LMFDB - Embedded newform 275.2.h.d.251.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(26,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			251.4
Root			$-1.33858 + 0.972539i$ of defining polynomial
Character	$\chi$	$=$	275.251
Dual form			275.2.h.d.126.4

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	−0.590581	−	0.806979i	$-0.701101\pi$
$2$	0.511294	−	1.57360i	0.361539	−	1.11270i	0.952120	−	0.305725i	$-0.0988988\pi$
$3$	1.59764	−	1.16075i	0.922396	−	0.670160i	−0.0217231	−	0.999764i	$-0.506915\pi$
$3$	1.59764	−	1.16075i	0.922396	−	0.670160i	0.944119	+	0.329604i	$0.106915\pi$
$4$	−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	$-0.160660\pi$
$7$	1.81468	+	1.31845i	0.685886	+	0.498326i	−0.189419	+	0.981896i	$0.560660\pi$
$8$	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	0.657794	+	0.753198i	$0.271490\pi$
$13$	−1.14329	+	3.51868i	−0.317091	+	0.975906i	−0.974885	+	0.222708i	$0.928510\pi$
$14$	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	$-0.186949\pi$
$17$	−0.687441	−	2.11573i	−0.166729	−	0.513139i	−0.999160	+	0.0409903i	$0.986949\pi$
$18$	−1.20444	−	0.875078i	−0.283890	−	0.206258i
$19$	−4.27714	+	3.10753i	−0.981244	+	0.712916i	−0.957986	−	0.286814i	$-0.907404\pi$
$19$	−4.27714	+	3.10753i	−0.981244	+	0.712916i	−0.0232580	+	0.999729i	$0.507404\pi$
$20$		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	$-0.631623\pi$
$23$	−3.85415			−0.803647			−0.401823	+	0.915717i	$0.631623\pi$
$24$	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	0.573541	−	0.819177i	$-0.305569\pi$
$29$	−0.152450	−	0.110762i	−0.0283093	−	0.0205679i	−0.601850	+	0.798609i	$0.705569\pi$
$30$		0			0
$31$	0.212253	−	0.653249i	0.0381218	−	0.117327i	−0.930185	−	0.367092i	$-0.880353\pi$
$31$	0.212253	−	0.653249i	0.0381218	−	0.117327i	0.968306	+	0.249765i	$0.0803534\pi$
$32$	−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	$-0.368374\pi$
$37$	−2.09791	−	1.52422i	−0.344894	−	0.250580i	−0.746724	+	0.665134i	$0.768374\pi$
$38$	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	−0.962124	−	0.272611i	$-0.912113\pi$
$41$	−6.40421	+	4.65293i	−1.00017	+	0.726666i	−0.0380448	+	0.999276i	$0.512113\pi$
$42$	2.26482	−	6.97041i	0.349470	−	1.07556i
$43$	8.41368			1.28307			0.641537	−	0.767092i	$-0.278297\pi$
$43$	8.41368			1.28307			0.641537	+	0.767092i	$0.278297\pi$
$44$	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	0.425486	−	0.904965i	$-0.360103\pi$
$47$	9.71886	−	7.06117i	1.41764	−	1.02998i	0.992155	−	0.125012i	$-0.0398969\pi$
$48$	−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	−0.201549	−	0.979479i	$-0.564597\pi$
$53$	3.91110	−	12.0371i	0.537231	−	1.65343i	0.738779	−	0.673947i	$-0.235403\pi$
$54$	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	0.605738	−	0.795664i	$-0.292878\pi$
$59$	0.278050	+	0.202015i	0.0361990	+	0.0263001i	−0.569539	+	0.821965i	$0.692878\pi$
$60$		0			0
$61$	0.535643	+	1.64854i	0.0685821	+	0.211074i	0.979474	−	0.201572i	$-0.0646049\pi$
$61$	0.535643	+	1.64854i	0.0685821	+	0.211074i	−0.910892	+	0.412645i	$0.864605\pi$
$62$	−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	$-0.487349\pi$
$67$	0.650461			0.0794664			0.0397332	+	0.999210i	$0.487349\pi$
$68$	−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	0.999396	−	0.0347464i	$-0.0110624\pi$
$71$	1.43619	+	4.42013i	0.170444	+	0.524573i	−0.828952	+	0.559320i	$0.811062\pi$
$72$	−0.580756	−	1.78738i	−0.0684427	−	0.210645i
$73$	7.16660	+	5.20684i	0.838787	+	0.609415i	0.922032	−	0.387115i	$-0.126528\pi$
$73$	7.16660	+	5.20684i	0.838787	+	0.609415i	−0.0832444	+	0.996529i	$0.526528\pi$
$74$	−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	0.742982	+	0.669311i	$0.233411\pi$
$79$	−2.23551	+	6.88019i	−0.251514	+	0.774082i	−0.994496	+	0.104770i	$0.966589\pi$
$80$		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	$-0.0441316\pi$
$83$	0.983185	+	3.02593i	0.107919	+	0.332139i	−0.882486	+	0.470339i	$0.844132\pi$
$84$	−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	$-0.863266\pi$
$97$	0.700884	−	2.15710i	0.0711640	−	0.219020i	0.980313	+	0.197451i	$0.0632665\pi$
$98$	−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	−0.675621	−	0.737249i	$-0.736124\pi$
$101$	3.05830	−	9.41247i	0.304312	−	0.936576i	0.979933	−	0.199327i	$-0.0638756\pi$
$102$	−5.88057	+	4.27249i	−0.582263	+	0.423039i
$103$	−8.28525	−	6.01958i	−0.816370	−	0.593127i	0.0993007	−	0.995057i	$-0.468339\pi$
$103$	−8.28525	−	6.01958i	−0.816370	−	0.593127i	−0.915670	+	0.401930i	$0.868339\pi$
$104$	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	$-0.861410\pi$
$107$	−8.12803	+	5.90536i	−0.785767	+	0.570893i	0.120937	+	0.992660i	$0.461410\pi$
$108$	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	$-0.703464\pi$
$113$	−0.187168	+	0.135985i	−0.0176073	+	0.0127924i	0.578947	+	0.815365i	$0.303464\pi$
$114$	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	$-0.134390\pi$
$127$	−0.751018	−	2.31140i	−0.0666421	−	0.205103i	−0.978832	+	0.204664i	$0.934390\pi$
$128$	−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	−0.818895	−	0.573943i	$-0.805413\pi$
$137$	−5.77920	−	17.7866i	−0.493750	−	1.51961i	0.325145	−	0.945664i	$-0.394587\pi$
$138$	3.89153	+	11.9769i	0.331269	+	1.01954i
$139$	−9.40675	−	6.83441i	−0.797870	−	0.579687i	0.112418	−	0.993661i	$-0.464140\pi$
$139$	−9.40675	−	6.83441i	−0.797870	−	0.579687i	−0.910289	+	0.413974i	$0.864140\pi$
$140$		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	0.997592	−	0.0693580i	$-0.0220951\pi$
$149$	1.82800	+	5.62600i	0.149755	+	0.460900i	−0.847836	+	0.530258i	$0.822095\pi$
$150$		0			0
$151$	−10.3375	+	7.51064i	−0.841254	+	0.611207i	−0.922721	−	0.385469i	$-0.874040\pi$
$151$	−10.3375	+	7.51064i	−0.841254	+	0.611207i	0.0814664	+	0.996676i	$0.474040\pi$
$152$	−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	$-0.894055\pi$
$157$	−11.6083	+	8.43394i	−0.926445	+	0.673102i	0.0186749	+	0.999826i	$0.494055\pi$
$158$	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	$-0.945370\pi$
$163$	−1.12085	+	3.44963i	−0.0877921	+	0.270196i	0.897516	+	0.440982i	$0.145370\pi$
$164$	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	$-0.947228\pi$
$167$	−1.18066	+	3.63370i	−0.0913623	+	0.281184i	0.894926	+	0.446214i	$0.147228\pi$
$168$	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	$-0.725524\pi$
$173$	−1.70472	+	1.23855i	−0.129607	+	0.0941651i	0.521093	+	0.853500i	$0.325524\pi$
$174$	−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	−0.729229	−	0.684270i	$-0.760121\pi$
$179$	−4.06448	+	2.95302i	−0.303793	+	0.220719i	0.425435	+	0.904989i	$0.360121\pi$
$180$		0			0
$181$	−4.83538	−	14.8818i	−0.359411	−	1.10615i	−0.953408	−	0.301685i	$-0.902451\pi$
$181$	−4.83538	−	14.8818i	−0.359411	−	1.10615i	0.593997	−	0.804467i	$-0.297549\pi$
$182$	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	0.492840	−	0.870120i	$-0.335959\pi$
$191$	−2.52078	−	1.83145i	−0.182397	−	0.132519i	−0.675237	+	0.737601i	$0.735959\pi$
$192$	−1.99815	−	6.14966i	−0.144204	−	0.443814i
$193$	−2.97780	−	9.16474i	−0.214347	−	0.659692i	−0.999199	−	0.0400095i	$-0.987261\pi$
$193$	−2.97780	−	9.16474i	−0.214347	−	0.659692i	0.784852	−	0.619683i	$-0.212739\pi$
$194$	−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	$-0.328577\pi$
$197$	14.3974			1.02577			0.512885	+	0.858457i	$0.328577\pi$
$198$	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	−0.996888	−	0.0788298i	$-0.974882\pi$
$211$	−2.09250	+	6.44005i	−0.144054	+	0.443352i	0.852834	+	0.522181i	$0.174882\pi$
$212$	−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	$-0.794279\pi$
$223$	−7.05242	+	5.12388i	−0.472265	+	0.343121i	0.326058	+	0.945350i	$0.394279\pi$
$224$	−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	$-0.259672\pi$
$227$	3.08028	+	2.23795i	0.204445	+	0.148538i	−0.480852	+	0.876802i	$0.659672\pi$
$228$	6.23044	−	4.52668i	0.412621	−	0.299787i
$229$	−0.838570	+	2.58085i	−0.0554142	+	0.170547i	−0.974933	−	0.222499i	$-0.928579\pi$
$229$	−0.838570	+	2.58085i	−0.0554142	+	0.170547i	0.919519	+	0.393046i	$0.128579\pi$
$230$		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	−0.786519	−	0.617566i	$-0.788119\pi$
$233$	3.24801	−	9.99634i	0.212784	−	0.654882i	0.999303	−	0.0373166i	$-0.0118810\pi$
$234$	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	−0.971963	−	0.235133i	$-0.924448\pi$
$239$	−16.2124	+	11.7790i	−1.04869	+	0.761919i	−0.0767288	+	0.997052i	$0.524448\pi$
$240$		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	0.394117	+	0.919060i	$0.371050\pi$
$251$	−7.36604	+	22.6703i	−0.464940	+	1.43094i	−0.859058	+	0.511879i	$0.828950\pi$
$252$	−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	$-0.0204391\pi$
$257$	19.9636	+	14.5044i	1.24529	+	0.904758i	0.247354	+	0.968925i	$0.420439\pi$
$258$	−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	$-0.553651\pi$
$263$	−5.44098			−0.335505			−0.167753	+	0.985829i	$0.553651\pi$
$264$	−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	0.867803	−	0.496909i	$-0.165532\pi$
$269$	−2.07213	−	6.37738i	−0.126340	−	0.388835i	−0.994143	+	0.108074i	$0.965532\pi$
$270$		0			0
$271$	4.09349	+	2.97409i	0.248662	+	0.180663i	0.705134	−	0.709075i	$-0.250887\pi$
$271$	4.09349	+	2.97409i	0.248662	+	0.180663i	−0.456472	+	0.889738i	$0.650887\pi$
$272$	−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	−0.801367	−	0.598173i	$-0.795893\pi$
$277$	3.30453	−	10.1703i	0.198550	−	0.611074i	0.999917	−	0.0129009i	$-0.00410661\pi$
$278$	−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	−0.994233	−	0.107238i	$-0.965799\pi$
$281$	−4.23963	−	13.0482i	−0.252915	−	0.778392i	0.741319	−	0.671153i	$-0.234201\pi$
$282$	−31.7559	−	23.0720i	−1.89103	−	1.37392i
$283$	−17.7735	+	12.9132i	−1.05653	+	0.767611i	−0.973442	−	0.228932i	$-0.926477\pi$
$283$	−17.7735	+	12.9132i	−1.05653	+	0.767611i	−0.0830832	+	0.996543i	$0.526477\pi$
$284$	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	$-0.165509\pi$
$293$	11.3570	+	8.25135i	0.663483	+	0.482049i	−0.204354	+	0.978897i	$0.565509\pi$
$294$	−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	$-0.437194\pi$
$307$	6.86951			0.392064			0.196032	+	0.980598i	$0.437194\pi$
$308$	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	−0.454398	−	0.890799i	$-0.650146\pi$
$311$	4.45087	−	3.23374i	0.252385	−	0.183369i	0.706783	+	0.707430i	$0.250146\pi$
$312$	12.3459	+	8.96982i	0.698949	+	0.507816i
$313$	−4.39793	−	13.5354i	−0.248586	−	0.765068i	−0.995026	−	0.0996156i	$-0.968239\pi$
$313$	−4.39793	−	13.5354i	−0.248586	−	0.765068i	0.746440	−	0.665452i	$-0.231761\pi$
$314$	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	0.647421	+	0.762132i	$0.275847\pi$
$317$	−5.77442	+	17.7718i	−0.324324	+	0.998166i	−0.971745	+	0.236033i	$0.924153\pi$
$318$	−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	0.969486	+	0.245146i	$0.0788359\pi$
$337$	27.5771	+	20.0360i	1.50222	+	1.09143i	0.532735	+	0.846282i	$0.321164\pi$
$338$	−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	$-0.130745\pi$
$347$	−1.11027	−	3.41707i	−0.0596026	−	0.183438i	−0.976425	+	0.215858i	$0.930745\pi$
$348$	0.222072	+	0.161345i	0.0119043	+	0.00864898i
$349$	5.15433	−	3.74484i	0.275905	−	0.200457i	−0.441224	−	0.897397i	$-0.645456\pi$
$349$	5.15433	−	3.74484i	0.275905	−	0.200457i	0.717129	+	0.696940i	$0.245456\pi$
$350$		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	$-0.394773\pi$
$353$	12.1971			0.649186			0.324593	+	0.945854i	$0.394773\pi$
$354$	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	−0.0614222	−	0.998112i	$-0.519564\pi$
$359$	−19.5093	−	14.1744i	−1.02966	−	0.748094i	−0.968241	+	0.250018i	$0.919564\pi$
$360$		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	$-0.478624\pi$
$367$	−16.4958	−	11.9849i	−0.861073	−	0.625606i	−0.928177	+	0.372140i	$0.878624\pi$
$368$	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	$-0.562368\pi$
$373$	−7.51997			−0.389369			−0.194685	+	0.980866i	$0.562368\pi$
$374$	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	0.948006	+	0.318254i	$0.103096\pi$
$379$	7.16649	+	22.0562i	0.368118	+	1.13295i	−0.579888	+	0.814696i	$0.696904\pi$
$380$		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	$-0.919859\pi$
$383$	−0.754123	+	2.32095i	−0.0385339	+	0.118595i	0.929939	+	0.367713i	$0.119859\pi$
$384$	−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	−0.995467	−	0.0951096i	$-0.969680\pi$
$389$	−27.4849	−	19.9689i	−1.39354	−	1.01246i	−0.398071	−	0.917355i	$-0.630320\pi$
$390$		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	$-0.257613\pi$
$397$	27.4961			1.37999			0.689995	+	0.723814i	$0.257613\pi$
$398$	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	0.935437	−	0.353494i	$-0.115006\pi$
$401$	−0.583247	−	1.79505i	−0.0291259	−	0.0896404i	−0.964563	+	0.263853i	$0.915006\pi$
$402$	−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	−0.792461	−	0.609923i	$-0.791201\pi$
$409$	4.18949	−	12.8939i	0.207157	−	0.637563i	0.999618	−	0.0276408i	$-0.00879945\pi$
$410$		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	−0.881842	−	0.471544i	$-0.843697\pi$
$421$	−14.4835	+	10.5229i	−0.705881	+	0.512853i	0.175961	+	0.984397i	$0.443697\pi$
$422$	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	−0.314662	−	0.949204i	$-0.601891\pi$
$431$	10.3353	−	31.8087i	0.497833	−	1.53217i	0.812495	−	0.582968i	$-0.198109\pi$
$432$	16.5459	−	12.0213i	0.796066	−	0.578376i
$433$	25.4771	+	18.5102i	1.22435	+	0.889543i	0.996454	−	0.0841428i	$-0.0268152\pi$
$433$	25.4771	+	18.5102i	1.22435	+	0.889543i	0.227897	+	0.973685i	$0.426815\pi$
$434$	−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	$-0.511583\pi$
$443$	19.0018	−	13.8056i	0.902805	−	0.655926i	0.939185	+	0.343412i	$0.111583\pi$
$444$	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	0.410011	+	0.912080i	$0.365525\pi$
$449$	−9.70066	+	29.8555i	−0.457802	+	1.40897i	−0.867814	+	0.496890i	$0.834475\pi$
$450$		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	−0.666903	−	0.745145i	$-0.732380\pi$
$457$	−12.0859	−	37.1964i	−0.565352	−	1.73998i	0.101550	−	0.994830i	$-0.467620\pi$
$458$	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	$-0.531195\pi$
$463$	−4.21081			−0.195693			−0.0978464	+	0.995202i	$0.531195\pi$
$464$	−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	$-0.0502440\pi$
$467$	2.07920	+	6.39912i	0.0962139	+	0.296116i	−0.891354	+	0.453307i	$0.850244\pi$
$468$	−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	0.983617	+	0.180272i	$0.0576977\pi$
$479$	6.43046	+	19.7909i	0.293815	+	0.904270i	−0.689802	+	0.723998i	$0.742302\pi$
$480$		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	$-0.816376\pi$
$487$	−12.7658	+	9.27489i	−0.578473	+	0.420285i	0.259700	+	0.965689i	$0.416376\pi$
$488$	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	0.176044	−	0.984382i	$-0.443670\pi$
$491$	−15.6386	−	11.3621i	−0.705759	−	0.512764i	−0.881803	+	0.471618i	$0.843670\pi$
$492$	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	0.969769	+	0.244026i	$0.0784684\pi$
$499$	33.5416	+	24.3694i	1.50153	+	1.09092i	0.531758	+	0.846896i	$0.321532\pi$
$500$		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	$-0.959619\pi$
$503$	−26.4236	+	19.1978i	−1.17817	+	0.855990i	−0.186205	+	0.982511i	$0.559619\pi$
$504$	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	−0.844770	−	0.535129i	$-0.820263\pi$
$509$	−13.4662	+	9.78379i	−0.596881	+	0.433659i	0.247890	+	0.968788i	$0.420263\pi$
$510$		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	0.310126	−	0.950696i	$-0.399629\pi$
$521$	−11.3717	−	8.26206i	−0.498205	−	0.361967i	−0.808331	+	0.588728i	$0.799629\pi$
$522$	0.0866924	+	0.266812i	0.00379442	+	0.0116780i
$523$	4.84159	+	14.9009i	0.211708	+	0.651570i	0.999371	+	0.0354635i	$0.0112908\pi$
$523$	4.84159	+	14.9009i	0.211708	+	0.651570i	−0.787663	+	0.616106i	$0.788709\pi$
$524$	−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	0.234461	+	0.972125i	$0.424667\pi$
$541$	−12.2489	+	37.6983i	−0.526623	+	1.62078i	−0.761084	+	0.648653i	$0.775333\pi$
$542$	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	−0.432895	+	0.901445i	$0.642508\pi$
$547$	−33.3043	+	24.1970i	−1.42399	+	1.03459i	−0.991097	+	0.133145i	$0.957492\pi$
$548$	−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	$-0.518153\pi$
$557$	−24.1702	−	17.5606i	−1.02412	−	0.744069i	−0.967124	+	0.254306i	$0.918153\pi$
$558$	−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	$-0.885521\pi$
$563$	0.666795	−	2.05218i	0.0281021	−	0.0864892i	0.964124	+	0.265453i	$0.0855214\pi$
$564$	−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	−0.599882	−	0.800088i	$-0.704786\pi$
$569$	−0.580298	+	0.421611i	−0.0243274	+	0.0176749i	0.575555	+	0.817763i	$0.304786\pi$
$570$		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	0.981001	+	0.194000i	$0.0621463\pi$
$577$	7.23952	+	22.2810i	0.301385	+	0.927568i	−0.679616	+	0.733568i	$0.737854\pi$
$578$	−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	$-0.285232\pi$
$587$	1.81814	+	1.32095i	0.0750425	+	0.0545216i	−0.549632	+	0.835407i	$0.685232\pi$
$588$	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	$-0.325337\pi$
$593$	25.4034			1.04319			0.521596	+	0.853193i	$0.325337\pi$
$594$	−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	−0.997732	−	0.0673118i	$-0.978558\pi$
$599$	−5.63194	−	17.3333i	−0.230115	−	0.708220i	0.767617	−	0.640909i	$-0.221442\pi$
$600$		0			0
$601$	28.0242	+	20.3608i	1.14313	+	0.830533i	0.987552	−	0.157290i	$-0.0502758\pi$
$601$	28.0242	+	20.3608i	1.14313	+	0.830533i	0.155579	+	0.987824i	$0.450276\pi$
$602$	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	−0.654809	−	0.755794i	$-0.727251\pi$
$607$	7.86394	−	24.2027i	0.319187	−	0.982358i	0.973996	−	0.226564i	$-0.0727491\pi$
$608$	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	$-0.430797\pi$
$613$	29.9835	−	21.7843i	1.21102	−	0.879859i	0.995323	+	0.0966016i	$0.0307973\pi$
$614$	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	$-0.687450\pi$
$617$	−27.5937			−1.11088			−0.555439	+	0.831557i	$0.687450\pi$
$618$	−10.3404	+	31.8246i	−0.415953	+	1.28017i
$619$	−16.5391	+	12.0164i	−0.664764	+	0.482979i	−0.868268	−	0.496095i	$-0.834767\pi$
$619$	−16.5391	+	12.0164i	−0.664764	+	0.482979i	0.203504	+	0.979074i	$0.434767\pi$
$620$		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	0.575494	−	0.817806i	$-0.304810\pi$
$631$	−0.614155	−	0.446210i	−0.0244491	−	0.0177633i	−0.599943	+	0.800043i	$0.704810\pi$
$632$	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	−0.323605	−	0.946192i	$-0.604895\pi$
$641$	12.0584	−	8.76094i	0.476278	−	0.346037i	0.799883	+	0.600156i	$0.204895\pi$
$642$	26.5579	+	19.2955i	1.04816	+	0.761531i
$643$	8.53955	+	26.2820i	0.336767	+	1.03646i	0.965845	+	0.259120i	$0.0834325\pi$
$643$	8.53955	+	26.2820i	0.336767	+	1.03646i	−0.629078	+	0.777342i	$0.716568\pi$
$644$	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	−0.676791	−	0.736175i	$-0.736630\pi$
$647$	7.71879	−	23.7560i	0.303457	−	0.933945i	0.980248	−	0.197770i	$-0.0633700\pi$
$648$	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	$-0.482797\pi$
$653$	−22.4607	−	16.3187i	−0.878956	−	0.638599i	−0.932975	+	0.359941i	$0.882797\pi$
$654$	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	−0.571158	−	0.820840i	$-0.693506\pi$
$673$	9.68673	−	29.8127i	0.373396	−	1.14920i	0.944554	−	0.328355i	$-0.106494\pi$
$674$	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	−0.950475	−	0.310801i	$-0.899403\pi$
$677$	−9.47642	−	29.1654i	−0.364209	−	1.12092i	0.586267	−	0.810118i	$-0.300597\pi$
$678$	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	$-0.519941\pi$
$683$	−3.27236			−0.125213			−0.0626066	+	0.998038i	$0.519941\pi$
$684$	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	0.470083	+	0.882622i	$0.344224\pi$
$691$	−11.2774	+	34.7084i	−0.429014	+	1.32037i	−0.899098	+	0.437748i	$0.855776\pi$
$692$	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	−0.431399	+	0.902161i	$0.641980\pi$
$701$	−37.6684	+	27.3677i	−1.42272	+	1.03366i	−0.991316	+	0.131502i	$0.958020\pi$
$702$	−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	−0.913929	−	0.405874i	$-0.866967\pi$
$709$	−11.0000	−	33.8544i	−0.413112	−	1.27143i	0.500817	−	0.865553i	$-0.333033\pi$
$710$		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	0.202337	−	0.979316i	$-0.435146\pi$
$719$	−17.8722	−	12.9849i	−0.666522	−	0.484256i	−0.868859	+	0.495060i	$0.835146\pi$
$720$		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	$-0.179885\pi$
$727$	45.5415			1.68904			0.844521	+	0.535522i	$0.179885\pi$
$728$	−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	$-0.367393\pi$
$733$	−9.20572	−	6.68835i	−0.340021	−	0.247040i	−0.744671	+	0.667432i	$0.767393\pi$
$734$	−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	−0.972679	−	0.232153i	$-0.925423\pi$
$739$	−1.34045	+	4.12547i	−0.0493091	+	0.151758i	0.923370	+	0.383911i	$0.125423\pi$
$740$		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	0.999963	+	0.00865478i	$0.00275494\pi$
$743$	5.34429	+	16.4480i	0.196063	+	0.603420i	−0.803900	+	0.594765i	$0.797245\pi$
$744$	−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	−0.0157586	−	0.999876i	$-0.505016\pi$
$751$	25.4946	−	18.5229i	0.930310	−	0.675910i	0.946069	+	0.323966i	$0.105016\pi$
$752$	−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	$-0.846077\pi$
$757$	2.86687	−	8.82332i	0.104198	−	0.320689i	0.989541	+	0.144249i	$0.0460766\pi$
$758$	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	−0.971641	−	0.236461i	$-0.924012\pi$
$761$	−1.28492	+	3.95459i	−0.0465784	+	0.143354i	0.925062	+	0.379815i	$0.124012\pi$
$762$	−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	$-0.651281\pi$
$773$	6.85852	−	4.98301i	0.246684	−	0.179226i	0.704256	+	0.709946i	$0.251281\pi$
$774$	−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	0.575508	+	0.817796i	$0.304804\pi$
$787$	16.5684	+	50.9924i	0.590601	+	1.81768i	0.0150924	+	0.999886i	$0.495196\pi$
$788$	−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	0.976792	+	0.214192i	$0.0687119\pi$
$797$	8.82082	+	27.1477i	0.312450	+	0.961621i	−0.664342	+	0.747429i	$0.731288\pi$
$798$	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	0.923865	+	0.382718i	$0.125012\pi$
$809$	11.4170	+	35.1378i	0.401399	+	1.23538i	−0.522466	+	0.852660i	$0.674988\pi$
$810$		0			0
$811$	31.0475	−	22.5573i	1.09022	−	0.792094i	0.110787	−	0.993844i	$-0.464663\pi$
$811$	31.0475	−	22.5573i	1.09022	−	0.792094i	0.979437	+	0.201750i	$0.0646629\pi$
$812$	−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	0.723006	−	0.690842i	$-0.242760\pi$
$821$	8.29214	+	6.02459i	0.289398	+	0.210260i	−0.433608	+	0.901101i	$0.642760\pi$
$822$	−49.4370	+	35.9181i	−1.72431	+	1.25279i
$823$	7.79637	−	23.9948i	0.271764	−	0.836405i	−0.718293	−	0.695741i	$-0.755076\pi$
$823$	7.79637	−	23.9948i	0.271764	−	0.836405i	0.990057	−	0.140664i	$-0.0449237\pi$
$824$	−21.3904			−0.745170
$825$		0			0
$826$	1.27555			0.0443820
$827$	−5.67001	+	17.4505i	−0.197165	+	0.606813i	0.802779	+	0.596277i	$0.203354\pi$
$827$	−5.67001	+	17.4505i	−0.197165	+	0.606813i	−0.999944	+	0.0105362i	$0.996646\pi$
$828$	2.06953	−	1.50360i	0.0719211	−	0.0522537i
$829$	−19.7259	−	14.3317i	−0.685110	−	0.497761i	0.189939	−	0.981796i	$-0.439171\pi$
$829$	−19.7259	−	14.3317i	−0.685110	−	0.497761i	−0.875049	+	0.484035i	$0.839171\pi$
$830$		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	0.188644	−	0.982046i	$-0.439591\pi$
$839$	34.2059	−	24.8520i	1.18092	−	0.857988i	0.992275	+	0.124058i	$0.0395908\pi$
$840$		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	$-0.0151411\pi$
$853$	4.75529	+	14.6353i	0.162818	+	0.501103i	−0.836051	+	0.548652i	$0.815141\pi$
$854$	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	$-0.288493\pi$
$857$	36.1038			1.23328			0.616641	+	0.787245i	$0.288493\pi$
$858$	−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	0.931889	+	0.362743i	$0.118160\pi$
$863$	11.4919	+	35.3685i	0.391190	+	1.20396i	−0.540699	+	0.841216i	$0.681840\pi$
$864$	−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	$-0.556576\pi$
$877$	20.8672	−	15.1609i	0.704634	−	0.511947i	0.881438	+	0.472299i	$0.156576\pi$
$878$	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	$-0.673369\pi$
$883$	4.01783	−	2.91912i	0.135211	−	0.0982364i	0.653335	+	0.757069i	$0.273369\pi$
$884$	−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	$-0.461389\pi$
$887$	−23.3994	−	17.0006i	−0.785674	−	0.570826i	−0.906677	+	0.421827i	$0.861389\pi$
$888$	−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	$-0.170614\pi$
$907$	−4.09531	−	12.6041i	−0.135983	−	0.418511i	−0.995742	+	0.0921887i	$0.970614\pi$
$908$	−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	−0.855822	−	0.517271i	$-0.826948\pi$
$911$	4.24361	−	13.0605i	0.140597	−	0.432713i	0.996419	+	0.0845580i	$0.0269478\pi$
$912$	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	0.494774	+	0.869022i	$0.335251\pi$
$919$	18.3494	+	56.4737i	0.605292	+	1.86290i	0.110517	+	0.993874i	$0.464749\pi$
$920$		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	0.999916	+	0.0129763i	$0.00413060\pi$
$929$	6.05305	+	18.6294i	0.198594	+	0.611210i	−0.801322	+	0.598234i	$0.795869\pi$
$930$		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	−0.507933	−	0.861397i	$-0.669590\pi$
$937$	12.5292	−	38.5608i	0.409310	−	1.25973i	0.917242	−	0.398329i	$-0.130410\pi$
$938$	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	0.948972	−	0.315361i	$-0.102126\pi$
$941$	−0.126602	−	0.389640i	−0.00412709	−	0.0127019i	−0.953099	+	0.302659i	$0.902126\pi$
$942$	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	$-0.487288\pi$
$947$	2.45729			0.0798511			0.0399256	+	0.999203i	$0.487288\pi$
$948$	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	−0.888841	−	0.458215i	$-0.848489\pi$
$953$	−49.3714	−	35.8704i	−1.59930	−	1.16196i	−0.710456	−	0.703742i	$-0.751511\pi$
$954$	−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	$-0.410808\pi$
$967$	17.1997			0.553106			0.276553	+	0.960999i	$0.410808\pi$
$968$	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	−0.882015	−	0.471221i	$-0.843813\pi$
$971$	−22.0125	+	15.9930i	−0.706415	+	0.513241i	0.175600	+	0.984462i	$0.443813\pi$
$972$	−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	$-0.999220\pi$
$977$	−5.92454	+	18.2339i	−0.189543	+	0.583353i	0.810454	+	0.585802i	$0.199220\pi$
$978$	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	$-0.174263\pi$
$983$	19.5219	+	14.1835i	0.622653	+	0.452384i	−0.231194	+	0.972908i	$0.574263\pi$
$984$	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	$-0.477935\pi$
$997$	−27.0950	−	19.6856i	−0.858106	−	0.623451i	−0.927369	+	0.374148i	$0.877935\pi$
$998$	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.251.4		16
5.2	odd	4		55.2.j.a.9.4	yes	16
5.3	odd	4		55.2.j.a.9.1	✓	16
5.4	even	2	inner	275.2.h.d.251.1		16
11.4	even	5		3025.2.a.bl.1.7		8
11.5	even	5	inner	275.2.h.d.126.4		16
11.7	odd	10		3025.2.a.bk.1.2		8
15.2	even	4		495.2.ba.a.64.1		16
15.8	even	4		495.2.ba.a.64.4		16
20.3	even	4		880.2.cd.c.449.1		16
20.7	even	4		880.2.cd.c.449.4		16
55.2	even	20		605.2.j.g.124.4		16
55.3	odd	20		605.2.j.h.444.1		16
55.4	even	10		3025.2.a.bl.1.2		8
55.7	even	20		605.2.b.f.364.2		8
55.8	even	20		605.2.j.g.444.4		16
55.13	even	20		605.2.j.g.124.1		16
55.17	even	20		605.2.j.d.269.4		16
55.18	even	20		605.2.b.f.364.7		8
55.27	odd	20		55.2.j.a.49.1	yes	16
55.28	even	20		605.2.j.d.269.1		16
55.29	odd	10		3025.2.a.bk.1.7		8
55.32	even	4		605.2.j.d.9.1		16
55.37	odd	20		605.2.b.g.364.7		8
55.38	odd	20		55.2.j.a.49.4	yes	16
55.42	odd	20		605.2.j.h.124.1		16
55.43	even	4		605.2.j.d.9.4		16
55.47	odd	20		605.2.j.h.444.4		16
55.48	odd	20		605.2.b.g.364.2		8
55.49	even	10	inner	275.2.h.d.126.1		16
55.52	even	20		605.2.j.g.444.1		16
55.53	odd	20		605.2.j.h.124.4		16
165.38	even	20		495.2.ba.a.379.1		16
165.137	even	20		495.2.ba.a.379.4		16
220.27	even	20		880.2.cd.c.49.1		16
220.203	even	20		880.2.cd.c.49.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	5.3	odd	4
55.2.j.a.9.4	yes	16	5.2	odd	4
55.2.j.a.49.1	yes	16	55.27	odd	20
55.2.j.a.49.4	yes	16	55.38	odd	20
275.2.h.d.126.1		16	55.49	even	10	inner
275.2.h.d.126.4		16	11.5	even	5	inner
275.2.h.d.251.1		16	5.4	even	2	inner
275.2.h.d.251.4		16	1.1	even	1	trivial
495.2.ba.a.64.1		16	15.2	even	4
495.2.ba.a.64.4		16	15.8	even	4
495.2.ba.a.379.1		16	165.38	even	20
495.2.ba.a.379.4		16	165.137	even	20
605.2.b.f.364.2		8	55.7	even	20
605.2.b.f.364.7		8	55.18	even	20
605.2.b.g.364.2		8	55.48	odd	20
605.2.b.g.364.7		8	55.37	odd	20
605.2.j.d.9.1		16	55.32	even	4
605.2.j.d.9.4		16	55.43	even	4
605.2.j.d.269.1		16	55.28	even	20
605.2.j.d.269.4		16	55.17	even	20
605.2.j.g.124.1		16	55.13	even	20
605.2.j.g.124.4		16	55.2	even	20
605.2.j.g.444.1		16	55.52	even	20
605.2.j.g.444.4		16	55.8	even	20
605.2.j.h.124.1		16	55.42	odd	20
605.2.j.h.124.4		16	55.53	odd	20
605.2.j.h.444.1		16	55.3	odd	20
605.2.j.h.444.4		16	55.47	odd	20
880.2.cd.c.49.1		16	220.27	even	20
880.2.cd.c.49.4		16	220.203	even	20
880.2.cd.c.449.1		16	20.3	even	4
880.2.cd.c.449.4		16	20.7	even	4
3025.2.a.bk.1.2		8	11.7	odd	10
3025.2.a.bk.1.7		8	55.29	odd	10
3025.2.a.bl.1.2		8	55.4	even	10
3025.2.a.bl.1.7		8	11.4	even	5

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 $\F_{q}$
Belyi maps

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more