LMFDB - Embedded newform 810.3.g.i.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(163,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 54 x^{9} + 921 x^{8} - 1350 x^{7} + 1458 x^{6} - 18792 x^{5} + 231804 x^{4} - 552420 x^{3} + \cdots + 656100 $ x^12 - 54x^9 + 921x^8 - 1350x^7 + 1458x^6 - 18792x^5 + 231804x^4 - 552420x^3 + 583200x^2 + 874800*x + 656100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.2
Root			$-3.24958 + 3.24958i$ of defining polynomial
Character	$\chi$	$=$	810.163
Dual form			810.3.g.i.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-1.76846 + 4.67681i) q^{5} +(-4.32826 + 4.32826i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-1.76846 + 4.67681i) q^{5} +(-4.32826 + 4.32826i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.90835 - 6.44527i) q^{10} -9.81423 q^{11} +(-13.2857 - 13.2857i) q^{13} -8.65652i q^{14} -4.00000 q^{16} +(18.6089 - 18.6089i) q^{17} -16.6095i q^{19} +(9.35362 + 3.53692i) q^{20} +(9.81423 - 9.81423i) q^{22} +(11.3765 + 11.3765i) q^{23} +(-18.7451 - 16.5415i) q^{25} +26.5713 q^{26} +(8.65652 + 8.65652i) q^{28} +34.0875i q^{29} +29.4950 q^{31} +(4.00000 - 4.00000i) q^{32} +37.2178i q^{34} +(-12.5881 - 27.8968i) q^{35} +(-27.3850 + 27.3850i) q^{37} +(16.6095 + 16.6095i) q^{38} +(-12.8905 + 5.81670i) q^{40} +22.4637 q^{41} +(-25.2230 - 25.2230i) q^{43} +19.6285i q^{44} -22.7530 q^{46} +(44.0549 - 44.0549i) q^{47} +11.5323i q^{49} +(35.2866 - 2.20360i) q^{50} +(-26.5713 + 26.5713i) q^{52} +(14.0186 + 14.0186i) q^{53} +(17.3561 - 45.8993i) q^{55} -17.3130 q^{56} +(-34.0875 - 34.0875i) q^{58} +21.0132i q^{59} +69.8487 q^{61} +(-29.4950 + 29.4950i) q^{62} +8.00000i q^{64} +(85.6298 - 38.6394i) q^{65} +(1.75875 - 1.75875i) q^{67} +(-37.2178 - 37.2178i) q^{68} +(40.4849 + 15.3087i) q^{70} +99.0623 q^{71} +(-0.175127 - 0.175127i) q^{73} -54.7700i q^{74} -33.2189 q^{76} +(42.4786 - 42.4786i) q^{77} -64.2928i q^{79} +(7.07384 - 18.7072i) q^{80} +(-22.4637 + 22.4637i) q^{82} +(-45.7761 - 45.7761i) q^{83} +(54.1211 + 119.939i) q^{85} +50.4459 q^{86} +(-19.6285 - 19.6285i) q^{88} -43.0842i q^{89} +115.008 q^{91} +(22.7530 - 22.7530i) q^{92} +88.1097i q^{94} +(77.6793 + 29.3732i) q^{95} +(117.314 - 117.314i) q^{97} +(-11.5323 - 11.5323i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 6 q^{7} + 24 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 6 * q^7 + 24 * q^8	$ 12 q - 12 q^{2} + 6 q^{7} + 24 q^{8} - 6 q^{10} - 12 q^{11} - 48 q^{16} + 18 q^{17} + 12 q^{20} + 12 q^{22} - 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} + 48 q^{32} + 168 q^{35} + 66 q^{37} - 36 q^{38} - 12 q^{40} + 24 q^{41} - 108 q^{43} + 108 q^{46} + 48 q^{47} + 54 q^{50} - 192 q^{53} - 276 q^{55} + 24 q^{56} - 60 q^{58} + 456 q^{61} - 72 q^{62} + 264 q^{65} - 12 q^{67} - 36 q^{68} - 174 q^{70} + 84 q^{71} - 216 q^{73} + 72 q^{76} - 48 q^{77} - 24 q^{82} - 246 q^{83} - 324 q^{85} + 216 q^{86} - 24 q^{88} + 612 q^{91} - 108 q^{92} + 432 q^{95} + 102 q^{97} - 12 q^{98}+O(q^{100}) $ 12 * q - 12 * q^2 + 6 * q^7 + 24 * q^8 - 6 * q^10 - 12 * q^11 - 48 * q^16 + 18 * q^17 + 12 * q^20 + 12 * q^22 - 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 + 48 * q^32 + 168 * q^35 + 66 * q^37 - 36 * q^38 - 12 * q^40 + 24 * q^41 - 108 * q^43 + 108 * q^46 + 48 * q^47 + 54 * q^50 - 192 * q^53 - 276 * q^55 + 24 * q^56 - 60 * q^58 + 456 * q^61 - 72 * q^62 + 264 * q^65 - 12 * q^67 - 36 * q^68 - 174 * q^70 + 84 * q^71 - 216 * q^73 + 72 * q^76 - 48 * q^77 - 24 * q^82 - 246 * q^83 - 324 * q^85 + 216 * q^86 - 24 * q^88 + 612 * q^91 - 108 * q^92 + 432 * q^95 + 102 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−1.76846	+	4.67681i	−0.353692	+	0.935362i
$5$	−1.76846	+	4.67681i	−0.353692	+	0.935362i
$6$		0			0
$7$	−4.32826	+	4.32826i	−0.618323	+	0.618323i	−0.945101	−	0.326778i	$-0.894037\pi$
$7$	−4.32826	+	4.32826i	−0.618323	+	0.618323i	0.326778	+	0.945101i	$0.394037\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	−2.90835	−	6.44527i	−0.290835	−	0.644527i
$11$	−9.81423			−0.892203			−0.446102	−	0.894982i	$-0.647188\pi$
$11$	−9.81423			−0.892203			−0.446102	+	0.894982i	$0.647188\pi$
$12$		0			0
$13$	−13.2857	−	13.2857i	−1.02197	−	1.02197i	−0.999753	−	0.0222219i	$-0.992926\pi$
$13$	−13.2857	−	13.2857i	−1.02197	−	1.02197i	−0.0222219	−	0.999753i	$-0.507074\pi$
$14$		−	8.65652i		−	0.618323i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	18.6089	−	18.6089i	1.09464	−	1.09464i	0.0996135	−	0.995026i	$-0.468239\pi$
$17$	18.6089	−	18.6089i	1.09464	−	1.09464i	0.995026	−	0.0996135i	$-0.0317606\pi$
$18$		0			0
$19$		−	16.6095i		−	0.874182i	−0.899417	−	0.437091i	$-0.856009\pi$
$19$		−	16.6095i		−	0.874182i	0.899417	−	0.437091i	$-0.143991\pi$
$20$	9.35362	+	3.53692i	0.467681	+	0.176846i
$21$		0			0
$22$	9.81423	−	9.81423i	0.446102	−	0.446102i
$23$	11.3765	+	11.3765i	0.494631	+	0.494631i	0.909762	−	0.415131i	$-0.136264\pi$
$23$	11.3765	+	11.3765i	0.494631	+	0.494631i	−0.415131	+	0.909762i	$0.636264\pi$
$24$		0			0
$25$	−18.7451	−	16.5415i	−0.749804	−	0.661660i
$26$	26.5713			1.02197
$27$		0			0
$28$	8.65652	+	8.65652i	0.309162	+	0.309162i
$29$			34.0875i			1.17543i	0.809067	+	0.587716i	$0.199973\pi$
$29$			34.0875i			1.17543i	−0.809067	+	0.587716i	$0.800027\pi$
$30$		0			0
$31$	29.4950			0.951453			0.475726	−	0.879593i	$-0.342185\pi$
$31$	29.4950			0.951453			0.475726	+	0.879593i	$0.342185\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$			37.2178i			1.09464i
$35$	−12.5881	−	27.8968i	−0.359660	−	0.797052i
$36$		0			0
$37$	−27.3850	+	27.3850i	−0.740135	+	0.740135i	−0.972604	−	0.232469i	$-0.925320\pi$
$37$	−27.3850	+	27.3850i	−0.740135	+	0.740135i	0.232469	+	0.972604i	$0.425320\pi$
$38$	16.6095	+	16.6095i	0.437091	+	0.437091i
$39$		0			0
$40$	−12.8905	+	5.81670i	−0.322263	+	0.145417i
$41$	22.4637			0.547895			0.273947	−	0.961745i	$-0.411671\pi$
$41$	22.4637			0.547895			0.273947	+	0.961745i	$0.411671\pi$
$42$		0			0
$43$	−25.2230	−	25.2230i	−0.586580	−	0.586580i	0.350123	−	0.936704i	$-0.386140\pi$
$43$	−25.2230	−	25.2230i	−0.586580	−	0.586580i	−0.936704	+	0.350123i	$0.886140\pi$
$44$			19.6285i			0.446102i
$45$		0			0
$46$	−22.7530			−0.494631
$47$	44.0549	−	44.0549i	0.937337	−	0.937337i	−0.0608118	−	0.998149i	$-0.519369\pi$
$47$	44.0549	−	44.0549i	0.937337	−	0.937337i	0.998149	+	0.0608118i	$0.0193690\pi$
$48$		0			0
$49$			11.5323i			0.235353i
$50$	35.2866	−	2.20360i	0.705732	−	0.0440720i
$51$		0			0
$52$	−26.5713	+	26.5713i	−0.510987	+	0.510987i
$53$	14.0186	+	14.0186i	0.264503	+	0.264503i	0.826880	−	0.562378i	$-0.190113\pi$
$53$	14.0186	+	14.0186i	0.264503	+	0.264503i	−0.562378	+	0.826880i	$0.690113\pi$
$54$		0			0
$55$	17.3561	−	45.8993i	0.315565	−	0.834533i
$56$	−17.3130			−0.309162
$57$		0			0
$58$	−34.0875	−	34.0875i	−0.587716	−	0.587716i
$59$			21.0132i			0.356155i	0.984016	+	0.178078i	$0.0569878\pi$
$59$			21.0132i			0.356155i	−0.984016	+	0.178078i	$0.943012\pi$
$60$		0			0
$61$	69.8487			1.14506			0.572530	−	0.819884i	$-0.305962\pi$
$61$	69.8487			1.14506			0.572530	+	0.819884i	$0.305962\pi$
$62$	−29.4950	+	29.4950i	−0.475726	+	0.475726i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	85.6298	−	38.6394i	1.31738	−	0.594452i
$66$		0			0
$67$	1.75875	−	1.75875i	0.0262499	−	0.0262499i	−0.693860	−	0.720110i	$-0.744091\pi$
$67$	1.75875	−	1.75875i	0.0262499	−	0.0262499i	0.720110	+	0.693860i	$0.244091\pi$
$68$	−37.2178	−	37.2178i	−0.547320	−	0.547320i
$69$		0			0
$70$	40.4849	+	15.3087i	0.578356	+	0.218696i
$71$	99.0623			1.39524			0.697622	−	0.716466i	$-0.254241\pi$
$71$	99.0623			1.39524			0.697622	+	0.716466i	$0.254241\pi$
$72$		0			0
$73$	−0.175127	−	0.175127i	−0.00239899	−	0.00239899i	0.705906	−	0.708305i	$-0.250540\pi$
$73$	−0.175127	−	0.175127i	−0.00239899	−	0.00239899i	−0.708305	+	0.705906i	$0.750540\pi$
$74$		−	54.7700i		−	0.740135i
$75$		0			0
$76$	−33.2189			−0.437091
$77$	42.4786	−	42.4786i	0.551670	−	0.551670i
$78$		0			0
$79$		−	64.2928i		−	0.813833i	−0.913465	−	0.406916i	$-0.866604\pi$
$79$		−	64.2928i		−	0.813833i	0.913465	−	0.406916i	$-0.133396\pi$
$80$	7.07384	−	18.7072i	0.0884230	−	0.233840i
$81$		0			0
$82$	−22.4637	+	22.4637i	−0.273947	+	0.273947i
$83$	−45.7761	−	45.7761i	−0.551519	−	0.551519i	0.375360	−	0.926879i	$-0.377519\pi$
$83$	−45.7761	−	45.7761i	−0.551519	−	0.551519i	−0.926879	+	0.375360i	$0.877519\pi$
$84$		0			0
$85$	54.1211	+	119.939i	0.636719	+	1.41105i
$86$	50.4459			0.586580
$87$		0			0
$88$	−19.6285	−	19.6285i	−0.223051	−	0.223051i
$89$		−	43.0842i		−	0.484092i	−0.970265	−	0.242046i	$-0.922182\pi$
$89$		−	43.0842i		−	0.484092i	0.970265	−	0.242046i	$-0.0778185\pi$
$90$		0			0
$91$	115.008			1.26382
$92$	22.7530	−	22.7530i	0.247315	−	0.247315i
$93$		0			0
$94$			88.1097i			0.937337i
$95$	77.6793	+	29.3732i	0.817677	+	0.309191i
$96$		0			0
$97$	117.314	−	117.314i	1.20942	−	1.20942i	0.238204	−	0.971215i	$-0.423441\pi$
$97$	117.314	−	117.314i	1.20942	−	1.20942i	0.971215	−	0.238204i	$-0.0765588\pi$
$98$	−11.5323	−	11.5323i	−0.117677	−	0.117677i
$99$		0			0
$100$	−33.0830	+	37.4902i	−0.330830	+	0.374902i
$101$	57.0465			0.564817			0.282408	−	0.959294i	$-0.408867\pi$
$101$	57.0465			0.564817			0.282408	+	0.959294i	$0.408867\pi$
$102$		0			0
$103$	−100.540	−	100.540i	−0.976120	−	0.976120i	0.0236018	−	0.999721i	$-0.492487\pi$
$103$	−100.540	−	100.540i	−0.976120	−	0.976120i	−0.999721	+	0.0236018i	$0.992487\pi$
$104$		−	53.1427i		−	0.510987i
$105$		0			0
$106$	−28.0373			−0.264503
$107$	−143.767	+	143.767i	−1.34362	+	1.34362i	−0.451197	+	0.892425i	$0.649003\pi$
$107$	−143.767	+	143.767i	−1.34362	+	1.34362i	−0.892425	+	0.451197i	$0.850997\pi$
$108$		0			0
$109$			16.4505i			0.150922i	0.997149	+	0.0754609i	$0.0240428\pi$
$109$			16.4505i			0.150922i	−0.997149	+	0.0754609i	$0.975957\pi$
$110$	28.5432	+	63.2554i	0.259484	+	0.575049i
$111$		0			0
$112$	17.3130	−	17.3130i	0.154581	−	0.154581i
$113$	−41.8286	−	41.8286i	−0.370165	−	0.370165i	0.497372	−	0.867537i	$-0.334298\pi$
$113$	−41.8286	−	41.8286i	−0.370165	−	0.370165i	−0.867537	+	0.497372i	$0.834298\pi$
$114$		0			0
$115$	−73.3247	+	33.0869i	−0.637606	+	0.287712i
$116$	68.1750			0.587716
$117$		0			0
$118$	−21.0132	−	21.0132i	−0.178078	−	0.178078i
$119$			161.088i			1.35368i
$120$		0			0
$121$	−24.6808			−0.203974
$122$	−69.8487	+	69.8487i	−0.572530	+	0.572530i
$123$		0			0
$124$		−	58.9901i		−	0.475726i
$125$	110.511	−	58.4143i	0.884091	−	0.467314i
$126$		0			0
$127$	17.2766	−	17.2766i	0.136036	−	0.136036i	−0.635810	−	0.771846i	$-0.719334\pi$
$127$	17.2766	−	17.2766i	0.136036	−	0.136036i	0.771846	+	0.635810i	$0.219334\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−46.9904	+	124.269i	−0.361464	+	0.955916i
$131$	94.9500			0.724809			0.362405	−	0.932021i	$-0.381956\pi$
$131$	94.9500			0.724809			0.362405	+	0.932021i	$0.381956\pi$
$132$		0			0
$133$	71.8901	+	71.8901i	0.540527	+	0.540527i
$134$			3.51749i			0.0262499i
$135$		0			0
$136$	74.4355			0.547320
$137$	126.860	−	126.860i	0.925985	−	0.925985i	−0.0714586	−	0.997444i	$-0.522765\pi$
$137$	126.860	−	126.860i	0.925985	−	0.925985i	0.997444	+	0.0714586i	$0.0227654\pi$
$138$		0			0
$139$		−	102.052i		−	0.734190i	−0.930183	−	0.367095i	$-0.880352\pi$
$139$		−	102.052i		−	0.734190i	0.930183	−	0.367095i	$-0.119648\pi$
$140$	−55.7936	+	25.1762i	−0.398526	+	0.179830i
$141$		0			0
$142$	−99.0623	+	99.0623i	−0.697622	+	0.697622i
$143$	130.389	+	130.389i	0.911809	+	0.911809i
$144$		0			0
$145$	−159.421	−	60.2824i	−1.09945	−	0.415741i
$146$	0.350253			0.00239899
$147$		0			0
$148$	54.7700	+	54.7700i	0.370068	+	0.370068i
$149$			103.426i			0.694133i	0.937841	+	0.347066i	$0.112822\pi$
$149$			103.426i			0.694133i	−0.937841	+	0.347066i	$0.887178\pi$
$150$		0			0
$151$	85.8926			0.568825			0.284413	−	0.958702i	$-0.408201\pi$
$151$	85.8926			0.568825			0.284413	+	0.958702i	$0.408201\pi$
$152$	33.2189	−	33.2189i	0.218545	−	0.218545i
$153$		0			0
$154$			84.9571i			0.551670i
$155$	−52.1608	+	137.943i	−0.336521	+	0.889953i
$156$		0			0
$157$	218.079	−	218.079i	1.38904	−	1.38904i	0.561694	−	0.827345i	$-0.310150\pi$
$157$	218.079	−	218.079i	1.38904	−	1.38904i	0.827345	−	0.561694i	$-0.189850\pi$
$158$	64.2928	+	64.2928i	0.406916	+	0.406916i
$159$		0			0
$160$	11.6334	+	25.7811i	0.0727087	+	0.161132i
$161$	−98.4810			−0.611683
$162$		0			0
$163$	18.9195	+	18.9195i	0.116071	+	0.116071i	0.762756	−	0.646686i	$-0.223846\pi$
$163$	18.9195	+	18.9195i	0.116071	+	0.116071i	−0.646686	+	0.762756i	$0.723846\pi$
$164$		−	44.9274i		−	0.273947i
$165$		0			0
$166$	91.5521			0.551519
$167$	16.6482	−	16.6482i	0.0996899	−	0.0996899i	−0.655503	−	0.755193i	$-0.727543\pi$
$167$	16.6482	−	16.6482i	0.0996899	−	0.0996899i	0.755193	+	0.655503i	$0.227543\pi$
$168$		0			0
$169$			184.018i			1.08887i
$170$	−174.060	−	65.8181i	−1.02388	−	0.387165i
$171$		0			0
$172$	−50.4459	+	50.4459i	−0.293290	+	0.293290i
$173$	−118.608	−	118.608i	−0.685596	−	0.685596i	0.275659	−	0.961255i	$-0.411104\pi$
$173$	−118.608	−	118.608i	−0.685596	−	0.685596i	−0.961255	+	0.275659i	$0.911104\pi$
$174$		0			0
$175$	152.730	−	9.53775i	0.872741	−	0.0545014i
$176$	39.2569			0.223051
$177$		0			0
$178$	43.0842	+	43.0842i	0.242046	+	0.242046i
$179$		−	199.747i		−	1.11590i	−0.829873	−	0.557952i	$-0.811587\pi$
$179$		−	199.747i		−	1.11590i	0.829873	−	0.557952i	$-0.188413\pi$
$180$		0			0
$181$	308.462			1.70421			0.852104	−	0.523373i	$-0.175326\pi$
$181$	308.462			1.70421			0.852104	+	0.523373i	$0.175326\pi$
$182$	−115.008	+	115.008i	−0.631911	+	0.631911i
$183$		0			0
$184$			45.5060i			0.247315i
$185$	−79.6452	−	176.504i	−0.430514	−	0.954074i
$186$		0			0
$187$	−182.632	+	182.632i	−0.976641	+	0.976641i
$188$	−88.1097	−	88.1097i	−0.468669	−	0.468669i
$189$		0			0
$190$	−107.052	+	48.3061i	−0.563434	+	0.254243i
$191$	−135.218			−0.707946			−0.353973	−	0.935256i	$-0.615169\pi$
$191$	−135.218			−0.707946			−0.353973	+	0.935256i	$0.615169\pi$
$192$		0			0
$193$	98.0015	+	98.0015i	0.507780	+	0.507780i	0.913844	−	0.406065i	$-0.133099\pi$
$193$	98.0015	+	98.0015i	0.507780	+	0.507780i	−0.406065	+	0.913844i	$0.633099\pi$
$194$			234.627i			1.20942i
$195$		0			0
$196$	23.0646			0.117677
$197$	−93.9540	+	93.9540i	−0.476924	+	0.476924i	−0.904146	−	0.427223i	$-0.859492\pi$
$197$	−93.9540	+	93.9540i	−0.476924	+	0.476924i	0.427223	+	0.904146i	$0.359492\pi$
$198$		0			0
$199$		−	315.420i		−	1.58503i	−0.609855	−	0.792513i	$-0.708772\pi$
$199$		−	315.420i		−	1.58503i	0.609855	−	0.792513i	$-0.291228\pi$
$200$	−4.40720	−	70.5732i	−0.0220360	−	0.352866i
$201$		0			0
$202$	−57.0465	+	57.0465i	−0.282408	+	0.282408i
$203$	−147.540	−	147.540i	−0.726797	−	0.726797i
$204$		0			0
$205$	−39.7261	+	105.058i	−0.193786	+	0.512480i
$206$	201.081			0.976120
$207$		0			0
$208$	53.1427	+	53.1427i	0.255494	+	0.255494i
$209$			163.009i			0.779948i
$210$		0			0
$211$	−119.592			−0.566787			−0.283393	−	0.959004i	$-0.591460\pi$
$211$	−119.592			−0.566787			−0.283393	+	0.959004i	$0.591460\pi$
$212$	28.0373	−	28.0373i	0.132251	−	0.132251i
$213$		0			0
$214$		−	287.535i		−	1.34362i
$215$	162.569	−	73.3572i	0.756134	−	0.341196i
$216$		0			0
$217$	−127.662	+	127.662i	−0.588305	+	0.588305i
$218$	−16.4505	−	16.4505i	−0.0754609	−	0.0754609i
$219$		0			0
$220$	−91.7986	−	34.7122i	−0.417266	−	0.157783i
$221$	−494.463			−2.23739
$222$		0			0
$223$	−197.471	−	197.471i	−0.885519	−	0.885519i	0.108570	−	0.994089i	$-0.465373\pi$
$223$	−197.471	−	197.471i	−0.885519	−	0.885519i	−0.994089	+	0.108570i	$0.965373\pi$
$224$			34.6261i			0.154581i
$225$		0			0
$226$	83.6572			0.370165
$227$	−236.566	+	236.566i	−1.04214	+	1.04214i	−0.0430688	+	0.999072i	$0.513713\pi$
$227$	−236.566	+	236.566i	−1.04214	+	1.04214i	−0.999072	+	0.0430688i	$0.986287\pi$
$228$		0			0
$229$		−	275.946i		−	1.20500i	−0.798117	−	0.602502i	$-0.794171\pi$
$229$		−	275.946i		−	1.20500i	0.798117	−	0.602502i	$-0.205829\pi$
$230$	40.2378	−	106.412i	0.174947	−	0.462659i
$231$		0			0
$232$	−68.1750	+	68.1750i	−0.293858	+	0.293858i
$233$	−171.730	−	171.730i	−0.737041	−	0.737041i	0.234963	−	0.972004i	$-0.424503\pi$
$233$	−171.730	−	171.730i	−0.737041	−	0.737041i	−0.972004	+	0.234963i	$0.924503\pi$
$234$		0			0
$235$	128.127	+	283.945i	0.545221	+	1.20828i
$236$	42.0263			0.178078
$237$		0			0
$238$	−161.088	−	161.088i	−0.676841	−	0.676841i
$239$		−	89.9823i		−	0.376495i	−0.982122	−	0.188247i	$-0.939719\pi$
$239$		−	89.9823i		−	0.376495i	0.982122	−	0.188247i	$-0.0602807\pi$
$240$		0			0
$241$	326.690			1.35556			0.677780	−	0.735265i	$-0.262942\pi$
$241$	326.690			1.35556			0.677780	+	0.735265i	$0.262942\pi$
$242$	24.6808	−	24.6808i	0.101987	−	0.101987i
$243$		0			0
$244$		−	139.697i		−	0.572530i
$245$	−53.9344	−	20.3944i	−0.220140	−	0.0832426i
$246$		0			0
$247$	−220.668	+	220.668i	−0.893392	+	0.893392i
$248$	58.9901	+	58.9901i	0.237863	+	0.237863i
$249$		0			0
$250$	−52.0971	+	168.926i	−0.208388	+	0.675703i
$251$	−214.382			−0.854110			−0.427055	−	0.904226i	$-0.640449\pi$
$251$	−214.382			−0.854110			−0.427055	+	0.904226i	$0.640449\pi$
$252$		0			0
$253$	−111.652	−	111.652i	−0.441311	−	0.441311i
$254$			34.5531i			0.136036i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−77.9744	+	77.9744i	−0.303402	+	0.303402i	−0.842343	−	0.538941i	$-0.818825\pi$
$257$	−77.9744	+	77.9744i	−0.303402	+	0.303402i	0.538941	+	0.842343i	$0.318825\pi$
$258$		0			0
$259$		−	237.059i		−	0.915285i
$260$	−77.2788	−	171.260i	−0.297226	−	0.658690i
$261$		0			0
$262$	−94.9500	+	94.9500i	−0.362405	+	0.362405i
$263$	−247.438	−	247.438i	−0.940829	−	0.940829i	0.0575155	−	0.998345i	$-0.481682\pi$
$263$	−247.438	−	247.438i	−0.940829	−	0.940829i	−0.998345	+	0.0575155i	$0.981682\pi$
$264$		0			0
$265$	−90.3539	+	40.7711i	−0.340958	+	0.153853i
$266$	−143.780			−0.540527
$267$		0			0
$268$	−3.51749	−	3.51749i	−0.0131250	−	0.0131250i
$269$			329.182i			1.22372i	0.790965	+	0.611862i	$0.209579\pi$
$269$			329.182i			1.22372i	−0.790965	+	0.611862i	$0.790421\pi$
$270$		0			0
$271$	−244.443			−0.902005			−0.451003	−	0.892523i	$-0.648934\pi$
$271$	−244.443			−0.902005			−0.451003	+	0.892523i	$0.648934\pi$
$272$	−74.4355	+	74.4355i	−0.273660	+	0.273660i
$273$		0			0
$274$			253.720i			0.925985i
$275$	183.969	+	162.342i	0.668977	+	0.590335i
$276$		0			0
$277$	178.411	−	178.411i	0.644082	−	0.644082i	−0.307474	−	0.951556i	$-0.599484\pi$
$277$	178.411	−	178.411i	0.644082	−	0.644082i	0.951556	+	0.307474i	$0.0994838\pi$
$278$	102.052	+	102.052i	0.367095	+	0.367095i
$279$		0			0
$280$	30.6174	−	80.9698i	0.109348	−	0.289178i
$281$	102.392			0.364383			0.182191	−	0.983263i	$-0.441681\pi$
$281$	102.392			0.364383			0.182191	+	0.983263i	$0.441681\pi$
$282$		0			0
$283$	−87.0854	−	87.0854i	−0.307722	−	0.307722i	0.536303	−	0.844025i	$-0.319820\pi$
$283$	−87.0854	−	87.0854i	−0.307722	−	0.307722i	−0.844025	+	0.536303i	$0.819820\pi$
$284$		−	198.125i		−	0.697622i
$285$		0			0
$286$	−260.777			−0.911809
$287$	−97.2287	+	97.2287i	−0.338776	+	0.338776i
$288$		0			0
$289$		−	403.580i		−	1.39647i
$290$	219.703	−	99.1384i	0.757598	−	0.341857i
$291$		0			0
$292$	−0.350253	+	0.350253i	−0.00119950	+	0.00119950i
$293$	52.5498	+	52.5498i	0.179351	+	0.179351i	0.791073	−	0.611722i	$-0.209523\pi$
$293$	52.5498	+	52.5498i	0.179351	+	0.179351i	−0.611722	+	0.791073i	$0.709523\pi$
$294$		0			0
$295$	−98.2746	−	37.1609i	−0.333134	−	0.125969i
$296$	−109.540			−0.370068
$297$		0			0
$298$	−103.426	−	103.426i	−0.347066	−	0.347066i
$299$		−	302.289i		−	1.01100i
$300$		0			0
$301$	218.343			0.725392
$302$	−85.8926	+	85.8926i	−0.284413	+	0.284413i
$303$		0			0
$304$			66.4378i			0.218545i
$305$	−123.525	+	326.669i	−0.404999	+	1.07105i
$306$		0			0
$307$	164.327	−	164.327i	0.535268	−	0.535268i	−0.386868	−	0.922135i	$-0.626443\pi$
$307$	164.327	−	164.327i	0.535268	−	0.535268i	0.922135	+	0.386868i	$0.126443\pi$
$308$	−84.9571	−	84.9571i	−0.275835	−	0.275835i
$309$		0			0
$310$	−85.7819	−	190.104i	−0.276716	−	0.613237i
$311$	240.496			0.773300			0.386650	−	0.922227i	$-0.373632\pi$
$311$	240.496			0.773300			0.386650	+	0.922227i	$0.373632\pi$
$312$		0			0
$313$	−274.314	−	274.314i	−0.876403	−	0.876403i	0.116757	−	0.993160i	$-0.462750\pi$
$313$	−274.314	−	274.314i	−0.876403	−	0.876403i	−0.993160	+	0.116757i	$0.962750\pi$
$314$			436.158i			1.38904i
$315$		0			0
$316$	−128.586			−0.406916
$317$	175.000	−	175.000i	0.552051	−	0.552051i	−0.374982	−	0.927032i	$-0.622351\pi$
$317$	175.000	−	175.000i	0.552051	−	0.552051i	0.927032	+	0.374982i	$0.122351\pi$
$318$		0			0
$319$		−	334.543i		−	1.04872i
$320$	−37.4145	−	14.1477i	−0.116920	−	0.0442115i
$321$		0			0
$322$	98.4810	−	98.4810i	0.305842	−	0.305842i
$323$	−309.083	−	309.083i	−0.956914	−	0.956914i
$324$		0			0
$325$	29.2763	+	468.806i	0.0900809	+	1.44248i
$326$	−37.8390			−0.116071
$327$		0			0
$328$	44.9274	+	44.9274i	0.136974	+	0.136974i
$329$			381.362i			1.15915i
$330$		0			0
$331$	241.485			0.729563			0.364781	−	0.931093i	$-0.381144\pi$
$331$	241.485			0.729563			0.364781	+	0.931093i	$0.381144\pi$
$332$	−91.5521	+	91.5521i	−0.275759	+	0.275759i
$333$		0			0
$334$			33.2964i			0.0996899i
$335$	5.11505	+	11.3356i	0.0152688	+	0.0338376i
$336$		0			0
$337$	−323.641	+	323.641i	−0.960360	+	0.960360i	−0.999244	−	0.0388841i	$-0.987620\pi$
$337$	−323.641	+	323.641i	−0.960360	+	0.960360i	0.0388841	+	0.999244i	$0.487620\pi$
$338$	−184.018	−	184.018i	−0.544433	−	0.544433i
$339$		0			0
$340$	239.878	−	108.242i	0.705525	−	0.318360i
$341$	−289.471			−0.848889
$342$		0			0
$343$	−262.000	−	262.000i	−0.763847	−	0.763847i
$344$		−	100.892i		−	0.293290i
$345$		0			0
$346$	237.216			0.685596
$347$	−148.684	+	148.684i	−0.428483	+	0.428483i	−0.888111	−	0.459628i	$-0.847983\pi$
$347$	−148.684	+	148.684i	−0.428483	+	0.428483i	0.459628	+	0.888111i	$0.347983\pi$
$348$		0			0
$349$		−	59.0300i		−	0.169141i	−0.996418	−	0.0845703i	$-0.973048\pi$
$349$		−	59.0300i		−	0.169141i	0.996418	−	0.0845703i	$-0.0269517\pi$
$350$	−143.192	+	162.267i	−0.409120	+	0.463621i
$351$		0			0
$352$	−39.2569	+	39.2569i	−0.111525	+	0.111525i
$353$	357.085	+	357.085i	1.01157	+	1.01157i	0.999932	+	0.0116395i	$0.00370506\pi$
$353$	357.085	+	357.085i	1.01157	+	1.01157i	0.0116395	+	0.999932i	$0.496295\pi$
$354$		0			0
$355$	−175.188	+	463.296i	−0.493487	+	1.30506i
$356$	−86.1684			−0.242046
$357$		0			0
$358$	199.747	+	199.747i	0.557952	+	0.557952i
$359$			152.761i			0.425519i	0.977105	+	0.212759i	$0.0682450\pi$
$359$			152.761i			0.425519i	−0.977105	+	0.212759i	$0.931755\pi$
$360$		0			0
$361$	85.1259			0.235806
$362$	−308.462	+	308.462i	−0.852104	+	0.852104i
$363$		0			0
$364$		−	230.015i		−	0.631911i
$365$	1.12874	−	0.509329i	0.00309243	−	0.00139542i
$366$		0			0
$367$	61.1377	−	61.1377i	0.166588	−	0.166588i	−0.618890	−	0.785478i	$-0.712417\pi$
$367$	61.1377	−	61.1377i	0.166588	−	0.166588i	0.785478	+	0.618890i	$0.212417\pi$
$368$	−45.5060	−	45.5060i	−0.123658	−	0.123658i
$369$		0			0
$370$	256.149	+	96.8585i	0.692294	+	0.261780i
$371$	−121.353			−0.327096
$372$		0			0
$373$	−40.0190	−	40.0190i	−0.107290	−	0.107290i	0.651424	−	0.758714i	$-0.274172\pi$
$373$	−40.0190	−	40.0190i	−0.107290	−	0.107290i	−0.758714	+	0.651424i	$0.774172\pi$
$374$		−	365.264i		−	0.976641i
$375$		0			0
$376$	176.219			0.468669
$377$	452.876	−	452.876i	1.20126	−	1.20126i
$378$		0			0
$379$			515.708i			1.36071i	0.732884	+	0.680353i	$0.238174\pi$
$379$			515.708i			1.36071i	−0.732884	+	0.680353i	$0.761826\pi$
$380$	58.7463	−	155.359i	0.154596	−	0.408838i
$381$		0			0
$382$	135.218	−	135.218i	0.353973	−	0.353973i
$383$	−219.183	−	219.183i	−0.572280	−	0.572280i	0.360485	−	0.932765i	$-0.382611\pi$
$383$	−219.183	−	219.183i	−0.572280	−	0.572280i	−0.932765	+	0.360485i	$0.882611\pi$
$384$		0			0
$385$	123.543	+	273.786i	0.320890	+	0.711132i
$386$	−196.003			−0.507780
$387$		0			0
$388$	−234.627	−	234.627i	−0.604710	−	0.604710i
$389$			56.3472i			0.144852i	0.997374	+	0.0724258i	$0.0230740\pi$
$389$			56.3472i			0.144852i	−0.997374	+	0.0724258i	$0.976926\pi$
$390$		0			0
$391$	423.408			1.08289
$392$	−23.0646	+	23.0646i	−0.0588383	+	0.0588383i
$393$		0			0
$394$		−	187.908i		−	0.476924i
$395$	300.685	+	113.699i	0.761228	+	0.287846i
$396$		0			0
$397$	−319.948	+	319.948i	−0.805914	+	0.805914i	−0.984013	−	0.178099i	$-0.943005\pi$
$397$	−319.948	+	319.948i	−0.805914	+	0.805914i	0.178099	+	0.984013i	$0.443005\pi$
$398$	315.420	+	315.420i	0.792513	+	0.792513i
$399$		0			0
$400$	74.9804	+	66.1660i	0.187451	+	0.165415i
$401$	231.122			0.576363			0.288181	−	0.957576i	$-0.406949\pi$
$401$	231.122			0.576363			0.288181	+	0.957576i	$0.406949\pi$
$402$		0			0
$403$	−391.862	−	391.862i	−0.972361	−	0.972361i
$404$		−	114.093i		−	0.282408i
$405$		0			0
$406$	295.079			0.726797
$407$	268.763	−	268.763i	0.660351	−	0.660351i
$408$		0			0
$409$			468.707i			1.14598i	0.819561	+	0.572992i	$0.194217\pi$
$409$			468.707i			1.14598i	−0.819561	+	0.572992i	$0.805783\pi$
$410$	−65.3323	−	144.785i	−0.159347	−	0.353133i
$411$		0			0
$412$	−201.081	+	201.081i	−0.488060	+	0.488060i
$413$	−90.9505	−	90.9505i	−0.220219	−	0.220219i
$414$		0			0
$415$	295.039	−	133.133i	0.710937	−	0.320802i
$416$	−106.285			−0.255494
$417$		0			0
$418$	−163.009	−	163.009i	−0.389974	−	0.389974i
$419$		−	90.7621i		−	0.216616i	−0.994117	−	0.108308i	$-0.965457\pi$
$419$		−	90.7621i		−	0.216616i	0.994117	−	0.108308i	$-0.0345433\pi$
$420$		0			0
$421$	−72.4132			−0.172003			−0.0860014	−	0.996295i	$-0.527409\pi$
$421$	−72.4132			−0.172003			−0.0860014	+	0.996295i	$0.527409\pi$
$422$	119.592	−	119.592i	0.283393	−	0.283393i
$423$		0			0
$424$			56.0746i			0.132251i
$425$	−656.644	+	41.0065i	−1.54504	+	0.0964859i
$426$		0			0
$427$	−302.323	+	302.323i	−0.708017	+	0.708017i
$428$	287.535	+	287.535i	0.671811	+	0.671811i
$429$		0			0
$430$	−89.2116	+	235.926i	−0.207469	+	0.548665i
$431$	36.9748			0.0857883			0.0428942	−	0.999080i	$-0.486342\pi$
$431$	36.9748			0.0857883			0.0428942	+	0.999080i	$0.486342\pi$
$432$		0			0
$433$	268.457	+	268.457i	0.619994	+	0.619994i	0.945530	−	0.325536i	$-0.105545\pi$
$433$	268.457	+	268.457i	0.619994	+	0.619994i	−0.325536	+	0.945530i	$0.605545\pi$
$434$		−	255.324i		−	0.588305i
$435$		0			0
$436$	32.9009			0.0754609
$437$	188.958	−	188.958i	0.432397	−	0.432397i
$438$		0			0
$439$			482.160i			1.09832i	0.835719	+	0.549158i	$0.185051\pi$
$439$			482.160i			1.09832i	−0.835719	+	0.549158i	$0.814949\pi$
$440$	126.511	−	57.0865i	0.287524	−	0.129742i
$441$		0			0
$442$	494.463	−	494.463i	1.11869	−	1.11869i
$443$	130.575	+	130.575i	0.294751	+	0.294751i	0.838954	−	0.544203i	$-0.183168\pi$
$443$	130.575	+	130.575i	0.294751	+	0.294751i	−0.544203	+	0.838954i	$0.683168\pi$
$444$		0			0
$445$	201.497	+	76.1927i	0.452801	+	0.171219i
$446$	394.942			0.885519
$447$		0			0
$448$	−34.6261	−	34.6261i	−0.0772904	−	0.0772904i
$449$		−	608.199i		−	1.35456i	−0.735724	−	0.677281i	$-0.763158\pi$
$449$		−	608.199i		−	1.35456i	0.735724	−	0.677281i	$-0.236842\pi$
$450$		0			0
$451$	−220.464			−0.488833
$452$	−83.6572	+	83.6572i	−0.185082	+	0.185082i
$453$		0			0
$454$		−	473.132i		−	1.04214i
$455$	−203.387	+	537.869i	−0.447003	+	1.18213i
$456$		0			0
$457$	−349.447	+	349.447i	−0.764654	+	0.764654i	−0.977160	−	0.212506i	$-0.931837\pi$
$457$	−349.447	+	349.447i	−0.764654	+	0.764654i	0.212506	+	0.977160i	$0.431837\pi$
$458$	275.946	+	275.946i	0.602502	+	0.602502i
$459$		0			0
$460$	66.1738	+	146.649i	0.143856	+	0.318803i
$461$	211.005			0.457711			0.228856	−	0.973460i	$-0.426502\pi$
$461$	211.005			0.457711			0.228856	+	0.973460i	$0.426502\pi$
$462$		0			0
$463$	37.9190	+	37.9190i	0.0818985	+	0.0818985i	0.746869	−	0.664971i	$-0.231556\pi$
$463$	37.9190	+	37.9190i	0.0818985	+	0.0818985i	−0.664971	+	0.746869i	$0.731556\pi$
$464$		−	136.350i		−	0.293858i
$465$		0			0
$466$	343.461			0.737041
$467$	401.408	−	401.408i	0.859547	−	0.859547i	−0.131738	−	0.991285i	$-0.542056\pi$
$467$	401.408	−	401.408i	0.859547	−	0.859547i	0.991285	+	0.131738i	$0.0420557\pi$
$468$		0			0
$469$			15.2246i			0.0324619i
$470$	−412.072	−	155.818i	−0.876750	−	0.331529i
$471$		0			0
$472$	−42.0263	+	42.0263i	−0.0890388	+	0.0890388i
$473$	247.544	+	247.544i	0.523349	+	0.523349i
$474$		0			0
$475$	−274.745	+	311.346i	−0.578411	+	0.655465i
$476$	322.176			0.676841
$477$		0			0
$478$	89.9823	+	89.9823i	0.188247	+	0.188247i
$479$			390.847i			0.815964i	0.912990	+	0.407982i	$0.133767\pi$
$479$			390.847i			0.815964i	−0.912990	+	0.407982i	$0.866233\pi$
$480$		0			0
$481$	727.656			1.51280
$482$	−326.690	+	326.690i	−0.677780	+	0.677780i
$483$		0			0
$484$			49.3616i			0.101987i
$485$	341.189	+	756.118i	0.703483	+	1.55901i
$486$		0			0
$487$	126.937	−	126.937i	0.260651	−	0.260651i	−0.564668	−	0.825318i	$-0.690996\pi$
$487$	126.937	−	126.937i	0.260651	−	0.260651i	0.825318	+	0.564668i	$0.190996\pi$
$488$	139.697	+	139.697i	0.286265	+	0.286265i
$489$		0			0
$490$	74.3288	−	33.5400i	0.151692	−	0.0684490i
$491$	24.8280			0.0505663			0.0252831	−	0.999680i	$-0.491951\pi$
$491$	24.8280			0.0505663			0.0252831	+	0.999680i	$0.491951\pi$
$492$		0			0
$493$	634.330	+	634.330i	1.28667	+	1.28667i
$494$		−	441.336i		−	0.893392i
$495$		0			0
$496$	−117.980			−0.237863
$497$	−428.768	+	428.768i	−0.862712	+	0.862712i
$498$		0			0
$499$		−	697.531i		−	1.39786i	−0.715191	−	0.698929i	$-0.753661\pi$
$499$		−	697.531i		−	1.39786i	0.715191	−	0.698929i	$-0.246339\pi$
$500$	−116.829	−	221.023i	−0.233657	−	0.442046i
$501$		0			0
$502$	214.382	−	214.382i	0.427055	−	0.427055i
$503$	206.750	+	206.750i	0.411033	+	0.411033i	0.882098	−	0.471065i	$-0.156130\pi$
$503$	206.750	+	206.750i	0.411033	+	0.411033i	−0.471065	+	0.882098i	$0.656130\pi$
$504$		0			0
$505$	−100.884	+	266.796i	−0.199771	+	0.528308i
$506$	223.304			0.441311
$507$		0			0
$508$	−34.5531	−	34.5531i	−0.0680180	−	0.0680180i
$509$		−	149.515i		−	0.293743i	−0.989156	−	0.146871i	$-0.953080\pi$
$509$		−	149.515i		−	0.293743i	0.989156	−	0.146871i	$-0.0469203\pi$
$510$		0			0
$511$	1.51599			0.00296671
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	155.949i		−	0.303402i
$515$	648.009	−	292.406i	1.25827	−	0.567779i
$516$		0			0
$517$	−432.365	+	432.365i	−0.836295	+	0.836295i
$518$	237.059	+	237.059i	0.457643	+	0.457643i
$519$		0			0
$520$	248.538	+	93.9807i	0.477958	+	0.180732i
$521$	468.376			0.898994			0.449497	−	0.893282i	$-0.351603\pi$
$521$	468.376			0.898994			0.449497	+	0.893282i	$0.351603\pi$
$522$		0			0
$523$	−666.842	−	666.842i	−1.27503	−	1.27503i	−0.943413	−	0.331620i	$-0.892405\pi$
$523$	−666.842	−	666.842i	−1.27503	−	1.27503i	−0.331620	−	0.943413i	$-0.607595\pi$
$524$		−	189.900i		−	0.362405i
$525$		0			0
$526$	494.876			0.940829
$527$	548.870	−	548.870i	1.04150	−	1.04150i
$528$		0			0
$529$		−	270.150i		−	0.510680i
$530$	49.5828	−	131.125i	0.0935524	−	0.247406i
$531$		0			0
$532$	143.780	−	143.780i	0.270263	−	0.270263i
$533$	−298.445	−	298.445i	−0.559935	−	0.559935i
$534$		0			0
$535$	−418.126	−	926.620i	−0.781544	−	1.73200i
$536$	7.03498			0.0131250
$537$		0			0
$538$	−329.182	−	329.182i	−0.611862	−	0.611862i
$539$		−	113.181i		−	0.209983i
$540$		0			0
$541$	896.813			1.65769			0.828847	−	0.559475i	$-0.188997\pi$
$541$	896.813			1.65769			0.828847	+	0.559475i	$0.188997\pi$
$542$	244.443	−	244.443i	0.451003	−	0.451003i
$543$		0			0
$544$		−	148.871i		−	0.273660i
$545$	−76.9357	−	29.0920i	−0.141166	−	0.0533798i
$546$		0			0
$547$	−442.260	+	442.260i	−0.808519	+	0.808519i	−0.984410	−	0.175891i	$-0.943719\pi$
$547$	−442.260	+	442.260i	−0.808519	+	0.808519i	0.175891	+	0.984410i	$0.443719\pi$
$548$	−253.720	−	253.720i	−0.462992	−	0.462992i
$549$		0			0
$550$	−346.311	+	21.6266i	−0.629656	+	0.0393211i
$551$	566.175			1.02754
$552$		0			0
$553$	278.276	+	278.276i	0.503211	+	0.503211i
$554$			356.822i			0.644082i
$555$		0			0
$556$	−204.105			−0.367095
$557$	285.633	−	285.633i	0.512806	−	0.512806i	−0.402579	−	0.915385i	$-0.631886\pi$
$557$	285.633	−	285.633i	0.512806	−	0.512806i	0.915385	+	0.402579i	$0.131886\pi$
$558$		0			0
$559$			670.208i			1.19894i
$560$	50.3524	+	111.587i	0.0899150	+	0.199263i
$561$		0			0
$562$	−102.392	+	102.392i	−0.182191	+	0.182191i
$563$	−318.473	−	318.473i	−0.565671	−	0.565671i	0.365242	−	0.930913i	$-0.380986\pi$
$563$	−318.473	−	318.473i	−0.565671	−	0.565671i	−0.930913	+	0.365242i	$0.880986\pi$
$564$		0			0
$565$	269.597	−	121.652i	0.477162	−	0.215314i
$566$	174.171			0.307722
$567$		0			0
$568$	198.125	+	198.125i	0.348811	+	0.348811i
$569$			94.0893i			0.165359i	0.996576	+	0.0826796i	$0.0263478\pi$
$569$			94.0893i			0.165359i	−0.996576	+	0.0826796i	$0.973652\pi$
$570$		0			0
$571$	13.8830			0.0243135			0.0121567	−	0.999926i	$-0.496130\pi$
$571$	13.8830			0.0243135			0.0121567	+	0.999926i	$0.496130\pi$
$572$	260.777	−	260.777i	0.455905	−	0.455905i
$573$		0			0
$574$		−	194.457i		−	0.338776i
$575$	−25.0693	−	401.438i	−0.0435987	−	0.698154i
$576$		0			0
$577$	332.492	−	332.492i	0.576242	−	0.576242i	−0.357624	−	0.933866i	$-0.616413\pi$
$577$	332.492	−	332.492i	0.576242	−	0.576242i	0.933866	+	0.357624i	$0.116413\pi$
$578$	403.580	+	403.580i	0.698236	+	0.698236i
$579$		0			0
$580$	−120.565	+	318.842i	−0.207870	+	0.549727i
$581$	396.261			0.682033
$582$		0			0
$583$	−137.582	−	137.582i	−0.235990	−	0.235990i
$584$		−	0.700506i		−	0.00119950i
$585$		0			0
$586$	−105.100			−0.179351
$587$	419.516	−	419.516i	0.714678	−	0.714678i	−0.252832	−	0.967510i	$-0.581362\pi$
$587$	419.516	−	419.516i	0.714678	−	0.714678i	0.967510	+	0.252832i	$0.0813621\pi$
$588$		0			0
$589$		−	489.897i		−	0.831743i
$590$	135.436	−	61.1136i	0.229552	−	0.103582i
$591$		0			0
$592$	109.540	−	109.540i	0.185034	−	0.185034i
$593$	−201.969	−	201.969i	−0.340589	−	0.340589i	0.516000	−	0.856589i	$-0.327421\pi$
$593$	−201.969	−	201.969i	−0.340589	−	0.340589i	−0.856589	+	0.516000i	$0.827421\pi$
$594$		0			0
$595$	−753.379	−	284.878i	−1.26618	−	0.478786i
$596$	206.852			0.347066
$597$		0			0
$598$	302.289	+	302.289i	0.505500	+	0.505500i
$599$		−	208.316i		−	0.347773i	−0.984766	−	0.173886i	$-0.944367\pi$
$599$		−	208.316i		−	0.347773i	0.984766	−	0.173886i	$-0.0556326\pi$
$600$		0			0
$601$	−395.704			−0.658409			−0.329204	−	0.944259i	$-0.606781\pi$
$601$	−395.704			−0.658409			−0.329204	+	0.944259i	$0.606781\pi$
$602$	−218.343	+	218.343i	−0.362696	+	0.362696i
$603$		0			0
$604$		−	171.785i		−	0.284413i
$605$	43.6470	−	115.427i	0.0721438	−	0.190789i
$606$		0			0
$607$	−135.427	+	135.427i	−0.223109	+	0.223109i	−0.809806	−	0.586698i	$-0.800428\pi$
$607$	−135.427	+	135.427i	−0.223109	+	0.223109i	0.586698	+	0.809806i	$0.300428\pi$
$608$	−66.4378	−	66.4378i	−0.109273	−	0.109273i
$609$		0			0
$610$	−203.144	−	450.193i	−0.333024	−	0.738022i
$611$	−1170.60			−1.91587
$612$		0			0
$613$	294.183	+	294.183i	0.479907	+	0.479907i	0.905102	−	0.425195i	$-0.139795\pi$
$613$	294.183	+	294.183i	0.479907	+	0.479907i	−0.425195	+	0.905102i	$0.639795\pi$
$614$			328.654i			0.535268i
$615$		0			0
$616$	169.914			0.275835
$617$	329.788	−	329.788i	0.534503	−	0.534503i	−0.387406	−	0.921909i	$-0.626629\pi$
$617$	329.788	−	329.788i	0.534503	−	0.534503i	0.921909	+	0.387406i	$0.126629\pi$
$618$		0			0
$619$		−	737.362i		−	1.19121i	−0.803276	−	0.595607i	$-0.796912\pi$
$619$		−	737.362i		−	1.19121i	0.803276	−	0.595607i	$-0.203088\pi$
$620$	275.885	+	104.322i	0.444976	+	0.168261i
$621$		0			0
$622$	−240.496	+	240.496i	−0.386650	+	0.386650i
$623$	186.480	+	186.480i	0.299325	+	0.299325i
$624$		0			0
$625$	77.7575	+	620.144i	0.124412	+	0.992231i
$626$	548.628			0.876403
$627$		0			0
$628$	−436.158	−	436.158i	−0.694520	−	0.694520i
$629$			1019.21i			1.62036i
$630$		0			0
$631$	−1070.18			−1.69601			−0.848004	−	0.529990i	$-0.822196\pi$
$631$	−1070.18			−1.69601			−0.848004	+	0.529990i	$0.822196\pi$
$632$	128.586	−	128.586i	0.203458	−	0.203458i
$633$		0			0
$634$			350.000i			0.552051i
$635$	50.2463	+	111.352i	0.0791280	+	0.175358i
$636$		0			0
$637$	153.215	−	153.215i	0.240525	−	0.240525i
$638$	334.543	+	334.543i	0.524362	+	0.524362i
$639$		0			0
$640$	51.5622	−	23.2668i	0.0805659	−	0.0363544i
$641$	−390.671			−0.609471			−0.304735	−	0.952437i	$-0.598568\pi$
$641$	−390.671			−0.609471			−0.304735	+	0.952437i	$0.598568\pi$
$642$		0			0
$643$	−337.514	−	337.514i	−0.524905	−	0.524905i	0.394144	−	0.919049i	$-0.371041\pi$
$643$	−337.514	−	337.514i	−0.524905	−	0.524905i	−0.919049	+	0.394144i	$0.871041\pi$
$644$			196.962i			0.305842i
$645$		0			0
$646$	618.167			0.956914
$647$	70.6685	−	70.6685i	0.109225	−	0.109225i	−0.650382	−	0.759607i	$-0.725391\pi$
$647$	70.6685	−	70.6685i	0.109225	−	0.109225i	0.759607	+	0.650382i	$0.225391\pi$
$648$		0			0
$649$		−	206.228i		−	0.317763i
$650$	−498.083	−	439.530i	−0.766281	−	0.676200i
$651$		0			0
$652$	37.8390	−	37.8390i	0.0580353	−	0.0580353i
$653$	298.337	+	298.337i	0.456871	+	0.456871i	0.897627	−	0.440756i	$-0.145290\pi$
$653$	298.337	+	298.337i	0.456871	+	0.456871i	−0.440756	+	0.897627i	$0.645290\pi$
$654$		0			0
$655$	−167.915	+	444.063i	−0.256359	+	0.677959i
$656$	−89.8547			−0.136974
$657$		0			0
$658$	−381.362	−	381.362i	−0.579577	−	0.579577i
$659$		−	320.219i		−	0.485916i	−0.970037	−	0.242958i	$-0.921882\pi$
$659$		−	320.219i		−	0.485916i	0.970037	−	0.242958i	$-0.0781178\pi$
$660$		0			0
$661$	−522.054			−0.789794			−0.394897	−	0.918725i	$-0.629220\pi$
$661$	−522.054			−0.789794			−0.394897	+	0.918725i	$0.629220\pi$
$662$	−241.485	+	241.485i	−0.364781	+	0.364781i
$663$		0			0
$664$		−	183.104i		−	0.275759i
$665$	−463.351	+	209.081i	−0.696768	+	0.314408i
$666$		0			0
$667$	−387.797	+	387.797i	−0.581405	+	0.581405i
$668$	−33.2964	−	33.2964i	−0.0498449	−	0.0498449i
$669$		0			0
$670$	−16.4506	−	6.22054i	−0.0245532	−	0.00928439i
$671$	−685.511			−1.02163
$672$		0			0
$673$	594.165	+	594.165i	0.882860	+	0.882860i	0.993824	−	0.110964i	$-0.0353939\pi$
$673$	594.165	+	594.165i	0.882860	+	0.882860i	−0.110964	+	0.993824i	$0.535394\pi$
$674$		−	647.282i		−	0.960360i
$675$		0			0
$676$	368.037			0.544433
$677$	151.272	−	151.272i	0.223444	−	0.223444i	−0.586503	−	0.809947i	$-0.699496\pi$
$677$	151.272	−	151.272i	0.223444	−	0.223444i	0.809947	+	0.586503i	$0.199496\pi$
$678$		0			0
$679$			1015.53i			1.49562i
$680$	−131.636	+	348.121i	−0.193583	+	0.511942i
$681$		0			0
$682$	289.471	−	289.471i	0.424445	−	0.424445i
$683$	850.365	+	850.365i	1.24504	+	1.24504i	0.957882	+	0.287162i	$0.0927118\pi$
$683$	850.365	+	850.365i	1.24504	+	1.24504i	0.287162	+	0.957882i	$0.407288\pi$
$684$		0			0
$685$	368.953	+	817.647i	0.538618	+	1.19364i
$686$	523.999			0.763847
$687$		0			0
$688$	100.892	+	100.892i	0.146645	+	0.146645i
$689$		−	372.494i		−	0.540630i
$690$		0			0
$691$	692.480			1.00214			0.501071	−	0.865406i	$-0.332939\pi$
$691$	692.480			1.00214			0.501071	+	0.865406i	$0.332939\pi$
$692$	−237.216	+	237.216i	−0.342798	+	0.342798i
$693$		0			0
$694$		−	297.367i		−	0.428483i
$695$	477.280	+	180.476i	0.686733	+	0.259677i
$696$		0			0
$697$	418.024	−	418.024i	0.599747	−	0.599747i
$698$	59.0300	+	59.0300i	0.0845703	+	0.0845703i
$699$		0			0
$700$	−19.0755	−	305.459i	−0.0272507	−	0.436370i
$701$	141.049			0.201211			0.100606	−	0.994926i	$-0.467922\pi$
$701$	141.049			0.201211			0.100606	+	0.994926i	$0.467922\pi$
$702$		0			0
$703$	454.850	+	454.850i	0.647013	+	0.647013i
$704$		−	78.5139i		−	0.111525i
$705$		0			0
$706$	−714.170			−1.01157
$707$	−246.912	+	246.912i	−0.349239	+	0.349239i
$708$		0			0
$709$			1132.12i			1.59678i	0.602139	+	0.798391i	$0.294315\pi$
$709$			1132.12i			1.59678i	−0.602139	+	0.798391i	$0.705685\pi$
$710$	−288.108	−	638.483i	−0.405786	−	0.899273i
$711$		0			0
$712$	86.1684	−	86.1684i	0.121023	−	0.121023i
$713$	335.551	+	335.551i	0.470618	+	0.470618i
$714$		0			0
$715$	−840.390	+	379.216i	−1.17537	+	0.530372i
$716$	−399.493			−0.557952
$717$		0			0
$718$	−152.761	−	152.761i	−0.212759	−	0.212759i
$719$			710.309i			0.987913i	0.869487	+	0.493956i	$0.164450\pi$
$719$			710.309i			0.987913i	−0.869487	+	0.493956i	$0.835550\pi$
$720$		0			0
$721$	870.330			1.20711
$722$	−85.1259	+	85.1259i	−0.117903	+	0.117903i
$723$		0			0
$724$		−	616.923i		−	0.852104i
$725$	563.859	−	638.974i	0.777736	−	0.881343i
$726$		0			0
$727$	592.419	−	592.419i	0.814881	−	0.814881i	−0.170480	−	0.985361i	$-0.554532\pi$
$727$	592.419	−	592.419i	0.814881	−	0.814881i	0.985361	+	0.170480i	$0.0545318\pi$
$728$	230.015	+	230.015i	0.315955	+	0.315955i
$729$		0			0
$730$	−0.619409	+	1.63807i	−0.000848505	+	0.00224393i
$731$	−938.742			−1.28419
$732$		0			0
$733$	−361.446	−	361.446i	−0.493105	−	0.493105i	0.416178	−	0.909283i	$-0.363369\pi$
$733$	−361.446	−	361.446i	−0.493105	−	0.493105i	−0.909283	+	0.416178i	$0.863369\pi$
$734$			122.275i			0.166588i
$735$		0			0
$736$	91.0121			0.123658
$737$	−17.2607	+	17.2607i	−0.0234203	+	0.0234203i
$738$		0			0
$739$		−	1107.09i		−	1.49809i	−0.662518	−	0.749046i	$-0.730512\pi$
$739$		−	1107.09i		−	1.49809i	0.662518	−	0.749046i	$-0.269488\pi$
$740$	−353.007	+	159.290i	−0.477037	+	0.215257i
$741$		0			0
$742$	121.353	−	121.353i	0.163548	−	0.163548i
$743$	812.741	+	812.741i	1.09386	+	1.09386i	0.995112	+	0.0987516i	$0.0314849\pi$
$743$	812.741	+	812.741i	1.09386	+	1.09386i	0.0987516	+	0.995112i	$0.468515\pi$
$744$		0			0
$745$	−483.703	−	182.904i	−0.649265	−	0.245509i
$746$	80.0380			0.107290
$747$		0			0
$748$	365.264	+	365.264i	0.488320	+	0.488320i
$749$		−	1244.53i		−	1.66158i
$750$		0			0
$751$	−425.371			−0.566406			−0.283203	−	0.959060i	$-0.591397\pi$
$751$	−425.371			−0.566406			−0.283203	+	0.959060i	$0.591397\pi$
$752$	−176.219	+	176.219i	−0.234334	+	0.234334i
$753$		0			0
$754$			905.751i			1.20126i
$755$	−151.898	+	401.704i	−0.201189	+	0.532058i
$756$		0			0
$757$	−148.304	+	148.304i	−0.195910	+	0.195910i	−0.798244	−	0.602334i	$-0.794238\pi$
$757$	−148.304	+	148.304i	−0.195910	+	0.195910i	0.602334	+	0.798244i	$0.294238\pi$
$758$	−515.708	−	515.708i	−0.680353	−	0.680353i
$759$		0			0
$760$	96.6122	+	214.105i	0.127121	+	0.281717i
$761$	−1177.06			−1.54673			−0.773366	−	0.633960i	$-0.781429\pi$
$761$	−1177.06			−1.54673			−0.773366	+	0.633960i	$0.781429\pi$
$762$		0			0
$763$	−71.2019	−	71.2019i	−0.0933184	−	0.0933184i
$764$			270.435i			0.353973i
$765$		0			0
$766$	438.366			0.572280
$767$	279.174	−	279.174i	0.363982	−	0.363982i
$768$		0			0
$769$			1212.45i			1.57665i	0.615257	+	0.788327i	$0.289052\pi$
$769$			1212.45i			1.57665i	−0.615257	+	0.788327i	$0.710948\pi$
$770$	−397.328	−	150.243i	−0.516011	−	0.195121i
$771$		0			0
$772$	196.003	−	196.003i	0.253890	−	0.253890i
$773$	243.631	+	243.631i	0.315176	+	0.315176i	0.846911	−	0.531735i	$-0.178460\pi$
$773$	243.631	+	243.631i	0.315176	+	0.315176i	−0.531735	+	0.846911i	$0.678460\pi$
$774$		0			0
$775$	−552.888	−	487.892i	−0.713403	−	0.629538i
$776$	469.255			0.604710
$777$		0			0
$778$	−56.3472	−	56.3472i	−0.0724258	−	0.0724258i
$779$		−	373.110i		−	0.478960i
$780$		0			0
$781$	−972.221			−1.24484
$782$	−423.408	+	423.408i	−0.541443	+	0.541443i
$783$		0			0
$784$		−	46.1292i		−	0.0588383i
$785$	634.250	+	1405.58i	0.807962	+	1.79055i
$786$		0			0
$787$	1029.11	−	1029.11i	1.30764	−	1.30764i	0.384529	−	0.923113i	$-0.374364\pi$
$787$	1029.11	−	1029.11i	1.30764	−	1.30764i	0.923113	−	0.384529i	$-0.125636\pi$
$788$	187.908	+	187.908i	0.238462	+	0.238462i
$789$		0			0
$790$	−414.384	+	186.986i	−0.524537	+	0.236691i
$791$	362.090			0.457763
$792$		0			0
$793$	−927.987	−	927.987i	−1.17022	−	1.17022i
$794$		−	639.895i		−	0.805914i
$795$		0			0
$796$	−630.840			−0.792513
$797$	571.758	−	571.758i	0.717387	−	0.717387i	−0.250682	−	0.968069i	$-0.580655\pi$
$797$	571.758	−	571.758i	0.717387	−	0.717387i	0.968069	+	0.250682i	$0.0806549\pi$
$798$		0			0
$799$		−	1639.62i		−	2.05209i
$800$	−141.146	+	8.81439i	−0.176433	+	0.0110180i
$801$		0			0
$802$	−231.122	+	231.122i	−0.288181	+	0.288181i
$803$	1.71873	+	1.71873i	0.00214039	+	0.00214039i
$804$		0			0
$805$	174.160	−	460.577i	0.216348	−	0.572145i
$806$	783.723			0.972361
$807$		0			0
$808$	114.093	+	114.093i	0.141204	+	0.141204i
$809$		−	1458.06i		−	1.80230i	−0.433507	−	0.901150i	$-0.642724\pi$
$809$		−	1458.06i		−	1.80230i	0.433507	−	0.901150i	$-0.357276\pi$
$810$		0			0
$811$	−723.861			−0.892554			−0.446277	−	0.894895i	$-0.647250\pi$
$811$	−723.861			−0.892554			−0.446277	+	0.894895i	$0.647250\pi$
$812$	−295.079	+	295.079i	−0.363398	+	0.363398i
$813$		0			0
$814$			537.526i			0.660351i
$815$	−121.941	+	55.0245i	−0.149621	+	0.0675147i
$816$		0			0
$817$	−418.940	+	418.940i	−0.512778	+	0.512778i
$818$	−468.707	−	468.707i	−0.572992	−	0.572992i
$819$		0			0
$820$	210.117	+	79.4523i	0.256240	+	0.0968930i
$821$	−824.427			−1.00417			−0.502087	−	0.864817i	$-0.667434\pi$
$821$	−824.427			−1.00417			−0.502087	+	0.864817i	$0.667434\pi$
$822$		0			0
$823$	−580.549	−	580.549i	−0.705406	−	0.705406i	0.260160	−	0.965566i	$-0.416225\pi$
$823$	−580.549	−	580.549i	−0.705406	−	0.705406i	−0.965566	+	0.260160i	$0.916225\pi$
$824$		−	402.161i		−	0.488060i
$825$		0			0
$826$	181.901			0.220219
$827$	533.414	−	533.414i	0.644999	−	0.644999i	−0.306781	−	0.951780i	$-0.599252\pi$
$827$	533.414	−	533.414i	0.644999	−	0.644999i	0.951780	+	0.306781i	$0.0992519\pi$
$828$		0			0
$829$			790.757i			0.953868i	0.878939	+	0.476934i	$0.158252\pi$
$829$			790.757i			0.953868i	−0.878939	+	0.476934i	$0.841748\pi$
$830$	−161.906	+	428.172i	−0.195068	+	0.515870i
$831$		0			0
$832$	106.285	−	106.285i	0.127747	−	0.127747i
$833$	214.603	+	214.603i	0.257627	+	0.257627i
$834$		0			0
$835$	48.4188	+	107.302i	0.0579866	+	0.128506i
$836$	326.018			0.389974
$837$		0			0
$838$	90.7621	+	90.7621i	0.108308	+	0.108308i
$839$			738.200i			0.879857i	0.898033	+	0.439928i	$0.144996\pi$
$839$			738.200i			0.879857i	−0.898033	+	0.439928i	$0.855004\pi$
$840$		0			0
$841$	−320.959			−0.381640
$842$	72.4132	−	72.4132i	0.0860014	−	0.0860014i
$843$		0			0
$844$			239.184i			0.283393i
$845$	−860.618	−	325.429i	−1.01848	−	0.385123i
$846$		0			0
$847$	106.825	−	106.825i	0.126122	−	0.126122i
$848$	−56.0746	−	56.0746i	−0.0661256	−	0.0661256i
$849$		0			0
$850$	615.637	−	697.650i	0.724279	−	0.820765i
$851$	−623.092			−0.732188
$852$		0			0
$853$	−847.815	−	847.815i	−0.993921	−	0.993921i	0.00606025	−	0.999982i	$-0.498071\pi$
$853$	−847.815	−	847.815i	−0.993921	−	0.993921i	−0.999982	+	0.00606025i	$0.998071\pi$
$854$		−	604.647i		−	0.708017i
$855$		0			0
$856$	−575.070			−0.671811
$857$	68.0430	−	68.0430i	0.0793967	−	0.0793967i	−0.666293	−	0.745690i	$-0.732120\pi$
$857$	68.0430	−	68.0430i	0.0793967	−	0.0793967i	0.745690	+	0.666293i	$0.232120\pi$
$858$		0			0
$859$			437.164i			0.508922i	0.967083	+	0.254461i	$0.0818981\pi$
$859$			437.164i			0.508922i	−0.967083	+	0.254461i	$0.918102\pi$
$860$	−146.714	−	325.138i	−0.170598	−	0.378067i
$861$		0			0
$862$	−36.9748	+	36.9748i	−0.0428942	+	0.0428942i
$863$	−817.757	−	817.757i	−0.947575	−	0.947575i	0.0511180	−	0.998693i	$-0.483722\pi$
$863$	−817.757	−	817.757i	−0.947575	−	0.947575i	−0.998693	+	0.0511180i	$0.983722\pi$
$864$		0			0
$865$	764.462	−	344.954i	0.883771	−	0.398791i
$866$	−536.915			−0.619994
$867$		0			0
$868$	255.324	+	255.324i	0.294153	+	0.294153i
$869$			630.984i			0.726104i
$870$		0			0
$871$	−46.7323			−0.0536536
$872$	−32.9009	+	32.9009i	−0.0377304	+	0.0377304i
$873$		0			0
$874$			377.915i			0.432397i
$875$	−225.490	+	731.155i	−0.257703	+	0.835605i
$876$		0			0
$877$	844.483	−	844.483i	0.962923	−	0.962923i	−0.0364140	−	0.999337i	$-0.511594\pi$
$877$	844.483	−	844.483i	0.962923	−	0.962923i	0.999337	+	0.0364140i	$0.0115935\pi$
$878$	−482.160	−	482.160i	−0.549158	−	0.549158i
$879$		0			0
$880$	−69.4243	+	183.597i	−0.0788913	+	0.208633i
$881$	727.798			0.826104			0.413052	−	0.910707i	$-0.364463\pi$
$881$	727.798			0.826104			0.413052	+	0.910707i	$0.364463\pi$
$882$		0			0
$883$	274.297	+	274.297i	0.310642	+	0.310642i	0.845158	−	0.534516i	$-0.179506\pi$
$883$	274.297	+	274.297i	0.310642	+	0.310642i	−0.534516	+	0.845158i	$0.679506\pi$
$884$			988.926i			1.11869i
$885$		0			0
$886$	−261.150			−0.294751
$887$	−709.487	+	709.487i	−0.799872	+	0.799872i	−0.983075	−	0.183203i	$-0.941353\pi$
$887$	−709.487	+	709.487i	−0.799872	+	0.799872i	0.183203	+	0.983075i	$0.441353\pi$
$888$		0			0
$889$			149.555i			0.168228i
$890$	−277.689	+	125.304i	−0.312010	+	0.140791i
$891$		0			0
$892$	−394.942	+	394.942i	−0.442760	+	0.442760i
$893$	−731.727	−	731.727i	−0.819403	−	0.819403i
$894$		0			0
$895$	934.177	+	353.244i	1.04377	+	0.394686i
$896$	69.2522			0.0772904
$897$		0			0
$898$	608.199	+	608.199i	0.677281	+	0.677281i
$899$			1005.41i			1.11837i
$900$		0			0
$901$	521.742			0.579070
$902$	220.464	−	220.464i	0.244417	−	0.244417i
$903$		0			0
$904$		−	167.314i		−	0.185082i
$905$	−545.502	+	1442.62i	−0.602765	+	1.59405i
$906$		0			0
$907$	−247.336	+	247.336i	−0.272696	+	0.272696i	−0.830185	−	0.557488i	$-0.811765\pi$
$907$	−247.336	+	247.336i	−0.272696	+	0.272696i	0.557488	+	0.830185i	$0.311765\pi$
$908$	473.132	+	473.132i	0.521070	+	0.521070i
$909$		0			0
$910$	−334.483	−	741.256i	−0.367563	−	0.814567i
$911$	−285.058			−0.312907			−0.156453	−	0.987685i	$-0.550006\pi$
$911$	−285.058			−0.312907			−0.156453	+	0.987685i	$0.550006\pi$
$912$		0			0
$913$	449.257	+	449.257i	0.492067	+	0.492067i
$914$		−	698.893i		−	0.764654i
$915$		0			0
$916$	−551.892			−0.602502
$917$	−410.969	+	410.969i	−0.448166	+	0.448166i
$918$		0			0
$919$		−	302.663i		−	0.329340i	−0.986349	−	0.164670i	$-0.947344\pi$
$919$		−	302.663i		−	0.329340i	0.986349	−	0.164670i	$-0.0526558\pi$
$920$	−212.823	−	80.4756i	−0.231329	−	0.0874735i
$921$		0			0
$922$	−211.005	+	211.005i	−0.228856	+	0.228856i
$923$	−1316.11	−	1316.11i	−1.42590	−	1.42590i
$924$		0			0
$925$	966.324	−	60.3455i	1.04467	−	0.0652384i
$926$	−75.8381			−0.0818985
$927$		0			0
$928$	136.350	+	136.350i	0.146929	+	0.146929i
$929$		−	406.988i		−	0.438093i	−0.975714	−	0.219046i	$-0.929705\pi$
$929$		−	406.988i		−	0.438093i	0.975714	−	0.219046i	$-0.0702946\pi$
$930$		0			0
$931$	191.545			0.205742
$932$	−343.461	+	343.461i	−0.368520	+	0.368520i
$933$		0			0
$934$			802.817i			0.859547i
$935$	−531.157	−	1177.11i	−0.568083	−	1.25894i
$936$		0			0
$937$	−299.583	+	299.583i	−0.319726	+	0.319726i	−0.848662	−	0.528936i	$-0.822591\pi$
$937$	−299.583	+	299.583i	−0.319726	+	0.319726i	0.528936	+	0.848662i	$0.322591\pi$
$938$	−15.2246	−	15.2246i	−0.0162309	−	0.0162309i
$939$		0			0
$940$	567.891	−	256.254i	0.604139	−	0.272611i
$941$	−1027.36			−1.09177			−0.545885	−	0.837860i	$-0.683806\pi$
$941$	−1027.36			−1.09177			−0.545885	+	0.837860i	$0.683806\pi$
$942$		0			0
$943$	255.558	+	255.558i	0.271006	+	0.271006i
$944$		−	84.0527i		−	0.0890388i
$945$		0			0
$946$	−495.088			−0.523349
$947$	−664.087	+	664.087i	−0.701254	+	0.701254i	−0.964680	−	0.263426i	$-0.915148\pi$
$947$	−664.087	+	664.087i	−0.701254	+	0.701254i	0.263426	+	0.964680i	$0.415148\pi$
$948$		0			0
$949$			4.65335i			0.00490342i
$950$	−36.6006	−	586.091i	−0.0385269	−	0.616938i
$951$		0			0
$952$	−322.176	+	322.176i	−0.338420	+	0.338420i
$953$	−625.070	−	625.070i	−0.655897	−	0.655897i	0.298509	−	0.954407i	$-0.403511\pi$
$953$	−625.070	−	625.070i	−0.655897	−	0.655897i	−0.954407	+	0.298509i	$0.903511\pi$
$954$		0			0
$955$	239.127	−	632.387i	0.250395	−	0.662186i
$956$	−179.965			−0.188247
$957$		0			0
$958$	−390.847	−	390.847i	−0.407982	−	0.407982i
$959$			1098.17i			1.14512i
$960$		0			0
$961$	−91.0424			−0.0947372
$962$	−727.656	+	727.656i	−0.756400	+	0.756400i
$963$		0			0
$964$		−	653.380i		−	0.677780i
$965$	−631.646	+	285.023i	−0.654556	+	0.295360i
$966$		0			0
$967$	731.246	−	731.246i	0.756200	−	0.756200i	−0.219428	−	0.975629i	$-0.570419\pi$
$967$	731.246	−	731.246i	0.756200	−	0.756200i	0.975629	+	0.219428i	$0.0704192\pi$
$968$	−49.3616	−	49.3616i	−0.0509934	−	0.0509934i
$969$		0			0
$970$	−1097.31	−	414.929i	−1.13124	−	0.427762i
$971$	−758.305			−0.780952			−0.390476	−	0.920613i	$-0.627690\pi$
$971$	−758.305			−0.780952			−0.390476	+	0.920613i	$0.627690\pi$
$972$		0			0
$973$	441.709	+	441.709i	0.453967	+	0.453967i
$974$			253.874i			0.260651i
$975$		0			0
$976$	−279.395			−0.286265
$977$	1106.34	−	1106.34i	1.13238	−	1.13238i	0.142603	−	0.989780i	$-0.454453\pi$
$977$	1106.34	−	1106.34i	1.13238	−	1.13238i	0.989780	−	0.142603i	$-0.0455473\pi$
$978$		0			0
$979$			422.838i			0.431908i
$980$	−40.7889	+	107.869i	−0.0416213	+	0.110070i
$981$		0			0
$982$	−24.8280	+	24.8280i	−0.0252831	+	0.0252831i
$983$	−209.129	−	209.129i	−0.212745	−	0.212745i	0.592687	−	0.805433i	$-0.298067\pi$
$983$	−209.129	−	209.129i	−0.212745	−	0.212745i	−0.805433	+	0.592687i	$0.798067\pi$
$984$		0			0
$985$	−273.251	−	605.559i	−0.277412	−	0.614781i
$986$	−1268.66			−1.28667
$987$		0			0
$988$	441.336	+	441.336i	0.446696	+	0.446696i
$989$		−	573.899i		−	0.580282i
$990$		0			0
$991$	1174.07			1.18473			0.592367	−	0.805668i	$-0.298194\pi$
$991$	1174.07			1.18473			0.592367	+	0.805668i	$0.298194\pi$
$992$	117.980	−	117.980i	0.118932	−	0.118932i
$993$		0			0
$994$		−	857.535i		−	0.862712i
$995$	1475.16	+	557.808i	1.48257	+	0.560611i
$996$		0			0
$997$	−119.979	+	119.979i	−0.120340	+	0.120340i	−0.764712	−	0.644372i	$-0.777119\pi$
$997$	−119.979	+	119.979i	−0.120340	+	0.120340i	0.644372	+	0.764712i	$0.277119\pi$
$998$	697.531	+	697.531i	0.698929	+	0.698929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.g.i.163.2		12
3.2	odd	2		810.3.g.k.163.5		12
5.2	odd	4	inner	810.3.g.i.487.2		12
9.2	odd	6		90.3.k.a.13.5	yes	24
9.4	even	3		270.3.l.b.73.6		24
9.5	odd	6		90.3.k.a.43.1	yes	24
9.7	even	3		270.3.l.b.253.3		24
15.2	even	4		810.3.g.k.487.5		12
45.2	even	12		90.3.k.a.67.1	yes	24
45.7	odd	12		270.3.l.b.37.6		24
45.22	odd	12		270.3.l.b.127.3		24
45.32	even	12		90.3.k.a.7.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.5	✓	24	45.32	even	12
90.3.k.a.13.5	yes	24	9.2	odd	6
90.3.k.a.43.1	yes	24	9.5	odd	6
90.3.k.a.67.1	yes	24	45.2	even	12
270.3.l.b.37.6		24	45.7	odd	12
270.3.l.b.73.6		24	9.4	even	3
270.3.l.b.127.3		24	45.22	odd	12
270.3.l.b.253.3		24	9.7	even	3
810.3.g.i.163.2		12	1.1	even	1	trivial
810.3.g.i.487.2		12	5.2	odd	4	inner
810.3.g.k.163.5		12	3.2	odd	2
810.3.g.k.487.5		12	15.2	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-1.76846 + 4.67681i) q^{5} +(-4.32826 + 4.32826i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-1.76846 + 4.67681i) q^{5} +(-4.32826 + 4.32826i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.90835 - 6.44527i) q^{10} -9.81423 q^{11} +(-13.2857 - 13.2857i) q^{13} -8.65652i q^{14} -4.00000 q^{16} +(18.6089 - 18.6089i) q^{17} -16.6095i q^{19} +(9.35362 + 3.53692i) q^{20} +(9.81423 - 9.81423i) q^{22} +(11.3765 + 11.3765i) q^{23} +(-18.7451 - 16.5415i) q^{25} +26.5713 q^{26} +(8.65652 + 8.65652i) q^{28} +34.0875i q^{29} +29.4950 q^{31} +(4.00000 - 4.00000i) q^{32} +37.2178i q^{34} +(-12.5881 - 27.8968i) q^{35} +(-27.3850 + 27.3850i) q^{37} +(16.6095 + 16.6095i) q^{38} +(-12.8905 + 5.81670i) q^{40} +22.4637 q^{41} +(-25.2230 - 25.2230i) q^{43} +19.6285i q^{44} -22.7530 q^{46} +(44.0549 - 44.0549i) q^{47} +11.5323i q^{49} +(35.2866 - 2.20360i) q^{50} +(-26.5713 + 26.5713i) q^{52} +(14.0186 + 14.0186i) q^{53} +(17.3561 - 45.8993i) q^{55} -17.3130 q^{56} +(-34.0875 - 34.0875i) q^{58} +21.0132i q^{59} +69.8487 q^{61} +(-29.4950 + 29.4950i) q^{62} +8.00000i q^{64} +(85.6298 - 38.6394i) q^{65} +(1.75875 - 1.75875i) q^{67} +(-37.2178 - 37.2178i) q^{68} +(40.4849 + 15.3087i) q^{70} +99.0623 q^{71} +(-0.175127 - 0.175127i) q^{73} -54.7700i q^{74} -33.2189 q^{76} +(42.4786 - 42.4786i) q^{77} -64.2928i q^{79} +(7.07384 - 18.7072i) q^{80} +(-22.4637 + 22.4637i) q^{82} +(-45.7761 - 45.7761i) q^{83} +(54.1211 + 119.939i) q^{85} +50.4459 q^{86} +(-19.6285 - 19.6285i) q^{88} -43.0842i q^{89} +115.008 q^{91} +(22.7530 - 22.7530i) q^{92} +88.1097i q^{94} +(77.6793 + 29.3732i) q^{95} +(117.314 - 117.314i) q^{97} +(-11.5323 - 11.5323i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 6 q^{7} + 24 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 6 * q^7 + 24 * q^8	\( 12 q - 12 q^{2} + 6 q^{7} + 24 q^{8} - 6 q^{10} - 12 q^{11} - 48 q^{16} + 18 q^{17} + 12 q^{20} + 12 q^{22} - 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} + 48 q^{32} + 168 q^{35} + 66 q^{37} - 36 q^{38} - 12 q^{40} + 24 q^{41} - 108 q^{43} + 108 q^{46} + 48 q^{47} + 54 q^{50} - 192 q^{53} - 276 q^{55} + 24 q^{56} - 60 q^{58} + 456 q^{61} - 72 q^{62} + 264 q^{65} - 12 q^{67} - 36 q^{68} - 174 q^{70} + 84 q^{71} - 216 q^{73} + 72 q^{76} - 48 q^{77} - 24 q^{82} - 246 q^{83} - 324 q^{85} + 216 q^{86} - 24 q^{88} + 612 q^{91} - 108 q^{92} + 432 q^{95} + 102 q^{97} - 12 q^{98}+O(q^{100}) \) 12 * q - 12 * q^2 + 6 * q^7 + 24 * q^8 - 6 * q^10 - 12 * q^11 - 48 * q^16 + 18 * q^17 + 12 * q^20 + 12 * q^22 - 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 + 48 * q^32 + 168 * q^35 + 66 * q^37 - 36 * q^38 - 12 * q^40 + 24 * q^41 - 108 * q^43 + 108 * q^46 + 48 * q^47 + 54 * q^50 - 192 * q^53 - 276 * q^55 + 24 * q^56 - 60 * q^58 + 456 * q^61 - 72 * q^62 + 264 * q^65 - 12 * q^67 - 36 * q^68 - 174 * q^70 + 84 * q^71 - 216 * q^73 + 72 * q^76 - 48 * q^77 - 24 * q^82 - 246 * q^83 - 324 * q^85 + 216 * q^86 - 24 * q^88 + 612 * q^91 - 108 * q^92 + 432 * q^95 + 102 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

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