LMFDB - Embedded newform 225.2.k.c.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Root			$0.409850 - 0.236627i$ of defining polynomial
Character	$\chi$	$=$	225.49
Dual form			225.2.k.c.124.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409850 - 0.236627i) q^{2} +(-1.64411 - 0.544899i) q^{3} +(-0.888015 + 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(2.21967 - 1.28153i) q^{7} +1.78702i q^{8} +(2.40617 + 1.79175i) q^{9} +O(q^{10})$	\(q+(0.409850 - 0.236627i) q^{2} +(-1.64411 - 0.544899i) q^{3} +(-0.888015 + 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(2.21967 - 1.28153i) q^{7} +1.78702i q^{8} +(2.40617 + 1.79175i) q^{9} +(3.08430 + 5.34217i) q^{11} +(2.29809 - 2.04490i) q^{12} +(1.84662 + 1.06615i) q^{13} +(0.606488 - 1.05047i) q^{14} +(-1.35317 - 2.34376i) q^{16} +3.16860i q^{17} +(1.41015 + 0.164982i) q^{18} -0.356267 q^{19} +(-4.34768 + 0.897469i) q^{21} +(2.52821 + 1.45966i) q^{22} +(-3.64854 - 2.10649i) q^{23} +(0.973748 - 2.93806i) q^{24} +1.00912 q^{26} +(-2.97968 - 4.25694i) q^{27} +4.55206i q^{28} +(0.843116 + 1.46032i) q^{29} +(4.12920 - 7.15199i) q^{31} +(-4.20441 - 2.42742i) q^{32} +(-2.15998 - 10.4637i) q^{33} +(0.749778 + 1.29865i) q^{34} +(-4.89257 + 2.10980i) q^{36} +3.63274i q^{37} +(-0.146016 + 0.0843024i) q^{38} +(-2.45510 - 2.75908i) q^{39} +(1.36677 - 2.36731i) q^{41} +(-1.56953 + 1.39661i) q^{42} +(6.64949 - 3.83908i) q^{43} -10.9556 q^{44} -1.99381 q^{46} +(-9.89770 + 5.71444i) q^{47} +(0.947643 + 4.59074i) q^{48} +(-0.215378 + 0.373046i) q^{49} +(1.72657 - 5.20952i) q^{51} +(-3.27966 + 1.89351i) q^{52} +9.43507i q^{53} +(-2.22853 - 1.03964i) q^{54} +(2.29012 + 3.96660i) q^{56} +(0.585740 + 0.194129i) q^{57} +(0.691103 + 0.399008i) q^{58} +(5.10795 - 8.84723i) q^{59} +(0.00549659 + 0.00952038i) q^{61} -3.90833i q^{62} +(7.63707 + 0.893512i) q^{63} +3.11511 q^{64} +(-3.36127 - 3.77745i) q^{66} +(-0.851145 - 0.491409i) q^{67} +(-4.87359 - 2.81377i) q^{68} +(4.85077 + 5.45138i) q^{69} -6.43507 q^{71} +(-3.20189 + 4.29988i) q^{72} -6.61467i q^{73} +(0.859605 + 1.48888i) q^{74} +(0.316370 - 0.547969i) q^{76} +(13.6923 + 7.90523i) q^{77} +(-1.65910 - 0.549868i) q^{78} +(-4.73569 - 8.20246i) q^{79} +(2.57930 + 8.62248i) q^{81} -1.29366i q^{82} +(9.02378 - 5.20988i) q^{83} +(2.48042 - 7.48407i) q^{84} +(1.81686 - 3.14690i) q^{86} +(-0.590444 - 2.86033i) q^{87} +(-9.54658 + 5.51172i) q^{88} +6.26940 q^{89} +5.46519 q^{91} +(6.47993 - 3.74119i) q^{92} +(-10.6860 + 9.50863i) q^{93} +(-2.70439 + 4.68413i) q^{94} +(5.58980 + 6.28191i) q^{96} +(6.24126 - 3.60339i) q^{97} +0.203858i q^{98} +(-2.15045 + 18.3804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.409850	−	0.236627i	0.289808	−	0.167321i	−0.348047	−	0.937477i	$-0.613155\pi$
$2$	0.409850	−	0.236627i	0.289808	−	0.167321i	0.637855	+	0.770156i	$0.279822\pi$
$3$	−1.64411	−	0.544899i	−0.949225	−	0.314598i
$3$	−1.64411	−	0.544899i	−0.949225	−	0.314598i
$4$	−0.888015	+	1.53809i	−0.444008	+	0.769044i
$5$		0			0
$5$		0			0
$6$	−0.802776	+	0.165713i	−0.327732	+	0.0676521i
$7$	2.21967	−	1.28153i	0.838956	−	0.484372i	−0.0179531	−	0.999839i	$-0.505715\pi$
$7$	2.21967	−	1.28153i	0.838956	−	0.484372i	0.856909	+	0.515467i	$0.172382\pi$
$8$			1.78702i			0.631808i
$9$	2.40617	+	1.79175i	0.802056	+	0.597248i
$10$		0			0
$11$	3.08430	+	5.34217i	0.929952	+	1.61072i	0.783397	+	0.621522i	$0.213485\pi$
$11$	3.08430	+	5.34217i	0.929952	+	1.61072i	0.146555	+	0.989202i	$0.453181\pi$
$12$	2.29809	−	2.04490i	0.663403	−	0.590312i
$13$	1.84662	+	1.06615i	0.512161	+	0.295696i	0.733722	−	0.679450i	$-0.237782\pi$
$13$	1.84662	+	1.06615i	0.512161	+	0.295696i	−0.221560	+	0.975147i	$0.571115\pi$
$14$	0.606488	−	1.05047i	0.162091	−	0.280750i
$15$		0			0
$16$	−1.35317	−	2.34376i	−0.338293	−	0.585941i
$17$			3.16860i			0.768500i	0.923229	+	0.384250i	$0.125540\pi$
$17$			3.16860i			0.768500i	−0.923229	+	0.384250i	$0.874460\pi$
$18$	1.41015	+	0.164982i	0.332374	+	0.0388867i
$19$	−0.356267			−0.0817332			−0.0408666	−	0.999165i	$-0.513012\pi$
$19$	−0.356267			−0.0817332			−0.0408666	+	0.999165i	$0.513012\pi$
$20$		0			0
$21$	−4.34768	+	0.897469i	−0.948740	+	0.195844i
$22$	2.52821	+	1.45966i	0.539015	+	0.311201i
$23$	−3.64854	−	2.10649i	−0.760774	−	0.439233i	0.0687995	−	0.997631i	$-0.478083\pi$
$23$	−3.64854	−	2.10649i	−0.760774	−	0.439233i	−0.829574	+	0.558397i	$0.811416\pi$
$24$	0.973748	−	2.93806i	0.198766	−	0.599728i
$25$		0			0
$26$	1.00912			0.197905
$27$	−2.97968	−	4.25694i	−0.573439	−	0.819248i
$28$			4.55206i			0.860259i
$29$	0.843116	+	1.46032i	0.156563	+	0.271174i	0.933627	−	0.358247i	$-0.116625\pi$
$29$	0.843116	+	1.46032i	0.156563	+	0.271174i	−0.777064	+	0.629421i	$0.783292\pi$
$30$		0			0
$31$	4.12920	−	7.15199i	0.741627	−	1.28453i	−0.210128	−	0.977674i	$-0.567388\pi$
$31$	4.12920	−	7.15199i	0.741627	−	1.28453i	0.951754	−	0.306861i	$-0.0992787\pi$
$32$	−4.20441	−	2.42742i	−0.743242	−	0.429111i
$33$	−2.15998	−	10.4637i	−0.376003	−	1.82150i
$34$	0.749778	+	1.29865i	0.128586	+	0.222717i
$35$		0			0
$36$	−4.89257	+	2.10980i	−0.815429	+	0.351634i
$37$			3.63274i			0.597219i	0.954375	+	0.298609i	$0.0965228\pi$
$37$			3.63274i			0.597219i	−0.954375	+	0.298609i	$0.903477\pi$
$38$	−0.146016	+	0.0843024i	−0.0236869	+	0.0136757i
$39$	−2.45510	−	2.75908i	−0.393131	−	0.441807i
$40$		0			0
$41$	1.36677	−	2.36731i	0.213453	−	0.369711i	−0.739340	−	0.673332i	$-0.764862\pi$
$41$	1.36677	−	2.36731i	0.213453	−	0.369711i	0.952793	+	0.303621i	$0.0981956\pi$
$42$	−1.56953	+	1.39661i	−0.242184	+	0.215501i
$43$	6.64949	−	3.83908i	1.01404	−	0.585455i	0.101666	−	0.994819i	$-0.467583\pi$
$43$	6.64949	−	3.83908i	1.01404	−	0.585455i	0.912371	+	0.409364i	$0.134249\pi$
$44$	−10.9556			−1.65162
$45$		0			0
$46$	−1.99381			−0.293971
$47$	−9.89770	+	5.71444i	−1.44373	+	0.833537i	−0.998096	−	0.0616792i	$-0.980354\pi$
$47$	−9.89770	+	5.71444i	−1.44373	+	0.833537i	−0.445632	+	0.895216i	$0.647021\pi$
$48$	0.947643	+	4.59074i	0.136780	+	0.662616i
$49$	−0.215378	+	0.373046i	−0.0307683	+	0.0532923i
$50$		0			0
$51$	1.72657	−	5.20952i	0.241768	−	0.729479i
$52$	−3.27966	+	1.89351i	−0.454807	+	0.262583i
$53$			9.43507i			1.29601i	0.761637	+	0.648003i	$0.224396\pi$
$53$			9.43507i			1.29601i	−0.761637	+	0.648003i	$0.775604\pi$
$54$	−2.22853	−	1.03964i	−0.303264	−	0.141477i
$55$		0			0
$56$	2.29012	+	3.96660i	0.306030	+	0.530059i
$57$	0.585740	+	0.194129i	0.0775832	+	0.0257131i
$58$	0.691103	+	0.399008i	0.0907462	+	0.0523924i
$59$	5.10795	−	8.84723i	0.664999	−	1.15181i	−0.314287	−	0.949328i	$-0.601765\pi$
$59$	5.10795	−	8.84723i	0.664999	−	1.15181i	0.979286	−	0.202484i	$-0.0649013\pi$
$60$		0			0
$61$	0.00549659	+	0.00952038i	0.000703767	+	0.00121896i	0.866377	−	0.499390i	$-0.166443\pi$
$61$	0.00549659	+	0.00952038i	0.000703767	+	0.00121896i	−0.865673	+	0.500609i	$0.833109\pi$
$62$		−	3.90833i		−	0.496358i
$63$	7.63707	+	0.893512i	0.962180	+	0.112572i
$64$	3.11511			0.389389
$65$		0			0
$66$	−3.36127	−	3.77745i	−0.413744	−	0.464972i
$67$	−0.851145	−	0.491409i	−0.103984	−	0.0600351i	0.447106	−	0.894481i	$-0.352455\pi$
$67$	−0.851145	−	0.491409i	−0.103984	−	0.0600351i	−0.551090	+	0.834446i	$0.685788\pi$
$68$	−4.87359	−	2.81377i	−0.591010	−	0.341220i
$69$	4.85077	+	5.45138i	0.583964	+	0.656269i
$70$		0			0
$71$	−6.43507			−0.763703			−0.381851	−	0.924224i	$-0.624713\pi$
$71$	−6.43507			−0.763703			−0.381851	+	0.924224i	$0.624713\pi$
$72$	−3.20189	+	4.29988i	−0.377346	+	0.506746i
$73$		−	6.61467i		−	0.774189i	−0.922040	−	0.387094i	$-0.873479\pi$
$73$		−	6.61467i		−	0.774189i	0.922040	−	0.387094i	$-0.126521\pi$
$74$	0.859605	+	1.48888i	0.0999271	+	0.173079i
$75$		0			0
$76$	0.316370	−	0.547969i	0.0362901	−	0.0628564i
$77$	13.6923	+	7.90523i	1.56038	+	0.900885i
$78$	−1.65910	−	0.549868i	−0.187856	−	0.0622603i
$79$	−4.73569	−	8.20246i	−0.532807	−	0.922848i	−0.999266	−	0.0383057i	$-0.987804\pi$
$79$	−4.73569	−	8.20246i	−0.532807	−	0.922848i	0.466459	−	0.884543i	$-0.345529\pi$
$80$		0			0
$81$	2.57930	+	8.62248i	0.286589	+	0.958054i
$82$		−	1.29366i		−	0.142860i
$83$	9.02378	−	5.20988i	0.990489	−	0.571859i	0.0850682	−	0.996375i	$-0.472889\pi$
$83$	9.02378	−	5.20988i	0.990489	−	0.571859i	0.905420	+	0.424516i	$0.139556\pi$
$84$	2.48042	−	7.48407i	0.270636	−	0.816579i
$85$		0			0
$86$	1.81686	−	3.14690i	0.195917	−	0.339339i
$87$	−0.590444	−	2.86033i	−0.0633023	−	0.306660i
$88$	−9.54658	+	5.51172i	−1.01767	+	0.587551i
$89$	6.26940			0.664555			0.332277	−	0.943182i	$-0.392183\pi$
$89$	6.26940			0.664555			0.332277	+	0.943182i	$0.392183\pi$
$90$		0			0
$91$	5.46519			0.572908
$92$	6.47993	−	3.74119i	0.675579	−	0.390046i
$93$	−10.6860	+	9.50863i	−1.10808	+	0.985999i
$94$	−2.70439	+	4.68413i	−0.278936	+	0.483131i
$95$		0			0
$96$	5.58980	+	6.28191i	0.570506	+	0.641145i
$97$	6.24126	−	3.60339i	0.633704	−	0.365869i	−0.148481	−	0.988915i	$-0.547438\pi$
$97$	6.24126	−	3.60339i	0.633704	−	0.365869i	0.782185	+	0.623046i	$0.214105\pi$
$98$			0.203858i			0.0205927i
$99$	−2.15045	+	18.3804i	−0.216128	+	1.84730i
$100$		0			0
$101$	−3.48547	−	6.03701i	−0.346817	−	0.600705i	0.638865	−	0.769319i	$-0.279404\pi$
$101$	−3.48547	−	6.03701i	−0.346817	−	0.600705i	−0.985682	+	0.168614i	$0.946071\pi$
$102$	−0.525079	−	2.54368i	−0.0519906	−	0.251862i
$103$	−5.29584	−	3.05756i	−0.521815	−	0.301270i	0.215862	−	0.976424i	$-0.430744\pi$
$103$	−5.29584	−	3.05756i	−0.521815	−	0.301270i	−0.737677	+	0.675154i	$0.764077\pi$
$104$	−1.90523	+	3.29996i	−0.186823	+	0.323588i
$105$		0			0
$106$	2.23260	+	3.86697i	0.216849	+	0.375593i
$107$		−	14.5349i		−	1.40514i	−0.711615	−	0.702570i	$-0.752036\pi$
$107$		−	14.5349i		−	1.40514i	0.711615	−	0.702570i	$-0.247964\pi$
$108$	9.19354	−	0.802776i	0.884649	−	0.0772471i
$109$	−1.90214			−0.182192			−0.0910958	−	0.995842i	$-0.529037\pi$
$109$	−1.90214			−0.182192			−0.0910958	+	0.995842i	$0.529037\pi$
$110$		0			0
$111$	1.97948	−	5.97261i	0.187884	−	0.566895i
$112$	−6.00719	−	3.46825i	−0.567626	−	0.327719i
$113$	−5.69780	−	3.28962i	−0.536004	−	0.309462i	0.207454	−	0.978245i	$-0.433482\pi$
$113$	−5.69780	−	3.28962i	−0.536004	−	0.309462i	−0.743458	+	0.668783i	$0.766816\pi$
$114$	0.286002	−	0.0590380i	0.0267866	−	0.00552942i
$115$		0			0
$116$	−2.99480			−0.278060
$117$	2.53302	+	5.87401i	0.234178	+	0.543053i
$118$		−	4.83472i		−	0.445072i
$119$	4.06065	+	7.03326i	0.372239	+	0.644737i
$120$		0			0
$121$	−13.5258	+	23.4274i	−1.22962	+	2.12977i
$122$	0.00450556	+	0.00260129i	0.000407914	+	0.000235509i
$123$	−3.53705	+	3.14736i	−0.318925	+	0.283788i
$124$	7.33359	+	12.7021i	0.658576	+	1.14069i
$125$		0			0
$126$	3.34149	−	1.44093i	0.297683	−	0.128368i
$127$		−	9.25840i		−	0.821550i	−0.911737	−	0.410775i	$-0.865258\pi$
$127$		−	9.25840i		−	0.821550i	0.911737	−	0.410775i	$-0.134742\pi$
$128$	9.68555	−	5.59196i	0.856090	−	0.494264i
$129$	−13.0244	+	2.68856i	−1.14673	+	0.236714i
$130$		0			0
$131$	−0.134698	+	0.233305i	−0.0117687	+	0.0203839i	−0.871850	−	0.489773i	$-0.837080\pi$
$131$	−0.134698	+	0.233305i	−0.0117687	+	0.0203839i	0.860081	+	0.510157i	$0.170413\pi$
$132$	18.0122	+	5.96972i	1.56776	+	0.519597i
$133$	−0.790794	+	0.456565i	−0.0685705	+	0.0395892i
$134$	−0.465123			−0.0401805
$135$		0			0
$136$	−5.66237			−0.485544
$137$	3.01046	−	1.73809i	0.257201	−	0.148495i	−0.365856	−	0.930671i	$-0.619224\pi$
$137$	3.01046	−	1.73809i	0.257201	−	0.148495i	0.623057	+	0.782176i	$0.285890\pi$
$138$	3.27804	+	1.08643i	0.279045	+	0.0924827i
$139$	7.37393	−	12.7720i	0.625448	−	1.08331i	−0.363006	−	0.931787i	$-0.618249\pi$
$139$	7.37393	−	12.7720i	0.625448	−	1.08331i	0.988454	−	0.151521i	$-0.0484172\pi$
$140$		0			0
$141$	19.3867	−	4.00189i	1.63265	−	0.337020i
$142$	−2.63742	+	1.52271i	−0.221327	+	0.127783i
$143$			13.1533i			1.09993i
$144$	0.943464	−	8.06403i	0.0786220	−	0.672002i
$145$		0			0
$146$	−1.56521	−	2.71103i	−0.129538	−	0.224366i
$147$	0.557378	−	0.495968i	0.0459717	−	0.0409068i
$148$	−5.58747	−	3.22593i	−0.459287	−	0.265170i
$149$	−5.07665	+	8.79301i	−0.415895	+	0.720352i	−0.995522	−	0.0945305i	$-0.969865\pi$
$149$	−5.07665	+	8.79301i	−0.415895	+	0.720352i	0.579627	+	0.814882i	$0.303198\pi$
$150$		0			0
$151$	5.15811	+	8.93410i	0.419761	+	0.727047i	0.995915	−	0.0902940i	$-0.0287807\pi$
$151$	5.15811	+	8.93410i	0.419761	+	0.727047i	−0.576155	+	0.817341i	$0.695447\pi$
$152$		−	0.636657i		−	0.0516397i
$153$	−5.67733	+	7.62420i	−0.458985	+	0.616380i
$154$	7.48237			0.602947
$155$		0			0
$156$	6.42388	−	1.32605i	0.514322	−	0.106169i
$157$	−0.920247	−	0.531305i	−0.0734437	−	0.0424028i	0.462828	−	0.886448i	$-0.346835\pi$
$157$	−0.920247	−	0.531305i	−0.0734437	−	0.0424028i	−0.536272	+	0.844045i	$0.680168\pi$
$158$	−3.88185	−	2.24119i	−0.308823	−	0.178299i
$159$	5.14117	−	15.5123i	0.407721	−	1.23020i
$160$		0			0
$161$	−10.7981			−0.851008
$162$	3.09744	+	2.92360i	0.243358	+	0.229699i
$163$			17.1386i			1.34240i	0.741278	+	0.671198i	$0.234220\pi$
$163$			17.1386i			1.34240i	−0.741278	+	0.671198i	$0.765780\pi$
$164$	2.42742	+	4.20441i	0.189549	+	0.328309i
$165$		0			0
$166$	2.46560	−	4.27054i	0.191368	−	0.331459i
$167$	3.78752	+	2.18672i	0.293087	+	0.169214i	0.639333	−	0.768930i	$-0.279210\pi$
$167$	3.78752	+	2.18672i	0.293087	+	0.169214i	−0.346246	+	0.938144i	$0.612544\pi$
$168$	−1.60380	−	7.76940i	−0.123736	−	0.599422i
$169$	−4.22666	−	7.32078i	−0.325127	−	0.563137i
$170$		0			0
$171$	−0.857238	−	0.638339i	−0.0655546	−	0.0488150i
$172$			13.6367i			1.03979i
$173$	12.6960	−	7.33005i	0.965260	−	0.557293i	0.0674723	−	0.997721i	$-0.478507\pi$
$173$	12.6960	−	7.33005i	0.965260	−	0.557293i	0.897788	+	0.440428i	$0.145173\pi$
$174$	−0.918827	−	1.03259i	−0.0696561	−	0.0782807i
$175$		0			0
$176$	8.34718	−	14.4577i	0.629192	−	1.08979i
$177$	−13.2189	+	11.7625i	−0.993591	+	0.884121i
$178$	2.56952	−	1.48351i	0.192593	−	0.111194i
$179$	6.87014			0.513499			0.256749	−	0.966478i	$-0.417349\pi$
$179$	6.87014			0.513499			0.256749	+	0.966478i	$0.417349\pi$
$180$		0			0
$181$	−10.9709			−0.815463			−0.407732	−	0.913102i	$-0.633680\pi$
$181$	−10.9709			−0.815463			−0.407732	+	0.913102i	$0.633680\pi$
$182$	2.23991	−	1.29321i	0.166033	−	0.0958593i
$183$	−0.00384933	−	0.0186476i	−0.000284551	−	0.00137847i
$184$	3.76434	−	6.52003i	0.277511	−	0.480663i
$185$		0			0
$186$	−2.12965	+	6.42570i	−0.156153	+	0.471155i
$187$	−16.9272	+	9.77294i	−1.23784	+	0.714668i
$188$		−	20.2980i		−	1.48039i
$189$	−12.0693	−	5.63046i	−0.877911	−	0.409556i
$190$		0			0
$191$	−6.86627	−	11.8927i	−0.496826	−	0.860528i	0.503167	−	0.864189i	$-0.332168\pi$
$191$	−6.86627	−	11.8927i	−0.496826	−	0.860528i	−0.999993	+	0.00366109i	$0.998835\pi$
$192$	−5.12158	−	1.69742i	−0.369618	−	0.122501i
$193$	−0.417748	−	0.241187i	−0.0300701	−	0.0173610i	0.484890	−	0.874575i	$-0.338860\pi$
$193$	−0.417748	−	0.241187i	−0.0300701	−	0.0173610i	−0.514960	+	0.857214i	$0.672193\pi$
$194$	1.70532	−	2.95370i	0.122435	−	0.212064i
$195$		0			0
$196$	−0.382518	−	0.662541i	−0.0273227	−	0.0473244i
$197$			5.53488i			0.394344i	0.980369	+	0.197172i	$0.0631757\pi$
$197$			5.53488i			0.394344i	−0.980369	+	0.197172i	$0.936824\pi$
$198$	3.46795	+	8.04209i	0.246457	+	0.571526i
$199$	−17.4590			−1.23764			−0.618818	−	0.785534i	$-0.712388\pi$
$199$	−17.4590			−1.23764			−0.618818	+	0.785534i	$0.712388\pi$
$200$		0			0
$201$	1.13160	+	1.27172i	0.0798172	+	0.0896999i
$202$	−2.85704	−	1.64951i	−0.201021	−	0.116059i
$203$	3.74288	+	2.16095i	0.262698	+	0.151669i
$204$	6.47948	+	7.28175i	0.453654	+	0.509825i
$205$		0			0
$206$	−2.89401			−0.201635
$207$	−5.00473	−	11.6058i	−0.347852	−	0.806661i
$208$		−	5.77073i		−	0.400128i
$209$	−1.09883	−	1.90324i	−0.0760079	−	0.131650i
$210$		0			0
$211$	0.818328	−	1.41739i	0.0563360	−	0.0975769i	−0.836482	−	0.547994i	$-0.815392\pi$
$211$	0.818328	−	1.41739i	0.0563360	−	0.0975769i	0.892818	+	0.450417i	$0.148725\pi$
$212$	−14.5120	−	8.37849i	−0.996686	−	0.575437i
$213$	10.5799	+	3.50647i	0.724926	+	0.240259i
$214$	−3.43935	−	5.95713i	−0.235109	−	0.407221i
$215$		0			0
$216$	7.60725	−	5.32475i	0.517608	−	0.362303i
$217$		−	21.1667i		−	1.43689i
$218$	−0.779592	+	0.450098i	−0.0528006	+	0.0304844i
$219$	−3.60433	+	10.8752i	−0.243558	+	0.734879i
$220$		0			0
$221$	−3.37820	+	5.85122i	−0.227243	+	0.393596i
$222$	−0.601992	−	2.91628i	−0.0404031	−	0.195728i
$223$	−6.70984	+	3.87393i	−0.449324	+	0.259417i	−0.707545	−	0.706669i	$-0.750197\pi$
$223$	−6.70984	+	3.87393i	−0.449324	+	0.259417i	0.258221	+	0.966086i	$0.416864\pi$
$224$	−12.4432			−0.831397
$225$		0			0
$226$	−3.11366			−0.207118
$227$	−9.75169	+	5.63014i	−0.647242	+	0.373685i	−0.787399	−	0.616444i	$-0.788573\pi$
$227$	−9.75169	+	5.63014i	−0.647242	+	0.373685i	0.140157	+	0.990129i	$0.455239\pi$
$228$	−0.818734	+	0.728529i	−0.0542220	+	0.0482480i
$229$	−5.23879	+	9.07384i	−0.346189	+	0.599616i	−0.985569	−	0.169274i	$-0.945858\pi$
$229$	−5.23879	+	9.07384i	−0.346189	+	0.599616i	0.639380	+	0.768891i	$0.279191\pi$
$230$		0			0
$231$	−18.2040	−	20.4579i	−1.19773	−	1.34603i
$232$	−2.60962	+	1.50667i	−0.171330	+	0.0989176i
$233$			2.90214i			0.190125i	0.995471	+	0.0950627i	$0.0303051\pi$
$233$			2.90214i			0.190125i	−0.995471	+	0.0950627i	$0.969695\pi$
$234$	2.42811	+	1.80808i	0.158731	+	0.118198i
$235$		0			0
$236$	9.07188	+	15.7130i	0.590529	+	1.02283i
$237$	3.31646	+	16.0662i	0.215427	+	1.04361i
$238$	3.32852	+	1.92172i	0.215756	+	0.124567i
$239$	8.17723	−	14.1634i	0.528941	−	0.916153i	−0.470489	−	0.882406i	$-0.655923\pi$
$239$	8.17723	−	14.1634i	0.528941	−	0.916153i	0.999430	−	0.0337471i	$-0.0107441\pi$
$240$		0			0
$241$	−8.76194	−	15.1761i	−0.564406	−	0.977580i	−0.997105	−	0.0760416i	$-0.975772\pi$
$241$	−8.76194	−	15.1761i	−0.564406	−	0.977580i	0.432698	−	0.901539i	$-0.357562\pi$
$242$			12.8023i			0.822965i
$243$	0.457745	−	15.5817i	0.0293644	−	0.999569i
$244$	−0.0195242			−0.00124991
$245$		0			0
$246$	−0.704913	+	2.12691i	−0.0449436	+	0.135607i
$247$	−0.657890	−	0.379833i	−0.0418605	−	0.0241682i
$248$	12.7808	+	7.37898i	0.811580	+	0.468566i
$249$	−17.6749	+	3.64854i	−1.12010	+	0.231217i
$250$		0			0
$251$	8.46999			0.534621			0.267311	−	0.963610i	$-0.413865\pi$
$251$	8.46999			0.534621			0.267311	+	0.963610i	$0.413865\pi$
$252$	−8.15613	+	10.9530i	−0.513788	+	0.689976i
$253$		−	25.9882i		−	1.63386i
$254$	−2.19079	−	3.79456i	−0.137462	−	0.238092i
$255$		0			0
$256$	−0.468695	+	0.811804i	−0.0292934	+	0.0507377i
$257$	2.48766	+	1.43625i	0.155176	+	0.0895910i	0.575577	−	0.817747i	$-0.304777\pi$
$257$	2.48766	+	1.43625i	0.155176	+	0.0895910i	−0.420401	+	0.907338i	$0.638111\pi$
$258$	−4.70186	+	4.18383i	−0.292725	+	0.260474i
$259$	4.65545	+	8.06348i	0.289276	+	0.501040i
$260$		0			0
$261$	−0.587841	+	5.02442i	−0.0363864	+	0.311004i
$262$			0.127493i			0.00787656i
$263$	−22.1909	+	12.8119i	−1.36835	+	0.790017i	−0.990717	−	0.135938i	$-0.956595\pi$
$263$	−22.1909	+	12.8119i	−1.36835	+	0.790017i	−0.377633	+	0.925955i	$0.623262\pi$
$264$	18.6989	−	3.85993i	1.15084	−	0.237562i
$265$		0			0
$266$	−0.216072	+	0.374247i	−0.0132482	+	0.0229465i
$267$	−10.3076	−	3.41619i	−0.630812	−	0.209068i
$268$	1.51166	−	0.872756i	0.0923392	−	0.0533121i
$269$	−0.337210			−0.0205600			−0.0102800	−	0.999947i	$-0.503272\pi$
$269$	−0.337210			−0.0205600			−0.0102800	+	0.999947i	$0.503272\pi$
$270$		0			0
$271$	21.5927			1.31166			0.655831	−	0.754908i	$-0.272318\pi$
$271$	21.5927			1.31166			0.655831	+	0.754908i	$0.272318\pi$
$272$	7.42646	−	4.28767i	0.450295	−	0.259978i
$273$	−8.98535	−	2.97798i	−0.543818	−	0.180236i
$274$	0.822560	−	1.42472i	0.0496927	−	0.0860702i
$275$		0			0
$276$	−12.6923	+	2.62000i	−0.763984	+	0.157705i
$277$	20.9004	−	12.0669i	1.25579	−	0.725028i	0.283533	−	0.958962i	$-0.408493\pi$
$277$	20.9004	−	12.0669i	1.25579	−	0.725028i	0.972252	+	0.233934i	$0.0751600\pi$
$278$		−	6.97949i		−	0.418602i
$279$	22.7501	−	9.81041i	1.36201	−	0.587334i
$280$		0			0
$281$	−1.68363	−	2.91613i	−0.100437	−	0.173962i	0.811428	−	0.584453i	$-0.198691\pi$
$281$	−1.68363	−	2.91613i	−0.100437	−	0.173962i	−0.911865	+	0.410491i	$0.865357\pi$
$282$	6.99868	−	6.22759i	0.416765	−	0.370848i
$283$	18.9224	+	10.9249i	1.12482	+	0.649415i	0.942627	−	0.333848i	$-0.108347\pi$
$283$	18.9224	+	10.9249i	1.12482	+	0.649415i	0.182193	+	0.983263i	$0.441681\pi$
$284$	5.71444	−	9.89770i	0.339090	−	0.587321i
$285$		0			0
$286$	3.11243	+	5.39088i	0.184042	+	0.318770i
$287$		−	7.00619i		−	0.413562i
$288$	−5.76721	−	13.3740i	−0.339836	−	0.788071i
$289$	6.95994			0.409408
$290$		0			0
$291$	−12.2248	+	2.52350i	−0.716629	+	0.147930i
$292$	10.1739	+	5.87393i	0.595385	+	0.343746i
$293$	11.9114	+	6.87702i	0.695869	+	0.401760i	0.805807	−	0.592179i	$-0.201732\pi$
$293$	11.9114	+	6.87702i	0.695869	+	0.401760i	−0.109938	+	0.993938i	$0.535065\pi$
$294$	0.111082	−	0.335163i	0.00647843	−	0.0195471i
$295$		0			0
$296$	−6.49179			−0.377328
$297$	13.5511	−	29.0476i	0.786312	−	1.68551i
$298$			4.80509i			0.278352i
$299$	−4.49166	−	7.77978i	−0.259759	−	0.449916i
$300$		0			0
$301$	9.83978	−	17.0430i	0.567155	−	0.982342i
$302$	4.22810	+	2.44110i	0.243300	+	0.140469i
$303$	2.44092	+	11.8247i	0.140227	+	0.679312i
$304$	0.482090	+	0.835004i	0.0276498	+	0.0478908i
$305$		0			0
$306$	−0.522764	+	4.46819i	−0.0298844	+	0.255430i
$307$			34.2183i			1.95294i	0.215644	+	0.976472i	$0.430815\pi$
$307$			34.2183i			1.95294i	−0.215644	+	0.976472i	$0.569185\pi$
$308$	−24.3179	+	14.0399i	−1.38564	+	0.799999i
$309$	7.04087	+	7.91265i	0.400541	+	0.450135i
$310$		0			0
$311$	−11.5199	+	19.9530i	−0.653232	+	1.13143i	0.329102	+	0.944294i	$0.393254\pi$
$311$	−11.5199	+	19.9530i	−0.653232	+	1.13143i	−0.982334	+	0.187136i	$0.940079\pi$
$312$	4.93055	−	4.38732i	0.279137	−	0.248383i
$313$	3.11016	−	1.79565i	0.175796	−	0.101496i	−0.409520	−	0.912301i	$-0.634304\pi$
$313$	3.11016	−	1.79565i	0.175796	−	0.101496i	0.585316	+	0.810805i	$0.300970\pi$
$314$	−0.502885			−0.0283794
$315$		0			0
$316$	16.8215			0.946281
$317$	11.4148	−	6.59033i	0.641118	−	0.370150i	−0.143927	−	0.989588i	$-0.545973\pi$
$317$	11.4148	−	6.59033i	0.641118	−	0.370150i	0.785045	+	0.619439i	$0.212640\pi$
$318$	−1.56351	−	7.57425i	−0.0876775	−	0.424743i
$319$	−5.20085	+	9.00813i	−0.291192	+	0.504359i
$320$		0			0
$321$	−7.92005	+	23.8969i	−0.442054	+	1.33379i
$322$	−4.42560	+	2.55512i	−0.246629	+	0.142391i
$323$		−	1.12887i		−	0.0628119i
$324$	−15.5526	−	3.68971i	−0.864033	−	0.204984i
$325$		0			0
$326$	4.05545	+	7.02424i	0.224611	+	0.389037i
$327$	3.12732	+	1.03647i	0.172941	+	0.0573171i
$328$	4.23044	+	2.44244i	0.233587	+	0.134861i
$329$	−14.6464	+	25.3683i	−0.807483	+	1.39860i
$330$		0			0
$331$	−0.591264	−	1.02410i	−0.0324988	−	0.0562896i	0.849319	−	0.527881i	$-0.177013\pi$
$331$	−0.591264	−	1.02410i	−0.0324988	−	0.0562896i	−0.881817	+	0.471591i	$0.843680\pi$
$332$			18.5058i			1.01564i
$333$	−6.50894	+	8.74099i	−0.356688	+	0.479003i
$334$	2.06975			0.113252
$335$		0			0
$336$	7.98661	+	8.97549i	0.435705	+	0.489653i
$337$	21.4770	+	12.3997i	1.16993	+	0.675457i	0.953662	−	0.300879i	$-0.0972799\pi$
$337$	21.4770	+	12.3997i	1.16993	+	0.675457i	0.216263	+	0.976335i	$0.430613\pi$
$338$	−3.46459	−	2.00028i	−0.188449	−	0.108801i
$339$	7.57527	+	8.51322i	0.411432	+	0.462375i
$340$		0			0
$341$	50.9428			2.75871
$342$	−0.502388	−	0.0587777i	−0.0271660	−	0.00317833i
$343$			19.0454i			1.02836i
$344$	6.86053	+	11.8828i	0.369895	+	0.640677i
$345$		0			0
$346$	3.46898	−	6.00845i	0.186493	−	0.323016i
$347$	−19.1991	−	11.0846i	−1.03066	−	0.595052i	−0.113486	−	0.993540i	$-0.536202\pi$
$347$	−19.1991	−	11.0846i	−1.03066	−	0.595052i	−0.917174	+	0.398488i	$0.869535\pi$
$348$	4.92376	+	1.63186i	0.263941	+	0.0874771i
$349$	7.45925	+	12.9198i	0.399285	+	0.691581i	0.993638	−	0.112623i	$-0.0359252\pi$
$349$	7.45925	+	12.9198i	0.399285	+	0.691581i	−0.594353	+	0.804204i	$0.702592\pi$
$350$		0			0
$351$	−0.963810	−	11.0377i	−0.0514444	−	0.589151i
$352$		−	29.9476i		−	1.59621i
$353$	−14.6484	+	8.45726i	−0.779656	+	0.450134i	−0.836308	−	0.548260i	$-0.815291\pi$
$353$	−14.6484	+	8.45726i	−0.779656	+	0.450134i	0.0566525	+	0.998394i	$0.481957\pi$
$354$	−2.63444	+	7.94880i	−0.140019	+	0.422474i
$355$		0			0
$356$	−5.56732	+	9.64288i	−0.295067	+	0.511072i
$357$	−2.84372	−	13.7761i	−0.150506	−	0.729107i
$358$	2.81573	−	1.62566i	0.148816	−	0.0859190i
$359$	−0.636657			−0.0336015			−0.0168007	−	0.999859i	$-0.505348\pi$
$359$	−0.636657			−0.0336015			−0.0168007	+	0.999859i	$0.505348\pi$
$360$		0			0
$361$	−18.8731			−0.993320
$362$	−4.49644	+	2.59602i	−0.236328	+	0.136444i
$363$	35.0035	−	31.1470i	1.83721	−	1.63479i
$364$	−4.85317	+	8.40594i	−0.254375	+	0.440591i
$365$		0			0
$366$	−0.00599018	−	0.00673187i	−0.000313112	−	0.000351880i
$367$	17.4053	−	10.0490i	0.908550	−	0.524552i	0.0285858	−	0.999591i	$-0.490900\pi$
$367$	17.4053	−	10.0490i	0.908550	−	0.524552i	0.879964	+	0.475040i	$0.157566\pi$
$368$			11.4018i			0.594358i
$369$	7.53028	−	3.24725i	0.392011	−	0.169045i
$370$		0			0
$371$	12.0913	+	20.9427i	0.627749	+	1.08729i
$372$	−5.13580	−	24.8797i	−0.266279	−	1.28995i
$373$	−17.0113	−	9.82146i	−0.880810	−	0.508536i	−0.00988448	−	0.999951i	$-0.503146\pi$
$373$	−17.0113	−	9.82146i	−0.880810	−	0.508536i	−0.870925	+	0.491415i	$0.836480\pi$
$374$	−4.62509	+	8.01088i	−0.239157	+	0.414233i
$375$		0			0
$376$	−10.2118	−	17.6874i	−0.526635	−	0.912159i
$377$			3.59555i			0.185180i
$378$	−6.27892	+	0.548272i	−0.322953	+	0.0282001i
$379$	7.94219			0.407963			0.203982	−	0.978975i	$-0.434612\pi$
$379$	7.94219			0.407963			0.203982	+	0.978975i	$0.434612\pi$
$380$		0			0
$381$	−5.04490	+	15.2218i	−0.258458	+	0.779836i
$382$	−5.62829	−	3.24949i	−0.287968	−	0.166259i
$383$	−27.0103	−	15.5944i	−1.38016	−	0.796836i	−0.387983	−	0.921667i	$-0.626828\pi$
$383$	−27.0103	−	15.5944i	−1.38016	−	0.796836i	−0.992178	+	0.124830i	$0.960161\pi$
$384$	−18.9711	+	3.91612i	−0.968116	+	0.199843i
$385$		0			0
$386$	−0.228285			−0.0116194
$387$	22.8785	+	2.67670i	1.16298	+	0.136064i
$388$			12.7995i			0.649795i
$389$	−15.7247	−	27.2360i	−0.797274	−	1.38092i	−0.921385	−	0.388650i	$-0.872941\pi$
$389$	−15.7247	−	27.2360i	−0.797274	−	1.38092i	0.124111	−	0.992268i	$-0.460392\pi$
$390$		0			0
$391$	6.67463	−	11.5608i	0.337550	−	0.584655i
$392$	−0.666642	−	0.384886i	−0.0336705	−	0.0194397i
$393$	0.348586	−	0.310180i	0.0175838	−	0.0156465i
$394$	1.30970	+	2.26847i	0.0659819	+	0.114284i
$395$		0			0
$396$	−26.3611	−	19.6297i	−1.32469	−	0.986429i
$397$			17.7174i			0.889211i	0.895726	+	0.444606i	$0.146656\pi$
$397$			17.7174i			0.889211i	−0.895726	+	0.444606i	$0.853344\pi$
$398$	−7.15558	+	4.13128i	−0.358677	+	0.207082i
$399$	1.54893	−	0.319738i	0.0775436	−	0.0160069i
$400$		0			0
$401$	3.57124	−	6.18556i	0.178339	−	0.308892i	−0.762973	−	0.646431i	$-0.776261\pi$
$401$	3.57124	−	6.18556i	0.178339	−	0.308892i	0.941312	+	0.337538i	$0.109594\pi$
$402$	0.764711	+	0.253445i	0.0381403	+	0.0126407i
$403$	15.2502	−	8.80468i	0.759665	−	0.438593i
$404$	12.3806			0.615958
$405$		0			0
$406$	2.04536			0.101509
$407$	−19.4067	+	11.2045i	−0.961955	+	0.555385i
$408$	9.30954	+	3.08542i	0.460891	+	0.152751i
$409$	12.3759	−	21.4357i	0.611948	−	1.05993i	−0.378964	−	0.925412i	$-0.623719\pi$
$409$	12.3759	−	21.4357i	0.611948	−	1.05993i	0.990912	−	0.134514i	$-0.0429472\pi$
$410$		0			0
$411$	−5.89661	+	1.21721i	−0.290858	+	0.0600404i
$412$	9.40558	−	5.43031i	0.463380	−	0.267532i
$413$		−	26.1839i		−	1.28843i
$414$	−4.79744	−	3.57240i	−0.235782	−	0.175574i
$415$		0			0
$416$	−5.17598	−	8.96505i	−0.253773	−	0.439548i
$417$	−19.0830	+	16.9805i	−0.934498	+	0.831539i
$418$	−0.900715	−	0.520028i	−0.0440554	−	0.0254354i
$419$	−5.32956	+	9.23106i	−0.260366	+	0.450967i	−0.966339	−	0.257272i	$-0.917176\pi$
$419$	−5.32956	+	9.23106i	−0.260366	+	0.450967i	0.705973	+	0.708238i	$0.250510\pi$
$420$		0			0
$421$	4.08931	+	7.08288i	0.199301	+	0.345199i	0.948302	−	0.317370i	$-0.102800\pi$
$421$	4.08931	+	7.08288i	0.199301	+	0.345199i	−0.749001	+	0.662569i	$0.769466\pi$
$422$		−	0.774555i		−	0.0377048i
$423$	−34.0544	−	3.98425i	−1.65578	−	0.193721i
$424$	−16.8607			−0.818828
$425$		0			0
$426$	5.16592	−	1.06638i	0.250290	−	0.0516660i
$427$	0.0244012	+	0.0140881i	0.00118086	+	0.000681769i
$428$	22.3559	+	12.9072i	1.08061	+	0.623893i
$429$	7.16722	−	21.6254i	0.346037	−	1.04408i
$430$		0			0
$431$	1.67248			0.0805604			0.0402802	−	0.999188i	$-0.487175\pi$
$431$	1.67248			0.0805604			0.0402802	+	0.999188i	$0.487175\pi$
$432$	−5.94524	+	12.7440i	−0.286040	+	0.613147i
$433$			9.95994i			0.478644i	0.970940	+	0.239322i	$0.0769252\pi$
$433$			9.95994i			0.478644i	−0.970940	+	0.239322i	$0.923075\pi$
$434$	−5.00863	−	8.67519i	−0.240422	−	0.416423i
$435$		0			0
$436$	1.68913	−	2.92565i	0.0808945	−	0.140113i
$437$	1.29985	+	0.750471i	0.0621805	+	0.0358999i
$438$	1.09614	+	5.31010i	0.0523754	+	0.253726i
$439$	6.40788	+	11.0988i	0.305832	+	0.529716i	0.977446	−	0.211185i	$-0.0677322\pi$
$439$	6.40788	+	11.0988i	0.305832	+	0.529716i	−0.671615	+	0.740901i	$0.734399\pi$
$440$		0			0
$441$	−1.18664	+	0.511709i	−0.0565067	+	0.0243671i
$442$			3.19750i			0.152090i
$443$	6.71520	−	3.87702i	0.319049	−	0.184203i	−0.331920	−	0.943308i	$-0.607696\pi$
$443$	6.71520	−	3.87702i	0.319049	−	0.184203i	0.650968	+	0.759105i	$0.274363\pi$
$444$	7.42859	+	8.34838i	0.352545	+	0.396196i
$445$		0			0
$446$	−1.83335	+	3.17546i	−0.0868118	+	0.150362i
$447$	13.1379	−	11.6904i	0.621399	−	0.552936i
$448$	6.91452	−	3.99210i	0.326681	−	0.188609i
$449$	33.3401			1.57342			0.786709	−	0.617324i	$-0.211783\pi$
$449$	33.3401			1.57342			0.786709	+	0.617324i	$0.211783\pi$
$450$		0			0
$451$	16.8621			0.794004
$452$	10.1195	−	5.84247i	0.475979	−	0.274807i
$453$	−3.61229	−	17.4993i	−0.169720	−	0.822187i
$454$	−2.66449	+	4.61503i	−0.125051	+	0.216594i
$455$		0			0
$456$	−0.346914	+	1.04673i	−0.0162457	+	0.0490177i
$457$	−33.0988	+	19.1096i	−1.54830	+	0.893910i	−0.550026	+	0.835148i	$0.685382\pi$
$457$	−33.0988	+	19.1096i	−1.54830	+	0.893910i	−0.998272	+	0.0587626i	$0.981285\pi$
$458$			4.95856i			0.231698i
$459$	13.4886	−	9.44142i	0.629592	−	0.440688i
$460$		0			0
$461$	−15.6517	−	27.1095i	−0.728971	−	1.26261i	−0.957319	−	0.289035i	$-0.906666\pi$
$461$	−15.6517	−	27.1095i	−0.728971	−	1.26261i	0.228348	−	0.973580i	$-0.426668\pi$
$462$	−12.3018	−	4.07714i	−0.572332	−	0.189686i
$463$	10.4661	+	6.04258i	0.486399	+	0.280823i	0.723079	−	0.690765i	$-0.242726\pi$
$463$	10.4661	+	6.04258i	0.486399	+	0.280823i	−0.236680	+	0.971588i	$0.576059\pi$
$464$	2.28176	−	3.95212i	0.105928	−	0.183473i
$465$		0			0
$466$	0.686725	+	1.18944i	0.0318119	+	0.0550998i
$467$		−	7.60466i		−	0.351902i	−0.984399	−	0.175951i	$-0.943700\pi$
$467$		−	7.60466i		−	0.351902i	0.984399	−	0.175951i	$-0.0563000\pi$
$468$	−11.2841	−	1.32020i	−0.521608	−	0.0610264i
$469$	−2.51901			−0.116317
$470$		0			0
$471$	1.22348	+	1.37496i	0.0563748	+	0.0633550i
$472$	15.8102	+	9.12803i	0.727724	+	0.420152i
$473$	41.0181	+	23.6818i	1.88601	+	1.08889i
$474$	5.16095	+	5.79997i	0.237050	+	0.266401i
$475$		0			0
$476$	−14.4237			−0.661108
$477$	−16.9052	+	22.7024i	−0.774038	+	1.03947i
$478$		−	7.73982i		−	0.354011i
$479$	−16.2417	−	28.1314i	−0.742101	−	1.28536i	−0.951537	−	0.307534i	$-0.900496\pi$
$479$	−16.2417	−	28.1314i	−0.742101	−	1.28536i	0.209437	−	0.977822i	$-0.432837\pi$
$480$		0			0
$481$	−3.87304	+	6.70830i	−0.176595	+	0.305872i
$482$	−7.18217	−	4.14663i	−0.327139	−	0.188874i
$483$	17.7532	+	5.88387i	0.807798	+	0.267725i
$484$	−24.0223	−	41.6079i	−1.09192	−	1.89127i
$485$		0			0
$486$	−3.49946	−	6.49450i	−0.158739	−	0.294596i
$487$		−	4.46121i		−	0.202157i	−0.994878	−	0.101078i	$-0.967771\pi$
$487$		−	4.46121i		−	0.202157i	0.994878	−	0.101078i	$-0.0322293\pi$
$488$	−0.0170131	+	0.00982254i	−0.000770148	+	0.000444645i
$489$	9.33879	−	28.1776i	0.422315	−	1.27424i
$490$		0			0
$491$	−16.4210	+	28.4420i	−0.741070	+	1.28357i	0.210938	+	0.977499i	$0.432348\pi$
$491$	−16.4210	+	28.4420i	−0.741070	+	1.28357i	−0.952008	+	0.306072i	$0.900985\pi$
$492$	−1.69995	−	8.23520i	−0.0766397	−	0.371271i
$493$	−4.62717	+	2.67150i	−0.208397	+	0.120318i
$494$	−0.359515			−0.0161754
$495$		0			0
$496$	−22.3501			−1.00355
$497$	−14.2837	+	8.24672i	−0.640713	+	0.369916i
$498$	−6.38073	+	5.67772i	−0.285927	+	0.254425i
$499$	−17.1010	+	29.6198i	−0.765547	+	1.32597i	0.174410	+	0.984673i	$0.444198\pi$
$499$	−17.1010	+	29.6198i	−0.765547	+	1.32597i	−0.939957	+	0.341293i	$0.889135\pi$
$500$		0			0
$501$	−5.03554	−	5.65902i	−0.224971	−	0.252827i
$502$	3.47143	−	2.00423i	0.154938	−	0.0894532i
$503$		−	22.1773i		−	0.988837i	−0.869224	−	0.494419i	$-0.835381\pi$
$503$		−	22.1773i		−	0.988837i	0.869224	−	0.494419i	$-0.164619\pi$
$504$	−1.59673	+	13.6476i	−0.0711238	+	0.607913i
$505$		0			0
$506$	−6.14951	−	10.6513i	−0.273379	−	0.473507i
$507$	2.95998	+	14.3392i	0.131457	+	0.636828i
$508$	14.2402	+	8.22160i	0.631808	+	0.364775i
$509$	−10.7816	+	18.6743i	−0.477887	+	0.827724i	−0.999679	−	0.0253489i	$-0.991930\pi$
$509$	−10.7816	+	18.6743i	−0.477887	+	0.827724i	0.521792	+	0.853073i	$0.325264\pi$
$510$		0			0
$511$	−8.47688	−	14.6824i	−0.374995	−	0.649510i
$512$			22.8115i			1.00813i
$513$	1.06156	+	1.51661i	0.0468690	+	0.0669598i
$514$	1.35943			0.0599617
$515$		0			0
$516$	7.43061	−	22.4201i	0.327114	−	0.986990i
$517$	−61.0550	−	35.2501i	−2.68520	−	1.55030i
$518$	3.81608	+	2.20321i	0.167669	+	0.0968037i
$519$	−24.8677	+	5.13332i	−1.09157	+	0.225328i
$520$		0			0
$521$	20.2626			0.887718			0.443859	−	0.896097i	$-0.353609\pi$
$521$	20.2626			0.887718			0.443859	+	0.896097i	$0.353609\pi$
$522$	0.947989	+	2.19836i	0.0414923	+	0.0962196i
$523$		−	31.8114i		−	1.39101i	−0.718520	−	0.695507i	$-0.755180\pi$
$523$		−	31.8114i		−	1.39101i	0.718520	−	0.695507i	$-0.244820\pi$
$524$	−0.239229	−	0.414356i	−0.0104507	−	0.0181012i
$525$		0			0
$526$	−6.06330	+	10.5019i	−0.264373	+	0.457907i
$527$	22.6618	+	13.0838i	0.987164	+	0.569940i
$528$	−21.6017	+	19.2217i	−0.940092	+	0.836517i
$529$	−2.62541	−	4.54735i	−0.114148	−	0.197711i
$530$		0			0
$531$	28.1426	−	12.1358i	1.22128	−	0.526649i
$532$		−	1.62175i		−	0.0703117i
$533$	5.04780	−	2.91435i	0.218645	−	0.126235i
$534$	−5.03292	+	1.03892i	−0.217796	+	0.0449585i
$535$		0			0
$536$	0.878159	−	1.52102i	0.0379307	−	0.0656978i
$537$	−11.2952	−	3.74354i	−0.487426	−	0.161546i
$538$	−0.138205	+	0.0797930i	−0.00595846	+	0.00344012i
$539$	−2.65717			−0.114452
$540$		0			0
$541$	−15.1315			−0.650553			−0.325277	−	0.945619i	$-0.605457\pi$
$541$	−15.1315			−0.650553			−0.325277	+	0.945619i	$0.605457\pi$
$542$	8.84977	−	5.10942i	0.380130	−	0.219468i
$543$	18.0374	+	5.97806i	0.774058	+	0.256543i
$544$	7.69153	−	13.3221i	0.329772	−	0.571181i
$545$		0			0
$546$	−4.38732	+	0.905653i	−0.187760	+	0.0387584i
$547$	−3.53982	+	2.04372i	−0.151352	+	0.0873831i	−0.573763	−	0.819021i	$-0.694517\pi$
$547$	−3.53982	+	2.04372i	−0.151352	+	0.0873831i	0.422411	+	0.906404i	$0.361184\pi$
$548$			6.17381i			0.263732i
$549$	−0.00383236	+	0.0327561i	−0.000163561	+	0.00139800i
$550$		0			0
$551$	−0.300374	−	0.520263i	−0.0127964	−	0.0221639i
$552$	−9.74174	+	8.66844i	−0.414636	+	0.368953i
$553$	−21.0233	−	12.1378i	−0.894003	−	0.516153i
$554$	5.71070	−	9.89123i	0.242625	−	0.420238i
$555$		0			0
$556$	13.0963	+	22.6835i	0.555408	+	0.961994i
$557$		−	13.1425i		−	0.556864i	−0.960456	−	0.278432i	$-0.910185\pi$
$557$		−	13.1425i		−	0.556864i	0.960456	−	0.278432i	$-0.0898147\pi$
$558$	7.00273	−	9.40410i	0.296449	−	0.398107i
$559$	16.3721			0.692467
$560$		0			0
$561$	33.1554	−	6.84411i	1.39982	−	0.288958i
$562$	−1.38007	−	0.796785i	−0.0582149	−	0.0336104i
$563$	−21.2368	−	12.2611i	−0.895023	−	0.516742i	−0.0194410	−	0.999811i	$-0.506189\pi$
$563$	−21.2368	−	12.2611i	−0.895023	−	0.516742i	−0.875582	+	0.483069i	$0.839522\pi$
$564$	−11.0604	+	33.3721i	−0.465727	+	1.40522i
$565$		0			0
$566$	10.3405			0.434642
$567$	16.7751	+	15.8336i	0.704489	+	0.664950i
$568$		−	11.4996i		−	0.482514i
$569$	11.3649	+	19.6846i	0.476442	+	0.825223i	0.999636	−	0.0269915i	$-0.00859271\pi$
$569$	11.3649	+	19.6846i	0.476442	+	0.825223i	−0.523193	+	0.852214i	$0.675259\pi$
$570$		0			0
$571$	0.247093	−	0.427977i	0.0103405	−	0.0179103i	−0.860809	−	0.508928i	$-0.830042\pi$
$571$	0.247093	−	0.427977i	0.0103405	−	0.0179103i	0.871149	+	0.491018i	$0.163375\pi$
$572$	−20.2309	−	11.6803i	−0.845897	−	0.488379i
$573$	4.80854	+	23.2943i	0.200879	+	0.973135i
$574$	−1.65786	−	2.87149i	−0.0691976	−	0.119854i
$575$		0			0
$576$	7.49549	+	5.58149i	0.312312	+	0.232562i
$577$		−	9.41187i		−	0.391821i	−0.980622	−	0.195911i	$-0.937234\pi$
$577$		−	9.41187i		−	0.391821i	0.980622	−	0.195911i	$-0.0627662\pi$
$578$	2.85254	−	1.64691i	0.118650	−	0.0685025i
$579$	0.555399	+	0.624167i	0.0230816	+	0.0259395i
$580$		0			0
$581$	13.3532	−	23.1284i	0.553984	−	0.959529i
$582$	−4.41320	+	3.92697i	−0.182933	+	0.162778i
$583$	−50.4037	+	29.1006i	−2.08751	+	1.20522i
$584$	11.8206			0.489139
$585$		0			0
$586$	6.50916			0.268891
$587$	8.63705	−	4.98661i	0.356489	−	0.205819i	−0.311050	−	0.950393i	$-0.600681\pi$
$587$	8.63705	−	4.98661i	0.356489	−	0.205819i	0.667540	+	0.744574i	$0.267347\pi$
$588$	0.267882	+	1.29772i	0.0110473	+	0.0535172i
$589$	−1.47110	+	2.54801i	−0.0606155	+	0.104989i
$590$		0			0
$591$	3.01595	−	9.09993i	0.124060	−	0.374321i
$592$	8.51428	−	4.91572i	0.349935	−	0.202035i
$593$		−	38.3421i		−	1.57452i	−0.616621	−	0.787260i	$-0.711499\pi$
$593$		−	38.3421i		−	1.57452i	0.616621	−	0.787260i	$-0.288501\pi$
$594$	−1.31955	−	15.1117i	−0.0541418	−	0.620042i
$595$		0			0
$596$	−9.01628	−	15.6167i	−0.369321	−	0.639683i
$597$	28.7044	+	9.51340i	1.17479	+	0.389358i
$598$	−3.68182	−	2.12570i	−0.150561	−	0.0869262i
$599$	−5.07665	+	8.79301i	−0.207426	+	0.359273i	−0.950903	−	0.309489i	$-0.899842\pi$
$599$	−5.07665	+	8.79301i	−0.207426	+	0.359273i	0.743477	+	0.668762i	$0.233175\pi$
$600$		0			0
$601$	10.6371	+	18.4241i	0.433898	+	0.751533i	0.997205	−	0.0747146i	$-0.0238046\pi$
$601$	10.6371	+	18.4241i	0.433898	+	0.751533i	−0.563307	+	0.826248i	$0.690471\pi$
$602$		−	9.31344i		−	0.379587i
$603$	−1.16752	−	2.70745i	−0.0475450	−	0.110256i
$604$	−18.3219			−0.745508
$605$		0			0
$606$	3.79846	+	4.26878i	0.154302	+	0.173407i
$607$	32.6799	+	18.8678i	1.32644	+	0.765819i	0.984747	−	0.173993i	$-0.0556671\pi$
$607$	32.6799	+	18.8678i	1.32644	+	0.765819i	0.341691	+	0.939812i	$0.389000\pi$
$608$	1.49789	+	0.864808i	0.0607475	+	0.0350726i
$609$	−4.97618	−	5.59232i	−0.201645	−	0.226612i
$610$		0			0
$611$	−24.3698			−0.985895
$612$	−6.68513	−	15.5026i	−0.270230	−	0.626657i
$613$			32.2633i			1.30310i	0.758605	+	0.651551i	$0.225881\pi$
$613$			32.2633i			1.30310i	−0.758605	+	0.651551i	$0.774119\pi$
$614$	8.09699	+	14.0244i	0.326768	+	0.565979i
$615$		0			0
$616$	−14.1268	+	24.4684i	−0.569186	+	0.985860i
$617$	22.5321	+	13.0089i	0.907108	+	0.523719i	0.879499	−	0.475900i	$-0.157878\pi$
$617$	22.5321	+	13.0089i	0.907108	+	0.523719i	0.0276084	+	0.999619i	$0.491211\pi$
$618$	4.75805	+	1.57694i	0.191397	+	0.0634339i
$619$	−5.94077	−	10.2897i	−0.238780	−	0.413578i	0.721585	−	0.692326i	$-0.243414\pi$
$619$	−5.94077	−	10.2897i	−0.238780	−	0.413578i	−0.960364	+	0.278748i	$0.910081\pi$
$620$		0			0
$621$	1.90429	+	21.8083i	0.0764165	+	0.875136i
$622$			10.9037i			0.437197i
$623$	13.9160	−	8.03440i	0.557532	−	0.321891i
$624$	−3.14447	+	9.48769i	−0.125879	+	0.379811i
$625$		0			0
$626$	0.849799	−	1.47189i	0.0339648	−	0.0588288i
$627$	0.769527	+	3.72788i	0.0307319	+	0.148877i
$628$	1.63439	−	0.943614i	0.0652191	−	0.0376543i
$629$	−11.5107			−0.458962
$630$		0			0
$631$	−13.2726			−0.528372			−0.264186	−	0.964472i	$-0.585103\pi$
$631$	−13.2726			−0.528372			−0.264186	+	0.964472i	$0.585103\pi$
$632$	14.6580	−	8.46279i	0.583063	−	0.336632i
$633$	−2.11775	+	1.88443i	−0.0841731	+	0.0748992i
$634$	3.11890	−	5.40210i	0.123867	−	0.214545i
$635$		0			0
$636$	19.2938	+	21.6827i	0.765048	+	0.859774i
$637$	−0.795445	+	0.459251i	−0.0315167	+	0.0181962i
$638$			4.92265i			0.194890i
$639$	−15.4839	−	11.5300i	−0.612533	−	0.456120i
$640$		0			0
$641$	−22.4075	−	38.8109i	−0.885042	−	1.53294i	−0.845665	−	0.533713i	$-0.820796\pi$
$641$	−22.4075	−	38.8109i	−0.885042	−	1.53294i	−0.0393765	−	0.999224i	$-0.512537\pi$
$642$	2.40862	+	11.6682i	0.0950606	+	0.460509i
$643$	−12.9259	−	7.46275i	−0.509747	−	0.294302i	0.222983	−	0.974822i	$-0.428421\pi$
$643$	−12.9259	−	7.46275i	−0.509747	−	0.294302i	−0.732729	+	0.680520i	$0.761754\pi$
$644$	9.58886	−	16.6084i	0.377854	−	0.654462i
$645$		0			0
$646$	−0.267121	−	0.462667i	−0.0105097	−	0.0182034i
$647$		−	41.2684i		−	1.62243i	−0.584749	−	0.811214i	$-0.698807\pi$
$647$		−	41.2684i		−	1.62243i	0.584749	−	0.811214i	$-0.301193\pi$
$648$	−15.4086	+	4.60927i	−0.605306	+	0.181069i
$649$	63.0179			2.47367
$650$		0			0
$651$	−11.5337	+	34.8003i	−0.452043	+	1.36393i
$652$	−26.3606	−	15.2193i	−1.03236	−	0.596034i
$653$	23.9241	+	13.8126i	0.936223	+	0.540528i	0.888774	−	0.458345i	$-0.151558\pi$
$653$	23.9241	+	13.8126i	0.936223	+	0.540528i	0.0474484	+	0.998874i	$0.484891\pi$
$654$	1.52699	−	0.315209i	0.0597100	−	0.0123256i
$655$		0			0
$656$	−7.39788			−0.288839
$657$	11.8518	−	15.9160i	0.462383	−	0.620943i
$658$			13.8630i			0.540435i
$659$	20.0112	+	34.6605i	0.779527	+	1.35018i	0.932215	+	0.361905i	$0.117874\pi$
$659$	20.0112	+	34.6605i	0.779527	+	1.35018i	−0.152688	+	0.988274i	$0.548793\pi$
$660$		0			0
$661$	−12.4965	+	21.6445i	−0.486056	+	0.841874i	−0.999872	−	0.0160270i	$-0.994898\pi$
$661$	−12.4965	+	21.6445i	−0.486056	+	0.841874i	0.513816	+	0.857901i	$0.328232\pi$
$662$	−0.484659	−	0.279818i	−0.0188368	−	0.0108754i
$663$	8.74245	−	7.77924i	0.339529	−	0.302121i
$664$	9.31018	+	16.1257i	0.361305	+	0.625799i
$665$		0			0
$666$	−0.599338	+	5.12269i	−0.0232239	+	0.198500i
$667$		−	7.10405i		−	0.275070i
$668$	−6.72675	+	3.88369i	−0.260266	+	0.150264i
$669$	13.1426	−	2.71296i	0.508122	−	0.104889i
$670$		0			0
$671$	−0.0339063	+	0.0587274i	−0.00130894	+	0.00226715i
$672$	20.4579	+	6.78030i	0.789182	+	0.261556i
$673$	35.3380	−	20.4024i	1.36218	−	0.786454i	0.372265	−	0.928126i	$-0.378581\pi$
$673$	35.3380	−	20.4024i	1.36218	−	0.786454i	0.989914	+	0.141672i	$0.0452479\pi$
$674$	11.7365			0.452072
$675$		0			0
$676$	15.0133			0.577436
$677$	35.6710	−	20.5947i	1.37095	−	0.791518i	0.379901	−	0.925027i	$-0.375958\pi$
$677$	35.6710	−	20.5947i	1.37095	−	0.791518i	0.991048	+	0.133509i	$0.0426246\pi$
$678$	5.11919	+	1.69663i	0.196601	+	0.0651587i
$679$	9.23569	−	15.9967i	0.354433	−	0.613896i
$680$		0			0
$681$	19.1007	−	3.94286i	0.731939	−	0.151091i
$682$	20.8789	−	12.0545i	0.799496	−	0.461589i
$683$		−	1.33820i		−	0.0512047i	−0.999672	−	0.0256023i	$-0.991850\pi$
$683$		−	1.33820i		−	0.0512047i	0.999672	−	0.0256023i	$-0.00815037\pi$
$684$	1.74306	−	0.751652i	0.0666476	−	0.0287401i
$685$		0			0
$686$	4.50667	+	7.80578i	0.172065	+	0.298026i
$687$	13.5574	−	12.0637i	0.517249	−	0.460261i
$688$	−17.9958	−	10.3899i	−0.686083	−	0.396110i
$689$	−10.0592	+	17.4230i	−0.383225	+	0.663764i
$690$		0			0
$691$	12.6407	+	21.8943i	0.480874	+	0.832898i	0.999759	−	0.0219459i	$-0.00698617\pi$
$691$	12.6407	+	21.8943i	0.480874	+	0.832898i	−0.518885	+	0.854844i	$0.673653\pi$
$692$			26.0368i			0.989770i
$693$	18.7817	+	43.5544i	0.713459	+	1.65449i
$694$	−10.4917			−0.398258
$695$		0			0
$696$	5.11148	−	1.05514i	0.193750	−	0.0399949i
$697$	7.50106	+	4.33074i	0.284123	+	0.164039i
$698$	6.11435	+	3.53012i	0.231432	+	0.133617i
$699$	1.58137	−	4.77142i	0.0598130	−	0.180472i
$700$		0			0
$701$	−18.2064			−0.687645			−0.343822	−	0.939035i	$-0.611722\pi$
$701$	−18.2064			−0.687645			−0.343822	+	0.939035i	$0.611722\pi$
$702$	−3.00685	−	4.29576i	−0.113486	−	0.162133i
$703$		−	1.29422i		−	0.0488126i
$704$	9.60795	+	16.6415i	0.362113	+	0.627199i
$705$		0			0
$706$	−4.00244	+	6.93242i	−0.150634	+	0.260905i
$707$	−15.4732	−	8.93344i	−0.581929	−	0.335977i
$708$	−6.35315	−	30.7770i	−0.238766	−	1.15667i
$709$	20.9103	+	36.2177i	0.785304	+	1.36019i	0.928818	+	0.370537i	$0.120826\pi$
$709$	20.9103	+	36.2177i	0.785304	+	1.36019i	−0.143514	+	0.989648i	$0.545840\pi$
$710$		0			0
$711$	3.30184	−	28.2216i	0.123829	−	1.05839i
$712$			11.2036i			0.419871i
$713$	−30.1312	+	17.3962i	−1.12842	+	0.651494i
$714$	−4.42529	−	4.97322i	−0.165612	−	0.186118i
$715$		0			0
$716$	−6.10079	+	10.5669i	−0.227997	+	0.394903i
$717$	−21.1619	+	18.8303i	−0.790304	+	0.703231i
$718$	−0.260934	+	0.150650i	−0.00973797	+	0.00562222i
$719$	−48.9786			−1.82660			−0.913298	−	0.407293i	$-0.866473\pi$
$719$	−48.9786			−1.82660			−0.913298	+	0.407293i	$0.866473\pi$
$720$		0			0
$721$	−15.6734			−0.583707
$722$	−7.73514	+	4.46588i	−0.287872	+	0.166203i
$723$	6.13610	+	29.7255i	0.228204	+	1.10550i
$724$	9.74236	−	16.8743i	0.362072	−	0.627127i
$725$		0			0
$726$	6.97598	−	21.0484i	0.258903	−	0.781179i
$727$	−37.9327	+	21.9005i	−1.40685	+	0.812243i	−0.995083	−	0.0990474i	$-0.968420\pi$
$727$	−37.9327	+	21.9005i	−1.40685	+	0.812243i	−0.411764	+	0.911291i	$0.635087\pi$
$728$			9.76642i			0.361968i
$729$	−9.24306	+	25.3686i	−0.342336	+	0.939578i
$730$		0			0
$731$	12.1645	+	21.0696i	0.449922	+	0.779287i
$732$	0.0320999	+	0.0106387i	0.00118645	+	0.000393219i
$733$	−5.87740	−	3.39332i	−0.217087	−	0.125335i	0.387514	−	0.921864i	$-0.373334\pi$
$733$	−5.87740	−	3.39332i	−0.217087	−	0.125335i	−0.604601	+	0.796529i	$0.706667\pi$
$734$	4.75572	−	8.23715i	0.175537	−	0.304039i
$735$		0			0
$736$	10.2267	+	17.7131i	0.376960	+	0.652913i
$737$		−	6.06261i		−	0.223319i
$738$	2.31790	−	3.11276i	0.0853232	−	0.114582i
$739$	−28.7245			−1.05665			−0.528324	−	0.849043i	$-0.677179\pi$
$739$	−28.7245			−1.05665			−0.528324	+	0.849043i	$0.677179\pi$
$740$		0			0
$741$	0.874670	+	0.982970i	0.0321318	+	0.0361103i
$742$	9.91125	+	5.72226i	0.363853	+	0.210071i
$743$	−27.2385	−	15.7262i	−0.999284	−	0.576937i	−0.0912477	−	0.995828i	$-0.529085\pi$
$743$	−27.2385	−	15.7262i	−0.999284	−	0.576937i	−0.908036	+	0.418891i	$0.862419\pi$
$744$	−16.9921	−	19.0961i	−0.622962	−	0.700096i
$745$		0			0
$746$	−9.29610			−0.340354
$747$	31.0475	+	3.63246i	1.13597	+	0.132905i
$748$		−	34.7141i		−	1.26927i
$749$	−18.6268	−	32.2626i	−0.680610	−	1.17885i
$750$		0			0
$751$	−5.47659	+	9.48574i	−0.199844	+	0.346139i	−0.948478	−	0.316844i	$-0.897377\pi$
$751$	−5.47659	+	9.48574i	−0.199844	+	0.346139i	0.748634	+	0.662984i	$0.230710\pi$
$752$	26.7866	+	15.4652i	0.976806	+	0.563959i
$753$	−13.9256	−	4.61530i	−0.507476	−	0.168191i
$754$	0.850804	+	1.47364i	0.0309845	+	0.0536667i
$755$		0			0
$756$	19.3778	−	13.5637i	0.704765	−	0.493306i
$757$		−	45.7942i		−	1.66442i	−0.554461	−	0.832210i	$-0.687075\pi$
$757$		−	45.7942i		−	1.66442i	0.554461	−	0.832210i	$-0.312925\pi$
$758$	3.25511	−	1.87934i	0.118231	−	0.0682607i
$759$	−14.1610	+	42.7273i	−0.514010	+	1.55090i
$760$		0			0
$761$	16.9569	−	29.3702i	0.614687	−	1.06467i	−0.375753	−	0.926720i	$-0.622616\pi$
$761$	16.9569	−	29.3702i	0.614687	−	1.06467i	0.990439	−	0.137948i	$-0.0440508\pi$
$762$	1.53424	+	7.43242i	0.0555796	+	0.269248i
$763$	−4.22212	+	2.43764i	−0.152851	+	0.0882485i
$764$	24.3894			0.882378
$765$		0			0
$766$	−14.7602			−0.533309
$767$	18.8649	−	10.8917i	0.681173	−	0.393275i
$768$	1.21294	−	1.07930i	0.0437680	−	0.0389459i
$769$	3.57986	−	6.20050i	0.129093	−	0.223596i	−0.794232	−	0.607614i	$-0.792127\pi$
$769$	3.57986	−	6.20050i	0.129093	−	0.223596i	0.923325	+	0.384018i	$0.125460\pi$
$770$		0			0
$771$	−3.30737	−	3.71688i	−0.119112	−	0.133860i
$772$	0.741933	−	0.428355i	0.0267027	−	0.0154168i
$773$			14.5998i			0.525117i	0.964916	+	0.262558i	$0.0845663\pi$
$773$			14.5998i			0.525117i	−0.964916	+	0.262558i	$0.915434\pi$
$774$	10.0101	−	4.31662i	0.359806	−	0.155158i
$775$		0			0
$776$	6.43935	+	11.1533i	0.231159	+	0.400379i
$777$	−3.26027	−	15.7940i	−0.116962	−	0.566606i
$778$	−12.8895	−	7.44178i	−0.462113	−	0.266801i
$779$	−0.486933	+	0.843393i	−0.0174462	+	0.0302177i
$780$		0			0
$781$	−19.8477	−	34.3772i	−0.710207	−	1.23011i
$782$		−	6.31760i		−	0.225917i
$783$	3.70428	−	7.94037i	0.132380	−	0.283766i
$784$	1.16578			0.0416348
$785$		0			0
$786$	0.0694710	−	0.209613i	0.00247795	−	0.00747663i
$787$	−15.9979	−	9.23638i	−0.570263	−	0.329242i	0.186991	−	0.982362i	$-0.440126\pi$
$787$	−15.9979	−	9.23638i	−0.570263	−	0.329242i	−0.757254	+	0.653120i	$0.773460\pi$
$788$	−8.51312	−	4.91505i	−0.303267	−	0.175092i
$789$	43.4654	−	8.97235i	1.54741	−	0.319424i
$790$		0			0
$791$	−16.8630			−0.599578
$792$	−32.8463	−	3.84291i	−1.16714	−	0.136552i
$793$			0.0234407i			0.000832405i
$794$	4.19242	+	7.26149i	0.148783	+	0.257700i
$795$		0			0
$796$	15.5039	−	26.8535i	0.549520	−	0.951796i
$797$	−35.5395	−	20.5187i	−1.25887	−	0.726810i	−0.286017	−	0.958225i	$-0.592331\pi$
$797$	−35.5395	−	20.5187i	−1.25887	−	0.726810i	−0.972855	+	0.231414i	$0.925665\pi$
$798$	0.559171	−	0.497564i	0.0197945	−	0.0176136i
$799$	−18.1068	−	31.3619i	−0.640573	−	1.10950i
$800$		0			0
$801$	15.0852	+	11.2332i	0.533010	+	0.396904i
$802$		−	3.38021i		−	0.119359i
$803$	35.3367	−	20.4016i	1.24700	−	0.719958i
$804$	−2.96089	+	0.611202i	−0.104423	+	0.0215554i
$805$		0			0
$806$	4.16686	−	7.21721i	0.146771	−	0.254215i
$807$	0.554408	+	0.183745i	0.0195161	+	0.00646814i
$808$	10.7883	−	6.22861i	0.379530	−	0.219122i
$809$	−7.19375			−0.252919			−0.126459	−	0.991972i	$-0.540361\pi$
$809$	−7.19375			−0.252919			−0.126459	+	0.991972i	$0.540361\pi$
$810$		0			0
$811$	38.2183			1.34203			0.671014	−	0.741445i	$-0.265859\pi$
$811$	38.2183			1.34203			0.671014	+	0.741445i	$0.265859\pi$
$812$	−6.64746	+	3.83791i	−0.233280	+	0.134684i
$813$	−35.5007	−	11.7658i	−1.24506	−	0.412646i
$814$	−5.30257	+	9.18431i	−0.185855	+	0.321910i
$815$		0			0
$816$	−14.5462	+	3.00271i	−0.509220	+	0.105116i
$817$	−2.36899	+	1.36774i	−0.0828805	+	0.0478511i
$818$		−	11.7139i		−	0.409566i
$819$	13.1502	+	9.79223i	0.459504	+	0.342168i
$820$		0			0
$821$	0.334280	+	0.578990i	0.0116665	+	0.0202069i	0.871800	−	0.489863i	$-0.162953\pi$
$821$	0.334280	+	0.578990i	0.0116665	+	0.0202069i	−0.860133	+	0.510069i	$0.829620\pi$
$822$	−2.12870	+	1.89417i	−0.0742470	+	0.0660668i
$823$	−1.23004	−	0.710165i	−0.0428766	−	0.0247548i	0.478408	−	0.878137i	$-0.341214\pi$
$823$	−1.23004	−	0.710165i	−0.0428766	−	0.0247548i	−0.521285	+	0.853383i	$0.674547\pi$
$824$	5.46393	−	9.46380i	0.190345	−	0.329687i
$825$		0			0
$826$	−6.19583	−	10.7315i	−0.215580	−	0.373396i
$827$			49.8169i			1.73230i	0.499782	+	0.866152i	$0.333414\pi$
$827$			49.8169i			1.73230i	−0.499782	+	0.866152i	$0.666586\pi$
$828$	22.2950	+	2.60845i	0.774807	+	0.0906498i
$829$	−36.4150			−1.26475			−0.632373	−	0.774664i	$-0.717919\pi$
$829$	−36.4150			−1.26475			−0.632373	+	0.774664i	$0.717919\pi$
$830$		0			0
$831$	−40.9378	+	8.45058i	−1.42012	+	0.293147i
$832$	5.75244	+	3.32117i	0.199430	+	0.115141i
$833$	−1.18204	−	0.682449i	−0.0409551	−	0.0236455i
$834$	−3.80312	+	11.4750i	−0.131691	+	0.397347i
$835$		0			0
$836$	3.90312			0.134992
$837$	−42.7493	+	3.73285i	−1.47763	+	0.129026i
$838$			5.04447i			0.174258i
$839$	−10.0445	−	17.3976i	−0.346774	−	0.600631i	0.638900	−	0.769290i	$-0.279390\pi$
$839$	−10.0445	−	17.3976i	−0.346774	−	0.600631i	−0.985674	+	0.168659i	$0.946056\pi$
$840$		0			0
$841$	13.0783	−	22.6523i	0.450976	−	0.781114i
$842$	3.35201	+	1.93528i	0.115518	+	0.0666942i
$843$	1.17907	+	5.71184i	0.0406092	+	0.196726i
$844$	1.45338	+	2.51732i	0.0500273	+	0.0866498i
$845$		0			0
$846$	−14.9000	+	6.42525i	−0.512272	+	0.220905i
$847$			69.3349i			2.38238i
$848$	22.1136	−	12.7673i	0.759383	−	0.438430i
$849$	−25.1575	−	28.2724i	−0.863402	−	0.970307i
$850$		0			0
$851$	7.65232	−	13.2542i	0.262318	−	0.454349i
$852$	−14.7884	+	13.1591i	−0.506642	+	0.450823i
$853$	−23.3034	+	13.4542i	−0.797892	+	0.460663i	−0.842733	−	0.538331i	$-0.819055\pi$
$853$	−23.3034	+	13.4542i	−0.797892	+	0.460663i	0.0448418	+	0.998994i	$0.485722\pi$
$854$	0.0133345			0.000456296
$855$		0			0
$856$	25.9742			0.887779
$857$	−42.2973	+	24.4204i	−1.44485	+	0.834184i	−0.998168	−	0.0605088i	$-0.980728\pi$
$857$	−42.2973	+	24.4204i	−1.44485	+	0.834184i	−0.446682	+	0.894693i	$0.647394\pi$
$858$	−2.17967	−	10.5591i	−0.0744128	−	0.360483i
$859$	−20.7047	+	35.8616i	−0.706435	+	1.22358i	0.259736	+	0.965680i	$0.416365\pi$
$859$	−20.7047	+	35.8616i	−0.706435	+	1.22358i	−0.966171	+	0.257902i	$0.916969\pi$
$860$		0			0
$861$	−3.81767	+	11.5189i	−0.130106	+	0.392564i
$862$	0.685465	−	0.395754i	0.0233470	−	0.0134794i
$863$			50.8101i			1.72960i	0.502119	+	0.864799i	$0.332554\pi$
$863$			50.8101i			1.72960i	−0.502119	+	0.864799i	$0.667446\pi$
$864$	2.19441	+	25.1308i	0.0746555	+	0.854969i
$865$		0			0
$866$	2.35679	+	4.08209i	0.0800871	+	0.138715i
$867$	−11.4429	−	3.79247i	−0.388621	−	0.128799i
$868$	32.5563	+	18.7964i	1.10503	+	0.637991i
$869$	29.2126	−	50.5977i	0.990970	−	1.71641i
$870$		0			0
$871$	−1.04783	−	1.81489i	−0.0355043	−	0.0614953i
$872$		−	3.39916i		−	0.115110i
$873$	21.4739	+	2.51237i	0.726781	+	0.0850310i
$874$	0.710328			0.0240272
$875$		0			0
$876$	−13.5263	−	15.2011i	−0.457013	−	0.513599i
$877$	0.354715	+	0.204795i	0.0119779	+	0.00691542i	0.505977	−	0.862547i	$-0.331132\pi$
$877$	0.354715	+	0.204795i	0.0119779	+	0.00691542i	−0.493999	+	0.869462i	$0.664465\pi$
$878$	5.25255	+	3.03256i	0.177265	+	0.102344i
$879$	−15.8362	−	17.7970i	−0.534143	−	0.600279i
$880$		0			0
$881$	−5.32851			−0.179522			−0.0897610	−	0.995963i	$-0.528610\pi$
$881$	−5.32851			−0.179522			−0.0897610	+	0.995963i	$0.528610\pi$
$882$	−0.365261	+	0.490516i	−0.0122990	+	0.0165165i
$883$			14.2064i			0.478083i	0.971009	+	0.239042i	$0.0768333\pi$
$883$			14.2064i			0.478083i	−0.971009	+	0.239042i	$0.923167\pi$
$884$	−5.99979	−	10.3919i	−0.201795	−	0.349519i
$885$		0			0
$886$	1.83482	−	3.17800i	0.0616419	−	0.106767i
$887$	6.26304	+	3.61597i	0.210292	+	0.121412i	0.601447	−	0.798913i	$-0.294591\pi$
$887$	6.26304	+	3.61597i	0.210292	+	0.121412i	−0.391155	+	0.920325i	$0.627924\pi$
$888$	10.6732	+	3.53737i	0.358169	+	0.118706i
$889$	−11.8649	−	20.5506i	−0.397936	−	0.689245i
$890$		0			0
$891$	−38.1074	+	40.3734i	−1.27665	+	1.35256i
$892$		−	13.7604i		−	0.460733i
$893$	3.52622	−	2.03586i	0.118000	−	0.0681276i
$894$	2.61829	−	7.90008i	0.0875688	−	0.264218i
$895$		0			0
$896$	14.3325	−	24.8246i	0.478815	−	0.829331i
$897$	3.14556	+	15.2383i	0.105027	+	0.508792i
$898$	13.6645	−	7.88919i	0.455989	−	0.263266i
$899$	13.9256			0.464444
$900$		0			0
$901$	−29.8960			−0.995981
$902$	6.91093	−	3.99003i	0.230109	−	0.132853i
$903$	−25.4644	+	22.6588i	−0.847401	+	0.754038i
$904$	5.87864	−	10.1821i	0.195521	−	0.338651i
$905$		0			0
$906$	−5.62130	−	6.31731i	−0.186755	−	0.209879i
$907$	33.6106	−	19.4051i	1.11602	−	0.644335i	0.175639	−	0.984455i	$-0.443801\pi$
$907$	33.6106	−	19.4051i	1.11602	−	0.644335i	0.940382	+	0.340120i	$0.110468\pi$
$908$		−	19.9986i		−	0.663677i
$909$	2.43015	−	20.7711i	0.0806031	−	0.688935i
$910$		0			0
$911$	20.1390	+	34.8819i	0.667236	+	1.15569i	0.978674	+	0.205421i	$0.0658563\pi$
$911$	20.1390	+	34.8819i	0.667236	+	1.15569i	−0.311437	+	0.950267i	$0.600810\pi$
$912$	−0.337614	−	1.63553i	−0.0111795	−	0.0541577i
$913$	55.6641	+	32.1377i	1.84221	+	1.06360i
$914$	−9.04371	+	15.6642i	−0.299139	+	0.518125i
$915$		0			0
$916$	−9.30424	−	16.1154i	−0.307421	−	0.532468i
$917$			0.690479i			0.0228016i
$918$	3.29419	−	7.06133i	0.108725	−	0.233059i
$919$	13.0468			0.430375			0.215187	−	0.976573i	$-0.430964\pi$
$919$	13.0468			0.430375			0.215187	+	0.976573i	$0.430964\pi$
$920$		0			0
$921$	18.6456	−	56.2586i	0.614392	−	1.85378i
$922$	−12.8297	−	7.40722i	−0.422523	−	0.243944i
$923$	−11.8832	−	6.86074i	−0.391139	−	0.225824i
$924$	47.6315	−	9.83234i	1.56696	−	0.323460i
$925$		0			0
$926$	5.71936			0.187950
$927$	−7.26433	−	16.8458i	−0.238592	−	0.553289i
$928$		−	8.18638i		−	0.268731i
$929$	0.146912	+	0.254460i	0.00482004	+	0.00834855i	0.868425	−	0.495820i	$-0.165132\pi$
$929$	0.146912	+	0.254460i	0.00482004	+	0.00834855i	−0.863605	+	0.504168i	$0.831799\pi$
$930$		0			0
$931$	0.0767321	−	0.132904i	0.00251479	−	0.00435575i
$932$	−4.46374	−	2.57714i	−0.146215	−	0.0844171i
$933$	29.8123	−	26.5277i	0.976010	−	0.868477i
$934$	−1.79947	−	3.11678i	−0.0588805	−	0.101984i
$935$		0			0
$936$	−10.4970	+	4.52657i	−0.343105	+	0.147956i
$937$		−	16.9141i		−	0.552559i	−0.961077	−	0.276280i	$-0.910898\pi$
$937$		−	16.9141i		−	0.552559i	0.961077	−	0.276280i	$-0.0891016\pi$
$938$	−1.03242	+	0.596067i	−0.0337097	+	0.0194623i
$939$	−6.09187	+	1.25752i	−0.198801	+	0.0410375i
$940$		0			0
$941$	−28.6046	+	49.5447i	−0.932485	+	1.61511i	−0.153426	+	0.988160i	$0.549031\pi$
$941$	−28.6046	+	49.5447i	−0.932485	+	1.61511i	−0.779059	+	0.626951i	$0.784303\pi$
$942$	0.826796	+	0.274022i	0.0269385	+	0.00892811i
$943$	−9.97342	+	5.75815i	−0.324779	+	0.187511i
$944$	−27.6478			−0.899858
$945$		0			0
$946$	22.4150			0.728775
$947$	−33.6664	+	19.4373i	−1.09401	+	0.631627i	−0.934641	−	0.355592i	$-0.884279\pi$
$947$	−33.6664	+	19.4373i	−1.09401	+	0.631627i	−0.159369	+	0.987219i	$0.550946\pi$
$948$	−27.6563	−	9.16600i	−0.898234	−	0.297698i
$949$	7.05222	−	12.2148i	0.228925	−	0.396509i
$950$		0			0
$951$	−22.3582	+	4.61529i	−0.725013	+	0.149661i
$952$	−12.5686	+	7.25648i	−0.407350	+	0.235184i
$953$			54.4516i			1.76386i	0.471381	+	0.881930i	$0.343756\pi$
$953$			54.4516i			1.76386i	−0.471381	+	0.881930i	$0.656244\pi$
$954$	−1.55662	+	13.3048i	−0.0503974	+	0.430760i
$955$		0			0
$956$	14.5230	+	25.1546i	0.469708	+	0.813557i
$957$	13.4593	−	11.9764i	0.435076	−	0.387141i
$958$	−13.3133	−	7.68644i	−0.430133	−	0.248338i
$959$	4.45482	−	7.71598i	0.143854	−	0.249162i
$960$		0			0
$961$	−18.6006	−	32.2172i	−0.600020	−	1.03926i
$962$			3.66587i			0.118192i
$963$	26.0428	−	34.9734i	0.839217	−	1.12700i
$964$	31.1229			1.00240
$965$		0			0
$966$	8.66844	−	1.78938i	0.278902	−	0.0575725i
$967$	16.9482	+	9.78507i	0.545018	+	0.314666i	0.747110	−	0.664700i	$-0.231441\pi$
$967$	16.9482	+	9.78507i	0.545018	+	0.314666i	−0.202092	+	0.979367i	$0.564774\pi$
$968$	−41.8654	−	24.1710i	−1.34560	−	0.776885i
$969$	−0.615120	+	1.85598i	−0.0197605	+	0.0596226i
$970$		0			0
$971$	6.31009			0.202500			0.101250	−	0.994861i	$-0.467716\pi$
$971$	6.31009			0.202500			0.101250	+	0.994861i	$0.467716\pi$
$972$	23.5596	+	14.5409i	0.755674	+	0.466399i
$973$		−	37.7995i		−	1.21180i
$974$	−1.05564	−	1.82843i	−0.0338250	−	0.0585866i
$975$		0			0
$976$	0.0148757	−	0.0257654i	0.000476158	−	0.000824731i
$977$	−6.42514	−	3.70955i	−0.205558	−	0.118679i	0.393687	−	0.919244i	$-0.371199\pi$
$977$	−6.42514	−	3.70955i	−0.205558	−	0.118679i	−0.599245	+	0.800565i	$0.704533\pi$
$978$	−2.84008	−	13.7584i	−0.0908158	−	0.439946i
$979$	19.3367	+	33.4922i	0.618004	+	1.07041i
$980$		0			0
$981$	−4.57686	−	3.40814i	−0.146128	−	0.108814i
$982$			15.5426i			0.495986i
$983$	9.51134	−	5.49137i	0.303365	−	0.175148i	−0.340589	−	0.940212i	$-0.610626\pi$
$983$	9.51134	−	5.49137i	0.303365	−	0.175148i	0.643953	+	0.765065i	$0.277293\pi$
$984$	−5.62440	−	6.32080i	−0.179299	−	0.201500i
$985$		0			0
$986$	−1.26430	+	2.18983i	−0.0402635	+	0.0697384i
$987$	37.9035	−	33.7274i	1.20648	−	1.07356i
$988$	1.16843	−	0.674595i	0.0371728	−	0.0214617i
$989$	−32.3479			−1.02860
$990$		0			0
$991$	−21.3721			−0.678908			−0.339454	−	0.940623i	$-0.610242\pi$
$991$	−21.3721			−0.678908			−0.339454	+	0.940623i	$0.610242\pi$
$992$	−34.7217	+	20.0466i	−1.10242	+	0.636480i
$993$	0.414069	+	2.00591i	0.0131401	+	0.0636555i
$994$	−3.90280	+	6.75984i	−0.123789	+	0.214409i
$995$		0			0
$996$	10.0838	−	30.4255i	0.319518	−	0.964070i
$997$	−26.4439	+	15.2674i	−0.837487	+	0.483524i	−0.856409	−	0.516297i	$-0.827310\pi$
$997$	−26.4439	+	15.2674i	−0.837487	+	0.483524i	0.0189220	+	0.999821i	$0.493977\pi$
$998$			16.1863i			0.512368i
$999$	15.4644	−	10.8244i	0.489271	−	0.342469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.k.c.49.5		16
3.2	odd	2		675.2.k.c.199.4		16
5.2	odd	4		225.2.e.c.76.3	✓	8
5.3	odd	4		225.2.e.e.76.2	yes	8
5.4	even	2	inner	225.2.k.c.49.4		16
9.2	odd	6		675.2.k.c.424.5		16
9.4	even	3		2025.2.b.n.649.5		8
9.5	odd	6		2025.2.b.o.649.4		8
9.7	even	3	inner	225.2.k.c.124.4		16
15.2	even	4		675.2.e.e.226.2		8
15.8	even	4		675.2.e.c.226.3		8
15.14	odd	2		675.2.k.c.199.5		16
45.2	even	12		675.2.e.e.451.2		8
45.4	even	6		2025.2.b.n.649.4		8
45.7	odd	12		225.2.e.c.151.3	yes	8
45.13	odd	12		2025.2.a.q.1.3		4
45.14	odd	6		2025.2.b.o.649.5		8
45.22	odd	12		2025.2.a.y.1.2		4
45.23	even	12		2025.2.a.z.1.2		4
45.29	odd	6		675.2.k.c.424.4		16
45.32	even	12		2025.2.a.p.1.3		4
45.34	even	6	inner	225.2.k.c.124.5		16
45.38	even	12		675.2.e.c.451.3		8
45.43	odd	12		225.2.e.e.151.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.3	✓	8	5.2	odd	4
225.2.e.c.151.3	yes	8	45.7	odd	12
225.2.e.e.76.2	yes	8	5.3	odd	4
225.2.e.e.151.2	yes	8	45.43	odd	12
225.2.k.c.49.4		16	5.4	even	2	inner
225.2.k.c.49.5		16	1.1	even	1	trivial
225.2.k.c.124.4		16	9.7	even	3	inner
225.2.k.c.124.5		16	45.34	even	6	inner
675.2.e.c.226.3		8	15.8	even	4
675.2.e.c.451.3		8	45.38	even	12
675.2.e.e.226.2		8	15.2	even	4
675.2.e.e.451.2		8	45.2	even	12
675.2.k.c.199.4		16	3.2	odd	2
675.2.k.c.199.5		16	15.14	odd	2
675.2.k.c.424.4		16	45.29	odd	6
675.2.k.c.424.5		16	9.2	odd	6
2025.2.a.p.1.3		4	45.32	even	12
2025.2.a.q.1.3		4	45.13	odd	12
2025.2.a.y.1.2		4	45.22	odd	12
2025.2.a.z.1.2		4	45.23	even	12
2025.2.b.n.649.4		8	45.4	even	6
2025.2.b.n.649.5		8	9.4	even	3
2025.2.b.o.649.4		8	9.5	odd	6
2025.2.b.o.649.5		8	45.14	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.409850 - 0.236627i) q^{2} +(-1.64411 - 0.544899i) q^{3} +(-0.888015 + 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(2.21967 - 1.28153i) q^{7} +1.78702i q^{8} +(2.40617 + 1.79175i) q^{9} +O(q^{10})\)	\(q+(0.409850 - 0.236627i) q^{2} +(-1.64411 - 0.544899i) q^{3} +(-0.888015 + 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(2.21967 - 1.28153i) q^{7} +1.78702i q^{8} +(2.40617 + 1.79175i) q^{9} +(3.08430 + 5.34217i) q^{11} +(2.29809 - 2.04490i) q^{12} +(1.84662 + 1.06615i) q^{13} +(0.606488 - 1.05047i) q^{14} +(-1.35317 - 2.34376i) q^{16} +3.16860i q^{17} +(1.41015 + 0.164982i) q^{18} -0.356267 q^{19} +(-4.34768 + 0.897469i) q^{21} +(2.52821 + 1.45966i) q^{22} +(-3.64854 - 2.10649i) q^{23} +(0.973748 - 2.93806i) q^{24} +1.00912 q^{26} +(-2.97968 - 4.25694i) q^{27} +4.55206i q^{28} +(0.843116 + 1.46032i) q^{29} +(4.12920 - 7.15199i) q^{31} +(-4.20441 - 2.42742i) q^{32} +(-2.15998 - 10.4637i) q^{33} +(0.749778 + 1.29865i) q^{34} +(-4.89257 + 2.10980i) q^{36} +3.63274i q^{37} +(-0.146016 + 0.0843024i) q^{38} +(-2.45510 - 2.75908i) q^{39} +(1.36677 - 2.36731i) q^{41} +(-1.56953 + 1.39661i) q^{42} +(6.64949 - 3.83908i) q^{43} -10.9556 q^{44} -1.99381 q^{46} +(-9.89770 + 5.71444i) q^{47} +(0.947643 + 4.59074i) q^{48} +(-0.215378 + 0.373046i) q^{49} +(1.72657 - 5.20952i) q^{51} +(-3.27966 + 1.89351i) q^{52} +9.43507i q^{53} +(-2.22853 - 1.03964i) q^{54} +(2.29012 + 3.96660i) q^{56} +(0.585740 + 0.194129i) q^{57} +(0.691103 + 0.399008i) q^{58} +(5.10795 - 8.84723i) q^{59} +(0.00549659 + 0.00952038i) q^{61} -3.90833i q^{62} +(7.63707 + 0.893512i) q^{63} +3.11511 q^{64} +(-3.36127 - 3.77745i) q^{66} +(-0.851145 - 0.491409i) q^{67} +(-4.87359 - 2.81377i) q^{68} +(4.85077 + 5.45138i) q^{69} -6.43507 q^{71} +(-3.20189 + 4.29988i) q^{72} -6.61467i q^{73} +(0.859605 + 1.48888i) q^{74} +(0.316370 - 0.547969i) q^{76} +(13.6923 + 7.90523i) q^{77} +(-1.65910 - 0.549868i) q^{78} +(-4.73569 - 8.20246i) q^{79} +(2.57930 + 8.62248i) q^{81} -1.29366i q^{82} +(9.02378 - 5.20988i) q^{83} +(2.48042 - 7.48407i) q^{84} +(1.81686 - 3.14690i) q^{86} +(-0.590444 - 2.86033i) q^{87} +(-9.54658 + 5.51172i) q^{88} +6.26940 q^{89} +5.46519 q^{91} +(6.47993 - 3.74119i) q^{92} +(-10.6860 + 9.50863i) q^{93} +(-2.70439 + 4.68413i) q^{94} +(5.58980 + 6.28191i) q^{96} +(6.24126 - 3.60339i) q^{97} +0.203858i q^{98} +(-2.15045 + 18.3804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Introduction

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