LMFDB - Embedded newform 925.2.y.b.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10002 + 1.21245i) q^{2} +(-0.586925 - 2.19044i) q^{3} +(1.94006 - 3.36028i) q^{4} +(3.88834 + 3.88834i) q^{6} +(0.132002 + 0.492639i) q^{7} +4.55908i q^{8} +(-1.85545 + 1.07124i) q^{9} -3.54199i q^{11} +(-8.49914 - 2.27734i) q^{12} +(3.22442 + 1.86162i) q^{13} +(-0.874506 - 0.874506i) q^{14} +(-1.64753 - 2.85361i) q^{16} +(2.57840 + 4.46592i) q^{17} +(2.59765 - 4.49927i) q^{18} +(1.61089 + 6.01191i) q^{19} +(1.00162 - 0.578285i) q^{21} +(4.29448 + 7.43826i) q^{22} +0.338516i q^{23} +(9.98638 - 2.67584i) q^{24} -9.02846 q^{26} +(-1.37503 - 1.37503i) q^{27} +(1.91150 + 0.512184i) q^{28} +(2.27033 + 2.27033i) q^{29} +(-5.38302 + 5.38302i) q^{31} +(-0.976852 - 0.563986i) q^{32} +(-7.75850 + 2.07889i) q^{33} +(-10.8294 - 6.25235i) q^{34} +8.31310i q^{36} +(5.22969 - 3.10650i) q^{37} +(-10.6720 - 10.6720i) q^{38} +(2.18526 - 8.15551i) q^{39} +(3.68619 + 2.12823i) q^{41} +(-1.40228 + 2.42882i) q^{42} +7.27408i q^{43} +(-11.9021 - 6.87167i) q^{44} +(-0.410433 - 0.710891i) q^{46} +(-5.08602 + 5.08602i) q^{47} +(-5.28368 + 5.28368i) q^{48} +(5.83691 - 3.36994i) q^{49} +(8.26899 - 8.26899i) q^{51} +(12.5111 - 7.22329i) q^{52} +(3.06455 - 11.4370i) q^{53} +(4.55474 + 1.22044i) q^{54} +(-2.24598 + 0.601809i) q^{56} +(12.2232 - 7.05709i) q^{57} +(-7.52039 - 2.01508i) q^{58} +(-4.75083 - 1.27298i) q^{59} +(3.52938 + 13.1718i) q^{61} +(4.77783 - 17.8311i) q^{62} +(-0.772660 - 0.772660i) q^{63} +9.32535 q^{64} +(13.7725 - 13.7725i) q^{66} +(6.51128 - 1.74469i) q^{67} +20.0090 q^{68} +(0.741497 - 0.198684i) q^{69} +(4.65903 - 8.06967i) q^{71} +(-4.88389 - 8.45915i) q^{72} +(3.04875 - 3.04875i) q^{73} +(-7.21600 + 12.8644i) q^{74} +(23.3269 + 6.25043i) q^{76} +(1.74492 - 0.467551i) q^{77} +(5.29903 + 19.7763i) q^{78} +(-0.309140 - 1.15373i) q^{79} +(-5.41860 + 9.38530i) q^{81} -10.3214 q^{82} +(-2.96248 + 11.0561i) q^{83} -4.48762i q^{84} +(-8.81944 - 15.2757i) q^{86} +(3.64049 - 6.30552i) q^{87} +16.1482 q^{88} +(3.23761 - 12.0829i) q^{89} +(-0.491475 + 1.83421i) q^{91} +(1.13751 + 0.656741i) q^{92} +(14.9506 + 8.63173i) q^{93} +(4.51421 - 16.8473i) q^{94} +(-0.662035 + 2.47075i) q^{96} +4.72808 q^{97} +(-8.17175 + 14.1539i) q^{98} +(3.79434 + 6.57199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.10002	+	1.21245i	−1.48494	+	0.857330i	−0.999853	−	0.0171367i	$-0.994545\pi$
$2$	−2.10002	+	1.21245i	−1.48494	+	0.857330i	−0.485086	+	0.874467i	$0.661212\pi$
$3$	−0.586925	−	2.19044i	−0.338862	−	1.26465i	−0.899622	−	0.436670i	$-0.856158\pi$
$3$	−0.586925	−	2.19044i	−0.338862	−	1.26465i	0.560760	−	0.827978i	$-0.310509\pi$
$4$	1.94006	−	3.36028i	0.970029	−	1.68014i
$5$		0			0
$5$		0			0
$6$	3.88834	+	3.88834i	1.58741	+	1.58741i
$7$	0.132002	+	0.492639i	0.0498922	+	0.186200i	0.986375	−	0.164514i	$-0.0526056\pi$
$7$	0.132002	+	0.492639i	0.0498922	+	0.186200i	−0.936483	+	0.350714i	$0.885939\pi$
$8$			4.55908i			1.61188i
$9$	−1.85545	+	1.07124i	−0.618483	+	0.357081i
$10$		0			0
$11$		−	3.54199i		−	1.06795i	−0.845500	−	0.533975i	$-0.820697\pi$
$11$		−	3.54199i		−	1.06795i	0.845500	−	0.533975i	$-0.179303\pi$
$12$	−8.49914	−	2.27734i	−2.45349	−	0.657411i
$13$	3.22442	+	1.86162i	0.894292	+	0.516320i	0.875344	−	0.483501i	$-0.160635\pi$
$13$	3.22442	+	1.86162i	0.894292	+	0.516320i	0.0189483	+	0.999820i	$0.493968\pi$
$14$	−0.874506	−	0.874506i	−0.233722	−	0.233722i
$15$		0			0
$16$	−1.64753	−	2.85361i	−0.411884	−	0.713404i
$17$	2.57840	+	4.46592i	0.625354	+	1.08315i	0.988472	+	0.151402i	$0.0483789\pi$
$17$	2.57840	+	4.46592i	0.625354	+	1.08315i	−0.363118	+	0.931743i	$0.618288\pi$
$18$	2.59765	−	4.49927i	0.612273	−	1.06049i
$19$	1.61089	+	6.01191i	0.369563	+	1.37923i	0.861129	+	0.508387i	$0.169758\pi$
$19$	1.61089	+	6.01191i	0.369563	+	1.37923i	−0.491566	+	0.870841i	$0.663575\pi$
$20$		0			0
$21$	1.00162	−	0.578285i	0.218571	−	0.126192i
$22$	4.29448	+	7.43826i	0.915586	+	1.58584i
$23$			0.338516i			0.0705855i	0.999377	+	0.0352927i	$0.0112364\pi$
$23$			0.338516i			0.0705855i	−0.999377	+	0.0352927i	$0.988764\pi$
$24$	9.98638	−	2.67584i	2.03846	−	0.546204i
$25$		0			0
$26$	−9.02846			−1.77063
$27$	−1.37503	−	1.37503i	−0.264624	−	0.264624i
$28$	1.91150	+	0.512184i	0.361239	+	0.0967937i
$29$	2.27033	+	2.27033i	0.421589	+	0.421589i	0.885751	−	0.464161i	$-0.153644\pi$
$29$	2.27033	+	2.27033i	0.421589	+	0.421589i	−0.464161	+	0.885751i	$0.653644\pi$
$30$		0			0
$31$	−5.38302	+	5.38302i	−0.966820	+	0.966820i	−0.999467	−	0.0326474i	$-0.989606\pi$
$31$	−5.38302	+	5.38302i	−0.966820	+	0.966820i	0.0326474	+	0.999467i	$0.489606\pi$
$32$	−0.976852	−	0.563986i	−0.172685	−	0.0996995i
$33$	−7.75850	+	2.07889i	−1.35058	+	0.361887i
$34$	−10.8294	−	6.25235i	−1.85723	−	1.07227i
$35$		0			0
$36$			8.31310i			1.38552i
$37$	5.22969	−	3.10650i	0.859756	−	0.510705i
$37$	5.22969	−	3.10650i	0.859756	−	0.510705i
$38$	−10.6720	−	10.6720i	−1.73123	−	1.73123i
$39$	2.18526	−	8.15551i	0.349922	−	1.30593i
$40$		0			0
$41$	3.68619	+	2.12823i	0.575687	+	0.332373i	0.759417	−	0.650604i	$-0.225484\pi$
$41$	3.68619	+	2.12823i	0.575687	+	0.332373i	−0.183731	+	0.982977i	$0.558817\pi$
$42$	−1.40228	+	2.42882i	−0.216376	+	0.374775i
$43$			7.27408i			1.10929i	0.832088	+	0.554643i	$0.187145\pi$
$43$			7.27408i			1.10929i	−0.832088	+	0.554643i	$0.812855\pi$
$44$	−11.9021	−	6.87167i	−1.79431	−	1.03594i
$45$		0			0
$46$	−0.410433	−	0.710891i	−0.0605150	−	0.104815i
$47$	−5.08602	+	5.08602i	−0.741872	+	0.741872i	−0.972938	−	0.231066i	$-0.925779\pi$
$47$	−5.08602	+	5.08602i	−0.741872	+	0.741872i	0.231066	+	0.972938i	$0.425779\pi$
$48$	−5.28368	+	5.28368i	−0.762633	+	0.762633i
$49$	5.83691	−	3.36994i	0.833844	−	0.481420i
$50$		0			0
$51$	8.26899	−	8.26899i	1.15789	−	1.15789i
$52$	12.5111	−	7.22329i	1.73498	−	1.00169i
$53$	3.06455	−	11.4370i	0.420948	−	1.57100i	−0.351668	−	0.936125i	$-0.614385\pi$
$53$	3.06455	−	11.4370i	0.420948	−	1.57100i	0.772616	−	0.634874i	$-0.218948\pi$
$54$	4.55474	+	1.22044i	0.619822	+	0.166081i
$55$		0			0
$56$	−2.24598	+	0.601809i	−0.300132	+	0.0804202i
$57$	12.2232	−	7.05709i	1.61901	−	0.934734i
$58$	−7.52039	−	2.01508i	−0.987476	−	0.264593i
$59$	−4.75083	−	1.27298i	−0.618505	−	0.165728i	−0.0640571	−	0.997946i	$-0.520404\pi$
$59$	−4.75083	−	1.27298i	−0.618505	−	0.165728i	−0.554448	+	0.832218i	$0.687071\pi$
$60$		0			0
$61$	3.52938	+	13.1718i	0.451890	+	1.68648i	0.697073	+	0.717001i	$0.254486\pi$
$61$	3.52938	+	13.1718i	0.451890	+	1.68648i	−0.245182	+	0.969477i	$0.578848\pi$
$62$	4.77783	−	17.8311i	0.606785	−	2.26455i
$63$	−0.772660	−	0.772660i	−0.0973460	−	0.0973460i
$64$	9.32535			1.16567
$65$		0			0
$66$	13.7725	−	13.7725i	1.69528	−	1.69528i
$67$	6.51128	−	1.74469i	0.795480	−	0.213148i	0.161881	−	0.986810i	$-0.448244\pi$
$67$	6.51128	−	1.74469i	0.795480	−	0.213148i	0.633599	+	0.773662i	$0.281577\pi$
$68$	20.0090			2.42645
$69$	0.741497	−	0.198684i	0.0892658	−	0.0239187i
$70$		0			0
$71$	4.65903	−	8.06967i	0.552925	−	0.957694i	−0.445137	−	0.895463i	$-0.646845\pi$
$71$	4.65903	−	8.06967i	0.552925	−	0.957694i	0.998062	−	0.0622314i	$-0.0198217\pi$
$72$	−4.88389	−	8.45915i	−0.575572	−	0.996920i
$73$	3.04875	−	3.04875i	0.356829	−	0.356829i	−0.505814	−	0.862643i	$-0.668808\pi$
$73$	3.04875	−	3.04875i	0.356829	−	0.356829i	0.862643	+	0.505814i	$0.168808\pi$
$74$	−7.21600	+	12.8644i	−0.838843	+	1.49546i
$75$		0			0
$76$	23.3269	+	6.25043i	2.67578	+	0.716974i
$77$	1.74492	−	0.467551i	0.198853	−	0.0532824i
$78$	5.29903	+	19.7763i	0.599997	+	2.23922i
$79$	−0.309140	−	1.15373i	−0.0347810	−	0.129804i	0.946352	−	0.323136i	$-0.104737\pi$
$79$	−0.309140	−	1.15373i	−0.0347810	−	0.129804i	−0.981133	+	0.193332i	$0.938071\pi$
$80$		0			0
$81$	−5.41860	+	9.38530i	−0.602067	+	1.04281i
$82$	−10.3214			−1.13981
$83$	−2.96248	+	11.0561i	−0.325174	+	1.21357i	0.588962	+	0.808161i	$0.299537\pi$
$83$	−2.96248	+	11.0561i	−0.325174	+	1.21357i	−0.914137	+	0.405406i	$0.867130\pi$
$84$		−	4.48762i		−	0.489640i
$85$		0			0
$86$	−8.81944	−	15.2757i	−0.951025	−	1.64722i
$87$	3.64049	−	6.30552i	0.390302	−	0.676023i
$88$	16.1482			1.72141
$89$	3.23761	−	12.0829i	0.343186	−	1.28079i	−0.551531	−	0.834155i	$-0.685956\pi$
$89$	3.23761	−	12.0829i	0.343186	−	1.28079i	0.894717	−	0.446634i	$-0.147377\pi$
$90$		0			0
$91$	−0.491475	+	1.83421i	−0.0515206	+	0.192278i
$92$	1.13751	+	0.656741i	0.118593	+	0.0684700i
$93$	14.9506	+	8.63173i	1.55030	+	0.895069i
$94$	4.51421	−	16.8473i	0.465606	−	1.73766i
$95$		0			0
$96$	−0.662035	+	2.47075i	−0.0675686	+	0.252170i
$97$	4.72808			0.480064			0.240032	−	0.970765i	$-0.422842\pi$
$97$	4.72808			0.480064			0.240032	+	0.970765i	$0.422842\pi$
$98$	−8.17175	+	14.1539i	−0.825472	+	1.42976i
$99$	3.79434	+	6.57199i	0.381345	+	0.660509i
$100$		0			0
$101$		−	7.82698i		−	0.778814i	−0.921066	−	0.389407i	$-0.872680\pi$
$101$		−	7.82698i		−	0.778814i	0.921066	−	0.389407i	$-0.127320\pi$
$102$	−7.33933	+	27.3908i	−0.726702	+	2.71209i
$103$	−4.11567			−0.405529			−0.202764	−	0.979228i	$-0.564993\pi$
$103$	−4.11567			−0.405529			−0.202764	+	0.979228i	$0.564993\pi$
$104$	−8.48727	+	14.7004i	−0.832246	+	1.44149i
$105$		0			0
$106$	7.43120	+	27.7336i	0.721782	+	2.69373i
$107$	4.12965	+	15.4121i	0.399229	+	1.48994i	0.814457	+	0.580224i	$0.197035\pi$
$107$	4.12965	+	15.4121i	0.399229	+	1.48994i	−0.415228	+	0.909717i	$0.636298\pi$
$108$	−7.28812	+	1.95285i	−0.701299	+	0.187913i
$109$	8.54823	+	2.29049i	0.818772	+	0.219389i	0.643809	−	0.765186i	$-0.277353\pi$
$109$	8.54823	+	2.29049i	0.818772	+	0.219389i	0.174962	+	0.984575i	$0.444020\pi$
$110$		0			0
$111$	−9.87402	−	9.63202i	−0.937200	−	0.914231i
$112$	1.18832	−	1.18832i	0.112286	−	0.112286i
$113$	−1.99398	−	3.45367i	−0.187578	−	0.324894i	0.756864	−	0.653572i	$-0.226730\pi$
$113$	−1.99398	−	3.45367i	−0.187578	−	0.324894i	−0.944442	+	0.328678i	$0.893397\pi$
$114$	−17.1127	+	29.6401i	−1.60275	+	2.77605i
$115$		0			0
$116$	12.0335	−	3.22437i	1.11728	−	0.299375i
$117$	−7.97699			−0.737473
$118$	11.5203	−	3.08684i	1.06053	−	0.284167i
$119$	−1.85973	+	1.85973i	−0.170481	+	0.170481i
$120$		0			0
$121$	−1.54571			−0.140519
$122$	−23.3819	−	23.3819i	−2.11690	−	2.11690i
$123$	2.49822	−	9.32348i	0.225257	−	0.840670i
$124$	7.64508	+	28.5318i	0.686549	+	2.56223i
$125$		0			0
$126$	2.55941	+	0.685792i	0.228011	+	0.0610952i
$127$	10.7680	+	2.88527i	0.955504	+	0.256027i	0.702696	−	0.711490i	$-0.251979\pi$
$127$	10.7680	+	2.88527i	0.955504	+	0.256027i	0.252808	+	0.967516i	$0.418646\pi$
$128$	−17.6297	+	10.1785i	−1.55826	+	0.899663i
$129$	15.9334	−	4.26934i	1.40286	−	0.375895i
$130$		0			0
$131$	−3.98701	−	1.06832i	−0.348347	−	0.0933393i	0.0804031	−	0.996762i	$-0.474379\pi$
$131$	−3.98701	−	1.06832i	−0.348347	−	0.0933393i	−0.428750	+	0.903423i	$0.641046\pi$
$132$	−8.06632	+	30.1039i	−0.702083	+	2.62021i
$133$	−2.74906	+	1.58717i	−0.238374	+	0.137625i
$134$	−11.5585	+	11.5585i	−0.998501	+	0.998501i
$135$		0			0
$136$	−20.3605	+	11.7552i	−1.74590	+	1.00800i
$137$	10.9312	−	10.9312i	0.933918	−	0.933918i	−0.0640304	−	0.997948i	$-0.520395\pi$
$137$	10.9312	−	10.9312i	0.933918	−	0.933918i	0.997948	+	0.0640304i	$0.0203955\pi$
$138$	−1.31627	+	1.31627i	−0.112048	+	0.112048i
$139$	−3.85294	−	6.67349i	−0.326802	−	0.566038i	0.655073	−	0.755566i	$-0.272638\pi$
$139$	−3.85294	−	6.67349i	−0.326802	−	0.566038i	−0.981875	+	0.189527i	$0.939304\pi$
$140$		0			0
$141$	14.1257	+	8.15548i	1.18960	+	0.686815i
$142$			22.5953i			1.89616i
$143$	6.59384	−	11.4209i	0.551404	−	0.955060i
$144$	6.11383	+	3.52982i	0.509486	+	0.294152i
$145$		0			0
$146$	−2.70599	+	10.0989i	−0.223949	+	0.835789i
$147$	−10.8075	−	10.8075i	−0.891385	−	0.891385i
$148$	−0.292792	−	23.6000i	−0.0240674	−	1.93991i
$149$		−	4.52038i		−	0.370324i	−0.982708	−	0.185162i	$-0.940719\pi$
$149$		−	4.52038i		−	0.370324i	0.982708	−	0.185162i	$-0.0592810\pi$
$150$		0			0
$151$	7.34080	+	4.23821i	0.597386	+	0.344901i	0.768013	−	0.640435i	$-0.221246\pi$
$151$	7.34080	+	4.23821i	0.597386	+	0.344901i	−0.170626	+	0.985336i	$0.554579\pi$
$152$	−27.4088	+	7.34417i	−2.22315	+	0.595691i
$153$	−9.56819	−	5.52419i	−0.773542	−	0.446605i
$154$	−3.09749	+	3.09749i	−0.249603	+	0.249603i
$155$		0			0
$156$	−23.1652	−	23.1652i	−1.85470	−	1.85470i
$157$	6.25734	+	1.67665i	0.499390	+	0.133811i	0.499717	−	0.866189i	$-0.333437\pi$
$157$	6.25734	+	1.67665i	0.499390	+	0.133811i	−0.000326679		1.00000i	$0.500104\pi$
$158$	2.04803	+	2.04803i	0.162933	+	0.162933i
$159$	−26.8508			−2.12940
$160$		0			0
$161$	−0.166766	+	0.0446849i	−0.0131430	+	0.00352166i
$162$		−	26.2791i		−	2.06468i
$163$	−5.44041	−	9.42307i	−0.426126	−	0.738072i	0.570399	−	0.821368i	$-0.306789\pi$
$163$	−5.44041	−	9.42307i	−0.426126	−	0.738072i	−0.996525	+	0.0832960i	$0.973455\pi$
$164$	14.3029	−	8.25776i	1.11687	−	0.644823i
$165$		0			0
$166$	−7.18370	−	26.8099i	−0.557563	−	2.08085i
$167$	0.0342983	−	0.0594064i	0.00265408	−	0.00459701i	−0.864695	−	0.502297i	$-0.832489\pi$
$167$	0.0342983	−	0.0594064i	0.00265408	−	0.00459701i	0.867349	+	0.497700i	$0.165822\pi$
$168$	2.63645	+	4.56646i	0.203406	+	0.352310i
$169$	0.431244	+	0.746936i	0.0331726	+	0.0574566i
$170$		0			0
$171$	−9.42915	−	9.42915i	−0.721065	−	0.721065i
$172$	24.4429	+	14.1121i	1.86376	+	1.07604i
$173$	−5.77870	−	1.54840i	−0.439346	−	0.117722i	0.0323639	−	0.999476i	$-0.489696\pi$
$173$	−5.77870	−	1.54840i	−0.439346	−	0.117722i	−0.471710	+	0.881754i	$0.656363\pi$
$174$			17.6556i			1.33847i
$175$		0			0
$176$	−10.1075	+	5.83556i	−0.761880	+	0.439872i
$177$			11.1535i			0.838351i
$178$	7.85087	+	29.2999i	0.588448	+	2.19612i
$179$	11.7111	+	11.7111i	0.875328	+	0.875328i	0.993047	−	0.117719i	$-0.0375583\pi$
$179$	11.7111	+	11.7111i	0.875328	+	0.875328i	−0.117719	+	0.993047i	$0.537558\pi$
$180$		0			0
$181$	−7.37562	+	12.7750i	−0.548226	+	0.949555i	0.450171	+	0.892943i	$0.351363\pi$
$181$	−7.37562	+	12.7750i	−0.548226	+	0.949555i	−0.998396	+	0.0566121i	$0.981970\pi$
$182$	−1.19178	−	4.44777i	−0.0883404	−	0.329691i
$183$	26.7805	−	15.4617i	1.97967	−	1.14296i
$184$	−1.54332			−0.113775
$185$		0			0
$186$	−41.8621			−3.06948
$187$	15.8183	−	9.13268i	1.15675	−	0.667848i
$188$	7.22327	+	26.9576i	0.526811	+	1.96609i
$189$	0.495886	−	0.858900i	0.0360704	−	0.0624758i
$190$		0			0
$191$	−5.10682	−	5.10682i	−0.369517	−	0.369517i	0.497784	−	0.867301i	$-0.334147\pi$
$191$	−5.10682	−	5.10682i	−0.369517	−	0.369517i	−0.867301	+	0.497784i	$0.834147\pi$
$192$	−5.47328	−	20.4266i	−0.395000	−	1.47416i
$193$		−	16.0854i		−	1.15785i	−0.815381	−	0.578925i	$-0.803472\pi$
$193$		−	16.0854i		−	1.15785i	0.815381	−	0.578925i	$-0.196528\pi$
$194$	−9.92906	+	5.73255i	−0.712865	+	0.411573i
$195$		0			0
$196$		−	26.1515i		−	1.86797i
$197$	1.27500	+	0.341636i	0.0908403	+	0.0243406i	0.303953	−	0.952687i	$-0.401693\pi$
$197$	1.27500	+	0.341636i	0.0908403	+	0.0243406i	−0.213113	+	0.977028i	$0.568360\pi$
$198$	−15.9364	−	9.20087i	−1.13255	−	0.653877i
$199$	−6.93417	−	6.93417i	−0.491550	−	0.491550i	0.417244	−	0.908794i	$-0.362996\pi$
$199$	−6.93417	−	6.93417i	−0.491550	−	0.491550i	−0.908794	+	0.417244i	$0.862996\pi$
$200$		0			0
$201$	−7.64327	−	13.2385i	−0.539115	−	0.933775i
$202$	9.48980	+	16.4368i	0.667700	+	1.15649i
$203$	−0.818764	+	1.41814i	−0.0574660	+	0.0995340i
$204$	−11.7438	−	43.8284i	−0.822230	−	3.06860i
$205$		0			0
$206$	8.64298	−	4.99003i	0.602185	−	0.347672i
$207$	−0.362633	−	0.628099i	−0.0252048	−	0.0436559i
$208$		−	12.2683i		−	0.850655i
$209$	21.2942	−	5.70575i	1.47295	−	0.394675i
$210$		0			0
$211$	20.0827			1.38255			0.691276	−	0.722591i	$-0.257049\pi$
$211$	20.0827			1.38255			0.691276	+	0.722591i	$0.257049\pi$
$212$	−32.4863	−	32.4863i	−2.23117	−	2.23117i
$213$	−20.4106	−	5.46900i	−1.39851	−	0.374730i
$214$	−27.3587	−	27.3587i	−1.87020	−	1.87020i
$215$		0			0
$216$	6.26887	−	6.26887i	0.426543	−	0.426543i
$217$	−3.36246	−	1.94132i	−0.228259	−	0.131785i
$218$	−20.7286	+	5.55420i	−1.40391	+	0.376178i
$219$	−8.46747	−	4.88870i	−0.572179	−	0.330348i
$220$		0			0
$221$			19.2000i			1.29153i
$222$	32.4140	+	8.25571i	2.17548	+	0.554087i
$223$	−7.38420	−	7.38420i	−0.494483	−	0.494483i	0.415233	−	0.909715i	$-0.363700\pi$
$223$	−7.38420	−	7.38420i	−0.494483	−	0.494483i	−0.909715	+	0.415233i	$0.863700\pi$
$224$	0.148895	−	0.555683i	0.00994844	−	0.0371281i
$225$		0			0
$226$	8.37480	+	4.83519i	0.557083	+	0.321632i
$227$	−7.02187	+	12.1622i	−0.466058	+	0.807236i	−0.999249	−	0.0387589i	$-0.987660\pi$
$227$	−7.02187	+	12.1622i	−0.466058	+	0.807236i	0.533190	+	0.845995i	$0.320993\pi$
$228$		−	54.7647i		−	3.62688i
$229$	−4.87436	−	2.81421i	−0.322107	−	0.185968i	0.330224	−	0.943902i	$-0.392876\pi$
$229$	−4.87436	−	2.81421i	−0.322107	−	0.185968i	−0.652331	+	0.757934i	$0.726209\pi$
$230$		0			0
$231$	−2.04828	−	3.54772i	−0.134767	−	0.233423i
$232$	−10.3506	+	10.3506i	−0.679552	+	0.679552i
$233$	0.663810	−	0.663810i	0.0434877	−	0.0434877i	−0.685029	−	0.728516i	$-0.740210\pi$
$233$	0.663810	−	0.663810i	0.0434877	−	0.0434877i	0.728516	+	0.685029i	$0.240210\pi$
$234$	16.7518	−	9.67168i	1.09510	−	0.632258i
$235$		0			0
$236$	−13.4945	+	13.4945i	−0.878414	+	0.878414i
$237$	−2.34572	+	1.35430i	−0.152371	+	0.0879714i
$238$	1.65065	−	6.16031i	0.106996	−	0.399313i
$239$	−16.2404	−	4.35161i	−1.05051	−	0.281482i	−0.308046	−	0.951372i	$-0.599675\pi$
$239$	−16.2404	−	4.35161i	−1.05051	−	0.281482i	−0.742461	+	0.669889i	$0.766342\pi$
$240$		0			0
$241$	−17.7499	+	4.75606i	−1.14337	+	0.306365i	−0.780305	−	0.625399i	$-0.784936\pi$
$241$	−17.7499	+	4.75606i	−1.14337	+	0.306365i	−0.363065	+	0.931764i	$0.618270\pi$
$242$	3.24602	−	1.87409i	0.208662	−	0.120471i
$243$	18.1032	+	4.85075i	1.16132	+	0.311176i
$244$	51.1082	+	13.6944i	3.27186	+	0.876693i
$245$		0			0
$246$	6.05792	+	22.6085i	0.386239	+	1.44146i
$247$	−5.99772	+	22.3838i	−0.381625	+	1.42425i
$248$	−24.5417	−	24.5417i	−1.55840	−	1.55840i
$249$	25.9565			1.64492
$250$		0			0
$251$	−5.87927	+	5.87927i	−0.371096	+	0.371096i	−0.867876	−	0.496780i	$-0.834516\pi$
$251$	−5.87927	+	5.87927i	−0.371096	+	0.371096i	0.496780	+	0.867876i	$0.334516\pi$
$252$	−4.09536	+	1.09735i	−0.257983	+	0.0691264i
$253$	1.19902			0.0753818
$254$	−26.1112	+	6.99649i	−1.63836	+	0.438999i
$255$		0			0
$256$	15.3565	−	26.5983i	0.959782	−	1.66239i
$257$	7.49045	+	12.9738i	0.467241	+	0.809286i	0.999300	−	0.0374219i	$-0.0119146\pi$
$257$	7.49045	+	12.9738i	0.467241	+	0.809286i	−0.532058	+	0.846708i	$0.678581\pi$
$258$	−28.2841	+	28.2841i	−1.76089	+	1.76089i
$259$	2.22071	+	2.16629i	0.137988	+	0.134606i
$260$		0			0
$261$	−6.64456	−	1.78040i	−0.411288	−	0.110204i
$262$	9.66809	−	2.59056i	0.597297	−	0.160045i
$263$	3.63934	+	13.5822i	0.224411	+	0.837514i	0.982640	+	0.185525i	$0.0593985\pi$
$263$	3.63934	+	13.5822i	0.224411	+	0.837514i	−0.758228	+	0.651989i	$0.773935\pi$
$264$	−9.47781	−	35.3717i	−0.583319	−	2.17698i
$265$		0			0
$266$	3.84873	−	6.66619i	0.235981	−	0.408730i
$267$	−28.3671			−1.73604
$268$	6.76961	−	25.2645i	0.413520	−	1.54328i
$269$			1.04920i			0.0639708i	0.999488	+	0.0319854i	$0.0101830\pi$
$269$			1.04920i			0.0639708i	−0.999488	+	0.0319854i	$0.989817\pi$
$270$		0			0
$271$	−6.57360	−	11.3858i	−0.399318	−	0.691638i	0.594324	−	0.804225i	$-0.297420\pi$
$271$	−6.57360	−	11.3858i	−0.399318	−	0.691638i	−0.993642	+	0.112587i	$0.964086\pi$
$272$	8.49601	−	14.7155i	0.515147	−	0.892260i
$273$	4.30618			0.260622
$274$	−9.70226	+	36.2093i	−0.586135	+	2.18749i
$275$		0			0
$276$	0.770916	−	2.87710i	0.0464037	−	0.173181i
$277$	−13.8716	−	8.00875i	−0.833461	−	0.481199i	0.0215750	−	0.999767i	$-0.493132\pi$
$277$	−13.8716	−	8.00875i	−0.833461	−	0.481199i	−0.855036	+	0.518568i	$0.826465\pi$
$278$	16.1825	+	9.34298i	0.970563	+	0.560355i
$279$	4.22139	−	15.7545i	0.252728	−	0.943195i
$280$		0			0
$281$	1.07217	−	4.00139i	0.0639603	−	0.238703i	−0.926544	−	0.376187i	$-0.877235\pi$
$281$	1.07217	−	4.00139i	0.0639603	−	0.238703i	0.990504	+	0.137484i	$0.0439016\pi$
$282$	−39.5524			−2.35531
$283$	10.2040	−	17.6738i	0.606563	−	1.05060i	−0.385239	−	0.922817i	$-0.625881\pi$
$283$	10.2040	−	17.6738i	0.606563	−	1.05060i	0.991802	−	0.127782i	$-0.0407857\pi$
$284$	−18.0776	−	31.3113i	−1.07271	−	1.85798i
$285$		0			0
$286$			31.9787i			1.89094i
$287$	−0.561861	+	2.09689i	−0.0331656	+	0.123776i
$288$	2.41666			0.142403
$289$	−4.79631	+	8.30746i	−0.282136	+	0.488674i
$290$		0			0
$291$	−2.77503	−	10.3566i	−0.162675	−	0.607112i
$292$	−4.32990	−	16.1594i	−0.253388	−	0.945657i
$293$	−14.8251	+	3.97236i	−0.866090	+	0.232068i	−0.664396	−	0.747381i	$-0.731311\pi$
$293$	−14.8251	+	3.97236i	−0.866090	+	0.232068i	−0.201694	+	0.979449i	$0.564644\pi$
$294$	35.7994	+	9.59242i	2.08786	+	0.559441i
$295$		0			0
$296$	14.1628	+	23.8426i	0.823195	+	1.38582i
$297$	−4.87034	+	4.87034i	−0.282606	+	0.282606i
$298$	5.48072	+	9.49289i	0.317490	+	0.549908i
$299$	−0.630188	+	1.09152i	−0.0364447	+	0.0631240i
$300$		0			0
$301$	−3.58350	+	0.960195i	−0.206549	+	0.0553447i
$302$	−20.5545			−1.18278
$303$	−17.1445	+	4.59385i	−0.984925	+	0.263910i
$304$	14.5017	−	14.5017i	0.831729	−	0.831729i
$305$		0			0
$306$	26.7912			1.53155
$307$	−12.4311	−	12.4311i	−0.709480	−	0.709480i	0.256946	−	0.966426i	$-0.417284\pi$
$307$	−12.4311	−	12.4311i	−0.709480	−	0.709480i	−0.966426	+	0.256946i	$0.917284\pi$
$308$	1.81415	−	6.77051i	0.103371	−	0.385785i
$309$	2.41559	+	9.01510i	0.137418	+	0.512851i
$310$		0			0
$311$	−14.7974	−	3.96496i	−0.839085	−	0.224832i	−0.186412	−	0.982472i	$-0.559686\pi$
$311$	−14.7974	−	3.96496i	−0.839085	−	0.224832i	−0.652673	+	0.757639i	$0.726353\pi$
$312$	37.1817	+	9.96279i	2.10500	+	0.564032i
$313$	−7.67727	+	4.43247i	−0.433945	+	0.250538i	−0.701026	−	0.713136i	$-0.747274\pi$
$313$	−7.67727	+	4.43247i	−0.433945	+	0.250538i	0.267081	+	0.963674i	$0.413941\pi$
$314$	−15.1734	+	4.06570i	−0.856285	+	0.229441i
$315$		0			0
$316$	−4.47659	−	1.19950i	−0.251828	−	0.0674771i
$317$	4.48626	−	16.7429i	0.251973	−	0.940377i	−0.717776	−	0.696274i	$-0.754840\pi$
$317$	4.48626	−	16.7429i	0.251973	−	0.940377i	0.969749	−	0.244103i	$-0.0784936\pi$
$318$	56.3872	−	32.5551i	3.16204	−	1.82560i
$319$	8.04149	−	8.04149i	0.450237	−	0.450237i
$320$		0			0
$321$	31.3354	−	18.0915i	1.74897	−	1.00977i
$322$	0.296034	−	0.296034i	0.0164974	−	0.0164974i
$323$	−22.6952	+	22.6952i	−1.26280	+	1.26280i
$324$	21.0248	+	36.4160i	1.16805	+	2.02311i
$325$		0			0
$326$	22.8500	+	13.1924i	1.26554	+	0.730661i
$327$		−	20.0687i		−	1.10980i
$328$	−9.70276	+	16.8057i	−0.535745	+	0.927938i
$329$	−3.17694	−	1.83421i	−0.175150	−	0.101123i
$330$		0			0
$331$	5.45207	−	20.3474i	0.299673	−	1.11839i	−0.637762	−	0.770234i	$-0.720140\pi$
$331$	5.45207	−	20.3474i	0.299673	−	1.11839i	0.937435	−	0.348161i	$-0.113194\pi$
$332$	31.4043	+	31.4043i	1.72353	+	1.72353i
$333$	−6.37561	+	11.3662i	−0.349381	+	0.622865i
$334$			0.166340i			0.00910170i
$335$		0			0
$336$	−3.30040	−	1.90549i	−0.180052	−	0.103953i
$337$	−31.0294	+	8.31429i	−1.69028	+	0.452908i	−0.970461	−	0.241257i	$-0.922440\pi$
$337$	−31.0294	+	8.31429i	−1.69028	+	0.452908i	−0.719816	+	0.694165i	$0.755774\pi$
$338$	−1.81124	−	1.04572i	−0.0985186	−	0.0568797i
$339$	−6.39473	+	6.39473i	−0.347314	+	0.347314i
$340$		0			0
$341$	19.0666	+	19.0666i	1.03252	+	1.03252i
$342$	31.2338	+	8.36906i	1.68893	+	0.452547i
$343$	4.95511	+	4.95511i	0.267551	+	0.267551i
$344$	−33.1632			−1.78804
$345$		0			0
$346$	14.0127	−	3.75470i	0.753329	−	0.201854i
$347$			3.43520i			0.184411i	0.995740	+	0.0922055i	$0.0293917\pi$
$347$			3.43520i			0.184411i	−0.995740	+	0.0922055i	$0.970608\pi$
$348$	−14.1255	−	24.4662i	−0.757209	−	1.31152i
$349$	2.54502	−	1.46937i	0.136232	−	0.0786533i	−0.430335	−	0.902669i	$-0.641605\pi$
$349$	2.54502	−	1.46937i	0.136232	−	0.0786533i	0.566567	+	0.824016i	$0.308271\pi$
$350$		0			0
$351$	−1.87389	−	6.99345i	−0.100021	−	0.373283i
$352$	−1.99763	+	3.46000i	−0.106474	+	0.184419i
$353$	−1.46544	−	2.53821i	−0.0779974	−	0.135095i	0.824388	−	0.566025i	$-0.191519\pi$
$353$	−1.46544	−	2.53821i	−0.0779974	−	0.135095i	−0.902386	+	0.430929i	$0.858186\pi$
$354$	−13.5231	−	23.4226i	−0.718743	−	1.24490i
$355$		0			0
$356$	−34.3209	−	34.3209i	−1.81900	−	1.81900i
$357$	5.16515	+	2.98210i	0.273369	+	0.157829i
$358$	−38.7926	−	10.3944i	−2.05025	−	0.549364i
$359$			33.4016i			1.76287i	0.472306	+	0.881435i	$0.343422\pi$
$359$			33.4016i			1.76287i	−0.472306	+	0.881435i	$0.656578\pi$
$360$		0			0
$361$	−17.0937	+	9.86904i	−0.899667	+	0.519423i
$362$		−	35.7702i		−	1.88004i
$363$	0.907216	+	3.38578i	0.0476165	+	0.177707i
$364$	5.20997	+	5.20997i	0.273077	+	0.273077i
$365$		0			0
$366$	−37.4931	+	64.9399i	−1.95980	+	3.39447i
$367$	1.84441	+	6.88341i	0.0962772	+	0.359311i	0.997210	−	0.0746473i	$-0.0237831\pi$
$367$	1.84441	+	6.88341i	0.0962772	+	0.359311i	−0.900933	+	0.433959i	$0.857116\pi$
$368$	0.965994	−	0.557717i	0.0503559	−	0.0290730i
$369$	−9.11939			−0.474737
$370$		0			0
$371$	6.03886			0.313522
$372$	58.0101	−	33.4921i	3.00768	−	1.73649i
$373$	8.66861	+	32.3517i	0.448843	+	1.67511i	0.705584	+	0.708626i	$0.250685\pi$
$373$	8.66861	+	32.3517i	0.448843	+	1.67511i	−0.256741	+	0.966480i	$0.582649\pi$
$374$	−22.1458	+	38.3576i	−1.14513	+	1.98343i
$375$		0			0
$376$	−23.1876	−	23.1876i	−1.19581	−	1.19581i
$377$	3.09400	+	11.5470i	0.159349	+	0.594699i
$378$			2.40494i			0.123697i
$379$	0.843406	−	0.486941i	0.0433229	−	0.0250125i	−0.478182	−	0.878261i	$-0.658704\pi$
$379$	0.843406	−	0.486941i	0.0433229	−	0.0250125i	0.521505	+	0.853248i	$0.325371\pi$
$380$		0			0
$381$		−	25.2800i		−	1.29513i
$382$	16.9162	+	4.53268i	0.865507	+	0.231912i
$383$	26.3897	+	15.2361i	1.34845	+	0.778527i	0.988030	−	0.154263i	$-0.0493003\pi$
$383$	26.3897	+	15.2361i	1.34845	+	0.778527i	0.360419	+	0.932790i	$0.382634\pi$
$384$	32.6427	+	32.6427i	1.66579	+	1.66579i
$385$		0			0
$386$	19.5027	+	33.7796i	0.992660	+	1.71934i
$387$	−7.79232	−	13.4967i	−0.396106	−	0.686075i
$388$	9.17275	−	15.8877i	0.465676	−	0.806574i
$389$	0.145105	+	0.541538i	0.00735710	+	0.0274571i	0.969507	−	0.245064i	$-0.0788091\pi$
$389$	0.145105	+	0.541538i	0.00735710	+	0.0274571i	−0.962150	+	0.272521i	$0.912142\pi$
$390$		0			0
$391$	−1.51179	+	0.872830i	−0.0764543	+	0.0441409i
$392$	15.3638	+	26.6110i	0.775991	+	1.34406i
$393$			9.36032i			0.472166i
$394$	−3.09175	+	0.828432i	−0.155760	+	0.0417358i
$395$		0			0
$396$	29.4449			1.47966
$397$	12.8419	+	12.8419i	0.644519	+	0.644519i	0.951663	−	0.307144i	$-0.0993735\pi$
$397$	12.8419	+	12.8419i	0.644519	+	0.644519i	−0.307144	+	0.951663i	$0.599373\pi$
$398$	22.9692	+	6.15458i	1.15134	+	0.308501i
$399$	5.09009	+	5.09009i	0.254823	+	0.254823i
$400$		0			0
$401$	19.2588	−	19.2588i	0.961739	−	0.961739i	−0.0375556	−	0.999295i	$-0.511957\pi$
$401$	19.2588	−	19.2588i	0.961739	−	0.961739i	0.999295	+	0.0375556i	$0.0119571\pi$
$402$	32.1021	+	18.5341i	1.60111	+	0.924399i
$403$	−27.3782	+	7.33598i	−1.36381	+	0.365431i
$404$	−26.3008	−	15.1848i	−1.30852	−	0.755472i
$405$		0			0
$406$		−	3.97083i		−	0.197069i
$407$	−11.0032	−	18.5235i	−0.545408	−	0.918177i
$408$	37.6990	+	37.6990i	1.86638	+	1.86638i
$409$	−4.51734	+	16.8590i	−0.223368	+	0.833622i	0.759683	+	0.650293i	$0.225354\pi$
$409$	−4.51734	+	16.8590i	−0.223368	+	0.833622i	−0.983052	+	0.183329i	$0.941313\pi$
$410$		0			0
$411$	−30.3600	−	17.5283i	−1.49755	−	0.864609i
$412$	−7.98463	+	13.8298i	−0.393375	+	0.681345i
$413$		−	2.50848i		−	0.123434i
$414$	1.52307	+	0.879348i	0.0748550	+	0.0432176i
$415$		0			0
$416$	−2.09985	−	3.63705i	−0.102954	−	0.178321i
$417$	−12.3565	+	12.3565i	−0.605099	+	0.605099i
$418$	−37.8002	+	37.8002i	−1.84887	+	1.84887i
$419$	28.8474	−	16.6550i	1.40929	−	0.813652i	0.413967	−	0.910292i	$-0.364143\pi$
$419$	28.8474	−	16.6550i	1.40929	−	0.813652i	0.995319	+	0.0966398i	$0.0308095\pi$
$420$		0			0
$421$	−22.7419	+	22.7419i	−1.10837	+	1.10837i	−0.115006	+	0.993365i	$0.536689\pi$
$421$	−22.7419	+	22.7419i	−1.10837	+	1.10837i	−0.993365	+	0.115006i	$0.963311\pi$
$422$	−42.1741	+	24.3493i	−2.05301	+	1.18530i
$423$	3.98848	−	14.8852i	0.193927	−	0.723744i
$424$	52.1425	+	13.9715i	2.53226	+	0.678517i
$425$		0			0
$426$	49.4936	−	13.2618i	2.39797	−	0.642534i
$427$	−6.02306	+	3.47742i	−0.291476	+	0.168284i
$428$	59.8007	+	16.0235i	2.89057	+	0.774527i
$429$	−28.8867	−	7.74018i	−1.39467	−	0.373699i
$430$		0			0
$431$	1.81621	+	6.77820i	0.0874840	+	0.326495i	0.995773	−	0.0918486i	$-0.0292776\pi$
$431$	1.81621	+	6.77820i	0.0874840	+	0.326495i	−0.908289	+	0.418343i	$0.862611\pi$
$432$	−1.65839	+	6.18921i	−0.0797895	+	0.297779i
$433$	25.1107	+	25.1107i	1.20674	+	1.20674i	0.972076	+	0.234667i	$0.0754000\pi$
$433$	25.1107	+	25.1107i	1.20674	+	1.20674i	0.234667	+	0.972076i	$0.424600\pi$
$434$	9.41498			0.451933
$435$		0			0
$436$	24.2807	−	24.2807i	1.16284	−	1.16284i
$437$	−2.03513	+	0.545311i	−0.0973534	+	0.0260858i
$438$	23.7092			1.13287
$439$	29.9057	−	8.01322i	1.42732	−	0.382450i	0.539247	−	0.842148i	$-0.318709\pi$
$439$	29.9057	−	8.01322i	1.42732	−	0.382450i	0.888076	+	0.459698i	$0.152042\pi$
$440$		0			0
$441$	−7.22006	+	12.5055i	−0.343812	+	0.595500i
$442$	−23.2790	−	40.3204i	−1.10727	−	1.91785i
$443$	−0.346705	+	0.346705i	−0.0164725	+	0.0164725i	−0.715295	−	0.698823i	$-0.753708\pi$
$443$	−0.346705	+	0.346705i	−0.0164725	+	0.0164725i	0.698823	+	0.715295i	$0.253708\pi$
$444$	−51.5224	+	14.4928i	−2.44515	+	0.687797i
$445$		0			0
$446$	24.4599	+	6.55402i	1.15821	+	0.310342i
$447$	−9.90160	+	2.65313i	−0.468329	+	0.125489i
$448$	1.23097	+	4.59403i	0.0581577	+	0.217048i
$449$	−0.545210	−	2.03475i	−0.0257301	−	0.0960259i	0.951867	−	0.306512i	$-0.0991620\pi$
$449$	−0.545210	−	2.03475i	−0.0257301	−	0.0960259i	−0.977597	+	0.210486i	$0.932495\pi$
$450$		0			0
$451$	7.53816	−	13.0565i	0.354958	−	0.614805i
$452$	−15.4737			−0.727824
$453$	4.97503	−	18.5671i	0.233747	−	0.872357i
$454$		−	34.0546i		−	1.59826i
$455$		0			0
$456$	32.1739	+	55.7268i	1.50668	+	2.60965i
$457$	15.6850	−	27.1673i	0.733715	−	1.27083i	−0.221570	−	0.975144i	$-0.571118\pi$
$457$	15.6850	−	27.1673i	0.733715	−	1.27083i	0.955285	−	0.295687i	$-0.0955485\pi$
$458$	13.6483			0.637745
$459$	2.59540	−	9.68615i	0.121143	−	0.452111i
$460$		0			0
$461$	−8.90787	+	33.2446i	−0.414881	+	1.54836i	0.370194	+	0.928955i	$0.379291\pi$
$461$	−8.90787	+	33.2446i	−0.414881	+	1.54836i	−0.785075	+	0.619401i	$0.787375\pi$
$462$	8.60286	+	4.96686i	0.400241	+	0.231079i
$463$	11.9951	+	6.92538i	0.557460	+	0.321850i	0.752125	−	0.659020i	$-0.229029\pi$
$463$	11.9951	+	6.92538i	0.557460	+	0.321850i	−0.194665	+	0.980870i	$0.562362\pi$
$464$	2.73820	−	10.2191i	0.127118	−	0.474409i
$465$		0			0
$466$	−0.589180	+	2.19885i	−0.0272932	+	0.101860i
$467$	12.9629			0.599850			0.299925	−	0.953963i	$-0.403038\pi$
$467$	12.9629			0.599850			0.299925	+	0.953963i	$0.403038\pi$
$468$	−15.4758	+	26.8049i	−0.715370	+	1.23906i
$469$	1.71901	+	2.97741i	0.0793764	+	0.137484i
$470$		0			0
$471$		−	14.6904i		−	0.676897i
$472$	5.80363	−	21.6594i	0.267134	−	0.996956i
$473$	25.7647			1.18466
$474$	3.28404	−	5.68813i	0.150841	−	0.261264i
$475$		0			0
$476$	2.64123	+	9.85721i	0.121061	+	0.451805i
$477$	6.56575	+	24.5037i	0.300625	+	1.12195i
$478$	39.3814	−	10.5522i	1.80126	−	0.482647i
$479$	−20.7631	−	5.56346i	−0.948691	−	0.254201i	−0.248884	−	0.968533i	$-0.580064\pi$
$479$	−20.7631	−	5.56346i	−0.948691	−	0.254201i	−0.699807	+	0.714332i	$0.746731\pi$
$480$		0			0
$481$	22.6458	−	0.280954i	1.03256	−	0.0128104i
$482$	31.5086	−	31.5086i	1.43518	−	1.43518i
$483$	0.195759	+	0.339064i	0.00890733	+	0.0154279i
$484$	−2.99877	+	5.19401i	−0.136308	+	0.236092i
$485$		0			0
$486$	−43.8984	+	11.7626i	−1.99127	+	0.533560i
$487$	11.9469			0.541367			0.270684	−	0.962668i	$-0.412750\pi$
$487$	11.9469			0.541367			0.270684	+	0.962668i	$0.412750\pi$
$488$	−60.0514	+	16.0907i	−2.71840	+	0.728393i
$489$	−17.4475	+	17.4475i	−0.789004	+	0.789004i
$490$		0			0
$491$	14.8679			0.670980			0.335490	−	0.942044i	$-0.391098\pi$
$491$	14.8679			0.670980			0.335490	+	0.942044i	$0.391098\pi$
$492$	−26.4828	−	26.4828i	−1.19394	−	1.19394i
$493$	−4.28529	+	15.9929i	−0.193000	+	0.720286i
$494$	−14.5438	−	54.2783i	−0.654358	−	2.44210i
$495$		0			0
$496$	24.2298	+	6.49235i	1.08795	+	0.291515i
$497$	4.59044	+	1.23000i	0.205909	+	0.0551732i
$498$	−54.5091	+	31.4709i	−2.44261	+	1.41024i
$499$	7.92150	−	2.12256i	0.354615	−	0.0950188i	−0.0771137	−	0.997022i	$-0.524570\pi$
$499$	7.92150	−	2.12256i	0.354615	−	0.0950188i	0.431729	+	0.902003i	$0.357904\pi$
$500$		0			0
$501$	−0.150256	−	0.0402611i	−0.00671296	−	0.00179873i
$502$	5.21828	−	19.4749i	0.232903	−	0.869207i
$503$	9.43924	−	5.44975i	0.420875	−	0.242992i	−0.274577	−	0.961565i	$-0.588538\pi$
$503$	9.43924	−	5.44975i	0.420875	−	0.242992i	0.695452	+	0.718573i	$0.255204\pi$
$504$	3.52262	−	3.52262i	0.156910	−	0.156910i
$505$		0			0
$506$	−2.51797	+	1.45375i	−0.111937	+	0.0646271i
$507$	1.38301	−	1.38301i	0.0614215	−	0.0614215i
$508$	30.5858	−	30.5858i	1.35703	−	1.35703i
$509$	18.1888	+	31.5039i	0.806204	+	1.39639i	0.915475	+	0.402374i	$0.131815\pi$
$509$	18.1888	+	31.5039i	0.806204	+	1.39639i	−0.109272	+	0.994012i	$0.534852\pi$
$510$		0			0
$511$	1.90437	+	1.09949i	0.0842445	+	0.0486386i
$512$			33.7617i			1.49207i
$513$	6.05154	−	10.4816i	0.267182	−	0.462773i
$514$	−31.4602	−	18.1636i	−1.38765	−	0.801160i
$515$		0			0
$516$	16.5655	−	61.8235i	0.729257	−	2.72163i
$517$	18.0146	+	18.0146i	0.792283	+	0.792283i
$518$	−7.29005	−	1.85675i	−0.320306	−	0.0815808i
$519$			13.5667i			0.595510i
$520$		0			0
$521$	−8.37998	−	4.83818i	−0.367134	−	0.211965i	0.305072	−	0.952329i	$-0.401320\pi$
$521$	−8.37998	−	4.83818i	−0.367134	−	0.211965i	−0.672205	+	0.740365i	$0.734653\pi$
$522$	16.1124	−	4.31729i	0.705218	−	0.188963i
$523$	−38.2833	−	22.1028i	−1.67401	−	0.966490i	−0.965357	−	0.260933i	$-0.915970\pi$
$523$	−38.2833	−	22.1028i	−1.67401	−	0.966490i	−0.708653	−	0.705557i	$-0.750697\pi$
$524$	−11.3249	+	11.3249i	−0.494730	+	0.494730i
$525$		0			0
$526$	−24.1104	−	24.1104i	−1.05126	−	1.05126i
$527$	−37.9198	−	10.1606i	−1.65181	−	0.442601i
$528$	18.7147	+	18.7147i	0.814455	+	0.814455i
$529$	22.8854			0.995018
$530$		0			0
$531$	10.1786	−	2.72735i	0.441713	−	0.118357i
$532$			12.3168i			0.534002i
$533$	7.92389	+	13.7246i	0.343222	+	0.594477i
$534$	59.5716	−	34.3937i	2.57791	−	1.48836i
$535$		0			0
$536$	7.95420	+	29.6855i	0.343569	+	1.28222i
$537$	18.7788	−	32.5259i	0.810367	−	1.40360i
$538$	−1.27210	−	2.20334i	−0.0548441	−	0.0949927i
$539$	−11.9363	−	20.6743i	−0.514133	−	0.890505i
$540$		0			0
$541$	0.733586	+	0.733586i	0.0315393	+	0.0315393i	0.722701	−	0.691161i	$-0.242901\pi$
$541$	0.733586	+	0.733586i	0.0315393	+	0.0315393i	−0.691161	+	0.722701i	$0.742901\pi$
$542$	27.6094	+	15.9403i	1.18592	+	0.684694i
$543$	32.3116	+	8.65788i	1.38663	+	0.371545i
$544$		−	5.81673i		−	0.249390i
$545$		0			0
$546$	−9.04307	+	5.22102i	−0.387008	+	0.223439i
$547$			11.8157i			0.505204i	0.967570	+	0.252602i	$0.0812864\pi$
$547$			11.8157i			0.505204i	−0.967570	+	0.252602i	$0.918714\pi$
$548$	−15.5248	−	57.9392i	−0.663185	−	2.47504i
$549$	−20.6588	−	20.6588i	−0.881696	−	0.881696i
$550$		0			0
$551$	−9.99178	+	17.3063i	−0.425664	+	0.737272i
$552$	0.905815	+	3.38055i	0.0385541	+	0.143886i
$553$	0.527563	−	0.304589i	0.0224343	−	0.0129524i
$554$	38.8408			1.65019
$555$		0			0
$556$	−29.8997			−1.26803
$557$	−5.59913	+	3.23266i	−0.237243	+	0.136972i	−0.613909	−	0.789377i	$-0.710404\pi$
$557$	−5.59913	+	3.23266i	−0.237243	+	0.136972i	0.376666	+	0.926349i	$0.377070\pi$
$558$	10.2364	+	38.2029i	0.433343	+	1.61726i
$559$	−13.5416	+	23.4547i	−0.572747	+	0.992027i
$560$		0			0
$561$	−29.2887	−	29.2887i	−1.23657	−	1.23657i
$562$	2.59990	+	9.70295i	0.109670	+	0.409294i
$563$			1.58134i			0.0666457i	0.999445	+	0.0333229i	$0.0106090\pi$
$563$			1.58134i			0.0666457i	−0.999445	+	0.0333229i	$0.989391\pi$
$564$	54.8094	−	31.6442i	2.30789	−	1.33246i
$565$		0			0
$566$			49.4871i			2.08010i
$567$	−5.33883	−	1.43054i	−0.224210	−	0.0600769i
$568$	36.7903	+	21.2409i	1.54369	+	0.891248i
$569$	−16.2660	−	16.2660i	−0.681906	−	0.681906i	0.278524	−	0.960429i	$-0.410155\pi$
$569$	−16.2660	−	16.2660i	−0.681906	−	0.681906i	−0.960429	+	0.278524i	$0.910155\pi$
$570$		0			0
$571$	9.98899	+	17.3014i	0.418026	+	0.724043i	0.995741	−	0.0921960i	$-0.0293886\pi$
$571$	9.98899	+	17.3014i	0.418026	+	0.724043i	−0.577715	+	0.816239i	$0.696055\pi$
$572$	−25.5849	−	44.3143i	−1.06976	−	1.85287i
$573$	−8.18884	+	14.1835i	−0.342094	+	0.592524i
$574$	−1.36245	−	5.08475i	−0.0568677	−	0.212233i
$575$		0			0
$576$	−17.3027	+	9.98973i	−0.720946	+	0.416239i
$577$	−1.76615	−	3.05906i	−0.0735258	−	0.127350i	0.826918	−	0.562322i	$-0.190092\pi$
$577$	−1.76615	−	3.05906i	−0.0735258	−	0.127350i	−0.900444	+	0.434971i	$0.856758\pi$
$578$		−	23.2611i		−	0.967535i
$579$	−35.2340	+	9.44091i	−1.46427	+	0.392351i
$580$		0			0
$581$	−5.83773			−0.242190
$582$	18.3844	+	18.3844i	0.762058	+	0.762058i
$583$	−40.5099	−	10.8546i	−1.67775	−	0.449552i
$584$	13.8995	+	13.8995i	0.575165	+	0.575165i
$585$		0			0
$586$	26.3167	−	26.3167i	1.08713	−	1.08713i
$587$	2.48280	+	1.43345i	0.102476	+	0.0591647i	0.550362	−	0.834926i	$-0.314490\pi$
$587$	2.48280	+	1.43345i	0.102476	+	0.0591647i	−0.447886	+	0.894091i	$0.647823\pi$
$588$	−57.2832	+	15.3490i	−2.36232	+	0.632982i
$589$	−41.0337	−	23.6908i	−1.69077	−	0.976164i
$590$		0			0
$591$		−	2.99333i		−	0.123129i
$592$	−17.4808	−	9.80546i	−0.718458	−	0.403002i
$593$	−29.6868	−	29.6868i	−1.21909	−	1.21909i	−0.967951	−	0.251137i	$-0.919195\pi$
$593$	−29.6868	−	29.6868i	−1.21909	−	1.21909i	−0.251137	−	0.967951i	$-0.580805\pi$
$594$	4.32279	−	16.1329i	0.177366	−	0.661939i
$595$		0			0
$596$	−15.1897	−	8.76980i	−0.622196	−	0.359225i
$597$	−11.1190	+	19.2587i	−0.455071	+	0.788206i
$598$		−	3.05628i		−	0.124980i
$599$	11.0786	+	6.39622i	0.452658	+	0.261342i	0.708952	−	0.705256i	$-0.249168\pi$
$599$	11.0786	+	6.39622i	0.452658	+	0.261342i	−0.256294	+	0.966599i	$0.582501\pi$
$600$		0			0
$601$	24.2575	+	42.0153i	0.989486	+	1.71384i	0.619997	+	0.784604i	$0.287134\pi$
$601$	24.2575	+	42.0153i	0.989486	+	1.71384i	0.369488	+	0.929235i	$0.379533\pi$
$602$	6.36123	−	6.36123i	0.259264	−	0.259264i
$603$	−10.2124	+	10.2124i	−0.415880	+	0.415880i
$604$	28.4832	−	16.4448i	1.15896	−	0.669128i
$605$		0			0
$606$	30.4340	−	30.4340i	1.23630	−	1.23630i
$607$	2.64364	−	1.52631i	0.107302	−	0.0619509i	−0.445389	−	0.895337i	$-0.646934\pi$
$607$	2.64364	−	1.52631i	0.107302	−	0.0619509i	0.552691	+	0.833386i	$0.313601\pi$
$608$	1.81703	−	6.78127i	0.0736905	−	0.275017i
$609$	3.58690	+	0.961107i	0.145349	+	0.0389460i
$610$		0			0
$611$	−25.8677	+	6.93122i	−1.04649	+	0.280407i
$612$	−37.1257	+	21.4345i	−1.50072	+	0.866439i
$613$	−26.2765	−	7.04077i	−1.06130	−	0.284374i	−0.314385	−	0.949296i	$-0.601798\pi$
$613$	−26.2765	−	7.04077i	−1.06130	−	0.284374i	−0.746913	+	0.664922i	$0.768465\pi$
$614$	41.1776	+	11.0335i	1.66179	+	0.445276i
$615$		0			0
$616$	2.13160	+	7.95525i	0.0858848	+	0.320526i
$617$	8.29972	−	30.9750i	0.334134	−	1.24701i	−0.570671	−	0.821179i	$-0.693317\pi$
$617$	8.29972	−	30.9750i	0.334134	−	1.24701i	0.904805	−	0.425827i	$-0.140017\pi$
$618$	−16.0031	−	16.0031i	−0.643740	−	0.643740i
$619$	−48.2130			−1.93785			−0.968923	−	0.247363i	$-0.920436\pi$
$619$	−48.2130			−1.93785			−0.968923	+	0.247363i	$0.920436\pi$
$620$		0			0
$621$	0.465469	−	0.465469i	0.0186786	−	0.0186786i
$622$	35.8822	−	9.61461i	1.43875	−	0.385511i
$623$	6.37990			0.255605
$624$	−26.8730	+	7.20059i	−1.07578	+	0.288254i
$625$		0			0
$626$	10.7483	−	18.6166i	0.429588	−	0.744068i
$627$	−24.9962	−	43.2946i	−0.998250	−	1.72902i
$628$	17.7736	−	17.7736i	0.709245	−	0.709245i
$629$	27.3576	+	15.3456i	1.09082	+	0.611869i
$630$		0			0
$631$	−34.6187	−	9.27605i	−1.37815	−	0.369274i	−0.507700	−	0.861534i	$-0.669504\pi$
$631$	−34.6187	−	9.27605i	−1.37815	−	0.369274i	−0.870448	+	0.492260i	$0.836171\pi$
$632$	5.25994	−	1.40940i	0.209229	−	0.0560627i
$633$	−11.7871	−	43.9899i	−0.468494	−	1.74844i
$634$	10.8787	+	40.5999i	0.432049	+	1.61243i
$635$		0			0
$636$	−52.0920	+	90.2261i	−2.06558	+	3.57770i
$637$	25.0942			0.994267
$638$	−7.13741	+	26.6372i	−0.282573	+	1.05458i
$639$			19.9638i			0.789757i
$640$		0			0
$641$	12.8244	+	22.2125i	0.506532	+	0.877339i	0.999971	+	0.00755909i	$0.00240616\pi$
$641$	12.8244	+	22.2125i	0.506532	+	0.877339i	−0.493439	+	0.869780i	$0.664261\pi$
$642$	−43.8699	+	75.9850i	−1.73141	+	2.99889i
$643$	−38.4606			−1.51674			−0.758369	−	0.651825i	$-0.774004\pi$
$643$	−38.4606			−1.51674			−0.758369	+	0.651825i	$0.774004\pi$
$644$	−0.173382	+	0.647072i	−0.00683223	+	0.0254982i
$645$		0			0
$646$	20.1437	−	75.1772i	0.792543	−	2.95781i
$647$	−8.15295	−	4.70711i	−0.320526	−	0.185056i	0.331101	−	0.943595i	$-0.392580\pi$
$647$	−8.15295	−	4.70711i	−0.320526	−	0.185056i	−0.651627	+	0.758540i	$0.725913\pi$
$648$	−42.7884	−	24.7039i	−1.68089	−	0.970460i
$649$	−4.50889	+	16.8274i	−0.176989	+	0.660533i
$650$		0			0
$651$	−2.27882	+	8.50466i	−0.0893138	+	0.333324i
$652$	−42.2189			−1.65342
$653$	−10.8330	+	18.7633i	−0.423928	+	0.734265i	−0.996320	−	0.0857155i	$-0.972682\pi$
$653$	−10.8330	+	18.7633i	−0.423928	+	0.734265i	0.572392	+	0.819980i	$0.306016\pi$
$654$	24.3322	+	42.1446i	0.951465	+	1.64799i
$655$		0			0
$656$		−	14.0253i		−	0.547596i
$657$	−2.39084	+	8.92275i	−0.0932757	+	0.348110i
$658$	8.89551			0.346783
$659$	−5.40133	+	9.35537i	−0.210406	+	0.364433i	−0.951842	−	0.306590i	$-0.900812\pi$
$659$	−5.40133	+	9.35537i	−0.210406	+	0.364433i	0.741436	+	0.671024i	$0.234145\pi$
$660$		0			0
$661$	−4.86688	−	18.1634i	−0.189300	−	0.706476i	−0.993669	−	0.112346i	$-0.964163\pi$
$661$	−4.86688	−	18.1634i	−0.189300	−	0.706476i	0.804370	−	0.594129i	$-0.202503\pi$
$662$	13.2207	+	49.3403i	0.513837	+	1.91767i
$663$	42.0564	−	11.2690i	1.63333	−	0.437650i
$664$	−50.4058	−	13.5062i	−1.95612	−	0.524142i
$665$		0			0
$666$	−0.392036	−	31.5994i	−0.0151911	−	1.22445i
$667$	−0.768543	+	0.768543i	−0.0297581	+	0.0297581i
$668$	−0.133081	−	0.230504i	−0.00514907	−	0.00891846i
$669$	−11.8406	+	20.5086i	−0.457786	+	0.792908i
$670$		0			0
$671$	46.6545	−	12.5010i	1.80108	−	0.482597i
$672$	−1.30458			−0.0503251
$673$	43.4302	−	11.6371i	1.67411	−	0.448577i	0.707896	−	0.706316i	$-0.249644\pi$
$673$	43.4302	−	11.6371i	1.67411	−	0.448577i	0.966214	+	0.257740i	$0.0829777\pi$
$674$	55.0817	−	55.0817i	2.12167	−	2.12167i
$675$		0			0
$676$	3.34655			0.128714
$677$	26.3401	+	26.3401i	1.01233	+	1.01233i	0.999923	+	0.0124109i	$0.00395062\pi$
$677$	26.3401	+	26.3401i	1.01233	+	1.01233i	0.0124109	+	0.999923i	$0.496049\pi$
$678$	5.67579	−	21.1823i	0.217978	−	0.813503i
$679$	0.624117	+	2.32924i	0.0239514	+	0.0893879i
$680$		0			0
$681$	30.7619	+	8.24263i	1.17880	+	0.315858i
$682$	−63.1576	−	16.9230i	−2.41843	−	0.648016i
$683$	19.6576	−	11.3493i	0.752178	−	0.434270i	−0.0743020	−	0.997236i	$-0.523673\pi$
$683$	19.6576	−	11.3493i	0.752178	−	0.434270i	0.826481	+	0.562965i	$0.190340\pi$
$684$	−49.9777	+	13.3915i	−1.91094	+	0.512036i
$685$		0			0
$686$	−16.4136	−	4.39802i	−0.626676	−	0.167917i
$687$	−3.30347	+	12.3287i	−0.126035	+	0.470369i
$688$	20.7574	−	11.9843i	0.791369	−	0.456897i
$689$	31.1728	−	31.1728i	1.18759	−	1.18759i
$690$		0			0
$691$	3.35727	−	1.93832i	0.127716	−	0.0737371i	−0.434781	−	0.900536i	$-0.643174\pi$
$691$	3.35727	−	1.93832i	0.127716	−	0.0737371i	0.562497	+	0.826799i	$0.309841\pi$
$692$	−16.4141	+	16.4141i	−0.623969	+	0.623969i
$693$	−2.73676	+	2.73676i	−0.103961	+	0.103961i
$694$	−4.16500	−	7.21398i	−0.158101	−	0.273839i
$695$		0			0
$696$	28.7474	+	16.5973i	1.08967	+	0.629120i
$697$			21.9497i			0.831403i
$698$	−3.56306	+	6.17139i	−0.134864	+	0.233591i
$699$	−1.84364	−	1.06443i	−0.0697329	−	0.0402603i
$700$		0			0
$701$	−0.649780	+	2.42501i	−0.0245418	+	0.0915914i	−0.977111	−	0.212732i	$-0.931764\pi$
$701$	−0.649780	+	2.42501i	−0.0245418	+	0.0915914i	0.952569	+	0.304324i	$0.0984304\pi$
$702$	12.4144	+	12.4144i	0.468551	+	0.468551i
$703$	27.1004	+	26.4362i	1.02211	+	0.997062i
$704$		−	33.0303i		−	1.24488i
$705$		0			0
$706$	6.15490	+	3.55353i	0.231643	+	0.133739i
$707$	3.85588	−	1.03318i	0.145015	−	0.0388567i
$708$	37.4790	+	21.6385i	1.40855	+	0.813224i
$709$	−1.48911	+	1.48911i	−0.0559246	+	0.0559246i	−0.734516	−	0.678591i	$-0.762591\pi$
$709$	−1.48911	+	1.48911i	−0.0559246	+	0.0559246i	0.678591	+	0.734516i	$0.262591\pi$
$710$		0			0
$711$	1.80952	+	1.80952i	0.0678621	+	0.0678621i
$712$	55.0871	+	14.7606i	2.06448	+	0.553175i
$713$	−1.82224	−	1.82224i	−0.0682434	−	0.0682434i
$714$	−14.4626			−0.541248
$715$		0			0
$716$	62.0727	−	16.6323i	2.31977	−	0.621579i
$717$			38.1277i			1.42391i
$718$	−40.4977	−	70.1441i	−1.51136	−	2.61775i
$719$	39.8189	−	22.9894i	1.48499	−	0.857361i	0.485138	−	0.874437i	$-0.338769\pi$
$719$	39.8189	−	22.9894i	1.48499	−	0.857361i	0.999854	+	0.0170766i	$0.00543590\pi$
$720$		0			0
$721$	−0.543277	−	2.02754i	−0.0202327	−	0.0755094i
$722$	23.9314	−	41.4504i	0.890634	−	1.54262i
$723$	20.8357	+	36.0885i	0.774888	+	1.34215i
$724$	28.6183	+	49.5683i	1.06359	+	1.84219i
$725$		0			0
$726$	−6.01025	−	6.01025i	−0.223061	−	0.223061i
$727$	−3.64009	−	2.10161i	−0.135003	−	0.0779443i	0.430977	−	0.902363i	$-0.358169\pi$
$727$	−3.64009	−	2.10161i	−0.135003	−	0.0779443i	−0.565981	+	0.824419i	$0.691502\pi$
$728$	−8.36233	−	2.24068i	−0.309928	−	0.0830451i
$729$		−	9.98935i		−	0.369976i
$730$		0			0
$731$	−32.4855	+	18.7555i	−1.20152	+	0.693697i
$732$		−	119.987i		−	4.43484i
$733$	6.69183	+	24.9742i	0.247168	+	0.922444i	0.972281	+	0.233814i	$0.0751208\pi$
$733$	6.69183	+	24.9742i	0.247168	+	0.922444i	−0.725113	+	0.688630i	$0.758213\pi$
$734$	−12.2191	−	12.2191i	−0.451014	−	0.451014i
$735$		0			0
$736$	0.190918	−	0.330680i	0.00703734	−	0.0121890i
$737$	−6.17969	−	23.0629i	−0.227632	−	0.849533i
$738$	19.1509	−	11.0568i	0.704955	−	0.407006i
$739$	21.1987			0.779807			0.389904	−	0.920856i	$-0.372508\pi$
$739$	21.1987			0.779807			0.389904	+	0.920856i	$0.372508\pi$
$740$		0			0
$741$	52.5504			1.93049
$742$	−12.6817	+	7.32180i	−0.465561	+	0.268792i
$743$	−12.0248	−	44.8773i	−0.441148	−	1.64639i	−0.725911	−	0.687789i	$-0.758582\pi$
$743$	−12.0248	−	44.8773i	−0.441148	−	1.64639i	0.284763	−	0.958598i	$-0.408085\pi$
$744$	−39.3528	+	68.1610i	−1.44274	+	2.49890i
$745$		0			0
$746$	−57.4290	−	57.4290i	−2.10262	−	2.10262i
$747$	−6.34708	−	23.6876i	−0.232227	−	0.866684i
$748$		−	70.8717i		−	2.59133i
$749$	−7.04747	+	4.06886i	−0.257509	+	0.148673i
$750$		0			0
$751$			15.3386i			0.559713i	0.960042	+	0.279857i	$0.0902869\pi$
$751$			15.3386i			0.559713i	−0.960042	+	0.279857i	$0.909713\pi$
$752$	22.8929	+	6.13414i	0.834819	+	0.223689i
$753$	16.3288	+	9.42747i	0.595056	+	0.343556i
$754$	−20.4976	−	20.4976i	−0.746477	−	0.746477i
$755$		0			0
$756$	−1.92410	−	3.33263i	−0.0699787	−	0.121207i
$757$	2.29300	+	3.97159i	0.0833404	+	0.144350i	0.904683	−	0.426086i	$-0.140108\pi$
$757$	2.29300	+	3.97159i	0.0833404	+	0.144350i	−0.821342	+	0.570435i	$0.806774\pi$
$758$	−1.18078	+	2.04517i	−0.0428879	+	0.0742840i
$759$	−0.703736	−	2.62638i	−0.0255440	−	0.0953315i
$760$		0			0
$761$	−36.6280	+	21.1472i	−1.32776	+	0.766584i	−0.984953	−	0.172821i	$-0.944712\pi$
$761$	−36.6280	+	21.1472i	−1.32776	+	0.766584i	−0.342809	+	0.939405i	$0.611378\pi$
$762$	30.6507	+	53.0886i	1.11036	+	1.92320i
$763$			4.51354i			0.163401i
$764$	−27.0679	+	7.25282i	−0.979281	+	0.262398i
$765$		0			0
$766$	−73.8918			−2.66982
$767$	−12.9489	−	12.9489i	−0.467556	−	0.467556i
$768$	−67.2749	−	18.0263i	−2.42757	−	0.650466i
$769$	−18.0202	−	18.0202i	−0.649824	−	0.649824i	0.303126	−	0.952950i	$-0.401970\pi$
$769$	−18.0202	−	18.0202i	−0.649824	−	0.649824i	−0.952950	+	0.303126i	$0.901970\pi$
$770$		0			0
$771$	24.0220	−	24.0220i	0.865132	−	0.865132i
$772$	−54.0513	−	31.2066i	−1.94535	−	1.12315i
$773$	−6.80793	+	1.82418i	−0.244864	+	0.0656112i	−0.379164	−	0.925330i	$-0.623788\pi$
$773$	−6.80793	+	1.82418i	−0.244864	+	0.0656112i	0.134299	+	0.990941i	$0.457122\pi$
$774$	32.7280	+	18.8955i	1.17639	+	0.679186i
$775$		0			0
$776$			21.5557i			0.773805i
$777$	3.44172	−	6.13578i	0.123471	−	0.220120i
$778$	−0.961310	−	0.961310i	−0.0344646	−	0.0344646i
$779$	−6.85666	+	25.5894i	−0.245665	+	0.916836i
$780$		0			0
$781$	−28.5827	−	16.5022i	−1.02277	−	0.590497i
$782$	2.11652	−	3.66592i	0.0756867	−	0.131093i
$783$		−	6.24354i		−	0.223126i
$784$	−19.2330	−	11.1042i	−0.686894	−	0.396578i
$785$		0			0
$786$	−11.3489	−	19.6569i	−0.404802	−	0.701137i
$787$	27.3926	−	27.3926i	0.976441	−	0.976441i	−0.0232881	−	0.999729i	$-0.507414\pi$
$787$	27.3926	−	27.3926i	0.976441	−	0.976441i	0.999729	+	0.0232881i	$0.00741351\pi$
$788$	3.62158	−	3.62158i	0.129013	−	0.129013i
$789$	27.6149	−	15.9435i	0.983116	−	0.567602i
$790$		0			0
$791$	1.43820	−	1.43820i	0.0511367	−	0.0511367i
$792$	−29.9622	+	17.2987i	−1.06466	+	0.614683i
$793$	−13.1407	+	49.0418i	−0.466640	+	1.74152i
$794$	−42.5385	−	11.3982i	−1.50964	−	0.404506i
$795$		0			0
$796$	−36.7534	+	9.84805i	−1.30269	+	0.349055i
$797$	−3.44250	+	1.98753i	−0.121939	+	0.0704018i	−0.559729	−	0.828676i	$-0.689095\pi$
$797$	−3.44250	+	1.98753i	−0.121939	+	0.0704018i	0.437790	+	0.899077i	$0.355761\pi$
$798$	−16.8608	−	4.51783i	−0.596865	−	0.159929i
$799$	−35.8276	−	9.59997i	−1.26749	−	0.339622i
$800$		0			0
$801$	6.93655	+	25.8875i	0.245091	+	0.914691i
$802$	−17.0936	+	63.7942i	−0.603596	+	2.25265i
$803$	−10.7986	−	10.7986i	−0.381076	−	0.381076i
$804$	−59.3136			−2.09183
$805$		0			0
$806$	48.6004	−	48.6004i	1.71188	−	1.71188i
$807$	2.29820	−	0.615801i	0.0809005	−	0.0216772i
$808$	35.6839			1.25535
$809$	4.43352	−	1.18796i	0.155874	−	0.0417664i	−0.180038	−	0.983660i	$-0.557622\pi$
$809$	4.43352	−	1.18796i	0.155874	−	0.0417664i	0.335912	+	0.941893i	$0.390955\pi$
$810$		0			0
$811$	−1.06741	+	1.84880i	−0.0374817	+	0.0649202i	−0.884158	−	0.467189i	$-0.845267\pi$
$811$	−1.06741	+	1.84880i	−0.0374817	+	0.0649202i	0.846676	+	0.532109i	$0.178600\pi$
$812$	3.17690	+	5.50255i	0.111487	+	0.193102i
$813$	−21.0817	+	21.0817i	−0.739366	+	0.739366i
$814$	45.5657	+	25.5590i	1.59708	+	0.895843i
$815$		0			0
$816$	−37.2199	−	9.97305i	−1.30296	−	0.349127i
$817$	−43.7312	+	11.7177i	−1.52996	+	0.409951i
$818$	−10.9541	−	40.8812i	−0.383001	−	1.42938i
$819$	−1.05298	−	3.92978i	−0.0367941	−	0.137317i
$820$		0			0
$821$	5.94240	−	10.2925i	0.207391	−	0.359212i	−0.743501	−	0.668735i	$-0.766836\pi$
$821$	5.94240	−	10.2925i	0.207391	−	0.359212i	0.950892	+	0.309523i	$0.100169\pi$
$822$	85.0087			2.96502
$823$	−3.87588	+	14.4650i	−0.135105	+	0.504217i	0.864893	+	0.501957i	$0.167386\pi$
$823$	−3.87588	+	14.4650i	−0.135105	+	0.504217i	−0.999997	+	0.00226077i	$0.999280\pi$
$824$		−	18.7637i		−	0.653663i
$825$		0			0
$826$	3.04140	+	5.26786i	0.105824	+	0.183292i
$827$	1.58873	−	2.75176i	0.0552456	−	0.0956881i	−0.837080	−	0.547080i	$-0.815739\pi$
$827$	1.58873	−	2.75176i	0.0552456	−	0.0956881i	0.892326	+	0.451392i	$0.149072\pi$
$828$	−2.81412			−0.0977974
$829$	−4.75678	+	17.7525i	−0.165210	+	0.616571i	0.832804	+	0.553569i	$0.186734\pi$
$829$	−4.75678	+	17.7525i	−0.165210	+	0.616571i	−0.998013	+	0.0630026i	$0.979932\pi$
$830$		0			0
$831$	−9.40108	+	35.0853i	−0.326120	+	1.21710i
$832$	30.0688	+	17.3602i	1.04245	+	0.601858i
$833$	30.0998	+	17.3781i	1.04290	+	0.602116i
$834$	10.9673	−	40.9304i	0.379765	−	1.41730i
$835$		0			0
$836$	22.1390	−	82.6238i	0.765693	−	2.85760i
$837$	14.8036			0.511688
$838$	−40.3867	+	69.9519i	−1.39514	+	2.41645i
$839$	1.61759	+	2.80176i	0.0558456	+	0.0967274i	0.892597	−	0.450856i	$-0.148881\pi$
$839$	1.61759	+	2.80176i	0.0558456	+	0.0967274i	−0.836751	+	0.547583i	$0.815548\pi$
$840$		0			0
$841$		−	18.6912i		−	0.644525i
$842$	20.1851	−	75.3317i	0.695624	−	2.59610i
$843$	−9.39407			−0.323549
$844$	38.9617	−	67.4836i	1.34112	−	2.32288i
$845$		0			0
$846$	9.67165	+	36.0951i	0.332518	+	1.24097i
$847$	−0.204037	−	0.761477i	−0.00701080	−	0.0261646i
$848$	−37.6859	+	10.0979i	−1.29414	+	0.346763i
$849$	−44.7023	−	11.9779i	−1.53418	−	0.411082i
$850$		0			0
$851$	1.05160	+	1.77033i	0.0360483	+	0.0606863i
$852$	−57.9751	+	57.9751i	−1.98619	+	1.98619i
$853$	−15.2299	−	26.3789i	−0.521461	−	0.903197i	−0.999688	−	0.0249611i	$-0.992054\pi$
$853$	−15.2299	−	26.3789i	−0.521461	−	0.903197i	0.478227	−	0.878236i	$-0.341280\pi$
$854$	8.43237	−	14.6053i	0.288550	−	0.499783i
$855$		0			0
$856$	−70.2650	+	18.8274i	−2.40161	+	0.643509i
$857$	−20.7543			−0.708954			−0.354477	−	0.935065i	$-0.615341\pi$
$857$	−20.7543			−0.708954			−0.354477	+	0.935065i	$0.615341\pi$
$858$	70.0473	−	18.7691i	2.39138	−	0.640767i
$859$	3.76826	−	3.76826i	0.128571	−	0.128571i	−0.639893	−	0.768464i	$-0.721021\pi$
$859$	3.76826	−	3.76826i	0.128571	−	0.128571i	0.768464	+	0.639893i	$0.221021\pi$
$860$		0			0
$861$	4.92288			0.167771
$862$	−12.0323	−	12.0323i	−0.409822	−	0.409822i
$863$	7.29310	−	27.2182i	0.248260	−	0.926519i	−0.723457	−	0.690370i	$-0.757448\pi$
$863$	7.29310	−	27.2182i	0.248260	−	0.926519i	0.971717	−	0.236149i	$-0.0758855\pi$
$864$	0.567703	+	2.11870i	0.0193136	+	0.0720795i
$865$		0			0
$866$	−83.1784	−	22.2876i	−2.82652	−	0.757363i
$867$	21.0120	+	5.63015i	0.713606	+	0.191210i
$868$	−13.0467	+	7.53253i	−0.442835	+	0.255671i
$869$	−4.08649	+	1.09497i	−0.138625	+	0.0371444i
$870$		0			0
$871$	24.2430	+	6.49590i	0.821444	+	0.220105i
$872$	−10.4425	+	38.9721i	−0.353629	+	1.31976i
$873$	−8.77271	+	5.06493i	−0.296911	+	0.171422i
$874$	3.61265	−	3.61265i	0.122200	−	0.122200i
$875$		0			0
$876$	−32.8548	+	18.9687i	−1.11006	+	0.640894i
$877$	9.40855	−	9.40855i	0.317704	−	0.317704i	−0.530181	−	0.847885i	$-0.677876\pi$
$877$	9.40855	−	9.40855i	0.317704	−	0.317704i	0.847885	+	0.530181i	$0.177876\pi$
$878$	−53.0871	+	53.0871i	−1.79160	+	1.79160i
$879$	17.4024	+	30.1419i	0.586969	+	1.01666i
$880$		0			0
$881$	−5.73392	−	3.31048i	−0.193181	−	0.111533i	0.400290	−	0.916388i	$-0.368909\pi$
$881$	−5.73392	−	3.31048i	−0.193181	−	0.111533i	−0.593471	+	0.804856i	$0.702243\pi$
$882$		−	35.0158i		−	1.17904i
$883$	18.1081	−	31.3641i	0.609385	−	1.05549i	−0.381957	−	0.924180i	$-0.624750\pi$
$883$	18.1081	−	31.3641i	0.609385	−	1.05549i	0.991342	−	0.131305i	$-0.0419169\pi$
$884$	64.5174	+	37.2491i	2.16995	+	1.25282i
$885$		0			0
$886$	0.307726	−	1.14845i	0.0103383	−	0.0385829i
$887$	10.3036	+	10.3036i	0.345961	+	0.345961i	0.858603	−	0.512642i	$-0.171333\pi$
$887$	10.3036	+	10.3036i	0.345961	+	0.345961i	−0.512642	+	0.858603i	$0.671333\pi$
$888$	43.9132	−	45.0165i	1.47363	−	1.51065i
$889$			5.68559i			0.190689i
$890$		0			0
$891$	33.2427	+	19.1927i	1.11367	+	0.642978i
$892$	−39.1388	+	10.4872i	−1.31046	+	0.351137i
$893$	−38.7697	−	22.3837i	−1.29738	−	0.749042i
$894$	17.5768	−	17.5768i	0.587856	−	0.587856i
$895$		0			0
$896$	−7.34150	−	7.34150i	−0.245262	−	0.245262i
$897$	2.76077	+	0.739746i	0.0921794	+	0.0246994i
$898$	3.61198	+	3.61198i	0.120533	+	0.120533i
$899$	−24.4425			−0.815202
$900$		0			0
$901$	58.9786	−	15.8033i	1.96486	−	0.526483i
$902$			36.5585i			1.21726i
$903$	4.20649	+	7.28585i	0.139983	+	0.242458i
$904$	15.7456	−	9.09072i	0.523691	−	0.302353i
$905$		0			0
$906$	12.0639	+	45.0232i	0.400797	+	1.49580i
$907$	5.54646	−	9.60675i	0.184167	−	0.318987i	−0.759128	−	0.650941i	$-0.774375\pi$
$907$	5.54646	−	9.60675i	0.184167	−	0.318987i	0.943296	+	0.331954i	$0.107708\pi$
$908$	27.2457	+	47.1909i	0.904180	+	1.56609i
$909$	8.38461	+	14.5226i	0.278100	+	0.481683i
$910$		0			0
$911$	2.08304	+	2.08304i	0.0690141	+	0.0690141i	0.740771	−	0.671757i	$-0.234460\pi$
$911$	2.08304	+	2.08304i	0.0690141	+	0.0690141i	−0.671757	+	0.740771i	$0.734460\pi$
$912$	−40.2764	−	23.2536i	−1.33369	−	0.770004i
$913$	39.1607	+	10.4931i	1.29603	+	0.347270i
$914$			76.0691i			2.51614i
$915$		0			0
$916$	−18.9131	+	10.9195i	−0.624906	+	0.360790i
$917$		−	2.10518i		−	0.0695191i
$918$	6.29356	+	23.4879i	0.207719	+	0.775216i
$919$	5.66143	+	5.66143i	0.186753	+	0.186753i	0.794291	−	0.607538i	$-0.207843\pi$
$919$	5.66143	+	5.66143i	0.186753	+	0.186753i	−0.607538	+	0.794291i	$0.707843\pi$
$920$		0			0
$921$	−19.9334	+	34.5256i	−0.656828	+	1.13766i
$922$	−21.6006	−	80.6147i	−0.711379	−	2.65490i
$923$	30.0453	−	17.3467i	0.988953	−	0.570972i
$924$	−15.8951			−0.522911
$925$		0			0
$926$	−33.5866			−1.10373
$927$	7.63641	−	4.40888i	0.250813	−	0.144807i
$928$	−0.937342	−	3.49821i	−0.0307697	−	0.114834i
$929$	11.4336	−	19.8035i	0.375124	−	0.649733i	−0.615222	−	0.788354i	$-0.710934\pi$
$929$	11.4336	−	19.8035i	0.375124	−	0.649733i	0.990346	+	0.138621i	$0.0442669\pi$
$930$		0			0
$931$	29.6624	+	29.6624i	0.972146	+	0.972146i
$932$	−0.942757	−	3.51842i	−0.0308810	−	0.115250i
$933$			34.7400i			1.13734i
$934$	−27.2223	+	15.7168i	−0.890740	+	0.514269i
$935$		0			0
$936$		−	36.3678i		−	1.18872i
$937$	−33.4153	−	8.95361i	−1.09163	−	0.292502i	−0.332279	−	0.943181i	$-0.607817\pi$
$937$	−33.4153	−	8.95361i	−1.09163	−	0.292502i	−0.759352	+	0.650680i	$0.774484\pi$
$938$	−7.21990	−	4.16841i	−0.235738	−	0.136104i
$939$	14.2150	+	14.2150i	0.463890	+	0.463890i
$940$		0			0
$941$	−7.81481	−	13.5357i	−0.254756	−	0.441250i	0.710074	−	0.704128i	$-0.248662\pi$
$941$	−7.81481	−	13.5357i	−0.254756	−	0.441250i	−0.964829	+	0.262878i	$0.915328\pi$
$942$	17.8113	+	30.8501i	0.580324	+	1.00515i
$943$	−0.720438	+	1.24784i	−0.0234607	+	0.0406351i
$944$	4.19456	+	15.6543i	0.136521	+	0.509504i
$945$		0			0
$946$	−54.1065	+	31.2384i	−1.75915	+	1.01565i
$947$	13.3898	+	23.1918i	0.435109	+	0.753631i	0.997305	−	0.0733735i	$-0.0233765\pi$
$947$	13.3898	+	23.1918i	0.435109	+	0.753631i	−0.562196	+	0.827004i	$0.690043\pi$
$948$			10.5097i			0.341339i
$949$	15.5060	−	4.15483i	0.503347	−	0.134872i
$950$		0			0
$951$	−39.3074			−1.27463
$952$	−8.47868	−	8.47868i	−0.274796	−	0.274796i
$953$	−8.42269	−	2.25685i	−0.272838	−	0.0731067i	0.119806	−	0.992797i	$-0.461773\pi$
$953$	−8.42269	−	2.25685i	−0.272838	−	0.0731067i	−0.392644	+	0.919691i	$0.628439\pi$
$954$	−43.4977	−	43.4977i	−1.40829	−	1.40829i
$955$		0			0
$956$	−46.1300	+	46.1300i	−1.49195	+	1.49195i
$957$	−22.3341	−	12.8946i	−0.721959	−	0.416823i
$958$	50.3484	−	13.4908i	1.62668	−	0.435868i
$959$	6.82809	+	3.94220i	0.220491	+	0.127300i
$960$		0			0
$961$		−	26.9539i		−	0.869480i
$962$	−47.2160	+	28.0469i	−1.52231	+	0.904268i
$963$	−24.1725	−	24.1725i	−0.778947	−	0.778947i
$964$	−18.4541	+	68.8716i	−0.594366	+	2.21820i
$965$		0			0
$966$	−0.822194	−	0.474694i	−0.0264537	−	0.0152730i
$967$	−18.3121	+	31.7175i	−0.588877	+	1.01996i	0.405503	+	0.914094i	$0.367096\pi$
$967$	−18.3121	+	31.7175i	−0.588877	+	1.01996i	−0.994380	+	0.105871i	$0.966237\pi$
$968$		−	7.04702i		−	0.226500i
$969$	63.0328	+	36.3920i	2.02491	+	1.16908i
$970$		0			0
$971$	13.4291	+	23.2599i	0.430961	+	0.746446i	0.996956	−	0.0779623i	$-0.0248414\pi$
$971$	13.4291	+	23.2599i	0.430961	+	0.746446i	−0.565996	+	0.824408i	$0.691508\pi$
$972$	51.4212	−	51.4212i	1.64934	−	1.64934i
$973$	2.77903	−	2.77903i	0.0890915	−	0.0890915i
$974$	−25.0888	+	14.4850i	−0.803897	+	0.464130i
$975$		0			0
$976$	31.7725	−	31.7725i	1.01701	−	1.01701i
$977$	−11.8665	+	6.85116i	−0.379645	+	0.219188i	−0.677664	−	0.735372i	$-0.737007\pi$
$977$	−11.8665	+	6.85116i	−0.379645	+	0.219188i	0.298019	+	0.954560i	$0.403674\pi$
$978$	15.4859	−	57.7943i	0.495186	−	1.84806i
$979$	−42.7977	−	11.4676i	−1.36782	−	0.366506i
$980$		0			0
$981$	−18.3145	+	4.90735i	−0.584736	+	0.156680i
$982$	−31.2230	+	18.0266i	−0.996365	+	0.575251i
$983$	15.2749	+	4.09290i	0.487194	+	0.130543i	0.494050	−	0.869433i	$-0.335516\pi$
$983$	15.2749	+	4.09290i	0.487194	+	0.130543i	−0.00685662	+	0.999976i	$0.502183\pi$
$984$	42.5065	+	11.3896i	1.35506	+	0.363087i
$985$		0			0
$986$	−10.3914	−	38.7812i	−0.330929	−	1.23504i
$987$	−2.15308	+	8.03542i	−0.0685334	+	0.255770i
$988$	63.5798	+	63.5798i	2.02274	+	2.02274i
$989$	−2.46239			−0.0782995
$990$		0			0
$991$	42.9379	−	42.9379i	1.36397	−	1.36397i	0.495169	−	0.868797i	$-0.335106\pi$
$991$	42.9379	−	42.9379i	1.36397	−	1.36397i	0.868797	−	0.495169i	$-0.164894\pi$
$992$	8.29436	−	2.22247i	0.263346	−	0.0705634i
$993$	−47.7696			−1.51592
$994$	−11.1313	+	2.98263i	−0.353064	+	0.0946033i
$995$		0			0
$996$	50.3571	−	87.2210i	1.59562	−	2.76370i
$997$	−19.5601	−	33.8791i	−0.619475	−	1.07296i	−0.989582	−	0.143973i	$-0.954012\pi$
$997$	−19.5601	−	33.8791i	−0.619475	−	1.07296i	0.370106	−	0.928989i	$-0.379321\pi$
$998$	−14.0618	+	14.0618i	−0.445119	+	0.445119i
$999$	−11.4625	−	2.91945i	−0.362658	−	0.0923674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.193.1		68
5.2	odd	4		925.2.t.b.82.1		68
5.3	odd	4		185.2.p.a.82.17	✓	68
5.4	even	2		185.2.u.a.8.17	yes	68
37.14	odd	12		925.2.t.b.643.1		68
185.14	odd	12		185.2.p.a.88.17	yes	68
185.88	even	12		185.2.u.a.162.17	yes	68
185.162	even	12	inner	925.2.y.b.532.1		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.17	✓	68	5.3	odd	4
185.2.p.a.88.17	yes	68	185.14	odd	12
185.2.u.a.8.17	yes	68	5.4	even	2
185.2.u.a.162.17	yes	68	185.88	even	12
925.2.t.b.82.1		68	5.2	odd	4
925.2.t.b.643.1		68	37.14	odd	12
925.2.y.b.193.1		68	1.1	even	1	trivial
925.2.y.b.532.1		68	185.162	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10002 + 1.21245i) q^{2} +(-0.586925 - 2.19044i) q^{3} +(1.94006 - 3.36028i) q^{4} +(3.88834 + 3.88834i) q^{6} +(0.132002 + 0.492639i) q^{7} +4.55908i q^{8} +(-1.85545 + 1.07124i) q^{9} -3.54199i q^{11} +(-8.49914 - 2.27734i) q^{12} +(3.22442 + 1.86162i) q^{13} +(-0.874506 - 0.874506i) q^{14} +(-1.64753 - 2.85361i) q^{16} +(2.57840 + 4.46592i) q^{17} +(2.59765 - 4.49927i) q^{18} +(1.61089 + 6.01191i) q^{19} +(1.00162 - 0.578285i) q^{21} +(4.29448 + 7.43826i) q^{22} +0.338516i q^{23} +(9.98638 - 2.67584i) q^{24} -9.02846 q^{26} +(-1.37503 - 1.37503i) q^{27} +(1.91150 + 0.512184i) q^{28} +(2.27033 + 2.27033i) q^{29} +(-5.38302 + 5.38302i) q^{31} +(-0.976852 - 0.563986i) q^{32} +(-7.75850 + 2.07889i) q^{33} +(-10.8294 - 6.25235i) q^{34} +8.31310i q^{36} +(5.22969 - 3.10650i) q^{37} +(-10.6720 - 10.6720i) q^{38} +(2.18526 - 8.15551i) q^{39} +(3.68619 + 2.12823i) q^{41} +(-1.40228 + 2.42882i) q^{42} +7.27408i q^{43} +(-11.9021 - 6.87167i) q^{44} +(-0.410433 - 0.710891i) q^{46} +(-5.08602 + 5.08602i) q^{47} +(-5.28368 + 5.28368i) q^{48} +(5.83691 - 3.36994i) q^{49} +(8.26899 - 8.26899i) q^{51} +(12.5111 - 7.22329i) q^{52} +(3.06455 - 11.4370i) q^{53} +(4.55474 + 1.22044i) q^{54} +(-2.24598 + 0.601809i) q^{56} +(12.2232 - 7.05709i) q^{57} +(-7.52039 - 2.01508i) q^{58} +(-4.75083 - 1.27298i) q^{59} +(3.52938 + 13.1718i) q^{61} +(4.77783 - 17.8311i) q^{62} +(-0.772660 - 0.772660i) q^{63} +9.32535 q^{64} +(13.7725 - 13.7725i) q^{66} +(6.51128 - 1.74469i) q^{67} +20.0090 q^{68} +(0.741497 - 0.198684i) q^{69} +(4.65903 - 8.06967i) q^{71} +(-4.88389 - 8.45915i) q^{72} +(3.04875 - 3.04875i) q^{73} +(-7.21600 + 12.8644i) q^{74} +(23.3269 + 6.25043i) q^{76} +(1.74492 - 0.467551i) q^{77} +(5.29903 + 19.7763i) q^{78} +(-0.309140 - 1.15373i) q^{79} +(-5.41860 + 9.38530i) q^{81} -10.3214 q^{82} +(-2.96248 + 11.0561i) q^{83} -4.48762i q^{84} +(-8.81944 - 15.2757i) q^{86} +(3.64049 - 6.30552i) q^{87} +16.1482 q^{88} +(3.23761 - 12.0829i) q^{89} +(-0.491475 + 1.83421i) q^{91} +(1.13751 + 0.656741i) q^{92} +(14.9506 + 8.63173i) q^{93} +(4.51421 - 16.8473i) q^{94} +(-0.662035 + 2.47075i) q^{96} +4.72808 q^{97} +(-8.17175 + 14.1539i) q^{98} +(3.79434 + 6.57199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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