LMFDB - Embedded newform 1805.2.b.k.1084.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, 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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.13
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.244477i q^{2} -2.73837i q^{3} +1.94023 q^{4} +(0.750459 - 2.10637i) q^{5} +0.669469 q^{6} +1.94027i q^{7} +0.963297i q^{8} -4.49866 q^{9} +O(q^{10})$	\(q+0.244477i q^{2} -2.73837i q^{3} +1.94023 q^{4} +(0.750459 - 2.10637i) q^{5} +0.669469 q^{6} +1.94027i q^{7} +0.963297i q^{8} -4.49866 q^{9} +(0.514961 + 0.183470i) q^{10} +4.23333 q^{11} -5.31307i q^{12} -1.26982i q^{13} -0.474352 q^{14} +(-5.76803 - 2.05503i) q^{15} +3.64496 q^{16} +2.46021i q^{17} -1.09982i q^{18} +(1.45606 - 4.08685i) q^{20} +5.31318 q^{21} +1.03495i q^{22} -5.13716i q^{23} +2.63786 q^{24} +(-3.87362 - 3.16149i) q^{25} +0.310443 q^{26} +4.10387i q^{27} +3.76457i q^{28} -8.64123 q^{29} +(0.502409 - 1.41015i) q^{30} +5.10084 q^{31} +2.81770i q^{32} -11.5924i q^{33} -0.601466 q^{34} +(4.08694 + 1.45609i) q^{35} -8.72843 q^{36} -11.0305i q^{37} -3.47724 q^{39} +(2.02906 + 0.722915i) q^{40} +2.49838 q^{41} +1.29895i q^{42} +4.46879i q^{43} +8.21364 q^{44} +(-3.37606 + 9.47585i) q^{45} +1.25592 q^{46} -6.76901i q^{47} -9.98123i q^{48} +3.23535 q^{49} +(0.772913 - 0.947013i) q^{50} +6.73697 q^{51} -2.46375i q^{52} +0.689802i q^{53} -1.00330 q^{54} +(3.17694 - 8.91697i) q^{55} -1.86906 q^{56} -2.11258i q^{58} -5.19336 q^{59} +(-11.1913 - 3.98724i) q^{60} +2.80281 q^{61} +1.24704i q^{62} -8.72862i q^{63} +6.60105 q^{64} +(-2.67472 - 0.952950i) q^{65} +2.83408 q^{66} +5.21227i q^{67} +4.77338i q^{68} -14.0674 q^{69} +(-0.355982 + 0.999163i) q^{70} +0.791916 q^{71} -4.33354i q^{72} +1.41576i q^{73} +2.69671 q^{74} +(-8.65733 + 10.6074i) q^{75} +8.21381i q^{77} -0.850107i q^{78} +6.06294 q^{79} +(2.73539 - 7.67764i) q^{80} -2.25806 q^{81} +0.610798i q^{82} +11.8522i q^{83} +10.3088 q^{84} +(5.18213 + 1.84629i) q^{85} -1.09252 q^{86} +23.6629i q^{87} +4.07795i q^{88} +2.23291 q^{89} +(-2.31663 - 0.825369i) q^{90} +2.46380 q^{91} -9.96727i q^{92} -13.9680i q^{93} +1.65487 q^{94} +7.71591 q^{96} +8.60981i q^{97} +0.790969i q^{98} -19.0443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.244477i			0.172872i	0.996257	+	0.0864358i	$0.0275477\pi$
$2$			0.244477i			0.172872i	−0.996257	+	0.0864358i	$0.972452\pi$
$3$		−	2.73837i		−	1.58100i	−0.612464	−	0.790499i	$-0.709821\pi$
$3$		−	2.73837i		−	1.58100i	0.612464	−	0.790499i	$-0.290179\pi$
$4$	1.94023			0.970115
$5$	0.750459	−	2.10637i	0.335615	−	0.941999i
$5$	0.750459	−	2.10637i	0.335615	−	0.941999i
$6$	0.669469			0.273309
$7$			1.94027i			0.733354i	0.930348	+	0.366677i	$0.119505\pi$
$7$			1.94027i			0.733354i	−0.930348	+	0.366677i	$0.880495\pi$
$8$			0.963297i			0.340577i
$9$	−4.49866			−1.49955
$10$	0.514961	+	0.183470i	0.162845	+	0.0580184i
$11$	4.23333			1.27640			0.638198	−	0.769872i	$-0.279680\pi$
$11$	4.23333			1.27640			0.638198	+	0.769872i	$0.279680\pi$
$12$		−	5.31307i		−	1.53375i
$13$		−	1.26982i		−	0.352186i	−0.984374	−	0.176093i	$-0.943654\pi$
$13$		−	1.26982i		−	0.352186i	0.984374	−	0.176093i	$-0.0563459\pi$
$14$	−0.474352			−0.126776
$15$	−5.76803	−	2.05503i	−1.48930	−	0.530607i
$16$	3.64496			0.911239
$17$			2.46021i			0.596689i	0.954458	+	0.298345i	$0.0964345\pi$
$17$			2.46021i			0.596689i	−0.954458	+	0.298345i	$0.903566\pi$
$18$		−	1.09982i		−	0.259230i
$19$		0			0
$19$		0			0
$20$	1.45606	−	4.08685i	0.325586	−	0.913848i
$21$	5.31318			1.15943
$22$			1.03495i			0.220653i
$23$		−	5.13716i		−	1.07117i	−0.844481	−	0.535586i	$-0.820091\pi$
$23$		−	5.13716i		−	1.07117i	0.844481	−	0.535586i	$-0.179909\pi$
$24$	2.63786			0.538451
$25$	−3.87362	−	3.16149i	−0.774725	−	0.632299i
$26$	0.310443			0.0608829
$27$			4.10387i			0.789791i
$28$			3.76457i			0.711438i
$29$	−8.64123			−1.60464			−0.802318	−	0.596897i	$-0.796400\pi$
$29$	−8.64123			−1.60464			−0.802318	+	0.596897i	$0.796400\pi$
$30$	0.502409	−	1.41015i	0.0917269	−	0.257457i
$31$	5.10084			0.916138			0.458069	−	0.888917i	$-0.348541\pi$
$31$	5.10084			0.916138			0.458069	+	0.888917i	$0.348541\pi$
$32$			2.81770i			0.498104i
$33$		−	11.5924i		−	2.01798i
$34$	−0.601466			−0.103151
$35$	4.08694	+	1.45609i	0.690819	+	0.246125i
$36$	−8.72843			−1.45474
$37$		−	11.0305i		−	1.81341i	−0.421770	−	0.906703i	$-0.638591\pi$
$37$		−	11.0305i		−	1.81341i	0.421770	−	0.906703i	$-0.361409\pi$
$38$		0			0
$39$	−3.47724			−0.556805
$40$	2.02906	+	0.722915i	0.320823	+	0.114303i
$41$	2.49838			0.390182			0.195091	−	0.980785i	$-0.437500\pi$
$41$	2.49838			0.390182			0.195091	+	0.980785i	$0.437500\pi$
$42$			1.29895i			0.200432i
$43$			4.46879i			0.681484i	0.940157	+	0.340742i	$0.110678\pi$
$43$			4.46879i			0.681484i	−0.940157	+	0.340742i	$0.889322\pi$
$44$	8.21364			1.23825
$45$	−3.37606	+	9.47585i	−0.503273	+	1.41258i
$46$	1.25592			0.185175
$47$		−	6.76901i		−	0.987362i	−0.869643	−	0.493681i	$-0.835651\pi$
$47$		−	6.76901i		−	0.987362i	0.869643	−	0.493681i	$-0.164349\pi$
$48$		−	9.98123i		−	1.44067i
$49$	3.23535			0.462192
$50$	0.772913	−	0.947013i	0.109306	−	0.133928i
$51$	6.73697			0.943364
$52$		−	2.46375i		−	0.341661i
$53$			0.689802i			0.0947515i	0.998877	+	0.0473758i	$0.0150858\pi$
$53$			0.689802i			0.0947515i	−0.998877	+	0.0473758i	$0.984914\pi$
$54$	−1.00330			−0.136532
$55$	3.17694	−	8.91697i	0.428378	−	1.20236i
$56$	−1.86906			−0.249763
$57$		0			0
$58$		−	2.11258i		−	0.277396i
$59$	−5.19336			−0.676118			−0.338059	−	0.941125i	$-0.609770\pi$
$59$	−5.19336			−0.676118			−0.338059	+	0.941125i	$0.609770\pi$
$60$	−11.1913	−	3.98724i	−1.44479	−	0.514750i
$61$	2.80281			0.358864			0.179432	−	0.983770i	$-0.442574\pi$
$61$	2.80281			0.358864			0.179432	+	0.983770i	$0.442574\pi$
$62$			1.24704i			0.158374i
$63$		−	8.72862i		−	1.09970i
$64$	6.60105			0.825131
$65$	−2.67472	−	0.952950i	−0.331759	−	0.118199i
$66$	2.83408			0.348851
$67$			5.21227i			0.636780i	0.947960	+	0.318390i	$0.103142\pi$
$67$			5.21227i			0.636780i	−0.947960	+	0.318390i	$0.896858\pi$
$68$			4.77338i			0.578858i
$69$	−14.0674			−1.69352
$70$	−0.355982	+	0.999163i	−0.0425480	+	0.119423i
$71$	0.791916			0.0939832			0.0469916	−	0.998895i	$-0.485037\pi$
$71$	0.791916			0.0939832			0.0469916	+	0.998895i	$0.485037\pi$
$72$		−	4.33354i		−	0.510713i
$73$			1.41576i			0.165702i	0.996562	+	0.0828512i	$0.0264026\pi$
$73$			1.41576i			0.165702i	−0.996562	+	0.0828512i	$0.973597\pi$
$74$	2.69671			0.313486
$75$	−8.65733	+	10.6074i	−0.999663	+	1.22484i
$76$		0			0
$77$			8.21381i			0.936050i
$78$		−	0.850107i		−	0.0962557i
$79$	6.06294			0.682134			0.341067	−	0.940039i	$-0.389212\pi$
$79$	6.06294			0.682134			0.341067	+	0.940039i	$0.389212\pi$
$80$	2.73539	−	7.67764i	0.305826	−	0.858387i
$81$	−2.25806			−0.250895
$82$			0.610798i			0.0674514i
$83$			11.8522i			1.30095i	0.759527	+	0.650476i	$0.225430\pi$
$83$			11.8522i			1.30095i	−0.759527	+	0.650476i	$0.774570\pi$
$84$	10.3088			1.12478
$85$	5.18213	+	1.84629i	0.562081	+	0.200258i
$86$	−1.09252			−0.117809
$87$			23.6629i			2.53692i
$88$			4.07795i			0.434711i
$89$	2.23291			0.236688			0.118344	−	0.992973i	$-0.462241\pi$
$89$	2.23291			0.236688			0.118344	+	0.992973i	$0.462241\pi$
$90$	−2.31663	−	0.825369i	−0.244194	−	0.0870016i
$91$	2.46380			0.258277
$92$		−	9.96727i		−	1.03916i
$93$		−	13.9680i		−	1.44841i
$94$	1.65487			0.170687
$95$		0			0
$96$	7.71591			0.787501
$97$			8.60981i			0.874194i	0.899414	+	0.437097i	$0.143993\pi$
$97$			8.60981i			0.874194i	−0.899414	+	0.437097i	$0.856007\pi$
$98$			0.790969i			0.0798999i
$99$	−19.0443			−1.91402
$100$	−7.51572	−	6.13403i	−0.751572	−	0.613403i
$101$	−13.4510			−1.33842			−0.669212	−	0.743071i	$-0.733368\pi$
$101$	−13.4510			−1.33842			−0.669212	+	0.743071i	$0.733368\pi$
$102$			1.64704i			0.163081i
$103$			4.03579i			0.397658i	0.980034	+	0.198829i	$0.0637139\pi$
$103$			4.03579i			0.397658i	−0.980034	+	0.198829i	$0.936286\pi$
$104$	1.22322			0.119946
$105$	3.98732	−	11.1915i	0.389123	−	1.09218i
$106$	−0.168641			−0.0163798
$107$		−	16.9589i		−	1.63948i	−0.572734	−	0.819741i	$-0.694117\pi$
$107$		−	16.9589i		−	1.63948i	0.572734	−	0.819741i	$-0.305883\pi$
$108$			7.96246i			0.766188i
$109$	−6.83567			−0.654739			−0.327369	−	0.944896i	$-0.606162\pi$
$109$	−6.83567			−0.654739			−0.327369	+	0.944896i	$0.606162\pi$
$110$	2.18000	+	0.776689i	0.207855	+	0.0740544i
$111$	−30.2056			−2.86699
$112$			7.07221i			0.668261i
$113$			5.92416i			0.557298i	0.960393	+	0.278649i	$0.0898867\pi$
$113$			5.92416i			0.557298i	−0.960393	+	0.278649i	$0.910113\pi$
$114$		0			0
$115$	−10.8208	−	3.85523i	−1.00904	−	0.359502i
$116$	−16.7660			−1.55668
$117$			5.71250i			0.528121i
$118$		−	1.26966i		−	0.116882i
$119$	−4.77348			−0.437584
$120$	1.97961	−	5.55632i	0.180712	−	0.507221i
$121$	6.92107			0.629188
$122$			0.685224i			0.0620373i
$123$		−	6.84150i		−	0.616877i
$124$	9.89681			0.888759
$125$	−9.56628	+	5.78673i	−0.855634	+	0.517581i
$126$	2.13395			0.190107
$127$			19.1802i			1.70197i	0.525193	+	0.850983i	$0.323993\pi$
$127$			19.1802i			1.70197i	−0.525193	+	0.850983i	$0.676007\pi$
$128$			7.24921i			0.640746i
$129$	12.2372			1.07742
$130$	0.232975	−	0.653909i	0.0204332	−	0.0573516i
$131$	−0.307990			−0.0269092			−0.0134546	−	0.999909i	$-0.504283\pi$
$131$	−0.307990			−0.0269092			−0.0134546	+	0.999909i	$0.504283\pi$
$132$		−	22.4920i		−	1.95767i
$133$		0			0
$134$	−1.27428			−0.110081
$135$	8.64429	+	3.07979i	0.743982	+	0.265066i
$136$	−2.36992			−0.203219
$137$			14.4994i			1.23876i	0.785090	+	0.619382i	$0.212617\pi$
$137$			14.4994i			1.23876i	−0.785090	+	0.619382i	$0.787383\pi$
$138$		−	3.43917i		−	0.292761i
$139$	−15.7973			−1.33991			−0.669955	−	0.742401i	$-0.733687\pi$
$139$	−15.7973			−1.33991			−0.669955	+	0.742401i	$0.733687\pi$
$140$	7.92960	+	2.82516i	0.670174	+	0.238769i
$141$	−18.5360			−1.56102
$142$			0.193606i			0.0162470i
$143$		−	5.37558i		−	0.449529i
$144$	−16.3974			−1.36645
$145$	−6.48489	+	18.2017i	−0.538540	+	1.51157i
$146$	−0.346122			−0.0286452
$147$		−	8.85957i		−	0.730725i
$148$		−	21.4017i		−	1.75921i
$149$	12.4650			1.02117			0.510585	−	0.859827i	$-0.329429\pi$
$149$	12.4650			1.02117			0.510585	+	0.859827i	$0.329429\pi$
$150$	−2.59327	−	2.11652i	−0.211740	−	0.172813i
$151$	13.8400			1.12629			0.563143	−	0.826360i	$-0.309592\pi$
$151$	13.8400			1.12629			0.563143	+	0.826360i	$0.309592\pi$
$152$		0			0
$153$		−	11.0677i		−	0.894767i
$154$	−2.00809			−0.161816
$155$	3.82797	−	10.7443i	0.307470	−	0.863001i
$156$	−6.74666			−0.540165
$157$			18.1970i			1.45228i	0.687549	+	0.726138i	$0.258687\pi$
$157$			18.1970i			1.45228i	−0.687549	+	0.726138i	$0.741313\pi$
$158$			1.48225i			0.117922i
$159$	1.88893			0.149802
$160$	5.93514	+	2.11457i	0.469214	+	0.167171i
$161$	9.96748			0.785548
$162$		−	0.552043i		−	0.0433726i
$163$		−	15.3337i		−	1.20103i	−0.799613	−	0.600516i	$-0.794962\pi$
$163$		−	15.3337i		−	1.20103i	0.799613	−	0.600516i	$-0.205038\pi$
$164$	4.84744			0.378522
$165$	−24.4180	−	8.69963i	−1.90094	−	0.677265i
$166$	−2.89760			−0.224897
$167$			6.21690i			0.481079i	0.970639	+	0.240539i	$0.0773243\pi$
$167$			6.21690i			0.481079i	−0.970639	+	0.240539i	$0.922676\pi$
$168$			5.11817i			0.394875i
$169$	11.3875			0.875965
$170$	−0.451376	+	1.26691i	−0.0346189	+	0.0971678i
$171$		0			0
$172$			8.67048i			0.661118i
$173$			2.76604i			0.210298i	0.994456	+	0.105149i	$0.0335319\pi$
$173$			2.76604i			0.210298i	−0.994456	+	0.105149i	$0.966468\pi$
$174$	−5.78503			−0.438562
$175$	6.13416	−	7.51588i	0.463699	−	0.568147i
$176$	15.4303			1.16310
$177$			14.2213i			1.06894i
$178$			0.545896i			0.0409167i
$179$	11.3783			0.850456			0.425228	−	0.905086i	$-0.360194\pi$
$179$	11.3783			0.850456			0.425228	+	0.905086i	$0.360194\pi$
$180$	−6.55033	+	18.3853i	−0.488233	+	1.37036i
$181$	3.56654			0.265099			0.132549	−	0.991176i	$-0.457684\pi$
$181$	3.56654			0.265099			0.132549	+	0.991176i	$0.457684\pi$
$182$			0.602344i			0.0446487i
$183$		−	7.67513i		−	0.567362i
$184$	4.94861			0.364816
$185$	−23.2344	−	8.27795i	−1.70823	−	0.608607i
$186$	3.41485			0.250389
$187$			10.4149i			0.761612i
$188$		−	13.1334i		−	0.957855i
$189$	−7.96263			−0.579196
$190$		0			0
$191$	−8.67323			−0.627573			−0.313786	−	0.949494i	$-0.601598\pi$
$191$	−8.67323			−0.627573			−0.313786	+	0.949494i	$0.601598\pi$
$192$		−	18.0761i		−	1.30453i
$193$		−	0.422110i		−	0.0303841i	−0.999885	−	0.0151921i	$-0.995164\pi$
$193$		−	0.422110i		−	0.0303841i	0.999885	−	0.0151921i	$-0.00483597\pi$
$194$	−2.10490			−0.151123
$195$	−2.60953	+	7.32438i	−0.186872	+	0.524510i
$196$	6.27732			0.448380
$197$		−	15.2415i		−	1.08591i	−0.839761	−	0.542956i	$-0.817305\pi$
$197$		−	15.2415i		−	1.08591i	0.839761	−	0.542956i	$-0.182695\pi$
$198$		−	4.65590i		−	0.330880i
$199$	−12.9264			−0.916331			−0.458166	−	0.888867i	$-0.651493\pi$
$199$	−12.9264			−0.916331			−0.458166	+	0.888867i	$0.651493\pi$
$200$	3.04546	−	3.73145i	0.215346	−	0.263853i
$201$	14.2731			1.00675
$202$		−	3.28846i		−	0.231376i
$203$		−	16.7663i		−	1.17677i
$204$	13.0713			0.915172
$205$	1.87493	−	5.26253i	0.130951	−	0.367551i
$206$	−0.986659			−0.0687438
$207$			23.1103i			1.60628i
$208$		−	4.62845i		−	0.320926i
$209$		0			0
$210$	2.73608	+	0.974809i	0.188807	+	0.0672682i
$211$	−4.44619			−0.306089			−0.153044	−	0.988219i	$-0.548908\pi$
$211$	−4.44619			−0.306089			−0.153044	+	0.988219i	$0.548908\pi$
$212$			1.33837i			0.0919199i
$213$		−	2.16856i		−	0.148587i
$214$	4.14608			0.283420
$215$	9.41294	+	3.35364i	0.641957	+	0.228717i
$216$	−3.95325			−0.268985
$217$			9.89701i			0.671853i
$218$		−	1.67117i		−	0.113186i
$219$	3.87688			0.261975
$220$	6.16399	−	17.3010i	0.415576	−	1.16643i
$221$	3.12404			0.210146
$222$		−	7.38459i		−	0.495621i
$223$			9.19893i			0.616006i	0.951385	+	0.308003i	$0.0996607\pi$
$223$			9.19893i			0.616006i	−0.951385	+	0.308003i	$0.900339\pi$
$224$	−5.46711			−0.365287
$225$	17.4261	+	14.2225i	1.16174	+	0.948165i
$226$	−1.44832			−0.0963411
$227$		−	0.600308i		−	0.0398438i	−0.999802	−	0.0199219i	$-0.993658\pi$
$227$		−	0.600308i		−	0.0398438i	0.999802	−	0.0199219i	$-0.00634176\pi$
$228$		0			0
$229$	7.11499			0.470172			0.235086	−	0.971975i	$-0.424463\pi$
$229$	7.11499			0.470172			0.235086	+	0.971975i	$0.424463\pi$
$230$	0.942515	−	2.64543i	0.0621476	−	0.174435i
$231$	22.4924			1.47989
$232$		−	8.32407i		−	0.546502i
$233$		−	20.1662i		−	1.32113i	−0.750767	−	0.660567i	$-0.770316\pi$
$233$		−	20.1662i		−	1.32113i	0.750767	−	0.660567i	$-0.229684\pi$
$234$	−1.39658			−0.0912971
$235$	−14.2581	−	5.07986i	−0.930094	−	0.331374i
$236$	−10.0763			−0.655912
$237$		−	16.6026i		−	1.07845i
$238$		−	1.16701i		−	0.0756459i
$239$	11.6342			0.752554			0.376277	−	0.926507i	$-0.377204\pi$
$239$	11.6342			0.752554			0.376277	+	0.926507i	$0.377204\pi$
$240$	−21.0242	−	7.49050i	−1.35711	−	0.483510i
$241$	25.5301			1.64454			0.822269	−	0.569100i	$-0.192708\pi$
$241$	25.5301			1.64454			0.822269	+	0.569100i	$0.192708\pi$
$242$			1.69205i			0.108769i
$243$			18.4950i			1.18646i
$244$	5.43811			0.348139
$245$	2.42799	−	6.81485i	0.155119	−	0.435385i
$246$	1.67259			0.106640
$247$		0			0
$248$			4.91362i			0.312015i
$249$	32.4558			2.05680
$250$	−1.41472	−	2.33874i	−0.0894750	−	0.147915i
$251$	15.3783			0.970669			0.485335	−	0.874328i	$-0.338698\pi$
$251$	15.3783			0.970669			0.485335	+	0.874328i	$0.338698\pi$
$252$		−	16.9355i		−	1.06684i
$253$		−	21.7473i		−	1.36724i
$254$	−4.68912			−0.294221
$255$	5.05582	−	14.1906i	0.316608	−	0.888648i
$256$	11.4298			0.714365
$257$			16.0534i			1.00139i	0.865625	+	0.500693i	$0.166921\pi$
$257$			16.0534i			1.00139i	−0.865625	+	0.500693i	$0.833079\pi$
$258$			2.99172i			0.186256i
$259$	21.4022			1.32987
$260$	−5.18958	−	1.84894i	−0.321844	−	0.114667i
$261$	38.8739			2.40624
$262$		−	0.0752965i		−	0.00465183i
$263$		−	14.2397i		−	0.878055i	−0.898474	−	0.439027i	$-0.855323\pi$
$263$		−	14.2397i		−	0.878055i	0.898474	−	0.439027i	$-0.144677\pi$
$264$	11.1669			0.687277
$265$	1.45298	+	0.517668i	0.0892559	+	0.0318001i
$266$		0			0
$267$		−	6.11453i		−	0.374203i
$268$			10.1130i			0.617750i
$269$	−16.2414			−0.990254			−0.495127	−	0.868821i	$-0.664879\pi$
$269$	−16.2414			−0.990254			−0.495127	+	0.868821i	$0.664879\pi$
$270$	−0.752938	+	2.11333i	−0.0458224	+	0.128613i
$271$	−5.92530			−0.359936			−0.179968	−	0.983672i	$-0.557599\pi$
$271$	−5.92530			−0.359936			−0.179968	+	0.983672i	$0.557599\pi$
$272$			8.96737i			0.543727i
$273$		−	6.74680i		−	0.408335i
$274$	−3.54476			−0.214147
$275$	−16.3983	−	13.3836i	−0.988856	−	0.807064i
$276$	−27.2941			−1.64291
$277$		−	6.30936i		−	0.379093i	−0.981872	−	0.189546i	$-0.939298\pi$
$277$		−	6.30936i		−	0.379093i	0.981872	−	0.189546i	$-0.0607017\pi$
$278$		−	3.86208i		−	0.231632i
$279$	−22.9469			−1.37380
$280$	−1.40265	+	3.93693i	−0.0838244	+	0.235277i
$281$	−2.67961			−0.159852			−0.0799261	−	0.996801i	$-0.525468\pi$
$281$	−2.67961			−0.159852			−0.0799261	+	0.996801i	$0.525468\pi$
$282$		−	4.53164i		−	0.269855i
$283$			31.0643i			1.84658i	0.384105	+	0.923290i	$0.374510\pi$
$283$			31.0643i			1.84658i	−0.384105	+	0.923290i	$0.625490\pi$
$284$	1.53650			0.0911745
$285$		0			0
$286$	1.31421			0.0777107
$287$			4.84754i			0.286142i
$288$		−	12.6759i		−	0.746933i
$289$	10.9474			0.643962
$290$	−4.44989	−	1.58541i	−0.261307	−	0.0930983i
$291$	23.5768			1.38210
$292$			2.74690i			0.160750i
$293$			0.865650i			0.0505718i	0.999680	+	0.0252859i	$0.00804961\pi$
$293$			0.865650i			0.0505718i	−0.999680	+	0.0252859i	$0.991950\pi$
$294$	2.16596			0.126322
$295$	−3.89740	+	10.9392i	−0.226916	+	0.636902i
$296$	10.6257			0.617604
$297$			17.3730i			1.00809i
$298$			3.04740i			0.176531i
$299$	−6.52329			−0.377251
$300$	−16.7972	+	20.5808i	−0.969788	+	1.18823i
$301$	−8.67067			−0.499769
$302$			3.38357i			0.194703i
$303$			36.8338i			2.11605i
$304$		0			0
$305$	2.10340	−	5.90377i	0.120440	−	0.338049i
$306$	2.70579			0.154680
$307$			8.99201i			0.513201i	0.966518	+	0.256601i	$0.0826025\pi$
$307$			8.99201i			0.513201i	−0.966518	+	0.256601i	$0.917397\pi$
$308$			15.9367i			0.908077i
$309$	11.0515			0.628696
$310$	2.62673	+	0.935852i	0.149188	+	0.0531528i
$311$	−11.4407			−0.648742			−0.324371	−	0.945930i	$-0.605153\pi$
$311$	−11.4407			−0.648742			−0.324371	+	0.945930i	$0.605153\pi$
$312$		−	3.34962i		−	0.189635i
$313$			7.86521i			0.444568i	0.974982	+	0.222284i	$0.0713512\pi$
$313$			7.86521i			0.444568i	−0.974982	+	0.222284i	$0.928649\pi$
$314$	−4.44875			−0.251057
$315$	−18.3857	−	6.55047i	−1.03592	−	0.369077i
$316$	11.7635			0.661749
$317$		−	16.5265i		−	0.928218i	−0.885778	−	0.464109i	$-0.846375\pi$
$317$		−	16.5265i		−	0.928218i	0.885778	−	0.464109i	$-0.153625\pi$
$318$			0.461801i			0.0258965i
$319$	−36.5812			−2.04815
$320$	4.95382	−	13.9043i	0.276927	−	0.777273i
$321$	−46.4398			−2.59202
$322$			2.43682i			0.135799i
$323$		0			0
$324$	−4.38115			−0.243397
$325$	−4.01454	+	4.91882i	−0.222687	+	0.272847i
$326$	3.74875			0.207624
$327$			18.7186i			1.03514i
$328$			2.40669i			0.132887i
$329$	13.1337			0.724085
$330$	2.12686	−	5.96963i	0.117080	−	0.328618i
$331$	7.91446			0.435018			0.217509	−	0.976058i	$-0.430207\pi$
$331$	7.91446			0.435018			0.217509	+	0.976058i	$0.430207\pi$
$332$			22.9961i			1.26207i
$333$			49.6225i			2.71930i
$334$	−1.51989			−0.0831648
$335$	10.9790	+	3.91159i	0.599846	+	0.213713i
$336$	19.3663			1.05652
$337$			19.0361i			1.03696i	0.855090	+	0.518480i	$0.173502\pi$
$337$			19.0361i			1.03696i	−0.855090	+	0.518480i	$0.826498\pi$
$338$			2.78400i			0.151429i
$339$	16.2225			0.881087
$340$	10.0545	+	3.58223i	0.545283	+	0.194274i
$341$	21.5935			1.16936
$342$		0			0
$343$			19.8594i			1.07230i
$344$	−4.30477			−0.232098
$345$	−10.5570	+	29.6313i	−0.568371	+	1.59529i
$346$	−0.676233			−0.0363545
$347$			5.46420i			0.293334i	0.989186	+	0.146667i	$0.0468545\pi$
$347$			5.46420i			0.293334i	−0.989186	+	0.146667i	$0.953145\pi$
$348$			45.9114i			2.46111i
$349$	6.26435			0.335323			0.167662	−	0.985845i	$-0.446378\pi$
$349$	6.26435			0.335323			0.167662	+	0.985845i	$0.446378\pi$
$350$	1.83746	+	1.49966i	0.0982165	+	0.0801603i
$351$	5.21120			0.278153
$352$			11.9283i			0.635779i
$353$		−	8.29398i		−	0.441444i	−0.975337	−	0.220722i	$-0.929159\pi$
$353$		−	8.29398i		−	0.441444i	0.975337	−	0.220722i	$-0.0708414\pi$
$354$	−3.47679			−0.184789
$355$	0.594300	−	1.66807i	0.0315422	−	0.0885321i
$356$	4.33237			0.229615
$357$			13.0715i			0.691820i
$358$			2.78174i			0.147020i
$359$	−13.0857			−0.690637			−0.345318	−	0.938486i	$-0.612229\pi$
$359$	−13.0857			−0.690637			−0.345318	+	0.938486i	$0.612229\pi$
$360$	−9.12806	−	3.25215i	−0.481091	−	0.171403i
$361$		0			0
$362$			0.871938i			0.0458281i
$363$		−	18.9524i		−	0.994745i
$364$	4.78035			0.250558
$365$	2.98212	+	1.06247i	0.156091	+	0.0556123i
$366$	1.87640			0.0980808
$367$		−	26.0942i		−	1.36211i	−0.732234	−	0.681053i	$-0.761522\pi$
$367$		−	26.0942i		−	1.36211i	0.732234	−	0.681053i	$-0.238478\pi$
$368$		−	18.7247i		−	0.976094i
$369$	−11.2394			−0.585099
$370$	2.02377	−	5.68028i	0.105211	−	0.295304i
$371$	−1.33840			−0.0694864
$372$		−	27.1011i		−	1.40513i
$373$			27.1969i			1.40820i	0.710101	+	0.704100i	$0.248649\pi$
$373$			27.1969i			1.40820i	−0.710101	+	0.704100i	$0.751351\pi$
$374$	−2.54620			−0.131661
$375$	15.8462	+	26.1960i	0.818294	+	1.35276i
$376$	6.52057			0.336273
$377$			10.9728i			0.565130i
$378$		−	1.94668i		−	0.100127i
$379$	−13.6999			−0.703714			−0.351857	−	0.936054i	$-0.614450\pi$
$379$	−13.6999			−0.703714			−0.351857	+	0.936054i	$0.614450\pi$
$380$		0			0
$381$	52.5224			2.69080
$382$		−	2.12041i		−	0.108490i
$383$			10.2515i			0.523827i	0.965091	+	0.261913i	$0.0843535\pi$
$383$			10.2515i			0.523827i	−0.965091	+	0.261913i	$0.915647\pi$
$384$	19.8510			1.01302
$385$	17.3014	+	6.16412i	0.881758	+	0.314153i
$386$	0.103196			0.00525255
$387$		−	20.1036i		−	1.02192i
$388$			16.7050i			0.848069i
$389$	5.05671			0.256385			0.128193	−	0.991749i	$-0.459082\pi$
$389$	5.05671			0.256385			0.128193	+	0.991749i	$0.459082\pi$
$390$	−1.79064	−	0.637971i	−0.0906728	−	0.0323049i
$391$	12.6385			0.639157
$392$			3.11660i			0.157412i
$393$			0.843389i			0.0425434i
$394$	3.72620			0.187723
$395$	4.54999	−	12.7708i	0.228935	−	0.642570i
$396$	−36.9503			−1.85682
$397$		−	23.8758i		−	1.19829i	−0.800640	−	0.599146i	$-0.795507\pi$
$397$		−	23.8758i		−	1.19829i	0.800640	−	0.599146i	$-0.204493\pi$
$398$		−	3.16022i		−	0.158408i
$399$		0			0
$400$	−14.1192	−	11.5235i	−0.705960	−	0.576176i
$401$	−24.7655			−1.23673			−0.618366	−	0.785891i	$-0.712205\pi$
$401$	−24.7655			−1.23673			−0.618366	+	0.785891i	$0.712205\pi$
$402$			3.48945i			0.174038i
$403$		−	6.47717i		−	0.322651i
$404$	−26.0981			−1.29843
$405$	−1.69458	+	4.75631i	−0.0842042	+	0.236343i
$406$	4.09899			0.203429
$407$		−	46.6958i		−	2.31463i
$408$			6.48970i			0.321288i
$409$	9.89998			0.489523			0.244761	−	0.969583i	$-0.421290\pi$
$409$	9.89998			0.489523			0.244761	+	0.969583i	$0.421290\pi$
$410$	1.28657	+	0.458379i	0.0635392	+	0.0226377i
$411$	39.7046			1.95848
$412$			7.83036i			0.385774i
$413$		−	10.0765i		−	0.495833i
$414$	−5.64995			−0.277680
$415$	24.9652	+	8.89461i	1.22549	+	0.436619i
$416$	3.57799			0.175425
$417$			43.2588i			2.11839i
$418$		0			0
$419$	−4.00810			−0.195808			−0.0979042	−	0.995196i	$-0.531214\pi$
$419$	−4.00810			−0.195808			−0.0979042	+	0.995196i	$0.531214\pi$
$420$	7.73632	−	21.7142i	0.377494	−	1.05954i
$421$	20.2781			0.988294			0.494147	−	0.869378i	$-0.335480\pi$
$421$	20.2781			0.988294			0.494147	+	0.869378i	$0.335480\pi$
$422$		−	1.08699i		−	0.0529140i
$423$			30.4515i			1.48060i
$424$	−0.664484			−0.0322702
$425$	7.77795	−	9.52994i	0.377286	−	0.462270i
$426$	0.530163			0.0256865
$427$			5.43822i			0.263174i
$428$		−	32.9043i		−	1.59049i
$429$	−14.7203			−0.710704
$430$	−0.819890	+	2.30125i	−0.0395386	+	0.110976i
$431$	13.4783			0.649229			0.324615	−	0.945846i	$-0.394765\pi$
$431$	13.4783			0.649229			0.324615	+	0.945846i	$0.394765\pi$
$432$			14.9584i			0.719689i
$433$			34.3776i			1.65208i	0.563611	+	0.826040i	$0.309412\pi$
$433$			34.3776i			1.65208i	−0.563611	+	0.826040i	$0.690588\pi$
$434$	−2.41959			−0.116144
$435$	49.8428	+	17.7580i	2.38978	+	0.851431i
$436$	−13.2628			−0.635172
$437$		0			0
$438$			0.947808i			0.0452880i
$439$	−23.4179			−1.11768			−0.558838	−	0.829277i	$-0.688753\pi$
$439$	−23.4179			−1.11768			−0.558838	+	0.829277i	$0.688753\pi$
$440$	8.58969	+	3.06034i	0.409498	+	0.145896i
$441$	−14.5547			−0.693082
$442$			0.763756i			0.0363282i
$443$		−	2.39888i		−	0.113974i	−0.998375	−	0.0569871i	$-0.981851\pi$
$443$		−	2.39888i		−	0.113974i	0.998375	−	0.0569871i	$-0.0181494\pi$
$444$	−58.6059			−2.78131
$445$	1.67571	−	4.70335i	0.0794362	−	0.222960i
$446$	−2.24893			−0.106490
$447$		−	34.1337i		−	1.61447i
$448$			12.8078i			0.605113i
$449$	−38.2019			−1.80286			−0.901430	−	0.432924i	$-0.857482\pi$
$449$	−38.2019			−1.80286			−0.901430	+	0.432924i	$0.857482\pi$
$450$	−3.47707	+	4.26029i	−0.163911	+	0.200832i
$451$	10.5765			0.498027
$452$			11.4942i			0.540644i
$453$		−	37.8991i		−	1.78065i
$454$	0.146762			0.00688786
$455$	1.84898	−	5.18969i	0.0866816	−	0.243296i
$456$		0			0
$457$		−	1.87605i		−	0.0877581i	−0.999037	−	0.0438790i	$-0.986028\pi$
$457$		−	1.87605i		−	0.0877581i	0.999037	−	0.0438790i	$-0.0139716\pi$
$458$			1.73945i			0.0812793i
$459$	−10.0964			−0.471260
$460$	−20.9948	−	7.48003i	−0.978888	−	0.348758i
$461$	16.8204			0.783402			0.391701	−	0.920092i	$-0.371887\pi$
$461$	16.8204			0.783402			0.391701	+	0.920092i	$0.371887\pi$
$462$			5.49889i			0.255831i
$463$		−	24.3641i		−	1.13230i	−0.824303	−	0.566148i	$-0.808433\pi$
$463$		−	24.3641i		−	1.13230i	0.824303	−	0.566148i	$-0.191567\pi$
$464$	−31.4969			−1.46221
$465$	−29.4218	−	10.4824i	−1.36440	−	0.486109i
$466$	4.93019			0.228386
$467$		−	13.6511i		−	0.631696i	−0.948810	−	0.315848i	$-0.897711\pi$
$467$		−	13.6511i		−	0.631696i	0.948810	−	0.315848i	$-0.102289\pi$
$468$			11.0836i			0.512338i
$469$	−10.1132			−0.466985
$470$	1.24191	−	3.48577i	0.0572851	−	0.160787i
$471$	49.8300			2.29604
$472$		−	5.00275i		−	0.230270i
$473$			18.9179i			0.869844i
$474$	4.05895			0.186434
$475$		0			0
$476$	−9.26166			−0.424507
$477$		−	3.10318i		−	0.142085i
$478$			2.84430i			0.130095i
$479$	21.7405			0.993351			0.496675	−	0.867936i	$-0.334554\pi$
$479$	21.7405			0.993351			0.496675	+	0.867936i	$0.334554\pi$
$480$	5.79047	−	16.2526i	0.264298	−	0.741826i
$481$	−14.0068			−0.638656
$482$			6.24153i			0.284294i
$483$		−	27.2946i		−	1.24195i
$484$	13.4285			0.610385
$485$	18.1355	+	6.46131i	0.823490	+	0.293393i
$486$	−4.52161			−0.205104
$487$			29.2454i			1.32524i	0.748957	+	0.662618i	$0.230555\pi$
$487$			29.2454i			1.32524i	−0.748957	+	0.662618i	$0.769445\pi$
$488$			2.69994i			0.122221i
$489$	−41.9894			−1.89883
$490$	1.66608	+	0.593589i	0.0752656	+	0.0268156i
$491$	−18.3556			−0.828375			−0.414188	−	0.910191i	$-0.635934\pi$
$491$	−18.3556			−0.828375			−0.414188	+	0.910191i	$0.635934\pi$
$492$		−	13.2741i		−	0.598442i
$493$		−	21.2593i		−	0.957469i
$494$		0			0
$495$	−14.2920	+	40.1144i	−0.642376	+	1.80301i
$496$	18.5923			0.834821
$497$			1.53653i			0.0689229i
$498$			7.93470i			0.355562i
$499$	−10.4159			−0.466279			−0.233140	−	0.972443i	$-0.574900\pi$
$499$	−10.4159			−0.466279			−0.233140	+	0.972443i	$0.574900\pi$
$500$	−18.5608	+	11.2276i	−0.830064	+	0.502113i
$501$	17.0242			0.760584
$502$			3.75964i			0.167801i
$503$			4.35731i			0.194283i	0.995271	+	0.0971413i	$0.0309699\pi$
$503$			4.35731i			0.194283i	−0.995271	+	0.0971413i	$0.969030\pi$
$504$	8.40825			0.374533
$505$	−10.0944	+	28.3328i	−0.449196	+	1.26079i
$506$	5.31672			0.236357
$507$		−	31.1833i		−	1.38490i
$508$			37.2140i			1.65110i
$509$	38.2608			1.69588			0.847941	−	0.530091i	$-0.177842\pi$
$509$	38.2608			1.69588			0.847941	+	0.530091i	$0.177842\pi$
$510$	3.46927	+	1.23603i	0.153622	+	0.0547324i
$511$	−2.74696			−0.121518
$512$			17.2928i			0.764239i
$513$		0			0
$514$	−3.92470			−0.173111
$515$	8.50088	+	3.02869i	0.374594	+	0.133460i
$516$	23.7430			1.04523
$517$		−	28.6555i		−	1.26027i
$518$			5.23235i			0.229896i
$519$	7.57442			0.332480
$520$	0.917974	−	2.57655i	0.0402558	−	0.112989i
$521$	−2.48812			−0.109007			−0.0545033	−	0.998514i	$-0.517358\pi$
$521$	−2.48812			−0.109007			−0.0545033	+	0.998514i	$0.517358\pi$
$522$			9.50379i			0.415970i
$523$			19.4533i			0.850635i	0.905044	+	0.425317i	$0.139837\pi$
$523$			19.4533i			0.850635i	−0.905044	+	0.425317i	$0.860163\pi$
$524$	−0.597571			−0.0261050
$525$	−20.5812	−	16.7976i	−0.898239	−	0.733106i
$526$	3.48127			0.151791
$527$			12.5492i			0.546650i
$528$		−	42.2538i		−	1.83886i
$529$	−3.39040			−0.147409
$530$	−0.126558	+	0.355221i	−0.00549733	+	0.0154298i
$531$	23.3631			1.01387
$532$		0			0
$533$		−	3.17251i		−	0.137417i
$534$	1.49486			0.0646891
$535$	−35.7219	−	12.7270i	−1.54439	−	0.550236i
$536$	−5.02096			−0.216873
$537$		−	31.1580i		−	1.34457i
$538$		−	3.97065i		−	0.171187i
$539$	13.6963			0.589941
$540$	16.7719	+	5.97550i	0.721749	+	0.257145i
$541$	14.4565			0.621535			0.310768	−	0.950486i	$-0.399414\pi$
$541$	14.4565			0.621535			0.310768	+	0.950486i	$0.399414\pi$
$542$		−	1.44860i		−	0.0622228i
$543$		−	9.76650i		−	0.419121i
$544$	−6.93215			−0.297214
$545$	−5.12989	+	14.3985i	−0.219740	+	0.616763i
$546$	1.64944			0.0705895
$547$		−	31.3961i		−	1.34240i	−0.741276	−	0.671200i	$-0.765779\pi$
$547$		−	31.3961i		−	1.34240i	0.741276	−	0.671200i	$-0.234221\pi$
$548$			28.1321i			1.20174i
$549$	−12.6089			−0.538135
$550$	3.27200	−	4.00902i	0.139518	−	0.170945i
$551$		0			0
$552$		−	13.5511i		−	0.576774i
$553$			11.7637i			0.500245i
$554$	1.54250			0.0655343
$555$	−22.6681	+	63.6243i	−0.962206	+	2.70070i
$556$	−30.6504			−1.29987
$557$			30.4484i			1.29014i	0.764124	+	0.645070i	$0.223172\pi$
$557$			30.4484i			1.29014i	−0.764124	+	0.645070i	$0.776828\pi$
$558$		−	5.61000i		−	0.237490i
$559$	5.67458			0.240009
$560$	14.8967	+	5.30740i	0.629501	+	0.224279i
$561$	28.5198			1.20411
$562$		−	0.655104i		−	0.0276339i
$563$		−	26.7012i		−	1.12532i	−0.826687	−	0.562661i	$-0.809777\pi$
$563$		−	26.7012i		−	1.12532i	0.826687	−	0.562661i	$-0.190223\pi$
$564$	−35.9642			−1.51437
$565$	12.4785	+	4.44584i	0.524975	+	0.187038i
$566$	−7.59451			−0.319221
$567$		−	4.38124i		−	0.183995i
$568$			0.762850i			0.0320085i
$569$	25.6513			1.07536			0.537679	−	0.843150i	$-0.319301\pi$
$569$	25.6513			1.07536			0.537679	+	0.843150i	$0.319301\pi$
$570$		0			0
$571$	2.93559			0.122851			0.0614253	−	0.998112i	$-0.480435\pi$
$571$	2.93559			0.122851			0.0614253	+	0.998112i	$0.480435\pi$
$572$		−	10.4299i		−	0.436095i
$573$			23.7505i			0.992191i
$574$	−1.18511			−0.0494657
$575$	−16.2411	+	19.8994i	−0.677301	+	0.829863i
$576$	−29.6959			−1.23733
$577$			17.7732i			0.739908i	0.929050	+	0.369954i	$0.120627\pi$
$577$			17.7732i			0.739908i	−0.929050	+	0.369954i	$0.879373\pi$
$578$			2.67638i			0.111323i
$579$	−1.15589			−0.0480373
$580$	−12.5822	+	35.3154i	−0.522446	+	1.46639i
$581$	−22.9965			−0.954057
$582$			5.76400i			0.238925i
$583$			2.92016i			0.120941i
$584$	−1.36380			−0.0564344
$585$	12.0327	+	4.28700i	0.497490	+	0.177246i
$586$	−0.211632			−0.00874243
$587$		−	23.1236i		−	0.954415i	−0.878791	−	0.477207i	$-0.841649\pi$
$587$		−	23.1236i		−	0.954415i	0.878791	−	0.477207i	$-0.158351\pi$
$588$		−	17.1896i		−	0.708887i
$589$		0			0
$590$	−2.67438	−	0.952826i	−0.110102	−	0.0392272i
$591$	−41.7368			−1.71682
$592$		−	40.2058i		−	1.65245i
$593$			17.1574i			0.704569i	0.935893	+	0.352284i	$0.114595\pi$
$593$			17.1574i			0.704569i	−0.935893	+	0.352284i	$0.885405\pi$
$594$	−4.24732			−0.174269
$595$	−3.58230	+	10.0547i	−0.146860	+	0.412204i
$596$	24.1849			0.990653
$597$			35.3973i			1.44872i
$598$		−	1.59480i		−	0.0652160i
$599$	13.3967			0.547376			0.273688	−	0.961819i	$-0.411756\pi$
$599$	13.3967			0.547376			0.273688	+	0.961819i	$0.411756\pi$
$600$	−10.2181	−	8.33958i	−0.417151	−	0.340462i
$601$	8.26251			0.337035			0.168517	−	0.985699i	$-0.446102\pi$
$601$	8.26251			0.337035			0.168517	+	0.985699i	$0.446102\pi$
$602$		−	2.11978i		−	0.0863958i
$603$		−	23.4482i		−	0.954885i
$604$	26.8528			1.09263
$605$	5.19398	−	14.5784i	0.211165	−	0.592695i
$606$	−9.00503			−0.365804
$607$			23.5191i			0.954612i	0.878737	+	0.477306i	$0.158387\pi$
$607$			23.5191i			0.954612i	−0.878737	+	0.477306i	$0.841613\pi$
$608$		0			0
$609$	−45.9124			−1.86046
$610$	1.44334	+	0.514233i	0.0584391	+	0.0208207i
$611$	−8.59545			−0.347735
$612$		−	21.4738i		−	0.868027i
$613$		−	29.8313i		−	1.20488i	−0.798166	−	0.602438i	$-0.794196\pi$
$613$		−	29.8313i		−	1.20488i	0.798166	−	0.602438i	$-0.205804\pi$
$614$	−2.19834			−0.0887179
$615$	−14.4107	−	5.13426i	−0.581098	−	0.207033i
$616$	−7.91234			−0.318797
$617$		−	11.5902i		−	0.466605i	−0.972404	−	0.233303i	$-0.925047\pi$
$617$		−	11.5902i		−	0.466605i	0.972404	−	0.233303i	$-0.0749533\pi$
$618$			2.70183i			0.108684i
$619$	−29.6697			−1.19253			−0.596264	−	0.802789i	$-0.703349\pi$
$619$	−29.6697			−1.19253			−0.596264	+	0.802789i	$0.703349\pi$
$620$	7.42714	−	20.8464i	0.298281	−	0.837211i
$621$	21.0823			0.846002
$622$		−	2.79699i		−	0.112149i
$623$			4.33246i			0.173576i
$624$	−12.6744			−0.507382
$625$	5.00991	+	24.4929i	0.200397	+	0.979715i
$626$	−1.92287			−0.0768532
$627$		0			0
$628$			35.3063i			1.40888i
$629$	27.1374			1.08204
$630$	1.60144	−	4.49489i	0.0638029	−	0.179081i
$631$	−24.4964			−0.975187			−0.487593	−	0.873071i	$-0.662125\pi$
$631$	−24.4964			−0.975187			−0.487593	+	0.873071i	$0.662125\pi$
$632$			5.84041i			0.232319i
$633$			12.1753i			0.483925i
$634$	4.04034			0.160463
$635$	40.4006	+	14.3939i	1.60325	+	0.571206i
$636$	3.66496			0.145325
$637$		−	4.10832i		−	0.162778i
$638$		−	8.94326i		−	0.354067i
$639$	−3.56256			−0.140933
$640$	15.2696	+	5.44024i	0.603582	+	0.215044i
$641$	12.3802			0.488989			0.244495	−	0.969651i	$-0.421378\pi$
$641$	12.3802			0.488989			0.244495	+	0.969651i	$0.421378\pi$
$642$		−	11.3535i		−	0.448086i
$643$			45.9092i			1.81048i	0.424898	+	0.905241i	$0.360310\pi$
$643$			45.9092i			1.81048i	−0.424898	+	0.905241i	$0.639690\pi$
$644$	19.3392			0.762072
$645$	9.18351	−	25.7761i	0.361600	−	1.01493i
$646$		0			0
$647$		−	33.6773i		−	1.32399i	−0.749508	−	0.661996i	$-0.769710\pi$
$647$		−	33.6773i		−	1.32399i	0.749508	−	0.661996i	$-0.230290\pi$
$648$		−	2.17518i		−	0.0854491i
$649$	−21.9852			−0.862994
$650$	−1.20254	−	0.981464i	−0.0471675	−	0.0384962i
$651$	27.1017			1.06220
$652$		−	29.7510i		−	1.16514i
$653$			19.6365i			0.768437i	0.923242	+	0.384219i	$0.125529\pi$
$653$			19.6365i			0.768437i	−0.923242	+	0.384219i	$0.874471\pi$
$654$	−4.57627			−0.178946
$655$	−0.231134	+	0.648742i	−0.00903114	+	0.0253484i
$656$	9.10651			0.355549
$657$		−	6.36903i		−	0.248479i
$658$			3.21090i			0.125174i
$659$	−20.7693			−0.809059			−0.404529	−	0.914525i	$-0.632565\pi$
$659$	−20.7693			−0.809059			−0.404529	+	0.914525i	$0.632565\pi$
$660$	−47.3765	−	16.8793i	−1.84413	−	0.657025i
$661$	13.2561			0.515603			0.257802	−	0.966198i	$-0.417002\pi$
$661$	13.2561			0.515603			0.257802	+	0.966198i	$0.417002\pi$
$662$			1.93490i			0.0752022i
$663$		−	8.55476i		−	0.332239i
$664$	−11.4172			−0.443074
$665$		0			0
$666$	−12.1316			−0.470089
$667$			44.3914i			1.71884i
$668$			12.0622i			0.466702i
$669$	25.1901			0.973904
$670$	−0.956296	+	2.68411i	−0.0369449	+	0.103696i
$671$	11.8652			0.458052
$672$			14.9710i			0.577517i
$673$			12.8576i			0.495624i	0.968808	+	0.247812i	$0.0797115\pi$
$673$			12.8576i			0.495624i	−0.968808	+	0.247812i	$0.920289\pi$
$674$	−4.65388			−0.179261
$675$	12.9744	−	15.8969i	0.499384	−	0.611871i
$676$	22.0945			0.849787
$677$			25.5573i			0.982245i	0.871091	+	0.491122i	$0.163413\pi$
$677$			25.5573i			0.982245i	−0.871091	+	0.491122i	$0.836587\pi$
$678$			3.96604i			0.152315i
$679$	−16.7054			−0.641093
$680$	−1.77852	+	4.99193i	−0.0682033	+	0.191432i
$681$	−1.64386			−0.0629930
$682$			5.27913i			0.202148i
$683$		−	22.8692i		−	0.875064i	−0.899203	−	0.437532i	$-0.855853\pi$
$683$		−	22.8692i		−	0.875064i	0.899203	−	0.437532i	$-0.144147\pi$
$684$		0			0
$685$	30.5411	+	10.8812i	1.16691	+	0.415748i
$686$	−4.85516			−0.185371
$687$		−	19.4835i		−	0.743340i
$688$			16.2886i			0.620995i
$689$	0.875927			0.0333701
$690$	−7.24417	−	2.58095i	−0.275781	−	0.0982552i
$691$	−32.3148			−1.22931			−0.614657	−	0.788795i	$-0.710705\pi$
$691$	−32.3148			−1.22931			−0.614657	+	0.788795i	$0.710705\pi$
$692$			5.36675i			0.204013i
$693$		−	36.9511i		−	1.40366i
$694$	−1.33587			−0.0507091
$695$	−11.8552	+	33.2750i	−0.449695	+	1.26219i
$696$	−22.7944			−0.864018
$697$			6.14656i			0.232818i
$698$			1.53149i			0.0579678i
$699$	−55.2226			−2.08871
$700$	11.9017	−	14.5825i	0.449841	−	0.551168i
$701$	34.7457			1.31233			0.656164	−	0.754618i	$-0.272178\pi$
$701$	34.7457			1.31233			0.656164	+	0.754618i	$0.272178\pi$
$702$			1.27402i			0.0480848i
$703$		0			0
$704$	27.9444			1.05319
$705$	−13.9105	+	39.0438i	−0.523901	+	1.47048i
$706$	2.02769			0.0763131
$707$		−	26.0986i		−	0.981539i
$708$			27.5927i			1.03700i
$709$	−8.00778			−0.300738			−0.150369	−	0.988630i	$-0.548046\pi$
$709$	−8.00778			−0.300738			−0.150369	+	0.988630i	$0.548046\pi$
$710$	0.407806	+	0.145293i	0.0153047	+	0.00545275i
$711$	−27.2751			−1.02290
$712$			2.15096i			0.0806105i
$713$		−	26.2038i		−	0.981341i
$714$	−3.19570			−0.119596
$715$	−11.3230	−	4.03415i	−0.423456	−	0.150869i
$716$	22.0766			0.825040
$717$		−	31.8587i		−	1.18979i
$718$		−	3.19916i		−	0.119391i
$719$	−14.2690			−0.532143			−0.266071	−	0.963953i	$-0.585726\pi$
$719$	−14.2690			−0.532143			−0.266071	+	0.963953i	$0.585726\pi$
$720$	−12.3056	+	34.5391i	−0.458602	+	1.28720i
$721$	−7.83053			−0.291624
$722$		0			0
$723$		−	69.9107i		−	2.60001i
$724$	6.91991			0.257177
$725$	33.4729	+	27.3192i	1.24315	+	1.01461i
$726$	4.63344			0.171963
$727$		−	3.13639i		−	0.116322i	−0.998307	−	0.0581612i	$-0.981476\pi$
$727$		−	3.13639i		−	0.116322i	0.998307	−	0.0581612i	$-0.0185237\pi$
$728$			2.37337i			0.0879631i
$729$	43.8720			1.62489
$730$	−0.259750	+	0.729061i	−0.00961378	+	0.0269838i
$731$	−10.9942			−0.406634
$732$		−	14.8915i		−	0.550407i
$733$			12.4004i			0.458020i	0.973424	+	0.229010i	$0.0735488\pi$
$733$			12.4004i			0.458020i	−0.973424	+	0.229010i	$0.926451\pi$
$734$	6.37944			0.235469
$735$	−18.6616	−	6.64874i	−0.688342	−	0.245243i
$736$	14.4750			0.533555
$737$			22.0653i			0.812784i
$738$		−	2.74777i		−	0.101147i
$739$	9.34314			0.343693			0.171846	−	0.985124i	$-0.445027\pi$
$739$	9.34314			0.343693			0.171846	+	0.985124i	$0.445027\pi$
$740$	−45.0801	−	16.0611i	−1.65718	−	0.590419i
$741$		0			0
$742$		−	0.327209i		−	0.0120122i
$743$		−	38.3186i		−	1.40577i	−0.711302	−	0.702887i	$-0.751894\pi$
$743$		−	38.3186i		−	1.40577i	0.711302	−	0.702887i	$-0.248106\pi$
$744$	13.4553			0.493295
$745$	9.35445	−	26.2559i	0.342720	−	0.961942i
$746$	−6.64901			−0.243438
$747$		−	53.3191i		−	1.95084i
$748$			20.2073i			0.738852i
$749$	32.9050			1.20232
$750$	−6.40433	+	3.87403i	−0.233853	+	0.141460i
$751$	−49.0370			−1.78939			−0.894693	−	0.446681i	$-0.852606\pi$
$751$	−49.0370			−1.78939			−0.894693	+	0.446681i	$0.852606\pi$
$752$		−	24.6728i		−	0.899723i
$753$		−	42.1114i		−	1.53463i
$754$	−2.68261			−0.0976949
$755$	10.3864	−	29.1523i	0.377999	−	1.06096i
$756$	−15.4493			−0.561887
$757$			36.7936i			1.33728i	0.743584	+	0.668642i	$0.233124\pi$
$757$			36.7936i			1.33728i	−0.743584	+	0.668642i	$0.766876\pi$
$758$		−	3.34930i		−	0.121652i
$759$	−59.5521			−2.16160
$760$		0			0
$761$	−0.255560			−0.00926406			−0.00463203	−	0.999989i	$-0.501474\pi$
$761$	−0.255560			−0.00926406			−0.00463203	+	0.999989i	$0.501474\pi$
$762$			12.8405i			0.465163i
$763$		−	13.2631i		−	0.480155i
$764$	−16.8281			−0.608818
$765$	−23.3126	−	8.30582i	−0.842870	−	0.300298i
$766$	−2.50626			−0.0905548
$767$			6.59465i			0.238119i
$768$		−	31.2991i		−	1.12941i
$769$	9.45643			0.341008			0.170504	−	0.985357i	$-0.445460\pi$
$769$	9.45643			0.341008			0.170504	+	0.985357i	$0.445460\pi$
$770$	−1.50699	+	4.22979i	−0.0543081	+	0.152431i
$771$	43.9602			1.58319
$772$		−	0.818991i		−	0.0294761i
$773$		−	30.2259i		−	1.08715i	−0.839360	−	0.543575i	$-0.817070\pi$
$773$		−	30.2259i		−	1.08715i	0.839360	−	0.543575i	$-0.182930\pi$
$774$	4.91486			0.176661
$775$	−19.7587	−	16.1263i	−0.709754	−	0.579273i
$776$	−8.29381			−0.297730
$777$		−	58.6071i		−	2.10252i
$778$			1.23625i			0.0443217i
$779$		0			0
$780$	−5.06309	+	14.2110i	−0.181288	+	0.508835i
$781$	3.35244			0.119960
$782$			3.08983i			0.110492i
$783$		−	35.4625i		−	1.26733i
$784$	11.7927			0.421168
$785$	38.3296	+	13.6561i	1.36804	+	0.487406i
$786$	−0.206190			−0.00735454
$787$		−	36.3976i		−	1.29743i	−0.761030	−	0.648717i	$-0.775306\pi$
$787$		−	36.3976i		−	1.29743i	0.761030	−	0.648717i	$-0.224694\pi$
$788$		−	29.5720i		−	1.05346i
$789$	−38.9934			−1.38820
$790$	3.12217	+	1.11237i	0.111082	+	0.0395763i
$791$	−11.4945			−0.408697
$792$		−	18.3453i		−	0.651872i
$793$		−	3.55908i		−	0.126387i
$794$	5.83709			0.207151
$795$	1.41756	−	3.97879i	0.0502758	−	0.141113i
$796$	−25.0803			−0.888947
$797$			19.2118i			0.680517i	0.940332	+	0.340258i	$0.110515\pi$
$797$			19.2118i			0.680517i	−0.940332	+	0.340258i	$0.889485\pi$
$798$		0			0
$799$	16.6532			0.589148
$800$	8.90815	−	10.9147i	0.314951	−	0.385894i
$801$	−10.0451			−0.354926
$802$		−	6.05461i		−	0.213796i
$803$			5.99338i			0.211502i
$804$	27.6931			0.976661
$805$	7.48019	−	20.9952i	0.263642	−	0.739985i
$806$	1.58352			0.0557771
$807$			44.4749i			1.56559i
$808$		−	12.9573i		−	0.455837i
$809$	43.0501			1.51356			0.756781	−	0.653669i	$-0.226771\pi$
$809$	43.0501			1.51356			0.756781	+	0.653669i	$0.226771\pi$
$810$	−1.16281	−	0.414286i	−0.0408570	−	0.0145565i
$811$	−31.3282			−1.10008			−0.550040	−	0.835138i	$-0.685388\pi$
$811$	−31.3282			−1.10008			−0.550040	+	0.835138i	$0.685388\pi$
$812$		−	32.5305i		−	1.14160i
$813$			16.2257i			0.569058i
$814$	11.4161			0.400133
$815$	−32.2986	−	11.5073i	−1.13137	−	0.403085i
$816$	24.5560			0.859631
$817$		0			0
$818$			2.42032i			0.0846245i
$819$	−11.0838			−0.387299
$820$	3.63781	−	10.2105i	0.127038	−	0.356567i
$821$	17.0708			0.595776			0.297888	−	0.954601i	$-0.403718\pi$
$821$	17.0708			0.595776			0.297888	+	0.954601i	$0.403718\pi$
$822$			9.70686i			0.338566i
$823$		−	36.3136i		−	1.26581i	−0.774228	−	0.632907i	$-0.781862\pi$
$823$		−	36.3136i		−	1.26581i	0.774228	−	0.632907i	$-0.218138\pi$
$824$	−3.88766			−0.135433
$825$	−36.6493	+	44.9046i	−1.27597	+	1.56338i
$826$	2.46348			0.0857155
$827$		−	19.3430i		−	0.672623i	−0.941751	−	0.336311i	$-0.890821\pi$
$827$		−	19.3430i		−	0.672623i	0.941751	−	0.336311i	$-0.109179\pi$
$828$			44.8393i			1.55828i
$829$	20.1843			0.701029			0.350514	−	0.936557i	$-0.386007\pi$
$829$	20.1843			0.701029			0.350514	+	0.936557i	$0.386007\pi$
$830$	−2.17453	+	6.10343i	−0.0754790	+	0.211853i
$831$	−17.2773			−0.599345
$832$		−	8.38217i		−	0.290600i
$833$			7.95964i			0.275785i
$834$	−10.5758			−0.366210
$835$	13.0951	+	4.66553i	0.453176	+	0.161457i
$836$		0			0
$837$			20.9332i			0.723557i
$838$		−	0.979889i		−	0.0338497i
$839$	−25.8209			−0.891437			−0.445719	−	0.895173i	$-0.647052\pi$
$839$	−25.8209			−0.891437			−0.445719	+	0.895173i	$0.647052\pi$
$840$	10.7808	+	3.84097i	0.371972	+	0.132526i
$841$	45.6708			1.57486
$842$			4.95753i			0.170848i
$843$			7.33776i			0.252726i
$844$	−8.62664			−0.296941
$845$	8.54589	−	23.9864i	0.293987	−	0.825158i
$846$	−7.44469			−0.255954
$847$			13.4288i			0.461418i
$848$			2.51430i			0.0863413i
$849$	85.0654			2.91944
$850$	2.32985	+	1.90153i	0.0799133	+	0.0652220i
$851$	−56.6655			−1.94247
$852$		−	4.20750i		−	0.144147i
$853$			14.3234i			0.490425i	0.969469	+	0.245212i	$0.0788577\pi$
$853$			14.3234i			0.490425i	−0.969469	+	0.245212i	$0.921142\pi$
$854$	−1.32952			−0.0454953
$855$		0			0
$856$	16.3365			0.558370
$857$		−	24.2649i		−	0.828874i	−0.910078	−	0.414437i	$-0.863979\pi$
$857$		−	24.2649i		−	0.828874i	0.910078	−	0.414437i	$-0.136021\pi$
$858$		−	3.59878i		−	0.122860i
$859$	−40.5232			−1.38263			−0.691317	−	0.722551i	$-0.742969\pi$
$859$	−40.5232			−1.38263			−0.691317	+	0.722551i	$0.742969\pi$
$860$	18.2633	+	6.50684i	0.622773	+	0.221881i
$861$	13.2744			0.452389
$862$			3.29515i			0.112233i
$863$			22.9160i			0.780069i	0.920800	+	0.390035i	$0.127537\pi$
$863$			22.9160i			0.780069i	−0.920800	+	0.390035i	$0.872463\pi$
$864$	−11.5635			−0.393398
$865$	5.82631	+	2.07580i	0.198100	+	0.0705792i
$866$	−8.40453			−0.285598
$867$		−	29.9779i		−	1.01810i
$868$			19.2025i			0.651775i
$869$	25.6664			0.870673
$870$	−4.34143	+	12.1854i	−0.147188	+	0.413125i
$871$	6.61866			0.224265
$872$		−	6.58478i		−	0.222989i
$873$		−	38.7326i		−	1.31090i
$874$		0			0
$875$	−11.2278	−	18.5612i	−0.379570	−	0.627483i
$876$	7.52203			0.254146
$877$		−	49.6951i		−	1.67808i	−0.544067	−	0.839042i	$-0.683116\pi$
$877$		−	49.6951i		−	1.67808i	0.544067	−	0.839042i	$-0.316884\pi$
$878$		−	5.72515i		−	0.193214i
$879$	2.37047			0.0799539
$880$	11.5798	−	32.5020i	0.390355	−	1.09564i
$881$	−11.0358			−0.371804			−0.185902	−	0.982568i	$-0.559521\pi$
$881$	−11.0358			−0.371804			−0.185902	+	0.982568i	$0.559521\pi$
$882$		−	3.55830i		−	0.119814i
$883$			22.1244i			0.744547i	0.928123	+	0.372273i	$0.121422\pi$
$883$			22.1244i			0.744547i	−0.928123	+	0.372273i	$0.878578\pi$
$884$	6.06135			0.203865
$885$	29.9554	+	10.6725i	1.00694	+	0.358753i
$886$	0.586472			0.0197029
$887$			20.0329i			0.672640i	0.941748	+	0.336320i	$0.109182\pi$
$887$			20.0329i			0.672640i	−0.941748	+	0.336320i	$0.890818\pi$
$888$		−	29.0970i		−	0.976430i
$889$	−37.2148			−1.24814
$890$	1.14986	+	0.409673i	0.0385435	+	0.0137323i
$891$	−9.55909			−0.320242
$892$			17.8481i			0.597597i
$893$		0			0
$894$	8.34491			0.279095
$895$	8.53896	−	23.9670i	0.285426	−	0.801129i
$896$	−14.0654			−0.469893
$897$			17.8632i			0.596433i
$898$		−	9.33951i		−	0.311663i
$899$	−44.0775			−1.47007
$900$	33.8107	+	27.5949i	1.12702	+	0.919830i
$901$	−1.69706			−0.0565372
$902$			2.58571i			0.0860947i
$903$			23.7435i			0.790133i
$904$	−5.70673			−0.189803
$905$	2.67654	−	7.51247i	0.0889713	−	0.249723i
$906$	9.26546			0.307824
$907$		−	0.681366i		−	0.0226244i	−0.999936	−	0.0113122i	$-0.996399\pi$
$907$		−	0.681366i		−	0.0226244i	0.999936	−	0.0113122i	$-0.00360086\pi$
$908$		−	1.16474i		−	0.0386531i
$909$	60.5114			2.00704
$910$	1.26876	+	0.452034i	0.0420590	+	0.0149848i
$911$	28.7169			0.951433			0.475716	−	0.879599i	$-0.342189\pi$
$911$	28.7169			0.951433			0.475716	+	0.879599i	$0.342189\pi$
$912$		0			0
$913$			50.1744i			1.66053i
$914$	0.458652			0.0151709
$915$	−16.1667	−	5.75987i	−0.534455	−	0.190416i
$916$	13.8047			0.456121
$917$		−	0.597584i		−	0.0197340i
$918$		−	2.46834i		−	0.0814674i
$919$	−6.91259			−0.228025			−0.114013	−	0.993479i	$-0.536370\pi$
$919$	−6.91259			−0.228025			−0.114013	+	0.993479i	$0.536370\pi$
$920$	3.71373	−	10.4236i	0.122438	−	0.343657i
$921$	24.6234			0.811370
$922$			4.11220i			0.135428i
$923$		−	1.00559i		−	0.0330995i
$924$	43.6405			1.43567
$925$	−34.8729	+	42.7281i	−1.14661	+	1.40489i
$926$	5.95647			0.195742
$927$		−	18.1556i		−	0.596309i
$928$		−	24.3484i		−	0.799276i
$929$	−40.8302			−1.33960			−0.669798	−	0.742544i	$-0.733619\pi$
$929$	−40.8302			−1.33960			−0.669798	+	0.742544i	$0.733619\pi$
$930$	2.56271	−	7.19296i	0.0840344	−	0.235866i
$931$		0			0
$932$		−	39.1272i		−	1.28165i
$933$			31.3288i			1.02566i
$934$	3.33737			0.109202
$935$	21.9377	+	7.81595i	0.717438	+	0.255609i
$936$	−5.50284			−0.179866
$937$		−	14.7439i		−	0.481664i	−0.970567	−	0.240832i	$-0.922580\pi$
$937$		−	14.7439i		−	0.481664i	0.970567	−	0.240832i	$-0.0774202\pi$
$938$		−	2.47245i		−	0.0807284i
$939$	21.5378			0.702861
$940$	−27.6639	−	9.85611i	−0.902298	−	0.321471i
$941$	−52.2137			−1.70212			−0.851059	−	0.525071i	$-0.824039\pi$
$941$	−52.2137			−1.70212			−0.851059	+	0.525071i	$0.824039\pi$
$942$			12.1823i			0.396921i
$943$		−	12.8346i		−	0.417952i
$944$	−18.9296			−0.616105
$945$	−5.97563	+	16.7723i	−0.194387	+	0.545602i
$946$	−4.62499			−0.150371
$947$		−	57.3403i		−	1.86331i	−0.363343	−	0.931655i	$-0.618365\pi$
$947$		−	57.3403i		−	1.86331i	0.363343	−	0.931655i	$-0.381635\pi$
$948$		−	32.2128i		−	1.04622i
$949$	1.79777			0.0583580
$950$		0			0
$951$	−45.2555			−1.46751
$952$		−	4.59828i		−	0.149031i
$953$			9.31765i			0.301828i	0.988547	+	0.150914i	$0.0482217\pi$
$953$			9.31765i			0.301828i	−0.988547	+	0.150914i	$0.951778\pi$
$954$	0.758657			0.0245624
$955$	−6.50890	+	18.2691i	−0.210623	+	0.591173i
$956$	22.5731			0.730065
$957$			100.173i			3.23812i
$958$			5.31507i			0.171722i
$959$	−28.1327			−0.908452
$960$	−38.0750	−	13.5654i	−1.22887	−	0.437820i
$961$	−4.98144			−0.160692
$962$		−	3.42435i		−	0.110405i
$963$			76.2925i			2.45849i
$964$	49.5343			1.59539
$965$	−0.889122	−	0.316776i	−0.0286218	−	0.0101974i
$966$	6.67292			0.214698
$967$			8.82697i			0.283856i	0.989877	+	0.141928i	$0.0453302\pi$
$967$			8.82697i			0.283856i	−0.989877	+	0.141928i	$0.954670\pi$
$968$			6.66705i			0.214287i
$969$		0			0
$970$	−1.57964	+	4.43371i	−0.0507193	+	0.142358i
$971$	55.9918			1.79686			0.898431	−	0.439114i	$-0.144708\pi$
$971$	55.9918			1.79686			0.898431	+	0.439114i	$0.144708\pi$
$972$			35.8846i			1.15100i
$973$		−	30.6511i		−	0.982628i
$974$	−7.14984			−0.229096
$975$	13.4695	+	10.9933i	0.431370	+	0.352067i
$976$	10.2161			0.327011
$977$			41.1034i			1.31501i	0.753449	+	0.657506i	$0.228389\pi$
$977$			41.1034i			1.31501i	−0.753449	+	0.657506i	$0.771611\pi$
$978$		−	10.2655i		−	0.328253i
$979$	9.45265			0.302108
$980$	4.71087	−	13.2224i	0.150483	−	0.422374i
$981$	30.7513			0.981815
$982$		−	4.48752i		−	0.143203i
$983$			2.49864i			0.0796941i	0.999206	+	0.0398471i	$0.0126871\pi$
$983$			2.49864i			0.0796941i	−0.999206	+	0.0398471i	$0.987313\pi$
$984$	6.59039			0.210094
$985$	−32.1043	−	11.4381i	−1.02293	−	0.364449i
$986$	5.19741			0.165519
$987$		−	35.9650i		−	1.14478i
$988$		0			0
$989$	22.9569			0.729986
$990$	−9.80706	−	3.49406i	−0.311689	−	0.111048i
$991$	17.4234			0.553471			0.276736	−	0.960946i	$-0.410747\pi$
$991$	17.4234			0.553471			0.276736	+	0.960946i	$0.410747\pi$
$992$			14.3727i			0.456332i
$993$		−	21.6727i		−	0.687762i
$994$	−0.375647			−0.0119148
$995$	−9.70076	+	27.2279i	−0.307535	+	0.863183i
$996$	62.9717			1.99533
$997$		−	12.8010i		−	0.405412i	−0.979240	−	0.202706i	$-0.935026\pi$
$997$		−	12.8010i		−	0.405412i	0.979240	−	0.202706i	$-0.0649736\pi$
$998$		−	2.54645i		−	0.0806065i
$999$	45.2679			1.43221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.13		24
5.2	odd	4		9025.2.a.cu.1.12		24
5.3	odd	4		9025.2.a.cu.1.13		24
5.4	even	2	inner	1805.2.b.k.1084.12		24
19.6	even	9		95.2.p.a.74.5	yes	48
19.16	even	9		95.2.p.a.9.4	✓	48
19.18	odd	2		1805.2.b.l.1084.12		24
57.35	odd	18		855.2.da.b.199.5		48
57.44	odd	18		855.2.da.b.739.4		48
95.18	even	4		9025.2.a.ct.1.12		24
95.37	even	4		9025.2.a.ct.1.13		24
95.44	even	18		95.2.p.a.74.4	yes	48
95.54	even	18		95.2.p.a.9.5	yes	48
95.63	odd	36		475.2.l.f.226.5		48
95.73	odd	36		475.2.l.f.351.5		48
95.82	odd	36		475.2.l.f.226.4		48
95.92	odd	36		475.2.l.f.351.4		48
95.94	odd	2		1805.2.b.l.1084.13		24
285.44	odd	18		855.2.da.b.739.5		48
285.149	odd	18		855.2.da.b.199.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.4	✓	48	19.16	even	9
95.2.p.a.9.5	yes	48	95.54	even	18
95.2.p.a.74.4	yes	48	95.44	even	18
95.2.p.a.74.5	yes	48	19.6	even	9
475.2.l.f.226.4		48	95.82	odd	36
475.2.l.f.226.5		48	95.63	odd	36
475.2.l.f.351.4		48	95.92	odd	36
475.2.l.f.351.5		48	95.73	odd	36
855.2.da.b.199.4		48	285.149	odd	18
855.2.da.b.199.5		48	57.35	odd	18
855.2.da.b.739.4		48	57.44	odd	18
855.2.da.b.739.5		48	285.44	odd	18
1805.2.b.k.1084.12		24	5.4	even	2	inner
1805.2.b.k.1084.13		24	1.1	even	1	trivial
1805.2.b.l.1084.12		24	19.18	odd	2
1805.2.b.l.1084.13		24	95.94	odd	2
9025.2.a.ct.1.12		24	95.18	even	4
9025.2.a.ct.1.13		24	95.37	even	4
9025.2.a.cu.1.12		24	5.2	odd	4
9025.2.a.cu.1.13		24	5.3	odd	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.244477i q^{2} -2.73837i q^{3} +1.94023 q^{4} +(0.750459 - 2.10637i) q^{5} +0.669469 q^{6} +1.94027i q^{7} +0.963297i q^{8} -4.49866 q^{9} +O(q^{10})\)	\(q+0.244477i q^{2} -2.73837i q^{3} +1.94023 q^{4} +(0.750459 - 2.10637i) q^{5} +0.669469 q^{6} +1.94027i q^{7} +0.963297i q^{8} -4.49866 q^{9} +(0.514961 + 0.183470i) q^{10} +4.23333 q^{11} -5.31307i q^{12} -1.26982i q^{13} -0.474352 q^{14} +(-5.76803 - 2.05503i) q^{15} +3.64496 q^{16} +2.46021i q^{17} -1.09982i q^{18} +(1.45606 - 4.08685i) q^{20} +5.31318 q^{21} +1.03495i q^{22} -5.13716i q^{23} +2.63786 q^{24} +(-3.87362 - 3.16149i) q^{25} +0.310443 q^{26} +4.10387i q^{27} +3.76457i q^{28} -8.64123 q^{29} +(0.502409 - 1.41015i) q^{30} +5.10084 q^{31} +2.81770i q^{32} -11.5924i q^{33} -0.601466 q^{34} +(4.08694 + 1.45609i) q^{35} -8.72843 q^{36} -11.0305i q^{37} -3.47724 q^{39} +(2.02906 + 0.722915i) q^{40} +2.49838 q^{41} +1.29895i q^{42} +4.46879i q^{43} +8.21364 q^{44} +(-3.37606 + 9.47585i) q^{45} +1.25592 q^{46} -6.76901i q^{47} -9.98123i q^{48} +3.23535 q^{49} +(0.772913 - 0.947013i) q^{50} +6.73697 q^{51} -2.46375i q^{52} +0.689802i q^{53} -1.00330 q^{54} +(3.17694 - 8.91697i) q^{55} -1.86906 q^{56} -2.11258i q^{58} -5.19336 q^{59} +(-11.1913 - 3.98724i) q^{60} +2.80281 q^{61} +1.24704i q^{62} -8.72862i q^{63} +6.60105 q^{64} +(-2.67472 - 0.952950i) q^{65} +2.83408 q^{66} +5.21227i q^{67} +4.77338i q^{68} -14.0674 q^{69} +(-0.355982 + 0.999163i) q^{70} +0.791916 q^{71} -4.33354i q^{72} +1.41576i q^{73} +2.69671 q^{74} +(-8.65733 + 10.6074i) q^{75} +8.21381i q^{77} -0.850107i q^{78} +6.06294 q^{79} +(2.73539 - 7.67764i) q^{80} -2.25806 q^{81} +0.610798i q^{82} +11.8522i q^{83} +10.3088 q^{84} +(5.18213 + 1.84629i) q^{85} -1.09252 q^{86} +23.6629i q^{87} +4.07795i q^{88} +2.23291 q^{89} +(-2.31663 - 0.825369i) q^{90} +2.46380 q^{91} -9.96727i q^{92} -13.9680i q^{93} +1.65487 q^{94} +7.71591 q^{96} +8.60981i q^{97} +0.790969i q^{98} -19.0443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

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