LMFDB - Embedded newform 300.2.m.b.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(61,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, 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("300.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.m (of order $5$, degree $4$, 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:	$2.39551206064$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.2
Root			$-1.21700 + 0.720348i$ of defining polynomial
Character	$\chi$	$=$	300.61
Dual form			300.2.m.b.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(-0.962197 - 2.01846i) q^{5} +1.50430 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.962197 - 2.01846i) q^{5} +1.50430 q^{7} +(-0.809017 - 0.587785i) q^{9} +(4.99517 - 3.62921i) q^{11} +(2.87714 + 2.09036i) q^{13} +(2.21700 - 0.291365i) q^{15} +(0.153180 + 0.471439i) q^{17} +(0.0963126 + 0.296420i) q^{19} +(-0.464854 + 1.43067i) q^{21} +(2.47611 - 1.79900i) q^{23} +(-3.14835 + 3.88431i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-0.0378031 + 0.116346i) q^{29} +(-0.909629 - 2.79955i) q^{31} +(1.90799 + 5.87218i) q^{33} +(-1.44743 - 3.03637i) q^{35} +(3.53298 + 2.56686i) q^{37} +(-2.87714 + 2.09036i) q^{39} +(-3.44096 - 2.50001i) q^{41} -3.62663 q^{43} +(-0.407987 + 2.19853i) q^{45} +(1.63227 - 5.02362i) q^{47} -4.73708 q^{49} -0.495700 q^{51} +(-2.65748 + 8.17888i) q^{53} +(-12.1317 - 6.59054i) q^{55} -0.311674 q^{57} +(-10.4222 - 7.57219i) q^{59} +(9.15882 - 6.65427i) q^{61} +(-1.21700 - 0.884205i) q^{63} +(1.45094 - 7.81873i) q^{65} +(4.09181 + 12.5933i) q^{67} +(0.945790 + 2.91084i) q^{69} +(1.00994 - 3.10827i) q^{71} +(-12.9174 + 9.38504i) q^{73} +(-2.72130 - 4.19458i) q^{75} +(7.51424 - 5.45941i) q^{77} +(-2.63513 + 8.11010i) q^{79} +(0.309017 + 0.951057i) q^{81} +(3.50367 + 10.7832i) q^{83} +(0.804191 - 0.762805i) q^{85} +(-0.0989699 - 0.0719058i) q^{87} +(-11.4335 + 8.30691i) q^{89} +(4.32808 + 3.14453i) q^{91} +2.94362 q^{93} +(0.505640 - 0.479617i) q^{95} +(-3.54837 + 10.9208i) q^{97} -6.17438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9	$ 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9} + 8 q^{11} + 5 q^{15} + 3 q^{17} + 5 q^{19} + 7 q^{21} - 7 q^{23} + 5 q^{25} + 2 q^{27} - 3 q^{29} - 3 q^{31} + 7 q^{33} - 10 q^{35} - q^{37} + 10 q^{41} - 12 q^{43} + 5 q^{45} - 33 q^{47} - 8 q^{49} - 8 q^{51} - 19 q^{53} - 15 q^{55} + 10 q^{57} - 38 q^{59} + 46 q^{61} + 3 q^{63} + 25 q^{65} - 8 q^{67} + 2 q^{69} - 25 q^{71} - 26 q^{73} - 5 q^{75} + 23 q^{77} - 16 q^{79} - 2 q^{81} + 8 q^{83} - 30 q^{85} + 3 q^{87} - 30 q^{89} + 25 q^{91} - 22 q^{93} - 25 q^{95} - 14 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9 + 8 * q^11 + 5 * q^15 + 3 * q^17 + 5 * q^19 + 7 * q^21 - 7 * q^23 + 5 * q^25 + 2 * q^27 - 3 * q^29 - 3 * q^31 + 7 * q^33 - 10 * q^35 - q^37 + 10 * q^41 - 12 * q^43 + 5 * q^45 - 33 * q^47 - 8 * q^49 - 8 * q^51 - 19 * q^53 - 15 * q^55 + 10 * q^57 - 38 * q^59 + 46 * q^61 + 3 * q^63 + 25 * q^65 - 8 * q^67 + 2 * q^69 - 25 * q^71 - 26 * q^73 - 5 * q^75 + 23 * q^77 - 16 * q^79 - 2 * q^81 + 8 * q^83 - 30 * q^85 + 3 * q^87 - 30 * q^89 + 25 * q^91 - 22 * q^93 - 25 * q^95 - 14 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	−0.962197	−	2.01846i	−0.430308	−	0.902682i
$5$	−0.962197	−	2.01846i	−0.430308	−	0.902682i
$6$		0			0
$7$	1.50430			0.568572			0.284286	−	0.958740i	$-0.408244\pi$
$7$	1.50430			0.568572			0.284286	+	0.958740i	$0.408244\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	4.99517	−	3.62921i	1.50610	−	1.09425i	0.538231	−	0.842797i	$-0.319093\pi$
$11$	4.99517	−	3.62921i	1.50610	−	1.09425i	0.967870	−	0.251450i	$-0.0809074\pi$
$12$		0			0
$13$	2.87714	+	2.09036i	0.797975	+	0.579763i	0.910319	−	0.413906i	$-0.135836\pi$
$13$	2.87714	+	2.09036i	0.797975	+	0.579763i	−0.112344	+	0.993669i	$0.535836\pi$
$14$		0			0
$15$	2.21700	−	0.291365i	0.572428	−	0.0752302i
$16$		0			0
$17$	0.153180	+	0.471439i	0.0371516	+	0.114341i	0.967912	−	0.251288i	$-0.0808541\pi$
$17$	0.153180	+	0.471439i	0.0371516	+	0.114341i	−0.930761	+	0.365629i	$0.880854\pi$
$18$		0			0
$19$	0.0963126	+	0.296420i	0.0220956	+	0.0680034i	0.961496	−	0.274818i	$-0.0886175\pi$
$19$	0.0963126	+	0.296420i	0.0220956	+	0.0680034i	−0.939401	+	0.342821i	$0.888618\pi$
$20$		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	$-0.596621\pi$
$23$	2.47611	−	1.79900i	0.516305	−	0.375117i	0.815210	+	0.579165i	$0.196621\pi$
$24$		0			0
$25$	−3.14835	+	3.88431i	−0.629671	+	0.776862i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	−0.0378031	+	0.116346i	−0.00701987	+	0.0216049i	−0.954505	−	0.298195i	$-0.903616\pi$
$29$	−0.0378031	+	0.116346i	−0.00701987	+	0.0216049i	0.947485	+	0.319800i	$0.103616\pi$
$30$		0			0
$31$	−0.909629	−	2.79955i	−0.163374	−	0.502814i	0.835539	−	0.549432i	$-0.185156\pi$
$31$	−0.909629	−	2.79955i	−0.163374	−	0.502814i	−0.998913	+	0.0466176i	$0.985156\pi$
$32$		0			0
$33$	1.90799	+	5.87218i	0.332138	+	1.02222i
$34$		0			0
$35$	−1.44743	−	3.03637i	−0.244661	−	0.513240i
$36$		0			0
$37$	3.53298	+	2.56686i	0.580818	+	0.421989i	0.839019	−	0.544102i	$-0.183130\pi$
$37$	3.53298	+	2.56686i	0.580818	+	0.421989i	−0.258201	+	0.966091i	$0.583130\pi$
$38$		0			0
$39$	−2.87714	+	2.09036i	−0.460711	+	0.334726i
$40$		0			0
$41$	−3.44096	−	2.50001i	−0.537388	−	0.390436i	0.285726	−	0.958311i	$-0.407765\pi$
$41$	−3.44096	−	2.50001i	−0.537388	−	0.390436i	−0.823114	+	0.567876i	$0.807765\pi$
$42$		0			0
$43$	−3.62663			−0.553056			−0.276528	−	0.961006i	$-0.589184\pi$
$43$	−3.62663			−0.553056			−0.276528	+	0.961006i	$0.589184\pi$
$44$		0			0
$45$	−0.407987	+	2.19853i	−0.0608191	+	0.327738i
$46$		0			0
$47$	1.63227	−	5.02362i	0.238091	−	0.732770i	−0.758605	−	0.651551i	$-0.774119\pi$
$47$	1.63227	−	5.02362i	0.238091	−	0.732770i	0.996696	−	0.0812191i	$-0.0258813\pi$
$48$		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	0.584928	+	0.811086i	$0.301123\pi$
$53$	−2.65748	+	8.17888i	−0.365033	+	1.12346i	−0.949960	+	0.312370i	$0.898877\pi$
$54$		0			0
$55$	−12.1317	−	6.59054i	−1.63584	−	0.888669i
$56$		0			0
$57$	−0.311674			−0.0412823
$58$		0			0
$59$	−10.4222	−	7.57219i	−1.35686	−	0.985815i	−0.998638	−	0.0521781i	$-0.983384\pi$
$59$	−10.4222	−	7.57219i	−1.35686	−	0.985815i	−0.358220	−	0.933637i	$-0.616616\pi$
$60$		0			0
$61$	9.15882	−	6.65427i	1.17267	−	0.851992i	0.181341	−	0.983420i	$-0.441956\pi$
$61$	9.15882	−	6.65427i	1.17267	−	0.851992i	0.991326	+	0.131428i	$0.0419562\pi$
$62$		0			0
$63$	−1.21700	−	0.884205i	−0.153328	−	0.111399i
$64$		0			0
$65$	1.45094	−	7.81873i	0.179967	−	0.969794i
$66$		0			0
$67$	4.09181	+	12.5933i	0.499894	+	1.53852i	0.809188	+	0.587550i	$0.199908\pi$
$67$	4.09181	+	12.5933i	0.499894	+	1.53852i	−0.309293	+	0.950967i	$0.600092\pi$
$68$		0			0
$69$	0.945790	+	2.91084i	0.113860	+	0.350424i
$70$		0			0
$71$	1.00994	−	3.10827i	0.119858	−	0.368884i	−0.873071	−	0.487592i	$-0.837875\pi$
$71$	1.00994	−	3.10827i	0.119858	−	0.368884i	0.992929	+	0.118708i	$0.0378753\pi$
$72$		0			0
$73$	−12.9174	+	9.38504i	−1.51187	+	1.09844i	−0.546527	+	0.837441i	$0.684050\pi$
$73$	−12.9174	+	9.38504i	−1.51187	+	1.09844i	−0.965340	+	0.260994i	$0.915950\pi$
$74$		0			0
$75$	−2.72130	−	4.19458i	−0.314229	−	0.484348i
$76$		0			0
$77$	7.51424	−	5.45941i	0.856327	−	0.622158i
$78$		0			0
$79$	−2.63513	+	8.11010i	−0.296475	+	0.912457i	0.686247	+	0.727369i	$0.259257\pi$
$79$	−2.63513	+	8.11010i	−0.296475	+	0.912457i	−0.982722	+	0.185088i	$0.940743\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	3.50367	+	10.7832i	0.384578	+	1.18361i	0.936786	+	0.349903i	$0.113785\pi$
$83$	3.50367	+	10.7832i	0.384578	+	1.18361i	−0.552208	+	0.833706i	$0.686215\pi$
$84$		0			0
$85$	0.804191	−	0.762805i	0.0872268	−	0.0827378i
$86$		0			0
$87$	−0.0989699	−	0.0719058i	−0.0106107	−	0.00770911i
$88$		0			0
$89$	−11.4335	+	8.30691i	−1.21195	+	0.880531i	−0.995406	−	0.0957428i	$-0.969477\pi$
$89$	−11.4335	+	8.30691i	−1.21195	+	0.880531i	−0.216541	+	0.976274i	$0.569477\pi$
$90$		0			0
$91$	4.32808	+	3.14453i	0.453706	+	0.329637i
$92$		0			0
$93$	2.94362			0.305239
$94$		0			0
$95$	0.505640	−	0.479617i	0.0518775	−	0.0492077i
$96$		0			0
$97$	−3.54837	+	10.9208i	−0.360282	+	1.10884i	0.592601	+	0.805497i	$0.298101\pi$
$97$	−3.54837	+	10.9208i	−0.360282	+	1.10884i	−0.952883	+	0.303339i	$0.901899\pi$
$98$		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	−0.00628354	−	0.999980i	$-0.502000\pi$
$103$	5.95307	−	18.3217i	0.586574	−	1.80529i	0.592857	−	0.805308i	$-0.298000\pi$
$104$		0			0
$105$	3.33504	−	0.438301i	0.325466	−	0.0427738i
$106$		0			0
$107$	8.63523			0.834799			0.417400	−	0.908723i	$-0.362942\pi$
$107$	8.63523			0.834799			0.417400	+	0.908723i	$0.362942\pi$
$108$		0			0
$109$	15.1200	+	10.9853i	1.44823	+	1.05220i	0.986241	+	0.165315i	$0.0528641\pi$
$109$	15.1200	+	10.9853i	1.44823	+	1.05220i	0.461989	+	0.886886i	$0.347136\pi$
$110$		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	$-0.391950\pi$
$113$	−4.89971	−	3.55985i	−0.460926	−	0.334883i	−0.793894	+	0.608056i	$0.791950\pi$
$114$		0			0
$115$	−6.01371	−	3.26694i	−0.560782	−	0.304643i
$116$		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
$125$	10.8697	+	2.61735i	0.972212	+	0.234103i
$126$		0			0
$127$	7.47988	−	5.43445i	0.663732	−	0.482230i	−0.204189	−	0.978931i	$-0.565456\pi$
$127$	7.47988	−	5.43445i	0.663732	−	0.482230i	0.867921	+	0.496702i	$0.165456\pi$
$128$		0			0
$129$	1.12069	−	3.44913i	0.0986714	−	0.303679i
$130$		0			0
$131$	5.87613	+	18.0849i	0.513399	+	1.58008i	0.786175	+	0.618003i	$0.212058\pi$
$131$	5.87613	+	18.0849i	0.513399	+	1.58008i	−0.272776	+	0.962078i	$0.587942\pi$
$132$		0			0
$133$	0.144883	+	0.445904i	0.0125630	+	0.0386648i
$134$		0			0
$135$	−1.96485	−	1.06740i	−0.169108	−	0.0918674i
$136$		0			0
$137$	−6.36053	−	4.62120i	−0.543417	−	0.394816i	0.281936	−	0.959433i	$-0.409024\pi$
$137$	−6.36053	−	4.62120i	−0.543417	−	0.394816i	−0.825352	+	0.564618i	$0.809024\pi$
$138$		0			0
$139$	11.1647	−	8.11165i	0.946980	−	0.688021i	−0.00311101	−	0.999995i	$-0.500990\pi$
$139$	11.1647	−	8.11165i	0.946980	−	0.688021i	0.950091	+	0.311974i	$0.100990\pi$
$140$		0			0
$141$	4.27335	+	3.10477i	0.359881	+	0.261469i
$142$		0			0
$143$	21.9582			1.83624
$144$		0			0
$145$	0.271214	−	0.0356438i	0.0225231	−	0.00296005i
$146$		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
$155$	−4.77554	+	4.52977i	−0.383580	+	0.363840i
$156$		0			0
$157$	−4.02750			−0.321429			−0.160715	−	0.987001i	$-0.551380\pi$
$157$	−4.02750			−0.321429			−0.160715	+	0.987001i	$0.551380\pi$
$158$		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	$-0.509509\pi$
$163$	−12.6360	−	9.18062i	−0.989732	−	0.719082i	−0.959862	+	0.280472i	$0.909509\pi$
$164$		0			0
$165$	10.0169	−	9.50139i	0.779814	−	0.739682i
$166$		0			0
$167$	3.66014	+	11.2647i	0.283230	+	0.871692i	0.986924	+	0.161189i	$0.0515327\pi$
$167$	3.66014	+	11.2647i	0.283230	+	0.871692i	−0.703694	+	0.710503i	$0.748467\pi$
$168$		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	$-0.890651\pi$
$173$	−11.9982	+	8.71717i	−0.912203	+	0.662754i	0.0293681	+	0.999569i	$0.490651\pi$
$174$		0			0
$175$	−4.73607	+	5.84317i	−0.358013	+	0.441702i
$176$		0			0
$177$	10.4222	−	7.57219i	0.783382	−	0.569161i
$178$		0			0
$179$	−0.295895	+	0.910670i	−0.0221162	+	0.0680667i	−0.961505	−	0.274786i	$-0.911393\pi$
$179$	−0.295895	+	0.910670i	−0.0221162	+	0.0680667i	0.939389	+	0.342852i	$0.111393\pi$
$180$		0			0
$181$	1.27971	+	3.93855i	0.0951202	+	0.292750i	0.987285	−	0.158960i	$-0.0508141\pi$
$181$	1.27971	+	3.93855i	0.0951202	+	0.292750i	−0.892165	+	0.451710i	$0.850814\pi$
$182$		0			0
$183$	3.49836	+	10.7668i	0.258606	+	0.795908i
$184$		0			0
$185$	1.78168	−	9.60099i	0.130992	−	0.705879i
$186$		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	0.968720	−	0.248156i	$-0.0798244\pi$
$191$	14.2634	+	10.3629i	1.03206	+	0.749836i	0.0633410	+	0.997992i	$0.479824\pi$
$192$		0			0
$193$	5.25392			0.378185			0.189093	−	0.981959i	$-0.439445\pi$
$193$	5.25392			0.378185			0.189093	+	0.981959i	$0.439445\pi$
$194$		0			0
$195$	6.98769	+	3.79605i	0.500399	+	0.271841i
$196$		0			0
$197$	−0.653870	+	2.01240i	−0.0465863	+	0.143378i	−0.971644	−	0.236449i	$-0.924016\pi$
$197$	−0.653870	+	2.01240i	−0.0465863	+	0.143378i	0.925058	+	0.379827i	$0.124016\pi$
$198$		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
$205$	−1.73528	+	9.35095i	−0.121197	+	0.653098i
$206$		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	0.121950	−	0.992536i	$-0.461085\pi$
$211$	16.0306	−	11.6469i	1.10359	−	0.801807i	0.981643	+	0.190729i	$0.0610853\pi$
$212$		0			0
$213$	2.64405	+	1.92102i	0.181168	+	0.131626i
$214$		0			0
$215$	3.48953	+	7.32021i	0.237984	+	0.499234i
$216$		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	$-0.770732\pi$
$223$	−5.32506	+	3.86888i	−0.356593	+	0.259080i	0.395037	+	0.918665i	$0.370732\pi$
$224$		0			0
$225$	4.83021	−	1.29192i	0.322014	−	0.0861278i
$226$		0			0
$227$	−9.53193	+	6.92535i	−0.632656	+	0.459652i	−0.857319	−	0.514785i	$-0.827872\pi$
$227$	−9.53193	+	6.92535i	−0.632656	+	0.459652i	0.224663	+	0.974436i	$0.427872\pi$
$228$		0			0
$229$	3.67417	−	11.3079i	0.242796	−	0.747250i	−0.753195	−	0.657798i	$-0.771488\pi$
$229$	3.67417	−	11.3079i	0.242796	−	0.747250i	0.995991	−	0.0894526i	$-0.0285117\pi$
$230$		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	$-0.152898\pi$
$233$	−1.56054	−	4.80285i	−0.102234	−	0.314645i	−0.989071	+	0.147437i	$0.952898\pi$
$234$		0			0
$235$	−11.7105	+	1.53903i	−0.763911	+	0.100396i
$236$		0			0
$237$	−6.89886	−	5.01232i	−0.448129	−	0.325585i
$238$		0			0
$239$	−2.16762	+	1.57487i	−0.140212	+	0.101870i	−0.655680	−	0.755039i	$-0.727618\pi$
$239$	−2.16762	+	1.57487i	−0.140212	+	0.101870i	0.515468	+	0.856909i	$0.327618\pi$
$240$		0			0
$241$	−10.2390	−	7.43906i	−0.659551	−	0.479192i	0.206960	−	0.978349i	$-0.433643\pi$
$241$	−10.2390	−	7.43906i	−0.659551	−	0.479192i	−0.866511	+	0.499157i	$0.833643\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	4.55801	+	9.56161i	0.291200	+	0.610869i
$246$		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
$255$	0.476961	+	1.00055i	0.0298685	+	0.0626569i
$256$		0			0
$257$	−27.7764			−1.73264			−0.866322	−	0.499486i	$-0.833522\pi$
$257$	−27.7764			−1.73264			−0.866322	+	0.499486i	$0.833522\pi$
$258$		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	$-0.417592\pi$
$263$	−9.47479	−	6.88384i	−0.584241	−	0.424476i	−0.840250	+	0.542198i	$0.817592\pi$
$264$		0			0
$265$	19.0658	−	2.50568i	1.17120	−	0.153923i
$266$		0			0
$267$	−4.36720	−	13.4409i	−0.267268	−	0.822568i
$268$		0			0
$269$	1.29979	+	4.00034i	0.0792496	+	0.243905i	0.982830	−	0.184513i	$-0.0590709\pi$
$269$	1.29979	+	4.00034i	0.0792496	+	0.243905i	−0.903580	+	0.428419i	$0.859071\pi$
$270$		0			0
$271$	−3.88308	+	11.9509i	−0.235880	+	0.725965i	0.761123	+	0.648608i	$0.224648\pi$
$271$	−3.88308	+	11.9509i	−0.235880	+	0.725965i	−0.997003	+	0.0773578i	$0.975352\pi$
$272$		0			0
$273$	−4.32808	+	3.14453i	−0.261947	+	0.190316i
$274$		0			0
$275$	−1.62962	+	30.8288i	−0.0982695	+	1.85905i
$276$		0			0
$277$	−25.7795	+	18.7299i	−1.54894	+	1.12537i	−0.604543	+	0.796573i	$0.706644\pi$
$277$	−25.7795	+	18.7299i	−1.54894	+	1.12537i	−0.944400	+	0.328800i	$0.893356\pi$
$278$		0			0
$279$	−0.909629	+	2.79955i	−0.0544581	+	0.167605i
$280$		0			0
$281$	5.03691	+	15.5020i	0.300477	+	0.924773i	0.981326	+	0.192350i	$0.0616108\pi$
$281$	5.03691	+	15.5020i	0.300477	+	0.924773i	−0.680849	+	0.732423i	$0.738389\pi$
$282$		0			0
$283$	−4.21205	−	12.9634i	−0.250381	−	0.770592i	−0.994705	−	0.102774i	$-0.967228\pi$
$283$	−4.21205	−	12.9634i	−0.250381	−	0.770592i	0.744324	−	0.667819i	$-0.232772\pi$
$284$		0			0
$285$	0.299892	+	0.629102i	0.0177641	+	0.0372648i
$286$		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	$-0.235768\pi$
$293$	25.2652			1.47601			0.738004	+	0.674796i	$0.235768\pi$
$294$		0			0
$295$	−5.25592	+	28.3228i	−0.306012	+	1.64902i
$296$		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
$305$	−22.2440	−	12.0840i	−1.27369	−	0.691927i
$306$		0			0
$307$	−7.01023			−0.400095			−0.200047	−	0.979786i	$-0.564110\pi$
$307$	−7.01023			−0.400095			−0.200047	+	0.979786i	$0.564110\pi$
$308$		0			0
$309$	15.5853	+	11.3234i	0.886619	+	0.644167i
$310$		0			0
$311$	−11.7403	+	8.52985i	−0.665733	+	0.483683i	−0.868594	−	0.495524i	$-0.834976\pi$
$311$	−11.7403	+	8.52985i	−0.665733	+	0.483683i	0.202861	+	0.979208i	$0.434976\pi$
$312$		0			0
$313$	−17.7334	−	12.8841i	−1.00235	−	0.728250i	−0.0397589	−	0.999209i	$-0.512659\pi$
$313$	−17.7334	−	12.8841i	−1.00235	−	0.728250i	−0.962591	+	0.270960i	$0.912659\pi$
$314$		0			0
$315$	−0.613734	+	3.30725i	−0.0345800	+	0.186343i
$316$		0			0
$317$	−10.4194	−	32.0675i	−0.585210	−	1.80109i	−0.598426	−	0.801178i	$-0.704207\pi$
$317$	−10.4194	−	32.0675i	−0.585210	−	1.80109i	0.0132156	−	0.999913i	$-0.495793\pi$
$318$		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
$325$	−17.1779	+	4.59450i	−0.952858	+	0.254857i
$326$		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	0.650645	+	0.759382i	$0.274498\pi$
$331$	10.3814	+	31.9508i	0.570616	+	1.75617i	−0.0800299	+	0.996792i	$0.525502\pi$
$332$		0			0
$333$	−1.34948	−	4.15326i	−0.0739509	−	0.227597i
$334$		0			0
$335$	21.4819	−	20.3764i	1.17368	−	1.11328i
$336$		0			0
$337$	−2.49603	−	1.81347i	−0.135967	−	0.0987859i	0.517723	−	0.855548i	$-0.326780\pi$
$337$	−2.49603	−	1.81347i	−0.135967	−	0.0987859i	−0.653690	+	0.756763i	$0.726780\pi$
$338$		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
$345$	4.96538	−	4.70984i	0.267327	−	0.253569i
$346$		0			0
$347$	3.88556	−	11.9585i	0.208588	−	0.641967i	−0.790959	−	0.611869i	$-0.790418\pi$
$347$	3.88556	−	11.9585i	0.208588	−	0.641967i	0.999547	−	0.0300984i	$-0.00958206\pi$
$348$		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	$-0.997150\pi$
$353$	−3.48923	+	10.7388i	−0.185713	+	0.571566i	0.814247	+	0.580519i	$0.197150\pi$
$354$		0			0
$355$	−7.24568	+	0.952250i	−0.384561	+	0.0505402i
$356$		0			0
$357$	−0.745682			−0.0394657
$358$		0			0
$359$	−15.7007	−	11.4072i	−0.828652	−	0.602051i	0.0905254	−	0.995894i	$-0.471145\pi$
$359$	−15.7007	−	11.4072i	−0.828652	−	0.602051i	−0.919178	+	0.393843i	$0.871145\pi$
$360$		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
$365$	31.3724	+	17.0430i	1.64211	+	0.892071i
$366$		0			0
$367$	5.42951	+	16.7103i	0.283418	+	0.872271i	0.986868	+	0.161526i	$0.0516417\pi$
$367$	5.42951	+	16.7103i	0.283418	+	0.872271i	−0.703450	+	0.710744i	$0.748358\pi$
$368$		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	$-0.439409\pi$
$373$	22.8195	−	16.5793i	1.18155	−	0.858446i	0.992346	+	0.123492i	$0.0394093\pi$
$374$		0			0
$375$	−5.84816	+	9.52885i	−0.301998	+	0.492068i
$376$		0			0
$377$	−0.351971	+	0.255722i	−0.0181274	+	0.0131703i
$378$		0			0
$379$	1.12118	−	3.45064i	0.0575912	−	0.177247i	−0.918123	−	0.396296i	$-0.870295\pi$
$379$	1.12118	−	3.45064i	0.0575912	−	0.177247i	0.975714	+	0.219049i	$0.0702954\pi$
$380$		0			0
$381$	2.85706	+	8.79313i	0.146372	+	0.450486i
$382$		0			0
$383$	−4.27519	−	13.1577i	−0.218452	−	0.672326i	−0.998890	−	0.0470934i	$-0.985004\pi$
$383$	−4.27519	−	13.1577i	−0.218452	−	0.672326i	0.780439	−	0.625232i	$-0.214996\pi$
$384$		0			0
$385$	−18.2498	−	9.91415i	−0.930095	−	0.505272i
$386$		0			0
$387$	2.93401	+	2.13168i	0.149144	+	0.108359i
$388$		0			0
$389$	16.9096	−	12.2855i	0.857348	−	0.622900i	−0.0698138	−	0.997560i	$-0.522241\pi$
$389$	16.9096	−	12.2855i	0.857348	−	0.622900i	0.927162	+	0.374660i	$0.122241\pi$
$390$		0			0
$391$	1.22741	+	0.891765i	0.0620727	+	0.0450985i
$392$		0			0
$393$	−19.0155			−0.959207
$394$		0			0
$395$	18.9054	−	2.48461i	0.951235	−	0.125014i
$396$		0			0
$397$	−4.77499	+	14.6959i	−0.239650	+	0.737566i	0.756821	+	0.653622i	$0.226752\pi$
$397$	−4.77499	+	14.6959i	−0.239650	+	0.737566i	−0.996471	+	0.0839436i	$0.973248\pi$
$398$		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
$405$	1.62233	−	1.53884i	0.0806144	−	0.0764657i
$406$		0			0
$407$	26.9635			1.33653
$408$		0			0
$409$	1.88712	+	1.37107i	0.0933119	+	0.0677951i	0.633463	−	0.773773i	$-0.281633\pi$
$409$	1.88712	+	1.37107i	0.0933119	+	0.0677951i	−0.540151	+	0.841568i	$0.681633\pi$
$410$		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
$415$	18.3942	−	17.4476i	0.902936	−	0.856468i
$416$		0			0
$417$	4.26455	+	13.1249i	0.208836	+	0.642730i
$418$		0			0
$419$	−1.55768	−	4.79405i	−0.0760977	−	0.234205i	0.905771	−	0.423768i	$-0.139293\pi$
$419$	−1.55768	−	4.79405i	−0.0760977	−	0.234205i	−0.981869	+	0.189563i	$0.939293\pi$
$420$		0			0
$421$	3.99823	−	12.3053i	0.194862	−	0.599724i	−0.805116	−	0.593117i	$-0.797897\pi$
$421$	3.99823	−	12.3053i	0.194862	−	0.599724i	0.999978	−	0.00660640i	$-0.00210290\pi$
$422$		0			0
$423$	−4.27335	+	3.10477i	−0.207777	+	0.150959i
$424$		0			0
$425$	−2.31348	−	0.889259i	−0.112220	−	0.0431354i
$426$		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	0.962028	−	0.272950i	$-0.0879994\pi$
$431$	0.483616	+	1.48842i	0.0232950	+	0.0716945i	−0.938733	+	0.344645i	$0.887999\pi$
$432$		0			0
$433$	7.99517	+	24.6066i	0.384224	+	1.18252i	0.937042	+	0.349217i	$0.113552\pi$
$433$	7.99517	+	24.6066i	0.384224	+	1.18252i	−0.552818	+	0.833302i	$0.686448\pi$
$434$		0			0
$435$	−0.0499105	+	0.268954i	−0.00239302	+	0.0128954i
$436$		0			0
$437$	0.771740	+	0.560702i	0.0369173	+	0.0268220i
$438$		0			0
$439$	−13.2446	+	9.62279i	−0.632132	+	0.459271i	−0.857138	−	0.515087i	$-0.827760\pi$
$439$	−13.2446	+	9.62279i	−0.632132	+	0.459271i	0.225006	+	0.974357i	$0.427760\pi$
$440$		0			0
$441$	3.83238	+	2.78439i	0.182494	+	0.132590i
$442$		0			0
$443$	28.1180			1.33593			0.667963	−	0.744194i	$-0.267166\pi$
$443$	28.1180			1.33593			0.667963	+	0.744194i	$0.267166\pi$
$444$		0			0
$445$	27.7684	+	15.0851i	1.31635	+	0.715104i
$446$		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
$455$	2.18265	−	11.7617i	0.102324	−	0.551398i
$456$		0			0
$457$	−0.321574			−0.0150426			−0.00752129	−	0.999972i	$-0.502394\pi$
$457$	−0.321574			−0.0150426			−0.00752129	+	0.999972i	$0.502394\pi$
$458$		0			0
$459$	0.401030	+	0.291365i	0.0187185	+	0.0135998i
$460$		0			0
$461$	6.21780	−	4.51749i	0.289592	−	0.210401i	−0.433499	−	0.901154i	$-0.642721\pi$
$461$	6.21780	−	4.51749i	0.289592	−	0.210401i	0.723090	+	0.690754i	$0.242721\pi$
$462$		0			0
$463$	−15.4555	−	11.2291i	−0.718279	−	0.521860i	0.167555	−	0.985863i	$-0.446413\pi$
$463$	−15.4555	−	11.2291i	−0.718279	−	0.521860i	−0.885834	+	0.464002i	$0.846413\pi$
$464$		0			0
$465$	−2.83234	−	5.94158i	−0.131347	−	0.275534i
$466$		0			0
$467$	−1.98372	−	6.10525i	−0.0917955	−	0.282517i	0.894610	−	0.446848i	$-0.147454\pi$
$467$	−1.98372	−	6.10525i	−0.0917955	−	0.282517i	−0.986405	+	0.164331i	$0.947454\pi$
$468$		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
$475$	−1.45461	−	0.559126i	−0.0667422	−	0.0256545i
$476$		0			0
$477$	6.95737	−	5.05483i	0.318556	−	0.231445i
$478$		0			0
$479$	10.3709	−	31.9183i	0.473858	−	1.45839i	−0.373633	−	0.927577i	$-0.621888\pi$
$479$	10.3709	−	31.9183i	0.473858	−	1.45839i	0.847491	−	0.530810i	$-0.178112\pi$
$480$		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
$485$	25.4573	−	3.34568i	1.15596	−	0.151920i
$486$		0			0
$487$	9.63578	+	7.00080i	0.436639	+	0.317237i	0.784298	−	0.620384i	$-0.213023\pi$
$487$	9.63578	+	7.00080i	0.436639	+	0.317237i	−0.347659	+	0.937621i	$0.613023\pi$
$488$		0			0
$489$	12.6360	−	9.18062i	0.571422	−	0.415162i
$490$		0			0
$491$	−12.6312	−	9.17712i	−0.570039	−	0.414158i	0.265080	−	0.964226i	$-0.414602\pi$
$491$	−12.6312	−	9.17712i	−0.570039	−	0.414158i	−0.835119	+	0.550069i	$0.814602\pi$
$492$		0			0
$493$	−0.0606408			−0.00273112
$494$		0			0
$495$	5.94096	+	12.4627i	0.267026	+	0.560158i
$496$		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	−0.472732	−	0.881206i	$-0.656732\pi$
$503$	9.59178	−	29.5204i	0.427676	−	1.31625i	0.900408	−	0.435046i	$-0.143268\pi$
$504$		0			0
$505$	14.2750	+	29.9456i	0.635230	+	1.33256i
$506$		0			0
$507$	0.352437			0.0156523
$508$		0			0
$509$	10.7945	+	7.84269i	0.478460	+	0.347621i	0.800729	−	0.599027i	$-0.204446\pi$
$509$	10.7945	+	7.84269i	0.478460	+	0.347621i	−0.322269	+	0.946648i	$0.604446\pi$
$510$		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
$515$	−42.7096	+	5.61302i	−1.88201	+	0.247339i
$516$		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	−0.594649	−	0.803985i	$-0.702709\pi$
$521$	8.19439	−	25.2197i	0.359003	−	1.10490i	0.953652	−	0.300912i	$-0.0972910\pi$
$522$		0			0
$523$	14.0888	−	10.2361i	0.616060	−	0.447594i	−0.235483	−	0.971878i	$-0.575667\pi$
$523$	14.0888	−	10.2361i	0.616060	−	0.447594i	0.851543	+	0.524285i	$0.175667\pi$
$524$		0			0
$525$	−4.09366	−	6.30991i	−0.178662	−	0.275387i
$526$		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
$535$	−8.30879	−	17.4299i	−0.359220	−	0.753559i
$536$		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	0.488638	−	0.872487i	$-0.337494\pi$
$541$	−4.42275	−	3.21332i	−0.190149	−	0.138151i	−0.678787	+	0.734335i	$0.737494\pi$
$542$		0			0
$543$	−4.14123			−0.177717
$544$		0			0
$545$	7.62499	−	41.0890i	0.326619	−	1.76006i
$546$		0			0
$547$	6.68894	−	20.5864i	0.285998	−	0.880212i	−0.700099	−	0.714046i	$-0.746861\pi$
$547$	6.68894	−	20.5864i	0.285998	−	0.880212i	0.986098	−	0.166167i	$-0.0531391\pi$
$548$		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
$555$	8.58052	+	4.66135i	0.364223	+	0.197863i
$556$		0			0
$557$	−2.58830			−0.109670			−0.0548349	−	0.998495i	$-0.517463\pi$
$557$	−2.58830			−0.109670			−0.0548349	+	0.998495i	$0.517463\pi$
$558$		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	$-0.437694\pi$
$563$	−16.0945	−	11.6933i	−0.678301	−	0.492815i	−0.872794	+	0.488089i	$0.837694\pi$
$564$		0			0
$565$	−2.47092	+	13.3151i	−0.103953	+	0.560172i
$566$		0			0
$567$	0.464854	+	1.43067i	0.0195220	+	0.0600827i
$568$		0			0
$569$	10.0215	+	30.8431i	0.420124	+	1.29301i	0.907587	+	0.419865i	$0.137923\pi$
$569$	10.0215	+	30.8431i	0.420124	+	1.29301i	−0.487463	+	0.873144i	$0.662077\pi$
$570$		0			0
$571$	4.23915	−	13.0468i	0.177403	−	0.545990i	−0.822332	−	0.569008i	$-0.807327\pi$
$571$	4.23915	−	13.0468i	0.177403	−	0.545990i	0.999735	+	0.0230176i	$0.00732739\pi$
$572$		0			0
$573$	−14.2634	+	10.3629i	−0.595861	+	0.432918i
$574$		0			0
$575$	−0.807801	+	15.2819i	−0.0336876	+	0.637298i
$576$		0			0
$577$	−19.9368	+	14.4849i	−0.829979	+	0.603015i	−0.919553	−	0.392965i	$-0.871449\pi$
$577$	−19.9368	+	14.4849i	−0.829979	+	0.603015i	0.0895741	+	0.995980i	$0.471449\pi$
$578$		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
$585$	−5.76957	+	5.47265i	−0.238542	+	0.226266i
$586$		0			0
$587$	−6.73236	−	4.89134i	−0.277874	−	0.201887i	0.440115	−	0.897941i	$-0.354938\pi$
$587$	−6.73236	−	4.89134i	−0.277874	−	0.201887i	−0.717990	+	0.696054i	$0.754938\pi$
$588$		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	$-0.352346\pi$
$593$	21.7904			0.894826			0.447413	+	0.894328i	$0.352346\pi$
$594$		0			0
$595$	1.20974	−	1.14749i	0.0495947	−	0.0470424i
$596$		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
$605$	−60.1316	+	7.90268i	−2.44470	+	0.321290i
$606$		0			0
$607$	32.9820			1.33870			0.669349	−	0.742948i	$-0.266573\pi$
$607$	32.9820			1.33870			0.669349	+	0.742948i	$0.266573\pi$
$608$		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	$-0.176116\pi$
$613$	15.2007	+	11.0440i	0.613951	+	0.446062i	−0.236852	+	0.971546i	$0.576116\pi$
$614$		0			0
$615$	−8.35705	−	4.53995i	−0.336989	−	0.183068i
$616$		0			0
$617$	12.1530	+	37.4030i	0.489260	+	1.50579i	0.825715	+	0.564087i	$0.190772\pi$
$617$	12.1530	+	37.4030i	0.489260	+	1.50579i	−0.336456	+	0.941699i	$0.609228\pi$
$618$		0			0
$619$	−4.95554	−	15.2516i	−0.199180	−	0.613013i	−0.999902	−	0.0139774i	$-0.995551\pi$
$619$	−4.95554	−	15.2516i	−0.199180	−	0.613013i	0.800722	−	0.599036i	$-0.204449\pi$
$620$		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
$625$	−5.17573	−	24.4584i	−0.207029	−	0.978335i
$626$		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	0.976346	−	0.216213i	$-0.0693705\pi$
$631$	1.49158	+	4.59061i	0.0593788	+	0.182749i	−0.916967	+	0.398962i	$0.869371\pi$
$632$		0			0
$633$	6.12315	+	18.8451i	0.243373	+	0.749026i
$634$		0			0
$635$	−18.1663	−	9.86883i	−0.720909	−	0.391632i
$636$		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	0.990816	−	0.135220i	$-0.0431742\pi$
$641$	29.5813	+	21.4921i	1.16839	+	0.848887i	0.177577	+	0.984107i	$0.443174\pi$
$642$		0			0
$643$	−18.3769			−0.724714			−0.362357	−	0.932039i	$-0.618028\pi$
$643$	−18.3769			−0.724714			−0.362357	+	0.932039i	$0.618028\pi$
$644$		0			0
$645$	−8.04026	+	1.05668i	−0.316585	+	0.0416066i
$646$		0			0
$647$	−12.7110	+	39.1206i	−0.499723	+	1.53799i	0.309743	+	0.950820i	$0.399757\pi$
$647$	−12.7110	+	39.1206i	−0.499723	+	1.53799i	−0.809465	+	0.587167i	$0.800243\pi$
$648$		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	0.726236	+	0.687446i	$0.241268\pi$
$653$	−6.78128	+	20.8706i	−0.265372	+	0.816731i	−0.991608	+	0.129285i	$0.958732\pi$
$654$		0			0
$655$	30.8496	−	29.2619i	1.20539	−	1.14336i
$656$		0			0
$657$	15.9668			0.622924
$658$		0			0
$659$	−17.1550	−	12.4638i	−0.668264	−	0.485522i	0.201179	−	0.979554i	$-0.435523\pi$
$659$	−17.1550	−	12.4638i	−0.668264	−	0.485522i	−0.869444	+	0.494032i	$0.835523\pi$
$660$		0			0
$661$	−14.5172	+	10.5473i	−0.564652	+	0.410244i	−0.833159	−	0.553034i	$-0.813470\pi$
$661$	−14.5172	+	10.5473i	−0.564652	+	0.410244i	0.268507	+	0.963278i	$0.413470\pi$
$662$		0			0
$663$	−1.42620	−	1.03619i	−0.0553890	−	0.0402425i
$664$		0			0
$665$	0.760633	−	0.721488i	0.0294961	−	0.0279781i
$666$		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	$-0.929915\pi$
$673$	−27.7504	+	20.1619i	−1.06970	+	0.777183i	−0.0938421	+	0.995587i	$0.529915\pi$
$674$		0			0
$675$	−0.263932	+	4.99303i	−0.0101587	+	0.192182i
$676$		0			0
$677$	3.35495	−	2.43752i	0.128941	−	0.0936814i	−0.521445	−	0.853285i	$-0.674607\pi$
$677$	3.35495	−	2.43752i	0.128941	−	0.0936814i	0.650387	+	0.759603i	$0.274607\pi$
$678$		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	$-0.0870956\pi$
$683$	0.654621	+	2.01472i	0.0250484	+	0.0770910i	−0.937751	+	0.347309i	$0.887096\pi$
$684$		0			0
$685$	−3.20761	+	17.2850i	−0.122557	+	0.660425i
$686$		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	0.647264	−	0.762266i	$-0.275913\pi$
$691$	3.21546	+	2.33617i	0.122322	+	0.0888721i	−0.524942	+	0.851138i	$0.675913\pi$
$692$		0			0
$693$	−9.28811			−0.352826
$694$		0			0
$695$	−27.1157	−	14.7305i	−1.02856	−	0.558761i
$696$		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
$705$	2.15505	−	11.6130i	0.0811637	−	0.437370i
$706$		0			0
$707$	−22.3176			−0.839338
$708$		0			0
$709$	−24.1421	−	17.5403i	−0.906676	−	0.658739i	0.0334959	−	0.999439i	$-0.489336\pi$
$709$	−24.1421	−	17.5403i	−0.906676	−	0.658739i	−0.940172	+	0.340700i	$0.889336\pi$
$710$		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
$715$	−21.1281	−	44.3217i	−0.790146	−	1.65754i
$716$		0			0
$717$	−0.827957	−	2.54819i	−0.0309206	−	0.0951639i
$718$		0			0
$719$	2.29734	+	7.07047i	0.0856762	+	0.263684i	0.984712	−	0.174191i	$-0.0557311\pi$
$719$	2.29734	+	7.07047i	0.0856762	+	0.263684i	−0.899036	+	0.437875i	$0.855731\pi$
$720$		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
$725$	−0.332907	−	0.513138i	−0.0123638	−	0.0190575i
$726$		0			0
$727$	12.8791	−	9.35722i	0.477660	−	0.347040i	−0.322759	−	0.946481i	$-0.604610\pi$
$727$	12.8791	−	9.35722i	0.477660	−	0.347040i	0.800419	+	0.599441i	$0.204610\pi$
$728$		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	0.959197	+	0.282738i	$0.0912428\pi$
$733$	9.45910	+	29.1121i	0.349380	+	1.07528i	−0.609817	+	0.792542i	$0.708757\pi$
$734$		0			0
$735$	−10.5021	+	1.38022i	−0.387377	+	0.0509103i
$736$		0			0
$737$	66.1430	+	48.0557i	2.43641	+	1.77015i
$738$		0			0
$739$	−20.9842	+	15.2459i	−0.771917	+	0.560830i	−0.902542	−	0.430602i	$-0.858301\pi$
$739$	−20.9842	+	15.2459i	−0.771917	+	0.560830i	0.130626	+	0.991432i	$0.458301\pi$
$740$		0			0
$741$	−0.896731	−	0.651513i	−0.0329422	−	0.0239339i
$742$		0			0
$743$	17.2136			0.631504			0.315752	−	0.948842i	$-0.397743\pi$
$743$	17.2136			0.631504			0.315752	+	0.948842i	$0.397743\pi$
$744$		0			0
$745$	−4.92807	−	10.3379i	−0.180550	−	0.378752i
$746$		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
$755$	12.4581	+	26.1341i	0.453397	+	0.951118i
$756$		0			0
$757$	−16.9118			−0.614669			−0.307335	−	0.951601i	$-0.599437\pi$
$757$	−16.9118			−0.614669			−0.307335	+	0.951601i	$0.599437\pi$
$758$		0			0
$759$	15.2884	+	11.1077i	0.554935	+	0.403184i
$760$		0			0
$761$	−0.422588	+	0.307028i	−0.0153188	+	0.0111297i	−0.595418	−	0.803416i	$-0.703014\pi$
$761$	−0.422588	+	0.307028i	−0.0153188	+	0.0111297i	0.580100	+	0.814546i	$0.303014\pi$
$762$		0			0
$763$	22.7450	+	16.5252i	0.823423	+	0.598252i
$764$		0			0
$765$	−1.09897	+	0.144430i	−0.0397333	+	0.00522188i
$766$		0			0
$767$	−14.1576	−	43.5725i	−0.511200	−	1.57331i
$768$		0			0
$769$	−11.7671	−	36.2154i	−0.424333	−	1.30596i	−0.903632	−	0.428310i	$-0.859109\pi$
$769$	−11.7671	−	36.2154i	−0.424333	−	1.30596i	0.479299	−	0.877651i	$-0.340891\pi$
$770$		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	$-0.566200\pi$
$773$	18.3577	−	13.3376i	0.660280	−	0.479721i	0.866757	+	0.498730i	$0.166200\pi$
$774$		0			0
$775$	13.7382	+	5.28070i	0.493489	+	0.189688i
$776$		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
$785$	3.87525	+	8.12934i	0.138314	+	0.290149i
$786$		0			0
$787$	−1.84384	−	1.33963i	−0.0657257	−	0.0477525i	0.554437	−	0.832226i	$-0.312934\pi$
$787$	−1.84384	−	1.33963i	−0.0657257	−	0.0477525i	−0.620163	+	0.784473i	$0.712934\pi$
$788$		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
$795$	−3.50860	+	18.9069i	−0.124437	+	0.670559i
$796$		0			0
$797$	6.06936	−	18.6796i	0.214988	−	0.661665i	−0.784167	−	0.620550i	$-0.786909\pi$
$797$	6.06936	−	18.6796i	0.214988	−	0.661665i	0.999154	−	0.0411143i	$-0.0130908\pi$
$798$		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
$805$	−9.04643	−	4.91445i	−0.318845	−	0.173212i
$806$		0			0
$807$	−4.20621			−0.148066
$808$		0			0
$809$	−9.05703	−	6.58032i	−0.318428	−	0.231352i	0.417076	−	0.908871i	$-0.363055\pi$
$809$	−9.05703	−	6.58032i	−0.318428	−	0.231352i	−0.735504	+	0.677520i	$0.763055\pi$
$810$		0			0
$811$	15.6132	−	11.3436i	0.548253	−	0.398329i	−0.278888	−	0.960324i	$-0.589966\pi$
$811$	15.6132	−	11.3436i	0.548253	−	0.398329i	0.827141	+	0.561995i	$0.189966\pi$
$812$		0			0
$813$	−10.1660	−	7.38606i	−0.356539	−	0.259040i
$814$		0			0
$815$	−6.37235	+	34.3389i	−0.223214	+	1.20284i
$816$		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	0.256818	+	0.966460i	$0.417326\pi$
$821$	−14.8716	+	45.7701i	−0.519023	+	1.59739i	−0.775841	+	0.630928i	$0.782674\pi$
$822$		0			0
$823$	−28.2356	+	20.5144i	−0.984232	+	0.715087i	−0.958650	−	0.284586i	$-0.908144\pi$
$823$	−28.2356	+	20.5144i	−0.984232	+	0.715087i	−0.0255817	+	0.999673i	$0.508144\pi$
$824$		0			0
$825$	−28.8164	−	11.0765i	−1.00326	−	0.385634i
$826$		0			0
$827$	−18.7401	+	13.6155i	−0.651656	+	0.473456i	−0.863835	−	0.503775i	$-0.831944\pi$
$827$	−18.7401	+	13.6155i	−0.651656	+	0.473456i	0.212179	+	0.977231i	$0.431944\pi$
$828$		0			0
$829$	6.70966	−	20.6502i	0.233036	−	0.717211i	−0.764340	−	0.644814i	$-0.776935\pi$
$829$	6.70966	−	20.6502i	0.233036	−	0.717211i	0.997376	−	0.0723976i	$-0.0230651\pi$
$830$		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
$835$	19.2156	−	18.2267i	0.664985	−	0.630762i
$836$		0			0
$837$	−2.38144	−	1.73022i	−0.0823146	−	0.0598051i
$838$		0			0
$839$	−8.40486	+	6.10649i	−0.290168	+	0.210819i	−0.723340	−	0.690492i	$-0.757394\pi$
$839$	−8.40486	+	6.10649i	−0.290168	+	0.210819i	0.433172	+	0.901311i	$0.357394\pi$
$840$		0			0
$841$	23.4494	+	17.0370i	0.808600	+	0.587482i
$842$		0			0
$843$	−16.2998			−0.561395
$844$		0			0
$845$	−0.571770	+	0.542345i	−0.0196695	+	0.0186572i
$846$		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	−0.600039	−	0.799970i	$-0.704848\pi$
$853$	10.3861	−	31.9651i	0.355613	−	1.09447i	0.955653	−	0.294495i	$-0.0951515\pi$
$854$		0			0
$855$	−0.690983	+	0.0908111i	−0.0236311	+	0.00310567i
$856$		0			0
$857$	46.0078			1.57160			0.785799	−	0.618482i	$-0.212252\pi$
$857$	46.0078			1.57160			0.785799	+	0.618482i	$0.212252\pi$
$858$		0			0
$859$	24.5549	+	17.8402i	0.837803	+	0.608700i	0.921756	−	0.387770i	$-0.126755\pi$
$859$	24.5549	+	17.8402i	0.837803	+	0.608700i	−0.0839529	+	0.996470i	$0.526755\pi$
$860$		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	$-0.260236\pi$
$863$	5.92243	+	4.30289i	0.201602	+	0.146472i	−0.482404	+	0.875949i	$0.660236\pi$
$864$		0			0
$865$	29.1398	+	15.8302i	0.990784	+	0.538241i
$866$		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
$875$	16.3512	+	3.93728i	0.552772	+	0.133104i
$876$		0			0
$877$	37.6546	−	27.3577i	1.27151	−	0.923803i	0.272244	−	0.962228i	$-0.412234\pi$
$877$	37.6546	−	27.3577i	1.27151	−	0.923803i	0.999261	+	0.0384252i	$0.0122341\pi$
$878$		0			0
$879$	−7.80737	+	24.0286i	−0.263336	+	0.810466i
$880$		0			0
$881$	−4.62663	−	14.2393i	−0.155875	−	0.479735i	0.842373	−	0.538894i	$-0.181158\pi$
$881$	−4.62663	−	14.2393i	−0.155875	−	0.479735i	−0.998249	+	0.0591598i	$0.981158\pi$
$882$		0			0
$883$	−2.70155	−	8.31451i	−0.0909144	−	0.279806i	0.895253	−	0.445558i	$-0.146995\pi$
$883$	−2.70155	−	8.31451i	−0.0909144	−	0.279806i	−0.986167	+	0.165752i	$0.946995\pi$
$884$		0			0
$885$	−25.3124	−	13.7509i	−0.850867	−	0.462231i
$886$		0			0
$887$	−13.3379	−	9.69054i	−0.447842	−	0.325376i	0.340901	−	0.940099i	$-0.389268\pi$
$887$	−13.3379	−	9.69054i	−0.447842	−	0.325376i	−0.788743	+	0.614723i	$0.789268\pi$
$888$		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
$895$	2.12286	−	0.278993i	0.0709594	−	0.00932570i
$896$		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
$905$	6.71846	−	6.37270i	0.223329	−	0.211836i
$906$		0			0
$907$	26.0243			0.864124			0.432062	−	0.901844i	$-0.357786\pi$
$907$	26.0243			0.864124			0.432062	+	0.901844i	$0.357786\pi$
$908$		0			0
$909$	12.0025	+	8.72029i	0.398096	+	0.289234i
$910$		0			0
$911$	41.7815	−	30.3560i	1.38428	−	1.00574i	0.387816	−	0.921737i	$-0.373229\pi$
$911$	41.7815	−	30.3560i	1.38428	−	1.00574i	0.996466	−	0.0840029i	$-0.0267705\pi$
$912$		0			0
$913$	56.6359	+	41.1484i	1.87437	+	1.36181i
$914$		0			0
$915$	18.3663	−	17.4211i	0.607172	−	0.575924i
$916$		0			0
$917$	8.83945	+	27.2050i	0.291904	+	0.898390i
$918$		0			0
$919$	−8.53835	−	26.2784i	−0.281654	−	0.866843i	−0.987382	−	0.158359i	$-0.949380\pi$
$919$	−8.53835	−	26.2784i	−0.281654	−	0.866843i	0.705727	−	0.708484i	$-0.250620\pi$
$920$		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
$925$	−21.0935	+	5.64180i	−0.693551	+	0.185501i
$926$		0			0
$927$	−15.5853	+	11.3234i	−0.511890	+	0.371910i
$928$		0			0
$929$	16.5946	−	51.0728i	0.544450	−	1.67565i	−0.177843	−	0.984059i	$-0.556912\pi$
$929$	16.5946	−	51.0728i	0.544450	−	1.67565i	0.722294	−	0.691587i	$-0.243088\pi$
$930$		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
$935$	1.24870	−	6.72892i	0.0408369	−	0.220059i
$936$		0			0
$937$	24.5304	+	17.8224i	0.801373	+	0.582232i	0.911317	−	0.411706i	$-0.135067\pi$
$937$	24.5304	+	17.8224i	0.801373	+	0.582232i	−0.109943	+	0.993938i	$0.535067\pi$
$938$		0			0
$939$	17.7334	−	12.8841i	0.578707	−	0.420455i
$940$		0			0
$941$	−38.3217	−	27.8423i	−1.24925	−	0.907635i	−0.251073	−	0.967968i	$-0.580784\pi$
$941$	−38.3217	−	27.8423i	−1.24925	−	0.907635i	−0.998178	+	0.0603335i	$0.980784\pi$
$942$		0			0
$943$	−13.0177			−0.423915
$944$		0			0
$945$	−2.95573	−	1.60569i	−0.0961499	−	0.0522332i
$946$		0			0
$947$	−6.68770	+	20.5826i	−0.217321	+	0.668845i	0.781660	+	0.623705i	$0.214373\pi$
$947$	−6.68770	+	20.5826i	−0.217321	+	0.668845i	−0.998981	+	0.0451402i	$0.985627\pi$
$948$		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	0.406540	+	0.913633i	$0.366735\pi$
$953$	−14.1813	+	43.6456i	−0.459378	+	1.41382i	−0.865918	+	0.500187i	$0.833265\pi$
$954$		0			0
$955$	7.19301	−	38.7612i	0.232760	−	1.25428i
$956$		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
$965$	−5.05530	−	10.6048i	−0.162736	−	0.341381i
$966$		0			0
$967$	−4.62587	−	14.2370i	−0.148758	−	0.457830i	0.848717	−	0.528847i	$-0.177375\pi$
$967$	−4.62587	−	14.2370i	−0.148758	−	0.457830i	−0.997475	+	0.0710173i	$0.977375\pi$
$968$		0			0
$969$	−0.0477422	−	0.146935i	−0.00153370	−	0.00472025i
$970$		0			0
$971$	−6.91563	+	21.2841i	−0.221933	+	0.683040i	0.776655	+	0.629926i	$0.216915\pi$
$971$	−6.91563	+	21.2841i	−0.221933	+	0.683040i	−0.998588	+	0.0531143i	$0.983085\pi$
$972$		0			0
$973$	16.7951	−	12.2023i	0.538426	−	0.391189i
$974$		0			0
$975$	0.938632	−	17.7569i	0.0300603	−	0.568676i
$976$		0			0
$977$	32.6588	−	23.7280i	1.04485	−	0.759127i	0.0736229	−	0.997286i	$-0.476544\pi$
$977$	32.6588	−	23.7280i	1.04485	−	0.759127i	0.971226	+	0.238159i	$0.0765439\pi$
$978$		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	−0.997702	−	0.0677498i	$-0.978418\pi$
$983$	−7.22264	−	22.2290i	−0.230367	−	0.708995i	0.767336	−	0.641245i	$-0.221582\pi$
$984$		0			0
$985$	4.69111	−	0.616520i	0.149471	−	0.0196439i
$986$		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	0.0607312	−	0.998154i	$-0.480657\pi$
$991$	−27.3815	−	19.8938i	−0.869803	−	0.631949i	−0.930534	+	0.366205i	$0.880657\pi$
$992$		0			0
$993$	−33.5950			−1.06611
$994$		0			0
$995$	−8.72741	−	18.3080i	−0.276677	−	0.580403i
$996$		0			0
$997$	1.71351	−	5.27364i	0.0542674	−	0.167018i	−0.920249	−	0.391332i	$-0.872014\pi$
$997$	1.71351	−	5.27364i	0.0542674	−	0.167018i	0.974517	+	0.224314i	$0.0720143\pi$
$998$		0			0
$999$	4.36700			0.138166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.m.b.61.2	✓	8
3.2	odd	2		900.2.n.b.361.1		8
5.2	odd	4		1500.2.o.b.949.4		16
5.3	odd	4		1500.2.o.b.949.1		16
5.4	even	2		1500.2.m.a.301.1		8
25.3	odd	20		7500.2.d.c.1249.2		8
25.4	even	10		7500.2.a.f.1.2		4
25.9	even	10		1500.2.m.a.1201.1		8
25.12	odd	20		1500.2.o.b.49.2		16
25.13	odd	20		1500.2.o.b.49.3		16
25.16	even	5	inner	300.2.m.b.241.2	yes	8
25.21	even	5		7500.2.a.e.1.3		4
25.22	odd	20		7500.2.d.c.1249.7		8
75.41	odd	10		900.2.n.b.541.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.2	✓	8	1.1	even	1	trivial
300.2.m.b.241.2	yes	8	25.16	even	5	inner
900.2.n.b.361.1		8	3.2	odd	2
900.2.n.b.541.1		8	75.41	odd	10
1500.2.m.a.301.1		8	5.4	even	2
1500.2.m.a.1201.1		8	25.9	even	10
1500.2.o.b.49.2		16	25.12	odd	20
1500.2.o.b.49.3		16	25.13	odd	20
1500.2.o.b.949.1		16	5.3	odd	4
1500.2.o.b.949.4		16	5.2	odd	4
7500.2.a.e.1.3		4	25.21	even	5
7500.2.a.f.1.2		4	25.4	even	10
7500.2.d.c.1249.2		8	25.3	odd	20
7500.2.d.c.1249.7		8	25.22	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.962197 - 2.01846i) q^{5} +1.50430 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.962197 - 2.01846i) q^{5} +1.50430 q^{7} +(-0.809017 - 0.587785i) q^{9} +(4.99517 - 3.62921i) q^{11} +(2.87714 + 2.09036i) q^{13} +(2.21700 - 0.291365i) q^{15} +(0.153180 + 0.471439i) q^{17} +(0.0963126 + 0.296420i) q^{19} +(-0.464854 + 1.43067i) q^{21} +(2.47611 - 1.79900i) q^{23} +(-3.14835 + 3.88431i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-0.0378031 + 0.116346i) q^{29} +(-0.909629 - 2.79955i) q^{31} +(1.90799 + 5.87218i) q^{33} +(-1.44743 - 3.03637i) q^{35} +(3.53298 + 2.56686i) q^{37} +(-2.87714 + 2.09036i) q^{39} +(-3.44096 - 2.50001i) q^{41} -3.62663 q^{43} +(-0.407987 + 2.19853i) q^{45} +(1.63227 - 5.02362i) q^{47} -4.73708 q^{49} -0.495700 q^{51} +(-2.65748 + 8.17888i) q^{53} +(-12.1317 - 6.59054i) q^{55} -0.311674 q^{57} +(-10.4222 - 7.57219i) q^{59} +(9.15882 - 6.65427i) q^{61} +(-1.21700 - 0.884205i) q^{63} +(1.45094 - 7.81873i) q^{65} +(4.09181 + 12.5933i) q^{67} +(0.945790 + 2.91084i) q^{69} +(1.00994 - 3.10827i) q^{71} +(-12.9174 + 9.38504i) q^{73} +(-2.72130 - 4.19458i) q^{75} +(7.51424 - 5.45941i) q^{77} +(-2.63513 + 8.11010i) q^{79} +(0.309017 + 0.951057i) q^{81} +(3.50367 + 10.7832i) q^{83} +(0.804191 - 0.762805i) q^{85} +(-0.0989699 - 0.0719058i) q^{87} +(-11.4335 + 8.30691i) q^{89} +(4.32808 + 3.14453i) q^{91} +2.94362 q^{93} +(0.505640 - 0.479617i) q^{95} +(-3.54837 + 10.9208i) q^{97} -6.17438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9	\( 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9} + 8 q^{11} + 5 q^{15} + 3 q^{17} + 5 q^{19} + 7 q^{21} - 7 q^{23} + 5 q^{25} + 2 q^{27} - 3 q^{29} - 3 q^{31} + 7 q^{33} - 10 q^{35} - q^{37} + 10 q^{41} - 12 q^{43} + 5 q^{45} - 33 q^{47} - 8 q^{49} - 8 q^{51} - 19 q^{53} - 15 q^{55} + 10 q^{57} - 38 q^{59} + 46 q^{61} + 3 q^{63} + 25 q^{65} - 8 q^{67} + 2 q^{69} - 25 q^{71} - 26 q^{73} - 5 q^{75} + 23 q^{77} - 16 q^{79} - 2 q^{81} + 8 q^{83} - 30 q^{85} + 3 q^{87} - 30 q^{89} + 25 q^{91} - 22 q^{93} - 25 q^{95} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9 + 8 * q^11 + 5 * q^15 + 3 * q^17 + 5 * q^19 + 7 * q^21 - 7 * q^23 + 5 * q^25 + 2 * q^27 - 3 * q^29 - 3 * q^31 + 7 * q^33 - 10 * q^35 - q^37 + 10 * q^41 - 12 * q^43 + 5 * q^45 - 33 * q^47 - 8 * q^49 - 8 * q^51 - 19 * q^53 - 15 * q^55 + 10 * q^57 - 38 * q^59 + 46 * q^61 + 3 * q^63 + 25 * q^65 - 8 * q^67 + 2 * q^69 - 25 * q^71 - 26 * q^73 - 5 * q^75 + 23 * q^77 - 16 * q^79 - 2 * q^81 + 8 * q^83 - 30 * q^85 + 3 * q^87 - 30 * q^89 + 25 * q^91 - 22 * q^93 - 25 * q^95 - 14 * q^97 - 2 * q^99

Introduction

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