LMFDB - Embedded newform 375.2.l.b.368.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(32,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("375.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.l (of order $20$, degree $8$, not 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			368.7
Character	$\chi$	$=$	375.368
Dual form			375.2.l.b.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74302 - 0.888111i) q^{2} +(1.31346 - 1.12908i) q^{3} +(1.07379 - 1.47795i) q^{4} +(1.28664 - 3.13450i) q^{6} +(0.551254 - 0.551254i) q^{7} +(-0.0529901 + 0.334566i) q^{8} +(0.450377 - 2.96600i) q^{9} +O(q^{10})$	\(q+(1.74302 - 0.888111i) q^{2} +(1.31346 - 1.12908i) q^{3} +(1.07379 - 1.47795i) q^{4} +(1.28664 - 3.13450i) q^{6} +(0.551254 - 0.551254i) q^{7} +(-0.0529901 + 0.334566i) q^{8} +(0.450377 - 2.96600i) q^{9} +(0.937544 + 0.304626i) q^{11} +(-0.258327 - 3.15362i) q^{12} +(-2.14163 + 4.20319i) q^{13} +(0.471270 - 1.45042i) q^{14} +(1.33382 + 4.10508i) q^{16} +(-3.38054 - 0.535425i) q^{17} +(-1.84912 - 5.56977i) q^{18} +(-3.79078 - 5.21756i) q^{19} +(0.101645 - 1.34646i) q^{21} +(1.90469 - 0.301674i) q^{22} +(0.435998 + 0.855694i) q^{23} +(0.308150 + 0.499270i) q^{24} +9.22822i q^{26} +(-2.75728 - 4.40425i) q^{27} +(-0.222792 - 1.40666i) q^{28} +(8.30669 + 6.03516i) q^{29} +(-2.73448 + 1.98672i) q^{31} +(5.49158 + 5.49158i) q^{32} +(1.57538 - 0.658442i) q^{33} +(-6.36785 + 2.06904i) q^{34} +(-3.89998 - 3.85050i) q^{36} +(-3.63316 - 1.85119i) q^{37} +(-11.2411 - 5.72765i) q^{38} +(1.93276 + 7.93880i) q^{39} +(3.89453 - 1.26541i) q^{41} +(-1.01864 - 2.43717i) q^{42} +(-4.93949 - 4.93949i) q^{43} +(1.45695 - 1.05853i) q^{44} +(1.51990 + 1.10427i) q^{46} +(0.732455 + 4.62454i) q^{47} +(6.38686 + 3.88589i) q^{48} +6.39224i q^{49} +(-5.04475 + 3.11362i) q^{51} +(3.91242 + 7.67856i) q^{52} +(3.42818 - 0.542970i) q^{53} +(-8.71745 - 5.22789i) q^{54} +(0.155220 + 0.213642i) q^{56} +(-10.8701 - 2.57300i) q^{57} +(19.8386 + 3.14212i) q^{58} +(0.172592 + 0.531183i) q^{59} +(2.95410 - 9.09178i) q^{61} +(-3.00182 + 5.89140i) q^{62} +(-1.38675 - 1.88329i) q^{63} +(6.23890 + 2.02714i) q^{64} +(2.16114 - 2.54678i) q^{66} +(-1.08040 + 6.82141i) q^{67} +(-4.42132 + 4.42132i) q^{68} +(1.53881 + 0.631649i) q^{69} +(5.08421 - 6.99781i) q^{71} +(0.968458 + 0.307850i) q^{72} +(-8.03649 + 4.09480i) q^{73} -7.97671 q^{74} -11.7818 q^{76} +(0.684752 - 0.348898i) q^{77} +(10.4194 + 12.1209i) q^{78} +(3.84334 - 5.28990i) q^{79} +(-8.59432 - 2.67164i) q^{81} +(5.66440 - 5.66440i) q^{82} +(0.223482 - 1.41101i) q^{83} +(-1.88085 - 1.59604i) q^{84} +(-12.9964 - 4.22279i) q^{86} +(17.7247 - 1.45191i) q^{87} +(-0.151598 + 0.297528i) q^{88} +(3.04398 - 9.36841i) q^{89} +(1.13644 + 3.49761i) q^{91} +(1.73284 + 0.274455i) q^{92} +(-1.34849 + 5.69692i) q^{93} +(5.38378 + 7.41014i) q^{94} +(13.4134 + 1.01259i) q^{96} +(-5.51558 + 0.873583i) q^{97} +(5.67701 + 11.1418i) q^{98} +(1.32577 - 2.64356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 20 q^{4} - 6 q^{6} + 20 q^{7} + 10 q^{9}+O(q^{10}) $ 64 * q + 20 * q^4 - 6 * q^6 + 20 * q^7 + 10 * q^9	$ 64 q + 20 q^{4} - 6 q^{6} + 20 q^{7} + 10 q^{9} + 40 q^{12} - 8 q^{16} + 10 q^{18} - 6 q^{21} - 30 q^{27} - 80 q^{28} - 12 q^{31} - 50 q^{33} - 20 q^{34} - 22 q^{36} - 120 q^{37} - 30 q^{39} + 60 q^{42} + 20 q^{43} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 100 q^{52} - 120 q^{54} - 70 q^{57} + 120 q^{58} - 12 q^{61} - 70 q^{63} + 100 q^{64} - 30 q^{66} - 60 q^{67} + 80 q^{69} - 40 q^{72} - 80 q^{73} - 64 q^{76} + 70 q^{78} + 60 q^{79} + 14 q^{81} + 60 q^{82} + 130 q^{84} + 100 q^{87} + 60 q^{88} - 12 q^{91} + 20 q^{93} - 260 q^{94} + 42 q^{96}+O(q^{100}) $ 64 * q + 20 * q^4 - 6 * q^6 + 20 * q^7 + 10 * q^9 + 40 * q^12 - 8 * q^16 + 10 * q^18 - 6 * q^21 - 30 * q^27 - 80 * q^28 - 12 * q^31 - 50 * q^33 - 20 * q^34 - 22 * q^36 - 120 * q^37 - 30 * q^39 + 60 * q^42 + 20 * q^43 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 100 * q^52 - 120 * q^54 - 70 * q^57 + 120 * q^58 - 12 * q^61 - 70 * q^63 + 100 * q^64 - 30 * q^66 - 60 * q^67 + 80 * q^69 - 40 * q^72 - 80 * q^73 - 64 * q^76 + 70 * q^78 + 60 * q^79 + 14 * q^81 + 60 * q^82 + 130 * q^84 + 100 * q^87 + 60 * q^88 - 12 * q^91 + 20 * q^93 - 260 * q^94 + 42 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.74302	−	0.888111i	1.23250	−	0.627989i	0.288354	−	0.957524i	$-0.406892\pi$
$2$	1.74302	−	0.888111i	1.23250	−	0.627989i	0.944143	+	0.329535i	$0.106892\pi$
$3$	1.31346	−	1.12908i	0.758329	−	0.651872i
$3$	1.31346	−	1.12908i	0.758329	−	0.651872i
$4$	1.07379	−	1.47795i	0.536895	−	0.738973i
$5$		0			0
$5$		0			0
$6$	1.28664	−	3.13450i	0.525270	−	1.27965i
$7$	0.551254	−	0.551254i	0.208355	−	0.208355i	−0.595213	−	0.803568i	$-0.702932\pi$
$7$	0.551254	−	0.551254i	0.208355	−	0.208355i	0.803568	+	0.595213i	$0.202932\pi$
$8$	−0.0529901	+	0.334566i	−0.0187348	+	0.118287i
$9$	0.450377	−	2.96600i	0.150126	−	0.988667i
$10$		0			0
$11$	0.937544	+	0.304626i	0.282680	+	0.0918483i	0.446925	−	0.894571i	$-0.352519\pi$
$11$	0.937544	+	0.304626i	0.282680	+	0.0918483i	−0.164245	+	0.986420i	$0.552519\pi$
$12$	−0.258327	−	3.15362i	−0.0745726	−	0.910372i
$13$	−2.14163	+	4.20319i	−0.593981	+	1.16575i	0.376914	+	0.926248i	$0.376985\pi$
$13$	−2.14163	+	4.20319i	−0.593981	+	1.16575i	−0.970895	+	0.239505i	$0.923015\pi$
$14$	0.471270	−	1.45042i	0.125952	−	0.387641i
$15$		0			0
$16$	1.33382	+	4.10508i	0.333455	+	1.02627i
$17$	−3.38054	−	0.535425i	−0.819901	−	0.129860i	−0.267627	−	0.963522i	$-0.586240\pi$
$17$	−3.38054	−	0.535425i	−0.819901	−	0.129860i	−0.552274	+	0.833663i	$0.686240\pi$
$18$	−1.84912	−	5.56977i	−0.435842	−	1.31281i
$19$	−3.79078	−	5.21756i	−0.869664	−	1.19699i	−0.979178	−	0.203004i	$-0.934930\pi$
$19$	−3.79078	−	5.21756i	−0.869664	−	1.19699i	0.109514	−	0.993985i	$-0.465070\pi$
$20$		0			0
$21$	0.101645	−	1.34646i	0.0221808	−	0.293822i
$22$	1.90469	−	0.301674i	0.406082	−	0.0643171i
$23$	0.435998	+	0.855694i	0.0909118	+	0.178424i	0.931985	−	0.362497i	$-0.118076\pi$
$23$	0.435998	+	0.855694i	0.0909118	+	0.178424i	−0.841073	+	0.540921i	$0.818076\pi$
$24$	0.308150	+	0.499270i	0.0629008	+	0.101913i
$25$		0			0
$26$			9.22822i			1.80980i
$27$	−2.75728	−	4.40425i	−0.530640	−	0.847598i
$28$	−0.222792	−	1.40666i	−0.0421038	−	0.265833i
$29$	8.30669	+	6.03516i	1.54251	+	1.12070i	0.948735	+	0.316073i	$0.102364\pi$
$29$	8.30669	+	6.03516i	1.54251	+	1.12070i	0.593778	+	0.804629i	$0.297636\pi$
$30$		0			0
$31$	−2.73448	+	1.98672i	−0.491128	+	0.356825i	−0.805618	−	0.592436i	$-0.798166\pi$
$31$	−2.73448	+	1.98672i	−0.491128	+	0.356825i	0.314490	+	0.949261i	$0.398166\pi$
$32$	5.49158	+	5.49158i	0.970784	+	0.970784i
$33$	1.57538	−	0.658442i	0.274238	−	0.114620i
$34$	−6.36785	+	2.06904i	−1.09208	+	0.354837i
$35$		0			0
$36$	−3.89998	−	3.85050i	−0.649997	−	0.641750i
$37$	−3.63316	−	1.85119i	−0.597288	−	0.304333i	0.129086	−	0.991633i	$-0.458796\pi$
$37$	−3.63316	−	1.85119i	−0.597288	−	0.304333i	−0.726374	+	0.687300i	$0.758796\pi$
$38$	−11.2411	−	5.72765i	−1.82355	−	0.929148i
$39$	1.93276	+	7.93880i	0.309489	+	1.27122i
$40$		0			0
$41$	3.89453	−	1.26541i	0.608223	−	0.197624i	0.0113186	−	0.999936i	$-0.496397\pi$
$41$	3.89453	−	1.26541i	0.608223	−	0.197624i	0.596905	+	0.802312i	$0.296397\pi$
$42$	−1.01864	−	2.43717i	−0.157179	−	0.376064i
$43$	−4.93949	−	4.93949i	−0.753265	−	0.753265i	0.221822	−	0.975087i	$-0.428799\pi$
$43$	−4.93949	−	4.93949i	−0.753265	−	0.753265i	−0.975087	+	0.221822i	$0.928799\pi$
$44$	1.45695	−	1.05853i	0.219643	−	0.159580i
$45$		0			0
$46$	1.51990	+	1.10427i	0.224097	+	0.162816i
$47$	0.732455	+	4.62454i	0.106840	+	0.674558i	0.981736	+	0.190248i	$0.0609293\pi$
$47$	0.732455	+	4.62454i	0.106840	+	0.674558i	−0.874897	+	0.484310i	$0.839071\pi$
$48$	6.38686	+	3.88589i	0.921865	+	0.560879i
$49$			6.39224i			0.913177i
$50$		0			0
$51$	−5.04475	+	3.11362i	−0.706407	+	0.435994i
$52$	3.91242	+	7.67856i	0.542555	+	1.06482i
$53$	3.42818	−	0.542970i	0.470896	−	0.0745826i	0.0835235	−	0.996506i	$-0.473383\pi$
$53$	3.42818	−	0.542970i	0.470896	−	0.0745826i	0.387373	+	0.921923i	$0.373383\pi$
$54$	−8.71745	−	5.22789i	−1.18629	−	0.711426i
$55$		0			0
$56$	0.155220	+	0.213642i	0.0207421	+	0.0285491i
$57$	−10.8701	−	2.57300i	−1.43978	−	0.340802i
$58$	19.8386	+	3.14212i	2.60493	+	0.412581i
$59$	0.172592	+	0.531183i	0.0224696	+	0.0691542i	0.961663	−	0.274236i	$-0.0884248\pi$
$59$	0.172592	+	0.531183i	0.0224696	+	0.0691542i	−0.939193	+	0.343390i	$0.888425\pi$
$60$		0			0
$61$	2.95410	−	9.09178i	0.378233	−	1.16408i	−0.563038	−	0.826431i	$-0.690367\pi$
$61$	2.95410	−	9.09178i	0.378233	−	1.16408i	0.941271	−	0.337652i	$-0.109633\pi$
$62$	−3.00182	+	5.89140i	−0.381231	+	0.748209i
$63$	−1.38675	−	1.88329i	−0.174714	−	0.237273i
$64$	6.23890	+	2.02714i	0.779862	+	0.253393i
$65$		0			0
$66$	2.16114	−	2.54678i	0.266017	−	0.313487i
$67$	−1.08040	+	6.82141i	−0.131992	+	0.833367i	0.829494	+	0.558515i	$0.188629\pi$
$67$	−1.08040	+	6.82141i	−0.131992	+	0.833367i	−0.961487	+	0.274852i	$0.911371\pi$
$68$	−4.42132	+	4.42132i	−0.536164	+	0.536164i
$69$	1.53881	+	0.631649i	0.185251	+	0.0760416i
$70$		0			0
$71$	5.08421	−	6.99781i	0.603385	−	0.830488i	−0.392628	−	0.919697i	$-0.628434\pi$
$71$	5.08421	−	6.99781i	0.603385	−	0.830488i	0.996013	+	0.0892096i	$0.0284341\pi$
$72$	0.968458	+	0.307850i	0.114134	+	0.0362804i
$73$	−8.03649	+	4.09480i	−0.940600	+	0.479260i	−0.855897	−	0.517147i	$-0.826994\pi$
$73$	−8.03649	+	4.09480i	−0.940600	+	0.479260i	−0.0847030	+	0.996406i	$0.526994\pi$
$74$	−7.97671			−0.927274
$75$		0			0
$76$	−11.7818			−1.35146
$77$	0.684752	−	0.348898i	0.0780347	−	0.0397607i
$78$	10.4194	+	12.1209i	1.17976	+	1.37243i
$79$	3.84334	−	5.28990i	0.432410	−	0.595161i	−0.536095	−	0.844158i	$-0.680101\pi$
$79$	3.84334	−	5.28990i	0.432410	−	0.595161i	0.968504	+	0.248997i	$0.0801010\pi$
$80$		0			0
$81$	−8.59432	−	2.67164i	−0.954925	−	0.296849i
$82$	5.66440	−	5.66440i	0.625528	−	0.625528i
$83$	0.223482	−	1.41101i	0.0245303	−	0.154878i	−0.972383	−	0.233392i	$-0.925017\pi$
$83$	0.223482	−	1.41101i	0.0245303	−	0.154878i	0.996913	+	0.0785138i	$0.0250175\pi$
$84$	−1.88085	−	1.59604i	−0.205218	−	0.174143i
$85$		0			0
$86$	−12.9964	−	4.22279i	−1.40144	−	0.455355i
$87$	17.7247	−	1.45191i	1.90029	−	0.155661i
$88$	−0.151598	+	0.297528i	−0.0161604	+	0.0317166i
$89$	3.04398	−	9.36841i	0.322661	−	0.993049i	−0.649824	−	0.760085i	$-0.725157\pi$
$89$	3.04398	−	9.36841i	0.322661	−	0.993049i	0.972485	−	0.232964i	$-0.0748426\pi$
$90$		0			0
$91$	1.13644	+	3.49761i	0.119131	+	0.366649i
$92$	1.73284	+	0.274455i	0.180661	+	0.0286139i
$93$	−1.34849	+	5.69692i	−0.139832	+	0.590743i
$94$	5.38378	+	7.41014i	0.555295	+	0.764297i
$95$		0			0
$96$	13.4134	+	1.01259i	1.36900	+	0.103347i
$97$	−5.51558	+	0.873583i	−0.560023	+	0.0886989i	−0.430028	−	0.902816i	$-0.641496\pi$
$97$	−5.51558	+	0.873583i	−0.560023	+	0.0886989i	−0.129995	+	0.991515i	$0.541496\pi$
$98$	5.67701	+	11.1418i	0.573465	+	1.12549i
$99$	1.32577	−	2.64356i	0.133245	−	0.265688i
$100$		0			0
$101$			3.43356i			0.341652i	0.985301	+	0.170826i	$0.0546437\pi$
$101$			3.43356i			0.341652i	−0.985301	+	0.170826i	$0.945356\pi$
$102$	−6.02784	+	9.90739i	−0.596845	+	0.980978i
$103$	−0.772999	−	4.88052i	−0.0761658	−	0.480892i	−0.996057	−	0.0887178i	$-0.971723\pi$
$103$	−0.772999	−	4.88052i	−0.0761658	−	0.480892i	0.919891	−	0.392174i	$-0.128277\pi$
$104$	−1.29276	−	0.939244i	−0.126765	−	0.0921004i
$105$		0			0
$106$	5.49315	−	3.99100i	0.533542	−	0.387641i
$107$	−2.44736	−	2.44736i	−0.236595	−	0.236595i	0.578844	−	0.815439i	$-0.303504\pi$
$107$	−2.44736	−	2.44736i	−0.236595	−	0.236595i	−0.815439	+	0.578844i	$0.803504\pi$
$108$	−9.46999	−	0.654121i	−0.911250	−	0.0629429i
$109$	2.20399	−	0.716119i	0.211104	−	0.0685918i	−0.201556	−	0.979477i	$-0.564600\pi$
$109$	2.20399	−	0.716119i	0.211104	−	0.0685918i	0.412660	+	0.910885i	$0.364600\pi$
$110$		0			0
$111$	−6.86216	+	1.67064i	−0.651327	+	0.158570i
$112$	2.99821	+	1.52767i	0.283305	+	0.144351i
$113$	2.90689	+	1.48114i	0.273457	+	0.139334i	0.585342	−	0.810786i	$-0.300960\pi$
$113$	2.90689	+	1.48114i	0.273457	+	0.139334i	−0.311885	+	0.950120i	$0.600960\pi$
$114$	−21.2318	+	5.16904i	−1.98854	+	0.484125i
$115$		0			0
$116$	17.8393	−	5.79634i	1.65634	−	0.538176i
$117$	11.5021	+	8.24509i	1.06337	+	0.762259i
$118$	0.772580	+	0.772580i	0.0711217	+	0.0711217i
$119$	−2.15869	+	1.56838i	−0.197887	+	0.143773i
$120$		0			0
$121$	−8.11300	−	5.89444i	−0.737545	−	0.535858i
$122$	−2.92547	−	18.4707i	−0.264859	−	1.67226i
$123$	3.68658	−	6.05929i	0.332408	−	0.546347i
$124$			6.17474i			0.554508i
$125$		0			0
$126$	−4.08970	−	2.05102i	−0.364339	−	0.182720i
$127$	−6.90244	−	13.5468i	−0.612493	−	1.20208i	−0.964001	−	0.265900i	$-0.914331\pi$
$127$	−6.90244	−	13.5468i	−0.612493	−	1.20208i	0.351508	−	0.936185i	$-0.385669\pi$
$128$	−2.66650	+	0.422332i	−0.235687	+	0.0373292i
$129$	−12.0649	−	0.910786i	−1.06225	−	0.0801903i
$130$		0			0
$131$	0.850285	+	1.17032i	0.0742897	+	0.102251i	0.844545	−	0.535485i	$-0.179871\pi$
$131$	0.850285	+	1.17032i	0.0742897	+	0.102251i	−0.770255	+	0.637736i	$0.779871\pi$
$132$	0.718483	−	3.03535i	0.0625360	−	0.264193i
$133$	−4.96588	−	0.786518i	−0.430597	−	0.0681998i
$134$	4.17500	+	12.8493i	0.360665	+	1.11001i
$135$		0			0
$136$	0.358270	−	1.10264i	0.0307214	−	0.0945507i
$137$	−4.30255	+	8.44422i	−0.367591	+	0.721438i	−0.998519	−	0.0544031i	$-0.982674\pi$
$137$	−4.30255	+	8.44422i	−0.367591	+	0.721438i	0.630928	+	0.775842i	$0.282674\pi$
$138$	3.24314	−	0.265660i	0.276075	−	0.0226145i
$139$	6.29917	+	2.04672i	0.534288	+	0.173601i	0.563720	−	0.825966i	$-0.309370\pi$
$139$	6.29917	+	2.04672i	0.534288	+	0.173601i	−0.0294316	+	0.999567i	$0.509370\pi$
$140$		0			0
$141$	6.18350	+	5.24717i	0.520745	+	0.441891i
$142$	2.64702	−	16.7126i	0.222133	−	1.40249i
$143$	−3.28827	+	3.28827i	−0.274979	+	0.274979i
$144$	12.7764	−	2.10728i	1.06470	−	0.175607i
$145$		0			0
$146$	−10.3711	+	14.2746i	−0.858318	+	1.18137i
$147$	7.21732	+	8.39598i	0.595274	+	0.692488i
$148$	−6.63721	+	3.38183i	−0.545575	+	0.277985i
$149$	−10.3466			−0.847626			−0.423813	−	0.905750i	$-0.639309\pi$
$149$	−10.3466			−0.847626			−0.423813	+	0.905750i	$0.639309\pi$
$150$		0			0
$151$	5.60298			0.455964			0.227982	−	0.973665i	$-0.426787\pi$
$151$	5.60298			0.455964			0.227982	+	0.973665i	$0.426787\pi$
$152$	1.94649	−	0.991787i	0.157881	−	0.0804445i
$153$	−3.11059	+	9.78554i	−0.251476	+	0.791114i
$154$	0.883672	−	1.21627i	0.0712083	−	0.0980098i
$155$		0			0
$156$	13.8085	+	5.66809i	1.10556	+	0.453811i
$157$	−7.18526	+	7.18526i	−0.573446	+	0.573446i	−0.933090	−	0.359644i	$-0.882898\pi$
$157$	−7.18526	+	7.18526i	−0.573446	+	0.573446i	0.359644	+	0.933090i	$0.382898\pi$
$158$	2.00098	−	12.6337i	0.159189	−	1.00508i
$159$	3.88973	−	4.58384i	0.308476	−	0.363522i
$160$		0			0
$161$	0.712050	+	0.231359i	0.0561174	+	0.0182337i
$162$	−17.3527	+	2.97600i	−1.36336	+	0.233817i
$163$	8.85172	−	17.3725i	0.693320	−	1.36072i	−0.228670	−	0.973504i	$-0.573438\pi$
$163$	8.85172	−	17.3725i	0.693320	−	1.36072i	0.921990	−	0.387214i	$-0.126562\pi$
$164$	2.31170	−	7.11469i	0.180514	−	0.555564i
$165$		0			0
$166$	−0.863599	−	2.65788i	−0.0670283	−	0.206292i
$167$	0.529779	+	0.0839087i	0.0409955	+	0.00649305i	0.176899	−	0.984229i	$-0.443394\pi$
$167$	0.529779	+	0.0839087i	0.0409955	+	0.00649305i	−0.135903	+	0.990722i	$0.543394\pi$
$168$	0.445094	+	0.105356i	0.0343397	+	0.00812840i
$169$	−5.43898	−	7.48611i	−0.418383	−	0.575855i
$170$		0			0
$171$	−17.1826	+	8.89358i	−1.31398	+	0.680109i
$172$	−12.6043	+	1.99632i	−0.961067	+	0.152218i
$173$	−7.23210	−	14.1938i	−0.549846	−	1.07913i	−0.983979	−	0.178285i	$-0.942945\pi$
$173$	−7.23210	−	14.1938i	−0.549846	−	1.07913i	0.434132	−	0.900849i	$-0.357055\pi$
$174$	29.6050	−	18.2722i	2.24435	−	1.38521i
$175$		0			0
$176$			4.25500i			0.320733i
$177$	0.826439	+	0.502821i	0.0621190	+	0.0377943i
$178$	−3.01448	−	19.0327i	−0.225945	−	1.42656i
$179$	14.7628	+	10.7258i	1.10342	+	0.801684i	0.981615	−	0.190870i	$-0.0611308\pi$
$179$	14.7628	+	10.7258i	1.10342	+	0.801684i	0.121808	+	0.992554i	$0.461131\pi$
$180$		0			0
$181$	8.42806	−	6.12334i	0.626453	−	0.455145i	−0.228717	−	0.973493i	$-0.573453\pi$
$181$	8.42806	−	6.12334i	0.626453	−	0.455145i	0.855170	+	0.518348i	$0.173453\pi$
$182$	5.08710	+	5.08710i	0.377081	+	0.377081i
$183$	−6.38520	−	15.2771i	−0.472008	−	1.12932i
$184$	−0.309390	+	0.100527i	−0.0228085	+	0.00741093i
$185$		0			0
$186$	2.70906	+	11.1274i	0.198638	+	0.815903i
$187$	−3.00630	−	1.53179i	−0.219842	−	0.112015i
$188$	7.62132	+	3.88326i	0.555842	+	0.283216i
$189$	−3.94782	−	0.907895i	−0.287162	−	0.0660396i
$190$		0			0
$191$	−16.3919	+	5.32604i	−1.18607	+	0.385379i	−0.834620	−	0.550826i	$-0.814313\pi$
$191$	−16.3919	+	5.32604i	−1.18607	+	0.385379i	−0.351454	+	0.936205i	$0.614313\pi$
$192$	10.4834	−	4.38161i	0.756571	−	0.316215i
$193$	13.5906	+	13.5906i	0.978276	+	0.978276i	0.999769	−	0.0214931i	$-0.00684200\pi$
$193$	13.5906	+	13.5906i	0.978276	+	0.978276i	−0.0214931	+	0.999769i	$0.506842\pi$
$194$	−8.83791	+	6.42112i	−0.634525	+	0.461009i
$195$		0			0
$196$	9.44738	+	6.86393i	0.674813	+	0.490280i
$197$	−0.334594	−	2.11254i	−0.0238388	−	0.150512i	0.972898	−	0.231236i	$-0.0742769\pi$
$197$	−0.334594	−	2.11254i	−0.0238388	−	0.150512i	−0.996737	+	0.0807236i	$0.974277\pi$
$198$	−0.0369342	−	5.78519i	−0.00262480	−	0.411136i
$199$		−	18.8648i		−	1.33729i	−0.743582	−	0.668644i	$-0.766875\pi$
$199$		−	18.8648i		−	1.33729i	0.743582	−	0.668644i	$-0.233125\pi$
$200$		0			0
$201$	6.28281	+	10.1795i	0.443155	+	0.718009i
$202$	3.04939	+	5.98476i	0.214554	+	0.421086i
$203$	7.90601	−	1.25219i	0.554893	−	0.0878864i
$204$	−0.815242	+	10.7993i	−0.0570784	+	0.756099i
$205$		0			0
$206$	−5.68179	−	7.82031i	−0.395869	−	0.544867i
$207$	2.73435	−	0.907785i	0.190051	−	0.0630954i
$208$	−20.1109	−	3.18526i	−1.39444	−	0.220858i
$209$	−1.96461	−	6.04646i	−0.135895	−	0.418242i
$210$		0			0
$211$	−1.54603	+	4.75818i	−0.106433	+	0.327567i	−0.990064	−	0.140617i	$-0.955091\pi$
$211$	−1.54603	+	4.75818i	−0.106433	+	0.327567i	0.883631	+	0.468184i	$0.155091\pi$
$212$	2.87866	−	5.64970i	0.197708	−	0.388023i
$213$	−1.22313	−	14.9318i	−0.0838076	−	1.02311i
$214$	−6.43931	−	2.09226i	−0.440182	−	0.143024i
$215$		0			0
$216$	1.61962	−	0.689113i	0.110201	−	0.0468882i
$217$	−0.412209	+	2.60258i	−0.0279825	+	0.176675i
$218$	3.20559	−	3.20559i	0.217110	−	0.217110i
$219$	−5.93231	+	14.4522i	−0.400868	+	0.976587i
$220$		0			0
$221$	9.49035	−	13.0623i	0.638390	−	0.878669i
$222$	−10.4771	+	9.00631i	−0.703179	+	0.604464i
$223$	−10.8469	+	5.52678i	−0.726363	+	0.370101i	−0.777746	−	0.628578i	$-0.783637\pi$
$223$	−10.8469	+	5.52678i	−0.726363	+	0.370101i	0.0513829	+	0.998679i	$0.483637\pi$
$224$	6.05452			0.404534
$225$		0			0
$226$	6.38217			0.424536
$227$	13.3560	−	6.80520i	0.886466	−	0.451677i	0.0494003	−	0.998779i	$-0.484269\pi$
$227$	13.3560	−	6.80520i	0.886466	−	0.451677i	0.837066	+	0.547102i	$0.184269\pi$
$228$	−15.4749	+	13.3025i	−1.02485	+	0.880980i
$229$	−9.00455	+	12.3937i	−0.595037	+	0.818999i	−0.995243	−	0.0974268i	$-0.968939\pi$
$229$	−9.00455	+	12.3937i	−0.595037	+	0.818999i	0.400205	+	0.916426i	$0.368939\pi$
$230$		0			0
$231$	0.505464	−	1.23140i	0.0332571	−	0.0810203i
$232$	−2.45933	+	2.45933i	−0.161463	+	0.161463i
$233$	−0.338659	+	2.13821i	−0.0221863	+	0.140079i	−0.996295	−	0.0860013i	$-0.972591\pi$
$233$	−0.338659	+	2.13821i	−0.0221863	+	0.140079i	0.974109	+	0.226080i	$0.0725911\pi$
$234$	27.3709	+	4.15618i	1.78929	+	0.271698i
$235$		0			0
$236$	0.970388	+	0.315298i	0.0631669	+	0.0205242i
$237$	−0.924610	−	11.2875i	−0.0600599	−	0.733203i
$238$	−2.36974	+	4.65087i	−0.153607	+	0.301471i
$239$	7.04340	−	21.6774i	0.455600	−	1.40219i	−0.414830	−	0.909899i	$-0.636159\pi$
$239$	7.04340	−	21.6774i	0.455600	−	1.40219i	0.870430	−	0.492293i	$-0.163841\pi$
$240$		0			0
$241$	−0.706155	−	2.17332i	−0.0454874	−	0.139996i	0.925733	−	0.378177i	$-0.123449\pi$
$241$	−0.706155	−	2.17332i	−0.0454874	−	0.139996i	−0.971221	+	0.238181i	$0.923449\pi$
$242$	−19.3760	−	3.06885i	−1.24554	−	0.197273i
$243$	−14.3048	+	6.19453i	−0.917654	+	0.397380i
$244$	−10.2651	−	14.1287i	−0.657154	−	0.904495i
$245$		0			0
$246$	1.04445	−	13.8355i	0.0665918	−	0.882120i
$247$	30.0488	−	4.75926i	1.91196	−	0.302825i
$248$	−0.519788	−	1.02014i	−0.0330066	−	0.0647791i
$249$	−1.29960	−	2.10564i	−0.0823587	−	0.133439i
$250$		0			0
$251$		−	14.3226i		−	0.904036i	−0.892009	−	0.452018i	$-0.850704\pi$
$251$		−	14.3226i		−	0.904036i	0.892009	−	0.452018i	$-0.149296\pi$
$252$	−4.27248	+	0.0272766i	−0.269141	+	0.00171827i
$253$	0.148100	+	0.935067i	0.00931097	+	0.0587871i
$254$	−24.0621	−	17.4822i	−1.50979	−	1.09693i
$255$		0			0
$256$	−14.8869	+	10.8160i	−0.930432	+	0.675998i
$257$	−4.31188	−	4.31188i	−0.268968	−	0.268968i	0.559716	−	0.828684i	$-0.310910\pi$
$257$	−4.31188	−	4.31188i	−0.268968	−	0.268968i	−0.828684	+	0.559716i	$0.810910\pi$
$258$	−21.8382	+	9.12744i	−1.35959	+	0.568250i
$259$	−3.02327	+	0.982320i	−0.187857	+	0.0610384i
$260$		0			0
$261$	21.6414	−	21.9195i	1.33957	−	1.35679i
$262$	2.52143	+	1.28473i	0.155774	+	0.0793711i
$263$	27.7729	+	14.1510i	1.71255	+	0.872587i	0.981795	+	0.189945i	$0.0608310\pi$
$263$	27.7729	+	14.1510i	1.71255	+	0.872587i	0.730753	+	0.682642i	$0.239169\pi$
$264$	0.136813	+	0.561958i	0.00842026	+	0.0345861i
$265$		0			0
$266$	−9.35412	+	3.03934i	−0.573538	+	0.186354i
$267$	−6.57948	−	15.7420i	−0.402658	−	0.963392i
$268$	8.92154	+	8.92154i	0.544970	+	0.544970i
$269$	−11.9339	+	8.67050i	−0.727624	+	0.528649i	−0.888811	−	0.458274i	$-0.848468\pi$
$269$	−11.9339	+	8.67050i	−0.727624	+	0.528649i	0.161187	+	0.986924i	$0.448468\pi$
$270$		0			0
$271$	19.8939	+	14.4538i	1.20847	+	0.878004i	0.995091	−	0.0989656i	$-0.0315534\pi$
$271$	19.8939	+	14.4538i	1.20847	+	0.878004i	0.213378	+	0.976970i	$0.431553\pi$
$272$	−2.31107	−	14.5915i	−0.140129	−	0.884741i
$273$	5.44174	+	3.31085i	0.329349	+	0.200382i
$274$			18.5395i			1.12001i
$275$		0			0
$276$	2.58590	−	1.59602i	0.155653	−	0.0960691i
$277$	−1.52140	−	2.98592i	−0.0914121	−	0.179406i	0.840773	−	0.541387i	$-0.182101\pi$
$277$	−1.52140	−	2.98592i	−0.0914121	−	0.179406i	−0.932186	+	0.361981i	$0.882101\pi$
$278$	12.7973	−	2.02689i	0.767529	−	0.121565i
$279$	4.66106	+	9.00525i	0.279050	+	0.539130i
$280$		0			0
$281$	0.291342	+	0.400997i	0.0173800	+	0.0239215i	0.817619	−	0.575760i	$-0.195294\pi$
$281$	0.291342	+	0.400997i	0.0173800	+	0.0239215i	−0.800239	+	0.599682i	$0.795294\pi$
$282$	15.4380	+	3.65426i	0.919320	+	0.217608i
$283$	22.6222	+	3.58300i	1.34475	+	0.212987i	0.786964	−	0.616999i	$-0.211652\pi$
$283$	22.6222	+	3.58300i	1.34475	+	0.212987i	0.557784	+	0.829986i	$0.311652\pi$
$284$	−4.88302	−	15.0284i	−0.289754	−	0.891770i
$285$		0			0
$286$	−2.81116	+	8.65186i	−0.166227	+	0.511595i
$287$	1.44931	−	2.84444i	0.0855502	−	0.167902i
$288$	18.7613	−	13.8148i	1.10552	−	0.814042i
$289$	−5.02660	−	1.63324i	−0.295682	−	0.0960730i
$290$		0			0
$291$	−6.25818	+	7.37493i	−0.366861	+	0.432326i
$292$	−2.57762	+	16.2745i	−0.150844	+	0.952390i
$293$	7.39973	−	7.39973i	0.432297	−	0.432297i	−0.457112	−	0.889409i	$-0.651116\pi$
$293$	7.39973	−	7.39973i	0.432297	−	0.432297i	0.889409	+	0.457112i	$0.151116\pi$
$294$	20.0365	+	8.22454i	1.16855	+	0.479665i
$295$		0			0
$296$	0.811866	−	1.11744i	0.0471888	−	0.0649498i
$297$	−1.24342	−	4.96911i	−0.0721508	−	0.288337i
$298$	−18.0343	+	9.18892i	−1.04470	+	0.532300i
$299$	−4.53039			−0.261999
$300$		0			0
$301$	−5.44583			−0.313892
$302$	9.76609	−	4.97607i	0.561975	−	0.286341i
$303$	3.87675	+	4.50987i	0.222714	+	0.259085i
$304$	16.3622	−	22.5207i	0.938439	−	1.29165i
$305$		0			0
$306$	3.26884	+	19.8189i	0.186867	+	1.13297i
$307$	6.95771	−	6.95771i	0.397097	−	0.397097i	−0.480111	−	0.877208i	$-0.659404\pi$
$307$	6.95771	−	6.95771i	0.397097	−	0.397097i	0.877208	+	0.480111i	$0.159404\pi$
$308$	0.219627	−	1.38667i	0.0125144	−	0.0790129i
$309$	−6.52578	−	5.53762i	−0.371239	−	0.315024i
$310$		0			0
$311$	−2.10692	−	0.684580i	−0.119473	−	0.0388190i	0.248671	−	0.968588i	$-0.420006\pi$
$311$	−2.10692	−	0.684580i	−0.119473	−	0.0388190i	−0.368143	+	0.929769i	$0.620006\pi$
$312$	−2.75847	+	0.225958i	−0.156168	+	0.0127924i
$313$	−10.9036	+	21.3996i	−0.616309	+	1.20958i	0.346158	+	0.938176i	$0.387486\pi$
$313$	−10.9036	+	21.3996i	−0.616309	+	1.20958i	−0.962467	+	0.271399i	$0.912514\pi$
$314$	−6.14271	+	18.9053i	−0.346653	+	1.06689i
$315$		0			0
$316$	−3.69125	−	11.3605i	−0.207649	−	0.639078i
$317$	−0.769521	−	0.121880i	−0.0432206	−	0.00684547i	0.134787	−	0.990875i	$-0.456965\pi$
$317$	−0.769521	−	0.121880i	−0.0432206	−	0.00684547i	−0.178007	+	0.984029i	$0.556965\pi$
$318$	2.70891	−	11.4442i	0.151908	−	0.641760i
$319$	5.94941	+	8.18866i	0.333103	+	0.458477i
$320$		0			0
$321$	−5.97777	−	0.451266i	−0.333647	−	0.0251872i
$322$	1.44659	−	0.229117i	0.0806152	−	0.0127682i
$323$	10.0213	+	19.6678i	0.557598	+	1.09435i
$324$	−13.1770	+	9.83316i	−0.732058	+	0.546287i
$325$		0			0
$326$		−	38.1418i		−	2.11248i
$327$	2.08631	−	3.42907i	0.115373	−	0.189628i
$328$	0.216992	+	1.37003i	0.0119814	+	0.0756473i
$329$	2.95306	+	2.14553i	0.162808	+	0.118287i
$330$		0			0
$331$	−12.1264	+	8.81032i	−0.666525	+	0.484259i	−0.868860	−	0.495057i	$-0.835147\pi$
$331$	−12.1264	+	8.81032i	−0.666525	+	0.484259i	0.202335	+	0.979316i	$0.435147\pi$
$332$	−1.84542	−	1.84542i	−0.101281	−	0.101281i
$333$	−7.12692	+	9.94222i	−0.390553	+	0.544830i
$334$	0.997933	−	0.324248i	0.0546044	−	0.0177421i
$335$		0			0
$336$	5.66290	−	1.37867i	0.308936	−	0.0752129i
$337$	21.4776	+	10.9434i	1.16996	+	0.596124i	0.927421	−	0.374019i	$-0.122020\pi$
$337$	21.4776	+	10.9434i	1.16996	+	0.596124i	0.242537	+	0.970142i	$0.422020\pi$
$338$	−16.1287	−	8.21799i	−0.877287	−	0.447000i
$339$	5.49041	−	1.33668i	0.298198	−	0.0725986i
$340$		0			0
$341$	−3.16890	+	1.02964i	−0.171606	+	0.0557581i
$342$	−22.0510	+	30.7616i	−1.19238	+	1.66340i
$343$	7.38253	+	7.38253i	0.398619	+	0.398619i
$344$	1.91433	−	1.39084i	0.103214	−	0.0749891i
$345$		0			0
$346$	−25.2113	−	18.3171i	−1.35537	−	0.984733i
$347$	5.05725	+	31.9302i	0.271487	+	1.71410i	0.626652	+	0.779299i	$0.284425\pi$
$347$	5.05725	+	31.9302i	0.271487	+	1.71410i	−0.355164	+	0.934804i	$0.615575\pi$
$348$	16.8868	−	27.7552i	0.905226	−	1.48783i
$349$			8.46821i			0.453293i	0.973977	+	0.226646i	$0.0727762\pi$
$349$			8.46821i			0.453293i	−0.973977	+	0.226646i	$0.927224\pi$
$350$		0			0
$351$	24.4169	−	2.15711i	1.30328	−	0.115138i
$352$	3.47572	+	6.82148i	0.185256	+	0.363586i
$353$	−33.2366	+	5.26415i	−1.76900	+	0.280183i	−0.954116	−	0.299437i	$-0.903201\pi$
$353$	−33.2366	+	5.26415i	−1.76900	+	0.280183i	−0.814887	+	0.579619i	$0.803201\pi$
$354$	1.88706	+	0.142455i	0.100296	+	0.00757141i
$355$		0			0
$356$	−10.5774	−	14.5586i	−0.560601	−	0.771602i
$357$	−1.06454	+	4.49734i	−0.0563416	+	0.238024i
$358$	35.2575	+	5.58424i	1.86342	+	0.295136i
$359$	2.38803	+	7.34959i	0.126035	+	0.387897i	0.994088	−	0.108575i	$-0.0346287\pi$
$359$	2.38803	+	7.34959i	0.126035	+	0.387897i	−0.868053	+	0.496471i	$0.834629\pi$
$360$		0			0
$361$	−6.98158	+	21.4871i	−0.367452	+	1.13090i
$362$	9.25203	−	18.1581i	0.486276	−	0.954370i
$363$	−17.3114	+	1.41805i	−0.908613	+	0.0744284i
$364$	6.38958	+	2.07610i	0.334905	+	0.108817i
$365$		0			0
$366$	−24.6973	−	20.9575i	−1.29095	−	1.09547i
$367$	−1.86431	+	11.7708i	−0.0973164	+	0.614431i	0.890036	+	0.455890i	$0.150679\pi$
$367$	−1.86431	+	11.7708i	−0.0973164	+	0.614431i	−0.987352	+	0.158541i	$0.949321\pi$
$368$	−2.93115	+	2.93115i	−0.152796	+	0.152796i
$369$	−1.99920	−	12.1211i	−0.104074	−	0.630998i
$370$		0			0
$371$	1.59048	−	2.18911i	0.0825737	−	0.113653i
$372$	6.97175	+	8.11030i	0.361468	+	0.420499i
$373$	22.5244	−	11.4767i	1.16627	−	0.594243i	0.239876	−	0.970804i	$-0.422893\pi$
$373$	22.5244	−	11.4767i	1.16627	−	0.594243i	0.926392	+	0.376560i	$0.122893\pi$
$374$	−6.60042			−0.341299
$375$		0			0
$376$	−1.58603			−0.0817931
$377$	−43.1568	+	21.9895i	−2.22269	+	1.13251i
$378$	−7.68743	+	1.92363i	−0.395399	+	0.0989409i
$379$	−11.2506	+	15.4851i	−0.577904	+	0.795416i	−0.993464	−	0.114150i	$-0.963586\pi$
$379$	−11.2506	+	15.4851i	−0.577904	+	0.795416i	0.415560	+	0.909566i	$0.363586\pi$
$380$		0			0
$381$	−24.3615	−	9.99987i	−1.24808	−	0.512309i
$382$	−23.8412	+	23.8412i	−1.21982	+	1.21982i
$383$	−3.31513	+	20.9309i	−0.169395	+	1.06952i	0.745700	+	0.666282i	$0.232115\pi$
$383$	−3.31513	+	20.9309i	−0.169395	+	1.06952i	−0.915095	+	0.403238i	$0.867885\pi$
$384$	−3.02551	+	3.56539i	−0.154395	+	0.181946i
$385$		0			0
$386$	35.7587	+	11.6187i	1.82007	+	0.591376i
$387$	−16.8752	+	12.4259i	−0.857812	+	0.631643i
$388$	−4.63148	+	9.08978i	−0.235128	+	0.461464i
$389$	−3.35765	+	10.3338i	−0.170240	+	0.523944i	−0.999384	−	0.0350902i	$-0.988828\pi$
$389$	−3.35765	+	10.3338i	−0.170240	+	0.523944i	0.829144	+	0.559035i	$0.188828\pi$
$390$		0			0
$391$	−1.01575	−	3.12615i	−0.0513686	−	0.158096i
$392$	−2.13863	−	0.338725i	−0.108017	−	0.0171082i
$393$	2.43819	+	0.577134i	0.122991	+	0.0291125i
$394$	−2.45937	−	3.38503i	−0.123901	−	0.170536i
$395$		0			0
$396$	−2.48344	−	4.79805i	−0.124797	−	0.241111i
$397$	−7.56976	+	1.19893i	−0.379915	+	0.0601727i	−0.343472	−	0.939163i	$-0.611603\pi$
$397$	−7.56976	+	1.19893i	−0.379915	+	0.0601727i	−0.0364437	+	0.999336i	$0.511603\pi$
$398$	−16.7540	−	32.8816i	−0.839802	−	1.64821i
$399$	−7.41055	+	4.57379i	−0.370991	+	0.228976i
$400$		0			0
$401$			20.7216i			1.03479i	0.855747	+	0.517395i	$0.173098\pi$
$401$			20.7216i			1.03479i	−0.855747	+	0.517395i	$0.826902\pi$
$402$	19.9916	+	12.1632i	0.997089	+	0.606648i
$403$	−2.49429	−	15.7484i	−0.124250	−	0.784481i
$404$	5.07463	+	3.68693i	0.252472	+	0.183432i
$405$		0			0
$406$	12.6682	−	9.20399i	0.628713	−	0.456786i
$407$	−2.84233	−	2.84233i	−0.140889	−	0.140889i
$408$	−0.774391	−	1.85279i	−0.0383380	−	0.0917270i
$409$	−30.3286	+	9.85436i	−1.49965	+	0.487267i	−0.939917	−	0.341404i	$-0.889098\pi$
$409$	−30.3286	+	9.85436i	−1.49965	+	0.487267i	−0.559736	+	0.828671i	$0.689098\pi$
$410$		0			0
$411$	3.88292	+	15.9491i	0.191530	+	0.786710i
$412$	−8.04319	−	4.09821i	−0.396259	−	0.201904i
$413$	0.387959	+	0.197675i	0.0190902	+	0.00972695i
$414$	3.95980	−	4.01069i	0.194614	−	0.197115i
$415$		0			0
$416$	−34.8431	+	11.3212i	−1.70832	+	0.555068i
$417$	10.5846	−	4.42394i	0.518332	−	0.216641i
$418$	−8.79427	−	8.79427i	−0.430142	−	0.430142i
$419$	10.4586	−	7.59860i	0.510935	−	0.371216i	−0.302243	−	0.953231i	$-0.597736\pi$
$419$	10.4586	−	7.59860i	0.510935	−	0.371216i	0.813178	+	0.582015i	$0.197736\pi$
$420$		0			0
$421$	−9.92844	−	7.21344i	−0.483883	−	0.351561i	0.318944	−	0.947773i	$-0.396672\pi$
$421$	−9.92844	−	7.21344i	−0.483883	−	0.351561i	−0.802827	+	0.596212i	$0.796672\pi$
$422$	1.53104	+	9.66663i	0.0745300	+	0.470564i
$423$	14.0463	−	0.0896750i	0.682953	−	0.00436015i
$424$			1.17572i			0.0570982i
$425$		0			0
$426$	−15.3931	−	24.9401i	−0.745796	−	1.20835i
$427$	−3.38342	−	6.64034i	−0.163735	−	0.321349i
$428$	−6.24502	+	0.989114i	−0.301864	+	0.0478106i
$429$	−0.606321	+	8.03174i	−0.0292735	+	0.387776i
$430$		0			0
$431$	23.6623	+	32.5684i	1.13977	+	1.56876i	0.768013	+	0.640434i	$0.221246\pi$
$431$	23.6623	+	32.5684i	1.13977	+	1.56876i	0.371760	+	0.928329i	$0.378754\pi$
$432$	14.4020	−	17.1933i	0.692919	−	0.827215i
$433$	−0.688486	−	0.109046i	−0.0330865	−	0.00524039i	0.139869	−	0.990170i	$-0.455332\pi$
$433$	−0.688486	−	0.109046i	−0.0330865	−	0.00524039i	−0.172956	+	0.984930i	$0.555332\pi$
$434$	1.59290	+	4.90243i	0.0764614	+	0.235324i
$435$		0			0
$436$	1.30824	−	4.02634i	0.0626532	−	0.192827i
$437$	2.81186	−	5.51859i	0.134510	−	0.263990i
$438$	2.49502	+	30.4589i	0.119217	+	1.45538i
$439$	32.6150	+	10.5973i	1.55663	+	0.505780i	0.955905	−	0.293677i	$-0.0948789\pi$
$439$	32.6150	+	10.5973i	1.55663	+	0.505780i	0.600724	+	0.799456i	$0.294879\pi$
$440$		0			0
$441$	18.9594	+	2.87892i	0.902828	+	0.137091i
$442$	4.94102	−	31.1964i	0.235020	−	1.48386i
$443$	20.2627	−	20.2627i	0.962712	−	0.962712i	−0.0366177	−	0.999329i	$-0.511658\pi$
$443$	20.2627	−	20.2627i	0.962712	−	0.962712i	0.999329	+	0.0366177i	$0.0116584\pi$
$444$	−4.89940	+	11.9358i	−0.232515	+	0.566449i
$445$		0			0
$446$	−13.9979	+	19.2665i	−0.662822	+	0.912296i
$447$	−13.5899	+	11.6821i	−0.642780	+	0.552544i
$448$	4.55669	−	2.32175i	0.215283	−	0.109692i
$449$	18.2524			0.861386			0.430693	−	0.902499i	$-0.358269\pi$
$449$	18.2524			0.861386			0.430693	+	0.902499i	$0.358269\pi$
$450$		0			0
$451$	4.03677			0.190084
$452$	5.31043	−	2.70580i	0.249782	−	0.127270i
$453$	7.35932	−	6.32619i	0.345771	−	0.297230i
$454$	17.2359	−	23.7231i	0.808919	−	1.11338i
$455$		0			0
$456$	1.43684	−	3.50041i	0.0672864	−	0.163922i
$457$	15.1979	−	15.1979i	0.710929	−	0.710929i	−0.255800	−	0.966730i	$-0.582339\pi$
$457$	15.1979	−	15.1979i	0.710929	−	0.710929i	0.966730	+	0.255800i	$0.0823390\pi$
$458$	−4.68809	+	29.5994i	−0.219060	+	1.38309i
$459$	6.96296	+	16.3650i	0.325003	+	0.763855i
$460$		0			0
$461$	17.1732	+	5.57990i	0.799835	+	0.259882i	0.680286	−	0.732946i	$-0.261855\pi$
$461$	17.1732	+	5.57990i	0.799835	+	0.259882i	0.119548	+	0.992828i	$0.461855\pi$
$462$	−0.212589	−	2.59526i	−0.00989054	−	0.120742i
$463$	−4.61839	+	9.06411i	−0.214635	+	0.421245i	−0.973072	−	0.230502i	$-0.925963\pi$
$463$	−4.61839	+	9.06411i	−0.214635	+	0.421245i	0.758437	+	0.651746i	$0.225963\pi$
$464$	−13.6952	+	42.1494i	−0.635782	+	1.95674i
$465$		0			0
$466$	1.30868	+	4.02770i	0.0606233	+	0.186579i
$467$	11.1130	+	1.76013i	0.514250	+	0.0814493i	0.408166	−	0.912908i	$-0.366169\pi$
$467$	11.1130	+	1.76013i	0.514250	+	0.0814493i	0.106085	+	0.994357i	$0.466169\pi$
$468$	24.5367	−	8.14599i	1.13421	−	0.376549i
$469$	3.16475	+	4.35591i	0.146135	+	0.201137i
$470$		0			0
$471$	−1.32488	+	17.5503i	−0.0610473	+	0.808674i
$472$	−0.186862	+	0.0295960i	−0.00860100	+	0.00136226i
$473$	−3.12629	−	6.13568i	−0.143747	−	0.282119i
$474$	−11.6362	−	18.8532i	−0.534467	−	0.865954i
$475$		0			0
$476$			4.87454i			0.223424i
$477$	−0.0664762	−	10.4125i	−0.00304374	−	0.476756i
$478$	−6.97514	−	44.0393i	−0.319035	−	2.01431i
$479$	−14.0049	−	10.1752i	−0.639901	−	0.464915i	0.219915	−	0.975519i	$-0.429422\pi$
$479$	−14.0049	−	10.1752i	−0.639901	−	0.464915i	−0.859816	+	0.510604i	$0.829422\pi$
$480$		0			0
$481$	15.5618	−	11.3063i	0.709556	−	0.515522i
$482$	−3.16099	−	3.16099i	−0.143979	−	0.143979i
$483$	1.19647	−	0.500077i	0.0544415	−	0.0227543i
$484$	−17.4233	+	5.66118i	−0.791969	+	0.257326i
$485$		0			0
$486$	−19.4321	+	23.5014i	−0.881457	+	1.06605i
$487$	−9.46599	−	4.82316i	−0.428945	−	0.218558i	0.226170	−	0.974088i	$-0.427380\pi$
$487$	−9.46599	−	4.82316i	−0.428945	−	0.218558i	−0.655115	+	0.755530i	$0.727380\pi$
$488$	2.88526	+	1.47011i	0.130610	+	0.0665490i
$489$	−7.98842	−	32.8124i	−0.361249	−	1.48383i
$490$		0			0
$491$	7.07290	−	2.29812i	0.319195	−	0.103713i	−0.145037	−	0.989426i	$-0.546330\pi$
$491$	7.07290	−	2.29812i	0.319195	−	0.103713i	0.464233	+	0.885713i	$0.346330\pi$
$492$	−4.99668	−	11.9550i	−0.225268	−	0.538972i
$493$	−24.8497	−	24.8497i	−1.11917	−	1.11917i
$494$	48.1487	−	34.9821i	2.16631	−	1.57392i
$495$		0			0
$496$	−11.8029	−	8.57533i	−0.529967	−	0.385044i
$497$	−1.05488	−	6.66027i	−0.0473179	−	0.298754i
$498$	−4.13526	−	2.51597i	−0.185305	−	0.112743i
$499$			22.9184i			1.02597i	0.858398	+	0.512985i	$0.171460\pi$
$499$			22.9184i			1.02597i	−0.858398	+	0.512985i	$0.828540\pi$
$500$		0			0
$501$	0.790585	−	0.487949i	0.0353207	−	0.0218000i
$502$	−12.7201	−	24.9646i	−0.567725	−	1.11422i
$503$	8.38878	−	1.32865i	0.374037	−	0.0592416i	0.0334140	−	0.999442i	$-0.489362\pi$
$503$	8.38878	−	1.32865i	0.374037	−	0.0592416i	0.340623	+	0.940200i	$0.389362\pi$
$504$	0.703570	−	0.364163i	0.0313395	−	0.0162211i
$505$		0			0
$506$	1.08858	+	1.49831i	0.0483934	+	0.0666078i
$507$	−15.5963	−	3.69172i	−0.692655	−	0.163955i
$508$	−27.4332	−	4.34500i	−1.21715	−	0.192778i
$509$	−0.901786	−	2.77541i	−0.0399710	−	0.123018i	0.929080	−	0.369879i	$-0.120601\pi$
$509$	−0.901786	−	2.77541i	−0.0399710	−	0.123018i	−0.969051	+	0.246861i	$0.920601\pi$
$510$		0			0
$511$	−2.17288	+	6.68742i	−0.0961223	+	0.295834i
$512$	−13.8910	+	27.2627i	−0.613902	+	1.20485i
$513$	−12.5272	+	31.0818i	−0.553087	+	1.37229i
$514$	−11.3451	−	3.68625i	−0.500411	−	0.162594i
$515$		0			0
$516$	−14.3013	+	16.8533i	−0.629578	+	0.741924i
$517$	−0.722048	+	4.55883i	−0.0317556	+	0.200497i
$518$	−4.39720	+	4.39720i	−0.193202	+	0.193202i
$519$	−25.5250	−	10.4775i	−1.12042	−	0.459909i
$520$		0			0
$521$	−4.48976	+	6.17962i	−0.196700	+	0.270734i	−0.895962	−	0.444132i	$-0.853512\pi$
$521$	−4.48976	+	6.17962i	−0.196700	+	0.270734i	0.699262	+	0.714866i	$0.253512\pi$
$522$	18.2544	−	57.4261i	0.798972	−	2.51347i
$523$	5.98876	−	3.05143i	0.261870	−	0.133430i	−0.318127	−	0.948048i	$-0.603054\pi$
$523$	5.98876	−	3.05143i	0.261870	−	0.133430i	0.579997	+	0.814619i	$0.303054\pi$
$524$	2.64269			0.115447
$525$		0			0
$526$	60.9762			2.65869
$527$	10.3078	−	5.25207i	0.449013	−	0.228784i
$528$	4.80422	+	5.58880i	0.209077	+	0.243221i
$529$	12.9769	−	17.8612i	0.564215	−	0.776575i
$530$		0			0
$531$	1.65322	−	0.272675i	0.0717437	−	0.0118331i
$532$	−6.49475	+	6.49475i	−0.281583	+	0.281583i
$533$	−3.02189	+	19.0795i	−0.130893	+	0.826423i
$534$	−25.4487	−	21.5952i	−1.10127	−	0.934514i
$535$		0			0
$536$	−2.22496	−	0.722933i	−0.0961037	−	0.0312260i
$537$	31.5007	−	2.58036i	1.35935	−	0.111351i
$538$	−13.1006	+	25.7114i	−0.564808	+	1.10850i
$539$	−1.94724	+	5.99300i	−0.0838737	+	0.258137i
$540$		0			0
$541$	−4.34775	−	13.3810i	−0.186924	−	0.575294i	0.813052	−	0.582191i	$-0.197804\pi$
$541$	−4.34775	−	13.3810i	−0.186924	−	0.575294i	−0.999976	+	0.00689744i	$0.997804\pi$
$542$	47.5119	+	7.52515i	2.04081	+	0.323233i
$543$	4.15624	−	17.5587i	0.178361	−	0.753516i
$544$	−15.6242	−	21.5048i	−0.669881	−	0.922012i
$545$		0			0
$546$	12.4254	+	0.938004i	0.531759	+	0.0401429i
$547$	−18.5296	+	2.93480i	−0.792269	+	0.125483i	−0.539436	−	0.842027i	$-0.681362\pi$
$547$	−18.5296	+	2.93480i	−0.792269	+	0.125483i	−0.252833	+	0.967510i	$0.581362\pi$
$548$	7.86007	+	15.4263i	0.335766	+	0.658977i
$549$	−25.6358	−	12.8566i	−1.09411	−	0.548706i
$550$		0			0
$551$		−	66.2186i		−	2.82101i
$552$	−0.292870	+	0.481363i	−0.0124654	+	0.0204882i
$553$	−0.797424	−	5.03474i	−0.0339099	−	0.214099i
$554$	−5.30365	−	3.85333i	−0.225331	−	0.163712i
$555$		0			0
$556$	9.78894	−	7.11208i	0.415143	−	0.301619i
$557$	−4.41902	−	4.41902i	−0.187240	−	0.187240i	0.607262	−	0.794502i	$-0.292268\pi$
$557$	−4.41902	−	4.41902i	−0.187240	−	0.187240i	−0.794502	+	0.607262i	$0.792268\pi$
$558$	16.1220	+	11.5568i	0.682497	+	0.489236i
$559$	31.3401	−	10.1830i	1.32555	−	0.430696i
$560$		0			0
$561$	−5.67817	+	1.38239i	−0.239732	+	0.0583646i
$562$	0.863943	+	0.440201i	0.0364432	+	0.0185688i
$563$	−39.3209	−	20.0350i	−1.65718	−	0.844375i	−0.995518	−	0.0945733i	$-0.969851\pi$
$563$	−39.3209	−	20.0350i	−1.65718	−	0.844375i	−0.661662	−	0.749802i	$-0.730149\pi$
$564$	14.3948	−	3.50453i	0.606132	−	0.147567i
$565$		0			0
$566$	42.6129	−	13.8458i	1.79115	−	0.581981i
$567$	−6.21041	+	3.26490i	−0.260813	+	0.137113i
$568$	2.07182	+	2.07182i	0.0869316	+	0.0869316i
$569$	−7.36407	+	5.35031i	−0.308718	+	0.224297i	−0.731346	−	0.682006i	$-0.761108\pi$
$569$	−7.36407	+	5.35031i	−0.308718	+	0.224297i	0.422628	+	0.906303i	$0.361108\pi$
$570$		0			0
$571$	14.7509	+	10.7172i	0.617307	+	0.448500i	0.851980	−	0.523575i	$-0.175402\pi$
$571$	14.7509	+	10.7172i	0.617307	+	0.448500i	−0.234673	+	0.972074i	$0.575402\pi$
$572$	1.32897	+	8.39081i	0.0555672	+	0.350837i
$573$	−15.5166	+	25.5032i	−0.648217	+	1.06541i
$574$		−	6.24505i		−	0.260663i
$575$		0			0
$576$	8.82236	−	17.5916i	0.367598	−	0.732983i
$577$	15.0501	+	29.5375i	0.626544	+	1.22966i	0.958156	+	0.286245i	$0.0924072\pi$
$577$	15.0501	+	29.5375i	0.626544	+	1.22966i	−0.331613	+	0.943416i	$0.607593\pi$
$578$	−10.2119	+	1.61741i	−0.424761	+	0.0672755i
$579$	33.1957	+	2.50596i	1.37957	+	0.104144i
$580$		0			0
$581$	−0.654629	−	0.901019i	−0.0271586	−	0.0373806i
$582$	−4.35835	+	18.4126i	−0.180660	+	0.763226i
$583$	3.37947	+	0.535255i	0.139963	+	0.0221680i
$584$	−0.944126	−	2.90572i	−0.0390682	−	0.120240i
$585$		0			0
$586$	6.32606	−	19.4696i	0.261327	−	0.804282i
$587$	13.4842	−	26.4642i	0.556551	−	1.09229i	−0.425725	−	0.904853i	$-0.639981\pi$
$587$	13.4842	−	26.4642i	0.556551	−	1.09229i	0.982276	−	0.187440i	$-0.0600190\pi$
$588$	20.1587	−	1.65129i	0.831331	−	0.0680979i
$589$	20.7316	+	6.73611i	0.854232	+	0.277557i
$590$		0			0
$591$	−2.82469	−	2.39697i	−0.116192	−	0.0985980i
$592$	2.75328	−	17.3835i	0.113159	−	0.714459i
$593$	15.2390	−	15.2390i	0.625792	−	0.625792i	−0.321215	−	0.947006i	$-0.604091\pi$
$593$	15.2390	−	15.2390i	0.625792	−	0.625792i	0.947006	+	0.321215i	$0.104091\pi$
$594$	−6.58043	−	7.55694i	−0.269998	−	0.310065i
$595$		0			0
$596$	−11.1101	+	15.2917i	−0.455087	+	0.626373i
$597$	−21.2998	−	24.7782i	−0.871741	−	1.01410i
$598$	−7.89653	+	4.02348i	−0.322913	+	0.164532i
$599$	29.5824			1.20870			0.604351	−	0.796718i	$-0.293432\pi$
$599$	29.5824			1.20870			0.604351	+	0.796718i	$0.293432\pi$
$600$		0			0
$601$	−27.6332			−1.12718			−0.563591	−	0.826054i	$-0.690581\pi$
$601$	−27.6332			−1.12718			−0.563591	+	0.826054i	$0.690581\pi$
$602$	−9.49216	+	4.83650i	−0.386871	+	0.197121i
$603$	19.7457	+	6.27669i	0.804107	+	0.255606i
$604$	6.01643	−	8.28091i	0.244805	−	0.336945i
$605$		0			0
$606$	10.7625	+	4.41778i	0.437197	+	0.179460i
$607$	20.2336	−	20.2336i	0.821256	−	0.821256i	−0.165032	−	0.986288i	$-0.552773\pi$
$607$	20.2336	−	20.2336i	0.821256	−	0.821256i	0.986288	+	0.165032i	$0.0527729\pi$
$608$	7.83528	−	49.4700i	0.317763	−	2.00627i
$609$	8.97044	−	10.5712i	0.363501	−	0.428366i
$610$		0			0
$611$	−21.0064	−	6.82540i	−0.849829	−	0.276126i
$612$	11.1224	+	15.1049i	0.449595	+	0.610579i
$613$	6.16521	−	12.0999i	0.249011	−	0.488711i	−0.732340	−	0.680940i	$-0.761572\pi$
$613$	6.16521	−	12.0999i	0.249011	−	0.488711i	0.981350	+	0.192229i	$0.0615716\pi$
$614$	5.94817	−	18.3066i	0.240049	−	0.738794i
$615$		0			0
$616$	0.0804445	+	0.247583i	0.00324120	+	0.00997540i
$617$	33.3556	+	5.28301i	1.34285	+	0.212686i	0.786153	−	0.618032i	$-0.212070\pi$
$617$	33.3556	+	5.28301i	1.34285	+	0.212686i	0.556694	+	0.830718i	$0.312070\pi$
$618$	−16.2926	−	3.85653i	−0.655383	−	0.155133i
$619$	−12.4660	−	17.1580i	−0.501052	−	0.689638i	0.481327	−	0.876541i	$-0.340155\pi$
$619$	−12.4660	−	17.1580i	−0.501052	−	0.689638i	−0.982378	+	0.186903i	$0.940155\pi$
$620$		0			0
$621$	2.56652	−	4.27963i	0.102991	−	0.171736i
$622$	−4.28038	+	0.677945i	−0.171628	+	0.0271831i
$623$	−3.48637	−	6.84238i	−0.139678	−	0.274134i
$624$	−30.0114	+	18.5230i	−1.20142	+	0.741515i
$625$		0			0
$626$			46.9834i			1.87783i
$627$	−9.40735	−	5.72361i	−0.375694	−	0.228579i
$628$	2.90396	+	18.3349i	0.115881	+	0.731642i
$629$	11.2909	+	8.20329i	0.450196	+	0.327087i
$630$		0			0
$631$	−6.46706	+	4.69860i	−0.257450	+	0.187048i	−0.709022	−	0.705186i	$-0.750863\pi$
$631$	−6.46706	+	4.69860i	−0.257450	+	0.187048i	0.451572	+	0.892235i	$0.350863\pi$
$632$	1.56616	+	1.56616i	0.0622986	+	0.0622986i
$633$	3.34170	+	7.99528i	0.132820	+	0.317784i
$634$	−1.44953	+	0.470981i	−0.0575682	+	0.0187050i
$635$		0			0
$636$	−2.59791	−	10.6709i	−0.103014	−	0.423129i
$637$	−26.8678	−	13.6898i	−1.06454	−	0.542410i
$638$	17.6424	+	8.98923i	0.698468	+	0.355887i
$639$	−18.4657	−	18.2314i	−0.730492	−	0.721224i
$640$		0			0
$641$	−39.9287	+	12.9736i	−1.57709	+	0.512427i	−0.961304	−	0.275488i	$-0.911160\pi$
$641$	−39.9287	+	12.9736i	−1.57709	+	0.512427i	−0.615784	+	0.787915i	$0.711160\pi$
$642$	−10.8201	+	4.52236i	−0.427036	+	0.178483i
$643$	−10.8134	−	10.8134i	−0.426437	−	0.426437i	0.460975	−	0.887413i	$-0.347500\pi$
$643$	−10.8134	−	10.8134i	−0.426437	−	0.426437i	−0.887413	+	0.460975i	$0.847500\pi$
$644$	1.10653	−	0.803941i	0.0436034	−	0.0316797i
$645$		0			0
$646$	34.9344	+	25.3813i	1.37448	+	0.998615i
$647$	0.0667390	+	0.421374i	0.00262378	+	0.0165659i	0.988965	−	0.148146i	$-0.0473306\pi$
$647$	0.0667390	+	0.421374i	0.00262378	+	0.0165659i	−0.986342	+	0.164712i	$0.947331\pi$
$648$	1.34925	−	2.73380i	0.0530037	−	0.107394i
$649$			0.550584i			0.0216123i
$650$		0			0
$651$	2.39709	+	3.88381i	0.0939494	+	0.152219i
$652$	−16.1707	−	31.7368i	−0.633293	−	1.24291i
$653$	−8.39719	+	1.32998i	−0.328608	+	0.0520463i	−0.318559	−	0.947903i	$-0.603199\pi$
$653$	−8.39719	+	1.32998i	−0.328608	+	0.0520463i	−0.0100490	+	0.999950i	$0.503199\pi$
$654$	0.591075	−	7.82978i	0.0231129	−	0.306169i
$655$		0			0
$656$	10.3892	+	14.2995i	0.405630	+	0.558302i
$657$	8.52571	+	25.6804i	0.332620	+	1.00189i
$658$	7.05270	+	1.11704i	0.274943	+	0.0435467i
$659$	−11.7433	−	36.1421i	−0.457453	−	1.40790i	−0.868231	−	0.496160i	$-0.834743\pi$
$659$	−11.7433	−	36.1421i	−0.457453	−	1.40790i	0.410778	−	0.911735i	$-0.365257\pi$
$660$		0			0
$661$	5.76600	−	17.7459i	0.224271	−	0.690236i	−0.774093	−	0.633071i	$-0.781794\pi$
$661$	5.76600	−	17.7459i	0.224271	−	0.690236i	0.998365	−	0.0571648i	$-0.0182061\pi$
$662$	−13.3119	+	26.1261i	−0.517382	+	1.01542i
$663$	−2.28314	−	27.8722i	−0.0886697	−	1.08247i
$664$	0.460233	+	0.149539i	0.0178605	+	0.00580323i
$665$		0			0
$666$	−3.59253	+	23.6589i	−0.139208	+	0.916765i
$667$	−1.54255	+	9.73930i	−0.0597279	+	0.377107i
$668$	0.692884	−	0.692884i	0.0268085	−	0.0268085i
$669$	−8.00689	+	19.5062i	−0.309564	+	0.754154i
$670$		0			0
$671$	5.53919	−	7.62404i	0.213838	−	0.294323i
$672$	7.95239	−	6.83601i	0.306770	−	0.263705i
$673$	13.5503	−	6.90421i	0.522325	−	0.266138i	−0.172888	−	0.984941i	$-0.555310\pi$
$673$	13.5503	−	6.90421i	0.522325	−	0.266138i	0.695213	+	0.718804i	$0.255310\pi$
$674$	47.1547			1.81633
$675$		0			0
$676$	−16.9044			−0.650169
$677$	−6.94944	+	3.54092i	−0.267089	+	0.136089i	−0.582407	−	0.812898i	$-0.697889\pi$
$677$	−6.94944	+	3.54092i	−0.267089	+	0.136089i	0.315318	+	0.948986i	$0.397889\pi$
$678$	8.38275	−	7.20595i	0.321938	−	0.276743i
$679$	−2.55892	+	3.52205i	−0.0982024	+	0.135164i
$680$		0			0
$681$	9.85899	−	24.0183i	0.377797	−	0.920382i
$682$	−4.60901	+	4.60901i	−0.176488	+	0.176488i
$683$	2.04378	−	12.9039i	0.0782029	−	0.493754i	−0.917235	−	0.398346i	$-0.869584\pi$
$683$	2.04378	−	12.9039i	0.0782029	−	0.493754i	0.995438	−	0.0954080i	$-0.0304156\pi$
$684$	−5.30624	+	34.9447i	−0.202889	+	1.33615i
$685$		0			0
$686$	19.4244	+	6.31136i	0.741626	+	0.240969i
$687$	2.16627	+	26.4455i	0.0826482	+	1.00896i
$688$	13.6886	−	26.8653i	0.521872	−	1.02423i
$689$	−5.05968	+	15.5721i	−0.192759	+	0.593250i
$690$		0			0
$691$	−13.0283	−	40.0970i	−0.495620	−	1.52536i	−0.815988	−	0.578068i	$-0.803807\pi$
$691$	−13.0283	−	40.0970i	−0.495620	−	1.52536i	0.320368	−	0.947293i	$-0.396193\pi$
$692$	−28.7434	−	4.55251i	−1.09266	−	0.173061i
$693$	−0.726436	−	2.18811i	−0.0275950	−	0.0831194i
$694$	37.1724	+	51.1634i	1.41105	+	1.94214i
$695$		0			0
$696$	−0.453474	+	6.00702i	−0.0171889	+	0.227695i
$697$	−13.8431	+	2.19254i	−0.524346	+	0.0830482i
$698$	7.52071	+	14.7602i	0.284663	+	0.558682i
$699$	1.96938	+	3.19083i	0.0744889	+	0.120688i
$700$		0			0
$701$			42.0365i			1.58770i	0.608116	+	0.793848i	$0.291925\pi$
$701$			42.0365i			1.58770i	−0.608116	+	0.793848i	$0.708075\pi$
$702$	40.6433	−	25.4448i	1.53398	−	0.960353i
$703$	4.11382	+	25.9737i	0.155156	+	0.979615i
$704$	5.23172	+	3.80106i	0.197178	+	0.143258i
$705$		0			0
$706$	−53.2567	+	38.6932i	−2.00434	+	1.45624i
$707$	1.89277	+	1.89277i	0.0711848	+	0.0711848i
$708$	1.63057	−	0.681508i	0.0612804	−	0.0256127i
$709$	28.0166	−	9.10314i	1.05219	−	0.341876i	0.268660	−	0.963235i	$-0.413419\pi$
$709$	28.0166	−	9.10314i	1.05219	−	0.341876i	0.783526	+	0.621359i	$0.213419\pi$
$710$		0			0
$711$	−13.9589	−	13.7818i	−0.523500	−	0.516858i
$712$	2.97305	+	1.51485i	0.111420	+	0.0567712i
$713$	−2.89225	−	1.47368i	−0.108316	−	0.0551896i
$714$	2.13862	+	8.78436i	0.0800358	+	0.328746i
$715$		0			0
$716$	31.7043	−	10.3014i	1.18485	−	0.384980i
$717$	−15.2241	−	36.4250i	−0.568555	−	1.36032i
$718$	10.6896	+	10.6896i	0.398933	+	0.398933i
$719$	−25.9550	+	18.8574i	−0.967957	+	0.703262i	−0.954985	−	0.296654i	$-0.904129\pi$
$719$	−25.9550	+	18.8574i	−0.967957	+	0.703262i	−0.0129720	+	0.999916i	$0.504129\pi$
$720$		0			0
$721$	−3.11653	−	2.26429i	−0.116066	−	0.0843265i
$722$	6.91392	+	43.6527i	0.257309	+	1.62459i
$723$	−3.38135	−	2.05728i	−0.125754	−	0.0765110i
$724$		−	19.0314i		−	0.707297i
$725$		0			0
$726$	−28.9146	+	17.8461i	−1.07312	+	0.662332i
$727$	21.4016	+	42.0031i	0.793742	+	1.55781i	0.829539	+	0.558448i	$0.188603\pi$
$727$	21.4016	+	42.0031i	0.793742	+	1.55781i	−0.0357969	+	0.999359i	$0.511397\pi$
$728$	−1.23040	+	0.194876i	−0.0456017	+	0.00722260i
$729$	−11.7948	+	24.2875i	−0.436843	+	0.899538i
$730$		0			0
$731$	14.0534	+	19.3428i	0.519784	+	0.715421i
$732$	−29.4351	−	6.96745i	−1.08795	−	0.257524i
$733$	−3.67592	−	0.582209i	−0.135773	−	0.0215044i	0.0881779	−	0.996105i	$-0.471896\pi$
$733$	−3.67592	−	0.582209i	−0.135773	−	0.0215044i	−0.223951	+	0.974600i	$0.571896\pi$
$734$	7.20426	+	22.1724i	0.265914	+	0.818399i
$735$		0			0
$736$	−2.30480	+	7.09343i	−0.0849559	+	0.261467i
$737$	−3.09091	+	6.06625i	−0.113855	+	0.223453i
$738$	−14.2495	−	19.3517i	−0.524531	−	0.712347i
$739$	−45.0233	−	14.6289i	−1.65621	−	0.538134i	−0.676136	−	0.736777i	$-0.736347\pi$
$739$	−45.0233	−	14.6289i	−1.65621	−	0.538134i	−0.980072	+	0.198643i	$0.936347\pi$
$740$		0			0
$741$	34.0945	−	40.1785i	1.25249	−	1.47599i
$742$	0.828062	−	5.22818i	0.0303991	−	0.191932i
$743$	−37.4947	+	37.4947i	−1.37555	+	1.37555i	−0.523556	+	0.851991i	$0.675395\pi$
$743$	−37.4947	+	37.4947i	−1.37555	+	1.37555i	−0.851991	+	0.523556i	$0.824605\pi$
$744$	−1.83454	−	0.753040i	−0.0672575	−	0.0276078i
$745$		0			0
$746$	29.0677	−	40.0083i	1.06424	−	1.46481i
$747$	−4.08440	−	1.29833i	−0.149440	−	0.0475035i
$748$	−5.49203	+	2.79833i	−0.200809	+	0.102317i
$749$	−2.69823			−0.0985913
$750$		0			0
$751$	−21.2697			−0.776142			−0.388071	−	0.921629i	$-0.626858\pi$
$751$	−21.2697			−0.776142			−0.388071	+	0.921629i	$0.626858\pi$
$752$	−18.0071	+	9.17508i	−0.656652	+	0.334581i
$753$	−16.1713	−	18.8123i	−0.589316	−	0.685557i
$754$	−55.6938	+	76.6559i	−2.02825	+	2.79164i
$755$		0			0
$756$	−5.58096	+	4.85978i	−0.202977	+	0.176749i
$757$	22.1455	−	22.1455i	0.804891	−	0.804891i	−0.178964	−	0.983856i	$-0.557275\pi$
$757$	22.1455	−	22.1455i	0.804891	−	0.804891i	0.983856	+	0.178964i	$0.0572747\pi$
$758$	−5.85746	+	36.9825i	−0.212752	+	1.34327i
$759$	1.25028	+	1.06096i	0.0453825	+	0.0385104i
$760$		0			0
$761$	−33.4555	−	10.8703i	−1.21276	−	0.394050i	−0.368320	−	0.929699i	$-0.620067\pi$
$761$	−33.4555	−	10.8703i	−1.21276	−	0.394050i	−0.844440	+	0.535649i	$0.820067\pi$
$762$	−51.3434	+	4.20576i	−1.85998	+	0.152359i
$763$	0.820194	−	1.60972i	0.0296930	−	0.0582758i
$764$	−9.72984	+	29.9454i	−0.352013	+	1.08339i
$765$		0			0
$766$	12.8106	+	39.4271i	0.462867	+	1.42456i
$767$	−2.60229	−	0.412162i	−0.0939632	−	0.0148823i
$768$	−7.34138	+	31.0148i	−0.264909	+	1.11915i
$769$	−17.0696	−	23.4943i	−0.615545	−	0.847225i	0.381474	−	0.924380i	$-0.375417\pi$
$769$	−17.0696	−	23.4943i	−0.615545	−	0.847225i	−0.997019	+	0.0771542i	$0.975417\pi$
$770$		0			0
$771$	−10.5319	−	0.795064i	−0.379299	−	0.0286335i
$772$	34.6798	−	5.49273i	1.24815	−	0.197688i
$773$	−17.9588	−	35.2461i	−0.645933	−	1.26771i	−0.949159	−	0.314796i	$-0.898064\pi$
$773$	−17.9588	−	35.2461i	−0.645933	−	1.26771i	0.303227	−	0.952918i	$-0.401936\pi$
$774$	−18.3781	+	36.6455i	−0.660587	+	1.31720i
$775$		0			0
$776$		−	1.89162i		−	0.0679051i
$777$	−2.86184	+	4.70374i	−0.102668	+	0.168746i
$778$	3.32511	+	20.9939i	0.119211	+	0.752669i
$779$	−21.3656	−	15.5230i	−0.765503	−	0.556170i
$780$		0			0
$781$	6.89839	−	5.01197i	0.246844	−	0.179342i
$782$	−4.54683	−	4.54683i	−0.162594	−	0.162594i
$783$	3.67644	−	53.2254i	0.131385	−	1.90212i
$784$	−26.2406	+	8.52609i	−0.937165	+	0.304503i
$785$		0			0
$786$	4.76237	−	1.15943i	0.169868	−	0.0413556i
$787$	−11.8192	−	6.02216i	−0.421307	−	0.214667i	0.230466	−	0.973080i	$-0.425975\pi$
$787$	−11.8192	−	6.02216i	−0.421307	−	0.214667i	−0.651774	+	0.758413i	$0.725975\pi$
$788$	−3.48151	−	1.77392i	−0.124024	−	0.0631931i
$789$	52.4562	−	12.7708i	1.86749	−	0.454654i
$790$		0			0
$791$	2.41892	−	0.785955i	0.0860069	−	0.0279453i
$792$	0.814192	+	0.583640i	0.0289311	+	0.0207388i
$793$	31.8878	+	31.8878i	1.13237	+	1.13237i
$794$	−12.1294	+	8.81254i	−0.430457	+	0.312745i
$795$		0			0
$796$	−27.8811	−	20.2568i	−0.988220	−	0.717984i
$797$	−3.63324	−	22.9393i	−0.128696	−	0.812553i	−0.964608	−	0.263690i	$-0.915061\pi$
$797$	−3.63324	−	22.9393i	−0.128696	−	0.812553i	0.835912	−	0.548864i	$-0.184939\pi$
$798$	−8.85466	+	14.5536i	−0.313452	+	0.515191i
$799$		−	16.0256i		−	0.566945i
$800$		0			0
$801$	−26.4158	−	13.2478i	−0.933355	−	0.468087i
$802$	18.4031	+	36.1181i	0.649836	+	1.27538i
$803$	−8.78194	+	1.39092i	−0.309908	+	0.0490846i
$804$	21.7912	+	1.64503i	0.768517	+	0.0580159i
$805$		0			0
$806$	−18.3339	−	25.2344i	−0.645783	−	0.888844i
$807$	−5.88513	+	24.8627i	−0.207166	+	0.875208i
$808$	−1.14875	−	0.181945i	−0.0404130	−	0.00640080i
$809$	7.57984	+	23.3283i	0.266493	+	0.820181i	0.991346	+	0.131277i	$0.0419077\pi$
$809$	7.57984	+	23.3283i	0.266493	+	0.820181i	−0.724853	+	0.688904i	$0.758092\pi$
$810$		0			0
$811$	−7.17737	+	22.0897i	−0.252032	+	0.775674i	0.742368	+	0.669992i	$0.233702\pi$
$811$	−7.17737	+	22.0897i	−0.252032	+	0.775674i	−0.994400	+	0.105682i	$0.966298\pi$
$812$	6.63873	−	13.0292i	0.232974	−	0.457237i
$813$	42.4493	−	3.47721i	1.48876	−	0.121951i
$814$	−7.47852	−	2.42992i	−0.262122	−	0.0851686i
$815$		0			0
$816$	−19.5104	−	16.5561i	−0.683002	−	0.579579i
$817$	−7.04756	+	44.4965i	−0.246563	+	1.55674i
$818$	−44.1115	+	44.1115i	−1.54232	+	1.54232i
$819$	10.8857	−	1.79544i	0.380378	−	0.0627379i
$820$		0			0
$821$	−14.1182	+	19.4320i	−0.492729	+	0.678183i	−0.980888	−	0.194572i	$-0.937668\pi$
$821$	−14.1182	+	19.4320i	−0.492729	+	0.678183i	0.488160	+	0.872754i	$0.337668\pi$
$822$	20.9325	+	24.3510i	0.730106	+	0.849340i
$823$	−26.7301	+	13.6197i	−0.931752	+	0.474751i	−0.852865	−	0.522132i	$-0.825137\pi$
$823$	−26.7301	+	13.6197i	−0.931752	+	0.474751i	−0.0788873	+	0.996884i	$0.525137\pi$
$824$	1.67382			0.0583102
$825$		0			0
$826$	0.851776			0.0296371
$827$	−6.22861	+	3.17364i	−0.216590	+	0.110358i	−0.558920	−	0.829222i	$-0.688784\pi$
$827$	−6.22861	+	3.17364i	−0.216590	+	0.110358i	0.342330	+	0.939580i	$0.388784\pi$
$828$	1.59447	−	5.01600i	0.0554115	−	0.174318i
$829$	−4.72836	+	6.50802i	−0.164223	+	0.226033i	−0.883195	−	0.469005i	$-0.844613\pi$
$829$	−4.72836	+	6.50802i	−0.164223	+	0.226033i	0.718973	+	0.695038i	$0.244613\pi$
$830$		0			0
$831$	−5.36963	−	2.20412i	−0.186270	−	0.0764601i
$832$	−21.8818	+	21.8818i	−0.758617	+	0.758617i
$833$	3.42256	−	21.6092i	0.118585	−	0.748715i
$834$	14.5202	−	17.1113i	0.502795	−	0.592516i
$835$		0			0
$836$	−11.0459	−	3.58904i	−0.382031	−	0.124129i
$837$	16.2897	+	6.56539i	0.563056	+	0.226933i
$838$	11.4811	−	22.5328i	0.396606	−	0.778384i
$839$	−3.47947	+	10.7087i	−0.120125	+	0.369706i	−0.992981	−	0.118271i	$-0.962265\pi$
$839$	−3.47947	+	10.7087i	−0.120125	+	0.369706i	0.872857	+	0.487977i	$0.162265\pi$
$840$		0			0
$841$	23.6164	+	72.6838i	0.814358	+	2.50634i
$842$	−23.7118	−	3.75557i	−0.817161	−	0.129426i
$843$	0.835423	+	0.197749i	0.0287735	+	0.00681084i
$844$	5.37223	+	7.39424i	0.184920	+	0.254520i
$845$		0			0
$846$	24.4032	−	12.6309i	0.839000	−	0.434261i
$847$	−7.72166	+	1.22299i	−0.265319	+	0.0420224i
$848$	6.80150	+	13.3487i	0.233565	+	0.458396i
$849$	33.7589	−	20.8360i	1.15860	−	0.715089i
$850$		0			0
$851$		−	3.91599i		−	0.134238i
$852$	−23.3818	−	14.2259i	−0.801049	−	0.487373i
$853$	2.39903	+	15.1469i	0.0821411	+	0.518619i	0.994111	+	0.108362i	$0.0345607\pi$
$853$	2.39903	+	15.1469i	0.0821411	+	0.518619i	−0.911970	+	0.410256i	$0.865439\pi$
$854$	−11.7947	−	8.56936i	−0.403607	−	0.293237i
$855$		0			0
$856$	0.948489	−	0.689118i	0.0324187	−	0.0235536i
$857$	−2.97404	−	2.97404i	−0.101591	−	0.101591i	0.654484	−	0.756076i	$-0.272886\pi$
$857$	−2.97404	−	2.97404i	−0.101591	−	0.101591i	−0.756076	+	0.654484i	$0.772886\pi$
$858$	6.07624	+	14.5379i	0.207440	+	0.496316i
$859$	24.1552	−	7.84850i	0.824165	−	0.267787i	0.133579	−	0.991038i	$-0.457353\pi$
$859$	24.1552	−	7.84850i	0.824165	−	0.267787i	0.690585	+	0.723251i	$0.257353\pi$
$860$		0			0
$861$	−1.30796	−	5.37245i	−0.0445753	−	0.183093i
$862$	70.1681	+	35.7524i	2.38993	+	1.21773i
$863$	12.0203	+	6.12466i	0.409177	+	0.208486i	0.646449	−	0.762957i	$-0.276253\pi$
$863$	12.0203	+	6.12466i	0.409177	+	0.208486i	−0.237272	+	0.971443i	$0.576253\pi$
$864$	9.04443	−	39.3281i	0.307698	−	1.33797i
$865$		0			0
$866$	−1.29689	+	0.421384i	−0.0440700	+	0.0143192i
$867$	−8.44631	+	3.53021i	−0.286852	+	0.119892i
$868$	3.40385	+	3.40385i	0.115534	+	0.115534i
$869$	5.21474	−	3.78873i	0.176898	−	0.128524i
$870$		0			0
$871$	−26.3578	−	19.1501i	−0.893100	−	0.648875i
$872$	0.122800	+	0.775327i	0.00415852	+	0.0262559i
$873$	0.106953	+	16.7527i	0.00361982	+	0.566992i
$874$		−	12.1162i		−	0.409837i
$875$		0			0
$876$	14.9895	+	24.2862i	0.506447	+	0.820556i
$877$	−6.83909	−	13.4225i	−0.230940	−	0.453245i	0.746235	−	0.665683i	$-0.231860\pi$
$877$	−6.83909	−	13.4225i	−0.230940	−	0.453245i	−0.977175	+	0.212438i	$0.931860\pi$
$878$	66.2600	−	10.4946i	2.23617	−	0.354174i
$879$	1.36443	−	18.0741i	0.0460210	−	0.609625i
$880$		0			0
$881$	−26.2832	−	36.1757i	−0.885504	−	1.21879i	−0.974866	−	0.222792i	$-0.928483\pi$
$881$	−26.2832	−	36.1757i	−0.885504	−	1.21879i	0.0893619	−	0.995999i	$-0.471517\pi$
$882$	35.6033	−	11.8200i	1.19883	−	0.398001i
$883$	−17.2484	−	2.73187i	−0.580454	−	0.0919349i	−0.140699	−	0.990052i	$-0.544935\pi$
$883$	−17.2484	−	2.73187i	−0.580454	−	0.0919349i	−0.439755	+	0.898118i	$0.644935\pi$
$884$	−9.11480	−	28.0525i	−0.306564	−	0.943506i
$885$		0			0
$886$	17.3227	−	53.3138i	0.581968	−	1.79111i
$887$	19.0088	−	37.3069i	0.638253	−	1.25264i	−0.314604	−	0.949223i	$-0.601872\pi$
$887$	19.0088	−	37.3069i	0.638253	−	1.25264i	0.952857	−	0.303420i	$-0.0981284\pi$
$888$	−0.195314	−	2.38437i	−0.00655432	−	0.0800143i
$889$	−11.2727	−	3.66273i	−0.378075	−	0.122844i
$890$		0			0
$891$	−7.24370	−	5.12283i	−0.242673	−	0.171621i
$892$	−3.47904	+	21.9658i	−0.116487	+	0.735468i
$893$	21.3522	−	21.3522i	0.714524	−	0.714524i
$894$	−13.3124	+	32.4314i	−0.445233	+	1.08467i
$895$		0			0
$896$	−1.23711	+	1.70273i	−0.0413288	+	0.0568842i
$897$	−5.95050	+	5.11515i	−0.198681	+	0.170790i
$898$	31.8143	−	16.2102i	1.06166	−	0.540941i
$899$	−34.7047			−1.15747
$900$		0			0
$901$	−11.8798			−0.395774
$902$	7.03615	−	3.58510i	0.234278	−	0.119371i
$903$	−7.15290	+	6.14875i	−0.238034	+	0.204618i
$904$	−0.649574	+	0.894062i	−0.0216045	+	0.0297361i
$905$		0			0
$906$	7.20905	−	17.5625i	0.239505	−	0.583476i
$907$	−3.29748	+	3.29748i	−0.109491	+	0.109491i	−0.759730	−	0.650239i	$-0.774669\pi$
$907$	−3.29748	+	3.29748i	−0.109491	+	0.109491i	0.650239	+	0.759730i	$0.274669\pi$
$908$	4.28379	−	27.0468i	0.142162	−	0.897578i
$909$	10.1840	+	1.54640i	0.337780	+	0.0512908i
$910$		0			0
$911$	32.2491	+	10.4784i	1.06846	+	0.347164i	0.789888	−	0.613251i	$-0.210139\pi$
$911$	32.2491	+	10.4784i	1.06846	+	0.347164i	0.278573	+	0.960415i	$0.410139\pi$
$912$	−3.93634	−	48.0543i	−0.130345	−	1.59124i
$913$	0.639354	−	1.25480i	0.0211595	−	0.0415279i
$914$	12.9928	−	39.9877i	0.429763	−	1.32267i
$915$		0			0
$916$	8.64822	+	26.6165i	0.285745	+	0.879433i
$917$	1.11387	+	0.176419i	0.0367831	+	0.00582587i
$918$	26.6705	+	22.3406i	0.880258	+	0.737351i
$919$	26.7422	+	36.8075i	0.882144	+	1.21417i	0.975822	+	0.218565i	$0.0701376\pi$
$919$	26.7422	+	36.8075i	0.882144	+	1.21417i	−0.0936779	+	0.995603i	$0.529862\pi$
$920$		0			0
$921$	1.28292	−	16.9945i	0.0422738	−	0.559987i
$922$	34.8887	−	5.52582i	1.14900	−	0.181983i
$923$	18.5246	+	36.3566i	0.609745	+	1.19669i
$924$	−1.27718	−	2.06932i	−0.0420162	−	0.0680755i
$925$		0			0
$926$			19.9005i			0.653972i
$927$	−14.8238	+	0.0946388i	−0.486876	+	0.00310835i
$928$	12.4743	+	78.7595i	0.409488	+	2.58541i
$929$	−28.1643	−	20.4626i	−0.924041	−	0.671355i	0.0204855	−	0.999790i	$-0.493479\pi$
$929$	−28.1643	−	20.4626i	−0.924041	−	0.671355i	−0.944527	+	0.328435i	$0.893479\pi$
$930$		0			0
$931$	33.3519	−	24.2315i	1.09306	−	0.794157i
$932$	2.79651	+	2.79651i	0.0916027	+	0.0916027i
$933$	−3.54031	+	1.47970i	−0.115905	+	0.0484432i
$934$	20.9334	−	6.80167i	0.684962	−	0.222558i
$935$		0			0
$936$	−3.36803	+	3.41131i	−0.110087	+	0.111502i
$937$	−25.5737	−	13.0305i	−0.835458	−	0.425687i	−0.0167239	−	0.999860i	$-0.505324\pi$
$937$	−25.5737	−	13.0305i	−0.835458	−	0.425687i	−0.818734	+	0.574173i	$0.805324\pi$
$938$	9.38474	+	4.78176i	0.306422	+	0.156130i
$939$	9.84021	+	40.4186i	0.321123	+	1.31901i
$940$		0			0
$941$	48.7206	−	15.8303i	1.58825	−	0.516053i	0.624083	−	0.781358i	$-0.285473\pi$
$941$	48.7206	−	15.8303i	1.58825	−	0.516053i	0.964164	+	0.265305i	$0.0854727\pi$
$942$	13.2773	+	31.7670i	0.432598	+	1.03503i
$943$	2.78081	+	2.78081i	0.0905556	+	0.0905556i
$944$	−1.95034	+	1.41701i	−0.0634782	+	0.0461196i
$945$		0			0
$946$	−10.8983	−	7.91810i	−0.354335	−	0.257440i
$947$	−4.38792	−	27.7042i	−0.142588	−	0.900267i	−0.950446	−	0.310890i	$-0.899373\pi$
$947$	−4.38792	−	27.7042i	−0.142588	−	0.900267i	0.807858	−	0.589377i	$-0.200627\pi$
$948$	−17.6752	−	10.7539i	−0.574063	−	0.349271i
$949$		−	42.5484i		−	1.38118i
$950$		0			0
$951$	−1.14835	+	0.708762i	−0.0372378	+	0.0229832i
$952$	−0.410338	−	0.805334i	−0.0132991	−	0.0261010i
$953$	−3.32321	+	0.526345i	−0.107649	+	0.0170500i	−0.210027	−	0.977696i	$-0.567355\pi$
$953$	−3.32321	+	0.526345i	−0.107649	+	0.0170500i	0.102377	+	0.994746i	$0.467355\pi$
$954$	−9.36333	−	18.0901i	−0.303149	−	0.585690i
$955$		0			0
$956$	−24.4748	−	33.6867i	−0.791573	−	1.08951i
$957$	17.0600	+	4.03818i	0.551470	+	0.130536i
$958$	−33.4475	−	5.29756i	−1.08064	−	0.171156i
$959$	2.28312	+	7.02671i	0.0737257	+	0.226904i
$960$		0			0
$961$	−6.04918	+	18.6175i	−0.195135	+	0.600563i
$962$	17.0832	−	33.5276i	0.550783	−	1.08097i
$963$	−8.36110	+	6.15663i	−0.269433	+	0.198395i
$964$	−3.97032	−	1.29003i	−0.127875	−	0.0415492i
$965$		0			0
$966$	1.64135	−	1.93424i	0.0528096	−	0.0622333i
$967$	4.46829	−	28.2117i	0.143690	−	0.907226i	−0.805516	−	0.592573i	$-0.798112\pi$
$967$	4.46829	−	28.2117i	0.143690	−	0.907226i	0.949207	−	0.314653i	$-0.101888\pi$
$968$	2.40199	−	2.40199i	0.0772028	−	0.0772028i
$969$	35.3690	+	14.5182i	1.13622	+	0.466393i
$970$		0			0
$971$	18.4852	−	25.4427i	0.593218	−	0.816495i	−0.401848	−	0.915706i	$-0.631632\pi$
$971$	18.4852	−	25.4427i	0.593218	−	0.816495i	0.995066	+	0.0992113i	$0.0316320\pi$
$972$	−6.20519	+	27.7934i	−0.199032	+	0.891473i
$973$	4.60071	−	2.34418i	0.147492	−	0.0751509i
$974$	−20.7829			−0.665926
$975$		0			0
$976$	41.2627			1.32079
$977$	4.10325	−	2.09071i	0.131275	−	0.0668877i	−0.387120	−	0.922029i	$-0.626530\pi$
$977$	4.10325	−	2.09071i	0.131275	−	0.0668877i	0.518394	+	0.855142i	$0.326530\pi$
$978$	−43.0650	−	50.0979i	−1.37707	−	1.60195i
$979$	5.70773	−	7.85601i	0.182420	−	0.251079i
$980$		0			0
$981$	−1.13138	−	6.85955i	−0.0361223	−	0.219009i
$982$	10.2872	−	10.2872i	0.328277	−	0.328277i
$983$	2.00270	−	12.6446i	0.0638763	−	0.403299i	−0.934946	−	0.354789i	$-0.884553\pi$
$983$	2.00270	−	12.6446i	0.0638763	−	0.403299i	0.998823	−	0.0485102i	$-0.0154473\pi$
$984$	1.83188	+	1.55449i	0.0583982	+	0.0495552i
$985$		0			0
$986$	−65.3827	−	21.2441i	−2.08221	−	0.676551i
$987$	6.30121	−	0.516160i	0.200570	−	0.0164295i
$988$	25.2322	−	49.5210i	0.802743	−	1.57547i
$989$	2.07308	−	6.38029i	0.0659202	−	0.202882i
$990$		0			0
$991$	−14.7045	−	45.2557i	−0.467103	−	1.43759i	−0.856319	−	0.516448i	$-0.827254\pi$
$991$	−14.7045	−	45.2557i	−0.467103	−	1.43759i	0.389216	−	0.921147i	$-0.372746\pi$
$992$	−25.9269	−	4.10641i	−0.823179	−	0.130379i
$993$	−5.98003	+	25.2636i	−0.189771	+	0.801717i
$994$	−7.75373	−	10.6721i	−0.245933	−	0.338498i
$995$		0			0
$996$	−4.50752	−	0.340275i	−0.142826	−	0.0107820i
$997$	−20.1708	+	3.19474i	−0.638816	+	0.101179i	−0.467437	−	0.884027i	$-0.654822\pi$
$997$	−20.1708	+	3.19474i	−0.638816	+	0.101179i	−0.171379	+	0.985205i	$0.554822\pi$
$998$	20.3541	+	39.9472i	0.644297	+	1.26451i
$999$	1.86457	+	21.1056i	0.0589924	+	0.667751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.l.b.368.7		64
3.2	odd	2	inner	375.2.l.b.368.2		64
5.2	odd	4		375.2.l.c.257.7		64
5.3	odd	4		75.2.l.a.47.2	yes	64
5.4	even	2		375.2.l.a.368.2		64
15.2	even	4		375.2.l.c.257.2		64
15.8	even	4		75.2.l.a.47.7	yes	64
15.14	odd	2		375.2.l.a.368.7		64
25.6	even	5		375.2.l.c.143.2		64
25.8	odd	20		375.2.l.a.107.7		64
25.17	odd	20	inner	375.2.l.b.107.2		64
25.19	even	10		75.2.l.a.8.7	yes	64
75.8	even	20		375.2.l.a.107.2		64
75.17	even	20	inner	375.2.l.b.107.7		64
75.44	odd	10		75.2.l.a.8.2	✓	64
75.56	odd	10		375.2.l.c.143.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.2	✓	64	75.44	odd	10
75.2.l.a.8.7	yes	64	25.19	even	10
75.2.l.a.47.2	yes	64	5.3	odd	4
75.2.l.a.47.7	yes	64	15.8	even	4
375.2.l.a.107.2		64	75.8	even	20
375.2.l.a.107.7		64	25.8	odd	20
375.2.l.a.368.2		64	5.4	even	2
375.2.l.a.368.7		64	15.14	odd	2
375.2.l.b.107.2		64	25.17	odd	20	inner
375.2.l.b.107.7		64	75.17	even	20	inner
375.2.l.b.368.2		64	3.2	odd	2	inner
375.2.l.b.368.7		64	1.1	even	1	trivial
375.2.l.c.143.2		64	25.6	even	5
375.2.l.c.143.7		64	75.56	odd	10
375.2.l.c.257.2		64	15.2	even	4
375.2.l.c.257.7		64	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.74302 - 0.888111i) q^{2} +(1.31346 - 1.12908i) q^{3} +(1.07379 - 1.47795i) q^{4} +(1.28664 - 3.13450i) q^{6} +(0.551254 - 0.551254i) q^{7} +(-0.0529901 + 0.334566i) q^{8} +(0.450377 - 2.96600i) q^{9} +O(q^{10})\)	\(q+(1.74302 - 0.888111i) q^{2} +(1.31346 - 1.12908i) q^{3} +(1.07379 - 1.47795i) q^{4} +(1.28664 - 3.13450i) q^{6} +(0.551254 - 0.551254i) q^{7} +(-0.0529901 + 0.334566i) q^{8} +(0.450377 - 2.96600i) q^{9} +(0.937544 + 0.304626i) q^{11} +(-0.258327 - 3.15362i) q^{12} +(-2.14163 + 4.20319i) q^{13} +(0.471270 - 1.45042i) q^{14} +(1.33382 + 4.10508i) q^{16} +(-3.38054 - 0.535425i) q^{17} +(-1.84912 - 5.56977i) q^{18} +(-3.79078 - 5.21756i) q^{19} +(0.101645 - 1.34646i) q^{21} +(1.90469 - 0.301674i) q^{22} +(0.435998 + 0.855694i) q^{23} +(0.308150 + 0.499270i) q^{24} +9.22822i q^{26} +(-2.75728 - 4.40425i) q^{27} +(-0.222792 - 1.40666i) q^{28} +(8.30669 + 6.03516i) q^{29} +(-2.73448 + 1.98672i) q^{31} +(5.49158 + 5.49158i) q^{32} +(1.57538 - 0.658442i) q^{33} +(-6.36785 + 2.06904i) q^{34} +(-3.89998 - 3.85050i) q^{36} +(-3.63316 - 1.85119i) q^{37} +(-11.2411 - 5.72765i) q^{38} +(1.93276 + 7.93880i) q^{39} +(3.89453 - 1.26541i) q^{41} +(-1.01864 - 2.43717i) q^{42} +(-4.93949 - 4.93949i) q^{43} +(1.45695 - 1.05853i) q^{44} +(1.51990 + 1.10427i) q^{46} +(0.732455 + 4.62454i) q^{47} +(6.38686 + 3.88589i) q^{48} +6.39224i q^{49} +(-5.04475 + 3.11362i) q^{51} +(3.91242 + 7.67856i) q^{52} +(3.42818 - 0.542970i) q^{53} +(-8.71745 - 5.22789i) q^{54} +(0.155220 + 0.213642i) q^{56} +(-10.8701 - 2.57300i) q^{57} +(19.8386 + 3.14212i) q^{58} +(0.172592 + 0.531183i) q^{59} +(2.95410 - 9.09178i) q^{61} +(-3.00182 + 5.89140i) q^{62} +(-1.38675 - 1.88329i) q^{63} +(6.23890 + 2.02714i) q^{64} +(2.16114 - 2.54678i) q^{66} +(-1.08040 + 6.82141i) q^{67} +(-4.42132 + 4.42132i) q^{68} +(1.53881 + 0.631649i) q^{69} +(5.08421 - 6.99781i) q^{71} +(0.968458 + 0.307850i) q^{72} +(-8.03649 + 4.09480i) q^{73} -7.97671 q^{74} -11.7818 q^{76} +(0.684752 - 0.348898i) q^{77} +(10.4194 + 12.1209i) q^{78} +(3.84334 - 5.28990i) q^{79} +(-8.59432 - 2.67164i) q^{81} +(5.66440 - 5.66440i) q^{82} +(0.223482 - 1.41101i) q^{83} +(-1.88085 - 1.59604i) q^{84} +(-12.9964 - 4.22279i) q^{86} +(17.7247 - 1.45191i) q^{87} +(-0.151598 + 0.297528i) q^{88} +(3.04398 - 9.36841i) q^{89} +(1.13644 + 3.49761i) q^{91} +(1.73284 + 0.274455i) q^{92} +(-1.34849 + 5.69692i) q^{93} +(5.38378 + 7.41014i) q^{94} +(13.4134 + 1.01259i) q^{96} +(-5.51558 + 0.873583i) q^{97} +(5.67701 + 11.1418i) q^{98} +(1.32577 - 2.64356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 20 q^{4} - 6 q^{6} + 20 q^{7} + 10 q^{9}+O(q^{10}) \) 64 * q + 20 * q^4 - 6 * q^6 + 20 * q^7 + 10 * q^9	\( 64 q + 20 q^{4} - 6 q^{6} + 20 q^{7} + 10 q^{9} + 40 q^{12} - 8 q^{16} + 10 q^{18} - 6 q^{21} - 30 q^{27} - 80 q^{28} - 12 q^{31} - 50 q^{33} - 20 q^{34} - 22 q^{36} - 120 q^{37} - 30 q^{39} + 60 q^{42} + 20 q^{43} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 100 q^{52} - 120 q^{54} - 70 q^{57} + 120 q^{58} - 12 q^{61} - 70 q^{63} + 100 q^{64} - 30 q^{66} - 60 q^{67} + 80 q^{69} - 40 q^{72} - 80 q^{73} - 64 q^{76} + 70 q^{78} + 60 q^{79} + 14 q^{81} + 60 q^{82} + 130 q^{84} + 100 q^{87} + 60 q^{88} - 12 q^{91} + 20 q^{93} - 260 q^{94} + 42 q^{96}+O(q^{100}) \) 64 * q + 20 * q^4 - 6 * q^6 + 20 * q^7 + 10 * q^9 + 40 * q^12 - 8 * q^16 + 10 * q^18 - 6 * q^21 - 30 * q^27 - 80 * q^28 - 12 * q^31 - 50 * q^33 - 20 * q^34 - 22 * q^36 - 120 * q^37 - 30 * q^39 + 60 * q^42 + 20 * q^43 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 100 * q^52 - 120 * q^54 - 70 * q^57 + 120 * q^58 - 12 * q^61 - 70 * q^63 + 100 * q^64 - 30 * q^66 - 60 * q^67 + 80 * q^69 - 40 * q^72 - 80 * q^73 - 64 * q^76 + 70 * q^78 + 60 * q^79 + 14 * q^81 + 60 * q^82 + 130 * q^84 + 100 * q^87 + 60 * q^88 - 12 * q^91 + 20 * q^93 - 260 * q^94 + 42 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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