LMFDB - Embedded newform 275.2.h.d.126.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} + 7x^{14} + 25x^{12} + 57x^{10} + 194x^{8} + 303x^{6} + 235x^{4} + 33x^{2} + 121 $ x^16 + 7x^14 + 25x^12 + 57x^10 + 194x^8 + 303x^6 + 235x^4 + 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			126.1
Root			$1.33858 + 0.972539i$ of defining polynomial
Character	$\chi$	$=$	275.126
Dual form			275.2.h.d.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.511294 - 1.57360i) q^{2} +(-1.59764 - 1.16075i) q^{3} +(-0.596764 + 0.433574i) q^{4} +(-1.00970 + 3.10753i) q^{6} +(-1.81468 + 1.31845i) q^{7} +(-1.68978 - 1.22769i) q^{8} +(0.278050 + 0.855749i) q^{9} +(-3.27115 + 0.547326i) q^{11} +1.45668 q^{12} +(1.14329 + 3.51868i) q^{13} +(3.00254 + 2.18148i) q^{14} +(-1.52381 + 4.68982i) q^{16} +(0.687441 - 2.11573i) q^{17} +(1.20444 - 0.875078i) q^{18} +(-4.27714 - 3.10753i) q^{19} +4.42960 q^{21} +(2.53379 + 4.86764i) q^{22} +3.85415 q^{23} +(1.27460 + 3.92282i) q^{24} +(4.95244 - 3.59816i) q^{26} +(-1.28164 + 3.94448i) q^{27} +(0.511294 - 1.57360i) q^{28} +(-0.152450 + 0.110762i) q^{29} +(0.212253 + 0.653249i) q^{31} +3.98166 q^{32} +(5.86142 + 2.92256i) q^{33} -3.68079 q^{34} +(-0.536960 - 0.390125i) q^{36} +(2.09791 - 1.52422i) q^{37} +(-2.70313 + 8.31938i) q^{38} +(2.25775 - 6.94864i) q^{39} +(-6.40421 - 4.65293i) q^{41} +(-2.26482 - 6.97041i) q^{42} -8.41368 q^{43} +(1.71480 - 1.74491i) q^{44} +(-1.97060 - 6.06490i) q^{46} +(-9.71886 - 7.06117i) q^{47} +(7.87822 - 5.72386i) q^{48} +(-0.608337 + 1.87227i) q^{49} +(-3.55411 + 2.58222i) q^{51} +(-2.20788 - 1.60412i) q^{52} +(-3.91110 - 12.0371i) q^{53} +6.86233 q^{54} +4.68506 q^{56} +(3.22626 + 9.92940i) q^{57} +(0.252241 + 0.183264i) q^{58} +(0.278050 - 0.202015i) q^{59} +(0.535643 - 1.64854i) q^{61} +(0.919429 - 0.668004i) q^{62} +(-1.63283 - 1.18632i) q^{63} +(1.01183 + 3.11409i) q^{64} +(1.60204 - 10.7178i) q^{66} -0.650461 q^{67} +(0.507084 + 1.56065i) q^{68} +(-6.15754 - 4.47371i) q^{69} +(1.43619 - 4.42013i) q^{71} +(0.580756 - 1.78738i) q^{72} +(-7.16660 + 5.20684i) q^{73} +(-3.47116 - 2.52195i) q^{74} +3.89979 q^{76} +(5.21449 - 5.30606i) q^{77} -12.0888 q^{78} +(-2.23551 - 6.88019i) q^{79} +(8.80999 - 6.40083i) q^{81} +(-4.04742 + 12.4567i) q^{82} +(-0.983185 + 3.02593i) q^{83} +(-2.64342 + 1.92056i) q^{84} +(4.30186 + 13.2398i) q^{86} +0.372127 q^{87} +(6.19946 + 3.09111i) q^{88} +9.92195 q^{89} +(-6.71389 - 4.87793i) q^{91} +(-2.30002 + 1.67106i) q^{92} +(0.419156 - 1.29003i) q^{93} +(-6.14226 + 18.9039i) q^{94} +(-6.36125 - 4.62172i) q^{96} +(-0.700884 - 2.15710i) q^{97} +3.25724 q^{98} +(-1.37792 - 2.64710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46}+ \cdots + 72 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.511294	−	1.57360i	−0.361539	−	1.11270i	−0.952120	−	0.305725i	$-0.901101\pi$
$2$	−0.511294	−	1.57360i	−0.361539	−	1.11270i	0.590581	−	0.806979i	$-0.298899\pi$
$3$	−1.59764	−	1.16075i	−0.922396	−	0.670160i	0.0217231	−	0.999764i	$-0.493085\pi$
$3$	−1.59764	−	1.16075i	−0.922396	−	0.670160i	−0.944119	+	0.329604i	$0.893085\pi$
$4$	−0.596764	+	0.433574i	−0.298382	+	0.216787i
$5$		0			0
$5$		0			0
$6$	−1.00970	+	3.10753i	−0.412207	+	1.26864i
$7$	−1.81468	+	1.31845i	−0.685886	+	0.498326i	−0.875305	−	0.483571i	$-0.839340\pi$
$7$	−1.81468	+	1.31845i	−0.685886	+	0.498326i	0.189419	+	0.981896i	$0.439340\pi$
$8$	−1.68978	−	1.22769i	−0.597426	−	0.434055i
$9$	0.278050	+	0.855749i	0.0926832	+	0.285250i
$10$		0			0
$11$	−3.27115	+	0.547326i	−0.986289	+	0.165025i
$11$	−3.27115	+	0.547326i	−0.986289	+	0.165025i
$12$	1.45668			0.420508
$13$	1.14329	+	3.51868i	0.317091	+	0.975906i	0.974885	+	0.222708i	$0.0714896\pi$
$13$	1.14329	+	3.51868i	0.317091	+	0.975906i	−0.657794	+	0.753198i	$0.728510\pi$
$14$	3.00254	+	2.18148i	0.802464	+	0.583024i
$15$		0			0
$16$	−1.52381	+	4.68982i	−0.380954	+	1.17245i
$17$	0.687441	−	2.11573i	0.166729	−	0.513139i	−0.832431	−	0.554129i	$-0.813051\pi$
$17$	0.687441	−	2.11573i	0.166729	−	0.513139i	0.999160	+	0.0409903i	$0.0130513\pi$
$18$	1.20444	−	0.875078i	0.283890	−	0.206258i
$19$	−4.27714	−	3.10753i	−0.981244	−	0.712916i	−0.0232580	−	0.999729i	$-0.507404\pi$
$19$	−4.27714	−	3.10753i	−0.981244	−	0.712916i	−0.957986	+	0.286814i	$0.907404\pi$
$20$		0			0
$21$	4.42960			0.966617
$22$	2.53379	+	4.86764i	0.540206	+	1.03778i
$23$	3.85415			0.803647			0.401823	−	0.915717i	$-0.368377\pi$
$23$	3.85415			0.803647			0.401823	+	0.915717i	$0.368377\pi$
$24$	1.27460	+	3.92282i	0.260177	+	0.800742i
$25$		0			0
$26$	4.95244	−	3.59816i	0.971253	−	0.705657i
$27$	−1.28164	+	3.94448i	−0.246652	+	0.759116i
$28$	0.511294	−	1.57360i	0.0966255	−	0.297383i
$29$	−0.152450	+	0.110762i	−0.0283093	+	0.0205679i	−0.601850	−	0.798609i	$-0.705569\pi$
$29$	−0.152450	+	0.110762i	−0.0283093	+	0.0205679i	0.573541	+	0.819177i	$0.305569\pi$
$30$		0			0
$31$	0.212253	+	0.653249i	0.0381218	+	0.117327i	0.968306	−	0.249765i	$-0.0803534\pi$
$31$	0.212253	+	0.653249i	0.0381218	+	0.117327i	−0.930185	+	0.367092i	$0.880353\pi$
$32$	3.98166			0.703866
$33$	5.86142	+	2.92256i	1.02034	+	0.508753i
$34$	−3.68079			−0.631251
$35$		0			0
$36$	−0.536960	−	0.390125i	−0.0894934	−	0.0650208i
$37$	2.09791	−	1.52422i	0.344894	−	0.250580i	−0.401830	−	0.915714i	$-0.631626\pi$
$37$	2.09791	−	1.52422i	0.344894	−	0.250580i	0.746724	+	0.665134i	$0.231626\pi$
$38$	−2.70313	+	8.31938i	−0.438506	+	1.34958i
$39$	2.25775	−	6.94864i	0.361529	−	1.11267i
$40$		0			0
$41$	−6.40421	−	4.65293i	−1.00017	−	0.726666i	−0.0380448	−	0.999276i	$-0.512113\pi$
$41$	−6.40421	−	4.65293i	−1.00017	−	0.726666i	−0.962124	+	0.272611i	$0.912113\pi$
$42$	−2.26482	−	6.97041i	−0.349470	−	1.07556i
$43$	−8.41368			−1.28307			−0.641537	−	0.767092i	$-0.721703\pi$
$43$	−8.41368			−1.28307			−0.641537	+	0.767092i	$0.721703\pi$
$44$	1.71480	−	1.74491i	0.258515	−	0.263055i
$45$		0			0
$46$	−1.97060	−	6.06490i	−0.290550	−	0.894220i
$47$	−9.71886	−	7.06117i	−1.41764	−	1.02998i	−0.992155	−	0.125012i	$-0.960103\pi$
$47$	−9.71886	−	7.06117i	−1.41764	−	1.02998i	−0.425486	−	0.904965i	$-0.639897\pi$
$48$	7.87822	−	5.72386i	1.13712	−	0.826168i
$49$	−0.608337	+	1.87227i	−0.0869053	+	0.267467i
$50$		0			0
$51$	−3.55411	+	2.58222i	−0.497676	+	0.361582i
$52$	−2.20788	−	1.60412i	−0.306178	−	0.222451i
$53$	−3.91110	−	12.0371i	−0.537231	−	1.65343i	−0.738779	−	0.673947i	$-0.764597\pi$
$53$	−3.91110	−	12.0371i	−0.537231	−	1.65343i	0.201549	−	0.979479i	$-0.435403\pi$
$54$	6.86233			0.933845
$55$		0			0
$56$	4.68506			0.626067
$57$	3.22626	+	9.92940i	0.427328	+	1.31518i
$58$	0.252241	+	0.183264i	0.0331209	+	0.0240638i
$59$	0.278050	−	0.202015i	0.0361990	−	0.0263001i	−0.569539	−	0.821965i	$-0.692878\pi$
$59$	0.278050	−	0.202015i	0.0361990	−	0.0263001i	0.605738	+	0.795664i	$0.292878\pi$
$60$		0			0
$61$	0.535643	−	1.64854i	0.0685821	−	0.211074i	−0.910892	−	0.412645i	$-0.864605\pi$
$61$	0.535643	−	1.64854i	0.0685821	−	0.211074i	0.979474	+	0.201572i	$0.0646049\pi$
$62$	0.919429	−	0.668004i	0.116768	−	0.0848366i
$63$	−1.63283	−	1.18632i	−0.205717	−	0.149462i
$64$	1.01183	+	3.11409i	0.126479	+	0.389261i
$65$		0			0
$66$	1.60204	−	10.7178i	0.197197	−	1.31927i
$67$	−0.650461			−0.0794664			−0.0397332	−	0.999210i	$-0.512651\pi$
$67$	−0.650461			−0.0794664			−0.0397332	+	0.999210i	$0.512651\pi$
$68$	0.507084	+	1.56065i	0.0614930	+	0.189256i
$69$	−6.15754	−	4.47371i	−0.741281	−	0.538572i
$70$		0			0
$71$	1.43619	−	4.42013i	0.170444	−	0.524573i	−0.828952	−	0.559320i	$-0.811062\pi$
$71$	1.43619	−	4.42013i	0.170444	−	0.524573i	0.999396	+	0.0347464i	$0.0110624\pi$
$72$	0.580756	−	1.78738i	0.0684427	−	0.210645i
$73$	−7.16660	+	5.20684i	−0.838787	+	0.609415i	−0.922032	−	0.387115i	$-0.873472\pi$
$73$	−7.16660	+	5.20684i	−0.838787	+	0.609415i	0.0832444	+	0.996529i	$0.473472\pi$
$74$	−3.47116	−	2.52195i	−0.403515	−	0.293171i
$75$		0			0
$76$	3.89979			0.447336
$77$	5.21449	−	5.30606i	0.594246	−	0.604682i
$78$	−12.0888			−1.36878
$79$	−2.23551	−	6.88019i	−0.251514	−	0.774082i	−0.994496	−	0.104770i	$-0.966589\pi$
$79$	−2.23551	−	6.88019i	−0.251514	−	0.774082i	0.742982	−	0.669311i	$-0.233411\pi$
$80$		0			0
$81$	8.80999	−	6.40083i	0.978888	−	0.711203i
$82$	−4.04742	+	12.4567i	−0.446963	+	1.37561i
$83$	−0.983185	+	3.02593i	−0.107919	+	0.332139i	−0.990404	−	0.138200i	$-0.955868\pi$
$83$	−0.983185	+	3.02593i	−0.107919	+	0.332139i	0.882486	+	0.470339i	$0.155868\pi$
$84$	−2.64342	+	1.92056i	−0.288421	+	0.209550i
$85$		0			0
$86$	4.30186	+	13.2398i	0.463882	+	1.42768i
$87$	0.372127			0.0398962
$88$	6.19946	+	3.09111i	0.660865	+	0.329514i
$89$	9.92195			1.05172			0.525862	−	0.850570i	$-0.323743\pi$
$89$	9.92195			1.05172			0.525862	+	0.850570i	$0.323743\pi$
$90$		0			0
$91$	−6.71389	−	4.87793i	−0.703807	−	0.511346i
$92$	−2.30002	+	1.67106i	−0.239793	+	0.174220i
$93$	0.419156	−	1.29003i	0.0434644	−	0.133770i
$94$	−6.14226	+	18.9039i	−0.633526	+	1.94979i
$95$		0			0
$96$	−6.36125	−	4.62172i	−0.649243	−	0.471703i
$97$	−0.700884	−	2.15710i	−0.0711640	−	0.219020i	0.909149	−	0.416472i	$-0.136734\pi$
$97$	−0.700884	−	2.15710i	−0.0711640	−	0.219020i	−0.980313	+	0.197451i	$0.936734\pi$
$98$	3.25724			0.329031
$99$	−1.37792	−	2.64710i	−0.138486	−	0.266044i
$100$		0			0
$101$	3.05830	+	9.41247i	0.304312	+	0.936576i	0.979933	+	0.199327i	$0.0638756\pi$
$101$	3.05830	+	9.41247i	0.304312	+	0.936576i	−0.675621	+	0.737249i	$0.736124\pi$
$102$	5.88057	+	4.27249i	0.582263	+	0.423039i
$103$	8.28525	−	6.01958i	0.816370	−	0.593127i	−0.0993007	−	0.995057i	$-0.531661\pi$
$103$	8.28525	−	6.01958i	0.816370	−	0.593127i	0.915670	+	0.401930i	$0.131661\pi$
$104$	2.38796	−	7.34938i	0.234159	−	0.720666i
$105$		0			0
$106$	−16.9419	+	12.3090i	−1.64554	+	1.19556i
$107$	8.12803	+	5.90536i	0.785767	+	0.570893i	0.906704	−	0.421767i	$-0.138590\pi$
$107$	8.12803	+	5.90536i	0.785767	+	0.570893i	−0.120937	+	0.992660i	$0.538590\pi$
$108$	−0.945389	−	2.90961i	−0.0909701	−	0.279977i
$109$	−8.80173			−0.843053			−0.421527	−	0.906816i	$-0.638506\pi$
$109$	−8.80173			−0.843053			−0.421527	+	0.906816i	$0.638506\pi$
$110$		0			0
$111$	−5.12094			−0.486058
$112$	−3.41803	−	10.5196i	−0.322973	−	0.994010i
$113$	0.187168	+	0.135985i	0.0176073	+	0.0127924i	0.596554	−	0.802573i	$-0.296536\pi$
$113$	0.187168	+	0.135985i	0.0176073	+	0.0127924i	−0.578947	+	0.815365i	$0.696536\pi$
$114$	13.9753	−	10.1537i	1.30891	−	0.950980i
$115$		0			0
$116$	0.0429534	−	0.132197i	0.00398812	−	0.0122742i
$117$	−2.69321	+	1.95673i	−0.248988	+	0.180900i
$118$	−0.460056	−	0.334250i	−0.0423516	−	0.0307702i
$119$	1.54198	+	4.74573i	0.141353	+	0.435040i
$120$		0			0
$121$	10.4009	−	3.58078i	0.945533	−	0.325525i
$122$	−2.86801			−0.259658
$123$	4.83071	+	14.8674i	0.435570	+	1.34055i
$124$	−0.409897	−	0.297808i	−0.0368098	−	0.0267439i
$125$		0			0
$126$	−1.03194	+	3.17598i	−0.0919324	+	0.282939i
$127$	0.751018	−	2.31140i	0.0666421	−	0.205103i	−0.912190	−	0.409767i	$-0.865610\pi$
$127$	0.751018	−	2.31140i	0.0666421	−	0.205103i	0.978832	+	0.204664i	$0.0656101\pi$
$128$	10.8255	−	7.86516i	0.956844	−	0.695188i
$129$	13.4420	+	9.76619i	1.18350	+	0.859865i
$130$		0			0
$131$	1.58846			0.138785			0.0693924	−	0.997589i	$-0.477894\pi$
$131$	1.58846			0.138785			0.0693924	+	0.997589i	$0.477894\pi$
$132$	−4.76503	+	0.797281i	−0.414743	+	0.0693944i
$133$	11.8588			1.02829
$134$	0.332577	+	1.02357i	0.0287302	+	0.0884226i
$135$		0			0
$136$	−3.75909	+	2.73114i	−0.322339	+	0.234193i
$137$	5.77920	−	17.7866i	0.493750	−	1.51961i	−0.325145	−	0.945664i	$-0.605413\pi$
$137$	5.77920	−	17.7866i	0.493750	−	1.51961i	0.818895	−	0.573943i	$-0.194587\pi$
$138$	−3.89153	+	11.9769i	−0.331269	+	1.01954i
$139$	−9.40675	+	6.83441i	−0.797870	+	0.579687i	−0.910289	−	0.413974i	$-0.864140\pi$
$139$	−9.40675	+	6.83441i	−0.797870	+	0.579687i	0.112418	+	0.993661i	$0.464140\pi$
$140$		0			0
$141$	7.33095	+	22.5624i	0.617378	+	1.90009i
$142$	−7.68984			−0.645317
$143$	−5.66573	−	10.8844i	−0.473792	−	0.910197i
$144$	−4.43700			−0.369750
$145$		0			0
$146$	11.8577	+	8.61514i	0.981352	+	0.712994i
$147$	3.14514	−	2.28508i	0.259407	−	0.188470i
$148$	−0.591094	+	1.81920i	−0.0485876	+	0.149537i
$149$	1.82800	−	5.62600i	0.149755	−	0.460900i	−0.847836	−	0.530258i	$-0.822095\pi$
$149$	1.82800	−	5.62600i	0.149755	−	0.460900i	0.997592	+	0.0693580i	$0.0220951\pi$
$150$		0			0
$151$	−10.3375	−	7.51064i	−0.841254	−	0.611207i	0.0814664	−	0.996676i	$-0.474040\pi$
$151$	−10.3375	−	7.51064i	−0.841254	−	0.611207i	−0.922721	+	0.385469i	$0.874040\pi$
$152$	3.41232	+	10.5020i	0.276776	+	0.851828i
$153$	2.00167			0.161826
$154$	−11.0158	−	5.49257i	−0.887675	−	0.442604i
$155$		0			0
$156$	1.66541	+	5.12560i	0.133339	+	0.410376i
$157$	11.6083	+	8.43394i	0.926445	+	0.673102i	0.945120	−	0.326724i	$-0.105945\pi$
$157$	11.6083	+	8.43394i	0.926445	+	0.673102i	−0.0186749	+	0.999826i	$0.505945\pi$
$158$	−9.68367	+	7.03560i	−0.770391	+	0.559722i
$159$	−7.72359	+	23.7708i	−0.612520	+	1.88514i
$160$		0			0
$161$	−6.99407	+	5.08149i	−0.551210	+	0.400478i
$162$	−14.5768	−	10.5907i	−1.14527	−	0.832084i
$163$	1.12085	+	3.44963i	0.0877921	+	0.270196i	0.985308	−	0.170785i	$-0.0546304\pi$
$163$	1.12085	+	3.44963i	0.0877921	+	0.270196i	−0.897516	+	0.440982i	$0.854630\pi$
$164$	5.83919			0.455964
$165$		0			0
$166$	5.26430			0.408589
$167$	1.18066	+	3.63370i	0.0913623	+	0.281184i	0.986289	−	0.165030i	$-0.0527720\pi$
$167$	1.18066	+	3.63370i	0.0913623	+	0.281184i	−0.894926	+	0.446214i	$0.852772\pi$
$168$	−7.48502	−	5.43819i	−0.577482	−	0.419565i
$169$	−0.556767	+	0.404515i	−0.0428282	+	0.0311165i
$170$		0			0
$171$	1.47000	−	4.52421i	0.112414	−	0.345975i
$172$	5.02098	−	3.64795i	0.382846	−	0.278154i
$173$	1.70472	+	1.23855i	0.129607	+	0.0941651i	0.650700	−	0.759335i	$-0.274476\pi$
$173$	1.70472	+	1.23855i	0.129607	+	0.0941651i	−0.521093	+	0.853500i	$0.674476\pi$
$174$	−0.190266	−	0.585579i	−0.0144240	−	0.0443926i
$175$		0			0
$176$	2.41777	−	16.1751i	0.182246	−	1.21925i
$177$	−0.678711			−0.0510151
$178$	−5.07303	−	15.6132i	−0.380240	−	1.17026i
$179$	−4.06448	−	2.95302i	−0.303793	−	0.220719i	0.425435	−	0.904989i	$-0.360121\pi$
$179$	−4.06448	−	2.95302i	−0.303793	−	0.220719i	−0.729229	+	0.684270i	$0.760121\pi$
$180$		0			0
$181$	−4.83538	+	14.8818i	−0.359411	+	1.10615i	0.593997	+	0.804467i	$0.297549\pi$
$181$	−4.83538	+	14.8818i	−0.359411	+	1.10615i	−0.953408	+	0.301685i	$0.902451\pi$
$182$	−4.24314	+	13.0590i	−0.314522	+	0.968000i
$183$	−2.76931	+	2.01202i	−0.204713	+	0.148733i
$184$	−6.51265	−	4.73172i	−0.480119	−	0.348827i
$185$		0			0
$186$	−2.24430			−0.164560
$187$	−1.09073	+	7.29712i	−0.0797622	+	0.533618i
$188$	8.86140			0.646284
$189$	−2.87481	−	8.84777i	−0.209112	−	0.643580i
$190$		0			0
$191$	−2.52078	+	1.83145i	−0.182397	+	0.132519i	−0.675237	−	0.737601i	$-0.735959\pi$
$191$	−2.52078	+	1.83145i	−0.182397	+	0.132519i	0.492840	+	0.870120i	$0.335959\pi$
$192$	1.99815	−	6.14966i	0.144204	−	0.443814i
$193$	2.97780	−	9.16474i	0.214347	−	0.659692i	−0.784852	−	0.619683i	$-0.787261\pi$
$193$	2.97780	−	9.16474i	0.214347	−	0.659692i	0.999199	−	0.0400095i	$-0.0127388\pi$
$194$	−3.03606	+	2.20582i	−0.217976	+	0.158369i
$195$		0			0
$196$	−0.448734	−	1.38106i	−0.0320524	−	0.0986472i
$197$	−14.3974			−1.02577			−0.512885	−	0.858457i	$-0.671423\pi$
$197$	−14.3974			−1.02577			−0.512885	+	0.858457i	$0.671423\pi$
$198$	−3.46096	+	3.52174i	−0.245960	+	0.250279i
$199$	14.7978			1.04899			0.524493	−	0.851415i	$-0.324255\pi$
$199$	14.7978			1.04899			0.524493	+	0.851415i	$0.324255\pi$
$200$		0			0
$201$	1.03920	+	0.755023i	0.0732995	+	0.0532552i
$202$	13.2478	−	9.62508i	0.932111	−	0.677218i
$203$	0.130616	−	0.401995i	0.00916745	−	0.0282145i
$204$	1.00138	−	3.08194i	0.0701109	−	0.215779i
$205$		0			0
$206$	−13.7086	−	9.95989i	−0.955125	−	0.693939i
$207$	1.07165	+	3.29819i	0.0744845	+	0.229240i
$208$	−18.2441			−1.26500
$209$	15.6920	+	7.82420i	1.08544	+	0.541211i
$210$		0			0
$211$	−2.09250	−	6.44005i	−0.144054	−	0.443352i	0.852834	−	0.522181i	$-0.174882\pi$
$211$	−2.09250	−	6.44005i	−0.144054	−	0.443352i	−0.996888	+	0.0788298i	$0.974882\pi$
$212$	7.55299	+	5.48756i	0.518741	+	0.376888i
$213$	−7.42518	+	5.39471i	−0.508765	+	0.369640i
$214$	5.13687	−	15.8097i	0.351149	−	1.08073i
$215$		0			0
$216$	7.00830	−	5.09183i	0.476854	−	0.346455i
$217$	−1.24645	−	0.905596i	−0.0846143	−	0.0614759i
$218$	4.50027	+	13.8504i	0.304797	+	0.938069i
$219$	17.4935			1.18210
$220$		0			0
$221$	8.23051			0.553644
$222$	2.61831	+	8.05832i	0.175729	+	0.540839i
$223$	7.05242	+	5.12388i	0.472265	+	0.343121i	0.798323	−	0.602229i	$-0.205721\pi$
$223$	7.05242	+	5.12388i	0.472265	+	0.343121i	−0.326058	+	0.945350i	$0.605721\pi$
$224$	−7.22547	+	5.24961i	−0.482772	+	0.350754i
$225$		0			0
$226$	0.118289	−	0.364056i	0.00786846	−	0.0242166i
$227$	−3.08028	+	2.23795i	−0.204445	+	0.148538i	−0.685297	−	0.728264i	$-0.740328\pi$
$227$	−3.08028	+	2.23795i	−0.204445	+	0.148538i	0.480852	+	0.876802i	$0.340328\pi$
$228$	−6.23044	−	4.52668i	−0.412621	−	0.299787i
$229$	−0.838570	−	2.58085i	−0.0554142	−	0.170547i	0.919519	−	0.393046i	$-0.128579\pi$
$229$	−0.838570	−	2.58085i	−0.0554142	−	0.170547i	−0.974933	+	0.222499i	$0.928579\pi$
$230$		0			0
$231$	−14.4899	+	2.42443i	−0.953364	+	0.159516i
$232$	0.393588			0.0258403
$233$	−3.24801	−	9.99634i	−0.212784	−	0.654882i	−0.999303	−	0.0373166i	$-0.988119\pi$
$233$	−3.24801	−	9.99634i	−0.212784	−	0.654882i	0.786519	−	0.617566i	$-0.211881\pi$
$234$	4.45614	+	3.23758i	0.291307	+	0.211647i
$235$		0			0
$236$	−0.0783415	+	0.241110i	−0.00509959	+	0.0156949i
$237$	−4.41466	+	13.5869i	−0.286763	+	0.882565i
$238$	6.67948	−	4.85293i	0.432966	−	0.314569i
$239$	−16.2124	−	11.7790i	−1.04869	−	0.761919i	−0.0767288	−	0.997052i	$-0.524448\pi$
$239$	−16.2124	−	11.7790i	−1.04869	−	0.761919i	−0.971963	+	0.235133i	$0.924448\pi$
$240$		0			0
$241$	28.4450			1.83230			0.916152	−	0.400832i	$-0.131279\pi$
$241$	28.4450			1.83230			0.916152	+	0.400832i	$0.131279\pi$
$242$	−10.9526	−	14.5360i	−0.704060	−	0.934408i
$243$	−9.06251			−0.581361
$244$	0.395112	+	1.21603i	0.0252944	+	0.0778483i
$245$		0			0
$246$	20.9254	−	15.2032i	1.33416	−	0.969321i
$247$	6.04438	−	18.6027i	0.384595	−	1.18366i
$248$	0.443329	−	1.36443i	0.0281514	−	0.0866411i
$249$	5.08313	−	3.69311i	0.322130	−	0.234041i
$250$		0			0
$251$	−7.36604	−	22.6703i	−0.464940	−	1.43094i	−0.859058	−	0.511879i	$-0.828950\pi$
$251$	−7.36604	−	22.6703i	−0.464940	−	1.43094i	0.394117	−	0.919060i	$-0.371050\pi$
$252$	1.48877			0.0937838
$253$	−12.6075	+	2.10948i	−0.792628	+	0.132622i
$254$	−4.02120			−0.252313
$255$		0			0
$256$	−12.6136	−	9.16432i	−0.788350	−	0.572770i
$257$	−19.9636	+	14.5044i	−1.24529	+	0.904758i	−0.997939	−	0.0641671i	$-0.979561\pi$
$257$	−19.9636	+	14.5044i	−1.24529	+	0.904758i	−0.247354	+	0.968925i	$0.579561\pi$
$258$	8.49527	−	26.1458i	0.528892	−	1.62776i
$259$	−1.79744	+	5.53196i	−0.111688	+	0.343739i
$260$		0			0
$261$	−0.137173	−	0.0996619i	−0.00849079	−	0.00616892i
$262$	−0.812172	−	2.49961i	−0.0501761	−	0.154426i
$263$	5.44098			0.335505			0.167753	−	0.985829i	$-0.446349\pi$
$263$	5.44098			0.335505			0.167753	+	0.985829i	$0.446349\pi$
$264$	−6.31647	−	12.1345i	−0.388752	−	0.746827i
$265$		0			0
$266$	−6.06332	−	18.6610i	−0.371766	−	1.14418i
$267$	−15.8517	−	11.5169i	−0.970107	−	0.704824i
$268$	0.388171	−	0.282023i	0.0237113	−	0.0172273i
$269$	−2.07213	+	6.37738i	−0.126340	+	0.388835i	−0.994143	−	0.108074i	$-0.965532\pi$
$269$	−2.07213	+	6.37738i	−0.126340	+	0.388835i	0.867803	+	0.496909i	$0.165532\pi$
$270$		0			0
$271$	4.09349	−	2.97409i	0.248662	−	0.180663i	−0.456472	−	0.889738i	$-0.650887\pi$
$271$	4.09349	−	2.97409i	0.248662	−	0.180663i	0.705134	+	0.709075i	$0.250887\pi$
$272$	8.87484	+	6.44795i	0.538116	+	0.390964i
$273$	5.06430	+	15.5863i	0.306505	+	0.943327i
$274$	−30.9438			−1.86938
$275$		0			0
$276$	5.61428			0.337940
$277$	−3.30453	−	10.1703i	−0.198550	−	0.611074i	−0.999917	−	0.0129009i	$-0.995893\pi$
$277$	−3.30453	−	10.1703i	−0.198550	−	0.611074i	0.801367	−	0.598173i	$-0.204107\pi$
$278$	15.5642	+	11.3081i	0.933481	+	0.678214i
$279$	−0.500000	+	0.363271i	−0.0299342	+	0.0217485i
$280$		0			0
$281$	−4.23963	+	13.0482i	−0.252915	+	0.778392i	0.741319	+	0.671153i	$0.234201\pi$
$281$	−4.23963	+	13.0482i	−0.252915	+	0.778392i	−0.994233	+	0.107238i	$0.965799\pi$
$282$	31.7559	−	23.0720i	1.89103	−	1.37392i
$283$	17.7735	+	12.9132i	1.05653	+	0.767611i	0.973442	−	0.228932i	$-0.0735233\pi$
$283$	17.7735	+	12.9132i	1.05653	+	0.767611i	0.0830832	+	0.996543i	$0.473523\pi$
$284$	1.05939	+	3.26047i	0.0628633	+	0.193473i
$285$		0			0
$286$	−14.2308	+	14.4807i	−0.841485	+	0.856263i
$287$	17.7563			1.04812
$288$	1.10710	+	3.40730i	0.0652365	+	0.200777i
$289$	9.74956	+	7.08347i	0.573504	+	0.416675i
$290$		0			0
$291$	−1.38410	+	4.25981i	−0.0811372	+	0.249715i
$292$	2.01922	−	6.21450i	0.118166	−	0.363676i
$293$	−11.3570	+	8.25135i	−0.663483	+	0.482049i	−0.867837	−	0.496848i	$-0.834491\pi$
$293$	−11.3570	+	8.25135i	−0.663483	+	0.482049i	0.204354	+	0.978897i	$0.434491\pi$
$294$	−5.20389	−	3.78085i	−0.303497	−	0.220504i
$295$		0			0
$296$	−5.41627			−0.314815
$297$	2.03352	−	13.6045i	0.117997	−	0.789412i
$298$	−9.78772			−0.566988
$299$	4.40641	+	13.5615i	0.254829	+	0.784283i
$300$		0			0
$301$	15.2682	−	11.0930i	0.880043	−	0.639389i
$302$	−6.53324	+	20.1073i	−0.375946	+	1.15704i
$303$	6.03949	−	18.5876i	0.346960	−	1.06783i
$304$	21.0913	−	15.3237i	1.20967	−	0.878877i
$305$		0			0
$306$	−1.02344	−	3.14983i	−0.0585064	−	0.180064i
$307$	−6.86951			−0.392064			−0.196032	−	0.980598i	$-0.562806\pi$
$307$	−6.86951			−0.392064			−0.196032	+	0.980598i	$0.562806\pi$
$308$	−0.811246	+	5.42733i	−0.0462251	+	0.309251i
$309$	−20.2241			−1.15051
$310$		0			0
$311$	4.45087	+	3.23374i	0.252385	+	0.183369i	0.706783	−	0.707430i	$-0.250146\pi$
$311$	4.45087	+	3.23374i	0.252385	+	0.183369i	−0.454398	+	0.890799i	$0.650146\pi$
$312$	−12.3459	+	8.96982i	−0.698949	+	0.507816i
$313$	4.39793	−	13.5354i	0.248586	−	0.765068i	−0.746440	−	0.665452i	$-0.768239\pi$
$313$	4.39793	−	13.5354i	0.248586	−	0.765068i	0.995026	−	0.0996156i	$-0.0317613\pi$
$314$	7.33639	−	22.5791i	0.414016	−	1.27421i
$315$		0			0
$316$	4.31714	+	3.13659i	0.242858	+	0.176447i
$317$	5.77442	+	17.7718i	0.324324	+	0.998166i	0.971745	+	0.236033i	$0.0758475\pi$
$317$	5.77442	+	17.7718i	0.324324	+	0.998166i	−0.647421	+	0.762132i	$0.724153\pi$
$318$	41.3547			2.31906
$319$	0.438065	−	0.445758i	0.0245269	−	0.0249577i
$320$		0			0
$321$	−6.13099	−	18.8693i	−0.342199	−	1.05318i
$322$	11.5723	+	8.40774i	0.644897	+	0.468545i
$323$	−9.51497	+	6.91303i	−0.529427	+	0.384651i
$324$	−2.48225	+	7.63957i	−0.137903	+	0.424420i
$325$		0			0
$326$	4.85526	−	3.52755i	0.268908	−	0.195373i
$327$	14.0620	+	10.2166i	0.777629	+	0.564981i
$328$	5.10930	+	15.7248i	0.282114	+	0.868257i
$329$	26.9464			1.48560
$330$		0			0
$331$	0.468249			0.0257373			0.0128686	−	0.999917i	$-0.495904\pi$
$331$	0.468249			0.0257373			0.0128686	+	0.999917i	$0.495904\pi$
$332$	−0.725237	−	2.23205i	−0.0398025	−	0.122500i
$333$	1.88767	+	1.37148i	0.103444	+	0.0751564i
$334$	5.11433	−	3.71578i	0.279844	−	0.203318i
$335$		0			0
$336$	−6.74988	+	20.7740i	−0.368236	+	1.13331i
$337$	−27.5771	+	20.0360i	−1.50222	+	1.09143i	−0.532735	+	0.846282i	$0.678836\pi$
$337$	−27.5771	+	20.0360i	−1.50222	+	1.09143i	−0.969486	+	0.245146i	$0.921164\pi$
$338$	0.921216	+	0.669303i	0.0501075	+	0.0364053i
$339$	−0.141181	−	0.434511i	−0.00766790	−	0.0235994i
$340$		0			0
$341$	−1.05185	−	2.02070i	−0.0569611	−	0.109427i
$342$	−7.87090			−0.425610
$343$	−6.21658	−	19.1327i	−0.335664	−	1.03307i
$344$	14.2172	+	10.3294i	0.766542	+	0.556925i
$345$		0			0
$346$	1.07737	−	3.31580i	0.0579198	−	0.178259i
$347$	1.11027	−	3.41707i	0.0596026	−	0.183438i	−0.916822	−	0.399296i	$-0.869255\pi$
$347$	1.11027	−	3.41707i	0.0596026	−	0.183438i	0.976425	+	0.215858i	$0.0692547\pi$
$348$	−0.222072	+	0.161345i	−0.0119043	+	0.00864898i
$349$	5.15433	+	3.74484i	0.275905	+	0.200457i	0.717129	−	0.696940i	$-0.245456\pi$
$349$	5.15433	+	3.74484i	0.275905	+	0.200457i	−0.441224	+	0.897397i	$0.645456\pi$
$350$		0			0
$351$	−15.3446			−0.819037
$352$	−13.0246	+	2.17927i	−0.694215	+	0.116156i
$353$	−12.1971			−0.649186			−0.324593	−	0.945854i	$-0.605227\pi$
$353$	−12.1971			−0.649186			−0.324593	+	0.945854i	$0.605227\pi$
$354$	0.347021	+	1.06802i	0.0184440	+	0.0567647i
$355$		0			0
$356$	−5.92106	+	4.30190i	−0.313815	+	0.228000i
$357$	3.04509	−	9.37181i	0.161163	−	0.496009i
$358$	−2.56873	+	7.90573i	−0.135761	+	0.417831i
$359$	−19.5093	+	14.1744i	−1.02966	+	0.748094i	−0.968241	−	0.250018i	$-0.919564\pi$
$359$	−19.5093	+	14.1744i	−1.02966	+	0.748094i	−0.0614222	+	0.998112i	$0.519564\pi$
$360$		0			0
$361$	2.76592	+	8.51262i	0.145575	+	0.448032i
$362$	25.8902			1.36076
$363$	−20.7732	−	6.35204i	−1.09031	−	0.333396i
$364$	6.12155			0.320856
$365$		0			0
$366$	4.58205	+	3.32905i	0.239507	+	0.174012i
$367$	16.4958	−	11.9849i	0.861073	−	0.625606i	−0.0671034	−	0.997746i	$-0.521376\pi$
$367$	16.4958	−	11.9849i	0.861073	−	0.625606i	0.928177	+	0.372140i	$0.121376\pi$
$368$	−5.87302	+	18.0753i	−0.306152	+	0.942239i
$369$	2.20105	−	6.77414i	0.114582	−	0.352648i
$370$		0			0
$371$	22.9677	+	16.6870i	1.19242	+	0.866347i
$372$	0.309186	+	0.951577i	0.0160305	+	0.0493370i
$373$	7.51997			0.389369			0.194685	−	0.980866i	$-0.437632\pi$
$373$	7.51997			0.389369			0.194685	+	0.980866i	$0.437632\pi$
$374$	12.0404	−	2.01460i	0.622596	−	0.104172i
$375$		0			0
$376$	7.75374	+	23.8636i	0.399869	+	1.23067i
$377$	−0.564029	−	0.409791i	−0.0290490	−	0.0211053i
$378$	−12.4530	+	9.04762i	−0.640512	+	0.465359i
$379$	7.16649	−	22.0562i	0.368118	−	1.13295i	−0.579888	−	0.814696i	$-0.696904\pi$
$379$	7.16649	−	22.0562i	0.368118	−	1.13295i	0.948006	−	0.318254i	$-0.103096\pi$
$380$		0			0
$381$	−3.88281	+	2.82103i	−0.198922	+	0.144526i
$382$	4.17083	+	3.03029i	0.213398	+	0.155043i
$383$	0.754123	+	2.32095i	0.0385339	+	0.118595i	0.968473	−	0.249118i	$-0.0801408\pi$
$383$	0.754123	+	2.32095i	0.0385339	+	0.118595i	−0.929939	+	0.367713i	$0.880141\pi$
$384$	−26.4246			−1.34848
$385$		0			0
$386$	−15.9442			−0.811537
$387$	−2.33942	−	7.20000i	−0.118919	−	0.365997i
$388$	1.35352	+	0.983393i	0.0687148	+	0.0499242i
$389$	−27.4849	+	19.9689i	−1.39354	+	1.01246i	−0.398071	+	0.917355i	$0.630320\pi$
$389$	−27.4849	+	19.9689i	−1.39354	+	1.01246i	−0.995467	+	0.0951096i	$0.969680\pi$
$390$		0			0
$391$	2.64950	−	8.15434i	0.133991	−	0.412383i
$392$	3.32653	−	2.41686i	0.168015	−	0.122070i
$393$	−2.53779	−	1.84381i	−0.128015	−	0.0930080i
$394$	7.36129	+	22.6557i	0.370856	+	1.14138i
$395$		0			0
$396$	1.97000	+	0.982264i	0.0989964	+	0.0493606i
$397$	−27.4961			−1.37999			−0.689995	−	0.723814i	$-0.742387\pi$
$397$	−27.4961			−1.37999			−0.689995	+	0.723814i	$0.742387\pi$
$398$	−7.56601	−	23.2858i	−0.379250	−	1.16721i
$399$	−18.9460	−	13.7651i	−0.948487	−	0.689116i
$400$		0			0
$401$	−0.583247	+	1.79505i	−0.0291259	+	0.0896404i	−0.964563	−	0.263853i	$-0.915006\pi$
$401$	−0.583247	+	1.79505i	−0.0291259	+	0.0896404i	0.935437	+	0.353494i	$0.115006\pi$
$402$	0.656768	−	2.02132i	0.0327566	−	0.100815i
$403$	−2.05591	+	1.49370i	−0.102412	+	0.0744067i
$404$	−5.90608	−	4.29102i	−0.293839	−	0.213486i
$405$		0			0
$406$	−0.699363			−0.0347088
$407$	−6.02834	+	6.13420i	−0.298814	+	0.304061i
$408$	9.17582			0.454271
$409$	4.18949	+	12.8939i	0.207157	+	0.637563i	0.999618	+	0.0276408i	$0.00879945\pi$
$409$	4.18949	+	12.8939i	0.207157	+	0.637563i	−0.792461	+	0.609923i	$0.791201\pi$
$410$		0			0
$411$	−29.8788	+	21.7082i	−1.47381	+	1.07079i
$412$	−2.33440	+	7.18454i	−0.115008	+	0.353957i
$413$	−0.238227	+	0.733187i	−0.0117224	+	0.0360778i
$414$	4.64210	−	3.37269i	0.228147	−	0.165758i
$415$		0			0
$416$	4.55219	+	14.0102i	0.223189	+	0.686906i
$417$	22.9616			1.12444
$418$	4.28893	−	28.6934i	0.209779	−	1.40344i
$419$	−22.1368			−1.08145			−0.540727	−	0.841198i	$-0.681851\pi$
$419$	−22.1368			−1.08145			−0.540727	+	0.841198i	$0.681851\pi$
$420$		0			0
$421$	−14.4835	−	10.5229i	−0.705881	−	0.512853i	0.175961	−	0.984397i	$-0.443697\pi$
$421$	−14.4835	−	10.5229i	−0.705881	−	0.512853i	−0.881842	+	0.471544i	$0.843697\pi$
$422$	−9.06419	+	6.58552i	−0.441238	+	0.320578i
$423$	3.34026	−	10.2803i	0.162409	−	0.499843i
$424$	−8.16902	+	25.1417i	−0.396723	+	1.22099i
$425$		0			0
$426$	12.2856	+	8.92599i	0.595238	+	0.432466i
$427$	1.20149	+	3.69780i	0.0581440	+	0.178949i
$428$	−7.41093			−0.358221
$429$	−3.58227	+	23.9658i	−0.172954	+	1.15708i
$430$		0			0
$431$	10.3353	+	31.8087i	0.497833	+	1.53217i	0.812495	+	0.582968i	$0.198109\pi$
$431$	10.3353	+	31.8087i	0.497833	+	1.53217i	−0.314662	+	0.949204i	$0.601891\pi$
$432$	−16.5459	−	12.0213i	−0.796066	−	0.578376i
$433$	−25.4771	+	18.5102i	−1.22435	+	0.889543i	−0.996454	−	0.0841428i	$-0.973185\pi$
$433$	−25.4771	+	18.5102i	−1.22435	+	0.889543i	−0.227897	+	0.973685i	$0.573185\pi$
$434$	−0.787747	+	2.42443i	−0.0378130	+	0.116377i
$435$		0			0
$436$	5.25255	−	3.81620i	0.251552	−	0.182763i
$437$	−16.4848	−	11.9769i	−0.788574	−	0.572932i
$438$	−8.94431	−	27.5277i	−0.427375	−	1.31533i
$439$	35.6208			1.70009			0.850045	−	0.526710i	$-0.176575\pi$
$439$	35.6208			1.70009			0.850045	+	0.526710i	$0.176575\pi$
$440$		0			0
$441$	−1.77134			−0.0843495
$442$	−4.20821	−	12.9515i	−0.200164	−	0.616041i
$443$	−19.0018	−	13.8056i	−0.902805	−	0.655926i	0.0363802	−	0.999338i	$-0.488417\pi$
$443$	−19.0018	−	13.8056i	−0.902805	−	0.655926i	−0.939185	+	0.343412i	$0.888417\pi$
$444$	3.05599	−	2.22031i	0.145031	−	0.105371i
$445$		0			0
$446$	4.45709	−	13.7175i	0.211049	−	0.649543i
$447$	−9.45086	+	6.86646i	−0.447011	+	0.324772i
$448$	−5.94191	−	4.31705i	−0.280729	−	0.203961i
$449$	−9.70066	−	29.8555i	−0.457802	−	1.40897i	−0.867814	−	0.496890i	$-0.834475\pi$
$449$	−9.70066	−	29.8555i	−0.457802	−	1.40897i	0.410011	−	0.912080i	$-0.365525\pi$
$450$		0			0
$451$	23.4958	+	11.7152i	1.10637	+	0.551649i
$452$	−0.170655			−0.00802692
$453$	7.79760	+	23.9985i	0.366363	+	1.12755i
$454$	5.09658	+	3.70288i	0.239194	+	0.173785i
$455$		0			0
$456$	6.73861	−	20.7393i	0.315564	−	0.971207i
$457$	12.0859	−	37.1964i	0.565352	−	1.73998i	−0.101550	−	0.994830i	$-0.532380\pi$
$457$	12.0859	−	37.1964i	0.565352	−	1.73998i	0.666903	−	0.745145i	$-0.267620\pi$
$458$	−3.63247	+	2.63915i	−0.169734	+	0.123319i
$459$	7.46440	+	5.42320i	0.348408	+	0.253133i
$460$		0			0
$461$	−8.88399			−0.413769			−0.206884	−	0.978365i	$-0.566332\pi$
$461$	−8.88399			−0.413769			−0.206884	+	0.978365i	$0.566332\pi$
$462$	11.2237	+	21.5617i	0.522173	+	1.00314i
$463$	4.21081			0.195693			0.0978464	−	0.995202i	$-0.468805\pi$
$463$	4.21081			0.195693			0.0978464	+	0.995202i	$0.468805\pi$
$464$	−0.287146	−	0.883744i	−0.0133304	−	0.0410268i
$465$		0			0
$466$	−14.0696	+	10.2221i	−0.651760	+	0.473531i
$467$	−2.07920	+	6.39912i	−0.0962139	+	0.296116i	−0.987568	−	0.157191i	$-0.949756\pi$
$467$	−2.07920	+	6.39912i	−0.0962139	+	0.296116i	0.891354	+	0.453307i	$0.149756\pi$
$468$	0.758822	−	2.33542i	0.0350766	−	0.107955i
$469$	1.18038	−	0.857597i	0.0545049	−	0.0396002i
$470$		0			0
$471$	−8.75618	−	26.9487i	−0.403463	−	1.24173i
$472$	−0.717854			−0.0330419
$473$	27.5224	−	4.60503i	1.26548	−	0.211740i
$474$	23.6376			1.08571
$475$		0			0
$476$	−2.97782	−	2.16352i	−0.136488	−	0.0991646i
$477$	9.21327	−	6.69383i	0.421847	−	0.306490i
$478$	−10.2461	+	31.5343i	−0.468647	+	1.44235i
$479$	6.43046	−	19.7909i	0.293815	−	0.904270i	−0.689802	−	0.723998i	$-0.742302\pi$
$479$	6.43046	−	19.7909i	0.293815	−	0.904270i	0.983617	−	0.180272i	$-0.0576977\pi$
$480$		0			0
$481$	7.76176	+	5.63925i	0.353906	+	0.257128i
$482$	−14.5437	−	44.7611i	−0.662450	−	2.03881i
$483$	17.0723			0.776818
$484$	−4.65433	+	6.64642i	−0.211560	+	0.302110i
$485$		0			0
$486$	4.63361	+	14.2608i	0.210185	+	0.646882i
$487$	12.7658	+	9.27489i	0.578473	+	0.420285i	0.838173	−	0.545404i	$-0.183624\pi$
$487$	12.7658	+	9.27489i	0.578473	+	0.420285i	−0.259700	+	0.965689i	$0.583624\pi$
$488$	−2.92902	+	2.12806i	−0.132590	+	0.0963326i
$489$	2.21345	−	6.81230i	0.100096	−	0.308063i
$490$		0			0
$491$	−15.6386	+	11.3621i	−0.705759	+	0.512764i	−0.881803	−	0.471618i	$-0.843670\pi$
$491$	−15.6386	+	11.3621i	−0.705759	+	0.512764i	0.176044	+	0.984382i	$0.443670\pi$
$492$	−9.32890	−	6.77784i	−0.420579	−	0.305569i
$493$	0.129541	+	0.398685i	0.00583422	+	0.0179559i
$494$	−32.3637			−1.45611
$495$		0			0
$496$	−3.38705			−0.152083
$497$	3.22148	+	9.91469i	0.144503	+	0.444734i
$498$	−8.41045	−	6.11055i	−0.376881	−	0.273820i
$499$	33.5416	−	24.3694i	1.50153	−	1.09092i	0.531758	−	0.846896i	$-0.321532\pi$
$499$	33.5416	−	24.3694i	1.50153	−	1.09092i	0.969769	−	0.244026i	$-0.0784684\pi$
$500$		0			0
$501$	2.33156	−	7.17579i	0.104166	−	0.320591i
$502$	−31.9078	+	23.1824i	−1.42412	+	1.03468i
$503$	26.4236	+	19.1978i	1.17817	+	0.855990i	0.991964	−	0.126521i	$-0.0403812\pi$
$503$	26.4236	+	19.1978i	1.17817	+	0.855990i	0.186205	+	0.982511i	$0.440381\pi$
$504$	1.30268	+	4.00923i	0.0580259	+	0.178585i
$505$		0			0
$506$	9.76563	+	18.7606i	0.434135	+	0.834012i
$507$	1.35905			0.0603576
$508$	0.553981	+	1.70498i	0.0245789	+	0.0756462i
$509$	−13.4662	−	9.78379i	−0.596881	−	0.433659i	0.247890	−	0.968788i	$-0.420263\pi$
$509$	−13.4662	−	9.78379i	−0.596881	−	0.433659i	−0.844770	+	0.535129i	$0.820263\pi$
$510$		0			0
$511$	6.14019	−	18.8975i	0.271626	−	0.835978i
$512$	0.298195	−	0.917749i	0.0131785	−	0.0405592i
$513$	17.7393	−	12.8884i	0.783211	−	0.569036i
$514$	33.0313	+	23.9987i	1.45695	+	1.05854i
$515$		0			0
$516$	−12.2561			−0.539543
$517$	35.6566	+	17.7788i	1.56818	+	0.781909i
$518$	9.62412			0.422860
$519$	−1.28587	−	3.95750i	−0.0564434	−	0.173715i
$520$		0			0
$521$	−11.3717	+	8.26206i	−0.498205	+	0.361967i	−0.808331	−	0.588728i	$-0.799629\pi$
$521$	−11.3717	+	8.26206i	−0.498205	+	0.361967i	0.310126	+	0.950696i	$0.399629\pi$
$522$	−0.0866924	+	0.266812i	−0.00379442	+	0.0116780i
$523$	−4.84159	+	14.9009i	−0.211708	+	0.651570i	0.787663	+	0.616106i	$0.211291\pi$
$523$	−4.84159	+	14.9009i	−0.211708	+	0.651570i	−0.999371	+	0.0354635i	$0.988709\pi$
$524$	−0.947937	+	0.688717i	−0.0414108	+	0.0300867i
$525$		0			0
$526$	−2.78194	−	8.56194i	−0.121298	−	0.373318i
$527$	1.52801			0.0665611
$528$	−22.6380	+	23.0356i	−0.985193	+	1.00249i
$529$	−8.14550			−0.354152
$530$		0			0
$531$	0.250186	+	0.181770i	0.0108571	+	0.00788817i
$532$	−7.07689	+	5.14166i	−0.306822	+	0.222919i
$533$	9.05031	−	27.8540i	0.392012	−	1.20649i
$534$	−10.0182	+	30.8327i	−0.433528	+	1.33426i
$535$		0			0
$536$	1.09913	+	0.798567i	0.0474753	+	0.0344928i
$537$	3.06584	+	9.43570i	0.132301	+	0.407180i
$538$	11.0949			0.478336
$539$	0.965221	−	6.45743i	0.0415750	−	0.278141i
$540$		0			0
$541$	−12.2489	−	37.6983i	−0.526623	−	1.62078i	−0.761084	−	0.648653i	$-0.775333\pi$
$541$	−12.2489	−	37.6983i	−0.526623	−	1.62078i	0.234461	−	0.972125i	$-0.424667\pi$
$542$	−6.77301	−	4.92088i	−0.290926	−	0.211370i
$543$	24.9992	−	18.1630i	1.07282	−	0.779448i
$544$	2.73716	−	8.42412i	0.117355	−	0.361181i
$545$		0			0
$546$	21.9373	−	15.9384i	0.938830	−	0.682100i
$547$	33.3043	+	24.1970i	1.42399	+	1.03459i	0.991097	+	0.133145i	$0.0425077\pi$
$547$	33.3043	+	24.1970i	1.42399	+	1.03459i	0.432895	+	0.901445i	$0.357492\pi$
$548$	4.26297	+	13.1201i	0.182105	+	0.560462i
$549$	1.55967			0.0665651
$550$		0			0
$551$	0.996247			0.0424415
$552$	4.91251	+	15.1191i	0.209090	+	0.643513i
$553$	13.1279	+	9.53798i	0.558255	+	0.405596i
$554$	−14.3144	+	10.4000i	−0.608161	+	0.441855i
$555$		0			0
$556$	2.65039	−	8.15705i	0.112401	−	0.345936i
$557$	24.1702	−	17.5606i	1.02412	−	0.744069i	0.0569987	−	0.998374i	$-0.481847\pi$
$557$	24.1702	−	17.5606i	1.02412	−	0.744069i	0.967124	+	0.254306i	$0.0818469\pi$
$558$	0.827291	+	0.601062i	0.0350220	+	0.0254450i
$559$	−9.61926	−	29.6050i	−0.406851	−	1.25216i
$560$		0			0
$561$	10.2127	−	10.3921i	0.431182	−	0.438754i
$562$	22.7004			0.957558
$563$	−0.666795	−	2.05218i	−0.0281021	−	0.0864892i	0.936022	−	0.351942i	$-0.114479\pi$
$563$	−0.666795	−	2.05218i	−0.0281021	−	0.0864892i	−0.964124	+	0.265453i	$0.914479\pi$
$564$	−14.1573	−	10.2859i	−0.596130	−	0.433114i
$565$		0			0
$566$	11.2328	−	34.5709i	0.472148	−	1.45312i
$567$	−7.54820	+	23.2310i	−0.316995	+	0.975610i
$568$	−7.85341	+	5.70583i	−0.329522	+	0.239411i
$569$	−0.580298	−	0.421611i	−0.0243274	−	0.0176749i	0.575555	−	0.817763i	$-0.304786\pi$
$569$	−0.580298	−	0.421611i	−0.0243274	−	0.0176749i	−0.599882	+	0.800088i	$0.704786\pi$
$570$		0			0
$571$	−21.6311			−0.905235			−0.452617	−	0.891705i	$-0.649510\pi$
$571$	−21.6311			−0.905235			−0.452617	+	0.891705i	$0.649510\pi$
$572$	8.10029	+	4.03888i	0.338690	+	0.168874i
$573$	6.15315			0.257051
$574$	−9.07866	−	27.9413i	−0.378936	−	1.16625i
$575$		0			0
$576$	−2.38354	+	1.73174i	−0.0993141	+	0.0721559i
$577$	−7.23952	+	22.2810i	−0.301385	+	0.927568i	0.679616	+	0.733568i	$0.262146\pi$
$577$	−7.23952	+	22.2810i	−0.301385	+	0.927568i	−0.981001	+	0.194000i	$0.937854\pi$
$578$	6.16167	−	18.9637i	0.256291	−	0.788784i
$579$	−15.3954	+	11.1854i	−0.639812	+	0.464851i
$580$		0			0
$581$	−2.20536	−	6.78739i	−0.0914936	−	0.281588i
$582$	7.41093			0.307193
$583$	19.3820	+	37.2346i	0.802722	+	1.54210i
$584$	18.5023			0.765633
$585$		0			0
$586$	18.7911	+	13.6525i	0.776253	+	0.563981i
$587$	−1.81814	+	1.32095i	−0.0750425	+	0.0545216i	−0.624674	−	0.780886i	$-0.714768\pi$
$587$	−1.81814	+	1.32095i	−0.0750425	+	0.0545216i	0.549632	+	0.835407i	$0.314768\pi$
$588$	−0.886154	+	2.72730i	−0.0365444	+	0.112472i
$589$	1.12215	−	3.45362i	0.0462374	−	0.142304i
$590$		0			0
$591$	23.0018	+	16.7118i	0.946167	+	0.687431i
$592$	3.95149	+	12.1615i	0.162405	+	0.499833i
$593$	−25.4034			−1.04319			−0.521596	−	0.853193i	$-0.674663\pi$
$593$	−25.4034			−1.04319			−0.521596	+	0.853193i	$0.674663\pi$
$594$	−22.4477	+	3.75594i	−0.921042	+	0.154108i
$595$		0			0
$596$	1.34841	+	4.14996i	0.0552328	+	0.169989i
$597$	−23.6415	−	17.1765i	−0.967580	−	0.702988i
$598$	19.0875	−	13.8678i	0.780544	−	0.567098i
$599$	−5.63194	+	17.3333i	−0.230115	+	0.708220i	0.767617	+	0.640909i	$0.221442\pi$
$599$	−5.63194	+	17.3333i	−0.230115	+	0.708220i	−0.997732	+	0.0673118i	$0.978558\pi$
$600$		0			0
$601$	28.0242	−	20.3608i	1.14313	−	0.830533i	0.155579	−	0.987824i	$-0.450276\pi$
$601$	28.0242	−	20.3608i	1.14313	−	0.830533i	0.987552	+	0.157290i	$0.0502758\pi$
$602$	−25.2625	−	18.3542i	−1.02962	−	0.748063i
$603$	−0.180860	−	0.556631i	−0.00736520	−	0.0226678i
$604$	9.42547			0.383517
$605$		0			0
$606$	−32.3375			−1.31362
$607$	−7.86394	−	24.2027i	−0.319187	−	0.982358i	−0.973996	−	0.226564i	$-0.927251\pi$
$607$	−7.86394	−	24.2027i	−0.319187	−	0.982358i	0.654809	−	0.755794i	$-0.272749\pi$
$608$	−17.0302	−	12.3731i	−0.690664	−	0.501797i
$609$	−0.675293	+	0.490629i	−0.0273643	+	0.0198813i
$610$		0			0
$611$	13.7345	−	42.2705i	0.555639	−	1.71008i
$612$	−1.19453	+	0.867874i	−0.0482858	+	0.0350817i
$613$	−29.9835	−	21.7843i	−1.21102	−	0.879859i	−0.215698	−	0.976460i	$-0.569203\pi$
$613$	−29.9835	−	21.7843i	−1.21102	−	0.879859i	−0.995323	+	0.0966016i	$0.969203\pi$
$614$	3.51234	+	10.8099i	0.141746	+	0.436251i
$615$		0			0
$616$	−15.3255	+	2.56426i	−0.617483	+	0.103317i
$617$	27.5937			1.11088			0.555439	−	0.831557i	$-0.312550\pi$
$617$	27.5937			1.11088			0.555439	+	0.831557i	$0.312550\pi$
$618$	10.3404	+	31.8246i	0.415953	+	1.28017i
$619$	−16.5391	−	12.0164i	−0.664764	−	0.482979i	0.203504	−	0.979074i	$-0.434767\pi$
$619$	−16.5391	−	12.0164i	−0.664764	−	0.482979i	−0.868268	+	0.496095i	$0.834767\pi$
$620$		0			0
$621$	−4.93964	+	15.2026i	−0.198221	+	0.610061i
$622$	2.81292	−	8.65728i	0.112788	−	0.347125i
$623$	−18.0052	+	13.0816i	−0.721364	+	0.524101i
$624$	29.1475	+	21.1769i	1.16683	+	0.847754i
$625$		0			0
$626$	−23.5480			−0.941167
$627$	−15.9882	−	30.7148i	−0.638507	−	1.22663i
$628$	−10.5842			−0.422354
$629$	−1.78265	−	5.48642i	−0.0710787	−	0.218758i
$630$		0			0
$631$	−0.614155	+	0.446210i	−0.0244491	+	0.0177633i	−0.599943	−	0.800043i	$-0.704810\pi$
$631$	−0.614155	+	0.446210i	−0.0244491	+	0.0177633i	0.575494	+	0.817806i	$0.304810\pi$
$632$	−4.66926	+	14.3705i	−0.185733	+	0.571627i
$633$	−4.13224	+	12.7177i	−0.164242	+	0.505485i
$634$	25.0133	−	18.1733i	0.993407	−	0.721752i
$635$		0			0
$636$	−5.69723	−	17.5343i	−0.225910	−	0.695279i
$637$	−7.28342			−0.288579
$638$	−0.925425	−	0.461426i	−0.0366379	−	0.0182680i
$639$	4.18186			0.165432
$640$		0			0
$641$	12.0584	+	8.76094i	0.476278	+	0.346037i	0.799883	−	0.600156i	$-0.204895\pi$
$641$	12.0584	+	8.76094i	0.476278	+	0.346037i	−0.323605	+	0.946192i	$0.604895\pi$
$642$	−26.5579	+	19.2955i	−1.04816	+	0.761531i
$643$	−8.53955	+	26.2820i	−0.336767	+	1.03646i	0.629078	+	0.777342i	$0.283432\pi$
$643$	−8.53955	+	26.2820i	−0.336767	+	1.03646i	−0.965845	+	0.259120i	$0.916568\pi$
$644$	1.97060	−	6.06490i	0.0776527	−	0.238990i
$645$		0			0
$646$	15.7433	+	11.4382i	0.619411	+	0.450029i
$647$	−7.71879	−	23.7560i	−0.303457	−	0.933945i	−0.980248	−	0.197770i	$-0.936630\pi$
$647$	−7.71879	−	23.7560i	−0.303457	−	0.933945i	0.676791	−	0.736175i	$-0.263370\pi$
$648$	−22.7452			−0.893514
$649$	−0.798974	+	0.813005i	−0.0313625	+	0.0319132i
$650$		0			0
$651$	0.940197	+	2.89363i	0.0368492	+	0.113410i
$652$	−2.16456	−	1.57264i	−0.0847706	−	0.0615895i
$653$	22.4607	−	16.3187i	0.878956	−	0.638599i	−0.0540191	−	0.998540i	$-0.517203\pi$
$653$	22.4607	−	16.3187i	0.878956	−	0.638599i	0.932975	+	0.359941i	$0.117203\pi$
$654$	8.88708	−	27.3516i	0.347513	−	1.06953i
$655$		0			0
$656$	31.5802	−	22.9444i	1.23300	−	0.895827i
$657$	−6.44842	−	4.68505i	−0.251577	−	0.182781i
$658$	−13.7775	−	42.4029i	−0.537105	−	1.65304i
$659$	−21.5863			−0.840883			−0.420442	−	0.907320i	$-0.638125\pi$
$659$	−21.5863			−0.840883			−0.420442	+	0.907320i	$0.638125\pi$
$660$		0			0
$661$	−16.0174			−0.623003			−0.311502	−	0.950246i	$-0.600832\pi$
$661$	−16.0174			−0.623003			−0.311502	+	0.950246i	$0.600832\pi$
$662$	−0.239413	−	0.736837i	−0.00930504	−	0.0286380i
$663$	−13.1494	−	9.55357i	−0.510679	−	0.371030i
$664$	5.37628	−	3.90609i	0.208640	−	0.151586i
$665$		0			0
$666$	1.19300	−	3.67167i	0.0462277	−	0.142274i
$667$	−0.587567	+	0.426892i	−0.0227507	+	0.0165293i
$668$	−2.28005	−	1.65656i	−0.0882180	−	0.0640941i
$669$	−5.31966	−	16.3722i	−0.205670	−	0.632986i
$670$		0			0
$671$	−0.849880	+	5.68579i	−0.0328093	+	0.219498i
$672$	17.6372			0.680368
$673$	−9.68673	−	29.8127i	−0.373396	−	1.14920i	−0.944554	−	0.328355i	$-0.893506\pi$
$673$	−9.68673	−	29.8127i	−0.373396	−	1.14920i	0.571158	−	0.820840i	$-0.306494\pi$
$674$	45.6286	+	33.1511i	1.75755	+	1.27693i
$675$		0			0
$676$	0.156871	−	0.482799i	0.00603350	−	0.0185692i
$677$	9.47642	−	29.1654i	0.364209	−	1.12092i	−0.586267	−	0.810118i	$-0.699403\pi$
$677$	9.47642	−	29.1654i	0.364209	−	1.12092i	0.950475	−	0.310801i	$-0.100597\pi$
$678$	−0.611561	+	0.444325i	−0.0234869	+	0.0170642i
$679$	4.11590	+	2.99038i	0.157954	+	0.114760i
$680$		0			0
$681$	7.51888			0.288124
$682$	−2.64198	+	2.68837i	−0.101166	+	0.102943i
$683$	3.27236			0.125213			0.0626066	−	0.998038i	$-0.480059\pi$
$683$	3.27236			0.125213			0.0626066	+	0.998038i	$0.480059\pi$
$684$	1.08433	+	3.33724i	0.0414606	+	0.127602i
$685$		0			0
$686$	−26.9287	+	19.5648i	−1.02814	+	0.746989i
$687$	−1.65600	+	5.09664i	−0.0631802	+	0.194449i
$688$	12.8209	−	39.4586i	0.488792	−	1.50435i
$689$	37.8832	−	27.5238i	1.44324	−	1.04857i
$690$		0			0
$691$	−11.2774	−	34.7084i	−0.429014	−	1.32037i	−0.899098	−	0.437748i	$-0.855776\pi$
$691$	−11.2774	−	34.7084i	−0.429014	−	1.32037i	0.470083	−	0.882622i	$-0.344224\pi$
$692$	−1.55431			−0.0590862
$693$	5.99054	+	2.98694i	0.227562	+	0.113465i
$694$	−5.94478			−0.225661
$695$		0			0
$696$	−0.628811	−	0.456858i	−0.0238350	−	0.0173172i
$697$	−14.2468	+	10.3509i	−0.539638	+	0.392070i
$698$	3.25750	−	10.0256i	0.123298	−	0.379473i
$699$	−6.41413	+	19.7407i	−0.242605	+	0.746660i
$700$		0			0
$701$	−37.6684	−	27.3677i	−1.42272	−	1.03366i	−0.991316	−	0.131502i	$-0.958020\pi$
$701$	−37.6684	−	27.3677i	−1.42272	−	1.03366i	−0.431399	−	0.902161i	$-0.641980\pi$
$702$	7.84562	+	24.1463i	0.296114	+	0.911345i
$703$	−13.7096			−0.517068
$704$	−5.01427	−	9.63285i	−0.188982	−	0.363052i
$705$		0			0
$706$	6.23630	+	19.1933i	0.234706	+	0.722351i
$707$	−17.9597	−	13.0485i	−0.675443	−	0.490738i
$708$	0.405030	−	0.294272i	0.0152220	−	0.0110594i
$709$	−11.0000	+	33.8544i	−0.413112	+	1.27143i	0.500817	+	0.865553i	$0.333033\pi$
$709$	−11.0000	+	33.8544i	−0.413112	+	1.27143i	−0.913929	+	0.405874i	$0.866967\pi$
$710$		0			0
$711$	5.26613	−	3.82607i	0.197495	−	0.143489i
$712$	−16.7659	−	12.1811i	−0.628327	−	0.456507i
$713$	0.818057	+	2.51772i	0.0306365	+	0.0942894i
$714$	−16.3044			−0.610178
$715$		0			0
$716$	3.70588			0.138495
$717$	12.2290	+	37.6371i	0.456702	+	1.40558i
$718$	32.2798	+	23.4526i	1.20467	+	0.875245i
$719$	−17.8722	+	12.9849i	−0.666522	+	0.484256i	−0.868859	−	0.495060i	$-0.835146\pi$
$719$	−17.8722	+	12.9849i	−0.666522	+	0.484256i	0.202337	+	0.979316i	$0.435146\pi$
$720$		0			0
$721$	−7.09862	+	21.8473i	−0.264366	+	0.813636i
$722$	11.9813	−	8.70490i	0.445896	−	0.323963i
$723$	−45.4448	−	33.0176i	−1.69011	−	1.22794i
$724$	−3.56677	−	10.9774i	−0.132558	−	0.407971i
$725$		0			0
$726$	0.625636	+	35.9365i	0.0232195	+	1.33373i
$727$	−45.5415			−1.68904			−0.844521	−	0.535522i	$-0.820115\pi$
$727$	−45.5415			−1.68904			−0.844521	+	0.535522i	$0.820115\pi$
$728$	5.35637	+	16.4852i	0.198520	+	0.610982i
$729$	−11.9514	−	8.68317i	−0.442643	−	0.321599i
$730$		0			0
$731$	−5.78391	+	17.8011i	−0.213926	+	0.658396i
$732$	0.780262	−	2.40140i	0.0288393	−	0.0887583i
$733$	9.20572	−	6.68835i	0.340021	−	0.247040i	−0.404650	−	0.914472i	$-0.632607\pi$
$733$	9.20572	−	6.68835i	0.340021	−	0.247040i	0.744671	+	0.667432i	$0.232607\pi$
$734$	−27.2936	−	19.8300i	−1.00743	−	0.731938i
$735$		0			0
$736$	15.3459			0.565659
$737$	2.12776	−	0.356014i	0.0783769	−	0.0131140i
$738$	−11.7852			−0.433818
$739$	−1.34045	−	4.12547i	−0.0493091	−	0.151758i	0.923370	−	0.383911i	$-0.125423\pi$
$739$	−1.34045	−	4.12547i	−0.0493091	−	0.151758i	−0.972679	+	0.232153i	$0.925423\pi$
$740$		0			0
$741$	−31.2498	+	22.7043i	−1.14799	+	0.834064i
$742$	14.5154	−	44.6740i	0.532879	−	1.64003i
$743$	−5.34429	+	16.4480i	−0.196063	+	0.603420i	0.803900	+	0.594765i	$0.202755\pi$
$743$	−5.34429	+	16.4480i	−0.196063	+	0.603420i	−0.999963	+	0.00865478i	$0.997245\pi$
$744$	−2.29204	+	1.66526i	−0.0840302	+	0.0610515i
$745$		0			0
$746$	−3.84491	−	11.8334i	−0.140772	−	0.433253i
$747$	−2.86281			−0.104745
$748$	−2.51293	−	4.82757i	−0.0918819	−	0.176513i
$749$	−22.5357			−0.823437
$750$		0			0
$751$	25.4946	+	18.5229i	0.930310	+	0.675910i	0.946069	−	0.323966i	$-0.105016\pi$
$751$	25.4946	+	18.5229i	0.930310	+	0.675910i	−0.0157586	+	0.999876i	$0.505016\pi$
$752$	47.9253	−	34.8198i	1.74766	−	1.26975i
$753$	−14.5464	+	44.7691i	−0.530099	+	1.63148i
$754$	−0.356463	+	1.09708i	−0.0129816	+	0.0399533i
$755$		0			0
$756$	5.55175	+	4.03358i	0.201915	+	0.146700i
$757$	−2.86687	−	8.82332i	−0.104198	−	0.320689i	0.885343	−	0.464938i	$-0.153923\pi$
$757$	−2.86687	−	8.82332i	−0.104198	−	0.320689i	−0.989541	+	0.144249i	$0.953923\pi$
$758$	−38.3718			−1.39373
$759$	22.5908	+	11.2640i	0.819995	+	0.408858i
$760$		0			0
$761$	−1.28492	−	3.95459i	−0.0465784	−	0.143354i	0.925062	−	0.379815i	$-0.124012\pi$
$761$	−1.28492	−	3.95459i	−0.0465784	−	0.143354i	−0.971641	+	0.236461i	$0.924012\pi$
$762$	6.42442	+	4.66762i	0.232732	+	0.169090i
$763$	15.9724	−	11.6046i	0.578239	−	0.420115i
$764$	0.710238	−	2.18589i	0.0256955	−	0.0790827i
$765$		0			0
$766$	3.26667	−	2.37338i	0.118030	−	0.0857536i
$767$	1.02872	+	0.747406i	0.0371448	+	0.0269873i
$768$	9.51446	+	29.2825i	0.343324	+	1.05664i
$769$	16.8800			0.608709			0.304355	−	0.952559i	$-0.401559\pi$
$769$	16.8800			0.608709			0.304355	+	0.952559i	$0.401559\pi$
$770$		0			0
$771$	48.7305			1.75499
$772$	2.19655	+	6.76028i	0.0790555	+	0.243308i
$773$	−6.85852	−	4.98301i	−0.246684	−	0.179226i	0.457572	−	0.889173i	$-0.348719\pi$
$773$	−6.85852	−	4.98301i	−0.246684	−	0.179226i	−0.704256	+	0.709946i	$0.748719\pi$
$774$	−10.1338	+	7.36263i	−0.364252	+	0.264644i
$775$		0			0
$776$	−1.46392	+	4.50548i	−0.0525517	+	0.161737i
$777$	9.29289	−	6.75168i	0.333381	−	0.242215i
$778$	45.4759	+	33.0402i	1.63039	+	1.18455i
$779$	12.9326	+	39.8025i	0.463359	+	1.42607i
$780$		0			0
$781$	−2.27873	+	15.2450i	−0.0815395	+	0.545509i
$782$	−14.1863			−0.507303
$783$	−0.241511	−	0.743294i	−0.00863089	−	0.0265632i
$784$	−7.85361	−	5.70598i	−0.280486	−	0.203785i
$785$		0			0
$786$	−1.60387	+	4.93620i	−0.0572080	+	0.176068i
$787$	−16.5684	+	50.9924i	−0.590601	+	1.81768i	−0.0150924	+	0.999886i	$0.504804\pi$
$787$	−16.5684	+	50.9924i	−0.590601	+	1.81768i	−0.575508	+	0.817796i	$0.695196\pi$
$788$	8.59183	−	6.24233i	0.306071	−	0.222374i
$789$	−8.69272	−	6.31563i	−0.309469	−	0.224842i
$790$		0			0
$791$	−0.518940			−0.0184514
$792$	−0.921459	+	6.16466i	−0.0327426	+	0.219052i
$793$	6.41307			0.227735
$794$	14.0586	+	43.2679i	0.498921	+	1.53552i
$795$		0			0
$796$	−8.83077	+	6.41593i	−0.312998	+	0.227407i
$797$	−8.82082	+	27.1477i	−0.312450	+	0.961621i	0.664342	+	0.747429i	$0.268712\pi$
$797$	−8.82082	+	27.1477i	−0.312450	+	0.961621i	−0.976792	+	0.214192i	$0.931288\pi$
$798$	−11.9738	+	36.8515i	−0.423867	+	1.30453i
$799$	−21.6206	+	15.7083i	−0.764883	+	0.555720i
$800$		0			0
$801$	2.75879	+	8.49070i	0.0974772	+	0.300004i
$802$	3.12290			0.110273
$803$	20.5932	−	20.9548i	0.726718	−	0.739480i
$804$	−0.947515			−0.0334163
$805$		0			0
$806$	3.40166	+	2.47145i	0.119819	+	0.0870532i
$807$	10.7131	−	7.78350i	0.377118	−	0.273992i
$808$	6.38780	−	19.6596i	0.224722	−	0.691623i
$809$	11.4170	−	35.1378i	0.401399	−	1.23538i	−0.522466	−	0.852660i	$-0.674988\pi$
$809$	11.4170	−	35.1378i	0.401399	−	1.23538i	0.923865	−	0.382718i	$-0.125012\pi$
$810$		0			0
$811$	31.0475	+	22.5573i	1.09022	+	0.792094i	0.979437	−	0.201750i	$-0.0646629\pi$
$811$	31.0475	+	22.5573i	1.09022	+	0.792094i	0.110787	+	0.993844i	$0.464663\pi$
$812$	0.0963477	+	0.296528i	0.00338114	+	0.0104061i
$813$	−9.99209			−0.350438
$814$	12.7350	+	6.34982i	0.446363	+	0.222561i
$815$		0			0
$816$	−6.69431	−	20.6030i	−0.234348	−	0.721248i
$817$	35.9865	+	26.1458i	1.25901	+	0.914724i
$818$	18.1478	−	13.1852i	0.634524	−	0.461008i
$819$	2.30749	−	7.10171i	0.0806301	−	0.248154i
$820$		0			0
$821$	8.29214	−	6.02459i	0.289398	−	0.210260i	−0.433608	−	0.901101i	$-0.642760\pi$
$821$	8.29214	−	6.02459i	0.289398	−	0.210260i	0.723006	+	0.690842i	$0.242760\pi$
$822$	49.4370	+	35.9181i	1.72431	+	1.25279i
$823$	−7.79637	−	23.9948i	−0.271764	−	0.836405i	−0.990057	−	0.140664i	$-0.955076\pi$
$823$	−7.79637	−	23.9948i	−0.271764	−	0.836405i	0.718293	−	0.695741i	$-0.244924\pi$
$824$	−21.3904			−0.745170
$825$		0			0
$826$	1.27555			0.0443820
$827$	5.67001	+	17.4505i	0.197165	+	0.606813i	0.999944	+	0.0105362i	$0.00335385\pi$
$827$	5.67001	+	17.4505i	0.197165	+	0.606813i	−0.802779	+	0.596277i	$0.796646\pi$
$828$	−2.06953	−	1.50360i	−0.0719211	−	0.0522537i
$829$	−19.7259	+	14.3317i	−0.685110	+	0.497761i	−0.875049	−	0.484035i	$-0.839171\pi$
$829$	−19.7259	+	14.3317i	−0.685110	+	0.497761i	0.189939	+	0.981796i	$0.439171\pi$
$830$		0			0
$831$	−6.52575	+	20.0842i	−0.226376	+	0.696713i
$832$	−9.80066	+	7.12060i	−0.339777	+	0.246862i
$833$	3.54301	+	2.57415i	0.122758	+	0.0891890i
$834$	−11.7401	−	36.1324i	−0.406528	−	1.25116i
$835$		0			0
$836$	−12.7568	+	2.13446i	−0.441203	+	0.0738217i
$837$	−2.84876			−0.0984676
$838$	11.3184	+	34.8345i	0.390988	+	1.20334i
$839$	34.2059	+	24.8520i	1.18092	+	0.857988i	0.992275	−	0.124058i	$-0.0395908\pi$
$839$	34.2059	+	24.8520i	1.18092	+	0.857988i	0.188644	+	0.982046i	$0.439591\pi$
$840$		0			0
$841$	−8.95052	+	27.5469i	−0.308639	+	0.949892i
$842$	−9.15347	+	28.1715i	−0.315449	+	0.970853i
$843$	21.9191	−	15.9252i	0.754935	−	0.548492i
$844$	4.04097	+	2.93594i	0.139096	+	0.101059i
$845$		0			0
$846$	−17.8849			−0.614895
$847$	−14.1532	+	20.2110i	−0.486311	+	0.694457i
$848$	62.4117			2.14323
$849$	−13.4066	−	41.2613i	−0.460113	−	1.41608i
$850$		0			0
$851$	8.08567	−	5.87458i	0.277173	−	0.201378i
$852$	2.09207	−	6.43874i	0.0716732	−	0.220587i
$853$	−4.75529	+	14.6353i	−0.162818	+	0.501103i	−0.998869	−	0.0475493i	$-0.984859\pi$
$853$	−4.75529	+	14.6353i	−0.162818	+	0.501103i	0.836051	+	0.548652i	$0.184859\pi$
$854$	5.20454	−	3.78132i	0.178096	−	0.129394i
$855$		0			0
$856$	−6.48458	−	19.9575i	−0.221638	−	0.682132i
$857$	−36.1038			−1.23328			−0.616641	−	0.787245i	$-0.711507\pi$
$857$	−36.1038			−1.23328			−0.616641	+	0.787245i	$0.711507\pi$
$858$	39.5442	−	6.61650i	1.35002	−	0.225884i
$859$	48.3509			1.64971			0.824855	−	0.565344i	$-0.191257\pi$
$859$	48.3509			1.64971			0.824855	+	0.565344i	$0.191257\pi$
$860$		0			0
$861$	−28.3680	−	20.6106i	−0.966781	−	0.702407i
$862$	44.7699	−	32.5272i	1.52487	−	1.10788i
$863$	−11.4919	+	35.3685i	−0.391190	+	1.20396i	0.540699	+	0.841216i	$0.318160\pi$
$863$	−11.4919	+	35.3685i	−0.391190	+	1.20396i	−0.931889	+	0.362743i	$0.881840\pi$
$864$	−5.10306	+	15.7056i	−0.173610	+	0.534316i
$865$		0			0
$866$	42.1539	+	30.6266i	1.43245	+	1.04073i
$867$	−7.35411	−	22.6336i	−0.249759	−	0.768679i
$868$	1.13648			0.0385745
$869$	11.0784	+	21.2826i	0.375809	+	0.721962i
$870$		0			0
$871$	−0.743664	−	2.28876i	−0.0251981	−	0.0775517i
$872$	14.8730	+	10.8058i	0.503662	+	0.365932i
$873$	1.65105	−	1.19956i	0.0558797	−	0.0405990i
$874$	−10.4183	+	32.0642i	−0.352403	+	1.08459i
$875$		0			0
$876$	−10.4395	+	7.58472i	−0.352717	+	0.256264i
$877$	−20.8672	−	15.1609i	−0.704634	−	0.511947i	0.176804	−	0.984246i	$-0.443424\pi$
$877$	−20.8672	−	15.1609i	−0.704634	−	0.511947i	−0.881438	+	0.472299i	$0.843424\pi$
$878$	−18.2127	−	56.0530i	−0.614649	−	1.89170i
$879$	27.7221			0.935044
$880$		0			0
$881$	−45.6820			−1.53906			−0.769532	−	0.638608i	$-0.779511\pi$
$881$	−45.6820			−1.53906			−0.769532	+	0.638608i	$0.779511\pi$
$882$	0.905675	+	2.78738i	0.0304957	+	0.0938560i
$883$	−4.01783	−	2.91912i	−0.135211	−	0.0982364i	0.518124	−	0.855306i	$-0.326631\pi$
$883$	−4.01783	−	2.91912i	−0.135211	−	0.0982364i	−0.653335	+	0.757069i	$0.726631\pi$
$884$	−4.91167	+	3.56853i	−0.165197	+	0.120023i
$885$		0			0
$886$	−12.0090	+	36.9600i	−0.403452	+	1.24170i
$887$	23.3994	−	17.0006i	0.785674	−	0.570826i	−0.121002	−	0.992652i	$-0.538611\pi$
$887$	23.3994	−	17.0006i	0.785674	−	0.570826i	0.906677	+	0.421827i	$0.138611\pi$
$888$	8.65324	+	6.28695i	0.290384	+	0.210976i
$889$	1.68459	+	5.18463i	0.0564993	+	0.173887i
$890$		0			0
$891$	−25.3155	+	25.7600i	−0.848100	+	0.862994i
$892$	−6.43021			−0.215299
$893$	19.6262	+	60.4033i	0.656766	+	2.02132i
$894$	15.6372	+	11.3611i	0.522987	+	0.379972i
$895$		0			0
$896$	−9.27501	+	28.5456i	−0.309856	+	0.953640i
$897$	8.70172	−	26.7811i	0.290542	−	0.894196i
$898$	−42.0208	+	30.5299i	−1.40225	+	1.01880i
$899$	−0.104713	−	0.0760785i	−0.00349237	−	0.00253736i
$900$		0			0
$901$	−28.1559			−0.938010
$902$	6.42186	−	42.9630i	0.213824	−	1.43051i
$903$	−37.2692			−1.24024
$904$	−0.149323	−	0.459570i	−0.00496642	−	0.0152851i
$905$		0			0
$906$	33.7773	−	24.5406i	1.12217	−	0.815307i
$907$	4.09531	−	12.6041i	0.135983	−	0.418511i	−0.859759	−	0.510700i	$-0.829386\pi$
$907$	4.09531	−	12.6041i	0.135983	−	0.418511i	0.995742	+	0.0921887i	$0.0293863\pi$
$908$	0.867880	−	2.67106i	0.0288016	−	0.0886422i
$909$	−7.20435	+	5.23427i	−0.238953	+	0.173610i
$910$		0			0
$911$	4.24361	+	13.0605i	0.140597	+	0.432713i	0.996419	−	0.0845580i	$-0.0269478\pi$
$911$	4.24361	+	13.0605i	0.140597	+	0.432713i	−0.855822	+	0.517271i	$0.826948\pi$
$912$	−51.4833			−1.70478
$913$	1.55997	−	10.4364i	0.0516276	−	0.345395i
$914$	−64.7117			−2.14047
$915$		0			0
$916$	1.61942	+	1.17658i	0.0535071	+	0.0388752i
$917$	−2.88256	+	2.09430i	−0.0951906	+	0.0691600i
$918$	4.71745	−	14.5188i	0.155699	−	0.479193i
$919$	18.3494	−	56.4737i	0.605292	−	1.86290i	0.110517	−	0.993874i	$-0.464749\pi$
$919$	18.3494	−	56.4737i	0.605292	−	1.86290i	0.494774	−	0.869022i	$-0.335251\pi$
$920$		0			0
$921$	10.9750	+	7.97379i	0.361638	+	0.262745i
$922$	4.54233	+	13.9798i	0.149594	+	0.460402i
$923$	17.1950			0.565981
$924$	7.59586	−	7.72925i	0.249885	−	0.254274i
$925$		0			0
$926$	−2.15296	−	6.62613i	−0.0707507	−	0.217748i
$927$	7.45496	+	5.41635i	0.244853	+	0.177896i
$928$	−0.607006	+	0.441016i	−0.0199259	+	0.0144770i
$929$	6.05305	−	18.6294i	0.198594	−	0.611210i	−0.801322	−	0.598234i	$-0.795869\pi$
$929$	6.05305	−	18.6294i	0.198594	−	0.611210i	0.999916	−	0.0129763i	$-0.00413060\pi$
$930$		0			0
$931$	8.42007	−	6.11754i	0.275957	−	0.200494i
$932$	6.27245	+	4.55720i	0.205461	+	0.149276i
$933$	−3.35730	−	10.3327i	−0.109913	−	0.338277i
$934$	11.1327			0.364275
$935$		0			0
$936$	6.95320			0.227272
$937$	−12.5292	−	38.5608i	−0.409310	−	1.25973i	−0.917242	−	0.398329i	$-0.869590\pi$
$937$	−12.5292	−	38.5608i	−0.409310	−	1.25973i	0.507933	−	0.861397i	$-0.330410\pi$
$938$	−1.95304	−	1.41896i	−0.0637689	−	0.0463308i
$939$	−22.7376	+	16.5198i	−0.742012	+	0.539104i
$940$		0			0
$941$	−0.126602	+	0.389640i	−0.00412709	+	0.0127019i	−0.953099	−	0.302659i	$-0.902126\pi$
$941$	−0.126602	+	0.389640i	−0.00412709	+	0.0127019i	0.948972	+	0.315361i	$0.102126\pi$
$942$	−37.9296	+	27.5575i	−1.23581	+	0.897870i
$943$	−24.6828	−	17.9331i	−0.803783	−	0.583982i
$944$	0.523717	+	1.61184i	0.0170455	+	0.0524608i
$945$		0			0
$946$	−21.3185	−	40.9548i	−0.693125	−	1.33156i
$947$	−2.45729			−0.0798511			−0.0399256	−	0.999203i	$-0.512712\pi$
$947$	−2.45729			−0.0798511			−0.0399256	+	0.999203i	$0.512712\pi$
$948$	−3.25643	−	10.0223i	−0.105764	−	0.325508i
$949$	−26.5147	−	19.2640i	−0.860703	−	0.625337i
$950$		0			0
$951$	11.4033	−	35.0956i	0.369776	−	1.13805i
$952$	3.22070	−	9.91230i	0.104384	−	0.321260i
$953$	49.3714	−	35.8704i	1.59930	−	1.16196i	0.710456	−	0.703742i	$-0.248489\pi$
$953$	49.3714	−	35.8704i	1.59930	−	1.16196i	0.888841	−	0.458215i	$-0.151511\pi$
$954$	−15.2441	−	11.0755i	−0.493546	−	0.358582i
$955$		0			0
$956$	14.7820			0.478085
$957$	−1.21728	+	0.203675i	−0.0393492	+	0.00658387i
$958$	−34.4309			−1.11241
$959$	12.9632	+	39.8965i	0.418603	+	1.28833i
$960$		0			0
$961$	24.6978	−	17.9440i	0.796705	−	0.578840i
$962$	4.90538	−	15.0972i	0.158156	−	0.486754i
$963$	−2.79351	+	8.59754i	−0.0900196	+	0.277052i
$964$	−16.9749	+	12.3330i	−0.546726	+	0.397220i
$965$		0			0
$966$	−8.72898	−	26.8650i	−0.280850	−	0.864369i
$967$	−17.1997			−0.553106			−0.276553	−	0.960999i	$-0.589192\pi$
$967$	−17.1997			−0.553106			−0.276553	+	0.960999i	$0.589192\pi$
$968$	−21.9712	−	6.71837i	−0.706182	−	0.215937i
$969$	23.2258			0.746119
$970$		0			0
$971$	−22.0125	−	15.9930i	−0.706415	−	0.513241i	0.175600	−	0.984462i	$-0.443813\pi$
$971$	−22.0125	−	15.9930i	−0.706415	−	0.513241i	−0.882015	+	0.471221i	$0.843813\pi$
$972$	5.40818	−	3.92927i	0.173467	−	0.126031i
$973$	8.05950	−	24.8046i	0.258376	−	0.795198i
$974$	8.06790	−	24.8304i	0.258512	−	0.795619i
$975$		0			0
$976$	6.91513	+	5.02414i	0.221348	+	0.160819i
$977$	5.92454	+	18.2339i	0.189543	+	0.583353i	0.999997	−	0.00244904i	$-0.000779555\pi$
$977$	5.92454	+	18.2339i	0.189543	+	0.583353i	−0.810454	+	0.585802i	$0.800780\pi$
$978$	−11.8516			−0.378971
$979$	−32.4562	+	5.43055i	−1.03730	+	0.173561i
$980$		0			0
$981$	−2.44732	−	7.53207i	−0.0781369	−	0.240481i
$982$	25.8753	+	18.7995i	0.825714	+	0.599916i
$983$	−19.5219	+	14.1835i	−0.622653	+	0.452384i	−0.853847	−	0.520524i	$-0.825737\pi$
$983$	−19.5219	+	14.1835i	−0.622653	+	0.452384i	0.231194	+	0.972908i	$0.425737\pi$
$984$	10.0898	−	31.0532i	0.321651	−	0.989939i
$985$		0			0
$986$	0.561138	−	0.407691i	0.0178703	−	0.0129835i
$987$	−43.0506	−	31.2781i	−1.37032	−	0.995593i
$988$	4.45858	+	13.7221i	0.141846	+	0.436558i
$989$	−32.4276			−1.03114
$990$		0			0
$991$	27.7081			0.880177			0.440089	−	0.897954i	$-0.354947\pi$
$991$	27.7081			0.880177			0.440089	+	0.897954i	$0.354947\pi$
$992$	0.845122	+	2.60102i	0.0268327	+	0.0825824i
$993$	−0.748092	−	0.543521i	−0.0237400	−	0.0172481i
$994$	13.9546	−	10.1386i	0.442614	−	0.321578i
$995$		0			0
$996$	−1.43219	+	4.40782i	−0.0453806	+	0.139667i
$997$	27.0950	−	19.6856i	0.858106	−	0.623451i	−0.0692628	−	0.997598i	$-0.522065\pi$
$997$	27.0950	−	19.6856i	0.858106	−	0.623451i	0.927369	+	0.374148i	$0.122065\pi$
$998$	−55.4972	−	40.3211i	−1.75673	−	1.27634i
$999$	3.32350	+	10.2287i	0.105151	+	0.323621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.d.126.1		16
5.2	odd	4		55.2.j.a.49.4	yes	16
5.3	odd	4		55.2.j.a.49.1	yes	16
5.4	even	2	inner	275.2.h.d.126.4		16
11.3	even	5		3025.2.a.bl.1.2		8
11.8	odd	10		3025.2.a.bk.1.7		8
11.9	even	5	inner	275.2.h.d.251.1		16
15.2	even	4		495.2.ba.a.379.1		16
15.8	even	4		495.2.ba.a.379.4		16
20.3	even	4		880.2.cd.c.49.1		16
20.7	even	4		880.2.cd.c.49.4		16
55.2	even	20		605.2.j.d.9.4		16
55.3	odd	20		605.2.b.g.364.7		8
55.7	even	20		605.2.j.g.124.1		16
55.8	even	20		605.2.b.f.364.2		8
55.9	even	10	inner	275.2.h.d.251.4		16
55.13	even	20		605.2.j.d.9.1		16
55.14	even	10		3025.2.a.bl.1.7		8
55.17	even	20		605.2.j.g.444.4		16
55.18	even	20		605.2.j.g.124.4		16
55.19	odd	10		3025.2.a.bk.1.2		8
55.27	odd	20		605.2.j.h.444.1		16
55.28	even	20		605.2.j.g.444.1		16
55.32	even	4		605.2.j.d.269.1		16
55.37	odd	20		605.2.j.h.124.4		16
55.38	odd	20		605.2.j.h.444.4		16
55.42	odd	20		55.2.j.a.9.1	✓	16
55.43	even	4		605.2.j.d.269.4		16
55.47	odd	20		605.2.b.g.364.2		8
55.48	odd	20		605.2.j.h.124.1		16
55.52	even	20		605.2.b.f.364.7		8
55.53	odd	20		55.2.j.a.9.4	yes	16
165.53	even	20		495.2.ba.a.64.1		16
165.152	even	20		495.2.ba.a.64.4		16
220.163	even	20		880.2.cd.c.449.4		16
220.207	even	20		880.2.cd.c.449.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	55.42	odd	20
55.2.j.a.9.4	yes	16	55.53	odd	20
55.2.j.a.49.1	yes	16	5.3	odd	4
55.2.j.a.49.4	yes	16	5.2	odd	4
275.2.h.d.126.1		16	1.1	even	1	trivial
275.2.h.d.126.4		16	5.4	even	2	inner
275.2.h.d.251.1		16	11.9	even	5	inner
275.2.h.d.251.4		16	55.9	even	10	inner
495.2.ba.a.64.1		16	165.53	even	20
495.2.ba.a.64.4		16	165.152	even	20
495.2.ba.a.379.1		16	15.2	even	4
495.2.ba.a.379.4		16	15.8	even	4
605.2.b.f.364.2		8	55.8	even	20
605.2.b.f.364.7		8	55.52	even	20
605.2.b.g.364.2		8	55.47	odd	20
605.2.b.g.364.7		8	55.3	odd	20
605.2.j.d.9.1		16	55.13	even	20
605.2.j.d.9.4		16	55.2	even	20
605.2.j.d.269.1		16	55.32	even	4
605.2.j.d.269.4		16	55.43	even	4
605.2.j.g.124.1		16	55.7	even	20
605.2.j.g.124.4		16	55.18	even	20
605.2.j.g.444.1		16	55.28	even	20
605.2.j.g.444.4		16	55.17	even	20
605.2.j.h.124.1		16	55.48	odd	20
605.2.j.h.124.4		16	55.37	odd	20
605.2.j.h.444.1		16	55.27	odd	20
605.2.j.h.444.4		16	55.38	odd	20
880.2.cd.c.49.1		16	20.3	even	4
880.2.cd.c.49.4		16	20.7	even	4
880.2.cd.c.449.1		16	220.207	even	20
880.2.cd.c.449.4		16	220.163	even	20
3025.2.a.bk.1.2		8	55.19	odd	10
3025.2.a.bk.1.7		8	11.8	odd	10
3025.2.a.bl.1.2		8	11.3	even	5
3025.2.a.bl.1.7		8	55.14	even	10

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.511294 - 1.57360i) q^{2} +(-1.59764 - 1.16075i) q^{3} +(-0.596764 + 0.433574i) q^{4} +(-1.00970 + 3.10753i) q^{6} +(-1.81468 + 1.31845i) q^{7} +(-1.68978 - 1.22769i) q^{8} +(0.278050 + 0.855749i) q^{9} +(-3.27115 + 0.547326i) q^{11} +1.45668 q^{12} +(1.14329 + 3.51868i) q^{13} +(3.00254 + 2.18148i) q^{14} +(-1.52381 + 4.68982i) q^{16} +(0.687441 - 2.11573i) q^{17} +(1.20444 - 0.875078i) q^{18} +(-4.27714 - 3.10753i) q^{19} +4.42960 q^{21} +(2.53379 + 4.86764i) q^{22} +3.85415 q^{23} +(1.27460 + 3.92282i) q^{24} +(4.95244 - 3.59816i) q^{26} +(-1.28164 + 3.94448i) q^{27} +(0.511294 - 1.57360i) q^{28} +(-0.152450 + 0.110762i) q^{29} +(0.212253 + 0.653249i) q^{31} +3.98166 q^{32} +(5.86142 + 2.92256i) q^{33} -3.68079 q^{34} +(-0.536960 - 0.390125i) q^{36} +(2.09791 - 1.52422i) q^{37} +(-2.70313 + 8.31938i) q^{38} +(2.25775 - 6.94864i) q^{39} +(-6.40421 - 4.65293i) q^{41} +(-2.26482 - 6.97041i) q^{42} -8.41368 q^{43} +(1.71480 - 1.74491i) q^{44} +(-1.97060 - 6.06490i) q^{46} +(-9.71886 - 7.06117i) q^{47} +(7.87822 - 5.72386i) q^{48} +(-0.608337 + 1.87227i) q^{49} +(-3.55411 + 2.58222i) q^{51} +(-2.20788 - 1.60412i) q^{52} +(-3.91110 - 12.0371i) q^{53} +6.86233 q^{54} +4.68506 q^{56} +(3.22626 + 9.92940i) q^{57} +(0.252241 + 0.183264i) q^{58} +(0.278050 - 0.202015i) q^{59} +(0.535643 - 1.64854i) q^{61} +(0.919429 - 0.668004i) q^{62} +(-1.63283 - 1.18632i) q^{63} +(1.01183 + 3.11409i) q^{64} +(1.60204 - 10.7178i) q^{66} -0.650461 q^{67} +(0.507084 + 1.56065i) q^{68} +(-6.15754 - 4.47371i) q^{69} +(1.43619 - 4.42013i) q^{71} +(0.580756 - 1.78738i) q^{72} +(-7.16660 + 5.20684i) q^{73} +(-3.47116 - 2.52195i) q^{74} +3.89979 q^{76} +(5.21449 - 5.30606i) q^{77} -12.0888 q^{78} +(-2.23551 - 6.88019i) q^{79} +(8.80999 - 6.40083i) q^{81} +(-4.04742 + 12.4567i) q^{82} +(-0.983185 + 3.02593i) q^{83} +(-2.64342 + 1.92056i) q^{84} +(4.30186 + 13.2398i) q^{86} +0.372127 q^{87} +(6.19946 + 3.09111i) q^{88} +9.92195 q^{89} +(-6.71389 - 4.87793i) q^{91} +(-2.30002 + 1.67106i) q^{92} +(0.419156 - 1.29003i) q^{93} +(-6.14226 + 18.9039i) q^{94} +(-6.36125 - 4.62172i) q^{96} +(-0.700884 - 2.15710i) q^{97} +3.25724 q^{98} +(-1.37792 - 2.64710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46}+ \cdots + 72 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Introduction

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