LMFDB - Embedded newform 1650.2.f.c.1649.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1650,2,Mod(1649,1650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1650.1649"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4,-8,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2051727616.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 37x^{4} + 36x^{2} + 4 $ x^8 + 11x^6 + 37x^4 + 36*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1649.1
Root			$-2.25619i$ of defining polynomial
Character	$\chi$	$=$	1650.1649
Dual form			1650.2.f.c.1649.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-1.73007 - 0.0828988i) q^{3} -1.00000 q^{4} +(-0.0828988 + 1.73007i) q^{6} -4.34658 q^{7} +1.00000i q^{8} +(2.98626 + 0.286841i) q^{9} +(-1.20394 + 3.09039i) q^{11} +(1.73007 + 0.0828988i) q^{12} +4.51238 q^{13} +4.34658i q^{14} +1.00000 q^{16} -2.72065i q^{17} +(0.286841 - 2.98626i) q^{18} +3.97251i q^{19} +(7.51987 + 0.360326i) q^{21} +(3.09039 + 1.20394i) q^{22} +1.66840 q^{23} +(0.0828988 - 1.73007i) q^{24} -4.51238i q^{26} +(-5.14264 - 0.743810i) q^{27} +4.34658 q^{28} -5.08606 q^{29} +9.74541 q^{31} -1.00000i q^{32} +(2.33909 - 5.24678i) q^{33} -2.72065 q^{34} +(-2.98626 - 0.286841i) q^{36} -5.60710i q^{37} +3.97251 q^{38} +(-7.80671 - 0.374071i) q^{39} -2.92026 q^{41} +(0.360326 - 7.51987i) q^{42} -3.25186 q^{43} +(1.20394 - 3.09039i) q^{44} -1.66840i q^{46} -9.25186 q^{47} +(-1.73007 - 0.0828988i) q^{48} +11.8928 q^{49} +(-0.225539 + 4.70691i) q^{51} -4.51238 q^{52} -3.05225 q^{53} +(-0.743810 + 5.14264i) q^{54} -4.34658i q^{56} +(0.329316 - 6.87271i) q^{57} +5.08606i q^{58} -5.43264i q^{59} -11.5646i q^{61} -9.74541i q^{62} +(-12.9800 - 1.24678i) q^{63} -1.00000 q^{64} +(-5.24678 - 2.33909i) q^{66} +12.3529i q^{67} +2.72065i q^{68} +(-2.88645 - 0.138309i) q^{69} -3.60710i q^{71} +(-0.286841 + 2.98626i) q^{72} -1.36502 q^{73} -5.60710 q^{74} -3.97251i q^{76} +(5.23303 - 13.4326i) q^{77} +(-0.374071 + 7.80671i) q^{78} -1.07107i q^{79} +(8.83544 + 1.71316i) q^{81} +2.92026i q^{82} -14.5887i q^{83} +(-7.51987 - 0.360326i) q^{84} +3.25186i q^{86} +(8.79922 + 0.421628i) q^{87} +(-3.09039 - 1.20394i) q^{88} +3.75791i q^{89} -19.6134 q^{91} -1.66840 q^{92} +(-16.8602 - 0.807883i) q^{93} +9.25186i q^{94} +(-0.0828988 + 1.73007i) q^{96} -12.7977i q^{97} -11.8928i q^{98} +(-4.48173 + 8.88336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{21} + 6 q^{22} + 8 q^{23} + 2 q^{24} - 10 q^{27} - 4 q^{29} - 4 q^{31} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 20 q^{38}+ \cdots + 10 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^21 + 6 * q^22 + 8 * q^23 + 2 * q^24 - 10 * q^27 - 4 * q^29 - 4 * q^31 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 20 * q^38 - 8 * q^39 + 16 * q^41 - 6 * q^42 + 8 * q^43 + 6 * q^44 - 40 * q^47 - 4 * q^48 + 4 * q^49 + 28 * q^51 - 4 * q^52 - 12 * q^53 - 22 * q^54 + 12 * q^57 - 32 * q^63 - 8 * q^64 - 18 * q^66 - 8 * q^69 + 12 * q^73 - 12 * q^74 - 8 * q^77 - 20 * q^78 + 2 * q^81 - 8 * q^84 + 36 * q^87 - 6 * q^88 - 48 * q^91 - 8 * q^92 - 2 * q^93 - 2 * q^96 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times$.

$n$	$551$	$727$	$1201$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.73007	−	0.0828988i	−0.998854	−	0.0478616i
$3$	−1.73007	−	0.0828988i	−0.998854	−	0.0478616i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−0.0828988	+	1.73007i	−0.0338433	+	0.706296i
$7$	−4.34658			−1.64285			−0.821427	−	0.570314i	$-0.806822\pi$
$7$	−4.34658			−1.64285			−0.821427	+	0.570314i	$0.806822\pi$
$8$			1.00000i			0.353553i
$9$	2.98626	+	0.286841i	0.995419	+	0.0956136i
$10$		0			0
$11$	−1.20394	+	3.09039i	−0.363002	+	0.931788i
$11$	−1.20394	+	3.09039i	−0.363002	+	0.931788i
$12$	1.73007	+	0.0828988i	0.499427	+	0.0239308i
$13$	4.51238			1.25151			0.625754	−	0.780020i	$-0.284791\pi$
$13$	4.51238			1.25151			0.625754	+	0.780020i	$0.284791\pi$
$14$			4.34658i			1.16167i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	2.72065i		−	0.659855i	−0.944006	−	0.329928i	$-0.892976\pi$
$17$		−	2.72065i		−	0.659855i	0.944006	−	0.329928i	$-0.107024\pi$
$18$	0.286841	−	2.98626i	0.0676090	−	0.703867i
$19$			3.97251i			0.911357i	0.890145	+	0.455678i	$0.150603\pi$
$19$			3.97251i			0.911357i	−0.890145	+	0.455678i	$0.849397\pi$
$20$		0			0
$21$	7.51987	+	0.360326i	1.64097	+	0.0786297i
$22$	3.09039	+	1.20394i	0.658874	+	0.256681i
$23$	1.66840			0.347886			0.173943	−	0.984756i	$-0.444349\pi$
$23$	1.66840			0.347886			0.173943	+	0.984756i	$0.444349\pi$
$24$	0.0828988	−	1.73007i	0.0169216	−	0.353148i
$25$		0			0
$26$		−	4.51238i		−	0.884950i
$27$	−5.14264	−	0.743810i	−0.989702	−	0.143146i
$28$	4.34658			0.821427
$29$	−5.08606			−0.944458			−0.472229	−	0.881476i	$-0.656550\pi$
$29$	−5.08606			−0.944458			−0.472229	+	0.881476i	$0.656550\pi$
$30$		0			0
$31$	9.74541			1.75033			0.875164	−	0.483827i	$-0.160754\pi$
$31$	9.74541			1.75033			0.875164	+	0.483827i	$0.160754\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.33909	−	5.24678i	0.407183	−	0.913347i
$34$	−2.72065			−0.466588
$35$		0			0
$36$	−2.98626	−	0.286841i	−0.497709	−	0.0478068i
$37$		−	5.60710i		−	0.921802i	−0.887452	−	0.460901i	$-0.847526\pi$
$37$		−	5.60710i		−	0.921802i	0.887452	−	0.460901i	$-0.152474\pi$
$38$	3.97251			0.644426
$39$	−7.80671	−	0.374071i	−1.25007	−	0.0598993i
$40$		0			0
$41$	−2.92026			−0.456069			−0.228034	−	0.973653i	$-0.573230\pi$
$41$	−2.92026			−0.456069			−0.228034	+	0.973653i	$0.573230\pi$
$42$	0.360326	−	7.51987i	0.0555996	−	1.16034i
$43$	−3.25186			−0.495904			−0.247952	−	0.968772i	$-0.579757\pi$
$43$	−3.25186			−0.495904			−0.247952	+	0.968772i	$0.579757\pi$
$44$	1.20394	−	3.09039i	0.181501	−	0.465894i
$45$		0			0
$46$		−	1.66840i		−	0.245993i
$47$	−9.25186			−1.34952			−0.674761	−	0.738036i	$-0.735753\pi$
$47$	−9.25186			−1.34952			−0.674761	+	0.738036i	$0.735753\pi$
$48$	−1.73007	−	0.0828988i	−0.249713	−	0.0119654i
$49$	11.8928			1.69897
$50$		0			0
$51$	−0.225539	+	4.70691i	−0.0315817	+	0.659099i
$52$	−4.51238			−0.625754
$53$	−3.05225			−0.419258			−0.209629	−	0.977781i	$-0.567226\pi$
$53$	−3.05225			−0.419258			−0.209629	+	0.977781i	$0.567226\pi$
$54$	−0.743810	+	5.14264i	−0.101220	+	0.699825i
$55$		0			0
$56$		−	4.34658i		−	0.580836i
$57$	0.329316	−	6.87271i	0.0436190	−	0.910312i
$58$			5.08606i			0.667833i
$59$		−	5.43264i		−	0.707270i	−0.935384	−	0.353635i	$-0.884946\pi$
$59$		−	5.43264i		−	0.707270i	0.935384	−	0.353635i	$-0.115054\pi$
$60$		0			0
$61$		−	11.5646i		−	1.48070i	−0.672222	−	0.740349i	$-0.734660\pi$
$61$		−	11.5646i		−	1.48070i	0.672222	−	0.740349i	$-0.265340\pi$
$62$		−	9.74541i		−	1.23767i
$63$	−12.9800	−	1.24678i	−1.63533	−	0.157079i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.24678	−	2.33909i	−0.645834	−	0.287922i
$67$			12.3529i			1.50915i	0.656215	+	0.754574i	$0.272156\pi$
$67$			12.3529i			1.50915i	−0.656215	+	0.754574i	$0.727844\pi$
$68$			2.72065i			0.329928i
$69$	−2.88645	−	0.138309i	−0.347488	−	0.0166504i
$70$		0			0
$71$		−	3.60710i		−	0.428084i	−0.976824	−	0.214042i	$-0.931337\pi$
$71$		−	3.60710i		−	0.428084i	0.976824	−	0.214042i	$-0.0686630\pi$
$72$	−0.286841	+	2.98626i	−0.0338045	+	0.351934i
$73$	−1.36502			−0.159763			−0.0798816	−	0.996804i	$-0.525454\pi$
$73$	−1.36502			−0.159763			−0.0798816	+	0.996804i	$0.525454\pi$
$74$	−5.60710			−0.651812
$75$		0			0
$76$		−	3.97251i		−	0.455678i
$77$	5.23303	−	13.4326i	0.596359	−	1.53079i
$78$	−0.374071	+	7.80671i	−0.0423552	+	0.883936i
$79$		−	1.07107i		−	0.120505i	−0.998183	−	0.0602526i	$-0.980809\pi$
$79$		−	1.07107i		−	0.120505i	0.998183	−	0.0602526i	$-0.0191906\pi$
$80$		0			0
$81$	8.83544	+	1.71316i	0.981716	+	0.190351i
$82$			2.92026i			0.322489i
$83$		−	14.5887i		−	1.60131i	−0.599123	−	0.800657i	$-0.704484\pi$
$83$		−	14.5887i		−	1.60131i	0.599123	−	0.800657i	$-0.295516\pi$
$84$	−7.51987	−	0.360326i	−0.820485	−	0.0393148i
$85$		0			0
$86$			3.25186i			0.350657i
$87$	8.79922	+	0.421628i	0.943375	+	0.0452033i
$88$	−3.09039	−	1.20394i	−0.329437	−	0.128341i
$89$			3.75791i			0.398338i	0.979965	+	0.199169i	$0.0638243\pi$
$89$			3.75791i			0.398338i	−0.979965	+	0.199169i	$0.936176\pi$
$90$		0			0
$91$	−19.6134			−2.05605
$92$	−1.66840			−0.173943
$93$	−16.8602	−	0.807883i	−1.74832	−	0.0837735i
$94$			9.25186i			0.954256i
$95$		0			0
$96$	−0.0828988	+	1.73007i	−0.00846082	+	0.176574i
$97$		−	12.7977i		−	1.29941i	−0.760188	−	0.649703i	$-0.774893\pi$
$97$		−	12.7977i		−	1.29941i	0.760188	−	0.649703i	$-0.225107\pi$
$98$		−	11.8928i		−	1.20135i
$99$	−4.48173	+	8.88336i	−0.450431	+	0.892811i
$100$		0			0
$101$	−6.73948			−0.670603			−0.335302	−	0.942111i	$-0.608838\pi$
$101$	−6.73948			−0.670603			−0.335302	+	0.942111i	$0.608838\pi$
$102$	4.70691	+	0.225539i	0.466053	+	0.0223317i
$103$			5.25186i			0.517481i	0.965947	+	0.258740i	$0.0833074\pi$
$103$			5.25186i			0.517481i	−0.965947	+	0.258740i	$0.916693\pi$
$104$			4.51238i			0.442475i
$105$		0			0
$106$			3.05225i			0.296461i
$107$		−	6.25707i		−	0.604894i	−0.953166	−	0.302447i	$-0.902196\pi$
$107$		−	6.25707i		−	0.604894i	0.953166	−	0.302447i	$-0.0978035\pi$
$108$	5.14264	+	0.743810i	0.494851	+	0.0715732i
$109$		−	17.9168i		−	1.71612i	−0.513550	−	0.858060i	$-0.671670\pi$
$109$		−	17.9168i		−	1.71612i	0.513550	−	0.858060i	$-0.328330\pi$
$110$		0			0
$111$	−0.464822	+	9.70066i	−0.0441190	+	0.920746i
$112$	−4.34658			−0.410713
$113$	8.51238			0.800777			0.400389	−	0.916345i	$-0.368875\pi$
$113$	8.51238			0.800777			0.400389	+	0.916345i	$0.368875\pi$
$114$	−6.87271	−	0.329316i	−0.643688	−	0.0308433i
$115$		0			0
$116$	5.08606			0.472229
$117$	13.4751	+	1.29433i	1.24578	+	0.119661i
$118$	−5.43264			−0.500115
$119$			11.8255i			1.08405i
$120$		0			0
$121$	−8.10105	−	7.44131i	−0.736459	−	0.676482i
$122$	−11.5646			−1.04701
$123$	5.05225	+	0.242086i	0.455546	+	0.0218282i
$124$	−9.74541			−0.875164
$125$		0			0
$126$	−1.24678	+	12.9800i	−0.111072	+	1.15635i
$127$	−8.95024			−0.794205			−0.397103	−	0.917774i	$-0.629984\pi$
$127$	−8.95024			−0.794205			−0.397103	+	0.917774i	$0.629984\pi$
$128$			1.00000i			0.0883883i
$129$	5.62593	+	0.269575i	0.495335	+	0.0237348i
$130$		0			0
$131$	12.3379			1.07797			0.538985	−	0.842316i	$-0.318808\pi$
$131$	12.3379			1.07797			0.538985	+	0.842316i	$0.318808\pi$
$132$	−2.33909	+	5.24678i	−0.203592	+	0.456673i
$133$		−	17.2668i		−	1.49723i
$134$	12.3529			1.06713
$135$		0			0
$136$	2.72065			0.233294
$137$	20.9416			1.78916			0.894580	−	0.446908i	$-0.147475\pi$
$137$	20.9416			1.78916			0.894580	+	0.446908i	$0.147475\pi$
$138$	−0.138309	+	2.88645i	−0.0117736	+	0.245711i
$139$		−	15.5458i		−	1.31858i	−0.751890	−	0.659289i	$-0.770857\pi$
$139$		−	15.5458i		−	1.31858i	0.751890	−	0.659289i	$-0.229143\pi$
$140$		0			0
$141$	16.0063	+	0.766968i	1.34798	+	0.0645903i
$142$	−3.60710			−0.302701
$143$	−5.43264	+	13.9450i	−0.454300	+	1.16614i
$144$	2.98626	+	0.286841i	0.248855	+	0.0239034i
$145$		0			0
$146$			1.36502i			0.112970i
$147$	−20.5753	−	0.985897i	−1.69702	−	0.0813154i
$148$			5.60710i			0.460901i
$149$	−23.2882			−1.90784			−0.953920	−	0.300061i	$-0.902993\pi$
$149$	−23.2882			−1.90784			−0.953920	+	0.300061i	$0.902993\pi$
$150$		0			0
$151$			10.8440i			0.882470i	0.897392	+	0.441235i	$0.145460\pi$
$151$			10.8440i			0.882470i	−0.897392	+	0.441235i	$0.854540\pi$
$152$	−3.97251			−0.322213
$153$	0.780394	−	8.12456i	0.0630911	−	0.656832i
$154$	−13.4326	−	5.23303i	−1.08243	−	0.421690i
$155$		0			0
$156$	7.80671	+	0.374071i	0.625037	+	0.0299496i
$157$			11.0861i			0.884764i	0.896827	+	0.442382i	$0.145866\pi$
$157$			11.0861i			0.884764i	−0.896827	+	0.442382i	$0.854134\pi$
$158$	−1.07107			−0.0852101
$159$	5.28059	+	0.253028i	0.418778	+	0.0200664i
$160$		0			0
$161$	−7.25186			−0.571527
$162$	1.71316	−	8.83544i	0.134599	−	0.694178i
$163$		−	4.16580i		−	0.326290i	−0.986602	−	0.163145i	$-0.947836\pi$
$163$		−	4.16580i		−	0.326290i	0.986602	−	0.163145i	$-0.0521639\pi$
$164$	2.92026			0.228034
$165$		0			0
$166$	−14.5887			−1.13230
$167$		−	8.78828i		−	0.680057i	−0.940415	−	0.340029i	$-0.889563\pi$
$167$		−	8.78828i		−	0.680057i	0.940415	−	0.340029i	$-0.110437\pi$
$168$	−0.360326	+	7.51987i	−0.0277998	+	0.580171i
$169$	7.36157			0.566275
$170$		0			0
$171$	−1.13948	+	11.8629i	−0.0871381	+	0.907181i
$172$	3.25186			0.247952
$173$			2.66319i			0.202479i	0.994862	+	0.101239i	$0.0322808\pi$
$173$			2.66319i			0.202479i	−0.994862	+	0.101239i	$0.967719\pi$
$174$	0.421628	−	8.79922i	0.0319636	−	0.667067i
$175$		0			0
$176$	−1.20394	+	3.09039i	−0.0907505	+	0.232947i
$177$	−0.450359	+	9.39883i	−0.0338511	+	0.706459i
$178$	3.75791			0.281668
$179$		−	11.2605i		−	0.841651i	−0.907142	−	0.420825i	$-0.861740\pi$
$179$		−	11.2605i		−	0.841651i	0.907142	−	0.420825i	$-0.138260\pi$
$180$		0			0
$181$	−0.711272			−0.0528684			−0.0264342	−	0.999651i	$-0.508415\pi$
$181$	−0.711272			−0.0528684			−0.0264342	+	0.999651i	$0.508415\pi$
$182$			19.6134i			1.45384i
$183$	−0.958694	+	20.0076i	−0.0708687	+	1.47900i
$184$			1.66840i			0.122996i
$185$		0			0
$186$	−0.807883	+	16.8602i	−0.0592368	+	1.23625i
$187$	8.40788	+	3.27551i	0.614845	+	0.239529i
$188$	9.25186			0.674761
$189$	22.3529	+	3.23303i	1.62593	+	0.235168i
$190$		0			0
$191$		−	19.5852i		−	1.41714i	−0.705642	−	0.708568i	$-0.749341\pi$
$191$		−	19.5852i		−	1.41714i	0.705642	−	0.708568i	$-0.250659\pi$
$192$	1.73007	+	0.0828988i	0.124857	+	0.00598270i
$193$	−8.82899			−0.635524			−0.317762	−	0.948170i	$-0.602931\pi$
$193$	−8.82899			−0.635524			−0.317762	+	0.948170i	$0.602931\pi$
$194$	−12.7977			−0.918818
$195$		0			0
$196$	−11.8928			−0.849484
$197$			12.9502i			0.922666i	0.887227	+	0.461333i	$0.152629\pi$
$197$			12.9502i			0.922666i	−0.887227	+	0.461333i	$0.847371\pi$
$198$	8.88336	+	4.48173i	0.631313	+	0.318503i
$199$	−1.17485			−0.0832830			−0.0416415	−	0.999133i	$-0.513259\pi$
$199$	−1.17485			−0.0832830			−0.0416415	+	0.999133i	$0.513259\pi$
$200$		0			0
$201$	1.02404	−	21.3713i	0.0722303	−	1.50742i
$202$			6.73948i			0.474188i
$203$	22.1070			1.55161
$204$	0.225539	−	4.70691i	0.0157909	−	0.329549i
$205$		0			0
$206$	5.25186			0.365914
$207$	4.98228	+	0.478566i	0.346293	+	0.0332627i
$208$	4.51238			0.312877
$209$	−12.2766	−	4.78267i	−0.849191	−	0.330824i
$210$		0			0
$211$		−	21.1498i		−	1.45602i	−0.685569	−	0.728008i	$-0.740446\pi$
$211$		−	21.1498i		−	1.45602i	0.685569	−	0.728008i	$-0.259554\pi$
$212$	3.05225			0.209629
$213$	−0.299024	+	6.24053i	−0.0204888	+	0.427594i
$214$	−6.25707			−0.427725
$215$		0			0
$216$	0.743810	−	5.14264i	0.0506099	−	0.349912i
$217$	−42.3592			−2.87553
$218$	−17.9168			−1.21348
$219$	2.36157	+	0.113158i	0.159580	+	0.00764652i
$220$		0			0
$221$		−	12.2766i		−	0.825815i
$222$	9.70066	+	0.464822i	0.651065	+	0.0311968i
$223$		−	22.6382i		−	1.51597i	−0.652275	−	0.757983i	$-0.726185\pi$
$223$		−	22.6382i		−	1.51597i	0.652275	−	0.757983i	$-0.273815\pi$
$224$			4.34658i			0.290418i
$225$		0			0
$226$		−	8.51238i		−	0.566235i
$227$			23.5758i			1.56478i	0.622789	+	0.782390i	$0.285999\pi$
$227$			23.5758i			1.56478i	−0.622789	+	0.782390i	$0.714001\pi$
$228$	−0.329316	+	6.87271i	−0.0218095	+	0.455156i
$229$	−3.50893			−0.231877			−0.115938	−	0.993256i	$-0.536988\pi$
$229$	−3.50893			−0.231877			−0.115938	+	0.993256i	$0.536988\pi$
$230$		0			0
$231$	−10.1670	+	22.8055i	−0.668942	+	1.50049i
$232$		−	5.08606i		−	0.333916i
$233$		−	9.84991i		−	0.645289i	−0.946520	−	0.322644i	$-0.895428\pi$
$233$		−	9.84991i		−	0.645289i	0.946520	−	0.322644i	$-0.104572\pi$
$234$	1.29433	−	13.4751i	0.0846133	−	0.880896i
$235$		0			0
$236$			5.43264i			0.353635i
$237$	−0.0887907	+	1.85303i	−0.00576758	+	0.120367i
$238$	11.8255			0.766536
$239$	24.1540			1.56239			0.781197	−	0.624285i	$-0.214610\pi$
$239$	24.1540			1.56239			0.781197	+	0.624285i	$0.214610\pi$
$240$		0			0
$241$			4.69316i			0.302313i	0.988510	+	0.151157i	$0.0482998\pi$
$241$			4.69316i			0.302313i	−0.988510	+	0.151157i	$0.951700\pi$
$242$	−7.44131	+	8.10105i	−0.478345	+	0.520755i
$243$	−15.1439	−	3.69633i	−0.971481	−	0.237119i
$244$			11.5646i			0.740349i
$245$		0			0
$246$	0.242086	−	5.05225i	0.0154349	−	0.322120i
$247$			17.9255i			1.14057i
$248$			9.74541i			0.618834i
$249$	−1.20938	+	25.2394i	−0.0766415	+	1.59948i
$250$		0			0
$251$			10.5424i			0.665427i	0.943028	+	0.332714i	$0.107964\pi$
$251$			10.5424i			0.665427i	−0.943028	+	0.332714i	$0.892036\pi$
$252$	12.9800	+	1.24678i	0.817663	+	0.0785395i
$253$	−2.00866	+	5.15603i	−0.126284	+	0.324157i
$254$			8.95024i			0.561588i
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.0334			0.688246			0.344123	−	0.938925i	$-0.388176\pi$
$257$	11.0334			0.688246			0.344123	+	0.938925i	$0.388176\pi$
$258$	0.269575	−	5.62593i	0.0167830	−	0.350255i
$259$			24.3717i			1.51439i
$260$		0			0
$261$	−15.1883	−	1.45889i	−0.940131	−	0.0903030i
$262$		−	12.3379i		−	0.762239i
$263$		−	30.8378i		−	1.90154i	−0.309897	−	0.950770i	$-0.600295\pi$
$263$		−	30.8378i		−	1.90154i	0.309897	−	0.950770i	$-0.399705\pi$
$264$	5.24678	+	2.33909i	0.322917	+	0.143961i
$265$		0			0
$266$	−17.2668			−1.05870
$267$	0.311526	−	6.50144i	0.0190651	−	0.397882i
$268$		−	12.3529i		−	0.754574i
$269$		−	9.58345i		−	0.584313i	−0.956370	−	0.292157i	$-0.905627\pi$
$269$		−	9.58345i		−	0.584313i	0.956370	−	0.292157i	$-0.0943729\pi$
$270$		0			0
$271$		−	21.3400i		−	1.29631i	−0.761507	−	0.648157i	$-0.775540\pi$
$271$		−	21.3400i		−	1.29631i	0.761507	−	0.648157i	$-0.224460\pi$
$272$		−	2.72065i		−	0.164964i
$273$	33.9325	+	1.62593i	2.05369	+	0.0984057i
$274$		−	20.9416i		−	1.26513i
$275$		0			0
$276$	2.88645	+	0.138309i	0.173744	+	0.00832521i
$277$	7.43264			0.446584			0.223292	−	0.974752i	$-0.428320\pi$
$277$	7.43264			0.446584			0.223292	+	0.974752i	$0.428320\pi$
$278$	−15.5458			−0.932375
$279$	29.1023	+	2.79538i	1.74231	+	0.167355i
$280$		0			0
$281$	20.0300			1.19489			0.597444	−	0.801911i	$-0.296183\pi$
$281$	20.0300			1.19489			0.597444	+	0.801911i	$0.296183\pi$
$282$	0.766968	−	16.0063i	0.0456723	−	0.953163i
$283$	5.98189			0.355587			0.177793	−	0.984068i	$-0.443104\pi$
$283$	5.98189			0.355587			0.177793	+	0.984068i	$0.443104\pi$
$284$			3.60710i			0.214042i
$285$		0			0
$286$	13.9450	+	5.43264i	0.824586	+	0.321239i
$287$	12.6932			0.749254
$288$	0.286841	−	2.98626i	0.0169023	−	0.175967i
$289$	9.59805			0.564591
$290$		0			0
$291$	−1.06091	+	22.1408i	−0.0621917	+	1.29792i
$292$	1.36502			0.0798816
$293$			22.9998i			1.34366i	0.740705	+	0.671830i	$0.234491\pi$
$293$			22.9998i			1.34366i	−0.740705	+	0.671830i	$0.765509\pi$
$294$	−0.985897	+	20.5753i	−0.0574987	+	1.19997i
$295$		0			0
$296$	5.60710			0.325906
$297$	8.49011	−	14.9973i	0.492646	−	0.870230i
$298$			23.2882i			1.34905i
$299$	7.52848			0.435383
$300$		0			0
$301$	14.1345			0.814697
$302$	10.8440			0.624001
$303$	11.6597	+	0.558695i	0.669835	+	0.0320962i
$304$			3.97251i			0.227839i
$305$		0			0
$306$	−8.12456	−	0.780394i	−0.464450	−	0.0446122i
$307$	27.2645			1.55607			0.778034	−	0.628222i	$-0.216217\pi$
$307$	27.2645			1.55607			0.778034	+	0.628222i	$0.216217\pi$
$308$	−5.23303	+	13.4326i	−0.298180	+	0.765396i
$309$	0.435373	−	9.08606i	0.0247675	−	0.516888i
$310$		0			0
$311$			0.0613019i			0.00347611i	0.999998	+	0.00173806i	$0.000553241\pi$
$311$			0.0613019i			0.00347611i	−0.999998	+	0.00173806i	$0.999447\pi$
$312$	0.374071	−	7.80671i	0.0211776	−	0.441968i
$313$			22.2766i			1.25915i	0.776940	+	0.629574i	$0.216771\pi$
$313$			22.2766i			1.25915i	−0.776940	+	0.629574i	$0.783229\pi$
$314$	11.0861			0.625623
$315$		0			0
$316$			1.07107i			0.0602526i
$317$	2.48169			0.139385			0.0696927	−	0.997569i	$-0.477798\pi$
$317$	2.48169			0.139385			0.0696927	+	0.997569i	$0.477798\pi$
$318$	0.253028	−	5.28059i	0.0141891	−	0.296121i
$319$	6.12332	−	15.7179i	0.342840	−	0.880035i
$320$		0			0
$321$	−0.518704	+	10.8251i	−0.0289512	+	0.604201i
$322$			7.25186i			0.404130i
$323$	10.8078			0.601363
$324$	−8.83544	−	1.71316i	−0.490858	−	0.0951755i
$325$		0			0
$326$	−4.16580			−0.230722
$327$	−1.48528	+	30.9973i	−0.0821363	+	1.71415i
$328$		−	2.92026i		−	0.161245i
$329$	40.2140			2.21707
$330$		0			0
$331$	−11.2519			−0.618458			−0.309229	−	0.950988i	$-0.600071\pi$
$331$	−11.2519			−0.618458			−0.309229	+	0.950988i	$0.600071\pi$
$332$			14.5887i			0.800657i
$333$	1.60835	−	16.7442i	0.0881368	−	0.917579i
$334$	−8.78828			−0.480873
$335$		0			0
$336$	7.51987	+	0.360326i	0.410243	+	0.0196574i
$337$	−0.968917			−0.0527803			−0.0263901	−	0.999652i	$-0.508401\pi$
$337$	−0.968917			−0.0527803			−0.0263901	+	0.999652i	$0.508401\pi$
$338$		−	7.36157i		−	0.400417i
$339$	−14.7270	−	0.705666i	−0.799860	−	0.0383265i
$340$		0			0
$341$	−11.7329	+	30.1171i	−0.635373	+	1.63093i
$342$	11.8629	+	1.13948i	0.641474	+	0.0616159i
$343$	−21.2668			−1.14830
$344$		−	3.25186i		−	0.175328i
$345$		0			0
$346$	2.66319			0.143174
$347$		−	1.59388i		−	0.0855641i	−0.999084	−	0.0427821i	$-0.986378\pi$
$347$		−	1.59388i		−	0.0855641i	0.999084	−	0.0427821i	$-0.0136221\pi$
$348$	−8.79922	−	0.421628i	−0.471688	−	0.0226016i
$349$			18.9416i			1.01392i	0.861970	+	0.506960i	$0.169231\pi$
$349$			18.9416i			1.01392i	−0.861970	+	0.506960i	$0.830769\pi$
$350$		0			0
$351$	−23.2055	−	3.35635i	−1.23862	−	0.179149i
$352$	3.09039	+	1.20394i	0.164718	+	0.0641703i
$353$	0.806322			0.0429162			0.0214581	−	0.999770i	$-0.493169\pi$
$353$	0.806322			0.0429162			0.0214581	+	0.999770i	$0.493169\pi$
$354$	9.39883	+	0.450359i	0.499542	+	0.0239363i
$355$		0			0
$356$		−	3.75791i		−	0.199169i
$357$	0.980323	−	20.4590i	0.0518842	−	1.08280i
$358$	−11.2605			−0.595137
$359$	−6.83531			−0.360754			−0.180377	−	0.983598i	$-0.557732\pi$
$359$	−6.83531			−0.360754			−0.180377	+	0.983598i	$0.557732\pi$
$360$		0			0
$361$	3.21916			0.169429
$362$			0.711272i			0.0373836i
$363$	13.3985	+	13.5455i	0.703237	+	0.710955i
$364$	19.6134			1.02802
$365$		0			0
$366$	20.0076	+	0.958694i	1.04581	+	0.0501117i
$367$			3.28873i			0.171670i	0.996309	+	0.0858351i	$0.0273558\pi$
$367$			3.28873i			0.171670i	−0.996309	+	0.0858351i	$0.972644\pi$
$368$	1.66840			0.0869716
$369$	−8.72065	−	0.837650i	−0.453979	−	0.0436063i
$370$		0			0
$371$	13.2668			0.688780
$372$	16.8602	+	0.807883i	0.874161	+	0.0418868i
$373$	11.3650			0.588458			0.294229	−	0.955735i	$-0.404937\pi$
$373$	11.3650			0.588458			0.294229	+	0.955735i	$0.404937\pi$
$374$	3.27551	−	8.40788i	0.169372	−	0.434761i
$375$		0			0
$376$		−	9.25186i		−	0.477128i
$377$	−22.9502			−1.18200
$378$	3.23303	−	22.3529i	0.166289	−	1.14971i
$379$	−26.1848			−1.34502			−0.672511	−	0.740087i	$-0.734784\pi$
$379$	−26.1848			−1.34502			−0.672511	+	0.740087i	$0.734784\pi$
$380$		0			0
$381$	15.4845	+	0.741964i	0.793295	+	0.0380120i
$382$	−19.5852			−1.00207
$383$	−18.7796			−0.959590			−0.479795	−	0.877381i	$-0.659289\pi$
$383$	−18.7796			−0.959590			−0.479795	+	0.877381i	$0.659289\pi$
$384$	0.0828988	−	1.73007i	0.00423041	−	0.0882871i
$385$		0			0
$386$			8.82899i			0.449384i
$387$	−9.71088	−	0.932765i	−0.493632	−	0.0474151i
$388$			12.7977i			0.649703i
$389$		−	24.4661i		−	1.24048i	−0.784413	−	0.620239i	$-0.787035\pi$
$389$		−	24.4661i		−	1.24048i	0.784413	−	0.620239i	$-0.212965\pi$
$390$		0			0
$391$		−	4.53915i		−	0.229555i
$392$			11.8928i			0.600676i
$393$	−21.3454	−	1.02280i	−1.07673	−	0.0515934i
$394$	12.9502			0.652424
$395$		0			0
$396$	4.48173	−	8.88336i	0.225215	−	0.446406i
$397$		−	34.0708i		−	1.70997i	−0.518656	−	0.854983i	$-0.673567\pi$
$397$		−	34.0708i		−	1.70997i	0.518656	−	0.854983i	$-0.326433\pi$
$398$			1.17485i			0.0588900i
$399$	−1.43140	+	29.8728i	−0.0716597	+	1.49551i
$400$		0			0
$401$			2.52416i			0.126051i	0.998012	+	0.0630254i	$0.0200749\pi$
$401$			2.52416i			0.126051i	−0.998012	+	0.0630254i	$0.979925\pi$
$402$	−21.3713	−	1.02404i	−1.06591	−	0.0510745i
$403$	43.9750			2.19055
$404$	6.73948			0.335302
$405$		0			0
$406$		−	22.1070i		−	1.09715i
$407$	17.3281	+	6.75063i	0.858924	+	0.334616i
$408$	−4.70691	−	0.225539i	−0.233027	−	0.0111658i
$409$			1.07974i			0.0533895i	0.999644	+	0.0266948i	$0.00849822\pi$
$409$			1.07974i			0.0533895i	−0.999644	+	0.0266948i	$0.991502\pi$
$410$		0			0
$411$	−36.2303	−	1.73603i	−1.78711	−	0.0856321i
$412$		−	5.25186i		−	0.258740i
$413$			23.6134i			1.16194i
$414$	0.478566	−	4.98228i	0.0235203	−	0.244866i
$415$		0			0
$416$		−	4.51238i		−	0.221238i
$417$	−1.28873	+	26.8953i	−0.0631093	+	1.31707i
$418$	−4.78267	+	12.2766i	−0.233928	+	0.600469i
$419$		−	27.6897i		−	1.35273i	−0.736566	−	0.676366i	$-0.763554\pi$
$419$		−	27.6897i		−	1.35273i	0.736566	−	0.676366i	$-0.236446\pi$
$420$		0			0
$421$	31.0847			1.51498			0.757488	−	0.652849i	$-0.226426\pi$
$421$	31.0847			1.51498			0.757488	+	0.652849i	$0.226426\pi$
$422$	−21.1498			−1.02956
$423$	−27.6284	−	2.65381i	−1.34334	−	0.129033i
$424$		−	3.05225i		−	0.148230i
$425$		0			0
$426$	6.24053	+	0.299024i	0.302354	+	0.0144878i
$427$			50.2666i			2.43257i
$428$			6.25707i			0.302447i
$429$	10.5549	−	23.6754i	0.509593	−	1.14306i
$430$		0			0
$431$	2.86529			0.138016			0.0690080	−	0.997616i	$-0.478017\pi$
$431$	2.86529			0.138016			0.0690080	+	0.997616i	$0.478017\pi$
$432$	−5.14264	−	0.743810i	−0.247425	−	0.0357866i
$433$			14.8158i			0.712000i	0.934486	+	0.356000i	$0.115860\pi$
$433$			14.8158i			0.712000i	−0.934486	+	0.356000i	$0.884140\pi$
$434$			42.3592i			2.03331i
$435$		0			0
$436$			17.9168i			0.858060i
$437$			6.62776i			0.317049i
$438$	0.113158	−	2.36157i	0.00540691	−	0.112840i
$439$		−	11.3108i		−	0.539836i	−0.962883	−	0.269918i	$-0.913003\pi$
$439$		−	11.3108i		−	0.539836i	0.962883	−	0.269918i	$-0.0869966\pi$
$440$		0			0
$441$	35.5149	+	3.41133i	1.69118	+	0.162444i
$442$	−12.2766			−0.583939
$443$	−1.60476			−0.0762447			−0.0381223	−	0.999273i	$-0.512138\pi$
$443$	−1.60476			−0.0762447			−0.0381223	+	0.999273i	$0.512138\pi$
$444$	0.464822	−	9.70066i	0.0220595	−	0.460373i
$445$		0			0
$446$	−22.6382			−1.07195
$447$	40.2900	+	1.93056i	1.90565	+	0.0913123i
$448$	4.34658			0.205357
$449$			4.00000i			0.188772i	0.995536	+	0.0943858i	$0.0300887\pi$
$449$			4.00000i			0.188772i	−0.995536	+	0.0943858i	$0.969911\pi$
$450$		0			0
$451$	3.51583	−	9.02476i	0.165554	−	0.424959i
$452$	−8.51238			−0.400389
$453$	0.898952	−	18.7608i	0.0422365	−	0.881459i
$454$	23.5758			1.10647
$455$		0			0
$456$	6.87271	+	0.329316i	0.321844	+	0.0154217i
$457$	−32.8716			−1.53767			−0.768835	−	0.639448i	$-0.779163\pi$
$457$	−32.8716			−1.53767			−0.768835	+	0.639448i	$0.779163\pi$
$458$			3.50893i			0.163962i
$459$	−2.02365	+	13.9913i	−0.0944559	+	0.653060i
$460$		0			0
$461$	15.9387			0.742339			0.371170	−	0.928565i	$-0.378957\pi$
$461$	15.9387			0.742339			0.371170	+	0.928565i	$0.378957\pi$
$462$	22.8055	+	10.1670i	1.06101	+	0.473014i
$463$		−	10.4842i		−	0.487241i	−0.969871	−	0.243620i	$-0.921665\pi$
$463$		−	10.4842i		−	0.487241i	0.969871	−	0.243620i	$-0.0783351\pi$
$464$	−5.08606			−0.236114
$465$		0			0
$466$	−9.84991			−0.456288
$467$	2.64436			0.122367			0.0611833	−	0.998127i	$-0.480513\pi$
$467$	2.64436			0.122367			0.0611833	+	0.998127i	$0.480513\pi$
$468$	−13.4751	−	1.29433i	−0.622888	−	0.0598306i
$469$		−	53.6929i		−	2.47931i
$470$		0			0
$471$	0.919021	−	19.1796i	0.0423463	−	0.883750i
$472$	5.43264			0.250058
$473$	3.91505	−	10.0495i	0.180014	−	0.462077i
$474$	1.85303	+	0.0887907i	0.0851124	+	0.00407829i
$475$		0			0
$476$		−	11.8255i		−	0.542023i
$477$	−9.11479	−	0.875509i	−0.417338	−	0.0400868i
$478$		−	24.1540i		−	1.10478i
$479$	28.6082			1.30714			0.653571	−	0.756865i	$-0.273270\pi$
$479$	28.6082			1.30714			0.653571	+	0.756865i	$0.273270\pi$
$480$		0			0
$481$		−	25.3014i		−	1.15364i
$482$	4.69316			0.213768
$483$	12.5462	+	0.601170i	0.570872	+	0.0273542i
$484$	8.10105	+	7.44131i	0.368229	+	0.338241i
$485$		0			0
$486$	−3.69633	+	15.1439i	−0.167669	+	0.686940i
$487$		−	25.5584i		−	1.15816i	−0.815269	−	0.579082i	$-0.803411\pi$
$487$		−	25.5584i		−	1.15816i	0.815269	−	0.579082i	$-0.196589\pi$
$488$	11.5646			0.523506
$489$	−0.345340	+	7.20710i	−0.0156168	+	0.325917i
$490$		0			0
$491$	−30.0732			−1.35718			−0.678592	−	0.734516i	$-0.737409\pi$
$491$	−30.0732			−1.35718			−0.678592	+	0.734516i	$0.737409\pi$
$492$	−5.05225	−	0.242086i	−0.227773	−	0.0109141i
$493$			13.8374i			0.623205i
$494$	17.9255			0.806505
$495$		0			0
$496$	9.74541			0.437582
$497$			15.6786i			0.703280i
$498$	25.2394	+	1.20938i	1.13100	+	0.0541937i
$499$	−13.6503			−0.611071			−0.305536	−	0.952181i	$-0.598835\pi$
$499$	−13.6503			−0.611071			−0.305536	+	0.952181i	$0.598835\pi$
$500$		0			0
$501$	−0.728538	+	15.2043i	−0.0325487	+	0.679278i
$502$	10.5424			0.470528
$503$			22.0495i			0.983139i	0.870838	+	0.491570i	$0.163577\pi$
$503$			22.0495i			0.983139i	−0.870838	+	0.491570i	$0.836423\pi$
$504$	1.24678	−	12.9800i	0.0555358	−	0.578175i
$505$		0			0
$506$	5.15603	+	2.00866i	0.229213	+	0.0892959i
$507$	−12.7360	−	0.610265i	−0.565626	−	0.0271028i
$508$	8.95024			0.397103
$509$		−	17.7660i		−	0.787464i	−0.919225	−	0.393732i	$-0.871184\pi$
$509$		−	17.7660i		−	0.787464i	0.919225	−	0.393732i	$-0.128816\pi$
$510$		0			0
$511$	5.93316			0.262467
$512$		−	1.00000i		−	0.0441942i
$513$	2.95479	−	20.4292i	0.130457	−	0.901971i
$514$		−	11.0334i		−	0.486663i
$515$		0			0
$516$	−5.62593	−	0.269575i	−0.247668	−	0.0118674i
$517$	11.1387	−	28.5919i	0.489879	−	1.25747i
$518$	24.3717			1.07083
$519$	0.220775	−	4.60749i	0.00969096	−	0.202247i
$520$		0			0
$521$		−	21.0074i		−	0.920352i	−0.887828	−	0.460176i	$-0.847786\pi$
$521$		−	21.0074i		−	0.920352i	0.887828	−	0.460176i	$-0.152214\pi$
$522$	−1.45889	+	15.1883i	−0.0638538	+	0.664773i
$523$	−41.7779			−1.82682			−0.913409	−	0.407042i	$-0.866560\pi$
$523$	−41.7779			−1.82682			−0.913409	+	0.407042i	$0.866560\pi$
$524$	−12.3379			−0.538985
$525$		0			0
$526$	−30.8378			−1.34459
$527$		−	26.5139i		−	1.15496i
$528$	2.33909	−	5.24678i	0.101796	−	0.228337i
$529$	−20.2164			−0.878975
$530$		0			0
$531$	1.55830	−	16.2233i	0.0676246	−	0.704030i
$532$			17.2668i			0.748613i
$533$	−13.1773			−0.570774
$534$	−6.50144	−	0.311526i	−0.281345	−	0.0134811i
$535$		0			0
$536$	−12.3529			−0.533564
$537$	−0.933483	+	19.4814i	−0.0402828	+	0.840686i
$538$	−9.58345			−0.413172
$539$	−14.3182	+	36.7533i	−0.616729	+	1.58308i
$540$		0			0
$541$			6.18327i			0.265840i	0.991127	+	0.132920i	$0.0424353\pi$
$541$			6.18327i			0.265840i	−0.991127	+	0.132920i	$0.957565\pi$
$542$	−21.3400			−0.916632
$543$	1.23055	+	0.0589636i	0.0528078	+	0.00253037i
$544$	−2.72065			−0.116647
$545$		0			0
$546$	1.62593	−	33.9325i	0.0695833	−	1.45218i
$547$	−21.2999			−0.910720			−0.455360	−	0.890307i	$-0.650489\pi$
$547$	−21.2999			−0.910720			−0.455360	+	0.890307i	$0.650489\pi$
$548$	−20.9416			−0.894580
$549$	3.31721	−	34.5349i	0.141575	−	1.47392i
$550$		0			0
$551$		−	20.2044i		−	0.860738i
$552$	0.138309	−	2.88645i	0.00588681	−	0.122855i
$553$			4.65551i			0.197972i
$554$		−	7.43264i		−	0.315783i
$555$		0			0
$556$			15.5458i			0.659289i
$557$		−	5.87740i		−	0.249033i	−0.992218	−	0.124517i	$-0.960262\pi$
$557$		−	5.87740i		−	0.249033i	0.992218	−	0.124517i	$-0.0397380\pi$
$558$	2.79538	−	29.1023i	0.118338	−	1.23200i
$559$	−14.6736			−0.620628
$560$		0			0
$561$	−14.2747	−	6.36385i	−0.602676	−	0.268682i
$562$		−	20.0300i		−	0.844913i
$563$			21.9442i			0.924839i	0.886661	+	0.462420i	$0.153019\pi$
$563$			21.9442i			0.924839i	−0.886661	+	0.462420i	$0.846981\pi$
$564$	−16.0063	−	0.766968i	−0.673988	−	0.0322952i
$565$		0			0
$566$		−	5.98189i		−	0.251438i
$567$	−38.4040	−	7.44639i	−1.61282	−	0.312719i
$568$	3.60710			0.151351
$569$	−15.7284			−0.659367			−0.329683	−	0.944092i	$-0.606942\pi$
$569$	−15.7284			−0.659367			−0.329683	+	0.944092i	$0.606942\pi$
$570$		0			0
$571$			39.4633i			1.65149i	0.564044	+	0.825745i	$0.309245\pi$
$571$			39.4633i			1.65149i	−0.564044	+	0.825745i	$0.690755\pi$
$572$	5.43264	−	13.9450i	0.227150	−	0.583071i
$573$	−1.62359	+	33.8837i	−0.0678265	+	1.41551i
$574$		−	12.6932i		−	0.529802i
$575$		0			0
$576$	−2.98626	−	0.286841i	−0.124427	−	0.0119517i
$577$		−	12.1721i		−	0.506732i	−0.967370	−	0.253366i	$-0.918462\pi$
$577$		−	12.1721i		−	0.506732i	0.967370	−	0.253366i	$-0.0815377\pi$
$578$		−	9.59805i		−	0.399226i
$579$	15.2747	+	0.731912i	0.634796	+	0.0304172i
$580$		0			0
$581$			63.4108i			2.63072i
$582$	22.1408	+	1.06091i	0.917765	+	0.0439762i
$583$	3.67473	−	9.43264i	0.152192	−	0.390660i
$584$		−	1.36502i		−	0.0564848i
$585$		0			0
$586$	22.9998			0.950111
$587$	−3.76175			−0.155264			−0.0776321	−	0.996982i	$-0.524736\pi$
$587$	−3.76175			−0.155264			−0.0776321	+	0.996982i	$0.524736\pi$
$588$	20.5753	+	0.985897i	0.848510	+	0.0406577i
$589$			38.7138i			1.59517i
$590$		0			0
$591$	1.07356	−	22.4048i	0.0441603	−	0.921609i
$592$		−	5.60710i		−	0.230451i
$593$			19.5389i			0.802367i	0.915998	+	0.401183i	$0.131401\pi$
$593$			19.5389i			0.802367i	−0.915998	+	0.401183i	$0.868599\pi$
$594$	−14.9973	−	8.49011i	−0.615345	−	0.348353i
$595$		0			0
$596$	23.2882			0.953920
$597$	2.03257	+	0.0973938i	0.0831876	+	0.00398606i
$598$		−	7.52848i		−	0.307862i
$599$		−	33.4776i		−	1.36786i	−0.729549	−	0.683929i	$-0.760270\pi$
$599$		−	33.4776i		−	1.36786i	0.729549	−	0.683929i	$-0.239730\pi$
$600$		0			0
$601$			22.9203i			0.934937i	0.884010	+	0.467469i	$0.154834\pi$
$601$			22.9203i			0.934937i	−0.884010	+	0.467469i	$0.845166\pi$
$602$		−	14.1345i		−	0.576078i
$603$	−3.54332	+	36.8889i	−0.144295	+	1.50223i
$604$		−	10.8440i		−	0.441235i
$605$		0			0
$606$	0.558695	−	11.6597i	0.0226954	−	0.473645i
$607$	−7.21187			−0.292721			−0.146360	−	0.989231i	$-0.546756\pi$
$607$	−7.21187			−0.292721			−0.146360	+	0.989231i	$0.546756\pi$
$608$	3.97251			0.161107
$609$	−38.2465	−	1.83264i	−1.54983	−	0.0742624i
$610$		0			0
$611$	−41.7479			−1.68894
$612$	−0.780394	+	8.12456i	−0.0315456	+	0.328416i
$613$	−10.9911			−0.443926			−0.221963	−	0.975055i	$-0.571246\pi$
$613$	−10.9911			−0.443926			−0.221963	+	0.975055i	$0.571246\pi$
$614$		−	27.2645i		−	1.10031i
$615$		0			0
$616$	13.4326	+	5.23303i	0.541217	+	0.210845i
$617$	9.52449			0.383442			0.191721	−	0.981450i	$-0.438593\pi$
$617$	9.52449			0.383442			0.191721	+	0.981450i	$0.438593\pi$
$618$	−9.08606	−	0.435373i	−0.365495	−	0.0175133i
$619$	−20.5329			−0.825287			−0.412644	−	0.910893i	$-0.635395\pi$
$619$	−20.5329			−0.825287			−0.412644	+	0.910893i	$0.635395\pi$
$620$		0			0
$621$	−8.58001	−	1.24098i	−0.344304	−	0.0497987i
$622$	0.0613019			0.00245798
$623$		−	16.3341i		−	0.654411i
$624$	−7.80671	−	0.374071i	−0.312519	−	0.0149748i
$625$		0			0
$626$	22.2766			0.890353
$627$	20.8429	+	9.29206i	0.832384	+	0.371089i
$628$		−	11.0861i		−	0.442382i
$629$	−15.2550			−0.608256
$630$		0			0
$631$	−29.6731			−1.18127			−0.590634	−	0.806940i	$-0.701122\pi$
$631$	−29.6731			−1.18127			−0.590634	+	0.806940i	$0.701122\pi$
$632$	1.07107			0.0426050
$633$	−1.75330	+	36.5906i	−0.0696873	+	1.45435i
$634$		−	2.48169i		−	0.0985604i
$635$		0			0
$636$	−5.28059	−	0.253028i	−0.209389	−	0.0100332i
$637$	53.6647			2.12627
$638$	−15.7179	−	6.12332i	−0.622279	−	0.242425i
$639$	1.03466	−	10.7717i	0.0409307	−	0.426123i
$640$		0			0
$641$			19.0947i			0.754196i	0.926173	+	0.377098i	$0.123078\pi$
$641$			19.0947i			0.754196i	−0.926173	+	0.377098i	$0.876922\pi$
$642$	10.8251	+	0.518704i	0.427235	+	0.0204716i
$643$		−	22.0663i		−	0.870209i	−0.900380	−	0.435104i	$-0.856711\pi$
$643$		−	22.0663i		−	0.870209i	0.900380	−	0.435104i	$-0.143289\pi$
$644$	7.25186			0.285763
$645$		0			0
$646$		−	10.8078i		−	0.425228i
$647$	18.5832			0.730581			0.365291	−	0.930894i	$-0.380970\pi$
$647$	18.5832			0.730581			0.365291	+	0.930894i	$0.380970\pi$
$648$	−1.71316	+	8.83544i	−0.0672993	+	0.347089i
$649$	16.7890	+	6.54059i	0.659026	+	0.256740i
$650$		0			0
$651$	73.2843	+	3.51153i	2.87224	+	0.137628i
$652$			4.16580i			0.163145i
$653$	−31.2063			−1.22120			−0.610598	−	0.791941i	$-0.709071\pi$
$653$	−31.2063			−1.22120			−0.610598	+	0.791941i	$0.709071\pi$
$654$	30.9973	+	1.48528i	1.21209	+	0.0580791i
$655$		0			0
$656$	−2.92026			−0.114017
$657$	−4.07629	−	0.391542i	−0.159031	−	0.0152755i
$658$		−	40.2140i		−	1.56770i
$659$	−26.6138			−1.03672			−0.518362	−	0.855161i	$-0.673458\pi$
$659$	−26.6138			−1.03672			−0.518362	+	0.855161i	$0.673458\pi$
$660$		0			0
$661$	−4.07452			−0.158481			−0.0792403	−	0.996856i	$-0.525249\pi$
$661$	−4.07452			−0.158481			−0.0792403	+	0.996856i	$0.525249\pi$
$662$			11.2519i			0.437316i
$663$	−1.01772	+	21.2394i	−0.0395248	+	0.824868i
$664$	14.5887			0.566150
$665$		0			0
$666$	−16.7442	−	1.60835i	−0.648826	−	0.0623221i
$667$	−8.48561			−0.328564
$668$			8.78828i			0.340029i
$669$	−1.87668	+	39.1656i	−0.0725566	+	1.51423i
$670$		0			0
$671$	35.7392	+	13.9231i	1.37970	+	0.537497i
$672$	0.360326	−	7.51987i	0.0138999	−	0.290085i
$673$	−0.828988			−0.0319551			−0.0159776	−	0.999872i	$-0.505086\pi$
$673$	−0.828988			−0.0319551			−0.0159776	+	0.999872i	$0.505086\pi$
$674$			0.968917i			0.0373213i
$675$		0			0
$676$	−7.36157			−0.283137
$677$		−	6.51415i		−	0.250359i	−0.992134	−	0.125179i	$-0.960049\pi$
$677$		−	6.51415i		−	0.250359i	0.992134	−	0.125179i	$-0.0399507\pi$
$678$	−0.705666	+	14.7270i	−0.0271009	+	0.565586i
$679$			55.6261i			2.13473i
$680$		0			0
$681$	1.95440	−	40.7876i	0.0748929	−	1.56299i
$682$	30.1171	+	11.7329i	1.15325	+	0.449276i
$683$	−8.99407			−0.344148			−0.172074	−	0.985084i	$-0.555047\pi$
$683$	−8.99407			−0.344148			−0.172074	+	0.985084i	$0.555047\pi$
$684$	1.13948	−	11.8629i	0.0435690	−	0.453591i
$685$		0			0
$686$			21.2668i			0.811972i
$687$	6.07068	+	0.290886i	0.231611	+	0.0110980i
$688$	−3.25186			−0.123976
$689$	−13.7729			−0.524706
$690$		0			0
$691$	−39.7848			−1.51348			−0.756742	−	0.653714i	$-0.773210\pi$
$691$	−39.7848			−1.51348			−0.756742	+	0.653714i	$0.773210\pi$
$692$		−	2.66319i		−	0.101239i
$693$	19.4802	−	38.6123i	0.739992	−	1.46676i
$694$	−1.59388			−0.0605030
$695$		0			0
$696$	−0.421628	+	8.79922i	−0.0159818	+	0.333534i
$697$			7.94502i			0.300939i
$698$	18.9416			0.716949
$699$	−0.816545	+	17.0410i	−0.0308846	+	0.644549i
$700$		0			0
$701$	40.4528			1.52788			0.763941	−	0.645286i	$-0.223262\pi$
$701$	40.4528			1.52788			0.763941	+	0.645286i	$0.223262\pi$
$702$	−3.35635	+	23.2055i	−0.126677	+	0.875837i
$703$	22.2743			0.840090
$704$	1.20394	−	3.09039i	0.0453753	−	0.116474i
$705$		0			0
$706$		−	0.806322i		−	0.0303463i
$707$	29.2937			1.10170
$708$	0.450359	−	9.39883i	0.0169255	−	0.353230i
$709$	31.3126			1.17597			0.587984	−	0.808872i	$-0.299922\pi$
$709$	31.3126			1.17597			0.587984	+	0.808872i	$0.299922\pi$
$710$		0			0
$711$	0.307228	−	3.19850i	0.0115219	−	0.119953i
$712$	−3.75791			−0.140834
$713$	16.2593			0.608915
$714$	−20.4590	−	0.980323i	−0.765657	−	0.0366877i
$715$		0			0
$716$			11.2605i			0.420825i
$717$	−41.7880	−	2.00234i	−1.56060	−	0.0747787i
$718$			6.83531i			0.255092i
$719$			49.2324i			1.83606i	0.396513	+	0.918029i	$0.370220\pi$
$719$			49.2324i			1.83606i	−0.396513	+	0.918029i	$0.629780\pi$
$720$		0			0
$721$		−	22.8276i		−	0.850145i
$722$		−	3.21916i		−	0.119805i
$723$	0.389058	−	8.11948i	0.0144692	−	0.301967i
$724$	0.711272			0.0264342
$725$		0			0
$726$	13.5455	−	13.3985i	0.502721	−	0.497264i
$727$			22.6682i			0.840716i	0.907358	+	0.420358i	$0.138095\pi$
$727$			22.6682i			0.840716i	−0.907358	+	0.420358i	$0.861905\pi$
$728$		−	19.6134i		−	0.726922i
$729$	25.8935	+	7.65030i	0.959018	+	0.283344i
$730$		0			0
$731$			8.84718i			0.327225i
$732$	0.958694	−	20.0076i	0.0354343	−	0.739501i
$733$	−0.210758			−0.00778452			−0.00389226	−	0.999992i	$-0.501239\pi$
$733$	−0.210758			−0.00778452			−0.00389226	+	0.999992i	$0.501239\pi$
$734$	3.28873			0.121389
$735$		0			0
$736$		−	1.66840i		−	0.0614982i
$737$	−38.1753	−	14.8722i	−1.40621	−	0.547824i
$738$	−0.837650	+	8.72065i	−0.0308343	+	0.321012i
$739$			14.8053i			0.544623i	0.962209	+	0.272312i	$0.0877881\pi$
$739$			14.8053i			0.544623i	−0.962209	+	0.272312i	$0.912212\pi$
$740$		0			0
$741$	1.48600	−	31.0123i	0.0545896	−	1.13926i
$742$		−	13.2668i		−	0.487041i
$743$		−	19.2717i		−	0.707009i	−0.935433	−	0.353504i	$-0.884990\pi$
$743$		−	19.2717i		−	0.707009i	0.935433	−	0.353504i	$-0.115010\pi$
$744$	0.807883	−	16.8602i	0.0296184	−	0.618125i
$745$		0			0
$746$		−	11.3650i		−	0.416103i
$747$	4.18462	−	43.5655i	0.153107	−	1.59398i
$748$	−8.40788	−	3.27551i	−0.307423	−	0.119764i
$749$			27.1969i			0.993752i
$750$		0			0
$751$	−24.6107			−0.898057			−0.449029	−	0.893517i	$-0.648230\pi$
$751$	−24.6107			−0.898057			−0.449029	+	0.893517i	$0.648230\pi$
$752$	−9.25186			−0.337381
$753$	0.873948	−	18.2390i	0.0318484	−	0.664665i
$754$			22.9502i			0.835798i
$755$		0			0
$756$	−22.3529	−	3.23303i	−0.812967	−	0.117584i
$757$			21.6166i			0.785670i	0.919609	+	0.392835i	$0.128506\pi$
$757$			21.6166i			0.785670i	−0.919609	+	0.392835i	$0.871494\pi$
$758$			26.1848i			0.951074i
$759$	3.90255	−	8.75375i	0.141653	−	0.317741i
$760$		0			0
$761$	−34.6751			−1.25697			−0.628485	−	0.777822i	$-0.716325\pi$
$761$	−34.6751			−1.25697			−0.628485	+	0.777822i	$0.716325\pi$
$762$	0.741964	−	15.4845i	0.0268785	−	0.560944i
$763$			77.8769i			2.81933i
$764$			19.5852i			0.708568i
$765$		0			0
$766$			18.7796i			0.678533i
$767$		−	24.5141i		−	0.885155i
$768$	−1.73007	−	0.0828988i	−0.0624284	−	0.00299135i
$769$			16.8772i			0.608606i	0.952575	+	0.304303i	$0.0984235\pi$
$769$			16.8772i			0.608606i	−0.952575	+	0.304303i	$0.901577\pi$
$770$		0			0
$771$	−19.0885	−	0.914657i	−0.687457	−	0.0329406i
$772$	8.82899			0.317762
$773$	−8.07701			−0.290510			−0.145255	−	0.989394i	$-0.546400\pi$
$773$	−8.07701			−0.290510			−0.145255	+	0.989394i	$0.546400\pi$
$774$	−0.932765	+	9.71088i	−0.0335276	+	0.349050i
$775$		0			0
$776$	12.7977			0.459409
$777$	2.02039	−	42.1647i	0.0724810	−	1.51265i
$778$	−24.4661			−0.877151
$779$		−	11.6008i		−	0.415641i
$780$		0			0
$781$	11.1474	+	4.34274i	0.398884	+	0.155396i
$782$	−4.53915			−0.162320
$783$	26.1558	+	3.78306i	0.934731	+	0.135196i
$784$	11.8928			0.424742
$785$		0			0
$786$	−1.02280	+	21.3454i	−0.0364820	+	0.761366i
$787$	15.2992			0.545356			0.272678	−	0.962105i	$-0.412091\pi$
$787$	15.2992			0.545356			0.272678	+	0.962105i	$0.412091\pi$
$788$		−	12.9502i		−	0.461333i
$789$	−2.55642	+	53.3514i	−0.0910108	+	1.89936i
$790$		0			0
$791$	−36.9998			−1.31556
$792$	−8.88336	−	4.48173i	−0.315657	−	0.159251i
$793$		−	52.1840i		−	1.85311i
$794$	−34.0708			−1.20913
$795$		0			0
$796$	1.17485			0.0416415
$797$	4.37200			0.154864			0.0774321	−	0.996998i	$-0.475328\pi$
$797$	4.37200			0.154864			0.0774321	+	0.996998i	$0.475328\pi$
$798$	29.8728	+	1.43140i	1.05748	+	0.0506710i
$799$			25.1711i			0.890489i
$800$		0			0
$801$	−1.07792	+	11.2221i	−0.0380865	+	0.396513i
$802$	2.52416			0.0891313
$803$	1.64340	−	4.21844i	0.0579944	−	0.148865i
$804$	−1.02404	+	21.3713i	−0.0361151	+	0.753709i
$805$		0			0
$806$		−	43.9750i		−	1.54895i
$807$	−0.794457	+	16.5800i	−0.0279662	+	0.583644i
$808$		−	6.73948i		−	0.237094i
$809$	16.6459			0.585237			0.292619	−	0.956229i	$-0.405473\pi$
$809$	16.6459			0.585237			0.292619	+	0.956229i	$0.405473\pi$
$810$		0			0
$811$			35.1018i			1.23259i	0.787515	+	0.616295i	$0.211367\pi$
$811$			35.1018i			1.23259i	−0.787515	+	0.616295i	$0.788633\pi$
$812$	−22.1070			−0.775803
$813$	−1.76906	+	36.9196i	−0.0620437	+	1.29483i
$814$	6.75063	−	17.3281i	0.236609	−	0.607351i
$815$		0			0
$816$	−0.225539	+	4.70691i	−0.00789544	+	0.164775i
$817$		−	12.9180i		−	0.451945i
$818$	1.07974			0.0377521
$819$	−58.5707	−	5.62593i	−2.04663	−	0.196586i
$820$		0			0
$821$	4.78900			0.167137			0.0835686	−	0.996502i	$-0.473368\pi$
$821$	4.78900			0.167137			0.0835686	+	0.996502i	$0.473368\pi$
$822$	−1.73603	+	36.2303i	−0.0605510	+	1.26368i
$823$		−	19.7053i		−	0.686883i	−0.939174	−	0.343441i	$-0.888407\pi$
$823$		−	19.7053i		−	0.686883i	0.939174	−	0.343441i	$-0.111593\pi$
$824$	−5.25186			−0.182957
$825$		0			0
$826$	23.6134			0.821616
$827$			49.7179i			1.72886i	0.502752	+	0.864431i	$0.332321\pi$
$827$			49.7179i			1.72886i	−0.502752	+	0.864431i	$0.667679\pi$
$828$	−4.98228	−	0.478566i	−0.173146	−	0.0166313i
$829$	−43.5766			−1.51348			−0.756738	−	0.653718i	$-0.773208\pi$
$829$	−43.5766			−1.51348			−0.756738	+	0.653718i	$0.773208\pi$
$830$		0			0
$831$	−12.8590	−	0.616157i	−0.446072	−	0.0213743i
$832$	−4.51238			−0.156439
$833$		−	32.3561i		−	1.12107i
$834$	26.8953	+	1.28873i	0.931307	+	0.0446250i
$835$		0			0
$836$	12.2766	+	4.78267i	0.424596	+	0.165412i
$837$	−50.1171	−	7.24874i	−1.73230	−	0.250553i
$838$	−27.6897			−0.956525
$839$			5.89727i			0.203596i	0.994805	+	0.101798i	$0.0324596\pi$
$839$			5.89727i			0.203596i	−0.994805	+	0.101798i	$0.967540\pi$
$840$		0			0
$841$	−3.13198			−0.107999
$842$		−	31.0847i		−	1.07125i
$843$	−34.6532	−	1.66046i	−1.19352	−	0.0571893i
$844$			21.1498i			0.728008i
$845$		0			0
$846$	−2.65381	+	27.6284i	−0.0912399	+	0.949884i
$847$	35.2119	+	32.3442i	1.20989	+	1.11136i
$848$	−3.05225			−0.104815
$849$	−10.3491	−	0.495892i	−0.355179	−	0.0170190i
$850$		0			0
$851$		−	9.35492i		−	0.320682i
$852$	0.299024	−	6.24053i	0.0102444	−	0.213797i
$853$	25.2919			0.865979			0.432990	−	0.901399i	$-0.357459\pi$
$853$	25.2919			0.865979			0.432990	+	0.901399i	$0.357459\pi$
$854$	50.2666			1.72009
$855$		0			0
$856$	6.25707			0.213862
$857$		−	25.0718i		−	0.856436i	−0.903675	−	0.428218i	$-0.859142\pi$
$857$		−	25.0718i		−	0.856436i	0.903675	−	0.428218i	$-0.140858\pi$
$858$	−23.6754	−	10.5549i	−0.808266	−	0.360337i
$859$	−12.2263			−0.417157			−0.208578	−	0.978006i	$-0.566884\pi$
$859$	−12.2263			−0.417157			−0.208578	+	0.978006i	$0.566884\pi$
$860$		0			0
$861$	−21.9600	−	1.05225i	−0.748395	−	0.0358605i
$862$		−	2.86529i		−	0.0975920i
$863$	−16.5713			−0.564095			−0.282048	−	0.959400i	$-0.591014\pi$
$863$	−16.5713			−0.564095			−0.282048	+	0.959400i	$0.591014\pi$
$864$	−0.743810	+	5.14264i	−0.0253049	+	0.174956i
$865$		0			0
$866$	14.8158			0.503460
$867$	−16.6053	−	0.795667i	−0.563944	−	0.0270223i
$868$	42.3592			1.43777
$869$	3.31004	+	1.28951i	0.112285	+	0.0437437i
$870$		0			0
$871$			55.7410i			1.88871i
$872$	17.9168			0.606740
$873$	3.67089	−	38.2171i	0.124241	−	1.29345i
$874$	6.62776			0.224187
$875$		0			0
$876$	−2.36157	−	0.113158i	−0.0797900	−	0.00382326i
$877$	−41.5248			−1.40219			−0.701096	−	0.713067i	$-0.747306\pi$
$877$	−41.5248			−1.40219			−0.701096	+	0.713067i	$0.747306\pi$
$878$	−11.3108			−0.381722
$879$	1.90665	−	39.7911i	0.0643098	−	1.34212i
$880$		0			0
$881$		−	18.8053i		−	0.633568i	−0.948498	−	0.316784i	$-0.897397\pi$
$881$		−	18.8053i		−	0.633568i	0.948498	−	0.316784i	$-0.102603\pi$
$882$	3.41133	−	35.5149i	0.114866	−	1.19585i
$883$			12.9252i			0.434966i	0.976064	+	0.217483i	$0.0697847\pi$
$883$			12.9252i			0.434966i	−0.976064	+	0.217483i	$0.930215\pi$
$884$			12.2766i			0.412907i
$885$		0			0
$886$			1.60476i			0.0539131i
$887$		−	43.1169i		−	1.44772i	−0.689945	−	0.723862i	$-0.742365\pi$
$887$		−	43.1169i		−	1.44772i	0.689945	−	0.723862i	$-0.257635\pi$
$888$	−9.70066	−	0.464822i	−0.325533	−	0.0155984i
$889$	38.9029			1.30476
$890$		0			0
$891$	−15.9317	+	25.2424i	−0.533732	+	0.845654i
$892$			22.6382i			0.757983i
$893$		−	36.7531i		−	1.22990i
$894$	1.93056	−	40.2900i	0.0645676	−	1.34750i
$895$		0			0
$896$		−	4.34658i		−	0.145209i
$897$	−13.0248	−	0.624101i	−0.434884	−	0.0208381i
$898$	4.00000			0.133482
$899$	−49.5658			−1.65311
$900$		0			0
$901$			8.30411i			0.276650i
$902$	−9.02476	−	3.51583i	−0.300492	−	0.117064i
$903$	−24.4536	−	1.17173i	−0.813764	−	0.0389927i
$904$			8.51238i			0.283118i
$905$		0			0
$906$	−18.7608	−	0.898952i	−0.623286	−	0.0298657i
$907$		−	16.4347i		−	0.545706i	−0.962056	−	0.272853i	$-0.912033\pi$
$907$		−	16.4347i		−	0.545706i	0.962056	−	0.272853i	$-0.0879673\pi$
$908$		−	23.5758i		−	0.782390i
$909$	−20.1258	−	1.93316i	−0.667531	−	0.0641188i
$910$		0			0
$911$		−	48.2030i		−	1.59704i	−0.601971	−	0.798518i	$-0.705618\pi$
$911$		−	48.2030i		−	1.59704i	0.601971	−	0.798518i	$-0.294382\pi$
$912$	0.329316	−	6.87271i	0.0109048	−	0.227578i
$913$	45.0847	+	17.5639i	1.49209	+	0.581281i
$914$			32.8716i			1.08730i
$915$		0			0
$916$	3.50893			0.115938
$917$	−53.6278			−1.77095
$918$	13.9913	+	2.02365i	0.461783	+	0.0667904i
$919$		−	33.3400i		−	1.09979i	−0.835235	−	0.549893i	$-0.814669\pi$
$919$		−	33.3400i		−	1.09979i	0.835235	−	0.549893i	$-0.185331\pi$
$920$		0			0
$921$	−47.1694	−	2.26019i	−1.55428	−	0.0744759i
$922$		−	15.9387i		−	0.524913i
$923$		−	16.2766i		−	0.535751i
$924$	10.1670	−	22.8055i	0.334471	−	0.750247i
$925$		0			0
$926$	−10.4842			−0.344531
$927$	−1.50645	+	15.6834i	−0.0494782	+	0.515110i
$928$			5.08606i			0.166958i
$929$		−	26.4142i		−	0.866622i	−0.901244	−	0.433311i	$-0.857345\pi$
$929$		−	26.4142i		−	0.866622i	0.901244	−	0.433311i	$-0.142655\pi$
$930$		0			0
$931$			47.2442i			1.54837i
$932$			9.84991i			0.322644i
$933$	0.00508185	−	0.106056i	0.000166372	−	0.00347213i
$934$		−	2.64436i		−	0.0865262i
$935$		0			0
$936$	−1.29433	+	13.4751i	−0.0423066	+	0.440448i
$937$	36.8009			1.20223			0.601116	−	0.799162i	$-0.294723\pi$
$937$	36.8009			1.20223			0.601116	+	0.799162i	$0.294723\pi$
$938$	−53.6929			−1.75314
$939$	1.84670	−	38.5400i	0.0602649	−	1.25771i
$940$		0			0
$941$	12.9934			0.423574			0.211787	−	0.977316i	$-0.432072\pi$
$941$	12.9934			0.423574			0.211787	+	0.977316i	$0.432072\pi$
$942$	−19.1796	−	0.919021i	−0.624906	−	0.0299433i
$943$	−4.87218			−0.158660
$944$		−	5.43264i		−	0.176817i
$945$		0			0
$946$	−10.0495	−	3.91505i	−0.326738	−	0.127289i
$947$	6.36307			0.206772			0.103386	−	0.994641i	$-0.467032\pi$
$947$	6.36307			0.206772			0.103386	+	0.994641i	$0.467032\pi$
$948$	0.0887907	−	1.85303i	0.00288379	−	0.0601836i
$949$	−6.15947			−0.199945
$950$		0			0
$951$	−4.29348	−	0.205729i	−0.139226	−	0.00667122i
$952$	−11.8255			−0.383268
$953$		−	29.7400i		−	0.963372i	−0.876344	−	0.481686i	$-0.840025\pi$
$953$		−	29.7400i		−	0.963372i	0.876344	−	0.481686i	$-0.159975\pi$
$954$	−0.875509	+	9.11479i	−0.0283456	+	0.295102i
$955$		0			0
$956$	−24.1540			−0.781197
$957$	−11.8967	+	26.6854i	−0.384567	+	0.862617i
$958$		−	28.6082i		−	0.924289i
$959$	−91.0243			−2.93933
$960$		0			0
$961$	63.9730			2.06365
$962$	−25.3014			−0.815749
$963$	1.79478	−	18.6852i	0.0578361	−	0.602123i
$964$		−	4.69316i		−	0.151157i
$965$		0			0
$966$	0.601170	−	12.5462i	0.0193423	−	0.403667i
$967$	36.5418			1.17510			0.587552	−	0.809186i	$-0.300092\pi$
$967$	36.5418			1.17510			0.587552	+	0.809186i	$0.300092\pi$
$968$	7.44131	−	8.10105i	0.239173	−	0.260378i
$969$	−18.6982	−	0.895955i	−0.600674	−	0.0287822i
$970$		0			0
$971$			22.7040i			0.728607i	0.931280	+	0.364304i	$0.118693\pi$
$971$			22.7040i			0.728607i	−0.931280	+	0.364304i	$0.881307\pi$
$972$	15.1439	+	3.69633i	0.485740	+	0.118560i
$973$			67.5711i			2.16623i
$974$	−25.5584			−0.818946
$975$		0			0
$976$		−	11.5646i		−	0.370175i
$977$	2.83708			0.0907662			0.0453831	−	0.998970i	$-0.485549\pi$
$977$	2.83708			0.0907662			0.0453831	+	0.998970i	$0.485549\pi$
$978$	7.20710	+	0.345340i	0.230458	+	0.0110427i
$979$	−11.6134	−	4.52431i	−0.371167	−	0.144598i
$980$		0			0
$981$	5.13927	−	53.5042i	0.164084	−	1.70826i
$982$			30.0732i			0.959673i
$983$	35.3487			1.12745			0.563724	−	0.825963i	$-0.309368\pi$
$983$	35.3487			1.12745			0.563724	+	0.825963i	$0.309368\pi$
$984$	−0.242086	+	5.05225i	−0.00771743	+	0.161060i
$985$		0			0
$986$	13.8374			0.440673
$987$	−69.5728	−	3.33369i	−2.21453	−	0.106112i
$988$		−	17.9255i		−	0.570285i
$989$	−5.42542			−0.172518
$990$		0			0
$991$	−20.0173			−0.635871			−0.317936	−	0.948112i	$-0.602990\pi$
$991$	−20.0173			−0.635871			−0.317936	+	0.948112i	$0.602990\pi$
$992$		−	9.74541i		−	0.309417i
$993$	19.4665	+	0.932765i	0.617749	+	0.0296004i
$994$	15.6786			0.497294
$995$		0			0
$996$	1.20938	−	25.2394i	0.0383208	−	0.799740i
$997$	6.80711			0.215583			0.107792	−	0.994174i	$-0.465622\pi$
$997$	6.80711			0.215583			0.107792	+	0.994174i	$0.465622\pi$
$998$			13.6503i			0.432093i
$999$	−4.17062	+	28.8353i	−0.131953	+	0.912309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.f.c.1649.1		8
3.2	odd	2		1650.2.f.f.1649.8		8
5.2	odd	4		1650.2.d.f.1451.6		8
5.3	odd	4		330.2.d.a.131.3	✓	8
5.4	even	2		1650.2.f.e.1649.8		8
11.10	odd	2		1650.2.f.d.1649.5		8
15.2	even	4		1650.2.d.c.1451.5		8
15.8	even	4		330.2.d.b.131.4	yes	8
15.14	odd	2		1650.2.f.d.1649.1		8
20.3	even	4		2640.2.f.b.1121.6		8
33.32	even	2		1650.2.f.e.1649.4		8
55.32	even	4		1650.2.d.c.1451.6		8
55.43	even	4		330.2.d.b.131.3	yes	8
55.54	odd	2		1650.2.f.f.1649.4		8
60.23	odd	4		2640.2.f.a.1121.5		8
165.32	odd	4		1650.2.d.f.1451.5		8
165.98	odd	4		330.2.d.a.131.4	yes	8
165.164	even	2	inner	1650.2.f.c.1649.5		8
220.43	odd	4		2640.2.f.a.1121.6		8
660.263	even	4		2640.2.f.b.1121.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.d.a.131.3	✓	8	5.3	odd	4
330.2.d.a.131.4	yes	8	165.98	odd	4
330.2.d.b.131.3	yes	8	55.43	even	4
330.2.d.b.131.4	yes	8	15.8	even	4
1650.2.d.c.1451.5		8	15.2	even	4
1650.2.d.c.1451.6		8	55.32	even	4
1650.2.d.f.1451.5		8	165.32	odd	4
1650.2.d.f.1451.6		8	5.2	odd	4
1650.2.f.c.1649.1		8	1.1	even	1	trivial
1650.2.f.c.1649.5		8	165.164	even	2	inner
1650.2.f.d.1649.1		8	15.14	odd	2
1650.2.f.d.1649.5		8	11.10	odd	2
1650.2.f.e.1649.4		8	33.32	even	2
1650.2.f.e.1649.8		8	5.4	even	2
1650.2.f.f.1649.4		8	55.54	odd	2
1650.2.f.f.1649.8		8	3.2	odd	2
2640.2.f.a.1121.5		8	60.23	odd	4
2640.2.f.a.1121.6		8	220.43	odd	4
2640.2.f.b.1121.5		8	660.263	even	4
2640.2.f.b.1121.6		8	20.3	even	4

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:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.73007 - 0.0828988i) q^{3} -1.00000 q^{4} +(-0.0828988 + 1.73007i) q^{6} -4.34658 q^{7} +1.00000i q^{8} +(2.98626 + 0.286841i) q^{9} +(-1.20394 + 3.09039i) q^{11} +(1.73007 + 0.0828988i) q^{12} +4.51238 q^{13} +4.34658i q^{14} +1.00000 q^{16} -2.72065i q^{17} +(0.286841 - 2.98626i) q^{18} +3.97251i q^{19} +(7.51987 + 0.360326i) q^{21} +(3.09039 + 1.20394i) q^{22} +1.66840 q^{23} +(0.0828988 - 1.73007i) q^{24} -4.51238i q^{26} +(-5.14264 - 0.743810i) q^{27} +4.34658 q^{28} -5.08606 q^{29} +9.74541 q^{31} -1.00000i q^{32} +(2.33909 - 5.24678i) q^{33} -2.72065 q^{34} +(-2.98626 - 0.286841i) q^{36} -5.60710i q^{37} +3.97251 q^{38} +(-7.80671 - 0.374071i) q^{39} -2.92026 q^{41} +(0.360326 - 7.51987i) q^{42} -3.25186 q^{43} +(1.20394 - 3.09039i) q^{44} -1.66840i q^{46} -9.25186 q^{47} +(-1.73007 - 0.0828988i) q^{48} +11.8928 q^{49} +(-0.225539 + 4.70691i) q^{51} -4.51238 q^{52} -3.05225 q^{53} +(-0.743810 + 5.14264i) q^{54} -4.34658i q^{56} +(0.329316 - 6.87271i) q^{57} +5.08606i q^{58} -5.43264i q^{59} -11.5646i q^{61} -9.74541i q^{62} +(-12.9800 - 1.24678i) q^{63} -1.00000 q^{64} +(-5.24678 - 2.33909i) q^{66} +12.3529i q^{67} +2.72065i q^{68} +(-2.88645 - 0.138309i) q^{69} -3.60710i q^{71} +(-0.286841 + 2.98626i) q^{72} -1.36502 q^{73} -5.60710 q^{74} -3.97251i q^{76} +(5.23303 - 13.4326i) q^{77} +(-0.374071 + 7.80671i) q^{78} -1.07107i q^{79} +(8.83544 + 1.71316i) q^{81} +2.92026i q^{82} -14.5887i q^{83} +(-7.51987 - 0.360326i) q^{84} +3.25186i q^{86} +(8.79922 + 0.421628i) q^{87} +(-3.09039 - 1.20394i) q^{88} +3.75791i q^{89} -19.6134 q^{91} -1.66840 q^{92} +(-16.8602 - 0.807883i) q^{93} +9.25186i q^{94} +(-0.0828988 + 1.73007i) q^{96} -12.7977i q^{97} -11.8928i q^{98} +(-4.48173 + 8.88336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{21} + 6 q^{22} + 8 q^{23} + 2 q^{24} - 10 q^{27} - 4 q^{29} - 4 q^{31} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 20 q^{38}+ \cdots + 10 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^21 + 6 * q^22 + 8 * q^23 + 2 * q^24 - 10 * q^27 - 4 * q^29 - 4 * q^31 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 20 * q^38 - 8 * q^39 + 16 * q^41 - 6 * q^42 + 8 * q^43 + 6 * q^44 - 40 * q^47 - 4 * q^48 + 4 * q^49 + 28 * q^51 - 4 * q^52 - 12 * q^53 - 22 * q^54 + 12 * q^57 - 32 * q^63 - 8 * q^64 - 18 * q^66 - 8 * q^69 + 12 * q^73 - 12 * q^74 - 8 * q^77 - 20 * q^78 + 2 * q^81 - 8 * q^84 + 36 * q^87 - 6 * q^88 - 48 * q^91 - 8 * q^92 - 2 * q^93 - 2 * q^96 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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