LMFDB - Embedded newform 1500.2.m.a.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1201.1
Root			$1.40799 - 0.132563i$ of defining polynomial
Character	$\chi$	$=$	1500.1201
Dual form			1500.2.m.a.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} -1.50430 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} -1.50430 q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.99517 + 3.62921i) q^{11} +(-2.87714 + 2.09036i) q^{13} +(-0.153180 + 0.471439i) q^{17} +(0.0963126 - 0.296420i) q^{19} +(-0.464854 - 1.43067i) q^{21} +(-2.47611 - 1.79900i) q^{23} +(-0.809017 - 0.587785i) q^{27} +(-0.0378031 - 0.116346i) q^{29} +(-0.909629 + 2.79955i) q^{31} +(-1.90799 + 5.87218i) q^{33} +(-3.53298 + 2.56686i) q^{37} +(-2.87714 - 2.09036i) q^{39} +(-3.44096 + 2.50001i) q^{41} +3.62663 q^{43} +(-1.63227 - 5.02362i) q^{47} -4.73708 q^{49} -0.495700 q^{51} +(2.65748 + 8.17888i) q^{53} +0.311674 q^{57} +(-10.4222 + 7.57219i) q^{59} +(9.15882 + 6.65427i) q^{61} +(1.21700 - 0.884205i) q^{63} +(-4.09181 + 12.5933i) q^{67} +(0.945790 - 2.91084i) q^{69} +(1.00994 + 3.10827i) q^{71} +(12.9174 + 9.38504i) q^{73} +(-7.51424 - 5.45941i) q^{77} +(-2.63513 - 8.11010i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-3.50367 + 10.7832i) q^{83} +(0.0989699 - 0.0719058i) q^{87} +(-11.4335 - 8.30691i) q^{89} +(4.32808 - 3.14453i) q^{91} -2.94362 q^{93} +(3.54837 + 10.9208i) q^{97} -6.17438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9} + 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} - 2 q^{27} - 3 q^{29} - 3 q^{31} - 7 q^{33} + q^{37} + 10 q^{41} + 12 q^{43} + 33 q^{47} - 8 q^{49} - 8 q^{51} + 19 q^{53} - 10 q^{57} - 38 q^{59} + 46 q^{61} - 3 q^{63} + 8 q^{67} + 2 q^{69} - 25 q^{71} + 26 q^{73} - 23 q^{77} - 16 q^{79} - 2 q^{81} - 8 q^{83} - 3 q^{87} - 30 q^{89} + 25 q^{91} + 22 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9 + 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 - 2 * q^27 - 3 * q^29 - 3 * q^31 - 7 * q^33 + q^37 + 10 * q^41 + 12 * q^43 + 33 * q^47 - 8 * q^49 - 8 * q^51 + 19 * q^53 - 10 * q^57 - 38 * q^59 + 46 * q^61 - 3 * q^63 + 8 * q^67 + 2 * q^69 - 25 * q^71 + 26 * q^73 - 23 * q^77 - 16 * q^79 - 2 * q^81 - 8 * q^83 - 3 * q^87 - 30 * q^89 + 25 * q^91 + 22 * q^93 + 14 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.50430			−0.568572			−0.284286	−	0.958740i	$-0.591756\pi$
$7$	−1.50430			−0.568572			−0.284286	+	0.958740i	$0.591756\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	4.99517	+	3.62921i	1.50610	+	1.09425i	0.967870	+	0.251450i	$0.0809074\pi$
$11$	4.99517	+	3.62921i	1.50610	+	1.09425i	0.538231	+	0.842797i	$0.319093\pi$
$12$		0			0
$13$	−2.87714	+	2.09036i	−0.797975	+	0.579763i	−0.910319	−	0.413906i	$-0.864164\pi$
$13$	−2.87714	+	2.09036i	−0.797975	+	0.579763i	0.112344	+	0.993669i	$0.464164\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.153180	+	0.471439i	−0.0371516	+	0.114341i	−0.967912	−	0.251288i	$-0.919146\pi$
$17$	−0.153180	+	0.471439i	−0.0371516	+	0.114341i	0.930761	+	0.365629i	$0.119146\pi$
$18$		0			0
$19$	0.0963126	−	0.296420i	0.0220956	−	0.0680034i	−0.939401	−	0.342821i	$-0.888618\pi$
$19$	0.0963126	−	0.296420i	0.0220956	−	0.0680034i	0.961496	+	0.274818i	$0.0886175\pi$
$20$		0			0
$21$	−0.464854	−	1.43067i	−0.101439	−	0.312199i
$22$		0			0
$23$	−2.47611	−	1.79900i	−0.516305	−	0.375117i	0.298905	−	0.954283i	$-0.403379\pi$
$23$	−2.47611	−	1.79900i	−0.516305	−	0.375117i	−0.815210	+	0.579165i	$0.803379\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	−0.0378031	−	0.116346i	−0.00701987	−	0.0216049i	0.947485	−	0.319800i	$-0.103616\pi$
$29$	−0.0378031	−	0.116346i	−0.00701987	−	0.0216049i	−0.954505	+	0.298195i	$0.903616\pi$
$30$		0			0
$31$	−0.909629	+	2.79955i	−0.163374	+	0.502814i	−0.998913	−	0.0466176i	$-0.985156\pi$
$31$	−0.909629	+	2.79955i	−0.163374	+	0.502814i	0.835539	+	0.549432i	$0.185156\pi$
$32$		0			0
$33$	−1.90799	+	5.87218i	−0.332138	+	1.02222i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.53298	+	2.56686i	−0.580818	+	0.421989i	−0.839019	−	0.544102i	$-0.816870\pi$
$37$	−3.53298	+	2.56686i	−0.580818	+	0.421989i	0.258201	+	0.966091i	$0.416870\pi$
$38$		0			0
$39$	−2.87714	−	2.09036i	−0.460711	−	0.334726i
$40$		0			0
$41$	−3.44096	+	2.50001i	−0.537388	+	0.390436i	−0.823114	−	0.567876i	$-0.807765\pi$
$41$	−3.44096	+	2.50001i	−0.537388	+	0.390436i	0.285726	+	0.958311i	$0.407765\pi$
$42$		0			0
$43$	3.62663			0.553056			0.276528	−	0.961006i	$-0.410816\pi$
$43$	3.62663			0.553056			0.276528	+	0.961006i	$0.410816\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.63227	−	5.02362i	−0.238091	−	0.732770i	−0.996696	−	0.0812191i	$-0.974119\pi$
$47$	−1.63227	−	5.02362i	−0.238091	−	0.732770i	0.758605	−	0.651551i	$-0.225881\pi$
$48$		0			0
$49$	−4.73708			−0.676726
$50$		0			0
$51$	−0.495700			−0.0694120
$52$		0			0
$53$	2.65748	+	8.17888i	0.365033	+	1.12346i	0.949960	+	0.312370i	$0.101123\pi$
$53$	2.65748	+	8.17888i	0.365033	+	1.12346i	−0.584928	+	0.811086i	$0.698877\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.311674			0.0412823
$58$		0			0
$59$	−10.4222	+	7.57219i	−1.35686	+	0.985815i	−0.358220	+	0.933637i	$0.616616\pi$
$59$	−10.4222	+	7.57219i	−1.35686	+	0.985815i	−0.998638	+	0.0521781i	$0.983384\pi$
$60$		0			0
$61$	9.15882	+	6.65427i	1.17267	+	0.851992i	0.991326	−	0.131428i	$-0.0419562\pi$
$61$	9.15882	+	6.65427i	1.17267	+	0.851992i	0.181341	+	0.983420i	$0.441956\pi$
$62$		0			0
$63$	1.21700	−	0.884205i	0.153328	−	0.111399i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.09181	+	12.5933i	−0.499894	+	1.53852i	0.309293	+	0.950967i	$0.399908\pi$
$67$	−4.09181	+	12.5933i	−0.499894	+	1.53852i	−0.809188	+	0.587550i	$0.800092\pi$
$68$		0			0
$69$	0.945790	−	2.91084i	0.113860	−	0.350424i
$70$		0			0
$71$	1.00994	+	3.10827i	0.119858	+	0.368884i	0.992929	−	0.118708i	$-0.0378753\pi$
$71$	1.00994	+	3.10827i	0.119858	+	0.368884i	−0.873071	+	0.487592i	$0.837875\pi$
$72$		0			0
$73$	12.9174	+	9.38504i	1.51187	+	1.09844i	0.965340	+	0.260994i	$0.0840504\pi$
$73$	12.9174	+	9.38504i	1.51187	+	1.09844i	0.546527	+	0.837441i	$0.315950\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.51424	−	5.45941i	−0.856327	−	0.622158i
$78$		0			0
$79$	−2.63513	−	8.11010i	−0.296475	−	0.912457i	−0.982722	−	0.185088i	$-0.940743\pi$
$79$	−2.63513	−	8.11010i	−0.296475	−	0.912457i	0.686247	−	0.727369i	$-0.259257\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−3.50367	+	10.7832i	−0.384578	+	1.18361i	0.552208	+	0.833706i	$0.313785\pi$
$83$	−3.50367	+	10.7832i	−0.384578	+	1.18361i	−0.936786	+	0.349903i	$0.886215\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.0989699	−	0.0719058i	0.0106107	−	0.00770911i
$88$		0			0
$89$	−11.4335	−	8.30691i	−1.21195	−	0.880531i	−0.216541	−	0.976274i	$-0.569477\pi$
$89$	−11.4335	−	8.30691i	−1.21195	−	0.880531i	−0.995406	+	0.0957428i	$0.969477\pi$
$90$		0			0
$91$	4.32808	−	3.14453i	0.453706	−	0.329637i
$92$		0			0
$93$	−2.94362			−0.305239
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.54837	+	10.9208i	0.360282	+	1.10884i	0.952883	+	0.303339i	$0.0981013\pi$
$97$	3.54837	+	10.9208i	0.360282	+	1.10884i	−0.592601	+	0.805497i	$0.701899\pi$
$98$		0			0
$99$	−6.17438			−0.620548
$100$		0			0
$101$	−14.8359			−1.47622			−0.738111	−	0.674679i	$-0.764282\pi$
$101$	−14.8359			−1.47622			−0.738111	+	0.674679i	$0.764282\pi$
$102$		0			0
$103$	−5.95307	−	18.3217i	−0.586574	−	1.80529i	−0.592857	−	0.805308i	$-0.702000\pi$
$103$	−5.95307	−	18.3217i	−0.586574	−	1.80529i	0.00628354	−	0.999980i	$-0.498000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.63523			−0.834799			−0.417400	−	0.908723i	$-0.637058\pi$
$107$	−8.63523			−0.834799			−0.417400	+	0.908723i	$0.637058\pi$
$108$		0			0
$109$	15.1200	−	10.9853i	1.44823	−	1.05220i	0.461989	−	0.886886i	$-0.347136\pi$
$109$	15.1200	−	10.9853i	1.44823	−	1.05220i	0.986241	−	0.165315i	$-0.0528641\pi$
$110$		0			0
$111$	−3.53298	−	2.56686i	−0.335335	−	0.243635i
$112$		0			0
$113$	4.89971	−	3.55985i	0.460926	−	0.334883i	−0.332968	−	0.942938i	$-0.608050\pi$
$113$	4.89971	−	3.55985i	0.460926	−	0.334883i	0.793894	+	0.608056i	$0.208050\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.09897	−	3.38228i	0.101600	−	0.312692i
$118$		0			0
$119$	0.230428	−	0.709186i	0.0211233	−	0.0650109i
$120$		0			0
$121$	8.38144	+	25.7954i	0.761949	+	2.34504i
$122$		0			0
$123$	−3.44096	−	2.50001i	−0.310261	−	0.225418i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.47988	−	5.43445i	−0.663732	−	0.482230i	0.204189	−	0.978931i	$-0.434544\pi$
$127$	−7.47988	−	5.43445i	−0.663732	−	0.482230i	−0.867921	+	0.496702i	$0.834544\pi$
$128$		0			0
$129$	1.12069	+	3.44913i	0.0986714	+	0.303679i
$130$		0			0
$131$	5.87613	−	18.0849i	0.513399	−	1.58008i	−0.272776	−	0.962078i	$-0.587942\pi$
$131$	5.87613	−	18.0849i	0.513399	−	1.58008i	0.786175	−	0.618003i	$-0.212058\pi$
$132$		0			0
$133$	−0.144883	+	0.445904i	−0.0125630	+	0.0386648i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.36053	−	4.62120i	0.543417	−	0.394816i	−0.281936	−	0.959433i	$-0.590976\pi$
$137$	6.36053	−	4.62120i	0.543417	−	0.394816i	0.825352	+	0.564618i	$0.190976\pi$
$138$		0			0
$139$	11.1647	+	8.11165i	0.946980	+	0.688021i	0.950091	−	0.311974i	$-0.100990\pi$
$139$	11.1647	+	8.11165i	0.946980	+	0.688021i	−0.00311101	+	0.999995i	$0.500990\pi$
$140$		0			0
$141$	4.27335	−	3.10477i	0.359881	−	0.261469i
$142$		0			0
$143$	−21.9582			−1.83624
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.46384	−	4.50523i	−0.120735	−	0.371585i
$148$		0			0
$149$	5.12168			0.419585			0.209792	−	0.977746i	$-0.432721\pi$
$149$	5.12168			0.419585			0.209792	+	0.977746i	$0.432721\pi$
$150$		0			0
$151$	−12.9476			−1.05366			−0.526829	−	0.849972i	$-0.676619\pi$
$151$	−12.9476			−1.05366			−0.526829	+	0.849972i	$0.676619\pi$
$152$		0			0
$153$	−0.153180	−	0.471439i	−0.0123839	−	0.0381136i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.02750			0.321429			0.160715	−	0.987001i	$-0.448620\pi$
$157$	4.02750			0.321429			0.160715	+	0.987001i	$0.448620\pi$
$158$		0			0
$159$	−6.95737	+	5.05483i	−0.551755	+	0.400874i
$160$		0			0
$161$	3.72481	+	2.70623i	0.293556	+	0.213281i
$162$		0			0
$163$	12.6360	−	9.18062i	0.989732	−	0.719082i	0.0298692	−	0.999554i	$-0.490491\pi$
$163$	12.6360	−	9.18062i	0.989732	−	0.719082i	0.959862	+	0.280472i	$0.0904909\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.66014	+	11.2647i	−0.283230	+	0.871692i	0.703694	+	0.710503i	$0.251533\pi$
$167$	−3.66014	+	11.2647i	−0.283230	+	0.871692i	−0.986924	+	0.161189i	$0.948467\pi$
$168$		0			0
$169$	−0.108909	+	0.335187i	−0.00837761	+	0.0257836i
$170$		0			0
$171$	0.0963126	+	0.296420i	0.00736521	+	0.0226678i
$172$		0			0
$173$	11.9982	+	8.71717i	0.912203	+	0.662754i	0.941571	−	0.336814i	$-0.109349\pi$
$173$	11.9982	+	8.71717i	0.912203	+	0.662754i	−0.0293681	+	0.999569i	$0.509349\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.4222	−	7.57219i	−0.783382	−	0.569161i
$178$		0			0
$179$	−0.295895	−	0.910670i	−0.0221162	−	0.0680667i	0.939389	−	0.342852i	$-0.111393\pi$
$179$	−0.295895	−	0.910670i	−0.0221162	−	0.0680667i	−0.961505	+	0.274786i	$0.911393\pi$
$180$		0			0
$181$	1.27971	−	3.93855i	0.0951202	−	0.292750i	−0.892165	−	0.451710i	$-0.850814\pi$
$181$	1.27971	−	3.93855i	0.0951202	−	0.292750i	0.987285	+	0.158960i	$0.0508141\pi$
$182$		0			0
$183$	−3.49836	+	10.7668i	−0.258606	+	0.795908i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.47611	+	1.79900i	−0.181071	+	0.131556i
$188$		0			0
$189$	1.21700	+	0.884205i	0.0885240	+	0.0643165i
$190$		0			0
$191$	14.2634	−	10.3629i	1.03206	−	0.749836i	0.0633410	−	0.997992i	$-0.479824\pi$
$191$	14.2634	−	10.3629i	1.03206	−	0.749836i	0.968720	+	0.248156i	$0.0798244\pi$
$192$		0			0
$193$	−5.25392			−0.378185			−0.189093	−	0.981959i	$-0.560555\pi$
$193$	−5.25392			−0.378185			−0.189093	+	0.981959i	$0.560555\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.653870	+	2.01240i	0.0465863	+	0.143378i	0.971644	−	0.236449i	$-0.0759836\pi$
$197$	0.653870	+	2.01240i	0.0465863	+	0.143378i	−0.925058	+	0.379827i	$0.875984\pi$
$198$		0			0
$199$	9.07029			0.642976			0.321488	−	0.946914i	$-0.395817\pi$
$199$	9.07029			0.642976			0.321488	+	0.946914i	$0.395817\pi$
$200$		0			0
$201$	−13.2414			−0.933975
$202$		0			0
$203$	0.0568672	+	0.175019i	0.00399130	+	0.0122840i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.06064			0.212729
$208$		0			0
$209$	1.55687	−	1.13113i	0.107691	−	0.0782419i
$210$		0			0
$211$	16.0306	+	11.6469i	1.10359	+	0.801807i	0.981643	−	0.190729i	$-0.0610853\pi$
$211$	16.0306	+	11.6469i	1.10359	+	0.801807i	0.121950	+	0.992536i	$0.461085\pi$
$212$		0			0
$213$	−2.64405	+	1.92102i	−0.181168	+	0.131626i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.36835	−	4.21136i	0.0928900	−	0.285886i
$218$		0			0
$219$	−4.93401	+	15.1853i	−0.333409	+	1.02613i
$220$		0			0
$221$	−0.544760	−	1.67660i	−0.0366445	−	0.112780i
$222$		0			0
$223$	5.32506	+	3.86888i	0.356593	+	0.259080i	0.751629	−	0.659586i	$-0.229268\pi$
$223$	5.32506	+	3.86888i	0.356593	+	0.259080i	−0.395037	+	0.918665i	$0.629268\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.53193	+	6.92535i	0.632656	+	0.459652i	0.857319	−	0.514785i	$-0.172128\pi$
$227$	9.53193	+	6.92535i	0.632656	+	0.459652i	−0.224663	+	0.974436i	$0.572128\pi$
$228$		0			0
$229$	3.67417	+	11.3079i	0.242796	+	0.747250i	0.995991	+	0.0894526i	$0.0285117\pi$
$229$	3.67417	+	11.3079i	0.242796	+	0.747250i	−0.753195	+	0.657798i	$0.771488\pi$
$230$		0			0
$231$	2.87018	−	8.83352i	0.188844	−	0.581203i
$232$		0			0
$233$	1.56054	−	4.80285i	0.102234	−	0.314645i	−0.886837	−	0.462082i	$-0.847102\pi$
$233$	1.56054	−	4.80285i	0.102234	−	0.314645i	0.989071	+	0.147437i	$0.0471025\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.89886	−	5.01232i	0.448129	−	0.325585i
$238$		0			0
$239$	−2.16762	−	1.57487i	−0.140212	−	0.101870i	0.515468	−	0.856909i	$-0.327618\pi$
$239$	−2.16762	−	1.57487i	−0.140212	−	0.101870i	−0.655680	+	0.755039i	$0.727618\pi$
$240$		0			0
$241$	−10.2390	+	7.43906i	−0.659551	+	0.479192i	−0.866511	−	0.499157i	$-0.833643\pi$
$241$	−10.2390	+	7.43906i	−0.659551	+	0.479192i	0.206960	+	0.978349i	$0.433643\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.342521	+	1.05417i	0.0217941	+	0.0670752i
$248$		0			0
$249$	−11.3381			−0.718524
$250$		0			0
$251$	−22.9068			−1.44586			−0.722932	−	0.690919i	$-0.757206\pi$
$251$	−22.9068			−1.44586			−0.722932	+	0.690919i	$0.757206\pi$
$252$		0			0
$253$	−5.83966	−	17.9726i	−0.367136	−	1.12993i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	27.7764			1.73264			0.866322	−	0.499486i	$-0.166478\pi$
$257$	27.7764			1.73264			0.866322	+	0.499486i	$0.166478\pi$
$258$		0			0
$259$	5.31466	−	3.86132i	0.330237	−	0.239931i
$260$		0			0
$261$	0.0989699	+	0.0719058i	0.00612608	+	0.00445086i
$262$		0			0
$263$	9.47479	−	6.88384i	0.584241	−	0.424476i	−0.256010	−	0.966674i	$-0.582408\pi$
$263$	9.47479	−	6.88384i	0.584241	−	0.424476i	0.840250	+	0.542198i	$0.182408\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	4.36720	−	13.4409i	0.267268	−	0.822568i
$268$		0			0
$269$	1.29979	−	4.00034i	0.0792496	−	0.243905i	−0.903580	−	0.428419i	$-0.859071\pi$
$269$	1.29979	−	4.00034i	0.0792496	−	0.243905i	0.982830	+	0.184513i	$0.0590709\pi$
$270$		0			0
$271$	−3.88308	−	11.9509i	−0.235880	−	0.725965i	−0.997003	−	0.0773578i	$-0.975352\pi$
$271$	−3.88308	−	11.9509i	−0.235880	−	0.725965i	0.761123	−	0.648608i	$-0.224648\pi$
$272$		0			0
$273$	4.32808	+	3.14453i	0.261947	+	0.190316i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	25.7795	+	18.7299i	1.54894	+	1.12537i	0.944400	+	0.328800i	$0.106644\pi$
$277$	25.7795	+	18.7299i	1.54894	+	1.12537i	0.604543	+	0.796573i	$0.293356\pi$
$278$		0			0
$279$	−0.909629	−	2.79955i	−0.0544581	−	0.167605i
$280$		0			0
$281$	5.03691	−	15.5020i	0.300477	−	0.924773i	−0.680849	−	0.732423i	$-0.738389\pi$
$281$	5.03691	−	15.5020i	0.300477	−	0.924773i	0.981326	−	0.192350i	$-0.0616108\pi$
$282$		0			0
$283$	4.21205	−	12.9634i	0.250381	−	0.770592i	−0.744324	−	0.667819i	$-0.767228\pi$
$283$	4.21205	−	12.9634i	0.250381	−	0.770592i	0.994705	−	0.102774i	$-0.0327718\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.17624	−	3.76076i	0.305544	−	0.221991i
$288$		0			0
$289$	13.5545	+	9.84792i	0.797323	+	0.579289i
$290$		0			0
$291$	−9.28975	+	6.74940i	−0.544575	+	0.395657i
$292$		0			0
$293$	−25.2652			−1.47601			−0.738004	−	0.674796i	$-0.764232\pi$
$293$	−25.2652			−1.47601			−0.738004	+	0.674796i	$0.764232\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.90799	−	5.87218i	−0.110713	−	0.340738i
$298$		0			0
$299$	10.8847			0.629477
$300$		0			0
$301$	−5.45554			−0.314452
$302$		0			0
$303$	−4.58453	−	14.1097i	−0.263374	−	0.810583i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	7.01023			0.400095			0.200047	−	0.979786i	$-0.435890\pi$
$307$	7.01023			0.400095			0.200047	+	0.979786i	$0.435890\pi$
$308$		0			0
$309$	15.5853	−	11.3234i	0.886619	−	0.644167i
$310$		0			0
$311$	−11.7403	−	8.52985i	−0.665733	−	0.483683i	0.202861	−	0.979208i	$-0.434976\pi$
$311$	−11.7403	−	8.52985i	−0.665733	−	0.483683i	−0.868594	+	0.495524i	$0.834976\pi$
$312$		0			0
$313$	17.7334	−	12.8841i	1.00235	−	0.728250i	0.0397589	−	0.999209i	$-0.487341\pi$
$313$	17.7334	−	12.8841i	1.00235	−	0.728250i	0.962591	+	0.270960i	$0.0873410\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.4194	−	32.0675i	0.585210	−	1.80109i	−0.0132156	−	0.999913i	$-0.504207\pi$
$317$	10.4194	−	32.0675i	0.585210	−	1.80109i	0.598426	−	0.801178i	$-0.295793\pi$
$318$		0			0
$319$	0.233411	−	0.718364i	0.0130685	−	0.0402207i
$320$		0			0
$321$	−2.66843	−	8.21259i	−0.148937	−	0.458382i
$322$		0			0
$323$	0.124991	+	0.0908111i	0.00695467	+	0.00505286i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	15.1200	+	10.9853i	0.836136	+	0.607488i
$328$		0			0
$329$	2.45543	+	7.55703i	0.135372	+	0.416632i
$330$		0			0
$331$	10.3814	−	31.9508i	0.570616	−	1.75617i	−0.0800299	−	0.996792i	$-0.525502\pi$
$331$	10.3814	−	31.9508i	0.570616	−	1.75617i	0.650645	−	0.759382i	$-0.274498\pi$
$332$		0			0
$333$	1.34948	−	4.15326i	0.0739509	−	0.227597i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.49603	−	1.81347i	0.135967	−	0.0987859i	−0.517723	−	0.855548i	$-0.673220\pi$
$337$	2.49603	−	1.81347i	0.135967	−	0.0987859i	0.653690	+	0.756763i	$0.273220\pi$
$338$		0			0
$339$	4.89971	+	3.55985i	0.266116	+	0.193345i
$340$		0			0
$341$	−14.7039	+	10.6830i	−0.796261	+	0.578518i
$342$		0			0
$343$	17.6561			0.953339
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.88556	−	11.9585i	−0.208588	−	0.641967i	−0.999547	−	0.0300984i	$-0.990418\pi$
$347$	−3.88556	−	11.9585i	−0.208588	−	0.641967i	0.790959	−	0.611869i	$-0.209582\pi$
$348$		0			0
$349$	13.3100			0.712466			0.356233	−	0.934397i	$-0.384061\pi$
$349$	13.3100			0.712466			0.356233	+	0.934397i	$0.384061\pi$
$350$		0			0
$351$	3.55634			0.189823
$352$		0			0
$353$	3.48923	+	10.7388i	0.185713	+	0.571566i	0.999960	−	0.00895265i	$-0.00284975\pi$
$353$	3.48923	+	10.7388i	0.185713	+	0.571566i	−0.814247	+	0.580519i	$0.802850\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.745682			0.0394657
$358$		0			0
$359$	−15.7007	+	11.4072i	−0.828652	+	0.602051i	−0.919178	−	0.393843i	$-0.871145\pi$
$359$	−15.7007	+	11.4072i	−0.828652	+	0.602051i	0.0905254	+	0.995894i	$0.471145\pi$
$360$		0			0
$361$	15.2927	+	11.1108i	0.804881	+	0.584780i
$362$		0			0
$363$	−21.9429	+	15.9424i	−1.15170	+	0.836761i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.42951	+	16.7103i	−0.283418	+	0.872271i	0.703450	+	0.710744i	$0.251642\pi$
$367$	−5.42951	+	16.7103i	−0.283418	+	0.872271i	−0.986868	+	0.161526i	$0.948358\pi$
$368$		0			0
$369$	1.31433	−	4.04510i	0.0684214	−	0.210579i
$370$		0			0
$371$	−3.99764	−	12.3035i	−0.207547	−	0.638765i
$372$		0			0
$373$	−22.8195	−	16.5793i	−1.18155	−	0.858446i	−0.189204	−	0.981938i	$-0.560591\pi$
$373$	−22.8195	−	16.5793i	−1.18155	−	0.858446i	−0.992346	+	0.123492i	$0.960591\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.351971	+	0.255722i	0.0181274	+	0.0131703i
$378$		0			0
$379$	1.12118	+	3.45064i	0.0575912	+	0.177247i	0.975714	−	0.219049i	$-0.0702954\pi$
$379$	1.12118	+	3.45064i	0.0575912	+	0.177247i	−0.918123	+	0.396296i	$0.870295\pi$
$380$		0			0
$381$	2.85706	−	8.79313i	0.146372	−	0.450486i
$382$		0			0
$383$	4.27519	−	13.1577i	0.218452	−	0.672326i	−0.780439	−	0.625232i	$-0.785004\pi$
$383$	4.27519	−	13.1577i	0.218452	−	0.672326i	0.998890	−	0.0470934i	$-0.0149958\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.93401	+	2.13168i	−0.149144	+	0.108359i
$388$		0			0
$389$	16.9096	+	12.2855i	0.857348	+	0.622900i	0.927162	−	0.374660i	$-0.122241\pi$
$389$	16.9096	+	12.2855i	0.857348	+	0.622900i	−0.0698138	+	0.997560i	$0.522241\pi$
$390$		0			0
$391$	1.22741	−	0.891765i	0.0620727	−	0.0450985i
$392$		0			0
$393$	19.0155			0.959207
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.77499	+	14.6959i	0.239650	+	0.737566i	0.996471	+	0.0839436i	$0.0267516\pi$
$397$	4.77499	+	14.6959i	0.239650	+	0.737566i	−0.756821	+	0.653622i	$0.773248\pi$
$398$		0			0
$399$	−0.468851			−0.0234719
$400$		0			0
$401$	2.25590			0.112654			0.0563271	−	0.998412i	$-0.482061\pi$
$401$	2.25590			0.112654			0.0563271	+	0.998412i	$0.482061\pi$
$402$		0			0
$403$	−3.23495	−	9.95616i	−0.161144	−	0.495952i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−26.9635			−1.33653
$408$		0			0
$409$	1.88712	−	1.37107i	0.0933119	−	0.0677951i	−0.540151	−	0.841568i	$-0.681633\pi$
$409$	1.88712	−	1.37107i	0.0933119	−	0.0677951i	0.633463	+	0.773773i	$0.281633\pi$
$410$		0			0
$411$	6.36053	+	4.62120i	0.313742	+	0.227947i
$412$		0			0
$413$	15.6781	−	11.3908i	0.771471	−	0.560507i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−4.26455	+	13.1249i	−0.208836	+	0.642730i
$418$		0			0
$419$	−1.55768	+	4.79405i	−0.0760977	+	0.234205i	−0.981869	−	0.189563i	$-0.939293\pi$
$419$	−1.55768	+	4.79405i	−0.0760977	+	0.234205i	0.905771	+	0.423768i	$0.139293\pi$
$420$		0			0
$421$	3.99823	+	12.3053i	0.194862	+	0.599724i	0.999978	+	0.00660640i	$0.00210290\pi$
$421$	3.99823	+	12.3053i	0.194862	+	0.599724i	−0.805116	+	0.593117i	$0.797897\pi$
$422$		0			0
$423$	4.27335	+	3.10477i	0.207777	+	0.150959i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−13.7776	−	10.0100i	−0.666745	−	0.484419i
$428$		0			0
$429$	−6.78545	−	20.8835i	−0.327605	−	1.00826i
$430$		0			0
$431$	0.483616	−	1.48842i	0.0232950	−	0.0716945i	−0.938733	−	0.344645i	$-0.887999\pi$
$431$	0.483616	−	1.48842i	0.0232950	−	0.0716945i	0.962028	+	0.272950i	$0.0879994\pi$
$432$		0			0
$433$	−7.99517	+	24.6066i	−0.384224	+	1.18252i	0.552818	+	0.833302i	$0.313552\pi$
$433$	−7.99517	+	24.6066i	−0.384224	+	1.18252i	−0.937042	+	0.349217i	$0.886448\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.771740	+	0.560702i	−0.0369173	+	0.0268220i
$438$		0			0
$439$	−13.2446	−	9.62279i	−0.632132	−	0.459271i	0.225006	−	0.974357i	$-0.427760\pi$
$439$	−13.2446	−	9.62279i	−0.632132	−	0.459271i	−0.857138	+	0.515087i	$0.827760\pi$
$440$		0			0
$441$	3.83238	−	2.78439i	0.182494	−	0.132590i
$442$		0			0
$443$	−28.1180			−1.33593			−0.667963	−	0.744194i	$-0.732834\pi$
$443$	−28.1180			−1.33593			−0.667963	+	0.744194i	$0.732834\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.58269	+	4.87101i	0.0748585	+	0.230391i
$448$		0			0
$449$	−2.65681			−0.125383			−0.0626914	−	0.998033i	$-0.519968\pi$
$449$	−2.65681			−0.125383			−0.0626914	+	0.998033i	$0.519968\pi$
$450$		0			0
$451$	−26.2613			−1.23659
$452$		0			0
$453$	−4.00101	−	12.3139i	−0.187984	−	0.578556i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.321574			0.0150426			0.00752129	−	0.999972i	$-0.497606\pi$
$457$	0.321574			0.0150426			0.00752129	+	0.999972i	$0.497606\pi$
$458$		0			0
$459$	0.401030	−	0.291365i	0.0187185	−	0.0135998i
$460$		0			0
$461$	6.21780	+	4.51749i	0.289592	+	0.210401i	0.723090	−	0.690754i	$-0.242721\pi$
$461$	6.21780	+	4.51749i	0.289592	+	0.210401i	−0.433499	+	0.901154i	$0.642721\pi$
$462$		0			0
$463$	15.4555	−	11.2291i	0.718279	−	0.521860i	−0.167555	−	0.985863i	$-0.553587\pi$
$463$	15.4555	−	11.2291i	0.718279	−	0.521860i	0.885834	+	0.464002i	$0.153587\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.98372	−	6.10525i	0.0917955	−	0.282517i	−0.894610	−	0.446848i	$-0.852546\pi$
$467$	1.98372	−	6.10525i	0.0917955	−	0.282517i	0.986405	+	0.164331i	$0.0525464\pi$
$468$		0			0
$469$	6.15531	−	18.9441i	0.284226	−	0.874757i
$470$		0			0
$471$	1.24457	+	3.83038i	0.0573466	+	0.176495i
$472$		0			0
$473$	18.1157	+	13.1618i	0.832959	+	0.605180i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.95737	−	5.05483i	−0.318556	−	0.231445i
$478$		0			0
$479$	10.3709	+	31.9183i	0.473858	+	1.45839i	0.847491	+	0.530810i	$0.178112\pi$
$479$	10.3709	+	31.9183i	0.473858	+	1.45839i	−0.373633	+	0.927577i	$0.621888\pi$
$480$		0			0
$481$	4.79920	−	14.7704i	0.218825	−	0.673473i
$482$		0			0
$483$	−1.42275	+	4.37878i	−0.0647374	+	0.199241i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−9.63578	+	7.00080i	−0.436639	+	0.317237i	−0.784298	−	0.620384i	$-0.786977\pi$
$487$	−9.63578	+	7.00080i	−0.436639	+	0.317237i	0.347659	+	0.937621i	$0.386977\pi$
$488$		0			0
$489$	12.6360	+	9.18062i	0.571422	+	0.415162i
$490$		0			0
$491$	−12.6312	+	9.17712i	−0.570039	+	0.414158i	−0.835119	−	0.550069i	$-0.814602\pi$
$491$	−12.6312	+	9.17712i	−0.570039	+	0.414158i	0.265080	+	0.964226i	$0.414602\pi$
$492$		0			0
$493$	0.0606408			0.00273112
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.51925	−	4.67577i	−0.0681477	−	0.209737i
$498$		0			0
$499$	30.9130			1.38386			0.691929	−	0.721966i	$-0.256761\pi$
$499$	30.9130			1.38386			0.691929	+	0.721966i	$0.256761\pi$
$500$		0			0
$501$	−11.8445			−0.529171
$502$		0			0
$503$	−9.59178	−	29.5204i	−0.427676	−	1.31625i	−0.900408	−	0.435046i	$-0.856732\pi$
$503$	−9.59178	−	29.5204i	−0.427676	−	1.31625i	0.472732	−	0.881206i	$-0.343268\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.352437			−0.0156523
$508$		0			0
$509$	10.7945	−	7.84269i	0.478460	−	0.347621i	−0.322269	−	0.946648i	$-0.604446\pi$
$509$	10.7945	−	7.84269i	0.478460	−	0.347621i	0.800729	+	0.599027i	$0.204446\pi$
$510$		0			0
$511$	−19.4316	−	14.1179i	−0.859605	−	0.624540i
$512$		0			0
$513$	−0.252150	+	0.183198i	−0.0111327	+	0.00808837i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	10.0783	−	31.0177i	0.443242	−	1.36416i
$518$		0			0
$519$	−4.58289	+	14.1047i	−0.201166	+	0.619127i
$520$		0			0
$521$	8.19439	+	25.2197i	0.359003	+	1.10490i	0.953652	+	0.300912i	$0.0972910\pi$
$521$	8.19439	+	25.2197i	0.359003	+	1.10490i	−0.594649	+	0.803985i	$0.702709\pi$
$522$		0			0
$523$	−14.0888	−	10.2361i	−0.616060	−	0.447594i	0.235483	−	0.971878i	$-0.424333\pi$
$523$	−14.0888	−	10.2361i	−0.616060	−	0.447594i	−0.851543	+	0.524285i	$0.824333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.18048	−	0.857670i	−0.0514226	−	0.0373607i
$528$		0			0
$529$	−4.21267	−	12.9653i	−0.183159	−	0.563707i
$530$		0			0
$531$	3.98094	−	12.2521i	0.172758	−	0.531694i
$532$		0			0
$533$	4.67421	−	14.3857i	0.202463	−	0.623116i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.774662	−	0.562825i	0.0334291	−	0.0242877i
$538$		0			0
$539$	−23.6626	−	17.1919i	−1.01922	−	0.740506i
$540$		0			0
$541$	−4.42275	+	3.21332i	−0.190149	+	0.138151i	−0.678787	−	0.734335i	$-0.737494\pi$
$541$	−4.42275	+	3.21332i	−0.190149	+	0.138151i	0.488638	+	0.872487i	$0.337494\pi$
$542$		0			0
$543$	4.14123			0.177717
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−6.68894	−	20.5864i	−0.285998	−	0.880212i	−0.986098	−	0.166167i	$-0.946861\pi$
$547$	−6.68894	−	20.5864i	−0.285998	−	0.880212i	0.700099	−	0.714046i	$-0.253139\pi$
$548$		0			0
$549$	−11.3209			−0.483165
$550$		0			0
$551$	−0.0381282			−0.00162432
$552$		0			0
$553$	3.96403	+	12.2000i	0.168568	+	0.518798i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.58830			0.109670			0.0548349	−	0.998495i	$-0.482537\pi$
$557$	2.58830			0.109670			0.0548349	+	0.998495i	$0.482537\pi$
$558$		0			0
$559$	−10.4343	+	7.58099i	−0.441325	+	0.320642i
$560$		0			0
$561$	−2.47611	−	1.79900i	−0.104541	−	0.0759538i
$562$		0			0
$563$	16.0945	−	11.6933i	0.678301	−	0.492815i	−0.194493	−	0.980904i	$-0.562306\pi$
$563$	16.0945	−	11.6933i	0.678301	−	0.492815i	0.872794	+	0.488089i	$0.162306\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.464854	+	1.43067i	−0.0195220	+	0.0600827i
$568$		0			0
$569$	10.0215	−	30.8431i	0.420124	−	1.29301i	−0.487463	−	0.873144i	$-0.662077\pi$
$569$	10.0215	−	30.8431i	0.420124	−	1.29301i	0.907587	−	0.419865i	$-0.137923\pi$
$570$		0			0
$571$	4.23915	+	13.0468i	0.177403	+	0.545990i	0.999735	−	0.0230176i	$-0.00732739\pi$
$571$	4.23915	+	13.0468i	0.177403	+	0.545990i	−0.822332	+	0.569008i	$0.807327\pi$
$572$		0			0
$573$	14.2634	+	10.3629i	0.595861	+	0.432918i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	19.9368	+	14.4849i	0.829979	+	0.603015i	0.919553	−	0.392965i	$-0.128551\pi$
$577$	19.9368	+	14.4849i	0.829979	+	0.603015i	−0.0895741	+	0.995980i	$0.528551\pi$
$578$		0			0
$579$	−1.62355	−	4.99677i	−0.0674724	−	0.207659i
$580$		0			0
$581$	5.27057	−	16.2212i	0.218660	−	0.672967i
$582$		0			0
$583$	−16.4083	+	50.4995i	−0.679561	+	2.09147i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.73236	−	4.89134i	0.277874	−	0.201887i	−0.440115	−	0.897941i	$-0.645062\pi$
$587$	6.73236	−	4.89134i	0.277874	−	0.201887i	0.717990	+	0.696054i	$0.245062\pi$
$588$		0			0
$589$	0.742234	+	0.539264i	0.0305832	+	0.0222200i
$590$		0			0
$591$	−1.71185	+	1.24373i	−0.0704162	+	0.0511604i
$592$		0			0
$593$	−21.7904			−0.894826			−0.447413	−	0.894328i	$-0.647654\pi$
$593$	−21.7904			−0.894826			−0.447413	+	0.894328i	$0.647654\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.80287	+	8.62636i	0.114714	+	0.353053i
$598$		0			0
$599$	10.6482			0.435074			0.217537	−	0.976052i	$-0.430198\pi$
$599$	10.6482			0.435074			0.217537	+	0.976052i	$0.430198\pi$
$600$		0			0
$601$	2.60740			0.106358			0.0531791	−	0.998585i	$-0.483065\pi$
$601$	2.60740			0.106358			0.0531791	+	0.998585i	$0.483065\pi$
$602$		0			0
$603$	−4.09181	−	12.5933i	−0.166631	−	0.512839i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−32.9820			−1.33870			−0.669349	−	0.742948i	$-0.733427\pi$
$607$	−32.9820			−1.33870			−0.669349	+	0.742948i	$0.733427\pi$
$608$		0			0
$609$	−0.148880	+	0.108168i	−0.00603294	+	0.00438318i
$610$		0			0
$611$	15.1975	+	11.0416i	0.614824	+	0.446696i
$612$		0			0
$613$	−15.2007	+	11.0440i	−0.613951	+	0.446062i	−0.850804	−	0.525484i	$-0.823884\pi$
$613$	−15.2007	+	11.0440i	−0.613951	+	0.446062i	0.236852	+	0.971546i	$0.423884\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.1530	+	37.4030i	−0.489260	+	1.50579i	0.336456	+	0.941699i	$0.390772\pi$
$617$	−12.1530	+	37.4030i	−0.489260	+	1.50579i	−0.825715	+	0.564087i	$0.809228\pi$
$618$		0			0
$619$	−4.95554	+	15.2516i	−0.199180	+	0.613013i	0.800722	+	0.599036i	$0.204449\pi$
$619$	−4.95554	+	15.2516i	−0.199180	+	0.613013i	−0.999902	+	0.0139774i	$0.995551\pi$
$620$		0			0
$621$	0.945790	+	2.91084i	0.0379532	+	0.116808i
$622$		0			0
$623$	17.1994	+	12.4961i	0.689079	+	0.500645i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.55687	+	1.13113i	0.0621753	+	0.0451730i
$628$		0			0
$629$	−0.668937	−	2.05878i	−0.0266722	−	0.0820887i
$630$		0			0
$631$	1.49158	−	4.59061i	0.0593788	−	0.182749i	−0.916967	−	0.398962i	$-0.869371\pi$
$631$	1.49158	−	4.59061i	0.0593788	−	0.182749i	0.976346	+	0.216213i	$0.0693705\pi$
$632$		0			0
$633$	−6.12315	+	18.8451i	−0.243373	+	0.749026i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	13.6293	−	9.90223i	0.540011	−	0.392341i
$638$		0			0
$639$	−2.64405	−	1.92102i	−0.104597	−	0.0759943i
$640$		0			0
$641$	29.5813	−	21.4921i	1.16839	−	0.848887i	0.177577	−	0.984107i	$-0.443174\pi$
$641$	29.5813	−	21.4921i	1.16839	−	0.848887i	0.990816	+	0.135220i	$0.0431742\pi$
$642$		0			0
$643$	18.3769			0.724714			0.362357	−	0.932039i	$-0.381972\pi$
$643$	18.3769			0.724714			0.362357	+	0.932039i	$0.381972\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.7110	+	39.1206i	0.499723	+	1.53799i	0.809465	+	0.587167i	$0.199757\pi$
$647$	12.7110	+	39.1206i	0.499723	+	1.53799i	−0.309743	+	0.950820i	$0.600243\pi$
$648$		0			0
$649$	−79.5419			−3.12229
$650$		0			0
$651$	4.42809			0.173550
$652$		0			0
$653$	6.78128	+	20.8706i	0.265372	+	0.816731i	0.991608	+	0.129285i	$0.0412681\pi$
$653$	6.78128	+	20.8706i	0.265372	+	0.816731i	−0.726236	+	0.687446i	$0.758732\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−15.9668			−0.622924
$658$		0			0
$659$	−17.1550	+	12.4638i	−0.668264	+	0.485522i	−0.869444	−	0.494032i	$-0.835523\pi$
$659$	−17.1550	+	12.4638i	−0.668264	+	0.485522i	0.201179	+	0.979554i	$0.435523\pi$
$660$		0			0
$661$	−14.5172	−	10.5473i	−0.564652	−	0.410244i	0.268507	−	0.963278i	$-0.413470\pi$
$661$	−14.5172	−	10.5473i	−0.564652	−	0.410244i	−0.833159	+	0.553034i	$0.813470\pi$
$662$		0			0
$663$	1.42620	−	1.03619i	0.0553890	−	0.0402425i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.115702	+	0.356094i	−0.00447999	+	0.0137880i
$668$		0			0
$669$	−2.03399	+	6.25999i	−0.0786387	+	0.242025i
$670$		0			0
$671$	21.6002	+	66.4785i	0.833865	+	2.56637i
$672$		0			0
$673$	27.7504	+	20.1619i	1.06970	+	0.777183i	0.975858	−	0.218404i	$-0.0700851\pi$
$673$	27.7504	+	20.1619i	1.06970	+	0.777183i	0.0938421	+	0.995587i	$0.470085\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.35495	−	2.43752i	−0.128941	−	0.0936814i	0.521445	−	0.853285i	$-0.325393\pi$
$677$	−3.35495	−	2.43752i	−0.128941	−	0.0936814i	−0.650387	+	0.759603i	$0.725393\pi$
$678$		0			0
$679$	−5.33781	−	16.4281i	−0.204846	−	0.630452i
$680$		0			0
$681$	−3.64087	+	11.2055i	−0.139519	+	0.429394i
$682$		0			0
$683$	−0.654621	+	2.01472i	−0.0250484	+	0.0770910i	−0.962799	−	0.270218i	$-0.912904\pi$
$683$	−0.654621	+	2.01472i	−0.0250484	+	0.0770910i	0.937751	+	0.347309i	$0.112904\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−9.61911	+	6.98869i	−0.366992	+	0.266635i
$688$		0			0
$689$	−24.7428	−	17.9767i	−0.942625	−	0.684857i
$690$		0			0
$691$	3.21546	−	2.33617i	0.122322	−	0.0888721i	−0.524942	−	0.851138i	$-0.675913\pi$
$691$	3.21546	−	2.33617i	0.122322	−	0.0888721i	0.647264	+	0.762266i	$0.275913\pi$
$692$		0			0
$693$	9.28811			0.352826
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.651515	−	2.00516i	−0.0246779	−	0.0759507i
$698$		0			0
$699$	5.05001			0.191009
$700$		0			0
$701$	−10.1954			−0.385076			−0.192538	−	0.981289i	$-0.561672\pi$
$701$	−10.1954			−0.385076			−0.192538	+	0.981289i	$0.561672\pi$
$702$		0			0
$703$	0.420597	+	1.29447i	0.0158631	+	0.0488217i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.3176			0.839338
$708$		0			0
$709$	−24.1421	+	17.5403i	−0.906676	+	0.658739i	−0.940172	−	0.340700i	$-0.889336\pi$
$709$	−24.1421	+	17.5403i	−0.906676	+	0.658739i	0.0334959	+	0.999439i	$0.489336\pi$
$710$		0			0
$711$	6.89886	+	5.01232i	0.258728	+	0.187977i
$712$		0			0
$713$	7.28873	−	5.29557i	0.272965	−	0.198321i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.827957	−	2.54819i	0.0309206	−	0.0951639i
$718$		0			0
$719$	2.29734	−	7.07047i	0.0856762	−	0.263684i	−0.899036	−	0.437875i	$-0.855731\pi$
$719$	2.29734	−	7.07047i	0.0856762	−	0.263684i	0.984712	+	0.174191i	$0.0557311\pi$
$720$		0			0
$721$	8.95520	+	27.5613i	0.333509	+	1.02644i
$722$		0			0
$723$	−10.2390	−	7.43906i	−0.380792	−	0.276662i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−12.8791	−	9.35722i	−0.477660	−	0.347040i	0.322759	−	0.946481i	$-0.395390\pi$
$727$	−12.8791	−	9.35722i	−0.477660	−	0.347040i	−0.800419	+	0.599441i	$0.795390\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−0.555527	+	1.70974i	−0.0205469	+	0.0632369i
$732$		0			0
$733$	−9.45910	+	29.1121i	−0.349380	+	1.07528i	0.609817	+	0.792542i	$0.291243\pi$
$733$	−9.45910	+	29.1121i	−0.349380	+	1.07528i	−0.959197	+	0.282738i	$0.908757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−66.1430	+	48.0557i	−2.43641	+	1.77015i
$738$		0			0
$739$	−20.9842	−	15.2459i	−0.771917	−	0.560830i	0.130626	−	0.991432i	$-0.458301\pi$
$739$	−20.9842	−	15.2459i	−0.771917	−	0.560830i	−0.902542	+	0.430602i	$0.858301\pi$
$740$		0			0
$741$	−0.896731	+	0.651513i	−0.0329422	+	0.0239339i
$742$		0			0
$743$	−17.2136			−0.631504			−0.315752	−	0.948842i	$-0.602257\pi$
$743$	−17.2136			−0.631504			−0.315752	+	0.948842i	$0.602257\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.50367	−	10.7832i	−0.128193	−	0.394536i
$748$		0			0
$749$	12.9900			0.474643
$750$		0			0
$751$	10.4020			0.379576			0.189788	−	0.981825i	$-0.439220\pi$
$751$	10.4020			0.379576			0.189788	+	0.981825i	$0.439220\pi$
$752$		0			0
$753$	−7.07859	−	21.7857i	−0.257958	−	0.793913i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	16.9118			0.614669			0.307335	−	0.951601i	$-0.400563\pi$
$757$	16.9118			0.614669			0.307335	+	0.951601i	$0.400563\pi$
$758$		0			0
$759$	15.2884	−	11.1077i	0.554935	−	0.403184i
$760$		0			0
$761$	−0.422588	−	0.307028i	−0.0153188	−	0.0111297i	0.580100	−	0.814546i	$-0.303014\pi$
$761$	−0.422588	−	0.307028i	−0.0153188	−	0.0111297i	−0.595418	+	0.803416i	$0.703014\pi$
$762$		0			0
$763$	−22.7450	+	16.5252i	−0.823423	+	0.598252i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.1576	−	43.5725i	0.511200	−	1.57331i
$768$		0			0
$769$	−11.7671	+	36.2154i	−0.424333	+	1.30596i	0.479299	+	0.877651i	$0.340891\pi$
$769$	−11.7671	+	36.2154i	−0.424333	+	1.30596i	−0.903632	+	0.428310i	$0.859109\pi$
$770$		0			0
$771$	8.58338	+	26.4169i	0.309123	+	0.951382i
$772$		0			0
$773$	−18.3577	−	13.3376i	−0.660280	−	0.479721i	0.206478	−	0.978451i	$-0.433800\pi$
$773$	−18.3577	−	13.3376i	−0.660280	−	0.479721i	−0.866757	+	0.498730i	$0.833800\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.31466	+	3.86132i	0.190662	+	0.138524i
$778$		0			0
$779$	0.409643	+	1.26075i	0.0146770	+	0.0451711i
$780$		0			0
$781$	−6.23574	+	19.1916i	−0.223132	+	0.686731i
$782$		0			0
$783$	−0.0378031	+	0.116346i	−0.00135097	+	0.00415787i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.84384	−	1.33963i	0.0657257	−	0.0477525i	−0.554437	−	0.832226i	$-0.687066\pi$
$787$	1.84384	−	1.33963i	0.0657257	−	0.0477525i	0.620163	+	0.784473i	$0.287066\pi$
$788$		0			0
$789$	9.47479	+	6.88384i	0.337312	+	0.245071i
$790$		0			0
$791$	−7.37064	+	5.35508i	−0.262070	+	0.190405i
$792$		0			0
$793$	−40.2611			−1.42971
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.06936	−	18.6796i	−0.214988	−	0.661665i	−0.999154	−	0.0411143i	$-0.986909\pi$
$797$	−6.06936	−	18.6796i	−0.214988	−	0.661665i	0.784167	−	0.620550i	$-0.213091\pi$
$798$		0			0
$799$	2.61836			0.0926310
$800$		0			0
$801$	14.1326			0.499349
$802$		0			0
$803$	30.4644	+	93.7598i	1.07507	+	3.30871i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.20621			0.148066
$808$		0			0
$809$	−9.05703	+	6.58032i	−0.318428	+	0.231352i	−0.735504	−	0.677520i	$-0.763055\pi$
$809$	−9.05703	+	6.58032i	−0.318428	+	0.231352i	0.417076	+	0.908871i	$0.363055\pi$
$810$		0			0
$811$	15.6132	+	11.3436i	0.548253	+	0.398329i	0.827141	−	0.561995i	$-0.189966\pi$
$811$	15.6132	+	11.3436i	0.548253	+	0.398329i	−0.278888	+	0.960324i	$0.589966\pi$
$812$		0			0
$813$	10.1660	−	7.38606i	0.356539	−	0.259040i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.349291	−	1.07501i	0.0122201	−	0.0376097i
$818$		0			0
$819$	−1.65318	+	5.08796i	−0.0577668	+	0.177788i
$820$		0			0
$821$	−14.8716	−	45.7701i	−0.519023	−	1.59739i	−0.775841	−	0.630928i	$-0.782674\pi$
$821$	−14.8716	−	45.7701i	−0.519023	−	1.59739i	0.256818	−	0.966460i	$-0.417326\pi$
$822$		0			0
$823$	28.2356	+	20.5144i	0.984232	+	0.715087i	0.958650	−	0.284586i	$-0.0918562\pi$
$823$	28.2356	+	20.5144i	0.984232	+	0.715087i	0.0255817	+	0.999673i	$0.491856\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.7401	+	13.6155i	0.651656	+	0.473456i	0.863835	−	0.503775i	$-0.168056\pi$
$827$	18.7401	+	13.6155i	0.651656	+	0.473456i	−0.212179	+	0.977231i	$0.568056\pi$
$828$		0			0
$829$	6.70966	+	20.6502i	0.233036	+	0.717211i	0.997376	+	0.0723976i	$0.0230651\pi$
$829$	6.70966	+	20.6502i	0.233036	+	0.717211i	−0.764340	+	0.644814i	$0.776935\pi$
$830$		0			0
$831$	−9.84691	+	30.3057i	−0.341585	+	1.05129i
$832$		0			0
$833$	0.725626	−	2.23325i	0.0251414	−	0.0773774i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.38144	−	1.73022i	0.0823146	−	0.0598051i
$838$		0			0
$839$	−8.40486	−	6.10649i	−0.290168	−	0.210819i	0.433172	−	0.901311i	$-0.357394\pi$
$839$	−8.40486	−	6.10649i	−0.290168	−	0.210819i	−0.723340	+	0.690492i	$0.757394\pi$
$840$		0			0
$841$	23.4494	−	17.0370i	0.808600	−	0.587482i
$842$		0			0
$843$	16.2998			0.561395
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.6082	−	38.8040i	−0.433223	−	1.33332i
$848$		0			0
$849$	13.6305			0.467797
$850$		0			0
$851$	13.3658			0.458174
$852$		0			0
$853$	−10.3861	−	31.9651i	−0.355613	−	1.09447i	−0.955653	−	0.294495i	$-0.904848\pi$
$853$	−10.3861	−	31.9651i	−0.355613	−	1.09447i	0.600039	−	0.799970i	$-0.295152\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−46.0078			−1.57160			−0.785799	−	0.618482i	$-0.787748\pi$
$857$	−46.0078			−1.57160			−0.785799	+	0.618482i	$0.787748\pi$
$858$		0			0
$859$	24.5549	−	17.8402i	0.837803	−	0.608700i	−0.0839529	−	0.996470i	$-0.526755\pi$
$859$	24.5549	−	17.8402i	0.837803	−	0.608700i	0.921756	+	0.387770i	$0.126755\pi$
$860$		0			0
$861$	5.17624	+	3.76076i	0.176406	+	0.128166i
$862$		0			0
$863$	−5.92243	+	4.30289i	−0.201602	+	0.146472i	−0.684006	−	0.729477i	$-0.739764\pi$
$863$	−5.92243	+	4.30289i	−0.201602	+	0.146472i	0.482404	+	0.875949i	$0.339764\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−5.17736	+	15.9343i	−0.175832	+	0.541156i
$868$		0			0
$869$	16.2703	−	50.0748i	0.551932	−	1.69867i
$870$		0			0
$871$	−14.5519	−	44.7861i	−0.493072	−	1.51752i
$872$		0			0
$873$	−9.28975	−	6.74940i	−0.314410	−	0.228433i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−37.6546	−	27.3577i	−1.27151	−	0.923803i	−0.272244	−	0.962228i	$-0.587766\pi$
$877$	−37.6546	−	27.3577i	−1.27151	−	0.923803i	−0.999261	+	0.0384252i	$0.987766\pi$
$878$		0			0
$879$	−7.80737	−	24.0286i	−0.263336	−	0.810466i
$880$		0			0
$881$	−4.62663	+	14.2393i	−0.155875	+	0.479735i	−0.998249	−	0.0591598i	$-0.981158\pi$
$881$	−4.62663	+	14.2393i	−0.155875	+	0.479735i	0.842373	+	0.538894i	$0.181158\pi$
$882$		0			0
$883$	2.70155	−	8.31451i	0.0909144	−	0.279806i	−0.895253	−	0.445558i	$-0.853005\pi$
$883$	2.70155	−	8.31451i	0.0909144	−	0.279806i	0.986167	+	0.165752i	$0.0530053\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.3379	−	9.69054i	0.447842	−	0.325376i	−0.340901	−	0.940099i	$-0.610732\pi$
$887$	13.3379	−	9.69054i	0.447842	−	0.325376i	0.788743	+	0.614723i	$0.210732\pi$
$888$		0			0
$889$	11.2520	+	8.17505i	0.377379	+	0.274182i
$890$		0			0
$891$	4.99517	−	3.62921i	0.167345	−	0.121583i
$892$		0			0
$893$	−1.64631			−0.0550916
$894$		0			0
$895$		0			0
$896$		0			0
$897$	3.36355	+	10.3519i	0.112306	+	0.345642i
$898$		0			0
$899$	0.360104			0.0120101
$900$		0			0
$901$	−4.26292			−0.142018
$902$		0			0
$903$	−1.68586	−	5.18853i	−0.0561018	−	0.172663i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−26.0243			−0.864124			−0.432062	−	0.901844i	$-0.642214\pi$
$907$	−26.0243			−0.864124			−0.432062	+	0.901844i	$0.642214\pi$
$908$		0			0
$909$	12.0025	−	8.72029i	0.398096	−	0.289234i
$910$		0			0
$911$	41.7815	+	30.3560i	1.38428	+	1.00574i	0.996466	+	0.0840029i	$0.0267705\pi$
$911$	41.7815	+	30.3560i	1.38428	+	1.00574i	0.387816	+	0.921737i	$0.373229\pi$
$912$		0			0
$913$	−56.6359	+	41.1484i	−1.87437	+	1.36181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.83945	+	27.2050i	−0.291904	+	0.898390i
$918$		0			0
$919$	−8.53835	+	26.2784i	−0.281654	+	0.866843i	0.705727	+	0.708484i	$0.250620\pi$
$919$	−8.53835	+	26.2784i	−0.281654	+	0.866843i	−0.987382	+	0.158359i	$0.949380\pi$
$920$		0			0
$921$	2.16628	+	6.66712i	0.0713813	+	0.219689i
$922$		0			0
$923$	−9.40316	−	6.83180i	−0.309509	−	0.224871i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	15.5853	+	11.3234i	0.511890	+	0.371910i
$928$		0			0
$929$	16.5946	+	51.0728i	0.544450	+	1.67565i	0.722294	+	0.691587i	$0.243088\pi$
$929$	16.5946	+	51.0728i	0.544450	+	1.67565i	−0.177843	+	0.984059i	$0.556912\pi$
$930$		0			0
$931$	−0.456241	+	1.40417i	−0.0149527	+	0.0460197i
$932$		0			0
$933$	4.48441	−	13.8016i	0.146813	−	0.451844i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−24.5304	+	17.8224i	−0.801373	+	0.582232i	−0.911317	−	0.411706i	$-0.864933\pi$
$937$	−24.5304	+	17.8224i	−0.801373	+	0.582232i	0.109943	+	0.993938i	$0.464933\pi$
$938$		0			0
$939$	17.7334	+	12.8841i	0.578707	+	0.420455i
$940$		0			0
$941$	−38.3217	+	27.8423i	−1.24925	+	0.907635i	−0.998178	−	0.0603335i	$-0.980784\pi$
$941$	−38.3217	+	27.8423i	−1.24925	+	0.907635i	−0.251073	+	0.967968i	$0.580784\pi$
$942$		0			0
$943$	13.0177			0.423915
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.68770	+	20.5826i	0.217321	+	0.668845i	0.998981	+	0.0451402i	$0.0143734\pi$
$947$	6.68770	+	20.5826i	0.217321	+	0.668845i	−0.781660	+	0.623705i	$0.785627\pi$
$948$		0			0
$949$	−56.7833			−1.84327
$950$		0			0
$951$	33.7178			1.09337
$952$		0			0
$953$	14.1813	+	43.6456i	0.459378	+	1.41382i	0.865918	+	0.500187i	$0.166735\pi$
$953$	14.1813	+	43.6456i	0.459378	+	1.41382i	−0.406540	+	0.913633i	$0.633265\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.755333			0.0244164
$958$		0			0
$959$	−9.56815	+	6.95167i	−0.308972	+	0.224481i
$960$		0			0
$961$	18.0695	+	13.1282i	0.582886	+	0.423492i
$962$		0			0
$963$	6.98605	−	5.07566i	0.225122	−	0.163561i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	4.62587	−	14.2370i	0.148758	−	0.457830i	−0.848717	−	0.528847i	$-0.822625\pi$
$967$	4.62587	−	14.2370i	0.148758	−	0.457830i	0.997475	+	0.0710173i	$0.0226246\pi$
$968$		0			0
$969$	−0.0477422	+	0.146935i	−0.00153370	+	0.00472025i
$970$		0			0
$971$	−6.91563	−	21.2841i	−0.221933	−	0.683040i	−0.998588	−	0.0531143i	$-0.983085\pi$
$971$	−6.91563	−	21.2841i	−0.221933	−	0.683040i	0.776655	−	0.629926i	$-0.216915\pi$
$972$		0			0
$973$	−16.7951	−	12.2023i	−0.538426	−	0.391189i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.6588	−	23.7280i	−1.04485	−	0.759127i	−0.0736229	−	0.997286i	$-0.523456\pi$
$977$	−32.6588	−	23.7280i	−1.04485	−	0.759127i	−0.971226	+	0.238159i	$0.923456\pi$
$978$		0			0
$979$	−26.9647	−	82.9889i	−0.861797	−	2.65234i
$980$		0			0
$981$	−5.77531	+	17.7746i	−0.184392	+	0.567499i
$982$		0			0
$983$	7.22264	−	22.2290i	0.230367	−	0.708995i	−0.767336	−	0.641245i	$-0.778418\pi$
$983$	7.22264	−	22.2290i	0.230367	−	0.708995i	0.997702	−	0.0677498i	$-0.0215820\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.42839	+	4.67050i	−0.204618	+	0.148664i
$988$		0			0
$989$	−8.97994	−	6.52431i	−0.285546	−	0.207461i
$990$		0			0
$991$	−27.3815	+	19.8938i	−0.869803	+	0.631949i	−0.930534	−	0.366205i	$-0.880657\pi$
$991$	−27.3815	+	19.8938i	−0.869803	+	0.631949i	0.0607312	+	0.998154i	$0.480657\pi$
$992$		0			0
$993$	33.5950			1.06611
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.71351	−	5.27364i	−0.0542674	−	0.167018i	0.920249	−	0.391332i	$-0.127986\pi$
$997$	−1.71351	−	5.27364i	−0.0542674	−	0.167018i	−0.974517	+	0.224314i	$0.927986\pi$
$998$		0			0
$999$	4.36700			0.138166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.a.1201.1		8
5.2	odd	4		1500.2.o.b.49.3		16
5.3	odd	4		1500.2.o.b.49.2		16
5.4	even	2		300.2.m.b.241.2	yes	8
15.14	odd	2		900.2.n.b.541.1		8
25.2	odd	20		1500.2.o.b.949.1		16
25.6	even	5		7500.2.a.f.1.2		4
25.8	odd	20		7500.2.d.c.1249.7		8
25.11	even	5	inner	1500.2.m.a.301.1		8
25.14	even	10		300.2.m.b.61.2	✓	8
25.17	odd	20		7500.2.d.c.1249.2		8
25.19	even	10		7500.2.a.e.1.3		4
25.23	odd	20		1500.2.o.b.949.4		16
75.14	odd	10		900.2.n.b.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.2	✓	8	25.14	even	10
300.2.m.b.241.2	yes	8	5.4	even	2
900.2.n.b.361.1		8	75.14	odd	10
900.2.n.b.541.1		8	15.14	odd	2
1500.2.m.a.301.1		8	25.11	even	5	inner
1500.2.m.a.1201.1		8	1.1	even	1	trivial
1500.2.o.b.49.2		16	5.3	odd	4
1500.2.o.b.49.3		16	5.2	odd	4
1500.2.o.b.949.1		16	25.2	odd	20
1500.2.o.b.949.4		16	25.23	odd	20
7500.2.a.e.1.3		4	25.19	even	10
7500.2.a.f.1.2		4	25.6	even	5
7500.2.d.c.1249.2		8	25.17	odd	20
7500.2.d.c.1249.7		8	25.8	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} -1.50430 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} -1.50430 q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.99517 + 3.62921i) q^{11} +(-2.87714 + 2.09036i) q^{13} +(-0.153180 + 0.471439i) q^{17} +(0.0963126 - 0.296420i) q^{19} +(-0.464854 - 1.43067i) q^{21} +(-2.47611 - 1.79900i) q^{23} +(-0.809017 - 0.587785i) q^{27} +(-0.0378031 - 0.116346i) q^{29} +(-0.909629 + 2.79955i) q^{31} +(-1.90799 + 5.87218i) q^{33} +(-3.53298 + 2.56686i) q^{37} +(-2.87714 - 2.09036i) q^{39} +(-3.44096 + 2.50001i) q^{41} +3.62663 q^{43} +(-1.63227 - 5.02362i) q^{47} -4.73708 q^{49} -0.495700 q^{51} +(2.65748 + 8.17888i) q^{53} +0.311674 q^{57} +(-10.4222 + 7.57219i) q^{59} +(9.15882 + 6.65427i) q^{61} +(1.21700 - 0.884205i) q^{63} +(-4.09181 + 12.5933i) q^{67} +(0.945790 - 2.91084i) q^{69} +(1.00994 + 3.10827i) q^{71} +(12.9174 + 9.38504i) q^{73} +(-7.51424 - 5.45941i) q^{77} +(-2.63513 - 8.11010i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-3.50367 + 10.7832i) q^{83} +(0.0989699 - 0.0719058i) q^{87} +(-11.4335 - 8.30691i) q^{89} +(4.32808 - 3.14453i) q^{91} -2.94362 q^{93} +(3.54837 + 10.9208i) q^{97} -6.17438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9} + 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} - 2 q^{27} - 3 q^{29} - 3 q^{31} - 7 q^{33} + q^{37} + 10 q^{41} + 12 q^{43} + 33 q^{47} - 8 q^{49} - 8 q^{51} + 19 q^{53} - 10 q^{57} - 38 q^{59} + 46 q^{61} - 3 q^{63} + 8 q^{67} + 2 q^{69} - 25 q^{71} + 26 q^{73} - 23 q^{77} - 16 q^{79} - 2 q^{81} - 8 q^{83} - 3 q^{87} - 30 q^{89} + 25 q^{91} + 22 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9 + 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 - 2 * q^27 - 3 * q^29 - 3 * q^31 - 7 * q^33 + q^37 + 10 * q^41 + 12 * q^43 + 33 * q^47 - 8 * q^49 - 8 * q^51 + 19 * q^53 - 10 * q^57 - 38 * q^59 + 46 * q^61 - 3 * q^63 + 8 * q^67 + 2 * q^69 - 25 * q^71 + 26 * q^73 - 23 * q^77 - 16 * q^79 - 2 * q^81 - 8 * q^83 - 3 * q^87 - 30 * q^89 + 25 * q^91 + 22 * q^93 + 14 * q^97 - 2 * q^99

Introduction

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