LMFDB - Embedded newform 950.2.f.c.493.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, degree $2$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 $ x^16 + 24x^14 + 212x^12 + 880x^10 + 1858x^8 + 1960x^6 + 892x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.1
Root			$1.04813i$ of defining polynomial
Character	$\chi$	$=$	950.493
Dual form			950.2.f.c.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.68553 + 1.68553i) q^{3} +1.00000i q^{4} +2.38370 q^{6} +(2.49494 - 2.49494i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.68204i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.68553 + 1.68553i) q^{3} +1.00000i q^{4} +2.38370 q^{6} +(2.49494 - 2.49494i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.68204i q^{9} -3.60618 q^{11} +(-1.68553 - 1.68553i) q^{12} +(-2.82127 + 2.82127i) q^{13} -3.52838 q^{14} -1.00000 q^{16} +(2.34102 - 2.34102i) q^{17} +(-1.89649 + 1.89649i) q^{18} +(1.57153 + 4.06575i) q^{19} +8.41061i q^{21} +(2.54995 + 2.54995i) q^{22} +(-0.793280 - 0.793280i) q^{23} +2.38370i q^{24} +3.98988 q^{26} +(-0.535925 - 0.535925i) q^{27} +(2.49494 + 2.49494i) q^{28} -4.81790 q^{29} +3.69603i q^{31} +(0.707107 + 0.707107i) q^{32} +(6.07833 - 6.07833i) q^{33} -3.31071 q^{34} +2.68204 q^{36} +(2.34615 + 2.34615i) q^{37} +(1.76368 - 3.98615i) q^{38} -9.51069i q^{39} -7.28874i q^{41} +(5.94720 - 5.94720i) q^{42} +(-1.22979 - 1.22979i) q^{43} -3.60618i q^{44} +1.12187i q^{46} +(-7.44945 + 7.44945i) q^{47} +(1.68553 - 1.68553i) q^{48} -5.44945i q^{49} +7.89174i q^{51} +(-2.82127 - 2.82127i) q^{52} +(-2.44629 + 2.44629i) q^{53} +0.757912i q^{54} -3.52838i q^{56} +(-9.50181 - 4.20410i) q^{57} +(3.40677 + 3.40677i) q^{58} -8.96359 q^{59} -11.6915 q^{61} +(2.61349 - 2.61349i) q^{62} +(-6.69154 - 6.69154i) q^{63} -1.00000i q^{64} -8.59606 q^{66} +(-8.19965 - 8.19965i) q^{67} +(2.34102 + 2.34102i) q^{68} +2.67420 q^{69} -15.8527i q^{71} +(-1.89649 - 1.89649i) q^{72} +(-7.33090 - 7.33090i) q^{73} -3.31796i q^{74} +(-4.06575 + 1.57153i) q^{76} +(-8.99719 + 8.99719i) q^{77} +(-6.72508 + 6.72508i) q^{78} -16.1990 q^{79} +9.85277 q^{81} +(-5.15392 + 5.15392i) q^{82} +(-1.38370 - 1.38370i) q^{83} -8.41061 q^{84} +1.73918i q^{86} +(8.12073 - 8.12073i) q^{87} +(-2.54995 + 2.54995i) q^{88} +11.9533 q^{89} +14.0778i q^{91} +(0.793280 - 0.793280i) q^{92} +(-6.22979 - 6.22979i) q^{93} +10.5351 q^{94} -2.38370 q^{96} +(3.46802 + 3.46802i) q^{97} +(-3.85334 + 3.85334i) q^{98} +9.67192i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) $ 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.68553	+	1.68553i	−0.973143	+	0.973143i	−0.999649	−	0.0265056i	$-0.991562\pi$
$3$	−1.68553	+	1.68553i	−0.973143	+	0.973143i	0.0265056	+	0.999649i	$0.491562\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.38370			0.973143
$7$	2.49494	−	2.49494i	0.942999	−	0.942999i	−0.0554621	−	0.998461i	$-0.517663\pi$
$7$	2.49494	−	2.49494i	0.942999	−	0.942999i	0.998461	+	0.0554621i	$0.0176632\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	2.68204i		−	0.894015i
$10$		0			0
$11$	−3.60618			−1.08730			−0.543652	−	0.839311i	$-0.682959\pi$
$11$	−3.60618			−1.08730			−0.543652	+	0.839311i	$0.682959\pi$
$12$	−1.68553	−	1.68553i	−0.486572	−	0.486572i
$13$	−2.82127	+	2.82127i	−0.782480	+	0.782480i	−0.980249	−	0.197769i	$-0.936630\pi$
$13$	−2.82127	+	2.82127i	−0.782480	+	0.782480i	0.197769	+	0.980249i	$0.436630\pi$
$14$	−3.52838			−0.942999
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.34102	−	2.34102i	0.567781	−	0.567781i	−0.363725	−	0.931506i	$-0.618495\pi$
$17$	2.34102	−	2.34102i	0.567781	−	0.567781i	0.931506	+	0.363725i	$0.118495\pi$
$18$	−1.89649	+	1.89649i	−0.447007	+	0.447007i
$19$	1.57153	+	4.06575i	0.360533	+	0.932747i
$19$	1.57153	+	4.06575i	0.360533	+	0.932747i
$20$		0			0
$21$			8.41061i			1.83535i
$22$	2.54995	+	2.54995i	0.543652	+	0.543652i
$23$	−0.793280	−	0.793280i	−0.165410	−	0.165410i	0.619548	−	0.784959i	$-0.287316\pi$
$23$	−0.793280	−	0.793280i	−0.165410	−	0.165410i	−0.784959	+	0.619548i	$0.787316\pi$
$24$			2.38370i			0.486572i
$25$		0			0
$26$	3.98988			0.782480
$27$	−0.535925	−	0.535925i	−0.103139	−	0.103139i
$28$	2.49494	+	2.49494i	0.471499	+	0.471499i
$29$	−4.81790			−0.894662			−0.447331	−	0.894369i	$-0.647625\pi$
$29$	−4.81790			−0.894662			−0.447331	+	0.894369i	$0.647625\pi$
$30$		0			0
$31$			3.69603i			0.663827i	0.943310	+	0.331914i	$0.107694\pi$
$31$			3.69603i			0.663827i	−0.943310	+	0.331914i	$0.892306\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	6.07833	−	6.07833i	1.05810	−	1.05810i
$34$	−3.31071			−0.567781
$35$		0			0
$36$	2.68204			0.447007
$37$	2.34615	+	2.34615i	0.385705	+	0.385705i	0.873152	−	0.487448i	$-0.162072\pi$
$37$	2.34615	+	2.34615i	0.385705	+	0.385705i	−0.487448	+	0.873152i	$0.662072\pi$
$38$	1.76368	−	3.98615i	0.286107	−	0.646640i
$39$		−	9.51069i		−	1.52293i
$40$		0			0
$41$		−	7.28874i		−	1.13831i	−0.822230	−	0.569155i	$-0.807270\pi$
$41$		−	7.28874i		−	1.13831i	0.822230	−	0.569155i	$-0.192730\pi$
$42$	5.94720	−	5.94720i	0.917673	−	0.917673i
$43$	−1.22979	−	1.22979i	−0.187541	−	0.187541i	0.607091	−	0.794632i	$-0.292336\pi$
$43$	−1.22979	−	1.22979i	−0.187541	−	0.187541i	−0.794632	+	0.607091i	$0.792336\pi$
$44$		−	3.60618i		−	0.543652i
$45$		0			0
$46$			1.12187i			0.165410i
$47$	−7.44945	+	7.44945i	−1.08661	+	1.08661i	−0.0907396	+	0.995875i	$0.528923\pi$
$47$	−7.44945	+	7.44945i	−1.08661	+	1.08661i	−0.995875	+	0.0907396i	$0.971077\pi$
$48$	1.68553	−	1.68553i	0.243286	−	0.243286i
$49$		−	5.44945i		−	0.778493i
$50$		0			0
$51$			7.89174i			1.10506i
$52$	−2.82127	−	2.82127i	−0.391240	−	0.391240i
$53$	−2.44629	+	2.44629i	−0.336023	+	0.336023i	−0.854868	−	0.518845i	$-0.826362\pi$
$53$	−2.44629	+	2.44629i	−0.336023	+	0.336023i	0.518845	+	0.854868i	$0.326362\pi$
$54$			0.757912i			0.103139i
$55$		0			0
$56$		−	3.52838i		−	0.471499i
$57$	−9.50181	−	4.20410i	−1.25855	−	0.556846i
$58$	3.40677	+	3.40677i	0.447331	+	0.447331i
$59$	−8.96359			−1.16696			−0.583480	−	0.812127i	$-0.698309\pi$
$59$	−8.96359			−1.16696			−0.583480	+	0.812127i	$0.698309\pi$
$60$		0			0
$61$	−11.6915			−1.49695			−0.748474	−	0.663164i	$-0.769213\pi$
$61$	−11.6915			−1.49695			−0.748474	+	0.663164i	$0.769213\pi$
$62$	2.61349	−	2.61349i	0.331914	−	0.331914i
$63$	−6.69154	−	6.69154i	−0.843055	−	0.843055i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−8.59606			−1.05810
$67$	−8.19965	−	8.19965i	−1.00175	−	1.00175i	−0.999998	−	0.00174823i	$-0.999444\pi$
$67$	−8.19965	−	8.19965i	−1.00175	−	1.00175i	−0.00174823	−	0.999998i	$-0.500556\pi$
$68$	2.34102	+	2.34102i	0.283891	+	0.283891i
$69$	2.67420			0.321936
$70$		0			0
$71$		−	15.8527i		−	1.88137i	−0.339283	−	0.940684i	$-0.610185\pi$
$71$		−	15.8527i		−	1.88137i	0.339283	−	0.940684i	$-0.389815\pi$
$72$	−1.89649	−	1.89649i	−0.223504	−	0.223504i
$73$	−7.33090	−	7.33090i	−0.858017	−	0.858017i	0.133087	−	0.991104i	$-0.457511\pi$
$73$	−7.33090	−	7.33090i	−0.858017	−	0.858017i	−0.991104	+	0.133087i	$0.957511\pi$
$74$		−	3.31796i		−	0.385705i
$75$		0			0
$76$	−4.06575	+	1.57153i	−0.466373	+	0.180266i
$77$	−8.99719	+	8.99719i	−1.02533	+	1.02533i
$78$	−6.72508	+	6.72508i	−0.761465	+	0.761465i
$79$	−16.1990			−1.82253			−0.911266	−	0.411818i	$-0.864894\pi$
$79$	−16.1990			−1.82253			−0.911266	+	0.411818i	$0.864894\pi$
$80$		0			0
$81$	9.85277			1.09475
$82$	−5.15392	+	5.15392i	−0.569155	+	0.569155i
$83$	−1.38370	−	1.38370i	−0.151881	−	0.151881i	0.627076	−	0.778958i	$-0.284251\pi$
$83$	−1.38370	−	1.38370i	−0.151881	−	0.151881i	−0.778958	+	0.627076i	$0.784251\pi$
$84$	−8.41061			−0.917673
$85$		0			0
$86$			1.73918i			0.187541i
$87$	8.12073	−	8.12073i	0.870634	−	0.870634i
$88$	−2.54995	+	2.54995i	−0.271826	+	0.271826i
$89$	11.9533			1.26705			0.633524	−	0.773723i	$-0.281608\pi$
$89$	11.9533			1.26705			0.633524	+	0.773723i	$0.281608\pi$
$90$		0			0
$91$			14.0778i			1.47576i
$92$	0.793280	−	0.793280i	0.0827052	−	0.0827052i
$93$	−6.22979	−	6.22979i	−0.645999	−	0.645999i
$94$	10.5351			1.08661
$95$		0			0
$96$	−2.38370			−0.243286
$97$	3.46802	+	3.46802i	0.352124	+	0.352124i	0.860899	−	0.508775i	$-0.169902\pi$
$97$	3.46802	+	3.46802i	0.352124	+	0.352124i	−0.508775	+	0.860899i	$0.669902\pi$
$98$	−3.85334	+	3.85334i	−0.389247	+	0.389247i
$99$			9.67192i			0.972065i
$100$		0			0
$101$	6.46456			0.643248			0.321624	−	0.946868i	$-0.395771\pi$
$101$	6.46456			0.643248			0.321624	+	0.946868i	$0.395771\pi$
$102$	5.58030	−	5.58030i	0.552532	−	0.552532i
$103$	−8.62475	+	8.62475i	−0.849822	+	0.849822i	−0.990111	−	0.140288i	$-0.955197\pi$
$103$	−8.62475	+	8.62475i	−0.849822	+	0.849822i	0.140288	+	0.990111i	$0.455197\pi$
$104$			3.98988i			0.391240i
$105$		0			0
$106$	3.45957			0.336023
$107$	−11.7924	−	11.7924i	−1.14001	−	1.14001i	−0.988448	−	0.151563i	$-0.951569\pi$
$107$	−11.7924	−	11.7924i	−1.14001	−	1.14001i	−0.151563	−	0.988448i	$-0.548431\pi$
$108$	0.535925	−	0.535925i	0.0515694	−	0.0515694i
$109$	18.4961			1.77160			0.885801	−	0.464065i	$-0.153610\pi$
$109$	18.4961			1.77160			0.885801	+	0.464065i	$0.153610\pi$
$110$		0			0
$111$	−7.90902			−0.750691
$112$	−2.49494	+	2.49494i	−0.235750	+	0.235750i
$113$	6.17528	−	6.17528i	0.580922	−	0.580922i	−0.354235	−	0.935156i	$-0.615259\pi$
$113$	6.17528	−	6.17528i	0.580922	−	0.580922i	0.935156	+	0.354235i	$0.115259\pi$
$114$	3.74605	+	9.69154i	0.350850	+	0.907696i
$115$		0			0
$116$		−	4.81790i		−	0.447331i
$117$	7.56677	+	7.56677i	0.699549	+	0.699549i
$118$	6.33822	+	6.33822i	0.583480	+	0.583480i
$119$		−	11.6814i		−	1.07083i
$120$		0			0
$121$	2.00451			0.182228
$122$	8.26717	+	8.26717i	0.748474	+	0.748474i
$123$	12.2854	+	12.2854i	1.10774	+	1.10774i
$124$	−3.69603			−0.331914
$125$		0			0
$126$			9.46327i			0.843055i
$127$	6.71439	+	6.71439i	0.595806	+	0.595806i	0.939194	−	0.343388i	$-0.111574\pi$
$127$	6.71439	+	6.71439i	0.595806	+	0.595806i	−0.343388	+	0.939194i	$0.611574\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	4.14569			0.365008
$130$		0			0
$131$	−7.36409			−0.643403			−0.321702	−	0.946841i	$-0.604255\pi$
$131$	−7.36409			−0.643403			−0.321702	+	0.946841i	$0.604255\pi$
$132$	6.07833	+	6.07833i	0.529051	+	0.529051i
$133$	14.0647	+	6.22294i	1.21956	+	0.539597i
$134$			11.5961i			1.00175i
$135$		0			0
$136$		−	3.31071i		−	0.283891i
$137$	−12.5579	+	12.5579i	−1.07289	+	1.07289i	−0.0757667	+	0.997126i	$0.524140\pi$
$137$	−12.5579	+	12.5579i	−1.07289	+	1.07289i	−0.997126	+	0.0757667i	$0.975860\pi$
$138$	−1.89095	−	1.89095i	−0.160968	−	0.160968i
$139$			10.3078i			0.874299i	0.899389	+	0.437150i	$0.144012\pi$
$139$			10.3078i			0.874299i	−0.899389	+	0.437150i	$0.855988\pi$
$140$		0			0
$141$		−	25.1126i		−	2.11486i
$142$	−11.2095	+	11.2095i	−0.940684	+	0.940684i
$143$	10.1740	−	10.1740i	0.850793	−	0.850793i
$144$			2.68204i			0.223504i
$145$		0			0
$146$			10.3675i			0.858017i
$147$	9.18523	+	9.18523i	0.757585	+	0.757585i
$148$	−2.34615	+	2.34615i	−0.192852	+	0.192852i
$149$			0.943747i			0.0773148i	0.999253	+	0.0386574i	$0.0123081\pi$
$149$			0.943747i			0.0773148i	−0.999253	+	0.0386574i	$0.987692\pi$
$150$		0			0
$151$		−	2.42082i		−	0.197004i	−0.995137	−	0.0985018i	$-0.968595\pi$
$151$		−	2.42082i		−	0.197004i	0.995137	−	0.0985018i	$-0.0314050\pi$
$152$	3.98615	+	1.76368i	0.323320	+	0.143053i
$153$	−6.27873	−	6.27873i	−0.507605	−	0.507605i
$154$	12.7240			1.02533
$155$		0			0
$156$	9.51069			0.761465
$157$	7.99439	−	7.99439i	0.638022	−	0.638022i	−0.312046	−	0.950067i	$-0.601014\pi$
$157$	7.99439	−	7.99439i	0.638022	−	0.638022i	0.950067	+	0.312046i	$0.101014\pi$
$158$	11.4544	+	11.4544i	0.911266	+	0.911266i
$159$		−	8.24660i		−	0.653998i
$160$		0			0
$161$	−3.95837			−0.311964
$162$	−6.96696	−	6.96696i	−0.547376	−	0.547376i
$163$	2.70447	+	2.70447i	0.211830	+	0.211830i	0.805045	−	0.593214i	$-0.202141\pi$
$163$	2.70447	+	2.70447i	0.211830	+	0.211830i	−0.593214	+	0.805045i	$0.702141\pi$
$164$	7.28874			0.569155
$165$		0			0
$166$			1.95685i			0.151881i
$167$	−1.55766	−	1.55766i	−0.120535	−	0.120535i	0.644266	−	0.764801i	$-0.277163\pi$
$167$	−1.55766	−	1.55766i	−0.120535	−	0.120535i	−0.764801	+	0.644266i	$0.777163\pi$
$168$	5.94720	+	5.94720i	0.458836	+	0.458836i
$169$		−	2.91914i		−	0.224550i
$170$		0			0
$171$	10.9045	−	4.21490i	0.833889	−	0.322321i
$172$	1.22979	−	1.22979i	0.0937703	−	0.0937703i
$173$	−5.06728	+	5.06728i	−0.385258	+	0.385258i	−0.872992	−	0.487734i	$-0.837824\pi$
$173$	−5.06728	+	5.06728i	−0.385258	+	0.385258i	0.487734	+	0.872992i	$0.337824\pi$
$174$	−11.4844			−0.870634
$175$		0			0
$176$	3.60618			0.271826
$177$	15.1084	−	15.1084i	1.13562	−	1.13562i
$178$	−8.45226	−	8.45226i	−0.633524	−	0.633524i
$179$	−13.5056			−1.00946			−0.504729	−	0.863278i	$-0.668408\pi$
$179$	−13.5056			−1.00946			−0.504729	+	0.863278i	$0.668408\pi$
$180$		0			0
$181$		−	10.9848i		−	0.816492i	−0.912872	−	0.408246i	$-0.866141\pi$
$181$		−	10.9848i		−	0.816492i	0.912872	−	0.408246i	$-0.133859\pi$
$182$	9.95451	−	9.95451i	0.737878	−	0.737878i
$183$	19.7065	−	19.7065i	1.45674	−	1.45674i
$184$	−1.12187			−0.0827052
$185$		0			0
$186$			8.81025i			0.645999i
$187$	−8.44214	+	8.44214i	−0.617350	+	0.617350i
$188$	−7.44945	−	7.44945i	−0.543307	−	0.543307i
$189$	−2.67420			−0.194520
$190$		0			0
$191$	−18.6006			−1.34589			−0.672945	−	0.739693i	$-0.734971\pi$
$191$	−18.6006			−1.34589			−0.672945	+	0.739693i	$0.734971\pi$
$192$	1.68553	+	1.68553i	0.121643	+	0.121643i
$193$	4.46428	−	4.46428i	0.321346	−	0.321346i	−0.527937	−	0.849283i	$-0.677034\pi$
$193$	4.46428	−	4.46428i	0.321346	−	0.321346i	0.849283	+	0.527937i	$0.177034\pi$
$194$		−	4.90452i		−	0.352124i
$195$		0			0
$196$	5.44945			0.389247
$197$	−2.14941	+	2.14941i	−0.153139	+	0.153139i	−0.779518	−	0.626379i	$-0.784536\pi$
$197$	−2.14941	+	2.14941i	−0.153139	+	0.153139i	0.626379	+	0.779518i	$0.284536\pi$
$198$	6.83908	−	6.83908i	0.486032	−	0.486032i
$199$			16.4298i			1.16468i	0.812945	+	0.582340i	$0.197863\pi$
$199$			16.4298i			1.16468i	−0.812945	+	0.582340i	$0.802137\pi$
$200$		0			0
$201$	27.6416			1.94969
$202$	−4.57113	−	4.57113i	−0.321624	−	0.321624i
$203$	−12.0204	+	12.0204i	−0.843665	+	0.843665i
$204$	−7.89174			−0.552532
$205$		0			0
$206$	12.1972			0.849822
$207$	−2.12761	+	2.12761i	−0.147879	+	0.147879i
$208$	2.82127	−	2.82127i	0.195620	−	0.195620i
$209$	−5.66720	−	14.6618i	−0.392008	−	1.01418i
$210$		0			0
$211$			5.51385i			0.379589i	0.981824	+	0.189795i	$0.0607822\pi$
$211$			5.51385i			0.379589i	−0.981824	+	0.189795i	$0.939218\pi$
$212$	−2.44629	−	2.44629i	−0.168012	−	0.168012i
$213$	26.7202	+	26.7202i	1.83084	+	1.83084i
$214$			16.6769i			1.14001i
$215$		0			0
$216$	−0.757912			−0.0515694
$217$	9.22138	+	9.22138i	0.625988	+	0.625988i
$218$	−13.0787	−	13.0787i	−0.885801	−	0.885801i
$219$	24.7130			1.66995
$220$		0			0
$221$			13.2093i			0.888555i
$222$	5.59252	+	5.59252i	0.375346	+	0.375346i
$223$	−2.06812	+	2.06812i	−0.138491	+	0.138491i	−0.772954	−	0.634462i	$-0.781222\pi$
$223$	−2.06812	+	2.06812i	−0.138491	+	0.138491i	0.634462	+	0.772954i	$0.281222\pi$
$224$	3.52838			0.235750
$225$		0			0
$226$	−8.73317			−0.580922
$227$	7.49970	+	7.49970i	0.497773	+	0.497773i	0.910744	−	0.412971i	$-0.135509\pi$
$227$	7.49970	+	7.49970i	0.497773	+	0.497773i	−0.412971	+	0.910744i	$0.635509\pi$
$228$	4.20410	−	9.50181i	0.278423	−	0.629273i
$229$			15.9203i			1.05204i	0.850471	+	0.526021i	$0.176317\pi$
$229$			15.9203i			1.05204i	−0.850471	+	0.526021i	$0.823683\pi$
$230$		0			0
$231$		−	30.3301i		−	1.99558i
$232$	−3.40677	+	3.40677i	−0.223665	+	0.223665i
$233$	−10.1360	−	10.1360i	−0.664032	−	0.664032i	0.292296	−	0.956328i	$-0.405581\pi$
$233$	−10.1360	−	10.1360i	−0.664032	−	0.664032i	−0.956328	+	0.292296i	$0.905581\pi$
$234$		−	10.7010i		−	0.699549i
$235$		0			0
$236$		−	8.96359i		−	0.583480i
$237$	27.3040	−	27.3040i	1.77358	−	1.77358i
$238$	−8.26001	+	8.26001i	−0.535417	+	0.535417i
$239$			5.15672i			0.333561i	0.985994	+	0.166780i	$0.0533371\pi$
$239$			5.15672i			0.333561i	−0.985994	+	0.166780i	$0.946663\pi$
$240$		0			0
$241$			16.0990i			1.03703i	0.855069	+	0.518514i	$0.173514\pi$
$241$			16.0990i			1.03703i	−0.855069	+	0.518514i	$0.826486\pi$
$242$	−1.41740	−	1.41740i	−0.0911140	−	0.0911140i
$243$	−14.9994	+	14.9994i	−0.962212	+	0.962212i
$244$		−	11.6915i		−	0.748474i
$245$		0			0
$246$		−	17.3742i		−	1.10774i
$247$	−15.9043	−	7.03688i	−1.01196	−	0.447746i
$248$	2.61349	+	2.61349i	0.165957	+	0.165957i
$249$	4.66456			0.295604
$250$		0			0
$251$	−10.1770			−0.642367			−0.321183	−	0.947017i	$-0.604081\pi$
$251$	−10.1770			−0.642367			−0.321183	+	0.947017i	$0.604081\pi$
$252$	6.69154	−	6.69154i	0.421527	−	0.421527i
$253$	2.86071	+	2.86071i	0.179851	+	0.179851i
$254$		−	9.49558i		−	0.595806i
$255$		0			0
$256$	1.00000			0.0625000
$257$	14.3142	+	14.3142i	0.892897	+	0.892897i	0.994795	−	0.101898i	$-0.0324915\pi$
$257$	14.3142	+	14.3142i	0.892897	+	0.892897i	−0.101898	+	0.994795i	$0.532491\pi$
$258$	−2.93145	−	2.93145i	−0.182504	−	0.182504i
$259$	11.7070			0.727438
$260$		0			0
$261$			12.9218i			0.799841i
$262$	5.20720	+	5.20720i	0.321702	+	0.321702i
$263$	3.50508	+	3.50508i	0.216133	+	0.216133i	0.806866	−	0.590734i	$-0.201162\pi$
$263$	3.50508	+	3.50508i	0.216133	+	0.216133i	−0.590734	+	0.806866i	$0.701162\pi$
$264$		−	8.59606i		−	0.529051i
$265$		0			0
$266$	−5.54494	−	14.3455i	−0.339982	−	0.879579i
$267$	−20.1477	+	20.1477i	−1.23302	+	1.23302i
$268$	8.19965	−	8.19965i	0.500873	−	0.500873i
$269$	3.44974			0.210334			0.105167	−	0.994455i	$-0.466462\pi$
$269$	3.44974			0.210334			0.105167	+	0.994455i	$0.466462\pi$
$270$		0			0
$271$	18.7321			1.13789			0.568946	−	0.822375i	$-0.307351\pi$
$271$	18.7321			1.13789			0.568946	+	0.822375i	$0.307351\pi$
$272$	−2.34102	+	2.34102i	−0.141945	+	0.141945i
$273$	−23.7286	−	23.7286i	−1.43612	−	1.43612i
$274$	17.7595			1.07289
$275$		0			0
$276$			2.67420i			0.160968i
$277$	4.82817	−	4.82817i	0.290096	−	0.290096i	−0.547022	−	0.837118i	$-0.684239\pi$
$277$	4.82817	−	4.82817i	0.290096	−	0.290096i	0.837118	+	0.547022i	$0.184239\pi$
$278$	7.28874	−	7.28874i	0.437150	−	0.437150i
$279$	9.91292			0.593471
$280$		0			0
$281$			0.795990i			0.0474848i	0.999718	+	0.0237424i	$0.00755814\pi$
$281$			0.795990i			0.0474848i	−0.999718	+	0.0237424i	$0.992442\pi$
$282$	−17.7573	+	17.7573i	−1.05743	+	1.05743i
$283$	−7.40831	−	7.40831i	−0.440378	−	0.440378i	0.451761	−	0.892139i	$-0.350796\pi$
$283$	−7.40831	−	7.40831i	−0.440378	−	0.440378i	−0.892139	+	0.451761i	$0.850796\pi$
$284$	15.8527			0.940684
$285$		0			0
$286$	−14.3882			−0.850793
$287$	−18.1850	−	18.1850i	−1.07342	−	1.07342i
$288$	1.89649	−	1.89649i	0.111752	−	0.111752i
$289$			6.03923i			0.355249i
$290$		0			0
$291$	−11.6909			−0.685334
$292$	7.33090	−	7.33090i	0.429009	−	0.429009i
$293$	14.8246	−	14.8246i	0.866062	−	0.866062i	−0.125972	−	0.992034i	$-0.540205\pi$
$293$	14.8246	−	14.8246i	0.866062	−	0.866062i	0.992034	+	0.125972i	$0.0402050\pi$
$294$		−	12.9899i		−	0.757585i
$295$		0			0
$296$	3.31796			0.192852
$297$	1.93264	+	1.93264i	0.112143	+	0.112143i
$298$	0.667330	−	0.667330i	0.0386574	−	0.0386574i
$299$	4.47612			0.258861
$300$		0			0
$301$	−6.13648			−0.353701
$302$	−1.71178	+	1.71178i	−0.0985018	+	0.0985018i
$303$	−10.8962	+	10.8962i	−0.625972	+	0.625972i
$304$	−1.57153	−	4.06575i	−0.0901332	−	0.233187i
$305$		0			0
$306$			8.87946i			0.507605i
$307$	15.0781	+	15.0781i	0.860551	+	0.860551i	0.991402	−	0.130851i	$-0.0417710\pi$
$307$	15.0781	+	15.0781i	0.860551	+	0.860551i	−0.130851	+	0.991402i	$0.541771\pi$
$308$	−8.99719	−	8.99719i	−0.512663	−	0.512663i
$309$		−	29.0746i		−	1.65400i
$310$		0			0
$311$	−1.77240			−0.100503			−0.0502517	−	0.998737i	$-0.516002\pi$
$311$	−1.77240			−0.100503			−0.0502517	+	0.998737i	$0.516002\pi$
$312$	−6.72508	−	6.72508i	−0.380732	−	0.380732i
$313$	−11.4579	−	11.4579i	−0.647638	−	0.647638i	0.304783	−	0.952422i	$-0.401416\pi$
$313$	−11.4579	−	11.4579i	−0.647638	−	0.647638i	−0.952422	+	0.304783i	$0.901416\pi$
$314$	−11.3058			−0.638022
$315$		0			0
$316$		−	16.1990i		−	0.911266i
$317$	−13.9316	−	13.9316i	−0.782479	−	0.782479i	0.197769	−	0.980249i	$-0.436630\pi$
$317$	−13.9316	−	13.9316i	−0.782479	−	0.782479i	−0.980249	+	0.197769i	$0.936630\pi$
$318$	−5.83122	+	5.83122i	−0.326999	+	0.326999i
$319$	17.3742			0.972768
$320$		0			0
$321$	39.7528			2.21879
$322$	2.79899	+	2.79899i	0.155982	+	0.155982i
$323$	13.1970	+	5.83903i	0.734300	+	0.324892i
$324$			9.85277i			0.547376i
$325$		0			0
$326$		−	3.82469i		−	0.211830i
$327$	−31.1757	+	31.1757i	−1.72402	+	1.72402i
$328$	−5.15392	−	5.15392i	−0.284578	−	0.284578i
$329$			37.1719i			2.04935i
$330$		0			0
$331$			14.3845i			0.790643i	0.918543	+	0.395322i	$0.129367\pi$
$331$			14.3845i			0.790643i	−0.918543	+	0.395322i	$0.870633\pi$
$332$	1.38370	−	1.38370i	0.0759406	−	0.0759406i
$333$	6.29248	−	6.29248i	0.344826	−	0.344826i
$334$			2.20286i			0.120535i
$335$		0			0
$336$		−	8.41061i		−	0.458836i
$337$	6.75600	+	6.75600i	0.368023	+	0.368023i	0.866756	−	0.498733i	$-0.166201\pi$
$337$	6.75600	+	6.75600i	0.368023	+	0.368023i	−0.498733	+	0.866756i	$0.666201\pi$
$338$	−2.06415	+	2.06415i	−0.112275	+	0.112275i
$339$			20.8173i			1.13064i
$340$		0			0
$341$		−	13.3285i		−	0.721781i
$342$	−10.6910	−	4.73027i	−0.578105	−	0.255784i
$343$	3.86852	+	3.86852i	0.208881	+	0.208881i
$344$	−1.73918			−0.0937703
$345$		0			0
$346$	7.16622			0.385258
$347$	8.48418	−	8.48418i	0.455454	−	0.455454i	−0.441706	−	0.897160i	$-0.645626\pi$
$347$	8.48418	−	8.48418i	0.455454	−	0.455454i	0.897160	+	0.441706i	$0.145626\pi$
$348$	8.12073	+	8.12073i	0.435317	+	0.435317i
$349$		−	19.6965i		−	1.05433i	−0.849763	−	0.527165i	$-0.823255\pi$
$349$		−	19.6965i		−	1.05433i	0.849763	−	0.527165i	$-0.176745\pi$
$350$		0			0
$351$	3.02398			0.161408
$352$	−2.54995	−	2.54995i	−0.135913	−	0.135913i
$353$	−5.40615	−	5.40615i	−0.287740	−	0.287740i	0.548446	−	0.836186i	$-0.315220\pi$
$353$	−5.40615	−	5.40615i	−0.287740	−	0.287740i	−0.836186	+	0.548446i	$0.815220\pi$
$354$	−21.3665			−1.13562
$355$		0			0
$356$			11.9533i			0.633524i
$357$	19.6894	+	19.6894i	1.04207	+	1.04207i
$358$	9.54992	+	9.54992i	0.504729	+	0.504729i
$359$		−	23.9039i		−	1.26160i	−0.775946	−	0.630800i	$-0.782727\pi$
$359$		−	23.9039i		−	1.26160i	0.775946	−	0.630800i	$-0.217273\pi$
$360$		0			0
$361$	−14.0606	+	12.7789i	−0.740032	+	0.672571i
$362$	−7.76741	+	7.76741i	−0.408246	+	0.408246i
$363$	−3.37866	+	3.37866i	−0.177334	+	0.177334i
$364$	−14.0778			−0.737878
$365$		0			0
$366$	−27.8692			−1.45674
$367$	20.3078	−	20.3078i	1.06006	−	1.06006i	0.0619832	−	0.998077i	$-0.480257\pi$
$367$	20.3078	−	20.3078i	1.06006	−	1.06006i	0.998077	−	0.0619832i	$-0.0197425\pi$
$368$	0.793280	+	0.793280i	0.0413526	+	0.0413526i
$369$	−19.5487			−1.01767
$370$		0			0
$371$			12.2067i			0.633739i
$372$	6.22979	−	6.22979i	0.322999	−	0.322999i
$373$	−17.8993	+	17.8993i	−0.926793	+	0.926793i	−0.997497	−	0.0707046i	$-0.977475\pi$
$373$	−17.8993	+	17.8993i	−0.926793	+	0.926793i	0.0707046	+	0.997497i	$0.477475\pi$
$374$	11.9390			0.617350
$375$		0			0
$376$			10.5351i			0.543307i
$377$	13.5926	−	13.5926i	0.700055	−	0.700055i
$378$	1.89095	+	1.89095i	0.0972598	+	0.0972598i
$379$	−10.1355			−0.520624			−0.260312	−	0.965524i	$-0.583826\pi$
$379$	−10.1355			−0.520624			−0.260312	+	0.965524i	$0.583826\pi$
$380$		0			0
$381$	−22.6347			−1.15961
$382$	13.1526	+	13.1526i	0.672945	+	0.672945i
$383$	2.46334	−	2.46334i	0.125871	−	0.125871i	−0.641365	−	0.767236i	$-0.721632\pi$
$383$	2.46334	−	2.46334i	0.125871	−	0.125871i	0.767236	+	0.641365i	$0.221632\pi$
$384$		−	2.38370i		−	0.121643i
$385$		0			0
$386$	−6.31345			−0.321346
$387$	−3.29834	+	3.29834i	−0.167664	+	0.167664i
$388$	−3.46802	+	3.46802i	−0.176062	+	0.176062i
$389$		−	1.19274i		−	0.0604742i	−0.999543	−	0.0302371i	$-0.990374\pi$
$389$		−	1.19274i		−	0.0604742i	0.999543	−	0.0302371i	$-0.00962623\pi$
$390$		0			0
$391$	−3.71417			−0.187834
$392$	−3.85334	−	3.85334i	−0.194623	−	0.194623i
$393$	12.4124	−	12.4124i	0.626124	−	0.626124i
$394$	3.03973			0.153139
$395$		0			0
$396$	−9.67192			−0.486032
$397$	17.8692	−	17.8692i	0.896828	−	0.896828i	−0.0983263	−	0.995154i	$-0.531349\pi$
$397$	17.8692	−	17.8692i	0.896828	−	0.896828i	0.995154	+	0.0983263i	$0.0313489\pi$
$398$	11.6176	−	11.6176i	0.582340	−	0.582340i
$399$	−34.1954	+	13.2175i	−1.71191	+	0.661702i
$400$		0			0
$401$			36.0282i			1.79916i	0.436756	+	0.899580i	$0.356127\pi$
$401$			36.0282i			1.79916i	−0.436756	+	0.899580i	$0.643873\pi$
$402$	−19.5455	−	19.5455i	−0.974843	−	0.974843i
$403$	−10.4275	−	10.4275i	−0.519431	−	0.519431i
$404$			6.46456i			0.321624i
$405$		0			0
$406$	16.9994			0.843665
$407$	−8.46063	−	8.46063i	−0.419378	−	0.419378i
$408$	5.58030	+	5.58030i	0.276266	+	0.276266i
$409$	11.5378			0.570505			0.285253	−	0.958452i	$-0.407922\pi$
$409$	11.5378			0.570505			0.285253	+	0.958452i	$0.407922\pi$
$410$		0			0
$411$		−	42.3335i		−	2.08816i
$412$	−8.62475	−	8.62475i	−0.424911	−	0.424911i
$413$	−22.3636	+	22.3636i	−1.10044	+	1.10044i
$414$	3.00890			0.147879
$415$		0			0
$416$	−3.98988			−0.195620
$417$	−17.3742	−	17.3742i	−0.850818	−	0.850818i
$418$	−6.36015	+	14.3748i	−0.311085	+	0.703093i
$419$		−	22.2072i		−	1.08489i	−0.840090	−	0.542447i	$-0.817498\pi$
$419$		−	22.2072i		−	1.08489i	0.840090	−	0.542447i	$-0.182502\pi$
$420$		0			0
$421$			14.1041i			0.687391i	0.939081	+	0.343695i	$0.111679\pi$
$421$			14.1041i			0.687391i	−0.939081	+	0.343695i	$0.888321\pi$
$422$	3.89888	−	3.89888i	0.189795	−	0.189795i
$423$	19.9798	+	19.9798i	0.971449	+	0.971449i
$424$			3.45957i			0.168012i
$425$		0			0
$426$		−	37.7881i		−	1.83084i
$427$	−29.1697	+	29.1697i	−1.41162	+	1.41162i
$428$	11.7924	−	11.7924i	0.570005	−	0.570005i
$429$			34.2972i			1.65589i
$430$		0			0
$431$		−	9.35994i		−	0.450853i	−0.974260	−	0.225426i	$-0.927623\pi$
$431$		−	9.35994i		−	0.450853i	0.974260	−	0.225426i	$-0.0723775\pi$
$432$	0.535925	+	0.535925i	0.0257847	+	0.0257847i
$433$	−7.84922	+	7.84922i	−0.377209	+	0.377209i	−0.870094	−	0.492885i	$-0.835942\pi$
$433$	−7.84922	+	7.84922i	−0.377209	+	0.377209i	0.492885	+	0.870094i	$0.335942\pi$
$434$		−	13.0410i		−	0.625988i
$435$		0			0
$436$			18.4961i			0.885801i
$437$	1.97862	−	4.47194i	0.0946501	−	0.213922i
$438$	−17.4747	−	17.4747i	−0.834973	−	0.834973i
$439$	−5.62426			−0.268431			−0.134216	−	0.990952i	$-0.542852\pi$
$439$	−5.62426			−0.268431			−0.134216	+	0.990952i	$0.542852\pi$
$440$		0			0
$441$	−14.6157			−0.695984
$442$	9.34040	−	9.34040i	0.444277	−	0.444277i
$443$	16.4365	+	16.4365i	0.780923	+	0.780923i	0.979987	−	0.199064i	$-0.0637900\pi$
$443$	16.4365	+	16.4365i	0.780923	+	0.780923i	−0.199064	+	0.979987i	$0.563790\pi$
$444$		−	7.90902i		−	0.375346i
$445$		0			0
$446$	2.92476			0.138491
$447$	−1.59072	−	1.59072i	−0.0752384	−	0.0752384i
$448$	−2.49494	−	2.49494i	−0.117875	−	0.117875i
$449$	−29.8772			−1.40999			−0.704996	−	0.709211i	$-0.749051\pi$
$449$	−29.8772			−1.40999			−0.704996	+	0.709211i	$0.749051\pi$
$450$		0			0
$451$			26.2845i			1.23769i
$452$	6.17528	+	6.17528i	0.290461	+	0.290461i
$453$	4.08038	+	4.08038i	0.191713	+	0.191713i
$454$		−	10.6062i		−	0.497773i
$455$		0			0
$456$	−9.69154	+	3.74605i	−0.453848	+	0.175425i
$457$	−7.57812	+	7.57812i	−0.354490	+	0.354490i	−0.861777	−	0.507287i	$-0.830648\pi$
$457$	−7.57812	+	7.57812i	−0.354490	+	0.354490i	0.507287	+	0.861777i	$0.330648\pi$
$458$	11.2573	−	11.2573i	0.526021	−	0.526021i
$459$	−2.50922			−0.117121
$460$		0			0
$461$	40.4141			1.88227			0.941136	−	0.338027i	$-0.109760\pi$
$461$	40.4141			1.88227			0.941136	+	0.338027i	$0.109760\pi$
$462$	−21.4466	+	21.4466i	−0.997788	+	0.997788i
$463$	20.5954	+	20.5954i	0.957151	+	0.957151i	0.999119	−	0.0419681i	$-0.0133628\pi$
$463$	20.5954	+	20.5954i	0.957151	+	0.957151i	−0.0419681	+	0.999119i	$0.513363\pi$
$464$	4.81790			0.223665
$465$		0			0
$466$			14.3345i			0.664032i
$467$	0.461754	−	0.461754i	0.0213674	−	0.0213674i	−0.696342	−	0.717710i	$-0.745190\pi$
$467$	0.461754	−	0.461754i	0.0213674	−	0.0213674i	0.717710	+	0.696342i	$0.245190\pi$
$468$	−7.56677	+	7.56677i	−0.349774	+	0.349774i
$469$	−40.9153			−1.88929
$470$		0			0
$471$			26.9496i			1.24177i
$472$	−6.33822	+	6.33822i	−0.291740	+	0.291740i
$473$	4.43482	+	4.43482i	0.203913	+	0.203913i
$474$	−38.6137			−1.77358
$475$		0			0
$476$	11.6814			0.535417
$477$	6.56105	+	6.56105i	0.300410	+	0.300410i
$478$	3.64635	−	3.64635i	0.166780	−	0.166780i
$479$			17.5046i			0.799806i	0.916558	+	0.399903i	$0.130956\pi$
$479$			17.5046i			0.799806i	−0.916558	+	0.399903i	$0.869044\pi$
$480$		0			0
$481$	−13.2382			−0.603612
$482$	11.3837	−	11.3837i	0.518514	−	0.518514i
$483$	6.67197	−	6.67197i	0.303585	−	0.303585i
$484$			2.00451i			0.0911140i
$485$		0			0
$486$	21.2124			0.962212
$487$	−4.02100	−	4.02100i	−0.182209	−	0.182209i	0.610109	−	0.792318i	$-0.291126\pi$
$487$	−4.02100	−	4.02100i	−0.182209	−	0.182209i	−0.792318	+	0.610109i	$0.791126\pi$
$488$	−8.26717	+	8.26717i	−0.374237	+	0.374237i
$489$	−9.11693			−0.412282
$490$		0			0
$491$	11.1117			0.501466			0.250733	−	0.968056i	$-0.419328\pi$
$491$	11.1117			0.501466			0.250733	+	0.968056i	$0.419328\pi$
$492$	−12.2854	+	12.2854i	−0.553869	+	0.553869i
$493$	−11.2788	+	11.2788i	−0.507972	+	0.507972i
$494$	6.27020	+	16.2218i	0.282110	+	0.729855i
$495$		0			0
$496$		−	3.69603i		−	0.165957i
$497$	−39.5515	−	39.5515i	−1.77413	−	1.77413i
$498$	−3.29834	−	3.29834i	−0.147802	−	0.147802i
$499$		−	1.00513i		−	0.0449959i	−0.999747	−	0.0224979i	$-0.992838\pi$
$499$		−	1.00513i		−	0.0449959i	0.999747	−	0.0224979i	$-0.00716192\pi$
$500$		0			0
$501$	5.25096			0.234596
$502$	7.19623	+	7.19623i	0.321183	+	0.321183i
$503$	8.12763	+	8.12763i	0.362393	+	0.362393i	0.864693	−	0.502300i	$-0.167513\pi$
$503$	8.12763	+	8.12763i	0.362393	+	0.362393i	−0.502300	+	0.864693i	$0.667513\pi$
$504$	−9.46327			−0.421527
$505$		0			0
$506$		−	4.04565i		−	0.179851i
$507$	4.92031	+	4.92031i	0.218519	+	0.218519i
$508$	−6.71439	+	6.71439i	−0.297903	+	0.297903i
$509$	−0.756343			−0.0335243			−0.0167622	−	0.999860i	$-0.505336\pi$
$509$	−0.756343			−0.0335243			−0.0167622	+	0.999860i	$0.505336\pi$
$510$		0			0
$511$	−36.5803			−1.61822
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.33672	−	3.02116i	0.0590175	−	0.133387i
$514$		−	20.2434i		−	0.892897i
$515$		0			0
$516$			4.14569i			0.182504i
$517$	26.8640	−	26.8640i	1.18148	−	1.18148i
$518$	−8.27810	−	8.27810i	−0.363719	−	0.363719i
$519$		−	17.0821i		−	0.749823i
$520$		0			0
$521$		−	18.2427i		−	0.799227i	−0.916684	−	0.399613i	$-0.869144\pi$
$521$		−	18.2427i		−	0.799227i	0.916684	−	0.399613i	$-0.130856\pi$
$522$	9.13711	−	9.13711i	0.399920	−	0.399920i
$523$	−8.67796	+	8.67796i	−0.379461	+	0.379461i	−0.870908	−	0.491447i	$-0.836468\pi$
$523$	−8.67796	+	8.67796i	−0.379461	+	0.379461i	0.491447	+	0.870908i	$0.336468\pi$
$524$		−	7.36409i		−	0.321702i
$525$		0			0
$526$		−	4.95693i		−	0.216133i
$527$	8.65249	+	8.65249i	0.376909	+	0.376909i
$528$	−6.07833	+	6.07833i	−0.264525	+	0.264525i
$529$		−	21.7414i		−	0.945279i
$530$		0			0
$531$			24.0407i			1.04328i
$532$	−6.22294	+	14.0647i	−0.269799	+	0.609780i
$533$	20.5635	+	20.5635i	0.890705	+	0.890705i
$534$	28.4931			1.23302
$535$		0			0
$536$	−11.5961			−0.500873
$537$	22.7642	−	22.7642i	0.982347	−	0.982347i
$538$	−2.43933	−	2.43933i	−0.105167	−	0.105167i
$539$			19.6517i			0.846458i
$540$		0			0
$541$	−4.92850			−0.211893			−0.105946	−	0.994372i	$-0.533787\pi$
$541$	−4.92850			−0.211893			−0.105946	+	0.994372i	$0.533787\pi$
$542$	−13.2456	−	13.2456i	−0.568946	−	0.568946i
$543$	18.5152	+	18.5152i	0.794563	+	0.794563i
$544$	3.31071			0.141945
$545$		0			0
$546$			33.5573i			1.43612i
$547$	−7.18633	−	7.18633i	−0.307265	−	0.307265i	0.536583	−	0.843848i	$-0.319715\pi$
$547$	−7.18633	−	7.18633i	−0.307265	−	0.307265i	−0.843848	+	0.536583i	$0.819715\pi$
$548$	−12.5579	−	12.5579i	−0.536446	−	0.536446i
$549$			31.3572i			1.33829i
$550$		0			0
$551$	−7.57145	−	19.5884i	−0.322555	−	0.834493i
$552$	1.89095	−	1.89095i	0.0804840	−	0.0804840i
$553$	−40.4156	+	40.4156i	−1.71865	+	1.71865i
$554$	−6.82806			−0.290096
$555$		0			0
$556$	−10.3078			−0.437150
$557$	7.00950	−	7.00950i	0.297002	−	0.297002i	−0.542837	−	0.839838i	$-0.682650\pi$
$557$	7.00950	−	7.00950i	0.297002	−	0.297002i	0.839838	+	0.542837i	$0.182650\pi$
$558$	−7.00950	−	7.00950i	−0.296736	−	0.296736i
$559$	6.93912			0.293493
$560$		0			0
$561$		−	28.4590i		−	1.20154i
$562$	0.562850	−	0.562850i	0.0237424	−	0.0237424i
$563$	8.09110	−	8.09110i	0.340999	−	0.340999i	−0.515744	−	0.856743i	$-0.672484\pi$
$563$	8.09110	−	8.09110i	0.340999	−	0.340999i	0.856743	+	0.515744i	$0.172484\pi$
$564$	25.1126			1.05743
$565$		0			0
$566$			10.4769i			0.440378i
$567$	24.5821	−	24.5821i	1.03235	−	1.03235i
$568$	−11.2095	−	11.2095i	−0.470342	−	0.470342i
$569$	4.14240			0.173659			0.0868293	−	0.996223i	$-0.472327\pi$
$569$	4.14240			0.173659			0.0868293	+	0.996223i	$0.472327\pi$
$570$		0			0
$571$	28.4072			1.18880			0.594402	−	0.804168i	$-0.297389\pi$
$571$	28.4072			1.18880			0.594402	+	0.804168i	$0.297389\pi$
$572$	10.1740	+	10.1740i	0.425396	+	0.425396i
$573$	31.3519	−	31.3519i	1.30974	−	1.30974i
$574$			25.7174i			1.07342i
$575$		0			0
$576$	−2.68204			−0.111752
$577$	−14.8815	+	14.8815i	−0.619523	+	0.619523i	−0.945409	−	0.325886i	$-0.894337\pi$
$577$	−14.8815	+	14.8815i	−0.619523	+	0.619523i	0.325886	+	0.945409i	$0.394337\pi$
$578$	4.27038	−	4.27038i	0.177624	−	0.177624i
$579$			15.0494i			0.625431i
$580$		0			0
$581$	−6.90452			−0.286448
$582$	8.26673	+	8.26673i	0.342667	+	0.342667i
$583$	8.82174	−	8.82174i	0.365359	−	0.365359i
$584$	−10.3675			−0.429009
$585$		0			0
$586$	−20.9651			−0.866062
$587$	1.83145	−	1.83145i	0.0755922	−	0.0755922i	−0.668300	−	0.743892i	$-0.732978\pi$
$587$	1.83145	−	1.83145i	0.0755922	−	0.0755922i	0.743892	+	0.668300i	$0.232978\pi$
$588$	−9.18523	+	9.18523i	−0.378793	+	0.378793i
$589$	−15.0271	+	5.80841i	−0.619182	+	0.239331i
$590$		0			0
$591$		−	7.24581i		−	0.298053i
$592$	−2.34615	−	2.34615i	−0.0964261	−	0.0964261i
$593$	3.73139	+	3.73139i	0.153230	+	0.153230i	0.779559	−	0.626329i	$-0.215443\pi$
$593$	3.73139	+	3.73139i	0.153230	+	0.153230i	−0.626329	+	0.779559i	$0.715443\pi$
$594$		−	2.73317i		−	0.112143i
$595$		0			0
$596$	−0.943747			−0.0386574
$597$	−27.6930	−	27.6930i	−1.13340	−	1.13340i
$598$	−3.16509	−	3.16509i	−0.129430	−	0.129430i
$599$	16.7816			0.685676			0.342838	−	0.939394i	$-0.388612\pi$
$599$	16.7816			0.685676			0.342838	+	0.939394i	$0.388612\pi$
$600$		0			0
$601$		−	35.7215i		−	1.45711i	−0.684988	−	0.728555i	$-0.740192\pi$
$601$		−	35.7215i		−	1.45711i	0.684988	−	0.728555i	$-0.259808\pi$
$602$	4.33915	+	4.33915i	0.176851	+	0.176851i
$603$	−21.9918	+	21.9918i	−0.895576	+	0.895576i
$604$	2.42082			0.0985018
$605$		0			0
$606$	15.4096			0.625972
$607$	10.4827	+	10.4827i	0.425481	+	0.425481i	0.887086	−	0.461605i	$-0.152726\pi$
$607$	10.4827	+	10.4827i	0.425481	+	0.425481i	−0.461605	+	0.887086i	$0.652726\pi$
$608$	−1.76368	+	3.98615i	−0.0715267	+	0.161660i
$609$		−	40.5215i		−	1.64201i
$610$		0			0
$611$		−	42.0339i		−	1.70051i
$612$	6.27873	−	6.27873i	0.253802	−	0.253802i
$613$	−24.0780	−	24.0780i	−0.972503	−	0.972503i	0.0271287	−	0.999632i	$-0.491364\pi$
$613$	−24.0780	−	24.0780i	−0.972503	−	0.972503i	−0.999632	+	0.0271287i	$0.991364\pi$
$614$		−	21.3236i		−	0.860551i
$615$		0			0
$616$			12.7240i			0.512663i
$617$	−32.1011	+	32.1011i	−1.29234	+	1.29234i	−0.359009	+	0.933334i	$0.616885\pi$
$617$	−32.1011	+	32.1011i	−1.29234	+	1.29234i	−0.933334	+	0.359009i	$0.883115\pi$
$618$	−20.5589	+	20.5589i	−0.826999	+	0.826999i
$619$		−	24.9836i		−	1.00418i	−0.864816	−	0.502089i	$-0.832565\pi$
$619$		−	24.9836i		−	1.00418i	0.864816	−	0.502089i	$-0.167435\pi$
$620$		0			0
$621$			0.850278i			0.0341205i
$622$	1.25327	+	1.25327i	0.0502517	+	0.0502517i
$623$	29.8228	−	29.8228i	1.19482	−	1.19482i
$624$			9.51069i			0.380732i
$625$		0			0
$626$			16.2039i			0.647638i
$627$	34.2652	+	15.1607i	1.36842	+	0.605460i
$628$	7.99439	+	7.99439i	0.319011	+	0.319011i
$629$	10.9848			0.437992
$630$		0			0
$631$	41.5056			1.65231			0.826156	−	0.563441i	$-0.190523\pi$
$631$	41.5056			1.65231			0.826156	+	0.563441i	$0.190523\pi$
$632$	−11.4544	+	11.4544i	−0.455633	+	0.455633i
$633$	−9.29378	−	9.29378i	−0.369395	−	0.369395i
$634$			19.7023i			0.782479i
$635$		0			0
$636$	8.24660			0.326999
$637$	15.3744	+	15.3744i	0.609155	+	0.609155i
$638$	−12.2854	−	12.2854i	−0.486384	−	0.486384i
$639$	−42.5176			−1.68197
$640$		0			0
$641$			33.0235i			1.30435i	0.758068	+	0.652176i	$0.226143\pi$
$641$			33.0235i			1.30435i	−0.758068	+	0.652176i	$0.773857\pi$
$642$	−28.1095	−	28.1095i	−1.10939	−	1.10939i
$643$	−35.1865	−	35.1865i	−1.38762	−	1.38762i	−0.830293	−	0.557327i	$-0.811827\pi$
$643$	−35.1865	−	35.1865i	−1.38762	−	1.38762i	−0.557327	−	0.830293i	$-0.688173\pi$
$644$		−	3.95837i		−	0.155982i
$645$		0			0
$646$	−5.20286	−	13.4605i	−0.204704	−	0.529596i
$647$	−8.42468	+	8.42468i	−0.331209	+	0.331209i	−0.853045	−	0.521837i	$-0.825247\pi$
$647$	−8.42468	+	8.42468i	−0.331209	+	0.331209i	0.521837	+	0.853045i	$0.325247\pi$
$648$	6.96696	−	6.96696i	0.273688	−	0.273688i
$649$	32.3243			1.26884
$650$		0			0
$651$	−31.0859			−1.21835
$652$	−2.70447	+	2.70447i	−0.105915	+	0.105915i
$653$	−24.1876	−	24.1876i	−0.946534	−	0.946534i	0.0521073	−	0.998641i	$-0.483406\pi$
$653$	−24.1876	−	24.1876i	−0.946534	−	0.946534i	−0.998641	+	0.0521073i	$0.983406\pi$
$654$	44.0891			1.72402
$655$		0			0
$656$			7.28874i			0.284578i
$657$	−19.6618	+	19.6618i	−0.767080	+	0.767080i
$658$	26.2845	−	26.2845i	1.02468	−	1.02468i
$659$	−1.84410			−0.0718358			−0.0359179	−	0.999355i	$-0.511435\pi$
$659$	−1.84410			−0.0718358			−0.0359179	+	0.999355i	$0.511435\pi$
$660$		0			0
$661$			7.65427i			0.297716i	0.988859	+	0.148858i	$0.0475598\pi$
$661$			7.65427i			0.297716i	−0.988859	+	0.148858i	$0.952440\pi$
$662$	10.1714	−	10.1714i	0.395322	−	0.395322i
$663$	−22.2647	−	22.2647i	−0.864691	−	0.864691i
$664$	−1.95685			−0.0759406
$665$		0			0
$666$	−8.89890			−0.344826
$667$	3.82195	+	3.82195i	0.147986	+	0.147986i
$668$	1.55766	−	1.55766i	0.0602675	−	0.0602675i
$669$		−	6.97175i		−	0.269544i
$670$		0			0
$671$	42.1618			1.62764
$672$	−5.94720	+	5.94720i	−0.229418	+	0.229418i
$673$	13.4288	−	13.4288i	0.517642	−	0.517642i	−0.399216	−	0.916857i	$-0.630717\pi$
$673$	13.4288	−	13.4288i	0.517642	−	0.517642i	0.916857	+	0.399216i	$0.130717\pi$
$674$		−	9.55443i		−	0.368023i
$675$		0			0
$676$	2.91914			0.112275
$677$	18.5770	+	18.5770i	0.713973	+	0.713973i	0.967364	−	0.253391i	$-0.0815460\pi$
$677$	18.5770	+	18.5770i	0.713973	+	0.713973i	−0.253391	+	0.967364i	$0.581546\pi$
$678$	14.7200	−	14.7200i	0.565320	−	0.565320i
$679$	17.3050			0.664105
$680$		0			0
$681$	−25.2820			−0.968808
$682$	−9.42471	+	9.42471i	−0.360891	+	0.360891i
$683$	−13.0496	+	13.0496i	−0.499329	+	0.499329i	−0.911229	−	0.411900i	$-0.864865\pi$
$683$	−13.0496	+	13.0496i	−0.499329	+	0.499329i	0.411900	+	0.911229i	$0.364865\pi$
$684$	4.21490	+	10.9045i	0.161161	+	0.416945i
$685$		0			0
$686$		−	5.47092i		−	0.208881i
$687$	−26.8342	−	26.8342i	−1.02379	−	1.02379i
$688$	1.22979	+	1.22979i	0.0468851	+	0.0468851i
$689$		−	13.8033i		−	0.525863i
$690$		0			0
$691$	−3.91335			−0.148871			−0.0744354	−	0.997226i	$-0.523715\pi$
$691$	−3.91335			−0.148871			−0.0744354	+	0.997226i	$0.523715\pi$
$692$	−5.06728	−	5.06728i	−0.192629	−	0.192629i
$693$	24.1309	+	24.1309i	0.916656	+	0.916656i
$694$	−11.9984			−0.455454
$695$		0			0
$696$		−	11.4844i		−	0.435317i
$697$	−17.0631	−	17.0631i	−0.646311	−	0.646311i
$698$	−13.9275	+	13.9275i	−0.527165	+	0.527165i
$699$	34.1691			1.29240
$700$		0			0
$701$	−11.8034			−0.445809			−0.222905	−	0.974840i	$-0.571554\pi$
$701$	−11.8034			−0.445809			−0.222905	+	0.974840i	$0.571554\pi$
$702$	−2.13828	−	2.13828i	−0.0807040	−	0.0807040i
$703$	−5.85182	+	13.2259i	−0.220706	+	0.498824i
$704$			3.60618i			0.135913i
$705$		0			0
$706$			7.64545i			0.287740i
$707$	16.1287	−	16.1287i	0.606582	−	0.606582i
$708$	15.1084	+	15.1084i	0.567810	+	0.567810i
$709$		−	18.5708i		−	0.697442i	−0.937227	−	0.348721i	$-0.886616\pi$
$709$		−	18.5708i		−	0.697442i	0.937227	−	0.348721i	$-0.113384\pi$
$710$		0			0
$711$			43.4465i			1.62937i
$712$	8.45226	−	8.45226i	0.316762	−	0.316762i
$713$	2.93199	−	2.93199i	0.109804	−	0.109804i
$714$		−	27.8450i		−	1.04207i
$715$		0			0
$716$		−	13.5056i		−	0.504729i
$717$	−8.69183	−	8.69183i	−0.324602	−	0.324602i
$718$	−16.9026	+	16.9026i	−0.630800	+	0.630800i
$719$			16.9860i			0.633472i	0.948514	+	0.316736i	$0.102587\pi$
$719$			16.9860i			0.633472i	−0.948514	+	0.316736i	$0.897413\pi$
$720$		0			0
$721$			43.0365i			1.60276i
$722$	18.9784	+	0.906344i	0.706302	+	0.0337306i
$723$	−27.1354	−	27.1354i	−1.00918	−	1.00918i
$724$	10.9848			0.408246
$725$		0			0
$726$	4.77815			0.177334
$727$	−9.80905	+	9.80905i	−0.363798	+	0.363798i	−0.865209	−	0.501411i	$-0.832814\pi$
$727$	−9.80905	+	9.80905i	−0.363798	+	0.363798i	0.501411	+	0.865209i	$0.332814\pi$
$728$	9.95451	+	9.95451i	0.368939	+	0.368939i
$729$		−	21.0057i		−	0.777987i
$730$		0			0
$731$	−5.75791			−0.212964
$732$	19.7065	+	19.7065i	0.728372	+	0.728372i
$733$	17.7230	+	17.7230i	0.654616	+	0.654616i	0.954101	−	0.299485i	$-0.0968150\pi$
$733$	17.7230	+	17.7230i	0.654616	+	0.654616i	−0.299485	+	0.954101i	$0.596815\pi$
$734$	−28.7196			−1.06006
$735$		0			0
$736$		−	1.12187i		−	0.0413526i
$737$	29.5694	+	29.5694i	1.08920	+	1.08920i
$738$	13.8230	+	13.8230i	0.508833	+	0.508833i
$739$		−	3.92303i		−	0.144311i	−0.997393	−	0.0721554i	$-0.977012\pi$
$739$		−	3.92303i		−	0.144311i	0.997393	−	0.0721554i	$-0.0229878\pi$
$740$		0			0
$741$	38.6681	−	14.9463i	1.42051	−	0.549066i
$742$	8.63142	−	8.63142i	0.316870	−	0.316870i
$743$	−16.5571	+	16.5571i	−0.607419	+	0.607419i	−0.942271	−	0.334852i	$-0.891314\pi$
$743$	−16.5571	+	16.5571i	−0.607419	+	0.607419i	0.334852	+	0.942271i	$0.391314\pi$
$744$	−8.81025			−0.322999
$745$		0			0
$746$	25.3135			0.926793
$747$	−3.71116	+	3.71116i	−0.135784	+	0.135784i
$748$	−8.44214	−	8.44214i	−0.308675	−	0.308675i
$749$	−58.8425			−2.15006
$750$		0			0
$751$		−	51.2938i		−	1.87174i	−0.352351	−	0.935868i	$-0.614618\pi$
$751$		−	51.2938i		−	1.87174i	0.352351	−	0.935868i	$-0.385382\pi$
$752$	7.44945	−	7.44945i	0.271654	−	0.271654i
$753$	17.1537	−	17.1537i	0.625115	−	0.625115i
$754$	−19.2228			−0.700055
$755$		0			0
$756$		−	2.67420i		−	0.0972598i
$757$	−4.31282	+	4.31282i	−0.156752	+	0.156752i	−0.781126	−	0.624374i	$-0.785354\pi$
$757$	−4.31282	+	4.31282i	−0.156752	+	0.156752i	0.624374	+	0.781126i	$0.285354\pi$
$758$	7.16686	+	7.16686i	0.260312	+	0.260312i
$759$	−9.64364			−0.350042
$760$		0			0
$761$	−16.6775			−0.604560			−0.302280	−	0.953219i	$-0.597748\pi$
$761$	−16.6775			−0.604560			−0.302280	+	0.953219i	$0.597748\pi$
$762$	16.0051	+	16.0051i	0.579804	+	0.579804i
$763$	46.1466	−	46.1466i	1.67062	−	1.67062i
$764$		−	18.6006i		−	0.672945i
$765$		0			0
$766$	−3.48369			−0.125871
$767$	25.2887	−	25.2887i	0.913123	−	0.913123i
$768$	−1.68553	+	1.68553i	−0.0608214	+	0.0608214i
$769$		−	47.3833i		−	1.70868i	−0.519711	−	0.854342i	$-0.673960\pi$
$769$		−	47.3833i		−	1.70868i	0.519711	−	0.854342i	$-0.326040\pi$
$770$		0			0
$771$	−48.2542			−1.73783
$772$	4.46428	+	4.46428i	0.160673	+	0.160673i
$773$	14.9288	−	14.9288i	0.536953	−	0.536953i	−0.385680	−	0.922633i	$-0.626033\pi$
$773$	14.9288	−	14.9288i	0.536953	−	0.536953i	0.922633	+	0.385680i	$0.126033\pi$
$774$	4.66456			0.167664
$775$		0			0
$776$	4.90452			0.176062
$777$	−19.7325	+	19.7325i	−0.707901	+	0.707901i
$778$	−0.843393	+	0.843393i	−0.0302371	+	0.0302371i
$779$	29.6342	−	11.4544i	1.06175	−	0.410398i
$780$		0			0
$781$			57.1676i			2.04562i
$782$	2.62632	+	2.62632i	0.0939169	+	0.0939169i
$783$	2.58203	+	2.58203i	0.0922743	+	0.0922743i
$784$			5.44945i			0.194623i
$785$		0			0
$786$	−17.5538			−0.626124
$787$	−26.6917	−	26.6917i	−0.951457	−	0.951457i	0.0474181	−	0.998875i	$-0.484901\pi$
$787$	−26.6917	−	26.6917i	−0.951457	−	0.951457i	−0.998875	+	0.0474181i	$0.984901\pi$
$788$	−2.14941	−	2.14941i	−0.0765696	−	0.0765696i
$789$	−11.8159			−0.420656
$790$		0			0
$791$		−	30.8139i		−	1.09562i
$792$	6.83908	+	6.83908i	0.243016	+	0.243016i
$793$	32.9850	−	32.9850i	1.17133	−	1.17133i
$794$	−25.2708			−0.896828
$795$		0			0
$796$	−16.4298			−0.582340
$797$	−6.51639	−	6.51639i	−0.230822	−	0.230822i	0.582213	−	0.813036i	$-0.302187\pi$
$797$	−6.51639	−	6.51639i	−0.230822	−	0.230822i	−0.813036	+	0.582213i	$0.802187\pi$
$798$	33.5260	+	14.8336i	1.18681	+	0.525105i
$799$			34.8787i			1.23392i
$800$		0			0
$801$		−	32.0593i		−	1.13276i
$802$	25.4758	−	25.4758i	0.899580	−	0.899580i
$803$	26.4365	+	26.4365i	0.932925	+	0.932925i
$804$			27.6416i			0.974843i
$805$		0			0
$806$			14.7467i			0.519431i
$807$	−5.81465	+	5.81465i	−0.204685	+	0.204685i
$808$	4.57113	−	4.57113i	0.160812	−	0.160812i
$809$			30.7224i			1.08014i	0.841619	+	0.540071i	$0.181603\pi$
$809$			30.7224i			1.08014i	−0.841619	+	0.540071i	$0.818397\pi$
$810$		0			0
$811$			10.8623i			0.381425i	0.981646	+	0.190713i	$0.0610799\pi$
$811$			10.8623i			0.381425i	−0.981646	+	0.190713i	$0.938920\pi$
$812$	−12.0204	−	12.0204i	−0.421832	−	0.421832i
$813$	−31.5735	+	31.5735i	−1.10733	+	1.10733i
$814$			11.9651i			0.419378i
$815$		0			0
$816$		−	7.89174i		−	0.276266i
$817$	3.06736	−	6.93264i	0.107313	−	0.242542i
$818$	−8.15843	−	8.15843i	−0.285253	−	0.285253i
$819$	37.7573			1.31935
$820$		0			0
$821$	0.400102			0.0139636			0.00698182	−	0.999976i	$-0.497778\pi$
$821$	0.400102			0.0139636			0.00698182	+	0.999976i	$0.497778\pi$
$822$	−29.9343	+	29.9343i	−1.04408	+	1.04408i
$823$	−29.3792	−	29.3792i	−1.02410	−	1.02410i	−0.999702	−	0.0243927i	$-0.992235\pi$
$823$	−29.3792	−	29.3792i	−1.02410	−	1.02410i	−0.0243927	−	0.999702i	$-0.507765\pi$
$824$			12.1972i			0.424911i
$825$		0			0
$826$	31.6269			1.10044
$827$	33.6189	+	33.6189i	1.16904	+	1.16904i	0.982434	+	0.186611i	$0.0597504\pi$
$827$	33.6189	+	33.6189i	1.16904	+	1.16904i	0.186611	+	0.982434i	$0.440250\pi$
$828$	−2.12761	−	2.12761i	−0.0739397	−	0.0739397i
$829$	−2.01789			−0.0700844			−0.0350422	−	0.999386i	$-0.511157\pi$
$829$	−2.01789			−0.0700844			−0.0350422	+	0.999386i	$0.511157\pi$
$830$		0			0
$831$			16.2761i			0.564611i
$832$	2.82127	+	2.82127i	0.0978100	+	0.0978100i
$833$	−12.7573	−	12.7573i	−0.442014	−	0.442014i
$834$			24.5708i			0.850818i
$835$		0			0
$836$	14.6618	−	5.66720i	0.507089	−	0.196004i
$837$	1.98080	−	1.98080i	0.0684663	−	0.0684663i
$838$	−15.7029	+	15.7029i	−0.542447	+	0.542447i
$839$	−4.97124			−0.171626			−0.0858132	−	0.996311i	$-0.527349\pi$
$839$	−4.97124			−0.171626			−0.0858132	+	0.996311i	$0.527349\pi$
$840$		0			0
$841$	−5.78783			−0.199580
$842$	9.97309	−	9.97309i	0.343695	−	0.343695i
$843$	−1.34167	−	1.34167i	−0.0462095	−	0.0462095i
$844$	−5.51385			−0.189795
$845$		0			0
$846$		−	28.2556i		−	0.971449i
$847$	5.00113	−	5.00113i	0.171841	−	0.171841i
$848$	2.44629	−	2.44629i	0.0840058	−	0.0840058i
$849$	24.9739			0.857102
$850$		0			0
$851$		−	3.72231i		−	0.127599i
$852$	−26.7202	+	26.7202i	−0.915420	+	0.915420i
$853$	−6.68142	−	6.68142i	−0.228767	−	0.228767i	0.583410	−	0.812178i	$-0.301718\pi$
$853$	−6.68142	−	6.68142i	−0.228767	−	0.228767i	−0.812178	+	0.583410i	$0.801718\pi$
$854$	41.2522			1.41162
$855$		0			0
$856$	−16.6769			−0.570005
$857$	8.71638	+	8.71638i	0.297746	+	0.297746i	0.840130	−	0.542384i	$-0.182478\pi$
$857$	8.71638	+	8.71638i	0.297746	+	0.297746i	−0.542384	+	0.840130i	$0.682478\pi$
$858$	24.2518	−	24.2518i	0.827943	−	0.827943i
$859$			12.9172i			0.440730i	0.975417	+	0.220365i	$0.0707249\pi$
$859$			12.9172i			0.440730i	−0.975417	+	0.220365i	$0.929275\pi$
$860$		0			0
$861$	61.3027			2.08919
$862$	−6.61848	+	6.61848i	−0.225426	+	0.225426i
$863$	1.85943	−	1.85943i	0.0632958	−	0.0632958i	−0.674750	−	0.738046i	$-0.735749\pi$
$863$	1.85943	−	1.85943i	0.0632958	−	0.0632958i	0.738046	+	0.674750i	$0.235749\pi$
$864$		−	0.757912i		−	0.0257847i
$865$		0			0
$866$	11.1005			0.377209
$867$	−10.1793	−	10.1793i	−0.345708	−	0.345708i
$868$	−9.22138	+	9.22138i	−0.312994	+	0.312994i
$869$	58.4165			1.98165
$870$		0			0
$871$	46.2669			1.56769
$872$	13.0787	−	13.0787i	0.442900	−	0.442900i
$873$	9.30138	−	9.30138i	0.314804	−	0.314804i
$874$	−4.56123	+	1.76304i	−0.154286	+	0.0596359i
$875$		0			0
$876$			24.7130i			0.834973i
$877$	8.71740	+	8.71740i	0.294366	+	0.294366i	0.838802	−	0.544437i	$-0.183256\pi$
$877$	8.71740	+	8.71740i	0.294366	+	0.294366i	−0.544437	+	0.838802i	$0.683256\pi$
$878$	3.97695	+	3.97695i	0.134216	+	0.134216i
$879$			49.9747i			1.68560i
$880$		0			0
$881$	−7.53174			−0.253751			−0.126875	−	0.991919i	$-0.540495\pi$
$881$	−7.53174			−0.253751			−0.126875	+	0.991919i	$0.540495\pi$
$882$	10.3348	+	10.3348i	0.347992	+	0.347992i
$883$	−21.3136	−	21.3136i	−0.717261	−	0.717261i	0.250783	−	0.968043i	$-0.419312\pi$
$883$	−21.3136	−	21.3136i	−0.717261	−	0.717261i	−0.968043	+	0.250783i	$0.919312\pi$
$884$	−13.2093			−0.444277
$885$		0			0
$886$		−	23.2448i		−	0.780923i
$887$	34.5779	+	34.5779i	1.16101	+	1.16101i	0.984254	+	0.176758i	$0.0565609\pi$
$887$	34.5779	+	34.5779i	1.16101	+	1.16101i	0.176758	+	0.984254i	$0.443439\pi$
$888$	−5.59252	+	5.59252i	−0.187673	+	0.187673i
$889$	33.5040			1.12369
$890$		0			0
$891$	−35.5308			−1.19033
$892$	−2.06812	−	2.06812i	−0.0692456	−	0.0692456i
$893$	−41.9946	−	18.5806i	−1.40530	−	0.621776i
$894$			2.24961i			0.0752384i
$895$		0			0
$896$			3.52838i			0.117875i
$897$	−7.54465	+	7.54465i	−0.251908	+	0.251908i
$898$	21.1264	+	21.1264i	0.704996	+	0.704996i
$899$		−	17.8071i		−	0.593901i
$900$		0			0
$901$			11.4536i			0.381576i
$902$	18.5859	−	18.5859i	0.618844	−	0.618844i
$903$	10.3432	−	10.3432i	0.344202	−	0.344202i
$904$		−	8.73317i		−	0.290461i
$905$		0			0
$906$		−	5.77052i		−	0.191713i
$907$	39.2776	+	39.2776i	1.30419	+	1.30419i	0.925539	+	0.378651i	$0.123612\pi$
$907$	39.2776	+	39.2776i	1.30419	+	1.30419i	0.378651	+	0.925539i	$0.376388\pi$
$908$	−7.49970	+	7.49970i	−0.248886	+	0.248886i
$909$		−	17.3382i		−	0.575073i
$910$		0			0
$911$		−	37.5759i		−	1.24495i	−0.782641	−	0.622473i	$-0.786128\pi$
$911$		−	37.5759i		−	1.24495i	0.782641	−	0.622473i	$-0.213872\pi$
$912$	9.50181	+	4.20410i	0.314636	+	0.139212i
$913$	4.98988	+	4.98988i	0.165141	+	0.165141i
$914$	10.7171			0.354490
$915$		0			0
$916$	−15.9203			−0.526021
$917$	−18.3730	+	18.3730i	−0.606729	+	0.606729i
$918$	1.77429	+	1.77429i	0.0585603	+	0.0585603i
$919$			2.21605i			0.0731008i	0.999332	+	0.0365504i	$0.0116369\pi$
$919$			2.21605i			0.0731008i	−0.999332	+	0.0365504i	$0.988363\pi$
$920$		0			0
$921$	−50.8292			−1.67488
$922$	−28.5771	−	28.5771i	−0.941136	−	0.941136i
$923$	44.7247	+	44.7247i	1.47213	+	1.47213i
$924$	30.3301			0.997788
$925$		0			0
$926$		−	29.1263i		−	0.957151i
$927$	23.1320	+	23.1320i	0.759754	+	0.759754i
$928$	−3.40677	−	3.40677i	−0.111833	−	0.111833i
$929$			5.42471i			0.177979i	0.996033	+	0.0889894i	$0.0283637\pi$
$929$			5.42471i			0.177979i	−0.996033	+	0.0889894i	$0.971636\pi$
$930$		0			0
$931$	22.1561	−	8.56395i	0.726137	−	0.280672i
$932$	10.1360	−	10.1360i	0.332016	−	0.332016i
$933$	2.98743	−	2.98743i	0.0978041	−	0.0978041i
$934$	−0.653019			−0.0213674
$935$		0			0
$936$	10.7010			0.349774
$937$	−5.49390	+	5.49390i	−0.179478	+	0.179478i	−0.791128	−	0.611650i	$-0.790506\pi$
$937$	−5.49390	+	5.49390i	−0.179478	+	0.179478i	0.611650	+	0.791128i	$0.290506\pi$
$938$	28.9315	+	28.9315i	0.944646	+	0.944646i
$939$	38.6253			1.26049
$940$		0			0
$941$		−	4.26821i		−	0.139140i	−0.997577	−	0.0695698i	$-0.977837\pi$
$941$		−	4.26821i		−	0.139140i	0.997577	−	0.0695698i	$-0.0221627\pi$
$942$	19.0563	−	19.0563i	0.620886	−	0.620886i
$943$	−5.78202	+	5.78202i	−0.188288	+	0.188288i
$944$	8.96359			0.291740
$945$		0			0
$946$		−	6.27179i		−	0.203913i
$947$	−1.89440	+	1.89440i	−0.0615596	+	0.0615596i	−0.737216	−	0.675657i	$-0.763860\pi$
$947$	−1.89440	+	1.89440i	−0.0615596	+	0.0615596i	0.675657	+	0.737216i	$0.263860\pi$
$948$	27.3040	+	27.3040i	0.886792	+	0.886792i
$949$	41.3649			1.34276
$950$		0			0
$951$	46.9645			1.52293
$952$	−8.26001	−	8.26001i	−0.267709	−	0.267709i
$953$	−21.6091	+	21.6091i	−0.699989	+	0.699989i	−0.964408	−	0.264419i	$-0.914820\pi$
$953$	−21.6091	+	21.6091i	−0.699989	+	0.699989i	0.264419	+	0.964408i	$0.414820\pi$
$954$		−	9.27873i		−	0.300410i
$955$		0			0
$956$	−5.15672			−0.166780
$957$	−29.2848	+	29.2848i	−0.946643	+	0.946643i
$958$	12.3776	−	12.3776i	0.399903	−	0.399903i
$959$			62.6623i			2.02347i
$960$		0			0
$961$	17.3393			0.559334
$962$	9.36085	+	9.36085i	0.301806	+	0.301806i
$963$	−31.6276	+	31.6276i	−1.01919	+	1.01919i
$964$	−16.0990			−0.518514
$965$		0			0
$966$	−9.43559			−0.303585
$967$	−31.6417	+	31.6417i	−1.01753	+	1.01753i	−0.0176851	+	0.999844i	$0.505630\pi$
$967$	−31.6417	+	31.6417i	−1.01753	+	1.01753i	−0.999844	+	0.0176851i	$0.994370\pi$
$968$	1.41740	−	1.41740i	0.0455570	−	0.0455570i
$969$	−32.0858	+	12.4021i	−1.03075	+	0.398412i
$970$		0			0
$971$			36.8855i			1.18371i	0.806043	+	0.591856i	$0.201605\pi$
$971$			36.8855i			1.18371i	−0.806043	+	0.591856i	$0.798395\pi$
$972$	−14.9994	−	14.9994i	−0.481106	−	0.481106i
$973$	25.7174	+	25.7174i	0.824463	+	0.824463i
$974$			5.68655i			0.182209i
$975$		0			0
$976$	11.6915			0.374237
$977$	−15.1069	−	15.1069i	−0.483314	−	0.483314i	0.422875	−	0.906188i	$-0.361021\pi$
$977$	−15.1069	−	15.1069i	−0.483314	−	0.483314i	−0.906188	+	0.422875i	$0.861021\pi$
$978$	6.44665	+	6.44665i	0.206141	+	0.206141i
$979$	−43.1057			−1.37766
$980$		0			0
$981$		−	49.6073i		−	1.58384i
$982$	−7.85718	−	7.85718i	−0.250733	−	0.250733i
$983$	−19.4222	+	19.4222i	−0.619472	+	0.619472i	−0.945396	−	0.325924i	$-0.894325\pi$
$983$	−19.4222	+	19.4222i	−0.619472	+	0.619472i	0.325924	+	0.945396i	$0.394325\pi$
$984$	17.3742			0.553869
$985$		0			0
$986$	15.9506			0.507972
$987$	−62.6544	−	62.6544i	−1.99431	−	1.99431i
$988$	7.03688	−	15.9043i	0.223873	−	0.505982i
$989$			1.95113i			0.0620423i
$990$		0			0
$991$		−	8.85318i		−	0.281231i	−0.990064	−	0.140615i	$-0.955092\pi$
$991$		−	8.85318i		−	0.281231i	0.990064	−	0.140615i	$-0.0449081\pi$
$992$	−2.61349	+	2.61349i	−0.0829784	+	0.0829784i
$993$	−24.2455	−	24.2455i	−0.769409	−	0.769409i
$994$			55.9343i			1.77413i
$995$		0			0
$996$			4.66456i			0.147802i
$997$	29.8865	−	29.8865i	0.946514	−	0.946514i	−0.0521268	−	0.998640i	$-0.516600\pi$
$997$	29.8865	−	29.8865i	0.946514	−	0.946514i	0.998640	+	0.0521268i	$0.0166000\pi$
$998$	−0.710735	+	0.710735i	−0.0224979	+	0.0224979i
$999$		−	2.51472i		−	0.0795622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.c.493.1		16
5.2	odd	4	inner	950.2.f.c.607.8		16
5.3	odd	4		190.2.f.b.37.1	✓	16
5.4	even	2		190.2.f.b.113.8	yes	16
15.8	even	4		1710.2.p.b.37.6		16
15.14	odd	2		1710.2.p.b.1063.2		16
19.18	odd	2	inner	950.2.f.c.493.8		16
95.18	even	4		190.2.f.b.37.8	yes	16
95.37	even	4	inner	950.2.f.c.607.1		16
95.94	odd	2		190.2.f.b.113.1	yes	16
285.113	odd	4		1710.2.p.b.37.2		16
285.284	even	2		1710.2.p.b.1063.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.b.37.1	✓	16	5.3	odd	4
190.2.f.b.37.8	yes	16	95.18	even	4
190.2.f.b.113.1	yes	16	95.94	odd	2
190.2.f.b.113.8	yes	16	5.4	even	2
950.2.f.c.493.1		16	1.1	even	1	trivial
950.2.f.c.493.8		16	19.18	odd	2	inner
950.2.f.c.607.1		16	95.37	even	4	inner
950.2.f.c.607.8		16	5.2	odd	4	inner
1710.2.p.b.37.2		16	285.113	odd	4
1710.2.p.b.37.6		16	15.8	even	4
1710.2.p.b.1063.2		16	15.14	odd	2
1710.2.p.b.1063.6		16	285.284	even	2

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.68553 + 1.68553i) q^{3} +1.00000i q^{4} +2.38370 q^{6} +(2.49494 - 2.49494i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.68204i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.68553 + 1.68553i) q^{3} +1.00000i q^{4} +2.38370 q^{6} +(2.49494 - 2.49494i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.68204i q^{9} -3.60618 q^{11} +(-1.68553 - 1.68553i) q^{12} +(-2.82127 + 2.82127i) q^{13} -3.52838 q^{14} -1.00000 q^{16} +(2.34102 - 2.34102i) q^{17} +(-1.89649 + 1.89649i) q^{18} +(1.57153 + 4.06575i) q^{19} +8.41061i q^{21} +(2.54995 + 2.54995i) q^{22} +(-0.793280 - 0.793280i) q^{23} +2.38370i q^{24} +3.98988 q^{26} +(-0.535925 - 0.535925i) q^{27} +(2.49494 + 2.49494i) q^{28} -4.81790 q^{29} +3.69603i q^{31} +(0.707107 + 0.707107i) q^{32} +(6.07833 - 6.07833i) q^{33} -3.31071 q^{34} +2.68204 q^{36} +(2.34615 + 2.34615i) q^{37} +(1.76368 - 3.98615i) q^{38} -9.51069i q^{39} -7.28874i q^{41} +(5.94720 - 5.94720i) q^{42} +(-1.22979 - 1.22979i) q^{43} -3.60618i q^{44} +1.12187i q^{46} +(-7.44945 + 7.44945i) q^{47} +(1.68553 - 1.68553i) q^{48} -5.44945i q^{49} +7.89174i q^{51} +(-2.82127 - 2.82127i) q^{52} +(-2.44629 + 2.44629i) q^{53} +0.757912i q^{54} -3.52838i q^{56} +(-9.50181 - 4.20410i) q^{57} +(3.40677 + 3.40677i) q^{58} -8.96359 q^{59} -11.6915 q^{61} +(2.61349 - 2.61349i) q^{62} +(-6.69154 - 6.69154i) q^{63} -1.00000i q^{64} -8.59606 q^{66} +(-8.19965 - 8.19965i) q^{67} +(2.34102 + 2.34102i) q^{68} +2.67420 q^{69} -15.8527i q^{71} +(-1.89649 - 1.89649i) q^{72} +(-7.33090 - 7.33090i) q^{73} -3.31796i q^{74} +(-4.06575 + 1.57153i) q^{76} +(-8.99719 + 8.99719i) q^{77} +(-6.72508 + 6.72508i) q^{78} -16.1990 q^{79} +9.85277 q^{81} +(-5.15392 + 5.15392i) q^{82} +(-1.38370 - 1.38370i) q^{83} -8.41061 q^{84} +1.73918i q^{86} +(8.12073 - 8.12073i) q^{87} +(-2.54995 + 2.54995i) q^{88} +11.9533 q^{89} +14.0778i q^{91} +(0.793280 - 0.793280i) q^{92} +(-6.22979 - 6.22979i) q^{93} +10.5351 q^{94} -2.38370 q^{96} +(3.46802 + 3.46802i) q^{97} +(-3.85334 + 3.85334i) q^{98} +9.67192i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) \) 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

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