0113751
$279$		0			0
$280$	−90.0000	+	30.0000i	−0.321429	+	0.107143i
$281$	262.907	+	151.789i	0.935611	+	0.540176i	0.888582	−	0.458718i	$-0.151691\pi$
$281$	262.907	+	151.789i	0.935611	+	0.540176i	0.0470296	+	0.998893i	$0.485025\pi$
$282$		0			0
$283$	−166.277	+	96.0000i	−0.587551	+	0.339223i	−0.764128	−	0.645064i	$-0.776831\pi$
$283$	−166.277	+	96.0000i	−0.587551	+	0.339223i	0.176578	+	0.984287i	$0.443497\pi$
$284$	−147.885	+	85.3815i	−0.520722	+	0.300639i
$285$		0			0
$286$	315.000	−	545.596i	1.10140	−	1.90768i
$287$	−142.302			−0.495828
$288$		0			0
$289$	−129.000			−0.446367
$290$	−150.360	+	734.773i	−0.518484	+	2.53370i
$291$		0			0
$292$	−140.296	+	81.0000i	−0.480466	+	0.277397i
$293$	−102.774	−	178.010i	−0.350765	−	0.607542i	0.635619	−	0.772003i	$-0.280745\pi$
$293$	−102.774	−	178.010i	−0.350765	−	0.607542i	−0.986384	+	0.164461i	$0.947412\pi$
$294$		0			0
$295$	38.0385	−	185.885i	0.128944	−	0.630117i
$296$			170.763i			0.576902i
$297$		0			0
$298$		−	240.000i		−	0.805369i
$299$	−402.576	−	232.427i	−1.34641	−	0.777349i
$300$		0			0
$301$	72.0000	+	124.708i	0.239203	+	0.414311i
$302$	−49.0153	−	84.8970i	−0.162302	−	0.281116i
$303$		0			0
$304$	−62.0000	+	107.387i	−0.203947	+	0.353247i
$305$	1.58114	+	4.74342i	0.00518406	+	0.0155522i
$306$		0			0
$307$			198.000i			0.644951i	0.946578	+	0.322476i	$0.104515\pi$
$307$			198.000i			0.644951i	−0.946578	+	0.322476i	$0.895485\pi$
$308$	85.3815	−	147.885i	0.277213	−	0.480146i
$309$		0			0
$310$	−167.846	+	189.282i	−0.541439	+	0.610587i
$311$	−427.224	+	246.658i	−1.37371	+	0.793111i	−0.991393	−	0.130920i	$-0.958207\pi$
$311$	−427.224	+	246.658i	−1.37371	+	0.793111i	−0.382316	+	0.924031i	$0.624874\pi$
$312$		0			0
$313$	355.936	+	205.500i	1.13718	+	0.656550i	0.945730	−	0.324953i	$-0.105349\pi$
$313$	355.936	+	205.500i	1.13718	+	0.656550i	0.191447	+	0.981503i	$0.438682\pi$
$314$			322.552i			1.02724i
$315$		0			0
$316$	−6.00000			−0.0189873
$317$	−126.491	+	219.089i	−0.399026	+	0.691133i	−0.993606	−	0.112904i	$-0.963985\pi$
$317$	−126.491	+	219.089i	−0.399026	+	0.691133i	0.594580	+	0.804036i	$0.297318\pi$
$318$		0			0
$319$	−225.000	−	389.711i	−0.705329	−	1.22167i
$320$	345.004	−	389.066i	1.07814	−	1.21583i
$321$		0			0
$322$	−181.865	−	105.000i	−0.564799	−	0.326087i
$323$	392.122			1.21400
$324$		0			0
$325$	315.000	+	420.000i	0.969231	+	1.29231i
$326$	−468.303	−	270.375i	−1.43651	−	0.829370i
$327$		0			0
$328$	−259.808	+	150.000i	−0.792096	+	0.457317i
$329$	−32.8634	+	18.9737i	−0.0998886	+	0.0576707i
$330$		0			0
$331$	−164.500	+	284.922i	−0.496979	+	0.860793i	−0.999994	−	0.00348502i	$-0.998891\pi$
$331$	−164.500	+	284.922i	−0.496979	+	0.860793i	0.503015	+	0.864278i	$0.332224\pi$
$332$	664.078			2.00024
$333$		0			0
$334$	−920.000			−2.75449
$335$	21.0504	−	102.868i	0.0628371	−	0.307069i
$336$		0			0
$337$	−329.956	+	190.500i	−0.979097	+	0.565282i	−0.901997	−	0.431741i	$-0.857899\pi$
$337$	−329.956	+	190.500i	−0.979097	+	0.565282i	−0.0770996	+	0.997023i	$0.524566\pi$
$338$	−430.070	−	744.903i	−1.27240	−	2.20385i
$339$		0			0
$340$	−371.769	−	76.0770i	−1.09344	−	0.223756i
$341$		−	151.789i		−	0.445130i
$342$		0			0
$343$			267.000i			0.778426i
$344$	262.907	+	151.789i	0.764264	+	0.441248i
$345$		0			0
$346$	40.0000	+	69.2820i	0.115607	+	0.200237i
$347$	58.5021	+	101.329i	0.168594	+	0.292013i	0.937926	−	0.346836i	$-0.112744\pi$
$347$	58.5021	+	101.329i	0.168594	+	0.292013i	−0.769332	+	0.638850i	$0.779411\pi$
$348$		0			0
$349$	−44.5000	+	77.0763i	−0.127507	+	0.220849i	−0.922710	−	0.385494i	$-0.874031\pi$
$349$	−44.5000	+	77.0763i	−0.127507	+	0.220849i	0.795203	+	0.606343i	$0.207364\pi$
$350$	142.302	+	189.737i	0.406579	+	0.542105i
$351$		0			0
$352$			360.000i			1.02273i
$353$	290.930	−	503.905i	0.824163	−	1.42749i	−0.0783943	−	0.996922i	$-0.524979\pi$
$353$	290.930	−	503.905i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141687\pi$
$354$		0			0
$355$	106.471	+	94.4134i	0.299919	+	0.265953i
$356$	−591.540	+	341.526i	−1.66163	+	0.959343i
$357$		0			0
$358$	−545.596	−	315.000i	−1.52401	−	0.879888i
$359$			85.3815i			0.237831i	0.992904	+	0.118916i	$0.0379418\pi$
$359$			85.3815i			0.237831i	−0.992904	+	0.118916i	$0.962058\pi$
$360$		0			0
$361$	600.000			1.66205
$362$	−162.857	+	282.077i	−0.449882	+	0.779219i
$363$		0			0
$364$	−189.000	−	327.358i	−0.519231	−	0.899334i
$365$	101.007	+	89.5684i	0.276733	+	0.245393i
$366$		0			0
$367$	44.1673	+	25.5000i	0.120347	+	0.0694823i	0.558965	−	0.829191i	$-0.311199\pi$
$367$	44.1673	+	25.5000i	0.120347	+	0.0694823i	−0.438618	+	0.898674i	$0.644532\pi$
$368$	88.5438			0.240608
$369$		0			0
$370$	405.000	−	135.000i	1.09459	−	0.364865i
$371$	106.806	+	61.6644i	0.287887	+	0.166211i
$372$		0			0
$373$	−205.248	+	118.500i	−0.550263	+	0.317694i	−0.749228	−	0.662312i	$-0.769575\pi$
$373$	−205.248	+	118.500i	−0.550263	+	0.317694i	0.198965	+	0.980007i	$0.436242\pi$
$374$	328.634	−	189.737i	0.878699	−	0.507317i
$375$		0			0
$376$	−40.0000	+	69.2820i	−0.106383	+	0.184261i
$377$	−996.117			−2.64222
$378$		0			0
$379$	−103.000			−0.271768			−0.135884	−	0.990725i	$-0.543387\pi$
$379$	−103.000			−0.271768			−0.135884	+	0.990725i	$0.543387\pi$
$380$	−911.119	−	186.447i	−2.39768	−	0.490649i
$381$		0			0
$382$	−727.461	+	420.000i	−1.90435	+	1.09948i
$383$	25.2982	+	43.8178i	0.0660528	+	0.114407i	0.897161	−	0.441705i	$-0.145626\pi$
$383$	25.2982	+	43.8178i	0.0660528	+	0.114407i	−0.831108	+	0.556111i	$0.812293\pi$
$384$		0			0
$385$	−139.413	−	28.5289i	−0.362113	−	0.0741009i
$386$		−	673.565i		−	1.74499i
$387$		0			0
$388$			558.000i			1.43814i
$389$	−230.043	−	132.816i	−0.591371	−	0.341428i	0.174268	−	0.984698i	$-0.444244\pi$
$389$	−230.043	−	132.816i	−0.591371	−	0.341428i	−0.765640	+	0.643270i	$0.777577\pi$
$390$		0			0
$391$	−140.000	−	242.487i	−0.358056	−	0.620172i
$392$	126.491	+	219.089i	0.322681	+	0.558901i
$393$		0			0
$394$	−380.000	+	658.179i	−0.964467	+	1.67051i
$395$	1.58114	+	4.74342i	0.00400288	+	0.0120086i
$396$		0			0
$397$		−	72.0000i		−	0.181360i	−0.995880	−	0.0906801i	$-0.971096\pi$
$397$		−	72.0000i		−	0.181360i	0.995880	−	0.0906801i	$-0.0289041\pi$
$398$	74.3135	−	128.715i	0.186717	−	0.323404i
$399$		0			0
$400$	−91.9615	−	39.2820i	−0.229904	−	0.0982051i
$401$	90.3742	−	52.1776i	0.225372	−	0.130119i	−0.383063	−	0.923722i	$-0.625131\pi$
$401$	90.3742	−	52.1776i	0.225372	−	0.130119i	0.608435	+	0.793603i	$0.291798\pi$
$402$		0			0
$403$	−290.985	−	168.000i	−0.722046	−	0.416873i
$404$		−	455.368i		−	1.12715i
$405$		0			0
$406$	−450.000			−1.10837
$407$	−128.072	+	221.828i	−0.314674	+	0.545031i
$408$		0			0
$409$	−68.5000	−	118.645i	−0.167482	−	0.290087i	0.770052	−	0.637981i	$-0.220230\pi$
$409$	−68.5000	−	118.645i	−0.167482	−	0.290087i	−0.937534	+	0.347894i	$0.886897\pi$
$410$	561.152	+	497.602i	1.36866	+	1.21366i
$411$		0			0
$412$	763.834	+	441.000i	1.85397	+	1.07039i
$413$	113.842			0.275646
$414$		0			0
$415$	−175.000	−	525.000i	−0.421687	−	1.26506i
$416$	690.130	+	398.447i	1.65897	+	0.957805i
$417$		0			0
$418$	805.404	−	465.000i	1.92680	−	1.11244i
$419$	−32.8634	+	18.9737i	−0.0784328	+	0.0452832i	−0.538704	−	0.842495i	$-0.681086\pi$
$419$	−32.8634	+	18.9737i	−0.0784328	+	0.0452832i	0.460271	+	0.887779i	$0.347752\pi$
$420$		0			0
$421$	315.500	−	546.462i	0.749406	−	1.29801i	−0.198701	−	0.980060i	$-0.563672\pi$
$421$	315.500	−	546.462i	0.749406	−	1.29801i	0.948108	−	0.317950i	$-0.102994\pi$
$422$	705.188			1.67106
$423$		0			0
$424$	260.000			0.613208
$425$	37.8257	+	313.957i	0.0890016	+	0.738723i
$426$		0			0
$427$	−2.59808	+	1.50000i	−0.00608449	+	0.00351288i
$428$	66.4078	+	115.022i	0.155158	+	0.268742i
$429$		0			0
$430$	152.154	−	743.538i	0.353846	−	1.72916i
$431$		−	540.749i		−	1.25464i	−0.778762	−	0.627320i	$-0.784152\pi$
$431$		−	540.749i		−	1.25464i	0.778762	−	0.627320i	$-0.215848\pi$
$432$		0			0
$433$			288.000i			0.665127i	0.943081	+	0.332564i	$0.107914\pi$
$433$			288.000i			0.665127i	−0.943081	+	0.332564i	$0.892086\pi$
$434$	−131.453	−	75.8947i	−0.302888	−	0.174872i
$435$		0			0
$436$	−312.000	−	540.400i	−0.715596	−	1.23945i
$437$	−343.107	−	594.279i	−0.785142	−	1.35991i
$438$		0			0
$439$	428.000	−	741.318i	0.974943	−	1.68865i	0.294820	−	0.955553i	$-0.404740\pi$
$439$	428.000	−	741.318i	0.974943	−	1.68865i	0.680123	−	0.733098i	$-0.261926\pi$
$440$	−284.605	+	94.8683i	−0.646830	+	0.215610i
$441$		0			0
$442$		−	840.000i		−	1.90045i
$443$	215.035	−	372.451i	0.485406	−	0.840748i	−0.514453	−	0.857518i	$-0.672005\pi$
$443$	215.035	−	372.451i	0.485406	−	0.840748i	0.999859	+	0.0167704i	$0.00533845\pi$
$444$		0			0
$445$	425.885	+	377.654i	0.957044	+	0.848660i
$446$	854.447	−	493.315i	1.91580	−	1.10609i
$447$		0			0
$448$	270.200	+	156.000i	0.603125	+	0.348214i
$449$			796.894i			1.77482i	0.460981	+	0.887410i	$0.347497\pi$
$449$			796.894i			1.77482i	−0.460981	+	0.887410i	$0.652503\pi$
$450$		0			0
$451$	−450.000			−0.997783
$452$	521.776	−	903.742i	1.15437	−	1.99943i
$453$		0			0
$454$	535.000	+	926.647i	1.17841	+	2.04107i
$455$	−208.993	+	235.684i	−0.459325	+	0.517987i
$456$		0			0
$457$	83.1384	+	48.0000i	0.181922	+	0.105033i	0.588195	−	0.808719i	$-0.299839\pi$
$457$	83.1384	+	48.0000i	0.181922	+	0.105033i	−0.406273	+	0.913752i	$0.633172\pi$
$458$	50.5964			0.110473
$459$		0			0
$460$	210.000	+	630.000i	0.456522	+	1.36957i
$461$	361.497	+	208.710i	0.784158	+	0.452734i	0.837902	−	0.545821i	$-0.183782\pi$
$461$	361.497	+	208.710i	0.784158	+	0.452734i	−0.0537438	+	0.998555i	$0.517115\pi$
$462$		0			0
$463$	−205.248	+	118.500i	−0.443300	+	0.255940i	−0.704997	−	0.709211i	$-0.749051\pi$
$463$	−205.248	+	118.500i	−0.443300	+	0.255940i	0.261696	+	0.965150i	$0.415718\pi$
$464$	164.317	−	94.8683i	0.354131	−	0.204458i
$465$		0			0
$466$	−80.0000	+	138.564i	−0.171674	+	0.297348i
$467$	−468.017			−1.00218			−0.501089	−	0.865396i	$-0.667067\pi$
$467$	−468.017			−1.00218			−0.501089	+	0.865396i	$0.667067\pi$
$468$		0			0
$469$	63.0000			0.134328
$470$	195.940	+	40.0961i	0.416893	+	0.0853108i
$471$		0			0
$472$	207.846	−	120.000i	0.440352	−	0.254237i
$473$	227.684	+	394.360i	0.481362	+	0.833743i
$474$		0			0
$475$	92.7018	+	769.436i	0.195162	+	1.61986i
$476$		−	227.684i		−	0.478328i
$477$		0			0
$478$		−	330.000i		−	0.690377i
$479$	−353.281	−	203.967i	−0.737539	−	0.425818i	0.0836350	−	0.996496i	$-0.473347\pi$
$479$	−353.281	−	203.967i	−0.737539	−	0.425818i	−0.821174	+	0.570678i	$0.806680\pi$
$480$		0			0
$481$	283.500	+	491.036i	0.589397	+	1.02087i
$482$	453.787	+	785.982i	0.941466	+	1.63067i
$483$		0			0
$484$	−93.0000	+	161.081i	−0.192149	+	0.332811i
$485$	441.138	−	147.046i	0.909562	−	0.303187i
$486$		0			0
$487$		−	261.000i		−	0.535934i	−0.963428	−	0.267967i	$-0.913648\pi$
$487$		−	261.000i		−	0.535934i	0.963428	−	0.267967i	$-0.0863519\pi$
$488$	−3.16228	+	5.47723i	−0.00648008	+	0.0112238i
$489$		0			0
$490$	419.615	−	473.205i	0.856358	−	0.965725i
$491$	−649.051	+	374.730i	−1.32190	+	0.763197i	−0.984031	−	0.177997i	$-0.943038\pi$
$491$	−649.051	+	374.730i	−1.32190	+	0.763197i	−0.337866	+	0.941194i	$0.609705\pi$
$492$		0			0
$493$	−519.615	−	300.000i	−1.05399	−	0.608519i
$494$		−	2058.64i		−	4.16729i
$495$		0			0
$496$	64.0000			0.129032
$497$	−42.6907	+	73.9425i	−0.0858969	+	0.148778i
$498$		0			0
$499$	53.0000	+	91.7987i	0.106212	+	0.183965i	0.914233	−	0.405189i	$-0.132794\pi$
$499$	53.0000	+	91.7987i	0.106212	+	0.183965i	−0.808020	+	0.589154i	$0.799461\pi$
$500$	61.3907	−	747.483i	0.122781	−	1.49497i
$501$		0			0
$502$	701.481	+	405.000i	1.39737	+	0.806773i
$503$	−382.636			−0.760707			−0.380353	−	0.924841i	$-0.624198\pi$
$503$	−382.636			−0.760707			−0.380353	+	0.924841i	$0.624198\pi$
$504$		0			0
$505$	−360.000	+	120.000i	−0.712871	+	0.237624i
$506$	−575.109	−	332.039i	−1.13658	−	0.656204i
$507$		0			0
$508$	748.246	−	432.000i	1.47293	−	0.850394i
$509$	139.669	−	80.6381i	0.274399	−	0.158425i	−0.356486	−	0.934301i	$-0.616025\pi$
$509$	139.669	−	80.6381i	0.274399	−	0.158425i	0.630885	+	0.775876i	$0.282692\pi$
$510$		0			0
$511$	−40.5000	+	70.1481i	−0.0792564	+	0.137276i
$512$	−252.982			−0.494106
$513$		0			0
$514$	880.000			1.71206
$515$	147.353	−	720.078i	0.286122	−	1.39821i
$516$		0			0
$517$	−103.923	+	60.0000i	−0.201012	+	0.116054i
$518$	128.072	+	221.828i	0.247244	+	0.428239i
$519$		0			0
$520$	−133.135	+	650.596i	−0.256028	+	1.25115i
$521$			369.986i			0.710147i	0.934838	+	0.355073i	$0.115544\pi$
$521$			369.986i			0.710147i	−0.934838	+	0.355073i	$0.884456\pi$
$522$		0			0
$523$		−	837.000i		−	1.60038i	−0.599745	−	0.800191i	$-0.704731\pi$
$523$		−	837.000i		−	1.60038i	0.599745	−	0.800191i	$-0.295269\pi$
$524$	−394.360	−	227.684i	−0.752596	−	0.434511i
$525$		0			0
$526$	−560.000	−	969.948i	−1.06464	−	1.84401i
$527$	−101.193	−	175.271i	−0.192017	−	0.332583i
$528$		0			0
$529$	19.5000	−	33.7750i	0.0368620	−	0.0638469i
$530$	−205.548	−	616.644i	−0.387827	−	1.16348i
$531$		0			0
$532$		−	558.000i		−	1.04887i
$533$	−498.059	+	862.663i	−0.934444	+	1.61850i
$534$		0			0
$535$	73.4327	−	82.8109i	0.137257	−	0.154787i
$536$	115.022	−	66.4078i	0.214593	−	0.123895i
$537$		0			0
$538$	311.769	+	180.000i	0.579497	+	0.334572i
$539$			379.473i			0.704032i
$540$		0			0
$541$	−511.000			−0.944547			−0.472274	−	0.881452i	$-0.656567\pi$
$541$	−511.000			−0.944547			−0.472274	+	0.881452i	$0.656567\pi$
$542$	−191.318	+	331.372i	−0.352985	+	0.611388i
$543$		0			0
$544$	240.000	+	415.692i	0.441176	+	0.764140i
$545$	−345.004	+	389.066i	−0.633036	+	0.713882i
$546$		0			0
$547$	−937.906	−	541.500i	−1.71464	−	0.989945i	−0.928044	−	0.372472i	$-0.878510\pi$
$547$	−937.906	−	541.500i	−1.71464	−	0.989945i	−0.786592	−	0.617473i	$-0.788156\pi$
$548$	322.552			0.588599
$549$		0			0
$550$	450.000	+	600.000i	0.818182	+	1.09091i
$551$	−1273.45	−	735.230i	−2.31117	−	1.33435i
$552$		0			0
$553$	−2.59808	+	1.50000i	−0.00469815	+	0.00271248i
$554$	−131.453	+	75.8947i	−0.237281	+	0.136994i
$555$		0			0
$556$	3.00000	−	5.19615i	0.00539568	−	0.00934560i
$557$	973.982			1.74862			0.874310	−	0.485368i	$-0.161314\pi$
$557$	973.982			1.74862			0.874310	+	0.485368i	$0.161314\pi$
$558$		0			0
$559$	1008.00			1.80322
$560$	12.0288	−	58.7819i	0.0214800	−	0.104968i
$561$		0			0
$562$	831.384	−	480.000i	1.47933	−	0.854093i
$563$	−240.333	−	416.269i	−0.426879	−	0.739377i	0.569714	−	0.821843i	$-0.307054\pi$
$563$	−240.333	−	416.269i	−0.426879	−	0.739377i	−0.996594	+	0.0824659i	$0.973720\pi$
$564$		0			0
$565$	−851.971	−	174.343i	−1.50791	−	0.308572i
$566$			607.157i			1.07272i
$567$		0			0
$568$			180.000i			0.316901i
$569$	558.677	+	322.552i	0.981858	+	0.566876i	0.902830	−	0.429997i	$-0.141485\pi$
$569$	558.677	+	322.552i	0.981858	+	0.566876i	0.0790272	+	0.996872i	$0.474819\pi$
$570$		0			0
$571$	−284.500	−	492.768i	−0.498249	−	0.862992i	0.501749	−	0.865013i	$-0.332690\pi$
$571$	−284.500	−	492.768i	−0.498249	−	0.862992i	−0.999998	+	0.00202106i	$0.999357\pi$
$572$	−597.670	−	1035.20i	−1.04488	−	1.80978i
$573$		0			0
$574$	−225.000	+	389.711i	−0.391986	+	0.678940i
$575$	442.719	−	332.039i	0.769946	−	0.577459i
$576$		0			0
$577$		−	837.000i		−	1.45061i	−0.688429	−	0.725303i	$-0.741700\pi$
$577$		−	837.000i		−	1.45061i	0.688429	−	0.725303i	$-0.258300\pi$
$578$	−203.967	+	353.281i	−0.352884	+	0.611213i
$579$		0			0
$580$	1064.71	+	944.134i	1.83571	+	1.62782i
$581$	287.554	−	166.020i	0.494930	−	0.285748i
$582$		0			0
$583$	337.750	+	195.000i	0.579331	+	0.334477i
$584$			170.763i			0.292402i
$585$		0			0
$586$	−650.000			−1.10922
$587$	314.647	−	544.984i	0.536025	−	0.928422i	−0.463088	−	0.886312i	$-0.653259\pi$
$587$	314.647	−	544.984i	0.536025	−	0.928422i	0.999113	−	0.0421101i	$-0.0134080\pi$
$588$		0			0
$589$	−248.000	−	429.549i	−0.421053	−	0.729285i
$590$	−448.922	−	398.082i	−0.760884	−	0.674715i
$591$		0			0
$592$	−93.5307	−	54.0000i	−0.157991	−	0.0912162i
$593$	641.942			1.08253			0.541267	−	0.840851i	$-0.317945\pi$
$593$	641.942			1.08253			0.541267	+	0.840851i	$0.317945\pi$
$594$		0			0
$595$	−180.000	+	60.0000i	−0.302521	+	0.100840i
$596$	−394.360	−	227.684i	−0.661678	−	0.382020i
$597$		0			0
$598$	−1273.06	+	735.000i	−2.12886	+	1.22910i
$599$	−550.461	+	317.809i	−0.918967	+	0.530566i	−0.883305	−	0.468798i	$-0.844687\pi$
$599$	−550.461	+	317.809i	−0.918967	+	0.530566i	−0.0356616	+	0.999364i	$0.511354\pi$
$600$		0			0
$601$	−112.000	+	193.990i	−0.186356	+	0.322778i	−0.944033	−	0.329852i	$-0.893001\pi$
$601$	−112.000	+	193.990i	−0.186356	+	0.322778i	0.757677	+	0.652630i	$0.226334\pi$
$602$	455.368			0.756425
$603$		0			0
$604$	−186.000			−0.307947
$605$	151.853	+	31.0745i	0.250997	+	0.0513627i
$606$		0			0
$607$	−127.306	+	73.5000i	−0.209729	+	0.121087i	−0.601186	−	0.799109i	$-0.705305\pi$
$607$	−127.306	+	73.5000i	−0.209729	+	0.121087i	0.391456	+	0.920197i	$0.371971\pi$
$608$	588.184	+	1018.76i	0.967407	+	1.67560i
$609$		0			0
$610$	15.4904	+	3.16987i	0.0253941	+	0.00519651i
$611$			265.631i			0.434748i
$612$		0			0
$613$			243.000i			0.396411i	0.980160	+	0.198206i	$0.0635114\pi$
$613$			243.000i			0.396411i	−0.980160	+	0.198206i	$0.936489\pi$
$614$	542.245	+	313.065i	0.883136	+	0.509879i
$615$		0			0
$616$	−90.0000	−	155.885i	−0.146104	−	0.253059i
$617$	39.5285	+	68.4653i	0.0640656	+	0.110965i	0.896279	−	0.443490i	$-0.146260\pi$
$617$	39.5285	+	68.4653i	0.0640656	+	0.110965i	−0.832214	+	0.554455i	$0.812927\pi$
$618$		0			0
$619$	600.500	−	1040.10i	0.970113	−	1.68029i	0.274913	−	0.961469i	$-0.411351\pi$
$619$	600.500	−	1040.10i	0.970113	−	1.68029i	0.695200	−	0.718816i	$-0.255316\pi$
$620$	151.789	+	455.368i	0.244821	+	0.734464i
$621$		0			0
$622$			1560.00i			2.50804i
$623$	−170.763	+	295.770i	−0.274098	+	0.474751i
$624$		0			0
$625$	−607.115	+	148.446i	−0.971384	+	0.237513i
$626$	1125.57	−	649.848i	1.79803	−	1.03810i
$627$		0			0
$628$	530.008	+	306.000i	0.843961	+	0.487261i
$629$			341.526i			0.542967i
$630$		0			0
$631$	−193.000			−0.305864			−0.152932	−	0.988237i	$-0.548872\pi$
$631$	−193.000			−0.305864			−0.152932	+	0.988237i	$0.548872\pi$
$632$	−3.16228	+	5.47723i	−0.00500360	+	0.00866650i
$633$		0			0
$634$	400.000	+	692.820i	0.630915	+	1.09278i
$635$	−538.706	−	477.698i	−0.848356	−	0.752281i
$636$		0			0
$637$	727.461	+	420.000i	1.14201	+	0.659341i
$638$	−1423.02			−2.23045
$639$		0			0
$640$	−280.000	−	840.000i	−0.437500	−	1.31250i
$641$	262.907	+	151.789i	0.410151	+	0.236801i	0.690855	−	0.722994i	$-0.257234\pi$
$641$	262.907	+	151.789i	0.410151	+	0.236801i	−0.280704	+	0.959795i	$0.590568\pi$
$642$		0			0
$643$	20.7846	−	12.0000i	0.0323244	−	0.0186625i	−0.483751	−	0.875206i	$-0.660726\pi$
$643$	20.7846	−	12.0000i	0.0323244	−	0.0186625i	0.516075	+	0.856543i	$0.327393\pi$
$644$	−345.065	+	199.223i	−0.535816	+	0.309353i
$645$		0			0
$646$	620.000	−	1073.87i	0.959752	−	1.66234i
$647$	−667.241			−1.03128			−0.515642	−	0.856804i	$-0.672446\pi$
$647$	−667.241			−1.03128			−0.515642	+	0.856804i	$0.672446\pi$
$648$		0			0
$649$	360.000			0.554700
$650$	1648.28	−	198.585i	2.53581	−	0.305515i
$651$		0			0
$652$	−888.542	+	513.000i	−1.36279	+	0.786810i
$653$	−202.386	−	350.542i	−0.309932	−	0.536818i	0.668415	−	0.743789i	$-0.266973\pi$
$653$	−202.386	−	350.542i	−0.309932	−	0.536818i	−0.978347	+	0.206970i	$0.933640\pi$
$654$		0			0
$655$	−76.0770	+	371.769i	−0.116148	+	0.567586i
$656$		−	189.737i		−	0.289233i
$657$		0			0
$658$			120.000i			0.182371i
$659$	−131.453	−	75.8947i	−0.199474	−	0.115166i	0.396936	−	0.917846i	$-0.370073\pi$
$659$	−131.453	−	75.8947i	−0.199474	−	0.115166i	−0.596410	+	0.802680i	$0.703407\pi$
$660$		0			0
$661$	−359.500	−	622.672i	−0.543873	−	0.942016i	−0.998677	−	0.0514240i	$-0.983624\pi$
$661$	−359.500	−	622.672i	−0.543873	−	0.942016i	0.454804	−	0.890592i	$-0.349709\pi$
$662$	520.195	+	901.004i	0.785793	+	1.36103i
$663$		0			0
$664$	350.000	−	606.218i	0.527108	−	0.912979i
$665$	−441.138	+	147.046i	−0.663365	+	0.221122i
$666$		0			0
$667$			1050.00i			1.57421i
$668$	−872.789	+	1511.71i	−1.30657	+	2.26305i
$669$		0			0
$670$	−248.433	−	220.298i	−0.370795	−	0.328803i
$671$	−8.21584	+	4.74342i	−0.0122442	+	0.00706918i
$672$		0			0
$673$	−1015.85	−	586.500i	−1.50943	−	0.871471i	−0.999940	−	0.0109960i	$-0.996500\pi$
$673$	−1015.85	−	586.500i	−1.50943	−	0.871471i	−0.509493	−	0.860475i	$-0.670167\pi$
$674$			1204.83i			1.78758i
$675$		0			0
$676$	−1632.00			−2.41420
$677$	−562.885	+	974.946i	−0.831441	+	1.44010i	0.0654549	+	0.997856i	$0.479150\pi$
$677$	−562.885	+	974.946i	−0.831441	+	1.44010i	−0.896896	+	0.442242i	$0.854183\pi$
$678$		0			0
$679$	139.500	+	241.621i	0.205449	+	0.355848i
$680$	−265.388	+	299.281i	−0.390276	+	0.440119i
$681$		0			0
$682$	−415.692	−	240.000i	−0.609519	−	0.351906i
$683$	−894.925			−1.31028			−0.655142	−	0.755505i	$-0.727391\pi$
$683$	−894.925			−1.31028			−0.655142	+	0.755505i	$0.727391\pi$
$684$		0			0
$685$	−85.0000	−	255.000i	−0.124088	−	0.372263i
$686$	731.210	+	422.164i	1.06590	+	0.615400i
$687$		0			0
$688$	−166.277	+	96.0000i	−0.241682	+	0.139535i
$689$	747.641	−	431.651i	1.08511	−	0.626489i
$690$		0			0
$691$	−436.000	+	755.174i	−0.630970	+	1.09287i	0.356384	+	0.934339i	$0.384009\pi$
$691$	−436.000	+	755.174i	−0.630970	+	1.09287i	−0.987354	+	0.158532i	$0.949324\pi$
$692$	151.789			0.219349
$693$		0			0
$694$	370.000			0.533141
$695$	−4.89849	−	1.00240i	−0.00704819	−	0.00144230i
$696$		0			0
$697$	−519.615	+	300.000i	−0.745502	+	0.430416i
$698$	140.721	+	243.737i	0.201607	+	0.349193i
$699$		0			0
$700$	446.769	−	53.8269i	0.638242	−	0.0768955i
$701$			1280.72i			1.82699i	0.406846	+	0.913497i	$0.366629\pi$
$701$			1280.72i			1.82699i	−0.406846	+	0.913497i	$0.633371\pi$
$702$		0			0
$703$			837.000i			1.19061i
$704$	854.447	+	493.315i	1.21370	+	0.700732i
$705$		0			0
$706$	−920.000	−	1593.49i	−1.30312	−	2.25706i
$707$	−113.842	−	197.180i	−0.161021	−	0.278897i
$708$		0			0
$709$	240.500	−	416.558i	0.339210	−	0.587529i	−0.645074	−	0.764120i	$-0.723174\pi$
$709$	240.500	−	416.558i	0.339210	−	0.587529i	0.984284	+	0.176591i	$0.0565069\pi$
$710$	426.907	−	142.302i	0.601278	−	0.200426i
$711$		0			0
$712$			720.000i			1.01124i
$713$	−177.088	+	306.725i	−0.248370	+	0.430189i
$714$		0			0
$715$	−660.894	+	745.298i	−0.924327	+	1.04237i
$716$	−1035.20	+	597.670i	−1.44580	+	0.834735i
$717$		0			0
$718$	233.827	+	135.000i	0.325664	+	0.188022i
$719$		−	939.196i		−	1.30625i	−0.757248	−	0.653127i	$-0.773457\pi$
$719$		−	939.196i		−	1.30625i	0.757248	−	0.653127i	$-0.226543\pi$
$720$		0			0
$721$	441.000			0.611650
$722$	948.683	−	1643.17i	1.31397	−	2.27586i
$723$		0			0
$724$	309.000	+	535.204i	0.426796	+	0.739232i
$725$	465.828	−	1090.53i	0.642521	−	1.50418i
$726$		0			0
$727$	−665.108	−	384.000i	−0.914866	−	0.528198i	−0.0328724	−	0.999460i	$-0.510465\pi$
$727$	−665.108	−	384.000i	−0.914866	−	0.528198i	−0.881994	+	0.471261i	$0.843799\pi$
$728$	−398.447			−0.547317
$729$		0			0
$730$	405.000	−	135.000i	0.554795	−	0.184932i
$731$	525.814	+	303.579i	0.719307	+	0.415292i
$732$		0			0
$733$	956.092	−	552.000i	1.30435	−	0.753070i	0.323207	−	0.946328i	$-0.395239\pi$
$733$	956.092	−	552.000i	1.30435	−	0.753070i	0.981148	+	0.193259i	$0.0619057\pi$
$734$	139.669	−	80.6381i	0.190285	−	0.109861i
$735$		0			0
$736$	420.000	−	727.461i	0.570652	−	0.988399i
$737$	199.223			0.270317
$738$		0			0
$739$	392.000			0.530447			0.265223	−	0.964187i	$-0.414554\pi$
$739$	392.000			0.530447			0.265223	+	0.964187i	$0.414554\pi$
$740$	162.389	−	793.555i	0.219445	−	1.07237i
$741$		0			0
$742$	337.750	−	195.000i	0.455189	−	0.262803i
$743$	499.640	+	865.402i	0.672463	+	1.16474i	0.977204	+	0.212304i	$0.0680968\pi$
$743$	499.640	+	865.402i	0.672463	+	1.16474i	−0.304741	+	0.952435i	$0.598570\pi$
$744$		0			0
$745$	−76.0770	+	371.769i	−0.102117	+	0.499019i
$746$			749.460i			1.00464i
$747$		0			0
$748$		−	720.000i		−	0.962567i
$749$	57.5109	+	33.2039i	0.0767835	+	0.0443310i
$750$		0			0
$751$	120.500	+	208.712i	0.160453	+	0.277912i	0.935031	−	0.354566i	$-0.115371\pi$
$751$	120.500	+	208.712i	0.160453	+	0.277912i	−0.774578	+	0.632478i	$0.782038\pi$
$752$	−25.2982	−	43.8178i	−0.0336413	−	0.0582684i
$753$		0			0
$754$	−1575.00	+	2727.98i	−2.08886	+	3.61801i
$755$	49.0153	+	147.046i	0.0649209	+	0.194763i
$756$		0			0
$757$		−	27.0000i		−	0.0356671i	−0.999841	−	0.0178336i	$-0.994323\pi$
$757$		−	27.0000i		−	0.0356671i	0.999841	−	0.0178336i	$-0.00567690\pi$
$758$	−162.857	+	282.077i	−0.214851	+	0.372133i
$759$		0			0
$760$	−650.404	+	733.468i	−0.855794	+	0.965089i
$761$	−599.756	+	346.269i	−0.788116	+	0.455019i	−0.839299	−	0.543670i	$-0.817034\pi$
$761$	−599.756	+	346.269i	−0.788116	+	0.455019i	0.0511829	+	0.998689i	$0.483701\pi$
$762$		0			0
$763$	−270.200	−	156.000i	−0.354128	−	0.204456i
$764$			1593.79i			2.08611i
$765$		0			0
$766$	160.000			0.208877
$767$	398.447	−	690.130i	0.519488	−	0.899779i
$768$		0			0
$769$	−563.500	−	976.011i	−0.732770	−	1.26919i	−0.955695	−	0.294359i	$-0.904894\pi$
$769$	−563.500	−	976.011i	−0.732770	−	1.26919i	0.222925	−	0.974836i	$-0.428439\pi$
$770$	−298.561	+	336.691i	−0.387742	+	0.437261i
$771$		0			0
$772$	−1106.78	−	639.000i	−1.43365	−	0.827720i
$773$	243.495			0.315000			0.157500	−	0.987519i	$-0.449656\pi$
$773$	243.495			0.315000			0.157500	+	0.987519i	$0.449656\pi$
$774$		0			0
$775$	320.000	−	240.000i	0.412903	−	0.309677i
$776$	509.382	+	294.092i	0.656420	+	0.378984i
$777$		0			0
$778$	−727.461	+	420.000i	−0.935040	+	0.539846i
$779$	−1273.45	+	735.230i	−1.63473	+	0.943812i
$780$		0			0
$781$	−135.000	+	233.827i	−0.172855	+	0.299394i
$782$	−885.438			−1.13227
$783$		0			0
$784$	−160.000			−0.204082
$785$	102.245	−	499.646i	0.130248	−	0.636492i
$786$		0			0
$787$	496.233	−	286.500i	0.630537	−	0.364041i	−0.150423	−	0.988622i	$-0.548064\pi$
$787$	496.233	−	286.500i	0.630537	−	0.364041i	0.780960	+	0.624581i	$0.214730\pi$
$788$	720.999	+	1248.81i	0.914974	+	1.58478i
$789$		0			0
$790$	15.4904	+	3.16987i	0.0196081	+	0.00401250i
$791$		−	521.776i		−	0.659641i
$792$		0			0
$793$			21.0000i			0.0264817i
$794$	−197.180	−	113.842i	−0.248338	−	0.143378i
$795$		0			0
$796$	−141.000	−	244.219i	−0.177136	−	0.306808i
$797$	−316.228	−	547.723i	−0.396773	−	0.687230i	0.596553	−	0.802574i	$-0.296537\pi$
$797$	−316.228	−	547.723i	−0.396773	−	0.687230i	−0.993326	+	0.115343i	$0.963203\pi$
$798$		0			0
$799$	−80.0000	+	138.564i	−0.100125	+	0.173422i
$800$	−758.947	+	569.210i	−0.948683	+	0.711512i
$801$		0			0
$802$		−	330.000i		−	0.411471i
$803$	−128.072	+	221.828i	−0.159492	+	0.276249i
$804$		0			0
$805$	248.433	+	220.298i	0.308612	+	0.273662i
$806$	−920.174	+	531.263i	−1.14165	+	0.659135i
$807$		0			0
$808$	−415.692	−	240.000i	−0.514471	−	0.297030i
$809$		−	1138.42i		−	1.40719i	−0.710599	−	0.703597i	$-0.751576\pi$
$809$		−	1138.42i		−	1.40719i	0.710599	−	0.703597i	$-0.248424\pi$
$810$		0			0
$811$	−376.000			−0.463625			−0.231813	−	0.972760i	$-0.574466\pi$
$811$	−376.000			−0.463625			−0.231813	+	0.972760i	$0.574466\pi$
$812$	−426.907	+	739.425i	−0.525748	+	0.910622i
$813$		0			0
$814$	405.000	+	701.481i	0.497543	+	0.861770i
$815$	639.714	+	567.267i	0.784925	+	0.696033i
$816$		0			0
$817$	1288.65	+	744.000i	1.57729	+	0.910649i
$818$	−433.232			−0.529624
$819$		0			0
$820$	1350.00	−	450.000i	1.64634	−	0.548780i
$821$	−32.8634	−	18.9737i	−0.0400284	−	0.0231104i	0.479852	−	0.877349i	$-0.340690\pi$
$821$	−32.8634	−	18.9737i	−0.0400284	−	0.0231104i	−0.519881	+	0.854239i	$0.674024\pi$
$822$		0			0
$823$	293.583	−	169.500i	0.356722	−	0.205954i	−0.310920	−	0.950436i	$-0.600637\pi$
$823$	293.583	−	169.500i	0.356722	−	0.205954i	0.667642	+	0.744482i	$0.267304\pi$
$824$	805.152	−	464.855i	0.977126	−	0.564144i
$825$		0			0
$826$	180.000	−	311.769i	0.217918	−	0.377444i
$827$	442.719			0.535331			0.267666	−	0.963512i	$-0.413748\pi$
$827$	442.719			0.535331			0.267666	+	0.963512i	$0.413748\pi$
$828$		0			0
$829$	−961.000			−1.15923			−0.579614	−	0.814891i	$-0.696797\pi$
$829$	−961.000			−1.15923			−0.579614	+	0.814891i	$0.696797\pi$
$830$	−1714.47	−	350.841i	−2.06563	−	0.422700i
$831$		0			0
$832$	1891.40	−	1092.00i	2.27332	−	1.31250i
$833$	252.982	+	438.178i	0.303700	+	0.526024i
$834$		0			0
$835$	1425.12	+	291.628i	1.70672	+	0.349255i
$836$		−	1764.55i		−	2.11071i
$837$		0			0
$838$			120.000i			0.143198i
$839$	−920.174	−	531.263i	−1.09675	−	0.633209i	−0.161385	−	0.986892i	$-0.551596\pi$
$839$	−920.174	−	531.263i	−1.09675	−	0.633209i	−0.935366	+	0.353682i	$0.884929\pi$
$840$		0			0
$841$	704.500	+	1220.23i	0.837693	+	1.45093i
$842$	−997.699	−	1728.06i	−1.18492	−	2.05233i
$843$		0			0
$844$	669.000	−	1158.74i	0.792654	−	1.37292i
$845$	430.070	+	1290.21i	0.508958	+	1.52687i
$846$		0			0
$847$			93.0000i			0.109799i
$848$	−82.2192	+	142.408i	−0.0969566	+	0.167934i
$849$		0			0
$850$	919.615	+	392.820i	1.08190	+	0.462142i
$851$	517.598	−	298.835i	0.608223	−	0.351158i
$852$		0			0
$853$	1057.42	+	610.500i	1.23964	+	0.715709i	0.969022	−	0.246976i	$-0.0794369\pi$
$853$	1057.42	+	610.500i	1.23964	+	0.715709i	0.270623	+	0.962685i	$0.412770\pi$
$854$			9.48683i			0.0111087i
$855$		0			0
$856$	140.000			0.163551
$857$	286.186	−	495.689i	0.333939	−	0.578400i	−0.649341	−	0.760497i	$-0.724955\pi$
$857$	286.186	−	495.689i	0.333939	−	0.578400i	0.983281	+	0.182097i	$0.0582886\pi$
$858$		0			0
$859$	−59.5000	−	103.057i	−0.0692666	−	0.119973i	0.829312	−	0.558786i	$-0.188733\pi$
$859$	−59.5000	−	103.057i	−0.0692666	−	0.119973i	−0.898579	+	0.438812i	$0.855399\pi$
$860$	−1077.41	−	955.397i	−1.25280	−	1.11093i
$861$		0			0
$862$	−1480.90	−	855.000i	−1.71799	−	0.991879i
$863$	442.719			0.513000			0.256500	−	0.966544i	$-0.417431\pi$
$863$	442.719			0.513000			0.256500	+	0.966544i	$0.417431\pi$
$864$		0			0
$865$	−40.0000	−	120.000i	−0.0462428	−	0.138728i
$866$	788.720	+	455.368i	0.910763	+	0.525829i
$867$		0			0
$868$	−249.415	+	144.000i	−0.287345	+	0.165899i
$869$	−8.21584	+	4.74342i	−0.00945436	+	0.00545848i
$870$		0			0
$871$	220.500	−	381.917i	0.253157	−	0.438481i
$872$	−657.754			−0.754305
$873$		0			0
$874$	−2170.00			−2.48284
$875$	−160.288	−	339.017i	−0.183186	−	0.387448i
$876$		0			0
$877$	106.521	−	61.5000i	0.121461	−	0.0701254i	−0.438039	−	0.898956i	$-0.644327\pi$
$877$	106.521	−	61.5000i	0.121461	−	0.0701254i	0.559499	+	0.828831i	$0.310993\pi$
$878$	−1353.45	−	2344.25i	−1.54152	−	2.66999i
$879$		0			0
$880$	38.0385	−	185.885i	0.0432255	−	0.211232i
$881$		−	996.117i		−	1.13067i	−0.824862	−	0.565333i	$-0.808748\pi$
$881$		−	996.117i		−	1.13067i	0.824862	−	0.565333i	$-0.191252\pi$
$882$		0			0
$883$		−	387.000i		−	0.438279i	−0.975694	−	0.219139i	$-0.929675\pi$
$883$		−	387.000i		−	0.438279i	0.975694	−	0.219139i	$-0.0703249\pi$
$884$	−1380.26	−	796.894i	−1.56138	−	0.901464i
$885$		0			0
$886$	−680.000	−	1177.79i	−0.767494	−	1.32934i
$887$	480.666	+	832.538i	0.541901	+	0.938600i	0.998795	+	0.0490789i	$0.0156286\pi$
$887$	480.666	+	832.538i	0.541901	+	0.938600i	−0.456894	+	0.889521i	$0.651038\pi$
$888$		0			0
$889$	216.000	−	374.123i	0.242970	−	0.420836i
$890$	1707.63	−	569.210i	1.91869	−	0.639562i
$891$		0			0
$892$		−	1872.00i		−	2.09865i
$893$	−196.061	+	339.588i	−0.219553	+	0.380278i
$894$		0			0
$895$	745.298	+	660.894i	0.832735	+	0.738429i
$896$	460.087	−	265.631i	0.513490	−	0.296464i
$897$		0			0
$898$	2182.38	+	1260.00i	2.43027	+	1.40312i
$899$			758.947i			0.844212i
$900$		0			0
$901$	520.000			0.577137
$902$	−711.512	+	1232.38i	−0.788816	+	1.36627i
$903$		0			0
$904$	−550.000	−	952.628i	−0.608407	−	1.05379i
$905$	341.687	−	385.325i	0.377555	−	0.425773i
$906$		0			0
$907$	−80.5404	−	46.5000i	−0.0887986	−	0.0512679i	0.454943	−	0.890520i	$-0.349660\pi$
$907$	−80.5404	−	46.5000i	−0.0887986	−	0.0512679i	−0.543742	+	0.839253i	$0.682993\pi$
$908$	2030.18			2.23588
$909$		0			0
$910$	315.000	+	945.000i	0.346154	+	1.03846i
$911$	460.087	+	265.631i	0.505035	+	0.291582i	0.730790	−	0.682602i	$-0.239152\pi$
$911$	460.087	+	265.631i	0.505035	+	0.291582i	−0.225755	+	0.974184i	$0.572485\pi$
$912$		0			0
$913$	909.327	−	525.000i	0.995977	−	0.575027i
$914$	262.907	−	151.789i	0.287644	−	0.166071i
$915$		0			0
$916$	48.0000	−	83.1384i	0.0524017	−	0.0907625i
$917$	−227.684			−0.248292
$918$		0			0
$919$	−376.000			−0.409140			−0.204570	−	0.978852i	$-0.565580\pi$
$919$	−376.000			−0.409140			−0.204570	+	0.978852i	$0.565580\pi$
$920$	685.788	+	140.336i	0.745422	+	0.152539i
$921$		0			0
$922$	1143.15	−	660.000i	1.23986	−	0.715835i
$923$	298.835	+	517.598i	0.323765	+	0.560778i
$924$		0			0
$925$	−670.154	+	80.7403i	−0.724491	+	0.0872868i
$926$			749.460i			0.809352i
$927$		0			0
$928$		−	1800.00i		−	1.93966i
$929$	1224.16	+	706.769i	1.31772	+	0.760785i	0.983361	−	0.181662i	$-0.0581476\pi$
$929$	1224.16	+	706.769i	1.31772	+	0.760785i	0.334357	+	0.942447i	$0.391481\pi$
$930$		0			0
$931$	620.000	+	1073.87i	0.665951	+	1.15346i
$932$	151.789	+	262.907i	0.162864	+	0.282089i
$933$		0			0
$934$	−740.000	+	1281.72i	−0.792291	+	1.37229i
$935$	−569.210	+	189.737i	−0.608781	+	0.202927i
$936$		0			0
$937$			243.000i			0.259338i	0.991557	+	0.129669i	$0.0413915\pi$
$937$			243.000i			0.259338i	−0.991557	+	0.129669i	$0.958608\pi$
$938$	99.6117	−	172.533i	0.106196	−	0.183937i
$939$		0			0
$940$	251.769	−	283.923i	0.267840	−	0.302046i
$941$	336.849	−	194.480i	0.357970	−	0.206674i	−0.310220	−	0.950665i	$-0.600403\pi$
$941$	336.849	−	194.480i	0.357970	−	0.206674i	0.668190	+	0.743991i	$0.267069\pi$
$942$		0			0
$943$	909.327	+	525.000i	0.964291	+	0.556734i
$944$			151.789i			0.160794i
$945$		0			0
$946$	1440.00			1.52220
$947$	158.114	−	273.861i	0.166963	−	0.289188i	−0.770388	−	0.637576i	$-0.779937\pi$
$947$	158.114	−	273.861i	0.166963	−	0.289188i	0.937351	+	0.348387i	$0.113271\pi$
$948$		0			0
$949$	283.500	+	491.036i	0.298736	+	0.517425i
$950$	2253.76	+	962.710i	2.37238	+	1.01338i
$951$		0			0
$952$	−207.846	−	120.000i	−0.218326	−	0.126050i
$953$	−1530.54			−1.60603			−0.803013	−	0.595962i	$-0.796771\pi$
$953$	−1530.54			−1.60603			−0.803013	+	0.595962i	$0.796771\pi$
$954$		0			0
$955$	1260.00	−	420.000i	1.31937	−	0.439791i
$956$	−542.245	−	313.065i	−0.567202	−	0.327474i
$957$		0			0
$958$	−1117.17	+	645.000i	−1.16615	+	0.673278i
$959$	139.669	−	80.6381i	0.145641	−	0.0840856i
$960$		0			0
$961$	352.500	−	610.548i	0.366805	−	0.635326i
$962$	1793.01			1.86384
$963$		0			0
$964$	1722.00			1.78631
$965$	−213.512	+	1043.38i	−0.221256	+	1.08122i
$966$		0			0
$967$	−205.248	+	118.500i	−0.212252	+	0.122544i	−0.602358	−	0.798226i	$-0.705772\pi$
$967$	−205.248	+	118.500i	−0.212252	+	0.122544i	0.390105	+	0.920770i	$0.372439\pi$
$968$	98.0306	+	169.794i	0.101271	+	0.175407i
$969$		0			0
$970$	294.798	−	1440.61i	0.303916	−	1.48516i
$971$		−	569.210i		−	0.586210i	−0.956080	−	0.293105i	$-0.905311\pi$
$971$		−	569.210i		−	0.586210i	0.956080	−	0.293105i	$-0.0946886\pi$
$972$		0			0
$973$		−	3.00000i		−	0.00308325i
$974$	−714.778	−	412.677i	−0.733858	−	0.423693i
$975$		0			0
$976$	−2.00000	−	3.46410i	−0.00204918	−	0.00354928i
$977$	257.726	+	446.394i	0.263793	+	0.456903i	0.967247	−	0.253838i	$-0.0816931\pi$
$977$	257.726	+	446.394i	0.263793	+	0.456903i	−0.703454	+	0.710741i	$0.748360\pi$
$978$		0			0
$979$	−540.000	+	935.307i	−0.551583	+	0.955370i
$980$	−379.473	−	1138.42i	−0.387218	−	1.16165i
$981$		0			0
$982$			2370.00i			2.41344i
$983$	314.647	−	544.984i	0.320088	−	0.554409i	−0.660418	−	0.750898i	$-0.729621\pi$
$983$	314.647	−	544.984i	0.320088	−	0.554409i	0.980506	+	0.196489i	$0.0629541\pi$
$984$		0			0
$985$	797.269	−	899.090i	0.809410	−	0.912781i
$986$	−1643.17	+	948.683i	−1.66650	+	0.962153i
$987$		0			0
$988$	−3382.70	−	1953.00i	−3.42378	−	1.97672i
$989$		−	1062.53i		−	1.07434i
$990$		0			0
$991$	−751.000			−0.757820			−0.378910	−	0.925433i	$-0.623701\pi$
$991$	−751.000			−0.757820			−0.378910	+	0.925433i	$0.623701\pi$
$992$	303.579	−	525.814i	0.306027	−	0.530054i
$993$		0			0
$994$	135.000	+	233.827i	0.135815	+	0.235238i
$995$	−155.915	+	175.828i	−0.156699	+	0.176711i
$996$		0			0
$997$	1330.22	+	768.000i	1.33422	+	0.770311i	0.985943	−	0.167082i	$-0.0534343\pi$
$997$	1330.22	+	768.000i	1.33422	+	0.770311i	0.348275	+	0.937393i	$0.386768\pi$
$998$	335.201			0.335873
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.i.269.3		8
3.2	odd	2	inner	405.3.h.i.269.2		8
5.4	even	2	inner	405.3.h.i.269.1		8
9.2	odd	6		135.3.d.g.134.4	yes	4
9.4	even	3	inner	405.3.h.i.134.4		8
9.5	odd	6	inner	405.3.h.i.134.1		8
9.7	even	3		135.3.d.g.134.1	✓	4
15.14	odd	2	inner	405.3.h.i.269.4		8
36.7	odd	6		2160.3.c.k.1889.1		4
36.11	even	6		2160.3.c.k.1889.4		4
45.2	even	12		675.3.c.f.26.2		2
45.4	even	6	inner	405.3.h.i.134.2		8
45.7	odd	12		675.3.c.f.26.1		2
45.14	odd	6	inner	405.3.h.i.134.3		8
45.29	odd	6		135.3.d.g.134.2	yes	4
45.34	even	6		135.3.d.g.134.3	yes	4
45.38	even	12		675.3.c.g.26.1		2
45.43	odd	12		675.3.c.g.26.2		2
180.79	odd	6		2160.3.c.k.1889.3		4
180.119	even	6		2160.3.c.k.1889.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.d.g.134.1	✓	4	9.7	even	3
135.3.d.g.134.2	yes	4	45.29	odd	6
135.3.d.g.134.3	yes	4	45.34	even	6
135.3.d.g.134.4	yes	4	9.2	odd	6
405.3.h.i.134.1		8	9.5	odd	6	inner
405.3.h.i.134.2		8	45.4	even	6	inner
405.3.h.i.134.3		8	45.14	odd	6	inner
405.3.h.i.134.4		8	9.4	even	3	inner
405.3.h.i.269.1		8	5.4	even	2	inner
405.3.h.i.269.2		8	3.2	odd	2	inner
405.3.h.i.269.3		8	1.1	even	1	trivial
405.3.h.i.269.4		8	15.14	odd	2	inner
675.3.c.f.26.1		2	45.7	odd	12
675.3.c.f.26.2		2	45.2	even	12
675.3.c.g.26.1		2	45.38	even	12
675.3.c.g.26.2		2	45.43	odd	12
2160.3.c.k.1889.1		4	36.7	odd	6
2160.3.c.k.1889.2		4	180.119	even	6
2160.3.c.k.1889.3		4	180.79	odd	6
2160.3.c.k.1889.4		4	36.11	even	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58114 - 2.73861i) q^{2} +(-3.00000 - 5.19615i) q^{4} +(-3.31735 + 3.74101i) q^{5} +(-2.59808 - 1.50000i) q^{7} -6.32456 q^{8} +(5.00000 + 15.0000i) q^{10} +(-8.21584 - 4.74342i) q^{11} +(-18.1865 + 10.5000i) q^{13} +(-8.21584 + 4.74342i) q^{14} +(2.00000 - 3.46410i) q^{16} -12.6491 q^{17} -31.0000 q^{19} +(29.3909 + 6.01441i) q^{20} +(-25.9808 + 15.0000i) q^{22} +(11.0680 + 19.1703i) q^{23} +(-2.99038 - 24.8205i) q^{25} +66.4078i q^{26} +18.0000i q^{28} +(41.0792 + 23.7171i) q^{29} +(8.00000 + 13.8564i) q^{31} +(-18.9737 - 32.8634i) q^{32} +(-20.0000 + 34.6410i) q^{34} +(14.2302 - 4.74342i) q^{35} -27.0000i q^{37} +(-49.0153 + 84.8970i) q^{38} +(20.9808 - 23.6603i) q^{40} +(41.0792 - 23.7171i) q^{41} +(-41.5692 - 24.0000i) q^{43} +56.9210i q^{44} +70.0000 q^{46} +(6.32456 - 10.9545i) q^{47} +(-20.0000 - 34.6410i) q^{49} +(-72.7020 - 31.0552i) q^{50} +(109.119 + 63.0000i) q^{52} -41.1096 q^{53} +(45.0000 - 15.0000i) q^{55} +(16.4317 + 9.48683i) q^{56} +(129.904 - 75.0000i) q^{58} +(-32.8634 + 18.9737i) q^{59} +(0.500000 - 0.866025i) q^{61} +50.5964 q^{62} -104.000 q^{64} +(21.0504 - 102.868i) q^{65} +(-18.1865 + 10.5000i) q^{67} +(37.9473 + 65.7267i) q^{68} +(9.50962 - 46.4711i) q^{70} -28.4605i q^{71} -27.0000i q^{73} +(-73.9425 - 42.6907i) q^{74} +(93.0000 + 161.081i) q^{76} +(14.2302 + 24.6475i) q^{77} +(0.500000 - 0.866025i) q^{79} +(6.32456 + 18.9737i) q^{80} -150.000i q^{82} +(-55.3399 + 95.8514i) q^{83} +(41.9615 - 47.3205i) q^{85} +(-131.453 + 75.8947i) q^{86} +(51.9615 + 30.0000i) q^{88} -113.842i q^{89} +63.0000 q^{91} +(66.4078 - 115.022i) q^{92} +(-20.0000 - 34.6410i) q^{94} +(102.838 - 115.971i) q^{95} +(-80.5404 - 46.5000i) q^{97} -126.491 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24 q^{4} + 40 q^{10} + 16 q^{16} - 248 q^{19} + 80 q^{25} + 64 q^{31} - 160 q^{34} - 40 q^{40} + 560 q^{46} - 160 q^{49} + 360 q^{55} + 4 q^{61} - 832 q^{64} + 180 q^{70} + 744 q^{76} + 4 q^{79} - 80 q^{85}+ \cdots - 160 q^{94}+O(q^{100}) \) 8 * q - 24 * q^4 + 40 * q^10 + 16 * q^16 - 248 * q^19 + 80 * q^25 + 64 * q^31 - 160 * q^34 - 40 * q^40 + 560 * q^46 - 160 * q^49 + 360 * q^55 + 4 * q^61 - 832 * q^64 + 180 * q^70 + 744 * q^76 + 4 * q^79 - 80 * q^85 + 504 * q^91 - 160 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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