LMFDB - Embedded newform 450.2.h.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	450.361
Dual form			450.2.h.c.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.690983 + 2.12663i) q^{10} +(2.92705 - 2.12663i) q^{11} +(5.23607 + 3.80423i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.381966 - 1.17557i) q^{17} +(-1.76393 - 5.42882i) q^{19} +(0.690983 + 2.12663i) q^{20} +(1.11803 - 3.44095i) q^{22} +(3.61803 - 2.62866i) q^{23} +(1.54508 - 4.75528i) q^{25} +6.47214 q^{26} +(0.809017 - 2.48990i) q^{28} +(-2.61803 + 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000 q^{32} +(-1.00000 - 0.726543i) q^{34} +(-4.73607 + 3.44095i) q^{35} +(-6.47214 - 4.70228i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(1.80902 + 1.31433i) q^{40} +(4.61803 + 3.35520i) q^{41} -7.70820 q^{43} +(-1.11803 - 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-0.527864 + 1.62460i) q^{47} -0.145898 q^{49} +(-1.54508 - 4.75528i) q^{50} +(5.23607 - 3.80423i) q^{52} +(0.645898 - 1.98787i) q^{53} +(-2.50000 + 7.69421i) q^{55} +(-0.809017 - 2.48990i) q^{56} +(2.61803 + 8.05748i) q^{58} +(-2.92705 - 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(5.35410 + 3.88998i) q^{62} +(-0.809017 + 0.587785i) q^{64} -14.4721 q^{65} +(-0.472136 - 1.45309i) q^{67} -1.23607 q^{68} +(-1.80902 + 5.56758i) q^{70} +(-1.70820 + 5.25731i) q^{71} +(-2.85410 + 2.07363i) q^{73} -8.00000 q^{74} -5.70820 q^{76} +(7.66312 - 5.56758i) q^{77} +(-1.73607 + 5.34307i) q^{79} +2.23607 q^{80} +5.70820 q^{82} +(-0.663119 - 2.04087i) q^{83} +(2.23607 + 1.62460i) q^{85} +(-6.23607 + 4.53077i) q^{86} +(-2.92705 - 2.12663i) q^{88} +(2.85410 - 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(-1.38197 - 4.25325i) q^{92} +(0.527864 + 1.62460i) q^{94} +(10.3262 + 7.50245i) q^{95} +(-1.04508 + 3.21644i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - 5 q^{5} + 6 q^{7} + q^{8} - 5 q^{10} + 5 q^{11} + 12 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} - 16 q^{19} + 5 q^{20} + 10 q^{23} - 5 q^{25} + 8 q^{26} + q^{28} - 6 q^{29} - 3 q^{31}+ \cdots + 4 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - 5 * q^5 + 6 * q^7 + q^8 - 5 * q^10 + 5 * q^11 + 12 * q^13 + 4 * q^14 - q^16 - 6 * q^17 - 16 * q^19 + 5 * q^20 + 10 * q^23 - 5 * q^25 + 8 * q^26 + q^28 - 6 * q^29 - 3 * q^31 - 4 * q^32 - 4 * q^34 - 10 * q^35 - 8 * q^37 - 14 * q^38 + 5 * q^40 + 14 * q^41 - 4 * q^43 + 10 * q^46 - 20 * q^47 - 14 * q^49 + 5 * q^50 + 12 * q^52 + 16 * q^53 - 10 * q^55 - q^56 + 6 * q^58 - 5 * q^59 + 8 * q^62 - q^64 - 40 * q^65 + 16 * q^67 + 4 * q^68 - 5 * q^70 + 20 * q^71 + 2 * q^73 - 32 * q^74 + 4 * q^76 + 15 * q^77 + 2 * q^79 - 4 * q^82 + 13 * q^83 - 16 * q^86 - 5 * q^88 - 2 * q^89 + 28 * q^91 - 10 * q^92 + 20 * q^94 + 10 * q^95 + 7 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$		0			0
$7$	2.61803			0.989524			0.494762	−	0.869029i	$-0.335255\pi$
$7$	2.61803			0.989524			0.494762	+	0.869029i	$0.335255\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$		0			0
$10$	−0.690983	+	2.12663i	−0.218508	+	0.672499i
$11$	2.92705	−	2.12663i	0.882539	−	0.641202i	−0.0513829	−	0.998679i	$-0.516363\pi$
$11$	2.92705	−	2.12663i	0.882539	−	0.641202i	0.933922	+	0.357477i	$0.116363\pi$
$12$		0			0
$13$	5.23607	+	3.80423i	1.45222	+	1.05510i	0.985305	+	0.170802i	$0.0546359\pi$
$13$	5.23607	+	3.80423i	1.45222	+	1.05510i	0.466919	+	0.884300i	$0.345364\pi$
$14$	2.11803	−	1.53884i	0.566068	−	0.411273i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.381966	−	1.17557i	−0.0926404	−	0.285118i	0.893991	−	0.448085i	$-0.147894\pi$
$17$	−0.381966	−	1.17557i	−0.0926404	−	0.285118i	−0.986632	+	0.162967i	$0.947894\pi$
$18$		0			0
$19$	−1.76393	−	5.42882i	−0.404674	−	1.24546i	−0.921167	−	0.389167i	$-0.872763\pi$
$19$	−1.76393	−	5.42882i	−0.404674	−	1.24546i	0.516494	−	0.856291i	$-0.327237\pi$
$20$	0.690983	+	2.12663i	0.154508	+	0.475528i
$21$		0			0
$22$	1.11803	−	3.44095i	0.238366	−	0.733614i
$23$	3.61803	−	2.62866i	0.754412	−	0.548113i	−0.142779	−	0.989755i	$-0.545604\pi$
$23$	3.61803	−	2.62866i	0.754412	−	0.548113i	0.897191	+	0.441642i	$0.145604\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	6.47214			1.26929
$27$		0			0
$28$	0.809017	−	2.48990i	0.152890	−	0.470547i
$29$	−2.61803	+	8.05748i	−0.486157	+	1.49624i	0.344142	+	0.938918i	$0.388170\pi$
$29$	−2.61803	+	8.05748i	−0.486157	+	1.49624i	−0.830299	+	0.557319i	$0.811830\pi$
$30$		0			0
$31$	2.04508	+	6.29412i	0.367308	+	1.13046i	0.948523	+	0.316708i	$0.102578\pi$
$31$	2.04508	+	6.29412i	0.367308	+	1.13046i	−0.581215	+	0.813750i	$0.697422\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−1.00000	−	0.726543i	−0.171499	−	0.124601i
$35$	−4.73607	+	3.44095i	−0.800542	+	0.581628i
$36$		0			0
$37$	−6.47214	−	4.70228i	−1.06401	−	0.773050i	−0.0891861	−	0.996015i	$-0.528427\pi$
$37$	−6.47214	−	4.70228i	−1.06401	−	0.773050i	−0.974827	+	0.222965i	$0.928427\pi$
$38$	−4.61803	−	3.35520i	−0.749144	−	0.544285i
$39$		0			0
$40$	1.80902	+	1.31433i	0.286031	+	0.207813i
$41$	4.61803	+	3.35520i	0.721216	+	0.523994i	0.886772	−	0.462206i	$-0.152942\pi$
$41$	4.61803	+	3.35520i	0.721216	+	0.523994i	−0.165557	+	0.986200i	$0.552942\pi$
$42$		0			0
$43$	−7.70820			−1.17549			−0.587745	−	0.809046i	$-0.699984\pi$
$43$	−7.70820			−1.17549			−0.587745	+	0.809046i	$0.699984\pi$
$44$	−1.11803	−	3.44095i	−0.168550	−	0.518743i
$45$		0			0
$46$	1.38197	−	4.25325i	0.203760	−	0.627108i
$47$	−0.527864	+	1.62460i	−0.0769969	+	0.236972i	−0.982145	−	0.188123i	$-0.939759\pi$
$47$	−0.527864	+	1.62460i	−0.0769969	+	0.236972i	0.905149	+	0.425096i	$0.139759\pi$
$48$		0			0
$49$	−0.145898			−0.0208426
$50$	−1.54508	−	4.75528i	−0.218508	−	0.672499i
$51$		0			0
$52$	5.23607	−	3.80423i	0.726112	−	0.527551i
$53$	0.645898	−	1.98787i	0.0887209	−	0.273055i	−0.896846	−	0.442344i	$-0.854147\pi$
$53$	0.645898	−	1.98787i	0.0887209	−	0.273055i	0.985566	+	0.169289i	$0.0541471\pi$
$54$		0			0
$55$	−2.50000	+	7.69421i	−0.337100	+	1.03749i
$56$	−0.809017	−	2.48990i	−0.108109	−	0.332727i
$57$		0			0
$58$	2.61803	+	8.05748i	0.343765	+	1.05800i
$59$	−2.92705	−	2.12663i	−0.381070	−	0.276863i	0.380717	−	0.924692i	$-0.375677\pi$
$59$	−2.92705	−	2.12663i	−0.381070	−	0.276863i	−0.761786	+	0.647829i	$0.775677\pi$
$60$		0			0
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	−0.721660	−	0.692247i	$-0.756621\pi$
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	0.435361	+	0.900256i	$0.356621\pi$
$62$	5.35410	+	3.88998i	0.679972	+	0.494028i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−14.4721			−1.79505
$66$		0			0
$67$	−0.472136	−	1.45309i	−0.0576806	−	0.177523i	0.918065	−	0.396430i	$-0.129751\pi$
$67$	−0.472136	−	1.45309i	−0.0576806	−	0.177523i	−0.975746	+	0.218907i	$0.929751\pi$
$68$	−1.23607			−0.149895
$69$		0			0
$70$	−1.80902	+	5.56758i	−0.216219	+	0.665453i
$71$	−1.70820	+	5.25731i	−0.202727	+	0.623928i	0.797073	+	0.603884i	$0.206381\pi$
$71$	−1.70820	+	5.25731i	−0.202727	+	0.623928i	−0.999799	+	0.0200445i	$0.993619\pi$
$72$		0			0
$73$	−2.85410	+	2.07363i	−0.334047	+	0.242700i	−0.742146	−	0.670238i	$-0.766192\pi$
$73$	−2.85410	+	2.07363i	−0.334047	+	0.242700i	0.408099	+	0.912938i	$0.366192\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$	−5.70820			−0.654776
$77$	7.66312	−	5.56758i	0.873293	−	0.634485i
$78$		0			0
$79$	−1.73607	+	5.34307i	−0.195323	+	0.601142i	0.804650	+	0.593750i	$0.202353\pi$
$79$	−1.73607	+	5.34307i	−0.195323	+	0.601142i	−0.999973	+	0.00739236i	$0.997647\pi$
$80$	2.23607			0.250000
$81$		0			0
$82$	5.70820			0.630366
$83$	−0.663119	−	2.04087i	−0.0727868	−	0.224015i	0.908044	−	0.418874i	$-0.137575\pi$
$83$	−0.663119	−	2.04087i	−0.0727868	−	0.224015i	−0.980831	+	0.194859i	$0.937575\pi$
$84$		0			0
$85$	2.23607	+	1.62460i	0.242536	+	0.176212i
$86$	−6.23607	+	4.53077i	−0.672453	+	0.488565i
$87$		0			0
$88$	−2.92705	−	2.12663i	−0.312025	−	0.226699i
$89$	2.85410	−	2.07363i	0.302534	−	0.219804i	−0.426152	−	0.904651i	$-0.640131\pi$
$89$	2.85410	−	2.07363i	0.302534	−	0.219804i	0.728686	+	0.684848i	$0.240131\pi$
$90$		0			0
$91$	13.7082	+	9.95959i	1.43701	+	1.04405i
$92$	−1.38197	−	4.25325i	−0.144080	−	0.443432i
$93$		0			0
$94$	0.527864	+	1.62460i	0.0544450	+	0.167565i
$95$	10.3262	+	7.50245i	1.05945	+	0.769735i
$96$		0			0
$97$	−1.04508	+	3.21644i	−0.106112	+	0.326580i	−0.989990	−	0.141138i	$-0.954924\pi$
$97$	−1.04508	+	3.21644i	−0.106112	+	0.326580i	0.883878	+	0.467718i	$0.154924\pi$
$98$	−0.118034	+	0.0857567i	−0.0119232	+	0.00866274i
$99$		0			0
$100$	−4.04508	−	2.93893i	−0.404508	−	0.293893i
$101$	−4.38197			−0.436022			−0.218011	−	0.975946i	$-0.569957\pi$
$101$	−4.38197			−0.436022			−0.218011	+	0.975946i	$0.569957\pi$
$102$		0			0
$103$	4.42705	−	13.6251i	0.436210	−	1.34252i	−0.455631	−	0.890169i	$-0.650586\pi$
$103$	4.42705	−	13.6251i	0.436210	−	1.34252i	0.891841	−	0.452348i	$-0.149414\pi$
$104$	2.00000	−	6.15537i	0.196116	−	0.603583i
$105$		0			0
$106$	−0.645898	−	1.98787i	−0.0627352	−	0.193079i
$107$	11.6180			1.12316			0.561579	−	0.827423i	$-0.310194\pi$
$107$	11.6180			1.12316			0.561579	+	0.827423i	$0.310194\pi$
$108$		0			0
$109$	−13.9443	−	10.1311i	−1.33562	−	0.970384i	−0.999593	−	0.0285313i	$-0.990917\pi$
$109$	−13.9443	−	10.1311i	−1.33562	−	0.970384i	−0.336026	−	0.941853i	$-0.609083\pi$
$110$	2.50000	+	7.69421i	0.238366	+	0.733614i
$111$		0			0
$112$	−2.11803	−	1.53884i	−0.200135	−	0.145407i
$113$	−15.5623	−	11.3067i	−1.46398	−	1.06364i	−0.982304	−	0.187292i	$-0.940029\pi$
$113$	−15.5623	−	11.3067i	−1.46398	−	1.06364i	−0.481674	−	0.876350i	$-0.659971\pi$
$114$		0			0
$115$	−3.09017	+	9.51057i	−0.288160	+	0.886865i
$116$	6.85410	+	4.97980i	0.636387	+	0.462363i
$117$		0			0
$118$	−3.61803			−0.333067
$119$	−1.00000	−	3.07768i	−0.0916698	−	0.282131i
$120$		0			0
$121$	0.645898	−	1.98787i	0.0587180	−	0.180715i
$122$	−0.854102	+	2.62866i	−0.0773268	+	0.237987i
$123$		0			0
$124$	6.61803			0.594317
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	−11.0172	+	8.00448i	−0.977620	+	0.710283i	−0.957176	−	0.289508i	$-0.906508\pi$
$127$	−11.0172	+	8.00448i	−0.977620	+	0.710283i	−0.0204448	+	0.999791i	$0.506508\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	−11.7082	+	8.50651i	−1.02688	+	0.746070i
$131$	5.52786	+	17.0130i	0.482972	+	1.48643i	0.834897	+	0.550406i	$0.185527\pi$
$131$	5.52786	+	17.0130i	0.482972	+	1.48643i	−0.351925	+	0.936028i	$0.614473\pi$
$132$		0			0
$133$	−4.61803	−	14.2128i	−0.400434	−	1.23241i
$134$	−1.23607	−	0.898056i	−0.106780	−	0.0775802i
$135$		0			0
$136$	−1.00000	+	0.726543i	−0.0857493	+	0.0623005i
$137$	−9.85410	−	7.15942i	−0.841893	−	0.611671i	0.0810060	−	0.996714i	$-0.474187\pi$
$137$	−9.85410	−	7.15942i	−0.841893	−	0.611671i	−0.922899	+	0.385043i	$0.874187\pi$
$138$		0			0
$139$	−8.47214	+	6.15537i	−0.718597	+	0.522091i	−0.885936	−	0.463808i	$-0.846483\pi$
$139$	−8.47214	+	6.15537i	−0.718597	+	0.522091i	0.167339	+	0.985899i	$0.446483\pi$
$140$	1.80902	+	5.56758i	0.152890	+	0.470547i
$141$		0			0
$142$	1.70820	+	5.25731i	0.143349	+	0.441184i
$143$	23.4164			1.95818
$144$		0			0
$145$	−5.85410	−	18.0171i	−0.486157	−	1.49624i
$146$	−1.09017	+	3.35520i	−0.0902231	+	0.277678i
$147$		0			0
$148$	−6.47214	+	4.70228i	−0.532006	+	0.386525i
$149$	−22.0902			−1.80970			−0.904849	−	0.425733i	$-0.860016\pi$
$149$	−22.0902			−1.80970			−0.904849	+	0.425733i	$0.860016\pi$
$150$		0			0
$151$	18.3262			1.49137			0.745684	−	0.666300i	$-0.232123\pi$
$151$	18.3262			1.49137			0.745684	+	0.666300i	$0.232123\pi$
$152$	−4.61803	+	3.35520i	−0.374572	+	0.272143i
$153$		0			0
$154$	2.92705	−	9.00854i	0.235868	−	0.725929i
$155$	−11.9721	−	8.69827i	−0.961625	−	0.698662i
$156$		0			0
$157$	8.65248			0.690543			0.345271	−	0.938503i	$-0.387787\pi$
$157$	8.65248			0.690543			0.345271	+	0.938503i	$0.387787\pi$
$158$	1.73607	+	5.34307i	0.138114	+	0.425072i
$159$		0			0
$160$	1.80902	−	1.31433i	0.143015	−	0.103907i
$161$	9.47214	−	6.88191i	0.746509	−	0.542370i
$162$		0			0
$163$	0.381966	+	0.277515i	0.0299179	+	0.0217366i	0.602644	−	0.798010i	$-0.294114\pi$
$163$	0.381966	+	0.277515i	0.0299179	+	0.0217366i	−0.572726	+	0.819747i	$0.694114\pi$
$164$	4.61803	−	3.35520i	0.360608	−	0.261997i
$165$		0			0
$166$	−1.73607	−	1.26133i	−0.134745	−	0.0978980i
$167$	−3.61803	−	11.1352i	−0.279972	−	0.861665i	−0.987861	−	0.155341i	$-0.950352\pi$
$167$	−3.61803	−	11.1352i	−0.279972	−	0.861665i	0.707889	−	0.706324i	$-0.249648\pi$
$168$		0			0
$169$	8.92705	+	27.4746i	0.686696	+	2.11343i
$170$	2.76393			0.211984
$171$		0			0
$172$	−2.38197	+	7.33094i	−0.181623	+	0.558979i
$173$	4.11803	−	2.99193i	0.313088	−	0.227472i	−0.420132	−	0.907463i	$-0.638016\pi$
$173$	4.11803	−	2.99193i	0.313088	−	0.227472i	0.733221	+	0.679991i	$0.238016\pi$
$174$		0			0
$175$	4.04508	−	12.4495i	0.305780	−	0.941093i
$176$	−3.61803			−0.272720
$177$		0			0
$178$	1.09017	−	3.35520i	0.0817117	−	0.251483i
$179$	−3.04508	+	9.37181i	−0.227600	+	0.700482i	0.770417	+	0.637540i	$0.220048\pi$
$179$	−3.04508	+	9.37181i	−0.227600	+	0.700482i	−0.998017	+	0.0629414i	$0.979952\pi$
$180$		0			0
$181$	−2.05573	−	6.32688i	−0.152801	−	0.470273i	0.845130	−	0.534560i	$-0.179523\pi$
$181$	−2.05573	−	6.32688i	−0.152801	−	0.470273i	−0.997931	+	0.0642869i	$0.979523\pi$
$182$	16.9443			1.25599
$183$		0			0
$184$	−3.61803	−	2.62866i	−0.266725	−	0.193787i
$185$	17.8885			1.31519
$186$		0			0
$187$	−3.61803	−	2.62866i	−0.264577	−	0.192226i
$188$	1.38197	+	1.00406i	0.100790	+	0.0732284i
$189$		0			0
$190$	12.7639			0.925993
$191$	3.47214	+	2.52265i	0.251235	+	0.182533i	0.706274	−	0.707939i	$-0.250375\pi$
$191$	3.47214	+	2.52265i	0.251235	+	0.182533i	−0.455039	+	0.890472i	$0.650375\pi$
$192$		0			0
$193$	17.8541			1.28517			0.642583	−	0.766216i	$-0.277863\pi$
$193$	17.8541			1.28517			0.642583	+	0.766216i	$0.277863\pi$
$194$	1.04508	+	3.21644i	0.0750327	+	0.230927i
$195$		0			0
$196$	−0.0450850	+	0.138757i	−0.00322036	+	0.00991123i
$197$	5.28115	−	16.2537i	0.376267	−	1.15803i	−0.566354	−	0.824162i	$-0.691646\pi$
$197$	5.28115	−	16.2537i	0.376267	−	1.15803i	0.942620	−	0.333867i	$-0.108354\pi$
$198$		0			0
$199$	19.5066			1.38278			0.691392	−	0.722480i	$-0.256998\pi$
$199$	19.5066			1.38278			0.691392	+	0.722480i	$0.256998\pi$
$200$	−5.00000			−0.353553
$201$		0			0
$202$	−3.54508	+	2.57565i	−0.249431	+	0.181222i
$203$	−6.85410	+	21.0948i	−0.481064	+	1.48056i
$204$		0			0
$205$	−12.7639			−0.891472
$206$	−4.42705	−	13.6251i	−0.308447	−	0.949303i
$207$		0			0
$208$	−2.00000	−	6.15537i	−0.138675	−	0.426798i
$209$	−16.7082	−	12.1392i	−1.15573	−	0.839687i
$210$		0			0
$211$	2.76393	−	2.00811i	0.190277	−	0.138244i	−0.488568	−	0.872526i	$-0.662481\pi$
$211$	2.76393	−	2.00811i	0.190277	−	0.138244i	0.678845	+	0.734281i	$0.262481\pi$
$212$	−1.69098	−	1.22857i	−0.116137	−	0.0843786i
$213$		0			0
$214$	9.39919	−	6.82891i	0.642515	−	0.466815i
$215$	13.9443	−	10.1311i	0.950991	−	0.690936i
$216$		0			0
$217$	5.35410	+	16.4782i	0.363460	+	1.11862i
$218$	−17.2361			−1.16737
$219$		0			0
$220$	6.54508	+	4.75528i	0.441270	+	0.320601i
$221$	2.47214	−	7.60845i	0.166294	−	0.511800i
$222$		0			0
$223$	6.54508	−	4.75528i	0.438291	−	0.318437i	−0.346664	−	0.937989i	$-0.612686\pi$
$223$	6.54508	−	4.75528i	0.438291	−	0.318437i	0.784956	+	0.619552i	$0.212686\pi$
$224$	−2.61803			−0.174925
$225$		0			0
$226$	−19.2361			−1.27956
$227$	−18.0172	+	13.0903i	−1.19584	+	0.868832i	−0.993870	−	0.110558i	$-0.964736\pi$
$227$	−18.0172	+	13.0903i	−1.19584	+	0.868832i	−0.201975	+	0.979391i	$0.564736\pi$
$228$		0			0
$229$	−1.70820	+	5.25731i	−0.112881	+	0.347413i	−0.991499	−	0.130113i	$-0.958466\pi$
$229$	−1.70820	+	5.25731i	−0.112881	+	0.347413i	0.878618	+	0.477525i	$0.158466\pi$
$230$	3.09017	+	9.51057i	0.203760	+	0.627108i
$231$		0			0
$232$	8.47214			0.556223
$233$	−5.76393	−	17.7396i	−0.377608	−	1.16216i	−0.941702	−	0.336447i	$-0.890775\pi$
$233$	−5.76393	−	17.7396i	−0.377608	−	1.16216i	0.564095	−	0.825710i	$-0.309225\pi$
$234$		0			0
$235$	−1.18034	−	3.63271i	−0.0769969	−	0.236972i
$236$	−2.92705	+	2.12663i	−0.190535	+	0.138432i
$237$		0			0
$238$	−2.61803	−	1.90211i	−0.169702	−	0.123296i
$239$	9.94427	−	7.22494i	0.643241	−	0.467342i	−0.217721	−	0.976011i	$-0.569862\pi$
$239$	9.94427	−	7.22494i	0.643241	−	0.467342i	0.860962	+	0.508669i	$0.169862\pi$
$240$		0			0
$241$	−7.73607	−	5.62058i	−0.498324	−	0.362054i	0.310052	−	0.950719i	$-0.399653\pi$
$241$	−7.73607	−	5.62058i	−0.498324	−	0.362054i	−0.808376	+	0.588666i	$0.799653\pi$
$242$	−0.645898	−	1.98787i	−0.0415199	−	0.127785i
$243$		0			0
$244$	0.854102	+	2.62866i	0.0546783	+	0.168282i
$245$	0.263932	−	0.191758i	0.0168620	−	0.0122510i
$246$		0			0
$247$	11.4164	−	35.1361i	0.726409	−	2.23566i
$248$	5.35410	−	3.88998i	0.339986	−	0.247014i
$249$		0			0
$250$	9.04508	+	6.57164i	0.572061	+	0.415627i
$251$	−13.5623			−0.856045			−0.428023	−	0.903768i	$-0.640790\pi$
$251$	−13.5623			−0.856045			−0.428023	+	0.903768i	$0.640790\pi$
$252$		0			0
$253$	5.00000	−	15.3884i	0.314347	−	0.967462i
$254$	−4.20820	+	12.9515i	−0.264046	+	0.812651i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$		0			0
$259$	−16.9443	−	12.3107i	−1.05287	−	0.764952i
$260$	−4.47214	+	13.7638i	−0.277350	+	0.853596i
$261$		0			0
$262$	14.4721	+	10.5146i	0.894092	+	0.649596i
$263$	−9.47214	−	6.88191i	−0.584077	−	0.424357i	0.256115	−	0.966646i	$-0.417558\pi$
$263$	−9.47214	−	6.88191i	−0.584077	−	0.424357i	−0.840192	+	0.542290i	$0.817558\pi$
$264$		0			0
$265$	1.44427	+	4.44501i	0.0887209	+	0.273055i
$266$	−12.0902	−	8.78402i	−0.741296	−	0.538583i
$267$		0			0
$268$	−1.52786			−0.0933292
$269$	2.80902	+	8.64527i	0.171269	+	0.527111i	0.999443	−	0.0333590i	$-0.0106205\pi$
$269$	2.80902	+	8.64527i	0.171269	+	0.527111i	−0.828175	+	0.560470i	$0.810620\pi$
$270$		0			0
$271$	−5.57295	+	17.1518i	−0.338533	+	1.04190i	0.626423	+	0.779483i	$0.284518\pi$
$271$	−5.57295	+	17.1518i	−0.338533	+	1.04190i	−0.964956	+	0.262413i	$0.915482\pi$
$272$	−0.381966	+	1.17557i	−0.0231601	+	0.0712794i
$273$		0			0
$274$	−12.1803			−0.735841
$275$	−5.59017	−	17.2048i	−0.337100	−	1.03749i
$276$		0			0
$277$	−13.7082	+	9.95959i	−0.823646	+	0.598414i	−0.917755	−	0.397148i	$-0.870000\pi$
$277$	−13.7082	+	9.95959i	−0.823646	+	0.598414i	0.0941084	+	0.995562i	$0.470000\pi$
$278$	−3.23607	+	9.95959i	−0.194086	+	0.597337i
$279$		0			0
$280$	4.73607	+	3.44095i	0.283034	+	0.205636i
$281$	−1.81966	−	5.60034i	−0.108552	−	0.334088i	0.881996	−	0.471257i	$-0.156200\pi$
$281$	−1.81966	−	5.60034i	−0.108552	−	0.334088i	−0.990548	+	0.137169i	$0.956200\pi$
$282$		0			0
$283$	1.41641	+	4.35926i	0.0841967	+	0.259131i	0.984288	−	0.176571i	$-0.0565004\pi$
$283$	1.41641	+	4.35926i	0.0841967	+	0.259131i	−0.900091	+	0.435701i	$0.856500\pi$
$284$	4.47214	+	3.24920i	0.265372	+	0.192804i
$285$		0			0
$286$	18.9443	−	13.7638i	1.12020	−	0.813872i
$287$	12.0902	+	8.78402i	0.713660	+	0.518504i
$288$		0			0
$289$	12.5172	−	9.09429i	0.736307	−	0.534958i
$290$	−15.3262	−	11.1352i	−0.899988	−	0.653879i
$291$		0			0
$292$	1.09017	+	3.35520i	0.0637974	+	0.196348i
$293$	22.0902			1.29052			0.645261	−	0.763962i	$-0.276749\pi$
$293$	22.0902			1.29052			0.645261	+	0.763962i	$0.276749\pi$
$294$		0			0
$295$	8.09017			0.471028
$296$	−2.47214	+	7.60845i	−0.143690	+	0.442232i
$297$		0			0
$298$	−17.8713	+	12.9843i	−1.03526	+	0.752159i
$299$	28.9443			1.67389
$300$		0			0
$301$	−20.1803			−1.16318
$302$	14.8262	−	10.7719i	0.853154	−	0.619853i
$303$		0			0
$304$	−1.76393	+	5.42882i	−0.101168	+	0.311364i
$305$	1.90983	−	5.87785i	0.109357	−	0.336565i
$306$		0			0
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$	−2.92705	−	9.00854i	−0.166784	−	0.513309i
$309$		0			0
$310$	−14.7984			−0.840491
$311$	−0.854102	+	0.620541i	−0.0484317	+	0.0351877i	−0.611738	−	0.791061i	$-0.709529\pi$
$311$	−0.854102	+	0.620541i	−0.0484317	+	0.0351877i	0.563306	+	0.826248i	$0.309529\pi$
$312$		0			0
$313$	13.1631	+	9.56357i	0.744023	+	0.540565i	0.893969	−	0.448130i	$-0.147910\pi$
$313$	13.1631	+	9.56357i	0.744023	+	0.540565i	−0.149945	+	0.988694i	$0.547910\pi$
$314$	7.00000	−	5.08580i	0.395033	−	0.287008i
$315$		0			0
$316$	4.54508	+	3.30220i	0.255681	+	0.185763i
$317$	6.35410	+	19.5559i	0.356882	+	1.09837i	0.954910	+	0.296895i	$0.0959510\pi$
$317$	6.35410	+	19.5559i	0.356882	+	1.09837i	−0.598028	+	0.801475i	$0.704049\pi$
$318$		0			0
$319$	9.47214	+	29.1522i	0.530338	+	1.63221i
$320$	0.690983	−	2.12663i	0.0386271	−	0.118882i
$321$		0			0
$322$	3.61803	−	11.1352i	0.201625	−	0.620538i
$323$	−5.70820	+	4.14725i	−0.317613	+	0.230759i
$324$		0			0
$325$	26.1803	−	19.0211i	1.45222	−	1.05510i
$326$	0.472136			0.0261492
$327$		0			0
$328$	1.76393	−	5.42882i	0.0973969	−	0.299757i
$329$	−1.38197	+	4.25325i	−0.0761903	+	0.234489i
$330$		0			0
$331$	−5.56231	−	17.1190i	−0.305732	−	0.940946i	−0.979403	−	0.201915i	$-0.935284\pi$
$331$	−5.56231	−	17.1190i	−0.305732	−	0.940946i	0.673671	−	0.739031i	$-0.264716\pi$
$332$	−2.14590			−0.117771
$333$		0			0
$334$	−9.47214	−	6.88191i	−0.518292	−	0.376561i
$335$	2.76393	+	2.00811i	0.151010	+	0.109715i
$336$		0			0
$337$	−0.736068	−	0.534785i	−0.0400962	−	0.0291316i	0.567557	−	0.823334i	$-0.307889\pi$
$337$	−0.736068	−	0.534785i	−0.0400962	−	0.0291316i	−0.607653	+	0.794203i	$0.707889\pi$
$338$	23.3713	+	16.9803i	1.27123	+	0.923604i
$339$		0			0
$340$	2.23607	−	1.62460i	0.121268	−	0.0881062i
$341$	19.3713	+	14.0741i	1.04902	+	0.762155i
$342$		0			0
$343$	−18.7082			−1.01015
$344$	2.38197	+	7.33094i	0.128427	+	0.395258i
$345$		0			0
$346$	1.57295	−	4.84104i	0.0845623	−	0.260256i
$347$	−6.35410	+	19.5559i	−0.341106	+	1.04982i	0.622529	+	0.782596i	$0.286105\pi$
$347$	−6.35410	+	19.5559i	−0.341106	+	1.04982i	−0.963636	+	0.267220i	$0.913895\pi$
$348$		0			0
$349$	−27.8885			−1.49284			−0.746420	−	0.665475i	$-0.768229\pi$
$349$	−27.8885			−1.49284			−0.746420	+	0.665475i	$0.768229\pi$
$350$	−4.04508	−	12.4495i	−0.216219	−	0.665453i
$351$		0			0
$352$	−2.92705	+	2.12663i	−0.156012	+	0.113350i
$353$	4.09017	−	12.5882i	0.217698	−	0.670005i	−0.781253	−	0.624214i	$-0.785419\pi$
$353$	4.09017	−	12.5882i	0.217698	−	0.670005i	0.998951	−	0.0457907i	$-0.0145807\pi$
$354$		0			0
$355$	−3.81966	−	11.7557i	−0.202727	−	0.623928i
$356$	−1.09017	−	3.35520i	−0.0577789	−	0.177825i
$357$		0			0
$358$	3.04508	+	9.37181i	0.160938	+	0.495315i
$359$	17.9443	+	13.0373i	0.947062	+	0.688081i	0.950110	−	0.311914i	$-0.100970\pi$
$359$	17.9443	+	13.0373i	0.947062	+	0.688081i	−0.00304782	+	0.999995i	$0.500970\pi$
$360$		0			0
$361$	−10.9894	+	7.98424i	−0.578387	+	0.420223i
$362$	−5.38197	−	3.91023i	−0.282870	−	0.205517i
$363$		0			0
$364$	13.7082	−	9.95959i	0.718505	−	0.522025i
$365$	2.43769	−	7.50245i	0.127595	−	0.392696i
$366$		0			0
$367$	−9.46149	−	29.1195i	−0.493886	−	1.52002i	−0.818686	−	0.574242i	$-0.805297\pi$
$367$	−9.46149	−	29.1195i	−0.493886	−	1.52002i	0.324800	−	0.945783i	$-0.394703\pi$
$368$	−4.47214			−0.233126
$369$		0			0
$370$	14.4721	−	10.5146i	0.752371	−	0.546629i
$371$	1.69098	−	5.20431i	0.0877915	−	0.270194i
$372$		0			0
$373$	9.32624	−	6.77591i	0.482894	−	0.350843i	−0.319551	−	0.947569i	$-0.603532\pi$
$373$	9.32624	−	6.77591i	0.482894	−	0.350843i	0.802445	+	0.596726i	$0.203532\pi$
$374$	−4.47214			−0.231249
$375$		0			0
$376$	1.70820			0.0880939
$377$	−44.3607	+	32.2299i	−2.28469	+	1.65993i
$378$		0			0
$379$	−6.23607	+	19.1926i	−0.320325	+	0.985860i	0.653181	+	0.757201i	$0.273434\pi$
$379$	−6.23607	+	19.1926i	−0.320325	+	0.985860i	−0.973507	+	0.228658i	$0.926566\pi$
$380$	10.3262	−	7.50245i	0.529725	−	0.384868i
$381$		0			0
$382$	4.29180			0.219587
$383$	6.18034	+	19.0211i	0.315801	+	0.971934i	0.975424	+	0.220338i	$0.0707160\pi$
$383$	6.18034	+	19.0211i	0.315801	+	0.971934i	−0.659623	+	0.751597i	$0.729284\pi$
$384$		0			0
$385$	−6.54508	+	20.1437i	−0.333568	+	1.02662i
$386$	14.4443	−	10.4944i	0.735194	−	0.534150i
$387$		0			0
$388$	2.73607	+	1.98787i	0.138903	+	0.100919i
$389$	−10.0172	+	7.27794i	−0.507893	+	0.369006i	−0.812024	−	0.583624i	$-0.801634\pi$
$389$	−10.0172	+	7.27794i	−0.507893	+	0.369006i	0.304131	+	0.952630i	$0.401634\pi$
$390$		0			0
$391$	−4.47214	−	3.24920i	−0.226166	−	0.164319i
$392$	0.0450850	+	0.138757i	0.00227713	+	0.00700830i
$393$		0			0
$394$	−5.28115	−	16.2537i	−0.266061	−	0.818850i
$395$	−3.88197	−	11.9475i	−0.195323	−	0.601142i
$396$		0			0
$397$	−9.50658	+	29.2582i	−0.477121	+	1.46843i	0.365954	+	0.930633i	$0.380743\pi$
$397$	−9.50658	+	29.2582i	−0.477121	+	1.46843i	−0.843075	+	0.537796i	$0.819257\pi$
$398$	15.7812	−	11.4657i	0.791038	−	0.574723i
$399$		0			0
$400$	−4.04508	+	2.93893i	−0.202254	+	0.146946i
$401$	−25.7082			−1.28381			−0.641903	−	0.766786i	$-0.721855\pi$
$401$	−25.7082			−1.28381			−0.641903	+	0.766786i	$0.721855\pi$
$402$		0			0
$403$	−13.2361	+	40.7364i	−0.659336	+	2.02923i
$404$	−1.35410	+	4.16750i	−0.0673691	+	0.207341i
$405$		0			0
$406$	6.85410	+	21.0948i	0.340163	+	1.04692i
$407$	−28.9443			−1.43471
$408$		0			0
$409$	−4.69098	−	3.40820i	−0.231954	−	0.168525i	0.465737	−	0.884923i	$-0.345789\pi$
$409$	−4.69098	−	3.40820i	−0.231954	−	0.168525i	−0.697691	+	0.716399i	$0.745789\pi$
$410$	−10.3262	+	7.50245i	−0.509977	+	0.370520i
$411$		0			0
$412$	−11.5902	−	8.42075i	−0.571007	−	0.414861i
$413$	−7.66312	−	5.56758i	−0.377077	−	0.273963i
$414$		0			0
$415$	3.88197	+	2.82041i	0.190558	+	0.138449i
$416$	−5.23607	−	3.80423i	−0.256719	−	0.186518i
$417$		0			0
$418$	−20.6525			−1.01015
$419$	0.954915	+	2.93893i	0.0466507	+	0.143576i	0.971669	−	0.236347i	$-0.0759504\pi$
$419$	0.954915	+	2.93893i	0.0466507	+	0.143576i	−0.925018	+	0.379923i	$0.875950\pi$
$420$		0			0
$421$	−7.03444	+	21.6498i	−0.342838	+	1.05515i	0.619893	+	0.784686i	$0.287176\pi$
$421$	−7.03444	+	21.6498i	−0.342838	+	1.05515i	−0.962731	+	0.270460i	$0.912824\pi$
$422$	1.05573	−	3.24920i	0.0513920	−	0.158168i
$423$		0			0
$424$	−2.09017			−0.101508
$425$	−6.18034			−0.299791
$426$		0			0
$427$	−5.85410	+	4.25325i	−0.283300	+	0.205829i
$428$	3.59017	−	11.0494i	0.173537	−	0.534093i
$429$		0			0
$430$	5.32624	−	16.3925i	0.256854	−	0.790515i
$431$	−5.20163	−	16.0090i	−0.250554	−	0.771124i	−0.994673	−	0.103078i	$-0.967131\pi$
$431$	−5.20163	−	16.0090i	−0.250554	−	0.771124i	0.744120	−	0.668046i	$-0.232869\pi$
$432$		0			0
$433$	4.79180	+	14.7476i	0.230279	+	0.708726i	0.997713	+	0.0675976i	$0.0215334\pi$
$433$	4.79180	+	14.7476i	0.230279	+	0.708726i	−0.767434	+	0.641128i	$0.778467\pi$
$434$	14.0172	+	10.1841i	0.672848	+	0.488853i
$435$		0			0
$436$	−13.9443	+	10.1311i	−0.667810	+	0.485192i
$437$	−20.6525	−	15.0049i	−0.987942	−	0.717782i
$438$		0			0
$439$	19.0172	−	13.8168i	0.907642	−	0.659441i	−0.0327751	−	0.999463i	$-0.510434\pi$
$439$	19.0172	−	13.8168i	0.907642	−	0.659441i	0.940418	+	0.340022i	$0.110434\pi$
$440$	8.09017			0.385684
$441$		0			0
$442$	−2.47214	−	7.60845i	−0.117588	−	0.361897i
$443$	−16.6180			−0.789547			−0.394773	−	0.918779i	$-0.629177\pi$
$443$	−16.6180			−0.789547			−0.394773	+	0.918779i	$0.629177\pi$
$444$		0			0
$445$	−2.43769	+	7.50245i	−0.115558	+	0.355650i
$446$	2.50000	−	7.69421i	0.118378	−	0.364331i
$447$		0			0
$448$	−2.11803	+	1.53884i	−0.100068	+	0.0727034i
$449$	27.7082			1.30763			0.653815	−	0.756654i	$-0.273167\pi$
$449$	27.7082			1.30763			0.653815	+	0.756654i	$0.273167\pi$
$450$		0			0
$451$	20.6525			0.972487
$452$	−15.5623	+	11.3067i	−0.731989	+	0.531821i
$453$		0			0
$454$	−6.88197	+	21.1805i	−0.322987	+	0.994051i
$455$	−37.8885			−1.77624
$456$		0			0
$457$	−4.09017			−0.191330			−0.0956650	−	0.995414i	$-0.530498\pi$
$457$	−4.09017			−0.191330			−0.0956650	+	0.995414i	$0.530498\pi$
$458$	1.70820	+	5.25731i	0.0798191	+	0.245658i
$459$		0			0
$460$	8.09017	+	5.87785i	0.377206	+	0.274056i
$461$	6.11803	−	4.44501i	0.284945	−	0.207025i	−0.436126	−	0.899885i	$-0.643650\pi$
$461$	6.11803	−	4.44501i	0.284945	−	0.207025i	0.721072	+	0.692861i	$0.243650\pi$
$462$		0			0
$463$	18.4721	+	13.4208i	0.858473	+	0.623717i	0.927469	−	0.373900i	$-0.121980\pi$
$463$	18.4721	+	13.4208i	0.858473	+	0.623717i	−0.0689961	+	0.997617i	$0.521980\pi$
$464$	6.85410	−	4.97980i	0.318194	−	0.231181i
$465$		0			0
$466$	−15.0902	−	10.9637i	−0.699039	−	0.507881i
$467$	−3.29837	−	10.1514i	−0.152631	−	0.469749i	0.845283	−	0.534320i	$-0.179432\pi$
$467$	−3.29837	−	10.1514i	−0.152631	−	0.469749i	−0.997913	+	0.0645710i	$0.979432\pi$
$468$		0			0
$469$	−1.23607	−	3.80423i	−0.0570763	−	0.175663i
$470$	−3.09017	−	2.24514i	−0.142539	−	0.103561i
$471$		0			0
$472$	−1.11803	+	3.44095i	−0.0514617	+	0.158383i
$473$	−22.5623	+	16.3925i	−1.03742	+	0.753727i
$474$		0			0
$475$	−28.5410			−1.30955
$476$	−3.23607			−0.148325
$477$		0			0
$478$	3.79837	−	11.6902i	0.173734	−	0.534697i
$479$	9.00000	−	27.6992i	0.411220	−	1.26561i	−0.504368	−	0.863489i	$-0.668274\pi$
$479$	9.00000	−	27.6992i	0.411220	−	1.26561i	0.915588	−	0.402117i	$-0.131726\pi$
$480$		0			0
$481$	−16.0000	−	49.2429i	−0.729537	−	2.24528i
$482$	−9.56231			−0.435551
$483$		0			0
$484$	−1.69098	−	1.22857i	−0.0768629	−	0.0558441i
$485$	−2.33688	−	7.19218i	−0.106112	−	0.326580i
$486$		0			0
$487$	−14.3992	−	10.4616i	−0.652489	−	0.474061i	0.211629	−	0.977350i	$-0.432123\pi$
$487$	−14.3992	−	10.4616i	−0.652489	−	0.474061i	−0.864118	+	0.503289i	$0.832123\pi$
$488$	2.23607	+	1.62460i	0.101222	+	0.0735421i
$489$		0			0
$490$	0.100813	−	0.310271i	0.00455427	−	0.0140166i
$491$	−20.4443	−	14.8536i	−0.922637	−	0.670335i	0.0215419	−	0.999768i	$-0.493142\pi$
$491$	−20.4443	−	14.8536i	−0.922637	−	0.670335i	−0.944179	+	0.329433i	$0.893142\pi$
$492$		0			0
$493$	10.4721			0.471641
$494$	−11.4164	−	35.1361i	−0.513648	−	1.58085i
$495$		0			0
$496$	2.04508	−	6.29412i	0.0918270	−	0.282615i
$497$	−4.47214	+	13.7638i	−0.200603	+	0.617392i
$498$		0			0
$499$	35.5967			1.59353			0.796765	−	0.604290i	$-0.206543\pi$
$499$	35.5967			1.59353			0.796765	+	0.604290i	$0.206543\pi$
$500$	11.1803			0.500000
$501$		0			0
$502$	−10.9721	+	7.97172i	−0.489710	+	0.355795i
$503$	−7.38197	+	22.7194i	−0.329146	+	1.01301i	0.640389	+	0.768051i	$0.278773\pi$
$503$	−7.38197	+	22.7194i	−0.329146	+	1.01301i	−0.969534	+	0.244955i	$0.921227\pi$
$504$		0			0
$505$	7.92705	−	5.75934i	0.352749	−	0.256287i
$506$	−5.00000	−	15.3884i	−0.222277	−	0.684099i
$507$		0			0
$508$	4.20820	+	12.9515i	0.186709	+	0.574631i
$509$	−14.1631	−	10.2901i	−0.627769	−	0.456101i	0.227857	−	0.973694i	$-0.426828\pi$
$509$	−14.1631	−	10.2901i	−0.627769	−	0.456101i	−0.855627	+	0.517593i	$0.826828\pi$
$510$		0			0
$511$	−7.47214	+	5.42882i	−0.330548	+	0.240157i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	17.7984	−	12.9313i	0.785053	−	0.570374i
$515$	9.89919	+	30.4666i	0.436210	+	1.34252i
$516$		0			0
$517$	1.90983	+	5.87785i	0.0839942	+	0.258508i
$518$	−20.9443			−0.920238
$519$		0			0
$520$	4.47214	+	13.7638i	0.196116	+	0.603583i
$521$	−4.38197	+	13.4863i	−0.191977	+	0.590846i	0.808021	+	0.589153i	$0.200539\pi$
$521$	−4.38197	+	13.4863i	−0.191977	+	0.590846i	−0.999999	+	0.00169226i	$0.999461\pi$
$522$		0			0
$523$	−8.94427	+	6.49839i	−0.391106	+	0.284155i	−0.765908	−	0.642950i	$-0.777710\pi$
$523$	−8.94427	+	6.49839i	−0.391106	+	0.284155i	0.374803	+	0.927105i	$0.377710\pi$
$524$	17.8885			0.781465
$525$		0			0
$526$	−11.7082			−0.510502
$527$	6.61803	−	4.80828i	0.288286	−	0.209452i
$528$		0			0
$529$	−0.927051	+	2.85317i	−0.0403066	+	0.124051i
$530$	3.78115	+	2.74717i	0.164243	+	0.119329i
$531$		0			0
$532$	−14.9443			−0.647916
$533$	11.4164	+	35.1361i	0.494500	+	1.52191i
$534$		0			0
$535$	−21.0172	+	15.2699i	−0.908654	+	0.660176i
$536$	−1.23607	+	0.898056i	−0.0533900	+	0.0387901i
$537$		0			0
$538$	7.35410	+	5.34307i	0.317058	+	0.230356i
$539$	−0.427051	+	0.310271i	−0.0183944	+	0.0133643i
$540$		0			0
$541$	21.1803	+	15.3884i	0.910614	+	0.661600i	0.941170	−	0.337933i	$-0.109728\pi$
$541$	21.1803	+	15.3884i	0.910614	+	0.661600i	−0.0305561	+	0.999533i	$0.509728\pi$
$542$	5.57295	+	17.1518i	0.239379	+	0.736732i
$543$		0			0
$544$	0.381966	+	1.17557i	0.0163767	+	0.0504022i
$545$	38.5410			1.65092
$546$		0			0
$547$	3.00000	−	9.23305i	0.128271	−	0.394777i	−0.866212	−	0.499677i	$-0.833452\pi$
$547$	3.00000	−	9.23305i	0.128271	−	0.394777i	0.994483	+	0.104900i	$0.0334522\pi$
$548$	−9.85410	+	7.15942i	−0.420946	+	0.305835i
$549$		0			0
$550$	−14.6353	−	10.6331i	−0.624049	−	0.453398i
$551$	48.3607			2.06023
$552$		0			0
$553$	−4.54508	+	13.9883i	−0.193277	+	0.594844i
$554$	−5.23607	+	16.1150i	−0.222459	+	0.684659i
$555$		0			0
$556$	3.23607	+	9.95959i	0.137240	+	0.422381i
$557$	18.3262			0.776508			0.388254	−	0.921552i	$-0.373078\pi$
$557$	18.3262			0.776508			0.388254	+	0.921552i	$0.373078\pi$
$558$		0			0
$559$	−40.3607	−	29.3238i	−1.70707	−	1.24026i
$560$	5.85410			0.247381
$561$		0			0
$562$	−4.76393	−	3.46120i	−0.200954	−	0.146002i
$563$	17.2082	+	12.5025i	0.725239	+	0.526917i	0.888054	−	0.459739i	$-0.152057\pi$
$563$	17.2082	+	12.5025i	0.725239	+	0.526917i	−0.162815	+	0.986657i	$0.552057\pi$
$564$		0			0
$565$	43.0132			1.80958
$566$	3.70820	+	2.69417i	0.155867	+	0.113244i
$567$		0			0
$568$	5.52786			0.231944
$569$	8.58359	+	26.4176i	0.359843	+	1.10748i	0.953148	+	0.302505i	$0.0978228\pi$
$569$	8.58359	+	26.4176i	0.359843	+	1.10748i	−0.593305	+	0.804978i	$0.702177\pi$
$570$		0			0
$571$	2.43769	−	7.50245i	0.102014	−	0.313968i	−0.887004	−	0.461762i	$-0.847217\pi$
$571$	2.43769	−	7.50245i	0.102014	−	0.313968i	0.989018	+	0.147794i	$0.0472174\pi$
$572$	7.23607	−	22.2703i	0.302555	−	0.931169i
$573$		0			0
$574$	14.9443			0.623762
$575$	−6.90983	−	21.2663i	−0.288160	−	0.886865i
$576$		0			0
$577$	−7.26393	+	5.27756i	−0.302401	+	0.219708i	−0.728629	−	0.684908i	$-0.759842\pi$
$577$	−7.26393	+	5.27756i	−0.302401	+	0.219708i	0.426228	+	0.904616i	$0.359842\pi$
$578$	4.78115	−	14.7149i	0.198870	−	0.612058i
$579$		0			0
$580$	−18.9443			−0.786618
$581$	−1.73607	−	5.34307i	−0.0720242	−	0.221668i
$582$		0			0
$583$	−2.33688	−	7.19218i	−0.0967837	−	0.297870i
$584$	2.85410	+	2.07363i	0.118104	+	0.0858073i
$585$		0			0
$586$	17.8713	−	12.9843i	0.738258	−	0.536376i
$587$	−0.781153	−	0.567541i	−0.0322416	−	0.0234249i	0.571548	−	0.820569i	$-0.306343\pi$
$587$	−0.781153	−	0.567541i	−0.0322416	−	0.0234249i	−0.603789	+	0.797144i	$0.706343\pi$
$588$		0			0
$589$	30.5623	−	22.2048i	1.25930	−	0.914933i
$590$	6.54508	−	4.75528i	0.269457	−	0.195772i
$591$		0			0
$592$	2.47214	+	7.60845i	0.101604	+	0.312705i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	5.85410	+	4.25325i	0.239995	+	0.174366i
$596$	−6.82624	+	21.0090i	−0.279614	+	0.860562i
$597$		0			0
$598$	23.4164	−	17.0130i	0.957568	−	0.695714i
$599$	−0.472136			−0.0192910			−0.00964548	−	0.999953i	$-0.503070\pi$
$599$	−0.472136			−0.0192910			−0.00964548	+	0.999953i	$0.503070\pi$
$600$		0			0
$601$	−7.72949			−0.315292			−0.157646	−	0.987496i	$-0.550391\pi$
$601$	−7.72949			−0.315292			−0.157646	+	0.987496i	$0.550391\pi$
$602$	−16.3262	+	11.8617i	−0.665408	+	0.483447i
$603$		0			0
$604$	5.66312	−	17.4293i	0.230429	−	0.709188i
$605$	1.44427	+	4.44501i	0.0587180	+	0.180715i
$606$		0			0
$607$	6.56231			0.266356			0.133178	−	0.991092i	$-0.457482\pi$
$607$	6.56231			0.266356			0.133178	+	0.991092i	$0.457482\pi$
$608$	1.76393	+	5.42882i	0.0715369	+	0.220168i
$609$		0			0
$610$	−1.90983	−	5.87785i	−0.0773268	−	0.237987i
$611$	−8.94427	+	6.49839i	−0.361847	+	0.262897i
$612$		0			0
$613$	−39.0344	−	28.3602i	−1.57659	−	1.14546i	−0.920481	−	0.390788i	$-0.872203\pi$
$613$	−39.0344	−	28.3602i	−1.57659	−	1.14546i	−0.656105	−	0.754669i	$-0.727797\pi$
$614$	8.09017	−	5.87785i	0.326493	−	0.237211i
$615$		0			0
$616$	−7.66312	−	5.56758i	−0.308756	−	0.224324i
$617$	−0.652476	−	2.00811i	−0.0262677	−	0.0808436i	0.937063	−	0.349160i	$-0.113533\pi$
$617$	−0.652476	−	2.00811i	−0.0262677	−	0.0808436i	−0.963331	+	0.268316i	$0.913533\pi$
$618$		0			0
$619$	−2.90983	−	8.95554i	−0.116956	−	0.359953i	0.875394	−	0.483410i	$-0.160602\pi$
$619$	−2.90983	−	8.95554i	−0.116956	−	0.359953i	−0.992350	+	0.123457i	$0.960602\pi$
$620$	−11.9721	+	8.69827i	−0.480813	+	0.349331i
$621$		0			0
$622$	−0.326238	+	1.00406i	−0.0130809	+	0.0402590i
$623$	7.47214	−	5.42882i	0.299365	−	0.217501i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	16.2705			0.650300
$627$		0			0
$628$	2.67376	−	8.22899i	0.106695	−	0.328373i
$629$	−3.05573	+	9.40456i	−0.121840	+	0.374985i
$630$		0			0
$631$	14.3607	+	44.1976i	0.571690	+	1.75948i	0.647184	+	0.762334i	$0.275946\pi$
$631$	14.3607	+	44.1976i	0.571690	+	1.75948i	−0.0754947	+	0.997146i	$0.524054\pi$
$632$	5.61803			0.223473
$633$		0			0
$634$	16.6353	+	12.0862i	0.660670	+	0.480005i
$635$	9.40983	−	28.9605i	0.373418	−	1.14926i
$636$		0			0
$637$	−0.763932	−	0.555029i	−0.0302681	−	0.0219911i
$638$	24.7984	+	18.0171i	0.981777	+	0.713303i
$639$		0			0
$640$	−0.690983	−	2.12663i	−0.0273135	−	0.0840623i
$641$	−11.1803	−	8.12299i	−0.441597	−	0.320839i	0.344672	−	0.938723i	$-0.387990\pi$
$641$	−11.1803	−	8.12299i	−0.441597	−	0.320839i	−0.786269	+	0.617884i	$0.787990\pi$
$642$		0			0
$643$	21.8885			0.863200			0.431600	−	0.902065i	$-0.357949\pi$
$643$	21.8885			0.863200			0.431600	+	0.902065i	$0.357949\pi$
$644$	−3.61803	−	11.1352i	−0.142571	−	0.438787i
$645$		0			0
$646$	−2.18034	+	6.71040i	−0.0857843	+	0.264017i
$647$	7.09017	−	21.8213i	0.278743	−	0.857884i	−0.709461	−	0.704744i	$-0.751062\pi$
$647$	7.09017	−	21.8213i	0.278743	−	0.857884i	0.988205	−	0.153139i	$-0.0489383\pi$
$648$		0			0
$649$	−13.0902			−0.513834
$650$	10.0000	−	30.7768i	0.392232	−	1.20717i
$651$		0			0
$652$	0.381966	−	0.277515i	0.0149589	−	0.0108683i
$653$	1.19098	−	3.66547i	0.0466068	−	0.143441i	−0.925045	−	0.379858i	$-0.875973\pi$
$653$	1.19098	−	3.66547i	0.0466068	−	0.143441i	0.971652	+	0.236417i	$0.0759730\pi$
$654$		0			0
$655$	−32.3607	−	23.5114i	−1.26444	−	0.918667i
$656$	−1.76393	−	5.42882i	−0.0688700	−	0.211960i
$657$		0			0
$658$	1.38197	+	4.25325i	0.0538746	+	0.165809i
$659$	−16.6803	−	12.1190i	−0.649774	−	0.472088i	0.213420	−	0.976960i	$-0.431540\pi$
$659$	−16.6803	−	12.1190i	−0.649774	−	0.472088i	−0.863194	+	0.504872i	$0.831540\pi$
$660$		0			0
$661$	24.6525	−	17.9111i	0.958870	−	0.696660i	0.00598211	−	0.999982i	$-0.498096\pi$
$661$	24.6525	−	17.9111i	0.958870	−	0.696660i	0.952888	+	0.303322i	$0.0980958\pi$
$662$	−14.5623	−	10.5801i	−0.565980	−	0.411209i
$663$		0			0
$664$	−1.73607	+	1.26133i	−0.0673725	+	0.0489490i
$665$	27.0344	+	19.6417i	1.04835	+	0.761671i
$666$		0			0
$667$	11.7082	+	36.0341i	0.453343	+	1.39525i
$668$	−11.7082			−0.453004
$669$		0			0
$670$	3.41641			0.131987
$671$	−3.09017	+	9.51057i	−0.119295	+	0.367151i
$672$		0			0
$673$	25.4443	−	18.4863i	0.980805	−	0.712596i	0.0229163	−	0.999737i	$-0.492705\pi$
$673$	25.4443	−	18.4863i	0.980805	−	0.712596i	0.957888	+	0.287141i	$0.0927049\pi$
$674$	−0.909830			−0.0350453
$675$		0			0
$676$	28.8885			1.11110
$677$	23.5344	−	17.0988i	0.904502	−	0.657159i	−0.0351163	−	0.999383i	$-0.511180\pi$
$677$	23.5344	−	17.0988i	0.904502	−	0.657159i	0.939618	+	0.342224i	$0.111180\pi$
$678$		0			0
$679$	−2.73607	+	8.42075i	−0.105001	+	0.323159i
$680$	0.854102	−	2.62866i	0.0327533	−	0.100804i
$681$		0			0
$682$	23.9443			0.916874
$683$	−10.3541	−	31.8666i	−0.396189	−	1.21934i	−0.928032	−	0.372501i	$-0.878500\pi$
$683$	−10.3541	−	31.8666i	−0.396189	−	1.21934i	0.531843	−	0.846843i	$-0.321500\pi$
$684$		0			0
$685$	27.2361			1.04064
$686$	−15.1353	+	10.9964i	−0.577867	+	0.419845i
$687$		0			0
$688$	6.23607	+	4.53077i	0.237748	+	0.172734i
$689$	10.9443	−	7.95148i	0.416944	−	0.302927i
$690$		0			0
$691$	−9.09017	−	6.60440i	−0.345806	−	0.251243i	0.401301	−	0.915946i	$-0.368558\pi$
$691$	−9.09017	−	6.60440i	−0.345806	−	0.251243i	−0.747108	+	0.664703i	$0.768558\pi$
$692$	−1.57295	−	4.84104i	−0.0597945	−	0.184029i
$693$		0			0
$694$	6.35410	+	19.5559i	0.241198	+	0.742332i
$695$	7.23607	−	22.2703i	0.274480	−	0.844762i
$696$		0			0
$697$	2.18034	−	6.71040i	0.0825863	−	0.254174i
$698$	−22.5623	+	16.3925i	−0.853996	+	0.620464i
$699$		0			0
$700$	−10.5902	−	7.69421i	−0.400271	−	0.290814i
$701$	−40.8328			−1.54223			−0.771117	−	0.636693i	$-0.780302\pi$
$701$	−40.8328			−1.54223			−0.771117	+	0.636693i	$0.780302\pi$
$702$		0			0
$703$	−14.1115	+	43.4306i	−0.532224	+	1.63802i
$704$	−1.11803	+	3.44095i	−0.0421375	+	0.129686i
$705$		0			0
$706$	−4.09017	−	12.5882i	−0.153936	−	0.473765i
$707$	−11.4721			−0.431454
$708$		0			0
$709$	35.3607	+	25.6910i	1.32800	+	0.964847i	0.999795	+	0.0202400i	$0.00644302\pi$
$709$	35.3607	+	25.6910i	1.32800	+	0.964847i	0.328203	+	0.944607i	$0.393557\pi$
$710$	−10.0000	−	7.26543i	−0.375293	−	0.272667i
$711$		0			0
$712$	−2.85410	−	2.07363i	−0.106962	−	0.0777124i
$713$	23.9443	+	17.3965i	0.896720	+	0.651505i
$714$		0			0
$715$	−42.3607	+	30.7768i	−1.58420	+	1.15099i
$716$	7.97214	+	5.79210i	0.297933	+	0.216461i
$717$		0			0
$718$	22.1803			0.827763
$719$	5.12461	+	15.7719i	0.191116	+	0.588194i	1.00000		0.000225882i	$7.19006e-5\pi$
$719$	5.12461	+	15.7719i	0.191116	+	0.588194i	−0.808884	+	0.587968i	$0.799928\pi$
$720$		0			0
$721$	11.5902	−	35.6709i	0.431640	−	1.32845i
$722$	−4.19756	+	12.9188i	−0.156217	+	0.480787i
$723$		0			0
$724$	−6.65248			−0.247237
$725$	34.2705	+	24.8990i	1.27277	+	0.924725i
$726$		0			0
$727$	6.94427	−	5.04531i	0.257549	−	0.187120i	−0.451517	−	0.892263i	$-0.649117\pi$
$727$	6.94427	−	5.04531i	0.257549	−	0.187120i	0.709066	+	0.705142i	$0.249117\pi$
$728$	5.23607	−	16.1150i	0.194062	−	0.597260i
$729$		0			0
$730$	−2.43769	−	7.50245i	−0.0902231	−	0.277678i
$731$	2.94427	+	9.06154i	0.108898	+	0.335153i
$732$		0			0
$733$	−11.0902	−	34.1320i	−0.409625	−	1.26070i	−0.916971	−	0.398953i	$-0.869374\pi$
$733$	−11.0902	−	34.1320i	−0.409625	−	1.26070i	0.507346	−	0.861742i	$-0.330626\pi$
$734$	−24.7705	−	17.9968i	−0.914296	−	0.664275i
$735$		0			0
$736$	−3.61803	+	2.62866i	−0.133363	+	0.0968935i
$737$	−4.47214	−	3.24920i	−0.164733	−	0.119686i
$738$		0			0
$739$	38.9787	−	28.3197i	1.43386	−	1.04176i	0.444573	−	0.895743i	$-0.353356\pi$
$739$	38.9787	−	28.3197i	1.43386	−	1.04176i	0.989283	−	0.146014i	$-0.0466444\pi$
$740$	5.52786	−	17.0130i	0.203208	−	0.625411i
$741$		0			0
$742$	−1.69098	−	5.20431i	−0.0620779	−	0.191056i
$743$	39.0132			1.43125			0.715627	−	0.698483i	$-0.246141\pi$
$743$	39.0132			1.43125			0.715627	+	0.698483i	$0.246141\pi$
$744$		0			0
$745$	39.9615	−	29.0337i	1.46408	−	1.06371i
$746$	3.56231	−	10.9637i	0.130425	−	0.401408i
$747$		0			0
$748$	−3.61803	+	2.62866i	−0.132288	+	0.0961132i
$749$	30.4164			1.11139
$750$		0			0
$751$	24.7984			0.904906			0.452453	−	0.891788i	$-0.350549\pi$
$751$	24.7984			0.904906			0.452453	+	0.891788i	$0.350549\pi$
$752$	1.38197	−	1.00406i	0.0503951	−	0.0366142i
$753$		0			0
$754$	−16.9443	+	52.1491i	−0.617074	+	1.89916i
$755$	−33.1525	+	24.0867i	−1.20654	+	0.876604i
$756$		0			0
$757$	−17.1246			−0.622405			−0.311202	−	0.950344i	$-0.600732\pi$
$757$	−17.1246			−0.622405			−0.311202	+	0.950344i	$0.600732\pi$
$758$	6.23607	+	19.1926i	0.226504	+	0.697108i
$759$		0			0
$760$	3.94427	−	12.1392i	0.143074	−	0.440336i
$761$	1.14590	−	0.832544i	0.0415388	−	0.0301797i	−0.566822	−	0.823840i	$-0.691827\pi$
$761$	1.14590	−	0.832544i	0.0415388	−	0.0301797i	0.608361	+	0.793661i	$0.291827\pi$
$762$		0			0
$763$	−36.5066	−	26.5236i	−1.32163	−	0.960218i
$764$	3.47214	−	2.52265i	0.125617	−	0.0912664i
$765$		0			0
$766$	16.1803	+	11.7557i	0.584619	+	0.424751i
$767$	−7.23607	−	22.2703i	−0.261279	−	0.804135i
$768$		0			0
$769$	7.62868	+	23.4787i	0.275097	+	0.846662i	0.989194	+	0.146615i	$0.0468377\pi$
$769$	7.62868	+	23.4787i	0.275097	+	0.846662i	−0.714097	+	0.700047i	$0.753162\pi$
$770$	6.54508	+	20.1437i	0.235868	+	0.725929i
$771$		0			0
$772$	5.51722	−	16.9803i	0.198569	−	0.611133i
$773$	−0.927051	+	0.673542i	−0.0333437	+	0.0242256i	−0.604332	−	0.796732i	$-0.706560\pi$
$773$	−0.927051	+	0.673542i	−0.0333437	+	0.0242256i	0.570989	+	0.820958i	$0.306560\pi$
$774$		0			0
$775$	33.0902			1.18863
$776$	3.38197			0.121406
$777$		0			0
$778$	−3.82624	+	11.7759i	−0.137177	+	0.422188i
$779$	10.0689	−	30.9888i	0.360755	−	1.11029i
$780$		0			0
$781$	6.18034	+	19.0211i	0.221150	+	0.680630i
$782$	−5.52786			−0.197676
$783$		0			0
$784$	0.118034	+	0.0857567i	0.00421550	+	0.00306274i
$785$	−15.6525	+	11.3722i	−0.558661	+	0.405891i
$786$		0			0
$787$	−22.7082	−	16.4985i	−0.809460	−	0.588107i	0.104214	−	0.994555i	$-0.466767\pi$
$787$	−22.7082	−	16.4985i	−0.809460	−	0.588107i	−0.913674	+	0.406448i	$0.866767\pi$
$788$	−13.8262	−	10.0453i	−0.492539	−	0.357851i
$789$		0			0
$790$	−10.1631	−	7.38394i	−0.361588	−	0.262709i
$791$	−40.7426	−	29.6013i	−1.44864	−	1.05250i
$792$		0			0
$793$	−17.8885			−0.635241
$794$	9.50658	+	29.2582i	0.337376	+	1.03834i
$795$		0			0
$796$	6.02786	−	18.5519i	0.213652	−	0.657553i
$797$	−0.465558	+	1.43284i	−0.0164909	+	0.0507538i	−0.958963	−	0.283530i	$-0.908494\pi$
$797$	−0.465558	+	1.43284i	−0.0164909	+	0.0507538i	0.942472	+	0.334284i	$0.108494\pi$
$798$		0			0
$799$	2.11146			0.0746979
$800$	−1.54508	+	4.75528i	−0.0546270	+	0.168125i
$801$		0			0
$802$	−20.7984	+	15.1109i	−0.734416	+	0.533585i
$803$	−3.94427	+	12.1392i	−0.139190	+	0.428384i
$804$		0			0
$805$	−8.09017	+	24.8990i	−0.285141	+	0.877574i
$806$	13.2361	+	40.7364i	0.466221	+	1.43488i
$807$		0			0
$808$	1.35410	+	4.16750i	0.0476371	+	0.146612i
$809$	−24.9443	−	18.1231i	−0.876994	−	0.637173i	0.0554606	−	0.998461i	$-0.482337\pi$
$809$	−24.9443	−	18.1231i	−0.876994	−	0.637173i	−0.932454	+	0.361288i	$0.882337\pi$
$810$		0			0
$811$	4.61803	−	3.35520i	0.162161	−	0.117817i	−0.503745	−	0.863852i	$-0.668045\pi$
$811$	4.61803	−	3.35520i	0.162161	−	0.117817i	0.665906	+	0.746035i	$0.268045\pi$
$812$	17.9443	+	13.0373i	0.629720	+	0.457519i
$813$		0			0
$814$	−23.4164	+	17.0130i	−0.820745	+	0.596306i
$815$	−1.05573			−0.0369805
$816$		0			0
$817$	13.5967	+	41.8465i	0.475690	+	1.46402i
$818$	−5.79837			−0.202735
$819$		0			0
$820$	−3.94427	+	12.1392i	−0.137740	+	0.423920i
$821$	13.9336	−	42.8833i	0.486287	−	1.49664i	−0.343821	−	0.939035i	$-0.611721\pi$
$821$	13.9336	−	42.8833i	0.486287	−	1.49664i	0.830108	−	0.557602i	$-0.188279\pi$
$822$		0			0
$823$	−2.39919	+	1.74311i	−0.0836304	+	0.0607610i	−0.628815	−	0.777555i	$-0.716460\pi$
$823$	−2.39919	+	1.74311i	−0.0836304	+	0.0607610i	0.545184	+	0.838316i	$0.316460\pi$
$824$	−14.3262			−0.499078
$825$		0			0
$826$	−9.47214			−0.329578
$827$	35.6803	−	25.9233i	1.24073	−	0.901441i	0.243080	−	0.970006i	$-0.421842\pi$
$827$	35.6803	−	25.9233i	1.24073	−	0.901441i	0.997647	+	0.0685652i	$0.0218421\pi$
$828$		0			0
$829$	8.00000	−	24.6215i	0.277851	−	0.855139i	−0.710599	−	0.703597i	$-0.751576\pi$
$829$	8.00000	−	24.6215i	0.277851	−	0.855139i	0.988451	−	0.151542i	$-0.0484239\pi$
$830$	4.79837			0.166554
$831$		0			0
$832$	−6.47214			−0.224381
$833$	0.0557281	+	0.171513i	0.00193086	+	0.00594259i
$834$		0			0
$835$	21.1803	+	15.3884i	0.732976	+	0.532538i
$836$	−16.7082	+	12.1392i	−0.577865	+	0.419844i
$837$		0			0
$838$	2.50000	+	1.81636i	0.0863611	+	0.0627450i
$839$	5.14590	−	3.73871i	0.177656	−	0.129075i	−0.495403	−	0.868663i	$-0.664980\pi$
$839$	5.14590	−	3.73871i	0.177656	−	0.129075i	0.673060	+	0.739588i	$0.264980\pi$
$840$		0			0
$841$	−34.6074	−	25.1437i	−1.19336	−	0.867026i
$842$	7.03444	+	21.6498i	0.242423	+	0.746101i
$843$		0			0
$844$	−1.05573	−	3.24920i	−0.0363397	−	0.111842i
$845$	−52.2599	−	37.9690i	−1.79779	−	1.30617i
$846$		0			0
$847$	1.69098	−	5.20431i	0.0581029	−	0.178822i
$848$	−1.69098	+	1.22857i	−0.0580686	+	0.0421893i
$849$		0			0
$850$	−5.00000	+	3.63271i	−0.171499	+	0.124601i
$851$	−35.7771			−1.22642
$852$		0			0
$853$	−13.4721	+	41.4630i	−0.461277	+	1.41967i	0.402328	+	0.915496i	$0.368201\pi$
$853$	−13.4721	+	41.4630i	−0.461277	+	1.41967i	−0.863605	+	0.504169i	$0.831799\pi$
$854$	−2.23607	+	6.88191i	−0.0765167	+	0.235494i
$855$		0			0
$856$	−3.59017	−	11.0494i	−0.122709	−	0.377661i
$857$	16.0689			0.548903			0.274451	−	0.961601i	$-0.411504\pi$
$857$	16.0689			0.548903			0.274451	+	0.961601i	$0.411504\pi$
$858$		0			0
$859$	1.85410	+	1.34708i	0.0632611	+	0.0459619i	0.618966	−	0.785417i	$-0.287552\pi$
$859$	1.85410	+	1.34708i	0.0632611	+	0.0459619i	−0.555705	+	0.831379i	$0.687552\pi$
$860$	−5.32624	−	16.3925i	−0.181623	−	0.558979i
$861$		0			0
$862$	−13.6180	−	9.89408i	−0.463832	−	0.336994i
$863$	−8.23607	−	5.98385i	−0.280359	−	0.203693i	0.438715	−	0.898626i	$-0.355434\pi$
$863$	−8.23607	−	5.98385i	−0.280359	−	0.203693i	−0.719074	+	0.694934i	$0.755434\pi$
$864$		0			0
$865$	−3.51722	+	10.8249i	−0.119589	+	0.368057i
$866$	12.5451	+	9.11454i	0.426299	+	0.309725i
$867$		0			0
$868$	17.3262			0.588091
$869$	6.28115	+	19.3314i	0.213074	+	0.655773i
$870$		0			0
$871$	3.05573	−	9.40456i	0.103539	−	0.318661i
$872$	−5.32624	+	16.3925i	−0.180369	+	0.555119i
$873$		0			0
$874$	−25.5279			−0.863493
$875$	9.04508	+	27.8379i	0.305780	+	0.941093i
$876$		0			0
$877$	30.0344	−	21.8213i	1.01419	−	0.736853i	0.0491070	−	0.998794i	$-0.484362\pi$
$877$	30.0344	−	21.8213i	1.01419	−	0.736853i	0.965084	+	0.261941i	$0.0843625\pi$
$878$	7.26393	−	22.3561i	0.245146	−	0.754481i
$879$		0			0
$880$	6.54508	−	4.75528i	0.220635	−	0.160301i
$881$	7.29180	+	22.4418i	0.245667	+	0.756085i	0.995526	+	0.0944874i	$0.0301212\pi$
$881$	7.29180	+	22.4418i	0.245667	+	0.756085i	−0.749859	+	0.661597i	$0.769879\pi$
$882$		0			0
$883$	−9.29180	−	28.5972i	−0.312694	−	0.962373i	−0.976693	−	0.214640i	$-0.931142\pi$
$883$	−9.29180	−	28.5972i	−0.312694	−	0.962373i	0.663999	−	0.747733i	$-0.268858\pi$
$884$	−6.47214	−	4.70228i	−0.217681	−	0.158155i
$885$		0			0
$886$	−13.4443	+	9.76784i	−0.451669	+	0.328157i
$887$	18.9443	+	13.7638i	0.636086	+	0.462144i	0.858503	−	0.512808i	$-0.171395\pi$
$887$	18.9443	+	13.7638i	0.636086	+	0.462144i	−0.222417	+	0.974952i	$0.571395\pi$
$888$		0			0
$889$	−28.8435	+	20.9560i	−0.967379	+	0.702842i
$890$	2.43769	+	7.50245i	0.0817117	+	0.251483i
$891$		0			0
$892$	−2.50000	−	7.69421i	−0.0837062	−	0.257621i
$893$	9.75078			0.326297
$894$		0			0
$895$	−6.80902	−	20.9560i	−0.227600	−	0.700482i
$896$	−0.809017	+	2.48990i	−0.0270274	+	0.0831817i
$897$		0			0
$898$	22.4164	−	16.2865i	0.748045	−	0.543487i
$899$	−56.0689			−1.87000
$900$		0			0
$901$	−2.58359			−0.0860719
$902$	16.7082	−	12.1392i	0.556322	−	0.404192i
$903$		0			0
$904$	−5.94427	+	18.2946i	−0.197704	+	0.608469i
$905$	12.0344	+	8.74353i	0.400038	+	0.290645i
$906$		0			0
$907$	30.4721			1.01181			0.505905	−	0.862589i	$-0.331159\pi$
$907$	30.4721			1.01181			0.505905	+	0.862589i	$0.331159\pi$
$908$	6.88197	+	21.1805i	0.228386	+	0.702900i
$909$		0			0
$910$	−30.6525	+	22.2703i	−1.01612	+	0.738254i
$911$	14.7082	−	10.6861i	0.487305	−	0.354047i	−0.316842	−	0.948478i	$-0.602623\pi$
$911$	14.7082	−	10.6861i	0.487305	−	0.354047i	0.804147	+	0.594431i	$0.202623\pi$
$912$		0			0
$913$	−6.28115	−	4.56352i	−0.207876	−	0.151031i
$914$	−3.30902	+	2.40414i	−0.109453	+	0.0795219i
$915$		0			0
$916$	4.47214	+	3.24920i	0.147764	+	0.107356i
$917$	14.4721	+	44.5407i	0.477912	+	1.47086i
$918$		0			0
$919$	−12.5836	−	38.7283i	−0.415094	−	1.27753i	−0.912166	−	0.409820i	$-0.865592\pi$
$919$	−12.5836	−	38.7283i	−0.415094	−	1.27753i	0.497072	−	0.867709i	$-0.334408\pi$
$920$	10.0000			0.329690
$921$		0			0
$922$	2.33688	−	7.19218i	0.0769611	−	0.236862i
$923$	−28.9443	+	21.0292i	−0.952712	+	0.692186i
$924$		0			0
$925$	−32.3607	+	23.5114i	−1.06401	+	0.773050i
$926$	22.8328			0.750333
$927$		0			0
$928$	2.61803	−	8.05748i	0.0859412	−	0.264500i
$929$	5.87539	−	18.0826i	0.192765	−	0.593270i	−0.807230	−	0.590237i	$-0.799034\pi$
$929$	5.87539	−	18.0826i	0.192765	−	0.593270i	0.999995	−	0.00303360i	$-0.000965627\pi$
$930$		0			0
$931$	0.257354	+	0.792055i	0.00843444	+	0.0259585i
$932$	−18.6525			−0.610982
$933$		0			0
$934$	−8.63525	−	6.27388i	−0.282554	−	0.205288i
$935$	10.0000			0.327035
$936$		0			0
$937$	7.02786	+	5.10604i	0.229590	+	0.166807i	0.696633	−	0.717428i	$-0.254681\pi$
$937$	7.02786	+	5.10604i	0.229590	+	0.166807i	−0.467043	+	0.884235i	$0.654681\pi$
$938$	−3.23607	−	2.35114i	−0.105661	−	0.0767675i
$939$		0			0
$940$	−3.81966			−0.124584
$941$	−3.59017	−	2.60841i	−0.117036	−	0.0850318i	0.527728	−	0.849414i	$-0.323044\pi$
$941$	−3.59017	−	2.60841i	−0.117036	−	0.0850318i	−0.644764	+	0.764382i	$0.723044\pi$
$942$		0			0
$943$	25.5279			0.831302
$944$	1.11803	+	3.44095i	0.0363889	+	0.111994i
$945$		0			0
$946$	−8.61803	+	26.5236i	−0.280196	+	0.862356i
$947$	10.3713	−	31.9196i	0.337023	−	1.03725i	−0.628694	−	0.777652i	$-0.716410\pi$
$947$	10.3713	−	31.9196i	0.337023	−	1.03725i	0.965717	−	0.259597i	$-0.0835897\pi$
$948$		0			0
$949$	−22.8328			−0.741185
$950$	−23.0902	+	16.7760i	−0.749144	+	0.544285i
$951$		0			0
$952$	−2.61803	+	1.90211i	−0.0848510	+	0.0616478i
$953$	−1.63932	+	5.04531i	−0.0531028	+	0.163434i	−0.974091	−	0.226157i	$-0.927384\pi$
$953$	−1.63932	+	5.04531i	−0.0531028	+	0.163434i	0.920988	+	0.389591i	$0.127384\pi$
$954$		0			0
$955$	−9.59675			−0.310543
$956$	−3.79837	−	11.6902i	−0.122848	−	0.378088i
$957$		0			0
$958$	−9.00000	−	27.6992i	−0.290777	−	0.894919i
$959$	−25.7984	−	18.7436i	−0.833073	−	0.605263i
$960$		0			0
$961$	−10.3541	+	7.52270i	−0.334003	+	0.242668i
$962$	−41.8885	−	30.4338i	−1.35054	−	0.981225i
$963$		0			0
$964$	−7.73607	+	5.62058i	−0.249162	+	0.181027i
$965$	−32.2984	+	23.4661i	−1.03972	+	0.755402i
$966$		0			0
$967$	3.37132	+	10.3759i	0.108414	+	0.333665i	0.990517	−	0.137393i	$-0.0438722\pi$
$967$	3.37132	+	10.3759i	0.108414	+	0.333665i	−0.882102	+	0.471058i	$0.843872\pi$
$968$	−2.09017			−0.0671806
$969$		0			0
$970$	−6.11803	−	4.44501i	−0.196438	−	0.142721i
$971$	4.39261	−	13.5191i	0.140966	−	0.433847i	−0.855505	−	0.517795i	$-0.826753\pi$
$971$	4.39261	−	13.5191i	0.140966	−	0.433847i	0.996470	+	0.0839479i	$0.0267529\pi$
$972$		0			0
$973$	−22.1803	+	16.1150i	−0.711069	+	0.516622i
$974$	−17.7984			−0.570297
$975$		0			0
$976$	2.76393			0.0884713
$977$	−0.618034	+	0.449028i	−0.0197727	+	0.0143657i	−0.597628	−	0.801774i	$-0.703890\pi$
$977$	−0.618034	+	0.449028i	−0.0197727	+	0.0143657i	0.577855	+	0.816139i	$0.303890\pi$
$978$		0			0
$979$	3.94427	−	12.1392i	0.126059	−	0.387971i
$980$	−0.100813	−	0.310271i	−0.00322036	−	0.00991123i
$981$		0			0
$982$	−25.2705			−0.806414
$983$	−12.4164	−	38.2138i	−0.396022	−	1.21883i	−0.928163	−	0.372174i	$-0.878612\pi$
$983$	−12.4164	−	38.2138i	−0.396022	−	1.21883i	0.532141	−	0.846656i	$-0.321388\pi$
$984$		0			0
$985$	11.8090	+	36.3444i	0.376267	+	1.15803i
$986$	8.47214	−	6.15537i	0.269808	−	0.196027i
$987$		0			0
$988$	−29.8885	−	21.7153i	−0.950881	−	0.690856i
$989$	−27.8885	+	20.2622i	−0.886804	+	0.644301i
$990$		0			0
$991$	−23.8262	−	17.3108i	−0.756865	−	0.549895i	0.141082	−	0.989998i	$-0.454942\pi$
$991$	−23.8262	−	17.3108i	−0.756865	−	0.549895i	−0.897947	+	0.440103i	$0.854942\pi$
$992$	−2.04508	−	6.29412i	−0.0649315	−	0.199839i
$993$		0			0
$994$	4.47214	+	13.7638i	0.141848	+	0.436562i
$995$	−35.2877	+	25.6380i	−1.11870	+	0.812780i
$996$		0			0
$997$	−1.72949	+	5.32282i	−0.0547735	+	0.168576i	−0.974701	−	0.223513i	$-0.928247\pi$
$997$	−1.72949	+	5.32282i	−0.0547735	+	0.168576i	0.919927	+	0.392089i	$0.128247\pi$
$998$	28.7984	−	20.9232i	0.911597	−	0.662314i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.c.361.1		4
3.2	odd	2		150.2.g.a.61.1	✓	4
15.2	even	4		750.2.h.b.199.1		8
15.8	even	4		750.2.h.b.199.2		8
15.14	odd	2		750.2.g.b.301.1		4
25.16	even	5	inner	450.2.h.c.91.1		4
75.29	odd	10		3750.2.a.d.1.1		2
75.38	even	20		750.2.h.b.49.1		8
75.41	odd	10		150.2.g.a.91.1	yes	4
75.47	even	20		3750.2.c.b.1249.4		4
75.53	even	20		3750.2.c.b.1249.1		4
75.59	odd	10		750.2.g.b.451.1		4
75.62	even	20		750.2.h.b.49.2		8
75.71	odd	10		3750.2.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.61.1	✓	4	3.2	odd	2
150.2.g.a.91.1	yes	4	75.41	odd	10
450.2.h.c.91.1		4	25.16	even	5	inner
450.2.h.c.361.1		4	1.1	even	1	trivial
750.2.g.b.301.1		4	15.14	odd	2
750.2.g.b.451.1		4	75.59	odd	10
750.2.h.b.49.1		8	75.38	even	20
750.2.h.b.49.2		8	75.62	even	20
750.2.h.b.199.1		8	15.2	even	4
750.2.h.b.199.2		8	15.8	even	4
3750.2.a.d.1.1		2	75.29	odd	10
3750.2.a.f.1.2		2	75.71	odd	10
3750.2.c.b.1249.1		4	75.53	even	20
3750.2.c.b.1249.4		4	75.47	even	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.690983 + 2.12663i) q^{10} +(2.92705 - 2.12663i) q^{11} +(5.23607 + 3.80423i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.381966 - 1.17557i) q^{17} +(-1.76393 - 5.42882i) q^{19} +(0.690983 + 2.12663i) q^{20} +(1.11803 - 3.44095i) q^{22} +(3.61803 - 2.62866i) q^{23} +(1.54508 - 4.75528i) q^{25} +6.47214 q^{26} +(0.809017 - 2.48990i) q^{28} +(-2.61803 + 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000 q^{32} +(-1.00000 - 0.726543i) q^{34} +(-4.73607 + 3.44095i) q^{35} +(-6.47214 - 4.70228i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(1.80902 + 1.31433i) q^{40} +(4.61803 + 3.35520i) q^{41} -7.70820 q^{43} +(-1.11803 - 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-0.527864 + 1.62460i) q^{47} -0.145898 q^{49} +(-1.54508 - 4.75528i) q^{50} +(5.23607 - 3.80423i) q^{52} +(0.645898 - 1.98787i) q^{53} +(-2.50000 + 7.69421i) q^{55} +(-0.809017 - 2.48990i) q^{56} +(2.61803 + 8.05748i) q^{58} +(-2.92705 - 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(5.35410 + 3.88998i) q^{62} +(-0.809017 + 0.587785i) q^{64} -14.4721 q^{65} +(-0.472136 - 1.45309i) q^{67} -1.23607 q^{68} +(-1.80902 + 5.56758i) q^{70} +(-1.70820 + 5.25731i) q^{71} +(-2.85410 + 2.07363i) q^{73} -8.00000 q^{74} -5.70820 q^{76} +(7.66312 - 5.56758i) q^{77} +(-1.73607 + 5.34307i) q^{79} +2.23607 q^{80} +5.70820 q^{82} +(-0.663119 - 2.04087i) q^{83} +(2.23607 + 1.62460i) q^{85} +(-6.23607 + 4.53077i) q^{86} +(-2.92705 - 2.12663i) q^{88} +(2.85410 - 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(-1.38197 - 4.25325i) q^{92} +(0.527864 + 1.62460i) q^{94} +(10.3262 + 7.50245i) q^{95} +(-1.04508 + 3.21644i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - 5 q^{5} + 6 q^{7} + q^{8} - 5 q^{10} + 5 q^{11} + 12 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} - 16 q^{19} + 5 q^{20} + 10 q^{23} - 5 q^{25} + 8 q^{26} + q^{28} - 6 q^{29} - 3 q^{31}+ \cdots + 4 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - 5 * q^5 + 6 * q^7 + q^8 - 5 * q^10 + 5 * q^11 + 12 * q^13 + 4 * q^14 - q^16 - 6 * q^17 - 16 * q^19 + 5 * q^20 + 10 * q^23 - 5 * q^25 + 8 * q^26 + q^28 - 6 * q^29 - 3 * q^31 - 4 * q^32 - 4 * q^34 - 10 * q^35 - 8 * q^37 - 14 * q^38 + 5 * q^40 + 14 * q^41 - 4 * q^43 + 10 * q^46 - 20 * q^47 - 14 * q^49 + 5 * q^50 + 12 * q^52 + 16 * q^53 - 10 * q^55 - q^56 + 6 * q^58 - 5 * q^59 + 8 * q^62 - q^64 - 40 * q^65 + 16 * q^67 + 4 * q^68 - 5 * q^70 + 20 * q^71 + 2 * q^73 - 32 * q^74 + 4 * q^76 + 15 * q^77 + 2 * q^79 - 4 * q^82 + 13 * q^83 - 16 * q^86 - 5 * q^88 - 2 * q^89 + 28 * q^91 - 10 * q^92 + 20 * q^94 + 10 * q^95 + 7 * q^97 + 4 * q^98

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