LMFDB - Embedded newform 1650.2.f.e.1649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1650,2,Mod(1649,1650)]

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

lf = mfeigenbasis(mf)

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")

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

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			$1.18994i$ of defining polynomial
Character	$\chi$	$=$	1650.1649
Dual form			1650.2.f.e.1649.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.03743 - 1.38699i) q^{3} -1.00000 q^{4} +(-1.38699 + 1.03743i) q^{6} -0.394100 q^{7} +1.00000i q^{8} +(-0.847487 + 2.87781i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.03743 - 1.38699i) q^{3} -1.00000 q^{4} +(-1.38699 + 1.03743i) q^{6} -0.394100 q^{7} +1.00000i q^{8} +(-0.847487 + 2.87781i) q^{9} +(3.26480 + 0.584041i) q^{11} +(1.03743 + 1.38699i) q^{12} -2.37988 q^{13} +0.394100i q^{14} +1.00000 q^{16} -0.906774i q^{17} +(2.87781 + 0.847487i) q^{18} +3.69497i q^{19} +(0.408850 + 0.546613i) q^{21} +(0.584041 - 3.26480i) q^{22} +3.54796 q^{23} +(1.38699 - 1.03743i) q^{24} +2.37988i q^{26} +(4.87070 - 1.81006i) q^{27} +0.394100 q^{28} +3.37573 q^{29} +3.66654 q^{31} -1.00000i q^{32} +(-2.57693 - 5.13414i) q^{33} -0.906774 q^{34} +(0.847487 - 2.87781i) q^{36} -4.58753i q^{37} +3.69497 q^{38} +(2.46896 + 3.30087i) q^{39} +8.14971 q^{41} +(0.546613 - 0.408850i) q^{42} -2.60175 q^{43} +(-3.26480 - 0.584041i) q^{44} -3.54796i q^{46} +3.39825 q^{47} +(-1.03743 - 1.38699i) q^{48} -6.84469 q^{49} +(-1.25769 + 0.940713i) q^{51} +2.37988 q^{52} +6.45474 q^{53} +(-1.81006 - 4.87070i) q^{54} -0.394100i q^{56} +(5.12489 - 3.83327i) q^{57} -3.37573i q^{58} -7.76983i q^{59} +12.8346i q^{61} -3.66654i q^{62} +(0.333995 - 1.13414i) q^{63} -1.00000 q^{64} +(-5.13414 + 2.57693i) q^{66} -11.9195i q^{67} +0.906774i q^{68} +(-3.68076 - 4.92099i) q^{69} +2.58753i q^{71} +(-2.87781 - 0.847487i) q^{72} +11.8911 q^{73} -4.58753 q^{74} -3.69497i q^{76} +(-1.28666 - 0.230170i) q^{77} +(3.30087 - 2.46896i) q^{78} +2.56633i q^{79} +(-7.56353 - 4.87781i) q^{81} -8.14971i q^{82} +1.69767i q^{83} +(-0.408850 - 0.546613i) q^{84} +2.60175i q^{86} +(-3.50208 - 4.68211i) q^{87} +(-0.584041 + 3.26480i) q^{88} -15.3036i q^{89} +0.937911 q^{91} -3.54796 q^{92} +(-3.80377 - 5.08545i) q^{93} -3.39825i q^{94} +(-1.38699 + 1.03743i) q^{96} -10.1213i q^{97} +6.84469i q^{98} +(-4.44763 + 8.90048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 8 * q^4 - 2 * q^6 - 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	−1.03743	−	1.38699i	−0.598959	−	0.800780i
$3$	−1.03743	−	1.38699i	−0.598959	−	0.800780i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.38699	+	1.03743i	−0.566237	+	0.423528i
$7$	−0.394100			−0.148956			−0.0744779	−	0.997223i	$-0.523729\pi$
$7$	−0.394100			−0.148956			−0.0744779	+	0.997223i	$0.523729\pi$
$8$			1.00000i			0.353553i
$9$	−0.847487	+	2.87781i	−0.282496	+	0.959269i
$10$		0			0
$11$	3.26480	+	0.584041i	0.984373	+	0.176095i
$11$	3.26480	+	0.584041i	0.984373	+	0.176095i
$12$	1.03743	+	1.38699i	0.299480	+	0.400390i
$13$	−2.37988			−0.660060			−0.330030	−	0.943970i	$-0.607059\pi$
$13$	−2.37988			−0.660060			−0.330030	+	0.943970i	$0.607059\pi$
$14$			0.394100i			0.105328i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.906774i		−	0.219925i	−0.993936	−	0.109963i	$-0.964927\pi$
$17$		−	0.906774i		−	0.219925i	0.993936	−	0.109963i	$-0.0350731\pi$
$18$	2.87781	+	0.847487i	0.678305	+	0.199755i
$19$			3.69497i			0.847685i	0.905736	+	0.423843i	$0.139319\pi$
$19$			3.69497i			0.847685i	−0.905736	+	0.423843i	$0.860681\pi$
$20$		0			0
$21$	0.408850	+	0.546613i	0.0892184	+	0.119281i
$22$	0.584041	−	3.26480i	0.124518	−	0.696057i
$23$	3.54796			0.739801			0.369901	−	0.929071i	$-0.379392\pi$
$23$	3.54796			0.739801			0.369901	+	0.929071i	$0.379392\pi$
$24$	1.38699	−	1.03743i	0.283118	−	0.211764i
$25$		0			0
$26$			2.37988i			0.466733i
$27$	4.87070	−	1.81006i	0.937366	−	0.348346i
$28$	0.394100			0.0744779
$29$	3.37573			0.626857			0.313429	−	0.949612i	$-0.398522\pi$
$29$	3.37573			0.626857			0.313429	+	0.949612i	$0.398522\pi$
$30$		0			0
$31$	3.66654			0.658530			0.329265	−	0.944238i	$-0.393199\pi$
$31$	3.66654			0.658530			0.329265	+	0.944238i	$0.393199\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.57693	−	5.13414i	−0.448586	−	0.893740i
$34$	−0.906774			−0.155510
$35$		0			0
$36$	0.847487	−	2.87781i	0.141248	−	0.479634i
$37$		−	4.58753i		−	0.754185i	−0.926176	−	0.377093i	$-0.876924\pi$
$37$		−	4.58753i		−	0.754185i	0.926176	−	0.377093i	$-0.123076\pi$
$38$	3.69497			0.599404
$39$	2.46896	+	3.30087i	0.395349	+	0.528563i
$40$		0			0
$41$	8.14971			1.27277			0.636386	−	0.771371i	$-0.280429\pi$
$41$	8.14971			1.27277			0.636386	+	0.771371i	$0.280429\pi$
$42$	0.546613	−	0.408850i	0.0843442	−	0.0630870i
$43$	−2.60175			−0.396763			−0.198381	−	0.980125i	$-0.563568\pi$
$43$	−2.60175			−0.396763			−0.198381	+	0.980125i	$0.563568\pi$
$44$	−3.26480	−	0.584041i	−0.492187	−	0.0880475i
$45$		0			0
$46$		−	3.54796i		−	0.523119i
$47$	3.39825			0.495686			0.247843	−	0.968800i	$-0.420278\pi$
$47$	3.39825			0.495686			0.247843	+	0.968800i	$0.420278\pi$
$48$	−1.03743	−	1.38699i	−0.149740	−	0.200195i
$49$	−6.84469			−0.977812
$50$		0			0
$51$	−1.25769	+	0.940713i	−0.176111	+	0.131726i
$52$	2.37988			0.330030
$53$	6.45474			0.886626			0.443313	−	0.896367i	$-0.353803\pi$
$53$	6.45474			0.886626			0.443313	+	0.896367i	$0.353803\pi$
$54$	−1.81006	−	4.87070i	−0.246318	−	0.662818i
$55$		0			0
$56$		−	0.394100i		−	0.0526638i
$57$	5.12489	−	3.83327i	0.678809	−	0.507729i
$58$		−	3.37573i		−	0.443255i
$59$		−	7.76983i		−	1.01155i	−0.862667	−	0.505773i	$-0.831207\pi$
$59$		−	7.76983i		−	1.01155i	0.862667	−	0.505773i	$-0.168793\pi$
$60$		0			0
$61$			12.8346i			1.64330i	0.569989	+	0.821652i	$0.306947\pi$
$61$			12.8346i			1.64330i	−0.569989	+	0.821652i	$0.693053\pi$
$62$		−	3.66654i		−	0.465651i
$63$	0.333995	−	1.13414i	0.0420794	−	0.142889i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.13414	+	2.57693i	−0.631969	+	0.317198i
$67$		−	11.9195i		−	1.45620i	−0.685469	−	0.728102i	$-0.740403\pi$
$67$		−	11.9195i		−	1.45620i	0.685469	−	0.728102i	$-0.259597\pi$
$68$			0.906774i			0.109963i
$69$	−3.68076	−	4.92099i	−0.443111	−	0.592418i
$70$		0			0
$71$			2.58753i			0.307083i	0.988142	+	0.153542i	$0.0490679\pi$
$71$			2.58753i			0.307083i	−0.988142	+	0.153542i	$0.950932\pi$
$72$	−2.87781	−	0.847487i	−0.339153	−	0.0998773i
$73$	11.8911			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$73$	11.8911			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$74$	−4.58753			−0.533290
$75$		0			0
$76$		−	3.69497i		−	0.423843i
$77$	−1.28666	−	0.230170i	−0.146628	−	0.0262303i
$78$	3.30087	−	2.46896i	0.373750	−	0.279554i
$79$			2.56633i			0.288735i	0.989524	+	0.144368i	$0.0461148\pi$
$79$			2.56633i			0.288735i	−0.989524	+	0.144368i	$0.953885\pi$
$80$		0			0
$81$	−7.56353	−	4.87781i	−0.840392	−	0.541978i
$82$		−	8.14971i		−	0.899985i
$83$			1.69767i			0.186344i	0.995650	+	0.0931720i	$0.0297006\pi$
$83$			1.69767i			0.186344i	−0.995650	+	0.0931720i	$0.970299\pi$
$84$	−0.408850	−	0.546613i	−0.0446092	−	0.0596404i
$85$		0			0
$86$			2.60175i			0.280554i
$87$	−3.50208	−	4.68211i	−0.375462	−	0.501974i
$88$	−0.584041	+	3.26480i	−0.0622590	+	0.348028i
$89$		−	15.3036i		−	1.62218i	−0.584924	−	0.811088i	$-0.698876\pi$
$89$		−	15.3036i		−	1.62218i	0.584924	−	0.811088i	$-0.301124\pi$
$90$		0			0
$91$	0.937911			0.0983198
$92$	−3.54796			−0.369901
$93$	−3.80377	−	5.08545i	−0.394432	−	0.527337i
$94$		−	3.39825i		−	0.350503i
$95$		0			0
$96$	−1.38699	+	1.03743i	−0.141559	+	0.105882i
$97$		−	10.1213i		−	1.02766i	−0.857892	−	0.513830i	$-0.828226\pi$
$97$		−	10.1213i		−	1.02766i	0.857892	−	0.513830i	$-0.171774\pi$
$98$			6.84469i			0.691418i
$99$	−4.44763	+	8.90048i	−0.447003	+	0.894532i
$100$		0			0
$101$	−3.01837			−0.300339			−0.150170	−	0.988660i	$-0.547982\pi$
$101$	−3.01837			−0.300339			−0.150170	+	0.988660i	$0.547982\pi$
$102$	0.940713	+	1.25769i	0.0931444	+	0.124530i
$103$		−	0.601748i		−	0.0592920i	−0.999560	−	0.0296460i	$-0.990562\pi$
$103$		−	0.601748i		−	0.0592920i	0.999560	−	0.0296460i	$-0.00943800\pi$
$104$		−	2.37988i		−	0.233367i
$105$		0			0
$106$		−	6.45474i		−	0.626940i
$107$			15.2456i			1.47385i	0.675974	+	0.736926i	$0.263723\pi$
$107$			15.2456i			1.47385i	−0.675974	+	0.736926i	$0.736277\pi$
$108$	−4.87070	+	1.81006i	−0.468683	+	0.174173i
$109$		−	18.3770i		−	1.76020i	−0.474793	−	0.880098i	$-0.657477\pi$
$109$		−	18.3770i		−	1.76020i	0.474793	−	0.880098i	$-0.342523\pi$
$110$		0			0
$111$	−6.36286	+	4.75923i	−0.603936	+	0.451726i
$112$	−0.394100			−0.0372389
$113$	−6.37988			−0.600169			−0.300084	−	0.953913i	$-0.597015\pi$
$113$	−6.37988			−0.600169			−0.300084	+	0.953913i	$0.597015\pi$
$114$	−3.83327	−	5.12489i	−0.359019	−	0.479990i
$115$		0			0
$116$	−3.37573			−0.313429
$117$	2.01692	−	6.84884i	0.186464	−	0.633175i
$118$	−7.76983			−0.715271
$119$			0.357360i			0.0327591i
$120$		0			0
$121$	10.3178	+	3.81355i	0.937981	+	0.346686i
$122$	12.8346			1.16199
$123$	−8.45474	−	11.3036i	−0.762338	−	1.01921i
$124$	−3.66654			−0.329265
$125$		0			0
$126$	−1.13414	−	0.333995i	−0.101037	−	0.0297546i
$127$	−22.0338			−1.95519			−0.977593	−	0.210502i	$-0.932490\pi$
$127$	−22.0338			−1.95519			−0.977593	+	0.210502i	$0.932490\pi$
$128$			1.00000i			0.0883883i
$129$	2.69913	+	3.60860i	0.237645	+	0.317720i
$130$		0			0
$131$	−1.97748			−0.172773			−0.0863865	−	0.996262i	$-0.527532\pi$
$131$	−1.97748			−0.172773			−0.0863865	+	0.996262i	$0.527532\pi$
$132$	2.57693	+	5.13414i	0.224293	+	0.446870i
$133$		−	1.45619i		−	0.126268i
$134$	−11.9195			−1.02969
$135$		0			0
$136$	0.906774			0.0777552
$137$	19.6172			1.67601			0.838006	−	0.545661i	$-0.183721\pi$
$137$	19.6172			1.67601			0.838006	+	0.545661i	$0.183721\pi$
$138$	−4.92099	+	3.68076i	−0.418903	+	0.313327i
$139$			18.7230i			1.58807i	0.607875	+	0.794033i	$0.292022\pi$
$139$			18.7230i			1.58807i	−0.607875	+	0.794033i	$0.707978\pi$
$140$		0			0
$141$	−3.52544	−	4.71334i	−0.296896	−	0.396935i
$142$	2.58753			0.217141
$143$	−7.76983	−	1.38995i	−0.649746	−	0.116233i
$144$	−0.847487	+	2.87781i	−0.0706239	+	0.239817i
$145$		0			0
$146$		−	11.8911i		−	0.984115i
$147$	7.10087	+	9.49352i	0.585670	+	0.783012i
$148$			4.58753i			0.377093i
$149$	22.0113			1.80324			0.901619	−	0.432532i	$-0.142380\pi$
$149$	22.0113			1.80324			0.901619	+	0.432532i	$0.142380\pi$
$150$		0			0
$151$		−	13.9278i		−	1.13343i	−0.823913	−	0.566716i	$-0.808214\pi$
$151$		−	13.9278i		−	1.13343i	0.823913	−	0.566716i	$-0.191786\pi$
$152$	−3.69497			−0.299702
$153$	2.60952	+	0.768479i	0.210967	+	0.0621279i
$154$	−0.230170	+	1.28666i	−0.0185477	+	0.103682i
$155$		0			0
$156$	−2.46896	−	3.30087i	−0.197675	−	0.264281i
$157$			2.62427i			0.209440i	0.994502	+	0.104720i	$0.0333946\pi$
$157$			2.62427i			0.209440i	−0.994502	+	0.104720i	$0.966605\pi$
$158$	2.56633			0.204167
$159$	−6.69632	−	8.95266i	−0.531053	−	0.709992i
$160$		0			0
$161$	−1.39825			−0.110198
$162$	−4.87781	+	7.56353i	−0.383237	+	0.594247i
$163$		−	6.77398i		−	0.530579i	−0.964169	−	0.265290i	$-0.914532\pi$
$163$		−	6.77398i		−	0.530579i	0.964169	−	0.265290i	$-0.0854676\pi$
$164$	−8.14971			−0.636386
$165$		0			0
$166$	1.69767			0.131765
$167$			16.7542i			1.29648i	0.761438	+	0.648238i	$0.224494\pi$
$167$			16.7542i			1.29648i	−0.761438	+	0.648238i	$0.775506\pi$
$168$	−0.546613	+	0.408850i	−0.0421721	+	0.0315435i
$169$	−7.33616			−0.564320
$170$		0			0
$171$	−10.6334	−	3.13144i	−0.813158	−	0.239467i
$172$	2.60175			0.198381
$173$			13.0959i			0.995665i	0.867273	+	0.497832i	$0.165871\pi$
$173$			13.0959i			0.995665i	−0.867273	+	0.497832i	$0.834129\pi$
$174$	−4.68211	+	3.50208i	−0.354950	+	0.265492i
$175$		0			0
$176$	3.26480	+	0.584041i	0.246093	+	0.0440237i
$177$	−10.7767	+	8.06064i	−0.810025	+	0.605875i
$178$	−15.3036			−1.14705
$179$			14.9816i			1.11978i	0.828567	+	0.559890i	$0.189157\pi$
$179$			14.9816i			1.11978i	−0.828567	+	0.559890i	$0.810843\pi$
$180$		0			0
$181$	23.9687			1.78158			0.890788	−	0.454419i	$-0.150153\pi$
$181$	23.9687			1.78158			0.890788	+	0.454419i	$0.150153\pi$
$182$		−	0.937911i		−	0.0695226i
$183$	17.8015	−	13.3150i	1.31592	−	0.984272i
$184$			3.54796i			0.261559i
$185$		0			0
$186$	−5.08545	+	3.80377i	−0.372884	+	0.278906i
$187$	0.529593	−	2.96043i	0.0387277	−	0.216488i
$188$	−3.39825			−0.247843
$189$	−1.91954	+	0.713344i	−0.139626	+	0.0518881i
$190$		0			0
$191$		−	21.9249i		−	1.58643i	−0.608940	−	0.793217i	$-0.708405\pi$
$191$		−	21.9249i		−	1.58643i	0.608940	−	0.793217i	$-0.291595\pi$
$192$	1.03743	+	1.38699i	0.0748699	+	0.100097i
$193$	21.8699			1.57423			0.787115	−	0.616806i	$-0.211574\pi$
$193$	21.8699			1.57423			0.787115	+	0.616806i	$0.211574\pi$
$194$	−10.1213			−0.726665
$195$		0			0
$196$	6.84469			0.488906
$197$		−	18.0338i		−	1.28486i	−0.766345	−	0.642429i	$-0.777927\pi$
$197$		−	18.0338i		−	1.28486i	0.766345	−	0.642429i	$-0.222073\pi$
$198$	8.90048	+	4.44763i	0.632530	+	0.316079i
$199$	3.81625			0.270527			0.135263	−	0.990810i	$-0.456812\pi$
$199$	3.81625			0.270527			0.135263	+	0.990810i	$0.456812\pi$
$200$		0			0
$201$	−16.5323	+	12.3657i	−1.16610	+	0.872207i
$202$			3.01837i			0.212372i
$203$	−1.33037			−0.0933740
$204$	1.25769	−	0.940713i	0.0880557	−	0.0658631i
$205$		0			0
$206$	−0.601748			−0.0419258
$207$	−3.00685	+	10.2103i	−0.208991	+	0.709668i
$208$	−2.37988			−0.165015
$209$	−2.15802	+	12.0633i	−0.149273	+	0.834439i
$210$		0			0
$211$		−	19.0903i		−	1.31423i	−0.753789	−	0.657116i	$-0.771776\pi$
$211$		−	19.0903i		−	1.31423i	0.753789	−	0.657116i	$-0.228224\pi$
$212$	−6.45474			−0.443313
$213$	3.58888	−	2.68438i	0.245906	−	0.183930i
$214$	15.2456			1.04217
$215$		0			0
$216$	1.81006	+	4.87070i	0.123159	+	0.331409i
$217$	−1.44498			−0.0980918
$218$	−18.3770			−1.24465
$219$	−12.3362	−	16.4929i	−0.833601	−	1.11448i
$220$		0			0
$221$			2.15802i			0.145164i
$222$	4.75923	+	6.36286i	0.319419	+	0.427047i
$223$			2.17815i			0.145860i	0.997337	+	0.0729298i	$0.0232349\pi$
$223$			2.17815i			0.145860i	−0.997337	+	0.0729298i	$0.976765\pi$
$224$			0.394100i			0.0263319i
$225$		0			0
$226$			6.37988i			0.424383i
$227$			6.83890i			0.453914i	0.973905	+	0.226957i	$0.0728776\pi$
$227$			6.83890i			0.453914i	−0.973905	+	0.226957i	$0.927122\pi$
$228$	−5.12489	+	3.83327i	−0.339404	+	0.253864i
$229$	23.8474			1.57588			0.787940	−	0.615752i	$-0.211148\pi$
$229$	23.8474			1.57588			0.787940	+	0.615752i	$0.211148\pi$
$230$		0			0
$231$	1.01557	+	2.02337i	0.0668195	+	0.133128i
$232$			3.37573i			0.221628i
$233$		−	10.5760i		−	0.692858i	−0.938076	−	0.346429i	$-0.887394\pi$
$233$		−	10.5760i		−	0.692858i	0.938076	−	0.346429i	$-0.112606\pi$
$234$	−6.84884	−	2.01692i	−0.447722	−	0.131850i
$235$		0			0
$236$			7.76983i			0.505773i
$237$	3.55948	−	2.66239i	0.231213	−	0.172941i
$238$	0.357360			0.0231642
$239$	22.4290			1.45081			0.725406	−	0.688322i	$-0.241652\pi$
$239$	22.4290			1.45081			0.725406	+	0.688322i	$0.241652\pi$
$240$		0			0
$241$			4.78820i			0.308435i	0.988037	+	0.154218i	$0.0492857\pi$
$241$			4.78820i			0.308435i	−0.988037	+	0.154218i	$0.950714\pi$
$242$	3.81355	−	10.3178i	0.245144	−	0.663253i
$243$	1.08115	+	15.5509i	0.0693556	+	0.997592i
$244$		−	12.8346i		−	0.821652i
$245$		0			0
$246$	−11.3036	+	8.45474i	−0.720690	+	0.539054i
$247$		−	8.79360i		−	0.559523i
$248$			3.66654i			0.232825i
$249$	2.35466	−	1.76121i	0.149220	−	0.111612i
$250$		0			0
$251$			11.5042i			0.726141i	0.931762	+	0.363071i	$0.118272\pi$
$251$			11.5042i			0.726141i	−0.931762	+	0.363071i	$0.881728\pi$
$252$	−0.333995	+	1.13414i	−0.0210397	+	0.0714443i
$253$	11.5834	+	2.07216i	0.728241	+	0.130275i
$254$			22.0338i			1.38253i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−16.3431			−1.01946			−0.509729	−	0.860335i	$-0.670254\pi$
$257$	−16.3431			−1.01946			−0.509729	+	0.860335i	$0.670254\pi$
$258$	3.60860	−	2.69913i	0.224662	−	0.168040i
$259$			1.80795i			0.112340i
$260$		0			0
$261$	−2.86089	+	9.71469i	−0.177084	+	0.601324i
$262$			1.97748i			0.122169i
$263$			3.23463i			0.199456i	0.995015	+	0.0997280i	$0.0317973\pi$
$263$			3.23463i			0.199456i	−0.995015	+	0.0997280i	$0.968203\pi$
$264$	5.13414	−	2.57693i	0.315985	−	0.158599i
$265$		0			0
$266$	−1.45619			−0.0892847
$267$	−21.2259	+	15.8764i	−1.29901	+	0.971617i
$268$			11.9195i			0.728102i
$269$			8.94622i			0.545460i	0.962091	+	0.272730i	$0.0879266\pi$
$269$			8.94622i			0.545460i	−0.962091	+	0.272730i	$0.912073\pi$
$270$		0			0
$271$		−	3.38297i		−	0.205501i	−0.994707	−	0.102750i	$-0.967236\pi$
$271$		−	3.38297i		−	0.205501i	0.994707	−	0.102750i	$-0.0327643\pi$
$272$		−	0.906774i		−	0.0549813i
$273$	−0.973015	−	1.30087i	−0.0588896	−	0.0787325i
$274$		−	19.6172i		−	1.18512i
$275$		0			0
$276$	3.68076	+	4.92099i	0.221555	+	0.296209i
$277$	5.76983			0.346675			0.173338	−	0.984862i	$-0.444545\pi$
$277$	5.76983			0.346675			0.173338	+	0.984862i	$0.444545\pi$
$278$	18.7230			1.12293
$279$	−3.10734	+	10.5516i	−0.186032	+	0.631707i
$280$		0			0
$281$	0.115874			0.00691245			0.00345623	−	0.999994i	$-0.498900\pi$
$281$	0.115874			0.00691245			0.00345623	+	0.999994i	$0.498900\pi$
$282$	−4.71334	+	3.52544i	−0.280676	+	0.209937i
$283$	−21.1805			−1.25905			−0.629524	−	0.776981i	$-0.716750\pi$
$283$	−21.1805			−1.25905			−0.629524	+	0.776981i	$0.716750\pi$
$284$		−	2.58753i		−	0.153542i
$285$		0			0
$286$	−1.38995	+	7.76983i	−0.0821893	+	0.459440i
$287$	−3.21180			−0.189587
$288$	2.87781	+	0.847487i	0.169576	+	0.0499386i
$289$	16.1778			0.951633
$290$		0			0
$291$	−14.0381	+	10.5001i	−0.822929	+	0.615526i
$292$	−11.8911			−0.695874
$293$		−	16.5143i		−	0.964776i	−0.875958	−	0.482388i	$-0.839769\pi$
$293$		−	16.5143i		−	0.964776i	0.875958	−	0.482388i	$-0.160231\pi$
$294$	9.49352	−	7.10087i	0.553673	−	0.414131i
$295$		0			0
$296$	4.58753			0.266645
$297$	16.9590	−	3.06479i	0.984060	−	0.177837i
$298$		−	22.0113i		−	1.27508i
$299$	−8.44373			−0.488314
$300$		0			0
$301$	1.02535			0.0591001
$302$	−13.9278			−0.801457
$303$	3.13134	+	4.18645i	0.179891	+	0.240505i
$304$			3.69497i			0.211921i
$305$		0			0
$306$	0.768479	−	2.60952i	0.0439310	−	0.149176i
$307$	17.6526			1.00749			0.503744	−	0.863853i	$-0.331955\pi$
$307$	17.6526			1.00749			0.503744	+	0.863853i	$0.331955\pi$
$308$	1.28666	+	0.230170i	0.0733140	+	0.0131152i
$309$	−0.834619	+	0.624270i	−0.0474798	+	0.0355135i
$310$		0			0
$311$			4.13549i			0.234502i	0.993102	+	0.117251i	$0.0374083\pi$
$311$			4.13549i			0.234502i	−0.993102	+	0.117251i	$0.962592\pi$
$312$	−3.30087	+	2.46896i	−0.186875	+	0.139777i
$313$			12.1580i			0.687212i	0.939114	+	0.343606i	$0.111648\pi$
$313$			12.1580i			0.687212i	−0.939114	+	0.343606i	$0.888352\pi$
$314$	2.62427			0.148096
$315$		0			0
$316$		−	2.56633i		−	0.144368i
$317$	−6.97195			−0.391584			−0.195792	−	0.980645i	$-0.562728\pi$
$317$	−6.97195			−0.391584			−0.195792	+	0.980645i	$0.562728\pi$
$318$	−8.95266	+	6.69632i	−0.502040	+	0.375511i
$319$	11.0211	+	1.97156i	0.617061	+	0.110386i
$320$		0			0
$321$	21.1456	−	15.8162i	1.18023	−	0.882777i
$322$			1.39825i			0.0779215i
$323$	3.35051			0.186427
$324$	7.56353	+	4.87781i	0.420196	+	0.270989i
$325$		0			0
$326$	−6.77398			−0.375176
$327$	−25.4887	+	19.0648i	−1.40953	+	1.05429i
$328$			8.14971i			0.449993i
$329$	−1.33925			−0.0738353
$330$		0			0
$331$	−5.39825			−0.296715			−0.148357	−	0.988934i	$-0.547399\pi$
$331$	−5.39825			−0.296715			−0.148357	+	0.988934i	$0.547399\pi$
$332$		−	1.69767i		−	0.0931720i
$333$	13.2020	+	3.88787i	0.723466	+	0.213054i
$334$	16.7542			0.916747
$335$		0			0
$336$	0.408850	+	0.546613i	0.0223046	+	0.0298202i
$337$	24.7657			1.34907			0.674536	−	0.738242i	$-0.264344\pi$
$337$	24.7657			1.34907			0.674536	+	0.738242i	$0.264344\pi$
$338$			7.33616i			0.399035i
$339$	6.61867	+	8.84884i	0.359477	+	0.480603i
$340$		0			0
$341$	11.9705	+	2.14141i	0.648239	+	0.115964i
$342$	−3.13144	+	10.6334i	−0.169329	+	0.574989i
$343$	5.45619			0.294607
$344$		−	2.60175i		−	0.140277i
$345$		0			0
$346$	13.0959			0.704041
$347$			30.3416i			1.62882i	0.580290	+	0.814410i	$0.302939\pi$
$347$			30.3416i			1.62882i	−0.580290	+	0.814410i	$0.697061\pi$
$348$	3.50208	+	4.68211i	0.187731	+	0.250987i
$349$			21.6172i			1.15714i	0.815632	+	0.578572i	$0.196390\pi$
$349$			21.6172i			1.15714i	−0.815632	+	0.578572i	$0.803610\pi$
$350$		0			0
$351$	−11.5917	+	4.30773i	−0.618718	+	0.229929i
$352$	0.584041	−	3.26480i	0.0311295	−	0.174014i
$353$	−7.70465			−0.410077			−0.205039	−	0.978754i	$-0.565732\pi$
$353$	−7.70465			−0.410077			−0.205039	+	0.978754i	$0.565732\pi$
$354$	8.06064	+	10.7767i	0.428418	+	0.572774i
$355$		0			0
$356$			15.3036i			0.811088i
$357$	0.495654	−	0.370735i	0.0262328	−	0.0196214i
$358$	14.9816			0.791804
$359$	−0.344467			−0.0181803			−0.00909014	−	0.999959i	$-0.502894\pi$
$359$	−0.344467			−0.0181803			−0.00909014	+	0.999959i	$0.502894\pi$
$360$		0			0
$361$	5.34717			0.281430
$362$		−	23.9687i		−	1.25976i
$363$	−5.41461	−	18.2670i	−0.284193	−	0.958767i
$364$	−0.937911			−0.0491599
$365$		0			0
$366$	−13.3150	−	17.8015i	−0.695986	−	0.930499i
$367$			27.9687i			1.45995i	0.683473	+	0.729976i	$0.260469\pi$
$367$			27.9687i			1.45995i	−0.683473	+	0.729976i	$0.739531\pi$
$368$	3.54796			0.184950
$369$	−6.90677	+	23.4533i	−0.359552	+	1.22093i
$370$		0			0
$371$	−2.54381			−0.132068
$372$	3.80377	+	5.08545i	0.197216	+	0.263669i
$373$	−21.8911			−1.13348			−0.566739	−	0.823897i	$-0.691795\pi$
$373$	−21.8911			−1.13348			−0.566739	+	0.823897i	$0.691795\pi$
$374$	−2.96043	−	0.529593i	−0.153080	−	0.0273846i
$375$		0			0
$376$			3.39825i			0.175251i
$377$	−8.03384			−0.413764
$378$	0.713344	+	1.91954i	0.0366905	+	0.0987305i
$379$	29.8023			1.53084			0.765422	−	0.643529i	$-0.222530\pi$
$379$	29.8023			1.53084			0.765422	+	0.643529i	$0.222530\pi$
$380$		0			0
$381$	22.8585	+	30.5607i	1.17108	+	1.56567i
$382$	−21.9249			−1.12178
$383$	31.3017			1.59944			0.799722	−	0.600370i	$-0.204980\pi$
$383$	31.3017			1.59944			0.799722	+	0.600370i	$0.204980\pi$
$384$	1.38699	−	1.03743i	0.0707796	−	0.0529410i
$385$		0			0
$386$		−	21.8699i		−	1.11315i
$387$	2.20495	−	7.48733i	0.112084	−	0.380602i
$388$			10.1213i			0.513830i
$389$			16.5733i			0.840300i	0.907455	+	0.420150i	$0.138023\pi$
$389$			16.5733i			0.840300i	−0.907455	+	0.420150i	$0.861977\pi$
$390$		0			0
$391$		−	3.21720i		−	0.162701i
$392$		−	6.84469i		−	0.345709i
$393$	2.05149	+	2.74274i	0.103484	+	0.138353i
$394$	−18.0338			−0.908532
$395$		0			0
$396$	4.44763	−	8.90048i	0.223502	−	0.447266i
$397$			3.94798i			0.198143i	0.995080	+	0.0990716i	$0.0315873\pi$
$397$			3.94798i			0.198143i	−0.995080	+	0.0990716i	$0.968413\pi$
$398$		−	3.81625i		−	0.191291i
$399$	−2.01972	+	1.51069i	−0.101112	+	0.0756291i
$400$		0			0
$401$		−	4.72486i		−	0.235948i	−0.993017	−	0.117974i	$-0.962360\pi$
$401$		−	4.72486i		−	0.235948i	0.993017	−	0.117974i	$-0.0376400\pi$
$402$	12.3657	+	16.5323i	0.616743	+	0.824556i
$403$	−8.72593			−0.434669
$404$	3.01837			0.150170
$405$		0			0
$406$			1.33037i			0.0660254i
$407$	2.67930	−	14.9774i	0.132808	−	0.742400i
$408$	−0.940713	−	1.25769i	−0.0465722	−	0.0622648i
$409$		−	12.1497i		−	0.600765i	−0.953819	−	0.300382i	$-0.902886\pi$
$409$		−	12.1497i		−	0.600765i	0.953819	−	0.300382i	$-0.0971143\pi$
$410$		0			0
$411$	−20.3514	−	27.2089i	−1.00386	−	1.34212i
$412$			0.601748i			0.0296460i
$413$			3.06209i			0.150676i
$414$	10.2103	+	3.00685i	0.501811	+	0.147779i
$415$		0			0
$416$			2.37988i			0.116683i
$417$	25.9687	−	19.4238i	1.27169	−	0.951187i
$418$	12.0633	+	2.15802i	0.590037	+	0.105552i
$419$		−	7.01547i		−	0.342728i	−0.985208	−	0.171364i	$-0.945183\pi$
$419$		−	7.01547i		−	0.342728i	0.985208	−	0.171364i	$-0.0548174\pi$
$420$		0			0
$421$	−13.0085			−0.633995			−0.316997	−	0.948426i	$-0.602675\pi$
$421$	−13.0085			−0.633995			−0.316997	+	0.948426i	$0.602675\pi$
$422$	−19.0903			−0.929302
$423$	−2.87997	+	9.77951i	−0.140029	+	0.475496i
$424$			6.45474i			0.313470i
$425$		0			0
$426$	−2.68438	−	3.58888i	−0.130058	−	0.173882i
$427$		−	5.05812i		−	0.244780i
$428$		−	15.2456i		−	0.736926i
$429$	6.13279	+	12.2187i	0.296094	+	0.589922i
$430$		0			0
$431$	−23.5397			−1.13387			−0.566933	−	0.823764i	$-0.691870\pi$
$431$	−23.5397			−1.13387			−0.566933	+	0.823764i	$0.691870\pi$
$432$	4.87070	−	1.81006i	0.234342	−	0.0870865i
$433$		−	3.05919i		−	0.147015i	−0.997295	−	0.0735076i	$-0.976581\pi$
$433$		−	3.05919i		−	0.147015i	0.997295	−	0.0735076i	$-0.0234193\pi$
$434$			1.44498i			0.0693614i
$435$		0			0
$436$			18.3770i			0.880098i
$437$			13.1096i			0.627119i
$438$	−16.4929	+	12.3362i	−0.788059	+	0.589445i
$439$		−	27.8461i		−	1.32902i	−0.747279	−	0.664510i	$-0.768640\pi$
$439$		−	27.8461i		−	1.32902i	0.747279	−	0.664510i	$-0.231360\pi$
$440$		0			0
$441$	5.80078	−	19.6977i	0.276228	−	0.937985i
$442$	2.15802			0.102646
$443$	−28.5213			−1.35509			−0.677544	−	0.735483i	$-0.736956\pi$
$443$	−28.5213			−1.35509			−0.677544	+	0.735483i	$0.736956\pi$
$444$	6.36286	−	4.75923i	0.301968	−	0.225863i
$445$		0			0
$446$	2.17815			0.103138
$447$	−22.8352	−	30.5295i	−1.08007	−	1.44400i
$448$	0.394100			0.0186195
$449$		−	4.00000i		−	0.188772i	−0.995536	−	0.0943858i	$-0.969911\pi$
$449$		−	4.00000i		−	0.188772i	0.995536	−	0.0943858i	$-0.0300887\pi$
$450$		0			0
$451$	26.6071	+	4.75976i	1.25288	+	0.224129i
$452$	6.37988			0.300084
$453$	−19.3178	+	14.4491i	−0.907629	+	0.678880i
$454$	6.83890			0.320965
$455$		0			0
$456$	3.83327	+	5.12489i	0.179509	+	0.239995i
$457$	−13.0651			−0.611160			−0.305580	−	0.952166i	$-0.598850\pi$
$457$	−13.0651			−0.611160			−0.305580	+	0.952166i	$0.598850\pi$
$458$		−	23.8474i		−	1.11432i
$459$	−1.64131	−	4.41662i	−0.0766100	−	0.206150i
$460$		0			0
$461$	20.1355			0.937803			0.468902	−	0.883250i	$-0.344650\pi$
$461$	20.1355			0.937803			0.468902	+	0.883250i	$0.344650\pi$
$462$	2.02337	−	1.01557i	0.0941355	−	0.0472485i
$463$			12.6071i			0.585904i	0.956127	+	0.292952i	$0.0946376\pi$
$463$			12.6071i			0.585904i	−0.956127	+	0.292952i	$0.905362\pi$
$464$	3.37573			0.156714
$465$		0			0
$466$	−10.5760			−0.489924
$467$	−14.9843			−0.693392			−0.346696	−	0.937978i	$-0.612696\pi$
$467$	−14.9843			−0.693392			−0.346696	+	0.937978i	$0.612696\pi$
$468$	−2.01692	+	6.84884i	−0.0932321	+	0.316588i
$469$			4.69749i			0.216910i
$470$		0			0
$471$	3.63984	−	2.72249i	0.167715	−	0.125446i
$472$	7.76983			0.357635
$473$	−8.49418	−	1.51953i	−0.390563	−	0.0698679i
$474$	−2.66239	−	3.55948i	−0.122287	−	0.163492i
$475$		0			0
$476$		−	0.357360i		−	0.0163796i
$477$	−5.47031	+	18.5755i	−0.250468	+	0.850513i
$478$		−	22.4290i		−	1.02588i
$479$	23.7060			1.08315			0.541577	−	0.840651i	$-0.317827\pi$
$479$	23.7060			1.08315			0.541577	+	0.840651i	$0.317827\pi$
$480$		0			0
$481$			10.9178i			0.497808i
$482$	4.78820			0.218097
$483$	1.45059	+	1.93936i	0.0660039	+	0.0882440i
$484$	−10.3178	−	3.81355i	−0.468991	−	0.173343i
$485$		0			0
$486$	15.5509	−	1.08115i	0.705404	−	0.0490418i
$487$			10.3279i			0.468000i	0.972237	+	0.234000i	$0.0751816\pi$
$487$			10.3279i			0.468000i	−0.972237	+	0.234000i	$0.924818\pi$
$488$	−12.8346			−0.580996
$489$	−9.39545	+	7.02752i	−0.424877	+	0.317795i
$490$		0			0
$491$	−21.1608			−0.954975			−0.477488	−	0.878638i	$-0.658452\pi$
$491$	−21.1608			−0.954975			−0.477488	+	0.878638i	$0.658452\pi$
$492$	8.45474	+	11.3036i	0.381169	+	0.509605i
$493$		−	3.06102i		−	0.137862i
$494$	−8.79360			−0.395643
$495$		0			0
$496$	3.66654			0.164632
$497$		−	1.01975i		−	0.0457418i
$498$	−1.76121	−	2.35466i	−0.0789219	−	0.105515i
$499$	−23.6325			−1.05794			−0.528968	−	0.848642i	$-0.677421\pi$
$499$	−23.6325			−1.05794			−0.528968	+	0.848642i	$0.677421\pi$
$500$		0			0
$501$	23.2379	−	17.3812i	1.03819	−	0.776536i
$502$	11.5042			0.513460
$503$			13.5195i			0.602806i	0.953497	+	0.301403i	$0.0974549\pi$
$503$			13.5195i			0.602806i	−0.953497	+	0.301403i	$0.902545\pi$
$504$	1.13414	+	0.333995i	0.0505187	+	0.0148773i
$505$		0			0
$506$	2.07216	−	11.5834i	0.0921185	−	0.514944i
$507$	7.61074	+	10.1752i	0.338005	+	0.451896i
$508$	22.0338			0.977593
$509$		−	31.0930i		−	1.37817i	−0.724679	−	0.689087i	$-0.758012\pi$
$509$		−	31.0930i		−	1.37817i	0.724679	−	0.689087i	$-0.241988\pi$
$510$		0			0
$511$	−4.68628			−0.207309
$512$		−	1.00000i		−	0.0441942i
$513$	6.68812	+	17.9971i	0.295288	+	0.794591i
$514$			16.3431i			0.720865i
$515$		0			0
$516$	−2.69913	−	3.60860i	−0.118822	−	0.158860i
$517$	11.0946	+	1.98472i	0.487940	+	0.0872878i
$518$	1.80795			0.0794365
$519$	18.1639	−	13.5861i	0.797308	−	0.596363i
$520$		0			0
$521$		−	2.40699i		−	0.105452i	−0.998609	−	0.0527261i	$-0.983209\pi$
$521$		−	2.40699i		−	0.105452i	0.998609	−	0.0527261i	$-0.0167910\pi$
$522$	9.71469	+	2.86089i	0.425201	+	0.125218i
$523$	−11.7967			−0.515833			−0.257917	−	0.966167i	$-0.583036\pi$
$523$	−11.7967			−0.515833			−0.257917	+	0.966167i	$0.583036\pi$
$524$	1.97748			0.0863865
$525$		0			0
$526$	3.23463			0.141037
$527$		−	3.32472i		−	0.144827i
$528$	−2.57693	−	5.13414i	−0.112147	−	0.223435i
$529$	−10.4120			−0.452694
$530$		0			0
$531$	22.3601	+	6.58483i	0.970344	+	0.285757i
$532$			1.45619i			0.0631338i
$533$	−19.3953			−0.840106
$534$	15.8764	+	21.2259i	0.687037	+	0.918535i
$535$		0			0
$536$	11.9195			0.514846
$537$	20.7794	−	15.5424i	0.896697	−	0.670702i
$538$	8.94622			0.385699
$539$	−22.3465	−	3.99758i	−0.962532	−	0.172188i
$540$		0			0
$541$			28.7472i			1.23594i	0.786203	+	0.617969i	$0.212044\pi$
$541$			28.7472i			1.23594i	−0.786203	+	0.617969i	$0.787956\pi$
$542$	−3.38297			−0.145311
$543$	−24.8658	−	33.2443i	−1.06709	−	1.42665i
$544$	−0.906774			−0.0388776
$545$		0			0
$546$	−1.30087	+	0.973015i	−0.0556723	+	0.0416412i
$547$	−19.6663			−0.840872			−0.420436	−	0.907322i	$-0.638123\pi$
$547$	−19.6663			−0.840872			−0.420436	+	0.907322i	$0.638123\pi$
$548$	−19.6172			−0.838006
$549$	−36.9355	−	10.8772i	−1.57637	−	0.464226i
$550$		0			0
$551$			12.4732i			0.531378i
$552$	4.92099	−	3.68076i	0.209451	−	0.156663i
$553$		−	1.01139i		−	0.0430087i
$554$		−	5.76983i		−	0.245137i
$555$		0			0
$556$		−	18.7230i		−	0.794033i
$557$		−	14.2710i		−	0.604681i	−0.953200	−	0.302341i	$-0.902232\pi$
$557$		−	14.2710i		−	0.604681i	0.953200	−	0.302341i	$-0.0977680\pi$
$558$	10.5516	+	3.10734i	0.446684	+	0.131544i
$559$	6.19185			0.261887
$560$		0			0
$561$	−4.65551	+	2.33670i	−0.196556	+	0.0986553i
$562$		−	0.115874i		−	0.00488784i
$563$			40.9573i			1.72614i	0.505082	+	0.863072i	$0.331462\pi$
$563$			40.9573i			1.72614i	−0.505082	+	0.863072i	$0.668538\pi$
$564$	3.52544	+	4.71334i	0.148448	+	0.198468i
$565$		0			0
$566$			21.1805i			0.890281i
$567$	2.98079	+	1.92234i	0.125181	+	0.0807308i
$568$	−2.58753			−0.108570
$569$	29.3162			1.22900			0.614500	−	0.788917i	$-0.289358\pi$
$569$	29.3162			1.22900			0.614500	+	0.788917i	$0.289358\pi$
$570$		0			0
$571$		−	19.6381i		−	0.821829i	−0.911674	−	0.410914i	$-0.865209\pi$
$571$		−	19.6381i		−	0.821829i	0.911674	−	0.410914i	$-0.134791\pi$
$572$	7.76983	+	1.38995i	0.324873	+	0.0581166i
$573$	−30.4097	+	22.7455i	−1.27038	+	0.950209i
$574$			3.21180i			0.134058i
$575$		0			0
$576$	0.847487	−	2.87781i	0.0353120	−	0.119909i
$577$			4.75146i			0.197806i	0.995097	+	0.0989029i	$0.0315333\pi$
$577$			4.75146i			0.197806i	−0.995097	+	0.0989029i	$0.968467\pi$
$578$		−	16.1778i		−	0.672906i
$579$	−22.6885	−	30.3334i	−0.942900	−	1.26061i
$580$		0			0
$581$		−	0.669053i		−	0.0277570i
$582$	10.5001	+	14.0381i	0.435243	+	0.581899i
$583$	21.0734	+	3.76983i	0.872771	+	0.156130i
$584$			11.8911i			0.492057i
$585$		0			0
$586$	−16.5143			−0.682200
$587$	23.3572			0.964056			0.482028	−	0.876156i	$-0.339900\pi$
$587$	23.3572			0.964056			0.482028	+	0.876156i	$0.339900\pi$
$588$	−7.10087	−	9.49352i	−0.292835	−	0.391506i
$589$			13.5478i			0.558226i
$590$		0			0
$591$	−25.0128	+	18.7088i	−1.02889	+	0.769577i
$592$		−	4.58753i		−	0.188546i
$593$		−	27.7315i		−	1.13880i	−0.822062	−	0.569398i	$-0.807176\pi$
$593$		−	27.7315i		−	1.13880i	0.822062	−	0.569398i	$-0.192824\pi$
$594$	−3.06479	−	16.9590i	−0.125750	−	0.695835i
$595$		0			0
$596$	−22.0113			−0.901619
$597$	−3.95908	−	5.29310i	−0.162034	−	0.216632i
$598$			8.44373i			0.345290i
$599$		−	9.59602i		−	0.392083i	−0.980596	−	0.196041i	$-0.937191\pi$
$599$		−	9.59602i		−	0.392083i	0.980596	−	0.196041i	$-0.0628087\pi$
$600$		0			0
$601$		−	11.8503i		−	0.483383i	−0.970353	−	0.241692i	$-0.922298\pi$
$601$		−	11.8503i		−	0.483383i	0.970353	−	0.241692i	$-0.0777023\pi$
$602$		−	1.02535i		−	0.0417901i
$603$	34.3021	+	10.1017i	1.39689	+	0.411371i
$604$			13.9278i			0.566716i
$605$		0			0
$606$	4.18645	−	3.13134i	0.170063	−	0.127202i
$607$	−23.9338			−0.971441			−0.485721	−	0.874114i	$-0.661443\pi$
$607$	−23.9338			−0.971441			−0.485721	+	0.874114i	$0.661443\pi$
$608$	3.69497			0.149851
$609$	1.38017	+	1.84522i	0.0559272	+	0.0747720i
$610$		0			0
$611$	−8.08744			−0.327183
$612$	−2.60952	−	0.768479i	−0.105484	−	0.0310639i
$613$	−38.0977			−1.53875			−0.769376	−	0.638797i	$-0.779432\pi$
$613$	−38.0977			−1.53875			−0.769376	+	0.638797i	$0.779432\pi$
$614$		−	17.6526i		−	0.712402i
$615$		0			0
$616$	0.230170	−	1.28666i	0.00927383	−	0.0518408i
$617$	−42.1905			−1.69853			−0.849263	−	0.527969i	$-0.822954\pi$
$617$	−42.1905			−1.69853			−0.849263	+	0.527969i	$0.822954\pi$
$618$	0.624270	+	0.834619i	0.0251118	+	0.0335733i
$619$	−23.2596			−0.934882			−0.467441	−	0.884024i	$-0.654824\pi$
$619$	−23.2596			−0.934882			−0.467441	+	0.884024i	$0.654824\pi$
$620$		0			0
$621$	17.2811	−	6.42202i	0.693465	−	0.257707i
$622$	4.13549			0.165818
$623$			6.03114i			0.241632i
$624$	2.46896	+	3.30087i	0.0988373	+	0.132141i
$625$		0			0
$626$	12.1580			0.485932
$627$	18.9705	−	9.52170i	0.757610	−	0.380260i
$628$		−	2.62427i		−	0.104720i
$629$	−4.15985			−0.165864
$630$		0			0
$631$	10.8902			0.433531			0.216765	−	0.976224i	$-0.430449\pi$
$631$	10.8902			0.433531			0.216765	+	0.976224i	$0.430449\pi$
$632$	−2.56633			−0.102083
$633$	−26.4781	+	19.8048i	−1.05241	+	0.787171i
$634$			6.97195i			0.276892i
$635$		0			0
$636$	6.69632	+	8.95266i	0.265527	+	0.354996i
$637$	16.2895			0.645415
$638$	1.97156	−	11.0211i	0.0780550	−	0.436328i
$639$	−7.44641	−	2.19290i	−0.294575	−	0.0867497i
$640$		0			0
$641$		−	20.2076i		−	0.798154i	−0.916917	−	0.399077i	$-0.869331\pi$
$641$		−	20.2076i		−	0.798154i	0.916917	−	0.399077i	$-0.130669\pi$
$642$	−15.8162	−	21.1456i	−0.624218	−	0.834549i
$643$			37.2937i			1.47072i	0.677677	+	0.735360i	$0.262987\pi$
$643$			37.2937i			1.47072i	−0.677677	+	0.735360i	$0.737013\pi$
$644$	1.39825			0.0550988
$645$		0			0
$646$		−	3.35051i		−	0.131824i
$647$	21.5681			0.847929			0.423965	−	0.905679i	$-0.360638\pi$
$647$	21.5681			0.847929			0.423965	+	0.905679i	$0.360638\pi$
$648$	4.87781	−	7.56353i	0.191618	−	0.297124i
$649$	4.53790	−	25.3669i	0.178128	−	0.995738i
$650$		0			0
$651$	1.49906	+	2.00418i	0.0587530	+	0.0785499i
$652$			6.77398i			0.265290i
$653$	32.8837			1.28684			0.643420	−	0.765513i	$-0.277515\pi$
$653$	32.8837			1.28684			0.643420	+	0.765513i	$0.277515\pi$
$654$	19.0648	+	25.4887i	0.745492	+	0.996687i
$655$		0			0
$656$	8.14971			0.318193
$657$	−10.0776	+	34.2203i	−0.393163	+	1.33506i
$658$			1.33925i			0.0522094i
$659$	−36.5278			−1.42292			−0.711460	−	0.702727i	$-0.751966\pi$
$659$	−36.5278			−1.42292			−0.711460	+	0.702727i	$0.751966\pi$
$660$		0			0
$661$	−30.7936			−1.19773			−0.598866	−	0.800849i	$-0.704382\pi$
$661$	−30.7936			−1.19773			−0.598866	+	0.800849i	$0.704382\pi$
$662$			5.39825i			0.209809i
$663$	2.99315	−	2.23879i	0.116244	−	0.0869472i
$664$	−1.69767			−0.0658825
$665$		0			0
$666$	3.88787	−	13.2020i	0.150652	−	0.511568i
$667$	11.9770			0.463750
$668$		−	16.7542i		−	0.648238i
$669$	3.02107	−	2.25967i	0.116801	−	0.0873639i
$670$		0			0
$671$	−7.49594	+	41.9024i	−0.289378	+	1.61762i
$672$	0.546613	−	0.408850i	0.0210861	−	0.0157717i
$673$	13.8699			0.534646			0.267323	−	0.963607i	$-0.413861\pi$
$673$	13.8699			0.534646			0.267323	+	0.963607i	$0.413861\pi$
$674$		−	24.7657i		−	0.953938i
$675$		0			0
$676$	7.33616			0.282160
$677$			36.4913i			1.40247i	0.712928	+	0.701237i	$0.247368\pi$
$677$			36.4913i			1.40247i	−0.712928	+	0.701237i	$0.752632\pi$
$678$	8.84884	−	6.61867i	0.339838	−	0.254188i
$679$			3.98879i			0.153076i
$680$		0			0
$681$	9.48549	−	7.09486i	0.363485	−	0.271876i
$682$	2.14141	−	11.9705i	0.0819987	−	0.458374i
$683$	11.3518			0.434366			0.217183	−	0.976131i	$-0.430313\pi$
$683$	11.3518			0.434366			0.217183	+	0.976131i	$0.430313\pi$
$684$	10.6334	+	3.13144i	0.406579	+	0.119734i
$685$		0			0
$686$		−	5.45619i		−	0.208318i
$687$	−24.7399	−	33.0761i	−0.943888	−	1.26193i
$688$	−2.60175			−0.0991907
$689$	−15.3615			−0.585227
$690$		0			0
$691$	−36.6578			−1.39453			−0.697265	−	0.716813i	$-0.745600\pi$
$691$	−36.6578			−1.39453			−0.697265	+	0.716813i	$0.745600\pi$
$692$		−	13.0959i		−	0.497832i
$693$	1.75281	−	3.50768i	0.0665837	−	0.133246i
$694$	30.3416			1.15175
$695$		0			0
$696$	4.68211	−	3.50208i	0.177475	−	0.132746i
$697$		−	7.38995i		−	0.279914i
$698$	21.6172			0.818224
$699$	−14.6688	+	10.9718i	−0.554826	+	0.414993i
$700$		0			0
$701$	1.64422			0.0621012			0.0310506	−	0.999518i	$-0.490115\pi$
$701$	1.64422			0.0621012			0.0310506	+	0.999518i	$0.490115\pi$
$702$	4.30773	+	11.5917i	0.162585	+	0.437500i
$703$	16.9508			0.639312
$704$	−3.26480	−	0.584041i	−0.123047	−	0.0220119i
$705$		0			0
$706$			7.70465i			0.289968i
$707$	1.18954			0.0447372
$708$	10.7767	−	8.06064i	0.405013	−	0.302937i
$709$	−48.7172			−1.82961			−0.914807	−	0.403892i	$-0.867657\pi$
$709$	−48.7172			−1.82961			−0.914807	+	0.403892i	$0.867657\pi$
$710$		0			0
$711$	−7.38541	−	2.17493i	−0.276974	−	0.0815664i
$712$	15.3036			0.573526
$713$	13.0087			0.487181
$714$	−0.370735	−	0.495654i	−0.0138744	−	0.0185494i
$715$		0			0
$716$		−	14.9816i		−	0.559890i
$717$	−23.2685	−	31.1088i	−0.868977	−	1.16178i
$718$			0.344467i			0.0128554i
$719$		−	22.9460i		−	0.855740i	−0.903840	−	0.427870i	$-0.859264\pi$
$719$		−	22.9460i		−	0.855740i	0.903840	−	0.427870i	$-0.140736\pi$
$720$		0			0
$721$			0.237149i			0.00883189i
$722$		−	5.34717i		−	0.199001i
$723$	6.64119	−	4.96741i	0.246988	−	0.184740i
$724$	−23.9687			−0.890788
$725$		0			0
$726$	−18.2670	+	5.41461i	−0.677951	+	0.200955i
$727$		−	22.0623i		−	0.818244i	−0.912480	−	0.409122i	$-0.865835\pi$
$727$		−	22.0623i		−	0.818244i	0.912480	−	0.409122i	$-0.134165\pi$
$728$			0.937911i			0.0347613i
$729$	20.4474	−	17.6325i	0.757310	−	0.653055i
$730$		0			0
$731$			2.35920i			0.0872581i
$732$	−17.8015	+	13.3150i	−0.657962	+	0.492136i
$733$	−27.0522			−0.999196			−0.499598	−	0.866257i	$-0.666519\pi$
$733$	−27.0522			−0.999196			−0.499598	+	0.866257i	$0.666519\pi$
$734$	27.9687			1.03234
$735$		0			0
$736$		−	3.54796i		−	0.130780i
$737$	6.96150	−	38.9149i	0.256430	−	1.43345i
$738$	23.4533	+	6.90677i	0.863327	+	0.254242i
$739$		−	28.2286i		−	1.03841i	−0.854651	−	0.519203i	$-0.826229\pi$
$739$		−	28.2286i		−	1.03841i	0.854651	−	0.519203i	$-0.173771\pi$
$740$		0			0
$741$	−12.1966	+	9.12273i	−0.448055	+	0.335132i
$742$			2.54381i			0.0933862i
$743$		−	4.98591i		−	0.182915i	−0.995809	−	0.0914576i	$-0.970847\pi$
$743$		−	4.98591i		−	0.182915i	0.995809	−	0.0914576i	$-0.0291526\pi$
$744$	5.08545	−	3.80377i	0.186442	−	0.139453i
$745$		0			0
$746$			21.8911i			0.801490i
$747$	−4.88558	−	1.43876i	−0.178754	−	0.0526414i
$748$	−0.529593	+	2.96043i	−0.0193638	+	0.108244i
$749$		−	6.00830i		−	0.219539i
$750$		0			0
$751$	7.87312			0.287294			0.143647	−	0.989629i	$-0.454117\pi$
$751$	7.87312			0.287294			0.143647	+	0.989629i	$0.454117\pi$
$752$	3.39825			0.123921
$753$	15.9563	−	11.9348i	0.581479	−	0.434929i
$754$			8.03384i			0.292575i
$755$		0			0
$756$	1.91954	−	0.713344i	0.0698130	−	0.0259441i
$757$		−	13.2250i		−	0.480669i	−0.970690	−	0.240335i	$-0.922743\pi$
$757$		−	13.2250i		−	0.480669i	0.970690	−	0.240335i	$-0.0772572\pi$
$758$		−	29.8023i		−	1.08247i
$759$	−9.14286	−	18.2158i	−0.331865	−	0.661190i
$760$		0			0
$761$	−40.3923			−1.46422			−0.732109	−	0.681187i	$-0.761464\pi$
$761$	−40.3923			−1.46422			−0.732109	+	0.681187i	$0.761464\pi$
$762$	30.5607	−	22.8585i	1.10710	−	0.828077i
$763$			7.24237i			0.262191i
$764$			21.9249i			0.793217i
$765$		0			0
$766$		−	31.3017i		−	1.13098i
$767$			18.4913i			0.667681i
$768$	−1.03743	−	1.38699i	−0.0374350	−	0.0500487i
$769$			14.2433i			0.513627i	0.966461	+	0.256814i	$0.0826727\pi$
$769$			14.2433i			0.513627i	−0.966461	+	0.256814i	$0.917327\pi$
$770$		0			0
$771$	16.9548	+	22.6678i	0.610613	+	0.816360i
$772$	−21.8699			−0.787115
$773$	7.21450			0.259488			0.129744	−	0.991548i	$-0.458585\pi$
$773$	7.21450			0.259488			0.129744	+	0.991548i	$0.458585\pi$
$774$	−7.48733	−	2.20495i	−0.269126	−	0.0792552i
$775$		0			0
$776$	10.1213			0.363333
$777$	2.50760	−	1.87561i	0.0899598	−	0.0672872i
$778$	16.5733			0.594182
$779$			30.1130i			1.07891i
$780$		0			0
$781$	−1.51122	+	8.44776i	−0.0540758	+	0.302285i
$782$	−3.21720			−0.115047
$783$	16.4422	−	6.11027i	0.587595	−	0.218363i
$784$	−6.84469			−0.244453
$785$		0			0
$786$	2.74274	−	2.05149i	0.0978304	−	0.0731742i
$787$	−8.68088			−0.309440			−0.154720	−	0.987958i	$-0.549448\pi$
$787$	−8.68088			−0.309440			−0.154720	+	0.987958i	$0.549448\pi$
$788$			18.0338i			0.642429i
$789$	4.48641	−	3.35570i	0.159720	−	0.119466i
$790$		0			0
$791$	2.51431			0.0893986
$792$	−8.90048	−	4.44763i	−0.316265	−	0.158040i
$793$		−	30.5449i		−	1.08468i
$794$	3.94798			0.140108
$795$		0			0
$796$	−3.81625			−0.135263
$797$	41.6239			1.47440			0.737198	−	0.675677i	$-0.236149\pi$
$797$	41.6239			1.47440			0.737198	+	0.675677i	$0.236149\pi$
$798$	1.51069	+	2.01972i	0.0534779	+	0.0714973i
$799$		−	3.08145i		−	0.109014i
$800$		0			0
$801$	44.0407	+	12.9696i	1.55610	+	0.458258i
$802$	−4.72486			−0.166841
$803$	38.8220	+	6.94489i	1.37000	+	0.245080i
$804$	16.5323	−	12.3657i	0.583049	−	0.436103i
$805$		0			0
$806$			8.72593i			0.307358i
$807$	12.4083	−	9.28105i	0.436793	−	0.326709i
$808$		−	3.01837i		−	0.106186i
$809$	7.92917			0.278775			0.139387	−	0.990238i	$-0.455487\pi$
$809$	7.92917			0.278775			0.139387	+	0.990238i	$0.455487\pi$
$810$		0			0
$811$		−	29.9743i		−	1.05254i	−0.850318	−	0.526269i	$-0.823590\pi$
$811$		−	29.9743i		−	1.05254i	0.850318	−	0.526269i	$-0.176410\pi$
$812$	1.33037			0.0466870
$813$	−4.69215	+	3.50959i	−0.164561	+	0.123087i
$814$	−14.9774	−	2.67930i	−0.524956	−	0.0939096i
$815$		0			0
$816$	−1.25769	+	0.940713i	−0.0440279	+	0.0329315i
$817$		−	9.61339i		−	0.336330i
$818$	−12.1497			−0.424805
$819$	−0.794867	+	2.69913i	−0.0277749	+	0.0943151i
$820$		0			0
$821$	−7.46210			−0.260429			−0.130215	−	0.991486i	$-0.541567\pi$
$821$	−7.46210			−0.260429			−0.130215	+	0.991486i	$0.541567\pi$
$822$	−27.2089	+	20.3514i	−0.949019	+	0.709838i
$823$		−	45.0224i		−	1.56938i	−0.619886	−	0.784692i	$-0.712821\pi$
$823$		−	45.0224i		−	1.56938i	0.619886	−	0.784692i	$-0.287179\pi$
$824$	0.601748			0.0209629
$825$		0			0
$826$	3.06209			0.106544
$827$			35.9716i			1.25085i	0.780283	+	0.625427i	$0.215075\pi$
$827$			35.9716i			1.25085i	−0.780283	+	0.625427i	$0.784925\pi$
$828$	3.00685	−	10.2103i	0.104495	−	0.354834i
$829$	7.50832			0.260775			0.130387	−	0.991463i	$-0.458378\pi$
$829$	7.50832			0.260775			0.130387	+	0.991463i	$0.458378\pi$
$830$		0			0
$831$	−5.98578	−	8.00270i	−0.207644	−	0.277611i
$832$	2.37988			0.0825076
$833$			6.20658i			0.215045i
$834$	−19.4238	−	25.9687i	−0.672591	−	0.899221i
$835$		0			0
$836$	2.15802	−	12.0633i	0.0746365	−	0.417219i
$837$	17.8586	−	6.63665i	0.617283	−	0.229396i
$838$	−7.01547			−0.242345
$839$			41.7806i			1.44243i	0.692713	+	0.721214i	$0.256415\pi$
$839$			41.7806i			1.44243i	−0.692713	+	0.721214i	$0.743585\pi$
$840$		0			0
$841$	−17.6044			−0.607050
$842$			13.0085i			0.448302i
$843$	−0.120211	−	0.160716i	−0.00414028	−	0.00553535i
$844$			19.0903i			0.657116i
$845$		0			0
$846$	9.77951	+	2.87997i	0.336226	+	0.0990156i
$847$	−4.06624	−	1.50292i	−0.139718	−	0.0516409i
$848$	6.45474			0.221657
$849$	21.9732	+	29.3771i	0.754118	+	1.00822i
$850$		0			0
$851$		−	16.2764i		−	0.557947i
$852$	−3.58888	+	2.68438i	−0.122953	+	0.0919652i
$853$	−35.6816			−1.22172			−0.610858	−	0.791740i	$-0.709175\pi$
$853$	−35.6816			−1.22172			−0.610858	+	0.791740i	$0.709175\pi$
$854$	−5.05812			−0.173085
$855$		0			0
$856$	−15.2456			−0.521085
$857$		−	39.8584i		−	1.36154i	−0.732499	−	0.680768i	$-0.761646\pi$
$857$		−	39.8584i		−	1.36154i	0.732499	−	0.680768i	$-0.238354\pi$
$858$	12.2187	−	6.13279i	0.417138	−	0.209370i
$859$	−44.9857			−1.53489			−0.767446	−	0.641113i	$-0.778473\pi$
$859$	−44.9857			−1.53489			−0.767446	+	0.641113i	$0.778473\pi$
$860$		0			0
$861$	3.33201	+	4.45474i	0.113555	+	0.151817i
$862$			23.5397i			0.801764i
$863$	−18.8644			−0.642153			−0.321076	−	0.947053i	$-0.604045\pi$
$863$	−18.8644			−0.642153			−0.321076	+	0.947053i	$0.604045\pi$
$864$	−1.81006	−	4.87070i	−0.0615795	−	0.165704i
$865$		0			0
$866$	−3.05919			−0.103955
$867$	−16.7833	−	22.4384i	−0.569989	−	0.762048i
$868$	1.44498			0.0490459
$869$	−1.49884	+	8.37856i	−0.0508448	+	0.284223i
$870$		0			0
$871$			28.3671i			0.961182i
$872$	18.3770			0.622323
$873$	29.1271	+	8.57765i	0.985802	+	0.290309i
$874$	13.1096			0.443440
$875$		0			0
$876$	12.3362	+	16.4929i	0.416800	+	0.557242i
$877$	−39.1853			−1.32319			−0.661597	−	0.749860i	$-0.730121\pi$
$877$	−39.1853			−1.32319			−0.661597	+	0.749860i	$0.730121\pi$
$878$	−27.8461			−0.939759
$879$	−22.9052	+	17.1324i	−0.772573	+	0.577862i
$880$		0			0
$881$			32.2286i			1.08581i	0.839794	+	0.542904i	$0.182675\pi$
$881$			32.2286i			1.08581i	−0.839794	+	0.542904i	$0.817325\pi$
$882$	−19.6977	−	5.80078i	−0.663255	−	0.195322i
$883$		−	44.2593i		−	1.48944i	−0.667375	−	0.744721i	$-0.732582\pi$
$883$		−	44.2593i		−	1.48944i	0.667375	−	0.744721i	$-0.267418\pi$
$884$		−	2.15802i		−	0.0725819i
$885$		0			0
$886$			28.5213i			0.958191i
$887$			28.6557i			0.962165i	0.876675	+	0.481082i	$0.159756\pi$
$887$			28.6557i			0.962165i	−0.876675	+	0.481082i	$0.840244\pi$
$888$	−4.75923	−	6.36286i	−0.159709	−	0.213524i
$889$	8.68353			0.291236
$890$		0			0
$891$	−21.8446	−	20.3425i	−0.731820	−	0.681498i
$892$		−	2.17815i		−	0.0729298i
$893$			12.5565i			0.420186i
$894$	−30.5295	+	22.8352i	−1.02106	+	0.763722i
$895$		0			0
$896$		−	0.394100i		−	0.0131660i
$897$	8.75976	+	11.7114i	0.292480	+	0.391032i
$898$	−4.00000			−0.133482
$899$	12.3772			0.412804
$900$		0			0
$901$		−	5.85299i		−	0.194991i
$902$	4.75976	−	26.6071i	0.158483	−	0.885921i
$903$	−1.06373	−	1.42215i	−0.0353986	−	0.0473262i
$904$		−	6.37988i		−	0.212192i
$905$		0			0
$906$	14.4491	+	19.3178i	0.480040	+	0.641791i
$907$			7.17532i			0.238253i	0.992879	+	0.119126i	$0.0380093\pi$
$907$			7.17532i			0.238253i	−0.992879	+	0.119126i	$0.961991\pi$
$908$		−	6.83890i		−	0.226957i
$909$	2.55803	−	8.68628i	0.0848445	−	0.288106i
$910$		0			0
$911$		−	32.0314i		−	1.06125i	−0.847607	−	0.530625i	$-0.821957\pi$
$911$		−	32.0314i		−	1.06125i	0.847607	−	0.530625i	$-0.178043\pi$
$912$	5.12489	−	3.83327i	0.169702	−	0.126932i
$913$	−0.991511	+	5.54256i	−0.0328142	+	0.183432i
$914$			13.0651i			0.432155i
$915$		0			0
$916$	−23.8474			−0.787940
$917$	0.779324			0.0257355
$918$	−4.41662	+	1.64131i	−0.145770	+	0.0541715i
$919$			8.61703i			0.284250i	0.989849	+	0.142125i	$0.0453934\pi$
$919$			8.61703i			0.284250i	−0.989849	+	0.142125i	$0.954607\pi$
$920$		0			0
$921$	−18.3133	−	24.4840i	−0.603445	−	0.806776i
$922$		−	20.1355i		−	0.663127i
$923$		−	6.15802i		−	0.202694i
$924$	−1.01557	−	2.02337i	−0.0334097	−	0.0665638i
$925$		0			0
$926$	12.6071			0.414297
$927$	1.73171	+	0.509974i	0.0568770	+	0.0167497i
$928$		−	3.37573i		−	0.110814i
$929$		−	2.05503i		−	0.0674235i	−0.999432	−	0.0337117i	$-0.989267\pi$
$929$		−	2.05503i		−	0.0674235i	0.999432	−	0.0337117i	$-0.0107328\pi$
$930$		0			0
$931$		−	25.2909i		−	0.828877i
$932$			10.5760i			0.346429i
$933$	5.73589	−	4.29028i	0.187785	−	0.140457i
$934$			14.9843i			0.490302i
$935$		0			0
$936$	6.84884	+	2.01692i	0.223861	+	0.0659251i
$937$	−19.8342			−0.647956			−0.323978	−	0.946065i	$-0.605020\pi$
$937$	−19.8342			−0.647956			−0.323978	+	0.946065i	$0.605020\pi$
$938$	4.69749			0.153378
$939$	16.8631	−	12.6131i	0.550305	−	0.411612i
$940$		0			0
$941$	−6.98887			−0.227831			−0.113915	−	0.993490i	$-0.536339\pi$
$941$	−6.98887			−0.227831			−0.113915	+	0.993490i	$0.536339\pi$
$942$	−2.72249	−	3.63984i	−0.0887036	−	0.118592i
$943$	28.9149			0.941598
$944$		−	7.76983i		−	0.252886i
$945$		0			0
$946$	−1.51953	+	8.49418i	−0.0494041	+	0.276170i
$947$	29.3913			0.955090			0.477545	−	0.878607i	$-0.341527\pi$
$947$	29.3913			0.955090			0.477545	+	0.878607i	$0.341527\pi$
$948$	−3.55948	+	2.66239i	−0.115607	+	0.0864703i
$949$	−28.2994			−0.918638
$950$		0			0
$951$	7.23290	+	9.67003i	0.234543	+	0.313572i
$952$	−0.357360			−0.0115821
$953$			0.203883i			0.00660443i	0.999995	+	0.00330221i	$0.00105113\pi$
$953$			0.203883i			0.00660443i	−0.999995	+	0.00330221i	$0.998949\pi$
$954$	18.5755	+	5.47031i	0.601403	+	0.177108i
$955$		0			0
$956$	−22.4290			−0.725406
$957$	−8.69902	−	17.3315i	−0.281200	−	0.560247i
$958$		−	23.7060i		−	0.765905i
$959$	−7.73114			−0.249652
$960$		0			0
$961$	−17.5565			−0.566339
$962$	10.9178			0.352003
$963$	−43.8740	−	12.9205i	−1.41382	−	0.416357i
$964$		−	4.78820i		−	0.154218i
$965$		0			0
$966$	1.93936	−	1.45059i	0.0623980	−	0.0466718i
$967$	55.4842			1.78425			0.892126	−	0.451786i	$-0.149213\pi$
$967$	55.4842			1.78425			0.892126	+	0.451786i	$0.149213\pi$
$968$	−3.81355	+	10.3178i	−0.122572	+	0.331626i
$969$	−3.47591	−	4.64712i	−0.111662	−	0.149287i
$970$		0			0
$971$		−	15.0321i		−	0.482402i	−0.970475	−	0.241201i	$-0.922459\pi$
$971$		−	15.0321i		−	0.482402i	0.970475	−	0.241201i	$-0.0775413\pi$
$972$	−1.08115	−	15.5509i	−0.0346778	−	0.498796i
$973$		−	7.37874i		−	0.236552i
$974$	10.3279			0.330926
$975$		0			0
$976$			12.8346i			0.410826i
$977$	44.5267			1.42454			0.712268	−	0.701908i	$-0.247668\pi$
$977$	44.5267			1.42454			0.712268	+	0.701908i	$0.247668\pi$
$978$	7.02752	+	9.39545i	0.224715	+	0.300433i
$979$	8.93791	−	49.9631i	0.285657	−	1.59683i
$980$		0			0
$981$	52.8854	+	15.5743i	1.68850	+	0.497248i
$982$			21.1608i			0.675270i
$983$	−20.2004			−0.644293			−0.322146	−	0.946690i	$-0.604404\pi$
$983$	−20.2004			−0.644293			−0.322146	+	0.946690i	$0.604404\pi$
$984$	11.3036	−	8.45474i	0.360345	−	0.269527i
$985$		0			0
$986$	−3.06102			−0.0974829
$987$	1.38938	+	1.85753i	0.0442243	+	0.0591258i
$988$			8.79360i			0.279762i
$989$	−9.23091			−0.293526
$990$		0			0
$991$	−39.1668			−1.24417			−0.622087	−	0.782949i	$-0.713715\pi$
$991$	−39.1668			−1.24417			−0.622087	+	0.782949i	$0.713715\pi$
$992$		−	3.66654i		−	0.116413i
$993$	5.60030	+	7.48733i	0.177720	+	0.237603i
$994$	−1.01975			−0.0323444
$995$		0			0
$996$	−2.35466	+	1.76121i	−0.0746102	+	0.0558062i
$997$	20.6426			0.653757			0.326878	−	0.945066i	$-0.394003\pi$
$997$	20.6426			0.653757			0.326878	+	0.945066i	$0.394003\pi$
$998$			23.6325i			0.748074i
$999$	−8.30370	−	22.3445i	−0.262717	−	0.706948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.f.e.1649.1		8
3.2	odd	2		1650.2.f.d.1649.8		8
5.2	odd	4		1650.2.d.f.1451.2		8
5.3	odd	4		330.2.d.a.131.7	✓	8
5.4	even	2		1650.2.f.c.1649.8		8
11.10	odd	2		1650.2.f.f.1649.5		8
15.2	even	4		1650.2.d.c.1451.1		8
15.8	even	4		330.2.d.b.131.8	yes	8
15.14	odd	2		1650.2.f.f.1649.1		8
20.3	even	4		2640.2.f.b.1121.2		8
33.32	even	2		1650.2.f.c.1649.4		8
55.32	even	4		1650.2.d.c.1451.2		8
55.43	even	4		330.2.d.b.131.7	yes	8
55.54	odd	2		1650.2.f.d.1649.4		8
60.23	odd	4		2640.2.f.a.1121.1		8
165.32	odd	4		1650.2.d.f.1451.1		8
165.98	odd	4		330.2.d.a.131.8	yes	8
165.164	even	2	inner	1650.2.f.e.1649.5		8
220.43	odd	4		2640.2.f.a.1121.2		8
660.263	even	4		2640.2.f.b.1121.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.d.a.131.7	✓	8	5.3	odd	4
330.2.d.a.131.8	yes	8	165.98	odd	4
330.2.d.b.131.7	yes	8	55.43	even	4
330.2.d.b.131.8	yes	8	15.8	even	4
1650.2.d.c.1451.1		8	15.2	even	4
1650.2.d.c.1451.2		8	55.32	even	4
1650.2.d.f.1451.1		8	165.32	odd	4
1650.2.d.f.1451.2		8	5.2	odd	4
1650.2.f.c.1649.4		8	33.32	even	2
1650.2.f.c.1649.8		8	5.4	even	2
1650.2.f.d.1649.4		8	55.54	odd	2
1650.2.f.d.1649.8		8	3.2	odd	2
1650.2.f.e.1649.1		8	1.1	even	1	trivial
1650.2.f.e.1649.5		8	165.164	even	2	inner
1650.2.f.f.1649.1		8	15.14	odd	2
1650.2.f.f.1649.5		8	11.10	odd	2
2640.2.f.a.1121.1		8	60.23	odd	4
2640.2.f.a.1121.2		8	220.43	odd	4
2640.2.f.b.1121.1		8	660.263	even	4
2640.2.f.b.1121.2		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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.03743 - 1.38699i) q^{3} -1.00000 q^{4} +(-1.38699 + 1.03743i) q^{6} -0.394100 q^{7} +1.00000i q^{8} +(-0.847487 + 2.87781i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.03743 - 1.38699i) q^{3} -1.00000 q^{4} +(-1.38699 + 1.03743i) q^{6} -0.394100 q^{7} +1.00000i q^{8} +(-0.847487 + 2.87781i) q^{9} +(3.26480 + 0.584041i) q^{11} +(1.03743 + 1.38699i) q^{12} -2.37988 q^{13} +0.394100i q^{14} +1.00000 q^{16} -0.906774i q^{17} +(2.87781 + 0.847487i) q^{18} +3.69497i q^{19} +(0.408850 + 0.546613i) q^{21} +(0.584041 - 3.26480i) q^{22} +3.54796 q^{23} +(1.38699 - 1.03743i) q^{24} +2.37988i q^{26} +(4.87070 - 1.81006i) q^{27} +0.394100 q^{28} +3.37573 q^{29} +3.66654 q^{31} -1.00000i q^{32} +(-2.57693 - 5.13414i) q^{33} -0.906774 q^{34} +(0.847487 - 2.87781i) q^{36} -4.58753i q^{37} +3.69497 q^{38} +(2.46896 + 3.30087i) q^{39} +8.14971 q^{41} +(0.546613 - 0.408850i) q^{42} -2.60175 q^{43} +(-3.26480 - 0.584041i) q^{44} -3.54796i q^{46} +3.39825 q^{47} +(-1.03743 - 1.38699i) q^{48} -6.84469 q^{49} +(-1.25769 + 0.940713i) q^{51} +2.37988 q^{52} +6.45474 q^{53} +(-1.81006 - 4.87070i) q^{54} -0.394100i q^{56} +(5.12489 - 3.83327i) q^{57} -3.37573i q^{58} -7.76983i q^{59} +12.8346i q^{61} -3.66654i q^{62} +(0.333995 - 1.13414i) q^{63} -1.00000 q^{64} +(-5.13414 + 2.57693i) q^{66} -11.9195i q^{67} +0.906774i q^{68} +(-3.68076 - 4.92099i) q^{69} +2.58753i q^{71} +(-2.87781 - 0.847487i) q^{72} +11.8911 q^{73} -4.58753 q^{74} -3.69497i q^{76} +(-1.28666 - 0.230170i) q^{77} +(3.30087 - 2.46896i) q^{78} +2.56633i q^{79} +(-7.56353 - 4.87781i) q^{81} -8.14971i q^{82} +1.69767i q^{83} +(-0.408850 - 0.546613i) q^{84} +2.60175i q^{86} +(-3.50208 - 4.68211i) q^{87} +(-0.584041 + 3.26480i) q^{88} -15.3036i q^{89} +0.937911 q^{91} -3.54796 q^{92} +(-3.80377 - 5.08545i) q^{93} -3.39825i q^{94} +(-1.38699 + 1.03743i) q^{96} -10.1213i q^{97} +6.84469i q^{98} +(-4.44763 + 8.90048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 8 * q^4 - 2 * q^6 - 2 * q^9	\( 8 q + 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} - 4 q^{12} - 4 q^{13} + 8 q^{16} + 8 q^{21} - 6 q^{22} - 8 q^{23} + 2 q^{24} + 10 q^{27} - 4 q^{29} - 4 q^{31} - 4 q^{33} - 4 q^{34} + 2 q^{36} + 20 q^{38} - 8 q^{39} + 16 q^{41} + 6 q^{42} - 8 q^{43} + 6 q^{44} + 40 q^{47} + 4 q^{48} + 4 q^{49} + 28 q^{51} + 4 q^{52} + 12 q^{53} - 22 q^{54} - 12 q^{57} + 32 q^{63} - 8 q^{64} - 18 q^{66} - 8 q^{69} - 12 q^{73} - 12 q^{74} + 8 q^{77} + 20 q^{78} + 2 q^{81} - 8 q^{84} - 36 q^{87} + 6 q^{88} - 48 q^{91} + 8 q^{92} + 2 q^{93} - 2 q^{96} + 10 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more