LMFDB - Embedded newform 315.2.be.b.311.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.2
Character	$\chi$	$=$	315.311
Dual form			315.2.be.b.236.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02825 - 1.17101i) q^{2} +(0.587320 - 1.62943i) q^{3} +(1.74252 + 3.01813i) q^{4} +1.00000 q^{5} +(-3.09931 + 2.61714i) q^{6} +(2.45764 - 0.979787i) q^{7} -3.47799i q^{8} +(-2.31011 - 1.91400i) q^{9} +O(q^{10})$	\(q+(-2.02825 - 1.17101i) q^{2} +(0.587320 - 1.62943i) q^{3} +(1.74252 + 3.01813i) q^{4} +1.00000 q^{5} +(-3.09931 + 2.61714i) q^{6} +(2.45764 - 0.979787i) q^{7} -3.47799i q^{8} +(-2.31011 - 1.91400i) q^{9} +(-2.02825 - 1.17101i) q^{10} -0.240982i q^{11} +(5.94127 - 1.06671i) q^{12} +(5.02640 + 2.90199i) q^{13} +(-6.13205 - 0.890673i) q^{14} +(0.587320 - 1.62943i) q^{15} +(-0.587714 + 1.01795i) q^{16} +(3.01284 - 5.21840i) q^{17} +(2.44416 + 6.58722i) q^{18} +(0.688475 - 0.397491i) q^{19} +(1.74252 + 3.01813i) q^{20} +(-0.153074 - 4.58002i) q^{21} +(-0.282192 + 0.488771i) q^{22} -0.396557i q^{23} +(-5.66715 - 2.04269i) q^{24} +1.00000 q^{25} +(-6.79651 - 11.7719i) q^{26} +(-4.47551 + 2.64004i) q^{27} +(7.23962 + 5.71020i) q^{28} +(-4.83674 + 2.79249i) q^{29} +(-3.09931 + 2.61714i) q^{30} +(-7.62683 + 4.40335i) q^{31} +(-3.64000 + 2.10155i) q^{32} +(-0.392665 - 0.141534i) q^{33} +(-12.2216 + 7.05613i) q^{34} +(2.45764 - 0.979787i) q^{35} +(1.75129 - 10.3074i) q^{36} +(-5.50596 - 9.53660i) q^{37} -1.86186 q^{38} +(7.68071 - 6.48578i) q^{39} -3.47799i q^{40} +(0.493886 - 0.855435i) q^{41} +(-5.05277 + 9.46865i) q^{42} +(2.80477 + 4.85800i) q^{43} +(0.727317 - 0.419917i) q^{44} +(-2.31011 - 1.91400i) q^{45} +(-0.464371 + 0.804314i) q^{46} +(1.05437 - 1.82622i) q^{47} +(1.31351 + 1.55550i) q^{48} +(5.08003 - 4.81594i) q^{49} +(-2.02825 - 1.17101i) q^{50} +(-6.73353 - 7.97410i) q^{51} +20.2271i q^{52} +(-0.327502 - 0.189083i) q^{53} +(12.1689 - 0.113794i) q^{54} -0.240982i q^{55} +(-3.40769 - 8.54766i) q^{56} +(-0.243330 - 1.35528i) q^{57} +13.0801 q^{58} +(7.36945 + 12.7643i) q^{59} +(5.94127 - 1.06671i) q^{60} +(-3.45074 - 1.99229i) q^{61} +20.6254 q^{62} +(-7.55274 - 2.44051i) q^{63} +12.1946 q^{64} +(5.02640 + 2.90199i) q^{65} +(0.630683 + 0.746879i) q^{66} +(-1.02677 - 1.77842i) q^{67} +20.9998 q^{68} +(-0.646163 - 0.232906i) q^{69} +(-6.13205 - 0.890673i) q^{70} +2.66240i q^{71} +(-6.65687 + 8.03454i) q^{72} +(-7.46653 - 4.31080i) q^{73} +25.7901i q^{74} +(0.587320 - 1.62943i) q^{75} +(2.39936 + 1.38527i) q^{76} +(-0.236111 - 0.592249i) q^{77} +(-23.1733 + 4.16059i) q^{78} +(0.939111 - 1.62659i) q^{79} +(-0.587714 + 1.01795i) q^{80} +(1.67322 + 8.84310i) q^{81} +(-2.00344 + 1.15669i) q^{82} +(-1.10515 - 1.91417i) q^{83} +(13.5564 - 8.44277i) q^{84} +(3.01284 - 5.21840i) q^{85} -13.1376i q^{86} +(1.70947 + 9.52124i) q^{87} -0.838134 q^{88} +(2.86854 + 4.96845i) q^{89} +(2.44416 + 6.58722i) q^{90} +(15.1964 + 2.20727i) q^{91} +(1.19686 - 0.691008i) q^{92} +(2.69558 + 15.0136i) q^{93} +(-4.27704 + 2.46935i) q^{94} +(0.688475 - 0.397491i) q^{95} +(1.28650 + 7.16542i) q^{96} +(13.7481 - 7.93745i) q^{97} +(-15.9431 + 3.81914i) q^{98} +(-0.461240 + 0.556696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.02825	−	1.17101i	−1.43419	−	0.828028i	−0.436750	−	0.899583i	$-0.643870\pi$
$2$	−2.02825	−	1.17101i	−1.43419	−	0.828028i	−0.997437	+	0.0715553i	$0.977204\pi$
$3$	0.587320	−	1.62943i	0.339089	−	0.940754i
$3$	0.587320	−	1.62943i	0.339089	−	0.940754i
$4$	1.74252	+	3.01813i	0.871260	+	1.50907i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−3.09931	+	2.61714i	−1.26529	+	1.06844i
$7$	2.45764	−	0.979787i	0.928902	−	0.370325i
$7$	2.45764	−	0.979787i	0.928902	−	0.370325i
$8$		−	3.47799i		−	1.22966i
$9$	−2.31011	−	1.91400i	−0.770037	−	0.638000i
$10$	−2.02825	−	1.17101i	−0.641388	−	0.370305i
$11$		−	0.240982i		−	0.0726589i	−0.999340	−	0.0363295i	$-0.988433\pi$
$11$		−	0.240982i		−	0.0726589i	0.999340	−	0.0363295i	$-0.0115666\pi$
$12$	5.94127	−	1.06671i	1.71510	−	0.307933i
$13$	5.02640	+	2.90199i	1.39407	+	0.804868i	0.993763	−	0.111513i	$-0.0355696\pi$
$13$	5.02640	+	2.90199i	1.39407	+	0.804868i	0.400309	+	0.916380i	$0.368903\pi$
$14$	−6.13205	−	0.890673i	−1.63886	−	0.238042i
$15$	0.587320	−	1.62943i	0.151645	−	0.420718i
$16$	−0.587714	+	1.01795i	−0.146928	+	0.254488i
$17$	3.01284	−	5.21840i	0.730722	−	1.26565i	−0.225853	−	0.974161i	$-0.572517\pi$
$17$	3.01284	−	5.21840i	0.730722	−	1.26565i	0.956575	−	0.291486i	$-0.0941496\pi$
$18$	2.44416	+	6.58722i	0.576094	+	1.55262i
$19$	0.688475	−	0.397491i	0.157947	−	0.0911908i	−0.418943	−	0.908012i	$-0.637599\pi$
$19$	0.688475	−	0.397491i	0.157947	−	0.0911908i	0.576890	+	0.816822i	$0.304266\pi$
$20$	1.74252	+	3.01813i	0.389639	+	0.674875i
$21$	−0.153074	−	4.58002i	−0.0334034	−	0.999442i
$22$	−0.282192	+	0.488771i	−0.0601636	+	0.104206i
$23$		−	0.396557i		−	0.0826878i	−0.999145	−	0.0413439i	$-0.986836\pi$
$23$		−	0.396557i		−	0.0826878i	0.999145	−	0.0413439i	$-0.0131639\pi$
$24$	−5.66715	−	2.04269i	−1.15680	−	0.416963i
$25$	1.00000			0.200000
$26$	−6.79651	−	11.7719i	−1.33291	−	2.30866i
$27$	−4.47551	+	2.64004i	−0.861312	+	0.508076i
$28$	7.23962	+	5.71020i	1.36816	+	1.07913i
$29$	−4.83674	+	2.79249i	−0.898160	+	0.518553i	−0.876603	−	0.481215i	$-0.840196\pi$
$29$	−4.83674	+	2.79249i	−0.898160	+	0.518553i	−0.0215574	+	0.999768i	$0.506862\pi$
$30$	−3.09931	+	2.61714i	−0.565854	+	0.477821i
$31$	−7.62683	+	4.40335i	−1.36982	+	0.790865i	−0.990905	−	0.134566i	$-0.957036\pi$
$31$	−7.62683	+	4.40335i	−1.36982	+	0.790865i	−0.378914	+	0.925432i	$0.623702\pi$
$32$	−3.64000	+	2.10155i	−0.643467	+	0.371506i
$33$	−0.392665	−	0.141534i	−0.0683542	−	0.0246379i
$34$	−12.2216	+	7.05613i	−2.09598	+	1.21012i
$35$	2.45764	−	0.979787i	0.415418	−	0.165614i
$36$	1.75129	−	10.3074i	0.291882	−	1.71790i
$37$	−5.50596	−	9.53660i	−0.905174	−	1.56781i	−0.820684	−	0.571383i	$-0.806407\pi$
$37$	−5.50596	−	9.53660i	−0.905174	−	1.56781i	−0.0844904	−	0.996424i	$-0.526926\pi$
$38$	−1.86186			−0.302034
$39$	7.68071	−	6.48578i	1.22990	−	1.03856i
$40$		−	3.47799i		−	0.549918i
$41$	0.493886	−	0.855435i	0.0771320	−	0.133596i	−0.824879	−	0.565309i	$-0.808757\pi$
$41$	0.493886	−	0.855435i	0.0771320	−	0.133596i	0.902011	+	0.431712i	$0.142090\pi$
$42$	−5.05277	+	9.46865i	−0.779659	+	1.46104i
$43$	2.80477	+	4.85800i	0.427723	+	0.740838i	0.996670	−	0.0815357i	$-0.0259825\pi$
$43$	2.80477	+	4.85800i	0.427723	+	0.740838i	−0.568947	+	0.822374i	$0.692649\pi$
$44$	0.727317	−	0.419917i	0.109647	−	0.0633048i
$45$	−2.31011	−	1.91400i	−0.344371	−	0.285322i
$46$	−0.464371	+	0.804314i	−0.0684678	+	0.118590i
$47$	1.05437	−	1.82622i	0.153796	−	0.266382i	−0.778824	−	0.627242i	$-0.784184\pi$
$47$	1.05437	−	1.82622i	0.153796	−	0.266382i	0.932620	+	0.360860i	$0.117517\pi$
$48$	1.31351	+	1.55550i	0.189588	+	0.224518i
$49$	5.08003	−	4.81594i	0.725719	−	0.687991i
$50$	−2.02825	−	1.17101i	−0.286837	−	0.165606i
$51$	−6.73353	−	7.97410i	−0.942883	−	1.11660i
$52$			20.2271i			2.80500i
$53$	−0.327502	−	0.189083i	−0.0449858	−	0.0259726i	0.477338	−	0.878720i	$-0.341602\pi$
$53$	−0.327502	−	0.189083i	−0.0449858	−	0.0259726i	−0.522324	+	0.852747i	$0.674935\pi$
$54$	12.1689	−	0.113794i	1.65598	−	0.0154854i
$55$		−	0.240982i		−	0.0324941i
$56$	−3.40769	−	8.54766i	−0.455372	−	1.14223i
$57$	−0.243330	−	1.35528i	−0.0322299	−	0.179511i
$58$	13.0801			1.71751
$59$	7.36945	+	12.7643i	0.959421	+	1.66177i	0.723911	+	0.689893i	$0.242343\pi$
$59$	7.36945	+	12.7643i	0.959421	+	1.66177i	0.235510	+	0.971872i	$0.424324\pi$
$60$	5.94127	−	1.06671i	0.767014	−	0.137712i
$61$	−3.45074	−	1.99229i	−0.441822	−	0.255086i	0.262548	−	0.964919i	$-0.415437\pi$
$61$	−3.45074	−	1.99229i	−0.441822	−	0.255086i	−0.704370	+	0.709833i	$0.748771\pi$
$62$	20.6254			2.61943
$63$	−7.55274	−	2.44051i	−0.951556	−	0.307476i
$64$	12.1946			1.52433
$65$	5.02640	+	2.90199i	0.623448	+	0.359948i
$66$	0.630683	+	0.746879i	0.0776318	+	0.0919345i
$67$	−1.02677	−	1.77842i	−0.125440	−	0.217269i	0.796465	−	0.604685i	$-0.206701\pi$
$67$	−1.02677	−	1.77842i	−0.125440	−	0.217269i	−0.921905	+	0.387416i	$0.873368\pi$
$68$	20.9998			2.54659
$69$	−0.646163	−	0.232906i	−0.0777889	−	0.0280386i
$70$	−6.13205	−	0.890673i	−0.732920	−	0.106456i
$71$			2.66240i			0.315968i	0.987442	+	0.157984i	$0.0504995\pi$
$71$			2.66240i			0.315968i	−0.987442	+	0.157984i	$0.949500\pi$
$72$	−6.65687	+	8.03454i	−0.784520	+	0.946879i
$73$	−7.46653	−	4.31080i	−0.873891	−	0.504541i	−0.00525172	−	0.999986i	$-0.501672\pi$
$73$	−7.46653	−	4.31080i	−0.873891	−	0.504541i	−0.868639	+	0.495445i	$0.835005\pi$
$74$			25.7901i			2.99804i
$75$	0.587320	−	1.62943i	0.0678179	−	0.188151i
$76$	2.39936	+	1.38527i	0.275226	+	0.158902i
$77$	−0.236111	−	0.592249i	−0.0269074	−	0.0674930i
$78$	−23.1733	+	4.16059i	−2.62386	+	0.471094i
$79$	0.939111	−	1.62659i	0.105658	−	0.183005i	−0.808349	−	0.588704i	$-0.799638\pi$
$79$	0.939111	−	1.62659i	0.105658	−	0.183005i	0.914007	+	0.405699i	$0.132972\pi$
$80$	−0.587714	+	1.01795i	−0.0657084	+	0.113810i
$81$	1.67322	+	8.84310i	0.185913	+	0.982566i
$82$	−2.00344	+	1.15669i	−0.221243	+	0.127735i
$83$	−1.10515	−	1.91417i	−0.121306	−	0.210108i	0.798977	−	0.601362i	$-0.205375\pi$
$83$	−1.10515	−	1.91417i	−0.121306	−	0.210108i	−0.920283	+	0.391254i	$0.872042\pi$
$84$	13.5564	−	8.44277i	1.47912	−	0.921182i
$85$	3.01284	−	5.21840i	0.326789	−	0.566015i
$86$		−	13.1376i		−	1.41667i
$87$	1.70947	+	9.52124i	0.183274	+	1.02078i
$88$	−0.838134			−0.0893454
$89$	2.86854	+	4.96845i	0.304064	+	0.526655i	0.977053	−	0.212998i	$-0.0683229\pi$
$89$	2.86854	+	4.96845i	0.304064	+	0.526655i	−0.672988	+	0.739653i	$0.734990\pi$
$90$	2.44416	+	6.58722i	0.257637	+	0.694354i
$91$	15.1964	+	2.20727i	1.59302	+	0.231384i
$92$	1.19686	−	0.691008i	0.124781	−	0.0720426i
$93$	2.69558	+	15.0136i	0.279519	+	1.55684i
$94$	−4.27704	+	2.46935i	−0.441143	+	0.254694i
$95$	0.688475	−	0.397491i	0.0706361	−	0.0407818i
$96$	1.28650	+	7.16542i	0.131303	+	0.731318i
$97$	13.7481	−	7.93745i	1.39591	−	0.805926i	0.401944	−	0.915664i	$-0.368334\pi$
$97$	13.7481	−	7.93745i	1.39591	−	0.805926i	0.993961	+	0.109738i	$0.0350011\pi$
$98$	−15.9431	+	3.81914i	−1.61049	+	0.385791i
$99$	−0.461240	+	0.556696i	−0.0463564	+	0.0559500i
$100$	1.74252	+	3.01813i	0.174252	+	0.301813i
$101$	0.331838			0.0330191			0.0165096	−	0.999864i	$-0.494745\pi$
$101$	0.331838			0.0330191			0.0165096	+	0.999864i	$0.494745\pi$
$102$	4.31952	+	24.0584i	0.427696	+	2.38214i
$103$			10.4715i			1.03179i	0.856652	+	0.515895i	$0.172540\pi$
$103$			10.4715i			1.03179i	−0.856652	+	0.515895i	$0.827460\pi$
$104$	10.0931	−	17.4818i	0.989710	−	1.71423i
$105$	−0.153074	−	4.58002i	−0.0149385	−	0.446964i
$106$	0.442836	+	0.767015i	0.0430120	+	0.0744990i
$107$	−0.490862	+	0.283399i	−0.0474534	+	0.0273972i	−0.523539	−	0.852002i	$-0.675389\pi$
$107$	−0.490862	+	0.283399i	−0.0474534	+	0.0273972i	0.476086	+	0.879399i	$0.342055\pi$
$108$	−15.7667	−	8.90736i	−1.51715	−	0.857111i
$109$	−2.43326	+	4.21452i	−0.233064	+	0.403678i	−0.958708	−	0.284392i	$-0.908208\pi$
$109$	−2.43326	+	4.21452i	−0.233064	+	0.403678i	0.725644	+	0.688070i	$0.241542\pi$
$110$	−0.282192	+	0.488771i	−0.0269060	+	0.0466025i
$111$	−18.7730	+	3.37056i	−1.78186	+	0.319919i
$112$	−0.447017	+	3.07759i	−0.0422392	+	0.290805i
$113$	13.6410	+	7.87562i	1.28324	+	0.740876i	0.977438	−	0.211221i	$-0.0677439\pi$
$113$	13.6410	+	7.87562i	1.28324	+	0.740876i	0.305797	+	0.952097i	$0.401077\pi$
$114$	−1.09351	+	3.03378i	−0.102417	+	0.284140i
$115$		−	0.396557i		−	0.0369791i
$116$	−16.8562	−	9.73195i	−1.56506	−	0.903589i
$117$	−6.05712	−	16.3244i	−0.559981	−	1.50919i
$118$		−	34.5187i		−	3.17771i
$119$	2.29158	−	15.7769i	0.210069	−	1.44627i
$120$	−5.66715	−	2.04269i	−0.517338	−	0.186472i
$121$	10.9419			0.994721
$122$	4.66597	+	8.08170i	0.422437	+	0.731683i
$123$	−1.10381	−	1.30717i	−0.0995268	−	0.117863i
$124$	−26.5798	−	15.3459i	−2.38694	−	1.37810i
$125$	1.00000			0.0894427
$126$	12.4610	+	13.7943i	1.11011	+	1.22889i
$127$	−12.0618			−1.07031			−0.535154	−	0.844754i	$-0.679746\pi$
$127$	−12.0618			−1.07031			−0.535154	+	0.844754i	$0.679746\pi$
$128$	−17.4537	−	10.0769i	−1.54270	−	0.890678i
$129$	9.56309	−	1.71698i	0.841983	−	0.151172i
$130$	−6.79651	−	11.7719i	−0.596094	−	1.03246i
$131$	−14.3505			−1.25381			−0.626905	−	0.779096i	$-0.715679\pi$
$131$	−14.3505			−1.25381			−0.626905	+	0.779096i	$0.715679\pi$
$132$	−0.257058	−	1.43174i	−0.0223741	−	0.124617i
$133$	1.30257	−	1.65145i	0.112947	−	0.143199i
$134$			4.80943i			0.415472i
$135$	−4.47551	+	2.64004i	−0.385191	+	0.227219i
$136$	−18.1495	−	10.4786i	−1.55631	−	0.898536i
$137$			2.15340i			0.183977i	0.995760	+	0.0919886i	$0.0293223\pi$
$137$			2.15340i			0.183977i	−0.995760	+	0.0919886i	$0.970678\pi$
$138$	1.03784	+	1.22905i	0.0883470	+	0.104624i
$139$	−13.8296	−	7.98451i	−1.17301	−	0.677237i	−0.218623	−	0.975810i	$-0.570156\pi$
$139$	−13.8296	−	7.98451i	−1.17301	−	0.677237i	−0.954387	+	0.298572i	$0.903490\pi$
$140$	7.23962	+	5.71020i	0.611860	+	0.482600i
$141$	−2.35646	−	2.79060i	−0.198449	−	0.235011i
$142$	3.11769	−	5.40000i	0.261631	−	0.453158i
$143$	0.699329	−	1.21127i	0.0584808	−	0.101292i
$144$	3.30604	−	1.22669i	0.275503	−	0.102224i
$145$	−4.83674	+	2.79249i	−0.401669	+	0.231904i
$146$	10.0960	+	17.4867i	0.835548	+	1.44721i
$147$	−4.86364	−	11.1061i	−0.401147	−	0.916014i
$148$	19.1885	−	33.2354i	1.57728	−	2.73194i
$149$			1.36724i			0.112009i	0.998431	+	0.0560044i	$0.0178361\pi$
$149$			1.36724i			0.112009i	−0.998431	+	0.0560044i	$0.982164\pi$
$150$	−3.09931	+	2.61714i	−0.253058	+	0.213688i
$151$	4.22191			0.343574			0.171787	−	0.985134i	$-0.445046\pi$
$151$	4.22191			0.343574			0.171787	+	0.985134i	$0.445046\pi$
$152$	−1.38247	−	2.39451i	−0.112133	−	0.194220i
$153$	−16.9480	+	6.28849i	−1.37016	+	0.508394i
$154$	−0.214637	+	1.47771i	−0.0172959	+	0.119078i
$155$	−7.62683	+	4.40335i	−0.612602	+	0.353686i
$156$	32.9588	+	11.8798i	2.63881	+	0.951145i
$157$	2.06559	−	1.19257i	0.164852	−	0.0951772i	−0.415304	−	0.909683i	$-0.636325\pi$
$157$	2.06559	−	1.19257i	0.164852	−	0.0951772i	0.580156	+	0.814505i	$0.302992\pi$
$158$	−3.80950	+	2.19941i	−0.303067	+	0.174976i
$159$	−0.500447	+	0.422590i	−0.0396880	+	0.0335136i
$160$	−3.64000	+	2.10155i	−0.287767	+	0.166142i
$161$	−0.388541	−	0.974596i	−0.0306213	−	0.0768089i
$162$	6.96165	−	19.8953i	0.546959	−	1.56312i
$163$	8.75207	+	15.1590i	0.685515	+	1.18735i	0.973275	+	0.229644i	$0.0737563\pi$
$163$	8.75207	+	15.1590i	0.685515	+	1.18735i	−0.287759	+	0.957703i	$0.592910\pi$
$164$	3.44242			0.268808
$165$	−0.392665	−	0.141534i	−0.0305689	−	0.0110184i
$166$			5.17655i			0.401778i
$167$	−8.17532	+	14.1601i	−0.632625	+	1.09574i	0.354388	+	0.935098i	$0.384689\pi$
$167$	−8.17532	+	14.1601i	−0.632625	+	1.09574i	−0.987013	+	0.160640i	$0.948644\pi$
$168$	−15.9293	+	0.532389i	−1.22897	+	0.0410747i
$169$	10.3431	+	17.9148i	0.795624	+	1.37806i
$170$	−12.2216	+	7.05613i	−0.937352	+	0.541180i
$171$	−2.35125	−	0.399492i	−0.179805	−	0.0305499i
$172$	−9.77473	+	16.9303i	−0.745316	+	1.29093i
$173$	9.25630	−	16.0324i	0.703743	−	1.21892i	−0.263400	−	0.964687i	$-0.584844\pi$
$173$	9.25630	−	16.0324i	0.703743	−	1.21892i	0.967143	−	0.254233i	$-0.0818229\pi$
$174$	7.68223	−	21.3132i	0.582388	−	1.61575i
$175$	2.45764	−	0.979787i	0.185780	−	0.0740649i
$176$	0.245308	+	0.141629i	0.0184908	+	0.0106757i
$177$	25.1267	−	4.51132i	1.88864	−	0.339092i
$178$		−	13.4363i		−	1.00709i
$179$	16.3655	+	9.44863i	1.22322	+	0.706224i	0.965602	−	0.260025i	$-0.0837307\pi$
$179$	16.3655	+	9.44863i	1.22322	+	0.706224i	0.257613	+	0.966248i	$0.417064\pi$
$180$	1.75129	−	10.3074i	0.130534	−	0.768268i
$181$			12.5008i			0.929175i	0.885527	+	0.464588i	$0.153797\pi$
$181$			12.5008i			0.929175i	−0.885527	+	0.464588i	$0.846203\pi$
$182$	−28.2374	−	22.2720i	−2.09309	−	1.65091i
$183$	−5.27299	+	4.45265i	−0.389791	+	0.329149i
$184$	−1.37922			−0.101677
$185$	−5.50596	−	9.53660i	−0.404806	−	0.701145i
$186$	12.1137	−	33.6078i	0.888223	−	2.46424i
$187$	−1.25754	−	0.726042i	−0.0919605	−	0.0530934i
$188$	7.34904			0.535984
$189$	−8.41253	+	10.8733i	−0.611922	+	0.790918i
$190$	−1.86186			−0.135074
$191$	7.55653	+	4.36277i	0.546771	+	0.315679i	0.747819	−	0.663903i	$-0.231101\pi$
$191$	7.55653	+	4.36277i	0.546771	+	0.315679i	−0.201047	+	0.979582i	$0.564435\pi$
$192$	7.16214	−	19.8703i	0.516883	−	1.43402i
$193$	−5.69624	−	9.86618i	−0.410025	−	0.710183i	0.584867	−	0.811129i	$-0.301147\pi$
$193$	−5.69624	−	9.86618i	−0.410025	−	0.710183i	−0.994892	+	0.100945i	$0.967813\pi$
$194$	−37.1793			−2.66932
$195$	7.68071	−	6.48578i	0.550027	−	0.464457i
$196$	23.3872	+	6.94036i	1.67051	+	0.495740i
$197$			18.6026i			1.32538i	0.748893	+	0.662690i	$0.230585\pi$
$197$			18.6026i			1.32538i	−0.748893	+	0.662690i	$0.769415\pi$
$198$	1.58740	−	0.589000i	0.112812	−	0.0418584i
$199$	−19.5486	−	11.2864i	−1.38577	−	0.800072i	−0.392931	−	0.919568i	$-0.628539\pi$
$199$	−19.5486	−	11.2864i	−1.38577	−	0.800072i	−0.992835	+	0.119496i	$0.961872\pi$
$200$		−	3.47799i		−	0.245931i
$201$	−3.50086	+	0.628554i	−0.246932	+	0.0443348i
$202$	−0.673050	−	0.388585i	−0.0473556	−	0.0273408i
$203$	−9.15094	+	11.6019i	−0.642270	+	0.814296i
$204$	12.3336	−	34.2177i	0.863524	−	2.39572i
$205$	0.493886	−	0.855435i	0.0344945	−	0.0597462i
$206$	12.2622	−	21.2388i	0.854350	−	1.47978i
$207$	−0.759009	+	0.916090i	−0.0527548	+	0.0636726i
$208$	−5.90817	+	3.41108i	−0.409658	+	0.236516i
$209$	−0.0957884	−	0.165910i	−0.00662582	−	0.0114763i
$210$	−5.05277	+	9.46865i	−0.348674	+	0.653399i
$211$	−4.97834	+	8.62274i	−0.342723	+	0.593614i	−0.984937	−	0.172911i	$-0.944683\pi$
$211$	−4.97834	+	8.62274i	−0.342723	+	0.593614i	0.642214	+	0.766525i	$0.278016\pi$
$212$		−	1.31793i		−	0.0905155i
$213$	4.33820	+	1.56368i	0.297249	+	0.107142i
$214$	1.32745			0.0907427
$215$	2.80477	+	4.85800i	0.191284	+	0.331313i
$216$	9.18204	+	15.5658i	0.624758	+	1.05912i
$217$	−14.4297	+	18.2945i	−0.979551	+	1.24191i
$218$	9.87049	−	5.69873i	0.668514	−	0.385967i
$219$	−11.4094	+	9.63439i	−0.770977	+	0.651032i
$220$	0.727317	−	0.419917i	0.0490357	−	0.0283108i
$221$	30.2875	−	17.4865i	2.03736	−	1.17627i
$222$	42.0232	+	15.1470i	2.82042	+	1.01660i
$223$	−2.06000	+	1.18934i	−0.137948	+	0.0796443i	−0.567386	−	0.823452i	$-0.692045\pi$
$223$	−2.06000	+	1.18934i	−0.137948	+	0.0796443i	0.429438	+	0.903096i	$0.358712\pi$
$224$	−6.88675	+	8.73130i	−0.460140	+	0.583384i
$225$	−2.31011	−	1.91400i	−0.154007	−	0.127600i
$226$	−18.4448	−	31.9474i	−1.22693	−	2.12511i
$227$	6.16323			0.409068			0.204534	−	0.978859i	$-0.434432\pi$
$227$	6.16323			0.409068			0.204534	+	0.978859i	$0.434432\pi$
$228$	3.66641	−	3.09601i	0.242814	−	0.205038i
$229$			26.8755i			1.77598i	0.459862	+	0.887990i	$0.347899\pi$
$229$			26.8755i			1.77598i	−0.459862	+	0.887990i	$0.652101\pi$
$230$	−0.464371	+	0.804314i	−0.0306197	+	0.0530349i
$231$	−1.10370	+	0.0368881i	−0.0726184	+	0.00242706i
$232$	9.71226	+	16.8221i	0.637641	+	1.10443i
$233$	1.10739	−	0.639354i	0.0725478	−	0.0418855i	−0.463287	−	0.886208i	$-0.653330\pi$
$233$	1.10739	−	0.639354i	0.0725478	−	0.0418855i	0.535835	+	0.844323i	$0.319997\pi$
$234$	−6.83072	+	40.2029i	−0.446538	+	2.62815i
$235$	1.05437	−	1.82622i	0.0687795	−	0.119130i
$236$	−25.6828	+	44.4840i	−1.67181	+	2.89566i
$237$	−2.09886	−	2.48555i	−0.136336	−	0.161454i
$238$	−23.1228	+	29.3160i	−1.49883	+	1.90027i
$239$	−10.8351	−	6.25563i	−0.700862	−	0.404643i	0.106806	−	0.994280i	$-0.465937\pi$
$239$	−10.8351	−	6.25563i	−0.700862	−	0.404643i	−0.807668	+	0.589637i	$0.799271\pi$
$240$	1.31351	+	1.55550i	0.0847865	+	0.100407i
$241$			11.4155i			0.735335i	0.929957	+	0.367667i	$0.119844\pi$
$241$			11.4155i			0.735335i	−0.929957	+	0.367667i	$0.880156\pi$
$242$	−22.1929	−	12.8131i	−1.42661	−	0.823656i
$243$	15.3920	+	2.46734i	0.987394	+	0.158280i
$244$		−	13.8864i		−	0.888986i
$245$	5.08003	−	4.81594i	0.324552	−	0.307679i
$246$	0.708084	+	3.94382i	0.0451458	+	0.251449i
$247$	4.61407			0.293586
$248$	15.3148	+	26.5260i	0.972492	+	1.68440i
$249$	−3.76810	+	0.676534i	−0.238793	+	0.0428736i
$250$	−2.02825	−	1.17101i	−0.128278	−	0.0740611i
$251$	3.48345			0.219873			0.109937	−	0.993939i	$-0.464935\pi$
$251$	3.48345			0.219873			0.109937	+	0.993939i	$0.464935\pi$
$252$	−5.79501	−	27.0478i	−0.365051	−	1.70385i
$253$	−0.0955632			−0.00600800
$254$	24.4642	+	14.1244i	1.53502	+	0.886245i
$255$	−6.73353	−	7.97410i	−0.421670	−	0.499357i
$256$	11.4056	+	19.7551i	0.712850	+	1.23469i
$257$	−25.6042			−1.59715			−0.798574	−	0.601897i	$-0.794412\pi$
$257$	−25.6042			−1.59715			−0.798574	+	0.601897i	$0.794412\pi$
$258$	−21.4069	−	7.71600i	−1.33274	−	0.480377i
$259$	−22.8755	−	18.0429i	−1.42142	−	1.12113i
$260$			20.2271i			1.25443i
$261$	16.5182	+	2.80655i	1.02245	+	0.173721i
$262$	29.1064	+	16.8046i	1.79820	+	1.03819i
$263$			1.93451i			0.119287i	0.998220	+	0.0596434i	$0.0189964\pi$
$263$			1.93451i			0.119287i	−0.998220	+	0.0596434i	$0.981004\pi$
$264$	−0.492253	+	1.36568i	−0.0302961	+	0.0840521i
$265$	−0.327502	−	0.189083i	−0.0201183	−	0.0116153i
$266$	−4.57580	+	1.82423i	−0.280560	+	0.111851i
$267$	9.78051	−	1.75602i	0.598557	−	0.107467i
$268$	3.57834	−	6.19787i	0.218582	−	0.378595i
$269$	5.96644	−	10.3342i	0.363780	−	0.630086i	−0.624799	−	0.780785i	$-0.714819\pi$
$269$	5.96644	−	10.3342i	0.363780	−	0.630086i	0.988580	+	0.150700i	$0.0481526\pi$
$270$	12.1689	−	0.113794i	0.740578	−	0.00692527i
$271$	−15.6502	+	9.03565i	−0.950682	+	0.548877i	−0.893293	−	0.449475i	$-0.851611\pi$
$271$	−15.6502	+	9.03565i	−0.950682	+	0.548877i	−0.0573895	+	0.998352i	$0.518278\pi$
$272$	3.54138	+	6.13385i	0.214728	+	0.371919i
$273$	12.5218	−	23.4652i	0.757852	−	1.42018i
$274$	2.52165	−	4.36762i	0.152338	−	0.263858i
$275$		−	0.240982i		−	0.0145318i
$276$	−0.423011	−	2.35605i	−0.0254623	−	0.141818i
$277$	18.3023			1.09968			0.549838	−	0.835271i	$-0.314689\pi$
$277$	18.3023			1.09968			0.549838	+	0.835271i	$0.314689\pi$
$278$	18.6999	+	32.3891i	1.12154	+	1.94257i
$279$	26.0468	+	4.42552i	1.55938	+	0.264949i
$280$	−3.40769	−	8.54766i	−0.203648	−	0.510821i
$281$	18.3680	−	10.6048i	1.09575	−	0.632629i	0.160645	−	0.987012i	$-0.448643\pi$
$281$	18.3680	−	10.6048i	1.09575	−	0.632629i	0.935100	+	0.354384i	$0.115309\pi$
$282$	1.51165	+	8.41946i	0.0900175	+	0.501371i
$283$	1.43261	−	0.827120i	0.0851601	−	0.0491672i	−0.456815	−	0.889562i	$-0.651010\pi$
$283$	1.43261	−	0.827120i	0.0851601	−	0.0491672i	0.541975	+	0.840394i	$0.317677\pi$
$284$	−8.03547	+	4.63928i	−0.476817	+	0.275291i
$285$	−0.243330	−	1.35528i	−0.0144137	−	0.0802798i
$286$	−2.83682	+	1.63784i	−0.167745	+	0.0968475i
$287$	0.375651	−	2.58626i	0.0221740	−	0.152662i
$288$	12.4312	+	2.11213i	0.732514	+	0.124459i
$289$	−9.65444	−	16.7220i	−0.567908	−	0.983646i
$290$	13.0801			0.768092
$291$	−4.85903	−	27.0634i	−0.284842	−	1.58648i
$292$		−	30.0466i		−	1.75835i
$293$	−11.7536	+	20.3579i	−0.686655	+	1.18932i	0.286259	+	0.958152i	$0.407588\pi$
$293$	−11.7536	+	20.3579i	−0.686655	+	1.18932i	−0.972914	+	0.231169i	$0.925745\pi$
$294$	−3.14065	+	28.2212i	−0.183166	+	1.64590i
$295$	7.36945	+	12.7643i	0.429066	+	0.743164i
$296$	−33.1682	+	19.1497i	−1.92786	+	1.11305i
$297$	0.636203	+	1.07852i	0.0369163	+	0.0625820i
$298$	1.60105	−	2.77310i	0.0927464	−	0.160641i
$299$	1.15080	−	1.99325i	0.0665527	−	0.115273i
$300$	5.94127	−	1.06671i	0.343019	−	0.0615866i
$301$	11.6529	+	9.19117i	0.671664	+	0.529770i
$302$	−8.56307	−	4.94389i	−0.492749	−	0.284489i
$303$	0.194895	−	0.540709i	0.0111964	−	0.0310629i
$304$			0.934445i			0.0535941i
$305$	−3.45074	−	1.99229i	−0.197589	−	0.114078i
$306$	41.7386	+	7.09165i	2.38604	+	0.405402i
$307$		−	15.5809i		−	0.889246i	−0.895718	−	0.444623i	$-0.853338\pi$
$307$		−	15.5809i		−	0.889246i	0.895718	−	0.444623i	$-0.146662\pi$
$308$	1.37606	−	1.74462i	0.0784082	−	0.0994090i
$309$	17.0626	+	6.15014i	0.970660	+	0.349869i
$310$	20.6254			1.17145
$311$	−9.23270	−	15.9915i	−0.523539	−	0.906796i	−0.999625	−	0.0273968i	$-0.991278\pi$
$311$	−9.23270	−	15.9915i	−0.523539	−	0.906796i	0.476086	−	0.879399i	$-0.342055\pi$
$312$	−22.5575	−	26.7134i	−1.27707	−	1.51235i
$313$	−14.3818	−	8.30334i	−0.812908	−	0.469333i	0.0350566	−	0.999385i	$-0.488839\pi$
$313$	−14.3818	−	8.30334i	−0.812908	−	0.469333i	−0.847965	+	0.530053i	$0.822172\pi$
$314$	−5.58602			−0.315237
$315$	−7.55274	−	2.44051i	−0.425549	−	0.137507i
$316$	6.54568			0.368223
$317$	−11.7602	−	6.78974i	−0.660517	−	0.381350i	0.131957	−	0.991255i	$-0.457874\pi$
$317$	−11.7602	−	6.78974i	−0.660517	−	0.381350i	−0.792474	+	0.609906i	$0.791207\pi$
$318$	1.50989	−	0.271089i	0.0846702	−	0.0152019i
$319$	0.672942	+	1.16557i	0.0376775	+	0.0652593i
$320$	12.1946			0.681699
$321$	0.173487	+	0.966273i	0.00968311	+	0.0539321i
$322$	−0.353203	+	2.43170i	−0.0196832	+	0.135514i
$323$		−	4.79032i		−	0.266540i
$324$	−23.7740	+	20.4593i	−1.32078	+	1.13663i
$325$	5.02640	+	2.90199i	0.278814	+	0.160974i
$326$		−	40.9950i		−	2.27050i
$327$	5.43819	+	6.44011i	0.300732	+	0.356139i
$328$	−2.97519	−	1.71773i	−0.164278	−	0.0948457i
$329$	0.801958	−	5.52126i	0.0442134	−	0.304397i
$330$	0.630683	+	0.746879i	0.0347180	+	0.0411143i
$331$	−14.8106	+	25.6528i	−0.814066	+	1.41000i	0.0959307	+	0.995388i	$0.469417\pi$
$331$	−14.8106	+	25.6528i	−0.814066	+	1.41000i	−0.909997	+	0.414616i	$0.863916\pi$
$332$	3.85149	−	6.67097i	0.211378	−	0.366117i
$333$	−5.53367	+	32.5690i	−0.303243	+	1.78477i
$334$	33.1631	−	19.1467i	1.81460	−	1.04766i
$335$	−1.02677	−	1.77842i	−0.0560986	−	0.0971655i
$336$	4.75219	+	2.53592i	0.259253	+	0.138346i
$337$	5.12883	−	8.88339i	0.279385	−	0.483909i	−0.691847	−	0.722044i	$-0.743203\pi$
$337$	5.12883	−	8.88339i	0.279385	−	0.483909i	0.971232	+	0.238135i	$0.0765361\pi$
$338$		−	48.4475i		−	2.63520i
$339$	20.8444	−	17.6016i	1.13211	−	0.955985i
$340$	20.9998			1.13887
$341$	1.06113	+	1.83793i	0.0574634	+	0.0995295i
$342$	4.30111	+	3.56360i	0.232577	+	0.192698i
$343$	7.76633	−	16.8132i	0.419342	−	0.907828i
$344$	16.8961	−	9.75496i	0.910976	−	0.525952i
$345$	−0.646163	−	0.232906i	−0.0347882	−	0.0125392i
$346$	−37.5481	+	21.6784i	−2.01860	+	1.16544i
$347$	24.6586	−	14.2367i	1.32374	−	0.764264i	0.339420	−	0.940635i	$-0.389769\pi$
$347$	24.6586	−	14.2367i	1.32374	−	0.764264i	0.984324	+	0.176371i	$0.0564360\pi$
$348$	−25.7576	+	21.7504i	−1.38075	+	1.16594i
$349$	1.01722	−	0.587291i	0.0544504	−	0.0314370i	−0.472528	−	0.881316i	$-0.656658\pi$
$349$	1.01722	−	0.587291i	0.0544504	−	0.0314370i	0.526978	+	0.849879i	$0.323325\pi$
$350$	−6.13205	−	0.890673i	−0.327772	−	0.0476085i
$351$	−30.1571	+	0.282004i	−1.60966	+	0.0150523i
$352$	0.506437	+	0.877175i	0.0269932	+	0.0467536i
$353$	−31.6082			−1.68234			−0.841168	−	0.540773i	$-0.818132\pi$
$353$	−31.6082			−1.68234			−0.841168	+	0.540773i	$0.818132\pi$
$354$	−56.2460	−	20.2736i	−2.98944	−	1.07753i
$355$			2.66240i			0.141305i
$356$	−9.99696	+	17.3153i	−0.529838	+	0.917706i
$357$	−24.3615	−	13.0001i	−1.28935	−	0.688037i
$358$	−22.1288	−	38.3283i	−1.16955	−	2.02571i
$359$	−19.5928	+	11.3119i	−1.03407	+	0.597019i	−0.918147	−	0.396240i	$-0.870315\pi$
$359$	−19.5928	+	11.3119i	−1.03407	+	0.597019i	−0.115920	+	0.993259i	$0.536982\pi$
$360$	−6.65687	+	8.03454i	−0.350848	+	0.423457i
$361$	−9.18400	+	15.9072i	−0.483368	+	0.837219i
$362$	14.6385	−	25.3546i	0.769383	−	1.33261i
$363$	6.42642	−	17.8291i	0.337299	−	0.935788i
$364$	19.8183	+	49.7111i	1.03876	+	2.60557i
$365$	−7.46653	−	4.31080i	−0.390816	−	0.225638i
$366$	15.9090	−	2.85635i	0.831577	−	0.149304i
$367$			9.82818i			0.513027i	0.966541	+	0.256514i	$0.0825738\pi$
$367$			9.82818i			0.513027i	−0.966541	+	0.256514i	$0.917426\pi$
$368$	0.403675	+	0.233062i	0.0210430	+	0.0121492i
$369$	−2.77823	+	1.03085i	−0.144629	+	0.0536640i
$370$			25.7901i			1.34076i
$371$	−0.990144	−	0.143817i	−0.0514057	−	0.00746663i
$372$	−40.6159	+	34.2971i	−2.10584	+	1.77822i
$373$	14.4369			0.747517			0.373758	−	0.927526i	$-0.378069\pi$
$373$	14.4369			0.747517			0.373758	+	0.927526i	$0.378069\pi$
$374$	1.70040	+	2.94518i	0.0879257	+	0.152292i
$375$	0.587320	−	1.62943i	0.0303291	−	0.0841436i
$376$	−6.35158	−	3.66709i	−0.327558	−	0.189116i
$377$	−32.4152			−1.66947
$378$	29.7954	−	12.2026i	1.53251	−	0.627636i
$379$	26.1822			1.34489			0.672444	−	0.740148i	$-0.265244\pi$
$379$	26.1822			1.34489			0.672444	+	0.740148i	$0.265244\pi$
$380$	2.39936	+	1.38527i	0.123085	+	0.0710630i
$381$	−7.08412	+	19.6538i	−0.362930	+	1.00690i
$382$	−10.2177	−	17.6975i	−0.522781	−	0.905484i
$383$	2.10791			0.107709			0.0538545	−	0.998549i	$-0.482849\pi$
$383$	2.10791			0.107709			0.0538545	+	0.998549i	$0.482849\pi$
$384$	−26.6705	+	22.5212i	−1.36102	+	1.14928i
$385$	−0.236111	−	0.592249i	−0.0120333	−	0.0301838i
$386$			26.6814i			1.35805i
$387$	2.81889	−	16.5908i	0.143292	−	0.843360i
$388$	47.9126	+	27.6623i	2.43239	+	1.40434i
$389$		−	28.3647i		−	1.43815i	−0.694933	−	0.719075i	$-0.744566\pi$
$389$		−	28.3647i		−	1.43815i	0.694933	−	0.719075i	$-0.255434\pi$
$390$	−23.1733	+	4.16059i	−1.17342	+	0.210680i
$391$	−2.06939	−	1.19476i	−0.104654	−	0.0604218i
$392$	−16.7498	−	17.6683i	−0.845992	−	0.892384i
$393$	−8.42835	+	23.3832i	−0.425154	+	1.17953i
$394$	21.7838	−	37.7307i	1.09745	−	1.90084i
$395$	0.939111	−	1.62659i	0.0472518	−	0.0818425i
$396$	−2.48390	−	0.422030i	−0.124821	−	0.0212078i
$397$	12.0308	−	6.94599i	0.603809	−	0.348609i	−0.166730	−	0.986003i	$-0.553321\pi$
$397$	12.0308	−	6.94599i	0.603809	−	0.348609i	0.770538	+	0.637394i	$0.219987\pi$
$398$	26.4330	+	45.7832i	1.32496	+	2.29491i
$399$	−1.92591	−	3.09238i	−0.0964159	−	0.154813i
$400$	−0.587714	+	1.01795i	−0.0293857	+	0.0508975i
$401$			21.0354i			1.05046i	0.850961	+	0.525229i	$0.176020\pi$
$401$			21.0354i			1.05046i	−0.850961	+	0.525229i	$0.823980\pi$
$402$	7.83666	+	2.82468i	0.390857	+	0.140882i
$403$	−51.1140			−2.54617
$404$	0.578235	+	1.00153i	0.0287683	+	0.0498281i
$405$	1.67322	+	8.84310i	0.0831427	+	0.439417i
$406$	32.1463	−	12.8157i	1.59539	−	0.636035i
$407$	−2.29815	+	1.32684i	−0.113915	+	0.0657690i
$408$	−27.7338	+	23.4191i	−1.37303	+	1.15942i
$409$	13.7622	−	7.94558i	0.680495	−	0.392884i	−0.119547	−	0.992829i	$-0.538144\pi$
$409$	13.7622	−	7.94558i	0.680495	−	0.392884i	0.800041	+	0.599945i	$0.204811\pi$
$410$	−2.00344	+	1.15669i	−0.0989430	+	0.0571248i
$411$	3.50882	+	1.26473i	0.173077	+	0.0623847i
$412$	−31.6044	+	18.2468i	−1.55704	+	0.898957i
$413$	30.6177	+	24.1495i	1.50660	+	1.18832i
$414$	2.61221	−	0.969249i	0.128383	−	0.0476360i
$415$	−1.10515	−	1.91417i	−0.0542496	−	0.0939631i
$416$	−24.3948			−1.19605
$417$	−21.1326	+	17.8449i	−1.03487	+	0.873870i
$418$			0.448676i			0.0219455i
$419$	17.4324	−	30.1939i	0.851631	−	1.47507i	−0.0281052	−	0.999605i	$-0.508947\pi$
$419$	17.4324	−	30.1939i	0.851631	−	1.47507i	0.879736	−	0.475463i	$-0.157719\pi$
$420$	13.5564	−	8.44277i	0.661483	−	0.411965i
$421$	3.61723	+	6.26523i	0.176293	+	0.305349i	0.940608	−	0.339495i	$-0.110256\pi$
$421$	3.61723	+	6.26523i	0.176293	+	0.305349i	−0.764315	+	0.644843i	$0.776923\pi$
$422$	20.1946	−	11.6594i	0.983058	−	0.567569i
$423$	−5.93110	+	2.20071i	−0.288380	+	0.107002i
$424$	−0.657630	+	1.13905i	−0.0319373	+	0.0553171i
$425$	3.01284	−	5.21840i	0.146144	−	0.253129i
$426$	−6.96785	−	8.25159i	−0.337594	−	0.399791i
$427$	−10.4327	−	1.51534i	−0.504875	−	0.0733325i
$428$	−1.71067	−	0.987658i	−0.0826885	−	0.0477402i
$429$	−1.56296	−	1.85092i	−0.0754604	−	0.0893630i
$430$		−	13.1376i		−	0.633553i
$431$	23.1880	+	13.3876i	1.11693	+	0.644859i	0.940615	−	0.339475i	$-0.110249\pi$
$431$	23.1880	+	13.3876i	1.11693	+	0.644859i	0.176314	+	0.984334i	$0.443583\pi$
$432$	−0.0571117	−	6.10743i	−0.00274779	−	0.293844i
$433$		−	11.2142i		−	0.538921i	−0.963011	−	0.269460i	$-0.913155\pi$
$433$		−	11.2142i		−	0.538921i	0.963011	−	0.269460i	$-0.0868453\pi$
$434$	50.6900	−	20.2085i	2.43320	−	0.970041i
$435$	1.70947	+	9.52124i	0.0819627	+	0.456508i
$436$	−16.9600			−0.812237
$437$	−0.157628	−	0.273019i	−0.00754036	−	0.0130603i
$438$	34.4230	−	6.18040i	1.64480	−	0.295311i
$439$	−14.6450	−	8.45528i	−0.698967	−	0.403548i	0.107996	−	0.994151i	$-0.465557\pi$
$439$	−14.6450	−	8.45528i	−0.698967	−	0.403548i	−0.806962	+	0.590603i	$0.798890\pi$
$440$	−0.838134			−0.0399565
$441$	−20.9531	+	1.40216i	−0.997768	+	0.0667695i
$442$	−81.9073			−3.89593
$443$	−11.8410	−	6.83642i	−0.562584	−	0.324808i	0.191598	−	0.981474i	$-0.438633\pi$
$443$	−11.8410	−	6.83642i	−0.562584	−	0.324808i	−0.754182	+	0.656665i	$0.771966\pi$
$444$	−42.8852	−	50.7862i	−2.03524	−	2.41021i
$445$	2.86854	+	4.96845i	0.135982	+	0.235527i
$446$	5.57092			0.263791
$447$	2.22783	+	0.803009i	0.105373	+	0.0379810i
$448$	29.9700	−	11.9481i	1.41595	−	0.564495i
$449$		−	10.8478i		−	0.511940i	−0.966685	−	0.255970i	$-0.917605\pi$
$449$		−	10.8478i		−	0.511940i	0.966685	−	0.255970i	$-0.0823948\pi$
$450$	2.44416	+	6.58722i	0.115219	+	0.310524i
$451$	−0.206145	−	0.119018i	−0.00970697	−	0.00560432i
$452$			54.8937i			2.58198i
$453$	2.47961	−	6.87932i	0.116502	−	0.323219i
$454$	−12.5005	−	7.21719i	−0.586679	−	0.338719i
$455$	15.1964	+	2.20727i	0.712420	+	0.103478i
$456$	−4.71365	+	0.846301i	−0.220737	+	0.0396317i
$457$	4.15591	−	7.19824i	0.194405	−	0.336719i	−0.752300	−	0.658820i	$-0.771056\pi$
$457$	4.15591	−	7.19824i	0.194405	−	0.336719i	0.946705	+	0.322101i	$0.104389\pi$
$458$	31.4714	−	54.5100i	1.47056	−	2.54709i
$459$	0.292776	+	31.3090i	0.0136656	+	1.46138i
$460$	1.19686	−	0.691008i	0.0558039	−	0.0322184i
$461$	0.892772	+	1.54633i	0.0415805	+	0.0720196i	0.886067	−	0.463558i	$-0.153427\pi$
$461$	0.892772	+	1.54633i	0.0415805	+	0.0720196i	−0.844486	+	0.535577i	$0.820094\pi$
$462$	2.28178	+	1.21763i	0.106158	+	0.0566492i
$463$	−2.30815	+	3.99784i	−0.107269	+	0.185795i	−0.914663	−	0.404217i	$-0.867544\pi$
$463$	−2.30815	+	3.99784i	−0.107269	+	0.185795i	0.807394	+	0.590013i	$0.200877\pi$
$464$		−	6.56475i		−	0.304761i
$465$	2.69558	+	15.0136i	0.125005	+	0.696239i
$466$	−2.99476			−0.138729
$467$	7.71918	+	13.3700i	0.357201	+	0.618690i	0.987492	−	0.157669i	$-0.0503978\pi$
$467$	7.71918	+	13.3700i	0.357201	+	0.618690i	−0.630291	+	0.776359i	$0.717065\pi$
$468$	38.7147	−	46.7269i	1.78959	−	2.15995i
$469$	−4.26592	−	3.36471i	−0.196982	−	0.155368i
$470$	−4.27704	+	2.46935i	−0.197285	+	0.113903i
$471$	−0.730048	−	4.06616i	−0.0336388	−	0.187359i
$472$	44.3940	−	25.6309i	2.04340	−	1.17976i
$473$	1.17069	−	0.675900i	0.0538285	−	0.0310779i
$474$	1.34640	+	7.49908i	0.0618424	+	0.344444i
$475$	0.688475	−	0.397491i	0.0315894	−	0.0182382i
$476$	51.6099	−	20.5753i	2.36554	−	0.943067i
$477$	0.394660	+	1.06364i	0.0180702	+	0.0487008i
$478$	14.6508	+	25.3759i	0.670111	+	1.16067i
$479$	−8.52828			−0.389667			−0.194834	−	0.980836i	$-0.562417\pi$
$479$	−8.52828			−0.389667			−0.194834	+	0.980836i	$0.562417\pi$
$480$	1.28650	+	7.16542i	0.0587204	+	0.327055i
$481$		−	63.9130i		−	2.91418i
$482$	13.3676	−	23.1534i	0.608878	−	1.05461i
$483$	−1.81624	+	0.0607024i	−0.0826417	+	0.00276205i
$484$	19.0665	+	33.0242i	0.866661	+	1.50110i
$485$	13.7481	−	7.93745i	0.624268	−	0.360421i
$486$	−28.3294	−	23.0285i	−1.28505	−	1.04459i
$487$	1.42319	−	2.46503i	0.0644907	−	0.111701i	−0.831977	−	0.554810i	$-0.812791\pi$
$487$	1.42319	−	2.46503i	0.0644907	−	0.111701i	0.896468	+	0.443109i	$0.146124\pi$
$488$	−6.92916	+	12.0017i	−0.313668	+	0.543289i
$489$	29.8409	−	5.35772i	1.34945	−	0.242284i
$490$	−15.9431	+	3.81914i	−0.720234	+	0.172531i
$491$	−30.4913	−	17.6042i	−1.37605	−	0.794465i	−0.384372	−	0.923178i	$-0.625582\pi$
$491$	−30.4913	−	17.6042i	−1.37605	−	0.794465i	−0.991682	+	0.128713i	$0.958915\pi$
$492$	2.02180	−	5.60920i	0.0911500	−	0.252882i
$493$			33.6534i			1.51567i
$494$	−9.35846	−	5.40311i	−0.421057	−	0.243097i
$495$	−0.461240	+	0.556696i	−0.0207312	+	0.0250216i
$496$		−	10.3516i		−	0.464802i
$497$	2.60858	+	6.54323i	0.117011	+	0.293504i
$498$	8.43485	+	3.04029i	0.377975	+	0.136239i
$499$	−14.4168			−0.645385			−0.322692	−	0.946504i	$-0.604588\pi$
$499$	−14.4168			−0.645385			−0.322692	+	0.946504i	$0.604588\pi$
$500$	1.74252	+	3.01813i	0.0779279	+	0.134975i
$501$	18.2714	+	21.6376i	0.816304	+	0.966698i
$502$	−7.06529	−	4.07915i	−0.315339	−	0.182061i
$503$	−3.65662			−0.163041			−0.0815204	−	0.996672i	$-0.525978\pi$
$503$	−3.65662			−0.163041			−0.0815204	+	0.996672i	$0.525978\pi$
$504$	−8.48808	+	26.2684i	−0.378089	+	1.17009i
$505$	0.331838			0.0147666
$506$	0.193826	+	0.111905i	0.00861660	+	0.00497480i
$507$	35.2657	−	6.33170i	1.56620	−	0.281200i
$508$	−21.0179	−	36.4040i	−0.932517	−	1.61517i
$509$	20.6591			0.915697			0.457849	−	0.889030i	$-0.348620\pi$
$509$	20.6591			0.915697			0.457849	+	0.889030i	$0.348620\pi$
$510$	4.31952	+	24.0584i	0.191271	+	1.06533i
$511$	−22.5737	−	3.27881i	−0.998604	−	0.145046i
$512$		−	13.1167i		−	0.579682i
$513$	−2.03188	+	3.59658i	−0.0897099	+	0.158793i
$514$	51.9317	+	29.9828i	2.29061	+	1.32248i
$515$			10.4715i			0.461430i
$516$	21.8460	+	25.8708i	0.961715	+	1.13890i
$517$	−0.440087	−	0.254084i	−0.0193550	−	0.0111746i
$518$	25.2688	+	63.3829i	1.11025	+	2.78488i
$519$	−20.6873	−	24.4987i	−0.908071	−	1.07537i
$520$	10.0931	−	17.4818i	0.442612	−	0.766626i
$521$	15.7853	−	27.3410i	0.691567	−	1.19783i	−0.279757	−	0.960071i	$-0.590254\pi$
$521$	15.7853	−	27.3410i	0.691567	−	1.19783i	0.971324	−	0.237758i	$-0.0764127\pi$
$522$	−30.2165	−	25.0354i	−1.32254	−	1.09577i
$523$	−31.3429	+	18.0958i	−1.37053	+	0.791274i	−0.990994	−	0.133904i	$-0.957249\pi$
$523$	−31.3429	+	18.0958i	−1.37053	+	0.791274i	−0.379533	+	0.925178i	$0.623915\pi$
$524$	−25.0061	−	43.3118i	−1.09239	−	1.89208i
$525$	−0.153074	−	4.58002i	−0.00668068	−	0.199888i
$526$	2.26532	−	3.92366i	0.0987728	−	0.171080i
$527$			53.0664i			2.31161i
$528$	0.374849	−	0.316532i	0.0163132	−	0.0137753i
$529$	22.8427			0.993163
$530$	0.442836	+	0.767015i	0.0192356	+	0.0333170i
$531$	7.40655	−	43.5920i	0.321417	−	1.89173i
$532$	7.25406	+	1.05364i	0.314503	+	0.0456813i
$533$	4.96493	−	2.86650i	0.215055	−	0.124162i
$534$	−21.8936	−	7.89142i	−0.947428	−	0.341495i
$535$	−0.490862	+	0.283399i	−0.0212218	+	0.0122524i
$536$	−6.18533	+	3.57110i	−0.267166	+	0.154248i
$537$	25.0077	−	21.1171i	1.07916	−	0.911272i
$538$	−24.2028	+	13.9735i	−1.04346	+	0.602440i
$539$	−1.16056	−	1.22420i	−0.0499887	−	0.0527300i
$540$	−15.7667	−	8.90736i	−0.678489	−	0.383312i
$541$	20.8272	+	36.0737i	0.895429	+	1.55093i	0.833273	+	0.552862i	$0.186465\pi$
$541$	20.8272	+	36.0737i	0.895429	+	1.55093i	0.0621567	+	0.998066i	$0.480202\pi$
$542$	42.3233			1.81794
$543$	20.3692	+	7.34196i	0.874126	+	0.315074i
$544$			25.3266i			1.08587i
$545$	−2.43326	+	4.21452i	−0.104229	+	0.180530i
$546$	−52.8752	+	32.9301i	−2.26285	+	1.40928i
$547$	12.2984	+	21.3015i	0.525843	+	0.910787i	0.999547	+	0.0301027i	$0.00958343\pi$
$547$	12.2984	+	21.3015i	0.525843	+	0.910787i	−0.473704	+	0.880684i	$0.657083\pi$
$548$	−6.49924	+	3.75234i	−0.277634	+	0.160292i
$549$	4.15836	+	11.2071i	0.177474	+	0.478308i
$550$	−0.282192	+	0.488771i	−0.0120327	+	0.0208413i
$551$	−2.21998	+	3.84513i	−0.0945745	+	0.163808i
$552$	−0.810044	+	2.24735i	−0.0344778	+	0.0956535i
$553$	0.714291	−	4.91770i	0.0303748	−	0.209122i
$554$	−37.1215	−	21.4321i	−1.57714	−	0.910563i
$555$	−18.7730	+	3.37056i	−0.796870	+	0.143072i
$556$		−	55.6527i		−	2.36020i
$557$	−1.86698	−	1.07790i	−0.0791065	−	0.0456722i	0.459925	−	0.887958i	$-0.347876\pi$
$557$	−1.86698	−	1.07790i	−0.0791065	−	0.0456722i	−0.539032	+	0.842286i	$0.681210\pi$
$558$	−47.6470	−	39.4771i	−2.01706	−	1.67120i
$559$			32.5577i			1.37704i
$560$	−0.447017	+	3.07759i	−0.0188899	+	0.130052i
$561$	−1.92162	+	1.62266i	−0.0811307	+	0.0685088i
$562$	−49.6732			−2.09534
$563$	0.453715	+	0.785857i	0.0191218	+	0.0331199i	0.875428	−	0.483349i	$-0.160580\pi$
$563$	0.453715	+	0.785857i	0.0191218	+	0.0331199i	−0.856306	+	0.516469i	$0.827246\pi$
$564$	4.31624	−	11.9748i	0.181747	−	0.504229i
$565$	13.6410	+	7.87562i	0.573880	+	0.331330i
$566$	−3.87426			−0.162847
$567$	12.7765	+	20.0938i	0.536563	+	0.843860i
$568$	9.25979			0.388532
$569$	−33.2443	−	19.1936i	−1.39367	−	0.804638i	−0.399954	−	0.916535i	$-0.630974\pi$
$569$	−33.2443	−	19.1936i	−1.39367	−	0.804638i	−0.993720	+	0.111897i	$0.964307\pi$
$570$	−1.09351	+	3.03378i	−0.0458021	+	0.127071i
$571$	−6.24499	−	10.8166i	−0.261345	−	0.452663i	0.705255	−	0.708954i	$-0.250833\pi$
$571$	−6.24499	−	10.8166i	−0.261345	−	0.452663i	−0.966600	+	0.256291i	$0.917499\pi$
$572$	4.87438			0.203808
$573$	11.5469	−	9.75053i	0.482380	−	0.407334i
$574$	−3.79044	+	4.80568i	−0.158210	+	0.200585i
$575$		−	0.396557i		−	0.0165376i
$576$	−28.1709	−	23.3405i	−1.17379	−	0.972519i
$577$	−18.9922	−	10.9652i	−0.790656	−	0.456485i	0.0495375	−	0.998772i	$-0.484225\pi$
$577$	−18.9922	−	10.9652i	−0.790656	−	0.456485i	−0.840193	+	0.542287i	$0.817559\pi$
$578$			45.2217i			1.88098i
$579$	−19.4218	+	3.48704i	−0.807143	+	0.144917i
$580$	−16.8562	−	9.73195i	−0.699917	−	0.404097i
$581$	−4.59154	−	3.62155i	−0.190489	−	0.150247i
$582$	−21.8361	+	60.5812i	−0.905137	+	2.51117i
$583$	−0.0455657	+	0.0789222i	−0.00188714	+	0.00326862i
$584$	−14.9929	+	25.9685i	−0.620412	+	1.07458i
$585$	−6.05712	−	16.3244i	−0.250431	−	0.674932i
$586$	47.6785	−	27.5272i	1.96958	−	1.13714i
$587$	2.41365	+	4.18057i	0.0996221	+	0.172550i	0.911528	−	0.411237i	$-0.134903\pi$
$587$	2.41365	+	4.18057i	0.0996221	+	0.172550i	−0.811906	+	0.583788i	$0.801570\pi$
$588$	25.0446	−	34.0317i	1.03282	−	1.40344i
$589$	−3.50059	+	6.06320i	−0.144239	+	0.249830i
$590$		−	34.5187i		−	1.42111i
$591$	30.3117	+	10.9257i	1.24686	+	0.449423i
$592$	12.9437			0.531983
$593$	−10.9883	−	19.0323i	−0.451236	−	0.781563i	0.547227	−	0.836984i	$-0.315683\pi$
$593$	−10.9883	−	19.0323i	−0.451236	−	0.781563i	−0.998463	+	0.0554206i	$0.982350\pi$
$594$	−0.0274223	−	2.93250i	−0.00112515	−	0.120322i
$595$	2.29158	−	15.7769i	0.0939456	−	0.646790i
$596$	−4.12652	+	2.38245i	−0.169029	+	0.0975888i
$597$	−29.8718	+	25.2245i	−1.22257	+	1.03237i
$598$	−4.66823	+	2.69520i	−0.190898	+	0.110215i
$599$	0.394818	−	0.227948i	0.0161318	−	0.00931371i	−0.491912	−	0.870645i	$-0.663702\pi$
$599$	0.394818	−	0.227948i	0.0161318	−	0.00931371i	0.508044	+	0.861331i	$0.330369\pi$
$600$	−5.66715	−	2.04269i	−0.231361	−	0.0833926i
$601$	17.3200	−	9.99972i	0.706498	−	0.407897i	−0.103265	−	0.994654i	$-0.532929\pi$
$601$	17.3200	−	9.99972i	0.706498	−	0.407897i	0.809763	+	0.586757i	$0.199596\pi$
$602$	−12.8721	−	32.2876i	−0.524627	−	1.31595i
$603$	−1.03194	+	6.07359i	−0.0420239	+	0.247336i
$604$	7.35676	+	12.7423i	0.299342	+	0.518476i
$605$	10.9419			0.444853
$606$	−1.02847	+	0.868466i	−0.0417787	+	0.0352790i
$607$		−	20.2057i		−	0.820122i	−0.912058	−	0.410061i	$-0.865507\pi$
$607$		−	20.2057i		−	0.820122i	0.912058	−	0.410061i	$-0.134493\pi$
$608$	−1.67070	+	2.89374i	−0.0677558	+	0.117357i
$609$	13.5301	+	21.7249i	0.548265	+	0.880338i
$610$	4.66597	+	8.08170i	0.188920	+	0.327218i
$611$	10.5994	−	6.11954i	0.428804	−	0.247570i
$612$	−48.5118	−	40.1935i	−1.96097	−	1.62473i
$613$	7.62154	−	13.2009i	0.307831	−	0.533179i	−0.670057	−	0.742310i	$-0.733730\pi$
$613$	7.62154	−	13.2009i	0.307831	−	0.533179i	0.977888	+	0.209131i	$0.0670635\pi$
$614$	−18.2453	+	31.6018i	−0.736321	+	1.27534i
$615$	−1.10381	−	1.30717i	−0.0445097	−	0.0527101i
$616$	−2.05984	+	0.821193i	−0.0829932	+	0.0330868i
$617$	−6.80537	−	3.92908i	−0.273974	−	0.158179i	0.356718	−	0.934212i	$-0.383896\pi$
$617$	−6.80537	−	3.92908i	−0.273974	−	0.158179i	−0.630692	+	0.776033i	$0.717229\pi$
$618$	−27.4054	−	32.4545i	−1.10241	−	1.30551i
$619$			4.71850i			0.189653i	0.995494	+	0.0948263i	$0.0302296\pi$
$619$			4.71850i			0.189653i	−0.995494	+	0.0948263i	$0.969770\pi$
$620$	−26.5798	−	15.3459i	−1.06747	−	0.616305i
$621$	1.04693	+	1.77479i	0.0420117	+	0.0712200i
$622$			43.2463i			1.73402i
$623$	11.9179	+	9.40013i	0.477479	+	0.376608i
$624$	2.08815	+	11.6304i	0.0835927	+	0.465587i
$625$	1.00000			0.0400000
$626$	19.4466	+	33.6824i	0.777241	+	1.34622i
$627$	−0.326598	+	0.0586384i	−0.0130431	+	0.00234179i
$628$	7.19865	+	4.15614i	0.287258	+	0.165848i
$629$	−66.3543			−2.64572
$630$	12.4610	+	13.7943i	0.496456	+	0.549577i
$631$	−24.0883			−0.958938			−0.479469	−	0.877559i	$-0.659171\pi$
$631$	−24.0883			−0.958938			−0.479469	+	0.877559i	$0.659171\pi$
$632$	−5.65726	−	3.26622i	−0.225034	−	0.129923i
$633$	11.1263	+	13.1762i	0.442231	+	0.523707i
$634$	15.9017	+	27.5425i	0.631537	+	1.09385i
$635$	−12.0618			−0.478656
$636$	−2.14747	−	0.774045i	−0.0851528	−	0.0306929i
$637$	39.5101	−	9.46459i	1.56545	−	0.375001i
$638$		−	3.15208i		−	0.124792i
$639$	5.09583	−	6.15043i	0.201588	−	0.243307i
$640$	−17.4537	−	10.0769i	−0.689916	−	0.398323i
$641$		−	3.97240i		−	0.156901i	−0.996918	−	0.0784503i	$-0.975003\pi$
$641$		−	3.97240i		−	0.156901i	0.996918	−	0.0784503i	$-0.0249972\pi$
$642$	0.779639	−	2.16299i	0.0307699	−	0.0853666i
$643$	13.2235	+	7.63462i	0.521486	+	0.301080i	0.737542	−	0.675301i	$-0.235986\pi$
$643$	13.2235	+	7.63462i	0.521486	+	0.301080i	−0.216057	+	0.976381i	$0.569320\pi$
$644$	2.26442	−	2.87092i	0.0892306	−	0.113130i
$645$	9.56309	−	1.71698i	0.376546	−	0.0676061i
$646$	−5.60950	+	9.71594i	−0.220703	+	0.382268i
$647$	−12.1791	+	21.0948i	−0.478809	+	0.829322i	−0.999705	−	0.0242984i	$-0.992265\pi$
$647$	−12.1791	+	21.0948i	−0.478809	+	0.829322i	0.520895	+	0.853621i	$0.325598\pi$
$648$	30.7562	−	5.81943i	1.20822	−	0.228609i
$649$	3.07596	−	1.77591i	0.120742	−	0.0697105i
$650$	−6.79651	−	11.7719i	−0.266581	−	0.461732i
$651$	21.3349	+	34.2570i	0.836181	+	1.34264i
$652$	−30.5013	+	52.8299i	−1.19452	+	2.06898i
$653$		−	34.0255i		−	1.33152i	−0.746166	−	0.665760i	$-0.768107\pi$
$653$		−	34.0255i		−	1.33152i	0.746166	−	0.665760i	$-0.231893\pi$
$654$	−3.48856	−	19.4303i	−0.136414	−	0.759784i
$655$	−14.3505			−0.560721
$656$	0.580527	+	1.00550i	0.0226658	+	0.0392583i
$657$	8.99763	+	24.2494i	0.351031	+	0.946057i
$658$	−8.09201	+	10.2594i	−0.315459	+	0.399952i
$659$	41.1434	−	23.7542i	1.60272	−	0.925331i	0.611779	−	0.791029i	$-0.290454\pi$
$659$	41.1434	−	23.7542i	1.60272	−	0.925331i	0.990940	−	0.134302i	$-0.0428792\pi$
$660$	−0.257058	−	1.43174i	−0.0100060	−	0.0557304i
$661$	−5.66794	+	3.27239i	−0.220457	+	0.127281i	−0.606162	−	0.795341i	$-0.707292\pi$
$661$	−5.66794	+	3.27239i	−0.220457	+	0.127281i	0.385705	+	0.922622i	$0.373958\pi$
$662$	60.0792	−	34.6867i	2.33504	−	1.34814i
$663$	−10.7046	−	59.6216i	−0.415733	−	2.31551i
$664$	−6.65748	+	3.84370i	−0.258360	+	0.149164i
$665$	1.30257	−	1.65145i	0.0505115	−	0.0640405i
$666$	49.3622	−	59.5779i	1.91275	−	2.30860i
$667$	1.10738	+	1.91804i	0.0428780	+	0.0742669i
$668$	−56.9826			−2.20472
$669$	0.728075	+	4.05516i	0.0281490	+	0.156782i
$670$			4.80943i			0.185805i
$671$	−0.480106	+	0.831568i	−0.0185343	+	0.0321023i
$672$	10.1823	+	16.3496i	0.392793	+	0.630698i
$673$	−5.47917	−	9.49020i	−0.211207	−	0.365820i	0.740886	−	0.671631i	$-0.234406\pi$
$673$	−5.47917	−	9.49020i	−0.211207	−	0.365820i	−0.952092	+	0.305810i	$0.901073\pi$
$674$	−20.8050	+	12.0118i	−0.801381	+	0.462677i
$675$	−4.47551	+	2.64004i	−0.172262	+	0.101615i
$676$	−36.0462	+	62.4338i	−1.38639	+	2.40130i
$677$	−9.78771	+	16.9528i	−0.376172	+	0.651549i	−0.990502	−	0.137500i	$-0.956093\pi$
$677$	−9.78771	+	16.9528i	−0.376172	+	0.651549i	0.614330	+	0.789050i	$0.289427\pi$
$678$	−62.8892	+	11.2913i	−2.41524	+	0.433639i
$679$	26.0109	−	32.9776i	0.998205	−	1.26556i
$680$	−18.1495	−	10.4786i	−0.696003	−	0.401837i
$681$	3.61979	−	10.0426i	0.138711	−	0.384832i
$682$		−	4.97037i		−	0.190325i
$683$	−26.1931	−	15.1226i	−1.00225	−	0.578649i	−0.0933363	−	0.995635i	$-0.529753\pi$
$683$	−26.1931	−	15.1226i	−1.00225	−	0.578649i	−0.908913	+	0.416986i	$0.863087\pi$
$684$	−2.89138	−	7.79252i	−0.110555	−	0.297954i
$685$			2.15340i			0.0822771i
$686$	−35.4404	+	25.0069i	−1.35312	+	0.954768i
$687$	43.7918	+	15.7845i	1.67076	+	0.602216i
$688$	−6.59361			−0.251379
$689$	−1.09744	−	1.90082i	−0.0418090	−	0.0724153i
$690$	1.03784	+	1.22905i	0.0395100	+	0.0467892i
$691$	37.6554	+	21.7404i	1.43248	+	0.827043i	0.997310	−	0.0733056i	$-0.0233549\pi$
$691$	37.6554	+	21.7404i	1.43248	+	0.827043i	0.435170	+	0.900348i	$0.356688\pi$
$692$	64.5172			2.45257
$693$	−0.588121	+	1.82008i	−0.0223409	+	0.0691390i
$694$	−66.6850			−2.53133
$695$	−13.8296	−	7.98451i	−0.524586	−	0.302870i
$696$	33.1148	−	5.94551i	1.25521	−	0.225364i
$697$	−2.97600	−	5.15458i	−0.112724	−	0.195244i
$698$	−2.75089			−0.104123
$699$	−0.391391	−	2.17993i	−0.0148038	−	0.0824526i
$700$	7.23962	+	5.71020i	0.273632	+	0.215825i
$701$		−	10.1452i		−	0.383179i	−0.981475	−	0.191589i	$-0.938636\pi$
$701$		−	10.1452i		−	0.383179i	0.981475	−	0.191589i	$-0.0613642\pi$
$702$	61.4962	+	34.7422i	2.32102	+	1.31126i
$703$	−7.58143	−	4.37714i	−0.285939	−	0.165087i
$704$		−	2.93868i		−	0.110756i
$705$	−2.35646	−	2.79060i	−0.0887492	−	0.105100i
$706$	64.1093	+	37.0135i	2.41278	+	1.39302i
$707$	0.815541	−	0.325131i	0.0306716	−	0.0122278i
$708$	57.3996	+	67.9748i	2.15721	+	2.55465i
$709$	16.5445	−	28.6560i	0.621343	−	1.07620i	−0.367893	−	0.929868i	$-0.619921\pi$
$709$	16.5445	−	28.6560i	0.621343	−	1.07620i	0.989236	−	0.146329i	$-0.0467459\pi$
$710$	3.11769	−	5.40000i	0.117005	−	0.202658i
$711$	−5.28274	+	1.96014i	−0.198118	+	0.0735110i
$712$	17.2802	−	9.97674i	0.647604	−	0.373894i
$713$	1.74618	+	3.02447i	0.0653949	+	0.113267i
$714$	34.1880	+	54.8949i	1.27945	+	2.05439i
$715$	0.699329	−	1.21127i	0.0261534	−	0.0452990i
$716$			65.8577i			2.46122i
$717$	−16.5568	+	13.9810i	−0.618324	+	0.522129i
$718$	52.9853			1.97739
$719$	6.27591	+	10.8702i	0.234052	+	0.405390i	0.958997	−	0.283417i	$-0.0914681\pi$
$719$	6.27591	+	10.8702i	0.234052	+	0.405390i	−0.724945	+	0.688807i	$0.758135\pi$
$720$	3.30604	−	1.22669i	0.123209	−	0.0457162i
$721$	10.2599	+	25.7353i	0.382097	+	0.958432i
$722$	37.2548	−	21.5091i	1.38648	−	0.800485i
$723$	18.6008	+	6.70454i	0.691769	+	0.249344i
$724$	−37.7290	+	21.7829i	−1.40219	+	0.809554i
$725$	−4.83674	+	2.79249i	−0.179632	+	0.103711i
$726$	−33.9124	+	28.6365i	−1.25861	+	1.06280i
$727$	24.1312	−	13.9322i	0.894978	−	0.516716i	0.0194103	−	0.999812i	$-0.493821\pi$
$727$	24.1312	−	13.9322i	0.894978	−	0.516716i	0.875567	+	0.483096i	$0.160488\pi$
$728$	7.67685	−	52.8530i	0.284523	−	1.95886i
$729$	13.0604	−	23.6311i	0.483717	−	0.875224i
$730$	10.0960	+	17.4867i	0.373669	+	0.647213i
$731$	33.8013			1.25019
$732$	−22.6270	−	8.15577i	−0.836317	−	0.301446i
$733$			17.7064i			0.654000i	0.945024	+	0.327000i	$0.106038\pi$
$733$			17.7064i			0.654000i	−0.945024	+	0.327000i	$0.893962\pi$
$734$	11.5089	−	19.9340i	0.424801	−	0.735776i
$735$	−4.86364	−	11.1061i	−0.179398	−	0.409654i
$736$	0.833386	+	1.44347i	0.0307190	+	0.0532069i
$737$	−0.428568	+	0.247434i	−0.0157865	+	0.00911435i
$738$	6.84207	+	1.16251i	0.251860	+	0.0427926i
$739$	7.88534	−	13.6578i	0.290067	−	0.502411i	−0.683758	−	0.729709i	$-0.739656\pi$
$739$	7.88534	−	13.6578i	0.290067	−	0.502411i	0.973825	+	0.227298i	$0.0729891\pi$
$740$	19.1885	−	33.2354i	0.705383	−	1.22176i
$741$	2.70993	−	7.51832i	0.0995519	−	0.276192i
$742$	1.83984	+	1.45116i	0.0675428	+	0.0532739i
$743$	11.7646	+	6.79232i	0.431603	+	0.249186i	0.700029	−	0.714114i	$-0.253170\pi$
$743$	11.7646	+	6.79232i	0.431603	+	0.249186i	−0.268426	+	0.963300i	$0.586504\pi$
$744$	52.2171	−	9.37520i	1.91437	−	0.343711i
$745$			1.36724i			0.0500918i
$746$	−29.2817	−	16.9058i	−1.07208	−	0.618965i
$747$	−1.11071	+	6.53720i	−0.0406388	+	0.239184i
$748$		−	5.06057i		−	0.185033i
$749$	−0.928693	+	1.17743i	−0.0339337	+	0.0430225i
$750$	−3.09931	+	2.61714i	−0.113171	+	0.0955643i
$751$	−36.8812			−1.34582			−0.672908	−	0.739726i	$-0.734955\pi$
$751$	−36.8812			−1.34582			−0.672908	+	0.739726i	$0.734955\pi$
$752$	1.23934	+	2.14659i	0.0451939	+	0.0782781i
$753$	2.04590	−	5.67605i	0.0745567	−	0.206847i
$754$	65.7459	+	37.9584i	2.39433	+	1.38236i
$755$	4.22191			0.153651
$756$	−47.4762	−	6.44316i	−1.72669	−	0.234335i
$757$	12.8740			0.467914			0.233957	−	0.972247i	$-0.424833\pi$
$757$	12.8740			0.467914			0.233957	+	0.972247i	$0.424833\pi$
$758$	−53.1039	−	30.6596i	−1.92882	−	1.11361i
$759$	−0.0561262	+	0.155714i	−0.00203725	+	0.00565206i
$760$	−1.38247	−	2.39451i	−0.0501475	−	0.0868580i
$761$	−34.7474			−1.25959			−0.629795	−	0.776761i	$-0.716861\pi$
$761$	−34.7474			−1.25959			−0.629795	+	0.776761i	$0.716861\pi$
$762$	37.3831	−	31.5673i	1.35425	−	1.14356i
$763$	−1.85074	+	12.7419i	−0.0670014	+	0.461287i
$764$			30.4088i			1.10015i
$765$	−16.9480	+	6.28849i	−0.612756	+	0.227361i
$766$	−4.27535	−	2.46837i	−0.154475	−	0.0891860i
$767$			85.5443i			3.08883i
$768$	38.8883	−	6.98211i	1.40326	−	0.251945i
$769$	26.0271	+	15.0267i	0.938560	+	0.541878i	0.889509	−	0.456918i	$-0.151047\pi$
$769$	26.0271	+	15.0267i	0.938560	+	0.541878i	0.0490513	+	0.998796i	$0.484380\pi$
$770$	−0.214637	+	1.47771i	−0.00773496	+	0.0532531i
$771$	−15.0379	+	41.7204i	−0.541576	+	1.50252i
$772$	19.8516	−	34.3841i	0.714476	−	1.23751i
$773$	−16.9927	+	29.4323i	−0.611186	+	1.05861i	0.379855	+	0.925046i	$0.375974\pi$
$773$	−16.9927	+	29.4323i	−0.611186	+	1.05861i	−0.991041	+	0.133559i	$0.957359\pi$
$774$	−25.1454	+	30.3494i	−0.903833	+	1.09089i
$775$	−7.62683	+	4.40335i	−0.273964	+	0.158173i
$776$	−27.6064	−	47.8156i	−0.991011	−	1.71648i
$777$	−42.8350	+	26.6772i	−1.53670	+	0.957039i
$778$	−33.2153	+	57.5307i	−1.19083	+	2.06257i
$779$		−	0.785261i		−	0.0281349i
$780$	32.9588	+	11.8798i	1.18011	+	0.425365i
$781$	0.641591			0.0229579
$782$	2.79815	+	4.84655i	0.100062	+	0.173312i
$783$	14.2746	−	25.2670i	0.510132	−	0.902970i
$784$	1.91678	+	8.00162i	0.0684563	+	0.285772i
$785$	2.06559	−	1.19257i	0.0737239	−	0.0425645i
$786$	44.4767	−	37.5572i	1.58643	−	1.33962i
$787$	−18.2990	+	10.5650i	−0.652290	+	0.376600i	−0.789333	−	0.613965i	$-0.789574\pi$
$787$	−18.2990	+	10.5650i	−0.652290	+	0.376600i	0.137043	+	0.990565i	$0.456240\pi$
$788$	−56.1452	+	32.4154i	−2.00009	+	1.15475i
$789$	3.15215	+	1.13618i	0.112220	+	0.0404489i
$790$	−3.80950	+	2.19941i	−0.135536	+	0.0782516i
$791$	41.2411	+	5.99023i	1.46636	+	0.212988i
$792$	1.93618	+	1.60419i	0.0687992	+	0.0570023i
$793$	−11.5632	−	20.0281i	−0.410621	−	0.711217i
$794$	−32.5352			−1.15463
$795$	−0.500447	+	0.422590i	−0.0177490	+	0.0149877i
$796$		−	78.6672i		−	2.78828i
$797$	−6.65988	+	11.5352i	−0.235905	+	0.408599i	−0.959535	−	0.281588i	$-0.909139\pi$
$797$	−6.65988	+	11.5352i	−0.235905	+	0.408599i	0.723630	+	0.690188i	$0.242472\pi$
$798$	0.285002	+	8.52737i	0.0100890	+	0.301865i
$799$	−6.35330	−	11.0042i	−0.224764	−	0.389302i
$800$	−3.64000	+	2.10155i	−0.128693	+	0.0743012i
$801$	2.88298	−	16.9680i	0.101865	−	0.599536i
$802$	24.6326	−	42.6650i	0.869808	−	1.50655i
$803$	−1.03883	+	1.79930i	−0.0366594	+	0.0634960i
$804$	−7.99739	−	9.47081i	−0.282046	−	0.334010i
$805$	−0.388541	−	0.974596i	−0.0136943	−	0.0343500i
$806$	103.672	+	59.8549i	3.65168	+	2.10830i
$807$	−13.3346	−	15.7914i	−0.469402	−	0.555883i
$808$		−	1.15413i		−	0.0406022i
$809$	−2.78023	−	1.60517i	−0.0977477	−	0.0564347i	0.450329	−	0.892863i	$-0.351307\pi$
$809$	−2.78023	−	1.60517i	−0.0977477	−	0.0564347i	−0.548077	+	0.836428i	$0.684640\pi$
$810$	6.96165	−	19.8953i	0.244607	−	0.699050i
$811$		−	26.0147i		−	0.913501i	−0.889595	−	0.456750i	$-0.849013\pi$
$811$		−	26.0147i		−	0.913501i	0.889595	−	0.456750i	$-0.150987\pi$
$812$	−50.9619	−	7.40216i	−1.78841	−	0.259765i
$813$	5.53131	+	30.8078i	0.193992	+	1.08048i
$814$	6.21496			0.217834
$815$	8.75207	+	15.1590i	0.306572	+	0.530998i
$816$	12.0746	−	2.16791i	0.422696	−	0.0758920i
$817$	3.86203	+	2.22974i	0.135115	+	0.0780088i
$818$	−37.2174			−1.30127
$819$	−30.8807	−	34.1850i	−1.07906	−	1.19452i
$820$	3.44242			0.120215
$821$	−29.6423	−	17.1140i	−1.03452	−	0.597283i	−0.116247	−	0.993220i	$-0.537086\pi$
$821$	−29.6423	−	17.1140i	−1.03452	−	0.597283i	−0.918277	+	0.395937i	$0.870420\pi$
$822$	−5.63573	−	6.67405i	−0.196569	−	0.232784i
$823$	−25.6594	−	44.4433i	−0.894429	−	1.54920i	−0.834509	−	0.550994i	$-0.814249\pi$
$823$	−25.6594	−	44.4433i	−0.894429	−	1.54920i	−0.0599200	−	0.998203i	$-0.519085\pi$
$824$	36.4198			1.26875
$825$	−0.392665	−	0.141534i	−0.0136708	−	0.00492757i
$826$	−33.8210	−	84.8348i	−1.17678	−	2.95178i
$827$		−	46.4687i		−	1.61587i	−0.589269	−	0.807937i	$-0.700584\pi$
$827$		−	46.4687i		−	1.61587i	0.589269	−	0.807937i	$-0.299416\pi$
$828$	−4.08747	−	0.694487i	−0.142049	−	0.0241351i
$829$	6.01685	+	3.47383i	0.208974	+	0.120651i	0.600834	−	0.799374i	$-0.294835\pi$
$829$	6.01685	+	3.47383i	0.208974	+	0.120651i	−0.391861	+	0.920025i	$0.628168\pi$
$830$			5.17655i			0.179681i
$831$	10.7493	−	29.8223i	0.372889	−	1.03453i
$832$	61.2949	+	35.3886i	2.12502	+	1.22688i
$833$	−9.82612	−	41.0193i	−0.340455	−	1.42123i
$834$	63.7587	−	11.4474i	2.20778	−	0.396391i
$835$	−8.17532	+	14.1601i	−0.282918	+	0.490029i
$836$	0.333826	−	0.578204i	0.0115456	−	0.0199976i
$837$	22.5089	−	39.8424i	0.778022	−	1.37715i
$838$	−70.7146	+	40.8271i	−2.44279	+	1.41035i
$839$	19.3614	+	33.5349i	0.668429	+	1.15775i	0.978343	+	0.206989i	$0.0663665\pi$
$839$	19.3614	+	33.5349i	0.668429	+	1.15775i	−0.309914	+	0.950765i	$0.600300\pi$
$840$	−15.9293	+	0.532389i	−0.549612	+	0.0183692i
$841$	1.09604	−	1.89840i	0.0377946	−	0.0654621i
$842$		−	16.9432i		−	0.583902i
$843$	−6.49189	−	36.1579i	−0.223592	−	1.24534i
$844$	−34.6995			−1.19440
$845$	10.3431	+	17.9148i	0.355814	+	0.616288i
$846$	14.6068	+	2.48178i	0.502191	+	0.0853254i
$847$	26.8914	−	10.7208i	0.923998	−	0.368370i
$848$	0.384955	−	0.222254i	0.0132194	−	0.00763222i
$849$	−0.506334	−	2.82013i	−0.0173774	−	0.0967868i
$850$	−12.2216	+	7.05613i	−0.419196	+	0.242023i
$851$	−3.78180	+	2.18342i	−0.129639	+	0.0748468i
$852$	2.84001	+	15.8180i	0.0972971	+	0.541916i
$853$	1.59392	−	0.920253i	0.0545749	−	0.0315089i	−0.472464	−	0.881350i	$-0.656635\pi$
$853$	1.59392	−	0.920253i	0.0545749	−	0.0315089i	0.527039	+	0.849841i	$0.323302\pi$
$854$	19.3856	+	15.2903i	0.663363	+	0.523223i
$855$	−2.35125	−	0.399492i	−0.0804111	−	0.0136623i
$856$	0.985660	+	1.70721i	0.0336891	+	0.0583513i
$857$	−34.0224			−1.16218			−0.581092	−	0.813838i	$-0.697374\pi$
$857$	−34.0224			−1.16218			−0.581092	+	0.813838i	$0.697374\pi$
$858$	1.00263	+	5.58435i	0.0342292	+	0.190647i
$859$		−	6.75581i		−	0.230505i	−0.993336	−	0.115253i	$-0.963232\pi$
$859$		−	6.75581i		−	0.230505i	0.993336	−	0.115253i	$-0.0367677\pi$
$860$	−9.77473	+	16.9303i	−0.333316	+	0.577320i
$861$	−3.99351	−	2.13106i	−0.136098	−	0.0726263i
$862$	−31.3540	−	54.3068i	−1.06792	−	1.84970i
$863$	9.99636	−	5.77140i	0.340280	−	0.196461i	−0.320116	−	0.947378i	$-0.603722\pi$
$863$	9.99636	−	5.77140i	0.340280	−	0.196461i	0.660396	+	0.750918i	$0.270388\pi$
$864$	10.7427	−	19.0153i	0.365473	−	0.646913i
$865$	9.25630	−	16.0324i	0.314724	−	0.545117i
$866$	−13.1319	+	22.7452i	−0.446241	+	0.772913i
$867$	−32.9176	+	5.91012i	−1.11794	+	0.200718i
$868$	−80.3594	−	11.6721i	−2.72758	−	0.396178i
$869$	−0.391979	−	0.226309i	−0.0132970	−	0.00767701i
$870$	7.68223	−	21.3132i	0.260452	−	0.722586i
$871$		−	11.9187i		−	0.403851i
$872$	14.6581	+	8.46284i	0.496385	+	0.286588i
$873$	−46.9518	−	7.97741i	−1.58908	−	0.269994i
$874$			0.738334i			0.0249745i
$875$	2.45764	−	0.979787i	0.0830836	−	0.0331228i
$876$	−48.9590	−	17.6470i	−1.65417	−	0.596237i
$877$	−48.2495			−1.62927			−0.814636	−	0.579973i	$-0.803063\pi$
$877$	−48.2495			−1.62927			−0.814636	+	0.579973i	$0.803063\pi$
$878$	19.8024	+	34.2988i	0.668299	+	1.15753i
$879$	26.2687	+	31.1084i	0.886021	+	1.04926i
$880$	0.245308	+	0.141629i	0.00826933	+	0.00477430i
$881$	−7.88554			−0.265671			−0.132835	−	0.991138i	$-0.542408\pi$
$881$	−7.88554			−0.265671			−0.132835	+	0.991138i	$0.542408\pi$
$882$	44.1401	+	21.6924i	1.48627	+	0.730420i
$883$	38.7887			1.30535			0.652673	−	0.757640i	$-0.273648\pi$
$883$	38.7887			1.30535			0.652673	+	0.757640i	$0.273648\pi$
$884$	105.553	+	60.9411i	3.55014	+	2.04967i
$885$	25.1267	−	4.51132i	0.844626	−	0.151646i
$886$	16.0110	+	27.7319i	0.537901	+	0.931671i
$887$	0.410828			0.0137943			0.00689714	−	0.999976i	$-0.497805\pi$
$887$	0.410828			0.0137943			0.00689714	+	0.999976i	$0.497805\pi$
$888$	11.7228	+	65.2924i	0.393390	+	2.19107i
$889$	−29.6435	+	11.8180i	−0.994212	+	0.396362i
$890$		−	13.4363i		−	0.450386i
$891$	2.13103	−	0.403215i	0.0713922	−	0.0135082i
$892$	−7.17919	−	4.14491i	−0.240377	−	0.138782i
$893$		−	1.67641i		−	0.0560990i
$894$	−3.57826	−	4.23751i	−0.119675	−	0.141723i
$895$	16.3655	+	9.44863i	0.547038	+	0.315833i
$896$	−52.7681	−	7.66451i	−1.76286	−	0.256053i
$897$	−2.57198	−	3.04584i	−0.0858759	−	0.101698i
$898$	−12.7029	+	22.0020i	−0.423900	+	0.734217i
$899$	24.5927	−	42.5957i	0.820211	−	1.42065i
$900$	1.75129	−	10.3074i	0.0583764	−	0.343580i
$901$	−1.97342	+	1.13936i	−0.0657443	+	0.0379575i
$902$	0.278741	+	0.482794i	0.00928107	+	0.0160753i
$903$	21.8204	−	13.5895i	0.726138	−	0.452231i
$904$	27.3913	−	47.4432i	0.911022	−	1.57794i
$905$			12.5008i			0.415540i
$906$	−13.0850	+	11.0493i	−0.434720	+	0.367089i
$907$	4.11936			0.136781			0.0683906	−	0.997659i	$-0.478214\pi$
$907$	4.11936			0.136781			0.0683906	+	0.997659i	$0.478214\pi$
$908$	10.7395	+	18.6014i	0.356404	+	0.617310i
$909$	−0.766583	−	0.635138i	−0.0254259	−	0.0210662i
$910$	−28.2374	−	22.2720i	−0.936060	−	0.738310i
$911$	−1.93982	+	1.11995i	−0.0642690	+	0.0371057i	−0.531790	−	0.846876i	$-0.678481\pi$
$911$	−1.93982	+	1.11995i	−0.0642690	+	0.0371057i	0.467521	+	0.883982i	$0.345147\pi$
$912$	1.52262	+	0.548818i	0.0504189	+	0.0181732i
$913$	−0.461282	+	0.266321i	−0.0152662	+	0.00881395i
$914$	−16.8584	+	9.73320i	−0.557626	+	0.321946i
$915$	−5.27299	+	4.45265i	−0.174320	+	0.147200i
$916$	−81.1137	+	46.8310i	−2.68007	+	1.54734i
$917$	−35.2685	+	14.0604i	−1.16467	+	0.464317i
$918$	36.0693	−	63.8452i	1.19046	−	2.10721i
$919$	4.42519	+	7.66466i	0.145974	+	0.252834i	0.929736	−	0.368227i	$-0.120035\pi$
$919$	4.42519	+	7.66466i	0.145974	+	0.252834i	−0.783762	+	0.621061i	$0.786702\pi$
$920$	−1.37922			−0.0454715
$921$	−25.3880	−	9.15095i	−0.836562	−	0.301534i
$922$		−	4.18177i		−	0.137719i
$923$	−7.72625	+	13.3823i	−0.254313	+	0.440483i
$924$	−2.03456	−	3.26685i	−0.0669321	−	0.107471i
$925$	−5.50596	−	9.53660i	−0.181035	−	0.313561i
$926$	9.36300	−	5.40573i	0.307687	−	0.177643i
$927$	20.0425	−	24.1904i	0.658281	−	0.794516i
$928$	11.7372	−	20.3293i	0.385291	−	0.667344i
$929$	−22.1259	+	38.3232i	−0.725927	+	1.25734i	0.232665	+	0.972557i	$0.425256\pi$
$929$	−22.1259	+	38.3232i	−0.725927	+	1.25734i	−0.958591	+	0.284785i	$0.908078\pi$
$930$	12.1137	−	33.6078i	0.397225	−	1.10204i
$931$	1.58319	−	5.33492i	0.0518868	−	0.174845i
$932$	3.85931	+	2.22818i	0.126416	+	0.0729863i
$933$	−31.4797	+	5.65194i	−1.03060	+	0.185036i
$934$		−	36.1569i		−	1.18309i
$935$	−1.25754	−	0.726042i	−0.0411260	−	0.0237441i
$936$	−56.7762	+	21.0666i	−1.85579	+	0.688583i
$937$		−	2.82353i		−	0.0922407i	−0.998936	−	0.0461203i	$-0.985314\pi$
$937$		−	2.82353i		−	0.0922407i	0.998936	−	0.0461203i	$-0.0146858\pi$
$938$	4.71222	+	11.8199i	0.153859	+	0.385933i
$939$	−21.9765	+	18.5575i	−0.717175	+	0.605601i
$940$	7.34904			0.239699
$941$	10.6229	+	18.3995i	0.346298	+	0.599805i	0.985589	−	0.169160i	$-0.0541054\pi$
$941$	10.6229	+	18.3995i	0.346298	+	0.599805i	−0.639291	+	0.768965i	$0.720772\pi$
$942$	−3.28078	+	9.10205i	−0.106894	+	0.296561i
$943$	−0.339228	−	0.195854i	−0.0110468	−	0.00637787i
$944$	−17.3245			−0.563865
$945$	−8.41253	+	10.8733i	−0.273660	+	0.353709i
$946$	−3.16594			−0.102933
$947$	31.5469	+	18.2136i	1.02514	+	0.591862i	0.915587	−	0.402119i	$-0.131726\pi$
$947$	31.5469	+	18.2136i	1.02514	+	0.591862i	0.109548	+	0.993982i	$0.465060\pi$
$948$	3.84441	−	10.6658i	0.124861	−	0.346408i
$949$	−25.0198	−	43.3356i	−0.812178	−	1.40673i
$950$	−1.86186			−0.0604068
$951$	−17.9704	+	15.1747i	−0.582731	+	0.492073i
$952$	−54.8719	−	7.97009i	−1.77841	−	0.258312i
$953$		−	58.8278i		−	1.90562i	−0.303569	−	0.952809i	$-0.598178\pi$
$953$		−	58.8278i		−	1.90562i	0.303569	−	0.952809i	$-0.401822\pi$
$954$	0.445065	−	2.61948i	0.0144095	−	0.0848087i
$955$	7.55653	+	4.36277i	0.244524	+	0.141176i
$956$		−	43.6022i		−	1.41020i
$957$	2.29445	−	0.411952i	0.0741690	−	0.0133165i
$958$	17.2974	+	9.98668i	0.558855	+	0.322655i
$959$	2.10987	+	5.29229i	0.0681313	+	0.170897i
$960$	7.16214	−	19.8703i	0.231157	−	0.641311i
$961$	23.2790	−	40.3204i	0.750936	−	1.30066i
$962$	−74.8426	+	129.631i	−2.41302	+	4.17948i
$963$	1.67637	+	0.284826i	0.0540203	+	0.00917838i
$964$	−34.4534	+	19.8917i	−1.10967	+	0.640668i
$965$	−5.69624	−	9.86618i	−0.183369	−	0.317604i
$966$	3.75486	+	2.00371i	0.120811	+	0.0644683i
$967$	13.3155	−	23.0631i	0.428196	−	0.741658i	−0.568517	−	0.822672i	$-0.692482\pi$
$967$	13.3155	−	23.0631i	0.428196	−	0.741658i	0.996713	+	0.0810139i	$0.0258158\pi$
$968$		−	38.0559i		−	1.22316i
$969$	−7.80550	−	2.81345i	−0.250749	−	0.0903810i
$970$	−37.1793			−1.19375
$971$	2.63348	+	4.56132i	0.0845124	+	0.146380i	0.905183	−	0.425021i	$-0.139733\pi$
$971$	2.63348	+	4.56132i	0.0845124	+	0.146380i	−0.820671	+	0.571401i	$0.806400\pi$
$972$	19.3740	+	50.7544i	0.621423	+	1.62795i
$973$	−41.8113	−	6.07305i	−1.34041	−	0.194693i
$974$	−5.77314	+	3.33312i	−0.184983	+	0.106800i
$975$	7.68071	−	6.48578i	0.245980	−	0.207711i
$976$	4.05610	−	2.34179i	0.129833	−	0.0749589i
$977$	41.0964	−	23.7270i	1.31479	−	0.759095i	0.331906	−	0.943313i	$-0.392308\pi$
$977$	41.0964	−	23.7270i	1.31479	−	0.759095i	0.982885	+	0.184218i	$0.0589751\pi$
$978$	−66.7986	−	24.0772i	−2.13598	−	0.769904i
$979$	1.19731	−	0.691266i	0.0382662	−	0.0220930i
$980$	23.3872	+	6.94036i	0.747077	+	0.221702i
$981$	13.6877	−	5.07876i	0.437014	−	0.162152i
$982$	41.2293	+	71.4112i	1.31568	+	2.27882i
$983$	−6.74330			−0.215078			−0.107539	−	0.994201i	$-0.534297\pi$
$983$	−6.74330			−0.215078			−0.107539	+	0.994201i	$0.534297\pi$
$984$	−4.54632	+	3.83902i	−0.144931	+	0.122384i
$985$			18.6026i			0.592728i
$986$	39.4084	−	68.2573i	1.25502	−	2.17376i
$987$	−8.52553	−	4.54949i	−0.271370	−	0.144812i
$988$	8.04011	+	13.9259i	0.255790	+	0.443041i
$989$	1.92647	−	1.11225i	0.0612583	−	0.0353675i
$990$	1.58740	−	0.589000i	0.0504510	−	0.0187196i
$991$	−1.97688	+	3.42405i	−0.0627976	+	0.108769i	−0.895715	−	0.444629i	$-0.853336\pi$
$991$	−1.97688	+	3.42405i	−0.0627976	+	0.108769i	0.832917	+	0.553397i	$0.186669\pi$
$992$	18.5078	−	32.0564i	0.587622	−	1.01779i
$993$	33.1009	+	39.1993i	1.05043	+	1.24395i
$994$	2.37133	−	16.3259i	0.0752139	−	0.517827i
$995$	−19.5486	−	11.2864i	−0.619733	−	0.357803i
$996$	−8.60785	−	10.1937i	−0.272750	−	0.323001i
$997$		−	18.5781i		−	0.588374i	−0.955748	−	0.294187i	$-0.904951\pi$
$997$		−	18.5781i		−	0.588374i	0.955748	−	0.294187i	$-0.0950488\pi$
$998$	29.2408	+	16.8822i	0.925602	+	0.534396i
$999$	49.8190	+	28.1452i	1.57620	+	0.890474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.311.2	yes	30
3.2	odd	2		945.2.be.b.206.14		30
7.5	odd	6		315.2.t.b.131.14	yes	30
9.2	odd	6		315.2.t.b.101.2	✓	30
9.7	even	3		945.2.t.b.521.14		30
21.5	even	6		945.2.t.b.341.2		30
63.47	even	6	inner	315.2.be.b.236.2	yes	30
63.61	odd	6		945.2.be.b.656.14		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.2	✓	30	9.2	odd	6
315.2.t.b.131.14	yes	30	7.5	odd	6
315.2.be.b.236.2	yes	30	63.47	even	6	inner
315.2.be.b.311.2	yes	30	1.1	even	1	trivial
945.2.t.b.341.2		30	21.5	even	6
945.2.t.b.521.14		30	9.7	even	3
945.2.be.b.206.14		30	3.2	odd	2
945.2.be.b.656.14		30	63.61	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02825 - 1.17101i) q^{2} +(0.587320 - 1.62943i) q^{3} +(1.74252 + 3.01813i) q^{4} +1.00000 q^{5} +(-3.09931 + 2.61714i) q^{6} +(2.45764 - 0.979787i) q^{7} -3.47799i q^{8} +(-2.31011 - 1.91400i) q^{9} +O(q^{10})\)	\(q+(-2.02825 - 1.17101i) q^{2} +(0.587320 - 1.62943i) q^{3} +(1.74252 + 3.01813i) q^{4} +1.00000 q^{5} +(-3.09931 + 2.61714i) q^{6} +(2.45764 - 0.979787i) q^{7} -3.47799i q^{8} +(-2.31011 - 1.91400i) q^{9} +(-2.02825 - 1.17101i) q^{10} -0.240982i q^{11} +(5.94127 - 1.06671i) q^{12} +(5.02640 + 2.90199i) q^{13} +(-6.13205 - 0.890673i) q^{14} +(0.587320 - 1.62943i) q^{15} +(-0.587714 + 1.01795i) q^{16} +(3.01284 - 5.21840i) q^{17} +(2.44416 + 6.58722i) q^{18} +(0.688475 - 0.397491i) q^{19} +(1.74252 + 3.01813i) q^{20} +(-0.153074 - 4.58002i) q^{21} +(-0.282192 + 0.488771i) q^{22} -0.396557i q^{23} +(-5.66715 - 2.04269i) q^{24} +1.00000 q^{25} +(-6.79651 - 11.7719i) q^{26} +(-4.47551 + 2.64004i) q^{27} +(7.23962 + 5.71020i) q^{28} +(-4.83674 + 2.79249i) q^{29} +(-3.09931 + 2.61714i) q^{30} +(-7.62683 + 4.40335i) q^{31} +(-3.64000 + 2.10155i) q^{32} +(-0.392665 - 0.141534i) q^{33} +(-12.2216 + 7.05613i) q^{34} +(2.45764 - 0.979787i) q^{35} +(1.75129 - 10.3074i) q^{36} +(-5.50596 - 9.53660i) q^{37} -1.86186 q^{38} +(7.68071 - 6.48578i) q^{39} -3.47799i q^{40} +(0.493886 - 0.855435i) q^{41} +(-5.05277 + 9.46865i) q^{42} +(2.80477 + 4.85800i) q^{43} +(0.727317 - 0.419917i) q^{44} +(-2.31011 - 1.91400i) q^{45} +(-0.464371 + 0.804314i) q^{46} +(1.05437 - 1.82622i) q^{47} +(1.31351 + 1.55550i) q^{48} +(5.08003 - 4.81594i) q^{49} +(-2.02825 - 1.17101i) q^{50} +(-6.73353 - 7.97410i) q^{51} +20.2271i q^{52} +(-0.327502 - 0.189083i) q^{53} +(12.1689 - 0.113794i) q^{54} -0.240982i q^{55} +(-3.40769 - 8.54766i) q^{56} +(-0.243330 - 1.35528i) q^{57} +13.0801 q^{58} +(7.36945 + 12.7643i) q^{59} +(5.94127 - 1.06671i) q^{60} +(-3.45074 - 1.99229i) q^{61} +20.6254 q^{62} +(-7.55274 - 2.44051i) q^{63} +12.1946 q^{64} +(5.02640 + 2.90199i) q^{65} +(0.630683 + 0.746879i) q^{66} +(-1.02677 - 1.77842i) q^{67} +20.9998 q^{68} +(-0.646163 - 0.232906i) q^{69} +(-6.13205 - 0.890673i) q^{70} +2.66240i q^{71} +(-6.65687 + 8.03454i) q^{72} +(-7.46653 - 4.31080i) q^{73} +25.7901i q^{74} +(0.587320 - 1.62943i) q^{75} +(2.39936 + 1.38527i) q^{76} +(-0.236111 - 0.592249i) q^{77} +(-23.1733 + 4.16059i) q^{78} +(0.939111 - 1.62659i) q^{79} +(-0.587714 + 1.01795i) q^{80} +(1.67322 + 8.84310i) q^{81} +(-2.00344 + 1.15669i) q^{82} +(-1.10515 - 1.91417i) q^{83} +(13.5564 - 8.44277i) q^{84} +(3.01284 - 5.21840i) q^{85} -13.1376i q^{86} +(1.70947 + 9.52124i) q^{87} -0.838134 q^{88} +(2.86854 + 4.96845i) q^{89} +(2.44416 + 6.58722i) q^{90} +(15.1964 + 2.20727i) q^{91} +(1.19686 - 0.691008i) q^{92} +(2.69558 + 15.0136i) q^{93} +(-4.27704 + 2.46935i) q^{94} +(0.688475 - 0.397491i) q^{95} +(1.28650 + 7.16542i) q^{96} +(13.7481 - 7.93745i) q^{97} +(-15.9431 + 3.81914i) q^{98} +(-0.461240 + 0.556696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more