LMFDB - Embedded newform 405.3.g.h.163.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(82,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 8 x^{17} + 245 x^{16} - 440 x^{15} + 422 x^{14} + 1724 x^{13} + \cdots + 11449 $ x^20 - 2x^19 + 2x^18 + 8x^17 + 245x^16 - 440x^15 + 422x^14 + 1724x^13 + 15070x^12 - 18240x^11 + 13542x^10 + 50064x^9 + 293818x^8 - 191648x^7 + 30530x^6 - 134164x^5 + 859529x^4 - 948950x^3 + 540800x^2 - 111280*x + 11449
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.5
Root			$0.134438 + 0.134438i$ of defining polynomial
Character	$\chi$	$=$	405.163
Dual form			405.3.g.h.82.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.134438 - 0.134438i) q^{2} +3.96385i q^{4} +(-3.28806 + 3.76678i) q^{5} +(-6.37245 + 6.37245i) q^{7} +(1.07064 + 1.07064i) q^{8} +(0.0643587 + 0.948439i) q^{10} +14.0822 q^{11} +(-9.47597 - 9.47597i) q^{13} +1.71340i q^{14} -15.5675 q^{16} +(-0.740694 + 0.740694i) q^{17} -7.09073i q^{19} +(-14.9310 - 13.0334i) q^{20} +(1.89318 - 1.89318i) q^{22} +(-13.9455 - 13.9455i) q^{23} +(-3.37732 - 24.7708i) q^{25} -2.54786 q^{26} +(-25.2594 - 25.2594i) q^{28} +7.13953i q^{29} -26.1565 q^{31} +(-6.37545 + 6.37545i) q^{32} +0.199155i q^{34} +(-3.05064 - 44.9566i) q^{35} +(-23.0151 + 23.0151i) q^{37} +(-0.953264 - 0.953264i) q^{38} +(-7.55323 + 0.512543i) q^{40} +72.0774 q^{41} +(8.82002 + 8.82002i) q^{43} +55.8198i q^{44} -3.74961 q^{46} +(-37.9887 + 37.9887i) q^{47} -32.2161i q^{49} +(-3.78418 - 2.87610i) q^{50} +(37.5614 - 37.5614i) q^{52} +(17.2907 + 17.2907i) q^{53} +(-46.3031 + 53.0446i) q^{55} -13.6452 q^{56} +(0.959823 + 0.959823i) q^{58} -31.8013i q^{59} -81.4634 q^{61} +(-3.51643 + 3.51643i) q^{62} -60.5560i q^{64} +(66.8515 - 4.53638i) q^{65} +(-46.9540 + 46.9540i) q^{67} +(-2.93600 - 2.93600i) q^{68} +(-6.45400 - 5.63375i) q^{70} -36.3928 q^{71} +(2.90991 + 2.90991i) q^{73} +6.18821i q^{74} +28.1066 q^{76} +(-89.7381 + 89.7381i) q^{77} +83.0025i q^{79} +(51.1870 - 58.6396i) q^{80} +(9.68994 - 9.68994i) q^{82} +(-37.6125 - 37.6125i) q^{83} +(-0.354588 - 5.22548i) q^{85} +2.37149 q^{86} +(15.0770 + 15.0770i) q^{88} -22.5436i q^{89} +120.770 q^{91} +(55.2780 - 55.2780i) q^{92} +10.2142i q^{94} +(26.7093 + 23.3148i) q^{95} +(-24.6841 + 24.6841i) q^{97} +(-4.33107 - 4.33107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.134438	−	0.134438i	0.0672190	−	0.0672190i	−0.672698	−	0.739917i	$-0.734865\pi$
$2$	0.134438	−	0.134438i	0.0672190	−	0.0672190i	0.739917	+	0.672698i	$0.234865\pi$
$3$		0			0
$3$		0			0
$4$			3.96385i			0.990963i
$5$	−3.28806	+	3.76678i	−0.657612	+	0.753357i
$5$	−3.28806	+	3.76678i	−0.657612	+	0.753357i
$6$		0			0
$7$	−6.37245	+	6.37245i	−0.910349	+	0.910349i	−0.996299	−	0.0859500i	$-0.972607\pi$
$7$	−6.37245	+	6.37245i	−0.910349	+	0.910349i	0.0859500	+	0.996299i	$0.472607\pi$
$8$	1.07064	+	1.07064i	0.133831	+	0.133831i
$9$		0			0
$10$	0.0643587	+	0.948439i	0.00643587	+	0.0948439i
$11$	14.0822			1.28020			0.640100	−	0.768292i	$-0.278893\pi$
$11$	14.0822			1.28020			0.640100	+	0.768292i	$0.278893\pi$
$12$		0			0
$13$	−9.47597	−	9.47597i	−0.728921	−	0.728921i	0.241484	−	0.970405i	$-0.422366\pi$
$13$	−9.47597	−	9.47597i	−0.728921	−	0.728921i	−0.970405	+	0.241484i	$0.922366\pi$
$14$			1.71340i			0.122386i
$15$		0			0
$16$	−15.5675			−0.972971
$17$	−0.740694	+	0.740694i	−0.0435702	+	0.0435702i	−0.728556	−	0.684986i	$-0.759808\pi$
$17$	−0.740694	+	0.740694i	−0.0435702	+	0.0435702i	0.684986	+	0.728556i	$0.259808\pi$
$18$		0			0
$19$		−	7.09073i		−	0.373196i	−0.982436	−	0.186598i	$-0.940254\pi$
$19$		−	7.09073i		−	0.373196i	0.982436	−	0.186598i	$-0.0597463\pi$
$20$	−14.9310	−	13.0334i	−0.746549	−	0.651669i
$21$		0			0
$22$	1.89318	−	1.89318i	0.0860538	−	0.0860538i
$23$	−13.9455	−	13.9455i	−0.606327	−	0.606327i	0.335658	−	0.941984i	$-0.391042\pi$
$23$	−13.9455	−	13.9455i	−0.606327	−	0.606327i	−0.941984	+	0.335658i	$0.891042\pi$
$24$		0			0
$25$	−3.37732	−	24.7708i	−0.135093	−	0.990833i
$26$	−2.54786			−0.0979947
$27$		0			0
$28$	−25.2594	−	25.2594i	−0.902123	−	0.902123i
$29$			7.13953i			0.246191i	0.992395	+	0.123095i	$0.0392821\pi$
$29$			7.13953i			0.246191i	−0.992395	+	0.123095i	$0.960718\pi$
$30$		0			0
$31$	−26.1565			−0.843759			−0.421879	−	0.906652i	$-0.638629\pi$
$31$	−26.1565			−0.843759			−0.421879	+	0.906652i	$0.638629\pi$
$32$	−6.37545	+	6.37545i	−0.199233	+	0.199233i
$33$		0			0
$34$			0.199155i			0.00585749i
$35$	−3.05064	−	44.9566i	−0.0871612	−	1.28447i
$36$		0			0
$37$	−23.0151	+	23.0151i	−0.622031	+	0.622031i	−0.946050	−	0.324020i	$-0.894966\pi$
$37$	−23.0151	+	23.0151i	−0.622031	+	0.622031i	0.324020	+	0.946050i	$0.394966\pi$
$38$	−0.953264	−	0.953264i	−0.0250859	−	0.0250859i
$39$		0			0
$40$	−7.55323	+	0.512543i	−0.188831	+	0.0128136i
$41$	72.0774			1.75799			0.878993	−	0.476834i	$-0.158216\pi$
$41$	72.0774			1.75799			0.878993	+	0.476834i	$0.158216\pi$
$42$		0			0
$43$	8.82002	+	8.82002i	0.205117	+	0.205117i	0.802188	−	0.597071i	$-0.203669\pi$
$43$	8.82002	+	8.82002i	0.205117	+	0.205117i	−0.597071	+	0.802188i	$0.703669\pi$
$44$			55.8198i			1.26863i
$45$		0			0
$46$	−3.74961			−0.0815133
$47$	−37.9887	+	37.9887i	−0.808270	+	0.808270i	−0.984372	−	0.176102i	$-0.943651\pi$
$47$	−37.9887	+	37.9887i	−0.808270	+	0.808270i	0.176102	+	0.984372i	$0.443651\pi$
$48$		0			0
$49$		−	32.2161i		−	0.657472i
$50$	−3.78418	−	2.87610i	−0.0756836	−	0.0575220i
$51$		0			0
$52$	37.5614	−	37.5614i	0.722334	−	0.722334i
$53$	17.2907	+	17.2907i	0.326240	+	0.326240i	0.851155	−	0.524915i	$-0.175903\pi$
$53$	17.2907	+	17.2907i	0.326240	+	0.326240i	−0.524915	+	0.851155i	$0.675903\pi$
$54$		0			0
$55$	−46.3031	+	53.0446i	−0.841875	+	0.964447i
$56$	−13.6452			−0.243665
$57$		0			0
$58$	0.959823	+	0.959823i	0.0165487	+	0.0165487i
$59$		−	31.8013i		−	0.539005i	−0.963000	−	0.269502i	$-0.913141\pi$
$59$		−	31.8013i		−	0.539005i	0.963000	−	0.269502i	$-0.0868592\pi$
$60$		0			0
$61$	−81.4634			−1.33547			−0.667733	−	0.744401i	$-0.732735\pi$
$61$	−81.4634			−1.33547			−0.667733	+	0.744401i	$0.732735\pi$
$62$	−3.51643	+	3.51643i	−0.0567166	+	0.0567166i
$63$		0			0
$64$		−	60.5560i		−	0.946187i
$65$	66.8515	−	4.53638i	1.02848	−	0.0697904i
$66$		0			0
$67$	−46.9540	+	46.9540i	−0.700806	+	0.700806i	−0.964584	−	0.263777i	$-0.915032\pi$
$67$	−46.9540	+	46.9540i	−0.700806	+	0.700806i	0.263777	+	0.964584i	$0.415032\pi$
$68$	−2.93600	−	2.93600i	−0.0431765	−	0.0431765i
$69$		0			0
$70$	−6.45400	−	5.63375i	−0.0922000	−	0.0804822i
$71$	−36.3928			−0.512574			−0.256287	−	0.966601i	$-0.582499\pi$
$71$	−36.3928			−0.512574			−0.256287	+	0.966601i	$0.582499\pi$
$72$		0			0
$73$	2.90991	+	2.90991i	0.0398617	+	0.0398617i	0.726757	−	0.686895i	$-0.241027\pi$
$73$	2.90991	+	2.90991i	0.0398617	+	0.0398617i	−0.686895	+	0.726757i	$0.741027\pi$
$74$			6.18821i			0.0836245i
$75$		0			0
$76$	28.1066			0.369824
$77$	−89.7381	+	89.7381i	−1.16543	+	1.16543i
$78$		0			0
$79$			83.0025i			1.05066i	0.850897	+	0.525332i	$0.176059\pi$
$79$			83.0025i			1.05066i	−0.850897	+	0.525332i	$0.823941\pi$
$80$	51.1870	−	58.6396i	0.639838	−	0.732995i
$81$		0			0
$82$	9.68994	−	9.68994i	0.118170	−	0.118170i
$83$	−37.6125	−	37.6125i	−0.453162	−	0.453162i	0.443241	−	0.896403i	$-0.353829\pi$
$83$	−37.6125	−	37.6125i	−0.453162	−	0.453162i	−0.896403	+	0.443241i	$0.853829\pi$
$84$		0			0
$85$	−0.354588	−	5.22548i	−0.00417162	−	0.0614762i
$86$	2.37149			0.0275755
$87$		0			0
$88$	15.0770	+	15.0770i	0.171330	+	0.171330i
$89$		−	22.5436i		−	0.253299i	−0.991948	−	0.126650i	$-0.959578\pi$
$89$		−	22.5436i		−	0.253299i	0.991948	−	0.126650i	$-0.0404224\pi$
$90$		0			0
$91$	120.770			1.32715
$92$	55.2780	−	55.2780i	0.600847	−	0.600847i
$93$		0			0
$94$			10.2142i			0.108662i
$95$	26.7093	+	23.3148i	0.281150	+	0.245418i
$96$		0			0
$97$	−24.6841	+	24.6841i	−0.254476	+	0.254476i	−0.822803	−	0.568327i	$-0.807591\pi$
$97$	−24.6841	+	24.6841i	−0.254476	+	0.254476i	0.568327	+	0.822803i	$0.307591\pi$
$98$	−4.33107	−	4.33107i	−0.0441946	−	0.0441946i
$99$		0			0
$100$	98.1879	−	13.3872i	0.981879	−	0.133872i
$101$	59.4566			0.588679			0.294340	−	0.955701i	$-0.404900\pi$
$101$	59.4566			0.588679			0.294340	+	0.955701i	$0.404900\pi$
$102$		0			0
$103$	55.6493	+	55.6493i	0.540285	+	0.540285i	0.923612	−	0.383328i	$-0.125222\pi$
$103$	55.6493	+	55.6493i	0.540285	+	0.540285i	−0.383328	+	0.923612i	$0.625222\pi$
$104$		−	20.2908i		−	0.195104i
$105$		0			0
$106$	4.64906			0.0438590
$107$	−50.6865	+	50.6865i	−0.473706	+	0.473706i	−0.903112	−	0.429406i	$-0.858723\pi$
$107$	−50.6865	+	50.6865i	−0.473706	+	0.473706i	0.429406	+	0.903112i	$0.358723\pi$
$108$		0			0
$109$			47.8364i			0.438866i	0.975628	+	0.219433i	$0.0704208\pi$
$109$			47.8364i			0.438866i	−0.975628	+	0.219433i	$0.929579\pi$
$110$	0.906312	+	13.3561i	0.00823920	+	0.121419i
$111$		0			0
$112$	99.2033	−	99.2033i	0.885744	−	0.885744i
$113$	−123.217	−	123.217i	−1.09042	−	1.09042i	−0.995484	−	0.0949318i	$-0.969737\pi$
$113$	−123.217	−	123.217i	−1.09042	−	1.09042i	−0.0949318	−	0.995484i	$-0.530263\pi$
$114$		0			0
$115$	98.3834	−	6.67605i	0.855508	−	0.0580526i
$116$	−28.3000			−0.243966
$117$		0			0
$118$	−4.27530	−	4.27530i	−0.0362313	−	0.0362313i
$119$		−	9.44007i		−	0.0793283i
$120$		0			0
$121$	77.3084			0.638912
$122$	−10.9518	+	10.9518i	−0.0897686	+	0.0897686i
$123$		0			0
$124$		−	103.681i		−	0.836134i
$125$	104.411	+	68.7263i	0.835289	+	0.549810i
$126$		0			0
$127$	16.3333	−	16.3333i	0.128608	−	0.128608i	−0.639873	−	0.768481i	$-0.721013\pi$
$127$	16.3333	−	16.3333i	0.128608	−	0.128608i	0.768481	+	0.639873i	$0.221013\pi$
$128$	−33.6428	−	33.6428i	−0.262834	−	0.262834i
$129$		0			0
$130$	8.37752	−	9.59724i	0.0644425	−	0.0738250i
$131$	55.2097			0.421448			0.210724	−	0.977546i	$-0.432418\pi$
$131$	55.2097			0.421448			0.210724	+	0.977546i	$0.432418\pi$
$132$		0			0
$133$	45.1853	+	45.1853i	0.339739	+	0.339739i
$134$			12.6248i			0.0942150i
$135$		0			0
$136$	−1.58604			−0.0116621
$137$	−138.629	+	138.629i	−1.01189	+	1.01189i	−0.0119610	+	0.999928i	$0.503807\pi$
$137$	−138.629	+	138.629i	−1.01189	+	1.01189i	−0.999928	+	0.0119610i	$0.996193\pi$
$138$		0			0
$139$			95.3049i			0.685647i	0.939400	+	0.342823i	$0.111383\pi$
$139$			95.3049i			0.685647i	−0.939400	+	0.342823i	$0.888617\pi$
$140$	178.201	−	12.0923i	1.27287	−	0.0863736i
$141$		0			0
$142$	−4.89257	+	4.89257i	−0.0344547	+	0.0344547i
$143$	−133.443	−	133.443i	−0.933165	−	0.933165i
$144$		0			0
$145$	−26.8931	−	23.4752i	−0.185469	−	0.161898i
$146$	0.782404			0.00535893
$147$		0			0
$148$	−91.2286	−	91.2286i	−0.616409	−	0.616409i
$149$			260.201i			1.74632i	0.487437	+	0.873158i	$0.337932\pi$
$149$			260.201i			1.74632i	−0.487437	+	0.873158i	$0.662068\pi$
$150$		0			0
$151$	257.828			1.70747			0.853735	−	0.520708i	$-0.174332\pi$
$151$	257.828			1.70747			0.853735	+	0.520708i	$0.174332\pi$
$152$	7.59165	−	7.59165i	0.0499451	−	0.0499451i
$153$		0			0
$154$			24.1284i			0.156678i
$155$	86.0042	−	98.5259i	0.554866	−	0.635651i
$156$		0			0
$157$	−32.8669	+	32.8669i	−0.209344	+	0.209344i	−0.803988	−	0.594645i	$-0.797293\pi$
$157$	−32.8669	+	32.8669i	−0.209344	+	0.209344i	0.594645	+	0.803988i	$0.297293\pi$
$158$	11.1587	+	11.1587i	0.0706246	+	0.0706246i
$159$		0			0
$160$	−3.05208	−	44.9778i	−0.0190755	−	0.281111i
$161$	177.734			1.10394
$162$		0			0
$163$	76.8331	+	76.8331i	0.471369	+	0.471369i	0.902357	−	0.430989i	$-0.141835\pi$
$163$	76.8331	+	76.8331i	0.471369	+	0.471369i	−0.430989	+	0.902357i	$0.641835\pi$
$164$			285.704i			1.74210i
$165$		0			0
$166$	−10.1131			−0.0609222
$167$	220.534	−	220.534i	1.32057	−	1.32057i	0.407248	−	0.913318i	$-0.366489\pi$
$167$	220.534	−	220.534i	1.32057	−	1.32057i	0.913318	−	0.407248i	$-0.133511\pi$
$168$		0			0
$169$			10.5882i			0.0626520i
$170$	−0.750173	−	0.654833i	−0.00441278	−	0.00385196i
$171$		0			0
$172$	−34.9612	+	34.9612i	−0.203263	+	0.203263i
$173$	−141.017	−	141.017i	−0.815127	−	0.815127i	0.170270	−	0.985397i	$-0.445536\pi$
$173$	−141.017	−	141.017i	−0.815127	−	0.815127i	−0.985397	+	0.170270i	$0.945536\pi$
$174$		0			0
$175$	179.373	+	136.329i	1.02499	+	0.779022i
$176$	−219.225			−1.24560
$177$		0			0
$178$	−3.03072	−	3.03072i	−0.0170265	−	0.0170265i
$179$			254.120i			1.41967i	0.704370	+	0.709833i	$0.251230\pi$
$179$			254.120i			1.41967i	−0.704370	+	0.709833i	$0.748770\pi$
$180$		0			0
$181$	−236.998			−1.30938			−0.654691	−	0.755896i	$-0.727201\pi$
$181$	−236.998			−1.30938			−0.654691	+	0.755896i	$0.727201\pi$
$182$	16.2361	−	16.2361i	0.0892094	−	0.0892094i
$183$		0			0
$184$		−	29.8614i		−	0.162290i
$185$	−11.0179	−	162.368i	−0.0595562	−	0.877666i
$186$		0			0
$187$	−10.4306	+	10.4306i	−0.0557786	+	0.0557786i
$188$	−150.582	−	150.582i	−0.800966	−	0.800966i
$189$		0			0
$190$	6.72513	−	0.456350i	0.0353954	−	0.00240184i
$191$	−54.5924			−0.285824			−0.142912	−	0.989735i	$-0.545647\pi$
$191$	−54.5924			−0.285824			−0.142912	+	0.989735i	$0.545647\pi$
$192$		0			0
$193$	141.584	+	141.584i	0.733597	+	0.733597i	0.971331	−	0.237733i	$-0.0764044\pi$
$193$	141.584	+	141.584i	0.733597	+	0.733597i	−0.237733	+	0.971331i	$0.576404\pi$
$194$			6.63697i			0.0342112i
$195$		0			0
$196$	127.700			0.651531
$197$	18.5367	−	18.5367i	0.0940948	−	0.0940948i	−0.658492	−	0.752587i	$-0.728806\pi$
$197$	18.5367	−	18.5367i	0.0940948	−	0.0940948i	0.752587	+	0.658492i	$0.228806\pi$
$198$		0			0
$199$			206.081i			1.03558i	0.855507	+	0.517792i	$0.173246\pi$
$199$			206.081i			1.03558i	−0.855507	+	0.517792i	$0.826754\pi$
$200$	22.9048	−	30.1367i	0.114524	−	0.150683i
$201$		0			0
$202$	7.99323	−	7.99323i	0.0395704	−	0.0395704i
$203$	−45.4962	−	45.4962i	−0.224119	−	0.224119i
$204$		0			0
$205$	−236.995	+	271.500i	−1.15607	+	1.32439i
$206$	14.9628			0.0726348
$207$		0			0
$208$	147.518	+	147.518i	0.709219	+	0.709219i
$209$		−	99.8531i		−	0.477766i
$210$		0			0
$211$	−242.747			−1.15046			−0.575230	−	0.817992i	$-0.695087\pi$
$211$	−242.747			−1.15046			−0.575230	+	0.817992i	$0.695087\pi$
$212$	−68.5378	+	68.5378i	−0.323292	+	0.323292i
$213$		0			0
$214$			13.6284i			0.0636840i
$215$	−62.2238	+	4.22235i	−0.289413	+	0.0196389i
$216$		0			0
$217$	166.681	−	166.681i	0.768115	−	0.768115i
$218$	6.43103	+	6.43103i	0.0295002	+	0.0295002i
$219$		0			0
$220$	−210.261	−	183.539i	−0.955732	−	0.834267i
$221$	14.0376			0.0635185
$222$		0			0
$223$	−145.501	−	145.501i	−0.652472	−	0.652472i	0.301116	−	0.953588i	$-0.402641\pi$
$223$	−145.501	−	145.501i	−0.652472	−	0.652472i	−0.953588	+	0.301116i	$0.902641\pi$
$224$		−	81.2544i		−	0.362743i
$225$		0			0
$226$	−33.1301			−0.146593
$227$	131.638	−	131.638i	0.579903	−	0.579903i	−0.354973	−	0.934876i	$-0.615510\pi$
$227$	131.638	−	131.638i	0.579903	−	0.579903i	0.934876	+	0.354973i	$0.115510\pi$
$228$		0			0
$229$		−	180.947i		−	0.790160i	−0.918647	−	0.395080i	$-0.870717\pi$
$229$		−	180.947i		−	0.790160i	0.918647	−	0.395080i	$-0.129283\pi$
$230$	12.3289	−	14.1240i	0.0536041	−	0.0614086i
$231$		0			0
$232$	−7.64389	+	7.64389i	−0.0329478	+	0.0329478i
$233$	−120.230	−	120.230i	−0.516010	−	0.516010i	0.400351	−	0.916362i	$-0.368888\pi$
$233$	−120.230	−	120.230i	−0.516010	−	0.516010i	−0.916362	+	0.400351i	$0.868888\pi$
$234$		0			0
$235$	−18.1861	−	268.004i	−0.0773877	−	1.14044i
$236$	126.056			0.534134
$237$		0			0
$238$	−1.26910	−	1.26910i	−0.00533237	−	0.00533237i
$239$			383.502i			1.60461i	0.596914	+	0.802306i	$0.296394\pi$
$239$			383.502i			1.60461i	−0.596914	+	0.802306i	$0.703606\pi$
$240$		0			0
$241$	−325.887			−1.35223			−0.676114	−	0.736797i	$-0.736337\pi$
$241$	−325.887			−1.35223			−0.676114	+	0.736797i	$0.736337\pi$
$242$	10.3932	−	10.3932i	0.0429470	−	0.0429470i
$243$		0			0
$244$		−	322.909i		−	1.32340i
$245$	121.351	+	105.929i	0.495311	+	0.432362i
$246$		0			0
$247$	−67.1916	+	67.1916i	−0.272031	+	0.272031i
$248$	−28.0043	−	28.0043i	−0.112921	−	0.112921i
$249$		0			0
$250$	23.2763	−	4.79740i	0.0931050	−	0.0191896i
$251$	428.941			1.70893			0.854465	−	0.519509i	$-0.173885\pi$
$251$	428.941			1.70893			0.854465	+	0.519509i	$0.173885\pi$
$252$		0			0
$253$	−196.383	−	196.383i	−0.776219	−	0.776219i
$254$		−	4.39162i		−	0.0172898i
$255$		0			0
$256$	233.178			0.910852
$257$	−260.509	+	260.509i	−1.01365	+	1.01365i	−0.0137462	+	0.999906i	$0.504376\pi$
$257$	−260.509	+	260.509i	−1.01365	+	1.01365i	−0.999906	+	0.0137462i	$0.995624\pi$
$258$		0			0
$259$		−	293.325i		−	1.13253i
$260$	17.9815	+	264.990i	0.0691597	+	1.01919i
$261$		0			0
$262$	7.42228	−	7.42228i	0.0283293	−	0.0283293i
$263$	46.6533	+	46.6533i	0.177389	+	0.177389i	0.790217	−	0.612828i	$-0.209968\pi$
$263$	46.6533	+	46.6533i	0.177389	+	0.177389i	−0.612828	+	0.790217i	$0.709968\pi$
$264$		0			0
$265$	−121.983	+	8.27748i	−0.460314	+	0.0312358i
$266$	12.1492			0.0456738
$267$		0			0
$268$	−186.119	−	186.119i	−0.694473	−	0.694473i
$269$		−	146.927i		−	0.546197i	−0.961986	−	0.273099i	$-0.911951\pi$
$269$		−	146.927i		−	0.546197i	0.961986	−	0.273099i	$-0.0880485\pi$
$270$		0			0
$271$	−45.0155			−0.166109			−0.0830544	−	0.996545i	$-0.526468\pi$
$271$	−45.0155			−0.166109			−0.0830544	+	0.996545i	$0.526468\pi$
$272$	11.5308	−	11.5308i	0.0423926	−	0.0423926i
$273$		0			0
$274$			37.2740i			0.136036i
$275$	−47.5602	−	348.828i	−0.172946	−	1.26846i
$276$		0			0
$277$	−112.252	+	112.252i	−0.405241	+	0.405241i	−0.880075	−	0.474834i	$-0.842508\pi$
$277$	−112.252	+	112.252i	−0.405241	+	0.405241i	0.474834	+	0.880075i	$0.342508\pi$
$278$	12.8126	+	12.8126i	0.0460885	+	0.0460885i
$279$		0			0
$280$	44.8664	−	51.3987i	0.160237	−	0.183567i
$281$	66.1874			0.235542			0.117771	−	0.993041i	$-0.462425\pi$
$281$	66.1874			0.235542			0.117771	+	0.993041i	$0.462425\pi$
$282$		0			0
$283$	−284.616	−	284.616i	−1.00571	−	1.00571i	−0.999984	−	0.00572739i	$-0.998177\pi$
$283$	−284.616	−	284.616i	−1.00571	−	1.00571i	−0.00572739	−	0.999984i	$-0.501823\pi$
$284$		−	144.256i		−	0.507942i
$285$		0			0
$286$	−35.8795			−0.125453
$287$	−459.310	+	459.310i	−1.60038	+	1.60038i
$288$		0			0
$289$			287.903i			0.996203i
$290$	−6.77140	+	0.459491i	−0.0233497	+	0.00158445i
$291$		0			0
$292$	−11.5344	+	11.5344i	−0.0395015	+	0.0395015i
$293$	153.537	+	153.537i	0.524017	+	0.524017i	0.918782	−	0.394765i	$-0.129174\pi$
$293$	153.537	+	153.537i	0.524017	+	0.524017i	−0.394765	+	0.918782i	$0.629174\pi$
$294$		0			0
$295$	119.789	+	104.565i	0.406063	+	0.354456i
$296$	−49.2820			−0.166493
$297$		0			0
$298$	34.9809	+	34.9809i	0.117386	+	0.117386i
$299$			264.295i			0.883928i
$300$		0			0
$301$	−112.410			−0.373456
$302$	34.6619	−	34.6619i	0.114774	−	0.114774i
$303$		0			0
$304$			110.385i			0.363109i
$305$	267.857	−	306.855i	0.878218	−	1.00608i
$306$		0			0
$307$	−219.096	+	219.096i	−0.713666	+	0.713666i	−0.967300	−	0.253634i	$-0.918374\pi$
$307$	−219.096	+	219.096i	−0.713666	+	0.713666i	0.253634	+	0.967300i	$0.418374\pi$
$308$	−355.708	−	355.708i	−1.15490	−	1.15490i
$309$		0			0
$310$	−1.68340	−	24.8079i	−0.00543032	−	0.0800253i
$311$	137.696			0.442751			0.221376	−	0.975189i	$-0.428945\pi$
$311$	137.696			0.442751			0.221376	+	0.975189i	$0.428945\pi$
$312$		0			0
$313$	4.66646	+	4.66646i	0.0149088	+	0.0149088i	0.714522	−	0.699613i	$-0.246644\pi$
$313$	4.66646	+	4.66646i	0.0149088	+	0.0149088i	−0.699613	+	0.714522i	$0.746644\pi$
$314$			8.83713i			0.0281437i
$315$		0			0
$316$	−329.010			−1.04117
$317$	−312.791	+	312.791i	−0.986721	+	0.986721i	−0.999913	−	0.0131919i	$-0.995801\pi$
$317$	−312.791	+	312.791i	−0.986721	+	0.986721i	0.0131919	+	0.999913i	$0.495801\pi$
$318$		0			0
$319$			100.540i			0.315173i
$320$	228.101	+	199.112i	0.712816	+	0.622224i
$321$		0			0
$322$	23.8942	−	23.8942i	0.0742056	−	0.0742056i
$323$	5.25206	+	5.25206i	0.0162603	+	0.0162603i
$324$		0			0
$325$	−202.724	+	266.731i	−0.623767	+	0.820711i
$326$	20.6586			0.0633699
$327$		0			0
$328$	77.1693	+	77.1693i	0.235272	+	0.235272i
$329$		−	484.162i		−	1.47162i
$330$		0			0
$331$	261.703			0.790642			0.395321	−	0.918543i	$-0.370633\pi$
$331$	261.703			0.790642			0.395321	+	0.918543i	$0.370633\pi$
$332$	149.090	−	149.090i	0.449067	−	0.449067i
$333$		0			0
$334$		−	59.2964i		−	0.177534i
$335$	−22.4780	−	331.253i	−0.0670986	−	0.988816i
$336$		0			0
$337$	−103.095	+	103.095i	−0.305921	+	0.305921i	−0.843325	−	0.537404i	$-0.819405\pi$
$337$	−103.095	+	103.095i	−0.305921	+	0.305921i	0.537404	+	0.843325i	$0.319405\pi$
$338$	1.42345	+	1.42345i	0.00421140	+	0.00421140i
$339$		0			0
$340$	20.7130	−	1.40553i	0.0609207	−	0.00413393i
$341$	−368.341			−1.08018
$342$		0			0
$343$	−106.954	−	106.954i	−0.311820	−	0.311820i
$344$			18.8862i			0.0549017i
$345$		0			0
$346$	−37.9161			−0.109584
$347$	−7.15939	+	7.15939i	−0.0206322	+	0.0206322i	−0.717348	−	0.696715i	$-0.754644\pi$
$347$	−7.15939	+	7.15939i	−0.0206322	+	0.0206322i	0.696715	+	0.717348i	$0.254644\pi$
$348$		0			0
$349$			108.665i			0.311362i	0.987807	+	0.155681i	$0.0497572\pi$
$349$			108.665i			0.311362i	−0.987807	+	0.155681i	$0.950243\pi$
$350$	42.4423	−	5.78670i	0.121264	−	0.0165334i
$351$		0			0
$352$	−89.7803	+	89.7803i	−0.255058	+	0.255058i
$353$	341.965	+	341.965i	0.968739	+	0.968739i	0.999526	−	0.0307868i	$-0.00980129\pi$
$353$	341.965	+	341.965i	0.968739	+	0.968739i	−0.0307868	+	0.999526i	$0.509801\pi$
$354$		0			0
$355$	119.662	−	137.084i	0.337075	−	0.386151i
$356$	89.3597			0.251010
$357$		0			0
$358$	34.1634	+	34.1634i	0.0954285	+	0.0954285i
$359$		−	279.063i		−	0.777333i	−0.921378	−	0.388667i	$-0.872936\pi$
$359$		−	279.063i		−	0.777333i	0.921378	−	0.388667i	$-0.127064\pi$
$360$		0			0
$361$	310.722			0.860724
$362$	−31.8616	+	31.8616i	−0.0880154	+	0.0880154i
$363$		0			0
$364$			478.716i			1.31515i
$365$	−20.5289	+	1.39304i	−0.0562436	+	0.00381655i
$366$		0			0
$367$	126.313	−	126.313i	0.344178	−	0.344178i	−0.513757	−	0.857935i	$-0.671747\pi$
$367$	126.313	−	126.313i	0.344178	−	0.344178i	0.857935	+	0.513757i	$0.171747\pi$
$368$	217.097	+	217.097i	0.589938	+	0.589938i
$369$		0			0
$370$	−23.3097	−	20.3472i	−0.0629991	−	0.0549925i
$371$	−220.368			−0.593984
$372$		0			0
$373$	−62.0733	−	62.0733i	−0.166416	−	0.166416i	0.618986	−	0.785402i	$-0.287544\pi$
$373$	−62.0733	−	62.0733i	−0.166416	−	0.166416i	−0.785402	+	0.618986i	$0.787544\pi$
$374$			2.80454i			0.00749876i
$375$		0			0
$376$	−81.3448			−0.216342
$377$	67.6540	−	67.6540i	0.179453	−	0.179453i
$378$		0			0
$379$		−	10.3793i		−	0.0273860i	−0.999906	−	0.0136930i	$-0.995641\pi$
$379$		−	10.3793i		−	0.0273860i	0.999906	−	0.0136930i	$-0.00435875\pi$
$380$	−92.4163	+	105.872i	−0.243201	+	0.278609i
$381$		0			0
$382$	−7.33929	+	7.33929i	−0.0192128	+	0.0192128i
$383$	−91.0926	−	91.0926i	−0.237840	−	0.237840i	0.578115	−	0.815955i	$-0.303788\pi$
$383$	−91.0926	−	91.0926i	−0.237840	−	0.237840i	−0.815955	+	0.578115i	$0.803788\pi$
$384$		0			0
$385$	−42.9598	−	633.088i	−0.111584	−	1.64438i
$386$	38.0686			0.0986233
$387$		0			0
$388$	−97.8443	−	97.8443i	−0.252176	−	0.252176i
$389$		−	733.647i		−	1.88598i	−0.332818	−	0.942991i	$-0.607999\pi$
$389$		−	733.647i		−	1.88598i	0.332818	−	0.942991i	$-0.392001\pi$
$390$		0			0
$391$	20.6587			0.0528356
$392$	34.4920	−	34.4920i	0.0879898	−	0.0879898i
$393$		0			0
$394$		−	4.98407i		−	0.0126499i
$395$	−312.652	−	272.917i	−0.791525	−	0.690930i
$396$		0			0
$397$	151.257	−	151.257i	0.381000	−	0.381000i	−0.490463	−	0.871462i	$-0.663172\pi$
$397$	151.257	−	151.257i	0.381000	−	0.381000i	0.871462	+	0.490463i	$0.163172\pi$
$398$	27.7051	+	27.7051i	0.0696109	+	0.0696109i
$399$		0			0
$400$	52.5766	+	385.621i	0.131442	+	0.964052i
$401$	6.54509			0.0163219			0.00816096	−	0.999967i	$-0.497402\pi$
$401$	6.54509			0.0163219			0.00816096	+	0.999967i	$0.497402\pi$
$402$		0			0
$403$	247.858	+	247.858i	0.615033	+	0.615033i
$404$			235.677i			0.583360i
$405$		0			0
$406$	−12.2328			−0.0301302
$407$	−324.104	+	324.104i	−0.796324	+	0.796324i
$408$		0			0
$409$		−	738.152i		−	1.80477i	−0.430927	−	0.902387i	$-0.641813\pi$
$409$		−	738.152i		−	1.80477i	0.430927	−	0.902387i	$-0.358187\pi$
$410$	4.63881	+	68.3610i	0.0113142	+	0.166734i
$411$		0			0
$412$	−220.586	+	220.586i	−0.535402	+	0.535402i
$413$	202.652	+	202.652i	0.490683	+	0.490683i
$414$		0			0
$415$	265.350	−	18.0060i	0.639398	−	0.0433879i
$416$	120.827			0.290450
$417$		0			0
$418$	−13.4241	−	13.4241i	−0.0321150	−	0.0321150i
$419$			271.788i			0.648660i	0.945944	+	0.324330i	$0.105139\pi$
$419$			271.788i			0.648660i	−0.945944	+	0.324330i	$0.894861\pi$
$420$		0			0
$421$	−205.993			−0.489293			−0.244647	−	0.969612i	$-0.578672\pi$
$421$	−205.993			−0.489293			−0.244647	+	0.969612i	$0.578672\pi$
$422$	−32.6344	+	32.6344i	−0.0773327	+	0.0773327i
$423$		0			0
$424$			37.0244i			0.0873217i
$425$	20.8492	+	15.8460i	0.0490569	+	0.0372848i
$426$		0			0
$427$	519.121	−	519.121i	1.21574	−	1.21574i
$428$	−200.914	−	200.914i	−0.469425	−	0.469425i
$429$		0			0
$430$	−7.79760	+	8.93289i	−0.0181340	+	0.0207742i
$431$	−238.470			−0.553294			−0.276647	−	0.960972i	$-0.589223\pi$
$431$	−238.470			−0.553294			−0.276647	+	0.960972i	$0.589223\pi$
$432$		0			0
$433$	79.6977	+	79.6977i	0.184059	+	0.184059i	0.793122	−	0.609063i	$-0.208454\pi$
$433$	79.6977	+	79.6977i	0.184059	+	0.184059i	−0.609063	+	0.793122i	$0.708454\pi$
$434$		−	44.8165i		−	0.103264i
$435$		0			0
$436$	−189.617			−0.434900
$437$	−98.8839	+	98.8839i	−0.226279	+	0.226279i
$438$		0			0
$439$			323.458i			0.736807i	0.929666	+	0.368404i	$0.120096\pi$
$439$			323.458i			0.736807i	−0.929666	+	0.368404i	$0.879904\pi$
$440$	−106.366	+	7.21774i	−0.241741	+	0.0164039i
$441$		0			0
$442$	1.88719	−	1.88719i	0.00426965	−	0.00426965i
$443$	534.164	+	534.164i	1.20579	+	1.20579i	0.972379	+	0.233410i	$0.0749883\pi$
$443$	534.164	+	534.164i	1.20579	+	1.20579i	0.233410	+	0.972379i	$0.425012\pi$
$444$		0			0
$445$	84.9170	+	74.1248i	0.190825	+	0.166573i
$446$	−39.1218			−0.0877170
$447$		0			0
$448$	385.890	+	385.890i	0.861361	+	0.861361i
$449$			514.733i			1.14640i	0.819416	+	0.573199i	$0.194298\pi$
$449$			514.733i			1.14640i	−0.819416	+	0.573199i	$0.805702\pi$
$450$		0			0
$451$	1015.01			2.25057
$452$	488.414	−	488.414i	1.08056	−	1.08056i
$453$		0			0
$454$		−	35.3943i		−	0.0779610i
$455$	−397.100	+	454.916i	−0.872747	+	0.999814i
$456$		0			0
$457$	402.961	−	402.961i	0.881754	−	0.881754i	−0.111959	−	0.993713i	$-0.535713\pi$
$457$	402.961	−	402.961i	0.881754	−	0.881754i	0.993713	+	0.111959i	$0.0357126\pi$
$458$	−24.3261	−	24.3261i	−0.0531137	−	0.0531137i
$459$		0			0
$460$	26.4629	+	389.977i	0.0575280	+	0.847777i
$461$	238.669			0.517720			0.258860	−	0.965915i	$-0.416653\pi$
$461$	238.669			0.517720			0.258860	+	0.965915i	$0.416653\pi$
$462$		0			0
$463$	583.314	+	583.314i	1.25986	+	1.25986i	0.951160	+	0.308698i	$0.0998934\pi$
$463$	583.314	+	583.314i	1.25986	+	1.25986i	0.308698	+	0.951160i	$0.400107\pi$
$464$		−	111.145i		−	0.239536i
$465$		0			0
$466$	−32.3271			−0.0693714
$467$	489.265	−	489.265i	1.04768	−	1.04768i	0.0488707	−	0.998805i	$-0.484438\pi$
$467$	489.265	−	489.265i	1.04768	−	1.04768i	0.998805	−	0.0488707i	$-0.0155622\pi$
$468$		0			0
$469$		−	598.424i		−	1.27596i
$470$	−38.4749	−	33.5851i	−0.0818614	−	0.0714576i
$471$		0			0
$472$	34.0479	−	34.0479i	0.0721353	−	0.0721353i
$473$	124.205	+	124.205i	0.262590	+	0.262590i
$474$		0			0
$475$	−175.643	+	23.9477i	−0.369775	+	0.0504162i
$476$	37.4190			0.0786114
$477$		0			0
$478$	51.5572	+	51.5572i	0.107860	+	0.107860i
$479$			164.885i			0.344228i	0.985077	+	0.172114i	$0.0550597\pi$
$479$			164.885i			0.344228i	−0.985077	+	0.172114i	$0.944940\pi$
$480$		0			0
$481$	436.182			0.906822
$482$	−43.8116	+	43.8116i	−0.0908954	+	0.0908954i
$483$		0			0
$484$			306.439i			0.633139i
$485$	−11.8169	−	174.143i	−0.0243647	−	0.359057i
$486$		0			0
$487$	326.960	−	326.960i	0.671376	−	0.671376i	−0.286657	−	0.958033i	$-0.592544\pi$
$487$	326.960	−	326.960i	0.671376	−	0.671376i	0.958033	+	0.286657i	$0.0925441\pi$
$488$	−87.2183	−	87.2183i	−0.178726	−	0.178726i
$489$		0			0
$490$	30.5550	−	2.07339i	0.0623572	−	0.00423140i
$491$	364.023			0.741391			0.370695	−	0.928755i	$-0.379119\pi$
$491$	364.023			0.741391			0.370695	+	0.928755i	$0.379119\pi$
$492$		0			0
$493$	−5.28820	−	5.28820i	−0.0107266	−	0.0107266i
$494$			18.0662i			0.0365713i
$495$		0			0
$496$	407.193			0.820953
$497$	231.911	−	231.911i	0.466622	−	0.466622i
$498$		0			0
$499$			408.276i			0.818189i	0.912492	+	0.409095i	$0.134155\pi$
$499$			408.276i			0.818189i	−0.912492	+	0.409095i	$0.865845\pi$
$500$	−272.421	+	413.871i	−0.544842	+	0.827741i
$501$		0			0
$502$	57.6660	−	57.6660i	0.114873	−	0.114873i
$503$	555.921	+	555.921i	1.10521	+	1.10521i	0.993771	+	0.111440i	$0.0355462\pi$
$503$	555.921	+	555.921i	1.10521	+	1.10521i	0.111440	+	0.993771i	$0.464454\pi$
$504$		0			0
$505$	−195.497	+	223.960i	−0.387123	+	0.443486i
$506$	−52.8028			−0.104353
$507$		0			0
$508$	64.7426	+	64.7426i	0.127446	+	0.127446i
$509$		−	524.197i		−	1.02986i	−0.857233	−	0.514928i	$-0.827819\pi$
$509$		−	524.197i		−	1.02986i	0.857233	−	0.514928i	$-0.172181\pi$
$510$		0			0
$511$	−37.0864			−0.0725762
$512$	165.919	−	165.919i	0.324061	−	0.324061i
$513$		0			0
$514$			70.0445i			0.136273i
$515$	−392.597	+	26.6407i	−0.762325	+	0.0517295i
$516$		0			0
$517$	−534.965	+	534.965i	−1.03475	+	1.03475i
$518$	−39.4341	−	39.4341i	−0.0761275	−	0.0761275i
$519$		0			0
$520$	76.4310	+	66.7173i	0.146983	+	0.128303i
$521$	−694.042			−1.33213			−0.666067	−	0.745892i	$-0.732023\pi$
$521$	−694.042			−1.33213			−0.666067	+	0.745892i	$0.732023\pi$
$522$		0			0
$523$	244.233	+	244.233i	0.466985	+	0.466985i	0.900936	−	0.433951i	$-0.142881\pi$
$523$	244.233	+	244.233i	0.466985	+	0.466985i	−0.433951	+	0.900936i	$0.642881\pi$
$524$			218.843i			0.417640i
$525$		0			0
$526$	12.5440			0.0238478
$527$	19.3740	−	19.3740i	0.0367628	−	0.0367628i
$528$		0			0
$529$		−	140.045i		−	0.264736i
$530$	−15.2864	+	17.5120i	−0.0288422	+	0.0330415i
$531$		0			0
$532$	−179.108	+	179.108i	−0.336669	+	0.336669i
$533$	−683.004	−	683.004i	−1.28143	−	1.28143i
$534$		0			0
$535$	−24.2648	−	357.585i	−0.0453549	−	0.668384i
$536$	−100.542			−0.187579
$537$		0			0
$538$	−19.7526	−	19.7526i	−0.0367148	−	0.0367148i
$539$		−	453.674i		−	0.841696i
$540$		0			0
$541$	−682.588			−1.26172			−0.630858	−	0.775899i	$-0.717297\pi$
$541$	−682.588			−1.26172			−0.630858	+	0.775899i	$0.717297\pi$
$542$	−6.05179	+	6.05179i	−0.0111657	+	0.0111657i
$543$		0			0
$544$		−	9.44451i		−	0.0173612i
$545$	−180.190	−	157.289i	−0.330623	−	0.288604i
$546$		0			0
$547$	−45.7308	+	45.7308i	−0.0836029	+	0.0836029i	−0.747672	−	0.664069i	$-0.768828\pi$
$547$	−45.7308	+	45.7308i	−0.0836029	+	0.0836029i	0.664069	+	0.747672i	$0.268828\pi$
$548$	−549.504	−	549.504i	−1.00275	−	1.00275i
$549$		0			0
$550$	−53.2896	−	40.5018i	−0.0968901	−	0.0736396i
$551$	50.6245			0.0918774
$552$		0			0
$553$	−528.929	−	528.929i	−0.956472	−	0.956472i
$554$			30.1818i			0.0544798i
$555$		0			0
$556$	−377.775			−0.679451
$557$	−66.9124	+	66.9124i	−0.120130	+	0.120130i	−0.764616	−	0.644486i	$-0.777071\pi$
$557$	−66.9124	+	66.9124i	−0.120130	+	0.120130i	0.644486	+	0.764616i	$0.277071\pi$
$558$		0			0
$559$		−	167.156i		−	0.299028i
$560$	47.4910	+	699.864i	0.0848054	+	1.24976i
$561$		0			0
$562$	8.89809	−	8.89809i	0.0158329	−	0.0158329i
$563$	100.610	+	100.610i	0.178703	+	0.178703i	0.790790	−	0.612087i	$-0.209670\pi$
$563$	100.610	+	100.610i	0.178703	+	0.178703i	−0.612087	+	0.790790i	$0.709670\pi$
$564$		0			0
$565$	869.276	−	58.9869i	1.53854	−	0.104402i
$566$	−76.5264			−0.135206
$567$		0			0
$568$	−38.9637	−	38.9637i	−0.0685981	−	0.0685981i
$569$			319.654i			0.561782i	0.959740	+	0.280891i	$0.0906299\pi$
$569$			319.654i			0.561782i	−0.959740	+	0.280891i	$0.909370\pi$
$570$		0			0
$571$	648.618			1.13593			0.567967	−	0.823051i	$-0.307730\pi$
$571$	648.618			1.13593			0.567967	+	0.823051i	$0.307730\pi$
$572$	528.947	−	528.947i	0.924732	−	0.924732i
$573$		0			0
$574$			123.497i			0.215152i
$575$	−298.343	+	392.540i	−0.518858	+	0.682679i
$576$		0			0
$577$	−519.616	+	519.616i	−0.900548	+	0.900548i	−0.995483	−	0.0949353i	$-0.969736\pi$
$577$	−519.616	+	519.616i	−0.900548	+	0.900548i	0.0949353	+	0.995483i	$0.469736\pi$
$578$	38.7051	+	38.7051i	0.0669638	+	0.0669638i
$579$		0			0
$580$	93.0522	−	106.600i	0.160435	−	0.183793i
$581$	479.367			0.825072
$582$		0			0
$583$	243.491	+	243.491i	0.417652	+	0.417652i
$584$			6.23095i			0.0106694i
$585$		0			0
$586$	41.2824			0.0704478
$587$	583.945	−	583.945i	0.994796	−	0.994796i	−0.00519094	−	0.999987i	$-0.501652\pi$
$587$	583.945	−	583.945i	0.994796	−	0.994796i	0.999987	+	0.00519094i	$0.00165233\pi$
$588$		0			0
$589$			185.469i			0.314888i
$590$	30.1616	−	2.04669i	0.0511213	−	0.00346896i
$591$		0			0
$592$	358.289	−	358.289i	0.605218	−	0.605218i
$593$	329.014	+	329.014i	0.554829	+	0.554829i	0.927831	−	0.373002i	$-0.121671\pi$
$593$	329.014	+	329.014i	0.554829	+	0.554829i	−0.373002	+	0.927831i	$0.621671\pi$
$594$		0			0
$595$	35.5587	+	31.0395i	0.0597625	+	0.0521672i
$596$	−1031.40			−1.73053
$597$		0			0
$598$	35.5312	+	35.5312i	0.0594168	+	0.0594168i
$599$		−	514.520i		−	0.858964i	−0.903075	−	0.429482i	$-0.858696\pi$
$599$		−	514.520i		−	0.858964i	0.903075	−	0.429482i	$-0.141304\pi$
$600$		0			0
$601$	39.4955			0.0657164			0.0328582	−	0.999460i	$-0.489539\pi$
$601$	39.4955			0.0657164			0.0328582	+	0.999460i	$0.489539\pi$
$602$	−15.1122	+	15.1122i	−0.0251033	+	0.0251033i
$603$		0			0
$604$			1021.99i			1.69204i
$605$	−254.195	+	291.204i	−0.420156	+	0.481329i
$606$		0			0
$607$	285.935	−	285.935i	0.471062	−	0.471062i	−0.431196	−	0.902258i	$-0.641908\pi$
$607$	285.935	−	285.935i	0.471062	−	0.471062i	0.902258	+	0.431196i	$0.141908\pi$
$608$	45.2066	+	45.2066i	0.0743529	+	0.0743529i
$609$		0			0
$610$	−5.24288	−	77.2631i	−0.00859488	−	0.126661i
$611$	719.960			1.17833
$612$		0			0
$613$	−559.593	−	559.593i	−0.912876	−	0.912876i	0.0836213	−	0.996498i	$-0.473351\pi$
$613$	−559.593	−	559.593i	−0.912876	−	0.912876i	−0.996498	+	0.0836213i	$0.973351\pi$
$614$			58.9095i			0.0959439i
$615$		0			0
$616$	−192.155			−0.311940
$617$	247.055	−	247.055i	0.400414	−	0.400414i	−0.477965	−	0.878379i	$-0.658625\pi$
$617$	247.055	−	247.055i	0.400414	−	0.400414i	0.878379	+	0.477965i	$0.158625\pi$
$618$		0			0
$619$		−	444.088i		−	0.717428i	−0.933448	−	0.358714i	$-0.883215\pi$
$619$		−	444.088i		−	0.717428i	0.933448	−	0.358714i	$-0.116785\pi$
$620$	390.542	+	340.908i	0.629907	+	0.549852i
$621$		0			0
$622$	18.5115	−	18.5115i	0.0297613	−	0.0297613i
$623$	143.658	+	143.658i	0.230591	+	0.230591i
$624$		0			0
$625$	−602.187	+	167.318i	−0.963500	+	0.267709i
$626$	1.25470			0.00200431
$627$		0			0
$628$	−130.280	−	130.280i	−0.207452	−	0.207452i
$629$		−	34.0943i		−	0.0542040i
$630$		0			0
$631$	−181.428			−0.287524			−0.143762	−	0.989612i	$-0.545920\pi$
$631$	−181.428			−0.287524			−0.143762	+	0.989612i	$0.545920\pi$
$632$	−88.8661	+	88.8661i	−0.140611	+	0.140611i
$633$		0			0
$634$			84.1019i			0.132653i
$635$	7.81912	+	115.229i	0.0123136	+	0.181462i
$636$		0			0
$637$	−305.279	+	305.279i	−0.479245	+	0.479245i
$638$	13.5164	+	13.5164i	0.0211856	+	0.0211856i
$639$		0			0
$640$	237.345	−	16.1056i	0.370851	−	0.0251650i
$641$	−88.7291			−0.138423			−0.0692114	−	0.997602i	$-0.522048\pi$
$641$	−88.7291			−0.138423			−0.0692114	+	0.997602i	$0.522048\pi$
$642$		0			0
$643$	303.712	+	303.712i	0.472337	+	0.472337i	0.902670	−	0.430333i	$-0.141604\pi$
$643$	303.712	+	303.712i	0.472337	+	0.472337i	−0.430333	+	0.902670i	$0.641604\pi$
$644$			704.512i			1.09396i
$645$		0			0
$646$	1.41215			0.00218600
$647$	237.290	−	237.290i	0.366755	−	0.366755i	−0.499537	−	0.866292i	$-0.666497\pi$
$647$	237.290	−	237.290i	0.366755	−	0.366755i	0.866292	+	0.499537i	$0.166497\pi$
$648$		0			0
$649$		−	447.832i		−	0.690034i
$650$	8.60495	+	63.1126i	0.0132384	+	0.0970964i
$651$		0			0
$652$	−304.555	+	304.555i	−0.467109	+	0.467109i
$653$	569.017	+	569.017i	0.871388	+	0.871388i	0.992624	−	0.121235i	$-0.0386856\pi$
$653$	569.017	+	569.017i	0.871388	+	0.871388i	−0.121235	+	0.992624i	$0.538686\pi$
$654$		0			0
$655$	−181.533	+	207.963i	−0.277149	+	0.317501i
$656$	−1122.07			−1.71047
$657$		0			0
$658$	−65.0897	−	65.0897i	−0.0989206	−	0.0989206i
$659$		−	470.246i		−	0.713575i	−0.934186	−	0.356787i	$-0.883872\pi$
$659$		−	470.246i		−	0.713575i	0.934186	−	0.356787i	$-0.116128\pi$
$660$		0			0
$661$	−759.159			−1.14850			−0.574251	−	0.818679i	$-0.694707\pi$
$661$	−759.159			−1.14850			−0.574251	+	0.818679i	$0.694707\pi$
$662$	35.1828	−	35.1828i	0.0531462	−	0.0531462i
$663$		0			0
$664$		−	80.5391i		−	0.121294i
$665$	−318.775	+	21.6313i	−0.479361	+	0.0325283i
$666$		0			0
$667$	99.5643	−	99.5643i	0.149272	−	0.149272i
$668$	874.166	+	874.166i	1.30863	+	1.30863i
$669$		0			0
$670$	−47.5549	−	41.5111i	−0.0709775	−	0.0619569i
$671$	−1147.18			−1.70966
$672$		0			0
$673$	−891.570	−	891.570i	−1.32477	−	1.32477i	−0.909865	−	0.414904i	$-0.863815\pi$
$673$	−891.570	−	891.570i	−1.32477	−	1.32477i	−0.414904	−	0.909865i	$-0.636185\pi$
$674$			27.7198i			0.0411273i
$675$		0			0
$676$	−41.9700			−0.0620858
$677$	70.5673	−	70.5673i	0.104235	−	0.104235i	−0.653066	−	0.757301i	$-0.726518\pi$
$677$	70.5673	−	70.5673i	0.104235	−	0.104235i	0.757301	+	0.653066i	$0.226518\pi$
$678$		0			0
$679$		−	314.597i		−	0.463324i
$680$	5.21499	−	5.97427i	0.00766911	−	0.00878569i
$681$		0			0
$682$	−49.5191	+	49.5191i	−0.0726086	+	0.0726086i
$683$	366.381	+	366.381i	0.536430	+	0.536430i	0.922478	−	0.386049i	$-0.126160\pi$
$683$	366.381	+	366.381i	0.536430	+	0.536430i	−0.386049	+	0.922478i	$0.626160\pi$
$684$		0			0
$685$	−66.3650	−	978.005i	−0.0968832	−	1.42774i
$686$	−28.7574			−0.0419205
$687$		0			0
$688$	−137.306	−	137.306i	−0.199573	−	0.199573i
$689$		−	327.693i		−	0.475606i
$690$		0			0
$691$	596.266			0.862903			0.431451	−	0.902136i	$-0.358002\pi$
$691$	596.266			0.862903			0.431451	+	0.902136i	$0.358002\pi$
$692$	558.971	−	558.971i	0.807761	−	0.807761i
$693$		0			0
$694$			1.92499i			0.00277376i
$695$	−358.993	−	313.368i	−0.516537	−	0.450889i
$696$		0			0
$697$	−53.3873	+	53.3873i	−0.0765959	+	0.0765959i
$698$	14.6088	+	14.6088i	0.0209294	+	0.0209294i
$699$		0			0
$700$	−540.388	+	711.006i	−0.771983	+	1.01572i
$701$	147.235			0.210036			0.105018	−	0.994470i	$-0.466510\pi$
$701$	147.235			0.210036			0.105018	+	0.994470i	$0.466510\pi$
$702$		0			0
$703$	163.194	+	163.194i	0.232140	+	0.232140i
$704$		−	852.761i		−	1.21131i
$705$		0			0
$706$	91.9461			0.130235
$707$	−378.884	+	378.884i	−0.535904	+	0.535904i
$708$		0			0
$709$		−	142.296i		−	0.200700i	−0.994952	−	0.100350i	$-0.968004\pi$
$709$		−	142.296i		−	0.200700i	0.994952	−	0.100350i	$-0.0319962\pi$
$710$	−2.34219	−	34.5163i	−0.00329886	−	0.0486145i
$711$		0			0
$712$	24.1362	−	24.1362i	0.0338992	−	0.0338992i
$713$	364.766	+	364.766i	0.511593	+	0.511593i
$714$		0			0
$715$	941.417	−	63.8822i	1.31667	−	0.0893457i
$716$	−1007.30			−1.40684
$717$		0			0
$718$	−37.5166	−	37.5166i	−0.0522515	−	0.0522515i
$719$		−	1075.81i		−	1.49626i	−0.663555	−	0.748128i	$-0.730953\pi$
$719$		−	1075.81i		−	1.49626i	0.663555	−	0.748128i	$-0.269047\pi$
$720$		0			0
$721$	−709.245			−0.983696
$722$	41.7728	−	41.7728i	0.0578570	−	0.0578570i
$723$		0			0
$724$		−	939.426i		−	1.29755i
$725$	176.852	−	24.1125i	0.243934	−	0.0332586i
$726$		0			0
$727$	−509.682	+	509.682i	−0.701075	+	0.701075i	−0.964641	−	0.263566i	$-0.915101\pi$
$727$	−509.682	+	509.682i	−0.701075	+	0.701075i	0.263566	+	0.964641i	$0.415101\pi$
$728$	129.302	+	129.302i	0.177613	+	0.177613i
$729$		0			0
$730$	−2.57259	+	2.94715i	−0.00352410	+	0.00403718i
$731$	−13.0659			−0.0178740
$732$		0			0
$733$	−863.447	−	863.447i	−1.17796	−	1.17796i	−0.980263	−	0.197700i	$-0.936653\pi$
$733$	−863.447	−	863.447i	−1.17796	−	1.17796i	−0.197700	−	0.980263i	$-0.563347\pi$
$734$		−	33.9626i		−	0.0462706i
$735$		0			0
$736$	177.818			0.241600
$737$	−661.216	+	661.216i	−0.897173	+	0.897173i
$738$		0			0
$739$		−	683.603i		−	0.925038i	−0.886609	−	0.462519i	$-0.846946\pi$
$739$		−	683.603i		−	0.925038i	0.886609	−	0.462519i	$-0.153054\pi$
$740$	643.603	−	43.6733i	0.869734	−	0.0590180i
$741$		0			0
$742$	−29.6259	+	29.6259i	−0.0399270	+	0.0399270i
$743$	559.077	+	559.077i	0.752459	+	0.752459i	0.974938	−	0.222479i	$-0.0714148\pi$
$743$	559.077	+	559.077i	0.752459	+	0.752459i	−0.222479	+	0.974938i	$0.571415\pi$
$744$		0			0
$745$	−980.121	−	855.557i	−1.31560	−	1.14840i
$746$	−16.6900			−0.0223727
$747$		0			0
$748$	−41.3454	−	41.3454i	−0.0552746	−	0.0552746i
$749$		−	645.994i		−	0.862475i
$750$		0			0
$751$	−653.724			−0.870472			−0.435236	−	0.900316i	$-0.643335\pi$
$751$	−653.724			−0.870472			−0.435236	+	0.900316i	$0.643335\pi$
$752$	591.391	−	591.391i	0.786424	−	0.786424i
$753$		0			0
$754$		−	18.1905i		−	0.0241254i
$755$	−847.754	+	971.182i	−1.12285	+	1.28633i
$756$		0			0
$757$	668.868	−	668.868i	0.883577	−	0.883577i	−0.110319	−	0.993896i	$-0.535187\pi$
$757$	668.868	−	668.868i	0.883577	−	0.883577i	0.993896	+	0.110319i	$0.0351874\pi$
$758$	−1.39537	−	1.39537i	−0.00184086	−	0.00184086i
$759$		0			0
$760$	3.63431	+	53.5579i	0.00478198	+	0.0704710i
$761$	−957.410			−1.25809			−0.629047	−	0.777367i	$-0.716555\pi$
$761$	−957.410			−1.25809			−0.629047	+	0.777367i	$0.716555\pi$
$762$		0			0
$763$	−304.835	−	304.835i	−0.399522	−	0.399522i
$764$		−	216.396i		−	0.283241i
$765$		0			0
$766$	−24.4926			−0.0319747
$767$	−301.348	+	301.348i	−0.392892	+	0.392892i
$768$		0			0
$769$			503.415i			0.654636i	0.944914	+	0.327318i	$0.106145\pi$
$769$			503.415i			0.654636i	−0.944914	+	0.327318i	$0.893855\pi$
$770$	−90.8865	−	79.3356i	−0.118034	−	0.103033i
$771$		0			0
$772$	−561.219	+	561.219i	−0.726968	+	0.726968i
$773$	−362.267	−	362.267i	−0.468651	−	0.468651i	0.432827	−	0.901477i	$-0.357516\pi$
$773$	−362.267	−	362.267i	−0.468651	−	0.468651i	−0.901477	+	0.432827i	$0.857516\pi$
$774$		0			0
$775$	88.3390	+	647.918i	0.113986	+	0.836024i
$776$	−52.8559			−0.0681132
$777$		0			0
$778$	−98.6300	−	98.6300i	−0.126774	−	0.126774i
$779$		−	511.082i		−	0.656074i
$780$		0			0
$781$	−512.490			−0.656198
$782$	2.77732	−	2.77732i	0.00355155	−	0.00355155i
$783$		0			0
$784$			501.526i			0.639701i
$785$	−15.7342	−	231.871i	−0.0200436	−	0.295377i
$786$		0			0
$787$	367.640	−	367.640i	0.467141	−	0.467141i	−0.433846	−	0.900987i	$-0.642844\pi$
$787$	367.640	−	367.640i	0.467141	−	0.467141i	0.900987	+	0.433846i	$0.142844\pi$
$788$	73.4767	+	73.4767i	0.0932445	+	0.0932445i
$789$		0			0
$790$	−78.7228	+	5.34193i	−0.0996491	+	0.00676194i
$791$	1570.39			1.98532
$792$		0			0
$793$	771.945	+	771.945i	0.973449	+	0.973449i
$794$		−	40.6693i		−	0.0512208i
$795$		0			0
$796$	−816.876			−1.02623
$797$	197.182	−	197.182i	0.247405	−	0.247405i	−0.572500	−	0.819905i	$-0.694026\pi$
$797$	197.182	−	197.182i	0.247405	−	0.247405i	0.819905	+	0.572500i	$0.194026\pi$
$798$		0			0
$799$		−	56.2760i		−	0.0704331i
$800$	179.457	+	136.393i	0.224321	+	0.170491i
$801$		0			0
$802$	0.879908	−	0.879908i	0.00109714	−	0.00109714i
$803$	40.9779	+	40.9779i	0.0510310	+	0.0510310i
$804$		0			0
$805$	−584.400	+	669.486i	−0.725963	+	0.831659i
$806$	66.6432			0.0826838
$807$		0			0
$808$	63.6569	+	63.6569i	0.0787833	+	0.0787833i
$809$		−	423.966i		−	0.524062i	−0.965060	−	0.262031i	$-0.915608\pi$
$809$		−	423.966i		−	0.524062i	0.965060	−	0.262031i	$-0.0843922\pi$
$810$		0			0
$811$	−1163.79			−1.43501			−0.717506	−	0.696552i	$-0.754716\pi$
$811$	−1163.79			−1.43501			−0.717506	+	0.696552i	$0.754716\pi$
$812$	180.340	−	180.340i	0.222094	−	0.222094i
$813$		0			0
$814$			87.1437i			0.107056i
$815$	−542.046	+	36.7819i	−0.665087	+	0.0451311i
$816$		0			0
$817$	62.5404	−	62.5404i	0.0765488	−	0.0765488i
$818$	−99.2357	−	99.2357i	−0.121315	−	0.121315i
$819$		0			0
$820$	−1076.19	−	939.413i	−1.31242	−	1.14563i
$821$	765.830			0.932801			0.466400	−	0.884574i	$-0.345551\pi$
$821$	765.830			0.932801			0.466400	+	0.884574i	$0.345551\pi$
$822$		0			0
$823$	699.482	+	699.482i	0.849917	+	0.849917i	0.990122	−	0.140205i	$-0.0447762\pi$
$823$	699.482	+	699.482i	0.849917	+	0.849917i	−0.140205	+	0.990122i	$0.544776\pi$
$824$			119.161i			0.144613i
$825$		0			0
$826$	54.4882			0.0659664
$827$	−260.100	+	260.100i	−0.314510	+	0.314510i	−0.846654	−	0.532144i	$-0.821387\pi$
$827$	−260.100	+	260.100i	−0.314510	+	0.314510i	0.532144	+	0.846654i	$0.321387\pi$
$828$		0			0
$829$			325.275i			0.392370i	0.980567	+	0.196185i	$0.0628553\pi$
$829$			325.275i			0.392370i	−0.980567	+	0.196185i	$0.937145\pi$
$830$	33.2524	−	38.0938i	0.0400632	−	0.0458962i
$831$		0			0
$832$	−573.827	+	573.827i	−0.689696	+	0.689696i
$833$	23.8623	+	23.8623i	0.0286462	+	0.0286462i
$834$		0			0
$835$	105.575	+	1555.84i	0.126437	+	1.86328i
$836$	395.803			0.473449
$837$		0			0
$838$	36.5387	+	36.5387i	0.0436022	+	0.0436022i
$839$		−	94.0811i		−	0.112135i	−0.998427	−	0.0560674i	$-0.982144\pi$
$839$		−	94.0811i		−	0.112135i	0.998427	−	0.0560674i	$-0.0178562\pi$
$840$		0			0
$841$	790.027			0.939390
$842$	−27.6932	+	27.6932i	−0.0328898	+	0.0328898i
$843$		0			0
$844$		−	962.213i		−	1.14006i
$845$	−39.8834	−	34.8146i	−0.0471993	−	0.0412007i
$846$		0			0
$847$	−492.644	+	492.644i	−0.581633	+	0.581633i
$848$	−269.174	−	269.174i	−0.317422	−	0.317422i
$849$		0			0
$850$	4.93323	−	0.672610i	0.00580380	−	0.000791306i
$851$	641.915			0.754307
$852$		0			0
$853$	721.055	+	721.055i	0.845316	+	0.845316i	0.989544	−	0.144228i	$-0.0460700\pi$
$853$	721.055	+	721.055i	0.845316	+	0.845316i	−0.144228	+	0.989544i	$0.546070\pi$
$854$		−	139.579i		−	0.163442i
$855$		0			0
$856$	−108.534			−0.126793
$857$	−1114.88	+	1114.88i	−1.30091	+	1.30091i	−0.373124	+	0.927781i	$0.621713\pi$
$857$	−1114.88	+	1114.88i	−1.30091	+	1.30091i	−0.927781	+	0.373124i	$0.878287\pi$
$858$		0			0
$859$			585.510i			0.681618i	0.940132	+	0.340809i	$0.110701\pi$
$859$			585.510i			0.681618i	−0.940132	+	0.340809i	$0.889299\pi$
$860$	−16.7368	−	246.646i	−0.0194614	−	0.286798i
$861$		0			0
$862$	−32.0594	+	32.0594i	−0.0371919	+	0.0371919i
$863$	−550.423	−	550.423i	−0.637802	−	0.637802i	0.312211	−	0.950013i	$-0.398930\pi$
$863$	−550.423	−	550.423i	−0.637802	−	0.637802i	−0.950013	+	0.312211i	$0.898930\pi$
$864$		0			0
$865$	994.853	−	67.5082i	1.15012	−	0.0780442i
$866$	21.4288			0.0247446
$867$		0			0
$868$	660.699	+	660.699i	0.761174	+	0.761174i
$869$			1168.86i			1.34506i
$870$		0			0
$871$	889.870			1.02167
$872$	−51.2158	+	51.2158i	−0.0587337	+	0.0587337i
$873$		0			0
$874$			26.5875i			0.0304205i
$875$	−1103.31	+	227.400i	−1.26092	+	0.259886i
$876$		0			0
$877$	646.130	−	646.130i	0.736750	−	0.736750i	−0.235197	−	0.971948i	$-0.575574\pi$
$877$	646.130	−	646.130i	0.736750	−	0.736750i	0.971948	+	0.235197i	$0.0755737\pi$
$878$	43.4851	+	43.4851i	0.0495274	+	0.0495274i
$879$		0			0
$880$	720.826	−	825.774i	0.819120	−	0.938380i
$881$	−459.689			−0.521781			−0.260891	−	0.965368i	$-0.584016\pi$
$881$	−459.689			−0.521781			−0.260891	+	0.965368i	$0.584016\pi$
$882$		0			0
$883$	107.163	+	107.163i	0.121362	+	0.121362i	0.765179	−	0.643817i	$-0.222650\pi$
$883$	107.163	+	107.163i	0.121362	+	0.121362i	−0.643817	+	0.765179i	$0.722650\pi$
$884$			55.6430i			0.0629445i
$885$		0			0
$886$	143.624			0.162104
$887$	−470.348	+	470.348i	−0.530268	+	0.530268i	−0.920652	−	0.390384i	$-0.872342\pi$
$887$	−470.348	+	470.348i	−0.530268	+	0.530268i	0.390384	+	0.920652i	$0.372342\pi$
$888$		0			0
$889$			208.166i			0.234157i
$890$	21.3813	−	1.45088i	0.0240239	−	0.00163020i
$891$		0			0
$892$	576.746	−	576.746i	0.646576	−	0.646576i
$893$	269.368	+	269.368i	0.301644	+	0.301644i
$894$		0			0
$895$	−957.216	−	835.563i	−1.06952	−	0.933589i
$896$	428.774			0.478542
$897$		0			0
$898$	69.1996	+	69.1996i	0.0770597	+	0.0770597i
$899$		−	186.745i		−	0.207725i
$900$		0			0
$901$	−25.6142			−0.0284287
$902$	136.456	−	136.456i	0.151281	−	0.151281i
$903$		0			0
$904$		−	263.843i		−	0.291862i
$905$	779.264	−	892.721i	0.861066	−	0.986432i
$906$		0			0
$907$	589.037	−	589.037i	0.649435	−	0.649435i	−0.303422	−	0.952856i	$-0.598129\pi$
$907$	589.037	−	589.037i	0.649435	−	0.649435i	0.952856	+	0.303422i	$0.0981291\pi$
$908$	521.794	+	521.794i	0.574663	+	0.574663i
$909$		0			0
$910$	7.77262	+	114.543i	0.00854134	+	0.125872i
$911$	77.5907			0.0851710			0.0425855	−	0.999093i	$-0.486441\pi$
$911$	77.5907			0.0851710			0.0425855	+	0.999093i	$0.486441\pi$
$912$		0			0
$913$	−529.666	−	529.666i	−0.580138	−	0.580138i
$914$		−	108.347i		−	0.118541i
$915$		0			0
$916$	717.246			0.783019
$917$	−351.821	+	351.821i	−0.383665	+	0.383665i
$918$		0			0
$919$			1478.95i			1.60930i	0.593750	+	0.804650i	$0.297647\pi$
$919$			1478.95i			1.60930i	−0.593750	+	0.804650i	$0.702353\pi$
$920$	112.481	+	98.1859i	0.122262	+	0.106724i
$921$		0			0
$922$	32.0861	−	32.0861i	0.0348006	−	0.0348006i
$923$	344.857	+	344.857i	0.373626	+	0.373626i
$924$		0			0
$925$	647.833	+	492.374i	0.700360	+	0.532296i
$926$	156.839			0.169373
$927$		0			0
$928$	−45.5177	−	45.5177i	−0.0490492	−	0.0490492i
$929$			1595.29i			1.71721i	0.512640	+	0.858604i	$0.328668\pi$
$929$			1595.29i			1.71721i	−0.512640	+	0.858604i	$0.671332\pi$
$930$		0			0
$931$	−228.436			−0.245366
$932$	476.576	−	476.576i	0.511347	−	0.511347i
$933$		0			0
$934$		−	131.551i		−	0.140847i
$935$	−4.99338	−	73.5863i	−0.00534051	−	0.0787019i
$936$		0			0
$937$	−921.265	+	921.265i	−0.983207	+	0.983207i	−0.999861	−	0.0166542i	$-0.994699\pi$
$937$	−921.265	+	921.265i	−0.983207	+	0.983207i	0.0166542	+	0.999861i	$0.494699\pi$
$938$	−80.4509	−	80.4509i	−0.0857686	−	0.0857686i
$939$		0			0
$940$	1062.33	−	72.0871i	1.13014	−	0.0766884i
$941$	1236.37			1.31389			0.656945	−	0.753939i	$-0.271848\pi$
$941$	1236.37			1.31389			0.656945	+	0.753939i	$0.271848\pi$
$942$		0			0
$943$	−1005.16	−	1005.16i	−1.06591	−	1.06591i
$944$			495.068i			0.524436i
$945$		0			0
$946$	33.3958			0.0353021
$947$	1142.74	−	1142.74i	1.20670	−	1.20670i	0.234605	−	0.972091i	$-0.424620\pi$
$947$	1142.74	−	1142.74i	1.20670	−	1.20670i	0.972091	−	0.234605i	$-0.0753795\pi$
$948$		0			0
$949$		−	55.1484i		−	0.0581121i
$950$	−20.3936	+	26.8326i	−0.0214670	+	0.0282449i
$951$		0			0
$952$	10.1070	−	10.1070i	0.0106165	−	0.0106165i
$953$	1074.57	+	1074.57i	1.12756	+	1.12756i	0.990573	+	0.136988i	$0.0437421\pi$
$953$	1074.57	+	1074.57i	1.12756	+	1.12756i	0.136988	+	0.990573i	$0.456258\pi$
$954$		0			0
$955$	179.503	−	205.638i	0.187961	−	0.215328i
$956$	−1520.15			−1.59011
$957$		0			0
$958$	22.1668	+	22.1668i	0.0231387	+	0.0231387i
$959$		−	1766.81i		−	1.84235i
$960$		0			0
$961$	−276.837			−0.288072
$962$	58.6394	−	58.6394i	0.0609557	−	0.0609557i
$963$		0			0
$964$		−	1291.77i		−	1.34001i
$965$	−998.855	+	67.7798i	−1.03508	+	0.0702381i
$966$		0			0
$967$	−127.404	+	127.404i	−0.131752	+	0.131752i	−0.769907	−	0.638156i	$-0.779698\pi$
$967$	−127.404	+	127.404i	−0.131752	+	0.131752i	0.638156	+	0.769907i	$0.279698\pi$
$968$	82.7698	+	82.7698i	0.0855060	+	0.0855060i
$969$		0			0
$970$	−25.0000	−	21.8228i	−0.0257732	−	0.0224977i
$971$	−40.8568			−0.0420770			−0.0210385	−	0.999779i	$-0.506697\pi$
$971$	−40.8568			−0.0420770			−0.0210385	+	0.999779i	$0.506697\pi$
$972$		0			0
$973$	−607.325	−	607.325i	−0.624178	−	0.624178i
$974$		−	87.9117i		−	0.0902584i
$975$		0			0
$976$	1268.18			1.29937
$977$	−552.078	+	552.078i	−0.565074	+	0.565074i	−0.930745	−	0.365670i	$-0.880840\pi$
$977$	−552.078	+	552.078i	−0.565074	+	0.565074i	0.365670	+	0.930745i	$0.380840\pi$
$978$		0			0
$979$		−	317.464i		−	0.324274i
$980$	−419.885	+	481.018i	−0.428454	+	0.490835i
$981$		0			0
$982$	48.9385	−	48.9385i	0.0498355	−	0.0498355i
$983$	363.474	+	363.474i	0.369760	+	0.369760i	0.867390	−	0.497630i	$-0.165796\pi$
$983$	363.474	+	363.474i	0.369760	+	0.369760i	−0.497630	+	0.867390i	$0.665796\pi$
$984$		0			0
$985$	8.87396	+	130.773i	0.00900909	+	0.132765i
$986$	−1.42187			−0.00144206
$987$		0			0
$988$	−266.338	−	266.338i	−0.269573	−	0.269573i
$989$		−	245.999i		−	0.248735i
$990$		0			0
$991$	941.294			0.949843			0.474922	−	0.880028i	$-0.342476\pi$
$991$	941.294			0.949843			0.474922	+	0.880028i	$0.342476\pi$
$992$	166.759	−	166.759i	0.168104	−	0.168104i
$993$		0			0
$994$		−	62.3553i		−	0.0627317i
$995$	−776.263	−	677.607i	−0.780164	−	0.681012i
$996$		0			0
$997$	942.532	−	942.532i	0.945368	−	0.945368i	−0.0532154	−	0.998583i	$-0.516947\pi$
$997$	942.532	−	942.532i	0.945368	−	0.945368i	0.998583	+	0.0532154i	$0.0169470\pi$
$998$	54.8879	+	54.8879i	0.0549979	+	0.0549979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.h.163.5		20
3.2	odd	2		405.3.g.g.163.6		20
5.2	odd	4	inner	405.3.g.h.82.5		20
9.2	odd	6		135.3.l.a.118.5		40
9.4	even	3		45.3.k.a.43.5	yes	40
9.5	odd	6		135.3.l.a.73.6		40
9.7	even	3		45.3.k.a.13.6	yes	40
15.2	even	4		405.3.g.g.82.6		20
45.2	even	12		135.3.l.a.37.6		40
45.4	even	6		225.3.o.b.43.6		40
45.7	odd	12		45.3.k.a.22.5	yes	40
45.13	odd	12		225.3.o.b.7.5		40
45.22	odd	12		45.3.k.a.7.6	✓	40
45.32	even	12		135.3.l.a.127.5		40
45.34	even	6		225.3.o.b.193.5		40
45.43	odd	12		225.3.o.b.157.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.6	✓	40	45.22	odd	12
45.3.k.a.13.6	yes	40	9.7	even	3
45.3.k.a.22.5	yes	40	45.7	odd	12
45.3.k.a.43.5	yes	40	9.4	even	3
135.3.l.a.37.6		40	45.2	even	12
135.3.l.a.73.6		40	9.5	odd	6
135.3.l.a.118.5		40	9.2	odd	6
135.3.l.a.127.5		40	45.32	even	12
225.3.o.b.7.5		40	45.13	odd	12
225.3.o.b.43.6		40	45.4	even	6
225.3.o.b.157.6		40	45.43	odd	12
225.3.o.b.193.5		40	45.34	even	6
405.3.g.g.82.6		20	15.2	even	4
405.3.g.g.163.6		20	3.2	odd	2
405.3.g.h.82.5		20	5.2	odd	4	inner
405.3.g.h.163.5		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134438 - 0.134438i) q^{2} +3.96385i q^{4} +(-3.28806 + 3.76678i) q^{5} +(-6.37245 + 6.37245i) q^{7} +(1.07064 + 1.07064i) q^{8} +(0.0643587 + 0.948439i) q^{10} +14.0822 q^{11} +(-9.47597 - 9.47597i) q^{13} +1.71340i q^{14} -15.5675 q^{16} +(-0.740694 + 0.740694i) q^{17} -7.09073i q^{19} +(-14.9310 - 13.0334i) q^{20} +(1.89318 - 1.89318i) q^{22} +(-13.9455 - 13.9455i) q^{23} +(-3.37732 - 24.7708i) q^{25} -2.54786 q^{26} +(-25.2594 - 25.2594i) q^{28} +7.13953i q^{29} -26.1565 q^{31} +(-6.37545 + 6.37545i) q^{32} +0.199155i q^{34} +(-3.05064 - 44.9566i) q^{35} +(-23.0151 + 23.0151i) q^{37} +(-0.953264 - 0.953264i) q^{38} +(-7.55323 + 0.512543i) q^{40} +72.0774 q^{41} +(8.82002 + 8.82002i) q^{43} +55.8198i q^{44} -3.74961 q^{46} +(-37.9887 + 37.9887i) q^{47} -32.2161i q^{49} +(-3.78418 - 2.87610i) q^{50} +(37.5614 - 37.5614i) q^{52} +(17.2907 + 17.2907i) q^{53} +(-46.3031 + 53.0446i) q^{55} -13.6452 q^{56} +(0.959823 + 0.959823i) q^{58} -31.8013i q^{59} -81.4634 q^{61} +(-3.51643 + 3.51643i) q^{62} -60.5560i q^{64} +(66.8515 - 4.53638i) q^{65} +(-46.9540 + 46.9540i) q^{67} +(-2.93600 - 2.93600i) q^{68} +(-6.45400 - 5.63375i) q^{70} -36.3928 q^{71} +(2.90991 + 2.90991i) q^{73} +6.18821i q^{74} +28.1066 q^{76} +(-89.7381 + 89.7381i) q^{77} +83.0025i q^{79} +(51.1870 - 58.6396i) q^{80} +(9.68994 - 9.68994i) q^{82} +(-37.6125 - 37.6125i) q^{83} +(-0.354588 - 5.22548i) q^{85} +2.37149 q^{86} +(15.0770 + 15.0770i) q^{88} -22.5436i q^{89} +120.770 q^{91} +(55.2780 - 55.2780i) q^{92} +10.2142i q^{94} +(26.7093 + 23.3148i) q^{95} +(-24.6841 + 24.6841i) q^{97} +(-4.33107 - 4.33107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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