LMFDB - Embedded newform 105.2.d.b.64.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("105.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.d (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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.6
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.2.d.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70928i q^{2} +1.00000i q^{3} -5.34017 q^{4} +(2.17009 + 0.539189i) q^{5} -2.70928 q^{6} -1.00000i q^{7} -9.04945i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.70928i q^{2} +1.00000i q^{3} -5.34017 q^{4} +(2.17009 + 0.539189i) q^{5} -2.70928 q^{6} -1.00000i q^{7} -9.04945i q^{8} -1.00000 q^{9} +(-1.46081 + 5.87936i) q^{10} +2.00000 q^{11} -5.34017i q^{12} +0.921622i q^{13} +2.70928 q^{14} +(-0.539189 + 2.17009i) q^{15} +13.8371 q^{16} -1.07838i q^{17} -2.70928i q^{18} -3.07838 q^{19} +(-11.5886 - 2.87936i) q^{20} +1.00000 q^{21} +5.41855i q^{22} +2.34017i q^{23} +9.04945 q^{24} +(4.41855 + 2.34017i) q^{25} -2.49693 q^{26} -1.00000i q^{27} +5.34017i q^{28} +6.68035 q^{29} +(-5.87936 - 1.46081i) q^{30} -7.75872 q^{31} +19.3896i q^{32} +2.00000i q^{33} +2.92162 q^{34} +(0.539189 - 2.17009i) q^{35} +5.34017 q^{36} -10.8371i q^{37} -8.34017i q^{38} -0.921622 q^{39} +(4.87936 - 19.6381i) q^{40} +6.49693 q^{41} +2.70928i q^{42} -6.52359i q^{43} -10.6803 q^{44} +(-2.17009 - 0.539189i) q^{45} -6.34017 q^{46} -4.68035i q^{47} +13.8371i q^{48} -1.00000 q^{49} +(-6.34017 + 11.9711i) q^{50} +1.07838 q^{51} -4.92162i q^{52} +3.75872i q^{53} +2.70928 q^{54} +(4.34017 + 1.07838i) q^{55} -9.04945 q^{56} -3.07838i q^{57} +18.0989i q^{58} -10.5236 q^{59} +(2.87936 - 11.5886i) q^{60} -4.15676 q^{61} -21.0205i q^{62} +1.00000i q^{63} -24.8576 q^{64} +(-0.496928 + 2.00000i) q^{65} -5.41855 q^{66} -4.68035i q^{67} +5.75872i q^{68} -2.34017 q^{69} +(5.87936 + 1.46081i) q^{70} +2.00000 q^{71} +9.04945i q^{72} +7.07838i q^{73} +29.3607 q^{74} +(-2.34017 + 4.41855i) q^{75} +16.4391 q^{76} -2.00000i q^{77} -2.49693i q^{78} -6.15676 q^{79} +(30.0277 + 7.46081i) q^{80} +1.00000 q^{81} +17.6020i q^{82} +6.83710i q^{83} -5.34017 q^{84} +(0.581449 - 2.34017i) q^{85} +17.6742 q^{86} +6.68035i q^{87} -18.0989i q^{88} -8.34017 q^{89} +(1.46081 - 5.87936i) q^{90} +0.921622 q^{91} -12.4969i q^{92} -7.75872i q^{93} +12.6803 q^{94} +(-6.68035 - 1.65983i) q^{95} -19.3896 q^{96} +8.43907i q^{97} -2.70928i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{14} + 26 q^{16} - 12 q^{19} - 30 q^{20} + 6 q^{21} + 18 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{29} - 10 q^{30} + 4 q^{31} + 24 q^{34} + 10 q^{36} - 12 q^{39} + 4 q^{40} + 4 q^{41} - 20 q^{44} - 2 q^{45} - 16 q^{46} - 6 q^{49} - 16 q^{50} + 2 q^{54} + 4 q^{55} - 18 q^{56} - 32 q^{59} - 8 q^{60} - 12 q^{61} - 26 q^{64} + 32 q^{65} - 4 q^{66} + 8 q^{69} + 10 q^{70} + 12 q^{71} + 88 q^{74} + 8 q^{75} + 4 q^{76} - 24 q^{79} + 46 q^{80} + 6 q^{81} - 10 q^{84} + 32 q^{85} - 8 q^{86} - 28 q^{89} + 12 q^{90} + 12 q^{91} + 32 q^{94} + 4 q^{95} - 58 q^{96} - 12 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^14 + 26 * q^16 - 12 * q^19 - 30 * q^20 + 6 * q^21 + 18 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^29 - 10 * q^30 + 4 * q^31 + 24 * q^34 + 10 * q^36 - 12 * q^39 + 4 * q^40 + 4 * q^41 - 20 * q^44 - 2 * q^45 - 16 * q^46 - 6 * q^49 - 16 * q^50 + 2 * q^54 + 4 * q^55 - 18 * q^56 - 32 * q^59 - 8 * q^60 - 12 * q^61 - 26 * q^64 + 32 * q^65 - 4 * q^66 + 8 * q^69 + 10 * q^70 + 12 * q^71 + 88 * q^74 + 8 * q^75 + 4 * q^76 - 24 * q^79 + 46 * q^80 + 6 * q^81 - 10 * q^84 + 32 * q^85 - 8 * q^86 - 28 * q^89 + 12 * q^90 + 12 * q^91 + 32 * q^94 + 4 * q^95 - 58 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			2.70928i			1.91575i	0.287190	+	0.957873i	$0.407279\pi$
$2$			2.70928i			1.91575i	−0.287190	+	0.957873i	$0.592721\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−5.34017			−2.67009
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$6$	−2.70928			−1.10606
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	9.04945i		−	3.19946i
$9$	−1.00000			−0.333333
$10$	−1.46081	+	5.87936i	−0.461949	+	1.85922i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		−	5.34017i		−	1.54158i
$13$			0.921622i			0.255612i	0.991799	+	0.127806i	$0.0407935\pi$
$13$			0.921622i			0.255612i	−0.991799	+	0.127806i	$0.959207\pi$
$14$	2.70928			0.724084
$15$	−0.539189	+	2.17009i	−0.139218	+	0.560314i
$16$	13.8371			3.45928
$17$		−	1.07838i		−	0.261545i	−0.991412	−	0.130773i	$-0.958254\pi$
$17$		−	1.07838i		−	0.261545i	0.991412	−	0.130773i	$-0.0417457\pi$
$18$		−	2.70928i		−	0.638582i
$19$	−3.07838			−0.706228			−0.353114	−	0.935580i	$-0.614877\pi$
$19$	−3.07838			−0.706228			−0.353114	+	0.935580i	$0.614877\pi$
$20$	−11.5886	−	2.87936i	−2.59130	−	0.643845i
$21$	1.00000			0.218218
$22$			5.41855i			1.15524i
$23$			2.34017i			0.487960i	0.969780	+	0.243980i	$0.0784531\pi$
$23$			2.34017i			0.487960i	−0.969780	+	0.243980i	$0.921547\pi$
$24$	9.04945			1.84721
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$	−2.49693			−0.489688
$27$		−	1.00000i		−	0.192450i
$28$			5.34017i			1.00920i
$29$	6.68035			1.24051			0.620255	−	0.784401i	$-0.287029\pi$
$29$	6.68035			1.24051			0.620255	+	0.784401i	$0.287029\pi$
$30$	−5.87936	−	1.46081i	−1.07342	−	0.266706i
$31$	−7.75872			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$31$	−7.75872			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$32$			19.3896i			3.42763i
$33$			2.00000i			0.348155i
$34$	2.92162			0.501054
$35$	0.539189	−	2.17009i	0.0911396	−	0.366812i
$36$	5.34017			0.890029
$37$		−	10.8371i		−	1.78161i	−0.454387	−	0.890804i	$-0.650142\pi$
$37$		−	10.8371i		−	1.78161i	0.454387	−	0.890804i	$-0.349858\pi$
$38$		−	8.34017i		−	1.35295i
$39$	−0.921622			−0.147578
$40$	4.87936	−	19.6381i	0.771495	−	3.10505i
$41$	6.49693			1.01465			0.507325	−	0.861755i	$-0.330634\pi$
$41$	6.49693			1.01465			0.507325	+	0.861755i	$0.330634\pi$
$42$			2.70928i			0.418050i
$43$		−	6.52359i		−	0.994838i	−0.867510	−	0.497419i	$-0.834281\pi$
$43$		−	6.52359i		−	0.994838i	0.867510	−	0.497419i	$-0.165719\pi$
$44$	−10.6803			−1.61012
$45$	−2.17009	−	0.539189i	−0.323497	−	0.0803775i
$46$	−6.34017			−0.934808
$47$		−	4.68035i		−	0.682699i	−0.939937	−	0.341349i	$-0.889116\pi$
$47$		−	4.68035i		−	0.682699i	0.939937	−	0.341349i	$-0.110884\pi$
$48$			13.8371i			1.99721i
$49$	−1.00000			−0.142857
$50$	−6.34017	+	11.9711i	−0.896636	+	1.69297i
$51$	1.07838			0.151003
$52$		−	4.92162i		−	0.682506i
$53$			3.75872i			0.516300i	0.966105	+	0.258150i	$0.0831129\pi$
$53$			3.75872i			0.516300i	−0.966105	+	0.258150i	$0.916887\pi$
$54$	2.70928			0.368686
$55$	4.34017	+	1.07838i	0.585229	+	0.145408i
$56$	−9.04945			−1.20928
$57$		−	3.07838i		−	0.407741i
$58$			18.0989i			2.37650i
$59$	−10.5236			−1.37005			−0.685027	−	0.728517i	$-0.740210\pi$
$59$	−10.5236			−1.37005			−0.685027	+	0.728517i	$0.740210\pi$
$60$	2.87936	−	11.5886i	0.371724	−	1.49609i
$61$	−4.15676			−0.532218			−0.266109	−	0.963943i	$-0.585738\pi$
$61$	−4.15676			−0.532218			−0.266109	+	0.963943i	$0.585738\pi$
$62$		−	21.0205i		−	2.66961i
$63$			1.00000i			0.125988i
$64$	−24.8576			−3.10720
$65$	−0.496928	+	2.00000i	−0.0616364	+	0.248069i
$66$	−5.41855			−0.666977
$67$		−	4.68035i		−	0.571795i	−0.958260	−	0.285898i	$-0.907708\pi$
$67$		−	4.68035i		−	0.571795i	0.958260	−	0.285898i	$-0.0922917\pi$
$68$			5.75872i			0.698348i
$69$	−2.34017			−0.281724
$70$	5.87936	+	1.46081i	0.702718	+	0.174600i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			9.04945i			1.06649i
$73$			7.07838i			0.828461i	0.910172	+	0.414231i	$0.135949\pi$
$73$			7.07838i			0.828461i	−0.910172	+	0.414231i	$0.864051\pi$
$74$	29.3607			3.41311
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$	16.4391			1.88569
$77$		−	2.00000i		−	0.227921i
$78$		−	2.49693i		−	0.282721i
$79$	−6.15676			−0.692689			−0.346345	−	0.938107i	$-0.612577\pi$
$79$	−6.15676			−0.692689			−0.346345	+	0.938107i	$0.612577\pi$
$80$	30.0277	+	7.46081i	3.35720	+	0.834144i
$81$	1.00000			0.111111
$82$			17.6020i			1.94381i
$83$			6.83710i			0.750469i	0.926930	+	0.375235i	$0.122438\pi$
$83$			6.83710i			0.750469i	−0.926930	+	0.375235i	$0.877562\pi$
$84$	−5.34017			−0.582661
$85$	0.581449	−	2.34017i	0.0630670	−	0.253827i
$86$	17.6742			1.90586
$87$			6.68035i			0.716208i
$88$		−	18.0989i		−	1.92935i
$89$	−8.34017			−0.884057			−0.442028	−	0.897001i	$-0.645741\pi$
$89$	−8.34017			−0.884057			−0.442028	+	0.897001i	$0.645741\pi$
$90$	1.46081	−	5.87936i	0.153983	−	0.619739i
$91$	0.921622			0.0966123
$92$		−	12.4969i		−	1.30289i
$93$		−	7.75872i		−	0.804542i
$94$	12.6803			1.30788
$95$	−6.68035	−	1.65983i	−0.685389	−	0.170295i
$96$	−19.3896			−1.97894
$97$			8.43907i			0.856858i	0.903576	+	0.428429i	$0.140933\pi$
$97$			8.43907i			0.856858i	−0.903576	+	0.428429i	$0.859067\pi$
$98$		−	2.70928i		−	0.273678i
$99$	−2.00000			−0.201008
$100$	−23.5958	−	12.4969i	−2.35958	−	1.24969i
$101$	−5.81658			−0.578772			−0.289386	−	0.957213i	$-0.593451\pi$
$101$	−5.81658			−0.578772			−0.289386	+	0.957213i	$0.593451\pi$
$102$			2.92162i			0.289284i
$103$		−	2.15676i		−	0.212511i	−0.994339	−	0.106256i	$-0.966114\pi$
$103$		−	2.15676i		−	0.212511i	0.994339	−	0.106256i	$-0.0338862\pi$
$104$	8.34017			0.817821
$105$	2.17009	+	0.539189i	0.211779	+	0.0526194i
$106$	−10.1834			−0.989101
$107$			16.4969i			1.59482i	0.603439	+	0.797409i	$0.293797\pi$
$107$			16.4969i			1.59482i	−0.603439	+	0.797409i	$0.706203\pi$
$108$			5.34017i			0.513858i
$109$	12.8371			1.22957			0.614786	−	0.788694i	$-0.289243\pi$
$109$	12.8371			1.22957			0.614786	+	0.788694i	$0.289243\pi$
$110$	−2.92162	+	11.7587i	−0.278566	+	1.12115i
$111$	10.8371			1.02861
$112$		−	13.8371i		−	1.30748i
$113$		−	5.23513i		−	0.492480i	−0.969209	−	0.246240i	$-0.920805\pi$
$113$		−	5.23513i		−	0.492480i	0.969209	−	0.246240i	$-0.0791951\pi$
$114$	8.34017			0.781129
$115$	−1.26180	+	5.07838i	−0.117663	+	0.473561i
$116$	−35.6742			−3.31227
$117$		−	0.921622i		−	0.0852040i
$118$		−	28.5113i		−	2.62468i
$119$	−1.07838			−0.0988547
$120$	19.6381	+	4.87936i	1.79270	+	0.445423i
$121$	−7.00000			−0.636364
$122$		−	11.2618i		−	1.01960i
$123$			6.49693i			0.585808i
$124$	41.4329			3.72079
$125$	8.32684	+	7.46081i	0.744775	+	0.667315i
$126$	−2.70928			−0.241361
$127$		−	1.84324i		−	0.163562i	−0.996650	−	0.0817808i	$-0.973939\pi$
$127$		−	1.84324i		−	0.163562i	0.996650	−	0.0817808i	$-0.0260607\pi$
$128$		−	28.5669i		−	2.52498i
$129$	6.52359			0.574370
$130$	−5.41855	−	1.34632i	−0.475238	−	0.118080i
$131$	1.47641			0.128995			0.0644973	−	0.997918i	$-0.479456\pi$
$131$	1.47641			0.128995			0.0644973	+	0.997918i	$0.479456\pi$
$132$		−	10.6803i		−	0.929605i
$133$			3.07838i			0.266929i
$134$	12.6803			1.09542
$135$	0.539189	−	2.17009i	0.0464060	−	0.186771i
$136$	−9.75872			−0.836804
$137$		−	4.43907i		−	0.379255i	−0.981856	−	0.189628i	$-0.939272\pi$
$137$		−	4.43907i		−	0.379255i	0.981856	−	0.189628i	$-0.0607281\pi$
$138$		−	6.34017i		−	0.539711i
$139$	−13.6020			−1.15370			−0.576852	−	0.816849i	$-0.695719\pi$
$139$	−13.6020			−1.15370			−0.576852	+	0.816849i	$0.695719\pi$
$140$	−2.87936	+	11.5886i	−0.243350	+	0.979419i
$141$	4.68035			0.394156
$142$			5.41855i			0.454715i
$143$			1.84324i			0.154140i
$144$	−13.8371			−1.15309
$145$	14.4969	+	3.60197i	1.20390	+	0.299127i
$146$	−19.1773			−1.58712
$147$		−	1.00000i		−	0.0824786i
$148$			57.8720i			4.75705i
$149$	−15.6742			−1.28408			−0.642040	−	0.766671i	$-0.721912\pi$
$149$	−15.6742			−1.28408			−0.642040	+	0.766671i	$0.721912\pi$
$150$	−11.9711	−	6.34017i	−0.977434	−	0.517673i
$151$	5.84324			0.475516			0.237758	−	0.971324i	$-0.423587\pi$
$151$	5.84324			0.475516			0.237758	+	0.971324i	$0.423587\pi$
$152$			27.8576i			2.25955i
$153$			1.07838i			0.0871817i
$154$	5.41855			0.436639
$155$	−16.8371	−	4.18342i	−1.35239	−	0.336020i
$156$	4.92162			0.394045
$157$		−	4.92162i		−	0.392788i	−0.980525	−	0.196394i	$-0.937077\pi$
$157$		−	4.92162i		−	0.392788i	0.980525	−	0.196394i	$-0.0629232\pi$
$158$		−	16.6803i		−	1.32702i
$159$	−3.75872			−0.298086
$160$	−10.4547	+	42.0772i	−0.826514	+	3.32649i
$161$	2.34017			0.184431
$162$			2.70928i			0.212861i
$163$		−	9.84324i		−	0.770982i	−0.922712	−	0.385491i	$-0.874032\pi$
$163$		−	9.84324i		−	0.770982i	0.922712	−	0.385491i	$-0.125968\pi$
$164$	−34.6947			−2.70920
$165$	−1.07838	+	4.34017i	−0.0839516	+	0.337882i
$166$	−18.5236			−1.43771
$167$			19.2039i			1.48605i	0.669266	+	0.743023i	$0.266609\pi$
$167$			19.2039i			1.48605i	−0.669266	+	0.743023i	$0.733391\pi$
$168$		−	9.04945i		−	0.698180i
$169$	12.1506			0.934662
$170$	6.34017	+	1.57531i	0.486269	+	0.120820i
$171$	3.07838			0.235409
$172$			34.8371i			2.65630i
$173$		−	22.4391i		−	1.70601i	−0.521902	−	0.853005i	$-0.674777\pi$
$173$		−	22.4391i		−	1.70601i	0.521902	−	0.853005i	$-0.325223\pi$
$174$	−18.0989			−1.37207
$175$	2.34017	−	4.41855i	0.176900	−	0.334011i
$176$	27.6742			2.08602
$177$		−	10.5236i		−	0.791001i
$178$		−	22.5958i		−	1.69363i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	11.5886	+	2.87936i	0.863766	+	0.214615i
$181$	−8.52359			−0.633553			−0.316777	−	0.948500i	$-0.602601\pi$
$181$	−8.52359			−0.633553			−0.316777	+	0.948500i	$0.602601\pi$
$182$			2.49693i			0.185085i
$183$		−	4.15676i		−	0.307276i
$184$	21.1773			1.56121
$185$	5.84324	−	23.5174i	0.429604	−	1.72904i
$186$	21.0205			1.54130
$187$		−	2.15676i		−	0.157718i
$188$			24.9939i			1.82286i
$189$	−1.00000			−0.0727393
$190$	4.49693	−	18.0989i	0.326241	−	1.31303i
$191$	15.3607			1.11146			0.555730	−	0.831363i	$-0.312439\pi$
$191$	15.3607			1.11146			0.555730	+	0.831363i	$0.312439\pi$
$192$		−	24.8576i		−	1.79394i
$193$			8.36683i			0.602258i	0.953583	+	0.301129i	$0.0973635\pi$
$193$			8.36683i			0.602258i	−0.953583	+	0.301129i	$0.902637\pi$
$194$	−22.8638			−1.64152
$195$	−2.00000	−	0.496928i	−0.143223	−	0.0355858i
$196$	5.34017			0.381441
$197$			11.7587i			0.837774i	0.908038	+	0.418887i	$0.137580\pi$
$197$			11.7587i			0.837774i	−0.908038	+	0.418887i	$0.862420\pi$
$198$		−	5.41855i		−	0.385080i
$199$	22.5958			1.60178			0.800888	−	0.598814i	$-0.204361\pi$
$199$	22.5958			1.60178			0.800888	+	0.598814i	$0.204361\pi$
$200$	21.1773	−	39.9854i	1.49746	−	2.82740i
$201$	4.68035			0.330126
$202$		−	15.7587i		−	1.10878i
$203$		−	6.68035i		−	0.468868i
$204$	−5.75872			−0.403191
$205$	14.0989	+	3.50307i	0.984710	+	0.244665i
$206$	5.84324			0.407118
$207$		−	2.34017i		−	0.162653i
$208$			12.7526i			0.884232i
$209$	−6.15676			−0.425872
$210$	−1.46081	+	5.87936i	−0.100806	+	0.405715i
$211$	−13.6742			−0.941371			−0.470685	−	0.882301i	$-0.655993\pi$
$211$	−13.6742			−0.941371			−0.470685	+	0.882301i	$0.655993\pi$
$212$		−	20.0722i		−	1.37857i
$213$			2.00000i			0.137038i
$214$	−44.6947			−3.05527
$215$	3.51745	−	14.1568i	0.239888	−	0.965483i
$216$	−9.04945			−0.615737
$217$			7.75872i			0.526696i
$218$			34.7792i			2.35555i
$219$	−7.07838			−0.478312
$220$	−23.1773	−	5.75872i	−1.56261	−	0.388253i
$221$	0.993857			0.0668541
$222$			29.3607i			1.97056i
$223$		−	21.6742i		−	1.45141i	−0.688005	−	0.725706i	$-0.741513\pi$
$223$		−	21.6742i		−	1.45141i	0.688005	−	0.725706i	$-0.258487\pi$
$224$	19.3896			1.29552
$225$	−4.41855	−	2.34017i	−0.294570	−	0.156012i
$226$	14.1834			0.943467
$227$			11.5174i			0.764440i	0.924071	+	0.382220i	$0.124840\pi$
$227$			11.5174i			0.764440i	−0.924071	+	0.382220i	$0.875160\pi$
$228$			16.4391i			1.08870i
$229$	−12.8371			−0.848300			−0.424150	−	0.905592i	$-0.639427\pi$
$229$	−12.8371			−0.848300			−0.424150	+	0.905592i	$0.639427\pi$
$230$	−13.7587	−	3.41855i	−0.907223	−	0.225413i
$231$	2.00000			0.131590
$232$		−	60.4534i		−	3.96896i
$233$		−	6.76487i		−	0.443181i	−0.975140	−	0.221591i	$-0.928875\pi$
$233$		−	6.76487i		−	0.443181i	0.975140	−	0.221591i	$-0.0711248\pi$
$234$	2.49693			0.163229
$235$	2.52359	−	10.1568i	0.164621	−	0.662554i
$236$	56.1978			3.65816
$237$		−	6.15676i		−	0.399924i
$238$		−	2.92162i		−	0.189381i
$239$	23.3607			1.51108			0.755539	−	0.655104i	$-0.227375\pi$
$239$	23.3607			1.51108			0.755539	+	0.655104i	$0.227375\pi$
$240$	−7.46081	+	30.0277i	−0.481593	+	1.93828i
$241$	−14.6803			−0.945644			−0.472822	−	0.881158i	$-0.656765\pi$
$241$	−14.6803			−0.945644			−0.472822	+	0.881158i	$0.656765\pi$
$242$		−	18.9649i		−	1.21911i
$243$			1.00000i			0.0641500i
$244$	22.1978			1.42107
$245$	−2.17009	−	0.539189i	−0.138642	−	0.0344475i
$246$	−17.6020			−1.12226
$247$		−	2.83710i		−	0.180520i
$248$			70.2122i			4.45848i
$249$	−6.83710			−0.433284
$250$	−20.2134	+	22.5597i	−1.27841	+	1.42680i
$251$	9.16290			0.578357			0.289179	−	0.957275i	$-0.406618\pi$
$251$	9.16290			0.578357			0.289179	+	0.957275i	$0.406618\pi$
$252$		−	5.34017i		−	0.336399i
$253$			4.68035i			0.294251i
$254$	4.99386			0.313342
$255$	2.34017	+	0.581449i	0.146547	+	0.0364118i
$256$	27.6803			1.73002
$257$			5.07838i			0.316781i	0.987377	+	0.158390i	$0.0506304\pi$
$257$			5.07838i			0.316781i	−0.987377	+	0.158390i	$0.949370\pi$
$258$			17.6742i			1.10035i
$259$	−10.8371			−0.673385
$260$	2.65368	−	10.6803i	0.164574	−	0.662367i
$261$	−6.68035			−0.413503
$262$			4.00000i			0.247121i
$263$			5.65983i			0.349000i	0.984657	+	0.174500i	$0.0558309\pi$
$263$			5.65983i			0.349000i	−0.984657	+	0.174500i	$0.944169\pi$
$264$	18.0989			1.11391
$265$	−2.02666	+	8.15676i	−0.124497	+	0.501066i
$266$	−8.34017			−0.511369
$267$		−	8.34017i		−	0.510410i
$268$			24.9939i			1.52674i
$269$	27.8576			1.69851			0.849255	−	0.527984i	$-0.177052\pi$
$269$	27.8576			1.69851			0.849255	+	0.527984i	$0.177052\pi$
$270$	5.87936	+	1.46081i	0.357807	+	0.0889021i
$271$	25.1194			1.52590			0.762948	−	0.646460i	$-0.223751\pi$
$271$	25.1194			1.52590			0.762948	+	0.646460i	$0.223751\pi$
$272$		−	14.9216i		−	0.904756i
$273$			0.921622i			0.0557791i
$274$	12.0267			0.726557
$275$	8.83710	+	4.68035i	0.532897	+	0.282235i
$276$	12.4969			0.752227
$277$			28.1978i			1.69424i	0.531401	+	0.847121i	$0.321666\pi$
$277$			28.1978i			1.69424i	−0.531401	+	0.847121i	$0.678334\pi$
$278$		−	36.8515i		−	2.21020i
$279$	7.75872			0.464503
$280$	−19.6381	−	4.87936i	−1.17360	−	0.291598i
$281$	−20.3545			−1.21425			−0.607125	−	0.794606i	$-0.707677\pi$
$281$	−20.3545			−1.21425			−0.607125	+	0.794606i	$0.707677\pi$
$282$			12.6803i			0.755104i
$283$			23.5174i			1.39797i	0.715138	+	0.698984i	$0.246364\pi$
$283$			23.5174i			1.39797i	−0.715138	+	0.698984i	$0.753636\pi$
$284$	−10.6803			−0.633762
$285$	1.65983	−	6.68035i	0.0983197	−	0.395710i
$286$	−4.99386			−0.295293
$287$		−	6.49693i		−	0.383502i
$288$		−	19.3896i		−	1.14254i
$289$	15.8371			0.931594
$290$	−9.75872	+	39.2762i	−0.573052	+	2.30638i
$291$	−8.43907			−0.494707
$292$		−	37.7998i		−	2.21206i
$293$		−	2.92162i		−	0.170683i	−0.996352	−	0.0853415i	$-0.972802\pi$
$293$		−	2.92162i		−	0.170683i	0.996352	−	0.0853415i	$-0.0271981\pi$
$294$	2.70928			0.158008
$295$	−22.8371	−	5.67420i	−1.32963	−	0.330365i
$296$	−98.0698			−5.70019
$297$		−	2.00000i		−	0.116052i
$298$		−	42.4657i		−	2.45997i
$299$	−2.15676			−0.124728
$300$	12.4969	−	23.5958i	0.721511	−	1.36231i
$301$	−6.52359			−0.376014
$302$			15.8310i			0.910969i
$303$		−	5.81658i		−	0.334154i
$304$	−42.5958			−2.44304
$305$	−9.02052	−	2.24128i	−0.516513	−	0.128335i
$306$	−2.92162			−0.167018
$307$			10.4703i			0.597570i	0.954321	+	0.298785i	$0.0965813\pi$
$307$			10.4703i			0.597570i	−0.954321	+	0.298785i	$0.903419\pi$
$308$			10.6803i			0.608569i
$309$	2.15676			0.122694
$310$	11.3340	−	45.6163i	0.643730	−	2.59083i
$311$	23.8310			1.35133			0.675665	−	0.737209i	$-0.263857\pi$
$311$	23.8310			1.35133			0.675665	+	0.737209i	$0.263857\pi$
$312$			8.34017i			0.472169i
$313$			32.7526i			1.85129i	0.378399	+	0.925643i	$0.376475\pi$
$313$			32.7526i			1.85129i	−0.378399	+	0.925643i	$0.623525\pi$
$314$	13.3340			0.752483
$315$	−0.539189	+	2.17009i	−0.0303799	+	0.122271i
$316$	32.8781			1.84954
$317$			17.9155i			1.00623i	0.864218	+	0.503117i	$0.167813\pi$
$317$			17.9155i			1.00623i	−0.864218	+	0.503117i	$0.832187\pi$
$318$		−	10.1834i		−	0.571058i
$319$	13.3607			0.748055
$320$	−53.9432	−	13.4030i	−3.01552	−	0.749248i
$321$	−16.4969			−0.920769
$322$			6.34017i			0.353324i
$323$			3.31965i			0.184710i
$324$	−5.34017			−0.296676
$325$	−2.15676	+	4.07223i	−0.119635	+	0.225887i
$326$	26.6681			1.47701
$327$			12.8371i			0.709893i
$328$		−	58.7936i		−	3.24633i
$329$	−4.68035			−0.258036
$330$	−11.7587	−	2.92162i	−0.647296	−	0.160830i
$331$	−1.36069			−0.0747904			−0.0373952	−	0.999301i	$-0.511906\pi$
$331$	−1.36069			−0.0747904			−0.0373952	+	0.999301i	$0.511906\pi$
$332$		−	36.5113i		−	2.00382i
$333$			10.8371i			0.593870i
$334$	−52.0288			−2.84689
$335$	2.52359	−	10.1568i	0.137878	−	0.554923i
$336$	13.8371			0.754876
$337$			25.3607i			1.38148i	0.723101	+	0.690742i	$0.242716\pi$
$337$			25.3607i			1.38148i	−0.723101	+	0.690742i	$0.757284\pi$
$338$			32.9194i			1.79058i
$339$	5.23513			0.284333
$340$	−3.10504	+	12.4969i	−0.168394	+	0.677741i
$341$	−15.5174			−0.840317
$342$			8.34017i			0.450985i
$343$			1.00000i			0.0539949i
$344$	−59.0349			−3.18295
$345$	−5.07838	−	1.26180i	−0.273411	−	0.0679328i
$346$	60.7936			3.26829
$347$		−	16.8638i		−	0.905294i	−0.891690	−	0.452647i	$-0.850480\pi$
$347$		−	16.8638i		−	0.905294i	0.891690	−	0.452647i	$-0.149520\pi$
$348$		−	35.6742i		−	1.91234i
$349$	−9.51745			−0.509457			−0.254729	−	0.967013i	$-0.581986\pi$
$349$	−9.51745			−0.509457			−0.254729	+	0.967013i	$0.581986\pi$
$350$	11.9711	+	6.34017i	0.639881	+	0.338897i
$351$	0.921622			0.0491926
$352$			38.7792i			2.06694i
$353$		−	35.7998i		−	1.90543i	−0.303867	−	0.952715i	$-0.598278\pi$
$353$		−	35.7998i		−	1.90543i	0.303867	−	0.952715i	$-0.401722\pi$
$354$	28.5113			1.51536
$355$	4.34017	+	1.07838i	0.230352	+	0.0572343i
$356$	44.5380			2.36051
$357$		−	1.07838i		−	0.0570738i
$358$		−	27.0928i		−	1.43190i
$359$	22.3135			1.17766			0.588831	−	0.808256i	$-0.299588\pi$
$359$	22.3135			1.17766			0.588831	+	0.808256i	$0.299588\pi$
$360$	−4.87936	+	19.6381i	−0.257165	+	1.03502i
$361$	−9.52359			−0.501242
$362$		−	23.0928i		−	1.21373i
$363$		−	7.00000i		−	0.367405i
$364$	−4.92162			−0.257963
$365$	−3.81658	+	15.3607i	−0.199769	+	0.804015i
$366$	11.2618			0.588663
$367$		−	20.3135i		−	1.06036i	−0.847886	−	0.530178i	$-0.822125\pi$
$367$		−	20.3135i		−	1.06036i	0.847886	−	0.530178i	$-0.177875\pi$
$368$			32.3812i			1.68799i
$369$	−6.49693			−0.338217
$370$	63.7152	+	15.8310i	3.31240	+	0.823012i
$371$	3.75872			0.195143
$372$			41.4329i			2.14820i
$373$		−	16.0000i		−	0.828449i	−0.910175	−	0.414224i	$-0.864053\pi$
$373$		−	16.0000i		−	0.828449i	0.910175	−	0.414224i	$-0.135947\pi$
$374$	5.84324			0.302147
$375$	−7.46081	+	8.32684i	−0.385275	+	0.429996i
$376$	−42.3545			−2.18427
$377$			6.15676i			0.317089i
$378$		−	2.70928i		−	0.139350i
$379$	−6.15676			−0.316251			−0.158126	−	0.987419i	$-0.550545\pi$
$379$	−6.15676			−0.316251			−0.158126	+	0.987419i	$0.550545\pi$
$380$	35.6742	+	8.86376i	1.83005	+	0.454701i
$381$	1.84324			0.0944323
$382$			41.6163i			2.12928i
$383$			26.8371i			1.37131i	0.727926	+	0.685656i	$0.240485\pi$
$383$			26.8371i			1.37131i	−0.727926	+	0.685656i	$0.759515\pi$
$384$	28.5669			1.45780
$385$	1.07838	−	4.34017i	0.0549592	−	0.221196i
$386$	−22.6681			−1.15377
$387$			6.52359i			0.331613i
$388$		−	45.0661i		−	2.28788i
$389$	5.63317			0.285613			0.142806	−	0.989751i	$-0.454387\pi$
$389$	5.63317			0.285613			0.142806	+	0.989751i	$0.454387\pi$
$390$	1.34632	−	5.41855i	0.0681734	−	0.274379i
$391$	2.52359			0.127623
$392$			9.04945i			0.457066i
$393$			1.47641i			0.0744750i
$394$	−31.8576			−1.60496
$395$	−13.3607	−	3.31965i	−0.672249	−	0.167030i
$396$	10.6803			0.536708
$397$		−	37.7998i		−	1.89712i	−0.316604	−	0.948558i	$-0.602543\pi$
$397$		−	37.7998i		−	1.89712i	0.316604	−	0.948558i	$-0.397457\pi$
$398$			61.2183i			3.06860i
$399$	−3.07838			−0.154112
$400$	61.1399	+	32.3812i	3.05700	+	1.61906i
$401$	−13.6332			−0.680808			−0.340404	−	0.940279i	$-0.610564\pi$
$401$	−13.6332			−0.680808			−0.340404	+	0.940279i	$0.610564\pi$
$402$			12.6803i			0.632438i
$403$		−	7.15061i		−	0.356197i
$404$	31.0616			1.54537
$405$	2.17009	+	0.539189i	0.107832	+	0.0267925i
$406$	18.0989			0.898233
$407$		−	21.6742i		−	1.07435i
$408$		−	9.75872i		−	0.483129i
$409$	−12.3545			−0.610893			−0.305447	−	0.952209i	$-0.598806\pi$
$409$	−12.3545			−0.610893			−0.305447	+	0.952209i	$0.598806\pi$
$410$	−9.49079	+	38.1978i	−0.468716	+	1.88645i
$411$	4.43907			0.218963
$412$			11.5174i			0.567424i
$413$			10.5236i			0.517832i
$414$	6.34017			0.311603
$415$	−3.68649	+	14.8371i	−0.180963	+	0.728325i
$416$	−17.8699			−0.876144
$417$		−	13.6020i		−	0.666091i
$418$		−	16.6803i		−	0.815862i
$419$	−28.9939			−1.41644			−0.708221	−	0.705991i	$-0.750502\pi$
$419$	−28.9939			−1.41644			−0.708221	+	0.705991i	$0.750502\pi$
$420$	−11.5886	−	2.87936i	−0.565468	−	0.140498i
$421$	−15.1629			−0.738994			−0.369497	−	0.929232i	$-0.620470\pi$
$421$	−15.1629			−0.738994			−0.369497	+	0.929232i	$0.620470\pi$
$422$		−	37.0472i		−	1.80343i
$423$			4.68035i			0.227566i
$424$	34.0144			1.65188
$425$	2.52359	−	4.76487i	0.122412	−	0.231130i
$426$	−5.41855			−0.262530
$427$			4.15676i			0.201159i
$428$		−	88.0965i		−	4.25830i
$429$	−1.84324			−0.0889927
$430$	38.3545	+	9.52973i	1.84962	+	0.459565i
$431$	−10.3135			−0.496784			−0.248392	−	0.968660i	$-0.579902\pi$
$431$	−10.3135			−0.496784			−0.248392	+	0.968660i	$0.579902\pi$
$432$		−	13.8371i		−	0.665738i
$433$			20.4391i			0.982239i	0.871092	+	0.491120i	$0.163412\pi$
$433$			20.4391i			0.982239i	−0.871092	+	0.491120i	$0.836588\pi$
$434$	−21.0205			−1.00902
$435$	−3.60197	+	14.4969i	−0.172701	+	0.695075i
$436$	−68.5523			−3.28306
$437$		−	7.20394i		−	0.344611i
$438$		−	19.1773i		−	0.916326i
$439$	16.9216			0.807625			0.403812	−	0.914842i	$-0.367685\pi$
$439$	16.9216			0.807625			0.403812	+	0.914842i	$0.367685\pi$
$440$	9.75872	−	39.2762i	0.465229	−	1.87242i
$441$	1.00000			0.0476190
$442$			2.69263i			0.128075i
$443$		−	12.8104i		−	0.608642i	−0.952569	−	0.304321i	$-0.901570\pi$
$443$		−	12.8104i		−	0.608642i	0.952569	−	0.304321i	$-0.0984296\pi$
$444$	−57.8720			−2.74648
$445$	−18.0989	−	4.49693i	−0.857970	−	0.213175i
$446$	58.7214			2.78054
$447$		−	15.6742i		−	0.741364i
$448$			24.8576i			1.17441i
$449$	14.6270			0.690292			0.345146	−	0.938549i	$-0.387829\pi$
$449$	14.6270			0.690292			0.345146	+	0.938549i	$0.387829\pi$
$450$	6.34017	−	11.9711i	0.298879	−	0.564322i
$451$	12.9939			0.611857
$452$			27.9565i			1.31496i
$453$			5.84324i			0.274540i
$454$	−31.2039			−1.46447
$455$	2.00000	+	0.496928i	0.0937614	+	0.0232964i
$456$	−27.8576			−1.30455
$457$		−	14.1568i		−	0.662225i	−0.943591	−	0.331113i	$-0.892576\pi$
$457$		−	14.1568i		−	0.662225i	0.943591	−	0.331113i	$-0.107424\pi$
$458$		−	34.7792i		−	1.62513i
$459$	−1.07838			−0.0503344
$460$	6.73820	−	27.1194i	0.314170	−	1.26445i
$461$	0.340173			0.0158434			0.00792172	−	0.999969i	$-0.497478\pi$
$461$	0.340173			0.0158434			0.00792172	+	0.999969i	$0.497478\pi$
$462$			5.41855i			0.252094i
$463$		−	9.84324i		−	0.457454i	−0.973491	−	0.228727i	$-0.926544\pi$
$463$		−	9.84324i		−	0.457454i	0.973491	−	0.228727i	$-0.0734564\pi$
$464$	92.4366			4.29126
$465$	4.18342	−	16.8371i	0.194001	−	0.780802i
$466$	18.3279			0.849023
$467$			11.5174i			0.532964i	0.963840	+	0.266482i	$0.0858613\pi$
$467$			11.5174i			0.532964i	−0.963840	+	0.266482i	$0.914139\pi$
$468$			4.92162i			0.227502i
$469$	−4.68035			−0.216118
$470$	27.5174	+	6.83710i	1.26929	+	0.315372i
$471$	4.92162			0.226776
$472$			95.2327i			4.38344i
$473$		−	13.0472i		−	0.599910i
$474$	16.6803			0.766154
$475$	−13.6020	−	7.20394i	−0.624101	−	0.330539i
$476$	5.75872			0.263951
$477$		−	3.75872i		−	0.172100i
$478$			63.2905i			2.89484i
$479$	19.5174			0.891775			0.445887	−	0.895089i	$-0.352888\pi$
$479$	19.5174			0.891775			0.445887	+	0.895089i	$0.352888\pi$
$480$	−42.0772	−	10.4547i	−1.92055	−	0.477188i
$481$	9.98771			0.455401
$482$		−	39.7731i		−	1.81162i
$483$			2.34017i			0.106482i
$484$	37.3812			1.69915
$485$	−4.55025	+	18.3135i	−0.206616	+	0.831574i
$486$	−2.70928			−0.122895
$487$		−	23.1506i		−	1.04905i	−0.851394	−	0.524527i	$-0.824242\pi$
$487$		−	23.1506i		−	1.04905i	0.851394	−	0.524527i	$-0.175758\pi$
$488$			37.6163i			1.70281i
$489$	9.84324			0.445127
$490$	1.46081	−	5.87936i	0.0659927	−	0.265602i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$		−	34.6947i		−	1.56416i
$493$		−	7.20394i		−	0.324449i
$494$	7.68649			0.345831
$495$	−4.34017	−	1.07838i	−0.195076	−	0.0484695i
$496$	−107.358			−4.82053
$497$		−	2.00000i		−	0.0897123i
$498$		−	18.5236i		−	0.830062i
$499$	−27.2039			−1.21782			−0.608908	−	0.793241i	$-0.708392\pi$
$499$	−27.2039			−1.21782			−0.608908	+	0.793241i	$0.708392\pi$
$500$	−44.4668	−	39.8420i	−1.98861	−	1.78179i
$501$	−19.2039			−0.857969
$502$			24.8248i			1.10799i
$503$		−	18.8371i		−	0.839905i	−0.907546	−	0.419952i	$-0.862047\pi$
$503$		−	18.8371i		−	0.839905i	0.907546	−	0.419952i	$-0.137953\pi$
$504$	9.04945			0.403094
$505$	−12.6225	−	3.13624i	−0.561693	−	0.139561i
$506$	−12.6803			−0.563710
$507$			12.1506i			0.539628i
$508$			9.84324i			0.436723i
$509$	−6.81044			−0.301867			−0.150934	−	0.988544i	$-0.548228\pi$
$509$	−6.81044			−0.301867			−0.150934	+	0.988544i	$0.548228\pi$
$510$	−1.57531	+	6.34017i	−0.0697557	+	0.280748i
$511$	7.07838			0.313129
$512$			17.8599i			0.789303i
$513$			3.07838i			0.135914i
$514$	−13.7587			−0.606871
$515$	1.16290	−	4.68035i	0.0512434	−	0.206241i
$516$	−34.8371			−1.53362
$517$		−	9.36069i		−	0.411683i
$518$		−	29.3607i		−	1.29003i
$519$	22.4391			0.984966
$520$	18.0989	+	4.49693i	0.793689	+	0.197203i
$521$	−25.8166			−1.13105			−0.565523	−	0.824733i	$-0.691325\pi$
$521$	−25.8166			−1.13105			−0.565523	+	0.824733i	$0.691325\pi$
$522$		−	18.0989i		−	0.792167i
$523$			4.00000i			0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$			4.00000i			0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	−7.88428			−0.344426
$525$	4.41855	+	2.34017i	0.192841	+	0.102134i
$526$	−15.3340			−0.668595
$527$			8.36683i			0.364465i
$528$			27.6742i			1.20437i
$529$	17.5236			0.761895
$530$	−22.0989	−	5.49079i	−0.959915	−	0.238504i
$531$	10.5236			0.456685
$532$		−	16.4391i		−	0.712724i
$533$			5.98771i			0.259357i
$534$	22.5958			0.977817
$535$	−8.89496	+	35.7998i	−0.384563	+	1.54776i
$536$	−42.3545			−1.82944
$537$		−	10.0000i		−	0.431532i
$538$			75.4740i			3.25391i
$539$	−2.00000			−0.0861461
$540$	−2.87936	+	11.5886i	−0.123908	+	0.498696i
$541$	25.8843			1.11285			0.556426	−	0.830897i	$-0.312172\pi$
$541$	25.8843			1.11285			0.556426	+	0.830897i	$0.312172\pi$
$542$			68.0554i			2.92323i
$543$		−	8.52359i		−	0.365782i
$544$	20.9093			0.896480
$545$	27.8576	+	6.92162i	1.19329	+	0.296490i
$546$	−2.49693			−0.106859
$547$		−	11.3197i		−	0.483993i	−0.970277	−	0.241997i	$-0.922198\pi$
$547$		−	11.3197i		−	0.483993i	0.970277	−	0.241997i	$-0.0778023\pi$
$548$			23.7054i			1.01264i
$549$	4.15676			0.177406
$550$	−12.6803	+	23.9421i	−0.540692	+	1.02090i
$551$	−20.5646			−0.876083
$552$			21.1773i			0.901365i
$553$			6.15676i			0.261812i
$554$	−76.3956			−3.24574
$555$	23.5174	+	5.84324i	0.998260	+	0.248032i
$556$	72.6369			3.08049
$557$			26.6491i			1.12916i	0.825378	+	0.564580i	$0.190962\pi$
$557$			26.6491i			1.12916i	−0.825378	+	0.564580i	$0.809038\pi$
$558$			21.0205i			0.889870i
$559$	6.01229			0.254293
$560$	7.46081	−	30.0277i	0.315277	−	1.26890i
$561$	2.15676			0.0910583
$562$		−	55.1461i		−	2.32620i
$563$			46.3545i			1.95361i	0.214128	+	0.976806i	$0.431309\pi$
$563$			46.3545i			1.95361i	−0.214128	+	0.976806i	$0.568691\pi$
$564$	−24.9939			−1.05243
$565$	2.82273	−	11.3607i	0.118753	−	0.477948i
$566$	−63.7152			−2.67815
$567$		−	1.00000i		−	0.0419961i
$568$		−	18.0989i		−	0.759413i
$569$	14.3668			0.602289			0.301145	−	0.953579i	$-0.402631\pi$
$569$	14.3668			0.602289			0.301145	+	0.953579i	$0.402631\pi$
$570$	18.0989	+	4.49693i	0.758079	+	0.188356i
$571$	38.7214			1.62044			0.810220	−	0.586126i	$-0.199348\pi$
$571$	38.7214			1.62044			0.810220	+	0.586126i	$0.199348\pi$
$572$		−	9.84324i		−	0.411567i
$573$			15.3607i			0.641702i
$574$	17.6020			0.734692
$575$	−5.47641	+	10.3402i	−0.228382	+	0.431215i
$576$	24.8576			1.03573
$577$		−	43.4740i		−	1.80984i	−0.425577	−	0.904922i	$-0.639929\pi$
$577$		−	43.4740i		−	1.80984i	0.425577	−	0.904922i	$-0.360071\pi$
$578$			42.9071i			1.78470i
$579$	−8.36683			−0.347714
$580$	−77.4161	−	19.2351i	−3.21453	−	0.798695i
$581$	6.83710			0.283651
$582$		−	22.8638i		−	0.947733i
$583$			7.51745i			0.311341i
$584$	64.0554			2.65063
$585$	0.496928	−	2.00000i	0.0205455	−	0.0826898i
$586$	7.91548			0.326985
$587$		−	36.0288i		−	1.48707i	−0.668699	−	0.743533i	$-0.733149\pi$
$587$		−	36.0288i		−	1.48707i	0.668699	−	0.743533i	$-0.266851\pi$
$588$			5.34017i			0.220225i
$589$	23.8843			0.984135
$590$	15.3730	−	61.8720i	0.632895	−	2.54723i
$591$	−11.7587			−0.483689
$592$		−	149.954i		−	6.16307i
$593$			31.4863i			1.29299i	0.762920	+	0.646493i	$0.223765\pi$
$593$			31.4863i			1.29299i	−0.762920	+	0.646493i	$0.776235\pi$
$594$	5.41855			0.222326
$595$	−2.34017	−	0.581449i	−0.0959377	−	0.0238371i
$596$	83.7030			3.42861
$597$			22.5958i			0.924786i
$598$		−	5.84324i		−	0.238948i
$599$	−29.0349			−1.18633			−0.593167	−	0.805080i	$-0.702123\pi$
$599$	−29.0349			−1.18633			−0.593167	+	0.805080i	$0.702123\pi$
$600$	39.9854	+	21.1773i	1.63240	+	0.864559i
$601$	15.3607			0.626576			0.313288	−	0.949658i	$-0.398570\pi$
$601$	15.3607			0.626576			0.313288	+	0.949658i	$0.398570\pi$
$602$		−	17.6742i		−	0.720347i
$603$			4.68035i			0.190598i
$604$	−31.2039			−1.26967
$605$	−15.1906	−	3.77432i	−0.617586	−	0.153448i
$606$	15.7587			0.640154
$607$			13.0472i			0.529569i	0.964308	+	0.264784i	$0.0853008\pi$
$607$			13.0472i			0.529569i	−0.964308	+	0.264784i	$0.914699\pi$
$608$		−	59.6886i		−	2.42069i
$609$	6.68035			0.270701
$610$	6.07223	−	24.4391i	0.245858	−	0.989509i
$611$	4.31351			0.174506
$612$		−	5.75872i		−	0.232783i
$613$		−	15.5174i		−	0.626744i	−0.949630	−	0.313372i	$-0.898541\pi$
$613$		−	15.5174i		−	0.626744i	0.949630	−	0.313372i	$-0.101459\pi$
$614$	−28.3668			−1.14479
$615$	−3.50307	+	14.0989i	−0.141257	+	0.568522i
$616$	−18.0989			−0.729225
$617$			22.7649i			0.916479i	0.888829	+	0.458240i	$0.151520\pi$
$617$			22.7649i			0.916479i	−0.888829	+	0.458240i	$0.848480\pi$
$618$			5.84324i			0.235050i
$619$	−7.92777			−0.318644			−0.159322	−	0.987227i	$-0.550931\pi$
$619$	−7.92777			−0.318644			−0.159322	+	0.987227i	$0.550931\pi$
$620$	89.9130	+	22.3402i	3.61099	+	0.897203i
$621$	2.34017			0.0939079
$622$			64.5646i			2.58881i
$623$			8.34017i			0.334142i
$624$	−12.7526			−0.510512
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	−88.7358			−3.54659
$627$		−	6.15676i		−	0.245877i
$628$			26.2823i			1.04878i
$629$	−11.6865			−0.465971
$630$	−5.87936	−	1.46081i	−0.234239	−	0.0582001i
$631$	19.2039			0.764497			0.382248	−	0.924060i	$-0.375150\pi$
$631$	19.2039			0.764497			0.382248	+	0.924060i	$0.375150\pi$
$632$			55.7152i			2.21623i
$633$		−	13.6742i		−	0.543501i
$634$	−48.5380			−1.92769
$635$	0.993857	−	4.00000i	0.0394400	−	0.158735i
$636$	20.0722			0.795916
$637$		−	0.921622i		−	0.0365160i
$638$			36.1978i			1.43308i
$639$	−2.00000			−0.0791188
$640$	15.4030	−	61.9926i	0.608855	−	2.45047i
$641$	−5.94668			−0.234880			−0.117440	−	0.993080i	$-0.537469\pi$
$641$	−5.94668			−0.234880			−0.117440	+	0.993080i	$0.537469\pi$
$642$		−	44.6947i		−	1.76396i
$643$		−	30.8904i		−	1.21820i	−0.793094	−	0.609100i	$-0.791531\pi$
$643$		−	30.8904i		−	1.21820i	0.793094	−	0.609100i	$-0.208469\pi$
$644$	−12.4969			−0.492448
$645$	14.1568	+	3.51745i	0.557422	+	0.138499i
$646$	−8.99386			−0.353859
$647$			19.2039i			0.754985i	0.926013	+	0.377492i	$0.123214\pi$
$647$			19.2039i			0.754985i	−0.926013	+	0.377492i	$0.876786\pi$
$648$		−	9.04945i		−	0.355496i
$649$	−21.0472			−0.826174
$650$	−11.0328	−	5.84324i	−0.432742	−	0.229191i
$651$	−7.75872			−0.304088
$652$			52.5646i			2.05859i
$653$		−	28.5548i		−	1.11744i	−0.829358	−	0.558718i	$-0.811294\pi$
$653$		−	28.5548i		−	1.11744i	0.829358	−	0.558718i	$-0.188706\pi$
$654$	−34.7792			−1.35998
$655$	3.20394	+	0.796064i	0.125188	+	0.0311048i
$656$	89.8987			3.50995
$657$		−	7.07838i		−	0.276154i
$658$		−	12.6803i		−	0.494331i
$659$	27.9877			1.09025			0.545123	−	0.838356i	$-0.316483\pi$
$659$	27.9877			1.09025			0.545123	+	0.838356i	$0.316483\pi$
$660$	5.75872	−	23.1773i	0.224158	−	0.902174i
$661$	−22.1445			−0.861320			−0.430660	−	0.902514i	$-0.641719\pi$
$661$	−22.1445			−0.861320			−0.430660	+	0.902514i	$0.641719\pi$
$662$		−	3.68649i		−	0.143279i
$663$			0.993857i			0.0385982i
$664$	61.8720			2.40110
$665$	−1.65983	+	6.68035i	−0.0643653	+	0.259053i
$666$	−29.3607			−1.13770
$667$			15.6332i			0.605319i
$668$		−	102.552i		−	3.96787i
$669$	21.6742			0.837973
$670$	27.5174	+	6.83710i	1.06309	+	0.264140i
$671$	−8.31351			−0.320940
$672$			19.3896i			0.747971i
$673$			2.21008i			0.0851923i	0.999092	+	0.0425962i	$0.0135629\pi$
$673$			2.21008i			0.0851923i	−0.999092	+	0.0425962i	$0.986437\pi$
$674$	−68.7091			−2.64658
$675$	2.34017	−	4.41855i	0.0900733	−	0.170070i
$676$	−64.8864			−2.49563
$677$		−	19.5486i		−	0.751315i	−0.926758	−	0.375658i	$-0.877417\pi$
$677$		−	19.5486i		−	0.751315i	0.926758	−	0.375658i	$-0.122583\pi$
$678$			14.1834i			0.544711i
$679$	8.43907			0.323862
$680$	−21.1773	−	5.26180i	−0.812111	−	0.201781i
$681$	−11.5174			−0.441350
$682$		−	42.0410i		−	1.60983i
$683$			11.8166i			0.452149i	0.974110	+	0.226074i	$0.0725893\pi$
$683$			11.8166i			0.452149i	−0.974110	+	0.226074i	$0.927411\pi$
$684$	−16.4391			−0.628564
$685$	2.39350	−	9.63317i	0.0914508	−	0.368064i
$686$	−2.70928			−0.103441
$687$		−	12.8371i		−	0.489766i
$688$		−	90.2676i		−	3.44142i
$689$	−3.46412			−0.131973
$690$	3.41855	−	13.7587i	0.130142	−	0.523786i
$691$	11.7587			0.447323			0.223661	−	0.974667i	$-0.428199\pi$
$691$	11.7587			0.447323			0.223661	+	0.974667i	$0.428199\pi$
$692$			119.829i			4.55520i
$693$			2.00000i			0.0759737i
$694$	45.6886			1.73431
$695$	−29.5174	−	7.33403i	−1.11966	−	0.278196i
$696$	60.4534			2.29148
$697$		−	7.00614i		−	0.265377i
$698$		−	25.7854i		−	0.975991i
$699$	6.76487			0.255871
$700$	−12.4969	+	23.5958i	−0.472339	+	0.891838i
$701$	9.94668			0.375681			0.187840	−	0.982200i	$-0.439851\pi$
$701$	9.94668			0.375681			0.187840	+	0.982200i	$0.439851\pi$
$702$			2.49693i			0.0942405i
$703$			33.3607i			1.25822i
$704$	−49.7152			−1.87371
$705$	10.1568	+	2.52359i	0.382526	+	0.0950439i
$706$	96.9914			3.65032
$707$			5.81658i			0.218755i
$708$			56.1978i			2.11204i
$709$	11.0472			0.414886			0.207443	−	0.978247i	$-0.433486\pi$
$709$	11.0472			0.414886			0.207443	+	0.978247i	$0.433486\pi$
$710$	−2.92162	+	11.7587i	−0.109647	+	0.441297i
$711$	6.15676			0.230896
$712$			75.4740i			2.82851i
$713$		−	18.1568i		−	0.679976i
$714$	2.92162			0.109339
$715$	−0.993857	+	4.00000i	−0.0371681	+	0.149592i
$716$	53.4017			1.99572
$717$			23.3607i			0.872421i
$718$			60.4534i			2.25610i
$719$	6.15676			0.229608			0.114804	−	0.993388i	$-0.463376\pi$
$719$	6.15676			0.229608			0.114804	+	0.993388i	$0.463376\pi$
$720$	−30.0277	−	7.46081i	−1.11907	−	0.278048i
$721$	−2.15676			−0.0803218
$722$		−	25.8020i		−	0.960252i
$723$		−	14.6803i		−	0.545968i
$724$	45.5174			1.69164
$725$	29.5174	+	15.6332i	1.09625	+	0.580601i
$726$	18.9649			0.703854
$727$		−	2.89043i		−	0.107200i	−0.998562	−	0.0536000i	$-0.982930\pi$
$727$		−	2.89043i		−	0.107200i	0.998562	−	0.0536000i	$-0.0170696\pi$
$728$		−	8.34017i		−	0.309107i
$729$	−1.00000			−0.0370370
$730$	−41.6163	−	10.3402i	−1.54029	−	0.382707i
$731$	−7.03489			−0.260195
$732$			22.1978i			0.820454i
$733$		−	25.7998i		−	0.952936i	−0.879192	−	0.476468i	$-0.841917\pi$
$733$		−	25.7998i		−	0.952936i	0.879192	−	0.476468i	$-0.158083\pi$
$734$	55.0349			2.03138
$735$	0.539189	−	2.17009i	0.0198883	−	0.0800448i
$736$	−45.3751			−1.67255
$737$		−	9.36069i		−	0.344806i
$738$		−	17.6020i		−	0.647937i
$739$	1.04718			0.0385212			0.0192606	−	0.999814i	$-0.493869\pi$
$739$	1.04718			0.0385212			0.0192606	+	0.999814i	$0.493869\pi$
$740$	−31.2039	+	125.587i	−1.14708	+	4.61668i
$741$	2.83710			0.104224
$742$			10.1834i			0.373845i
$743$		−	9.97334i		−	0.365886i	−0.983123	−	0.182943i	$-0.941438\pi$
$743$		−	9.97334i		−	0.365886i	0.983123	−	0.182943i	$-0.0585624\pi$
$744$	−70.2122			−2.57410
$745$	−34.0144	−	8.45136i	−1.24619	−	0.309634i
$746$	43.3484			1.58710
$747$		−	6.83710i		−	0.250156i
$748$			11.5174i			0.421120i
$749$	16.4969			0.602785
$750$	−22.5597	−	20.2134i	−0.823764	−	0.738089i
$751$	3.26633			0.119190			0.0595950	−	0.998223i	$-0.481019\pi$
$751$	3.26633			0.119190			0.0595950	+	0.998223i	$0.481019\pi$
$752$		−	64.7624i		−	2.36164i
$753$			9.16290i			0.333915i
$754$	−16.6803			−0.607462
$755$	12.6803	+	3.15061i	0.461485	+	0.114663i
$756$	5.34017			0.194220
$757$			49.9877i			1.81683i	0.418065	+	0.908417i	$0.362708\pi$
$757$			49.9877i			1.81683i	−0.418065	+	0.908417i	$0.637292\pi$
$758$		−	16.6803i		−	0.605857i
$759$	−4.68035			−0.169886
$760$	−15.0205	+	60.4534i	−0.544851	+	2.19288i
$761$	2.61265			0.0947083			0.0473542	−	0.998878i	$-0.484921\pi$
$761$	2.61265			0.0947083			0.0473542	+	0.998878i	$0.484921\pi$
$762$			4.99386i			0.180908i
$763$		−	12.8371i		−	0.464734i
$764$	−82.0288			−2.96770
$765$	−0.581449	+	2.34017i	−0.0210223	+	0.0846091i
$766$	−72.7091			−2.62709
$767$		−	9.69878i		−	0.350202i
$768$			27.6803i			0.998828i
$769$	15.6742			0.565226			0.282613	−	0.959234i	$-0.408799\pi$
$769$	15.6742			0.565226			0.282613	+	0.959234i	$0.408799\pi$
$770$	11.7587	+	2.92162i	0.423755	+	0.105288i
$771$	−5.07838			−0.182893
$772$		−	44.6803i		−	1.60808i
$773$			5.81205i			0.209045i	0.994523	+	0.104522i	$0.0333314\pi$
$773$			5.81205i			0.209045i	−0.994523	+	0.104522i	$0.966669\pi$
$774$	−17.6742			−0.635286
$775$	−34.2823	−	18.1568i	−1.23146	−	0.652210i
$776$	76.3689			2.74148
$777$		−	10.8371i		−	0.388779i
$778$			15.2618i			0.547162i
$779$	−20.0000			−0.716574
$780$	10.6803	+	2.65368i	0.382418	+	0.0950171i
$781$	4.00000			0.143131
$782$			6.83710i			0.244494i
$783$		−	6.68035i		−	0.238736i
$784$	−13.8371			−0.494182
$785$	2.65368	−	10.6803i	0.0947140	−	0.381198i
$786$	−4.00000			−0.142675
$787$		−	39.3484i		−	1.40262i	−0.712857	−	0.701310i	$-0.752599\pi$
$787$		−	39.3484i		−	1.40262i	0.712857	−	0.701310i	$-0.247401\pi$
$788$		−	62.7936i		−	2.23693i
$789$	−5.65983			−0.201495
$790$	8.99386	−	36.1978i	0.319987	−	1.28786i
$791$	−5.23513			−0.186140
$792$			18.0989i			0.643116i
$793$		−	3.83096i		−	0.136041i
$794$	102.410			3.63439
$795$	−8.15676	−	2.02666i	−0.289290	−	0.0718783i
$796$	−120.666			−4.27688
$797$		−	28.2823i		−	1.00181i	−0.865502	−	0.500905i	$-0.833000\pi$
$797$		−	28.2823i		−	1.00181i	0.865502	−	0.500905i	$-0.167000\pi$
$798$		−	8.34017i		−	0.295239i
$799$	−5.04718			−0.178556
$800$	−45.3751	+	85.6740i	−1.60425	+	3.02903i
$801$	8.34017			0.294686
$802$		−	36.9360i		−	1.30426i
$803$			14.1568i			0.499581i
$804$	−24.9939			−0.881465
$805$	5.07838	+	1.26180i	0.178989	+	0.0444724i
$806$	19.3730			0.682384
$807$			27.8576i			0.980635i
$808$			52.6369i			1.85176i
$809$	15.6742			0.551076			0.275538	−	0.961290i	$-0.411144\pi$
$809$	15.6742			0.551076			0.275538	+	0.961290i	$0.411144\pi$
$810$	−1.46081	+	5.87936i	−0.0513277	+	0.206580i
$811$	−42.1666			−1.48067			−0.740335	−	0.672238i	$-0.765333\pi$
$811$	−42.1666			−1.48067			−0.740335	+	0.672238i	$0.765333\pi$
$812$			35.6742i			1.25192i
$813$			25.1194i			0.880976i
$814$	58.7214			2.05818
$815$	5.30737	−	21.3607i	0.185909	−	0.748232i
$816$	14.9216			0.522361
$817$			20.0821i			0.702583i
$818$		−	33.4719i		−	1.17032i
$819$	−0.921622			−0.0322041
$820$	−75.2905	−	18.7070i	−2.62926	−	0.653277i
$821$	−39.0472			−1.36276			−0.681378	−	0.731932i	$-0.738619\pi$
$821$	−39.0472			−1.36276			−0.681378	+	0.731932i	$0.738619\pi$
$822$			12.0267i			0.419478i
$823$		−	36.5646i		−	1.27456i	−0.770631	−	0.637281i	$-0.780059\pi$
$823$		−	36.5646i		−	1.27456i	0.770631	−	0.637281i	$-0.219941\pi$
$824$	−19.5174			−0.679922
$825$	−4.68035	+	8.83710i	−0.162949	+	0.307668i
$826$	−28.5113			−0.992035
$827$		−	50.2245i		−	1.74648i	−0.487294	−	0.873238i	$-0.662016\pi$
$827$		−	50.2245i		−	1.74648i	0.487294	−	0.873238i	$-0.337984\pi$
$828$			12.4969i			0.434298i
$829$	−32.8371			−1.14048			−0.570240	−	0.821478i	$-0.693150\pi$
$829$	−32.8371			−1.14048			−0.570240	+	0.821478i	$0.693150\pi$
$830$	−40.1978	−	9.98771i	−1.39529	−	0.346679i
$831$	−28.1978			−0.978171
$832$		−	22.9093i		−	0.794238i
$833$			1.07838i			0.0373636i
$834$	36.8515			1.27606
$835$	−10.3545	+	41.6742i	−0.358334	+	1.44220i
$836$	32.8781			1.13711
$837$			7.75872i			0.268181i
$838$		−	78.5523i		−	2.71355i
$839$	13.3607			0.461262			0.230631	−	0.973041i	$-0.425921\pi$
$839$	13.3607			0.461262			0.230631	+	0.973041i	$0.425921\pi$
$840$	4.87936	−	19.6381i	0.168354	−	0.677578i
$841$	15.6270			0.538863
$842$		−	41.0805i		−	1.41573i
$843$		−	20.3545i		−	0.701048i
$844$	73.0226			2.51354
$845$	26.3679	+	6.55148i	0.907083	+	0.225378i
$846$	−12.6803			−0.435959
$847$			7.00000i			0.240523i
$848$			52.0098i			1.78603i
$849$	−23.5174			−0.807117
$850$	12.9093	+	6.83710i	0.442787	+	0.234511i
$851$	25.3607			0.869353
$852$		−	10.6803i		−	0.365903i
$853$		−	39.6430i		−	1.35735i	−0.734438	−	0.678675i	$-0.762554\pi$
$853$		−	39.6430i		−	1.35735i	0.734438	−	0.678675i	$-0.237446\pi$
$854$	−11.2618			−0.385371
$855$	6.68035	+	1.65983i	0.228463	+	0.0567649i
$856$	149.288			5.10256
$857$			29.7054i			1.01472i	0.861735	+	0.507359i	$0.169378\pi$
$857$			29.7054i			1.01472i	−0.861735	+	0.507359i	$0.830622\pi$
$858$		−	4.99386i		−	0.170487i
$859$	3.07838			0.105033			0.0525164	−	0.998620i	$-0.483276\pi$
$859$	3.07838			0.105033			0.0525164	+	0.998620i	$0.483276\pi$
$860$	−18.7838	+	75.5995i	−0.640521	+	2.57792i
$861$	6.49693			0.221415
$862$		−	27.9421i		−	0.951713i
$863$		−	6.39350i		−	0.217637i	−0.994062	−	0.108819i	$-0.965293\pi$
$863$		−	6.39350i		−	0.217637i	0.994062	−	0.108819i	$-0.0347068\pi$
$864$	19.3896			0.659648
$865$	12.0989	−	48.6947i	0.411375	−	1.65567i
$866$	−55.3751			−1.88172
$867$			15.8371i			0.537856i
$868$		−	41.4329i		−	1.40633i
$869$	−12.3135			−0.417707
$870$	−39.2762	−	9.75872i	−1.33159	−	0.330852i
$871$	4.31351			0.146158
$872$		−	116.169i		−	3.93397i
$873$		−	8.43907i		−	0.285619i
$874$	19.5174			0.660188
$875$	7.46081	−	8.32684i	0.252221	−	0.281499i
$876$	37.7998			1.27714
$877$			1.21622i			0.0410689i	0.999789	+	0.0205345i	$0.00653678\pi$
$877$			1.21622i			0.0410689i	−0.999789	+	0.0205345i	$0.993463\pi$
$878$			45.8453i			1.54721i
$879$	2.92162			0.0985439
$880$	60.0554	+	14.9216i	2.02447	+	0.503008i
$881$	15.9733			0.538155			0.269078	−	0.963118i	$-0.413281\pi$
$881$	15.9733			0.538155			0.269078	+	0.963118i	$0.413281\pi$
$882$			2.70928i			0.0912260i
$883$			11.6865i			0.393282i	0.980476	+	0.196641i	$0.0630033\pi$
$883$			11.6865i			0.393282i	−0.980476	+	0.196641i	$0.936997\pi$
$884$	−5.30737			−0.178506
$885$	5.67420	−	22.8371i	0.190736	−	0.767661i
$886$	34.7070			1.16600
$887$			25.6209i			0.860265i	0.902766	+	0.430132i	$0.141533\pi$
$887$			25.6209i			0.860265i	−0.902766	+	0.430132i	$0.858467\pi$
$888$		−	98.0698i		−	3.29101i
$889$	−1.84324			−0.0618204
$890$	12.1834	−	49.0349i	0.408389	−	1.64365i
$891$	2.00000			0.0670025
$892$			115.744i			3.87540i
$893$			14.4079i			0.482141i
$894$	42.4657			1.42027
$895$	−21.7009	−	5.39189i	−0.725380	−	0.180231i
$896$	−28.5669			−0.954353
$897$		−	2.15676i		−	0.0720120i
$898$			39.6286i			1.32242i
$899$	−51.8310			−1.72866
$900$	23.5958	+	12.4969i	0.786528	+	0.416564i
$901$	4.05332			0.135036
$902$			35.2039i			1.17216i
$903$		−	6.52359i		−	0.217091i
$904$	−47.3751			−1.57567
$905$	−18.4969	−	4.59583i	−0.614859	−	0.152770i
$906$	−15.8310			−0.525948
$907$			57.7563i			1.91777i	0.283802	+	0.958883i	$0.408404\pi$
$907$			57.7563i			1.91777i	−0.283802	+	0.958883i	$0.591596\pi$
$908$		−	61.5052i		−	2.04112i
$909$	5.81658			0.192924
$910$	−1.34632	+	5.41855i	−0.0446299	+	0.179623i
$911$	−35.9877			−1.19233			−0.596163	−	0.802863i	$-0.703309\pi$
$911$	−35.9877			−1.19233			−0.596163	+	0.802863i	$0.703309\pi$
$912$		−	42.5958i		−	1.41049i
$913$			13.6742i			0.452550i
$914$	38.3545			1.26866
$915$	2.24128	−	9.02052i	0.0740943	−	0.298209i
$916$	68.5523			2.26503
$917$		−	1.47641i		−	0.0487553i
$918$		−	2.92162i		−	0.0964279i
$919$	−46.7214			−1.54120			−0.770598	−	0.637321i	$-0.780042\pi$
$919$	−46.7214			−1.54120			−0.770598	+	0.637321i	$0.780042\pi$
$920$	45.9565	+	11.4186i	1.51514	+	0.376458i
$921$	−10.4703			−0.345007
$922$			0.921622i			0.0303520i
$923$			1.84324i			0.0606711i
$924$	−10.6803			−0.351358
$925$	25.3607	−	47.8843i	0.833854	−	1.57443i
$926$	26.6681			0.876367
$927$			2.15676i			0.0708371i
$928$			129.529i			4.25201i
$929$	53.0493			1.74049			0.870245	−	0.492619i	$-0.163960\pi$
$929$	53.0493			1.74049			0.870245	+	0.492619i	$0.163960\pi$
$930$	45.6163	+	11.3340i	1.49582	+	0.371657i
$931$	3.07838			0.100890
$932$			36.1256i			1.18333i
$933$			23.8310i			0.780191i
$934$	−31.2039			−1.02102
$935$	1.16290	−	4.68035i	0.0380308	−	0.153064i
$936$	−8.34017			−0.272607
$937$			16.1256i			0.526799i	0.964687	+	0.263400i	$0.0848437\pi$
$937$			16.1256i			0.526799i	−0.964687	+	0.263400i	$0.915156\pi$
$938$		−	12.6803i		−	0.414028i
$939$	−32.7526			−1.06884
$940$	−13.4764	+	54.2388i	−0.439552	+	1.76908i
$941$	24.7070			0.805425			0.402713	−	0.915326i	$-0.368067\pi$
$941$	24.7070			0.805425			0.402713	+	0.915326i	$0.368067\pi$
$942$			13.3340i			0.434446i
$943$			15.2039i			0.495108i
$944$	−145.616			−4.73940
$945$	−2.17009	−	0.539189i	−0.0705929	−	0.0175398i
$946$	35.3484			1.14928
$947$			6.53797i			0.212455i	0.994342	+	0.106228i	$0.0338772\pi$
$947$			6.53797i			0.212455i	−0.994342	+	0.106228i	$0.966123\pi$
$948$			32.8781i			1.06783i
$949$	−6.52359			−0.211765
$950$	19.5174	−	36.8515i	0.633230	−	1.19562i
$951$	−17.9155			−0.580949
$952$			9.75872i			0.316282i
$953$			6.11327i			0.198028i	0.995086	+	0.0990142i	$0.0315689\pi$
$953$			6.11327i			0.198028i	−0.995086	+	0.0990142i	$0.968431\pi$
$954$	10.1834			0.329700
$955$	33.3340	+	8.28231i	1.07866	+	0.268009i
$956$	−124.750			−4.03471
$957$			13.3607i			0.431890i
$958$			52.8781i			1.70842i
$959$	−4.43907			−0.143345
$960$	13.4030	−	53.9432i	0.432578	−	1.74101i
$961$	29.1978			0.941864
$962$			27.0595i			0.872432i
$963$		−	16.4969i		−	0.531606i
$964$	78.3956			2.52495
$965$	−4.51130	+	18.1568i	−0.145224	+	0.584487i
$966$	−6.34017			−0.203992
$967$			25.6209i			0.823912i	0.911204	+	0.411956i	$0.135154\pi$
$967$			25.6209i			0.823912i	−0.911204	+	0.411956i	$0.864846\pi$
$968$			63.3461i			2.03602i
$969$	−3.31965			−0.106643
$970$	−49.6163	−	12.3279i	−1.59308	−	0.395825i
$971$	4.05332			0.130077			0.0650387	−	0.997883i	$-0.479283\pi$
$971$	4.05332			0.130077			0.0650387	+	0.997883i	$0.479283\pi$
$972$		−	5.34017i		−	0.171286i
$973$			13.6020i			0.436059i
$974$	62.7214			2.00972
$975$	−4.07223	−	2.15676i	−0.130416	−	0.0690715i
$976$	−57.5174			−1.84109
$977$			3.81205i			0.121958i	0.998139	+	0.0609791i	$0.0194223\pi$
$977$			3.81205i			0.121958i	−0.998139	+	0.0609791i	$0.980578\pi$
$978$			26.6681i			0.852751i
$979$	−16.6803			−0.533106
$980$	11.5886	+	2.87936i	0.370185	+	0.0919778i
$981$	−12.8371			−0.409857
$982$			5.41855i			0.172913i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	58.7936			1.87427
$985$	−6.34017	+	25.5174i	−0.202015	+	0.813053i
$986$	19.5174			0.621562
$987$		−	4.68035i		−	0.148977i
$988$			15.1506i			0.482005i
$989$	15.2663			0.485441
$990$	2.92162	−	11.7587i	0.0928553	−	0.373717i
$991$	−42.4079			−1.34713			−0.673565	−	0.739128i	$-0.735238\pi$
$991$	−42.4079			−1.34713			−0.673565	+	0.739128i	$0.735238\pi$
$992$		−	150.439i		−	4.77643i
$993$		−	1.36069i		−	0.0431803i
$994$	5.41855			0.171866
$995$	49.0349	+	12.1834i	1.55451	+	0.386240i
$996$	36.5113			1.15690
$997$		−	43.4740i		−	1.37683i	−0.725315	−	0.688417i	$-0.758306\pi$
$997$		−	43.4740i		−	1.37683i	0.725315	−	0.688417i	$-0.241694\pi$
$998$		−	73.7030i		−	2.33303i
$999$	−10.8371			−0.342871

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.d.b.64.6	yes	6
3.2	odd	2		315.2.d.e.64.1		6
4.3	odd	2		1680.2.t.k.1009.3		6
5.2	odd	4		525.2.a.j.1.1		3
5.3	odd	4		525.2.a.k.1.3		3
5.4	even	2	inner	105.2.d.b.64.1	✓	6
7.2	even	3		735.2.q.e.214.6		12
7.3	odd	6		735.2.q.f.79.1		12
7.4	even	3		735.2.q.e.79.1		12
7.5	odd	6		735.2.q.f.214.6		12
7.6	odd	2		735.2.d.b.589.6		6
12.11	even	2		5040.2.t.v.1009.1		6
15.2	even	4		1575.2.a.x.1.3		3
15.8	even	4		1575.2.a.w.1.1		3
15.14	odd	2		315.2.d.e.64.6		6
20.3	even	4		8400.2.a.dj.1.2		3
20.7	even	4		8400.2.a.dg.1.2		3
20.19	odd	2		1680.2.t.k.1009.6		6
21.20	even	2		2205.2.d.l.1324.1		6
35.4	even	6		735.2.q.e.79.6		12
35.9	even	6		735.2.q.e.214.1		12
35.13	even	4		3675.2.a.bj.1.3		3
35.19	odd	6		735.2.q.f.214.1		12
35.24	odd	6		735.2.q.f.79.6		12
35.27	even	4		3675.2.a.bi.1.1		3
35.34	odd	2		735.2.d.b.589.1		6
60.59	even	2		5040.2.t.v.1009.2		6
105.104	even	2		2205.2.d.l.1324.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.1	✓	6	5.4	even	2	inner
105.2.d.b.64.6	yes	6	1.1	even	1	trivial
315.2.d.e.64.1		6	3.2	odd	2
315.2.d.e.64.6		6	15.14	odd	2
525.2.a.j.1.1		3	5.2	odd	4
525.2.a.k.1.3		3	5.3	odd	4
735.2.d.b.589.1		6	35.34	odd	2
735.2.d.b.589.6		6	7.6	odd	2
735.2.q.e.79.1		12	7.4	even	3
735.2.q.e.79.6		12	35.4	even	6
735.2.q.e.214.1		12	35.9	even	6
735.2.q.e.214.6		12	7.2	even	3
735.2.q.f.79.1		12	7.3	odd	6
735.2.q.f.79.6		12	35.24	odd	6
735.2.q.f.214.1		12	35.19	odd	6
735.2.q.f.214.6		12	7.5	odd	6
1575.2.a.w.1.1		3	15.8	even	4
1575.2.a.x.1.3		3	15.2	even	4
1680.2.t.k.1009.3		6	4.3	odd	2
1680.2.t.k.1009.6		6	20.19	odd	2
2205.2.d.l.1324.1		6	21.20	even	2
2205.2.d.l.1324.6		6	105.104	even	2
3675.2.a.bi.1.1		3	35.27	even	4
3675.2.a.bj.1.3		3	35.13	even	4
5040.2.t.v.1009.1		6	12.11	even	2
5040.2.t.v.1009.2		6	60.59	even	2
8400.2.a.dg.1.2		3	20.7	even	4
8400.2.a.dj.1.2		3	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.70928i q^{2} +1.00000i q^{3} -5.34017 q^{4} +(2.17009 + 0.539189i) q^{5} -2.70928 q^{6} -1.00000i q^{7} -9.04945i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.70928i q^{2} +1.00000i q^{3} -5.34017 q^{4} +(2.17009 + 0.539189i) q^{5} -2.70928 q^{6} -1.00000i q^{7} -9.04945i q^{8} -1.00000 q^{9} +(-1.46081 + 5.87936i) q^{10} +2.00000 q^{11} -5.34017i q^{12} +0.921622i q^{13} +2.70928 q^{14} +(-0.539189 + 2.17009i) q^{15} +13.8371 q^{16} -1.07838i q^{17} -2.70928i q^{18} -3.07838 q^{19} +(-11.5886 - 2.87936i) q^{20} +1.00000 q^{21} +5.41855i q^{22} +2.34017i q^{23} +9.04945 q^{24} +(4.41855 + 2.34017i) q^{25} -2.49693 q^{26} -1.00000i q^{27} +5.34017i q^{28} +6.68035 q^{29} +(-5.87936 - 1.46081i) q^{30} -7.75872 q^{31} +19.3896i q^{32} +2.00000i q^{33} +2.92162 q^{34} +(0.539189 - 2.17009i) q^{35} +5.34017 q^{36} -10.8371i q^{37} -8.34017i q^{38} -0.921622 q^{39} +(4.87936 - 19.6381i) q^{40} +6.49693 q^{41} +2.70928i q^{42} -6.52359i q^{43} -10.6803 q^{44} +(-2.17009 - 0.539189i) q^{45} -6.34017 q^{46} -4.68035i q^{47} +13.8371i q^{48} -1.00000 q^{49} +(-6.34017 + 11.9711i) q^{50} +1.07838 q^{51} -4.92162i q^{52} +3.75872i q^{53} +2.70928 q^{54} +(4.34017 + 1.07838i) q^{55} -9.04945 q^{56} -3.07838i q^{57} +18.0989i q^{58} -10.5236 q^{59} +(2.87936 - 11.5886i) q^{60} -4.15676 q^{61} -21.0205i q^{62} +1.00000i q^{63} -24.8576 q^{64} +(-0.496928 + 2.00000i) q^{65} -5.41855 q^{66} -4.68035i q^{67} +5.75872i q^{68} -2.34017 q^{69} +(5.87936 + 1.46081i) q^{70} +2.00000 q^{71} +9.04945i q^{72} +7.07838i q^{73} +29.3607 q^{74} +(-2.34017 + 4.41855i) q^{75} +16.4391 q^{76} -2.00000i q^{77} -2.49693i q^{78} -6.15676 q^{79} +(30.0277 + 7.46081i) q^{80} +1.00000 q^{81} +17.6020i q^{82} +6.83710i q^{83} -5.34017 q^{84} +(0.581449 - 2.34017i) q^{85} +17.6742 q^{86} +6.68035i q^{87} -18.0989i q^{88} -8.34017 q^{89} +(1.46081 - 5.87936i) q^{90} +0.921622 q^{91} -12.4969i q^{92} -7.75872i q^{93} +12.6803 q^{94} +(-6.68035 - 1.65983i) q^{95} -19.3896 q^{96} +8.43907i q^{97} -2.70928i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{14} + 26 q^{16} - 12 q^{19} - 30 q^{20} + 6 q^{21} + 18 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{29} - 10 q^{30} + 4 q^{31} + 24 q^{34} + 10 q^{36} - 12 q^{39} + 4 q^{40} + 4 q^{41} - 20 q^{44} - 2 q^{45} - 16 q^{46} - 6 q^{49} - 16 q^{50} + 2 q^{54} + 4 q^{55} - 18 q^{56} - 32 q^{59} - 8 q^{60} - 12 q^{61} - 26 q^{64} + 32 q^{65} - 4 q^{66} + 8 q^{69} + 10 q^{70} + 12 q^{71} + 88 q^{74} + 8 q^{75} + 4 q^{76} - 24 q^{79} + 46 q^{80} + 6 q^{81} - 10 q^{84} + 32 q^{85} - 8 q^{86} - 28 q^{89} + 12 q^{90} + 12 q^{91} + 32 q^{94} + 4 q^{95} - 58 q^{96} - 12 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^14 + 26 * q^16 - 12 * q^19 - 30 * q^20 + 6 * q^21 + 18 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^29 - 10 * q^30 + 4 * q^31 + 24 * q^34 + 10 * q^36 - 12 * q^39 + 4 * q^40 + 4 * q^41 - 20 * q^44 - 2 * q^45 - 16 * q^46 - 6 * q^49 - 16 * q^50 + 2 * q^54 + 4 * q^55 - 18 * q^56 - 32 * q^59 - 8 * q^60 - 12 * q^61 - 26 * q^64 + 32 * q^65 - 4 * q^66 + 8 * q^69 + 10 * q^70 + 12 * q^71 + 88 * q^74 + 8 * q^75 + 4 * q^76 - 24 * q^79 + 46 * q^80 + 6 * q^81 - 10 * q^84 + 32 * q^85 - 8 * q^86 - 28 * q^89 + 12 * q^90 + 12 * q^91 + 32 * q^94 + 4 * q^95 - 58 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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